Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 690) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.24264 | −1.27920 | −0.639602 | − | 0.768706i | \(-0.720901\pi\) | ||||
−0.639602 | + | 0.768706i | \(0.720901\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.828427 | −0.229764 | −0.114882 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114882 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.82843 | 1.65614 | 0.828068 | − | 0.560627i | \(-0.189440\pi\) | ||||
0.828068 | + | 0.560627i | \(0.189440\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 6.24264 | 1.43216 | 0.716080 | − | 0.698018i | \(-0.245935\pi\) | ||||
0.716080 | + | 0.698018i | \(0.245935\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | −4.24264 | −0.904534 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.828427 | −0.162468 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 3.65685 | 0.679061 | 0.339530 | − | 0.940595i | \(-0.389732\pi\) | ||||
0.339530 | + | 0.940595i | \(0.389732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −4.24264 | −0.738549 | ||||||||
\(34\) | 6.82843 | 1.17107 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.585786 | 0.0963027 | 0.0481513 | − | 0.998840i | \(-0.484667\pi\) | ||||
0.0481513 | + | 0.998840i | \(0.484667\pi\) | |||||||
\(38\) | 6.24264 | 1.01269 | ||||||||
\(39\) | −0.828427 | −0.132655 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.82843 | −1.06642 | −0.533211 | − | 0.845983i | \(-0.679015\pi\) | ||||
−0.533211 | + | 0.845983i | \(0.679015\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | 10.2426 | 1.56199 | 0.780994 | − | 0.624538i | \(-0.214713\pi\) | ||||
0.780994 | + | 0.624538i | \(0.214713\pi\) | |||||||
\(44\) | −4.24264 | −0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −0.828427 | −0.120839 | −0.0604193 | − | 0.998173i | \(-0.519244\pi\) | ||||
−0.0604193 | + | 0.998173i | \(0.519244\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.82843 | 0.956171 | ||||||||
\(52\) | −0.828427 | −0.114882 | ||||||||
\(53\) | 10.5858 | 1.45407 | 0.727035 | − | 0.686601i | \(-0.240898\pi\) | ||||
0.727035 | + | 0.686601i | \(0.240898\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 6.24264 | 0.826858 | ||||||||
\(58\) | 3.65685 | 0.480168 | ||||||||
\(59\) | 8.48528 | 1.10469 | 0.552345 | − | 0.833616i | \(-0.313733\pi\) | ||||
0.552345 | + | 0.833616i | \(0.313733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.585786 | −0.0750023 | −0.0375011 | − | 0.999297i | \(-0.511940\pi\) | ||||
−0.0375011 | + | 0.999297i | \(0.511940\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.24264 | −0.522233 | ||||||||
\(67\) | −3.41421 | −0.417113 | −0.208556 | − | 0.978010i | \(-0.566876\pi\) | ||||
−0.208556 | + | 0.978010i | \(0.566876\pi\) | |||||||
\(68\) | 6.82843 | 0.828068 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 7.65685 | 0.896167 | 0.448084 | − | 0.893992i | \(-0.352107\pi\) | ||||
0.448084 | + | 0.893992i | \(0.352107\pi\) | |||||||
\(74\) | 0.585786 | 0.0680963 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.24264 | 0.716080 | ||||||||
\(77\) | 8.48528 | 0.966988 | ||||||||
\(78\) | −0.828427 | −0.0938009 | ||||||||
\(79\) | −3.65685 | −0.411428 | −0.205714 | − | 0.978612i | \(-0.565952\pi\) | ||||
−0.205714 | + | 0.978612i | \(0.565952\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.82843 | −0.754074 | ||||||||
\(83\) | 1.41421 | 0.155230 | 0.0776151 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776151 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.2426 | 1.10449 | ||||||||
\(87\) | 3.65685 | 0.392056 | ||||||||
\(88\) | −4.24264 | −0.452267 | ||||||||
\(89\) | 9.17157 | 0.972185 | 0.486092 | − | 0.873907i | \(-0.338422\pi\) | ||||
0.486092 | + | 0.873907i | \(0.338422\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.65685 | 0.173686 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 6.00000 | 0.622171 | ||||||||
\(94\) | −0.828427 | −0.0854457 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | −4.24264 | −0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3137 | 1.32476 | 0.662382 | − | 0.749166i | \(-0.269546\pi\) | ||||
0.662382 | + | 0.749166i | \(0.269546\pi\) | |||||||
\(102\) | 6.82843 | 0.676115 | ||||||||
\(103\) | 16.1421 | 1.59053 | 0.795266 | − | 0.606261i | \(-0.207331\pi\) | ||||
0.795266 | + | 0.606261i | \(0.207331\pi\) | |||||||
\(104\) | −0.828427 | −0.0812340 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.5858 | 1.02818 | ||||||||
\(107\) | 0.928932 | 0.0898033 | 0.0449016 | − | 0.998991i | \(-0.485703\pi\) | ||||
0.0449016 | + | 0.998991i | \(0.485703\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 12.5858 | 1.20550 | 0.602750 | − | 0.797930i | \(-0.294072\pi\) | ||||
0.602750 | + | 0.797930i | \(0.294072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.585786 | 0.0556004 | ||||||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | −16.9706 | −1.59646 | −0.798228 | − | 0.602355i | \(-0.794229\pi\) | ||||
−0.798228 | + | 0.602355i | \(0.794229\pi\) | |||||||
\(114\) | 6.24264 | 0.584677 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.65685 | 0.339530 | ||||||||
\(117\) | −0.828427 | −0.0765881 | ||||||||
\(118\) | 8.48528 | 0.781133 | ||||||||
\(119\) | −13.6569 | −1.25192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −0.585786 | −0.0530346 | ||||||||
\(123\) | −6.82843 | −0.615699 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 10.2426 | 0.901814 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.6569 | −1.89217 | −0.946084 | − | 0.323921i | \(-0.894999\pi\) | ||||
−0.946084 | + | 0.323921i | \(0.894999\pi\) | |||||||
\(132\) | −4.24264 | −0.369274 | ||||||||
\(133\) | −12.4853 | −1.08261 | ||||||||
\(134\) | −3.41421 | −0.294943 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.82843 | 0.585533 | ||||||||
\(137\) | −8.48528 | −0.724947 | −0.362473 | − | 0.931994i | \(-0.618068\pi\) | ||||
−0.362473 | + | 0.931994i | \(0.618068\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −16.9706 | −1.43942 | −0.719712 | − | 0.694273i | \(-0.755726\pi\) | ||||
−0.719712 | + | 0.694273i | \(0.755726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.828427 | −0.0697661 | ||||||||
\(142\) | −5.65685 | −0.474713 | ||||||||
