Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(781,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.w (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 781.3 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.781 |
Dual form | 1560.2.w.c.781.4 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 1.00000 | ||||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 2.00000 | 1.00000 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | − 1.41421i | − 0.577350i | ||||||||
\(7\) | −0.585786 | −0.221406 | −0.110703 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110703 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | − 1.41421i | − 0.447214i | ||||||||
\(11\) | − 4.82843i | − 1.45583i | −0.685670 | − | 0.727913i | \(-0.740491\pi\) | ||||
0.685670 | − | 0.727913i | \(-0.259509\pi\) | |||||||
\(12\) | − 2.00000i | − 0.577350i | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −0.828427 | −0.221406 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −1.41421 | −0.342997 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(18\) | −1.41421 | −0.333333 | ||||||||
\(19\) | 0.242641i | 0.0556656i | 0.999613 | + | 0.0278328i | \(0.00886060\pi\) | ||||
−0.999613 | + | 0.0278328i | \(0.991139\pi\) | |||||||
\(20\) | − 2.00000i | − 0.447214i | ||||||||
\(21\) | 0.585786i | 0.127829i | ||||||||
\(22\) | − 6.82843i | − 1.45583i | ||||||||
\(23\) | 4.24264 | 0.884652 | 0.442326 | − | 0.896854i | \(-0.354153\pi\) | ||||
0.442326 | + | 0.896854i | \(0.354153\pi\) | |||||||
\(24\) | − 2.82843i | − 0.577350i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 1.41421i | 0.277350i | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.17157 | −0.221406 | ||||||||
\(29\) | − 10.2426i | − 1.90201i | −0.309175 | − | 0.951005i | \(-0.600053\pi\) | ||||
0.309175 | − | 0.951005i | \(-0.399947\pi\) | |||||||
\(30\) | −1.41421 | −0.258199 | ||||||||
\(31\) | 1.17157 | 0.210421 | 0.105210 | − | 0.994450i | \(-0.466448\pi\) | ||||
0.105210 | + | 0.994450i | \(0.466448\pi\) | |||||||
\(32\) | 5.65685 | 1.00000 | ||||||||
\(33\) | −4.82843 | −0.840521 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0.585786i | 0.0990160i | ||||||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | − 6.48528i | − 1.06617i | −0.846061 | − | 0.533087i | \(-0.821032\pi\) | ||||
0.846061 | − | 0.533087i | \(-0.178968\pi\) | |||||||
\(38\) | 0.343146i | 0.0556656i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | − 2.82843i | − 0.447214i | ||||||||
\(41\) | −5.17157 | −0.807664 | −0.403832 | − | 0.914833i | \(-0.632322\pi\) | ||||
−0.403832 | + | 0.914833i | \(0.632322\pi\) | |||||||
\(42\) | 0.828427i | 0.127829i | ||||||||
\(43\) | 4.82843i | 0.736328i | 0.929761 | + | 0.368164i | \(0.120014\pi\) | ||||
−0.929761 | + | 0.368164i | \(0.879986\pi\) | |||||||
\(44\) | − 9.65685i | − 1.45583i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 1.65685 | 0.241677 | 0.120839 | − | 0.992672i | \(-0.461442\pi\) | ||||
0.120839 | + | 0.992672i | \(0.461442\pi\) | |||||||
\(48\) | − 4.00000i | − 0.577350i | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | −1.41421 | −0.200000 | ||||||||
\(51\) | 1.41421i | 0.198030i | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | 0.343146i | 0.0471347i | 0.999722 | + | 0.0235673i | \(0.00750241\pi\) | ||||
−0.999722 | + | 0.0235673i | \(0.992498\pi\) | |||||||
\(54\) | 1.41421i | 0.192450i | ||||||||
\(55\) | −4.82843 | −0.651065 | ||||||||
\(56\) | −1.65685 | −0.221406 | ||||||||
\(57\) | 0.242641 | 0.0321385 | ||||||||
\(58\) | − 14.4853i | − 1.90201i | ||||||||
\(59\) | 3.17157i | 0.412904i | 0.978457 | + | 0.206452i | \(0.0661917\pi\) | ||||
−0.978457 | + | 0.206452i | \(0.933808\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | 8.00000i | 1.02430i | 0.858898 | + | 0.512148i | \(0.171150\pi\) | ||||
−0.858898 | + | 0.512148i | \(0.828850\pi\) | |||||||
\(62\) | 1.65685 | 0.210421 | ||||||||
\(63\) | 0.585786 | 0.0738022 | ||||||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | −6.82843 | −0.840521 | ||||||||
\(67\) | 1.17157i | 0.143130i | 0.997436 | + | 0.0715652i | \(0.0227994\pi\) | ||||
−0.997436 | + | 0.0715652i | \(0.977201\pi\) | |||||||
\(68\) | −2.82843 | −0.342997 | ||||||||
\(69\) | − 4.24264i | − 0.510754i | ||||||||
\(70\) | 0.828427i | 0.0990160i | ||||||||
\(71\) | 4.82843 | 0.573029 | 0.286514 | − | 0.958076i | \(-0.407503\pi\) | ||||
0.286514 | + | 0.958076i | \(0.407503\pi\) | |||||||
\(72\) | −2.82843 | −0.333333 | ||||||||
\(73\) | 8.58579 | 1.00489 | 0.502445 | − | 0.864609i | \(-0.332434\pi\) | ||||
0.502445 | + | 0.864609i | \(0.332434\pi\) | |||||||
\(74\) | − 9.17157i | − 1.06617i | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0.485281i | 0.0556656i | ||||||||
\(77\) | 2.82843i | 0.322329i | ||||||||
\(78\) | 1.41421 | 0.160128 | ||||||||
\(79\) | −1.65685 | −0.186411 | −0.0932053 | − | 0.995647i | \(-0.529711\pi\) | ||||
−0.0932053 | + | 0.995647i | \(0.529711\pi\) | |||||||
\(80\) | − 4.00000i | − 0.447214i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −7.31371 | −0.807664 | ||||||||
\(83\) | 7.65685i | 0.840449i | 0.907420 | + | 0.420224i | \(0.138049\pi\) | ||||
−0.907420 | + | 0.420224i | \(0.861951\pi\) | |||||||
\(84\) | 1.17157i | 0.127829i | ||||||||
\(85\) | 1.41421i | 0.153393i | ||||||||
\(86\) | 6.82843i | 0.736328i | ||||||||
\(87\) | −10.2426 | −1.09813 | ||||||||
\(88\) | − 13.6569i | − 1.45583i | ||||||||
\(89\) | 7.65685 | 0.811625 | 0.405812 | − | 0.913956i | \(-0.366989\pi\) | ||||
0.405812 | + | 0.913956i | \(0.366989\pi\) | |||||||
\(90\) | 1.41421i | 0.149071i | ||||||||
\(91\) | − 0.585786i | − 0.0614071i | ||||||||
\(92\) | 8.48528 | 0.884652 | ||||||||
\(93\) | − 1.17157i | − 0.121486i | ||||||||
\(94\) | 2.34315 | 0.241677 | ||||||||
\(95\) | 0.242641 | 0.0248944 | ||||||||
\(96\) | − 5.65685i | − 0.577350i | ||||||||
\(97\) | 6.72792 | 0.683117 | 0.341558 | − | 0.939861i | \(-0.389045\pi\) | ||||
0.341558 | + | 0.939861i | \(0.389045\pi\) | |||||||
\(98\) | −9.41421 | −0.950979 | ||||||||
\(99\) | 4.82843i | 0.485275i | ||||||||
\(100\) | −2.00000 | −0.200000 | ||||||||
\(101\) | 0.585786i | 0.0582879i | 0.999575 | + | 0.0291440i | \(0.00927813\pi\) | ||||
−0.999575 | + | 0.0291440i | \(0.990722\pi\) | |||||||
\(102\) | 2.00000i | 0.198030i | ||||||||
\(103\) | 7.65685 | 0.754452 | 0.377226 | − | 0.926121i | \(-0.376878\pi\) | ||||
0.377226 | + | 0.926121i | \(0.376878\pi\) | |||||||
\(104\) | 2.82843i | 0.277350i | ||||||||
\(105\) | 0.585786 | 0.0571669 | ||||||||
\(106\) | 0.485281i | 0.0471347i | ||||||||
\(107\) | − 1.17157i | − 0.113260i | −0.998395 | − | 0.0566301i | \(-0.981964\pi\) | ||||
0.998395 | − | 0.0566301i | \(-0.0180356\pi\) | |||||||
\(108\) | 2.00000i | 0.192450i | ||||||||
\(109\) | − 4.24264i | − 0.406371i | −0.979140 | − | 0.203186i | \(-0.934871\pi\) | ||||
0.979140 | − | 0.203186i | \(-0.0651295\pi\) | |||||||
\(110\) | −6.82843 | −0.651065 | ||||||||
\(111\) | −6.48528 | −0.615556 | ||||||||
\(112\) | −2.34315 | −0.221406 | ||||||||
\(113\) | 10.5858 | 0.995827 | 0.497914 | − | 0.867227i | \(-0.334100\pi\) | ||||
0.497914 | + | 0.867227i | \(0.334100\pi\) | |||||||
\(114\) | 0.343146 | 0.0321385 | ||||||||
