Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, 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("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 643.8 | ||
Character | \(\chi\) | \(=\) | 690.643 |
Dual form | 690.2.j.b.367.8 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.52094 | + | 1.63913i | −0.680187 | + | 0.733039i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.68754 | + | 2.68754i | 1.01580 | + | 1.01580i | 0.999873 | + | 0.0159226i | \(0.00506854\pi\) |
0.0159226 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.0835670 | + | 2.23451i | 0.0264262 | + | 0.706613i | ||||
\(11\) | 0.403497i | 0.121659i | 0.998148 | + | 0.0608295i | \(0.0193746\pi\) | ||||
−0.998148 | + | 0.0608295i | \(0.980625\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −2.12629 | − | 2.12629i | −0.589728 | − | 0.589728i | 0.347830 | − | 0.937558i | \(-0.386919\pi\) |
−0.937558 | + | 0.347830i | \(0.886919\pi\) | |||||||
\(14\) | 3.80076 | 1.01580 | ||||||||
\(15\) | −2.23451 | + | 0.0835670i | −0.576947 | + | 0.0215769i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.95666 | + | 4.95666i | 1.20217 | + | 1.20217i | 0.973506 | + | 0.228662i | \(0.0734349\pi\) |
0.228662 | + | 0.973506i | \(0.426565\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | −5.20795 | −1.19479 | −0.597393 | − | 0.801949i | \(-0.703797\pi\) | ||||
−0.597393 | + | 0.801949i | \(0.703797\pi\) | |||||||
\(20\) | 1.63913 | + | 1.52094i | 0.366520 | + | 0.340093i | ||||
\(21\) | 3.80076i | 0.829394i | ||||||||
\(22\) | 0.285316 | + | 0.285316i | 0.0608295 | + | 0.0608295i | ||||
\(23\) | 2.47384 | + | 4.10854i | 0.515832 | + | 0.856690i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −0.373462 | − | 4.98603i | −0.0746924 | − | 0.997207i | ||||
\(26\) | −3.00703 | −0.589728 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 2.68754 | − | 2.68754i | 0.507898 | − | 0.507898i | ||||
\(29\) | 9.42076i | 1.74939i | 0.484673 | + | 0.874695i | \(0.338939\pi\) | ||||
−0.484673 | + | 0.874695i | \(0.661061\pi\) | |||||||
\(30\) | −1.52094 | + | 1.63913i | −0.277685 | + | 0.299262i | ||||
\(31\) | 3.33683 | 0.599312 | 0.299656 | − | 0.954047i | \(-0.403128\pi\) | ||||
0.299656 | + | 0.954047i | \(0.403128\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −0.285316 | + | 0.285316i | −0.0496671 | + | 0.0496671i | ||||
\(34\) | 7.00978 | 1.20217 | ||||||||
\(35\) | −8.49282 | + | 0.317618i | −1.43555 | + | 0.0536873i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.17130 | − | 2.17130i | −0.356959 | − | 0.356959i | 0.505732 | − | 0.862691i | \(-0.331223\pi\) |
−0.862691 | + | 0.505732i | \(0.831223\pi\) | |||||||
\(38\) | −3.68258 | + | 3.68258i | −0.597393 | + | 0.597393i | ||||
\(39\) | − | 3.00703i | − | 0.481511i | ||||||
\(40\) | 2.23451 | − | 0.0835670i | 0.353306 | − | 0.0132131i | ||||
\(41\) | 5.69885 | 0.890011 | 0.445006 | − | 0.895528i | \(-0.353202\pi\) | ||||
0.445006 | + | 0.895528i | \(0.353202\pi\) | |||||||
\(42\) | 2.68754 | + | 2.68754i | 0.414697 | + | 0.414697i | ||||
\(43\) | 2.56936 | − | 2.56936i | 0.391824 | − | 0.391824i | −0.483513 | − | 0.875337i | \(-0.660639\pi\) |
0.875337 | + | 0.483513i | \(0.160639\pi\) | |||||||
\(44\) | 0.403497 | 0.0608295 | ||||||||
\(45\) | −1.63913 | − | 1.52094i | −0.244346 | − | 0.226729i | ||||
\(46\) | 4.65445 | + | 1.15590i | 0.686261 | + | 0.170429i | ||||
