Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5445,2,Mod(1,5445)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5445, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5445.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5445.a (trivial) |
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: | yes |
Analytic conductor: | \(43.4785439006\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.48704.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 6x^{2} + 4x + 6 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 495) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.69696\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5445.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69696 | 1.90704 | 0.953519 | − | 0.301334i | \(-0.0974317\pi\) | ||||
0.953519 | + | 0.301334i | \(0.0974317\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.27358 | 2.63679 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.13176 | 1.56166 | 0.780830 | − | 0.624744i | \(-0.214796\pi\) | ||||
0.780830 | + | 0.624744i | \(0.214796\pi\) | |||||||
\(8\) | 8.82872 | 3.12142 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.69696 | −0.852853 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.73785 | −0.759342 | −0.379671 | − | 0.925122i | \(-0.623963\pi\) | ||||
−0.379671 | + | 0.925122i | \(0.623963\pi\) | |||||||
\(14\) | 11.1432 | 2.97814 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.2635 | 3.31588 | ||||||||
\(17\) | 2.41541 | 0.585822 | 0.292911 | − | 0.956140i | \(-0.405376\pi\) | ||||
0.292911 | + | 0.956140i | \(0.405376\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.15325 | 0.264574 | 0.132287 | − | 0.991211i | \(-0.457768\pi\) | ||||
0.132287 | + | 0.991211i | \(0.457768\pi\) | |||||||
\(20\) | −5.27358 | −1.17921 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.54717 | 1.78221 | 0.891104 | − | 0.453799i | \(-0.149932\pi\) | ||||
0.891104 | + | 0.453799i | \(0.149932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.38386 | −1.44809 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 21.7892 | 4.11777 | ||||||||
\(29\) | −1.67756 | −0.311515 | −0.155757 | − | 0.987795i | \(-0.549782\pi\) | ||||
−0.155757 | + | 0.987795i | \(0.549782\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2635 | −1.84338 | −0.921692 | − | 0.387922i | \(-0.873193\pi\) | ||||
−0.921692 | + | 0.387922i | \(0.873193\pi\) | |||||||
\(32\) | 18.1137 | 3.20209 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.51425 | 1.11718 | ||||||||
\(35\) | −4.13176 | −0.698396 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.71636 | 0.939764 | 0.469882 | − | 0.882729i | \(-0.344297\pi\) | ||||
0.469882 | + | 0.882729i | \(0.344297\pi\) | |||||||
\(38\) | 3.11028 | 0.504553 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.82872 | −1.39594 | ||||||||
\(41\) | −9.11028 | −1.42279 | −0.711393 | − | 0.702794i | \(-0.751935\pi\) | ||||
−0.711393 | + | 0.702794i | \(0.751935\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.13176 | −1.24008 | −0.620041 | − | 0.784569i | \(-0.712884\pi\) | ||||
−0.620041 | + | 0.784569i | \(0.712884\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 23.0514 | 3.39874 | ||||||||
\(47\) | −1.47569 | −0.215252 | −0.107626 | − | 0.994191i | \(-0.534325\pi\) | ||||
−0.107626 | + | 0.994191i | \(0.534325\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.0715 | 1.43878 | ||||||||
\(50\) | 2.69696 | 0.381408 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.4383 | −2.00223 | ||||||||
\(53\) | 2.54717 | 0.349881 | 0.174940 | − | 0.984579i | \(-0.444027\pi\) | ||||
0.174940 | + | 0.984579i | \(0.444027\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 36.4782 | 4.87460 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.52431 | −0.594070 | ||||||||
\(59\) | 8.24066 | 1.07284 | 0.536422 | − | 0.843950i | \(-0.319776\pi\) | ||||
0.536422 | + | 0.843950i | \(0.319776\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.47569 | −0.445017 | −0.222509 | − | 0.974931i | \(-0.571425\pi\) | ||||
−0.222509 | + | 0.974931i | \(0.571425\pi\) | |||||||
\(62\) | −27.6803 | −3.51540 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 22.3249 | 2.79062 | ||||||||
\(65\) | 2.73785 | 0.339588 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.3350 | 1.87347 | 0.936734 | − | 0.350041i | \(-0.113832\pi\) | ||||
0.936734 | + | 0.350041i | \(0.113832\pi\) | |||||||
\(68\) | 12.7378 | 1.54469 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −11.1432 | −1.33187 | ||||||||
\(71\) | −2.54717 | −0.302293 | −0.151147 | − | 0.988511i | \(-0.548297\pi\) | ||||
−0.151147 | + | 0.988511i | \(0.548297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.73785 | −0.320441 | −0.160220 | − | 0.987081i | \(-0.551220\pi\) | ||||
−0.160220 | + | 0.987081i | \(0.551220\pi\) | |||||||
\(74\) | 15.4168 | 1.79216 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.08178 | 0.697628 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.15325 | −0.579786 | −0.289893 | − | 0.957059i | \(-0.593620\pi\) | ||||
−0.289893 | + | 0.957059i | \(0.593620\pi\) | |||||||
\(80\) | −13.2635 | −1.48291 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −24.5700 | −2.71331 | ||||||||
\(83\) | 9.28502 | 1.01916 | 0.509582 | − | 0.860422i | \(-0.329800\pi\) | ||||
0.509582 | + | 0.860422i | \(0.329800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.41541 | −0.261988 | ||||||||
\(86\) | −21.9310 | −2.36488 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.78783 | −0.507509 | −0.253755 | − | 0.967269i | \(-0.581666\pi\) | ||||
−0.253755 | + | 0.967269i | \(0.581666\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.3121 | −1.18583 | ||||||||
\(92\) | 45.0742 | 4.69931 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.97989 | −0.410494 | ||||||||
\(95\) | −1.15325 | −0.118321 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.24066 | 0.430574 | 0.215287 | − | 0.976551i | \(-0.430931\pi\) | ||||
0.215287 | + | 0.976551i | \(0.430931\pi\) | |||||||
\(98\) | 27.1624 | 2.74381 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.27358 | 0.527358 | ||||||||
\(101\) | −13.9411 | −1.38719 | −0.693595 | − | 0.720365i | \(-0.743974\pi\) | ||||
−0.693595 | + | 0.720365i | \(0.743974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.5042 | −1.82327 | −0.911636 | − | 0.410998i | \(-0.865180\pi\) | ||||
−0.911636 | + | 0.410998i | \(0.865180\pi\) | |||||||
\(104\) | −24.1717 | −2.37023 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.86961 | 0.667236 | ||||||||
