Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (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: | \(30.7424047782\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.1 | ||
Root | \(-1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.q.1849.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | − 3.23607i | − 1.86834i | −0.356822 | − | 0.934172i | \(-0.616140\pi\) | ||||
0.356822 | − | 0.934172i | \(-0.383860\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.23607 | −1.32112 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −7.47214 | −2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 3.23607i | 0.934172i | ||||||||
\(13\) | 1.23607i | 0.342824i | 0.985199 | + | 0.171412i | \(0.0548329\pi\) | ||||
−0.985199 | + | 0.171412i | \(0.945167\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.47214i | 1.56972i | 0.619671 | + | 0.784862i | \(0.287266\pi\) | ||||
−0.619671 | + | 0.784862i | \(0.712734\pi\) | |||||||
\(18\) | 7.47214i | 1.76120i | ||||||||
\(19\) | 2.76393 | 0.634089 | 0.317045 | − | 0.948411i | \(-0.397309\pi\) | ||||
0.317045 | + | 0.948411i | \(0.397309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | − 1.00000i | − 0.213201i | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 3.23607 | 0.660560 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.23607 | 0.242413 | ||||||||
\(27\) | 14.4721i | 2.78516i | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 3.23607i | − 0.563327i | ||||||||
\(34\) | 6.47214 | 1.10996 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.47214 | 1.24536 | ||||||||
\(37\) | 10.9443i | 1.79923i | 0.436687 | + | 0.899614i | \(0.356152\pi\) | ||||
−0.436687 | + | 0.899614i | \(0.643848\pi\) | |||||||
\(38\) | − 2.76393i | − 0.448369i | ||||||||
\(39\) | 4.00000 | 0.640513 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.47214 | 1.01078 | 0.505389 | − | 0.862892i | \(-0.331349\pi\) | ||||
0.505389 | + | 0.862892i | \(0.331349\pi\) | |||||||
\(42\) | 3.23607i | 0.499336i | ||||||||
\(43\) | − 1.52786i | − 0.232997i | −0.993191 | − | 0.116499i | \(-0.962833\pi\) | ||||
0.993191 | − | 0.116499i | \(-0.0371670\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | 0.589768 | ||||||||
\(47\) | 2.00000i | 0.291730i | 0.989305 | + | 0.145865i | \(0.0465965\pi\) | ||||
−0.989305 | + | 0.145865i | \(0.953403\pi\) | |||||||
\(48\) | − 3.23607i | − 0.467086i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.9443 | 2.93278 | ||||||||
\(52\) | − 1.23607i | − 0.171412i | ||||||||
\(53\) | − 0.472136i | − 0.0648529i | −0.999474 | − | 0.0324264i | \(-0.989677\pi\) | ||||
0.999474 | − | 0.0324264i | \(-0.0103235\pi\) | |||||||
\(54\) | 14.4721 | 1.96941 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | − 8.94427i | − 1.18470i | ||||||||
\(58\) | − 4.47214i | − 0.587220i | ||||||||
\(59\) | −7.23607 | −0.942056 | −0.471028 | − | 0.882118i | \(-0.656117\pi\) | ||||
−0.471028 | + | 0.882118i | \(0.656117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.23607 | −0.670410 | −0.335205 | − | 0.942145i | \(-0.608806\pi\) | ||||
−0.335205 | + | 0.942145i | \(0.608806\pi\) | |||||||
\(62\) | − 2.00000i | − 0.254000i | ||||||||
\(63\) | 7.47214i | 0.941401i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.23607 | −0.398332 | ||||||||
\(67\) | 15.4164i | 1.88341i | 0.336434 | + | 0.941707i | \(0.390779\pi\) | ||||
−0.336434 | + | 0.941707i | \(0.609221\pi\) | |||||||
\(68\) | − 6.47214i | − 0.784862i | ||||||||
\(69\) | 12.9443 | 1.55831 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.47214 | −0.293389 | −0.146694 | − | 0.989182i | \(-0.546863\pi\) | ||||
−0.146694 | + | 0.989182i | \(0.546863\pi\) | |||||||
\(72\) | − 7.47214i | − 0.880600i | ||||||||
\(73\) | − 4.94427i | − 0.578683i | −0.957226 | − | 0.289342i | \(-0.906564\pi\) | ||||
0.957226 | − | 0.289342i | \(-0.0934364\pi\) | |||||||
\(74\) | 10.9443 | 1.27225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.76393 | −0.317045 | ||||||||
\(77\) | − 1.00000i | − 0.113961i | ||||||||
\(78\) | − 4.00000i | − 0.452911i | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | − 6.47214i | − 0.714728i | ||||||||
\(83\) | 10.1803i | 1.11744i | 0.829357 | + | 0.558719i | \(0.188707\pi\) | ||||
−0.829357 | + | 0.558719i | \(0.811293\pi\) | |||||||
\(84\) | 3.23607 | 0.353084 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.52786 | −0.164754 | ||||||||
\(87\) | − 14.4721i | − 1.55158i | ||||||||
\(88\) | 1.00000i | 0.106600i | ||||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | 0.129575 | ||||||||
\(92\) | − 4.00000i | − 0.417029i | ||||||||
\(93\) | − 6.47214i | − 0.671129i | ||||||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.23607 | −0.330280 | ||||||||
\(97\) | − 3.52786i | − 0.358200i | −0.983831 | − | 0.179100i | \(-0.942681\pi\) | ||||
0.983831 | − | 0.179100i | \(-0.0573186\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | −7.47214 | −0.750978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1803 | −1.41100 | −0.705498 | − | 0.708712i | \(-0.749277\pi\) | ||||
−0.705498 | + | 0.708712i | \(0.749277\pi\) | |||||||
\(102\) | − 20.9443i | − 2.07379i | ||||||||
\(103\) | 2.94427i | 0.290108i | 0.989424 | + | 0.145054i | \(0.0463355\pi\) | ||||
−0.989424 | + | 0.145054i | \(0.953664\pi\) | |||||||
\(104\) | −1.23607 | −0.121206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.472136 | −0.0458579 | ||||||||
\(107\) | 6.47214i | 0.625685i | 0.949805 | + | 0.312842i | \(0.101281\pi\) | ||||
−0.949805 | + | 0.312842i | \(0.898719\pi\) | |||||||
\(108\) | − 14.4721i | − 1.39258i | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 35.4164 | 3.36158 | ||||||||
\(112\) | − 1.00000i | − 0.0944911i | ||||||||
\(113\) | 8.47214i | 0.796992i | 0.917170 | + | 0.398496i | \(0.130468\pi\) | ||||
−0.917170 | + | 0.398496i | \(0.869532\pi\) | |||||||
\(114\) | −8.94427 | −0.837708 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.47214 | −0.415227 | ||||||||
\(117\) | − 9.23607i | − 0.853875i | ||||||||
\(118\) | 7.23607i | 0.666134i | ||||||||
\(119\) | 6.47214 | 0.593300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 5.23607i | 0.474051i | ||||||||
\(123\) | − 20.9443i | − 1.88848i | ||||||||
\(124\) | −2.00000 | −0.179605 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 7.47214 | 0.665671 | ||||||||
\(127\) | 12.0000i | 1.06483i | 0.846484 | + | 0.532414i | \(0.178715\pi\) | ||||
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.94427 | −0.435319 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.23607 | 0.806959 | 0.403480 | − | 0.914989i | \(-0.367801\pi\) | ||||
0.403480 | + | 0.914989i | \(0.367801\pi\) | |||||||
\(132\) | 3.23607i | 0.281664i | ||||||||
\(133\) | − 2.76393i | − 0.239663i | ||||||||
