Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(809,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1620.809");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.b (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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 809.24 | ||
Character | \(\chi\) | \(=\) | 1620.809 |
Dual form | 1620.3.b.b.809.23 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.90327 | + | 0.978759i | 0.980653 | + | 0.195752i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 7.34726i | − | 1.04961i | −0.851223 | − | 0.524804i | \(-0.824138\pi\) | ||
0.851223 | − | 0.524804i | \(-0.175862\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.64692i | 0.876993i | 0.898733 | + | 0.438496i | \(0.144489\pi\) | ||||
−0.898733 | + | 0.438496i | \(0.855511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.6859i | 1.28353i | 0.766901 | + | 0.641765i | \(0.221798\pi\) | ||||
−0.766901 | + | 0.641765i | \(0.778202\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.4743 | 0.910251 | 0.455125 | − | 0.890427i | \(-0.349594\pi\) | ||||
0.455125 | + | 0.890427i | \(0.349594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.4865 | −0.920344 | −0.460172 | − | 0.887830i | \(-0.652212\pi\) | ||||
−0.460172 | + | 0.887830i | \(0.652212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −10.5819 | −0.460080 | −0.230040 | − | 0.973181i | \(-0.573886\pi\) | ||||
−0.230040 | + | 0.973181i | \(0.573886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.0841 | + | 9.59823i | 0.923363 | + | 0.383929i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 41.8058i | 1.44158i | 0.693154 | + | 0.720789i | \(0.256220\pi\) | ||||
−0.693154 | + | 0.720789i | \(0.743780\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −48.7281 | −1.57187 | −0.785937 | − | 0.618306i | \(-0.787819\pi\) | ||||
−0.785937 | + | 0.618306i | \(0.787819\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.19120 | − | 36.0256i | 0.205463 | − | 1.02930i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 20.4792i | 0.553492i | 0.960943 | + | 0.276746i | \(0.0892561\pi\) | ||||
−0.960943 | + | 0.276746i | \(0.910744\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 27.9021i | 0.680540i | 0.940328 | + | 0.340270i | \(0.110518\pi\) | ||||
−0.940328 | + | 0.340270i | \(0.889482\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 30.2091i | 0.702538i | 0.936275 | + | 0.351269i | \(0.114250\pi\) | ||||
−0.936275 | + | 0.351269i | \(0.885750\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 42.1251 | 0.896279 | 0.448139 | − | 0.893964i | \(-0.352087\pi\) | ||||
0.448139 | + | 0.893964i | \(0.352087\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.98225 | −0.101679 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −90.4314 | −1.70625 | −0.853127 | − | 0.521704i | \(-0.825297\pi\) | ||||
−0.853127 | + | 0.521704i | \(0.825297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.44201 | + | 47.3014i | −0.171673 | + | 0.860026i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 55.4367i | − | 0.939605i | −0.882771 | − | 0.469803i | \(-0.844325\pi\) | ||
0.882771 | − | 0.469803i | \(-0.155675\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 116.758 | 1.91407 | 0.957034 | − | 0.289977i | \(-0.0936478\pi\) | ||||
0.957034 | + | 0.289977i | \(0.0936478\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.3315 | + | 81.8154i | −0.251253 | + | 1.25870i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17.2837i | 0.257966i | 0.991647 | + | 0.128983i | \(0.0411713\pi\) | ||||
−0.991647 | + | 0.128983i | \(0.958829\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 38.4861i | 0.542058i | 0.962571 | + | 0.271029i | \(0.0873640\pi\) | ||||
−0.962571 | + | 0.271029i | \(0.912636\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.38815i | 0.101208i | 0.998719 | + | 0.0506038i | \(0.0161146\pi\) | ||||
−0.998719 | + | 0.0506038i | \(0.983885\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 70.8784 | 0.920499 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.6993 | 0.299992 | 0.149996 | − | 0.988687i | \(-0.452074\pi\) | ||||
0.149996 | + | 0.988687i | \(0.452074\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.26989 | −0.0514444 | −0.0257222 | − | 0.999669i | \(-0.508189\pi\) | ||||
−0.0257222 | + | 0.999669i | \(0.508189\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 75.8744 | + | 15.1456i | 0.892641 | + | 0.178183i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 145.034i | − | 1.62959i | −0.579746 | − | 0.814797i | \(-0.696848\pi\) | ||
0.579746 | − | 0.814797i | \(-0.303152\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 122.596 | 1.34720 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −85.7411 | − | 17.1151i | −0.902538 | − | 0.180159i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 102.700i | 1.05876i | 0.848385 | + | 0.529379i | \(0.177575\pi\) | ||||
−0.848385 | + | 0.529379i | \(0.822425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 110.861i | − | 1.09763i | −0.835943 | − | 0.548816i | \(-0.815079\pi\) | ||
0.835943 | − | 0.548816i | \(-0.184921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 187.849i | 1.82378i | 0.410438 | + | 0.911888i | \(0.365376\pi\) | ||||
−0.410438 | + | 0.911888i | \(0.634624\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 121.767 | 1.13801 | 0.569005 | − | 0.822334i | \(-0.307328\pi\) | ||||
0.569005 | + | 0.822334i | \(0.307328\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −45.3350 | −0.415918 | −0.207959 | − | 0.978138i | \(-0.566682\pi\) | ||||
