Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(1149,1150)]
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([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.1149");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(31.3352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1149.4 | ||
Character | \(\chi\) | \(=\) | 1150.1149 |
Dual form | 1150.3.c.c.1149.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | − | 5.41949i | − | 1.80650i | −0.429117 | − | 0.903249i | \(-0.641175\pi\) | ||
0.429117 | − | 0.903249i | \(-0.358825\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 7.66432 | 1.27739 | ||||||||
\(7\) | 8.24199 | 1.17743 | 0.588713 | − | 0.808342i | \(-0.299635\pi\) | ||||
0.588713 | + | 0.808342i | \(0.299635\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −20.3709 | −2.26343 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8246i | 1.43860i | 0.694702 | + | 0.719298i | \(0.255536\pi\) | ||||
−0.694702 | + | 0.719298i | \(0.744464\pi\) | |||||||
\(12\) | 10.8390i | 0.903249i | ||||||||
\(13\) | − | 14.3219i | − | 1.10169i | −0.834609 | − | 0.550843i | \(-0.814306\pi\) | ||
0.834609 | − | 0.550843i | \(-0.185694\pi\) | |||||||
\(14\) | 11.6559i | 0.832566i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −10.1666 | −0.598034 | −0.299017 | − | 0.954248i | \(-0.596659\pi\) | ||||
−0.299017 | + | 0.954248i | \(0.596659\pi\) | |||||||
\(18\) | − | 28.8088i | − | 1.60049i | ||||||
\(19\) | 36.5359i | 1.92294i | 0.274904 | + | 0.961472i | \(0.411354\pi\) | ||||
−0.274904 | + | 0.961472i | \(0.588646\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 44.6674i | − | 2.12702i | ||||||
\(22\) | −22.3793 | −1.01724 | ||||||||
\(23\) | −5.84663 | + | 22.2445i | −0.254201 | + | 0.967151i | ||||
\(24\) | −15.3286 | −0.638693 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 20.2543 | 0.779010 | ||||||||
\(27\) | 61.6245i | 2.28239i | ||||||||
\(28\) | −16.4840 | −0.588713 | ||||||||
\(29\) | −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 | \(0.742905\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 85.7611 | 2.59882 | ||||||||
\(34\) | − | 14.3777i | − | 0.422874i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 40.7418 | 1.13172 | ||||||||
\(37\) | −63.6379 | −1.71994 | −0.859972 | − | 0.510341i | \(-0.829519\pi\) | ||||
−0.859972 | + | 0.510341i | \(0.829519\pi\) | |||||||
\(38\) | −51.6696 | −1.35973 | ||||||||
\(39\) | −77.6175 | −1.99019 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −37.0921 | −0.904685 | −0.452342 | − | 0.891844i | \(-0.649412\pi\) | ||||
−0.452342 | + | 0.891844i | \(0.649412\pi\) | |||||||
\(42\) | 63.1692 | 1.50403 | ||||||||
\(43\) | −6.00126 | −0.139564 | −0.0697821 | − | 0.997562i | \(-0.522230\pi\) | ||||
−0.0697821 | + | 0.997562i | \(0.522230\pi\) | |||||||
\(44\) | − | 31.6491i | − | 0.719298i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −31.4584 | − | 8.26838i | −0.683879 | − | 0.179747i | ||||
\(47\) | 32.4676i | 0.690800i | 0.938455 | + | 0.345400i | \(0.112257\pi\) | ||||
−0.938455 | + | 0.345400i | \(0.887743\pi\) | |||||||
\(48\) | − | 21.6780i | − | 0.451624i | ||||||
\(49\) | 18.9303 | 0.386333 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 55.0977i | 1.08035i | ||||||||
\(52\) | 28.6438i | 0.550843i | ||||||||
\(53\) | 36.6640 | 0.691774 | 0.345887 | − | 0.938276i | \(-0.387578\pi\) | ||||
0.345887 | + | 0.938276i | \(0.387578\pi\) | |||||||
\(54\) | −87.1502 | −1.61389 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 23.3119i | − | 0.416283i | ||||||
\(57\) | 198.006 | 3.47379 | ||||||||
\(58\) | − | 9.14336i | − | 0.157644i | ||||||
\(59\) | −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 | \(-0.150945\pi\) | |||||||
\(62\) | − | 60.6028i | − | 0.977464i | ||||||
\(63\) | −167.897 | −2.66503 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 121.284i | 1.83764i | ||||||||
\(67\) | 4.45984 | 0.0665648 | 0.0332824 | − | 0.999446i | \(-0.489404\pi\) | ||||
0.0332824 | + | 0.999446i | \(0.489404\pi\) | |||||||
\(68\) | 20.3331 | 0.299017 | ||||||||
\(69\) | 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 | \(0.186111\pi\) | |||||||
\(72\) | 57.6176i | 0.800245i | ||||||||
\(73\) | 82.2675i | 1.12695i | 0.826133 | + | 0.563476i | \(0.190536\pi\) | ||||
−0.826133 | + | 0.563476i | \(0.809464\pi\) | |||||||
\(74\) | − | 89.9976i | − | 1.21618i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 73.0718i | − | 0.961472i | ||||||
\(77\) | 130.426i | 1.69384i | ||||||||
\(78\) | − | 109.768i | − | 1.40728i | ||||||
\(79\) | 133.084i | 1.68461i | 0.538999 | + | 0.842307i | \(0.318803\pi\) | ||||
−0.538999 | + | 0.842307i | \(0.681197\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 150.636 | 1.85970 | ||||||||
\(82\) | − | 52.4561i | − | 0.639709i | ||||||
\(83\) | 67.5614 | 0.813993 | 0.406996 | − | 0.913430i | \(-0.366576\pi\) | ||||
0.406996 | + | 0.913430i | \(0.366576\pi\) | |||||||
\(84\) | 89.3348i | 1.06351i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 8.48707i | − | 0.0986868i | ||||||
\(87\) | 35.0388i | 0.402745i | ||||||||
\(88\) | 44.7586 | 0.508620 | ||||||||
\(89\) | − | 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 | ||||||
\(92\) | 11.6933 | − | 44.4890i | 0.127101 | − | 0.483576i | ||||
\(93\) | 232.240i | 2.49720i | ||||||||
\(94\) | −45.9161 | −0.488470 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 30.6573 | 0.319347 | ||||||||
\(97\) | −98.6666 | −1.01718 | −0.508591 | − | 0.861008i | \(-0.669833\pi\) | ||||
−0.508591 | + | 0.861008i | \(0.669833\pi\) | |||||||
\(98\) | 26.7715i | 0.273179i | ||||||||
\(99\) | − | 322.360i | − | 3.25617i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −75.6811 | −0.749318 | −0.374659 | − | 0.927163i | \(-0.622240\pi\) | ||||
−0.374659 | + | 0.927163i | \(0.622240\pi\) | |||||||
\(102\) | −77.9199 | −0.763920 | ||||||||
\(103\) | −86.8499 | −0.843203 | −0.421602 | − | 0.906781i | \(-0.638532\pi\) | ||||
−0.421602 | + | 0.906781i | \(0.638532\pi\) | |||||||
\(104\) | −40.5085 | −0.389505 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 51.8508i | 0.489158i | ||||||||
\(107\) | −5.55552 | −0.0519208 | −0.0259604 | − | 0.999663i | \(-0.508264\pi\) | ||||
−0.0259604 | + | 0.999663i | \(0.508264\pi\) | |||||||
\(108\) | − | 123.249i | − | 1.14119i | ||||||
\(109\) | 71.0003i | 0.651379i | 0.945477 | + | 0.325689i | \(0.105596\pi\) | ||||
−0.945477 | + | 0.325689i | \(0.894404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 344.885i | 3.10707i | ||||||||
\(112\) | 32.9679 | 0.294357 | ||||||||
\(113\) | 100.763 | 0.891707 | 0.445854 | − | 0.895106i | \(-0.352900\pi\) | ||||
0.445854 | + | 0.895106i | \(0.352900\pi\) | |||||||
\(114\) | 280.023i | 2.45634i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.9307 | 0.111471 | ||||||||
