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: | \(\Q(\sqrt{-3}, \sqrt{-7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - x^{2} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 336) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.3 | ||
Root | \(1.39564 - 0.228425i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.k.1471.1 |
$q$-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 | ||||||||
\(5\) | 0.417424 | 0.0834849 | 0.0417424 | − | 0.999128i | \(-0.486709\pi\) | ||||
0.0417424 | + | 0.999128i | \(0.486709\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 18.4249i | − 1.67499i | −0.546444 | − | 0.837496i | \(-0.684019\pi\) | ||||
0.546444 | − | 0.837496i | \(-0.315981\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.16515 | 0.0896270 | 0.0448135 | − | 0.998995i | \(-0.485731\pi\) | ||||
0.0448135 | + | 0.998995i | \(0.485731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.723000i | 0.0482000i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.417424 | −0.0245544 | −0.0122772 | − | 0.999925i | \(-0.503908\pi\) | ||||
−0.0122772 | + | 0.999925i | \(0.503908\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.1660i | 1.11400i | 0.830512 | + | 0.557000i | \(0.188048\pi\) | ||||
−0.830512 | + | 0.557000i | \(0.811952\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 16.9789i | − 0.738213i | −0.929387 | − | 0.369107i | \(-0.879664\pi\) | ||||
0.929387 | − | 0.369107i | \(-0.120336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.8258 | −0.993030 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.33030 | 0.149321 | 0.0746604 | − | 0.997209i | \(-0.476213\pi\) | ||||
0.0746604 | + | 0.997209i | \(0.476213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.7846i | 0.670471i | 0.942134 | + | 0.335236i | \(0.108816\pi\) | ||||
−0.942134 | + | 0.335236i | \(0.891184\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 31.9129 | 0.967057 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −61.1652 | −1.65311 | −0.826556 | − | 0.562854i | \(-0.809703\pi\) | ||||
−0.826556 | + | 0.562854i | \(0.809703\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.01810i | 0.0517462i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.07803 | 0.221415 | 0.110708 | − | 0.993853i | \(-0.464688\pi\) | ||||
0.110708 | + | 0.993853i | \(0.464688\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.30960i | − 0.169991i | −0.996381 | − | 0.0849954i | \(-0.972912\pi\) | ||||
0.996381 | − | 0.0849954i | \(-0.0270876\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.25227 | −0.0278283 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 19.3386i | 0.411460i | 0.978609 | + | 0.205730i | \(0.0659568\pi\) | ||||
−0.978609 | + | 0.205730i | \(0.934043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 0.723000i | − 0.0141765i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 92.1561 | 1.73879 | 0.869397 | − | 0.494115i | \(-0.164508\pi\) | ||||
0.869397 | + | 0.494115i | \(0.164508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 7.69100i | − 0.139836i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −36.6606 | −0.643169 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 99.2036i | 1.68142i | 0.541487 | + | 0.840709i | \(0.317861\pi\) | ||||
−0.541487 | + | 0.840709i | \(0.682139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −78.6606 | −1.28952 | −0.644759 | − | 0.764386i | \(-0.723042\pi\) | ||||
−0.644759 | + | 0.764386i | \(0.723042\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.486363 | 0.00748250 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 77.6562i | 1.15905i | 0.814955 | + | 0.579524i | \(0.196762\pi\) | ||||
−0.814955 | + | 0.579524i | \(0.803238\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 29.4083 | 0.426208 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 43.9289i | 0.618717i | 0.950945 | + | 0.309359i | \(0.100114\pi\) | ||||
−0.950945 | + | 0.309359i | \(0.899886\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 53.8258 | 0.737339 | 0.368670 | − | 0.929561i | \(-0.379813\pi\) | ||||
0.368670 | + | 0.929561i | \(0.379813\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 42.9995i | − 0.573326i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.7642i | 0.946383i | 0.880960 | + | 0.473191i | \(0.156898\pi\) | ||||
−0.880960 | + | 0.473191i | \(0.843102\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 32.5118i | 0.391709i | 0.980633 | + | 0.195854i | \(0.0627480\pi\) | ||||
−0.980633 | + | 0.195854i | \(0.937252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.174243 | −0.00204992 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.50030i | 0.0862104i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −81.9129 | −0.920369 | −0.460185 | − | 0.887823i | \(-0.652217\pi\) | ||||
−0.460185 | + | 0.887823i | \(0.652217\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −36.0000 | −0.387097 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.83521i | 0.0930022i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 30.1742 | 0.311075 | 0.155537 | − | 0.987830i | \(-0.450289\pi\) | ||||
0.155537 | + | 0.987830i | \(0.450289\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 55.2747i | 0.558331i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −183.060 | −1.81247 | −0.906237 | − | 0.422770i | \(-0.861058\pi\) | ||||
−0.906237 | + | 0.422770i | \(0.861058\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 30.9862i | 0.300837i | 0.988622 | + | 0.150419i | \(0.0480621\pi\) | ||||
−0.988622 | + | 0.150419i | \(0.951938\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 118.010i | 1.10290i | 0.834209 | + | 0.551448i | \(0.185925\pi\) | ||||
−0.834209 | + | 0.551448i | \(0.814075\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 85.3394 | 0.782930 | 0.391465 | − | 0.920193i | \(-0.371968\pi\) | ||||
0.391465 | + | 0.920193i | \(0.371968\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 105.941i | − 0.954425i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 70.6606 | 0.625315 | 0.312658 | − | 0.949866i | \(-0.398781\pi\) | ||||
