Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.a (trivial) |
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: | yes |
Analytic conductor: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 17x^{6} + 37x^{5} + 105x^{4} - 117x^{3} - 238x^{2} + 42x + 90 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.14759\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.25098 | −1.00667 | −0.503334 | − | 0.864092i | \(-0.667894\pi\) | ||||
−0.503334 | + | 0.864092i | \(0.667894\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0.744783 | 0.281502 | 0.140751 | − | 0.990045i | \(-0.455048\pi\) | ||||
0.140751 | + | 0.990045i | \(0.455048\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.25098 | 0.711822 | ||||||||
\(11\) | 2.33248 | 0.703269 | 0.351635 | − | 0.936137i | \(-0.385626\pi\) | ||||
0.351635 | + | 0.936137i | \(0.385626\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.46972 | 0.407627 | 0.203813 | − | 0.979010i | \(-0.434666\pi\) | ||||
0.203813 | + | 0.979010i | \(0.434666\pi\) | |||||||
\(14\) | −0.744783 | −0.199052 | ||||||||
\(15\) | 2.25098 | 0.581200 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 6.67430 | 1.53119 | 0.765595 | − | 0.643323i | \(-0.222445\pi\) | ||||
0.765595 | + | 0.643323i | \(0.222445\pi\) | |||||||
\(20\) | −2.25098 | −0.503334 | ||||||||
\(21\) | −0.744783 | −0.162525 | ||||||||
\(22\) | −2.33248 | −0.497287 | ||||||||
\(23\) | −3.70644 | −0.772847 | −0.386423 | − | 0.922322i | \(-0.626290\pi\) | ||||
−0.386423 | + | 0.922322i | \(0.626290\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0.0669086 | 0.0133817 | ||||||||
\(26\) | −1.46972 | −0.288236 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.744783 | 0.140751 | ||||||||
\(29\) | 2.98937 | 0.555112 | 0.277556 | − | 0.960709i | \(-0.410476\pi\) | ||||
0.277556 | + | 0.960709i | \(0.410476\pi\) | |||||||
\(30\) | −2.25098 | −0.410971 | ||||||||
\(31\) | −0.755138 | −0.135627 | −0.0678134 | − | 0.997698i | \(-0.521602\pi\) | ||||
−0.0678134 | + | 0.997698i | \(0.521602\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.33248 | −0.406033 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −1.67649 | −0.283379 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.9072 | 1.79314 | 0.896568 | − | 0.442907i | \(-0.146053\pi\) | ||||
0.896568 | + | 0.442907i | \(0.146053\pi\) | |||||||
\(38\) | −6.67430 | −1.08271 | ||||||||
\(39\) | −1.46972 | −0.235343 | ||||||||
\(40\) | 2.25098 | 0.355911 | ||||||||
\(41\) | 1.43420 | 0.223985 | 0.111992 | − | 0.993709i | \(-0.464277\pi\) | ||||
0.111992 | + | 0.993709i | \(0.464277\pi\) | |||||||
\(42\) | 0.744783 | 0.114923 | ||||||||
\(43\) | −2.14336 | −0.326859 | −0.163429 | − | 0.986555i | \(-0.552256\pi\) | ||||
−0.163429 | + | 0.986555i | \(0.552256\pi\) | |||||||
\(44\) | 2.33248 | 0.351635 | ||||||||
\(45\) | −2.25098 | −0.335556 | ||||||||
\(46\) | 3.70644 | 0.546485 | ||||||||
\(47\) | 7.97412 | 1.16315 | 0.581573 | − | 0.813494i | \(-0.302438\pi\) | ||||
0.581573 | + | 0.813494i | \(0.302438\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.44530 | −0.920757 | ||||||||
\(50\) | −0.0669086 | −0.00946230 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 1.46972 | 0.203813 | ||||||||
\(53\) | −0.555658 | −0.0763255 | −0.0381627 | − | 0.999272i | \(-0.512151\pi\) | ||||
−0.0381627 | + | 0.999272i | \(0.512151\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −5.25037 | −0.707959 | ||||||||
\(56\) | −0.744783 | −0.0995258 | ||||||||
\(57\) | −6.67430 | −0.884033 | ||||||||
\(58\) | −2.98937 | −0.392524 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 2.25098 | 0.290600 | ||||||||
\(61\) | 7.27359 | 0.931288 | 0.465644 | − | 0.884972i | \(-0.345823\pi\) | ||||
0.465644 | + | 0.884972i | \(0.345823\pi\) | |||||||
\(62\) | 0.755138 | 0.0959026 | ||||||||
\(63\) | 0.744783 | 0.0938338 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.30831 | −0.410345 | ||||||||
\(66\) | 2.33248 | 0.287109 | ||||||||
\(67\) | 11.3321 | 1.38444 | 0.692219 | − | 0.721687i | \(-0.256633\pi\) | ||||
0.692219 | + | 0.721687i | \(0.256633\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | 3.70644 | 0.446203 | ||||||||
\(70\) | 1.67649 | 0.200379 | ||||||||
\(71\) | −9.47926 | −1.12498 | −0.562490 | − | 0.826804i | \(-0.690157\pi\) | ||||
−0.562490 | + | 0.826804i | \(0.690157\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −0.684684 | −0.0801362 | −0.0400681 | − | 0.999197i | \(-0.512757\pi\) | ||||
−0.0400681 | + | 0.999197i | \(0.512757\pi\) | |||||||
\(74\) | −10.9072 | −1.26794 | ||||||||
\(75\) | −0.0669086 | −0.00772594 | ||||||||
\(76\) | 6.67430 | 0.765595 | ||||||||
\(77\) | 1.73719 | 0.197971 | ||||||||
\(78\) | 1.46972 | 0.166413 | ||||||||
\(79\) | 2.55312 | 0.287249 | 0.143624 | − | 0.989632i | \(-0.454124\pi\) | ||||
0.143624 | + | 0.989632i | \(0.454124\pi\) | |||||||
\(80\) | −2.25098 | −0.251667 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.43420 | −0.158381 | ||||||||
\(83\) | −10.4910 | −1.15154 | −0.575771 | − | 0.817611i | \(-0.695298\pi\) | ||||
−0.575771 | + | 0.817611i | \(0.695298\pi\) | |||||||
\(84\) | −0.744783 | −0.0812625 | ||||||||
\(85\) | 2.25098 | 0.244153 | ||||||||
\(86\) | 2.14336 | 0.231124 | ||||||||
\(87\) | −2.98937 | −0.320494 | ||||||||
\(88\) | −2.33248 | −0.248643 | ||||||||
\(89\) | −4.18370 | −0.443471 | −0.221735 | − | 0.975107i | \(-0.571172\pi\) | ||||
−0.221735 | + | 0.975107i | \(0.571172\pi\) | |||||||
\(90\) | 2.25098 | 0.237274 | ||||||||
\(91\) | 1.09462 | 0.114748 | ||||||||
\(92\) | −3.70644 | −0.386423 | ||||||||
\(93\) | 0.755138 | 0.0783042 | ||||||||
\(94\) | −7.97412 | −0.822468 | ||||||||
\(95\) | −15.0237 | −1.54140 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.31411 | 0.641101 | 0.320550 | − | 0.947231i | \(-0.396132\pi\) | ||||
0.320550 | + | 0.947231i | \(0.396132\pi\) | |||||||
\(98\) | 6.44530 | 0.651073 | ||||||||
\(99\) | 2.33248 | 0.234423 | ||||||||
\(100\) | 0.0669086 | 0.00669086 | ||||||||
\(101\) | −11.3149 | −1.12588 | −0.562938 | − | 0.826499i | \(-0.690329\pi\) | ||||
−0.562938 | + | 0.826499i | \(0.690329\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −15.6380 | −1.54086 | −0.770430 | − | 0.637525i | \(-0.779958\pi\) | ||||
−0.770430 | + | 0.637525i | \(0.779958\pi\) | |||||||
\(104\) | −1.46972 | −0.144118 | ||||||||
\(105\) | 1.67649 | 0.163609 | ||||||||
\(106\) | 0.555658 | 0.0539703 | ||||||||
\(107\) | 10.6721 | 1.03171 | 0.515853 | − | 0.856677i | \(-0.327475\pi\) | ||||
0.515853 | + | 0.856677i | \(0.327475\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −10.7884 | −1.03334 | −0.516672 | − | 0.856184i | \(-0.672829\pi\) | ||||
−0.516672 | + | 0.856184i | \(0.672829\pi\) | |||||||
\(110\) | 5.25037 | 0.500603 | ||||||||
\(111\) | −10.9072 | −1.03527 | ||||||||
\(112\) | 0.744783 | 0.0703754 | ||||||||
\(113\) | 2.51807 | 0.236880 | 0.118440 | − | 0.992961i | \(-0.462211\pi\) | ||||
0.118440 | + | 0.992961i | \(0.462211\pi\) | |||||||
\(114\) | 6.67430 | 0.625106 | ||||||||
\(115\) | 8.34313 | 0.778000 | ||||||||
\(116\) | 2.98937 | 0.277556 | ||||||||
