Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(551,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1150.551");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.d (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: | \(31.3352304014\) |
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: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.15 | ||
Root | \(0.0431371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.551 |
Dual form | 1150.3.d.b.551.16 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 5.41949 | 1.80650 | 0.903249 | − | 0.429117i | \(-0.141175\pi\) | ||||
0.903249 | + | 0.429117i | \(0.141175\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 7.66432 | 1.27739 | ||||||||
\(7\) | − | 8.24199i | − | 1.17743i | −0.808342 | − | 0.588713i | \(-0.799635\pi\) | ||
0.808342 | − | 0.588713i | \(-0.200365\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 20.3709 | 2.26343 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8246i | 1.43860i | 0.694702 | + | 0.719298i | \(0.255536\pi\) | ||||
−0.694702 | + | 0.719298i | \(0.744464\pi\) | |||||||
\(12\) | 10.8390 | 0.903249 | ||||||||
\(13\) | 14.3219 | 1.10169 | 0.550843 | − | 0.834609i | \(-0.314306\pi\) | ||||
0.550843 | + | 0.834609i | \(0.314306\pi\) | |||||||
\(14\) | − | 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 | \(0.903341\pi\) | |||||||
\(18\) | 28.8088 | 1.60049 | ||||||||
\(19\) | − | 36.5359i | − | 1.92294i | −0.274904 | − | 0.961472i | \(-0.588646\pi\) | ||
0.274904 | − | 0.961472i | \(-0.411354\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 44.6674i | − | 2.12702i | ||||||
\(22\) | 22.3793i | 1.01724i | ||||||||
\(23\) | −22.2445 | − | 5.84663i | −0.967151 | − | 0.254201i | ||||
\(24\) | 15.3286 | 0.638693 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 20.2543 | 0.779010 | ||||||||
\(27\) | 61.6245 | 2.28239 | ||||||||
\(28\) | − | 16.4840i | − | 0.588713i | ||||||
\(29\) | 6.46533 | 0.222942 | 0.111471 | − | 0.993768i | \(-0.464444\pi\) | ||||
0.111471 | + | 0.993768i | \(0.464444\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 85.7611i | 2.59882i | ||||||||
\(34\) | 14.3777i | 0.422874i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 40.7418 | 1.13172 | ||||||||
\(37\) | 63.6379i | 1.71994i | 0.510341 | + | 0.859972i | \(0.329519\pi\) | ||||
−0.510341 | + | 0.859972i | \(0.670481\pi\) | |||||||
\(38\) | − | 51.6696i | − | 1.35973i | ||||||
\(39\) | 77.6175 | 1.99019 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −37.0921 | −0.904685 | −0.452342 | − | 0.891844i | \(-0.649412\pi\) | ||||
−0.452342 | + | 0.891844i | \(0.649412\pi\) | |||||||
\(42\) | − | 63.1692i | − | 1.50403i | ||||||
\(43\) | − | 6.00126i | − | 0.139564i | −0.997562 | − | 0.0697821i | \(-0.977770\pi\) | ||
0.997562 | − | 0.0697821i | \(-0.0222304\pi\) | |||||||
\(44\) | 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 | \(0.387743\pi\) | |||||||
\(48\) | 21.6780 | 0.451624 | ||||||||
\(49\) | −18.9303 | −0.386333 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 55.0977i | 1.08035i | ||||||||
\(52\) | 28.6438 | 0.550843 | ||||||||
\(53\) | 36.6640i | 0.691774i | 0.938276 | + | 0.345887i | \(0.112422\pi\) | ||||
−0.938276 | + | 0.345887i | \(0.887578\pi\) | |||||||
\(54\) | 87.1502 | 1.61389 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 23.3119i | − | 0.416283i | ||||||
\(57\) | − | 198.006i | − | 3.47379i | ||||||
\(58\) | 9.14336 | 0.157644 | ||||||||
\(59\) | 6.65851 | 0.112856 | 0.0564280 | − | 0.998407i | \(-0.482029\pi\) | ||||
0.0564280 | + | 0.998407i | \(0.482029\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | − | 167.897i | − | 2.66503i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 121.284i | 1.83764i | ||||||||
\(67\) | − | 4.45984i | − | 0.0665648i | −0.999446 | − | 0.0332824i | \(-0.989404\pi\) | ||
0.999446 | − | 0.0332824i | \(-0.0105961\pi\) | |||||||
\(68\) | 20.3331i | 0.299017i | ||||||||
\(69\) | −120.554 | − | 31.6858i | −1.74716 | − | 0.459214i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 118.412 | 1.66777 | 0.833886 | − | 0.551937i | \(-0.186111\pi\) | ||||
0.833886 | + | 0.551937i | \(0.186111\pi\) | |||||||
\(72\) | 57.6176 | 0.800245 | ||||||||
\(73\) | −82.2675 | −1.12695 | −0.563476 | − | 0.826133i | \(-0.690536\pi\) | ||||
−0.563476 | + | 0.826133i | \(0.690536\pi\) | |||||||
\(74\) | 89.9976i | 1.21618i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 73.0718i | − | 0.961472i | ||||||
\(77\) | 130.426 | 1.69384 | ||||||||
\(78\) | 109.768 | 1.40728 | ||||||||
\(79\) | − | 133.084i | − | 1.68461i | −0.538999 | − | 0.842307i | \(-0.681197\pi\) | ||
0.538999 | − | 0.842307i | \(-0.318803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 150.636 | 1.85970 | ||||||||
\(82\) | −52.4561 | −0.639709 | ||||||||
\(83\) | 67.5614i | 0.813993i | 0.913430 | + | 0.406996i | \(0.133424\pi\) | ||||
−0.913430 | + | 0.406996i | \(0.866576\pi\) | |||||||
\(84\) | − | 89.3348i | − | 1.06351i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.48707i | − | 0.0986868i | ||||||
\(87\) | 35.0388 | 0.402745 | ||||||||
\(88\) | 44.7586i | 0.508620i | ||||||||
\(89\) | 104.729i | 1.17673i | 0.808595 | + | 0.588365i | \(0.200228\pi\) | ||||
−0.808595 | + | 0.588365i | \(0.799772\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 118.041i | − | 1.29715i | ||||||
\(92\) | −44.4890 | − | 11.6933i | −0.483576 | − | 0.127101i | ||||
\(93\) | −232.240 | −2.49720 | ||||||||
\(94\) | 45.9161 | 0.488470 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 30.6573 | 0.319347 | ||||||||
\(97\) | 98.6666i | 1.01718i | 0.861008 | + | 0.508591i | \(0.169833\pi\) | ||||
−0.861008 | + | 0.508591i | \(0.830167\pi\) | |||||||
\(98\) | −26.7715 | −0.273179 | ||||||||
\(99\) | 322.360i | 3.25617i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −75.6811 | −0.749318 | −0.374659 | − | 0.927163i | \(-0.622240\pi\) | ||||
−0.374659 | + | 0.927163i | \(0.622240\pi\) | |||||||
\(102\) | 77.9199i | 0.763920i | ||||||||
\(103\) | − | 86.8499i | − | 0.843203i | −0.906781 | − | 0.421602i | \(-0.861468\pi\) | ||
0.906781 | − | 0.421602i | \(-0.138532\pi\) | |||||||
\(104\) | 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 | \(0.991736\pi\) | |||||||
\(108\) | 123.249 | 1.14119 | ||||||||
\(109\) | − | 71.0003i | − | 0.651379i | −0.945477 | − | 0.325689i | \(-0.894404\pi\) | ||
