Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(151,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.151");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.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: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 42x^{12} + 677x^{10} + 5313x^{8} + 21125x^{6} + 40138x^{4} + 30565x^{2} + 3675 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.7 | ||
Root | \(-0.382406i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.151 |
Dual form | 475.3.c.i.151.8 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.382406i | − | 0.191203i | −0.995420 | − | 0.0956015i | \(-0.969523\pi\) | ||
0.995420 | − | 0.0956015i | \(-0.0304775\pi\) | |||||||
\(3\) | 3.15259i | 1.05086i | 0.850836 | + | 0.525432i | \(0.176096\pi\) | ||||
−0.850836 | + | 0.525432i | \(0.823904\pi\) | |||||||
\(4\) | 3.85377 | 0.963441 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.20557 | 0.200928 | ||||||||
\(7\) | −4.26742 | −0.609632 | −0.304816 | − | 0.952411i | \(-0.598595\pi\) | ||||
−0.304816 | + | 0.952411i | \(0.598595\pi\) | |||||||
\(8\) | − | 3.00333i | − | 0.375416i | ||||||
\(9\) | −0.938823 | −0.104314 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.61517 | −0.874107 | −0.437053 | − | 0.899436i | \(-0.643978\pi\) | ||||
−0.437053 | + | 0.899436i | \(0.643978\pi\) | |||||||
\(12\) | 12.1493i | 1.01245i | ||||||||
\(13\) | 22.7853i | 1.75272i | 0.481658 | + | 0.876359i | \(0.340035\pi\) | ||||
−0.481658 | + | 0.876359i | \(0.659965\pi\) | |||||||
\(14\) | 1.63189i | 0.116564i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.2666 | 0.891661 | ||||||||
\(17\) | −25.9136 | −1.52433 | −0.762165 | − | 0.647383i | \(-0.775863\pi\) | ||||
−0.762165 | + | 0.647383i | \(0.775863\pi\) | |||||||
\(18\) | 0.359012i | 0.0199451i | ||||||||
\(19\) | 8.03195 | + | 17.2188i | 0.422734 | + | 0.906254i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 13.4534i | − | 0.640640i | ||||||
\(22\) | 3.67690i | 0.167132i | ||||||||
\(23\) | 24.5299 | 1.06652 | 0.533260 | − | 0.845952i | \(-0.320967\pi\) | ||||
0.533260 | + | 0.845952i | \(0.320967\pi\) | |||||||
\(24\) | 9.46826 | 0.394511 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.71325 | 0.335125 | ||||||||
\(27\) | 25.4136i | 0.941244i | ||||||||
\(28\) | −16.4457 | −0.587345 | ||||||||
\(29\) | 21.2643i | 0.733253i | 0.930368 | + | 0.366627i | \(0.119487\pi\) | ||||
−0.930368 | + | 0.366627i | \(0.880513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.67661i | 0.215375i | 0.994185 | + | 0.107687i | \(0.0343445\pi\) | ||||
−0.994185 | + | 0.107687i | \(0.965655\pi\) | |||||||
\(32\) | − | 17.4689i | − | 0.545904i | ||||||
\(33\) | − | 30.3127i | − | 0.918567i | ||||||
\(34\) | 9.90952i | 0.291456i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.61800 | −0.100500 | ||||||||
\(37\) | 35.0237i | 0.946587i | 0.880905 | + | 0.473293i | \(0.156935\pi\) | ||||
−0.880905 | + | 0.473293i | \(0.843065\pi\) | |||||||
\(38\) | 6.58458 | − | 3.07147i | 0.173278 | − | 0.0808280i | ||||
\(39\) | −71.8328 | −1.84187 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 72.2427i | − | 1.76202i | −0.473101 | − | 0.881008i | \(-0.656865\pi\) | ||
0.473101 | − | 0.881008i | \(-0.343135\pi\) | |||||||
\(42\) | −5.14468 | −0.122492 | ||||||||
\(43\) | −50.2869 | −1.16946 | −0.584731 | − | 0.811227i | \(-0.698800\pi\) | ||||
−0.584731 | + | 0.811227i | \(0.698800\pi\) | |||||||
\(44\) | −37.0546 | −0.842151 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 9.38040i | − | 0.203922i | ||||||
\(47\) | 36.1970 | 0.770149 | 0.385075 | − | 0.922885i | \(-0.374176\pi\) | ||||
0.385075 | + | 0.922885i | \(0.374176\pi\) | |||||||
\(48\) | 44.9766i | 0.937014i | ||||||||
\(49\) | −30.7891 | −0.628349 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 81.6950i | − | 1.60186i | ||||||
\(52\) | 87.8094i | 1.68864i | ||||||||
\(53\) | − | 2.29775i | − | 0.0433537i | −0.999765 | − | 0.0216768i | \(-0.993100\pi\) | ||
0.999765 | − | 0.0216768i | \(-0.00690050\pi\) | |||||||
\(54\) | 9.71831 | 0.179969 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.8165i | 0.228866i | ||||||||
\(57\) | −54.2839 | + | 25.3214i | −0.952349 | + | 0.444236i | ||||
\(58\) | 8.13162 | 0.140200 | ||||||||
\(59\) | 19.0722i | 0.323257i | 0.986852 | + | 0.161629i | \(0.0516747\pi\) | ||||
−0.986852 | + | 0.161629i | \(0.948325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 50.6664 | 0.830596 | 0.415298 | − | 0.909685i | \(-0.363677\pi\) | ||||
0.415298 | + | 0.909685i | \(0.363677\pi\) | |||||||
\(62\) | 2.55318 | 0.0411803 | ||||||||
\(63\) | 4.00636 | 0.0635930 | ||||||||
\(64\) | 50.3861 | 0.787282 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11.5918 | −0.175633 | ||||||||
\(67\) | − | 9.20576i | − | 0.137399i | −0.997637 | − | 0.0686997i | \(-0.978115\pi\) | ||
0.997637 | − | 0.0686997i | \(-0.0218850\pi\) | |||||||
\(68\) | −99.8650 | −1.46860 | ||||||||
\(69\) | 77.3328i | 1.12077i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 116.977i | 1.64756i | 0.566909 | + | 0.823780i | \(0.308139\pi\) | ||||
−0.566909 | + | 0.823780i | \(0.691861\pi\) | |||||||
\(72\) | 2.81959i | 0.0391610i | ||||||||
\(73\) | 49.2115 | 0.674130 | 0.337065 | − | 0.941481i | \(-0.390566\pi\) | ||||
0.337065 | + | 0.941481i | \(0.390566\pi\) | |||||||
\(74\) | 13.3933 | 0.180990 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 30.9532 | + | 66.3573i | 0.407279 | + | 0.873122i | ||||
\(77\) | 41.0320 | 0.532883 | ||||||||
\(78\) | 27.4693i | 0.352171i | ||||||||
\(79\) | − | 87.5706i | − | 1.10849i | −0.832354 | − | 0.554244i | \(-0.813007\pi\) | ||
0.832354 | − | 0.554244i | \(-0.186993\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −88.5680 | −1.09343 | ||||||||
\(82\) | −27.6260 | −0.336903 | ||||||||
\(83\) | 33.8601 | 0.407953 | 0.203976 | − | 0.978976i | \(-0.434613\pi\) | ||||
0.203976 | + | 0.978976i | \(0.434613\pi\) | |||||||
\(84\) | − | 51.8464i | − | 0.617219i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 19.2300i | 0.223605i | ||||||||
\(87\) | −67.0378 | −0.770549 | ||||||||
\(88\) | 28.8775i | 0.328154i | ||||||||
\(89\) | − | 7.05272i | − | 0.0792440i | −0.999215 | − | 0.0396220i | \(-0.987385\pi\) | ||
0.999215 | − | 0.0396220i | \(-0.0126154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 97.2347i | − | 1.06851i | ||||||
\(92\) | 94.5326 | 1.02753 | ||||||||
\(93\) | −21.0486 | −0.226329 | ||||||||
\(94\) | − | 13.8420i | − | 0.147255i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 55.0724 | 0.573671 | ||||||||
\(97\) | 16.0742i | 0.165714i | 0.996561 | + | 0.0828568i | \(0.0264044\pi\) | ||||
−0.996561 | + | 0.0828568i | \(0.973596\pi\) | |||||||
\(98\) | 11.7739i | 0.120142i | ||||||||
\(99\) | 9.02695 | 0.0911813 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 42.2774 | 0.418588 | 0.209294 | − | 0.977853i | \(-0.432883\pi\) | ||||
0.209294 | + | 0.977853i | \(0.432883\pi\) | |||||||
\(102\) | −31.2407 | −0.306281 | ||||||||
\(103\) | − | 50.6822i | − | 0.492060i | −0.969262 | − | 0.246030i | \(-0.920874\pi\) | ||
0.969262 | − | 0.246030i | \(-0.0791262\pi\) | |||||||
\(104\) | 68.4318 | 0.657999 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.878672 | −0.00828936 | ||||||||
\(107\) | − | 115.511i | − | 1.07954i | −0.841811 | − | 0.539772i | \(-0.818510\pi\) | ||
0.841811 | − | 0.539772i | \(-0.181490\pi\) | |||||||