\(134\) | 15.4164 | 1.33177 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.47214 | −0.554981 | ||||||||
\(137\) | − 15.8885i | − 1.35745i | −0.734393 | − | 0.678725i | \(-0.762533\pi\) | ||||
0.734393 | − | 0.678725i | \(-0.237467\pi\) | |||||||
\(138\) | − 12.9443i | − 1.10189i | ||||||||
\(139\) | 8.29180 | 0.703301 | 0.351650 | − | 0.936131i | \(-0.385621\pi\) | ||||
0.351650 | + | 0.936131i | \(0.385621\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.47214 | 0.545052 | ||||||||
\(142\) | 2.47214i | 0.207457i | ||||||||
\(143\) | 1.23607i | 0.103365i | ||||||||
\(144\) | −7.47214 | −0.622678 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.94427 | −0.409191 | ||||||||
\(147\) | 3.23607i | 0.266906i | ||||||||
\(148\) | − 10.9443i | − 0.899614i | ||||||||
\(149\) | −22.3607 | −1.83186 | −0.915929 | − | 0.401340i | \(-0.868545\pi\) | ||||
−0.915929 | + | 0.401340i | \(0.868545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 2.76393i | 0.224184i | ||||||||
\(153\) | − 48.3607i | − 3.90973i | ||||||||
\(154\) | −1.00000 | −0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | − 18.6525i | − 1.48863i | −0.667829 | − | 0.744315i | \(-0.732776\pi\) | ||||
0.667829 | − | 0.744315i | \(-0.267224\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.52786 | −0.121168 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | 0.315244 | ||||||||
\(162\) | − 24.4164i | − 1.91833i | ||||||||
\(163\) | 7.41641i | 0.580898i | 0.956890 | + | 0.290449i | \(0.0938046\pi\) | ||||
−0.956890 | + | 0.290449i | \(0.906195\pi\) | |||||||
\(164\) | −6.47214 | −0.505389 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 10.1803 | 0.790148 | ||||||||
\(167\) | 15.4164i | 1.19296i | 0.802629 | + | 0.596479i | \(0.203434\pi\) | ||||
−0.802629 | + | 0.596479i | \(0.796566\pi\) | |||||||
\(168\) | − 3.23607i | − 0.249668i | ||||||||
\(169\) | 11.4721 | 0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −20.6525 | −1.57933 | ||||||||
\(172\) | 1.52786i | 0.116499i | ||||||||
\(173\) | 1.23607i | 0.0939765i | 0.998895 | + | 0.0469883i | \(0.0149623\pi\) | ||||
−0.998895 | + | 0.0469883i | \(0.985038\pi\) | |||||||
\(174\) | −14.4721 | −1.09713 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 23.4164i | 1.76008i | ||||||||
\(178\) | 10.0000i | 0.749532i | ||||||||
\(179\) | −8.94427 | −0.668526 | −0.334263 | − | 0.942480i | \(-0.608487\pi\) | ||||
−0.334263 | + | 0.942480i | \(0.608487\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.76393 | 0.354100 | 0.177050 | − | 0.984202i | \(-0.443345\pi\) | ||||
0.177050 | + | 0.984202i | \(0.443345\pi\) | |||||||
\(182\) | − 1.23607i | − 0.0916235i | ||||||||
\(183\) | 16.9443i | 1.25256i | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.47214 | −0.474560 | ||||||||
\(187\) | 6.47214i | 0.473289i | ||||||||
\(188\) | − 2.00000i | − 0.145865i | ||||||||
\(189\) | 14.4721 | 1.05269 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.47214 | 0.468307 | 0.234154 | − | 0.972200i | \(-0.424768\pi\) | ||||
0.234154 | + | 0.972200i | \(0.424768\pi\) | |||||||
\(192\) | 3.23607i | 0.233543i | ||||||||
\(193\) | 2.94427i | 0.211933i | 0.994370 | + | 0.105967i | \(0.0337937\pi\) | ||||
−0.994370 | + | 0.105967i | \(0.966206\pi\) | |||||||
\(194\) | −3.52786 | −0.253286 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − 18.0000i | − 1.28245i | −0.767354 | − | 0.641223i | \(-0.778427\pi\) | ||||
0.767354 | − | 0.641223i | \(-0.221573\pi\) | |||||||
\(198\) | 7.47214i | 0.531022i | ||||||||
\(199\) | −1.05573 | −0.0748386 | −0.0374193 | − | 0.999300i | \(-0.511914\pi\) | ||||
−0.0374193 | + | 0.999300i | \(0.511914\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.8885 | 3.51887 | ||||||||
\(202\) | 14.1803i | 0.997725i | ||||||||
\(203\) | − 4.47214i | − 0.313882i | ||||||||
\(204\) | −20.9443 | −1.46639 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.94427 | 0.205137 | ||||||||
\(207\) | − 29.8885i | − 2.07740i | ||||||||
\(208\) | 1.23607i | 0.0857059i | ||||||||
\(209\) | 2.76393 | 0.191185 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.4721 | −1.54705 | −0.773523 | − | 0.633768i | \(-0.781507\pi\) | ||||
−0.773523 | + | 0.633768i | \(0.781507\pi\) | |||||||
\(212\) | 0.472136i | 0.0324264i | ||||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | 6.47214 | 0.442426 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.4721 | −0.984704 | ||||||||
\(217\) | − 2.00000i | − 0.135769i | ||||||||
\(218\) | − 10.0000i | − 0.677285i | ||||||||
\(219\) | −16.0000 | −1.08118 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | − 35.4164i | − 2.37699i | ||||||||
\(223\) | 8.47214i | 0.567336i | 0.958923 | + | 0.283668i | \(0.0915514\pi\) | ||||
−0.958923 | + | 0.283668i | \(0.908449\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.47214 | 0.563558 | ||||||||
\(227\) | 14.7639i | 0.979917i | 0.871746 | + | 0.489958i | \(0.162988\pi\) | ||||
−0.871746 | + | 0.489958i | \(0.837012\pi\) | |||||||
\(228\) | 8.94427i | 0.592349i | ||||||||
\(229\) | −12.7639 | −0.843464 | −0.421732 | − | 0.906720i | \(-0.638578\pi\) | ||||
−0.421732 | + | 0.906720i | \(0.638578\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.23607 | −0.212918 | ||||||||
\(232\) | 4.47214i | 0.293610i | ||||||||
\(233\) | 2.94427i | 0.192886i | 0.995339 | + | 0.0964428i | \(0.0307465\pi\) | ||||
−0.995339 | + | 0.0964428i | \(0.969254\pi\) | |||||||
\(234\) | −9.23607 | −0.603781 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.23607 | 0.471028 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 6.47214i | − 0.419526i | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4164 | −0.735395 | −0.367698 | − | 0.929945i | \(-0.619854\pi\) | ||||
−0.367698 | + | 0.929945i | \(0.619854\pi\) | |||||||
\(242\) | − 1.00000i | − 0.0642824i | ||||||||
\(243\) | − 35.5967i | − 2.28353i | ||||||||
\(244\) | 5.23607 | 0.335205 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −20.9443 | −1.33536 | ||||||||
\(247\) | 3.41641i | 0.217381i | ||||||||
\(248\) | 2.00000i | 0.127000i | ||||||||
\(249\) | 32.9443 | 2.08776 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.7639 | 1.56309 | 0.781543 | − | 0.623852i | \(-0.214433\pi\) | ||||
0.781543 | + | 0.623852i | \(0.214433\pi\) | |||||||
\(252\) | − 7.47214i | − 0.470700i | ||||||||
\(253\) | 4.00000i | 0.251478i | ||||||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.9443i | 0.682685i | 0.939939 | + | 0.341342i | \(0.110882\pi\) | ||||
−0.939939 | + | 0.341342i | \(0.889118\pi\) | |||||||
\(258\) | 4.94427i | 0.307817i | ||||||||
\(259\) | 10.9443 | 0.680044 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33.4164 | −2.06842 | ||||||||
\(262\) | − 9.23607i | − 0.570606i | ||||||||
