Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1200,3,Mod(193,1200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1200, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1200.193");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1200.bg (of order \(4\), degree \(2\), not 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: | \(32.6976317232\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1057.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1200.1057 |
Dual form | 1200.3.bg.c.193.2 |
$q$-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 \(\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(577\) | \(751\) | \(901\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.325765 | − | 0.325765i | −0.0465379 | − | 0.0465379i | 0.683455 | − | 0.729993i | \(-0.260477\pi\) |
−0.729993 | + | 0.683455i | \(0.760477\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.7980 | 1.07254 | 0.536271 | − | 0.844046i | \(-0.319833\pi\) | ||||
0.536271 | + | 0.844046i | \(0.319833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.67423 | − | 3.67423i | 0.282633 | − | 0.282633i | −0.551525 | − | 0.834158i | \(-0.685954\pi\) |
0.834158 | + | 0.551525i | \(0.185954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.3485 | + | 11.3485i | 0.667557 | + | 0.667557i | 0.957150 | − | 0.289593i | \(-0.0935199\pi\) |
−0.289593 | + | 0.957150i | \(0.593520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.3939i | 1.59968i | 0.600215 | + | 0.799839i | \(0.295082\pi\) | ||||
−0.600215 | + | 0.799839i | \(0.704918\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.797959 | −0.0379980 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.55051 | + | 9.55051i | −0.415240 | + | 0.415240i | −0.883559 | − | 0.468320i | \(-0.844860\pi\) |
0.468320 | + | 0.883559i | \(0.344860\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 15.3939i | − | 0.530823i | −0.964135 | − | 0.265412i | \(-0.914492\pi\) | ||
0.964135 | − | 0.265412i | \(-0.0855079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21.2020 | 0.683937 | 0.341968 | − | 0.939711i | \(-0.388906\pi\) | ||||
0.341968 | + | 0.939711i | \(0.388906\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 14.4495 | − | 14.4495i | 0.437863 | − | 0.437863i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10102 | + | 3.10102i | 0.0838114 | + | 0.0838114i | 0.747770 | − | 0.663958i | \(-0.231125\pi\) |
−0.663958 | + | 0.747770i | \(0.731125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 9.00000i | − | 0.230769i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18.2020 | 0.443952 | 0.221976 | − | 0.975052i | \(-0.428749\pi\) | ||||
0.221976 | + | 0.975052i | \(0.428749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19.4268 | + | 19.4268i | −0.451786 | + | 0.451786i | −0.895947 | − | 0.444161i | \(-0.853502\pi\) |
0.444161 | + | 0.895947i | \(0.353502\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −27.7526 | − | 27.7526i | −0.590480 | − | 0.590480i | 0.347281 | − | 0.937761i | \(-0.387105\pi\) |
−0.937761 | + | 0.347281i | \(0.887105\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 48.7878i | − | 0.995668i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 27.7980 | 0.545058 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 56.8990 | − | 56.8990i | 1.07357 | − | 1.07357i | 0.0764957 | − | 0.997070i | \(-0.475627\pi\) |
0.997070 | − | 0.0764957i | \(-0.0243732\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37.2247 | + | 37.2247i | 0.653066 | + | 0.653066i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 82.0000i | 1.38983i | 0.719092 | + | 0.694915i | \(0.244558\pi\) | ||||
−0.719092 | + | 0.694915i | \(0.755442\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 94.5959 | 1.55075 | 0.775376 | − | 0.631499i | \(-0.217560\pi\) | ||||
0.775376 | + | 0.631499i | \(0.217560\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.977296 | + | 0.977296i | −0.0155126 | + | 0.0155126i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.7298 | + | 12.7298i | 0.189998 | + | 0.189998i | 0.795695 | − | 0.605697i | \(-0.207106\pi\) |
−0.605697 | + | 0.795695i | \(0.707106\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 23.3939i | 0.339042i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 77.7980 | 1.09575 | 0.547873 | − | 0.836562i | \(-0.315438\pi\) | ||||
0.547873 | + | 0.836562i | \(0.315438\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 90.2929 | − | 90.2929i | 1.23689 | − | 1.23689i | 0.275622 | − | 0.961266i | \(-0.411116\pi\) |
0.961266 | − | 0.275622i | \(-0.0888840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.84337 | − | 3.84337i | −0.0499139 | − | 0.0499139i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 103.980i | 1.31620i | 0.752932 | + | 0.658099i | \(0.228639\pi\) | ||||
−0.752932 | + | 0.658099i | \(0.771361\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −22.8536 | + | 22.8536i | −0.275344 | + | 0.275344i | −0.831247 | − | 0.555903i | \(-0.812373\pi\) |
0.555903 | + | 0.831247i | \(0.312373\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.8536 | − | 18.8536i | −0.216708 | − | 0.216708i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 159.596i | 1.79321i | 0.442829 | + | 0.896606i | \(0.353975\pi\) | ||||
−0.442829 | + | 0.896606i | \(0.646025\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39388 | −0.0263063 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25.9671 | − | 25.9671i | 0.279216 | − | 0.279216i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −56.7298 | − | 56.7298i | −0.584844 | − | 0.584844i | 0.351387 | − | 0.936230i | \(-0.385710\pi\) |
−0.936230 | + | 0.351387i | \(0.885710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 35.3939i | − | 0.357514i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 46.2020 | 0.457446 | 0.228723 | − | 0.973492i | \(-0.426545\pi\) | ||||
0.228723 | + | 0.973492i | \(0.426545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 141.576 | − | 141.576i | 1.37452 | − | 1.37452i | 0.520905 | − | 0.853615i | \(-0.325595\pi\) |
0.853615 | − | 0.520905i | \(-0.174405\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −114.384 | − | 114.384i | −1.06901 | − | 1.06901i | −0.997436 | − | 0.0715708i | \(-0.977199\pi\) |
−0.0715708 | − | 0.997436i | \(-0.522801\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 160.171i | − | 1.46946i | −0.678358 | − | 0.734731i | \(-0.737308\pi\) | ||