−0.207959 | + | 0.978138i | \(0.566682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.2092 | −0.169993 | −0.0849963 | − | 0.996381i | \(-0.527088\pi\) | ||||
−0.0849963 | + | 0.996381i | \(0.527088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −51.8856 | − | 10.3571i | −0.451179 | − | 0.0900616i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 113.693i | − | 0.955407i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.9369 | 0.230884 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 103.793 | + | 69.6564i | 0.830344 | + | 0.557251i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 179.244i | 1.41137i | 0.708527 | + | 0.705684i | \(0.249360\pi\) | ||||
−0.708527 | + | 0.705684i | \(0.750640\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 84.9928i | − | 0.648800i | −0.945920 | − | 0.324400i | \(-0.894838\pi\) | ||
0.945920 | − | 0.324400i | \(-0.105162\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 128.478i | 0.966001i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −66.0739 | −0.482291 | −0.241146 | − | 0.970489i | \(-0.577523\pi\) | ||||
−0.241146 | + | 0.970489i | \(0.577523\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.42041 | −0.0677728 | −0.0338864 | − | 0.999426i | \(-0.510788\pi\) | ||||
−0.0338864 | + | 0.999426i | \(0.510788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −160.967 | −1.12565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.9178 | + | 204.985i | −0.282191 | + | 1.41369i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 124.758i | 0.837305i | 0.908146 | + | 0.418653i | \(0.137498\pi\) | ||||
−0.908146 | + | 0.418653i | \(0.862502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −291.962 | −1.93353 | −0.966763 | − | 0.255674i | \(-0.917703\pi\) | ||||
−0.966763 | + | 0.255674i | \(0.917703\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −238.927 | − | 47.6931i | −1.54146 | − | 0.307697i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 143.269i | 0.912543i | 0.889840 | + | 0.456272i | \(0.150815\pi\) | ||||
−0.889840 | + | 0.456272i | \(0.849185\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 77.7476i | 0.482904i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 228.204i | − | 1.40002i | −0.714132 | − | 0.700011i | \(-0.753178\pi\) | ||
0.714132 | − | 0.700011i | \(-0.246822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −60.7552 | −0.363804 | −0.181902 | − | 0.983317i | \(-0.558225\pi\) | ||||
−0.181902 | + | 0.983317i | \(0.558225\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −109.419 | −0.647449 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 277.631 | 1.60480 | 0.802400 | − | 0.596786i | \(-0.203556\pi\) | ||||
0.802400 | + | 0.596786i | \(0.203556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 70.5207 | − | 169.605i | 0.402976 | − | 0.969169i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 272.749i | 1.52374i | 0.647731 | + | 0.761869i | \(0.275718\pi\) | ||||
−0.647731 | + | 0.761869i | \(0.724282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −110.378 | −0.609824 | −0.304912 | − | 0.952380i | \(-0.598627\pi\) | ||||
−0.304912 | + | 0.952380i | \(0.598627\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −20.0442 | + | 100.415i | −0.108347 | + | 0.542784i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 149.279i | 0.798283i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 33.6071i | − | 0.175954i | −0.996123 | − | 0.0879768i | \(-0.971960\pi\) | ||
0.996123 | − | 0.0879768i | \(-0.0280401\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 270.684i | 1.40251i | 0.712911 | + | 0.701255i | \(0.247376\pi\) | ||||
−0.712911 | + | 0.701255i | \(0.752624\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 63.0978 | 0.320293 | 0.160147 | − | 0.987093i | \(-0.448803\pi\) | ||||
0.160147 | + | 0.987093i | \(0.448803\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 283.032 | 1.42227 | 0.711135 | − | 0.703056i | \(-0.248182\pi\) | ||||
0.711135 | + | 0.703056i | \(0.248182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 307.158 | 1.51309 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −27.3095 | + | 136.812i | −0.133217 | + | 0.667374i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 168.691i | − | 0.807135i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 113.862 | 0.539633 | 0.269816 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269816 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −29.5674 | + | 148.123i | −0.137523 | + | 0.688946i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 358.018i | 1.64985i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 258.202i | 1.16833i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 217.858i | 0.976941i | 0.872580 | + | 0.488471i | \(0.162445\pi\) | ||||
−0.872580 | + | 0.488471i | \(0.837555\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −52.9198 | −0.233127 | −0.116563 | − | 0.993183i | \(-0.537188\pi\) | ||||
−0.116563 | + | 0.993183i | \(0.537188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 391.321 | 1.70883 | 0.854413 | − | 0.519595i | \(-0.173917\pi\) | ||||
0.854413 | + | 0.519595i | \(0.173917\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −178.384 | −0.765596 | −0.382798 | − | 0.923832i | \(-0.625039\pi\) | ||||
−0.382798 | + | 0.923832i | \(0.625039\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 206.551 | + | 41.2303i | 0.878939 | + | 0.175448i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 363.155i | − | 1.51948i | −0.650229 | − | 0.759738i | \(-0.725327\pi\) | ||
