Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (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: | \(79.2985670477\) |
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: | \( x^{16} - 2 x^{15} + 2 x^{14} + 58 x^{13} + 178264 x^{12} - 331354 x^{11} + 307862 x^{10} + \cdots + 22\!\cdots\!01 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.2 | ||
Root | \(-6.36140 - 6.36140i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.b.223.10 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −10.6345 | −0.951180 | −0.475590 | − | 0.879667i | \(-0.657765\pi\) | ||||
−0.475590 | + | 0.879667i | \(0.657765\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 18.0158 | − | 4.29303i | 0.972763 | − | 0.231802i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.02265 | −0.137671 | −0.0688357 | − | 0.997628i | \(-0.521928\pi\) | ||||
−0.0688357 | + | 0.997628i | \(0.521928\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 80.6582 | 1.72081 | 0.860406 | − | 0.509608i | \(-0.170210\pi\) | ||||
0.860406 | + | 0.509608i | \(0.170210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 31.9036i | 0.549164i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 31.3183i | 0.446811i | 0.974726 | + | 0.223406i | \(0.0717175\pi\) | ||||
−0.974726 | + | 0.223406i | \(0.928283\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 74.0722i | 0.894385i | 0.894438 | + | 0.447193i | \(0.147576\pi\) | ||||
−0.894438 | + | 0.447193i | \(0.852424\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −12.8791 | − | 54.0475i | −0.133831 | − | 0.561625i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 37.3407i | − | 0.338525i | −0.985571 | − | 0.169263i | \(-0.945861\pi\) | ||
0.985571 | − | 0.169263i | \(-0.0541386\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.9070 | −0.0952563 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 242.998i | 1.55599i | 0.628271 | + | 0.777994i | \(0.283763\pi\) | ||||
−0.628271 | + | 0.777994i | \(0.716237\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −284.926 | −1.65078 | −0.825390 | − | 0.564563i | \(-0.809045\pi\) | ||||
−0.825390 | + | 0.564563i | \(0.809045\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.0679i | 0.0794846i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −191.590 | + | 45.6543i | −0.925273 | + | 0.220485i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 167.404i | − | 0.743813i | −0.928270 | − | 0.371906i | \(-0.878704\pi\) | ||
0.928270 | − | 0.371906i | \(-0.121296\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 241.975i | − | 0.993512i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 270.989i | − | 1.03223i | −0.856519 | − | 0.516115i | \(-0.827378\pi\) | ||
0.856519 | − | 0.516115i | \(-0.172622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 169.804 | 0.602205 | 0.301103 | − | 0.953592i | \(-0.402645\pi\) | ||||
0.301103 | + | 0.953592i | \(0.402645\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 95.7107 | 0.317060 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −639.550 | −1.98485 | −0.992425 | − | 0.122848i | \(-0.960797\pi\) | ||||
−0.992425 | + | 0.122848i | \(0.960797\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 306.140 | − | 154.685i | 0.892536 | − | 0.450976i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 93.9548 | 0.257967 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 534.235i | 1.38458i | 0.721619 | + | 0.692291i | \(0.243398\pi\) | ||||
−0.721619 | + | 0.692291i | \(0.756602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 53.4134 | 0.130950 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 222.217 | 0.516374 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 56.9436i | 0.125651i | 0.998025 | + | 0.0628257i | \(0.0200112\pi\) | ||||
−0.998025 | + | 0.0628257i | \(0.979989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −217.266 | −0.456033 | −0.228016 | − | 0.973657i | \(-0.573224\pi\) | ||||
−0.228016 | + | 0.973657i | \(0.573224\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −162.142 | + | 38.6372i | −0.324254 | + | 0.0772672i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −857.761 | −1.63680 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 684.081 | 1.24737 | 0.623685 | − | 0.781676i | \(-0.285635\pi\) | ||||
0.623685 | + | 0.781676i | \(0.285635\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −112.022 | −0.195448 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 966.305i | 1.61520i | 0.589730 | + | 0.807601i | \(0.299234\pi\) | ||||
−0.589730 | + | 0.807601i | \(0.700766\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 325.451i | 0.521797i | 0.965366 | + | 0.260898i | \(0.0840188\pi\) | ||||
−0.965366 | + | 0.260898i | \(0.915981\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 35.7211i | 0.0549962i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −90.4871 | + | 21.5624i | −0.133922 | + | 0.0319125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 856.194i | − | 1.21936i | −0.792648 | − | 0.609679i | \(-0.791298\pi\) | ||
0.792648 | − | 0.609679i | \(-0.208702\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 459.647i | − | 0.607865i | −0.952694 | − | 0.303932i | \(-0.901700\pi\) | ||
0.952694 | − | 0.303932i | \(-0.0982997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 333.055i | − | 0.424998i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 728.995 | 0.898351 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1077.84i | 1.28372i | 0.766822 | + | 0.641860i | \(0.221837\pi\) | ||||
−0.766822 | + | 0.641860i | \(0.778163\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1453.12 | − | 346.268i | 1.67394 | − | 0.398887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 854.778i | 0.953079i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 787.722i | − | 0.850722i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1225.31i | 1.28259i | 0.767293 | + | 0.641297i | \(0.221603\pi\) | ||||
−0.767293 | + | 0.641297i | \(0.778397\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 45.2038 | 0.0458905 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1513.47 | −1.49105 | −0.745523 | − | 0.666480i | \(-0.767800\pi\) | ||||
−0.745523 | + | 0.666480i | \(0.767800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 997.456 | 0.954197 | 0.477098 | − | 0.878850i | \(-0.341689\pi\) | ||||
0.477098 | + | 0.878850i | \(0.341689\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 136.963 | + | 574.769i | 0.127297 | + | 0.534207i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 959.164 | 0.866597 | 0.433299 | − | 0.901250i | \(-0.357350\pi\) | ||||
0.433299 | + | 0.901250i | \(0.357350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 717.352i | 0.630365i | 0.949031 | + | 0.315183i | \(0.102066\pi\) | ||||
−0.949031 | + | 0.315183i | \(0.897934\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −502.212 | −0.429440 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 940.776 | 0.783193 | 0.391596 | − | 0.920137i | \(-0.371923\pi\) | ||||
