Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.1 | ||
Root | \(2.69978 - 0.355433i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.e.1273.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.99671 | − | 1.00656i | −0.892955 | − | 0.450147i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.700141 | + | 2.12363i | 0.221404 | + | 0.671551i | ||||
\(11\) | −3.10780 | −0.937038 | −0.468519 | − | 0.883453i | \(-0.655212\pi\) | ||||
−0.468519 | + | 0.883453i | \(0.655212\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 3.40812 | + | 3.40812i | 0.945243 | + | 0.945243i | 0.998577 | − | 0.0533341i | \(-0.0169848\pi\) |
−0.0533341 | + | 0.998577i | \(0.516985\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.700141 | + | 2.12363i | 0.180776 | + | 0.548319i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.76725 | − | 3.76725i | 0.913692 | − | 0.913692i | −0.0828688 | − | 0.996560i | \(-0.526408\pi\) |
0.996560 | + | 0.0828688i | \(0.0264083\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 7.23346 | 1.65947 | 0.829735 | − | 0.558158i | \(-0.188492\pi\) | ||||
0.829735 | + | 0.558158i | \(0.188492\pi\) | |||||||
\(20\) | 1.00656 | − | 1.99671i | 0.225073 | − | 0.446477i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.19755 | + | 2.19755i | 0.468519 | + | 0.468519i | ||||
\(23\) | −3.72349 | + | 3.72349i | −0.776401 | + | 0.776401i | −0.979217 | − | 0.202816i | \(-0.934991\pi\) |
0.202816 | + | 0.979217i | \(0.434991\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 2.97368 | + | 4.01961i | 0.594736 | + | 0.803921i | ||||
\(26\) | − | 4.81981i | − | 0.945243i | ||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.49359i | − | 0.834438i | −0.908806 | − | 0.417219i | \(-0.863005\pi\) | ||
0.908806 | − | 0.417219i | \(-0.136995\pi\) | |||||||
\(30\) | 1.00656 | − | 1.99671i | 0.183772 | − | 0.364547i | ||||
\(31\) | − | 9.22503i | − | 1.65686i | −0.560089 | − | 0.828432i | \(-0.689233\pi\) | ||
0.560089 | − | 0.828432i | \(-0.310767\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 2.19755 | + | 2.19755i | 0.382544 | + | 0.382544i | ||||
\(34\) | −5.32769 | −0.913692 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −2.54080 | − | 2.54080i | −0.417705 | − | 0.417705i | 0.466707 | − | 0.884412i | \(-0.345440\pi\) |
−0.884412 | + | 0.466707i | \(0.845440\pi\) | |||||||
\(38\) | −5.11483 | − | 5.11483i | −0.829735 | − | 0.829735i | ||||
\(39\) | − | 4.81981i | − | 0.771787i | ||||||
\(40\) | −2.12363 | + | 0.700141i | −0.335775 | + | 0.110702i | ||||
\(41\) | 2.51851i | 0.393326i | 0.980471 | + | 0.196663i | \(0.0630104\pi\) | ||||
−0.980471 | + | 0.196663i | \(0.936990\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.86848 | + | 3.86848i | −0.589938 | + | 0.589938i | −0.937615 | − | 0.347677i | \(-0.886971\pi\) |
0.347677 | + | 0.937615i | \(0.386971\pi\) | |||||||
\(44\) | − | 3.10780i | − | 0.468519i | ||||||
\(45\) | 1.00656 | − | 1.99671i | 0.150049 | − | 0.297652i | ||||
\(46\) | 5.26581 | 0.776401 | ||||||||
\(47\) | −2.88813 | + | 2.88813i | −0.421277 | + | 0.421277i | −0.885643 | − | 0.464366i | \(-0.846282\pi\) |
0.464366 | + | 0.885643i | \(0.346282\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.739583 | − | 4.94500i | 0.104593 | − | 0.699328i | ||||
\(51\) | −5.32769 | −0.746026 | ||||||||
\(52\) | −3.40812 | + | 3.40812i | −0.472621 | + | 0.472621i | ||||
\(53\) | 2.43203 | − | 2.43203i | 0.334066 | − | 0.334066i | −0.520063 | − | 0.854128i | \(-0.674091\pi\) |
0.854128 | + | 0.520063i | \(0.174091\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 6.20538 | + | 3.12819i | 0.836733 | + | 0.421805i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.11483 | − | 5.11483i | −0.677476 | − | 0.677476i | ||||
\(58\) | −3.17745 | + | 3.17745i | −0.417219 | + | 0.417219i | ||||
\(59\) | −1.33238 | −0.173461 | −0.0867303 | − | 0.996232i | \(-0.527642\pi\) | ||||
−0.0867303 | + | 0.996232i | \(0.527642\pi\) | |||||||
\(60\) | −2.12363 | + | 0.700141i | −0.274159 | + | 0.0903878i | ||||
\(61\) | − | 12.5538i | − | 1.60735i | −0.595071 | − | 0.803673i | \(-0.702876\pi\) | ||
0.595071 | − | 0.803673i | \(-0.297124\pi\) | |||||||
\(62\) | −6.52308 | + | 6.52308i | −0.828432 | + | 0.828432i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −3.37454 | − | 10.2355i | −0.418561 | − | 1.26956i | ||||
\(66\) | − | 3.10780i | − | 0.382544i | ||||||
\(67\) | −4.71136 | − | 4.71136i | −0.575584 | − | 0.575584i | 0.358099 | − | 0.933684i | \(-0.383425\pi\) |
−0.933684 | + | 0.358099i | \(0.883425\pi\) | |||||||
\(68\) | 3.76725 | + | 3.76725i | 0.456846 | + | 0.456846i | ||||
\(69\) | 5.26581 | 0.633929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.22738 | 1.09509 | 0.547544 | − | 0.836777i | \(-0.315563\pi\) | ||||
0.547544 | + | 0.836777i | \(0.315563\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 5.82099 | + | 5.82099i | 0.681296 | + | 0.681296i | 0.960292 | − | 0.278996i | \(-0.0900017\pi\) |
−0.278996 | + | 0.960292i | \(0.590002\pi\) | |||||||
\(74\) | 3.59323i | 0.417705i | ||||||||
\(75\) | 0.739583 | − | 4.94500i | 0.0853997 | − | 0.570999i | ||||
\(76\) | 7.23346i | 0.829735i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.40812 | + | 3.40812i | −0.385894 | + | 0.385894i | ||||
\(79\) | − | 1.91436i | − | 0.215383i | −0.994184 | − | 0.107691i | \(-0.965654\pi\) | ||
0.994184 | − | 0.107691i | \(-0.0343458\pi\) | |||||||
\(80\) | 1.99671 | + | 1.00656i | 0.223239 | + | 0.112537i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 1.78086 | − | 1.78086i | 0.196663 | − | 0.196663i | ||||
\(83\) | −8.97250 | − | 8.97250i | −0.984860 | − | 0.984860i | 0.0150269 | − | 0.999887i | \(-0.495217\pi\) |
−0.999887 | + | 0.0150269i | \(0.995217\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3140 | + | 3.73013i | −1.22718 | + | 0.404590i | ||||
\(86\) | 5.47086 | 0.589938 | ||||||||
\(87\) | −3.17745 | + | 3.17745i | −0.340658 | + | 0.340658i | ||||
\(88\) | −2.19755 | + | 2.19755i | −0.234260 | + | 0.234260i | ||||
\(89\) | −4.07354 | −0.431794 | −0.215897 | − | 0.976416i | \(-0.569268\pi\) | ||||
−0.215897 | + | 0.976416i | \(0.569268\pi\) | |||||||
\(90\) | −2.12363 | + | 0.700141i | −0.223850 | + | 0.0738013i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.72349 | − | 3.72349i | −0.388201 | − | 0.388201i | ||||
\(93\) | −6.52308 | + | 6.52308i | −0.676412 | + | 0.676412i | ||||
\(94\) | 4.08444 | 0.421277 | ||||||||
\(95\) | −14.4431 | − | 7.28091i | −1.48183 | − | 0.747005i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −2.69423 | + | 2.69423i | −0.273558 | + | 0.273558i | −0.830531 | − | 0.556973i | \(-0.811963\pi\) |
0.556973 | + | 0.830531i | \(0.311963\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.10780i | − | 0.312346i | ||||||
\(100\) | −4.01961 | + | 2.97368i | −0.401961 | + | 0.297368i | ||||
\(101\) | − | 7.86244i | − | 0.782342i | −0.920318 | − | 0.391171i | \(-0.872070\pi\) | ||
0.920318 | − | 0.391171i | \(-0.127930\pi\) | |||||||
\(102\) | 3.76725 | + | 3.76725i | 0.373013 | + | 0.373013i | ||||
\(103\) | −8.36587 | − | 8.36587i | −0.824313 | − | 0.824313i | 0.162410 | − | 0.986723i | \(-0.448073\pi\) |
−0.986723 | + | 0.162410i | \(0.948073\pi\) | |||||||
\(104\) | 4.81981 | 0.472621 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.43942 | −0.334066 | ||||||||
\(107\) | −1.52895 | − | 1.52895i | −0.147809 | − | 0.147809i | 0.629329 | − | 0.777139i | \(-0.283330\pi\) |
−0.777139 | + | 0.629329i | \(0.783330\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 0.565551i | 0.0541700i | 0.999633 | + | 0.0270850i | \(0.00862248\pi\) | ||||
−0.999633 | + | 0.0270850i | \(0.991378\pi\) | |||||||
\(110\) | −2.17590 | − | 6.59983i | −0.207464 | − | 0.629269i | ||||
\(111\) | 3.59323i | 0.341054i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.98231 | − | 9.98231i | 0.939057 | − | 0.939057i | −0.0591899 | − | 0.998247i | \(-0.518852\pi\) |
0.998247 | + | 0.0591899i | \(0.0188518\pi\) | |||||||
\(114\) | 7.23346i | 0.677476i | ||||||||
\(115\) | 11.1826 | − | 3.68681i | 1.04279 | − | 0.343797i | ||||
\(116\) | 4.49359 | 0.417219 | ||||||||
\(117\) | −3.40812 | + | 3.40812i | −0.315081 | + | 0.315081i | ||||
\(118\) | 0.942132 | + | 0.942132i | 0.0867303 | + | 0.0867303i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.99671 | + | 1.00656i | 0.182274 | + | 0.0918858i | ||||
\(121\) | −1.34155 | −0.121959 | ||||||||
\(122\) | −8.87686 | + | 8.87686i | −0.803673 | + | 0.803673i | ||||
\(123\) | 1.78086 | − | 1.78086i | 0.160575 | − | 0.160575i | ||||
\(124\) | 9.22503 | 0.828432 | ||||||||
\(125\) | −1.89159 | − | 11.0192i | −0.169189 | − | 0.985584i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.14534 | − | 2.14534i | −0.190368 | − | 0.190368i | 0.605487 | − | 0.795855i | \(-0.292978\pi\) |
