Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(13,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.13");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.v (of order \(8\), degree \(4\), 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: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{8}]$ |
Embedding invariants
Embedding label | 69.1 | ||
Root | \(-1.28897 - 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.69 |
Dual form | 224.3.v.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.99607 | − | 0.125246i | −0.998037 | − | 0.0626229i | ||||
\(3\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(4\) | 3.96863 | + | 0.500000i | 0.992157 | + | 0.125000i | ||||
\(5\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.94975 | + | 4.94975i | 0.707107 | + | 0.707107i | ||||
\(8\) | −7.85905 | − | 1.49509i | −0.982382 | − | 0.186886i | ||||
\(9\) | −6.36396 | + | 6.36396i | −0.707107 | + | 0.707107i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.978370 | − | 2.36199i | 0.0889427 | − | 0.214727i | −0.873149 | − | 0.487454i | \(-0.837926\pi\) |
0.962091 | + | 0.272727i | \(0.0879257\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(14\) | −9.26013 | − | 10.5000i | −0.661438 | − | 0.750000i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.5000 | + | 3.96863i | 0.968750 | + | 0.248039i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 13.5000 | − | 11.9059i | 0.750000 | − | 0.661438i | ||||
\(19\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.24873 | + | 4.59218i | −0.102215 | + | 0.208735i | ||||
\(23\) | −30.1660 | + | 30.1660i | −1.31157 | + | 1.31157i | −0.391304 | + | 0.920261i | \(0.627976\pi\) |
−0.920261 | + | 0.391304i | \(0.872024\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.6777 | + | 17.6777i | 0.707107 | + | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 17.1688 | + | 22.1186i | 0.613172 | + | 0.789949i | ||||
\(29\) | 15.9922 | + | 38.6086i | 0.551455 | + | 1.33133i | 0.916386 | + | 0.400295i | \(0.131093\pi\) |
−0.364931 | + | 0.931034i | \(0.618907\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −30.4421 | − | 9.86299i | −0.951316 | − | 0.308218i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −28.4382 | + | 22.0742i | −0.789949 | + | 0.613172i | ||||
\(37\) | 40.7639 | + | 16.8850i | 1.10173 | + | 0.456351i | 0.858082 | − | 0.513514i | \(-0.171656\pi\) |
0.243646 | + | 0.969864i | \(0.421656\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −30.9438 | + | 74.7051i | −0.719624 | + | 1.73733i | −0.0452058 | + | 0.998978i | \(0.514394\pi\) |
−0.674419 | + | 0.738349i | \(0.735606\pi\) | |||||||
\(44\) | 5.06378 | − | 8.88469i | 0.115086 | − | 0.201925i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 63.9918 | − | 56.4354i | 1.39113 | − | 1.22686i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000i | 1.00000i | ||||||||
\(50\) | −33.0719 | − | 37.5000i | −0.661438 | − | 0.750000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 38.2953 | − | 92.4529i | 0.722552 | − | 1.74439i | 0.0566038 | − | 0.998397i | \(-0.481973\pi\) |
0.665948 | − | 0.745998i | \(-0.268027\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −31.5000 | − | 46.3006i | −0.562500 | − | 0.826797i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −27.0860 | − | 79.0685i | −0.467001 | − | 1.36325i | ||||
\(59\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −63.0000 | −1.00000 | ||||||||
\(64\) | 59.5294 | + | 23.5000i | 0.930147 | + | 0.367188i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.16924 | + | 12.4797i | 0.0771529 | + | 0.186264i | 0.957750 | − | 0.287602i | \(-0.0928581\pi\) |
−0.880597 | + | 0.473866i | \(0.842858\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −59.8665 | − | 59.8665i | −0.843190 | − | 0.843190i | 0.146082 | − | 0.989272i | \(-0.453334\pi\) |
−0.989272 | + | 0.146082i | \(0.953334\pi\) | |||||||
\(72\) | 59.5294 | − | 40.5000i | 0.826797 | − | 0.562500i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | −79.2531 | − | 38.8092i | −1.07099 | − | 0.524448i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.5340 | − | 6.84859i | 0.214727 | − | 0.0889427i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 156.268i | − | 1.97807i | −0.147669 | − | 0.989037i | \(-0.547177\pi\) | ||
0.147669 | − | 0.989037i | \(-0.452823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 81.0000i | − | 1.00000i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 71.1227 | − | 145.241i | 0.827008 | − | 1.68885i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.2205 | + | 17.1003i | −0.127505 | + | 0.194321i | ||||
