Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,3,Mod(319,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.e (of order \(2\), degree \(1\), 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: | \(17.4387369191\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{14} + 104x^{12} - 208x^{10} - 352x^{8} + 2312x^{6} + 2497x^{4} - 9072x^{2} + 5184 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{38} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.15 | ||
Root | \(0.332843 - 1.47845i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 640.319 |
Dual form | 640.3.e.i.319.4 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.62258i | 1.20753i | 0.797163 | + | 0.603764i | \(0.206333\pi\) | ||||
−0.797163 | + | 0.603764i | \(0.793667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.96837 | − | 0.561553i | 0.993673 | − | 0.112311i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.45101 | 0.921573 | 0.460786 | − | 0.887511i | \(-0.347567\pi\) | ||||
0.460786 | + | 0.887511i | \(0.347567\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.12311 | −0.458123 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.94566 | −0.358696 | −0.179348 | − | 0.983786i | \(-0.557399\pi\) | ||||
−0.179348 | + | 0.983786i | \(0.557399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.5167 | 1.19359 | 0.596797 | − | 0.802392i | \(-0.296440\pi\) | ||||
0.596797 | + | 0.802392i | \(0.296440\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.03427 | + | 17.9983i | 0.135618 | + | 1.19989i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 25.4535i | − | 1.49726i | −0.662987 | − | 0.748631i | \(-0.730711\pi\) | ||
0.662987 | − | 0.748631i | \(-0.269289\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.0510 | 1.68689 | 0.843447 | − | 0.537213i | \(-0.180523\pi\) | ||||
0.843447 | + | 0.537213i | \(0.180523\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 23.3693i | 1.11282i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.2845 | −0.664543 | −0.332271 | − | 0.943184i | \(-0.607815\pi\) | ||||
−0.332271 | + | 0.943184i | \(0.607815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.3693 | − | 5.58000i | 0.974773 | − | 0.223200i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17.6670i | 0.654332i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 34.7386i | − | 1.19788i | −0.800792 | − | 0.598942i | \(-0.795588\pi\) | ||
0.800792 | − | 0.598942i | \(-0.204412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.2140i | 0.652065i | 0.945359 | + | 0.326032i | \(0.105712\pi\) | ||||
−0.945359 | + | 0.326032i | \(0.894288\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 14.2935i | − | 0.433135i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 32.0510 | − | 3.62258i | 0.915742 | − | 0.103502i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.93673 | 0.268560 | 0.134280 | − | 0.990943i | \(-0.457128\pi\) | ||||
0.134280 | + | 0.990943i | \(0.457128\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 56.2106i | 1.44130i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −42.3542 | −1.03303 | −0.516514 | − | 0.856279i | \(-0.672771\pi\) | ||||
−0.516514 | + | 0.856279i | \(0.672771\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 52.9460i | − | 1.23130i | −0.788019 | − | 0.615651i | \(-0.788893\pi\) | ||
0.788019 | − | 0.615651i | \(-0.211107\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −20.4851 | + | 2.31534i | −0.455224 | + | 0.0514520i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −21.6377 | −0.460377 | −0.230189 | − | 0.973146i | \(-0.573934\pi\) | ||||
−0.230189 | + | 0.973146i | \(0.573934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.38447 | −0.150704 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 92.2073 | 1.80799 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −35.3902 | −0.667740 | −0.333870 | − | 0.942619i | \(-0.608355\pi\) | ||||
−0.333870 | + | 0.942619i | \(0.608355\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.6035 | + | 2.21569i | −0.356427 | + | 0.0402853i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 116.107i | 2.03697i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 16.2684 | 0.275735 | 0.137867 | − | 0.990451i | \(-0.455975\pi\) | ||||
0.137867 | + | 0.990451i | \(0.455975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 77.3390i | 1.26785i | 0.773393 | + | 0.633926i | \(0.218558\pi\) | ||||
−0.773393 | + | 0.633926i | \(0.781442\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −26.5982 | −0.422194 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 77.0928 | − | 8.71346i | 1.18604 | − | 0.134053i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.0444i | 0.209617i | 0.994492 | + | 0.104809i | \(0.0334230\pi\) | ||||
−0.994492 | + | 0.104809i | \(0.966577\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 55.3693i | − | 0.802454i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 107.990i | 1.52098i | 0.649347 | + | 0.760492i | \(0.275042\pi\) | ||||
−0.649347 | + | 0.760492i | \(0.724958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 93.7873i | 1.28476i | 0.766387 | + | 0.642379i | \(0.222052\pi\) | ||||
−0.766387 | + | 0.642379i | \(0.777948\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 20.2140 | + | 88.2799i | 0.269520 | + | 1.17706i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −25.4535 | −0.330564 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 92.2073i | 1.16718i | 0.812048 | + | 0.583590i | \(0.198353\pi\) | ||||
−0.812048 | + | 0.583590i | \(0.801647\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −101.108 | −1.24825 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 26.7509i | 0.322300i | 0.986930 | + | 0.161150i | \(0.0515202\pi\) | ||||
−0.986930 | + | 0.161150i | \(0.948480\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.2935 | − | 126.462i | −0.168158 | − | 1.48779i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 125.844 | 1.44648 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 27.7538 | 0.311840 | 0.155920 | − | 0.987770i | \(-0.450166\pi\) | ||||
0.155920 | + | 0.987770i | \(0.450166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 100.099 | 1.09998 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −73.2269 | −0.787386 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 159.241 | − | 17.9983i | 1.67622 | − | 0.189456i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 133.534i | − | 1.37664i | −0.725406 | − | 0.688321i | \(-0.758348\pi\) | ||
0.725406 | − | 0.688321i | \(-0.241652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.2684 | 0.164327 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 148.708i | 1.47236i | 0.676786 | + | 0.736180i | \(0.263372\pi\) | ||||
−0.676786 | + | 0.736180i | \(0.736628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −146.089 | −1.41834 | −0.709168 | − | 0.705040i | \(-0.750929\pi\) | ||||
−0.709168 | + | 0.705040i | \(0.750929\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.1231 | + | 116.107i | 0.124982 | + | 1.10578i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 35.2790i | 0.329710i | 0.986318 | + | 0.164855i | \(0.0527157\pi\) | ||||
