Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,3,Mod(701,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.d (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: | \(36.7848356886\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.1 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.701 |
Dual form | 1350.3.d.l.701.3 |
$q$-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 \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.41421i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.24264 | −1.17752 | −0.588760 | − | 0.808308i | \(-0.700384\pi\) | ||||
−0.588760 | + | 0.808308i | \(0.700384\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 3.00000i | − 0.272727i | −0.990659 | − | 0.136364i | \(-0.956458\pi\) | ||||
0.990659 | − | 0.136364i | \(-0.0435416\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.4853 | 1.03733 | 0.518665 | − | 0.854978i | \(-0.326429\pi\) | ||||
0.518665 | + | 0.854978i | \(0.326429\pi\) | |||||||
\(14\) | 11.6569i | 0.832632i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 16.2426i | 0.955449i | 0.878510 | + | 0.477725i | \(0.158538\pi\) | ||||
−0.878510 | + | 0.477725i | \(0.841462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.9706 | 1.31424 | 0.657120 | − | 0.753786i | \(-0.271774\pi\) | ||||
0.657120 | + | 0.753786i | \(0.271774\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.24264 | −0.192847 | ||||||||
\(23\) | − 23.4853i | − 1.02110i | −0.859848 | − | 0.510550i | \(-0.829442\pi\) | ||||
0.859848 | − | 0.510550i | \(-0.170558\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 19.0711i | − 0.733503i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.4853 | 0.588760 | ||||||||
\(29\) | − 40.9706i | − 1.41278i | −0.707824 | − | 0.706389i | \(-0.750323\pi\) | ||||
0.707824 | − | 0.706389i | \(-0.249677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.2132 | −0.426232 | −0.213116 | − | 0.977027i | \(-0.568361\pi\) | ||||
−0.213116 | + | 0.977027i | \(0.568361\pi\) | |||||||
\(32\) | − 5.65685i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 22.9706 | 0.675605 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14.4558 | −0.390698 | −0.195349 | − | 0.980734i | \(-0.562584\pi\) | ||||
−0.195349 | + | 0.980734i | \(0.562584\pi\) | |||||||
\(38\) | − 35.3137i | − 0.929308i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 14.7868i | − 0.360654i | −0.983607 | − | 0.180327i | \(-0.942284\pi\) | ||||
0.983607 | − | 0.180327i | \(-0.0577155\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −44.9706 | −1.04583 | −0.522914 | − | 0.852386i | \(-0.675155\pi\) | ||||
−0.522914 | + | 0.852386i | \(0.675155\pi\) | |||||||
\(44\) | 6.00000i | 0.136364i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −33.2132 | −0.722026 | ||||||||
\(47\) | 23.4853i | 0.499687i | 0.968286 | + | 0.249843i | \(0.0803791\pi\) | ||||
−0.968286 | + | 0.249843i | \(0.919621\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.9411 | 0.386554 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −26.9706 | −0.518665 | ||||||||
\(53\) | 74.9117i | 1.41343i | 0.707499 | + | 0.706714i | \(0.249823\pi\) | ||||
−0.707499 | + | 0.706714i | \(0.750177\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 23.3137i | − 0.416316i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −57.9411 | −0.998985 | ||||||||
\(59\) | − 17.0589i | − 0.289133i | −0.989495 | − | 0.144567i | \(-0.953821\pi\) | ||||
0.989495 | − | 0.144567i | \(-0.0461788\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.3675 | −1.56340 | −0.781701 | − | 0.623653i | \(-0.785648\pi\) | ||||
−0.781701 | + | 0.623653i | \(0.785648\pi\) | |||||||
\(62\) | 18.6863i | 0.301392i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −81.0955 | −1.21038 | −0.605190 | − | 0.796081i | \(-0.706903\pi\) | ||||
−0.605190 | + | 0.796081i | \(0.706903\pi\) | |||||||
\(68\) | − 32.4853i | − 0.477725i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 89.4853i | − 1.26036i | −0.776451 | − | 0.630178i | \(-0.782982\pi\) | ||||
0.776451 | − | 0.630178i | \(-0.217018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.08831 | 0.0697029 | 0.0348515 | − | 0.999393i | \(-0.488904\pi\) | ||||
0.0348515 | + | 0.999393i | \(0.488904\pi\) | |||||||
\(74\) | 20.4437i | 0.276266i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −49.9411 | −0.657120 | ||||||||
\(77\) | 24.7279i | 0.321142i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.81623 | −0.0229903 | −0.0114952 | − | 0.999934i | \(-0.503659\pi\) | ||||
−0.0114952 | + | 0.999934i | \(0.503659\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −20.9117 | −0.255021 | ||||||||
\(83\) | − 109.882i | − 1.32388i | −0.749556 | − | 0.661941i | \(-0.769733\pi\) | ||||
0.749556 | − | 0.661941i | \(-0.230267\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 63.5980i | 0.739511i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.48528 | 0.0964237 | ||||||||
\(89\) | − 40.2426i | − 0.452165i | −0.974108 | − | 0.226082i | \(-0.927408\pi\) | ||||
0.974108 | − | 0.226082i | \(-0.0725918\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −111.154 | −1.22148 | ||||||||
\(92\) | 46.9706i | 0.510550i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 33.2132 | 0.353332 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −160.765 | −1.65737 | −0.828683 | − | 0.559718i | \(-0.810909\pi\) | ||||
−0.828683 | + | 0.559718i | \(0.810909\pi\) | |||||||
\(98\) | − 26.7868i | − 0.273335i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 171.037i | − 1.69343i | −0.532046 | − | 0.846716i | \(-0.678576\pi\) | ||||
0.532046 | − | 0.846716i | \(-0.321424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −117.095 | −1.13685 | −0.568425 | − | 0.822735i | \(-0.692447\pi\) | ||||
−0.568425 | + | 0.822735i | \(0.692447\pi\) | |||||||
\(104\) | 38.1421i | 0.366751i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 105.941 | 0.999445 | ||||||||
\(107\) | − 135.853i | − 1.26965i | −0.772655 | − | 0.634826i | \(-0.781072\pi\) | ||||
0.772655 | − | 0.634826i | \(-0.218928\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 188.853 | 1.73259 | 0.866297 | − | 0.499529i | \(-0.166493\pi\) | ||||