\(263\) | 12.9443i | 0.798178i | 0.916912 | + | 0.399089i | \(0.130674\pi\) | ||||
−0.916912 | + | 0.399089i | \(0.869326\pi\) | |||||||
\(264\) | 3.23607 | 0.199166 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.76393 | −0.169468 | ||||||||
\(267\) | 32.3607i | 1.98044i | ||||||||
\(268\) | − 15.4164i | − 0.941707i | ||||||||
\(269\) | 27.2361 | 1.66061 | 0.830306 | − | 0.557307i | \(-0.188166\pi\) | ||||
0.830306 | + | 0.557307i | \(0.188166\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.9443 | −1.02929 | −0.514646 | − | 0.857403i | \(-0.672076\pi\) | ||||
−0.514646 | + | 0.857403i | \(0.672076\pi\) | |||||||
\(272\) | 6.47214i | 0.392431i | ||||||||
\(273\) | − 4.00000i | − 0.242091i | ||||||||
\(274\) | −15.8885 | −0.959862 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −12.9443 | −0.779154 | ||||||||
\(277\) | − 12.4721i | − 0.749378i | −0.927151 | − | 0.374689i | \(-0.877749\pi\) | ||||
0.927151 | − | 0.374689i | \(-0.122251\pi\) | |||||||
\(278\) | − 8.29180i | − 0.497309i | ||||||||
\(279\) | −14.9443 | −0.894690 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.8328 | −1.48140 | −0.740701 | − | 0.671835i | \(-0.765506\pi\) | ||||
−0.740701 | + | 0.671835i | \(0.765506\pi\) | |||||||
\(282\) | − 6.47214i | − 0.385410i | ||||||||
\(283\) | − 16.6525i | − 0.989887i | −0.868925 | − | 0.494943i | \(-0.835189\pi\) | ||||
0.868925 | − | 0.494943i | \(-0.164811\pi\) | |||||||
\(284\) | 2.47214 | 0.146694 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.23607 | 0.0730902 | ||||||||
\(287\) | − 6.47214i | − 0.382038i | ||||||||
\(288\) | 7.47214i | 0.440300i | ||||||||
\(289\) | −24.8885 | −1.46403 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4164 | −0.669242 | ||||||||
\(292\) | 4.94427i | 0.289342i | ||||||||
\(293\) | 4.65248i | 0.271801i | 0.990723 | + | 0.135900i | \(0.0433927\pi\) | ||||
−0.990723 | + | 0.135900i | \(0.956607\pi\) | |||||||
\(294\) | 3.23607 | 0.188731 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.9443 | −0.636123 | ||||||||
\(297\) | 14.4721i | 0.839759i | ||||||||
\(298\) | 22.3607i | 1.29532i | ||||||||
\(299\) | −4.94427 | −0.285935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.52786 | −0.0880646 | ||||||||
\(302\) | − 12.0000i | − 0.690522i | ||||||||
\(303\) | 45.8885i | 2.63623i | ||||||||
\(304\) | 2.76393 | 0.158522 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −48.3607 | −2.76460 | ||||||||
\(307\) | − 32.0689i | − 1.83027i | −0.403150 | − | 0.915134i | \(-0.632085\pi\) | ||||
0.403150 | − | 0.915134i | \(-0.367915\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | 9.52786 | 0.542021 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.41641 | 0.307136 | 0.153568 | − | 0.988138i | \(-0.450924\pi\) | ||||
0.153568 | + | 0.988138i | \(0.450924\pi\) | |||||||
\(312\) | 4.00000i | 0.226455i | ||||||||
\(313\) | 28.4721i | 1.60934i | 0.593722 | + | 0.804670i | \(0.297658\pi\) | ||||
−0.593722 | + | 0.804670i | \(0.702342\pi\) | |||||||
\(314\) | −18.6525 | −1.05262 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.0557i | 0.733283i | 0.930362 | + | 0.366641i | \(0.119492\pi\) | ||||
−0.930362 | + | 0.366641i | \(0.880508\pi\) | |||||||
\(318\) | 1.52786i | 0.0856784i | ||||||||
\(319\) | 4.47214 | 0.250392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.9443 | 1.16900 | ||||||||
\(322\) | − 4.00000i | − 0.222911i | ||||||||
\(323\) | 17.8885i | 0.995345i | ||||||||
\(324\) | −24.4164 | −1.35647 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.41641 | 0.410757 | ||||||||
\(327\) | − 32.3607i | − 1.78955i | ||||||||
\(328\) | 6.47214i | 0.357364i | ||||||||
\(329\) | 2.00000 | 0.110264 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.944272 | 0.0519019 | 0.0259509 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259509 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(332\) | − 10.1803i | − 0.558719i | ||||||||
\(333\) | − 81.7771i | − 4.48136i | ||||||||
\(334\) | 15.4164 | 0.843548 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.23607 | −0.176542 | ||||||||
\(337\) | − 18.0000i | − 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | − 11.4721i | − 0.624002i | ||||||||
\(339\) | 27.4164 | 1.48905 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 20.6525i | 1.11676i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 1.52786 | 0.0823769 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.23607 | 0.0664514 | ||||||||
\(347\) | 6.47214i | 0.347442i | 0.984795 | + | 0.173721i | \(0.0555792\pi\) | ||||
−0.984795 | + | 0.173721i | \(0.944421\pi\) | |||||||
\(348\) | 14.4721i | 0.775788i | ||||||||
\(349\) | −8.29180 | −0.443850 | −0.221925 | − | 0.975064i | \(-0.571234\pi\) | ||||
−0.221925 | + | 0.975064i | \(0.571234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | − 1.00000i | − 0.0533002i | ||||||||
\(353\) | − 34.9443i | − 1.85990i | −0.367691 | − | 0.929948i | \(-0.619852\pi\) | ||||
0.367691 | − | 0.929948i | \(-0.380148\pi\) | |||||||
\(354\) | 23.4164 | 1.24457 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | − 20.9443i | − 1.10849i | ||||||||
\(358\) | 8.94427i | 0.472719i | ||||||||
\(359\) | 26.8328 | 1.41618 | 0.708091 | − | 0.706121i | \(-0.249557\pi\) | ||||
0.708091 | + | 0.706121i | \(0.249557\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.3607 | −0.597931 | ||||||||
\(362\) | − 4.76393i | − 0.250387i | ||||||||
\(363\) | − 3.23607i | − 0.169850i | ||||||||
\(364\) | −1.23607 | −0.0647876 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 16.9443 | 0.885691 | ||||||||
\(367\) | − 21.4164i | − 1.11793i | −0.829192 | − | 0.558964i | \(-0.811199\pi\) | ||||
0.829192 | − | 0.558964i | \(-0.188801\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | −48.3607 | −2.51756 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.472136 | −0.0245121 | ||||||||
\(372\) | 6.47214i | 0.335565i | ||||||||
\(373\) | − 6.00000i | − 0.310668i | −0.987862 | − | 0.155334i | \(-0.950355\pi\) | ||||
0.987862 | − | 0.155334i | \(-0.0496454\pi\) | |||||||
\(374\) | 6.47214 | 0.334666 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.00000 | −0.103142 | ||||||||
\(377\) | 5.52786i | 0.284699i | ||||||||
\(378\) | − 14.4721i | − 0.744366i | ||||||||
\(379\) | −5.52786 | −0.283947 | −0.141974 | − | 0.989870i | \(-0.545345\pi\) | ||||
−0.141974 | + | 0.989870i | \(0.545345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.8328 | 1.98947 | ||||||||
\(382\) | − 6.47214i | − 0.331143i | ||||||||
\(383\) | 11.8885i | 0.607476i | 0.952756 | + | 0.303738i | \(0.0982348\pi\) | ||||
−0.952756 | + | 0.303738i | \(0.901765\pi\) | |||||||
\(384\) | 3.23607 | 0.165140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.94427 | 0.149859 | ||||||||