\(89\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −134.801 | + | 104.635i | −1.46522 | + | 1.13733i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 6.13705 | − | 97.8077i | 0.0626229 | − | 0.998037i | ||||
\(99\) | 8.80533 | + | 21.2579i | 0.0889427 | + | 0.214727i | ||||
\(100\) | 61.3172 | + | 78.9949i | 0.613172 | + | 0.789949i | ||||
\(101\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −88.0195 | + | 179.747i | −0.830373 | + | 1.69572i | ||||
\(107\) | −10.1775 | + | 24.5707i | −0.0951169 | + | 0.229632i | −0.964276 | − | 0.264901i | \(-0.914661\pi\) |
0.869159 | + | 0.494533i | \(0.164661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 157.826 | − | 65.3739i | 1.44795 | − | 0.599760i | 0.486239 | − | 0.873826i | \(-0.338369\pi\) |
0.961711 | + | 0.274066i | \(0.0883686\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 57.0774 | + | 96.3648i | 0.509620 | + | 0.860400i | ||||
\(113\) | 127.044i | 1.12429i | 0.827040 | + | 0.562144i | \(0.190023\pi\) | ||||
−0.827040 | + | 0.562144i | \(0.809977\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 44.1628 | + | 161.219i | 0.380713 | + | 1.38982i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 80.9381 | + | 80.9381i | 0.668910 | + | 0.668910i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 125.753 | + | 7.89049i | 0.998037 | + | 0.0626229i | ||||
\(127\) | −253.992 | −1.99994 | −0.999969 | − | 0.00787402i | \(-0.997494\pi\) | ||||
−0.999969 | + | 0.00787402i | \(0.997494\pi\) | |||||||
\(128\) | −115.882 | − | 54.3636i | −0.905327 | − | 0.424715i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.75517 | − | 25.5578i | −0.0653371 | − | 0.190730i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.8301 | + | 18.8301i | −0.137446 | + | 0.137446i | −0.772482 | − | 0.635036i | \(-0.780985\pi\) |
0.635036 | + | 0.772482i | \(0.280985\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 112.000 | + | 126.996i | 0.788732 | + | 0.894338i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −123.898 | + | 73.3852i | −0.860400 | + | 0.509620i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 153.334 | + | 87.3921i | 1.03604 | + | 0.590487i | ||||
\(149\) | 109.556 | − | 264.490i | 0.735272 | − | 1.77510i | 0.111111 | − | 0.993808i | \(-0.464559\pi\) |
0.624161 | − | 0.781296i | \(-0.285441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 73.5020 | − | 73.5020i | 0.486768 | − | 0.486768i | −0.420517 | − | 0.907285i | \(-0.638151\pi\) |
0.907285 | + | 0.420517i | \(0.138151\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −33.8608 | + | 11.5995i | −0.219875 | + | 0.0753214i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(158\) | −19.5719 | + | 311.922i | −0.123873 | + | 1.97419i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −298.628 | −1.85483 | ||||||||
\(162\) | −10.1449 | + | 161.682i | −0.0626229 | + | 0.998037i | ||||
\(163\) | 20.3324 | + | 49.0868i | 0.124739 | + | 0.301146i | 0.973896 | − | 0.226994i | \(-0.0728897\pi\) |
−0.849158 | + | 0.528140i | \(0.822890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 119.501 | − | 119.501i | 0.707107 | − | 0.707107i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −160.157 | + | 281.005i | −0.931146 | + | 1.63375i | ||||
\(173\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 175.000i | 1.00000i | ||||||||
\(176\) | 24.5386 | − | 32.7281i | 0.139424 | − | 0.185955i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 211.247 | − | 87.5013i | 1.18015 | − | 0.488834i | 0.295615 | − | 0.955307i | \(-0.404476\pi\) |
0.884535 | + | 0.466473i | \(0.154476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 282.177 | − | 191.975i | 1.53357 | − | 1.04334i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −75.1937 | −0.393684 | −0.196842 | − | 0.980435i | \(-0.563069\pi\) | ||||
−0.196842 | + | 0.980435i | \(0.563069\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −225.559 | −1.16870 | −0.584349 | − | 0.811502i | \(-0.698650\pi\) | ||||
−0.584349 | + | 0.811502i | \(0.698650\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.5000 | + | 194.463i | −0.125000 | + | 0.992157i | ||||
\(197\) | 135.160 | + | 55.9851i | 0.686092 | + | 0.284189i | 0.698371 | − | 0.715736i | \(-0.253909\pi\) |
−0.0122790 | + | 0.999925i | \(0.503909\pi\) | |||||||
\(198\) | −14.9136 | − | 43.5353i | −0.0753214 | − | 0.219875i | ||||
\(199\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(200\) | −112.500 | − | 165.359i | −0.562500 | − | 0.826797i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −111.945 | + | 270.260i | −0.551455 | + | 1.33133i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 383.951i | − | 1.85483i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 349.538 | − | 144.783i | 1.65658 | − | 0.686176i | 0.658768 | − | 0.752346i | \(-0.271078\pi\) |