0.866297 | + | 0.499529i | \(0.166493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −32.9706 | −0.294380 | ||||||||
\(113\) | 69.2132i | 0.612506i | 0.951950 | + | 0.306253i | \(0.0990754\pi\) | ||||
−0.951950 | + | 0.306253i | \(0.900925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 81.9411i | 0.706389i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.1249 | −0.204448 | ||||||||
\(119\) | − 133.882i | − 1.12506i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 112.000 | 0.925620 | ||||||||
\(122\) | 134.870i | 1.10549i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 26.4264 | 0.213116 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −206.919 | −1.62928 | −0.814641 | − | 0.579965i | \(-0.803066\pi\) | ||||
−0.814641 | + | 0.579965i | \(0.803066\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 155.735i | 1.18882i | 0.804163 | + | 0.594409i | \(0.202614\pi\) | ||||
−0.804163 | + | 0.594409i | \(0.797386\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −205.823 | −1.54754 | ||||||||
\(134\) | 114.686i | 0.855868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −45.9411 | −0.337802 | ||||||||
\(137\) | − 23.1472i | − 0.168958i | −0.996425 | − | 0.0844788i | \(-0.973077\pi\) | ||||
0.996425 | − | 0.0844788i | \(-0.0269225\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 61.0955 | 0.439536 | 0.219768 | − | 0.975552i | \(-0.429470\pi\) | ||||
0.219768 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −126.551 | −0.891206 | ||||||||
\(143\) | − 40.4558i | − 0.282908i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − 7.19596i | − 0.0492874i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 28.9117 | 0.195349 | ||||||||
\(149\) | 140.007i | 0.939645i | 0.882761 | + | 0.469823i | \(0.155682\pi\) | ||||
−0.882761 | + | 0.469823i | \(0.844318\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 29.0883 | 0.192638 | 0.0963189 | − | 0.995351i | \(-0.469293\pi\) | ||||
0.0963189 | + | 0.995351i | \(0.469293\pi\) | |||||||
\(152\) | 70.6274i | 0.464654i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 34.9706 | 0.227082 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −185.706 | −1.18284 | −0.591419 | − | 0.806364i | \(-0.701432\pi\) | ||||
−0.591419 | + | 0.806364i | \(0.701432\pi\) | |||||||
\(158\) | 2.56854i | 0.0162566i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 193.581i | 1.20236i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 241.698 | 1.48281 | 0.741406 | − | 0.671056i | \(-0.234159\pi\) | ||||
0.741406 | + | 0.671056i | \(0.234159\pi\) | |||||||
\(164\) | 29.5736i | 0.180327i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −155.397 | −0.936126 | ||||||||
\(167\) | − 286.279i | − 1.71425i | −0.515111 | − | 0.857123i | \(-0.672249\pi\) | ||||
0.515111 | − | 0.857123i | \(-0.327751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8528 | 0.0760522 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 89.9411 | 0.522914 | ||||||||
\(173\) | 220.846i | 1.27656i | 0.769802 | + | 0.638282i | \(0.220355\pi\) | ||||
−0.769802 | + | 0.638282i | \(0.779645\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − 12.0000i | − 0.0681818i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −56.9117 | −0.319729 | ||||||||
\(179\) | − 245.912i | − 1.37381i | −0.726748 | − | 0.686904i | \(-0.758969\pi\) | ||||
0.726748 | − | 0.686904i | \(-0.241031\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −267.309 | −1.47684 | −0.738422 | − | 0.674339i | \(-0.764429\pi\) | ||||
−0.738422 | + | 0.674339i | \(0.764429\pi\) | |||||||
\(182\) | 157.196i | 0.863714i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 66.4264 | 0.361013 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 48.7279 | 0.260577 | ||||||||
\(188\) | − 46.9706i | − 0.249843i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 346.441i | − 1.81383i | −0.421318 | − | 0.906913i | \(-0.638432\pi\) | ||||
0.421318 | − | 0.906913i | \(-0.361568\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 34.9117 | 0.180890 | 0.0904448 | − | 0.995901i | \(-0.471171\pi\) | ||||
0.0904448 | + | 0.995901i | \(0.471171\pi\) | |||||||
\(194\) | 227.355i | 1.17193i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −37.8823 | −0.193277 | ||||||||
\(197\) | − 189.941i | − 0.964168i | −0.876125 | − | 0.482084i | \(-0.839880\pi\) | ||||
0.876125 | − | 0.482084i | \(-0.160120\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 137.213 | 0.689514 | 0.344757 | − | 0.938692i | \(-0.387961\pi\) | ||||
0.344757 | + | 0.938692i | \(0.387961\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −241.882 | −1.19744 | ||||||||
\(203\) | 337.706i | 1.66357i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 165.598i | 0.803874i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 53.9411 | 0.259332 | ||||||||
\(209\) | − 74.9117i | − 0.358429i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −173.706 | −0.823249 | −0.411625 | − | 0.911353i | \(-0.635039\pi\) | ||||
−0.411625 | + | 0.911353i | \(0.635039\pi\) | |||||||
\(212\) | − 149.823i | − 0.706714i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −192.125 | −0.897780 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 108.912 | 0.501897 | ||||||||
\(218\) | − 267.078i | − 1.22513i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 219.037i | 0.991116i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −167.029 | −0.749011 | −0.374505 | − | 0.927225i | \(-0.622188\pi\) | ||||
−0.374505 | + | 0.927225i | \(0.622188\pi\) | |||||||
\(224\) | 46.6274i | 0.208158i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 97.8823 | 0.433107 | ||||||||
\(227\) | 295.441i | 1.30150i | 0.759292 | + | 0.650750i | \(0.225546\pi\) | ||||
−0.759292 | + | 0.650750i | \(0.774454\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −189.485 | −0.827447 | −0.413723 | − | 0.910403i | \(-0.635772\pi\) | ||||
−0.413723 | + | 0.910403i | \(0.635772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 115.882 | 0.499492 | ||||||||
\(233\) | 139.757i | 0.599817i | 0.953968 | + | 0.299908i | \(0.0969562\pi\) | ||||
−0.953968 | + | 0.299908i | \(0.903044\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 34.1177i | 0.144567i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −189.338 | −0.795538 | ||||||||
