Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,2,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.39738203537\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.3 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.2.b.c.99.2 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.618034i | 0.437016i | 0.975835 | + | 0.218508i | \(0.0701190\pi\) | ||||
−0.975835 | + | 0.218508i | \(0.929881\pi\) | |||||||
\(3\) | − 3.23607i | − 1.86834i | −0.356822 | − | 0.934172i | \(-0.616140\pi\) | ||||
0.356822 | − | 0.934172i | \(-0.383860\pi\) | |||||||
\(4\) | 1.61803 | 0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | 0.816497 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | −7.47214 | −2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.236068 | −0.0711772 | −0.0355886 | − | 0.999367i | \(-0.511331\pi\) | ||||
−0.0355886 | + | 0.999367i | \(0.511331\pi\) | |||||||
\(12\) | − 5.23607i | − 1.51152i | ||||||||
\(13\) | 1.23607i | 0.342824i | 0.985199 | + | 0.171412i | \(0.0548329\pi\) | ||||
−0.985199 | + | 0.171412i | \(0.945167\pi\) | |||||||
\(14\) | 0.618034 | 0.165177 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | − 2.47214i | − 0.599581i | −0.954005 | − | 0.299791i | \(-0.903083\pi\) | ||||
0.954005 | − | 0.299791i | \(-0.0969168\pi\) | |||||||
\(18\) | − 4.61803i | − 1.08848i | ||||||||
\(19\) | 4.47214 | 1.02598 | 0.512989 | − | 0.858395i | \(-0.328538\pi\) | ||||
0.512989 | + | 0.858395i | \(0.328538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | − 0.145898i | − 0.0311056i | ||||||||
\(23\) | 6.23607i | 1.30031i | 0.759802 | + | 0.650155i | \(0.225296\pi\) | ||||
−0.759802 | + | 0.650155i | \(0.774704\pi\) | |||||||
\(24\) | 7.23607 | 1.47706 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.763932 | −0.149819 | ||||||||
\(27\) | 14.4721i | 2.78516i | ||||||||
\(28\) | − 1.61803i | − 0.305780i | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.70820 | 0.666013 | 0.333007 | − | 0.942925i | \(-0.391937\pi\) | ||||
0.333007 | + | 0.942925i | \(0.391937\pi\) | |||||||
\(32\) | 5.61803i | 0.993137i | ||||||||
\(33\) | 0.763932i | 0.132983i | ||||||||
\(34\) | 1.52786 | 0.262027 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.0902 | −2.01503 | ||||||||
\(37\) | − 3.00000i | − 0.493197i | −0.969118 | − | 0.246598i | \(-0.920687\pi\) | ||||
0.969118 | − | 0.246598i | \(-0.0793129\pi\) | |||||||
\(38\) | 2.76393i | 0.448369i | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.76393 | 0.744001 | 0.372001 | − | 0.928232i | \(-0.378672\pi\) | ||||
0.372001 | + | 0.928232i | \(0.378672\pi\) | |||||||
\(42\) | − 2.00000i | − 0.308607i | ||||||||
\(43\) | 1.76393i | 0.268997i | 0.990914 | + | 0.134499i | \(0.0429424\pi\) | ||||
−0.990914 | + | 0.134499i | \(0.957058\pi\) | |||||||
\(44\) | −0.381966 | −0.0575835 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.85410 | −0.568256 | ||||||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | − 6.00000i | − 0.866025i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | −1.12022 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | 8.47214i | 1.16374i | 0.813283 | + | 0.581869i | \(0.197678\pi\) | ||||
−0.813283 | + | 0.581869i | \(0.802322\pi\) | |||||||
\(54\) | −8.94427 | −1.21716 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | 0.298807 | ||||||||
\(57\) | − 14.4721i | − 1.91688i | ||||||||
\(58\) | − 3.09017i | − 0.405759i | ||||||||
\(59\) | −11.7082 | −1.52428 | −0.762139 | − | 0.647413i | \(-0.775851\pi\) | ||||
−0.762139 | + | 0.647413i | \(0.775851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.70820 | −1.24301 | −0.621504 | − | 0.783411i | \(-0.713478\pi\) | ||||
−0.621504 | + | 0.783411i | \(0.713478\pi\) | |||||||
\(62\) | 2.29180i | 0.291058i | ||||||||
\(63\) | 7.47214i | 0.941401i | ||||||||
\(64\) | 0.236068 | 0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.472136 | −0.0581159 | ||||||||
\(67\) | 4.23607i | 0.517518i | 0.965942 | + | 0.258759i | \(0.0833136\pi\) | ||||
−0.965942 | + | 0.258759i | \(0.916686\pi\) | |||||||
\(68\) | − 4.00000i | − 0.485071i | ||||||||
\(69\) | 20.1803 | 2.42943 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.70820 | 1.03347 | 0.516737 | − | 0.856144i | \(-0.327147\pi\) | ||||
0.516737 | + | 0.856144i | \(0.327147\pi\) | |||||||
\(72\) | − 16.7082i | − 1.96908i | ||||||||
\(73\) | − 8.76393i | − 1.02574i | −0.858466 | − | 0.512870i | \(-0.828582\pi\) | ||||
0.858466 | − | 0.512870i | \(-0.171418\pi\) | |||||||
\(74\) | 1.85410 | 0.215535 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.23607 | 0.830034 | ||||||||
\(77\) | 0.236068i | 0.0269024i | ||||||||
\(78\) | 2.47214i | 0.279914i | ||||||||
\(79\) | 11.1803 | 1.25789 | 0.628943 | − | 0.777451i | \(-0.283488\pi\) | ||||
0.628943 | + | 0.777451i | \(0.283488\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 2.94427i | 0.325140i | ||||||||
\(83\) | − 7.70820i | − 0.846085i | −0.906110 | − | 0.423043i | \(-0.860962\pi\) | ||||
0.906110 | − | 0.423043i | \(-0.139038\pi\) | |||||||
\(84\) | −5.23607 | −0.571302 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.09017 | −0.117556 | ||||||||
\(87\) | 16.1803i | 1.73471i | ||||||||
\(88\) | − 0.527864i | − 0.0562705i | ||||||||
\(89\) | −17.2361 | −1.82702 | −0.913510 | − | 0.406817i | \(-0.866639\pi\) | ||||
−0.913510 | + | 0.406817i | \(0.866639\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | 0.129575 | ||||||||
\(92\) | 10.0902i | 1.05197i | ||||||||
\(93\) | − 12.0000i | − 1.24434i | ||||||||
\(94\) | −1.23607 | −0.127491 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 18.1803 | 1.85552 | ||||||||
\(97\) | − 5.23607i | − 0.531642i | −0.964022 | − | 0.265821i | \(-0.914357\pi\) | ||||
0.964022 | − | 0.265821i | \(-0.0856430\pi\) | |||||||
\(98\) | − 0.618034i | − 0.0624309i | ||||||||
\(99\) | 1.76393 | 0.177282 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.76393 | 0.474029 | 0.237014 | − | 0.971506i | \(-0.423831\pi\) | ||||
0.237014 | + | 0.971506i | \(0.423831\pi\) | |||||||
\(102\) | − 4.94427i | − 0.489556i | ||||||||
\(103\) | 8.47214i | 0.834784i | 0.908726 | + | 0.417392i | \(0.137056\pi\) | ||||
−0.908726 | + | 0.417392i | \(0.862944\pi\) | |||||||
\(104\) | −2.76393 | −0.271026 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.23607 | −0.508572 | ||||||||
\(107\) | − 8.00000i | − 0.773389i | −0.922208 | − | 0.386695i | \(-0.873617\pi\) | ||||
0.922208 | − | 0.386695i | \(-0.126383\pi\) | |||||||
\(108\) | 23.4164i | 2.25324i | ||||||||
\(109\) | −8.41641 | −0.806146 | −0.403073 | − | 0.915168i | \(-0.632058\pi\) | ||||
−0.403073 | + | 0.915168i | \(0.632058\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.70820 | −0.921462 | ||||||||
\(112\) | − 1.85410i | − 0.175196i | ||||||||
\(113\) | − 14.4164i | − 1.35618i | −0.734978 | − | 0.678091i | \(-0.762808\pi\) | ||||
0.734978 | − | 0.678091i | \(-0.237192\pi\) | |||||||
\(114\) | 8.94427 | 0.837708 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.09017 | −0.751153 | ||||||||