−0.795855 | + | 0.605487i | \(0.792978\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 5.47086 | 0.481682 | ||||||||
\(130\) | −4.85142 | + | 9.62375i | −0.425498 | + | 0.844059i | ||||
\(131\) | − | 8.77339i | − | 0.766534i | −0.923638 | − | 0.383267i | \(-0.874799\pi\) | ||
0.923638 | − | 0.383267i | \(-0.125201\pi\) | |||||||
\(132\) | −2.19755 | + | 2.19755i | −0.191272 | + | 0.191272i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.66287i | 0.575584i | ||||||||
\(135\) | −2.12363 | + | 0.700141i | −0.182773 | + | 0.0602585i | ||||
\(136\) | − | 5.32769i | − | 0.456846i | ||||||
\(137\) | −9.62030 | − | 9.62030i | −0.821918 | − | 0.821918i | 0.164465 | − | 0.986383i | \(-0.447410\pi\) |
−0.986383 | + | 0.164465i | \(0.947410\pi\) | |||||||
\(138\) | −3.72349 | − | 3.72349i | −0.316965 | − | 0.316965i | ||||
\(139\) | 10.9145 | 0.925753 | 0.462876 | − | 0.886423i | \(-0.346817\pi\) | ||||
0.462876 | + | 0.886423i | \(0.346817\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.08444 | 0.343972 | ||||||||
\(142\) | −6.52474 | − | 6.52474i | −0.547544 | − | 0.547544i | ||||
\(143\) | −10.5918 | − | 10.5918i | −0.885729 | − | 0.885729i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −4.52306 | + | 8.97238i | −0.375620 | + | 0.745115i | ||||
\(146\) | − | 8.23213i | − | 0.681296i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.54080 | − | 2.54080i | 0.208852 | − | 0.208852i | ||||
\(149\) | − | 2.09021i | − | 0.171237i | −0.996328 | − | 0.0856183i | \(-0.972713\pi\) | ||
0.996328 | − | 0.0856183i | \(-0.0272866\pi\) | |||||||
\(150\) | −4.01961 | + | 2.97368i | −0.328200 | + | 0.242800i | ||||
\(151\) | 4.04236 | 0.328963 | 0.164481 | − | 0.986380i | \(-0.447405\pi\) | ||||
0.164481 | + | 0.986380i | \(0.447405\pi\) | |||||||
\(152\) | 5.11483 | − | 5.11483i | 0.414867 | − | 0.414867i | ||||
\(153\) | 3.76725 | + | 3.76725i | 0.304564 | + | 0.304564i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.28554 | + | 18.4197i | −0.745832 | + | 1.47950i | ||||
\(156\) | 4.81981 | 0.385894 | ||||||||
\(157\) | −0.640337 | + | 0.640337i | −0.0511044 | + | 0.0511044i | −0.732197 | − | 0.681093i | \(-0.761505\pi\) |
0.681093 | + | 0.732197i | \(0.261505\pi\) | |||||||
\(158\) | −1.35366 | + | 1.35366i | −0.107691 | + | 0.107691i | ||||
\(159\) | −3.43942 | −0.272763 | ||||||||
\(160\) | −0.700141 | − | 2.12363i | −0.0553510 | − | 0.167888i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −5.21998 | + | 5.21998i | −0.408860 | + | 0.408860i | −0.881341 | − | 0.472481i | \(-0.843359\pi\) |
0.472481 | + | 0.881341i | \(0.343359\pi\) | |||||||
\(164\) | −2.51851 | −0.196663 | ||||||||
\(165\) | −2.17590 | − | 6.59983i | −0.169394 | − | 0.513796i | ||||
\(166\) | 12.6890i | 0.984860i | ||||||||
\(167\) | 0.610646 | − | 0.610646i | 0.0472532 | − | 0.0472532i | −0.683085 | − | 0.730339i | \(-0.739362\pi\) |
0.730339 | + | 0.683085i | \(0.239362\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2306i | 0.786967i | ||||||||
\(170\) | 10.6378 | + | 5.36264i | 0.815885 | + | 0.411295i | ||||
\(171\) | 7.23346i | 0.553157i | ||||||||
\(172\) | −3.86848 | − | 3.86848i | −0.294969 | − | 0.294969i | ||||
\(173\) | 2.47309 | + | 2.47309i | 0.188026 | + | 0.188026i | 0.794842 | − | 0.606816i | \(-0.207554\pi\) |
−0.606816 | + | 0.794842i | \(0.707554\pi\) | |||||||
\(174\) | 4.49359 | 0.340658 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.10780 | 0.234260 | ||||||||
\(177\) | 0.942132 | + | 0.942132i | 0.0708150 | + | 0.0708150i | ||||
\(178\) | 2.88043 | + | 2.88043i | 0.215897 | + | 0.215897i | ||||
\(179\) | 18.0618i | 1.35000i | 0.737816 | + | 0.675002i | \(0.235857\pi\) | ||||
−0.737816 | + | 0.675002i | \(0.764143\pi\) | |||||||
\(180\) | 1.99671 | + | 1.00656i | 0.148826 | + | 0.0750245i | ||||
\(181\) | − | 21.7257i | − | 1.61486i | −0.589965 | − | 0.807429i | \(-0.700858\pi\) | ||
0.589965 | − | 0.807429i | \(-0.299142\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.87686 | + | 8.87686i | −0.656196 | + | 0.656196i | ||||
\(184\) | 5.26581i | 0.388201i | ||||||||
\(185\) | 2.51577 | + | 7.63069i | 0.184963 | + | 0.561020i | ||||
\(186\) | 9.22503 | 0.676412 | ||||||||
\(187\) | −11.7079 | + | 11.7079i | −0.856164 | + | 0.856164i | ||||
\(188\) | −2.88813 | − | 2.88813i | −0.210639 | − | 0.210639i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.06444 | + | 15.3612i | 0.367413 | + | 1.11442i | ||||
\(191\) | 16.5825 | 1.19986 | 0.599932 | − | 0.800051i | \(-0.295194\pi\) | ||||
0.599932 | + | 0.800051i | \(0.295194\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −1.49728 | + | 1.49728i | −0.107777 | + | 0.107777i | −0.758939 | − | 0.651162i | \(-0.774282\pi\) |
0.651162 | + | 0.758939i | \(0.274282\pi\) | |||||||
\(194\) | 3.81022 | 0.273558 | ||||||||
\(195\) | −4.85142 | + | 9.62375i | −0.347418 | + | 0.689171i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.22531 | − | 1.22531i | −0.0872995 | − | 0.0872995i | 0.662108 | − | 0.749408i | \(-0.269662\pi\) |
−0.749408 | + | 0.662108i | \(0.769662\pi\) | |||||||
\(198\) | −2.19755 | + | 2.19755i | −0.156173 | + | 0.156173i | ||||
\(199\) | 7.87801 | 0.558458 | 0.279229 | − | 0.960225i | \(-0.409921\pi\) | ||||
0.279229 | + | 0.960225i | \(0.409921\pi\) | |||||||
\(200\) | 4.94500 | + | 0.739583i | 0.349664 | + | 0.0522964i | ||||
\(201\) | 6.66287i | 0.469963i | ||||||||
\(202\) | −5.55958 | + | 5.55958i | −0.391171 | + | 0.391171i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 5.32769i | − | 0.373013i | ||||||
\(205\) | 2.53503 | − | 5.02873i | 0.177054 | − | 0.351222i | ||||
\(206\) | 11.8311i | 0.824313i | ||||||||
\(207\) | −3.72349 | − | 3.72349i | −0.258800 | − | 0.258800i | ||||
\(208\) | −3.40812 | − | 3.40812i | −0.236311 | − | 0.236311i | ||||
\(209\) | −22.4802 | −1.55499 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9995 | −1.10145 | −0.550724 | − | 0.834687i | \(-0.685648\pi\) | ||||
−0.550724 | + | 0.834687i | \(0.685648\pi\) | |||||||
\(212\) | 2.43203 | + | 2.43203i | 0.167033 | + | 0.167033i | ||||
\(213\) | −6.52474 | − | 6.52474i | −0.447068 | − | 0.447068i | ||||
\(214\) | 2.16226i | 0.147809i | ||||||||
\(215\) | 11.6181 | − | 3.83037i | 0.792347 | − | 0.261229i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.399905 | − | 0.399905i | 0.0270850 | − | 0.0270850i | ||||
\(219\) | − | 8.23213i | − | 0.556276i | ||||||
\(220\) | −3.12819 | + | 6.20538i | −0.210902 | + | 0.418366i | ||||
\(221\) | 25.6785 | 1.72732 | ||||||||
\(222\) | 2.54080 | − | 2.54080i | 0.170527 | − | 0.170527i | ||||
\(223\) | 1.20707 | + | 1.20707i | 0.0808314 | + | 0.0808314i | 0.746367 | − | 0.665535i | \(-0.231797\pi\) |
−0.665535 | + | 0.746367i | \(0.731797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.01961 | + | 2.97368i | −0.267974 | + | 0.198245i | ||||
\(226\) | −14.1171 | −0.939057 | ||||||||
\(227\) | −4.81749 | + | 4.81749i | −0.319748 | + | 0.319748i | −0.848670 | − | 0.528922i | \(-0.822596\pi\) |
0.528922 | + | 0.848670i | \(0.322596\pi\) | |||||||
\(228\) | 5.11483 | − | 5.11483i | 0.338738 | − | 0.338738i | ||||
\(229\) | 19.8143 | 1.30936 | 0.654682 | − | 0.755904i | \(-0.272802\pi\) | ||||
0.654682 | + | 0.755904i | \(0.272802\pi\) | |||||||
\(230\) | −10.5143 | − | 5.30035i | −0.693291 | − | 0.349495i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.17745 | − | 3.17745i | −0.208610 | − | 0.208610i | ||||
\(233\) | 12.7261 | − | 12.7261i | 0.833714 | − | 0.833714i | −0.154309 | − | 0.988023i | \(-0.549315\pi\) |
0.988023 | + | 0.154309i | \(0.0493150\pi\) | |||||||
\(234\) | 4.81981 | 0.315081 | ||||||||
\(235\) | 8.67383 | − | 2.85968i | 0.565818 | − | 0.186545i | ||||
\(236\) | − | 1.33238i | − | 0.0867303i | ||||||
\(237\) | −1.35366 | + | 1.35366i | −0.0879296 | + | 0.0879296i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.6409i | − | 1.72325i | −0.507542 | − | 0.861627i | \(-0.669446\pi\) | ||
0.507542 | − | 0.861627i | \(-0.330554\pi\) | |||||||
\(240\) | −0.700141 | − | 2.12363i | −0.0451939 | − | 0.137080i | ||||
\(241\) | − | 14.4248i | − | 0.929185i | −0.885525 | − | 0.464592i | \(-0.846201\pi\) | ||
0.885525 | − | 0.464592i | \(-0.153799\pi\) | |||||||
\(242\) | 0.948618 | + | 0.948618i | 0.0609795 | + | 0.0609795i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 12.5538 | 0.803673 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.51851 | −0.160575 | ||||||||
\(247\) | 24.6525 | + | 24.6525i | 1.56860 | + | 1.56860i | ||||
\(248\) | −6.52308 | − | 6.52308i | −0.414216 | − | 0.414216i | ||||
\(249\) | 12.6890i | 0.804135i | ||||||||
\(250\) | −6.45416 | + | 9.12928i | −0.408197 | + | 0.577386i | ||||
\(251\) | − | 26.4573i | − | 1.66997i | −0.550271 | − | 0.834986i | \(-0.685476\pi\) | ||
0.550271 | − | 0.834986i | \(-0.314524\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.5719 | − | 11.5719i | 0.727518 | − | 0.727518i | ||||