\(107\) | 13.7663 | 1.33084 | 0.665421 | − | 0.746468i | \(-0.268252\pi\) | ||||
0.665421 | + | 0.746468i | \(0.268252\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.7878 | −1.22485 | −0.612426 | − | 0.790528i | \(-0.709806\pi\) | ||||
−0.612426 | + | 0.790528i | \(0.709806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 54.8018 | 5.17828 | ||||||||
\(113\) | 14.8107 | 1.39327 | 0.696637 | − | 0.717424i | \(-0.254679\pi\) | ||||
0.696637 | + | 0.717424i | \(0.254679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.54717 | −0.797028 | ||||||||
\(116\) | −8.84675 | −0.821400 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 22.2247 | 2.04595 | ||||||||
\(119\) | 9.97989 | 0.914855 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −9.37380 | −0.848664 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −54.1256 | −4.86062 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9626 | −1.15024 | −0.575121 | − | 0.818068i | \(-0.695045\pi\) | ||||
−0.575121 | + | 0.818068i | \(0.695045\pi\) | |||||||
\(128\) | 23.9820 | 2.11973 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.38386 | 0.647607 | ||||||||
\(131\) | −1.47569 | −0.128932 | −0.0644660 | − | 0.997920i | \(-0.520534\pi\) | ||||
−0.0644660 | + | 0.997920i | \(0.520534\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.76497 | 0.413175 | ||||||||
\(134\) | 41.3579 | 3.57278 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.3249 | 1.82860 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.889725 | 0.0754655 | 0.0377327 | − | 0.999288i | \(-0.487986\pi\) | ||||
0.0377327 | + | 0.999288i | \(0.487986\pi\) | |||||||
\(140\) | −21.7892 | −1.84152 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.86961 | −0.576485 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.67756 | 0.139314 | ||||||||
\(146\) | −7.38386 | −0.611093 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 30.1457 | 2.47796 | ||||||||
\(149\) | 12.7289 | 1.04279 | 0.521397 | − | 0.853314i | \(-0.325411\pi\) | ||||
0.521397 | + | 0.853314i | \(0.325411\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.15325 | 0.0938504 | 0.0469252 | − | 0.998898i | \(-0.485058\pi\) | ||||
0.0469252 | + | 0.998898i | \(0.485058\pi\) | |||||||
\(152\) | 10.1818 | 0.825849 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2635 | 0.824386 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.95702 | −0.315805 | −0.157902 | − | 0.987455i | \(-0.550473\pi\) | ||||
−0.157902 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(158\) | −13.8981 | −1.10567 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −18.1137 | −1.43202 | ||||||||
\(161\) | 35.3149 | 2.78320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.07148 | 0.240577 | 0.120288 | − | 0.992739i | \(-0.461618\pi\) | ||||
0.120288 | + | 0.992739i | \(0.461618\pi\) | |||||||
\(164\) | −48.0438 | −3.75159 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.0413 | 1.94358 | ||||||||
\(167\) | 2.71498 | 0.210092 | 0.105046 | − | 0.994467i | \(-0.466501\pi\) | ||||
0.105046 | + | 0.994467i | \(0.466501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50419 | −0.423399 | ||||||||
\(170\) | −6.51425 | −0.499620 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −42.8835 | −3.26984 | ||||||||
\(173\) | 14.4154 | 1.09598 | 0.547992 | − | 0.836484i | \(-0.315393\pi\) | ||||
0.547992 | + | 0.836484i | \(0.315393\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.13176 | 0.312332 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.9126 | −0.967839 | ||||||||
\(179\) | −10.7878 | −0.806321 | −0.403160 | − | 0.915129i | \(-0.632088\pi\) | ||||
−0.403160 | + | 0.915129i | \(0.632088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.50419 | −0.483453 | −0.241726 | − | 0.970344i | \(-0.577714\pi\) | ||||
−0.241726 | + | 0.970344i | \(0.577714\pi\) | |||||||
\(182\) | −30.5084 | −2.26143 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 75.4606 | 5.56303 | ||||||||
\(185\) | −5.71636 | −0.420275 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −7.78220 | −0.567575 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.11028 | −0.225643 | ||||||||
\(191\) | −15.8822 | −1.14919 | −0.574597 | − | 0.818437i | \(-0.694841\pi\) | ||||
−0.574597 | + | 0.818437i | \(0.694841\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.83219 | 0.275847 | 0.137923 | − | 0.990443i | \(-0.455957\pi\) | ||||
0.137923 | + | 0.990443i | \(0.455957\pi\) | |||||||
\(194\) | 11.4369 | 0.821121 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 53.1128 | 3.79377 | ||||||||
\(197\) | −2.67893 | −0.190866 | −0.0954331 | − | 0.995436i | \(-0.530424\pi\) | ||||
−0.0954331 | + | 0.995436i | \(0.530424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.78783 | 0.481177 | 0.240588 | − | 0.970627i | \(-0.422660\pi\) | ||||
0.240588 | + | 0.970627i | \(0.422660\pi\) | |||||||
\(200\) | 8.82872 | 0.624285 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −37.5985 | −2.64542 | ||||||||
\(203\) | −6.93128 | −0.486480 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.11028 | 0.636289 | ||||||||
\(206\) | −49.9050 | −3.47705 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −36.3135 | −2.51789 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.6803 | −1.21716 | −0.608581 | − | 0.793491i | \(-0.708261\pi\) | ||||
−0.608581 | + | 0.793491i | \(0.708261\pi\) | |||||||
\(212\) | 13.4327 | 0.922563 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 37.1273 | 2.53797 | ||||||||
\(215\) | 8.13176 | 0.554582 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −42.4065 | −2.87874 | ||||||||
\(218\) | −34.4883 | −2.33584 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.61301 | −0.444839 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.83081 | −0.591355 | −0.295677 | − | 0.955288i | \(-0.595545\pi\) | ||||
−0.295677 | + | 0.955288i | \(0.595545\pi\) | |||||||
\(224\) | 74.8417 | 5.00057 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 39.9438 | 2.65702 | ||||||||
\(227\) | 10.4972 | 0.696723 | 0.348361 | − | 0.937360i | \(-0.386738\pi\) | ||||
0.348361 | + | 0.937360i | \(0.386738\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.95139 | 0.327197 | 0.163598 | − | 0.986527i | \(-0.447690\pi\) | ||||
0.163598 | + | 0.986527i | \(0.447690\pi\) | |||||||
\(230\) | −23.0514 | −1.51996 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.8107 | −0.972370 | ||||||||