0.650229 | − | 0.759738i | \(-0.274673\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 180.644 | 0.749559 | 0.374780 | − | 0.927114i | \(-0.377718\pi\) | ||||
0.374780 | + | 0.927114i | \(0.377718\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.4293 | − | 4.87642i | −0.0997115 | − | 0.0199038i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 291.778i | − | 1.18129i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 73.5509i | 0.293032i | 0.989208 | + | 0.146516i | \(0.0468059\pi\) | ||||
−0.989208 | + | 0.146516i | \(0.953194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 102.082i | − | 0.403487i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −144.952 | −0.564014 | −0.282007 | − | 0.959412i | \(-0.591000\pi\) | ||||
−0.282007 | + | 0.959412i | \(0.591000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 150.466 | 0.580950 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 328.862 | 1.25043 | 0.625213 | − | 0.780454i | \(-0.285012\pi\) | ||||
0.625213 | + | 0.780454i | \(0.285012\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −443.409 | − | 88.5106i | −1.67324 | − | 0.334002i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 355.832i | − | 1.32280i | −0.750035 | − | 0.661398i | \(-0.769963\pi\) | ||
0.750035 | − | 0.661398i | \(-0.230037\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −128.345 | −0.473599 | −0.236799 | − | 0.971559i | \(-0.576098\pi\) | ||||
−0.236799 | + | 0.971559i | \(0.576098\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −92.5934 | + | 222.690i | −0.336703 | + | 0.809782i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 270.554i | − | 0.976729i | −0.872640 | − | 0.488365i | \(-0.837594\pi\) | ||
0.872640 | − | 0.488365i | \(-0.162406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 525.118i | 1.86875i | 0.356295 | + | 0.934374i | \(0.384040\pi\) | ||||
−0.356295 | + | 0.934374i | \(0.615960\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 209.596i | 0.740623i | 0.928908 | + | 0.370311i | \(0.120749\pi\) | ||||
−0.928908 | + | 0.370311i | \(0.879251\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 205.004 | 0.714300 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −49.5472 | −0.171444 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 119.736 | 0.408654 | 0.204327 | − | 0.978903i | \(-0.434499\pi\) | ||||
0.204327 | + | 0.978903i | \(0.434499\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 54.2592 | − | 271.821i | 0.183929 | − | 0.921427i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 176.568i | − | 0.590527i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 221.954 | 0.737390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 572.496 | + | 114.278i | 1.87704 | + | 0.374682i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 435.735i | − | 1.41933i | −0.704538 | − | 0.709666i | \(-0.748846\pi\) | ||
0.704538 | − | 0.709666i | \(-0.251154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 68.4104i | 0.219969i | 0.993933 | + | 0.109985i | \(0.0350801\pi\) | ||||
−0.993933 | + | 0.109985i | \(0.964920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 43.9371i | 0.140374i | 0.997534 | + | 0.0701870i | \(0.0223596\pi\) | ||||
−0.997534 | + | 0.0701870i | \(0.977640\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −267.533 | −0.843953 | −0.421977 | − | 0.906607i | \(-0.638664\pi\) | ||||
−0.421977 | + | 0.906607i | \(0.638664\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −403.297 | −1.26425 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −270.591 | −0.837743 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −160.155 | + | 385.178i | −0.492785 | + | 1.18516i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 309.504i | − | 0.940742i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 72.1231 | 0.217894 | 0.108947 | − | 0.994048i | \(-0.465252\pi\) | ||||
0.108947 | + | 0.994048i | \(0.465252\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.9166 | + | 84.7468i | −0.0504974 | + | 0.252976i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 195.792i | 0.580987i | 0.956877 | + | 0.290493i | \(0.0938194\pi\) | ||||
−0.956877 | + | 0.290493i | \(0.906181\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 470.076i | − | 1.37852i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 323.410i | − | 0.942886i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −126.817 | −0.365466 | −0.182733 | − | 0.983163i | \(-0.558494\pi\) | ||||
−0.182733 | + | 0.983163i | \(0.558494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 130.553 | 0.374077 | 0.187038 | − | 0.982353i | \(-0.440111\pi\) | ||||
0.187038 | + | 0.982353i | \(0.440111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −261.256 | −0.740102 | −0.370051 | − | 0.929011i | \(-0.620660\pi\) | ||||
−0.370051 | + | 0.929011i | \(0.620660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −37.6687 | + | 188.708i | −0.106109 | + | 0.531571i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 390.386i | − | 1.08743i | −0.839271 | − | 0.543713i | \(-0.817018\pi\) | ||
0.839271 | − | 0.543713i | \(-0.182982\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −55.2213 | −0.152968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.23121 | + | 36.2261i | −0.0198115 | + | 0.0992495i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 84.3330i | − | 0.229790i | −0.993378 | − | 0.114895i | \(-0.963347\pi\) | ||