\(115\) | − 4.24264i | − 0.395628i | ||||||||
\(116\) | − 20.4853i | − 1.90201i | ||||||||
\(117\) | − 1.00000i | − 0.0924500i | ||||||||
\(118\) | 4.48528i | 0.412904i | ||||||||
\(119\) | 0.828427 | 0.0759418 | ||||||||
\(120\) | −2.82843 | −0.258199 | ||||||||
\(121\) | −12.3137 | −1.11943 | ||||||||
\(122\) | 11.3137i | 1.02430i | ||||||||
\(123\) | 5.17157i | 0.466305i | ||||||||
\(124\) | 2.34315 | 0.210421 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0.828427 | 0.0738022 | ||||||||
\(127\) | −18.9706 | −1.68337 | −0.841683 | − | 0.539973i | \(-0.818435\pi\) | ||||
−0.841683 | + | 0.539973i | \(0.818435\pi\) | |||||||
\(128\) | 11.3137 | 1.00000 | ||||||||
\(129\) | 4.82843 | 0.425119 | ||||||||
\(130\) | 1.41421 | 0.124035 | ||||||||
\(131\) | 10.2426i | 0.894904i | 0.894308 | + | 0.447452i | \(0.147668\pi\) | ||||
−0.894308 | + | 0.447452i | \(0.852332\pi\) | |||||||
\(132\) | −9.65685 | −0.840521 | ||||||||
\(133\) | − 0.142136i | − 0.0123247i | ||||||||
\(134\) | 1.65685i | 0.143130i | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −8.48528 | −0.724947 | −0.362473 | − | 0.931994i | \(-0.618068\pi\) | ||||
−0.362473 | + | 0.931994i | \(0.618068\pi\) | |||||||
\(138\) | − 6.00000i | − 0.510754i | ||||||||
\(139\) | 17.1716i | 1.45647i | 0.685325 | + | 0.728237i | \(0.259660\pi\) | ||||
−0.685325 | + | 0.728237i | \(0.740340\pi\) | |||||||
\(140\) | 1.17157i | 0.0990160i | ||||||||
\(141\) | − 1.65685i | − 0.139532i | ||||||||
\(142\) | 6.82843 | 0.573029 | ||||||||
\(143\) | 4.82843 | 0.403773 | ||||||||
\(144\) | −4.00000 | −0.333333 | ||||||||
\(145\) | −10.2426 | −0.850605 | ||||||||
\(146\) | 12.1421 | 1.00489 | ||||||||
\(147\) | 6.65685i | 0.549048i | ||||||||
\(148\) | − 12.9706i | − 1.06617i | ||||||||
\(149\) | 11.1716i | 0.915211i | 0.889155 | + | 0.457605i | \(0.151293\pi\) | ||||
−0.889155 | + | 0.457605i | \(0.848707\pi\) | |||||||
\(150\) | 1.41421i | 0.115470i | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0.686292i | 0.0556656i | ||||||||
\(153\) | 1.41421 | 0.114332 | ||||||||
\(154\) | 4.00000i | 0.322329i | ||||||||
\(155\) | − 1.17157i | − 0.0941030i | ||||||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | − 6.82843i | − 0.544968i | −0.962160 | − | 0.272484i | \(-0.912155\pi\) | ||||
0.962160 | − | 0.272484i | \(-0.0878452\pi\) | |||||||
\(158\) | −2.34315 | −0.186411 | ||||||||
\(159\) | 0.343146 | 0.0272132 | ||||||||
\(160\) | − 5.65685i | − 0.447214i | ||||||||
\(161\) | −2.48528 | −0.195868 | ||||||||
\(162\) | 1.41421 | 0.111111 | ||||||||
\(163\) | − 8.00000i | − 0.626608i | −0.949653 | − | 0.313304i | \(-0.898564\pi\) | ||||
0.949653 | − | 0.313304i | \(-0.101436\pi\) | |||||||
\(164\) | −10.3431 | −0.807664 | ||||||||
\(165\) | 4.82843i | 0.375893i | ||||||||
\(166\) | 10.8284i | 0.840449i | ||||||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 1.65685i | 0.127829i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 2.00000i | 0.153393i | ||||||||
\(171\) | − 0.242641i | − 0.0185552i | ||||||||
\(172\) | 9.65685i | 0.736328i | ||||||||
\(173\) | − 12.1421i | − 0.923149i | −0.887101 | − | 0.461575i | \(-0.847285\pi\) | ||||
0.887101 | − | 0.461575i | \(-0.152715\pi\) | |||||||
\(174\) | −14.4853 | −1.09813 | ||||||||
\(175\) | 0.585786 | 0.0442813 | ||||||||
\(176\) | − 19.3137i | − 1.45583i | ||||||||
\(177\) | 3.17157 | 0.238390 | ||||||||
\(178\) | 10.8284 | 0.811625 | ||||||||
\(179\) | 15.8995i | 1.18838i | 0.804323 | + | 0.594192i | \(0.202528\pi\) | ||||
−0.804323 | + | 0.594192i | \(0.797472\pi\) | |||||||
\(180\) | 2.00000i | 0.149071i | ||||||||
\(181\) | 6.82843i | 0.507553i | 0.967263 | + | 0.253776i | \(0.0816728\pi\) | ||||
−0.967263 | + | 0.253776i | \(0.918327\pi\) | |||||||
\(182\) | − 0.828427i | − 0.0614071i | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 12.0000 | 0.884652 | ||||||||
\(185\) | −6.48528 | −0.476807 | ||||||||
\(186\) | − 1.65685i | − 0.121486i | ||||||||
\(187\) | 6.82843i | 0.499344i | ||||||||
\(188\) | 3.31371 | 0.241677 | ||||||||
\(189\) | − 0.585786i | − 0.0426097i | ||||||||
\(190\) | 0.343146 | 0.0248944 | ||||||||
\(191\) | 15.7990 | 1.14317 | 0.571587 | − | 0.820541i | \(-0.306328\pi\) | ||||
0.571587 | + | 0.820541i | \(0.306328\pi\) | |||||||
\(192\) | − 8.00000i | − 0.577350i | ||||||||
\(193\) | 3.41421 | 0.245760 | 0.122880 | − | 0.992422i | \(-0.460787\pi\) | ||||
0.122880 | + | 0.992422i | \(0.460787\pi\) | |||||||
\(194\) | 9.51472 | 0.683117 | ||||||||
\(195\) | − 1.00000i | − 0.0716115i | ||||||||
\(196\) | −13.3137 | −0.950979 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 6.82843i | 0.485275i | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −2.82843 | −0.200000 | ||||||||
\(201\) | 1.17157 | 0.0826364 | ||||||||
\(202\) | 0.828427i | 0.0582879i | ||||||||
\(203\) | 6.00000i | 0.421117i | ||||||||
\(204\) | 2.82843i | 0.198030i | ||||||||
\(205\) | 5.17157i | 0.361198i | ||||||||
\(206\) | 10.8284 | 0.754452 | ||||||||
\(207\) | −4.24264 | −0.294884 | ||||||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | 1.17157 | 0.0810394 | ||||||||
\(210\) | 0.828427 | 0.0571669 | ||||||||
\(211\) | 24.9706i | 1.71904i | 0.511098 | + | 0.859522i | \(0.329239\pi\) | ||||
−0.511098 | + | 0.859522i | \(0.670761\pi\) | |||||||
\(212\) | 0.686292i | 0.0471347i | ||||||||
\(213\) | − 4.82843i | − 0.330838i | ||||||||
\(214\) | − 1.65685i | − 0.113260i | ||||||||
\(215\) | 4.82843 | 0.329296 | ||||||||
\(216\) | 2.82843i | 0.192450i | ||||||||
\(217\) | −0.686292 | −0.0465885 | ||||||||
\(218\) | − 6.00000i | − 0.406371i | ||||||||
\(219\) | − 8.58579i | − 0.580174i | ||||||||
\(220\) | −9.65685 | −0.651065 | ||||||||
\(221\) | − 1.41421i | − 0.0951303i | ||||||||
\(222\) | −9.17157 | −0.615556 | ||||||||
\(223\) | 27.2132 | 1.82233 | 0.911165 | − | 0.412041i | \(-0.135184\pi\) | ||||
0.911165 | + | 0.412041i | \(0.135184\pi\) | |||||||
\(224\) | −3.31371 | −0.221406 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 14.9706 | 0.995827 | ||||||||
\(227\) | 15.3137i | 1.01641i | 0.861237 | + | 0.508203i | \(0.169690\pi\) | ||||
−0.861237 | + | 0.508203i | \(0.830310\pi\) | |||||||
\(228\) | 0.485281 | 0.0321385 | ||||||||
\(229\) | 5.89949i | 0.389850i | 0.980818 | + | 0.194925i | \(0.0624463\pi\) | ||||
−0.980818 | + | 0.194925i | \(0.937554\pi\) | |||||||
\(230\) | − 6.00000i | − 0.395628i | ||||||||
\(231\) | 2.82843 | 0.186097 | ||||||||
\(232\) | − 28.9706i | − 1.90201i | ||||||||
\(233\) | 22.5858 | 1.47964 | 0.739822 | − | 0.672803i | \(-0.234910\pi\) | ||||
0.739822 | + | 0.672803i | \(0.234910\pi\) | |||||||
\(234\) | − 1.41421i | − 0.0924500i | ||||||||
\(235\) | − 1.65685i | − 0.108081i | ||||||||
\(236\) | 6.34315i | 0.412904i | ||||||||
\(237\) | 1.65685i | 0.107624i | ||||||||
\(238\) | 1.17157 | 0.0759418 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | −4.00000 | −0.258199 | ||||||||
\(241\) | −1.51472 | −0.0975716 | −0.0487858 | − | 0.998809i | \(-0.515535\pi\) | ||||
−0.0487858 | + | 0.998809i | \(0.515535\pi\) | |||||||
\(242\) | −17.4142 | −1.11943 | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 16.0000i | 1.02430i | ||||||||
\(245\) | 6.65685i | 0.425291i | ||||||||
