Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,3,Mod(97,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.67030659073\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.97 |
Dual form | 98.3.b.b.97.1 |
$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 4.18154i | 1.39385i | 0.717146 | + | 0.696923i | \(0.245448\pi\) | ||||
−0.717146 | + | 0.696923i | \(0.754552\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 3.16693i | 0.633386i | 0.948528 | + | 0.316693i | \(0.102572\pi\) | ||||
−0.948528 | + | 0.316693i | \(0.897428\pi\) | |||||||
\(6\) | − 5.91359i | − 0.985599i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −8.48528 | −0.942809 | ||||||||
\(10\) | − 4.47871i | − 0.447871i | ||||||||
\(11\) | −13.2426 | −1.20388 | −0.601938 | − | 0.798543i | \(-0.705605\pi\) | ||||
−0.601938 | + | 0.798543i | \(0.705605\pi\) | |||||||
\(12\) | 8.36308i | 0.696923i | ||||||||
\(13\) | 5.49333i | 0.422563i | 0.977425 | + | 0.211282i | \(0.0677638\pi\) | ||||
−0.977425 | + | 0.211282i | \(0.932236\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.2426 | −0.882843 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 13.5592i | 0.797602i | 0.917037 | + | 0.398801i | \(0.130574\pi\) | ||||
−0.917037 | + | 0.398801i | \(0.869426\pi\) | |||||||
\(18\) | 12.0000 | 0.666667 | ||||||||
\(19\) | − 0.717439i | − 0.0377599i | −0.999822 | − | 0.0188800i | \(-0.993990\pi\) | ||||
0.999822 | − | 0.0188800i | \(-0.00601004\pi\) | |||||||
\(20\) | 6.33386i | 0.316693i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 18.7279 | 0.851269 | ||||||||
\(23\) | −2.27208 | −0.0987860 | −0.0493930 | − | 0.998779i | \(-0.515729\pi\) | ||||
−0.0493930 | + | 0.998779i | \(0.515729\pi\) | |||||||
\(24\) | − 11.8272i | − 0.492799i | ||||||||
\(25\) | 14.9706 | 0.598823 | ||||||||
\(26\) | − 7.76874i | − 0.298798i | ||||||||
\(27\) | 2.15232i | 0.0797154i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 20.4853 | 0.706389 | 0.353195 | − | 0.935550i | \(-0.385095\pi\) | ||||
0.353195 | + | 0.935550i | \(0.385095\pi\) | |||||||
\(30\) | 18.7279 | 0.624264 | ||||||||
\(31\) | − 24.6180i | − 0.794129i | −0.917791 | − | 0.397064i | \(-0.870029\pi\) | ||||
0.917791 | − | 0.397064i | \(-0.129971\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − 55.3746i | − 1.67802i | ||||||||
\(34\) | − 19.1757i | − 0.563990i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.9706 | −0.471405 | ||||||||
\(37\) | 64.9411 | 1.75517 | 0.877583 | − | 0.479425i | \(-0.159155\pi\) | ||||
0.877583 | + | 0.479425i | \(0.159155\pi\) | |||||||
\(38\) | 1.01461i | 0.0267003i | ||||||||
\(39\) | −22.9706 | −0.588989 | ||||||||
\(40\) | − 8.95743i | − 0.223936i | ||||||||
\(41\) | 21.0308i | 0.512946i | 0.966551 | + | 0.256473i | \(0.0825605\pi\) | ||||
−0.966551 | + | 0.256473i | \(0.917439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.48528 | 0.150820 | 0.0754102 | − | 0.997153i | \(-0.475973\pi\) | ||||
0.0754102 | + | 0.997153i | \(0.475973\pi\) | |||||||
\(44\) | −26.4853 | −0.601938 | ||||||||
\(45\) | − 26.8723i | − 0.597162i | ||||||||
\(46\) | 3.21320 | 0.0698522 | ||||||||
\(47\) | 47.7800i | 1.01660i | 0.861181 | + | 0.508298i | \(0.169725\pi\) | ||||
−0.861181 | + | 0.508298i | \(0.830275\pi\) | |||||||
\(48\) | 16.7262i | 0.348462i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −21.1716 | −0.423431 | ||||||||
\(51\) | −56.6985 | −1.11173 | ||||||||
\(52\) | 10.9867i | 0.211282i | ||||||||
\(53\) | 22.0294 | 0.415650 | 0.207825 | − | 0.978166i | \(-0.433362\pi\) | ||||
0.207825 | + | 0.978166i | \(0.433362\pi\) | |||||||
\(54\) | − 3.04384i | − 0.0563673i | ||||||||
\(55\) | − 41.9385i | − 0.762518i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000 | 0.0526316 | ||||||||
\(58\) | −28.9706 | −0.499492 | ||||||||
\(59\) | 83.7539i | 1.41956i | 0.704425 | + | 0.709779i | \(0.251205\pi\) | ||||
−0.704425 | + | 0.709779i | \(0.748795\pi\) | |||||||
\(60\) | −26.4853 | −0.441421 | ||||||||
\(61\) | 66.2593i | 1.08622i | 0.839662 | + | 0.543109i | \(0.182753\pi\) | ||||
−0.839662 | + | 0.543109i | \(0.817247\pi\) | |||||||
\(62\) | 34.8151i | 0.561534i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −17.3970 | −0.267646 | ||||||||
\(66\) | 78.3116i | 1.18654i | ||||||||
\(67\) | 92.6396 | 1.38268 | 0.691340 | − | 0.722529i | \(-0.257021\pi\) | ||||
0.691340 | + | 0.722529i | \(0.257021\pi\) | |||||||
\(68\) | 27.1185i | 0.398801i | ||||||||
\(69\) | − 9.50079i | − 0.137693i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48.4264 | −0.682062 | −0.341031 | − | 0.940052i | \(-0.610776\pi\) | ||||
−0.341031 | + | 0.940052i | \(0.610776\pi\) | |||||||
\(72\) | 24.0000 | 0.333333 | ||||||||
\(73\) | − 130.991i | − 1.79439i | −0.441634 | − | 0.897195i | \(-0.645601\pi\) | ||||
0.441634 | − | 0.897195i | \(-0.354399\pi\) | |||||||
\(74\) | −91.8406 | −1.24109 | ||||||||
\(75\) | 62.6000i | 0.834667i | ||||||||
\(76\) | − 1.43488i | − 0.0188800i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 32.4853 | 0.416478 | ||||||||
\(79\) | −76.2132 | −0.964724 | −0.482362 | − | 0.875972i | \(-0.660221\pi\) | ||||
−0.482362 | + | 0.875972i | \(0.660221\pi\) | |||||||
\(80\) | 12.6677i | 0.158346i | ||||||||
\(81\) | −85.3675 | −1.05392 | ||||||||
\(82\) | − 29.7420i | − 0.362708i | ||||||||
\(83\) | − 107.981i | − 1.30098i | −0.759514 | − | 0.650491i | \(-0.774563\pi\) | ||||
0.759514 | − | 0.650491i | \(-0.225437\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −42.9411 | −0.505190 | ||||||||
\(86\) | −9.17157 | −0.106646 | ||||||||
\(87\) | 85.6600i | 0.984598i | ||||||||
\(88\) | 37.4558 | 0.425635 | ||||||||
\(89\) | − 167.907i | − 1.88659i | −0.331949 | − | 0.943297i | \(-0.607706\pi\) | ||||
0.331949 | − | 0.943297i | \(-0.392294\pi\) | |||||||
\(90\) | 38.0031i | 0.422257i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.54416 | −0.0493930 | ||||||||
\(93\) | 102.941 | 1.10689 | ||||||||
\(94\) | − 67.5711i | − 0.718841i | ||||||||
\(95\) | 2.27208 | 0.0239166 | ||||||||
\(96\) | − 23.6544i | − 0.246400i | ||||||||
\(97\) | − 25.5816i | − 0.263728i | −0.991268 | − | 0.131864i | \(-0.957904\pi\) | ||||
0.991268 | − | 0.131864i | \(-0.0420962\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 112.368 | 1.13503 | ||||||||
\(100\) | 29.9411 | 0.299411 | ||||||||
\(101\) | − 28.5024i | − 0.282202i | −0.989995 | − | 0.141101i | \(-0.954936\pi\) | ||||
0.989995 | − | 0.141101i | \(-0.0450642\pi\) | |||||||
\(102\) | 80.1838 | 0.786115 | ||||||||
\(103\) | 56.4912i | 0.548458i | 0.961664 | + | 0.274229i | \(0.0884227\pi\) | ||||
−0.961664 | + | 0.274229i | \(0.911577\pi\) | |||||||
\(104\) | − 15.5375i | − 0.149399i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −31.1543 | −0.293909 | ||||||||
\(107\) | 47.6102 | 0.444955 | 0.222477 | − | 0.974938i | \(-0.428586\pi\) | ||||
0.222477 | + | 0.974938i | \(0.428586\pi\) | |||||||
\(108\) | 4.30463i | 0.0398577i | ||||||||
\(109\) | 75.3087 | 0.690905 | 0.345453 | − | 0.938436i | \(-0.387725\pi\) | ||||
0.345453 | + | 0.938436i | \(0.387725\pi\) | |||||||
\(110\) | 59.3100i | 0.539182i | ||||||||
\(111\) | 271.554i | 2.44643i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 85.4558 | 0.756246 | 0.378123 | − | 0.925755i | \(-0.376570\pi\) | ||||
0.378123 | + | 0.925755i | \(0.376570\pi\) | |||||||
\(114\) | −4.24264 | −0.0372161 | ||||||||
\(115\) | − 7.19551i | − 0.0625696i | ||||||||
\(116\) | 40.9706 | 0.353195 | ||||||||
