Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.1 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.l.1471.3 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.58579 | 0.917157 | 0.458579 | − | 0.888654i | \(-0.348359\pi\) | ||||
0.458579 | + | 0.888654i | \(0.348359\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 0.594346i | − 0.0540314i | −0.999635 | − | 0.0270157i | \(-0.991400\pi\) | ||||
0.999635 | − | 0.0270157i | \(-0.00860042\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.10051 | 0.161577 | 0.0807887 | − | 0.996731i | \(-0.474256\pi\) | ||||
0.0807887 | + | 0.996731i | \(0.474256\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 7.94282i | − 0.529521i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.07107 | −0.0630040 | −0.0315020 | − | 0.999504i | \(-0.510029\pi\) | ||||
−0.0315020 | + | 0.999504i | \(0.510029\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 14.6969i | 0.773523i | 0.922180 | + | 0.386762i | \(0.126406\pi\) | ||||
−0.922180 | + | 0.386762i | \(0.873594\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 21.3790i | − 0.929520i | −0.885437 | − | 0.464760i | \(-0.846141\pi\) | ||||
0.885437 | − | 0.464760i | \(-0.153859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.97056 | −0.158823 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.5147 | 0.534990 | 0.267495 | − | 0.963559i | \(-0.413804\pi\) | ||||
0.267495 | + | 0.963559i | \(0.413804\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 37.1626i | − 1.19879i | −0.800452 | − | 0.599397i | \(-0.795407\pi\) | ||||
0.800452 | − | 0.599397i | \(-0.204593\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.02944 | −0.0311951 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 33.9411 | 0.917328 | 0.458664 | − | 0.888610i | \(-0.348328\pi\) | ||||
0.458664 | + | 0.888610i | \(0.348328\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 3.63818i | − 0.0932867i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −27.8995 | −0.680475 | −0.340238 | − | 0.940339i | \(-0.610508\pi\) | ||||
−0.340238 | + | 0.940339i | \(0.610508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 28.2052i | − 0.655935i | −0.944689 | − | 0.327967i | \(-0.893636\pi\) | ||||
0.944689 | − | 0.327967i | \(-0.106364\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.7574 | −0.305719 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.840532i | 0.0178837i | 0.999960 | + | 0.00894183i | \(0.00284631\pi\) | ||||
−0.999960 | + | 0.00894183i | \(0.997154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85514i | 0.0363754i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 28.9117 | 0.545504 | 0.272752 | − | 0.962084i | \(-0.412066\pi\) | ||||
0.272752 | + | 0.962084i | \(0.412066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 2.72554i | − 0.0495553i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 25.4558 | 0.446594 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 92.5882i | − 1.56929i | −0.619944 | − | 0.784646i | \(-0.712845\pi\) | ||||
0.619944 | − | 0.784646i | \(-0.287155\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 81.9828 | 1.34398 | 0.671990 | − | 0.740560i | \(-0.265440\pi\) | ||||
0.671990 | + | 0.740560i | \(0.265440\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.63247 | 0.148192 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9867i | 0.163980i | 0.996633 | + | 0.0819899i | \(0.0261275\pi\) | ||||
−0.996633 | + | 0.0819899i | \(0.973872\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −37.0294 | −0.536659 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 89.9647i | − 1.26711i | −0.773698 | − | 0.633554i | \(-0.781595\pi\) | ||||
0.773698 | − | 0.633554i | \(-0.218405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −37.4975 | −0.513664 | −0.256832 | − | 0.966456i | \(-0.582679\pi\) | ||||
−0.256832 | + | 0.966456i | \(0.582679\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.87722i | 0.0916962i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.42058i | 0.0939313i | 0.998897 | + | 0.0469657i | \(0.0149551\pi\) | ||||
−0.998897 | + | 0.0469657i | \(0.985045\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 64.0349i | − 0.771505i | −0.922602 | − | 0.385752i | \(-0.873942\pi\) | ||||
0.922602 | − | 0.385752i | \(-0.126058\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.91169 | −0.0577846 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 26.8723i | − 0.308877i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.12994 | −0.0351679 | −0.0175839 | − | 0.999845i | \(-0.505597\pi\) | ||||
−0.0175839 | + | 0.999845i | \(0.505597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −64.3675 | −0.692124 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 67.3970i | 0.709442i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 92.4437 | 0.953027 | 0.476514 | − | 0.879167i | \(-0.341900\pi\) | ||||
0.476514 | + | 0.879167i | \(0.341900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.78304i | 0.0180105i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 34.3259 | 0.339860 | 0.169930 | − | 0.985456i | \(-0.445646\pi\) | ||||
0.169930 | + | 0.985456i | \(0.445646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 95.9504i | − 0.931557i | −0.884901 | − | 0.465778i | \(-0.845774\pi\) | ||||
0.884901 | − | 0.465778i | \(-0.154226\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 171.914i | 1.60668i | 0.595523 | + | 0.803338i | \(0.296945\pi\) | ||||
−0.595523 | + | 0.803338i | \(0.703055\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96.8528 | −0.888558 | −0.444279 | − | 0.895888i | \(-0.646540\pi\) | ||||
−0.444279 | + | 0.895888i | \(0.646540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 58.7878i | − 0.529619i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 115.823 | 1.02499 | 0.512493 | − | 0.858692i | \(-0.328722\pi\) | ||||
