Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(1077,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.1077");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.c (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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1077.11 | ||
Root | \(-1.29724 - 0.347596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1077 |
Dual form | 1078.2.c.b.1077.6 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 1.55924i | − | 0.900225i | −0.892972 | − | 0.450113i | \(-0.851384\pi\) | ||
0.892972 | − | 0.450113i | \(-0.148616\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.01909i | 0.455752i | 0.973690 | + | 0.227876i | \(0.0731780\pi\) | ||||
−0.973690 | + | 0.227876i | \(0.926822\pi\) | |||||||
\(6\) | 1.55924 | 0.636555 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.568783 | 0.189594 | ||||||||
\(10\) | −1.01909 | −0.322265 | ||||||||
\(11\) | 3.09335 | + | 1.19633i | 0.932679 | + | 0.360708i | ||||
\(12\) | 1.55924i | 0.450113i | ||||||||
\(13\) | 0.167247 | 0.0463859 | 0.0231929 | − | 0.999731i | \(-0.492617\pi\) | ||||
0.0231929 | + | 0.999731i | \(0.492617\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.58900 | 0.410279 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.95232 | −0.716042 | −0.358021 | − | 0.933713i | \(-0.616548\pi\) | ||||
−0.358021 | + | 0.933713i | \(0.616548\pi\) | |||||||
\(18\) | 0.568783i | 0.134064i | ||||||||
\(19\) | −0.311700 | −0.0715090 | −0.0357545 | − | 0.999361i | \(-0.511383\pi\) | ||||
−0.0357545 | + | 0.999361i | \(0.511383\pi\) | |||||||
\(20\) | − | 1.01909i | − | 0.227876i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.19633 | + | 3.09335i | −0.255059 | + | 0.659503i | ||||
\(23\) | −0.475438 | −0.0991358 | −0.0495679 | − | 0.998771i | \(-0.515784\pi\) | ||||
−0.0495679 | + | 0.998771i | \(0.515784\pi\) | |||||||
\(24\) | −1.55924 | −0.318278 | ||||||||
\(25\) | 3.96145 | 0.792291 | ||||||||
\(26\) | 0.167247i | 0.0327998i | ||||||||
\(27\) | − | 5.56458i | − | 1.07090i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.89701i | 0.352266i | 0.984366 | + | 0.176133i | \(0.0563589\pi\) | ||||
−0.984366 | + | 0.176133i | \(0.943641\pi\) | |||||||
\(30\) | 1.58900i | 0.290111i | ||||||||
\(31\) | 2.54997i | 0.457987i | 0.973428 | + | 0.228994i | \(0.0735435\pi\) | ||||
−0.973428 | + | 0.228994i | \(0.926456\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.86537 | − | 4.82325i | 0.324719 | − | 0.839621i | ||||
\(34\) | − | 2.95232i | − | 0.506318i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.568783 | −0.0947972 | ||||||||
\(37\) | 6.09335 | 1.00174 | 0.500870 | − | 0.865523i | \(-0.333014\pi\) | ||||
0.500870 | + | 0.865523i | \(0.333014\pi\) | |||||||
\(38\) | − | 0.311700i | − | 0.0505645i | ||||||
\(39\) | − | 0.260777i | − | 0.0417577i | ||||||
\(40\) | 1.01909 | 0.161132 | ||||||||
\(41\) | 10.2084 | 1.59428 | 0.797138 | − | 0.603797i | \(-0.206346\pi\) | ||||
0.797138 | + | 0.603797i | \(0.206346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1222i | 1.54363i | 0.635848 | + | 0.771814i | \(0.280650\pi\) | ||||
−0.635848 | + | 0.771814i | \(0.719350\pi\) | |||||||
\(44\) | −3.09335 | − | 1.19633i | −0.466339 | − | 0.180354i | ||||
\(45\) | 0.579642i | 0.0864080i | ||||||||
\(46\) | − | 0.475438i | − | 0.0700996i | ||||||
\(47\) | − | 3.79859i | − | 0.554082i | −0.960858 | − | 0.277041i | \(-0.910646\pi\) | ||
0.960858 | − | 0.277041i | \(-0.0893538\pi\) | |||||||
\(48\) | − | 1.55924i | − | 0.225056i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.96145i | 0.560234i | ||||||||
\(51\) | 4.60336i | 0.644599i | ||||||||
\(52\) | −0.167247 | −0.0231929 | ||||||||
\(53\) | 8.42157 | 1.15679 | 0.578396 | − | 0.815756i | \(-0.303679\pi\) | ||||
0.578396 | + | 0.815756i | \(0.303679\pi\) | |||||||
\(54\) | 5.56458 | 0.757243 | ||||||||
\(55\) | −1.21917 | + | 3.15240i | −0.164393 | + | 0.425070i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.486014i | 0.0643742i | ||||||||
\(58\) | −1.89701 | −0.249090 | ||||||||
\(59\) | − | 6.24251i | − | 0.812706i | −0.913716 | − | 0.406353i | \(-0.866800\pi\) | ||
0.913716 | − | 0.406353i | \(-0.133200\pi\) | |||||||
\(60\) | −1.58900 | −0.205140 | ||||||||
\(61\) | 11.8792 | 1.52098 | 0.760488 | − | 0.649352i | \(-0.224960\pi\) | ||||
0.760488 | + | 0.649352i | \(0.224960\pi\) | |||||||
\(62\) | −2.54997 | −0.323846 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.170440i | 0.0211404i | ||||||||
\(66\) | 4.82325 | + | 1.86537i | 0.593702 | + | 0.229611i | ||||
\(67\) | −10.3830 | −1.26849 | −0.634244 | − | 0.773133i | \(-0.718689\pi\) | ||||
−0.634244 | + | 0.773133i | \(0.718689\pi\) | |||||||
\(68\) | 2.95232 | 0.358021 | ||||||||
\(69\) | 0.741321i | 0.0892445i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5206 | 1.72328 | 0.861639 | − | 0.507522i | \(-0.169439\pi\) | ||||
0.861639 | + | 0.507522i | \(0.169439\pi\) | |||||||
\(72\) | − | 0.568783i | − | 0.0670318i | ||||||
\(73\) | −9.70771 | −1.13620 | −0.568101 | − | 0.822959i | \(-0.692322\pi\) | ||||
−0.568101 | + | 0.822959i | \(0.692322\pi\) | |||||||
\(74\) | 6.09335i | 0.708337i | ||||||||
\(75\) | − | 6.17684i | − | 0.713240i | ||||||
\(76\) | 0.311700 | 0.0357545 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.260777 | 0.0295272 | ||||||||
\(79\) | − | 7.00567i | − | 0.788200i | −0.919068 | − | 0.394100i | \(-0.871056\pi\) | ||
0.919068 | − | 0.394100i | \(-0.128944\pi\) | |||||||
\(80\) | 1.01909i | 0.113938i | ||||||||
\(81\) | −6.97014 | −0.774459 | ||||||||
\(82\) | 10.2084i | 1.12732i | ||||||||
\(83\) | 14.6915 | 1.61261 | 0.806303 | − | 0.591502i | \(-0.201465\pi\) | ||||
0.806303 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.00868i | − | 0.326337i | ||||||
\(86\) | −10.1222 | −1.09151 | ||||||||
\(87\) | 2.95789 | 0.317119 | ||||||||
\(88\) | 1.19633 | − | 3.09335i | 0.127530 | − | 0.329752i | ||||
\(89\) | 6.90094i | 0.731498i | 0.930714 | + | 0.365749i | \(0.119187\pi\) | ||||
−0.930714 | + | 0.365749i | \(0.880813\pi\) | |||||||
\(90\) | −0.579642 | −0.0610997 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.475438 | 0.0495679 | ||||||||
\(93\) | 3.97600 | 0.412292 | ||||||||
\(94\) | 3.79859 | 0.391795 | ||||||||
\(95\) | − | 0.317651i | − | 0.0325903i | ||||||
\(96\) | 1.55924 | 0.159139 | ||||||||
\(97\) | 11.0218i | 1.11909i | 0.828799 | + | 0.559547i | \(0.189025\pi\) | ||||
−0.828799 | + | 0.559547i | \(0.810975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.75944 | + | 0.680455i | 0.176831 | + | 0.0683883i | ||||
\(100\) | −3.96145 | −0.396145 | ||||||||
\(101\) | −5.33504 | −0.530856 | −0.265428 | − | 0.964131i | \(-0.585513\pi\) | ||||
−0.265428 | + | 0.964131i | \(0.585513\pi\) | |||||||
\(102\) | −4.60336 | −0.455801 | ||||||||
\(103\) | − | 12.4533i | − | 1.22706i | −0.789672 | − | 0.613529i | \(-0.789749\pi\) | ||
0.789672 | − | 0.613529i | \(-0.210251\pi\) | |||||||
\(104\) | − | 0.167247i | − | 0.0163999i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.42157i | 0.817975i | ||||||||
\(107\) | − | 7.25414i | − | 0.701284i | −0.936510 | − | 0.350642i | \(-0.885963\pi\) | ||
0.936510 | − | 0.350642i | \(-0.114037\pi\) | |||||||
\(108\) | 5.56458i | 0.535452i | ||||||||
\(109\) | 1.16743i | 0.111820i | 0.998436 | + | 0.0559098i | \(0.0178059\pi\) | ||||
−0.998436 | + | 0.0559098i | \(0.982194\pi\) | |||||||
\(110\) | −3.15240 | − | 1.21917i | −0.300570 | − | 0.116244i | ||||
\(111\) | − | 9.50096i | − | 0.901791i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.40135 | −0.790333 | −0.395166 | − | 0.918610i | \(-0.629313\pi\) | ||||
−0.395166 | + | 0.918610i | \(0.629313\pi\) | |||||||
