Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6762,2,Mod(1,6762)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6762, 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("6762.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6762.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: | \(53.9948418468\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.16448.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 7x^{2} + 8x + 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.87996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6762.1 |
$q$-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 | ||||||||
\(5\) | −3.87996 | −1.73517 | −0.867586 | − | 0.497288i | \(-0.834329\pi\) | ||||
−0.867586 | + | 0.497288i | \(0.834329\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.87996 | −1.22695 | ||||||||
\(11\) | 2.65867 | 0.801618 | 0.400809 | − | 0.916162i | \(-0.368729\pi\) | ||||
0.400809 | + | 0.916162i | \(0.368729\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −4.19292 | −1.16291 | −0.581453 | − | 0.813580i | \(-0.697516\pi\) | ||||
−0.581453 | + | 0.813580i | \(0.697516\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.87996 | −1.00180 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.75992 | 0.426844 | 0.213422 | − | 0.976960i | \(-0.431539\pi\) | ||||
0.213422 | + | 0.976960i | \(0.431539\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −0.585786 | −0.134389 | −0.0671943 | − | 0.997740i | \(-0.521405\pi\) | ||||
−0.0671943 | + | 0.997740i | \(0.521405\pi\) | |||||||
\(20\) | −3.87996 | −0.867586 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.65867 | 0.566830 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 10.0541 | 2.01082 | ||||||||
\(26\) | −4.19292 | −0.822299 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.63551 | 0.489402 | 0.244701 | − | 0.969599i | \(-0.421310\pi\) | ||||
0.244701 | + | 0.969599i | \(0.421310\pi\) | |||||||
\(30\) | −3.87996 | −0.708381 | ||||||||
\(31\) | −0.585786 | −0.105210 | −0.0526052 | − | 0.998615i | \(-0.516752\pi\) | ||||
−0.0526052 | + | 0.998615i | \(0.516752\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.65867 | 0.462814 | ||||||||
\(34\) | 1.75992 | 0.301824 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.95284 | −1.30744 | −0.653719 | − | 0.756737i | \(-0.726792\pi\) | ||||
−0.653719 | + | 0.756737i | \(0.726792\pi\) | |||||||
\(38\) | −0.585786 | −0.0950271 | ||||||||
\(39\) | −4.19292 | −0.671404 | ||||||||
\(40\) | −3.87996 | −0.613476 | ||||||||
\(41\) | −11.3671 | −1.77524 | −0.887618 | − | 0.460581i | \(-0.847641\pi\) | ||||
−0.887618 | + | 0.460581i | \(0.847641\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.85158 | 0.434863 | 0.217431 | − | 0.976076i | \(-0.430232\pi\) | ||||
0.217431 | + | 0.976076i | \(0.430232\pi\) | |||||||
\(44\) | 2.65867 | 0.400809 | ||||||||
\(45\) | −3.87996 | −0.578390 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 4.70839 | 0.686789 | 0.343394 | − | 0.939191i | \(-0.388423\pi\) | ||||
0.343394 | + | 0.939191i | \(0.388423\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.0541 | 1.42186 | ||||||||
\(51\) | 1.75992 | 0.246438 | ||||||||
\(52\) | −4.19292 | −0.581453 | ||||||||
\(53\) | −4.55560 | −0.625760 | −0.312880 | − | 0.949793i | \(-0.601294\pi\) | ||||
−0.312880 | + | 0.949793i | \(0.601294\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −10.3155 | −1.39094 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.585786 | −0.0775893 | ||||||||
\(58\) | 2.63551 | 0.346059 | ||||||||
\(59\) | −1.83024 | −0.238277 | −0.119138 | − | 0.992878i | \(-0.538013\pi\) | ||||
−0.119138 | + | 0.992878i | \(0.538013\pi\) | |||||||
\(60\) | −3.87996 | −0.500901 | ||||||||
\(61\) | 1.80005 | 0.230473 | 0.115236 | − | 0.993338i | \(-0.463237\pi\) | ||||
0.115236 | + | 0.993338i | \(0.463237\pi\) | |||||||
\(62\) | −0.585786 | −0.0743950 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 16.2684 | 2.01784 | ||||||||
\(66\) | 2.65867 | 0.327259 | ||||||||
\(67\) | 0.931495 | 0.113800 | 0.0569001 | − | 0.998380i | \(-0.481878\pi\) | ||||
0.0569001 | + | 0.998380i | \(0.481878\pi\) | |||||||
\(68\) | 1.75992 | 0.213422 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.65867 | −0.315526 | −0.157763 | − | 0.987477i | \(-0.550428\pi\) | ||||
−0.157763 | + | 0.987477i | \(0.550428\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −1.02838 | −0.120362 | −0.0601811 | − | 0.998187i | \(-0.519168\pi\) | ||||
−0.0601811 | + | 0.998187i | \(0.519168\pi\) | |||||||
\(74\) | −7.95284 | −0.924499 | ||||||||
\(75\) | 10.0541 | 1.16095 | ||||||||
\(76\) | −0.585786 | −0.0671943 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.19292 | −0.474755 | ||||||||
\(79\) | −8.65867 | −0.974176 | −0.487088 | − | 0.873353i | \(-0.661941\pi\) | ||||
−0.487088 | + | 0.873353i | \(0.661941\pi\) | |||||||
\(80\) | −3.87996 | −0.433793 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −11.3671 | −1.25528 | ||||||||
\(83\) | −13.7297 | −1.50703 | −0.753517 | − | 0.657428i | \(-0.771644\pi\) | ||||
−0.753517 | + | 0.657428i | \(0.771644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.82843 | −0.740647 | ||||||||
\(86\) | 2.85158 | 0.307494 | ||||||||
\(87\) | 2.63551 | 0.282556 | ||||||||
\(88\) | 2.65867 | 0.283415 | ||||||||
\(89\) | 0.216077 | 0.0229041 | 0.0114520 | − | 0.999934i | \(-0.496355\pi\) | ||||
0.0114520 | + | 0.999934i | \(0.496355\pi\) | |||||||
\(90\) | −3.87996 | −0.408984 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −0.585786 | −0.0607432 | ||||||||
\(94\) | 4.70839 | 0.485633 | ||||||||
\(95\) | 2.27283 | 0.233187 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −8.80527 | −0.894040 | −0.447020 | − | 0.894524i | \(-0.647515\pi\) | ||||
−0.447020 | + | 0.894524i | \(0.647515\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.65867 | 0.267206 | ||||||||
\(100\) | 10.0541 | 1.00541 | ||||||||
\(101\) | 11.1439 | 1.10886 | 0.554432 | − | 0.832229i | \(-0.312936\pi\) | ||||
0.554432 | + | 0.832229i | \(0.312936\pi\) | |||||||
\(102\) | 1.75992 | 0.174258 | ||||||||
\(103\) | −1.80708 | −0.178057 | −0.0890285 | − | 0.996029i | \(-0.528376\pi\) | ||||
−0.0890285 | + | 0.996029i | \(0.528376\pi\) | |||||||
\(104\) | −4.19292 | −0.411150 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.55560 | −0.442479 | ||||||||
\(107\) | −7.55741 | −0.730602 | −0.365301 | − | 0.930889i | \(-0.619034\pi\) | ||||
−0.365301 | + | 0.930889i | \(0.619034\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 2.81883 | 0.269995 | 0.134998 | − | 0.990846i | \(-0.456897\pi\) | ||||
0.134998 | + | 0.990846i | \(0.456897\pi\) | |||||||
\(110\) | −10.3155 | −0.983546 | ||||||||
\(111\) | −7.95284 | −0.754850 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.61151 | −0.433814 | −0.216907 | − | 0.976192i | \(-0.569597\pi\) | ||||