\(246\) | 7.31371i | 0.466305i | ||||||||
\(247\) | −0.242641 | −0.0154389 | ||||||||
\(248\) | 3.31371 | 0.210421 | ||||||||
\(249\) | 7.65685 | 0.485233 | ||||||||
\(250\) | 1.41421i | 0.0894427i | ||||||||
\(251\) | 2.92893i | 0.184873i | 0.995719 | + | 0.0924363i | \(0.0294654\pi\) | ||||
−0.995719 | + | 0.0924363i | \(0.970535\pi\) | |||||||
\(252\) | 1.17157 | 0.0738022 | ||||||||
\(253\) | − 20.4853i | − 1.28790i | ||||||||
\(254\) | −26.8284 | −1.68337 | ||||||||
\(255\) | 1.41421 | 0.0885615 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −10.1005 | −0.630052 | −0.315026 | − | 0.949083i | \(-0.602013\pi\) | ||||
−0.315026 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(258\) | 6.82843 | 0.425119 | ||||||||
\(259\) | 3.79899i | 0.236058i | ||||||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 10.2426i | 0.634004i | ||||||||
\(262\) | 14.4853i | 0.894904i | ||||||||
\(263\) | 4.24264 | 0.261612 | 0.130806 | − | 0.991408i | \(-0.458243\pi\) | ||||
0.130806 | + | 0.991408i | \(0.458243\pi\) | |||||||
\(264\) | −13.6569 | −0.840521 | ||||||||
\(265\) | 0.343146 | 0.0210793 | ||||||||
\(266\) | − 0.201010i | − 0.0123247i | ||||||||
\(267\) | − 7.65685i | − 0.468592i | ||||||||
\(268\) | 2.34315i | 0.143130i | ||||||||
\(269\) | − 15.2132i | − 0.927565i | −0.885949 | − | 0.463783i | \(-0.846492\pi\) | ||||
0.885949 | − | 0.463783i | \(-0.153508\pi\) | |||||||
\(270\) | 1.41421 | 0.0860663 | ||||||||
\(271\) | 1.65685 | 0.100647 | 0.0503234 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503234 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(272\) | −5.65685 | −0.342997 | ||||||||
\(273\) | −0.585786 | −0.0354534 | ||||||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | 4.82843i | 0.291165i | ||||||||
\(276\) | − 8.48528i | − 0.510754i | ||||||||
\(277\) | − 13.1716i | − 0.791403i | −0.918379 | − | 0.395702i | \(-0.870501\pi\) | ||||
0.918379 | − | 0.395702i | \(-0.129499\pi\) | |||||||
\(278\) | 24.2843i | 1.45647i | ||||||||
\(279\) | −1.17157 | −0.0701402 | ||||||||
\(280\) | 1.65685i | 0.0990160i | ||||||||
\(281\) | −27.6569 | −1.64987 | −0.824935 | − | 0.565228i | \(-0.808788\pi\) | ||||
−0.824935 | + | 0.565228i | \(0.808788\pi\) | |||||||
\(282\) | − 2.34315i | − 0.139532i | ||||||||
\(283\) | 16.1421i | 0.959550i | 0.877391 | + | 0.479775i | \(0.159282\pi\) | ||||
−0.877391 | + | 0.479775i | \(0.840718\pi\) | |||||||
\(284\) | 9.65685 | 0.573029 | ||||||||
\(285\) | − 0.242641i | − 0.0143728i | ||||||||
\(286\) | 6.82843 | 0.403773 | ||||||||
\(287\) | 3.02944 | 0.178822 | ||||||||
\(288\) | −5.65685 | −0.333333 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | −14.4853 | −0.850605 | ||||||||
\(291\) | − 6.72792i | − 0.394398i | ||||||||
\(292\) | 17.1716 | 1.00489 | ||||||||
\(293\) | 7.31371i | 0.427271i | 0.976913 | + | 0.213636i | \(0.0685306\pi\) | ||||
−0.976913 | + | 0.213636i | \(0.931469\pi\) | |||||||
\(294\) | 9.41421i | 0.549048i | ||||||||
\(295\) | 3.17157 | 0.184656 | ||||||||
\(296\) | − 18.3431i | − 1.06617i | ||||||||
\(297\) | 4.82843 | 0.280174 | ||||||||
\(298\) | 15.7990i | 0.915211i | ||||||||
\(299\) | 4.24264i | 0.245358i | ||||||||
\(300\) | 2.00000i | 0.115470i | ||||||||
\(301\) | − 2.82843i | − 0.163028i | ||||||||
\(302\) | −16.9706 | −0.976546 | ||||||||
\(303\) | 0.585786 | 0.0336526 | ||||||||
\(304\) | 0.970563i | 0.0556656i | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 2.00000 | 0.114332 | ||||||||
\(307\) | − 3.31371i | − 0.189123i | −0.995519 | − | 0.0945617i | \(-0.969855\pi\) | ||||
0.995519 | − | 0.0945617i | \(-0.0301450\pi\) | |||||||
\(308\) | 5.65685i | 0.322329i | ||||||||
\(309\) | − 7.65685i | − 0.435583i | ||||||||
\(310\) | − 1.65685i | − 0.0941030i | ||||||||
\(311\) | 14.1421 | 0.801927 | 0.400963 | − | 0.916094i | \(-0.368675\pi\) | ||||
0.400963 | + | 0.916094i | \(0.368675\pi\) | |||||||
\(312\) | 2.82843 | 0.160128 | ||||||||
\(313\) | 16.8284 | 0.951199 | 0.475599 | − | 0.879662i | \(-0.342231\pi\) | ||||
0.475599 | + | 0.879662i | \(0.342231\pi\) | |||||||
\(314\) | − 9.65685i | − 0.544968i | ||||||||
\(315\) | − 0.585786i | − 0.0330053i | ||||||||
\(316\) | −3.31371 | −0.186411 | ||||||||
\(317\) | 20.6274i | 1.15855i | 0.815132 | + | 0.579276i | \(0.196664\pi\) | ||||
−0.815132 | + | 0.579276i | \(0.803336\pi\) | |||||||
\(318\) | 0.485281 | 0.0272132 | ||||||||
\(319\) | −49.4558 | −2.76900 | ||||||||
\(320\) | − 8.00000i | − 0.447214i | ||||||||
\(321\) | −1.17157 | −0.0653908 | ||||||||
\(322\) | −3.51472 | −0.195868 | ||||||||
\(323\) | − 0.343146i | − 0.0190931i | ||||||||
\(324\) | 2.00000 | 0.111111 | ||||||||
\(325\) | − 1.00000i | − 0.0554700i | ||||||||
\(326\) | − 11.3137i | − 0.626608i | ||||||||
\(327\) | −4.24264 | −0.234619 | ||||||||
\(328\) | −14.6274 | −0.807664 | ||||||||
\(329\) | −0.970563 | −0.0535089 | ||||||||
\(330\) | 6.82843i | 0.375893i | ||||||||
\(331\) | 33.6985i | 1.85224i | 0.377234 | + | 0.926118i | \(0.376875\pi\) | ||||
−0.377234 | + | 0.926118i | \(0.623125\pi\) | |||||||
\(332\) | 15.3137i | 0.840449i | ||||||||
\(333\) | 6.48528i | 0.355391i | ||||||||
\(334\) | 28.0000 | 1.53209 | ||||||||
\(335\) | 1.17157 | 0.0640099 | ||||||||
\(336\) | 2.34315i | 0.127829i | ||||||||
\(337\) | −34.4853 | −1.87853 | −0.939266 | − | 0.343189i | \(-0.888493\pi\) | ||||
−0.939266 | + | 0.343189i | \(0.888493\pi\) | |||||||
\(338\) | −1.41421 | −0.0769231 | ||||||||
\(339\) | − 10.5858i | − 0.574941i | ||||||||
\(340\) | 2.82843i | 0.153393i | ||||||||
\(341\) | − 5.65685i | − 0.306336i | ||||||||
\(342\) | − 0.343146i | − 0.0185552i | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 13.6569i | 0.736328i | ||||||||
\(345\) | −4.24264 | −0.228416 | ||||||||
\(346\) | − 17.1716i | − 0.923149i | ||||||||
\(347\) | 11.3137i | 0.607352i | 0.952775 | + | 0.303676i | \(0.0982140\pi\) | ||||
−0.952775 | + | 0.303676i | \(0.901786\pi\) | |||||||
\(348\) | −20.4853 | −1.09813 | ||||||||
\(349\) | − 20.7279i | − 1.10954i | −0.832004 | − | 0.554770i | \(-0.812806\pi\) | ||||
0.832004 | − | 0.554770i | \(-0.187194\pi\) | |||||||
\(350\) | 0.828427 | 0.0442813 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | − 27.3137i | − 1.45583i | ||||||||
\(353\) | 6.14214 | 0.326913 | 0.163456 | − | 0.986551i | \(-0.447736\pi\) | ||||
0.163456 | + | 0.986551i | \(0.447736\pi\) | |||||||
\(354\) | 4.48528 | 0.238390 | ||||||||
\(355\) | − 4.82843i | − 0.256266i | ||||||||
\(356\) | 15.3137 | 0.811625 | ||||||||
\(357\) | − 0.828427i | − 0.0438450i | ||||||||
\(358\) | 22.4853i | 1.18838i | ||||||||
\(359\) | 23.1716 | 1.22295 | 0.611474 | − | 0.791264i | \(-0.290577\pi\) | ||||
0.611474 | + | 0.791264i | \(0.290577\pi\) | |||||||
\(360\) | 2.82843i | 0.149071i | ||||||||
\(361\) | 18.9411 | 0.996901 | ||||||||
\(362\) | 9.65685i | 0.507553i | ||||||||
\(363\) | 12.3137i | 0.646302i | ||||||||
\(364\) | − 1.17157i | − 0.0614071i | ||||||||
\(365\) | − 8.58579i | − 0.449401i | ||||||||
\(366\) | 11.3137 | 0.591377 | ||||||||
\(367\) | −26.0000 | −1.35719 | −0.678594 | − | 0.734513i | \(-0.737411\pi\) | ||||
−0.678594 | + | 0.734513i | \(0.737411\pi\) | |||||||
\(368\) | 16.9706 | 0.884652 | ||||||||