0.678358 | − | 0.734731i | \(-0.262692\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.59592 | 0.0684317 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −21.2122 | + | 21.2122i | −0.187719 | + | 0.187719i | −0.794709 | − | 0.606990i | \(-0.792377\pi\) |
0.606990 | + | 0.794709i | \(0.292377\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.0227 | − | 11.0227i | −0.0942111 | − | 0.0942111i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.39388i | − | 0.0621334i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.1918 | 0.150346 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 22.2929 | − | 22.2929i | 0.181243 | − | 0.181243i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 112.495 | + | 112.495i | 0.885787 | + | 0.885787i | 0.994115 | − | 0.108329i | \(-0.0345498\pi\) |
−0.108329 | + | 0.994115i | \(0.534550\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 47.5857i | 0.368881i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 144.586 | 1.10371 | 0.551854 | − | 0.833941i | \(-0.313921\pi\) | ||||
0.551854 | + | 0.833941i | \(0.313921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.90127 | − | 9.90127i | 0.0744457 | − | 0.0744457i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.6617 | + | 15.6617i | 0.114319 | + | 0.114319i | 0.761952 | − | 0.647633i | \(-0.224241\pi\) |
−0.647633 | + | 0.761952i | \(0.724241\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 97.1918i | 0.699222i | 0.936895 | + | 0.349611i | \(0.113686\pi\) | ||||
−0.936895 | + | 0.349611i | \(0.886314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −67.9796 | −0.482125 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 43.3485 | − | 43.3485i | 0.303136 | − | 0.303136i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −59.7526 | − | 59.7526i | −0.406480 | − | 0.406480i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 177.151i | 1.18893i | 0.804120 | + | 0.594466i | \(0.202637\pi\) | ||||
−0.804120 | + | 0.594466i | \(0.797363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −112.778 | −0.746871 | −0.373436 | − | 0.927656i | \(-0.621820\pi\) | ||||
−0.373436 | + | 0.927656i | \(0.621820\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.0454 | − | 34.0454i | 0.222519 | − | 0.222519i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −152.911 | − | 152.911i | −0.973958 | − | 0.973958i | 0.0257110 | − | 0.999669i | \(-0.491815\pi\) |
−0.999669 | + | 0.0257110i | \(0.991815\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 139.373i | − | 0.876563i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.22245 | 0.0386488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 156.573 | − | 156.573i | 0.960572 | − | 0.960572i | −0.0386798 | − | 0.999252i | \(-0.512315\pi\) |
0.999252 | + | 0.0386798i | \(0.0123152\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.81837 | + | 3.81837i | 0.0228645 | + | 0.0228645i | 0.718447 | − | 0.695582i | \(-0.244853\pi\) |
−0.695582 | + | 0.718447i | \(0.744853\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 142.000i | 0.840237i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 91.1816 | 0.533226 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −157.015 | + | 157.015i | −0.907600 | + | 0.907600i | −0.996078 | − | 0.0884782i | \(-0.971800\pi\) |
0.0884782 | + | 0.996078i | \(0.471800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 100.429 | + | 100.429i | 0.567396 | + | 0.567396i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2327i | 0.0739255i | 0.999317 | + | 0.0369627i | \(0.0117683\pi\) | ||||
−0.999317 | + | 0.0369627i | \(0.988232\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 236.959 | 1.30917 | 0.654583 | − | 0.755990i | \(-0.272844\pi\) | ||||
0.654583 | + | 0.755990i | \(0.272844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 115.856 | − | 115.856i | 0.633092 | − | 0.633092i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 133.889 | + | 133.889i | 0.715983 | + | 0.715983i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.39388i | 0.0126660i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.2020 | 0.126712 | 0.0633561 | − | 0.997991i | \(-0.479820\pi\) | ||||
0.0633561 | + | 0.997991i | \(0.479820\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −63.7401 | + | 63.7401i | −0.330259 | + | 0.330259i | −0.852685 | − | 0.522426i | \(-0.825027\pi\) |
0.522426 | + | 0.852685i | \(0.325027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −245.914 | − | 245.914i | −1.24829 | − | 1.24829i | −0.956473 | − | 0.291820i | \(-0.905739\pi\) |
−0.291820 | − | 0.956473i | \(-0.594261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 102.798i | − | 0.516573i | −0.966068 | − | 0.258286i | \(-0.916842\pi\) | ||
0.966068 | − | 0.258286i | \(-0.0831578\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.1816 | 0.155132 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.01479 | + | 5.01479i | −0.0247034 | + | 0.0247034i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28.6515 | + | 28.6515i | 0.138413 | + | 0.138413i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 358.586i | 1.71572i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.43470 | 0.0304962 | 0.0152481 | − | 0.999884i | \(-0.495146\pi\) | ||||
0.0152481 | + | 0.999884i | \(0.495146\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 95.2827 | − | 95.2827i | 0.447336 | − | 0.447336i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.90689 | − | 6.90689i | −0.0318290 | − | 0.0318290i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 221.171i | − | 1.00992i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 83.3939 | 0.377348 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 33.3156 | − | 33.3156i | 0.149397 | − | 0.149397i | −0.628452 | − | 0.777849i | \(-0.716311\pi\) |
0.777849 | + | 0.628452i | \(0.216311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −72.5857 | − | 72.5857i | −0.319761 | − | 0.319761i | 0.528914 | − | 0.848675i | \(-0.322599\pi\) |
−0.848675 | + | 0.528914i | \(0.822599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 295.788i | − | 1.29165i | −0.763486 | − | 0.645825i | \(-0.776514\pi\) | ||
0.763486 | − | 0.645825i | \(-0.223486\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.41429 | −0.0407545 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −39.2827 | + | 39.2827i | −0.168595 | + | 0.168595i | −0.786362 | − | 0.617767i | \(-0.788038\pi\) |
