Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3356224.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 8x^{4} + 16x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.5 | ||
Root | \(-0.254102i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.q.4049.2 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.93543i | 1.11742i | 0.829362 | + | 0.558711i | \(0.188704\pi\) | ||||
−0.829362 | + | 0.558711i | \(0.811296\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.93543i | 1.86542i | 0.360630 | + | 0.932709i | \(0.382562\pi\) | ||||
−0.360630 | + | 0.932709i | \(0.617438\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.745898 | −0.248633 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.745898 | 0.224897 | 0.112448 | − | 0.993658i | \(-0.464131\pi\) | ||||
0.112448 | + | 0.993658i | \(0.464131\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.74590i | − 0.484225i | −0.970248 | − | 0.242113i | \(-0.922160\pi\) | ||||
0.970248 | − | 0.242113i | \(-0.0778403\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 6.10856i | − 1.48154i | −0.671757 | − | 0.740772i | \(-0.734460\pi\) | ||||
0.671757 | − | 0.740772i | \(-0.265540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.44364 | −1.24886 | −0.624428 | − | 0.781083i | \(-0.714668\pi\) | ||||
−0.624428 | + | 0.781083i | \(0.714668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.55220 | −2.08446 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.36266i | 0.839595i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.66492 | 0.309169 | 0.154584 | − | 0.987980i | \(-0.450596\pi\) | ||||
0.154584 | + | 0.987980i | \(0.450596\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.61676 | −0.290379 | −0.145190 | − | 0.989404i | \(-0.546379\pi\) | ||||
−0.145190 | + | 0.989404i | \(0.546379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.44364i | 0.251305i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.34625i | 0.714520i | 0.934005 | + | 0.357260i | \(0.116289\pi\) | ||||
−0.934005 | + | 0.357260i | \(0.883711\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.37907 | 0.541084 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.95184 | −1.08569 | −0.542847 | − | 0.839831i | \(-0.682654\pi\) | ||||
−0.542847 | + | 0.839831i | \(0.682654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.01641i | − 0.764995i | −0.923957 | − | 0.382497i | \(-0.875064\pi\) | ||||
0.923957 | − | 0.382497i | \(-0.124936\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.68133i | 0.391112i | 0.980693 | + | 0.195556i | \(0.0626512\pi\) | ||||
−0.980693 | + | 0.195556i | \(0.937349\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.3585 | −2.47978 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.8227 | 1.65551 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 13.7417i | − 1.88757i | −0.330558 | − | 0.943786i | \(-0.607237\pi\) | ||||
0.330558 | − | 0.943786i | \(-0.392763\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 10.5358i | − 1.39550i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.2171 | −1.59053 | −0.795267 | − | 0.606260i | \(-0.792669\pi\) | ||||
−0.795267 | + | 0.606260i | \(0.792669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.9794 | −1.78988 | −0.894941 | − | 0.446185i | \(-0.852782\pi\) | ||||
−0.894941 | + | 0.446185i | \(0.852782\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 3.68133i | − 0.463804i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.1044i | 1.60096i | 0.599362 | + | 0.800478i | \(0.295421\pi\) | ||||
−0.599362 | + | 0.800478i | \(0.704579\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.93543 | −0.232999 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.67716 | −1.14847 | −0.574234 | − | 0.818691i | \(-0.694700\pi\) | ||||
−0.574234 | + | 0.818691i | \(0.694700\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 5.69774i | − 0.666870i | −0.942773 | − | 0.333435i | \(-0.891792\pi\) | ||||
0.942773 | − | 0.333435i | \(-0.108208\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.68133i | 0.419527i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3791 | −1.16774 | −0.583868 | − | 0.811848i | \(-0.698462\pi\) | ||||
−0.583868 | + | 0.811848i | \(0.698462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6813 | −1.18681 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 0.637339i | − 0.0699570i | −0.999388 | − | 0.0349785i | \(-0.988864\pi\) | ||||
0.999388 | − | 0.0349785i | \(-0.0111363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.22235i | 0.345472i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.72532 | −0.288884 | −0.144442 | − | 0.989513i | \(-0.546139\pi\) | ||||
−0.144442 | + | 0.989513i | \(0.546139\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.61676 | 0.903282 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.12914i | − 0.324476i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.12497i | 0.723431i | 0.932289 | + | 0.361715i | \(0.117809\pi\) | ||||
−0.932289 | + | 0.361715i | \(0.882191\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.556364 | −0.0559167 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.9753 | 1.49009 | 0.745047 | − | 0.667012i | \(-0.232427\pi\) | ||||
0.745047 | + | 0.667012i | \(0.232427\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8667i | 1.07073i | 0.844622 | + | 0.535364i | \(0.179825\pi\) | ||||
−0.844622 | + | 0.535364i | \(0.820175\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.49180i | − 0.724259i | −0.932128 | − | 0.362130i | \(-0.882050\pi\) | ||||
0.932128 | − | 0.362130i | \(-0.117950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.3309 | 1.75578 | 0.877891 | − | 0.478860i | \(-0.158950\pi\) | ||||