\(117\) | − 46.6124i | − 0.398397i | ||||||||
\(118\) | − 118.446i | − 1.00378i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 37.4558 | 0.312132 | ||||||||
\(121\) | 54.3675 | 0.449318 | ||||||||
\(122\) | − 93.7048i | − 0.768072i | ||||||||
\(123\) | −87.9411 | −0.714968 | ||||||||
\(124\) | − 49.2360i | − 0.397064i | ||||||||
\(125\) | 126.584i | 1.01267i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −60.6619 | −0.477653 | −0.238826 | − | 0.971062i | \(-0.576763\pi\) | ||||
−0.238826 | + | 0.971062i | \(0.576763\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 27.1185i | 0.210221i | ||||||||
\(130\) | 24.6030 | 0.189254 | ||||||||
\(131\) | − 132.948i | − 1.01487i | −0.861691 | − | 0.507434i | \(-0.830594\pi\) | ||||
0.861691 | − | 0.507434i | \(-0.169406\pi\) | |||||||
\(132\) | − 110.749i | − 0.839010i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −131.012 | −0.977703 | ||||||||
\(135\) | −6.81623 | −0.0504906 | ||||||||
\(136\) | − 38.3513i | − 0.281995i | ||||||||
\(137\) | −117.426 | −0.857127 | −0.428564 | − | 0.903512i | \(-0.640980\pi\) | ||||
−0.428564 | + | 0.903512i | \(0.640980\pi\) | |||||||
\(138\) | 13.4361i | 0.0973633i | ||||||||
\(139\) | − 68.5857i | − 0.493422i | −0.969089 | − | 0.246711i | \(-0.920650\pi\) | ||||
0.969089 | − | 0.246711i | \(-0.0793499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −199.794 | −1.41698 | ||||||||
\(142\) | 68.4853 | 0.482291 | ||||||||
\(143\) | − 72.7461i | − 0.508714i | ||||||||
\(144\) | −33.9411 | −0.235702 | ||||||||
\(145\) | 64.8754i | 0.447417i | ||||||||
\(146\) | 185.249i | 1.26883i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 129.882 | 0.877583 | ||||||||
\(149\) | −26.3970 | −0.177161 | −0.0885804 | − | 0.996069i | \(-0.528233\pi\) | ||||
−0.0885804 | + | 0.996069i | \(0.528233\pi\) | |||||||
\(150\) | − 88.5298i | − 0.590199i | ||||||||
\(151\) | −134.213 | −0.888829 | −0.444415 | − | 0.895821i | \(-0.646588\pi\) | ||||
−0.444415 | + | 0.895821i | \(0.646588\pi\) | |||||||
\(152\) | 2.02922i | 0.0133502i | ||||||||
\(153\) | − 115.054i | − 0.751986i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 77.9634 | 0.502990 | ||||||||
\(156\) | −45.9411 | −0.294494 | ||||||||
\(157\) | 226.695i | 1.44392i | 0.691937 | + | 0.721958i | \(0.256757\pi\) | ||||
−0.691937 | + | 0.721958i | \(0.743243\pi\) | |||||||
\(158\) | 107.782 | 0.682163 | ||||||||
\(159\) | 92.1170i | 0.579352i | ||||||||
\(160\) | − 17.9149i | − 0.111968i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 120.728 | 0.745234 | ||||||||
\(163\) | −91.9777 | −0.564280 | −0.282140 | − | 0.959373i | \(-0.591044\pi\) | ||||
−0.282140 | + | 0.959373i | \(0.591044\pi\) | |||||||
\(164\) | 42.0616i | 0.256473i | ||||||||
\(165\) | 175.368 | 1.06283 | ||||||||
\(166\) | 152.709i | 0.919933i | ||||||||
\(167\) | − 203.482i | − 1.21845i | −0.792996 | − | 0.609227i | \(-0.791480\pi\) | ||||
0.792996 | − | 0.609227i | \(-0.208520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 138.823 | 0.821440 | ||||||||
\(170\) | 60.7279 | 0.357223 | ||||||||
\(171\) | 6.08767i | 0.0356004i | ||||||||
\(172\) | 12.9706 | 0.0754102 | ||||||||
\(173\) | 70.8101i | 0.409307i | 0.978834 | + | 0.204654i | \(0.0656068\pi\) | ||||
−0.978834 | + | 0.204654i | \(0.934393\pi\) | |||||||
\(174\) | − 121.142i | − 0.696216i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −52.9706 | −0.300969 | ||||||||
\(177\) | −350.220 | −1.97865 | ||||||||
\(178\) | 237.456i | 1.33402i | ||||||||
\(179\) | 108.816 | 0.607912 | 0.303956 | − | 0.952686i | \(-0.401692\pi\) | ||||
0.303956 | + | 0.952686i | \(0.401692\pi\) | |||||||
\(180\) | − 53.7446i | − 0.298581i | ||||||||
\(181\) | 99.6607i | 0.550611i | 0.961357 | + | 0.275306i | \(0.0887791\pi\) | ||||
−0.961357 | + | 0.275306i | \(0.911221\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −277.066 | −1.51402 | ||||||||
\(184\) | 6.42641 | 0.0349261 | ||||||||
\(185\) | 205.664i | 1.11170i | ||||||||
\(186\) | −145.581 | −0.782692 | ||||||||
\(187\) | − 179.560i | − 0.960214i | ||||||||
\(188\) | 95.5600i | 0.508298i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.21320 | −0.0169116 | ||||||||
\(191\) | 69.9045 | 0.365992 | 0.182996 | − | 0.983114i | \(-0.441420\pi\) | ||||
0.182996 | + | 0.983114i | \(0.441420\pi\) | |||||||
\(192\) | 33.4523i | 0.174231i | ||||||||
\(193\) | −32.3381 | −0.167555 | −0.0837774 | − | 0.996484i | \(-0.526698\pi\) | ||||
−0.0837774 | + | 0.996484i | \(0.526698\pi\) | |||||||
\(194\) | 36.1779i | 0.186484i | ||||||||
\(195\) | − 72.7461i | − 0.373057i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 277.103 | 1.40661 | 0.703306 | − | 0.710887i | \(-0.251706\pi\) | ||||
0.703306 | + | 0.710887i | \(0.251706\pi\) | |||||||
\(198\) | −158.912 | −0.802584 | ||||||||
\(199\) | − 167.444i | − 0.841429i | −0.907193 | − | 0.420715i | \(-0.861779\pi\) | ||||
0.907193 | − | 0.420715i | \(-0.138221\pi\) | |||||||
\(200\) | −42.3431 | −0.211716 | ||||||||
\(201\) | 387.376i | 1.92725i | ||||||||
\(202\) | 40.3084i | 0.199547i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −113.397 | −0.555867 | ||||||||
\(205\) | −66.6030 | −0.324893 | ||||||||
\(206\) | − 79.8907i | − 0.387819i | ||||||||
\(207\) | 19.2792 | 0.0931363 | ||||||||
\(208\) | 21.9733i | 0.105641i | ||||||||
\(209\) | 9.50079i | 0.0454583i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −128.073 | −0.606982 | −0.303491 | − | 0.952834i | \(-0.598152\pi\) | ||||
−0.303491 | + | 0.952834i | \(0.598152\pi\) | |||||||
\(212\) | 44.0589 | 0.207825 | ||||||||
\(213\) | − 202.497i | − 0.950690i | ||||||||
\(214\) | −67.3310 | −0.314631 | ||||||||
\(215\) | 20.5384i | 0.0955276i | ||||||||
\(216\) | − 6.08767i | − 0.0281837i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −106.503 | −0.488544 | ||||||||
\(219\) | 547.742 | 2.50111 | ||||||||
\(220\) | − 83.8770i | − 0.381259i | ||||||||
\(221\) | −74.4853 | −0.337037 | ||||||||
\(222\) | − 384.035i | − 1.72989i | ||||||||
\(223\) | 417.169i | 1.87071i | 0.353705 | + | 0.935357i | \(0.384922\pi\) | ||||
−0.353705 | + | 0.935357i | \(0.615078\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −127.029 | −0.564575 | ||||||||
\(226\) | −120.853 | −0.534747 | ||||||||
\(227\) | − 232.260i | − 1.02317i | −0.859232 | − | 0.511586i | \(-0.829058\pi\) | ||||
0.859232 | − | 0.511586i | \(-0.170942\pi\) | |||||||
\(228\) | 6.00000 | 0.0263158 | ||||||||
\(229\) | − 83.6221i | − 0.365162i | −0.983191 | − | 0.182581i | \(-0.941555\pi\) | ||||
0.983191 | − | 0.182581i | \(-0.0584452\pi\) | |||||||
\(230\) | 10.1760i | 0.0442434i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −57.9411 | −0.249746 | ||||||||
\(233\) | 219.073 | 0.940228 | 0.470114 | − | 0.882606i | \(-0.344213\pi\) | ||||
0.470114 | + | 0.882606i | \(0.344213\pi\) | |||||||
\(234\) | 65.9199i | 0.281709i | ||||||||
\(235\) | −151.316 | −0.643897 | ||||||||
\(236\) | 167.508i | 0.709779i | ||||||||
\(237\) | − 318.689i | − 1.34468i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 193.103 | 0.807961 | 0.403980 | − | 0.914768i | \(-0.367626\pi\) | ||||
0.403980 | + | 0.914768i | \(0.367626\pi\) | |||||||
\(240\) | −52.9706 | −0.220711 | ||||||||
\(241\) | − 49.5332i | − 0.205532i | −0.994706 | − | 0.102766i | \(-0.967231\pi\) | ||||
0.994706 | − | 0.102766i | \(-0.0327692\pi\) | |||||||
\(242\) | −76.8873 | −0.317716 | ||||||||
\(243\) | − 337.597i | − 1.38929i | ||||||||