0.617767 | + | 0.786362i | \(0.288038\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 127.348 | + | 127.348i | 0.537335 | + | 0.537335i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 89.7571i | − | 0.375553i | −0.982212 | − | 0.187776i | \(-0.939872\pi\) | ||
0.982212 | − | 0.187776i | \(-0.0601280\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.23266 | −0.0175629 | −0.00878144 | − | 0.999961i | \(-0.502795\pi\) | ||||
−0.00878144 | + | 0.999961i | \(0.502795\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 111.674 | + | 111.674i | 0.452122 | + | 0.452122i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 55.9796i | 0.224818i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −299.151 | −1.19184 | −0.595918 | − | 0.803045i | \(-0.703212\pi\) | ||||
−0.595918 | + | 0.803045i | \(0.703212\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −112.677 | + | 112.677i | −0.445362 | + | 0.445362i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 229.262 | + | 229.262i | 0.892071 | + | 0.892071i | 0.994718 | − | 0.102647i | \(-0.0327312\pi\) |
−0.102647 | + | 0.994718i | \(0.532731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.02041i | − | 0.00780081i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −46.1816 | −0.176941 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −207.464 | + | 207.464i | −0.788838 | + | 0.788838i | −0.981304 | − | 0.192466i | \(-0.938351\pi\) |
0.192466 | + | 0.981304i | \(0.438351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 195.464 | + | 195.464i | 0.732076 | + | 0.732076i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 100.161i | 0.372347i | 0.982517 | + | 0.186173i | \(0.0596086\pi\) | ||||
−0.982517 | + | 0.186173i | \(0.940391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −168.424 | −0.621493 | −0.310746 | − | 0.950493i | \(-0.600579\pi\) | ||||
−0.310746 | + | 0.950493i | \(0.600579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.93189 | + | 2.93189i | −0.0107395 | + | 0.0107395i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −137.563 | − | 137.563i | −0.496617 | − | 0.496617i | 0.413766 | − | 0.910383i | \(-0.364213\pi\) |
−0.910383 | + | 0.413766i | \(0.864213\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 63.6061i | − | 0.227979i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −254.586 | −0.905999 | −0.452999 | − | 0.891511i | \(-0.649646\pi\) | ||||
−0.452999 | + | 0.891511i | \(0.649646\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −121.472 | + | 121.472i | −0.429230 | + | 0.429230i | −0.888366 | − | 0.459136i | \(-0.848159\pi\) |
0.459136 | + | 0.888366i | \(0.348159\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.92959 | − | 5.92959i | −0.0206606 | − | 0.0206606i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 31.4245i | − | 0.108735i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −138.959 | −0.477523 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −353.510 | + | 353.510i | −1.20652 | + | 1.20652i | −0.234370 | + | 0.972147i | \(0.575303\pi\) |
−0.972147 | + | 0.234370i | \(0.924697\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −43.3485 | − | 43.3485i | −0.145954 | − | 0.145954i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 70.1816i | 0.234721i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.6571 | 0.0420503 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 56.5857 | − | 56.5857i | 0.186752 | − | 0.186752i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 142.396 | + | 142.396i | 0.463831 | + | 0.463831i | 0.899909 | − | 0.436078i | \(-0.143633\pi\) |
−0.436078 | + | 0.899909i | \(0.643633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 346.788i | − | 1.12229i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 479.535 | 1.54191 | 0.770956 | − | 0.636888i | \(-0.219779\pi\) | ||||
0.770956 | + | 0.636888i | \(0.219779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 53.6288 | − | 53.6288i | 0.171338 | − | 0.171338i | −0.616229 | − | 0.787567i | \(-0.711340\pi\) |
0.787567 | + | 0.616229i | \(0.211340\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −78.0704 | − | 78.0704i | −0.246279 | − | 0.246279i | 0.573163 | − | 0.819442i | \(-0.305716\pi\) |
−0.819442 | + | 0.573163i | \(0.805716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 181.616i | − | 0.569330i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −280.182 | −0.872840 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −344.924 | + | 344.924i | −1.06788 | + | 1.06788i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −196.169 | − | 196.169i | −0.599906 | − | 0.599906i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.0816i | 0.0549594i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −120.424 | −0.363820 | −0.181910 | − | 0.983315i | \(-0.558228\pi\) | ||||
−0.181910 | + | 0.983315i | \(0.558228\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.30306 | − | 9.30306i | 0.0279371 | − | 0.0279371i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 468.062 | + | 468.062i | 1.38891 | + | 1.38891i | 0.827619 | + | 0.561291i | \(0.189695\pi\) |
0.561291 | + | 0.827619i | \(0.310305\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 51.9592i | 0.153272i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 250.141 | 0.733551 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −31.8559 | + | 31.8559i | −0.0928742 | + | 0.0928742i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −194.318 | − | 194.318i | −0.559994 | − | 0.559994i | 0.369312 | − | 0.929306i | \(-0.379593\pi\) |
−0.929306 | + | 0.369312i | \(0.879593\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 599.576i | − | 1.71798i | −0.511991 | − | 0.858991i | \(-0.671092\pi\) | ||
0.511991 | − | 0.858991i | \(-0.328908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.0000 | −0.0769231 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −146.409 | + | 146.409i | −0.414755 | + | 0.414755i | −0.883391 | − | 0.468636i | \(-0.844746\pi\) |
0.468636 | + | 0.883391i | \(0.344746\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.05561 | − | 9.05561i | −0.0253659 | − | 0.0253659i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 452.949i | 1.26170i | 0.775906 | + | 0.630848i | \(0.217293\pi\) | ||||
−0.775906 | + | 0.630848i | \(0.782707\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −562.788 | −1.55897 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 22.2804 | − | 22.2804i | 0.0613784 | − | 0.0613784i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −221.901 | − | 221.901i | −0.604636 | − | 0.604636i | 0.336904 | − | 0.941539i | \(-0.390620\pi\) |