0.391596 | + | 0.920137i | \(0.371923\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 397.101i | 0.321999i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −725.924 | −0.573604 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 134.450 | + | 564.224i | 0.103572 | + | 0.434642i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1305.77 | −0.981047 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −812.968 | −0.595958 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1455.94 | 1.04179 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2089.41i | 1.45988i | 0.683509 | + | 0.729942i | \(0.260453\pi\) | ||||
−0.683509 | + | 0.729942i | \(0.739547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 509.411i | − | 0.347683i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 892.922i | 0.595534i | 0.954639 | + | 0.297767i | \(0.0962418\pi\) | ||||
−0.954639 | + | 0.297767i | \(0.903758\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 317.994 | + | 1334.47i | 0.207320 | + | 0.870025i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 287.132i | − | 0.183055i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1440.52 | −0.898338 | −0.449169 | − | 0.893447i | \(-0.648280\pi\) | ||||
−0.449169 | + | 0.893447i | \(0.648280\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2001.02i | 1.22104i | 0.792001 | + | 0.610520i | \(0.209040\pi\) | ||||
−0.792001 | + | 0.610520i | \(0.790960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1918.65i | 1.14595i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −405.118 | −0.236907 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2584.17i | − | 1.48003i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −464.055 | − | 918.420i | −0.260371 | − | 0.515306i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1978.85i | 1.08801i | 0.839081 | + | 0.544006i | \(0.183093\pi\) | ||||
−0.839081 | + | 0.544006i | \(0.816907\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1906.09i | − | 1.02725i | −0.858014 | − | 0.513626i | \(-0.828302\pi\) | ||
0.858014 | − | 0.513626i | \(-0.171698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 281.864i | − | 0.148937i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3030.05 | 1.57019 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 280.991 | 0.142838 | 0.0714188 | − | 0.997446i | \(-0.477247\pi\) | ||||
0.0714188 | + | 0.997446i | \(0.477247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1602.70 | 0.799388 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −160.305 | − | 672.724i | −0.0784707 | − | 0.329305i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2809.63 | 1.35011 | 0.675053 | − | 0.737770i | \(-0.264121\pi\) | ||||
0.675053 | + | 0.737770i | \(0.264121\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 160.240i | − | 0.0756042i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −101.283 | −0.0469310 | −0.0234655 | − | 0.999725i | \(-0.507470\pi\) | ||||
−0.0234655 | + | 0.999725i | \(0.507470\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4308.75 | 1.96120 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 666.650i | − | 0.298128i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 408.564 | 0.179552 | 0.0897761 | − | 0.995962i | \(-0.471385\pi\) | ||||
0.0897761 | + | 0.995962i | \(0.471385\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −214.515 | + | 51.1172i | −0.0926618 | + | 0.0220806i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 170.831 | 0.0725449 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1624.36 | 0.678272 | 0.339136 | − | 0.940737i | \(-0.389865\pi\) | ||||
0.339136 | + | 0.940737i | \(0.389865\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1303.28 | −0.535203 | −0.267601 | − | 0.963530i | \(-0.586231\pi\) | ||||
−0.267601 | + | 0.963530i | \(0.586231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 651.797i | 0.263291i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1780.26i | 0.707500i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 157.301i | − | 0.0615131i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 115.912 | + | 486.427i | 0.0446103 | + | 0.187208i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 117.261i | − | 0.0444226i | −0.999753 | − | 0.0222113i | \(-0.992929\pi\) | ||
0.999753 | − | 0.0222113i | \(-0.00707066\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 292.337 | 0.109030 | 0.0545151 | − | 0.998513i | \(-0.482639\pi\) | ||||
0.0545151 | + | 0.998513i | \(0.482639\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2573.28i | 0.945009i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4190.92i | 1.51569i | 0.652436 | + | 0.757843i | \(0.273747\pi\) | ||||
−0.652436 | + | 0.757843i | \(0.726253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1747.17 | 0.622381 | 0.311191 | − | 0.950347i | \(-0.399272\pi\) | ||||
0.311191 | + | 0.950347i | \(0.399272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 2052.24i | − | 0.720169i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1043.20 | + | 4377.82i | 0.360681 | + | 1.51361i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2881.84i | 0.981837i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 336.067i | 0.112842i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 372.038i | − | 0.123131i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 628.802 | 0.205159 | 0.102579 | − | 0.994725i | \(-0.467290\pi\) | ||||
0.102579 | + | 0.994725i | \(0.467290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2898.91 | 0.932537 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1805.78 | −0.572806 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5133.17 | + | 1223.19i | −1.60582 | + | 0.382654i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 976.353 | 0.301260 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2526.08i | 0.768879i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2081.12 | 0.624942 | 0.312471 | − | 0.949927i | \(-0.398843\pi\) | ||||
0.312471 | + | 0.949927i | \(0.398843\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 107.163 | 0.0317521 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 806.786i | − | 0.235896i | −0.993020 | − | 0.117948i | \(-0.962368\pi\) | ||
0.993020 | − | 0.117948i | \(-0.0376315\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1726.29 | −0.498152 | −0.249076 | − | 0.968484i | \(-0.580127\pi\) | ||||
−0.249076 | + | 0.968484i | \(0.580127\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 64.6871 | + | 271.461i | 0.0184247 | + | 0.0773197i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2208.17 | 0.620868 | 0.310434 | − | 0.950595i | \(-0.399526\pi\) | ||||
