Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4650,2,Mod(3349,4650)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4650, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4650.3349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4650 = 2 \cdot 3 \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4650.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(37.1304369399\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 930) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3349.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4650.3349 |
Dual form | 4650.2.d.bd.3349.4 |
$q$-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 \(\left(\mathbb{Z}/4650\mathbb{Z}\right)^\times\).
\(n\) | \(1801\) | \(2977\) | \(3101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | − 2.56155i | − 0.968176i | −0.875019 | − | 0.484088i | \(-0.839151\pi\) | ||||
0.875019 | − | 0.484088i | \(-0.160849\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56155 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −2.56155 | −0.684604 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.12311i | 0.757464i | 0.925506 | + | 0.378732i | \(0.123640\pi\) | ||||
−0.925506 | + | 0.378732i | \(0.876360\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 7.68466 | 1.76298 | 0.881491 | − | 0.472201i | \(-0.156540\pi\) | ||||
0.881491 | + | 0.472201i | \(0.156540\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.56155 | −0.558977 | ||||||||
\(22\) | − 2.56155i | − 0.546125i | ||||||||
\(23\) | 1.43845i | 0.299937i | 0.988691 | + | 0.149968i | \(0.0479172\pi\) | ||||
−0.988691 | + | 0.149968i | \(0.952083\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.56155i | 0.484088i | ||||||||
\(29\) | −7.12311 | −1.32273 | −0.661364 | − | 0.750065i | \(-0.730022\pi\) | ||||
−0.661364 | + | 0.750065i | \(0.730022\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 2.56155i | − 0.445909i | ||||||||
\(34\) | 3.12311 | 0.535608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 3.12311i | 0.513435i | 0.966486 | + | 0.256718i | \(0.0826411\pi\) | ||||
−0.966486 | + | 0.256718i | \(0.917359\pi\) | |||||||
\(38\) | − 7.68466i | − 1.24662i | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.12311 | 1.11244 | 0.556221 | − | 0.831034i | \(-0.312251\pi\) | ||||
0.556221 | + | 0.831034i | \(0.312251\pi\) | |||||||
\(42\) | 2.56155i | 0.395256i | ||||||||
\(43\) | 12.8078i | 1.95317i | 0.215142 | + | 0.976583i | \(0.430979\pi\) | ||||
−0.215142 | + | 0.976583i | \(0.569021\pi\) | |||||||
\(44\) | −2.56155 | −0.386169 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.43845 | 0.212087 | ||||||||
\(47\) | − 5.12311i | − 0.747282i | −0.927573 | − | 0.373641i | \(-0.878109\pi\) | ||||
0.927573 | − | 0.373641i | \(-0.121891\pi\) | |||||||
\(48\) | − 1.00000i | − 0.144338i | ||||||||
\(49\) | 0.438447 | 0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.12311 | 0.437322 | ||||||||
\(52\) | − 2.00000i | − 0.277350i | ||||||||
\(53\) | 7.43845i | 1.02175i | 0.859655 | + | 0.510875i | \(0.170678\pi\) | ||||
−0.859655 | + | 0.510875i | \(0.829322\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.56155 | 0.342302 | ||||||||
\(57\) | − 7.68466i | − 1.01786i | ||||||||
\(58\) | 7.12311i | 0.935310i | ||||||||
\(59\) | 13.1231 | 1.70848 | 0.854241 | − | 0.519877i | \(-0.174022\pi\) | ||||
0.854241 | + | 0.519877i | \(0.174022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | 0.768221 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(62\) | − 1.00000i | − 0.127000i | ||||||||
\(63\) | 2.56155i | 0.322725i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.56155 | −0.315305 | ||||||||
\(67\) | 15.3693i | 1.87766i | 0.344380 | + | 0.938830i | \(0.388089\pi\) | ||||
−0.344380 | + | 0.938830i | \(0.611911\pi\) | |||||||
\(68\) | − 3.12311i | − 0.378732i | ||||||||
\(69\) | 1.43845 | 0.173169 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.68466 | −0.912001 | −0.456001 | − | 0.889979i | \(-0.650719\pi\) | ||||
−0.456001 | + | 0.889979i | \(0.650719\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 10.8078i | − 1.26495i | −0.774580 | − | 0.632477i | \(-0.782038\pi\) | ||||
0.774580 | − | 0.632477i | \(-0.217962\pi\) | |||||||
\(74\) | 3.12311 | 0.363054 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.68466 | −0.881491 | ||||||||
\(77\) | − 6.56155i | − 0.747758i | ||||||||
\(78\) | − 2.00000i | − 0.226455i | ||||||||
\(79\) | 4.31534 | 0.485514 | 0.242757 | − | 0.970087i | \(-0.421948\pi\) | ||||
0.242757 | + | 0.970087i | \(0.421948\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 7.12311i | − 0.786615i | ||||||||
\(83\) | 14.2462i | 1.56372i | 0.623451 | + | 0.781862i | \(0.285730\pi\) | ||||
−0.623451 | + | 0.781862i | \(0.714270\pi\) | |||||||
\(84\) | 2.56155 | 0.279488 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.8078 | 1.38110 | ||||||||
\(87\) | 7.12311i | 0.763677i | ||||||||
\(88\) | 2.56155i | 0.273062i | ||||||||
\(89\) | 13.6847 | 1.45057 | 0.725285 | − | 0.688448i | \(-0.241708\pi\) | ||||
0.725285 | + | 0.688448i | \(0.241708\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.12311 | 0.537047 | ||||||||
\(92\) | − 1.43845i | − 0.149968i | ||||||||
\(93\) | − 1.00000i | − 0.103695i | ||||||||
\(94\) | −5.12311 | −0.528408 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | − 0.438447i | − 0.0442899i | ||||||||
\(99\) | −2.56155 | −0.257446 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.561553 | −0.0558766 | −0.0279383 | − | 0.999610i | \(-0.508894\pi\) | ||||
−0.0279383 | + | 0.999610i | \(0.508894\pi\) | |||||||
\(102\) | − 3.12311i | − 0.309234i | ||||||||
\(103\) | − 1.75379i | − 0.172806i | −0.996260 | − | 0.0864030i | \(-0.972463\pi\) | ||||
0.996260 | − | 0.0864030i | \(-0.0275373\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.43845 | 0.722486 | ||||||||
\(107\) | 2.56155i | 0.247635i | 0.992305 | + | 0.123817i | \(0.0395137\pi\) | ||||
−0.992305 | + | 0.123817i | \(0.960486\pi\) | |||||||
\(108\) | − 1.00000i | − 0.0962250i | ||||||||
\(109\) | −5.36932 | −0.514287 | −0.257144 | − | 0.966373i | \(-0.582781\pi\) | ||||
−0.257144 | + | 0.966373i | \(0.582781\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.12311 | 0.296432 | ||||||||
\(112\) | − 2.56155i | − 0.242044i | ||||||||
\(113\) | − 1.68466i | − 0.158479i | −0.996856 | − | 0.0792397i | \(-0.974751\pi\) | ||||
0.996856 | − | 0.0792397i | \(-0.0252492\pi\) | |||||||
\(114\) | −7.68466 | −0.719734 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.12311 | 0.661364 | ||||||||
\(117\) | − 2.00000i | − 0.184900i | ||||||||