\(47\) | 8.64413 | − | 8.64413i | 1.26088 | − | 1.26088i | 0.310208 | − | 0.950669i | \(-0.399601\pi\) |
0.950669 | − | 0.310208i | \(-0.100399\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | 7.44578i | 1.06368i | ||||||||
\(50\) | −3.78974 | − | 3.26158i | −0.535950 | − | 0.461257i | ||||
\(51\) | 7.00978i | 0.981566i | ||||||||
\(52\) | −2.12629 | + | 2.12629i | −0.294864 | + | 0.294864i | ||||
\(53\) | 1.47608 | − | 1.47608i | 0.202755 | − | 0.202755i | −0.598424 | − | 0.801179i | \(-0.704206\pi\) |
0.801179 | + | 0.598424i | \(0.204206\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −0.661382 | − | 0.613696i | −0.0891808 | − | 0.0827508i | ||||
\(56\) | − | 3.80076i | − | 0.507898i | ||||||
\(57\) | −3.68258 | − | 3.68258i | −0.487769 | − | 0.487769i | ||||
\(58\) | 6.66148 | + | 6.66148i | 0.874695 | + | 0.874695i | ||||
\(59\) | − | 13.4003i | − | 1.74458i | −0.488992 | − | 0.872288i | \(-0.662635\pi\) | ||
0.488992 | − | 0.872288i | \(-0.337365\pi\) | |||||||
\(60\) | 0.0835670 | + | 2.23451i | 0.0107885 | + | 0.288473i | ||||
\(61\) | − | 7.51118i | − | 0.961708i | −0.876801 | − | 0.480854i | \(-0.840327\pi\) | ||
0.876801 | − | 0.480854i | \(-0.159673\pi\) | |||||||
\(62\) | 2.35950 | − | 2.35950i | 0.299656 | − | 0.299656i | ||||
\(63\) | −2.68754 | + | 2.68754i | −0.338599 | + | 0.338599i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 6.71923 | − | 0.251289i | 0.833418 | − | 0.0311685i | ||||
\(66\) | 0.403497i | 0.0496671i | ||||||||
\(67\) | −4.60755 | − | 4.60755i | −0.562902 | − | 0.562902i | 0.367229 | − | 0.930131i | \(-0.380307\pi\) |
−0.930131 | + | 0.367229i | \(0.880307\pi\) | |||||||
\(68\) | 4.95666 | − | 4.95666i | 0.601084 | − | 0.601084i | ||||
\(69\) | −1.15590 | + | 4.65445i | −0.139154 | + | 0.560330i | ||||
\(70\) | −5.78074 | + | 6.22992i | −0.690931 | + | 0.744618i | ||||
\(71\) | −5.45281 | −0.647129 | −0.323565 | − | 0.946206i | \(-0.604881\pi\) | ||||
−0.323565 | + | 0.946206i | \(0.604881\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 1.06175 | + | 1.06175i | 0.124269 | + | 0.124269i | 0.766506 | − | 0.642237i | \(-0.221994\pi\) |
−0.642237 | + | 0.766506i | \(0.721994\pi\) | |||||||
\(74\) | −3.07068 | −0.356959 | ||||||||
\(75\) | 3.26158 | − | 3.78974i | 0.376615 | − | 0.437601i | ||||
\(76\) | 5.20795i | 0.597393i | ||||||||
\(77\) | −1.08442 | + | 1.08442i | −0.123581 | + | 0.123581i | ||||
\(78\) | −2.12629 | − | 2.12629i | −0.240755 | − | 0.240755i | ||||
\(79\) | −0.383565 | −0.0431544 | −0.0215772 | − | 0.999767i | \(-0.506869\pi\) | ||||
−0.0215772 | + | 0.999767i | \(0.506869\pi\) | |||||||
\(80\) | 1.52094 | − | 1.63913i | 0.170047 | − | 0.183260i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.02970 | − | 4.02970i | 0.445006 | − | 0.445006i | ||||
\(83\) | −12.3708 | + | 12.3708i | −1.35787 | + | 1.35787i | −0.481328 | + | 0.876540i | \(0.659846\pi\) |
−0.876540 | + | 0.481328i | \(0.840154\pi\) | |||||||
\(84\) | 3.80076 | 0.414697 | ||||||||
\(85\) | −15.6634 | + | 0.585786i | −1.69893 | + | 0.0635375i | ||||
\(86\) | − | 3.63363i | − | 0.391824i | ||||||
\(87\) | −6.66148 | + | 6.66148i | −0.714186 | + | 0.714186i | ||||
\(88\) | 0.285316 | − | 0.285316i | 0.0304147 | − | 0.0304147i | ||||
\(89\) | −6.23158 | −0.660546 | −0.330273 | − | 0.943885i | \(-0.607141\pi\) | ||||
−0.330273 | + | 0.943885i | \(0.607141\pi\) | |||||||
\(90\) | −2.23451 | + | 0.0835670i | −0.235538 | + | 0.00880874i | ||||
