Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(257,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.r (of order \(4\), degree \(2\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.257 |
Dual form | 600.2.r.d.593.2 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 1.70711 | − | 0.292893i | 0.985599 | − | 0.169102i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00000 | − | 3.00000i | −1.13389 | − | 1.13389i | −0.989524 | − | 0.144370i | \(-0.953885\pi\) |
−0.144370 | − | 0.989524i | \(-0.546115\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82843 | − | 1.00000i | 0.942809 | − | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264 | − | 4.24264i | 1.02899 | − | 1.02899i | 0.0294245 | − | 0.999567i | \(-0.490633\pi\) |
0.999567 | − | 0.0294245i | \(-0.00936746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | − | 4.24264i | −1.30931 | − | 0.925820i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | + | 2.82843i | 0.589768 | + | 0.589768i | 0.937568 | − | 0.347801i | \(-0.113071\pi\) |
−0.347801 | + | 0.937568i | \(0.613071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.53553 | − | 2.53553i | 0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.41421 | −0.262613 | −0.131306 | − | 0.991342i | \(-0.541917\pi\) | ||||
−0.131306 | + | 0.991342i | \(0.541917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | −0.359211 | −0.179605 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179605 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.414214 | − | 2.41421i | −0.0721053 | − | 0.420261i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | + | 2.00000i | 0.328798 | + | 0.328798i | 0.852129 | − | 0.523331i | \(-0.175311\pi\) |
−0.523331 | + | 0.852129i | \(0.675311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | − | 2.00000i | 0.304997 | − | 0.304997i | −0.537968 | − | 0.842965i | \(-0.680808\pi\) |
0.842965 | + | 0.537968i | \(0.180808\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65685 | + | 5.65685i | −0.825137 | + | 0.825137i | −0.986840 | − | 0.161703i | \(-0.948301\pi\) |
0.161703 | + | 0.986840i | \(0.448301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.00000 | − | 8.48528i | 0.840168 | − | 1.18818i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528 | + | 8.48528i | 1.16554 | + | 1.16554i | 0.983243 | + | 0.182300i | \(0.0583542\pi\) |
0.182300 | + | 0.983243i | \(0.441646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.17157 | − | 6.82843i | −0.155179 | − | 0.904447i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.41421 | −0.184115 | −0.0920575 | − | 0.995754i | \(-0.529344\pi\) | ||||
−0.0920575 | + | 0.995754i | \(0.529344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.4853 | − | 5.48528i | −1.44701 | − | 0.691080i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | − | 4.00000i | −0.488678 | − | 0.488678i | 0.419211 | − | 0.907889i | \(-0.362307\pi\) |
−0.907889 | + | 0.419211i | \(0.862307\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.65685 | + | 4.00000i | 0.681005 | + | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.82843i | 0.335673i | 0.985815 | + | 0.167836i | \(0.0536780\pi\) | ||||
−0.985815 | + | 0.167836i | \(0.946322\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.00000 | + | 3.00000i | −0.351123 | + | 0.351123i | −0.860527 | − | 0.509404i | \(-0.829866\pi\) |
0.509404 | + | 0.860527i | \(0.329866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.24264 | + | 4.24264i | −0.483494 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.0000i | − | 1.12509i | −0.826767 | − | 0.562544i | \(-0.809823\pi\) | ||
0.826767 | − | 0.562544i | \(-0.190177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.82843 | − | 2.82843i | −0.310460 | − | 0.310460i | 0.534628 | − | 0.845088i | \(-0.320452\pi\) |
−0.845088 | + | 0.534628i | \(0.820452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.41421 | + | 0.414214i | −0.258831 | + | 0.0444084i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.82843 | 0.299813 | 0.149906 | − | 0.988700i | \(-0.452103\pi\) | ||||
0.149906 | + | 0.988700i | \(0.452103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.41421 | + | 0.585786i | −0.354037 | + | 0.0607432i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0000 | + | 13.0000i | 1.31995 | + | 1.31995i | 0.913812 | + | 0.406138i | \(0.133125\pi\) |
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.41421 | − | 4.00000i | −0.142134 | − | 0.402015i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.5563i | 1.54791i | 0.633238 | + | 0.773957i | \(0.281726\pi\) | ||||
−0.633238 | + | 0.773957i | \(0.718274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.0000 | − | 11.0000i | 1.08386 | − | 1.08386i | 0.0877167 | − | 0.996145i | \(-0.472043\pi\) |
0.996145 | − | 0.0877167i | \(-0.0279570\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.82843 | − | 2.82843i | 0.273434 | − | 0.273434i | −0.557047 | − | 0.830481i | \(-0.688066\pi\) |
0.830481 | + | 0.557047i | \(0.188066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 10.0000i | − | 0.957826i | −0.877862 | − | 0.478913i | \(-0.841031\pi\) | ||
0.877862 | − | 0.478913i | \(-0.158969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | + | 2.82843i | 0.379663 | + | 0.268462i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.24264 | − | 4.24264i | −0.399114 | − | 0.399114i | 0.478806 | − | 0.877920i | \(-0.341070\pi\) |
−0.877920 | + | 0.478806i | \(0.841070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.4558 | −2.33353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.65685 | + | 9.65685i | 0.149394 | + | 0.870729i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000 | + | 3.00000i | 0.266207 | + | 0.266207i | 0.827570 | − | 0.561363i | \(-0.189723\pi\) |