\(118\) | − 13.1231i | − 1.20808i | ||||||||
\(119\) | 8.00000 | 0.733359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.43845 | −0.403495 | ||||||||
\(122\) | − 6.00000i | − 0.543214i | ||||||||
\(123\) | − 7.12311i | − 0.642269i | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.56155 | 0.228201 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 12.8078 | 1.12766 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.3693 | −1.34282 | −0.671412 | − | 0.741085i | \(-0.734312\pi\) | ||||
−0.671412 | + | 0.741085i | \(0.734312\pi\) | |||||||
\(132\) | 2.56155i | 0.222955i | ||||||||
\(133\) | − 19.6847i | − 1.70688i | ||||||||
\(134\) | 15.3693 | 1.32771 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.12311 | −0.267804 | ||||||||
\(137\) | − 20.2462i | − 1.72975i | −0.501987 | − | 0.864875i | \(-0.667397\pi\) | ||||
0.501987 | − | 0.864875i | \(-0.332603\pi\) | |||||||
\(138\) | − 1.43845i | − 0.122449i | ||||||||
\(139\) | 17.1231 | 1.45236 | 0.726181 | − | 0.687503i | \(-0.241293\pi\) | ||||
0.726181 | + | 0.687503i | \(0.241293\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.12311 | −0.431443 | ||||||||
\(142\) | 7.68466i | 0.644882i | ||||||||
\(143\) | 5.12311i | 0.428416i | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.8078 | −0.894457 | ||||||||
\(147\) | − 0.438447i | − 0.0361625i | ||||||||
\(148\) | − 3.12311i | − 0.256718i | ||||||||
\(149\) | −17.0540 | −1.39712 | −0.698558 | − | 0.715553i | \(-0.746175\pi\) | ||||
−0.698558 | + | 0.715553i | \(0.746175\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(152\) | 7.68466i | 0.623308i | ||||||||
\(153\) | − 3.12311i | − 0.252488i | ||||||||
\(154\) | −6.56155 | −0.528745 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | − 17.0540i | − 1.36106i | −0.732722 | − | 0.680528i | \(-0.761751\pi\) | ||||
0.732722 | − | 0.680528i | \(-0.238249\pi\) | |||||||
\(158\) | − 4.31534i | − 0.343310i | ||||||||
\(159\) | 7.43845 | 0.589907 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.68466 | 0.290392 | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 15.3693i | − 1.20382i | −0.798565 | − | 0.601909i | \(-0.794407\pi\) | ||||
0.798565 | − | 0.601909i | \(-0.205593\pi\) | |||||||
\(164\) | −7.12311 | −0.556221 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.2462 | 1.10572 | ||||||||
\(167\) | 6.56155i | 0.507748i | 0.967237 | + | 0.253874i | \(0.0817049\pi\) | ||||
−0.967237 | + | 0.253874i | \(0.918295\pi\) | |||||||
\(168\) | − 2.56155i | − 0.197628i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.68466 | −0.587661 | ||||||||
\(172\) | − 12.8078i | − 0.976583i | ||||||||
\(173\) | 8.24621i | 0.626948i | 0.949597 | + | 0.313474i | \(0.101493\pi\) | ||||
−0.949597 | + | 0.313474i | \(0.898507\pi\) | |||||||
\(174\) | 7.12311 | 0.540001 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.56155 | 0.193084 | ||||||||
\(177\) | − 13.1231i | − 0.986393i | ||||||||
\(178\) | − 13.6847i | − 1.02571i | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0540 | −0.970294 | −0.485147 | − | 0.874433i | \(-0.661234\pi\) | ||||
−0.485147 | + | 0.874433i | \(0.661234\pi\) | |||||||
\(182\) | − 5.12311i | − 0.379750i | ||||||||
\(183\) | − 6.00000i | − 0.443533i | ||||||||
\(184\) | −1.43845 | −0.106044 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.00000 | −0.0733236 | ||||||||
\(187\) | 8.00000i | 0.585018i | ||||||||
\(188\) | 5.12311i | 0.373641i | ||||||||
\(189\) | 2.56155 | 0.186326 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.2462 | −1.03082 | −0.515410 | − | 0.856944i | \(-0.672360\pi\) | ||||
−0.515410 | + | 0.856944i | \(0.672360\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 14.4924i | 1.04319i | 0.853194 | + | 0.521594i | \(0.174662\pi\) | ||||
−0.853194 | + | 0.521594i | \(0.825338\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.438447 | −0.0313177 | ||||||||
\(197\) | − 6.00000i | − 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 2.56155i | 0.182042i | ||||||||
\(199\) | 16.8078 | 1.19147 | 0.595735 | − | 0.803181i | \(-0.296861\pi\) | ||||
0.595735 | + | 0.803181i | \(0.296861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.3693 | 1.08407 | ||||||||
\(202\) | 0.561553i | 0.0395107i | ||||||||
\(203\) | 18.2462i | 1.28063i | ||||||||
\(204\) | −3.12311 | −0.218661 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.75379 | −0.122192 | ||||||||
\(207\) | − 1.43845i | − 0.0999790i | ||||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 19.6847 | 1.36162 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.6847 | −1.63052 | −0.815260 | − | 0.579096i | \(-0.803406\pi\) | ||||
−0.815260 | + | 0.579096i | \(0.803406\pi\) | |||||||
\(212\) | − 7.43845i | − 0.510875i | ||||||||
\(213\) | 7.68466i | 0.526544i | ||||||||
\(214\) | 2.56155 | 0.175104 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | − 2.56155i | − 0.173890i | ||||||||
\(218\) | 5.36932i | 0.363656i | ||||||||
\(219\) | −10.8078 | −0.730321 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.24621 | −0.420166 | ||||||||
\(222\) | − 3.12311i | − 0.209609i | ||||||||
\(223\) | − 21.1231i | − 1.41451i | −0.706960 | − | 0.707254i | \(-0.749934\pi\) | ||||
0.706960 | − | 0.707254i | \(-0.250066\pi\) | |||||||
\(224\) | −2.56155 | −0.171151 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.68466 | −0.112062 | ||||||||
\(227\) | − 7.68466i | − 0.510049i | −0.966935 | − | 0.255024i | \(-0.917917\pi\) | ||||
0.966935 | − | 0.255024i | \(-0.0820835\pi\) | |||||||
\(228\) | 7.68466i | 0.508929i | ||||||||
\(229\) | 16.5616 | 1.09442 | 0.547209 | − | 0.836996i | \(-0.315690\pi\) | ||||
0.547209 | + | 0.836996i | \(0.315690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.56155 | −0.431718 | ||||||||
\(232\) | − 7.12311i | − 0.467655i | ||||||||
\(233\) | − 17.0540i | − 1.11724i | −0.829423 | − | 0.558622i | \(-0.811330\pi\) | ||||
0.829423 | − | 0.558622i | \(-0.188670\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −13.1231 | −0.854241 | ||||||||
\(237\) | − 4.31534i | − 0.280312i | ||||||||
\(238\) | − 8.00000i | − 0.518563i | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.2462 | 0.788848 | 0.394424 | − | 0.918929i | \(-0.370944\pi\) | ||||
0.394424 | + | 0.918929i | \(0.370944\pi\) | |||||||
\(242\) | 4.43845i | 0.285314i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −6.00000 | −0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.12311 | −0.454153 | ||||||||
\(247\) | 15.3693i | 0.977926i | ||||||||
\(248\) | 1.00000i | 0.0635001i | ||||||||