−0.216907 | + | 0.976192i | \(0.569597\pi\) | |||||||
\(114\) | −0.585786 | −0.0548639 | ||||||||
\(115\) | 3.87996 | 0.361808 | ||||||||
\(116\) | 2.63551 | 0.244701 | ||||||||
\(117\) | −4.19292 | −0.387635 | ||||||||
\(118\) | −1.83024 | −0.168487 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.87996 | −0.354190 | ||||||||
\(121\) | −3.93149 | −0.357409 | ||||||||
\(122\) | 1.80005 | 0.162969 | ||||||||
\(123\) | −11.3671 | −1.02493 | ||||||||
\(124\) | −0.585786 | −0.0526052 | ||||||||
\(125\) | −19.6097 | −1.75394 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.51025 | −0.843898 | −0.421949 | − | 0.906619i | \(-0.638654\pi\) | ||||
−0.421949 | + | 0.906619i | \(0.638654\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.85158 | 0.251068 | ||||||||
\(130\) | 16.2684 | 1.42683 | ||||||||
\(131\) | 19.0069 | 1.66064 | 0.830322 | − | 0.557284i | \(-0.188157\pi\) | ||||
0.830322 | + | 0.557284i | \(0.188157\pi\) | |||||||
\(132\) | 2.65867 | 0.231407 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.931495 | 0.0804689 | ||||||||
\(135\) | −3.87996 | −0.333934 | ||||||||
\(136\) | 1.75992 | 0.150912 | ||||||||
\(137\) | −8.71095 | −0.744227 | −0.372113 | − | 0.928187i | \(-0.621367\pi\) | ||||
−0.372113 | + | 0.928187i | \(0.621367\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | 9.34049 | 0.792250 | 0.396125 | − | 0.918197i | \(-0.370355\pi\) | ||||
0.396125 | + | 0.918197i | \(0.370355\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.70839 | 0.396518 | ||||||||
\(142\) | −2.65867 | −0.223110 | ||||||||
\(143\) | −11.1476 | −0.932207 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −10.2257 | −0.849196 | ||||||||
\(146\) | −1.02838 | −0.0851090 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.95284 | −0.653719 | ||||||||
\(149\) | 1.62410 | 0.133052 | 0.0665259 | − | 0.997785i | \(-0.478808\pi\) | ||||
0.0665259 | + | 0.997785i | \(0.478808\pi\) | |||||||
\(150\) | 10.0541 | 0.820914 | ||||||||
\(151\) | −6.39543 | −0.520453 | −0.260226 | − | 0.965548i | \(-0.583797\pi\) | ||||
−0.260226 | + | 0.965548i | \(0.583797\pi\) | |||||||
\(152\) | −0.585786 | −0.0475136 | ||||||||
\(153\) | 1.75992 | 0.142281 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.27283 | 0.182558 | ||||||||
\(156\) | −4.19292 | −0.335702 | ||||||||
\(157\) | −21.2736 | −1.69782 | −0.848908 | − | 0.528540i | \(-0.822740\pi\) | ||||
−0.848908 | + | 0.528540i | \(0.822740\pi\) | |||||||
\(158\) | −8.65867 | −0.688846 | ||||||||
\(159\) | −4.55560 | −0.361282 | ||||||||
\(160\) | −3.87996 | −0.306738 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −8.48528 | −0.664619 | −0.332309 | − | 0.943170i | \(-0.607828\pi\) | ||||
−0.332309 | + | 0.943170i | \(0.607828\pi\) | |||||||
\(164\) | −11.3671 | −0.887618 | ||||||||
\(165\) | −10.3155 | −0.803062 | ||||||||
\(166\) | −13.7297 | −1.06563 | ||||||||
\(167\) | −21.8292 | −1.68919 | −0.844596 | − | 0.535404i | \(-0.820159\pi\) | ||||
−0.844596 | + | 0.535404i | \(0.820159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.58057 | 0.352351 | ||||||||
\(170\) | −6.82843 | −0.523716 | ||||||||
\(171\) | −0.585786 | −0.0447962 | ||||||||
\(172\) | 2.85158 | 0.217431 | ||||||||
\(173\) | −20.4940 | −1.55813 | −0.779066 | − | 0.626942i | \(-0.784306\pi\) | ||||
−0.779066 | + | 0.626942i | \(0.784306\pi\) | |||||||
\(174\) | 2.63551 | 0.199797 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.65867 | 0.200404 | ||||||||
\(177\) | −1.83024 | −0.137569 | ||||||||
\(178\) | 0.216077 | 0.0161956 | ||||||||
\(179\) | −26.6166 | −1.98942 | −0.994710 | − | 0.102721i | \(-0.967245\pi\) | ||||
−0.994710 | + | 0.102721i | \(0.967245\pi\) | |||||||
\(180\) | −3.87996 | −0.289195 | ||||||||
\(181\) | −21.6390 | −1.60842 | −0.804209 | − | 0.594347i | \(-0.797410\pi\) | ||||
−0.804209 | + | 0.594347i | \(0.797410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.80005 | 0.133064 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 30.8567 | 2.26863 | ||||||||
\(186\) | −0.585786 | −0.0429519 | ||||||||
\(187\) | 4.67904 | 0.342166 | ||||||||
\(188\) | 4.70839 | 0.343394 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.27283 | 0.164888 | ||||||||
\(191\) | 2.23645 | 0.161824 | 0.0809121 | − | 0.996721i | \(-0.474217\pi\) | ||||
0.0809121 | + | 0.996721i | \(0.474217\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 1.19473 | 0.0859986 | 0.0429993 | − | 0.999075i | \(-0.486309\pi\) | ||||
0.0429993 | + | 0.999075i | \(0.486309\pi\) | |||||||
\(194\) | −8.80527 | −0.632181 | ||||||||
\(195\) | 16.2684 | 1.16500 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5788 | 0.896199 | 0.448100 | − | 0.893984i | \(-0.352101\pi\) | ||||
0.448100 | + | 0.893984i | \(0.352101\pi\) | |||||||
\(198\) | 2.65867 | 0.188943 | ||||||||
\(199\) | −2.73858 | −0.194132 | −0.0970662 | − | 0.995278i | \(-0.530946\pi\) | ||||
−0.0970662 | + | 0.995278i | \(0.530946\pi\) | |||||||
\(200\) | 10.0541 | 0.710932 | ||||||||
\(201\) | 0.931495 | 0.0657026 | ||||||||
\(202\) | 11.1439 | 0.784085 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.75992 | 0.123219 | ||||||||
\(205\) | 44.1037 | 3.08034 | ||||||||
\(206\) | −1.80708 | −0.125905 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −4.19292 | −0.290727 | ||||||||
\(209\) | −1.55741 | −0.107728 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.58654 | 0.522279 | 0.261139 | − | 0.965301i | \(-0.415902\pi\) | ||||
0.261139 | + | 0.965301i | \(0.415902\pi\) | |||||||
\(212\) | −4.55560 | −0.312880 | ||||||||
\(213\) | −2.65867 | −0.182169 | ||||||||
\(214\) | −7.55741 | −0.516614 | ||||||||
\(215\) | −11.0640 | −0.754561 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.81883 | 0.190916 | ||||||||
\(219\) | −1.02838 | −0.0694912 | ||||||||
\(220\) | −10.3155 | −0.695472 | ||||||||
\(221\) | −7.37921 | −0.496379 | ||||||||
\(222\) | −7.95284 | −0.533760 | ||||||||
\(223\) | 13.4433 | 0.900233 | 0.450116 | − | 0.892970i | \(-0.351383\pi\) | ||||
0.450116 | + | 0.892970i | \(0.351383\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0541 | 0.670273 | ||||||||
\(226\) | −4.61151 | −0.306753 | ||||||||
\(227\) | 1.84721 | 0.122604 | 0.0613018 | − | 0.998119i | \(-0.480475\pi\) | ||||
0.0613018 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(228\) | −0.585786 | −0.0387947 | ||||||||
\(229\) | 13.0471 | 0.862174 | 0.431087 | − | 0.902310i | \(-0.358130\pi\) | ||||
0.431087 | + | 0.902310i | \(0.358130\pi\) | |||||||
\(230\) | 3.87996 | 0.255837 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.63551 | 0.173030 | ||||||||
\(233\) | 12.5556 | 0.822545 | 0.411272 | − | 0.911513i | \(-0.365085\pi\) | ||||
0.411272 | + | 0.911513i | \(0.365085\pi\) | |||||||
\(234\) | −4.19292 | −0.274100 | ||||||||
\(235\) | −18.2684 | −1.19170 | ||||||||
\(236\) | −1.83024 | −0.119138 | ||||||||