\(143\) | 3.51472 | 0.293916 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.65685 | 0.633686 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | 0.585786 | 0.0481513 | ||||||||
\(149\) | 12.7279 | 1.04271 | 0.521356 | − | 0.853339i | \(-0.325426\pi\) | ||||
0.521356 | + | 0.853339i | \(0.325426\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.34315 | −0.353440 | −0.176720 | − | 0.984261i | \(-0.556549\pi\) | ||||
−0.176720 | + | 0.984261i | \(0.556549\pi\) | |||||||
\(152\) | 6.24264 | 0.506345 | ||||||||
\(153\) | 6.82843 | 0.552046 | ||||||||
\(154\) | 8.48528 | 0.683763 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.828427 | −0.0663273 | ||||||||
\(157\) | 21.0711 | 1.68165 | 0.840827 | − | 0.541304i | \(-0.182069\pi\) | ||||
0.840827 | + | 0.541304i | \(0.182069\pi\) | |||||||
\(158\) | −3.65685 | −0.290924 | ||||||||
\(159\) | 10.5858 | 0.839507 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 6.82843 | 0.534844 | 0.267422 | − | 0.963580i | \(-0.413828\pi\) | ||||
0.267422 | + | 0.963580i | \(0.413828\pi\) | |||||||
\(164\) | −6.82843 | −0.533211 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.41421 | 0.109764 | ||||||||
\(167\) | −3.17157 | −0.245424 | −0.122712 | − | 0.992442i | \(-0.539159\pi\) | ||||
−0.122712 | + | 0.992442i | \(0.539159\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | −12.3137 | −0.947208 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.24264 | 0.477387 | ||||||||
\(172\) | 10.2426 | 0.780994 | ||||||||
\(173\) | 8.82843 | 0.671213 | 0.335606 | − | 0.942002i | \(-0.391059\pi\) | ||||
0.335606 | + | 0.942002i | \(0.391059\pi\) | |||||||
\(174\) | 3.65685 | 0.277225 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.24264 | −0.319801 | ||||||||
\(177\) | 8.48528 | 0.637793 | ||||||||
\(178\) | 9.17157 | 0.687438 | ||||||||
\(179\) | −21.6569 | −1.61871 | −0.809355 | − | 0.587320i | \(-0.800183\pi\) | ||||
−0.809355 | + | 0.587320i | \(0.800183\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.3848 | −1.51519 | −0.757594 | − | 0.652726i | \(-0.773625\pi\) | ||||
−0.757594 | + | 0.652726i | \(0.773625\pi\) | |||||||
\(182\) | 1.65685 | 0.122814 | ||||||||
\(183\) | −0.585786 | −0.0433026 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −28.9706 | −2.11854 | ||||||||
\(188\) | −0.828427 | −0.0604193 | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8284 | −0.783517 | −0.391759 | − | 0.920068i | \(-0.628133\pi\) | ||||
−0.391759 | + | 0.920068i | \(0.628133\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −20.9706 | −1.50949 | −0.754747 | − | 0.656016i | \(-0.772240\pi\) | ||||
−0.754747 | + | 0.656016i | \(0.772240\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 20.6274 | 1.46964 | 0.734821 | − | 0.678261i | \(-0.237266\pi\) | ||||
0.734821 | + | 0.678261i | \(0.237266\pi\) | |||||||
\(198\) | −4.24264 | −0.301511 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.41421 | −0.240820 | ||||||||
\(202\) | 13.3137 | 0.936749 | ||||||||
\(203\) | −7.31371 | −0.513322 | ||||||||
\(204\) | 6.82843 | 0.478086 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16.1421 | 1.12468 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | −0.828427 | −0.0574411 | ||||||||
\(209\) | −26.4853 | −1.83203 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.51472 | −0.241963 | −0.120982 | − | 0.992655i | \(-0.538604\pi\) | ||||
−0.120982 | + | 0.992655i | \(0.538604\pi\) | |||||||
\(212\) | 10.5858 | 0.727035 | ||||||||
\(213\) | −5.65685 | −0.387601 | ||||||||
\(214\) | 0.928932 | 0.0635005 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −12.0000 | −0.814613 | ||||||||
\(218\) | 12.5858 | 0.852417 | ||||||||
\(219\) | 7.65685 | 0.517402 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.65685 | −0.380521 | ||||||||
\(222\) | 0.585786 | 0.0393154 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.9706 | −1.12887 | ||||||||
\(227\) | −22.3848 | −1.48573 | −0.742865 | − | 0.669441i | \(-0.766534\pi\) | ||||
−0.742865 | + | 0.669441i | \(0.766534\pi\) | |||||||
\(228\) | 6.24264 | 0.413429 | ||||||||
\(229\) | 10.2426 | 0.676853 | 0.338426 | − | 0.940993i | \(-0.390105\pi\) | ||||
0.338426 | + | 0.940993i | \(0.390105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.48528 | 0.558291 | ||||||||
\(232\) | 3.65685 | 0.240084 | ||||||||
\(233\) | 2.14214 | 0.140336 | 0.0701680 | − | 0.997535i | \(-0.477646\pi\) | ||||
0.0701680 | + | 0.997535i | \(0.477646\pi\) | |||||||
\(234\) | −0.828427 | −0.0541560 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.48528 | 0.552345 | ||||||||
\(237\) | −3.65685 | −0.237538 | ||||||||
\(238\) | −13.6569 | −0.885242 | ||||||||
\(239\) | −16.8284 | −1.08854 | −0.544270 | − | 0.838910i | \(-0.683193\pi\) | ||||
−0.544270 | + | 0.838910i | \(0.683193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.48528 | 0.417754 | 0.208877 | − | 0.977942i | \(-0.433019\pi\) | ||||
0.208877 | + | 0.977942i | \(0.433019\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.585786 | −0.0375011 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.82843 | −0.435365 | ||||||||
\(247\) | −5.17157 | −0.329059 | ||||||||
\(248\) | 6.00000 | 0.381000 | ||||||||
\(249\) | 1.41421 | 0.0896221 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.727922 | 0.0459460 | 0.0229730 | − | 0.999736i | \(-0.492687\pi\) | ||||
0.0229730 | + | 0.999736i | \(0.492687\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 4.24264 | 0.266733 | ||||||||
\(254\) | −2.00000 | −0.125491 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000 | 1.12281 | 0.561405 | − | 0.827541i | \(-0.310261\pi\) | ||||
0.561405 | + | 0.827541i | \(0.310261\pi\) | |||||||
\(258\) | 10.2426 | 0.637679 | ||||||||
\(259\) | −1.17157 | −0.0727980 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65685 | 0.226354 | ||||||||
\(262\) | −21.6569 | −1.33796 | ||||||||
\(263\) | −6.34315 | −0.391135 | −0.195568 | − | 0.980690i | \(-0.562655\pi\) | ||||
−0.195568 | + | 0.980690i | \(0.562655\pi\) | |||||||
\(264\) | −4.24264 | −0.261116 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −12.4853 | −0.765522 | ||||||||
\(267\) | 9.17157 | 0.561291 | ||||||||
\(268\) | −3.41421 | −0.208556 | ||||||||
\(269\) | −19.1716 | −1.16891 | −0.584456 | − | 0.811426i | \(-0.698692\pi\) | ||||