0.512493 | + | 0.858692i | \(0.328722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 98.0393i | − 0.852516i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.30152 | −0.0538591 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 120.647 | 0.997081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 48.3233i | 0.392873i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −132.853 | −1.06282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 228.919i | − 1.80251i | −0.433286 | − | 0.901256i | \(-0.642646\pi\) | ||||
0.433286 | − | 0.901256i | \(-0.357354\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −48.8528 | −0.378704 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 32.9600i | − 0.251603i | −0.992055 | − | 0.125801i | \(-0.959850\pi\) | ||||
0.992055 | − | 0.125801i | \(-0.0401502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23.8284i | 0.176507i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 101.574 | 0.741413 | 0.370707 | − | 0.928750i | \(-0.379116\pi\) | ||||
0.370707 | + | 0.928750i | \(0.379116\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 211.004i | − 1.51802i | −0.651081 | − | 0.759008i | \(-0.725684\pi\) | ||||
0.651081 | − | 0.759008i | \(-0.274316\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.45584 | 0.0103251 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.24843i | − 0.00873026i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 71.1472 | 0.490670 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 52.9117 | 0.355112 | 0.177556 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177556 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 255.936i | 1.69494i | 0.530845 | + | 0.847469i | \(0.321875\pi\) | ||||
−0.530845 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.21320 | 0.0210013 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 170.420i | − 1.09948i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 40.9289 | 0.260694 | 0.130347 | − | 0.991468i | \(-0.458391\pi\) | ||||
0.130347 | + | 0.991468i | \(0.458391\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 50.0765i | − 0.314947i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 245.849i | 1.50828i | 0.656715 | + | 0.754139i | \(0.271945\pi\) | ||||
−0.656715 | + | 0.754139i | \(0.728055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.72078 | −0.0286108 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 92.7922i | − 0.555642i | −0.960633 | − | 0.277821i | \(-0.910388\pi\) | ||||
0.960633 | − | 0.277821i | \(-0.0896122\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −164.588 | −0.973893 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 44.0908i | − 0.257841i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −188.267 | −1.08825 | −0.544124 | − | 0.839005i | \(-0.683138\pi\) | ||||
−0.544124 | + | 0.839005i | \(0.683138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −160.368 | −0.906031 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 174.292i | 0.973697i | 0.873486 | + | 0.486849i | \(0.161854\pi\) | ||||
−0.873486 | + | 0.486849i | \(0.838146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 138.988 | 0.767888 | 0.383944 | − | 0.923356i | \(-0.374565\pi\) | ||||
0.383944 | + | 0.923356i | \(0.374565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 141.998i | − 0.775947i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 155.647 | 0.841334 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.636585i | 0.00340420i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 51.9615i | 0.272050i | 0.990705 | + | 0.136025i | \(0.0434327\pi\) | ||||
−0.990705 | + | 0.136025i | \(0.956567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8234 | 0.0819864 | 0.0409932 | − | 0.999159i | \(-0.486948\pi\) | ||||
0.0409932 | + | 0.999159i | \(0.486948\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 16.6839i | − 0.0855586i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −148.912 | −0.755897 | −0.377948 | − | 0.925827i | \(-0.623370\pi\) | ||||
−0.377948 | + | 0.925827i | \(0.623370\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 135.202i | − 0.679407i | −0.940533 | − | 0.339703i | \(-0.889673\pi\) | ||||
0.940533 | − | 0.339703i | \(-0.110327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.0294 | 0.0946738 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −127.941 | −0.624103 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 64.1369i | 0.309840i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.73506 | 0.0417946 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 100.645i | − 0.476992i | −0.971143 | − | 0.238496i | \(-0.923346\pi\) | ||||
0.971143 | − | 0.238496i | \(-0.0766545\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −155.823 | −0.731565 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 129.343i | − 0.601595i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 64.9475i | 0.296564i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.24978 | −0.0101800 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 100.357i | − 0.450031i | −0.974355 | − | 0.225016i | \(-0.927757\pi\) | ||||
0.974355 | − | 0.225016i | \(-0.0722433\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.9117 | 0.0529408 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 379.803i | − 1.67314i | −0.547860 | − | 0.836570i | \(-0.684557\pi\) | ||||
0.547860 | − | 0.836570i | \(-0.315443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8995 | 0.0956310 | 0.0478155 | − | 0.998856i | \(-0.484774\pi\) | ||||
0.0478155 | + | 0.998856i | \(0.484774\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 102.780 | 0.441114 | 0.220557 | − | 0.975374i | \(-0.429212\pi\) | ||||
0.220557 | + | 0.975374i | \(0.429212\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.85450i | 0.0164021i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.8528 | 0.0542313 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 376.483i | − 1.57524i | −0.616160 | − | 0.787621i | \(-0.711313\pi\) | ||||
