Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | −0.316697 | −0.182845 | −0.0914224 | − | 0.995812i | \(-0.529141\pi\) | ||||
−0.0914224 | + | 0.995812i | \(0.529141\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.633871 | −0.283476 | −0.141738 | − | 0.989904i | \(-0.545269\pi\) | ||||
−0.141738 | + | 0.989904i | \(0.545269\pi\) | |||||||
\(6\) | −0.316697 | −0.129291 | ||||||||
\(7\) | 1.30218 | 0.492177 | 0.246089 | − | 0.969247i | \(-0.420855\pi\) | ||||
0.246089 | + | 0.969247i | \(0.420855\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.89970 | −0.966568 | ||||||||
\(10\) | −0.633871 | −0.200448 | ||||||||
\(11\) | −3.28199 | −0.989559 | −0.494779 | − | 0.869019i | \(-0.664751\pi\) | ||||
−0.494779 | + | 0.869019i | \(0.664751\pi\) | |||||||
\(12\) | −0.316697 | −0.0914224 | ||||||||
\(13\) | 2.72112 | 0.754704 | 0.377352 | − | 0.926070i | \(-0.376835\pi\) | ||||
0.377352 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(14\) | 1.30218 | 0.348022 | ||||||||
\(15\) | 0.200745 | 0.0518321 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.85122 | 1.90420 | 0.952101 | − | 0.305785i | \(-0.0989187\pi\) | ||||
0.952101 | + | 0.305785i | \(0.0989187\pi\) | |||||||
\(18\) | −2.89970 | −0.683467 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −0.633871 | −0.141738 | ||||||||
\(21\) | −0.412396 | −0.0899921 | ||||||||
\(22\) | −3.28199 | −0.699724 | ||||||||
\(23\) | 5.94658 | 1.23995 | 0.619973 | − | 0.784623i | \(-0.287143\pi\) | ||||
0.619973 | + | 0.784623i | \(0.287143\pi\) | |||||||
\(24\) | −0.316697 | −0.0646454 | ||||||||
\(25\) | −4.59821 | −0.919642 | ||||||||
\(26\) | 2.72112 | 0.533656 | ||||||||
\(27\) | 1.86842 | 0.359577 | ||||||||
\(28\) | 1.30218 | 0.246089 | ||||||||
\(29\) | 4.86917 | 0.904182 | 0.452091 | − | 0.891972i | \(-0.350678\pi\) | ||||
0.452091 | + | 0.891972i | \(0.350678\pi\) | |||||||
\(30\) | 0.200745 | 0.0366508 | ||||||||
\(31\) | −10.3129 | −1.85225 | −0.926127 | − | 0.377211i | \(-0.876883\pi\) | ||||
−0.926127 | + | 0.377211i | \(0.876883\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.03940 | 0.180936 | ||||||||
\(34\) | 7.85122 | 1.34647 | ||||||||
\(35\) | −0.825413 | −0.139520 | ||||||||
\(36\) | −2.89970 | −0.483284 | ||||||||
\(37\) | 6.38504 | 1.04969 | 0.524847 | − | 0.851196i | \(-0.324122\pi\) | ||||
0.524847 | + | 0.851196i | \(0.324122\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −0.861770 | −0.137994 | ||||||||
\(40\) | −0.633871 | −0.100224 | ||||||||
\(41\) | 6.73152 | 1.05129 | 0.525643 | − | 0.850705i | \(-0.323825\pi\) | ||||
0.525643 | + | 0.850705i | \(0.323825\pi\) | |||||||
\(42\) | −0.412396 | −0.0636340 | ||||||||
\(43\) | −8.64507 | −1.31836 | −0.659180 | − | 0.751985i | \(-0.729097\pi\) | ||||
−0.659180 | + | 0.751985i | \(0.729097\pi\) | |||||||
\(44\) | −3.28199 | −0.494779 | ||||||||
\(45\) | 1.83804 | 0.273998 | ||||||||
\(46\) | 5.94658 | 0.876775 | ||||||||
\(47\) | −4.92688 | −0.718660 | −0.359330 | − | 0.933211i | \(-0.616995\pi\) | ||||
−0.359330 | + | 0.933211i | \(0.616995\pi\) | |||||||
\(48\) | −0.316697 | −0.0457112 | ||||||||
\(49\) | −5.30433 | −0.757761 | ||||||||
\(50\) | −4.59821 | −0.650285 | ||||||||
\(51\) | −2.48646 | −0.348173 | ||||||||
\(52\) | 2.72112 | 0.377352 | ||||||||
\(53\) | 6.78791 | 0.932391 | 0.466195 | − | 0.884682i | \(-0.345624\pi\) | ||||
0.466195 | + | 0.884682i | \(0.345624\pi\) | |||||||
\(54\) | 1.86842 | 0.254259 | ||||||||
\(55\) | 2.08036 | 0.280516 | ||||||||
\(56\) | 1.30218 | 0.174011 | ||||||||
\(57\) | 0.316697 | 0.0419475 | ||||||||
\(58\) | 4.86917 | 0.639353 | ||||||||
\(59\) | 6.46212 | 0.841297 | 0.420648 | − | 0.907224i | \(-0.361803\pi\) | ||||
0.420648 | + | 0.907224i | \(0.361803\pi\) | |||||||
\(60\) | 0.200745 | 0.0259160 | ||||||||
\(61\) | 8.88569 | 1.13770 | 0.568848 | − | 0.822443i | \(-0.307389\pi\) | ||||
0.568848 | + | 0.822443i | \(0.307389\pi\) | |||||||
\(62\) | −10.3129 | −1.30974 | ||||||||
\(63\) | −3.77593 | −0.475723 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.72484 | −0.213940 | ||||||||
\(66\) | 1.03940 | 0.127941 | ||||||||
\(67\) | −9.62712 | −1.17614 | −0.588070 | − | 0.808810i | \(-0.700112\pi\) | ||||
−0.588070 | + | 0.808810i | \(0.700112\pi\) | |||||||
\(68\) | 7.85122 | 0.952101 | ||||||||
\(69\) | −1.88326 | −0.226718 | ||||||||
\(70\) | −0.825413 | −0.0986558 | ||||||||
\(71\) | −15.4994 | −1.83944 | −0.919721 | − | 0.392571i | \(-0.871586\pi\) | ||||
−0.919721 | + | 0.392571i | \(0.871586\pi\) | |||||||
\(72\) | −2.89970 | −0.341733 | ||||||||
\(73\) | 11.9836 | 1.40258 | 0.701290 | − | 0.712876i | \(-0.252608\pi\) | ||||
0.701290 | + | 0.712876i | \(0.252608\pi\) | |||||||
\(74\) | 6.38504 | 0.742246 | ||||||||
\(75\) | 1.45624 | 0.168152 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −4.27374 | −0.487038 | ||||||||
\(78\) | −0.861770 | −0.0975762 | ||||||||
\(79\) | −10.1395 | −1.14079 | −0.570393 | − | 0.821372i | \(-0.693209\pi\) | ||||
−0.570393 | + | 0.821372i | \(0.693209\pi\) | |||||||
\(80\) | −0.633871 | −0.0708689 | ||||||||
\(81\) | 8.10739 | 0.900821 | ||||||||
\(82\) | 6.73152 | 0.743372 | ||||||||
\(83\) | 9.02471 | 0.990590 | 0.495295 | − | 0.868725i | \(-0.335060\pi\) | ||||
0.495295 | + | 0.868725i | \(0.335060\pi\) | |||||||
\(84\) | −0.412396 | −0.0449961 | ||||||||
\(85\) | −4.97666 | −0.539795 | ||||||||
\(86\) | −8.64507 | −0.932221 | ||||||||
\(87\) | −1.54205 | −0.165325 | ||||||||
\(88\) | −3.28199 | −0.349862 | ||||||||
\(89\) | 1.81210 | 0.192082 | 0.0960411 | − | 0.995377i | \(-0.469382\pi\) | ||||
0.0960411 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(90\) | 1.83804 | 0.193746 | ||||||||
\(91\) | 3.54339 | 0.371448 | ||||||||
\(92\) | 5.94658 | 0.619973 | ||||||||
\(93\) | 3.26607 | 0.338675 | ||||||||
\(94\) | −4.92688 | −0.508169 | ||||||||
\(95\) | 0.633871 | 0.0650338 | ||||||||
\(96\) | −0.316697 | −0.0323227 | ||||||||
\(97\) | 11.7199 | 1.18998 | 0.594989 | − | 0.803734i | \(-0.297156\pi\) | ||||
0.594989 | + | 0.803734i | \(0.297156\pi\) | |||||||
\(98\) | −5.30433 | −0.535818 | ||||||||
\(99\) | 9.51681 | 0.956475 | ||||||||
\(100\) | −4.59821 | −0.459821 | ||||||||
\(101\) | −8.56010 | −0.851761 | −0.425881 | − | 0.904779i | \(-0.640036\pi\) | ||||
−0.425881 | + | 0.904779i | \(0.640036\pi\) | |||||||
\(102\) | −2.48646 | −0.246196 | ||||||||
\(103\) | 14.5743 | 1.43605 | 0.718024 | − | 0.696018i | \(-0.245047\pi\) | ||||
0.718024 | + | 0.696018i | \(0.245047\pi\) | |||||||
\(104\) | 2.72112 | 0.266828 | ||||||||
\(105\) | 0.261406 | 0.0255106 | ||||||||
\(106\) | 6.78791 | 0.659300 | ||||||||
\(107\) | 0.0386434 | 0.00373580 | 0.00186790 | − | 0.999998i | \(-0.499405\pi\) | ||||
0.00186790 | + | 0.999998i | \(0.499405\pi\) | |||||||
\(108\) | 1.86842 | 0.179788 | ||||||||
\(109\) | −10.5277 | −1.00837 | −0.504187 | − | 0.863594i | \(-0.668208\pi\) | ||||
−0.504187 | + | 0.863594i | \(0.668208\pi\) | |||||||
\(110\) | 2.08036 | 0.198355 | ||||||||
\(111\) | −2.02212 | −0.191931 | ||||||||
\(112\) | 1.30218 | 0.123044 | ||||||||
\(113\) | 9.61364 | 0.904375 | 0.452188 | − | 0.891923i | \(-0.350644\pi\) | ||||