0.945477 | − | 0.325689i | \(-0.105596\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 344.885i | 3.10707i | ||||||||
\(112\) | − | 32.9679i | − | 0.294357i | ||||||
\(113\) | 100.763i | 0.891707i | 0.895106 | + | 0.445854i | \(0.147100\pi\) | ||||
−0.895106 | + | 0.445854i | \(0.852900\pi\) | |||||||
\(114\) | − | 280.023i | − | 2.45634i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.9307 | 0.111471 | ||||||||
\(117\) | 291.750 | 2.49359 | ||||||||
\(118\) | 9.41655 | 0.0798013 | ||||||||
\(119\) | 83.7927 | 0.704141 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −129.417 | −1.06956 | ||||||||
\(122\) | − | 78.7849i | − | 0.645778i | ||||||
\(123\) | −201.020 | −1.63431 | ||||||||
\(124\) | −85.7053 | −0.691172 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 237.442i | − | 1.88446i | ||||||
\(127\) | 43.9602 | 0.346143 | 0.173072 | − | 0.984909i | \(-0.444631\pi\) | ||||
0.173072 | + | 0.984909i | \(0.444631\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 32.5238i | − | 0.252123i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −44.4134 | −0.339033 | −0.169517 | − | 0.985527i | \(-0.554221\pi\) | ||||
−0.169517 | + | 0.985527i | \(0.554221\pi\) | |||||||
\(132\) | 171.522i | 1.29941i | ||||||||
\(133\) | −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 | \(-0.0524321\pi\) | |||||||
\(138\) | −170.489 | − | 44.8105i | −1.23543 | − | 0.324713i | ||||
\(139\) | −139.796 | −1.00573 | −0.502864 | − | 0.864365i | \(-0.667720\pi\) | ||||
−0.502864 | + | 0.864365i | \(0.667720\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 175.958 | 1.24793 | ||||||||
\(142\) | 167.460 | 1.17929 | ||||||||
\(143\) | 226.638i | 1.58488i | ||||||||
\(144\) | 81.4836 | 0.565858 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −116.344 | −0.796875 | ||||||||
\(147\) | −102.593 | −0.697910 | ||||||||
\(148\) | 127.276i | 0.859972i | ||||||||
\(149\) | − | 25.4227i | − | 0.170622i | −0.996354 | − | 0.0853111i | \(-0.972812\pi\) | ||
0.996354 | − | 0.0853111i | \(-0.0271884\pi\) | |||||||
\(150\) | 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 | ||||||
\(153\) | 207.102i | 1.35361i | ||||||||
\(154\) | 184.450 | 1.19773 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 155.235 | 0.995097 | ||||||||
\(157\) | 74.5874i | 0.475079i | 0.971378 | + | 0.237539i | \(0.0763409\pi\) | ||||
−0.971378 | + | 0.237539i | \(0.923659\pi\) | |||||||
\(158\) | − | 188.210i | − | 1.19120i | ||||||
\(159\) | 198.700i | 1.24969i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −48.1878 | + | 183.339i | −0.299303 | + | 1.13875i | ||||
\(162\) | 213.031 | 1.31501 | ||||||||
\(163\) | 18.3238 | 0.112416 | 0.0562080 | − | 0.998419i | \(-0.482099\pi\) | ||||
0.0562080 | + | 0.998419i | \(0.482099\pi\) | |||||||
\(164\) | −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 | \(0.566213\pi\) | |||||||
\(168\) | − | 126.338i | − | 0.752014i | ||||||
\(169\) | 36.1174 | 0.213712 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 744.270i | − | 4.35245i | ||||||
\(172\) | − | 12.0025i | − | 0.0697821i | ||||||
\(173\) | −118.707 | −0.686166 | −0.343083 | − | 0.939305i | \(-0.611471\pi\) | ||||
−0.343083 | + | 0.939305i | \(0.611471\pi\) | |||||||
\(174\) | 49.5523 | 0.284784 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 63.2982i | 0.359649i | ||||||||
\(177\) | 36.0857 | 0.203874 | ||||||||
\(178\) | 148.109i | 0.832074i | ||||||||
\(179\) | −278.892 | −1.55806 | −0.779029 | − | 0.626988i | \(-0.784288\pi\) | ||||
−0.779029 | + | 0.626988i | \(0.784288\pi\) | |||||||
\(180\) | 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 | ||||||
\(183\) | − | 301.916i | − | 1.64982i | ||||||
\(184\) | −62.9169 | − | 16.5368i | −0.341940 | − | 0.0898737i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −328.436 | −1.76579 | ||||||||
\(187\) | −160.882 | −0.860329 | ||||||||
\(188\) | 64.9352 | 0.345400 | ||||||||
\(189\) | − | 507.908i | − | 2.68735i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.53406i | 0.0289741i | 0.999895 | + | 0.0144871i | \(0.00461154\pi\) | ||||
−0.999895 | + | 0.0144871i | \(0.995388\pi\) | |||||||
\(192\) | 43.3559 | 0.225812 | ||||||||
\(193\) | 72.0460 | 0.373295 | 0.186648 | − | 0.982427i | \(-0.440238\pi\) | ||||
0.186648 | + | 0.982427i | \(0.440238\pi\) | |||||||
\(194\) | 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 | \(0.661230\pi\) | |||||||
\(198\) | 455.887i | 2.30246i | ||||||||
\(199\) | − | 172.543i | − | 0.867051i | −0.901141 | − | 0.433525i | \(-0.857269\pi\) | ||
0.901141 | − | 0.433525i | \(-0.142731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 24.1701i | − | 0.120249i | ||||||
\(202\) | −107.029 | −0.529848 | ||||||||
\(203\) | − | 53.2871i | − | 0.262498i | ||||||
\(204\) | 110.195i | 0.540173i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 122.824i | − | 0.596235i | ||||||
\(207\) | −453.140 | − | 119.101i | −2.18908 | − | 0.575368i | ||||
\(208\) | 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 | ||||||||
\(213\) | 641.732 | 3.01282 | ||||||||
\(214\) | 7.85670i | 0.0367135i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 174.300 | 0.806947 | ||||||||
\(217\) | 353.191i | 1.62761i | ||||||||
\(218\) | − | 100.410i | − | 0.460594i | ||||||
\(219\) | −445.848 | −2.03584 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 145.605i | 0.658845i | ||||||||
\(222\) | 487.741i | 2.19703i | ||||||||
\(223\) | 441.580 | 1.98018 | 0.990089 | − | 0.140440i | \(-0.0448517\pi\) | ||||
0.990089 | + | 0.140440i | \(0.0448517\pi\) | |||||||
\(224\) | − | 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 | \(0.961398\pi\) | |||||||
\(228\) | − | 396.012i | − | 1.73690i | ||||||
\(229\) | 322.300i | 1.40743i | 0.710485 | + | 0.703713i | \(0.248476\pi\) | ||||
−0.710485 | + | 0.703713i | \(0.751524\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 706.841 | 3.05992 | ||||||||
\(232\) | 18.2867 | 0.0788220 | ||||||||
\(233\) | −159.208 | −0.683296 | −0.341648 | − | 0.939828i | \(-0.610985\pi\) | ||||
−0.341648 | + | 0.939828i | \(0.610985\pi\) | |||||||
\(234\) | 412.597 | 1.76324 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.3170 | 0.0564280 | ||||||||
\(237\) | − | 721.250i | − | 3.04325i | ||||||
\(238\) | 118.501 | 0.497903 | ||||||||
\(239\) | 32.1990 | 0.134724 | 0.0673620 | − | 0.997729i | \(-0.478542\pi\) | ||||
