Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.510062 | −0.360668 | −0.180334 | − | 0.983605i | \(-0.557718\pi\) | ||||
−0.180334 | + | 0.983605i | \(0.557718\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.73984 | −0.869918 | ||||||||
\(5\) | −1.60726 | −0.718787 | −0.359394 | − | 0.933186i | \(-0.617016\pi\) | ||||
−0.359394 | + | 0.933186i | \(0.617016\pi\) | |||||||
\(6\) | 0.510062 | 0.208232 | ||||||||
\(7\) | −0.772958 | −0.292151 | −0.146075 | − | 0.989273i | \(-0.546664\pi\) | ||||
−0.146075 | + | 0.989273i | \(0.546664\pi\) | |||||||
\(8\) | 1.90755 | 0.674420 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.819801 | 0.259244 | ||||||||
\(11\) | 5.11481 | 1.54217 | 0.771086 | − | 0.636731i | \(-0.219714\pi\) | ||||
0.771086 | + | 0.636731i | \(0.219714\pi\) | |||||||
\(12\) | 1.73984 | 0.502248 | ||||||||
\(13\) | −4.25469 | −1.18004 | −0.590019 | − | 0.807389i | \(-0.700880\pi\) | ||||
−0.590019 | + | 0.807389i | \(0.700880\pi\) | |||||||
\(14\) | 0.394257 | 0.105369 | ||||||||
\(15\) | 1.60726 | 0.414992 | ||||||||
\(16\) | 2.50671 | 0.626676 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −0.510062 | −0.120223 | ||||||||
\(19\) | 0.139644 | 0.0320366 | 0.0160183 | − | 0.999872i | \(-0.494901\pi\) | ||||
0.0160183 | + | 0.999872i | \(0.494901\pi\) | |||||||
\(20\) | 2.79637 | 0.625286 | ||||||||
\(21\) | 0.772958 | 0.168673 | ||||||||
\(22\) | −2.60887 | −0.556213 | ||||||||
\(23\) | 2.39815 | 0.500048 | 0.250024 | − | 0.968240i | \(-0.419561\pi\) | ||||
0.250024 | + | 0.968240i | \(0.419561\pi\) | |||||||
\(24\) | −1.90755 | −0.389377 | ||||||||
\(25\) | −2.41672 | −0.483345 | ||||||||
\(26\) | 2.17016 | 0.425603 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.34482 | 0.254147 | ||||||||
\(29\) | 7.73479 | 1.43631 | 0.718157 | − | 0.695881i | \(-0.244986\pi\) | ||||
0.718157 | + | 0.695881i | \(0.244986\pi\) | |||||||
\(30\) | −0.819801 | −0.149674 | ||||||||
\(31\) | −0.727102 | −0.130591 | −0.0652957 | − | 0.997866i | \(-0.520799\pi\) | ||||
−0.0652957 | + | 0.997866i | \(0.520799\pi\) | |||||||
\(32\) | −5.09367 | −0.900443 | ||||||||
\(33\) | −5.11481 | −0.890374 | ||||||||
\(34\) | 0.510062 | 0.0874749 | ||||||||
\(35\) | 1.24234 | 0.209994 | ||||||||
\(36\) | −1.73984 | −0.289973 | ||||||||
\(37\) | 1.12804 | 0.185449 | 0.0927246 | − | 0.995692i | \(-0.470442\pi\) | ||||
0.0927246 | + | 0.995692i | \(0.470442\pi\) | |||||||
\(38\) | −0.0712273 | −0.0115546 | ||||||||
\(39\) | 4.25469 | 0.681296 | ||||||||
\(40\) | −3.06592 | −0.484765 | ||||||||
\(41\) | −4.55066 | −0.710693 | −0.355347 | − | 0.934735i | \(-0.615637\pi\) | ||||
−0.355347 | + | 0.934735i | \(0.615637\pi\) | |||||||
\(42\) | −0.394257 | −0.0608351 | ||||||||
\(43\) | −10.1625 | −1.54977 | −0.774886 | − | 0.632101i | \(-0.782193\pi\) | ||||
−0.774886 | + | 0.632101i | \(0.782193\pi\) | |||||||
\(44\) | −8.89893 | −1.34156 | ||||||||
\(45\) | −1.60726 | −0.239596 | ||||||||
\(46\) | −1.22320 | −0.180352 | ||||||||
\(47\) | 5.80251 | 0.846383 | 0.423191 | − | 0.906040i | \(-0.360910\pi\) | ||||
0.423191 | + | 0.906040i | \(0.360910\pi\) | |||||||
\(48\) | −2.50671 | −0.361812 | ||||||||
\(49\) | −6.40254 | −0.914648 | ||||||||
\(50\) | 1.23268 | 0.174327 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 7.40247 | 1.02654 | ||||||||
\(53\) | −8.80818 | −1.20990 | −0.604948 | − | 0.796265i | \(-0.706806\pi\) | ||||
−0.604948 | + | 0.796265i | \(0.706806\pi\) | |||||||
\(54\) | 0.510062 | 0.0694107 | ||||||||
\(55\) | −8.22081 | −1.10849 | ||||||||
\(56\) | −1.47445 | −0.197032 | ||||||||
\(57\) | −0.139644 | −0.0184964 | ||||||||
\(58\) | −3.94522 | −0.518033 | ||||||||
\(59\) | 2.77156 | 0.360827 | 0.180413 | − | 0.983591i | \(-0.442256\pi\) | ||||
0.180413 | + | 0.983591i | \(0.442256\pi\) | |||||||
\(60\) | −2.79637 | −0.361009 | ||||||||
\(61\) | 6.83036 | 0.874538 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(62\) | 0.370867 | 0.0471001 | ||||||||
\(63\) | −0.772958 | −0.0973836 | ||||||||
\(64\) | −2.41532 | −0.301915 | ||||||||
\(65\) | 6.83838 | 0.848197 | ||||||||
\(66\) | 2.60887 | 0.321130 | ||||||||
\(67\) | −9.93419 | −1.21365 | −0.606827 | − | 0.794834i | \(-0.707558\pi\) | ||||
−0.606827 | + | 0.794834i | \(0.707558\pi\) | |||||||
\(68\) | 1.73984 | 0.210986 | ||||||||
\(69\) | −2.39815 | −0.288703 | ||||||||
\(70\) | −0.633672 | −0.0757383 | ||||||||
\(71\) | −9.38080 | −1.11330 | −0.556648 | − | 0.830748i | \(-0.687913\pi\) | ||||
−0.556648 | + | 0.830748i | \(0.687913\pi\) | |||||||
\(72\) | 1.90755 | 0.224807 | ||||||||
\(73\) | 14.8634 | 1.73963 | 0.869815 | − | 0.493379i | \(-0.164238\pi\) | ||||
0.869815 | + | 0.493379i | \(0.164238\pi\) | |||||||
\(74\) | −0.575372 | −0.0668857 | ||||||||
\(75\) | 2.41672 | 0.279059 | ||||||||
\(76\) | −0.242959 | −0.0278693 | ||||||||
\(77\) | −3.95353 | −0.450547 | ||||||||
\(78\) | −2.17016 | −0.245722 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −4.02892 | −0.450447 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.32112 | 0.256325 | ||||||||
\(83\) | 0.155778 | 0.0170989 | 0.00854944 | − | 0.999963i | \(-0.497279\pi\) | ||||
0.00854944 | + | 0.999963i | \(0.497279\pi\) | |||||||
\(84\) | −1.34482 | −0.146732 | ||||||||
\(85\) | 1.60726 | 0.174332 | ||||||||
\(86\) | 5.18352 | 0.558954 | ||||||||
\(87\) | −7.73479 | −0.829256 | ||||||||
\(88\) | 9.75674 | 1.04007 | ||||||||
\(89\) | 1.13427 | 0.120232 | 0.0601160 | − | 0.998191i | \(-0.480853\pi\) | ||||
0.0601160 | + | 0.998191i | \(0.480853\pi\) | |||||||
\(90\) | 0.819801 | 0.0864146 | ||||||||
\(91\) | 3.28870 | 0.344749 | ||||||||
\(92\) | −4.17238 | −0.435001 | ||||||||
\(93\) | 0.727102 | 0.0753969 | ||||||||
\(94\) | −2.95964 | −0.305263 | ||||||||
\(95\) | −0.224445 | −0.0230275 | ||||||||
\(96\) | 5.09367 | 0.519871 | ||||||||
\(97\) | 10.1795 | 1.03357 | 0.516784 | − | 0.856116i | \(-0.327129\pi\) | ||||
0.516784 | + | 0.856116i | \(0.327129\pi\) | |||||||
\(98\) | 3.26569 | 0.329885 | ||||||||
\(99\) | 5.11481 | 0.514058 | ||||||||
\(100\) | 4.20470 | 0.420470 | ||||||||
\(101\) | 1.50689 | 0.149941 | 0.0749706 | − | 0.997186i | \(-0.476114\pi\) | ||||
0.0749706 | + | 0.997186i | \(0.476114\pi\) | |||||||
\(102\) | −0.510062 | −0.0505037 | ||||||||
\(103\) | −16.7719 | −1.65258 | −0.826291 | − | 0.563243i | \(-0.809553\pi\) | ||||
−0.826291 | + | 0.563243i | \(0.809553\pi\) | |||||||
\(104\) | −8.11603 | −0.795842 | ||||||||
\(105\) | −1.24234 | −0.121240 | ||||||||
\(106\) | 4.49272 | 0.436371 | ||||||||
\(107\) | −9.35639 | −0.904517 | −0.452258 | − | 0.891887i | \(-0.649381\pi\) | ||||
−0.452258 | + | 0.891887i | \(0.649381\pi\) | |||||||
\(108\) | 1.73984 | 0.167416 | ||||||||
\(109\) | −1.19641 | −0.114595 | −0.0572975 | − | 0.998357i | \(-0.518248\pi\) | ||||
−0.0572975 | + | 0.998357i | \(0.518248\pi\) | |||||||
\(110\) | 4.19312 | 0.399799 | ||||||||
\(111\) | −1.12804 | −0.107069 | ||||||||
\(112\) | −1.93758 | −0.183084 | ||||||||
\(113\) | −9.37198 | −0.881642 | −0.440821 | − | 0.897595i | \(-0.645313\pi\) | ||||
−0.440821 | + | 0.897595i | \(0.645313\pi\) | |||||||
\(114\) | 0.0712273 | 0.00667105 | ||||||||
\(115\) | −3.85444 | −0.359428 | ||||||||