\(108\) | 97.9380i | 0.906833i | ||||||||
\(109\) | 108.668i | 0.996957i | 0.866902 | + | 0.498478i | \(0.166108\pi\) | ||||
−0.866902 | + | 0.498478i | \(0.833892\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −110.415 | −0.994734 | ||||||||
\(112\) | −60.8815 | −0.543585 | ||||||||
\(113\) | − | 40.1073i | − | 0.354932i | −0.984127 | − | 0.177466i | \(-0.943210\pi\) | ||
0.984127 | − | 0.177466i | \(-0.0567900\pi\) | |||||||
\(114\) | 9.68307 | + | 20.7585i | 0.0849392 | + | 0.182092i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 81.9478i | 0.706447i | ||||||||
\(117\) | − | 21.3914i | − | 0.182833i | ||||||
\(118\) | 7.29332 | 0.0618078 | ||||||||
\(119\) | 110.584 | 0.929280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −28.5484 | −0.235938 | ||||||||
\(122\) | − | 19.3751i | − | 0.158813i | ||||||
\(123\) | 227.752 | 1.85164 | ||||||||
\(124\) | 25.7301i | 0.207501i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 1.53206i | − | 0.0121592i | ||||||
\(127\) | − | 149.933i | − | 1.18057i | −0.807194 | − | 0.590287i | \(-0.799015\pi\) | ||
0.807194 | − | 0.590287i | \(-0.200985\pi\) | |||||||
\(128\) | − | 89.1437i | − | 0.696435i | ||||||
\(129\) | − | 158.534i | − | 1.22894i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 235.661 | 1.79894 | 0.899471 | − | 0.436980i | \(-0.143952\pi\) | ||||
0.899471 | + | 0.436980i | \(0.143952\pi\) | |||||||
\(132\) | − | 116.818i | − | 0.884985i | ||||||
\(133\) | −34.2757 | − | 73.4800i | −0.257712 | − | 0.552481i | ||||
\(134\) | −3.52034 | −0.0262712 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 77.8270i | 0.572258i | ||||||||
\(137\) | 90.1819 | 0.658262 | 0.329131 | − | 0.944284i | \(-0.393244\pi\) | ||||
0.329131 | + | 0.944284i | \(0.393244\pi\) | |||||||
\(138\) | 29.5726 | 0.214294 | ||||||||
\(139\) | 193.273 | 1.39045 | 0.695225 | − | 0.718792i | \(-0.255305\pi\) | ||||
0.695225 | + | 0.718792i | \(0.255305\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 114.114i | 0.809322i | ||||||||
\(142\) | 44.7326 | 0.315019 | ||||||||
\(143\) | − | 219.085i | − | 1.53206i | ||||||
\(144\) | −13.3938 | −0.0930124 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 18.8188i | − | 0.128896i | ||||||
\(147\) | − | 97.0654i | − | 0.660309i | ||||||
\(148\) | 134.973i | 0.911981i | ||||||||
\(149\) | −158.141 | −1.06135 | −0.530673 | − | 0.847577i | \(-0.678061\pi\) | ||||
−0.530673 | + | 0.847577i | \(0.678061\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 155.289i | − | 1.02841i | −0.857669 | − | 0.514203i | \(-0.828088\pi\) | ||
0.857669 | − | 0.514203i | \(-0.171912\pi\) | |||||||
\(152\) | 51.7138 | − | 24.1226i | 0.340222 | − | 0.158701i | ||||
\(153\) | 24.3283 | 0.159008 | ||||||||
\(154\) | − | 15.6909i | − | 0.101889i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −276.827 | −1.77453 | ||||||||
\(157\) | 226.052 | 1.43982 | 0.719910 | − | 0.694068i | \(-0.244183\pi\) | ||||
0.719910 | + | 0.694068i | \(0.244183\pi\) | |||||||
\(158\) | −33.4875 | −0.211946 | ||||||||
\(159\) | 7.24385 | 0.0455588 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −104.680 | −0.650184 | ||||||||
\(162\) | 33.8689i | 0.209068i | ||||||||
\(163\) | −83.8369 | −0.514337 | −0.257169 | − | 0.966367i | \(-0.582790\pi\) | ||||
−0.257169 | + | 0.966367i | \(0.582790\pi\) | |||||||
\(164\) | − | 278.406i | − | 1.69760i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 12.9483i | − | 0.0780018i | ||||||
\(167\) | − | 162.067i | − | 0.970462i | −0.874386 | − | 0.485231i | \(-0.838736\pi\) | ||
0.874386 | − | 0.485231i | \(-0.161264\pi\) | |||||||
\(168\) | −40.4051 | −0.240506 | ||||||||
\(169\) | −350.172 | −2.07202 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.54058 | − | 16.1654i | −0.0440969 | − | 0.0945347i | ||||
\(172\) | −193.794 | −1.12671 | ||||||||
\(173\) | − | 294.504i | − | 1.70234i | −0.524894 | − | 0.851168i | \(-0.675895\pi\) | ||
0.524894 | − | 0.851168i | \(-0.324105\pi\) | |||||||
\(174\) | 25.6356i | 0.147331i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −137.176 | −0.779407 | ||||||||
\(177\) | −60.1267 | −0.339699 | ||||||||
\(178\) | −2.69700 | −0.0151517 | ||||||||
\(179\) | 203.585i | 1.13735i | 0.822563 | + | 0.568674i | \(0.192543\pi\) | ||||
−0.822563 | + | 0.568674i | \(0.807457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 298.958i | 1.65170i | 0.563888 | + | 0.825851i | \(0.309305\pi\) | ||||
−0.563888 | + | 0.825851i | \(0.690695\pi\) | |||||||
\(182\) | −37.1832 | −0.204303 | ||||||||
\(183\) | 159.730i | 0.872843i | ||||||||
\(184\) | − | 73.6715i | − | 0.400388i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 8.04912i | 0.0432748i | ||||||||
\(187\) | 249.164 | 1.33243 | ||||||||
\(188\) | 139.495 | 0.741994 | ||||||||
\(189\) | − | 108.451i | − | 0.573812i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 123.188 | 0.644963 | 0.322481 | − | 0.946576i | \(-0.395483\pi\) | ||||
0.322481 | + | 0.946576i | \(0.395483\pi\) | |||||||
\(192\) | 158.847i | 0.827326i | ||||||||
\(193\) | − | 68.6578i | − | 0.355740i | −0.984054 | − | 0.177870i | \(-0.943079\pi\) | ||
0.984054 | − | 0.177870i | \(-0.0569207\pi\) | |||||||
\(194\) | 6.14688 | 0.0316849 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −118.654 | −0.605377 | ||||||||
\(197\) | 68.1228 | 0.345801 | 0.172901 | − | 0.984939i | \(-0.444686\pi\) | ||||
0.172901 | + | 0.984939i | \(0.444686\pi\) | |||||||
\(198\) | − | 3.45196i | − | 0.0174341i | ||||||
\(199\) | 263.929 | 1.32628 | 0.663139 | − | 0.748496i | \(-0.269224\pi\) | ||||
0.663139 | + | 0.748496i | \(0.269224\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 29.0220 | 0.144388 | ||||||||
\(202\) | − | 16.1671i | − | 0.0800354i | ||||||
\(203\) | − | 90.7440i | − | 0.447015i | ||||||
\(204\) | − | 314.833i | − | 1.54330i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −19.3812 | −0.0940834 | ||||||||
\(207\) | −23.0293 | −0.111253 | ||||||||
\(208\) | 325.069i | 1.56283i | ||||||||
\(209\) | −77.2286 | − | 165.562i | −0.369515 | − | 0.792162i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 411.603i | 1.95072i | 0.220613 | + | 0.975362i | \(0.429194\pi\) | ||||
−0.220613 | + | 0.975362i | \(0.570806\pi\) | |||||||
\(212\) | − | 8.85497i | − | 0.0417687i | ||||||
\(213\) | −368.780 | −1.73136 | ||||||||
\(214\) | −44.1722 | −0.206412 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 76.3253 | 0.353358 | ||||||||
\(217\) | − | 28.4919i | − | 0.131299i | ||||||
\(218\) | 41.5554 | 0.190621 | ||||||||
\(219\) | 155.144i | 0.708418i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 590.450i | − | 2.67172i | ||||||
\(222\) | 42.2235i | 0.190196i | ||||||||
\(223\) | 123.041i | 0.551751i | 0.961193 | + | 0.275876i | \(0.0889678\pi\) | ||||
−0.961193 | + | 0.275876i | \(0.911032\pi\) | |||||||
\(224\) | 74.5474i | 0.332801i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.3373 | −0.0678641 | ||||||||
\(227\) | − | 278.989i | − | 1.22903i | −0.788907 | − | 0.614513i | \(-0.789352\pi\) | ||
0.788907 | − | 0.614513i | \(-0.210648\pi\) | |||||||
\(228\) | −209.197 | + | 97.5829i | −0.917532 | + | 0.427995i | ||||
\(229\) | −11.9531 | −0.0521969 | −0.0260984 | − | 0.999659i | \(-0.508308\pi\) | ||||
−0.0260984 | + | 0.999659i | \(0.508308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 129.357i | 0.559988i | ||||||||