0.997808 | + | 0.0661700i | \(0.0210780\pi\) | |||||||
\(212\) | 198.206 | − | 347.764i | 0.934934 | − | 1.64039i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.3924 | − | 47.7702i | 0.109310 | − | 0.223225i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −323.221 | + | 110.724i | −1.48267 | + | 0.507908i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | −101.861 | − | 199.500i | −0.454739 | − | 0.890625i | ||||
\(225\) | −225.000 | −1.00000 | ||||||||
\(226\) | 15.9118 | − | 253.590i | 0.0704061 | − | 1.12208i | ||||
\(227\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −67.9601 | − | 327.337i | −0.292932 | − | 1.41093i | ||||
\(233\) | −223.826 | + | 223.826i | −0.960627 | + | 0.960627i | −0.999254 | − | 0.0386266i | \(-0.987702\pi\) |
0.0386266 | + | 0.999254i | \(0.487702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 423.320i | − | 1.77121i | −0.464435 | − | 0.885607i | \(-0.653743\pi\) | ||
0.464435 | − | 0.885607i | \(-0.346257\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | −151.421 | − | 171.696i | −0.625708 | − | 0.709486i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(252\) | −250.023 | − | 31.5000i | −0.992157 | − | 0.125000i | ||||
\(253\) | 41.7384 | + | 100.765i | 0.164974 | + | 0.398282i | ||||
\(254\) | 506.987 | + | 31.8115i | 1.99601 | + | 0.125242i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 224.500 | + | 123.027i | 0.876953 | + | 0.480576i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 118.195 | + | 285.348i | 0.456351 | + | 1.10173i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −347.477 | − | 143.930i | −1.33133 | − | 0.551455i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 352.139 | + | 352.139i | 1.33893 | + | 1.33893i | 0.897095 | + | 0.441837i | \(0.145673\pi\) |
0.441837 | + | 0.897095i | \(0.354327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.2750 | + | 52.1117i | 0.0532648 | + | 0.194447i | ||||
\(269\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.9446 | − | 35.2278i | 0.145783 | − | 0.128569i | ||||
\(275\) | 59.0499 | − | 24.4593i | 0.214727 | − | 0.0889427i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 207.009 | − | 499.763i | 0.747323 | − | 1.80420i | 0.174237 | − | 0.984704i | \(-0.444254\pi\) |
0.573087 | − | 0.819495i | \(-0.305746\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 332.158 | + | 332.158i | 1.18206 | + | 1.18206i | 0.979210 | + | 0.202847i | \(0.0650194\pi\) |
0.202847 | + | 0.979210i | \(0.434981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(284\) | −207.655 | − | 267.521i | −0.731178 | − | 0.941976i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 256.500 | − | 130.965i | 0.890625 | − | 0.454739i | ||||
\(289\) | −289.000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −295.121 | − | 193.646i | −0.997031 | − | 0.654208i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −251.807 | + | 514.221i | −0.844991 | + | 1.72557i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −522.935 | + | 216.607i | −1.73733 | + | 0.719624i | ||||
\(302\) | −155.921 | + | 137.510i | −0.516295 | + | 0.455330i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(308\) | 69.0414 | − | 18.9125i | 0.224160 | − | 0.0614043i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 78.1339 | − | 620.169i | 0.247259 | − | 1.96256i | ||||
\(317\) | 237.250 | + | 572.771i | 0.748421 | + | 1.80685i | 0.567543 | + | 0.823344i | \(0.307894\pi\) |
0.180879 | + | 0.983505i | \(0.442106\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 106.840 | 0.334920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 596.084 | + | 37.4019i | 1.85119 | + | 0.116155i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 40.5000 | − | 321.459i | 0.125000 | − | 0.992157i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −34.4371 | − | 100.527i | −0.105635 | − | 0.308366i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −252.050 | + | 608.503i | −0.761481 | + | 1.83838i | −0.287755 | + | 0.957704i | \(0.592909\pi\) |
−0.473725 | + | 0.880673i | \(0.657091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −366.875 | + | 151.965i | −1.10173 | + | 0.456351i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 289.193i | − | 0.858139i | −0.903272 | − | 0.429069i | \(-0.858842\pi\) | ||
0.903272 | − | 0.429069i | \(-0.141158\pi\) | |||||||
\(338\) | −253.500 | + | 223.566i | −0.750000 | + | 0.661438i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −242.538 | + | 242.538i | −0.707107 | + | 0.707107i | ||||