\(117\) | − 9.23607i | − 0.853875i | ||||||||
\(118\) | − 7.23607i | − 0.666134i | ||||||||
\(119\) | −2.47214 | −0.226620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9443 | −0.994934 | ||||||||
\(122\) | − 6.00000i | − 0.543214i | ||||||||
\(123\) | − 15.4164i | − 1.39005i | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.61803 | −0.411407 | ||||||||
\(127\) | − 13.6525i | − 1.21146i | −0.795670 | − | 0.605731i | \(-0.792881\pi\) | ||||
0.795670 | − | 0.605731i | \(-0.207119\pi\) | |||||||
\(128\) | 11.3820i | 1.00603i | ||||||||
\(129\) | 5.70820 | 0.502579 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9443 | −1.48043 | −0.740214 | − | 0.672371i | \(-0.765276\pi\) | ||||
−0.740214 | + | 0.672371i | \(0.765276\pi\) | |||||||
\(132\) | 1.23607i | 0.107586i | ||||||||
\(133\) | − 4.47214i | − 0.387783i | ||||||||
\(134\) | −2.61803 | −0.226164 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.52786 | 0.474010 | ||||||||
\(137\) | 10.9443i | 0.935032i | 0.883985 | + | 0.467516i | \(0.154851\pi\) | ||||
−0.883985 | + | 0.467516i | \(0.845149\pi\) | |||||||
\(138\) | 12.4721i | 1.06170i | ||||||||
\(139\) | −10.6525 | −0.903531 | −0.451766 | − | 0.892137i | \(-0.649206\pi\) | ||||
−0.451766 | + | 0.892137i | \(0.649206\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.47214 | 0.545052 | ||||||||
\(142\) | 5.38197i | 0.451645i | ||||||||
\(143\) | − 0.291796i | − 0.0244012i | ||||||||
\(144\) | −13.8541 | −1.15451 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.41641 | 0.448265 | ||||||||
\(147\) | 3.23607i | 0.266906i | ||||||||
\(148\) | − 4.85410i | − 0.399005i | ||||||||
\(149\) | −3.94427 | −0.323127 | −0.161564 | − | 0.986862i | \(-0.551654\pi\) | ||||
−0.161564 | + | 0.986862i | \(0.551654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.2361 | −1.64679 | −0.823394 | − | 0.567470i | \(-0.807922\pi\) | ||||
−0.823394 | + | 0.567470i | \(0.807922\pi\) | |||||||
\(152\) | 10.0000i | 0.811107i | ||||||||
\(153\) | 18.4721i | 1.49338i | ||||||||
\(154\) | −0.145898 | −0.0117568 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.47214 | 0.518186 | ||||||||
\(157\) | − 0.763932i | − 0.0609684i | −0.999535 | − | 0.0304842i | \(-0.990295\pi\) | ||||
0.999535 | − | 0.0304842i | \(-0.00970493\pi\) | |||||||
\(158\) | 6.90983i | 0.549717i | ||||||||
\(159\) | 27.4164 | 2.17426 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.23607 | 0.491471 | ||||||||
\(162\) | 15.0902i | 1.18560i | ||||||||
\(163\) | − 1.52786i | − 0.119672i | −0.998208 | − | 0.0598358i | \(-0.980942\pi\) | ||||
0.998208 | − | 0.0598358i | \(-0.0190577\pi\) | |||||||
\(164\) | 7.70820 | 0.601910 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.76393 | 0.369753 | ||||||||
\(167\) | − 5.23607i | − 0.405179i | −0.979264 | − | 0.202590i | \(-0.935064\pi\) | ||||
0.979264 | − | 0.202590i | \(-0.0649357\pi\) | |||||||
\(168\) | − 7.23607i | − 0.558275i | ||||||||
\(169\) | 11.4721 | 0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33.4164 | −2.55542 | ||||||||
\(172\) | 2.85410i | 0.217623i | ||||||||
\(173\) | − 11.5279i | − 0.876447i | −0.898866 | − | 0.438224i | \(-0.855608\pi\) | ||||
0.898866 | − | 0.438224i | \(-0.144392\pi\) | |||||||
\(174\) | −10.0000 | −0.758098 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.437694 | −0.0329924 | ||||||||
\(177\) | 37.8885i | 2.84788i | ||||||||
\(178\) | − 10.6525i | − 0.798437i | ||||||||
\(179\) | 23.4164 | 1.75022 | 0.875112 | − | 0.483920i | \(-0.160787\pi\) | ||||
0.875112 | + | 0.483920i | \(0.160787\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.18034 | 0.608040 | 0.304020 | − | 0.952666i | \(-0.401671\pi\) | ||||
0.304020 | + | 0.952666i | \(0.401671\pi\) | |||||||
\(182\) | 0.763932i | 0.0566264i | ||||||||
\(183\) | 31.4164i | 2.32237i | ||||||||
\(184\) | −13.9443 | −1.02799 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.41641 | 0.543797 | ||||||||
\(187\) | 0.583592i | 0.0426765i | ||||||||
\(188\) | 3.23607i | 0.236015i | ||||||||
\(189\) | 14.4721 | 1.05269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47214 | 0.468307 | 0.234154 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234154 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(192\) | − 0.763932i | − 0.0551320i | ||||||||
\(193\) | 12.4164i | 0.893753i | 0.894596 | + | 0.446876i | \(0.147464\pi\) | ||||
−0.894596 | + | 0.446876i | \(0.852536\pi\) | |||||||
\(194\) | 3.23607 | 0.232336 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.61803 | −0.115574 | ||||||||
\(197\) | 1.47214i | 0.104885i | 0.998624 | + | 0.0524427i | \(0.0167007\pi\) | ||||
−0.998624 | + | 0.0524427i | \(0.983299\pi\) | |||||||
\(198\) | 1.09017i | 0.0774750i | ||||||||
\(199\) | −7.23607 | −0.512951 | −0.256476 | − | 0.966551i | \(-0.582561\pi\) | ||||
−0.256476 | + | 0.966551i | \(0.582561\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.7082 | 0.966902 | ||||||||
\(202\) | 2.94427i | 0.207158i | ||||||||
\(203\) | 5.00000i | 0.350931i | ||||||||
\(204\) | −12.9443 | −0.906280 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.23607 | −0.364814 | ||||||||
\(207\) | − 46.5967i | − 3.23870i | ||||||||
\(208\) | 2.29180i | 0.158907i | ||||||||
\(209\) | −1.05573 | −0.0730262 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 13.7082i | 0.941483i | ||||||||
\(213\) | − 28.1803i | − 1.93089i | ||||||||
\(214\) | 4.94427 | 0.337983 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −32.3607 | −2.20187 | ||||||||
\(217\) | − 3.70820i | − 0.251729i | ||||||||
\(218\) | − 5.20163i | − 0.352299i | ||||||||
\(219\) | −28.3607 | −1.91644 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.05573 | 0.205551 | ||||||||
\(222\) | − 6.00000i | − 0.402694i | ||||||||
\(223\) | 20.1803i | 1.35138i | 0.737188 | + | 0.675688i | \(0.236153\pi\) | ||||
−0.737188 | + | 0.675688i | \(0.763847\pi\) | |||||||
\(224\) | 5.61803 | 0.375371 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.90983 | 0.592673 | ||||||||
\(227\) | − 21.4164i | − 1.42146i | −0.703466 | − | 0.710728i | \(-0.748365\pi\) | ||||
0.703466 | − | 0.710728i | \(-0.251635\pi\) | |||||||
\(228\) | − 23.4164i | − 1.55079i | ||||||||
\(229\) | 4.47214 | 0.295527 | 0.147764 | − | 0.989023i | \(-0.452793\pi\) | ||||
0.147764 | + | 0.989023i | \(0.452793\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.763932 | 0.0502630 | ||||||||
\(232\) | − 11.1803i | − 0.734025i | ||||||||
\(233\) | 7.94427i | 0.520447i | 0.965548 | + | 0.260223i | \(0.0837962\pi\) | ||||
−0.965548 | + | 0.260223i | \(0.916204\pi\) | |||||||
\(234\) | 5.70820 | 0.373157 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −18.9443 | −1.23317 | ||||||||
\(237\) | − 36.1803i | − 2.35017i | ||||||||
\(238\) | − 1.52786i | − 0.0990367i | ||||||||
\(239\) | 5.52786 | 0.357568 | 0.178784 | − | 0.983888i | \(-0.442784\pi\) | ||||
0.178784 | + | 0.983888i | \(0.442784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.52786 | −0.227250 | −0.113625 | − | 0.993524i | \(-0.536246\pi\) | ||||