0.616160 | − | 0.787621i | \(-0.288687\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −221.179 | −0.917754 | −0.458877 | − | 0.888500i | \(-0.651748\pi\) | ||||
−0.458877 | + | 0.888500i | \(0.651748\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.8710i | 0.124984i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −110.912 | −0.445428 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 298.753i | − 1.19025i | −0.803632 | − | 0.595126i | \(-0.797102\pi\) | ||||
0.803632 | − | 0.595126i | \(-0.202898\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.7065 | −0.0502233 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.50729i | 0.0333619i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −344.517 | −1.34053 | −0.670266 | − | 0.742121i | \(-0.733820\pi\) | ||||
−0.670266 | + | 0.742121i | \(0.733820\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −46.5442 | −0.178330 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 227.136i | 0.863635i | 0.901961 | + | 0.431818i | \(0.142128\pi\) | ||||
−0.901961 | + | 0.431818i | \(0.857872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 132.583 | 0.500313 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.42122i | 0.0203042i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 470.590 | 1.74941 | 0.874703 | − | 0.484660i | \(-0.161057\pi\) | ||||
0.874703 | + | 0.484660i | \(0.161057\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 156.419i | 0.577193i | 0.957451 | + | 0.288596i | \(0.0931885\pi\) | ||||
−0.957451 | + | 0.288596i | \(0.906811\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.35989i | 0.00858141i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −279.823 | −1.01019 | −0.505096 | − | 0.863063i | \(-0.668543\pi\) | ||||
−0.505096 | + | 0.863063i | \(0.668543\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 111.488i | 0.399598i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 134.309 | 0.477967 | 0.238983 | − | 0.971024i | \(-0.423186\pi\) | ||||
0.238983 | + | 0.971024i | \(0.423186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 490.858i | − 1.73448i | −0.497890 | − | 0.867240i | \(-0.665892\pi\) | ||||
0.497890 | − | 0.867240i | \(-0.334108\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 116.735 | 0.409597 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −287.853 | −0.996030 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 160.117i | − 0.550231i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −154.056 | −0.525788 | −0.262894 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262894 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 424.590i | − 1.43929i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.08831 | 0.0103984 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 44.9066i | − 0.150189i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 59.4542i | − 0.196219i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 375.955 | 1.23264 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.1023i | 0.0752517i | 0.999292 | + | 0.0376258i | \(0.0119795\pi\) | ||||
−0.999292 | + | 0.0376258i | \(0.988020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −166.191 | −0.537835 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 364.061i | − 1.17062i | −0.810811 | − | 0.585308i | \(-0.800974\pi\) | ||||
0.810811 | − | 0.585308i | \(-0.199026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −194.704 | −0.622056 | −0.311028 | − | 0.950401i | \(-0.600673\pi\) | ||||
−0.311028 | + | 0.950401i | \(0.600673\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 414.735 | 1.30831 | 0.654156 | − | 0.756359i | \(-0.273024\pi\) | ||||
0.654156 | + | 0.756359i | \(0.273024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 9.22111i | − 0.0289063i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 297.765 | 0.927615 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 15.7414i | − 0.0487350i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.34019 | −0.0256621 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 167.754i | 0.513009i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 70.6747i | − 0.213519i | −0.994285 | − | 0.106759i | \(-0.965953\pi\) | ||||
0.994285 | − | 0.106759i | \(-0.0340474\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −101.823 | −0.305776 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 50.3824i | 0.150395i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −134.558 | −0.399283 | −0.199642 | − | 0.979869i | \(-0.563978\pi\) | ||||
−0.199642 | + | 0.979869i | \(0.563978\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 200.612i | − 0.591776i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.0874 | −0.0647726 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −169.809 | −0.492200 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 352.744i | − 1.01655i | −0.861194 | − | 0.508277i | \(-0.830283\pi\) | ||||
0.861194 | − | 0.508277i | \(-0.169717\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −168.042 | −0.481495 | −0.240747 | − | 0.970588i | \(-0.577393\pi\) | ||||
−0.240747 | + | 0.970588i | \(0.577393\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.9145i | 0.0310956i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 406.659 | 1.15201 | 0.576004 | − | 0.817447i | \(-0.304611\pi\) | ||||
0.576004 | + | 0.817447i | \(0.304611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 412.559i | − 1.16214i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 81.3554i | − 0.226617i | −0.993560 | − | 0.113308i | \(-0.963855\pi\) | ||||
0.993560 | − | 0.113308i | \(-0.0361448\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 145.000 | 0.401662 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 208.966i | − 0.575665i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −171.955 | −0.471111 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 54.1525i | 0.147554i | 0.997275 | + | 0.0737772i | \(0.0235054\pi\) | ||||