\(117\) | 291.750i | 2.49359i | ||||||||
\(118\) | − | 9.41655i | − | 0.0798013i | ||||||
\(119\) | −83.7927 | −0.704141 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −129.417 | −1.06956 | ||||||||
\(122\) | 78.7849 | 0.645778 | ||||||||
\(123\) | 201.020i | 1.63431i | ||||||||
\(124\) | 85.7053 | 0.691172 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 237.442i | − | 1.88446i | ||||||
\(127\) | 43.9602i | 0.346143i | 0.984909 | + | 0.173072i | \(0.0553692\pi\) | ||||
−0.984909 | + | 0.173072i | \(0.944631\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 32.5238i | 0.252123i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −44.4134 | −0.339033 | −0.169517 | − | 0.985527i | \(-0.554221\pi\) | ||||
−0.169517 | + | 0.985527i | \(0.554221\pi\) | |||||||
\(132\) | −171.522 | −1.29941 | ||||||||
\(133\) | 301.129i | 2.26412i | ||||||||
\(134\) | 6.30717i | 0.0470684i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28.7554i | 0.211437i | ||||||||
\(137\) | 44.9295 | 0.327953 | 0.163976 | − | 0.986464i | \(-0.447568\pi\) | ||||
0.163976 | + | 0.986464i | \(0.447568\pi\) | |||||||
\(138\) | −44.8105 | + | 170.489i | −0.324713 | + | 1.23543i | ||||
\(139\) | 139.796 | 1.00573 | 0.502864 | − | 0.864365i | \(-0.332280\pi\) | ||||
0.502864 | + | 0.864365i | \(0.332280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 175.958 | 1.24793 | ||||||||
\(142\) | 167.460i | 1.17929i | ||||||||
\(143\) | 226.638 | 1.58488 | ||||||||
\(144\) | −81.4836 | −0.565858 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −116.344 | −0.796875 | ||||||||
\(147\) | − | 102.593i | − | 0.697910i | ||||||
\(148\) | 127.276 | 0.859972 | ||||||||
\(149\) | 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 | \(0.555650\pi\) | |||||||
\(152\) | 103.339 | 0.679863 | ||||||||
\(153\) | 207.102 | 1.35361 | ||||||||
\(154\) | −184.450 | −1.19773 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 155.235 | 0.995097 | ||||||||
\(157\) | −74.5874 | −0.475079 | −0.237539 | − | 0.971378i | \(-0.576341\pi\) | ||||
−0.237539 | + | 0.971378i | \(0.576341\pi\) | |||||||
\(158\) | −188.210 | −1.19120 | ||||||||
\(159\) | − | 198.700i | − | 1.24969i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −48.1878 | + | 183.339i | −0.299303 | + | 1.13875i | ||||
\(162\) | 213.031i | 1.31501i | ||||||||
\(163\) | − | 18.3238i | − | 0.112416i | −0.998419 | − | 0.0562080i | \(-0.982099\pi\) | ||
0.998419 | − | 0.0562080i | \(-0.0179010\pi\) | |||||||
\(164\) | 74.1842 | 0.452342 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 95.5462i | 0.575580i | ||||||||
\(167\) | − | 68.9768i | − | 0.413035i | −0.978443 | − | 0.206517i | \(-0.933787\pi\) | ||
0.978443 | − | 0.206517i | \(-0.0662130\pi\) | |||||||
\(168\) | −126.338 | −0.752014 | ||||||||
\(169\) | −36.1174 | −0.213712 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 744.270i | − | 4.35245i | ||||||
\(172\) | 12.0025 | 0.0697821 | ||||||||
\(173\) | 118.707i | 0.686166i | 0.939305 | + | 0.343083i | \(0.111471\pi\) | ||||
−0.939305 | + | 0.343083i | \(0.888529\pi\) | |||||||
\(174\) | −49.5523 | −0.284784 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 63.2982i | 0.359649i | ||||||||
\(177\) | 36.0857i | 0.203874i | ||||||||
\(178\) | 148.109 | 0.832074 | ||||||||
\(179\) | 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 | \(0.941539\pi\) | |||||||
\(182\) | 166.935 | 0.917227 | ||||||||
\(183\) | −301.916 | −1.64982 | ||||||||
\(184\) | 62.9169 | + | 16.5368i | 0.341940 | + | 0.0898737i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −328.436 | −1.76579 | ||||||||
\(187\) | − | 160.882i | − | 0.860329i | ||||||
\(188\) | − | 64.9352i | − | 0.345400i | ||||||
\(189\) | 507.908i | 2.68735i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.53406i | 0.0289741i | 0.999895 | + | 0.0144871i | \(0.00461154\pi\) | ||||
−0.999895 | + | 0.0144871i | \(0.995388\pi\) | |||||||
\(192\) | 43.3559i | 0.225812i | ||||||||
\(193\) | − | 72.0460i | − | 0.373295i | −0.982427 | − | 0.186648i | \(-0.940238\pi\) | ||
0.982427 | − | 0.186648i | \(-0.0597623\pi\) | |||||||
\(194\) | − | 139.536i | − | 0.719256i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −37.8606 | −0.193167 | ||||||||
\(197\) | − | 191.143i | − | 0.970271i | −0.874439 | − | 0.485136i | \(-0.838770\pi\) | ||
0.874439 | − | 0.485136i | \(-0.161230\pi\) | |||||||
\(198\) | 455.887 | 2.30246 | ||||||||
\(199\) | 172.543i | 0.867051i | 0.901141 | + | 0.433525i | \(0.142731\pi\) | ||||
−0.901141 | + | 0.433525i | \(0.857269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 24.1701i | − | 0.120249i | ||||||
\(202\) | − | 107.029i | − | 0.529848i | ||||||
\(203\) | −53.2871 | −0.262498 | ||||||||
\(204\) | − | 110.195i | − | 0.540173i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 122.824i | − | 0.596235i | ||||||
\(207\) | 119.101 | − | 453.140i | 0.575368 | − | 2.18908i | ||||
\(208\) | − | 57.2877i | − | 0.275422i | ||||||
\(209\) | −578.165 | −2.76634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −334.039 | −1.58312 | −0.791561 | − | 0.611090i | \(-0.790731\pi\) | ||||
−0.791561 | + | 0.611090i | \(0.790731\pi\) | |||||||
\(212\) | −73.3281 | −0.345887 | ||||||||
\(213\) | − | 641.732i | − | 3.01282i | ||||||
\(214\) | − | 7.85670i | − | 0.0367135i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 174.300 | 0.806947 | ||||||||
\(217\) | −353.191 | −1.62761 | ||||||||
\(218\) | −100.410 | −0.460594 | ||||||||
\(219\) | 445.848 | 2.03584 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 145.605i | 0.658845i | ||||||||
\(222\) | −487.741 | −2.19703 | ||||||||
\(223\) | − | 441.580i | − | 1.98018i | −0.140440 | − | 0.990089i | \(-0.544852\pi\) | ||
0.140440 | − | 0.990089i | \(-0.455148\pi\) | |||||||
\(224\) | 46.6237i | 0.208142i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 142.500i | 0.630532i | ||||||||
\(227\) | −54.9222 | −0.241948 | −0.120974 | − | 0.992656i | \(-0.538602\pi\) | ||||
−0.120974 | + | 0.992656i | \(0.538602\pi\) | |||||||
\(228\) | −396.012 | −1.73690 | ||||||||
\(229\) | − | 322.300i | − | 1.40743i | −0.710485 | − | 0.703713i | \(-0.751524\pi\) | ||
0.710485 | − | 0.703713i | \(-0.248476\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 706.841 | 3.05992 | ||||||||
\(232\) | 18.2867i | 0.0788220i | ||||||||
\(233\) | 159.208i | 0.683296i | 0.939828 | + | 0.341648i | \(0.110985\pi\) | ||||
−0.939828 | + | 0.341648i | \(0.889015\pi\) | |||||||
\(234\) | −412.597 | −1.76324 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.3170 | 0.0564280 | ||||||||
\(237\) | 721.250 | 3.04325 | ||||||||
\(238\) | − | 118.501i | − | 0.497903i | ||||||
\(239\) | −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 | \(0.973669\pi\) | |||||||
\(242\) | − | 183.023i | − | 0.756292i | ||||||
\(243\) | − | 261.748i | − | 1.07715i | ||||||