\(232\) | 63.8638 | 0.275275 | ||||||||
\(233\) | 215.911 | 0.926658 | 0.463329 | − | 0.886186i | \(-0.346655\pi\) | ||||
0.463329 | + | 0.886186i | \(0.346655\pi\) | |||||||
\(234\) | −8.18020 | −0.0349581 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 73.4997i | 0.311439i | ||||||||
\(237\) | 276.074 | 1.16487 | ||||||||
\(238\) | − | 42.2881i | − | 0.177681i | ||||||
\(239\) | −3.19514 | −0.0133688 | −0.00668438 | − | 0.999978i | \(-0.502128\pi\) | ||||
−0.00668438 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 68.7508i | − | 0.285273i | −0.989775 | − | 0.142637i | \(-0.954442\pi\) | ||
0.989775 | − | 0.142637i | \(-0.0455580\pi\) | |||||||
\(242\) | 10.9171i | 0.0451120i | ||||||||
\(243\) | − | 50.4964i | − | 0.207804i | ||||||
\(244\) | 195.256 | 0.800231 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 87.0936i | − | 0.354039i | ||||||
\(247\) | −392.337 | + | 183.011i | −1.58841 | + | 0.740934i | ||||
\(248\) | 20.0521 | 0.0808550 | ||||||||
\(249\) | 106.747i | 0.428703i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.9054 | 0.107193 | 0.0535964 | − | 0.998563i | \(-0.482932\pi\) | ||||
0.0535964 | + | 0.998563i | \(0.482932\pi\) | |||||||
\(252\) | 15.4396 | 0.0612681 | ||||||||
\(253\) | −235.860 | −0.932251 | ||||||||
\(254\) | −57.3352 | −0.225729 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 167.455 | 0.654122 | ||||||||
\(257\) | 413.078i | 1.60731i | 0.595097 | + | 0.803654i | \(0.297114\pi\) | ||||
−0.595097 | + | 0.803654i | \(0.702886\pi\) | |||||||
\(258\) | −60.6243 | −0.234978 | ||||||||
\(259\) | − | 149.461i | − | 0.577070i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 19.9635i | − | 0.0764883i | ||||||
\(262\) | − | 90.1184i | − | 0.343963i | ||||||
\(263\) | 227.053 | 0.863319 | 0.431660 | − | 0.902037i | \(-0.357928\pi\) | ||||
0.431660 | + | 0.902037i | \(0.357928\pi\) | |||||||
\(264\) | −91.0390 | −0.344845 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −28.0992 | + | 13.1072i | −0.105636 | + | 0.0492754i | ||||
\(267\) | 22.2343 | 0.0832746 | ||||||||
\(268\) | − | 35.4768i | − | 0.132376i | ||||||
\(269\) | 404.662i | 1.50432i | 0.658981 | + | 0.752160i | \(0.270988\pi\) | ||||
−0.658981 | + | 0.752160i | \(0.729012\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 162.057 | 0.597995 | 0.298997 | − | 0.954254i | \(-0.403348\pi\) | ||||
0.298997 | + | 0.954254i | \(0.403348\pi\) | |||||||
\(272\) | −369.698 | −1.35918 | ||||||||
\(273\) | 306.541 | 1.12286 | ||||||||
\(274\) | − | 34.4861i | − | 0.125862i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 298.023i | 1.07979i | ||||||||
\(277\) | −433.591 | −1.56531 | −0.782654 | − | 0.622456i | \(-0.786135\pi\) | ||||
−0.782654 | + | 0.622456i | \(0.786135\pi\) | |||||||
\(278\) | − | 73.9086i | − | 0.265858i | ||||||
\(279\) | − | 6.26816i | − | 0.0224665i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 521.733i | − | 1.85670i | −0.371704 | − | 0.928351i | \(-0.621226\pi\) | ||
0.371704 | − | 0.928351i | \(-0.378774\pi\) | |||||||
\(282\) | 43.6380 | 0.154745 | ||||||||
\(283\) | 375.661 | 1.32742 | 0.663712 | − | 0.747988i | \(-0.268980\pi\) | ||||
0.663712 | + | 0.747988i | \(0.268980\pi\) | |||||||
\(284\) | 450.801i | 1.58733i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −83.7794 | −0.292935 | ||||||||
\(287\) | 308.290i | 1.07418i | ||||||||
\(288\) | 16.4002i | 0.0569453i | ||||||||
\(289\) | 382.515 | 1.32358 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −50.6754 | −0.174142 | ||||||||
\(292\) | 189.649 | 0.649484 | ||||||||
\(293\) | 145.752i | 0.497448i | 0.968574 | + | 0.248724i | \(0.0800113\pi\) | ||||
−0.968574 | + | 0.248724i | \(0.919989\pi\) | |||||||
\(294\) | −37.1184 | −0.126253 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 105.188 | 0.355364 | ||||||||
\(297\) | − | 244.356i | − | 0.822748i | ||||||
\(298\) | 60.4739i | 0.202933i | ||||||||
\(299\) | 558.923i | 1.86931i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 214.595 | 0.712941 | ||||||||
\(302\) | −59.3835 | −0.196634 | ||||||||
\(303\) | 133.283i | 0.439879i | ||||||||
\(304\) | 114.588 | + | 245.654i | 0.376935 | + | 0.808071i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 9.30329i | − | 0.0304029i | ||||||
\(307\) | 199.397i | 0.649502i | 0.945800 | + | 0.324751i | \(0.105281\pi\) | ||||
−0.945800 | + | 0.324751i | \(0.894719\pi\) | |||||||
\(308\) | 158.128 | 0.513402 | ||||||||
\(309\) | 159.780 | 0.517088 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 309.298 | 0.994528 | 0.497264 | − | 0.867599i | \(-0.334338\pi\) | ||||
0.497264 | + | 0.867599i | \(0.334338\pi\) | |||||||
\(312\) | 215.738i | 0.691467i | ||||||||
\(313\) | −315.997 | −1.00957 | −0.504787 | − | 0.863244i | \(-0.668429\pi\) | ||||
−0.504787 | + | 0.863244i | \(0.668429\pi\) | |||||||
\(314\) | − | 86.4435i | − | 0.275298i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 337.477i | − | 1.06796i | ||||||
\(317\) | 59.9579i | 0.189142i | 0.995518 | + | 0.0945708i | \(0.0301479\pi\) | ||||
−0.995518 | + | 0.0945708i | \(0.969852\pi\) | |||||||
\(318\) | − | 2.77009i | − | 0.00871098i | ||||||
\(319\) | − | 204.460i | − | 0.640942i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 364.159 | 1.13445 | ||||||||
\(322\) | 40.0301i | 0.124317i | ||||||||
\(323\) | −208.137 | − | 446.202i | −0.644386 | − | 1.38143i | ||||
\(324\) | −341.320 | −1.05346 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 32.0598i | 0.0983428i | ||||||||
\(327\) | −342.587 | −1.04767 | ||||||||
\(328\) | −216.968 | −0.661489 | ||||||||
\(329\) | −154.468 | −0.469508 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 125.718i | − | 0.379814i | −0.981802 | − | 0.189907i | \(-0.939181\pi\) | ||
0.981802 | − | 0.189907i | \(-0.0608186\pi\) | |||||||
\(332\) | 130.489 | 0.393039 | ||||||||
\(333\) | − | 32.8811i | − | 0.0987420i | ||||||
\(334\) | −61.9755 | −0.185555 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 191.934i | − | 0.571233i | ||||||
\(337\) | 124.397i | 0.369130i | 0.982820 | + | 0.184565i | \(0.0590877\pi\) | ||||
−0.982820 | + | 0.184565i | \(0.940912\pi\) | |||||||
\(338\) | 133.908i | 0.396177i | ||||||||
\(339\) | 126.442 | 0.372985 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 64.1968i | − | 0.188260i | ||||||
\(342\) | −6.18176 | + | 2.88356i | −0.0180753 | + | 0.00843147i | ||||
\(343\) | 340.494 | 0.992694 | ||||||||
\(344\) | 151.028i | 0.439035i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −112.620 | −0.325492 | ||||||||
\(347\) | 155.887 | 0.449241 | 0.224621 | − | 0.974446i | \(-0.427886\pi\) | ||||
0.224621 | + | 0.974446i | \(0.427886\pi\) | |||||||
\(348\) | −258.348 | −0.742379 | ||||||||
\(349\) | −546.288 | −1.56530 | −0.782648 | − | 0.622465i | \(-0.786131\pi\) | ||||
−0.782648 | + | 0.622465i | \(0.786131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −579.057 | −1.64974 | ||||||||
\(352\) | 167.967i | 0.477179i | ||||||||
\(353\) | −491.756 | −1.39308 | −0.696538 | − | 0.717520i | \(-0.745277\pi\) | ||||
−0.696538 | + | 0.717520i | \(0.745277\pi\) | |||||||
\(354\) | 22.9928i | 0.0649515i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 27.1795i | − | 0.0763469i | ||||||
\(357\) | 348.627i | 0.976546i | ||||||||
\(358\) | 77.8522 | 0.217464 | ||||||||
\(359\) | −175.785 | −0.489651 | −0.244825 | − | 0.969567i | \(-0.578731\pi\) | ||||
