Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(701,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.3 | ||
Character | \(\chi\) | \(=\) | 1050.701 |
Dual form | 1050.3.e.e.701.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | −1.28756 | + | 2.70965i | −0.429186 | + | 0.903216i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.83202 | − | 1.82088i | −0.638670 | − | 0.303481i | ||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −5.68438 | − | 6.97766i | −0.631598 | − | 0.775296i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.4698i | 0.951802i | 0.879499 | + | 0.475901i | \(0.157878\pi\) | ||||
−0.879499 | + | 0.475901i | \(0.842122\pi\) | |||||||
\(12\) | 2.57512 | − | 5.41930i | 0.214593 | − | 0.451608i | ||||
\(13\) | −11.9937 | −0.922595 | −0.461297 | − | 0.887246i | \(-0.652616\pi\) | ||||
−0.461297 | + | 0.887246i | \(0.652616\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 29.1133i | 1.71254i | 0.516525 | + | 0.856272i | \(0.327225\pi\) | ||||
−0.516525 | + | 0.856272i | \(0.672775\pi\) | |||||||
\(18\) | 9.86791 | − | 8.03893i | 0.548217 | − | 0.446607i | ||||
\(19\) | −20.3176 | −1.06935 | −0.534673 | − | 0.845059i | \(-0.679565\pi\) | ||||
−0.534673 | + | 0.845059i | \(0.679565\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.40656 | − | 7.16905i | 0.162217 | − | 0.341384i | ||||
\(22\) | −14.8066 | −0.673026 | ||||||||
\(23\) | 7.71572i | 0.335466i | 0.985832 | + | 0.167733i | \(0.0536446\pi\) | ||||
−0.985832 | + | 0.167733i | \(0.946355\pi\) | |||||||
\(24\) | 7.66404 | + | 3.64177i | 0.319335 | + | 0.151740i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 16.9617i | − | 0.652373i | ||||||
\(27\) | 26.2260 | − | 6.41851i | 0.971333 | − | 0.237723i | ||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | − | 47.4046i | − | 1.63464i | −0.576182 | − | 0.817321i | \(-0.695458\pi\) | ||
0.576182 | − | 0.817321i | \(-0.304542\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −35.5084 | −1.14543 | −0.572717 | − | 0.819753i | \(-0.694110\pi\) | ||||
−0.572717 | + | 0.819753i | \(0.694110\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −28.3695 | − | 13.4805i | −0.859683 | − | 0.408501i | ||||
\(34\) | −41.1724 | −1.21095 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.3688 | + | 13.9553i | 0.315799 | + | 0.387648i | ||||
\(37\) | 58.0907 | 1.57002 | 0.785009 | − | 0.619485i | \(-0.212658\pi\) | ||||
0.785009 | + | 0.619485i | \(0.212658\pi\) | |||||||
\(38\) | − | 28.7334i | − | 0.756142i | ||||||
\(39\) | 15.4426 | − | 32.4988i | 0.395965 | − | 0.833302i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 52.5850i | − | 1.28256i | −0.767307 | − | 0.641280i | \(-0.778404\pi\) | ||
0.767307 | − | 0.641280i | \(-0.221596\pi\) | |||||||
\(42\) | 10.1386 | + | 4.81761i | 0.241395 | + | 0.114705i | ||||
\(43\) | 15.7629 | 0.366578 | 0.183289 | − | 0.983059i | \(-0.441326\pi\) | ||||
0.183289 | + | 0.983059i | \(0.441326\pi\) | |||||||
\(44\) | − | 20.9396i | − | 0.475901i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.9117 | −0.237210 | ||||||||
\(47\) | − | 85.2023i | − | 1.81281i | −0.422405 | − | 0.906407i | \(-0.638814\pi\) | ||
0.422405 | − | 0.906407i | \(-0.361186\pi\) | |||||||
\(48\) | −5.15024 | + | 10.8386i | −0.107297 | + | 0.225804i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −78.8867 | − | 37.4850i | −1.54680 | − | 0.735001i | ||||
\(52\) | 23.9875 | 0.461297 | ||||||||
\(53\) | 42.7649i | 0.806885i | 0.915005 | + | 0.403443i | \(0.132187\pi\) | ||||
−0.915005 | + | 0.403443i | \(0.867813\pi\) | |||||||
\(54\) | 9.07715 | + | 37.0892i | 0.168095 | + | 0.686836i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | 26.1601 | − | 55.0535i | 0.458949 | − | 0.965850i | ||||
\(58\) | 67.0403 | 1.15587 | ||||||||
\(59\) | 37.9769i | 0.643676i | 0.946795 | + | 0.321838i | \(0.104301\pi\) | ||||
−0.946795 | + | 0.321838i | \(0.895699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 53.5108 | 0.877226 | 0.438613 | − | 0.898676i | \(-0.355470\pi\) | ||||
0.438613 | + | 0.898676i | \(0.355470\pi\) | |||||||
\(62\) | − | 50.2165i | − | 0.809944i | ||||||
\(63\) | 15.0395 | + | 18.4612i | 0.238722 | + | 0.293034i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 19.0643 | − | 40.1206i | 0.288854 | − | 0.607888i | ||||
\(67\) | −27.6366 | −0.412487 | −0.206243 | − | 0.978501i | \(-0.566124\pi\) | ||||
−0.206243 | + | 0.978501i | \(0.566124\pi\) | |||||||
\(68\) | − | 58.2265i | − | 0.856272i | ||||||
\(69\) | −20.9069 | − | 9.93444i | −0.302998 | − | 0.143977i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 58.0688i | − | 0.817871i | −0.912563 | − | 0.408935i | \(-0.865900\pi\) | ||
0.912563 | − | 0.408935i | \(-0.134100\pi\) | |||||||
\(72\) | −19.7358 | + | 16.0779i | −0.274109 | + | 0.223304i | ||||
\(73\) | 67.8080 | 0.928877 | 0.464438 | − | 0.885605i | \(-0.346256\pi\) | ||||
0.464438 | + | 0.885605i | \(0.346256\pi\) | |||||||
\(74\) | 82.1526i | 1.11017i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 40.6352 | 0.534673 | ||||||||
\(77\) | − | 27.7005i | − | 0.359747i | ||||||
\(78\) | 45.9602 | + | 21.8392i | 0.589234 | + | 0.279990i | ||||
\(79\) | −19.2994 | −0.244296 | −0.122148 | − | 0.992512i | \(-0.538978\pi\) | ||||
−0.122148 | + | 0.992512i | \(0.538978\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −16.3756 | + | 79.3274i | −0.202168 | + | 0.979351i | ||||
\(82\) | 74.3664 | 0.906907 | ||||||||
\(83\) | 33.6998i | 0.406021i | 0.979177 | + | 0.203011i | \(0.0650726\pi\) | ||||
−0.979177 | + | 0.203011i | \(0.934927\pi\) | |||||||
\(84\) | −6.81312 | + | 14.3381i | −0.0811086 | + | 0.170692i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 22.2920i | 0.259210i | ||||||||
\(87\) | 128.450 | + | 61.0363i | 1.47643 | + | 0.701566i | ||||
\(88\) | 29.6131 | 0.336513 | ||||||||
\(89\) | 46.8325i | 0.526208i | 0.964768 | + | 0.263104i | \(0.0847462\pi\) | ||||
−0.964768 | + | 0.263104i | \(0.915254\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 31.7324 | 0.348708 | ||||||||
\(92\) | − | 15.4314i | − | 0.167733i | ||||||
\(93\) | 45.7192 | − | 96.2153i | 0.491604 | − | 1.03457i | ||||
\(94\) | 120.494 | 1.28185 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −15.3281 | − | 7.28354i | −0.159668 | − | 0.0758702i | ||||
\(97\) | −65.1337 | −0.671482 | −0.335741 | − | 0.941954i | \(-0.608987\pi\) | ||||
−0.335741 | + | 0.941954i | \(0.608987\pi\) | |||||||
\(98\) | 9.89949i | 0.101015i | ||||||||
\(99\) | 73.0549 | − | 59.5145i | 0.737928 | − | 0.601156i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 171.169i | − | 1.69474i | −0.531000 | − | 0.847372i | \(-0.678184\pi\) | ||
0.531000 | − | 0.847372i | \(-0.321816\pi\) | |||||||
\(102\) | 53.0119 | − | 111.563i | 0.519724 | − | 1.09375i | ||||
\(103\) | −129.879 | −1.26096 | −0.630481 | − | 0.776205i | \(-0.717142\pi\) | ||||
−0.630481 | + | 0.776205i | \(0.717142\pi\) | |||||||
\(104\) | 33.9234i | 0.326186i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −60.4787 | −0.570554 | ||||||||
\(107\) | 29.1627i | 0.272549i | 0.990671 | + | 0.136274i | \(0.0435128\pi\) | ||||
−0.990671 | + | 0.136274i | \(0.956487\pi\) | |||||||
\(108\) | −52.4520 | + | 12.8370i | −0.485667 | + | 0.118861i | ||||
\(109\) | −19.3296 | −0.177336 | −0.0886680 | − | 0.996061i | \(-0.528261\pi\) | ||||
−0.0886680 | + | 0.996061i | \(0.528261\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −74.7952 | + | 157.405i | −0.673830 | + | 1.41807i | ||||
\(112\) | −10.5830 | −0.0944911 | ||||||||
\(113\) | 28.5568i | 0.252715i | 0.991985 | + | 0.126358i | \(0.0403287\pi\) | ||||
−0.991985 | + | 0.126358i | \(0.959671\pi\) | |||||||
\(114\) | 77.8574 | + | 36.9959i | 0.682959 | + | 0.324526i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 94.8092i | 0.817321i | ||||||||
\(117\) | 68.1769 | + | 83.6882i | 0.582709 | + | 0.715284i | ||||
\(118\) | −53.7074 | −0.455148 | ||||||||
\(119\) | − | 77.0264i | − | 0.647281i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.3828 | 0.0940727 | ||||||||