\(239\) | − 260.397i | − 1.08953i | −0.838590 | − | 0.544764i | \(-0.816619\pi\) | ||||
0.838590 | − | 0.544764i | \(-0.183381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −85.8528 | −0.356236 | −0.178118 | − | 0.984009i | \(-0.557001\pi\) | ||||
−0.178118 | + | 0.984009i | \(0.557001\pi\) | |||||||
\(242\) | − 158.392i | − 0.654512i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 190.735 | 0.781701 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 336.735 | 1.36330 | ||||||||
\(248\) | − 37.3726i | − 0.150696i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 340.529i | 1.35669i | 0.734744 | + | 0.678345i | \(0.237302\pi\) | ||||
−0.734744 | + | 0.678345i | \(0.762698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −70.4558 | −0.278482 | ||||||||
\(254\) | 292.627i | 1.15208i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 375.889i | − 1.46260i | −0.682053 | − | 0.731302i | \(-0.738913\pi\) | ||||
0.682053 | − | 0.731302i | \(-0.261087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 119.154 | 0.460055 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 220.243 | 0.840621 | ||||||||
\(263\) | − 265.014i | − 1.00766i | −0.863803 | − | 0.503829i | \(-0.831924\pi\) | ||||
0.863803 | − | 0.503829i | \(-0.168076\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 291.078i | 1.09428i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 162.191 | 0.605190 | ||||||||
\(269\) | 157.706i | 0.586266i | 0.956072 | + | 0.293133i | \(0.0946979\pi\) | ||||
−0.956072 | + | 0.293133i | \(0.905302\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −58.1766 | −0.214674 | −0.107337 | − | 0.994223i | \(-0.534232\pi\) | ||||
−0.107337 | + | 0.994223i | \(0.534232\pi\) | |||||||
\(272\) | 64.9706i | 0.238862i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −32.7351 | −0.119471 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −170.118 | −0.614143 | −0.307072 | − | 0.951686i | \(-0.599349\pi\) | ||||
−0.307072 | + | 0.951686i | \(0.599349\pi\) | |||||||
\(278\) | − 86.4020i | − 0.310799i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 222.323i | − 0.791185i | −0.918426 | − | 0.395592i | \(-0.870539\pi\) | ||||
0.918426 | − | 0.395592i | \(-0.129461\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.9706 | 0.0882352 | 0.0441176 | − | 0.999026i | \(-0.485952\pi\) | ||||
0.0441176 | + | 0.999026i | \(0.485952\pi\) | |||||||
\(284\) | 178.971i | 0.630178i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −57.2132 | −0.200046 | ||||||||
\(287\) | 121.882i | 0.424677i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 25.1766 | 0.0871163 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10.1766 | −0.0348515 | ||||||||
\(293\) | 506.683i | 1.72929i | 0.502379 | + | 0.864647i | \(0.332458\pi\) | ||||
−0.502379 | + | 0.864647i | \(0.667542\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 40.8873i | − 0.138133i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 198.000 | 0.664430 | ||||||||
\(299\) | − 316.706i | − 1.05922i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 370.676 | 1.23148 | ||||||||
\(302\) | − 41.1371i | − 0.136216i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 99.8823 | 0.328560 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −216.360 | −0.704757 | −0.352378 | − | 0.935858i | \(-0.614627\pi\) | ||||
−0.352378 | + | 0.935858i | \(0.614627\pi\) | |||||||
\(308\) | − 49.4558i | − 0.160571i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.0437i | 0.0451567i | 0.999745 | + | 0.0225783i | \(0.00718752\pi\) | ||||
−0.999745 | + | 0.0225783i | \(0.992812\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 372.617 | 1.19047 | 0.595235 | − | 0.803551i | \(-0.297059\pi\) | ||||
0.595235 | + | 0.803551i | \(0.297059\pi\) | |||||||
\(314\) | 262.627i | 0.836393i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.63247 | 0.0114952 | ||||||||
\(317\) | 60.4996i | 0.190850i | 0.995437 | + | 0.0954252i | \(0.0304211\pi\) | ||||
−0.995437 | + | 0.0954252i | \(0.969579\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −122.912 | −0.385303 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 273.765 | 0.850200 | ||||||||
\(323\) | 405.588i | 1.25569i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − 341.813i | − 1.04851i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 41.8234 | 0.127510 | ||||||||
\(329\) | − 193.581i | − 0.588391i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 473.110 | 1.42933 | 0.714667 | − | 0.699465i | \(-0.246578\pi\) | ||||
0.714667 | + | 0.699465i | \(0.246578\pi\) | |||||||
\(332\) | 219.765i | 0.661941i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −404.860 | −1.21216 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 615.529 | 1.82650 | 0.913248 | − | 0.407405i | \(-0.133566\pi\) | ||||
0.913248 | + | 0.407405i | \(0.133566\pi\) | |||||||
\(338\) | − 18.1766i | − 0.0537770i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.6396i | 0.116245i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 247.765 | 0.722345 | ||||||||
\(344\) | − 127.196i | − 0.369756i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 312.323 | 0.902667 | ||||||||
\(347\) | 190.294i | 0.548399i | 0.961673 | + | 0.274199i | \(0.0884128\pi\) | ||||
−0.961673 | + | 0.274199i | \(0.911587\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −273.470 | −0.783582 | −0.391791 | − | 0.920054i | \(-0.628144\pi\) | ||||
−0.391791 | + | 0.920054i | \(0.628144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −16.9706 | −0.0482118 | ||||||||
\(353\) | − 562.087i | − 1.59232i | −0.605089 | − | 0.796158i | \(-0.706862\pi\) | ||||
0.605089 | − | 0.796158i | \(-0.293138\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 80.4853i | 0.226082i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −347.772 | −0.971429 | ||||||||
\(359\) | 256.955i | 0.715753i | 0.933769 | + | 0.357877i | \(0.116499\pi\) | ||||
−0.933769 | + | 0.357877i | \(0.883501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 262.529 | 0.727227 | ||||||||
\(362\) | 378.032i | 1.04429i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 222.309 | 0.610738 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −190.177 | −0.518192 | −0.259096 | − | 0.965852i | \(-0.583425\pi\) | ||||