\(244\) | 132.519i | 0.543109i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 124.368 | 0.505559 | ||||||||
\(247\) | 3.94113 | 0.0159560 | ||||||||
\(248\) | 69.6302i | 0.280767i | ||||||||
\(249\) | 451.529 | 1.81337 | ||||||||
\(250\) | − 179.017i | − 0.716067i | ||||||||
\(251\) | − 162.524i | − 0.647507i | −0.946141 | − | 0.323754i | \(-0.895055\pi\) | ||||
0.946141 | − | 0.323754i | \(-0.104945\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0883 | 0.118926 | ||||||||
\(254\) | 85.7889 | 0.337752 | ||||||||
\(255\) | − 179.560i | − 0.704157i | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − 99.1595i | − 0.385835i | −0.981215 | − | 0.192917i | \(-0.938205\pi\) | ||||
0.981215 | − | 0.192917i | \(-0.0617949\pi\) | |||||||
\(258\) | − 38.3513i | − 0.148648i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −34.7939 | −0.133823 | ||||||||
\(261\) | −173.823 | −0.665990 | ||||||||
\(262\) | 188.016i | 0.717620i | ||||||||
\(263\) | 434.345 | 1.65150 | 0.825751 | − | 0.564034i | \(-0.190751\pi\) | ||||
0.825751 | + | 0.564034i | \(0.190751\pi\) | |||||||
\(264\) | 156.623i | 0.593269i | ||||||||
\(265\) | 69.7657i | 0.263267i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 702.110 | 2.62962 | ||||||||
\(268\) | 185.279 | 0.691340 | ||||||||
\(269\) | 91.4083i | 0.339808i | 0.985461 | + | 0.169904i | \(0.0543457\pi\) | ||||
−0.985461 | + | 0.169904i | \(0.945654\pi\) | |||||||
\(270\) | 9.63961 | 0.0357023 | ||||||||
\(271\) | 17.0954i | 0.0630828i | 0.999502 | + | 0.0315414i | \(0.0100416\pi\) | ||||
−0.999502 | + | 0.0315414i | \(0.989958\pi\) | |||||||
\(272\) | 54.2369i | 0.199400i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 166.066 | 0.606080 | ||||||||
\(275\) | −198.250 | −0.720908 | ||||||||
\(276\) | − 19.0016i | − 0.0688463i | ||||||||
\(277\) | −400.411 | −1.44553 | −0.722764 | − | 0.691095i | \(-0.757129\pi\) | ||||
−0.722764 | + | 0.691095i | \(0.757129\pi\) | |||||||
\(278\) | 96.9948i | 0.348902i | ||||||||
\(279\) | 208.891i | 0.748712i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −538.690 | −1.91705 | −0.958524 | − | 0.285012i | \(-0.908002\pi\) | ||||
−0.958524 | + | 0.285012i | \(0.908002\pi\) | |||||||
\(282\) | 282.551 | 1.00195 | ||||||||
\(283\) | 309.209i | 1.09261i | 0.837586 | + | 0.546306i | \(0.183966\pi\) | ||||
−0.837586 | + | 0.546306i | \(0.816034\pi\) | |||||||
\(284\) | −96.8528 | −0.341031 | ||||||||
\(285\) | 9.50079i | 0.0333361i | ||||||||
\(286\) | 102.879i | 0.359715i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 48.0000 | 0.166667 | ||||||||
\(289\) | 105.147 | 0.363831 | ||||||||
\(290\) | − 91.7477i | − 0.316371i | ||||||||
\(291\) | 106.971 | 0.367596 | ||||||||
\(292\) | − 261.981i | − 0.897195i | ||||||||
\(293\) | − 327.391i | − 1.11738i | −0.829378 | − | 0.558688i | \(-0.811305\pi\) | ||||
0.829378 | − | 0.558688i | \(-0.188695\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −265.243 | −0.899128 | ||||||||
\(296\) | −183.681 | −0.620545 | ||||||||
\(297\) | − 28.5024i | − 0.0959675i | ||||||||
\(298\) | 37.3310 | 0.125272 | ||||||||
\(299\) | − 12.4813i | − 0.0417434i | ||||||||
\(300\) | 125.200i | 0.417333i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 189.806 | 0.628497 | ||||||||
\(303\) | 119.184 | 0.393346 | ||||||||
\(304\) | − 2.86976i | − 0.00943999i | ||||||||
\(305\) | −209.839 | −0.687995 | ||||||||
\(306\) | 162.711i | 0.531735i | ||||||||
\(307\) | − 256.140i | − 0.834331i | −0.908831 | − | 0.417165i | \(-0.863024\pi\) | ||||
0.908831 | − | 0.417165i | \(-0.136976\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −236.220 | −0.764467 | ||||||||
\(310\) | −110.257 | −0.355668 | ||||||||
\(311\) | − 216.332i | − 0.695602i | −0.937568 | − | 0.347801i | \(-0.886928\pi\) | ||||
0.937568 | − | 0.347801i | \(-0.113072\pi\) | |||||||
\(312\) | 64.9706 | 0.208239 | ||||||||
\(313\) | 156.818i | 0.501017i | 0.968114 | + | 0.250509i | \(0.0805978\pi\) | ||||
−0.968114 | + | 0.250509i | \(0.919402\pi\) | |||||||
\(314\) | − 320.595i | − 1.02100i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −152.426 | −0.482362 | ||||||||
\(317\) | −448.029 | −1.41334 | −0.706671 | − | 0.707542i | \(-0.749804\pi\) | ||||
−0.706671 | + | 0.707542i | \(0.749804\pi\) | |||||||
\(318\) | − 130.273i | − 0.409664i | ||||||||
\(319\) | −271.279 | −0.850405 | ||||||||
\(320\) | 25.3354i | 0.0791732i | ||||||||
\(321\) | 199.084i | 0.620199i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.72792 | 0.0301174 | ||||||||
\(324\) | −170.735 | −0.526960 | ||||||||
\(325\) | 82.2382i | 0.253041i | ||||||||
\(326\) | 130.076 | 0.399006 | ||||||||
\(327\) | 314.906i | 0.963016i | ||||||||
\(328\) | − 59.4841i | − 0.181354i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −248.007 | −0.751537 | ||||||||
\(331\) | −55.0071 | −0.166185 | −0.0830924 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830924 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(332\) | − 215.963i | − 0.650491i | ||||||||
\(333\) | −551.044 | −1.65479 | ||||||||
\(334\) | 287.767i | 0.861577i | ||||||||
\(335\) | 293.383i | 0.875770i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −111.632 | −0.331254 | −0.165627 | − | 0.986189i | \(-0.552965\pi\) | ||||
−0.165627 | + | 0.986189i | \(0.552965\pi\) | |||||||
\(338\) | −196.326 | −0.580846 | ||||||||
\(339\) | 357.337i | 1.05409i | ||||||||
\(340\) | −85.8823 | −0.252595 | ||||||||
\(341\) | 326.007i | 0.956033i | ||||||||
\(342\) | − 8.60927i | − 0.0251733i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.3431 | −0.0533231 | ||||||||
\(345\) | 30.0883 | 0.0872125 | ||||||||
\(346\) | − 100.141i | − 0.289424i | ||||||||
\(347\) | 377.257 | 1.08720 | 0.543598 | − | 0.839346i | \(-0.317062\pi\) | ||||
0.543598 | + | 0.839346i | \(0.317062\pi\) | |||||||
\(348\) | 171.320i | 0.492299i | ||||||||
\(349\) | 204.034i | 0.584624i | 0.956323 | + | 0.292312i | \(0.0944246\pi\) | ||||
−0.956323 | + | 0.292312i | \(0.905575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.8234 | −0.0336848 | ||||||||
\(352\) | 74.9117 | 0.212817 | ||||||||
\(353\) | 417.076i | 1.18152i | 0.806848 | + | 0.590759i | \(0.201172\pi\) | ||||
−0.806848 | + | 0.590759i | \(0.798828\pi\) | |||||||
\(354\) | 495.286 | 1.39911 | ||||||||
\(355\) | − 153.363i | − 0.432008i | ||||||||
\(356\) | − 335.814i | − 0.943297i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −153.889 | −0.429859 | ||||||||
\(359\) | −178.831 | −0.498135 | −0.249068 | − | 0.968486i | \(-0.580124\pi\) | ||||
−0.249068 | + | 0.968486i | \(0.580124\pi\) | |||||||
\(360\) | 76.0063i | 0.211129i | ||||||||
\(361\) | 360.485 | 0.998574 | ||||||||
\(362\) | − 140.941i | − 0.389341i | ||||||||
\(363\) | 227.340i | 0.626281i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 414.838 | 1.13654 | ||||||||
\(366\) | 391.831 | 1.07058 | ||||||||
\(367\) | 628.993i | 1.71388i | 0.515418 | + | 0.856939i | \(0.327637\pi\) | ||||
−0.515418 | + | 0.856939i | \(0.672363\pi\) | |||||||
\(368\) | −9.08831 | −0.0246965 | ||||||||
\(369\) | − 178.452i | − 0.483610i | ||||||||
\(370\) | − 290.853i | − 0.786088i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 205.882 | 0.553447 | ||||||||
\(373\) | −255.558 | −0.685143 | −0.342572 | − | 0.939492i | \(-0.611298\pi\) | ||||
−0.342572 | + | 0.939492i | \(0.611298\pi\) | |||||||
\(374\) | 253.936i | 0.678974i | ||||||||
\(375\) | −529.316 | −1.41151 | ||||||||
\(376\) | − 135.142i | − 0.359421i | ||||||||