\(122\) | 75.6757i | 0.620292i | ||||||||
\(123\) | 142.487 | + | 67.7063i | 1.15843 | + | 0.550457i | ||||
\(124\) | 71.0169 | 0.572717 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −26.1080 | + | 21.2690i | −0.207207 | + | 0.168802i | ||||
\(127\) | 162.116 | 1.27650 | 0.638252 | − | 0.769828i | \(-0.279658\pi\) | ||||
0.638252 | + | 0.769828i | \(0.279658\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | −20.2956 | + | 42.7118i | −0.157330 | + | 0.331099i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 49.5756i | 0.378440i | 0.981935 | + | 0.189220i | \(0.0605959\pi\) | ||||
−0.981935 | + | 0.189220i | \(0.939404\pi\) | |||||||
\(132\) | 56.7391 | + | 26.9610i | 0.429841 | + | 0.204250i | ||||
\(133\) | 53.7553 | 0.404175 | ||||||||
\(134\) | − | 39.0840i | − | 0.291672i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 82.3447 | 0.605476 | ||||||||
\(137\) | − | 212.721i | − | 1.55271i | −0.630297 | − | 0.776354i | \(-0.717067\pi\) | ||
0.630297 | − | 0.776354i | \(-0.282933\pi\) | |||||||
\(138\) | 14.0494 | − | 29.5668i | 0.101807 | − | 0.214252i | ||||
\(139\) | −74.1650 | −0.533561 | −0.266780 | − | 0.963757i | \(-0.585960\pi\) | ||||
−0.266780 | + | 0.963757i | \(0.585960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 230.868 | + | 109.703i | 1.63736 | + | 0.778036i | ||||
\(142\) | 82.1217 | 0.578322 | ||||||||
\(143\) | − | 125.572i | − | 0.878128i | ||||||
\(144\) | −22.7375 | − | 27.9107i | −0.157899 | − | 0.193824i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 95.8950i | 0.656815i | ||||||||
\(147\) | −9.01292 | + | 18.9675i | −0.0613124 | + | 0.129031i | ||||
\(148\) | −116.181 | −0.785009 | ||||||||
\(149\) | 23.1598i | 0.155435i | 0.996975 | + | 0.0777176i | \(0.0247632\pi\) | ||||
−0.996975 | + | 0.0777176i | \(0.975237\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 75.1469 | 0.497661 | 0.248831 | − | 0.968547i | \(-0.419954\pi\) | ||||
0.248831 | + | 0.968547i | \(0.419954\pi\) | |||||||
\(152\) | 57.4668i | 0.378071i | ||||||||
\(153\) | 203.143 | − | 165.491i | 1.32773 | − | 1.08164i | ||||
\(154\) | 39.1745 | 0.254380 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −30.8853 | + | 64.9976i | −0.197983 | + | 0.416651i | ||||
\(157\) | 66.6968 | 0.424820 | 0.212410 | − | 0.977181i | \(-0.431869\pi\) | ||||
0.212410 | + | 0.977181i | \(0.431869\pi\) | |||||||
\(158\) | − | 27.2934i | − | 0.172743i | ||||||
\(159\) | −115.878 | − | 55.0624i | −0.728792 | − | 0.346304i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 20.4139i | − | 0.126794i | ||||||
\(162\) | −112.186 | − | 23.1586i | −0.692506 | − | 0.142954i | ||||
\(163\) | −248.817 | −1.52648 | −0.763241 | − | 0.646114i | \(-0.776393\pi\) | ||||
−0.763241 | + | 0.646114i | \(0.776393\pi\) | |||||||
\(164\) | 105.170i | 0.641280i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −47.6587 | −0.287100 | ||||||||
\(167\) | 92.0222i | 0.551031i | 0.961297 | + | 0.275516i | \(0.0888485\pi\) | ||||
−0.961297 | + | 0.275516i | \(0.911151\pi\) | |||||||
\(168\) | −20.2771 | − | 9.63521i | −0.120697 | − | 0.0573525i | ||||
\(169\) | −25.1504 | −0.148819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 115.493 | + | 141.769i | 0.675397 | + | 0.829060i | ||||
\(172\) | −31.5257 | −0.183289 | ||||||||
\(173\) | − | 233.473i | − | 1.34956i | −0.738021 | − | 0.674778i | \(-0.764239\pi\) | ||
0.738021 | − | 0.674778i | \(-0.235761\pi\) | |||||||
\(174\) | −86.3183 | + | 181.655i | −0.496082 | + | 1.04400i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 41.8793i | 0.237951i | ||||||||
\(177\) | −102.904 | − | 48.8975i | −0.581379 | − | 0.276257i | ||||
\(178\) | −66.2311 | −0.372085 | ||||||||
\(179\) | − | 185.252i | − | 1.03493i | −0.855705 | − | 0.517465i | \(-0.826876\pi\) | ||
0.855705 | − | 0.517465i | \(-0.173124\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −146.372 | −0.808684 | −0.404342 | − | 0.914608i | \(-0.632499\pi\) | ||||
−0.404342 | + | 0.914608i | \(0.632499\pi\) | |||||||
\(182\) | 44.8764i | 0.246574i | ||||||||
\(183\) | −68.8983 | + | 144.995i | −0.376493 | + | 0.792324i | ||||
\(184\) | 21.8233 | 0.118605 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 136.069 | + | 64.6567i | 0.731554 | + | 0.347617i | ||||
\(187\) | −304.811 | −1.63000 | ||||||||
\(188\) | 170.405i | 0.906407i | ||||||||
\(189\) | −69.3875 | + | 16.9818i | −0.367129 | + | 0.0898507i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 83.4780i | − | 0.437057i | −0.975831 | − | 0.218529i | \(-0.929874\pi\) | ||
0.975831 | − | 0.218529i | \(-0.0701257\pi\) | |||||||
\(192\) | 10.3005 | − | 21.6772i | 0.0536483 | − | 0.112902i | ||||
\(193\) | 88.5046 | 0.458573 | 0.229287 | − | 0.973359i | \(-0.426361\pi\) | ||||
0.229287 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(194\) | − | 92.1130i | − | 0.474809i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 36.9343i | 0.187484i | 0.995597 | + | 0.0937419i | \(0.0298828\pi\) | ||||
−0.995597 | + | 0.0937419i | \(0.970117\pi\) | |||||||
\(198\) | 84.1662 | + | 103.315i | 0.425082 | + | 0.521794i | ||||
\(199\) | 205.101 | 1.03066 | 0.515330 | − | 0.856992i | \(-0.327669\pi\) | ||||
0.515330 | + | 0.856992i | \(0.327669\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 35.5838 | − | 74.8854i | 0.177034 | − | 0.372564i | ||||
\(202\) | 242.070 | 1.19836 | ||||||||
\(203\) | 125.421i | 0.617837i | ||||||||
\(204\) | 157.773 | + | 74.9701i | 0.773399 | + | 0.367500i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 183.677i | − | 0.891634i | ||||||
\(207\) | 53.8377 | − | 43.8591i | 0.260085 | − | 0.211880i | ||||
\(208\) | −47.9749 | −0.230649 | ||||||||
\(209\) | − | 212.721i | − | 1.01781i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 49.4829 | 0.234516 | 0.117258 | − | 0.993101i | \(-0.462590\pi\) | ||||
0.117258 | + | 0.993101i | \(0.462590\pi\) | |||||||
\(212\) | − | 85.5298i | − | 0.403443i | ||||||
\(213\) | 157.346 | + | 74.7670i | 0.738714 | + | 0.351019i | ||||
\(214\) | −41.2423 | −0.192721 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −18.1543 | − | 74.1783i | −0.0840477 | − | 0.343418i | ||||
\(217\) | 93.9465 | 0.432933 | ||||||||
\(218\) | − | 27.3362i | − | 0.125395i | ||||||
\(219\) | −87.3069 | + | 183.736i | −0.398661 | + | 0.838976i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 349.177i | − | 1.57998i | ||||||
\(222\) | −222.605 | − | 105.776i | −1.00272 | − | 0.476470i | ||||
\(223\) | −1.69928 | −0.00762011 | −0.00381005 | − | 0.999993i | \(-0.501213\pi\) | ||||
−0.00381005 | + | 0.999993i | \(0.501213\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −40.3855 | −0.178697 | ||||||||
\(227\) | 206.970i | 0.911762i | 0.890041 | + | 0.455881i | \(0.150676\pi\) | ||||
−0.890041 | + | 0.455881i | \(0.849324\pi\) | |||||||
\(228\) | −52.3202 | + | 110.107i | −0.229474 | + | 0.482925i | ||||
\(229\) | 7.02543 | 0.0306787 | 0.0153394 | − | 0.999882i | \(-0.495117\pi\) | ||||
0.0153394 | + | 0.999882i | \(0.495117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 75.0587 | + | 35.6661i | 0.324930 | + | 0.154399i | ||||
\(232\) | −134.081 | −0.577933 | ||||||||
\(233\) | 116.672i | 0.500738i | 0.968151 | + | 0.250369i | \(0.0805519\pi\) | ||||
−0.968151 | + | 0.250369i | \(0.919448\pi\) | |||||||
\(234\) | −118.353 | + | 96.4168i | −0.505782 | + | 0.412037i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 75.9538i | − | 0.321838i | ||||||
\(237\) | 24.8491 | − | 52.2945i | 0.104848 | − | 0.220652i | ||||
\(238\) | 108.932 | 0.457697 | ||||||||
\(239\) | − | 157.119i | − | 0.657400i | −0.944434 | − | 0.328700i | \(-0.893389\pi\) | ||
0.944434 | − | 0.328700i | \(-0.106611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −287.032 | −1.19101 | −0.595503 | − | 0.803353i | \(-0.703047\pi\) | ||||
−0.595503 | + | 0.803353i | \(0.703047\pi\) | |||||||
\(242\) | 16.0977i | 0.0665194i | ||||||||
\(243\) | −193.865 | − | 146.511i | −0.797797 | − | 0.602926i | ||||