\(114\) | −0.486014 | −0.0455194 | ||||||||
\(115\) | − | 0.484515i | − | 0.0451813i | ||||||
\(116\) | − | 1.89701i | − | 0.176133i | ||||||
\(117\) | 0.0951271 | 0.00879450 | ||||||||
\(118\) | 6.24251 | 0.574670 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 1.58900i | − | 0.145056i | ||||||
\(121\) | 8.13757 | + | 7.40135i | 0.739779 | + | 0.672850i | ||||
\(122\) | 11.8792i | 1.07549i | ||||||||
\(123\) | − | 15.9172i | − | 1.43521i | ||||||
\(124\) | − | 2.54997i | − | 0.228994i | ||||||
\(125\) | 9.13254i | 0.816839i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.53324i | − | 0.313525i | −0.987636 | − | 0.156762i | \(-0.949894\pi\) | ||
0.987636 | − | 0.156762i | \(-0.0501057\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 15.7830 | 1.38961 | ||||||||
\(130\) | −0.170440 | −0.0149485 | ||||||||
\(131\) | −13.9797 | −1.22141 | −0.610705 | − | 0.791858i | \(-0.709114\pi\) | ||||
−0.610705 | + | 0.791858i | \(0.709114\pi\) | |||||||
\(132\) | −1.86537 | + | 4.82325i | −0.162359 | + | 0.419810i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 10.3830i | − | 0.896957i | ||||||
\(135\) | 5.67081 | 0.488066 | ||||||||
\(136\) | 2.95232i | 0.253159i | ||||||||
\(137\) | −7.01058 | −0.598954 | −0.299477 | − | 0.954104i | \(-0.596812\pi\) | ||||
−0.299477 | + | 0.954104i | \(0.596812\pi\) | |||||||
\(138\) | −0.741321 | −0.0631054 | ||||||||
\(139\) | −11.4615 | −0.972148 | −0.486074 | − | 0.873918i | \(-0.661571\pi\) | ||||
−0.486074 | + | 0.873918i | \(0.661571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.92291 | −0.498799 | ||||||||
\(142\) | 14.5206i | 1.21854i | ||||||||
\(143\) | 0.517352 | + | 0.200083i | 0.0432631 | + | 0.0167318i | ||||
\(144\) | 0.568783 | 0.0473986 | ||||||||
\(145\) | −1.93323 | −0.160546 | ||||||||
\(146\) | − | 9.70771i | − | 0.803416i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.09335 | −0.500870 | ||||||||
\(149\) | − | 14.1568i | − | 1.15977i | −0.814698 | − | 0.579886i | \(-0.803097\pi\) | ||
0.814698 | − | 0.579886i | \(-0.196903\pi\) | |||||||
\(150\) | 6.17684 | 0.504337 | ||||||||
\(151\) | 23.3040i | 1.89646i | 0.317591 | + | 0.948228i | \(0.397126\pi\) | ||||
−0.317591 | + | 0.948228i | \(0.602874\pi\) | |||||||
\(152\) | 0.311700i | 0.0252822i | ||||||||
\(153\) | −1.67923 | −0.135758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59865 | −0.208728 | ||||||||
\(156\) | 0.260777i | 0.0208789i | ||||||||
\(157\) | − | 4.03261i | − | 0.321837i | −0.986968 | − | 0.160919i | \(-0.948554\pi\) | ||
0.986968 | − | 0.160919i | \(-0.0514456\pi\) | |||||||
\(158\) | 7.00567 | 0.557342 | ||||||||
\(159\) | − | 13.1312i | − | 1.04137i | ||||||
\(160\) | −1.01909 | −0.0805662 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 6.97014i | − | 0.547626i | ||||||
\(163\) | −5.53988 | −0.433917 | −0.216958 | − | 0.976181i | \(-0.569614\pi\) | ||||
−0.216958 | + | 0.976181i | \(0.569614\pi\) | |||||||
\(164\) | −10.2084 | −0.797138 | ||||||||
\(165\) | 4.91534 | + | 1.90098i | 0.382658 | + | 0.147991i | ||||
\(166\) | 14.6915i | 1.14029i | ||||||||
\(167\) | −21.2252 | −1.64245 | −0.821226 | − | 0.570603i | \(-0.806709\pi\) | ||||
−0.821226 | + | 0.570603i | \(0.806709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9720 | −0.997848 | ||||||||
\(170\) | 3.00868 | 0.230755 | ||||||||
\(171\) | −0.177290 | −0.0135577 | ||||||||
\(172\) | − | 10.1222i | − | 0.771814i | ||||||
\(173\) | −15.0655 | −1.14541 | −0.572706 | − | 0.819761i | \(-0.694106\pi\) | ||||
−0.572706 | + | 0.819761i | \(0.694106\pi\) | |||||||
\(174\) | 2.95789i | 0.224237i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.09335 | + | 1.19633i | 0.233170 | + | 0.0901771i | ||||
\(177\) | −9.73355 | −0.731618 | ||||||||
\(178\) | −6.90094 | −0.517247 | ||||||||
\(179\) | −2.16176 | −0.161577 | −0.0807887 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807887 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(180\) | − | 0.579642i | − | 0.0432040i | ||||||
\(181\) | 5.39285i | 0.400848i | 0.979709 | + | 0.200424i | \(0.0642319\pi\) | ||||
−0.979709 | + | 0.200424i | \(0.935768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.5225i | − | 1.36922i | ||||||
\(184\) | 0.475438i | 0.0350498i | ||||||||
\(185\) | 6.20968i | 0.456544i | ||||||||
\(186\) | 3.97600i | 0.291534i | ||||||||
\(187\) | −9.13254 | − | 3.53196i | −0.667837 | − | 0.258283i | ||||
\(188\) | 3.79859i | 0.277041i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.317651 | 0.0230448 | ||||||||
\(191\) | 6.00000 | 0.434145 | 0.217072 | − | 0.976156i | \(-0.430349\pi\) | ||||
0.217072 | + | 0.976156i | \(0.430349\pi\) | |||||||
\(192\) | 1.55924i | 0.112528i | ||||||||
\(193\) | 9.59958i | 0.690993i | 0.938420 | + | 0.345496i | \(0.112289\pi\) | ||||
−0.938420 | + | 0.345496i | \(0.887711\pi\) | |||||||
\(194\) | −11.0218 | −0.791319 | ||||||||
\(195\) | 0.265756 | 0.0190311 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8180i | 1.05574i | 0.849325 | + | 0.527870i | \(0.177009\pi\) | ||||
−0.849325 | + | 0.527870i | \(0.822991\pi\) | |||||||
\(198\) | −0.680455 | + | 1.75944i | −0.0483579 | + | 0.125038i | ||||
\(199\) | − | 4.11030i | − | 0.291371i | −0.989331 | − | 0.145686i | \(-0.953461\pi\) | ||
0.989331 | − | 0.145686i | \(-0.0465388\pi\) | |||||||
\(200\) | − | 3.96145i | − | 0.280117i | ||||||
\(201\) | 16.1896i | 1.14193i | ||||||||
\(202\) | − | 5.33504i | − | 0.375372i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 4.60336i | − | 0.322300i | ||||||
\(205\) | 10.4032i | 0.726594i | ||||||||
\(206\) | 12.4533 | 0.867661 | ||||||||
\(207\) | −0.270422 | −0.0187956 | ||||||||
\(208\) | 0.167247 | 0.0115965 | ||||||||
\(209\) | −0.964197 | − | 0.372898i | −0.0666949 | − | 0.0257939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.52456i | − | 0.518012i | −0.965876 | − | 0.259006i | \(-0.916605\pi\) | ||
0.965876 | − | 0.259006i | \(-0.0833950\pi\) | |||||||
\(212\) | −8.42157 | −0.578396 | ||||||||
\(213\) | − | 22.6410i | − | 1.55134i | ||||||
\(214\) | 7.25414 | 0.495883 | ||||||||
\(215\) | −10.3155 | −0.703511 | ||||||||
\(216\) | −5.56458 | −0.378621 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.16743 | −0.0790685 | ||||||||
\(219\) | 15.1366i | 1.02284i | ||||||||
\(220\) | 1.21917 | − | 3.15240i | 0.0821967 | − | 0.212535i | ||||
\(221\) | −0.493765 | −0.0332142 | ||||||||
\(222\) | 9.50096 | 0.637663 | ||||||||
\(223\) | 13.5885i | 0.909951i | 0.890504 | + | 0.454975i | \(0.150352\pi\) | ||||
−0.890504 | + | 0.454975i | \(0.849648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.25321 | 0.150214 | ||||||||
\(226\) | − | 8.40135i | − | 0.558850i | ||||||
\(227\) | −21.6635 | −1.43786 | −0.718929 | − | 0.695084i | \(-0.755367\pi\) | ||||
−0.718929 | + | 0.695084i | \(0.755367\pi\) | |||||||
\(228\) | − | 0.486014i | − | 0.0321871i | ||||||
\(229\) | 30.0632i | 1.98663i | 0.115421 | + | 0.993317i | \(0.463178\pi\) | ||||
−0.115421 | + | 0.993317i | \(0.536822\pi\) | |||||||
\(230\) | 0.484515 | 0.0319480 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.89701 | 0.124545 | ||||||||
\(233\) | − | 16.1916i | − | 1.06075i | −0.847764 | − | 0.530373i | \(-0.822052\pi\) | ||
0.847764 | − | 0.530373i | \(-0.177948\pi\) | |||||||
\(234\) | 0.0951271i | 0.00621865i | ||||||||
\(235\) | 3.87112 | 0.252524 | ||||||||
\(236\) | 6.24251i | 0.406353i | ||||||||
\(237\) | −10.9235 | −0.709558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.0701i | − | 1.68633i | −0.537652 | − | 0.843167i | \(-0.680689\pi\) | ||
0.537652 | − | 0.843167i | \(-0.319311\pi\) | |||||||
\(240\) | 1.58900 | 0.102570 | ||||||||
\(241\) | 13.2044 | 0.850572 | 0.425286 | − | 0.905059i | \(-0.360173\pi\) | ||||