0.310434 | + | 0.950595i | \(0.399526\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6801.31 | 1.88795 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2568.58 | −0.703997 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1379.52i | − | 0.373362i | −0.982421 | − | 0.186681i | \(-0.940227\pi\) | ||
0.982421 | − | 0.186681i | \(-0.0597731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5254.27i | − | 1.40439i | −0.711986 | − | 0.702194i | \(-0.752204\pi\) | ||
0.711986 | − | 0.702194i | \(-0.247796\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3255.65 | + | 1645.00i | −0.848963 | + | 0.428960i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5974.53i | 1.53907i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1378.94 | −0.350951 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4235.01i | − | 1.06499i | −0.846434 | − | 0.532493i | \(-0.821255\pi\) | ||
0.846434 | − | 0.532493i | \(-0.178745\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 187.549i | 0.0466052i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −999.164 | −0.245373 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3842.32i | 0.932596i | 0.884628 | + | 0.466298i | \(0.154413\pi\) | ||||
−0.884628 | + | 0.466298i | \(0.845587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −718.670 | − | 3015.92i | −0.172417 | − | 0.723554i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2186.99i | − | 0.518663i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 5327.10i | − | 1.24898i | −0.781031 | − | 0.624492i | \(-0.785306\pi\) | ||
0.781031 | − | 0.624492i | \(-0.214694\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5681.33i | − | 1.31699i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3233.53 | 0.741156 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7196.26 | −1.63109 | −0.815546 | − | 0.578692i | \(-0.803563\pi\) | ||||
−0.815546 | + | 0.578692i | \(0.803563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3998.83 | −0.896352 | −0.448176 | − | 0.893945i | \(-0.647926\pi\) | ||||
−0.448176 | + | 0.893945i | \(0.647926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1038.80 | − | 4359.37i | −0.230298 | − | 0.966452i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 59.8048 | 0.0131141 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6116.25i | 1.32668i | 0.748319 | + | 0.663339i | \(0.230861\pi\) | ||||
−0.748319 | + | 0.663339i | \(0.769139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2564.33 | 0.550260 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6280.80 | 1.33338 | 0.666692 | − | 0.745333i | \(-0.267710\pi\) | ||||
0.666692 | + | 0.745333i | \(0.267710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 894.355i | 0.187858i | 0.995579 | + | 0.0939292i | \(0.0299427\pi\) | ||||
−0.995579 | + | 0.0939292i | \(0.970057\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2363.17 | −0.491164 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1163.36 | − | 4882.10i | −0.239273 | − | 1.00412i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3932.17 | 0.800360 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3675.94 | 0.740506 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6903.17 | 1.37641 | 0.688204 | − | 0.725517i | \(-0.258399\pi\) | ||||
0.688204 | + | 0.725517i | \(0.258399\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 605.568i | − | 0.119517i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 135.611i | − | 0.0264949i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3011.84i | − | 0.582539i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3059.15 | − | 728.972i | 0.585803 | − | 0.139592i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4540.40i | 0.860855i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2310.51 | 0.433769 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7933.97i | 1.47497i | 0.675364 | + | 0.737485i | \(0.263987\pi\) | ||||
−0.675364 | + | 0.737485i | \(0.736013\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2992.37i | − | 0.550906i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6215.65 | −1.13330 | −0.566652 | − | 0.823957i | \(-0.691762\pi\) | ||||
−0.566652 | + | 0.823957i | \(0.691762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3466.13i | 0.625933i | 0.949764 | + | 0.312966i | \(0.101323\pi\) | ||||
−0.949764 | + | 0.312966i | \(0.898677\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1724.31 | − | 410.888i | 0.308424 | − | 0.0734950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1277.86i | 0.226409i | 0.993572 | + | 0.113204i | \(0.0361115\pi\) | ||||
−0.993572 | + | 0.113204i | \(0.963888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1220.50i | − | 0.214215i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 2877.49i | − | 0.500330i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2319.81 | −0.399622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −960.400 | −0.163918 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2152.05 | 0.363942 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11522.0 | + | 2745.61i | −1.93079 | + | 0.460092i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3351.13 | −0.556480 | −0.278240 | − | 0.960512i | \(-0.589751\pi\) | ||||
−0.278240 | + | 0.960512i | \(0.589751\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1506.64i | 0.247938i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7274.87 | −1.18647 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5362.98 | −0.866885 | −0.433442 | − | 0.901181i | \(-0.642701\pi\) | ||||
−0.433442 | + | 0.901181i | \(0.642701\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 2822.33i | − | 0.452177i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1431.08 | 0.227265 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4851.30 | − | 4101.04i | 0.763689 | − | 0.645584i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1191.30 | 0.185906 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3355.31 | 0.519084 | 0.259542 | − | 0.965732i | \(-0.416428\pi\) | ||||
0.259542 | + | 0.965732i | \(0.416428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5141.54 | −0.788597 | −0.394298 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394298 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2177.77i | 0.331171i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8307.43i | 1.25258i | 0.779591 | + | 0.626289i | \(0.215427\pi\) | ||||
−0.779591 | + | 0.626289i | \(0.784573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 10276.2i | − | 1.53635i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1692.67 | − | 403.350i | 0.250940 | − | 0.0597971i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10202.5i | 1.49991i | 0.661489 | + | 0.749955i | \(0.269925\pi\) | ||||
−0.661489 | + | 0.749955i | \(0.730075\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1372.31 | 0.200075 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3917.32i | 0.566408i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3461.02i | − | 0.496323i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5765.85 | 0.820095 | 0.410047 | − | 0.912064i | \(-0.365512\pi\) | ||||