\(244\) | −107.022 | −0.438613 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −95.7511 | + | 201.507i | −0.389232 | + | 0.819133i | ||||
\(247\) | 243.684 | 0.986573 | ||||||||
\(248\) | 100.433i | 0.404972i | ||||||||
\(249\) | −91.3145 | − | 43.3905i | −0.366725 | − | 0.174259i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 161.056i | 0.641658i | 0.947137 | + | 0.320829i | \(0.103961\pi\) | ||||
−0.947137 | + | 0.320829i | \(0.896039\pi\) | |||||||
\(252\) | −30.0789 | − | 36.9223i | −0.119361 | − | 0.146517i | ||||
\(253\) | −80.7822 | −0.319297 | ||||||||
\(254\) | 229.267i | 0.902625i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 356.900i | − | 1.38871i | −0.719630 | − | 0.694357i | \(-0.755689\pi\) | ||
0.719630 | − | 0.694357i | \(-0.244311\pi\) | |||||||
\(258\) | −60.4036 | − | 28.7023i | −0.234122 | − | 0.111249i | ||||
\(259\) | −153.693 | −0.593411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −330.774 | + | 269.466i | −1.26733 | + | 1.03244i | ||||
\(262\) | −70.1105 | −0.267597 | ||||||||
\(263\) | 126.259i | 0.480071i | 0.970764 | + | 0.240036i | \(0.0771591\pi\) | ||||
−0.970764 | + | 0.240036i | \(0.922841\pi\) | |||||||
\(264\) | −38.1287 | + | 80.2412i | −0.144427 | + | 0.303944i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 76.0214i | 0.285795i | ||||||||
\(267\) | −126.900 | − | 60.2996i | −0.475279 | − | 0.225841i | ||||
\(268\) | 55.2732 | 0.206243 | ||||||||
\(269\) | − | 356.319i | − | 1.32461i | −0.749236 | − | 0.662304i | \(-0.769579\pi\) | ||
0.749236 | − | 0.662304i | \(-0.230421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −422.588 | −1.55937 | −0.779683 | − | 0.626175i | \(-0.784620\pi\) | ||||
−0.779683 | + | 0.626175i | \(0.784620\pi\) | |||||||
\(272\) | 116.453i | 0.428136i | ||||||||
\(273\) | −40.8574 | + | 85.9837i | −0.149661 | + | 0.314959i | ||||
\(274\) | 300.833 | 1.09793 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 41.8137 | + | 19.8689i | 0.151499 | + | 0.0719887i | ||||
\(277\) | −267.379 | −0.965266 | −0.482633 | − | 0.875823i | \(-0.660320\pi\) | ||||
−0.482633 | + | 0.875823i | \(0.660320\pi\) | |||||||
\(278\) | − | 104.885i | − | 0.377284i | ||||||
\(279\) | 201.843 | + | 247.766i | 0.723453 | + | 0.888050i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 417.470i | − | 1.48566i | −0.669480 | − | 0.742830i | \(-0.733483\pi\) | ||
0.669480 | − | 0.742830i | \(-0.266517\pi\) | |||||||
\(282\) | −155.143 | + | 326.497i | −0.550154 | + | 1.15779i | ||||
\(283\) | −56.1781 | −0.198509 | −0.0992546 | − | 0.995062i | \(-0.531646\pi\) | ||||
−0.0992546 | + | 0.995062i | \(0.531646\pi\) | |||||||
\(284\) | 116.138i | 0.408935i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 177.586 | 0.620930 | ||||||||
\(287\) | 139.127i | 0.484762i | ||||||||
\(288\) | 39.4716 | − | 32.1557i | 0.137054 | − | 0.111652i | ||||
\(289\) | −558.582 | −1.93281 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 83.8635 | − | 176.489i | 0.288191 | − | 0.606493i | ||||
\(292\) | −135.616 | −0.464438 | ||||||||
\(293\) | 35.8668i | 0.122412i | 0.998125 | + | 0.0612062i | \(0.0194947\pi\) | ||||
−0.998125 | + | 0.0612062i | \(0.980505\pi\) | |||||||
\(294\) | −26.8241 | − | 12.7462i | −0.0912386 | − | 0.0433544i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 164.305i | − | 0.555085i | ||||||
\(297\) | 67.2007 | + | 274.582i | 0.226265 | + | 0.924517i | ||||
\(298\) | −32.7530 | −0.109909 | ||||||||
\(299\) | − | 92.5402i | − | 0.309499i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −41.7046 | −0.138553 | ||||||||
\(302\) | 106.274i | 0.351900i | ||||||||
\(303\) | 463.808 | + | 220.390i | 1.53072 | + | 0.727361i | ||||
\(304\) | −81.2703 | −0.267337 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 234.039 | + | 287.287i | 0.764835 | + | 0.938846i | ||||
\(307\) | −496.572 | −1.61750 | −0.808749 | − | 0.588154i | \(-0.799855\pi\) | ||||
−0.808749 | + | 0.588154i | \(0.799855\pi\) | |||||||
\(308\) | 55.4011i | 0.179874i | ||||||||
\(309\) | 167.227 | − | 351.926i | 0.541188 | − | 1.13892i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 49.5016i | 0.159169i | 0.996828 | + | 0.0795846i | \(0.0253594\pi\) | ||||
−0.996828 | + | 0.0795846i | \(0.974641\pi\) | |||||||
\(312\) | −91.9204 | − | 43.6784i | −0.294617 | − | 0.139995i | ||||
\(313\) | −219.172 | −0.700229 | −0.350114 | − | 0.936707i | \(-0.613857\pi\) | ||||
−0.350114 | + | 0.936707i | \(0.613857\pi\) | |||||||
\(314\) | 94.3235i | 0.300393i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 38.5987 | 0.122148 | ||||||||
\(317\) | − | 96.3016i | − | 0.303791i | −0.988397 | − | 0.151895i | \(-0.951462\pi\) | ||
0.988397 | − | 0.151895i | \(-0.0485377\pi\) | |||||||
\(318\) | 77.8700 | − | 163.876i | 0.244874 | − | 0.515333i | ||||
\(319\) | 496.318 | 1.55586 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −79.0206 | − | 37.5487i | −0.246170 | − | 0.116974i | ||||
\(322\) | 28.8696 | 0.0896570 | ||||||||
\(323\) | − | 591.511i | − | 1.83130i | ||||||
\(324\) | 32.7512 | − | 158.655i | 0.101084 | − | 0.489675i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 351.880i | − | 1.07939i | ||||||
\(327\) | 24.8880 | − | 52.3764i | 0.0761102 | − | 0.160173i | ||||
\(328\) | −148.733 | −0.453453 | ||||||||
\(329\) | 225.424i | 0.685180i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 538.706 | 1.62751 | 0.813755 | − | 0.581208i | \(-0.197420\pi\) | ||||
0.813755 | + | 0.581208i | \(0.197420\pi\) | |||||||
\(332\) | − | 67.3995i | − | 0.203011i | ||||||
\(333\) | −330.209 | − | 405.337i | −0.991620 | − | 1.21723i | ||||
\(334\) | −130.139 | −0.389638 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 13.6262 | − | 28.6762i | 0.0405543 | − | 0.0853459i | ||||
\(337\) | −202.735 | −0.601589 | −0.300794 | − | 0.953689i | \(-0.597252\pi\) | ||||
−0.300794 | + | 0.953689i | \(0.597252\pi\) | |||||||
\(338\) | − | 35.5681i | − | 0.105231i | ||||||
\(339\) | −77.3790 | − | 36.7686i | −0.228257 | − | 0.108462i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 371.767i | − | 1.09023i | ||||||
\(342\) | −200.492 | + | 163.332i | −0.586234 | + | 0.477578i | ||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | − | 44.5841i | − | 0.129605i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 330.181 | 0.954280 | ||||||||
\(347\) | 139.011i | 0.400607i | 0.979734 | + | 0.200304i | \(0.0641928\pi\) | ||||
−0.979734 | + | 0.200304i | \(0.935807\pi\) | |||||||
\(348\) | −256.900 | − | 122.073i | −0.738217 | − | 0.350783i | ||||
\(349\) | −452.984 | −1.29795 | −0.648974 | − | 0.760811i | \(-0.724801\pi\) | ||||
−0.648974 | + | 0.760811i | \(0.724801\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −314.547 | + | 76.9819i | −0.896147 | + | 0.219322i | ||||
\(352\) | −59.2263 | −0.168256 | ||||||||
\(353\) | 453.499i | 1.28470i | 0.766412 | + | 0.642349i | \(0.222040\pi\) | ||||
−0.766412 | + | 0.642349i | \(0.777960\pi\) | |||||||
\(354\) | 69.1515 | − | 145.528i | 0.195343 | − | 0.411097i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 93.6650i | − | 0.263104i | ||||||
\(357\) | 208.715 | + | 99.1761i | 0.584635 | + | 0.277804i | ||||
\(358\) | 261.986 | 0.731806 | ||||||||
\(359\) | − | 150.308i | − | 0.418686i | −0.977842 | − | 0.209343i | \(-0.932868\pi\) | ||
0.977842 | − | 0.209343i | \(-0.0671324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.8039 | 0.143501 | ||||||||
\(362\) | − | 207.001i | − | 0.571826i | ||||||
\(363\) | −14.6560 | + | 30.8434i | −0.0403747 | + | 0.0849680i | ||||
\(364\) | −63.4649 | −0.174354 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −205.054 | − | 97.4369i | −0.560258 | − | 0.266221i | ||||
\(367\) | −382.992 | −1.04357 | −0.521787 | − | 0.853076i | \(-0.674735\pi\) | ||||
−0.521787 | + | 0.853076i | \(0.674735\pi\) | |||||||
\(368\) | 30.8629i | 0.0838665i | ||||||||
\(369\) | −366.920 | + | 298.913i | −0.994364 | + | 0.810062i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 113.145i | − | 0.304974i | ||||||