\(387\) | 11.4164i | 0.580329i | ||||||||
\(388\) | 3.52786i | 0.179100i | ||||||||
\(389\) | −6.58359 | −0.333801 | −0.166901 | − | 0.985974i | \(-0.553376\pi\) | ||||
−0.166901 | + | 0.985974i | \(0.553376\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8885 | −1.30924 | ||||||||
\(392\) | − 1.00000i | − 0.0505076i | ||||||||
\(393\) | − 29.8885i | − 1.50768i | ||||||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.47214 | 0.375489 | ||||||||
\(397\) | 10.2918i | 0.516530i | 0.966074 | + | 0.258265i | \(0.0831508\pi\) | ||||
−0.966074 | + | 0.258265i | \(0.916849\pi\) | |||||||
\(398\) | 1.05573i | 0.0529189i | ||||||||
\(399\) | −8.94427 | −0.447774 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.3607 | −1.51614 | −0.758070 | − | 0.652173i | \(-0.773857\pi\) | ||||
−0.758070 | + | 0.652173i | \(0.773857\pi\) | |||||||
\(402\) | − 49.8885i | − 2.48821i | ||||||||
\(403\) | 2.47214i | 0.123146i | ||||||||
\(404\) | 14.1803 | 0.705498 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | 10.9443i | 0.542487i | ||||||||
\(408\) | 20.9443i | 1.03690i | ||||||||
\(409\) | 23.4164 | 1.15787 | 0.578933 | − | 0.815375i | \(-0.303469\pi\) | ||||
0.578933 | + | 0.815375i | \(0.303469\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −51.4164 | −2.53618 | ||||||||
\(412\) | − 2.94427i | − 0.145054i | ||||||||
\(413\) | 7.23607i | 0.356064i | ||||||||
\(414\) | −29.8885 | −1.46894 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.23607 | 0.0606032 | ||||||||
\(417\) | − 26.8328i | − 1.31401i | ||||||||
\(418\) | − 2.76393i | − 0.135188i | ||||||||
\(419\) | −12.7639 | −0.623559 | −0.311779 | − | 0.950155i | \(-0.600925\pi\) | ||||
−0.311779 | + | 0.950155i | \(0.600925\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.52786 | 0.366886 | 0.183443 | − | 0.983030i | \(-0.441276\pi\) | ||||
0.183443 | + | 0.983030i | \(0.441276\pi\) | |||||||
\(422\) | 22.4721i | 1.09393i | ||||||||
\(423\) | − 14.9443i | − 0.726615i | ||||||||
\(424\) | 0.472136 | 0.0229289 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | 5.23607i | 0.253391i | ||||||||
\(428\) | − 6.47214i | − 0.312842i | ||||||||
\(429\) | 4.00000 | 0.193122 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 40.9443 | 1.97222 | 0.986108 | − | 0.166105i | \(-0.0531190\pi\) | ||||
0.986108 | + | 0.166105i | \(0.0531190\pi\) | |||||||
\(432\) | 14.4721i | 0.696291i | ||||||||
\(433\) | 19.5279i | 0.938449i | 0.883079 | + | 0.469225i | \(0.155467\pi\) | ||||
−0.883079 | + | 0.469225i | \(0.844533\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 11.0557i | 0.528867i | ||||||||
\(438\) | 16.0000i | 0.764510i | ||||||||
\(439\) | 8.94427 | 0.426887 | 0.213443 | − | 0.976955i | \(-0.431532\pi\) | ||||
0.213443 | + | 0.976955i | \(0.431532\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 8.00000i | 0.380521i | ||||||||
\(443\) | − 7.05573i | − 0.335228i | −0.985853 | − | 0.167614i | \(-0.946394\pi\) | ||||
0.985853 | − | 0.167614i | \(-0.0536062\pi\) | |||||||
\(444\) | −35.4164 | −1.68079 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.47214 | 0.401167 | ||||||||
\(447\) | 72.3607i | 3.42254i | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | −1.05573 | −0.0498229 | −0.0249114 | − | 0.999690i | \(-0.507930\pi\) | ||||
−0.0249114 | + | 0.999690i | \(0.507930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.47214 | 0.304761 | ||||||||
\(452\) | − 8.47214i | − 0.398496i | ||||||||
\(453\) | − 38.8328i | − 1.82452i | ||||||||
\(454\) | 14.7639 | 0.692906 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.94427 | 0.418854 | ||||||||
\(457\) | − 9.05573i | − 0.423609i | −0.977312 | − | 0.211805i | \(-0.932066\pi\) | ||||
0.977312 | − | 0.211805i | \(-0.0679340\pi\) | |||||||
\(458\) | 12.7639i | 0.596419i | ||||||||
\(459\) | −93.6656 | −4.37194 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.2361 | 1.36166 | 0.680830 | − | 0.732442i | \(-0.261619\pi\) | ||||
0.680830 | + | 0.732442i | \(0.261619\pi\) | |||||||
\(462\) | 3.23607i | 0.150556i | ||||||||
\(463\) | − 21.5279i | − 1.00048i | −0.865885 | − | 0.500242i | \(-0.833244\pi\) | ||||
0.865885 | − | 0.500242i | \(-0.166756\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.94427 | 0.136391 | ||||||||
\(467\) | − 13.1246i | − 0.607335i | −0.952778 | − | 0.303667i | \(-0.901789\pi\) | ||||
0.952778 | − | 0.303667i | \(-0.0982111\pi\) | |||||||
\(468\) | 9.23607i | 0.426937i | ||||||||
\(469\) | 15.4164 | 0.711864 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −60.3607 | −2.78127 | ||||||||
\(472\) | − 7.23607i | − 0.333067i | ||||||||
\(473\) | − 1.52786i | − 0.0702513i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.47214 | −0.296650 | ||||||||
\(477\) | 3.52786i | 0.161530i | ||||||||
\(478\) | 20.0000i | 0.914779i | ||||||||
\(479\) | 32.3607 | 1.47860 | 0.739299 | − | 0.673378i | \(-0.235157\pi\) | ||||
0.739299 | + | 0.673378i | \(0.235157\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.5279 | −0.616818 | ||||||||
\(482\) | 11.4164i | 0.520003i | ||||||||
\(483\) | − 12.9443i | − 0.588985i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −35.5967 | −1.61470 | ||||||||
\(487\) | 0.944272i | 0.0427890i | 0.999771 | + | 0.0213945i | \(0.00681061\pi\) | ||||
−0.999771 | + | 0.0213945i | \(0.993189\pi\) | |||||||
\(488\) | − 5.23607i | − 0.237026i | ||||||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.944272 | 0.0426144 | 0.0213072 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213072 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(492\) | 20.9443i | 0.944241i | ||||||||
\(493\) | 28.9443i | 1.30358i | ||||||||
\(494\) | 3.41641 | 0.153711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 2.47214i | 0.110890i | ||||||||
\(498\) | − 32.9443i | − 1.47627i | ||||||||
\(499\) | −12.3607 | −0.553340 | −0.276670 | − | 0.960965i | \(-0.589231\pi\) | ||||
−0.276670 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 49.8885 | 2.22886 | ||||||||
\(502\) | − 24.7639i | − 1.10527i | ||||||||
\(503\) | 4.00000i | 0.178351i | 0.996016 | + | 0.0891756i | \(0.0284232\pi\) | ||||
−0.996016 | + | 0.0891756i | \(0.971577\pi\) | |||||||
\(504\) | −7.47214 | −0.332835 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | − 37.1246i | − 1.64876i | ||||||||
\(508\) | − 12.0000i | − 0.532414i | ||||||||
\(509\) | 34.0689 | 1.51008 | 0.755038 | − | 0.655681i | \(-0.227618\pi\) | ||||
0.755038 | + | 0.655681i | \(0.227618\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.94427 | −0.218722 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 40.0000i | 1.76604i | ||||||||
\(514\) | 10.9443 | 0.482731 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.94427 | 0.217659 | ||||||||
\(517\) | 2.00000i | 0.0879599i | ||||||||