0.425286 | + | 0.905059i | \(0.360173\pi\) | |||||||
\(242\) | −7.40135 | + | 8.13757i | −0.475777 | + | 0.523103i | ||||
\(243\) | − | 5.82564i | − | 0.373715i | ||||||
\(244\) | −11.8792 | −0.760488 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.9172 | 1.01485 | ||||||||
\(247\) | −0.0521308 | −0.00331700 | ||||||||
\(248\) | 2.54997 | 0.161923 | ||||||||
\(249\) | − | 22.9076i | − | 1.45171i | ||||||
\(250\) | −9.13254 | −0.577593 | ||||||||
\(251\) | − | 28.9829i | − | 1.82939i | −0.404149 | − | 0.914693i | \(-0.632432\pi\) | ||
0.404149 | − | 0.914693i | \(-0.367568\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.47070 | − | 0.568783i | −0.0924618 | − | 0.0357591i | ||||
\(254\) | 3.53324 | 0.221695 | ||||||||
\(255\) | −4.69125 | −0.293777 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.98602i | 0.435776i | 0.975974 | + | 0.217888i | \(0.0699167\pi\) | ||||
−0.975974 | + | 0.217888i | \(0.930083\pi\) | |||||||
\(258\) | 15.7830i | 0.982605i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 0.170440i | − | 0.0105702i | ||||||
\(261\) | 1.07899i | 0.0667877i | ||||||||
\(262\) | − | 13.9797i | − | 0.863668i | ||||||
\(263\) | − | 4.47070i | − | 0.275675i | −0.990455 | − | 0.137837i | \(-0.955985\pi\) | ||
0.990455 | − | 0.137837i | \(-0.0440152\pi\) | |||||||
\(264\) | −4.82325 | − | 1.86537i | −0.296851 | − | 0.114805i | ||||
\(265\) | 8.58235i | 0.527210i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7602 | 0.658513 | ||||||||
\(268\) | 10.3830 | 0.634244 | ||||||||
\(269\) | − | 2.21730i | − | 0.135191i | −0.997713 | − | 0.0675956i | \(-0.978467\pi\) | ||
0.997713 | − | 0.0675956i | \(-0.0215328\pi\) | |||||||
\(270\) | 5.67081i | 0.345115i | ||||||||
\(271\) | 22.5122 | 1.36752 | 0.683759 | − | 0.729708i | \(-0.260344\pi\) | ||||
0.683759 | + | 0.729708i | \(0.260344\pi\) | |||||||
\(272\) | −2.95232 | −0.179011 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 7.01058i | − | 0.423524i | ||||||
\(275\) | 12.2541 | + | 4.73922i | 0.738952 | + | 0.285786i | ||||
\(276\) | − | 0.741321i | − | 0.0446223i | ||||||
\(277\) | − | 24.4658i | − | 1.47001i | −0.678063 | − | 0.735004i | \(-0.737180\pi\) | ||
0.678063 | − | 0.735004i | \(-0.262820\pi\) | |||||||
\(278\) | − | 11.4615i | − | 0.687413i | ||||||
\(279\) | 1.45038i | 0.0868319i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.3532i | − | 0.677273i | −0.940917 | − | 0.338636i | \(-0.890034\pi\) | ||
0.940917 | − | 0.338636i | \(-0.109966\pi\) | |||||||
\(282\) | − | 5.92291i | − | 0.352704i | ||||||
\(283\) | 21.6537 | 1.28718 | 0.643589 | − | 0.765371i | \(-0.277445\pi\) | ||||
0.643589 | + | 0.765371i | \(0.277445\pi\) | |||||||
\(284\) | −14.5206 | −0.861639 | ||||||||
\(285\) | −0.495293 | −0.0293386 | ||||||||
\(286\) | −0.200083 | + | 0.517352i | −0.0118312 | + | 0.0305916i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.568783i | 0.0335159i | ||||||||
\(289\) | −8.28382 | −0.487283 | ||||||||
\(290\) | − | 1.93323i | − | 0.113523i | ||||||
\(291\) | 17.1856 | 1.00744 | ||||||||
\(292\) | 9.70771 | 0.568101 | ||||||||
\(293\) | −12.1233 | −0.708249 | −0.354124 | − | 0.935198i | \(-0.615221\pi\) | ||||
−0.354124 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.36169 | 0.370392 | ||||||||
\(296\) | − | 6.09335i | − | 0.354168i | ||||||
\(297\) | 6.65709 | − | 17.2132i | 0.386284 | − | 0.998808i | ||||
\(298\) | 14.1568 | 0.820083 | ||||||||
\(299\) | −0.0795155 | −0.00459850 | ||||||||
\(300\) | 6.17684i | 0.356620i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −23.3040 | −1.34100 | ||||||||
\(303\) | 8.31858i | 0.477890i | ||||||||
\(304\) | −0.311700 | −0.0178772 | ||||||||
\(305\) | 12.1060i | 0.693187i | ||||||||
\(306\) | − | 1.67923i | − | 0.0959952i | ||||||
\(307\) | −9.65817 | −0.551221 | −0.275610 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275610 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.4176 | −1.10463 | ||||||||
\(310\) | − | 2.59865i | − | 0.147593i | ||||||
\(311\) | 17.6778i | 1.00242i | 0.865327 | + | 0.501208i | \(0.167111\pi\) | ||||
−0.865327 | + | 0.501208i | \(0.832889\pi\) | |||||||
\(312\) | −0.260777 | −0.0147636 | ||||||||
\(313\) | − | 28.8103i | − | 1.62846i | −0.580545 | − | 0.814228i | \(-0.697161\pi\) | ||
0.580545 | − | 0.814228i | \(-0.302839\pi\) | |||||||
\(314\) | 4.03261 | 0.227573 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00567i | 0.394100i | ||||||||
\(317\) | 10.3456 | 0.581066 | 0.290533 | − | 0.956865i | \(-0.406167\pi\) | ||||
0.290533 | + | 0.956865i | \(0.406167\pi\) | |||||||
\(318\) | 13.1312 | 0.736362 | ||||||||
\(319\) | −2.26946 | + | 5.86811i | −0.127065 | + | 0.328551i | ||||
\(320\) | − | 1.01909i | − | 0.0569689i | ||||||
\(321\) | −11.3109 | −0.631314 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.920239 | 0.0512034 | ||||||||
\(324\) | 6.97014 | 0.387230 | ||||||||
\(325\) | 0.662540 | 0.0367511 | ||||||||
\(326\) | − | 5.53988i | − | 0.306826i | ||||||
\(327\) | 1.82030 | 0.100663 | ||||||||
\(328\) | − | 10.2084i | − | 0.563662i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.90098 | + | 4.91534i | −0.104646 | + | 0.270580i | ||||
\(331\) | −26.8448 | −1.47553 | −0.737763 | − | 0.675060i | \(-0.764118\pi\) | ||||
−0.737763 | + | 0.675060i | \(0.764118\pi\) | |||||||
\(332\) | −14.6915 | −0.806303 | ||||||||
\(333\) | 3.46579 | 0.189924 | ||||||||
\(334\) | − | 21.2252i | − | 1.16139i | ||||||
\(335\) | − | 10.5813i | − | 0.578116i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5505i | 0.792614i | 0.918118 | + | 0.396307i | \(0.129708\pi\) | ||||
−0.918118 | + | 0.396307i | \(0.870292\pi\) | |||||||
\(338\) | − | 12.9720i | − | 0.705585i | ||||||
\(339\) | 13.0997i | 0.711477i | ||||||||
\(340\) | 3.00868i | 0.163169i | ||||||||
\(341\) | −3.05061 | + | 7.88792i | −0.165200 | + | 0.427155i | ||||
\(342\) | − | 0.177290i | − | 0.00958674i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.1222 | 0.545755 | ||||||||
\(345\) | −0.755474 | −0.0406733 | ||||||||
\(346\) | − | 15.0655i | − | 0.809928i | ||||||
\(347\) | − | 28.5417i | − | 1.53220i | −0.642721 | − | 0.766101i | \(-0.722194\pi\) | ||
0.642721 | − | 0.766101i | \(-0.277806\pi\) | |||||||
\(348\) | −2.95789 | −0.158559 | ||||||||
\(349\) | 34.6026 | 1.85224 | 0.926118 | − | 0.377235i | \(-0.123125\pi\) | ||||
0.926118 | + | 0.377235i | \(0.123125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.930656i | − | 0.0496748i | ||||||
\(352\) | −1.19633 | + | 3.09335i | −0.0637648 | + | 0.164876i | ||||
\(353\) | 16.9203i | 0.900579i | 0.892883 | + | 0.450289i | \(0.148679\pi\) | ||||
−0.892883 | + | 0.450289i | \(0.851321\pi\) | |||||||
\(354\) | − | 9.73355i | − | 0.517332i | ||||||
\(355\) | 14.7978i | 0.785386i | ||||||||
\(356\) | − | 6.90094i | − | 0.365749i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.16176i | − | 0.114252i | ||||||
\(359\) | − | 30.3511i | − | 1.60187i | −0.598752 | − | 0.800934i | \(-0.704337\pi\) | ||
0.598752 | − | 0.800934i | \(-0.295663\pi\) | |||||||
\(360\) | 0.579642 | 0.0305498 | ||||||||
\(361\) | −18.9028 | −0.994886 | ||||||||
\(362\) | −5.39285 | −0.283442 | ||||||||
\(363\) | 11.5405 | − | 12.6884i | 0.605717 | − | 0.665968i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.89304i | − | 0.517825i | ||||||
\(366\) | 18.5225 | 0.968186 | ||||||||
\(367\) | 17.4215i | 0.909395i | 0.890646 | + | 0.454698i | \(0.150253\pi\) | ||||
−0.890646 | + | 0.454698i | \(0.849747\pi\) | |||||||
\(368\) | −0.475438 | −0.0247839 | ||||||||
\(369\) | 5.80634 | 0.302266 | ||||||||
\(370\) | −6.20968 | −0.322826 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.97600 | −0.206146 | ||||||||