0.452188 | + | 0.891923i | \(0.350644\pi\) | |||||||
\(114\) | 0.316697 | 0.0296613 | ||||||||
\(115\) | −3.76936 | −0.351495 | ||||||||
\(116\) | 4.86917 | 0.452091 | ||||||||
\(117\) | −7.89045 | −0.729472 | ||||||||
\(118\) | 6.46212 | 0.594887 | ||||||||
\(119\) | 10.2237 | 0.937205 | ||||||||
\(120\) | 0.200745 | 0.0183254 | ||||||||
\(121\) | −0.228513 | −0.0207739 | ||||||||
\(122\) | 8.88569 | 0.804473 | ||||||||
\(123\) | −2.13185 | −0.192222 | ||||||||
\(124\) | −10.3129 | −0.926127 | ||||||||
\(125\) | 6.08402 | 0.544172 | ||||||||
\(126\) | −3.77593 | −0.336387 | ||||||||
\(127\) | −1.39508 | −0.123793 | −0.0618967 | − | 0.998083i | \(-0.519715\pi\) | ||||
−0.0618967 | + | 0.998083i | \(0.519715\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 2.73786 | 0.241055 | ||||||||
\(130\) | −1.72484 | −0.151278 | ||||||||
\(131\) | −9.10667 | −0.795653 | −0.397827 | − | 0.917461i | \(-0.630235\pi\) | ||||
−0.397827 | + | 0.917461i | \(0.630235\pi\) | |||||||
\(132\) | 1.03940 | 0.0904678 | ||||||||
\(133\) | −1.30218 | −0.112913 | ||||||||
\(134\) | −9.62712 | −0.831656 | ||||||||
\(135\) | −1.18433 | −0.101931 | ||||||||
\(136\) | 7.85122 | 0.673237 | ||||||||
\(137\) | 22.7634 | 1.94481 | 0.972405 | − | 0.233298i | \(-0.0749517\pi\) | ||||
0.972405 | + | 0.233298i | \(0.0749517\pi\) | |||||||
\(138\) | −1.88326 | −0.160314 | ||||||||
\(139\) | 17.9297 | 1.52077 | 0.760387 | − | 0.649470i | \(-0.225009\pi\) | ||||
0.760387 | + | 0.649470i | \(0.225009\pi\) | |||||||
\(140\) | −0.825413 | −0.0697602 | ||||||||
\(141\) | 1.56033 | 0.131403 | ||||||||
\(142\) | −15.4994 | −1.30068 | ||||||||
\(143\) | −8.93071 | −0.746823 | ||||||||
\(144\) | −2.89970 | −0.241642 | ||||||||
\(145\) | −3.08642 | −0.256314 | ||||||||
\(146\) | 11.9836 | 0.991774 | ||||||||
\(147\) | 1.67986 | 0.138553 | ||||||||
\(148\) | 6.38504 | 0.524847 | ||||||||
\(149\) | 12.6405 | 1.03555 | 0.517775 | − | 0.855517i | \(-0.326760\pi\) | ||||
0.517775 | + | 0.855517i | \(0.326760\pi\) | |||||||
\(150\) | 1.45624 | 0.118901 | ||||||||
\(151\) | 21.7335 | 1.76865 | 0.884324 | − | 0.466875i | \(-0.154620\pi\) | ||||
0.884324 | + | 0.466875i | \(0.154620\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −22.7662 | −1.84054 | ||||||||
\(154\) | −4.27374 | −0.344388 | ||||||||
\(155\) | 6.53706 | 0.525069 | ||||||||
\(156\) | −0.861770 | −0.0689968 | ||||||||
\(157\) | 6.16246 | 0.491818 | 0.245909 | − | 0.969293i | \(-0.420914\pi\) | ||||
0.245909 | + | 0.969293i | \(0.420914\pi\) | |||||||
\(158\) | −10.1395 | −0.806658 | ||||||||
\(159\) | −2.14971 | −0.170483 | ||||||||
\(160\) | −0.633871 | −0.0501119 | ||||||||
\(161\) | 7.74351 | 0.610274 | ||||||||
\(162\) | 8.10739 | 0.636977 | ||||||||
\(163\) | −11.7577 | −0.920934 | −0.460467 | − | 0.887677i | \(-0.652318\pi\) | ||||
−0.460467 | + | 0.887677i | \(0.652318\pi\) | |||||||
\(164\) | 6.73152 | 0.525643 | ||||||||
\(165\) | −0.658843 | −0.0512909 | ||||||||
\(166\) | 9.02471 | 0.700453 | ||||||||
\(167\) | −5.50355 | −0.425877 | −0.212939 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212939 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(168\) | −0.412396 | −0.0318170 | ||||||||
\(169\) | −5.59549 | −0.430423 | ||||||||
\(170\) | −4.97666 | −0.381693 | ||||||||
\(171\) | 2.89970 | 0.221746 | ||||||||
\(172\) | −8.64507 | −0.659180 | ||||||||
\(173\) | 13.2067 | 1.00409 | 0.502044 | − | 0.864842i | \(-0.332582\pi\) | ||||
0.502044 | + | 0.864842i | \(0.332582\pi\) | |||||||
\(174\) | −1.54205 | −0.116902 | ||||||||
\(175\) | −5.98769 | −0.452627 | ||||||||
\(176\) | −3.28199 | −0.247390 | ||||||||
\(177\) | −2.04653 | −0.153827 | ||||||||
\(178\) | 1.81210 | 0.135823 | ||||||||
\(179\) | 22.4263 | 1.67622 | 0.838109 | − | 0.545503i | \(-0.183661\pi\) | ||||
0.838109 | + | 0.545503i | \(0.183661\pi\) | |||||||
\(180\) | 1.83804 | 0.136999 | ||||||||
\(181\) | 12.5002 | 0.929134 | 0.464567 | − | 0.885538i | \(-0.346210\pi\) | ||||
0.464567 | + | 0.885538i | \(0.346210\pi\) | |||||||
\(182\) | 3.54339 | 0.262653 | ||||||||
\(183\) | −2.81407 | −0.208022 | ||||||||
\(184\) | 5.94658 | 0.438387 | ||||||||
\(185\) | −4.04729 | −0.297563 | ||||||||
\(186\) | 3.26607 | 0.239480 | ||||||||
\(187\) | −25.7677 | −1.88432 | ||||||||
\(188\) | −4.92688 | −0.359330 | ||||||||
\(189\) | 2.43301 | 0.176976 | ||||||||
\(190\) | 0.633871 | 0.0459858 | ||||||||
\(191\) | 25.8064 | 1.86729 | 0.933644 | − | 0.358203i | \(-0.116610\pi\) | ||||
0.933644 | + | 0.358203i | \(0.116610\pi\) | |||||||
\(192\) | −0.316697 | −0.0228556 | ||||||||
\(193\) | 9.81184 | 0.706272 | 0.353136 | − | 0.935572i | \(-0.385115\pi\) | ||||
0.353136 | + | 0.935572i | \(0.385115\pi\) | |||||||
\(194\) | 11.7199 | 0.841442 | ||||||||
\(195\) | 0.546251 | 0.0391178 | ||||||||
\(196\) | −5.30433 | −0.378881 | ||||||||
\(197\) | −9.53236 | −0.679152 | −0.339576 | − | 0.940579i | \(-0.610284\pi\) | ||||
−0.339576 | + | 0.940579i | \(0.610284\pi\) | |||||||
\(198\) | 9.51681 | 0.676330 | ||||||||
\(199\) | 16.1514 | 1.14494 | 0.572470 | − | 0.819926i | \(-0.305985\pi\) | ||||
0.572470 | + | 0.819926i | \(0.305985\pi\) | |||||||
\(200\) | −4.59821 | −0.325142 | ||||||||
\(201\) | 3.04887 | 0.215051 | ||||||||
\(202\) | −8.56010 | −0.602286 | ||||||||
\(203\) | 6.34053 | 0.445018 | ||||||||
\(204\) | −2.48646 | −0.174087 | ||||||||
\(205\) | −4.26692 | −0.298014 | ||||||||
\(206\) | 14.5743 | 1.01544 | ||||||||
\(207\) | −17.2433 | −1.19849 | ||||||||
\(208\) | 2.72112 | 0.188676 | ||||||||
\(209\) | 3.28199 | 0.227020 | ||||||||
\(210\) | 0.261406 | 0.0180387 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 6.78791 | 0.466195 | ||||||||
\(213\) | 4.90861 | 0.336333 | ||||||||
\(214\) | 0.0386434 | 0.00264161 | ||||||||
\(215\) | 5.47986 | 0.373723 | ||||||||
\(216\) | 1.86842 | 0.127130 | ||||||||
\(217\) | −13.4293 | −0.911638 | ||||||||
\(218\) | −10.5277 | −0.713029 | ||||||||
\(219\) | −3.79518 | −0.256454 | ||||||||
\(220\) | 2.08036 | 0.140258 | ||||||||
\(221\) | 21.3641 | 1.43711 | ||||||||
\(222\) | −2.02212 | −0.135716 | ||||||||
\(223\) | 6.01217 | 0.402604 | 0.201302 | − | 0.979529i | \(-0.435483\pi\) | ||||
0.201302 | + | 0.979529i | \(0.435483\pi\) | |||||||
\(224\) | 1.30218 | 0.0870055 | ||||||||
\(225\) | 13.3334 | 0.888896 | ||||||||
\(226\) | 9.61364 | 0.639490 | ||||||||
\(227\) | 0.456059 | 0.0302697 | 0.0151348 | − | 0.999885i | \(-0.495182\pi\) | ||||
0.0151348 | + | 0.999885i | \(0.495182\pi\) | |||||||
\(228\) | 0.316697 | 0.0209737 | ||||||||
\(229\) | 6.93276 | 0.458129 | 0.229065 | − | 0.973411i | \(-0.426433\pi\) | ||||
0.229065 | + | 0.973411i | \(0.426433\pi\) | |||||||
\(230\) | −3.76936 | −0.248544 | ||||||||
\(231\) | 1.35348 | 0.0890525 | ||||||||
\(232\) | 4.86917 | 0.319677 | ||||||||
\(233\) | 8.39227 | 0.549796 | 0.274898 | − | 0.961473i | \(-0.411356\pi\) | ||||
0.274898 | + | 0.961473i | \(0.411356\pi\) | |||||||
\(234\) | −7.89045 | −0.515815 | ||||||||
\(235\) | 3.12301 | 0.203723 | ||||||||
\(236\) | 6.46212 | 0.420648 | ||||||||
\(237\) | 3.21115 | 0.208587 | ||||||||
\(238\) | 10.2237 | 0.662704 | ||||||||
\(239\) | −2.25755 | −0.146029 | −0.0730143 | − | 0.997331i | \(-0.523262\pi\) | ||||