\(116\) | −13.4573 | −1.24948 | ||||||||
\(117\) | −4.25469 | −0.393346 | ||||||||
\(118\) | −1.41367 | −0.130139 | ||||||||
\(119\) | 0.772958 | 0.0708569 | ||||||||
\(120\) | 3.06592 | 0.279879 | ||||||||
\(121\) | 15.1613 | 1.37830 | ||||||||
\(122\) | −3.48391 | −0.315418 | ||||||||
\(123\) | 4.55066 | 0.410319 | ||||||||
\(124\) | 1.26504 | 0.113604 | ||||||||
\(125\) | 11.9206 | 1.06621 | ||||||||
\(126\) | 0.394257 | 0.0351232 | ||||||||
\(127\) | −10.1118 | −0.897281 | −0.448641 | − | 0.893712i | \(-0.648092\pi\) | ||||
−0.448641 | + | 0.893712i | \(0.648092\pi\) | |||||||
\(128\) | 11.4193 | 1.00933 | ||||||||
\(129\) | 10.1625 | 0.894761 | ||||||||
\(130\) | −3.48800 | −0.305918 | ||||||||
\(131\) | 14.9108 | 1.30276 | 0.651382 | − | 0.758750i | \(-0.274190\pi\) | ||||
0.651382 | + | 0.758750i | \(0.274190\pi\) | |||||||
\(132\) | 8.89893 | 0.774552 | ||||||||
\(133\) | −0.107939 | −0.00935952 | ||||||||
\(134\) | 5.06705 | 0.437727 | ||||||||
\(135\) | 1.60726 | 0.138331 | ||||||||
\(136\) | −1.90755 | −0.163571 | ||||||||
\(137\) | 12.8494 | 1.09780 | 0.548898 | − | 0.835889i | \(-0.315047\pi\) | ||||
0.548898 | + | 0.835889i | \(0.315047\pi\) | |||||||
\(138\) | 1.22320 | 0.104126 | ||||||||
\(139\) | −8.69363 | −0.737384 | −0.368692 | − | 0.929552i | \(-0.620194\pi\) | ||||
−0.368692 | + | 0.929552i | \(0.620194\pi\) | |||||||
\(140\) | −2.16147 | −0.182678 | ||||||||
\(141\) | −5.80251 | −0.488659 | ||||||||
\(142\) | 4.78479 | 0.401531 | ||||||||
\(143\) | −21.7619 | −1.81982 | ||||||||
\(144\) | 2.50671 | 0.208892 | ||||||||
\(145\) | −12.4318 | −1.03240 | ||||||||
\(146\) | −7.58126 | −0.627429 | ||||||||
\(147\) | 6.40254 | 0.528072 | ||||||||
\(148\) | −1.96261 | −0.161326 | ||||||||
\(149\) | 2.99949 | 0.245728 | 0.122864 | − | 0.992424i | \(-0.460792\pi\) | ||||
0.122864 | + | 0.992424i | \(0.460792\pi\) | |||||||
\(150\) | −1.23268 | −0.100648 | ||||||||
\(151\) | 16.8985 | 1.37518 | 0.687591 | − | 0.726099i | \(-0.258668\pi\) | ||||
0.687591 | + | 0.726099i | \(0.258668\pi\) | |||||||
\(152\) | 0.266379 | 0.0216062 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 2.01655 | 0.162498 | ||||||||
\(155\) | 1.16864 | 0.0938674 | ||||||||
\(156\) | −7.40247 | −0.592672 | ||||||||
\(157\) | −4.67973 | −0.373483 | −0.186741 | − | 0.982409i | \(-0.559793\pi\) | ||||
−0.186741 | + | 0.982409i | \(0.559793\pi\) | |||||||
\(158\) | −0.510062 | −0.0405784 | ||||||||
\(159\) | 8.80818 | 0.698534 | ||||||||
\(160\) | 8.18684 | 0.647227 | ||||||||
\(161\) | −1.85367 | −0.146089 | ||||||||
\(162\) | −0.510062 | −0.0400743 | ||||||||
\(163\) | 16.9424 | 1.32703 | 0.663517 | − | 0.748161i | \(-0.269063\pi\) | ||||
0.663517 | + | 0.748161i | \(0.269063\pi\) | |||||||
\(164\) | 7.91740 | 0.618245 | ||||||||
\(165\) | 8.22081 | 0.639989 | ||||||||
\(166\) | −0.0794566 | −0.00616703 | ||||||||
\(167\) | 5.73607 | 0.443870 | 0.221935 | − | 0.975061i | \(-0.428763\pi\) | ||||
0.221935 | + | 0.975061i | \(0.428763\pi\) | |||||||
\(168\) | 1.47445 | 0.113757 | ||||||||
\(169\) | 5.10239 | 0.392491 | ||||||||
\(170\) | −0.819801 | −0.0628759 | ||||||||
\(171\) | 0.139644 | 0.0106789 | ||||||||
\(172\) | 17.6812 | 1.34818 | ||||||||
\(173\) | −10.7165 | −0.814763 | −0.407382 | − | 0.913258i | \(-0.633558\pi\) | ||||
−0.407382 | + | 0.913258i | \(0.633558\pi\) | |||||||
\(174\) | 3.94522 | 0.299086 | ||||||||
\(175\) | 1.86803 | 0.141209 | ||||||||
\(176\) | 12.8213 | 0.966443 | ||||||||
\(177\) | −2.77156 | −0.208324 | ||||||||
\(178\) | −0.578546 | −0.0433638 | ||||||||
\(179\) | 7.40907 | 0.553780 | 0.276890 | − | 0.960902i | \(-0.410696\pi\) | ||||
0.276890 | + | 0.960902i | \(0.410696\pi\) | |||||||
\(180\) | 2.79637 | 0.208429 | ||||||||
\(181\) | 19.6108 | 1.45766 | 0.728829 | − | 0.684696i | \(-0.240065\pi\) | ||||
0.728829 | + | 0.684696i | \(0.240065\pi\) | |||||||
\(182\) | −1.67744 | −0.124340 | ||||||||
\(183\) | −6.83036 | −0.504915 | ||||||||
\(184\) | 4.57458 | 0.337243 | ||||||||
\(185\) | −1.81306 | −0.133299 | ||||||||
\(186\) | −0.370867 | −0.0271933 | ||||||||
\(187\) | −5.11481 | −0.374032 | ||||||||
\(188\) | −10.0954 | −0.736284 | ||||||||
\(189\) | 0.772958 | 0.0562244 | ||||||||
\(190\) | 0.114481 | 0.00830530 | ||||||||
\(191\) | −4.69270 | −0.339552 | −0.169776 | − | 0.985483i | \(-0.554304\pi\) | ||||
−0.169776 | + | 0.985483i | \(0.554304\pi\) | |||||||
\(192\) | 2.41532 | 0.174311 | ||||||||
\(193\) | 26.9839 | 1.94235 | 0.971173 | − | 0.238376i | \(-0.0766151\pi\) | ||||
0.971173 | + | 0.238376i | \(0.0766151\pi\) | |||||||
\(194\) | −5.19216 | −0.372775 | ||||||||
\(195\) | −6.83838 | −0.489707 | ||||||||
\(196\) | 11.1394 | 0.795669 | ||||||||
\(197\) | −4.65075 | −0.331352 | −0.165676 | − | 0.986180i | \(-0.552981\pi\) | ||||
−0.165676 | + | 0.986180i | \(0.552981\pi\) | |||||||
\(198\) | −2.60887 | −0.185404 | ||||||||
\(199\) | 4.56935 | 0.323913 | 0.161956 | − | 0.986798i | \(-0.448220\pi\) | ||||
0.161956 | + | 0.986798i | \(0.448220\pi\) | |||||||
\(200\) | −4.61002 | −0.325977 | ||||||||
\(201\) | 9.93419 | 0.700704 | ||||||||
\(202\) | −0.768608 | −0.0540790 | ||||||||
\(203\) | −5.97866 | −0.419620 | ||||||||
\(204\) | −1.73984 | −0.121813 | ||||||||
\(205\) | 7.31408 | 0.510837 | ||||||||
\(206\) | 8.55470 | 0.596034 | ||||||||
\(207\) | 2.39815 | 0.166683 | ||||||||
\(208\) | −10.6653 | −0.739502 | ||||||||
\(209\) | 0.714255 | 0.0494060 | ||||||||
\(210\) | 0.633672 | 0.0437275 | ||||||||
\(211\) | −0.130965 | −0.00901598 | −0.00450799 | − | 0.999990i | \(-0.501435\pi\) | ||||
−0.00450799 | + | 0.999990i | \(0.501435\pi\) | |||||||
\(212\) | 15.3248 | 1.05251 | ||||||||
\(213\) | 9.38080 | 0.642762 | ||||||||
\(214\) | 4.77234 | 0.326230 | ||||||||
\(215\) | 16.3338 | 1.11396 | ||||||||
\(216\) | −1.90755 | −0.129792 | ||||||||
\(217\) | 0.562019 | 0.0381523 | ||||||||
\(218\) | 0.610242 | 0.0413308 | ||||||||
\(219\) | −14.8634 | −1.00438 | ||||||||
\(220\) | 14.3029 | 0.964299 | ||||||||
\(221\) | 4.25469 | 0.286201 | ||||||||
\(222\) | 0.575372 | 0.0386165 | ||||||||
\(223\) | 20.5196 | 1.37409 | 0.687045 | − | 0.726614i | \(-0.258907\pi\) | ||||
0.687045 | + | 0.726614i | \(0.258907\pi\) | |||||||
\(224\) | 3.93719 | 0.263065 | ||||||||
\(225\) | −2.41672 | −0.161115 | ||||||||
\(226\) | 4.78029 | 0.317980 | ||||||||
\(227\) | 6.91983 | 0.459285 | 0.229643 | − | 0.973275i | \(-0.426244\pi\) | ||||
0.229643 | + | 0.973275i | \(0.426244\pi\) | |||||||
\(228\) | 0.242959 | 0.0160903 | ||||||||
\(229\) | 23.6514 | 1.56293 | 0.781463 | − | 0.623951i | \(-0.214474\pi\) | ||||
0.781463 | + | 0.623951i | \(0.214474\pi\) | |||||||
\(230\) | 1.96600 | 0.129634 | ||||||||
\(231\) | 3.95353 | 0.260123 | ||||||||
\(232\) | 14.7545 | 0.968679 | ||||||||
\(233\) | −2.04570 | −0.134018 | −0.0670092 | − | 0.997752i | \(-0.521346\pi\) | ||||
−0.0670092 | + | 0.997752i | \(0.521346\pi\) | |||||||
\(234\) | 2.17016 | 0.141868 | ||||||||
\(235\) | −9.32612 | −0.608369 | ||||||||
\(236\) | −4.82207 | −0.313890 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −0.394257 | −0.0255559 | ||||||||
\(239\) | −6.32016 | −0.408817 | −0.204409 | − | 0.978886i | \(-0.565527\pi\) | ||||