−0.113625 | + | 0.993524i | \(0.536246\pi\) | |||||||
\(242\) | − 6.76393i | − 0.434802i | ||||||||
\(243\) | − 35.5967i | − 2.28353i | ||||||||
\(244\) | −15.7082 | −1.00561 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.52786 | 0.607474 | ||||||||
\(247\) | 5.52786i | 0.351730i | ||||||||
\(248\) | 8.29180i | 0.526530i | ||||||||
\(249\) | −24.9443 | −1.58078 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.47214 | 0.408518 | 0.204259 | − | 0.978917i | \(-0.434522\pi\) | ||||
0.204259 | + | 0.978917i | \(0.434522\pi\) | |||||||
\(252\) | 12.0902i | 0.761609i | ||||||||
\(253\) | − 1.47214i | − 0.0925524i | ||||||||
\(254\) | 8.43769 | 0.529428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 12.6525i | 0.789240i | 0.918844 | + | 0.394620i | \(0.129124\pi\) | ||||
−0.918844 | + | 0.394620i | \(0.870876\pi\) | |||||||
\(258\) | 3.52786i | 0.219635i | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 37.3607 | 2.31257 | ||||||||
\(262\) | − 10.4721i | − 0.646971i | ||||||||
\(263\) | 16.2361i | 1.00116i | 0.865691 | + | 0.500579i | \(0.166880\pi\) | ||||
−0.865691 | + | 0.500579i | \(0.833120\pi\) | |||||||
\(264\) | −1.70820 | −0.105133 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.76393 | 0.169468 | ||||||||
\(267\) | 55.7771i | 3.41350i | ||||||||
\(268\) | 6.85410i | 0.418681i | ||||||||
\(269\) | 11.7082 | 0.713862 | 0.356931 | − | 0.934131i | \(-0.383823\pi\) | ||||
0.356931 | + | 0.934131i | \(0.383823\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7082 | 1.44017 | 0.720085 | − | 0.693885i | \(-0.244103\pi\) | ||||
0.720085 | + | 0.693885i | \(0.244103\pi\) | |||||||
\(272\) | − 4.58359i | − 0.277921i | ||||||||
\(273\) | − 4.00000i | − 0.242091i | ||||||||
\(274\) | −6.76393 | −0.408624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 32.6525 | 1.96545 | ||||||||
\(277\) | 19.8885i | 1.19499i | 0.801874 | + | 0.597493i | \(0.203837\pi\) | ||||
−0.801874 | + | 0.597493i | \(0.796163\pi\) | |||||||
\(278\) | − 6.58359i | − 0.394858i | ||||||||
\(279\) | −27.7082 | −1.65885 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.3607 | −0.916341 | −0.458171 | − | 0.888864i | \(-0.651495\pi\) | ||||
−0.458171 | + | 0.888864i | \(0.651495\pi\) | |||||||
\(282\) | 4.00000i | 0.238197i | ||||||||
\(283\) | 17.4164i | 1.03530i | 0.855593 | + | 0.517649i | \(0.173193\pi\) | ||||
−0.855593 | + | 0.517649i | \(0.826807\pi\) | |||||||
\(284\) | 14.0902 | 0.836098 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.180340 | 0.0106637 | ||||||||
\(287\) | − 4.76393i | − 0.281206i | ||||||||
\(288\) | − 41.9787i | − 2.47362i | ||||||||
\(289\) | 10.8885 | 0.640503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.9443 | −0.993291 | ||||||||
\(292\) | − 14.1803i | − 0.829842i | ||||||||
\(293\) | − 31.1246i | − 1.81832i | −0.416448 | − | 0.909160i | \(-0.636725\pi\) | ||||
0.416448 | − | 0.909160i | \(-0.363275\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.70820 | 0.389906 | ||||||||
\(297\) | − 3.41641i | − 0.198240i | ||||||||
\(298\) | − 2.43769i | − 0.141212i | ||||||||
\(299\) | −7.70820 | −0.445777 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.76393 | 0.101671 | ||||||||
\(302\) | − 12.5066i | − 0.719673i | ||||||||
\(303\) | − 15.4164i | − 0.885649i | ||||||||
\(304\) | 8.29180 | 0.475567 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −11.4164 | −0.652633 | ||||||||
\(307\) | − 4.58359i | − 0.261599i | −0.991409 | − | 0.130800i | \(-0.958246\pi\) | ||||
0.991409 | − | 0.130800i | \(-0.0417545\pi\) | |||||||
\(308\) | 0.381966i | 0.0217645i | ||||||||
\(309\) | 27.4164 | 1.55966 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3607 | 1.38137 | 0.690684 | − | 0.723157i | \(-0.257310\pi\) | ||||
0.690684 | + | 0.723157i | \(0.257310\pi\) | |||||||
\(312\) | 8.94427i | 0.506370i | ||||||||
\(313\) | 19.5279i | 1.10378i | 0.833917 | + | 0.551890i | \(0.186093\pi\) | ||||
−0.833917 | + | 0.551890i | \(0.813907\pi\) | |||||||
\(314\) | 0.472136 | 0.0266442 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0902 | 1.01765 | ||||||||
\(317\) | − 25.3607i | − 1.42440i | −0.701978 | − | 0.712199i | \(-0.747699\pi\) | ||||
0.701978 | − | 0.712199i | \(-0.252301\pi\) | |||||||
\(318\) | 16.9443i | 0.950188i | ||||||||
\(319\) | 1.18034 | 0.0660863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −25.8885 | −1.44496 | ||||||||
\(322\) | 3.85410i | 0.214781i | ||||||||
\(323\) | − 11.0557i | − 0.615157i | ||||||||
\(324\) | 39.5066 | 2.19481 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.944272 | 0.0522984 | ||||||||
\(327\) | 27.2361i | 1.50616i | ||||||||
\(328\) | 10.6525i | 0.588185i | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.7082 | −1.35809 | −0.679043 | − | 0.734099i | \(-0.737605\pi\) | ||||
−0.679043 | + | 0.734099i | \(0.737605\pi\) | |||||||
\(332\) | − 12.4721i | − 0.684497i | ||||||||
\(333\) | 22.4164i | 1.22841i | ||||||||
\(334\) | 3.23607 | 0.177070 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −6.00000 | −0.327327 | ||||||||
\(337\) | 16.4721i | 0.897294i | 0.893709 | + | 0.448647i | \(0.148094\pi\) | ||||
−0.893709 | + | 0.448647i | \(0.851906\pi\) | |||||||
\(338\) | 7.09017i | 0.385654i | ||||||||
\(339\) | −46.6525 | −2.53381 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.875388 | −0.0474049 | ||||||||
\(342\) | − 20.6525i | − 1.11676i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | −3.94427 | −0.212661 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.12461 | 0.383022 | ||||||||
\(347\) | − 20.2361i | − 1.08633i | −0.839626 | − | 0.543165i | \(-0.817226\pi\) | ||||
0.839626 | − | 0.543165i | \(-0.182774\pi\) | |||||||
\(348\) | 26.1803i | 1.40341i | ||||||||
\(349\) | −4.47214 | −0.239388 | −0.119694 | − | 0.992811i | \(-0.538191\pi\) | ||||
−0.119694 | + | 0.992811i | \(0.538191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | − 1.32624i | − 0.0706887i | ||||||||
\(353\) | − 2.18034i | − 0.116048i | −0.998315 | − | 0.0580239i | \(-0.981520\pi\) | ||||
0.998315 | − | 0.0580239i | \(-0.0184800\pi\) | |||||||
\(354\) | −23.4164 | −1.24457 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −27.8885 | −1.47809 | ||||||||
\(357\) | 8.00000i | 0.423405i | ||||||||
\(358\) | 14.4721i | 0.764876i | ||||||||
\(359\) | 30.1246 | 1.58992 | 0.794958 | − | 0.606664i | \(-0.207493\pi\) | ||||
0.794958 | + | 0.606664i | \(0.207493\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 5.05573i | 0.265723i | ||||||||
\(363\) | 35.4164i | 1.85888i | ||||||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.4164 | −1.01491 | ||||||||
\(367\) | 37.1246i | 1.93789i | 0.247278 | + | 0.968944i | \(0.420464\pi\) | ||||
−0.247278 | + | 0.968944i | \(0.579536\pi\) | |||||||
\(368\) | 11.5623i | 0.602727i | ||||||||
\(369\) | −35.5967 | −1.85309 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.47214 | 0.439851 | ||||||||
\(372\) | − 19.4164i | − 1.00669i | ||||||||
\(373\) | − 37.8328i | − 1.95891i | −0.201665 | − | 0.979454i | \(-0.564635\pi\) | ||||