\(373\) | − | 9.15211i | − | 0.473878i | −0.971524 | − | 0.236939i | \(-0.923856\pi\) | ||
0.971524 | − | 0.236939i | \(-0.0761442\pi\) | |||||||
\(374\) | 3.53196 | − | 9.13254i | 0.182633 | − | 0.472232i | ||||
\(375\) | 14.2398 | 0.735339 | ||||||||
\(376\) | −3.79859 | −0.195898 | ||||||||
\(377\) | 0.317269i | 0.0163402i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.15382 | −0.316100 | −0.158050 | − | 0.987431i | \(-0.550521\pi\) | ||||
−0.158050 | + | 0.987431i | \(0.550521\pi\) | |||||||
\(380\) | 0.317651i | 0.0162952i | ||||||||
\(381\) | −5.50916 | −0.282243 | ||||||||
\(382\) | 6.00000i | 0.306987i | ||||||||
\(383\) | 12.9651i | 0.662484i | 0.943546 | + | 0.331242i | \(0.107468\pi\) | ||||
−0.943546 | + | 0.331242i | \(0.892532\pi\) | |||||||
\(384\) | −1.55924 | −0.0795694 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.59958 | −0.488606 | ||||||||
\(387\) | 5.75737i | 0.292663i | ||||||||
\(388\) | − | 11.0218i | − | 0.559547i | ||||||
\(389\) | 5.16647 | 0.261950 | 0.130975 | − | 0.991386i | \(-0.458189\pi\) | ||||
0.130975 | + | 0.991386i | \(0.458189\pi\) | |||||||
\(390\) | 0.265756i | 0.0134571i | ||||||||
\(391\) | 1.40365 | 0.0709854 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.7976i | 1.09954i | ||||||||
\(394\) | −14.8180 | −0.746521 | ||||||||
\(395\) | 7.13942 | 0.359223 | ||||||||
\(396\) | −1.75944 | − | 0.680455i | −0.0884154 | − | 0.0341942i | ||||
\(397\) | 9.25712i | 0.464602i | 0.972644 | + | 0.232301i | \(0.0746254\pi\) | ||||
−0.972644 | + | 0.232301i | \(0.925375\pi\) | |||||||
\(398\) | 4.11030 | 0.206030 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.96145 | 0.198073 | ||||||||
\(401\) | −30.9248 | −1.54431 | −0.772155 | − | 0.635435i | \(-0.780821\pi\) | ||||
−0.772155 | + | 0.635435i | \(0.780821\pi\) | |||||||
\(402\) | −16.1896 | −0.807463 | ||||||||
\(403\) | 0.426473i | 0.0212441i | ||||||||
\(404\) | 5.33504 | 0.265428 | ||||||||
\(405\) | − | 7.10320i | − | 0.352961i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.8488 | + | 7.28968i | 0.934301 | + | 0.361336i | ||||
\(408\) | 4.60336 | 0.227900 | ||||||||
\(409\) | −23.8397 | −1.17880 | −0.589399 | − | 0.807842i | \(-0.700635\pi\) | ||||
−0.589399 | + | 0.807842i | \(0.700635\pi\) | |||||||
\(410\) | −10.4032 | −0.513780 | ||||||||
\(411\) | 10.9311i | 0.539193i | ||||||||
\(412\) | 12.4533i | 0.613529i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 0.270422i | − | 0.0132905i | ||||||
\(415\) | 14.9720i | 0.734948i | ||||||||
\(416\) | 0.167247i | 0.00819994i | ||||||||
\(417\) | 17.8711i | 0.875152i | ||||||||
\(418\) | 0.372898 | − | 0.964197i | 0.0182390 | − | 0.0471604i | ||||
\(419\) | − | 5.03426i | − | 0.245940i | −0.992410 | − | 0.122970i | \(-0.960758\pi\) | ||
0.992410 | − | 0.122970i | \(-0.0392418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9250 | −0.824872 | −0.412436 | − | 0.910987i | \(-0.635322\pi\) | ||||
−0.412436 | + | 0.910987i | \(0.635322\pi\) | |||||||
\(422\) | 7.52456 | 0.366290 | ||||||||
\(423\) | − | 2.16058i | − | 0.105051i | ||||||
\(424\) | − | 8.42157i | − | 0.408988i | ||||||
\(425\) | −11.6955 | −0.567314 | ||||||||
\(426\) | 22.6410 | 1.09696 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.25414i | 0.350642i | ||||||||
\(429\) | 0.311976 | − | 0.806673i | 0.0150624 | − | 0.0389465i | ||||
\(430\) | − | 10.3155i | − | 0.497457i | ||||||
\(431\) | − | 5.99907i | − | 0.288965i | −0.989507 | − | 0.144482i | \(-0.953848\pi\) | ||
0.989507 | − | 0.144482i | \(-0.0461517\pi\) | |||||||
\(432\) | − | 5.56458i | − | 0.267726i | ||||||
\(433\) | 36.1175i | 1.73570i | 0.496829 | + | 0.867849i | \(0.334498\pi\) | ||||
−0.496829 | + | 0.867849i | \(0.665502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.01436i | 0.144527i | ||||||||
\(436\) | − | 1.16743i | − | 0.0559098i | ||||||
\(437\) | 0.148194 | 0.00708909 | ||||||||
\(438\) | −15.1366 | −0.723255 | ||||||||
\(439\) | 11.3496 | 0.541688 | 0.270844 | − | 0.962623i | \(-0.412697\pi\) | ||||
0.270844 | + | 0.962623i | \(0.412697\pi\) | |||||||
\(440\) | 3.15240 | + | 1.21917i | 0.150285 | + | 0.0581219i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.493765i | − | 0.0234860i | ||||||
\(443\) | −4.75076 | −0.225715 | −0.112858 | − | 0.993611i | \(-0.536000\pi\) | ||||
−0.112858 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(444\) | 9.50096i | 0.450896i | ||||||||
\(445\) | −7.03268 | −0.333381 | ||||||||
\(446\) | −13.5885 | −0.643432 | ||||||||
\(447\) | −22.0738 | −1.04406 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.33297 | 0.346064 | 0.173032 | − | 0.984916i | \(-0.444644\pi\) | ||||
0.173032 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(450\) | 2.25321i | 0.106217i | ||||||||
\(451\) | 31.5780 | + | 12.2126i | 1.48695 | + | 0.575069i | ||||
\(452\) | 8.40135 | 0.395166 | ||||||||
\(453\) | 36.3365 | 1.70724 | ||||||||
\(454\) | − | 21.6635i | − | 1.01672i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.486014 | 0.0227597 | ||||||||
\(457\) | 13.5176i | 0.632326i | 0.948705 | + | 0.316163i | \(0.102395\pi\) | ||||
−0.948705 | + | 0.316163i | \(0.897605\pi\) | |||||||
\(458\) | −30.0632 | −1.40476 | ||||||||
\(459\) | 16.4284i | 0.766812i | ||||||||
\(460\) | 0.484515i | 0.0225906i | ||||||||
\(461\) | 18.5730 | 0.865033 | 0.432516 | − | 0.901626i | \(-0.357626\pi\) | ||||
0.432516 | + | 0.901626i | \(0.357626\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.2849 | 1.31451 | 0.657256 | − | 0.753667i | \(-0.271717\pi\) | ||||
0.657256 | + | 0.753667i | \(0.271717\pi\) | |||||||
\(464\) | 1.89701i | 0.0880665i | ||||||||
\(465\) | 4.05191i | 0.187903i | ||||||||
\(466\) | 16.1916 | 0.750061 | ||||||||
\(467\) | − | 21.5792i | − | 0.998564i | −0.866439 | − | 0.499282i | \(-0.833597\pi\) | ||
0.866439 | − | 0.499282i | \(-0.166403\pi\) | |||||||
\(468\) | −0.0951271 | −0.00439725 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.87112i | 0.178561i | ||||||||
\(471\) | −6.28779 | −0.289726 | ||||||||
\(472\) | −6.24251 | −0.287335 | ||||||||
\(473\) | −12.1096 | + | 31.3116i | −0.556800 | + | 1.43971i | ||||
\(474\) | − | 10.9235i | − | 0.501733i | ||||||
\(475\) | −1.23479 | −0.0566559 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.79005 | 0.219321 | ||||||||
\(478\) | 26.0701 | 1.19242 | ||||||||
\(479\) | −6.93560 | −0.316896 | −0.158448 | − | 0.987367i | \(-0.550649\pi\) | ||||
−0.158448 | + | 0.987367i | \(0.550649\pi\) | |||||||
\(480\) | 1.58900i | 0.0725278i | ||||||||
\(481\) | 1.01909 | 0.0464666 | ||||||||
\(482\) | 13.2044i | 0.601445i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.13757 | − | 7.40135i | −0.369889 | − | 0.336425i | ||||
\(485\) | −11.2322 | −0.510029 | ||||||||
\(486\) | 5.82564 | 0.264256 | ||||||||
\(487\) | −12.1740 | −0.551658 | −0.275829 | − | 0.961207i | \(-0.588952\pi\) | ||||
−0.275829 | + | 0.961207i | \(0.588952\pi\) | |||||||
\(488\) | − | 11.8792i | − | 0.537746i | ||||||
\(489\) | 8.63798i | 0.390623i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.37152i | − | 0.107025i | −0.998567 | − | 0.0535125i | \(-0.982958\pi\) | ||
0.998567 | − | 0.0535125i | \(-0.0170417\pi\) | |||||||
\(492\) | 15.9172i | 0.717604i | ||||||||
\(493\) | − | 5.60058i | − | 0.252237i | ||||||
\(494\) | − | 0.0521308i | − | 0.00234548i | ||||||
\(495\) | −0.693446 | + | 1.79303i | −0.0311681 | + | 0.0805909i | ||||
\(496\) | 2.54997i | 0.114497i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 22.9076 | 1.02651 | ||||||||
\(499\) | −3.92892 | −0.175883 | −0.0879413 | − | 0.996126i | \(-0.528029\pi\) | ||||
−0.0879413 | + | 0.996126i | \(0.528029\pi\) | |||||||
\(500\) | − | 9.13254i | − | 0.408420i | ||||||