\(254\) | 3.03397i | 0.190368i | ||||||||
\(255\) | 10.6378 | + | 5.36264i | 0.666167 | + | 0.335821i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.93021 | + | 7.93021i | −0.494673 | + | 0.494673i | −0.909775 | − | 0.415102i | \(-0.863746\pi\) |
0.415102 | + | 0.909775i | \(0.363746\pi\) | |||||||
\(258\) | −3.86848 | − | 3.86848i | −0.240841 | − | 0.240841i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 10.2355 | − | 3.37454i | 0.634778 | − | 0.209280i | ||||
\(261\) | 4.49359 | 0.278146 | ||||||||
\(262\) | −6.20372 | + | 6.20372i | −0.383267 | + | 0.383267i | ||||
\(263\) | −4.85012 | + | 4.85012i | −0.299071 | + | 0.299071i | −0.840650 | − | 0.541579i | \(-0.817827\pi\) |
0.541579 | + | 0.840650i | \(0.317827\pi\) | |||||||
\(264\) | 3.10780 | 0.191272 | ||||||||
\(265\) | −7.30405 | + | 2.40807i | −0.448684 | + | 0.147927i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.88043 | + | 2.88043i | 0.176279 | + | 0.176279i | ||||
\(268\) | 4.71136 | − | 4.71136i | 0.287792 | − | 0.287792i | ||||
\(269\) | 8.98064 | 0.547559 | 0.273780 | − | 0.961792i | \(-0.411726\pi\) | ||||
0.273780 | + | 0.961792i | \(0.411726\pi\) | |||||||
\(270\) | 1.99671 | + | 1.00656i | 0.121516 | + | 0.0612572i | ||||
\(271\) | − | 8.97179i | − | 0.544998i | −0.962156 | − | 0.272499i | \(-0.912150\pi\) | ||
0.962156 | − | 0.272499i | \(-0.0878501\pi\) | |||||||
\(272\) | −3.76725 | + | 3.76725i | −0.228423 | + | 0.228423i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.6052i | 0.821918i | ||||||||
\(275\) | −9.24161 | − | 12.4922i | −0.557290 | − | 0.753305i | ||||
\(276\) | 5.26581i | 0.316965i | ||||||||
\(277\) | −17.4734 | − | 17.4734i | −1.04988 | − | 1.04988i | −0.998689 | − | 0.0511860i | \(-0.983700\pi\) |
−0.0511860 | − | 0.998689i | \(-0.516300\pi\) | |||||||
\(278\) | −7.71769 | − | 7.71769i | −0.462876 | − | 0.462876i | ||||
\(279\) | 9.22503 | 0.552288 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.4916 | 1.10312 | 0.551558 | − | 0.834137i | \(-0.314034\pi\) | ||||
0.551558 | + | 0.834137i | \(0.314034\pi\) | |||||||
\(282\) | −2.88813 | − | 2.88813i | −0.171986 | − | 0.171986i | ||||
\(283\) | 3.93983 | + | 3.93983i | 0.234198 | + | 0.234198i | 0.814443 | − | 0.580244i | \(-0.197043\pi\) |
−0.580244 | + | 0.814443i | \(0.697043\pi\) | |||||||
\(284\) | 9.22738i | 0.547544i | ||||||||
\(285\) | 5.06444 | + | 15.3612i | 0.299992 | + | 0.909919i | ||||
\(286\) | 14.9790i | 0.885729i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 11.3843i | − | 0.669665i | ||||||
\(290\) | 9.54272 | − | 3.14614i | 0.560368 | − | 0.184748i | ||||
\(291\) | 3.81022 | 0.223359 | ||||||||
\(292\) | −5.82099 | + | 5.82099i | −0.340648 | + | 0.340648i | ||||
\(293\) | 17.6465 | + | 17.6465i | 1.03092 | + | 1.03092i | 0.999507 | + | 0.0314115i | \(0.0100002\pi\) |
0.0314115 | + | 0.999507i | \(0.490000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.66037 | + | 1.34112i | 0.154892 | + | 0.0780828i | ||||
\(296\) | −3.59323 | −0.208852 | ||||||||
\(297\) | −2.19755 | + | 2.19755i | −0.127515 | + | 0.127515i | ||||
\(298\) | −1.47800 | + | 1.47800i | −0.0856183 | + | 0.0856183i | ||||
\(299\) | −25.3802 | −1.46778 | ||||||||
\(300\) | 4.94500 | + | 0.739583i | 0.285500 | + | 0.0426998i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.85838 | − | 2.85838i | −0.164481 | − | 0.164481i | ||||
\(303\) | −5.55958 | + | 5.55958i | −0.319390 | + | 0.319390i | ||||
\(304\) | −7.23346 | −0.414867 | ||||||||
\(305\) | −12.6361 | + | 25.0662i | −0.723542 | + | 1.43529i | ||||
\(306\) | − | 5.32769i | − | 0.304564i | ||||||
\(307\) | 11.4807 | − | 11.4807i | 0.655239 | − | 0.655239i | −0.299011 | − | 0.954250i | \(-0.596657\pi\) |
0.954250 | + | 0.299011i | \(0.0966566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.8311i | 0.673049i | ||||||||
\(310\) | 19.5906 | − | 6.45882i | 1.11267 | − | 0.366836i | ||||
\(311\) | − | 13.1349i | − | 0.744809i | −0.928070 | − | 0.372405i | \(-0.878533\pi\) | ||
0.928070 | − | 0.372405i | \(-0.121467\pi\) | |||||||
\(312\) | −3.40812 | − | 3.40812i | −0.192947 | − | 0.192947i | ||||
\(313\) | 17.9946 | + | 17.9946i | 1.01711 | + | 1.01711i | 0.999851 | + | 0.0172640i | \(0.00549556\pi\) |
0.0172640 | + | 0.999851i | \(0.494504\pi\) | |||||||
\(314\) | 0.905573 | 0.0511044 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.91436 | 0.107691 | ||||||||
\(317\) | 13.4535 | + | 13.4535i | 0.755626 | + | 0.755626i | 0.975523 | − | 0.219897i | \(-0.0705722\pi\) |
−0.219897 | + | 0.975523i | \(0.570572\pi\) | |||||||
\(318\) | 2.43203 | + | 2.43203i | 0.136382 | + | 0.136382i | ||||
\(319\) | 13.9652i | 0.781901i | ||||||||
\(320\) | −1.00656 | + | 1.99671i | −0.0562684 | + | 0.111619i | ||||
\(321\) | 2.16226i | 0.120686i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.2502 | − | 27.2502i | 1.51624 | − | 1.51624i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −3.56465 | + | 23.8340i | −0.197731 | + | 1.32207i | ||||
\(326\) | 7.38217 | 0.408860 | ||||||||
\(327\) | 0.399905 | − | 0.399905i | 0.0221148 | − | 0.0221148i | ||||
\(328\) | 1.78086 | + | 1.78086i | 0.0983314 | + | 0.0983314i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.12819 | + | 6.20538i | −0.172201 | + | 0.341595i | ||||
\(331\) | −20.9381 | −1.15086 | −0.575430 | − | 0.817851i | \(-0.695165\pi\) | ||||
−0.575430 | + | 0.817851i | \(0.695165\pi\) | |||||||
\(332\) | 8.97250 | − | 8.97250i | 0.492430 | − | 0.492430i | ||||
\(333\) | 2.54080 | − | 2.54080i | 0.139235 | − | 0.139235i | ||||
\(334\) | −0.863584 | −0.0472532 | ||||||||
\(335\) | 4.66495 | + | 14.1495i | 0.254873 | + | 0.773068i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.272770 | + | 0.272770i | 0.0148587 | + | 0.0148587i | 0.714497 | − | 0.699638i | \(-0.246656\pi\) |
−0.699638 | + | 0.714497i | \(0.746656\pi\) | |||||||
\(338\) | 7.23411 | − | 7.23411i | 0.393484 | − | 0.393484i | ||||
\(339\) | −14.1171 | −0.766737 | ||||||||
\(340\) | −3.73013 | − | 11.3140i | −0.202295 | − | 0.613590i | ||||
\(341\) | 28.6696i | 1.55255i | ||||||||
\(342\) | 5.11483 | − | 5.11483i | 0.276578 | − | 0.276578i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.47086i | 0.294969i | ||||||||
\(345\) | −10.5143 | − | 5.30035i | −0.566070 | − | 0.285361i | ||||
\(346\) | − | 3.49748i | − | 0.188026i | ||||||
\(347\) | −10.6964 | − | 10.6964i | −0.574214 | − | 0.574214i | 0.359089 | − | 0.933303i | \(-0.383087\pi\) |
−0.933303 | + | 0.359089i | \(0.883087\pi\) | |||||||
\(348\) | −3.17745 | − | 3.17745i | −0.170329 | − | 0.170329i | ||||
\(349\) | −15.2733 | −0.817563 | −0.408781 | − | 0.912632i | \(-0.634046\pi\) | ||||
−0.408781 | + | 0.912632i | \(0.634046\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.81981 | 0.257262 | ||||||||
\(352\) | −2.19755 | − | 2.19755i | −0.117130 | − | 0.117130i | ||||
\(353\) | 21.2321 | + | 21.2321i | 1.13007 | + | 1.13007i | 0.990165 | + | 0.139903i | \(0.0446790\pi\) |
0.139903 | + | 0.990165i | \(0.455321\pi\) | |||||||
\(354\) | − | 1.33238i | − | 0.0708150i | ||||||
\(355\) | −18.4244 | − | 9.28790i | −0.977864 | − | 0.492950i | ||||
\(356\) | − | 4.07354i | − | 0.215897i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7716 | − | 12.7716i | 0.675002 | − | 0.675002i | ||||
\(359\) | 11.7244i | 0.618792i | 0.950933 | + | 0.309396i | \(0.100127\pi\) | ||||
−0.950933 | + | 0.309396i | \(0.899873\pi\) | |||||||
\(360\) | −0.700141 | − | 2.12363i | −0.0369006 | − | 0.111925i | ||||
\(361\) | 33.3230 | 1.75384 | ||||||||
\(362\) | −15.3624 | + | 15.3624i | −0.807429 | + | 0.807429i | ||||
\(363\) | 0.948618 | + | 0.948618i | 0.0497895 | + | 0.0497895i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.76365 | − | 17.4820i | −0.301683 | − | 0.915049i | ||||
\(366\) | 12.5538 | 0.656196 | ||||||||
\(367\) | −21.4951 | + | 21.4951i | −1.12204 | + | 1.12204i | −0.130600 | + | 0.991435i | \(0.541690\pi\) |
−0.991435 | + | 0.130600i | \(0.958310\pi\) | |||||||
\(368\) | 3.72349 | − | 3.72349i | 0.194100 | − | 0.194100i | ||||
\(369\) | −2.51851 | −0.131109 | ||||||||
\(370\) | 3.61680 | − | 7.17463i | 0.188028 | − | 0.372991i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.52308 | − | 6.52308i | −0.338206 | − | 0.338206i | ||||
\(373\) | 21.3303 | − | 21.3303i | 1.10444 | − | 1.10444i | 0.110572 | − | 0.993868i | \(-0.464732\pi\) |
0.993868 | − | 0.110572i | \(-0.0352681\pi\) | |||||||
\(374\) | 16.5574 | 0.856164 | ||||||||
\(375\) | −6.45416 | + | 9.12928i | −0.333292 | + | 0.471434i | ||||
\(376\) | 4.08444i | 0.210639i | ||||||||
\(377\) | 15.3147 | − | 15.3147i | 0.788746 | − | 0.788746i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.44115i | − | 0.228127i | −0.993473 | − | 0.114063i | \(-0.963613\pi\) | ||
0.993473 | − | 0.114063i | \(-0.0363867\pi\) | |||||||