−0.0730143 | + | 0.997331i | \(0.523262\pi\) | |||||||
\(240\) | 0.200745 | 0.0129580 | ||||||||
\(241\) | 5.14424 | 0.331370 | 0.165685 | − | 0.986179i | \(-0.447017\pi\) | ||||
0.165685 | + | 0.986179i | \(0.447017\pi\) | |||||||
\(242\) | −0.228513 | −0.0146894 | ||||||||
\(243\) | −8.17283 | −0.524287 | ||||||||
\(244\) | 8.88569 | 0.568848 | ||||||||
\(245\) | 3.36226 | 0.214807 | ||||||||
\(246\) | −2.13185 | −0.135922 | ||||||||
\(247\) | −2.72112 | −0.173141 | ||||||||
\(248\) | −10.3129 | −0.654871 | ||||||||
\(249\) | −2.85809 | −0.181124 | ||||||||
\(250\) | 6.08402 | 0.384788 | ||||||||
\(251\) | 25.9841 | 1.64010 | 0.820052 | − | 0.572289i | \(-0.193944\pi\) | ||||
0.820052 | + | 0.572289i | \(0.193944\pi\) | |||||||
\(252\) | −3.77593 | −0.237861 | ||||||||
\(253\) | −19.5166 | −1.22700 | ||||||||
\(254\) | −1.39508 | −0.0875352 | ||||||||
\(255\) | 1.57609 | 0.0986987 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.5572 | −1.15756 | −0.578782 | − | 0.815482i | \(-0.696472\pi\) | ||||
−0.578782 | + | 0.815482i | \(0.696472\pi\) | |||||||
\(258\) | 2.73786 | 0.170452 | ||||||||
\(259\) | 8.31447 | 0.516636 | ||||||||
\(260\) | −1.72484 | −0.106970 | ||||||||
\(261\) | −14.1191 | −0.873953 | ||||||||
\(262\) | −9.10667 | −0.562612 | ||||||||
\(263\) | −20.5112 | −1.26477 | −0.632386 | − | 0.774653i | \(-0.717924\pi\) | ||||
−0.632386 | + | 0.774653i | \(0.717924\pi\) | |||||||
\(264\) | 1.03940 | 0.0639704 | ||||||||
\(265\) | −4.30266 | −0.264310 | ||||||||
\(266\) | −1.30218 | −0.0798417 | ||||||||
\(267\) | −0.573886 | −0.0351212 | ||||||||
\(268\) | −9.62712 | −0.588070 | ||||||||
\(269\) | −11.6832 | −0.712339 | −0.356170 | − | 0.934421i | \(-0.615917\pi\) | ||||
−0.356170 | + | 0.934421i | \(0.615917\pi\) | |||||||
\(270\) | −1.18433 | −0.0720763 | ||||||||
\(271\) | 16.9254 | 1.02814 | 0.514072 | − | 0.857747i | \(-0.328136\pi\) | ||||
0.514072 | + | 0.857747i | \(0.328136\pi\) | |||||||
\(272\) | 7.85122 | 0.476050 | ||||||||
\(273\) | −1.12218 | −0.0679174 | ||||||||
\(274\) | 22.7634 | 1.37519 | ||||||||
\(275\) | 15.0913 | 0.910039 | ||||||||
\(276\) | −1.88326 | −0.113359 | ||||||||
\(277\) | −10.7834 | −0.647910 | −0.323955 | − | 0.946072i | \(-0.605013\pi\) | ||||
−0.323955 | + | 0.946072i | \(0.605013\pi\) | |||||||
\(278\) | 17.9297 | 1.07535 | ||||||||
\(279\) | 29.9044 | 1.79033 | ||||||||
\(280\) | −0.825413 | −0.0493279 | ||||||||
\(281\) | 0.140080 | 0.00835650 | 0.00417825 | − | 0.999991i | \(-0.498670\pi\) | ||||
0.00417825 | + | 0.999991i | \(0.498670\pi\) | |||||||
\(282\) | 1.56033 | 0.0929161 | ||||||||
\(283\) | 15.7665 | 0.937221 | 0.468610 | − | 0.883405i | \(-0.344755\pi\) | ||||
0.468610 | + | 0.883405i | \(0.344755\pi\) | |||||||
\(284\) | −15.4994 | −0.919721 | ||||||||
\(285\) | −0.200745 | −0.0118911 | ||||||||
\(286\) | −8.93071 | −0.528084 | ||||||||
\(287\) | 8.76565 | 0.517420 | ||||||||
\(288\) | −2.89970 | −0.170867 | ||||||||
\(289\) | 44.6417 | 2.62598 | ||||||||
\(290\) | −3.08642 | −0.181241 | ||||||||
\(291\) | −3.71166 | −0.217581 | ||||||||
\(292\) | 11.9836 | 0.701290 | ||||||||
\(293\) | −19.3202 | −1.12870 | −0.564349 | − | 0.825536i | \(-0.690873\pi\) | ||||
−0.564349 | + | 0.825536i | \(0.690873\pi\) | |||||||
\(294\) | 1.67986 | 0.0979716 | ||||||||
\(295\) | −4.09615 | −0.238487 | ||||||||
\(296\) | 6.38504 | 0.371123 | ||||||||
\(297\) | −6.13213 | −0.355822 | ||||||||
\(298\) | 12.6405 | 0.732245 | ||||||||
\(299\) | 16.1814 | 0.935792 | ||||||||
\(300\) | 1.45624 | 0.0840759 | ||||||||
\(301\) | −11.2574 | −0.648867 | ||||||||
\(302\) | 21.7335 | 1.25062 | ||||||||
\(303\) | 2.71095 | 0.155740 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −5.63238 | −0.322509 | ||||||||
\(306\) | −22.7662 | −1.30146 | ||||||||
\(307\) | −12.9088 | −0.736745 | −0.368372 | − | 0.929678i | \(-0.620085\pi\) | ||||
−0.368372 | + | 0.929678i | \(0.620085\pi\) | |||||||
\(308\) | −4.27374 | −0.243519 | ||||||||
\(309\) | −4.61563 | −0.262574 | ||||||||
\(310\) | 6.53706 | 0.371280 | ||||||||
\(311\) | 16.1837 | 0.917694 | 0.458847 | − | 0.888515i | \(-0.348263\pi\) | ||||
0.458847 | + | 0.888515i | \(0.348263\pi\) | |||||||
\(312\) | −0.861770 | −0.0487881 | ||||||||
\(313\) | −30.7000 | −1.73526 | −0.867632 | − | 0.497206i | \(-0.834359\pi\) | ||||
−0.867632 | + | 0.497206i | \(0.834359\pi\) | |||||||
\(314\) | 6.16246 | 0.347768 | ||||||||
\(315\) | 2.39345 | 0.134856 | ||||||||
\(316\) | −10.1395 | −0.570393 | ||||||||
\(317\) | 13.8118 | 0.775748 | 0.387874 | − | 0.921712i | \(-0.373210\pi\) | ||||
0.387874 | + | 0.921712i | \(0.373210\pi\) | |||||||
\(318\) | −2.14971 | −0.120550 | ||||||||
\(319\) | −15.9806 | −0.894741 | ||||||||
\(320\) | −0.633871 | −0.0354345 | ||||||||
\(321\) | −0.0122382 | −0.000683071 0 | ||||||||
\(322\) | 7.74351 | 0.431529 | ||||||||
\(323\) | −7.85122 | −0.436854 | ||||||||
\(324\) | 8.10739 | 0.450411 | ||||||||
\(325\) | −12.5123 | −0.694057 | ||||||||
\(326\) | −11.7577 | −0.651199 | ||||||||
\(327\) | 3.33410 | 0.184376 | ||||||||
\(328\) | 6.73152 | 0.371686 | ||||||||
\(329\) | −6.41569 | −0.353708 | ||||||||
\(330\) | −0.658843 | −0.0362681 | ||||||||
\(331\) | −13.2313 | −0.727256 | −0.363628 | − | 0.931544i | \(-0.618462\pi\) | ||||
−0.363628 | + | 0.931544i | \(0.618462\pi\) | |||||||
\(332\) | 9.02471 | 0.495295 | ||||||||
\(333\) | −18.5147 | −1.01460 | ||||||||
\(334\) | −5.50355 | −0.301141 | ||||||||
\(335\) | 6.10235 | 0.333407 | ||||||||
\(336\) | −0.412396 | −0.0224980 | ||||||||
\(337\) | 20.4876 | 1.11603 | 0.558016 | − | 0.829830i | \(-0.311563\pi\) | ||||
0.558016 | + | 0.829830i | \(0.311563\pi\) | |||||||
\(338\) | −5.59549 | −0.304355 | ||||||||
\(339\) | −3.04461 | −0.165360 | ||||||||
\(340\) | −4.97666 | −0.269897 | ||||||||
\(341\) | 33.8469 | 1.83291 | ||||||||
\(342\) | 2.89970 | 0.156798 | ||||||||
\(343\) | −16.0224 | −0.865130 | ||||||||
\(344\) | −8.64507 | −0.466111 | ||||||||
\(345\) | 1.19374 | 0.0642690 | ||||||||
\(346\) | 13.2067 | 0.709997 | ||||||||
\(347\) | −23.1980 | −1.24533 | −0.622667 | − | 0.782487i | \(-0.713951\pi\) | ||||
−0.622667 | + | 0.782487i | \(0.713951\pi\) | |||||||
\(348\) | −1.54205 | −0.0826625 | ||||||||
\(349\) | −2.16227 | −0.115743 | −0.0578717 | − | 0.998324i | \(-0.518431\pi\) | ||||
−0.0578717 | + | 0.998324i | \(0.518431\pi\) | |||||||
\(350\) | −5.98769 | −0.320055 | ||||||||
\(351\) | 5.08419 | 0.271374 | ||||||||
\(352\) | −3.28199 | −0.174931 | ||||||||
\(353\) | −15.5308 | −0.826623 | −0.413311 | − | 0.910590i | \(-0.635628\pi\) | ||||
−0.413311 | + | 0.910590i | \(0.635628\pi\) | |||||||
\(354\) | −2.04653 | −0.108772 | ||||||||
\(355\) | 9.82463 | 0.521437 | ||||||||
\(356\) | 1.81210 | 0.0960411 | ||||||||
\(357\) | −3.23781 | −0.171363 | ||||||||
\(358\) | 22.4263 | 1.18526 | ||||||||
\(359\) | −21.9983 | −1.16102 | −0.580512 | − | 0.814252i | \(-0.697148\pi\) | ||||
−0.580512 | + | 0.814252i | \(0.697148\pi\) | |||||||
\(360\) | 1.83804 | 0.0968731 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 12.5002 | 0.656997 | ||||||||
\(363\) | 0.0723694 | 0.00379841 | ||||||||