−0.986318 | + | 0.164855i | \(0.947284\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 24.1383i | 0.221452i | 0.993851 | + | 0.110726i | \(0.0353176\pi\) | ||||
−0.993851 | + | 0.110726i | \(0.964682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 35.9966i | 0.324294i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 181.308i | − | 1.60449i | −0.596993 | − | 0.802246i | \(-0.703638\pi\) | ||
0.596993 | − | 0.802246i | \(-0.296362\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −75.9389 | + | 8.58305i | −0.660338 | + | 0.0746352i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −63.9771 | −0.546813 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 164.201i | − | 1.37984i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −105.432 | −0.871337 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 153.431i | − | 1.24741i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 117.942 | − | 41.4081i | 0.943538 | − | 0.331265i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −191.453 | −1.50751 | −0.753753 | − | 0.657158i | \(-0.771758\pi\) | ||||
−0.753753 | + | 0.657158i | \(0.771758\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 191.801 | 1.48683 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −224.357 | −1.71265 | −0.856324 | − | 0.516439i | \(-0.827257\pi\) | ||||
−0.856324 | + | 0.516439i | \(0.827257\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 206.761 | 1.55460 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.92093 | + | 87.7759i | 0.0734884 | + | 0.650192i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 55.8000i | − | 0.407299i | −0.979044 | − | 0.203650i | \(-0.934720\pi\) | ||
0.979044 | − | 0.203650i | \(-0.0652803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 115.395 | 0.830183 | 0.415092 | − | 0.909780i | \(-0.363750\pi\) | ||||
0.415092 | + | 0.909780i | \(0.363750\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 78.3845i | − | 0.555918i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −61.2237 | −0.428138 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.5076 | − | 172.594i | −0.134535 | − | 1.19031i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 26.7509i | − | 0.181979i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 52.6307i | 0.353226i | 0.984280 | + | 0.176613i | \(0.0565141\pi\) | ||||
−0.984280 | + | 0.176613i | \(0.943486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 231.762i | − | 1.53485i | −0.641138 | − | 0.767425i | \(-0.721538\pi\) | ||
0.641138 | − | 0.767425i | \(-0.278462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 104.947i | 0.685930i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.3512 | + | 100.431i | 0.0732338 | + | 0.647939i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 162.658 | 1.03604 | 0.518018 | − | 0.855370i | \(-0.326670\pi\) | ||||
0.518018 | + | 0.855370i | \(0.326670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 128.204i | − | 0.806314i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −98.6004 | −0.612425 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 293.319i | − | 1.79951i | −0.436400 | − | 0.899753i | \(-0.643747\pi\) | ||
0.436400 | − | 0.899753i | \(-0.356253\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.02653 | − | 71.0152i | −0.0486457 | − | 0.430395i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 246.934 | 1.47865 | 0.739324 | − | 0.673350i | \(-0.235145\pi\) | ||||
0.739324 | + | 0.673350i | \(0.235145\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 71.7689 | 0.424668 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −132.150 | −0.772804 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 76.8967 | 0.444490 | 0.222245 | − | 0.974991i | \(-0.428662\pi\) | ||||
0.222245 | + | 0.974991i | \(0.428662\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 157.207 | − | 35.9966i | 0.898324 | − | 0.205695i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 58.9335i | 0.332957i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −284.999 | −1.59217 | −0.796086 | − | 0.605183i | \(-0.793100\pi\) | ||||
−0.796086 | + | 0.605183i | \(0.793100\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 176.769i | 0.976624i | 0.872669 | + | 0.488312i | \(0.162387\pi\) | ||||
−0.872669 | + | 0.488312i | \(0.837613\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −280.167 | −1.53097 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 49.3693 | − | 5.58000i | 0.266861 | − | 0.0301622i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 100.431i | 0.537062i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 113.970i | 0.603014i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 265.271i | − | 1.38885i | −0.719564 | − | 0.694426i | \(-0.755659\pi\) | ||
0.719564 | − | 0.694426i | \(-0.244341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 82.6273i | − | 0.428121i | −0.976820 | − | 0.214060i | \(-0.931331\pi\) | ||
0.976820 | − | 0.214060i | \(-0.0686689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 31.5652 | + | 279.275i | 0.161873 | + | 1.43218i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 180.771 | 0.917621 | 0.458811 | − | 0.888534i | \(-0.348276\pi\) | ||||
0.458811 | + | 0.888534i | \(0.348276\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 171.120i | 0.859901i | 0.902852 | + | 0.429951i | \(0.141469\pi\) | ||||
−0.902852 | + | 0.429951i | \(0.858531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −50.8769 | −0.253119 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 224.099i | − | 1.10394i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −210.431 | + | 23.7841i | −1.02649 | + | 0.116020i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 63.0196 | 0.304442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −126.462 | −0.605082 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −96.1529 | −0.455701 | −0.227851 | − | 0.973696i | \(-0.573170\pi\) | ||||
−0.227851 | + | 0.973696i | \(0.573170\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −391.202 | −1.83663 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.7320 | − | 263.055i | −0.138288 | − | 1.22351i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 130.401i | 0.600925i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −339.752 | −1.55138 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 394.955i | − | 1.78712i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −79.8803 | −0.358208 | −0.179104 | − | 0.983830i | \(-0.557320\pi\) | ||||
−0.179104 | + | 0.983830i | \(0.557320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −100.477 | + | 23.0069i | −0.446566 | + | 0.102253i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 229.897i | 1.01276i | 0.862310 | + | 0.506381i | \(0.169017\pi\) | ||||
−0.862310 | + | 0.506381i | \(0.830983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 132.277i | − | 0.577627i | −0.957385 | − | 0.288813i | \(-0.906739\pi\) | ||
0.957385 | − | 0.288813i | \(-0.0932607\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 92.2073i | − | 0.399166i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 81.2535i | 0.348727i | 0.984681 | + | 0.174364i | \(0.0557868\pi\) | ||||