−0.584456 | + | 0.811426i | \(0.698692\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.65685 | 0.586612 | 0.293306 | − | 0.956019i | \(-0.405245\pi\) | ||||
0.293306 | + | 0.956019i | \(0.405245\pi\) | |||||||
\(272\) | 6.82843 | 0.414034 | ||||||||
\(273\) | 1.65685 | 0.100277 | ||||||||
\(274\) | −8.48528 | −0.512615 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 13.5147 | 0.812021 | 0.406010 | − | 0.913868i | \(-0.366920\pi\) | ||||
0.406010 | + | 0.913868i | \(0.366920\pi\) | |||||||
\(278\) | −16.9706 | −1.01783 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.85786 | −0.110831 | −0.0554154 | − | 0.998463i | \(-0.517648\pi\) | ||||
−0.0554154 | + | 0.998463i | \(0.517648\pi\) | |||||||
\(282\) | −0.828427 | −0.0493321 | ||||||||
\(283\) | 15.2132 | 0.904331 | 0.452166 | − | 0.891934i | \(-0.350652\pi\) | ||||
0.452166 | + | 0.891934i | \(0.350652\pi\) | |||||||
\(284\) | −5.65685 | −0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.51472 | 0.207830 | ||||||||
\(287\) | 13.6569 | 0.806139 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 29.6274 | 1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 7.65685 | 0.448084 | ||||||||
\(293\) | 20.0416 | 1.17084 | 0.585422 | − | 0.810729i | \(-0.300929\pi\) | ||||
0.585422 | + | 0.810729i | \(0.300929\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.585786 | 0.0340481 | ||||||||
\(297\) | −4.24264 | −0.246183 | ||||||||
\(298\) | 12.7279 | 0.737309 | ||||||||
\(299\) | 0.828427 | 0.0479092 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.4853 | −1.18075 | ||||||||
\(302\) | −4.34315 | −0.249920 | ||||||||
\(303\) | 13.3137 | 0.764853 | ||||||||
\(304\) | 6.24264 | 0.358040 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.82843 | 0.390355 | ||||||||
\(307\) | 25.4558 | 1.45284 | 0.726421 | − | 0.687250i | \(-0.241182\pi\) | ||||
0.726421 | + | 0.687250i | \(0.241182\pi\) | |||||||
\(308\) | 8.48528 | 0.483494 | ||||||||
\(309\) | 16.1421 | 0.918294 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7990 | −1.23611 | −0.618054 | − | 0.786136i | \(-0.712079\pi\) | ||||
−0.618054 | + | 0.786136i | \(0.712079\pi\) | |||||||
\(312\) | −0.828427 | −0.0469005 | ||||||||
\(313\) | 18.0000 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(314\) | 21.0711 | 1.18911 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.65685 | −0.205714 | ||||||||
\(317\) | −14.4853 | −0.813574 | −0.406787 | − | 0.913523i | \(-0.633351\pi\) | ||||
−0.406787 | + | 0.913523i | \(0.633351\pi\) | |||||||
\(318\) | 10.5858 | 0.593621 | ||||||||
\(319\) | −15.5147 | −0.868657 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.928932 | 0.0518479 | ||||||||
\(322\) | 2.00000 | 0.111456 | ||||||||
\(323\) | 42.6274 | 2.37185 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.82843 | 0.378192 | ||||||||
\(327\) | 12.5858 | 0.695996 | ||||||||
\(328\) | −6.82843 | −0.377037 | ||||||||
\(329\) | 1.65685 | 0.0913453 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.4853 | −1.12597 | −0.562986 | − | 0.826466i | \(-0.690348\pi\) | ||||
−0.562986 | + | 0.826466i | \(0.690348\pi\) | |||||||
\(332\) | 1.41421 | 0.0776151 | ||||||||
\(333\) | 0.585786 | 0.0321009 | ||||||||
\(334\) | −3.17157 | −0.173541 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | −0.109109 | ||||||||
\(337\) | −26.4853 | −1.44275 | −0.721373 | − | 0.692547i | \(-0.756488\pi\) | ||||
−0.721373 | + | 0.692547i | \(0.756488\pi\) | |||||||
\(338\) | −12.3137 | −0.669777 | ||||||||
\(339\) | −16.9706 | −0.921714 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.4558 | −1.37851 | ||||||||
\(342\) | 6.24264 | 0.337563 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 10.2426 | 0.552246 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.82843 | 0.474619 | ||||||||
\(347\) | −31.7990 | −1.70706 | −0.853530 | − | 0.521044i | \(-0.825543\pi\) | ||||
−0.853530 | + | 0.521044i | \(0.825543\pi\) | |||||||
\(348\) | 3.65685 | 0.196028 | ||||||||
\(349\) | 2.68629 | 0.143794 | 0.0718969 | − | 0.997412i | \(-0.477095\pi\) | ||||
0.0718969 | + | 0.997412i | \(0.477095\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.828427 | −0.0442182 | ||||||||
\(352\) | −4.24264 | −0.226134 | ||||||||
\(353\) | 2.14214 | 0.114014 | 0.0570072 | − | 0.998374i | \(-0.481844\pi\) | ||||
0.0570072 | + | 0.998374i | \(0.481844\pi\) | |||||||
\(354\) | 8.48528 | 0.450988 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 9.17157 | 0.486092 | ||||||||
\(357\) | −13.6569 | −0.722797 | ||||||||
\(358\) | −21.6569 | −1.14460 | ||||||||
\(359\) | 19.7990 | 1.04495 | 0.522475 | − | 0.852654i | \(-0.325009\pi\) | ||||
0.522475 | + | 0.852654i | \(0.325009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.9706 | 1.05108 | ||||||||
\(362\) | −20.3848 | −1.07140 | ||||||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 1.65685 | 0.0868428 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.585786 | −0.0306195 | ||||||||
\(367\) | 1.02944 | 0.0537362 | 0.0268681 | − | 0.999639i | \(-0.491447\pi\) | ||||
0.0268681 | + | 0.999639i | \(0.491447\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −6.82843 | −0.355474 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.1716 | −1.09917 | ||||||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | −23.2132 | −1.20193 | −0.600967 | − | 0.799274i | \(-0.705218\pi\) | ||||
−0.600967 | + | 0.799274i | \(0.705218\pi\) | |||||||
\(374\) | −28.9706 | −1.49803 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.828427 | −0.0427229 | ||||||||
\(377\) | −3.02944 | −0.156024 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 23.2132 | 1.19238 | 0.596191 | − | 0.802843i | \(-0.296680\pi\) | ||||
0.596191 | + | 0.802843i | \(0.296680\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | −0.102463 | ||||||||
\(382\) | −10.8284 | −0.554031 | ||||||||
\(383\) | 26.6274 | 1.36060 | 0.680299 | − | 0.732935i | \(-0.261850\pi\) | ||||
0.680299 | + | 0.732935i | \(0.261850\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.9706 | −1.06737 | ||||||||
\(387\) | 10.2426 | 0.520663 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | −30.3848 | −1.54057 | −0.770285 | − | 0.637700i | \(-0.779886\pi\) | ||||
−0.770285 | + | 0.637700i | \(0.779886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.82843 | −0.345328 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | −21.6569 | −1.09244 | ||||||||