−0.204409 | + | 0.978886i | \(0.565527\pi\) | |||||||
\(240\) | 4.02892 | 0.260066 | ||||||||
\(241\) | 10.5071 | 0.676820 | 0.338410 | − | 0.940999i | \(-0.390111\pi\) | ||||
0.338410 | + | 0.940999i | \(0.390111\pi\) | |||||||
\(242\) | −7.73318 | −0.497108 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.8837 | −0.760777 | ||||||||
\(245\) | 10.2905 | 0.657437 | ||||||||
\(246\) | −2.32112 | −0.147989 | ||||||||
\(247\) | −0.594144 | −0.0378045 | ||||||||
\(248\) | −1.38698 | −0.0880734 | ||||||||
\(249\) | −0.155778 | −0.00987205 | ||||||||
\(250\) | −6.08024 | −0.384548 | ||||||||
\(251\) | 19.6393 | 1.23962 | 0.619810 | − | 0.784752i | \(-0.287210\pi\) | ||||
0.619810 | + | 0.784752i | \(0.287210\pi\) | |||||||
\(252\) | 1.34482 | 0.0847157 | ||||||||
\(253\) | 12.2661 | 0.771161 | ||||||||
\(254\) | 5.15767 | 0.323621 | ||||||||
\(255\) | −1.60726 | −0.100650 | ||||||||
\(256\) | −0.993913 | −0.0621195 | ||||||||
\(257\) | 29.8255 | 1.86047 | 0.930233 | − | 0.366970i | \(-0.119605\pi\) | ||||
0.930233 | + | 0.366970i | \(0.119605\pi\) | |||||||
\(258\) | −5.18352 | −0.322712 | ||||||||
\(259\) | −0.871930 | −0.0541791 | ||||||||
\(260\) | −11.8977 | −0.737862 | ||||||||
\(261\) | 7.73479 | 0.478771 | ||||||||
\(262\) | −7.60544 | −0.469866 | ||||||||
\(263\) | −10.2391 | −0.631369 | −0.315685 | − | 0.948864i | \(-0.602234\pi\) | ||||
−0.315685 | + | 0.948864i | \(0.602234\pi\) | |||||||
\(264\) | −9.75674 | −0.600486 | ||||||||
\(265\) | 14.1570 | 0.869658 | ||||||||
\(266\) | 0.0550557 | 0.00337568 | ||||||||
\(267\) | −1.13427 | −0.0694159 | ||||||||
\(268\) | 17.2839 | 1.05578 | ||||||||
\(269\) | −18.5321 | −1.12992 | −0.564961 | − | 0.825118i | \(-0.691109\pi\) | ||||
−0.564961 | + | 0.825118i | \(0.691109\pi\) | |||||||
\(270\) | −0.819801 | −0.0498915 | ||||||||
\(271\) | −5.63643 | −0.342388 | −0.171194 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171194 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(272\) | −2.50671 | −0.151991 | ||||||||
\(273\) | −3.28870 | −0.199041 | ||||||||
\(274\) | −6.55398 | −0.395940 | ||||||||
\(275\) | −12.3611 | −0.745401 | ||||||||
\(276\) | 4.17238 | 0.251148 | ||||||||
\(277\) | −22.8345 | −1.37199 | −0.685996 | − | 0.727606i | \(-0.740633\pi\) | ||||
−0.685996 | + | 0.727606i | \(0.740633\pi\) | |||||||
\(278\) | 4.43429 | 0.265951 | ||||||||
\(279\) | −0.727102 | −0.0435304 | ||||||||
\(280\) | 2.36983 | 0.141624 | ||||||||
\(281\) | −0.819303 | −0.0488755 | −0.0244378 | − | 0.999701i | \(-0.507780\pi\) | ||||
−0.0244378 | + | 0.999701i | \(0.507780\pi\) | |||||||
\(282\) | 2.95964 | 0.176244 | ||||||||
\(283\) | −5.08478 | −0.302259 | −0.151129 | − | 0.988514i | \(-0.548291\pi\) | ||||
−0.151129 | + | 0.988514i | \(0.548291\pi\) | |||||||
\(284\) | 16.3211 | 0.968477 | ||||||||
\(285\) | 0.224445 | 0.0132950 | ||||||||
\(286\) | 11.0999 | 0.656353 | ||||||||
\(287\) | 3.51747 | 0.207630 | ||||||||
\(288\) | −5.09367 | −0.300148 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.34099 | 0.372355 | ||||||||
\(291\) | −10.1795 | −0.596731 | ||||||||
\(292\) | −25.8599 | −1.51334 | ||||||||
\(293\) | −8.50443 | −0.496834 | −0.248417 | − | 0.968653i | \(-0.579910\pi\) | ||||
−0.248417 | + | 0.968653i | \(0.579910\pi\) | |||||||
\(294\) | −3.26569 | −0.190459 | ||||||||
\(295\) | −4.45462 | −0.259358 | ||||||||
\(296\) | 2.15180 | 0.125071 | ||||||||
\(297\) | −5.11481 | −0.296791 | ||||||||
\(298\) | −1.52992 | −0.0886262 | ||||||||
\(299\) | −10.2034 | −0.590076 | ||||||||
\(300\) | −4.20470 | −0.242759 | ||||||||
\(301\) | 7.85521 | 0.452767 | ||||||||
\(302\) | −8.61929 | −0.495984 | ||||||||
\(303\) | −1.50689 | −0.0865686 | ||||||||
\(304\) | 0.350048 | 0.0200766 | ||||||||
\(305\) | −10.9781 | −0.628607 | ||||||||
\(306\) | 0.510062 | 0.0291583 | ||||||||
\(307\) | 28.5827 | 1.63130 | 0.815651 | − | 0.578545i | \(-0.196379\pi\) | ||||
0.815651 | + | 0.578545i | \(0.196379\pi\) | |||||||
\(308\) | 6.87850 | 0.391939 | ||||||||
\(309\) | 16.7719 | 0.954119 | ||||||||
\(310\) | −0.596079 | −0.0338550 | ||||||||
\(311\) | 7.63659 | 0.433031 | 0.216516 | − | 0.976279i | \(-0.430531\pi\) | ||||
0.216516 | + | 0.976279i | \(0.430531\pi\) | |||||||
\(312\) | 8.11603 | 0.459480 | ||||||||
\(313\) | −10.8842 | −0.615210 | −0.307605 | − | 0.951514i | \(-0.599527\pi\) | ||||
−0.307605 | + | 0.951514i | \(0.599527\pi\) | |||||||
\(314\) | 2.38695 | 0.134703 | ||||||||
\(315\) | 1.24234 | 0.0699981 | ||||||||
\(316\) | −1.73984 | −0.0978735 | ||||||||
\(317\) | 17.6907 | 0.993606 | 0.496803 | − | 0.867863i | \(-0.334507\pi\) | ||||
0.496803 | + | 0.867863i | \(0.334507\pi\) | |||||||
\(318\) | −4.49272 | −0.251939 | ||||||||
\(319\) | 39.5619 | 2.21504 | ||||||||
\(320\) | 3.88204 | 0.217013 | ||||||||
\(321\) | 9.35639 | 0.522223 | ||||||||
\(322\) | 0.945485 | 0.0526898 | ||||||||
\(323\) | −0.139644 | −0.00777003 | ||||||||
\(324\) | −1.73984 | −0.0966576 | ||||||||
\(325\) | 10.2824 | 0.570365 | ||||||||
\(326\) | −8.64169 | −0.478619 | ||||||||
\(327\) | 1.19641 | 0.0661614 | ||||||||
\(328\) | −8.68060 | −0.479306 | ||||||||
\(329\) | −4.48510 | −0.247271 | ||||||||
\(330\) | −4.19312 | −0.230824 | ||||||||
\(331\) | 3.98286 | 0.218918 | 0.109459 | − | 0.993991i | \(-0.465088\pi\) | ||||
0.109459 | + | 0.993991i | \(0.465088\pi\) | |||||||
\(332\) | −0.271029 | −0.0148746 | ||||||||
\(333\) | 1.12804 | 0.0618164 | ||||||||
\(334\) | −2.92575 | −0.160090 | ||||||||
\(335\) | 15.9668 | 0.872360 | ||||||||
\(336\) | 1.93758 | 0.105704 | ||||||||
\(337\) | 3.26509 | 0.177861 | 0.0889305 | − | 0.996038i | \(-0.471655\pi\) | ||||
0.0889305 | + | 0.996038i | \(0.471655\pi\) | |||||||
\(338\) | −2.60253 | −0.141559 | ||||||||
\(339\) | 9.37198 | 0.509016 | ||||||||
\(340\) | −2.79637 | −0.151654 | ||||||||
\(341\) | −3.71898 | −0.201394 | ||||||||
\(342\) | −0.0712273 | −0.00385153 | ||||||||
\(343\) | 10.3596 | 0.559366 | ||||||||
\(344\) | −19.3855 | −1.04520 | ||||||||
\(345\) | 3.85444 | 0.207516 | ||||||||
\(346\) | 5.46610 | 0.293859 | ||||||||
\(347\) | 14.7628 | 0.792507 | 0.396253 | − | 0.918141i | \(-0.370310\pi\) | ||||
0.396253 | + | 0.918141i | \(0.370310\pi\) | |||||||
\(348\) | 13.4573 | 0.721385 | ||||||||
\(349\) | 20.3942 | 1.09167 | 0.545837 | − | 0.837891i | \(-0.316212\pi\) | ||||
0.545837 | + | 0.837891i | \(0.316212\pi\) | |||||||
\(350\) | −0.952809 | −0.0509298 | ||||||||
\(351\) | 4.25469 | 0.227099 | ||||||||
\(352\) | −26.0532 | −1.38864 | ||||||||
\(353\) | −22.1391 | −1.17834 | −0.589172 | − | 0.808008i | \(-0.700546\pi\) | ||||
−0.589172 | + | 0.808008i | \(0.700546\pi\) | |||||||
\(354\) | 1.41367 | 0.0751357 | ||||||||
\(355\) | 15.0774 | 0.800223 | ||||||||
\(356\) | −1.97344 | −0.104592 | ||||||||
\(357\) | −0.772958 | −0.0409093 | ||||||||
\(358\) | −3.77908 | −0.199731 | ||||||||
\(359\) | −3.75177 | −0.198011 | −0.0990054 | − | 0.995087i | \(-0.531566\pi\) | ||||
−0.0990054 | + | 0.995087i | \(0.531566\pi\) | |||||||
\(360\) | −3.06592 | −0.161588 | ||||||||
\(361\) | −18.9805 | −0.998974 | ||||||||
\(362\) | −10.0027 | −0.525731 | ||||||||
\(363\) | −15.1613 | −0.795760 | ||||||||