\(380\) | 7.28091 | − | 14.4431i | 0.373503 | − | 0.740916i | ||||
\(381\) | 3.03397i | 0.155435i | ||||||||
\(382\) | −11.7256 | − | 11.7256i | −0.599932 | − | 0.599932i | ||||
\(383\) | 15.7414 | + | 15.7414i | 0.804350 | + | 0.804350i | 0.983772 | − | 0.179422i | \(-0.0574227\pi\) |
−0.179422 | + | 0.983772i | \(0.557423\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.11748 | 0.107777 | ||||||||
\(387\) | −3.86848 | − | 3.86848i | −0.196646 | − | 0.196646i | ||||
\(388\) | −2.69423 | − | 2.69423i | −0.136779 | − | 0.136779i | ||||
\(389\) | − | 12.6880i | − | 0.643307i | −0.946857 | − | 0.321653i | \(-0.895761\pi\) | ||
0.946857 | − | 0.321653i | \(-0.104239\pi\) | |||||||
\(390\) | 10.2355 | − | 3.37454i | 0.518294 | − | 0.170877i | ||||
\(391\) | 28.0546i | 1.41878i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.20372 | + | 6.20372i | −0.312936 | + | 0.312936i | ||||
\(394\) | 1.73285i | 0.0872995i | ||||||||
\(395\) | −1.92692 | + | 3.82242i | −0.0969538 | + | 0.192327i | ||||
\(396\) | 3.10780 | 0.156173 | ||||||||
\(397\) | 15.3969 | − | 15.3969i | 0.772748 | − | 0.772748i | −0.205838 | − | 0.978586i | \(-0.565992\pi\) |
0.978586 | + | 0.205838i | \(0.0659920\pi\) | |||||||
\(398\) | −5.57060 | − | 5.57060i | −0.279229 | − | 0.279229i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.97368 | − | 4.01961i | −0.148684 | − | 0.200980i | ||||
\(401\) | 26.3077 | 1.31374 | 0.656872 | − | 0.754002i | \(-0.271879\pi\) | ||||
0.656872 | + | 0.754002i | \(0.271879\pi\) | |||||||
\(402\) | 4.71136 | − | 4.71136i | 0.234981 | − | 0.234981i | ||||
\(403\) | 31.4400 | − | 31.4400i | 1.56614 | − | 1.56614i | ||||
\(404\) | 7.86244 | 0.391171 | ||||||||
\(405\) | 1.99671 | + | 1.00656i | 0.0992172 | + | 0.0500163i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.89630 | + | 7.89630i | 0.391405 | + | 0.391405i | ||||
\(408\) | −3.76725 | + | 3.76725i | −0.186507 | + | 0.186507i | ||||
\(409\) | −2.34651 | −0.116027 | −0.0580137 | − | 0.998316i | \(-0.518477\pi\) | ||||
−0.0580137 | + | 0.998316i | \(0.518477\pi\) | |||||||
\(410\) | −5.34839 | + | 1.76331i | −0.264138 | + | 0.0870838i | ||||
\(411\) | 13.6052i | 0.671093i | ||||||||
\(412\) | 8.36587 | − | 8.36587i | 0.412157 | − | 0.412157i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.26581i | 0.258800i | ||||||||
\(415\) | 8.88411 | + | 26.9468i | 0.436104 | + | 1.32277i | ||||
\(416\) | 4.81981i | 0.236311i | ||||||||
\(417\) | −7.71769 | − | 7.71769i | −0.377937 | − | 0.377937i | ||||
\(418\) | 15.8959 | + | 15.8959i | 0.777494 | + | 0.777494i | ||||
\(419\) | 1.03087 | 0.0503614 | 0.0251807 | − | 0.999683i | \(-0.491984\pi\) | ||||
0.0251807 | + | 0.999683i | \(0.491984\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.6945 | 1.39849 | 0.699243 | − | 0.714884i | \(-0.253521\pi\) | ||||
0.699243 | + | 0.714884i | \(0.253521\pi\) | |||||||
\(422\) | 11.3133 | + | 11.3133i | 0.550724 | + | 0.550724i | ||||
\(423\) | −2.88813 | − | 2.88813i | −0.140426 | − | 0.140426i | ||||
\(424\) | − | 3.43942i | − | 0.167033i | ||||||
\(425\) | 26.3454 | + | 3.94027i | 1.27794 | + | 0.191131i | ||||
\(426\) | 9.22738i | 0.447068i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.52895 | − | 1.52895i | 0.0739047 | − | 0.0739047i | ||||
\(429\) | 14.9790i | 0.723194i | ||||||||
\(430\) | −10.9237 | − | 5.50674i | −0.526788 | − | 0.265559i | ||||
\(431\) | −24.2775 | −1.16941 | −0.584704 | − | 0.811247i | \(-0.698789\pi\) | ||||
−0.584704 | + | 0.811247i | \(0.698789\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −19.1704 | − | 19.1704i | −0.921271 | − | 0.921271i | 0.0758481 | − | 0.997119i | \(-0.475834\pi\) |
−0.997119 | + | 0.0758481i | \(0.975834\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.54272 | − | 3.14614i | 0.457538 | − | 0.150846i | ||||
\(436\) | −0.565551 | −0.0270850 | ||||||||
\(437\) | −26.9337 | + | 26.9337i | −1.28841 | + | 1.28841i | ||||
\(438\) | −5.82099 | + | 5.82099i | −0.278138 | + | 0.278138i | ||||
\(439\) | −14.5989 | −0.696769 | −0.348385 | − | 0.937352i | \(-0.613270\pi\) | ||||
−0.348385 | + | 0.937352i | \(0.613270\pi\) | |||||||
\(440\) | 6.59983 | − | 2.17590i | 0.314634 | − | 0.103732i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.1574 | − | 18.1574i | −0.863660 | − | 0.863660i | ||||
\(443\) | −16.0790 | + | 16.0790i | −0.763938 | + | 0.763938i | −0.977032 | − | 0.213094i | \(-0.931646\pi\) |
0.213094 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(444\) | −3.59323 | −0.170527 | ||||||||
\(445\) | 8.13367 | + | 4.10026i | 0.385573 | + | 0.194371i | ||||
\(446\) | − | 1.70706i | − | 0.0808314i | ||||||
\(447\) | −1.47800 | + | 1.47800i | −0.0699071 | + | 0.0699071i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 41.8564i | 1.97532i | 0.156600 | + | 0.987662i | \(0.449947\pi\) | ||||
−0.156600 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(450\) | 4.94500 | + | 0.739583i | 0.233109 | + | 0.0348643i | ||||
\(451\) | − | 7.82705i | − | 0.368561i | ||||||
\(452\) | 9.98231 | + | 9.98231i | 0.469528 | + | 0.469528i | ||||
\(453\) | −2.85838 | − | 2.85838i | −0.134298 | − | 0.134298i | ||||
\(454\) | 6.81296 | 0.319748 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.23346 | −0.338738 | ||||||||
\(457\) | 18.7798 | + | 18.7798i | 0.878480 | + | 0.878480i | 0.993377 | − | 0.114897i | \(-0.0366539\pi\) |
−0.114897 | + | 0.993377i | \(0.536654\pi\) | |||||||
\(458\) | −14.0108 | − | 14.0108i | −0.654682 | − | 0.654682i | ||||
\(459\) | − | 5.32769i | − | 0.248675i | ||||||
\(460\) | 3.68681 | + | 11.1826i | 0.171898 | + | 0.521393i | ||||
\(461\) | − | 16.5608i | − | 0.771313i | −0.922642 | − | 0.385656i | \(-0.873975\pi\) | ||
0.922642 | − | 0.385656i | \(-0.126025\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.0305 | + | 19.0305i | −0.884424 | + | 0.884424i | −0.993981 | − | 0.109557i | \(-0.965057\pi\) |
0.109557 | + | 0.993981i | \(0.465057\pi\) | |||||||
\(464\) | 4.49359i | 0.208610i | ||||||||
\(465\) | 19.5906 | − | 6.45882i | 0.908490 | − | 0.299521i | ||||
\(466\) | −17.9974 | −0.833714 | ||||||||
\(467\) | −9.62124 | + | 9.62124i | −0.445218 | + | 0.445218i | −0.893761 | − | 0.448543i | \(-0.851943\pi\) |
0.448543 | + | 0.893761i | \(0.351943\pi\) | |||||||
\(468\) | −3.40812 | − | 3.40812i | −0.157540 | − | 0.157540i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.15542 | − | 4.11123i | −0.376182 | − | 0.189637i | ||||
\(471\) | 0.905573 | 0.0417266 | ||||||||
\(472\) | −0.942132 | + | 0.942132i | −0.0433652 | + | 0.0433652i | ||||
\(473\) | 12.0225 | − | 12.0225i | 0.552795 | − | 0.552795i | ||||
\(474\) | 1.91436 | 0.0879296 | ||||||||
\(475\) | 21.5100 | + | 29.0757i | 0.986946 | + | 1.33408i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.43203 | + | 2.43203i | 0.111355 | + | 0.111355i | ||||
\(478\) | −18.8379 | + | 18.8379i | −0.861627 | + | 0.861627i | ||||
\(479\) | −1.32529 | −0.0605539 | −0.0302769 | − | 0.999542i | \(-0.509639\pi\) | ||||
−0.0302769 | + | 0.999542i | \(0.509639\pi\) | |||||||
\(480\) | −1.00656 | + | 1.99671i | −0.0459429 | + | 0.0911368i | ||||
\(481\) | − | 17.3187i | − | 0.789664i | ||||||
\(482\) | −10.1999 | + | 10.1999i | −0.464592 | + | 0.464592i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 1.34155i | − | 0.0609795i | ||||||
\(485\) | 8.09149 | − | 2.66769i | 0.367416 | − | 0.121133i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 22.6570 | + | 22.6570i | 1.02669 | + | 1.02669i | 0.999634 | + | 0.0270532i | \(0.00861234\pi\) |
0.0270532 | + | 0.999634i | \(0.491388\pi\) | |||||||
\(488\) | −8.87686 | − | 8.87686i | −0.401837 | − | 0.401837i | ||||
\(489\) | 7.38217 | 0.333833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3460 | −1.00846 | −0.504231 | − | 0.863569i | \(-0.668224\pi\) | ||||
−0.504231 | + | 0.863569i | \(0.668224\pi\) | |||||||
\(492\) | 1.78086 | + | 1.78086i | 0.0802873 | + | 0.0802873i | ||||
\(493\) | −16.9285 | − | 16.9285i | −0.762419 | − | 0.762419i | ||||
\(494\) | − | 34.8639i | − | 1.56860i | ||||||
\(495\) | −3.12819 | + | 6.20538i | −0.140602 | + | 0.278911i | ||||
\(496\) | 9.22503i | 0.414216i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 8.97250 | − | 8.97250i | 0.402067 | − | 0.402067i | ||||
\(499\) | − | 10.8523i | − | 0.485817i | −0.970049 | − | 0.242908i | \(-0.921899\pi\) | ||
0.970049 | − | 0.242908i | \(-0.0781014\pi\) | |||||||
\(500\) | 11.0192 | − | 1.89159i | 0.492792 | − | 0.0845947i | ||||
\(501\) | −0.863584 | −0.0385821 | ||||||||
\(502\) | −18.7082 | + | 18.7082i | −0.834986 | + | 0.834986i | ||||
\(503\) | −2.64043 | − | 2.64043i | −0.117731 | − | 0.117731i | 0.645787 | − | 0.763518i | \(-0.276529\pi\) |
−0.763518 | + | 0.645787i | \(0.776529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.91401 | + | 15.6990i | −0.352169 | + | 0.698596i | ||||