−0.259096 | + | 0.965852i | \(0.583425\pi\) | |||||||
\(368\) | − 93.9411i | − 0.255275i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 617.470i | − 1.66434i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 225.882 | 0.605582 | 0.302791 | − | 0.953057i | \(-0.402082\pi\) | ||||
0.302791 | + | 0.953057i | \(0.402082\pi\) | |||||||
\(374\) | − 68.9117i | − 0.184256i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −66.4264 | −0.176666 | ||||||||
\(377\) | − 552.500i | − 1.46552i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −479.051 | −1.26399 | −0.631993 | − | 0.774974i | \(-0.717763\pi\) | ||||
−0.631993 | + | 0.774974i | \(0.717763\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −489.941 | −1.28257 | ||||||||
\(383\) | − 281.662i | − 0.735410i | −0.929943 | − | 0.367705i | \(-0.880144\pi\) | ||||
0.929943 | − | 0.367705i | \(-0.119856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 49.3726i | − 0.127908i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 321.529 | 0.828683 | ||||||||
\(389\) | − 632.382i | − 1.62566i | −0.582501 | − | 0.812830i | \(-0.697926\pi\) | ||||
0.582501 | − | 0.812830i | \(-0.302074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 381.463 | 0.975609 | ||||||||
\(392\) | 53.5736i | 0.136667i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −268.617 | −0.681770 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 511.632 | 1.28874 | 0.644372 | − | 0.764712i | \(-0.277119\pi\) | ||||
0.644372 | + | 0.764712i | \(0.277119\pi\) | |||||||
\(398\) | − 194.049i | − 0.487560i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 695.418i | 1.73421i | 0.498125 | + | 0.867105i | \(0.334022\pi\) | ||||
−0.498125 | + | 0.867105i | \(0.665978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −178.184 | −0.442143 | ||||||||
\(404\) | 342.073i | 0.846716i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 477.588 | 1.17632 | ||||||||
\(407\) | 43.3675i | 0.106554i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −508.411 | −1.24306 | −0.621530 | − | 0.783391i | \(-0.713488\pi\) | ||||
−0.621530 | + | 0.783391i | \(0.713488\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 234.191 | 0.568425 | ||||||||
\(413\) | 140.610i | 0.340460i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 76.2843i | − 0.183376i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −105.941 | −0.253448 | ||||||||
\(419\) | 53.6468i | 0.128035i | 0.997949 | + | 0.0640176i | \(0.0203914\pi\) | ||||
−0.997949 | + | 0.0640176i | \(0.979609\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 203.749 | 0.483965 | 0.241983 | − | 0.970281i | \(-0.422202\pi\) | ||||
0.241983 | + | 0.970281i | \(0.422202\pi\) | |||||||
\(422\) | 245.657i | 0.582125i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −211.882 | −0.499722 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 786.080 | 1.84094 | ||||||||
\(428\) | 271.706i | 0.634826i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 808.456i | − 1.87577i | −0.346950 | − | 0.937884i | \(-0.612782\pi\) | ||||
0.346950 | − | 0.937884i | \(-0.387218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −632.706 | −1.46121 | −0.730607 | − | 0.682798i | \(-0.760763\pi\) | ||||
−0.730607 | + | 0.682798i | \(0.760763\pi\) | |||||||
\(434\) | − 154.024i | − 0.354895i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −377.706 | −0.866297 | ||||||||
\(437\) | − 586.441i | − 1.34197i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.8305 | −0.0952859 | −0.0476430 | − | 0.998864i | \(-0.515171\pi\) | ||||
−0.0476430 | + | 0.998864i | \(0.515171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 309.765 | 0.700825 | ||||||||
\(443\) | − 487.617i | − 1.10072i | −0.834929 | − | 0.550358i | \(-0.814491\pi\) | ||||
0.834929 | − | 0.550358i | \(-0.185509\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 236.215i | 0.529631i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 65.9411 | 0.147190 | ||||||||
\(449\) | − 26.7868i | − 0.0596588i | −0.999555 | − | 0.0298294i | \(-0.990504\pi\) | ||||
0.999555 | − | 0.0298294i | \(-0.00949640\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −44.3604 | −0.0983601 | ||||||||
\(452\) | − 138.426i | − 0.306253i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 417.816 | 0.920300 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 523.382 | 1.14526 | 0.572628 | − | 0.819815i | \(-0.305924\pi\) | ||||
0.572628 | + | 0.819815i | \(0.305924\pi\) | |||||||
\(458\) | 267.973i | 0.585093i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 471.058i | − 1.02182i | −0.859635 | − | 0.510909i | \(-0.829309\pi\) | ||||
0.859635 | − | 0.510909i | \(-0.170691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 238.912 | 0.516008 | 0.258004 | − | 0.966144i | \(-0.416935\pi\) | ||||
0.258004 | + | 0.966144i | \(0.416935\pi\) | |||||||
\(464\) | − 163.882i | − 0.353195i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 197.647 | 0.424135 | ||||||||
\(467\) | 472.882i | 1.01260i | 0.862359 | + | 0.506298i | \(0.168986\pi\) | ||||
−0.862359 | + | 0.506298i | \(0.831014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 668.441 | 1.42525 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 48.2498 | 0.102224 | ||||||||
\(473\) | 134.912i | 0.285226i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 267.765i | 0.562530i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −368.257 | −0.770412 | ||||||||
\(479\) | 179.647i | 0.375045i | 0.982260 | + | 0.187523i | \(0.0600458\pi\) | ||||
−0.982260 | + | 0.187523i | \(0.939954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −194.941 | −0.405283 | ||||||||
\(482\) | 121.414i | 0.251897i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −224.000 | −0.462810 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 368.874 | 0.757442 | 0.378721 | − | 0.925511i | \(-0.376364\pi\) | ||||
0.378721 | + | 0.925511i | \(0.376364\pi\) | |||||||
\(488\) | − 269.740i | − 0.552746i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 745.882i | − 1.51911i | −0.650444 | − | 0.759554i | \(-0.725417\pi\) | ||||