−0.244825 | + | 0.969567i | \(0.578731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −231.976 | + | 276.601i | −0.642592 | + | 0.766209i | ||||
\(362\) | 114.323 | 0.315811 | ||||||||
\(363\) | − | 90.0015i | − | 0.247938i | ||||||
\(364\) | − | 374.720i | − | 1.02945i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 61.0818 | 0.166890 | ||||||||
\(367\) | 450.517 | 1.22757 | 0.613783 | − | 0.789475i | \(-0.289647\pi\) | ||||
0.613783 | + | 0.789475i | \(0.289647\pi\) | |||||||
\(368\) | 349.958 | 0.950973 | ||||||||
\(369\) | 67.8231i | 0.183802i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.80546i | 0.0264298i | ||||||||
\(372\) | −81.1164 | −0.218055 | ||||||||
\(373\) | 566.983i | 1.52006i | 0.649887 | + | 0.760031i | \(0.274816\pi\) | ||||
−0.649887 | + | 0.760031i | \(0.725184\pi\) | |||||||
\(374\) | − | 95.2817i | − | 0.254764i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 108.712i | − | 0.289126i | ||||||
\(377\) | −484.515 | −1.28519 | ||||||||
\(378\) | −41.4722 | −0.109715 | ||||||||
\(379\) | − | 333.683i | − | 0.880431i | −0.897892 | − | 0.440216i | \(-0.854902\pi\) | ||
0.897892 | − | 0.440216i | \(-0.145098\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 472.677 | 1.24062 | ||||||||
\(382\) | − | 47.1078i | − | 0.123319i | ||||||
\(383\) | − | 14.7262i | − | 0.0384496i | −0.999815 | − | 0.0192248i | \(-0.993880\pi\) | ||
0.999815 | − | 0.0192248i | \(-0.00611982\pi\) | |||||||
\(384\) | 281.033 | 0.731858 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.2552 | −0.0680186 | ||||||||
\(387\) | 47.2105 | 0.121991 | ||||||||
\(388\) | 61.9463i | 0.159655i | ||||||||
\(389\) | −522.712 | −1.34373 | −0.671866 | − | 0.740673i | \(-0.734507\pi\) | ||||
−0.671866 | + | 0.740673i | \(0.734507\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −635.659 | −1.62573 | ||||||||
\(392\) | 92.4697i | 0.235892i | ||||||||
\(393\) | 742.944i | 1.89044i | ||||||||
\(394\) | − | 26.0506i | − | 0.0661182i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 34.7877 | 0.0878478 | ||||||||
\(397\) | −207.249 | −0.522037 | −0.261019 | − | 0.965334i | \(-0.584058\pi\) | ||||
−0.261019 | + | 0.965334i | \(0.584058\pi\) | |||||||
\(398\) | − | 100.928i | − | 0.253588i | ||||||
\(399\) | 231.652 | − | 108.057i | 0.580582 | − | 0.270820i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 279.133i | − | 0.696093i | −0.937477 | − | 0.348047i | \(-0.886845\pi\) | ||
0.937477 | − | 0.348047i | \(-0.113155\pi\) | |||||||
\(402\) | − | 11.0982i | − | 0.0276074i | ||||||
\(403\) | −152.129 | −0.377491 | ||||||||
\(404\) | 162.927 | 0.403285 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34.7011 | −0.0854706 | ||||||||
\(407\) | − | 336.759i | − | 0.827418i | ||||||
\(408\) | −245.357 | −0.601365 | ||||||||
\(409\) | 511.459i | 1.25051i | 0.780420 | + | 0.625256i | \(0.215005\pi\) | ||||
−0.780420 | + | 0.625256i | \(0.784995\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 284.307i | 0.691744i | ||||||||
\(412\) | − | 195.317i | − | 0.474071i | ||||||
\(413\) | − | 81.3891i | − | 0.197068i | ||||||
\(414\) | 8.80653i | 0.0212718i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 398.036 | 0.956816 | ||||||||
\(417\) | 609.309i | 1.46117i | ||||||||
\(418\) | −63.3119 | + | 29.5327i | −0.151464 | + | 0.0706523i | ||||
\(419\) | −486.210 | −1.16041 | −0.580203 | − | 0.814472i | \(-0.697027\pi\) | ||||
−0.580203 | + | 0.814472i | \(0.697027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 499.876i | − | 1.18735i | −0.804704 | − | 0.593676i | \(-0.797676\pi\) | ||
0.804704 | − | 0.593676i | \(-0.202324\pi\) | |||||||
\(422\) | 157.399 | 0.372984 | ||||||||
\(423\) | −33.9826 | −0.0803371 | ||||||||
\(424\) | −6.90088 | −0.0162757 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 141.024i | 0.331041i | ||||||||
\(427\) | −216.215 | −0.506358 | ||||||||
\(428\) | − | 445.153i | − | 1.04008i | ||||||
\(429\) | 690.685 | 1.60999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 666.010i | − | 1.54527i | −0.634852 | − | 0.772634i | \(-0.718939\pi\) | ||
0.634852 | − | 0.772634i | \(-0.281061\pi\) | |||||||
\(432\) | 362.565i | 0.839270i | ||||||||
\(433\) | 36.6550i | 0.0846536i | 0.999104 | + | 0.0423268i | \(0.0134771\pi\) | ||||
−0.999104 | + | 0.0423268i | \(0.986523\pi\) | |||||||
\(434\) | −10.8955 | −0.0251048 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 418.782i | 0.960509i | ||||||||
\(437\) | 197.023 | + | 422.377i | 0.450854 | + | 0.966537i | ||||
\(438\) | 59.3278 | 0.135452 | ||||||||
\(439\) | − | 206.265i | − | 0.469852i | −0.972013 | − | 0.234926i | \(-0.924515\pi\) | ||
0.972013 | − | 0.234926i | \(-0.0754848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 28.9055 | 0.0655454 | ||||||||
\(442\) | −225.792 | −0.510841 | ||||||||
\(443\) | −611.151 | −1.37957 | −0.689787 | − | 0.724012i | \(-0.742296\pi\) | ||||
−0.689787 | + | 0.724012i | \(0.742296\pi\) | |||||||
\(444\) | −425.515 | −0.958367 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 47.0515 | 0.105497 | ||||||||
\(447\) | − | 498.552i | − | 1.11533i | ||||||
\(448\) | −215.019 | −0.479952 | ||||||||
\(449\) | 0.285011i | 0.000634768i | 1.00000 | 0.000317384i | \(0.000101026\pi\) | |||||
−1.00000 | 0.000317384i | \(0.999899\pi\) | ||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 694.626i | 1.54019i | ||||||||
\(452\) | − | 154.564i | − | 0.341956i | ||||||
\(453\) | 489.563 | 1.08071 | ||||||||
\(454\) | −106.687 | −0.234994 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 76.0486 | + | 163.032i | 0.166773 | + | 0.357527i | ||||
\(457\) | 333.707 | 0.730213 | 0.365107 | − | 0.930966i | \(-0.381033\pi\) | ||||
0.365107 | + | 0.930966i | \(0.381033\pi\) | |||||||
\(458\) | 4.57093i | 0.00998020i | ||||||||
\(459\) | − | 658.558i | − | 1.43477i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −888.555 | −1.92745 | −0.963725 | − | 0.266895i | \(-0.914002\pi\) | ||||
−0.963725 | + | 0.266895i | \(0.914002\pi\) | |||||||
\(462\) | 49.4670 | 0.107071 | ||||||||
\(463\) | 245.546 | 0.530337 | 0.265169 | − | 0.964202i | \(-0.414572\pi\) | ||||
0.265169 | + | 0.964202i | \(0.414572\pi\) | |||||||
\(464\) | 303.369i | 0.653813i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 82.5658i | − | 0.177180i | ||||||
\(467\) | 32.4279 | 0.0694389 | 0.0347194 | − | 0.999397i | \(-0.488946\pi\) | ||||
0.0347194 | + | 0.999397i | \(0.488946\pi\) | |||||||
\(468\) | − | 82.4375i | − | 0.176148i | ||||||
\(469\) | 39.2849i | 0.0837631i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 712.648i | 1.51305i | ||||||||
\(472\) | 57.2800 | 0.121356 | ||||||||
\(473\) | 483.517 | 1.02223 | ||||||||
\(474\) | − | 105.572i | − | 0.222727i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 426.166 | 0.895307 | ||||||||
\(477\) | 2.15718i | 0.00452238i | ||||||||
\(478\) | 1.22184i | 0.00255615i | ||||||||
\(479\) | −345.842 | −0.722008 | −0.361004 | − | 0.932564i | \(-0.617566\pi\) | ||||
−0.361004 | + | 0.932564i | \(0.617566\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −798.027 | −1.65910 | ||||||||
\(482\) | −26.2907 | −0.0545451 | ||||||||
\(483\) | − | 330.012i | − | 0.683255i | ||||||
\(484\) | −110.019 | −0.227312 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.3101 | −0.0397328 | ||||||||
\(487\) | − | 345.826i | − | 0.710114i | −0.934845 | − | 0.355057i | \(-0.884461\pi\) | ||
0.934845 | − | 0.355057i | \(-0.115539\pi\) | |||||||