\(372\) | −91.4384 | + | 192.431i | −0.245802 | + | 0.517287i | ||||
\(373\) | −80.3409 | −0.215391 | −0.107696 | − | 0.994184i | \(-0.534347\pi\) | ||||
−0.107696 | + | 0.994184i | \(0.534347\pi\) | |||||||
\(374\) | − | 431.067i | − | 1.15259i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −240.988 | −0.640927 | ||||||||
\(377\) | 568.558i | 1.50811i | ||||||||
\(378\) | −24.0159 | − | 98.1287i | −0.0635341 | − | 0.259600i | ||||
\(379\) | 636.088 | 1.67833 | 0.839166 | − | 0.543875i | \(-0.183044\pi\) | ||||
0.839166 | + | 0.543875i | \(0.183044\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −208.734 | + | 439.277i | −0.547858 | + | 1.15296i | ||||
\(382\) | 118.056 | 0.309046 | ||||||||
\(383\) | 343.675i | 0.897323i | 0.893702 | + | 0.448661i | \(0.148099\pi\) | ||||
−0.893702 | + | 0.448661i | \(0.851901\pi\) | |||||||
\(384\) | 30.6562 | + | 14.5671i | 0.0798338 | + | 0.0379351i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 125.164i | 0.324260i | ||||||||
\(387\) | −89.6021 | − | 109.988i | −0.231530 | − | 0.284207i | ||||
\(388\) | 130.267 | 0.335741 | ||||||||
\(389\) | − | 520.410i | − | 1.33782i | −0.743345 | − | 0.668908i | \(-0.766762\pi\) | ||
0.743345 | − | 0.668908i | \(-0.233238\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −224.630 | −0.574500 | ||||||||
\(392\) | − | 19.7990i | − | 0.0505076i | ||||||
\(393\) | −134.333 | − | 63.8316i | −0.341813 | − | 0.162421i | ||||
\(394\) | −52.2330 | −0.132571 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −146.110 | + | 119.029i | −0.368964 | + | 0.300578i | ||||
\(397\) | −184.320 | −0.464281 | −0.232140 | − | 0.972682i | \(-0.574573\pi\) | ||||
−0.232140 | + | 0.972682i | \(0.574573\pi\) | |||||||
\(398\) | 290.057i | 0.728787i | ||||||||
\(399\) | −69.2131 | + | 145.658i | −0.173466 | + | 0.365057i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 10.1322i | − | 0.0252674i | −0.999920 | − | 0.0126337i | \(-0.995978\pi\) | ||
0.999920 | − | 0.0126337i | \(-0.00402154\pi\) | |||||||
\(402\) | 105.904 | + | 50.3230i | 0.263443 | + | 0.125182i | ||||
\(403\) | 425.879 | 1.05677 | ||||||||
\(404\) | 342.338i | 0.847372i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −177.372 | −0.436876 | ||||||||
\(407\) | 608.199i | 1.49435i | ||||||||
\(408\) | −106.024 | + | 223.125i | −0.259862 | + | 0.546876i | ||||
\(409\) | 802.483 | 1.96206 | 0.981031 | − | 0.193853i | \(-0.0620985\pi\) | ||||
0.981031 | + | 0.193853i | \(0.0620985\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 576.399 | + | 273.891i | 1.40243 | + | 0.666402i | ||||
\(412\) | 259.758 | 0.630481 | ||||||||
\(413\) | − | 100.477i | − | 0.243287i | ||||||
\(414\) | 62.0261 | + | 76.1380i | 0.149822 | + | 0.183908i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 67.8468i | − | 0.163093i | ||||||
\(417\) | 95.4918 | − | 200.961i | 0.228997 | − | 0.481921i | ||||
\(418\) | 300.834 | 0.719697 | ||||||||
\(419\) | 27.2524i | 0.0650414i | 0.999471 | + | 0.0325207i | \(0.0103535\pi\) | ||||
−0.999471 | + | 0.0325207i | \(0.989647\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 792.513 | 1.88245 | 0.941227 | − | 0.337775i | \(-0.109674\pi\) | ||||
0.941227 | + | 0.337775i | \(0.109674\pi\) | |||||||
\(422\) | 69.9793i | 0.165828i | ||||||||
\(423\) | −594.513 | + | 484.322i | −1.40547 | + | 1.14497i | ||||
\(424\) | 120.957 | 0.285277 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −105.737 | + | 222.521i | −0.248208 | + | 0.522349i | ||||
\(427\) | −141.576 | −0.331560 | ||||||||
\(428\) | − | 58.3254i | − | 0.136274i | ||||||
\(429\) | 340.257 | + | 161.682i | 0.793139 | + | 0.376880i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 483.889i | 1.12271i | 0.827574 | + | 0.561357i | \(0.189720\pi\) | ||||
−0.827574 | + | 0.561357i | \(0.810280\pi\) | |||||||
\(432\) | 104.904 | − | 25.6741i | 0.242833 | − | 0.0594307i | ||||
\(433\) | −567.937 | −1.31163 | −0.655816 | − | 0.754920i | \(-0.727675\pi\) | ||||
−0.655816 | + | 0.754920i | \(0.727675\pi\) | |||||||
\(434\) | 132.860i | 0.306130i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.6592 | 0.0886680 | ||||||||
\(437\) | − | 156.765i | − | 0.358729i | ||||||
\(438\) | −259.842 | − | 123.471i | −0.593246 | − | 0.281896i | ||||
\(439\) | −834.645 | −1.90124 | −0.950621 | − | 0.310355i | \(-0.899552\pi\) | ||||
−0.950621 | + | 0.310355i | \(0.899552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.7907 | − | 48.8437i | −0.0902283 | − | 0.110757i | ||||
\(442\) | 493.810 | 1.11722 | ||||||||
\(443\) | − | 543.969i | − | 1.22792i | −0.789337 | − | 0.613960i | \(-0.789576\pi\) | ||
0.789337 | − | 0.613960i | \(-0.210424\pi\) | |||||||
\(444\) | 149.590 | − | 314.810i | 0.336915 | − | 0.709033i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 2.40315i | − | 0.00538823i | ||||||
\(447\) | −62.7550 | − | 29.8197i | −0.140392 | − | 0.0667107i | ||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | 308.306i | 0.686649i | 0.939217 | + | 0.343325i | \(0.111553\pi\) | ||||
−0.939217 | + | 0.343325i | \(0.888447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 550.555 | 1.22074 | ||||||||
\(452\) | − | 57.1137i | − | 0.126358i | ||||||
\(453\) | −96.7560 | + | 203.622i | −0.213589 | + | 0.449496i | ||||
\(454\) | −292.700 | −0.644713 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −155.715 | − | 73.9919i | −0.341480 | − | 0.162263i | ||||
\(457\) | −475.765 | −1.04106 | −0.520530 | − | 0.853843i | \(-0.674266\pi\) | ||||
−0.520530 | + | 0.853843i | \(0.674266\pi\) | |||||||
\(458\) | 9.93545i | 0.0216931i | ||||||||
\(459\) | 186.864 | + | 763.524i | 0.407111 | + | 1.66345i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 764.494i | − | 1.65834i | −0.558998 | − | 0.829169i | \(-0.688814\pi\) | ||
0.558998 | − | 0.829169i | \(-0.311186\pi\) | |||||||
\(462\) | −50.4395 | + | 106.149i | −0.109176 | + | 0.229760i | ||||
\(463\) | −558.506 | −1.20628 | −0.603138 | − | 0.797637i | \(-0.706083\pi\) | ||||
−0.603138 | + | 0.797637i | \(0.706083\pi\) | |||||||
\(464\) | − | 189.618i | − | 0.408661i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −164.999 | −0.354075 | ||||||||
\(467\) | 251.321i | 0.538160i | 0.963118 | + | 0.269080i | \(0.0867196\pi\) | ||||
−0.963118 | + | 0.269080i | \(0.913280\pi\) | |||||||
\(468\) | −136.354 | − | 167.376i | −0.291354 | − | 0.357642i | ||||
\(469\) | 73.1196 | 0.155905 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −85.8761 | + | 180.725i | −0.182327 | + | 0.383705i | ||||
\(472\) | 107.415 | 0.227574 | ||||||||
\(473\) | 165.034i | 0.348910i | ||||||||
\(474\) | 73.9556 | + | 35.1419i | 0.156024 | + | 0.0741391i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 154.053i | 0.323641i | ||||||||
\(477\) | 298.399 | − | 243.092i | 0.625575 | − | 0.509627i | ||||
\(478\) | 222.199 | 0.464852 | ||||||||
\(479\) | 343.617i | 0.717363i | 0.933460 | + | 0.358681i | \(0.116774\pi\) | ||||
−0.933460 | + | 0.358681i | \(0.883226\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −696.724 | −1.44849 | ||||||||
\(482\) | − | 405.925i | − | 0.842169i | ||||||
\(483\) | 55.3144 | + | 26.2841i | 0.114523 | + | 0.0544184i | ||||
\(484\) | −22.7656 | −0.0470363 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 207.198 | − | 274.166i | 0.426333 | − | 0.564128i | ||||
\(487\) | −909.858 | −1.86829 | −0.934146 | − | 0.356892i | \(-0.883837\pi\) | ||||
−0.934146 | + | 0.356892i | \(0.883837\pi\) | |||||||
\(488\) | − | 151.351i | − | 0.310146i | ||||||
\(489\) | 320.366 | − | 674.206i | 0.655146 | − | 1.37874i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 584.882i | − | 1.19121i | −0.803279 | − | 0.595603i | \(-0.796913\pi\) | ||
0.803279 | − | 0.595603i | \(-0.203087\pi\) | |||||||
\(492\) | −284.973 | − | 135.413i | −0.579214 | − | 0.275229i | ||||
\(493\) | 1380.10 | 2.79940 | ||||||||
\(494\) | 344.621i | 0.697612i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −142.034 | −0.286358 | ||||||||