0.410047 | + | 0.912064i | \(0.365512\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2438.90i | 0.344077i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2293.48 | + | 9624.68i | 0.320948 | + | 1.34687i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5679.15i | 0.788352i | 0.919035 | + | 0.394176i | \(0.128970\pi\) | ||||
−0.919035 | + | 0.394176i | \(0.871030\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 4367.82i | − | 0.601475i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19599.8i | 2.67757i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6030.20 | 0.817284 | 0.408642 | − | 0.912695i | \(-0.366003\pi\) | ||||
0.408642 | + | 0.912695i | \(0.366003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6268.23 | 0.842864 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1734.63 | 0.231425 | 0.115712 | − | 0.993283i | \(-0.463085\pi\) | ||||
0.115712 | + | 0.993283i | \(0.463085\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 962.287 | − | 229.305i | 0.127384 | − | 0.0303545i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1528.23 | −0.200735 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 9051.11i | − | 1.17972i | −0.807507 | − | 0.589858i | \(-0.799184\pi\) | ||
0.807507 | − | 0.589858i | \(-0.200816\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1169.45 | 0.151257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2678.77 | 0.343832 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9105.21i | 1.15983i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 422.728 | 0.0534411 | 0.0267206 | − | 0.999643i | \(-0.491494\pi\) | ||||
0.0267206 | + | 0.999643i | \(0.491494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4003.41 | − | 953.982i | 0.502309 | − | 0.119696i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2221.19 | −0.276610 | −0.138305 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138305 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22981.6 | −2.84068 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −861.396 | −0.105687 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 840.812i | 0.102402i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5178.51i | 0.626066i | 0.949742 | + | 0.313033i | \(0.101345\pi\) | ||||
−0.949742 | + | 0.313033i | \(0.898655\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4321.57i | 0.518655i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 244.461 | + | 1025.89i | 0.0291262 | + | 0.122229i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4888.12i | 0.578189i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6003.07 | 0.704968 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 8420.46i | − | 0.981782i | −0.871221 | − | 0.490891i | \(-0.836671\pi\) | ||
0.871221 | − | 0.490891i | \(-0.163329\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14115.9i | 1.63413i | 0.576548 | + | 0.817063i | \(0.304399\pi\) | ||||
−0.576548 | + | 0.817063i | \(0.695601\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5755.95 | 0.661617 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 372.908i | − | 0.0425616i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3914.22 | + | 932.727i | −0.443612 | + | 0.105709i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1215.35i | 0.136778i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 9628.09i | − | 1.07603i | −0.842935 | − | 0.538015i | \(-0.819174\pi\) | ||
0.842935 | − | 0.538015i | \(-0.180826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1048.69i | 0.116390i | 0.998305 | + | 0.0581952i | \(0.0185346\pi\) | ||||
−0.998305 | + | 0.0581952i | \(0.981465\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7752.51 | −0.854493 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2765.91 | 0.302772 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5992.62 | 0.651508 | 0.325754 | − | 0.945455i | \(-0.394382\pi\) | ||||
0.325754 | + | 0.945455i | \(0.394382\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2755.26 | + | 1392.16i | −0.297512 | + | 0.150325i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14401.7 | 1.54457 | 0.772286 | − | 0.635275i | \(-0.219113\pi\) | ||||
0.772286 | + | 0.635275i | \(0.219113\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 11462.3i | − | 1.22105i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5936.56 | 0.628164 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12503.5 | −1.31420 | −0.657100 | − | 0.753803i | \(-0.728217\pi\) | ||||
−0.657100 | + | 0.753803i | \(0.728217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1361.08i | 0.142109i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5718.26 | −0.593084 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −15453.3 | + | 3682.39i | −1.59222 | + | 0.379414i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2149.64 | −0.220035 | −0.110018 | − | 0.993930i | \(-0.535091\pi\) | ||||
−0.110018 | + | 0.993930i | \(0.535091\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −845.593 | −0.0859889 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14484.2 | 1.46334 | 0.731668 | − | 0.681661i | \(-0.238742\pi\) | ||||
0.731668 | + | 0.681661i | \(0.238742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6792.36i | 0.681788i | 0.940102 | + | 0.340894i | \(0.110730\pi\) | ||||
−0.940102 | + | 0.340894i | \(0.889270\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 9090.15i | − | 0.906549i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 3760.27i | − | 0.372600i | −0.982493 | − | 0.186300i | \(-0.940350\pi\) | ||
0.982493 | − | 0.186300i | \(-0.0596497\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12324.3 | − | 2936.78i | 1.21340 | − | 0.289142i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 842.973i | − | 0.0824674i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −852.864 | −0.0829064 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 881.980i | − | 0.0851958i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 4808.11i | − | 0.461527i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8749.41 | −0.834594 | −0.417297 | − | 0.908770i | \(-0.637023\pi\) | ||||
−0.417297 | + | 0.908770i | \(0.637023\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 13502.5i | − | 1.27996i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2018.17 | + | 480.914i | −0.190124 | + | 0.0453051i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 13030.6i | − | 1.21998i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13362.5i | − | 1.24335i | −0.783274 | − | 0.621677i | \(-0.786452\pi\) | ||
0.783274 | − | 0.621677i | \(-0.213548\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8428.89i | − | 0.779483i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7703.62 | −0.708064 | −0.354032 | − | 0.935233i | \(-0.615190\pi\) | ||||