\(364\) | 3.54339 | 0.185724 | ||||||||
\(365\) | −7.59608 | −0.397597 | ||||||||
\(366\) | −2.81407 | −0.147094 | ||||||||
\(367\) | 25.2122 | 1.31607 | 0.658033 | − | 0.752989i | \(-0.271389\pi\) | ||||
0.658033 | + | 0.752989i | \(0.271389\pi\) | |||||||
\(368\) | 5.94658 | 0.309987 | ||||||||
\(369\) | −19.5194 | −1.01614 | ||||||||
\(370\) | −4.04729 | −0.210409 | ||||||||
\(371\) | 8.83907 | 0.458902 | ||||||||
\(372\) | 3.26607 | 0.169338 | ||||||||
\(373\) | 22.5197 | 1.16603 | 0.583013 | − | 0.812463i | \(-0.301873\pi\) | ||||
0.583013 | + | 0.812463i | \(0.301873\pi\) | |||||||
\(374\) | −25.7677 | −1.33241 | ||||||||
\(375\) | −1.92679 | −0.0994990 | ||||||||
\(376\) | −4.92688 | −0.254085 | ||||||||
\(377\) | 13.2496 | 0.682389 | ||||||||
\(378\) | 2.43301 | 0.125141 | ||||||||
\(379\) | −18.1362 | −0.931594 | −0.465797 | − | 0.884892i | \(-0.654232\pi\) | ||||
−0.465797 | + | 0.884892i | \(0.654232\pi\) | |||||||
\(380\) | 0.633871 | 0.0325169 | ||||||||
\(381\) | 0.441817 | 0.0226350 | ||||||||
\(382\) | 25.8064 | 1.32037 | ||||||||
\(383\) | 18.7929 | 0.960271 | 0.480135 | − | 0.877194i | \(-0.340588\pi\) | ||||
0.480135 | + | 0.877194i | \(0.340588\pi\) | |||||||
\(384\) | −0.316697 | −0.0161614 | ||||||||
\(385\) | 2.70900 | 0.138064 | ||||||||
\(386\) | 9.81184 | 0.499410 | ||||||||
\(387\) | 25.0681 | 1.27428 | ||||||||
\(388\) | 11.7199 | 0.594989 | ||||||||
\(389\) | 26.0243 | 1.31949 | 0.659743 | − | 0.751492i | \(-0.270665\pi\) | ||||
0.659743 | + | 0.751492i | \(0.270665\pi\) | |||||||
\(390\) | 0.546251 | 0.0276605 | ||||||||
\(391\) | 46.6879 | 2.36111 | ||||||||
\(392\) | −5.30433 | −0.267909 | ||||||||
\(393\) | 2.88405 | 0.145481 | ||||||||
\(394\) | −9.53236 | −0.480233 | ||||||||
\(395\) | 6.42715 | 0.323385 | ||||||||
\(396\) | 9.51681 | 0.478238 | ||||||||
\(397\) | 13.7105 | 0.688110 | 0.344055 | − | 0.938949i | \(-0.388199\pi\) | ||||
0.344055 | + | 0.938949i | \(0.388199\pi\) | |||||||
\(398\) | 16.1514 | 0.809594 | ||||||||
\(399\) | 0.412396 | 0.0206456 | ||||||||
\(400\) | −4.59821 | −0.229910 | ||||||||
\(401\) | −37.7874 | −1.88701 | −0.943506 | − | 0.331355i | \(-0.892494\pi\) | ||||
−0.943506 | + | 0.331355i | \(0.892494\pi\) | |||||||
\(402\) | 3.04887 | 0.152064 | ||||||||
\(403\) | −28.0627 | −1.39790 | ||||||||
\(404\) | −8.56010 | −0.425881 | ||||||||
\(405\) | −5.13904 | −0.255361 | ||||||||
\(406\) | 6.34053 | 0.314675 | ||||||||
\(407\) | −20.9557 | −1.03873 | ||||||||
\(408\) | −2.48646 | −0.123098 | ||||||||
\(409\) | −20.1267 | −0.995199 | −0.497599 | − | 0.867407i | \(-0.665785\pi\) | ||||
−0.497599 | + | 0.867407i | \(0.665785\pi\) | |||||||
\(410\) | −4.26692 | −0.210728 | ||||||||
\(411\) | −7.20910 | −0.355599 | ||||||||
\(412\) | 14.5743 | 0.718024 | ||||||||
\(413\) | 8.41484 | 0.414067 | ||||||||
\(414\) | −17.2433 | −0.847462 | ||||||||
\(415\) | −5.72050 | −0.280808 | ||||||||
\(416\) | 2.72112 | 0.133414 | ||||||||
\(417\) | −5.67826 | −0.278066 | ||||||||
\(418\) | 3.28199 | 0.160528 | ||||||||
\(419\) | −29.3823 | −1.43542 | −0.717709 | − | 0.696343i | \(-0.754809\pi\) | ||||
−0.717709 | + | 0.696343i | \(0.754809\pi\) | |||||||
\(420\) | 0.261406 | 0.0127553 | ||||||||
\(421\) | 3.09990 | 0.151080 | 0.0755400 | − | 0.997143i | \(-0.475932\pi\) | ||||
0.0755400 | + | 0.997143i | \(0.475932\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | 14.2865 | 0.694634 | ||||||||
\(424\) | 6.78791 | 0.329650 | ||||||||
\(425\) | −36.1016 | −1.75118 | ||||||||
\(426\) | 4.90861 | 0.237823 | ||||||||
\(427\) | 11.5708 | 0.559948 | ||||||||
\(428\) | 0.0386434 | 0.00186790 | ||||||||
\(429\) | 2.82832 | 0.136553 | ||||||||
\(430\) | 5.47986 | 0.264262 | ||||||||
\(431\) | 1.55279 | 0.0747953 | 0.0373977 | − | 0.999300i | \(-0.488093\pi\) | ||||
0.0373977 | + | 0.999300i | \(0.488093\pi\) | |||||||
\(432\) | 1.86842 | 0.0898942 | ||||||||
\(433\) | −9.38182 | −0.450862 | −0.225431 | − | 0.974259i | \(-0.572379\pi\) | ||||
−0.225431 | + | 0.974259i | \(0.572379\pi\) | |||||||
\(434\) | −13.4293 | −0.644625 | ||||||||
\(435\) | 0.977460 | 0.0468656 | ||||||||
\(436\) | −10.5277 | −0.504187 | ||||||||
\(437\) | −5.94658 | −0.284463 | ||||||||
\(438\) | −3.79518 | −0.181341 | ||||||||
\(439\) | 7.35006 | 0.350799 | 0.175400 | − | 0.984497i | \(-0.443878\pi\) | ||||
0.175400 | + | 0.984497i | \(0.443878\pi\) | |||||||
\(440\) | 2.08036 | 0.0991773 | ||||||||
\(441\) | 15.3810 | 0.732428 | ||||||||
\(442\) | 21.3641 | 1.01619 | ||||||||
\(443\) | −19.9342 | −0.947104 | −0.473552 | − | 0.880766i | \(-0.657028\pi\) | ||||
−0.473552 | + | 0.880766i | \(0.657028\pi\) | |||||||
\(444\) | −2.02212 | −0.0959656 | ||||||||
\(445\) | −1.14864 | −0.0544507 | ||||||||
\(446\) | 6.01217 | 0.284684 | ||||||||
\(447\) | −4.00321 | −0.189345 | ||||||||
\(448\) | 1.30218 | 0.0615222 | ||||||||
\(449\) | −14.5104 | −0.684787 | −0.342394 | − | 0.939557i | \(-0.611238\pi\) | ||||
−0.342394 | + | 0.939557i | \(0.611238\pi\) | |||||||
\(450\) | 13.3334 | 0.628544 | ||||||||
\(451\) | −22.0928 | −1.04031 | ||||||||
\(452\) | 9.61364 | 0.452188 | ||||||||
\(453\) | −6.88292 | −0.323388 | ||||||||
\(454\) | 0.456059 | 0.0214039 | ||||||||
\(455\) | −2.24605 | −0.105296 | ||||||||
\(456\) | 0.316697 | 0.0148307 | ||||||||
\(457\) | 9.65001 | 0.451409 | 0.225704 | − | 0.974196i | \(-0.427532\pi\) | ||||
0.225704 | + | 0.974196i | \(0.427532\pi\) | |||||||
\(458\) | 6.93276 | 0.323946 | ||||||||
\(459\) | 14.6693 | 0.684707 | ||||||||
\(460\) | −3.76936 | −0.175747 | ||||||||
\(461\) | −3.51618 | −0.163765 | −0.0818824 | − | 0.996642i | \(-0.526093\pi\) | ||||
−0.0818824 | + | 0.996642i | \(0.526093\pi\) | |||||||
\(462\) | 1.35348 | 0.0629696 | ||||||||
\(463\) | −14.2805 | −0.663672 | −0.331836 | − | 0.943337i | \(-0.607668\pi\) | ||||
−0.331836 | + | 0.943337i | \(0.607668\pi\) | |||||||
\(464\) | 4.86917 | 0.226045 | ||||||||
\(465\) | −2.07026 | −0.0960062 | ||||||||
\(466\) | 8.39227 | 0.388765 | ||||||||
\(467\) | −7.93248 | −0.367071 | −0.183536 | − | 0.983013i | \(-0.558754\pi\) | ||||
−0.183536 | + | 0.983013i | \(0.558754\pi\) | |||||||
\(468\) | −7.89045 | −0.364736 | ||||||||
\(469\) | −12.5362 | −0.578869 | ||||||||
\(470\) | 3.12301 | 0.144054 | ||||||||
\(471\) | −1.95163 | −0.0899264 | ||||||||
\(472\) | 6.46212 | 0.297443 | ||||||||
\(473\) | 28.3731 | 1.30459 | ||||||||
\(474\) | 3.21115 | 0.147493 | ||||||||
\(475\) | 4.59821 | 0.210980 | ||||||||
\(476\) | 10.2237 | 0.468602 | ||||||||
\(477\) | −19.6829 | −0.901219 | ||||||||
\(478\) | −2.25755 | −0.103258 | ||||||||
\(479\) | 21.1612 | 0.966878 | 0.483439 | − | 0.875378i | \(-0.339388\pi\) | ||||
0.483439 | + | 0.875378i | \(0.339388\pi\) | |||||||
\(480\) | 0.200745 | 0.00916270 | ||||||||
\(481\) | 17.3745 | 0.792208 | ||||||||
\(482\) | 5.14424 | 0.234314 | ||||||||
\(483\) | −2.45234 | −0.111585 | ||||||||
\(484\) | −0.228513 | −0.0103870 | ||||||||
\(485\) | −7.42892 | −0.337330 | ||||||||
\(486\) | −8.17283 | −0.370727 | ||||||||
\(487\) | −17.4317 | −0.789908 | −0.394954 | − | 0.918701i | \(-0.629239\pi\) | ||||
−0.394954 | + | 0.918701i | \(0.629239\pi\) | |||||||