\(488\) | − | 152.168i | − | 0.311819i | ||||||
\(489\) | − | 264.303i | − | 0.540498i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 122.626 | 0.249748 | 0.124874 | − | 0.992173i | \(-0.460147\pi\) | ||||
0.124874 | + | 0.992173i | \(0.460147\pi\) | |||||||
\(492\) | 877.701 | 1.78395 | ||||||||
\(493\) | − | 551.036i | − | 1.11772i | ||||||
\(494\) | 69.9844 | + | 150.032i | 0.141669 | + | 0.303708i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 95.2523i | 0.192041i | ||||||||
\(497\) | − | 499.190i | − | 1.00441i | ||||||
\(498\) | 40.8207 | 0.0819693 | ||||||||
\(499\) | 4.16222 | 0.00834111 | 0.00417056 | − | 0.999991i | \(-0.498672\pi\) | ||||
0.00417056 | + | 0.999991i | \(0.498672\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 510.931 | 1.01982 | ||||||||
\(502\) | − | 10.2888i | − | 0.0204956i | ||||||
\(503\) | 444.782 | 0.884258 | 0.442129 | − | 0.896951i | \(-0.354223\pi\) | ||||
0.442129 | + | 0.896951i | \(0.354223\pi\) | |||||||
\(504\) | − | 12.0324i | − | 0.0238738i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 90.1942i | 0.178249i | ||||||||
\(507\) | − | 1103.95i | − | 2.17741i | ||||||
\(508\) | − | 577.806i | − | 1.13741i | ||||||
\(509\) | − | 39.1447i | − | 0.0769051i | −0.999260 | − | 0.0384526i | \(-0.987757\pi\) | ||
0.999260 | − | 0.0384526i | \(-0.0122429\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −210.006 | −0.410971 | ||||||||
\(512\) | − | 420.611i | − | 0.821505i | ||||||
\(513\) | −437.592 | + | 204.121i | −0.853006 | + | 0.397896i | ||||
\(514\) | 157.964 | 0.307322 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 610.952i | − | 1.18402i | ||||||
\(517\) | −348.041 | −0.673193 | ||||||||
\(518\) | −57.1548 | −0.110337 | ||||||||
\(519\) | 928.450 | 1.78892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 93.5181i | − | 0.179497i | −0.995964 | − | 0.0897487i | \(-0.971394\pi\) | ||
0.995964 | − | 0.0897487i | \(-0.0286064\pi\) | |||||||
\(522\) | −7.63415 | −0.0146248 | ||||||||
\(523\) | 831.457i | 1.58978i | 0.606751 | + | 0.794892i | \(0.292473\pi\) | ||||
−0.606751 | + | 0.794892i | \(0.707527\pi\) | |||||||
\(524\) | 908.184 | 1.73318 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 86.8264i | − | 0.165069i | ||||||
\(527\) | − | 173.015i | − | 0.328302i | ||||||
\(528\) | − | 432.458i | − | 0.819050i | ||||||
\(529\) | 72.7180 | 0.137463 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 17.9054i | − | 0.0337201i | ||||||
\(532\) | −132.091 | − | 283.175i | −0.248291 | − | 0.532283i | ||||
\(533\) | 1646.07 | 3.08832 | ||||||||
\(534\) | − | 8.50254i | − | 0.0159224i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −27.6479 | −0.0515819 | ||||||||
\(537\) | −641.821 | −1.19520 | ||||||||
\(538\) | 154.745 | 0.287630 | ||||||||
\(539\) | 296.042 | 0.549244 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 663.633 | 1.22668 | 0.613339 | − | 0.789820i | \(-0.289826\pi\) | ||||
0.613339 | + | 0.789820i | \(0.289826\pi\) | |||||||
\(542\) | − | 61.9714i | − | 0.114338i | ||||||
\(543\) | −942.492 | −1.73571 | ||||||||
\(544\) | 452.683i | 0.832138i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 117.223i | − | 0.214695i | ||||||
\(547\) | − | 110.471i | − | 0.201957i | −0.994889 | − | 0.100979i | \(-0.967803\pi\) | ||
0.994889 | − | 0.100979i | \(-0.0321974\pi\) | |||||||
\(548\) | 347.540 | 0.634197 | ||||||||
\(549\) | −47.5668 | −0.0866425 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −366.147 | + | 170.794i | −0.664514 | + | 0.309971i | ||||
\(552\) | 232.256 | 0.420753 | ||||||||
\(553\) | 373.701i | 0.675770i | ||||||||
\(554\) | 165.808i | 0.299292i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 744.827 | 1.33962 | ||||||||
\(557\) | −697.017 | −1.25138 | −0.625688 | − | 0.780073i | \(-0.715182\pi\) | ||||
−0.625688 | + | 0.780073i | \(0.715182\pi\) | |||||||
\(558\) | −2.39698 | −0.00429567 | ||||||||
\(559\) | − | 1145.80i | − | 2.04974i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 785.511i | 1.40020i | ||||||||
\(562\) | −199.514 | −0.355007 | ||||||||
\(563\) | − | 576.361i | − | 1.02373i | −0.859065 | − | 0.511866i | \(-0.828954\pi\) | ||
0.859065 | − | 0.511866i | \(-0.171046\pi\) | |||||||
\(564\) | 439.770i | 0.779734i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 143.655i | − | 0.253808i | ||||||
\(567\) | 377.957 | 0.666591 | ||||||||
\(568\) | 351.320 | 0.618520 | ||||||||
\(569\) | 616.679i | 1.08379i | 0.840445 | + | 0.541897i | \(0.182294\pi\) | ||||
−0.840445 | + | 0.541897i | \(0.817706\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 251.262 | 0.440039 | 0.220019 | − | 0.975496i | \(-0.429388\pi\) | ||||
0.220019 | + | 0.975496i | \(0.429388\pi\) | |||||||
\(572\) | − | 844.302i | − | 1.47605i | ||||||
\(573\) | 388.361i | 0.677768i | ||||||||
\(574\) | 117.892 | 0.205387 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −47.3036 | −0.0821243 | ||||||||
\(577\) | 814.466 | 1.41155 | 0.705777 | − | 0.708434i | \(-0.250598\pi\) | ||||
0.705777 | + | 0.708434i | \(0.250598\pi\) | |||||||
\(578\) | − | 146.276i | − | 0.253073i | ||||||
\(579\) | 216.450 | 0.373834 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −144.495 | −0.248701 | ||||||||
\(582\) | 19.3786i | 0.0332965i | ||||||||
\(583\) | 22.0932i | 0.0378958i | ||||||||
\(584\) | − | 147.798i | − | 0.253079i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 55.7366 | 0.0951136 | ||||||||
\(587\) | 954.562 | 1.62617 | 0.813085 | − | 0.582145i | \(-0.197786\pi\) | ||||
0.813085 | + | 0.582145i | \(0.197786\pi\) | |||||||
\(588\) | − | 374.067i | − | 0.636169i | ||||||
\(589\) | −114.963 | + | 53.6262i | −0.195184 | + | 0.0910462i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 214.763i | 0.363390i | ||||||||
\(592\) | 499.668i | 0.844034i | ||||||||
\(593\) | −730.770 | −1.23233 | −0.616163 | − | 0.787618i | \(-0.711314\pi\) | ||||
−0.616163 | + | 0.787618i | \(0.711314\pi\) | |||||||
\(594\) | −93.4432 | −0.157312 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −609.437 | −1.02255 | ||||||||
\(597\) | 832.061i | 1.39374i | ||||||||
\(598\) | 213.736 | 0.357417 | ||||||||
\(599\) | − | 195.522i | − | 0.326414i | −0.986592 | − | 0.163207i | \(-0.947816\pi\) | ||
0.986592 | − | 0.163207i | \(-0.0521838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 385.902i | 0.642100i | 0.947062 | + | 0.321050i | \(0.104036\pi\) | ||||
−0.947062 | + | 0.321050i | \(0.895964\pi\) | |||||||
\(602\) | − | 82.0626i | − | 0.136317i | ||||||
\(603\) | 8.64258i | 0.0143326i | ||||||||
\(604\) | − | 598.448i | − | 0.990808i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 50.9684 | 0.0841062 | ||||||||
\(607\) | − | 368.570i | − | 0.607200i | −0.952800 | − | 0.303600i | \(-0.901811\pi\) | ||
0.952800 | − | 0.303600i | \(-0.0981886\pi\) | |||||||
\(608\) | 300.794 | − | 140.310i | 0.494728 | − | 0.230772i | ||||
\(609\) | 286.079 | 0.469751 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 824.761i | 1.34986i | ||||||||
\(612\) | 93.7555 | 0.153195 | ||||||||
\(613\) | −675.526 | −1.10200 | −0.551000 | − | 0.834505i | \(-0.685754\pi\) | ||||
−0.551000 | + | 0.834505i | \(0.685754\pi\) | |||||||
\(614\) | 76.2507 | 0.124187 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 123.233i | − | 0.200053i | ||||||
\(617\) | −433.371 | −0.702384 | −0.351192 | − | 0.936303i | \(-0.614224\pi\) | ||||