\(237\) | −8.65867 | −0.562441 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.2540 | −1.56886 | −0.784429 | − | 0.620219i | \(-0.787044\pi\) | ||||
−0.784429 | + | 0.620219i | \(0.787044\pi\) | |||||||
\(240\) | −3.87996 | −0.250450 | ||||||||
\(241\) | −17.7227 | −1.14162 | −0.570810 | − | 0.821082i | \(-0.693371\pi\) | ||||
−0.570810 | + | 0.821082i | \(0.693371\pi\) | |||||||
\(242\) | −3.93149 | −0.252726 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.80005 | 0.115236 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.3671 | −0.724737 | ||||||||
\(247\) | 2.45615 | 0.156281 | ||||||||
\(248\) | −0.585786 | −0.0371975 | ||||||||
\(249\) | −13.7297 | −0.870087 | ||||||||
\(250\) | −19.6097 | −1.24023 | ||||||||
\(251\) | 26.3037 | 1.66027 | 0.830137 | − | 0.557560i | \(-0.188262\pi\) | ||||
0.830137 | + | 0.557560i | \(0.188262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.65867 | −0.167149 | ||||||||
\(254\) | −9.51025 | −0.596726 | ||||||||
\(255\) | −6.82843 | −0.427613 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.7643 | 0.920971 | 0.460486 | − | 0.887667i | \(-0.347675\pi\) | ||||
0.460486 | + | 0.887667i | \(0.347675\pi\) | |||||||
\(258\) | 2.85158 | 0.177532 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.2684 | 1.00892 | ||||||||
\(261\) | 2.63551 | 0.163134 | ||||||||
\(262\) | 19.0069 | 1.17425 | ||||||||
\(263\) | 3.81583 | 0.235294 | 0.117647 | − | 0.993055i | \(-0.462465\pi\) | ||||
0.117647 | + | 0.993055i | \(0.462465\pi\) | |||||||
\(264\) | 2.65867 | 0.163630 | ||||||||
\(265\) | 17.6755 | 1.08580 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.216077 | 0.0132237 | ||||||||
\(268\) | 0.931495 | 0.0569001 | ||||||||
\(269\) | 19.7551 | 1.20449 | 0.602245 | − | 0.798311i | \(-0.294273\pi\) | ||||
0.602245 | + | 0.798311i | \(0.294273\pi\) | |||||||
\(270\) | −3.87996 | −0.236127 | ||||||||
\(271\) | −24.4966 | −1.48806 | −0.744031 | − | 0.668145i | \(-0.767089\pi\) | ||||
−0.744031 | + | 0.668145i | \(0.767089\pi\) | |||||||
\(272\) | 1.75992 | 0.106711 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.71095 | −0.526248 | ||||||||
\(275\) | 26.7305 | 1.61191 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −2.21245 | −0.132933 | −0.0664667 | − | 0.997789i | \(-0.521173\pi\) | ||||
−0.0664667 | + | 0.997789i | \(0.521173\pi\) | |||||||
\(278\) | 9.34049 | 0.560205 | ||||||||
\(279\) | −0.585786 | −0.0350701 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.92009 | 0.233853 | 0.116926 | − | 0.993141i | \(-0.462696\pi\) | ||||
0.116926 | + | 0.993141i | \(0.462696\pi\) | |||||||
\(282\) | 4.70839 | 0.280380 | ||||||||
\(283\) | −25.7484 | −1.53058 | −0.765292 | − | 0.643683i | \(-0.777406\pi\) | ||||
−0.765292 | + | 0.643683i | \(0.777406\pi\) | |||||||
\(284\) | −2.65867 | −0.157763 | ||||||||
\(285\) | 2.27283 | 0.134631 | ||||||||
\(286\) | −11.1476 | −0.659170 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −13.9027 | −0.817804 | ||||||||
\(290\) | −10.2257 | −0.600472 | ||||||||
\(291\) | −8.80527 | −0.516174 | ||||||||
\(292\) | −1.02838 | −0.0601811 | ||||||||
\(293\) | 25.8379 | 1.50947 | 0.754734 | − | 0.656031i | \(-0.227766\pi\) | ||||
0.754734 | + | 0.656031i | \(0.227766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.10126 | 0.413451 | ||||||||
\(296\) | −7.95284 | −0.462249 | ||||||||
\(297\) | 2.65867 | 0.154271 | ||||||||
\(298\) | 1.62410 | 0.0940818 | ||||||||
\(299\) | 4.19292 | 0.242483 | ||||||||
\(300\) | 10.0541 | 0.580474 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.39543 | −0.368016 | ||||||||
\(303\) | 11.1439 | 0.640203 | ||||||||
\(304\) | −0.585786 | −0.0335972 | ||||||||
\(305\) | −6.98413 | −0.399910 | ||||||||
\(306\) | 1.75992 | 0.100608 | ||||||||
\(307\) | 19.2889 | 1.10087 | 0.550437 | − | 0.834877i | \(-0.314461\pi\) | ||||
0.550437 | + | 0.834877i | \(0.314461\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.80708 | −0.102801 | ||||||||
\(310\) | 2.27283 | 0.129088 | ||||||||
\(311\) | 17.4433 | 0.989121 | 0.494561 | − | 0.869143i | \(-0.335329\pi\) | ||||
0.494561 | + | 0.869143i | \(0.335329\pi\) | |||||||
\(312\) | −4.19292 | −0.237377 | ||||||||
\(313\) | 15.3225 | 0.866076 | 0.433038 | − | 0.901376i | \(-0.357442\pi\) | ||||
0.433038 | + | 0.901376i | \(0.357442\pi\) | |||||||
\(314\) | −21.2736 | −1.20054 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.65867 | −0.487088 | ||||||||
\(317\) | 27.4123 | 1.53963 | 0.769814 | − | 0.638268i | \(-0.220349\pi\) | ||||
0.769814 | + | 0.638268i | \(0.220349\pi\) | |||||||
\(318\) | −4.55560 | −0.255465 | ||||||||
\(319\) | 7.00694 | 0.392313 | ||||||||
\(320\) | −3.87996 | −0.216896 | ||||||||
\(321\) | −7.55741 | −0.421814 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.03094 | −0.0573629 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −42.1560 | −2.33839 | ||||||||
\(326\) | −8.48528 | −0.469956 | ||||||||
\(327\) | 2.81883 | 0.155882 | ||||||||
\(328\) | −11.3671 | −0.627641 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −10.3155 | −0.567851 | ||||||||
\(331\) | 5.99638 | 0.329591 | 0.164795 | − | 0.986328i | \(-0.447304\pi\) | ||||
0.164795 | + | 0.986328i | \(0.447304\pi\) | |||||||
\(332\) | −13.7297 | −0.753517 | ||||||||
\(333\) | −7.95284 | −0.435813 | ||||||||
\(334\) | −21.8292 | −1.19444 | ||||||||
\(335\) | −3.61416 | −0.197463 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.63648 | −0.415985 | −0.207993 | − | 0.978130i | \(-0.566693\pi\) | ||||
−0.207993 | + | 0.978130i | \(0.566693\pi\) | |||||||
\(338\) | 4.58057 | 0.249150 | ||||||||
\(339\) | −4.61151 | −0.250463 | ||||||||
\(340\) | −6.82843 | −0.370323 | ||||||||
\(341\) | −1.55741 | −0.0843385 | ||||||||
\(342\) | −0.585786 | −0.0316757 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.85158 | 0.153747 | ||||||||
\(345\) | 3.87996 | 0.208890 | ||||||||
\(346\) | −20.4940 | −1.10177 | ||||||||
\(347\) | 32.7660 | 1.75897 | 0.879486 | − | 0.475925i | \(-0.157887\pi\) | ||||
0.879486 | + | 0.475925i | \(0.157887\pi\) | |||||||
\(348\) | 2.63551 | 0.141278 | ||||||||
\(349\) | −36.5403 | −1.95596 | −0.977980 | − | 0.208699i | \(-0.933077\pi\) | ||||
−0.977980 | + | 0.208699i | \(0.933077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.19292 | −0.223801 | ||||||||
\(352\) | 2.65867 | 0.141707 | ||||||||
\(353\) | −2.90096 | −0.154402 | −0.0772012 | − | 0.997016i | \(-0.524598\pi\) | ||||
−0.0772012 | + | 0.997016i | \(0.524598\pi\) | |||||||
\(354\) | −1.83024 | −0.0972761 | ||||||||
\(355\) | 10.3155 | 0.547491 | ||||||||
\(356\) | 0.216077 | 0.0114520 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.6166 | −1.40673 | ||||||||
\(359\) | −26.5499 | −1.40125 | −0.700626 | − | 0.713529i | \(-0.747096\pi\) | ||||
−0.700626 | + | 0.713529i | \(0.747096\pi\) | |||||||
\(360\) | −3.87996 | −0.204492 | ||||||||
\(361\) | −18.6569 | −0.981940 | ||||||||
\(362\) | −21.6390 | −1.13732 | ||||||||