−0.984681 | + | 0.174364i | \(0.944213\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −107.504 | + | 12.1507i | −0.457465 | + | 0.0517052i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −334.028 | −1.40940 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 317.050i | − | 1.32657i | −0.748368 | − | 0.663284i | \(-0.769162\pi\) | ||
0.748368 | − | 0.663284i | \(-0.230838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 446.725 | 1.85363 | 0.926816 | − | 0.375516i | \(-0.122534\pi\) | ||||
0.926816 | + | 0.375516i | \(0.122534\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 207.269i | − | 0.852960i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −36.6888 | + | 4.14677i | −0.149750 | + | 0.0169256i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 497.326 | 2.01347 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −96.9072 | −0.389186 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −253.434 | −1.00970 | −0.504848 | − | 0.863208i | \(-0.668451\pi\) | ||||
−0.504848 | + | 0.863208i | \(0.668451\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 60.3073 | 0.238369 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 458.119 | − | 51.7793i | 1.79655 | − | 0.203056i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 85.7608i | 0.333700i | 0.985982 | + | 0.166850i | \(0.0533595\pi\) | ||||
−0.985982 | + | 0.166850i | \(0.946641\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 64.1020 | 0.247498 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 143.231i | 0.548778i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −302.587 | −1.15052 | −0.575260 | − | 0.817971i | \(-0.695099\pi\) | ||||
−0.575260 | + | 0.817971i | \(0.695099\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −175.831 | + | 19.8735i | −0.663515 | + | 0.0749942i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 100.540i | 0.376556i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 173.339i | 0.644383i | 0.946675 | + | 0.322191i | \(0.104419\pi\) | ||||
−0.946675 | + | 0.322191i | \(0.895581\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 195.766i | 0.722383i | 0.932492 | + | 0.361191i | \(0.117630\pi\) | ||||
−0.932492 | + | 0.361191i | \(0.882370\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 362.615i | 1.32826i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −96.1529 | + | 22.0168i | −0.349647 | + | 0.0800609i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −365.213 | −1.31846 | −0.659228 | − | 0.751943i | \(-0.729117\pi\) | ||||
−0.659228 | + | 0.751943i | \(0.729117\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 83.3445i | − | 0.298726i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 268.756 | 0.956426 | 0.478213 | − | 0.878244i | \(-0.341285\pi\) | ||||
0.478213 | + | 0.878244i | \(0.341285\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 43.6357i | 0.154190i | 0.997024 | + | 0.0770949i | \(0.0245644\pi\) | ||||
−0.997024 | + | 0.0770949i | \(0.975436\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 65.2004 | + | 576.864i | 0.228773 | + | 2.02408i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −273.227 | −0.952011 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −358.879 | −1.24180 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 483.739 | 1.66233 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 226.098 | 0.771667 | 0.385833 | − | 0.922569i | \(-0.373914\pi\) | ||||
0.385833 | + | 0.922569i | \(0.373914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 80.8271 | − | 9.13554i | 0.273990 | − | 0.0309679i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 69.7077i | − | 0.234706i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −237.165 | −0.793195 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 341.555i | − | 1.13473i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −538.708 | −1.77791 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43.4299 | + | 384.248i | 0.142393 | + | 1.25983i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 172.436i | 0.561682i | 0.959754 | + | 0.280841i | \(0.0906133\pi\) | ||||
−0.959754 | + | 0.280841i | \(0.909387\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 529.218i | − | 1.71268i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 78.9131i | 0.253740i | 0.991919 | + | 0.126870i | \(0.0404931\pi\) | ||||
−0.991919 | + | 0.126870i | \(0.959507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 338.922i | − | 1.08282i | −0.840760 | − | 0.541408i | \(-0.817891\pi\) | ||
0.840760 | − | 0.541408i | \(-0.182109\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −132.150 | + | 14.9363i | −0.419522 | + | 0.0474168i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 101.278 | 0.319487 | 0.159744 | − | 0.987159i | \(-0.448933\pi\) | ||||
0.159744 | + | 0.987159i | \(0.448933\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 137.067i | 0.429676i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −127.801 | −0.398134 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 815.808i | − | 2.52572i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 378.132 | − | 86.5834i | 1.16348 | − | 0.266410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −87.4428 | −0.267409 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −139.585 | −0.424271 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 153.335 | 0.463248 | 0.231624 | − | 0.972805i | \(-0.425596\pi\) | ||||
0.231624 | + | 0.972805i | \(0.425596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40.9702 | −0.123034 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.88666 | + | 69.7776i | 0.0235423 | + | 0.208291i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 146.454i | − | 0.434581i | −0.976107 | − | 0.217291i | \(-0.930278\pi\) | ||
0.976107 | − | 0.217291i | \(-0.0697219\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 656.802 | 1.93747 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 79.7575i | − | 0.233893i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −363.737 | −1.06046 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.0928 | − | 275.095i | −0.0901240 | − | 0.797377i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 332.832i | − | 0.959169i | −0.877496 | − | 0.479585i | \(-0.840787\pi\) | ||
0.877496 | − | 0.479585i | \(-0.159213\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 307.170i | 0.880145i | 0.897962 | + | 0.440072i | \(0.145047\pi\) | ||||
−0.897962 | + | 0.440072i | \(0.854953\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 274.133i | 0.781007i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 177.788i | 0.503650i | 0.967773 | + | 0.251825i | \(0.0810308\pi\) | ||||
−0.967773 | + | 0.251825i | \(0.918969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 60.6420 | + | 536.533i | 0.170823 | + | 1.51136i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 594.830 | 1.66619 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 447.742i | − | 1.24719i | −0.781746 | − | 0.623596i | \(-0.785671\pi\) | ||
0.781746 | − | 0.623596i | \(-0.214329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 666.265 | 1.84561 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 381.935i | − | 1.05216i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 52.6665 | + | 465.970i | 0.144292 | + | 1.27663i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 417.312 | 1.13709 | 0.568545 | − | 0.822652i | \(-0.307506\pi\) | ||||