−0.997275 | + | 0.0737772i | \(0.976495\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 83.6985 | 0.226825 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −523.470 | −1.40341 | −0.701703 | − | 0.712470i | \(-0.747576\pi\) | ||||
−0.701703 | + | 0.712470i | \(0.747576\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 230.108i | 0.613621i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.5887 | 0.0864423 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 43.9466i | − 0.115954i | −0.998318 | − | 0.0579770i | \(-0.981535\pi\) | ||||
0.998318 | − | 0.0579770i | \(-0.0184650\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −396.500 | −1.04068 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 456.854i | 1.19283i | 0.802677 | + | 0.596415i | \(0.203409\pi\) | ||||
−0.802677 | + | 0.596415i | \(0.796591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 84.6156i | 0.218645i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 175.279 | 0.450589 | 0.225295 | − | 0.974291i | \(-0.427666\pi\) | ||||
0.225295 | + | 0.974291i | \(0.427666\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22.8983i | 0.0585635i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −57.0883 | −0.145263 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 34.0292i | 0.0861498i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 182.600 | 0.459950 | 0.229975 | − | 0.973197i | \(-0.426136\pi\) | ||||
0.229975 | + | 0.973197i | \(0.426136\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 755.897 | 1.88503 | 0.942514 | − | 0.334166i | \(-0.108454\pi\) | ||||
0.942514 | + | 0.334166i | \(0.108454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 78.0603i | − 0.193698i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 41.2721 | 0.101906 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 20.1728i | − 0.0495645i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −662.704 | −1.62030 | −0.810151 | − | 0.586221i | \(-0.800615\pi\) | ||||
−0.810151 | + | 0.586221i | \(0.800615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 175.931i | − 0.428055i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 293.650i | − 0.707591i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −365.470 | −0.876427 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 268.951i | 0.641889i | 0.947098 | + | 0.320945i | \(0.104000\pi\) | ||||
−0.947098 | + | 0.320945i | \(0.896000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 445.294 | 1.05770 | 0.528852 | − | 0.848714i | \(-0.322623\pi\) | ||||
0.528852 | + | 0.848714i | \(0.322623\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.52160i | − 0.00596122i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.25274 | 0.0100065 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.16234 | −0.00504042 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 270.182i | 0.626873i | 0.949609 | + | 0.313437i | \(0.101480\pi\) | ||||
−0.949609 | + | 0.313437i | \(0.898520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −283.591 | −0.654944 | −0.327472 | − | 0.944861i | \(-0.606197\pi\) | ||||
−0.327472 | + | 0.944861i | \(0.606197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 123.231i | − 0.283289i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 314.205 | 0.719005 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 426.186i | 0.970812i | 0.874289 | + | 0.485406i | \(0.161328\pi\) | ||||
−0.874289 | + | 0.485406i | \(0.838672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 183.801i | 0.414901i | 0.978245 | + | 0.207451i | \(0.0665167\pi\) | ||||
−0.978245 | + | 0.207451i | \(0.933483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3532 | −0.0322545 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 91.6457i | − 0.205024i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 290.353 | 0.646666 | 0.323333 | − | 0.946285i | \(-0.395197\pi\) | ||||
0.323333 | + | 0.946285i | \(0.395197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5819i | 0.0367671i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 443.294 | 0.978573 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −277.647 | −0.607542 | −0.303771 | − | 0.952745i | \(-0.598246\pi\) | ||||
−0.303771 | + | 0.952745i | \(0.598246\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 5.56543i | − 0.0121251i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −293.002 | −0.635579 | −0.317790 | − | 0.948161i | \(-0.602941\pi\) | ||||
−0.317790 | + | 0.948161i | \(0.602941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 240.518i | 0.519477i | 0.965679 | + | 0.259738i | \(0.0836363\pi\) | ||||
−0.965679 | + | 0.259738i | \(0.916364\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −295.176 | −0.634787 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 370.582i | − 0.793537i | −0.917919 | − | 0.396768i | \(-0.870132\pi\) | ||||
0.917919 | − | 0.396768i | \(-0.129868\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 70.8910i | − 0.150512i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.7636 | −0.0354411 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 58.3551i | − 0.122853i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −86.7351 | −0.181835 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 613.885i | 1.28160i | 0.767709 | + | 0.640798i | \(0.221396\pi\) | ||||
−0.767709 | + | 0.640798i | \(0.778604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 71.2935 | 0.148219 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 423.927 | 0.874076 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 514.860i | 1.05721i | 0.848868 | + | 0.528604i | \(0.177284\pi\) | ||||
−0.848868 | + | 0.528604i | \(0.822716\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 425.823 | 0.870804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 306.097i | 0.623415i | 0.950178 | + | 0.311707i | \(0.100901\pi\) | ||||