\(506\) | −16.3651 | −0.727518 | ||||||||
\(507\) | 7.23411 | − | 7.23411i | 0.321278 | − | 0.321278i | ||||
\(508\) | 2.14534 | − | 2.14534i | 0.0951842 | − | 0.0951842i | ||||
\(509\) | 17.4093 | 0.771653 | 0.385827 | − | 0.922571i | \(-0.373916\pi\) | ||||
0.385827 | + | 0.922571i | \(0.373916\pi\) | |||||||
\(510\) | −3.73013 | − | 11.3140i | −0.165173 | − | 0.500994i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 5.11483 | − | 5.11483i | 0.225825 | − | 0.225825i | ||||
\(514\) | 11.2150 | 0.494673 | ||||||||
\(515\) | 8.28345 | + | 25.1249i | 0.365012 | + | 1.10714i | ||||
\(516\) | 5.47086i | 0.240841i | ||||||||
\(517\) | 8.97575 | − | 8.97575i | 0.394753 | − | 0.394753i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.49748i | − | 0.153522i | ||||||
\(520\) | −9.62375 | − | 4.85142i | −0.422029 | − | 0.212749i | ||||
\(521\) | 7.09577i | 0.310871i | 0.987846 | + | 0.155436i | \(0.0496781\pi\) | ||||
−0.987846 | + | 0.155436i | \(0.950322\pi\) | |||||||
\(522\) | −3.17745 | − | 3.17745i | −0.139073 | − | 0.139073i | ||||
\(523\) | −2.49227 | − | 2.49227i | −0.108979 | − | 0.108979i | 0.650515 | − | 0.759494i | \(-0.274553\pi\) |
−0.759494 | + | 0.650515i | \(0.774553\pi\) | |||||||
\(524\) | 8.77339 | 0.383267 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.85911 | 0.299071 | ||||||||
\(527\) | −34.7530 | − | 34.7530i | −1.51386 | − | 1.51386i | ||||
\(528\) | −2.19755 | − | 2.19755i | −0.0956361 | − | 0.0956361i | ||||
\(529\) | − | 4.72876i | − | 0.205598i | ||||||
\(530\) | 6.86751 | + | 3.46198i | 0.298305 | + | 0.150379i | ||||
\(531\) | − | 1.33238i | − | 0.0578202i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −8.58340 | + | 8.58340i | −0.371788 | + | 0.371788i | ||||
\(534\) | − | 4.07354i | − | 0.176279i | ||||||
\(535\) | 1.51389 | + | 4.59185i | 0.0654511 | + | 0.198523i | ||||
\(536\) | −6.66287 | −0.287792 | ||||||||
\(537\) | 12.7716 | − | 12.7716i | 0.551137 | − | 0.551137i | ||||
\(538\) | −6.35027 | − | 6.35027i | −0.273780 | − | 0.273780i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.700141 | − | 2.12363i | −0.0301293 | − | 0.0913865i | ||||
\(541\) | 20.3951 | 0.876853 | 0.438426 | − | 0.898767i | \(-0.355536\pi\) | ||||
0.438426 | + | 0.898767i | \(0.355536\pi\) | |||||||
\(542\) | −6.34402 | + | 6.34402i | −0.272499 | + | 0.272499i | ||||
\(543\) | −15.3624 | + | 15.3624i | −0.659263 | + | 0.659263i | ||||
\(544\) | 5.32769 | 0.228423 | ||||||||
\(545\) | 0.569261 | − | 1.12924i | 0.0243845 | − | 0.0483713i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.79499 | − | 8.79499i | −0.376047 | − | 0.376047i | 0.493627 | − | 0.869674i | \(-0.335671\pi\) |
−0.869674 | + | 0.493627i | \(0.835671\pi\) | |||||||
\(548\) | 9.62030 | − | 9.62030i | 0.410959 | − | 0.410959i | ||||
\(549\) | 12.5538 | 0.535782 | ||||||||
\(550\) | −2.29848 | + | 15.3681i | −0.0980075 | + | 0.655298i | ||||
\(551\) | − | 32.5042i | − | 1.38473i | ||||||
\(552\) | 3.72349 | − | 3.72349i | 0.158482 | − | 0.158482i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.7111i | 1.04988i | ||||||||
\(555\) | 3.61680 | − | 7.17463i | 0.153525 | − | 0.304546i | ||||
\(556\) | 10.9145i | 0.462876i | ||||||||
\(557\) | −12.7022 | − | 12.7022i | −0.538210 | − | 0.538210i | 0.384793 | − | 0.923003i | \(-0.374273\pi\) |
−0.923003 | + | 0.384793i | \(0.874273\pi\) | |||||||
\(558\) | −6.52308 | − | 6.52308i | −0.276144 | − | 0.276144i | ||||
\(559\) | −26.3685 | −1.11527 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.5574 | 0.699055 | ||||||||
\(562\) | −13.0755 | − | 13.0755i | −0.551558 | − | 0.551558i | ||||
\(563\) | −30.7771 | − | 30.7771i | −1.29710 | − | 1.29710i | −0.930300 | − | 0.366799i | \(-0.880454\pi\) |
−0.366799 | − | 0.930300i | \(-0.619546\pi\) | |||||||
\(564\) | 4.08444i | 0.171986i | ||||||||
\(565\) | −29.9795 | + | 9.88397i | −1.26125 | + | 0.415822i | ||||
\(566\) | − | 5.57176i | − | 0.234198i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.52474 | − | 6.52474i | 0.273772 | − | 0.273772i | ||||
\(569\) | − | 18.1826i | − | 0.762255i | −0.924522 | − | 0.381128i | \(-0.875536\pi\) | ||
0.924522 | − | 0.381128i | \(-0.124464\pi\) | |||||||
\(570\) | 7.28091 | − | 14.4431i | 0.304964 | − | 0.604955i | ||||
\(571\) | −27.3134 | −1.14303 | −0.571516 | − | 0.820591i | \(-0.693644\pi\) | ||||
−0.571516 | + | 0.820591i | \(0.693644\pi\) | |||||||
\(572\) | 10.5918 | − | 10.5918i | 0.442864 | − | 0.442864i | ||||
\(573\) | −11.7256 | − | 11.7256i | −0.489843 | − | 0.489843i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −26.0394 | − | 3.89450i | −1.08592 | − | 0.162412i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −17.5022 | + | 17.5022i | −0.728625 | + | 0.728625i | −0.970346 | − | 0.241721i | \(-0.922288\pi\) |
0.241721 | + | 0.970346i | \(0.422288\pi\) | |||||||
\(578\) | −8.04992 | + | 8.04992i | −0.334832 | + | 0.334832i | ||||
\(579\) | 2.11748 | 0.0879995 | ||||||||
\(580\) | −8.97238 | − | 4.52306i | −0.372558 | − | 0.187810i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.69423 | − | 2.69423i | −0.111679 | − | 0.111679i | ||||
\(583\) | −7.55829 | + | 7.55829i | −0.313032 | + | 0.313032i | ||||
\(584\) | 8.23213 | 0.340648 | ||||||||
\(585\) | 10.2355 | − | 3.37454i | 0.423186 | − | 0.139520i | ||||
\(586\) | − | 24.9559i | − | 1.03092i | ||||||
\(587\) | −25.7187 | + | 25.7187i | −1.06153 | + | 1.06153i | −0.0635463 | + | 0.997979i | \(0.520241\pi\) |
−0.997979 | + | 0.0635463i | \(0.979759\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 66.7289i | − | 2.74952i | ||||||
\(590\) | −0.932851 | − | 2.82947i | −0.0384049 | − | 0.116488i | ||||
\(591\) | 1.73285i | 0.0712798i | ||||||||
\(592\) | 2.54080 | + | 2.54080i | 0.104426 | + | 0.104426i | ||||
\(593\) | −19.5784 | − | 19.5784i | −0.803988 | − | 0.803988i | 0.179728 | − | 0.983716i | \(-0.442478\pi\) |
−0.983716 | + | 0.179728i | \(0.942478\pi\) | |||||||
\(594\) | 3.10780 | 0.127515 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.09021 | 0.0856183 | ||||||||
\(597\) | −5.57060 | − | 5.57060i | −0.227989 | − | 0.227989i | ||||
\(598\) | 17.9465 | + | 17.9465i | 0.733888 | + | 0.733888i | ||||
\(599\) | 21.9587i | 0.897207i | 0.893731 | + | 0.448603i | \(0.148078\pi\) | ||||
−0.893731 | + | 0.448603i | \(0.851922\pi\) | |||||||
\(600\) | −2.97368 | − | 4.01961i | −0.121400 | − | 0.164100i | ||||
\(601\) | 7.04092i | 0.287205i | 0.989635 | + | 0.143603i | \(0.0458687\pi\) | ||||
−0.989635 | + | 0.143603i | \(0.954131\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.71136 | − | 4.71136i | 0.191861 | − | 0.191861i | ||||
\(604\) | 4.04236i | 0.164481i | ||||||||
\(605\) | 2.67868 | + | 1.35035i | 0.108904 | + | 0.0548994i | ||||
\(606\) | 7.86244 | 0.319390 | ||||||||
\(607\) | 16.6691 | − | 16.6691i | 0.676576 | − | 0.676576i | −0.282647 | − | 0.959224i | \(-0.591213\pi\) |
0.959224 | + | 0.282647i | \(0.0912127\pi\) | |||||||
\(608\) | 5.11483 | + | 5.11483i | 0.207434 | + | 0.207434i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 26.6596 | − | 8.78941i | 1.07941 | − | 0.355873i | ||||
\(611\) | −19.6862 | −0.796419 | ||||||||
\(612\) | −3.76725 | + | 3.76725i | −0.152282 | + | 0.152282i | ||||
\(613\) | −9.85213 | + | 9.85213i | −0.397924 | + | 0.397924i | −0.877500 | − | 0.479576i | \(-0.840790\pi\) |
0.479576 | + | 0.877500i | \(0.340790\pi\) | |||||||
\(614\) | −16.2362 | −0.655239 | ||||||||
\(615\) | −5.34839 | + | 1.76331i | −0.215668 | + | 0.0711036i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.68360 | + | 9.68360i | 0.389847 | + | 0.389847i | 0.874633 | − | 0.484786i | \(-0.161102\pi\) |
−0.484786 | + | 0.874633i | \(0.661102\pi\) | |||||||
\(618\) | 8.36587 | − | 8.36587i | 0.336525 | − | 0.336525i | ||||
\(619\) | −12.4190 | −0.499162 | −0.249581 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249581 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(620\) | −18.4197 | − | 9.28554i | −0.739752 | − | 0.372916i | ||||
\(621\) | 5.26581i | 0.211310i | ||||||||
\(622\) | −9.28775 | + | 9.28775i | −0.372405 | + | 0.372405i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.81981i | 0.192947i | ||||||||
\(625\) | −7.31447 | + | 23.9060i | −0.292579 | + | 0.956241i | ||||
\(626\) | − | 25.4482i | − | 1.01711i | ||||||
\(627\) | 15.8959 | + | 15.8959i | 0.634821 | + | 0.634821i | ||||
\(628\) | −0.640337 | − | 0.640337i | −0.0255522 | − | 0.0255522i | ||||
\(629\) | −19.1436 | −0.763306 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.546516 | −0.0217565 | −0.0108782 | − | 0.999941i | \(-0.503463\pi\) | ||||
−0.0108782 | + | 0.999941i | \(0.503463\pi\) | |||||||
\(632\) | −1.35366 | − | 1.35366i | −0.0538457 | − | 0.0538457i | ||||
\(633\) | 11.3133 | + | 11.3133i | 0.449665 | + | 0.449665i | ||||
\(634\) | − | 19.0262i | − | 0.755626i | ||||||