0.568545 | + | 0.822652i | \(0.307506\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 174.631 | 0.473254 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −228.302 | −0.615371 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −206.225 | −0.552882 | −0.276441 | − | 0.961031i | \(-0.589155\pi\) | ||||
−0.276441 | + | 0.961031i | \(0.589155\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 150.004 | + | 427.255i | 0.400012 | + | 1.13935i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 539.030i | − | 1.42979i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 573.943 | 1.51436 | 0.757181 | − | 0.653205i | \(-0.226576\pi\) | ||||
0.757181 | + | 0.653205i | \(0.226576\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 693.555i | − | 1.82035i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 144.219 | 0.376551 | 0.188275 | − | 0.982116i | \(-0.439710\pi\) | ||||
0.188275 | + | 0.982116i | \(0.439710\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −126.462 | + | 14.2935i | −0.328473 | + | 0.0371259i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 218.302i | 0.564087i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 470.358i | 1.20915i | 0.796550 | + | 0.604573i | \(0.206656\pi\) | ||||
−0.796550 | + | 0.604573i | \(0.793344\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 389.043i | 0.994995i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 812.751i | − | 2.06807i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 51.7793 | + | 458.119i | 0.131087 | + | 1.15980i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 337.011 | 0.848895 | 0.424448 | − | 0.905453i | \(-0.360468\pi\) | ||||
0.424448 | + | 0.905453i | \(0.360468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 749.009i | 1.87722i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 228.739 | 0.570421 | 0.285210 | − | 0.958465i | \(-0.407937\pi\) | ||||
0.285210 | + | 0.958465i | \(0.407937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 313.655i | 0.778301i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −502.341 | + | 56.7775i | −1.24035 | + | 0.140191i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −39.2069 | −0.0963315 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −576.263 | −1.40896 | −0.704478 | − | 0.709726i | \(-0.748819\pi\) | ||||
−0.704478 | + | 0.709726i | \(0.748819\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 202.140 | 0.491825 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 104.947 | 0.254110 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0220 | + | 132.908i | 0.0361976 | + | 0.320260i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 418.030i | 1.00247i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −435.905 | −1.04035 | −0.520173 | − | 0.854061i | \(-0.674133\pi\) | ||||
−0.520173 | + | 0.854061i | \(0.674133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 429.616i | 1.02046i | 0.860037 | + | 0.510232i | \(0.170441\pi\) | ||||
−0.860037 | + | 0.510232i | \(0.829559\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 89.2147 | 0.210909 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −142.030 | − | 620.283i | −0.334189 | − | 1.45949i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 498.915i | 1.16842i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 221.788i | − | 0.516988i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 690.856i | − | 1.60291i | −0.598053 | − | 0.801457i | \(-0.704059\pi\) | ||
0.598053 | − | 0.801457i | \(-0.295941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 70.0935i | 0.161879i | 0.996719 | + | 0.0809393i | \(0.0257920\pi\) | ||||
−0.996719 | + | 0.0809393i | \(0.974208\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 625.237 | − | 70.6678i | 1.43733 | − | 0.162455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −489.883 | −1.12101 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 816.571i | 1.86007i | 0.367469 | + | 0.930036i | \(0.380224\pi\) | ||||
−0.367469 | + | 0.930036i | \(0.619776\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 30.4470 | 0.0690407 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 199.242i | 0.449756i | 0.974387 | + | 0.224878i | \(0.0721984\pi\) | ||||
−0.974387 | + | 0.224878i | \(0.927802\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 137.891 | − | 15.5852i | 0.309867 | − | 0.0350230i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −190.659 | −0.426530 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.00187 | −0.00668567 | −0.00334283 | − | 0.999994i | \(-0.501064\pi\) | ||||
−0.00334283 | + | 0.999994i | \(0.501064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 167.115 | 0.370543 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 839.579 | 1.85337 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 497.326 | − | 56.2106i | 1.09303 | − | 0.123540i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 345.188i | 0.755336i | 0.925941 | + | 0.377668i | \(0.123274\pi\) | ||||
−0.925941 | + | 0.377668i | \(0.876726\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 449.685 | 0.979706 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 799.663i | − | 1.73463i | −0.497763 | − | 0.867313i | \(-0.665845\pi\) | ||
0.497763 | − | 0.867313i | \(-0.334155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −245.737 | −0.530749 | −0.265375 | − | 0.964145i | \(-0.585496\pi\) | ||||
−0.265375 | + | 0.964145i | \(0.585496\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −363.818 | + | 41.1208i | −0.782405 | + | 0.0884318i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 331.439i | − | 0.709719i | −0.934920 | − | 0.354860i | \(-0.884529\pi\) | ||
0.934920 | − | 0.354860i | \(-0.115471\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 90.6004i | 0.193178i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 589.240i | 1.25104i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 208.907i | 0.441663i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 781.060 | − | 178.844i | 1.64434 | − | 0.376515i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 145.918 | 0.305907 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 310.676i | 0.648592i | 0.945956 | + | 0.324296i | \(0.105127\pi\) | ||||
−0.945956 | + | 0.324296i | \(0.894873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 154.186 | 0.320552 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 357.188i | − | 0.739520i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −74.9865 | − | 663.447i | −0.154611 | − | 1.36793i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −173.615 | −0.356498 | −0.178249 | − | 0.983985i | \(-0.557043\pi\) | ||||
−0.178249 | + | 0.983985i | \(0.557043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1062.57 | 2.17295 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 470.930 | 0.959125 | 0.479563 | − | 0.877508i | \(-0.340795\pi\) | ||||