\(501\) | 33.0950i | 1.47858i | ||||||||
\(502\) | 28.9829 | 1.29357 | ||||||||
\(503\) | 19.8703 | 0.885971 | 0.442986 | − | 0.896529i | \(-0.353919\pi\) | ||||
0.442986 | + | 0.896529i | \(0.353919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.43689i | − | 0.241938i | ||||||
\(506\) | 0.568783 | − | 1.47070i | 0.0252855 | − | 0.0653804i | ||||
\(507\) | 20.2265i | 0.898288i | ||||||||
\(508\) | 3.53324i | 0.156762i | ||||||||
\(509\) | 15.2927i | 0.677836i | 0.940816 | + | 0.338918i | \(0.110061\pi\) | ||||
−0.940816 | + | 0.338918i | \(0.889939\pi\) | |||||||
\(510\) | − | 4.69125i | − | 0.207732i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.73448i | 0.0765792i | ||||||||
\(514\) | −6.98602 | −0.308140 | ||||||||
\(515\) | 12.6910 | 0.559234 | ||||||||
\(516\) | −15.7830 | −0.694807 | ||||||||
\(517\) | 4.54439 | − | 11.7504i | 0.199862 | − | 0.516780i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4907i | 1.03113i | ||||||||
\(520\) | 0.170440 | 0.00747427 | ||||||||
\(521\) | 0.140713i | 0.00616475i | 0.999995 | + | 0.00308237i | \(0.000981152\pi\) | ||||
−0.999995 | + | 0.00308237i | \(0.999019\pi\) | |||||||
\(522\) | −1.07899 | −0.0472260 | ||||||||
\(523\) | −9.12307 | −0.398924 | −0.199462 | − | 0.979906i | \(-0.563919\pi\) | ||||
−0.199462 | + | 0.979906i | \(0.563919\pi\) | |||||||
\(524\) | 13.9797 | 0.610705 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.47070 | 0.194932 | ||||||||
\(527\) | − | 7.52831i | − | 0.327938i | ||||||
\(528\) | 1.86537 | − | 4.82325i | 0.0811797 | − | 0.209905i | ||||
\(529\) | −22.7740 | −0.990172 | ||||||||
\(530\) | −8.58235 | −0.372794 | ||||||||
\(531\) | − | 3.55064i | − | 0.154085i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.70731 | 0.0739519 | ||||||||
\(534\) | 10.7602i | 0.465639i | ||||||||
\(535\) | 7.39263 | 0.319611 | ||||||||
\(536\) | 10.3830i | 0.448478i | ||||||||
\(537\) | 3.37069i | 0.145456i | ||||||||
\(538\) | 2.21730 | 0.0955946 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.67081 | −0.244033 | ||||||||
\(541\) | 25.0259i | 1.07595i | 0.842962 | + | 0.537973i | \(0.180810\pi\) | ||||
−0.842962 | + | 0.537973i | \(0.819190\pi\) | |||||||
\(542\) | 22.5122i | 0.966981i | ||||||||
\(543\) | 8.40873 | 0.360853 | ||||||||
\(544\) | − | 2.95232i | − | 0.126580i | ||||||
\(545\) | −1.18972 | −0.0509620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.7246i | 1.57023i | 0.619348 | + | 0.785116i | \(0.287397\pi\) | ||||
−0.619348 | + | 0.785116i | \(0.712603\pi\) | |||||||
\(548\) | 7.01058 | 0.299477 | ||||||||
\(549\) | 6.75670 | 0.288369 | ||||||||
\(550\) | −4.73922 | + | 12.2541i | −0.202081 | + | 0.522518i | ||||
\(551\) | − | 0.591299i | − | 0.0251902i | ||||||
\(552\) | 0.741321 | 0.0315527 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.4658 | 1.03945 | ||||||||
\(555\) | 9.68235 | 0.410993 | ||||||||
\(556\) | 11.4615 | 0.486074 | ||||||||
\(557\) | − | 38.7766i | − | 1.64302i | −0.570195 | − | 0.821509i | \(-0.693132\pi\) | ||
0.570195 | − | 0.821509i | \(-0.306868\pi\) | |||||||
\(558\) | −1.45038 | −0.0613994 | ||||||||
\(559\) | 1.69291i | 0.0716025i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.50716 | + | 14.2398i | −0.232512 | + | 0.601204i | ||||
\(562\) | 11.3532 | 0.478904 | ||||||||
\(563\) | −43.2493 | −1.82274 | −0.911371 | − | 0.411586i | \(-0.864975\pi\) | ||||
−0.911371 | + | 0.411586i | \(0.864975\pi\) | |||||||
\(564\) | 5.92291 | 0.249399 | ||||||||
\(565\) | − | 8.56175i | − | 0.360195i | ||||||
\(566\) | 21.6537i | 0.910172i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 14.5206i | − | 0.609270i | ||||||
\(569\) | 21.3369i | 0.894490i | 0.894412 | + | 0.447245i | \(0.147595\pi\) | ||||
−0.894412 | + | 0.447245i | \(0.852405\pi\) | |||||||
\(570\) | − | 0.495293i | − | 0.0207455i | ||||||
\(571\) | 22.5948i | 0.945564i | 0.881179 | + | 0.472782i | \(0.156750\pi\) | ||||
−0.881179 | + | 0.472782i | \(0.843250\pi\) | |||||||
\(572\) | −0.517352 | − | 0.200083i | −0.0216316 | − | 0.00836589i | ||||
\(573\) | − | 9.35542i | − | 0.390828i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.88343 | −0.0785443 | ||||||||
\(576\) | −0.568783 | −0.0236993 | ||||||||
\(577\) | 33.8740i | 1.41019i | 0.709110 | + | 0.705097i | \(0.249097\pi\) | ||||
−0.709110 | + | 0.705097i | \(0.750903\pi\) | |||||||
\(578\) | − | 8.28382i | − | 0.344561i | ||||||
\(579\) | 14.9680 | 0.622049 | ||||||||
\(580\) | 1.93323 | 0.0802729 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.1856i | 0.712365i | ||||||||
\(583\) | 26.0508 | + | 10.0750i | 1.07892 | + | 0.417265i | ||||
\(584\) | 9.70771i | 0.401708i | ||||||||
\(585\) | 0.0969432i | 0.00400811i | ||||||||
\(586\) | − | 12.1233i | − | 0.500807i | ||||||
\(587\) | − | 6.07819i | − | 0.250874i | −0.992102 | − | 0.125437i | \(-0.959967\pi\) | ||
0.992102 | − | 0.125437i | \(-0.0400332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.794825i | − | 0.0327502i | ||||||
\(590\) | 6.36169i | 0.261907i | ||||||||
\(591\) | 23.1048 | 0.950404 | ||||||||
\(592\) | 6.09335 | 0.250435 | ||||||||
\(593\) | −1.61839 | −0.0664594 | −0.0332297 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332297 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(594\) | 17.2132 | + | 6.65709i | 0.706264 | + | 0.273144i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.1568i | 0.579886i | ||||||||
\(597\) | −6.40892 | −0.262300 | ||||||||
\(598\) | − | 0.0795155i | − | 0.00325163i | ||||||
\(599\) | 5.27910 | 0.215698 | 0.107849 | − | 0.994167i | \(-0.465604\pi\) | ||||
0.107849 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(600\) | −6.17684 | −0.252168 | ||||||||
\(601\) | 32.7945 | 1.33771 | 0.668857 | − | 0.743391i | \(-0.266784\pi\) | ||||
0.668857 | + | 0.743391i | \(0.266784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.90569 | −0.240498 | ||||||||
\(604\) | − | 23.3040i | − | 0.948228i | ||||||
\(605\) | −7.54265 | + | 8.29292i | −0.306652 | + | 0.337155i | ||||
\(606\) | −8.31858 | −0.337919 | ||||||||
\(607\) | 0.665819 | 0.0270248 | 0.0135124 | − | 0.999909i | \(-0.495699\pi\) | ||||
0.0135124 | + | 0.999909i | \(0.495699\pi\) | |||||||
\(608\) | − | 0.311700i | − | 0.0126411i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1060 | −0.490158 | ||||||||
\(611\) | − | 0.635302i | − | 0.0257016i | ||||||
\(612\) | 1.67923 | 0.0678788 | ||||||||
\(613\) | 4.29442i | 0.173450i | 0.996232 | + | 0.0867251i | \(0.0276402\pi\) | ||||
−0.996232 | + | 0.0867251i | \(0.972360\pi\) | |||||||
\(614\) | − | 9.65817i | − | 0.389772i | ||||||
\(615\) | 16.2211 | 0.654098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9913 | −1.24766 | −0.623831 | − | 0.781559i | \(-0.714425\pi\) | ||||
−0.623831 | + | 0.781559i | \(0.714425\pi\) | |||||||
\(618\) | − | 19.4176i | − | 0.781091i | ||||||
\(619\) | 0.791382i | 0.0318083i | 0.999874 | + | 0.0159042i | \(0.00506266\pi\) | ||||
−0.999874 | + | 0.0159042i | \(0.994937\pi\) | |||||||
\(620\) | 2.59865 | 0.104364 | ||||||||
\(621\) | 2.64561i | 0.106165i | ||||||||
\(622\) | −17.6778 | −0.708815 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 0.260777i | − | 0.0104394i | ||||||
\(625\) | 10.5004 | 0.420015 | ||||||||
\(626\) | 28.8103 | 1.15149 | ||||||||
\(627\) | −0.581436 | + | 1.50341i | −0.0232203 | + | 0.0600404i | ||||
\(628\) | 4.03261i | 0.160919i | ||||||||
\(629\) | −17.9895 | −0.717288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.3677 | −1.36816 | −0.684078 | − | 0.729409i | \(-0.739795\pi\) | ||||
−0.684078 | + | 0.729409i | \(0.739795\pi\) | |||||||
\(632\) | −7.00567 | −0.278671 | ||||||||
\(633\) | −11.7326 | −0.466328 | ||||||||
\(634\) | 10.3456i | 0.410876i | ||||||||