\(635\) | 2.12421 | + | 6.44304i | 0.0842966 | + | 0.255684i | ||||
\(636\) | − | 3.43942i | − | 0.136382i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 9.87488 | − | 9.87488i | 0.390950 | − | 0.390950i | ||||
\(639\) | 9.22738i | 0.365029i | ||||||||
\(640\) | 2.12363 | − | 0.700141i | 0.0839438 | − | 0.0276755i | ||||
\(641\) | 8.75118 | 0.345651 | 0.172825 | − | 0.984952i | \(-0.444710\pi\) | ||||
0.172825 | + | 0.984952i | \(0.444710\pi\) | |||||||
\(642\) | 1.52895 | − | 1.52895i | 0.0603429 | − | 0.0603429i | ||||
\(643\) | −10.2080 | − | 10.2080i | −0.402565 | − | 0.402565i | 0.476571 | − | 0.879136i | \(-0.341879\pi\) |
−0.879136 | + | 0.476571i | \(0.841879\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.9237 | − | 5.50674i | −0.430120 | − | 0.216828i | ||||
\(646\) | −38.5377 | −1.51624 | ||||||||
\(647\) | 16.9715 | − | 16.9715i | 0.667219 | − | 0.667219i | −0.289852 | − | 0.957071i | \(-0.593606\pi\) |
0.957071 | + | 0.289852i | \(0.0936062\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 4.14077 | 0.162539 | ||||||||
\(650\) | 19.3737 | − | 14.3326i | 0.759901 | − | 0.562169i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.21998 | − | 5.21998i | −0.204430 | − | 0.204430i | ||||
\(653\) | −26.5386 | + | 26.5386i | −1.03854 | + | 1.03854i | −0.0393104 | + | 0.999227i | \(0.512516\pi\) |
−0.999227 | + | 0.0393104i | \(0.987484\pi\) | |||||||
\(654\) | −0.565551 | −0.0221148 | ||||||||
\(655\) | −8.83093 | + | 17.5179i | −0.345053 | + | 0.684480i | ||||
\(656\) | − | 2.51851i | − | 0.0983314i | ||||||
\(657\) | −5.82099 | + | 5.82099i | −0.227099 | + | 0.227099i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.4591i | 1.18652i | 0.805011 | + | 0.593259i | \(0.202159\pi\) | ||||
−0.805011 | + | 0.593259i | \(0.797841\pi\) | |||||||
\(660\) | 6.59983 | − | 2.17590i | 0.256898 | − | 0.0846968i | ||||
\(661\) | − | 27.5737i | − | 1.07249i | −0.844062 | − | 0.536246i | \(-0.819842\pi\) | ||
0.844062 | − | 0.536246i | \(-0.180158\pi\) | |||||||
\(662\) | 14.8054 | + | 14.8054i | 0.575430 | + | 0.575430i | ||||
\(663\) | −18.1574 | − | 18.1574i | −0.705176 | − | 0.705176i | ||||
\(664\) | −12.6890 | −0.492430 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.59323 | −0.139235 | ||||||||
\(667\) | 16.7318 | + | 16.7318i | 0.647859 | + | 0.647859i | ||||
\(668\) | 0.610646 | + | 0.610646i | 0.0236266 | + | 0.0236266i | ||||
\(669\) | − | 1.70706i | − | 0.0659986i | ||||||
\(670\) | 6.70657 | − | 13.3038i | 0.259097 | − | 0.513971i | ||||
\(671\) | 39.0147i | 1.50615i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.77420 | + | 8.77420i | −0.338221 | + | 0.338221i | −0.855697 | − | 0.517477i | \(-0.826871\pi\) |
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(674\) | − | 0.385754i | − | 0.0148587i | ||||||
\(675\) | 4.94500 | + | 0.739583i | 0.190333 | + | 0.0284666i | ||||
\(676\) | −10.2306 | −0.393484 | ||||||||
\(677\) | 20.9822 | − | 20.9822i | 0.806412 | − | 0.806412i | −0.177677 | − | 0.984089i | \(-0.556858\pi\) |
0.984089 | + | 0.177677i | \(0.0568583\pi\) | |||||||
\(678\) | 9.98231 | + | 9.98231i | 0.383368 | + | 0.383368i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −5.36264 | + | 10.6378i | −0.205648 | + | 0.407943i | ||||
\(681\) | 6.81296 | 0.261073 | ||||||||
\(682\) | 20.2725 | − | 20.2725i | 0.776273 | − | 0.776273i | ||||
\(683\) | 29.5234 | − | 29.5234i | 1.12968 | − | 1.12968i | 0.139451 | − | 0.990229i | \(-0.455466\pi\) |
0.990229 | − | 0.139451i | \(-0.0445337\pi\) | |||||||
\(684\) | −7.23346 | −0.276578 | ||||||||
\(685\) | 9.52552 | + | 28.8923i | 0.363952 | + | 1.10392i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.0108 | − | 14.0108i | −0.534546 | − | 0.534546i | ||||
\(688\) | 3.86848 | − | 3.86848i | 0.147485 | − | 0.147485i | ||||
\(689\) | 16.5773 | 0.631546 | ||||||||
\(690\) | 3.68681 | + | 11.1826i | 0.140354 | + | 0.425716i | ||||
\(691\) | − | 45.1068i | − | 1.71594i | −0.513697 | − | 0.857972i | \(-0.671724\pi\) | ||
0.513697 | − | 0.857972i | \(-0.328276\pi\) | |||||||
\(692\) | −2.47309 | + | 2.47309i | −0.0940129 | + | 0.0940129i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15.1270i | 0.574214i | ||||||||
\(695\) | −21.7930 | − | 10.9860i | −0.826655 | − | 0.416725i | ||||
\(696\) | 4.49359i | 0.170329i | ||||||||
\(697\) | 9.48786 | + | 9.48786i | 0.359378 | + | 0.359378i | ||||
\(698\) | 10.7999 | + | 10.7999i | 0.408781 | + | 0.408781i | ||||
\(699\) | −17.9974 | −0.680725 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.29359 | −0.0866278 | −0.0433139 | − | 0.999062i | \(-0.513792\pi\) | ||||
−0.0433139 | + | 0.999062i | \(0.513792\pi\) | |||||||
\(702\) | −3.40812 | − | 3.40812i | −0.128631 | − | 0.128631i | ||||
\(703\) | −18.3788 | − | 18.3788i | −0.693168 | − | 0.693168i | ||||
\(704\) | 3.10780i | 0.117130i | ||||||||
\(705\) | −8.15542 | − | 4.11123i | −0.307151 | − | 0.154838i | ||||
\(706\) | − | 30.0267i | − | 1.13007i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.942132 | + | 0.942132i | −0.0354075 | + | 0.0354075i | ||||
\(709\) | − | 48.2598i | − | 1.81243i | −0.422812 | − | 0.906217i | \(-0.638957\pi\) | ||
0.422812 | − | 0.906217i | \(-0.361043\pi\) | |||||||
\(710\) | 6.46046 | + | 19.5955i | 0.242457 | + | 0.735407i | ||||
\(711\) | 1.91436 | 0.0717942 | ||||||||
\(712\) | −2.88043 | + | 2.88043i | −0.107949 | + | 0.107949i | ||||
\(713\) | 34.3493 | + | 34.3493i | 1.28639 | + | 1.28639i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.4874 | + | 31.8099i | 0.392207 | + | 1.18962i | ||||
\(716\) | −18.0618 | −0.675002 | ||||||||
\(717\) | −18.8379 | + | 18.8379i | −0.703516 | + | 0.703516i | ||||
\(718\) | 8.29043 | − | 8.29043i | 0.309396 | − | 0.309396i | ||||
\(719\) | −25.0470 | −0.934096 | −0.467048 | − | 0.884232i | \(-0.654682\pi\) | ||||
−0.467048 | + | 0.884232i | \(0.654682\pi\) | |||||||
\(720\) | −1.00656 | + | 1.99671i | −0.0375122 | + | 0.0744129i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −23.5629 | − | 23.5629i | −0.876920 | − | 0.876920i | ||||
\(723\) | −10.1999 | + | 10.1999i | −0.379338 | + | 0.379338i | ||||
\(724\) | 21.7257 | 0.807429 | ||||||||
\(725\) | 18.0625 | − | 13.3625i | 0.670823 | − | 0.496270i | ||||
\(726\) | − | 1.34155i | − | 0.0497895i | ||||||
\(727\) | 17.1495 | − | 17.1495i | 0.636039 | − | 0.636039i | −0.313537 | − | 0.949576i | \(-0.601514\pi\) |
0.949576 | + | 0.313537i | \(0.101514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −8.28612 | + | 16.4372i | −0.306683 | + | 0.608366i | ||||
\(731\) | 29.1471i | 1.07804i | ||||||||
\(732\) | −8.87686 | − | 8.87686i | −0.328098 | − | 0.328098i | ||||
\(733\) | 5.25687 | + | 5.25687i | 0.194167 | + | 0.194167i | 0.797494 | − | 0.603327i | \(-0.206159\pi\) |
−0.603327 | + | 0.797494i | \(0.706159\pi\) | |||||||
\(734\) | 30.3987 | 1.12204 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.26581 | −0.194100 | ||||||||
\(737\) | 14.6420 | + | 14.6420i | 0.539345 | + | 0.539345i | ||||
\(738\) | 1.78086 | + | 1.78086i | 0.0655543 | + | 0.0655543i | ||||
\(739\) | 8.35457i | 0.307328i | 0.988123 | + | 0.153664i | \(0.0491073\pi\) | ||||
−0.988123 | + | 0.153664i | \(0.950893\pi\) | |||||||
\(740\) | −7.63069 | + | 2.51577i | −0.280510 | + | 0.0924814i | ||||
\(741\) | − | 34.8639i | − | 1.28076i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.5565 | + | 20.5565i | −0.754146 | + | 0.754146i | −0.975250 | − | 0.221104i | \(-0.929034\pi\) |
0.221104 | + | 0.975250i | \(0.429034\pi\) | |||||||
\(744\) | 9.22503i | 0.338206i | ||||||||
\(745\) | −2.10392 | + | 4.17354i | −0.0770816 | + | 0.152907i | ||||
\(746\) | −30.1656 | −1.10444 | ||||||||
\(747\) | 8.97250 | − | 8.97250i | 0.328287 | − | 0.328287i | ||||
\(748\) | −11.7079 | − | 11.7079i | −0.428082 | − | 0.428082i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 11.0192 | − | 1.89159i | 0.402363 | − | 0.0690712i | ||||
\(751\) | −34.6297 | −1.26366 | −0.631828 | − | 0.775109i | \(-0.717695\pi\) | ||||
−0.631828 | + | 0.775109i | \(0.717695\pi\) | |||||||
\(752\) | 2.88813 | − | 2.88813i | 0.105319 | − | 0.105319i | ||||
\(753\) | −18.7082 | + | 18.7082i | −0.681763 | + | 0.681763i | ||||
\(754\) | −21.6582 | −0.788746 | ||||||||
\(755\) | −8.07141 | − | 4.06887i | −0.293749 | − | 0.148082i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.7332 | − | 24.7332i | −0.898945 | − | 0.898945i | 0.0963983 | − | 0.995343i | \(-0.469268\pi\) |
−0.995343 | + | 0.0963983i | \(0.969268\pi\) | |||||||
\(758\) | −3.14037 | + | 3.14037i | −0.114063 | + | 0.114063i | ||||
\(759\) | −16.3651 | −0.594016 | ||||||||
\(760\) | −15.3612 | + | 5.06444i | −0.557209 | + | 0.183707i | ||||
\(761\) | 37.5984i | 1.36294i | 0.731845 | + | 0.681471i | \(0.238659\pi\) | ||||
−0.731845 | + | 0.681471i | \(0.761341\pi\) | |||||||