0.479563 | + | 0.877508i | \(0.340795\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −884.219 | −1.79355 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 80.8271 | − | 9.13554i | 0.163287 | − | 0.0184556i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 696.644i | 1.40170i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −114.424 | −0.229307 | −0.114653 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114653 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 894.540i | 1.78551i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −279.067 | −0.554806 | −0.277403 | − | 0.960754i | \(-0.589474\pi\) | ||||
−0.277403 | + | 0.960754i | \(0.589474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 83.5076 | + | 738.837i | 0.165362 | + | 1.46304i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 259.989i | 0.512799i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 332.155i | 0.652564i | 0.945272 | + | 0.326282i | \(0.105796\pi\) | ||||
−0.945272 | + | 0.326282i | \(0.894204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 605.023i | 1.18400i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 566.243i | 1.10379i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −725.821 | + | 82.0364i | −1.40936 | + | 0.159294i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 85.3750 | 0.165135 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 278.565i | 0.536734i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −746.924 | −1.43364 | −0.716818 | − | 0.697260i | \(-0.754402\pi\) | ||||
−0.716818 | + | 0.697260i | \(0.754402\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 584.018i | − | 1.11667i | −0.829616 | − | 0.558335i | \(-0.811441\pi\) | ||
0.829616 | − | 0.558335i | \(-0.188559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 130.401 | + | 569.494i | 0.248382 | + | 1.08475i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 514.517 | 0.976312 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −295.384 | −0.558383 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −67.0761 | −0.126320 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −657.198 | −1.23302 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.8110 | + | 175.279i | 0.0370300 | + | 0.327624i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1032.43i | − | 1.92259i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.1366 | 0.0540567 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 271.905i | − | 0.502598i | −0.967910 | − | 0.251299i | \(-0.919142\pi\) | ||
0.967910 | − | 0.251299i | \(-0.0808577\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −640.360 | −1.17930 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.5549 | + | 119.928i | 0.0248714 | + | 0.220051i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.1146i | 0.0349445i | 0.999847 | + | 0.0174722i | \(0.00556187\pi\) | ||||
−0.999847 | + | 0.0174722i | \(0.994438\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 318.877i | − | 0.580832i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1113.41i | − | 2.02070i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 594.830i | 1.07564i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 20.2140 | + | 178.844i | 0.0364216 | + | 0.322242i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −868.015 | −1.55837 | −0.779187 | − | 0.626791i | \(-0.784368\pi\) | ||||
−0.779187 | + | 0.626791i | \(0.784368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 821.548i | − | 1.46967i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −363.818 | −0.648517 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 912.726i | 1.62118i | 0.585612 | + | 0.810592i | \(0.300854\pi\) | ||||
−0.585612 | + | 0.810592i | \(0.699146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −101.814 | − | 900.803i | −0.180202 | − | 1.59434i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −652.248 | −1.15035 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 115.434 | 0.202871 | 0.101436 | − | 0.994842i | \(-0.467656\pi\) | ||||
0.101436 | + | 0.994842i | \(0.467656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 347.158 | 0.607982 | 0.303991 | − | 0.952675i | \(-0.401681\pi\) | ||||
0.303991 | + | 0.952675i | \(0.401681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 960.965 | 1.67708 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −372.472 | + | 85.2874i | −0.647778 | + | 0.148326i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 70.4792i | 0.122148i | 0.998133 | + | 0.0610738i | \(0.0194525\pi\) | ||||
−0.998133 | + | 0.0610738i | \(0.980547\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 299.324 | 0.516968 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 172.570i | 0.297022i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 139.638 | 0.239515 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −317.862 | + | 35.9265i | −0.543353 | + | 0.0614129i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 461.461i | − | 0.786134i | −0.919510 | − | 0.393067i | \(-0.871414\pi\) | ||
0.919510 | − | 0.393067i | \(-0.128586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 647.879i | 1.09996i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 654.859i | 1.10805i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 222.428i | 0.375090i | 0.982256 | + | 0.187545i | \(0.0600531\pi\) | ||||
−0.982256 | + | 0.187545i | \(0.939947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −92.2073 | − | 815.808i | −0.154970 | − | 1.37111i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −619.898 | −1.03835 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 206.571i | − | 0.344861i | −0.985022 | − | 0.172430i | \(-0.944838\pi\) | ||
0.985022 | − | 0.172430i | \(-0.0551620\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −102.941 | −0.171283 | −0.0856416 | − | 0.996326i | \(-0.527294\pi\) | ||||
−0.0856416 | + | 0.996326i | \(0.527294\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 57.9064i | − | 0.0960306i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −523.824 | + | 59.2055i | −0.865824 | + | 0.0978604i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 857.703 | 1.41302 | 0.706510 | − | 0.707703i | \(-0.250269\pi\) | ||||
0.706510 | + | 0.707703i | \(0.250269\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 811.818 | 1.33303 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −335.747 | −0.549504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −299.711 | −0.488925 | −0.244462 | − | 0.969659i | \(-0.578611\pi\) | ||||
−0.244462 | + | 0.969659i | \(0.578611\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −86.1599 | − | 762.304i | −0.140097 | − | 1.23952i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 189.334i | − | 0.306863i | −0.988159 | − | 0.153431i | \(-0.950968\pi\) | ||
0.988159 | − | 0.153431i | \(-0.0490324\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −269.762 | −0.435803 | −0.217901 | − | 0.975971i | \(-0.569921\pi\) | ||||
−0.217901 | + | 0.975971i | \(0.569921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 270.030i | − | 0.434831i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 179.040 | 0.287384 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 562.727 | − | 271.962i | 0.900364 | − | 0.435138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 458.119i | − | 0.730653i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 252.924i | − | 0.402105i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 569.026i | 0.901785i | 0.892578 | + | 0.450892i | \(0.148894\pi\) | ||||
