Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,3,Mod(91,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.c (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: | \(56.4034147226\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.15 | ||
Root | \(-0.0431371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.91 |
Dual form | 2070.3.c.a.91.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.24199i | 1.17743i | 0.808342 | + | 0.588713i | \(0.200365\pi\) | ||||
−0.808342 | + | 0.588713i | \(0.799635\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | − | 15.8246i | − | 1.43860i | −0.694702 | − | 0.719298i | \(-0.744464\pi\) | ||
0.694702 | − | 0.719298i | \(-0.255536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.3219 | −1.10169 | −0.550843 | − | 0.834609i | \(-0.685694\pi\) | ||||
−0.550843 | + | 0.834609i | \(0.685694\pi\) | |||||||
\(14\) | 11.6559i | 0.832566i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 10.1666i | 0.598034i | 0.954248 | + | 0.299017i | \(0.0966587\pi\) | ||||
−0.954248 | + | 0.299017i | \(0.903341\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 36.5359i | − | 1.92294i | −0.274904 | − | 0.961472i | \(-0.588646\pi\) | ||
0.274904 | − | 0.961472i | \(-0.411354\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 22.3793i | − | 1.01724i | ||||||
\(23\) | −22.2445 | − | 5.84663i | −0.967151 | − | 0.254201i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −20.2543 | −0.779010 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.4840i | 0.588713i | ||||||||
\(29\) | −6.46533 | −0.222942 | −0.111471 | − | 0.993768i | \(-0.535556\pi\) | ||||
−0.111471 | + | 0.993768i | \(0.535556\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.8526 | −1.38234 | −0.691172 | − | 0.722691i | \(-0.742905\pi\) | ||||
−0.691172 | + | 0.722691i | \(0.742905\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 14.3777i | 0.422874i | ||||||||
\(35\) | −18.4296 | −0.526561 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 63.6379i | − | 1.71994i | −0.510341 | − | 0.859972i | \(-0.670481\pi\) | ||
0.510341 | − | 0.859972i | \(-0.329519\pi\) | |||||||
\(38\) | − | 51.6696i | − | 1.35973i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 37.0921 | 0.904685 | 0.452342 | − | 0.891844i | \(-0.350588\pi\) | ||||
0.452342 | + | 0.891844i | \(0.350588\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00126i | 0.139564i | 0.997562 | + | 0.0697821i | \(0.0222304\pi\) | ||||
−0.997562 | + | 0.0697821i | \(0.977770\pi\) | |||||||
\(44\) | − | 31.6491i | − | 0.719298i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −31.4584 | − | 8.26838i | −0.683879 | − | 0.179747i | ||||
\(47\) | 32.4676 | 0.690800 | 0.345400 | − | 0.938455i | \(-0.387743\pi\) | ||||
0.345400 | + | 0.938455i | \(0.387743\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.9303 | −0.386333 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −28.6438 | −0.550843 | ||||||||
\(53\) | 36.6640i | 0.691774i | 0.938276 | + | 0.345887i | \(0.112422\pi\) | ||||
−0.938276 | + | 0.345887i | \(0.887578\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 35.3848 | 0.643360 | ||||||||
\(56\) | 23.3119i | 0.416283i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.14336 | −0.157644 | ||||||||
\(59\) | −6.65851 | −0.112856 | −0.0564280 | − | 0.998407i | \(-0.517971\pi\) | ||||
−0.0564280 | + | 0.998407i | \(0.517971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 55.7093i | − | 0.913268i | −0.889655 | − | 0.456634i | \(-0.849055\pi\) | ||
0.889655 | − | 0.456634i | \(-0.150945\pi\) | |||||||
\(62\) | −60.6028 | −0.977464 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 32.0248i | − | 0.492689i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.45984i | 0.0665648i | 0.999446 | + | 0.0332824i | \(0.0105961\pi\) | ||||
−0.999446 | + | 0.0332824i | \(0.989404\pi\) | |||||||
\(68\) | 20.3331i | 0.299017i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −26.0634 | −0.372335 | ||||||||
\(71\) | −118.412 | −1.66777 | −0.833886 | − | 0.551937i | \(-0.813889\pi\) | ||||
−0.833886 | + | 0.551937i | \(0.813889\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 82.2675 | 1.12695 | 0.563476 | − | 0.826133i | \(-0.309464\pi\) | ||||
0.563476 | + | 0.826133i | \(0.309464\pi\) | |||||||
\(74\) | − | 89.9976i | − | 1.21618i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 73.0718i | − | 0.961472i | ||||||
\(77\) | 130.426 | 1.69384 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 133.084i | − | 1.68461i | −0.538999 | − | 0.842307i | \(-0.681197\pi\) | ||
0.538999 | − | 0.842307i | \(-0.318803\pi\) | |||||||
\(80\) | 8.94427i | 0.111803i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 52.4561 | 0.639709 | ||||||||
\(83\) | 67.5614i | 0.813993i | 0.913430 | + | 0.406996i | \(0.133424\pi\) | ||||
−0.913430 | + | 0.406996i | \(0.866576\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.7331 | −0.267449 | ||||||||
\(86\) | 8.48707i | 0.0986868i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 44.7586i | − | 0.508620i | ||||||
\(89\) | − | 104.729i | − | 1.17673i | −0.808595 | − | 0.588365i | \(-0.799772\pi\) | ||
0.808595 | − | 0.588365i | \(-0.200228\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 118.041i | − | 1.29715i | ||||||
\(92\) | −44.4890 | − | 11.6933i | −0.483576 | − | 0.127101i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 45.9161 | 0.488470 | ||||||||
\(95\) | 81.6968 | 0.859966 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 98.6666i | − | 1.01718i | −0.861008 | − | 0.508591i | \(-0.830167\pi\) | ||
0.861008 | − | 0.508591i | \(-0.169833\pi\) | |||||||
\(98\) | −26.7715 | −0.273179 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 75.6811 | 0.749318 | 0.374659 | − | 0.927163i | \(-0.377760\pi\) | ||||
0.374659 | + | 0.927163i | \(0.377760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 86.8499i | 0.843203i | 0.906781 | + | 0.421602i | \(0.138532\pi\) | ||||
−0.906781 | + | 0.421602i | \(0.861468\pi\) | |||||||
\(104\) | −40.5085 | −0.389505 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51.8508i | 0.489158i | ||||||||
\(107\) | 5.55552i | 0.0519208i | 0.999663 | + | 0.0259604i | \(0.00826438\pi\) | ||||
−0.999663 | + | 0.0259604i | \(0.991736\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 71.0003i | − | 0.651379i | −0.945477 | − | 0.325689i | \(-0.894404\pi\) | ||
0.945477 | − | 0.325689i | \(-0.105596\pi\) | |||||||
\(110\) | 50.0416 | 0.454924 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 32.9679i | 0.294357i | ||||||||
\(113\) | 100.763i | 0.891707i | 0.895106 | + | 0.445854i | \(0.147100\pi\) | ||||
−0.895106 | + | 0.445854i | \(0.852900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.0735 | − | 49.7402i | 0.113682 | − | 0.432523i | ||||
\(116\) | −12.9307 | −0.111471 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.41655 | −0.0798013 | ||||||||
\(119\) | −83.7927 | −0.704141 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −129.417 | −1.06956 | ||||||||
\(122\) | − | 78.7849i | − | 0.645778i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −85.7053 | −0.691172 | ||||||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −43.9602 | −0.346143 | −0.173072 | − | 0.984909i | \(-0.555369\pi\) | ||||
−0.173072 | + | 0.984909i | \(0.555369\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | − | 45.2899i | − | 0.348384i | ||||||
\(131\) | 44.4134 | 0.339033 | 0.169517 | − | 0.985527i | \(-0.445779\pi\) | ||||
0.169517 | + | 0.985527i | \(0.445779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 301.129 | 2.26412 | ||||||||
\(134\) | 6.30717i | 0.0470684i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28.7554i | 0.211437i | ||||||||
\(137\) | − | 44.9295i | − | 0.327953i | −0.986464 | − | 0.163976i | \(-0.947568\pi\) | ||
0.986464 | − | 0.163976i | \(-0.0524321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −139.796 | −1.00573 | −0.502864 | − | 0.864365i | \(-0.667720\pi\) | ||||
−0.502864 | + | 0.864365i | \(0.667720\pi\) | |||||||
\(140\) | −36.8593 | −0.263281 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −167.460 | −1.17929 | ||||||||
\(143\) | 226.638i | 1.58488i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 14.4569i | − | 0.0997029i | ||||||
\(146\) | 116.344 | 0.796875 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 127.276i | − | 0.859972i | ||||||
\(149\) | 25.4227i | 0.170622i | 0.996354 | + | 0.0853111i | \(0.0271884\pi\) | ||||
−0.996354 | + | 0.0853111i | \(0.972812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −52.5299 | −0.347880 | −0.173940 | − | 0.984756i | \(-0.555650\pi\) | ||||
−0.173940 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(152\) | − | 103.339i | − | 0.679863i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 184.450 | 1.19773 | ||||||||
\(155\) | − | 95.8214i | − | 0.618203i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 74.5874i | − | 0.475079i | −0.971378 | − | 0.237539i | \(-0.923659\pi\) | ||
0.971378 | − | 0.237539i | \(-0.0763409\pi\) | |||||||
\(158\) | − | 188.210i | − | 1.19120i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 48.1878 | − | 183.339i | 0.299303 | − | 1.13875i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.3238 | −0.112416 | −0.0562080 | − | 0.998419i | \(-0.517901\pi\) | ||||
−0.0562080 | + | 0.998419i | \(0.517901\pi\) | |||||||
\(164\) | 74.1842 | 0.452342 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 95.5462i | 0.575580i | ||||||||
\(167\) | −68.9768 | −0.413035 | −0.206517 | − | 0.978443i | \(-0.566213\pi\) | ||||
−0.206517 | + | 0.978443i | \(0.566213\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.1174 | 0.213712 | ||||||||
\(170\) | −32.1495 | −0.189115 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.0025i | 0.0697821i | ||||||||
\(173\) | −118.707 | −0.686166 | −0.343083 | − | 0.939305i | \(-0.611471\pi\) | ||||
−0.343083 | + | 0.939305i | \(0.611471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 41.2099i | − | 0.235485i | ||||||
\(176\) | − | 63.2982i | − | 0.359649i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 148.109i | − | 0.832074i | ||||||
\(179\) | 278.892 | 1.55806 | 0.779029 | − | 0.626988i | \(-0.215712\pi\) | ||||
0.779029 | + | 0.626988i | \(0.215712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 66.1123i | 0.365261i | 0.983182 | + | 0.182631i | \(0.0584613\pi\) | ||||
−0.983182 | + | 0.182631i | \(0.941539\pi\) | |||||||
\(182\) | − | 166.935i | − | 0.917227i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −62.9169 | − | 16.5368i | −0.341940 | − | 0.0898737i | ||||
\(185\) | 142.299 | 0.769182 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 160.882 | 0.860329 | ||||||||
\(188\) | 64.9352 | 0.345400 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 115.537 | 0.608088 | ||||||||
\(191\) | − | 5.53406i | − | 0.0289741i | −0.999895 | − | 0.0144871i | \(-0.995388\pi\) | ||
0.999895 | − | 0.0144871i | \(-0.00461154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −72.0460 | −0.373295 | −0.186648 | − | 0.982427i | \(-0.559762\pi\) | ||||
−0.186648 | + | 0.982427i | \(0.559762\pi\) | |||||||
\(194\) | − | 139.536i | − | 0.719256i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −37.8606 | −0.193167 | ||||||||
\(197\) | −191.143 | −0.970271 | −0.485136 | − | 0.874439i | \(-0.661230\pi\) | ||||
−0.485136 | + | 0.874439i | \(0.661230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 172.543i | − | 0.867051i | −0.901141 | − | 0.433525i | \(-0.857269\pi\) | ||
0.901141 | − | 0.433525i | \(-0.142731\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 107.029 | 0.529848 | ||||||||
\(203\) | − | 53.2871i | − | 0.262498i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 82.9404i | 0.404587i | ||||||||
\(206\) | 122.824i | 0.596235i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −57.2877 | −0.275422 | ||||||||
\(209\) | −578.165 | −2.76634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −334.039 | −1.58312 | −0.791561 | − | 0.611090i | \(-0.790731\pi\) | ||||
−0.791561 | + | 0.611090i | \(0.790731\pi\) | |||||||
\(212\) | 73.3281i | 0.345887i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.85670i | 0.0367135i | ||||||||
\(215\) | −13.4192 | −0.0624150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 353.191i | − | 1.62761i | ||||||
\(218\) | − | 100.410i | − | 0.460594i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 70.7696 | 0.321680 | ||||||||
\(221\) | − | 145.605i | − | 0.658845i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −441.580 | −1.98018 | −0.990089 | − | 0.140440i | \(-0.955148\pi\) | ||||
−0.990089 | + | 0.140440i | \(0.955148\pi\) | |||||||
\(224\) | 46.6237i | 0.208142i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 142.500i | 0.630532i | ||||||||
\(227\) | 54.9222i | 0.241948i | 0.992656 | + | 0.120974i | \(0.0386018\pi\) | ||||
−0.992656 | + | 0.120974i | \(0.961398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 322.300i | 1.40743i | 0.710485 | + | 0.703713i | \(0.248476\pi\) | ||||
−0.710485 | + | 0.703713i | \(0.751524\pi\) | |||||||
\(230\) | 18.4887 | − | 70.3432i | 0.0803855 | − | 0.305840i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.2867 | −0.0788220 | ||||||||
\(233\) | −159.208 | −0.683296 | −0.341648 | − | 0.939828i | \(-0.610985\pi\) | ||||
−0.341648 | + | 0.939828i | \(0.610985\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 72.5998i | 0.308935i | ||||||||
\(236\) | −13.3170 | −0.0564280 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −118.501 | −0.497903 | ||||||||
\(239\) | −32.1990 | −0.134724 | −0.0673620 | − | 0.997729i | \(-0.521458\pi\) | ||||
−0.0673620 | + | 0.997729i | \(0.521458\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 39.8259i | 0.165253i | 0.996581 | + | 0.0826263i | \(0.0263308\pi\) | ||||
−0.996581 | + | 0.0826263i | \(0.973669\pi\) | |||||||
\(242\) | −183.023 | −0.756292 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 111.419i | − | 0.456634i | ||||||
\(245\) | − | 42.3295i | − | 0.172773i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 523.265i | 2.11848i | ||||||||
\(248\) | −121.206 | −0.488732 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | − | 232.529i | − | 0.926410i | −0.886251 | − | 0.463205i | \(-0.846699\pi\) | ||
0.886251 | − | 0.463205i | \(-0.153301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −92.5203 | + | 352.009i | −0.365693 | + | 1.39134i | ||||
\(254\) | −62.1691 | −0.244760 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −325.160 | −1.26521 | −0.632606 | − | 0.774473i | \(-0.718015\pi\) | ||||
−0.632606 | + | 0.774473i | \(0.718015\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 524.503 | 2.02511 | ||||||||
\(260\) | − | 64.0496i | − | 0.246344i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 62.8100 | 0.239733 | ||||||||
\(263\) | − | 4.94890i | − | 0.0188171i | −0.999956 | − | 0.00940855i | \(-0.997005\pi\) | ||
0.999956 | − | 0.00940855i | \(-0.00299488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −81.9833 | −0.309371 | ||||||||
\(266\) | 425.860 | 1.60098 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.91969i | 0.0332824i | ||||||||
\(269\) | −235.047 | −0.873781 | −0.436891 | − | 0.899515i | \(-0.643920\pi\) | ||||
−0.436891 | + | 0.899515i | \(0.643920\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −53.5224 | −0.197500 | −0.0987498 | − | 0.995112i | \(-0.531484\pi\) | ||||
−0.0987498 | + | 0.995112i | \(0.531484\pi\) | |||||||
\(272\) | 40.6663i | 0.149508i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 63.5399i | − | 0.231898i | ||||||
\(275\) | 79.1228i | 0.287719i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −143.576 | −0.518326 | −0.259163 | − | 0.965834i | \(-0.583447\pi\) | ||||
−0.259163 | + | 0.965834i | \(0.583447\pi\) | |||||||
\(278\) | −197.702 | −0.711157 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −52.1269 | −0.186167 | ||||||||
\(281\) | 187.330i | 0.666656i | 0.942811 | + | 0.333328i | \(0.108172\pi\) | ||||
−0.942811 | + | 0.333328i | \(0.891828\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 486.156i | − | 1.71787i | −0.512087 | − | 0.858934i | \(-0.671127\pi\) | ||
0.512087 | − | 0.858934i | \(-0.328873\pi\) | |||||||
\(284\) | −236.824 | −0.833886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 320.515i | 1.12068i | ||||||||
\(287\) | 305.712i | 1.06520i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 185.641 | 0.642356 | ||||||||
\(290\) | − | 20.4452i | − | 0.0705006i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 164.535 | 0.563476 | ||||||||
\(293\) | − | 240.733i | − | 0.821616i | −0.911722 | − | 0.410808i | \(-0.865247\pi\) | ||
0.911722 | − | 0.410808i | \(-0.134753\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 14.8889i | − | 0.0504708i | ||||||
\(296\) | − | 179.995i | − | 0.608092i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 35.9531i | 0.120648i | ||||||||
\(299\) | 318.584 | + | 83.7350i | 1.06550 | + | 0.280050i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.4623 | −0.164327 | ||||||||
\(302\) | −74.2885 | −0.245988 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 146.144i | − | 0.480736i | ||||||
\(305\) | 124.570 | 0.408426 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 338.091 | 1.10127 | 0.550636 | − | 0.834745i | \(-0.314385\pi\) | ||||
0.550636 | + | 0.834745i | \(0.314385\pi\) | |||||||
\(308\) | 260.852 | 0.846920 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 135.512i | − | 0.437135i | ||||||
\(311\) | 131.884 | 0.424066 | 0.212033 | − | 0.977263i | \(-0.431992\pi\) | ||||
0.212033 | + | 0.977263i | \(0.431992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 160.254i | − | 0.511994i | −0.966678 | − | 0.255997i | \(-0.917596\pi\) | ||
0.966678 | − | 0.255997i | \(-0.0824038\pi\) | |||||||
\(314\) | − | 105.482i | − | 0.335931i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 266.169i | − | 0.842307i | ||||||
\(317\) | 525.687 | 1.65832 | 0.829160 | − | 0.559012i | \(-0.188819\pi\) | ||||
0.829160 | + | 0.559012i | \(0.188819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 102.311i | 0.320724i | ||||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 68.1479 | − | 259.280i | 0.211639 | − | 0.805218i | ||||
\(323\) | 371.445 | 1.14998 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 71.6096 | 0.220337 | ||||||||
\(326\) | −25.9138 | −0.0794901 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 104.912 | 0.319854 | ||||||||
\(329\) | 267.598i | 0.813367i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.120137 | 0.000362953 | 0.000181477 | − | 1.00000i | \(-0.499942\pi\) | ||||
0.000181477 | 1.00000i | \(0.499942\pi\) | ||||||||
\(332\) | 135.123i | 0.406996i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −97.5480 | −0.292060 | ||||||||
\(335\) | −9.97251 | −0.0297687 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 652.946i | 1.93752i | 0.247992 | + | 0.968762i | \(0.420229\pi\) | ||||
−0.247992 | + | 0.968762i | \(0.579771\pi\) | |||||||
\(338\) | 51.0777 | 0.151117 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −45.4663 | −0.133724 | ||||||||
\(341\) | 678.124i | 1.98863i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 247.834i | 0.722548i | ||||||||
\(344\) | 16.9741i | 0.0493434i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −167.877 | −0.485193 | ||||||||
\(347\) | 468.304 | 1.34958 | 0.674789 | − | 0.738010i | \(-0.264234\pi\) | ||||
0.674789 | + | 0.738010i | \(0.264234\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 182.288 | 0.522315 | 0.261157 | − | 0.965296i | \(-0.415896\pi\) | ||||
0.261157 | + | 0.965296i | \(0.415896\pi\) | |||||||
\(350\) | − | 58.2796i | − | 0.166513i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 89.5172i | − | 0.254310i | ||||||
\(353\) | 301.039 | 0.852802 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 264.777i | − | 0.745850i | ||||||
\(356\) | − | 209.458i | − | 0.588365i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 394.413 | 1.10171 | ||||||||
\(359\) | − | 24.6772i | − | 0.0687388i | −0.999409 | − | 0.0343694i | \(-0.989058\pi\) | ||
0.999409 | − | 0.0343694i | \(-0.0109423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −973.874 | −2.69771 | ||||||||
\(362\) | 93.4969i | 0.258279i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 236.082i | − | 0.648577i | ||||||
\(365\) | 183.956i | 0.503988i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 427.508i | − | 1.16487i | −0.812877 | − | 0.582435i | \(-0.802100\pi\) | ||
0.812877 | − | 0.582435i | \(-0.197900\pi\) | |||||||
\(368\) | −88.9779 | − | 23.3865i | −0.241788 | − | 0.0635503i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 201.241 | 0.543894 | ||||||||
\(371\) | −302.184 | −0.814513 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 338.652i | − | 0.907913i | −0.891024 | − | 0.453957i | \(-0.850012\pi\) | ||
0.891024 | − | 0.453957i | \(-0.149988\pi\) | |||||||
\(374\) | 227.521 | 0.608344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 91.8323 | 0.244235 | ||||||||
\(377\) | 92.5959 | 0.245612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 287.157i | − | 0.757671i | −0.925464 | − | 0.378835i | \(-0.876325\pi\) | ||
0.925464 | − | 0.378835i | \(-0.123675\pi\) | |||||||
\(380\) | 163.394 | 0.429983 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 7.82634i | − | 0.0204878i | ||||||
\(383\) | − | 682.661i | − | 1.78240i | −0.453606 | − | 0.891202i | \(-0.649863\pi\) | ||
0.453606 | − | 0.891202i | \(-0.350137\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 291.641i | 0.757509i | ||||||||
\(386\) | −101.888 | −0.263960 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 197.333i | − | 0.508591i | ||||||
\(389\) | 543.886i | 1.39816i | 0.715041 | + | 0.699082i | \(0.246408\pi\) | ||||
−0.715041 | + | 0.699082i | \(0.753592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.4402 | − | 226.150i | 0.152021 | − | 0.578389i | ||||
\(392\) | −53.5430 | −0.136589 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −270.318 | −0.686085 | ||||||||
\(395\) | 297.586 | 0.753382 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 99.6609 | 0.251035 | 0.125517 | − | 0.992091i | \(-0.459941\pi\) | ||||
0.125517 | + | 0.992091i | \(0.459941\pi\) | |||||||
\(398\) | − | 244.013i | − | 0.613097i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 404.668i | 1.00915i | 0.863369 | + | 0.504573i | \(0.168350\pi\) | ||||
−0.863369 | + | 0.504573i | \(0.831650\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 613.732 | 1.52291 | ||||||||
\(404\) | 151.362 | 0.374659 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 75.3594i | − | 0.185614i | ||||||
\(407\) | −1007.04 | −2.47430 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 701.478 | 1.71510 | 0.857552 | − | 0.514397i | \(-0.171984\pi\) | ||||
0.857552 | + | 0.514397i | \(0.171984\pi\) | |||||||
\(410\) | 117.295i | 0.286087i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 173.700i | 0.421602i | ||||||||
\(413\) | − | 54.8793i | − | 0.132880i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −151.072 | −0.364029 | ||||||||
\(416\) | −81.0170 | −0.194752 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −817.648 | −1.95610 | ||||||||
\(419\) | − | 685.089i | − | 1.63506i | −0.575888 | − | 0.817529i | \(-0.695343\pi\) | ||
0.575888 | − | 0.817529i | \(-0.304657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 205.326i | 0.487711i | 0.969812 | + | 0.243856i | \(0.0784123\pi\) | ||||
−0.969812 | + | 0.243856i | \(0.921588\pi\) | |||||||
\(422\) | −472.402 | −1.11944 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 103.702i | 0.244579i | ||||||||
\(425\) | − | 50.8329i | − | 0.119607i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 459.156 | 1.07531 | ||||||||
\(428\) | 11.1110i | 0.0259604i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.9777 | −0.0441341 | ||||||||
\(431\) | 355.926i | 0.825814i | 0.910773 | + | 0.412907i | \(0.135487\pi\) | ||||
−0.910773 | + | 0.412907i | \(0.864513\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.2870i | 0.0399238i | 0.999801 | + | 0.0199619i | \(0.00635449\pi\) | ||||
−0.999801 | + | 0.0199619i | \(0.993646\pi\) | |||||||
\(434\) | − | 499.487i | − | 1.15089i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 142.001i | − | 0.325689i | ||||||
\(437\) | −213.612 | + | 812.723i | −0.488815 | + | 1.85978i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −458.708 | −1.04489 | −0.522447 | − | 0.852672i | \(-0.674981\pi\) | ||||
−0.522447 | + | 0.852672i | \(0.674981\pi\) | |||||||
\(440\) | 100.083 | 0.227462 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 205.916i | − | 0.465874i | ||||||
\(443\) | 196.292 | 0.443096 | 0.221548 | − | 0.975149i | \(-0.428889\pi\) | ||||
0.221548 | + | 0.975149i | \(0.428889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 234.181 | 0.526250 | ||||||||
\(446\) | −624.488 | −1.40020 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 65.9359i | 0.147178i | ||||||||
\(449\) | 344.536 | 0.767341 | 0.383671 | − | 0.923470i | \(-0.374660\pi\) | ||||
0.383671 | + | 0.923470i | \(0.374660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 586.966i | − | 1.30148i | ||||||
\(452\) | 201.526i | 0.445854i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 77.6717i | 0.171083i | ||||||||
\(455\) | 263.948 | 0.580105 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 122.214i | 0.267426i | 0.991020 | + | 0.133713i | \(0.0426900\pi\) | ||||
−0.991020 | + | 0.133713i | \(0.957310\pi\) | |||||||
\(458\) | 455.802i | 0.995200i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 26.1469 | − | 99.4803i | 0.0568411 | − | 0.216262i | ||||
\(461\) | −218.326 | −0.473593 | −0.236796 | − | 0.971559i | \(-0.576097\pi\) | ||||
−0.236796 | + | 0.971559i | \(0.576097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −455.380 | −0.983542 | −0.491771 | − | 0.870725i | \(-0.663650\pi\) | ||||
−0.491771 | + | 0.870725i | \(0.663650\pi\) | |||||||
\(464\) | −25.8613 | −0.0557356 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −225.154 | −0.483163 | ||||||||
\(467\) | 350.332i | 0.750176i | 0.926989 | + | 0.375088i | \(0.122388\pi\) | ||||
−0.926989 | + | 0.375088i | \(0.877612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −36.7580 | −0.0783752 | ||||||||
\(470\) | 102.672i | 0.218450i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.8331 | −0.0399006 | ||||||||
\(473\) | 94.9673 | 0.200777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 182.680i | 0.384589i | ||||||||
\(476\) | −167.585 | −0.352070 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −45.5363 | −0.0952643 | ||||||||
\(479\) | 743.178i | 1.55152i | 0.631028 | + | 0.775760i | \(0.282633\pi\) | ||||
−0.631028 | + | 0.775760i | \(0.717367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 911.417i | 1.89484i | ||||||||
\(482\) | 56.3223i | 0.116851i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −258.833 | −0.534779 | ||||||||
\(485\) | 220.625 | 0.454897 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −366.770 | −0.753122 | −0.376561 | − | 0.926392i | \(-0.622893\pi\) | ||||
−0.376561 | + | 0.926392i | \(0.622893\pi\) | |||||||
\(488\) | − | 157.570i | − | 0.322889i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − | 59.8629i | − | 0.122169i | ||||||
\(491\) | −127.024 | −0.258704 | −0.129352 | − | 0.991599i | \(-0.541290\pi\) | ||||
−0.129352 | + | 0.991599i | \(0.541290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 65.7302i | − | 0.133327i | ||||||
\(494\) | 740.008i | 1.49799i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −171.411 | −0.345586 | ||||||||
\(497\) | − | 975.948i | − | 1.96368i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 523.599 | 1.04930 | 0.524648 | − | 0.851319i | \(-0.324197\pi\) | ||||
0.524648 | + | 0.851319i | \(0.324197\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 328.845i | − | 0.655071i | ||||||