\(233\) | −3.89110 | −0.254914 | −0.127457 | − | 0.991844i | \(-0.540682\pi\) | ||||
−0.127457 | + | 0.991844i | \(0.540682\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.47569 | 0.0962637 | ||||||||
\(236\) | 43.4578 | 2.82886 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.9153 | 1.74466 | ||||||||
\(239\) | −15.6186 | −1.01029 | −0.505143 | − | 0.863036i | \(-0.668560\pi\) | ||||
−0.505143 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.2635 | 0.661132 | 0.330566 | − | 0.943783i | \(-0.392760\pi\) | ||||
0.330566 | + | 0.943783i | \(0.392760\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −18.3294 | −1.17342 | ||||||||
\(245\) | −10.0715 | −0.643443 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.15743 | −0.200902 | ||||||||
\(248\) | −90.6138 | −5.75398 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.69696 | −0.170571 | ||||||||
\(251\) | 19.6415 | 1.23976 | 0.619881 | − | 0.784696i | \(-0.287181\pi\) | ||||
0.619881 | + | 0.784696i | \(0.287181\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −34.9595 | −2.19356 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.0285 | 1.25178 | ||||||||
\(257\) | 1.16919 | 0.0729320 | 0.0364660 | − | 0.999335i | \(-0.488390\pi\) | ||||
0.0364660 | + | 0.999335i | \(0.488390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.6186 | 1.46759 | ||||||||
\(260\) | 14.4383 | 0.895424 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.97989 | −0.245878 | ||||||||
\(263\) | 8.93553 | 0.550989 | 0.275494 | − | 0.961303i | \(-0.411158\pi\) | ||||
0.275494 | + | 0.961303i | \(0.411158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.54717 | −0.156471 | ||||||||
\(266\) | 12.8509 | 0.787941 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 80.8704 | 4.93995 | ||||||||
\(269\) | 14.9514 | 0.911602 | 0.455801 | − | 0.890082i | \(-0.349353\pi\) | ||||
0.455801 | + | 0.890082i | \(0.349353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.7289 | 1.38068 | 0.690342 | − | 0.723483i | \(-0.257460\pi\) | ||||
0.690342 | + | 0.723483i | \(0.257460\pi\) | |||||||
\(272\) | 32.0368 | 1.94252 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.1818 | 0.977575 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.1387 | 1.33019 | 0.665093 | − | 0.746761i | \(-0.268392\pi\) | ||||
0.665093 | + | 0.746761i | \(0.268392\pi\) | |||||||
\(278\) | 2.39955 | 0.143915 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −36.4782 | −2.17999 | ||||||||
\(281\) | −19.9841 | −1.19215 | −0.596075 | − | 0.802929i | \(-0.703274\pi\) | ||||
−0.596075 | + | 0.802929i | \(0.703274\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −24.2775 | −1.44315 | −0.721573 | − | 0.692339i | \(-0.756580\pi\) | ||||
−0.721573 | + | 0.692339i | \(0.756580\pi\) | |||||||
\(284\) | −13.4327 | −0.797085 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −37.6415 | −2.22191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.1658 | −0.656813 | ||||||||
\(290\) | 4.52431 | 0.265676 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.4383 | −0.844936 | ||||||||
\(293\) | −16.4182 | −0.959159 | −0.479579 | − | 0.877498i | \(-0.659211\pi\) | ||||
−0.479579 | + | 0.877498i | \(0.659211\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.24066 | −0.479790 | ||||||||
\(296\) | 50.4681 | 2.93340 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 34.3294 | 1.98865 | ||||||||
\(299\) | −23.4008 | −1.35331 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −33.5985 | −1.93659 | ||||||||
\(302\) | 3.11028 | 0.178976 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 15.2962 | 0.877297 | ||||||||
\(305\) | 3.47569 | 0.199018 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.44390 | −0.310700 | −0.155350 | − | 0.987859i | \(-0.549651\pi\) | ||||
−0.155350 | + | 0.987859i | \(0.549651\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 27.6803 | 1.57214 | ||||||||
\(311\) | −28.2864 | −1.60397 | −0.801987 | − | 0.597341i | \(-0.796224\pi\) | ||||
−0.801987 | + | 0.597341i | \(0.796224\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.8107 | 1.28934 | 0.644668 | − | 0.764462i | \(-0.276995\pi\) | ||||
0.644668 | + | 0.764462i | \(0.276995\pi\) | |||||||
\(314\) | −10.6719 | −0.602252 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.1761 | −1.52878 | ||||||||
\(317\) | −23.8593 | −1.34007 | −0.670036 | − | 0.742328i | \(-0.733721\pi\) | ||||
−0.670036 | + | 0.742328i | \(0.733721\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −22.3249 | −1.24800 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 95.2428 | 5.30767 | ||||||||
\(323\) | 2.78557 | 0.154993 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.73785 | −0.151868 | ||||||||
\(326\) | 8.28364 | 0.458788 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −80.4321 | −4.44112 | ||||||||
\(329\) | −6.09722 | −0.336151 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.9084 | −1.03930 | −0.519650 | − | 0.854379i | \(-0.673938\pi\) | ||||
−0.519650 | + | 0.854379i | \(0.673938\pi\) | |||||||
\(332\) | 48.9653 | 2.68732 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.32220 | 0.400653 | ||||||||
\(335\) | −15.3350 | −0.837841 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.6630 | −1.34348 | −0.671740 | − | 0.740787i | \(-0.734453\pi\) | ||||
−0.671740 | + | 0.740787i | \(0.734453\pi\) | |||||||
\(338\) | −14.8446 | −0.807439 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.7378 | −0.690807 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6906 | 0.685229 | ||||||||
\(344\) | −71.7931 | −3.87082 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.8778 | 2.09008 | ||||||||
\(347\) | −15.5056 | −0.832383 | −0.416191 | − | 0.909277i | \(-0.636635\pi\) | ||||
−0.416191 | + | 0.909277i | \(0.636635\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.4841 | −1.09649 | −0.548244 | − | 0.836319i | \(-0.684703\pi\) | ||||
−0.548244 | + | 0.836319i | \(0.684703\pi\) | |||||||
\(350\) | 11.1432 | 0.595629 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.9799 | 1.16987 | 0.584936 | − | 0.811080i | \(-0.301120\pi\) | ||||
0.584936 | + | 0.811080i | \(0.301120\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.54717 | 0.135190 | ||||||||
\(356\) | −25.2490 | −1.33820 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −29.0943 | −1.53768 | ||||||||
\(359\) | −19.6962 | −1.03953 | −0.519764 | − | 0.854310i | \(-0.673980\pi\) | ||||
−0.519764 | + | 0.854310i | \(0.673980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6700 | −0.930000 | ||||||||