\(369\) | 5.17157 | 0.269221 | ||||||||
\(370\) | −9.17157 | −0.476807 | ||||||||
\(371\) | − 0.201010i | − 0.0104359i | ||||||||
\(372\) | − 2.34315i | − 0.121486i | ||||||||
\(373\) | − 22.8284i | − 1.18201i | −0.806667 | − | 0.591006i | \(-0.798731\pi\) | ||||
0.806667 | − | 0.591006i | \(-0.201269\pi\) | |||||||
\(374\) | 9.65685i | 0.499344i | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 4.68629 | 0.241677 | ||||||||
\(377\) | 10.2426 | 0.527523 | ||||||||
\(378\) | − 0.828427i | − 0.0426097i | ||||||||
\(379\) | 1.89949i | 0.0975705i | 0.998809 | + | 0.0487853i | \(0.0155350\pi\) | ||||
−0.998809 | + | 0.0487853i | \(0.984465\pi\) | |||||||
\(380\) | 0.485281 | 0.0248944 | ||||||||
\(381\) | 18.9706i | 0.971891i | ||||||||
\(382\) | 22.3431 | 1.14317 | ||||||||
\(383\) | 35.7990 | 1.82924 | 0.914621 | − | 0.404311i | \(-0.132489\pi\) | ||||
0.914621 | + | 0.404311i | \(0.132489\pi\) | |||||||
\(384\) | − 11.3137i | − 0.577350i | ||||||||
\(385\) | 2.82843 | 0.144150 | ||||||||
\(386\) | 4.82843 | 0.245760 | ||||||||
\(387\) | − 4.82843i | − 0.245443i | ||||||||
\(388\) | 13.4558 | 0.683117 | ||||||||
\(389\) | 27.4142i | 1.38996i | 0.719031 | + | 0.694978i | \(0.244586\pi\) | ||||
−0.719031 | + | 0.694978i | \(0.755414\pi\) | |||||||
\(390\) | − 1.41421i | − 0.0716115i | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | −18.8284 | −0.950979 | ||||||||
\(393\) | 10.2426 | 0.516673 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.65685i | 0.0833654i | ||||||||
\(396\) | 9.65685i | 0.485275i | ||||||||
\(397\) | 10.6863i | 0.536330i | 0.963373 | + | 0.268165i | \(0.0864172\pi\) | ||||
−0.963373 | + | 0.268165i | \(0.913583\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.142136 | −0.00711568 | ||||||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −10.1421 | −0.506474 | −0.253237 | − | 0.967404i | \(-0.581495\pi\) | ||||
−0.253237 | + | 0.967404i | \(0.581495\pi\) | |||||||
\(402\) | 1.65685 | 0.0826364 | ||||||||
\(403\) | 1.17157i | 0.0583602i | ||||||||
\(404\) | 1.17157i | 0.0582879i | ||||||||
\(405\) | − 1.00000i | − 0.0496904i | ||||||||
\(406\) | 8.48528i | 0.421117i | ||||||||
\(407\) | −31.3137 | −1.55216 | ||||||||
\(408\) | 4.00000i | 0.198030i | ||||||||
\(409\) | −5.79899 | −0.286742 | −0.143371 | − | 0.989669i | \(-0.545794\pi\) | ||||
−0.143371 | + | 0.989669i | \(0.545794\pi\) | |||||||
\(410\) | 7.31371i | 0.361198i | ||||||||
\(411\) | 8.48528i | 0.418548i | ||||||||
\(412\) | 15.3137 | 0.754452 | ||||||||
\(413\) | − 1.85786i | − 0.0914195i | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | 7.65685 | 0.375860 | ||||||||
\(416\) | 5.65685i | 0.277350i | ||||||||
\(417\) | 17.1716 | 0.840896 | ||||||||
\(418\) | 1.65685 | 0.0810394 | ||||||||
\(419\) | − 0.100505i | − 0.00490999i | −0.999997 | − | 0.00245500i | \(-0.999219\pi\) | ||||
0.999997 | − | 0.00245500i | \(-0.000781451\pi\) | |||||||
\(420\) | 1.17157 | 0.0571669 | ||||||||
\(421\) | 7.27208i | 0.354419i | 0.984173 | + | 0.177210i | \(0.0567071\pi\) | ||||
−0.984173 | + | 0.177210i | \(0.943293\pi\) | |||||||
\(422\) | 35.3137i | 1.71904i | ||||||||
\(423\) | −1.65685 | −0.0805590 | ||||||||
\(424\) | 0.970563i | 0.0471347i | ||||||||
\(425\) | 1.41421 | 0.0685994 | ||||||||
\(426\) | − 6.82843i | − 0.330838i | ||||||||
\(427\) | − 4.68629i | − 0.226786i | ||||||||
\(428\) | − 2.34315i | − 0.113260i | ||||||||
\(429\) | − 4.82843i | − 0.233119i | ||||||||
\(430\) | 6.82843 | 0.329296 | ||||||||
\(431\) | 19.3137 | 0.930309 | 0.465154 | − | 0.885230i | \(-0.345999\pi\) | ||||
0.465154 | + | 0.885230i | \(0.345999\pi\) | |||||||
\(432\) | 4.00000i | 0.192450i | ||||||||
\(433\) | −34.4853 | −1.65726 | −0.828628 | − | 0.559799i | \(-0.810878\pi\) | ||||
−0.828628 | + | 0.559799i | \(0.810878\pi\) | |||||||
\(434\) | −0.970563 | −0.0465885 | ||||||||
\(435\) | 10.2426i | 0.491097i | ||||||||
\(436\) | − 8.48528i | − 0.406371i | ||||||||
\(437\) | 1.02944i | 0.0492447i | ||||||||
\(438\) | − 12.1421i | − 0.580174i | ||||||||
\(439\) | −31.6569 | −1.51090 | −0.755450 | − | 0.655207i | \(-0.772582\pi\) | ||||
−0.755450 | + | 0.655207i | \(0.772582\pi\) | |||||||
\(440\) | −13.6569 | −0.651065 | ||||||||
\(441\) | 6.65685 | 0.316993 | ||||||||
\(442\) | − 2.00000i | − 0.0951303i | ||||||||
\(443\) | − 13.6569i | − 0.648857i | −0.945910 | − | 0.324428i | \(-0.894828\pi\) | ||||
0.945910 | − | 0.324428i | \(-0.105172\pi\) | |||||||
\(444\) | −12.9706 | −0.615556 | ||||||||
\(445\) | − 7.65685i | − 0.362970i | ||||||||
\(446\) | 38.4853 | 1.82233 | ||||||||
\(447\) | 11.1716 | 0.528397 | ||||||||
\(448\) | −4.68629 | −0.221406 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 1.41421 | 0.0666667 | ||||||||
\(451\) | 24.9706i | 1.17582i | ||||||||
\(452\) | 21.1716 | 0.995827 | ||||||||
\(453\) | 12.0000i | 0.563809i | ||||||||
\(454\) | 21.6569i | 1.01641i | ||||||||
\(455\) | −0.585786 | −0.0274621 | ||||||||
\(456\) | 0.686292 | 0.0321385 | ||||||||
\(457\) | 5.75736 | 0.269318 | 0.134659 | − | 0.990892i | \(-0.457006\pi\) | ||||
0.134659 | + | 0.990892i | \(0.457006\pi\) | |||||||
\(458\) | 8.34315i | 0.389850i | ||||||||
\(459\) | − 1.41421i | − 0.0660098i | ||||||||
\(460\) | − 8.48528i | − 0.395628i | ||||||||
\(461\) | − 35.6569i | − 1.66071i | −0.557238 | − | 0.830353i | \(-0.688139\pi\) | ||||
0.557238 | − | 0.830353i | \(-0.311861\pi\) | |||||||
\(462\) | 4.00000 | 0.186097 | ||||||||
\(463\) | −34.7279 | −1.61394 | −0.806972 | − | 0.590590i | \(-0.798895\pi\) | ||||
−0.806972 | + | 0.590590i | \(0.798895\pi\) | |||||||
\(464\) | − 40.9706i | − 1.90201i | ||||||||
\(465\) | −1.17157 | −0.0543304 | ||||||||
\(466\) | 31.9411 | 1.47964 | ||||||||
\(467\) | − 35.1127i | − 1.62482i | −0.583085 | − | 0.812411i | \(-0.698155\pi\) | ||||
0.583085 | − | 0.812411i | \(-0.301845\pi\) | |||||||
\(468\) | − 2.00000i | − 0.0924500i | ||||||||
\(469\) | − 0.686292i | − 0.0316900i | ||||||||
\(470\) | − 2.34315i | − 0.108081i | ||||||||
\(471\) | −6.82843 | −0.314637 | ||||||||
\(472\) | 8.97056i | 0.412904i | ||||||||
\(473\) | 23.3137 | 1.07197 | ||||||||
\(474\) | 2.34315i | 0.107624i | ||||||||
\(475\) | − 0.242641i | − 0.0111331i | ||||||||
\(476\) | 1.65685 | 0.0759418 | ||||||||
\(477\) | − 0.343146i | − 0.0157116i | ||||||||
\(478\) | −16.0000 | −0.731823 | ||||||||
\(479\) | 11.3137 | 0.516937 | 0.258468 | − | 0.966020i | \(-0.416782\pi\) | ||||
0.258468 | + | 0.966020i | \(0.416782\pi\) | |||||||
\(480\) | −5.65685 | −0.258199 | ||||||||
\(481\) | 6.48528 | 0.295703 | ||||||||
\(482\) | −2.14214 | −0.0975716 | ||||||||
\(483\) | 2.48528i | 0.113084i | ||||||||
\(484\) | −24.6274 | −1.11943 | ||||||||
\(485\) | − 6.72792i | − 0.305499i | ||||||||
\(486\) | − 1.41421i | − 0.0641500i | ||||||||
\(487\) | −28.3848 | −1.28624 | −0.643118 | − | 0.765767i | \(-0.722360\pi\) | ||||
−0.643118 | + | 0.765767i | \(0.722360\pi\) | |||||||
\(488\) | 22.6274i | 1.02430i | ||||||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 9.41421i | 0.425291i | ||||||||
\(491\) | − 40.8701i | − 1.84444i | −0.386666 | − | 0.922220i | \(-0.626373\pi\) | ||||
0.386666 | − | 0.922220i | \(-0.373627\pi\) | |||||||
\(492\) | 10.3431i | 0.466305i | ||||||||