\(518\) | − 10.9443i | − 0.480864i | ||||||||
\(519\) | 4.00000 | 0.175581 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.3607 | 1.50537 | 0.752684 | − | 0.658382i | \(-0.228759\pi\) | ||||
0.752684 | + | 0.658382i | \(0.228759\pi\) | |||||||
\(522\) | 33.4164i | 1.46260i | ||||||||
\(523\) | − 27.7082i | − 1.21160i | −0.795619 | − | 0.605798i | \(-0.792854\pi\) | ||||
0.795619 | − | 0.605798i | \(-0.207146\pi\) | |||||||
\(524\) | −9.23607 | −0.403480 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.9443 | 0.564397 | ||||||||
\(527\) | 12.9443i | 0.563861i | ||||||||
\(528\) | − 3.23607i | − 0.140832i | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 54.0689 | 2.34639 | ||||||||
\(532\) | 2.76393i | 0.119832i | ||||||||
\(533\) | 8.00000i | 0.346518i | ||||||||
\(534\) | 32.3607 | 1.40038 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.4164 | −0.665887 | ||||||||
\(537\) | 28.9443i | 1.24904i | ||||||||
\(538\) | − 27.2361i | − 1.17423i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.05573 | −0.389336 | −0.194668 | − | 0.980869i | \(-0.562363\pi\) | ||||
−0.194668 | + | 0.980869i | \(0.562363\pi\) | |||||||
\(542\) | 16.9443i | 0.727819i | ||||||||
\(543\) | − 15.4164i | − 0.661581i | ||||||||
\(544\) | 6.47214 | 0.277491 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.00000 | −0.171184 | ||||||||
\(547\) | − 16.9443i | − 0.724485i | −0.932084 | − | 0.362242i | \(-0.882011\pi\) | ||||
0.932084 | − | 0.362242i | \(-0.117989\pi\) | |||||||
\(548\) | 15.8885i | 0.678725i | ||||||||
\(549\) | 39.1246 | 1.66980 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.3607 | 0.526583 | ||||||||
\(552\) | 12.9443i | 0.550945i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.4721 | −0.529890 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.29180 | −0.351650 | ||||||||
\(557\) | 28.8328i | 1.22169i | 0.791752 | + | 0.610843i | \(0.209169\pi\) | ||||
−0.791752 | + | 0.610843i | \(0.790831\pi\) | |||||||
\(558\) | 14.9443i | 0.632641i | ||||||||
\(559\) | 1.88854 | 0.0798769 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.9443 | 0.884268 | ||||||||
\(562\) | 24.8328i | 1.04751i | ||||||||
\(563\) | 26.7639i | 1.12797i | 0.825787 | + | 0.563983i | \(0.190732\pi\) | ||||
−0.825787 | + | 0.563983i | \(0.809268\pi\) | |||||||
\(564\) | −6.47214 | −0.272526 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −16.6525 | −0.699956 | ||||||||
\(567\) | − 24.4164i | − 1.02539i | ||||||||
\(568\) | − 2.47214i | − 0.103729i | ||||||||
\(569\) | −16.8328 | −0.705668 | −0.352834 | − | 0.935686i | \(-0.614782\pi\) | ||||
−0.352834 | + | 0.935686i | \(0.614782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −45.8885 | −1.92038 | −0.960188 | − | 0.279355i | \(-0.909879\pi\) | ||||
−0.960188 | + | 0.279355i | \(0.909879\pi\) | |||||||
\(572\) | − 1.23607i | − 0.0516826i | ||||||||
\(573\) | − 20.9443i | − 0.874960i | ||||||||
\(574\) | −6.47214 | −0.270142 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.47214 | 0.311339 | ||||||||
\(577\) | − 9.05573i | − 0.376995i | −0.982074 | − | 0.188497i | \(-0.939638\pi\) | ||||
0.982074 | − | 0.188497i | \(-0.0603617\pi\) | |||||||
\(578\) | 24.8885i | 1.03523i | ||||||||
\(579\) | 9.52786 | 0.395965 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.1803 | 0.422352 | ||||||||
\(582\) | 11.4164i | 0.473225i | ||||||||
\(583\) | − 0.472136i | − 0.0195539i | ||||||||
\(584\) | 4.94427 | 0.204595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.65248 | 0.192192 | ||||||||
\(587\) | 28.1803i | 1.16313i | 0.813501 | + | 0.581564i | \(0.197559\pi\) | ||||
−0.813501 | + | 0.581564i | \(0.802441\pi\) | |||||||
\(588\) | − 3.23607i | − 0.133453i | ||||||||
\(589\) | 5.52786 | 0.227772 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −58.2492 | −2.39605 | ||||||||
\(592\) | 10.9443i | 0.449807i | ||||||||
\(593\) | 24.0000i | 0.985562i | 0.870153 | + | 0.492781i | \(0.164020\pi\) | ||||
−0.870153 | + | 0.492781i | \(0.835980\pi\) | |||||||
\(594\) | 14.4721 | 0.593799 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.3607 | 0.915929 | ||||||||
\(597\) | 3.41641i | 0.139824i | ||||||||
\(598\) | 4.94427i | 0.202186i | ||||||||
\(599\) | −12.3607 | −0.505044 | −0.252522 | − | 0.967591i | \(-0.581260\pi\) | ||||
−0.252522 | + | 0.967591i | \(0.581260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.8328 | 0.768207 | 0.384103 | − | 0.923290i | \(-0.374511\pi\) | ||||
0.384103 | + | 0.923290i | \(0.374511\pi\) | |||||||
\(602\) | 1.52786i | 0.0622711i | ||||||||
\(603\) | − 115.193i | − 4.69104i | ||||||||
\(604\) | −12.0000 | −0.488273 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 45.8885 | 1.86409 | ||||||||
\(607\) | 32.0000i | 1.29884i | 0.760430 | + | 0.649420i | \(0.224988\pi\) | ||||
−0.760430 | + | 0.649420i | \(0.775012\pi\) | |||||||
\(608\) | − 2.76393i | − 0.112092i | ||||||||
\(609\) | −14.4721 | −0.586441 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.47214 | −0.100012 | ||||||||
\(612\) | 48.3607i | 1.95486i | ||||||||
\(613\) | 19.5279i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(614\) | −32.0689 | −1.29419 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | 5.41641i | 0.218056i | 0.994039 | + | 0.109028i | \(0.0347739\pi\) | ||||
−0.994039 | + | 0.109028i | \(0.965226\pi\) | |||||||
\(618\) | − 9.52786i | − 0.383267i | ||||||||
\(619\) | 48.5410 | 1.95103 | 0.975514 | − | 0.219937i | \(-0.0705851\pi\) | ||||
0.975514 | + | 0.219937i | \(0.0705851\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −57.8885 | −2.32299 | ||||||||
\(622\) | − 5.41641i | − 0.217178i | ||||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | 4.00000 | 0.160128 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 28.4721 | 1.13798 | ||||||||
\(627\) | − 8.94427i | − 0.357200i | ||||||||
\(628\) | 18.6525i | 0.744315i | ||||||||
\(629\) | −70.8328 | −2.82429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.58359 | −0.182470 | −0.0912350 | − | 0.995829i | \(-0.529081\pi\) | ||||
−0.0912350 | + | 0.995829i | \(0.529081\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 72.7214i | 2.89041i | ||||||||
\(634\) | 13.0557 | 0.518509 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.52786 | 0.0605838 | ||||||||
\(637\) | − 1.23607i | − 0.0489748i | ||||||||
\(638\) | − 4.47214i | − 0.177054i | ||||||||
\(639\) | 18.4721 | 0.730746 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.4721 | 1.44056 | 0.720281 | − | 0.693682i | \(-0.244013\pi\) | ||||
0.720281 | + | 0.693682i | \(0.244013\pi\) | |||||||
\(642\) | − 20.9443i | − 0.826604i | ||||||||
\(643\) | − 23.2361i | − 0.916341i | −0.888864 | − | 0.458171i | \(-0.848505\pi\) | ||||
0.888864 | − | 0.458171i | \(-0.151495\pi\) | |||||||
\(644\) | −4.00000 | −0.157622 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.8885 | 0.703815 | ||||||||
\(647\) | − 24.8328i | − 0.976279i | −0.872766 | − | 0.488139i | \(-0.837676\pi\) | ||||
0.872766 | − | 0.488139i | \(-0.162324\pi\) | |||||||
\(648\) | 24.4164i | 0.959167i | ||||||||
\(649\) | −7.23607 | −0.284041 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.47214 | −0.253663 | ||||||||
\(652\) | − 7.41641i | − 0.290449i | ||||||||
\(653\) | 1.63932i | 0.0641516i | 0.999485 | + | 0.0320758i | \(0.0102118\pi\) | ||||
−0.999485 | + | 0.0320758i | \(0.989788\pi\) | |||||||
\(654\) | −32.3607 | −1.26540 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.47214 | 0.252694 | ||||||||
\(657\) | 36.9443i | 1.44133i | ||||||||
\(658\) | − 2.00000i | − 0.0779681i | ||||||||
\(659\) | −43.4164 | −1.69126 | −0.845632 | − | 0.533767i | \(-0.820776\pi\) | ||||
−0.845632 | + | 0.533767i | \(0.820776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.1246 | 1.44398 | 0.721990 | − | 0.691903i | \(-0.243228\pi\) | ||||
0.721990 | + | 0.691903i | \(0.243228\pi\) | |||||||
\(662\) | − 0.944272i | − 0.0367002i | ||||||||
\(663\) | 25.8885i | 1.00543i | ||||||||
\(664\) | −10.1803 | −0.395074 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −81.7771 | −3.16880 | ||||||||
\(667\) | 17.8885i | 0.692647i | ||||||||
\(668\) | − 15.4164i | − 0.596479i | ||||||||
\(669\) | 27.4164 | 1.05998 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.23607 | −0.202136 | ||||||||
\(672\) | 3.23607i | 0.124834i | ||||||||
\(673\) | 31.8885i | 1.22921i | 0.788834 | + | 0.614607i | \(0.210685\pi\) | ||||
−0.788834 | + | 0.614607i | \(0.789315\pi\) | |||||||
\(674\) | −18.0000 | −0.693334 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.4721 | −0.441236 | ||||||||
\(677\) | − 32.0689i | − 1.23251i | −0.787548 | − | 0.616254i | \(-0.788650\pi\) | ||||
0.787548 | − | 0.616254i | \(-0.211350\pi\) | |||||||
\(678\) | − 27.4164i | − 1.05292i | ||||||||
\(679\) | −3.52786 | −0.135387 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.7771 | 1.83082 | ||||||||
\(682\) | − 2.00000i | − 0.0765840i | ||||||||
\(683\) | 15.0557i | 0.576091i | 0.957617 | + | 0.288046i | \(0.0930055\pi\) | ||||
−0.957617 | + | 0.288046i | \(0.906994\pi\) | |||||||
\(684\) | 20.6525 | 0.789667 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 41.3050i | 1.57588i | ||||||||
\(688\) | − 1.52786i | − 0.0582493i | ||||||||
\(689\) | 0.583592 | 0.0222331 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6525 | −0.709574 | −0.354787 | − | 0.934947i | \(-0.615447\pi\) | ||||
−0.354787 | + | 0.934947i | \(0.615447\pi\) | |||||||
\(692\) | − 1.23607i | − 0.0469883i | ||||||||
\(693\) | 7.47214i | 0.283843i | ||||||||
\(694\) | 6.47214 | 0.245679 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 14.4721 | 0.548565 | ||||||||
\(697\) | 41.8885i | 1.58664i | ||||||||
\(698\) | 8.29180i | 0.313849i | ||||||||
\(699\) | 9.52786 | 0.360377 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.7214 | 1.76464 | 0.882321 | − | 0.470649i | \(-0.155980\pi\) | ||||
0.882321 | + | 0.470649i | \(0.155980\pi\) | |||||||
\(702\) | 17.8885i | 0.675160i | ||||||||
\(703\) | 30.2492i | 1.14087i | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −34.9443 | −1.31515 | ||||||||
\(707\) | 14.1803i | 0.533307i | ||||||||
\(708\) | − 23.4164i | − 0.880042i | ||||||||
\(709\) | 4.47214 | 0.167955 | 0.0839773 | − | 0.996468i | \(-0.473238\pi\) | ||||
0.0839773 | + | 0.996468i | \(0.473238\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 10.0000i | − 0.374766i | ||||||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | −20.9443 | −0.783820 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.94427 | 0.334263 | ||||||||
\(717\) | 64.7214i | 2.41706i | ||||||||
\(718\) | − 26.8328i | − 1.00139i | ||||||||
\(719\) | 36.8328 | 1.37363 | 0.686816 | − | 0.726831i | \(-0.259008\pi\) | ||||
0.686816 | + | 0.726831i | \(0.259008\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.94427 | 0.109650 | ||||||||
\(722\) | 11.3607i | 0.422801i | ||||||||
\(723\) | 36.9443i | 1.37397i | ||||||||
\(724\) | −4.76393 | −0.177050 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.23607 | −0.120102 | ||||||||
\(727\) | − 18.0000i | − 0.667583i | −0.942647 | − | 0.333792i | \(-0.891672\pi\) | ||||
0.942647 | − | 0.333792i | \(-0.108328\pi\) | |||||||
\(728\) | 1.23607i | 0.0458117i | ||||||||
\(729\) | −41.9443 | −1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.88854 | 0.365741 | ||||||||
\(732\) | − 16.9443i | − 0.626278i | ||||||||
\(733\) | 8.87539i | 0.327820i | 0.986475 | + | 0.163910i | \(0.0524107\pi\) | ||||
−0.986475 | + | 0.163910i | \(0.947589\pi\) | |||||||
\(734\) | −21.4164 | −0.790494 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | 0.147442 | ||||||||
\(737\) | 15.4164i | 0.567871i | ||||||||
\(738\) | 48.3607i | 1.78018i | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.0557 | 0.406142 | ||||||||
\(742\) | 0.472136i | 0.0173327i | ||||||||
\(743\) | − 13.8885i | − 0.509521i | −0.967004 | − | 0.254761i | \(-0.918003\pi\) | ||||
0.967004 | − | 0.254761i | \(-0.0819967\pi\) | |||||||
\(744\) | 6.47214 | 0.237280 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −6.00000 | −0.219676 | ||||||||
\(747\) | − 76.0689i | − 2.78321i | ||||||||
\(748\) | − 6.47214i | − 0.236645i | ||||||||
\(749\) | 6.47214 | 0.236487 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.944272 | 0.0344570 | 0.0172285 | − | 0.999852i | \(-0.494516\pi\) | ||||
0.0172285 | + | 0.999852i | \(0.494516\pi\) | |||||||
\(752\) | 2.00000i | 0.0729325i | ||||||||
\(753\) | − 80.1378i | − 2.92038i | ||||||||
\(754\) | 5.52786 | 0.201313 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −14.4721 | −0.526346 | ||||||||
\(757\) | − 39.3050i | − 1.42856i | −0.699859 | − | 0.714281i | \(-0.746754\pi\) | ||||
0.699859 | − | 0.714281i | \(-0.253246\pi\) | |||||||
\(758\) | 5.52786i | 0.200781i | ||||||||
\(759\) | 12.9443 | 0.469847 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.4164 | 0.558844 | 0.279422 | − | 0.960168i | \(-0.409857\pi\) | ||||
0.279422 | + | 0.960168i | \(0.409857\pi\) | |||||||
\(762\) | − 38.8328i | − 1.40676i | ||||||||
\(763\) | − 10.0000i | − 0.362024i | ||||||||
\(764\) | −6.47214 | −0.234154 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.8885 | 0.429551 | ||||||||
\(767\) | − 8.94427i | − 0.322959i | ||||||||
\(768\) | − 3.23607i | − 0.116772i | ||||||||
\(769\) | 16.5836 | 0.598020 | 0.299010 | − | 0.954250i | \(-0.403344\pi\) | ||||
0.299010 | + | 0.954250i | \(0.403344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.4164 | 1.27549 | ||||||||
\(772\) | − 2.94427i | − 0.105967i | ||||||||
\(773\) | 2.29180i | 0.0824302i | 0.999150 | + | 0.0412151i | \(0.0131229\pi\) | ||||
−0.999150 | + | 0.0412151i | \(0.986877\pi\) | |||||||
\(774\) | 11.4164 | 0.410354 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.52786 | 0.126643 | ||||||||
\(777\) | − 35.4164i | − 1.27056i | ||||||||
\(778\) | 6.58359i | 0.236033i | ||||||||
\(779\) | 17.8885 | 0.640924 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.47214 | −0.0884600 | ||||||||
\(782\) | 25.8885i | 0.925772i | ||||||||
\(783\) | 64.7214i | 2.31295i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −29.8885 | −1.06609 | ||||||||
\(787\) | 5.81966i | 0.207448i | 0.994606 | + | 0.103724i | \(0.0330759\pi\) | ||||
−0.994606 | + | 0.103724i | \(0.966924\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 41.8885 | 1.49127 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.47214 | 0.301234 | ||||||||
\(792\) | − 7.47214i | − 0.265511i | ||||||||
\(793\) | − 6.47214i | − 0.229832i | ||||||||
\(794\) | 10.2918 | 0.365242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.05573 | 0.0374193 | ||||||||
\(797\) | − 7.59675i | − 0.269091i | −0.990907 | − | 0.134545i | \(-0.957043\pi\) | ||||
0.990907 | − | 0.134545i | \(-0.0429574\pi\) | |||||||
\(798\) | 8.94427i | 0.316624i | ||||||||
\(799\) | −12.9443 | −0.457935 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 74.7214 | 2.64015 | ||||||||
\(802\) | 30.3607i | 1.07207i | ||||||||
\(803\) | − 4.94427i | − 0.174480i | ||||||||
\(804\) | −49.8885 | −1.75943 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.47214 | 0.0870773 | ||||||||
\(807\) | − 88.1378i | − 3.10260i | ||||||||
\(808\) | − 14.1803i | − 0.498863i | ||||||||
\(809\) | 38.9443 | 1.36921 | 0.684604 | − | 0.728915i | \(-0.259975\pi\) | ||||
0.684604 | + | 0.728915i | \(0.259975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.23607 | 0.324322 | 0.162161 | − | 0.986764i | \(-0.448154\pi\) | ||||
0.162161 | + | 0.986764i | \(0.448154\pi\) | |||||||
\(812\) | 4.47214i | 0.156941i | ||||||||
\(813\) | 54.8328i | 1.92307i | ||||||||
\(814\) | 10.9443 | 0.383597 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.9443 | 0.733196 | ||||||||
\(817\) | − 4.22291i | − 0.147741i | ||||||||
\(818\) | − 23.4164i | − 0.818736i | ||||||||
\(819\) | −9.23607 | −0.322734 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.4164 | 0.887039 | 0.443519 | − | 0.896265i | \(-0.353730\pi\) | ||||
0.443519 | + | 0.896265i | \(0.353730\pi\) | |||||||
\(822\) | 51.4164i | 1.79335i | ||||||||
\(823\) | 34.2492i | 1.19385i | 0.802296 | + | 0.596926i | \(0.203612\pi\) | ||||
−0.802296 | + | 0.596926i | \(0.796388\pi\) | |||||||
\(824\) | −2.94427 | −0.102569 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.23607 | 0.251775 | ||||||||
\(827\) | 0.944272i | 0.0328356i | 0.999865 | + | 0.0164178i | \(0.00522618\pi\) | ||||
−0.999865 | + | 0.0164178i | \(0.994774\pi\) | |||||||
\(828\) | 29.8885i | 1.03870i | ||||||||
\(829\) | 1.70820 | 0.0593284 | 0.0296642 | − | 0.999560i | \(-0.490556\pi\) | ||||
0.0296642 | + | 0.999560i | \(0.490556\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −40.3607 | −1.40010 | ||||||||
\(832\) | − 1.23607i | − 0.0428529i | ||||||||
\(833\) | − 6.47214i | − 0.224246i | ||||||||
\(834\) | −26.8328 | −0.929144 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.76393 | −0.0955926 | ||||||||
\(837\) | 28.9443i | 1.00046i | ||||||||
\(838\) | 12.7639i | 0.440923i | ||||||||
\(839\) | 36.8328 | 1.27161 | 0.635805 | − | 0.771850i | \(-0.280668\pi\) | ||||
0.635805 | + | 0.771850i | \(0.280668\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | − 7.52786i | − 0.259427i | ||||||||
\(843\) | 80.3607i | 2.76777i | ||||||||
\(844\) | 22.4721 | 0.773523 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −14.9443 | −0.513795 | ||||||||
\(847\) | − 1.00000i | − 0.0343604i | ||||||||
\(848\) | − 0.472136i | − 0.0162132i | ||||||||
\(849\) | −53.8885 | −1.84945 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43.7771 | −1.50066 | ||||||||
\(852\) | − 8.00000i | − 0.274075i | ||||||||
\(853\) | − 34.5410i | − 1.18266i | −0.806429 | − | 0.591331i | \(-0.798603\pi\) | ||||
0.806429 | − | 0.591331i | \(-0.201397\pi\) | |||||||
\(854\) | 5.23607 | 0.179175 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.47214 | −0.221213 | ||||||||
\(857\) | 37.5279i | 1.28193i | 0.767571 | + | 0.640964i | \(0.221465\pi\) | ||||
−0.767571 | + | 0.640964i | \(0.778535\pi\) | |||||||
\(858\) | − 4.00000i | − 0.136558i | ||||||||
\(859\) | 25.1246 | 0.857241 | 0.428620 | − | 0.903485i | \(-0.359000\pi\) | ||||
0.428620 | + | 0.903485i | \(0.359000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.9443 | −0.713779 | ||||||||
\(862\) | − 40.9443i | − 1.39457i | ||||||||
\(863\) | 27.4164i | 0.933265i | 0.884451 | + | 0.466633i | \(0.154533\pi\) | ||||
−0.884451 | + | 0.466633i | \(0.845467\pi\) | |||||||
\(864\) | 14.4721 | 0.492352 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 19.5279 | 0.663584 | ||||||||
\(867\) | 80.5410i | 2.73532i | ||||||||
\(868\) | 2.00000i | 0.0678844i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.0557 | −0.645679 | ||||||||
\(872\) | 10.0000i | 0.338643i | ||||||||
\(873\) | 26.3607i | 0.892174i | ||||||||
\(874\) | 11.0557 | 0.373966 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | − 26.9443i | − 0.909843i | −0.890531 | − | 0.454922i | \(-0.849667\pi\) | ||||
0.890531 | − | 0.454922i | \(-0.150333\pi\) | |||||||
\(878\) | − 8.94427i | − 0.301855i | ||||||||
\(879\) | 15.0557 | 0.507817 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.8328 | −0.836639 | −0.418319 | − | 0.908300i | \(-0.637381\pi\) | ||||
−0.418319 | + | 0.908300i | \(0.637381\pi\) | |||||||
\(882\) | − 7.47214i | − 0.251600i | ||||||||
\(883\) | 50.8328i | 1.71066i | 0.518083 | + | 0.855330i | \(0.326646\pi\) | ||||
−0.518083 | + | 0.855330i | \(0.673354\pi\) | |||||||
\(884\) | 8.00000 | 0.269069 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.05573 | −0.237042 | ||||||||
\(887\) | − 0.360680i | − 0.0121104i | −0.999982 | − | 0.00605522i | \(-0.998073\pi\) | ||||
0.999982 | − | 0.00605522i | \(-0.00192745\pi\) | |||||||
\(888\) | 35.4164i | 1.18850i | ||||||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 24.4164 | 0.817980 | ||||||||
\(892\) | − 8.47214i | − 0.283668i | ||||||||
\(893\) | 5.52786i | 0.184983i | ||||||||
\(894\) | 72.3607 | 2.42010 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 16.0000i | 0.534224i | ||||||||
\(898\) | 1.05573i | 0.0352301i | ||||||||
\(899\) | 8.94427 | 0.298308 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.05573 | 0.101801 | ||||||||
\(902\) | − 6.47214i | − 0.215499i | ||||||||
\(903\) | 4.94427i | 0.164535i | ||||||||
\(904\) | −8.47214 | −0.281779 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −38.8328 | −1.29013 | ||||||||
\(907\) | − 20.3607i | − 0.676065i | −0.941134 | − | 0.338033i | \(-0.890239\pi\) | ||||
0.941134 | − | 0.338033i | \(-0.109761\pi\) | |||||||
\(908\) | − 14.7639i | − 0.489958i | ||||||||
\(909\) | 105.957 | 3.51439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.0000 | −0.927681 | −0.463841 | − | 0.885919i | \(-0.653529\pi\) | ||||
−0.463841 | + | 0.885919i | \(0.653529\pi\) | |||||||
\(912\) | − 8.94427i | − 0.296174i | ||||||||
\(913\) | 10.1803i | 0.336920i | ||||||||
\(914\) | −9.05573 | −0.299537 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.7639 | 0.421732 | ||||||||
\(917\) | − 9.23607i | − 0.305002i | ||||||||
\(918\) | 93.6656i | 3.09143i | ||||||||
\(919\) | 57.8885 | 1.90957 | 0.954783 | − | 0.297302i | \(-0.0960869\pi\) | ||||
0.954783 | + | 0.297302i | \(0.0960869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −103.777 | −3.41957 | ||||||||
\(922\) | − 29.2361i | − 0.962839i | ||||||||
\(923\) | − 3.05573i | − 0.100581i | ||||||||
\(924\) | 3.23607 | 0.106459 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.5279 | −0.707450 | ||||||||
\(927\) | − 22.0000i | − 0.722575i | ||||||||
\(928\) | − 4.47214i | − 0.146805i | ||||||||
\(929\) | 40.2492 | 1.32053 | 0.660267 | − | 0.751031i | \(-0.270443\pi\) | ||||
0.660267 | + | 0.751031i | \(0.270443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.76393 | −0.0905842 | ||||||||
\(932\) | − 2.94427i | − 0.0964428i | ||||||||
\(933\) | − 17.5279i | − 0.573837i | ||||||||
\(934\) | −13.1246 | −0.429450 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.23607 | 0.301890 | ||||||||
\(937\) | 20.9443i | 0.684220i | 0.939660 | + | 0.342110i | \(0.111141\pi\) | ||||
−0.939660 | + | 0.342110i | \(0.888859\pi\) | |||||||
\(938\) | − 15.4164i | − 0.503364i | ||||||||
\(939\) | 92.1378 | 3.00680 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.1803 | −1.11425 | −0.557124 | − | 0.830430i | \(-0.688095\pi\) | ||||
−0.557124 | + | 0.830430i | \(0.688095\pi\) | |||||||
\(942\) | 60.3607i | 1.96666i | ||||||||
\(943\) | 25.8885i | 0.843047i | ||||||||
\(944\) | −7.23607 | −0.235514 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.52786 | −0.0496751 | ||||||||
\(947\) | 0.944272i | 0.0306847i | 0.999882 | + | 0.0153424i | \(0.00488382\pi\) | ||||
−0.999882 | + | 0.0153424i | \(0.995116\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.11146 | 0.198386 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.2492 | 1.37002 | ||||||||
\(952\) | 6.47214i | 0.209763i | ||||||||
\(953\) | 5.05573i | 0.163771i | 0.996642 | + | 0.0818855i | \(0.0260942\pi\) | ||||
−0.996642 | + | 0.0818855i | \(0.973906\pi\) | |||||||
\(954\) | 3.52786 | 0.114219 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.0000 | 0.646846 | ||||||||
\(957\) | − 14.4721i | − 0.467818i | ||||||||
\(958\) | − 32.3607i | − 1.04553i | ||||||||
\(959\) | −15.8885 | −0.513068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 13.5279i | 0.436156i | ||||||||
\(963\) | − 48.3607i | − 1.55840i | ||||||||
\(964\) | 11.4164 | 0.367698 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.9443 | −0.416475 | ||||||||
\(967\) | − 10.1115i | − 0.325163i | −0.986695 | − | 0.162581i | \(-0.948018\pi\) | ||||
0.986695 | − | 0.162581i | \(-0.0519820\pi\) | |||||||
\(968\) | 1.00000i | 0.0321412i | ||||||||
\(969\) | 57.8885 | 1.85965 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.5410 | −0.530827 | −0.265413 | − | 0.964135i | \(-0.585508\pi\) | ||||
−0.265413 | + | 0.964135i | \(0.585508\pi\) | |||||||
\(972\) | 35.5967i | 1.14177i | ||||||||
\(973\) | − 8.29180i | − 0.265823i | ||||||||
\(974\) | 0.944272 | 0.0302564 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.23607 | −0.167602 | ||||||||
\(977\) | − 24.8328i | − 0.794472i | −0.917716 | − | 0.397236i | \(-0.869969\pi\) | ||||
0.917716 | − | 0.397236i | \(-0.130031\pi\) | |||||||
\(978\) | − 24.0000i | − 0.767435i | ||||||||
\(979\) | −10.0000 | −0.319601 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −74.7214 | −2.38567 | ||||||||
\(982\) | − 0.944272i | − 0.0301329i | ||||||||
\(983\) | 14.0000i | 0.446531i | 0.974758 | + | 0.223265i | \(0.0716716\pi\) | ||||
−0.974758 | + | 0.223265i | \(0.928328\pi\) | |||||||
\(984\) | 20.9443 | 0.667679 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 28.9443 | 0.921773 | ||||||||
\(987\) | − 6.47214i | − 0.206010i | ||||||||
\(988\) | − 3.41641i | − 0.108690i | ||||||||
\(989\) | 6.11146 | 0.194333 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.3607 | 1.40916 | 0.704582 | − | 0.709623i | \(-0.251135\pi\) | ||||
0.704582 | + | 0.709623i | \(0.251135\pi\) | |||||||
\(992\) | − 2.00000i | − 0.0635001i | ||||||||
\(993\) | − 3.05573i | − 0.0969706i | ||||||||
\(994\) | 2.47214 | 0.0784114 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −32.9443 | −1.04388 | ||||||||
\(997\) | − 1.81966i | − 0.0576292i | −0.999585 | − | 0.0288146i | \(-0.990827\pi\) | ||||
0.999585 | − | 0.0288146i | \(-0.00917324\pi\) | |||||||
\(998\) | 12.3607i | 0.391270i | ||||||||
\(999\) | −158.387 | −5.01114 |
(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 | 3850.2.c.q.1849.1 | 4 | ||
5.2 | odd | 4 | 154.2.a.d.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 3850.2.a.bj.1.2 | 2 | |||
5.4 | even | 2 | inner | 3850.2.c.q.1849.4 | 4 | ||
15.2 | even | 4 | 1386.2.a.m.1.1 | 2 | |||
20.7 | even | 4 | 1232.2.a.p.1.2 | 2 | |||
35.2 | odd | 12 | 1078.2.e.q.67.2 | 4 | |||
35.12 | even | 12 | 1078.2.e.n.67.1 | 4 | |||
35.17 | even | 12 | 1078.2.e.n.177.1 | 4 | |||
35.27 | even | 4 | 1078.2.a.w.1.2 | 2 | |||
35.32 | odd | 12 | 1078.2.e.q.177.2 | 4 | |||
40.27 | even | 4 | 4928.2.a.bk.1.1 | 2 | |||
40.37 | odd | 4 | 4928.2.a.bt.1.2 | 2 | |||
55.32 | even | 4 | 1694.2.a.l.1.1 | 2 | |||
105.62 | odd | 4 | 9702.2.a.cu.1.2 | 2 | |||
140.27 | odd | 4 | 8624.2.a.bf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.a.d.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1078.2.a.w.1.2 | 2 | 35.27 | even | 4 | |||
1078.2.e.n.67.1 | 4 | 35.12 | even | 12 | |||
1078.2.e.n.177.1 | 4 | 35.17 | even | 12 | |||
1078.2.e.q.67.2 | 4 | 35.2 | odd | 12 | |||
1078.2.e.q.177.2 | 4 | 35.32 | odd | 12 | |||
1232.2.a.p.1.2 | 2 | 20.7 | even | 4 | |||
1386.2.a.m.1.1 | 2 | 15.2 | even | 4 | |||
1694.2.a.l.1.1 | 2 | 55.32 | even | 4 | |||
3850.2.a.bj.1.2 | 2 | 5.3 | odd | 4 | |||
3850.2.c.q.1849.1 | 4 | 1.1 | even | 1 | trivial | ||
3850.2.c.q.1849.4 | 4 | 5.4 | even | 2 | inner | ||
4928.2.a.bk.1.1 | 2 | 40.27 | even | 4 | |||
4928.2.a.bt.1.2 | 2 | 40.37 | odd | 4 | |||
8624.2.a.bf.1.1 | 2 | 140.27 | odd | 4 | |||
9702.2.a.cu.1.2 | 2 | 105.62 | odd | 4 |