\(362\) | −17.5415 | −0.921963 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −59.6555 | −3.12680 | ||||||||
\(365\) | 2.73785 | 0.143305 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.2635 | −1.47534 | −0.737672 | − | 0.675159i | \(-0.764075\pi\) | ||||
−0.737672 | + | 0.675159i | \(0.764075\pi\) | |||||||
\(368\) | 113.366 | 5.90959 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.4168 | −0.801480 | ||||||||
\(371\) | 10.5243 | 0.546395 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.78921 | 0.506866 | 0.253433 | − | 0.967353i | \(-0.418440\pi\) | ||||
0.253433 | + | 0.967353i | \(0.418440\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −13.0285 | −0.671893 | ||||||||
\(377\) | 4.59290 | 0.236546 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.66162 | 0.290818 | 0.145409 | − | 0.989372i | \(-0.453550\pi\) | ||||
0.145409 | + | 0.989372i | \(0.453550\pi\) | |||||||
\(380\) | −6.08178 | −0.311989 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −42.8336 | −2.19156 | ||||||||
\(383\) | 26.5042 | 1.35430 | 0.677150 | − | 0.735845i | \(-0.263215\pi\) | ||||
0.677150 | + | 0.735845i | \(0.263215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.3352 | 0.526050 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 22.3635 | 1.13533 | ||||||||
\(389\) | 15.3551 | 0.778535 | 0.389268 | − | 0.921125i | \(-0.372728\pi\) | ||||
0.389268 | + | 0.921125i | \(0.372728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.6449 | 1.04406 | ||||||||
\(392\) | 88.9183 | 4.49105 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.22497 | −0.363989 | ||||||||
\(395\) | 5.15325 | 0.259288 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.7677 | 0.841548 | 0.420774 | − | 0.907166i | \(-0.361759\pi\) | ||||
0.420774 | + | 0.907166i | \(0.361759\pi\) | |||||||
\(398\) | 18.3065 | 0.917622 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.2635 | 0.663176 | ||||||||
\(401\) | 26.0457 | 1.30066 | 0.650331 | − | 0.759651i | \(-0.274630\pi\) | ||||
0.650331 | + | 0.759651i | \(0.274630\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.1000 | 1.39976 | ||||||||
\(404\) | −73.5195 | −3.65773 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.6934 | −0.927736 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.4495 | −1.11005 | −0.555027 | − | 0.831832i | \(-0.687292\pi\) | ||||
−0.555027 | + | 0.831832i | \(0.687292\pi\) | |||||||
\(410\) | 24.5700 | 1.21343 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −97.5834 | −4.80759 | ||||||||
\(413\) | 34.0485 | 1.67542 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.28502 | −0.455784 | ||||||||
\(416\) | −49.5927 | −2.43148 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.8822 | −1.36213 | −0.681067 | − | 0.732221i | \(-0.738484\pi\) | ||||
−0.681067 | + | 0.732221i | \(0.738484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5985 | 0.760226 | 0.380113 | − | 0.924940i | \(-0.375885\pi\) | ||||
0.380113 | + | 0.924940i | \(0.375885\pi\) | |||||||
\(422\) | −47.6831 | −2.32118 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.4883 | 1.09213 | ||||||||
\(425\) | 2.41541 | 0.117164 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.3608 | −0.694965 | ||||||||
\(428\) | 72.5980 | 3.50916 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.9310 | 1.05761 | ||||||||
\(431\) | 2.95139 | 0.142163 | 0.0710817 | − | 0.997470i | \(-0.477355\pi\) | ||||
0.0710817 | + | 0.997470i | \(0.477355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.2864 | 1.16713 | 0.583565 | − | 0.812067i | \(-0.301657\pi\) | ||||
0.583565 | + | 0.812067i | \(0.301657\pi\) | |||||||
\(434\) | −114.369 | −5.48986 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −67.4377 | −3.22968 | ||||||||
\(437\) | 9.85705 | 0.471527 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.1103 | 0.912084 | 0.456042 | − | 0.889958i | \(-0.349267\pi\) | ||||
0.456042 | + | 0.889958i | \(0.349267\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.8350 | −0.848325 | ||||||||
\(443\) | 1.97714 | 0.0939365 | 0.0469683 | − | 0.998896i | \(-0.485044\pi\) | ||||
0.0469683 | + | 0.998896i | \(0.485044\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.78783 | 0.226965 | ||||||||
\(446\) | −23.8163 | −1.12774 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 92.2414 | 4.35800 | ||||||||
\(449\) | −15.1719 | −0.716008 | −0.358004 | − | 0.933720i | \(-0.616543\pi\) | ||||
−0.358004 | + | 0.933720i | \(0.616543\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 78.1055 | 3.67377 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 28.3105 | 1.32868 | ||||||||
\(455\) | 11.3121 | 0.530321 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.17056 | 0.288647 | 0.144323 | − | 0.989531i | \(-0.453899\pi\) | ||||
0.144323 | + | 0.989531i | \(0.453899\pi\) | |||||||
\(458\) | 13.3537 | 0.623977 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −45.0742 | −2.10160 | ||||||||
\(461\) | −23.1990 | −1.08048 | −0.540242 | − | 0.841510i | \(-0.681667\pi\) | ||||
−0.540242 | + | 0.841510i | \(0.681667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.39809 | −0.0649750 | −0.0324875 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324875 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(464\) | −22.2503 | −1.03295 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.4941 | −0.486131 | ||||||||
\(467\) | 22.6901 | 1.04997 | 0.524987 | − | 0.851110i | \(-0.324070\pi\) | ||||
0.524987 | + | 0.851110i | \(0.324070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.3606 | 2.92572 | ||||||||
\(470\) | 3.97989 | 0.183578 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 72.7545 | 3.34880 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.15325 | 0.0529149 | ||||||||
\(476\) | 52.6298 | 2.41228 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −42.1228 | −1.92665 | ||||||||
\(479\) | −24.7906 | −1.13271 | −0.566355 | − | 0.824161i | \(-0.691647\pi\) | ||||
−0.566355 | + | 0.824161i | \(0.691647\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6505 | −0.713602 | ||||||||
\(482\) | 27.6803 | 1.26080 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.24066 | −0.192559 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.7191 | −1.52796 | −0.763979 | − | 0.645241i | \(-0.776757\pi\) | ||||
−0.763979 | + | 0.645241i | \(0.776757\pi\) | |||||||
\(488\) | −30.6859 | −1.38909 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −27.1624 | −1.22707 | ||||||||