\(394\) | 20.6274 | 1.03919 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.24264 | −0.213201 | ||||||||
\(397\) | −19.6569 | −0.986549 | −0.493275 | − | 0.869874i | \(-0.664200\pi\) | ||||
−0.493275 | + | 0.869874i | \(0.664200\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | −12.4853 | −0.625046 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.97056 | 0.248218 | 0.124109 | − | 0.992269i | \(-0.460393\pi\) | ||||
0.124109 | + | 0.992269i | \(0.460393\pi\) | |||||||
\(402\) | −3.41421 | −0.170285 | ||||||||
\(403\) | −4.97056 | −0.247601 | ||||||||
\(404\) | 13.3137 | 0.662382 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.31371 | −0.362973 | ||||||||
\(407\) | −2.48528 | −0.123191 | ||||||||
\(408\) | 6.82843 | 0.338058 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.48528 | −0.418548 | ||||||||
\(412\) | 16.1421 | 0.795266 | ||||||||
\(413\) | −16.9706 | −0.835067 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.828427 | −0.0406170 | ||||||||
\(417\) | −16.9706 | −0.831052 | ||||||||
\(418\) | −26.4853 | −1.29544 | ||||||||
\(419\) | −39.0711 | −1.90875 | −0.954373 | − | 0.298616i | \(-0.903475\pi\) | ||||
−0.954373 | + | 0.298616i | \(0.903475\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.75736 | 0.0856485 | 0.0428242 | − | 0.999083i | \(-0.486364\pi\) | ||||
0.0428242 | + | 0.999083i | \(0.486364\pi\) | |||||||
\(422\) | −3.51472 | −0.171094 | ||||||||
\(423\) | −0.828427 | −0.0402795 | ||||||||
\(424\) | 10.5858 | 0.514091 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.65685 | −0.274075 | ||||||||
\(427\) | 1.17157 | 0.0566964 | ||||||||
\(428\) | 0.928932 | 0.0449016 | ||||||||
\(429\) | 3.51472 | 0.169692 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.48528 | −0.408722 | −0.204361 | − | 0.978896i | \(-0.565512\pi\) | ||||
−0.204361 | + | 0.978896i | \(0.565512\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −6.97056 | −0.334984 | −0.167492 | − | 0.985873i | \(-0.553567\pi\) | ||||
−0.167492 | + | 0.985873i | \(0.553567\pi\) | |||||||
\(434\) | −12.0000 | −0.576018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.5858 | 0.602750 | ||||||||
\(437\) | −6.24264 | −0.298626 | ||||||||
\(438\) | 7.65685 | 0.365859 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −5.65685 | −0.269069 | ||||||||
\(443\) | −0.686292 | −0.0326067 | −0.0163033 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163033 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(444\) | 0.585786 | 0.0278002 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.0000 | 0.757622 | ||||||||
\(447\) | 12.7279 | 0.602010 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | −17.1716 | −0.810377 | −0.405188 | − | 0.914233i | \(-0.632794\pi\) | ||||
−0.405188 | + | 0.914233i | \(0.632794\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9706 | 1.36417 | ||||||||
\(452\) | −16.9706 | −0.798228 | ||||||||
\(453\) | −4.34315 | −0.204059 | ||||||||
\(454\) | −22.3848 | −1.05057 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.24264 | 0.292338 | ||||||||
\(457\) | 34.9706 | 1.63585 | 0.817927 | − | 0.575322i | \(-0.195123\pi\) | ||||
0.817927 | + | 0.575322i | \(0.195123\pi\) | |||||||
\(458\) | 10.2426 | 0.478607 | ||||||||
\(459\) | 6.82843 | 0.318724 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.17157 | −0.334013 | −0.167007 | − | 0.985956i | \(-0.553410\pi\) | ||||
−0.167007 | + | 0.985956i | \(0.553410\pi\) | |||||||
\(462\) | 8.48528 | 0.394771 | ||||||||
\(463\) | −30.9706 | −1.43932 | −0.719662 | − | 0.694325i | \(-0.755703\pi\) | ||||
−0.719662 | + | 0.694325i | \(0.755703\pi\) | |||||||
\(464\) | 3.65685 | 0.169765 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.14214 | 0.0992325 | ||||||||
\(467\) | −31.3553 | −1.45095 | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(468\) | −0.828427 | −0.0382941 | ||||||||
\(469\) | 6.82843 | 0.315307 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.0711 | 0.970904 | ||||||||
\(472\) | 8.48528 | 0.390567 | ||||||||
\(473\) | −43.4558 | −1.99810 | ||||||||
\(474\) | −3.65685 | −0.167965 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −13.6569 | −0.625961 | ||||||||
\(477\) | 10.5858 | 0.484690 | ||||||||
\(478\) | −16.8284 | −0.769714 | ||||||||
\(479\) | 27.3137 | 1.24800 | 0.623998 | − | 0.781426i | \(-0.285507\pi\) | ||||
0.623998 | + | 0.781426i | \(0.285507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.485281 | −0.0221269 | ||||||||
\(482\) | 6.48528 | 0.295396 | ||||||||
\(483\) | 2.00000 | 0.0910032 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 39.9411 | 1.80991 | 0.904953 | − | 0.425512i | \(-0.139906\pi\) | ||||
0.904953 | + | 0.425512i | \(0.139906\pi\) | |||||||
\(488\) | −0.585786 | −0.0265173 | ||||||||
\(489\) | 6.82843 | 0.308792 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.6274 | −0.840644 | −0.420322 | − | 0.907375i | \(-0.638083\pi\) | ||||
−0.420322 | + | 0.907375i | \(0.638083\pi\) | |||||||
\(492\) | −6.82843 | −0.307849 | ||||||||
\(493\) | 24.9706 | 1.12462 | ||||||||
\(494\) | −5.17157 | −0.232680 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 11.3137 | 0.507489 | ||||||||
\(498\) | 1.41421 | 0.0633724 | ||||||||
\(499\) | −37.4558 | −1.67675 | −0.838377 | − | 0.545091i | \(-0.816495\pi\) | ||||
−0.838377 | + | 0.545091i | \(0.816495\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.17157 | −0.141695 | ||||||||
\(502\) | 0.727922 | 0.0324888 | ||||||||
\(503\) | −6.14214 | −0.273864 | −0.136932 | − | 0.990580i | \(-0.543724\pi\) | ||||
−0.136932 | + | 0.990580i | \(0.543724\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.24264 | 0.188608 | ||||||||
\(507\) | −12.3137 | −0.546871 | ||||||||
\(508\) | −2.00000 | −0.0887357 | ||||||||
\(509\) | −10.9706 | −0.486262 | −0.243131 | − | 0.969994i | \(-0.578174\pi\) | ||||
−0.243131 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.3137 | −0.677439 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 6.24264 | 0.275619 | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 10.2426 | 0.450907 | ||||||||
\(517\) | 3.51472 | 0.154577 | ||||||||
\(518\) | −1.17157 | −0.0514760 | ||||||||
\(519\) | 8.82843 | 0.387525 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.2843 | 1.76489 | 0.882443 | − | 0.470419i | \(-0.155897\pi\) | ||||