\(364\) | −5.72179 | −0.299904 | ||||||||
\(365\) | −23.8893 | −1.25042 | ||||||||
\(366\) | 3.48391 | 0.182107 | ||||||||
\(367\) | 7.71466 | 0.402702 | 0.201351 | − | 0.979519i | \(-0.435467\pi\) | ||||
0.201351 | + | 0.979519i | \(0.435467\pi\) | |||||||
\(368\) | 6.01145 | 0.313368 | ||||||||
\(369\) | −4.55066 | −0.236898 | ||||||||
\(370\) | 0.924771 | 0.0480766 | ||||||||
\(371\) | 6.80835 | 0.353472 | ||||||||
\(372\) | −1.26504 | −0.0655892 | ||||||||
\(373\) | −26.9773 | −1.39683 | −0.698417 | − | 0.715691i | \(-0.746112\pi\) | ||||
−0.698417 | + | 0.715691i | \(0.746112\pi\) | |||||||
\(374\) | 2.60887 | 0.134901 | ||||||||
\(375\) | −11.9206 | −0.615576 | ||||||||
\(376\) | 11.0686 | 0.570818 | ||||||||
\(377\) | −32.9091 | −1.69491 | ||||||||
\(378\) | −0.394257 | −0.0202784 | ||||||||
\(379\) | 25.9799 | 1.33450 | 0.667249 | − | 0.744835i | \(-0.267472\pi\) | ||||
0.667249 | + | 0.744835i | \(0.267472\pi\) | |||||||
\(380\) | 0.390497 | 0.0200321 | ||||||||
\(381\) | 10.1118 | 0.518046 | ||||||||
\(382\) | 2.39357 | 0.122465 | ||||||||
\(383\) | −12.2388 | −0.625374 | −0.312687 | − | 0.949856i | \(-0.601229\pi\) | ||||
−0.312687 | + | 0.949856i | \(0.601229\pi\) | |||||||
\(384\) | −11.4193 | −0.582739 | ||||||||
\(385\) | 6.35434 | 0.323847 | ||||||||
\(386\) | −13.7635 | −0.700543 | ||||||||
\(387\) | −10.1625 | −0.516591 | ||||||||
\(388\) | −17.7106 | −0.899120 | ||||||||
\(389\) | 9.76147 | 0.494926 | 0.247463 | − | 0.968897i | \(-0.420403\pi\) | ||||
0.247463 | + | 0.968897i | \(0.420403\pi\) | |||||||
\(390\) | 3.48800 | 0.176622 | ||||||||
\(391\) | −2.39815 | −0.121280 | ||||||||
\(392\) | −12.2131 | −0.616857 | ||||||||
\(393\) | −14.9108 | −0.752151 | ||||||||
\(394\) | 2.37217 | 0.119508 | ||||||||
\(395\) | −1.60726 | −0.0808699 | ||||||||
\(396\) | −8.89893 | −0.447188 | ||||||||
\(397\) | −17.6259 | −0.884617 | −0.442309 | − | 0.896863i | \(-0.645840\pi\) | ||||
−0.442309 | + | 0.896863i | \(0.645840\pi\) | |||||||
\(398\) | −2.33065 | −0.116825 | ||||||||
\(399\) | 0.107939 | 0.00540372 | ||||||||
\(400\) | −6.05801 | −0.302901 | ||||||||
\(401\) | −0.0129089 | −0.000644641 0 | −0.000322321 | − | 1.00000i | \(-0.500103\pi\) | ||||
−0.000322321 | 1.00000i | \(0.500103\pi\) | ||||||||
\(402\) | −5.06705 | −0.252722 | ||||||||
\(403\) | 3.09359 | 0.154103 | ||||||||
\(404\) | −2.62174 | −0.130437 | ||||||||
\(405\) | −1.60726 | −0.0798653 | ||||||||
\(406\) | 3.04949 | 0.151344 | ||||||||
\(407\) | 5.76973 | 0.285995 | ||||||||
\(408\) | 1.90755 | 0.0944377 | ||||||||
\(409\) | 6.07683 | 0.300480 | 0.150240 | − | 0.988650i | \(-0.451995\pi\) | ||||
0.150240 | + | 0.988650i | \(0.451995\pi\) | |||||||
\(410\) | −3.73063 | −0.184243 | ||||||||
\(411\) | −12.8494 | −0.633813 | ||||||||
\(412\) | 29.1803 | 1.43761 | ||||||||
\(413\) | −2.14230 | −0.105416 | ||||||||
\(414\) | −1.22320 | −0.0601172 | ||||||||
\(415\) | −0.250376 | −0.0122905 | ||||||||
\(416\) | 21.6720 | 1.06256 | ||||||||
\(417\) | 8.69363 | 0.425729 | ||||||||
\(418\) | −0.364314 | −0.0178192 | ||||||||
\(419\) | 6.81338 | 0.332856 | 0.166428 | − | 0.986054i | \(-0.446777\pi\) | ||||
0.166428 | + | 0.986054i | \(0.446777\pi\) | |||||||
\(420\) | 2.16147 | 0.105469 | ||||||||
\(421\) | 11.4340 | 0.557257 | 0.278628 | − | 0.960399i | \(-0.410120\pi\) | ||||
0.278628 | + | 0.960399i | \(0.410120\pi\) | |||||||
\(422\) | 0.0668001 | 0.00325178 | ||||||||
\(423\) | 5.80251 | 0.282128 | ||||||||
\(424\) | −16.8020 | −0.815979 | ||||||||
\(425\) | 2.41672 | 0.117228 | ||||||||
\(426\) | −4.78479 | −0.231824 | ||||||||
\(427\) | −5.27958 | −0.255497 | ||||||||
\(428\) | 16.2786 | 0.786856 | ||||||||
\(429\) | 21.7619 | 1.05068 | ||||||||
\(430\) | −8.33126 | −0.401769 | ||||||||
\(431\) | 24.9948 | 1.20396 | 0.601980 | − | 0.798511i | \(-0.294379\pi\) | ||||
0.601980 | + | 0.798511i | \(0.294379\pi\) | |||||||
\(432\) | −2.50671 | −0.120604 | ||||||||
\(433\) | 9.79759 | 0.470842 | 0.235421 | − | 0.971893i | \(-0.424353\pi\) | ||||
0.235421 | + | 0.971893i | \(0.424353\pi\) | |||||||
\(434\) | −0.286665 | −0.0137603 | ||||||||
\(435\) | 12.4318 | 0.596059 | ||||||||
\(436\) | 2.08155 | 0.0996883 | ||||||||
\(437\) | 0.334888 | 0.0160199 | ||||||||
\(438\) | 7.58126 | 0.362246 | ||||||||
\(439\) | 17.0727 | 0.814837 | 0.407418 | − | 0.913242i | \(-0.366429\pi\) | ||||
0.407418 | + | 0.913242i | \(0.366429\pi\) | |||||||
\(440\) | −15.6816 | −0.747591 | ||||||||
\(441\) | −6.40254 | −0.304883 | ||||||||
\(442\) | −2.17016 | −0.103224 | ||||||||
\(443\) | −32.3480 | −1.53690 | −0.768449 | − | 0.639911i | \(-0.778971\pi\) | ||||
−0.768449 | + | 0.639911i | \(0.778971\pi\) | |||||||
\(444\) | 1.96261 | 0.0931414 | ||||||||
\(445\) | −1.82306 | −0.0864212 | ||||||||
\(446\) | −10.4662 | −0.495591 | ||||||||
\(447\) | −2.99949 | −0.141871 | ||||||||
\(448\) | 1.86694 | 0.0882047 | ||||||||
\(449\) | −17.3359 | −0.818134 | −0.409067 | − | 0.912504i | \(-0.634146\pi\) | ||||
−0.409067 | + | 0.912504i | \(0.634146\pi\) | |||||||
\(450\) | 1.23268 | 0.0581090 | ||||||||
\(451\) | −23.2757 | −1.09601 | ||||||||
\(452\) | 16.3057 | 0.766957 | ||||||||
\(453\) | −16.8985 | −0.793961 | ||||||||
\(454\) | −3.52954 | −0.165650 | ||||||||
\(455\) | −5.28578 | −0.247801 | ||||||||
\(456\) | −0.266379 | −0.0124743 | ||||||||
\(457\) | 3.37493 | 0.157873 | 0.0789363 | − | 0.996880i | \(-0.474848\pi\) | ||||
0.0789363 | + | 0.996880i | \(0.474848\pi\) | |||||||
\(458\) | −12.0637 | −0.563698 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 6.70610 | 0.312673 | ||||||||
\(461\) | −2.57908 | −0.120120 | −0.0600599 | − | 0.998195i | \(-0.519129\pi\) | ||||
−0.0600599 | + | 0.998195i | \(0.519129\pi\) | |||||||
\(462\) | −2.01655 | −0.0938182 | ||||||||
\(463\) | 2.05356 | 0.0954372 | 0.0477186 | − | 0.998861i | \(-0.484805\pi\) | ||||
0.0477186 | + | 0.998861i | \(0.484805\pi\) | |||||||
\(464\) | 19.3888 | 0.900104 | ||||||||
\(465\) | −1.16864 | −0.0541944 | ||||||||
\(466\) | 1.04344 | 0.0483362 | ||||||||
\(467\) | −4.60299 | −0.213001 | −0.106500 | − | 0.994313i | \(-0.533965\pi\) | ||||
−0.106500 | + | 0.994313i | \(0.533965\pi\) | |||||||
\(468\) | 7.40247 | 0.342179 | ||||||||
\(469\) | 7.67871 | 0.354570 | ||||||||
\(470\) | 4.75690 | 0.219420 | ||||||||
\(471\) | 4.67973 | 0.215630 | ||||||||
\(472\) | 5.28689 | 0.243349 | ||||||||
\(473\) | −51.9794 | −2.39002 | ||||||||
\(474\) | 0.510062 | 0.0234279 | ||||||||
\(475\) | −0.337482 | −0.0154847 | ||||||||
\(476\) | −1.34482 | −0.0616398 | ||||||||
\(477\) | −8.80818 | −0.403299 | ||||||||
\(478\) | 3.22367 | 0.147447 | ||||||||
\(479\) | −5.94766 | −0.271755 | −0.135878 | − | 0.990726i | \(-0.543385\pi\) | ||||
−0.135878 | + | 0.990726i | \(0.543385\pi\) | |||||||
\(480\) | −8.18684 | −0.373677 | ||||||||
\(481\) | −4.79948 | −0.218837 | ||||||||
\(482\) | −5.35926 | −0.244108 | ||||||||
\(483\) | 1.85367 | 0.0843448 | ||||||||
\(484\) | −26.3781 | −1.19901 | ||||||||
\(485\) | −16.3610 | −0.742916 | ||||||||
\(486\) | 0.510062 | 0.0231369 | ||||||||
\(487\) | 20.3347 | 0.921454 | 0.460727 | − | 0.887542i | \(-0.347589\pi\) | ||||
0.460727 | + | 0.887542i | \(0.347589\pi\) | |||||||