\(491\) | 6.90566 | 0.311648 | 0.155824 | − | 0.987785i | \(-0.450197\pi\) | ||||
0.155824 | + | 0.987785i | \(0.450197\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.05198 | −0.182492 | ||||||||
\(494\) | −8.51546 | −0.383129 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −136.131 | −6.11244 | ||||||||
\(497\) | −10.5243 | −0.472080 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.26078 | −0.101206 | −0.0506031 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506031 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(500\) | −5.27358 | −0.235842 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 52.9723 | 2.36427 | ||||||||
\(503\) | 20.5999 | 0.918504 | 0.459252 | − | 0.888306i | \(-0.348117\pi\) | ||||
0.459252 | + | 0.888306i | \(0.348117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9411 | 0.620370 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −68.3592 | −3.03295 | ||||||||
\(509\) | 7.43272 | 0.329449 | 0.164725 | − | 0.986340i | \(-0.447326\pi\) | ||||
0.164725 | + | 0.986340i | \(0.447326\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3121 | −0.500420 | ||||||||
\(512\) | 6.05208 | 0.267466 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.15325 | 0.139084 | ||||||||
\(515\) | 18.5042 | 0.815392 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 63.6985 | 2.79875 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.1717 | 1.06000 | ||||||||
\(521\) | 35.0084 | 1.53375 | 0.766873 | − | 0.641799i | \(-0.221812\pi\) | ||||
0.766873 | + | 0.641799i | \(0.221812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.52986 | 0.0668960 | 0.0334480 | − | 0.999440i | \(-0.489351\pi\) | ||||
0.0334480 | + | 0.999440i | \(0.489351\pi\) | |||||||
\(524\) | −7.78220 | −0.339967 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0988 | 1.05076 | ||||||||
\(527\) | −24.7906 | −1.07989 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.0541 | 2.17627 | ||||||||
\(530\) | −6.86961 | −0.298397 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 25.1285 | 1.08946 | ||||||||
\(533\) | 24.9425 | 1.08038 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.7663 | −0.595171 | ||||||||
\(536\) | 135.388 | 5.84789 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 40.3233 | 1.73846 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.6700 | −0.716700 | −0.358350 | − | 0.933587i | \(-0.616660\pi\) | ||||
−0.358350 | + | 0.933587i | \(0.616660\pi\) | |||||||
\(542\) | 61.2990 | 2.63302 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 43.7520 | 1.87585 | ||||||||
\(545\) | 12.7878 | 0.547771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.25234 | 0.0963032 | 0.0481516 | − | 0.998840i | \(-0.484667\pi\) | ||||
0.0481516 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(548\) | 31.6415 | 1.35166 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.93465 | −0.0824188 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.2920 | −0.905429 | ||||||||
\(554\) | 59.7071 | 2.53671 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.69204 | 0.198987 | ||||||||
\(557\) | −11.9911 | −0.508078 | −0.254039 | − | 0.967194i | \(-0.581759\pi\) | ||||
−0.254039 | + | 0.967194i | \(0.581759\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2635 | 0.941647 | ||||||||
\(560\) | −54.8018 | −2.31580 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −53.8962 | −2.27347 | ||||||||
\(563\) | −19.4598 | −0.820134 | −0.410067 | − | 0.912055i | \(-0.634495\pi\) | ||||
−0.410067 | + | 0.912055i | \(0.634495\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.8107 | −0.623091 | ||||||||
\(566\) | −65.4753 | −2.75213 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −22.4883 | −0.943586 | ||||||||
\(569\) | 19.7205 | 0.826728 | 0.413364 | − | 0.910566i | \(-0.364354\pi\) | ||||
0.413364 | + | 0.910566i | \(0.364354\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.41678 | −0.226685 | −0.113343 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113343 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −101.518 | −4.23726 | ||||||||
\(575\) | 8.54717 | 0.356442 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.42708 | 0.267563 | 0.133781 | − | 0.991011i | \(-0.457288\pi\) | ||||
0.133781 | + | 0.991011i | \(0.457288\pi\) | |||||||
\(578\) | −30.1137 | −1.25257 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.84675 | 0.367341 | ||||||||
\(581\) | 38.3635 | 1.59159 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −24.1717 | −1.00023 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −44.2791 | −1.82915 | ||||||||
\(587\) | −44.9883 | −1.85686 | −0.928432 | − | 0.371502i | \(-0.878843\pi\) | ||||
−0.928432 | + | 0.371502i | \(0.878843\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.8364 | −0.487712 | ||||||||
\(590\) | −22.2247 | −0.914978 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 75.8191 | 3.11615 | ||||||||
\(593\) | 21.3892 | 0.878348 | 0.439174 | − | 0.898402i | \(-0.355271\pi\) | ||||
0.439174 | + | 0.898402i | \(0.355271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.97989 | −0.409135 | ||||||||
\(596\) | 67.1270 | 2.74963 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −63.1111 | −2.58081 | ||||||||
\(599\) | 26.9514 | 1.10120 | 0.550602 | − | 0.834768i | \(-0.314398\pi\) | ||||
0.550602 | + | 0.834768i | \(0.314398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.42708 | −0.262166 | −0.131083 | − | 0.991371i | \(-0.541845\pi\) | ||||
−0.131083 | + | 0.991371i | \(0.541845\pi\) | |||||||
\(602\) | −90.6138 | −3.69314 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 6.08178 | 0.247464 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9626 | −0.526135 | −0.263067 | − | 0.964777i | \(-0.584734\pi\) | ||||
−0.263067 | + | 0.964777i | \(0.584734\pi\) | |||||||
\(608\) | 20.8897 | 0.847190 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.37380 | 0.379534 | ||||||||
\(611\) | 4.04023 | 0.163450 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.4771 | 0.988620 | 0.494310 | − | 0.869286i | \(-0.335421\pi\) | ||||
0.494310 | + | 0.869286i | \(0.335421\pi\) | |||||||
\(614\) | −14.6820 | −0.592517 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9453 | 0.480898 | 0.240449 | − | 0.970662i | \(-0.422705\pi\) | ||||
0.240449 | + | 0.970662i | \(0.422705\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18.9084 | −0.759993 | −0.379997 | − | 0.924988i | \(-0.624075\pi\) | ||||
−0.379997 | + | 0.924988i | \(0.624075\pi\) | |||||||