\(244\) | 111.419i | 0.456634i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −284.286 | −1.15563 | ||||||||
\(247\) | 523.265 | 2.11848 | ||||||||
\(248\) | 121.206i | 0.488732i | ||||||||
\(249\) | − | 366.148i | − | 1.47048i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 232.529i | 0.926410i | 0.886251 | + | 0.463205i | \(0.153301\pi\) | ||||
−0.886251 | + | 0.463205i | \(0.846699\pi\) | |||||||
\(252\) | 335.793 | 1.33251 | ||||||||
\(253\) | −352.009 | − | 92.5203i | −1.39134 | − | 0.365693i | ||||
\(254\) | −62.1691 | −0.244760 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 325.160i | − | 1.26521i | −0.774473 | − | 0.632606i | \(-0.781985\pi\) | ||
0.774473 | − | 0.632606i | \(-0.218015\pi\) | |||||||
\(258\) | −45.9956 | −0.178278 | ||||||||
\(259\) | −524.503 | −2.02511 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 131.705 | 0.504615 | ||||||||
\(262\) | − | 62.8100i | − | 0.239733i | ||||||
\(263\) | −4.94890 | −0.0188171 | −0.00940855 | − | 0.999956i | \(-0.502995\pi\) | ||||
−0.00940855 | + | 0.999956i | \(0.502995\pi\) | |||||||
\(264\) | − | 242.569i | − | 0.918822i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −425.860 | −1.60098 | ||||||||
\(267\) | −567.578 | −2.12576 | ||||||||
\(268\) | −8.91969 | −0.0332824 | ||||||||
\(269\) | −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 | \(0.531484\pi\) | |||||||
\(272\) | −40.6663 | −0.149508 | ||||||||
\(273\) | −639.723 | −2.34331 | ||||||||
\(274\) | 63.5399i | 0.231898i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −241.108 | − | 63.3715i | −0.873578 | − | 0.229607i | ||||
\(277\) | 143.576i | 0.518326i | 0.965834 | + | 0.259163i | \(0.0834468\pi\) | ||||
−0.965834 | + | 0.259163i | \(0.916553\pi\) | |||||||
\(278\) | 197.702i | 0.711157i | ||||||||
\(279\) | 872.947 | 3.12884 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 187.330i | − | 0.666656i | −0.942811 | − | 0.333328i | \(-0.891828\pi\) | ||
0.942811 | − | 0.333328i | \(-0.108172\pi\) | |||||||
\(282\) | 248.842i | 0.882419i | ||||||||
\(283\) | 486.156 | 1.71787 | 0.858934 | − | 0.512087i | \(-0.171127\pi\) | ||||
0.858934 | + | 0.512087i | \(0.171127\pi\) | |||||||
\(284\) | −236.824 | −0.833886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 320.515i | 1.12068i | ||||||||
\(287\) | −305.712 | −1.06520 | ||||||||
\(288\) | − | 115.235i | − | 0.400122i | ||||||
\(289\) | −185.641 | −0.642356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 534.723i | 1.83754i | ||||||||
\(292\) | − | 164.535i | − | 0.563476i | ||||||
\(293\) | −240.733 | −0.821616 | −0.410808 | − | 0.911722i | \(-0.634753\pi\) | ||||
−0.410808 | + | 0.911722i | \(0.634753\pi\) | |||||||
\(294\) | 145.088 | 0.493497 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 179.995i | 0.608092i | ||||||||
\(297\) | −975.181 | −3.28344 | ||||||||
\(298\) | −35.9531 | −0.120648 | ||||||||
\(299\) | 318.584 | + | 83.7350i | 1.06550 | + | 0.280050i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.4623 | −0.164327 | ||||||||
\(302\) | − | 74.2885i | − | 0.245988i | ||||||
\(303\) | 410.153i | 1.35364i | ||||||||
\(304\) | 146.144i | 0.480736i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 292.887i | 0.957147i | ||||||||
\(307\) | − | 338.091i | − | 1.10127i | −0.834745 | − | 0.550636i | \(-0.814385\pi\) | ||
0.834745 | − | 0.550636i | \(-0.185615\pi\) | |||||||
\(308\) | − | 260.852i | − | 0.846920i | ||||||
\(309\) | 470.683i | 1.52324i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −131.884 | −0.424066 | −0.212033 | − | 0.977263i | \(-0.568008\pi\) | ||||
−0.212033 | + | 0.977263i | \(0.568008\pi\) | |||||||
\(312\) | 219.536i | 0.703640i | ||||||||
\(313\) | 160.254 | 0.511994 | 0.255997 | − | 0.966678i | \(-0.417596\pi\) | ||||
0.255997 | + | 0.966678i | \(0.417596\pi\) | |||||||
\(314\) | − | 105.482i | − | 0.335931i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 266.169i | − | 0.842307i | ||||||
\(317\) | 525.687i | 1.65832i | 0.559012 | + | 0.829160i | \(0.311181\pi\) | ||||
−0.559012 | + | 0.829160i | \(0.688819\pi\) | |||||||
\(318\) | 281.005 | 0.883663 | ||||||||
\(319\) | − | 102.311i | − | 0.320724i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 30.1081i | 0.0937948i | ||||||||
\(322\) | −259.280 | − | 68.1479i | −0.805218 | − | 0.211639i | ||||
\(323\) | − | 371.445i | − | 1.14998i | ||||||
\(324\) | −301.271 | −0.929849 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 25.9138 | 0.0794901 | ||||||||
\(327\) | 384.786 | 1.17671 | ||||||||
\(328\) | 104.912i | 0.319854i | ||||||||
\(329\) | 267.598i | 0.813367i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.120137 | 0.000362953 | 0.000181477 | − | 1.00000i | \(-0.499942\pi\) | ||||
0.000181477 | 1.00000i | \(0.499942\pi\) | ||||||||
\(332\) | −135.123 | −0.406996 | ||||||||
\(333\) | 1296.36 | 3.89298 | ||||||||
\(334\) | 97.5480 | 0.292060 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 178.670i | − | 0.531755i | ||||||
\(337\) | 652.946 | 1.93752 | 0.968762 | − | 0.247992i | \(-0.0797706\pi\) | ||||
0.968762 | + | 0.247992i | \(0.0797706\pi\) | |||||||
\(338\) | − | 51.0777i | − | 0.151117i | ||||||
\(339\) | − | 546.084i | − | 1.61087i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 678.124i | − | 1.98863i | ||||||
\(342\) | 1052.56 | 3.07765 | ||||||||
\(343\) | −247.834 | −0.722548 | ||||||||
\(344\) | 16.9741i | 0.0493434i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −167.877 | −0.485193 | ||||||||
\(347\) | 468.304i | 1.34958i | 0.738010 | + | 0.674789i | \(0.235766\pi\) | ||||
−0.738010 | + | 0.674789i | \(0.764234\pi\) | |||||||
\(348\) | − | 70.0776i | − | 0.201372i | ||||||
\(349\) | −182.288 | −0.522315 | −0.261157 | − | 0.965296i | \(-0.584104\pi\) | ||||
−0.261157 | + | 0.965296i | \(0.584104\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 882.581 | 2.51448 | ||||||||
\(352\) | −89.5172 | −0.254310 | ||||||||
\(353\) | − | 301.039i | − | 0.852802i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) | ||
0.904534 | − | 0.426401i | \(-0.140219\pi\) | |||||||
\(354\) | −51.0329 | −0.144161 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 209.458i | 0.588365i | ||||||||
\(357\) | 454.114i | 1.27203i | ||||||||
\(358\) | 394.413i | 1.10171i | ||||||||
\(359\) | − | 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 | ||||||||
\(362\) | −93.4969 | −0.258279 | ||||||||
\(363\) | 701.372i | 1.93215i | ||||||||
\(364\) | 236.082i | 0.648577i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | − | 426.974i | − | 1.16660i | ||||||
\(367\) | −427.508 | −1.16487 | −0.582435 | − | 0.812877i | \(-0.697900\pi\) | ||||
−0.582435 | + | 0.812877i | \(0.697900\pi\) | |||||||
\(368\) | −23.3865 | + | 88.9779i | −0.0635503 | + | 0.241788i | ||||