\(488\) | 13.0292 | 0.589806 | ||||||||
\(489\) | −16.9424 | −0.766163 | ||||||||
\(490\) | −5.24881 | −0.237117 | ||||||||
\(491\) | 20.9077 | 0.943550 | 0.471775 | − | 0.881719i | \(-0.343614\pi\) | ||||
0.471775 | + | 0.881719i | \(0.343614\pi\) | |||||||
\(492\) | −7.91740 | −0.356944 | ||||||||
\(493\) | −7.73479 | −0.348357 | ||||||||
\(494\) | 0.303050 | 0.0136349 | ||||||||
\(495\) | −8.22081 | −0.369498 | ||||||||
\(496\) | −1.82263 | −0.0818385 | ||||||||
\(497\) | 7.25097 | 0.325250 | ||||||||
\(498\) | 0.0794566 | 0.00356054 | ||||||||
\(499\) | −17.1176 | −0.766289 | −0.383145 | − | 0.923688i | \(-0.625159\pi\) | ||||
−0.383145 | + | 0.923688i | \(0.625159\pi\) | |||||||
\(500\) | −20.7399 | −0.927515 | ||||||||
\(501\) | −5.73607 | −0.256269 | ||||||||
\(502\) | −10.0172 | −0.447092 | ||||||||
\(503\) | −14.9037 | −0.664523 | −0.332261 | − | 0.943187i | \(-0.607812\pi\) | ||||
−0.332261 | + | 0.943187i | \(0.607812\pi\) | |||||||
\(504\) | −1.47445 | −0.0656774 | ||||||||
\(505\) | −2.42196 | −0.107776 | ||||||||
\(506\) | −6.25645 | −0.278133 | ||||||||
\(507\) | −5.10239 | −0.226605 | ||||||||
\(508\) | 17.5930 | 0.780561 | ||||||||
\(509\) | 19.4362 | 0.861493 | 0.430747 | − | 0.902473i | \(-0.358250\pi\) | ||||
0.430747 | + | 0.902473i | \(0.358250\pi\) | |||||||
\(510\) | 0.819801 | 0.0363014 | ||||||||
\(511\) | −11.4888 | −0.508234 | ||||||||
\(512\) | −22.3317 | −0.986929 | ||||||||
\(513\) | −0.139644 | −0.00616545 | ||||||||
\(514\) | −15.2129 | −0.671011 | ||||||||
\(515\) | 26.9567 | 1.18786 | ||||||||
\(516\) | −17.6812 | −0.778369 | ||||||||
\(517\) | 29.6787 | 1.30527 | ||||||||
\(518\) | 0.444739 | 0.0195407 | ||||||||
\(519\) | 10.7165 | 0.470404 | ||||||||
\(520\) | 13.0445 | 0.572041 | ||||||||
\(521\) | 33.2196 | 1.45538 | 0.727688 | − | 0.685908i | \(-0.240595\pi\) | ||||
0.727688 | + | 0.685908i | \(0.240595\pi\) | |||||||
\(522\) | −3.94522 | −0.172678 | ||||||||
\(523\) | 8.57448 | 0.374936 | 0.187468 | − | 0.982271i | \(-0.439972\pi\) | ||||
0.187468 | + | 0.982271i | \(0.439972\pi\) | |||||||
\(524\) | −25.9424 | −1.13330 | ||||||||
\(525\) | −1.86803 | −0.0815273 | ||||||||
\(526\) | 5.22257 | 0.227715 | ||||||||
\(527\) | 0.727102 | 0.0316730 | ||||||||
\(528\) | −12.8213 | −0.557976 | ||||||||
\(529\) | −17.2489 | −0.749952 | ||||||||
\(530\) | −7.22095 | −0.313658 | ||||||||
\(531\) | 2.77156 | 0.120276 | ||||||||
\(532\) | 0.187797 | 0.00814202 | ||||||||
\(533\) | 19.3616 | 0.838646 | ||||||||
\(534\) | 0.578546 | 0.0250361 | ||||||||
\(535\) | 15.0381 | 0.650155 | ||||||||
\(536\) | −18.9500 | −0.818513 | ||||||||
\(537\) | −7.40907 | −0.319725 | ||||||||
\(538\) | 9.45252 | 0.407527 | ||||||||
\(539\) | −32.7477 | −1.41055 | ||||||||
\(540\) | −2.79637 | −0.120336 | ||||||||
\(541\) | −24.7280 | −1.06314 | −0.531570 | − | 0.847014i | \(-0.678398\pi\) | ||||
−0.531570 | + | 0.847014i | \(0.678398\pi\) | |||||||
\(542\) | 2.87493 | 0.123489 | ||||||||
\(543\) | −19.6108 | −0.841579 | ||||||||
\(544\) | 5.09367 | 0.218389 | ||||||||
\(545\) | 1.92293 | 0.0823694 | ||||||||
\(546\) | 1.67744 | 0.0717878 | ||||||||
\(547\) | 16.7662 | 0.716872 | 0.358436 | − | 0.933554i | \(-0.383310\pi\) | ||||
0.358436 | + | 0.933554i | \(0.383310\pi\) | |||||||
\(548\) | −22.3558 | −0.954993 | ||||||||
\(549\) | 6.83036 | 0.291513 | ||||||||
\(550\) | 6.30492 | 0.268842 | ||||||||
\(551\) | 1.08012 | 0.0460147 | ||||||||
\(552\) | −4.57458 | −0.194707 | ||||||||
\(553\) | −0.772958 | −0.0328695 | ||||||||
\(554\) | 11.6470 | 0.494834 | ||||||||
\(555\) | 1.81306 | 0.0769600 | ||||||||
\(556\) | 15.1255 | 0.641464 | ||||||||
\(557\) | 15.3333 | 0.649691 | 0.324845 | − | 0.945767i | \(-0.394688\pi\) | ||||
0.324845 | + | 0.945767i | \(0.394688\pi\) | |||||||
\(558\) | 0.370867 | 0.0157000 | ||||||||
\(559\) | 43.2384 | 1.82879 | ||||||||
\(560\) | 3.11419 | 0.131598 | ||||||||
\(561\) | 5.11481 | 0.215947 | ||||||||
\(562\) | 0.417896 | 0.0176279 | ||||||||
\(563\) | −20.4118 | −0.860254 | −0.430127 | − | 0.902768i | \(-0.641531\pi\) | ||||
−0.430127 | + | 0.902768i | \(0.641531\pi\) | |||||||
\(564\) | 10.0954 | 0.425094 | ||||||||
\(565\) | 15.0632 | 0.633713 | ||||||||
\(566\) | 2.59355 | 0.109015 | ||||||||
\(567\) | −0.772958 | −0.0324612 | ||||||||
\(568\) | −17.8943 | −0.750830 | ||||||||
\(569\) | −0.929251 | −0.0389562 | −0.0194781 | − | 0.999810i | \(-0.506200\pi\) | ||||
−0.0194781 | + | 0.999810i | \(0.506200\pi\) | |||||||
\(570\) | −0.114481 | −0.00479507 | ||||||||
\(571\) | −31.4706 | −1.31700 | −0.658502 | − | 0.752579i | \(-0.728810\pi\) | ||||
−0.658502 | + | 0.752579i | \(0.728810\pi\) | |||||||
\(572\) | 37.8622 | 1.58310 | ||||||||
\(573\) | 4.69270 | 0.196040 | ||||||||
\(574\) | −1.79413 | −0.0748854 | ||||||||
\(575\) | −5.79566 | −0.241696 | ||||||||
\(576\) | −2.41532 | −0.100638 | ||||||||
\(577\) | 13.3141 | 0.554275 | 0.277137 | − | 0.960830i | \(-0.410614\pi\) | ||||
0.277137 | + | 0.960830i | \(0.410614\pi\) | |||||||
\(578\) | −0.510062 | −0.0212158 | ||||||||
\(579\) | −26.9839 | −1.12141 | ||||||||
\(580\) | 21.6293 | 0.898107 | ||||||||
\(581\) | −0.120410 | −0.00499545 | ||||||||
\(582\) | 5.19216 | 0.215222 | ||||||||
\(583\) | −45.0521 | −1.86587 | ||||||||
\(584\) | 28.3527 | 1.17324 | ||||||||
\(585\) | 6.83838 | 0.282732 | ||||||||
\(586\) | 4.33779 | 0.179192 | ||||||||
\(587\) | 40.0412 | 1.65268 | 0.826339 | − | 0.563173i | \(-0.190420\pi\) | ||||
0.826339 | + | 0.563173i | \(0.190420\pi\) | |||||||
\(588\) | −11.1394 | −0.459380 | ||||||||
\(589\) | −0.101536 | −0.00418371 | ||||||||
\(590\) | 2.27213 | 0.0935422 | ||||||||
\(591\) | 4.65075 | 0.191306 | ||||||||
\(592\) | 2.82767 | 0.116217 | ||||||||
\(593\) | 30.6403 | 1.25825 | 0.629123 | − | 0.777306i | \(-0.283414\pi\) | ||||
0.629123 | + | 0.777306i | \(0.283414\pi\) | |||||||
\(594\) | 2.60887 | 0.107043 | ||||||||
\(595\) | −1.24234 | −0.0509311 | ||||||||
\(596\) | −5.21862 | −0.213763 | ||||||||
\(597\) | −4.56935 | −0.187011 | ||||||||
\(598\) | 5.20435 | 0.212822 | ||||||||
\(599\) | −0.634987 | −0.0259449 | −0.0129724 | − | 0.999916i | \(-0.504129\pi\) | ||||
−0.0129724 | + | 0.999916i | \(0.504129\pi\) | |||||||
\(600\) | 4.61002 | 0.188203 | ||||||||
\(601\) | −8.64444 | −0.352614 | −0.176307 | − | 0.984335i | \(-0.556415\pi\) | ||||
−0.176307 | + | 0.984335i | \(0.556415\pi\) | |||||||
\(602\) | −4.00665 | −0.163299 | ||||||||
\(603\) | −9.93419 | −0.404552 | ||||||||
\(604\) | −29.4006 | −1.19630 | ||||||||
\(605\) | −24.3680 | −0.990702 | ||||||||
\(606\) | 0.768608 | 0.0312226 | ||||||||
\(607\) | 17.2389 | 0.699704 | 0.349852 | − | 0.936805i | \(-0.386232\pi\) | ||||
0.349852 | + | 0.936805i | \(0.386232\pi\) | |||||||
\(608\) | −0.711303 | −0.0288472 | ||||||||
\(609\) | 5.97866 | 0.242268 | ||||||||
\(610\) | 5.59953 | 0.226719 | ||||||||
\(611\) | −24.6879 | −0.998764 | ||||||||
\(612\) | 1.73984 | 0.0703287 | ||||||||
\(613\) | −20.7633 | −0.838624 | −0.419312 | − | 0.907842i | \(-0.637729\pi\) | ||||
−0.419312 | + | 0.907842i | \(0.637729\pi\) | |||||||
\(614\) | −14.5790 | −0.588359 | ||||||||
\(615\) | −7.31408 | −0.294932 | ||||||||