\(503\) | 646.170i | 1.28463i | 0.766440 | + | 0.642316i | \(0.222026\pi\) | ||||
−0.766440 | + | 0.642316i | \(0.777974\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 169.228i | 0.335105i | ||||||||
\(506\) | −130.844 | + | 497.816i | −0.258584 | + | 0.983826i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −87.9203 | −0.173072 | ||||||||
\(509\) | 605.436 | 1.18946 | 0.594731 | − | 0.803925i | \(-0.297259\pi\) | ||||
0.594731 | + | 0.803925i | \(0.297259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 678.047i | 1.32690i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −459.845 | −0.894641 | ||||||||
\(515\) | −194.202 | −0.377092 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 513.786i | − | 0.993783i | ||||||
\(518\) | 741.759 | 1.43197 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 90.5798i | − | 0.174192i | ||||||
\(521\) | − | 655.952i | − | 1.25902i | −0.776990 | − | 0.629512i | \(-0.783255\pi\) | ||
0.776990 | − | 0.629512i | \(-0.216745\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 317.109i | 0.606328i | 0.952938 | + | 0.303164i | \(0.0980430\pi\) | ||||
−0.952938 | + | 0.303164i | \(0.901957\pi\) | |||||||
\(524\) | 88.8267 | 0.169517 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 6.99880i | − | 0.0133057i | ||||||
\(527\) | − | 435.665i | − | 0.826688i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 460.634 | + | 260.111i | 0.870763 | + | 0.491702i | ||||
\(530\) | −115.942 | −0.218758 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 602.257 | 1.13206 | ||||||||
\(533\) | −531.230 | −0.996679 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.4225 | −0.0232197 | ||||||||
\(536\) | 12.6143i | 0.0235342i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −332.407 | −0.617856 | ||||||||
\(539\) | 299.564i | 0.555777i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −222.888 | −0.411992 | −0.205996 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205996 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(542\) | −75.6921 | −0.139653 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 57.5108i | 0.105718i | ||||||||
\(545\) | 158.762 | 0.291306 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −552.627 | −1.01029 | −0.505144 | − | 0.863035i | \(-0.668561\pi\) | ||||
−0.505144 | + | 0.863035i | \(0.668561\pi\) | |||||||
\(548\) | − | 89.8590i | − | 0.163976i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 111.897i | 0.203448i | ||||||||
\(551\) | 236.217i | 0.428706i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1096.88 | 1.98351 | ||||||||
\(554\) | −203.048 | −0.366512 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −279.592 | −0.502864 | ||||||||
\(557\) | 110.000i | 0.197486i | 0.995113 | + | 0.0987430i | \(0.0314822\pi\) | ||||
−0.995113 | + | 0.0987430i | \(0.968518\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 85.9496i | − | 0.153756i | ||||||
\(560\) | −73.7186 | −0.131640 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 264.925i | 0.471397i | ||||||||
\(563\) | 360.367i | 0.640084i | 0.947403 | + | 0.320042i | \(0.103697\pi\) | ||||
−0.947403 | + | 0.320042i | \(0.896303\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −225.313 | −0.398784 | ||||||||
\(566\) | − | 687.529i | − | 1.21472i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −334.919 | −0.589646 | ||||||||
\(569\) | 532.981i | 0.936698i | 0.883544 | + | 0.468349i | \(0.155151\pi\) | ||||
−0.883544 | + | 0.468349i | \(0.844849\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 582.697i | 1.02048i | 0.860031 | + | 0.510242i | \(0.170444\pi\) | ||||
−0.860031 | + | 0.510242i | \(0.829556\pi\) | |||||||
\(572\) | 453.276i | 0.792441i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 432.343i | 0.753210i | ||||||||
\(575\) | 111.222 | + | 29.2332i | 0.193430 | + | 0.0508403i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −869.422 | −1.50680 | −0.753399 | − | 0.657564i | \(-0.771587\pi\) | ||||
−0.753399 | + | 0.657564i | \(0.771587\pi\) | |||||||
\(578\) | 262.536 | 0.454214 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 28.9138i | − | 0.0498514i | ||||||
\(581\) | −556.840 | −0.958416 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 580.192 | 0.995183 | ||||||||
\(584\) | 232.688 | 0.398438 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 340.449i | − | 0.580970i | ||||||
\(587\) | 403.118 | 0.686742 | 0.343371 | − | 0.939200i | \(-0.388431\pi\) | ||||
0.343371 | + | 0.939200i | \(0.388431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1565.66i | 2.65817i | ||||||||
\(590\) | − | 21.0560i | − | 0.0356882i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 254.552i | − | 0.429986i | ||||||
\(593\) | 668.332 | 1.12703 | 0.563517 | − | 0.826104i | \(-0.309448\pi\) | ||||
0.563517 | + | 0.826104i | \(0.309448\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 187.366i | − | 0.314901i | ||||||
\(596\) | 50.8454i | 0.0853111i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 450.545 | + | 118.419i | 0.753420 | + | 0.198025i | ||||
\(599\) | −866.946 | −1.44732 | −0.723661 | − | 0.690155i | \(-0.757542\pi\) | ||||
−0.723661 | + | 0.690155i | \(0.757542\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 544.425 | 0.905866 | 0.452933 | − | 0.891545i | \(-0.350378\pi\) | ||||
0.452933 | + | 0.891545i | \(0.350378\pi\) | |||||||
\(602\) | −69.9503 | −0.116196 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −105.060 | −0.173940 | ||||||||
\(605\) | − | 289.384i | − | 0.478321i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.2820 | 0.0383559 | 0.0191779 | − | 0.999816i | \(-0.493895\pi\) | ||||
0.0191779 | + | 0.999816i | \(0.493895\pi\) | |||||||
\(608\) | − | 206.678i | − | 0.339932i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 176.168 | 0.288801 | ||||||||
\(611\) | −464.999 | −0.761045 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 559.419i | 0.912592i | 0.889828 | + | 0.456296i | \(0.150824\pi\) | ||||
−0.889828 | + | 0.456296i | \(0.849176\pi\) | |||||||
\(614\) | 478.133 | 0.778718 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 368.900 | 0.598863 | ||||||||
\(617\) | − | 1080.07i | − | 1.75052i | −0.483649 | − | 0.875262i | \(-0.660689\pi\) | ||
0.483649 | − | 0.875262i | \(-0.339311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 729.225i | − | 1.17807i | −0.808107 | − | 0.589035i | \(-0.799508\pi\) | ||
0.808107 | − | 0.589035i | \(-0.200492\pi\) | |||||||
\(620\) | − | 191.643i | − | 0.309101i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 186.513 | 0.299860 | ||||||||
\(623\) | 863.175 | 1.38551 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − | 226.634i | − | 0.362035i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 149.175i | − | 0.237539i | ||||||
\(629\) | 646.980 | 1.02858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 386.633i | − | 0.612731i | −0.951914 | − | 0.306365i | \(-0.900887\pi\) | ||