\(762\) | 2.14534 | − | 2.14534i | 0.0777176 | − | 0.0777176i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16.5825i | 0.599932i | ||||||||
\(765\) | −3.73013 | − | 11.3140i | −0.134863 | − | 0.409060i | ||||
\(766\) | − | 22.2618i | − | 0.804350i | ||||||
\(767\) | −4.54090 | − | 4.54090i | −0.163962 | − | 0.163962i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | −23.9494 | −0.863638 | −0.431819 | − | 0.901960i | \(-0.642128\pi\) | ||||
−0.431819 | + | 0.901960i | \(0.642128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.2150 | 0.403899 | ||||||||
\(772\) | −1.49728 | − | 1.49728i | −0.0538884 | − | 0.0538884i | ||||
\(773\) | −0.0264874 | − | 0.0264874i | −0.000952685 | − | 0.000952685i | 0.706630 | − | 0.707583i | \(-0.250214\pi\) |
−0.707583 | + | 0.706630i | \(0.750214\pi\) | |||||||
\(774\) | 5.47086i | 0.196646i | ||||||||
\(775\) | 37.0810 | − | 27.4323i | 1.33199 | − | 0.985396i | ||||
\(776\) | 3.81022i | 0.136779i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.97176 | + | 8.97176i | −0.321653 | + | 0.321653i | ||||
\(779\) | 18.2176i | 0.652712i | ||||||||
\(780\) | −9.62375 | − | 4.85142i | −0.344586 | − | 0.173709i | ||||
\(781\) | −28.6769 | −1.02614 | ||||||||
\(782\) | 19.8376 | − | 19.8376i | 0.709391 | − | 0.709391i | ||||
\(783\) | −3.17745 | − | 3.17745i | −0.113553 | − | 0.113553i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.92310 | − | 0.634028i | 0.0686384 | − | 0.0226294i | ||||
\(786\) | 8.77339 | 0.312936 | ||||||||
\(787\) | 18.4576 | − | 18.4576i | 0.657942 | − | 0.657942i | −0.296951 | − | 0.954893i | \(-0.595970\pi\) |
0.954893 | + | 0.296951i | \(0.0959696\pi\) | |||||||
\(788\) | 1.22531 | − | 1.22531i | 0.0436498 | − | 0.0436498i | ||||
\(789\) | 6.85911 | 0.244191 | ||||||||
\(790\) | 4.06540 | − | 1.34032i | 0.144640 | − | 0.0476866i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.19755 | − | 2.19755i | −0.0780865 | − | 0.0780865i | ||||
\(793\) | 42.7848 | − | 42.7848i | 1.51933 | − | 1.51933i | ||||
\(794\) | −21.7745 | −0.772748 | ||||||||
\(795\) | 6.86751 | + | 3.46198i | 0.243565 | + | 0.122784i | ||||
\(796\) | 7.87801i | 0.279229i | ||||||||
\(797\) | 0.973551 | − | 0.973551i | 0.0344850 | − | 0.0344850i | −0.689654 | − | 0.724139i | \(-0.742237\pi\) |
0.724139 | + | 0.689654i | \(0.242237\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.7606i | 0.769835i | ||||||||
\(800\) | −0.739583 | + | 4.94500i | −0.0261482 | + | 0.174832i | ||||
\(801\) | − | 4.07354i | − | 0.143931i | ||||||
\(802\) | −18.6024 | − | 18.6024i | −0.656872 | − | 0.656872i | ||||
\(803\) | −18.0905 | − | 18.0905i | −0.638400 | − | 0.638400i | ||||
\(804\) | −6.66287 | −0.234981 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −44.4629 | −1.56614 | ||||||||
\(807\) | −6.35027 | − | 6.35027i | −0.223540 | − | 0.223540i | ||||
\(808\) | −5.55958 | − | 5.55958i | −0.195585 | − | 0.195585i | ||||
\(809\) | 40.1730i | 1.41241i | 0.708009 | + | 0.706203i | \(0.249593\pi\) | ||||
−0.708009 | + | 0.706203i | \(0.750407\pi\) | |||||||
\(810\) | −0.700141 | − | 2.12363i | −0.0246004 | − | 0.0746167i | ||||
\(811\) | − | 24.5727i | − | 0.862866i | −0.902145 | − | 0.431433i | \(-0.858008\pi\) | ||
0.902145 | − | 0.431433i | \(-0.141992\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.34402 | + | 6.34402i | −0.222494 | + | 0.222494i | ||||
\(814\) | − | 11.1671i | − | 0.391405i | ||||||
\(815\) | 15.6770 | − | 5.16855i | 0.549141 | − | 0.181047i | ||||
\(816\) | 5.32769 | 0.186507 | ||||||||
\(817\) | −27.9825 | + | 27.9825i | −0.978984 | + | 0.978984i | ||||
\(818\) | 1.65923 | + | 1.65923i | 0.0580137 | + | 0.0580137i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.02873 | + | 2.53503i | 0.175611 | + | 0.0885271i | ||||
\(821\) | −49.0817 | −1.71296 | −0.856482 | − | 0.516177i | \(-0.827355\pi\) | ||||
−0.856482 | + | 0.516177i | \(0.827355\pi\) | |||||||
\(822\) | 9.62030 | − | 9.62030i | 0.335547 | − | 0.335547i | ||||
\(823\) | 20.7131 | − | 20.7131i | 0.722014 | − | 0.722014i | −0.247001 | − | 0.969015i | \(-0.579445\pi\) |
0.969015 | + | 0.247001i | \(0.0794452\pi\) | |||||||
\(824\) | −11.8311 | −0.412157 | ||||||||
\(825\) | −2.29848 | + | 15.3681i | −0.0800228 | + | 0.535048i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.8882 | + | 14.8882i | 0.517712 | + | 0.517712i | 0.916879 | − | 0.399166i | \(-0.130700\pi\) |
−0.399166 | + | 0.916879i | \(0.630700\pi\) | |||||||
\(828\) | 3.72349 | − | 3.72349i | 0.129400 | − | 0.129400i | ||||
\(829\) | 36.7688 | 1.27703 | 0.638516 | − | 0.769609i | \(-0.279549\pi\) | ||||
0.638516 | + | 0.769609i | \(0.279549\pi\) | |||||||
\(830\) | 12.7723 | − | 25.3363i | 0.443332 | − | 0.879435i | ||||
\(831\) | 24.7111i | 0.857219i | ||||||||
\(832\) | 3.40812 | − | 3.40812i | 0.118155 | − | 0.118155i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.9145i | 0.377937i | ||||||||
\(835\) | −1.83393 | + | 0.604630i | −0.0634659 | + | 0.0209241i | ||||
\(836\) | − | 22.4802i | − | 0.777494i | ||||||
\(837\) | −6.52308 | − | 6.52308i | −0.225471 | − | 0.225471i | ||||
\(838\) | −0.728937 | − | 0.728937i | −0.0251807 | − | 0.0251807i | ||||
\(839\) | −11.6715 | −0.402944 | −0.201472 | − | 0.979494i | \(-0.564573\pi\) | ||||
−0.201472 | + | 0.979494i | \(0.564573\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.80767 | 0.303713 | ||||||||
\(842\) | −20.2901 | − | 20.2901i | −0.699243 | − | 0.699243i | ||||
\(843\) | −13.0755 | − | 13.0755i | −0.450345 | − | 0.450345i | ||||
\(844\) | − | 15.9995i | − | 0.550724i | ||||||
\(845\) | 10.2977 | − | 20.4275i | 0.354251 | − | 0.702726i | ||||
\(846\) | 4.08444i | 0.140426i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.43203 | + | 2.43203i | −0.0835164 | + | 0.0835164i | ||||
\(849\) | − | 5.57176i | − | 0.191222i | ||||||
\(850\) | −15.8428 | − | 21.4152i | −0.543405 | − | 0.734536i | ||||
\(851\) | 18.9213 | 0.648613 | ||||||||
\(852\) | 6.52474 | − | 6.52474i | 0.223534 | − | 0.223534i | ||||
\(853\) | −19.6499 | − | 19.6499i | −0.672801 | − | 0.672801i | 0.285560 | − | 0.958361i | \(-0.407821\pi\) |
−0.958361 | + | 0.285560i | \(0.907821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.28091 | − | 14.4431i | 0.249002 | − | 0.493944i | ||||
\(856\) | −2.16226 | −0.0739047 | ||||||||
\(857\) | 39.6746 | − | 39.6746i | 1.35526 | − | 1.35526i | 0.475596 | − | 0.879664i | \(-0.342233\pi\) |
0.879664 | − | 0.475596i | \(-0.157767\pi\) | |||||||
\(858\) | 10.5918 | − | 10.5918i | 0.361597 | − | 0.361597i | ||||
\(859\) | 19.0290 | 0.649261 | 0.324630 | − | 0.945841i | \(-0.394760\pi\) | ||||
0.324630 | + | 0.945841i | \(0.394760\pi\) | |||||||
\(860\) | 3.83037 | + | 11.6181i | 0.130615 | + | 0.396173i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.1668 | + | 17.1668i | 0.584704 | + | 0.584704i | ||||
\(863\) | −14.5855 | + | 14.5855i | −0.496495 | + | 0.496495i | −0.910345 | − | 0.413850i | \(-0.864184\pi\) |
0.413850 | + | 0.910345i | \(0.364184\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.44873 | − | 7.42736i | −0.0832593 | − | 0.252538i | ||||
\(866\) | 27.1111i | 0.921271i | ||||||||
\(867\) | −8.04992 | + | 8.04992i | −0.273389 | + | 0.273389i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.94947i | 0.201822i | ||||||||
\(870\) | −8.97238 | − | 4.52306i | −0.304192 | − | 0.153346i | ||||
\(871\) | − | 32.1138i | − | 1.08813i | ||||||
\(872\) | 0.399905 | + | 0.399905i | 0.0135425 | + | 0.0135425i | ||||
\(873\) | −2.69423 | − | 2.69423i | −0.0911859 | − | 0.0911859i | ||||
\(874\) | 38.0900 | 1.28841 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.23213 | 0.278138 | ||||||||
\(877\) | −20.1153 | − | 20.1153i | −0.679245 | − | 0.679245i | 0.280585 | − | 0.959829i | \(-0.409472\pi\) |
−0.959829 | + | 0.280585i | \(0.909472\pi\) | |||||||
\(878\) | 10.3230 | + | 10.3230i | 0.348385 | + | 0.348385i | ||||
\(879\) | − | 24.9559i | − | 0.841741i | ||||||
\(880\) | −6.20538 | − | 3.12819i | −0.209183 | − | 0.105451i | ||||
\(881\) | 17.6227i | 0.593724i | 0.954920 | + | 0.296862i | \(0.0959401\pi\) | ||||
−0.954920 | + | 0.296862i | \(0.904060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.03577 | + | 4.03577i | −0.135814 | + | 0.135814i | −0.771746 | − | 0.635931i | \(-0.780616\pi\) |
0.635931 | + | 0.771746i | \(0.280616\pi\) | |||||||
\(884\) | 25.6785i | 0.863660i | ||||||||
\(885\) | −0.932851 | − | 2.82947i | −0.0313574 | − | 0.0951117i | ||||
\(886\) | 22.7392 | 0.763938 | ||||||||
\(887\) | 10.5767 | − | 10.5767i | 0.355130 | − | 0.355130i | −0.506884 | − | 0.862014i | \(-0.669203\pi\) |
0.862014 | + | 0.506884i | \(0.169203\pi\) | |||||||
\(888\) | 2.54080 | + | 2.54080i | 0.0852636 | + | 0.0852636i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.85205 | − | 8.65069i | −0.0956010 | − | 0.289972i | ||||