0.312658 | + | 0.949866i | \(0.398781\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 7.08741i | − 0.0616296i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.49545 | −0.0298757 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −218.477 | −1.80560 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.7236i | 0.127834i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −20.7985 | −0.166388 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 133.241i | 1.04914i | 0.851367 | + | 0.524571i | \(0.175774\pi\) | ||||
−0.851367 | + | 0.524571i | \(0.824226\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.6606 | 0.0981442 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 41.1878i | 0.314411i | 0.987566 | + | 0.157205i | \(0.0502485\pi\) | ||||
−0.987566 | + | 0.157205i | \(0.949752\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 2.16900i | − 0.0160667i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −52.5045 | −0.383245 | −0.191622 | − | 0.981469i | \(-0.561375\pi\) | ||||
−0.191622 | + | 0.981469i | \(0.561375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 265.179i | − 1.90776i | −0.300187 | − | 0.953880i | \(-0.597049\pi\) | ||||
0.300187 | − | 0.953880i | \(-0.402951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.4955 | −0.237556 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 21.4678i | − 0.150125i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.80757 | 0.0124660 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −121.826 | −0.817623 | −0.408811 | − | 0.912619i | \(-0.634057\pi\) | ||||
−0.408811 | + | 0.912619i | \(0.634057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 142.378i | − 0.942901i | −0.881892 | − | 0.471451i | \(-0.843731\pi\) | ||||
0.881892 | − | 0.471451i | \(-0.156269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.25227 | 0.00818479 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.67600i | 0.0559742i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −241.652 | −1.53918 | −0.769591 | − | 0.638537i | \(-0.779540\pi\) | ||||
−0.769591 | + | 0.638537i | \(0.779540\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 159.619i | 1.00389i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 32.4322i | 0.198971i | 0.995039 | + | 0.0994853i | \(0.0317196\pi\) | ||||
−0.995039 | + | 0.0994853i | \(0.968280\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.3212 | 0.0807346 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 28.7774i | 0.172320i | 0.996281 | + | 0.0861599i | \(0.0274596\pi\) | ||||
−0.996281 | + | 0.0861599i | \(0.972540\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −167.642 | −0.991967 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 63.4980i | − 0.371334i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −210.399 | −1.21618 | −0.608090 | − | 0.793868i | \(-0.708064\pi\) | ||||
−0.608090 | + | 0.793868i | \(0.708064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −171.826 | −0.970767 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 286.575i | − 1.60098i | −0.599347 | − | 0.800489i | \(-0.704573\pi\) | ||||
0.599347 | − | 0.800489i | \(-0.295427\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 182.174 | 1.00649 | 0.503244 | − | 0.864144i | \(-0.332140\pi\) | ||||
0.503244 | + | 0.864144i | \(0.332140\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 136.244i | − 0.744504i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −25.5318 | −0.138010 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.69100i | 0.0411284i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 192.695i | 1.00887i | 0.863449 | + | 0.504436i | \(0.168300\pi\) | ||||
−0.863449 | + | 0.504436i | \(0.831700\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 141.826 | 0.734848 | 0.367424 | − | 0.930053i | \(-0.380240\pi\) | ||||
0.367424 | + | 0.930053i | \(0.380240\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.842405i | 0.00432002i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 31.8439 | 0.161644 | 0.0808222 | − | 0.996729i | \(-0.474245\pi\) | ||||
0.0808222 | + | 0.996729i | \(0.474245\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 146.796i | 0.737667i | 0.929496 | + | 0.368833i | \(0.120243\pi\) | ||||
−0.929496 | + | 0.368833i | \(0.879757\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −134.505 | −0.669177 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.78939 | 0.0184848 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 50.9367i | 0.246071i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 389.982 | 1.86594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 274.999i | − 1.30331i | −0.758514 | − | 0.651656i | \(-0.774074\pi\) | ||||
0.758514 | − | 0.651656i | \(-0.225926\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −76.0871 | −0.357217 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 3.05121i | − 0.0141917i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 93.2289i | 0.425703i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.486363 | −0.00220074 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 257.647i | 1.15537i | 0.816261 | + | 0.577684i | \(0.196043\pi\) | ||||
−0.816261 | + | 0.577684i | \(0.803957\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 74.4773 | 0.331010 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 291.064i | 1.28222i | 0.767449 | + | 0.641110i | \(0.221526\pi\) | ||||
−0.767449 | + | 0.641110i | \(0.778474\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 227.459 | 0.993271 | 0.496636 | − | 0.867959i | \(-0.334569\pi\) | ||||
0.496636 | + | 0.867959i | \(0.334569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −442.138 | −1.89759 | −0.948794 | − | 0.315896i | \(-0.897695\pi\) | ||||