\(363\) | −3.93149 | −0.206350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.99006 | 0.208849 | ||||||||
\(366\) | 1.80005 | 0.0940902 | ||||||||
\(367\) | −26.6833 | −1.39286 | −0.696429 | − | 0.717626i | \(-0.745229\pi\) | ||||
−0.696429 | + | 0.717626i | \(0.745229\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −11.3671 | −0.591745 | ||||||||
\(370\) | 30.8567 | 1.60416 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.585786 | −0.0303716 | ||||||||
\(373\) | 9.13038 | 0.472753 | 0.236377 | − | 0.971662i | \(-0.424040\pi\) | ||||
0.236377 | + | 0.971662i | \(0.424040\pi\) | |||||||
\(374\) | 4.67904 | 0.241948 | ||||||||
\(375\) | −19.6097 | −1.01264 | ||||||||
\(376\) | 4.70839 | 0.242817 | ||||||||
\(377\) | −11.0505 | −0.569128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.9288 | −1.74281 | −0.871404 | − | 0.490567i | \(-0.836790\pi\) | ||||
−0.871404 | + | 0.490567i | \(0.836790\pi\) | |||||||
\(380\) | 2.27283 | 0.116594 | ||||||||
\(381\) | −9.51025 | −0.487225 | ||||||||
\(382\) | 2.23645 | 0.114427 | ||||||||
\(383\) | −30.8008 | −1.57385 | −0.786924 | − | 0.617050i | \(-0.788328\pi\) | ||||
−0.786924 | + | 0.617050i | \(0.788328\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.19473 | 0.0608102 | ||||||||
\(387\) | 2.85158 | 0.144954 | ||||||||
\(388\) | −8.80527 | −0.447020 | ||||||||
\(389\) | −2.38221 | −0.120783 | −0.0603915 | − | 0.998175i | \(-0.519235\pi\) | ||||
−0.0603915 | + | 0.998175i | \(0.519235\pi\) | |||||||
\(390\) | 16.2684 | 0.823780 | ||||||||
\(391\) | −1.75992 | −0.0890031 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 19.0069 | 0.958773 | ||||||||
\(394\) | 12.5788 | 0.633709 | ||||||||
\(395\) | 33.5953 | 1.69036 | ||||||||
\(396\) | 2.65867 | 0.133603 | ||||||||
\(397\) | 3.21064 | 0.161137 | 0.0805687 | − | 0.996749i | \(-0.474326\pi\) | ||||
0.0805687 | + | 0.996749i | \(0.474326\pi\) | |||||||
\(398\) | −2.73858 | −0.137272 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0541 | 0.502705 | ||||||||
\(401\) | 36.2591 | 1.81069 | 0.905346 | − | 0.424675i | \(-0.139612\pi\) | ||||
0.905346 | + | 0.424675i | \(0.139612\pi\) | |||||||
\(402\) | 0.931495 | 0.0464587 | ||||||||
\(403\) | 2.45615 | 0.122350 | ||||||||
\(404\) | 11.1439 | 0.554432 | ||||||||
\(405\) | −3.87996 | −0.192797 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.1439 | −1.04807 | ||||||||
\(408\) | 1.75992 | 0.0871291 | ||||||||
\(409\) | −4.28896 | −0.212075 | −0.106038 | − | 0.994362i | \(-0.533816\pi\) | ||||
−0.106038 | + | 0.994362i | \(0.533816\pi\) | |||||||
\(410\) | 44.1037 | 2.17813 | ||||||||
\(411\) | −8.71095 | −0.429679 | ||||||||
\(412\) | −1.80708 | −0.0890285 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 53.2708 | 2.61496 | ||||||||
\(416\) | −4.19292 | −0.205575 | ||||||||
\(417\) | 9.34049 | 0.457406 | ||||||||
\(418\) | −1.55741 | −0.0761754 | ||||||||
\(419\) | 29.3422 | 1.43346 | 0.716730 | − | 0.697350i | \(-0.245638\pi\) | ||||
0.716730 | + | 0.697350i | \(0.245638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.27186 | −0.256935 | −0.128467 | − | 0.991714i | \(-0.541006\pi\) | ||||
−0.128467 | + | 0.991714i | \(0.541006\pi\) | |||||||
\(422\) | 7.58654 | 0.369307 | ||||||||
\(423\) | 4.70839 | 0.228930 | ||||||||
\(424\) | −4.55560 | −0.221239 | ||||||||
\(425\) | 17.6944 | 0.858306 | ||||||||
\(426\) | −2.65867 | −0.128813 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.55741 | −0.365301 | ||||||||
\(429\) | −11.1476 | −0.538210 | ||||||||
\(430\) | −11.0640 | −0.533555 | ||||||||
\(431\) | −6.70463 | −0.322951 | −0.161475 | − | 0.986877i | \(-0.551625\pi\) | ||||
−0.161475 | + | 0.986877i | \(0.551625\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −26.3751 | −1.26750 | −0.633752 | − | 0.773536i | \(-0.718486\pi\) | ||||
−0.633752 | + | 0.773536i | \(0.718486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.2257 | −0.490283 | ||||||||
\(436\) | 2.81883 | 0.134998 | ||||||||
\(437\) | 0.585786 | 0.0280220 | ||||||||
\(438\) | −1.02838 | −0.0491377 | ||||||||
\(439\) | −8.18589 | −0.390691 | −0.195346 | − | 0.980734i | \(-0.562583\pi\) | ||||
−0.195346 | + | 0.980734i | \(0.562583\pi\) | |||||||
\(440\) | −10.3155 | −0.491773 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.37921 | −0.350993 | ||||||||
\(443\) | 3.45037 | 0.163932 | 0.0819660 | − | 0.996635i | \(-0.473880\pi\) | ||||
0.0819660 | + | 0.996635i | \(0.473880\pi\) | |||||||
\(444\) | −7.95284 | −0.377425 | ||||||||
\(445\) | −0.838369 | −0.0397425 | ||||||||
\(446\) | 13.4433 | 0.636561 | ||||||||
\(447\) | 1.62410 | 0.0768175 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 39.1515 | 1.84767 | 0.923837 | − | 0.382787i | \(-0.125036\pi\) | ||||
0.923837 | + | 0.382787i | \(0.125036\pi\) | |||||||
\(450\) | 10.0541 | 0.473955 | ||||||||
\(451\) | −30.2212 | −1.42306 | ||||||||
\(452\) | −4.61151 | −0.216907 | ||||||||
\(453\) | −6.39543 | −0.300484 | ||||||||
\(454\) | 1.84721 | 0.0866939 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.585786 | −0.0274320 | ||||||||
\(457\) | 16.7872 | 0.785274 | 0.392637 | − | 0.919694i | \(-0.371563\pi\) | ||||
0.392637 | + | 0.919694i | \(0.371563\pi\) | |||||||
\(458\) | 13.0471 | 0.609649 | ||||||||
\(459\) | 1.75992 | 0.0821461 | ||||||||
\(460\) | 3.87996 | 0.180904 | ||||||||
\(461\) | −34.3170 | −1.59830 | −0.799152 | − | 0.601130i | \(-0.794718\pi\) | ||||
−0.799152 | + | 0.601130i | \(0.794718\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.75033 | −0.360188 | −0.180094 | − | 0.983649i | \(-0.557640\pi\) | ||||
−0.180094 | + | 0.983649i | \(0.557640\pi\) | |||||||
\(464\) | 2.63551 | 0.122350 | ||||||||
\(465\) | 2.27283 | 0.105400 | ||||||||
\(466\) | 12.5556 | 0.581627 | ||||||||
\(467\) | −19.9023 | −0.920967 | −0.460484 | − | 0.887668i | \(-0.652324\pi\) | ||||
−0.460484 | + | 0.887668i | \(0.652324\pi\) | |||||||
\(468\) | −4.19292 | −0.193818 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −18.2684 | −0.842657 | ||||||||
\(471\) | −21.2736 | −0.980235 | ||||||||
\(472\) | −1.83024 | −0.0842436 | ||||||||
\(473\) | 7.58141 | 0.348594 | ||||||||
\(474\) | −8.65867 | −0.397706 | ||||||||
\(475\) | −5.88955 | −0.270231 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.55560 | −0.208587 | ||||||||
\(478\) | −24.2540 | −1.10935 | ||||||||
\(479\) | 12.4661 | 0.569591 | 0.284795 | − | 0.958588i | \(-0.408074\pi\) | ||||
0.284795 | + | 0.958588i | \(0.408074\pi\) | |||||||
\(480\) | −3.87996 | −0.177095 | ||||||||
\(481\) | 33.3456 | 1.52043 | ||||||||
\(482\) | −17.7227 | −0.807247 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.93149 | −0.178704 | ||||||||
\(485\) | 34.1641 | 1.55131 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −40.4859 | −1.83459 | −0.917296 | − | 0.398205i | \(-0.869633\pi\) | ||||
−0.917296 | + | 0.398205i | \(0.869633\pi\) | |||||||