\(891\) | 3.10780 | 0.104115 | ||||||||
\(892\) | −1.20707 | + | 1.20707i | −0.0404157 | + | 0.0404157i | ||||
\(893\) | −20.8912 | + | 20.8912i | −0.699097 | + | 0.699097i | ||||
\(894\) | 2.09021 | 0.0699071 | ||||||||
\(895\) | 18.1803 | − | 36.0642i | 0.607700 | − | 1.20549i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.9465 | + | 17.9465i | 0.599217 | + | 0.599217i | ||||
\(898\) | 29.5969 | − | 29.5969i | 0.987662 | − | 0.987662i | ||||
\(899\) | −41.4535 | −1.38255 | ||||||||
\(900\) | −2.97368 | − | 4.01961i | −0.0991226 | − | 0.133987i | ||||
\(901\) | − | 18.3242i | − | 0.610466i | ||||||
\(902\) | −5.53456 | + | 5.53456i | −0.184281 | + | 0.184281i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 14.1171i | − | 0.469528i | ||||||
\(905\) | −21.8682 | + | 43.3798i | −0.726923 | + | 1.44199i | ||||
\(906\) | 4.04236i | 0.134298i | ||||||||
\(907\) | −12.3104 | − | 12.3104i | −0.408761 | − | 0.408761i | 0.472545 | − | 0.881306i | \(-0.343335\pi\) |
−0.881306 | + | 0.472545i | \(0.843335\pi\) | |||||||
\(908\) | −4.81749 | − | 4.81749i | −0.159874 | − | 0.159874i | ||||
\(909\) | 7.86244 | 0.260781 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.74129 | 0.322743 | 0.161372 | − | 0.986894i | \(-0.448408\pi\) | ||||
0.161372 | + | 0.986894i | \(0.448408\pi\) | |||||||
\(912\) | 5.11483 | + | 5.11483i | 0.169369 | + | 0.169369i | ||||
\(913\) | 27.8848 | + | 27.8848i | 0.922852 | + | 0.922852i | ||||
\(914\) | − | 26.5586i | − | 0.878480i | ||||||
\(915\) | 26.6596 | − | 8.78941i | 0.881338 | − | 0.290569i | ||||
\(916\) | 19.8143i | 0.654682i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.76725 | + | 3.76725i | −0.124338 | + | 0.124338i | ||||
\(919\) | 23.1175i | 0.762575i | 0.924456 | + | 0.381288i | \(0.124519\pi\) | ||||
−0.924456 | + | 0.381288i | \(0.875481\pi\) | |||||||
\(920\) | 5.30035 | − | 10.5143i | 0.174747 | − | 0.346646i | ||||
\(921\) | −16.2362 | −0.535001 | ||||||||
\(922\) | −11.7102 | + | 11.7102i | −0.385656 | + | 0.385656i | ||||
\(923\) | 31.4480 | + | 31.4480i | 1.03512 | + | 1.03512i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.65749 | − | 17.7685i | 0.0873778 | − | 0.584225i | ||||
\(926\) | 26.9132 | 0.884424 | ||||||||
\(927\) | 8.36587 | − | 8.36587i | 0.274771 | − | 0.274771i | ||||
\(928\) | 3.17745 | − | 3.17745i | 0.104305 | − | 0.104305i | ||||
\(929\) | 18.3779 | 0.602958 | 0.301479 | − | 0.953473i | \(-0.402520\pi\) | ||||
0.301479 | + | 0.953473i | \(0.402520\pi\) | |||||||
\(930\) | −18.4197 | − | 9.28554i | −0.604005 | − | 0.304485i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.7261 | + | 12.7261i | 0.416857 | + | 0.416857i | ||||
\(933\) | −9.28775 | + | 9.28775i | −0.304067 | + | 0.304067i | ||||
\(934\) | 13.6065 | 0.445218 | ||||||||
\(935\) | 35.1618 | − | 11.5925i | 1.14992 | − | 0.379116i | ||||
\(936\) | 4.81981i | 0.157540i | ||||||||
\(937\) | −12.6455 | + | 12.6455i | −0.413111 | + | 0.413111i | −0.882821 | − | 0.469710i | \(-0.844358\pi\) |
0.469710 | + | 0.882821i | \(0.344358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 25.4482i | − | 0.830471i | ||||||
\(940\) | 2.85968 | + | 8.67383i | 0.0932725 | + | 0.282909i | ||||
\(941\) | 51.6202i | 1.68277i | 0.540436 | + | 0.841385i | \(0.318259\pi\) | ||||
−0.540436 | + | 0.841385i | \(0.681741\pi\) | |||||||
\(942\) | −0.640337 | − | 0.640337i | −0.0208633 | − | 0.0208633i | ||||
\(943\) | −9.37766 | − | 9.37766i | −0.305379 | − | 0.305379i | ||||
\(944\) | 1.33238 | 0.0433652 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.0024 | −0.552795 | ||||||||
\(947\) | 36.9153 | + | 36.9153i | 1.19959 | + | 1.19959i | 0.974290 | + | 0.225297i | \(0.0723352\pi\) |
0.225297 | + | 0.974290i | \(0.427665\pi\) | |||||||
\(948\) | −1.35366 | − | 1.35366i | −0.0439648 | − | 0.0439648i | ||||
\(949\) | 39.6773i | 1.28798i | ||||||||
\(950\) | 5.34974 | − | 35.7695i | 0.173569 | − | 1.16051i | ||||
\(951\) | − | 19.0262i | − | 0.616966i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.900242 | − | 0.900242i | 0.0291617 | − | 0.0291617i | −0.692376 | − | 0.721537i | \(-0.743436\pi\) |
0.721537 | + | 0.692376i | \(0.243436\pi\) | |||||||
\(954\) | − | 3.43942i | − | 0.111355i | ||||||
\(955\) | −33.1103 | − | 16.6912i | −1.07142 | − | 0.540115i | ||||
\(956\) | 26.6409 | 0.861627 | ||||||||
\(957\) | 9.87488 | − | 9.87488i | 0.319210 | − | 0.319210i | ||||
\(958\) | 0.937119 | + | 0.937119i | 0.0302769 | + | 0.0302769i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.12363 | − | 0.700141i | 0.0685399 | − | 0.0225969i | ||||
\(961\) | −54.1012 | −1.74520 | ||||||||
\(962\) | −12.2462 | + | 12.2462i | −0.394832 | + | 0.394832i | ||||
\(963\) | 1.52895 | − | 1.52895i | 0.0492698 | − | 0.0492698i | ||||
\(964\) | 14.4248 | 0.464592 | ||||||||
\(965\) | 4.49674 | − | 1.48253i | 0.144755 | − | 0.0477244i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.5119 | + | 39.5119i | 1.27062 | + | 1.27062i | 0.945765 | + | 0.324852i | \(0.105314\pi\) |
0.324852 | + | 0.945765i | \(0.394686\pi\) | |||||||
\(968\) | −0.948618 | + | 0.948618i | −0.0304897 | + | 0.0304897i | ||||
\(969\) | −38.5377 | −1.23801 | ||||||||
\(970\) | −7.60789 | − | 3.83521i | −0.244275 | − | 0.123141i | ||||
\(971\) | 0.110632i | 0.00355034i | 0.999998 | + | 0.00177517i | \(0.000565055\pi\) | ||||
−0.999998 | + | 0.00177517i | \(0.999435\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 32.0419i | − | 1.02669i | ||||||
\(975\) | 19.3737 | − | 14.3326i | 0.620456 | − | 0.459009i | ||||
\(976\) | 12.5538i | 0.401837i | ||||||||
\(977\) | 5.61031 | + | 5.61031i | 0.179490 | + | 0.179490i | 0.791133 | − | 0.611644i | \(-0.209491\pi\) |
−0.611644 | + | 0.791133i | \(0.709491\pi\) | |||||||
\(978\) | −5.21998 | − | 5.21998i | −0.166917 | − | 0.166917i | ||||
\(979\) | 12.6598 | 0.404608 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.565551 | −0.0180567 | ||||||||
\(982\) | 15.8010 | + | 15.8010i | 0.504231 | + | 0.504231i | ||||
\(983\) | 23.5138 | + | 23.5138i | 0.749973 | + | 0.749973i | 0.974474 | − | 0.224501i | \(-0.0720752\pi\) |
−0.224501 | + | 0.974474i | \(0.572075\pi\) | |||||||
\(984\) | − | 2.51851i | − | 0.0802873i | ||||||
\(985\) | 1.21324 | + | 3.67992i | 0.0386569 | + | 0.117252i | ||||
\(986\) | 23.9404i | 0.762419i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.6525 | + | 24.6525i | −0.784301 | + | 0.784301i | ||||
\(989\) | − | 28.8085i | − | 0.916057i | ||||||
\(990\) | 6.59983 | − | 2.17590i | 0.209756 | − | 0.0691546i | ||||
\(991\) | −14.3373 | −0.455439 | −0.227720 | − | 0.973727i | \(-0.573127\pi\) | ||||
−0.227720 | + | 0.973727i | \(0.573127\pi\) | |||||||
\(992\) | 6.52308 | − | 6.52308i | 0.207108 | − | 0.207108i | ||||
\(993\) | 14.8054 | + | 14.8054i | 0.469837 | + | 0.469837i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.7301 | − | 7.92969i | −0.498677 | − | 0.251388i | ||||
\(996\) | −12.6890 | −0.402067 | ||||||||
\(997\) | −21.5103 | + | 21.5103i | −0.681239 | + | 0.681239i | −0.960279 | − | 0.279040i | \(-0.909984\pi\) |
0.279040 | + | 0.960279i | \(0.409984\pi\) | |||||||
\(998\) | −7.67375 | + | 7.67375i | −0.242908 | + | 0.242908i | ||||
\(999\) | −3.59323 | −0.113685 |
(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 | 1470.2.m.e.97.1 | 16 | ||
5.3 | odd | 4 | 1470.2.m.d.1273.4 | 16 | |||
7.4 | even | 3 | 210.2.u.b.187.4 | yes | 16 | ||
7.5 | odd | 6 | 210.2.u.a.157.1 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.d.97.4 | 16 | |||
21.5 | even | 6 | 630.2.bv.a.577.4 | 16 | |||
21.11 | odd | 6 | 630.2.bv.b.397.1 | 16 | |||
35.4 | even | 6 | 1050.2.bc.g.607.2 | 16 | |||
35.12 | even | 12 | 1050.2.bc.g.493.2 | 16 | |||
35.13 | even | 4 | inner | 1470.2.m.e.1273.1 | 16 | ||
35.18 | odd | 12 | 210.2.u.a.103.1 | ✓ | 16 | ||
35.19 | odd | 6 | 1050.2.bc.h.157.4 | 16 | |||
35.32 | odd | 12 | 1050.2.bc.h.943.4 | 16 | |||
35.33 | even | 12 | 210.2.u.b.73.4 | yes | 16 | ||
105.53 | even | 12 | 630.2.bv.a.523.4 | 16 | |||
105.68 | odd | 12 | 630.2.bv.b.73.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.103.1 | ✓ | 16 | 35.18 | odd | 12 | ||
210.2.u.a.157.1 | yes | 16 | 7.5 | odd | 6 | ||
210.2.u.b.73.4 | yes | 16 | 35.33 | even | 12 | ||
210.2.u.b.187.4 | yes | 16 | 7.4 | even | 3 | ||
630.2.bv.a.523.4 | 16 | 105.53 | even | 12 | |||
630.2.bv.a.577.4 | 16 | 21.5 | even | 6 | |||
630.2.bv.b.73.1 | 16 | 105.68 | odd | 12 | |||
630.2.bv.b.397.1 | 16 | 21.11 | odd | 6 | |||
1050.2.bc.g.493.2 | 16 | 35.12 | even | 12 | |||
1050.2.bc.g.607.2 | 16 | 35.4 | even | 6 | |||
1050.2.bc.h.157.4 | 16 | 35.19 | odd | 6 | |||
1050.2.bc.h.943.4 | 16 | 35.32 | odd | 12 | |||
1470.2.m.d.97.4 | 16 | 7.6 | odd | 2 | |||
1470.2.m.d.1273.4 | 16 | 5.3 | odd | 4 | |||
1470.2.m.e.97.1 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.e.1273.1 | 16 | 35.13 | even | 4 | inner |