\(369\) | 755.599 | 2.04769 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 302.184 | 0.814513 | ||||||||
\(372\) | − | 464.479i | − | 1.24860i | ||||||
\(373\) | 338.652 | 0.907913 | 0.453957 | − | 0.891024i | \(-0.350012\pi\) | ||||
0.453957 | + | 0.891024i | \(0.350012\pi\) | |||||||
\(374\) | 227.521 | 0.608344 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 91.8323 | 0.244235 | ||||||||
\(377\) | 92.5959i | 0.245612i | ||||||||
\(378\) | −718.291 | −1.90024 | ||||||||
\(379\) | 287.157i | 0.757671i | 0.925464 | + | 0.378835i | \(0.123675\pi\) | ||||
−0.925464 | + | 0.378835i | \(0.876325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 238.242 | 0.625307 | ||||||||
\(382\) | −7.82634 | −0.0204878 | ||||||||
\(383\) | −682.661 | −1.78240 | −0.891202 | − | 0.453606i | \(-0.850137\pi\) | ||||
−0.891202 | + | 0.453606i | \(0.850137\pi\) | |||||||
\(384\) | −61.3146 | −0.159673 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 101.888 | 0.263960 | ||||||||
\(387\) | 122.251 | 0.315894 | ||||||||
\(388\) | 197.333 | 0.508591 | ||||||||
\(389\) | 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 | ||||
\(392\) | − | 53.5430i | − | 0.136589i | ||||||
\(393\) | 240.698i | 0.612463i | ||||||||
\(394\) | 270.318 | 0.686085 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 644.721i | 1.62808i | ||||||||
\(397\) | − | 99.6609i | − | 0.251035i | −0.992091 | − | 0.125517i | \(-0.959941\pi\) | ||
0.992091 | − | 0.125517i | \(-0.0400591\pi\) | |||||||
\(398\) | −244.013 | −0.613097 | ||||||||
\(399\) | 1631.96 | 4.09014 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 404.668i | − | 1.00915i | −0.863369 | − | 0.504573i | \(-0.831650\pi\) | ||
0.863369 | − | 0.504573i | \(-0.168350\pi\) | |||||||
\(402\) | 34.1817 | 0.0850290 | ||||||||
\(403\) | 613.732i | 1.52291i | ||||||||
\(404\) | 151.362 | 0.374659 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 75.3594i | − | 0.185614i | ||||||
\(407\) | − | 1007.04i | − | 2.47430i | ||||||
\(408\) | 155.840 | 0.381960 | ||||||||
\(409\) | −701.478 | −1.71510 | −0.857552 | − | 0.514397i | \(-0.828016\pi\) | ||||
−0.857552 | + | 0.514397i | \(0.828016\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 243.495i | − | 0.592446i | ||||||
\(412\) | 173.700 | 0.421602 | ||||||||
\(413\) | −54.8793 | −0.132880 | ||||||||
\(414\) | 640.837 | + | 168.434i | 1.54792 | + | 0.406847i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 81.0170 | 0.194752 | ||||||||
\(417\) | − | 757.625i | − | 1.81685i | ||||||
\(418\) | − | 817.648i | − | 1.95610i | ||||||
\(419\) | − | 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 | \(0.921588\pi\) | |||||||
\(422\) | − | 472.402i | − | 1.11944i | ||||||
\(423\) | − | 661.395i | − | 1.56358i | ||||||
\(424\) | − | 103.702i | − | 0.244579i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 907.546 | 2.13039 | ||||||||
\(427\) | − | 459.156i | − | 1.07531i | ||||||
\(428\) | 11.1110 | 0.0259604 | ||||||||
\(429\) | − | 1228.26i | − | 2.86308i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 355.926i | − | 0.825814i | −0.910773 | − | 0.412907i | \(-0.864513\pi\) | ||
0.910773 | − | 0.412907i | \(-0.135487\pi\) | |||||||
\(432\) | 246.498i | 0.570597i | ||||||||
\(433\) | −17.2870 | −0.0399238 | −0.0199619 | − | 0.999801i | \(-0.506354\pi\) | ||||
−0.0199619 | + | 0.999801i | \(0.506354\pi\) | |||||||
\(434\) | − | 499.487i | − | 1.15089i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 142.001i | − | 0.325689i | ||||||
\(437\) | −812.723 | − | 213.612i | −1.85978 | − | 0.488815i | ||||
\(438\) | 630.524i | 1.43955i | ||||||||
\(439\) | 458.708 | 1.04489 | 0.522447 | − | 0.852672i | \(-0.325019\pi\) | ||||
0.522447 | + | 0.852672i | \(0.325019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −385.628 | −0.874439 | ||||||||
\(442\) | −205.916 | −0.465874 | ||||||||
\(443\) | − | 196.292i | − | 0.443096i | −0.975149 | − | 0.221548i | \(-0.928889\pi\) | ||
0.975149 | − | 0.221548i | \(-0.0711110\pi\) | |||||||
\(444\) | − | 689.771i | − | 1.55354i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 624.488 | 1.40020 | ||||||||
\(447\) | 137.778 | 0.308228 | ||||||||
\(448\) | −65.9359 | −0.147178 | ||||||||
\(449\) | 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 | ||||||
\(452\) | −201.526 | −0.445854 | ||||||||
\(453\) | 284.685i | 0.628445i | ||||||||
\(454\) | − | 77.6717i | − | 0.171083i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 560.046i | − | 1.22817i | ||||||
\(457\) | 122.214 | 0.267426 | 0.133713 | − | 0.991020i | \(-0.457310\pi\) | ||||
0.133713 | + | 0.991020i | \(0.457310\pi\) | |||||||
\(458\) | 455.802 | 0.995200 | ||||||||
\(459\) | − | 626.510i | − | 1.36495i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 218.326 | 0.473593 | 0.236796 | − | 0.971559i | \(-0.423903\pi\) | ||||
0.236796 | + | 0.971559i | \(0.423903\pi\) | |||||||
\(462\) | 999.625i | 2.16369i | ||||||||
\(463\) | − | 455.380i | − | 0.983542i | −0.870725 | − | 0.491771i | \(-0.836350\pi\) | ||
0.870725 | − | 0.491771i | \(-0.163650\pi\) | |||||||
\(464\) | −25.8613 | −0.0557356 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −225.154 | −0.483163 | ||||||||
\(467\) | −350.332 | −0.750176 | −0.375088 | − | 0.926989i | \(-0.622388\pi\) | ||||
−0.375088 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(468\) | − | 583.501i | − | 1.24680i | ||||||
\(469\) | 36.7580 | 0.0783752 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 404.226i | 0.858229i | ||||||||
\(472\) | 18.8331i | 0.0399006i | ||||||||
\(473\) | − | 94.9673i | − | 0.200777i | ||||||
\(474\) | 1020.00i | 2.15190i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 167.585 | 0.352070 | ||||||||
\(477\) | −746.879 | −1.56578 | ||||||||
\(478\) | − | 45.5363i | − | 0.0952643i | ||||||
\(479\) | 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 | ||||||||
\(482\) | −56.3223 | −0.116851 | ||||||||
\(483\) | 993.603 | + | 261.154i | 2.05715 | + | 0.540691i | ||||
\(484\) | 258.833 | 0.534779 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 370.167 | 0.761660 | ||||||||
\(487\) | 366.770i | 0.753122i | 0.926392 | + | 0.376561i | \(0.122893\pi\) | ||||
−0.926392 | + | 0.376561i | \(0.877107\pi\) | |||||||
\(488\) | −157.570 | −0.322889 | ||||||||
\(489\) | −99.3057 | −0.203079 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 127.024 | 0.258704 | 0.129352 | − | 0.991599i | \(-0.458710\pi\) | ||||
0.129352 | + | 0.991599i | \(0.458710\pi\) | |||||||
\(492\) | − | 402.041i | − | 0.817156i | ||||||
\(493\) | 65.7302 | 0.133327 | ||||||||
\(494\) | 740.008i | 1.49799i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −171.411 | −0.345586 | ||||||||
\(497\) | 975.948 | 1.96368 | ||||||||
\(498\) | 517.812 | 1.03978 | ||||||||
\(499\) | −523.599 | −1.04930 | −0.524648 | − | 0.851319i | \(-0.675803\pi\) | ||||