\(488\) | 1.80005 | 0.0814845 | ||||||||
\(489\) | −8.48528 | −0.383718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.7599 | 1.61382 | 0.806911 | − | 0.590673i | \(-0.201138\pi\) | ||||
0.806911 | + | 0.590673i | \(0.201138\pi\) | |||||||
\(492\) | −11.3671 | −0.512466 | ||||||||
\(493\) | 4.63829 | 0.208898 | ||||||||
\(494\) | 2.45615 | 0.110508 | ||||||||
\(495\) | −10.3155 | −0.463648 | ||||||||
\(496\) | −0.585786 | −0.0263026 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −13.7297 | −0.615244 | ||||||||
\(499\) | −18.3291 | −0.820523 | −0.410261 | − | 0.911968i | \(-0.634562\pi\) | ||||
−0.410261 | + | 0.911968i | \(0.634562\pi\) | |||||||
\(500\) | −19.6097 | −0.876972 | ||||||||
\(501\) | −21.8292 | −0.975256 | ||||||||
\(502\) | 26.3037 | 1.17399 | ||||||||
\(503\) | −3.19389 | −0.142408 | −0.0712042 | − | 0.997462i | \(-0.522684\pi\) | ||||
−0.0712042 | + | 0.997462i | \(0.522684\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43.2381 | −1.92407 | ||||||||
\(506\) | −2.65867 | −0.118192 | ||||||||
\(507\) | 4.58057 | 0.203430 | ||||||||
\(508\) | −9.51025 | −0.421949 | ||||||||
\(509\) | 29.5917 | 1.31163 | 0.655814 | − | 0.754923i | \(-0.272326\pi\) | ||||
0.655814 | + | 0.754923i | \(0.272326\pi\) | |||||||
\(510\) | −6.82843 | −0.302368 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.585786 | −0.0258631 | ||||||||
\(514\) | 14.7643 | 0.651225 | ||||||||
\(515\) | 7.01140 | 0.308959 | ||||||||
\(516\) | 2.85158 | 0.125534 | ||||||||
\(517\) | 12.5180 | 0.550542 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.4940 | −0.899588 | ||||||||
\(520\) | 16.2684 | 0.713415 | ||||||||
\(521\) | 38.8474 | 1.70194 | 0.850968 | − | 0.525217i | \(-0.176016\pi\) | ||||
0.850968 | + | 0.525217i | \(0.176016\pi\) | |||||||
\(522\) | 2.63551 | 0.115353 | ||||||||
\(523\) | −41.6214 | −1.81997 | −0.909987 | − | 0.414636i | \(-0.863909\pi\) | ||||
−0.909987 | + | 0.414636i | \(0.863909\pi\) | |||||||
\(524\) | 19.0069 | 0.830322 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.81583 | 0.166378 | ||||||||
\(527\) | −1.03094 | −0.0449084 | ||||||||
\(528\) | 2.65867 | 0.115704 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 17.6755 | 0.767777 | ||||||||
\(531\) | −1.83024 | −0.0794256 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 47.6611 | 2.06443 | ||||||||
\(534\) | 0.216077 | 0.00935055 | ||||||||
\(535\) | 29.3225 | 1.26772 | ||||||||
\(536\) | 0.931495 | 0.0402344 | ||||||||
\(537\) | −26.6166 | −1.14859 | ||||||||
\(538\) | 19.7551 | 0.851703 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.87996 | −0.166967 | ||||||||
\(541\) | 4.70185 | 0.202148 | 0.101074 | − | 0.994879i | \(-0.467772\pi\) | ||||
0.101074 | + | 0.994879i | \(0.467772\pi\) | |||||||
\(542\) | −24.4966 | −1.05222 | ||||||||
\(543\) | −21.6390 | −0.928620 | ||||||||
\(544\) | 1.75992 | 0.0754560 | ||||||||
\(545\) | −10.9370 | −0.468488 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.5764 | 1.69217 | 0.846083 | − | 0.533052i | \(-0.178955\pi\) | ||||
0.846083 | + | 0.533052i | \(0.178955\pi\) | |||||||
\(548\) | −8.71095 | −0.372113 | ||||||||
\(549\) | 1.80005 | 0.0768243 | ||||||||
\(550\) | 26.7305 | 1.13979 | ||||||||
\(551\) | −1.54385 | −0.0657700 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.21245 | −0.0939981 | ||||||||
\(555\) | 30.8567 | 1.30979 | ||||||||
\(556\) | 9.34049 | 0.396125 | ||||||||
\(557\) | 9.65685 | 0.409174 | 0.204587 | − | 0.978848i | \(-0.434415\pi\) | ||||
0.204587 | + | 0.978848i | \(0.434415\pi\) | |||||||
\(558\) | −0.585786 | −0.0247983 | ||||||||
\(559\) | −11.9565 | −0.505705 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.67904 | 0.197549 | ||||||||
\(562\) | 3.92009 | 0.165359 | ||||||||
\(563\) | 1.05635 | 0.0445199 | 0.0222599 | − | 0.999752i | \(-0.492914\pi\) | ||||
0.0222599 | + | 0.999752i | \(0.492914\pi\) | |||||||
\(564\) | 4.70839 | 0.198259 | ||||||||
\(565\) | 17.8925 | 0.752742 | ||||||||
\(566\) | −25.7484 | −1.08229 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.65867 | −0.111555 | ||||||||
\(569\) | 6.60276 | 0.276802 | 0.138401 | − | 0.990376i | \(-0.455804\pi\) | ||||
0.138401 | + | 0.990376i | \(0.455804\pi\) | |||||||
\(570\) | 2.27283 | 0.0951983 | ||||||||
\(571\) | 0.686292 | 0.0287204 | 0.0143602 | − | 0.999897i | \(-0.495429\pi\) | ||||
0.0143602 | + | 0.999897i | \(0.495429\pi\) | |||||||
\(572\) | −11.1476 | −0.466103 | ||||||||
\(573\) | 2.23645 | 0.0934292 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.0541 | −0.419285 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 34.5565 | 1.43860 | 0.719302 | − | 0.694697i | \(-0.244462\pi\) | ||||
0.719302 | + | 0.694697i | \(0.244462\pi\) | |||||||
\(578\) | −13.9027 | −0.578275 | ||||||||
\(579\) | 1.19473 | 0.0496513 | ||||||||
\(580\) | −10.2257 | −0.424598 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −8.80527 | −0.364990 | ||||||||
\(583\) | −12.1118 | −0.501620 | ||||||||
\(584\) | −1.02838 | −0.0425545 | ||||||||
\(585\) | 16.2684 | 0.672614 | ||||||||
\(586\) | 25.8379 | 1.06735 | ||||||||
\(587\) | −13.5829 | −0.560627 | −0.280313 | − | 0.959909i | \(-0.590438\pi\) | ||||
−0.280313 | + | 0.959909i | \(0.590438\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.343146 | 0.0141391 | ||||||||
\(590\) | 7.10126 | 0.292354 | ||||||||
\(591\) | 12.5788 | 0.517421 | ||||||||
\(592\) | −7.95284 | −0.326860 | ||||||||
\(593\) | 19.3331 | 0.793916 | 0.396958 | − | 0.917837i | \(-0.370066\pi\) | ||||
0.396958 | + | 0.917837i | \(0.370066\pi\) | |||||||
\(594\) | 2.65867 | 0.109086 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.62410 | 0.0665259 | ||||||||
\(597\) | −2.73858 | −0.112082 | ||||||||
\(598\) | 4.19292 | 0.171461 | ||||||||
\(599\) | 17.6241 | 0.720101 | 0.360051 | − | 0.932933i | \(-0.382759\pi\) | ||||
0.360051 | + | 0.932933i | \(0.382759\pi\) | |||||||
\(600\) | 10.0541 | 0.410457 | ||||||||
\(601\) | 29.3990 | 1.19921 | 0.599604 | − | 0.800297i | \(-0.295325\pi\) | ||||
0.599604 | + | 0.800297i | \(0.295325\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.931495 | 0.0379334 | ||||||||
\(604\) | −6.39543 | −0.260226 | ||||||||
\(605\) | 15.2540 | 0.620165 | ||||||||
\(606\) | 11.1439 | 0.452692 | ||||||||
\(607\) | 41.8755 | 1.69967 | 0.849837 | − | 0.527046i | \(-0.176700\pi\) | ||||
0.849837 | + | 0.527046i | \(0.176700\pi\) | |||||||
\(608\) | −0.585786 | −0.0237568 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.98413 | −0.282779 | ||||||||
\(611\) | −19.7419 | −0.798671 | ||||||||
\(612\) | 1.75992 | 0.0711406 | ||||||||
\(613\) | −2.75333 | −0.111206 | −0.0556031 | − | 0.998453i | \(-0.517708\pi\) | ||||
−0.0556031 | + | 0.998453i | \(0.517708\pi\) | |||||||
\(614\) | 19.2889 | 0.778435 | ||||||||
\(615\) | 44.1037 | 1.77843 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.6274 | −0.508361 | −0.254180 | − | 0.967157i | \(-0.581806\pi\) | ||||