−0.941539 | + | 0.336904i | \(0.890620\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 54.6061i | − | 0.147984i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −37.0714 | −0.0999230 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 243.518 | − | 243.518i | 0.652862 | − | 0.652862i | −0.300819 | − | 0.953681i | \(-0.597260\pi\) |
0.953681 | + | 0.300819i | \(0.0972600\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −56.5607 | − | 56.5607i | −0.150028 | − | 0.150028i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 164.839i | − | 0.434931i | −0.976068 | − | 0.217465i | \(-0.930221\pi\) | ||
0.976068 | − | 0.217465i | \(-0.0697789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 275.555 | 0.723242 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −455.110 | + | 455.110i | −1.18828 | + | 1.18828i | −0.210734 | + | 0.977543i | \(0.567585\pi\) |
−0.977543 | + | 0.210734i | \(0.932415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 58.2804 | + | 58.2804i | 0.150595 | + | 0.150595i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 619.696i | − | 1.59305i | −0.604607 | − | 0.796524i | \(-0.706670\pi\) | ||
0.604607 | − | 0.796524i | \(-0.293330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −216.767 | −0.554392 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 177.081 | − | 177.081i | 0.450587 | − | 0.450587i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 108.952 | + | 108.952i | 0.274439 | + | 0.274439i | 0.830884 | − | 0.556445i | \(-0.187835\pi\) |
−0.556445 | + | 0.830884i | \(0.687835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 24.2531i | − | 0.0607846i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −412.182 | −1.02788 | −0.513942 | − | 0.857825i | \(-0.671815\pi\) | ||||
−0.513942 | + | 0.857825i | \(0.671815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 77.9013 | − | 77.9013i | 0.193303 | − | 0.193303i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.5857 | + | 36.5857i | 0.0898912 | + | 0.0898912i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.86939i | 0.0143506i | 0.999974 | + | 0.00717530i | \(0.00228399\pi\) | ||||
−0.999974 | + | 0.00717530i | \(0.997716\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.3633 | 0.0933413 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.7128 | − | 26.7128i | 0.0646798 | − | 0.0646798i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 119.035 | + | 119.035i | 0.285456 | + | 0.285456i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 517.757i | 1.23570i | 0.786297 | + | 0.617849i | \(0.211996\pi\) | ||||
−0.786297 | + | 0.617849i | \(0.788004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −770.322 | −1.82974 | −0.914872 | − | 0.403743i | \(-0.867709\pi\) | ||||
−0.914872 | + | 0.403743i | \(0.867709\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −83.2577 | + | 83.2577i | −0.196827 | + | 0.196827i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.8161 | − | 30.8161i | −0.0721688 | − | 0.0721688i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 106.182i | − | 0.247510i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −674.504 | −1.56497 | −0.782487 | − | 0.622667i | \(-0.786049\pi\) | ||||
−0.782487 | + | 0.622667i | \(0.786049\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 116.796 | − | 116.796i | 0.269736 | − | 0.269736i | −0.559258 | − | 0.828994i | \(-0.688914\pi\) |
0.828994 | + | 0.559258i | \(0.188914\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −290.277 | − | 290.277i | −0.664250 | − | 0.664250i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 133.141i | − | 0.303282i | −0.988436 | − | 0.151641i | \(-0.951544\pi\) | ||
0.988436 | − | 0.151641i | \(-0.0484558\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −146.363 | −0.331889 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −41.3031 | + | 41.3031i | −0.0932349 | + | 0.0932349i | −0.752186 | − | 0.658951i | \(-0.771000\pi\) |
0.658951 | + | 0.752186i | \(0.271000\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 216.965 | + | 216.965i | 0.485380 | + | 0.485380i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 424.767i | 0.946030i | 0.881054 | + | 0.473015i | \(0.156834\pi\) | ||||
−0.881054 | + | 0.473015i | \(0.843166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 214.747 | 0.476157 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −138.124 | + | 138.124i | −0.304909 | + | 0.304909i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 553.798 | + | 553.798i | 1.21181 | + | 1.21181i | 0.970430 | + | 0.241381i | \(0.0776005\pi\) |
0.241381 | + | 0.970430i | \(0.422400\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 83.3939i | − | 0.181686i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.6469 | 0.0230953 | 0.0115477 | − | 0.999933i | \(-0.496324\pi\) | ||||
0.0115477 | + | 0.999933i | \(0.496324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −435.464 | + | 435.464i | −0.940528 | + | 0.940528i | −0.998328 | − | 0.0578005i | \(-0.981591\pi\) |
0.0578005 | + | 0.998328i | \(0.481591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −344.974 | − | 344.974i | −0.738702 | − | 0.738702i | 0.233625 | − | 0.972327i | \(-0.424941\pi\) |
−0.972327 | + | 0.233625i | \(0.924941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.29389i | − | 0.0176842i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −374.555 | −0.795234 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −229.196 | + | 229.196i | −0.484559 | + | 0.484559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −170.697 | − | 170.697i | −0.357855 | − | 0.357855i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 349.555i | 0.729760i | 0.931055 | + | 0.364880i | \(0.118890\pi\) | ||||
−0.931055 | + | 0.364880i | \(0.881110\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.7878 | 0.0473758 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.62092 | − | 7.62092i | 0.0157783 | − | 0.0157783i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −345.785 | − | 345.785i | −0.710032 | − | 0.710032i | 0.256510 | − | 0.966542i | \(-0.417427\pi\) |
−0.966542 | + | 0.256510i | \(0.917427\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 383.524i | − | 0.784304i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −611.192 | −1.24479 | −0.622395 | − | 0.782703i | \(-0.713840\pi\) | ||||
−0.622395 | + | 0.782703i | \(0.713840\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 174.697 | − | 174.697i | 0.354355 | − | 0.354355i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.3439 | − | 25.3439i | −0.0509937 | − | 0.0509937i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 716.292i | − | 1.43545i | −0.696324 | − | 0.717727i | \(-0.745182\pi\) | ||
0.696324 | − | 0.717727i | \(-0.254818\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.35306 | 0.0186688 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −503.333 | + | 503.333i | −1.00066 | + | 1.00066i | −0.000661543 | 1.00000i | \(0.500211\pi\) | |
−1.00000 | 0.000661543i | \(0.999789\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 173.914 | + | 173.914i | 0.343025 | + | 0.343025i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 811.090i | − | 1.59350i | −0.604311 | − | 0.796748i | \(-0.706552\pi\) | ||
0.604311 | − | 0.796748i | \(-0.293448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −58.8286 | −0.115124 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 111.674 | − | 111.674i | 0.217689 | − | 0.217689i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −327.423 | − | 327.423i | −0.633314 | − | 0.633314i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 384.606i | 0.741052i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −247.880 | −0.475777 | −0.237888 | − | 0.971293i | \(-0.576455\pi\) | ||||
−0.237888 | + | 0.971293i | \(0.576455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −478.578 | + | 478.578i | −0.915063 | + | 0.915063i | −0.996665 | − | 0.0816023i | \(-0.973996\pi\) |
0.0816023 | + | 0.996665i | \(0.473996\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 240.611 | + | 240.611i | 0.456567 | + | 0.456567i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 346.576i | 0.655152i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 246.000 | 0.463277 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 66.8786 | − | 66.8786i | 0.125476 | − | 0.125476i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.2066 | + | 16.2066i | 0.0301799 | + | 0.0301799i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 575.596i | − | 1.06790i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 522.110 | 0.965084 | 0.482542 | − | 0.875873i | \(-0.339714\pi\) | ||||
0.482542 | + | 0.875873i | \(0.339714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 290.215 | − | 290.215i | 0.534465 | − | 0.534465i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −150.384 | − | 150.384i | −0.274924 | − | 0.274924i | 0.556154 | − | 0.831079i | \(-0.312276\pi\) |
−0.831079 | + | 0.556154i | \(0.812276\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 283.788i | − | 0.516918i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 467.880 | 0.849146 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.8730 | − | 33.8730i | 0.0612531 | − | 0.0612531i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.1464 | − | 41.1464i | −0.0738715 | − | 0.0738715i | 0.669206 | − | 0.743077i | \(-0.266635\pi\) |
−0.743077 | + | 0.669206i | \(0.766635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 142.757i | 0.255379i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 327.959 | 0.584597 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 634.954 | − | 634.954i | 1.12780 | − | 1.12780i | 0.137270 | − | 0.990534i | \(-0.456167\pi\) |
0.990534 | − | 0.137270i | \(-0.0438329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.93189 | + | 2.93189i | 0.00517088 | + | 0.00517088i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 775.271i | 1.36252i | 0.732044 | + | 0.681258i | \(0.238567\pi\) | ||||
−0.732044 | + | 0.681258i | \(0.761433\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 151.929 | 0.266075 | 0.133037 | − | 0.991111i | \(-0.457527\pi\) | ||||
0.133037 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 29.6413 | − | 29.6413i | 0.0517301 | − | 0.0517301i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 302.875 | + | 302.875i | 0.524914 | + | 0.524914i | 0.919051 | − | 0.394138i | \(-0.128957\pi\) |
−0.394138 | + | 0.919051i | \(0.628957\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 156.131i | 0.269656i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8898 | 0.0256279 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 671.292 | − | 671.292i | 1.15144 | − | 1.15144i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 102.374 | + | 102.374i | 0.174403 | + | 0.174403i | 0.788911 | − | 0.614508i | \(-0.210645\pi\) |
−0.614508 | + | 0.788911i | \(0.710645\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 644.412i | 1.09408i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −602.363 | −1.01923 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 177.576 | − | 177.576i | 0.299453 | − | 0.299453i | −0.541347 | − | 0.840799i | \(-0.682085\pi\) |
0.840799 | + | 0.541347i | \(0.182085\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −125.901 | − | 125.901i | −0.210890 | − | 0.210890i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 248.282i | 0.414494i | 0.978289 | + | 0.207247i | \(0.0664503\pi\) | ||||
−0.978289 | + | 0.207247i | \(0.933550\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −469.706 | −0.781541 | −0.390770 | − | 0.920488i | \(-0.627791\pi\) | ||||
−0.390770 | + | 0.920488i | \(0.627791\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.1895 | − | 38.1895i | 0.0633326 | − | 0.0633326i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −385.666 | − | 385.666i | −0.635365 | − | 0.635365i | 0.314044 | − | 0.949408i | \(-0.398316\pi\) |
−0.949408 | + | 0.314044i | \(0.898316\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.2837i | 0.0201702i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −203.939 | −0.333779 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −520.232 | + | 520.232i | −0.848665 | + | 0.848665i | −0.989967 | − | 0.141302i | \(-0.954871\pi\) |
0.141302 | + | 0.989967i | \(0.454871\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −120.767 | − | 120.767i | −0.195733 | − | 0.195733i | 0.602435 | − | 0.798168i | \(-0.294197\pi\) |
−0.798168 | + | 0.602435i | \(0.794197\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 795.039i | − | 1.28439i | −0.766540 | − | 0.642196i | \(-0.778023\pi\) | ||
0.766540 | − | 0.642196i | \(-0.221977\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 70.1816 | 0.113014 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.9908 | − | 51.9908i | 0.0834524 | − | 0.0834524i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 439.176 | + | 439.176i | 0.700440 | + | 0.700440i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.3837i | 0.111898i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 834.271 | 1.32214 | 0.661071 | − | 0.750323i | \(-0.270102\pi\) | ||||
0.661071 | + | 0.750323i | \(0.270102\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.88086 | − | 7.88086i | 0.0124500 | − | 0.0124500i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −179.258 | − | 179.258i | −0.281409 | − | 0.281409i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 233.394i | − | 0.365249i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 858.665 | 1.33957 | 0.669786 | − | 0.742554i | \(-0.266386\pi\) | ||||
0.669786 | + | 0.742554i | \(0.266386\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 425.040 | − | 425.040i | 0.661026 | − | 0.661026i | −0.294596 | − | 0.955622i | \(-0.595185\pi\) |
0.955622 | + | 0.294596i | \(0.0951850\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 727.373 | + | 727.373i | 1.12422 | + | 1.12422i | 0.991099 | + | 0.133126i | \(0.0425014\pi\) |
0.133126 | + | 0.991099i | \(0.457499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 967.433i | 1.49065i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.9184 | −0.0259883 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −561.773 | + | 561.773i | −0.860296 | + | 0.860296i | −0.991372 | − | 0.131077i | \(-0.958157\pi\) |
0.131077 | + | 0.991372i | \(0.458157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −270.879 | − | 270.879i | −0.412296 | − | 0.412296i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 678.606i | 1.02975i | 0.857265 | + | 0.514876i | \(0.172162\pi\) | ||||
−0.857265 | + | 0.514876i | \(0.827838\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −241.069 | −0.364704 | −0.182352 | − | 0.983233i | \(-0.558371\pi\) | ||||
−0.182352 | + | 0.983233i | \(0.558371\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 102.136 | − | 102.136i | 0.154052 | − | 0.154052i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 147.019 | + | 147.019i | 0.220419 | + | 0.220419i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 81.6061i | − | 0.121982i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1116.04 | 1.66325 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 39.6867 | − | 39.6867i | 0.0589699 | − | 0.0589699i | −0.677007 | − | 0.735977i | \(-0.736723\pi\) |
0.735977 | + | 0.677007i | \(0.236723\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −285.873 | − | 285.873i | −0.422264 | − | 0.422264i | 0.463718 | − | 0.885983i | \(-0.346515\pi\) |
−0.885983 | + | 0.463718i | \(0.846515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.9612i | 0.0544348i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −177.798 | −0.261084 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 180.767 | − | 180.767i | 0.264667 | − | 0.264667i | −0.562280 | − | 0.826947i | \(-0.690076\pi\) |
0.826947 | + | 0.562280i | \(0.190076\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −362.265 | − | 362.265i | −0.527314 | − | 0.527314i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 418.120i | − | 0.606851i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 265.273 | 0.383898 | 0.191949 | − | 0.981405i | \(-0.438519\pi\) | ||||
0.191949 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.5301 | + | 11.5301i | −0.0166380 | + | 0.0166380i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 206.565 | + | 206.565i | 0.296363 | + | 0.296363i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 96.2225i | 0.137657i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1371.27 | 1.95616 | 0.978082 | − | 0.208219i | \(-0.0667665\pi\) | ||||
0.978082 | + | 0.208219i | \(0.0667665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −94.2520 | + | 94.2520i | −0.134071 | + | 0.134071i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.0510 | − | 15.0510i | −0.0212886 | − | 0.0212886i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 213.829i | 0.301592i | 0.988565 | + | 0.150796i | \(0.0481836\pi\) | ||||
−0.988565 | + | 0.150796i | \(0.951816\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 311.939 | 0.438732 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −202.490 | + | 202.490i | −0.283998 | + | 0.283998i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −109.930 | − | 109.930i | −0.153319 | − | 0.153319i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1102.34i | − | 1.53316i | −0.642150 | − | 0.766579i | \(-0.721957\pi\) | ||
0.642150 | − | 0.766579i | \(-0.278043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −92.2408 | −0.127935 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.18392 | + | 5.18392i | −0.00717002 | + | 0.00717002i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −119.593 | − | 119.593i | −0.164502 | − | 0.164502i | 0.620056 | − | 0.784558i | \(-0.287110\pi\) |
−0.784558 | + | 0.620056i | \(0.787110\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −440.929 | −0.603185 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −206.697 | + | 206.697i | −0.281988 | + | 0.281988i | −0.833901 | − | 0.551914i | \(-0.813898\pi\) |
0.551914 | + | 0.833901i | \(0.313898\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 150.186 | + | 150.186i | 0.203780 | + | 0.203780i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 179.131i | − | 0.242396i | −0.992628 | − | 0.121198i | \(-0.961326\pi\) | ||
0.992628 | − | 0.121198i | \(-0.0386736\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 273.545 | 0.369156 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 984.777 | − | 984.777i | 1.32541 | − | 1.32541i | 0.416076 | − | 0.909330i | \(-0.363405\pi\) |
0.909330 | − | 0.416076i | \(-0.136595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 68.5607 | + | 68.5607i | 0.0917814 | + | 0.0917814i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 74.5245i | 0.0994986i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −343.576 | −0.457491 | −0.228745 | − | 0.973486i | \(-0.573462\pi\) | ||||
−0.228745 | + | 0.973486i | \(0.573462\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −366.384 | + | 366.384i | −0.486565 | + | 0.486565i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 585.588 | + | 585.588i | 0.773564 | + | 0.773564i | 0.978728 | − | 0.205164i | \(-0.0657726\pi\) |
−0.205164 | + | 0.978728i | \(0.565773\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 276.000i | 0.363636i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −477.857 | −0.627933 | −0.313967 | − | 0.949434i | \(-0.601658\pi\) | ||||
−0.313967 | + | 0.949434i | \(0.601658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.1783 | + | 52.1783i | −0.0683857 | + | 0.0683857i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 301.287 | + | 301.287i | 0.392813 | + | 0.392813i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1116.56i | 1.45196i | 0.687717 | + | 0.725979i | \(0.258613\pi\) | ||||
−0.687717 | + | 0.725979i | \(0.741387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 561.576 | 0.728373 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 375.151 | − | 375.151i | 0.485318 | − | 0.485318i | −0.421507 | − | 0.906825i | \(-0.638499\pi\) |
0.906825 | + | 0.421507i | \(0.138499\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.47449 | − | 2.47449i | −0.00318467 | − | 0.00318467i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 553.231i | 0.710180i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 917.857 | 1.17523 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −56.5607 | + | 56.5607i | −0.0722359 | + | 0.0722359i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 559.229 | + | 559.229i | 0.710584 | + | 0.710584i | 0.966657 | − | 0.256074i | \(-0.0824290\pi\) |
−0.256074 | + | 0.966657i | \(0.582429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 508.182i | 0.644083i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.8204 | 0.0174721 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 347.568 | − | 347.568i | 0.438295 | − | 0.438295i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −437.839 | − | 437.839i | −0.549359 | − | 0.549359i | 0.376897 | − | 0.926255i | \(-0.376991\pi\) |
−0.926255 | + | 0.376897i | \(0.876991\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 629.898i | − | 0.788358i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 478.788 | 0.597738 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1065.27 | − | 1065.27i | 1.32661 | − | 1.32661i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 122.672 | + | 122.672i | 0.152010 | + | 0.152010i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 210.565i | 0.260278i | 0.991496 | + | 0.130139i | \(0.0415424\pi\) | ||||
−0.991496 | + | 0.130139i | \(0.958458\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 858.818 | 1.05896 | 0.529481 | − | 0.848322i | \(-0.322387\pi\) | ||||
0.529481 | + | 0.848322i | \(0.322387\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −206.277 | + | 206.277i | −0.253723 | + | 0.253723i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −590.455 | − | 590.455i | −0.722712 | − | 0.722712i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.18163i | 0.00876878i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −637.878 | −0.776952 | −0.388476 | − | 0.921459i | \(-0.626998\pi\) | ||||
−0.388476 | + | 0.921459i | \(0.626998\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 636.855 | − | 636.855i | 0.773821 | − | 0.773821i | −0.204951 | − | 0.978772i | \(-0.565704\pi\) |
0.978772 | + | 0.204951i | \(0.0657035\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 43.7684 | + | 43.7684i | 0.0529243 | + | 0.0529243i | 0.733074 | − | 0.680149i | \(-0.238085\pi\) |
−0.680149 | + | 0.733074i | \(0.738085\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 325.110i | − | 0.392172i | −0.980587 | − | 0.196086i | \(-0.937177\pi\) | ||
0.980587 | − | 0.196086i | \(-0.0628231\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −336.959 | −0.405486 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 553.666 | − | 553.666i | 0.664665 | − | 0.664665i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −77.9013 | − | 77.9013i | −0.0930720 | − | 0.0930720i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 279.394i | − | 0.333008i | −0.986041 | − | 0.166504i | \(-0.946752\pi\) | ||
0.986041 | − | 0.166504i | \(-0.0532479\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 604.029 | 0.718227 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −311.803 | + | 311.803i | −0.369873 | + | 0.369873i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.92627 | − | 5.92627i | −0.00699678 | − | 0.00699678i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 297.545i | 0.350465i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −59.2327 | −0.0696036 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 708.269 | − | 708.269i | 0.830327 | − | 0.830327i | −0.157234 | − | 0.987561i | \(-0.550258\pi\) |
0.987561 | + | 0.157234i | \(0.0502577\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 77.9888 | + | 77.9888i | 0.0910021 | + | 0.0910021i | 0.751142 | − | 0.660140i | \(-0.229503\pi\) |
−0.660140 | + | 0.751142i | \(0.729503\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 937.837i | 1.09178i | 0.837858 | + | 0.545889i | \(0.183808\pi\) | ||||
−0.837858 | + | 0.545889i | \(0.816192\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.5245 | −0.0168693 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1144.00 | + | 1144.00i | −1.32561 | + | 1.32561i | −0.416449 | + | 0.909159i | \(0.636726\pi\) |
−0.909159 | + | 0.416449i | \(0.863274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.4870 | − | 38.4870i | −0.0443910 | − | 0.0443910i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1226.75i | 1.41168i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 93.5449 | 0.107399 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −170.190 | + | 170.190i | −0.194948 | + | 0.194948i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 191.740 | + | 191.740i | 0.218632 | + | 0.218632i | 0.807922 | − | 0.589290i | \(-0.200592\pi\) |
−0.589290 | + | 0.807922i | \(0.700592\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 865.918i | 0.985118i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1300.97 | 1.47669 | 0.738347 | − | 0.674421i | \(-0.235607\pi\) | ||||
0.738347 | + | 0.674421i | \(0.235607\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 316.623 | − | 316.623i | 0.358577 | − | 0.358577i | −0.504711 | − | 0.863288i | \(-0.668401\pi\) |
0.863288 | + | 0.504711i | \(0.168401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −426.894 | − | 426.894i | −0.481279 | − | 0.481279i | 0.424261 | − | 0.905540i | \(-0.360534\pi\) |