\(488\) | 8.88569 | 0.402236 | ||||||||
\(489\) | 3.72362 | 0.168388 | ||||||||
\(490\) | 3.36226 | 0.151891 | ||||||||
\(491\) | −40.2231 | −1.81525 | −0.907623 | − | 0.419787i | \(-0.862105\pi\) | ||||
−0.907623 | + | 0.419787i | \(0.862105\pi\) | |||||||
\(492\) | −2.13185 | −0.0961112 | ||||||||
\(493\) | 38.2289 | 1.72174 | ||||||||
\(494\) | −2.72112 | −0.122429 | ||||||||
\(495\) | −6.03243 | −0.271138 | ||||||||
\(496\) | −10.3129 | −0.463064 | ||||||||
\(497\) | −20.1830 | −0.905332 | ||||||||
\(498\) | −2.85809 | −0.128074 | ||||||||
\(499\) | −18.6263 | −0.833828 | −0.416914 | − | 0.908946i | \(-0.636888\pi\) | ||||
−0.416914 | + | 0.908946i | \(0.636888\pi\) | |||||||
\(500\) | 6.08402 | 0.272086 | ||||||||
\(501\) | 1.74296 | 0.0778695 | ||||||||
\(502\) | 25.9841 | 1.15973 | ||||||||
\(503\) | −1.00162 | −0.0446601 | −0.0223301 | − | 0.999751i | \(-0.507108\pi\) | ||||
−0.0223301 | + | 0.999751i | \(0.507108\pi\) | |||||||
\(504\) | −3.77593 | −0.168193 | ||||||||
\(505\) | 5.42600 | 0.241454 | ||||||||
\(506\) | −19.5166 | −0.867620 | ||||||||
\(507\) | 1.77207 | 0.0787006 | ||||||||
\(508\) | −1.39508 | −0.0618967 | ||||||||
\(509\) | −9.65915 | −0.428134 | −0.214067 | − | 0.976819i | \(-0.568671\pi\) | ||||
−0.214067 | + | 0.976819i | \(0.568671\pi\) | |||||||
\(510\) | 1.57609 | 0.0697905 | ||||||||
\(511\) | 15.6049 | 0.690318 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.86842 | −0.0824926 | ||||||||
\(514\) | −18.5572 | −0.818522 | ||||||||
\(515\) | −9.23822 | −0.407085 | ||||||||
\(516\) | 2.73786 | 0.120528 | ||||||||
\(517\) | 16.1700 | 0.711156 | ||||||||
\(518\) | 8.31447 | 0.365317 | ||||||||
\(519\) | −4.18252 | −0.183592 | ||||||||
\(520\) | −1.72484 | −0.0756392 | ||||||||
\(521\) | −39.0538 | −1.71098 | −0.855489 | − | 0.517822i | \(-0.826743\pi\) | ||||
−0.855489 | + | 0.517822i | \(0.826743\pi\) | |||||||
\(522\) | −14.1191 | −0.617978 | ||||||||
\(523\) | 41.0561 | 1.79526 | 0.897628 | − | 0.440754i | \(-0.145289\pi\) | ||||
0.897628 | + | 0.440754i | \(0.145289\pi\) | |||||||
\(524\) | −9.10667 | −0.397827 | ||||||||
\(525\) | 1.89628 | 0.0827605 | ||||||||
\(526\) | −20.5112 | −0.894329 | ||||||||
\(527\) | −80.9690 | −3.52707 | ||||||||
\(528\) | 1.03940 | 0.0452339 | ||||||||
\(529\) | 12.3618 | 0.537468 | ||||||||
\(530\) | −4.30266 | −0.186896 | ||||||||
\(531\) | −18.7382 | −0.813170 | ||||||||
\(532\) | −1.30218 | −0.0564566 | ||||||||
\(533\) | 18.3173 | 0.793410 | ||||||||
\(534\) | −0.573886 | −0.0248345 | ||||||||
\(535\) | −0.0244949 | −0.00105901 | ||||||||
\(536\) | −9.62712 | −0.415828 | ||||||||
\(537\) | −7.10232 | −0.306488 | ||||||||
\(538\) | −11.6832 | −0.503700 | ||||||||
\(539\) | 17.4088 | 0.749849 | ||||||||
\(540\) | −1.18433 | −0.0509656 | ||||||||
\(541\) | −0.289335 | −0.0124395 | −0.00621973 | − | 0.999981i | \(-0.501980\pi\) | ||||
−0.00621973 | + | 0.999981i | \(0.501980\pi\) | |||||||
\(542\) | 16.9254 | 0.727008 | ||||||||
\(543\) | −3.95878 | −0.169887 | ||||||||
\(544\) | 7.85122 | 0.336618 | ||||||||
\(545\) | 6.67323 | 0.285850 | ||||||||
\(546\) | −1.12218 | −0.0480248 | ||||||||
\(547\) | −7.33466 | −0.313607 | −0.156804 | − | 0.987630i | \(-0.550119\pi\) | ||||
−0.156804 | + | 0.987630i | \(0.550119\pi\) | |||||||
\(548\) | 22.7634 | 0.972405 | ||||||||
\(549\) | −25.7659 | −1.09966 | ||||||||
\(550\) | 15.0913 | 0.643495 | ||||||||
\(551\) | −4.86917 | −0.207434 | ||||||||
\(552\) | −1.88326 | −0.0801569 | ||||||||
\(553\) | −13.2035 | −0.561469 | ||||||||
\(554\) | −10.7834 | −0.458142 | ||||||||
\(555\) | 1.28176 | 0.0544078 | ||||||||
\(556\) | 17.9297 | 0.760387 | ||||||||
\(557\) | 11.7624 | 0.498389 | 0.249195 | − | 0.968453i | \(-0.419834\pi\) | ||||
0.249195 | + | 0.968453i | \(0.419834\pi\) | |||||||
\(558\) | 29.9044 | 1.26595 | ||||||||
\(559\) | −23.5243 | −0.994971 | ||||||||
\(560\) | −0.825413 | −0.0348801 | ||||||||
\(561\) | 8.16053 | 0.344538 | ||||||||
\(562\) | 0.140080 | 0.00590894 | ||||||||
\(563\) | −16.8546 | −0.710337 | −0.355169 | − | 0.934802i | \(-0.615577\pi\) | ||||
−0.355169 | + | 0.934802i | \(0.615577\pi\) | |||||||
\(564\) | 1.56033 | 0.0657016 | ||||||||
\(565\) | −6.09381 | −0.256368 | ||||||||
\(566\) | 15.7665 | 0.662715 | ||||||||
\(567\) | 10.5573 | 0.443364 | ||||||||
\(568\) | −15.4994 | −0.650341 | ||||||||
\(569\) | −30.4909 | −1.27824 | −0.639122 | − | 0.769106i | \(-0.720702\pi\) | ||||
−0.639122 | + | 0.769106i | \(0.720702\pi\) | |||||||
\(570\) | −0.200745 | −0.00840827 | ||||||||
\(571\) | −9.28553 | −0.388588 | −0.194294 | − | 0.980943i | \(-0.562242\pi\) | ||||
−0.194294 | + | 0.980943i | \(0.562242\pi\) | |||||||
\(572\) | −8.93071 | −0.373412 | ||||||||
\(573\) | −8.17281 | −0.341424 | ||||||||
\(574\) | 8.76565 | 0.365871 | ||||||||
\(575\) | −27.3436 | −1.14031 | ||||||||
\(576\) | −2.89970 | −0.120821 | ||||||||
\(577\) | 41.2739 | 1.71825 | 0.859127 | − | 0.511762i | \(-0.171007\pi\) | ||||
0.859127 | + | 0.511762i | \(0.171007\pi\) | |||||||
\(578\) | 44.6417 | 1.85685 | ||||||||
\(579\) | −3.10738 | −0.129138 | ||||||||
\(580\) | −3.08642 | −0.128157 | ||||||||
\(581\) | 11.7518 | 0.487546 | ||||||||
\(582\) | −3.71166 | −0.153853 | ||||||||
\(583\) | −22.2779 | −0.922655 | ||||||||
\(584\) | 11.9836 | 0.495887 | ||||||||
\(585\) | 5.00152 | 0.206788 | ||||||||
\(586\) | −19.3202 | −0.798111 | ||||||||
\(587\) | −13.3476 | −0.550915 | −0.275457 | − | 0.961313i | \(-0.588829\pi\) | ||||
−0.275457 | + | 0.961313i | \(0.588829\pi\) | |||||||
\(588\) | 1.67986 | 0.0692764 | ||||||||
\(589\) | 10.3129 | 0.424936 | ||||||||
\(590\) | −4.09615 | −0.168636 | ||||||||
\(591\) | 3.01886 | 0.124179 | ||||||||
\(592\) | 6.38504 | 0.262424 | ||||||||
\(593\) | −28.3630 | −1.16473 | −0.582364 | − | 0.812928i | \(-0.697872\pi\) | ||||
−0.582364 | + | 0.812928i | \(0.697872\pi\) | |||||||
\(594\) | −6.13213 | −0.251604 | ||||||||
\(595\) | −6.48051 | −0.265675 | ||||||||
\(596\) | 12.6405 | 0.517775 | ||||||||
\(597\) | −5.11508 | −0.209346 | ||||||||
\(598\) | 16.1814 | 0.661705 | ||||||||
\(599\) | 30.7521 | 1.25650 | 0.628248 | − | 0.778013i | \(-0.283772\pi\) | ||||
0.628248 | + | 0.778013i | \(0.283772\pi\) | |||||||
\(600\) | 1.45624 | 0.0594506 | ||||||||
\(601\) | 35.3404 | 1.44156 | 0.720782 | − | 0.693162i | \(-0.243783\pi\) | ||||
0.720782 | + | 0.693162i | \(0.243783\pi\) | |||||||
\(602\) | −11.2574 | −0.458818 | ||||||||
\(603\) | 27.9158 | 1.13682 | ||||||||
\(604\) | 21.7335 | 0.884324 | ||||||||
\(605\) | 0.144848 | 0.00588891 | ||||||||
\(606\) | 2.71095 | 0.110125 | ||||||||
\(607\) | −30.2690 | −1.22858 | −0.614290 | − | 0.789080i | \(-0.710557\pi\) | ||||
−0.614290 | + | 0.789080i | \(0.710557\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −2.00802 | −0.0813692 | ||||||||
\(610\) | −5.63238 | −0.228048 | ||||||||
\(611\) | −13.4067 | −0.542375 | ||||||||
\(612\) | −22.7662 | −0.920270 | ||||||||
\(613\) | −19.8122 | −0.800207 | −0.400103 | − | 0.916470i | \(-0.631026\pi\) | ||||
−0.400103 | + | 0.916470i | \(0.631026\pi\) | |||||||
\(614\) | −12.9088 | −0.520957 | ||||||||
\(615\) | 1.35132 | 0.0544904 | ||||||||
\(616\) | −4.27374 | −0.172194 | ||||||||