0.993378 | − | 0.114895i | \(-0.0366532\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 664.423i | 1.79090i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 177.161i | 0.474963i | 0.971392 | + | 0.237482i | \(0.0763219\pi\) | ||||
−0.971392 | + | 0.237482i | \(0.923678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −697.566 | −1.85031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −291.976 | −0.770386 | −0.385193 | − | 0.922836i | \(-0.625865\pi\) | ||||
−0.385193 | + | 0.922836i | \(0.625865\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −273.531 | −0.714179 | −0.357090 | − | 0.934070i | \(-0.616231\pi\) | ||||
−0.357090 | + | 0.934070i | \(0.616231\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 347.536 | + | 69.3729i | 0.902691 | + | 0.180189i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 237.978i | − | 0.611769i | −0.952069 | − | 0.305885i | \(-0.901048\pi\) | ||
0.952069 | − | 0.305885i | \(-0.0989522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −163.746 | −0.418789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 116.204 | + | 23.1959i | 0.294188 | + | 0.0587239i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 76.9037i | 0.193712i | 0.995298 | + | 0.0968560i | \(0.0308786\pi\) | ||||
−0.995298 | + | 0.0968560i | \(0.969121\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 546.297i | − | 1.36234i | −0.732127 | − | 0.681169i | \(-0.761472\pi\) | ||
0.732127 | − | 0.681169i | \(-0.238528\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 813.072i | − | 2.01755i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −197.561 | −0.485409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −562.102 | −1.37433 | −0.687166 | − | 0.726500i | \(-0.741146\pi\) | ||||
−0.687166 | + | 0.726500i | \(0.741146\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −407.308 | −0.986218 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.9364 | − | 4.17919i | −0.0504492 | − | 0.0100703i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 242.077i | − | 0.577749i | −0.957367 | − | 0.288874i | \(-0.906719\pi\) | ||
0.957367 | − | 0.288874i | \(-0.0932810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.2005 | 0.0384809 | 0.0192405 | − | 0.999815i | \(-0.493875\pi\) | ||||
0.0192405 | + | 0.999815i | \(0.493875\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 357.209 | + | 148.526i | 0.840491 | + | 0.349472i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 857.852i | − | 2.00902i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 50.0624i | − | 0.116154i | −0.998312 | − | 0.0580770i | \(-0.981503\pi\) | ||
0.998312 | − | 0.0580770i | \(-0.0184969\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 452.725i | − | 1.04556i | −0.852469 | − | 0.522778i | \(-0.824896\pi\) | ||
0.852469 | − | 0.522778i | \(-0.175104\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 185.040 | 0.423432 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 230.278 | 0.524551 | 0.262275 | − | 0.964993i | \(-0.415527\pi\) | ||||
0.262275 | + | 0.964993i | \(0.415527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 597.848 | 1.34954 | 0.674772 | − | 0.738027i | \(-0.264242\pi\) | ||||
0.674772 | + | 0.738027i | \(0.264242\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 141.953 | − | 711.140i | 0.318996 | − | 1.59807i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 642.091i | − | 1.43005i | −0.699101 | − | 0.715023i | \(-0.746416\pi\) | ||
0.699101 | − | 0.715023i | \(-0.253584\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −269.170 | −0.596828 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 601.119 | + | 119.992i | 1.32114 | + | 0.263718i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 88.4182i | 0.193475i | 0.995310 | + | 0.0967376i | \(0.0308408\pi\) | ||||
−0.995310 | + | 0.0967376i | \(0.969159\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 487.138i | − | 1.05670i | −0.849027 | − | 0.528349i | \(-0.822811\pi\) | ||
0.849027 | − | 0.528349i | \(-0.177189\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 627.882i | − | 1.35612i | −0.735008 | − | 0.678058i | \(-0.762822\pi\) | ||
0.735008 | − | 0.678058i | \(-0.237178\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 323.410 | 0.692527 | 0.346263 | − | 0.938137i | \(-0.387450\pi\) | ||||
0.346263 | + | 0.938137i | \(0.387450\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 126.988 | 0.270764 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −291.425 | −0.616121 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −403.660 | − | 167.840i | −0.849811 | − | 0.353347i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 158.394i | − | 0.330677i | −0.986237 | − | 0.165339i | \(-0.947128\pi\) | ||
0.986237 | − | 0.165339i | \(-0.0528717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −341.714 | −0.710424 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −100.518 | + | 503.564i | −0.207254 | + | 1.03828i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 108.301i | 0.222385i | 0.993799 | + | 0.111192i | \(0.0354670\pi\) | ||||
−0.993799 | + | 0.111192i | \(0.964533\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 679.140i | 1.38318i | 0.722291 | + | 0.691589i | \(0.243089\pi\) | ||||
−0.722291 | + | 0.691589i | \(0.756911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 646.913i | 1.31220i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 282.768 | 0.568949 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −74.3129 | −0.148924 | −0.0744618 | − | 0.997224i | \(-0.523724\pi\) | ||||