\(497\) | 153.636i | 0.309126i | ||||||||
\(498\) | 61.3634 | − | 129.138i | 0.123220 | − | 0.259314i | ||||
\(499\) | −903.199 | −1.81002 | −0.905009 | − | 0.425392i | \(-0.860136\pi\) | ||||
−0.905009 | + | 0.425392i | \(0.860136\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −249.348 | − | 118.484i | −0.497700 | − | 0.236495i | ||||
\(502\) | −227.768 | −0.453720 | ||||||||
\(503\) | − | 188.576i | − | 0.374903i | −0.982274 | − | 0.187452i | \(-0.939977\pi\) | ||
0.982274 | − | 0.187452i | \(-0.0600228\pi\) | |||||||
\(504\) | 52.2161 | − | 42.5380i | 0.103603 | − | 0.0844008i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 114.243i | − | 0.225777i | ||||||
\(507\) | 32.3827 | − | 68.1488i | 0.0638711 | − | 0.134416i | ||||
\(508\) | −324.232 | −0.638252 | ||||||||
\(509\) | 526.061i | 1.03352i | 0.856131 | + | 0.516759i | \(0.172862\pi\) | ||||
−0.856131 | + | 0.516759i | \(0.827138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −179.403 | −0.351083 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −532.849 | + | 130.409i | −1.03869 | + | 0.254208i | ||||
\(514\) | 504.732 | 0.981970 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 40.5912 | − | 85.4236i | 0.0786652 | − | 0.165550i | ||||
\(517\) | 892.053 | 1.72544 | ||||||||
\(518\) | − | 217.355i | − | 0.419605i | ||||||
\(519\) | 632.630 | + | 300.611i | 1.21894 | + | 0.579211i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 636.046i | 1.22082i | 0.792087 | + | 0.610408i | \(0.208995\pi\) | ||||
−0.792087 | + | 0.610408i | \(0.791005\pi\) | |||||||
\(522\) | −381.082 | − | 467.784i | −0.730043 | − | 0.896139i | ||||
\(523\) | 662.926 | 1.26755 | 0.633773 | − | 0.773519i | \(-0.281506\pi\) | ||||
0.633773 | + | 0.773519i | \(0.281506\pi\) | |||||||
\(524\) | − | 99.1513i | − | 0.189220i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −178.557 | −0.339461 | ||||||||
\(527\) | − | 1033.77i | − | 1.96161i | ||||||
\(528\) | −113.478 | − | 53.9221i | −0.214921 | − | 0.102125i | ||||
\(529\) | 469.468 | 0.887463 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 264.990 | − | 215.875i | 0.499040 | − | 0.406545i | ||||
\(532\) | −107.511 | −0.202087 | ||||||||
\(533\) | 630.690i | 1.18328i | ||||||||
\(534\) | 85.2765 | − | 179.463i | 0.159694 | − | 0.336073i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 78.1681i | 0.145836i | ||||||||
\(537\) | 501.969 | + | 238.523i | 0.934765 | + | 0.444178i | ||||
\(538\) | 503.912 | 0.936639 | ||||||||
\(539\) | 73.2888i | 0.135972i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −299.602 | −0.553793 | −0.276897 | − | 0.960900i | \(-0.589306\pi\) | ||||
−0.276897 | + | 0.960900i | \(0.589306\pi\) | |||||||
\(542\) | − | 597.630i | − | 1.10264i | ||||||
\(543\) | 188.462 | − | 396.616i | 0.347076 | − | 0.730416i | ||||
\(544\) | −164.689 | −0.302738 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −121.599 | − | 57.7811i | −0.222709 | − | 0.105826i | ||||
\(547\) | −177.699 | −0.324862 | −0.162431 | − | 0.986720i | \(-0.551933\pi\) | ||||
−0.162431 | + | 0.986720i | \(0.551933\pi\) | |||||||
\(548\) | 425.442i | 0.776354i | ||||||||
\(549\) | −304.176 | − | 373.380i | −0.554054 | − | 0.680110i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 963.147i | 1.74800i | ||||||||
\(552\) | −28.0989 | + | 59.1336i | −0.0509037 | + | 0.107126i | ||||
\(553\) | 51.0613 | 0.0923351 | ||||||||
\(554\) | − | 378.131i | − | 0.682546i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 148.330 | 0.266780 | ||||||||
\(557\) | − | 227.747i | − | 0.408882i | −0.978879 | − | 0.204441i | \(-0.934462\pi\) | ||
0.978879 | − | 0.204441i | \(-0.0655377\pi\) | |||||||
\(558\) | −350.394 | + | 285.450i | −0.627946 | + | 0.511559i | ||||
\(559\) | −189.055 | −0.338203 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 392.462 | − | 825.930i | 0.699575 | − | 1.47225i | ||||
\(562\) | 590.392 | 1.05052 | ||||||||
\(563\) | 271.221i | 0.481742i | 0.970557 | + | 0.240871i | \(0.0774330\pi\) | ||||
−0.970557 | + | 0.240871i | \(0.922567\pi\) | |||||||
\(564\) | −461.736 | − | 219.406i | −0.818682 | − | 0.389018i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 79.4479i | − | 0.140367i | ||||||
\(567\) | 43.3258 | − | 209.881i | 0.0764123 | − | 0.370160i | ||||
\(568\) | −164.243 | −0.289161 | ||||||||
\(569\) | − | 63.1031i | − | 0.110902i | −0.998461 | − | 0.0554509i | \(-0.982340\pi\) | ||
0.998461 | − | 0.0554509i | \(-0.0176596\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 130.175 | 0.227977 | 0.113988 | − | 0.993482i | \(-0.463637\pi\) | ||||
0.113988 | + | 0.993482i | \(0.463637\pi\) | |||||||
\(572\) | 251.144i | 0.439064i | ||||||||
\(573\) | 226.196 | + | 107.483i | 0.394757 | + | 0.187579i | ||||
\(574\) | −196.755 | −0.342779 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 45.4751 | + | 55.8213i | 0.0789497 | + | 0.0969120i | ||||
\(577\) | −371.832 | −0.644424 | −0.322212 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322212 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(578\) | − | 789.954i | − | 1.36670i | ||||||
\(579\) | −113.955 | + | 239.816i | −0.196813 | + | 0.414190i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 89.1612i | − | 0.153462i | ||||||
\(582\) | 249.594 | + | 118.601i | 0.428855 | + | 0.203782i | ||||
\(583\) | −447.741 | −0.767995 | ||||||||
\(584\) | − | 191.790i | − | 0.328408i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −50.7233 | −0.0865586 | ||||||||
\(587\) | 824.490i | 1.40458i | 0.711890 | + | 0.702291i | \(0.247840\pi\) | ||||
−0.711890 | + | 0.702291i | \(0.752160\pi\) | |||||||
\(588\) | 18.0258 | − | 37.9351i | 0.0306562 | − | 0.0645154i | ||||
\(589\) | 721.445 | 1.22486 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −100.079 | − | 47.5551i | −0.169338 | − | 0.0804655i | ||||
\(592\) | 232.363 | 0.392504 | ||||||||
\(593\) | 148.957i | 0.251192i | 0.992081 | + | 0.125596i | \(0.0400843\pi\) | ||||
−0.992081 | + | 0.125596i | \(0.959916\pi\) | |||||||
\(594\) | −388.317 | + | 95.0361i | −0.653732 | + | 0.159994i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 46.3197i | − | 0.0777176i | ||||||
\(597\) | −264.080 | + | 555.752i | −0.442345 | + | 0.930909i | ||||
\(598\) | 130.872 | 0.218849 | ||||||||
\(599\) | 98.6062i | 0.164618i | 0.996607 | + | 0.0823090i | \(0.0262294\pi\) | ||||
−0.996607 | + | 0.0823090i | \(0.973771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 244.192 | 0.406310 | 0.203155 | − | 0.979147i | \(-0.434880\pi\) | ||||
0.203155 | + | 0.979147i | \(0.434880\pi\) | |||||||
\(602\) | − | 58.9792i | − | 0.0979721i | ||||||
\(603\) | 157.097 | + | 192.839i | 0.260526 | + | 0.319799i | ||||
\(604\) | −150.294 | −0.248831 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −311.679 | + | 655.924i | −0.514322 | + | 1.08238i | ||||
\(607\) | 504.707 | 0.831478 | 0.415739 | − | 0.909484i | \(-0.363523\pi\) | ||||
0.415739 | + | 0.909484i | \(0.363523\pi\) | |||||||
\(608\) | − | 114.934i | − | 0.189035i | ||||||
\(609\) | −339.846 | − | 161.487i | −0.558040 | − | 0.265167i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1021.89i | 1.67249i | ||||||||
\(612\) | −406.285 | + | 330.982i | −0.663865 | + | 0.540820i | ||||
\(613\) | −416.536 | −0.679503 | −0.339752 | − | 0.940515i | \(-0.610343\pi\) | ||||
−0.339752 | + | 0.940515i | \(0.610343\pi\) | |||||||
\(614\) | − | 702.259i | − | 1.14374i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −78.3490 | −0.127190 | ||||||||
\(617\) | 132.241i | 0.214330i | 0.994241 | + | 0.107165i | \(0.0341773\pi\) | ||||
−0.994241 | + | 0.107165i | \(0.965823\pi\) | |||||||
\(618\) | 497.699 | + | 236.495i | 0.805338 | + | 0.382677i | ||||
\(619\) | −669.449 | −1.08150 | −0.540751 | − | 0.841183i | \(-0.681860\pi\) | ||||
−0.540751 | + | 0.841183i | \(0.681860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 49.5234 | + | 202.352i | 0.0797479 | + | 0.325849i | ||||
\(622\) | −70.0059 | −0.112550 | ||||||||
\(623\) | − | 123.907i | − | 0.198888i | ||||||