−0.351192 | + | 0.936303i | \(0.614224\pi\) | |||||||
\(618\) | − | 61.1009i | − | 0.0988688i | ||||||
\(619\) | 316.106 | 0.510672 | 0.255336 | − | 0.966852i | \(-0.417814\pi\) | ||||
0.255336 | + | 0.966852i | \(0.417814\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 623.394i | 1.00385i | ||||||||
\(622\) | − | 118.277i | − | 0.190157i | ||||||
\(623\) | 30.0969i | 0.0483097i | ||||||||
\(624\) | −1024.81 | −1.64232 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 120.839i | 0.193034i | ||||||||
\(627\) | 521.949 | − | 243.470i | 0.832454 | − | 0.388309i | ||||
\(628\) | 871.150 | 1.38718 | ||||||||
\(629\) | − | 907.591i | − | 1.44291i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −614.891 | −0.974471 | −0.487235 | − | 0.873271i | \(-0.661995\pi\) | ||||
−0.487235 | + | 0.873271i | \(0.661995\pi\) | |||||||
\(632\) | −263.003 | −0.416144 | ||||||||
\(633\) | −1297.61 | −2.04994 | ||||||||
\(634\) | 22.9283 | 0.0361645 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 27.9161 | 0.0438932 | ||||||||
\(637\) | − | 701.540i | − | 1.10132i | ||||||
\(638\) | −78.1869 | −0.122550 | ||||||||
\(639\) | − | 109.821i | − | 0.171863i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.80543i | 0.00593670i | 0.999996 | + | 0.00296835i | \(0.000944857\pi\) | ||||
−0.999996 | + | 0.00296835i | \(0.999055\pi\) | |||||||
\(642\) | − | 139.257i | − | 0.216911i | ||||||
\(643\) | −786.552 | −1.22325 | −0.611627 | − | 0.791146i | \(-0.709485\pi\) | ||||
−0.611627 | + | 0.791146i | \(0.709485\pi\) | |||||||
\(644\) | −403.411 | −0.626414 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −170.630 | + | 79.5927i | −0.264134 | + | 0.123209i | ||||
\(647\) | 766.493 | 1.18469 | 0.592344 | − | 0.805685i | \(-0.298203\pi\) | ||||
0.592344 | + | 0.805685i | \(0.298203\pi\) | |||||||
\(648\) | 265.999i | 0.410492i | ||||||||
\(649\) | − | 183.382i | − | 0.282561i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 89.8234 | 0.137978 | ||||||||
\(652\) | −323.088 | −0.495534 | ||||||||
\(653\) | −360.741 | −0.552436 | −0.276218 | − | 0.961095i | \(-0.589081\pi\) | ||||
−0.276218 | + | 0.961095i | \(0.589081\pi\) | |||||||
\(654\) | 131.007i | 0.200317i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1030.66i | − | 1.57112i | ||||||
\(657\) | −46.2008 | −0.0703209 | ||||||||
\(658\) | 59.0695i | 0.0897713i | ||||||||
\(659\) | − | 594.422i | − | 0.902006i | −0.892522 | − | 0.451003i | \(-0.851066\pi\) | ||
0.892522 | − | 0.451003i | \(-0.148934\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 143.641i | − | 0.217309i | −0.994080 | − | 0.108655i | \(-0.965346\pi\) | ||
0.994080 | − | 0.108655i | \(-0.0346542\pi\) | |||||||
\(662\) | −48.0755 | −0.0726215 | ||||||||
\(663\) | 1861.45 | 2.80761 | ||||||||
\(664\) | − | 101.693i | − | 0.153152i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.5739 | −0.0188798 | ||||||||
\(667\) | 521.613i | 0.782029i | ||||||||
\(668\) | − | 624.569i | − | 0.934983i | ||||||
\(669\) | −387.896 | −0.579815 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −487.166 | −0.726030 | ||||||||
\(672\) | −235.017 | −0.349728 | ||||||||
\(673\) | − | 80.3740i | − | 0.119426i | −0.998216 | − | 0.0597132i | \(-0.980981\pi\) | ||
0.998216 | − | 0.0597132i | \(-0.0190186\pi\) | |||||||
\(674\) | 47.5701 | 0.0705788 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1349.48 | −1.99627 | ||||||||
\(677\) | 643.046i | 0.949846i | 0.880027 | + | 0.474923i | \(0.157524\pi\) | ||||
−0.880027 | + | 0.474923i | \(0.842476\pi\) | |||||||
\(678\) | − | 48.3522i | − | 0.0713159i | ||||||
\(679\) | − | 68.5955i | − | 0.101024i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 879.538 | 1.29154 | ||||||||
\(682\) | −24.5492 | −0.0359959 | ||||||||
\(683\) | 1189.25i | 1.74121i | 0.491982 | + | 0.870606i | \(0.336273\pi\) | ||||
−0.491982 | + | 0.870606i | \(0.663727\pi\) | |||||||
\(684\) | −29.0596 | − | 62.2978i | −0.0424848 | − | 0.0910786i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 130.207i | − | 0.189806i | ||||||
\(687\) | − | 37.6832i | − | 0.0548518i | ||||||
\(688\) | −717.421 | −1.04276 | ||||||||
\(689\) | 52.3549 | 0.0759868 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 454.252 | 0.657383 | 0.328692 | − | 0.944437i | \(-0.393392\pi\) | ||||
0.328692 | + | 0.944437i | \(0.393392\pi\) | |||||||
\(692\) | − | 1134.95i | − | 1.64010i | ||||||
\(693\) | −38.5218 | −0.0555870 | ||||||||
\(694\) | − | 59.6120i | − | 0.0858963i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 201.336i | 0.289276i | ||||||||
\(697\) | 1872.07i | 2.68589i | ||||||||
\(698\) | 208.904i | 0.299289i | ||||||||
\(699\) | 680.680i | 0.973791i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −183.307 | −0.261494 | −0.130747 | − | 0.991416i | \(-0.541738\pi\) | ||||
−0.130747 | + | 0.991416i | \(0.541738\pi\) | |||||||
\(702\) | 221.435i | 0.315434i | ||||||||
\(703\) | −603.067 | + | 281.309i | −0.857848 | + | 0.400155i | ||||
\(704\) | −484.471 | −0.688169 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 188.050i | 0.266360i | ||||||||
\(707\) | −180.416 | −0.255185 | ||||||||
\(708\) | −231.714 | −0.327280 | ||||||||
\(709\) | 1209.49 | 1.70591 | 0.852953 | − | 0.521987i | \(-0.174809\pi\) | ||||
0.852953 | + | 0.521987i | \(0.174809\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 82.2133i | 0.115631i | ||||||||
\(712\) | −21.1816 | −0.0297495 | ||||||||
\(713\) | 163.777i | 0.229701i | ||||||||
\(714\) | 133.317 | 0.186719 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 784.570i | 1.09577i | ||||||||
\(717\) | − | 10.0730i | − | 0.0140487i | ||||||
\(718\) | 67.2211i | 0.0936227i | ||||||||
\(719\) | −721.858 | −1.00397 | −0.501987 | − | 0.864875i | \(-0.667398\pi\) | ||||
−0.501987 | + | 0.864875i | \(0.667398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 216.283i | 0.299976i | ||||||||
\(722\) | 105.774 | + | 88.7089i | 0.146501 | + | 0.122866i | ||||
\(723\) | 216.743 | 0.299783 | ||||||||
\(724\) | 1152.11i | 1.59132i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −34.4171 | −0.0474065 | ||||||||
\(727\) | −141.344 | −0.194421 | −0.0972103 | − | 0.995264i | \(-0.530992\pi\) | ||||
−0.0972103 | + | 0.995264i | \(0.530992\pi\) | |||||||
\(728\) | −292.028 | −0.401137 | ||||||||
\(729\) | −637.918 | −0.875059 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1303.11 | 1.78265 | ||||||||
\(732\) | 615.563i | 0.840933i | ||||||||
\(733\) | −270.218 | −0.368647 | −0.184324 | − | 0.982866i | \(-0.559009\pi\) | ||||
−0.184324 | + | 0.982866i | \(0.559009\pi\) | |||||||
\(734\) | − | 172.280i | − | 0.234714i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 428.512i | − | 0.582217i | ||||||
\(737\) | 88.5150i | 0.120102i | ||||||||
\(738\) | 25.9360 | 0.0351436 | ||||||||
\(739\) | −955.610 | −1.29311 | −0.646556 | − | 0.762866i | \(-0.723791\pi\) | ||||
−0.646556 | + | 0.762866i | \(0.723791\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −576.958 | − | 1236.88i | −0.778620 | − | 1.66920i | ||||
\(742\) | 3.74967 | 0.00505346 | ||||||||
\(743\) | − | 1090.15i | − | 1.46722i | −0.679569 | − | 0.733612i | \(-0.737833\pi\) | ||
0.679569 | − | 0.733612i | \(-0.262167\pi\) | |||||||
\(744\) | 63.2159i | 0.0849676i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 216.818 | 0.290640 | ||||||||
\(747\) | −31.7886 | −0.0425551 | ||||||||