\(616\) | −7.54155 | −0.303858 | ||||||||
\(617\) | −12.7284 | −0.512426 | −0.256213 | − | 0.966620i | \(-0.582475\pi\) | ||||
−0.256213 | + | 0.966620i | \(0.582475\pi\) | |||||||
\(618\) | −8.55470 | −0.344120 | ||||||||
\(619\) | 25.1062 | 1.00910 | 0.504552 | − | 0.863381i | \(-0.331658\pi\) | ||||
0.504552 | + | 0.863381i | \(0.331658\pi\) | |||||||
\(620\) | −2.03324 | −0.0816570 | ||||||||
\(621\) | −2.39815 | −0.0962343 | ||||||||
\(622\) | −3.89513 | −0.156181 | ||||||||
\(623\) | −0.876740 | −0.0351258 | ||||||||
\(624\) | 10.6653 | 0.426952 | ||||||||
\(625\) | −7.07583 | −0.283033 | ||||||||
\(626\) | 5.55160 | 0.221887 | ||||||||
\(627\) | −0.714255 | −0.0285246 | ||||||||
\(628\) | 8.14196 | 0.324900 | ||||||||
\(629\) | −1.12804 | −0.0449781 | ||||||||
\(630\) | −0.633672 | −0.0252461 | ||||||||
\(631\) | −19.8552 | −0.790422 | −0.395211 | − | 0.918590i | \(-0.629328\pi\) | ||||
−0.395211 | + | 0.918590i | \(0.629328\pi\) | |||||||
\(632\) | 1.90755 | 0.0758782 | ||||||||
\(633\) | 0.130965 | 0.00520538 | ||||||||
\(634\) | −9.02333 | −0.358362 | ||||||||
\(635\) | 16.2523 | 0.644954 | ||||||||
\(636\) | −15.3248 | −0.607667 | ||||||||
\(637\) | 27.2408 | 1.07932 | ||||||||
\(638\) | −20.1790 | −0.798896 | ||||||||
\(639\) | −9.38080 | −0.371099 | ||||||||
\(640\) | −18.3538 | −0.725496 | ||||||||
\(641\) | 0.862217 | 0.0340555 | 0.0170278 | − | 0.999855i | \(-0.494580\pi\) | ||||
0.0170278 | + | 0.999855i | \(0.494580\pi\) | |||||||
\(642\) | −4.77234 | −0.188349 | ||||||||
\(643\) | 9.91531 | 0.391022 | 0.195511 | − | 0.980702i | \(-0.437364\pi\) | ||||
0.195511 | + | 0.980702i | \(0.437364\pi\) | |||||||
\(644\) | 3.22508 | 0.127086 | ||||||||
\(645\) | −16.3338 | −0.643143 | ||||||||
\(646\) | 0.0712273 | 0.00280240 | ||||||||
\(647\) | 29.4141 | 1.15639 | 0.578193 | − | 0.815900i | \(-0.303758\pi\) | ||||
0.578193 | + | 0.815900i | \(0.303758\pi\) | |||||||
\(648\) | 1.90755 | 0.0749356 | ||||||||
\(649\) | 14.1760 | 0.556457 | ||||||||
\(650\) | −5.24467 | −0.205713 | ||||||||
\(651\) | −0.562019 | −0.0220273 | ||||||||
\(652\) | −29.4771 | −1.15441 | ||||||||
\(653\) | −9.23466 | −0.361380 | −0.180690 | − | 0.983540i | \(-0.557833\pi\) | ||||
−0.180690 | + | 0.983540i | \(0.557833\pi\) | |||||||
\(654\) | −0.610242 | −0.0238623 | ||||||||
\(655\) | −23.9655 | −0.936410 | ||||||||
\(656\) | −11.4072 | −0.445375 | ||||||||
\(657\) | 14.8634 | 0.579876 | ||||||||
\(658\) | 2.28768 | 0.0891829 | ||||||||
\(659\) | 9.05610 | 0.352775 | 0.176388 | − | 0.984321i | \(-0.443559\pi\) | ||||
0.176388 | + | 0.984321i | \(0.443559\pi\) | |||||||
\(660\) | −14.3029 | −0.556739 | ||||||||
\(661\) | 38.1014 | 1.48197 | 0.740985 | − | 0.671521i | \(-0.234359\pi\) | ||||
0.740985 | + | 0.671521i | \(0.234359\pi\) | |||||||
\(662\) | −2.03150 | −0.0789567 | ||||||||
\(663\) | −4.25469 | −0.165238 | ||||||||
\(664\) | 0.297155 | 0.0115318 | ||||||||
\(665\) | 0.173486 | 0.00672751 | ||||||||
\(666\) | −0.575372 | −0.0222952 | ||||||||
\(667\) | 18.5492 | 0.718226 | ||||||||
\(668\) | −9.97983 | −0.386131 | ||||||||
\(669\) | −20.5196 | −0.793332 | ||||||||
\(670\) | −8.14406 | −0.314632 | ||||||||
\(671\) | 34.9360 | 1.34869 | ||||||||
\(672\) | −3.93719 | −0.151881 | ||||||||
\(673\) | −19.4204 | −0.748601 | −0.374300 | − | 0.927308i | \(-0.622117\pi\) | ||||
−0.374300 | + | 0.927308i | \(0.622117\pi\) | |||||||
\(674\) | −1.66540 | −0.0641488 | ||||||||
\(675\) | 2.41672 | 0.0930197 | ||||||||
\(676\) | −8.87732 | −0.341435 | ||||||||
\(677\) | 42.4802 | 1.63265 | 0.816323 | − | 0.577596i | \(-0.196009\pi\) | ||||
0.816323 | + | 0.577596i | \(0.196009\pi\) | |||||||
\(678\) | −4.78029 | −0.183586 | ||||||||
\(679\) | −7.86830 | −0.301958 | ||||||||
\(680\) | 3.06592 | 0.117573 | ||||||||
\(681\) | −6.91983 | −0.265168 | ||||||||
\(682\) | 1.89691 | 0.0726366 | ||||||||
\(683\) | 4.77934 | 0.182876 | 0.0914382 | − | 0.995811i | \(-0.470854\pi\) | ||||
0.0914382 | + | 0.995811i | \(0.470854\pi\) | |||||||
\(684\) | −0.242959 | −0.00928975 | ||||||||
\(685\) | −20.6523 | −0.789082 | ||||||||
\(686\) | −5.28404 | −0.201745 | ||||||||
\(687\) | −23.6514 | −0.902356 | ||||||||
\(688\) | −25.4745 | −0.971206 | ||||||||
\(689\) | 37.4761 | 1.42772 | ||||||||
\(690\) | −1.96600 | −0.0748445 | ||||||||
\(691\) | 19.9362 | 0.758408 | 0.379204 | − | 0.925313i | \(-0.376198\pi\) | ||||
0.379204 | + | 0.925313i | \(0.376198\pi\) | |||||||
\(692\) | 18.6450 | 0.708777 | ||||||||
\(693\) | −3.95353 | −0.150182 | ||||||||
\(694\) | −7.52993 | −0.285832 | ||||||||
\(695\) | 13.9729 | 0.530022 | ||||||||
\(696\) | −14.7545 | −0.559267 | ||||||||
\(697\) | 4.55066 | 0.172368 | ||||||||
\(698\) | −10.4023 | −0.393733 | ||||||||
\(699\) | 2.04570 | 0.0773756 | ||||||||
\(700\) | −3.25006 | −0.122841 | ||||||||
\(701\) | 17.0991 | 0.645823 | 0.322912 | − | 0.946429i | \(-0.395338\pi\) | ||||
0.322912 | + | 0.946429i | \(0.395338\pi\) | |||||||
\(702\) | −2.17016 | −0.0819072 | ||||||||
\(703\) | 0.157525 | 0.00594117 | ||||||||
\(704\) | −12.3539 | −0.465605 | ||||||||
\(705\) | 9.32612 | 0.351242 | ||||||||
\(706\) | 11.2923 | 0.424991 | ||||||||
\(707\) | −1.16476 | −0.0438054 | ||||||||
\(708\) | 4.82207 | 0.181224 | ||||||||
\(709\) | −1.41763 | −0.0532403 | −0.0266201 | − | 0.999646i | \(-0.508474\pi\) | ||||
−0.0266201 | + | 0.999646i | \(0.508474\pi\) | |||||||
\(710\) | −7.69039 | −0.288615 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 2.16367 | 0.0810868 | ||||||||
\(713\) | −1.74370 | −0.0653020 | ||||||||
\(714\) | 0.394257 | 0.0147547 | ||||||||
\(715\) | 34.9770 | 1.30807 | ||||||||
\(716\) | −12.8906 | −0.481743 | ||||||||
\(717\) | 6.32016 | 0.236031 | ||||||||
\(718\) | 1.91364 | 0.0714162 | ||||||||
\(719\) | −34.4537 | −1.28491 | −0.642453 | − | 0.766325i | \(-0.722083\pi\) | ||||
−0.642453 | + | 0.766325i | \(0.722083\pi\) | |||||||
\(720\) | −4.02892 | −0.150149 | ||||||||
\(721\) | 12.9640 | 0.482803 | ||||||||
\(722\) | 9.68123 | 0.360298 | ||||||||
\(723\) | −10.5071 | −0.390762 | ||||||||
\(724\) | −34.1195 | −1.26804 | ||||||||
\(725\) | −18.6928 | −0.694235 | ||||||||
\(726\) | 7.73318 | 0.287005 | ||||||||
\(727\) | 31.6046 | 1.17215 | 0.586076 | − | 0.810256i | \(-0.300672\pi\) | ||||
0.586076 | + | 0.810256i | \(0.300672\pi\) | |||||||
\(728\) | 6.27335 | 0.232506 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.1850 | 0.450988 | ||||||||
\(731\) | 10.1625 | 0.375875 | ||||||||
\(732\) | 11.8837 | 0.439235 | ||||||||
\(733\) | 18.3870 | 0.679138 | 0.339569 | − | 0.940581i | \(-0.389719\pi\) | ||||
0.339569 | + | 0.940581i | \(0.389719\pi\) | |||||||
\(734\) | −3.93495 | −0.145242 | ||||||||
\(735\) | −10.2905 | −0.379572 | ||||||||
\(736\) | −12.2154 | −0.450265 | ||||||||
\(737\) | −50.8115 | −1.87166 | ||||||||
\(738\) | 2.32112 | 0.0854415 | ||||||||
\(739\) | 7.42605 | 0.273172 | 0.136586 | − | 0.990628i | \(-0.456387\pi\) | ||||
0.136586 | + | 0.990628i | \(0.456387\pi\) | |||||||
\(740\) | 3.15442 | 0.115959 | ||||||||
\(741\) | 0.594144 | 0.0218264 | ||||||||
\(742\) | −3.47268 | −0.127486 | ||||||||
\(743\) | 10.9476 | 0.401628 | 0.200814 | − | 0.979629i | \(-0.435641\pi\) | ||||