−0.354032 | + | 0.935233i | \(0.615190\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7610.29 | −0.695234 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −480.721 | −0.0436501 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4148.37 | + | 17408.8i | 0.374406 | + | 1.57121i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10522.8 | −0.944019 | −0.472009 | − | 0.881594i | \(-0.656471\pi\) | ||||
−0.472009 | + | 0.881594i | \(0.656471\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 303.848i | 0.0270956i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20002.0 | −1.77305 | −0.886527 | − | 0.462678i | \(-0.846889\pi\) | ||||
−0.886527 | + | 0.462678i | \(0.846889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16095.0 | 1.41825 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12926.3i | − | 1.13230i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18691.1 | −1.62764 | −0.813819 | − | 0.581118i | \(-0.802615\pi\) | ||||
−0.813819 | + | 0.581118i | \(0.802615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1397.17 | + | 5863.27i | 0.120953 | + | 0.507585i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1999.95 | −0.172125 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10607.5 | −0.907613 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3212.24 | 0.273257 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 1225.69i | − | 0.103665i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7044.44i | − | 0.592365i | −0.955131 | − | 0.296183i | \(-0.904286\pi\) | ||
0.955131 | − | 0.296183i | \(-0.0957137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5379.79i | − | 0.449793i | −0.974383 | − | 0.224897i | \(-0.927796\pi\) | ||
0.974383 | − | 0.224897i | \(-0.0722045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 153.352 | + | 643.545i | 0.0127482 | + | 0.0534983i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 8923.38i | − | 0.737588i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10772.7 | 0.885401 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 512.493i | − | 0.0418838i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 21857.5i | − | 1.77627i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10200.2 | −0.824290 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4873.09i | − | 0.391600i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1537.63 | + | 776.927i | −0.122877 | + | 0.0620865i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 20045.6i | − | 1.59303i | −0.604621 | − | 0.796513i | \(-0.706675\pi\) | ||
0.604621 | − | 0.796513i | \(-0.293325\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3909.83i | 0.308999i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7628.69i | − | 0.599591i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10939.2 | −0.855079 | −0.427539 | − | 0.903997i | \(-0.640619\pi\) | ||||
−0.427539 | + | 0.903997i | \(0.640619\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1955.39 | 0.152011 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17999.4 | −1.39165 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3675.66 | − | 15425.0i | −0.282649 | − | 1.18615i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5340.79 | 0.408475 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10198.6i | 0.775817i | 0.921698 | + | 0.387909i | \(0.126802\pi\) | ||||
−0.921698 | + | 0.387909i | \(0.873198\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13696.1 | 1.03628 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −471.902 | −0.0355146 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17772.4i | − | 1.33040i | −0.746663 | − | 0.665202i | \(-0.768345\pi\) | ||
0.746663 | − | 0.665202i | \(-0.231655\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10004.7 | −0.744957 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1459.28 | − | 347.735i | 0.108085 | − | 0.0257557i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −22205.7 | −1.63604 | −0.818022 | − | 0.575187i | \(-0.804929\pi\) | ||||
−0.818022 | + | 0.575187i | \(0.804929\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12606.3 | 0.923918 | 0.461959 | − | 0.886901i | \(-0.347147\pi\) | ||||
0.461959 | + | 0.886901i | \(0.347147\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −351.784 | −0.0256474 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 444.617i | 0.0322467i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 7952.14i | − | 0.573747i | −0.957968 | − | 0.286874i | \(-0.907384\pi\) | ||
0.957968 | − | 0.286874i | \(-0.0926159\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 877.010i | − | 0.0629487i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1973.28 | − | 8280.91i | −0.140904 | − | 0.591308i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2683.27i | − | 0.190617i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7719.85 | 0.545601 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9107.77i | 0.640405i | 0.947349 | + | 0.320203i | \(0.103751\pi\) | ||||
−0.947349 | + | 0.320203i | \(0.896249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 21105.1i | − | 1.47643i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12572.7 | 0.875082 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16773.3i | 1.16155i | 0.814066 | + | 0.580773i | \(0.197249\pi\) | ||||
−0.814066 | + | 0.580773i | \(0.802751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1429.81 | − | 6000.25i | −0.0985153 | − | 0.413422i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 5241.52i | − | 0.359332i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6931.31i | 0.472798i | 0.971656 | + | 0.236399i | \(0.0759672\pi\) | ||||
−0.971656 | + | 0.236399i | \(0.924033\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 7300.46i | − | 0.495494i | −0.968825 | − | 0.247747i | \(-0.920310\pi\) | ||
0.968825 | − | 0.247747i | \(-0.0796902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6156.73 | −0.415790 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13886.3 | 0.933152 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20396.1 | 1.36384 | 0.681920 | − | 0.731427i | \(-0.261145\pi\) | ||||
0.681920 | + | 0.731427i | \(0.261145\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13133.5 | − | 3129.60i | 0.873882 | − | 0.208239i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −51585.0 | −3.41556 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 11938.4i | − | 0.786602i | −0.919410 | − | 0.393301i | \(-0.871333\pi\) | ||
0.919410 | − | 0.393301i | \(-0.128667\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8645.52 | 0.566864 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18423.2 | 1.20209 | 0.601045 | − | 0.799215i | \(-0.294751\pi\) | ||||
0.601045 | + | 0.799215i | \(0.294751\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8807.50i | 0.571896i | 0.958245 | + | 0.285948i | \(0.0923084\pi\) | ||||