\(635\) | 3.60070 | 0.142889 | ||||||||
\(636\) | 13.1312i | 0.520687i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.86811 | − | 2.26946i | −0.232321 | − | 0.0898488i | ||||
\(639\) | 8.25907 | 0.326724 | ||||||||
\(640\) | 1.01909 | 0.0402831 | ||||||||
\(641\) | 4.95879 | 0.195860 | 0.0979301 | − | 0.995193i | \(-0.468778\pi\) | ||||
0.0979301 | + | 0.995193i | \(0.468778\pi\) | |||||||
\(642\) | − | 11.3109i | − | 0.446406i | ||||||
\(643\) | − | 48.1404i | − | 1.89847i | −0.314562 | − | 0.949237i | \(-0.601858\pi\) | ||
0.314562 | − | 0.949237i | \(-0.398142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.0843i | 0.633318i | ||||||||
\(646\) | 0.920239i | 0.0362063i | ||||||||
\(647\) | 3.16572i | 0.124457i | 0.998062 | + | 0.0622287i | \(0.0198208\pi\) | ||||
−0.998062 | + | 0.0622287i | \(0.980179\pi\) | |||||||
\(648\) | 6.97014i | 0.273813i | ||||||||
\(649\) | 7.46813 | − | 19.3102i | 0.293150 | − | 0.757993i | ||||
\(650\) | 0.662540i | 0.0259869i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.53988 | 0.216958 | ||||||||
\(653\) | −22.1211 | −0.865667 | −0.432833 | − | 0.901474i | \(-0.642486\pi\) | ||||
−0.432833 | + | 0.901474i | \(0.642486\pi\) | |||||||
\(654\) | 1.82030i | 0.0711794i | ||||||||
\(655\) | − | 14.2466i | − | 0.556660i | ||||||
\(656\) | 10.2084 | 0.398569 | ||||||||
\(657\) | −5.52158 | −0.215417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.6258i | − | 0.959286i | −0.877464 | − | 0.479643i | \(-0.840766\pi\) | ||
0.877464 | − | 0.479643i | \(-0.159234\pi\) | |||||||
\(660\) | −4.91534 | − | 1.90098i | −0.191329 | − | 0.0739956i | ||||
\(661\) | − | 27.7365i | − | 1.07882i | −0.842042 | − | 0.539412i | \(-0.818647\pi\) | ||
0.842042 | − | 0.539412i | \(-0.181353\pi\) | |||||||
\(662\) | − | 26.8448i | − | 1.04335i | ||||||
\(663\) | 0.769897i | 0.0299003i | ||||||||
\(664\) | − | 14.6915i | − | 0.570143i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.46579i | 0.134297i | ||||||||
\(667\) | − | 0.901912i | − | 0.0349222i | ||||||
\(668\) | 21.2252 | 0.821226 | ||||||||
\(669\) | 21.1876 | 0.819161 | ||||||||
\(670\) | 10.5813 | 0.408789 | ||||||||
\(671\) | 36.7465 | + | 14.2115i | 1.41858 | + | 0.548629i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.9518i | − | 0.614897i | −0.951565 | − | 0.307449i | \(-0.900525\pi\) | ||
0.951565 | − | 0.307449i | \(-0.0994752\pi\) | |||||||
\(674\) | −14.5505 | −0.560463 | ||||||||
\(675\) | − | 22.0438i | − | 0.848466i | ||||||
\(676\) | 12.9720 | 0.498924 | ||||||||
\(677\) | 15.0515 | 0.578475 | 0.289238 | − | 0.957257i | \(-0.406598\pi\) | ||||
0.289238 | + | 0.957257i | \(0.406598\pi\) | |||||||
\(678\) | −13.0997 | −0.503091 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00868 | −0.115378 | ||||||||
\(681\) | 33.7785i | 1.29440i | ||||||||
\(682\) | −7.88792 | − | 3.05061i | −0.302044 | − | 0.116814i | ||||
\(683\) | −5.29346 | −0.202549 | −0.101274 | − | 0.994859i | \(-0.532292\pi\) | ||||
−0.101274 | + | 0.994859i | \(0.532292\pi\) | |||||||
\(684\) | 0.177290 | 0.00677885 | ||||||||
\(685\) | − | 7.14442i | − | 0.272974i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.8756 | 1.78842 | ||||||||
\(688\) | 10.1222i | 0.385907i | ||||||||
\(689\) | 1.40848 | 0.0536588 | ||||||||
\(690\) | − | 0.755474i | − | 0.0287604i | ||||||
\(691\) | − | 27.0303i | − | 1.02828i | −0.857706 | − | 0.514140i | \(-0.828111\pi\) | ||
0.857706 | − | 0.514140i | \(-0.171889\pi\) | |||||||
\(692\) | 15.0655 | 0.572706 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.5417 | 1.08343 | ||||||||
\(695\) | − | 11.6803i | − | 0.443058i | ||||||
\(696\) | − | 2.95789i | − | 0.112118i | ||||||
\(697\) | −30.1383 | −1.14157 | ||||||||
\(698\) | 34.6026i | 1.30973i | ||||||||
\(699\) | −25.2465 | −0.954911 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9250i | 0.752555i | 0.926507 | + | 0.376278i | \(0.122796\pi\) | ||||
−0.926507 | + | 0.376278i | \(0.877204\pi\) | |||||||
\(702\) | 0.930656 | 0.0351254 | ||||||||
\(703\) | −1.89930 | −0.0716334 | ||||||||
\(704\) | −3.09335 | − | 1.19633i | −0.116585 | − | 0.0450886i | ||||
\(705\) | − | 6.03598i | − | 0.227328i | ||||||
\(706\) | −16.9203 | −0.636805 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.73355 | 0.365809 | ||||||||
\(709\) | 9.96825 | 0.374365 | 0.187183 | − | 0.982325i | \(-0.440064\pi\) | ||||
0.187183 | + | 0.982325i | \(0.440064\pi\) | |||||||
\(710\) | −14.7978 | −0.555352 | ||||||||
\(711\) | − | 3.98471i | − | 0.149438i | ||||||
\(712\) | 6.90094 | 0.258623 | ||||||||
\(713\) | − | 1.21235i | − | 0.0454029i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.203903 | + | 0.527228i | −0.00762553 | + | 0.0197172i | ||||
\(716\) | 2.16176 | 0.0807887 | ||||||||
\(717\) | −40.6494 | −1.51808 | ||||||||
\(718\) | 30.3511 | 1.13269 | ||||||||
\(719\) | 41.2017i | 1.53656i | 0.640112 | + | 0.768282i | \(0.278888\pi\) | ||||
−0.640112 | + | 0.768282i | \(0.721112\pi\) | |||||||
\(720\) | 0.579642i | 0.0216020i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.9028i | − | 0.703491i | ||||||
\(723\) | − | 20.5888i | − | 0.765706i | ||||||
\(724\) | − | 5.39285i | − | 0.200424i | ||||||
\(725\) | 7.51492i | 0.279097i | ||||||||
\(726\) | 12.6884 | + | 11.5405i | 0.470910 | + | 0.428306i | ||||
\(727\) | 0.0415718i | 0.00154181i | 1.00000 | 0.000770906i | \(0.000245387\pi\) | |||||
−1.00000 | 0.000770906i | \(0.999755\pi\) | ||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9940 | −1.11089 | ||||||||
\(730\) | 9.89304 | 0.366158 | ||||||||
\(731\) | − | 29.8841i | − | 1.10530i | ||||||
\(732\) | 18.5225i | 0.684611i | ||||||||
\(733\) | 8.80809 | 0.325334 | 0.162667 | − | 0.986681i | \(-0.447990\pi\) | ||||
0.162667 | + | 0.986681i | \(0.447990\pi\) | |||||||
\(734\) | −17.4215 | −0.643040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.475438i | − | 0.0175249i | ||||||
\(737\) | −32.1183 | − | 12.4216i | −1.18309 | − | 0.457554i | ||||
\(738\) | 5.80634i | 0.213734i | ||||||||
\(739\) | − | 32.7938i | − | 1.20634i | −0.797612 | − | 0.603170i | \(-0.793904\pi\) | ||
0.797612 | − | 0.603170i | \(-0.206096\pi\) | |||||||
\(740\) | − | 6.20968i | − | 0.228272i | ||||||
\(741\) | 0.0812842i | 0.00298605i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7575i | 0.944952i | 0.881344 | + | 0.472476i | \(0.156640\pi\) | ||||
−0.881344 | + | 0.472476i | \(0.843360\pi\) | |||||||
\(744\) | − | 3.97600i | − | 0.145767i | ||||||
\(745\) | 14.4271 | 0.528568 | ||||||||
\(746\) | 9.15211 | 0.335083 | ||||||||
\(747\) | 8.35631 | 0.305741 | ||||||||
\(748\) | 9.13254 | + | 3.53196i | 0.333919 | + | 0.129141i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.2398i | 0.519963i | ||||||||
\(751\) | 11.4658 | 0.418393 | 0.209196 | − | 0.977874i | \(-0.432915\pi\) | ||||
0.209196 | + | 0.977874i | \(0.432915\pi\) | |||||||
\(752\) | − | 3.79859i | − | 0.138521i | ||||||
\(753\) | −45.1912 | −1.64686 | ||||||||
\(754\) | −0.317269 | −0.0115542 | ||||||||
\(755\) | −23.7489 | −0.864313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.9741 | 0.798661 | 0.399331 | − | 0.916807i | \(-0.369243\pi\) | ||||
0.399331 | + | 0.916807i | \(0.369243\pi\) | |||||||
\(758\) | − | 6.15382i | − | 0.223517i | ||||||
\(759\) | −0.886868 | + | 2.29316i | −0.0321913 | + | 0.0832365i | ||||
\(760\) | −0.317651 | −0.0115224 | ||||||||
\(761\) | 26.0095 | 0.942843 | 0.471421 | − | 0.881908i | \(-0.343741\pi\) | ||||
0.471421 | + | 0.881908i | \(0.343741\pi\) | |||||||
\(762\) | − | 5.50916i | − | 0.199576i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | − | 1.71129i | − | 0.0618718i | ||||||
\(766\) | −12.9651 | −0.468447 | ||||||||