0.200814 | + | 0.979629i | \(0.435641\pi\) | |||||||
\(744\) | 1.38698 | 0.0508492 | ||||||||
\(745\) | −4.82095 | −0.176626 | ||||||||
\(746\) | 13.7601 | 0.503794 | ||||||||
\(747\) | 0.155778 | 0.00569963 | ||||||||
\(748\) | 8.89893 | 0.325377 | ||||||||
\(749\) | 7.23210 | 0.264255 | ||||||||
\(750\) | 6.08024 | 0.222019 | ||||||||
\(751\) | 26.8378 | 0.979324 | 0.489662 | − | 0.871912i | \(-0.337120\pi\) | ||||
0.489662 | + | 0.871912i | \(0.337120\pi\) | |||||||
\(752\) | 14.5452 | 0.530408 | ||||||||
\(753\) | −19.6393 | −0.715695 | ||||||||
\(754\) | 16.7857 | 0.611299 | ||||||||
\(755\) | −27.1603 | −0.988463 | ||||||||
\(756\) | −1.34482 | −0.0489107 | ||||||||
\(757\) | 8.31975 | 0.302386 | 0.151193 | − | 0.988504i | \(-0.451688\pi\) | ||||
0.151193 | + | 0.988504i | \(0.451688\pi\) | |||||||
\(758\) | −13.2514 | −0.481311 | ||||||||
\(759\) | −12.2661 | −0.445230 | ||||||||
\(760\) | −0.428139 | −0.0155302 | ||||||||
\(761\) | −51.2196 | −1.85671 | −0.928355 | − | 0.371695i | \(-0.878777\pi\) | ||||
−0.928355 | + | 0.371695i | \(0.878777\pi\) | |||||||
\(762\) | −5.15767 | −0.186843 | ||||||||
\(763\) | 0.924772 | 0.0334790 | ||||||||
\(764\) | 8.16452 | 0.295382 | ||||||||
\(765\) | 1.60726 | 0.0581105 | ||||||||
\(766\) | 6.24256 | 0.225553 | ||||||||
\(767\) | −11.7921 | −0.425790 | ||||||||
\(768\) | 0.993913 | 0.0358647 | ||||||||
\(769\) | −25.2340 | −0.909961 | −0.454981 | − | 0.890501i | \(-0.650354\pi\) | ||||
−0.454981 | + | 0.890501i | \(0.650354\pi\) | |||||||
\(770\) | −3.24111 | −0.116801 | ||||||||
\(771\) | −29.8255 | −1.07414 | ||||||||
\(772\) | −46.9476 | −1.68968 | ||||||||
\(773\) | −9.41633 | −0.338682 | −0.169341 | − | 0.985558i | \(-0.554164\pi\) | ||||
−0.169341 | + | 0.985558i | \(0.554164\pi\) | |||||||
\(774\) | 5.18352 | 0.186318 | ||||||||
\(775\) | 1.75720 | 0.0631206 | ||||||||
\(776\) | 19.4178 | 0.697060 | ||||||||
\(777\) | 0.871930 | 0.0312803 | ||||||||
\(778\) | −4.97895 | −0.178504 | ||||||||
\(779\) | −0.635474 | −0.0227682 | ||||||||
\(780\) | 11.8977 | 0.426005 | ||||||||
\(781\) | −47.9810 | −1.71690 | ||||||||
\(782\) | 1.22320 | 0.0437417 | ||||||||
\(783\) | −7.73479 | −0.276419 | ||||||||
\(784\) | −16.0493 | −0.573188 | ||||||||
\(785\) | 7.52153 | 0.268455 | ||||||||
\(786\) | 7.60544 | 0.271277 | ||||||||
\(787\) | 5.75429 | 0.205118 | 0.102559 | − | 0.994727i | \(-0.467297\pi\) | ||||
0.102559 | + | 0.994727i | \(0.467297\pi\) | |||||||
\(788\) | 8.09154 | 0.288249 | ||||||||
\(789\) | 10.2391 | 0.364521 | ||||||||
\(790\) | 0.819801 | 0.0291672 | ||||||||
\(791\) | 7.24415 | 0.257572 | ||||||||
\(792\) | 9.75674 | 0.346691 | ||||||||
\(793\) | −29.0611 | −1.03199 | ||||||||
\(794\) | 8.99029 | 0.319053 | ||||||||
\(795\) | −14.1570 | −0.502097 | ||||||||
\(796\) | −7.94993 | −0.281778 | ||||||||
\(797\) | −14.0063 | −0.496127 | −0.248064 | − | 0.968744i | \(-0.579794\pi\) | ||||
−0.248064 | + | 0.968744i | \(0.579794\pi\) | |||||||
\(798\) | −0.0550557 | −0.00194895 | ||||||||
\(799\) | −5.80251 | −0.205278 | ||||||||
\(800\) | 12.3100 | 0.435224 | ||||||||
\(801\) | 1.13427 | 0.0400773 | ||||||||
\(802\) | 0.00658435 | 0.000232502 0 | ||||||||
\(803\) | 76.0234 | 2.68281 | ||||||||
\(804\) | −17.2839 | −0.609555 | ||||||||
\(805\) | 2.97932 | 0.105007 | ||||||||
\(806\) | −1.57792 | −0.0555800 | ||||||||
\(807\) | 18.5321 | 0.652361 | ||||||||
\(808\) | 2.87447 | 0.101123 | ||||||||
\(809\) | −7.04469 | −0.247678 | −0.123839 | − | 0.992302i | \(-0.539521\pi\) | ||||
−0.123839 | + | 0.992302i | \(0.539521\pi\) | |||||||
\(810\) | 0.819801 | 0.0288049 | ||||||||
\(811\) | 33.5005 | 1.17636 | 0.588181 | − | 0.808730i | \(-0.299844\pi\) | ||||
0.588181 | + | 0.808730i | \(0.299844\pi\) | |||||||
\(812\) | 10.4019 | 0.365035 | ||||||||
\(813\) | 5.63643 | 0.197678 | ||||||||
\(814\) | −2.94292 | −0.103149 | ||||||||
\(815\) | −27.2309 | −0.953855 | ||||||||
\(816\) | 2.50671 | 0.0877522 | ||||||||
\(817\) | −1.41914 | −0.0496495 | ||||||||
\(818\) | −3.09956 | −0.108374 | ||||||||
\(819\) | 3.28870 | 0.114916 | ||||||||
\(820\) | −12.7253 | −0.444387 | ||||||||
\(821\) | −18.0776 | −0.630914 | −0.315457 | − | 0.948940i | \(-0.602158\pi\) | ||||
−0.315457 | + | 0.948940i | \(0.602158\pi\) | |||||||
\(822\) | 6.55398 | 0.228596 | ||||||||
\(823\) | 35.3510 | 1.23226 | 0.616129 | − | 0.787645i | \(-0.288700\pi\) | ||||
0.616129 | + | 0.787645i | \(0.288700\pi\) | |||||||
\(824\) | −31.9932 | −1.11453 | ||||||||
\(825\) | 12.3611 | 0.430357 | ||||||||
\(826\) | 1.09271 | 0.0380202 | ||||||||
\(827\) | −50.3601 | −1.75119 | −0.875597 | − | 0.483043i | \(-0.839532\pi\) | ||||
−0.875597 | + | 0.483043i | \(0.839532\pi\) | |||||||
\(828\) | −4.17238 | −0.145000 | ||||||||
\(829\) | 22.8922 | 0.795080 | 0.397540 | − | 0.917585i | \(-0.369864\pi\) | ||||
0.397540 | + | 0.917585i | \(0.369864\pi\) | |||||||
\(830\) | 0.127707 | 0.00443278 | ||||||||
\(831\) | 22.8345 | 0.792120 | ||||||||
\(832\) | 10.2764 | 0.356272 | ||||||||
\(833\) | 6.40254 | 0.221835 | ||||||||
\(834\) | −4.43429 | −0.153547 | ||||||||
\(835\) | −9.21934 | −0.319048 | ||||||||
\(836\) | −1.24269 | −0.0429792 | ||||||||
\(837\) | 0.727102 | 0.0251323 | ||||||||
\(838\) | −3.47525 | −0.120050 | ||||||||
\(839\) | −30.6388 | −1.05777 | −0.528885 | − | 0.848694i | \(-0.677390\pi\) | ||||
−0.528885 | + | 0.848694i | \(0.677390\pi\) | |||||||
\(840\) | −2.36983 | −0.0817669 | ||||||||
\(841\) | 30.8269 | 1.06300 | ||||||||
\(842\) | −5.83203 | −0.200985 | ||||||||
\(843\) | 0.819303 | 0.0282183 | ||||||||
\(844\) | 0.227857 | 0.00784317 | ||||||||
\(845\) | −8.20085 | −0.282118 | ||||||||
\(846\) | −2.95964 | −0.101754 | ||||||||
\(847\) | −11.7190 | −0.402670 | ||||||||
\(848\) | −22.0795 | −0.758213 | ||||||||
\(849\) | 5.08478 | 0.174509 | ||||||||
\(850\) | −1.23268 | −0.0422805 | ||||||||
\(851\) | 2.70522 | 0.0927336 | ||||||||
\(852\) | −16.3211 | −0.559150 | ||||||||
\(853\) | −28.1815 | −0.964917 | −0.482459 | − | 0.875919i | \(-0.660256\pi\) | ||||
−0.482459 | + | 0.875919i | \(0.660256\pi\) | |||||||
\(854\) | 2.69291 | 0.0921496 | ||||||||
\(855\) | −0.224445 | −0.00767584 | ||||||||
\(856\) | −17.8478 | −0.610024 | ||||||||
\(857\) | −6.97770 | −0.238354 | −0.119177 | − | 0.992873i | \(-0.538026\pi\) | ||||
−0.119177 | + | 0.992873i | \(0.538026\pi\) | |||||||
\(858\) | −11.0999 | −0.378945 | ||||||||
\(859\) | 24.4451 | 0.834055 | 0.417027 | − | 0.908894i | \(-0.363072\pi\) | ||||
0.417027 | + | 0.908894i | \(0.363072\pi\) | |||||||
\(860\) | −28.4182 | −0.969051 | ||||||||
\(861\) | −3.51747 | −0.119875 | ||||||||
\(862\) | −12.7489 | −0.434230 | ||||||||
\(863\) | 11.4944 | 0.391275 | 0.195637 | − | 0.980676i | \(-0.437322\pi\) | ||||
0.195637 | + | 0.980676i | \(0.437322\pi\) | |||||||
\(864\) | 5.09367 | 0.173290 | ||||||||
\(865\) | 17.2242 | 0.585642 | ||||||||
\(866\) | −4.99738 | −0.169818 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −0.977821 | −0.0331894 | ||||||||
\(869\) | 5.11481 | 0.173508 | ||||||||
\(870\) | −6.34099 | −0.214980 | ||||||||
\(871\) | 42.2669 | 1.43216 | ||||||||
\(872\) | −2.28220 | −0.0772852 | ||||||||
\(873\) | 10.1795 | 0.344523 | ||||||||
\(874\) | −0.170814 | −0.00577786 | ||||||||
\(875\) | −9.21411 | −0.311494 | ||||||||
\(876\) | 25.8599 | 0.873725 | ||||||||
\(877\) | −9.31690 | −0.314609 | −0.157305 | − | 0.987550i | \(-0.550280\pi\) | ||||
−0.157305 | + | 0.987550i | \(0.550280\pi\) | |||||||
\(878\) | −8.70815 | −0.293886 | ||||||||
\(879\) | 8.50443 | 0.286847 | ||||||||
\(880\) | −20.6072 | −0.694667 | ||||||||
\(881\) | −3.16807 | −0.106735 | −0.0533674 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533674 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(882\) | 3.26569 | 0.109962 | ||||||||
\(883\) | −17.8681 | −0.601308 | −0.300654 | − | 0.953733i | \(-0.597205\pi\) | ||||
−0.300654 | + | 0.953733i | \(0.597205\pi\) | |||||||
\(884\) | −7.40247 | −0.248972 | ||||||||
\(885\) | 4.45462 | 0.149740 | ||||||||
\(886\) | 16.4995 | 0.554311 | ||||||||
\(887\) | −6.52473 | −0.219079 | −0.109540 | − | 0.993982i | \(-0.534938\pi\) | ||||
−0.109540 | + | 0.993982i | \(0.534938\pi\) | |||||||
\(888\) | −2.15180 | −0.0722096 | ||||||||
\(889\) | 7.81603 | 0.262141 | ||||||||
\(890\) | 0.929872 | 0.0311694 | ||||||||
\(891\) | 5.11481 | 0.171353 | ||||||||
\(892\) | −35.7007 | −1.19535 | ||||||||
\(893\) | 0.810288 | 0.0271153 | ||||||||
\(894\) | 1.52992 | 0.0511683 | ||||||||
\(895\) | −11.9083 | −0.398050 | ||||||||
\(896\) | −8.82665 | −0.294878 | ||||||||
\(897\) | 10.2034 | 0.340681 | ||||||||
\(898\) | 8.84241 | 0.295075 | ||||||||
\(899\) | −5.62398 | −0.187570 | ||||||||
\(900\) | 4.20470 | 0.140157 | ||||||||
\(901\) | 8.80818 | 0.293443 | ||||||||
\(902\) | 11.8721 | 0.395297 | ||||||||
\(903\) | −7.85521 | −0.261405 | ||||||||
\(904\) | −17.8775 | −0.594597 | ||||||||
\(905\) | −31.5196 | −1.04775 | ||||||||
\(906\) | 8.61929 | 0.286357 | ||||||||
\(907\) | 5.15987 | 0.171331 | 0.0856653 | − | 0.996324i | \(-0.472698\pi\) | ||||
0.0856653 | + | 0.996324i | \(0.472698\pi\) | |||||||
\(908\) | −12.0394 | −0.399540 | ||||||||
\(909\) | 1.50689 | 0.0499804 | ||||||||
\(910\) | 2.69608 | 0.0893741 | ||||||||
\(911\) | 4.85421 | 0.160827 | 0.0804136 | − | 0.996762i | \(-0.474376\pi\) | ||||
0.0804136 | + | 0.996762i | \(0.474376\pi\) | |||||||
\(912\) | −0.350048 | −0.0115912 | ||||||||
\(913\) | 0.796776 | 0.0263694 | ||||||||
\(914\) | −1.72142 | −0.0569396 | ||||||||
\(915\) | 10.9781 | 0.362926 | ||||||||
\(916\) | −41.1495 | −1.35962 | ||||||||
\(917\) | −11.5254 | −0.380603 | ||||||||
\(918\) | −0.510062 | −0.0168346 | ||||||||
\(919\) | −12.5063 | −0.412545 | −0.206273 | − | 0.978495i | \(-0.566133\pi\) | ||||
−0.206273 | + | 0.978495i | \(0.566133\pi\) | |||||||
\(920\) | −7.35253 | −0.242406 | ||||||||
\(921\) | −28.5827 | −0.941832 | ||||||||
\(922\) | 1.31549 | 0.0433234 | ||||||||
\(923\) | 39.9124 | 1.31373 | ||||||||
\(924\) | −6.87850 | −0.226286 | ||||||||
\(925\) | −2.72617 | −0.0896359 | ||||||||
\(926\) | −1.04745 | −0.0344212 | ||||||||
\(927\) | −16.7719 | −0.550861 | ||||||||
\(928\) | −39.3985 | −1.29332 | ||||||||
\(929\) | −27.2787 | −0.894987 | −0.447493 | − | 0.894287i | \(-0.647683\pi\) | ||||
−0.447493 | + | 0.894287i | \(0.647683\pi\) | |||||||
\(930\) | 0.596079 | 0.0195462 | ||||||||
\(931\) | −0.894079 | −0.0293022 | ||||||||
\(932\) | 3.55919 | 0.116585 | ||||||||
\(933\) | −7.63659 | −0.250011 | ||||||||
\(934\) | 2.34781 | 0.0768226 | ||||||||
\(935\) | 8.22081 | 0.268849 | ||||||||
\(936\) | −8.11603 | −0.265281 | ||||||||
\(937\) | 11.8756 | 0.387958 | 0.193979 | − | 0.981006i | \(-0.437861\pi\) | ||||
0.193979 | + | 0.981006i | \(0.437861\pi\) | |||||||
\(938\) | −3.91662 | −0.127882 | ||||||||
\(939\) | 10.8842 | 0.355191 | ||||||||
\(940\) | 16.2259 | 0.529232 | ||||||||
\(941\) | 48.3497 | 1.57615 | 0.788077 | − | 0.615576i | \(-0.211077\pi\) | ||||
0.788077 | + | 0.615576i | \(0.211077\pi\) | |||||||
\(942\) | −2.38695 | −0.0777711 | ||||||||
\(943\) | −10.9131 | −0.355381 | ||||||||
\(944\) | 6.94750 | 0.226122 | ||||||||
\(945\) | −1.24234 | −0.0404134 | ||||||||
\(946\) | 26.5127 | 0.862003 | ||||||||
\(947\) | 17.4820 | 0.568090 | 0.284045 | − | 0.958811i | \(-0.408324\pi\) | ||||
0.284045 | + | 0.958811i | \(0.408324\pi\) | |||||||
\(948\) | 1.73984 | 0.0565073 | ||||||||
\(949\) | −63.2391 | −2.05283 | ||||||||
\(950\) | 0.172137 | 0.00558485 | ||||||||
\(951\) | −17.6907 | −0.573659 | ||||||||
\(952\) | 1.47445 | 0.0477874 | ||||||||
\(953\) | −13.9910 | −0.453213 | −0.226606 | − | 0.973986i | \(-0.572763\pi\) | ||||
−0.226606 | + | 0.973986i | \(0.572763\pi\) | |||||||
\(954\) | 4.49272 | 0.145457 | ||||||||
\(955\) | 7.54237 | 0.244065 | ||||||||
\(956\) | 10.9960 | 0.355637 | ||||||||
\(957\) | −39.5619 | −1.27886 | ||||||||
\(958\) | 3.03368 | 0.0980136 | ||||||||
\(959\) | −9.93203 | −0.320722 | ||||||||
\(960\) | −3.88204 | −0.125292 | ||||||||
\(961\) | −30.4713 | −0.982946 | ||||||||
\(962\) | 2.44803 | 0.0789277 | ||||||||
\(963\) | −9.35639 | −0.301506 | ||||||||
\(964\) | −18.2806 | −0.588778 | ||||||||
\(965\) | −43.3701 | −1.39613 | ||||||||
\(966\) | −0.945485 | −0.0304205 | ||||||||
\(967\) | 20.8099 | 0.669202 | 0.334601 | − | 0.942360i | \(-0.391398\pi\) | ||||
0.334601 | + | 0.942360i | \(0.391398\pi\) | |||||||
\(968\) | 28.9208 | 0.929551 | ||||||||
\(969\) | 0.139644 | 0.00448603 | ||||||||
\(970\) | 8.34514 | 0.267946 | ||||||||
\(971\) | −49.2271 | −1.57977 | −0.789886 | − | 0.613254i | \(-0.789860\pi\) | ||||
−0.789886 | + | 0.613254i | \(0.789860\pi\) | |||||||
\(972\) | 1.73984 | 0.0558053 | ||||||||
\(973\) | 6.71981 | 0.215427 | ||||||||
\(974\) | −10.3720 | −0.332339 | ||||||||
\(975\) | −10.2824 | −0.329301 | ||||||||
\(976\) | 17.1217 | 0.548052 | ||||||||
\(977\) | 50.1669 | 1.60498 | 0.802490 | − | 0.596665i | \(-0.203508\pi\) | ||||
0.802490 | + | 0.596665i | \(0.203508\pi\) | |||||||
\(978\) | 8.64169 | 0.276331 | ||||||||
\(979\) | 5.80155 | 0.185418 | ||||||||
\(980\) | −17.9038 | −0.571917 | ||||||||
\(981\) | −1.19641 | −0.0381983 | ||||||||
\(982\) | −10.6642 | −0.340308 | ||||||||
\(983\) | 42.1134 | 1.34321 | 0.671605 | − | 0.740909i | \(-0.265605\pi\) | ||||
0.671605 | + | 0.740909i | \(0.265605\pi\) | |||||||
\(984\) | 8.68060 | 0.276727 | ||||||||
\(985\) | 7.47495 | 0.238172 | ||||||||
\(986\) | 3.94522 | 0.125641 | ||||||||
\(987\) | 4.48510 | 0.142762 | ||||||||
\(988\) | 1.03371 | 0.0328868 | ||||||||
\(989\) | −24.3713 | −0.774961 | ||||||||
\(990\) | 4.19312 | 0.133266 | ||||||||
\(991\) | 1.69004 | 0.0536860 | 0.0268430 | − | 0.999640i | \(-0.491455\pi\) | ||||
0.0268430 | + | 0.999640i | \(0.491455\pi\) | |||||||
\(992\) | 3.70362 | 0.117590 | ||||||||
\(993\) | −3.98286 | −0.126392 | ||||||||
\(994\) | −3.69844 | −0.117307 | ||||||||
\(995\) | −7.34413 | −0.232824 | ||||||||
\(996\) | 0.271029 | 0.00858788 | ||||||||
\(997\) | 11.6609 | 0.369305 | 0.184653 | − | 0.982804i | \(-0.440884\pi\) | ||||
0.184653 | + | 0.982804i | \(0.440884\pi\) | |||||||
\(998\) | 8.73104 | 0.276376 | ||||||||
\(999\) | −1.12804 | −0.0356897 |
(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 | 4029.2.a.l.1.14 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.14 | ✓ | 32 | 1.1 | even | 1 | trivial |