\(377\) | 112.532i | 0.298494i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 219.750 | 0.579816 | 0.289908 | − | 0.957055i | \(-0.406375\pi\) | ||||
0.289908 | + | 0.957055i | \(0.406375\pi\) | |||||||
\(380\) | 4.54416 | 0.0119583 | ||||||||
\(381\) | − 253.660i | − 0.665775i | ||||||||
\(382\) | −98.8600 | −0.258796 | ||||||||
\(383\) | − 17.0357i | − 0.0444797i | −0.999753 | − | 0.0222398i | \(-0.992920\pi\) | ||||
0.999753 | − | 0.0222398i | \(-0.00707974\pi\) | |||||||
\(384\) | − 47.3087i | − 0.123200i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 45.7330 | 0.118479 | ||||||||
\(387\) | −55.0294 | −0.142195 | ||||||||
\(388\) | − 51.1632i | − 0.131864i | ||||||||
\(389\) | −152.220 | −0.391312 | −0.195656 | − | 0.980673i | \(-0.562684\pi\) | ||||
−0.195656 | + | 0.980673i | \(0.562684\pi\) | |||||||
\(390\) | 102.879i | 0.263791i | ||||||||
\(391\) | − 30.8076i | − 0.0787919i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 555.926 | 1.41457 | ||||||||
\(394\) | −391.882 | −0.994625 | ||||||||
\(395\) | − 241.362i | − 0.611042i | ||||||||
\(396\) | 224.735 | 0.567513 | ||||||||
\(397\) | − 372.722i | − 0.938845i | −0.882974 | − | 0.469423i | \(-0.844462\pi\) | ||||
0.882974 | − | 0.469423i | \(-0.155538\pi\) | |||||||
\(398\) | 236.802i | 0.594980i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 59.8823 | 0.149706 | ||||||||
\(401\) | 651.573 | 1.62487 | 0.812435 | − | 0.583052i | \(-0.198142\pi\) | ||||
0.812435 | + | 0.583052i | \(0.198142\pi\) | |||||||
\(402\) | − 547.833i | − 1.36277i | ||||||||
\(403\) | 135.235 | 0.335570 | ||||||||
\(404\) | − 57.0047i | − 0.141101i | ||||||||
\(405\) | − 270.353i | − 0.667538i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −859.992 | −2.11300 | ||||||||
\(408\) | 160.368 | 0.393058 | ||||||||
\(409\) | − 533.565i | − 1.30456i | −0.757978 | − | 0.652280i | \(-0.773813\pi\) | ||||
0.757978 | − | 0.652280i | \(-0.226187\pi\) | |||||||
\(410\) | 94.1909 | 0.229734 | ||||||||
\(411\) | − 491.023i | − 1.19470i | ||||||||
\(412\) | 112.982i | 0.274229i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −27.2649 | −0.0658573 | ||||||||
\(415\) | 341.970 | 0.824023 | ||||||||
\(416\) | − 31.0749i | − 0.0746994i | ||||||||
\(417\) | 286.794 | 0.687755 | ||||||||
\(418\) | − 13.4361i | − 0.0321439i | ||||||||
\(419\) | − 534.252i | − 1.27507i | −0.770423 | − | 0.637533i | \(-0.779955\pi\) | ||||
0.770423 | − | 0.637533i | \(-0.220045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 157.220 | 0.373445 | 0.186723 | − | 0.982413i | \(-0.440213\pi\) | ||||
0.186723 | + | 0.982413i | \(0.440213\pi\) | |||||||
\(422\) | 181.123 | 0.429201 | ||||||||
\(423\) | − 405.427i | − 0.958455i | ||||||||
\(424\) | −62.3087 | −0.146954 | ||||||||
\(425\) | 202.989i | 0.477622i | ||||||||
\(426\) | 286.374i | 0.672239i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 95.2203 | 0.222477 | ||||||||
\(429\) | 304.191 | 0.709070 | ||||||||
\(430\) | − 29.0457i | − 0.0675482i | ||||||||
\(431\) | −228.536 | −0.530246 | −0.265123 | − | 0.964215i | \(-0.585413\pi\) | ||||
−0.265123 | + | 0.964215i | \(0.585413\pi\) | |||||||
\(432\) | 8.60927i | 0.0199289i | ||||||||
\(433\) | 47.5549i | 0.109827i | 0.998491 | + | 0.0549133i | \(0.0174882\pi\) | ||||
−0.998491 | + | 0.0549133i | \(0.982512\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −271.279 | −0.623630 | ||||||||
\(436\) | 150.617 | 0.345453 | ||||||||
\(437\) | 1.63008i | 0.00373015i | ||||||||
\(438\) | −774.624 | −1.76855 | ||||||||
\(439\) | − 73.8540i | − 0.168232i | −0.996456 | − | 0.0841161i | \(-0.973193\pi\) | ||||
0.996456 | − | 0.0841161i | \(-0.0268067\pi\) | |||||||
\(440\) | 118.620i | 0.269591i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 105.338 | 0.238321 | ||||||||
\(443\) | 234.640 | 0.529661 | 0.264830 | − | 0.964295i | \(-0.414684\pi\) | ||||
0.264830 | + | 0.964295i | \(0.414684\pi\) | |||||||
\(444\) | 543.108i | 1.22322i | ||||||||
\(445\) | 531.749 | 1.19494 | ||||||||
\(446\) | − 589.966i | − 1.32279i | ||||||||
\(447\) | − 110.380i | − 0.246935i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −255.161 | −0.568288 | −0.284144 | − | 0.958782i | \(-0.591709\pi\) | ||||
−0.284144 | + | 0.958782i | \(0.591709\pi\) | |||||||
\(450\) | 179.647 | 0.399215 | ||||||||
\(451\) | − 278.503i | − 0.617524i | ||||||||
\(452\) | 170.912 | 0.378123 | ||||||||
\(453\) | − 561.218i | − 1.23889i | ||||||||
\(454\) | 328.465i | 0.723492i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.48528 | −0.0186081 | ||||||||
\(457\) | −145.735 | −0.318895 | −0.159448 | − | 0.987206i | \(-0.550971\pi\) | ||||
−0.159448 | + | 0.987206i | \(0.550971\pi\) | |||||||
\(458\) | 118.259i | 0.258208i | ||||||||
\(459\) | −29.1838 | −0.0635812 | ||||||||
\(460\) | − 14.3910i | − 0.0312848i | ||||||||
\(461\) | 888.329i | 1.92696i | 0.267777 | + | 0.963481i | \(0.413711\pi\) | ||||
−0.267777 | + | 0.963481i | \(0.586289\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 234.014 | 0.505430 | 0.252715 | − | 0.967541i | \(-0.418676\pi\) | ||||
0.252715 | + | 0.967541i | \(0.418676\pi\) | |||||||
\(464\) | 81.9411 | 0.176597 | ||||||||
\(465\) | 326.007i | 0.701091i | ||||||||
\(466\) | −309.816 | −0.664842 | ||||||||
\(467\) | 786.618i | 1.68441i | 0.539159 | + | 0.842204i | \(0.318742\pi\) | ||||
−0.539159 | + | 0.842204i | \(0.681258\pi\) | |||||||
\(468\) | − 93.2248i | − 0.199198i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 213.993 | 0.455304 | ||||||||
\(471\) | −947.933 | −2.01260 | ||||||||
\(472\) | − 236.892i | − 0.501889i | ||||||||
\(473\) | −85.8823 | −0.181569 | ||||||||
\(474\) | 450.694i | 0.950831i | ||||||||
\(475\) | − 10.7405i | − 0.0226115i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −186.926 | −0.391878 | ||||||||
\(478\) | −273.088 | −0.571314 | ||||||||
\(479\) | − 736.932i | − 1.53848i | −0.638960 | − | 0.769240i | \(-0.720635\pi\) | ||||
0.638960 | − | 0.769240i | \(-0.279365\pi\) | |||||||
\(480\) | 74.9117 | 0.156066 | ||||||||
\(481\) | 356.743i | 0.741669i | ||||||||
\(482\) | 70.0505i | 0.145333i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 108.735 | 0.224659 | ||||||||
\(485\) | 81.0152 | 0.167042 | ||||||||
\(486\) | 477.434i | 0.982375i | ||||||||
\(487\) | 270.698 | 0.555849 | 0.277925 | − | 0.960603i | \(-0.410353\pi\) | ||||
0.277925 | + | 0.960603i | \(0.410353\pi\) | |||||||
\(488\) | − 187.410i | − 0.384036i | ||||||||
\(489\) | − 384.609i | − 0.786520i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 760.161 | 1.54819 | 0.774094 | − | 0.633070i | \(-0.218206\pi\) | ||||
0.774094 | + | 0.633070i | \(0.218206\pi\) | |||||||
\(492\) | −175.882 | −0.357484 | ||||||||
\(493\) | 277.765i | 0.563417i | ||||||||
\(494\) | −5.57359 | −0.0112826 | ||||||||
\(495\) | 355.860i | 0.718909i | ||||||||
\(496\) | − 98.4720i | − 0.198532i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −638.558 | −1.28225 | ||||||||
\(499\) | 125.492 | 0.251488 | 0.125744 | − | 0.992063i | \(-0.459868\pi\) | ||||
0.125744 | + | 0.992063i | \(0.459868\pi\) | |||||||
\(500\) | 253.168i | 0.506336i | ||||||||
\(501\) | 850.867 | 1.69834 | ||||||||
\(502\) | 229.844i | 0.457857i | ||||||||
\(503\) | 117.083i | 0.232770i | 0.993204 | + | 0.116385i | \(0.0371306\pi\) | ||||
−0.993204 | + | 0.116385i | \(0.962869\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 90.2649 | 0.178742 | ||||||||
\(506\) | −42.5513 | −0.0840935 | ||||||||
\(507\) | 580.496i | 1.14496i | ||||||||