−0.0744618 | + | 0.997224i | \(0.523724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 278.694 | 0.554063 | 0.277031 | − | 0.960861i | \(-0.410649\pi\) | ||||
0.277031 | + | 0.960861i | \(0.410649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 108.506 | − | 543.580i | 0.214863 | − | 1.07640i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 276.468i | 0.543160i | 0.962416 | + | 0.271580i | \(0.0875461\pi\) | ||||
−0.962416 | + | 0.271580i | \(0.912454\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 54.2827 | 0.106228 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −183.859 | + | 921.074i | −0.357008 | + | 1.78849i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 406.378i | 0.786030i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 929.478i | 1.78403i | 0.452008 | + | 0.892014i | \(0.350708\pi\) | ||||
−0.452008 | + | 0.892014i | \(0.649292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 217.275i | − | 0.415439i | −0.978188 | − | 0.207719i | \(-0.933396\pi\) | ||
0.978188 | − | 0.207719i | \(-0.0666041\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −754.032 | −1.43080 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −417.024 | −0.788326 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −465.572 | −0.873493 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 597.057 | + | 119.181i | 1.11599 | + | 0.222768i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 48.0634i | − | 0.0891714i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 393.139 | 0.726690 | 0.363345 | − | 0.931655i | \(-0.381635\pi\) | ||||
0.363345 | + | 0.931655i | \(0.381635\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −222.290 | − | 44.3721i | −0.407871 | − | 0.0814166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 876.683i | − | 1.60271i | −0.598188 | − | 0.801356i | \(-0.704112\pi\) | ||
0.598188 | − | 0.801356i | \(-0.295888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 731.038i | − | 1.32675i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 174.125i | − | 0.314874i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 546.180 | 0.980575 | 0.490287 | − | 0.871561i | \(-0.336892\pi\) | ||||
0.490287 | + | 0.871561i | \(0.336892\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −504.066 | −0.901728 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 948.666 | 1.68502 | 0.842510 | − | 0.538681i | \(-0.181077\pi\) | ||||
0.842510 | + | 0.538681i | \(0.181077\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −94.1877 | − | 18.8011i | −0.166704 | − | 0.0332764i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 116.957i | − | 0.205548i | −0.994705 | − | 0.102774i | \(-0.967228\pi\) | ||
0.994705 | − | 0.102774i | \(-0.0327719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −143.844 | −0.251916 | −0.125958 | − | 0.992036i | \(-0.540200\pi\) | ||||
−0.125958 | + | 0.992036i | \(0.540200\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −244.272 | − | 101.567i | −0.424821 | − | 0.176638i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 665.087i | − | 1.15266i | −0.817216 | − | 0.576332i | \(-0.804484\pi\) | ||
0.817216 | − | 0.576332i | \(-0.195516\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.3720i | 0.0539965i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 872.385i | − | 1.49637i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 223.307 | 0.380421 | 0.190210 | − | 0.981743i | \(-0.439083\pi\) | ||||
0.190210 | + | 0.981743i | \(0.439083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 852.086 | 1.44666 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 320.932 | 0.541200 | 0.270600 | − | 0.962692i | \(-0.412778\pi\) | ||||
0.270600 | + | 0.962692i | \(0.412778\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 111.278 | − | 557.469i | 0.187023 | − | 0.936923i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 619.547i | − | 1.03430i | −0.855894 | − | 0.517151i | \(-0.826992\pi\) | ||
0.855894 | − | 0.517151i | \(-0.173008\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −583.311 | −0.970567 | −0.485283 | − | 0.874357i | \(-0.661284\pi\) | ||||
−0.485283 | + | 0.874357i | \(0.661284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 136.982 | + | 27.3435i | 0.226417 | + | 0.0451959i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 149.646i | − | 0.246533i | −0.992374 | − | 0.123267i | \(-0.960663\pi\) | ||
0.992374 | − | 0.123267i | \(-0.0393370\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 702.895i | 1.15040i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 775.281i | 1.26473i | 0.774669 | + | 0.632367i | \(0.217916\pi\) | ||||
−0.774669 | + | 0.632367i | \(0.782084\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1195.51 | 1.93761 | 0.968807 | − | 0.247817i | \(-0.0797132\pi\) | ||||
0.968807 | + | 0.247817i | \(0.0797132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −835.072 | −1.34907 | −0.674533 | − | 0.738244i | \(-0.735655\pi\) | ||||
−0.674533 | + | 0.738244i | \(0.735655\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1065.60 | −1.71044 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 440.748 | + | 443.132i | 0.705197 | + | 0.709012i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 316.901i | 0.503817i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 378.090 | 0.599191 | 0.299596 | − | 0.954066i | \(-0.403148\pi\) | ||||