\(249\) | 14.2462 | 0.902817 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.4924 | 1.04099 | 0.520496 | − | 0.853864i | \(-0.325747\pi\) | ||||
0.520496 | + | 0.853864i | \(0.325747\pi\) | |||||||
\(252\) | − 2.56155i | − 0.161363i | ||||||||
\(253\) | 3.68466i | 0.231652i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.68466i | 0.105086i | 0.998619 | + | 0.0525431i | \(0.0167327\pi\) | ||||
−0.998619 | + | 0.0525431i | \(0.983267\pi\) | |||||||
\(258\) | − 12.8078i | − 0.797377i | ||||||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.12311 | 0.440909 | ||||||||
\(262\) | 15.3693i | 0.949520i | ||||||||
\(263\) | − 20.4924i | − 1.26362i | −0.775125 | − | 0.631808i | \(-0.782313\pi\) | ||||
0.775125 | − | 0.631808i | \(-0.217687\pi\) | |||||||
\(264\) | 2.56155 | 0.157653 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19.6847 | −1.20694 | ||||||||
\(267\) | − 13.6847i | − 0.837487i | ||||||||
\(268\) | − 15.3693i | − 0.938830i | ||||||||
\(269\) | 0.246211 | 0.0150118 | 0.00750588 | − | 0.999972i | \(-0.497611\pi\) | ||||
0.00750588 | + | 0.999972i | \(0.497611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.0540 | 1.64341 | 0.821706 | − | 0.569912i | \(-0.193023\pi\) | ||||
0.821706 | + | 0.569912i | \(0.193023\pi\) | |||||||
\(272\) | 3.12311i | 0.189366i | ||||||||
\(273\) | − 5.12311i | − 0.310064i | ||||||||
\(274\) | −20.2462 | −1.22312 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.43845 | −0.0865843 | ||||||||
\(277\) | 5.36932i | 0.322611i | 0.986905 | + | 0.161305i | \(0.0515704\pi\) | ||||
−0.986905 | + | 0.161305i | \(0.948430\pi\) | |||||||
\(278\) | − 17.1231i | − 1.02698i | ||||||||
\(279\) | −1.00000 | −0.0598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.87689 | 0.290931 | 0.145466 | − | 0.989363i | \(-0.453532\pi\) | ||||
0.145466 | + | 0.989363i | \(0.453532\pi\) | |||||||
\(282\) | 5.12311i | 0.305077i | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 7.68466 | 0.456001 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.12311 | 0.302936 | ||||||||
\(287\) | − 18.2462i | − 1.07704i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 7.24621 | 0.426248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | 10.8078i | 0.632477i | ||||||||
\(293\) | 26.4924i | 1.54770i | 0.633367 | + | 0.773852i | \(0.281673\pi\) | ||||
−0.633367 | + | 0.773852i | \(0.718327\pi\) | |||||||
\(294\) | −0.438447 | −0.0255708 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.12311 | −0.181527 | ||||||||
\(297\) | 2.56155i | 0.148636i | ||||||||
\(298\) | 17.0540i | 0.987910i | ||||||||
\(299\) | −2.87689 | −0.166375 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.8078 | 1.89101 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.561553i | 0.0322604i | ||||||||
\(304\) | 7.68466 | 0.440745 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.12311 | −0.178536 | ||||||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 6.56155i | 0.373879i | ||||||||
\(309\) | −1.75379 | −0.0997696 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.75379 | −0.0994482 | −0.0497241 | − | 0.998763i | \(-0.515834\pi\) | ||||
−0.0497241 | + | 0.998763i | \(0.515834\pi\) | |||||||
\(312\) | 2.00000i | 0.113228i | ||||||||
\(313\) | − 10.0000i | − 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | −17.0540 | −0.962412 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.31534 | −0.242757 | ||||||||
\(317\) | − 16.8769i | − 0.947901i | −0.880552 | − | 0.473950i | \(-0.842828\pi\) | ||||
0.880552 | − | 0.473950i | \(-0.157172\pi\) | |||||||
\(318\) | − 7.43845i | − 0.417127i | ||||||||
\(319\) | −18.2462 | −1.02159 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.56155 | 0.142972 | ||||||||
\(322\) | − 3.68466i | − 0.205338i | ||||||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.3693 | −0.851228 | ||||||||
\(327\) | 5.36932i | 0.296924i | ||||||||
\(328\) | 7.12311i | 0.393308i | ||||||||
\(329\) | −13.1231 | −0.723500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.24621 | −0.343323 | −0.171661 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171661 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(332\) | − 14.2462i | − 0.781862i | ||||||||
\(333\) | − 3.12311i | − 0.171145i | ||||||||
\(334\) | 6.56155 | 0.359032 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.56155 | −0.139744 | ||||||||
\(337\) | 10.0000i | 0.544735i | 0.962193 | + | 0.272367i | \(0.0878066\pi\) | ||||
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(338\) | − 9.00000i | − 0.489535i | ||||||||
\(339\) | −1.68466 | −0.0914981 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.56155 | 0.138716 | ||||||||
\(342\) | 7.68466i | 0.415539i | ||||||||
\(343\) | − 19.0540i | − 1.02882i | ||||||||
\(344\) | −12.8078 | −0.690548 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.24621 | 0.443319 | ||||||||
\(347\) | − 14.2462i | − 0.764777i | −0.924002 | − | 0.382388i | \(-0.875102\pi\) | ||||
0.924002 | − | 0.382388i | \(-0.124898\pi\) | |||||||
\(348\) | − 7.12311i | − 0.381839i | ||||||||
\(349\) | −5.36932 | −0.287413 | −0.143706 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143706 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | − 2.56155i | − 0.136531i | ||||||||
\(353\) | − 0.246211i | − 0.0131045i | −0.999979 | − | 0.00655225i | \(-0.997914\pi\) | ||||
0.999979 | − | 0.00655225i | \(-0.00208566\pi\) | |||||||
\(354\) | −13.1231 | −0.697485 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −13.6847 | −0.725285 | ||||||||
\(357\) | − 8.00000i | − 0.423405i | ||||||||
\(358\) | − 12.0000i | − 0.634220i | ||||||||
\(359\) | 31.6847 | 1.67225 | 0.836126 | − | 0.548537i | \(-0.184815\pi\) | ||||
0.836126 | + | 0.548537i | \(0.184815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.0540 | 2.10810 | ||||||||
\(362\) | 13.0540i | 0.686102i | ||||||||
\(363\) | 4.43845i | 0.232958i | ||||||||
\(364\) | −5.12311 | −0.268524 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.00000 | −0.313625 | ||||||||
\(367\) | − 15.3693i | − 0.802272i | −0.916019 | − | 0.401136i | \(-0.868616\pi\) | ||||
0.916019 | − | 0.401136i | \(-0.131384\pi\) | |||||||
\(368\) | 1.43845i | 0.0749842i | ||||||||
\(369\) | −7.12311 | −0.370814 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.0540 | 0.989233 | ||||||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | − 5.68466i | − 0.294340i | −0.989111 | − | 0.147170i | \(-0.952983\pi\) | ||||
0.989111 | − | 0.147170i | \(-0.0470165\pi\) | |||||||
\(374\) | 8.00000 | 0.413670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.12311 | 0.264204 | ||||||||
\(377\) | − 14.2462i | − 0.733717i | ||||||||