\(117\) | 1.46972 | 0.135876 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −0.744783 | −0.0682741 | ||||||||
\(120\) | −2.25098 | −0.205485 | ||||||||
\(121\) | −5.55953 | −0.505412 | ||||||||
\(122\) | −7.27359 | −0.658520 | ||||||||
\(123\) | −1.43420 | −0.129318 | ||||||||
\(124\) | −0.755138 | −0.0678134 | ||||||||
\(125\) | 11.1043 | 0.993198 | ||||||||
\(126\) | −0.744783 | −0.0663505 | ||||||||
\(127\) | 13.6560 | 1.21177 | 0.605887 | − | 0.795550i | \(-0.292818\pi\) | ||||
0.605887 | + | 0.795550i | \(0.292818\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.14336 | 0.188712 | ||||||||
\(130\) | 3.30831 | 0.290158 | ||||||||
\(131\) | −15.8779 | −1.38725 | −0.693627 | − | 0.720334i | \(-0.743988\pi\) | ||||
−0.693627 | + | 0.720334i | \(0.743988\pi\) | |||||||
\(132\) | −2.33248 | −0.203016 | ||||||||
\(133\) | 4.97091 | 0.431032 | ||||||||
\(134\) | −11.3321 | −0.978946 | ||||||||
\(135\) | 2.25098 | 0.193733 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 5.50898 | 0.470664 | 0.235332 | − | 0.971915i | \(-0.424382\pi\) | ||||
0.235332 | + | 0.971915i | \(0.424382\pi\) | |||||||
\(138\) | −3.70644 | −0.315513 | ||||||||
\(139\) | −15.0899 | −1.27991 | −0.639956 | − | 0.768412i | \(-0.721047\pi\) | ||||
−0.639956 | + | 0.768412i | \(0.721047\pi\) | |||||||
\(140\) | −1.67649 | −0.141689 | ||||||||
\(141\) | −7.97412 | −0.671542 | ||||||||
\(142\) | 9.47926 | 0.795482 | ||||||||
\(143\) | 3.42809 | 0.286671 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −6.72902 | −0.558814 | ||||||||
\(146\) | 0.684684 | 0.0566648 | ||||||||
\(147\) | 6.44530 | 0.531599 | ||||||||
\(148\) | 10.9072 | 0.896568 | ||||||||
\(149\) | −10.7904 | −0.883985 | −0.441993 | − | 0.897019i | \(-0.645728\pi\) | ||||
−0.441993 | + | 0.897019i | \(0.645728\pi\) | |||||||
\(150\) | 0.0669086 | 0.00546306 | ||||||||
\(151\) | −0.577797 | −0.0470205 | −0.0235102 | − | 0.999724i | \(-0.507484\pi\) | ||||
−0.0235102 | + | 0.999724i | \(0.507484\pi\) | |||||||
\(152\) | −6.67430 | −0.541357 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −1.73719 | −0.139987 | ||||||||
\(155\) | 1.69980 | 0.136531 | ||||||||
\(156\) | −1.46972 | −0.117672 | ||||||||
\(157\) | 19.5006 | 1.55632 | 0.778159 | − | 0.628068i | \(-0.216154\pi\) | ||||
0.778159 | + | 0.628068i | \(0.216154\pi\) | |||||||
\(158\) | −2.55312 | −0.203115 | ||||||||
\(159\) | 0.555658 | 0.0440665 | ||||||||
\(160\) | 2.25098 | 0.177956 | ||||||||
\(161\) | −2.76050 | −0.217558 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 3.10700 | 0.243359 | 0.121679 | − | 0.992569i | \(-0.461172\pi\) | ||||
0.121679 | + | 0.992569i | \(0.461172\pi\) | |||||||
\(164\) | 1.43420 | 0.111992 | ||||||||
\(165\) | 5.25037 | 0.408740 | ||||||||
\(166\) | 10.4910 | 0.814263 | ||||||||
\(167\) | −2.31460 | −0.179109 | −0.0895546 | − | 0.995982i | \(-0.528544\pi\) | ||||
−0.0895546 | + | 0.995982i | \(0.528544\pi\) | |||||||
\(168\) | 0.744783 | 0.0574613 | ||||||||
\(169\) | −10.8399 | −0.833841 | ||||||||
\(170\) | −2.25098 | −0.172642 | ||||||||
\(171\) | 6.67430 | 0.510397 | ||||||||
\(172\) | −2.14336 | −0.163429 | ||||||||
\(173\) | 8.26013 | 0.628006 | 0.314003 | − | 0.949422i | \(-0.398330\pi\) | ||||
0.314003 | + | 0.949422i | \(0.398330\pi\) | |||||||
\(174\) | 2.98937 | 0.226624 | ||||||||
\(175\) | 0.0498324 | 0.00376697 | ||||||||
\(176\) | 2.33248 | 0.175817 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 4.18370 | 0.313581 | ||||||||
\(179\) | −5.00744 | −0.374274 | −0.187137 | − | 0.982334i | \(-0.559921\pi\) | ||||
−0.187137 | + | 0.982334i | \(0.559921\pi\) | |||||||
\(180\) | −2.25098 | −0.167778 | ||||||||
\(181\) | 4.27999 | 0.318129 | 0.159064 | − | 0.987268i | \(-0.449152\pi\) | ||||
0.159064 | + | 0.987268i | \(0.449152\pi\) | |||||||
\(182\) | −1.09462 | −0.0811388 | ||||||||
\(183\) | −7.27359 | −0.537679 | ||||||||
\(184\) | 3.70644 | 0.273243 | ||||||||
\(185\) | −24.5519 | −1.80509 | ||||||||
\(186\) | −0.755138 | −0.0553694 | ||||||||
\(187\) | −2.33248 | −0.170568 | ||||||||
\(188\) | 7.97412 | 0.581573 | ||||||||
\(189\) | −0.744783 | −0.0541750 | ||||||||
\(190\) | 15.0237 | 1.08994 | ||||||||
\(191\) | −0.847670 | −0.0613353 | −0.0306676 | − | 0.999530i | \(-0.509763\pi\) | ||||
−0.0306676 | + | 0.999530i | \(0.509763\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 14.5718 | 1.04890 | 0.524451 | − | 0.851441i | \(-0.324271\pi\) | ||||
0.524451 | + | 0.851441i | \(0.324271\pi\) | |||||||
\(194\) | −6.31411 | −0.453327 | ||||||||
\(195\) | 3.30831 | 0.236913 | ||||||||
\(196\) | −6.44530 | −0.460378 | ||||||||
\(197\) | 5.93431 | 0.422802 | 0.211401 | − | 0.977399i | \(-0.432197\pi\) | ||||
0.211401 | + | 0.977399i | \(0.432197\pi\) | |||||||
\(198\) | −2.33248 | −0.165762 | ||||||||
\(199\) | −21.4599 | −1.52125 | −0.760625 | − | 0.649191i | \(-0.775108\pi\) | ||||
−0.760625 | + | 0.649191i | \(0.775108\pi\) | |||||||
\(200\) | −0.0669086 | −0.00473115 | ||||||||
\(201\) | −11.3321 | −0.799306 | ||||||||
\(202\) | 11.3149 | 0.796115 | ||||||||
\(203\) | 2.22643 | 0.156265 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −3.22836 | −0.225479 | ||||||||
\(206\) | 15.6380 | 1.08955 | ||||||||
\(207\) | −3.70644 | −0.257616 | ||||||||
\(208\) | 1.46972 | 0.101907 | ||||||||
\(209\) | 15.5677 | 1.07684 | ||||||||
\(210\) | −1.67649 | −0.115689 | ||||||||
\(211\) | 12.1102 | 0.833698 | 0.416849 | − | 0.908976i | \(-0.363134\pi\) | ||||
0.416849 | + | 0.908976i | \(0.363134\pi\) | |||||||
\(212\) | −0.555658 | −0.0381627 | ||||||||
\(213\) | 9.47926 | 0.649508 | ||||||||
\(214\) | −10.6721 | −0.729527 | ||||||||
\(215\) | 4.82465 | 0.329038 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −0.562414 | −0.0381792 | ||||||||
\(218\) | 10.7884 | 0.730684 | ||||||||
\(219\) | 0.684684 | 0.0462666 | ||||||||
\(220\) | −5.25037 | −0.353980 | ||||||||
\(221\) | −1.46972 | −0.0988640 | ||||||||
\(222\) | 10.9072 | 0.732044 | ||||||||
\(223\) | 12.2515 | 0.820419 | 0.410209 | − | 0.911991i | \(-0.365456\pi\) | ||||
0.410209 | + | 0.911991i | \(0.365456\pi\) | |||||||
\(224\) | −0.744783 | −0.0497629 | ||||||||
\(225\) | 0.0669086 | 0.00446057 | ||||||||
\(226\) | −2.51807 | −0.167500 | ||||||||
\(227\) | 25.7155 | 1.70679 | 0.853397 | − | 0.521261i | \(-0.174538\pi\) | ||||
0.853397 | + | 0.521261i | \(0.174538\pi\) | |||||||
\(228\) | −6.67430 | −0.442017 | ||||||||
\(229\) | −1.91198 | −0.126347 | −0.0631736 | − | 0.998003i | \(-0.520122\pi\) | ||||
−0.0631736 | + | 0.998003i | \(0.520122\pi\) | |||||||
\(230\) | −8.34313 | −0.550129 | ||||||||
\(231\) | −1.73719 | −0.114299 | ||||||||
\(232\) | −2.98937 | −0.196262 | ||||||||
\(233\) | 12.2211 | 0.800634 | 0.400317 | − | 0.916377i | \(-0.368900\pi\) | ||||
0.400317 | + | 0.916377i | \(0.368900\pi\) | |||||||
\(234\) | −1.46972 | −0.0960785 | ||||||||
\(235\) | −17.9496 | −1.17090 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −2.55312 | −0.165843 | ||||||||
\(238\) | 0.744783 | 0.0482771 | ||||||||
\(239\) | 17.2655 | 1.11681 | 0.558405 | − | 0.829569i | \(-0.311414\pi\) | ||||
0.558405 | + | 0.829569i | \(0.311414\pi\) | |||||||