\(748\) | 960.219 | 1.28372 | ||||||||
\(749\) | 492.935i | 0.658125i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 729.113i | − | 0.970856i | −0.874277 | − | 0.485428i | \(-0.838664\pi\) | ||
0.874277 | − | 0.485428i | \(-0.161336\pi\) | |||||||
\(752\) | 516.407 | 0.686712 | ||||||||
\(753\) | 84.8216i | 0.112645i | ||||||||
\(754\) | 185.282i | 0.245732i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 417.943i | − | 0.552835i | ||||||
\(757\) | 200.136 | 0.264381 | 0.132191 | − | 0.991224i | \(-0.457799\pi\) | ||||
0.132191 | + | 0.991224i | \(0.457799\pi\) | |||||||
\(758\) | −127.603 | −0.168341 | ||||||||
\(759\) | − | 743.569i | − | 0.979669i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 649.201 | 0.853090 | 0.426545 | − | 0.904466i | \(-0.359731\pi\) | ||||
0.426545 | + | 0.904466i | \(0.359731\pi\) | |||||||
\(762\) | − | 180.754i | − | 0.237211i | ||||||
\(763\) | − | 463.734i | − | 0.607777i | ||||||
\(764\) | 474.737 | 0.621384 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.63138 | −0.00735168 | ||||||||
\(767\) | −434.566 | −0.566579 | ||||||||
\(768\) | 527.917i | 0.687392i | ||||||||
\(769\) | −975.651 | −1.26873 | −0.634363 | − | 0.773035i | \(-0.718738\pi\) | ||||
−0.634363 | + | 0.773035i | \(0.718738\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1302.27 | −1.68906 | ||||||||
\(772\) | − | 264.591i | − | 0.342735i | ||||||
\(773\) | − | 1411.33i | − | 1.82579i | −0.408196 | − | 0.912894i | \(-0.633842\pi\) | ||
0.408196 | − | 0.912894i | \(-0.366158\pi\) | |||||||
\(774\) | − | 18.0536i | − | 0.0233250i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 48.2761 | 0.0622115 | ||||||||
\(777\) | 471.189 | 0.606421 | ||||||||
\(778\) | 199.888i | 0.256926i | ||||||||
\(779\) | 1243.93 | − | 580.249i | 1.59683 | − | 0.744864i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 1124.75i | − | 1.44014i | ||||||
\(782\) | 243.080i | 0.310844i | ||||||||
\(783\) | −540.403 | −0.690170 | ||||||||
\(784\) | −439.255 | −0.560274 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 284.106 | 0.361458 | ||||||||
\(787\) | 318.102i | 0.404196i | 0.979365 | + | 0.202098i | \(0.0647759\pi\) | ||||
−0.979365 | + | 0.202098i | \(0.935224\pi\) | |||||||
\(788\) | 262.529 | 0.333159 | ||||||||
\(789\) | 715.805i | 0.907230i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 171.155i | 0.216378i | ||||||||
\(792\) | − | 27.1109i | − | 0.0342309i | ||||||
\(793\) | 1154.45i | 1.45580i | ||||||||
\(794\) | 79.2532i | 0.0998152i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1017.12 | 1.27779 | ||||||||
\(797\) | − | 27.1975i | − | 0.0341249i | −0.999854 | − | 0.0170624i | \(-0.994569\pi\) | ||
0.999854 | − | 0.0170624i | \(-0.00543141\pi\) | |||||||
\(798\) | −41.3218 | − | 88.5853i | −0.0517817 | − | 0.111009i | ||||
\(799\) | −937.995 | −1.17396 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.62125i | 0.00826623i | ||||||||
\(802\) | −106.742 | −0.133095 | ||||||||
\(803\) | −473.177 | −0.589261 | ||||||||
\(804\) | 111.844 | 0.139109 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 58.1750i | 0.0721774i | ||||||||
\(807\) | −1275.73 | −1.58083 | ||||||||
\(808\) | − | 126.973i | − | 0.157145i | ||||||
\(809\) | 1023.22 | 1.26480 | 0.632398 | − | 0.774643i | \(-0.282071\pi\) | ||||
0.632398 | + | 0.774643i | \(0.282071\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1153.64i | 1.42249i | 0.702944 | + | 0.711245i | \(0.251869\pi\) | ||||
−0.702944 | + | 0.711245i | \(0.748131\pi\) | |||||||
\(812\) | − | 349.706i | − | 0.430673i | ||||||
\(813\) | 510.898i | 0.628411i | ||||||||
\(814\) | −128.779 | −0.158205 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 1165.51i | − | 1.42832i | ||||||
\(817\) | −403.901 | − | 865.880i | −0.494371 | − | 1.05983i | ||||
\(818\) | 195.585 | 0.239102 | ||||||||
\(819\) | 91.2862i | 0.111461i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 201.567 | 0.245515 | 0.122757 | − | 0.992437i | \(-0.460826\pi\) | ||||
0.122757 | + | 0.992437i | \(0.460826\pi\) | |||||||
\(822\) | 108.721 | 0.132263 | ||||||||
\(823\) | −194.061 | −0.235797 | −0.117898 | − | 0.993026i | \(-0.537616\pi\) | ||||
−0.117898 | + | 0.993026i | \(0.537616\pi\) | |||||||
\(824\) | −152.215 | −0.184727 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −31.1237 | −0.0376800 | ||||||||
\(827\) | − | 252.357i | − | 0.305147i | −0.988292 | − | 0.152574i | \(-0.951244\pi\) | ||
0.988292 | − | 0.152574i | \(-0.0487561\pi\) | |||||||
\(828\) | −88.7494 | −0.107185 | ||||||||
\(829\) | − | 80.0611i | − | 0.0965756i | −0.998833 | − | 0.0482878i | \(-0.984624\pi\) | ||
0.998833 | − | 0.0482878i | \(-0.0153765\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1366.93i | − | 1.64493i | ||||||
\(832\) | 1148.06i | 1.37988i | ||||||||
\(833\) | 797.856 | 0.957811 | ||||||||
\(834\) | 233.004 | 0.279381 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −297.621 | − | 638.037i | −0.356006 | − | 0.763202i | ||||
\(837\) | −169.677 | −0.202720 | ||||||||
\(838\) | 185.930i | 0.221873i | ||||||||
\(839\) | 1347.70i | 1.60632i | 0.595765 | + | 0.803159i | \(0.296849\pi\) | ||||
−0.595765 | + | 0.803159i | \(0.703151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 388.828 | 0.462340 | ||||||||
\(842\) | −191.155 | −0.227025 | ||||||||
\(843\) | 1644.81 | 1.95114 | ||||||||
\(844\) | 1586.22i | 1.87941i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 12.9952i | 0.0153607i | ||||||||
\(847\) | 121.828 | 0.143835 | ||||||||
\(848\) | − | 32.7810i | − | 0.0386568i | ||||||
\(849\) | 1184.31i | 1.39494i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 859.130i | 1.00955i | ||||||||
\(852\) | −1421.19 | −1.66806 | ||||||||
\(853\) | 1254.19 | 1.47033 | 0.735165 | − | 0.677888i | \(-0.237105\pi\) | ||||
0.735165 | + | 0.677888i | \(0.237105\pi\) | |||||||
\(854\) | 82.6819i | 0.0968172i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −346.918 | −0.405278 | ||||||||
\(857\) | 1044.59i | 1.21889i | 0.792828 | + | 0.609445i | \(0.208608\pi\) | ||||
−0.792828 | + | 0.609445i | \(0.791392\pi\) | |||||||
\(858\) | − | 264.122i | − | 0.307835i | ||||||
\(859\) | 803.394 | 0.935267 | 0.467634 | − | 0.883922i | \(-0.345107\pi\) | ||||
0.467634 | + | 0.883922i | \(0.345107\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −971.912 | −1.12882 | ||||||||
\(862\) | −254.686 | −0.295460 | ||||||||
\(863\) | 852.534i | 0.987873i | 0.869498 | + | 0.493936i | \(0.164442\pi\) | ||||
−0.869498 | + | 0.493936i | \(0.835558\pi\) | |||||||
\(864\) | 443.948 | 0.513829 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.0171 | 0.0161860 | ||||||||
\(867\) | 1205.91i | 1.39090i | ||||||||
\(868\) | − | 109.801i | − | 0.126499i | ||||||
\(869\) | 842.007i | 0.968937i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 209.756 | 0.240822 | ||||||||
\(872\) | 326.366 | 0.374274 | ||||||||
\(873\) | − | 15.0908i | − | 0.0172862i | ||||||
\(874\) | 161.519 | − | 75.3429i | 0.184805 | − | 0.0862046i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 597.887i | 0.682519i | ||||||||
\(877\) | 134.051i | 0.152852i | 0.997075 | + | 0.0764260i | \(0.0243509\pi\) | ||||
−0.997075 | + | 0.0764260i | \(0.975649\pi\) | |||||||
\(878\) | −78.8771 | −0.0898372 | ||||||||
\(879\) | −459.497 | −0.522750 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1395.05 | 1.58348 | 0.791742 | − | 0.610855i | \(-0.209174\pi\) | ||||