0.951914 | − | 0.306365i | \(-0.0991129\pi\) | |||||||
\(632\) | − | 376.420i | − | 0.595601i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 743.434 | 1.17261 | ||||||||
\(635\) | − | 98.2979i | − | 0.154800i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 271.118 | 0.425618 | ||||||||
\(638\) | 144.690i | 0.226786i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | − | 676.123i | − | 1.05479i | −0.849619 | − | 0.527397i | \(-0.823168\pi\) | ||
0.849619 | − | 0.527397i | \(-0.176832\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1063.72i | 1.65430i | 0.561980 | + | 0.827151i | \(0.310040\pi\) | ||||
−0.561980 | + | 0.827151i | \(0.689960\pi\) | |||||||
\(644\) | 96.3757 | − | 366.677i | 0.149652 | − | 0.569375i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 525.303 | 0.813162 | ||||||||
\(647\) | 157.776 | 0.243857 | 0.121929 | − | 0.992539i | \(-0.461092\pi\) | ||||
0.121929 | + | 0.992539i | \(0.461092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 105.368i | 0.162354i | ||||||||
\(650\) | 101.271 | 0.155802 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −36.6476 | −0.0562080 | ||||||||
\(653\) | −41.1895 | −0.0630773 | −0.0315386 | − | 0.999503i | \(-0.510041\pi\) | ||||
−0.0315386 | + | 0.999503i | \(0.510041\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 99.3113i | 0.151620i | ||||||||
\(656\) | 148.368 | 0.226171 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 378.440i | 0.575137i | ||||||||
\(659\) | 19.2526i | 0.0292149i | 0.999893 | + | 0.0146075i | \(0.00464986\pi\) | ||||
−0.999893 | + | 0.0146075i | \(0.995350\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 75.8322i | 0.114724i | 0.998353 | + | 0.0573618i | \(0.0182688\pi\) | ||||
−0.998353 | + | 0.0573618i | \(0.981731\pi\) | |||||||
\(662\) | 0.169900 | 0.000256647 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 191.092i | 0.287790i | ||||||||
\(665\) | 673.344i | 1.01255i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 143.818 | + | 37.8004i | 0.215619 | + | 0.0566722i | ||||
\(668\) | −137.954 | −0.206517 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.1033 | −0.0210497 | ||||||||
\(671\) | −881.576 | −1.31382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.6902 | 0.0188561 | 0.00942807 | − | 0.999956i | \(-0.496999\pi\) | ||||
0.00942807 | + | 0.999956i | \(0.496999\pi\) | |||||||
\(674\) | 923.405i | 1.37004i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 72.2347 | 0.106856 | ||||||||
\(677\) | − | 233.185i | − | 0.344439i | −0.985059 | − | 0.172220i | \(-0.944906\pi\) | ||
0.985059 | − | 0.172220i | \(-0.0550939\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 813.209 | 1.19766 | ||||||||
\(680\) | −64.2991 | −0.0945574 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 959.012i | 1.40618i | ||||||||
\(683\) | −367.020 | −0.537364 | −0.268682 | − | 0.963229i | \(-0.586588\pi\) | ||||
−0.268682 | + | 0.963229i | \(0.586588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 100.465 | 0.146665 | ||||||||
\(686\) | 350.490i | 0.510918i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24.0051i | 0.0348911i | ||||||||
\(689\) | − | 525.099i | − | 0.762118i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1186.21 | −1.71666 | −0.858332 | − | 0.513095i | \(-0.828499\pi\) | ||||
−0.858332 | + | 0.513095i | \(0.828499\pi\) | |||||||
\(692\) | −237.413 | −0.343083 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 662.282 | 0.954296 | ||||||||
\(695\) | − | 312.594i | − | 0.449775i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 377.099i | 0.541032i | ||||||||
\(698\) | 257.794 | 0.369332 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 82.4199i | − | 0.117743i | ||||||
\(701\) | 848.508i | 1.21043i | 0.796064 | + | 0.605213i | \(0.206912\pi\) | ||||
−0.796064 | + | 0.605213i | \(0.793088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2325.07 | −3.30736 | ||||||||
\(704\) | − | 126.596i | − | 0.179825i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 425.733 | 0.603022 | ||||||||
\(707\) | 623.763i | 0.882267i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 533.757i | − | 0.752831i | −0.926451 | − | 0.376416i | \(-0.877156\pi\) | ||
0.926451 | − | 0.376416i | \(-0.122844\pi\) | |||||||
\(710\) | − | 374.451i | − | 0.527396i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 296.218i | − | 0.416037i | ||||||
\(713\) | 953.235 | + | 250.544i | 1.33694 | + | 0.351394i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −506.778 | −0.708780 | ||||||||
\(716\) | 557.785 | 0.779029 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 34.8989i | − | 0.0486057i | ||||||
\(719\) | −1210.11 | −1.68304 | −0.841520 | − | 0.540225i | \(-0.818339\pi\) | ||||
−0.841520 | + | 0.540225i | \(0.818339\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −715.816 | −0.992810 | ||||||||
\(722\) | −1377.27 | −1.90757 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 132.225i | 0.182631i | ||||||||
\(725\) | 32.3266 | 0.0445885 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.43604i | 0.00335081i | 0.999999 | + | 0.00167540i | \(0.000533298\pi\) | ||||
−0.999999 | + | 0.00167540i | \(0.999467\pi\) | |||||||
\(728\) | − | 333.870i | − | 0.458613i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 260.153i | 0.356373i | ||||||||
\(731\) | −61.0123 | −0.0834641 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 495.146i | − | 0.675506i | −0.941235 | − | 0.337753i | \(-0.890333\pi\) | ||
0.941235 | − | 0.337753i | \(-0.109667\pi\) | |||||||
\(734\) | − | 604.587i | − | 0.823688i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −125.834 | − | 33.0735i | −0.170970 | − | 0.0449369i | ||||
\(737\) | 70.5751 | 0.0957599 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1235.77 | 1.67222 | 0.836112 | − | 0.548559i | \(-0.184823\pi\) | ||||
0.836112 | + | 0.548559i | \(0.184823\pi\) | |||||||
\(740\) | 284.597 | 0.384591 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −427.353 | −0.575948 | ||||||||
\(743\) | 1030.67i | 1.38717i | 0.720373 | + | 0.693587i | \(0.243971\pi\) | ||||
−0.720373 | + | 0.693587i | \(0.756029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −56.8469 | −0.0763045 | ||||||||
\(746\) | − | 478.926i | − | 0.641992i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 321.763 | 0.430164 | ||||||||
\(749\) | −45.7885 | −0.0611329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1112.44i | − | 1.48128i | −0.671903 | − | 0.740639i | \(-0.734523\pi\) | ||
0.671903 | − | 0.740639i | \(-0.265477\pi\) | |||||||
\(752\) | 129.870 | 0.172700 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 130.950 | 0.173674 | ||||||||
\(755\) | − | 117.460i | − | 0.155577i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 483.738i | 0.639019i | 0.947583 | + | 0.319510i | \(0.103518\pi\) | ||||
−0.947583 | + | 0.319510i | \(0.896482\pi\) | |||||||
\(758\) | − | 406.102i | − | 0.535754i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 231.073 | 0.304044 | ||||||||
\(761\) | −833.341 | −1.09506 | −0.547530 | − | 0.836786i | \(-0.684432\pi\) | ||||
−0.547530 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 585.183 | 0.766951 | ||||||||
\(764\) | − | 11.0681i | − | 0.0144871i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 965.428i | − | 1.26035i | ||||||
\(767\) | 95.3626 | 0.124332 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 356.518i | − | 0.463613i | −0.972762 | − | 0.231806i | \(-0.925536\pi\) | ||
0.972762 | − | 0.231806i | \(-0.0744636\pi\) | |||||||
\(770\) | 412.442i | 0.535640i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −144.092 | −0.186648 | ||||||||
\(773\) | − | 286.633i | − | 0.370805i | −0.982663 | − | 0.185403i | \(-0.940641\pi\) | ||
0.982663 | − | 0.185403i | \(-0.0593589\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 214.263 | 0.276469 | ||||||||
\(776\) | − | 279.071i | − | 0.359628i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 769.171i | 0.988651i | ||||||||
\(779\) | − | 1355.19i | − | 1.73966i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1873.81i | 2.39925i | ||||||||
\(782\) | 84.0611 | − | 319.825i | 0.107495 | − | 0.408983i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −75.7213 | −0.0965833 | ||||||||
\(785\) | 166.782 | 0.212462 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 930.798i | 1.18272i | 0.806409 | + | 0.591359i | \(0.201408\pi\) | ||||
−0.806409 | + | 0.591359i | \(0.798592\pi\) | |||||||
\(788\) | −382.287 | −0.485136 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 420.850 | 0.532721 | ||||||||
\(791\) | −830.487 | −1.04992 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 797.865i | 1.00613i | ||||||||
\(794\) | 140.942 | 0.177509 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 345.086i | − | 0.433525i | ||||||
\(797\) | 1493.90i | 1.87441i | 0.348785 | + | 0.937203i | \(0.386594\pi\) | ||||
−0.348785 | + | 0.937203i | \(0.613406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 330.084i | 0.413122i | ||||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 572.286i | 0.713574i | ||||||||
\(803\) | − | 1301.85i | − | 1.62123i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 409.958 | + | 107.751i | 0.509264 | + | 0.133853i | ||||
\(806\) | 867.948 | 1.07686 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 214.059 | 0.264924 | ||||||||
\(809\) | 850.318 | 1.05107 | 0.525537 | − | 0.850771i | \(-0.323865\pi\) | ||||
0.525537 | + | 0.850771i | \(0.323865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1050.33 | 1.29510 | 0.647552 | − | 0.762022i | \(-0.275793\pi\) | ||||
0.647552 | + | 0.762022i | \(0.275793\pi\) | |||||||
\(812\) | − | 106.574i | − | 0.131249i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1424.17 | −1.74960 | ||||||||
\(815\) | − | 40.9733i | − | 0.0502739i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 219.262 | 0.268374 | ||||||||
\(818\) | 992.039 | 1.21276 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 165.881i | 0.202294i | ||||||||
\(821\) | 461.343 | 0.561929 | 0.280964 | − | 0.959718i | \(-0.409346\pi\) | ||||
0.280964 | + | 0.959718i | \(0.409346\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 101.176 | 0.122936 | 0.0614680 | − | 0.998109i | \(-0.480422\pi\) | ||||
0.0614680 | + | 0.998109i | \(0.480422\pi\) | |||||||
\(824\) | 245.649i | 0.298117i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 77.6111i | − | 0.0939601i | ||||||
\(827\) | − | 718.169i | − | 0.868403i | −0.900816 | − | 0.434202i | \(-0.857031\pi\) | ||
0.900816 | − | 0.434202i | \(-0.142969\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 634.298 | 0.765137 | 0.382568 | − | 0.923927i | \(-0.375040\pi\) | ||||
0.382568 | + | 0.923927i | \(0.375040\pi\) | |||||||
\(830\) | −213.648 | −0.257407 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −114.575 | −0.137711 | ||||||||
\(833\) | − | 192.456i | − | 0.231040i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 154.237i | − | 0.184715i | ||||||
\(836\) | −1156.33 | −1.38317 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 968.862i | − | 1.15616i | ||||||
\(839\) | 133.138i | 0.158687i | 0.996847 | + | 0.0793434i | \(0.0252824\pi\) | ||||
−0.996847 | + | 0.0793434i | \(0.974718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −799.200 | −0.950297 | ||||||||
\(842\) | 290.375i | 0.344864i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −668.078 | −0.791561 | ||||||||
\(845\) | 80.7609i | 0.0955750i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1066.65i | − | 1.25933i | ||||||
\(848\) | 146.656i | 0.172944i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 71.8885i | − | 0.0845747i | ||||||
\(851\) | −372.068 | + | 1415.59i | −0.437212 | + | 1.66345i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 728.808 | 0.854406 | 0.427203 | − | 0.904156i | \(-0.359499\pi\) | ||||
0.427203 | + | 0.904156i | \(0.359499\pi\) | |||||||
\(854\) | 649.344 | 0.760356 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7134i | 0.0183568i | ||||||||
\(857\) | −1137.95 | −1.32783 | −0.663914 | − | 0.747809i | \(-0.731106\pi\) | ||||
−0.663914 | + | 0.747809i | \(0.731106\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −782.016 | −0.910379 | −0.455190 | − | 0.890395i | \(-0.650429\pi\) | ||||
−0.455190 | + | 0.890395i | \(0.650429\pi\) | |||||||
\(860\) | −26.8385 | −0.0312075 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 503.355i | 0.583939i | ||||||||
\(863\) | 324.868 | 0.376440 | 0.188220 | − | 0.982127i | \(-0.439728\pi\) | ||||
0.188220 | + | 0.982127i | \(0.439728\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 265.436i | − | 0.306863i | ||||||
\(866\) | 24.4475i | 0.0282304i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 706.382i | − | 0.813804i | ||||||
\(869\) | −2106.00 | −2.42348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 63.8735i | − | 0.0733336i | ||||||
\(872\) | − | 200.819i | − | 0.230297i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −302.093 | + | 1149.36i | −0.345644 | + | 1.31506i | ||||
\(875\) | 92.1482 | 0.105312 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −411.966 | −0.469745 | −0.234872 | − | 0.972026i | \(-0.575467\pi\) | ||||
−0.234872 | + | 0.972026i | \(0.575467\pi\) | |||||||
\(878\) | −648.712 | −0.738852 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 141.539 | 0.160840 | ||||||||
\(881\) | 1082.39i | 1.22859i | 0.789076 | + | 0.614296i | \(0.210560\pi\) | ||||
−0.789076 | + | 0.614296i | \(0.789440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1343.48 | 1.52149 | 0.760746 | − | 0.649049i | \(-0.224833\pi\) | ||||
0.760746 | + | 0.649049i | \(0.224833\pi\) | |||||||
\(884\) | − | 291.210i | − | 0.329423i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 277.598 | 0.313316 | ||||||||
\(887\) | −377.176 | −0.425227 | −0.212613 | − | 0.977136i | \(-0.568197\pi\) | ||||