\(493\) | 14.4853i | 0.652384i | ||||||||
\(494\) | −0.343146 | −0.0154389 | ||||||||
\(495\) | 4.82843 | 0.217022 | ||||||||
\(496\) | 4.68629 | 0.210421 | ||||||||
\(497\) | −2.82843 | −0.126872 | ||||||||
\(498\) | 10.8284 | 0.485233 | ||||||||
\(499\) | 2.58579i | 0.115756i | 0.998324 | + | 0.0578778i | \(0.0184334\pi\) | ||||
−0.998324 | + | 0.0578778i | \(0.981567\pi\) | |||||||
\(500\) | 2.00000i | 0.0894427i | ||||||||
\(501\) | − 19.7990i | − 0.884554i | ||||||||
\(502\) | 4.14214i | 0.184873i | ||||||||
\(503\) | −10.5858 | −0.471997 | −0.235998 | − | 0.971753i | \(-0.575836\pi\) | ||||
−0.235998 | + | 0.971753i | \(0.575836\pi\) | |||||||
\(504\) | 1.65685 | 0.0738022 | ||||||||
\(505\) | 0.585786 | 0.0260672 | ||||||||
\(506\) | − 28.9706i | − 1.28790i | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | −37.9411 | −1.68337 | ||||||||
\(509\) | − 24.6274i | − 1.09159i | −0.837918 | − | 0.545796i | \(-0.816228\pi\) | ||||
0.837918 | − | 0.545796i | \(-0.183772\pi\) | |||||||
\(510\) | 2.00000 | 0.0885615 | ||||||||
\(511\) | −5.02944 | −0.222489 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −0.242641 | −0.0107128 | ||||||||
\(514\) | −14.2843 | −0.630052 | ||||||||
\(515\) | − 7.65685i | − 0.337401i | ||||||||
\(516\) | 9.65685 | 0.425119 | ||||||||
\(517\) | − 8.00000i | − 0.351840i | ||||||||
\(518\) | 5.37258i | 0.236058i | ||||||||
\(519\) | −12.1421 | −0.532981 | ||||||||
\(520\) | 2.82843 | 0.124035 | ||||||||
\(521\) | 3.17157 | 0.138949 | 0.0694746 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694746 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(522\) | 14.4853i | 0.634004i | ||||||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | 20.4853i | 0.894904i | ||||||||
\(525\) | − 0.585786i | − 0.0255658i | ||||||||
\(526\) | 6.00000 | 0.261612 | ||||||||
\(527\) | −1.65685 | −0.0721737 | ||||||||
\(528\) | −19.3137 | −0.840521 | ||||||||
\(529\) | −5.00000 | −0.217391 | ||||||||
\(530\) | 0.485281 | 0.0210793 | ||||||||
\(531\) | − 3.17157i | − 0.137635i | ||||||||
\(532\) | − 0.284271i | − 0.0123247i | ||||||||
\(533\) | − 5.17157i | − 0.224006i | ||||||||
\(534\) | − 10.8284i | − 0.468592i | ||||||||
\(535\) | −1.17157 | −0.0506515 | ||||||||
\(536\) | 3.31371i | 0.143130i | ||||||||
\(537\) | 15.8995 | 0.686114 | ||||||||
\(538\) | − 21.5147i | − 0.927565i | ||||||||
\(539\) | 32.1421i | 1.38446i | ||||||||
\(540\) | 2.00000 | 0.0860663 | ||||||||
\(541\) | − 28.7279i | − 1.23511i | −0.786528 | − | 0.617555i | \(-0.788123\pi\) | ||||
0.786528 | − | 0.617555i | \(-0.211877\pi\) | |||||||
\(542\) | 2.34315 | 0.100647 | ||||||||
\(543\) | 6.82843 | 0.293036 | ||||||||
\(544\) | −8.00000 | −0.342997 | ||||||||
\(545\) | −4.24264 | −0.181735 | ||||||||
\(546\) | −0.828427 | −0.0354534 | ||||||||
\(547\) | − 28.0000i | − 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | −16.9706 | −0.724947 | ||||||||
\(549\) | − 8.00000i | − 0.341432i | ||||||||
\(550\) | 6.82843i | 0.291165i | ||||||||
\(551\) | 2.48528 | 0.105877 | ||||||||
\(552\) | − 12.0000i | − 0.510754i | ||||||||
\(553\) | 0.970563 | 0.0412725 | ||||||||
\(554\) | − 18.6274i | − 0.791403i | ||||||||
\(555\) | 6.48528i | 0.275285i | ||||||||
\(556\) | 34.3431i | 1.45647i | ||||||||
\(557\) | − 29.3137i | − 1.24206i | −0.783786 | − | 0.621031i | \(-0.786714\pi\) | ||||
0.783786 | − | 0.621031i | \(-0.213286\pi\) | |||||||
\(558\) | −1.65685 | −0.0701402 | ||||||||
\(559\) | −4.82843 | −0.204221 | ||||||||
\(560\) | 2.34315i | 0.0990160i | ||||||||
\(561\) | 6.82843 | 0.288296 | ||||||||
\(562\) | −39.1127 | −1.64987 | ||||||||
\(563\) | − 6.34315i | − 0.267332i | −0.991026 | − | 0.133666i | \(-0.957325\pi\) | ||||
0.991026 | − | 0.133666i | \(-0.0426749\pi\) | |||||||
\(564\) | − 3.31371i | − 0.139532i | ||||||||
\(565\) | − 10.5858i | − 0.445347i | ||||||||
\(566\) | 22.8284i | 0.959550i | ||||||||
\(567\) | −0.585786 | −0.0246007 | ||||||||
\(568\) | 13.6569 | 0.573029 | ||||||||
\(569\) | −24.8284 | −1.04086 | −0.520431 | − | 0.853904i | \(-0.674229\pi\) | ||||
−0.520431 | + | 0.853904i | \(0.674229\pi\) | |||||||
\(570\) | − 0.343146i | − 0.0143728i | ||||||||
\(571\) | − 30.1421i | − 1.26141i | −0.776023 | − | 0.630705i | \(-0.782766\pi\) | ||||
0.776023 | − | 0.630705i | \(-0.217234\pi\) | |||||||
\(572\) | 9.65685 | 0.403773 | ||||||||
\(573\) | − 15.7990i | − 0.660012i | ||||||||
\(574\) | 4.28427 | 0.178822 | ||||||||
\(575\) | −4.24264 | −0.176930 | ||||||||
\(576\) | −8.00000 | −0.333333 | ||||||||
\(577\) | 36.8701 | 1.53492 | 0.767460 | − | 0.641096i | \(-0.221520\pi\) | ||||
0.767460 | + | 0.641096i | \(0.221520\pi\) | |||||||
\(578\) | −21.2132 | −0.882353 | ||||||||
\(579\) | − 3.41421i | − 0.141890i | ||||||||
\(580\) | −20.4853 | −0.850605 | ||||||||
\(581\) | − 4.48528i | − 0.186081i | ||||||||
\(582\) | − 9.51472i | − 0.394398i | ||||||||
\(583\) | 1.65685 | 0.0686199 | ||||||||
\(584\) | 24.2843 | 1.00489 | ||||||||
\(585\) | −1.00000 | −0.0413449 | ||||||||
\(586\) | 10.3431i | 0.427271i | ||||||||
\(587\) | 5.65685i | 0.233483i | 0.993162 | + | 0.116742i | \(0.0372450\pi\) | ||||
−0.993162 | + | 0.116742i | \(0.962755\pi\) | |||||||
\(588\) | 13.3137i | 0.549048i | ||||||||
\(589\) | 0.284271i | 0.0117132i | ||||||||
\(590\) | 4.48528 | 0.184656 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 25.9411i | − 1.06617i | ||||||||
\(593\) | 18.3431 | 0.753263 | 0.376631 | − | 0.926363i | \(-0.377082\pi\) | ||||
0.376631 | + | 0.926363i | \(0.377082\pi\) | |||||||
\(594\) | 6.82843 | 0.280174 | ||||||||
\(595\) | − 0.828427i | − 0.0339622i | ||||||||
\(596\) | 22.3431i | 0.915211i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6.00000i | 0.245358i | ||||||||
\(599\) | −21.9411 | −0.896490 | −0.448245 | − | 0.893911i | \(-0.647951\pi\) | ||||
−0.448245 | + | 0.893911i | \(0.647951\pi\) | |||||||
\(600\) | 2.82843i | 0.115470i | ||||||||
\(601\) | −44.2843 | −1.80639 | −0.903197 | − | 0.429227i | \(-0.858786\pi\) | ||||
−0.903197 | + | 0.429227i | \(0.858786\pi\) | |||||||
\(602\) | − 4.00000i | − 0.163028i | ||||||||
\(603\) | − 1.17157i | − 0.0477101i | ||||||||
\(604\) | −24.0000 | −0.976546 | ||||||||
\(605\) | 12.3137i | 0.500623i | ||||||||
\(606\) | 0.828427 | 0.0336526 | ||||||||
\(607\) | −14.9706 | −0.607636 | −0.303818 | − | 0.952730i | \(-0.598262\pi\) | ||||
−0.303818 | + | 0.952730i | \(0.598262\pi\) | |||||||
\(608\) | 1.37258i | 0.0556656i | ||||||||
\(609\) | 6.00000 | 0.243132 | ||||||||
\(610\) | 11.3137 | 0.458079 | ||||||||
\(611\) | 1.65685i | 0.0670291i | ||||||||
\(612\) | 2.82843 | 0.114332 | ||||||||
\(613\) | 31.1716i | 1.25901i | 0.776997 | + | 0.629504i | \(0.216742\pi\) | ||||
−0.776997 | + | 0.629504i | \(0.783258\pi\) | |||||||
\(614\) | − 4.68629i | − 0.189123i | ||||||||
\(615\) | 5.17157 | 0.208538 | ||||||||
\(616\) | 8.00000i | 0.322329i | ||||||||
\(617\) | 37.4558 | 1.50792 | 0.753958 | − | 0.656923i | \(-0.228142\pi\) | ||||
0.753958 | + | 0.656923i | \(0.228142\pi\) | |||||||
\(618\) | − 10.8284i | − 0.435583i | ||||||||
\(619\) | − 11.2721i | − 0.453063i | −0.974004 | − | 0.226532i | \(-0.927261\pi\) | ||||
0.974004 | − | 0.226532i | \(-0.0727386\pi\) | |||||||