−0.254180 | + | 0.967157i | \(0.581806\pi\) | |||||||
\(618\) | −1.80708 | −0.0726915 | ||||||||
\(619\) | 6.55547 | 0.263486 | 0.131743 | − | 0.991284i | \(-0.457943\pi\) | ||||
0.131743 | + | 0.991284i | \(0.457943\pi\) | |||||||
\(620\) | 2.27283 | 0.0912790 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 17.4433 | 0.699414 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.19292 | −0.167851 | ||||||||
\(625\) | 25.8144 | 1.03257 | ||||||||
\(626\) | 15.3225 | 0.612409 | ||||||||
\(627\) | −1.55741 | −0.0621970 | ||||||||
\(628\) | −21.2736 | −0.848908 | ||||||||
\(629\) | −13.9964 | −0.558072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.20202 | 0.246898 | 0.123449 | − | 0.992351i | \(-0.460604\pi\) | ||||
0.123449 | + | 0.992351i | \(0.460604\pi\) | |||||||
\(632\) | −8.65867 | −0.344423 | ||||||||
\(633\) | 7.58654 | 0.301538 | ||||||||
\(634\) | 27.4123 | 1.08868 | ||||||||
\(635\) | 36.8994 | 1.46431 | ||||||||
\(636\) | −4.55560 | −0.180641 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.00694 | 0.277407 | ||||||||
\(639\) | −2.65867 | −0.105175 | ||||||||
\(640\) | −3.87996 | −0.153369 | ||||||||
\(641\) | 42.4796 | 1.67784 | 0.838922 | − | 0.544252i | \(-0.183186\pi\) | ||||
0.838922 | + | 0.544252i | \(0.183186\pi\) | |||||||
\(642\) | −7.55741 | −0.298267 | ||||||||
\(643\) | −6.70754 | −0.264520 | −0.132260 | − | 0.991215i | \(-0.542223\pi\) | ||||
−0.132260 | + | 0.991215i | \(0.542223\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0640 | −0.435646 | ||||||||
\(646\) | −1.03094 | −0.0405617 | ||||||||
\(647\) | −3.62154 | −0.142377 | −0.0711887 | − | 0.997463i | \(-0.522679\pi\) | ||||
−0.0711887 | + | 0.997463i | \(0.522679\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −4.86599 | −0.191007 | ||||||||
\(650\) | −42.1560 | −1.65349 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.48528 | −0.332309 | ||||||||
\(653\) | 11.4998 | 0.450023 | 0.225011 | − | 0.974356i | \(-0.427758\pi\) | ||||
0.225011 | + | 0.974356i | \(0.427758\pi\) | |||||||
\(654\) | 2.81883 | 0.110225 | ||||||||
\(655\) | −73.7462 | −2.88150 | ||||||||
\(656\) | −11.3671 | −0.443809 | ||||||||
\(657\) | −1.02838 | −0.0401208 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.5953 | −0.685415 | −0.342708 | − | 0.939442i | \(-0.611344\pi\) | ||||
−0.342708 | + | 0.939442i | \(0.611344\pi\) | |||||||
\(660\) | −10.3155 | −0.401531 | ||||||||
\(661\) | 36.5477 | 1.42154 | 0.710771 | − | 0.703424i | \(-0.248346\pi\) | ||||
0.710771 | + | 0.703424i | \(0.248346\pi\) | |||||||
\(662\) | 5.99638 | 0.233056 | ||||||||
\(663\) | −7.37921 | −0.286585 | ||||||||
\(664\) | −13.7297 | −0.532817 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7.95284 | −0.308166 | ||||||||
\(667\) | −2.63551 | −0.102047 | ||||||||
\(668\) | −21.8292 | −0.844596 | ||||||||
\(669\) | 13.4433 | 0.519750 | ||||||||
\(670\) | −3.61416 | −0.139627 | ||||||||
\(671\) | 4.78574 | 0.184751 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.8016 | −0.724750 | −0.362375 | − | 0.932032i | \(-0.618034\pi\) | ||||
−0.362375 | + | 0.932032i | \(0.618034\pi\) | |||||||
\(674\) | −7.63648 | −0.294146 | ||||||||
\(675\) | 10.0541 | 0.386982 | ||||||||
\(676\) | 4.58057 | 0.176176 | ||||||||
\(677\) | 26.3232 | 1.01168 | 0.505842 | − | 0.862626i | \(-0.331182\pi\) | ||||
0.505842 | + | 0.862626i | \(0.331182\pi\) | |||||||
\(678\) | −4.61151 | −0.177104 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −6.82843 | −0.261858 | ||||||||
\(681\) | 1.84721 | 0.0707853 | ||||||||
\(682\) | −1.55741 | −0.0596363 | ||||||||
\(683\) | 31.8381 | 1.21825 | 0.609125 | − | 0.793074i | \(-0.291521\pi\) | ||||
0.609125 | + | 0.793074i | \(0.291521\pi\) | |||||||
\(684\) | −0.585786 | −0.0223981 | ||||||||
\(685\) | 33.7981 | 1.29136 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.0471 | 0.497777 | ||||||||
\(688\) | 2.85158 | 0.108716 | ||||||||
\(689\) | 19.1013 | 0.727700 | ||||||||
\(690\) | 3.87996 | 0.147708 | ||||||||
\(691\) | 43.8825 | 1.66937 | 0.834685 | − | 0.550728i | \(-0.185650\pi\) | ||||
0.834685 | + | 0.550728i | \(0.185650\pi\) | |||||||
\(692\) | −20.4940 | −0.779066 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 32.7660 | 1.24378 | ||||||||
\(695\) | −36.2407 | −1.37469 | ||||||||
\(696\) | 2.63551 | 0.0998987 | ||||||||
\(697\) | −20.0051 | −0.757748 | ||||||||
\(698\) | −36.5403 | −1.38307 | ||||||||
\(699\) | 12.5556 | 0.474896 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.6317 | −1.11917 | −0.559586 | − | 0.828772i | \(-0.689040\pi\) | ||||
−0.559586 | + | 0.828772i | \(0.689040\pi\) | |||||||
\(702\) | −4.19292 | −0.158252 | ||||||||
\(703\) | 4.65867 | 0.175705 | ||||||||
\(704\) | 2.65867 | 0.100202 | ||||||||
\(705\) | −18.2684 | −0.688026 | ||||||||
\(706\) | −2.90096 | −0.109179 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.83024 | −0.0687846 | ||||||||
\(709\) | 43.7151 | 1.64176 | 0.820878 | − | 0.571104i | \(-0.193485\pi\) | ||||
0.820878 | + | 0.571104i | \(0.193485\pi\) | |||||||
\(710\) | 10.3155 | 0.387135 | ||||||||
\(711\) | −8.65867 | −0.324725 | ||||||||
\(712\) | 0.216077 | 0.00809781 | ||||||||
\(713\) | 0.585786 | 0.0219379 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.2521 | 1.61754 | ||||||||
\(716\) | −26.6166 | −0.994710 | ||||||||
\(717\) | −24.2540 | −0.905780 | ||||||||
\(718\) | −26.5499 | −0.990835 | ||||||||
\(719\) | −16.6333 | −0.620316 | −0.310158 | − | 0.950685i | \(-0.600382\pi\) | ||||
−0.310158 | + | 0.950685i | \(0.600382\pi\) | |||||||
\(720\) | −3.87996 | −0.144598 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.6569 | −0.694336 | ||||||||
\(723\) | −17.7227 | −0.659114 | ||||||||
\(724\) | −21.6390 | −0.804209 | ||||||||
\(725\) | 26.4977 | 0.984098 | ||||||||
\(726\) | −3.93149 | −0.145911 | ||||||||
\(727\) | −27.5058 | −1.02013 | −0.510067 | − | 0.860135i | \(-0.670379\pi\) | ||||
−0.510067 | + | 0.860135i | \(0.670379\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.99006 | 0.147679 | ||||||||
\(731\) | 5.01857 | 0.185618 | ||||||||
\(732\) | 1.80005 | 0.0665318 | ||||||||
\(733\) | 0.448776 | 0.0165759 | 0.00828795 | − | 0.999966i | \(-0.497362\pi\) | ||||
0.00828795 | + | 0.999966i | \(0.497362\pi\) | |||||||
\(734\) | −26.6833 | −0.984899 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 2.47653 | 0.0912243 | ||||||||
\(738\) | −11.3671 | −0.418427 | ||||||||
\(739\) | 42.0614 | 1.54725 | 0.773626 | − | 0.633642i | \(-0.218441\pi\) | ||||
0.773626 | + | 0.633642i | \(0.218441\pi\) | |||||||
\(740\) | 30.8567 | 1.13432 | ||||||||
\(741\) | 2.45615 | 0.0902291 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −45.5005 | −1.66925 | −0.834625 | − | 0.550818i | \(-0.814316\pi\) | ||||
−0.834625 | + | 0.550818i | \(0.814316\pi\) | |||||||
\(744\) | −0.585786 | −0.0214760 | ||||||||