0.877891 | + | 0.478860i | \(0.158950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.41188 | −0.798420 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 0.379068i | − 0.0356597i | −0.999841 | − | 0.0178299i | \(-0.994324\pi\) | ||||
0.999841 | − | 0.0178299i | \(-0.00567572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.30226i | 0.120394i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 30.1484 | 2.76370 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4436 | −0.949421 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 13.4548i | − 1.21318i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.64852i | 0.235018i | 0.993072 | + | 0.117509i | \(0.0374909\pi\) | ||||
−0.993072 | + | 0.117509i | \(0.962509\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.70892 | 0.854822 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.53579 | −0.483664 | −0.241832 | − | 0.970318i | \(-0.577748\pi\) | ||||
−0.241832 | + | 0.970318i | \(0.577748\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 26.8667i | − 2.32964i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.16896i | 0.527050i | 0.964653 | + | 0.263525i | \(0.0848851\pi\) | ||||
−0.964653 | + | 0.263525i | \(0.915115\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.7693 | 1.76163 | 0.880815 | − | 0.473460i | \(-0.156995\pi\) | ||||
0.880815 | + | 0.473460i | \(0.156995\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.18953 | −0.437038 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1.30226i | − 0.108901i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 33.5962i | − 2.77097i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.06457 | 0.0872128 | 0.0436064 | − | 0.999049i | \(-0.486115\pi\) | ||||
0.0436064 | + | 0.999049i | \(0.486115\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.6608 | −1.03032 | −0.515159 | − | 0.857095i | \(-0.672267\pi\) | ||||
−0.515159 | + | 0.857095i | \(0.672267\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.55636i | 0.368360i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.8873i | 1.18813i | 0.804416 | + | 0.594067i | \(0.202479\pi\) | ||||
−0.804416 | + | 0.594067i | \(0.797521\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 26.5962 | 2.10921 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.93543 | −0.388967 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.72949i | − 0.527094i | −0.964646 | − | 0.263547i | \(-0.915108\pi\) | ||||
0.964646 | − | 0.263547i | \(-0.0848925\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 2.98359i | − 0.230877i | −0.993315 | − | 0.115439i | \(-0.963173\pi\) | ||||
0.993315 | − | 0.115439i | \(-0.0368274\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.95184 | 0.765526 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.06040 | 0.310506 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.8503i | 1.20508i | 0.798091 | + | 0.602538i | \(0.205844\pi\) | ||||
−0.798091 | + | 0.602538i | \(0.794156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 23.6454i | − 1.77730i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.02759 | −0.226292 | −0.113146 | − | 0.993578i | \(-0.536093\pi\) | ||||
−0.113146 | + | 0.993578i | \(0.536093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.82270 | 0.135481 | 0.0677403 | − | 0.997703i | \(-0.478421\pi\) | ||||
0.0677403 | + | 0.997703i | \(0.478421\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 27.0562i | − 2.00005i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 4.55636i | − 0.333194i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.5316 | −1.56619 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.6126 | 1.41912 | 0.709559 | − | 0.704646i | \(-0.248894\pi\) | ||||
0.709559 | + | 0.704646i | \(0.248894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.335076i | 0.0241193i | 0.999927 | + | 0.0120597i | \(0.00383880\pi\) | ||||
−0.999927 | + | 0.0120597i | \(0.996161\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.5316i | − 1.46282i | −0.681939 | − | 0.731409i | \(-0.738863\pi\) | ||||
0.681939 | − | 0.731409i | \(-0.261137\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.7253 | −1.18563 | −0.592813 | − | 0.805340i | \(-0.701983\pi\) | ||||
−0.592813 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.3627 | −1.78894 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.21712i | 0.576729i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 0.745898i | − 0.0518435i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.06040 | −0.280864 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.3955 | −0.922183 | −0.461091 | − | 0.887353i | \(-0.652542\pi\) | ||||
−0.461091 | + | 0.887353i | \(0.652542\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 18.7295i | − 1.28332i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 7.97942i | − 0.541679i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.0276 | 0.745175 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.6649 | −0.717400 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.27468i | − 0.0853587i | −0.999089 | − | 0.0426794i | \(-0.986411\pi\) | ||||
0.999089 | − | 0.0426794i | \(-0.0135894\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.57978i | 0.237598i | 0.992918 | + | 0.118799i | \(0.0379045\pi\) | ||||
−0.992918 | + | 0.118799i | \(0.962096\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.4119 | −0.688036 | −0.344018 | − | 0.938963i | \(-0.611788\pi\) | ||||
−0.344018 | + | 0.938963i | \(0.611788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.12497 | −0.468788 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 3.06040i | − 0.200493i | −0.994963 | − | 0.100247i | \(-0.968037\pi\) | ||||