\(378\) | − 2.56155i | − 0.131752i | ||||||||
\(379\) | 7.05398 | 0.362338 | 0.181169 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181169 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.2462i | 0.728900i | ||||||||
\(383\) | − 10.2462i | − 0.523557i | −0.965128 | − | 0.261778i | \(-0.915691\pi\) | ||||
0.965128 | − | 0.261778i | \(-0.0843090\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.4924 | 0.737645 | ||||||||
\(387\) | − 12.8078i | − 0.651055i | ||||||||
\(388\) | − 6.00000i | − 0.304604i | ||||||||
\(389\) | −7.75379 | −0.393133 | −0.196566 | − | 0.980491i | \(-0.562979\pi\) | ||||
−0.196566 | + | 0.980491i | \(0.562979\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.49242 | −0.227192 | ||||||||
\(392\) | 0.438447i | 0.0221449i | ||||||||
\(393\) | 15.3693i | 0.775279i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.56155 | 0.128723 | ||||||||
\(397\) | − 9.05398i | − 0.454406i | −0.973847 | − | 0.227203i | \(-0.927042\pi\) | ||||
0.973847 | − | 0.227203i | \(-0.0729581\pi\) | |||||||
\(398\) | − 16.8078i | − 0.842497i | ||||||||
\(399\) | −19.6847 | −0.985466 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.6847 | −0.683379 | −0.341690 | − | 0.939813i | \(-0.610999\pi\) | ||||
−0.341690 | + | 0.939813i | \(0.610999\pi\) | |||||||
\(402\) | − 15.3693i | − 0.766552i | ||||||||
\(403\) | 2.00000i | 0.0996271i | ||||||||
\(404\) | 0.561553 | 0.0279383 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.2462 | 0.905544 | ||||||||
\(407\) | 8.00000i | 0.396545i | ||||||||
\(408\) | 3.12311i | 0.154617i | ||||||||
\(409\) | 37.3693 | 1.84779 | 0.923897 | − | 0.382642i | \(-0.124986\pi\) | ||||
0.923897 | + | 0.382642i | \(0.124986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.2462 | −0.998672 | ||||||||
\(412\) | 1.75379i | 0.0864030i | ||||||||
\(413\) | − 33.6155i | − 1.65411i | ||||||||
\(414\) | −1.43845 | −0.0706958 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | − 17.1231i | − 0.838522i | ||||||||
\(418\) | − 19.6847i | − 0.962808i | ||||||||
\(419\) | −5.75379 | −0.281091 | −0.140545 | − | 0.990074i | \(-0.544886\pi\) | ||||
−0.140545 | + | 0.990074i | \(0.544886\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.4924 | −0.706317 | −0.353159 | − | 0.935563i | \(-0.614892\pi\) | ||||
−0.353159 | + | 0.935563i | \(0.614892\pi\) | |||||||
\(422\) | 23.6847i | 1.15295i | ||||||||
\(423\) | 5.12311i | 0.249094i | ||||||||
\(424\) | −7.43845 | −0.361243 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.68466 | 0.372323 | ||||||||
\(427\) | − 15.3693i | − 0.743773i | ||||||||
\(428\) | − 2.56155i | − 0.123817i | ||||||||
\(429\) | 5.12311 | 0.247346 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.2462 | −1.45691 | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||||
−0.728454 | + | 0.685094i | \(0.759761\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 35.3002i | 1.69642i | 0.529661 | + | 0.848209i | \(0.322319\pi\) | ||||
−0.529661 | + | 0.848209i | \(0.677681\pi\) | |||||||
\(434\) | −2.56155 | −0.122958 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.36932 | 0.257144 | ||||||||
\(437\) | 11.0540i | 0.528783i | ||||||||
\(438\) | 10.8078i | 0.516415i | ||||||||
\(439\) | −9.61553 | −0.458924 | −0.229462 | − | 0.973318i | \(-0.573697\pi\) | ||||
−0.229462 | + | 0.973318i | \(0.573697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.438447 | −0.0208784 | ||||||||
\(442\) | 6.24621i | 0.297102i | ||||||||
\(443\) | 23.0540i | 1.09533i | 0.836699 | + | 0.547664i | \(0.184483\pi\) | ||||
−0.836699 | + | 0.547664i | \(0.815517\pi\) | |||||||
\(444\) | −3.12311 | −0.148216 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −21.1231 | −1.00021 | ||||||||
\(447\) | 17.0540i | 0.806625i | ||||||||
\(448\) | 2.56155i | 0.121022i | ||||||||
\(449\) | −10.4924 | −0.495168 | −0.247584 | − | 0.968866i | \(-0.579637\pi\) | ||||
−0.247584 | + | 0.968866i | \(0.579637\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.2462 | 0.859181 | ||||||||
\(452\) | 1.68466i | 0.0792397i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.68466 | −0.360659 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.68466 | 0.359867 | ||||||||
\(457\) | 24.7386i | 1.15722i | 0.815603 | + | 0.578612i | \(0.196406\pi\) | ||||
−0.815603 | + | 0.578612i | \(0.803594\pi\) | |||||||
\(458\) | − 16.5616i | − 0.773871i | ||||||||
\(459\) | −3.12311 | −0.145774 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.36932 | 0.436373 | 0.218186 | − | 0.975907i | \(-0.429986\pi\) | ||||
0.218186 | + | 0.975907i | \(0.429986\pi\) | |||||||
\(462\) | 6.56155i | 0.305271i | ||||||||
\(463\) | 30.7386i | 1.42855i | 0.699867 | + | 0.714273i | \(0.253242\pi\) | ||||
−0.699867 | + | 0.714273i | \(0.746758\pi\) | |||||||
\(464\) | −7.12311 | −0.330682 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.0540 | −0.790010 | ||||||||
\(467\) | 9.75379i | 0.451352i | 0.974202 | + | 0.225676i | \(0.0724590\pi\) | ||||
−0.974202 | + | 0.225676i | \(0.927541\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | 39.3693 | 1.81791 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.0540 | −0.785806 | ||||||||
\(472\) | 13.1231i | 0.604040i | ||||||||
\(473\) | 32.8078i | 1.50850i | ||||||||
\(474\) | −4.31534 | −0.198210 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | − 7.43845i | − 0.340583i | ||||||||
\(478\) | 24.0000i | 1.09773i | ||||||||
\(479\) | −10.5616 | −0.482570 | −0.241285 | − | 0.970454i | \(-0.577569\pi\) | ||||
−0.241285 | + | 0.970454i | \(0.577569\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.24621 | −0.284803 | ||||||||
\(482\) | − 12.2462i | − 0.557800i | ||||||||
\(483\) | − 3.68466i | − 0.167658i | ||||||||
\(484\) | 4.43845 | 0.201748 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − 24.0000i | − 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | 6.00000i | 0.271607i | ||||||||
\(489\) | −15.3693 | −0.695025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.9309 | −1.17024 | −0.585122 | − | 0.810945i | \(-0.698953\pi\) | ||||
−0.585122 | + | 0.810945i | \(0.698953\pi\) | |||||||
\(492\) | 7.12311i | 0.321134i | ||||||||
\(493\) | − 22.2462i | − 1.00192i | ||||||||
\(494\) | 15.3693 | 0.691498 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 19.6847i | 0.882978i | ||||||||
\(498\) | − 14.2462i | − 0.638388i | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.56155 | 0.293149 | ||||||||
\(502\) | − 16.4924i | − 0.736093i | ||||||||
\(503\) | 26.2462i | 1.17026i | 0.810939 | + | 0.585130i | \(0.198957\pi\) | ||||