\(508\) | −121.324 | −0.238826 | ||||||||
\(509\) | − 662.925i | − 1.30241i | −0.758903 | − | 0.651204i | \(-0.774264\pi\) | ||||
0.758903 | − | 0.651204i | \(-0.225736\pi\) | |||||||
\(510\) | 253.936i | 0.497914i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 1.54416 | 0.00301005 | ||||||||
\(514\) | 140.233i | 0.272826i | ||||||||
\(515\) | −178.904 | −0.347386 | ||||||||
\(516\) | 54.2369i | 0.105110i | ||||||||
\(517\) | − 632.733i | − 1.22386i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −296.095 | −0.570511 | ||||||||
\(520\) | 49.2061 | 0.0946270 | ||||||||
\(521\) | 47.1383i | 0.0904765i | 0.998976 | + | 0.0452383i | \(0.0144047\pi\) | ||||
−0.998976 | + | 0.0452383i | \(0.985595\pi\) | |||||||
\(522\) | 245.823 | 0.470926 | ||||||||
\(523\) | 499.471i | 0.955011i | 0.878629 | + | 0.477506i | \(0.158459\pi\) | ||||
−0.878629 | + | 0.477506i | \(0.841541\pi\) | |||||||
\(524\) | − 265.895i | − 0.507434i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −614.257 | −1.16779 | ||||||||
\(527\) | 333.801 | 0.633399 | ||||||||
\(528\) | − 221.499i | − 0.419505i | ||||||||
\(529\) | −523.838 | −0.990241 | ||||||||
\(530\) | − 98.6635i | − 0.186158i | ||||||||
\(531\) | − 710.675i | − 1.33837i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −115.529 | −0.216752 | ||||||||
\(534\) | −992.933 | −1.85943 | ||||||||
\(535\) | 150.778i | 0.281828i | ||||||||
\(536\) | −262.024 | −0.488851 | ||||||||
\(537\) | 455.019i | 0.847336i | ||||||||
\(538\) | − 129.271i | − 0.240280i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −13.6325 | −0.0252453 | ||||||||
\(541\) | 498.809 | 0.922013 | 0.461007 | − | 0.887397i | \(-0.347488\pi\) | ||||
0.461007 | + | 0.887397i | \(0.347488\pi\) | |||||||
\(542\) | − 24.1766i | − 0.0446063i | ||||||||
\(543\) | −416.735 | −0.767468 | ||||||||
\(544\) | − 76.7026i | − 0.140997i | ||||||||
\(545\) | 238.497i | 0.437609i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −279.897 | −0.511694 | −0.255847 | − | 0.966717i | \(-0.582354\pi\) | ||||
−0.255847 | + | 0.966717i | \(0.582354\pi\) | |||||||
\(548\) | −234.853 | −0.428564 | ||||||||
\(549\) | − 562.229i | − 1.02410i | ||||||||
\(550\) | 280.368 | 0.509759 | ||||||||
\(551\) | − 14.6969i | − 0.0266732i | ||||||||
\(552\) | 26.8723i | 0.0486817i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 566.267 | 1.02214 | ||||||||
\(555\) | −859.992 | −1.54954 | ||||||||
\(556\) | − 137.171i | − 0.246711i | ||||||||
\(557\) | −261.780 | −0.469981 | −0.234991 | − | 0.971998i | \(-0.575506\pi\) | ||||
−0.234991 | + | 0.971998i | \(0.575506\pi\) | |||||||
\(558\) | − 295.416i | − 0.529419i | ||||||||
\(559\) | 35.6258i | 0.0637312i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 750.838 | 1.33839 | ||||||||
\(562\) | 761.823 | 1.35556 | ||||||||
\(563\) | 485.062i | 0.861567i | 0.902455 | + | 0.430784i | \(0.141763\pi\) | ||||
−0.902455 | + | 0.430784i | \(0.858237\pi\) | |||||||
\(564\) | −399.588 | −0.708489 | ||||||||
\(565\) | 270.633i | 0.478996i | ||||||||
\(566\) | − 437.287i | − 0.772593i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 136.971 | 0.241145 | ||||||||
\(569\) | −453.999 | −0.797890 | −0.398945 | − | 0.916975i | \(-0.630623\pi\) | ||||
−0.398945 | + | 0.916975i | \(0.630623\pi\) | |||||||
\(570\) | − 13.4361i | − 0.0235722i | ||||||||
\(571\) | −231.537 | −0.405494 | −0.202747 | − | 0.979231i | \(-0.564987\pi\) | ||||
−0.202747 | + | 0.979231i | \(0.564987\pi\) | |||||||
\(572\) | − 145.492i | − 0.254357i | ||||||||
\(573\) | 292.309i | 0.510137i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −34.0143 | −0.0591553 | ||||||||
\(576\) | −67.8823 | −0.117851 | ||||||||
\(577\) | − 651.267i | − 1.12871i | −0.825531 | − | 0.564356i | \(-0.809124\pi\) | ||||
0.825531 | − | 0.564356i | \(-0.190876\pi\) | |||||||
\(578\) | −148.701 | −0.257267 | ||||||||
\(579\) | − 135.223i | − 0.233546i | ||||||||
\(580\) | 129.751i | 0.223708i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −151.279 | −0.259930 | ||||||||
\(583\) | −291.728 | −0.500391 | ||||||||
\(584\) | 370.497i | 0.634413i | ||||||||
\(585\) | 147.618 | 0.252339 | ||||||||
\(586\) | 463.001i | 0.790104i | ||||||||
\(587\) | 823.029i | 1.40209i | 0.713116 | + | 0.701046i | \(0.247283\pi\) | ||||
−0.713116 | + | 0.701046i | \(0.752717\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.6619 | −0.0299863 | ||||||||
\(590\) | 375.110 | 0.635779 | ||||||||
\(591\) | 1158.72i | 1.96060i | ||||||||
\(592\) | 259.765 | 0.438791 | ||||||||
\(593\) | − 808.418i | − 1.36327i | −0.731694 | − | 0.681634i | \(-0.761270\pi\) | ||||
0.731694 | − | 0.681634i | \(-0.238730\pi\) | |||||||
\(594\) | 40.3084i | 0.0678593i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −52.7939 | −0.0885804 | ||||||||
\(597\) | 700.176 | 1.17282 | ||||||||
\(598\) | 17.6512i | 0.0295170i | ||||||||
\(599\) | 530.845 | 0.886218 | 0.443109 | − | 0.896468i | \(-0.353875\pi\) | ||||
0.443109 | + | 0.896468i | \(0.353875\pi\) | |||||||
\(600\) | − 177.060i | − 0.295099i | ||||||||
\(601\) | − 936.503i | − 1.55824i | −0.626874 | − | 0.779121i | \(-0.715666\pi\) | ||||
0.626874 | − | 0.779121i | \(-0.284334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −786.073 | −1.30360 | ||||||||
\(604\) | −268.426 | −0.444415 | ||||||||
\(605\) | 172.178i | 0.284592i | ||||||||
\(606\) | −168.551 | −0.278137 | ||||||||
\(607\) | 602.121i | 0.991962i | 0.868333 | + | 0.495981i | \(0.165191\pi\) | ||||
−0.868333 | + | 0.495981i | \(0.834809\pi\) | |||||||
\(608\) | 4.05845i | 0.00667508i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 296.756 | 0.486486 | ||||||||
\(611\) | −262.471 | −0.429576 | ||||||||
\(612\) | − 230.108i | − 0.375993i | ||||||||
\(613\) | 1096.90 | 1.78939 | 0.894695 | − | 0.446677i | \(-0.147393\pi\) | ||||
0.894695 | + | 0.446677i | \(0.147393\pi\) | |||||||
\(614\) | 362.236i | 0.589961i | ||||||||
\(615\) | − 278.503i | − 0.452851i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −432.956 | −0.701712 | −0.350856 | − | 0.936429i | \(-0.614109\pi\) | ||||
−0.350856 | + | 0.936429i | \(0.614109\pi\) | |||||||
\(618\) | 334.066 | 0.540560 | ||||||||
\(619\) | − 225.110i | − 0.363668i | −0.983329 | − | 0.181834i | \(-0.941797\pi\) | ||||
0.983329 | − | 0.181834i | \(-0.0582034\pi\) | |||||||
\(620\) | 155.927 | 0.251495 | ||||||||
\(621\) | − 4.89023i | − 0.00787477i | ||||||||
\(622\) | 305.940i | 0.491865i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −91.8823 | −0.147247 | ||||||||
\(625\) | −26.6182 | −0.0425891 | ||||||||
\(626\) | − 221.775i | − 0.354273i | ||||||||
\(627\) | −39.7279 | −0.0633619 | ||||||||
\(628\) | 453.389i | 0.721958i | ||||||||
\(629\) | 880.552i | 1.39992i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 750.514 | 1.18940 | 0.594702 | − | 0.803946i | \(-0.297270\pi\) | ||||
0.594702 | + | 0.803946i | \(0.297270\pi\) | |||||||
\(632\) | 215.563 | 0.341081 | ||||||||
\(633\) | − 535.543i | − 0.846040i | ||||||||
\(634\) | 633.609 | 0.999384 | ||||||||
\(635\) | − 192.112i | − 0.302538i | ||||||||
\(636\) | 184.234i | 0.289676i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 383.647 | 0.601327 | ||||||||
\(639\) | 410.912 | 0.643054 | ||||||||
\(640\) | − 35.8297i | − 0.0559839i | ||||||||
\(641\) | −1161.85 | −1.81256 | −0.906281 | − | 0.422675i | \(-0.861091\pi\) | ||||
−0.906281 | + | 0.422675i | \(0.861091\pi\) | |||||||
\(642\) | − 281.547i | − 0.438547i | ||||||||