0.994963 | − | 0.100247i | \(-0.0319632\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 20.0880i | − 1.30485i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1895 | 1.24127 | 0.620634 | − | 0.784100i | \(-0.286875\pi\) | ||||
0.620634 | + | 0.784100i | \(0.286875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.346255 | 0.0223042 | 0.0111521 | − | 0.999938i | \(-0.496450\pi\) | ||||
0.0111521 | + | 0.999938i | \(0.496450\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 7.58501i | − 0.486579i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.50403i | 0.604727i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.23353 | 0.0781715 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.3861 | 0.908041 | 0.454021 | − | 0.890991i | \(-0.349989\pi\) | ||||
0.454021 | + | 0.890991i | \(0.349989\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.745898i | 0.0468942i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.28586i | 0.0802095i | 0.999195 | + | 0.0401047i | \(0.0127692\pi\) | ||||
−0.999195 | + | 0.0401047i | \(0.987231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −21.4506 | −1.33288 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.24186 | −0.0768694 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 28.2294i | − 1.74070i | −0.492437 | − | 0.870348i | \(-0.663894\pi\) | ||||
0.492437 | − | 0.870348i | \(-0.336106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 5.27468i | − 0.322805i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.4395 | 1.18525 | 0.592623 | − | 0.805480i | \(-0.298093\pi\) | ||||
0.592623 | + | 0.805480i | \(0.298093\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.42723 | −0.390426 | −0.195213 | − | 0.980761i | \(-0.562540\pi\) | ||||
−0.195213 | + | 0.980761i | \(0.562540\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.6772i | 1.00935i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.08514i | 0.245452i | 0.992441 | + | 0.122726i | \(0.0391637\pi\) | ||||
−0.992441 | + | 0.122726i | \(0.960836\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.20594 | 0.0721978 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.38741 | −0.381041 | −0.190520 | − | 0.981683i | \(-0.561018\pi\) | ||||
−0.190520 | + | 0.981683i | \(0.561018\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4835i | 1.27706i | 0.769597 | + | 0.638530i | \(0.220457\pi\) | ||||
−0.769597 | + | 0.638530i | \(0.779543\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 34.3103i | − 2.02527i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −20.3145 | −1.19497 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.7899 | −0.808378 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.1208i | 0.941787i | 0.882190 | + | 0.470894i | \(0.156068\pi\) | ||||
−0.882190 | + | 0.470894i | \(0.843932\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.25410i | 0.188822i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.74590 | 0.100968 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.7581 | 1.42704 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 28.9836i | 1.66506i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.96302i | − 0.397400i | −0.980060 | − | 0.198700i | \(-0.936328\pi\) | ||||
0.980060 | − | 0.198700i | \(-0.0636720\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.0318 | −1.19645 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.14031 | −0.234776 | −0.117388 | − | 0.993086i | \(-0.537452\pi\) | ||||
−0.117388 | + | 0.993086i | \(0.537452\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.26528i | − 0.354135i | −0.984199 | − | 0.177067i | \(-0.943339\pi\) | ||||
0.984199 | − | 0.177067i | \(-0.0566610\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.53996i | 0.535817i | 0.963444 | + | 0.267909i | \(0.0863326\pi\) | ||||
−0.963444 | + | 0.267909i | \(0.913667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.24186 | 0.0695310 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.4999 | 0.809304 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.2528i | 1.85023i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 35.4782i | 1.96195i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.2335 | −0.729588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.3023 | −0.786123 | −0.393062 | − | 0.919512i | \(-0.628584\pi\) | ||||
−0.393062 | + | 0.919512i | \(0.628584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 3.24186i | − 0.177653i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 3.34731i | − 0.182340i | −0.995835 | − | 0.0911699i | \(-0.970939\pi\) | ||||
0.995835 | − | 0.0911699i | \(-0.0290606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.733661 | 0.0398470 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.20594 | −0.0653054 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 51.1236i | − 2.76042i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 23.9383i | − 1.28507i | −0.766255 | − | 0.642537i | \(-0.777882\pi\) | ||||
0.766255 | − | 0.642537i | \(-0.222118\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9149 | 0.637788 | 0.318894 | − | 0.947790i | \(-0.396689\pi\) | ||||
0.318894 | + | 0.947790i | \(0.396689\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.61676 | 0.406553 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2447i | 1.34364i | 0.740714 | + | 0.671820i | \(0.234487\pi\) | ||||
−0.740714 | + | 0.671820i | \(0.765513\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 58.3502i | 3.08822i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.4671 | −1.08021 | −0.540105 | − | 0.841598i | \(-0.681615\pi\) | ||||