−0.892578 | + | 0.450892i | \(0.851106\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 348.322i | − | 0.550272i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −951.209 | + | 107.511i | −1.49797 | + | 0.169309i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −114.583 | −0.179879 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 445.254i | − | 0.696798i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −173.093 | −0.270036 | −0.135018 | − | 0.990843i | \(-0.543109\pi\) | ||||
−0.135018 | + | 0.990843i | \(0.543109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 551.298i | − | 0.857384i | −0.903451 | − | 0.428692i | \(-0.858974\pi\) | ||
0.903451 | − | 0.428692i | \(-0.141026\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 952.938 | − | 107.706i | 1.47742 | − | 0.166987i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −518.940 | −0.802071 | −0.401036 | − | 0.916062i | \(-0.631350\pi\) | ||||
−0.401036 | + | 0.916062i | \(0.631350\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −64.1893 | −0.0989050 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −472.388 | −0.725634 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −150.509 | −0.230489 | −0.115245 | − | 0.993337i | \(-0.536765\pi\) | ||||
−0.115245 | + | 0.993337i | \(0.536765\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1114.69 | + | 125.988i | −1.70181 | + | 0.192348i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 386.695i | − | 0.588577i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −397.420 | −0.603065 | −0.301533 | − | 0.953456i | \(-0.597498\pi\) | ||||
−0.301533 | + | 0.953456i | \(0.597498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 673.953i | 1.01960i | 0.860294 | + | 0.509798i | \(0.170280\pi\) | ||||
−0.860294 | + | 0.509798i | \(0.829720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1430.76 | 2.15800 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1027.27 | − | 116.107i | 1.54476 | − | 0.174597i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 530.962i | 0.796045i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 289.373i | − | 0.432546i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 305.153i | − | 0.454774i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1132.10i | − | 1.68217i | −0.540903 | − | 0.841085i | \(-0.681917\pi\) | ||
0.540903 | − | 0.841085i | \(-0.318083\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 98.5816 | + | 430.532i | 0.146047 | + | 0.637825i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1088.08 | 1.60721 | 0.803605 | − | 0.595163i | \(-0.202912\pi\) | ||||
0.803605 | + | 0.595163i | \(0.202912\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 861.431i | − | 1.26868i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −832.820 | −1.22294 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.4045i | − | 0.0357313i | −0.999840 | − | 0.0178657i | \(-0.994313\pi\) | ||
0.999840 | − | 0.0178657i | \(-0.00568712\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31.3346 | − | 277.235i | −0.0457440 | − | 0.404722i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 479.183 | 0.697500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −549.140 | −0.797010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 349.646 | 0.506001 | 0.253000 | − | 0.967466i | \(-0.418583\pi\) | ||||
0.253000 | + | 0.967466i | \(0.418583\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 104.947 | 0.151439 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 573.327 | − | 64.8007i | 0.824931 | − | 0.0932384i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1078.06i | 1.54671i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −294.347 | −0.421098 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 819.714i | 1.16935i | 0.811268 | + | 0.584675i | \(0.198778\pi\) | ||||
−0.811268 | + | 0.584675i | \(0.801222\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 318.482 | 0.453033 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −44.0170 | − | 389.443i | −0.0624355 | − | 0.552401i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 959.319i | 1.35689i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 719.231i | − | 1.01443i | −0.861819 | − | 0.507215i | \(-0.830675\pi\) | ||
0.861819 | − | 0.507215i | \(-0.169325\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 380.180i | − | 0.534712i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 308.961i | − | 0.433325i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −304.182 | + | 34.3803i | −0.425429 | + | 0.0480844i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1148.54 | 1.60187 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 600.046i | − | 0.834556i | −0.908779 | − | 0.417278i | \(-0.862984\pi\) | ||
0.908779 | − | 0.417278i | \(-0.137016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −942.419 | −1.30710 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1618.30i | 2.23831i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −193.842 | − | 846.557i | −0.267368 | − | 1.16766i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −452.279 | −0.622117 | −0.311059 | − | 0.950391i | \(-0.600684\pi\) | ||||
−0.311059 | + | 0.950391i | \(0.600684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −159.121 | −0.218273 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1347.66 | −1.84358 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 773.541 | 1.05531 | 0.527654 | − | 0.849459i | \(-0.323072\pi\) | ||||
0.527654 | + | 0.849459i | \(0.323072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.0220 | − | 132.908i | −0.0204381 | − | 0.180827i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 55.4142i | − | 0.0751889i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.5394 | 0.0467381 | 0.0233690 | − | 0.999727i | \(-0.492561\pi\) | ||||
0.0233690 | + | 0.999727i | \(0.492561\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1801.61i | 2.43132i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 396.078 | 0.533079 | 0.266539 | − | 0.963824i | \(-0.414120\pi\) | ||||
0.266539 | + | 0.963824i | \(0.414120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.5549 | + | 261.488i | 0.0396710 | + | 0.350991i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 110.297i | − | 0.147653i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 227.585i | 0.303852i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 850.079i | − | 1.13193i | −0.824429 | − | 0.565965i | \(-0.808504\pi\) | ||
0.824429 | − | 0.565965i | \(-0.191496\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 918.084i | − | 1.21924i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −130.147 | − | 1151.48i | −0.172380 | − | 1.52514i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 458.313 | 0.605433 | 0.302717 | − | 0.953081i | \(-0.402106\pi\) | ||||
0.302717 | + | 0.953081i | \(0.402106\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 218.468i | 0.287837i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 788.678 | 1.03637 | 0.518185 | − | 0.855268i | \(-0.326608\pi\) | ||||