\(617\) | 3.39011 | 0.136481 | 0.0682403 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682403 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(618\) | −4.61563 | −0.185668 | ||||||||
\(619\) | 38.3541 | 1.54158 | 0.770791 | − | 0.637088i | \(-0.219861\pi\) | ||||
0.770791 | + | 0.637088i | \(0.219861\pi\) | |||||||
\(620\) | 6.53706 | 0.262535 | ||||||||
\(621\) | 11.1107 | 0.445856 | ||||||||
\(622\) | 16.1837 | 0.648908 | ||||||||
\(623\) | 2.35968 | 0.0945385 | ||||||||
\(624\) | −0.861770 | −0.0344984 | ||||||||
\(625\) | 19.1346 | 0.765382 | ||||||||
\(626\) | −30.7000 | −1.22702 | ||||||||
\(627\) | −1.03940 | −0.0415095 | ||||||||
\(628\) | 6.16246 | 0.245909 | ||||||||
\(629\) | 50.1304 | 1.99883 | ||||||||
\(630\) | 2.39345 | 0.0953575 | ||||||||
\(631\) | 33.9402 | 1.35114 | 0.675569 | − | 0.737297i | \(-0.263898\pi\) | ||||
0.675569 | + | 0.737297i | \(0.263898\pi\) | |||||||
\(632\) | −10.1395 | −0.403329 | ||||||||
\(633\) | 0.316697 | 0.0125876 | ||||||||
\(634\) | 13.8118 | 0.548537 | ||||||||
\(635\) | 0.884301 | 0.0350924 | ||||||||
\(636\) | −2.14971 | −0.0852414 | ||||||||
\(637\) | −14.4337 | −0.571885 | ||||||||
\(638\) | −15.9806 | −0.632677 | ||||||||
\(639\) | 44.9437 | 1.77795 | ||||||||
\(640\) | −0.633871 | −0.0250559 | ||||||||
\(641\) | 19.7731 | 0.780990 | 0.390495 | − | 0.920605i | \(-0.372304\pi\) | ||||
0.390495 | + | 0.920605i | \(0.372304\pi\) | |||||||
\(642\) | −0.0122382 | −0.000483004 0 | ||||||||
\(643\) | −37.2279 | −1.46813 | −0.734063 | − | 0.679081i | \(-0.762379\pi\) | ||||
−0.734063 | + | 0.679081i | \(0.762379\pi\) | |||||||
\(644\) | 7.74351 | 0.305137 | ||||||||
\(645\) | −1.73545 | −0.0683333 | ||||||||
\(646\) | −7.85122 | −0.308902 | ||||||||
\(647\) | 39.8723 | 1.56754 | 0.783770 | − | 0.621051i | \(-0.213294\pi\) | ||||
0.783770 | + | 0.621051i | \(0.213294\pi\) | |||||||
\(648\) | 8.10739 | 0.318488 | ||||||||
\(649\) | −21.2087 | −0.832513 | ||||||||
\(650\) | −12.5123 | −0.490772 | ||||||||
\(651\) | 4.25300 | 0.166688 | ||||||||
\(652\) | −11.7577 | −0.460467 | ||||||||
\(653\) | −15.0879 | −0.590434 | −0.295217 | − | 0.955430i | \(-0.595392\pi\) | ||||
−0.295217 | + | 0.955430i | \(0.595392\pi\) | |||||||
\(654\) | 3.33410 | 0.130374 | ||||||||
\(655\) | 5.77245 | 0.225548 | ||||||||
\(656\) | 6.73152 | 0.262822 | ||||||||
\(657\) | −34.7490 | −1.35569 | ||||||||
\(658\) | −6.41569 | −0.250109 | ||||||||
\(659\) | −27.2238 | −1.06049 | −0.530245 | − | 0.847844i | \(-0.677900\pi\) | ||||
−0.530245 | + | 0.847844i | \(0.677900\pi\) | |||||||
\(660\) | −0.658843 | −0.0256454 | ||||||||
\(661\) | 8.89511 | 0.345980 | 0.172990 | − | 0.984924i | \(-0.444657\pi\) | ||||
0.172990 | + | 0.984924i | \(0.444657\pi\) | |||||||
\(662\) | −13.2313 | −0.514248 | ||||||||
\(663\) | −6.76595 | −0.262768 | ||||||||
\(664\) | 9.02471 | 0.350227 | ||||||||
\(665\) | 0.825413 | 0.0320082 | ||||||||
\(666\) | −18.5147 | −0.717431 | ||||||||
\(667\) | 28.9549 | 1.12114 | ||||||||
\(668\) | −5.50355 | −0.212939 | ||||||||
\(669\) | −1.90403 | −0.0736141 | ||||||||
\(670\) | 6.10235 | 0.235754 | ||||||||
\(671\) | −29.1628 | −1.12582 | ||||||||
\(672\) | −0.412396 | −0.0159085 | ||||||||
\(673\) | −7.04337 | −0.271502 | −0.135751 | − | 0.990743i | \(-0.543345\pi\) | ||||
−0.135751 | + | 0.990743i | \(0.543345\pi\) | |||||||
\(674\) | 20.4876 | 0.789153 | ||||||||
\(675\) | −8.59136 | −0.330682 | ||||||||
\(676\) | −5.59549 | −0.215211 | ||||||||
\(677\) | 44.6504 | 1.71605 | 0.858027 | − | 0.513604i | \(-0.171690\pi\) | ||||
0.858027 | + | 0.513604i | \(0.171690\pi\) | |||||||
\(678\) | −3.04461 | −0.116927 | ||||||||
\(679\) | 15.2614 | 0.585680 | ||||||||
\(680\) | −4.97666 | −0.190846 | ||||||||
\(681\) | −0.144432 | −0.00553466 | ||||||||
\(682\) | 33.8469 | 1.29607 | ||||||||
\(683\) | 17.4383 | 0.667259 | 0.333629 | − | 0.942704i | \(-0.391727\pi\) | ||||
0.333629 | + | 0.942704i | \(0.391727\pi\) | |||||||
\(684\) | 2.89970 | 0.110873 | ||||||||
\(685\) | −14.4291 | −0.551307 | ||||||||
\(686\) | −16.0224 | −0.611740 | ||||||||
\(687\) | −2.19558 | −0.0837666 | ||||||||
\(688\) | −8.64507 | −0.329590 | ||||||||
\(689\) | 18.4707 | 0.703679 | ||||||||
\(690\) | 1.19374 | 0.0454451 | ||||||||
\(691\) | 43.9575 | 1.67222 | 0.836110 | − | 0.548561i | \(-0.184824\pi\) | ||||
0.836110 | + | 0.548561i | \(0.184824\pi\) | |||||||
\(692\) | 13.2067 | 0.502044 | ||||||||
\(693\) | 12.3926 | 0.470756 | ||||||||
\(694\) | −23.1980 | −0.880583 | ||||||||
\(695\) | −11.3651 | −0.431103 | ||||||||
\(696\) | −1.54205 | −0.0584512 | ||||||||
\(697\) | 52.8507 | 2.00186 | ||||||||
\(698\) | −2.16227 | −0.0818430 | ||||||||
\(699\) | −2.65780 | −0.100527 | ||||||||
\(700\) | −5.98769 | −0.226313 | ||||||||
\(701\) | 32.3793 | 1.22295 | 0.611475 | − | 0.791264i | \(-0.290576\pi\) | ||||
0.611475 | + | 0.791264i | \(0.290576\pi\) | |||||||
\(702\) | 5.08419 | 0.191890 | ||||||||
\(703\) | −6.38504 | −0.240816 | ||||||||
\(704\) | −3.28199 | −0.123695 | ||||||||
\(705\) | −0.989046 | −0.0372496 | ||||||||
\(706\) | −15.5308 | −0.584511 | ||||||||
\(707\) | −11.1468 | −0.419218 | ||||||||
\(708\) | −2.04653 | −0.0769134 | ||||||||
\(709\) | −22.7288 | −0.853596 | −0.426798 | − | 0.904347i | \(-0.640359\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640359\pi\) | |||||||
\(710\) | 9.82463 | 0.368712 | ||||||||
\(711\) | 29.4016 | 1.10265 | ||||||||
\(712\) | 1.81210 | 0.0679113 | ||||||||
\(713\) | −61.3266 | −2.29670 | ||||||||
\(714\) | −3.23781 | −0.121172 | ||||||||
\(715\) | 5.66092 | 0.211706 | ||||||||
\(716\) | 22.4263 | 0.838109 | ||||||||
\(717\) | 0.714957 | 0.0267006 | ||||||||
\(718\) | −21.9983 | −0.820968 | ||||||||
\(719\) | 21.6467 | 0.807284 | 0.403642 | − | 0.914917i | \(-0.367744\pi\) | ||||
0.403642 | + | 0.914917i | \(0.367744\pi\) | |||||||
\(720\) | 1.83804 | 0.0684996 | ||||||||
\(721\) | 18.9783 | 0.706791 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −1.62916 | −0.0605892 | ||||||||
\(724\) | 12.5002 | 0.464567 | ||||||||
\(725\) | −22.3894 | −0.831523 | ||||||||
\(726\) | 0.0723694 | 0.00268588 | ||||||||
\(727\) | 23.8204 | 0.883451 | 0.441726 | − | 0.897150i | \(-0.354366\pi\) | ||||
0.441726 | + | 0.897150i | \(0.354366\pi\) | |||||||
\(728\) | 3.54339 | 0.131327 | ||||||||
\(729\) | −21.7339 | −0.804958 | ||||||||
\(730\) | −7.59608 | −0.281144 | ||||||||
\(731\) | −67.8743 | −2.51042 | ||||||||
\(732\) | −2.81407 | −0.104011 | ||||||||
\(733\) | 16.1370 | 0.596032 | 0.298016 | − | 0.954561i | \(-0.403675\pi\) | ||||
0.298016 | + | 0.954561i | \(0.403675\pi\) | |||||||
\(734\) | 25.2122 | 0.930599 | ||||||||
\(735\) | −1.06482 | −0.0392763 | ||||||||
\(736\) | 5.94658 | 0.219194 | ||||||||
\(737\) | 31.5961 | 1.16386 | ||||||||
\(738\) | −19.5194 | −0.718520 | ||||||||
\(739\) | 52.5146 | 1.93178 | 0.965889 | − | 0.258955i | \(-0.0833780\pi\) | ||||
0.965889 | + | 0.258955i | \(0.0833780\pi\) | |||||||
\(740\) | −4.04729 | −0.148781 | ||||||||
\(741\) | 0.861770 | 0.0316579 | ||||||||
\(742\) | 8.83907 | 0.324493 | ||||||||
\(743\) | −6.84173 | −0.250999 | −0.125499 | − | 0.992094i | \(-0.540053\pi\) | ||||