0.650444 | − | 0.759554i | \(-0.274583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 665.470 | 1.34984 | ||||||||
\(494\) | − 476.215i | − 0.963999i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −52.8528 | −0.106558 | ||||||||
\(497\) | 737.595i | 1.48409i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −771.294 | −1.54568 | −0.772839 | − | 0.634602i | \(-0.781164\pi\) | ||||
−0.772839 | + | 0.634602i | \(0.781164\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 481.581 | 0.959324 | ||||||||
\(503\) | − 32.2355i | − 0.0640865i | −0.999486 | − | 0.0320432i | \(-0.989799\pi\) | ||||
0.999486 | − | 0.0320432i | \(-0.0102014\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 99.6396i | 0.196916i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 413.838 | 0.814641 | ||||||||
\(509\) | 31.7574i | 0.0623917i | 0.999513 | + | 0.0311958i | \(0.00993155\pi\) | ||||
−0.999513 | + | 0.0311958i | \(0.990068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.9411 | −0.0820766 | ||||||||
\(512\) | − 22.6274i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −531.588 | −1.03422 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 70.4558 | 0.136278 | ||||||||
\(518\) | − 168.510i | − 0.325308i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 487.404i | 0.935517i | 0.883856 | + | 0.467758i | \(0.154938\pi\) | ||||
−0.883856 | + | 0.467758i | \(0.845062\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −304.353 | −0.581937 | −0.290969 | − | 0.956733i | \(-0.593978\pi\) | ||||
−0.290969 | + | 0.956733i | \(0.593978\pi\) | |||||||
\(524\) | − 311.470i | − 0.594409i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −374.787 | −0.712522 | ||||||||
\(527\) | − 214.617i | − 0.407243i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.5584 | −0.0426436 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 411.647 | 0.773772 | ||||||||
\(533\) | − 199.404i | − 0.374117i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 229.373i | − 0.427934i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 223.029 | 0.414553 | ||||||||
\(539\) | − 56.8234i | − 0.105424i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 112.574 | 0.208084 | 0.104042 | − | 0.994573i | \(-0.466822\pi\) | ||||
0.104042 | + | 0.994573i | \(0.466822\pi\) | |||||||
\(542\) | 82.2742i | 0.151797i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 91.8823 | 0.168901 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 157.470 | 0.287880 | 0.143940 | − | 0.989586i | \(-0.454023\pi\) | ||||
0.143940 | + | 0.989586i | \(0.454023\pi\) | |||||||
\(548\) | 46.2944i | 0.0844788i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1023.06i | − 1.85673i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.9706 | 0.0270715 | ||||||||
\(554\) | 240.583i | 0.434265i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −122.191 | −0.219768 | ||||||||
\(557\) | 156.978i | 0.281827i | 0.990022 | + | 0.140914i | \(0.0450040\pi\) | ||||
−0.990022 | + | 0.140914i | \(0.954996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −606.441 | −1.08487 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −314.412 | −0.559452 | ||||||||
\(563\) | 81.3229i | 0.144446i | 0.997389 | + | 0.0722229i | \(0.0230093\pi\) | ||||
−0.997389 | + | 0.0722229i | \(0.976991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − 35.3137i | − 0.0623917i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 253.103 | 0.445603 | ||||||||
\(569\) | 479.022i | 0.841867i | 0.907092 | + | 0.420933i | \(0.138297\pi\) | ||||
−0.907092 | + | 0.420933i | \(0.861703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 631.418 | 1.10581 | 0.552906 | − | 0.833244i | \(-0.313519\pi\) | ||||
0.552906 | + | 0.833244i | \(0.313519\pi\) | |||||||
\(572\) | 80.9117i | 0.141454i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 172.368 | 0.300292 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −945.912 | −1.63936 | −0.819681 | − | 0.572820i | \(-0.805849\pi\) | ||||
−0.819681 | + | 0.572820i | \(0.805849\pi\) | |||||||
\(578\) | − 35.6051i | − 0.0616006i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 905.720i | 1.55890i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 224.735 | 0.385480 | ||||||||
\(584\) | 14.3919i | 0.0246437i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 716.558 | 1.22280 | ||||||||
\(587\) | 847.529i | 1.44383i | 0.691981 | + | 0.721916i | \(0.256738\pi\) | ||||
−0.691981 | + | 0.721916i | \(0.743262\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −329.941 | −0.560172 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −57.8234 | −0.0976746 | ||||||||
\(593\) | − 268.118i | − 0.452138i | −0.974111 | − | 0.226069i | \(-0.927413\pi\) | ||||
0.974111 | − | 0.226069i | \(-0.0725875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 280.014i | − 0.469823i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −447.889 | −0.748979 | ||||||||
\(599\) | 817.176i | 1.36423i | 0.731243 | + | 0.682117i | \(0.238940\pi\) | ||||
−0.731243 | + | 0.682117i | \(0.761060\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −602.706 | −1.00284 | −0.501419 | − | 0.865205i | \(-0.667188\pi\) | ||||
−0.501419 | + | 0.865205i | \(0.667188\pi\) | |||||||
\(602\) | − 524.215i | − 0.870790i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −58.1766 | −0.0963189 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 842.551 | 1.38806 | 0.694029 | − | 0.719947i | \(-0.255834\pi\) | ||||
0.694029 | + | 0.719947i | \(0.255834\pi\) | |||||||
\(608\) | − 141.255i | − 0.232327i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 316.706i | 0.518340i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 50.8377 | 0.0829326 | 0.0414663 | − | 0.999140i | \(-0.486797\pi\) | ||||
0.0414663 | + | 0.999140i | \(0.486797\pi\) | |||||||
\(614\) | 305.980i | 0.498338i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −69.9411 | −0.113541 | ||||||||
\(617\) | − 167.272i | − 0.271105i | −0.990770 | − | 0.135553i | \(-0.956719\pi\) | ||||
0.990770 | − | 0.135553i | \(-0.0432810\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 892.403 | 1.44169 | 0.720843 | − | 0.693099i | \(-0.243755\pi\) | ||||