0.518185 | + | 0.855268i | \(0.326608\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 155.716i | 0.204084i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 58.9335 | + | 521.417i | 0.0770372 | + | 0.681590i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 252.432 | 0.329116 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 980.098 | 1.27451 | 0.637255 | − | 0.770653i | \(-0.280070\pi\) | ||||
0.637255 | + | 0.770653i | \(0.280070\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −310.676 | −0.402951 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 193.305 | 0.250071 | 0.125036 | − | 0.992152i | \(-0.460095\pi\) | ||||
0.125036 | + | 0.992152i | \(0.460095\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 112.794 | + | 492.602i | 0.145541 | + | 0.635615i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 232.215i | 0.298861i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1357.49 | −1.74261 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 426.091i | − | 0.545571i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 613.726 | 0.783813 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 808.142 | − | 91.3408i | 1.02948 | − | 0.116358i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 679.927i | − | 0.863948i | −0.901886 | − | 0.431974i | \(-0.857817\pi\) | ||
0.901886 | − | 0.431974i | \(-0.142183\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1096.15i | − | 1.38928i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1169.62i | − | 1.47866i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1200.05i | 1.51330i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −71.9933 | − | 636.964i | −0.0905576 | − | 0.801212i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 324.477 | 0.407124 | 0.203562 | − | 0.979062i | \(-0.434748\pi\) | ||||
0.203562 | + | 0.979062i | \(0.434748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 550.755i | 0.689306i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −114.432 | −0.142861 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 370.052i | − | 0.460837i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −489.883 | + | 55.3693i | −0.608550 | + | 0.0687818i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −627.935 | −0.778110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −392.712 | −0.485429 | −0.242714 | − | 0.970098i | \(-0.578038\pi\) | ||||
−0.242714 | + | 0.970098i | \(0.578038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −606.480 | −0.747818 | −0.373909 | − | 0.927465i | \(-0.621983\pi\) | ||||
−0.373909 | + | 0.927465i | \(0.621983\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −709.178 | −0.872297 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −164.714 | − | 1457.32i | −0.202103 | − | 1.78812i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1696.97i | − | 2.07707i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −412.717 | −0.503928 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 750.634i | 0.914293i | 0.889391 | + | 0.457146i | \(0.151128\pi\) | ||||
−0.889391 | + | 0.457146i | \(0.848872\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −557.389 | −0.677265 | −0.338632 | − | 0.940919i | \(-0.609964\pi\) | ||||
−0.338632 | + | 0.940919i | \(0.609964\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −79.7575 | − | 348.322i | −0.0966758 | − | 0.422208i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1394.76i | − | 1.68652i | −0.537502 | − | 0.843262i | \(-0.680632\pi\) | ||
0.537502 | − | 0.843262i | \(-0.319368\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 392.570i | − | 0.473547i | −0.971565 | − | 0.236773i | \(-0.923910\pi\) | ||
0.971565 | − | 0.236773i | \(-0.0760899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1323.01i | − | 1.59207i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 187.960i | 0.225643i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1226.86 | − | 138.667i | 1.46929 | − | 0.166068i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −357.120 | −0.426667 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 10.8057i | − | 0.0128793i | −0.999979 | − | 0.00643963i | \(-0.997950\pi\) | ||
0.999979 | − | 0.00643963i | \(-0.00204981\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −365.773 | −0.434926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 973.590i | 1.15491i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 356.574 | − | 40.3021i | 0.421981 | − | 0.0476947i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −680.142 | −0.803001 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −158.074 | −0.186188 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −151.878 | −0.178470 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −222.965 | −0.261389 | −0.130695 | − | 0.991423i | \(-0.541721\pi\) | ||||
−0.130695 | + | 0.991423i | \(0.541721\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −656.567 | + | 74.2090i | −0.767915 | + | 0.0867941i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1258.77i | 1.46880i | 0.678714 | + | 0.734402i | \(0.262537\pi\) | ||||
−0.678714 | + | 0.734402i | \(0.737463\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −667.122 | −0.776626 | −0.388313 | − | 0.921527i | \(-0.626942\pi\) | ||||
−0.388313 | + | 0.921527i | \(0.626942\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 989.788i | − | 1.14958i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 235.010 | 0.272317 | 0.136159 | − | 0.990687i | \(-0.456524\pi\) | ||||
0.136159 | + | 0.990687i | \(0.456524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 382.051 | − | 43.1816i | 0.441678 | − | 0.0499209i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1300.07i | − | 1.49950i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 363.818i | − | 0.418663i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 217.923i | 0.250198i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 550.576i | 0.630671i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 760.846 | − | 267.124i | 0.869539 | − | 0.305285i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1577.19 | −1.79840 | −0.899198 | − | 0.437543i | \(-0.855849\pi\) | ||||
−0.899198 | + | 0.437543i | \(0.855849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 819.060i | 0.931809i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −220.324 | −0.250084 | −0.125042 | − | 0.992151i | \(-0.539907\pi\) | ||||
−0.125042 | + | 0.992151i | \(0.539907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1144.57i | 1.29623i | 0.761542 | + | 0.648115i | \(0.224442\pi\) | ||||
−0.761542 | + | 0.648115i | \(0.775558\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.0943 | + | 292.803i | 0.0373946 | + | 0.330851i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −773.413 | −0.871942 | −0.435971 | − | 0.899961i | \(-0.643595\pi\) | ||||
