Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(1,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, 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("475.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.66064384.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 9x^{4} + 13x^{2} - 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.68667\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.82254 | −1.28873 | −0.644364 | − | 0.764719i | \(-0.722878\pi\) | ||||
−0.644364 | + | 0.764719i | \(0.722878\pi\) | |||||||
\(3\) | −2.31446 | −1.33625 | −0.668127 | − | 0.744047i | \(-0.732904\pi\) | ||||
−0.668127 | + | 0.744047i | \(0.732904\pi\) | |||||||
\(4\) | 1.32164 | 0.660819 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.21819 | 1.72207 | ||||||||
\(7\) | −1.45033 | −0.548172 | −0.274086 | − | 0.961705i | \(-0.588375\pi\) | ||||
−0.274086 | + | 0.961705i | \(0.588375\pi\) | |||||||
\(8\) | 1.23634 | 0.437112 | ||||||||
\(9\) | 2.35673 | 0.785575 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.89655 | −1.17485 | −0.587427 | − | 0.809277i | \(-0.699859\pi\) | ||||
−0.587427 | + | 0.809277i | \(0.699859\pi\) | |||||||
\(12\) | −3.05888 | −0.883022 | ||||||||
\(13\) | −3.05888 | −0.848380 | −0.424190 | − | 0.905573i | \(-0.639441\pi\) | ||||
−0.424190 | + | 0.905573i | \(0.639441\pi\) | |||||||
\(14\) | 2.64327 | 0.706445 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.89655 | −1.22414 | ||||||||
\(17\) | −3.92301 | −0.951469 | −0.475735 | − | 0.879589i | \(-0.657818\pi\) | ||||
−0.475735 | + | 0.879589i | \(0.657818\pi\) | |||||||
\(18\) | −4.29522 | −1.01239 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.35673 | 0.732498 | ||||||||
\(22\) | 7.10160 | 1.51407 | ||||||||
\(23\) | 5.37334 | 1.12042 | 0.560209 | − | 0.828351i | \(-0.310721\pi\) | ||||
0.560209 | + | 0.828351i | \(0.310721\pi\) | |||||||
\(24\) | −2.86146 | −0.584093 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.57491 | 1.09333 | ||||||||
\(27\) | 1.48883 | 0.286526 | ||||||||
\(28\) | −1.91681 | −0.362242 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.43637 | −1.51522 | −0.757609 | − | 0.652709i | \(-0.773632\pi\) | ||||
−0.757609 | + | 0.652709i | \(0.773632\pi\) | |||||||
\(32\) | 6.45146 | 1.14047 | ||||||||
\(33\) | 9.01841 | 1.56990 | ||||||||
\(34\) | 7.14982 | 1.22618 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.11474 | 0.519123 | ||||||||
\(37\) | 5.95953 | 0.979741 | 0.489871 | − | 0.871795i | \(-0.337044\pi\) | ||||
0.489871 | + | 0.871795i | \(0.337044\pi\) | |||||||
\(38\) | 1.82254 | 0.295654 | ||||||||
\(39\) | 7.07965 | 1.13365 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4364 | 1.62989 | 0.814944 | − | 0.579540i | \(-0.196768\pi\) | ||||
0.814944 | + | 0.579540i | \(0.196768\pi\) | |||||||
\(42\) | −6.11775 | −0.943990 | ||||||||
\(43\) | 1.45033 | 0.221173 | 0.110586 | − | 0.993867i | \(-0.464727\pi\) | ||||
0.110586 | + | 0.993867i | \(0.464727\pi\) | |||||||
\(44\) | −5.14982 | −0.776365 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.79310 | −1.44391 | ||||||||
\(47\) | −4.90686 | −0.715739 | −0.357869 | − | 0.933772i | \(-0.616497\pi\) | ||||
−0.357869 | + | 0.933772i | \(0.616497\pi\) | |||||||
\(48\) | 11.3329 | 1.63576 | ||||||||
\(49\) | −4.89655 | −0.699507 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.07965 | 1.27140 | ||||||||
\(52\) | −4.04272 | −0.560625 | ||||||||
\(53\) | 4.23127 | 0.581209 | 0.290605 | − | 0.956843i | \(-0.406144\pi\) | ||||
0.290605 | + | 0.956843i | \(0.406144\pi\) | |||||||
\(54\) | −2.71345 | −0.369254 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.79310 | −0.239613 | ||||||||
\(57\) | 2.31446 | 0.306558 | ||||||||
\(58\) | −10.9352 | −1.43586 | ||||||||
\(59\) | 3.35673 | 0.437008 | 0.218504 | − | 0.975836i | \(-0.429882\pi\) | ||||
0.218504 | + | 0.975836i | \(0.429882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3329 | 1.32300 | 0.661498 | − | 0.749947i | \(-0.269921\pi\) | ||||
0.661498 | + | 0.749947i | \(0.269921\pi\) | |||||||
\(62\) | 15.3756 | 1.95270 | ||||||||
\(63\) | −3.41802 | −0.430631 | ||||||||
\(64\) | −1.96491 | −0.245614 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −16.4364 | −2.02318 | ||||||||
\(67\) | 9.84404 | 1.20264 | 0.601320 | − | 0.799008i | \(-0.294642\pi\) | ||||
0.601320 | + | 0.799008i | \(0.294642\pi\) | |||||||
\(68\) | −5.18479 | −0.628749 | ||||||||
\(69\) | −12.4364 | −1.49716 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.64327 | 1.02577 | 0.512884 | − | 0.858458i | \(-0.328577\pi\) | ||||
0.512884 | + | 0.858458i | \(0.328577\pi\) | |||||||
\(72\) | 2.91372 | 0.343385 | ||||||||
\(73\) | 2.43418 | 0.284899 | 0.142449 | − | 0.989802i | \(-0.454502\pi\) | ||||
0.142449 | + | 0.989802i | \(0.454502\pi\) | |||||||
\(74\) | −10.8615 | −1.26262 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.32164 | −0.151602 | ||||||||
\(77\) | 5.65127 | 0.644022 | ||||||||
\(78\) | −12.9029 | −1.46097 | ||||||||
\(79\) | −12.4364 | −1.39920 | −0.699601 | − | 0.714534i | \(-0.746639\pi\) | ||||
−0.699601 | + | 0.714534i | \(0.746639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.5160 | −1.16845 | ||||||||
\(82\) | −19.0207 | −2.10048 | ||||||||
\(83\) | −12.6635 | −1.39000 | −0.694999 | − | 0.719011i | \(-0.744595\pi\) | ||||
−0.694999 | + | 0.719011i | \(0.744595\pi\) | |||||||
\(84\) | 4.43637 | 0.484048 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.64327 | −0.285032 | ||||||||
\(87\) | −13.8868 | −1.48882 | ||||||||
\(88\) | −4.81746 | −0.513543 | ||||||||
\(89\) | 12.3662 | 1.31081 | 0.655407 | − | 0.755276i | \(-0.272497\pi\) | ||||
0.655407 | + | 0.755276i | \(0.272497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.43637 | 0.465058 | ||||||||
\(92\) | 7.10160 | 0.740393 | ||||||||
\(93\) | 19.5256 | 2.02472 | ||||||||
\(94\) | 8.94292 | 0.922392 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −14.9316 | −1.52395 | ||||||||
\(97\) | −3.05888 | −0.310582 | −0.155291 | − | 0.987869i | \(-0.549631\pi\) | ||||
−0.155291 | + | 0.987869i | \(0.549631\pi\) | |||||||
\(98\) | 8.92414 | 0.901474 | ||||||||
\(99\) | −9.18310 | −0.922936 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.35673 | 0.334007 | 0.167003 | − | 0.985956i | \(-0.446591\pi\) | ||||
0.167003 | + | 0.985956i | \(0.446591\pi\) | |||||||
\(102\) | −16.5480 | −1.63849 | ||||||||
\(103\) | −13.0611 | −1.28695 | −0.643476 | − | 0.765466i | \(-0.722508\pi\) | ||||
−0.643476 | + | 0.765466i | \(0.722508\pi\) | |||||||
\(104\) | −3.78181 | −0.370837 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.71164 | −0.749020 | ||||||||
\(107\) | 5.77099 | 0.557903 | 0.278951 | − | 0.960305i | \(-0.410013\pi\) | ||||
0.278951 | + | 0.960305i | \(0.410013\pi\) | |||||||
\(108\) | 1.96770 | 0.189342 | ||||||||
\(109\) | 6.64327 | 0.636310 | 0.318155 | − | 0.948039i | \(-0.396937\pi\) | ||||
0.318155 | + | 0.948039i | \(0.396937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.7931 | −1.30918 | ||||||||