−0.125499 | + | 0.992094i | \(0.540053\pi\) | |||||||
\(744\) | 3.26607 | 0.119740 | ||||||||
\(745\) | −8.01245 | −0.293553 | ||||||||
\(746\) | 22.5197 | 0.824505 | ||||||||
\(747\) | −26.1690 | −0.957473 | ||||||||
\(748\) | −25.7677 | −0.942159 | ||||||||
\(749\) | 0.0503206 | 0.00183867 | ||||||||
\(750\) | −1.92679 | −0.0703564 | ||||||||
\(751\) | 7.49789 | 0.273602 | 0.136801 | − | 0.990599i | \(-0.456318\pi\) | ||||
0.136801 | + | 0.990599i | \(0.456318\pi\) | |||||||
\(752\) | −4.92688 | −0.179665 | ||||||||
\(753\) | −8.22909 | −0.299885 | ||||||||
\(754\) | 13.2496 | 0.482522 | ||||||||
\(755\) | −13.7762 | −0.501368 | ||||||||
\(756\) | 2.43301 | 0.0884878 | ||||||||
\(757\) | 1.81117 | 0.0658283 | 0.0329141 | − | 0.999458i | \(-0.489521\pi\) | ||||
0.0329141 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(758\) | −18.1362 | −0.658736 | ||||||||
\(759\) | 6.18085 | 0.224351 | ||||||||
\(760\) | 0.633871 | 0.0229929 | ||||||||
\(761\) | −12.4752 | −0.452226 | −0.226113 | − | 0.974101i | \(-0.572602\pi\) | ||||
−0.226113 | + | 0.974101i | \(0.572602\pi\) | |||||||
\(762\) | 0.441817 | 0.0160054 | ||||||||
\(763\) | −13.7090 | −0.496299 | ||||||||
\(764\) | 25.8064 | 0.933644 | ||||||||
\(765\) | 14.4308 | 0.521748 | ||||||||
\(766\) | 18.7929 | 0.679014 | ||||||||
\(767\) | 17.5842 | 0.634930 | ||||||||
\(768\) | −0.316697 | −0.0114278 | ||||||||
\(769\) | −4.38194 | −0.158017 | −0.0790084 | − | 0.996874i | \(-0.525175\pi\) | ||||
−0.0790084 | + | 0.996874i | \(0.525175\pi\) | |||||||
\(770\) | 2.70900 | 0.0976257 | ||||||||
\(771\) | 5.87699 | 0.211655 | ||||||||
\(772\) | 9.81184 | 0.353136 | ||||||||
\(773\) | 2.17024 | 0.0780582 | 0.0390291 | − | 0.999238i | \(-0.487573\pi\) | ||||
0.0390291 | + | 0.999238i | \(0.487573\pi\) | |||||||
\(774\) | 25.0681 | 0.901055 | ||||||||
\(775\) | 47.4209 | 1.70341 | ||||||||
\(776\) | 11.7199 | 0.420721 | ||||||||
\(777\) | −2.63316 | −0.0944642 | ||||||||
\(778\) | 26.0243 | 0.933017 | ||||||||
\(779\) | −6.73152 | −0.241182 | ||||||||
\(780\) | 0.546251 | 0.0195589 | ||||||||
\(781\) | 50.8690 | 1.82024 | ||||||||
\(782\) | 46.6879 | 1.66956 | ||||||||
\(783\) | 9.09763 | 0.325123 | ||||||||
\(784\) | −5.30433 | −0.189440 | ||||||||
\(785\) | −3.90620 | −0.139418 | ||||||||
\(786\) | 2.88405 | 0.102871 | ||||||||
\(787\) | 24.3865 | 0.869283 | 0.434642 | − | 0.900603i | \(-0.356875\pi\) | ||||
0.434642 | + | 0.900603i | \(0.356875\pi\) | |||||||
\(788\) | −9.53236 | −0.339576 | ||||||||
\(789\) | 6.49581 | 0.231257 | ||||||||
\(790\) | 6.42715 | 0.228668 | ||||||||
\(791\) | 12.5187 | 0.445113 | ||||||||
\(792\) | 9.51681 | 0.338165 | ||||||||
\(793\) | 24.1790 | 0.858623 | ||||||||
\(794\) | 13.7105 | 0.486567 | ||||||||
\(795\) | 1.36264 | 0.0483277 | ||||||||
\(796\) | 16.1514 | 0.572470 | ||||||||
\(797\) | −25.2277 | −0.893610 | −0.446805 | − | 0.894631i | \(-0.647438\pi\) | ||||
−0.446805 | + | 0.894631i | \(0.647438\pi\) | |||||||
\(798\) | 0.412396 | 0.0145986 | ||||||||
\(799\) | −38.6821 | −1.36847 | ||||||||
\(800\) | −4.59821 | −0.162571 | ||||||||
\(801\) | −5.25455 | −0.185661 | ||||||||
\(802\) | −37.7874 | −1.33432 | ||||||||
\(803\) | −39.3303 | −1.38793 | ||||||||
\(804\) | 3.04887 | 0.107526 | ||||||||
\(805\) | −4.90838 | −0.172998 | ||||||||
\(806\) | −28.0627 | −0.988467 | ||||||||
\(807\) | 3.70004 | 0.130248 | ||||||||
\(808\) | −8.56010 | −0.301143 | ||||||||
\(809\) | −11.7622 | −0.413537 | −0.206768 | − | 0.978390i | \(-0.566295\pi\) | ||||
−0.206768 | + | 0.978390i | \(0.566295\pi\) | |||||||
\(810\) | −5.13904 | −0.180567 | ||||||||
\(811\) | 46.9368 | 1.64817 | 0.824087 | − | 0.566464i | \(-0.191689\pi\) | ||||
0.824087 | + | 0.566464i | \(0.191689\pi\) | |||||||
\(812\) | 6.34053 | 0.222509 | ||||||||
\(813\) | −5.36021 | −0.187991 | ||||||||
\(814\) | −20.9557 | −0.734496 | ||||||||
\(815\) | 7.45286 | 0.261062 | ||||||||
\(816\) | −2.48646 | −0.0870434 | ||||||||
\(817\) | 8.64507 | 0.302453 | ||||||||
\(818\) | −20.1267 | −0.703712 | ||||||||
\(819\) | −10.2748 | −0.359030 | ||||||||
\(820\) | −4.26692 | −0.149007 | ||||||||
\(821\) | 2.44949 | 0.0854878 | 0.0427439 | − | 0.999086i | \(-0.486390\pi\) | ||||
0.0427439 | + | 0.999086i | \(0.486390\pi\) | |||||||
\(822\) | −7.20910 | −0.251446 | ||||||||
\(823\) | −15.8230 | −0.551554 | −0.275777 | − | 0.961222i | \(-0.588935\pi\) | ||||
−0.275777 | + | 0.961222i | \(0.588935\pi\) | |||||||
\(824\) | 14.5743 | 0.507720 | ||||||||
\(825\) | −4.77936 | −0.166396 | ||||||||
\(826\) | 8.41484 | 0.292790 | ||||||||
\(827\) | −29.8591 | −1.03830 | −0.519151 | − | 0.854683i | \(-0.673752\pi\) | ||||
−0.519151 | + | 0.854683i | \(0.673752\pi\) | |||||||
\(828\) | −17.2433 | −0.599246 | ||||||||
\(829\) | −39.4678 | −1.37078 | −0.685388 | − | 0.728178i | \(-0.740367\pi\) | ||||
−0.685388 | + | 0.728178i | \(0.740367\pi\) | |||||||
\(830\) | −5.72050 | −0.198561 | ||||||||
\(831\) | 3.41506 | 0.118467 | ||||||||
\(832\) | 2.72112 | 0.0943379 | ||||||||
\(833\) | −41.6455 | −1.44293 | ||||||||
\(834\) | −5.67826 | −0.196622 | ||||||||
\(835\) | 3.48854 | 0.120726 | ||||||||
\(836\) | 3.28199 | 0.113510 | ||||||||
\(837\) | −19.2688 | −0.666028 | ||||||||
\(838\) | −29.3823 | −1.01499 | ||||||||
\(839\) | −29.3345 | −1.01274 | −0.506370 | − | 0.862316i | \(-0.669013\pi\) | ||||
−0.506370 | + | 0.862316i | \(0.669013\pi\) | |||||||
\(840\) | 0.261406 | 0.00901935 | ||||||||
\(841\) | −5.29120 | −0.182455 | ||||||||
\(842\) | 3.09990 | 0.106830 | ||||||||
\(843\) | −0.0443630 | −0.00152794 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | 3.54682 | 0.122014 | ||||||||
\(846\) | 14.2865 | 0.491180 | ||||||||
\(847\) | −0.297565 | −0.0102245 | ||||||||
\(848\) | 6.78791 | 0.233098 | ||||||||
\(849\) | −4.99319 | −0.171366 | ||||||||
\(850\) | −36.1016 | −1.23827 | ||||||||
\(851\) | 37.9691 | 1.30157 | ||||||||
\(852\) | 4.90861 | 0.168166 | ||||||||
\(853\) | 20.6330 | 0.706461 | 0.353231 | − | 0.935536i | \(-0.385083\pi\) | ||||
0.353231 | + | 0.935536i | \(0.385083\pi\) | |||||||
\(854\) | 11.5708 | 0.395943 | ||||||||
\(855\) | −1.83804 | −0.0628596 | ||||||||
\(856\) | 0.0386434 | 0.00132080 | ||||||||
\(857\) | 11.7409 | 0.401063 | 0.200531 | − | 0.979687i | \(-0.435733\pi\) | ||||
0.200531 | + | 0.979687i | \(0.435733\pi\) | |||||||
\(858\) | 2.82832 | 0.0965574 | ||||||||
\(859\) | −22.3891 | −0.763906 | −0.381953 | − | 0.924182i | \(-0.624748\pi\) | ||||
−0.381953 | + | 0.924182i | \(0.624748\pi\) | |||||||
\(860\) | 5.47986 | 0.186862 | ||||||||
\(861\) | −2.77605 | −0.0946075 | ||||||||
\(862\) | 1.55279 | 0.0528883 | ||||||||
\(863\) | −37.9279 | −1.29108 | −0.645540 | − | 0.763727i | \(-0.723368\pi\) | ||||
−0.645540 | + | 0.763727i | \(0.723368\pi\) | |||||||
\(864\) | 1.86842 | 0.0635648 | ||||||||
\(865\) | −8.37135 | −0.284634 | ||||||||
\(866\) | −9.38182 | −0.318807 | ||||||||
\(867\) | −14.1379 | −0.480147 | ||||||||
\(868\) | −13.4293 | −0.455819 | ||||||||
\(869\) | 33.2779 | 1.12887 | ||||||||
\(870\) | 0.977460 | 0.0331390 | ||||||||
\(871\) | −26.1966 | −0.887636 | ||||||||
\(872\) | −10.5277 | −0.356514 | ||||||||