\(240\) | 2.25098 | 0.145300 | ||||||||
\(241\) | 9.82240 | 0.632717 | 0.316358 | − | 0.948640i | \(-0.397540\pi\) | ||||
0.316358 | + | 0.948640i | \(0.397540\pi\) | |||||||
\(242\) | 5.55953 | 0.357380 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.27359 | 0.465644 | ||||||||
\(245\) | 14.5082 | 0.926897 | ||||||||
\(246\) | 1.43420 | 0.0914415 | ||||||||
\(247\) | 9.80935 | 0.624154 | ||||||||
\(248\) | 0.755138 | 0.0479513 | ||||||||
\(249\) | 10.4910 | 0.664843 | ||||||||
\(250\) | −11.1043 | −0.702297 | ||||||||
\(251\) | −5.65216 | −0.356761 | −0.178380 | − | 0.983962i | \(-0.557086\pi\) | ||||
−0.178380 | + | 0.983962i | \(0.557086\pi\) | |||||||
\(252\) | 0.744783 | 0.0469169 | ||||||||
\(253\) | −8.64521 | −0.543519 | ||||||||
\(254\) | −13.6560 | −0.856854 | ||||||||
\(255\) | −2.25098 | −0.140962 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.49579 | −0.218061 | −0.109031 | − | 0.994038i | \(-0.534775\pi\) | ||||
−0.109031 | + | 0.994038i | \(0.534775\pi\) | |||||||
\(258\) | −2.14336 | −0.133439 | ||||||||
\(259\) | 8.12351 | 0.504770 | ||||||||
\(260\) | −3.30831 | −0.205172 | ||||||||
\(261\) | 2.98937 | 0.185037 | ||||||||
\(262\) | 15.8779 | 0.980937 | ||||||||
\(263\) | 0.649961 | 0.0400783 | 0.0200392 | − | 0.999799i | \(-0.493621\pi\) | ||||
0.0200392 | + | 0.999799i | \(0.493621\pi\) | |||||||
\(264\) | 2.33248 | 0.143554 | ||||||||
\(265\) | 1.25077 | 0.0768345 | ||||||||
\(266\) | −4.97091 | −0.304786 | ||||||||
\(267\) | 4.18370 | 0.256038 | ||||||||
\(268\) | 11.3321 | 0.692219 | ||||||||
\(269\) | −2.49731 | −0.152264 | −0.0761318 | − | 0.997098i | \(-0.524257\pi\) | ||||
−0.0761318 | + | 0.997098i | \(0.524257\pi\) | |||||||
\(270\) | −2.25098 | −0.136990 | ||||||||
\(271\) | 25.5431 | 1.55163 | 0.775816 | − | 0.630959i | \(-0.217339\pi\) | ||||
0.775816 | + | 0.630959i | \(0.217339\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −1.09462 | −0.0662495 | ||||||||
\(274\) | −5.50898 | −0.332810 | ||||||||
\(275\) | 0.156063 | 0.00941095 | ||||||||
\(276\) | 3.70644 | 0.223102 | ||||||||
\(277\) | −3.79244 | −0.227866 | −0.113933 | − | 0.993488i | \(-0.536345\pi\) | ||||
−0.113933 | + | 0.993488i | \(0.536345\pi\) | |||||||
\(278\) | 15.0899 | 0.905034 | ||||||||
\(279\) | −0.755138 | −0.0452089 | ||||||||
\(280\) | 1.67649 | 0.100190 | ||||||||
\(281\) | 22.4667 | 1.34025 | 0.670127 | − | 0.742247i | \(-0.266240\pi\) | ||||
0.670127 | + | 0.742247i | \(0.266240\pi\) | |||||||
\(282\) | 7.97412 | 0.474852 | ||||||||
\(283\) | 17.1466 | 1.01926 | 0.509630 | − | 0.860394i | \(-0.329782\pi\) | ||||
0.509630 | + | 0.860394i | \(0.329782\pi\) | |||||||
\(284\) | −9.47926 | −0.562490 | ||||||||
\(285\) | 15.0237 | 0.889928 | ||||||||
\(286\) | −3.42809 | −0.202707 | ||||||||
\(287\) | 1.06817 | 0.0630521 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 6.72902 | 0.395141 | ||||||||
\(291\) | −6.31411 | −0.370140 | ||||||||
\(292\) | −0.684684 | −0.0400681 | ||||||||
\(293\) | −15.5636 | −0.909236 | −0.454618 | − | 0.890687i | \(-0.650224\pi\) | ||||
−0.454618 | + | 0.890687i | \(0.650224\pi\) | |||||||
\(294\) | −6.44530 | −0.375897 | ||||||||
\(295\) | −2.25098 | −0.131057 | ||||||||
\(296\) | −10.9072 | −0.633969 | ||||||||
\(297\) | −2.33248 | −0.135344 | ||||||||
\(298\) | 10.7904 | 0.625072 | ||||||||
\(299\) | −5.44743 | −0.315033 | ||||||||
\(300\) | −0.0669086 | −0.00386297 | ||||||||
\(301\) | −1.59633 | −0.0920112 | ||||||||
\(302\) | 0.577797 | 0.0332485 | ||||||||
\(303\) | 11.3149 | 0.650025 | ||||||||
\(304\) | 6.67430 | 0.382798 | ||||||||
\(305\) | −16.3727 | −0.937498 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 5.47777 | 0.312633 | 0.156317 | − | 0.987707i | \(-0.450038\pi\) | ||||
0.156317 | + | 0.987707i | \(0.450038\pi\) | |||||||
\(308\) | 1.73719 | 0.0989857 | ||||||||
\(309\) | 15.6380 | 0.889616 | ||||||||
\(310\) | −1.69980 | −0.0965422 | ||||||||
\(311\) | −22.2670 | −1.26264 | −0.631322 | − | 0.775521i | \(-0.717487\pi\) | ||||
−0.631322 | + | 0.775521i | \(0.717487\pi\) | |||||||
\(312\) | 1.46972 | 0.0832064 | ||||||||
\(313\) | 16.5391 | 0.934847 | 0.467424 | − | 0.884033i | \(-0.345182\pi\) | ||||
0.467424 | + | 0.884033i | \(0.345182\pi\) | |||||||
\(314\) | −19.5006 | −1.10048 | ||||||||
\(315\) | −1.67649 | −0.0944596 | ||||||||
\(316\) | 2.55312 | 0.143624 | ||||||||
\(317\) | −1.48690 | −0.0835125 | −0.0417562 | − | 0.999128i | \(-0.513295\pi\) | ||||
−0.0417562 | + | 0.999128i | \(0.513295\pi\) | |||||||
\(318\) | −0.555658 | −0.0311598 | ||||||||
\(319\) | 6.97265 | 0.390394 | ||||||||
\(320\) | −2.25098 | −0.125834 | ||||||||
\(321\) | −10.6721 | −0.595656 | ||||||||
\(322\) | 2.76050 | 0.153836 | ||||||||
\(323\) | −6.67430 | −0.371368 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0.0983368 | 0.00545475 | ||||||||
\(326\) | −3.10700 | −0.172081 | ||||||||
\(327\) | 10.7884 | 0.596601 | ||||||||
\(328\) | −1.43420 | −0.0791906 | ||||||||
\(329\) | 5.93899 | 0.327427 | ||||||||
\(330\) | −5.25037 | −0.289023 | ||||||||
\(331\) | −11.7250 | −0.644465 | −0.322232 | − | 0.946661i | \(-0.604433\pi\) | ||||
−0.322232 | + | 0.946661i | \(0.604433\pi\) | |||||||
\(332\) | −10.4910 | −0.575771 | ||||||||
\(333\) | 10.9072 | 0.597712 | ||||||||
\(334\) | 2.31460 | 0.126649 | ||||||||
\(335\) | −25.5084 | −1.39367 | ||||||||
\(336\) | −0.744783 | −0.0406312 | ||||||||
\(337\) | 3.94487 | 0.214891 | 0.107445 | − | 0.994211i | \(-0.465733\pi\) | ||||
0.107445 | + | 0.994211i | \(0.465733\pi\) | |||||||
\(338\) | 10.8399 | 0.589614 | ||||||||
\(339\) | −2.51807 | −0.136763 | ||||||||
\(340\) | 2.25098 | 0.122077 | ||||||||
\(341\) | −1.76135 | −0.0953822 | ||||||||
\(342\) | −6.67430 | −0.360905 | ||||||||
\(343\) | −10.0138 | −0.540696 | ||||||||
\(344\) | 2.14336 | 0.115562 | ||||||||
\(345\) | −8.34313 | −0.449179 | ||||||||
\(346\) | −8.26013 | −0.444068 | ||||||||
\(347\) | −6.95425 | −0.373323 | −0.186662 | − | 0.982424i | \(-0.559767\pi\) | ||||
−0.186662 | + | 0.982424i | \(0.559767\pi\) | |||||||
\(348\) | −2.98937 | −0.160247 | ||||||||
\(349\) | 1.00105 | 0.0535847 | 0.0267924 | − | 0.999641i | \(-0.491471\pi\) | ||||
0.0267924 | + | 0.999641i | \(0.491471\pi\) | |||||||
\(350\) | −0.0498324 | −0.00266365 | ||||||||
\(351\) | −1.46972 | −0.0784478 | ||||||||
\(352\) | −2.33248 | −0.124322 | ||||||||
\(353\) | −1.04474 | −0.0556060 | −0.0278030 | − | 0.999613i | \(-0.508851\pi\) | ||||
−0.0278030 | + | 0.999613i | \(0.508851\pi\) | |||||||
\(354\) | 1.00000 | 0.0531494 | ||||||||
\(355\) | 21.3376 | 1.13248 | ||||||||
\(356\) | −4.18370 | −0.221735 | ||||||||
\(357\) | 0.744783 | 0.0394181 | ||||||||
\(358\) | 5.00744 | 0.264651 | ||||||||
\(359\) | 2.08008 | 0.109782 | 0.0548912 | − | 0.998492i | \(-0.482519\pi\) | ||||
0.0548912 | + | 0.998492i | \(0.482519\pi\) | |||||||
\(360\) | 2.25098 | 0.118637 | ||||||||
\(361\) | 25.5463 | 1.34454 | ||||||||
\(362\) | −4.27999 | −0.224951 | ||||||||
\(363\) | 5.55953 | 0.291800 | ||||||||
\(364\) | 1.09462 | 0.0573738 | ||||||||
\(365\) | 1.54121 | 0.0806705 | ||||||||
\(366\) | 7.27359 | 0.380197 | ||||||||
\(367\) | 3.17815 | 0.165898 | 0.0829491 | − | 0.996554i | \(-0.473566\pi\) | ||||
0.0829491 | + | 0.996554i | \(0.473566\pi\) | |||||||
\(368\) | −3.70644 | −0.193212 | ||||||||
\(369\) | 1.43420 | 0.0746616 | ||||||||
\(370\) | 24.5519 | 1.27639 | ||||||||
\(371\) | −0.413845 | −0.0214857 | ||||||||
\(372\) | 0.755138 | 0.0391521 | ||||||||
\(373\) | 24.6572 | 1.27670 | 0.638350 | − | 0.769746i | \(-0.279617\pi\) | ||||
0.638350 | + | 0.769746i | \(0.279617\pi\) | |||||||
\(374\) | 2.33248 | 0.120610 | ||||||||
\(375\) | −11.1043 | −0.573423 | ||||||||
\(376\) | −7.97412 | −0.411234 | ||||||||
\(377\) | 4.39354 | 0.226279 | ||||||||
\(378\) | 0.744783 | 0.0383075 | ||||||||
\(379\) | 37.0811 | 1.90473 | 0.952363 | − | 0.304966i | \(-0.0986452\pi\) | ||||
0.952363 | + | 0.304966i | \(0.0986452\pi\) | |||||||
\(380\) | −15.0237 | −0.770701 | ||||||||
\(381\) | −13.6560 | −0.699618 | ||||||||
\(382\) | 0.847670 | 0.0433706 | ||||||||
\(383\) | 6.62748 | 0.338648 | 0.169324 | − | 0.985560i | \(-0.445841\pi\) | ||||
0.169324 | + | 0.985560i | \(0.445841\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −3.91038 | −0.199292 | ||||||||
\(386\) | −14.5718 | −0.741686 | ||||||||
\(387\) | −2.14336 | −0.108953 | ||||||||
\(388\) | 6.31411 | 0.320550 | ||||||||
\(389\) | −11.4197 | −0.579001 | −0.289500 | − | 0.957178i | \(-0.593489\pi\) | ||||
−0.289500 | + | 0.957178i | \(0.593489\pi\) | |||||||
\(390\) | −3.30831 | −0.167523 | ||||||||
\(391\) | 3.70644 | 0.187443 | ||||||||
\(392\) | 6.44530 | 0.325537 | ||||||||
\(393\) | 15.8779 | 0.800932 | ||||||||
\(394\) | −5.93431 | −0.298966 | ||||||||
\(395\) | −5.74702 | −0.289164 | ||||||||
\(396\) | 2.33248 | 0.117212 | ||||||||
\(397\) | 11.8768 | 0.596077 | 0.298039 | − | 0.954554i | \(-0.403668\pi\) | ||||
0.298039 | + | 0.954554i | \(0.403668\pi\) | |||||||
\(398\) | 21.4599 | 1.07569 | ||||||||
\(399\) | −4.97091 | −0.248857 | ||||||||
\(400\) | 0.0669086 | 0.00334543 | ||||||||
\(401\) | 23.7385 | 1.18544 | 0.592721 | − | 0.805407i | \(-0.298053\pi\) | ||||
0.592721 | + | 0.805407i | \(0.298053\pi\) | |||||||
\(402\) | 11.3321 | 0.565195 | ||||||||
\(403\) | −1.10984 | −0.0552851 | ||||||||
\(404\) | −11.3149 | −0.562938 | ||||||||
\(405\) | −2.25098 | −0.111852 | ||||||||
\(406\) | −2.22643 | −0.110496 | ||||||||
\(407\) | 25.4409 | 1.26106 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −28.1905 | −1.39393 | −0.696966 | − | 0.717105i | \(-0.745467\pi\) | ||||
−0.696966 | + | 0.717105i | \(0.745467\pi\) | |||||||
\(410\) | 3.22836 | 0.159437 | ||||||||
\(411\) | −5.50898 | −0.271738 | ||||||||
\(412\) | −15.6380 | −0.770430 | ||||||||
\(413\) | 0.744783 | 0.0366484 | ||||||||
\(414\) | 3.70644 | 0.182162 | ||||||||
\(415\) | 23.6151 | 1.15922 | ||||||||
\(416\) | −1.46972 | −0.0720589 | ||||||||
\(417\) | 15.0899 | 0.738957 | ||||||||
\(418\) | −15.5677 | −0.761440 | ||||||||
\(419\) | −7.02938 | −0.343408 | −0.171704 | − | 0.985149i | \(-0.554927\pi\) | ||||
−0.171704 | + | 0.985149i | \(0.554927\pi\) | |||||||
\(420\) | 1.67649 | 0.0818044 | ||||||||
\(421\) | −10.5205 | −0.512740 | −0.256370 | − | 0.966579i | \(-0.582526\pi\) | ||||
−0.256370 | + | 0.966579i | \(0.582526\pi\) | |||||||
\(422\) | −12.1102 | −0.589513 | ||||||||
\(423\) | 7.97412 | 0.387715 | ||||||||
\(424\) | 0.555658 | 0.0269851 | ||||||||
\(425\) | −0.0669086 | −0.00324554 | ||||||||
\(426\) | −9.47926 | −0.459272 | ||||||||
\(427\) | 5.41725 | 0.262159 | ||||||||
\(428\) | 10.6721 | 0.515853 | ||||||||
\(429\) | −3.42809 | −0.165510 | ||||||||
\(430\) | −4.82465 | −0.232665 | ||||||||
\(431\) | 9.69352 | 0.466920 | 0.233460 | − | 0.972366i | \(-0.424995\pi\) | ||||
0.233460 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −1.13605 | −0.0545949 | −0.0272975 | − | 0.999627i | \(-0.508690\pi\) | ||||
−0.0272975 | + | 0.999627i | \(0.508690\pi\) | |||||||
\(434\) | 0.562414 | 0.0269967 | ||||||||
\(435\) | 6.72902 | 0.322632 | ||||||||
\(436\) | −10.7884 | −0.516672 | ||||||||
\(437\) | −24.7379 | −1.18338 | ||||||||
\(438\) | −0.684684 | −0.0327154 | ||||||||
\(439\) | 32.1368 | 1.53381 | 0.766903 | − | 0.641763i | \(-0.221797\pi\) | ||||
0.766903 | + | 0.641763i | \(0.221797\pi\) | |||||||
\(440\) | 5.25037 | 0.250301 | ||||||||
\(441\) | −6.44530 | −0.306919 | ||||||||
\(442\) | 1.46972 | 0.0699074 | ||||||||
\(443\) | −18.1819 | −0.863847 | −0.431924 | − | 0.901910i | \(-0.642165\pi\) | ||||
−0.431924 | + | 0.901910i | \(0.642165\pi\) | |||||||
\(444\) | −10.9072 | −0.517633 | ||||||||
\(445\) | 9.41742 | 0.446428 | ||||||||
\(446\) | −12.2515 | −0.580124 | ||||||||
\(447\) | 10.7904 | 0.510369 | ||||||||
\(448\) | 0.744783 | 0.0351877 | ||||||||
\(449\) | 21.9530 | 1.03602 | 0.518012 | − | 0.855373i | \(-0.326672\pi\) | ||||
0.518012 | + | 0.855373i | \(0.326672\pi\) | |||||||
\(450\) | −0.0669086 | −0.00315410 | ||||||||
\(451\) | 3.34525 | 0.157522 | ||||||||
\(452\) | 2.51807 | 0.118440 | ||||||||
\(453\) | 0.577797 | 0.0271473 | ||||||||
\(454\) | −25.7155 | −1.20689 | ||||||||
\(455\) | −2.46397 | −0.115513 | ||||||||
\(456\) | 6.67430 | 0.312553 | ||||||||
\(457\) | −2.49031 | −0.116492 | −0.0582459 | − | 0.998302i | \(-0.518551\pi\) | ||||
−0.0582459 | + | 0.998302i | \(0.518551\pi\) | |||||||
\(458\) | 1.91198 | 0.0893410 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 8.34313 | 0.389000 | ||||||||
\(461\) | 40.8264 | 1.90148 | 0.950738 | − | 0.309995i | \(-0.100327\pi\) | ||||
0.950738 | + | 0.309995i | \(0.100327\pi\) | |||||||
\(462\) | 1.73719 | 0.0808215 | ||||||||
\(463\) | 0.959874 | 0.0446091 | 0.0223046 | − | 0.999751i | \(-0.492900\pi\) | ||||
0.0223046 | + | 0.999751i | \(0.492900\pi\) | |||||||
\(464\) | 2.98937 | 0.138778 | ||||||||
\(465\) | −1.69980 | −0.0788264 | ||||||||
\(466\) | −12.2211 | −0.566134 | ||||||||
\(467\) | 7.88116 | 0.364696 | 0.182348 | − | 0.983234i | \(-0.441630\pi\) | ||||
0.182348 | + | 0.983234i | \(0.441630\pi\) | |||||||
\(468\) | 1.46972 | 0.0679378 | ||||||||
\(469\) | 8.43997 | 0.389722 | ||||||||
\(470\) | 17.9496 | 0.827953 | ||||||||
\(471\) | −19.5006 | −0.898540 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | −4.99934 | −0.229870 | ||||||||
\(474\) | 2.55312 | 0.117269 | ||||||||
\(475\) | 0.446568 | 0.0204900 | ||||||||
\(476\) | −0.744783 | −0.0341371 | ||||||||
\(477\) | −0.555658 | −0.0254418 | ||||||||
\(478\) | −17.2655 | −0.789703 | ||||||||
\(479\) | 22.3279 | 1.02019 | 0.510093 | − | 0.860119i | \(-0.329611\pi\) | ||||
0.510093 | + | 0.860119i | \(0.329611\pi\) | |||||||
\(480\) | −2.25098 | −0.102743 | ||||||||
\(481\) | 16.0305 | 0.730930 | ||||||||
\(482\) | −9.82240 | −0.447398 | ||||||||
\(483\) | 2.76050 | 0.125607 | ||||||||
\(484\) | −5.55953 | −0.252706 | ||||||||
\(485\) | −14.2129 | −0.645376 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 8.35612 | 0.378652 | 0.189326 | − | 0.981914i | \(-0.439370\pi\) | ||||
0.189326 | + | 0.981914i | \(0.439370\pi\) | |||||||
\(488\) | −7.27359 | −0.329260 | ||||||||
\(489\) | −3.10700 | −0.140503 | ||||||||
\(490\) | −14.5082 | −0.655415 | ||||||||
\(491\) | −24.1809 | −1.09127 | −0.545635 | − | 0.838023i | \(-0.683711\pi\) | ||||
−0.545635 | + | 0.838023i | \(0.683711\pi\) | |||||||
\(492\) | −1.43420 | −0.0646589 | ||||||||
\(493\) | −2.98937 | −0.134635 | ||||||||
\(494\) | −9.80935 | −0.441343 | ||||||||
\(495\) | −5.25037 | −0.235986 | ||||||||
\(496\) | −0.755138 | −0.0339067 | ||||||||
\(497\) | −7.05999 | −0.316684 | ||||||||
\(498\) | −10.4910 | −0.470115 | ||||||||
\(499\) | 20.7556 | 0.929149 | 0.464574 | − | 0.885534i | \(-0.346207\pi\) | ||||
0.464574 | + | 0.885534i | \(0.346207\pi\) | |||||||
\(500\) | 11.1043 | 0.496599 | ||||||||
\(501\) | 2.31460 | 0.103409 | ||||||||
\(502\) | 5.65216 | 0.252268 | ||||||||
\(503\) | 7.78502 | 0.347117 | 0.173558 | − | 0.984824i | \(-0.444473\pi\) | ||||
0.173558 | + | 0.984824i | \(0.444473\pi\) | |||||||
\(504\) | −0.744783 | −0.0331753 | ||||||||
\(505\) | 25.4696 | 1.13338 | ||||||||
\(506\) | 8.64521 | 0.384326 | ||||||||
\(507\) | 10.8399 | 0.481418 | ||||||||
\(508\) | 13.6560 | 0.605887 | ||||||||
\(509\) | 9.16778 | 0.406355 | 0.203177 | − | 0.979142i | \(-0.434873\pi\) | ||||
0.203177 | + | 0.979142i | \(0.434873\pi\) | |||||||
\(510\) | 2.25098 | 0.0996750 | ||||||||
\(511\) | −0.509941 | −0.0225584 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −6.67430 | −0.294678 | ||||||||
\(514\) | 3.49579 | 0.154193 | ||||||||
\(515\) | 35.2009 | 1.55114 | ||||||||
\(516\) | 2.14336 | 0.0943560 | ||||||||
\(517\) | 18.5995 | 0.818005 | ||||||||
\(518\) | −8.12351 | −0.356926 | ||||||||
\(519\) | −8.26013 | −0.362580 | ||||||||
\(520\) | 3.30831 | 0.145079 | ||||||||
\(521\) | 23.1482 | 1.01414 | 0.507070 | − | 0.861905i | \(-0.330729\pi\) | ||||
0.507070 | + | 0.861905i | \(0.330729\pi\) | |||||||
\(522\) | −2.98937 | −0.130841 | ||||||||
\(523\) | 7.35421 | 0.321577 | 0.160789 | − | 0.986989i | \(-0.448596\pi\) | ||||
0.160789 | + | 0.986989i | \(0.448596\pi\) | |||||||
\(524\) | −15.8779 | −0.693627 | ||||||||
\(525\) | −0.0498324 | −0.00217486 | ||||||||
\(526\) | −0.649961 | −0.0283397 | ||||||||
\(527\) | 0.755138 | 0.0328943 | ||||||||
\(528\) | −2.33248 | −0.101508 | ||||||||
\(529\) | −9.26229 | −0.402708 | ||||||||
\(530\) | −1.25077 | −0.0543302 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 4.97091 | 0.215516 | ||||||||
\(533\) | 2.10788 | 0.0913022 | ||||||||
\(534\) | −4.18370 | −0.181046 | ||||||||
\(535\) | −24.0226 | −1.03859 | ||||||||
\(536\) | −11.3321 | −0.489473 | ||||||||
\(537\) | 5.00744 | 0.216087 | ||||||||
\(538\) | 2.49731 | 0.107667 | ||||||||
\(539\) | −15.0335 | −0.647540 | ||||||||
\(540\) | 2.25098 | 0.0968667 | ||||||||
\(541\) | 10.8733 | 0.467478 | 0.233739 | − | 0.972299i | \(-0.424904\pi\) | ||||
0.233739 | + | 0.972299i | \(0.424904\pi\) | |||||||
\(542\) | −25.5431 | −1.09717 | ||||||||
\(543\) | −4.27999 | −0.183672 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 24.2845 | 1.04023 | ||||||||
\(546\) | 1.09462 | 0.0468455 | ||||||||
\(547\) | −37.6511 | −1.60984 | −0.804922 | − | 0.593380i | \(-0.797793\pi\) | ||||
−0.804922 | + | 0.593380i | \(0.797793\pi\) | |||||||
\(548\) | 5.50898 | 0.235332 | ||||||||
\(549\) | 7.27359 | 0.310429 | ||||||||
\(550\) | −0.156063 | −0.00665455 | ||||||||
\(551\) | 19.9520 | 0.849983 | ||||||||
\(552\) | −3.70644 | −0.157757 | ||||||||
\(553\) | 1.90152 | 0.0808609 | ||||||||
\(554\) | 3.79244 | 0.161125 | ||||||||
\(555\) | 24.5519 | 1.04217 | ||||||||
\(556\) | −15.0899 | −0.639956 | ||||||||
\(557\) | −10.0391 | −0.425369 | −0.212684 | − | 0.977121i | \(-0.568221\pi\) | ||||
−0.212684 | + | 0.977121i | \(0.568221\pi\) | |||||||
\(558\) | 0.755138 | 0.0319675 | ||||||||
\(559\) | −3.15013 | −0.133236 | ||||||||
\(560\) | −1.67649 | −0.0708447 | ||||||||
\(561\) | 2.33248 | 0.0984774 | ||||||||
\(562\) | −22.4667 | −0.947702 | ||||||||
\(563\) | 31.4267 | 1.32448 | 0.662240 | − | 0.749292i | \(-0.269606\pi\) | ||||
0.662240 | + | 0.749292i | \(0.269606\pi\) | |||||||
\(564\) | −7.97412 | −0.335771 | ||||||||
\(565\) | −5.66813 | −0.238460 | ||||||||
\(566\) | −17.1466 | −0.720725 | ||||||||
\(567\) | 0.744783 | 0.0312779 | ||||||||
\(568\) | 9.47926 | 0.397741 | ||||||||
\(569\) | −5.84319 | −0.244959 | −0.122480 | − | 0.992471i | \(-0.539085\pi\) | ||||
−0.122480 | + | 0.992471i | \(0.539085\pi\) | |||||||
\(570\) | −15.0237 | −0.629274 | ||||||||
\(571\) | −0.366490 | −0.0153371 | −0.00766856 | − | 0.999971i | \(-0.502441\pi\) | ||||
−0.00766856 | + | 0.999971i | \(0.502441\pi\) | |||||||
\(572\) | 3.42809 | 0.143336 | ||||||||
\(573\) | 0.847670 | 0.0354119 | ||||||||
\(574\) | −1.06817 | −0.0445846 | ||||||||
\(575\) | −0.247993 | −0.0103420 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −37.0890 | −1.54403 | −0.772017 | − | 0.635602i | \(-0.780752\pi\) | ||||
−0.772017 | + | 0.635602i | \(0.780752\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | −14.5718 | −0.605584 | ||||||||
\(580\) | −6.72902 | −0.279407 | ||||||||
\(581\) | −7.81356 | −0.324161 | ||||||||
\(582\) | 6.31411 | 0.261728 | ||||||||
\(583\) | −1.29606 | −0.0536774 | ||||||||
\(584\) | 0.684684 | 0.0283324 | ||||||||
\(585\) | −3.30831 | −0.136782 | ||||||||
\(586\) | 15.5636 | 0.642927 | ||||||||
\(587\) | 23.6078 | 0.974400 | 0.487200 | − | 0.873290i | \(-0.338018\pi\) | ||||
0.487200 | + | 0.873290i | \(0.338018\pi\) | |||||||
\(588\) | 6.44530 | 0.265800 | ||||||||
\(589\) | −5.04002 | −0.207670 | ||||||||
\(590\) | 2.25098 | 0.0926714 | ||||||||
\(591\) | −5.93431 | −0.244105 | ||||||||
\(592\) | 10.9072 | 0.448284 | ||||||||
\(593\) | 4.17885 | 0.171605 | 0.0858023 | − | 0.996312i | \(-0.472655\pi\) | ||||
0.0858023 | + | 0.996312i | \(0.472655\pi\) | |||||||
\(594\) | 2.33248 | 0.0957028 | ||||||||
\(595\) | 1.67649 | 0.0687294 | ||||||||
\(596\) | −10.7904 | −0.441993 | ||||||||
\(597\) | 21.4599 | 0.878294 | ||||||||
\(598\) | 5.44743 | 0.222762 | ||||||||
\(599\) | −2.29628 | −0.0938234 | −0.0469117 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469117 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(600\) | 0.0669086 | 0.00273153 | ||||||||
\(601\) | −12.9374 | −0.527726 | −0.263863 | − | 0.964560i | \(-0.584997\pi\) | ||||
−0.263863 | + | 0.964560i | \(0.584997\pi\) | |||||||
\(602\) | 1.59633 | 0.0650618 | ||||||||
\(603\) | 11.3321 | 0.461480 | ||||||||
\(604\) | −0.577797 | −0.0235102 | ||||||||
\(605\) | 12.5144 | 0.508783 | ||||||||
\(606\) | −11.3149 | −0.459637 | ||||||||
\(607\) | −30.7070 | −1.24636 | −0.623179 | − | 0.782079i | \(-0.714159\pi\) | ||||
−0.623179 | + | 0.782079i | \(0.714159\pi\) | |||||||
\(608\) | −6.67430 | −0.270679 | ||||||||
\(609\) | −2.22643 | −0.0902196 | ||||||||
\(610\) | 16.3727 | 0.662911 | ||||||||
\(611\) | 11.7197 | 0.474129 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 20.2545 | 0.818072 | 0.409036 | − | 0.912518i | \(-0.365865\pi\) | ||||
0.409036 | + | 0.912518i | \(0.365865\pi\) | |||||||
\(614\) | −5.47777 | −0.221065 | ||||||||
\(615\) | 3.22836 | 0.130180 | ||||||||
\(616\) | −1.73719 | −0.0699935 | ||||||||
\(617\) | −11.9815 | −0.482357 | −0.241178 | − | 0.970481i | \(-0.577534\pi\) | ||||
−0.241178 | + | 0.970481i | \(0.577534\pi\) | |||||||
\(618\) | −15.6380 | −0.629053 | ||||||||
\(619\) | 40.8104 | 1.64031 | 0.820153 | − | 0.572144i | \(-0.193888\pi\) | ||||
0.820153 | + | 0.572144i | \(0.193888\pi\) | |||||||
\(620\) | 1.69980 | 0.0682656 | ||||||||
\(621\) | 3.70644 | 0.148734 | ||||||||
\(622\) | 22.2670 | 0.892824 | ||||||||
\(623\) | −3.11595 | −0.124838 | ||||||||
\(624\) | −1.46972 | −0.0588358 | ||||||||
\(625\) | −25.3301 | −1.01320 | ||||||||
\(626\) | −16.5391 | −0.661037 | ||||||||
\(627\) | −15.5677 | −0.621713 | ||||||||
\(628\) | 19.5006 | 0.778159 | ||||||||
\(629\) | −10.9072 | −0.434899 | ||||||||
\(630\) | 1.67649 | 0.0667930 | ||||||||
\(631\) | 4.38106 | 0.174407 | 0.0872036 | − | 0.996191i | \(-0.472207\pi\) | ||||
0.0872036 | + | 0.996191i | \(0.472207\pi\) | |||||||
\(632\) | −2.55312 | −0.101558 | ||||||||
\(633\) | −12.1102 | −0.481336 | ||||||||
\(634\) | 1.48690 | 0.0590522 | ||||||||
\(635\) | −30.7394 | −1.21986 | ||||||||
\(636\) | 0.555658 | 0.0220333 | ||||||||
\(637\) | −9.47278 | −0.375325 | ||||||||
\(638\) | −6.97265 | −0.276050 | ||||||||
\(639\) | −9.47926 | −0.374994 | ||||||||
\(640\) | 2.25098 | 0.0889778 | ||||||||
\(641\) | 32.8368 | 1.29698 | 0.648488 | − | 0.761225i | \(-0.275402\pi\) | ||||
0.648488 | + | 0.761225i | \(0.275402\pi\) | |||||||
\(642\) | 10.6721 | 0.421192 | ||||||||
\(643\) | 12.7254 | 0.501840 | 0.250920 | − | 0.968008i | \(-0.419267\pi\) | ||||
0.250920 | + | 0.968008i | \(0.419267\pi\) | |||||||
\(644\) | −2.76050 | −0.108779 | ||||||||
\(645\) | −4.82465 | −0.189970 | ||||||||
\(646\) | 6.67430 | 0.262597 | ||||||||
\(647\) | 37.0464 | 1.45645 | 0.728223 | − | 0.685341i | \(-0.240347\pi\) | ||||
0.728223 | + | 0.685341i | \(0.240347\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 2.33248 | 0.0915579 | ||||||||
\(650\) | −0.0983368 | −0.00385709 | ||||||||
\(651\) | 0.562414 | 0.0220427 | ||||||||
\(652\) | 3.10700 | 0.121679 | ||||||||
\(653\) | −37.8018 | −1.47930 | −0.739650 | − | 0.672992i | \(-0.765009\pi\) | ||||
−0.739650 | + | 0.672992i | \(0.765009\pi\) | |||||||
\(654\) | −10.7884 | −0.421861 | ||||||||
\(655\) | 35.7407 | 1.39651 | ||||||||
\(656\) | 1.43420 | 0.0559962 | ||||||||
\(657\) | −0.684684 | −0.0267121 | ||||||||
\(658\) | −5.93899 | −0.231526 | ||||||||
\(659\) | −24.9348 | −0.971321 | −0.485661 | − | 0.874147i | \(-0.661421\pi\) | ||||
−0.485661 | + | 0.874147i | \(0.661421\pi\) | |||||||
\(660\) | 5.25037 | 0.204370 | ||||||||
\(661\) | 25.3582 | 0.986321 | 0.493160 | − | 0.869938i | \(-0.335842\pi\) | ||||
0.493160 | + | 0.869938i | \(0.335842\pi\) | |||||||
\(662\) | 11.7250 | 0.455705 | ||||||||
\(663\) | 1.46972 | 0.0570791 | ||||||||
\(664\) | 10.4910 | 0.407132 | ||||||||
\(665\) | −11.1894 | −0.433907 | ||||||||
\(666\) | −10.9072 | −0.422646 | ||||||||
\(667\) | −11.0799 | −0.429017 | ||||||||
\(668\) | −2.31460 | −0.0895546 | ||||||||
\(669\) | −12.2515 | −0.473669 | ||||||||
\(670\) | 25.5084 | 0.985474 | ||||||||
\(671\) | 16.9655 | 0.654946 | ||||||||
\(672\) | 0.744783 | 0.0287306 | ||||||||
\(673\) | 5.89157 | 0.227103 | 0.113552 | − | 0.993532i | \(-0.463777\pi\) | ||||
0.113552 | + | 0.993532i | \(0.463777\pi\) | |||||||
\(674\) | −3.94487 | −0.151951 | ||||||||
\(675\) | −0.0669086 | −0.00257531 | ||||||||
\(676\) | −10.8399 | −0.416920 | ||||||||
\(677\) | −40.5600 | −1.55885 | −0.779423 | − | 0.626498i | \(-0.784488\pi\) | ||||
−0.779423 | + | 0.626498i | \(0.784488\pi\) | |||||||
\(678\) | 2.51807 | 0.0967060 | ||||||||
\(679\) | 4.70264 | 0.180471 | ||||||||
\(680\) | −2.25098 | −0.0863211 | ||||||||
\(681\) | −25.7155 | −0.985418 | ||||||||
\(682\) | 1.76135 | 0.0674454 | ||||||||
\(683\) | 10.6717 | 0.408342 | 0.204171 | − | 0.978935i | \(-0.434550\pi\) | ||||
0.204171 | + | 0.978935i | \(0.434550\pi\) | |||||||
\(684\) | 6.67430 | 0.255198 | ||||||||
\(685\) | −12.4006 | −0.473803 | ||||||||
\(686\) | 10.0138 | 0.382330 | ||||||||
\(687\) | 1.91198 | 0.0729466 | ||||||||
\(688\) | −2.14336 | −0.0817147 | ||||||||
\(689\) | −0.816661 | −0.0311123 | ||||||||
\(690\) | 8.34313 | 0.317617 | ||||||||
\(691\) | 11.1727 | 0.425029 | 0.212514 | − | 0.977158i | \(-0.431835\pi\) | ||||
0.212514 | + | 0.977158i | \(0.431835\pi\) | |||||||
\(692\) | 8.26013 | 0.314003 | ||||||||
\(693\) | 1.73719 | 0.0659905 | ||||||||
\(694\) | 6.95425 | 0.263980 | ||||||||
\(695\) | 33.9671 | 1.28845 | ||||||||
\(696\) | 2.98937 | 0.113312 | ||||||||
\(697\) | −1.43420 | −0.0543243 | ||||||||
\(698\) | −1.00105 | −0.0378901 | ||||||||
\(699\) | −12.2211 | −0.462246 | ||||||||
\(700\) | 0.0498324 | 0.00188349 | ||||||||
\(701\) | −2.61307 | −0.0986943 | −0.0493472 | − | 0.998782i | \(-0.515714\pi\) | ||||
−0.0493472 | + | 0.998782i | \(0.515714\pi\) | |||||||
\(702\) | 1.46972 | 0.0554710 | ||||||||
\(703\) | 72.7981 | 2.74563 | ||||||||
\(704\) | 2.33248 | 0.0879087 | ||||||||
\(705\) | 17.9496 | 0.676021 | ||||||||
\(706\) | 1.04474 | 0.0393194 | ||||||||
\(707\) | −8.42716 | −0.316936 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 4.99299 | 0.187516 | 0.0937579 | − | 0.995595i | \(-0.470112\pi\) | ||||
0.0937579 | + | 0.995595i | \(0.470112\pi\) | |||||||
\(710\) | −21.3376 | −0.800786 | ||||||||
\(711\) | 2.55312 | 0.0957495 | ||||||||
\(712\) | 4.18370 | 0.156791 | ||||||||
\(713\) | 2.79888 | 0.104819 | ||||||||
\(714\) | −0.744783 | −0.0278728 | ||||||||
\(715\) | −7.71656 | −0.288583 | ||||||||
\(716\) | −5.00744 | −0.187137 | ||||||||
\(717\) | −17.2655 | −0.644790 | ||||||||
\(718\) | −2.08008 | −0.0776279 | ||||||||
\(719\) | 24.6175 | 0.918079 | 0.459039 | − | 0.888416i | \(-0.348194\pi\) | ||||
0.459039 | + | 0.888416i | \(0.348194\pi\) | |||||||
\(720\) | −2.25098 | −0.0838891 | ||||||||
\(721\) | −11.6469 | −0.433754 | ||||||||
\(722\) | −25.5463 | −0.950736 | ||||||||
\(723\) | −9.82240 | −0.365299 | ||||||||
\(724\) | 4.27999 | 0.159064 | ||||||||
\(725\) | 0.200015 | 0.00742836 | ||||||||
\(726\) | −5.55953 | −0.206334 | ||||||||
\(727\) | −8.21807 | −0.304791 | −0.152396 | − | 0.988320i | \(-0.548699\pi\) | ||||
−0.152396 | + | 0.988320i | \(0.548699\pi\) | |||||||
\(728\) | −1.09462 | −0.0405694 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.54121 | −0.0570427 | ||||||||
\(731\) | 2.14336 | 0.0792749 | ||||||||
\(732\) | −7.27359 | −0.268840 | ||||||||
\(733\) | −22.9140 | −0.846348 | −0.423174 | − | 0.906049i | \(-0.639084\pi\) | ||||
−0.423174 | + | 0.906049i | \(0.639084\pi\) | |||||||
\(734\) | −3.17815 | −0.117308 | ||||||||
\(735\) | −14.5082 | −0.535144 | ||||||||
\(736\) | 3.70644 | 0.136621 | ||||||||
\(737\) | 26.4319 | 0.973633 | ||||||||
\(738\) | −1.43420 | −0.0527937 | ||||||||
\(739\) | −5.90809 | −0.217333 | −0.108666 | − | 0.994078i | \(-0.534658\pi\) | ||||
−0.108666 | + | 0.994078i | \(0.534658\pi\) | |||||||
\(740\) | −24.5519 | −0.902546 | ||||||||
\(741\) | −9.80935 | −0.360355 | ||||||||
\(742\) | 0.413845 | 0.0151927 | ||||||||
\(743\) | 32.8388 | 1.20474 | 0.602370 | − | 0.798217i | \(-0.294223\pi\) | ||||
0.602370 | + | 0.798217i | \(0.294223\pi\) | |||||||
\(744\) | −0.755138 | −0.0276847 | ||||||||
\(745\) | 24.2890 | 0.889880 | ||||||||
\(746\) | −24.6572 | −0.902764 | ||||||||
\(747\) | −10.4910 | −0.383847 | ||||||||
\(748\) | −2.33248 | −0.0852839 | ||||||||
\(749\) | 7.94837 | 0.290427 | ||||||||
\(750\) | 11.1043 | 0.405471 | ||||||||
\(751\) | 18.5529 | 0.677003 | 0.338502 | − | 0.940966i | \(-0.390080\pi\) | ||||
0.338502 | + | 0.940966i | \(0.390080\pi\) | |||||||
\(752\) | 7.97412 | 0.290786 | ||||||||
\(753\) | 5.65216 | 0.205976 | ||||||||
\(754\) | −4.39354 | −0.160003 | ||||||||
\(755\) | 1.30061 | 0.0473340 | ||||||||
\(756\) | −0.744783 | −0.0270875 | ||||||||
\(757\) | −9.78140 | −0.355511 | −0.177756 | − | 0.984075i | \(-0.556884\pi\) | ||||
−0.177756 | + | 0.984075i | \(0.556884\pi\) | |||||||
\(758\) | −37.0811 | −1.34684 | ||||||||
\(759\) | 8.64521 | 0.313801 | ||||||||
\(760\) | 15.0237 | 0.544968 | ||||||||
\(761\) | −10.8795 | −0.394380 | −0.197190 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197190 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(762\) | 13.6560 | 0.494705 | ||||||||
\(763\) | −8.03503 | −0.290888 | ||||||||
\(764\) | −0.847670 | −0.0306676 | ||||||||
\(765\) | 2.25098 | 0.0813843 | ||||||||
\(766\) | −6.62748 | −0.239461 | ||||||||
\(767\) | 1.46972 | 0.0530685 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −2.02800 | −0.0731314 | −0.0365657 | − | 0.999331i | \(-0.511642\pi\) | ||||
−0.0365657 | + | 0.999331i | \(0.511642\pi\) | |||||||
\(770\) | 3.91038 | 0.140920 | ||||||||
\(771\) | 3.49579 | 0.125898 | ||||||||
\(772\) | 14.5718 | 0.524451 | ||||||||
\(773\) | −13.4984 | −0.485503 | −0.242751 | − | 0.970089i | \(-0.578050\pi\) | ||||
−0.242751 | + | 0.970089i | \(0.578050\pi\) | |||||||
\(774\) | 2.14336 | 0.0770413 | ||||||||
\(775\) | −0.0505252 | −0.00181492 | ||||||||
\(776\) | −6.31411 | −0.226663 | ||||||||
\(777\) | −8.12351 | −0.291429 | ||||||||
\(778\) | 11.4197 | 0.409415 | ||||||||
\(779\) | 9.57231 | 0.342964 | ||||||||
\(780\) | 3.30831 | 0.118456 | ||||||||
\(781\) | −22.1102 | −0.791165 | ||||||||
\(782\) | −3.70644 | −0.132542 | ||||||||
\(783\) | −2.98937 | −0.106831 | ||||||||
\(784\) | −6.44530 | −0.230189 | ||||||||
\(785\) | −43.8955 | −1.56670 | ||||||||
\(786\) | −15.8779 | −0.566344 | ||||||||
\(787\) | 51.1250 | 1.82241 | 0.911204 | − | 0.411956i | \(-0.135154\pi\) | ||||
0.911204 | + | 0.411956i | \(0.135154\pi\) | |||||||
\(788\) | 5.93431 | 0.211401 | ||||||||
\(789\) | −0.649961 | −0.0231392 | ||||||||
\(790\) | 5.74702 | 0.204470 | ||||||||
\(791\) | 1.87542 | 0.0666822 | ||||||||
\(792\) | −2.33248 | −0.0828811 | ||||||||
\(793\) | 10.6901 | 0.379618 | ||||||||
\(794\) | −11.8768 | −0.421490 | ||||||||
\(795\) | −1.25077 | −0.0443604 | ||||||||
\(796\) | −21.4599 | −0.760625 | ||||||||
\(797\) | −23.5439 | −0.833967 | −0.416983 | − | 0.908914i | \(-0.636913\pi\) | ||||
−0.416983 | + | 0.908914i | \(0.636913\pi\) | |||||||
\(798\) | 4.97091 | 0.175968 | ||||||||
\(799\) | −7.97412 | −0.282104 | ||||||||
\(800\) | −0.0669086 | −0.00236558 | ||||||||
\(801\) | −4.18370 | −0.147824 | ||||||||
\(802\) | −23.7385 | −0.838235 | ||||||||
\(803\) | −1.59701 | −0.0563573 | ||||||||
\(804\) | −11.3321 | −0.399653 | ||||||||
\(805\) | 6.21382 | 0.219008 | ||||||||
\(806\) | 1.10984 | 0.0390925 | ||||||||
\(807\) | 2.49731 | 0.0879094 | ||||||||
\(808\) | 11.3149 | 0.398057 | ||||||||
\(809\) | 9.00040 | 0.316437 | 0.158219 | − | 0.987404i | \(-0.449425\pi\) | ||||
0.158219 | + | 0.987404i | \(0.449425\pi\) | |||||||
\(810\) | 2.25098 | 0.0790914 | ||||||||
\(811\) | −34.6240 | −1.21581 | −0.607906 | − | 0.794009i | \(-0.707990\pi\) | ||||
−0.607906 | + | 0.794009i | \(0.707990\pi\) | |||||||
\(812\) | 2.22643 | 0.0781325 | ||||||||
\(813\) | −25.5431 | −0.895835 | ||||||||
\(814\) | −25.4409 | −0.891702 | ||||||||
\(815\) | −6.99379 | −0.244982 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | −14.3054 | −0.500483 | ||||||||
\(818\) | 28.1905 | 0.985658 | ||||||||
\(819\) | 1.09462 | 0.0382492 | ||||||||
\(820\) | −3.22836 | −0.112739 | ||||||||
\(821\) | 22.8376 | 0.797038 | 0.398519 | − | 0.917160i | \(-0.369524\pi\) | ||||
0.398519 | + | 0.917160i | \(0.369524\pi\) | |||||||
\(822\) | 5.50898 | 0.192148 | ||||||||
\(823\) | 17.0312 | 0.593672 | 0.296836 | − | 0.954928i | \(-0.404069\pi\) | ||||
0.296836 | + | 0.954928i | \(0.404069\pi\) | |||||||
\(824\) | 15.6380 | 0.544776 | ||||||||
\(825\) | −0.156063 | −0.00543342 | ||||||||
\(826\) | −0.744783 | −0.0259143 | ||||||||
\(827\) | 20.9520 | 0.728573 | 0.364287 | − | 0.931287i | \(-0.381313\pi\) | ||||
0.364287 | + | 0.931287i | \(0.381313\pi\) | |||||||
\(828\) | −3.70644 | −0.128808 | ||||||||
\(829\) | −13.6782 | −0.475065 | −0.237532 | − | 0.971380i | \(-0.576339\pi\) | ||||
−0.237532 | + | 0.971380i | \(0.576339\pi\) | |||||||
\(830\) | −23.6151 | −0.819693 | ||||||||
\(831\) | 3.79244 | 0.131558 | ||||||||
\(832\) | 1.46972 | 0.0509533 | ||||||||
\(833\) | 6.44530 | 0.223316 | ||||||||
\(834\) | −15.0899 | −0.522522 | ||||||||
\(835\) | 5.21012 | 0.180304 | ||||||||
\(836\) | 15.5677 | 0.538420 | ||||||||
\(837\) | 0.755138 | 0.0261014 | ||||||||
\(838\) | 7.02938 | 0.242826 | ||||||||
\(839\) | 11.2419 | 0.388115 | 0.194058 | − | 0.980990i | \(-0.437835\pi\) | ||||
0.194058 | + | 0.980990i | \(0.437835\pi\) | |||||||
\(840\) | −1.67649 | −0.0578444 | ||||||||
\(841\) | −20.0637 | −0.691850 | ||||||||
\(842\) | 10.5205 | 0.362562 | ||||||||
\(843\) | −22.4667 | −0.773796 | ||||||||
\(844\) | 12.1102 | 0.416849 | ||||||||
\(845\) | 24.4005 | 0.839401 | ||||||||
\(846\) | −7.97412 | −0.274156 | ||||||||
\(847\) | −4.14065 | −0.142274 | ||||||||
\(848\) | −0.555658 | −0.0190814 | ||||||||
\(849\) | −17.1466 | −0.588470 | ||||||||
\(850\) | 0.0669086 | 0.00229495 | ||||||||
\(851\) | −40.4270 | −1.38582 | ||||||||
\(852\) | 9.47926 | 0.324754 | ||||||||
\(853\) | −5.13625 | −0.175862 | −0.0879309 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879309 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(854\) | −5.41725 | −0.185374 | ||||||||
\(855\) | −15.0237 | −0.513800 | ||||||||
\(856\) | −10.6721 | −0.364763 | ||||||||
\(857\) | 26.3242 | 0.899219 | 0.449609 | − | 0.893225i | \(-0.351563\pi\) | ||||
0.449609 | + | 0.893225i | \(0.351563\pi\) | |||||||
\(858\) | 3.42809 | 0.117033 | ||||||||
\(859\) | −26.1048 | −0.890686 | −0.445343 | − | 0.895360i | \(-0.646918\pi\) | ||||
−0.445343 | + | 0.895360i | \(0.646918\pi\) | |||||||
\(860\) | 4.82465 | 0.164519 | ||||||||
\(861\) | −1.06817 | −0.0364031 | ||||||||
\(862\) | −9.69352 | −0.330163 | ||||||||
\(863\) | 30.1483 | 1.02626 | 0.513130 | − | 0.858311i | \(-0.328486\pi\) | ||||
0.513130 | + | 0.858311i | \(0.328486\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −18.5934 | −0.632194 | ||||||||
\(866\) | 1.13605 | 0.0386044 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −0.562414 | −0.0190896 | ||||||||
\(869\) | 5.95511 | 0.202013 | ||||||||
\(870\) | −6.72902 | −0.228135 | ||||||||
\(871\) | 16.6550 | 0.564334 | ||||||||
\(872\) | 10.7884 | 0.365342 | ||||||||
\(873\) | 6.31411 | 0.213700 | ||||||||
\(874\) | 24.7379 | 0.836773 | ||||||||
\(875\) | 8.27029 | 0.279587 | ||||||||
\(876\) | 0.684684 | 0.0231333 | ||||||||
\(877\) | −5.93599 | −0.200444 | −0.100222 | − | 0.994965i | \(-0.531955\pi\) | ||||
−0.100222 | + | 0.994965i | \(0.531955\pi\) | |||||||
\(878\) | −32.1368 | −1.08456 | ||||||||
\(879\) | 15.5636 | 0.524948 | ||||||||
\(880\) | −5.25037 | −0.176990 | ||||||||
\(881\) | −54.0924 | −1.82242 | −0.911210 | − | 0.411941i | \(-0.864851\pi\) | ||||
−0.911210 | + | 0.411941i | \(0.864851\pi\) | |||||||
\(882\) | 6.44530 | 0.217024 | ||||||||
\(883\) | −19.6268 | −0.660493 | −0.330247 | − | 0.943895i | \(-0.607132\pi\) | ||||
−0.330247 | + | 0.943895i | \(0.607132\pi\) | |||||||
\(884\) | −1.46972 | −0.0494320 | ||||||||
\(885\) | 2.25098 | 0.0756658 | ||||||||
\(886\) | 18.1819 | 0.610832 | ||||||||
\(887\) | −16.7715 | −0.563133 | −0.281566 | − | 0.959542i | \(-0.590854\pi\) | ||||
−0.281566 | + | 0.959542i | \(0.590854\pi\) | |||||||
\(888\) | 10.9072 | 0.366022 | ||||||||
\(889\) | 10.1708 | 0.341116 | ||||||||
\(890\) | −9.41742 | −0.315673 | ||||||||
\(891\) | 2.33248 | 0.0781410 | ||||||||
\(892\) | 12.2515 | 0.410209 | ||||||||
\(893\) | 53.2217 | 1.78100 | ||||||||
\(894\) | −10.7904 | −0.360885 | ||||||||
\(895\) | 11.2716 | 0.376770 | ||||||||
\(896\) | −0.744783 | −0.0248815 | ||||||||
\(897\) | 5.44743 | 0.181884 | ||||||||
\(898\) | −21.9530 | −0.732580 | ||||||||
\(899\) | −2.25739 | −0.0752881 | ||||||||
\(900\) | 0.0669086 | 0.00223029 | ||||||||
\(901\) | 0.555658 | 0.0185117 | ||||||||
\(902\) | −3.34525 | −0.111385 | ||||||||
\(903\) | 1.59633 | 0.0531227 | ||||||||
\(904\) | −2.51807 | −0.0837499 | ||||||||
\(905\) | −9.63416 | −0.320250 | ||||||||
\(906\) | −0.577797 | −0.0191960 | ||||||||
\(907\) | 36.4018 | 1.20870 | 0.604351 | − | 0.796718i | \(-0.293432\pi\) | ||||
0.604351 | + | 0.796718i | \(0.293432\pi\) | |||||||
\(908\) | 25.7155 | 0.853397 | ||||||||
\(909\) | −11.3149 | −0.375292 | ||||||||
\(910\) | 2.46397 | 0.0816798 | ||||||||
\(911\) | 42.4720 | 1.40716 | 0.703579 | − | 0.710617i | \(-0.251584\pi\) | ||||
0.703579 | + | 0.710617i | \(0.251584\pi\) | |||||||
\(912\) | −6.67430 | −0.221008 | ||||||||
\(913\) | −24.4702 | −0.809844 | ||||||||
\(914\) | 2.49031 | 0.0823721 | ||||||||
\(915\) | 16.3727 | 0.541265 | ||||||||
\(916\) | −1.91198 | −0.0631736 | ||||||||
\(917\) | −11.8256 | −0.390514 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 23.3770 | 0.771135 | 0.385568 | − | 0.922680i | \(-0.374006\pi\) | ||||
0.385568 | + | 0.922680i | \(0.374006\pi\) | |||||||
\(920\) | −8.34313 | −0.275065 | ||||||||
\(921\) | −5.47777 | −0.180499 | ||||||||
\(922\) | −40.8264 | −1.34455 | ||||||||
\(923\) | −13.9318 | −0.458572 | ||||||||
\(924\) | −1.73719 | −0.0571494 | ||||||||
\(925\) | 0.729786 | 0.0239952 | ||||||||
\(926\) | −0.959874 | −0.0315434 | ||||||||
\(927\) | −15.6380 | −0.513620 | ||||||||
\(928\) | −2.98937 | −0.0981310 | ||||||||
\(929\) | −20.7973 | −0.682338 | −0.341169 | − | 0.940002i | \(-0.610823\pi\) | ||||
−0.341169 | + | 0.940002i | \(0.610823\pi\) | |||||||
\(930\) | 1.69980 | 0.0557387 | ||||||||
\(931\) | −43.0179 | −1.40985 | ||||||||
\(932\) | 12.2211 | 0.400317 | ||||||||
\(933\) | 22.2670 | 0.728988 | ||||||||
\(934\) | −7.88116 | −0.257879 | ||||||||
\(935\) | 5.25037 | 0.171705 | ||||||||
\(936\) | −1.46972 | −0.0480393 | ||||||||
\(937\) | 31.5794 | 1.03165 | 0.515827 | − | 0.856692i | \(-0.327485\pi\) | ||||
0.515827 | + | 0.856692i | \(0.327485\pi\) | |||||||
\(938\) | −8.43997 | −0.275575 | ||||||||
\(939\) | −16.5391 | −0.539734 | ||||||||
\(940\) | −17.9496 | −0.585451 | ||||||||
\(941\) | 15.2842 | 0.498250 | 0.249125 | − | 0.968471i | \(-0.419857\pi\) | ||||
0.249125 | + | 0.968471i | \(0.419857\pi\) | |||||||
\(942\) | 19.5006 | 0.635364 | ||||||||
\(943\) | −5.31579 | −0.173106 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | 1.67649 | 0.0545363 | ||||||||
\(946\) | 4.99934 | 0.162542 | ||||||||
\(947\) | 2.83073 | 0.0919863 | 0.0459932 | − | 0.998942i | \(-0.485355\pi\) | ||||
0.0459932 | + | 0.998942i | \(0.485355\pi\) | |||||||
\(948\) | −2.55312 | −0.0829215 | ||||||||
\(949\) | −1.00629 | −0.0326656 | ||||||||
\(950\) | −0.446568 | −0.0144886 | ||||||||
\(951\) | 1.48690 | 0.0482159 | ||||||||
\(952\) | 0.744783 | 0.0241386 | ||||||||
\(953\) | −20.5895 | −0.666959 | −0.333479 | − | 0.942757i | \(-0.608223\pi\) | ||||
−0.333479 | + | 0.942757i | \(0.608223\pi\) | |||||||
\(954\) | 0.555658 | 0.0179901 | ||||||||
\(955\) | 1.90809 | 0.0617443 | ||||||||
\(956\) | 17.2655 | 0.558405 | ||||||||
\(957\) | −6.97265 | −0.225394 | ||||||||
\(958\) | −22.3279 | −0.721381 | ||||||||
\(959\) | 4.10300 | 0.132493 | ||||||||
\(960\) | 2.25098 | 0.0726501 | ||||||||
\(961\) | −30.4298 | −0.981605 | ||||||||
\(962\) | −16.0305 | −0.516845 | ||||||||
\(963\) | 10.6721 | 0.343902 | ||||||||
\(964\) | 9.82240 | 0.316358 | ||||||||
\(965\) | −32.8009 | −1.05590 | ||||||||
\(966\) | −2.76050 | −0.0888175 | ||||||||
\(967\) | 39.4564 | 1.26883 | 0.634416 | − | 0.772992i | \(-0.281241\pi\) | ||||
0.634416 | + | 0.772992i | \(0.281241\pi\) | |||||||
\(968\) | 5.55953 | 0.178690 | ||||||||
\(969\) | 6.67430 | 0.214410 | ||||||||
\(970\) | 14.2129 | 0.456350 | ||||||||
\(971\) | 38.7634 | 1.24398 | 0.621989 | − | 0.783026i | \(-0.286325\pi\) | ||||
0.621989 | + | 0.783026i | \(0.286325\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −11.2387 | −0.360297 | ||||||||
\(974\) | −8.35612 | −0.267747 | ||||||||
\(975\) | −0.0983368 | −0.00314930 | ||||||||
\(976\) | 7.27359 | 0.232822 | ||||||||
\(977\) | 42.3730 | 1.35563 | 0.677816 | − | 0.735231i | \(-0.262926\pi\) | ||||
0.677816 | + | 0.735231i | \(0.262926\pi\) | |||||||
\(978\) | 3.10700 | 0.0993508 | ||||||||
\(979\) | −9.75839 | −0.311880 | ||||||||
\(980\) | 14.5082 | 0.463449 | ||||||||
\(981\) | −10.7884 | −0.344448 | ||||||||
\(982\) | 24.1809 | 0.771644 | ||||||||
\(983\) | 5.05137 | 0.161114 | 0.0805568 | − | 0.996750i | \(-0.474330\pi\) | ||||
0.0805568 | + | 0.996750i | \(0.474330\pi\) | |||||||
\(984\) | 1.43420 | 0.0457207 | ||||||||
\(985\) | −13.3580 | −0.425622 | ||||||||
\(986\) | 2.98937 | 0.0952010 | ||||||||
\(987\) | −5.93899 | −0.189040 | ||||||||
\(988\) | 9.80935 | 0.312077 | ||||||||
\(989\) | 7.94422 | 0.252612 | ||||||||
\(990\) | 5.25037 | 0.166868 | ||||||||
\(991\) | 29.3763 | 0.933169 | 0.466584 | − | 0.884477i | \(-0.345484\pi\) | ||||
0.466584 | + | 0.884477i | \(0.345484\pi\) | |||||||
\(992\) | 0.755138 | 0.0239757 | ||||||||
\(993\) | 11.7250 | 0.372082 | ||||||||
\(994\) | 7.05999 | 0.223929 | ||||||||
\(995\) | 48.3058 | 1.53140 | ||||||||
\(996\) | 10.4910 | 0.332422 | ||||||||
\(997\) | 19.7134 | 0.624329 | 0.312165 | − | 0.950028i | \(-0.398946\pi\) | ||||
0.312165 | + | 0.950028i | \(0.398946\pi\) | |||||||
\(998\) | −20.7556 | −0.657007 | ||||||||
\(999\) | −10.9072 | −0.345089 |
(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 | 6018.2.a.s.1.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.s.1.2 | ✓ | 8 | 1.1 | even | 1 | trivial |