0.299596 | + | 0.954066i | \(0.403148\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −175.436 | + | 878.880i | −0.276278 | + | 1.38406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 83.1333i | − | 0.130508i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 81.4809i | − | 0.127115i | −0.997978 | − | 0.0635577i | \(-0.979755\pi\) | ||
0.997978 | − | 0.0635577i | \(-0.0202447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 849.766i | − | 1.32157i | −0.750577 | − | 0.660783i | \(-0.770225\pi\) | ||
0.750577 | − | 0.660783i | \(-0.229775\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −569.387 | −0.880042 | −0.440021 | − | 0.897988i | \(-0.645029\pi\) | ||||
−0.440021 | + | 0.897988i | \(0.645029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 534.793 | 0.824027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −940.392 | −1.44011 | −0.720055 | − | 0.693917i | \(-0.755883\pi\) | ||||
−0.720055 | + | 0.693917i | \(0.755883\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 83.1875 | − | 416.742i | 0.127004 | − | 0.636248i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1263.48i | − | 1.91726i | −0.284651 | − | 0.958631i | \(-0.591878\pi\) | ||
0.284651 | − | 0.958631i | \(-0.408122\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 131.621 | 0.199125 | 0.0995623 | − | 0.995031i | \(-0.468256\pi\) | ||||
0.0995623 | + | 0.995031i | \(0.468256\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −125.749 | + | 629.962i | −0.189096 | + | 0.947312i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 442.382i | − | 0.663242i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1126.36i | 1.67862i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 238.795i | − | 0.354822i | −0.984137 | − | 0.177411i | \(-0.943228\pi\) | ||
0.984137 | − | 0.177411i | \(-0.0567722\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −351.521 | −0.519233 | −0.259617 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259617 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 754.561 | 1.11128 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1067.52 | 1.56299 | 0.781495 | − | 0.623911i | \(-0.214457\pi\) | ||||
0.781495 | + | 0.623911i | \(0.214457\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −323.978 | − | 64.6704i | −0.472961 | − | 0.0944094i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1508.93i | − | 2.19003i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 462.586 | 0.669444 | 0.334722 | − | 0.942317i | \(-0.391358\pi\) | ||||
0.334722 | + | 0.942317i | \(0.391358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −46.1908 | − | 9.22031i | −0.0664616 | − | 0.0132666i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 431.765i | 0.619462i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 519.309i | 0.740812i | 0.928870 | + | 0.370406i | \(0.120781\pi\) | ||||
−0.928870 | + | 0.370406i | \(0.879219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 358.110i | − | 0.509403i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −814.523 | −1.15208 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −625.144 | −0.881727 | −0.440863 | − | 0.897574i | \(-0.645328\pi\) | ||||
−0.440863 | + | 0.897574i | \(0.645328\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 515.634 | 0.723189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −789.266 | − | 157.548i | −1.10387 | − | 0.220347i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1385.24i | − | 1.92662i | −0.268400 | − | 0.963308i | \(-0.586495\pi\) | ||
0.268400 | − | 0.963308i | \(-0.413505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1380.18 | 1.91425 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −401.261 | + | 965.047i | −0.553464 | + | 1.33110i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1358.49i | 1.86863i | 0.356451 | + | 0.934314i | \(0.383987\pi\) | ||||
−0.356451 | + | 0.934314i | \(0.616013\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 467.464i | 0.639486i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 926.431i | − | 1.26389i | −0.775013 | − | 0.631945i | \(-0.782257\pi\) | ||
0.775013 | − | 0.631945i | \(-0.217743\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −166.735 | −0.226235 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −693.908 | −0.938983 | −0.469491 | − | 0.882937i | \(-0.655563\pi\) | ||||
−0.469491 | + | 0.882937i | \(0.655563\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 100.379 | 0.135099 | 0.0675497 | − | 0.997716i | \(-0.478482\pi\) | ||||
0.0675497 | + | 0.997716i | \(0.478482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −122.108 | + | 611.724i | −0.163904 | + | 0.821106i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 894.655i | − | 1.19447i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.71806 | 0.00628237 | 0.00314118 | − | 0.999995i | \(-0.499000\pi\) | ||||
0.00314118 | + | 0.999995i | \(0.499000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1431.57 | − | 285.761i | −1.89612 | − | 0.378491i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 133.356i | − | 0.176163i | −0.996113 | − | 0.0880816i | \(-0.971926\pi\) | ||
0.996113 | − | 0.0880816i | \(-0.0280736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 219.732i | − | 0.288741i | −0.989524 | − | 0.144371i | \(-0.953884\pi\) | ||
0.989524 | − | 0.144371i | \(-0.0461157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 333.088i | 0.436551i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 925.011 | 1.20601 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −638.833 | −0.830732 | −0.415366 | − | 0.909654i | \(-0.636346\pi\) | ||||