\(643\) | 121.957i | 0.189669i | 0.995493 | + | 0.0948347i | \(0.0302322\pi\) | ||||
−0.995493 | + | 0.0948347i | \(0.969768\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −85.8823 | −0.133151 | ||||||||
\(646\) | −13.7574 | −0.0212962 | ||||||||
\(647\) | 158.775i | 0.245403i | 0.992444 | + | 0.122701i | \(0.0391557\pi\) | ||||
−0.992444 | + | 0.122701i | \(0.960844\pi\) | |||||||
\(648\) | 241.456 | 0.372617 | ||||||||
\(649\) | − 1109.12i | − 1.70897i | ||||||||
\(650\) | − 116.302i | − 0.178927i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −183.955 | −0.282140 | ||||||||
\(653\) | −390.941 | −0.598685 | −0.299342 | − | 0.954146i | \(-0.596767\pi\) | ||||
−0.299342 | + | 0.954146i | \(0.596767\pi\) | |||||||
\(654\) | − 445.345i | − 0.680955i | ||||||||
\(655\) | 421.036 | 0.642803 | ||||||||
\(656\) | 84.1232i | 0.128237i | ||||||||
\(657\) | 1111.49i | 1.69177i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −331.955 | −0.503726 | −0.251863 | − | 0.967763i | \(-0.581043\pi\) | ||||
−0.251863 | + | 0.967763i | \(0.581043\pi\) | |||||||
\(660\) | 350.735 | 0.531417 | ||||||||
\(661\) | − 647.820i | − 0.980061i | −0.871705 | − | 0.490031i | \(-0.836986\pi\) | ||||
0.871705 | − | 0.490031i | \(-0.163014\pi\) | |||||||
\(662\) | 77.7918 | 0.117510 | ||||||||
\(663\) | − 311.463i | − 0.469779i | ||||||||
\(664\) | 305.418i | 0.459967i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 779.294 | 1.17011 | ||||||||
\(667\) | −46.5442 | −0.0697813 | ||||||||
\(668\) | − 406.963i | − 0.609227i | ||||||||
\(669\) | −1744.41 | −2.60749 | ||||||||
\(670\) | − 414.906i | − 0.619263i | ||||||||
\(671\) | − 877.448i | − 1.30767i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 100.956 | 0.150009 | 0.0750047 | − | 0.997183i | \(-0.476103\pi\) | ||||
0.0750047 | + | 0.997183i | \(0.476103\pi\) | |||||||
\(674\) | 157.872 | 0.234232 | ||||||||
\(675\) | 32.2214i | 0.0477354i | ||||||||
\(676\) | 277.647 | 0.410720 | ||||||||
\(677\) | 743.177i | 1.09775i | 0.835905 | + | 0.548875i | \(0.184944\pi\) | ||||
−0.835905 | + | 0.548875i | \(0.815056\pi\) | |||||||
\(678\) | − 505.351i | − 0.745355i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 121.456 | 0.178612 | ||||||||
\(681\) | 971.205 | 1.42615 | ||||||||
\(682\) | − 461.044i | − 0.676017i | ||||||||
\(683\) | 4.43442 | 0.00649256 | 0.00324628 | − | 0.999995i | \(-0.498967\pi\) | ||||
0.00324628 | + | 0.999995i | \(0.498967\pi\) | |||||||
\(684\) | 12.1753i | 0.0178002i | ||||||||
\(685\) | − 371.881i | − 0.542892i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 349.669 | 0.508980 | ||||||||
\(688\) | 25.9411 | 0.0377051 | ||||||||
\(689\) | 121.015i | 0.175638i | ||||||||
\(690\) | −42.5513 | −0.0616685 | ||||||||
\(691\) | − 977.169i | − 1.41414i | −0.707145 | − | 0.707069i | \(-0.750017\pi\) | ||||
0.707145 | − | 0.707069i | \(-0.249983\pi\) | |||||||
\(692\) | 141.620i | 0.204654i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −533.522 | −0.768763 | ||||||||
\(695\) | 217.206 | 0.312527 | ||||||||
\(696\) | − 242.283i | − 0.348108i | ||||||||
\(697\) | −285.161 | −0.409127 | ||||||||
\(698\) | − 288.547i | − 0.413392i | ||||||||
\(699\) | 916.063i | 1.31053i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −840.177 | −1.19854 | −0.599270 | − | 0.800547i | \(-0.704542\pi\) | ||||
−0.599270 | + | 0.800547i | \(0.704542\pi\) | |||||||
\(702\) | 16.7208 | 0.0238188 | ||||||||
\(703\) | − 46.5913i | − 0.0662750i | ||||||||
\(704\) | −105.941 | −0.150485 | ||||||||
\(705\) | − 632.733i | − 0.897494i | ||||||||
\(706\) | − 589.835i | − 0.835460i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −700.441 | −0.989323 | ||||||||
\(709\) | 682.558 | 0.962705 | 0.481352 | − | 0.876527i | \(-0.340146\pi\) | ||||
0.481352 | + | 0.876527i | \(0.340146\pi\) | |||||||
\(710\) | 216.888i | 0.305476i | ||||||||
\(711\) | 646.690 | 0.909551 | ||||||||
\(712\) | 474.913i | 0.667012i | ||||||||
\(713\) | 55.9340i | 0.0784488i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 230.382 | 0.322212 | ||||||||
\(716\) | 217.632 | 0.303956 | ||||||||
\(717\) | 807.466i | 1.12617i | ||||||||
\(718\) | 252.905 | 0.352235 | ||||||||
\(719\) | 137.625i | 0.191412i | 0.995410 | + | 0.0957060i | \(0.0305109\pi\) | ||||
−0.995410 | + | 0.0957060i | \(0.969489\pi\) | |||||||
\(720\) | − 107.489i | − 0.149290i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −509.803 | −0.706099 | ||||||||
\(723\) | 207.125 | 0.286480 | ||||||||
\(724\) | 199.321i | 0.275306i | ||||||||
\(725\) | 306.676 | 0.423002 | ||||||||
\(726\) | − 321.507i | − 0.442848i | ||||||||
\(727\) | 264.137i | 0.363325i | 0.983361 | + | 0.181662i | \(0.0581478\pi\) | ||||
−0.983361 | + | 0.181662i | \(0.941852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 643.368 | 0.882534 | ||||||||
\(730\) | −586.669 | −0.803656 | ||||||||
\(731\) | 87.9354i | 0.120295i | ||||||||
\(732\) | −554.132 | −0.757011 | ||||||||
\(733\) | 579.319i | 0.790340i | 0.918608 | + | 0.395170i | \(0.129314\pi\) | ||||
−0.918608 | + | 0.395170i | \(0.870686\pi\) | |||||||
\(734\) | − 889.530i | − 1.21189i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.8528 | 0.0174631 | ||||||||
\(737\) | −1226.79 | −1.66458 | ||||||||
\(738\) | 252.370i | 0.341964i | ||||||||
\(739\) | −198.095 | −0.268059 | −0.134029 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134029 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(740\) | 411.328i | 0.555848i | ||||||||
\(741\) | 16.4800i | 0.0222402i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 976.690 | 1.31452 | 0.657261 | − | 0.753663i | \(-0.271715\pi\) | ||||
0.657261 | + | 0.753663i | \(0.271715\pi\) | |||||||
\(744\) | −291.161 | −0.391346 | ||||||||
\(745\) | − 83.5973i | − 0.112211i | ||||||||
\(746\) | 361.414 | 0.484469 | ||||||||
\(747\) | 916.253i | 1.22658i | ||||||||
\(748\) | − 359.120i | − 0.480107i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 748.566 | 0.998087 | ||||||||
\(751\) | −835.330 | −1.11229 | −0.556145 | − | 0.831085i | \(-0.687720\pi\) | ||||
−0.556145 | + | 0.831085i | \(0.687720\pi\) | |||||||
\(752\) | 191.120i | 0.254149i | ||||||||
\(753\) | 679.602 | 0.902526 | ||||||||
\(754\) | − 159.145i | − 0.211067i | ||||||||
\(755\) | − 425.044i | − 0.562972i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 104.221 | 0.137677 | 0.0688383 | − | 0.997628i | \(-0.478071\pi\) | ||||
0.0688383 | + | 0.997628i | \(0.478071\pi\) | |||||||
\(758\) | −310.774 | −0.409992 | ||||||||
\(759\) | 125.815i | 0.165765i | ||||||||
\(760\) | −6.42641 | −0.00845580 | ||||||||
\(761\) | − 547.080i | − 0.718897i | −0.933165 | − | 0.359448i | \(-0.882965\pi\) | ||||
0.933165 | − | 0.359448i | \(-0.117035\pi\) | |||||||
\(762\) | 358.730i | 0.470774i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 139.809 | 0.182996 | ||||||||
\(765\) | 364.368 | 0.476297 | ||||||||
\(766\) | 24.0921i | 0.0314519i | ||||||||
\(767\) | −460.087 | −0.599853 | ||||||||
\(768\) | 66.9046i | 0.0871154i | ||||||||
\(769\) | − 341.205i | − 0.443700i | −0.975081 | − | 0.221850i | \(-0.928790\pi\) | ||||
0.975081 | − | 0.221850i | \(-0.0712095\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 414.640 | 0.537795 | ||||||||
\(772\) | −64.6762 | −0.0837774 | ||||||||
\(773\) | 490.993i | 0.635179i | 0.948228 | + | 0.317590i | \(0.102873\pi\) | ||||
−0.948228 | + | 0.317590i | \(0.897127\pi\) | |||||||
\(774\) | 77.8234 | 0.100547 | ||||||||