\(344\) | 354.880 | − | 540.847i | 1.03163 | − | 1.57223i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 631.092 | + | 261.407i | 1.81871 | + | 0.753334i | 0.976945 | + | 0.213490i | \(0.0684831\pi\) |
0.841765 | + | 0.539844i | \(0.181517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(350\) | 21.9180 | − | 349.313i | 0.0626229 | − | 0.998037i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −53.0800 | + | 62.2544i | −0.150795 | + | 0.176859i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −432.624 | + | 148.201i | −1.20845 | + | 0.413970i | ||||
\(359\) | 475.162 | + | 475.162i | 1.32357 | + | 1.32357i | 0.910864 | + | 0.412708i | \(0.135417\pi\) |
0.412708 | + | 0.910864i | \(0.364583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 255.266 | − | 255.266i | 0.707107 | − | 0.707107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | −587.291 | + | 347.856i | −1.59590 | + | 0.945260i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 647.170 | − | 268.067i | 1.74439 | − | 0.722552i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.65880 | − | 23.3184i | 0.0258949 | − | 0.0625158i | −0.910403 | − | 0.413722i | \(-0.864228\pi\) |
0.936298 | + | 0.351206i | \(0.114228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −596.475 | − | 247.068i | −1.57381 | − | 0.651894i | −0.586393 | − | 0.810026i | \(-0.699453\pi\) |
−0.987418 | + | 0.158132i | \(0.949453\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 150.092 | + | 9.41769i | 0.392911 | + | 0.0246536i | ||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 450.232 | + | 28.2503i | 1.16640 | + | 0.0731873i | ||||
\(387\) | −278.495 | − | 672.346i | −0.719624 | − | 1.73733i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −578.727 | − | 239.716i | −1.48773 | − | 0.616238i | −0.516908 | − | 0.856041i | \(-0.672917\pi\) |
−0.970821 | + | 0.239804i | \(0.922917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 73.2595 | − | 385.094i | 0.186886 | − | 0.982382i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −262.778 | − | 128.679i | −0.666949 | − | 0.326596i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 24.3161 | + | 88.7675i | 0.0614043 | + | 0.224160i | ||||
\(397\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 203.848 | + | 344.160i | 0.509620 | + | 0.860400i | ||||
\(401\) | 759.181i | 1.89322i | 0.322381 | + | 0.946610i | \(0.395517\pi\) | ||||
−0.322381 | + | 0.946610i | \(0.604483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 257.300 | − | 525.438i | 0.633744 | − | 1.29418i | ||||
\(407\) | 79.7644 | − | 79.7644i | 0.195981 | − | 0.195981i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −48.0882 | + | 766.394i | −0.116155 | + | 1.85119i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 433.539 | + | 179.578i | 1.02978 | + | 0.426551i | 0.832635 | − | 0.553823i | \(-0.186832\pi\) |
0.197150 | + | 0.980373i | \(0.436832\pi\) | |||||||
\(422\) | −715.837 | + | 245.220i | −1.69630 | + | 0.581090i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −439.190 | + | 669.337i | −1.03583 | + | 1.57863i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −52.6761 | + | 92.4231i | −0.123075 | + | 0.215942i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 162.000i | 0.375870i | 0.982181 | + | 0.187935i | \(0.0601794\pi\) | ||||
−0.982181 | + | 0.187935i | \(0.939821\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 659.041 | − | 180.531i | 1.51156 | − | 0.414063i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −311.834 | − | 311.834i | −0.707107 | − | 0.707107i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −460.494 | − | 190.743i | −1.03949 | − | 0.430571i | −0.203361 | − | 0.979104i | \(-0.565187\pi\) |
−0.836129 | + | 0.548533i | \(0.815187\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 178.336 | + | 410.975i | 0.398072 | + | 0.917354i | ||||
\(449\) | 84.6640 | 0.188561 | 0.0942807 | − | 0.995546i | \(-0.469945\pi\) | ||||
0.0942807 | + | 0.995546i | \(0.469945\pi\) | |||||||
\(450\) | 449.117 | + | 28.1803i | 0.998037 | + | 0.0626229i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −63.5222 | + | 504.192i | −0.140536 | + | 1.11547i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 179.600 | − | 179.600i | 0.392997 | − | 0.392997i | −0.482757 | − | 0.875754i | \(-0.660365\pi\) |
0.875754 | + | 0.482757i | \(0.160365\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 27.5911i | − | 0.0595920i | −0.999556 | − | 0.0297960i | \(-0.990514\pi\) | ||
0.999556 | − | 0.0297960i | \(-0.00948576\pi\) | |||||||