−0.810939 | + | 0.585130i | \(0.801043\pi\) | |||||||
\(504\) | −2.56155 | −0.114101 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.68466 | 0.163803 | ||||||||
\(507\) | − 9.00000i | − 0.399704i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.6155 | −0.869443 | −0.434721 | − | 0.900565i | \(-0.643153\pi\) | ||||
−0.434721 | + | 0.900565i | \(0.643153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.6847 | −1.22470 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 7.68466i | 0.339286i | ||||||||
\(514\) | 1.68466 | 0.0743071 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −12.8078 | −0.563830 | ||||||||
\(517\) | − 13.1231i | − 0.577154i | ||||||||
\(518\) | − 8.00000i | − 0.351500i | ||||||||
\(519\) | 8.24621 | 0.361968 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.2462 | −1.41273 | −0.706366 | − | 0.707847i | \(-0.749667\pi\) | ||||
−0.706366 | + | 0.707847i | \(0.749667\pi\) | |||||||
\(522\) | − 7.12311i | − 0.311770i | ||||||||
\(523\) | − 22.4233i | − 0.980502i | −0.871581 | − | 0.490251i | \(-0.836905\pi\) | ||||
0.871581 | − | 0.490251i | \(-0.163095\pi\) | |||||||
\(524\) | 15.3693 | 0.671412 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.4924 | −0.893512 | ||||||||
\(527\) | 3.12311i | 0.136045i | ||||||||
\(528\) | − 2.56155i | − 0.111477i | ||||||||
\(529\) | 20.9309 | 0.910038 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.1231 | −0.569494 | ||||||||
\(532\) | 19.6847i | 0.853438i | ||||||||
\(533\) | 14.2462i | 0.617072i | ||||||||
\(534\) | −13.6847 | −0.592193 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.3693 | −0.663853 | ||||||||
\(537\) | − 12.0000i | − 0.517838i | ||||||||
\(538\) | − 0.246211i | − 0.0106149i | ||||||||
\(539\) | 1.12311 | 0.0483756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.7538 | 0.849282 | 0.424641 | − | 0.905362i | \(-0.360400\pi\) | ||||
0.424641 | + | 0.905362i | \(0.360400\pi\) | |||||||
\(542\) | − 27.0540i | − 1.16207i | ||||||||
\(543\) | 13.0540i | 0.560200i | ||||||||
\(544\) | 3.12311 | 0.133902 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.12311 | −0.219249 | ||||||||
\(547\) | − 26.8769i | − 1.14917i | −0.818444 | − | 0.574587i | \(-0.805163\pi\) | ||||
0.818444 | − | 0.574587i | \(-0.194837\pi\) | |||||||
\(548\) | 20.2462i | 0.864875i | ||||||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −54.7386 | −2.33194 | ||||||||
\(552\) | 1.43845i | 0.0612244i | ||||||||
\(553\) | − 11.0540i | − 0.470063i | ||||||||
\(554\) | 5.36932 | 0.228120 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.1231 | −0.726181 | ||||||||
\(557\) | 26.8078i | 1.13588i | 0.823069 | + | 0.567941i | \(0.192260\pi\) | ||||
−0.823069 | + | 0.567941i | \(0.807740\pi\) | |||||||
\(558\) | 1.00000i | 0.0423334i | ||||||||
\(559\) | −25.6155 | −1.08342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | − 4.87689i | − 0.205719i | ||||||||
\(563\) | 16.4924i | 0.695073i | 0.937667 | + | 0.347536i | \(0.112982\pi\) | ||||
−0.937667 | + | 0.347536i | \(0.887018\pi\) | |||||||
\(564\) | 5.12311 | 0.215722 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 2.56155i | − 0.107575i | ||||||||
\(568\) | − 7.68466i | − 0.322441i | ||||||||
\(569\) | −30.8078 | −1.29153 | −0.645764 | − | 0.763537i | \(-0.723461\pi\) | ||||
−0.645764 | + | 0.763537i | \(0.723461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.1231 | 1.72095 | 0.860474 | − | 0.509494i | \(-0.170167\pi\) | ||||
0.860474 | + | 0.509494i | \(0.170167\pi\) | |||||||
\(572\) | − 5.12311i | − 0.214208i | ||||||||
\(573\) | 14.2462i | 0.595144i | ||||||||
\(574\) | −18.2462 | −0.761582 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − 15.1231i | − 0.629583i | −0.949161 | − | 0.314792i | \(-0.898065\pi\) | ||||
0.949161 | − | 0.314792i | \(-0.101935\pi\) | |||||||
\(578\) | − 7.24621i | − 0.301403i | ||||||||
\(579\) | 14.4924 | 0.602285 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.4924 | 1.51396 | ||||||||
\(582\) | − 6.00000i | − 0.248708i | ||||||||
\(583\) | 19.0540i | 0.789135i | ||||||||
\(584\) | 10.8078 | 0.447228 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.4924 | 1.09439 | ||||||||
\(587\) | 0.492423i | 0.0203245i | 0.999948 | + | 0.0101622i | \(0.00323479\pi\) | ||||
−0.999948 | + | 0.0101622i | \(0.996765\pi\) | |||||||
\(588\) | 0.438447i | 0.0180813i | ||||||||
\(589\) | 7.68466 | 0.316641 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 3.12311i | 0.128359i | ||||||||
\(593\) | − 30.0000i | − 1.23195i | −0.787765 | − | 0.615976i | \(-0.788762\pi\) | ||||
0.787765 | − | 0.615976i | \(-0.211238\pi\) | |||||||
\(594\) | 2.56155 | 0.105102 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.0540 | 0.698558 | ||||||||
\(597\) | − 16.8078i | − 0.687896i | ||||||||
\(598\) | 2.87689i | 0.117645i | ||||||||
\(599\) | −38.4233 | −1.56993 | −0.784967 | − | 0.619538i | \(-0.787320\pi\) | ||||
−0.784967 | + | 0.619538i | \(0.787320\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.00000 | 0.0815817 | 0.0407909 | − | 0.999168i | \(-0.487012\pi\) | ||||
0.0407909 | + | 0.999168i | \(0.487012\pi\) | |||||||
\(602\) | − 32.8078i | − 1.33714i | ||||||||
\(603\) | − 15.3693i | − 0.625887i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.561553 | 0.0228115 | ||||||||
\(607\) | − 7.05398i | − 0.286312i | −0.989700 | − | 0.143156i | \(-0.954275\pi\) | ||||
0.989700 | − | 0.143156i | \(-0.0457251\pi\) | |||||||
\(608\) | − 7.68466i | − 0.311654i | ||||||||
\(609\) | 18.2462 | 0.739374 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.2462 | 0.414517 | ||||||||
\(612\) | 3.12311i | 0.126244i | ||||||||
\(613\) | 2.00000i | 0.0807792i | 0.999184 | + | 0.0403896i | \(0.0128599\pi\) | ||||
−0.999184 | + | 0.0403896i | \(0.987140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.56155 | 0.264372 | ||||||||
\(617\) | 15.4384i | 0.621528i | 0.950487 | + | 0.310764i | \(0.100585\pi\) | ||||
−0.950487 | + | 0.310764i | \(0.899415\pi\) | |||||||
\(618\) | 1.75379i | 0.0705477i | ||||||||
\(619\) | −11.3693 | −0.456971 | −0.228486 | − | 0.973547i | \(-0.573377\pi\) | ||||
−0.228486 | + | 0.973547i | \(0.573377\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.43845 | −0.0577229 | ||||||||
\(622\) | 1.75379i | 0.0703205i | ||||||||
\(623\) | − 35.0540i | − 1.40441i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | − 19.6847i | − 0.786130i | ||||||||
\(628\) | 17.0540i | 0.680528i | ||||||||
\(629\) | −9.75379 | −0.388909 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3002 | 1.16642 | 0.583211 | − | 0.812321i | \(-0.301796\pi\) | ||||