0.201665 | − | 0.979454i | \(-0.435365\pi\) | |||||||
\(374\) | −0.360680 | −0.0186503 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.47214 | −0.230633 | ||||||||
\(377\) | − 6.18034i | − 0.318304i | ||||||||
\(378\) | 8.94427i | 0.460044i | ||||||||
\(379\) | 11.1803 | 0.574295 | 0.287148 | − | 0.957886i | \(-0.407293\pi\) | ||||
0.287148 | + | 0.957886i | \(0.407293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −44.1803 | −2.26343 | ||||||||
\(382\) | 4.00000i | 0.204658i | ||||||||
\(383\) | − 33.2361i | − 1.69828i | −0.528165 | − | 0.849142i | \(-0.677120\pi\) | ||||
0.528165 | − | 0.849142i | \(-0.322880\pi\) | |||||||
\(384\) | 36.8328 | 1.87962 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.67376 | −0.390584 | ||||||||
\(387\) | − 13.1803i | − 0.669994i | ||||||||
\(388\) | − 8.47214i | − 0.430108i | ||||||||
\(389\) | −2.88854 | −0.146455 | −0.0732275 | − | 0.997315i | \(-0.523330\pi\) | ||||
−0.0732275 | + | 0.997315i | \(0.523330\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.4164 | 0.779641 | ||||||||
\(392\) | − 2.23607i | − 0.112938i | ||||||||
\(393\) | 54.8328i | 2.76595i | ||||||||
\(394\) | −0.909830 | −0.0458366 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.85410 | 0.143424 | ||||||||
\(397\) | − 9.05573i | − 0.454494i | −0.973837 | − | 0.227247i | \(-0.927028\pi\) | ||||
0.973837 | − | 0.227247i | \(-0.0729725\pi\) | |||||||
\(398\) | − 4.47214i | − 0.224168i | ||||||||
\(399\) | −14.4721 | −0.724513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.52786 | 0.126236 | 0.0631178 | − | 0.998006i | \(-0.479896\pi\) | ||||
0.0631178 | + | 0.998006i | \(0.479896\pi\) | |||||||
\(402\) | 8.47214i | 0.422552i | ||||||||
\(403\) | 4.58359i | 0.228325i | ||||||||
\(404\) | 7.70820 | 0.383497 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.09017 | −0.153363 | ||||||||
\(407\) | 0.708204i | 0.0351044i | ||||||||
\(408\) | − 17.8885i | − 0.885615i | ||||||||
\(409\) | −24.4721 | −1.21007 | −0.605035 | − | 0.796199i | \(-0.706841\pi\) | ||||
−0.605035 | + | 0.796199i | \(0.706841\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.4164 | 1.74696 | ||||||||
\(412\) | 13.7082i | 0.675355i | ||||||||
\(413\) | 11.7082i | 0.576123i | ||||||||
\(414\) | 28.7984 | 1.41536 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.94427 | −0.340471 | ||||||||
\(417\) | 34.4721i | 1.68811i | ||||||||
\(418\) | − 0.652476i | − 0.0319136i | ||||||||
\(419\) | 26.1803 | 1.27899 | 0.639497 | − | 0.768794i | \(-0.279143\pi\) | ||||
0.639497 | + | 0.768794i | \(0.279143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | −0.633581 | −0.316791 | − | 0.948495i | \(-0.602605\pi\) | ||||
−0.316791 | + | 0.948495i | \(0.602605\pi\) | |||||||
\(422\) | 7.41641i | 0.361025i | ||||||||
\(423\) | − 14.9443i | − 0.726615i | ||||||||
\(424\) | −18.9443 | −0.920015 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 17.4164 | 0.843828 | ||||||||
\(427\) | 9.70820i | 0.469813i | ||||||||
\(428\) | − 12.9443i | − 0.625685i | ||||||||
\(429\) | −0.944272 | −0.0455899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.5279 | 0.844288 | 0.422144 | − | 0.906529i | \(-0.361278\pi\) | ||||
0.422144 | + | 0.906529i | \(0.361278\pi\) | |||||||
\(432\) | 26.8328i | 1.29099i | ||||||||
\(433\) | − 28.3607i | − 1.36293i | −0.731852 | − | 0.681464i | \(-0.761344\pi\) | ||||
0.731852 | − | 0.681464i | \(-0.238656\pi\) | |||||||
\(434\) | 2.29180 | 0.110010 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.6180 | −0.652186 | ||||||||
\(437\) | 27.8885i | 1.33409i | ||||||||
\(438\) | − 17.5279i | − 0.837514i | ||||||||
\(439\) | 8.29180 | 0.395746 | 0.197873 | − | 0.980228i | \(-0.436597\pi\) | ||||
0.197873 | + | 0.980228i | \(0.436597\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 1.88854i | 0.0898289i | ||||||||
\(443\) | − 19.4164i | − 0.922501i | −0.887270 | − | 0.461251i | \(-0.847401\pi\) | ||||
0.887270 | − | 0.461251i | \(-0.152599\pi\) | |||||||
\(444\) | −15.7082 | −0.745478 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.4721 | −0.590573 | ||||||||
\(447\) | 12.7639i | 0.603713i | ||||||||
\(448\) | − 0.236068i | − 0.0111532i | ||||||||
\(449\) | −20.5279 | −0.968770 | −0.484385 | − | 0.874855i | \(-0.660957\pi\) | ||||
−0.484385 | + | 0.874855i | \(0.660957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.12461 | −0.0529559 | ||||||||
\(452\) | − 23.3262i | − 1.09717i | ||||||||
\(453\) | 65.4853i | 3.07677i | ||||||||
\(454\) | 13.2361 | 0.621199 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 32.3607 | 1.51543 | ||||||||
\(457\) | 12.5279i | 0.586029i | 0.956108 | + | 0.293014i | \(0.0946584\pi\) | ||||
−0.956108 | + | 0.293014i | \(0.905342\pi\) | |||||||
\(458\) | 2.76393i | 0.129150i | ||||||||
\(459\) | 35.7771 | 1.66993 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.1803 | −0.660444 | −0.330222 | − | 0.943903i | \(-0.607124\pi\) | ||||
−0.330222 | + | 0.943903i | \(0.607124\pi\) | |||||||
\(462\) | 0.472136i | 0.0219658i | ||||||||
\(463\) | − 13.8885i | − 0.645455i | −0.946492 | − | 0.322728i | \(-0.895400\pi\) | ||||
0.946492 | − | 0.322728i | \(-0.104600\pi\) | |||||||
\(464\) | −9.27051 | −0.430373 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.90983 | −0.227443 | ||||||||
\(467\) | − 6.94427i | − 0.321343i | −0.987008 | − | 0.160671i | \(-0.948634\pi\) | ||||
0.987008 | − | 0.160671i | \(-0.0513659\pi\) | |||||||
\(468\) | − 14.9443i | − 0.690799i | ||||||||
\(469\) | 4.23607 | 0.195603 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.47214 | −0.113910 | ||||||||
\(472\) | − 26.1803i | − 1.20505i | ||||||||
\(473\) | − 0.416408i | − 0.0191465i | ||||||||
\(474\) | 22.3607 | 1.02706 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | − 63.3050i | − 2.89853i | ||||||||
\(478\) | 3.41641i | 0.156263i | ||||||||
\(479\) | 26.1803 | 1.19621 | 0.598105 | − | 0.801418i | \(-0.295921\pi\) | ||||
0.598105 | + | 0.801418i | \(0.295921\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.70820 | 0.169080 | ||||||||
\(482\) | − 2.18034i | − 0.0993118i | ||||||||
\(483\) | − 20.1803i | − 0.918237i | ||||||||
\(484\) | −17.7082 | −0.804918 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0000 | 0.997940 | ||||||||
\(487\) | − 5.76393i | − 0.261189i | −0.991436 | − | 0.130594i | \(-0.958311\pi\) | ||||
0.991436 | − | 0.130594i | \(-0.0416885\pi\) | |||||||
\(488\) | − 21.7082i | − 0.982684i | ||||||||
\(489\) | −4.94427 | −0.223588 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.76393 | −0.260123 | −0.130061 | − | 0.991506i | \(-0.541517\pi\) | ||||
−0.130061 | + | 0.991506i | \(0.541517\pi\) | |||||||
\(492\) | − 24.9443i | − 1.12457i | ||||||||
\(493\) | 12.3607i | 0.556697i | ||||||||
\(494\) | −3.41641 | −0.153711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.87539 | 0.308714 | ||||||||
\(497\) | − 8.70820i | − 0.390616i | ||||||||
\(498\) | − 15.4164i | − 0.690826i | ||||||||