\(464\) | 94.6560 | + | 661.900i | 0.204000 | + | 1.42651i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 474.807 | − | 418.740i | 1.01890 | − | 0.898584i | ||||
\(467\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.1847 | + | 87.3576i | −0.0771529 | + | 0.186264i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 146.178 | + | 146.178i | 0.309045 | + | 0.309045i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 344.657 | + | 832.076i | 0.722552 | + | 1.74439i | ||||
\(478\) | −53.0191 | + | 844.979i | −0.110919 | + | 1.76774i | ||||
\(479\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 280.744 | + | 361.682i | 0.580050 | + | 0.747277i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 245.486 | + | 245.486i | 0.504078 | + | 0.504078i | 0.912703 | − | 0.408624i | \(-0.133991\pi\) |
−0.408624 | + | 0.912703i | \(0.633991\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 222.027 | − | 536.019i | 0.452193 | − | 1.09169i | −0.519294 | − | 0.854596i | \(-0.673805\pi\) |
0.971487 | − | 0.237094i | \(-0.0761949\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 592.648i | − | 1.19245i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −707.625 | + | 293.108i | −1.41809 | + | 0.587391i | −0.954379 | − | 0.298597i | \(-0.903481\pi\) |
−0.463708 | + | 0.885988i | \(0.653481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 495.120 | + | 94.1907i | 0.982382 | + | 0.186886i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −70.6926 | − | 206.363i | −0.139709 | − | 0.407832i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1008.00 | − | 126.996i | −1.98425 | − | 0.249992i | ||||
\(509\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −432.710 | − | 273.690i | −0.845137 | − | 0.534550i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −200.187 | − | 584.378i | −0.386462 | − | 1.12814i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | 675.564 | + | 330.815i | 1.29418 | + | 0.633744i | ||||
\(523\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −658.792 | − | 747.000i | −1.25246 | − | 1.42015i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1290.98i | − | 2.44041i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −21.9671 | − | 105.807i | −0.0409835 | − | 0.197401i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 115.738 | + | 47.9401i | 0.214727 | + | 0.0889427i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −392.486 | − | 947.545i | −0.725483 | − | 1.75147i | −0.657091 | − | 0.753811i | \(-0.728213\pi\) |
−0.0683919 | − | 0.997659i | \(-0.521787\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −399.982 | − | 965.641i | −0.731228 | − | 1.76534i | −0.638463 | − | 0.769653i | \(-0.720429\pi\) |
−0.0927652 | − | 0.995688i | \(-0.529571\pi\) | |||||||
\(548\) | −84.1445 | + | 65.3144i | −0.153548 | + | 0.119187i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −120.931 | + | 41.4267i | −0.219875 | + | 0.0753214i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 773.486 | − | 773.486i | 1.39871 | − | 1.39871i | ||||
\(554\) | −475.798 | + | 971.637i | −0.858841 | + | 1.75386i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 683.144 | − | 282.968i | 1.22647 | − | 0.508021i | 0.327009 | − | 0.945021i | \(-0.393959\pi\) |
0.899461 | + | 0.437000i | \(0.143959\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −621.411 | − | 704.614i | −1.10571 | − | 1.25376i | ||||
\(563\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 400.930 | − | 400.930i | 0.707107 | − | 0.707107i | ||||
\(568\) | 380.988 | + | 560.000i | 0.670754 | + | 0.985915i | ||||
\(569\) | 658.532 | + | 658.532i | 1.15735 | + | 1.15735i | 0.985044 | + | 0.172306i | \(0.0551217\pi\) |
0.172306 | + | 0.985044i | \(0.444878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −893.751 | − | 370.204i | −1.56524 | − | 0.648343i | −0.579249 | − | 0.815151i | \(-0.696654\pi\) |
−0.985989 | + | 0.166807i | \(0.946654\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1066.53 | −1.85483 | ||||||||
\(576\) | −528.396 | + | 229.290i | −0.917354 | + | 0.398072i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 576.866 | + | 36.1960i | 0.998037 | + | 0.0626229i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −180.906 | − | 180.906i | −0.310302 | − | 0.310302i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 564.831 | + | 423.494i | 0.954106 | + | 0.715361i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 567.030 | − | 994.886i | 0.951393 | − | 1.66927i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 123.037 | − | 123.037i | 0.205403 | − | 0.205403i | −0.596907 | − | 0.802310i | \(-0.703604\pi\) |
0.802310 | + | 0.596907i | \(0.203604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(602\) | 1070.95 | − | 366.868i | 1.77898 | − | 0.609415i | ||||