\(767\) | − | 1.04404i | − | 0.0376981i | ||||||
\(768\) | − | 1.55924i | − | 0.0562641i | ||||||
\(769\) | 40.8753 | 1.47400 | 0.737001 | − | 0.675891i | \(-0.236241\pi\) | ||||
0.737001 | + | 0.675891i | \(0.236241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8929 | 0.392296 | ||||||||
\(772\) | − | 9.59958i | − | 0.345496i | ||||||
\(773\) | − | 47.1382i | − | 1.69544i | −0.530441 | − | 0.847722i | \(-0.677974\pi\) | ||
0.530441 | − | 0.847722i | \(-0.322026\pi\) | |||||||
\(774\) | −5.75737 | −0.206944 | ||||||||
\(775\) | 10.1016i | 0.362859i | ||||||||
\(776\) | 11.0218 | 0.395659 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.16647i | 0.185227i | ||||||||
\(779\) | −3.18195 | −0.114005 | ||||||||
\(780\) | −0.265756 | −0.00951557 | ||||||||
\(781\) | 44.9172 | + | 17.3715i | 1.60726 | + | 0.621601i | ||||
\(782\) | 1.40365i | 0.0501943i | ||||||||
\(783\) | 10.5561 | 0.377243 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.10960 | 0.146678 | ||||||||
\(786\) | −21.7976 | −0.777495 | ||||||||
\(787\) | 24.1491 | 0.860823 | 0.430411 | − | 0.902633i | \(-0.358368\pi\) | ||||
0.430411 | + | 0.902633i | \(0.358368\pi\) | |||||||
\(788\) | − | 14.8180i | − | 0.527870i | ||||||
\(789\) | −6.97087 | −0.248169 | ||||||||
\(790\) | 7.13942i | 0.254009i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.680455 | − | 1.75944i | 0.0241789 | − | 0.0625191i | ||||
\(793\) | 1.98676 | 0.0705518 | ||||||||
\(794\) | −9.25712 | −0.328523 | ||||||||
\(795\) | 13.3819 | 0.474607 | ||||||||
\(796\) | 4.11030i | 0.145686i | ||||||||
\(797\) | − | 20.3073i | − | 0.719321i | −0.933083 | − | 0.359660i | \(-0.882893\pi\) | ||
0.933083 | − | 0.359660i | \(-0.117107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2147i | 0.396746i | ||||||||
\(800\) | 3.96145i | 0.140059i | ||||||||
\(801\) | 3.92514i | 0.138688i | ||||||||
\(802\) | − | 30.9248i | − | 1.09199i | ||||||
\(803\) | −30.0293 | − | 11.6137i | −1.05971 | − | 0.409837i | ||||
\(804\) | − | 16.1896i | − | 0.570963i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.426473 | −0.0150219 | ||||||||
\(807\) | −3.45729 | −0.121703 | ||||||||
\(808\) | 5.33504i | 0.187686i | ||||||||
\(809\) | − | 27.0778i | − | 0.952006i | −0.879444 | − | 0.476003i | \(-0.842085\pi\) | ||
0.879444 | − | 0.476003i | \(-0.157915\pi\) | |||||||
\(810\) | 7.10320 | 0.249581 | ||||||||
\(811\) | −23.5808 | −0.828033 | −0.414016 | − | 0.910269i | \(-0.635874\pi\) | ||||
−0.414016 | + | 0.910269i | \(0.635874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 35.1018i | − | 1.23107i | ||||||
\(814\) | −7.28968 | + | 18.8488i | −0.255503 | + | 0.660651i | ||||
\(815\) | − | 5.64564i | − | 0.197758i | ||||||
\(816\) | 4.60336i | 0.161150i | ||||||||
\(817\) | − | 3.15511i | − | 0.110383i | ||||||
\(818\) | − | 23.8397i | − | 0.833535i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 10.4032i | − | 0.363297i | ||||||
\(821\) | − | 33.9767i | − | 1.18580i | −0.805277 | − | 0.592898i | \(-0.797984\pi\) | ||
0.805277 | − | 0.592898i | \(-0.202016\pi\) | |||||||
\(822\) | −10.9311 | −0.381267 | ||||||||
\(823\) | −11.8007 | −0.411345 | −0.205673 | − | 0.978621i | \(-0.565938\pi\) | ||||
−0.205673 | + | 0.978621i | \(0.565938\pi\) | |||||||
\(824\) | −12.4533 | −0.433831 | ||||||||
\(825\) | 7.38957 | − | 19.1071i | 0.257272 | − | 0.665224i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.0595i | − | 0.593217i | −0.954999 | − | 0.296609i | \(-0.904144\pi\) | ||
0.954999 | − | 0.296609i | \(-0.0958557\pi\) | |||||||
\(828\) | 0.270422 | 0.00939780 | ||||||||
\(829\) | 25.1016i | 0.871816i | 0.899991 | + | 0.435908i | \(0.143573\pi\) | ||||
−0.899991 | + | 0.435908i | \(0.856427\pi\) | |||||||
\(830\) | −14.9720 | −0.519687 | ||||||||
\(831\) | −38.1479 | −1.32334 | ||||||||
\(832\) | −0.167247 | −0.00579823 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.8711 | −0.618826 | ||||||||
\(835\) | − | 21.6304i | − | 0.748550i | ||||||
\(836\) | 0.964197 | + | 0.372898i | 0.0333474 | + | 0.0128969i | ||||
\(837\) | 14.1895 | 0.490460 | ||||||||
\(838\) | 5.03426 | 0.173906 | ||||||||
\(839\) | 41.1030i | 1.41903i | 0.704688 | + | 0.709517i | \(0.251087\pi\) | ||||
−0.704688 | + | 0.709517i | \(0.748913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.4014 | 0.875909 | ||||||||
\(842\) | − | 16.9250i | − | 0.583272i | ||||||
\(843\) | −17.7023 | −0.609698 | ||||||||
\(844\) | 7.52456i | 0.259006i | ||||||||
\(845\) | − | 13.2197i | − | 0.454771i | ||||||
\(846\) | 2.16058 | 0.0742822 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.42157 | 0.289198 | ||||||||
\(849\) | − | 33.7632i | − | 1.15875i | ||||||
\(850\) | − | 11.6955i | − | 0.401151i | ||||||
\(851\) | −2.89701 | −0.0993082 | ||||||||
\(852\) | 22.6410i | 0.775669i | ||||||||
\(853\) | −52.7195 | −1.80508 | −0.902541 | − | 0.430605i | \(-0.858300\pi\) | ||||
−0.902541 | + | 0.430605i | \(0.858300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.180675i | − | 0.00617894i | ||||||
\(856\) | −7.25414 | −0.247941 | ||||||||
\(857\) | −21.8774 | −0.747319 | −0.373659 | − | 0.927566i | \(-0.621897\pi\) | ||||
−0.373659 | + | 0.927566i | \(0.621897\pi\) | |||||||
\(858\) | 0.806673 | + | 0.311976i | 0.0275394 | + | 0.0106507i | ||||
\(859\) | 13.6865i | 0.466978i | 0.972359 | + | 0.233489i | \(0.0750142\pi\) | ||||
−0.972359 | + | 0.233489i | \(0.924986\pi\) | |||||||
\(860\) | 10.3155 | 0.351755 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.99907 | 0.204329 | ||||||||
\(863\) | 30.0480 | 1.02285 | 0.511423 | − | 0.859329i | \(-0.329119\pi\) | ||||
0.511423 | + | 0.859329i | \(0.329119\pi\) | |||||||
\(864\) | 5.56458 | 0.189311 | ||||||||
\(865\) | − | 15.3532i | − | 0.522023i | ||||||
\(866\) | −36.1175 | −1.22732 | ||||||||
\(867\) | 12.9164i | 0.438665i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.38113 | − | 21.6710i | 0.284310 | − | 0.735137i | ||||
\(870\) | −3.01436 | −0.102196 | ||||||||
\(871\) | −1.73653 | −0.0588399 | ||||||||
\(872\) | 1.16743 | 0.0395342 | ||||||||
\(873\) | 6.26901i | 0.212174i | ||||||||
\(874\) | 0.148194i | 0.00501275i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 15.1366i | − | 0.511418i | ||||||
\(877\) | 14.1782i | 0.478762i | 0.970926 | + | 0.239381i | \(0.0769446\pi\) | ||||
−0.970926 | + | 0.239381i | \(0.923055\pi\) | |||||||
\(878\) | 11.3496i | 0.383031i | ||||||||
\(879\) | 18.9030i | 0.637583i | ||||||||
\(880\) | −1.21917 | + | 3.15240i | −0.0410984 | + | 0.106267i | ||||
\(881\) | 22.3264i | 0.752196i | 0.926580 | + | 0.376098i | \(0.122734\pi\) | ||||
−0.926580 | + | 0.376098i | \(0.877266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.45618 | −0.149962 | −0.0749812 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749812 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(884\) | 0.493765 | 0.0166071 | ||||||||
\(885\) | − | 9.91938i | − | 0.333436i | ||||||
\(886\) | − | 4.75076i | − | 0.159605i | ||||||
\(887\) | −9.00141 | −0.302238 | −0.151119 | − | 0.988516i | \(-0.548288\pi\) | ||||
−0.151119 | + | 0.988516i | \(0.548288\pi\) | |||||||
\(888\) | −9.50096 | −0.318831 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.03268i | − | 0.235736i | ||||||
\(891\) | −21.5610 | − | 8.33861i | −0.722322 | − | 0.279354i | ||||
\(892\) | − | 13.5885i | − | 0.454975i | ||||||
\(893\) | 1.18402i | 0.0396218i | ||||||||
\(894\) | − | 22.0738i | − | 0.738259i | ||||||
\(895\) | − | 2.20303i | − | 0.0736391i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.123983i | 0.00413968i | ||||||||
\(898\) | 7.33297i | 0.244704i | ||||||||
\(899\) | −4.83731 | −0.161333 | ||||||||
\(900\) | −2.25321 | −0.0751070 | ||||||||
\(901\) | −24.8632 | −0.828312 | ||||||||