0.0673620 | + | 0.997729i | \(0.478542\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 261.748 | 1.07715 | ||||||||
\(244\) | − | 111.419i | − | 0.456634i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −284.286 | −1.15563 | ||||||||
\(247\) | − | 523.265i | − | 2.11848i | ||||||
\(248\) | −121.206 | −0.488732 | ||||||||
\(249\) | 366.148i | 1.47048i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 232.529i | 0.926410i | 0.886251 | + | 0.463205i | \(0.153301\pi\) | ||||
−0.886251 | + | 0.463205i | \(0.846699\pi\) | |||||||
\(252\) | − | 335.793i | − | 1.33251i | ||||||
\(253\) | 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 | \(0.718015\pi\) | |||||||
\(258\) | − | 45.9956i | − | 0.178278i | ||||||
\(259\) | 524.503 | 2.02511 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 131.705 | 0.504615 | ||||||||
\(262\) | −62.8100 | −0.239733 | ||||||||
\(263\) | − | 4.94890i | − | 0.0188171i | −0.999956 | − | 0.00940855i | \(-0.997005\pi\) | ||
0.999956 | − | 0.00940855i | \(-0.00299488\pi\) | |||||||
\(264\) | 242.569i | 0.918822i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −425.860 | −1.60098 | ||||||||
\(267\) | 567.578i | 2.12576i | ||||||||
\(268\) | − | 8.91969i | − | 0.0332824i | ||||||
\(269\) | 235.047 | 0.873781 | 0.436891 | − | 0.899515i | \(-0.356080\pi\) | ||||
0.436891 | + | 0.899515i | \(0.356080\pi\) | |||||||
\(270\) | 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 | ||||||||
\(273\) | − | 639.723i | − | 2.34331i | ||||||
\(274\) | − | 63.5399i | − | 0.231898i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −241.108 | − | 63.3715i | −0.873578 | − | 0.229607i | ||||
\(277\) | 143.576 | 0.518326 | 0.259163 | − | 0.965834i | \(-0.416553\pi\) | ||||
0.259163 | + | 0.965834i | \(0.416553\pi\) | |||||||
\(278\) | −197.702 | −0.711157 | ||||||||
\(279\) | −872.947 | −3.12884 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 187.330i | − | 0.666656i | −0.942811 | − | 0.333328i | \(-0.891828\pi\) | ||
0.942811 | − | 0.333328i | \(-0.108172\pi\) | |||||||
\(282\) | 248.842 | 0.882419 | ||||||||
\(283\) | 486.156i | 1.71787i | 0.512087 | + | 0.858934i | \(0.328873\pi\) | ||||
−0.512087 | + | 0.858934i | \(0.671127\pi\) | |||||||
\(284\) | 236.824 | 0.833886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 320.515i | 1.12068i | ||||||||
\(287\) | 305.712i | 1.06520i | ||||||||
\(288\) | 115.235 | 0.400122 | ||||||||
\(289\) | 185.641 | 0.642356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 534.723i | 1.83754i | ||||||||
\(292\) | −164.535 | −0.563476 | ||||||||
\(293\) | − | 240.733i | − | 0.821616i | −0.911722 | − | 0.410808i | \(-0.865247\pi\) | ||
0.911722 | − | 0.410808i | \(-0.134753\pi\) | |||||||
\(294\) | −145.088 | −0.493497 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 179.995i | 0.608092i | ||||||||
\(297\) | 975.181i | 3.28344i | ||||||||
\(298\) | − | 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 | ||||||||
\(303\) | −410.153 | −1.35364 | ||||||||
\(304\) | − | 146.144i | − | 0.480736i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 292.887i | 0.957147i | ||||||||
\(307\) | −338.091 | −1.10127 | −0.550636 | − | 0.834745i | \(-0.685615\pi\) | ||||
−0.550636 | + | 0.834745i | \(0.685615\pi\) | |||||||
\(308\) | 260.852 | 0.846920 | ||||||||
\(309\) | − | 470.683i | − | 1.52324i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −131.884 | −0.424066 | −0.212033 | − | 0.977263i | \(-0.568008\pi\) | ||||
−0.212033 | + | 0.977263i | \(0.568008\pi\) | |||||||
\(312\) | 219.536 | 0.703640 | ||||||||
\(313\) | 160.254i | 0.511994i | 0.966678 | + | 0.255997i | \(0.0824038\pi\) | ||||
−0.966678 | + | 0.255997i | \(0.917596\pi\) | |||||||
\(314\) | 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 | \(0.188819\pi\) | |||||||
\(318\) | 281.005i | 0.883663i | ||||||||
\(319\) | 102.311i | 0.320724i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.1081i | 0.0937948i | ||||||||
\(322\) | −68.1479 | + | 259.280i | −0.211639 | + | 0.805218i | ||||
\(323\) | 371.445 | 1.14998 | ||||||||
\(324\) | 301.271 | 0.929849 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.9138 | 0.0794901 | ||||||||
\(327\) | − | 384.786i | − | 1.17671i | ||||||
\(328\) | −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 | ||||||||
\(333\) | 1296.36i | 3.89298i | ||||||||
\(334\) | −97.5480 | −0.292060 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 178.670i | − | 0.531755i | ||||||
\(337\) | − | 652.946i | − | 1.93752i | −0.247992 | − | 0.968762i | \(-0.579771\pi\) | ||
0.247992 | − | 0.968762i | \(-0.420229\pi\) | |||||||
\(338\) | 51.0777 | 0.151117 | ||||||||
\(339\) | 546.084i | 1.61087i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 678.124i | − | 1.98863i | ||||||
\(342\) | − | 1052.56i | − | 3.07765i | ||||||
\(343\) | − | 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 | \(0.264234\pi\) | |||||||
\(348\) | 70.0776 | 0.201372 | ||||||||
\(349\) | 182.288 | 0.522315 | 0.261157 | − | 0.965296i | \(-0.415896\pi\) | ||||
0.261157 | + | 0.965296i | \(0.415896\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 882.581 | 2.51448 | ||||||||
\(352\) | 89.5172i | 0.254310i | ||||||||
\(353\) | 301.039 | 0.852802 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(354\) | 51.0329 | 0.144161 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 209.458i | 0.588365i | ||||||||
\(357\) | 454.114 | 1.27203 | ||||||||
\(358\) | −394.413 | −1.10171 | ||||||||
\(359\) | 24.6772i | 0.0687388i | 0.999409 | + | 0.0343694i | \(0.0109423\pi\) | ||||
−0.999409 | + | 0.0343694i | \(0.989058\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −973.874 | −2.69771 | ||||||||
\(362\) | 93.4969i | 0.258279i | ||||||||
\(363\) | −701.372 | −1.93215 | ||||||||
\(364\) | − | 236.082i | − | 0.648577i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 426.974i | − | 1.16660i | ||||||
\(367\) | 427.508i | 1.16487i | 0.812877 | + | 0.582435i | \(0.197900\pi\) | ||||
−0.812877 | + | 0.582435i | \(0.802100\pi\) | |||||||
\(368\) | −88.9779 | − | 23.3865i | −0.241788 | − | 0.0635503i | ||||
\(369\) | −755.599 | −2.04769 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 302.184 | 0.814513 | ||||||||
\(372\) | −464.479 | −1.24860 | ||||||||
\(373\) | 338.652i | 0.907913i | 0.891024 | + | 0.453957i | \(0.149988\pi\) | ||||
−0.891024 | + | 0.453957i | \(0.850012\pi\) | |||||||