−0.540105 | + | 0.841598i | \(0.681615\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6332 | 0.559641 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 20.2130i | − 1.06090i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 36.4999i | − 1.90528i | −0.304104 | − | 0.952639i | \(-0.598357\pi\) | ||||
0.304104 | − | 0.952639i | \(-0.401643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.18537 | 0.269939 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 67.8214 | 3.52111 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.57978i | 0.288910i | 0.989511 | + | 0.144455i | \(0.0461429\pi\) | ||||
−0.989511 | + | 0.144455i | \(0.953857\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.90679i | − 0.149707i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −36.6168 | −1.88088 | −0.940438 | − | 0.339964i | \(-0.889585\pi\) | ||||
−0.940438 | + | 0.339964i | \(0.889585\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.12603 | −0.262614 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.7581i | 1.46947i | 0.678353 | + | 0.734736i | \(0.262694\pi\) | ||||
−0.678353 | + | 0.734736i | \(0.737306\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.74173i | 0.190203i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.3913 | −1.33809 | −0.669046 | − | 0.743221i | \(-0.733297\pi\) | ||||
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.10856 | 0.308923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 10.7141i | − 0.540457i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.08931i | 0.0546710i | 0.999626 | + | 0.0273355i | \(0.00870225\pi\) | ||||
−0.999626 | + | 0.0273355i | \(0.991298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 51.9987 | 2.60319 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5962 | −1.12840 | −0.564200 | − | 0.825638i | \(-0.690815\pi\) | ||||
−0.564200 | + | 0.825638i | \(0.690815\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.82270i | 0.140609i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.24186i | 0.160693i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0510 | 0.793671 | 0.396835 | − | 0.917890i | \(-0.370108\pi\) | ||||
0.396835 | + | 0.917890i | \(0.370108\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.9396 | −0.588937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 60.2968i | − 2.96701i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.1976i | 1.96849i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.4342 | 1.19369 | 0.596845 | − | 0.802356i | \(-0.296421\pi\) | ||||
0.596845 | + | 0.802356i | \(0.296421\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.3473 | −0.553034 | −0.276517 | − | 0.961009i | \(-0.589180\pi\) | ||||
−0.276517 | + | 0.961009i | \(0.589180\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 2.00000i | − 0.0972433i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 68.9945i | − 3.33888i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.52044 | 0.121688 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.83805 | 0.377546 | 0.188773 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188773 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.9023i | 1.82147i | 0.412990 | + | 0.910735i | \(0.364484\pi\) | ||||
−0.412990 | + | 0.910735i | \(0.635516\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.44364i | − 0.260404i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7704 | 0.848134 | 0.424067 | − | 0.905631i | \(-0.360602\pi\) | ||||
0.424067 | + | 0.905631i | \(0.360602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.9477 | 0.616556 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 16.9466i | − 0.805158i | −0.915385 | − | 0.402579i | \(-0.868114\pi\) | ||||
0.915385 | − | 0.402579i | \(-0.131886\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.06040i | 0.0974535i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.0890 | 0.995253 | 0.497627 | − | 0.867391i | \(-0.334205\pi\) | ||||
0.497627 | + | 0.867391i | \(0.334205\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.18537 | −0.244169 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 24.5040i | − 1.15130i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.1372i | 0.614532i | 0.951624 | + | 0.307266i | \(0.0994142\pi\) | ||||
−0.951624 | + | 0.307266i | \(0.900586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 26.6496 | 1.24390 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.5439 | −0.677375 | −0.338687 | − | 0.940899i | \(-0.609983\pi\) | ||||
−0.338687 | + | 0.940899i | \(0.609983\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 19.4283i | − 0.902909i | −0.892294 | − | 0.451455i | \(-0.850905\pi\) | ||||
0.892294 | − | 0.451455i | \(-0.149095\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 3.61259i | − 0.167171i | −0.996501 | − | 0.0835855i | \(-0.973363\pi\) | ||||
0.996501 | − | 0.0835855i | \(-0.0266372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −64.6758 | −2.98645 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.8133 | −1.32765 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3.74173i | − 0.172045i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.2499i | 0.469312i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.13720 | −0.234725 | −0.117362 | − | 0.993089i | \(-0.537444\pi\) | ||||
−0.117362 | + | 0.993089i | \(0.537444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.58812 | 0.345988 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 9.55220i | − 0.434640i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 24.7693i | − 1.12240i | −0.827679 | − | 0.561202i | \(-0.810339\pi\) | ||||
0.827679 | − | 0.561202i | \(-0.189661\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.0245 | 0.588987 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.54413 | 0.159944 | 0.0799721 | − | 0.996797i | \(-0.474517\pi\) | ||||
0.0799721 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 10.1703i | − 0.458047i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 47.7610i | − 2.14237i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.5358 | −1.41174 | −0.705868 | − | 0.708344i | \(-0.749443\pi\) | ||||
−0.705868 | + | 0.708344i | \(0.749443\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.77454 | 0.257988 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 32.2346i | 1.43727i | 0.695388 | + | 0.718635i | \(0.255233\pi\) | ||||
−0.695388 | + | 0.718635i | \(0.744767\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.2611i | 0.855416i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.302263 | −0.0133976 | −0.00669878 | − | 0.999978i | \(-0.502132\pi\) | ||||
−0.00669878 | + | 0.999978i | \(0.502132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.1208 | 1.24399 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 23.7487i | − 1.04853i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.00000i | 0.0879599i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −30.6772 | −1.34658 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3463 | −1.32949 | −0.664747 | − | 0.747069i | \(-0.731461\pi\) | ||||
−0.664747 | + | 0.747069i | \(0.731461\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 42.5878i | 1.86224i | 0.364717 | + | 0.931118i | \(0.381166\pi\) | ||||
−0.364717 | + | 0.931118i | \(0.618834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.87609i | 0.430209i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.11273 | 0.395459 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.1372i | 0.525721i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 5.85969i | − 0.252864i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.9477 | −0.557696 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.9313 | 1.67379 | 0.836893 | − | 0.547367i | \(-0.184370\pi\) | ||||
0.836893 | + | 0.547367i | \(0.184370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.52772i | 0.151389i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.6004i | 0.709780i | 0.934908 | + | 0.354890i | \(0.115482\pi\) | ||||
−0.934908 | + | 0.354890i | \(0.884518\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.4272 | 0.445023 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.06324 | −0.386107 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 51.2252i | − 2.17832i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.4506i | 0.739408i | 0.929150 | + | 0.369704i | \(0.120541\pi\) | ||||
−0.929150 | + | 0.369704i | \(0.879459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.75814 | −0.370430 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.81853 | 0.372319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 8.25827i | − 0.348045i | −0.984742 | − | 0.174022i | \(-0.944324\pi\) | ||||
0.984742 | − | 0.174022i | \(-0.0556765\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 52.7170i | − 2.21391i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.4178 | 1.73633 | 0.868163 | − | 0.496279i | \(-0.165301\pi\) | ||||
0.868163 | + | 0.496279i | \(0.165301\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.19059 | 0.300917 | 0.150458 | − | 0.988616i | \(-0.451925\pi\) | ||||
0.150458 | + | 0.988616i | \(0.451925\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.9588i | 1.58575i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.3103i | 1.63651i | 0.574855 | + | 0.818255i | \(0.305058\pi\) | ||||
−0.574855 | + | 0.818255i | \(0.694942\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.648517 | −0.0269515 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.14554 | 0.130499 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 10.2499i | − 0.424509i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.7899i | 1.18829i | 0.804359 | + | 0.594143i | \(0.202509\pi\) | ||||
−0.804359 | + | 0.594143i | \(0.797491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.80107 | 0.362642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.7376 | 1.63458 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.8873i | 1.67904i | 0.543330 | + | 0.839519i | \(0.317163\pi\) | ||||
−0.543330 | + | 0.839519i | \(0.682837\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 32.3707i | − 1.32485i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.1801 | −0.783679 | −0.391840 | − | 0.920034i | \(-0.628161\pi\) | ||||
−0.391840 | + | 0.920034i | \(0.628161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.36683 | 0.137336 | 0.0686679 | − | 0.997640i | \(-0.478125\pi\) | ||||
0.0686679 | + | 0.997640i | \(0.478125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 9.77454i | − 0.398050i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.1924i | 0.535462i | 0.963494 | + | 0.267731i | \(0.0862738\pi\) | ||||
−0.963494 | + | 0.267731i | \(0.913726\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.9037 | −0.644450 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.68133 | 0.189386 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 32.6207i | − 1.31754i | −0.752346 | − | 0.658768i | \(-0.771078\pi\) | ||||
0.752346 | − | 0.658768i | \(-0.228922\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 41.7212i | 1.67963i | 0.542872 | + | 0.839815i | \(0.317337\pi\) | ||||
−0.542872 | + | 0.839815i | \(0.682663\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.339245 | 0.0136354 | 0.00681771 | − | 0.999977i | \(-0.497830\pi\) | ||||
0.00681771 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.36266 | −0.175068 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 13.4506i | − 0.538889i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.85863i | − 0.313843i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26.5494 | 1.05859 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.71725 | 0.147982 | 0.0739908 | − | 0.997259i | \(-0.476426\pi\) | ||||
0.0739908 | + | 0.997259i | \(0.476426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 25.9260i | − 1.03047i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 30.3062i | 1.20077i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.21818 | 0.285547 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.0328 | −0.870244 | −0.435122 | − | 0.900372i | \(-0.643295\pi\) | ||||
−0.435122 | + | 0.900372i | \(0.643295\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.6842i | 0.973449i | 0.873556 | + | 0.486724i | \(0.161808\pi\) | ||||
−0.873556 | + | 0.486724i | \(0.838192\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.1731i | 1.26486i | 0.774619 | + | 0.632428i | \(0.217942\pi\) | ||||
−0.774619 | + | 0.632428i | \(0.782058\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.11273 | −0.357706 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.4436 | 0.605284 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.9466i | 1.05450i | 0.849709 | + | 0.527251i | \(0.176777\pi\) | ||||
−0.849709 | + | 0.527251i | \(0.823223\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.24993i | 0.165806i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.7417 | 0.769029 | 0.384514 | − | 0.923119i | \(-0.374369\pi\) | ||||
0.384514 | + | 0.923119i | \(0.374369\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.28692 | −0.0500552 | −0.0250276 | − | 0.999687i | \(-0.507967\pi\) | ||||
−0.0250276 | + | 0.999687i | \(0.507967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 20.6412i | − 0.801639i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.66492i | 0.0644661i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.46705 | 0.0953817 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.4272 | −0.402539 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 12.4970i | − 0.481725i | −0.970559 | − | 0.240862i | \(-0.922570\pi\) | ||||
0.970559 | − | 0.240862i | \(-0.0774303\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 2.69251i | − 0.103482i | −0.998661 | − | 0.0517408i | \(-0.983523\pi\) | ||||
0.998661 | − | 0.0517408i | \(-0.0164770\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.1648 | −1.34950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.92842 | −0.265498 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.72115i | 0.104122i | 0.998644 | + | 0.0520610i | \(0.0165790\pi\) | ||||
−0.998644 | + | 0.0520610i | \(0.983421\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 20.1515i | − 0.768827i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.9917 | −0.914010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.3051 | 1.45719 | 0.728597 | − | 0.684942i | \(-0.240173\pi\) | ||||
0.728597 | + | 0.684942i | \(0.240173\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 2.74590i | − 0.104308i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.4657i | 1.60850i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.92319 | 0.224036 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.8472 | 1.50501 | 0.752504 | − | 0.658588i | \(-0.228846\pi\) | ||||
0.752504 | + | 0.658588i | \(0.228846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 23.6594i | − 0.892332i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 73.9094i | 2.77965i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.8995 | 1.68624 | 0.843118 | − | 0.537728i | \(-0.180717\pi\) | ||||
0.843118 | + | 0.537728i | \(0.180717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.74173 | 0.290338 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 1.61676i | − 0.0605482i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 37.1400i | 1.38702i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.5400 | 1.17624 | 0.588121 | − | 0.808773i | \(-0.299868\pi\) | ||||
0.588121 | + | 0.808773i | \(0.299868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −53.6318 | −1.99735 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.670152i | 0.0249232i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 48.9219i | − 1.81441i | −0.420687 | − | 0.907206i | \(-0.638211\pi\) | ||||
0.420687 | − | 0.907206i | \(-0.361789\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.3637 | −0.643101 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.6430 | −1.13337 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.1536i | 0.522776i | 0.965234 | + | 0.261388i | \(0.0841801\pi\) | ||||
−0.965234 | + | 0.261388i | \(0.915820\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.77454i | 0.360050i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.46421 | −0.164219 | −0.0821093 | − | 0.996623i | \(-0.526166\pi\) | ||||
−0.0821093 | + | 0.996623i | \(0.526166\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.3944 | −0.675736 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.2898i | 1.25797i | 0.777418 | + | 0.628985i | \(0.216529\pi\) | ||||
−0.777418 | + | 0.628985i | \(0.783471\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.475390i | 0.0173936i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.9753 | 1.35105 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.28275 | −0.302242 | −0.151121 | − | 0.988515i | \(-0.548288\pi\) | ||||