0.720843 | + | 0.693099i | \(0.243755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.8608 | 0.0319306 | ||||||||
\(623\) | 331.706i | 0.532433i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 526.960i | − 0.841790i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 371.411 | 0.591419 | ||||||||
\(629\) | − 234.801i | − 0.373293i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −95.0294 | −0.150601 | −0.0753007 | − | 0.997161i | \(-0.523992\pi\) | ||||
−0.0753007 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(632\) | − 5.13708i | − 0.00812830i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 85.5593 | 0.134952 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 255.426 | 0.400983 | ||||||||
\(638\) | 173.823i | 0.272450i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1129.23i | 1.76167i | 0.473428 | + | 0.880833i | \(0.343017\pi\) | ||||
−0.473428 | + | 0.880833i | \(0.656983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1041.83 | 1.62027 | 0.810133 | − | 0.586247i | \(-0.199395\pi\) | ||||
0.810133 | + | 0.586247i | \(0.199395\pi\) | |||||||
\(644\) | − 387.161i | − 0.601182i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 573.588 | 0.887907 | ||||||||
\(647\) | − 588.131i | − 0.909013i | −0.890744 | − | 0.454506i | \(-0.849816\pi\) | ||||
0.890744 | − | 0.454506i | \(-0.150184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −51.1766 | −0.0788546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −483.397 | −0.741406 | ||||||||
\(653\) | 127.861i | 0.195805i | 0.995196 | + | 0.0979026i | \(0.0312134\pi\) | ||||
−0.995196 | + | 0.0979026i | \(0.968787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 59.1472i | − 0.0901634i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −273.765 | −0.416055 | ||||||||
\(659\) | − 1151.79i | − 1.74779i | −0.486115 | − | 0.873895i | \(-0.661587\pi\) | ||||
0.486115 | − | 0.873895i | \(-0.338413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 492.986 | 0.745818 | 0.372909 | − | 0.927868i | \(-0.378360\pi\) | ||||
0.372909 | + | 0.927868i | \(0.378360\pi\) | |||||||
\(662\) | − 669.078i | − 1.01069i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 310.794 | 0.468063 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −962.205 | −1.44259 | ||||||||
\(668\) | 572.558i | 0.857123i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 286.103i | 0.426382i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 620.088 | 0.921379 | 0.460690 | − | 0.887561i | \(-0.347602\pi\) | ||||
0.460690 | + | 0.887561i | \(0.347602\pi\) | |||||||
\(674\) | − 870.489i | − 1.29153i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.7056 | −0.0380261 | ||||||||
\(677\) | − 733.581i | − 1.08358i | −0.840515 | − | 0.541788i | \(-0.817748\pi\) | ||||
0.840515 | − | 0.541788i | \(-0.182252\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1325.12 | 1.95158 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 56.0589 | 0.0821978 | ||||||||
\(683\) | − 810.588i | − 1.18681i | −0.804906 | − | 0.593403i | \(-0.797784\pi\) | ||||
0.804906 | − | 0.593403i | \(-0.202216\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − 350.392i | − 0.510775i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −179.882 | −0.261457 | ||||||||
\(689\) | 1010.21i | 1.46619i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −665.477 | −0.963064 | −0.481532 | − | 0.876428i | \(-0.659919\pi\) | ||||
−0.481532 | + | 0.876428i | \(0.659919\pi\) | |||||||
\(692\) | − 441.691i | − 0.638282i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 269.117 | 0.387776 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 240.177 | 0.344586 | ||||||||
\(698\) | 386.745i | 0.554076i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1210.32i | 1.72656i | 0.504729 | + | 0.863278i | \(0.331593\pi\) | ||||
−0.504729 | + | 0.863278i | \(0.668407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −360.971 | −0.513472 | ||||||||
\(704\) | 24.0000i | 0.0340909i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −794.912 | −1.12594 | ||||||||
\(707\) | 1409.79i | 1.99405i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −65.8671 | −0.0929014 | −0.0464507 | − | 0.998921i | \(-0.514791\pi\) | ||||
−0.0464507 | + | 0.998921i | \(0.514791\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 113.823 | 0.159864 | ||||||||
\(713\) | 310.316i | 0.435226i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 491.823i | 0.686904i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 363.390 | 0.506114 | ||||||||
\(719\) | 11.8385i | 0.0164653i | 0.999966 | + | 0.00823263i | \(0.00262056\pi\) | ||||
−0.999966 | + | 0.00823263i | \(0.997379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 965.176 | 1.33866 | ||||||||
\(722\) | − 371.272i | − 0.514227i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 534.617 | 0.738422 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −171.294 | −0.235617 | −0.117808 | − | 0.993036i | \(-0.537587\pi\) | ||||
−0.117808 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(728\) | − 314.392i | − 0.431857i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 730.441i | − 0.999235i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −197.191 | −0.269019 | −0.134509 | − | 0.990912i | \(-0.542946\pi\) | ||||
−0.134509 | + | 0.990912i | \(0.542946\pi\) | |||||||
\(734\) | 268.950i | 0.366417i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −132.853 | −0.180507 | ||||||||
\(737\) | 243.286i | 0.330104i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 140.728 | 0.190430 | 0.0952151 | − | 0.995457i | \(-0.469646\pi\) | ||||
0.0952151 | + | 0.995457i | \(0.469646\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −873.235 | −1.17687 | ||||||||
\(743\) | − 399.073i | − 0.537111i | −0.963264 | − | 0.268555i | \(-0.913454\pi\) | ||||
0.963264 | − | 0.268555i | \(-0.0865462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − 319.446i | − 0.428211i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −97.4558 | −0.130289 | ||||||||
\(749\) | 1119.79i | 1.49504i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −93.8234 | −0.124931 | −0.0624656 | − | 0.998047i | \(-0.519896\pi\) | ||||
−0.0624656 | + | 0.998047i | \(0.519896\pi\) | |||||||