0.583211 | + | 0.812321i | \(0.301796\pi\) | |||||||
\(632\) | 4.31534i | 0.171655i | ||||||||
\(633\) | 23.6847i | 0.941381i | ||||||||
\(634\) | −16.8769 | −0.670267 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.43845 | −0.294954 | ||||||||
\(637\) | 0.876894i | 0.0347438i | ||||||||
\(638\) | 18.2462i | 0.722374i | ||||||||
\(639\) | 7.68466 | 0.304000 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.50758 | −0.217536 | −0.108768 | − | 0.994067i | \(-0.534691\pi\) | ||||
−0.108768 | + | 0.994067i | \(0.534691\pi\) | |||||||
\(642\) | − 2.56155i | − 0.101096i | ||||||||
\(643\) | − 7.05398i | − 0.278182i | −0.990280 | − | 0.139091i | \(-0.955582\pi\) | ||||
0.990280 | − | 0.139091i | \(-0.0444180\pi\) | |||||||
\(644\) | −3.68466 | −0.145196 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | 0.944267 | ||||||||
\(647\) | 45.9309i | 1.80573i | 0.429925 | + | 0.902864i | \(0.358540\pi\) | ||||
−0.429925 | + | 0.902864i | \(0.641460\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 33.6155 | 1.31952 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.56155 | −0.100395 | ||||||||
\(652\) | 15.3693i | 0.601909i | ||||||||
\(653\) | 40.2462i | 1.57496i | 0.616343 | + | 0.787478i | \(0.288614\pi\) | ||||
−0.616343 | + | 0.787478i | \(0.711386\pi\) | |||||||
\(654\) | 5.36932 | 0.209957 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.12311 | 0.278111 | ||||||||
\(657\) | 10.8078i | 0.421651i | ||||||||
\(658\) | 13.1231i | 0.511592i | ||||||||
\(659\) | 30.7386 | 1.19741 | 0.598704 | − | 0.800971i | \(-0.295683\pi\) | ||||
0.598704 | + | 0.800971i | \(0.295683\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.4924 | 1.03044 | 0.515218 | − | 0.857059i | \(-0.327711\pi\) | ||||
0.515218 | + | 0.857059i | \(0.327711\pi\) | |||||||
\(662\) | 6.24621i | 0.242766i | ||||||||
\(663\) | 6.24621i | 0.242583i | ||||||||
\(664\) | −14.2462 | −0.552860 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.12311 | −0.121018 | ||||||||
\(667\) | − 10.2462i | − 0.396735i | ||||||||
\(668\) | − 6.56155i | − 0.253874i | ||||||||
\(669\) | −21.1231 | −0.816666 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3693 | 0.593326 | ||||||||
\(672\) | 2.56155i | 0.0988140i | ||||||||
\(673\) | 11.7538i | 0.453075i | 0.974002 | + | 0.226538i | \(0.0727406\pi\) | ||||
−0.974002 | + | 0.226538i | \(0.927259\pi\) | |||||||
\(674\) | 10.0000 | 0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | − 32.4233i | − 1.24613i | −0.782171 | − | 0.623064i | \(-0.785888\pi\) | ||||
0.782171 | − | 0.623064i | \(-0.214112\pi\) | |||||||
\(678\) | 1.68466i | 0.0646989i | ||||||||
\(679\) | 15.3693 | 0.589820 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.68466 | −0.294477 | ||||||||
\(682\) | − 2.56155i | − 0.0980869i | ||||||||
\(683\) | 31.6847i | 1.21238i | 0.795320 | + | 0.606190i | \(0.207303\pi\) | ||||
−0.795320 | + | 0.606190i | \(0.792697\pi\) | |||||||
\(684\) | 7.68466 | 0.293830 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −19.0540 | −0.727484 | ||||||||
\(687\) | − 16.5616i | − 0.631863i | ||||||||
\(688\) | 12.8078i | 0.488291i | ||||||||
\(689\) | −14.8769 | −0.566765 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0540 | 0.572680 | 0.286340 | − | 0.958128i | \(-0.407561\pi\) | ||||
0.286340 | + | 0.958128i | \(0.407561\pi\) | |||||||
\(692\) | − 8.24621i | − 0.313474i | ||||||||
\(693\) | 6.56155i | 0.249253i | ||||||||
\(694\) | −14.2462 | −0.540779 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.12311 | −0.270001 | ||||||||
\(697\) | 22.2462i | 0.842635i | ||||||||
\(698\) | 5.36932i | 0.203232i | ||||||||
\(699\) | −17.0540 | −0.645041 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.19224 | 0.196108 | 0.0980540 | − | 0.995181i | \(-0.468738\pi\) | ||||
0.0980540 | + | 0.995181i | \(0.468738\pi\) | |||||||
\(702\) | 2.00000i | 0.0754851i | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | −2.56155 | −0.0965422 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.246211 | −0.00926628 | ||||||||
\(707\) | 1.43845i | 0.0540984i | ||||||||
\(708\) | 13.1231i | 0.493197i | ||||||||
\(709\) | −17.0540 | −0.640475 | −0.320238 | − | 0.947337i | \(-0.603763\pi\) | ||||
−0.320238 | + | 0.947337i | \(0.603763\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.31534 | −0.161838 | ||||||||
\(712\) | 13.6847i | 0.512854i | ||||||||
\(713\) | 1.43845i | 0.0538703i | ||||||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 24.0000i | 0.896296i | ||||||||
\(718\) | − 31.6847i | − 1.18246i | ||||||||
\(719\) | 34.8769 | 1.30069 | 0.650344 | − | 0.759640i | \(-0.274625\pi\) | ||||
0.650344 | + | 0.759640i | \(0.274625\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.49242 | −0.167307 | ||||||||
\(722\) | − 40.0540i | − 1.49065i | ||||||||
\(723\) | − 12.2462i | − 0.455441i | ||||||||
\(724\) | 13.0540 | 0.485147 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.43845 | 0.164726 | ||||||||
\(727\) | − 23.0540i | − 0.855025i | −0.904010 | − | 0.427512i | \(-0.859390\pi\) | ||||
0.904010 | − | 0.427512i | \(-0.140610\pi\) | |||||||
\(728\) | 5.12311i | 0.189875i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.0000 | −1.47945 | ||||||||
\(732\) | 6.00000i | 0.221766i | ||||||||
\(733\) | − 6.49242i | − 0.239803i | −0.992786 | − | 0.119902i | \(-0.961742\pi\) | ||||
0.992786 | − | 0.119902i | \(-0.0382579\pi\) | |||||||
\(734\) | −15.3693 | −0.567292 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.43845 | 0.0530219 | ||||||||
\(737\) | 39.3693i | 1.45019i | ||||||||
\(738\) | 7.12311i | 0.262205i | ||||||||
\(739\) | −52.9848 | −1.94908 | −0.974540 | − | 0.224216i | \(-0.928018\pi\) | ||||
−0.974540 | + | 0.224216i | \(0.928018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.3693 | 0.564606 | ||||||||
\(742\) | − 19.0540i | − 0.699493i | ||||||||
\(743\) | − 50.4233i | − 1.84985i | −0.380148 | − | 0.924926i | \(-0.624127\pi\) | ||||
0.380148 | − | 0.924926i | \(-0.375873\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −5.68466 | −0.208130 | ||||||||
\(747\) | − 14.2462i | − 0.521242i | ||||||||
\(748\) | − 8.00000i | − 0.292509i | ||||||||
\(749\) | 6.56155 | 0.239754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 45.1231 | 1.64657 | 0.823283 | − | 0.567631i | \(-0.192140\pi\) | ||||
0.823283 | + | 0.567631i | \(0.192140\pi\) | |||||||
\(752\) | − 5.12311i | − 0.186820i | ||||||||
\(753\) | − 16.4924i | − 0.601017i | ||||||||
\(754\) | −14.2462 | −0.518816 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.56155 | −0.0931628 | ||||||||