0.882443 | + | 0.470419i | \(0.155897\pi\) | |||||||
\(522\) | 3.65685 | 0.160056 | ||||||||
\(523\) | −17.0711 | −0.746466 | −0.373233 | − | 0.927738i | \(-0.621751\pi\) | ||||
−0.373233 | + | 0.927738i | \(0.621751\pi\) | |||||||
\(524\) | −21.6569 | −0.946084 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.34315 | −0.276574 | ||||||||
\(527\) | 40.9706 | 1.78471 | ||||||||
\(528\) | −4.24264 | −0.184637 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.48528 | 0.368230 | ||||||||
\(532\) | −12.4853 | −0.541306 | ||||||||
\(533\) | 5.65685 | 0.245026 | ||||||||
\(534\) | 9.17157 | 0.396893 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.41421 | −0.147472 | ||||||||
\(537\) | −21.6569 | −0.934562 | ||||||||
\(538\) | −19.1716 | −0.826545 | ||||||||
\(539\) | 12.7279 | 0.548230 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.9411 | −1.37326 | −0.686628 | − | 0.727009i | \(-0.740910\pi\) | ||||
−0.686628 | + | 0.727009i | \(0.740910\pi\) | |||||||
\(542\) | 9.65685 | 0.414797 | ||||||||
\(543\) | −20.3848 | −0.874794 | ||||||||
\(544\) | 6.82843 | 0.292766 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.65685 | 0.0709068 | ||||||||
\(547\) | 12.4853 | 0.533832 | 0.266916 | − | 0.963720i | \(-0.413995\pi\) | ||||
0.266916 | + | 0.963720i | \(0.413995\pi\) | |||||||
\(548\) | −8.48528 | −0.362473 | ||||||||
\(549\) | −0.585786 | −0.0250008 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.8284 | 0.972524 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 7.31371 | 0.311011 | ||||||||
\(554\) | 13.5147 | 0.574185 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.9706 | −0.719712 | ||||||||
\(557\) | 38.8701 | 1.64698 | 0.823489 | − | 0.567333i | \(-0.192025\pi\) | ||||
0.823489 | + | 0.567333i | \(0.192025\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −8.48528 | −0.358889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.9706 | −1.22314 | ||||||||
\(562\) | −1.85786 | −0.0783693 | ||||||||
\(563\) | −2.10051 | −0.0885257 | −0.0442629 | − | 0.999020i | \(-0.514094\pi\) | ||||
−0.0442629 | + | 0.999020i | \(0.514094\pi\) | |||||||
\(564\) | −0.828427 | −0.0348831 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.2132 | 0.639459 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | −5.65685 | −0.237356 | ||||||||
\(569\) | 14.3431 | 0.601296 | 0.300648 | − | 0.953735i | \(-0.402797\pi\) | ||||
0.300648 | + | 0.953735i | \(0.402797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.2721 | −0.722814 | −0.361407 | − | 0.932408i | \(-0.617703\pi\) | ||||
−0.361407 | + | 0.932408i | \(0.617703\pi\) | |||||||
\(572\) | 3.51472 | 0.146958 | ||||||||
\(573\) | −10.8284 | −0.452364 | ||||||||
\(574\) | 13.6569 | 0.570026 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 24.6274 | 1.02525 | 0.512626 | − | 0.858612i | \(-0.328673\pi\) | ||||
0.512626 | + | 0.858612i | \(0.328673\pi\) | |||||||
\(578\) | 29.6274 | 1.23234 | ||||||||
\(579\) | −20.9706 | −0.871507 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.82843 | −0.117343 | ||||||||
\(582\) | −6.00000 | −0.248708 | ||||||||
\(583\) | −44.9117 | −1.86005 | ||||||||
\(584\) | 7.65685 | 0.316843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.0416 | 0.827912 | ||||||||
\(587\) | 21.1716 | 0.873844 | 0.436922 | − | 0.899499i | \(-0.356069\pi\) | ||||
0.436922 | + | 0.899499i | \(0.356069\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | 37.4558 | 1.54334 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.6274 | 0.848499 | ||||||||
\(592\) | 0.585786 | 0.0240757 | ||||||||
\(593\) | −23.6569 | −0.971471 | −0.485735 | − | 0.874106i | \(-0.661448\pi\) | ||||
−0.485735 | + | 0.874106i | \(0.661448\pi\) | |||||||
\(594\) | −4.24264 | −0.174078 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.7279 | 0.521356 | ||||||||
\(597\) | −14.0000 | −0.572982 | ||||||||
\(598\) | 0.828427 | 0.0338769 | ||||||||
\(599\) | −11.8579 | −0.484499 | −0.242250 | − | 0.970214i | \(-0.577885\pi\) | ||||
−0.242250 | + | 0.970214i | \(0.577885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.9706 | 0.529080 | 0.264540 | − | 0.964375i | \(-0.414780\pi\) | ||||
0.264540 | + | 0.964375i | \(0.414780\pi\) | |||||||
\(602\) | −20.4853 | −0.834918 | ||||||||
\(603\) | −3.41421 | −0.139038 | ||||||||
\(604\) | −4.34315 | −0.176720 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.3137 | 0.540832 | ||||||||
\(607\) | 16.9706 | 0.688814 | 0.344407 | − | 0.938820i | \(-0.388080\pi\) | ||||
0.344407 | + | 0.938820i | \(0.388080\pi\) | |||||||
\(608\) | 6.24264 | 0.253173 | ||||||||
\(609\) | −7.31371 | −0.296366 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.686292 | 0.0277644 | ||||||||
\(612\) | 6.82843 | 0.276023 | ||||||||
\(613\) | −5.75736 | −0.232538 | −0.116269 | − | 0.993218i | \(-0.537093\pi\) | ||||
−0.116269 | + | 0.993218i | \(0.537093\pi\) | |||||||
\(614\) | 25.4558 | 1.02731 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.48528 | 0.341882 | ||||||||
\(617\) | −8.68629 | −0.349697 | −0.174848 | − | 0.984595i | \(-0.555944\pi\) | ||||
−0.174848 | + | 0.984595i | \(0.555944\pi\) | |||||||
\(618\) | 16.1421 | 0.649332 | ||||||||
\(619\) | 23.2132 | 0.933017 | 0.466509 | − | 0.884517i | \(-0.345512\pi\) | ||||
0.466509 | + | 0.884517i | \(0.345512\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −21.7990 | −0.874060 | ||||||||
\(623\) | −18.3431 | −0.734903 | ||||||||
\(624\) | −0.828427 | −0.0331636 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.0000 | 0.719425 | ||||||||
\(627\) | −26.4853 | −1.05772 | ||||||||
\(628\) | 21.0711 | 0.840827 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.8284 | 1.62535 | 0.812677 | − | 0.582714i | \(-0.198009\pi\) | ||||
0.812677 | + | 0.582714i | \(0.198009\pi\) | |||||||
\(632\) | −3.65685 | −0.145462 | ||||||||
\(633\) | −3.51472 | −0.139698 | ||||||||
\(634\) | −14.4853 | −0.575284 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.5858 | 0.419754 | ||||||||
\(637\) | 2.48528 | 0.0984704 | ||||||||
\(638\) | −15.5147 | −0.614234 | ||||||||
\(639\) | −5.65685 | −0.223782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.2843 | 1.90711 | 0.953557 | − | 0.301213i | \(-0.0973914\pi\) | ||||
0.953557 | + | 0.301213i | \(0.0973914\pi\) | |||||||