−0.212613 | + | 0.977136i | \(0.568197\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 362.319i | − | 0.407558i | ||||||
\(890\) | 331.182 | 0.372115 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −883.160 | −0.990089 | ||||||||
\(893\) | − | 1186.23i | − | 1.32837i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 623.622i | 0.696785i | ||||||||
\(896\) | 93.2474i | 0.104071i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 487.248 | 0.542592 | ||||||||
\(899\) | 277.056 | 0.308183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −372.748 | −0.413704 | ||||||||
\(902\) | − | 830.095i | − | 0.920283i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 285.001i | 0.315266i | ||||||||
\(905\) | −147.832 | −0.163350 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 295.704i | − | 0.326024i | −0.986624 | − | 0.163012i | \(-0.947879\pi\) | ||
0.986624 | − | 0.163012i | \(-0.0521209\pi\) | |||||||
\(908\) | 109.844i | 0.120974i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 373.279 | 0.410196 | ||||||||
\(911\) | − | 419.625i | − | 0.460620i | −0.973117 | − | 0.230310i | \(-0.926026\pi\) | ||
0.973117 | − | 0.230310i | \(-0.0739740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1069.13 | 1.17101 | ||||||||
\(914\) | 172.836i | 0.189099i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 644.601i | 0.703713i | ||||||||
\(917\) | 366.054i | 0.399187i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1654.94i | − | 1.80080i | −0.435062 | − | 0.900401i | \(-0.643274\pi\) | ||
0.435062 | − | 0.900401i | \(-0.356726\pi\) | |||||||
\(920\) | 36.9773 | − | 140.686i | 0.0401928 | − | 0.152920i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −308.760 | −0.334881 | ||||||||
\(923\) | 1695.88 | 1.83736 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 318.190i | 0.343989i | ||||||||
\(926\) | −644.004 | −0.695469 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −36.5734 | −0.0394110 | ||||||||
\(929\) | 1291.79 | 1.39052 | 0.695260 | − | 0.718758i | \(-0.255289\pi\) | ||||
0.695260 | + | 0.718758i | \(0.255289\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 691.637i | 0.742897i | ||||||||
\(932\) | −318.416 | −0.341648 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 495.445i | 0.530455i | ||||||||
\(935\) | 359.742i | 0.384751i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 212.428i | − | 0.226711i | −0.993554 | − | 0.113355i | \(-0.963840\pi\) | ||
0.993554 | − | 0.113355i | \(-0.0361599\pi\) | |||||||
\(938\) | −51.9836 | −0.0554196 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 145.200i | 0.154468i | ||||||||
\(941\) | − | 980.930i | − | 1.04243i | −0.853424 | − | 0.521217i | \(-0.825478\pi\) | ||
0.853424 | − | 0.521217i | \(-0.174522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −825.094 | − | 216.864i | −0.874967 | − | 0.229972i | ||||
\(944\) | −26.6340 | −0.0282140 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 134.304 | 0.141970 | ||||||||
\(947\) | 953.755 | 1.00713 | 0.503567 | − | 0.863956i | \(-0.332021\pi\) | ||||
0.503567 | + | 0.863956i | \(0.332021\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1178.23 | −1.24155 | ||||||||
\(950\) | 258.348i | 0.271945i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −237.002 | −0.248951 | ||||||||
\(953\) | 248.522i | 0.260779i | 0.991463 | + | 0.130389i | \(0.0416227\pi\) | ||||
−0.991463 | + | 0.130389i | \(0.958377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.3745 | 0.0129576 | ||||||||
\(956\) | −64.3981 | −0.0673620 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1051.01i | 1.09709i | ||||||||
\(959\) | 370.308 | 0.386140 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 875.349 | 0.910873 | ||||||||
\(962\) | 1288.94i | 1.33985i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 79.6517i | 0.0826263i | ||||||||
\(965\) | − | 161.100i | − | 0.166943i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1112.21 | −1.15016 | −0.575081 | − | 0.818096i | \(-0.695030\pi\) | ||||
−0.575081 | + | 0.818096i | \(0.695030\pi\) | |||||||
\(968\) | −366.045 | −0.378146 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 312.011 | 0.321661 | ||||||||
\(971\) | 548.535i | 0.564918i | 0.959279 | + | 0.282459i | \(0.0911500\pi\) | ||||
−0.959279 | + | 0.282459i | \(0.908850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1152.20i | − | 1.18417i | ||||||
\(974\) | −518.692 | −0.532538 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 222.837i | − | 0.228317i | ||||||
\(977\) | 262.933i | 0.269122i | 0.990905 | + | 0.134561i | \(0.0429625\pi\) | ||||
−0.990905 | + | 0.134561i | \(0.957038\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1657.29 | −1.69284 | ||||||||
\(980\) | − | 84.6590i | − | 0.0863867i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −179.639 | −0.182932 | ||||||||
\(983\) | − | 1516.23i | − | 1.54245i | −0.636562 | − | 0.771226i | \(-0.719644\pi\) | ||
0.636562 | − | 0.771226i | \(-0.280356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 427.410i | − | 0.433918i | ||||||
\(986\) | − | 92.9566i | − | 0.0942765i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1046.53i | 1.05924i | ||||||||
\(989\) | 35.0872 | − | 133.495i | 0.0354774 | − | 0.134980i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 705.633 | 0.712042 | 0.356021 | − | 0.934478i | \(-0.384133\pi\) | ||||
0.356021 | + | 0.934478i | \(0.384133\pi\) | |||||||
\(992\) | −242.411 | −0.244366 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1380.20i | − | 1.38853i | ||||||
\(995\) | 385.818 | 0.387757 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 480.892 | 0.482339 | 0.241169 | − | 0.970483i | \(-0.422469\pi\) | ||||
0.241169 | + | 0.970483i | \(0.422469\pi\) | |||||||
\(998\) | 740.481 | 0.741965 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2070.3.c.a.91.15 | 16 | ||
3.2 | odd | 2 | 230.3.d.a.91.1 | ✓ | 16 | ||
12.11 | even | 2 | 1840.3.k.d.321.15 | 16 | |||
15.2 | even | 4 | 1150.3.c.c.1149.29 | 32 | |||
15.8 | even | 4 | 1150.3.c.c.1149.4 | 32 | |||
15.14 | odd | 2 | 1150.3.d.b.551.15 | 16 | |||
23.22 | odd | 2 | inner | 2070.3.c.a.91.10 | 16 | ||
69.68 | even | 2 | 230.3.d.a.91.2 | yes | 16 | ||
276.275 | odd | 2 | 1840.3.k.d.321.16 | 16 | |||
345.68 | odd | 4 | 1150.3.c.c.1149.30 | 32 | |||
345.137 | odd | 4 | 1150.3.c.c.1149.3 | 32 | |||
345.344 | even | 2 | 1150.3.d.b.551.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.1 | ✓ | 16 | 3.2 | odd | 2 | ||
230.3.d.a.91.2 | yes | 16 | 69.68 | even | 2 | ||
1150.3.c.c.1149.3 | 32 | 345.137 | odd | 4 | |||
1150.3.c.c.1149.4 | 32 | 15.8 | even | 4 | |||
1150.3.c.c.1149.29 | 32 | 15.2 | even | 4 | |||
1150.3.c.c.1149.30 | 32 | 345.68 | odd | 4 | |||
1150.3.d.b.551.15 | 16 | 15.14 | odd | 2 | |||
1150.3.d.b.551.16 | 16 | 345.344 | even | 2 | |||
1840.3.k.d.321.15 | 16 | 12.11 | even | 2 | |||
1840.3.k.d.321.16 | 16 | 276.275 | odd | 2 | |||
2070.3.c.a.91.10 | 16 | 23.22 | odd | 2 | inner | ||
2070.3.c.a.91.15 | 16 | 1.1 | even | 1 | trivial |