−0.950178 | + | 0.311707i | \(0.899099\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.6173 | −0.0337065 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.17663i | 0.0165184i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 443.609i | 0.888996i | 0.895780 | + | 0.444498i | \(0.146618\pi\) | ||||
−0.895780 | + | 0.444498i | \(0.853382\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −160.721 | −0.320800 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 95.3138i | 0.189491i | 0.995502 | + | 0.0947453i | \(0.0302037\pi\) | ||||
−0.995502 | + | 0.0947453i | \(0.969796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 157.411 | 0.311705 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 285.075i | 0.562277i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −641.439 | −1.26019 | −0.630097 | − | 0.776517i | \(-0.716985\pi\) | ||||
−0.630097 | + | 0.776517i | \(0.716985\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −76.3675 | −0.148865 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 440.008i | − 0.854384i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.499567 | 0.000966280 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 326.088i | 0.628301i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 948.718 | 1.82096 | 0.910478 | − | 0.413558i | \(-0.135714\pi\) | ||||
0.910478 | + | 0.413558i | \(0.135714\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 451.606i | − 0.863492i | −0.901995 | − | 0.431746i | \(-0.857898\pi\) | ||||
0.901995 | − | 0.431746i | \(-0.142102\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 39.8037i | 0.0755288i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 71.9403 | 0.135993 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 277.765i | 0.523097i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58.6030 | −0.109949 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 788.363i | 1.47358i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 301.882 | 0.562164 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −438.764 | −0.811023 | −0.405512 | − | 0.914090i | \(-0.632907\pi\) | ||||
−0.405512 | + | 0.914090i | \(0.632907\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 240.734i | − 0.443341i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −444.146 | −0.814947 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 651.132i | 1.19037i | 0.803589 | + | 0.595184i | \(0.202921\pi\) | ||||
−0.803589 | + | 0.595184i | \(0.797079\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −245.948 | −0.447993 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 228.019i | 0.413827i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 269.588i | − 0.485744i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 912.205 | 1.63771 | 0.818856 | − | 0.573999i | \(-0.194609\pi\) | ||||
0.818856 | + | 0.573999i | \(0.194609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 59.2451i | − 0.105984i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10260 | 0.00196541 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 523.002i | 0.928956i | 0.885585 | + | 0.464478i | \(0.153758\pi\) | ||||
−0.885585 | + | 0.464478i | \(0.846242\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 531.141 | 0.940073 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1005.34 | 1.76685 | 0.883425 | − | 0.468572i | \(-0.155231\pi\) | ||||
0.883425 | + | 0.468572i | \(0.155231\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 722.383i | − 1.26512i | −0.774512 | − | 0.632560i | \(-0.782004\pi\) | ||||
0.774512 | − | 0.632560i | \(-0.217996\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 90.0000 | 0.157068 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 84.8865i | 0.147629i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −614.060 | −1.06423 | −0.532114 | − | 0.846672i | \(-0.678602\pi\) | ||||
−0.532114 | + | 0.846672i | \(0.678602\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 27.4069i | − 0.0473349i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 17.1835i | − 0.0294743i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −28.8974 | −0.0493973 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 140.066i | − 0.238613i | −0.992857 | − | 0.119307i | \(-0.961933\pi\) | ||||
0.992857 | − | 0.119307i | \(-0.0380671\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 546.177 | 0.927295 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 257.923i | 0.436417i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 649.841 | 1.09585 | 0.547926 | − | 0.836527i | \(-0.315417\pi\) | ||||
0.547926 | + | 0.836527i | \(0.315417\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −234.177 | −0.392256 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 707.560i | 1.18123i | 0.806952 | + | 0.590617i | \(0.201116\pi\) | ||||
−0.806952 | + | 0.590617i | \(0.798884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −279.057 | −0.464321 | −0.232160 | − | 0.972678i | \(-0.574579\pi\) | ||||
−0.232160 | + | 0.972678i | \(0.574579\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 32.9600i | − 0.0546600i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 553.260 | 0.914480 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 795.724i | 1.31091i | 0.755233 | + | 0.655456i | \(0.227524\pi\) | ||||
−0.755233 | + | 0.655456i | \(0.772476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.76554i | 0.00288959i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −557.470 | −0.909413 | −0.454706 | − | 0.890641i | \(-0.650256\pi\) | ||||
−0.454706 | + | 0.890641i | \(0.650256\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 221.601i | 0.360326i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 832.514 | 1.34929 | 0.674647 | − | 0.738141i | \(-0.264296\pi\) | ||||