\(642\) | 0.928932 | 0.0366620 | ||||||||
\(643\) | 4.38478 | 0.172919 | 0.0864593 | − | 0.996255i | \(-0.472445\pi\) | ||||
0.0864593 | + | 0.996255i | \(0.472445\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 42.6274 | 1.67715 | ||||||||
\(647\) | −18.3431 | −0.721143 | −0.360572 | − | 0.932731i | \(-0.617418\pi\) | ||||
−0.360572 | + | 0.932731i | \(0.617418\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | 6.82843 | 0.267422 | ||||||||
\(653\) | −7.45584 | −0.291770 | −0.145885 | − | 0.989302i | \(-0.546603\pi\) | ||||
−0.145885 | + | 0.989302i | \(0.546603\pi\) | |||||||
\(654\) | 12.5858 | 0.492143 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.82843 | −0.266605 | ||||||||
\(657\) | 7.65685 | 0.298722 | ||||||||
\(658\) | 1.65685 | 0.0645909 | ||||||||
\(659\) | −45.8995 | −1.78799 | −0.893995 | − | 0.448076i | \(-0.852109\pi\) | ||||
−0.893995 | + | 0.448076i | \(0.852109\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.7279 | 1.35076 | 0.675380 | − | 0.737470i | \(-0.263980\pi\) | ||||
0.675380 | + | 0.737470i | \(0.263980\pi\) | |||||||
\(662\) | −20.4853 | −0.796183 | ||||||||
\(663\) | −5.65685 | −0.219694 | ||||||||
\(664\) | 1.41421 | 0.0548821 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.585786 | 0.0226988 | ||||||||
\(667\) | −3.65685 | −0.141594 | ||||||||
\(668\) | −3.17157 | −0.122712 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.48528 | 0.0959432 | ||||||||
\(672\) | −2.00000 | −0.0771517 | ||||||||
\(673\) | 27.9411 | 1.07705 | 0.538526 | − | 0.842609i | \(-0.318982\pi\) | ||||
0.538526 | + | 0.842609i | \(0.318982\pi\) | |||||||
\(674\) | −26.4853 | −1.02017 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3137 | −0.473604 | ||||||||
\(677\) | −40.5269 | −1.55758 | −0.778788 | − | 0.627287i | \(-0.784165\pi\) | ||||
−0.778788 | + | 0.627287i | \(0.784165\pi\) | |||||||
\(678\) | −16.9706 | −0.651751 | ||||||||
\(679\) | 12.0000 | 0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.3848 | −0.857786 | ||||||||
\(682\) | −25.4558 | −0.974755 | ||||||||
\(683\) | −8.48528 | −0.324680 | −0.162340 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162340 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(684\) | 6.24264 | 0.238693 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | 10.2426 | 0.390781 | ||||||||
\(688\) | 10.2426 | 0.390497 | ||||||||
\(689\) | −8.76955 | −0.334093 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.1716 | −0.501070 | −0.250535 | − | 0.968108i | \(-0.580607\pi\) | ||||
−0.250535 | + | 0.968108i | \(0.580607\pi\) | |||||||
\(692\) | 8.82843 | 0.335606 | ||||||||
\(693\) | 8.48528 | 0.322329 | ||||||||
\(694\) | −31.7990 | −1.20707 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.65685 | 0.138613 | ||||||||
\(697\) | −46.6274 | −1.76614 | ||||||||
\(698\) | 2.68629 | 0.101678 | ||||||||
\(699\) | 2.14214 | 0.0810230 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1838 | −1.44218 | −0.721090 | − | 0.692841i | \(-0.756359\pi\) | ||||
−0.721090 | + | 0.692841i | \(0.756359\pi\) | |||||||
\(702\) | −0.828427 | −0.0312670 | ||||||||
\(703\) | 3.65685 | 0.137921 | ||||||||
\(704\) | −4.24264 | −0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.14214 | 0.0806203 | ||||||||
\(707\) | −26.6274 | −1.00143 | ||||||||
\(708\) | 8.48528 | 0.318896 | ||||||||
\(709\) | 32.5858 | 1.22378 | 0.611892 | − | 0.790941i | \(-0.290409\pi\) | ||||
0.611892 | + | 0.790941i | \(0.290409\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.65685 | −0.137143 | ||||||||
\(712\) | 9.17157 | 0.343719 | ||||||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | −13.6569 | −0.511095 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −21.6569 | −0.809355 | ||||||||
\(717\) | −16.8284 | −0.628469 | ||||||||
\(718\) | 19.7990 | 0.738892 | ||||||||
\(719\) | −0.142136 | −0.00530076 | −0.00265038 | − | 0.999996i | \(-0.500844\pi\) | ||||
−0.00265038 | + | 0.999996i | \(0.500844\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.2843 | −1.20233 | ||||||||
\(722\) | 19.9706 | 0.743227 | ||||||||
\(723\) | 6.48528 | 0.241190 | ||||||||
\(724\) | −20.3848 | −0.757594 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | 0.259794 | ||||||||
\(727\) | −20.3431 | −0.754486 | −0.377243 | − | 0.926114i | \(-0.623128\pi\) | ||||
−0.377243 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(728\) | 1.65685 | 0.0614071 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 69.9411 | 2.58687 | ||||||||
\(732\) | −0.585786 | −0.0216513 | ||||||||
\(733\) | 11.4142 | 0.421594 | 0.210797 | − | 0.977530i | \(-0.432394\pi\) | ||||
0.210797 | + | 0.977530i | \(0.432394\pi\) | |||||||
\(734\) | 1.02944 | 0.0379972 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 14.4853 | 0.533572 | ||||||||
\(738\) | −6.82843 | −0.251358 | ||||||||
\(739\) | −2.62742 | −0.0966511 | −0.0483255 | − | 0.998832i | \(-0.515388\pi\) | ||||
−0.0483255 | + | 0.998832i | \(0.515388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.17157 | −0.189982 | ||||||||
\(742\) | −21.1716 | −0.777233 | ||||||||
\(743\) | 13.6569 | 0.501021 | 0.250511 | − | 0.968114i | \(-0.419401\pi\) | ||||
0.250511 | + | 0.968114i | \(0.419401\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.2132 | −0.849896 | ||||||||
\(747\) | 1.41421 | 0.0517434 | ||||||||
\(748\) | −28.9706 | −1.05927 | ||||||||
\(749\) | −1.85786 | −0.0678849 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.1716 | −1.57535 | −0.787677 | − | 0.616089i | \(-0.788716\pi\) | ||||
−0.787677 | + | 0.616089i | \(0.788716\pi\) | |||||||
\(752\) | −0.828427 | −0.0302096 | ||||||||
\(753\) | 0.727922 | 0.0265270 | ||||||||
\(754\) | −3.02944 | −0.110326 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | −0.0727393 | ||||||||
\(757\) | 33.7574 | 1.22693 | 0.613466 | − | 0.789721i | \(-0.289775\pi\) | ||||
0.613466 | + | 0.789721i | \(0.289775\pi\) | |||||||
\(758\) | 23.2132 | 0.843142 | ||||||||
\(759\) | 4.24264 | 0.153998 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.6569 | −1.29256 | −0.646280 | − | 0.763100i | \(-0.723676\pi\) | ||||
−0.646280 | + | 0.763100i | \(0.723676\pi\) | |||||||
\(762\) | −2.00000 | −0.0724524 | ||||||||
\(763\) | −25.1716 | −0.911272 | ||||||||