\(752\) | 93.9411i | 0.124922i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −781.352 | −1.03628 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −763.573 | −1.00868 | −0.504341 | − | 0.863504i | \(-0.668265\pi\) | ||||
−0.504341 | + | 0.863504i | \(0.668265\pi\) | |||||||
\(758\) | 677.480i | 0.893773i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 212.214i | 0.278862i | 0.990232 | + | 0.139431i | \(0.0445274\pi\) | ||||
−0.990232 | + | 0.139431i | \(0.955473\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1556.65 | −2.04016 | ||||||||
\(764\) | 692.881i | 0.906913i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −398.330 | −0.520013 | ||||||||
\(767\) | − 230.044i | − 0.299927i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.79307 | 0.0101340 | 0.00506702 | − | 0.999987i | \(-0.498387\pi\) | ||||
0.00506702 | + | 0.999987i | \(0.498387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −69.8234 | −0.0904448 | ||||||||
\(773\) | 549.442i | 0.710791i | 0.934716 | + | 0.355396i | \(0.115654\pi\) | ||||
−0.934716 | + | 0.355396i | \(0.884346\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − 454.711i | − 0.585967i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −894.323 | −1.14952 | ||||||||
\(779\) | − 369.235i | − 0.473985i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −268.456 | −0.343733 | ||||||||
\(782\) | − 539.470i | − 0.689860i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 75.7645 | 0.0966384 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −332.764 | −0.422825 | −0.211413 | − | 0.977397i | \(-0.567806\pi\) | ||||
−0.211413 | + | 0.977397i | \(0.567806\pi\) | |||||||
\(788\) | 379.882i | 0.482084i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 570.500i | − 0.721238i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1286.06 | −1.62176 | ||||||||
\(794\) | − 723.556i | − 0.911280i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −274.426 | −0.344757 | ||||||||
\(797\) | 656.029i | 0.823122i | 0.911382 | + | 0.411561i | \(0.135016\pi\) | ||||
−0.911382 | + | 0.411561i | \(0.864984\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −381.463 | −0.477426 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 983.470 | 1.22627 | ||||||||
\(803\) | − 15.2649i | − 0.0190099i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 251.990i | 0.312643i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 483.765 | 0.598718 | ||||||||
\(809\) | 475.736i | 0.588054i | 0.955797 | + | 0.294027i | \(0.0949956\pi\) | ||||
−0.955797 | + | 0.294027i | \(0.905004\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −991.433 | −1.22248 | −0.611241 | − | 0.791445i | \(-0.709329\pi\) | ||||
−0.611241 | + | 0.791445i | \(0.709329\pi\) | |||||||
\(812\) | − 675.411i | − 0.831787i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 61.3310 | 0.0753452 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1122.94 | −1.37447 | ||||||||
\(818\) | 719.002i | 0.878976i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1201.83i | 1.46386i | 0.681379 | + | 0.731931i | \(0.261381\pi\) | ||||
−0.681379 | + | 0.731931i | \(0.738619\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 423.383 | 0.514438 | 0.257219 | − | 0.966353i | \(-0.417194\pi\) | ||||
0.257219 | + | 0.966353i | \(0.417194\pi\) | |||||||
\(824\) | − 331.196i | − 0.401937i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 198.853 | 0.240742 | ||||||||
\(827\) | 225.323i | 0.272458i | 0.990677 | + | 0.136229i | \(0.0434983\pi\) | ||||
−0.990677 | + | 0.136229i | \(0.956502\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −602.279 | −0.726513 | −0.363256 | − | 0.931689i | \(-0.618335\pi\) | ||||
−0.363256 | + | 0.931689i | \(0.618335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −107.882 | −0.129666 | ||||||||
\(833\) | 307.654i | 0.369332i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 149.823i | 0.179215i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 75.8680 | 0.0905346 | ||||||||
\(839\) | 784.279i | 0.934779i | 0.884052 | + | 0.467389i | \(0.154805\pi\) | ||||
−0.884052 | + | 0.467389i | \(0.845195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −837.587 | −0.995942 | ||||||||
\(842\) | − 288.145i | − 0.342215i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 347.411 | 0.411625 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −923.176 | −1.08994 | ||||||||
\(848\) | 299.647i | 0.353357i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 339.500i | 0.398942i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −763.043 | −0.894540 | −0.447270 | − | 0.894399i | \(-0.647604\pi\) | ||||
−0.447270 | + | 0.894399i | \(0.647604\pi\) | |||||||
\(854\) | − 1111.69i | − 1.30174i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 384.250 | 0.448890 | ||||||||
\(857\) | − 527.294i | − 0.615278i | −0.951503 | − | 0.307639i | \(-0.900461\pi\) | ||||
0.951503 | − | 0.307639i | \(-0.0995390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −426.558 | −0.496576 | −0.248288 | − | 0.968686i | \(-0.579868\pi\) | ||||
−0.248288 | + | 0.968686i | \(0.579868\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1143.33 | −1.32637 | ||||||||
\(863\) | − 705.442i | − 0.817429i | −0.912662 | − | 0.408715i | \(-0.865977\pi\) | ||||
0.912662 | − | 0.408715i | \(-0.134023\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 894.781i | 1.03323i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −217.823 | −0.250949 | ||||||||
\(869\) | 5.44870i | 0.00627008i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1093.60 | −1.25556 | ||||||||
\(872\) | 534.156i | 0.612565i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −829.352 | −0.948916 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 488.368 | 0.556862 | 0.278431 | − | 0.960456i | \(-0.410186\pi\) | ||||
0.278431 | + | 0.960456i | \(0.410186\pi\) | |||||||
\(878\) | 59.1573i | 0.0673773i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 217.060i | 0.246379i | 0.992383 | + | 0.123189i | \(0.0393123\pi\) | ||||
−0.992383 | + | 0.123189i | \(0.960688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.1392 | −0.0228077 | −0.0114038 | − | 0.999935i | \(-0.503630\pi\) | ||||