\(374\) | −227.521 | −0.608344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 91.8323 | 0.244235 | ||||||||
\(377\) | 92.5959 | 0.245612 | ||||||||
\(378\) | − | 718.291i | − | 1.90024i | ||||||
\(379\) | − | 287.157i | − | 0.757671i | −0.925464 | − | 0.378835i | \(-0.876325\pi\) | ||
0.925464 | − | 0.378835i | \(-0.123675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 238.242 | 0.625307 | ||||||||
\(382\) | 7.82634i | 0.0204878i | ||||||||
\(383\) | − | 682.661i | − | 1.78240i | −0.453606 | − | 0.891202i | \(-0.649863\pi\) | ||
0.453606 | − | 0.891202i | \(-0.350137\pi\) | |||||||
\(384\) | 61.3146 | 0.159673 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 101.888 | 0.263960 | ||||||||
\(387\) | − | 122.251i | − | 0.315894i | ||||||
\(388\) | 197.333i | 0.508591i | ||||||||
\(389\) | − | 543.886i | − | 1.39816i | −0.715041 | − | 0.699082i | \(-0.753592\pi\) | ||
0.715041 | − | 0.699082i | \(-0.246408\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 59.4402 | − | 226.150i | 0.152021 | − | 0.578389i | ||||
\(392\) | −53.5430 | −0.136589 | ||||||||
\(393\) | −240.698 | −0.612463 | ||||||||
\(394\) | −270.318 | −0.686085 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 644.721i | 1.62808i | ||||||||
\(397\) | −99.6609 | −0.251035 | −0.125517 | − | 0.992091i | \(-0.540059\pi\) | ||||
−0.125517 | + | 0.992091i | \(0.540059\pi\) | |||||||
\(398\) | − | 244.013i | − | 0.613097i | ||||||
\(399\) | −1631.96 | −4.09014 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 404.668i | − | 1.00915i | −0.863369 | − | 0.504573i | \(-0.831650\pi\) | ||
0.863369 | − | 0.504573i | \(-0.168350\pi\) | |||||||
\(402\) | − | 34.1817i | − | 0.0850290i | ||||||
\(403\) | −613.732 | −1.52291 | ||||||||
\(404\) | −151.362 | −0.374659 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 75.3594i | − | 0.185614i | ||||||
\(407\) | −1007.04 | −2.47430 | ||||||||
\(408\) | 155.840i | 0.381960i | ||||||||
\(409\) | 701.478 | 1.71510 | 0.857552 | − | 0.514397i | \(-0.171984\pi\) | ||||
0.857552 | + | 0.514397i | \(0.171984\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 243.495i | − | 0.592446i | ||||||
\(412\) | − | 173.700i | − | 0.421602i | ||||||
\(413\) | − | 54.8793i | − | 0.132880i | ||||||
\(414\) | −640.837 | − | 168.434i | −1.54792 | − | 0.406847i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 81.0170 | 0.194752 | ||||||||
\(417\) | −757.625 | −1.81685 | ||||||||
\(418\) | 817.648 | 1.95610 | ||||||||
\(419\) | 685.089i | 1.63506i | 0.575888 | + | 0.817529i | \(0.304657\pi\) | ||||
−0.575888 | + | 0.817529i | \(0.695343\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | 661.395 | 1.56358 | ||||||||
\(424\) | 103.702i | 0.244579i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 907.546 | 2.13039 | ||||||||
\(427\) | −459.156 | −1.07531 | ||||||||
\(428\) | 11.1110i | 0.0259604i | ||||||||
\(429\) | 1228.26i | 2.86308i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 355.926i | − | 0.825814i | −0.910773 | − | 0.412907i | \(-0.864513\pi\) | ||
0.910773 | − | 0.412907i | \(-0.135487\pi\) | |||||||
\(432\) | 246.498 | 0.570597 | ||||||||
\(433\) | − | 17.2870i | − | 0.0399238i | −0.999801 | − | 0.0199619i | \(-0.993646\pi\) | ||
0.999801 | − | 0.0199619i | \(-0.00635449\pi\) | |||||||
\(434\) | 499.487i | 1.15089i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 142.001i | − | 0.325689i | ||||||
\(437\) | −213.612 | + | 812.723i | −0.488815 | + | 1.85978i | ||||
\(438\) | −630.524 | −1.43955 | ||||||||
\(439\) | −458.708 | −1.04489 | −0.522447 | − | 0.852672i | \(-0.674981\pi\) | ||||
−0.522447 | + | 0.852672i | \(0.674981\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −385.628 | −0.874439 | ||||||||
\(442\) | 205.916i | 0.465874i | ||||||||
\(443\) | 196.292 | 0.443096 | 0.221548 | − | 0.975149i | \(-0.428889\pi\) | ||||
0.221548 | + | 0.975149i | \(0.428889\pi\) | |||||||
\(444\) | 689.771i | 1.55354i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 624.488 | 1.40020 | ||||||||
\(447\) | − | 137.778i | − | 0.308228i | ||||||
\(448\) | − | 65.9359i | − | 0.147178i | ||||||
\(449\) | −344.536 | −0.767341 | −0.383671 | − | 0.923470i | \(-0.625340\pi\) | ||||
−0.383671 | + | 0.923470i | \(0.625340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 586.966i | − | 1.30148i | ||||||
\(452\) | 201.526i | 0.445854i | ||||||||
\(453\) | −284.685 | −0.628445 | ||||||||
\(454\) | 77.6717i | 0.171083i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 560.046i | − | 1.22817i | ||||||
\(457\) | − | 122.214i | − | 0.267426i | −0.991020 | − | 0.133713i | \(-0.957310\pi\) | ||
0.991020 | − | 0.133713i | \(-0.0426900\pi\) | |||||||
\(458\) | 455.802i | 0.995200i | ||||||||
\(459\) | 626.510i | 1.36495i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 218.326 | 0.473593 | 0.236796 | − | 0.971559i | \(-0.423903\pi\) | ||||
0.236796 | + | 0.971559i | \(0.423903\pi\) | |||||||
\(462\) | 999.625 | 2.16369 | ||||||||
\(463\) | 455.380 | 0.983542 | 0.491771 | − | 0.870725i | \(-0.336350\pi\) | ||||
0.491771 | + | 0.870725i | \(0.336350\pi\) | |||||||
\(464\) | 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 | \(0.877612\pi\) | |||||||
\(468\) | 583.501 | 1.24680 | ||||||||
\(469\) | −36.7580 | −0.0783752 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 404.226i | 0.858229i | ||||||||
\(472\) | 18.8331 | 0.0399006 | ||||||||
\(473\) | 94.9673 | 0.200777 | ||||||||
\(474\) | − | 1020.00i | − | 2.15190i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 167.585 | 0.352070 | ||||||||
\(477\) | 746.879i | 1.56578i | ||||||||
\(478\) | 45.5363 | 0.0952643 | ||||||||
\(479\) | − | 743.178i | − | 1.55152i | −0.631028 | − | 0.775760i | \(-0.717367\pi\) | ||
0.631028 | − | 0.775760i | \(-0.282633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 911.417i | 1.89484i | ||||||||
\(482\) | 56.3223i | 0.116851i | ||||||||
\(483\) | −261.154 | + | 993.603i | −0.540691 | + | 2.05715i | ||||
\(484\) | −258.833 | −0.534779 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 370.167 | 0.761660 | ||||||||
\(487\) | 366.770 | 0.753122 | 0.376561 | − | 0.926392i | \(-0.377107\pi\) | ||||
0.376561 | + | 0.926392i | \(0.377107\pi\) | |||||||
\(488\) | − | 157.570i | − | 0.322889i | ||||||
\(489\) | 99.3057 | 0.203079 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 127.024 | 0.258704 | 0.129352 | − | 0.991599i | \(-0.458710\pi\) | ||||