\(764\) | −10.8284 | −0.391759 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 26.6274 | 0.962088 | ||||||||
\(767\) | −7.02944 | −0.253818 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 6.20101 | 0.223614 | 0.111807 | − | 0.993730i | \(-0.464336\pi\) | ||||
0.111807 | + | 0.993730i | \(0.464336\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | −20.9706 | −0.754747 | ||||||||
\(773\) | −31.0711 | −1.11755 | −0.558774 | − | 0.829320i | \(-0.688728\pi\) | ||||
−0.558774 | + | 0.829320i | \(0.688728\pi\) | |||||||
\(774\) | 10.2426 | 0.368164 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | −1.17157 | −0.0420299 | ||||||||
\(778\) | −30.3848 | −1.08935 | ||||||||
\(779\) | −42.6274 | −1.52729 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | −6.82843 | −0.244184 | ||||||||
\(783\) | 3.65685 | 0.130685 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −21.6569 | −0.772474 | ||||||||
\(787\) | −22.7279 | −0.810163 | −0.405081 | − | 0.914281i | \(-0.632757\pi\) | ||||
−0.405081 | + | 0.914281i | \(0.632757\pi\) | |||||||
\(788\) | 20.6274 | 0.734821 | ||||||||
\(789\) | −6.34315 | −0.225822 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 33.9411 | 1.20681 | ||||||||
\(792\) | −4.24264 | −0.150756 | ||||||||
\(793\) | 0.485281 | 0.0172328 | ||||||||
\(794\) | −19.6569 | −0.697596 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | −18.5858 | −0.658342 | −0.329171 | − | 0.944270i | \(-0.606769\pi\) | ||||
−0.329171 | + | 0.944270i | \(0.606769\pi\) | |||||||
\(798\) | −12.4853 | −0.441974 | ||||||||
\(799\) | −5.65685 | −0.200125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.17157 | 0.324062 | ||||||||
\(802\) | 4.97056 | 0.175517 | ||||||||
\(803\) | −32.4853 | −1.14638 | ||||||||
\(804\) | −3.41421 | −0.120410 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.97056 | −0.175081 | ||||||||
\(807\) | −19.1716 | −0.674871 | ||||||||
\(808\) | 13.3137 | 0.468375 | ||||||||
\(809\) | −9.31371 | −0.327453 | −0.163726 | − | 0.986506i | \(-0.552351\pi\) | ||||
−0.163726 | + | 0.986506i | \(0.552351\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.17157 | 0.0411395 | 0.0205697 | − | 0.999788i | \(-0.493452\pi\) | ||||
0.0205697 | + | 0.999788i | \(0.493452\pi\) | |||||||
\(812\) | −7.31371 | −0.256661 | ||||||||
\(813\) | 9.65685 | 0.338681 | ||||||||
\(814\) | −2.48528 | −0.0871091 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.82843 | 0.239043 | ||||||||
\(817\) | 63.9411 | 2.23702 | ||||||||
\(818\) | 18.0000 | 0.629355 | ||||||||
\(819\) | 1.65685 | 0.0578952 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.3137 | −1.02306 | −0.511528 | − | 0.859267i | \(-0.670920\pi\) | ||||
−0.511528 | + | 0.859267i | \(0.670920\pi\) | |||||||
\(822\) | −8.48528 | −0.295958 | ||||||||
\(823\) | −24.2843 | −0.846496 | −0.423248 | − | 0.906014i | \(-0.639110\pi\) | ||||
−0.423248 | + | 0.906014i | \(0.639110\pi\) | |||||||
\(824\) | 16.1421 | 0.562338 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.9706 | −0.590481 | ||||||||
\(827\) | 37.8995 | 1.31789 | 0.658947 | − | 0.752189i | \(-0.271002\pi\) | ||||
0.658947 | + | 0.752189i | \(0.271002\pi\) | |||||||
\(828\) | −1.00000 | −0.0347524 | ||||||||
\(829\) | −6.28427 | −0.218262 | −0.109131 | − | 0.994027i | \(-0.534807\pi\) | ||||
−0.109131 | + | 0.994027i | \(0.534807\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.5147 | 0.468820 | ||||||||
\(832\) | −0.828427 | −0.0287205 | ||||||||
\(833\) | −20.4853 | −0.709773 | ||||||||
\(834\) | −16.9706 | −0.587643 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −26.4853 | −0.916013 | ||||||||
\(837\) | 6.00000 | 0.207390 | ||||||||
\(838\) | −39.0711 | −1.34969 | ||||||||
\(839\) | 33.9411 | 1.17178 | 0.585889 | − | 0.810391i | \(-0.300745\pi\) | ||||
0.585889 | + | 0.810391i | \(0.300745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.6274 | −0.538876 | ||||||||
\(842\) | 1.75736 | 0.0605626 | ||||||||
\(843\) | −1.85786 | −0.0639882 | ||||||||
\(844\) | −3.51472 | −0.120982 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.828427 | −0.0284819 | ||||||||
\(847\) | −14.0000 | −0.481046 | ||||||||
\(848\) | 10.5858 | 0.363517 | ||||||||
\(849\) | 15.2132 | 0.522116 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.585786 | −0.0200805 | ||||||||
\(852\) | −5.65685 | −0.193801 | ||||||||
\(853\) | −21.3137 | −0.729767 | −0.364884 | − | 0.931053i | \(-0.618891\pi\) | ||||
−0.364884 | + | 0.931053i | \(0.618891\pi\) | |||||||
\(854\) | 1.17157 | 0.0400904 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.928932 | 0.0317502 | ||||||||
\(857\) | −50.8284 | −1.73627 | −0.868133 | − | 0.496332i | \(-0.834680\pi\) | ||||
−0.868133 | + | 0.496332i | \(0.834680\pi\) | |||||||
\(858\) | 3.51472 | 0.119991 | ||||||||
\(859\) | 24.2843 | 0.828569 | 0.414284 | − | 0.910148i | \(-0.364032\pi\) | ||||
0.414284 | + | 0.910148i | \(0.364032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13.6569 | 0.465424 | ||||||||
\(862\) | −8.48528 | −0.289010 | ||||||||
\(863\) | −22.6274 | −0.770246 | −0.385123 | − | 0.922865i | \(-0.625841\pi\) | ||||
−0.385123 | + | 0.922865i | \(0.625841\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.97056 | −0.236869 | ||||||||
\(867\) | 29.6274 | 1.00620 | ||||||||
\(868\) | −12.0000 | −0.407307 | ||||||||
\(869\) | 15.5147 | 0.526301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.82843 | 0.0958376 | ||||||||
\(872\) | 12.5858 | 0.426209 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | −6.24264 | −0.211160 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.65685 | 0.258701 | ||||||||
\(877\) | −16.8284 | −0.568256 | −0.284128 | − | 0.958786i | \(-0.591704\pi\) | ||||
−0.284128 | + | 0.958786i | \(0.591704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.0416 | 0.675987 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.1421 | 0.880751 | 0.440375 | − | 0.897814i | \(-0.354845\pi\) | ||||
0.440375 | + | 0.897814i | \(0.354845\pi\) | |||||||
\(882\) | −3.00000 | −0.101015 | ||||||||
\(883\) | 18.8284 | 0.633627 | 0.316814 | − | 0.948488i | \(-0.397387\pi\) | ||||
0.316814 | + | 0.948488i | \(0.397387\pi\) | |||||||
\(884\) | −5.65685 | −0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.686292 | −0.0230564 | ||||||||
\(887\) | 36.4264 | 1.22308 | 0.611540 | − | 0.791214i | \(-0.290551\pi\) | ||||