−0.561363 | + | 0.827570i | \(0.689723\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82843 | − | 4.00000i | 0.249029 | − | 0.352180i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5563i | 1.35916i | 0.733599 | + | 0.679582i | \(0.237839\pi\) | ||||
−0.733599 | + | 0.679582i | \(0.762161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | + | 12.0000i | −1.04053 | + | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.7279 | + | 12.7279i | −1.08742 | + | 1.08742i | −0.0916263 | + | 0.995793i | \(0.529207\pi\) |
−0.995793 | + | 0.0916263i | \(0.970793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000i | 1.35710i | 0.734553 | + | 0.678551i | \(0.237392\pi\) | ||||
−0.734553 | + | 0.678551i | \(0.762608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | + | 11.3137i | −0.673722 | + | 0.952786i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.22183 | + | 18.7782i | 0.265732 | + | 1.54880i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24264 | −0.347571 | −0.173785 | − | 0.984784i | \(-0.555600\pi\) | ||||
−0.173785 | + | 0.984784i | \(0.555600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.75736 | − | 16.2426i | 0.627145 | − | 1.31314i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.00000 | − | 8.00000i | −0.638470 | − | 0.638470i | 0.311708 | − | 0.950178i | \(-0.399099\pi\) |
−0.950178 | + | 0.311708i | \(0.899099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 16.9706 | + | 12.0000i | 1.34585 | + | 0.951662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 16.9706i | − | 1.33747i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.0000 | + | 12.0000i | −0.939913 | + | 0.939913i | −0.998294 | − | 0.0583818i | \(-0.981406\pi\) |
0.0583818 | + | 0.998294i | \(0.481406\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | − | 11.3137i | −0.305888 | − | 0.865181i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.89949 | − | 9.89949i | −0.752645 | − | 0.752645i | 0.222327 | − | 0.974972i | \(-0.428635\pi\) |
−0.974972 | + | 0.222327i | \(0.928635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.41421 | + | 0.414214i | −0.181463 | + | 0.0311342i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.5563 | 1.16274 | 0.581368 | − | 0.813641i | \(-0.302518\pi\) | ||||
0.581368 | + | 0.813641i | \(0.302518\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.2426 | + | 1.75736i | −0.757158 | + | 0.129908i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.00000 | − | 6.00000i | −0.438763 | − | 0.438763i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.2132 | − | 6.00000i | −1.54303 | − | 0.436436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 2.82843i | − | 0.204658i | −0.994751 | − | 0.102329i | \(-0.967371\pi\) | ||
0.994751 | − | 0.102329i | \(-0.0326294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | − | 7.00000i | 0.503871 | − | 0.503871i | −0.408768 | − | 0.912639i | \(-0.634041\pi\) |
0.912639 | + | 0.408768i | \(0.134041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.00000 | − | 5.65685i | −0.564276 | − | 0.399004i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.24264 | + | 4.24264i | 0.297775 | + | 0.297775i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8284 | + | 5.17157i | 0.752628 | + | 0.359449i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.828427 | + | 4.82843i | 0.0567629 | + | 0.330838i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | + | 6.00000i | 0.407307 | + | 0.407307i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.24264 | + | 6.00000i | −0.286691 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.00000 | + | 3.00000i | −0.200895 | + | 0.200895i | −0.800383 | − | 0.599489i | \(-0.795371\pi\) |
0.599489 | + | 0.800383i | \(0.295371\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.24264 | + | 4.24264i | −0.281594 | + | 0.281594i | −0.833744 | − | 0.552151i | \(-0.813807\pi\) |
0.552151 | + | 0.833744i | \(0.313807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.00000 | + | 8.48528i | −0.394771 | + | 0.558291i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.07107 | + | 7.07107i | 0.463241 | + | 0.463241i | 0.899716 | − | 0.436475i | \(-0.143773\pi\) |
−0.436475 | + | 0.899716i | \(0.643773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.92893 | − | 17.0711i | −0.190255 | − | 1.10889i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.4558 | 1.64660 | 0.823301 | − | 0.567605i | \(-0.192130\pi\) | ||||
0.823301 | + | 0.567605i | \(0.192130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.0000 | 1.28831 | 0.644157 | − | 0.764894i | \(-0.277208\pi\) | ||||
0.644157 | + | 0.764894i | \(0.277208\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.2929 | − | 11.7071i | 0.660289 | − | 0.751011i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.65685 | − | 4.00000i | −0.358489 | − | 0.253490i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.7279i | 0.803379i | 0.915776 | + | 0.401690i | \(0.131577\pi\) | ||||
−0.915776 | + | 0.401690i | \(0.868423\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | − | 4.00000i | 0.251478 | − | 0.251478i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.5563 | − | 15.5563i | 0.970378 | − | 0.970378i | −0.0291953 | − | 0.999574i | \(-0.509294\pi\) |
0.999574 | + | 0.0291953i | \(0.00929448\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.00000 | + | 1.41421i | −0.247594 | + | 0.0875376i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.3137 | + | 11.3137i | 0.697633 | + | 0.697633i | 0.963899 | − | 0.266266i | \(-0.0857901\pi\) |
−0.266266 | + | 0.963899i | \(0.585790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.82843 | − | 0.828427i | 0.295495 | − | 0.0506989i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.89949 | −0.603583 | −0.301791 | − | 0.953374i | \(-0.597585\pi\) | ||||
−0.301791 | + | 0.953374i | \(0.597585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | −1.45790 | −0.728948 | − | 0.684569i | \(-0.759990\pi\) | ||||
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | − | 2.00000i | −0.120168 | − | 0.120168i | 0.644465 | − | 0.764634i | \(-0.277080\pi\) |
−0.764634 | + | 0.644465i | \(0.777080\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | + | 2.00000i | −0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 25.4558i | − | 1.51857i | −0.650759 | − | 0.759284i | \(-0.725549\pi\) | ||
0.650759 | − | 0.759284i | \(-0.274451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | − | 4.00000i | 0.237775 | − | 0.237775i | −0.578153 | − | 0.815928i | \(-0.696226\pi\) |
0.815928 | + | 0.578153i | \(0.196226\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9706 | − | 16.9706i | 1.00174 | − | 1.00174i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 19.0000i | − | 1.11765i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 26.0000 | + | 18.3848i | 1.52415 | + | 1.07773i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.65685 | + | 5.65685i | 0.330477 | + | 0.330477i | 0.852768 | − | 0.522291i | \(-0.174922\pi\) |
−0.522291 | + | 0.852768i | \(0.674922\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.58579 | − | 6.41421i | −0.208068 | − | 0.372190i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.0000 | −0.691669 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.55635 | + | 26.5563i | 0.261755 | + | 1.52562i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0000 | − | 10.0000i | −0.570730 | − | 0.570730i | 0.361602 | − | 0.932332i | \(-0.382230\pi\) |
−0.932332 | + | 0.361602i | \(0.882230\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.5563 | − | 22.0000i | 0.884970 | − | 1.25154i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.1127i | − | 1.76424i | −0.471025 | − | 0.882120i | \(-0.656116\pi\) | ||
0.471025 | − | 0.882120i | \(-0.343884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0000 | − | 15.0000i | 0.847850 | − | 0.847850i | −0.142014 | − | 0.989865i | \(-0.545358\pi\) |
0.989865 | + | 0.142014i | \(0.0453579\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.41421 | − | 1.41421i | 0.0794301 | − | 0.0794301i | −0.666276 | − | 0.745706i | \(-0.732113\pi\) |
0.745706 | + | 0.666276i | \(0.232113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.00000i | 0.111979i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00000 | − | 5.65685i | 0.223258 | − | 0.315735i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.9706 | − | 16.9706i | −0.944267 | − | 0.944267i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.92893 | − | 17.0711i | −0.161970 | − | 0.944032i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 33.9411 | 1.87123 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | −0.879440 | −0.439720 | − | 0.898135i | \(-0.644922\pi\) | ||||
−0.439720 | + | 0.898135i | \(0.644922\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.65685 | + | 3.65685i | 0.419593 | + | 0.200394i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.0000 | − | 15.0000i | −0.817102 | − | 0.817102i | 0.168585 | − | 0.985687i | \(-0.446080\pi\) |
−0.985687 | + | 0.168585i | \(0.946080\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.48528 | − | 6.00000i | −0.460857 | − | 0.325875i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.82843i | 0.153168i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.7279 | − | 12.7279i | 0.683271 | − | 0.683271i | −0.277465 | − | 0.960736i | \(-0.589494\pi\) |
0.960736 | + | 0.277465i | \(0.0894943\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2.00000i | − | 0.107058i | −0.998566 | − | 0.0535288i | \(-0.982953\pi\) | ||
0.998566 | − | 0.0535288i | \(-0.0170469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.3848 | − | 18.3848i | −0.978523 | − | 0.978523i | 0.0212513 | − | 0.999774i | \(-0.493235\pi\) |
−0.999774 | + | 0.0212513i | \(0.993235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −43.4558 | + | 7.45584i | −2.29993 | + | 0.394605i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.6274 | 1.19423 | 0.597115 | − | 0.802156i | \(-0.296314\pi\) | ||||
0.597115 | + | 0.802156i | \(0.296314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3640 | − | 2.63604i | 0.806399 | − | 0.138356i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.00000 | + | 7.00000i | 0.365397 | + | 0.365397i | 0.865795 | − | 0.500398i | \(-0.166813\pi\) |
−0.500398 | + | 0.865795i | \(0.666813\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.65685 | + | 16.0000i | 0.294484 | + | 0.832927i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 50.9117i | − | 2.64320i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0000 | + | 12.0000i | −0.621336 | + | 0.621336i | −0.945873 | − | 0.324537i | \(-0.894792\pi\) |
0.324537 | + | 0.945873i | \(0.394792\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0000i | 1.23280i | 0.787434 | + | 0.616399i | \(0.211409\pi\) | ||||
−0.787434 | + | 0.616399i | \(0.788591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.00000 | + | 4.24264i | 0.307389 | + | 0.217357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.65685 | − | 7.65685i | 0.185888 | − | 0.389220i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.7279 | −0.645331 | −0.322666 | − | 0.946513i | \(-0.604579\pi\) | ||||
−0.322666 | + | 0.946513i | \(0.604579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.55635 | + | 26.5563i | 0.229837 | + | 1.33959i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000 | + | 10.0000i | 0.501886 | + | 0.501886i | 0.912024 | − | 0.410138i | \(-0.134519\pi\) |
−0.410138 | + | 0.912024i | \(0.634519\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.9706 | + | 24.0000i | −0.849591 | + | 1.20150i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1421i | 0.706225i | 0.935581 | + | 0.353112i | \(0.114877\pi\) | ||||
−0.935581 | + | 0.353112i | \(0.885123\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.82843 | − | 2.82843i | 0.140200 | − | 0.140200i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.0000 | + | 25.4558i | −0.887875 | + | 1.25564i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.24264 | + | 4.24264i | 0.208767 | + | 0.208767i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.68629 | + | 27.3137i | 0.229489 | + | 1.33756i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.0416 | −1.17451 | −0.587255 | − | 0.809402i | \(-0.699792\pi\) | ||||
−0.587255 | + | 0.809402i | \(0.699792\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.0000 | −1.65706 | −0.828529 | − | 0.559946i | \(-0.810822\pi\) | ||||
−0.828529 | + | 0.559946i | \(0.810822\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.3431 | + | 21.6569i | −0.502901 | + | 1.05299i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | + | 18.0000i | 0.871081 | + | 0.871081i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.6274i | 1.08992i | 0.838461 | + | 0.544962i | \(0.183456\pi\) | ||||
−0.838461 | + | 0.544962i | \(0.816544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.00000 | − | 1.00000i | 0.0480569 | − | 0.0480569i | −0.682670 | − | 0.730727i | \(-0.739181\pi\) |
0.730727 | + | 0.682670i | \(0.239181\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.3137 | − | 11.3137i | 0.541208 | − | 0.541208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 8.00000i | − | 0.381819i | −0.981608 | − | 0.190910i | \(-0.938856\pi\) | ||
0.981608 | − | 0.190910i | \(-0.0611437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.0000 | + | 31.1127i | 0.523810 | + | 1.48156i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.07107 | − | 7.07107i | −0.335957 | − | 0.335957i | 0.518887 | − | 0.854843i | \(-0.326347\pi\) |
−0.854843 | + | 0.518887i | \(0.826347\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.24264 | + | 1.24264i | −0.342565 | + | 0.0587749i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.7990 | −0.934372 | −0.467186 | − | 0.884159i | \(-0.654732\pi\) | ||||
−0.467186 | + | 0.884159i | \(0.654732\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.00000 | 0.376705 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.6569 | − | 2.34315i | 0.641655 | − | 0.110091i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.00000 | − | 1.00000i | −0.0467780 | − | 0.0467780i | 0.683331 | − | 0.730109i | \(-0.260531\pi\) |
−0.730109 | + | 0.683331i | \(0.760531\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.48528 | − | 30.0000i | 0.396059 | − | 1.40028i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 32.5269i | − | 1.51493i | −0.652876 | − | 0.757465i | \(-0.726438\pi\) | ||
0.652876 | − | 0.757465i | \(-0.273562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.00000 | + | 1.00000i | −0.0464739 | + | 0.0464739i | −0.729962 | − | 0.683488i | \(-0.760462\pi\) |
0.683488 | + | 0.729962i | \(0.260462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.4558 | + | 25.4558i | −1.17796 | + | 1.17796i | −0.197692 | + | 0.980264i | \(0.563345\pi\) |
−0.980264 | + | 0.197692i | \(0.936655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.0000 | − | 11.3137i | −0.737241 | − | 0.521308i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.82843 | − | 2.82843i | −0.130051 | − | 0.130051i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.4853 | + | 15.5147i | 1.48740 | + | 0.710370i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.82843 | −0.129234 | −0.0646171 | − | 0.997910i | \(-0.520583\pi\) | ||||
−0.0646171 | + | 0.997910i | \(0.520583\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.97056 | − | 28.9706i | −0.226168 | − | 1.31821i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00000 | + | 3.00000i | 0.135943 | + | 0.135943i | 0.771804 | − | 0.635861i | \(-0.219355\pi\) |
−0.635861 | + | 0.771804i | \(0.719355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.9706 | + | 24.0000i | −0.767435 | + | 1.08532i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5563i | 0.702048i | 0.936366 | + | 0.351024i | \(0.114166\pi\) | ||||
−0.936366 | + | 0.351024i | \(0.885834\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 6.00000i | −0.270226 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.48528 | − | 8.48528i | 0.380617 | − | 0.380617i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.0000i | − | 0.895323i | −0.894203 | − | 0.447661i | \(-0.852257\pi\) | ||
0.894203 | − | 0.447661i | \(-0.147743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | − | 25.4558i | −1.13502 | − | 1.13502i | −0.989330 | − | 0.145690i | \(-0.953460\pi\) |
−0.145690 | − | 0.989330i | \(-0.546540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.80761 | + | 22.1924i | 0.169102 | + | 0.985599i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.1838 | 1.69247 | 0.846233 | − | 0.532813i | \(-0.178865\pi\) | ||||
0.846233 | + | 0.532813i | \(0.178865\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.0000 | 0.796273 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.1421 | − | 18.1421i | −0.447786 | − | 0.800995i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 8.00000i | 0.351840 | + | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.7990 | − | 14.0000i | −0.869079 | − | 0.614532i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.48528i | 0.371747i | 0.982574 | + | 0.185873i | \(0.0595115\pi\) | ||||
−0.982574 | + | 0.185873i | \(0.940489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.0000 | + | 24.0000i | −1.04945 | + | 1.04945i | −0.0507346 | + | 0.998712i | \(0.516156\pi\) |
−0.998712 | + | 0.0507346i | \(0.983844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.48528 | + | 8.48528i | −0.369625 | + | 0.369625i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 7.00000i | − | 0.304348i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | + | 1.41421i | −0.173585 | + | 0.0613716i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 26.5563 | − | 4.55635i | 1.14599 | − | 0.196621i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5563 | 0.670059 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.0000 | 0.601907 | 0.300954 | − | 0.953639i | \(-0.402695\pi\) | ||||
0.300954 | + | 0.953639i | \(0.402695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.0711 | − | 2.92893i | 0.732590 | − | 0.125693i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.0000 | − | 30.0000i | −1.28271 | − | 1.28271i | −0.939121 | − | 0.343586i | \(-0.888358\pi\) |
−0.343586 | − | 0.939121i | \(-0.611642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.9706 | + | 6.00000i | −0.724286 | + | 0.256074i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.65685i | 0.240990i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.0000 | + | 30.0000i | −1.27573 | + | 1.27573i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.9706 | + | 16.9706i | −0.719066 | + | 0.719066i | −0.968414 | − | 0.249348i | \(-0.919784\pi\) |
0.249348 | + | 0.968414i | \(0.419784\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.0000 | − | 8.48528i | −0.506640 | − | 0.358249i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.0416 | + | 24.0416i | 1.01323 | + | 1.01323i | 0.999911 | + | 0.0133227i | \(0.00424086\pi\) |
0.0133227 | + | 0.999911i | \(0.495759\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −37.9706 | − | 4.02944i | −1.59461 | − | 0.169220i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1421 | −0.592869 | −0.296435 | − | 0.955053i | \(-0.595798\pi\) | ||||
−0.296435 | + | 0.955053i | \(0.595798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.828427 | − | 4.82843i | −0.0346080 | − | 0.201710i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.0000 | − | 21.0000i | −0.874241 | − | 0.874241i | 0.118690 | − | 0.992931i | \(-0.462131\pi\) |
−0.992931 | + | 0.118690i | \(0.962131\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.89949 | − | 14.0000i | 0.411409 | − | 0.581820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.9706i | 0.704058i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | − | 12.0000i | 0.496989 | − | 0.496989i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.7990 | + | 19.7990i | −0.817192 | + | 0.817192i | −0.985700 | − | 0.168508i | \(-0.946105\pi\) |
0.168508 | + | 0.985700i | \(0.446105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.41421 | + | 1.41421i | 0.0580748 | + | 0.0580748i | 0.735548 | − | 0.677473i | \(-0.236925\pi\) |
−0.677473 | + | 0.735548i | \(0.736925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3137 | 0.462266 | 0.231133 | − | 0.972922i | \(-0.425757\pi\) | ||||
0.231133 | + | 0.972922i | \(0.425757\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −15.3137 | − | 7.31371i | −0.623622 | − | 0.297837i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.0000 | + | 25.0000i | 1.01472 | + | 1.01472i | 0.999890 | + | 0.0148286i | \(0.00472028\pi\) |
0.0148286 | + | 0.999890i | \(0.495280\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.48528 | + | 6.00000i | 0.343841 | + | 0.243132i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.0000 | − | 30.0000i | 1.21169 | − | 1.21169i | 0.241218 | − | 0.970471i | \(-0.422453\pi\) |
0.970471 | − | 0.241218i | \(-0.0775467\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.24264 | + | 4.24264i | −0.170802 | + | 0.170802i | −0.787332 | − | 0.616530i | \(-0.788538\pi\) |
0.616530 | + | 0.787332i | \(0.288538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 48.0000i | 1.92928i | 0.263566 | + | 0.964641i | \(0.415101\pi\) | ||||
−0.263566 | + | 0.964641i | \(0.584899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.0000 | + | 5.65685i | 0.802572 | + | 0.227002i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.48528 | − | 8.48528i | −0.339956 | − | 0.339956i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.65685 | + | 1.65685i | −0.385658 | + | 0.0661684i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.9706 | 0.676661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.0000 | 1.35352 | 0.676759 | − | 0.736204i | \(-0.263384\pi\) | ||||
0.676759 | + | 0.736204i | \(0.263384\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.3137 | + | 4.68629i | −1.08562 | + | 0.186263i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.82843 | + | 8.00000i | 0.111891 | + | 0.316475i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.2843i | 1.11716i | 0.829450 | + | 0.558581i | \(0.188654\pi\) | ||||
−0.829450 | + | 0.558581i | \(0.811346\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.00000 | + | 8.00000i | −0.315489 | + | 0.315489i | −0.847032 | − | 0.531542i | \(-0.821613\pi\) |
0.531542 | + | 0.847032i | \(0.321613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.82843 | + | 2.82843i | −0.111197 | + | 0.111197i | −0.760516 | − | 0.649319i | \(-0.775054\pi\) |
0.649319 | + | 0.760516i | \(0.275054\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.00000i | 0.0785069i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | + | 8.48528i | 0.470317 | + | 0.332564i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.24264 | − | 4.24264i | −0.166027 | − | 0.166027i | 0.619203 | − | 0.785231i | \(-0.287456\pi\) |
−0.785231 | + | 0.619203i | \(0.787456\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.48528 | + | 11.4853i | −0.214001 | + | 0.448084i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.6690 | −1.81797 | −0.908984 | − | 0.416831i | \(-0.863141\pi\) | ||||
−0.908984 | + | 0.416831i | \(0.863141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | − | 4.00000i | −0.154881 | − | 0.154881i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.24264 | + | 6.00000i | −0.164030 | + | 0.231973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.48528i | 0.327571i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0000 | − | 19.0000i | 0.732396 | − | 0.732396i | −0.238698 | − | 0.971094i | \(-0.576721\pi\) |
0.971094 | + | 0.238698i | \(0.0767205\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.3848 | + | 18.3848i | −0.706584 | + | 0.706584i | −0.965815 | − | 0.259231i | \(-0.916531\pi\) |
0.259231 | + | 0.965815i | \(0.416531\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 78.0000i | − | 2.99337i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | + | 8.48528i | −0.229920 | + | 0.325157i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.4558 | + | 25.4558i | 0.974041 | + | 0.974041i | 0.999671 | − | 0.0256307i | \(-0.00815939\pi\) |
−0.0256307 | + | 0.999671i | \(0.508159\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.75736 | − | 10.2426i | −0.0670474 | − | 0.390781i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.75736 | + | 16.2426i | −0.294678 | + | 0.617007i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | + | 24.0000i | 0.909065 | + | 0.909065i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.1421 | + | 10.0000i | 0.534905 | + | 0.378235i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41421i | 0.0534141i | 0.999643 | + | 0.0267071i | \(0.00850213\pi\) | ||||
−0.999643 | + | 0.0267071i | \(0.991498\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | − | 8.00000i | 0.301726 | − | 0.301726i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 46.6690 | − | 46.6690i | 1.75517 | − | 1.75517i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 6.00000i | − | 0.225335i | −0.993633 | − | 0.112667i | \(-0.964061\pi\) | ||
0.993633 | − | 0.112667i | \(-0.0359394\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0000 | − | 28.2843i | −0.375029 | − | 1.06074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.65685 | − | 5.65685i | −0.211851 | − | 0.211851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 43.4558 | − | 7.45584i | 1.62289 | − | 0.278444i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.2548 | −1.68772 | −0.843860 | − | 0.536563i | \(-0.819722\pi\) | ||||
−0.843860 | + | 0.536563i | \(0.819722\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −66.0000 | −2.45797 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 34.1421 | − | 5.85786i | 1.26976 | − | 0.217856i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0000 | + | 15.0000i | 0.556319 | + | 0.556319i | 0.928257 | − | 0.371938i | \(-0.121307\pi\) |
−0.371938 | + | 0.928257i | \(0.621307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | − | 23.0000i | 0.523783 | − | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 16.9706i | − | 0.627679i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | + | 14.0000i | −0.517102 | + | 0.517102i | −0.916693 | − | 0.399592i | \(-0.869152\pi\) |
0.399592 | + | 0.916693i | \(0.369152\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.65685 | + | 5.65685i | −0.208373 | + | 0.208373i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0000i | 0.588570i | 0.955718 | + | 0.294285i | \(0.0950814\pi\) | ||||
−0.955718 | + | 0.294285i | \(0.904919\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4558 | − | 25.4558i | −0.933884 | − | 0.933884i | 0.0640616 | − | 0.997946i | \(-0.479595\pi\) |
−0.997946 | + | 0.0640616i | \(0.979595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8284 | − | 5.17157i | −0.396191 | − | 0.189218i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.9706 | −0.620091 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.0000 | −1.09472 | −0.547358 | − | 0.836899i | \(-0.684366\pi\) | ||||
−0.547358 | + | 0.836899i | \(0.684366\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.72792 | + | 21.7279i | 0.135853 | + | 0.791809i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.00000 | + | 6.00000i | 0.218074 | + | 0.218074i | 0.807686 | − | 0.589613i | \(-0.200720\pi\) |
−0.589613 | + | 0.807686i | \(0.700720\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.65685 | − | 8.00000i | 0.205331 | − | 0.290382i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.7990i | − | 0.717713i | −0.933393 | − | 0.358856i | \(-0.883167\pi\) | ||
0.933393 | − | 0.358856i | \(-0.116833\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −30.0000 | + | 30.0000i | −1.08607 | + | 1.08607i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0000i | 0.360609i | 0.983611 | + | 0.180305i | \(0.0577084\pi\) | ||||
−0.983611 | + | 0.180305i | \(0.942292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | − | 31.1127i | 0.792311 | − | 1.12050i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.3848 | − | 18.3848i | −0.661254 | − | 0.661254i | 0.294421 | − | 0.955676i | \(-0.404873\pi\) |
−0.955676 | + | 0.294421i | \(0.904873\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.51472 | − | 20.4853i | −0.126090 | − | 0.734905i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.6274 | 0.810711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.41421 | + | 3.58579i | −0.229225 | + | 0.128146i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0000 | + | 12.0000i | 0.427754 | + | 0.427754i | 0.887863 | − | 0.460109i | \(-0.152190\pi\) |
−0.460109 | + | 0.887863i | \(0.652190\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6274 | + | 16.0000i | 0.805557 | + | 0.569615i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.4558i | 0.905106i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.2132 | − | 21.2132i | 0.751410 | − | 0.751410i | −0.223332 | − | 0.974742i | \(-0.571693\pi\) |
0.974742 | + | 0.223332i | \(0.0716935\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.0000i | 1.69812i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.00000 | − | 2.82843i | 0.282666 | − | 0.0999376i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.24264 | + | 4.24264i | 0.149720 | + | 0.149720i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.8995 | + | 2.89949i | −0.594890 | + | 0.102067i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.2548 | 1.59108 | 0.795538 | − | 0.605904i | \(-0.207189\pi\) | ||||
0.795538 | + | 0.605904i | \(0.207189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.9706 | + | 7.02944i | −1.43690 | + | 0.246533i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.00000 | − | 8.00000i | −0.279885 | − | 0.279885i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 26.8701i | − | 0.937771i | −0.883259 | − | 0.468886i | \(-0.844656\pi\) | ||
0.883259 | − | 0.468886i | \(-0.155344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.0000 | − | 29.0000i | 1.01088 | − | 1.01088i | 0.0109363 | − | 0.999940i | \(-0.496519\pi\) |
0.999940 | − | 0.0109363i | \(-0.00348119\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.7279 | − | 12.7279i | 0.442593 | − | 0.442593i | −0.450289 | − | 0.892883i | \(-0.648679\pi\) |
0.892883 | + | 0.450289i | \(0.148679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000i | 0.486240i | 0.969996 | + | 0.243120i | \(0.0781709\pi\) | ||||
−0.969996 | + | 0.243120i | \(0.921829\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.00000 | − | 2.82843i | −0.138758 | − | 0.0981170i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 46.6690 | + | 46.6690i | 1.61699 | + | 1.61699i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.07107 | + | 5.07107i | −0.313542 | + | 0.175282i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −39.5980 | −1.36707 | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||||
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0000 | −0.931034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.45584 | − | 43.4558i | −0.256793 | − | 1.49670i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.0000 | − | 27.0000i | −0.927731 | − | 0.927731i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.65685 | − | 8.00000i | 0.194143 | − | 0.274559i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.3137i | 0.387829i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0000 | − | 18.0000i | 0.616308 | − | 0.616308i | −0.328274 | − | 0.944582i | \(-0.606467\pi\) |
0.944582 | + | 0.328274i | \(0.106467\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.7279 | + | 12.7279i | −0.434778 | + | 0.434778i | −0.890250 | − | 0.455472i | \(-0.849470\pi\) |
0.455472 | + | 0.890250i | \(0.349470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.0000i | − | 1.36478i | −0.730987 | − | 0.682391i | \(-0.760940\pi\) | ||
0.730987 | − | 0.682391i | \(-0.239060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.0000 | − | 33.9411i | 0.817918 | − | 1.15671i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.4558 | + | 25.4558i | 0.866527 | + | 0.866527i | 0.992086 | − | 0.125559i | \(-0.0400725\pi\) |
−0.125559 | + | 0.992086i | \(0.540072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.56497 | − | 32.4350i | −0.188996 | − | 1.10155i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.1421 | −0.479739 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 49.7696 | + | 23.7696i | 1.68444 | + | 0.804477i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.0000 | − | 36.0000i | −1.21563 | − | 1.21563i | −0.969146 | − | 0.246488i | \(-0.920724\pi\) |
−0.246488 | − | 0.969146i | \(-0.579276\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.3137 | + | 8.00000i | 0.381602 | + | 0.269833i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.7990i | 0.667045i | 0.942742 | + | 0.333522i | \(0.108237\pi\) | ||||
−0.942742 | + | 0.333522i | \(0.891763\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | − | 12.0000i | 0.403832 | − | 0.403832i | −0.475749 | − | 0.879581i | \(-0.657823\pi\) |
0.879581 | + | 0.475749i | \(0.157823\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.7696 | + | 36.7696i | −1.23460 | + | 1.23460i | −0.272423 | + | 0.962178i | \(0.587825\pi\) |
−0.962178 | + | 0.272423i | \(0.912175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 18.0000i | − | 0.603701i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.00000 | − | 9.89949i | −0.268010 | − | 0.331646i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.6274 | + | 22.6274i | 0.757198 | + | 0.757198i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.82843 | 0.0943333 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 72.0000 | 2.39867 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.4853 | + | 3.51472i | −0.681707 | + | 0.116963i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0000 | + | 26.0000i | 0.863316 | + | 0.863316i | 0.991722 | − | 0.128406i | \(-0.0409860\pi\) |
−0.128406 | + | 0.991722i | \(0.540986\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.5563 | + | 44.0000i | 0.515972 | + | 1.45939i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.65685i | 0.187420i | 0.995600 | + | 0.0937100i | \(0.0298726\pi\) | ||||
−0.995600 | + | 0.0937100i | \(0.970127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.00000 | + | 4.00000i | −0.132381 | + | 0.132381i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46.6690 | − | 46.6690i | 1.54115 | − | 1.54115i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.00000i | − | 0.0659739i | −0.999456 | − | 0.0329870i | \(-0.989498\pi\) | ||
0.999456 | − | 0.0329870i | \(-0.0105020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | − | 14.1421i | −0.659022 | − | 0.465999i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.1127 | − | 42.1127i | 0.660588 | − | 1.38316i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.7696 | −1.20637 | −0.603185 | − | 0.797601i | \(-0.706102\pi\) | ||||
−0.603185 | + | 0.797601i | \(0.706102\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.0000 | 1.44204 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.11270 | − | 53.1127i | −0.298336 | − | 1.73883i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.0000 | − | 11.0000i | −0.359354 | − | 0.359354i | 0.504221 | − | 0.863575i | \(-0.331780\pi\) |
−0.863575 | + | 0.504221i | \(0.831780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.2132 | − | 30.0000i | 0.692267 | − | 0.979013i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.1838i | 1.24476i | 0.782717 | + | 0.622378i | \(0.213833\pi\) | ||||
−0.782717 | + | 0.622378i | \(0.786167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | + | 16.0000i | −0.521032 | + | 0.521032i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5563 | + | 15.5563i | −0.505513 | + | 0.505513i | −0.913146 | − | 0.407633i | \(-0.866354\pi\) |
0.407633 | + | 0.913146i | \(0.366354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.00000 | − | 2.82843i | 0.0648544 | − | 0.0917180i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.2132 | + | 21.2132i | 0.687163 | + | 0.687163i | 0.961604 | − | 0.274441i | \(-0.0884928\pi\) |
−0.274441 | + | 0.961604i | \(0.588493\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.585786 | + | 3.41421i | 0.0189358 | + | 0.110366i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 76.3675 | 2.46604 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.17157 | − | 10.8284i | 0.166652 | − | 0.348941i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.0000 | − | 15.0000i | −0.482367 | − | 0.482367i | 0.423520 | − | 0.905887i | \(-0.360795\pi\) |
−0.905887 | + | 0.423520i | \(0.860795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.9411 | − | 24.0000i | −1.09035 | − | 0.770991i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 41.0122i | − | 1.31614i | −0.752955 | − | 0.658072i | \(-0.771372\pi\) | ||
0.752955 | − | 0.658072i | \(-0.228628\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.0000 | − | 48.0000i | 1.53881 | − | 1.53881i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.2132 | + | 21.2132i | −0.678671 | + | 0.678671i | −0.959699 | − | 0.281029i | \(-0.909324\pi\) |
0.281029 | + | 0.959699i | \(0.409324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.00000i | − | 0.127841i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | − | 28.2843i | −0.319275 | − | 0.903047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.48528 | − | 8.48528i | −0.270638 | − | 0.270638i | 0.558719 | − | 0.829357i | \(-0.311293\pi\) |
−0.829357 | + | 0.558719i | \(0.811293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.9411 | − | 9.94113i | 1.84429 | − | 0.316430i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3137 | 0.359755 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.3137 | + | 4.68629i | −0.866774 | + | 0.148715i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0000 | − | 24.0000i | −0.760088 | − | 0.760088i | 0.216250 | − | 0.976338i | \(-0.430617\pi\) |
−0.976338 | + | 0.216250i | \(0.930617\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.1421 | + | 4.00000i | 0.447437 | + | 0.126554i |
(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 | 600.2.r.d.257.2 | 4 | ||
3.2 | odd | 2 | inner | 600.2.r.d.257.1 | 4 | ||
4.3 | odd | 2 | 1200.2.v.c.257.1 | 4 | |||
5.2 | odd | 4 | 120.2.r.a.113.2 | yes | 4 | ||
5.3 | odd | 4 | inner | 600.2.r.d.593.1 | 4 | ||
5.4 | even | 2 | 120.2.r.a.17.1 | ✓ | 4 | ||
12.11 | even | 2 | 1200.2.v.c.257.2 | 4 | |||
15.2 | even | 4 | 120.2.r.a.113.1 | yes | 4 | ||
15.8 | even | 4 | inner | 600.2.r.d.593.2 | 4 | ||
15.14 | odd | 2 | 120.2.r.a.17.2 | yes | 4 | ||
20.3 | even | 4 | 1200.2.v.c.593.2 | 4 | |||
20.7 | even | 4 | 240.2.v.d.113.1 | 4 | |||
20.19 | odd | 2 | 240.2.v.d.17.2 | 4 | |||
40.19 | odd | 2 | 960.2.v.b.257.1 | 4 | |||
40.27 | even | 4 | 960.2.v.b.833.2 | 4 | |||
40.29 | even | 2 | 960.2.v.l.257.2 | 4 | |||
40.37 | odd | 4 | 960.2.v.l.833.1 | 4 | |||
60.23 | odd | 4 | 1200.2.v.c.593.1 | 4 | |||
60.47 | odd | 4 | 240.2.v.d.113.2 | 4 | |||
60.59 | even | 2 | 240.2.v.d.17.1 | 4 | |||
120.29 | odd | 2 | 960.2.v.l.257.1 | 4 | |||
120.59 | even | 2 | 960.2.v.b.257.2 | 4 | |||
120.77 | even | 4 | 960.2.v.l.833.2 | 4 | |||
120.107 | odd | 4 | 960.2.v.b.833.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.2.r.a.17.1 | ✓ | 4 | 5.4 | even | 2 | ||
120.2.r.a.17.2 | yes | 4 | 15.14 | odd | 2 | ||
120.2.r.a.113.1 | yes | 4 | 15.2 | even | 4 | ||
120.2.r.a.113.2 | yes | 4 | 5.2 | odd | 4 | ||
240.2.v.d.17.1 | 4 | 60.59 | even | 2 | |||
240.2.v.d.17.2 | 4 | 20.19 | odd | 2 | |||
240.2.v.d.113.1 | 4 | 20.7 | even | 4 | |||
240.2.v.d.113.2 | 4 | 60.47 | odd | 4 | |||
600.2.r.d.257.1 | 4 | 3.2 | odd | 2 | inner | ||
600.2.r.d.257.2 | 4 | 1.1 | even | 1 | trivial | ||
600.2.r.d.593.1 | 4 | 5.3 | odd | 4 | inner | ||
600.2.r.d.593.2 | 4 | 15.8 | even | 4 | inner | ||
960.2.v.b.257.1 | 4 | 40.19 | odd | 2 | |||
960.2.v.b.257.2 | 4 | 120.59 | even | 2 | |||
960.2.v.b.833.1 | 4 | 120.107 | odd | 4 | |||
960.2.v.b.833.2 | 4 | 40.27 | even | 4 | |||
960.2.v.l.257.1 | 4 | 120.29 | odd | 2 | |||
960.2.v.l.257.2 | 4 | 40.29 | even | 2 | |||
960.2.v.l.833.1 | 4 | 40.37 | odd | 4 | |||
960.2.v.l.833.2 | 4 | 120.77 | even | 4 | |||
1200.2.v.c.257.1 | 4 | 4.3 | odd | 2 | |||
1200.2.v.c.257.2 | 4 | 12.11 | even | 2 | |||
1200.2.v.c.593.1 | 4 | 60.23 | odd | 4 | |||
1200.2.v.c.593.2 | 4 | 20.3 | even | 4 |