\(620\) | 54.1256 | 2.17374 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −76.2872 | −3.05884 | ||||||||
\(623\) | −19.7822 | −0.792557 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 61.5195 | 2.45881 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.8677 | −0.832712 | ||||||||
\(629\) | 13.8073 | 0.550534 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8364 | −0.471201 | −0.235601 | − | 0.971850i | \(-0.575706\pi\) | ||||
−0.235601 | + | 0.971850i | \(0.575706\pi\) | |||||||
\(632\) | −45.4966 | −1.80976 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −64.3476 | −2.55557 | ||||||||
\(635\) | 12.9626 | 0.514404 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.5742 | −1.09253 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.9820 | −0.947971 | ||||||||
\(641\) | 12.2206 | 0.482683 | 0.241341 | − | 0.970440i | \(-0.422413\pi\) | ||||
0.241341 | + | 0.970440i | \(0.422413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.84257 | −0.348717 | −0.174358 | − | 0.984682i | \(-0.555785\pi\) | ||||
−0.174358 | + | 0.984682i | \(0.555785\pi\) | |||||||
\(644\) | 186.236 | 7.33873 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.51258 | 0.295578 | ||||||||
\(647\) | −9.40985 | −0.369939 | −0.184970 | − | 0.982744i | \(-0.559219\pi\) | ||||
−0.184970 | + | 0.982744i | \(0.559219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.38386 | −0.289619 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.1977 | 0.634350 | ||||||||
\(653\) | −22.7449 | −0.890075 | −0.445038 | − | 0.895512i | \(-0.646810\pi\) | ||||
−0.445038 | + | 0.895512i | \(0.646810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.47569 | 0.0576602 | ||||||||
\(656\) | −120.834 | −4.71779 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.4440 | −0.641052 | ||||||||
\(659\) | −20.3635 | −0.793249 | −0.396625 | − | 0.917981i | \(-0.629819\pi\) | ||||
−0.396625 | + | 0.917981i | \(0.629819\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6616 | 0.453585 | 0.226792 | − | 0.973943i | \(-0.427176\pi\) | ||||
0.226792 | + | 0.973943i | \(0.427176\pi\) | |||||||
\(662\) | −50.9952 | −1.98198 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 81.9748 | 3.18124 | ||||||||
\(665\) | −4.76497 | −0.184778 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.3384 | −0.555184 | ||||||||
\(668\) | 14.3177 | 0.553968 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −41.3579 | −1.59779 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0070 | −1.15669 | −0.578343 | − | 0.815794i | \(-0.696300\pi\) | ||||
−0.578343 | + | 0.815794i | \(0.696300\pi\) | |||||||
\(674\) | −66.5151 | −2.56207 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.0268 | −1.11642 | ||||||||
\(677\) | 51.4695 | 1.97813 | 0.989067 | − | 0.147466i | \(-0.0471116\pi\) | ||||
0.989067 | + | 0.147466i | \(0.0471116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.5214 | 0.672411 | ||||||||
\(680\) | −21.3249 | −0.817774 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.6186 | 1.05680 | 0.528399 | − | 0.848996i | \(-0.322793\pi\) | ||||
0.528399 | + | 0.848996i | \(0.322793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 34.2261 | 1.30676 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −107.856 | −4.11197 | ||||||||
\(689\) | −6.97376 | −0.265679 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.2344 | −1.30234 | −0.651169 | − | 0.758933i | \(-0.725721\pi\) | ||||
−0.651169 | + | 0.758933i | \(0.725721\pi\) | |||||||
\(692\) | 76.0209 | 2.88988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −41.8179 | −1.58738 | ||||||||
\(695\) | −0.889725 | −0.0337492 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.0050 | −0.833499 | ||||||||
\(698\) | −55.2447 | −2.09104 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.7892 | 0.823555 | ||||||||
\(701\) | 11.8524 | 0.447658 | 0.223829 | − | 0.974628i | \(-0.428144\pi\) | ||||
0.223829 | + | 0.974628i | \(0.428144\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.59241 | 0.248637 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 59.2788 | 2.23099 | ||||||||
\(707\) | −57.6013 | −2.16632 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.1658 | −1.05779 | −0.528895 | − | 0.848687i | \(-0.677393\pi\) | ||||
−0.528895 | + | 0.848687i | \(0.677393\pi\) | |||||||
\(710\) | 6.86961 | 0.257812 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −42.2705 | −1.58415 | ||||||||
\(713\) | −87.7241 | −3.28529 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −56.8906 | −2.12610 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −53.1200 | −1.98242 | ||||||||
\(719\) | −26.2663 | −0.979567 | −0.489783 | − | 0.871844i | \(-0.662924\pi\) | ||||
−0.489783 | + | 0.871844i | \(0.662924\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −76.4550 | −2.84733 | ||||||||
\(722\) | −47.6553 | −1.77355 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −34.3004 | −1.27476 | ||||||||
\(725\) | −1.67756 | −0.0623030 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1401 | 0.784042 | 0.392021 | − | 0.919956i | \(-0.371776\pi\) | ||||
0.392021 | + | 0.919956i | \(0.371776\pi\) | |||||||
\(728\) | −99.8717 | −3.70149 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.38386 | 0.273289 | ||||||||
\(731\) | −19.6415 | −0.726467 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.86406 | −0.142722 | −0.0713611 | − | 0.997451i | \(-0.522734\pi\) | ||||
−0.0713611 | + | 0.997451i | \(0.522734\pi\) | |||||||
\(734\) | −76.2256 | −2.81354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 154.821 | 5.70679 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.0298 | 0.516094 | 0.258047 | − | 0.966132i | \(-0.416921\pi\) | ||||
0.258047 | + | 0.966132i | \(0.416921\pi\) | |||||||
\(740\) | −30.1457 | −1.10818 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.3836 | 1.04200 | ||||||||
\(743\) | −26.2934 | −0.964611 | −0.482306 | − | 0.876003i | \(-0.660201\pi\) | ||||
−0.482306 | + | 0.876003i | \(0.660201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7289 | −0.466352 | ||||||||
\(746\) | 26.4011 | 0.966613 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 56.8793 | 2.07832 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.2206 | 1.39469 | 0.697344 | − | 0.716737i | \(-0.254365\pi\) | ||||
0.697344 | + | 0.716737i | \(0.254365\pi\) | |||||||
\(752\) | −19.5729 | −0.713751 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.3869 | 0.451103 | ||||||||