\(620\) | − 2.34315i | − 0.0941030i | ||||||||
\(621\) | 4.24264i | 0.170251i | ||||||||
\(622\) | 20.0000 | 0.801927 | ||||||||
\(623\) | −4.48528 | −0.179699 | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.7990 | 0.951199 | ||||||||
\(627\) | − 1.17157i | − 0.0467881i | ||||||||
\(628\) | − 13.6569i | − 0.544968i | ||||||||
\(629\) | 9.17157i | 0.365695i | ||||||||
\(630\) | − 0.828427i | − 0.0330053i | ||||||||
\(631\) | −36.4853 | −1.45246 | −0.726228 | − | 0.687454i | \(-0.758728\pi\) | ||||
−0.726228 | + | 0.687454i | \(0.758728\pi\) | |||||||
\(632\) | −4.68629 | −0.186411 | ||||||||
\(633\) | 24.9706 | 0.992491 | ||||||||
\(634\) | 29.1716i | 1.15855i | ||||||||
\(635\) | 18.9706i | 0.752824i | ||||||||
\(636\) | 0.686292 | 0.0272132 | ||||||||
\(637\) | − 6.65685i | − 0.263754i | ||||||||
\(638\) | −69.9411 | −2.76900 | ||||||||
\(639\) | −4.82843 | −0.191010 | ||||||||
\(640\) | − 11.3137i | − 0.447214i | ||||||||
\(641\) | −37.7990 | −1.49297 | −0.746485 | − | 0.665402i | \(-0.768260\pi\) | ||||
−0.746485 | + | 0.665402i | \(0.768260\pi\) | |||||||
\(642\) | −1.65685 | −0.0653908 | ||||||||
\(643\) | − 42.1421i | − 1.66192i | −0.556329 | − | 0.830962i | \(-0.687791\pi\) | ||||
0.556329 | − | 0.830962i | \(-0.312209\pi\) | |||||||
\(644\) | −4.97056 | −0.195868 | ||||||||
\(645\) | − 4.82843i | − 0.190119i | ||||||||
\(646\) | − 0.485281i | − 0.0190931i | ||||||||
\(647\) | −10.1005 | −0.397092 | −0.198546 | − | 0.980092i | \(-0.563622\pi\) | ||||
−0.198546 | + | 0.980092i | \(0.563622\pi\) | |||||||
\(648\) | 2.82843 | 0.111111 | ||||||||
\(649\) | 15.3137 | 0.601116 | ||||||||
\(650\) | − 1.41421i | − 0.0554700i | ||||||||
\(651\) | 0.686292i | 0.0268979i | ||||||||
\(652\) | − 16.0000i | − 0.626608i | ||||||||
\(653\) | − 40.1421i | − 1.57088i | −0.618936 | − | 0.785442i | \(-0.712436\pi\) | ||||
0.618936 | − | 0.785442i | \(-0.287564\pi\) | |||||||
\(654\) | −6.00000 | −0.234619 | ||||||||
\(655\) | 10.2426 | 0.400213 | ||||||||
\(656\) | −20.6863 | −0.807664 | ||||||||
\(657\) | −8.58579 | −0.334963 | ||||||||
\(658\) | −1.37258 | −0.0535089 | ||||||||
\(659\) | 6.92893i | 0.269913i | 0.990852 | + | 0.134956i | \(0.0430894\pi\) | ||||
−0.990852 | + | 0.134956i | \(0.956911\pi\) | |||||||
\(660\) | 9.65685i | 0.375893i | ||||||||
\(661\) | − 4.24264i | − 0.165020i | −0.996590 | − | 0.0825098i | \(-0.973706\pi\) | ||||
0.996590 | − | 0.0825098i | \(-0.0262936\pi\) | |||||||
\(662\) | 47.6569i | 1.85224i | ||||||||
\(663\) | −1.41421 | −0.0549235 | ||||||||
\(664\) | 21.6569i | 0.840449i | ||||||||
\(665\) | −0.142136 | −0.00551178 | ||||||||
\(666\) | 9.17157i | 0.355391i | ||||||||
\(667\) | − 43.4558i | − 1.68262i | ||||||||
\(668\) | 39.5980 | 1.53209 | ||||||||
\(669\) | − 27.2132i | − 1.05212i | ||||||||
\(670\) | 1.65685 | 0.0640099 | ||||||||
\(671\) | 38.6274 | 1.49119 | ||||||||
\(672\) | 3.31371i | 0.127829i | ||||||||
\(673\) | 35.9411 | 1.38543 | 0.692714 | − | 0.721212i | \(-0.256415\pi\) | ||||
0.692714 | + | 0.721212i | \(0.256415\pi\) | |||||||
\(674\) | −48.7696 | −1.87853 | ||||||||
\(675\) | − 1.00000i | − 0.0384900i | ||||||||
\(676\) | −2.00000 | −0.0769231 | ||||||||
\(677\) | 37.1127i | 1.42636i | 0.700983 | + | 0.713178i | \(0.252745\pi\) | ||||
−0.700983 | + | 0.713178i | \(0.747255\pi\) | |||||||
\(678\) | − 14.9706i | − 0.574941i | ||||||||
\(679\) | −3.94113 | −0.151247 | ||||||||
\(680\) | 4.00000i | 0.153393i | ||||||||
\(681\) | 15.3137 | 0.586823 | ||||||||
\(682\) | − 8.00000i | − 0.306336i | ||||||||
\(683\) | 22.9706i | 0.878944i | 0.898256 | + | 0.439472i | \(0.144834\pi\) | ||||
−0.898256 | + | 0.439472i | \(0.855166\pi\) | |||||||
\(684\) | − 0.485281i | − 0.0185552i | ||||||||
\(685\) | 8.48528i | 0.324206i | ||||||||
\(686\) | 11.3137 | 0.431959 | ||||||||
\(687\) | 5.89949 | 0.225080 | ||||||||
\(688\) | 19.3137i | 0.736328i | ||||||||
\(689\) | −0.343146 | −0.0130728 | ||||||||
\(690\) | −6.00000 | −0.228416 | ||||||||
\(691\) | 23.2721i | 0.885312i | 0.896692 | + | 0.442656i | \(0.145964\pi\) | ||||
−0.896692 | + | 0.442656i | \(0.854036\pi\) | |||||||
\(692\) | − 24.2843i | − 0.923149i | ||||||||
\(693\) | − 2.82843i | − 0.107443i | ||||||||
\(694\) | 16.0000i | 0.607352i | ||||||||
\(695\) | 17.1716 | 0.651355 | ||||||||
\(696\) | −28.9706 | −1.09813 | ||||||||
\(697\) | 7.31371 | 0.277026 | ||||||||
\(698\) | − 29.3137i | − 1.10954i | ||||||||
\(699\) | − 22.5858i | − 0.854273i | ||||||||
\(700\) | 1.17157 | 0.0442813 | ||||||||
\(701\) | − 46.2426i | − 1.74656i | −0.487218 | − | 0.873280i | \(-0.661988\pi\) | ||||
0.487218 | − | 0.873280i | \(-0.338012\pi\) | |||||||
\(702\) | −1.41421 | −0.0533761 | ||||||||
\(703\) | 1.57359 | 0.0593492 | ||||||||
\(704\) | − 38.6274i | − 1.45583i | ||||||||
\(705\) | −1.65685 | −0.0624007 | ||||||||
\(706\) | 8.68629 | 0.326913 | ||||||||
\(707\) | − 0.343146i | − 0.0129053i | ||||||||
\(708\) | 6.34315 | 0.238390 | ||||||||
\(709\) | − 13.8995i | − 0.522006i | −0.965338 | − | 0.261003i | \(-0.915947\pi\) | ||||
0.965338 | − | 0.261003i | \(-0.0840533\pi\) | |||||||
\(710\) | − 6.82843i | − 0.256266i | ||||||||
\(711\) | 1.65685 | 0.0621369 | ||||||||
\(712\) | 21.6569 | 0.811625 | ||||||||
\(713\) | 4.97056 | 0.186149 | ||||||||
\(714\) | − 1.17157i | − 0.0438450i | ||||||||
\(715\) | − 4.82843i | − 0.180573i | ||||||||
\(716\) | 31.7990i | 1.18838i | ||||||||
\(717\) | 11.3137i | 0.422518i | ||||||||
\(718\) | 32.7696 | 1.22295 | ||||||||
\(719\) | 42.4264 | 1.58224 | 0.791119 | − | 0.611662i | \(-0.209499\pi\) | ||||
0.791119 | + | 0.611662i | \(0.209499\pi\) | |||||||
\(720\) | 4.00000i | 0.149071i | ||||||||
\(721\) | −4.48528 | −0.167041 | ||||||||
\(722\) | 26.7868 | 0.996901 | ||||||||
\(723\) | 1.51472i | 0.0563330i | ||||||||
\(724\) | 13.6569i | 0.507553i | ||||||||
\(725\) | 10.2426i | 0.380402i | ||||||||
\(726\) | 17.4142i | 0.646302i | ||||||||
\(727\) | 23.1716 | 0.859386 | 0.429693 | − | 0.902975i | \(-0.358622\pi\) | ||||
0.429693 | + | 0.902975i | \(0.358622\pi\) | |||||||
\(728\) | − 1.65685i | − 0.0614071i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | − 12.1421i | − 0.449401i | ||||||||
\(731\) | − 6.82843i | − 0.252559i | ||||||||
\(732\) | 16.0000 | 0.591377 | ||||||||
\(733\) | 42.9706i | 1.58715i | 0.608470 | + | 0.793577i | \(0.291784\pi\) | ||||
−0.608470 | + | 0.793577i | \(0.708216\pi\) | |||||||
\(734\) | −36.7696 | −1.35719 | ||||||||
\(735\) | 6.65685 | 0.245542 | ||||||||
\(736\) | 24.0000 | 0.884652 | ||||||||
\(737\) | 5.65685 | 0.208373 | ||||||||
\(738\) | 7.31371 | 0.269221 | ||||||||
\(739\) | 0.242641i | 0.00892568i | 0.999990 | + | 0.00446284i | \(0.00142057\pi\) | ||||
−0.999990 | + | 0.00446284i | \(0.998579\pi\) | |||||||
\(740\) | −12.9706 | −0.476807 | ||||||||
\(741\) | 0.242641i | 0.00891363i | ||||||||
\(742\) | − 0.284271i | − 0.0104359i | ||||||||
\(743\) | 33.1716 | 1.21695 | 0.608473 | − | 0.793574i | \(-0.291782\pi\) | ||||
0.608473 | + | 0.793574i | \(0.291782\pi\) | |||||||
\(744\) | − 3.31371i | − 0.121486i | ||||||||
\(745\) | 11.1716 | 0.409295 | ||||||||
\(746\) | − 32.2843i | − 1.18201i | ||||||||
\(747\) | − 7.65685i | − 0.280150i | ||||||||
\(748\) | 13.6569i | 0.499344i | ||||||||