\(499\) | −11.0557 | −0.494922 | −0.247461 | − | 0.968898i | \(-0.579596\pi\) | ||||
−0.247461 | + | 0.968898i | \(0.579596\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.9443 | −0.757014 | ||||||||
\(502\) | 4.00000i | 0.178529i | ||||||||
\(503\) | − 8.11146i | − 0.361672i | −0.983513 | − | 0.180836i | \(-0.942120\pi\) | ||||
0.983513 | − | 0.180836i | \(-0.0578803\pi\) | |||||||
\(504\) | −16.7082 | −0.744243 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.909830 | 0.0404469 | ||||||||
\(507\) | − 37.1246i | − 1.64876i | ||||||||
\(508\) | − 22.0902i | − 0.980093i | ||||||||
\(509\) | −40.6525 | −1.80189 | −0.900945 | − | 0.433934i | \(-0.857125\pi\) | ||||
−0.900945 | + | 0.433934i | \(0.857125\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.76393 | −0.387694 | ||||||||
\(512\) | 18.7082i | 0.826794i | ||||||||
\(513\) | 64.7214i | 2.85752i | ||||||||
\(514\) | −7.81966 | −0.344910 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.23607 | 0.406595 | ||||||||
\(517\) | − 0.472136i | − 0.0207645i | ||||||||
\(518\) | − 1.85410i | − 0.0814646i | ||||||||
\(519\) | −37.3050 | −1.63751 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 23.0902i | 1.01063i | ||||||||
\(523\) | 16.3607i | 0.715403i | 0.933836 | + | 0.357701i | \(0.116439\pi\) | ||||
−0.933836 | + | 0.357701i | \(0.883561\pi\) | |||||||
\(524\) | −27.4164 | −1.19769 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.0344 | −0.437522 | ||||||||
\(527\) | − 9.16718i | − 0.399329i | ||||||||
\(528\) | 1.41641i | 0.0616412i | ||||||||
\(529\) | −15.8885 | −0.690806 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 87.4853 | 3.79654 | ||||||||
\(532\) | − 7.23607i | − 0.313723i | ||||||||
\(533\) | 5.88854i | 0.255061i | ||||||||
\(534\) | −34.4721 | −1.49176 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9.47214 | −0.409134 | ||||||||
\(537\) | − 75.7771i | − 3.27002i | ||||||||
\(538\) | 7.23607i | 0.311969i | ||||||||
\(539\) | 0.236068 | 0.0101682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.9443 | 0.685498 | 0.342749 | − | 0.939427i | \(-0.388642\pi\) | ||||
0.342749 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(542\) | 14.6525i | 0.629378i | ||||||||
\(543\) | − 26.4721i | − 1.13603i | ||||||||
\(544\) | 13.8885 | 0.595466 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2.47214 | 0.105798 | ||||||||
\(547\) | 9.76393i | 0.417476i | 0.977972 | + | 0.208738i | \(0.0669355\pi\) | ||||
−0.977972 | + | 0.208738i | \(0.933064\pi\) | |||||||
\(548\) | 17.7082i | 0.756457i | ||||||||
\(549\) | 72.5410 | 3.09598 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.3607 | −0.952597 | ||||||||
\(552\) | 45.1246i | 1.92063i | ||||||||
\(553\) | − 11.1803i | − 0.475436i | ||||||||
\(554\) | −12.2918 | −0.522228 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.2361 | −0.730972 | ||||||||
\(557\) | 9.11146i | 0.386065i | 0.981192 | + | 0.193032i | \(0.0618322\pi\) | ||||
−0.981192 | + | 0.193032i | \(0.938168\pi\) | |||||||
\(558\) | − 17.1246i | − 0.724943i | ||||||||
\(559\) | −2.18034 | −0.0922186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.88854 | 0.0797344 | ||||||||
\(562\) | − 9.49342i | − 0.400456i | ||||||||
\(563\) | 17.4164i | 0.734014i | 0.930218 | + | 0.367007i | \(0.119618\pi\) | ||||
−0.930218 | + | 0.367007i | \(0.880382\pi\) | |||||||
\(564\) | 10.4721 | 0.440956 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.7639 | −0.452442 | ||||||||
\(567\) | − 24.4164i | − 1.02539i | ||||||||
\(568\) | 19.4721i | 0.817033i | ||||||||
\(569\) | 3.94427 | 0.165352 | 0.0826762 | − | 0.996576i | \(-0.473653\pi\) | ||||
0.0826762 | + | 0.996576i | \(0.473653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.5967 | 1.53153 | 0.765763 | − | 0.643123i | \(-0.222362\pi\) | ||||
0.765763 | + | 0.643123i | \(0.222362\pi\) | |||||||
\(572\) | − 0.472136i | − 0.0197410i | ||||||||
\(573\) | − 20.9443i | − 0.874960i | ||||||||
\(574\) | 2.94427 | 0.122892 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.76393 | −0.0734972 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 6.72949i | 0.279910i | ||||||||
\(579\) | 40.1803 | 1.66984 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.70820 | −0.319790 | ||||||||
\(582\) | − 10.4721i | − 0.434084i | ||||||||
\(583\) | − 2.00000i | − 0.0828315i | ||||||||
\(584\) | 19.5967 | 0.810919 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 19.2361 | 0.794635 | ||||||||
\(587\) | 24.7639i | 1.02212i | 0.859546 | + | 0.511058i | \(0.170746\pi\) | ||||
−0.859546 | + | 0.511058i | \(0.829254\pi\) | |||||||
\(588\) | 5.23607i | 0.215932i | ||||||||
\(589\) | 16.5836 | 0.683315 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.76393 | 0.195962 | ||||||||
\(592\) | − 5.56231i | − 0.228609i | ||||||||
\(593\) | − 37.3050i | − 1.53193i | −0.642882 | − | 0.765965i | \(-0.722261\pi\) | ||||
0.642882 | − | 0.765965i | \(-0.277739\pi\) | |||||||
\(594\) | 2.11146 | 0.0866341 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.38197 | −0.261416 | ||||||||
\(597\) | 23.4164i | 0.958370i | ||||||||
\(598\) | − 4.76393i | − 0.194812i | ||||||||
\(599\) | 11.1803 | 0.456816 | 0.228408 | − | 0.973565i | \(-0.426648\pi\) | ||||
0.228408 | + | 0.973565i | \(0.426648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −36.9443 | −1.50699 | −0.753494 | − | 0.657455i | \(-0.771633\pi\) | ||||
−0.753494 | + | 0.657455i | \(0.771633\pi\) | |||||||
\(602\) | 1.09017i | 0.0444320i | ||||||||
\(603\) | − 31.6525i | − 1.28899i | ||||||||
\(604\) | −32.7426 | −1.33228 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.52786 | 0.387043 | ||||||||
\(607\) | 7.12461i | 0.289179i | 0.989492 | + | 0.144590i | \(0.0461862\pi\) | ||||
−0.989492 | + | 0.144590i | \(0.953814\pi\) | |||||||
\(608\) | 25.1246i | 1.01894i | ||||||||
\(609\) | 16.1803 | 0.655660 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.47214 | −0.100012 | ||||||||
\(612\) | 29.8885i | 1.20817i | ||||||||
\(613\) | − 44.4164i | − 1.79396i | −0.442069 | − | 0.896981i | \(-0.645755\pi\) | ||||
0.442069 | − | 0.896981i | \(-0.354245\pi\) | |||||||
\(614\) | 2.83282 | 0.114323 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.527864 | −0.0212682 | ||||||||
\(617\) | 5.94427i | 0.239307i | 0.992816 | + | 0.119654i | \(0.0381784\pi\) | ||||
−0.992816 | + | 0.119654i | \(0.961822\pi\) | |||||||
\(618\) | 16.9443i | 0.681599i | ||||||||
\(619\) | 11.7082 | 0.470592 | 0.235296 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235296 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −90.2492 | −3.62158 | ||||||||
\(622\) | 15.0557i | 0.603680i | ||||||||
\(623\) | 17.2361i | 0.690548i | ||||||||
\(624\) | 7.41641 | 0.296894 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.0689 | −0.482370 | ||||||||
\(627\) | 3.41641i | 0.136438i | ||||||||
\(628\) | − 1.23607i | − 0.0493245i | ||||||||
\(629\) | −7.41641 | −0.295712 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.6525 | 1.10083 | 0.550414 | − | 0.834892i | \(-0.314470\pi\) | ||||