−0.905540 | + | 0.424261i | \(0.860534\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 73.2939i | − | 0.0824453i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −106.182 | −0.119171 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 843.508 | − | 843.508i | 0.944577 | − | 0.944577i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 85.9546 | + | 85.9546i | 0.0958245 | + | 0.0958245i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 326.382i | − | 0.363050i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1291.43 | 1.43333 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5018 | − | 15.5018i | 0.0171670 | − | 0.0171670i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −591.687 | − | 591.687i | −0.652356 | − | 0.652356i | 0.301204 | − | 0.953560i | \(-0.402612\pi\) |
−0.953560 | + | 0.301204i | \(0.902612\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 138.606i | − | 0.152482i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 972.947 | 1.06800 | 0.533999 | − | 0.845485i | \(-0.320688\pi\) | ||||
0.533999 | + | 0.845485i | \(0.320688\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −269.626 | + | 269.626i | −0.295318 | + | 0.295318i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −47.1010 | − | 47.1010i | −0.0513643 | − | 0.0513643i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 226.031i | 0.245953i | 0.992410 | + | 0.122976i | \(0.0392439\pi\) | ||||
−0.992410 | + | 0.122976i | \(0.960756\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 348.798 | 0.378717 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 285.848 | − | 285.848i | 0.309694 | − | 0.309694i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −424.727 | − | 424.727i | −0.458173 | − | 0.458173i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1161.66i | − | 1.25044i | −0.780450 | − | 0.625218i | \(-0.785010\pi\) | ||
0.780450 | − | 0.625218i | \(-0.214990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1482.85 | 1.59275 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 587.308 | − | 587.308i | 0.629483 | − | 0.629483i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −927.997 | − | 927.997i | −0.990391 | − | 0.990391i | 0.00956294 | − | 0.999954i | \(-0.496956\pi\) |
−0.999954 | + | 0.00956294i | \(0.996956\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 131.363i | − | 0.139897i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1039.86 | −1.10506 | −0.552528 | − | 0.833495i | \(-0.686337\pi\) | ||||
−0.552528 | + | 0.833495i | \(0.686337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −173.839 | + | 173.839i | −0.184347 | + | 0.184347i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1203.27 | − | 1203.27i | −1.27061 | − | 1.27061i | −0.945769 | − | 0.324840i | \(-0.894689\pi\) |
−0.324840 | − | 0.945769i | \(-0.605311\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 663.514i | − | 0.699172i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −191.233 | −0.201086 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1002.66 | − | 1002.66i | 1.05211 | − | 1.05211i | 0.0535393 | − | 0.998566i | \(-0.482950\pi\) |
0.998566 | − | 0.0535393i | \(-0.0170502\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −222.434 | − | 222.434i | −0.232428 | − | 0.232428i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 10.2041i | − | 0.0106404i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −511.473 | −0.532230 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −343.151 | + | 343.151i | −0.356335 | + | 0.356335i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −382.434 | − | 382.434i | −0.395485 | − | 0.395485i | 0.481152 | − | 0.876637i | \(-0.340218\pi\) |
−0.876637 | + | 0.481152i | \(0.840218\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 844.888i | 0.871917i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1241.64 | −1.27872 | −0.639360 | − | 0.768908i | \(-0.720801\pi\) | ||||
−0.639360 | + | 0.768908i | \(0.720801\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.6617 | − | 31.6617i | 0.0325403 | − | 0.0325403i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1155.44 | + | 1155.44i | 1.18264 | + | 1.18264i | 0.979058 | + | 0.203582i | \(0.0652584\pi\) |
0.203582 | + | 0.979058i | \(0.434742\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1882.91i | 1.92330i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −480.514 | −0.489821 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 582.352 | − | 582.352i | 0.592423 | − | 0.592423i | −0.345862 | − | 0.938285i | \(-0.612414\pi\) |
0.938285 | + | 0.345862i | \(0.112414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.1454 | + | 22.1454i | 0.0224371 | + | 0.0224371i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 371.071i | − | 0.375199i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1762.94 | −1.77895 | −0.889474 | − | 0.456987i | \(-0.848929\pi\) | ||||
−0.889474 | + | 0.456987i | \(0.848929\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −147.489 | + | 147.489i | −0.148529 | + | 0.148529i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −734.170 | − | 734.170i | −0.736380 | − | 0.736380i | 0.235496 | − | 0.971875i | \(-0.424329\pi\) |
−0.971875 | + | 0.235496i | \(0.924329\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 22.7878i | − | 0.0228106i |
(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 | 1200.3.bg.c.1057.2 | 4 | ||
4.3 | odd | 2 | 600.3.u.g.457.1 | yes | 4 | ||
5.2 | odd | 4 | 1200.3.bg.n.193.1 | 4 | |||
5.3 | odd | 4 | inner | 1200.3.bg.c.193.2 | 4 | ||
5.4 | even | 2 | 1200.3.bg.n.1057.1 | 4 | |||
12.11 | even | 2 | 1800.3.v.p.1657.1 | 4 | |||
20.3 | even | 4 | 600.3.u.g.193.1 | yes | 4 | ||
20.7 | even | 4 | 600.3.u.b.193.2 | ✓ | 4 | ||
20.19 | odd | 2 | 600.3.u.b.457.2 | yes | 4 | ||
60.23 | odd | 4 | 1800.3.v.p.793.1 | 4 | |||
60.47 | odd | 4 | 1800.3.v.i.793.2 | 4 | |||
60.59 | even | 2 | 1800.3.v.i.1657.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.3.u.b.193.2 | ✓ | 4 | 20.7 | even | 4 | ||
600.3.u.b.457.2 | yes | 4 | 20.19 | odd | 2 | ||
600.3.u.g.193.1 | yes | 4 | 20.3 | even | 4 | ||
600.3.u.g.457.1 | yes | 4 | 4.3 | odd | 2 | ||
1200.3.bg.c.193.2 | 4 | 5.3 | odd | 4 | inner | ||
1200.3.bg.c.1057.2 | 4 | 1.1 | even | 1 | trivial | ||
1200.3.bg.n.193.1 | 4 | 5.2 | odd | 4 | |||
1200.3.bg.n.1057.1 | 4 | 5.4 | even | 2 | |||
1800.3.v.i.793.2 | 4 | 60.47 | odd | 4 | |||
1800.3.v.i.1657.2 | 4 | 60.59 | even | 2 | |||
1800.3.v.p.793.1 | 4 | 60.23 | odd | 4 | |||
1800.3.v.p.1657.1 | 4 | 12.11 | even | 2 |