−0.415366 | + | 0.909654i | \(0.636346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1244.36 | 1.60978 | 0.804888 | − | 0.593426i | \(-0.202225\pi\) | ||||
0.804888 | + | 0.593426i | \(0.202225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1124.84 | − | 467.704i | −1.45141 | − | 0.603489i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 487.911i | − | 0.626330i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −371.273 | −0.475381 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −140.226 | + | 702.488i | −0.178632 | + | 0.894889i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1138.73i | − | 1.44693i | −0.690360 | − | 0.723466i | \(-0.742548\pi\) | ||
0.690360 | − | 0.723466i | \(-0.257452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 141.135i | 0.178426i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1948.21i | 2.45676i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1365.72 | 1.71357 | 0.856785 | − | 0.515673i | \(-0.172458\pi\) | ||||
0.856785 | + | 0.515673i | \(0.172458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 651.855 | 0.815839 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −71.2729 | −0.0887582 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −76.0962 | + | 381.217i | −0.0945294 | + | 0.473562i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 504.881i | 0.624080i | 0.950069 | + | 0.312040i | \(0.101012\pi\) | ||||
−0.950069 | + | 0.312040i | \(0.898988\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1484.09 | −1.82995 | −0.914974 | − | 0.403514i | \(-0.867789\pi\) | ||||
−0.914974 | + | 0.403514i | \(0.867789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 223.356 | − | 1118.94i | 0.274057 | − | 1.37294i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 528.253i | − | 0.646576i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 396.424i | − | 0.482855i | −0.970419 | − | 0.241428i | \(-0.922384\pi\) | ||
0.970419 | − | 0.241428i | \(-0.0776156\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 711.138i | 0.864080i | 0.901854 | + | 0.432040i | \(0.142206\pi\) | ||||
−0.901854 | + | 0.432040i | \(0.857794\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −296.720 | −0.358791 | −0.179396 | − | 0.983777i | \(-0.557414\pi\) | ||||
−0.179396 | + | 0.983777i | \(0.557414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 252.785 | 0.304928 | 0.152464 | − | 0.988309i | \(-0.451279\pi\) | ||||
0.152464 | + | 0.988309i | \(0.451279\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −77.0967 | −0.0925530 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −297.899 | − | 59.4647i | −0.356765 | − | 0.0712152i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 291.010i | 0.346854i | 0.984847 | + | 0.173427i | \(0.0554840\pi\) | ||||
−0.984847 | + | 0.173427i | \(0.944516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −906.722 | −1.07815 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −536.510 | − | 107.095i | −0.634923 | − | 0.126739i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 205.260i | − | 0.242338i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 216.708i | − | 0.254651i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 43.6198i | 0.0511370i | 0.999673 | + | 0.0255685i | \(0.00813959\pi\) | ||||
−0.999673 | + | 0.0255685i | \(0.991860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 343.361 | 0.400654 | 0.200327 | − | 0.979729i | \(-0.435799\pi\) | ||||
0.200327 | + | 0.979729i | \(0.435799\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4882 | 0.0180305 | 0.00901526 | − | 0.999959i | \(-0.497130\pi\) | ||||
0.00901526 | + | 0.999959i | \(0.497130\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −880.604 | −1.02040 | −0.510199 | − | 0.860056i | \(-0.670428\pi\) | ||||
−0.510199 | + | 0.860056i | \(0.670428\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1361.30 | + | 271.733i | 1.57375 | + | 0.314143i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 228.626i | 0.263091i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −288.395 | −0.331108 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 511.784 | − | 762.594i | 0.584896 | − | 0.871536i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1243.43i | 1.41783i | 0.705296 | + | 0.708913i | \(0.250814\pi\) | ||||
−0.705296 | + | 0.708913i | \(0.749186\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1006.63i | − | 1.14260i | −0.820742 | − | 0.571299i | \(-0.806440\pi\) | ||
0.820742 | − | 0.571299i | \(-0.193560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 765.263i | 0.866662i | 0.901235 | + | 0.433331i | \(0.142662\pi\) | ||||
−0.901235 | + | 0.433331i | \(0.857338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 676.959 | 0.763200 | 0.381600 | − | 0.924328i | \(-0.375373\pi\) | ||||
0.381600 | + | 0.924328i | \(0.375373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1316.95 | 1.48138 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −736.622 | −0.824885 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −266.956 | + | 1337.36i | −0.298274 | + | 1.49426i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2037.12i | − | 2.26598i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1399.36 | −1.55312 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −541.214 | − | 108.034i | −0.598026 | − | 0.119374i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.4353i | − | 0.0258383i | −0.999917 | − | 0.0129191i | \(-0.995888\pi\) | ||
0.999917 | − | 0.0129191i | \(-0.00411240\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1253.82i | 1.37631i | 0.725563 | + | 0.688156i | \(0.241580\pi\) | ||||