0.550414 | + | 0.834892i | \(0.314470\pi\) | |||||||
\(632\) | 25.0000i | 0.994447i | ||||||||
\(633\) | − 38.8328i | − 1.54347i | ||||||||
\(634\) | 15.6738 | 0.622485 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 44.3607 | 1.75902 | ||||||||
\(637\) | − 1.23607i | − 0.0489748i | ||||||||
\(638\) | 0.729490i | 0.0288808i | ||||||||
\(639\) | −65.0689 | −2.57409 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.8328 | 1.73129 | 0.865646 | − | 0.500656i | \(-0.166908\pi\) | ||||
0.865646 | + | 0.500656i | \(0.166908\pi\) | |||||||
\(642\) | − 16.0000i | − 0.631470i | ||||||||
\(643\) | 18.4721i | 0.728470i | 0.931307 | + | 0.364235i | \(0.118669\pi\) | ||||
−0.931307 | + | 0.364235i | \(0.881331\pi\) | |||||||
\(644\) | 10.0902 | 0.397608 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.83282 | 0.268834 | ||||||||
\(647\) | 19.8885i | 0.781899i | 0.920412 | + | 0.390950i | \(0.127853\pi\) | ||||
−0.920412 | + | 0.390950i | \(0.872147\pi\) | |||||||
\(648\) | 54.5967i | 2.14476i | ||||||||
\(649\) | 2.76393 | 0.108494 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | − 2.47214i | − 0.0968163i | ||||||||
\(653\) | 25.0557i | 0.980506i | 0.871580 | + | 0.490253i | \(0.163096\pi\) | ||||
−0.871580 | + | 0.490253i | \(0.836904\pi\) | |||||||
\(654\) | −16.8328 | −0.658215 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.83282 | 0.344864 | ||||||||
\(657\) | 65.4853i | 2.55482i | ||||||||
\(658\) | 1.23607i | 0.0481869i | ||||||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.7214 | −1.66167 | −0.830834 | − | 0.556520i | \(-0.812136\pi\) | ||||
−0.830834 | + | 0.556520i | \(0.812136\pi\) | |||||||
\(662\) | − 15.2705i | − 0.593505i | ||||||||
\(663\) | − 9.88854i | − 0.384039i | ||||||||
\(664\) | 17.2361 | 0.668889 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.8541 | −0.536836 | ||||||||
\(667\) | − 31.1803i | − 1.20731i | ||||||||
\(668\) | − 8.47214i | − 0.327797i | ||||||||
\(669\) | 65.3050 | 2.52484 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.29180 | 0.0884738 | ||||||||
\(672\) | − 18.1803i | − 0.701322i | ||||||||
\(673\) | 19.5279i | 0.752744i | 0.926469 | + | 0.376372i | \(0.122829\pi\) | ||||
−0.926469 | + | 0.376372i | \(0.877171\pi\) | |||||||
\(674\) | −10.1803 | −0.392132 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.5623 | 0.713935 | ||||||||
\(677\) | 14.3607i | 0.551926i | 0.961168 | + | 0.275963i | \(0.0889967\pi\) | ||||
−0.961168 | + | 0.275963i | \(0.911003\pi\) | |||||||
\(678\) | − 28.8328i | − 1.10732i | ||||||||
\(679\) | −5.23607 | −0.200942 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −69.3050 | −2.65577 | ||||||||
\(682\) | − 0.541020i | − 0.0207167i | ||||||||
\(683\) | 14.1246i | 0.540463i | 0.962795 | + | 0.270232i | \(0.0871003\pi\) | ||||
−0.962795 | + | 0.270232i | \(0.912900\pi\) | |||||||
\(684\) | −54.0689 | −2.06738 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.618034 | −0.0235966 | ||||||||
\(687\) | − 14.4721i | − 0.552146i | ||||||||
\(688\) | 3.27051i | 0.124687i | ||||||||
\(689\) | −10.4721 | −0.398957 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.18034 | −0.159028 | −0.0795138 | − | 0.996834i | \(-0.525337\pi\) | ||||
−0.0795138 | + | 0.996834i | \(0.525337\pi\) | |||||||
\(692\) | − 18.6525i | − 0.709061i | ||||||||
\(693\) | − 1.76393i | − 0.0670062i | ||||||||
\(694\) | 12.5066 | 0.474743 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −36.1803 | −1.37141 | ||||||||
\(697\) | − 11.7771i | − 0.446089i | ||||||||
\(698\) | − 2.76393i | − 0.104616i | ||||||||
\(699\) | 25.7082 | 0.972374 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.0557 | −1.09742 | −0.548710 | − | 0.836013i | \(-0.684881\pi\) | ||||
−0.548710 | + | 0.836013i | \(0.684881\pi\) | |||||||
\(702\) | − 11.0557i | − 0.417272i | ||||||||
\(703\) | − 13.4164i | − 0.506009i | ||||||||
\(704\) | −0.0557281 | −0.00210033 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.34752 | 0.0507147 | ||||||||
\(707\) | − 4.76393i | − 0.179166i | ||||||||
\(708\) | 61.3050i | 2.30398i | ||||||||
\(709\) | 12.1115 | 0.454855 | 0.227428 | − | 0.973795i | \(-0.426968\pi\) | ||||
0.227428 | + | 0.973795i | \(0.426968\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −83.5410 | −3.13303 | ||||||||
\(712\) | − 38.5410i | − 1.44439i | ||||||||
\(713\) | 23.1246i | 0.866024i | ||||||||
\(714\) | −4.94427 | −0.185035 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 37.8885 | 1.41596 | ||||||||
\(717\) | − 17.8885i | − 0.668060i | ||||||||
\(718\) | 18.6180i | 0.694819i | ||||||||
\(719\) | −16.1803 | −0.603425 | −0.301712 | − | 0.953399i | \(-0.597558\pi\) | ||||
−0.301712 | + | 0.953399i | \(0.597558\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.47214 | 0.315519 | ||||||||
\(722\) | 0.618034i | 0.0230008i | ||||||||
\(723\) | 11.4164i | 0.424581i | ||||||||
\(724\) | 13.2361 | 0.491915 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −21.8885 | −0.812360 | ||||||||
\(727\) | 3.05573i | 0.113331i | 0.998393 | + | 0.0566653i | \(0.0180468\pi\) | ||||
−0.998393 | + | 0.0566653i | \(0.981953\pi\) | |||||||
\(728\) | 2.76393i | 0.102438i | ||||||||
\(729\) | −41.9443 | −1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.36068 | 0.161286 | ||||||||
\(732\) | 50.8328i | 1.87883i | ||||||||
\(733\) | 4.00000i | 0.147743i | 0.997268 | + | 0.0738717i | \(0.0235355\pi\) | ||||
−0.997268 | + | 0.0738717i | \(0.976464\pi\) | |||||||
\(734\) | −22.9443 | −0.846889 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −35.0344 | −1.29139 | ||||||||
\(737\) | − 1.00000i | − 0.0368355i | ||||||||
\(738\) | − 22.0000i | − 0.809831i | ||||||||
\(739\) | −25.6525 | −0.943642 | −0.471821 | − | 0.881694i | \(-0.656403\pi\) | ||||
−0.471821 | + | 0.881694i | \(0.656403\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.8885 | 0.657152 | ||||||||
\(742\) | 5.23607i | 0.192222i | ||||||||
\(743\) | − 10.4721i | − 0.384185i | −0.981377 | − | 0.192093i | \(-0.938473\pi\) | ||||
0.981377 | − | 0.192093i | \(-0.0615274\pi\) | |||||||
\(744\) | 26.8328 | 0.983739 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 23.3820 | 0.856075 | ||||||||
\(747\) | 57.5967i | 2.10735i | ||||||||
\(748\) | 0.944272i | 0.0345260i | ||||||||
\(749\) | −8.00000 | −0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.05573 | 0.111505 | 0.0557526 | − | 0.998445i | \(-0.482244\pi\) | ||||
0.0557526 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(752\) | 3.70820i | 0.135224i | ||||||||
\(753\) | − 20.9443i | − 0.763252i | ||||||||
\(754\) | 3.81966 | 0.139104 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 23.4164 | 0.851647 | ||||||||
\(757\) | − 19.5836i | − 0.711778i | −0.934528 | − | 0.355889i | \(-0.884178\pi\) | ||||
0.934528 | − | 0.355889i | \(-0.115822\pi\) | |||||||
\(758\) | 6.90983i | 0.250976i | ||||||||
\(759\) | −4.76393 | −0.172920 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.7771 | 1.00692 | 0.503459 | − | 0.864019i | \(-0.332060\pi\) | ||||