0.611540 | + | 0.791214i | \(0.290551\pi\) | |||||||
\(888\) | 0.585786 | 0.0196577 | ||||||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.24264 | −0.142134 | ||||||||
\(892\) | 16.0000 | 0.535720 | ||||||||
\(893\) | −5.17157 | −0.173060 | ||||||||
\(894\) | 12.7279 | 0.425685 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0.828427 | 0.0276604 | ||||||||
\(898\) | −17.1716 | −0.573023 | ||||||||
\(899\) | 21.9411 | 0.731778 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 72.2843 | 2.40814 | ||||||||
\(902\) | 28.9706 | 0.964614 | ||||||||
\(903\) | −20.4853 | −0.681707 | ||||||||
\(904\) | −16.9706 | −0.564433 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.34315 | −0.144291 | ||||||||
\(907\) | −15.2132 | −0.505146 | −0.252573 | − | 0.967578i | \(-0.581277\pi\) | ||||
−0.252573 | + | 0.967578i | \(0.581277\pi\) | |||||||
\(908\) | −22.3848 | −0.742865 | ||||||||
\(909\) | 13.3137 | 0.441588 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.7990 | −1.31860 | −0.659300 | − | 0.751880i | \(-0.729147\pi\) | ||||
−0.659300 | + | 0.751880i | \(0.729147\pi\) | |||||||
\(912\) | 6.24264 | 0.206714 | ||||||||
\(913\) | −6.00000 | −0.198571 | ||||||||
\(914\) | 34.9706 | 1.15672 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.2426 | 0.338426 | ||||||||
\(917\) | 43.3137 | 1.43034 | ||||||||
\(918\) | 6.82843 | 0.225372 | ||||||||
\(919\) | 38.9706 | 1.28552 | 0.642760 | − | 0.766068i | \(-0.277789\pi\) | ||||
0.642760 | + | 0.766068i | \(0.277789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.4558 | 0.838799 | ||||||||
\(922\) | −7.17157 | −0.236183 | ||||||||
\(923\) | 4.68629 | 0.154251 | ||||||||
\(924\) | 8.48528 | 0.279145 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −30.9706 | −1.01776 | ||||||||
\(927\) | 16.1421 | 0.530177 | ||||||||
\(928\) | 3.65685 | 0.120042 | ||||||||
\(929\) | 13.8579 | 0.454662 | 0.227331 | − | 0.973818i | \(-0.427000\pi\) | ||||
0.227331 | + | 0.973818i | \(0.427000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.7279 | −0.613783 | ||||||||
\(932\) | 2.14214 | 0.0701680 | ||||||||
\(933\) | −21.7990 | −0.713667 | ||||||||
\(934\) | −31.3553 | −1.02598 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −0.828427 | −0.0270780 | ||||||||
\(937\) | −40.4264 | −1.32067 | −0.660337 | − | 0.750970i | \(-0.729586\pi\) | ||||
−0.660337 | + | 0.750970i | \(0.729586\pi\) | |||||||
\(938\) | 6.82843 | 0.222956 | ||||||||
\(939\) | 18.0000 | 0.587408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.443651 | −0.0144626 | −0.00723130 | − | 0.999974i | \(-0.502302\pi\) | ||||
−0.00723130 | + | 0.999974i | \(0.502302\pi\) | |||||||
\(942\) | 21.0711 | 0.686532 | ||||||||
\(943\) | 6.82843 | 0.222364 | ||||||||
\(944\) | 8.48528 | 0.276172 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.4558 | −1.41287 | ||||||||
\(947\) | −49.4558 | −1.60710 | −0.803549 | − | 0.595238i | \(-0.797058\pi\) | ||||
−0.803549 | + | 0.595238i | \(0.797058\pi\) | |||||||
\(948\) | −3.65685 | −0.118769 | ||||||||
\(949\) | −6.34315 | −0.205907 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.4853 | −0.469717 | ||||||||
\(952\) | −13.6569 | −0.442621 | ||||||||
\(953\) | −56.0833 | −1.81672 | −0.908358 | − | 0.418194i | \(-0.862663\pi\) | ||||
−0.908358 | + | 0.418194i | \(0.862663\pi\) | |||||||
\(954\) | 10.5858 | 0.342727 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16.8284 | −0.544270 | ||||||||
\(957\) | −15.5147 | −0.501520 | ||||||||
\(958\) | 27.3137 | 0.882466 | ||||||||
\(959\) | 16.9706 | 0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −0.485281 | −0.0156461 | ||||||||
\(963\) | 0.928932 | 0.0299344 | ||||||||
\(964\) | 6.48528 | 0.208877 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.00000 | 0.0643489 | ||||||||
\(967\) | −28.9706 | −0.931630 | −0.465815 | − | 0.884882i | \(-0.654239\pi\) | ||||
−0.465815 | + | 0.884882i | \(0.654239\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 42.6274 | 1.36939 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.3848 | −1.74529 | −0.872645 | − | 0.488355i | \(-0.837597\pi\) | ||||
−0.872645 | + | 0.488355i | \(0.837597\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 33.9411 | 1.08810 | ||||||||
\(974\) | 39.9411 | 1.27980 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.585786 | −0.0187506 | ||||||||
\(977\) | −19.7990 | −0.633426 | −0.316713 | − | 0.948521i | \(-0.602579\pi\) | ||||
−0.316713 | + | 0.948521i | \(0.602579\pi\) | |||||||
\(978\) | 6.82843 | 0.218349 | ||||||||
\(979\) | −38.9117 | −1.24362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.5858 | 0.401833 | ||||||||
\(982\) | −18.6274 | −0.594425 | ||||||||
\(983\) | −3.51472 | −0.112102 | −0.0560511 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560511 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(984\) | −6.82843 | −0.217682 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 24.9706 | 0.795225 | ||||||||
\(987\) | 1.65685 | 0.0527383 | ||||||||
\(988\) | −5.17157 | −0.164530 | ||||||||
\(989\) | −10.2426 | −0.325697 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.9411 | −0.506387 | −0.253193 | − | 0.967416i | \(-0.581481\pi\) | ||||
−0.253193 | + | 0.967416i | \(0.581481\pi\) | |||||||
\(992\) | 6.00000 | 0.190500 | ||||||||
\(993\) | −20.4853 | −0.650081 | ||||||||
\(994\) | 11.3137 | 0.358849 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.41421 | 0.0448111 | ||||||||
\(997\) | −13.0294 | −0.412646 | −0.206323 | − | 0.978484i | \(-0.566150\pi\) | ||||
−0.206323 | + | 0.978484i | \(0.566150\pi\) | |||||||
\(998\) | −37.4558 | −1.18564 | ||||||||
\(999\) | 0.585786 | 0.0185335 |
(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 | 3450.2.a.bk.1.1 | 2 | ||
5.2 | odd | 4 | 690.2.d.b.139.3 | yes | 4 | ||
5.3 | odd | 4 | 690.2.d.b.139.1 | ✓ | 4 | ||
5.4 | even | 2 | 3450.2.a.bg.1.1 | 2 | |||
15.2 | even | 4 | 2070.2.d.a.829.2 | 4 | |||
15.8 | even | 4 | 2070.2.d.a.829.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.b.139.1 | ✓ | 4 | 5.3 | odd | 4 | ||
690.2.d.b.139.3 | yes | 4 | 5.2 | odd | 4 | ||
2070.2.d.a.829.2 | 4 | 15.2 | even | 4 | |||
2070.2.d.a.829.4 | 4 | 15.8 | even | 4 | |||
3450.2.a.bg.1.1 | 2 | 5.4 | even | 2 | |||
3450.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial |