Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(191,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.191");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + x^{12} + 14 x^{11} - 42 x^{10} + 28 x^{9} + 132 x^{8} - 440 x^{7} + 528 x^{6} + \cdots + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{25} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.10 | ||
Root | \(1.57398 - 1.23393i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.191 |
Dual form | 1216.3.d.d.191.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 2.90118i | 0.967060i | 0.875328 | + | 0.483530i | \(0.160646\pi\) | ||||
−0.875328 | + | 0.483530i | \(0.839354\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.66290 | −0.732580 | −0.366290 | − | 0.930501i | \(-0.619372\pi\) | ||||
−0.366290 | + | 0.930501i | \(0.619372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.93414i | − 0.276306i | −0.990411 | − | 0.138153i | \(-0.955883\pi\) | ||||
0.990411 | − | 0.138153i | \(-0.0441166\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.583162 | 0.0647958 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.752428i | 0.0684025i | 0.999415 | + | 0.0342013i | \(0.0108887\pi\) | ||||
−0.999415 | + | 0.0342013i | \(0.989111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0118 | 1.00091 | 0.500453 | − | 0.865763i | \(-0.333167\pi\) | ||||
0.500453 | + | 0.865763i | \(0.333167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 10.6267i | − 0.708449i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −23.9304 | −1.40767 | −0.703836 | − | 0.710363i | \(-0.748531\pi\) | ||||
−0.703836 | + | 0.710363i | \(0.748531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.35890i | − 0.229416i | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.61130 | 0.267205 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.26712i | 0.272483i | 0.990676 | + | 0.136242i | \(0.0435024\pi\) | ||||
−0.990676 | + | 0.136242i | \(0.956498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.5832 | −0.463326 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.8025i | 1.02972i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −33.1165 | −1.14195 | −0.570974 | − | 0.820968i | \(-0.693434\pi\) | ||||
−0.570974 | + | 0.820968i | \(0.693434\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 17.5328i | − 0.565574i | −0.959183 | − | 0.282787i | \(-0.908741\pi\) | ||||
0.959183 | − | 0.282787i | \(-0.0912589\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.18293 | −0.0661493 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.08457i | 0.202416i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −41.5073 | −1.12182 | −0.560910 | − | 0.827877i | \(-0.689549\pi\) | ||||
−0.560910 | + | 0.827877i | \(0.689549\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 37.7495i | 0.967937i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.51661 | −0.134551 | −0.0672757 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672757 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 84.5402i | − 1.96605i | −0.183468 | − | 0.983026i | \(-0.558733\pi\) | ||||
0.183468 | − | 0.983026i | \(-0.441267\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.13607 | −0.0474681 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 18.3582i | − 0.390599i | −0.980744 | − | 0.195300i | \(-0.937432\pi\) | ||||
0.980744 | − | 0.195300i | \(-0.0625679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 45.2591 | 0.923655 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 69.4264i | − 1.36130i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 41.2010 | 0.777377 | 0.388688 | − | 0.921369i | \(-0.372928\pi\) | ||||
0.388688 | + | 0.921369i | \(0.372928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.75607i | − 0.0501103i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.6459 | 0.221859 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 69.5279i | 1.17844i | 0.807973 | + | 0.589219i | \(0.200565\pi\) | ||||
−0.807973 | + | 0.589219i | \(0.799435\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −87.6461 | −1.43682 | −0.718411 | − | 0.695619i | \(-0.755130\pi\) | ||||
−0.718411 | + | 0.695619i | \(0.755130\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.12792i | − 0.0179035i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −47.6609 | −0.733244 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 105.121i | − 1.56897i | −0.620145 | − | 0.784487i | \(-0.712926\pi\) | ||||
0.620145 | − | 0.784487i | \(-0.287074\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.1820 | −0.263508 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 74.9540i | − 1.05569i | −0.849341 | − | 0.527845i | \(-0.823000\pi\) | ||||
0.849341 | − | 0.527845i | \(-0.177000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 48.7353 | 0.667607 | 0.333803 | − | 0.942643i | \(-0.391668\pi\) | ||||
0.333803 | + | 0.942643i | \(0.391668\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 33.6048i | − 0.448064i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.45530 | 0.0189000 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 95.9473i | − 1.21452i | −0.794502 | − | 0.607261i | \(-0.792268\pi\) | ||||
0.794502 | − | 0.607261i | \(-0.207732\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −75.4115 | −0.931006 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 65.8722i | − 0.793641i | −0.917896 | − | 0.396821i | \(-0.870114\pi\) | ||||
0.917896 | − | 0.396821i | \(-0.129886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 87.6548 | 1.03123 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 96.0768i | − 1.10433i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.38934 | 0.0380825 | 0.0190412 | − | 0.999819i | \(-0.493939\pi\) | ||||
0.0190412 | + | 0.999819i | \(0.493939\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 25.1667i | − 0.276557i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 50.8657 | 0.546943 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.9662i | 0.168065i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −23.5177 | −0.242451 | −0.121225 | − | 0.992625i | \(-0.538682\pi\) | ||||
−0.121225 | + | 0.992625i | \(0.538682\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.438788i | 0.00443220i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 153.325 | 1.51807 | 0.759035 | − | 0.651050i | \(-0.225671\pi\) | ||||
0.759035 | + | 0.651050i | \(0.225671\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 114.566i | − 1.11229i | −0.831084 | − | 0.556147i | \(-0.812279\pi\) | ||||
0.831084 | − | 0.556147i | \(-0.187721\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20.5536 | −0.195749 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 161.991i | 1.51393i | 0.653454 | + | 0.756966i | \(0.273319\pi\) | ||||
−0.653454 | + | 0.756966i | \(0.726681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −120.924 | −1.10939 | −0.554696 | − | 0.832053i | \(-0.687166\pi\) | ||||
−0.554696 | + | 0.832053i | \(0.687166\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 120.420i | − 1.08487i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −91.1817 | −0.806918 | −0.403459 | − | 0.914998i | \(-0.632192\pi\) | ||||
−0.403459 | + | 0.914998i | \(0.632192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 22.9558i | − 0.199616i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.58799 | 0.0648546 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 46.2849i | 0.388948i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.434 | 0.995321 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 16.0047i | − 0.130119i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 134.000 | 1.07200 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.974i | 1.51160i | 0.654800 | + | 0.755802i | \(0.272753\pi\) | ||||
−0.654800 | + | 0.755802i | \(0.727247\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 245.266 | 1.90129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 92.3292i | − 0.704803i | −0.935849 | − | 0.352401i | \(-0.885365\pi\) | ||||
0.935849 | − | 0.352401i | \(-0.114635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.43073 | −0.0633890 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 101.838i | − 0.754353i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.46732 | −0.0180097 | −0.00900483 | − | 0.999959i | \(-0.502866\pi\) | ||||
−0.00900483 | + | 0.999959i | \(0.502866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 245.321i | − 1.76490i | −0.470409 | − | 0.882448i | \(-0.655894\pi\) | ||||
0.470409 | − | 0.882448i | \(-0.344106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 53.2603 | 0.377733 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.79043i | 0.0684646i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 121.302 | 0.836568 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 131.305i | 0.893229i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −52.3645 | −0.351439 | −0.175720 | − | 0.984440i | \(-0.556225\pi\) | ||||
−0.175720 | + | 0.984440i | \(0.556225\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 25.3459i | − 0.167853i | −0.996472 | − | 0.0839267i | \(-0.973254\pi\) | ||||
0.996472 | − | 0.0839267i | \(-0.0267461\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.9553 | −0.0912113 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 64.2208i | 0.414328i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 54.8571 | 0.349408 | 0.174704 | − | 0.984621i | \(-0.444103\pi\) | ||||
0.174704 | + | 0.984621i | \(0.444103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 119.531i | 0.751770i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.1215 | 0.0752888 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 26.8048i | 0.164446i | 0.996614 | + | 0.0822232i | \(0.0262020\pi\) | ||||
−0.996614 | + | 0.0822232i | \(0.973798\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.99585 | 0.0484597 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 62.7282i | − 0.375618i | −0.982206 | − | 0.187809i | \(-0.939861\pi\) | ||||
0.982206 | − | 0.187809i | \(-0.0601386\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.306683 | 0.00181469 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.54195i | − 0.0148652i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −328.974 | −1.90159 | −0.950793 | − | 0.309827i | \(-0.899729\pi\) | ||||
−0.950793 | + | 0.309827i | \(0.899729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.4035i | 0.128020i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −201.713 | −1.13962 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 335.845i | − 1.87623i | −0.346327 | − | 0.938114i | \(-0.612571\pi\) | ||||
0.346327 | − | 0.938114i | \(-0.387429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 58.9250 | 0.325552 | 0.162776 | − | 0.986663i | \(-0.447955\pi\) | ||||
0.162776 | + | 0.986663i | \(0.447955\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 254.277i | − 1.38949i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 152.037 | 0.821823 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 18.0059i | − 0.0962883i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 53.7740 | 0.284518 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 98.6857i | − 0.516679i | −0.966054 | − | 0.258339i | \(-0.916825\pi\) | ||||
0.966054 | − | 0.258339i | \(-0.0831753\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −278.391 | −1.44244 | −0.721220 | − | 0.692706i | \(-0.756418\pi\) | ||||
−0.721220 | + | 0.692706i | \(0.756418\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 138.273i | − 0.709091i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 47.3378 | 0.240293 | 0.120147 | − | 0.992756i | \(-0.461664\pi\) | ||||
0.120147 | + | 0.992756i | \(0.461664\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 251.355i | 1.26309i | 0.775340 | + | 0.631545i | \(0.217579\pi\) | ||||
−0.775340 | + | 0.631545i | \(0.782421\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 304.975 | 1.51729 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 64.0520i | 0.315527i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.2068 | 0.0985697 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.65475i | 0.0176558i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.27976 | 0.0156926 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 38.9936i | − 0.184804i | −0.995722 | − | 0.0924019i | \(-0.970546\pi\) | ||||
0.995722 | − | 0.0924019i | \(-0.0294544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 217.455 | 1.02092 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 309.662i | 1.44029i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −33.9109 | −0.156272 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 141.390i | 0.645615i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −311.378 | −1.40895 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 189.466i | − 0.849622i | −0.905282 | − | 0.424811i | \(-0.860340\pi\) | ||||
0.905282 | − | 0.424811i | \(-0.139660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.75486 | −0.0300216 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 167.625i | 0.738438i | 0.929342 | + | 0.369219i | \(0.120375\pi\) | ||||
−0.929342 | + | 0.369219i | \(0.879625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −203.355 | −0.888013 | −0.444006 | − | 0.896024i | \(-0.646443\pi\) | ||||
−0.444006 | + | 0.896024i | \(0.646443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.22209i | 0.0182775i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −200.769 | −0.861671 | −0.430836 | − | 0.902430i | \(-0.641781\pi\) | ||||
−0.430836 | + | 0.902430i | \(0.641781\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 67.2441i | 0.286145i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 278.360 | 1.17452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 165.710i | 0.693349i | 0.937986 | + | 0.346674i | \(0.112689\pi\) | ||||
−0.937986 | + | 0.346674i | \(0.887311\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −396.818 | −1.64655 | −0.823273 | − | 0.567646i | \(-0.807854\pi\) | ||||
−0.823273 | + | 0.567646i | \(0.807854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 31.4401i | 0.129383i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −165.780 | −0.676651 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 56.7171i | − 0.229624i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 191.107 | 0.767498 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 249.643i | 0.994592i | 0.867581 | + | 0.497296i | \(0.165674\pi\) | ||||
−0.867581 | + | 0.497296i | \(0.834326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.71555 | −0.0186385 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 254.302i | 0.997263i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.5770 | 0.0956302 | 0.0478151 | − | 0.998856i | \(-0.484774\pi\) | ||||
0.0478151 | + | 0.998856i | \(0.484774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 80.2811i | 0.309966i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −19.3123 | −0.0739934 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 343.809i | − 1.30726i | −0.756816 | − | 0.653628i | \(-0.773246\pi\) | ||||
0.756816 | − | 0.653628i | \(-0.226754\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −150.915 | −0.569491 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.83308i | 0.0368280i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −64.7826 | −0.240828 | −0.120414 | − | 0.992724i | \(-0.538422\pi\) | ||||
−0.120414 | + | 0.992724i | \(0.538422\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 113.329i | − 0.418189i | −0.977895 | − | 0.209095i | \(-0.932948\pi\) | ||||
0.977895 | − | 0.209095i | \(-0.0670517\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 73.0130 | 0.267447 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 8.71549i | − 0.0316927i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 42.8037 | 0.154526 | 0.0772629 | − | 0.997011i | \(-0.475382\pi\) | ||||
0.0772629 | + | 0.997011i | \(0.475382\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 10.2245i | − 0.0366468i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −202.018 | −0.718924 | −0.359462 | − | 0.933160i | \(-0.617040\pi\) | ||||
−0.359462 | + | 0.933160i | \(0.617040\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 77.5872i | 0.274160i | 0.990560 | + | 0.137080i | \(0.0437717\pi\) | ||||
−0.990560 | + | 0.137080i | \(0.956228\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −46.3208 | −0.162529 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.6699i | 0.0371774i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 283.665 | 0.981540 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 68.2291i | − 0.234464i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −327.131 | −1.11649 | −0.558243 | − | 0.829677i | \(-0.688524\pi\) | ||||
−0.558243 | + | 0.829677i | \(0.688524\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 254.674i | − 0.863300i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −20.9193 | −0.0704355 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 81.5464i | 0.272730i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −163.513 | −0.543232 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 444.823i | 1.46806i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 321.039 | 1.05259 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 268.290i | − 0.873910i | −0.899483 | − | 0.436955i | \(-0.856057\pi\) | ||||
0.899483 | − | 0.436955i | \(-0.143943\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 332.377 | 1.07566 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 449.497i | − 1.44533i | −0.691199 | − | 0.722664i | \(-0.742917\pi\) | ||||
0.691199 | − | 0.722664i | \(-0.257083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −283.901 | −0.907032 | −0.453516 | − | 0.891248i | \(-0.649830\pi\) | ||||
−0.453516 | + | 0.891248i | \(0.649830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.13146i | 0.0131157i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 553.100 | 1.74480 | 0.872398 | − | 0.488797i | \(-0.162564\pi\) | ||||
0.872398 | + | 0.488797i | \(0.162564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 24.9178i | − 0.0781121i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −469.964 | −1.46406 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 104.310i | 0.322942i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −150.718 | −0.463747 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 350.822i | − 1.07285i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −35.5073 | −0.107925 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 280.828i | 0.848422i | 0.905563 | + | 0.424211i | \(0.139448\pi\) | ||||
−0.905563 | + | 0.424211i | \(0.860552\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.2055 | −0.0726892 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 385.049i | 1.14940i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 93.1413 | 0.276384 | 0.138192 | − | 0.990405i | \(-0.455871\pi\) | ||||
0.138192 | + | 0.990405i | \(0.455871\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 264.534i | − 0.780337i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.1922 | 0.0386867 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 182.311i | − 0.531518i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 66.5989 | 0.193040 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 221.251i | − 0.637612i | −0.947820 | − | 0.318806i | \(-0.896718\pi\) | ||||
0.947820 | − | 0.318806i | \(-0.103282\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 227.761 | 0.652611 | 0.326306 | − | 0.945264i | \(-0.394196\pi\) | ||||
0.326306 | + | 0.945264i | \(0.394196\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 361.760i | 1.03065i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −169.824 | −0.481089 | −0.240545 | − | 0.970638i | \(-0.577326\pi\) | ||||
−0.240545 | + | 0.970638i | \(0.577326\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 274.549i | 0.773378i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −134.281 | −0.376136 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 585.928i | 1.63211i | 0.577972 | + | 0.816056i | \(0.303844\pi\) | ||||
−0.577972 | + | 0.816056i | \(0.696156\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 349.400i | 0.962535i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −178.512 | −0.489075 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 428.832i | 1.16848i | 0.811581 | + | 0.584239i | \(0.198607\pi\) | ||||
−0.811581 | + | 0.584239i | \(0.801393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.21708 | −0.00871837 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 79.6886i | − 0.214794i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 127.502 | 0.341830 | 0.170915 | − | 0.985286i | \(-0.445328\pi\) | ||||
0.170915 | + | 0.985286i | \(0.445328\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 388.759i | 1.03669i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −430.905 | −1.14298 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 244.665i | 0.645555i | 0.946475 | + | 0.322777i | \(0.104616\pi\) | ||||
−0.946475 | + | 0.322777i | \(0.895384\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −556.950 | −1.46181 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 685.025i | 1.78858i | 0.447491 | + | 0.894288i | \(0.352318\pi\) | ||||
−0.447491 | + | 0.894288i | \(0.647682\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.33063 | −0.0138458 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 49.3007i | − 0.127392i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −290.167 | −0.745931 | −0.372966 | − | 0.927845i | \(-0.621659\pi\) | ||||
−0.372966 | + | 0.927845i | \(0.621659\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 149.975i | − 0.383567i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 267.863 | 0.681586 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 351.445i | 0.889735i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −317.752 | −0.800384 | −0.400192 | − | 0.916431i | \(-0.631057\pi\) | ||||
−0.400192 | + | 0.916431i | \(0.631057\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 24.4591i | − 0.0613009i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 445.424 | 1.11078 | 0.555392 | − | 0.831589i | \(-0.312568\pi\) | ||||
0.555392 | + | 0.831589i | \(0.312568\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 228.133i | − 0.566087i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 276.225 | 0.682036 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 31.2313i | − 0.0767353i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 571.233 | 1.39666 | 0.698328 | − | 0.715778i | \(-0.253928\pi\) | ||||
0.698328 | + | 0.715778i | \(0.253928\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 7.15815i | − 0.0174164i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 134.477 | 0.325610 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 241.283i | 0.581406i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 711.719 | 1.70676 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 308.595i | 0.736502i | 0.929726 | + | 0.368251i | \(0.120043\pi\) | ||||
−0.929726 | + | 0.368251i | \(0.879957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.8298 | −0.0922324 | −0.0461162 | − | 0.998936i | \(-0.514684\pi\) | ||||
−0.0461162 | + | 0.998936i | \(0.514684\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 10.7058i | − 0.0253092i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 277.190 | 0.652212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 169.520i | 0.397003i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.4038 | −0.0662093 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 479.659i | 1.11290i | 0.830881 | + | 0.556450i | \(0.187837\pi\) | ||||
−0.830881 | + | 0.556450i | \(0.812163\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 434.901 | 1.00439 | 0.502195 | − | 0.864754i | \(-0.332526\pi\) | ||||
0.502195 | + | 0.864754i | \(0.332526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 351.920i | 0.809011i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.3177 | 0.0625120 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 25.4779i | − 0.0580363i | −0.999579 | − | 0.0290182i | \(-0.990762\pi\) | ||||
0.999579 | − | 0.0290182i | \(-0.00923807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 26.3934 | 0.0598490 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 805.631i | 1.81858i | 0.416164 | + | 0.909290i | \(0.363374\pi\) | ||||
−0.416164 | + | 0.909290i | \(0.636626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.4148 | −0.0278985 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 151.919i | − 0.339863i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −106.288 | −0.236721 | −0.118360 | − | 0.992971i | \(-0.537764\pi\) | ||||
−0.118360 | + | 0.992971i | \(0.537764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 4.15085i | − 0.00920366i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 73.5328 | 0.162324 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 92.1830i | 0.202600i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −730.620 | −1.59873 | −0.799365 | − | 0.600846i | \(-0.794831\pi\) | ||||
−0.799365 | + | 0.600846i | \(0.794831\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 665.325i | − 1.44951i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 854.696 | 1.85401 | 0.927003 | − | 0.375055i | \(-0.122376\pi\) | ||||
0.927003 | + | 0.375055i | \(0.122376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 769.128i | − 1.66118i | −0.556882 | − | 0.830591i | \(-0.688003\pi\) | ||||
0.556882 | − | 0.830591i | \(-0.311997\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −186.316 | −0.400680 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 54.2556i | 0.116179i | 0.998311 | + | 0.0580895i | \(0.0185009\pi\) | ||||
−0.998311 | + | 0.0580895i | \(0.981499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −203.320 | −0.433517 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 159.150i | 0.337899i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 63.6104 | 0.134483 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 50.4898i | 0.106294i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.0269 | 0.0503708 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 512.359i | 1.06964i | 0.844965 | + | 0.534821i | \(0.179621\pi\) | ||||
−0.844965 | + | 0.534821i | \(0.820379\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −540.085 | −1.12284 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35.1666i | 0.0728088i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 86.1431 | 0.177615 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 445.189i | 0.914146i | 0.889429 | + | 0.457073i | \(0.151102\pi\) | ||||
−0.889429 | + | 0.457073i | \(0.848898\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −77.7654 | −0.159030 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 219.288i | − 0.446615i | −0.974748 | − | 0.223308i | \(-0.928315\pi\) | ||||
0.974748 | − | 0.223308i | \(-0.0716855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 792.492 | 1.60749 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 1.60724i | − 0.00324694i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −144.972 | −0.291694 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 277.168i | − 0.555446i | −0.960661 | − | 0.277723i | \(-0.910420\pi\) | ||||
0.960661 | − | 0.277723i | \(-0.0895798\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 181.986 | 0.363245 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 328.913i | − 0.653903i | −0.945041 | − | 0.326951i | \(-0.893979\pi\) | ||||
0.945041 | − | 0.326951i | \(-0.106021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −561.614 | −1.11211 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.889743i | 0.00175492i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 371.573 | 0.730006 | 0.365003 | − | 0.931006i | \(-0.381068\pi\) | ||||
0.365003 | + | 0.931006i | \(0.381068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 94.2610i | − 0.184464i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 121.188 | 0.236234 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 419.645i | 0.814845i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.8132 | 0.0267180 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 954.413i | − 1.83895i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −607.799 | −1.16660 | −0.583300 | − | 0.812256i | \(-0.698239\pi\) | ||||
−0.583300 | + | 0.812256i | \(0.698239\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 384.474i | 0.735131i | 0.929998 | + | 0.367566i | \(0.119809\pi\) | ||||
−0.929998 | + | 0.367566i | \(0.880191\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −64.9965 | −0.123803 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 419.567i | 0.796142i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 489.723 | 0.925753 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 40.5460i | 0.0763579i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −71.7809 | −0.134673 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 593.356i | − 1.10908i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 974.346 | 1.81442 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.0542i | 0.0631803i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 382.676 | 0.707350 | 0.353675 | − | 0.935368i | \(-0.384932\pi\) | ||||
0.353675 | + | 0.935368i | \(0.384932\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 170.952i | 0.314828i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 442.932 | 0.812719 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 179.104i | 0.327430i | 0.986508 | + | 0.163715i | \(0.0523477\pi\) | ||||
−0.986508 | + | 0.163715i | \(0.947652\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −51.1119 | −0.0931000 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 144.351i | 0.261981i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −185.576 | −0.335580 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 441.087i | 0.794752i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −720.325 | −1.29322 | −0.646612 | − | 0.762819i | \(-0.723815\pi\) | ||||
−0.646612 | + | 0.762819i | \(0.723815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1100.02i | − 1.96783i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 52.2384 | 0.0931165 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 175.948i | − 0.312519i | −0.987716 | − | 0.156260i | \(-0.950056\pi\) | ||||
0.987716 | − | 0.156260i | \(-0.0499436\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 333.989 | 0.591132 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 145.857i | 0.257243i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −547.930 | −0.962971 | −0.481485 | − | 0.876454i | \(-0.659903\pi\) | ||||
−0.481485 | + | 0.876454i | \(0.659903\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 376.007i | 0.658507i | 0.944242 | + | 0.329253i | \(0.106797\pi\) | ||||
−0.944242 | + | 0.329253i | \(0.893203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 286.305 | 0.499659 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 72.5930i | − 0.126249i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 458.453 | 0.794546 | 0.397273 | − | 0.917700i | \(-0.369957\pi\) | ||||
0.397273 | + | 0.917700i | \(0.369957\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 807.662i | − 1.39493i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −127.406 | −0.219288 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.0008i | 0.0531745i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.7940 | −0.0475112 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 335.174i | 0.570995i | 0.958379 | + | 0.285497i | \(0.0921588\pi\) | ||||
−0.958379 | + | 0.285497i | \(0.907841\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −76.4236 | −0.129752 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 137.335i | 0.232378i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −280.543 | −0.473092 | −0.236546 | − | 0.971620i | \(-0.576015\pi\) | ||||
−0.236546 | + | 0.971620i | \(0.576015\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 169.537i | − 0.284936i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −729.225 | −1.22148 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 677.612i | 1.13124i | 0.824667 | + | 0.565619i | \(0.191363\pi\) | ||||
−0.824667 | + | 0.565619i | \(0.808637\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 177.699 | 0.295672 | 0.147836 | − | 0.989012i | \(-0.452769\pi\) | ||||
0.147836 | + | 0.989012i | \(0.452769\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 61.3028i | − 0.101663i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −441.137 | −0.729152 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 826.068i | 1.36090i | 0.732793 | + | 0.680451i | \(0.238216\pi\) | ||||
−0.732793 | + | 0.680451i | \(0.761784\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −185.826 | −0.305134 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 238.873i | − 0.390954i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −839.090 | −1.36883 | −0.684413 | − | 0.729095i | \(-0.739941\pi\) | ||||
−0.684413 | + | 0.729095i | \(0.739941\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 58.6235i | 0.0953227i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 615.452 | 0.997491 | 0.498746 | − | 0.866748i | \(-0.333794\pi\) | ||||
0.498746 | + | 0.866748i | \(0.333794\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 118.351i | 0.191197i | 0.995420 | + | 0.0955984i | \(0.0304765\pi\) | ||||
−0.995420 | + | 0.0955984i | \(0.969524\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −174.241 | −0.280582 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 6.55547i | − 0.0105224i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −201.251 | −0.322002 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.51516i | 0.0151757i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 993.288 | 1.57915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 665.915i | 1.05533i | 0.849452 | + | 0.527667i | \(0.176933\pi\) | ||||
−0.849452 | + | 0.527667i | \(0.823067\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 113.127 | 0.178716 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 703.181i | − 1.10737i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 588.902 | 0.924493 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 43.7104i | − 0.0684043i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 396.009 | 0.617798 | 0.308899 | − | 0.951095i | \(-0.400039\pi\) | ||||
0.308899 | + | 0.951095i | \(0.400039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 890.406i | − 1.38477i | −0.721529 | − | 0.692384i | \(-0.756560\pi\) | ||||
0.721529 | − | 0.692384i | \(-0.243440\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −898.386 | −1.39285 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1022.42i | − 1.58025i | −0.612945 | − | 0.790126i | \(-0.710015\pi\) | ||||
0.612945 | − | 0.790126i | \(-0.289985\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −52.3147 | −0.0806082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 98.3816i | − 0.151124i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −298.828 | −0.457623 | −0.228811 | − | 0.973471i | \(-0.573484\pi\) | ||||
−0.228811 | + | 0.973471i | \(0.573484\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 338.193i | 0.516324i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 28.4206 | 0.0432581 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 76.0870i | − 0.115458i | −0.998332 | − | 0.0577292i | \(-0.981614\pi\) | ||||
0.998332 | − | 0.0577292i | \(-0.0183860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 63.4958 | 0.0960602 | 0.0480301 | − | 0.998846i | \(-0.484706\pi\) | ||||
0.0480301 | + | 0.998846i | \(0.484706\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 903.362i | − 1.36254i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.8809 | 0.0464375 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 207.545i | − 0.311162i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 549.674 | 0.821636 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 65.9474i | − 0.0982822i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −814.516 | −1.21028 | −0.605138 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605138 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 322.040i | − 0.477097i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −127.732 | −0.188673 | −0.0943365 | − | 0.995540i | \(-0.530073\pi\) | ||||
−0.0943365 | + | 0.995540i | \(0.530073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.4866i | 0.0669906i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −486.311 | −0.714113 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 518.648i | 0.759367i | 0.925116 | + | 0.379684i | \(0.123967\pi\) | ||||
−0.925116 | + | 0.379684i | \(0.876033\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.03756 | 0.0131935 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 589.969i | − 0.858761i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 536.098 | 0.778082 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 1279.00i | − 1.85094i | −0.378823 | − | 0.925469i | \(-0.623671\pi\) | ||||
0.378823 | − | 0.925469i | \(-0.376329\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.848678 | 0.00122464 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 898.585i | 1.29293i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 132.015 | 0.189404 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 582.468i | − 0.833287i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −189.067 | −0.269710 | −0.134855 | − | 0.990865i | \(-0.543057\pi\) | ||||
−0.134855 | + | 0.990865i | \(0.543057\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 180.926i | 0.257363i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −195.087 | −0.276719 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 296.552i | − 0.419452i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −722.894 | −1.01960 | −0.509798 | − | 0.860294i | \(-0.670280\pi\) | ||||
−0.509798 | + | 0.860294i | \(0.670280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 55.9528i | − 0.0786960i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 109.880 | 0.154109 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 35.8614i | − 0.0501558i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −480.755 | −0.670509 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 768.781i | − 1.06924i | −0.845094 | − | 0.534618i | \(-0.820455\pi\) | ||||
0.845094 | − | 0.534618i | \(-0.179545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −221.588 | −0.307334 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 1151.24i | − 1.59231i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 383.594 | 0.529095 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1092.23i | − 1.50238i | −0.660085 | − | 0.751191i | \(-0.729480\pi\) | ||||
0.660085 | − | 0.751191i | \(-0.270520\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −769.916 | −1.05613 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2023.08i | 2.76756i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −571.768 | −0.780038 | −0.390019 | − | 0.920807i | \(-0.627532\pi\) | ||||
−0.390019 | + | 0.920807i | \(0.627532\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 480.956i | − 0.654362i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 79.0961 | 0.107322 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 299.431i | − 0.405184i | −0.979263 | − | 0.202592i | \(-0.935063\pi\) | ||||
0.979263 | − | 0.202592i | \(-0.0649365\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 164.546 | 0.222060 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.0943i | 0.0216612i | 0.999941 | + | 0.0108306i | \(0.00344755\pi\) | ||||
−0.999941 | + | 0.0108306i | \(0.996552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 191.806 | 0.257458 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 38.4142i | − 0.0514246i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 313.313 | 0.418309 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 699.482i | − 0.931401i | −0.884942 | − | 0.465701i | \(-0.845802\pi\) | ||||
0.884942 | − | 0.465701i | \(-0.154198\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −724.258 | −0.961830 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 92.8393i | 0.122966i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.5679 | −0.0152812 | −0.00764062 | − | 0.999971i | \(-0.502432\pi\) | ||||
−0.00764062 | + | 0.999971i | \(0.502432\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 13.6807i | − 0.0180246i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −354.338 | −0.465622 | −0.232811 | − | 0.972522i | \(-0.574792\pi\) | ||||
−0.232811 | + | 0.972522i | \(0.574792\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 233.884i | 0.306532i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 51.1170 | 0.0668195 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 904.682i | 1.17951i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 847.602 | 1.10221 | 0.551106 | − | 0.834435i | \(-0.314206\pi\) | ||||
0.551106 | + | 0.834435i | \(0.314206\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 71.3021i | 0.0924801i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −712.408 | −0.921615 | −0.460807 | − | 0.887500i | \(-0.652440\pi\) | ||||
−0.460807 | + | 0.887500i | \(0.652440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 203.085i | 0.262045i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −232.910 | −0.299755 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0463i | 0.0308682i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.3975 | 0.0722119 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 920.720i | − 1.17589i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −200.936 | −0.255970 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 514.229i | 0.653404i | 0.945127 | + | 0.326702i | \(0.105937\pi\) | ||||
−0.945127 | + | 0.326702i | \(0.894063\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 997.450 | 1.26420 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 176.358i | 0.222956i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1140.43 | −1.43812 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 437.831i | − 0.550731i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −934.459 | −1.17247 | −0.586235 | − | 0.810141i | \(-0.699391\pi\) | ||||
−0.586235 | + | 0.810141i | \(0.699391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 439.319i | 0.549836i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.97654 | 0.00246759 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.6698i | 0.0456660i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −44.3998 | −0.0551551 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 187.946i | − 0.232895i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1126.44 | 1.39239 | 0.696195 | − | 0.717853i | \(-0.254875\pi\) | ||||
0.696195 | + | 0.717853i | \(0.254875\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 938.339i | 1.15702i | 0.815677 | + | 0.578508i | \(0.196365\pi\) | ||||
−0.815677 | + | 0.578508i | \(0.803635\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 328.789 | 0.404414 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 98.1832i | − 0.120470i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −368.502 | −0.451043 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 14.6763i | − 0.0179197i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −509.877 | −0.621044 | −0.310522 | − | 0.950566i | \(-0.600504\pi\) | ||||
−0.310522 | + | 0.950566i | \(0.600504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 791.322i | 0.961509i | 0.876855 | + | 0.480754i | \(0.159637\pi\) | ||||
−0.876855 | + | 0.480754i | \(0.840363\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.2852 | 0.0306487 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 725.787i | − 0.877615i | −0.898581 | − | 0.438807i | \(-0.855401\pi\) | ||||
0.898581 | − | 0.438807i | \(-0.144599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 987.501 | 1.19120 | 0.595598 | − | 0.803283i | \(-0.296915\pi\) | ||||
0.595598 | + | 0.803283i | \(0.296915\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 124.181i | 0.149436i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1083.07 | −1.30020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 229.767i | 0.275170i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 487.455 | 0.582383 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 1549.38i | − 1.84670i | −0.383959 | − | 0.923350i | \(-0.625439\pi\) | ||||
0.383959 | − | 0.923350i | \(-0.374561\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 255.702 | 0.304045 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 586.089i | − 0.695242i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.12335 | −0.00132941 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 232.936i | − 0.275013i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −225.094 | −0.265129 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 260.131i | − 0.305677i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 108.740 | 0.127480 | 0.0637399 | − | 0.997967i | \(-0.479697\pi\) | ||||
0.0637399 | + | 0.997967i | \(0.479697\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.31089i | 0.0108899i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −958.909 | −1.11891 | −0.559457 | − | 0.828860i | \(-0.688990\pi\) | ||||
−0.559457 | + | 0.828860i | \(0.688990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1060.62i | − 1.23471i | −0.786684 | − | 0.617356i | \(-0.788204\pi\) | ||||
0.786684 | − | 0.617356i | \(-0.211796\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.9553 | −0.0359527 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 838.621i | 0.971751i | 0.874028 | + | 0.485875i | \(0.161499\pi\) | ||||
−0.874028 | + | 0.485875i | \(0.838501\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1205.00 | 1.39306 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 822.963i | 0.949208i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 72.1934 | 0.0830764 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1367.82i | − 1.57040i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.7147 | −0.0157098 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 259.176i | − 0.296201i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1453.86 | −1.65776 | −0.828882 | − | 0.559424i | \(-0.811022\pi\) | ||||
−0.828882 | + | 0.559424i | \(0.811022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 949.064i | − 1.07971i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 156.229 | 0.177332 | 0.0886659 | − | 0.996061i | \(-0.471740\pi\) | ||||
0.0886659 | + | 0.996061i | \(0.471740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 37.1369i | − 0.0420577i | −0.999779 | − | 0.0210288i | \(-0.993306\pi\) | ||||
0.999779 | − | 0.0210288i | \(-0.00669418\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 738.854 | 0.834863 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 490.932i | 0.553474i | 0.960946 | + | 0.276737i | \(0.0892532\pi\) | ||||
−0.960946 | + | 0.276737i | \(0.910747\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 371.305 | 0.417666 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 56.7417i | − 0.0636831i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −80.0214 | −0.0896096 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1230.17i | 1.37449i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −236.581 | −0.263747 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 580.624i | 0.645856i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −985.957 | −1.09429 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 474.380i | − 0.525338i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −215.836 | −0.238493 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 167.806i | − 0.185012i | −0.995712 | − | 0.0925060i | \(-0.970512\pi\) | ||||
0.995712 | − | 0.0925060i | \(-0.0294877\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 89.4134 | 0.0983645 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1217.97i | − 1.33696i | −0.743730 | − | 0.668481i | \(-0.766945\pi\) | ||||
0.743730 | − | 0.668481i | \(-0.233055\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.5641 | 0.0542871 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 931.391i | 1.01791i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −178.578 | −0.194741 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1037.14i | − 1.12855i | −0.825585 | − | 0.564277i | \(-0.809155\pi\) | ||||
0.825585 | − | 0.564277i | \(-0.190845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 778.358 | 0.845123 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 975.286i | − 1.05665i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 480.786 | 0.519769 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 66.8108i | − 0.0720720i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −98.9780 | −0.106543 | −0.0532713 | − | 0.998580i | \(-0.516965\pi\) | ||||
−0.0532713 | + | 0.998580i | \(0.516965\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 197.280i | − 0.211901i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1304.07 | 1.39772 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 65.9539i | 0.0705389i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1744.65 | 1.86195 | 0.930974 | − | 0.365084i | \(-0.118960\pi\) | ||||
0.930974 | + | 0.365084i | \(0.118960\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 823.647i | − 0.877154i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 723.767 | 0.769147 | 0.384574 | − | 0.923094i | \(-0.374348\pi\) | ||||
0.384574 | + | 0.923094i | \(0.374348\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 34.5732i | − 0.0366630i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −196.969 | −0.208432 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 819.583i | 0.865452i | 0.901526 | + | 0.432726i | \(0.142448\pi\) | ||||
−0.901526 | + | 0.432726i | \(0.857552\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 634.133 | 0.668212 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1604.64i | 1.68732i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1777.86 | 1.86554 | 0.932771 | − | 0.360470i | \(-0.117384\pi\) | ||||
0.932771 | + | 0.360470i | \(0.117384\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 361.476i | 0.378509i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 72.2909 | 0.0755391 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.77216i | 0.00497618i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 653.601 | 0.680126 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 94.4669i | 0.0980965i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1019.72 | 1.05670 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1306.29i | 1.35087i | 0.737421 | + | 0.675433i | \(0.236043\pi\) | ||||
−0.737421 | + | 0.675433i | \(0.763957\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −302.623 | −0.312304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 940.020i | − 0.968094i | −0.875042 | − | 0.484047i | \(-0.839166\pi\) | ||||
0.875042 | − | 0.484047i | \(-0.160834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −474.485 | −0.487652 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 437.259i | − 0.448471i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −549.002 | −0.561927 | −0.280963 | − | 0.959719i | \(-0.590654\pi\) | ||||
−0.280963 | + | 0.959719i | \(0.590654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.55023i | 0.00260494i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −70.5182 | −0.0718840 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 506.118i | − 0.514871i | −0.966295 | − | 0.257436i | \(-0.917122\pi\) | ||||
0.966295 | − | 0.257436i | \(-0.0828775\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −173.394 | −0.176034 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 103.013i | − 0.104370i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 529.823 | 0.535716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 213.024i | − 0.214959i | −0.994207 | − | 0.107479i | \(-0.965722\pi\) | ||||
0.994207 | − | 0.107479i | \(-0.0342780\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −814.731 | −0.820474 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 920.687i | − 0.925314i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 940.041 | 0.942870 | 0.471435 | − | 0.881901i | \(-0.343736\pi\) | ||||
0.471435 | + | 0.881901i | \(0.343736\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 1154.01i | − 1.15516i |
(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 | 1216.3.d.d.191.10 | 14 | ||
4.3 | odd | 2 | inner | 1216.3.d.d.191.5 | 14 | ||
8.3 | odd | 2 | 76.3.b.b.39.11 | ✓ | 14 | ||
8.5 | even | 2 | 76.3.b.b.39.12 | yes | 14 | ||
24.5 | odd | 2 | 684.3.g.b.343.3 | 14 | |||
24.11 | even | 2 | 684.3.g.b.343.4 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.b.b.39.11 | ✓ | 14 | 8.3 | odd | 2 | ||
76.3.b.b.39.12 | yes | 14 | 8.5 | even | 2 | ||
684.3.g.b.343.3 | 14 | 24.5 | odd | 2 | |||
684.3.g.b.343.4 | 14 | 24.11 | even | 2 | |||
1216.3.d.d.191.5 | 14 | 4.3 | odd | 2 | inner | ||
1216.3.d.d.191.10 | 14 | 1.1 | even | 1 | trivial |