−0.524648 | + | 0.851319i | \(0.675803\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −373.819 | −0.746147 | ||||||||
\(502\) | −328.845 | −0.655071 | ||||||||
\(503\) | 646.170 | 1.28463 | 0.642316 | − | 0.766440i | \(-0.277974\pi\) | ||||
0.642316 | + | 0.766440i | \(0.277974\pi\) | |||||||
\(504\) | 474.884i | 0.942229i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 130.844 | − | 497.816i | 0.258584 | − | 0.983826i | ||||
\(507\) | 195.738i | 0.386070i | ||||||||
\(508\) | − | 87.9203i | − | 0.173072i | ||||||
\(509\) | 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 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −2251.51 | −4.38891 | ||||||||
\(514\) | 459.845 | 0.894641 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 65.0476i | − | 0.126061i | ||||||
\(517\) | −513.786 | −0.993783 | ||||||||
\(518\) | − | 741.759i | − | 1.43197i | ||||||
\(519\) | 643.330 | 1.23956 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 655.952i | 1.25902i | 0.776990 | + | 0.629512i | \(0.216745\pi\) | ||||
−0.776990 | + | 0.629512i | \(0.783255\pi\) | |||||||
\(522\) | 186.258i | 0.356817i | ||||||||
\(523\) | −317.109 | −0.606328 | −0.303164 | − | 0.952938i | \(-0.598043\pi\) | ||||
−0.303164 | + | 0.952938i | \(0.598043\pi\) | |||||||
\(524\) | 88.8267 | 0.169517 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 6.99880i | − | 0.0133057i | ||||||
\(527\) | 435.665 | 0.826688 | ||||||||
\(528\) | 343.044 | 0.649705 | ||||||||
\(529\) | −460.634 | − | 260.111i | −0.870763 | − | 0.491702i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 135.640 | 0.255442 | ||||||||
\(532\) | − | 602.257i | − | 1.13206i | ||||||
\(533\) | 531.230i | 0.996679i | ||||||||
\(534\) | − | 802.677i | − | 1.50314i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 12.6143i | − | 0.0235342i | ||||||
\(537\) | − | 1511.46i | − | 2.81463i | ||||||
\(538\) | − | 332.407i | − | 0.617856i | ||||||
\(539\) | 299.564i | 0.555777i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −222.888 | −0.411992 | −0.205996 | − | 0.978553i | \(-0.566043\pi\) | ||||
−0.205996 | + | 0.978553i | \(0.566043\pi\) | |||||||
\(542\) | − | 75.6921i | − | 0.139653i | ||||||
\(543\) | 358.295 | 0.659844 | ||||||||
\(544\) | − | 57.5108i | − | 0.105718i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 904.704i | − | 1.65697i | ||||||
\(547\) | 552.627i | 1.01029i | 0.863035 | + | 0.505144i | \(0.168561\pi\) | ||||
−0.863035 | + | 0.505144i | \(0.831439\pi\) | |||||||
\(548\) | −89.8590 | −0.163976 | ||||||||
\(549\) | 1134.85i | 2.06712i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 236.217i | − | 0.428706i | ||||||
\(552\) | 89.6209 | − | 340.978i | 0.162357 | − | 0.617713i | ||||
\(553\) | 1096.88i | 1.98351i | ||||||||
\(554\) | −203.048 | −0.366512 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −279.592 | −0.502864 | ||||||||
\(557\) | −110.000 | −0.197486 | −0.0987430 | − | 0.995113i | \(-0.531482\pi\) | ||||
−0.0987430 | + | 0.995113i | \(0.531482\pi\) | |||||||
\(558\) | 1234.53i | 2.21243i | ||||||||
\(559\) | 85.9496i | 0.153756i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −871.896 | −1.55418 | ||||||||
\(562\) | 264.925 | 0.471397 | ||||||||
\(563\) | 360.367 | 0.640084 | 0.320042 | − | 0.947403i | \(-0.396303\pi\) | ||||
0.320042 | + | 0.947403i | \(0.396303\pi\) | |||||||
\(564\) | −351.916 | −0.623965 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 687.529i | 1.21472i | ||||||||
\(567\) | 1241.54 | 2.18966 | ||||||||
\(568\) | − | 334.919i | − | 0.589646i | ||||||
\(569\) | 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 | \(0.829556\pi\) | |||||||
\(572\) | −453.276 | −0.792441 | ||||||||
\(573\) | 29.9918 | 0.0523417 | ||||||||
\(574\) | − | 432.343i | − | 0.753210i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 162.967 | 0.282929 | ||||||||
\(577\) | 869.422i | 1.50680i | 0.657564 | + | 0.753399i | \(0.271587\pi\) | ||||
−0.657564 | + | 0.753399i | \(0.728413\pi\) | |||||||
\(578\) | − | 262.536i | − | 0.454214i | ||||||
\(579\) | −390.453 | −0.674357 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 556.840 | 0.958416 | ||||||||
\(582\) | −756.212 | −1.29933 | ||||||||
\(583\) | 580.192i | 0.995183i | ||||||||
\(584\) | 232.688 | 0.398438 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 340.449i | − | 0.580970i | ||||||
\(587\) | 403.118i | 0.686742i | 0.939200 | + | 0.343371i | \(0.111569\pi\) | ||||
−0.939200 | + | 0.343371i | \(0.888431\pi\) | |||||||
\(588\) | 205.185i | 0.348955i | ||||||||
\(589\) | − | 1565.66i | − | 2.65817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1035.90 | −1.75279 | ||||||||
\(592\) | −254.552 | −0.429986 | ||||||||
\(593\) | − | 668.332i | − | 1.12703i | −0.826104 | − | 0.563517i | \(-0.809448\pi\) | ||
0.826104 | − | 0.563517i | \(-0.190552\pi\) | |||||||
\(594\) | − | 1379.11i | − | 2.32174i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 50.8454i | − | 0.0853111i | ||||||
\(597\) | 935.096 | 1.56632 | ||||||||
\(598\) | −118.419 | + | 450.545i | −0.198025 | + | 0.753420i | ||||
\(599\) | −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 | \(0.350378\pi\) | |||||||
\(602\) | − | 69.9503i | − | 0.116196i | ||||||
\(603\) | −90.8511 | −0.150665 | ||||||||
\(604\) | 105.060 | 0.173940 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −580.044 | −0.957169 | ||||||||
\(607\) | − | 23.2820i | − | 0.0383559i | −0.999816 | − | 0.0191779i | \(-0.993895\pi\) | ||
0.999816 | − | 0.0191779i | \(-0.00610490\pi\) | |||||||
\(608\) | −206.678 | −0.339932 | ||||||||
\(609\) | 288.789i | 0.474202i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 464.999 | 0.761045 | ||||||||
\(612\) | −414.205 | −0.676805 | ||||||||
\(613\) | −559.419 | −0.912592 | −0.456296 | − | 0.889828i | \(-0.650824\pi\) | ||||
−0.456296 | + | 0.889828i | \(0.650824\pi\) | |||||||
\(614\) | 478.133 | 0.778718 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 368.900 | 0.598863 | ||||||||
\(617\) | 1080.07 | 1.75052 | 0.875262 | − | 0.483649i | \(-0.160689\pi\) | ||||
0.875262 | + | 0.483649i | \(0.160689\pi\) | |||||||
\(618\) | −665.646 | −1.07710 | ||||||||
\(619\) | 729.225i | 1.17807i | 0.808107 | + | 0.589035i | \(0.200492\pi\) | ||||
−0.808107 | + | 0.589035i | \(0.799508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1370.81 | − | 360.296i | −2.20742 | − | 0.580187i | ||||
\(622\) | − | 186.513i | − | 0.299860i | ||||||
\(623\) | − | 863.175i | − | 1.38551i | ||||||
\(624\) | −310.470 | −0.497548 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 226.634i | 0.362035i | ||||||||
\(627\) | 3133.36i | 4.99738i | ||||||||
\(628\) | 149.175 | 0.237539 | ||||||||
\(629\) | 646.980 | 1.02858 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 386.633i | − | 0.612731i | −0.951914 | − | 0.306365i | \(-0.900887\pi\) | ||