\(603\) | −112.317 | − | 46.5232i | −0.186264 | − | 0.0771529i | ||||
\(604\) | 328.453 | − | 254.951i | 0.543796 | − | 0.422104i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −612.624 | − | 253.757i | −0.999386 | − | 0.413959i | −0.177814 | − | 0.984064i | \(-0.556903\pi\) |
−0.821572 | + | 0.570105i | \(0.806903\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −140.181 | + | 29.1037i | −0.227566 | + | 0.0472462i | ||||
\(617\) | 778.265 | − | 778.265i | 1.26137 | − | 1.26137i | 0.310939 | − | 0.950430i | \(-0.399356\pi\) |
0.950430 | − | 0.310939i | \(-0.100644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000i | 1.00000i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −538.799 | + | 538.799i | −0.853881 | + | 0.853881i | −0.990609 | − | 0.136728i | \(-0.956341\pi\) |
0.136728 | + | 0.990609i | \(0.456341\pi\) | |||||||
\(632\) | −233.635 | + | 1228.12i | −0.369675 | + | 1.94322i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −401.831 | − | 1173.01i | −0.633802 | − | 1.85017i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −213.260 | − | 13.3812i | −0.334263 | − | 0.0209737i | ||||
\(639\) | 761.976 | 1.19245 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 98.7379 | 0.154037 | 0.0770186 | − | 0.997030i | \(-0.475460\pi\) | ||||
0.0770186 | + | 0.997030i | \(0.475460\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(644\) | −1185.14 | − | 149.314i | −1.84029 | − | 0.231854i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | −121.102 | + | 636.583i | −0.186886 | + | 0.982382i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 56.1484 | + | 204.973i | 0.0861171 | + | 0.314376i | ||||
\(653\) | −1206.23 | + | 499.635i | −1.84721 | + | 0.765138i | −0.914242 | + | 0.405169i | \(0.867213\pi\) |
−0.932964 | + | 0.359969i | \(0.882787\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 115.914 | − | 48.0130i | 0.175893 | − | 0.0728574i | −0.292999 | − | 0.956113i | \(-0.594653\pi\) |
0.468892 | + | 0.883255i | \(0.344653\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(662\) | 579.323 | − | 1183.05i | 0.875110 | − | 1.78708i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 751.344 | − | 257.383i | 1.12814 | − | 0.386462i | ||||
\(667\) | −1647.09 | − | 682.246i | −2.46940 | − | 1.02286i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1269.96 | 1.88701 | 0.943507 | − | 0.331352i | \(-0.107505\pi\) | ||||
0.943507 | + | 0.331352i | \(0.107505\pi\) | |||||||
\(674\) | −36.2202 | + | 577.250i | −0.0537391 | + | 0.856454i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 534.006 | − | 414.505i | 0.789949 | − | 0.613172i | ||||
\(677\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −98.6625 | + | 238.192i | −0.144455 | + | 0.348744i | −0.979502 | − | 0.201433i | \(-0.935440\pi\) |
0.835048 | + | 0.550178i | \(0.185440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 514.500 | − | 453.746i | 0.750000 | − | 0.661438i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −776.106 | + | 1035.12i | −1.12806 | + | 1.50454i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −61.6373 | + | 148.806i | −0.0889427 | + | 0.214727i | ||||
\(694\) | −1226.97 | − | 600.830i | −1.76796 | − | 0.865749i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −87.5000 | + | 694.510i | −0.125000 | + | 0.992157i | ||||
\(701\) | 242.149 | + | 584.599i | 0.345434 | + | 0.833950i | 0.997147 | + | 0.0754851i | \(0.0240505\pi\) |
−0.651713 | + | 0.758465i | \(0.725949\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 113.749 | − | 117.616i | 0.161575 | − | 0.167069i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1291.86 | + | 535.106i | 1.82209 | + | 0.754734i | 0.974612 | + | 0.223900i | \(0.0718789\pi\) |
0.847476 | + | 0.530834i | \(0.178121\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 994.482 | + | 994.482i | 1.39871 | + | 1.39871i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 882.111 | − | 241.637i | 1.23200 | − | 0.337481i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −888.947 | − | 1007.97i | −1.23809 | − | 1.40386i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −541.500 | + | 477.558i | −0.750000 | + | 0.661438i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −399.805 | + | 965.214i | −0.551455 | + | 1.33133i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 515.481 | + | 515.481i | 0.707107 | + | 0.707107i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1215.84 | − | 620.790i | 1.65196 | − | 0.843464i | ||||
\(737\) | 34.5343 | 0.0468580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 312.569 | + | 754.607i | 0.422961 | + | 1.02112i | 0.981469 | + | 0.191620i | \(0.0613741\pi\) |
−0.558508 | + | 0.829499i | \(0.688626\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1325.37 | + | 454.026i | −1.78622 | + | 0.611895i | ||||
\(743\) | −683.810 | − | 683.810i | −0.920337 | − | 0.920337i | 0.0767160 | − | 0.997053i | \(-0.475557\pi\) |
−0.997053 | + | 0.0767160i | \(0.975557\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −22.2002 | + | 45.3355i | −0.0297590 | + | 0.0607715i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −171.995 | + | 71.2425i | −0.229632 | + | 0.0951169i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1269.96i | 1.69103i | 0.533955 | + | 0.845513i | \(0.320705\pi\) | ||||
−0.533955 | + | 0.845513i | \(0.679295\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −407.368 | + | 983.472i | −0.538134 | + | 1.29917i | 0.387890 | + | 0.921706i | \(0.373204\pi\) |
−0.926024 | + | 0.377465i | \(0.876796\pi\) | |||||||
\(758\) | 1159.66 | + | 567.872i | 1.52990 | + | 0.749171i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1104.79 | + | 457.617i | 1.44795 | + | 0.599760i | ||||
\(764\) | −298.416 | − | 37.5968i | −0.390596 | − | 0.0492105i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −895.158 | − | 112.779i | −1.15953 | − | 0.146087i | ||||
\(773\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(774\) | 471.688 | + | 1376.93i | 0.609415 | + | 1.77898i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1125.16 | + | 550.975i | 1.44622 | + | 0.708194i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −199.976 | + | 82.8328i | −0.256051 | + | 0.106060i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −194.463 | + | 759.500i | −0.248039 | + | 0.968750i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(788\) | 508.407 | + | 289.764i | 0.645187 | + | 0.367721i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −628.838 | + | 628.838i | −0.794991 | + | 0.794991i | ||||
\(792\) | −37.4190 | − | 180.232i | −0.0472462 | − | 0.227566i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −363.791 | − | 712.500i | −0.454739 | − | 0.890625i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 95.0843 | − | 1515.38i | 0.118559 | − | 1.88950i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1137.46 | + | 1137.46i | −1.40601 | + | 1.40601i | −0.626964 | + | 0.779048i | \(0.715703\pi\) |
−0.779048 | + | 0.626964i | \(0.784297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(812\) | −579.399 | + | 1016.59i | −0.713546 | + | 1.25196i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −169.206 | + | 149.226i | −0.207870 | + | 0.183324i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 579.898 | − | 1400.00i | 0.706331 | − | 1.70523i | −0.00264006 | − | 0.999997i | \(-0.500840\pi\) |
0.708971 | − | 0.705238i | \(-0.249160\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −439.820 | + | 439.820i | −0.534411 | + | 0.534411i | −0.921882 | − | 0.387471i | \(-0.873349\pi\) |
0.387471 | + | 0.921882i | \(0.373349\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1291.40 | + | 534.917i | 1.56155 | + | 0.646817i | 0.985358 | − | 0.170496i | \(-0.0545369\pi\) |
0.576195 | + | 0.817312i | \(0.304537\pi\) | |||||||
\(828\) | 191.975 | − | 1523.76i | 0.231854 | − | 1.84029i | ||||
\(829\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −640.195 | + | 640.195i | −0.761230 | + | 0.761230i | ||||
\(842\) | −842.885 | − | 412.750i | −1.00105 | − | 0.490201i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1459.58 | − | 399.822i | 1.72936 | − | 0.473722i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 801.246i | 0.945982i | ||||||||
\(848\) | 960.488 | − | 1281.04i | 1.13265 | − | 1.51066i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1739.04 | + | 720.333i | −2.04352 | + | 0.846455i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 116.721 | − | 177.886i | 0.136356 | − | 0.207811i | ||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.2898 | − | 323.364i | 0.0235381 | − | 0.375132i | ||||
\(863\) | 1504.48 | 1.74331 | 0.871655 | − | 0.490119i | \(-0.163047\pi\) | ||||
0.871655 | + | 0.490119i | \(0.163047\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −369.104 | − | 152.888i | −0.424745 | − | 0.175935i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1338.11 | + | 277.812i | −1.53453 | + | 0.318591i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1618.72 | − | 670.498i | 1.84575 | − | 0.764536i | 0.905046 | − | 0.425314i | \(-0.139836\pi\) |
0.940706 | − | 0.339222i | \(-0.110164\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 583.388 | + | 661.500i | 0.661438 | + | 0.750000i | ||||
\(883\) | −1137.51 | + | 471.174i | −1.28824 | + | 0.533606i | −0.918460 | − | 0.395514i | \(-0.870566\pi\) |
−0.369778 | + | 0.929120i | \(0.620566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 895.291 | + | 438.412i | 1.01049 | + | 0.494822i | ||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1257.20 | − | 1257.20i | −1.41417 | − | 1.41417i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −191.322 | − | 79.2480i | −0.214727 | − | 0.0889427i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −304.500 | − | 842.672i | −0.339844 | − | 0.940482i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −168.996 | − | 10.6038i | −0.188191 | − | 0.0118083i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −892.941 | − | 112.500i | −0.992157 | − | 0.125000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 189.943 | − | 998.449i | 0.210114 | − | 1.10448i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 584.951 | − | 1412.20i | 0.644929 | − | 1.55700i | −0.175022 | − | 0.984564i | \(-0.556000\pi\) |
0.819952 | − | 0.572433i | \(-0.194000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 931.304i | − | 1.02229i | −0.859495 | − | 0.511144i | \(-0.829222\pi\) | ||
0.859495 | − | 0.511144i | \(-0.170778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −380.988 | + | 336.000i | −0.416836 | + | 0.367615i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1257.20 | − | 1257.20i | 1.36801 | − | 1.36801i | 0.504725 | − | 0.863280i | \(-0.331594\pi\) |
0.863280 | − | 0.504725i | \(-0.168406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 422.124 | + | 1019.10i | 0.456351 | + | 1.10173i | ||||
\(926\) | −3.45567 | + | 55.0739i | −0.00373182 | + | 0.0594750i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −106.040 | − | 1333.06i | −0.114267 | − | 1.43648i | ||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1000.20 | + | 776.369i | −1.07317 | + | 0.833014i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | 83.1686 | − | 169.840i | 0.0886658 | − | 0.181066i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −273.475 | − | 310.091i | −0.289085 | − | 0.327792i | ||||
\(947\) | 1686.79 | − | 698.692i | 1.78119 | − | 0.737795i | 0.788807 | − | 0.614641i | \(-0.210699\pi\) |
0.992388 | − | 0.123154i | \(-0.0393008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1342.81 | − | 1342.81i | −1.40904 | − | 1.40904i | −0.764953 | − | 0.644086i | \(-0.777238\pi\) |
−0.644086 | − | 0.764953i | \(-0.722762\pi\) | |||||||
\(954\) | −583.748 | − | 1704.05i | −0.611895 | − | 1.78622i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 211.660 | − | 1680.00i | 0.221402 | − | 1.75732i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −186.408 | −0.194377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 961.000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −91.5975 | − | 221.136i | −0.0951169 | − | 0.229632i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −785.470 | − | 785.470i | −0.812276 | − | 0.812276i | 0.172699 | − | 0.984975i | \(-0.444751\pi\) |
−0.984975 | + | 0.172699i | \(0.944751\pi\) | |||||||
\(968\) | −515.087 | − | 757.107i | −0.532115 | − | 0.782135i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −459.263 | − | 520.755i | −0.471522 | − | 0.534656i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1947.27i | 1.99311i | 0.0829069 | + | 0.996557i | \(0.473580\pi\) | ||||
−0.0829069 | + | 0.996557i | \(0.526420\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −588.365 | + | 1420.44i | −0.599760 | + | 1.44795i | ||||
\(982\) | −510.316 | + | 1042.13i | −0.519670 | + | 1.06123i | ||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1320.10 | − | 3187.01i | −1.33478 | − | 3.22245i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.39458 | −0.00645266 | −0.00322633 | − | 0.999995i | \(-0.501027\pi\) | ||||
−0.00322633 | + | 0.999995i | \(0.501027\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −74.2267 | + | 1182.97i | −0.0746748 | + | 1.19011i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(998\) | 1449.18 | − | 496.438i | 1.45209 | − | 0.497433i | ||||
\(999\) | 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 | 224.3.v.a.69.1 | yes | 8 | |
7.6 | odd | 2 | CM | 224.3.v.a.69.1 | yes | 8 | |
32.13 | even | 8 | inner | 224.3.v.a.13.1 | ✓ | 8 | |
224.13 | odd | 8 | inner | 224.3.v.a.13.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.v.a.13.1 | ✓ | 8 | 32.13 | even | 8 | inner | |
224.3.v.a.13.1 | ✓ | 8 | 224.13 | odd | 8 | inner | |
224.3.v.a.69.1 | yes | 8 | 1.1 | even | 1 | trivial | |
224.3.v.a.69.1 | yes | 8 | 7.6 | odd | 2 | CM |