0.503459 | + | 0.864019i | \(0.332060\pi\) | |||||||
\(762\) | − 27.3050i | − 0.989154i | ||||||||
\(763\) | 8.41641i | 0.304694i | ||||||||
\(764\) | 10.4721 | 0.378869 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20.5410 | 0.742177 | ||||||||
\(767\) | − 14.4721i | − 0.522559i | ||||||||
\(768\) | 21.2361i | 0.766291i | ||||||||
\(769\) | 43.0132 | 1.55109 | 0.775547 | − | 0.631290i | \(-0.217474\pi\) | ||||
0.775547 | + | 0.631290i | \(0.217474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40.9443 | 1.47457 | ||||||||
\(772\) | 20.0902i | 0.723061i | ||||||||
\(773\) | 50.1803i | 1.80486i | 0.430835 | + | 0.902431i | \(0.358219\pi\) | ||||
−0.430835 | + | 0.902431i | \(0.641781\pi\) | |||||||
\(774\) | 8.14590 | 0.292798 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.7082 | 0.420300 | ||||||||
\(777\) | 9.70820i | 0.348280i | ||||||||
\(778\) | − 1.78522i | − 0.0640032i | ||||||||
\(779\) | 21.3050 | 0.763329 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.05573 | −0.0735597 | ||||||||
\(782\) | 9.52786i | 0.340716i | ||||||||
\(783\) | − 72.3607i | − 2.58596i | ||||||||
\(784\) | −1.85410 | −0.0662179 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −33.8885 | −1.20876 | ||||||||
\(787\) | − 40.7639i | − 1.45308i | −0.687126 | − | 0.726539i | \(-0.741128\pi\) | ||||
0.687126 | − | 0.726539i | \(-0.258872\pi\) | |||||||
\(788\) | 2.38197i | 0.0848540i | ||||||||
\(789\) | 52.5410 | 1.87051 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.4164 | −0.512588 | ||||||||
\(792\) | 3.94427i | 0.140154i | ||||||||
\(793\) | − 12.0000i | − 0.426132i | ||||||||
\(794\) | 5.59675 | 0.198621 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.7082 | −0.414986 | ||||||||
\(797\) | 35.4164i | 1.25451i | 0.778813 | + | 0.627257i | \(0.215822\pi\) | ||||
−0.778813 | + | 0.627257i | \(0.784178\pi\) | |||||||
\(798\) | − 8.94427i | − 0.316624i | ||||||||
\(799\) | 4.94427 | 0.174916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 128.790 | 4.55058 | ||||||||
\(802\) | 1.56231i | 0.0551669i | ||||||||
\(803\) | 2.06888i | 0.0730093i | ||||||||
\(804\) | 22.1803 | 0.782240 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.83282 | −0.0997817 | ||||||||
\(807\) | − 37.8885i | − 1.33374i | ||||||||
\(808\) | 10.6525i | 0.374753i | ||||||||
\(809\) | −29.4721 | −1.03619 | −0.518093 | − | 0.855325i | \(-0.673358\pi\) | ||||
−0.518093 | + | 0.855325i | \(0.673358\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7214 | −1.50015 | −0.750075 | − | 0.661353i | \(-0.769983\pi\) | ||||
−0.750075 | + | 0.661353i | \(0.769983\pi\) | |||||||
\(812\) | 8.09017i | 0.283909i | ||||||||
\(813\) | − 76.7214i | − 2.69074i | ||||||||
\(814\) | −0.437694 | −0.0153412 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −14.8328 | −0.519252 | ||||||||
\(817\) | 7.88854i | 0.275985i | ||||||||
\(818\) | − 15.1246i | − 0.528820i | ||||||||
\(819\) | −9.23607 | −0.322734 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.8328 | 1.00627 | 0.503136 | − | 0.864207i | \(-0.332179\pi\) | ||||
0.503136 | + | 0.864207i | \(0.332179\pi\) | |||||||
\(822\) | 21.8885i | 0.763451i | ||||||||
\(823\) | − 31.6525i | − 1.10334i | −0.834064 | − | 0.551668i | \(-0.813992\pi\) | ||||
0.834064 | − | 0.551668i | \(-0.186008\pi\) | |||||||
\(824\) | −18.9443 | −0.659955 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.23607 | −0.251775 | ||||||||
\(827\) | − 41.5410i | − 1.44452i | −0.691620 | − | 0.722261i | \(-0.743103\pi\) | ||||
0.691620 | − | 0.722261i | \(-0.256897\pi\) | |||||||
\(828\) | − 75.3951i | − 2.62016i | ||||||||
\(829\) | 7.63932 | 0.265325 | 0.132662 | − | 0.991161i | \(-0.457647\pi\) | ||||
0.132662 | + | 0.991161i | \(0.457647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 64.3607 | 2.23265 | ||||||||
\(832\) | 0.291796i | 0.0101162i | ||||||||
\(833\) | 2.47214i | 0.0856544i | ||||||||
\(834\) | −21.3050 | −0.737730 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.70820 | −0.0590795 | ||||||||
\(837\) | 53.6656i | 1.85496i | ||||||||
\(838\) | 16.1803i | 0.558941i | ||||||||
\(839\) | 30.6525 | 1.05824 | 0.529120 | − | 0.848547i | \(-0.322522\pi\) | ||||
0.529120 | + | 0.848547i | \(0.322522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | − 8.03444i | − 0.276885i | ||||||||
\(843\) | 49.7082i | 1.71204i | ||||||||
\(844\) | 19.4164 | 0.668340 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.23607 | 0.317543 | ||||||||
\(847\) | 10.9443i | 0.376050i | ||||||||
\(848\) | 15.7082i | 0.539422i | ||||||||
\(849\) | 56.3607 | 1.93429 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.7082 | 0.641309 | ||||||||
\(852\) | − 45.5967i | − 1.56212i | ||||||||
\(853\) | 27.4164i | 0.938720i | 0.883007 | + | 0.469360i | \(0.155515\pi\) | ||||
−0.883007 | + | 0.469360i | \(0.844485\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 17.8885 | 0.611418 | ||||||||
\(857\) | 15.8197i | 0.540389i | 0.962806 | + | 0.270195i | \(0.0870881\pi\) | ||||
−0.962806 | + | 0.270195i | \(0.912912\pi\) | |||||||
\(858\) | − 0.583592i | − 0.0199235i | ||||||||
\(859\) | −22.3607 | −0.762937 | −0.381468 | − | 0.924382i | \(-0.624581\pi\) | ||||
−0.381468 | + | 0.924382i | \(0.624581\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.4164 | −0.525390 | ||||||||
\(862\) | 10.8328i | 0.368967i | ||||||||
\(863\) | 18.3475i | 0.624557i | 0.949991 | + | 0.312278i | \(0.101092\pi\) | ||||
−0.949991 | + | 0.312278i | \(0.898908\pi\) | |||||||
\(864\) | −81.3050 | −2.76605 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17.5279 | 0.595621 | ||||||||
\(867\) | − 35.2361i | − 1.19668i | ||||||||
\(868\) | − 6.00000i | − 0.203653i | ||||||||
\(869\) | −2.63932 | −0.0895328 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.23607 | −0.177417 | ||||||||
\(872\) | − 18.8197i | − 0.637314i | ||||||||
\(873\) | 39.1246i | 1.32417i | ||||||||
\(874\) | −17.2361 | −0.583019 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −45.8885 | −1.55043 | ||||||||
\(877\) | − 30.3607i | − 1.02521i | −0.858625 | − | 0.512604i | \(-0.828681\pi\) | ||||
0.858625 | − | 0.512604i | \(-0.171319\pi\) | |||||||
\(878\) | 5.12461i | 0.172947i | ||||||||
\(879\) | −100.721 | −3.39725 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.81966 | 0.196069 | 0.0980347 | − | 0.995183i | \(-0.468744\pi\) | ||||
0.0980347 | + | 0.995183i | \(0.468744\pi\) | |||||||
\(882\) | 4.61803i | 0.155497i | ||||||||
\(883\) | − 1.40325i | − 0.0472232i | −0.999721 | − | 0.0236116i | \(-0.992483\pi\) | ||||
0.999721 | − | 0.0236116i | \(-0.00751650\pi\) | |||||||
\(884\) | 4.94427 | 0.166294 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | 21.3475i | 0.716780i | 0.933572 | + | 0.358390i | \(0.116674\pi\) | ||||
−0.933572 | + | 0.358390i | \(0.883326\pi\) | |||||||
\(888\) | − 21.7082i | − 0.728480i | ||||||||
\(889\) | −13.6525 | −0.457889 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.76393 | −0.193099 | ||||||||
\(892\) | 32.6525i | 1.09329i | ||||||||