−0.958245 | + | 0.285948i | \(0.907692\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1008.20 | 0.0651492 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4627.20 | + | 19418.2i | 0.297568 | + | 1.24875i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13994.8 | −0.895670 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1116.12 | −0.0710899 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5242.81 | 0.332344 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1067.09i | − | 0.0673223i | −0.999433 | − | 0.0336611i | \(-0.989283\pi\) | ||
0.999433 | − | 0.0336611i | \(-0.0107167\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1886.41i | − | 0.118449i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 22219.9i | − | 1.38861i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24692.7 | − | 12476.6i | 1.53589 | − | 0.776046i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 8696.74i | − | 0.538400i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7062.71 | −0.435195 | −0.217598 | − | 0.976039i | \(-0.569822\pi\) | ||||
−0.217598 | + | 0.976039i | \(0.569822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12546.4i | 0.769490i | 0.923023 | + | 0.384745i | \(0.125711\pi\) | ||||
−0.923023 | + | 0.384745i | \(0.874289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5417.34i | 0.330709i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −405.177 | −0.0246200 | −0.0123100 | − | 0.999924i | \(-0.503918\pi\) | ||||
−0.0123100 | + | 0.999924i | \(0.503918\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 286.008i | − | 0.0172986i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3669.58 | + | 15399.5i | 0.220925 | + | 0.927120i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2647.84i | 0.158680i | 0.996848 | + | 0.0793401i | \(0.0252813\pi\) | ||||
−0.996848 | + | 0.0793401i | \(0.974719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 9495.79i | − | 0.566460i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2929.06i | − | 0.173932i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9246.93 | −0.546600 | −0.273300 | − | 0.961929i | \(-0.588115\pi\) | ||||
−0.273300 | + | 0.961929i | \(0.588115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22699.7 | −1.33573 | −0.667863 | − | 0.744284i | \(-0.732791\pi\) | ||||
−0.667863 | + | 0.744284i | \(0.732791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7578.23 | 0.443912 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3381.71 | − | 14191.5i | −0.197199 | − | 0.827551i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9073.74 | 0.526742 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6243.36i | − | 0.360811i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1091.25 | 0.0627827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3196.22 | −0.183069 | −0.0915343 | − | 0.995802i | \(-0.529177\pi\) | ||||
−0.0915343 | + | 0.995802i | \(0.529177\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 321.490i | − | 0.0183321i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21840.2 | −1.23987 | −0.619933 | − | 0.784655i | \(-0.712840\pi\) | ||||
−0.619933 | + | 0.784655i | \(0.712840\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5260.30 | + | 22075.0i | 0.297307 | + | 1.24766i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2420.36 | −0.136194 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7500.96 | −0.420229 | −0.210114 | − | 0.977677i | \(-0.567384\pi\) | ||||
−0.210114 | + | 0.977677i | \(0.567384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15319.3 | 0.854481 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5178.88i | 0.287608i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 43090.4i | 2.38261i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32124.5i | − | 1.76856i | −0.466960 | − | 0.884278i | \(-0.654651\pi\) | ||
0.466960 | − | 0.884278i | \(-0.345349\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 814.384 | − | 194.061i | 0.0446405 | − | 0.0106375i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 21279.9i | − | 1.16143i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8486.92 | 0.461212 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 6624.52i | − | 0.358458i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22998.8i | 1.23916i | 0.784933 | + | 0.619581i | \(0.212697\pi\) | ||||
−0.784933 | + | 0.619581i | \(0.787303\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12400.0 | 0.665255 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 20403.9i | − | 1.09001i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27266.4 | + | 6497.35i | −1.45043 | + | 0.345627i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 4735.32i | − | 0.250831i | −0.992104 | − | 0.125415i | \(-0.959974\pi\) | ||
0.992104 | − | 0.125415i | \(-0.0400263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7705.75i | 0.406453i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10639.3i | 0.558831i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4308.23 | 0.225341 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4138.55 | −0.215561 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33697.1 | −1.74783 | −0.873914 | − | 0.486081i | \(-0.838426\pi\) | ||||
−0.873914 | + | 0.486081i | \(0.838426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17970.0 | − | 4282.11i | 0.928207 | − | 0.221184i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15762.8 | −0.810823 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2893.39i | − | 0.148218i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2679.22 | 0.136680 | 0.0683402 | − | 0.997662i | \(-0.478230\pi\) | ||||
0.0683402 | + | 0.997662i | \(0.478230\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5317.96i | 0.269072i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23133.2 | 1.16568 | 0.582841 | − | 0.812586i | \(-0.301941\pi\) | ||||
0.582841 | + | 0.812586i | \(0.301941\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4935.00 | + | 9766.95i | 0.247660 | + | 0.490149i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3435.90 | −0.171727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7748.32 | −0.385692 | −0.192846 | − | 0.981229i | \(-0.561772\pi\) | ||||
−0.192846 | + | 0.981229i | \(0.561772\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17923.6 | 0.888583 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 34547.9i | − | 1.70584i | −0.522043 | − | 0.852919i | \(-0.674830\pi\) | ||
0.522043 | − | 0.852919i | \(-0.325170\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 21044.1i | − | 1.03490i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4136.82i | 0.202622i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17280.1 | − | 4117.72i | 0.842994 | − | 0.200879i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 363.938i | 0.0176835i | 0.999961 | + | 0.00884174i | \(0.00281445\pi\) | ||||