\(624\) | 61.7706 | − | 129.995i | 0.0989913 | − | 0.208326i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 309.955i | − | 0.495137i | ||||||
\(627\) | 576.400 | + | 273.891i | 0.919299 | + | 0.436829i | ||||
\(628\) | −133.394 | −0.212410 | ||||||||
\(629\) | 1691.21i | 2.68873i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 590.546 | 0.935889 | 0.467944 | − | 0.883758i | \(-0.344995\pi\) | ||||
0.467944 | + | 0.883758i | \(0.344995\pi\) | |||||||
\(632\) | 54.5869i | 0.0863716i | ||||||||
\(633\) | −63.7121 | + | 134.081i | −0.100651 | + | 0.211819i | ||||
\(634\) | 136.191 | 0.214812 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 231.756 | + | 110.125i | 0.364396 | + | 0.173152i | ||||
\(637\) | −83.9561 | −0.131799 | ||||||||
\(638\) | 701.900i | 1.10016i | ||||||||
\(639\) | −405.185 | + | 330.085i | −0.634092 | + | 0.516565i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 542.271i | − | 0.845977i | −0.906135 | − | 0.422989i | \(-0.860981\pi\) | ||
0.906135 | − | 0.422989i | \(-0.139019\pi\) | |||||||
\(642\) | 53.1019 | − | 111.752i | 0.0827132 | − | 0.174069i | ||||
\(643\) | 546.024 | 0.849181 | 0.424591 | − | 0.905385i | \(-0.360418\pi\) | ||||
0.424591 | + | 0.905385i | \(0.360418\pi\) | |||||||
\(644\) | 40.8277i | 0.0633971i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 836.523 | 1.29493 | ||||||||
\(647\) | − | 801.011i | − | 1.23804i | −0.785376 | − | 0.619020i | \(-0.787530\pi\) | ||
0.785376 | − | 0.619020i | \(-0.212470\pi\) | |||||||
\(648\) | 224.372 | + | 46.3172i | 0.346253 | + | 0.0714772i | ||||
\(649\) | −397.611 | −0.612652 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −120.962 | + | 254.562i | −0.185809 | + | 0.391032i | ||||
\(652\) | 497.633 | 0.763241 | ||||||||
\(653\) | − | 1193.82i | − | 1.82821i | −0.405482 | − | 0.914103i | \(-0.632896\pi\) | ||
0.405482 | − | 0.914103i | \(-0.367104\pi\) | |||||||
\(654\) | 74.0715 | + | 35.1970i | 0.113259 | + | 0.0538180i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 210.340i | − | 0.320640i | ||||||
\(657\) | −385.447 | − | 473.142i | −0.586677 | − | 0.720155i | ||||
\(658\) | −318.798 | −0.484495 | ||||||||
\(659\) | − | 1234.84i | − | 1.87381i | −0.349579 | − | 0.936907i | \(-0.613675\pi\) | ||
0.349579 | − | 0.936907i | \(-0.386325\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −660.309 | −0.998954 | −0.499477 | − | 0.866327i | \(-0.666475\pi\) | ||||
−0.499477 | + | 0.866327i | \(0.666475\pi\) | |||||||
\(662\) | 761.845i | 1.15082i | ||||||||
\(663\) | 946.146 | + | 449.586i | 1.42707 | + | 0.678108i | ||||
\(664\) | 95.3174 | 0.143550 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 573.233 | − | 466.987i | 0.860711 | − | 0.701181i | ||||
\(667\) | 365.761 | 0.548367 | ||||||||
\(668\) | − | 184.044i | − | 0.275516i | ||||||
\(669\) | 2.18793 | − | 4.60446i | 0.00327045 | − | 0.00688260i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 560.248i | 0.834945i | ||||||||
\(672\) | 40.5543 | + | 19.2704i | 0.0603487 | + | 0.0286762i | ||||
\(673\) | 372.706 | 0.553798 | 0.276899 | − | 0.960899i | \(-0.410693\pi\) | ||||
0.276899 | + | 0.960899i | \(0.410693\pi\) | |||||||
\(674\) | − | 286.711i | − | 0.425387i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 50.3009 | 0.0744096 | ||||||||
\(677\) | − | 762.928i | − | 1.12693i | −0.826142 | − | 0.563463i | \(-0.809469\pi\) | ||
0.826142 | − | 0.563463i | \(-0.190531\pi\) | |||||||
\(678\) | 51.9987 | − | 109.430i | 0.0766942 | − | 0.161402i | ||||
\(679\) | 172.328 | 0.253796 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −560.816 | − | 266.486i | −0.823518 | − | 0.391316i | ||||
\(682\) | 525.758 | 0.770906 | ||||||||
\(683\) | 28.2779i | 0.0414024i | 0.999786 | + | 0.0207012i | \(0.00658987\pi\) | ||||
−0.999786 | + | 0.0207012i | \(0.993410\pi\) | |||||||
\(684\) | −230.986 | − | 283.538i | −0.337698 | − | 0.414530i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | −9.04565 | + | 19.0364i | −0.0131669 | + | 0.0277095i | ||||
\(688\) | 63.0514 | 0.0916445 | ||||||||
\(689\) | − | 512.911i | − | 0.744428i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −587.034 | −0.849543 | −0.424771 | − | 0.905301i | \(-0.639645\pi\) | ||||
−0.424771 | + | 0.905301i | \(0.639645\pi\) | |||||||
\(692\) | 466.946i | 0.674778i | ||||||||
\(693\) | −193.285 | + | 157.460i | −0.278911 | + | 0.227216i | ||||
\(694\) | −196.591 | −0.283272 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 172.637 | − | 363.311i | 0.248041 | − | 0.521999i | ||||
\(697\) | 1530.92 | 2.19644 | ||||||||
\(698\) | − | 640.616i | − | 0.917787i | ||||||
\(699\) | −316.140 | − | 150.222i | −0.452274 | − | 0.214910i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 221.461i | 0.315922i | 0.987445 | + | 0.157961i | \(0.0504920\pi\) | ||||
−0.987445 | + | 0.157961i | \(0.949508\pi\) | |||||||
\(702\) | −108.869 | − | 444.837i | −0.155084 | − | 0.633671i | ||||
\(703\) | −1180.26 | −1.67889 | ||||||||
\(704\) | − | 83.7586i | − | 0.118975i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −641.344 | −0.908419 | ||||||||
\(707\) | 452.871i | 0.640553i | ||||||||
\(708\) | 205.808 | + | 97.7950i | 0.290689 | + | 0.138129i | ||||
\(709\) | 1187.65 | 1.67511 | 0.837553 | − | 0.546356i | \(-0.183986\pi\) | ||||
0.837553 | + | 0.546356i | \(0.183986\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 109.705 | + | 134.665i | 0.154297 | + | 0.189402i | ||||
\(712\) | 132.462 | 0.186043 | ||||||||
\(713\) | − | 273.973i | − | 0.384254i | ||||||
\(714\) | −140.256 | + | 295.167i | −0.196437 | + | 0.413399i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 370.505i | 0.517465i | ||||||||
\(717\) | 425.736 | + | 202.300i | 0.593774 | + | 0.282147i | ||||
\(718\) | 212.568 | 0.296055 | ||||||||
\(719\) | 611.937i | 0.851095i | 0.904936 | + | 0.425547i | \(0.139918\pi\) | ||||
−0.904936 | + | 0.425547i | \(0.860082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 343.628 | 0.476599 | ||||||||
\(722\) | 73.2618i | 0.101471i | ||||||||
\(723\) | 369.571 | − | 777.757i | 0.511164 | − | 1.07574i | ||||
\(724\) | 292.744 | 0.404342 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −43.6191 | − | 20.7268i | −0.0600814 | − | 0.0285492i | ||||
\(727\) | 1136.33 | 1.56304 | 0.781520 | − | 0.623881i | \(-0.214445\pi\) | ||||
0.781520 | + | 0.623881i | \(0.214445\pi\) | |||||||
\(728\) | − | 89.7529i | − | 0.123287i | ||||||
\(729\) | 646.605 | − | 336.664i | 0.886976 | − | 0.461816i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 458.908i | 0.627781i | ||||||||
\(732\) | 137.797 | − | 289.991i | 0.188247 | − | 0.396162i | ||||
\(733\) | 401.450 | 0.547681 | 0.273840 | − | 0.961775i | \(-0.411706\pi\) | ||||
0.273840 | + | 0.961775i | \(0.411706\pi\) | |||||||
\(734\) | − | 541.632i | − | 0.737919i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −43.6467 | −0.0593026 | ||||||||
\(737\) | − | 289.350i | − | 0.392606i | ||||||
\(738\) | −422.727 | − | 518.904i | −0.572801 | − | 0.703121i | ||||
\(739\) | 75.9398 | 0.102760 | 0.0513801 | − | 0.998679i | \(-0.483638\pi\) | ||||
0.0513801 | + | 0.998679i | \(0.483638\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −313.757 | + | 660.297i | −0.423424 | + | 0.891088i | ||||
\(742\) | 160.012 | 0.215649 | ||||||||
\(743\) | − | 308.906i | − | 0.415755i | −0.978155 | − | 0.207877i | \(-0.933345\pi\) | ||
0.978155 | − | 0.207877i | \(-0.0666555\pi\) | |||||||
\(744\) | −272.138 | − | 129.313i | −0.365777 | − | 0.173808i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 113.619i | − | 0.152305i | ||||||
\(747\) | 235.146 | − | 191.562i | 0.314787 | − | 0.256442i | ||||
\(748\) | 609.621 | 0.815002 | ||||||||
\(749\) | − | 77.1572i | − | 0.103014i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 629.294 | 0.837941 | 0.418971 | − | 0.908000i | \(-0.362391\pi\) | ||||
0.418971 | + | 0.908000i | \(0.362391\pi\) | |||||||
\(752\) | − | 340.809i | − | 0.453204i | ||||||