−0.435971 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1235.07 | −1.38928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 398.937 | 0.447741 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −693.510 | −0.776607 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1415.98 | + | 160.042i | −1.58210 | + | 0.178818i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 859.151i | − | 0.957805i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 702.207 | 0.781098 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 900.803i | 0.999781i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1237.31 | 1.37022 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 99.2651 | + | 878.253i | 0.109685 | + | 0.970445i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 271.474i | 0.299310i | 0.988738 | + | 0.149655i | \(0.0478163\pi\) | ||||
−0.988738 | + | 0.149655i | \(0.952184\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 613.140i | − | 0.674522i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 663.176i | 0.727965i | 0.931406 | + | 0.363983i | \(0.118583\pi\) | ||||
−0.931406 | + | 0.363983i | \(0.881417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 105.550i | − | 0.115608i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1391.97 | + | 157.329i | −1.52128 | + | 0.171944i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1447.33 | −1.57833 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1017.31i | − | 1.10698i | −0.832856 | − | 0.553490i | \(-0.813296\pi\) | ||
0.832856 | − | 0.553490i | \(-0.186704\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −624.665 | −0.678246 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1675.65i | 1.81544i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 242.151 | − | 55.4470i | 0.261785 | − | 0.0599427i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 602.338 | 0.649772 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −800.790 | −0.861991 | −0.430996 | − | 0.902354i | \(-0.641838\pi\) | ||||
−0.430996 | + | 0.902354i | \(0.641838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −236.680 | −0.254221 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −285.869 | −0.306398 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 56.3971 | + | 498.976i | 0.0603177 | + | 0.533664i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 795.927i | 0.849441i | 0.905324 | + | 0.424721i | \(0.139628\pi\) | ||||
−0.905324 | + | 0.424721i | \(0.860372\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1227.77 | 1.30753 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 159.663i | − | 0.169674i | −0.996395 | − | 0.0848368i | \(-0.972963\pi\) | ||
0.996395 | − | 0.0848368i | \(-0.0270369\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 647.362 | 0.686492 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 64.0000 | + | 566.243i | 0.0677249 | + | 0.599199i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 138.776i | − | 0.146543i | −0.997312 | − | 0.0732716i | \(-0.976656\pi\) | ||
0.997312 | − | 0.0732716i | \(-0.0233440\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1455.27i | 1.53348i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 366.886i | 0.385790i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 141.561i | − | 0.148542i | −0.997238 | − | 0.0742711i | \(-0.976337\pi\) | ||
0.997238 | − | 0.0742711i | \(-0.0236630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −148.963 | − | 1317.96i | −0.155983 | − | 1.38006i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −496.535 | −0.518846 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 359.966i | − | 0.375356i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 552.394 | 0.574811 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 145.459i | − | 0.151048i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −46.3996 | − | 410.523i | −0.0480825 | − | 0.425412i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 278.872 | 0.288389 | 0.144194 | − | 0.989549i | \(-0.453941\pi\) | ||||
0.144194 | + | 0.989549i | \(0.453941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2955.33 | 3.04988 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 88.2616 | 0.0908977 | 0.0454488 | − | 0.998967i | \(-0.485528\pi\) | ||||
0.0454488 | + | 0.998967i | \(0.485528\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 744.417 | 0.765074 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 313.655 | + | 1369.81i | 0.321698 | + | 1.40494i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 521.989i | 0.534277i | 0.963658 | + | 0.267139i | \(0.0860782\pi\) | ||||
−0.963658 | + | 0.267139i | \(0.913922\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −109.507 | −0.111856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 99.5246i | − | 0.101452i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1819.43 | 1.85090 | 0.925448 | − | 0.378876i | \(-0.123689\pi\) | ||||
0.925448 | + | 0.378876i | \(0.123689\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 898.138 | − | 101.513i | 0.911815 | − | 0.103059i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 505.659i | − | 0.512319i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 809.252i | 0.818253i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 593.672i | 0.599063i | 0.954086 | + | 0.299532i | \(0.0968304\pi\) | ||||
−0.954086 | + | 0.299532i | \(0.903170\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 555.469i | 0.559385i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 96.0931 | + | 850.189i | 0.0965760 | + | 0.854461i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −639.235 | −0.641158 | −0.320579 | − | 0.947222i | \(-0.603878\pi\) | ||||
−0.320579 | + | 0.947222i | \(0.603878\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 175.552i | 0.175727i |
(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 | 640.3.e.i.319.15 | yes | 16 | |
4.3 | odd | 2 | inner | 640.3.e.i.319.3 | yes | 16 | |
5.4 | even | 2 | inner | 640.3.e.i.319.1 | ✓ | 16 | |
8.3 | odd | 2 | inner | 640.3.e.i.319.14 | yes | 16 | |
8.5 | even | 2 | inner | 640.3.e.i.319.2 | yes | 16 | |
16.3 | odd | 4 | 1280.3.h.l.1279.7 | 8 | |||
16.5 | even | 4 | 1280.3.h.h.1279.8 | 8 | |||
16.11 | odd | 4 | 1280.3.h.h.1279.2 | 8 | |||
16.13 | even | 4 | 1280.3.h.l.1279.1 | 8 | |||
20.19 | odd | 2 | inner | 640.3.e.i.319.13 | yes | 16 | |
40.19 | odd | 2 | inner | 640.3.e.i.319.4 | yes | 16 | |
40.29 | even | 2 | inner | 640.3.e.i.319.16 | yes | 16 | |
80.19 | odd | 4 | 1280.3.h.l.1279.2 | 8 | |||
80.29 | even | 4 | 1280.3.h.l.1279.8 | 8 | |||
80.59 | odd | 4 | 1280.3.h.h.1279.7 | 8 | |||
80.69 | even | 4 | 1280.3.h.h.1279.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
640.3.e.i.319.1 | ✓ | 16 | 5.4 | even | 2 | inner | |
640.3.e.i.319.2 | yes | 16 | 8.5 | even | 2 | inner | |
640.3.e.i.319.3 | yes | 16 | 4.3 | odd | 2 | inner | |
640.3.e.i.319.4 | yes | 16 | 40.19 | odd | 2 | inner | |
640.3.e.i.319.13 | yes | 16 | 20.19 | odd | 2 | inner | |
640.3.e.i.319.14 | yes | 16 | 8.3 | odd | 2 | inner | |
640.3.e.i.319.15 | yes | 16 | 1.1 | even | 1 | trivial | |
640.3.e.i.319.16 | yes | 16 | 40.29 | even | 2 | inner | |
1280.3.h.h.1279.1 | 8 | 80.69 | even | 4 | |||
1280.3.h.h.1279.2 | 8 | 16.11 | odd | 4 | |||
1280.3.h.h.1279.7 | 8 | 80.59 | odd | 4 | |||
1280.3.h.h.1279.8 | 8 | 16.5 | even | 4 | |||
1280.3.h.l.1279.1 | 8 | 16.13 | even | 4 | |||
1280.3.h.l.1279.2 | 8 | 80.19 | odd | 4 | |||
1280.3.h.l.1279.7 | 8 | 16.3 | odd | 4 | |||
1280.3.h.l.1279.8 | 8 | 80.29 | even | 4 |