0.951914 | − | 0.306365i | \(-0.0991129\pi\) | |||||||
\(632\) | 376.420 | 0.595601 | ||||||||
\(633\) | 1810.32i | 2.85991i | ||||||||
\(634\) | −743.434 | −1.17261 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 397.401i | 0.624844i | ||||||||
\(637\) | − | 271.118i | − | 0.425618i | ||||||
\(638\) | 144.690 | 0.226786 | ||||||||
\(639\) | −2412.15 | −3.77489 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 676.123i | 1.05479i | 0.849619 | + | 0.527397i | \(0.176832\pi\) | ||||
−0.849619 | + | 0.527397i | \(0.823168\pi\) | |||||||
\(642\) | −42.5793 | −0.0663229 | ||||||||
\(643\) | −1063.72 | −1.65430 | −0.827151 | − | 0.561980i | \(-0.810040\pi\) | ||||
−0.827151 | + | 0.561980i | \(0.810040\pi\) | |||||||
\(644\) | 96.3757 | − | 366.677i | 0.149652 | − | 0.569375i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 525.303 | 0.813162 | ||||||||
\(647\) | 157.776i | 0.243857i | 0.992539 | + | 0.121929i | \(0.0389079\pi\) | ||||
−0.992539 | + | 0.121929i | \(0.961092\pi\) | |||||||
\(648\) | − | 426.062i | − | 0.657503i | ||||||
\(649\) | − | 105.368i | − | 0.162354i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1914.12i | 2.94027i | ||||||||
\(652\) | 36.6476i | 0.0562080i | ||||||||
\(653\) | 41.1895i | 0.0630773i | 0.999503 | + | 0.0315386i | \(0.0100407\pi\) | ||||
−0.999503 | + | 0.0315386i | \(0.989959\pi\) | |||||||
\(654\) | 544.169i | 0.832063i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −148.368 | −0.226171 | ||||||||
\(657\) | − | 1675.86i | − | 2.55078i | ||||||
\(658\) | −378.440 | −0.575137 | ||||||||
\(659\) | 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 | \(0.981731\pi\) | |||||||
\(662\) | 0.169900i | 0.000256647i | ||||||||
\(663\) | 789.104 | 1.19020 | ||||||||
\(664\) | − | 191.092i | − | 0.287790i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1833.33i | 2.75275i | ||||||||
\(667\) | 37.8004 | − | 143.818i | 0.0566722 | − | 0.215619i | ||||
\(668\) | 137.954i | 0.206517i | ||||||||
\(669\) | −2393.14 | −3.57719 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 881.576 | 1.31382 | ||||||||
\(672\) | 252.677 | 0.376007 | ||||||||
\(673\) | 12.6902i | 0.0188561i | 0.999956 | + | 0.00942807i | \(0.00300109\pi\) | ||||
−0.999956 | + | 0.00942807i | \(0.996999\pi\) | |||||||
\(674\) | 923.405i | 1.37004i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 72.2347 | 0.106856 | ||||||||
\(677\) | 233.185 | 0.344439 | 0.172220 | − | 0.985059i | \(-0.444906\pi\) | ||||
0.172220 | + | 0.985059i | \(0.444906\pi\) | |||||||
\(678\) | 772.279 | 1.13906 | ||||||||
\(679\) | −813.209 | −1.19766 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 297.650i | 0.437078i | ||||||||
\(682\) | 959.012 | 1.40618 | ||||||||
\(683\) | 367.020i | 0.537364i | 0.963229 | + | 0.268682i | \(0.0865881\pi\) | ||||
−0.963229 | + | 0.268682i | \(0.913412\pi\) | |||||||
\(684\) | 1488.54i | 2.17623i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 350.490i | − | 0.510918i | ||||||
\(687\) | −1746.70 | −2.54251 | ||||||||
\(688\) | −24.0051 | −0.0348911 | ||||||||
\(689\) | − | 525.099i | − | 0.762118i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1186.21 | −1.71666 | −0.858332 | − | 0.513095i | \(-0.828499\pi\) | ||||
−0.858332 | + | 0.513095i | \(0.828499\pi\) | |||||||
\(692\) | − | 237.413i | − | 0.343083i | ||||||
\(693\) | − | 2656.89i | − | 3.83390i | ||||||
\(694\) | −662.282 | −0.954296 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 99.1047 | 0.142392 | ||||||||
\(697\) | 377.099 | 0.541032 | ||||||||
\(698\) | − | 257.794i | − | 0.369332i | ||||||
\(699\) | 862.826 | 1.23437 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 848.508i | − | 1.21043i | −0.796064 | − | 0.605213i | \(-0.793088\pi\) | ||
0.796064 | − | 0.605213i | \(-0.206912\pi\) | |||||||
\(702\) | 1248.16i | 1.77800i | ||||||||
\(703\) | − | 2325.07i | − | 3.30736i | ||||||
\(704\) | − | 126.596i | − | 0.179825i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 425.733 | 0.603022 | ||||||||
\(707\) | −623.763 | −0.882267 | ||||||||
\(708\) | − | 72.1715i | − | 0.101937i | ||||||
\(709\) | 533.757i | 0.752831i | 0.926451 | + | 0.376416i | \(0.122844\pi\) | ||||
−0.926451 | + | 0.376416i | \(0.877156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2711.05i | − | 3.81301i | ||||||
\(712\) | −296.218 | −0.416037 | ||||||||
\(713\) | 250.544 | − | 953.235i | 0.351394 | − | 1.33694i | ||||
\(714\) | −642.214 | −0.899460 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −557.785 | −0.779029 | ||||||||
\(717\) | 174.502i | 0.243379i | ||||||||
\(718\) | 34.8989 | 0.0486057 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | − | 1377.27i | − | 1.90757i | ||||||
\(723\) | 215.836 | 0.298528 | ||||||||
\(724\) | − | 132.225i | − | 0.182631i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −991.890 | −1.36624 | ||||||||
\(727\) | 2.43604 | 0.00335081 | 0.00167540 | − | 0.999999i | \(-0.499467\pi\) | ||||
0.00167540 | + | 0.999999i | \(0.499467\pi\) | |||||||
\(728\) | −333.870 | −0.458613 | ||||||||
\(729\) | −62.8190 | −0.0861715 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 61.0123 | 0.0834641 | ||||||||
\(732\) | 603.833 | 0.824908 | ||||||||
\(733\) | 495.146 | 0.675506 | 0.337753 | − | 0.941235i | \(-0.390333\pi\) | ||||
0.337753 | + | 0.941235i | \(0.390333\pi\) | |||||||
\(734\) | − | 604.587i | − | 0.823688i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −125.834 | − | 33.0735i | −0.170970 | − | 0.0449369i | ||||
\(737\) | 70.5751i | 0.0957599i | ||||||||
\(738\) | 1068.58i | 1.44794i | ||||||||
\(739\) | −1235.77 | −1.67222 | −0.836112 | − | 0.548559i | \(-0.815177\pi\) | ||||
−0.836112 | + | 0.548559i | \(0.815177\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 2835.83i | − | 3.82703i | ||||||
\(742\) | 427.353i | 0.575948i | ||||||||
\(743\) | 1030.67 | 1.38717 | 0.693587 | − | 0.720373i | \(-0.256029\pi\) | ||||
0.693587 | + | 0.720373i | \(0.256029\pi\) | |||||||
\(744\) | 656.873 | 0.882894 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 478.926i | 0.641992i | ||||||||
\(747\) | −1376.29 | −1.84242 | ||||||||
\(748\) | 321.763i | 0.430164i | ||||||||
\(749\) | −45.7885 | −0.0611329 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1112.44i | − | 1.48128i | −0.671903 | − | 0.740639i | \(-0.734523\pi\) | ||
0.671903 | − | 0.740639i | \(-0.265477\pi\) | |||||||
\(752\) | 129.870i | 0.172700i | ||||||||
\(753\) | 1260.19 | 1.67356 | ||||||||
\(754\) | −130.950 | −0.173674 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 1015.82i | − | 1.34367i | ||||||
\(757\) | 483.738 | 0.639019 | 0.319510 | − | 0.947583i | \(-0.396482\pi\) | ||||
0.319510 | + | 0.947583i | \(0.396482\pi\) | |||||||
\(758\) | −406.102 | −0.535754 | ||||||||