\(753\) | −436.405 | − | 207.369i | −0.579555 | − | 0.275391i | ||||
\(754\) | −804.063 | −1.06640 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 138.775 | − | 33.9636i | 0.183565 | − | 0.0449254i | ||||
\(757\) | 526.381 | 0.695351 | 0.347676 | − | 0.937615i | \(-0.386971\pi\) | ||||
0.347676 | + | 0.937615i | \(0.386971\pi\) | |||||||
\(758\) | 899.564i | 1.18676i | ||||||||
\(759\) | 104.012 | − | 218.891i | 0.137038 | − | 0.288394i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 955.908i | 1.25612i | 0.778164 | + | 0.628061i | \(0.216151\pi\) | ||||
−0.778164 | + | 0.628061i | \(0.783849\pi\) | |||||||
\(762\) | −621.232 | − | 295.194i | −0.815265 | − | 0.387394i | ||||
\(763\) | 51.1414 | 0.0670267 | ||||||||
\(764\) | 166.956i | 0.218529i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −486.029 | −0.634503 | ||||||||
\(767\) | − | 455.485i | − | 0.593852i | ||||||
\(768\) | −20.6010 | + | 43.3544i | −0.0268242 | + | 0.0564510i | ||||
\(769\) | −1062.16 | −1.38123 | −0.690613 | − | 0.723225i | \(-0.742659\pi\) | ||||
−0.690613 | + | 0.723225i | \(0.742659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 967.072 | + | 459.530i | 1.25431 | + | 0.596018i | ||||
\(772\) | −177.009 | −0.229287 | ||||||||
\(773\) | − | 548.202i | − | 0.709188i | −0.935020 | − | 0.354594i | \(-0.884619\pi\) | ||
0.935020 | − | 0.354594i | \(-0.115381\pi\) | |||||||
\(774\) | 155.546 | − | 126.717i | 0.200964 | − | 0.163716i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 184.226i | 0.237405i | ||||||||
\(777\) | 197.889 | − | 416.455i | 0.254684 | − | 0.535978i | ||||
\(778\) | 735.971 | 0.945979 | ||||||||
\(779\) | 1068.40i | 1.37150i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 607.970 | 0.778451 | ||||||||
\(782\) | − | 317.674i | − | 0.406233i | ||||||
\(783\) | −304.267 | − | 1243.23i | −0.388592 | − | 1.58778i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 90.2715 | − | 189.975i | 0.114849 | − | 0.241698i | ||||
\(787\) | 590.574 | 0.750412 | 0.375206 | − | 0.926942i | \(-0.377572\pi\) | ||||
0.375206 | + | 0.926942i | \(0.377572\pi\) | |||||||
\(788\) | − | 73.8686i | − | 0.0937419i | ||||||
\(789\) | −342.117 | − | 162.566i | −0.433608 | − | 0.206040i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 75.5543i | − | 0.0955174i | ||||||
\(792\) | −168.332 | − | 206.631i | −0.212541 | − | 0.260897i | ||||
\(793\) | −641.794 | −0.809324 | ||||||||
\(794\) | − | 260.667i | − | 0.328296i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −410.203 | −0.515330 | ||||||||
\(797\) | − | 913.353i | − | 1.14599i | −0.819560 | − | 0.572994i | \(-0.805782\pi\) | ||
0.819560 | − | 0.572994i | \(-0.194218\pi\) | |||||||
\(798\) | −205.991 | − | 97.8821i | −0.258134 | − | 0.122659i | ||||
\(799\) | 2480.52 | 3.10453 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 326.781 | − | 266.214i | 0.407967 | − | 0.332352i | ||||
\(802\) | 14.3292 | 0.0178668 | ||||||||
\(803\) | 709.938i | 0.884107i | ||||||||
\(804\) | −71.1675 | + | 149.771i | −0.0885168 | + | 0.186282i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 602.283i | 0.747250i | ||||||||
\(807\) | 965.500 | + | 458.782i | 1.19641 | + | 0.568504i | ||||
\(808\) | −484.139 | −0.599182 | ||||||||
\(809\) | − | 287.495i | − | 0.355370i | −0.984087 | − | 0.177685i | \(-0.943139\pi\) | ||
0.984087 | − | 0.177685i | \(-0.0568609\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 319.747 | 0.394262 | 0.197131 | − | 0.980377i | \(-0.436838\pi\) | ||||
0.197131 | + | 0.980377i | \(0.436838\pi\) | |||||||
\(812\) | − | 250.842i | − | 0.308918i | ||||||
\(813\) | 544.107 | − | 1145.06i | 0.669258 | − | 1.40844i | ||||
\(814\) | −860.123 | −1.05666 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −315.547 | − | 149.940i | −0.386699 | − | 0.183750i | ||||
\(817\) | −320.263 | −0.391999 | ||||||||
\(818\) | 1134.88i | 1.38739i | ||||||||
\(819\) | −180.379 | − | 221.418i | −0.220243 | − | 0.270352i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1361.35i | − | 1.65816i | −0.559130 | − | 0.829080i | \(-0.688865\pi\) | ||
0.559130 | − | 0.829080i | \(-0.311135\pi\) | |||||||
\(822\) | −387.340 | + | 815.152i | −0.471217 | + | 0.991669i | ||||
\(823\) | −68.4196 | −0.0831344 | −0.0415672 | − | 0.999136i | \(-0.513235\pi\) | ||||
−0.0415672 | + | 0.999136i | \(0.513235\pi\) | |||||||
\(824\) | 367.353i | 0.445817i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 142.097 | 0.172030 | ||||||||
\(827\) | − | 1072.36i | − | 1.29668i | −0.761349 | − | 0.648342i | \(-0.775463\pi\) | ||
0.761349 | − | 0.648342i | \(-0.224537\pi\) | |||||||
\(828\) | −107.675 | + | 87.7182i | −0.130043 | + | 0.105940i | ||||
\(829\) | 970.657 | 1.17088 | 0.585438 | − | 0.810717i | \(-0.300922\pi\) | ||||
0.585438 | + | 0.810717i | \(0.300922\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 344.266 | − | 724.502i | 0.414279 | − | 0.871844i | ||||
\(832\) | 95.9498 | 0.115324 | ||||||||
\(833\) | 203.793i | 0.244649i | ||||||||
\(834\) | 284.202 | + | 135.046i | 0.340769 | + | 0.161925i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 425.443i | 0.508903i | ||||||||
\(837\) | −931.244 | + | 227.911i | −1.11260 | + | 0.272296i | ||||
\(838\) | −38.5407 | −0.0459912 | ||||||||
\(839\) | 980.187i | 1.16828i | 0.811653 | + | 0.584140i | \(0.198568\pi\) | ||||
−0.811653 | + | 0.584140i | \(0.801432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1406.20 | −1.67206 | ||||||||
\(842\) | 1120.78i | 1.33110i | ||||||||
\(843\) | 1131.20 | + | 537.518i | 1.34187 | + | 0.637625i | ||||
\(844\) | −98.9657 | −0.117258 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −684.935 | − | 840.768i | −0.809616 | − | 0.993816i | ||||
\(847\) | −30.1160 | −0.0355561 | ||||||||
\(848\) | 171.060i | 0.201721i | ||||||||
\(849\) | 72.3327 | − | 152.223i | 0.0851975 | − | 0.179297i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 448.211i | 0.526688i | ||||||||
\(852\) | −314.692 | − | 149.534i | −0.369357 | − | 0.175509i | ||||
\(853\) | −34.7970 | −0.0407936 | −0.0203968 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203968 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(854\) | − | 200.219i | − | 0.234448i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 82.4845 | 0.0963605 | ||||||||
\(857\) | 79.5168i | 0.0927851i | 0.998923 | + | 0.0463926i | \(0.0147725\pi\) | ||||
−0.998923 | + | 0.0463926i | \(0.985227\pi\) | |||||||
\(858\) | −228.652 | + | 481.195i | −0.266495 | + | 0.560834i | ||||
\(859\) | 311.130 | 0.362200 | 0.181100 | − | 0.983465i | \(-0.442034\pi\) | ||||
0.181100 | + | 0.983465i | \(0.442034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −376.984 | − | 179.134i | −0.437845 | − | 0.208053i | ||||
\(862\) | −684.323 | −0.793878 | ||||||||
\(863\) | − | 145.121i | − | 0.168159i | −0.996459 | − | 0.0840796i | \(-0.973205\pi\) | ||
0.996459 | − | 0.0840796i | \(-0.0267950\pi\) | |||||||
\(864\) | 36.3086 | + | 148.357i | 0.0420238 | + | 0.171709i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 803.184i | − | 0.927465i | ||||||
\(867\) | 719.207 | − | 1513.56i | 0.829535 | − | 1.74574i | ||||
\(868\) | −187.893 | −0.216467 | ||||||||
\(869\) | − | 202.061i | − | 0.232521i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 331.466 | 0.380558 | ||||||||
\(872\) | 54.6724i | 0.0626977i | ||||||||
\(873\) | 370.245 | + | 454.481i | 0.424106 | + | 0.520597i | ||||
\(874\) | 221.699 | 0.253660 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 174.614 | − | 367.472i | 0.199331 | − | 0.419488i | ||||
\(877\) | −595.173 | −0.678647 | −0.339324 | − | 0.940670i | \(-0.610198\pi\) | ||||
−0.339324 | + | 0.940670i | \(0.610198\pi\) | |||||||
\(878\) | − | 1180.37i | − | 1.34438i | ||||||
\(879\) | −97.1865 | − | 46.1807i | −0.110565 | − | 0.0525377i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 321.893i | − | 0.365372i | −0.983171 | − | 0.182686i | \(-0.941521\pi\) | ||
0.983171 | − | 0.182686i | \(-0.0584792\pi\) | |||||||