−0.0114038 | + | 0.999935i | \(0.503630\pi\) | |||||||
\(884\) | − 438.073i | − 0.495558i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −689.595 | −0.778324 | ||||||||
\(887\) | − 63.5727i | − 0.0716716i | −0.999358 | − | 0.0358358i | \(-0.988591\pi\) | ||||
0.999358 | − | 0.0358358i | \(-0.0114093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1705.56 | 1.91851 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 334.059 | 0.374505 | ||||||||
\(893\) | 586.441i | 0.656709i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 93.2548i | − 0.104079i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −37.8823 | −0.0421851 | ||||||||
\(899\) | 541.352i | 0.602172i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1216.76 | −1.35046 | ||||||||
\(902\) | 62.7351i | 0.0695511i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −195.765 | −0.216554 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −582.558 | −0.642292 | −0.321146 | − | 0.947030i | \(-0.604068\pi\) | ||||
−0.321146 | + | 0.947030i | \(0.604068\pi\) | |||||||
\(908\) | − 590.881i | − 0.650750i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1683.69i | 1.84818i | 0.382179 | + | 0.924088i | \(0.375174\pi\) | ||||
−0.382179 | + | 0.924088i | \(0.624826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −329.647 | −0.361059 | ||||||||
\(914\) | − 740.174i | − 0.809818i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 378.971 | 0.413723 | ||||||||
\(917\) | − 1283.67i | − 1.39986i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1299.32 | 1.41384 | 0.706922 | − | 0.707292i | \(-0.250083\pi\) | ||||
0.706922 | + | 0.707292i | \(0.250083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −666.177 | −0.722534 | ||||||||
\(923\) | − 1206.73i | − 1.30740i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − 337.872i | − 0.364873i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −231.765 | −0.249746 | ||||||||
\(929\) | 1636.74i | 1.76183i | 0.473272 | + | 0.880916i | \(0.343073\pi\) | ||||
−0.473272 | + | 0.880916i | \(0.656927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 472.971 | 0.508024 | ||||||||
\(932\) | − 279.515i | − 0.299908i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 668.756 | 0.716013 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1084.38 | −1.15729 | −0.578645 | − | 0.815579i | \(-0.696418\pi\) | ||||
−0.578645 | + | 0.815579i | \(0.696418\pi\) | |||||||
\(938\) | − 945.318i | − 1.00780i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 773.138i | − 0.821614i | −0.911722 | − | 0.410807i | \(-0.865247\pi\) | ||||
0.911722 | − | 0.410807i | \(-0.134753\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −347.272 | −0.368263 | ||||||||
\(944\) | − 68.2355i | − 0.0722834i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 190.794 | 0.201685 | ||||||||
\(947\) | 849.442i | 0.896982i | 0.893787 | + | 0.448491i | \(0.148038\pi\) | ||||
−0.893787 | + | 0.448491i | \(0.851962\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 68.6173 | 0.0723049 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 378.676 | 0.397769 | ||||||||
\(953\) | 1537.35i | 1.61317i | 0.591117 | + | 0.806586i | \(0.298687\pi\) | ||||
−0.591117 | + | 0.806586i | \(0.701313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 520.794i | 0.544764i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 254.059 | 0.265197 | ||||||||
\(959\) | 190.794i | 0.198951i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −786.411 | −0.818326 | ||||||||
\(962\) | 275.688i | 0.286578i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 171.706 | 0.178118 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −974.234 | −1.00748 | −0.503740 | − | 0.863855i | \(-0.668043\pi\) | ||||
−0.503740 | + | 0.863855i | \(0.668043\pi\) | |||||||
\(968\) | 316.784i | 0.327256i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 771.500i | − 0.794541i | −0.917702 | − | 0.397271i | \(-0.869957\pi\) | ||||
0.917702 | − | 0.397271i | \(-0.130043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −503.588 | −0.517562 | ||||||||
\(974\) | − 521.667i | − 0.535592i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −381.470 | −0.390851 | ||||||||
\(977\) | − 580.118i | − 0.593775i | −0.954913 | − | 0.296887i | \(-0.904051\pi\) | ||||
0.954913 | − | 0.296887i | \(-0.0959486\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −120.728 | −0.123318 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1054.84 | −1.07417 | ||||||||
\(983\) | − 1086.02i | − 1.10480i | −0.833580 | − | 0.552398i | \(-0.813713\pi\) | ||||
0.833580 | − | 0.552398i | \(-0.186287\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 941.117i | − 0.954480i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −673.470 | −0.681650 | ||||||||
\(989\) | 1056.15i | 1.06789i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −159.294 | −0.160740 | −0.0803701 | − | 0.996765i | \(-0.525610\pi\) | ||||
−0.0803701 | + | 0.996765i | \(0.525610\pi\) | |||||||
\(992\) | 74.7452i | 0.0753479i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1043.12 | 1.04941 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 100.427 | 0.100729 | 0.0503647 | − | 0.998731i | \(-0.483962\pi\) | ||||
0.0503647 | + | 0.998731i | \(0.483962\pi\) | |||||||
\(998\) | 1090.77i | 1.09296i | ||||||||
\(999\) | 0 | 0 |
(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 | 1350.3.d.l.701.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 1350.3.d.l.701.3 | yes | 4 | |
5.2 | odd | 4 | 1350.3.b.a.1349.3 | 4 | |||
5.3 | odd | 4 | 1350.3.b.f.1349.2 | 4 | |||
5.4 | even | 2 | 1350.3.d.n.701.4 | yes | 4 | ||
15.2 | even | 4 | 1350.3.b.f.1349.1 | 4 | |||
15.8 | even | 4 | 1350.3.b.a.1349.4 | 4 | |||
15.14 | odd | 2 | 1350.3.d.n.701.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.3.b.a.1349.3 | 4 | 5.2 | odd | 4 | |||
1350.3.b.a.1349.4 | 4 | 15.8 | even | 4 | |||
1350.3.b.f.1349.1 | 4 | 15.2 | even | 4 | |||
1350.3.b.f.1349.2 | 4 | 5.3 | odd | 4 | |||
1350.3.d.l.701.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1350.3.d.l.701.3 | yes | 4 | 3.2 | odd | 2 | inner | |
1350.3.d.n.701.2 | yes | 4 | 15.14 | odd | 2 | ||
1350.3.d.n.701.4 | yes | 4 | 5.4 | even | 2 |