\(757\) | − 10.0000i | − 0.363456i | −0.983349 | − | 0.181728i | \(-0.941831\pi\) | ||||
0.983349 | − | 0.181728i | \(-0.0581691\pi\) | |||||||
\(758\) | − 7.05398i | − 0.256212i | ||||||||
\(759\) | 3.68466 | 0.133745 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.4233 | −0.740344 | −0.370172 | − | 0.928963i | \(-0.620701\pi\) | ||||
−0.370172 | + | 0.928963i | \(0.620701\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.7538i | 0.497921i | ||||||||
\(764\) | 14.2462 | 0.515410 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.2462 | −0.370211 | ||||||||
\(767\) | 26.2462i | 0.947696i | ||||||||
\(768\) | − 1.00000i | − 0.0360844i | ||||||||
\(769\) | 20.5616 | 0.741469 | 0.370734 | − | 0.928739i | \(-0.379106\pi\) | ||||
0.370734 | + | 0.928739i | \(0.379106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.68466 | 0.0606715 | ||||||||
\(772\) | − 14.4924i | − 0.521594i | ||||||||
\(773\) | − 11.4384i | − 0.411412i | −0.978614 | − | 0.205706i | \(-0.934051\pi\) | ||||
0.978614 | − | 0.205706i | \(-0.0659491\pi\) | |||||||
\(774\) | −12.8078 | −0.460366 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | − 8.00000i | − 0.286998i | ||||||||
\(778\) | 7.75379i | 0.277987i | ||||||||
\(779\) | 54.7386 | 1.96122 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.6847 | −0.704372 | ||||||||
\(782\) | 4.49242i | 0.160649i | ||||||||
\(783\) | − 7.12311i | − 0.254559i | ||||||||
\(784\) | 0.438447 | 0.0156588 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 15.3693 | 0.548205 | ||||||||
\(787\) | 17.9309i | 0.639166i | 0.947558 | + | 0.319583i | \(0.103543\pi\) | ||||
−0.947558 | + | 0.319583i | \(0.896457\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | −20.4924 | −0.729550 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.31534 | −0.153436 | ||||||||
\(792\) | − 2.56155i | − 0.0910208i | ||||||||
\(793\) | 12.0000i | 0.426132i | ||||||||
\(794\) | −9.05398 | −0.321314 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.8078 | −0.595735 | ||||||||
\(797\) | 26.9848i | 0.955852i | 0.878400 | + | 0.477926i | \(0.158611\pi\) | ||||
−0.878400 | + | 0.477926i | \(0.841389\pi\) | |||||||
\(798\) | 19.6847i | 0.696829i | ||||||||
\(799\) | 16.0000 | 0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.6847 | −0.483524 | ||||||||
\(802\) | 13.6847i | 0.483222i | ||||||||
\(803\) | − 27.6847i | − 0.976970i | ||||||||
\(804\) | −15.3693 | −0.542034 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.00000 | 0.0704470 | ||||||||
\(807\) | − 0.246211i | − 0.00866705i | ||||||||
\(808\) | − 0.561553i | − 0.0197554i | ||||||||
\(809\) | 37.6847 | 1.32492 | 0.662461 | − | 0.749096i | \(-0.269512\pi\) | ||||
0.662461 | + | 0.749096i | \(0.269512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.6695 | −0.866263 | −0.433132 | − | 0.901331i | \(-0.642592\pi\) | ||||
−0.433132 | + | 0.901331i | \(0.642592\pi\) | |||||||
\(812\) | − 18.2462i | − 0.640316i | ||||||||
\(813\) | − 27.0540i | − 0.948824i | ||||||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.12311 | 0.109331 | ||||||||
\(817\) | 98.4233i | 3.44340i | ||||||||
\(818\) | − 37.3693i | − 1.30659i | ||||||||
\(819\) | −5.12311 | −0.179016 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.6155 | 0.684587 | 0.342293 | − | 0.939593i | \(-0.388796\pi\) | ||||
0.342293 | + | 0.939593i | \(0.388796\pi\) | |||||||
\(822\) | 20.2462i | 0.706168i | ||||||||
\(823\) | − 25.6155i | − 0.892901i | −0.894808 | − | 0.446451i | \(-0.852688\pi\) | ||||
0.894808 | − | 0.446451i | \(-0.147312\pi\) | |||||||
\(824\) | 1.75379 | 0.0610961 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −33.6155 | −1.16963 | ||||||||
\(827\) | − 1.75379i | − 0.0609852i | −0.999535 | − | 0.0304926i | \(-0.990292\pi\) | ||||
0.999535 | − | 0.0304926i | \(-0.00970760\pi\) | |||||||
\(828\) | 1.43845i | 0.0499895i | ||||||||
\(829\) | −24.4233 | −0.848256 | −0.424128 | − | 0.905602i | \(-0.639419\pi\) | ||||
−0.424128 | + | 0.905602i | \(0.639419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.36932 | 0.186260 | ||||||||
\(832\) | − 2.00000i | − 0.0693375i | ||||||||
\(833\) | 1.36932i | 0.0474440i | ||||||||
\(834\) | −17.1231 | −0.592925 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −19.6847 | −0.680808 | ||||||||
\(837\) | 1.00000i | 0.0345651i | ||||||||
\(838\) | 5.75379i | 0.198761i | ||||||||
\(839\) | −6.06913 | −0.209530 | −0.104765 | − | 0.994497i | \(-0.533409\pi\) | ||||
−0.104765 | + | 0.994497i | \(0.533409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.7386 | 0.749608 | ||||||||
\(842\) | 14.4924i | 0.499442i | ||||||||
\(843\) | − 4.87689i | − 0.167969i | ||||||||
\(844\) | 23.6847 | 0.815260 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.12311 | 0.176136 | ||||||||
\(847\) | 11.3693i | 0.390654i | ||||||||
\(848\) | 7.43845i | 0.255437i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.49242 | −0.153998 | ||||||||
\(852\) | − 7.68466i | − 0.263272i | ||||||||
\(853\) | 47.7926i | 1.63639i | 0.574942 | + | 0.818194i | \(0.305024\pi\) | ||||
−0.574942 | + | 0.818194i | \(0.694976\pi\) | |||||||
\(854\) | −15.3693 | −0.525927 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.56155 | −0.0875521 | ||||||||
\(857\) | − 29.2311i | − 0.998514i | −0.866454 | − | 0.499257i | \(-0.833606\pi\) | ||||
0.866454 | − | 0.499257i | \(-0.166394\pi\) | |||||||
\(858\) | − 5.12311i | − 0.174900i | ||||||||
\(859\) | −26.7386 | −0.912310 | −0.456155 | − | 0.889900i | \(-0.650774\pi\) | ||||
−0.456155 | + | 0.889900i | \(0.650774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.2462 | −0.621829 | ||||||||
\(862\) | 30.2462i | 1.03019i | ||||||||
\(863\) | 39.5464i | 1.34618i | 0.739563 | + | 0.673088i | \(0.235032\pi\) | ||||
−0.739563 | + | 0.673088i | \(0.764968\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 35.3002 | 1.19955 | ||||||||
\(867\) | − 7.24621i | − 0.246094i | ||||||||
\(868\) | 2.56155i | 0.0869448i | ||||||||
\(869\) | 11.0540 | 0.374980 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.7386 | −1.04154 | ||||||||
\(872\) | − 5.36932i | − 0.181828i | ||||||||
\(873\) | − 6.00000i | − 0.203069i | ||||||||
\(874\) | 11.0540 | 0.373906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.8078 | 0.365161 | ||||||||
\(877\) | 50.0000i | 1.68838i | 0.536044 | + | 0.844190i | \(0.319918\pi\) | ||||
−0.536044 | + | 0.844190i | \(0.680082\pi\) | |||||||
\(878\) | 9.61553i | 0.324508i | ||||||||
\(879\) | 26.4924 | 0.893567 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.50758 | 0.320318 | 0.160159 | − | 0.987091i | \(-0.448799\pi\) | ||||