\(759\) | −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 | \(0.315568\pi\) | |||||||
\(762\) | 336.925i | 0.442158i | ||||||||
\(763\) | 585.183i | 0.766951i | ||||||||
\(764\) | − | 11.0681i | − | 0.0144871i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 965.428i | − | 1.26035i | ||||||
\(767\) | 95.3626i | 0.124332i | ||||||||
\(768\) | − | 86.7119i | − | 0.112906i | ||||||
\(769\) | 356.518i | 0.463613i | 0.972762 | + | 0.231806i | \(0.0744636\pi\) | ||||
−0.972762 | + | 0.231806i | \(0.925536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1762.20 | −2.28560 | ||||||||
\(772\) | 144.092i | 0.186648i | ||||||||
\(773\) | −286.633 | −0.370805 | −0.185403 | − | 0.982663i | \(-0.559359\pi\) | ||||
−0.185403 | + | 0.982663i | \(0.559359\pi\) | |||||||
\(774\) | 172.889i | 0.223371i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 279.071i | 0.359628i | ||||||||
\(777\) | 2842.54i | 3.65835i | ||||||||
\(778\) | −769.171 | −0.988651 | ||||||||
\(779\) | − | 1355.19i | − | 1.73966i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1873.81i | 2.39925i | ||||||||
\(782\) | 319.825 | + | 84.0611i | 0.408983 | + | 0.107495i | ||||
\(783\) | − | 398.423i | − | 0.508841i | ||||||
\(784\) | 75.7213 | 0.0965833 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −340.398 | −0.433077 | ||||||||
\(787\) | 930.798 | 1.18272 | 0.591359 | − | 0.806409i | \(-0.298592\pi\) | ||||
0.591359 | + | 0.806409i | \(0.298592\pi\) | |||||||
\(788\) | 382.287i | 0.485136i | ||||||||
\(789\) | 26.8205i | 0.0339931i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 830.487 | 1.04992 | ||||||||
\(792\) | −911.773 | −1.15123 | ||||||||
\(793\) | −797.865 | −1.00613 | ||||||||
\(794\) | 140.942 | 0.177509 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 345.086i | − | 0.433525i | ||||||
\(797\) | −1493.90 | −1.87441 | −0.937203 | − | 0.348785i | \(-0.886594\pi\) | ||||
−0.937203 | + | 0.348785i | \(0.886594\pi\) | |||||||
\(798\) | 2307.95i | 2.89216i | ||||||||
\(799\) | − | 330.084i | − | 0.413122i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2133.42i | 2.66345i | ||||||||
\(802\) | 572.286 | 0.713574 | ||||||||
\(803\) | −1301.85 | −1.62123 | ||||||||
\(804\) | 48.3402i | 0.0601246i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −867.948 | −1.07686 | ||||||||
\(807\) | 1273.84i | 1.57848i | ||||||||
\(808\) | 214.059i | 0.264924i | ||||||||
\(809\) | 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 | \(0.275793\pi\) | |||||||
\(812\) | 106.574 | 0.131249 | ||||||||
\(813\) | 290.064i | 0.356783i | ||||||||
\(814\) | 1424.17 | 1.74960 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 220.391i | 0.270087i | ||||||||
\(817\) | − | 219.262i | − | 0.268374i | ||||||
\(818\) | − | 992.039i | − | 1.21276i | ||||||
\(819\) | 2404.60i | 2.93602i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −461.343 | −0.561929 | −0.280964 | − | 0.959718i | \(-0.590654\pi\) | ||||
−0.280964 | + | 0.959718i | \(0.590654\pi\) | |||||||
\(822\) | 344.354 | 0.418922 | ||||||||
\(823\) | 101.176i | 0.122936i | 0.998109 | + | 0.0614680i | \(0.0195782\pi\) | ||||
−0.998109 | + | 0.0614680i | \(0.980422\pi\) | |||||||
\(824\) | 245.649i | 0.298117i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 77.6111i | − | 0.0939601i | ||||||
\(827\) | 718.169 | 0.868403 | 0.434202 | − | 0.900816i | \(-0.357031\pi\) | ||||
0.434202 | + | 0.900816i | \(0.357031\pi\) | |||||||
\(828\) | −238.202 | + | 906.280i | −0.287684 | + | 1.09454i | ||||
\(829\) | −634.298 | −0.765137 | −0.382568 | − | 0.923927i | \(-0.624960\pi\) | ||||
−0.382568 | + | 0.923927i | \(0.624960\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 778.111 | 0.936356 | ||||||||
\(832\) | 114.575i | 0.137711i | ||||||||
\(833\) | −192.456 | −0.231040 | ||||||||
\(834\) | 1071.44 | 1.28470 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1156.33 | 1.38317 | ||||||||
\(837\) | − | 2640.77i | − | 3.15505i | ||||||
\(838\) | 968.862 | 1.15616 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | −290.375 | −0.344864 | ||||||||
\(843\) | −1015.23 | −1.20431 | ||||||||
\(844\) | 668.078 | 0.791561 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 935.353 | 1.10562 | ||||||||
\(847\) | −1066.65 | −1.25933 | ||||||||
\(848\) | 146.656 | 0.172944 | ||||||||
\(849\) | − | 2634.72i | − | 3.10332i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 372.068 | − | 1415.59i | 0.437212 | − | 1.66345i | ||||
\(852\) | 1283.46i | 1.50641i | ||||||||
\(853\) | 728.808i | 0.854406i | 0.904156 | + | 0.427203i | \(0.140501\pi\) | ||||
−0.904156 | + | 0.427203i | \(0.859499\pi\) | |||||||
\(854\) | 649.344 | 0.760356 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.7134i | 0.0183568i | ||||||||
\(857\) | − | 1137.95i | − | 1.32783i | −0.747809 | − | 0.663914i | \(-0.768894\pi\) | ||
0.747809 | − | 0.663914i | \(-0.231106\pi\) | |||||||
\(858\) | 1737.03 | 2.02451 | ||||||||
\(859\) | 782.016 | 0.910379 | 0.455190 | − | 0.890395i | \(-0.349571\pi\) | ||||
0.455190 | + | 0.890395i | \(0.349571\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1656.81i | 1.92428i | ||||||||
\(862\) | 503.355 | 0.583939 | ||||||||
\(863\) | − | 324.868i | − | 0.376440i | −0.982127 | − | 0.188220i | \(-0.939728\pi\) | ||
0.982127 | − | 0.188220i | \(-0.0602718\pi\) | |||||||
\(864\) | −348.601 | −0.403473 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 24.4475i | − | 0.0282304i | ||||||
\(867\) | 1006.08i | 1.16041i | ||||||||
\(868\) | 706.382 | 0.813804 | ||||||||
\(869\) | −2106.00 | −2.42348 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 63.8735i | − | 0.0733336i | ||||||
\(872\) | 200.819 | 0.230297 | ||||||||
\(873\) | 2009.93 | 2.30232 | ||||||||
\(874\) | 302.093 | − | 1149.36i | 0.345644 | − | 1.31506i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −891.696 | −1.01792 | ||||||||
\(877\) | 411.966i | 0.469745i | 0.972026 | + | 0.234872i | \(0.0754672\pi\) | ||||
−0.972026 | + | 0.234872i | \(0.924533\pi\) | |||||||
\(878\) | 648.712i | 0.738852i | ||||||||
\(879\) | 1304.65i | 1.48425i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1082.39i | − | 1.22859i | −0.789076 | − | 0.614296i | \(-0.789440\pi\) | ||
0.789076 | − | 0.614296i | \(-0.210560\pi\) | |||||||
\(882\) | − | 545.360i | − | 0.618322i | ||||||
\(883\) | 1343.48i | 1.52149i | 0.649049 | + | 0.760746i | \(0.275167\pi\) | ||||
−0.649049 | + | 0.760746i | \(0.724833\pi\) | |||||||
\(884\) | − | 291.210i | − | 0.329423i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 277.598 | 0.313316 | ||||||||
\(887\) | − | 377.176i | − | 0.425227i | −0.977136 | − | 0.212613i | \(-0.931803\pi\) | ||
0.977136 | − | 0.212613i | \(-0.0681975\pi\) | |||||||
\(888\) | 975.483 | 1.09852 | ||||||||
\(889\) | 362.319i | 0.407558i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2383.74i | 2.67535i | ||||||||