−0.948794 | + | 0.315896i | \(0.897695\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.07241i | 0.0343507i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −129.495 | −0.546394 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 182.191i | 0.762306i | 0.924512 | + | 0.381153i | \(0.124473\pi\) | ||||
−0.924512 | + | 0.381153i | \(0.875527\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −354.450 | −1.47075 | −0.735373 | − | 0.677662i | \(-0.762993\pi\) | ||||
−0.735373 | + | 0.677662i | \(0.762993\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.6616i | 0.0998446i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −56.3121 | −0.226153 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 388.822i | 1.54909i | 0.632518 | + | 0.774545i | \(0.282021\pi\) | ||||
−0.632518 | + | 0.774545i | \(0.717979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −312.835 | −1.23650 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 0.301798i | − 0.00118352i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −302.922 | −1.17868 | −0.589342 | − | 0.807883i | \(-0.700613\pi\) | ||||
−0.589342 | + | 0.807883i | \(0.700613\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.9909 | −0.0497736 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 46.6783i | 0.177484i | 0.996055 | + | 0.0887421i | \(0.0282847\pi\) | ||||
−0.996055 | + | 0.0887421i | \(0.971715\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 38.4682 | 0.145163 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 141.877i | − 0.531376i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 260.033 | 0.966664 | 0.483332 | − | 0.875437i | \(-0.339426\pi\) | ||||
0.483332 | + | 0.875437i | \(0.339426\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 115.650i | 0.426754i | 0.976970 | + | 0.213377i | \(0.0684462\pi\) | ||||
−0.976970 | + | 0.213377i | \(0.931554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 457.412i | 1.66332i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 221.826 | 0.800815 | 0.400408 | − | 0.916337i | \(-0.368869\pi\) | ||||
0.400408 | + | 0.916337i | \(0.368869\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 62.3538i | − 0.223490i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −376.468 | −1.33974 | −0.669872 | − | 0.742476i | \(-0.733651\pi\) | ||||
−0.669872 | + | 0.742476i | \(0.733651\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.7128i | 0.0979251i | 0.998801 | + | 0.0489626i | \(0.0155915\pi\) | ||||
−0.998801 | + | 0.0489626i | \(0.984408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.3030 | −0.0536948 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −288.826 | −0.999397 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 52.2633i | 0.179599i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 547.161 | 1.86744 | 0.933722 | − | 0.357998i | \(-0.116540\pi\) | ||||
0.933722 | + | 0.357998i | \(0.116540\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 41.4100i | 0.140373i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −95.7386 | −0.322352 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 19.7830i | − 0.0661639i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 317.069i | − 1.04643i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −32.8348 | −0.107655 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 564.013i | − 1.83718i | −0.395215 | − | 0.918589i | \(-0.629330\pi\) | ||||
0.395215 | − | 0.918589i | \(-0.370670\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −53.6697 | −0.173688 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 397.435i | − 1.27793i | −0.769238 | − | 0.638963i | \(-0.779364\pi\) | ||||
0.769238 | − | 0.638963i | \(-0.220636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −519.909 | −1.66105 | −0.830526 | − | 0.556980i | \(-0.811960\pi\) | ||||
−0.830526 | + | 0.556980i | \(0.811960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 100.156 | 0.315950 | 0.157975 | − | 0.987443i | \(-0.449504\pi\) | ||||
0.157975 | + | 0.987443i | \(0.449504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 79.7854i | − 0.250111i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −204.399 | −0.636758 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 8.83521i | − 0.0273536i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28.9258 | −0.0890024 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 147.812i | 0.452025i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 72.9368i | − 0.220353i | −0.993912 | − | 0.110176i | \(-0.964858\pi\) | ||||
0.993912 | − | 0.110176i | \(-0.0351416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 183.495 | 0.551037 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.4156i | 0.0967630i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 358.936 | 1.06509 | 0.532547 | − | 0.846401i | \(-0.321235\pi\) | ||||
0.532547 | + | 0.846401i | \(0.321235\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 122.388i | 0.361026i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 382.955 | 1.12303 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.2758 | 0.0355819 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 357.827i | − 1.03120i | −0.856829 | − | 0.515601i | \(-0.827569\pi\) | ||||
0.856829 | − | 0.515601i | \(-0.172431\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −482.624 | −1.38288 | −0.691439 | − | 0.722435i | \(-0.743023\pi\) | ||||
−0.691439 | + | 0.722435i | \(0.743023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 6.05430i | − 0.0172487i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −535.023 | −1.51565 | −0.757824 | − | 0.652459i | \(-0.773737\pi\) | ||||
−0.757824 | + | 0.652459i | \(0.773737\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.3370i | 0.0516535i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 572.920i | 1.59588i | 0.602739 | + | 0.797939i | \(0.294076\pi\) | ||||
−0.602739 | + | 0.797939i | \(0.705924\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −87.0000 | −0.240997 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 378.414i | − 1.04246i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 22.4682 | 0.0615567 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 272.107i | − 0.741436i | −0.928746 | − | 0.370718i | \(-0.879112\pi\) | ||||
0.928746 | − | 0.370718i | \(-0.120888\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.2341 | −0.0738051 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −297.339 | −0.797157 | −0.398578 | − | 0.917134i | \(-0.630496\pi\) | ||||
−0.398578 | + | 0.917134i | \(0.630496\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 36.0240i | − 0.0960641i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.04546 | 0.0133832 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 147.240i | − 0.388496i | −0.980952 | − | 0.194248i | \(-0.937773\pi\) | ||||
0.980952 | − | 0.194248i | \(-0.0622267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −230.780 | −0.605723 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 339.101i | − 0.885380i | −0.896675 | − | 0.442690i | \(-0.854024\pi\) | ||||
0.896675 | − | 0.442690i | \(-0.145976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 21.9288i | 0.0566636i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −457.579 | −1.17630 | −0.588148 | − | 0.808754i | \(-0.700143\pi\) | ||||
−0.588148 | + | 0.808754i | \(0.700143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.08741i | 0.0181264i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −71.3394 | −0.181525 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 31.2084i | 0.0790086i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −174.312 | −0.439073 | −0.219537 | − | 0.975604i | \(-0.570455\pi\) | ||||
−0.219537 | + | 0.975604i | \(0.570455\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 260.468 | 0.649547 | 0.324773 | − | 0.945792i | \(-0.394712\pi\) | ||||
0.324773 | + | 0.945792i | \(0.394712\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.2172i | 0.0600923i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.75682 | 0.00927610 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1126.96i | 2.76895i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 134.174 | 0.328054 | 0.164027 | − | 0.986456i | \(-0.447552\pi\) | ||||
0.164027 | + | 0.986456i | \(0.447552\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 90.9405i | − 0.221267i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.5712i | 0.0327017i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 459.303 | 1.10145 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 342.835i | 0.818222i | 0.912485 | + | 0.409111i | \(0.134161\pi\) | ||||
−0.912485 | + | 0.409111i | \(0.865839\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 186.486 | 0.442960 | 0.221480 | − | 0.975165i | \(-0.428911\pi\) | ||||
0.221480 | + | 0.975165i | \(0.428911\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 58.0158i | − 0.137153i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.3629 | 0.0243832 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 37.1833 | 0.0866744 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 114.577i | 0.265841i | 0.991127 | + | 0.132920i | \(0.0424355\pi\) | ||||
−0.991127 | + | 0.132920i | \(0.957565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −289.027 | −0.667499 | −0.333750 | − | 0.942662i | \(-0.608314\pi\) | ||||
−0.333750 | + | 0.942662i | \(0.608314\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.13081i | 0.00719726i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 359.376 | 0.822370 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 730.894i | 1.66491i | 0.554095 | + | 0.832453i | \(0.313064\pi\) | ||||
−0.554095 | + | 0.832453i | \(0.686936\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 186.848i | − 0.421778i | −0.977510 | − | 0.210889i | \(-0.932364\pi\) | ||||
0.977510 | − | 0.210889i | \(-0.0676358\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.1924 | −0.0768369 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 211.008i | − 0.472055i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 673.652 | 1.50034 | 0.750169 | − | 0.661246i | \(-0.229972\pi\) | ||||
0.750169 | + | 0.661246i | \(0.229972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 167.262i | − 0.370869i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 246.606 | 0.544384 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 199.982 | 0.437597 | 0.218798 | − | 0.975770i | \(-0.429786\pi\) | ||||
0.218798 | + | 0.975770i | \(0.429786\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.16900i | 0.00472549i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 348.904 | 0.756841 | 0.378421 | − | 0.925634i | \(-0.376467\pi\) | ||||
0.378421 | + | 0.925634i | \(0.376467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 5.80061i | − 0.0125283i | −0.999980 | − | 0.00626416i | \(-0.998006\pi\) | ||||
0.999980 | − | 0.00626416i | \(-0.00199396\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.0273 | −0.0323167 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 756.716i | − 1.62038i | −0.586169 | − | 0.810189i | \(-0.699365\pi\) | ||||
0.586169 | − | 0.810189i | \(-0.300635\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − 418.553i | − 0.888647i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −134.679 | −0.284733 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 525.462i | − 1.10624i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −276.468 | −0.579598 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 810.076i | 1.69118i | 0.533832 | + | 0.845591i | \(0.320751\pi\) | ||||
−0.533832 | + | 0.845591i | \(0.679249\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −71.2667 | −0.148164 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.5955 | 0.0259700 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 739.888i | 1.51928i | 0.650345 | + | 0.759639i | \(0.274624\pi\) | ||||
−0.650345 | + | 0.759639i | \(0.725376\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −56.1742 | −0.114876 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 332.244i | − 0.676667i | −0.941026 | − | 0.338334i | \(-0.890137\pi\) | ||||
0.941026 | − | 0.338334i | \(-0.109863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.80757 | −0.00366648 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.0730i | 0.0466122i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 156.075i | 0.312776i | 0.987696 | + | 0.156388i | \(0.0499850\pi\) | ||||
−0.987696 | + | 0.156388i | \(0.950015\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −49.8439 | −0.0994889 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 812.348i | 1.61501i | 0.589864 | + | 0.807503i | \(0.299181\pi\) | ||||
−0.589864 | + | 0.807503i | \(0.700819\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −76.4136 | −0.151314 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 290.365i | − 0.572712i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 261.078 | 0.512923 | 0.256462 | − | 0.966554i | \(-0.417443\pi\) | ||||
0.256462 | + | 0.966554i | \(0.417443\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 109.982 | 0.214390 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.9344i | 0.0251153i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 356.312 | 0.689192 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 364.422i | − 0.702162i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 752.831 | 1.44497 | 0.722487 | − | 0.691385i | \(-0.242999\pi\) | ||||
0.722487 | + | 0.691385i | \(0.242999\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 282.531i | − 0.540212i | −0.962831 | − | 0.270106i | \(-0.912941\pi\) | ||||
0.962831 | − | 0.270106i | \(-0.0870587\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.67600i | − 0.0164630i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 240.717 | 0.455041 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 297.611i | − 0.560473i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.5773 | 0.0198448 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.2602i | 0.0920752i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 496.363 | 0.924326 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −254.138 | −0.469756 | −0.234878 | − | 0.972025i | \(-0.575469\pi\) | ||||
−0.234878 | + | 0.972025i | \(0.575469\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 315.535i | 0.581096i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.6227 | 0.0653628 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 696.777i | − 1.27382i | −0.770940 | − | 0.636908i | \(-0.780213\pi\) | ||||
0.770940 | − | 0.636908i | \(-0.219787\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 235.982 | 0.429839 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 91.6552i | 0.166343i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 44.2224i | − 0.0796800i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 640.395 | 1.14972 | 0.574861 | − | 0.818251i | \(-0.305056\pi\) | ||||
0.574861 | + | 0.818251i | \(0.305056\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 8.51680i | − 0.0152358i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.3212 | −0.0237455 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 734.025i | 1.30377i | 0.758316 | + | 0.651887i | \(0.226022\pi\) | ||||
−0.758316 | + | 0.651887i | \(0.773978\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 29.4955 | 0.0522043 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1129.13 | 1.98441 | 0.992205 | − | 0.124620i | \(-0.0397711\pi\) | ||||
0.992205 | + | 0.124620i | \(0.0397711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 345.664i | 0.605366i | 0.953091 | + | 0.302683i | \(0.0978823\pi\) | ||||
−0.953091 | + | 0.302683i | \(0.902118\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −333.757 | −0.582473 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 421.514i | 0.733068i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 820.330 | 1.42172 | 0.710858 | − | 0.703335i | \(-0.248307\pi\) | ||||
0.710858 | + | 0.703335i | \(0.248307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 245.649i | 0.424265i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1697.97i | − 2.91246i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.45909 | −0.00249417 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 736.154i | 1.25410i | 0.778981 | + | 0.627048i | \(0.215737\pi\) | ||||
−0.778981 | + | 0.627048i | \(0.784263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −439.927 | −0.746905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 55.1553i | 0.0933254i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −381.354 | −0.643092 | −0.321546 | − | 0.946894i | \(-0.604203\pi\) | ||||
−0.321546 | + | 0.946894i | \(0.604203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −254.258 | −0.425892 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 539.281i | − 0.900301i | −0.892953 | − | 0.450151i | \(-0.851370\pi\) | ||||
0.892953 | − | 0.450151i | \(-0.148630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −938.276 | −1.56119 | −0.780595 | − | 0.625037i | \(-0.785084\pi\) | ||||
−0.780595 | + | 0.625037i | \(0.785084\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 232.969i | − 0.386349i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −91.1977 | −0.150740 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 274.077i | 0.451527i | 0.974182 | + | 0.225764i | \(0.0724877\pi\) | ||||
−0.974182 | + | 0.225764i | \(0.927512\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.5324i | 0.0368779i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −907.836 | −1.48097 | −0.740486 | − | 0.672071i | \(-0.765405\pi\) | ||||
−0.740486 | + | 0.672071i | \(0.765405\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.56342i | 0.0106722i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 289.753 | 0.469616 | 0.234808 | − | 0.972042i | \(-0.424554\pi\) | ||||
0.234808 | + | 0.972042i | \(0.424554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 908.391i | 1.46751i | 0.679412 | + | 0.733757i | \(0.262235\pi\) | ||||
−0.679412 | + | 0.733757i | \(0.737765\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −88.2250 | −0.142069 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 611.962 | 0.979139 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 675.468i | 1.07730i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.5318 | 0.0405911 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 437.319i | 0.693057i | 0.938039 | + | 0.346529i | \(0.112640\pi\) | ||||
−0.938039 | + | 0.346529i | \(0.887360\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 476.312 | 0.752468 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 55.6181i | 0.0875875i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 131.787i | − 0.206239i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −766.450 | −1.19571 | −0.597855 | − | 0.801604i | \(-0.703980\pi\) | ||||
−0.597855 | + | 0.801604i | \(0.703980\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 191.257i | 0.297445i | 0.988879 | + | 0.148722i | \(0.0475161\pi\) | ||||
−0.988879 | + | 0.148722i | \(0.952484\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.28484 | 0.00819356 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1017.92i | − 1.57330i | −0.617402 | − | 0.786648i | \(-0.711815\pi\) | ||||
0.617402 | − | 0.786648i | \(-0.288185\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1827.82 | 2.81636 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 548.330 | 0.839709 | 0.419855 | − | 0.907591i | \(-0.362081\pi\) | ||||
0.419855 | + | 0.907591i | \(0.362081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.1928i | 0.0262485i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −161.477 | −0.245780 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 569.789i | − 0.864627i | −0.901723 | − | 0.432313i | \(-0.857697\pi\) | ||||
0.901723 | − | 0.432313i | \(-0.142303\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 171.633 | 0.259657 | 0.129829 | − | 0.991536i | \(-0.458557\pi\) | ||||
0.129829 | + | 0.991536i | \(0.458557\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 0.842405i | − 0.00127060i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 73.5238i | − 0.110231i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −446.258 | −0.667052 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1449.31i | 2.15993i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 279.423 | 0.415190 | 0.207595 | − | 0.978215i | \(-0.433436\pi\) | ||||
0.207595 | + | 0.978215i | \(0.433436\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 128.998i | 0.191109i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −719.960 | −1.06346 | −0.531728 | − | 0.846915i | \(-0.678457\pi\) | ||||
−0.531728 | + | 0.846915i | \(0.678457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −504.138 | −0.740291 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1066.95i | − 1.56215i | −0.624434 | − | 0.781077i | \(-0.714670\pi\) | ||||
0.624434 | − | 0.781077i | \(-0.285330\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.9167 | −0.0319951 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 393.971i | 0.573465i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 107.376 | 0.155843 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 716.497i | − 1.03690i | −0.855108 | − | 0.518449i | \(-0.826509\pi\) | ||||
0.855108 | − | 0.518449i | \(-0.173491\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 110.692i | − 0.159269i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.78939 | −0.00543671 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 765.805i | − 1.09557i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1080.02 | 1.54068 | 0.770341 | − | 0.637632i | \(-0.220086\pi\) | ||||
0.770341 | + | 0.637632i | \(0.220086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1294.62i | − 1.84157i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.9818 | −0.0198324 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 773.891 | 1.09152 | 0.545762 | − | 0.837940i | \(-0.316240\pi\) | ||||
0.545762 | + | 0.837940i | \(0.316240\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 224.293i | − 0.315461i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 352.900 | 0.494951 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 8.96118i | − 0.0125331i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −315.564 | −0.440118 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 680.204i | 0.946042i | 0.881051 | + | 0.473021i | \(0.156837\pi\) | ||||
−0.881051 | + | 0.473021i | \(0.843163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 613.925i | − 0.849136i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −107.503 | −0.148280 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 984.982i | − 1.35486i | −0.735588 | − | 0.677429i | \(-0.763094\pi\) | ||||
0.735588 | − | 0.677429i | \(-0.236906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.05121i | 0.00417402i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 893.056 | 1.21836 | 0.609179 | − | 0.793033i | \(-0.291499\pi\) | ||||
0.609179 | + | 0.793033i | \(0.291499\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1430.81 | 1.94140 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 467.035i | − 0.631983i | −0.948762 | − | 0.315991i | \(-0.897663\pi\) | ||||
0.948762 | − | 0.315991i | \(-0.102337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −42.7152 | −0.0576453 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1012.07i | 1.36214i | 0.732220 | + | 0.681068i | \(0.238484\pi\) | ||||
−0.732220 | + | 0.681068i | \(0.761516\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −50.8530 | −0.0682591 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 97.5355i | − 0.130570i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 450.715i | − 0.600153i | −0.953915 | − | 0.300076i | \(-0.902988\pi\) | ||||
0.953915 | − | 0.300076i | \(-0.0970121\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −673.459 | −0.894368 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 59.4321i | − 0.0787180i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −429.303 | −0.567111 | −0.283556 | − | 0.958956i | \(-0.591514\pi\) | ||||
−0.283556 | + | 0.958956i | \(0.591514\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 541.846i | − 0.713894i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 341.390 | 0.448607 | 0.224304 | − | 0.974519i | \(-0.427989\pi\) | ||||
0.224304 | + | 0.974519i | \(0.427989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.522729 | 0.000683306 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 115.587i | 0.150700i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −181.064 | −0.235453 | −0.117727 | − | 0.993046i | \(-0.537561\pi\) | ||||
−0.117727 | + | 0.993046i | \(0.537561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 524.676i | − 0.680514i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1211.23 | 1.56693 | 0.783463 | − | 0.621438i | \(-0.213451\pi\) | ||||
0.783463 | + | 0.621438i | \(0.213451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 515.994i | − 0.665798i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 192.146i | 0.246657i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 809.386 | 1.03635 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 22.5009i | − 0.0287368i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −100.871 | −0.128498 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1070.85i | − 1.36068i | −0.732898 | − | 0.680339i | \(-0.761833\pi\) | ||||
0.732898 | − | 0.680339i | \(-0.238167\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −80.8492 | −0.102471 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −91.6515 | −0.115576 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 66.6288i | 0.0838099i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1498.33 | −1.87996 | −0.939979 | − | 0.341232i | \(-0.889156\pi\) | ||||
−0.939979 | + | 0.341232i | \(0.889156\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 8.07241i | − 0.0101031i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 245.739 | 0.306790 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 991.735i | − 1.23504i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 450.390i | 0.558104i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −416.221 | −0.514489 | −0.257244 | − | 0.966346i | \(-0.582814\pi\) | ||||
−0.257244 | + | 0.966346i | \(0.582814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 326.103i | − 0.402100i | −0.979581 | − | 0.201050i | \(-0.935565\pi\) | ||||
0.979581 | − | 0.201050i | \(-0.0644354\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −200.312 | −0.246386 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.5380i | 0.0166110i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 154.715 | 0.189370 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 952.468 | 1.16013 | 0.580066 | − | 0.814570i | \(-0.303027\pi\) | ||||
0.580066 | + | 0.814570i | \(0.303027\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 486.483i | 0.591110i | 0.955326 | + | 0.295555i | \(0.0955045\pi\) | ||||
−0.955326 | + | 0.295555i | \(0.904496\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −792.261 | −0.960317 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 542.110i | − 0.655513i | −0.944762 | − | 0.327757i | \(-0.893707\pi\) | ||||
0.944762 | − | 0.327757i | \(-0.106293\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −161.826 | −0.195206 | −0.0976030 | − | 0.995225i | \(-0.531118\pi\) | ||||
−0.0976030 | + | 0.995225i | \(0.531118\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 384.213i | 0.462351i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0124i | 0.0143861i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 108.000 | 0.129032 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1103.95i | 1.31580i | 0.753107 | + | 0.657898i | \(0.228554\pi\) | ||||
−0.753107 | + | 0.657898i | \(0.771446\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −822.248 | −0.977703 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 652.062i | − 0.773502i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −69.9780 | −0.0828142 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −48.0000 | −0.0565371 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1038.52i | 1.22035i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −851.873 | −0.998678 | −0.499339 | − | 0.866407i | \(-0.666424\pi\) | ||||
−0.499339 | + | 0.866407i | \(0.666424\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 26.5056i | − 0.0310007i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1331.79 | −1.55401 | −0.777004 | − | 0.629495i | \(-0.783262\pi\) | ||||
−0.777004 | + | 0.629495i | \(0.783262\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 569.479i | − 0.662956i | −0.943463 | − | 0.331478i | \(-0.892453\pi\) | ||||
0.943463 | − | 0.331478i | \(-0.107547\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 161.931i | − 0.187637i | −0.995589 | − | 0.0938184i | \(-0.970093\pi\) | ||||
0.995589 | − | 0.0938184i | \(-0.0299073\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −87.8258 | −0.101533 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 500.261i | − 0.577002i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1377.52 | 1.58518 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 90.4813i | 0.103882i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −90.5227 | −0.103692 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1299.18 | 1.48139 | 0.740693 | − | 0.671844i | \(-0.234497\pi\) | ||||
0.740693 | + | 0.671844i | \(0.234497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 947.711i | 1.07817i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 725.492 | 0.823487 | 0.411743 | − | 0.911300i | \(-0.364920\pi\) | ||||
0.411743 | + | 0.911300i | \(0.364920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 1016.70i | − 1.15141i | −0.817656 | − | 0.575707i | \(-0.804727\pi\) | ||||
0.817656 | − | 0.575707i | \(-0.195273\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −71.7242 | −0.0810443 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 884.857i | − 0.997584i | −0.866722 | − | 0.498792i | \(-0.833777\pi\) | ||||
0.866722 | − | 0.498792i | \(-0.166223\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 165.824i | − 0.186110i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −409.321 | −0.458366 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 119.623i | − 0.133658i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.2652 | 0.0381997 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 90.0037i | 0.100115i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.4682 | −0.0426950 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 76.0440 | 0.0840265 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.1036i | 0.0398055i | 0.999802 | + | 0.0199028i | \(0.00633567\pi\) | ||||
−0.999802 | + | 0.0199028i | \(0.993664\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 549.180 | 0.604158 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 497.091i | 0.545654i | 0.962063 | + | 0.272827i | \(0.0879587\pi\) | ||||
−0.962063 | + | 0.272827i | \(0.912041\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 599.027 | 0.656109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 56.8716i | − 0.0621548i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 231.141i | − 0.251514i | −0.992061 | − | 0.125757i | \(-0.959864\pi\) | ||||
0.992061 | − | 0.125757i | \(-0.0401360\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 976.900 | 1.06069 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 51.1838i | 0.0554538i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1518.47 | 1.64159 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 92.9586i | − 0.100279i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 249.775 | 0.268864 | 0.134432 | − | 0.990923i | \(-0.457079\pi\) | ||||
0.134432 | + | 0.990923i | \(0.457079\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 688.377 | 0.737811 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.21041i | 0.00343360i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 910.827 | 0.972068 | 0.486034 | − | 0.873940i | \(-0.338443\pi\) | ||||
0.486034 | + | 0.873940i | \(0.338443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 900.509i | − 0.959008i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 777.042 | 0.825762 | 0.412881 | − | 0.910785i | \(-0.364523\pi\) | ||||
0.412881 | + | 0.910785i | \(0.364523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 154.135i | − 0.163452i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1245.72i | 1.31544i | 0.753264 | + | 0.657718i | \(0.228478\pi\) | ||||
−0.753264 | + | 0.657718i | \(0.771522\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.7152 | 0.0660855 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 173.475i | 0.182414i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −510.000 | −0.535152 | −0.267576 | − | 0.963537i | \(-0.586223\pi\) | ||||
−0.267576 | + | 0.963537i | \(0.586223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 80.4354i | 0.0842256i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 138.192 | 0.144402 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 529.000 | 0.550468 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 354.030i | − 0.367632i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 59.2015 | 0.0613487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 171.315i | 0.177161i | 0.996069 | + | 0.0885805i | \(0.0282331\pi\) | ||||
−0.996069 | + | 0.0885805i | \(0.971767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.3030 | 0.0157926 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 977.069i | − 1.00625i | −0.864214 | − | 0.503125i | \(-0.832183\pi\) | ||||
0.864214 | − | 0.503125i | \(-0.167817\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − 50.1009i | − 0.0513855i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −448.468 | −0.459026 | −0.229513 | − | 0.973306i | \(-0.573713\pi\) | ||||
−0.229513 | + | 0.973306i | \(0.573713\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1509.24i | 1.54161i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −256.018 | −0.260977 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 563.377i | − 0.573120i | −0.958062 | − | 0.286560i | \(-0.907488\pi\) | ||||
0.958062 | − | 0.286560i | \(-0.0925117\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2924 | 0.0134949 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −124.109 | −0.125489 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1231.85i | 1.24304i | 0.783398 | + | 0.621521i | \(0.213485\pi\) | ||||
−0.783398 | + | 0.621521i | \(0.786515\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 126.330 | 0.127221 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61.2761i | 0.0615840i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −352.882 | −0.353944 | −0.176972 | − | 0.984216i | \(-0.556630\pi\) | ||||
−0.176972 | + | 0.984216i | \(0.556630\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 317.823i | 0.318142i |
(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.k.1471.3 | 4 | ||
4.3 | odd | 2 | inner | 2352.3.m.k.1471.1 | 4 | ||
7.6 | odd | 2 | 336.3.m.a.127.2 | ✓ | 4 | ||
21.20 | even | 2 | 1008.3.m.f.127.2 | 4 | |||
28.27 | even | 2 | 336.3.m.a.127.4 | yes | 4 | ||
56.13 | odd | 2 | 1344.3.m.c.127.3 | 4 | |||
56.27 | even | 2 | 1344.3.m.c.127.1 | 4 | |||
84.83 | odd | 2 | 1008.3.m.f.127.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.3.m.a.127.2 | ✓ | 4 | 7.6 | odd | 2 | ||
336.3.m.a.127.4 | yes | 4 | 28.27 | even | 2 | ||
1008.3.m.f.127.1 | 4 | 84.83 | odd | 2 | |||
1008.3.m.f.127.2 | 4 | 21.20 | even | 2 | |||
1344.3.m.c.127.1 | 4 | 56.27 | even | 2 | |||
1344.3.m.c.127.3 | 4 | 56.13 | odd | 2 | |||
2352.3.m.k.1471.1 | 4 | 4.3 | odd | 2 | inner | ||
2352.3.m.k.1471.3 | 4 | 1.1 | even | 1 | trivial |