0.791742 | + | 0.610855i | \(0.209174\pi\) | |||||||
\(882\) | − | 11.0536i | − | 0.0125325i | ||||||
\(883\) | −879.025 | −0.995498 | −0.497749 | − | 0.867321i | \(-0.665840\pi\) | ||||
−0.497749 | + | 0.867321i | \(0.665840\pi\) | |||||||
\(884\) | − | 2275.46i | − | 2.57405i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 233.708i | 0.263779i | ||||||||
\(887\) | 1198.89i | 1.35163i | 0.737072 | + | 0.675814i | \(0.236208\pi\) | ||||
−0.737072 | + | 0.675814i | \(0.763792\pi\) | |||||||
\(888\) | 331.614i | 0.373439i | ||||||||
\(889\) | 639.827i | 0.719715i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 851.597 | 0.955776 | ||||||||
\(892\) | 474.170i | 0.531580i | ||||||||
\(893\) | 290.733 | + | 623.270i | 0.325568 | + | 0.697951i | ||||
\(894\) | −190.650 | −0.213254 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 380.414i | 0.424569i | ||||||||
\(897\) | −1762.06 | −1.96439 | ||||||||
\(898\) | 0.108990 | 0.000121370 | ||||||||
\(899\) | −141.974 | −0.157924 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 59.5429i | 0.0660853i | ||||||||
\(902\) | 265.629 | 0.294489 | ||||||||
\(903\) | 676.531i | 0.749204i | ||||||||
\(904\) | −120.455 | −0.133247 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 187.212i | − | 0.206636i | ||||||
\(907\) | − | 793.689i | − | 0.875071i | −0.899201 | − | 0.437535i | \(-0.855851\pi\) | ||
0.899201 | − | 0.437535i | \(-0.144149\pi\) | |||||||
\(908\) | − | 1075.16i | − | 1.18409i | ||||||
\(909\) | −39.6910 | −0.0436645 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 136.125i | 0.149423i | 0.997205 | + | 0.0747116i | \(0.0238036\pi\) | ||||
−0.997205 | + | 0.0747116i | \(0.976196\pi\) | |||||||
\(912\) | −774.445 | + | 361.250i | −0.849172 | + | 0.396108i | ||||
\(913\) | −325.571 | −0.356594 | ||||||||
\(914\) | − | 127.612i | − | 0.139619i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.0644 | −0.0502886 | ||||||||
\(917\) | −1005.67 | −1.09669 | ||||||||
\(918\) | −251.836 | −0.274332 | ||||||||
\(919\) | 124.377 | 0.135339 | 0.0676695 | − | 0.997708i | \(-0.478444\pi\) | ||||
0.0676695 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −628.617 | −0.682538 | ||||||||
\(922\) | 339.789i | 0.368534i | ||||||||
\(923\) | −2665.36 | −2.88771 | ||||||||
\(924\) | 498.512i | 0.539515i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 93.8984i | − | 0.101402i | ||||||
\(927\) | 47.5816i | 0.0513286i | ||||||||
\(928\) | 371.465 | 0.400286 | ||||||||
\(929\) | 412.151 | 0.443650 | 0.221825 | − | 0.975086i | \(-0.428799\pi\) | ||||
0.221825 | + | 0.975086i | \(0.428799\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −247.296 | − | 530.152i | −0.265624 | − | 0.569443i | ||||
\(932\) | 832.071 | 0.892780 | ||||||||
\(933\) | 975.090i | 1.04511i | ||||||||
\(934\) | − | 12.4006i | − | 0.0132769i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −64.2454 | −0.0686382 | ||||||||
\(937\) | 703.752 | 0.751069 | 0.375535 | − | 0.926808i | \(-0.377459\pi\) | ||||
0.375535 | + | 0.926808i | \(0.377459\pi\) | |||||||
\(938\) | 15.0228 | 0.0160158 | ||||||||
\(939\) | − | 996.209i | − | 1.06092i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 556.128i | − | 0.590997i | −0.955343 | − | 0.295498i | \(-0.904514\pi\) | ||
0.955343 | − | 0.295498i | \(-0.0954857\pi\) | |||||||
\(942\) | 272.521 | 0.289300 | ||||||||
\(943\) | − | 1772.11i | − | 1.87922i | ||||||
\(944\) | 272.095i | 0.288236i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 184.900i | − | 0.195454i | ||||||
\(947\) | 729.330 | 0.770148 | 0.385074 | − | 0.922886i | \(-0.374176\pi\) | ||||
0.385074 | + | 0.922886i | \(0.374176\pi\) | |||||||
\(948\) | 1063.93 | 1.12228 | ||||||||
\(949\) | 1121.30i | 1.18156i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −189.023 | −0.198762 | ||||||||
\(952\) | − | 332.121i | − | 0.348867i | ||||||
\(953\) | 1856.42i | 1.94798i | 0.226592 | + | 0.973990i | \(0.427242\pi\) | ||||
−0.226592 | + | 0.973990i | \(0.572758\pi\) | |||||||
\(954\) | 0.824918 | 0.000864693 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.3133 | −0.0128800 | ||||||||
\(957\) | 644.580 | 0.673542 | ||||||||
\(958\) | 132.252i | 0.138050i | ||||||||
\(959\) | −384.845 | −0.401298 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 916.423 | 0.953614 | ||||||||
\(962\) | 305.171i | 0.317225i | ||||||||
\(963\) | 108.445i | 0.112611i | ||||||||
\(964\) | − | 264.949i | − | 0.274844i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −126.199 | −0.130640 | ||||||||
\(967\) | 1029.19 | 1.06432 | 0.532158 | − | 0.846645i | \(-0.321381\pi\) | ||||
0.532158 | + | 0.846645i | \(0.321381\pi\) | |||||||
\(968\) | 85.7403i | 0.0885747i | ||||||||
\(969\) | 1406.69 | − | 656.170i | 1.45169 | − | 0.677162i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 231.062i | − | 0.237963i | −0.992896 | − | 0.118981i | \(-0.962037\pi\) | ||
0.992896 | − | 0.118981i | \(-0.0379629\pi\) | |||||||
\(972\) | − | 194.601i | − | 0.200207i | ||||||
\(973\) | −824.776 | −0.847663 | ||||||||
\(974\) | −132.246 | −0.135776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 722.835 | 0.740610 | ||||||||
\(977\) | 491.283i | 0.502849i | 0.967877 | + | 0.251424i | \(0.0808990\pi\) | ||||
−0.967877 | + | 0.251424i | \(0.919101\pi\) | |||||||
\(978\) | −101.071 | −0.103345 | ||||||||
\(979\) | 67.8131i | 0.0692677i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 102.020i | − | 0.103996i | ||||||
\(982\) | − | 46.8930i | − | 0.0477525i | ||||||
\(983\) | 363.273i | 0.369555i | 0.982780 | + | 0.184778i | \(0.0591565\pi\) | ||||
−0.982780 | + | 0.184778i | \(0.940844\pi\) | |||||||
\(984\) | − | 684.012i | − | 0.695135i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −210.719 | −0.213711 | ||||||||
\(987\) | − | 486.974i | − | 0.493388i | ||||||
\(988\) | −1511.97 | + | 705.280i | −1.53034 | + | 0.713846i | ||||
\(989\) | −1233.53 | −1.24725 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 548.658i | 0.553640i | 0.960922 | + | 0.276820i | \(0.0892806\pi\) | ||||
−0.960922 | + | 0.276820i | \(0.910719\pi\) | |||||||
\(992\) | 116.633 | 0.117574 | ||||||||
\(993\) | 396.338 | 0.399132 | ||||||||
\(994\) | −190.893 | −0.192045 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 411.378i | 0.413030i | ||||||||
\(997\) | −863.800 | −0.866400 | −0.433200 | − | 0.901298i | \(-0.642616\pi\) | ||||
−0.433200 | + | 0.901298i | \(0.642616\pi\) | |||||||
\(998\) | − | 1.59166i | − | 0.00159485i | ||||||
\(999\) | −890.078 | −0.890969 |
(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 | 475.3.c.i.151.7 | yes | 14 | |
5.2 | odd | 4 | 475.3.d.d.474.16 | 28 | |||
5.3 | odd | 4 | 475.3.d.d.474.13 | 28 | |||
5.4 | even | 2 | 475.3.c.h.151.8 | yes | 14 | ||
19.18 | odd | 2 | inner | 475.3.c.i.151.8 | yes | 14 | |
95.18 | even | 4 | 475.3.d.d.474.15 | 28 | |||
95.37 | even | 4 | 475.3.d.d.474.14 | 28 | |||
95.94 | odd | 2 | 475.3.c.h.151.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.3.c.h.151.7 | ✓ | 14 | 95.94 | odd | 2 | ||
475.3.c.h.151.8 | yes | 14 | 5.4 | even | 2 | ||
475.3.c.i.151.7 | yes | 14 | 1.1 | even | 1 | trivial | |
475.3.c.i.151.8 | yes | 14 | 19.18 | odd | 2 | inner | |
475.3.d.d.474.13 | 28 | 5.3 | odd | 4 | |||
475.3.d.d.474.14 | 28 | 95.37 | even | 4 | |||
475.3.d.d.474.15 | 28 | 95.18 | even | 4 | |||
475.3.d.d.474.16 | 28 | 5.2 | odd | 4 |