\(902\) | −12.2126 | + | 31.5780i | −0.406635 | + | 1.05143i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.40135i | 0.279425i | ||||||||
\(905\) | −5.49581 | −0.182687 | ||||||||
\(906\) | 36.3365i | 1.20720i | ||||||||
\(907\) | 21.3743 | 0.709723 | 0.354862 | − | 0.934919i | \(-0.384528\pi\) | ||||
0.354862 | + | 0.934919i | \(0.384528\pi\) | |||||||
\(908\) | 21.6635 | 0.718929 | ||||||||
\(909\) | −3.03448 | −0.100647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4299 | −0.941924 | −0.470962 | − | 0.882153i | \(-0.656093\pi\) | ||||
−0.470962 | + | 0.882153i | \(0.656093\pi\) | |||||||
\(912\) | 0.486014i | 0.0160935i | ||||||||
\(913\) | 45.4460 | + | 17.5760i | 1.50404 | + | 0.581681i | ||||
\(914\) | −13.5176 | −0.447122 | ||||||||
\(915\) | 18.8761 | 0.624025 | ||||||||
\(916\) | − | 30.0632i | − | 0.993317i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.4284 | −0.542218 | ||||||||
\(919\) | − | 21.0525i | − | 0.694459i | −0.937780 | − | 0.347229i | \(-0.887122\pi\) | ||
0.937780 | − | 0.347229i | \(-0.112878\pi\) | |||||||
\(920\) | −0.484515 | −0.0159740 | ||||||||
\(921\) | 15.0594i | 0.496223i | ||||||||
\(922\) | 18.5730i | 0.611670i | ||||||||
\(923\) | 2.42852 | 0.0799357 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1385 | 0.793669 | ||||||||
\(926\) | 28.2849i | 0.929501i | ||||||||
\(927\) | − | 7.08322i | − | 0.232643i | ||||||
\(928\) | −1.89701 | −0.0622724 | ||||||||
\(929\) | 12.4772i | 0.409363i | 0.978829 | + | 0.204681i | \(0.0656158\pi\) | ||||
−0.978829 | + | 0.204681i | \(0.934384\pi\) | |||||||
\(930\) | −4.05191 | −0.132867 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.1916i | 0.530373i | ||||||||
\(933\) | 27.5639 | 0.902400 | ||||||||
\(934\) | 21.5792 | 0.706092 | ||||||||
\(935\) | 3.59939 | − | 9.30689i | 0.117713 | − | 0.304368i | ||||
\(936\) | − | 0.0951271i | − | 0.00310933i | ||||||
\(937\) | −43.2128 | −1.41170 | −0.705850 | − | 0.708362i | \(-0.749435\pi\) | ||||
−0.705850 | + | 0.708362i | \(0.749435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44.9221 | −1.46598 | ||||||||
\(940\) | −3.87112 | −0.126262 | ||||||||
\(941\) | 15.4751 | 0.504473 | 0.252236 | − | 0.967666i | \(-0.418834\pi\) | ||||
0.252236 | + | 0.967666i | \(0.418834\pi\) | |||||||
\(942\) | − | 6.28779i | − | 0.204867i | ||||||
\(943\) | −4.85344 | −0.158050 | ||||||||
\(944\) | − | 6.24251i | − | 0.203176i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.3116 | − | 12.1096i | −1.01803 | − | 0.393717i | ||||
\(947\) | 33.4977 | 1.08853 | 0.544264 | − | 0.838914i | \(-0.316809\pi\) | ||||
0.544264 | + | 0.838914i | \(0.316809\pi\) | |||||||
\(948\) | 10.9235 | 0.354779 | ||||||||
\(949\) | −1.62358 | −0.0527037 | ||||||||
\(950\) | − | 1.23479i | − | 0.0400617i | ||||||
\(951\) | − | 16.1312i | − | 0.523091i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.4820i | − | 0.825444i | −0.910857 | − | 0.412722i | \(-0.864578\pi\) | ||
0.910857 | − | 0.412722i | \(-0.135422\pi\) | |||||||
\(954\) | 4.79005i | 0.155084i | ||||||||
\(955\) | 6.11455i | 0.197862i | ||||||||
\(956\) | 26.0701i | 0.843167i | ||||||||
\(957\) | 9.14976 | + | 3.53862i | 0.295770 | + | 0.114387i | ||||
\(958\) | − | 6.93560i | − | 0.224079i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.58900 | −0.0512849 | ||||||||
\(961\) | 24.4977 | 0.790248 | ||||||||
\(962\) | 1.01909i | 0.0328568i | ||||||||
\(963\) | − | 4.12603i | − | 0.132960i | ||||||
\(964\) | −13.2044 | −0.425286 | ||||||||
\(965\) | −9.78285 | −0.314921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.6417i | − | 1.27479i | −0.770537 | − | 0.637395i | \(-0.780012\pi\) | ||
0.770537 | − | 0.637395i | \(-0.219988\pi\) | |||||||
\(968\) | 7.40135 | − | 8.13757i | 0.237888 | − | 0.261551i | ||||
\(969\) | − | 1.43487i | − | 0.0460946i | ||||||
\(970\) | − | 11.2322i | − | 0.360645i | ||||||
\(971\) | − | 19.0620i | − | 0.611730i | −0.952075 | − | 0.305865i | \(-0.901054\pi\) | ||
0.952075 | − | 0.305865i | \(-0.0989456\pi\) | |||||||
\(972\) | 5.82564i | 0.186858i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 12.1740i | − | 0.390081i | ||||||
\(975\) | − | 1.03306i | − | 0.0330843i | ||||||
\(976\) | 11.8792 | 0.380244 | ||||||||
\(977\) | 47.6697 | 1.52509 | 0.762544 | − | 0.646936i | \(-0.223950\pi\) | ||||
0.762544 | + | 0.646936i | \(0.223950\pi\) | |||||||
\(978\) | −8.63798 | −0.276212 | ||||||||
\(979\) | −8.25583 | + | 21.3470i | −0.263857 | + | 0.682252i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.664016i | 0.0212004i | ||||||||
\(982\) | 2.37152 | 0.0756782 | ||||||||
\(983\) | − | 46.4625i | − | 1.48192i | −0.671548 | − | 0.740961i | \(-0.734370\pi\) | ||
0.671548 | − | 0.740961i | \(-0.265630\pi\) | |||||||
\(984\) | −15.9172 | −0.507423 | ||||||||
\(985\) | −15.1009 | −0.481155 | ||||||||
\(986\) | 5.60058 | 0.178359 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0521308 | 0.00165850 | ||||||||
\(989\) | − | 4.81251i | − | 0.153029i | ||||||
\(990\) | −1.79303 | − | 0.693446i | −0.0569864 | − | 0.0220392i | ||||
\(991\) | −14.5718 | −0.462887 | −0.231444 | − | 0.972848i | \(-0.574345\pi\) | ||||
−0.231444 | + | 0.972848i | \(0.574345\pi\) | |||||||
\(992\) | −2.54997 | −0.0809615 | ||||||||
\(993\) | 41.8575i | 1.32831i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.18877 | 0.132793 | ||||||||
\(996\) | 22.9076i | 0.725855i | ||||||||
\(997\) | −4.11696 | −0.130385 | −0.0651927 | − | 0.997873i | \(-0.520766\pi\) | ||||
−0.0651927 | + | 0.997873i | \(0.520766\pi\) | |||||||
\(998\) | − | 3.92892i | − | 0.124368i | ||||||
\(999\) | − | 33.9069i | − | 1.07277i |
(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 | 1078.2.c.b.1077.11 | 16 | ||
7.2 | even | 3 | 154.2.i.a.87.7 | yes | 16 | ||
7.3 | odd | 6 | 154.2.i.a.131.3 | yes | 16 | ||
7.4 | even | 3 | 1078.2.i.c.901.2 | 16 | |||
7.5 | odd | 6 | 1078.2.i.c.1011.6 | 16 | |||
7.6 | odd | 2 | inner | 1078.2.c.b.1077.14 | 16 | ||
11.10 | odd | 2 | inner | 1078.2.c.b.1077.3 | 16 | ||
21.2 | odd | 6 | 1386.2.bk.c.703.2 | 16 | |||
21.17 | even | 6 | 1386.2.bk.c.901.6 | 16 | |||
28.3 | even | 6 | 1232.2.bn.b.593.3 | 16 | |||
28.23 | odd | 6 | 1232.2.bn.b.241.4 | 16 | |||
77.10 | even | 6 | 154.2.i.a.131.7 | yes | 16 | ||
77.32 | odd | 6 | 1078.2.i.c.901.6 | 16 | |||
77.54 | even | 6 | 1078.2.i.c.1011.2 | 16 | |||
77.65 | odd | 6 | 154.2.i.a.87.3 | ✓ | 16 | ||
77.76 | even | 2 | inner | 1078.2.c.b.1077.6 | 16 | ||
231.65 | even | 6 | 1386.2.bk.c.703.6 | 16 | |||
231.164 | odd | 6 | 1386.2.bk.c.901.2 | 16 | |||
308.87 | odd | 6 | 1232.2.bn.b.593.4 | 16 | |||
308.219 | even | 6 | 1232.2.bn.b.241.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.3 | ✓ | 16 | 77.65 | odd | 6 | ||
154.2.i.a.87.7 | yes | 16 | 7.2 | even | 3 | ||
154.2.i.a.131.3 | yes | 16 | 7.3 | odd | 6 | ||
154.2.i.a.131.7 | yes | 16 | 77.10 | even | 6 | ||
1078.2.c.b.1077.3 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.c.b.1077.6 | 16 | 77.76 | even | 2 | inner | ||
1078.2.c.b.1077.11 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.c.b.1077.14 | 16 | 7.6 | odd | 2 | inner | ||
1078.2.i.c.901.2 | 16 | 7.4 | even | 3 | |||
1078.2.i.c.901.6 | 16 | 77.32 | odd | 6 | |||
1078.2.i.c.1011.2 | 16 | 77.54 | even | 6 | |||
1078.2.i.c.1011.6 | 16 | 7.5 | odd | 6 | |||
1232.2.bn.b.241.3 | 16 | 308.219 | even | 6 | |||
1232.2.bn.b.241.4 | 16 | 28.23 | odd | 6 | |||
1232.2.bn.b.593.3 | 16 | 28.3 | even | 6 | |||
1232.2.bn.b.593.4 | 16 | 308.87 | odd | 6 | |||
1386.2.bk.c.703.2 | 16 | 21.2 | odd | 6 | |||
1386.2.bk.c.703.6 | 16 | 231.65 | even | 6 | |||
1386.2.bk.c.901.2 | 16 | 231.164 | odd | 6 | |||
1386.2.bk.c.901.6 | 16 | 21.17 | even | 6 |