0.129352 | + | 0.991599i | \(0.458710\pi\) | |||||||
\(492\) | −402.041 | −0.817156 | ||||||||
\(493\) | 65.7302i | 0.133327i | ||||||||
\(494\) | − | 740.008i | − | 1.49799i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −171.411 | −0.345586 | ||||||||
\(497\) | − | 975.948i | − | 1.96368i | ||||||
\(498\) | 517.812i | 1.03978i | ||||||||
\(499\) | 523.599 | 1.04930 | 0.524648 | − | 0.851319i | \(-0.324197\pi\) | ||||
0.524648 | + | 0.851319i | \(0.324197\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −373.819 | −0.746147 | ||||||||
\(502\) | 328.845i | 0.655071i | ||||||||
\(503\) | 646.170i | 1.28463i | 0.766440 | + | 0.642316i | \(0.222026\pi\) | ||||
−0.766440 | + | 0.642316i | \(0.777974\pi\) | |||||||
\(504\) | − | 474.884i | − | 0.942229i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 130.844 | − | 497.816i | 0.258584 | − | 0.983826i | ||||
\(507\) | 195.738 | 0.386070 | ||||||||
\(508\) | 87.9203 | 0.173072 | ||||||||
\(509\) | −605.436 | −1.18946 | −0.594731 | − | 0.803925i | \(-0.702741\pi\) | ||||
−0.594731 | + | 0.803925i | \(0.702741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 678.047i | 1.32690i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 2251.51i | − | 4.38891i | ||||||
\(514\) | −459.845 | −0.894641 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 65.0476i | − | 0.126061i | ||||||
\(517\) | 513.786i | 0.993783i | ||||||||
\(518\) | 741.759 | 1.43197 | ||||||||
\(519\) | −643.330 | −1.23956 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 655.952i | 1.25902i | 0.776990 | + | 0.629512i | \(0.216745\pi\) | ||||
−0.776990 | + | 0.629512i | \(0.783255\pi\) | |||||||
\(522\) | 186.258 | 0.356817 | ||||||||
\(523\) | − | 317.109i | − | 0.606328i | −0.952938 | − | 0.303164i | \(-0.901957\pi\) | ||
0.952938 | − | 0.303164i | \(-0.0980430\pi\) | |||||||
\(524\) | −88.8267 | −0.169517 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 6.99880i | − | 0.0133057i | ||||||
\(527\) | − | 435.665i | − | 0.826688i | ||||||
\(528\) | 343.044i | 0.649705i | ||||||||
\(529\) | 460.634 | + | 260.111i | 0.870763 | + | 0.491702i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 135.640 | 0.255442 | ||||||||
\(532\) | −602.257 | −1.13206 | ||||||||
\(533\) | −531.230 | −0.996679 | ||||||||
\(534\) | 802.677i | 1.50314i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.6143i | − | 0.0235342i | ||||||
\(537\) | −1511.46 | −2.81463 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 358.295i | 0.659844i | ||||||||
\(544\) | 57.5108i | 0.105718i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 904.704i | − | 1.65697i | ||||||
\(547\) | 552.627 | 1.01029 | 0.505144 | − | 0.863035i | \(-0.331439\pi\) | ||||
0.505144 | + | 0.863035i | \(0.331439\pi\) | |||||||
\(548\) | − | 89.8590i | − | 0.163976i | ||||||
\(549\) | − | 1134.85i | − | 2.06712i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 236.217i | − | 0.428706i | ||||||
\(552\) | −340.978 | − | 89.6209i | −0.617713 | − | 0.162357i | ||||
\(553\) | −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 | \(0.968518\pi\) | |||||||
\(558\) | −1234.53 | −2.21243 | ||||||||
\(559\) | − | 85.9496i | − | 0.153756i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −871.896 | −1.55418 | ||||||||
\(562\) | − | 264.925i | − | 0.471397i | ||||||
\(563\) | 360.367i | 0.640084i | 0.947403 | + | 0.320042i | \(0.103697\pi\) | ||||
−0.947403 | + | 0.320042i | \(0.896303\pi\) | |||||||
\(564\) | 351.916 | 0.623965 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 687.529i | 1.21472i | ||||||||
\(567\) | − | 1241.54i | − | 2.18966i | ||||||
\(568\) | 334.919 | 0.589646 | ||||||||
\(569\) | − | 532.981i | − | 0.936698i | −0.883544 | − | 0.468349i | \(-0.844849\pi\) | ||
0.883544 | − | 0.468349i | \(-0.155151\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | 29.9918i | 0.0523417i | ||||||||
\(574\) | 432.343i | 0.753210i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 162.967 | 0.282929 | ||||||||
\(577\) | 869.422 | 1.50680 | 0.753399 | − | 0.657564i | \(-0.228413\pi\) | ||||
0.753399 | + | 0.657564i | \(0.228413\pi\) | |||||||
\(578\) | 262.536 | 0.454214 | ||||||||
\(579\) | 390.453 | 0.674357 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 556.840 | 0.958416 | ||||||||
\(582\) | 756.212i | 1.29933i | ||||||||
\(583\) | −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 | \(0.388431\pi\) | |||||||
\(588\) | −205.185 | −0.348955 | ||||||||
\(589\) | 1565.66i | 2.65817i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1035.90 | −1.75279 | ||||||||
\(592\) | 254.552i | 0.429986i | ||||||||
\(593\) | 668.332 | 1.12703 | 0.563517 | − | 0.826104i | \(-0.309448\pi\) | ||||
0.563517 | + | 0.826104i | \(0.309448\pi\) | |||||||
\(594\) | 1379.11i | 2.32174i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 50.8454i | − | 0.0853111i | ||||||
\(597\) | − | 935.096i | − | 1.56632i | ||||||
\(598\) | −450.545 | − | 118.419i | −0.753420 | − | 0.198025i | ||||
\(599\) | 866.946 | 1.44732 | 0.723661 | − | 0.690155i | \(-0.242458\pi\) | ||||
0.723661 | + | 0.690155i | \(0.242458\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | − | 90.8511i | − | 0.150665i | ||||||
\(604\) | −105.060 | −0.173940 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −580.044 | −0.957169 | ||||||||
\(607\) | −23.2820 | −0.0383559 | −0.0191779 | − | 0.999816i | \(-0.506105\pi\) | ||||
−0.0191779 | + | 0.999816i | \(0.506105\pi\) | |||||||
\(608\) | − | 206.678i | − | 0.339932i | ||||||
\(609\) | − | 288.789i | − | 0.474202i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 464.999 | 0.761045 | ||||||||
\(612\) | 414.205i | 0.676805i | ||||||||
\(613\) | − | 559.419i | − | 0.912592i | −0.889828 | − | 0.456296i | \(-0.849176\pi\) | ||
0.889828 | − | 0.456296i | \(-0.150824\pi\) | |||||||
\(614\) | −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 | \(-0.339311\pi\) | |||||||
\(618\) | − | 665.646i | − | 1.07710i | ||||||
\(619\) | − | 729.225i | − | 1.17807i | −0.808107 | − | 0.589035i | \(-0.799508\pi\) | ||
0.808107 | − | 0.589035i | \(-0.200492\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1370.81 | − | 360.296i | −2.20742 | − | 0.580187i | ||||
\(622\) | −186.513 | −0.299860 | ||||||||
\(623\) | 863.175 | 1.38551 | ||||||||
\(624\) | 310.470 | 0.497548 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 226.634i | 0.362035i | ||||||||
\(627\) | 3133.36 | 4.99738 | ||||||||
\(628\) | 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 | ||||||
\(633\) | −1810.32 | −2.85991 | ||||||||
\(634\) | 743.434 | 1.17261 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 397.401i | 0.624844i | ||||||||
\(637\) | −271.118 | −0.425618 | ||||||||
\(638\) | 144.690i | 0.226786i | ||||||||
\(639\) | 2412.15 | 3.77489 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 676.123i | 1.05479i | 0.849619 | + | 0.527397i | \(0.176832\pi\) | ||||
−0.849619 | + | 0.527397i | \(0.823168\pi\) | |||||||
\(642\) | 42.5793i | 0.0663229i | ||||||||
\(643\) | − | 1063.72i | − | 1.65430i | −0.561980 | − | 0.827151i | \(-0.689960\pi\) | ||
0.561980 | − | 0.827151i | \(-0.310040\pi\) | |||||||
\(644\) | −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 | \(0.461092\pi\) | |||||||
\(648\) | 426.062 | 0.657503 | ||||||||
\(649\) | 105.368i | 0.162354i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1914.12i | 2.94027i | ||||||||
\(652\) | 36.6476 | 0.0562080 | ||||||||
\(653\) | −41.1895 | −0.0630773 | −0.0315386 | − | 0.999503i | \(-0.510041\pi\) | ||||
−0.0315386 | + | 0.999503i | \(0.510041\pi\) | |||||||
\(654\) | − | 544.169i | − | 0.832063i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −148.368 | −0.226171 | ||||||||
\(657\) | −1675.86 | −2.55078 | ||||||||
\(658\) | − | 378.440i | − | 0.575137i | ||||||
\(659\) | − | 19.2526i | − | 0.0292149i | −0.999893 | − | 0.0146075i | \(-0.995350\pi\) | ||
0.999893 | − | 0.0146075i | \(-0.00464986\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 789.104i | 1.19020i | ||||||||
\(664\) | 191.092i | 0.287790i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1833.33i | 2.75275i | ||||||||
\(667\) | −143.818 | − | 37.8004i | −0.215619 | − | 0.0566722i | ||||
\(668\) | −137.954 | −0.206517 | ||||||||
\(669\) | 2393.14 | 3.57719 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 881.576 | 1.31382 | ||||||||
\(672\) | − | 252.677i | − | 0.376007i | ||||||
\(673\) | −12.6902 | −0.0188561 | −0.00942807 | − | 0.999956i | \(-0.503001\pi\) | ||||
−0.00942807 | + | 0.999956i | \(0.503001\pi\) | |||||||
\(674\) | − | 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 | \(-0.0550939\pi\) | |||||||
\(678\) | 772.279i | 1.13906i | ||||||||
\(679\) | 813.209 | 1.19766 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 297.650i | 0.437078i | ||||||||
\(682\) | − | 959.012i | − | 1.40618i | ||||||
\(683\) | −367.020 | −0.537364 | −0.268682 | − | 0.963229i | \(-0.586588\pi\) | ||||
−0.268682 | + | 0.963229i | \(0.586588\pi\) | |||||||
\(684\) | − | 1488.54i | − | 2.17623i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 350.490i | − | 0.510918i | ||||||
\(687\) | 1746.70i | 2.54251i | ||||||||
\(688\) | − | 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 | ||||||||
\(693\) | 2656.89 | 3.83390 | ||||||||
\(694\) | 662.282 | 0.954296 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 99.1047 | 0.142392 | ||||||||
\(697\) | − | 377.099i | − | 0.541032i | ||||||
\(698\) | 257.794 | 0.369332 | ||||||||
\(699\) | −862.826 | −1.23437 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 848.508i | − | 1.21043i | −0.796064 | − | 0.605213i | \(-0.793088\pi\) | ||
0.796064 | − | 0.605213i | \(-0.206912\pi\) | |||||||
\(702\) | 1248.16 | 1.77800 | ||||||||
\(703\) | 2325.07 | 3.30736 | ||||||||
\(704\) | 126.596i | 0.179825i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 425.733 | 0.603022 | ||||||||
\(707\) | 623.763i | 0.882267i | ||||||||
\(708\) | 72.1715 | 0.101937 | ||||||||
\(709\) | − | 533.757i | − | 0.752831i | −0.926451 | − | 0.376416i | \(-0.877156\pi\) | ||
0.926451 | − | 0.376416i | \(-0.122844\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2711.05i | − | 3.81301i | ||||||
\(712\) | 296.218i | 0.416037i | ||||||||
\(713\) | 953.235 | + | 250.544i | 1.33694 | + | 0.351394i | ||||
\(714\) | 642.214 | 0.899460 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −557.785 | −0.779029 | ||||||||
\(717\) | 174.502 | 0.243379 | ||||||||
\(718\) | 34.8989i | 0.0486057i | ||||||||
\(719\) | 1210.11 | 1.68304 | 0.841520 | − | 0.540225i | \(-0.181661\pi\) | ||||
0.841520 | + | 0.540225i | \(0.181661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −715.816 | −0.992810 | ||||||||
\(722\) | −1377.27 | −1.90757 | ||||||||
\(723\) | 215.836i | 0.298528i | ||||||||
\(724\) | 132.225i | 0.182631i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −991.890 | −1.36624 | ||||||||
\(727\) | − | 2.43604i | − | 0.00335081i | −0.999999 | − | 0.00167540i | \(-0.999467\pi\) | ||
0.999999 | − | 0.00167540i | \(-0.000533298\pi\) | |||||||
\(728\) | − | 333.870i | − | 0.458613i | ||||||
\(729\) | 62.8190 | 0.0861715 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 61.0123 | 0.0834641 | ||||||||
\(732\) | − | 603.833i | − | 0.824908i | ||||||
\(733\) | 495.146i | 0.675506i | 0.941235 | + | 0.337753i | \(0.109667\pi\) | ||||
−0.941235 | + | 0.337753i | \(0.890333\pi\) | |||||||
\(734\) | 604.587i | 0.823688i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −125.834 | − | 33.0735i | −0.170970 | − | 0.0449369i | ||||
\(737\) | 70.5751 | 0.0957599 | ||||||||
\(738\) | −1068.58 | −1.44794 | ||||||||
\(739\) | 1235.77 | 1.67222 | 0.836112 | − | 0.548559i | \(-0.184823\pi\) | ||||
0.836112 | + | 0.548559i | \(0.184823\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2835.83i | − | 3.82703i | ||||||
\(742\) | 427.353 | 0.575948 | ||||||||
\(743\) | 1030.67i | 1.38717i | 0.720373 | + | 0.693587i | \(0.243971\pi\) | ||||
−0.720373 | + | 0.693587i | \(0.756029\pi\) | |||||||
\(744\) | −656.873 | −0.882894 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 478.926i | 0.641992i | ||||||||
\(747\) | 1376.29i | 1.84242i | ||||||||
\(748\) | −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 | ||||||||
\(753\) | 1260.19i | 1.67356i | ||||||||
\(754\) | 130.950 | 0.173674 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 1015.82i | − | 1.34367i | ||||||
\(757\) | − | 483.738i | − | 0.639019i | −0.947583 | − | 0.319510i | \(-0.896482\pi\) | ||
0.947583 | − | 0.319510i | \(-0.103518\pi\) | |||||||
\(758\) | − | 406.102i | − | 0.535754i | ||||||
\(759\) | 501.413 | − | 1907.71i | 0.660624 | − | 2.51345i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 833.341 | 1.09506 | 0.547530 | − | 0.836786i | \(-0.315568\pi\) | ||||
0.547530 | + | 0.836786i | \(0.315568\pi\) | |||||||
\(762\) | 336.925 | 0.442158 | ||||||||
\(763\) | −585.183 | −0.766951 | ||||||||
\(764\) | 11.0681i | 0.0144871i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 965.428i | − | 1.26035i | ||||||
\(767\) | 95.3626 | 0.124332 | ||||||||
\(768\) | 86.7119 | 0.112906 | ||||||||
\(769\) | − | 356.518i | − | 0.463613i | −0.972762 | − | 0.231806i | \(-0.925536\pi\) | ||
0.972762 | − | 0.231806i | \(-0.0744636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1762.20 | −2.28560 | ||||||||
\(772\) | 144.092 | 0.186648 | ||||||||
\(773\) | − | 286.633i | − | 0.370805i | −0.982663 | − | 0.185403i | \(-0.940641\pi\) | ||
0.982663 | − | 0.185403i | \(-0.0593589\pi\) | |||||||
\(774\) | − | 172.889i | − | 0.223371i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 279.071i | 0.359628i | ||||||||
\(777\) | 2842.54 | 3.65835 | ||||||||
\(778\) | − | 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 | ||||
\(783\) | 398.423 | 0.508841 | ||||||||
\(784\) | −75.7213 | −0.0965833 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −340.398 | −0.433077 | ||||||||
\(787\) | − | 930.798i | − | 1.18272i | −0.806409 | − | 0.591359i | \(-0.798592\pi\) | ||
0.806409 | − | 0.591359i | \(-0.201408\pi\) | |||||||
\(788\) | −382.287 | −0.485136 | ||||||||
\(789\) | − | 26.8205i | − | 0.0339931i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 830.487 | 1.04992 | ||||||||
\(792\) | 911.773i | 1.15123i | ||||||||
\(793\) | − | 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 | \(0.613406\pi\) | |||||||
\(798\) | −2307.95 | −2.89216 | ||||||||
\(799\) | 330.084i | 0.413122i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2133.42i | 2.66345i | ||||||||
\(802\) | − | 572.286i | − | 0.713574i | ||||||
\(803\) | − | 1301.85i | − | 1.62123i | ||||||
\(804\) | − | 48.3402i | − | 0.0601246i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −867.948 | −1.07686 | ||||||||
\(807\) | 1273.84 | 1.57848 | ||||||||
\(808\) | −214.059 | −0.264924 | ||||||||
\(809\) | −850.318 | −1.05107 | −0.525537 | − | 0.850771i | \(-0.676135\pi\) | ||||
−0.525537 | + | 0.850771i | \(0.676135\pi\) | |||||||
\(810\) | 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 | ||||||
\(813\) | −290.064 | −0.356783 | ||||||||
\(814\) | −1424.17 | −1.74960 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 220.391i | 0.270087i | ||||||||
\(817\) | −219.262 | −0.268374 | ||||||||
\(818\) | 992.039 | 1.21276 | ||||||||
\(819\) | − | 2404.60i | − | 2.93602i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −461.343 | −0.561929 | −0.280964 | − | 0.959718i | \(-0.590654\pi\) | ||||
−0.280964 | + | 0.959718i | \(0.590654\pi\) | |||||||
\(822\) | − | 344.354i | − | 0.418922i | ||||||
\(823\) | −101.176 | −0.122936 | −0.0614680 | − | 0.998109i | \(-0.519578\pi\) | ||||
−0.0614680 | + | 0.998109i | \(0.519578\pi\) | |||||||
\(824\) | − | 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 | \(-0.142969\pi\) | |||||||
\(828\) | −906.280 | − | 238.202i | −1.09454 | − | 0.287684i | ||||
\(829\) | 634.298 | 0.765137 | 0.382568 | − | 0.923927i | \(-0.375040\pi\) | ||||
0.382568 | + | 0.923927i | \(0.375040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 778.111 | 0.936356 | ||||||||
\(832\) | 114.575 | 0.137711 | ||||||||
\(833\) | − | 192.456i | − | 0.231040i | ||||||
\(834\) | −1071.44 | −1.28470 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1156.33 | 1.38317 | ||||||||
\(837\) | −2640.77 | −3.15505 | ||||||||
\(838\) | 968.862i | 1.15616i | ||||||||
\(839\) | − | 133.138i | − | 0.158687i | −0.996847 | − | 0.0793434i | \(-0.974718\pi\) | ||
0.996847 | − | 0.0793434i | \(-0.0252824\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −799.200 | −0.950297 | ||||||||
\(842\) | 290.375i | 0.344864i | ||||||||
\(843\) | − | 1015.23i | − | 1.20431i | ||||||
\(844\) | −668.078 | −0.791561 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 935.353 | 1.10562 | ||||||||
\(847\) | 1066.65i | 1.25933i | ||||||||
\(848\) | 146.656i | 0.172944i | ||||||||
\(849\) | 2634.72i | 3.10332i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 372.068 | − | 1415.59i | 0.437212 | − | 1.66345i | ||||
\(852\) | 1283.46 | 1.50641 | ||||||||
\(853\) | −728.808 | −0.854406 | −0.427203 | − | 0.904156i | \(-0.640501\pi\) | ||||
−0.427203 | + | 0.904156i | \(0.640501\pi\) | |||||||
\(854\) | −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 | \(0.731106\pi\) | |||||||
\(858\) | 1737.03i | 2.02451i | ||||||||
\(859\) | −782.016 | −0.910379 | −0.455190 | − | 0.890395i | \(-0.650429\pi\) | ||||
−0.455190 | + | 0.890395i | \(0.650429\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1656.81i | 1.92428i | ||||||||
\(862\) | − | 503.355i | − | 0.583939i | ||||||
\(863\) | 324.868 | 0.376440 | 0.188220 | − | 0.982127i | \(-0.439728\pi\) | ||||
0.188220 | + | 0.982127i | \(0.439728\pi\) | |||||||
\(864\) | 348.601 | 0.403473 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 24.4475i | − | 0.0282304i | ||||||
\(867\) | 1006.08 | 1.16041 | ||||||||
\(868\) | 706.382i | 0.813804i | ||||||||
\(869\) | 2106.00 | 2.42348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 63.8735i | − | 0.0733336i | ||||||
\(872\) | − | 200.819i | − | 0.230297i | ||||||
\(873\) | 2009.93i | 2.30232i | ||||||||
\(874\) | −302.093 | + | 1149.36i | −0.345644 | + | 1.31506i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −891.696 | −1.01792 | ||||||||
\(877\) | 411.966 | 0.469745 | 0.234872 | − | 0.972026i | \(-0.424533\pi\) | ||||
0.234872 | + | 0.972026i | \(0.424533\pi\) | |||||||
\(878\) | −648.712 | −0.738852 | ||||||||
\(879\) | − | 1304.65i | − | 1.48425i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1082.39i | − | 1.22859i | −0.789076 | − | 0.614296i | \(-0.789440\pi\) | ||
0.789076 | − | 0.614296i | \(-0.210560\pi\) | |||||||
\(882\) | −545.360 | −0.618322 | ||||||||
\(883\) | −1343.48 | −1.52149 | −0.760746 | − | 0.649049i | \(-0.775167\pi\) | ||||
−0.760746 | + | 0.649049i | \(0.775167\pi\) | |||||||
\(884\) | 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 | \(0.568197\pi\) | |||||||
\(888\) | 975.483i | 1.09852i | ||||||||
\(889\) | − | 362.319i | − | 0.407558i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2383.74i | 2.67535i | ||||||||
\(892\) | 883.160 | 0.990089 | ||||||||
\(893\) | − | 1186.23i | − | 1.32837i | ||||||
\(894\) | − | 194.848i | − | 0.217950i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 93.2474i | − | 0.104071i | ||||||
\(897\) | −1726.56 | − | 453.801i | −1.92482 | − | 0.505910i | ||||
\(898\) | −487.248 | −0.542592 | ||||||||
\(899\) | −277.056 | −0.308183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −372.748 | −0.413704 | ||||||||
\(902\) | − | 830.095i | − | 0.920283i | ||||||
\(903\) | −268.061 | −0.296856 | ||||||||
\(904\) | 285.001i | 0.315266i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −402.606 | −0.444378 | ||||||||
\(907\) | 295.704i | 0.326024i | 0.986624 | + | 0.163012i | \(0.0521209\pi\) | ||||
−0.986624 | + | 0.163012i | \(0.947879\pi\) | |||||||
\(908\) | 109.844i | 0.120974i | ||||||||
\(909\) | −1541.69 | −1.69603 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 419.625i | 0.460620i | 0.973117 | + | 0.230310i | \(0.0739740\pi\) | ||||
−0.973117 | + | 0.230310i | \(0.926026\pi\) | |||||||
\(912\) | − | 792.025i | − | 0.868448i | ||||||
\(913\) | −1069.13 | −1.17101 | ||||||||
\(914\) | − | 172.836i | − | 0.189099i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 644.601i | 0.703713i | ||||||||
\(917\) | 366.054i | 0.399187i | ||||||||
\(918\) | 886.019i | 0.965163i | ||||||||
\(919\) | − | 1654.94i | − | 1.80080i | −0.435062 | − | 0.900401i | \(-0.643274\pi\) | ||
0.435062 | − | 0.900401i | \(-0.356726\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1832.28 | −1.98945 | ||||||||
\(922\) | 308.760 | 0.334881 | ||||||||
\(923\) | 1695.88 | 1.83736 | ||||||||
\(924\) | 1413.68 | 1.52996 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 644.004 | 0.695469 | ||||||||
\(927\) | − | 1769.21i | − | 1.90853i | ||||||
\(928\) | 36.5734 | 0.0394110 | ||||||||
\(929\) | −1291.79 | −1.39052 | −0.695260 | − | 0.718758i | \(-0.744711\pi\) | ||||
−0.695260 | + | 0.718758i | \(0.744711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 691.637i | 0.742897i | ||||||||
\(932\) | −318.416 | −0.341648 | ||||||||
\(933\) | −714.747 | −0.766074 | ||||||||
\(934\) | 495.445i | 0.530455i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 825.195 | 0.881618 | ||||||||
\(937\) | 212.428i | 0.226711i | 0.993554 | + | 0.113355i | \(0.0361599\pi\) | ||||
−0.993554 | + | 0.113355i | \(0.963840\pi\) | |||||||
\(938\) | −51.9836 | −0.0554196 | ||||||||
\(939\) | 868.496i | 0.924916i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 980.930i | 1.04243i | 0.853424 | + | 0.521217i | \(0.174522\pi\) | ||||
−0.853424 | + | 0.521217i | \(0.825478\pi\) | |||||||
\(942\) | 571.661i | 0.606859i | ||||||||
\(943\) | 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 | \(0.332021\pi\) | |||||||
\(948\) | − | 1442.50i | − | 1.52162i | ||||||
\(949\) | −1178.23 | −1.24155 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2848.96 | 2.99575 | ||||||||
\(952\) | 237.002 | 0.248951 | ||||||||
\(953\) | 248.522i | 0.260779i | 0.991463 | + | 0.130389i | \(0.0416227\pi\) | ||||
−0.991463 | + | 0.130389i | \(0.958377\pi\) | |||||||
\(954\) | 1056.25i | 1.10718i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 64.3981 | 0.0673620 | ||||||||
\(957\) | 554.473i | 0.579387i | ||||||||
\(958\) | − | 1051.01i | − | 1.09709i | ||||||
\(959\) | −370.308 | −0.386140 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 875.349 | 0.910873 | ||||||||
\(962\) | 1288.94i | 1.33985i | ||||||||
\(963\) | 113.171i | 0.117519i | ||||||||
\(964\) | 79.6517i | 0.0826263i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −369.327 | + | 1405.17i | −0.382326 | + | 1.45462i | ||||
\(967\) | 1112.21 | 1.15016 | 0.575081 | − | 0.818096i | \(-0.304970\pi\) | ||||
0.575081 | + | 0.818096i | \(0.304970\pi\) | |||||||
\(968\) | −366.045 | −0.378146 | ||||||||
\(969\) | 2013.04 | 2.07745 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 548.535i | − | 0.564918i | −0.959279 | − | 0.282459i | \(-0.908850\pi\) | ||
0.959279 | − | 0.282459i | \(-0.0911500\pi\) | |||||||
\(972\) | 523.495 | 0.538575 | ||||||||
\(973\) | 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 | \(0.957038\pi\) | |||||||
\(978\) | 140.439 | 0.143599 | ||||||||
\(979\) | −1657.29 | −1.69284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1446.34i | − | 1.47435i | ||||||
\(982\) | 179.639 | 0.182932 | ||||||||
\(983\) | − | 1516.23i | − | 1.54245i | −0.636562 | − | 0.771226i | \(-0.719644\pi\) | ||
0.636562 | − | 0.771226i | \(-0.280356\pi\) | |||||||
\(984\) | −568.571 | −0.577816 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 92.9566i | 0.0942765i | ||||||||
\(987\) | − | 1450.24i | − | 1.46934i | ||||||
\(988\) | − | 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 | ||||||||
\(993\) | 0.651084 | 0.000655674 | ||||||||
\(994\) | − | 1380.20i | − | 1.38853i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 732.297i | 0.735238i | ||||||||
\(997\) | −480.892 | −0.482339 | −0.241169 | − | 0.970483i | \(-0.577531\pi\) | ||||
−0.241169 | + | 0.970483i | \(0.577531\pi\) | |||||||
\(998\) | 740.481 | 0.741965 | ||||||||
\(999\) | 3921.66i | 3.92558i |
(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 | 1150.3.d.b.551.15 | 16 | ||
5.2 | odd | 4 | 1150.3.c.c.1149.4 | 32 | |||
5.3 | odd | 4 | 1150.3.c.c.1149.29 | 32 | |||
5.4 | even | 2 | 230.3.d.a.91.1 | ✓ | 16 | ||
15.14 | odd | 2 | 2070.3.c.a.91.15 | 16 | |||
20.19 | odd | 2 | 1840.3.k.d.321.15 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.d.b.551.16 | 16 | ||
115.22 | even | 4 | 1150.3.c.c.1149.30 | 32 | |||
115.68 | even | 4 | 1150.3.c.c.1149.3 | 32 | |||
115.114 | odd | 2 | 230.3.d.a.91.2 | yes | 16 | ||
345.344 | even | 2 | 2070.3.c.a.91.10 | 16 | |||
460.459 | even | 2 | 1840.3.k.d.321.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.1 | ✓ | 16 | 5.4 | even | 2 | ||
230.3.d.a.91.2 | yes | 16 | 115.114 | odd | 2 | ||
1150.3.c.c.1149.3 | 32 | 115.68 | even | 4 | |||
1150.3.c.c.1149.4 | 32 | 5.2 | odd | 4 | |||
1150.3.c.c.1149.29 | 32 | 5.3 | odd | 4 | |||
1150.3.c.c.1149.30 | 32 | 115.22 | even | 4 | |||
1150.3.d.b.551.15 | 16 | 1.1 | even | 1 | trivial | ||
1150.3.d.b.551.16 | 16 | 23.22 | odd | 2 | inner | ||
1840.3.k.d.321.15 | 16 | 20.19 | odd | 2 | |||
1840.3.k.d.321.16 | 16 | 460.459 | even | 2 | |||
2070.3.c.a.91.10 | 16 | 345.344 | even | 2 | |||
2070.3.c.a.91.15 | 16 | 15.14 | odd | 2 |