\(873\) | −33.9843 | −1.15019 | ||||||||
\(874\) | −5.94658 | −0.201146 | ||||||||
\(875\) | 7.92249 | 0.267829 | ||||||||
\(876\) | −3.79518 | −0.128227 | ||||||||
\(877\) | 30.0165 | 1.01358 | 0.506792 | − | 0.862068i | \(-0.330831\pi\) | ||||
0.506792 | + | 0.862068i | \(0.330831\pi\) | |||||||
\(878\) | 7.35006 | 0.248052 | ||||||||
\(879\) | 6.11864 | 0.206377 | ||||||||
\(880\) | 2.08036 | 0.0701289 | ||||||||
\(881\) | −24.7663 | −0.834399 | −0.417199 | − | 0.908815i | \(-0.636988\pi\) | ||||
−0.417199 | + | 0.908815i | \(0.636988\pi\) | |||||||
\(882\) | 15.3810 | 0.517905 | ||||||||
\(883\) | −13.1762 | −0.443413 | −0.221707 | − | 0.975113i | \(-0.571163\pi\) | ||||
−0.221707 | + | 0.975113i | \(0.571163\pi\) | |||||||
\(884\) | 21.3641 | 0.718554 | ||||||||
\(885\) | 1.29724 | 0.0436062 | ||||||||
\(886\) | −19.9342 | −0.669703 | ||||||||
\(887\) | 16.7332 | 0.561846 | 0.280923 | − | 0.959730i | \(-0.409360\pi\) | ||||
0.280923 | + | 0.959730i | \(0.409360\pi\) | |||||||
\(888\) | −2.02212 | −0.0678579 | ||||||||
\(889\) | −1.81665 | −0.0609283 | ||||||||
\(890\) | −1.14864 | −0.0385024 | ||||||||
\(891\) | −26.6084 | −0.891415 | ||||||||
\(892\) | 6.01217 | 0.201302 | ||||||||
\(893\) | 4.92688 | 0.164872 | ||||||||
\(894\) | −4.00321 | −0.133887 | ||||||||
\(895\) | −14.2154 | −0.475167 | ||||||||
\(896\) | 1.30218 | 0.0435027 | ||||||||
\(897\) | −5.12458 | −0.171105 | ||||||||
\(898\) | −14.5104 | −0.484218 | ||||||||
\(899\) | −50.2153 | −1.67478 | ||||||||
\(900\) | 13.3334 | 0.444448 | ||||||||
\(901\) | 53.2934 | 1.77546 | ||||||||
\(902\) | −22.0928 | −0.735610 | ||||||||
\(903\) | 3.56519 | 0.118642 | ||||||||
\(904\) | 9.61364 | 0.319745 | ||||||||
\(905\) | −7.92353 | −0.263387 | ||||||||
\(906\) | −6.88292 | −0.228670 | ||||||||
\(907\) | 56.2603 | 1.86809 | 0.934047 | − | 0.357151i | \(-0.116252\pi\) | ||||
0.934047 | + | 0.357151i | \(0.116252\pi\) | |||||||
\(908\) | 0.456059 | 0.0151348 | ||||||||
\(909\) | 24.8217 | 0.823285 | ||||||||
\(910\) | −2.24605 | −0.0744559 | ||||||||
\(911\) | 16.4810 | 0.546040 | 0.273020 | − | 0.962008i | \(-0.411978\pi\) | ||||
0.273020 | + | 0.962008i | \(0.411978\pi\) | |||||||
\(912\) | 0.316697 | 0.0104869 | ||||||||
\(913\) | −29.6190 | −0.980247 | ||||||||
\(914\) | 9.65001 | 0.319194 | ||||||||
\(915\) | 1.78376 | 0.0589691 | ||||||||
\(916\) | 6.93276 | 0.229065 | ||||||||
\(917\) | −11.8585 | −0.391603 | ||||||||
\(918\) | 14.6693 | 0.484161 | ||||||||
\(919\) | −23.7440 | −0.783243 | −0.391621 | − | 0.920126i | \(-0.628086\pi\) | ||||
−0.391621 | + | 0.920126i | \(0.628086\pi\) | |||||||
\(920\) | −3.76936 | −0.124272 | ||||||||
\(921\) | 4.08818 | 0.134710 | ||||||||
\(922\) | −3.51618 | −0.115799 | ||||||||
\(923\) | −42.1758 | −1.38823 | ||||||||
\(924\) | 1.35348 | 0.0445262 | ||||||||
\(925\) | −29.3597 | −0.965343 | ||||||||
\(926\) | −14.2805 | −0.469287 | ||||||||
\(927\) | −42.2611 | −1.38804 | ||||||||
\(928\) | 4.86917 | 0.159838 | ||||||||
\(929\) | 16.3866 | 0.537629 | 0.268814 | − | 0.963192i | \(-0.413368\pi\) | ||||
0.268814 | + | 0.963192i | \(0.413368\pi\) | |||||||
\(930\) | −2.07026 | −0.0678866 | ||||||||
\(931\) | 5.30433 | 0.173842 | ||||||||
\(932\) | 8.39227 | 0.274898 | ||||||||
\(933\) | −5.12533 | −0.167796 | ||||||||
\(934\) | −7.93248 | −0.259559 | ||||||||
\(935\) | 16.3334 | 0.534159 | ||||||||
\(936\) | −7.89045 | −0.257907 | ||||||||
\(937\) | −4.14264 | −0.135334 | −0.0676670 | − | 0.997708i | \(-0.521556\pi\) | ||||
−0.0676670 | + | 0.997708i | \(0.521556\pi\) | |||||||
\(938\) | −12.5362 | −0.409322 | ||||||||
\(939\) | 9.72258 | 0.317284 | ||||||||
\(940\) | 3.12301 | 0.101861 | ||||||||
\(941\) | 30.2726 | 0.986858 | 0.493429 | − | 0.869786i | \(-0.335743\pi\) | ||||
0.493429 | + | 0.869786i | \(0.335743\pi\) | |||||||
\(942\) | −1.95163 | −0.0635875 | ||||||||
\(943\) | 40.0295 | 1.30354 | ||||||||
\(944\) | 6.46212 | 0.210324 | ||||||||
\(945\) | −1.54222 | −0.0501683 | ||||||||
\(946\) | 28.3731 | 0.922488 | ||||||||
\(947\) | −19.0803 | −0.620028 | −0.310014 | − | 0.950732i | \(-0.600334\pi\) | ||||
−0.310014 | + | 0.950732i | \(0.600334\pi\) | |||||||
\(948\) | 3.21115 | 0.104293 | ||||||||
\(949\) | 32.6090 | 1.05853 | ||||||||
\(950\) | 4.59821 | 0.149186 | ||||||||
\(951\) | −4.37415 | −0.141841 | ||||||||
\(952\) | 10.2237 | 0.331352 | ||||||||
\(953\) | −9.67680 | −0.313462 | −0.156731 | − | 0.987641i | \(-0.550096\pi\) | ||||
−0.156731 | + | 0.987641i | \(0.550096\pi\) | |||||||
\(954\) | −19.6829 | −0.637258 | ||||||||
\(955\) | −16.3579 | −0.529331 | ||||||||
\(956\) | −2.25755 | −0.0730143 | ||||||||
\(957\) | 5.06100 | 0.163599 | ||||||||
\(958\) | 21.1612 | 0.683686 | ||||||||
\(959\) | 29.6421 | 0.957192 | ||||||||
\(960\) | 0.200745 | 0.00647901 | ||||||||
\(961\) | 75.3563 | 2.43085 | ||||||||
\(962\) | 17.3745 | 0.560176 | ||||||||
\(963\) | −0.112054 | −0.00361090 | ||||||||
\(964\) | 5.14424 | 0.165685 | ||||||||
\(965\) | −6.21944 | −0.200211 | ||||||||
\(966\) | −2.45234 | −0.0789028 | ||||||||
\(967\) | −1.57849 | −0.0507607 | −0.0253804 | − | 0.999678i | \(-0.508080\pi\) | ||||
−0.0253804 | + | 0.999678i | \(0.508080\pi\) | |||||||
\(968\) | −0.228513 | −0.00734470 | ||||||||
\(969\) | 2.48646 | 0.0798765 | ||||||||
\(970\) | −7.42892 | −0.238528 | ||||||||
\(971\) | −15.3795 | −0.493552 | −0.246776 | − | 0.969073i | \(-0.579371\pi\) | ||||
−0.246776 | + | 0.969073i | \(0.579371\pi\) | |||||||
\(972\) | −8.17283 | −0.262144 | ||||||||
\(973\) | 23.3476 | 0.748491 | ||||||||
\(974\) | −17.4317 | −0.558549 | ||||||||
\(975\) | 3.96260 | 0.126905 | ||||||||
\(976\) | 8.88569 | 0.284424 | ||||||||
\(977\) | −32.8029 | −1.04946 | −0.524729 | − | 0.851269i | \(-0.675833\pi\) | ||||
−0.524729 | + | 0.851269i | \(0.675833\pi\) | |||||||
\(978\) | 3.72362 | 0.119068 | ||||||||
\(979\) | −5.94730 | −0.190077 | ||||||||
\(980\) | 3.36226 | 0.107403 | ||||||||
\(981\) | 30.5273 | 0.974663 | ||||||||
\(982\) | −40.2231 | −1.28357 | ||||||||
\(983\) | 19.2148 | 0.612858 | 0.306429 | − | 0.951894i | \(-0.400866\pi\) | ||||
0.306429 | + | 0.951894i | \(0.400866\pi\) | |||||||
\(984\) | −2.13185 | −0.0679609 | ||||||||
\(985\) | 6.04228 | 0.192523 | ||||||||
\(986\) | 38.2289 | 1.21746 | ||||||||
\(987\) | 2.03183 | 0.0646737 | ||||||||
\(988\) | −2.72112 | −0.0865704 | ||||||||
\(989\) | −51.4085 | −1.63470 | ||||||||
\(990\) | −6.03243 | −0.191723 | ||||||||
\(991\) | −12.3138 | −0.391160 | −0.195580 | − | 0.980688i | \(-0.562659\pi\) | ||||
−0.195580 | + | 0.980688i | \(0.562659\pi\) | |||||||
\(992\) | −10.3129 | −0.327436 | ||||||||
\(993\) | 4.19030 | 0.132975 | ||||||||
\(994\) | −20.1830 | −0.640167 | ||||||||
\(995\) | −10.2379 | −0.324563 | ||||||||
\(996\) | −2.85809 | −0.0905622 | ||||||||
\(997\) | −46.7594 | −1.48088 | −0.740442 | − | 0.672121i | \(-0.765384\pi\) | ||||
−0.740442 | + | 0.672121i | \(0.765384\pi\) | |||||||
\(998\) | −18.6263 | −0.589606 | ||||||||
\(999\) | 11.9299 | 0.377446 |
(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 | 8018.2.a.j.1.20 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.20 | ✓ | 47 | 1.1 | even | 1 | trivial |