\(775\) | − 368.545i | − 0.475542i | ||||||||
\(776\) | 72.3557i | 0.0932419i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 215.272 | 0.276699 | ||||||||
\(779\) | 15.0883 | 0.0193688 | ||||||||
\(780\) | − 145.492i | − 0.186529i | ||||||||
\(781\) | 641.294 | 0.821118 | ||||||||
\(782\) | 43.5686i | 0.0557143i | ||||||||
\(783\) | 44.0908i | 0.0563101i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −717.926 | −0.914555 | ||||||||
\(786\) | −786.198 | −1.00025 | ||||||||
\(787\) | − 300.455i | − 0.381773i | −0.981612 | − | 0.190887i | \(-0.938864\pi\) | ||||
0.981612 | − | 0.190887i | \(-0.0611363\pi\) | |||||||
\(788\) | 554.205 | 0.703306 | ||||||||
\(789\) | 1816.23i | 2.30194i | ||||||||
\(790\) | 341.337i | 0.432072i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −317.823 | −0.401292 | ||||||||
\(793\) | −363.984 | −0.458996 | ||||||||
\(794\) | 527.108i | 0.663864i | ||||||||
\(795\) | −291.728 | −0.366953 | ||||||||
\(796\) | − 334.889i | − 0.420715i | ||||||||
\(797\) | − 370.072i | − 0.464331i | −0.972676 | − | 0.232165i | \(-0.925419\pi\) | ||||
0.972676 | − | 0.232165i | \(-0.0745811\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −647.860 | −0.810838 | ||||||||
\(800\) | −84.6863 | −0.105858 | ||||||||
\(801\) | 1424.74i | 1.77870i | ||||||||
\(802\) | −921.463 | −1.14896 | ||||||||
\(803\) | 1734.66i | 2.16022i | ||||||||
\(804\) | 774.753i | 0.963623i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −191.251 | −0.237284 | ||||||||
\(807\) | −382.227 | −0.473640 | ||||||||
\(808\) | 80.6168i | 0.0997733i | ||||||||
\(809\) | 491.235 | 0.607213 | 0.303607 | − | 0.952797i | \(-0.401809\pi\) | ||||
0.303607 | + | 0.952797i | \(0.401809\pi\) | |||||||
\(810\) | 382.337i | 0.472021i | ||||||||
\(811\) | 156.802i | 0.193344i | 0.995316 | + | 0.0966722i | \(0.0308199\pi\) | ||||
−0.995316 | + | 0.0966722i | \(0.969180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −71.4853 | −0.0879278 | ||||||||
\(814\) | 1216.21 | 1.49412 | ||||||||
\(815\) | − 291.287i | − 0.357407i | ||||||||
\(816\) | −226.794 | −0.277934 | ||||||||
\(817\) | − 4.65279i | − 0.00569497i | ||||||||
\(818\) | 754.575i | 0.922463i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −133.206 | −0.162446 | ||||||||
\(821\) | −430.632 | −0.524522 | −0.262261 | − | 0.964997i | \(-0.584468\pi\) | ||||
−0.262261 | + | 0.964997i | \(0.584468\pi\) | |||||||
\(822\) | 694.412i | 0.844783i | ||||||||
\(823\) | −708.741 | −0.861168 | −0.430584 | − | 0.902550i | \(-0.641692\pi\) | ||||
−0.430584 | + | 0.902550i | \(0.641692\pi\) | |||||||
\(824\) | − 159.781i | − 0.193909i | ||||||||
\(825\) | − 828.990i | − 1.00484i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1460.10 | −1.76554 | −0.882770 | − | 0.469805i | \(-0.844324\pi\) | ||||
−0.882770 | + | 0.469805i | \(0.844324\pi\) | |||||||
\(828\) | 38.5584 | 0.0465682 | ||||||||
\(829\) | 257.608i | 0.310745i | 0.987856 | + | 0.155373i | \(0.0496578\pi\) | ||||
−0.987856 | + | 0.155373i | \(0.950342\pi\) | |||||||
\(830\) | −483.618 | −0.582673 | ||||||||
\(831\) | − 1674.34i | − 2.01484i | ||||||||
\(832\) | 43.9466i | 0.0528204i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −405.588 | −0.486316 | ||||||||
\(835\) | 644.412 | 0.771751 | ||||||||
\(836\) | 19.0016i | 0.0227292i | ||||||||
\(837\) | 52.9857 | 0.0633043 | ||||||||
\(838\) | 755.547i | 0.901607i | ||||||||
\(839\) | − 213.621i | − 0.254613i | −0.991863 | − | 0.127307i | \(-0.959367\pi\) | ||||
0.991863 | − | 0.127307i | \(-0.0406332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −421.353 | −0.501015 | ||||||||
\(842\) | −222.343 | −0.264065 | ||||||||
\(843\) | − 2252.56i | − 2.67207i | ||||||||
\(844\) | −256.146 | −0.303491 | ||||||||
\(845\) | 439.644i | 0.520288i | ||||||||
\(846\) | 573.360i | 0.677730i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 88.1177 | 0.103912 | ||||||||
\(849\) | −1292.97 | −1.52293 | ||||||||
\(850\) | − 287.070i | − 0.337730i | ||||||||
\(851\) | −147.551 | −0.173386 | ||||||||
\(852\) | − 404.994i | − 0.475345i | ||||||||
\(853\) | − 1127.37i | − 1.32165i | −0.750539 | − | 0.660826i | \(-0.770206\pi\) | ||||
0.750539 | − | 0.660826i | \(-0.229794\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.2792 | −0.0225488 | ||||||||
\(856\) | −134.662 | −0.157315 | ||||||||
\(857\) | − 1270.42i | − 1.48241i | −0.671280 | − | 0.741204i | \(-0.734255\pi\) | ||||
0.671280 | − | 0.741204i | \(-0.265745\pi\) | |||||||
\(858\) | −430.191 | −0.501388 | ||||||||
\(859\) | − 255.753i | − 0.297733i | −0.988857 | − | 0.148867i | \(-0.952438\pi\) | ||||
0.988857 | − | 0.148867i | \(-0.0475625\pi\) | |||||||
\(860\) | 41.0768i | 0.0477638i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 323.199 | 0.374941 | ||||||||
\(863\) | 1114.73 | 1.29169 | 0.645844 | − | 0.763469i | \(-0.276506\pi\) | ||||
0.645844 | + | 0.763469i | \(0.276506\pi\) | |||||||
\(864\) | − 12.1753i | − 0.0140918i | ||||||||
\(865\) | −224.251 | −0.259249 | ||||||||
\(866\) | − 67.2528i | − 0.0776591i | ||||||||
\(867\) | 439.677i | 0.507125i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1009.26 | 1.16141 | ||||||||
\(870\) | 383.647 | 0.440973 | ||||||||
\(871\) | 508.900i | 0.584270i | ||||||||
\(872\) | −213.005 | −0.244272 | ||||||||
\(873\) | 217.067i | 0.248645i | ||||||||
\(874\) | − 2.30528i | − 0.00263762i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1095.48 | 1.25055 | ||||||||
\(877\) | −1101.81 | −1.25634 | −0.628169 | − | 0.778077i | \(-0.716195\pi\) | ||||
−0.628169 | + | 0.778077i | \(0.716195\pi\) | |||||||
\(878\) | 104.445i | 0.118958i | ||||||||
\(879\) | 1369.00 | 1.55745 | ||||||||
\(880\) | − 167.754i | − 0.190630i | ||||||||
\(881\) | 217.067i | 0.246387i | 0.992383 | + | 0.123194i | \(0.0393136\pi\) | ||||
−0.992383 | + | 0.123194i | \(0.960686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −516.544 | −0.584988 | −0.292494 | − | 0.956267i | \(-0.594485\pi\) | ||||
−0.292494 | + | 0.956267i | \(0.594485\pi\) | |||||||
\(884\) | −148.971 | −0.168519 | ||||||||
\(885\) | − 1109.12i | − 1.25325i | ||||||||
\(886\) | −331.831 | −0.374527 | ||||||||
\(887\) | − 1129.81i | − 1.27374i | −0.770970 | − | 0.636872i | \(-0.780228\pi\) | ||||
0.770970 | − | 0.636872i | \(-0.219772\pi\) | |||||||
\(888\) | − 768.071i | − 0.864944i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −752.007 | −0.844952 | ||||||||
\(891\) | 1130.49 | 1.26879 | ||||||||
\(892\) | 834.339i | 0.935357i | ||||||||
\(893\) | 34.2792 | 0.0383866 | ||||||||
\(894\) | 156.101i | 0.174609i | ||||||||
\(895\) | 344.613i | 0.385043i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 52.1909 | 0.0581838 | ||||||||
\(898\) | 360.853 | 0.401841 | ||||||||
\(899\) | − 504.306i | − 0.560964i | ||||||||
\(900\) | −254.059 | −0.282288 | ||||||||
\(901\) | 298.702i | 0.331523i | ||||||||
\(902\) | 393.863i | 0.436655i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −241.706 | −0.267373 | ||||||||
\(905\) | −315.618 | −0.348749 | ||||||||
\(906\) | 793.682i | 0.876029i | ||||||||
\(907\) | 60.0223 | 0.0661767 | 0.0330884 | − | 0.999452i | \(-0.489466\pi\) | ||||
0.0330884 | + | 0.999452i | \(0.489466\pi\) | |||||||
\(908\) | − 464.520i | − 0.511586i | ||||||||
\(909\) | 241.851i | 0.266062i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1422.25 | 1.56120 | 0.780598 | − | 0.625033i | \(-0.214915\pi\) | ||||
0.780598 | + | 0.625033i | \(0.214915\pi\) | |||||||
\(912\) | 12.0000 | 0.0131579 | ||||||||