\(755\) | −1.15325 | −0.0419712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.6158 | −1.33082 | −0.665411 | − | 0.746477i | \(-0.731744\pi\) | ||||
−0.665411 | + | 0.746477i | \(0.731744\pi\) | |||||||
\(758\) | 15.2692 | 0.554601 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10.1818 | −0.369331 | ||||||||
\(761\) | −51.6803 | −1.87341 | −0.936705 | − | 0.350120i | \(-0.886141\pi\) | ||||
−0.936705 | + | 0.350120i | \(0.886141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.8363 | −1.91280 | ||||||||
\(764\) | −83.7560 | −3.03019 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 71.4807 | 2.58270 | ||||||||
\(767\) | −22.5617 | −0.814655 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.4841 | −1.60414 | −0.802068 | − | 0.597232i | \(-0.796267\pi\) | ||||
−0.802068 | + | 0.597232i | \(0.796267\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.2094 | 0.727351 | ||||||||
\(773\) | 0.973762 | 0.0350238 | 0.0175119 | − | 0.999847i | \(-0.494426\pi\) | ||||
0.0175119 | + | 0.999847i | \(0.494426\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.2635 | −0.368677 | ||||||||
\(776\) | 37.4396 | 1.34400 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41.4121 | 1.48470 | ||||||||
\(779\) | −10.5065 | −0.376433 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 55.6784 | 1.99106 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 133.583 | 4.77083 | ||||||||
\(785\) | 3.95702 | 0.141232 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.5382 | 1.08857 | 0.544285 | − | 0.838900i | \(-0.316801\pi\) | ||||
0.544285 | + | 0.838900i | \(0.316801\pi\) | |||||||
\(788\) | −14.1276 | −0.503274 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.8981 | 0.494473 | ||||||||
\(791\) | 61.1943 | 2.17582 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.51592 | 0.337920 | ||||||||
\(794\) | 45.2218 | 1.60486 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 35.7962 | 1.26876 | ||||||||
\(797\) | 26.7247 | 0.946639 | 0.473319 | − | 0.880891i | \(-0.343056\pi\) | ||||
0.473319 | + | 0.880891i | \(0.343056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.56440 | −0.126099 | ||||||||
\(800\) | 18.1137 | 0.640417 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 70.2442 | 2.48041 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.3149 | −1.24469 | ||||||||
\(806\) | 75.7845 | 2.66939 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −123.082 | −4.33001 | ||||||||
\(809\) | 17.0327 | 0.598837 | 0.299418 | − | 0.954122i | \(-0.403207\pi\) | ||||
0.299418 | + | 0.954122i | \(0.403207\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23.1103 | −0.811512 | −0.405756 | − | 0.913982i | \(-0.632992\pi\) | ||||
−0.405756 | + | 0.913982i | \(0.632992\pi\) | |||||||
\(812\) | −36.5527 | −1.28275 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.07148 | −0.107589 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37798 | −0.328094 | ||||||||
\(818\) | −60.5453 | −2.11692 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 48.0438 | 1.67776 | ||||||||
\(821\) | 28.3476 | 0.989337 | 0.494668 | − | 0.869082i | \(-0.335290\pi\) | ||||
0.494668 | + | 0.869082i | \(0.335290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4585 | −0.364559 | −0.182280 | − | 0.983247i | \(-0.558348\pi\) | ||||
−0.182280 | + | 0.983247i | \(0.558348\pi\) | |||||||
\(824\) | −163.368 | −5.69121 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 91.8273 | 3.19508 | ||||||||
\(827\) | 45.2672 | 1.57409 | 0.787047 | − | 0.616893i | \(-0.211609\pi\) | ||||
0.787047 | + | 0.616893i | \(0.211609\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.9855 | −0.798320 | −0.399160 | − | 0.916881i | \(-0.630698\pi\) | ||||
−0.399160 | + | 0.916881i | \(0.630698\pi\) | |||||||
\(830\) | −25.0413 | −0.869196 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −61.1223 | −2.11903 | ||||||||
\(833\) | 24.3267 | 0.842870 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.71498 | −0.0939559 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −75.1971 | −2.59764 | ||||||||
\(839\) | −20.1547 | −0.695818 | −0.347909 | − | 0.937528i | \(-0.613108\pi\) | ||||
−0.347909 | + | 0.937528i | \(0.613108\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1858 | −0.902959 | ||||||||
\(842\) | 42.0686 | 1.44978 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −93.2386 | −3.20941 | ||||||||
\(845\) | 5.50419 | 0.189350 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 33.7845 | 1.16016 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.51425 | 0.223437 | ||||||||
\(851\) | 48.8587 | 1.67485 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.2705 | 1.31036 | 0.655179 | − | 0.755474i | \(-0.272593\pi\) | ||||
0.655179 | + | 0.755474i | \(0.272593\pi\) | |||||||
\(854\) | −38.7303 | −1.32533 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 121.539 | 4.15413 | ||||||||
\(857\) | 9.51250 | 0.324941 | 0.162470 | − | 0.986713i | \(-0.448054\pi\) | ||||
0.162470 | + | 0.986713i | \(0.448054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.61865 | −0.0552275 | −0.0276137 | − | 0.999619i | \(-0.508791\pi\) | ||||
−0.0276137 | + | 0.999619i | \(0.508791\pi\) | |||||||
\(860\) | 42.8835 | 1.46232 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.95977 | 0.271111 | ||||||||
\(863\) | 46.0229 | 1.56664 | 0.783318 | − | 0.621621i | \(-0.213526\pi\) | ||||
0.783318 | + | 0.621621i | \(0.213526\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.4154 | −0.490138 | ||||||||
\(866\) | 65.4994 | 2.22576 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −223.634 | −7.59064 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −41.9849 | −1.42260 | ||||||||
\(872\) | −112.900 | −3.82328 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 26.5841 | 0.899219 | ||||||||
\(875\) | −4.13176 | −0.139679 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.7630 | 0.971257 | 0.485628 | − | 0.874165i | \(-0.338591\pi\) | ||||
0.485628 | + | 0.874165i | \(0.338591\pi\) | |||||||
\(878\) | 51.5396 | 1.73938 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.3149 | −0.785499 | −0.392749 | − | 0.919646i | \(-0.628476\pi\) | ||||
−0.392749 | + | 0.919646i | \(0.628476\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6616 | 0.998193 | 0.499097 | − | 0.866546i | \(-0.333665\pi\) | ||||
0.499097 | + | 0.866546i | \(0.333665\pi\) | |||||||
\(884\) | −34.8743 | −1.17295 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.33225 | 0.179141 | ||||||||
\(887\) | −20.3364 | −0.682829 | −0.341414 | − | 0.939913i | \(-0.610906\pi\) | ||||