\(892\) | 883.160i | 0.990089i | ||||||||
\(893\) | −1186.23 | −1.32837 | ||||||||
\(894\) | 194.848i | 0.217950i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 93.2474i | − | 0.104071i | ||||||
\(897\) | 453.801 | − | 1726.56i | 0.505910 | − | 1.92482i | ||||
\(898\) | 487.248i | 0.542592i | ||||||||
\(899\) | 277.056 | 0.308183 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −372.748 | −0.413704 | ||||||||
\(902\) | 830.095 | 0.920283 | ||||||||
\(903\) | 268.061i | 0.296856i | ||||||||
\(904\) | − | 285.001i | − | 0.315266i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −402.606 | −0.444378 | ||||||||
\(907\) | −295.704 | −0.326024 | −0.163012 | − | 0.986624i | \(-0.552121\pi\) | ||||
−0.163012 | + | 0.986624i | \(0.552121\pi\) | |||||||
\(908\) | 109.844 | 0.120974 | ||||||||
\(909\) | 1541.69 | 1.69603 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 419.625i | 0.460620i | 0.973117 | + | 0.230310i | \(0.0739740\pi\) | ||||
−0.973117 | + | 0.230310i | \(0.926026\pi\) | |||||||
\(912\) | 792.025 | 0.868448 | ||||||||
\(913\) | 1069.13i | 1.17101i | ||||||||
\(914\) | 172.836i | 0.189099i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 644.601i | 0.703713i | ||||||||
\(917\) | −366.054 | −0.399187 | ||||||||
\(918\) | 886.019 | 0.965163 | ||||||||
\(919\) | 1654.94i | 1.80080i | 0.435062 | + | 0.900401i | \(0.356726\pi\) | ||||
−0.435062 | + | 0.900401i | \(0.643274\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1832.28 | −1.98945 | ||||||||
\(922\) | 308.760i | 0.334881i | ||||||||
\(923\) | − | 1695.88i | − | 1.83736i | ||||||
\(924\) | −1413.68 | −1.52996 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 644.004 | 0.695469 | ||||||||
\(927\) | 1769.21 | 1.90853 | ||||||||
\(928\) | − | 36.5734i | − | 0.0394110i | ||||||
\(929\) | 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 | ||||||||
\(932\) | − | 318.416i | − | 0.341648i | ||||||
\(933\) | 714.747i | 0.766074i | ||||||||
\(934\) | − | 495.445i | − | 0.530455i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 825.195 | 0.881618 | ||||||||
\(937\) | −212.428 | −0.226711 | −0.113355 | − | 0.993554i | \(-0.536160\pi\) | ||||
−0.113355 | + | 0.993554i | \(0.536160\pi\) | |||||||
\(938\) | 51.9836i | 0.0554196i | ||||||||
\(939\) | − | 868.496i | − | 0.924916i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 980.930i | 1.04243i | 0.853424 | + | 0.521217i | \(0.174522\pi\) | ||||
−0.853424 | + | 0.521217i | \(0.825478\pi\) | |||||||
\(942\) | −571.661 | −0.606859 | ||||||||
\(943\) | 216.864 | − | 825.094i | 0.229972 | − | 0.874967i | ||||
\(944\) | −26.6340 | −0.0282140 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 134.304 | 0.141970 | ||||||||
\(947\) | 953.755i | 1.00713i | 0.863956 | + | 0.503567i | \(0.167979\pi\) | ||||
−0.863956 | + | 0.503567i | \(0.832021\pi\) | |||||||
\(948\) | −1442.50 | −1.52162 | ||||||||
\(949\) | 1178.23 | 1.24155 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2848.96 | 2.99575 | ||||||||
\(952\) | 237.002i | 0.248951i | ||||||||
\(953\) | 248.522 | 0.260779 | 0.130389 | − | 0.991463i | \(-0.458377\pi\) | ||||
0.130389 | + | 0.991463i | \(0.458377\pi\) | |||||||
\(954\) | − | 1056.25i | − | 1.10718i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 64.3981 | 0.0673620 | ||||||||
\(957\) | −554.473 | −0.579387 | ||||||||
\(958\) | −1051.01 | −1.09709 | ||||||||
\(959\) | 370.308 | 0.386140 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 875.349 | 0.910873 | ||||||||
\(962\) | −1288.94 | −1.33985 | ||||||||
\(963\) | 113.171 | 0.117519 | ||||||||
\(964\) | − | 79.6517i | − | 0.0826263i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −369.327 | + | 1405.17i | −0.382326 | + | 1.45462i | ||||
\(967\) | 1112.21i | 1.15016i | 0.818096 | + | 0.575081i | \(0.195030\pi\) | ||||
−0.818096 | + | 0.575081i | \(0.804970\pi\) | |||||||
\(968\) | 366.045i | 0.378146i | ||||||||
\(969\) | −2013.04 | −2.07745 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 548.535i | − | 0.564918i | −0.959279 | − | 0.282459i | \(-0.908850\pi\) | ||
0.959279 | − | 0.282459i | \(-0.0911500\pi\) | |||||||
\(972\) | 523.495i | 0.538575i | ||||||||
\(973\) | 1152.20 | 1.18417 | ||||||||
\(974\) | −518.692 | −0.532538 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 222.837i | − | 0.228317i | ||||||
\(977\) | −262.933 | −0.269122 | −0.134561 | − | 0.990905i | \(-0.542962\pi\) | ||||
−0.134561 | + | 0.990905i | \(0.542962\pi\) | |||||||
\(978\) | − | 140.439i | − | 0.143599i | ||||||
\(979\) | 1657.29 | 1.69284 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1446.34i | − | 1.47435i | ||||||
\(982\) | 179.639i | 0.182932i | ||||||||
\(983\) | −1516.23 | −1.54245 | −0.771226 | − | 0.636562i | \(-0.780356\pi\) | ||||
−0.771226 | + | 0.636562i | \(0.780356\pi\) | |||||||
\(984\) | 568.571 | 0.577816 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 92.9566i | 0.0942765i | ||||||||
\(987\) | 1450.24 | 1.46934 | ||||||||
\(988\) | −1046.53 | −1.05924 | ||||||||
\(989\) | 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 | \(0.384133\pi\) | |||||||
\(992\) | − | 242.411i | − | 0.244366i | ||||||
\(993\) | − | 0.651084i | − | 0.000655674i | ||||||
\(994\) | 1380.20i | 1.38853i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 732.297i | 0.735238i | ||||||||
\(997\) | − | 480.892i | − | 0.482339i | −0.970483 | − | 0.241169i | \(-0.922469\pi\) | ||
0.970483 | − | 0.241169i | \(-0.0775310\pi\) | |||||||
\(998\) | − | 740.481i | − | 0.741965i | ||||||
\(999\) | − | 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.c.c.1149.4 | 32 | ||
5.2 | odd | 4 | 230.3.d.a.91.1 | ✓ | 16 | ||
5.3 | odd | 4 | 1150.3.d.b.551.15 | 16 | |||
5.4 | even | 2 | inner | 1150.3.c.c.1149.29 | 32 | ||
15.2 | even | 4 | 2070.3.c.a.91.15 | 16 | |||
20.7 | even | 4 | 1840.3.k.d.321.15 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.c.c.1149.30 | 32 | ||
115.22 | even | 4 | 230.3.d.a.91.2 | yes | 16 | ||
115.68 | even | 4 | 1150.3.d.b.551.16 | 16 | |||
115.114 | odd | 2 | inner | 1150.3.c.c.1149.3 | 32 | ||
345.137 | odd | 4 | 2070.3.c.a.91.10 | 16 | |||
460.367 | odd | 4 | 1840.3.k.d.321.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.1 | ✓ | 16 | 5.2 | odd | 4 | ||
230.3.d.a.91.2 | yes | 16 | 115.22 | even | 4 | ||
1150.3.c.c.1149.3 | 32 | 115.114 | odd | 2 | inner | ||
1150.3.c.c.1149.4 | 32 | 1.1 | even | 1 | trivial | ||
1150.3.c.c.1149.29 | 32 | 5.4 | even | 2 | inner | ||
1150.3.c.c.1149.30 | 32 | 23.22 | odd | 2 | inner | ||
1150.3.d.b.551.15 | 16 | 5.3 | odd | 4 | |||
1150.3.d.b.551.16 | 16 | 115.68 | even | 4 | |||
1840.3.k.d.321.15 | 16 | 20.7 | even | 4 | |||
1840.3.k.d.321.16 | 16 | 460.367 | odd | 4 | |||
2070.3.c.a.91.10 | 16 | 345.137 | odd | 4 | |||
2070.3.c.a.91.15 | 16 | 15.2 | even | 4 |