\(913\) | 1429.96i | 1.56622i | ||||||||
\(914\) | 206.101 | 0.225493 | ||||||||
\(915\) | − 877.448i | − 0.958960i | ||||||||
\(916\) | − 167.244i | − 0.182581i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 41.2721 | 0.0449587 | ||||||||
\(919\) | 1669.70 | 1.81686 | 0.908432 | − | 0.418033i | \(-0.137280\pi\) | ||||
0.908432 | + | 0.418033i | \(0.137280\pi\) | |||||||
\(920\) | 20.3520i | 0.0221217i | ||||||||
\(921\) | 1071.06 | 1.16293 | ||||||||
\(922\) | − 1256.29i | − 1.36257i | ||||||||
\(923\) | − 266.022i | − 0.288215i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 972.205 | 1.05103 | ||||||||
\(926\) | −330.946 | −0.357393 | ||||||||
\(927\) | − 479.344i | − 0.517092i | ||||||||
\(928\) | −115.882 | −0.124873 | ||||||||
\(929\) | 968.860i | 1.04291i | 0.853280 | + | 0.521453i | \(0.174610\pi\) | ||||
−0.853280 | + | 0.521453i | \(0.825390\pi\) | |||||||
\(930\) | − 461.044i | − 0.495746i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 438.146 | 0.470114 | ||||||||
\(933\) | 904.602 | 0.969563 | ||||||||
\(934\) | − 1112.45i | − 1.19106i | ||||||||
\(935\) | 568.654 | 0.608186 | ||||||||
\(936\) | 131.840i | 0.140854i | ||||||||
\(937\) | 1212.57i | 1.29410i | 0.762449 | + | 0.647049i | \(0.223997\pi\) | ||||
−0.762449 | + | 0.647049i | \(0.776003\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −655.742 | −0.698341 | ||||||||
\(940\) | −302.632 | −0.321949 | ||||||||
\(941\) | 1494.06i | 1.58774i | 0.608087 | + | 0.793870i | \(0.291937\pi\) | ||||
−0.608087 | + | 0.793870i | \(0.708063\pi\) | |||||||
\(942\) | 1340.58 | 1.42312 | ||||||||
\(943\) | − 47.7836i | − 0.0506719i | ||||||||
\(944\) | 335.016i | 0.354889i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 121.456 | 0.128389 | ||||||||
\(947\) | 775.462 | 0.818862 | 0.409431 | − | 0.912341i | \(-0.365727\pi\) | ||||
0.409431 | + | 0.912341i | \(0.365727\pi\) | |||||||
\(948\) | − 637.377i | − 0.672339i | ||||||||
\(949\) | 719.574 | 0.758244 | ||||||||
\(950\) | 15.1893i | 0.0159887i | ||||||||
\(951\) | − 1873.45i | − 1.96998i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1055.40 | 1.10745 | 0.553723 | − | 0.832701i | \(-0.313206\pi\) | ||||
0.553723 | + | 0.832701i | \(0.313206\pi\) | |||||||
\(954\) | 264.353 | 0.277100 | ||||||||
\(955\) | 221.383i | 0.231814i | ||||||||
\(956\) | 386.205 | 0.403980 | ||||||||
\(957\) | − 1134.37i | − 1.18533i | ||||||||
\(958\) | 1042.18i | 1.08787i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −105.941 | −0.110355 | ||||||||
\(961\) | 354.955 | 0.369360 | ||||||||
\(962\) | − 504.510i | − 0.524439i | ||||||||
\(963\) | −403.986 | −0.419507 | ||||||||
\(964\) | − 99.0663i | − 0.102766i | ||||||||
\(965\) | − 102.412i | − 0.106127i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1221.63 | 1.26332 | 0.631661 | − | 0.775245i | \(-0.282373\pi\) | ||||
0.631661 | + | 0.775245i | \(0.282373\pi\) | |||||||
\(968\) | −153.775 | −0.158858 | ||||||||
\(969\) | 40.6777i | 0.0419791i | ||||||||
\(970\) | −114.573 | −0.118116 | ||||||||
\(971\) | − 526.259i | − 0.541976i | −0.962583 | − | 0.270988i | \(-0.912650\pi\) | ||||
0.962583 | − | 0.270988i | \(-0.0873504\pi\) | |||||||
\(972\) | − 675.194i | − 0.694644i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −382.825 | −0.393045 | ||||||||
\(975\) | −343.882 | −0.352700 | ||||||||
\(976\) | 265.037i | 0.271555i | ||||||||
\(977\) | −1000.10 | −1.02365 | −0.511823 | − | 0.859091i | \(-0.671030\pi\) | ||||
−0.511823 | + | 0.859091i | \(0.671030\pi\) | |||||||
\(978\) | 543.919i | 0.556154i | ||||||||
\(979\) | 2223.53i | 2.27123i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −639.015 | −0.651392 | ||||||||
\(982\) | −1075.03 | −1.09473 | ||||||||
\(983\) | − 1075.70i | − 1.09430i | −0.837033 | − | 0.547152i | \(-0.815712\pi\) | ||||
0.837033 | − | 0.547152i | \(-0.184288\pi\) | |||||||
\(984\) | 248.735 | 0.252780 | ||||||||
\(985\) | 877.564i | 0.890928i | ||||||||
\(986\) | − 392.819i | − 0.398396i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.88225 | 0.00797799 | ||||||||
\(989\) | −14.7351 | −0.0148990 | ||||||||
\(990\) | − 503.262i | − 0.508345i | ||||||||
\(991\) | −1876.03 | −1.89307 | −0.946536 | − | 0.322597i | \(-0.895444\pi\) | ||||
−0.946536 | + | 0.322597i | \(0.895444\pi\) | |||||||
\(992\) | 139.260i | 0.140383i | ||||||||
\(993\) | − 230.015i | − 0.231636i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 530.285 | 0.532949 | ||||||||
\(996\) | 903.058 | 0.906685 | ||||||||
\(997\) | − 582.224i | − 0.583976i | −0.956422 | − | 0.291988i | \(-0.905683\pi\) | ||||
0.956422 | − | 0.291988i | \(-0.0943167\pi\) | |||||||
\(998\) | −177.473 | −0.177829 | ||||||||
\(999\) | 139.774i | 0.139914i |
(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 | 98.3.b.b.97.2 | 4 | ||
3.2 | odd | 2 | 882.3.c.f.685.3 | 4 | |||
4.3 | odd | 2 | 784.3.c.e.97.1 | 4 | |||
7.2 | even | 3 | 14.3.d.a.3.2 | ✓ | 4 | ||
7.3 | odd | 6 | 14.3.d.a.5.2 | yes | 4 | ||
7.4 | even | 3 | 98.3.d.a.19.2 | 4 | |||
7.5 | odd | 6 | 98.3.d.a.31.2 | 4 | |||
7.6 | odd | 2 | inner | 98.3.b.b.97.1 | 4 | ||
21.2 | odd | 6 | 126.3.n.c.73.1 | 4 | |||
21.5 | even | 6 | 882.3.n.b.325.1 | 4 | |||
21.11 | odd | 6 | 882.3.n.b.19.1 | 4 | |||
21.17 | even | 6 | 126.3.n.c.19.1 | 4 | |||
21.20 | even | 2 | 882.3.c.f.685.4 | 4 | |||
28.3 | even | 6 | 112.3.s.b.33.2 | 4 | |||
28.11 | odd | 6 | 784.3.s.c.705.1 | 4 | |||
28.19 | even | 6 | 784.3.s.c.129.1 | 4 | |||
28.23 | odd | 6 | 112.3.s.b.17.2 | 4 | |||
28.27 | even | 2 | 784.3.c.e.97.4 | 4 | |||
35.2 | odd | 12 | 350.3.i.a.199.1 | 8 | |||
35.3 | even | 12 | 350.3.i.a.299.1 | 8 | |||
35.9 | even | 6 | 350.3.k.a.101.1 | 4 | |||
35.17 | even | 12 | 350.3.i.a.299.4 | 8 | |||
35.23 | odd | 12 | 350.3.i.a.199.4 | 8 | |||
35.24 | odd | 6 | 350.3.k.a.201.1 | 4 | |||
56.3 | even | 6 | 448.3.s.c.257.1 | 4 | |||
56.37 | even | 6 | 448.3.s.d.129.2 | 4 | |||
56.45 | odd | 6 | 448.3.s.d.257.2 | 4 | |||
56.51 | odd | 6 | 448.3.s.c.129.1 | 4 | |||
84.23 | even | 6 | 1008.3.cg.l.577.1 | 4 | |||
84.59 | odd | 6 | 1008.3.cg.l.145.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.3.d.a.3.2 | ✓ | 4 | 7.2 | even | 3 | ||
14.3.d.a.5.2 | yes | 4 | 7.3 | odd | 6 | ||
98.3.b.b.97.1 | 4 | 7.6 | odd | 2 | inner | ||
98.3.b.b.97.2 | 4 | 1.1 | even | 1 | trivial | ||
98.3.d.a.19.2 | 4 | 7.4 | even | 3 | |||
98.3.d.a.31.2 | 4 | 7.5 | odd | 6 | |||
112.3.s.b.17.2 | 4 | 28.23 | odd | 6 | |||
112.3.s.b.33.2 | 4 | 28.3 | even | 6 | |||
126.3.n.c.19.1 | 4 | 21.17 | even | 6 | |||
126.3.n.c.73.1 | 4 | 21.2 | odd | 6 | |||
350.3.i.a.199.1 | 8 | 35.2 | odd | 12 | |||
350.3.i.a.199.4 | 8 | 35.23 | odd | 12 | |||
350.3.i.a.299.1 | 8 | 35.3 | even | 12 | |||
350.3.i.a.299.4 | 8 | 35.17 | even | 12 | |||
350.3.k.a.101.1 | 4 | 35.9 | even | 6 | |||
350.3.k.a.201.1 | 4 | 35.24 | odd | 6 | |||
448.3.s.c.129.1 | 4 | 56.51 | odd | 6 | |||
448.3.s.c.257.1 | 4 | 56.3 | even | 6 | |||
448.3.s.d.129.2 | 4 | 56.37 | even | 6 | |||
448.3.s.d.257.2 | 4 | 56.45 | odd | 6 | |||
784.3.c.e.97.1 | 4 | 4.3 | odd | 2 | |||
784.3.c.e.97.4 | 4 | 28.27 | even | 2 | |||
784.3.s.c.129.1 | 4 | 28.19 | even | 6 | |||
784.3.s.c.705.1 | 4 | 28.11 | odd | 6 | |||
882.3.c.f.685.3 | 4 | 3.2 | odd | 2 | |||
882.3.c.f.685.4 | 4 | 21.20 | even | 2 | |||
882.3.n.b.19.1 | 4 | 21.11 | odd | 6 | |||
882.3.n.b.325.1 | 4 | 21.5 | even | 6 | |||
1008.3.cg.l.145.1 | 4 | 84.59 | odd | 6 | |||
1008.3.cg.l.577.1 | 4 | 84.23 | even | 6 |