−0.341414 | + | 0.939913i | \(0.610906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −53.5583 | −1.79629 | ||||||||
\(890\) | 12.9126 | 0.432831 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46.5700 | −1.55928 | ||||||||
\(893\) | −1.70185 | −0.0569502 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.7878 | 0.360598 | ||||||||
\(896\) | 99.0879 | 3.31029 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40.9181 | −1.36545 | ||||||||
\(899\) | 17.2177 | 0.574241 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.15245 | 0.204968 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 130.760 | 4.34900 | ||||||||
\(905\) | 6.50419 | 0.216207 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.87942 | 0.328041 | 0.164020 | − | 0.986457i | \(-0.447554\pi\) | ||||
0.164020 | + | 0.986457i | \(0.447554\pi\) | |||||||
\(908\) | 55.3578 | 1.83711 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 30.5084 | 1.01134 | ||||||||
\(911\) | 7.22343 | 0.239323 | 0.119662 | − | 0.992815i | \(-0.461819\pi\) | ||||
0.119662 | + | 0.992815i | \(0.461819\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 16.6418 | 0.550460 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.1116 | 0.862751 | ||||||||
\(917\) | −6.09722 | −0.201348 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.7233 | −1.17840 | −0.589201 | − | 0.807986i | \(-0.700557\pi\) | ||||
−0.589201 | + | 0.807986i | \(0.700557\pi\) | |||||||
\(920\) | −75.4606 | −2.48786 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −62.5667 | −2.06052 | ||||||||
\(923\) | 6.97376 | 0.229544 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.71636 | 0.187953 | ||||||||
\(926\) | −3.77060 | −0.123910 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.3869 | −0.997497 | ||||||||
\(929\) | −1.12621 | −0.0369498 | −0.0184749 | − | 0.999829i | \(-0.505881\pi\) | ||||
−0.0184749 | + | 0.999829i | \(0.505881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.6150 | 0.380665 | ||||||||
\(932\) | −20.5200 | −0.672157 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 61.1943 | 2.00234 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.127587 | 0.00416807 | 0.00208404 | − | 0.999998i | \(-0.499337\pi\) | ||||
0.00208404 | + | 0.999998i | \(0.499337\pi\) | |||||||
\(938\) | 170.881 | 5.57946 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.78220 | 0.253827 | ||||||||
\(941\) | −1.41403 | −0.0460961 | −0.0230480 | − | 0.999734i | \(-0.507337\pi\) | ||||
−0.0230480 | + | 0.999734i | \(0.507337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −77.8671 | −2.53570 | ||||||||
\(944\) | 109.300 | 3.55742 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −37.1943 | −1.20865 | −0.604326 | − | 0.796737i | \(-0.706558\pi\) | ||||
−0.604326 | + | 0.796737i | \(0.706558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.49581 | 0.243324 | ||||||||
\(950\) | 3.11028 | 0.100911 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 88.1097 | 2.85565 | ||||||||
\(953\) | 16.5041 | 0.534621 | 0.267310 | − | 0.963610i | \(-0.413865\pi\) | ||||
0.267310 | + | 0.963610i | \(0.413865\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.8822 | 0.513935 | ||||||||
\(956\) | −82.3663 | −2.66391 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −66.8592 | −2.16012 | ||||||||
\(959\) | 24.7906 | 0.800530 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.3400 | 2.39807 | ||||||||
\(962\) | −42.2088 | −1.36087 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 54.1256 | 1.74327 | ||||||||
\(965\) | −3.83219 | −0.123362 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.60471 | 0.115920 | 0.0579598 | − | 0.998319i | \(-0.481540\pi\) | ||||
0.0579598 | + | 0.998319i | \(0.481540\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.4369 | −0.367217 | ||||||||
\(971\) | 29.6214 | 0.950596 | 0.475298 | − | 0.879825i | \(-0.342340\pi\) | ||||
0.475298 | + | 0.879825i | \(0.342340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.67613 | 0.117851 | ||||||||
\(974\) | −90.9390 | −2.91387 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −46.1000 | −1.47562 | ||||||||
\(977\) | −52.7157 | −1.68653 | −0.843263 | − | 0.537501i | \(-0.819368\pi\) | ||||
−0.843263 | + | 0.537501i | \(0.819368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −53.1128 | −1.69663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.6243 | 0.594325 | ||||||||
\(983\) | 29.2602 | 0.933254 | 0.466627 | − | 0.884454i | \(-0.345469\pi\) | ||||
0.466627 | + | 0.884454i | \(0.345469\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.67893 | 0.0853579 | ||||||||
\(986\) | −10.9280 | −0.348019 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.6510 | −0.529738 | ||||||||
\(989\) | −69.5036 | −2.21008 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1776 | 1.21275 | 0.606375 | − | 0.795179i | \(-0.292623\pi\) | ||||
0.606375 | + | 0.795179i | \(0.292623\pi\) | |||||||
\(992\) | −185.911 | −5.90268 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −28.3836 | −0.900274 | ||||||||
\(995\) | −6.78783 | −0.215189 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.1500 | 1.27156 | 0.635781 | − | 0.771870i | \(-0.280678\pi\) | ||||
0.635781 | + | 0.771870i | \(0.280678\pi\) | |||||||
\(998\) | −6.09722 | −0.193004 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5445.2.a.bs.1.4 | 4 | ||
3.2 | odd | 2 | 5445.2.a.bh.1.1 | 4 | |||
11.10 | odd | 2 | 495.2.a.f.1.1 | ✓ | 4 | ||
33.32 | even | 2 | 495.2.a.g.1.4 | yes | 4 | ||
44.43 | even | 2 | 7920.2.a.cm.1.4 | 4 | |||
55.32 | even | 4 | 2475.2.c.t.199.1 | 8 | |||
55.43 | even | 4 | 2475.2.c.t.199.8 | 8 | |||
55.54 | odd | 2 | 2475.2.a.bj.1.4 | 4 | |||
132.131 | odd | 2 | 7920.2.a.cn.1.4 | 4 | |||
165.32 | odd | 4 | 2475.2.c.s.199.8 | 8 | |||
165.98 | odd | 4 | 2475.2.c.s.199.1 | 8 | |||
165.164 | even | 2 | 2475.2.a.bf.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
495.2.a.f.1.1 | ✓ | 4 | 11.10 | odd | 2 | ||
495.2.a.g.1.4 | yes | 4 | 33.32 | even | 2 | ||
2475.2.a.bf.1.1 | 4 | 165.164 | even | 2 | |||
2475.2.a.bj.1.4 | 4 | 55.54 | odd | 2 | |||
2475.2.c.s.199.1 | 8 | 165.98 | odd | 4 | |||
2475.2.c.s.199.8 | 8 | 165.32 | odd | 4 | |||
2475.2.c.t.199.1 | 8 | 55.32 | even | 4 | |||
2475.2.c.t.199.8 | 8 | 55.43 | even | 4 | |||
5445.2.a.bh.1.1 | 4 | 3.2 | odd | 2 | |||
5445.2.a.bs.1.4 | 4 | 1.1 | even | 1 | trivial | ||
7920.2.a.cm.1.4 | 4 | 44.43 | even | 2 | |||
7920.2.a.cn.1.4 | 4 | 132.131 | odd | 2 |