−0.999961 | + | 0.00884174i | \(0.997186\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12705.0 | −0.614870 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20270.3i | 0.977102i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31211.6i | − | 1.49855i | −0.662258 | − | 0.749276i | \(-0.730402\pi\) | ||
0.662258 | − | 0.749276i | \(-0.269598\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 562.648 | 0.0269075 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23313.8i | 1.11055i | 0.831668 | + | 0.555273i | \(0.187386\pi\) | ||||
−0.831668 | + | 0.555273i | \(0.812614\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3079.61 | + | 12923.7i | 0.146120 | + | 0.613196i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2997.49i | 0.141666i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4592.97i | 0.216223i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10415.1i | − | 0.488400i | −0.969725 | − | 0.244200i | \(-0.921475\pi\) | ||
0.969725 | − | 0.244200i | \(-0.0785253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11527.0 | 0.538435 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26311.8 | 1.22428 | 0.612140 | − | 0.790749i | \(-0.290309\pi\) | ||||
0.612140 | + | 0.790749i | \(0.290309\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3392.62 | 0.157247 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9047.77 | + | 2156.01i | −0.417744 | + | 0.0995450i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20072.8 | 0.923212 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4853.41i | − | 0.222367i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6560.96 | −0.299450 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2988.20 | −0.135864 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17169.8i | 0.777684i | 0.921304 | + | 0.388842i | \(0.127125\pi\) | ||||
−0.921304 | + | 0.388842i | \(0.872875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15981.3 | −0.721102 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16948.9 | − | 4038.78i | 0.761861 | − | 0.181545i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17524.3 | −0.784747 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17044.0 | −0.760362 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 874.370 | 0.0388604 | 0.0194302 | − | 0.999811i | \(-0.493815\pi\) | ||||
0.0194302 | + | 0.999811i | \(0.493815\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20029.6i | − | 0.886854i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 9700.58i | − | 0.427906i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1634.63i | − | 0.0718365i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1704.76 | + | 7154.10i | 0.0746398 | + | 0.313228i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21588.8i | 0.941712i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 33010.4 | 1.43459 | 0.717296 | − | 0.696769i | \(-0.245380\pi\) | ||||
0.717296 | + | 0.696769i | \(0.245380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20230.9i | 0.875958i | 0.898985 | + | 0.437979i | \(0.144306\pi\) | ||||
−0.898985 | + | 0.437979i | \(0.855694\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11996.5i | 0.517509i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29879.0 | −1.28419 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12577.7i | 0.538603i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13078.1 | + | 3116.41i | −0.557981 | + | 0.132962i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4732.53i | − | 0.201177i | −0.994928 | − | 0.100589i | \(-0.967927\pi\) | ||
0.994928 | − | 0.100589i | \(-0.0320726\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41290.9i | 1.74886i | 0.485152 | + | 0.874430i | \(0.338764\pi\) | ||||
−0.485152 | + | 0.874430i | \(0.661236\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 179.415i | − | 0.00757141i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21503.5 | 0.904170 | 0.452085 | − | 0.891975i | \(-0.350680\pi\) | ||||
0.452085 | + | 0.891975i | \(0.350680\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36515.6 | −1.52984 | −0.764922 | − | 0.644123i | \(-0.777223\pi\) | ||||
−0.764922 | + | 0.644123i | \(0.777223\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18348.7 | 0.765958 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4844.46 | + | 9587.77i | 0.201501 | + | 0.398795i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1077.09 | 0.0446399 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7693.00i | − | 0.317693i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17897.1 | 0.736443 | 0.368222 | − | 0.929738i | \(-0.379967\pi\) | ||||
0.368222 | + | 0.929738i | \(0.379967\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34659.2 | −1.42110 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 18842.4i | − | 0.769830i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45821.5 | −1.86545 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23524.6 | + | 5605.72i | −0.954326 | + | 0.227408i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2683.07 | 0.108460 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6250.99 | −0.251799 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35335.7 | 1.41837 | 0.709187 | − | 0.705021i | \(-0.249062\pi\) | ||||
0.709187 | + | 0.705021i | \(0.249062\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7089.50i | 0.283574i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.07218i | 8.25955e-5i | 1.00000 | 4.12977e-5i | \(1.31455e-5\pi\) | |||||
−1.00000 | 4.12977e-5i | \(0.999987\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 38481.3i | − | 1.52848i | −0.644930 | − | 0.764241i | \(-0.723114\pi\) | ||
0.644930 | − | 0.764241i | \(-0.276886\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14646.3 | + | 3490.09i | −0.579726 | + | 0.138144i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2091.21i | − | 0.0824861i | −0.999149 | − | 0.0412431i | \(-0.986868\pi\) | ||
0.999149 | − | 0.0412431i | \(-0.0131318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4344.88 | −0.170787 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 11796.5i | − | 0.462088i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4300.36i | 0.167871i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55176.8 | 2.14649 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 11027.8i | − | 0.427531i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26230.0 | − | 6250.39i | 1.01341 | − | 0.241488i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15517.2i | 0.597467i | 0.954337 | + | 0.298734i | \(0.0965642\pi\) | ||||
−0.954337 | + | 0.298734i | \(0.903436\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 20709.5i | − | 0.794670i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47831.0i | 1.82913i | 0.404434 | + | 0.914567i | \(0.367469\pi\) | ||||
−0.404434 | + | 0.914567i | \(0.632531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50738.9 | −1.93375 | −0.966874 | − | 0.255254i | \(-0.917841\pi\) | ||||