\(893\) | 8.94427i | 0.299309i | ||||||||
\(894\) | −7.88854 | −0.263832 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.3820 | 0.380245 | ||||||||
\(897\) | 24.9443i | 0.832865i | ||||||||
\(898\) | − 12.6869i | − 0.423368i | ||||||||
\(899\) | −18.5410 | −0.618378 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9443 | 0.697755 | ||||||||
\(902\) | − 0.695048i | − 0.0231426i | ||||||||
\(903\) | − 5.70820i | − 0.189957i | ||||||||
\(904\) | 32.2361 | 1.07216 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −40.4721 | −1.34460 | ||||||||
\(907\) | − 34.8328i | − 1.15660i | −0.815823 | − | 0.578302i | \(-0.803715\pi\) | ||||
0.815823 | − | 0.578302i | \(-0.196285\pi\) | |||||||
\(908\) | − 34.6525i | − 1.14998i | ||||||||
\(909\) | −35.5967 | −1.18067 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.819660 | 0.0271566 | 0.0135783 | − | 0.999908i | \(-0.495678\pi\) | ||||
0.0135783 | + | 0.999908i | \(0.495678\pi\) | |||||||
\(912\) | − 26.8328i | − 0.888523i | ||||||||
\(913\) | 1.81966i | 0.0602220i | ||||||||
\(914\) | −7.74265 | −0.256104 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.23607 | 0.239086 | ||||||||
\(917\) | 16.9443i | 0.559549i | ||||||||
\(918\) | 22.1115i | 0.729787i | ||||||||
\(919\) | 27.7639 | 0.915848 | 0.457924 | − | 0.888991i | \(-0.348593\pi\) | ||||
0.457924 | + | 0.888991i | \(0.348593\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.8328 | −0.488758 | ||||||||
\(922\) | − 8.76393i | − 0.288625i | ||||||||
\(923\) | 10.7639i | 0.354299i | ||||||||
\(924\) | 1.23607 | 0.0406637 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.58359 | 0.282074 | ||||||||
\(927\) | − 63.3050i | − 2.07921i | ||||||||
\(928\) | − 28.0902i | − 0.922105i | ||||||||
\(929\) | −38.2918 | −1.25631 | −0.628157 | − | 0.778087i | \(-0.716190\pi\) | ||||
−0.628157 | + | 0.778087i | \(0.716190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.47214 | −0.146568 | ||||||||
\(932\) | 12.8541i | 0.421050i | ||||||||
\(933\) | − 78.8328i | − 2.58087i | ||||||||
\(934\) | 4.29180 | 0.140432 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.6525 | 0.675047 | ||||||||
\(937\) | − 35.2361i | − 1.15111i | −0.817762 | − | 0.575556i | \(-0.804786\pi\) | ||||
0.817762 | − | 0.575556i | \(-0.195214\pi\) | |||||||
\(938\) | 2.61803i | 0.0854818i | ||||||||
\(939\) | 63.1935 | 2.06224 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.23607 | −0.170691 | −0.0853455 | − | 0.996351i | \(-0.527199\pi\) | ||||
−0.0853455 | + | 0.996351i | \(0.527199\pi\) | |||||||
\(942\) | − 1.52786i | − 0.0497805i | ||||||||
\(943\) | 29.7082i | 0.967432i | ||||||||
\(944\) | −21.7082 | −0.706542 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.257354 | 0.00836731 | ||||||||
\(947\) | − 34.8328i | − 1.13191i | −0.824435 | − | 0.565957i | \(-0.808507\pi\) | ||||
0.824435 | − | 0.565957i | \(-0.191493\pi\) | |||||||
\(948\) | − 58.5410i | − 1.90132i | ||||||||
\(949\) | 10.8328 | 0.351648 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −82.0689 | −2.66127 | ||||||||
\(952\) | − 5.52786i | − 0.179159i | ||||||||
\(953\) | 3.47214i | 0.112474i | 0.998417 | + | 0.0562368i | \(0.0179102\pi\) | ||||
−0.998417 | + | 0.0562368i | \(0.982090\pi\) | |||||||
\(954\) | 39.1246 | 1.26671 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.94427 | 0.289278 | ||||||||
\(957\) | − 3.81966i | − 0.123472i | ||||||||
\(958\) | 16.1803i | 0.522763i | ||||||||
\(959\) | 10.9443 | 0.353409 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.2492 | −0.556427 | ||||||||
\(962\) | 2.29180i | 0.0738905i | ||||||||
\(963\) | 59.7771i | 1.92629i | ||||||||
\(964\) | −5.70820 | −0.183849 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 12.4721 | 0.401284 | ||||||||
\(967\) | 14.1115i | 0.453794i | 0.973919 | + | 0.226897i | \(0.0728580\pi\) | ||||
−0.973919 | + | 0.226897i | \(0.927142\pi\) | |||||||
\(968\) | − 24.4721i | − 0.786564i | ||||||||
\(969\) | −35.7771 | −1.14933 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | − 57.5967i | − 1.84742i | ||||||||
\(973\) | 10.6525i | 0.341503i | ||||||||
\(974\) | 3.56231 | 0.114144 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.0000 | −0.576166 | ||||||||
\(977\) | 11.4721i | 0.367026i | 0.983017 | + | 0.183513i | \(0.0587470\pi\) | ||||
−0.983017 | + | 0.183513i | \(0.941253\pi\) | |||||||
\(978\) | − 3.05573i | − 0.0977114i | ||||||||
\(979\) | 4.06888 | 0.130042 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 62.8885 | 2.00788 | ||||||||
\(982\) | − 3.56231i | − 0.113678i | ||||||||
\(983\) | − 34.5410i | − 1.10169i | −0.834608 | − | 0.550844i | \(-0.814306\pi\) | ||||
0.834608 | − | 0.550844i | \(-0.185694\pi\) | |||||||
\(984\) | 34.4721 | 1.09893 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.63932 | −0.243286 | ||||||||
\(987\) | − 6.47214i | − 0.206010i | ||||||||
\(988\) | 8.94427i | 0.284555i | ||||||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1803 | 0.418687 | 0.209344 | − | 0.977842i | \(-0.432867\pi\) | ||||
0.209344 | + | 0.977842i | \(0.432867\pi\) | |||||||
\(992\) | 20.8328i | 0.661443i | ||||||||
\(993\) | 79.9574i | 2.53737i | ||||||||
\(994\) | 5.38197 | 0.170706 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −40.3607 | −1.27888 | ||||||||
\(997\) | 45.4164i | 1.43835i | 0.694828 | + | 0.719176i | \(0.255481\pi\) | ||||
−0.694828 | + | 0.719176i | \(0.744519\pi\) | |||||||
\(998\) | − 6.83282i | − 0.216289i | ||||||||
\(999\) | 43.4164 | 1.37363 |
(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 | 175.2.b.c.99.3 | 4 | ||
3.2 | odd | 2 | 1575.2.d.k.1324.2 | 4 | |||
4.3 | odd | 2 | 2800.2.g.s.449.4 | 4 | |||
5.2 | odd | 4 | 175.2.a.e.1.1 | yes | 2 | ||
5.3 | odd | 4 | 175.2.a.d.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 175.2.b.c.99.2 | 4 | ||
7.6 | odd | 2 | 1225.2.b.k.99.3 | 4 | |||
15.2 | even | 4 | 1575.2.a.n.1.2 | 2 | |||
15.8 | even | 4 | 1575.2.a.s.1.1 | 2 | |||
15.14 | odd | 2 | 1575.2.d.k.1324.3 | 4 | |||
20.3 | even | 4 | 2800.2.a.bh.1.1 | 2 | |||
20.7 | even | 4 | 2800.2.a.bp.1.2 | 2 | |||
20.19 | odd | 2 | 2800.2.g.s.449.1 | 4 | |||
35.13 | even | 4 | 1225.2.a.n.1.2 | 2 | |||
35.27 | even | 4 | 1225.2.a.u.1.1 | 2 | |||
35.34 | odd | 2 | 1225.2.b.k.99.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.a.d.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
175.2.a.e.1.1 | yes | 2 | 5.2 | odd | 4 | ||
175.2.b.c.99.2 | 4 | 5.4 | even | 2 | inner | ||
175.2.b.c.99.3 | 4 | 1.1 | even | 1 | trivial | ||
1225.2.a.n.1.2 | 2 | 35.13 | even | 4 | |||
1225.2.a.u.1.1 | 2 | 35.27 | even | 4 | |||
1225.2.b.k.99.2 | 4 | 35.34 | odd | 2 | |||
1225.2.b.k.99.3 | 4 | 7.6 | odd | 2 | |||
1575.2.a.n.1.2 | 2 | 15.2 | even | 4 | |||
1575.2.a.s.1.1 | 2 | 15.8 | even | 4 | |||
1575.2.d.k.1324.2 | 4 | 3.2 | odd | 2 | |||
1575.2.d.k.1324.3 | 4 | 15.14 | odd | 2 | |||
2800.2.a.bh.1.1 | 2 | 20.3 | even | 4 | |||
2800.2.a.bp.1.2 | 2 | 20.7 | even | 4 | |||
2800.2.g.s.449.1 | 4 | 20.19 | odd | 2 | |||
2800.2.g.s.449.4 | 4 | 4.3 | odd | 2 |