\(882\) | 69.0754 | − | 56.2725i | 0.0783167 | − | 0.0638010i | ||||
\(883\) | 944.347 | 1.06948 | 0.534738 | − | 0.845018i | \(-0.320410\pi\) | ||||
0.534738 | + | 0.845018i | \(0.320410\pi\) | |||||||
\(884\) | 698.353i | 0.789992i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 769.288 | 0.868271 | ||||||||
\(887\) | 1184.20i | 1.33506i | 0.744584 | + | 0.667528i | \(0.232648\pi\) | ||||
−0.744584 | + | 0.667528i | \(0.767352\pi\) | |||||||
\(888\) | 445.209 | + | 211.553i | 0.501362 | + | 0.238235i | ||||
\(889\) | −428.919 | −0.482473 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −830.544 | − | 171.450i | −0.932148 | − | 0.192424i | ||||
\(892\) | 3.39857 | 0.00381005 | ||||||||
\(893\) | 1731.10i | 1.93853i | ||||||||
\(894\) | 42.1714 | − | 88.7490i | 0.0471716 | − | 0.0992718i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 250.751 | + | 119.151i | 0.279545 | + | 0.132833i | ||||
\(898\) | −436.010 | −0.485534 | ||||||||
\(899\) | 1683.26i | 1.87237i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1245.03 | −1.38183 | ||||||||
\(902\) | 778.603i | 0.863196i | ||||||||
\(903\) | 53.6972 | − | 113.005i | 0.0594653 | − | 0.125144i | ||||
\(904\) | 80.7709 | 0.0893484 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −287.964 | − | 136.834i | −0.317841 | − | 0.151031i | ||||
\(907\) | −291.663 | −0.321569 | −0.160785 | − | 0.986990i | \(-0.551402\pi\) | ||||
−0.160785 | + | 0.986990i | \(0.551402\pi\) | |||||||
\(908\) | − | 413.940i | − | 0.455881i | ||||||
\(909\) | −1194.36 | + | 972.991i | −1.31393 | + | 1.07040i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1318.03i | 1.44679i | 0.690434 | + | 0.723395i | \(0.257420\pi\) | ||||
−0.690434 | + | 0.723395i | \(0.742580\pi\) | |||||||
\(912\) | 104.640 | − | 220.214i | 0.114737 | − | 0.241463i | ||||
\(913\) | −352.831 | −0.386452 | ||||||||
\(914\) | − | 672.833i | − | 0.736141i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0509 | −0.0153394 | ||||||||
\(917\) | − | 131.165i | − | 0.143037i | ||||||
\(918\) | −1079.79 | + | 264.265i | −1.17624 | + | 0.287871i | ||||
\(919\) | 569.882 | 0.620111 | 0.310056 | − | 0.950718i | \(-0.399652\pi\) | ||||
0.310056 | + | 0.950718i | \(0.399652\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 639.366 | − | 1345.53i | 0.694208 | − | 1.46095i | ||||
\(922\) | 1081.16 | 1.17262 | ||||||||
\(923\) | 696.462i | 0.754563i | ||||||||
\(924\) | −150.117 | − | 71.3322i | −0.162465 | − | 0.0771994i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 789.847i | − | 0.852966i | ||||||
\(927\) | 738.282 | + | 906.252i | 0.796421 | + | 0.977618i | ||||
\(928\) | 268.161 | 0.288967 | ||||||||
\(929\) | − | 198.562i | − | 0.213737i | −0.994273 | − | 0.106869i | \(-0.965918\pi\) | ||
0.994273 | − | 0.106869i | \(-0.0340824\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −142.223 | −0.152764 | ||||||||
\(932\) | − | 233.344i | − | 0.250369i | ||||||
\(933\) | −134.132 | − | 63.7363i | −0.143764 | − | 0.0683133i | ||||
\(934\) | −355.421 | −0.380537 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 236.706 | − | 192.834i | 0.252891 | − | 0.206019i | ||||
\(937\) | −1307.73 | −1.39566 | −0.697828 | − | 0.716266i | \(-0.745850\pi\) | ||||
−0.697828 | + | 0.716266i | \(0.745850\pi\) | |||||||
\(938\) | 103.407i | 0.110242i | ||||||||
\(939\) | 282.196 | − | 593.878i | 0.300529 | − | 0.632458i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1542.60i | − | 1.63932i | −0.572853 | − | 0.819658i | \(-0.694163\pi\) | ||
0.572853 | − | 0.819658i | \(-0.305837\pi\) | |||||||
\(942\) | −255.584 | − | 121.447i | −0.271320 | − | 0.128925i | ||||
\(943\) | 405.731 | 0.430255 | ||||||||
\(944\) | 151.908i | 0.160919i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −233.394 | −0.246716 | ||||||||
\(947\) | − | 377.167i | − | 0.398276i | −0.979971 | − | 0.199138i | \(-0.936186\pi\) | ||
0.979971 | − | 0.199138i | \(-0.0638142\pi\) | |||||||
\(948\) | −49.6982 | + | 104.589i | −0.0524242 | + | 0.110326i | ||||
\(949\) | −813.271 | −0.856977 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 260.943 | + | 123.994i | 0.274388 | + | 0.130383i | ||||
\(952\) | −217.864 | −0.228848 | ||||||||
\(953\) | 673.763i | 0.706991i | 0.935436 | + | 0.353496i | \(0.115007\pi\) | ||||
−0.935436 | + | 0.353496i | \(0.884993\pi\) | |||||||
\(954\) | 343.784 | + | 422.000i | 0.360361 | + | 0.442348i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 314.237i | 0.328700i | ||||||||
\(957\) | −639.039 | + | 1344.85i | −0.667752 | + | 1.40527i | ||||
\(958\) | −485.947 | −0.507252 | ||||||||
\(959\) | 562.807i | 0.586869i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 299.849 | 0.312017 | ||||||||
\(962\) | − | 985.316i | − | 1.02424i | ||||||
\(963\) | 203.487 | − | 165.772i | 0.211306 | − | 0.172141i | ||||
\(964\) | 574.065 | 0.595503 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −37.1713 | + | 78.2264i | −0.0384796 | + | 0.0809797i | ||||
\(967\) | −1121.04 | −1.15929 | −0.579647 | − | 0.814867i | \(-0.696810\pi\) | ||||
−0.579647 | + | 0.814867i | \(0.696810\pi\) | |||||||
\(968\) | − | 32.1954i | − | 0.0332597i | ||||||
\(969\) | 1602.79 | + | 761.605i | 1.65406 | + | 0.785970i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1490.39i | − | 1.53490i | −0.641108 | − | 0.767451i | \(-0.721525\pi\) | ||
0.641108 | − | 0.767451i | \(-0.278475\pi\) | |||||||
\(972\) | 387.730 | + | 293.022i | 0.398899 | + | 0.301463i | ||||
\(973\) | 196.222 | 0.201667 | ||||||||
\(974\) | − | 1286.73i | − | 1.32108i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 214.043 | 0.219306 | ||||||||
\(977\) | 1171.66i | 1.19924i | 0.800284 | + | 0.599621i | \(0.204682\pi\) | ||||
−0.800284 | + | 0.599621i | \(0.795318\pi\) | |||||||
\(978\) | 953.471 | + | 453.066i | 0.974919 | + | 0.463258i | ||||
\(979\) | −490.328 | −0.500846 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 109.877 | + | 134.876i | 0.112005 | + | 0.137488i | ||||
\(982\) | 827.148 | 0.842309 | ||||||||
\(983\) | − | 1018.78i | − | 1.03639i | −0.855261 | − | 0.518197i | \(-0.826603\pi\) | ||
0.855261 | − | 0.518197i | \(-0.173397\pi\) | |||||||
\(984\) | 191.502 | − | 403.013i | 0.194616 | − | 0.409566i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1951.76i | 1.97947i | ||||||||
\(987\) | −610.820 | − | 290.247i | −0.618865 | − | 0.294070i | ||||
\(988\) | −487.367 | −0.493287 | ||||||||
\(989\) | 121.622i | 0.122974i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −240.455 | −0.242639 | −0.121320 | − | 0.992613i | \(-0.538713\pi\) | ||||
−0.121320 | + | 0.992613i | \(0.538713\pi\) | |||||||
\(992\) | − | 200.866i | − | 0.202486i | ||||||
\(993\) | −693.615 | + | 1459.70i | −0.698505 | + | 1.46999i | ||||
\(994\) | −217.274 | −0.218585 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 182.629 | + | 86.7809i | 0.183362 | + | 0.0871294i | ||||
\(997\) | −723.800 | −0.725978 | −0.362989 | − | 0.931793i | \(-0.618244\pi\) | ||||
−0.362989 | + | 0.931793i | \(0.618244\pi\) | |||||||
\(998\) | − | 1277.32i | − | 1.27988i | ||||||
\(999\) | 1523.49 | − | 372.856i | 1.52501 | − | 0.373229i |
(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 | 1050.3.e.e.701.3 | 24 | ||
3.2 | odd | 2 | inner | 1050.3.e.e.701.1 | 24 | ||
5.2 | odd | 4 | 210.3.c.a.29.10 | yes | 24 | ||
5.3 | odd | 4 | 210.3.c.a.29.15 | yes | 24 | ||
5.4 | even | 2 | inner | 1050.3.e.e.701.2 | 24 | ||
15.2 | even | 4 | 210.3.c.a.29.16 | yes | 24 | ||
15.8 | even | 4 | 210.3.c.a.29.9 | ✓ | 24 | ||
15.14 | odd | 2 | inner | 1050.3.e.e.701.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.9 | ✓ | 24 | 15.8 | even | 4 | ||
210.3.c.a.29.10 | yes | 24 | 5.2 | odd | 4 | ||
210.3.c.a.29.15 | yes | 24 | 5.3 | odd | 4 | ||
210.3.c.a.29.16 | yes | 24 | 15.2 | even | 4 | ||
1050.3.e.e.701.1 | 24 | 3.2 | odd | 2 | inner | ||
1050.3.e.e.701.2 | 24 | 5.4 | even | 2 | inner | ||
1050.3.e.e.701.3 | 24 | 1.1 | even | 1 | trivial | ||
1050.3.e.e.701.4 | 24 | 15.14 | odd | 2 | inner |