\(745\) | −6.30146 | −0.230868 | ||||||||
\(746\) | 9.13038 | 0.334287 | ||||||||
\(747\) | −13.7297 | −0.502345 | ||||||||
\(748\) | 4.67904 | 0.171083 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −19.6097 | −0.716045 | ||||||||
\(751\) | −23.6860 | −0.864314 | −0.432157 | − | 0.901798i | \(-0.642247\pi\) | ||||
−0.432157 | + | 0.901798i | \(0.642247\pi\) | |||||||
\(752\) | 4.70839 | 0.171697 | ||||||||
\(753\) | 26.3037 | 0.958559 | ||||||||
\(754\) | −11.0505 | −0.402434 | ||||||||
\(755\) | 24.8140 | 0.903075 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4424 | 1.32452 | 0.662261 | − | 0.749273i | \(-0.269597\pi\) | ||||
0.662261 | + | 0.749273i | \(0.269597\pi\) | |||||||
\(758\) | −33.9288 | −1.23235 | ||||||||
\(759\) | −2.65867 | −0.0965035 | ||||||||
\(760\) | 2.27283 | 0.0824442 | ||||||||
\(761\) | −30.5757 | −1.10837 | −0.554183 | − | 0.832395i | \(-0.686969\pi\) | ||||
−0.554183 | + | 0.832395i | \(0.686969\pi\) | |||||||
\(762\) | −9.51025 | −0.344520 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.23645 | 0.0809121 | ||||||||
\(765\) | −6.82843 | −0.246882 | ||||||||
\(766\) | −30.8008 | −1.11288 | ||||||||
\(767\) | 7.67404 | 0.277094 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 8.43180 | 0.304059 | 0.152029 | − | 0.988376i | \(-0.451419\pi\) | ||||
0.152029 | + | 0.988376i | \(0.451419\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.7643 | 0.531723 | ||||||||
\(772\) | 1.19473 | 0.0429993 | ||||||||
\(773\) | −15.0072 | −0.539770 | −0.269885 | − | 0.962893i | \(-0.586986\pi\) | ||||
−0.269885 | + | 0.962893i | \(0.586986\pi\) | |||||||
\(774\) | 2.85158 | 0.102498 | ||||||||
\(775\) | −5.88955 | −0.211559 | ||||||||
\(776\) | −8.80527 | −0.316091 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.38221 | −0.0854065 | ||||||||
\(779\) | 6.65867 | 0.238571 | ||||||||
\(780\) | 16.2684 | 0.582501 | ||||||||
\(781\) | −7.06851 | −0.252931 | ||||||||
\(782\) | −1.75992 | −0.0629347 | ||||||||
\(783\) | 2.63551 | 0.0941854 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 82.5407 | 2.94600 | ||||||||
\(786\) | 19.0069 | 0.677955 | ||||||||
\(787\) | 35.9774 | 1.28245 | 0.641227 | − | 0.767351i | \(-0.278426\pi\) | ||||
0.641227 | + | 0.767351i | \(0.278426\pi\) | |||||||
\(788\) | 12.5788 | 0.448100 | ||||||||
\(789\) | 3.81583 | 0.135847 | ||||||||
\(790\) | 33.5953 | 1.19527 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.65867 | 0.0944716 | ||||||||
\(793\) | −7.54747 | −0.268018 | ||||||||
\(794\) | 3.21064 | 0.113941 | ||||||||
\(795\) | 17.6755 | 0.626887 | ||||||||
\(796\) | −2.73858 | −0.0970662 | ||||||||
\(797\) | −36.1450 | −1.28032 | −0.640162 | − | 0.768240i | \(-0.721133\pi\) | ||||
−0.640162 | + | 0.768240i | \(0.721133\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.28639 | 0.293152 | ||||||||
\(800\) | 10.0541 | 0.355466 | ||||||||
\(801\) | 0.216077 | 0.00763469 | ||||||||
\(802\) | 36.2591 | 1.28035 | ||||||||
\(803\) | −2.73411 | −0.0964846 | ||||||||
\(804\) | 0.931495 | 0.0328513 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.45615 | 0.0865144 | ||||||||
\(807\) | 19.7551 | 0.695413 | ||||||||
\(808\) | 11.1439 | 0.392043 | ||||||||
\(809\) | 31.0261 | 1.09082 | 0.545410 | − | 0.838169i | \(-0.316374\pi\) | ||||
0.545410 | + | 0.838169i | \(0.316374\pi\) | |||||||
\(810\) | −3.87996 | −0.136328 | ||||||||
\(811\) | 2.38036 | 0.0835859 | 0.0417929 | − | 0.999126i | \(-0.486693\pi\) | ||||
0.0417929 | + | 0.999126i | \(0.486693\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −24.4966 | −0.859133 | ||||||||
\(814\) | −21.1439 | −0.741095 | ||||||||
\(815\) | 32.9226 | 1.15323 | ||||||||
\(816\) | 1.75992 | 0.0616096 | ||||||||
\(817\) | −1.67042 | −0.0584406 | ||||||||
\(818\) | −4.28896 | −0.149960 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 44.1037 | 1.54017 | ||||||||
\(821\) | −53.2725 | −1.85922 | −0.929612 | − | 0.368540i | \(-0.879858\pi\) | ||||
−0.929612 | + | 0.368540i | \(0.879858\pi\) | |||||||
\(822\) | −8.71095 | −0.303829 | ||||||||
\(823\) | −44.8240 | −1.56247 | −0.781233 | − | 0.624240i | \(-0.785409\pi\) | ||||
−0.781233 | + | 0.624240i | \(0.785409\pi\) | |||||||
\(824\) | −1.80708 | −0.0629527 | ||||||||
\(825\) | 26.7305 | 0.930636 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.6878 | −0.858479 | −0.429239 | − | 0.903191i | \(-0.641218\pi\) | ||||
−0.429239 | + | 0.903191i | \(0.641218\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | 24.3483 | 0.845650 | 0.422825 | − | 0.906211i | \(-0.361038\pi\) | ||||
0.422825 | + | 0.906211i | \(0.361038\pi\) | |||||||
\(830\) | 53.2708 | 1.84906 | ||||||||
\(831\) | −2.21245 | −0.0767491 | ||||||||
\(832\) | −4.19292 | −0.145363 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 9.34049 | 0.323435 | ||||||||
\(835\) | 84.6964 | 2.93104 | ||||||||
\(836\) | −1.55741 | −0.0538642 | ||||||||
\(837\) | −0.585786 | −0.0202477 | ||||||||
\(838\) | 29.3422 | 1.01361 | ||||||||
\(839\) | −36.5215 | −1.26086 | −0.630431 | − | 0.776246i | \(-0.717122\pi\) | ||||
−0.630431 | + | 0.776246i | \(0.717122\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0541 | −0.760486 | ||||||||
\(842\) | −5.27186 | −0.181680 | ||||||||
\(843\) | 3.92009 | 0.135015 | ||||||||
\(844\) | 7.58654 | 0.261139 | ||||||||
\(845\) | −17.7724 | −0.611390 | ||||||||
\(846\) | 4.70839 | 0.161878 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.55560 | −0.156440 | ||||||||
\(849\) | −25.7484 | −0.883684 | ||||||||
\(850\) | 17.6944 | 0.606914 | ||||||||
\(851\) | 7.95284 | 0.272620 | ||||||||
\(852\) | −2.65867 | −0.0910844 | ||||||||
\(853\) | 14.1893 | 0.485832 | 0.242916 | − | 0.970047i | \(-0.421896\pi\) | ||||
0.242916 | + | 0.970047i | \(0.421896\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.27283 | 0.0777291 | ||||||||
\(856\) | −7.55741 | −0.258307 | ||||||||
\(857\) | 36.5314 | 1.24789 | 0.623944 | − | 0.781469i | \(-0.285529\pi\) | ||||
0.623944 | + | 0.781469i | \(0.285529\pi\) | |||||||
\(858\) | −11.1476 | −0.380572 | ||||||||
\(859\) | 1.93415 | 0.0659924 | 0.0329962 | − | 0.999455i | \(-0.489495\pi\) | ||||
0.0329962 | + | 0.999455i | \(0.489495\pi\) | |||||||
\(860\) | −11.0640 | −0.377281 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.70463 | −0.228361 | ||||||||
\(863\) | −13.0081 | −0.442802 | −0.221401 | − | 0.975183i | \(-0.571063\pi\) | ||||
−0.221401 | + | 0.975183i | \(0.571063\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 79.5160 | 2.70363 | ||||||||
\(866\) | −26.3751 | −0.896261 | ||||||||
\(867\) | −13.9027 | −0.472160 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.0205 | −0.780917 | ||||||||
\(870\) | −10.2257 | −0.346683 | ||||||||
\(871\) | −3.90568 | −0.132339 | ||||||||
\(872\) | 2.81883 | 0.0954578 | ||||||||
\(873\) | −8.80527 | −0.298013 | ||||||||
\(874\) | 0.585786 | 0.0198145 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.02838 | −0.0347456 | ||||||||