−0.151121 | + | 0.988515i | \(0.548288\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 27.8433i | 1.01467i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.32985i | 0.121025i | 0.998167 | + | 0.0605127i | \(0.0192736\pi\) | ||||
−0.998167 | + | 0.0605127i | \(0.980726\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.44364 | −0.0524007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.4077 | −0.667279 | −0.333640 | − | 0.942701i | \(-0.608277\pi\) | ||||
−0.333640 | + | 0.942701i | \(0.608277\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 90.4710i | 3.27527i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.3298i | 0.770176i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −51.4506 | −1.85536 | −0.927679 | − | 0.373379i | \(-0.878199\pi\) | ||||
−0.927679 | + | 0.373379i | \(0.878199\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.48869 | −0.0896279 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 17.4506i | − 0.627656i | −0.949480 | − | 0.313828i | \(-0.898388\pi\) | ||||
0.949480 | − | 0.313828i | \(-0.101612\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 41.5163i | − 1.48939i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.8433 | 1.35588 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.21818 | −0.258287 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.26350i | 0.259576i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 21.2335i | − 0.756893i | −0.925623 | − | 0.378447i | \(-0.876458\pi\) | ||||
0.925623 | − | 0.378447i | \(-0.123542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.6360 | 1.94509 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.87086 | 0.0665203 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.4067i | 0.866706i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 25.3215i | − 0.896934i | −0.893799 | − | 0.448467i | \(-0.851970\pi\) | ||||
0.893799 | − | 0.448467i | \(-0.148030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3791 | 0.579450 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.03281 | 0.0718259 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.24993i | − 0.149977i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.6238i | 1.32442i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.14137 | −0.215919 | −0.107960 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107960 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.5051 | 0.544457 | 0.272229 | − | 0.962233i | \(-0.412239\pi\) | ||||
0.272229 | + | 0.962233i | \(0.412239\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 12.4395i | − 0.436271i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.3075i | 0.955368i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.42723 | −0.224586 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4835 | −0.749778 | −0.374889 | − | 0.927070i | \(-0.622319\pi\) | ||||
−0.374889 | + | 0.927070i | \(0.622319\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 40.1565i | − 1.39977i | −0.714258 | − | 0.699883i | \(-0.753235\pi\) | ||||
0.714258 | − | 0.699883i | \(-0.246765\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.0573i | 1.32338i | 0.749777 | + | 0.661691i | \(0.230161\pi\) | ||||
−0.749777 | + | 0.661691i | \(0.769839\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 51.2580 | 1.78026 | 0.890132 | − | 0.455703i | \(-0.150612\pi\) | ||||
0.890132 | + | 0.455703i | \(0.150612\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.90652 | −0.274274 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 106.035i | 3.67391i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 7.05339i | − 0.243801i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.4200 | −1.56807 | −0.784035 | − | 0.620716i | \(-0.786842\pi\) | ||||
−0.784035 | + | 0.620716i | \(0.786842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.2280 | −0.904415 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 12.3624i | − 0.425783i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 51.5439i | − 1.77107i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −41.5798 | −1.42701 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.34625 | −0.148988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 40.0867i | − 1.37254i | −0.727346 | − | 0.686270i | \(-0.759247\pi\) | ||||
0.727346 | − | 0.686270i | \(-0.240753\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 3.63423i | − 0.124143i | −0.998072 | − | 0.0620715i | \(-0.980229\pi\) | ||||
0.998072 | − | 0.0620715i | \(-0.0197707\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.7529 | 1.28811 | 0.644056 | − | 0.764978i | \(-0.277250\pi\) | ||||
0.644056 | + | 0.764978i | \(0.277250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 66.4053 | 2.26309 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.94555i | 0.134308i | 0.997743 | + | 0.0671541i | \(0.0213919\pi\) | ||||
−0.997743 | + | 0.0671541i | \(0.978608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 39.3173i | − 1.33529i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.74173 | −0.262620 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.8789 | 0.775223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 5.31450i | − 0.179869i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 8.64958i | − 0.292075i | −0.989279 | − | 0.146038i | \(-0.953348\pi\) | ||||
0.989279 | − | 0.146038i | \(-0.0466521\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.2007 | −1.05237 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.1760 | −1.89262 | −0.946308 | − | 0.323266i | \(-0.895219\pi\) | ||||
−0.946308 | + | 0.323266i | \(0.895219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.1054i | 0.407381i | 0.979035 | + | 0.203690i | \(0.0652936\pi\) | ||||