−0.966874 | + | 0.255254i | \(0.917841\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1816.70 | −0.0690032 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6294.31 | 0.238267 | 0.119133 | − | 0.992878i | \(-0.461988\pi\) | ||||
0.119133 | + | 0.992878i | \(0.461988\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8969.89 | + | 37642.5i | 0.338403 | + | 1.42012i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −406.834 | −0.0152968 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 47372.9i | − | 1.77522i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17274.3 | −0.645159 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9035.51 | −0.336329 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 69236.5i | − | 2.56860i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16731.3 | −0.618647 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2186.92 | − | 9177.46i | −0.0805936 | − | 0.338213i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13859.7 | 0.509074 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28639.8 | 1.04848 | 0.524239 | − | 0.851571i | \(-0.324350\pi\) | ||||
0.524239 | + | 0.851571i | \(0.324350\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13621.2 | 0.497015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 28088.6i | − | 1.02153i | −0.859719 | − | 0.510767i | \(-0.829361\pi\) | ||
0.859719 | − | 0.510767i | \(-0.170639\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2308.64i | 0.0836856i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 6931.54i | − | 0.250437i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3833.34 | + | 16086.7i | 0.138046 | + | 0.579313i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 143.830i | 0.00516270i | 0.999997 | + | 0.00258135i | \(0.000821670\pi\) | ||||
−0.999997 | + | 0.00258135i | \(0.999178\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23801.9 | 0.851574 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 77940.4i | 2.77946i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1993.29i | 0.0708528i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8977.10 | −0.318066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12743.0i | 0.450037i | 0.974355 | + | 0.225018i | \(0.0722442\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11457.8 | + | 22676.4i | 0.403347 | + | 0.798271i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18647.0i | 0.654313i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1672.82i | 0.0585101i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1125.79i | 0.0392509i | 0.999807 | + | 0.0196254i | \(0.00624737\pi\) | ||||
−0.999807 | + | 0.0196254i | \(0.993753\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10398.4 | 0.361382 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8478.11 | 0.293707 | 0.146854 | − | 0.989158i | \(-0.453085\pi\) | ||||
0.146854 | + | 0.989158i | \(0.453085\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10118.9 | −0.349436 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1232.67 | − | 5172.92i | −0.0424324 | − | 0.178069i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40984.8 | 1.40636 | 0.703182 | − | 0.711010i | \(-0.251762\pi\) | ||||
0.703182 | + | 0.711010i | \(0.251762\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26250.3i | 0.897915i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3833.57 | 0.130717 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32319.7 | −1.09857 | −0.549285 | − | 0.835635i | \(-0.685100\pi\) | ||||
−0.549285 | + | 0.835635i | \(0.685100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1247.02i | 0.0422539i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3661.49 | −0.123677 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25952.2 | + | 6184.21i | −0.873870 | + | 0.208236i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51391.7 | 1.72508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8632.48 | −0.288866 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3108.86 | −0.103707 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 186.698i | − | 0.00620870i | −0.999995 | − | 0.00310435i | \(-0.999012\pi\) | ||
0.999995 | − | 0.00310435i | \(-0.000988147\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6959.44i | 0.230722i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 38237.7i | − | 1.26375i | −0.775068 | − | 0.631877i | \(-0.782285\pi\) | ||
0.775068 | − | 0.631877i | \(-0.217715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8590.45 | + | 36050.1i | 0.283039 | + | 1.18778i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2881.20i | 0.0946382i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −39341.4 | −1.28827 | −0.644137 | − | 0.764910i | \(-0.722783\pi\) | ||||
−0.644137 | + | 0.764910i | \(0.722783\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 5413.62i | − | 0.176731i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6456.16i | − | 0.210122i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33595.5 | −1.09006 | −0.545031 | − | 0.838416i | \(-0.683482\pi\) | ||||
−0.545031 | + | 0.838416i | \(0.683482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 44568.4i | − | 1.44169i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8236.82 | + | 34566.1i | 0.265634 | + | 1.11474i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 6340.59i | − | 0.203862i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13906.6i | 0.445770i | 0.974845 | + | 0.222885i | \(0.0715475\pi\) | ||||
−0.974845 | + | 0.222885i | \(0.928453\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10053.4i | 0.321284i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18580.4 | −0.591997 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37389.4 | −1.18770 | −0.593848 | − | 0.804577i | \(-0.702392\pi\) | ||||
−0.593848 | + | 0.804577i | \(0.702392\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4519.91 | 0.143147 |
(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 | 1344.4.p.b.223.2 | yes | 16 | |
4.3 | odd | 2 | inner | 1344.4.p.b.223.9 | yes | 16 | |
7.6 | odd | 2 | 1344.4.p.a.223.15 | yes | 16 | ||
8.3 | odd | 2 | 1344.4.p.a.223.7 | ✓ | 16 | ||
8.5 | even | 2 | 1344.4.p.a.223.16 | yes | 16 | ||
28.27 | even | 2 | 1344.4.p.a.223.8 | yes | 16 | ||
56.13 | odd | 2 | inner | 1344.4.p.b.223.1 | yes | 16 | |
56.27 | even | 2 | inner | 1344.4.p.b.223.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.a.223.7 | ✓ | 16 | 8.3 | odd | 2 | ||
1344.4.p.a.223.8 | yes | 16 | 28.27 | even | 2 | ||
1344.4.p.a.223.15 | yes | 16 | 7.6 | odd | 2 | ||
1344.4.p.a.223.16 | yes | 16 | 8.5 | even | 2 | ||
1344.4.p.b.223.1 | yes | 16 | 56.13 | odd | 2 | inner | |
1344.4.p.b.223.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1344.4.p.b.223.9 | yes | 16 | 4.3 | odd | 2 | inner | |
1344.4.p.b.223.10 | yes | 16 | 56.27 | even | 2 | inner |