0.160159 | + | 0.987091i | \(0.448799\pi\) | |||||||
\(882\) | 0.438447i | 0.0147633i | ||||||||
\(883\) | 30.4233i | 1.02383i | 0.859038 | + | 0.511913i | \(0.171063\pi\) | ||||
−0.859038 | + | 0.511913i | \(0.828937\pi\) | |||||||
\(884\) | 6.24621 | 0.210083 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.0540 | 0.774513 | ||||||||
\(887\) | 32.6307i | 1.09563i | 0.836599 | + | 0.547816i | \(0.184540\pi\) | ||||
−0.836599 | + | 0.547816i | \(0.815460\pi\) | |||||||
\(888\) | 3.12311i | 0.104805i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.56155 | 0.0858152 | ||||||||
\(892\) | 21.1231i | 0.707254i | ||||||||
\(893\) | − 39.3693i | − 1.31744i | ||||||||
\(894\) | 17.0540 | 0.570370 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.56155 | 0.0855755 | ||||||||
\(897\) | 2.87689i | 0.0960567i | ||||||||
\(898\) | 10.4924i | 0.350137i | ||||||||
\(899\) | −7.12311 | −0.237569 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −23.2311 | −0.773939 | ||||||||
\(902\) | − 18.2462i | − 0.607532i | ||||||||
\(903\) | − 32.8078i | − 1.09177i | ||||||||
\(904\) | 1.68466 | 0.0560309 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 24.0000i | − 0.796907i | −0.917189 | − | 0.398453i | \(-0.869547\pi\) | ||||
0.917189 | − | 0.398453i | \(-0.130453\pi\) | |||||||
\(908\) | 7.68466i | 0.255024i | ||||||||
\(909\) | 0.561553 | 0.0186255 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.5076 | −0.381263 | −0.190632 | − | 0.981662i | \(-0.561054\pi\) | ||||
−0.190632 | + | 0.981662i | \(0.561054\pi\) | |||||||
\(912\) | − 7.68466i | − 0.254464i | ||||||||
\(913\) | 36.4924i | 1.20772i | ||||||||
\(914\) | 24.7386 | 0.818281 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.5616 | −0.547209 | ||||||||
\(917\) | 39.3693i | 1.30009i | ||||||||
\(918\) | 3.12311i | 0.103078i | ||||||||
\(919\) | 1.61553 | 0.0532914 | 0.0266457 | − | 0.999645i | \(-0.491517\pi\) | ||||
0.0266457 | + | 0.999645i | \(0.491517\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 9.36932i | − 0.308562i | ||||||||
\(923\) | − 15.3693i | − 0.505887i | ||||||||
\(924\) | 6.56155 | 0.215859 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.7386 | 1.01013 | ||||||||
\(927\) | 1.75379i | 0.0576020i | ||||||||
\(928\) | 7.12311i | 0.233827i | ||||||||
\(929\) | −7.43845 | −0.244048 | −0.122024 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122024 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.36932 | 0.110425 | ||||||||
\(932\) | 17.0540i | 0.558622i | ||||||||
\(933\) | 1.75379i | 0.0574165i | ||||||||
\(934\) | 9.75379 | 0.319154 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | − 41.3693i | − 1.35148i | −0.737142 | − | 0.675738i | \(-0.763825\pi\) | ||||
0.737142 | − | 0.675738i | \(-0.236175\pi\) | |||||||
\(938\) | − 39.3693i | − 1.28545i | ||||||||
\(939\) | −10.0000 | −0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.63068 | 0.0857578 | 0.0428789 | − | 0.999080i | \(-0.486347\pi\) | ||||
0.0428789 | + | 0.999080i | \(0.486347\pi\) | |||||||
\(942\) | 17.0540i | 0.555649i | ||||||||
\(943\) | 10.2462i | 0.333663i | ||||||||
\(944\) | 13.1231 | 0.427121 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.8078 | 1.06667 | ||||||||
\(947\) | 9.12311i | 0.296461i | 0.988953 | + | 0.148231i | \(0.0473578\pi\) | ||||
−0.988953 | + | 0.148231i | \(0.952642\pi\) | |||||||
\(948\) | 4.31534i | 0.140156i | ||||||||
\(949\) | 21.6155 | 0.701670 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.8769 | −0.547271 | ||||||||
\(952\) | 8.00000i | 0.259281i | ||||||||
\(953\) | 16.1080i | 0.521788i | 0.965367 | + | 0.260894i | \(0.0840173\pi\) | ||||
−0.965367 | + | 0.260894i | \(0.915983\pi\) | |||||||
\(954\) | −7.43845 | −0.240829 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | 18.2462i | 0.589816i | ||||||||
\(958\) | 10.5616i | 0.341228i | ||||||||
\(959\) | −51.8617 | −1.67470 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 6.24621i | 0.201386i | ||||||||
\(963\) | − 2.56155i | − 0.0825449i | ||||||||
\(964\) | −12.2462 | −0.394424 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.68466 | −0.118552 | ||||||||
\(967\) | 42.2462i | 1.35855i | 0.733885 | + | 0.679273i | \(0.237705\pi\) | ||||
−0.733885 | + | 0.679273i | \(0.762295\pi\) | |||||||
\(968\) | − 4.43845i | − 0.142657i | ||||||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.1231 | −1.19134 | −0.595669 | − | 0.803230i | \(-0.703113\pi\) | ||||
−0.595669 | + | 0.803230i | \(0.703113\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − 43.8617i | − 1.40614i | ||||||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | 0.192055 | ||||||||
\(977\) | − 42.9848i | − 1.37521i | −0.726086 | − | 0.687604i | \(-0.758663\pi\) | ||||
0.726086 | − | 0.687604i | \(-0.241337\pi\) | |||||||
\(978\) | 15.3693i | 0.491457i | ||||||||
\(979\) | 35.0540 | 1.12033 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.36932 | 0.171429 | ||||||||
\(982\) | 25.9309i | 0.827487i | ||||||||
\(983\) | 40.9848i | 1.30721i | 0.756834 | + | 0.653607i | \(0.226745\pi\) | ||||
−0.756834 | + | 0.653607i | \(0.773255\pi\) | |||||||
\(984\) | 7.12311 | 0.227076 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22.2462 | −0.708464 | ||||||||
\(987\) | 13.1231i | 0.417713i | ||||||||
\(988\) | − 15.3693i | − 0.488963i | ||||||||
\(989\) | −18.4233 | −0.585827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35.6847 | 1.13356 | 0.566780 | − | 0.823869i | \(-0.308189\pi\) | ||||
0.566780 | + | 0.823869i | \(0.308189\pi\) | |||||||
\(992\) | − 1.00000i | − 0.0317500i | ||||||||
\(993\) | 6.24621i | 0.198218i | ||||||||
\(994\) | 19.6847 | 0.624359 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.2462 | −0.451408 | ||||||||
\(997\) | 29.5076i | 0.934514i | 0.884121 | + | 0.467257i | \(0.154758\pi\) | ||||
−0.884121 | + | 0.467257i | \(0.845242\pi\) | |||||||
\(998\) | 20.0000i | 0.633089i | ||||||||
\(999\) | −3.12311 | −0.0988107 |
(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 | 4650.2.d.bd.3349.1 | 4 | ||
5.2 | odd | 4 | 930.2.a.p.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 4650.2.a.ce.1.1 | 2 | |||
5.4 | even | 2 | inner | 4650.2.d.bd.3349.4 | 4 | ||
15.2 | even | 4 | 2790.2.a.be.1.2 | 2 | |||
20.7 | even | 4 | 7440.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.a.p.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
2790.2.a.be.1.2 | 2 | 15.2 | even | 4 | |||
4650.2.a.ce.1.1 | 2 | 5.3 | odd | 4 | |||
4650.2.d.bd.3349.1 | 4 | 1.1 | even | 1 | trivial | ||
4650.2.d.bd.3349.4 | 4 | 5.4 | even | 2 | inner | ||
7440.2.a.bl.1.1 | 2 | 20.7 | even | 4 |