0.674647 | + | 0.738141i | \(0.264296\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 593.125i | 0.958198i | 0.877761 | + | 0.479099i | \(0.159037\pi\) | ||||
−0.877761 | + | 0.479099i | \(0.840963\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 111.088 | 0.178886 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −509.971 | −0.815953 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 15.1296i | − 0.0241301i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.3532 | −0.0577953 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 921.620i | 1.46057i | 0.683142 | + | 0.730285i | \(0.260613\pi\) | ||||
−0.683142 | + | 0.730285i | \(0.739387\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −174.323 | −0.275392 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1049.77i | − 1.65319i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 269.894i | 0.422369i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 79.4861 | 0.124003 | 0.0620017 | − | 0.998076i | \(-0.480252\pi\) | ||||
0.0620017 | + | 0.998076i | \(0.480252\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 669.310i | 1.04092i | 0.853887 | + | 0.520459i | \(0.174239\pi\) | ||||
−0.853887 | + | 0.520459i | \(0.825761\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −224.029 | −0.347331 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 396.360i | 0.612612i | 0.951933 | + | 0.306306i | \(0.0990931\pi\) | ||||
−0.951933 | + | 0.306306i | \(0.900907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.0294 | −0.0847911 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1008.04 | 1.54371 | 0.771855 | − | 0.635798i | \(-0.219329\pi\) | ||||
0.771855 | + | 0.635798i | \(0.219329\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 151.147i | − 0.230759i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 112.492 | 0.171221 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 897.287i | 1.36159i | 0.732475 | + | 0.680794i | \(0.238365\pi\) | ||||
−0.732475 | + | 0.680794i | \(0.761635\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −797.658 | −1.20674 | −0.603372 | − | 0.797460i | \(-0.706177\pi\) | ||||
−0.603372 | + | 0.797460i | \(0.706177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.89674i | 0.00587743i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 331.688i | − 0.497284i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −173.823 | −0.259826 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 48.7261i | − 0.0726172i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −961.352 | −1.42846 | −0.714229 | − | 0.699912i | \(-0.753223\pi\) | ||||
−0.714229 | + | 0.699912i | \(0.753223\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 20.6316i | − 0.0305654i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −881.855 | −1.30259 | −0.651296 | − | 0.758824i | \(-0.725774\pi\) | ||||
−0.651296 | + | 0.758824i | \(0.725774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −657.838 | −0.965988 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1299.58i | − 1.90275i | −0.308031 | − | 0.951376i | \(-0.599670\pi\) | ||||
0.308031 | − | 0.951376i | \(-0.400330\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 465.795 | 0.679992 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 37.9310i | − 0.0552126i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 60.7291 | 0.0881410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 556.141i | − 0.804835i | −0.915456 | − | 0.402418i | \(-0.868170\pi\) | ||||
0.915456 | − | 0.402418i | \(-0.131830\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 967.621i | − 1.39226i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.8823 | 0.0428727 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 178.020i | − 0.254678i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −394.690 | −0.563039 | −0.281520 | − | 0.959555i | \(-0.590838\pi\) | ||||
−0.281520 | + | 0.959555i | \(0.590838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 498.831i | 0.709574i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.67619 | 0.00946977 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −90.0303 | −0.126982 | −0.0634910 | − | 0.997982i | \(-0.520223\pi\) | ||||
−0.0634910 | + | 0.997982i | \(0.520223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 22.2617i | − 0.0313104i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −794.498 | −1.11430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 5.72502i | − 0.00800702i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −652.087 | −0.909466 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1379.78i | 1.91903i | 0.281660 | + | 0.959514i | \(0.409115\pi\) | ||||
−0.281660 | + | 0.959514i | \(0.590885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 383.093i | 0.529866i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −61.6022 | −0.0849685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 655.250i | 0.901306i | 0.892699 | + | 0.450653i | \(0.148809\pi\) | ||||
−0.892699 | + | 0.450653i | \(0.851191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.2097i | 0.0413265i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 354.488 | 0.483613 | 0.241806 | − | 0.970325i | \(-0.422260\pi\) | ||||
0.241806 | + | 0.970325i | \(0.422260\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.52987 | 0.00886007 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1053.46i | − 1.42552i | −0.701408 | − | 0.712760i | \(-0.747445\pi\) | ||||
0.701408 | − | 0.712760i | \(-0.252555\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.4701 | 0.0721594 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1248.25i | 1.68001i | 0.542578 | + | 0.840005i | \(0.317448\pi\) | ||||
−0.542578 | + | 0.840005i | \(0.682552\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 242.642 | 0.325694 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 192.105i | 0.257168i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 573.325i | − 0.763415i | −0.924283 | − | 0.381708i | \(-0.875336\pi\) | ||||
0.924283 | − | 0.381708i | \(-0.124664\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −517.456 | −0.687192 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1173.67i | 1.55452i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 86.9117 | 0.114811 | 0.0574053 | − | 0.998351i | \(-0.481717\pi\) | ||||
0.0574053 | + | 0.998351i | \(0.481717\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 22.0083i | 0.0289964i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −850.659 | −1.11782 | −0.558909 | − | 0.829229i | \(-0.688780\pi\) | ||||
−0.558909 | + | 0.829229i | \(0.688780\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.7351 | 0.0192615 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 194.482i | − 0.253562i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 809.762 | 1.05301 | 0.526503 | − | 0.850173i | \(-0.323503\pi\) | ||||
0.526503 | + | 0.850173i | \(0.323503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 596.721i | 0.773957i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1155.03 | 1.49421 | 0.747106 | − | 0.664704i | \(-0.231443\pi\) | ||||
0.747106 | + | 0.664704i | \(0.231443\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 147.556i | 0.190395i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 410.037i | − 0.526363i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.4701 | −0.0684637 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 80.6168i | 0.102959i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 187.691 | 0.239097 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 61.8964i | 0.0786486i | 0.999227 | + | 0.0393243i | \(0.0125205\pi\) | ||||
−0.999227 | + | 0.0393243i | \(0.987479\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 393.411 | 0.498620 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 172.205 | 0.217157 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 229.640i | − 0.288856i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −60.6750 | −0.0761292 | −0.0380646 | − | 0.999275i | \(-0.512119\pi\) | ||||
−0.0380646 | + | 0.999275i | \(0.512119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 0.900267i | − 0.00112674i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.38983 | 0.0117226 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22.2865i | 0.0277540i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 815.086i | − 1.01002i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1363.53 | 1.68545 | 0.842724 | − | 0.538346i | \(-0.180951\pi\) | ||||
0.842724 | + | 0.538346i | \(0.180951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 8.60927i | − 0.0106156i | −0.999986 | − | 0.00530781i | \(-0.998310\pi\) | ||||
0.999986 | − | 0.00530781i | \(-0.00168954\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 270.926 | 0.333242 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1127.41i | 1.38333i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 414.530 | 0.507381 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −322.029 | −0.392239 | −0.196120 | − | 0.980580i | \(-0.562834\pi\) | ||||
−0.196120 | + | 0.980580i | \(0.562834\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 645.800i | 0.784690i | 0.919818 | + | 0.392345i | \(0.128336\pi\) | ||||
−0.919818 | + | 0.392345i | \(0.871664\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.08745 | 0.00495448 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 679.608i | 0.821775i | 0.911686 | + | 0.410887i | \(0.134781\pi\) | ||||
−0.911686 | + | 0.410887i | \(0.865219\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 245.719 | 0.296404 | 0.148202 | − | 0.988957i | \(-0.452651\pi\) | ||||
0.148202 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 484.668i | 0.583235i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 425.525i | − 0.509611i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 193.103 | 0.230708 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 706.701i | 0.842314i | 0.906988 | + | 0.421157i | \(0.138376\pi\) | ||||
−0.906988 | + | 0.421157i | \(0.861624\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −600.294 | −0.713785 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 232.629i | − 0.275954i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −754.765 | −0.893213 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −850.191 | −1.00140 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 725.626i | − 0.852674i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 272.194 | 0.319102 | 0.159551 | − | 0.987190i | \(-0.448995\pi\) | ||||
0.159551 | + | 0.987190i | \(0.448995\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 202.191i | − 0.236481i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1005.87 | 1.17371 | 0.586855 | − | 0.809692i | \(-0.300366\pi\) | ||||
0.586855 | + | 0.809692i | \(0.300366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 323.765i | 0.376910i | 0.982082 | + | 0.188455i | \(0.0603479\pi\) | ||||
−0.982082 | + | 0.188455i | \(0.939652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 759.250i | − 0.879780i | −0.898052 | − | 0.439890i | \(-0.855017\pi\) | ||||
0.898052 | − | 0.439890i | \(-0.144983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −863.352 | −0.998095 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 498.576i | 0.575058i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.41039 | 0.00507525 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.0775i | 0.0264954i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −277.331 | −0.317676 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 529.352 | 0.603595 | 0.301797 | − | 0.953372i | \(-0.402413\pi\) | ||||
0.301797 | + | 0.953372i | \(0.402413\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 266.833i | 0.303564i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −80.1005 | −0.0909200 | −0.0454600 | − | 0.998966i | \(-0.514475\pi\) | ||||
−0.0454600 | + | 0.998966i | \(0.514475\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 869.964i | 0.985237i | 0.870245 | + | 0.492619i | \(0.163960\pi\) | ||||
−0.870245 | + | 0.492619i | \(0.836040\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −735.411 | −0.830973 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 639.508i | 0.720979i | 0.932763 | + | 0.360490i | \(0.117390\pi\) | ||||
−0.932763 | + | 0.360490i | \(0.882610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 5.34911i | − 0.00600349i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.3532 | −0.0138334 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 799.265i | 0.893033i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −77.7805 | −0.0867118 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 576.567i | − 0.641343i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.9664 | −0.0343689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 637.368 | 0.704274 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 1329.03i | − 1.46530i | −0.680606 | − | 0.732650i | \(-0.738283\pi\) | ||||
0.680606 | − | 0.732650i | \(-0.261717\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −102.978 | −0.113287 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 397.879i | − 0.436750i | −0.975865 | − | 0.218375i | \(-0.929924\pi\) | ||||
0.975865 | − | 0.218375i | \(-0.0700756\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −38.0589 | −0.0416855 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 651.174i | − 0.711665i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1282.34i | − 1.39537i | −0.716405 | − | 0.697684i | \(-0.754214\pi\) | ||||
0.716405 | − | 0.697684i | \(-0.245786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.0143 | 0.0434466 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 188.971i | − 0.204736i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −134.765 | −0.145692 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 287.851i | 0.310519i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −148.336 | −0.159673 | −0.0798364 | − | 0.996808i | \(-0.525440\pi\) | ||||
−0.0798364 | + | 0.996808i | \(0.525440\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −630.573 | −0.675855 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.91924i | 0.00312218i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 414.032 | 0.441869 | 0.220935 | − | 0.975289i | \(-0.429089\pi\) | ||||
0.220935 | + | 0.975289i | \(0.429089\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 337.236i | 0.359144i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 345.266 | 0.366914 | 0.183457 | − | 0.983028i | \(-0.441271\pi\) | ||||
0.183457 | + | 0.983028i | \(0.441271\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 596.462i | 0.632515i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 966.773i | 1.02088i | 0.859914 | + | 0.510440i | \(0.170517\pi\) | ||||
−0.859914 | + | 0.510440i | \(0.829483\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −78.7636 | −0.0829965 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 718.342i | − 0.755355i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −366.764 | −0.384852 | −0.192426 | − | 0.981312i | \(-0.561635\pi\) | ||||
−0.192426 | + | 0.981312i | \(0.561635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 238.284i | 0.249513i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15.9714 | −0.0166891 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −420.060 | −0.437107 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 515.743i | − 0.535559i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 72.5626 | 0.0751944 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 563.850i | 0.583092i | 0.956557 | + | 0.291546i | \(0.0941697\pi\) | ||||
−0.956557 | + | 0.291546i | \(0.905830\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −27.2649 | −0.0281372 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 257.159i | − 0.264840i | −0.991194 | − | 0.132420i | \(-0.957725\pi\) | ||||
0.991194 | − | 0.132420i | \(-0.0422747\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4456i | 0.0148160i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −741.131 | −0.758578 | −0.379289 | − | 0.925278i | \(-0.623831\pi\) | ||||
−0.379289 | + | 0.925278i | \(0.623831\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.86027i | 0.00190017i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 290.558 | 0.296186 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 512.687i | 0.521553i | 0.965399 | + | 0.260777i | \(0.0839786\pi\) | ||||
−0.965399 | + | 0.260777i | \(0.916021\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −682.877 | −0.693276 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −602.997 | −0.609704 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 220.633i | 0.222637i | 0.993785 | + | 0.111319i | \(0.0355074\pi\) | ||||
−0.993785 | + | 0.111319i | \(0.964493\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −122.412 | −0.123275 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 620.007i | − 0.623123i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −895.071 | −0.897764 | −0.448882 | − | 0.893591i | \(-0.648178\pi\) | ||||
−0.448882 | + | 0.893591i | \(0.648178\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 176.363i | 0.176540i |
(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 | 2352.3.m.l.1471.1 | yes | 4 | |
4.3 | odd | 2 | inner | 2352.3.m.l.1471.3 | yes | 4 | |
7.6 | odd | 2 | 2352.3.m.d.1471.4 | yes | 4 | ||
28.27 | even | 2 | 2352.3.m.d.1471.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.3.m.d.1471.2 | ✓ | 4 | 28.27 | even | 2 | ||
2352.3.m.d.1471.4 | yes | 4 | 7.6 | odd | 2 | ||
2352.3.m.l.1471.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2352.3.m.l.1471.3 | yes | 4 | 4.3 | odd | 2 | inner |