−0.979035 | + | 0.203690i | \(0.934706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 24.7058i | − 0.829540i | −0.909926 | − | 0.414770i | \(-0.863862\pi\) | ||||
0.909926 | − | 0.414770i | \(-0.136138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.0716 | −0.438407 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.96719 | −0.266911 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 14.5962i | − 0.488443i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.37907i | 0.112824i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.69179 | −0.0897761 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −83.9422 | −2.79652 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47.9177i | 1.59460i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.7170i | 0.754305i | 0.926151 | + | 0.377153i | \(0.123097\pi\) | ||||
−0.926151 | + | 0.377153i | \(0.876903\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.1700 | −0.370486 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −12.3156 | −0.408033 | −0.204016 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204016 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 0.475390i | − 0.0157331i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 27.3215i | − 0.902236i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.2088 | −1.52429 | −0.762144 | − | 0.647408i | \(-0.775853\pi\) | ||||
−0.762144 | + | 0.647408i | \(0.775853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.4764 | 0.444064 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.8953i | 0.556117i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 8.10545i | − 0.266218i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.12391 | −0.299346 | −0.149673 | − | 0.988736i | \(-0.547822\pi\) | ||||
−0.149673 | + | 0.988736i | \(0.547822\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 94.4933 | 3.09689 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 8.01330i | − 0.262344i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 33.9190i | − 1.10809i | −0.832488 | − | 0.554043i | \(-0.813084\pi\) | ||||
0.832488 | − | 0.554043i | \(-0.186916\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.1260 | 0.395718 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −37.2926 | −1.21570 | −0.607852 | − | 0.794050i | \(-0.707969\pi\) | ||||
−0.607852 | + | 0.794050i | \(0.707969\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.95184i | − 0.226383i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.7047i | 1.09526i | 0.836722 | + | 0.547629i | \(0.184469\pi\) | ||||
−0.836722 | + | 0.547629i | \(0.815531\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.94767 | −0.322915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.4639 | −0.598734 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.4465i | 1.56934i | 0.619917 | + | 0.784668i | \(0.287166\pi\) | ||||
−0.619917 | + | 0.784668i | \(0.712834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.40354i | 0.0776955i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −30.4465 | −0.983168 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3861 | −0.915680 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.58812i | 0.180075i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 28.2528i | − 0.908548i | −0.890862 | − | 0.454274i | \(-0.849899\pi\) | ||||
0.890862 | − | 0.454274i | \(-0.150101\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −64.3585 | −2.06749 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.65553 | 0.0531284 | 0.0265642 | − | 0.999647i | \(-0.491543\pi\) | ||||
0.0265642 | + | 0.999647i | \(0.491543\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 102.506i | 3.28618i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 11.1630i | − 0.357136i | −0.983928 | − | 0.178568i | \(-0.942854\pi\) | ||||
0.983928 | − | 0.178568i | \(-0.0571465\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.03281 | −0.0649690 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.6730 | −0.436545 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 15.0615i | − 0.480386i | −0.970725 | − | 0.240193i | \(-0.922789\pi\) | ||||
0.970725 | − | 0.240193i | \(-0.0772107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 25.6126i | − 0.815258i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.01641 | 0.159512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.8971 | −1.39444 | −0.697219 | − | 0.716858i | \(-0.745579\pi\) | ||||
−0.697219 | + | 0.716858i | \(0.745579\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 27.6811i | − 0.878432i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.5655i | 1.22138i | 0.791869 | + | 0.610691i | \(0.209108\pi\) | ||||
−0.791869 | + | 0.610691i | \(0.790892\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −18.9612 | −0.599907 |
(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 | 4600.2.e.q.4049.5 | 6 | ||
5.2 | odd | 4 | 4600.2.a.v.1.3 | 3 | |||
5.3 | odd | 4 | 920.2.a.i.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 4600.2.e.q.4049.2 | 6 | ||
15.8 | even | 4 | 8280.2.a.bl.1.3 | 3 | |||
20.3 | even | 4 | 1840.2.a.q.1.3 | 3 | |||
20.7 | even | 4 | 9200.2.a.ci.1.1 | 3 | |||
40.3 | even | 4 | 7360.2.a.cf.1.1 | 3 | |||
40.13 | odd | 4 | 7360.2.a.bw.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.i.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
1840.2.a.q.1.3 | 3 | 20.3 | even | 4 | |||
4600.2.a.v.1.3 | 3 | 5.2 | odd | 4 | |||
4600.2.e.q.4049.2 | 6 | 5.4 | even | 2 | inner | ||
4600.2.e.q.4049.5 | 6 | 1.1 | even | 1 | trivial | ||
7360.2.a.bw.1.3 | 3 | 40.13 | odd | 4 | |||
7360.2.a.cf.1.1 | 3 | 40.3 | even | 4 | |||
8280.2.a.bl.1.3 | 3 | 15.8 | even | 4 | |||
9200.2.a.ci.1.1 | 3 | 20.7 | even | 4 |