\(749\) | 0.686292i | 0.0250765i | ||||||||
\(750\) | 1.41421 | 0.0516398 | ||||||||
\(751\) | −1.02944 | −0.0375647 | −0.0187823 | − | 0.999824i | \(-0.505979\pi\) | ||||
−0.0187823 | + | 0.999824i | \(0.505979\pi\) | |||||||
\(752\) | 6.62742 | 0.241677 | ||||||||
\(753\) | 2.92893 | 0.106736 | ||||||||
\(754\) | 14.4853 | 0.527523 | ||||||||
\(755\) | 12.0000i | 0.436725i | ||||||||
\(756\) | − 1.17157i | − 0.0426097i | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 2.68629i | 0.0975705i | ||||||||
\(759\) | −20.4853 | −0.743569 | ||||||||
\(760\) | 0.686292 | 0.0248944 | ||||||||
\(761\) | −25.4558 | −0.922774 | −0.461387 | − | 0.887199i | \(-0.652648\pi\) | ||||
−0.461387 | + | 0.887199i | \(0.652648\pi\) | |||||||
\(762\) | 26.8284i | 0.971891i | ||||||||
\(763\) | 2.48528i | 0.0899732i | ||||||||
\(764\) | 31.5980 | 1.14317 | ||||||||
\(765\) | − 1.41421i | − 0.0511310i | ||||||||
\(766\) | 50.6274 | 1.82924 | ||||||||
\(767\) | −3.17157 | −0.114519 | ||||||||
\(768\) | − 16.0000i | − 0.577350i | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 4.00000 | 0.144150 | ||||||||
\(771\) | 10.1005i | 0.363761i | ||||||||
\(772\) | 6.82843 | 0.245760 | ||||||||
\(773\) | − 13.6569i | − 0.491203i | −0.969371 | − | 0.245601i | \(-0.921015\pi\) | ||||
0.969371 | − | 0.245601i | \(-0.0789854\pi\) | |||||||
\(774\) | − 6.82843i | − 0.245443i | ||||||||
\(775\) | −1.17157 | −0.0420841 | ||||||||
\(776\) | 19.0294 | 0.683117 | ||||||||
\(777\) | 3.79899 | 0.136288 | ||||||||
\(778\) | 38.7696i | 1.38996i | ||||||||
\(779\) | − 1.25483i | − 0.0449591i | ||||||||
\(780\) | − 2.00000i | − 0.0716115i | ||||||||
\(781\) | − 23.3137i | − 0.834230i | ||||||||
\(782\) | −8.48528 | −0.303433 | ||||||||
\(783\) | 10.2426 | 0.366042 | ||||||||
\(784\) | −26.6274 | −0.950979 | ||||||||
\(785\) | −6.82843 | −0.243717 | ||||||||
\(786\) | 14.4853 | 0.516673 | ||||||||
\(787\) | 13.6569i | 0.486814i | 0.969924 | + | 0.243407i | \(0.0782651\pi\) | ||||
−0.969924 | + | 0.243407i | \(0.921735\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 4.24264i | − 0.151042i | ||||||||
\(790\) | 2.34315i | 0.0833654i | ||||||||
\(791\) | −6.20101 | −0.220483 | ||||||||
\(792\) | 13.6569i | 0.485275i | ||||||||
\(793\) | −8.00000 | −0.284088 | ||||||||
\(794\) | 15.1127i | 0.536330i | ||||||||
\(795\) | − 0.343146i | − 0.0121701i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.7696i | 1.37329i | 0.726994 | + | 0.686644i | \(0.240917\pi\) | ||||
−0.726994 | + | 0.686644i | \(0.759083\pi\) | |||||||
\(798\) | −0.201010 | −0.00711568 | ||||||||
\(799\) | −2.34315 | −0.0828945 | ||||||||
\(800\) | −5.65685 | −0.200000 | ||||||||
\(801\) | −7.65685 | −0.270542 | ||||||||
\(802\) | −14.3431 | −0.506474 | ||||||||
\(803\) | − 41.4558i | − 1.46294i | ||||||||
\(804\) | 2.34315 | 0.0826364 | ||||||||
\(805\) | 2.48528i | 0.0875947i | ||||||||
\(806\) | 1.65685i | 0.0583602i | ||||||||
\(807\) | −15.2132 | −0.535530 | ||||||||
\(808\) | 1.65685i | 0.0582879i | ||||||||
\(809\) | −49.1127 | −1.72671 | −0.863355 | − | 0.504597i | \(-0.831641\pi\) | ||||
−0.863355 | + | 0.504597i | \(0.831641\pi\) | |||||||
\(810\) | − 1.41421i | − 0.0496904i | ||||||||
\(811\) | − 45.6985i | − 1.60469i | −0.596860 | − | 0.802345i | \(-0.703585\pi\) | ||||
0.596860 | − | 0.802345i | \(-0.296415\pi\) | |||||||
\(812\) | 12.0000i | 0.421117i | ||||||||
\(813\) | − 1.65685i | − 0.0581084i | ||||||||
\(814\) | −44.2843 | −1.55216 | ||||||||
\(815\) | −8.00000 | −0.280228 | ||||||||
\(816\) | 5.65685i | 0.198030i | ||||||||
\(817\) | −1.17157 | −0.0409881 | ||||||||
\(818\) | −8.20101 | −0.286742 | ||||||||
\(819\) | 0.585786i | 0.0204690i | ||||||||
\(820\) | 10.3431i | 0.361198i | ||||||||
\(821\) | 20.1421i | 0.702965i | 0.936194 | + | 0.351483i | \(0.114322\pi\) | ||||
−0.936194 | + | 0.351483i | \(0.885678\pi\) | |||||||
\(822\) | 12.0000i | 0.418548i | ||||||||
\(823\) | 21.3137 | 0.742949 | 0.371475 | − | 0.928443i | \(-0.378852\pi\) | ||||
0.371475 | + | 0.928443i | \(0.378852\pi\) | |||||||
\(824\) | 21.6569 | 0.754452 | ||||||||
\(825\) | 4.82843 | 0.168104 | ||||||||
\(826\) | − 2.62742i | − 0.0914195i | ||||||||
\(827\) | 37.3137i | 1.29752i | 0.760991 | + | 0.648762i | \(0.224713\pi\) | ||||
−0.760991 | + | 0.648762i | \(0.775287\pi\) | |||||||
\(828\) | −8.48528 | −0.294884 | ||||||||
\(829\) | − 7.02944i | − 0.244142i | −0.992521 | − | 0.122071i | \(-0.961046\pi\) | ||||
0.992521 | − | 0.122071i | \(-0.0389536\pi\) | |||||||
\(830\) | 10.8284 | 0.375860 | ||||||||
\(831\) | −13.1716 | −0.456917 | ||||||||
\(832\) | 8.00000i | 0.277350i | ||||||||
\(833\) | 9.41421 | 0.326183 | ||||||||
\(834\) | 24.2843 | 0.840896 | ||||||||
\(835\) | − 19.7990i | − 0.685172i | ||||||||
\(836\) | 2.34315 | 0.0810394 | ||||||||
\(837\) | 1.17157i | 0.0404955i | ||||||||
\(838\) | − 0.142136i | − 0.00490999i | ||||||||
\(839\) | −45.6569 | −1.57625 | −0.788125 | − | 0.615515i | \(-0.788948\pi\) | ||||
−0.788125 | + | 0.615515i | \(0.788948\pi\) | |||||||
\(840\) | 1.65685 | 0.0571669 | ||||||||
\(841\) | −75.9117 | −2.61764 | ||||||||
\(842\) | 10.2843i | 0.354419i | ||||||||
\(843\) | 27.6569i | 0.952553i | ||||||||
\(844\) | 49.9411i | 1.71904i | ||||||||
\(845\) | 1.00000i | 0.0344010i | ||||||||
\(846\) | −2.34315 | −0.0805590 | ||||||||
\(847\) | 7.21320 | 0.247849 | ||||||||
\(848\) | 1.37258i | 0.0471347i | ||||||||
\(849\) | 16.1421 | 0.553997 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | − 27.5147i | − 0.943192i | ||||||||
\(852\) | − 9.65685i | − 0.330838i | ||||||||
\(853\) | 47.9411i | 1.64147i | 0.571307 | + | 0.820736i | \(0.306437\pi\) | ||||
−0.571307 | + | 0.820736i | \(0.693563\pi\) | |||||||
\(854\) | − 6.62742i | − 0.226786i | ||||||||
\(855\) | −0.242641 | −0.00829814 | ||||||||
\(856\) | − 3.31371i | − 0.113260i | ||||||||
\(857\) | −23.5563 | −0.804670 | −0.402335 | − | 0.915493i | \(-0.631801\pi\) | ||||
−0.402335 | + | 0.915493i | \(0.631801\pi\) | |||||||
\(858\) | − 6.82843i | − 0.233119i | ||||||||
\(859\) | − 13.9411i | − 0.475665i | −0.971306 | − | 0.237833i | \(-0.923563\pi\) | ||||
0.971306 | − | 0.237833i | \(-0.0764369\pi\) | |||||||
\(860\) | 9.65685 | 0.329296 | ||||||||
\(861\) | − 3.02944i | − 0.103243i | ||||||||
\(862\) | 27.3137 | 0.930309 | ||||||||
\(863\) | 26.1421 | 0.889889 | 0.444944 | − | 0.895558i | \(-0.353223\pi\) | ||||
0.444944 | + | 0.895558i | \(0.353223\pi\) | |||||||
\(864\) | 5.65685i | 0.192450i | ||||||||
\(865\) | −12.1421 | −0.412845 | ||||||||
\(866\) | −48.7696 | −1.65726 | ||||||||
\(867\) | 15.0000i | 0.509427i | ||||||||
\(868\) | −1.37258 | −0.0465885 | ||||||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 14.4853i | 0.491097i | ||||||||
\(871\) | −1.17157 | −0.0396972 | ||||||||
\(872\) | − 12.0000i | − 0.406371i | ||||||||
\(873\) | −6.72792 | −0.227706 | ||||||||
\(874\) | 1.45584i | 0.0492447i | ||||||||
\(875\) | − 0.585786i | − 0.0198032i | ||||||||
\(876\) | − 17.1716i | − 0.580174i | ||||||||
\(877\) | − 36.4264i | − 1.23003i | −0.788514 | − | 0.615016i | \(-0.789149\pi\) | ||||
0.788514 | − | 0.615016i | \(-0.210851\pi\) | |||||||
\(878\) | −44.7696 | −1.51090 | ||||||||