−0.725563 | + | 0.688156i | \(0.758420\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 41.1913i | − | 0.0451164i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −624.464 | −0.680986 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1113.99 | 1.21217 | 0.606087 | − | 0.795398i | \(-0.292738\pi\) | ||||
0.606087 | + | 0.795398i | \(0.292738\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −642.176 | −0.695748 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −196.564 | + | 472.744i | −0.212502 | + | 0.511074i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 635.968i | 0.684573i | 0.939596 | + | 0.342286i | \(0.111201\pi\) | ||||
−0.939596 | + | 0.342286i | \(0.888799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 87.1223 | 0.0935792 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −146.108 | + | 731.955i | −0.156265 | + | 0.782839i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 81.1236i | − | 0.0865780i | −0.999063 | − | 0.0432890i | \(-0.986216\pi\) | ||
0.999063 | − | 0.0432890i | \(-0.0137836\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 338.123i | − | 0.359323i | −0.983729 | − | 0.179661i | \(-0.942500\pi\) | ||
0.983729 | − | 0.179661i | \(-0.0575002\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 295.256i | − | 0.313103i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −389.778 | −0.411592 | −0.205796 | − | 0.978595i | \(-0.565978\pi\) | ||||
−0.205796 | + | 0.978595i | \(0.565978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −123.278 | −0.129903 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1439.63 | 1.51063 | 0.755314 | − | 0.655363i | \(-0.227484\pi\) | ||||
0.755314 | + | 0.655363i | \(0.227484\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.8933 | − | 164.785i | 0.0344432 | − | 0.172550i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 485.462i | 0.506217i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1413.43 | 1.47079 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −264.935 | + | 1327.24i | −0.274544 | + | 1.37538i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 665.617i | 0.688332i | 0.938909 | + | 0.344166i | \(0.111838\pi\) | ||||
−0.938909 | + | 0.344166i | \(0.888162\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 437.415i | − | 0.450479i | −0.974303 | − | 0.225239i | \(-0.927684\pi\) | ||
0.974303 | − | 0.225239i | \(-0.0723164\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 69.2142i | 0.0711349i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1236.61 | −1.26572 | −0.632862 | − | 0.774265i | \(-0.718120\pi\) | ||||
−0.632862 | + | 0.774265i | \(0.718120\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1399.13 | 1.42914 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1273.34 | −1.29536 | −0.647680 | − | 0.761913i | \(-0.724261\pi\) | ||||
−0.647680 | + | 0.761913i | \(0.724261\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 309.385 | + | 61.7575i | 0.314097 | + | 0.0626980i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 319.668i | − | 0.323224i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 443.540 | 0.447568 | 0.223784 | − | 0.974639i | \(-0.428159\pi\) | ||||
0.223784 | + | 0.974639i | \(0.428159\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1387.78 | + | 277.020i | 1.39475 | + | 0.278412i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 557.980i | − | 0.559659i | −0.960050 | − | 0.279830i | \(-0.909722\pi\) | ||
0.960050 | − | 0.279830i | \(-0.0902780\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1620.3.b.b.809.24 | 24 | ||
3.2 | odd | 2 | inner | 1620.3.b.b.809.1 | 24 | ||
5.4 | even | 2 | inner | 1620.3.b.b.809.2 | 24 | ||
9.2 | odd | 6 | 180.3.t.a.149.1 | yes | 24 | ||
9.4 | even | 3 | 180.3.t.a.29.12 | yes | 24 | ||
9.5 | odd | 6 | 540.3.t.a.89.7 | 24 | |||
9.7 | even | 3 | 540.3.t.a.449.3 | 24 | |||
15.14 | odd | 2 | inner | 1620.3.b.b.809.23 | 24 | ||
45.2 | even | 12 | 900.3.p.f.401.7 | 24 | |||
45.4 | even | 6 | 180.3.t.a.29.1 | ✓ | 24 | ||
45.7 | odd | 12 | 2700.3.p.f.2501.3 | 24 | |||
45.13 | odd | 12 | 900.3.p.f.101.6 | 24 | |||
45.14 | odd | 6 | 540.3.t.a.89.3 | 24 | |||
45.22 | odd | 12 | 900.3.p.f.101.7 | 24 | |||
45.23 | even | 12 | 2700.3.p.f.1601.10 | 24 | |||
45.29 | odd | 6 | 180.3.t.a.149.12 | yes | 24 | ||
45.32 | even | 12 | 2700.3.p.f.1601.3 | 24 | |||
45.34 | even | 6 | 540.3.t.a.449.7 | 24 | |||
45.38 | even | 12 | 900.3.p.f.401.6 | 24 | |||
45.43 | odd | 12 | 2700.3.p.f.2501.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.t.a.29.1 | ✓ | 24 | 45.4 | even | 6 | ||
180.3.t.a.29.12 | yes | 24 | 9.4 | even | 3 | ||
180.3.t.a.149.1 | yes | 24 | 9.2 | odd | 6 | ||
180.3.t.a.149.12 | yes | 24 | 45.29 | odd | 6 | ||
540.3.t.a.89.3 | 24 | 45.14 | odd | 6 | |||
540.3.t.a.89.7 | 24 | 9.5 | odd | 6 | |||
540.3.t.a.449.3 | 24 | 9.7 | even | 3 | |||
540.3.t.a.449.7 | 24 | 45.34 | even | 6 | |||
900.3.p.f.101.6 | 24 | 45.13 | odd | 12 | |||
900.3.p.f.101.7 | 24 | 45.22 | odd | 12 | |||
900.3.p.f.401.6 | 24 | 45.38 | even | 12 | |||
900.3.p.f.401.7 | 24 | 45.2 | even | 12 | |||
1620.3.b.b.809.1 | 24 | 3.2 | odd | 2 | inner | ||
1620.3.b.b.809.2 | 24 | 5.4 | even | 2 | inner | ||
1620.3.b.b.809.23 | 24 | 15.14 | odd | 2 | inner | ||
1620.3.b.b.809.24 | 24 | 1.1 | even | 1 | trivial | ||
2700.3.p.f.1601.3 | 24 | 45.32 | even | 12 | |||
2700.3.p.f.1601.10 | 24 | 45.23 | even | 12 | |||
2700.3.p.f.2501.3 | 24 | 45.7 | odd | 12 | |||
2700.3.p.f.2501.10 | 24 | 45.43 | odd | 12 |