\(112\) | 7.10160 | 0.671038 | ||||||||
\(113\) | 9.41606 | 0.885789 | 0.442894 | − | 0.896574i | \(-0.353952\pi\) | ||||
0.442894 | + | 0.896574i | \(0.353952\pi\) | |||||||
\(114\) | −4.21819 | −0.395069 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.92982 | 0.736266 | ||||||||
\(117\) | −7.20893 | −0.666466 | ||||||||
\(118\) | −6.11775 | −0.563185 | ||||||||
\(119\) | 5.68965 | 0.521569 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.18310 | 0.380282 | ||||||||
\(122\) | −18.8321 | −1.70498 | ||||||||
\(123\) | −24.1546 | −2.17794 | ||||||||
\(124\) | −11.1498 | −1.00128 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 6.22947 | 0.554966 | ||||||||
\(127\) | −11.0934 | −0.984383 | −0.492192 | − | 0.870487i | \(-0.663804\pi\) | ||||
−0.492192 | + | 0.870487i | \(0.663804\pi\) | |||||||
\(128\) | −9.32179 | −0.823938 | ||||||||
\(129\) | −3.35673 | −0.295543 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.61000 | 0.402778 | 0.201389 | − | 0.979511i | \(-0.435455\pi\) | ||||
0.201389 | + | 0.979511i | \(0.435455\pi\) | |||||||
\(132\) | 11.9191 | 1.03742 | ||||||||
\(133\) | 1.45033 | 0.125759 | ||||||||
\(134\) | −17.9411 | −1.54988 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.85018 | −0.415899 | ||||||||
\(137\) | 13.1808 | 1.12612 | 0.563058 | − | 0.826417i | \(-0.309625\pi\) | ||||
0.563058 | + | 0.826417i | \(0.309625\pi\) | |||||||
\(138\) | 22.6657 | 1.92944 | ||||||||
\(139\) | 1.18310 | 0.100349 | 0.0501745 | − | 0.998740i | \(-0.484022\pi\) | ||||
0.0501745 | + | 0.998740i | \(0.484022\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3567 | 0.956409 | ||||||||
\(142\) | −15.7527 | −1.32194 | ||||||||
\(143\) | 11.9191 | 0.996722 | ||||||||
\(144\) | −11.5398 | −0.961652 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.43637 | −0.367157 | ||||||||
\(147\) | 11.3329 | 0.934719 | ||||||||
\(148\) | 7.87634 | 0.647431 | ||||||||
\(149\) | 5.46018 | 0.447315 | 0.223658 | − | 0.974668i | \(-0.428200\pi\) | ||||
0.223658 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.07965 | −0.413376 | −0.206688 | − | 0.978407i | \(-0.566268\pi\) | ||||
−0.206688 | + | 0.978407i | \(0.566268\pi\) | |||||||
\(152\) | −1.23634 | −0.100280 | ||||||||
\(153\) | −9.24546 | −0.747451 | ||||||||
\(154\) | −10.2996 | −0.829969 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.35673 | 0.749138 | ||||||||
\(157\) | −6.11775 | −0.488250 | −0.244125 | − | 0.969744i | \(-0.578501\pi\) | ||||
−0.244125 | + | 0.969744i | \(0.578501\pi\) | |||||||
\(158\) | 22.6657 | 1.80319 | ||||||||
\(159\) | −9.79310 | −0.776643 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.79310 | −0.614182 | ||||||||
\(162\) | 19.1658 | 1.50581 | ||||||||
\(163\) | 16.4365 | 1.28740 | 0.643701 | − | 0.765277i | \(-0.277398\pi\) | ||||
0.643701 | + | 0.765277i | \(0.277398\pi\) | |||||||
\(164\) | 13.7931 | 1.07706 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.0796 | 1.79133 | ||||||||
\(167\) | 3.80329 | 0.294308 | 0.147154 | − | 0.989114i | \(-0.452989\pi\) | ||||
0.147154 | + | 0.989114i | \(0.452989\pi\) | |||||||
\(168\) | 4.15006 | 0.320184 | ||||||||
\(169\) | −3.64327 | −0.280252 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.35673 | −0.180223 | ||||||||
\(172\) | 1.91681 | 0.146155 | ||||||||
\(173\) | 11.3838 | 0.865491 | 0.432746 | − | 0.901516i | \(-0.357545\pi\) | ||||
0.432746 | + | 0.901516i | \(0.357545\pi\) | |||||||
\(174\) | 25.3091 | 1.91868 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 19.0796 | 1.43818 | ||||||||
\(177\) | −7.76901 | −0.583954 | ||||||||
\(178\) | −22.5378 | −1.68928 | ||||||||
\(179\) | 10.0702 | 0.752680 | 0.376340 | − | 0.926482i | \(-0.377182\pi\) | ||||
0.376340 | + | 0.926482i | \(0.377182\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.573097 | 0.0425980 | 0.0212990 | − | 0.999773i | \(-0.493220\pi\) | ||||
0.0212990 | + | 0.999773i | \(0.493220\pi\) | |||||||
\(182\) | −8.08545 | −0.599333 | ||||||||
\(183\) | −23.9151 | −1.76786 | ||||||||
\(184\) | 6.64327 | 0.489749 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −35.5862 | −2.60931 | ||||||||
\(187\) | 15.2862 | 1.11784 | ||||||||
\(188\) | −6.48509 | −0.472973 | ||||||||
\(189\) | −2.15930 | −0.157066 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.18310 | −0.230321 | −0.115160 | − | 0.993347i | \(-0.536738\pi\) | ||||
−0.115160 | + | 0.993347i | \(0.536738\pi\) | |||||||
\(192\) | 4.54771 | 0.328203 | ||||||||
\(193\) | −3.05888 | −0.220183 | −0.110091 | − | 0.993921i | \(-0.535114\pi\) | ||||
−0.110091 | + | 0.993921i | \(0.535114\pi\) | |||||||
\(194\) | 5.57491 | 0.400255 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.47146 | −0.462247 | ||||||||
\(197\) | −21.4933 | −1.53134 | −0.765669 | − | 0.643235i | \(-0.777592\pi\) | ||||
−0.765669 | + | 0.643235i | \(0.777592\pi\) | |||||||
\(198\) | 16.7365 | 1.18941 | ||||||||
\(199\) | −4.81690 | −0.341461 | −0.170731 | − | 0.985318i | \(-0.554613\pi\) | ||||
−0.170731 | + | 0.985318i | \(0.554613\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −22.7836 | −1.60703 | ||||||||
\(202\) | −6.11775 | −0.430444 | ||||||||
\(203\) | −8.70197 | −0.610758 | ||||||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 23.8044 | 1.65853 | ||||||||
\(207\) | 12.6635 | 0.880173 | ||||||||
\(208\) | 14.9779 | 1.03853 | ||||||||
\(209\) | 3.89655 | 0.269530 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5066 | 0.723301 | 0.361650 | − | 0.932314i | \(-0.382213\pi\) | ||||
0.361650 | + | 0.932314i | \(0.382213\pi\) | |||||||
\(212\) | 5.59220 | 0.384074 | ||||||||
\(213\) | −20.0045 | −1.37069 | ||||||||
\(214\) | −10.5178 | −0.718984 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.84070 | 0.125244 | ||||||||
\(217\) | 12.2355 | 0.830600 | ||||||||
\(218\) | −12.1076 | −0.820031 | ||||||||
\(219\) | −5.63380 | −0.380697 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 25.1384 | 1.68718 | ||||||||
\(223\) | 16.8947 | 1.13136 | 0.565678 | − | 0.824626i | \(-0.308615\pi\) | ||||
0.565678 | + | 0.824626i | \(0.308615\pi\) | |||||||
\(224\) | −9.35673 | −0.625173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.1611 | −1.14154 | ||||||||
\(227\) | −17.1342 | −1.13724 | −0.568618 | − | 0.822602i | \(-0.692522\pi\) | ||||
−0.568618 | + | 0.822602i | \(0.692522\pi\) | |||||||
\(228\) | 3.05888 | 0.202579 | ||||||||
\(229\) | 25.0464 | 1.65511 | 0.827555 | − | 0.561384i | \(-0.189731\pi\) | ||||
0.827555 | + | 0.561384i | \(0.189731\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.0796 | −0.860578 | ||||||||
\(232\) | 7.41804 | 0.487018 | ||||||||
\(233\) | −19.2986 | −1.26429 | −0.632147 | − | 0.774849i | \(-0.717826\pi\) | ||||
−0.632147 | + | 0.774849i | \(0.717826\pi\) | |||||||
\(234\) | 13.1385 | 0.858893 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.43637 | 0.288783 | ||||||||
\(237\) | 28.7835 | 1.86969 | ||||||||
\(238\) | −10.3696 | −0.672161 | ||||||||
\(239\) | 18.7693 | 1.21408 | 0.607042 | − | 0.794669i | \(-0.292356\pi\) | ||||
0.607042 | + | 0.794669i | \(0.292356\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4364 | −0.929929 | −0.464964 | − | 0.885329i | \(-0.653933\pi\) | ||||
−0.464964 | + | 0.885329i | \(0.653933\pi\) | |||||||
\(242\) | −7.62385 | −0.490079 | ||||||||
\(243\) | 19.8724 | 1.27482 | ||||||||
\(244\) | 13.6564 | 0.874260 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 44.0226 | 2.80678 | ||||||||
\(247\) | 3.05888 | 0.194632 | ||||||||
\(248\) | −10.4302 | −0.662320 | ||||||||
\(249\) | 29.3091 | 1.85739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.9762 | −0.692811 | −0.346406 | − | 0.938085i | \(-0.612598\pi\) | ||||
−0.346406 | + | 0.938085i | \(0.612598\pi\) | |||||||
\(252\) | −4.51739 | −0.284569 | ||||||||
\(253\) | −20.9375 | −1.31633 | ||||||||
\(254\) | 20.2182 | 1.26860 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.9191 | 1.30745 | ||||||||
\(257\) | 17.6392 | 1.10030 | 0.550150 | − | 0.835066i | \(-0.314570\pi\) | ||||
0.550150 | + | 0.835066i | \(0.314570\pi\) | |||||||
\(258\) | 6.11775 | 0.380875 | ||||||||
\(259\) | −8.64327 | −0.537067 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.1404 | 0.875266 | ||||||||
\(262\) | −8.40189 | −0.519071 | ||||||||
\(263\) | 1.68976 | 0.104195 | 0.0520975 | − | 0.998642i | \(-0.483409\pi\) | ||||
0.0520975 | + | 0.998642i | \(0.483409\pi\) | |||||||
\(264\) | 11.1498 | 0.686224 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.64327 | −0.162070 | ||||||||
\(267\) | −28.6211 | −1.75158 | ||||||||
\(268\) | 13.0102 | 0.794727 | ||||||||
\(269\) | −27.1022 | −1.65245 | −0.826226 | − | 0.563339i | \(-0.809516\pi\) | ||||
−0.826226 | + | 0.563339i | \(0.809516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9524 | 1.45500 | 0.727502 | − | 0.686105i | \(-0.240681\pi\) | ||||
0.727502 | + | 0.686105i | \(0.240681\pi\) | |||||||
\(272\) | 19.2092 | 1.16473 | ||||||||
\(273\) | −10.2678 | −0.621436 | ||||||||
\(274\) | −24.0226 | −1.45126 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −16.4364 | −0.989353 | ||||||||
\(277\) | −8.23549 | −0.494822 | −0.247411 | − | 0.968911i | \(-0.579580\pi\) | ||||
−0.247411 | + | 0.968911i | \(0.579580\pi\) | |||||||
\(278\) | −2.15624 | −0.129323 | ||||||||
\(279\) | −19.8822 | −1.19032 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4364 | −0.622582 | −0.311291 | − | 0.950315i | \(-0.600761\pi\) | ||||
−0.311291 | + | 0.950315i | \(0.600761\pi\) | |||||||
\(282\) | −20.6980 | −1.23255 | ||||||||
\(283\) | 10.4687 | 0.622302 | 0.311151 | − | 0.950361i | \(-0.399286\pi\) | ||||
0.311151 | + | 0.950361i | \(0.399286\pi\) | |||||||
\(284\) | 11.4233 | 0.677847 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −21.7229 | −1.28450 | ||||||||
\(287\) | −15.1362 | −0.893459 | ||||||||
\(288\) | 15.2043 | 0.895923 | ||||||||
\(289\) | −1.61000 | −0.0947059 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.07965 | 0.415016 | ||||||||
\(292\) | 3.21710 | 0.188266 | ||||||||
\(293\) | 16.4668 | 0.961999 | 0.481000 | − | 0.876721i | \(-0.340274\pi\) | ||||
0.481000 | + | 0.876721i | \(0.340274\pi\) | |||||||
\(294\) | −20.6546 | −1.20460 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.36801 | 0.428257 | ||||||||
\(297\) | −5.80131 | −0.336626 | ||||||||
\(298\) | −9.95137 | −0.576467 | ||||||||
\(299\) | −16.4364 | −0.950540 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.10345 | −0.121241 | ||||||||
\(302\) | 9.25784 | 0.532729 | ||||||||
\(303\) | −7.76901 | −0.446318 | ||||||||
\(304\) | 4.89655 | 0.280836 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 16.8502 | 0.963260 | ||||||||
\(307\) | −7.87634 | −0.449526 | −0.224763 | − | 0.974413i | \(-0.572161\pi\) | ||||
−0.224763 | + | 0.974413i | \(0.572161\pi\) | |||||||
\(308\) | 7.46893 | 0.425582 | ||||||||
\(309\) | 30.2295 | 1.71969 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.89655 | 0.220953 | 0.110477 | − | 0.993879i | \(-0.464762\pi\) | ||||
0.110477 | + | 0.993879i | \(0.464762\pi\) | |||||||
\(312\) | 8.75286 | 0.495533 | ||||||||
\(313\) | −7.76901 | −0.439130 | −0.219565 | − | 0.975598i | \(-0.570464\pi\) | ||||
−0.219565 | + | 0.975598i | \(0.570464\pi\) | |||||||
\(314\) | 11.1498 | 0.629221 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.4364 | −0.924618 | ||||||||
\(317\) | −19.0510 | −1.07001 | −0.535005 | − | 0.844849i | \(-0.679690\pi\) | ||||
−0.535005 | + | 0.844849i | \(0.679690\pi\) | |||||||
\(318\) | 17.8483 | 1.00088 | ||||||||
\(319\) | −23.3793 | −1.30899 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.3567 | −0.745500 | ||||||||
\(322\) | 14.2032 | 0.791514 | ||||||||
\(323\) | 3.92301 | 0.218282 | ||||||||
\(324\) | −13.8984 | −0.772131 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −29.9560 | −1.65911 | ||||||||
\(327\) | −15.3756 | −0.850272 | ||||||||
\(328\) | 12.9029 | 0.712444 | ||||||||
\(329\) | 7.11655 | 0.392348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | −16.7365 | −0.918536 | ||||||||
\(333\) | 14.0450 | 0.769660 | ||||||||
\(334\) | −6.93164 | −0.379282 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −16.4364 | −0.896678 | ||||||||
\(337\) | 6.89249 | 0.375458 | 0.187729 | − | 0.982221i | \(-0.439887\pi\) | ||||
0.187729 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(338\) | 6.64000 | 0.361168 | ||||||||
\(339\) | −21.7931 | −1.18364 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 32.8727 | 1.78016 | ||||||||
\(342\) | 4.29522 | 0.232259 | ||||||||
\(343\) | 17.2539 | 0.931623 | ||||||||
\(344\) | 1.79310 | 0.0966774 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.7473 | −1.11538 | ||||||||
\(347\) | 30.5503 | 1.64002 | 0.820012 | − | 0.572346i | \(-0.193967\pi\) | ||||
0.820012 | + | 0.572346i | \(0.193967\pi\) | |||||||
\(348\) | −18.3533 | −0.983838 | ||||||||
\(349\) | 16.7693 | 0.897640 | 0.448820 | − | 0.893622i | \(-0.351844\pi\) | ||||
0.448820 | + | 0.893622i | \(0.351844\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.55416 | −0.243083 | ||||||||
\(352\) | −25.1384 | −1.33988 | ||||||||
\(353\) | −29.0999 | −1.54883 | −0.774417 | − | 0.632676i | \(-0.781956\pi\) | ||||
−0.774417 | + | 0.632676i | \(0.781956\pi\) | |||||||
\(354\) | 14.1593 | 0.752558 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.3436 | 0.866210 | ||||||||
\(357\) | −13.1685 | −0.696949 | ||||||||
\(358\) | −18.3533 | −0.970000 | ||||||||
\(359\) | −11.6896 | −0.616956 | −0.308478 | − | 0.951231i | \(-0.599820\pi\) | ||||
−0.308478 | + | 0.951231i | \(0.599820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −1.04449 | −0.0548972 | ||||||||
\(363\) | −9.68161 | −0.508153 | ||||||||
\(364\) | 5.86328 | 0.307319 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 43.5862 | 2.27829 | ||||||||
\(367\) | 4.20095 | 0.219288 | 0.109644 | − | 0.993971i | \(-0.465029\pi\) | ||||
0.109644 | + | 0.993971i | \(0.465029\pi\) | |||||||
\(368\) | −26.3108 | −1.37155 | ||||||||
\(369\) | 24.5957 | 1.28040 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.13672 | −0.318603 | ||||||||
\(372\) | 25.8058 | 1.33797 | ||||||||
\(373\) | 16.9456 | 0.877412 | 0.438706 | − | 0.898631i | \(-0.355437\pi\) | ||||
0.438706 | + | 0.898631i | \(0.355437\pi\) | |||||||
\(374\) | −27.8596 | −1.44059 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.06655 | −0.312858 | ||||||||
\(377\) | −18.3533 | −0.945241 | ||||||||
\(378\) | 3.93539 | 0.202415 | ||||||||
\(379\) | 10.3662 | 0.532476 | 0.266238 | − | 0.963907i | \(-0.414219\pi\) | ||||
0.266238 | + | 0.963907i | \(0.414219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 25.6753 | 1.31539 | ||||||||
\(382\) | 5.80131 | 0.296821 | ||||||||
\(383\) | −20.5907 | −1.05214 | −0.526068 | − | 0.850442i | \(-0.676334\pi\) | ||||
−0.526068 | + | 0.850442i | \(0.676334\pi\) | |||||||
\(384\) | 21.5749 | 1.10099 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.57491 | 0.283756 | ||||||||
\(387\) | 3.41802 | 0.173748 | ||||||||
\(388\) | −4.04272 | −0.205238 | ||||||||
\(389\) | 8.10345 | 0.410861 | 0.205431 | − | 0.978672i | \(-0.434141\pi\) | ||||
0.205431 | + | 0.978672i | \(0.434141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0796 | −1.06604 | ||||||||
\(392\) | −6.05380 | −0.305763 | ||||||||
\(393\) | −10.6697 | −0.538213 | ||||||||
\(394\) | 39.1724 | 1.97348 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.1367 | −0.609893 | ||||||||
\(397\) | −3.46891 | −0.174100 | −0.0870499 | − | 0.996204i | \(-0.527744\pi\) | ||||
−0.0870499 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(398\) | 8.77898 | 0.440050 | ||||||||
\(399\) | −3.35673 | −0.168046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9524 | −0.796625 | −0.398312 | − | 0.917250i | \(-0.630404\pi\) | ||||
−0.398312 | + | 0.917250i | \(0.630404\pi\) | |||||||
\(402\) | 41.5240 | 2.07103 | ||||||||
\(403\) | 25.8058 | 1.28548 | ||||||||
\(404\) | 4.43637 | 0.220718 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.8596 | 0.787101 | ||||||||
\(407\) | −23.2216 | −1.15105 | ||||||||
\(408\) | 11.2255 | 0.555747 | ||||||||
\(409\) | −3.92982 | −0.194317 | −0.0971586 | − | 0.995269i | \(-0.530975\pi\) | ||||
−0.0971586 | + | 0.995269i | \(0.530975\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −30.5066 | −1.50478 | ||||||||
\(412\) | −17.2621 | −0.850442 | ||||||||
\(413\) | −4.86835 | −0.239556 | ||||||||
\(414\) | −23.0796 | −1.13430 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −19.7342 | −0.967549 | ||||||||
\(417\) | −2.73823 | −0.134092 | ||||||||
\(418\) | −7.10160 | −0.347351 | ||||||||
\(419\) | −34.2996 | −1.67565 | −0.837824 | − | 0.545941i | \(-0.816172\pi\) | ||||
−0.837824 | + | 0.545941i | \(0.816172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0891 | −1.27151 | −0.635753 | − | 0.771893i | \(-0.719310\pi\) | ||||
−0.635753 | + | 0.771893i | \(0.719310\pi\) | |||||||
\(422\) | −19.1486 | −0.932138 | ||||||||
\(423\) | −11.5641 | −0.562267 | ||||||||
\(424\) | 5.23129 | 0.254054 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 36.4589 | 1.76644 | ||||||||
\(427\) | −14.9861 | −0.725229 | ||||||||
\(428\) | 7.62715 | 0.368672 | ||||||||
\(429\) | −27.5862 | −1.33187 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2996 | 0.496117 | 0.248058 | − | 0.968745i | \(-0.420208\pi\) | ||||
0.248058 | + | 0.968745i | \(0.420208\pi\) | |||||||
\(432\) | −7.29014 | −0.350747 | ||||||||
\(433\) | 36.2319 | 1.74119 | 0.870596 | − | 0.491999i | \(-0.163734\pi\) | ||||
0.870596 | + | 0.491999i | \(0.163734\pi\) | |||||||
\(434\) | −22.2996 | −1.07042 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.78000 | 0.420486 | ||||||||
\(437\) | −5.37334 | −0.257042 | ||||||||
\(438\) | 10.2678 | 0.490615 | ||||||||
\(439\) | −24.0891 | −1.14971 | −0.574855 | − | 0.818255i | \(-0.694942\pi\) | ||||
−0.574855 | + | 0.818255i | \(0.694942\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.5398 | −0.549515 | ||||||||
\(442\) | −21.8704 | −1.04027 | ||||||||
\(443\) | 5.52337 | 0.262423 | 0.131212 | − | 0.991354i | \(-0.458113\pi\) | ||||
0.131212 | + | 0.991354i | \(0.458113\pi\) | |||||||
\(444\) | −18.2295 | −0.865132 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −30.7913 | −1.45801 | ||||||||
\(447\) | −12.6374 | −0.597727 | ||||||||
\(448\) | 2.84977 | 0.134639 | ||||||||
\(449\) | 7.92982 | 0.374231 | 0.187116 | − | 0.982338i | \(-0.440086\pi\) | ||||
0.187116 | + | 0.982338i | \(0.440086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.6658 | −1.91488 | ||||||||
\(452\) | 12.4446 | 0.585346 | ||||||||
\(453\) | 11.7566 | 0.552375 | ||||||||
\(454\) | 31.2277 | 1.46559 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.86146 | 0.134000 | ||||||||
\(457\) | 22.6534 | 1.05968 | 0.529840 | − | 0.848098i | \(-0.322252\pi\) | ||||
0.529840 | + | 0.848098i | \(0.322252\pi\) | |||||||
\(458\) | −45.6479 | −2.13299 | ||||||||
\(459\) | −5.84070 | −0.272621 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3900 | 0.623634 | 0.311817 | − | 0.950142i | \(-0.399062\pi\) | ||||
0.311817 | + | 0.950142i | \(0.399062\pi\) | |||||||
\(462\) | 23.8381 | 1.10905 | ||||||||
\(463\) | 16.9029 | 0.785546 | 0.392773 | − | 0.919635i | \(-0.371516\pi\) | ||||
0.392773 | + | 0.919635i | \(0.371516\pi\) | |||||||
\(464\) | −29.3793 | −1.36390 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 35.1724 | 1.62933 | ||||||||
\(467\) | 22.2501 | 1.02961 | 0.514807 | − | 0.857306i | \(-0.327864\pi\) | ||||
0.514807 | + | 0.857306i | \(0.327864\pi\) | |||||||
\(468\) | −9.52759 | −0.440413 | ||||||||
\(469\) | −14.2771 | −0.659254 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.1593 | 0.652426 | ||||||||
\(472\) | 4.15006 | 0.191022 | ||||||||
\(473\) | −5.65127 | −0.259846 | ||||||||
\(474\) | −52.4589 | −2.40952 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.51965 | 0.344663 | ||||||||
\(477\) | 9.97194 | 0.456584 | ||||||||
\(478\) | −34.2077 | −1.56462 | ||||||||
\(479\) | 0.366196 | 0.0167319 | 0.00836597 | − | 0.999965i | \(-0.497337\pi\) | ||||
0.00836597 | + | 0.999965i | \(0.497337\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.2295 | −0.831192 | ||||||||
\(482\) | 26.3108 | 1.19842 | ||||||||
\(483\) | 18.0368 | 0.820704 | ||||||||
\(484\) | 5.52854 | 0.251297 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −36.2182 | −1.64289 | ||||||||
\(487\) | 26.8461 | 1.21651 | 0.608257 | − | 0.793740i | \(-0.291869\pi\) | ||||
0.608257 | + | 0.793740i | \(0.291869\pi\) | |||||||
\(488\) | 12.7750 | 0.578298 | ||||||||
\(489\) | −38.0415 | −1.72030 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.7266 | −1.07076 | −0.535382 | − | 0.844610i | \(-0.679832\pi\) | ||||
−0.535382 | + | 0.844610i | \(0.679832\pi\) | |||||||
\(492\) | −31.9236 | −1.43923 | ||||||||
\(493\) | −23.5381 | −1.06010 | ||||||||
\(494\) | −5.57491 | −0.250827 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 41.3091 | 1.85483 | ||||||||
\(497\) | −12.5356 | −0.562298 | ||||||||
\(498\) | −53.4169 | −2.39367 | ||||||||
\(499\) | 6.81690 | 0.305166 | 0.152583 | − | 0.988291i | \(-0.451241\pi\) | ||||
0.152583 | + | 0.988291i | \(0.451241\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.80257 | −0.393270 | ||||||||
\(502\) | 20.0045 | 0.892845 | ||||||||
\(503\) | 23.4102 | 1.04381 | 0.521904 | − | 0.853004i | \(-0.325222\pi\) | ||||
0.521904 | + | 0.853004i | \(0.325222\pi\) | |||||||
\(504\) | −4.22584 | −0.188234 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 38.1593 | 1.69639 | ||||||||
\(507\) | 8.43221 | 0.374488 | ||||||||
\(508\) | −14.6615 | −0.650499 | ||||||||
\(509\) | 16.9204 | 0.749981 | 0.374991 | − | 0.927029i | \(-0.377646\pi\) | ||||
0.374991 | + | 0.927029i | \(0.377646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.53035 | −0.156174 | ||||||||
\(512\) | −19.4823 | −0.861003 | ||||||||
\(513\) | −1.48883 | −0.0657336 | ||||||||
\(514\) | −32.1480 | −1.41799 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.43637 | −0.195300 | ||||||||
\(517\) | 19.1198 | 0.840888 | ||||||||
\(518\) | 15.7527 | 0.692133 | ||||||||
\(519\) | −26.3473 | −1.15652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.49345 | −0.153051 | −0.0765254 | − | 0.997068i | \(-0.524383\pi\) | ||||
−0.0765254 | + | 0.997068i | \(0.524383\pi\) | |||||||
\(522\) | −25.7713 | −1.12798 | ||||||||
\(523\) | 14.9271 | 0.652714 | 0.326357 | − | 0.945247i | \(-0.394179\pi\) | ||||
0.326357 | + | 0.945247i | \(0.394179\pi\) | |||||||
\(524\) | 6.09275 | 0.266163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.07965 | −0.134279 | ||||||||
\(527\) | 33.0960 | 1.44168 | ||||||||
\(528\) | −44.1591 | −1.92178 | ||||||||
\(529\) | 5.87275 | 0.255337 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.91088 | 0.343303 | ||||||||
\(532\) | 1.91681 | 0.0831041 | ||||||||
\(533\) | −31.9236 | −1.38276 | ||||||||
\(534\) | 52.1629 | 2.25731 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.1706 | 0.525689 | ||||||||
\(537\) | −23.3070 | −1.00577 | ||||||||
\(538\) | 49.3948 | 2.12956 | ||||||||
\(539\) | 19.0796 | 0.821819 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.6991 | −0.545978 | −0.272989 | − | 0.962017i | \(-0.588012\pi\) | ||||
−0.272989 | + | 0.962017i | \(0.588012\pi\) | |||||||
\(542\) | −43.6541 | −1.87510 | ||||||||
\(543\) | −1.32641 | −0.0569217 | ||||||||
\(544\) | −25.3091 | −1.08512 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.7135 | 0.800862 | ||||||||
\(547\) | 31.8162 | 1.36036 | 0.680182 | − | 0.733043i | \(-0.261901\pi\) | ||||
0.680182 | + | 0.733043i | \(0.261901\pi\) | |||||||
\(548\) | 17.4203 | 0.744158 | ||||||||
\(549\) | 24.3519 | 1.03931 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | −15.3756 | −0.654429 | ||||||||
\(553\) | 18.0368 | 0.767003 | ||||||||
\(554\) | 15.0095 | 0.637691 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.56363 | 0.0663125 | ||||||||
\(557\) | 9.64731 | 0.408770 | 0.204385 | − | 0.978891i | \(-0.434481\pi\) | ||||
0.204385 | + | 0.978891i | \(0.434481\pi\) | |||||||
\(558\) | 36.2361 | 1.53399 | ||||||||
\(559\) | −4.43637 | −0.187639 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.3793 | −1.49372 | ||||||||
\(562\) | 19.0207 | 0.802338 | ||||||||
\(563\) | 4.28216 | 0.180471 | 0.0902357 | − | 0.995920i | \(-0.471238\pi\) | ||||
0.0902357 | + | 0.995920i | \(0.471238\pi\) | |||||||
\(564\) | 15.0095 | 0.632013 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −19.0796 | −0.801977 | ||||||||
\(567\) | 15.2517 | 0.640510 | ||||||||
\(568\) | 10.6860 | 0.448376 | ||||||||
\(569\) | 42.2295 | 1.77035 | 0.885176 | − | 0.465257i | \(-0.154038\pi\) | ||||
0.885176 | + | 0.465257i | \(0.154038\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.2200 | −0.804332 | −0.402166 | − | 0.915567i | \(-0.631743\pi\) | ||||
−0.402166 | + | 0.915567i | \(0.631743\pi\) | |||||||
\(572\) | 15.7527 | 0.658653 | ||||||||
\(573\) | 7.36715 | 0.307767 | ||||||||
\(574\) | 27.5862 | 1.15143 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.63076 | −0.192948 | ||||||||
\(577\) | 40.7919 | 1.69819 | 0.849096 | − | 0.528239i | \(-0.177148\pi\) | ||||
0.849096 | + | 0.528239i | \(0.177148\pi\) | |||||||
\(578\) | 2.93428 | 0.122050 | ||||||||
\(579\) | 7.07965 | 0.294220 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 18.3662 | 0.761958 | ||||||||
\(582\) | −12.9029 | −0.534843 | ||||||||
\(583\) | −16.4873 | −0.682836 | ||||||||
\(584\) | 3.00947 | 0.124533 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −30.0113 | −1.23975 | ||||||||
\(587\) | 31.8851 | 1.31604 | 0.658019 | − | 0.753001i | \(-0.271395\pi\) | ||||
0.658019 | + | 0.753001i | \(0.271395\pi\) | |||||||
\(588\) | 14.9779 | 0.617680 | ||||||||
\(589\) | 8.43637 | 0.347615 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 49.7455 | 2.04626 | ||||||||
\(592\) | −29.1811 | −1.19934 | ||||||||
\(593\) | 38.8973 | 1.59732 | 0.798660 | − | 0.601783i | \(-0.205543\pi\) | ||||
0.798660 | + | 0.601783i | \(0.205543\pi\) | |||||||
\(594\) | 10.5731 | 0.433819 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.21637 | 0.295594 | ||||||||
\(597\) | 11.1485 | 0.456279 | ||||||||
\(598\) | 29.9559 | 1.22499 | ||||||||
\(599\) | 28.1629 | 1.15071 | 0.575353 | − | 0.817905i | \(-0.304865\pi\) | ||||
0.575353 | + | 0.817905i | \(0.304865\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.56363 | −0.226945 | −0.113473 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113473 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(602\) | 3.83361 | 0.156246 | ||||||||
\(603\) | 23.1997 | 0.944764 | ||||||||
\(604\) | −6.71345 | −0.273166 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 14.1593 | 0.575182 | ||||||||
\(607\) | −33.9986 | −1.37996 | −0.689980 | − | 0.723828i | \(-0.742381\pi\) | ||||
−0.689980 | + | 0.723828i | \(0.742381\pi\) | |||||||
\(608\) | −6.45146 | −0.261641 | ||||||||
\(609\) | 20.1404 | 0.816128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0095 | 0.607218 | ||||||||
\(612\) | −12.2191 | −0.493929 | ||||||||
\(613\) | −17.5703 | −0.709659 | −0.354830 | − | 0.934931i | \(-0.615461\pi\) | ||||
−0.354830 | + | 0.934931i | \(0.615461\pi\) | |||||||
\(614\) | 14.3549 | 0.579317 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.98690 | 0.281510 | ||||||||
\(617\) | 13.0791 | 0.526544 | 0.263272 | − | 0.964722i | \(-0.415198\pi\) | ||||
0.263272 | + | 0.964722i | \(0.415198\pi\) | |||||||
\(618\) | −55.0943 | −2.21622 | ||||||||
\(619\) | −18.9393 | −0.761234 | −0.380617 | − | 0.924733i | \(-0.624288\pi\) | ||||
−0.380617 | + | 0.924733i | \(0.624288\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | 0.321029 | ||||||||
\(622\) | −7.10160 | −0.284748 | ||||||||
\(623\) | −17.9350 | −0.718552 | ||||||||
\(624\) | −34.6658 | −1.38774 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 14.1593 | 0.565919 | ||||||||
\(627\) | −9.01841 | −0.360161 | ||||||||
\(628\) | −8.08545 | −0.322645 | ||||||||
\(629\) | −23.3793 | −0.932194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.6896 | 1.26154 | 0.630772 | − | 0.775968i | \(-0.282738\pi\) | ||||
0.630772 | + | 0.775968i | \(0.282738\pi\) | |||||||
\(632\) | −15.3756 | −0.611608 | ||||||||
\(633\) | −24.3170 | −0.966514 | ||||||||
\(634\) | 34.7211 | 1.37895 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.9429 | −0.513220 | ||||||||
\(637\) | 14.9779 | 0.593448 | ||||||||
\(638\) | 42.6096 | 1.68693 | ||||||||
\(639\) | 20.3698 | 0.805818 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.9750 | 1.89490 | 0.947449 | − | 0.319908i | \(-0.103652\pi\) | ||||
0.947449 | + | 0.319908i | \(0.103652\pi\) | |||||||
\(642\) | 24.3431 | 0.960746 | ||||||||
\(643\) | 0.200927 | 0.00792378 | 0.00396189 | − | 0.999992i | \(-0.498739\pi\) | ||||
0.00396189 | + | 0.999992i | \(0.498739\pi\) | |||||||
\(644\) | −10.2996 | −0.405863 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.14982 | −0.281306 | ||||||||
\(647\) | −1.58798 | −0.0624299 | −0.0312150 | − | 0.999513i | \(-0.509938\pi\) | ||||
−0.0312150 | + | 0.999513i | \(0.509938\pi\) | |||||||
\(648\) | −13.0014 | −0.510743 | ||||||||
\(649\) | −13.0796 | −0.513421 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −28.3186 | −1.10989 | ||||||||
\(652\) | 21.7230 | 0.850739 | ||||||||
\(653\) | 33.5624 | 1.31340 | 0.656700 | − | 0.754152i | \(-0.271952\pi\) | ||||
0.656700 | + | 0.754152i | \(0.271952\pi\) | |||||||
\(654\) | 28.0226 | 1.09577 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −51.1022 | −1.99521 | ||||||||
\(657\) | 5.73669 | 0.223809 | ||||||||
\(658\) | −12.9702 | −0.505630 | ||||||||
\(659\) | 15.3567 | 0.598213 | 0.299107 | − | 0.954220i | \(-0.403311\pi\) | ||||
0.299107 | + | 0.954220i | \(0.403311\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8026 | 0.497962 | 0.248981 | − | 0.968508i | \(-0.419904\pi\) | ||||
0.248981 | + | 0.968508i | \(0.419904\pi\) | |||||||
\(662\) | −14.5803 | −0.566679 | ||||||||
\(663\) | −27.7735 | −1.07863 | ||||||||
\(664\) | −15.6564 | −0.607585 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.5975 | −0.991882 | ||||||||
\(667\) | 32.2400 | 1.24834 | ||||||||
\(668\) | 5.02657 | 0.194484 | ||||||||
\(669\) | −39.1022 | −1.51178 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −40.2627 | −1.55433 | ||||||||
\(672\) | 21.6558 | 0.835389 | ||||||||
\(673\) | −7.82545 | −0.301649 | −0.150824 | − | 0.988561i | \(-0.548193\pi\) | ||||
−0.150824 | + | 0.988561i | \(0.548193\pi\) | |||||||
\(674\) | −12.5618 | −0.483863 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.81509 | −0.185196 | ||||||||
\(677\) | −21.6516 | −0.832137 | −0.416069 | − | 0.909333i | \(-0.636592\pi\) | ||||
−0.416069 | + | 0.909333i | \(0.636592\pi\) | |||||||
\(678\) | 39.7187 | 1.52539 | ||||||||
\(679\) | 4.43637 | 0.170252 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.6564 | 1.51964 | ||||||||
\(682\) | −59.9118 | −2.29414 | ||||||||
\(683\) | −6.38751 | −0.244411 | −0.122206 | − | 0.992505i | \(-0.538997\pi\) | ||||
−0.122206 | + | 0.992505i | \(0.538997\pi\) | |||||||
\(684\) | −3.11474 | −0.119095 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −31.4458 | −1.20061 | ||||||||
\(687\) | −57.9688 | −2.21165 | ||||||||
\(688\) | −7.10160 | −0.270746 | ||||||||
\(689\) | −12.9429 | −0.493086 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.4958 | 1.69270 | 0.846351 | − | 0.532626i | \(-0.178795\pi\) | ||||
0.846351 | + | 0.532626i | \(0.178795\pi\) | |||||||
\(692\) | 15.0452 | 0.571933 | ||||||||
\(693\) | 13.3185 | 0.505928 | ||||||||
\(694\) | −55.6789 | −2.11354 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −17.1688 | −0.650780 | ||||||||
\(697\) | −40.9420 | −1.55079 | ||||||||
\(698\) | −30.5626 | −1.15681 | ||||||||
\(699\) | 44.6658 | 1.68942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.5160 | 0.661571 | 0.330785 | − | 0.943706i | \(-0.392686\pi\) | ||||
0.330785 | + | 0.943706i | \(0.392686\pi\) | |||||||
\(702\) | 8.30011 | 0.313268 | ||||||||
\(703\) | −5.95953 | −0.224768 | ||||||||
\(704\) | 7.65638 | 0.288560 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.0357 | 1.99602 | ||||||||
\(707\) | −4.86835 | −0.183093 | ||||||||
\(708\) | −10.2678 | −0.385888 | ||||||||
\(709\) | 11.4269 | 0.429146 | 0.214573 | − | 0.976708i | \(-0.431164\pi\) | ||||
0.214573 | + | 0.976708i | \(0.431164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −29.3091 | −1.09918 | ||||||||
\(712\) | 15.2888 | 0.572973 | ||||||||
\(713\) | −45.3315 | −1.69768 | ||||||||
\(714\) | 24.0000 | 0.898177 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 13.3091 | 0.497385 | ||||||||
\(717\) | −43.4408 | −1.62233 | ||||||||
\(718\) | 21.3048 | 0.795088 | ||||||||
\(719\) | 15.8965 | 0.592841 | 0.296421 | − | 0.955057i | \(-0.404207\pi\) | ||||
0.296421 | + | 0.955057i | \(0.404207\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.9429 | 0.705471 | ||||||||
\(722\) | −1.82254 | −0.0678278 | ||||||||
\(723\) | 33.4124 | 1.24262 | ||||||||
\(724\) | 0.757427 | 0.0281495 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 17.6451 | 0.654871 | ||||||||
\(727\) | −41.9905 | −1.55734 | −0.778670 | − | 0.627434i | \(-0.784105\pi\) | ||||
−0.778670 | + | 0.627434i | \(0.784105\pi\) | |||||||
\(728\) | 5.48487 | 0.203283 | ||||||||
\(729\) | −14.4458 | −0.535031 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.68965 | −0.210439 | ||||||||
\(732\) | −31.6071 | −1.16823 | ||||||||
\(733\) | 0.632884 | 0.0233761 | 0.0116881 | − | 0.999932i | \(-0.496279\pi\) | ||||
0.0116881 | + | 0.999932i | \(0.496279\pi\) | |||||||
\(734\) | −7.65638 | −0.282602 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.6658 | 1.27780 | ||||||||
\(737\) | −38.3578 | −1.41293 | ||||||||
\(738\) | −44.8265 | −1.65009 | ||||||||
\(739\) | −29.5493 | −1.08699 | −0.543494 | − | 0.839413i | \(-0.682899\pi\) | ||||
−0.543494 | + | 0.839413i | \(0.682899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.07965 | −0.260077 | ||||||||
\(742\) | 11.1844 | 0.410592 | ||||||||
\(743\) | 31.3374 | 1.14966 | 0.574829 | − | 0.818274i | \(-0.305069\pi\) | ||||
0.574829 | + | 0.818274i | \(0.305069\pi\) | |||||||
\(744\) | 24.1404 | 0.885028 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −30.8840 | −1.13074 | ||||||||
\(747\) | −29.8443 | −1.09195 | ||||||||
\(748\) | 20.2028 | 0.738688 | ||||||||
\(749\) | −8.36983 | −0.305827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0131 | 0.912741 | 0.456371 | − | 0.889790i | \(-0.349149\pi\) | ||||
0.456371 | + | 0.889790i | \(0.349149\pi\) | |||||||
\(752\) | 24.0267 | 0.876163 | ||||||||
\(753\) | 25.4040 | 0.925772 | ||||||||
\(754\) | 33.4495 | 1.21816 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.85381 | −0.103792 | ||||||||
\(757\) | 32.0900 | 1.16633 | 0.583165 | − | 0.812354i | \(-0.301814\pi\) | ||||
0.583165 | + | 0.812354i | \(0.301814\pi\) | |||||||
\(758\) | −18.8928 | −0.686216 | ||||||||
\(759\) | 48.4589 | 1.75895 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −40.4922 | −1.46784 | −0.733921 | − | 0.679235i | \(-0.762312\pi\) | ||||
−0.733921 | + | 0.679235i | \(0.762312\pi\) | |||||||
\(762\) | −46.7942 | −1.69517 | ||||||||
\(763\) | −9.63492 | −0.348808 | ||||||||
\(764\) | −4.20690 | −0.152200 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.5273 | 1.35592 | ||||||||
\(767\) | −10.2678 | −0.370749 | ||||||||
\(768\) | −48.4165 | −1.74708 | ||||||||
\(769\) | 3.09398 | 0.111572 | 0.0557859 | − | 0.998443i | \(-0.482234\pi\) | ||||
0.0557859 | + | 0.998443i | \(0.482234\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.8251 | −1.47028 | ||||||||
\(772\) | −4.04272 | −0.145501 | ||||||||
\(773\) | 1.96350 | 0.0706220 | 0.0353110 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353110 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(774\) | −6.22947 | −0.223914 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.78181 | −0.135759 | ||||||||
\(777\) | 20.0045 | 0.717658 | ||||||||
\(778\) | −14.7688 | −0.529488 | ||||||||
\(779\) | −10.4364 | −0.373922 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −33.6789 | −1.20513 | ||||||||
\(782\) | 38.4184 | 1.37384 | ||||||||
\(783\) | 8.93300 | 0.319239 | ||||||||
\(784\) | 23.9762 | 0.856293 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.4458 | 0.693610 | ||||||||
\(787\) | 0.107331 | 0.00382595 | 0.00191297 | − | 0.999998i | \(-0.499391\pi\) | ||||
0.00191297 | + | 0.999998i | \(0.499391\pi\) | |||||||
\(788\) | −28.4064 | −1.01194 | ||||||||
\(789\) | −3.91088 | −0.139231 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.6564 | −0.485565 | ||||||||
\(792\) | −11.3534 | −0.403427 | ||||||||
\(793\) | −31.6071 | −1.12240 | ||||||||
\(794\) | 6.32222 | 0.224367 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.36620 | −0.225644 | ||||||||
\(797\) | 8.32068 | 0.294734 | 0.147367 | − | 0.989082i | \(-0.452920\pi\) | ||||
0.147367 | + | 0.989082i | \(0.452920\pi\) | |||||||
\(798\) | 6.11775 | 0.216566 | ||||||||
\(799\) | 19.2496 | 0.681003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 29.1437 | 1.02974 | ||||||||
\(802\) | 29.0738 | 1.02663 | ||||||||
\(803\) | −9.48489 | −0.334714 | ||||||||
\(804\) | −30.1117 | −1.06196 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −47.0320 | −1.65663 | ||||||||
\(807\) | 62.7270 | 2.20810 | ||||||||
\(808\) | 4.15006 | 0.145998 | ||||||||
\(809\) | −27.6231 | −0.971177 | −0.485588 | − | 0.874188i | \(-0.661395\pi\) | ||||
−0.485588 | + | 0.874188i | \(0.661395\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.0095 | 0.807972 | 0.403986 | − | 0.914765i | \(-0.367624\pi\) | ||||
0.403986 | + | 0.914765i | \(0.367624\pi\) | |||||||
\(812\) | −11.5008 | −0.403600 | ||||||||
\(813\) | −55.4369 | −1.94426 | ||||||||
\(814\) | 42.3222 | 1.48339 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −44.4589 | −1.55637 | ||||||||
\(817\) | −1.45033 | −0.0507405 | ||||||||
\(818\) | 7.16224 | 0.250422 | ||||||||
\(819\) | 10.4553 | 0.365338 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.1355 | 1.08664 | 0.543318 | − | 0.839527i | \(-0.317168\pi\) | ||||
0.543318 | + | 0.839527i | \(0.317168\pi\) | |||||||
\(822\) | 55.5993 | 1.93925 | ||||||||
\(823\) | −20.4201 | −0.711800 | −0.355900 | − | 0.934524i | \(-0.615826\pi\) | ||||
−0.355900 | + | 0.934524i | \(0.615826\pi\) | |||||||
\(824\) | −16.1480 | −0.562543 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.87275 | 0.308722 | ||||||||
\(827\) | 0.902638 | 0.0313878 | 0.0156939 | − | 0.999877i | \(-0.495004\pi\) | ||||
0.0156939 | + | 0.999877i | \(0.495004\pi\) | |||||||
\(828\) | 16.7365 | 0.581634 | ||||||||
\(829\) | −13.4971 | −0.468773 | −0.234386 | − | 0.972143i | \(-0.575308\pi\) | ||||
−0.234386 | + | 0.972143i | \(0.575308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 19.0607 | 0.661209 | ||||||||
\(832\) | 6.01042 | 0.208374 | ||||||||
\(833\) | 19.2092 | 0.665560 | ||||||||
\(834\) | 4.99053 | 0.172808 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.14982 | 0.178110 | ||||||||
\(837\) | −12.5603 | −0.434149 | ||||||||
\(838\) | 62.5123 | 2.15945 | ||||||||
\(839\) | 33.1022 | 1.14282 | 0.571408 | − | 0.820666i | \(-0.306397\pi\) | ||||
0.571408 | + | 0.820666i | \(0.306397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 47.5484 | 1.63862 | ||||||||
\(843\) | 24.1546 | 0.831928 | ||||||||
\(844\) | 13.8858 | 0.477971 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 21.0760 | 0.724608 | ||||||||
\(847\) | −6.06686 | −0.208460 | ||||||||
\(848\) | −20.7186 | −0.711480 | ||||||||
\(849\) | −24.2295 | −0.831553 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.0226 | 1.09772 | ||||||||
\(852\) | −26.4387 | −0.905775 | ||||||||
\(853\) | −50.9097 | −1.74312 | −0.871558 | − | 0.490293i | \(-0.836890\pi\) | ||||
−0.871558 | + | 0.490293i | \(0.836890\pi\) | |||||||
\(854\) | 27.3128 | 0.934623 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.13491 | 0.243866 | ||||||||
\(857\) | −21.2333 | −0.725317 | −0.362659 | − | 0.931922i | \(-0.618131\pi\) | ||||
−0.362659 | + | 0.931922i | \(0.618131\pi\) | |||||||
\(858\) | 50.2768 | 1.71642 | ||||||||
\(859\) | 29.4827 | 1.00594 | 0.502969 | − | 0.864304i | \(-0.332241\pi\) | ||||
0.502969 | + | 0.864304i | \(0.332241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 35.0320 | 1.19389 | ||||||||
\(862\) | −18.7715 | −0.639359 | ||||||||
\(863\) | −25.7755 | −0.877408 | −0.438704 | − | 0.898632i | \(-0.644562\pi\) | ||||
−0.438704 | + | 0.898632i | \(0.644562\pi\) | |||||||
\(864\) | 9.60514 | 0.326773 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −66.0339 | −2.24392 | ||||||||
\(867\) | 3.72628 | 0.126551 | ||||||||
\(868\) | 16.1709 | 0.548876 | ||||||||
\(869\) | 48.4589 | 1.64386 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.1117 | −1.02030 | ||||||||
\(872\) | 8.21335 | 0.278139 | ||||||||
\(873\) | −7.20893 | −0.243985 | ||||||||
\(874\) | 9.79310 | 0.331257 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.44584 | −0.251572 | ||||||||
\(877\) | −54.2687 | −1.83252 | −0.916261 | − | 0.400581i | \(-0.868808\pi\) | ||||
−0.916261 | + | 0.400581i | \(0.868808\pi\) | |||||||
\(878\) | 43.9033 | 1.48166 | ||||||||
\(879\) | −38.1117 | −1.28548 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.4922 | −0.959927 | −0.479964 | − | 0.877288i | \(-0.659350\pi\) | ||||
−0.479964 | + | 0.877288i | \(0.659350\pi\) | |||||||
\(882\) | 21.0317 | 0.708176 | ||||||||
\(883\) | −40.5264 | −1.36382 | −0.681911 | − | 0.731435i | \(-0.738851\pi\) | ||||
−0.681911 | + | 0.731435i | \(0.738851\pi\) | |||||||
\(884\) | 15.8596 | 0.533418 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.0665 | −0.338192 | ||||||||
\(887\) | 11.4705 | 0.385142 | 0.192571 | − | 0.981283i | \(-0.438317\pi\) | ||||
0.192571 | + | 0.981283i | \(0.438317\pi\) | |||||||
\(888\) | −17.0530 | −0.572260 | ||||||||
\(889\) | 16.0891 | 0.539612 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 40.9762 | 1.37275 | ||||||||
\(892\) | 22.3287 | 0.747621 | ||||||||
\(893\) | 4.90686 | 0.164202 | ||||||||
\(894\) | 23.0320 | 0.770307 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.5197 | 0.451660 | ||||||||
\(897\) | 38.0413 | 1.27016 | ||||||||
\(898\) | −14.4524 | −0.482282 | ||||||||
\(899\) | −50.6182 | −1.68821 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.5993 | −0.553003 | ||||||||
\(902\) | 74.1150 | 2.46776 | ||||||||
\(903\) | 4.86835 | 0.162009 | ||||||||
\(904\) | 11.6415 | 0.387189 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.4269 | −0.711861 | ||||||||
\(907\) | 48.1000 | 1.59714 | 0.798568 | − | 0.601905i | \(-0.205591\pi\) | ||||
0.798568 | + | 0.601905i | \(0.205591\pi\) | |||||||
\(908\) | −22.6452 | −0.751506 | ||||||||
\(909\) | 7.91088 | 0.262387 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.8062 | −0.424288 | −0.212144 | − | 0.977238i | \(-0.568045\pi\) | ||||
−0.212144 | + | 0.977238i | \(0.568045\pi\) | |||||||
\(912\) | −11.3329 | −0.375269 | ||||||||
\(913\) | 49.3439 | 1.63304 | ||||||||
\(914\) | −41.2865 | −1.36564 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.1022 | 1.09373 | ||||||||
\(917\) | −6.68601 | −0.220792 | ||||||||
\(918\) | 10.6449 | 0.351334 | ||||||||
\(919\) | −38.7135 | −1.27704 | −0.638519 | − | 0.769606i | \(-0.720453\pi\) | ||||
−0.638519 | + | 0.769606i | \(0.720453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2295 | 0.600682 | ||||||||
\(922\) | −24.4038 | −0.803695 | ||||||||
\(923\) | −26.4387 | −0.870241 | ||||||||
\(924\) | −17.2865 | −0.568686 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −30.8062 | −1.01235 | ||||||||
\(927\) | −30.7815 | −1.01100 | ||||||||
\(928\) | 38.7087 | 1.27068 | ||||||||
\(929\) | −36.0189 | −1.18174 | −0.590872 | − | 0.806766i | \(-0.701216\pi\) | ||||
−0.590872 | + | 0.806766i | \(0.701216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89655 | 0.160478 | ||||||||
\(932\) | −25.5058 | −0.835469 | ||||||||
\(933\) | −9.01841 | −0.295249 | ||||||||
\(934\) | −40.5517 | −1.32689 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.91270 | −0.291321 | ||||||||
\(937\) | −45.2421 | −1.47799 | −0.738997 | − | 0.673709i | \(-0.764700\pi\) | ||||
−0.738997 | + | 0.673709i | \(0.764700\pi\) | |||||||
\(938\) | 26.0205 | 0.849599 | ||||||||
\(939\) | 17.9811 | 0.586790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.7455 | −0.382892 | −0.191446 | − | 0.981503i | \(-0.561318\pi\) | ||||
−0.191446 | + | 0.981503i | \(0.561318\pi\) | |||||||
\(942\) | −25.8058 | −0.840799 | ||||||||
\(943\) | 56.0781 | 1.82616 | ||||||||
\(944\) | −16.4364 | −0.534958 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.2996 | 0.334870 | ||||||||
\(947\) | −13.7752 | −0.447635 | −0.223817 | − | 0.974631i | \(-0.571852\pi\) | ||||
−0.223817 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(948\) | 38.0413 | 1.23552 | ||||||||
\(949\) | −7.44584 | −0.241702 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.0927 | 1.42981 | ||||||||
\(952\) | 7.03434 | 0.227984 | ||||||||
\(953\) | 9.01421 | 0.291999 | 0.145999 | − | 0.989285i | \(-0.453360\pi\) | ||||
0.145999 | + | 0.989285i | \(0.453360\pi\) | |||||||
\(954\) | −18.1742 | −0.588412 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.8062 | 0.802290 | ||||||||
\(957\) | 54.1105 | 1.74914 | ||||||||
\(958\) | −0.667406 | −0.0215629 | ||||||||
\(959\) | −19.1166 | −0.617306 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.1724 | 1.29588 | ||||||||
\(962\) | 33.2239 | 1.07118 | ||||||||
\(963\) | 13.6006 | 0.438274 | ||||||||
\(964\) | −19.0796 | −0.614514 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −32.8727 | −1.05766 | ||||||||
\(967\) | 30.3232 | 0.975129 | 0.487564 | − | 0.873087i | \(-0.337885\pi\) | ||||
0.487564 | + | 0.873087i | \(0.337885\pi\) | |||||||
\(968\) | 5.17173 | 0.166226 | ||||||||
\(969\) | −9.07965 | −0.291680 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.5636 | −1.01292 | −0.506462 | − | 0.862262i | \(-0.669047\pi\) | ||||
−0.506462 | + | 0.862262i | \(0.669047\pi\) | |||||||
\(972\) | 26.2641 | 0.842422 | ||||||||
\(973\) | −1.71588 | −0.0550086 | ||||||||
\(974\) | −48.9280 | −1.56775 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −50.5957 | −1.61953 | ||||||||
\(977\) | 43.1285 | 1.37980 | 0.689902 | − | 0.723903i | \(-0.257654\pi\) | ||||
0.689902 | + | 0.723903i | \(0.257654\pi\) | |||||||
\(978\) | 69.3320 | 2.21699 | ||||||||
\(979\) | −48.1855 | −1.54002 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6564 | 0.499870 | ||||||||
\(982\) | 43.2425 | 1.37992 | ||||||||
\(983\) | 7.81570 | 0.249282 | 0.124641 | − | 0.992202i | \(-0.460222\pi\) | ||||
0.124641 | + | 0.992202i | \(0.460222\pi\) | |||||||
\(984\) | −29.8633 | −0.952006 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 42.8989 | 1.36618 | ||||||||
\(987\) | −16.4710 | −0.524277 | ||||||||
\(988\) | 4.04272 | 0.128616 | ||||||||
\(989\) | 7.79310 | 0.247806 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5197 | −0.747126 | −0.373563 | − | 0.927605i | \(-0.621864\pi\) | ||||
−0.373563 | + | 0.927605i | \(0.621864\pi\) | |||||||
\(992\) | −54.4269 | −1.72806 | ||||||||
\(993\) | −18.5157 | −0.587577 | ||||||||
\(994\) | 22.8465 | 0.724648 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.7360 | 1.22740 | ||||||||
\(997\) | −33.6395 | −1.06537 | −0.532686 | − | 0.846313i | \(-0.678817\pi\) | ||||
−0.532686 | + | 0.846313i | \(0.678817\pi\) | |||||||
\(998\) | −12.4240 | −0.393276 | ||||||||
\(999\) | 8.87275 | 0.280721 |
(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 | 475.2.a.j.1.2 | 6 | ||
3.2 | odd | 2 | 4275.2.a.br.1.5 | 6 | |||
4.3 | odd | 2 | 7600.2.a.ck.1.5 | 6 | |||
5.2 | odd | 4 | 95.2.b.b.39.2 | ✓ | 6 | ||
5.3 | odd | 4 | 95.2.b.b.39.5 | yes | 6 | ||
5.4 | even | 2 | inner | 475.2.a.j.1.5 | 6 | ||
15.2 | even | 4 | 855.2.c.d.514.5 | 6 | |||
15.8 | even | 4 | 855.2.c.d.514.2 | 6 | |||
15.14 | odd | 2 | 4275.2.a.br.1.2 | 6 | |||
19.18 | odd | 2 | 9025.2.a.bx.1.5 | 6 | |||
20.3 | even | 4 | 1520.2.d.h.609.5 | 6 | |||
20.7 | even | 4 | 1520.2.d.h.609.2 | 6 | |||
20.19 | odd | 2 | 7600.2.a.ck.1.2 | 6 | |||
95.18 | even | 4 | 1805.2.b.e.1084.2 | 6 | |||
95.37 | even | 4 | 1805.2.b.e.1084.5 | 6 | |||
95.94 | odd | 2 | 9025.2.a.bx.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.b.b.39.2 | ✓ | 6 | 5.2 | odd | 4 | ||
95.2.b.b.39.5 | yes | 6 | 5.3 | odd | 4 | ||
475.2.a.j.1.2 | 6 | 1.1 | even | 1 | trivial | ||
475.2.a.j.1.5 | 6 | 5.4 | even | 2 | inner | ||
855.2.c.d.514.2 | 6 | 15.8 | even | 4 | |||
855.2.c.d.514.5 | 6 | 15.2 | even | 4 | |||
1520.2.d.h.609.2 | 6 | 20.7 | even | 4 | |||
1520.2.d.h.609.5 | 6 | 20.3 | even | 4 | |||
1805.2.b.e.1084.2 | 6 | 95.18 | even | 4 | |||
1805.2.b.e.1084.5 | 6 | 95.37 | even | 4 | |||
4275.2.a.br.1.2 | 6 | 15.14 | odd | 2 | |||
4275.2.a.br.1.5 | 6 | 3.2 | odd | 2 | |||
7600.2.a.ck.1.2 | 6 | 20.19 | odd | 2 | |||
7600.2.a.ck.1.5 | 6 | 4.3 | odd | 2 | |||
9025.2.a.bx.1.2 | 6 | 95.94 | odd | 2 | |||
9025.2.a.bx.1.5 | 6 | 19.18 | odd | 2 |