\(877\) | 0.988246 | 0.0333707 | 0.0166854 | − | 0.999861i | \(-0.494689\pi\) | ||||
0.0166854 | + | 0.999861i | \(0.494689\pi\) | |||||||
\(878\) | −8.18589 | −0.276260 | ||||||||
\(879\) | 25.8379 | 0.871492 | ||||||||
\(880\) | −10.3155 | −0.347736 | ||||||||
\(881\) | 4.71492 | 0.158850 | 0.0794249 | − | 0.996841i | \(-0.474692\pi\) | ||||
0.0794249 | + | 0.996841i | \(0.474692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.0253 | 0.438337 | 0.219168 | − | 0.975687i | \(-0.429666\pi\) | ||||
0.219168 | + | 0.975687i | \(0.429666\pi\) | |||||||
\(884\) | −7.37921 | −0.248190 | ||||||||
\(885\) | 7.10126 | 0.238706 | ||||||||
\(886\) | 3.45037 | 0.115917 | ||||||||
\(887\) | 20.9615 | 0.703818 | 0.351909 | − | 0.936034i | \(-0.385533\pi\) | ||||
0.351909 | + | 0.936034i | \(0.385533\pi\) | |||||||
\(888\) | −7.95284 | −0.266880 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.838369 | −0.0281022 | ||||||||
\(891\) | 2.65867 | 0.0890687 | ||||||||
\(892\) | 13.4433 | 0.450116 | ||||||||
\(893\) | −2.75811 | −0.0922966 | ||||||||
\(894\) | 1.62410 | 0.0543182 | ||||||||
\(895\) | 103.271 | 3.45199 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.19292 | 0.139997 | ||||||||
\(898\) | 39.1515 | 1.30650 | ||||||||
\(899\) | −1.54385 | −0.0514901 | ||||||||
\(900\) | 10.0541 | 0.335137 | ||||||||
\(901\) | −8.01750 | −0.267102 | ||||||||
\(902\) | −30.2212 | −1.00626 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.61151 | −0.153376 | ||||||||
\(905\) | 83.9586 | 2.79088 | ||||||||
\(906\) | −6.39543 | −0.212474 | ||||||||
\(907\) | −28.6969 | −0.952865 | −0.476432 | − | 0.879211i | \(-0.658070\pi\) | ||||
−0.476432 | + | 0.879211i | \(0.658070\pi\) | |||||||
\(908\) | 1.84721 | 0.0613018 | ||||||||
\(909\) | 11.1439 | 0.369621 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.5199 | 1.60754 | 0.803768 | − | 0.594943i | \(-0.202825\pi\) | ||||
0.803768 | + | 0.594943i | \(0.202825\pi\) | |||||||
\(912\) | −0.585786 | −0.0193973 | ||||||||
\(913\) | −36.5028 | −1.20807 | ||||||||
\(914\) | 16.7872 | 0.555272 | ||||||||
\(915\) | −6.98413 | −0.230888 | ||||||||
\(916\) | 13.0471 | 0.431087 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.75992 | 0.0580861 | ||||||||
\(919\) | −8.80492 | −0.290448 | −0.145224 | − | 0.989399i | \(-0.546390\pi\) | ||||
−0.145224 | + | 0.989399i | \(0.546390\pi\) | |||||||
\(920\) | 3.87996 | 0.127919 | ||||||||
\(921\) | 19.2889 | 0.635590 | ||||||||
\(922\) | −34.3170 | −1.13017 | ||||||||
\(923\) | 11.1476 | 0.366927 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −79.9586 | −2.62902 | ||||||||
\(926\) | −7.75033 | −0.254692 | ||||||||
\(927\) | −1.80708 | −0.0593523 | ||||||||
\(928\) | 2.63551 | 0.0865148 | ||||||||
\(929\) | 54.7130 | 1.79508 | 0.897538 | − | 0.440937i | \(-0.145354\pi\) | ||||
0.897538 | + | 0.440937i | \(0.145354\pi\) | |||||||
\(930\) | 2.27283 | 0.0745290 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.5556 | 0.411272 | ||||||||
\(933\) | 17.4433 | 0.571069 | ||||||||
\(934\) | −19.9023 | −0.651222 | ||||||||
\(935\) | −18.1545 | −0.593716 | ||||||||
\(936\) | −4.19292 | −0.137050 | ||||||||
\(937\) | 38.8531 | 1.26927 | 0.634637 | − | 0.772810i | \(-0.281149\pi\) | ||||
0.634637 | + | 0.772810i | \(0.281149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.3225 | 0.500029 | ||||||||
\(940\) | −18.2684 | −0.595848 | ||||||||
\(941\) | −19.1134 | −0.623079 | −0.311540 | − | 0.950233i | \(-0.600845\pi\) | ||||
−0.311540 | + | 0.950233i | \(0.600845\pi\) | |||||||
\(942\) | −21.2736 | −0.693131 | ||||||||
\(943\) | 11.3671 | 0.370162 | ||||||||
\(944\) | −1.83024 | −0.0595692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.58141 | 0.246493 | ||||||||
\(947\) | 13.6992 | 0.445164 | 0.222582 | − | 0.974914i | \(-0.428551\pi\) | ||||
0.222582 | + | 0.974914i | \(0.428551\pi\) | |||||||
\(948\) | −8.65867 | −0.281220 | ||||||||
\(949\) | 4.31190 | 0.139970 | ||||||||
\(950\) | −5.88955 | −0.191082 | ||||||||
\(951\) | 27.4123 | 0.888905 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.6603 | −1.28472 | −0.642361 | − | 0.766402i | \(-0.722045\pi\) | ||||
−0.642361 | + | 0.766402i | \(0.722045\pi\) | |||||||
\(954\) | −4.55560 | −0.147493 | ||||||||
\(955\) | −8.67736 | −0.280793 | ||||||||
\(956\) | −24.2540 | −0.784429 | ||||||||
\(957\) | 7.00694 | 0.226502 | ||||||||
\(958\) | 12.4661 | 0.402761 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.87996 | −0.125225 | ||||||||
\(961\) | −30.6569 | −0.988931 | ||||||||
\(962\) | 33.3456 | 1.07511 | ||||||||
\(963\) | −7.55741 | −0.243534 | ||||||||
\(964\) | −17.7227 | −0.570810 | ||||||||
\(965\) | −4.63551 | −0.149222 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.1953 | 0.585120 | 0.292560 | − | 0.956247i | \(-0.405493\pi\) | ||||
0.292560 | + | 0.956247i | \(0.405493\pi\) | |||||||
\(968\) | −3.93149 | −0.126363 | ||||||||
\(969\) | −1.03094 | −0.0331185 | ||||||||
\(970\) | 34.1641 | 1.09694 | ||||||||
\(971\) | 6.56691 | 0.210742 | 0.105371 | − | 0.994433i | \(-0.466397\pi\) | ||||
0.105371 | + | 0.994433i | \(0.466397\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −40.4859 | −1.29725 | ||||||||
\(975\) | −42.1560 | −1.35007 | ||||||||
\(976\) | 1.80005 | 0.0576182 | ||||||||
\(977\) | −56.9952 | −1.82344 | −0.911719 | − | 0.410814i | \(-0.865245\pi\) | ||||
−0.911719 | + | 0.410814i | \(0.865245\pi\) | |||||||
\(978\) | −8.48528 | −0.271329 | ||||||||
\(979\) | 0.574476 | 0.0183603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.81883 | 0.0899985 | ||||||||
\(982\) | 35.7599 | 1.14114 | ||||||||
\(983\) | −29.3964 | −0.937599 | −0.468800 | − | 0.883304i | \(-0.655313\pi\) | ||||
−0.468800 | + | 0.883304i | \(0.655313\pi\) | |||||||
\(984\) | −11.3671 | −0.362368 | ||||||||
\(985\) | −48.8051 | −1.55506 | ||||||||
\(986\) | 4.63829 | 0.147713 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.45615 | 0.0781407 | ||||||||
\(989\) | −2.85158 | −0.0906751 | ||||||||
\(990\) | −10.3155 | −0.327849 | ||||||||
\(991\) | −31.2354 | −0.992225 | −0.496112 | − | 0.868258i | \(-0.665240\pi\) | ||||
−0.496112 | + | 0.868258i | \(0.665240\pi\) | |||||||
\(992\) | −0.585786 | −0.0185987 | ||||||||
\(993\) | 5.99638 | 0.190289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.6256 | 0.336853 | ||||||||
\(996\) | −13.7297 | −0.435043 | ||||||||
\(997\) | 42.7089 | 1.35260 | 0.676302 | − | 0.736624i | \(-0.263581\pi\) | ||||
0.676302 | + | 0.736624i | \(0.263581\pi\) | |||||||
\(998\) | −18.3291 | −0.580197 | ||||||||
\(999\) | −7.95284 | −0.251617 |
(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 | 6762.2.a.co.1.1 | yes | 4 | |
7.6 | odd | 2 | 6762.2.a.cn.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6762.2.a.cn.1.4 | ✓ | 4 | 7.6 | odd | 2 | ||
6762.2.a.co.1.1 | yes | 4 | 1.1 | even | 1 | trivial |