\(879\) | 7.31371 | 0.246685 | ||||||||
\(880\) | −19.3137 | −0.651065 | ||||||||
\(881\) | −51.9411 | −1.74994 | −0.874970 | − | 0.484176i | \(-0.839119\pi\) | ||||
−0.874970 | + | 0.484176i | \(0.839119\pi\) | |||||||
\(882\) | 9.41421 | 0.316993 | ||||||||
\(883\) | 4.97056i | 0.167273i | 0.996496 | + | 0.0836364i | \(0.0266534\pi\) | ||||
−0.996496 | + | 0.0836364i | \(0.973347\pi\) | |||||||
\(884\) | − 2.82843i | − 0.0951303i | ||||||||
\(885\) | − 3.17157i | − 0.106611i | ||||||||
\(886\) | − 19.3137i | − 0.648857i | ||||||||
\(887\) | 0.928932 | 0.0311905 | 0.0155952 | − | 0.999878i | \(-0.495036\pi\) | ||||
0.0155952 | + | 0.999878i | \(0.495036\pi\) | |||||||
\(888\) | −18.3431 | −0.615556 | ||||||||
\(889\) | 11.1127 | 0.372708 | ||||||||
\(890\) | − 10.8284i | − 0.362970i | ||||||||
\(891\) | − 4.82843i | − 0.161758i | ||||||||
\(892\) | 54.4264 | 1.82233 | ||||||||
\(893\) | 0.402020i | 0.0134531i | ||||||||
\(894\) | 15.7990 | 0.528397 | ||||||||
\(895\) | 15.8995 | 0.531462 | ||||||||
\(896\) | −6.62742 | −0.221406 | ||||||||
\(897\) | 4.24264 | 0.141658 | ||||||||
\(898\) | −8.48528 | −0.283158 | ||||||||
\(899\) | − 12.0000i | − 0.400222i | ||||||||
\(900\) | 2.00000 | 0.0666667 | ||||||||
\(901\) | − 0.485281i | − 0.0161671i | ||||||||
\(902\) | 35.3137i | 1.17582i | ||||||||
\(903\) | −2.82843 | −0.0941242 | ||||||||
\(904\) | 29.9411 | 0.995827 | ||||||||
\(905\) | 6.82843 | 0.226985 | ||||||||
\(906\) | 16.9706i | 0.563809i | ||||||||
\(907\) | − 32.4264i | − 1.07670i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) | ||||
0.842721 | − | 0.538351i | \(-0.180952\pi\) | |||||||
\(908\) | 30.6274i | 1.01641i | ||||||||
\(909\) | − 0.585786i | − 0.0194293i | ||||||||
\(910\) | −0.828427 | −0.0274621 | ||||||||
\(911\) | 32.4853 | 1.07629 | 0.538143 | − | 0.842854i | \(-0.319126\pi\) | ||||
0.538143 | + | 0.842854i | \(0.319126\pi\) | |||||||
\(912\) | 0.970563 | 0.0321385 | ||||||||
\(913\) | 36.9706 | 1.22355 | ||||||||
\(914\) | 8.14214 | 0.269318 | ||||||||
\(915\) | − 8.00000i | − 0.264472i | ||||||||
\(916\) | 11.7990i | 0.389850i | ||||||||
\(917\) | − 6.00000i | − 0.198137i | ||||||||
\(918\) | − 2.00000i | − 0.0660098i | ||||||||
\(919\) | 27.9411 | 0.921693 | 0.460846 | − | 0.887480i | \(-0.347546\pi\) | ||||
0.460846 | + | 0.887480i | \(0.347546\pi\) | |||||||
\(920\) | − 12.0000i | − 0.395628i | ||||||||
\(921\) | −3.31371 | −0.109190 | ||||||||
\(922\) | − 50.4264i | − 1.66071i | ||||||||
\(923\) | 4.82843i | 0.158930i | ||||||||
\(924\) | 5.65685 | 0.186097 | ||||||||
\(925\) | 6.48528i | 0.213235i | ||||||||
\(926\) | −49.1127 | −1.61394 | ||||||||
\(927\) | −7.65685 | −0.251484 | ||||||||
\(928\) | − 57.9411i | − 1.90201i | ||||||||
\(929\) | 18.0000 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(930\) | −1.65685 | −0.0543304 | ||||||||
\(931\) | − 1.61522i | − 0.0529368i | ||||||||
\(932\) | 45.1716 | 1.47964 | ||||||||
\(933\) | − 14.1421i | − 0.462993i | ||||||||
\(934\) | − 49.6569i | − 1.62482i | ||||||||
\(935\) | 6.82843 | 0.223313 | ||||||||
\(936\) | − 2.82843i | − 0.0924500i | ||||||||
\(937\) | 30.9706 | 1.01176 | 0.505882 | − | 0.862603i | \(-0.331167\pi\) | ||||
0.505882 | + | 0.862603i | \(0.331167\pi\) | |||||||
\(938\) | − 0.970563i | − 0.0316900i | ||||||||
\(939\) | − 16.8284i | − 0.549175i | ||||||||
\(940\) | − 3.31371i | − 0.108081i | ||||||||
\(941\) | − 10.2010i | − 0.332543i | −0.986080 | − | 0.166272i | \(-0.946827\pi\) | ||||
0.986080 | − | 0.166272i | \(-0.0531729\pi\) | |||||||
\(942\) | −9.65685 | −0.314637 | ||||||||
\(943\) | −21.9411 | −0.714501 | ||||||||
\(944\) | 12.6863i | 0.412904i | ||||||||
\(945\) | −0.585786 | −0.0190556 | ||||||||
\(946\) | 32.9706 | 1.07197 | ||||||||
\(947\) | − 37.5980i | − 1.22177i | −0.791719 | − | 0.610885i | \(-0.790814\pi\) | ||||
0.791719 | − | 0.610885i | \(-0.209186\pi\) | |||||||
\(948\) | 3.31371i | 0.107624i | ||||||||
\(949\) | 8.58579i | 0.278706i | ||||||||
\(950\) | − 0.343146i | − 0.0111331i | ||||||||
\(951\) | 20.6274 | 0.668890 | ||||||||
\(952\) | 2.34315 | 0.0759418 | ||||||||
\(953\) | −48.3259 | −1.56543 | −0.782715 | − | 0.622381i | \(-0.786166\pi\) | ||||
−0.782715 | + | 0.622381i | \(0.786166\pi\) | |||||||
\(954\) | − 0.485281i | − 0.0157116i | ||||||||
\(955\) | − 15.7990i | − 0.511243i | ||||||||
\(956\) | −22.6274 | −0.731823 | ||||||||
\(957\) | 49.4558i | 1.59868i | ||||||||
\(958\) | 16.0000 | 0.516937 | ||||||||
\(959\) | 4.97056 | 0.160508 | ||||||||
\(960\) | −8.00000 | −0.258199 | ||||||||
\(961\) | −29.6274 | −0.955723 | ||||||||
\(962\) | 9.17157 | 0.295703 | ||||||||
\(963\) | 1.17157i | 0.0377534i | ||||||||
\(964\) | −3.02944 | −0.0975716 | ||||||||
\(965\) | − 3.41421i | − 0.109907i | ||||||||
\(966\) | 3.51472i | 0.113084i | ||||||||
\(967\) | 8.38478 | 0.269636 | 0.134818 | − | 0.990870i | \(-0.456955\pi\) | ||||
0.134818 | + | 0.990870i | \(0.456955\pi\) | |||||||
\(968\) | −34.8284 | −1.11943 | ||||||||
\(969\) | −0.343146 | −0.0110234 | ||||||||
\(970\) | − 9.51472i | − 0.305499i | ||||||||
\(971\) | − 24.5858i | − 0.788995i | −0.918897 | − | 0.394498i | \(-0.870919\pi\) | ||||
0.918897 | − | 0.394498i | \(-0.129081\pi\) | |||||||
\(972\) | − 2.00000i | − 0.0641500i | ||||||||
\(973\) | − 10.0589i | − 0.322473i | ||||||||
\(974\) | −40.1421 | −1.28624 | ||||||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | 32.0000i | 1.02430i | ||||||||
\(977\) | 18.3431 | 0.586849 | 0.293425 | − | 0.955982i | \(-0.405205\pi\) | ||||
0.293425 | + | 0.955982i | \(0.405205\pi\) | |||||||
\(978\) | −11.3137 | −0.361773 | ||||||||
\(979\) | − 36.9706i | − 1.18158i | ||||||||
\(980\) | 13.3137i | 0.425291i | ||||||||
\(981\) | 4.24264i | 0.135457i | ||||||||
\(982\) | − 57.7990i | − 1.84444i | ||||||||
\(983\) | −39.7990 | −1.26939 | −0.634695 | − | 0.772762i | \(-0.718874\pi\) | ||||
−0.634695 | + | 0.772762i | \(0.718874\pi\) | |||||||
\(984\) | 14.6274i | 0.466305i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.4853i | 0.652384i | ||||||||
\(987\) | 0.970563i | 0.0308934i | ||||||||
\(988\) | −0.485281 | −0.0154389 | ||||||||
\(989\) | 20.4853i | 0.651394i | ||||||||
\(990\) | 6.82843 | 0.217022 | ||||||||
\(991\) | 48.9706 | 1.55560 | 0.777801 | − | 0.628511i | \(-0.216335\pi\) | ||||
0.777801 | + | 0.628511i | \(0.216335\pi\) | |||||||
\(992\) | 6.62742 | 0.210421 | ||||||||
\(993\) | 33.6985 | 1.06939 | ||||||||
\(994\) | −4.00000 | −0.126872 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 15.3137 | 0.485233 | ||||||||
\(997\) | − 8.48528i | − 0.268732i | −0.990932 | − | 0.134366i | \(-0.957100\pi\) | ||||
0.990932 | − | 0.134366i | \(-0.0428997\pi\) | |||||||
\(998\) | 3.65685i | 0.115756i | ||||||||
\(999\) | 6.48528 | 0.205185 |
(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 | 1560.2.w.c.781.3 | ✓ | 4 | |
4.3 | odd | 2 | 6240.2.w.d.3121.3 | 4 | |||
8.3 | odd | 2 | 6240.2.w.d.3121.1 | 4 | |||
8.5 | even | 2 | inner | 1560.2.w.c.781.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.w.c.781.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1560.2.w.c.781.4 | yes | 4 | 8.5 | even | 2 | inner | |
6240.2.w.d.3121.1 | 4 | 8.3 | odd | 2 | |||
6240.2.w.d.3121.3 | 4 | 4.3 | odd | 2 |