\(91\) | − | 11.4290i | − | 1.19809i | ||||||
\(92\) | 4.10854 | − | 2.47384i | 0.428345 | − | 0.257916i | ||||
\(93\) | 2.35950 | + | 2.35950i | 0.244668 | + | 0.244668i | ||||
\(94\) | − | 12.2247i | − | 1.26088i | ||||||
\(95\) | 7.92100 | − | 8.53649i | 0.812678 | − | 0.875825i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −8.25631 | − | 8.25631i | −0.838301 | − | 0.838301i | 0.150334 | − | 0.988635i | \(-0.451965\pi\) |
−0.988635 | + | 0.150334i | \(0.951965\pi\) | |||||||
\(98\) | 5.26496 | + | 5.26496i | 0.531841 | + | 0.531841i | ||||
\(99\) | −0.403497 | −0.0405530 | ||||||||
\(100\) | −4.98603 | + | 0.373462i | −0.498603 | + | 0.0373462i | ||||
\(101\) | −7.08442 | −0.704926 | −0.352463 | − | 0.935826i | \(-0.614656\pi\) | ||||
−0.352463 | + | 0.935826i | \(0.614656\pi\) | |||||||
\(102\) | 4.95666 | + | 4.95666i | 0.490783 | + | 0.490783i | ||||
\(103\) | 6.87041 | − | 6.87041i | 0.676961 | − | 0.676961i | −0.282350 | − | 0.959311i | \(-0.591114\pi\) |
0.959311 | + | 0.282350i | \(0.0911140\pi\) | |||||||
\(104\) | 3.00703i | 0.294864i | ||||||||
\(105\) | −6.22992 | − | 5.78074i | −0.607978 | − | 0.564143i | ||||
\(106\) | − | 2.08749i | − | 0.202755i | ||||||
\(107\) | 3.14660 | + | 3.14660i | 0.304194 | + | 0.304194i | 0.842652 | − | 0.538458i | \(-0.180993\pi\) |
−0.538458 | + | 0.842652i | \(0.680993\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 12.6901 | 1.21549 | 0.607744 | − | 0.794133i | \(-0.292075\pi\) | ||||
0.607744 | + | 0.794133i | \(0.292075\pi\) | |||||||
\(110\) | −0.901617 | + | 0.0337191i | −0.0859658 | + | 0.00321499i | ||||
\(111\) | − | 3.07068i | − | 0.291456i | ||||||
\(112\) | −2.68754 | − | 2.68754i | −0.253949 | − | 0.253949i | ||||
\(113\) | 8.96499 | − | 8.96499i | 0.843356 | − | 0.843356i | −0.145938 | − | 0.989294i | \(-0.546620\pi\) |
0.989294 | + | 0.145938i | \(0.0466200\pi\) | |||||||
\(114\) | −5.20795 | −0.487769 | ||||||||
\(115\) | −10.4970 | − | 2.19392i | −0.978849 | − | 0.204584i | ||||
\(116\) | 9.42076 | 0.874695 | ||||||||
\(117\) | 2.12629 | − | 2.12629i | 0.196576 | − | 0.196576i | ||||
\(118\) | −9.47547 | − | 9.47547i | −0.872288 | − | 0.872288i | ||||
\(119\) | 26.6425i | 2.44231i | ||||||||
\(120\) | 1.63913 | + | 1.52094i | 0.149631 | + | 0.138843i | ||||
\(121\) | 10.8372 | 0.985199 | ||||||||
\(122\) | −5.31121 | − | 5.31121i | −0.480854 | − | 0.480854i | ||||
\(123\) | 4.02970 | + | 4.02970i | 0.363346 | + | 0.363346i | ||||
\(124\) | − | 3.33683i | − | 0.299656i | ||||||
\(125\) | 8.74075 | + | 6.97132i | 0.781796 | + | 0.623534i | ||||
\(126\) | 3.80076i | 0.338599i | ||||||||
\(127\) | −9.84286 | + | 9.84286i | −0.873413 | + | 0.873413i | −0.992843 | − | 0.119430i | \(-0.961893\pi\) |
0.119430 | + | 0.992843i | \(0.461893\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 3.63363 | 0.319923 | ||||||||
\(130\) | 4.57353 | − | 4.92890i | 0.401125 | − | 0.432293i | ||||
\(131\) | −1.09419 | −0.0955998 | −0.0477999 | − | 0.998857i | \(-0.515221\pi\) | ||||
−0.0477999 | + | 0.998857i | \(0.515221\pi\) | |||||||
\(132\) | 0.285316 | + | 0.285316i | 0.0248335 | + | 0.0248335i | ||||
\(133\) | −13.9966 | − | 13.9966i | −1.21366 | − | 1.21366i | ||||
\(134\) | −6.51606 | −0.562902 | ||||||||
\(135\) | −0.0835670 | − | 2.23451i | −0.00719230 | − | 0.192316i | ||||
\(136\) | − | 7.00978i | − | 0.601084i | ||||||
\(137\) | −13.9152 | − | 13.9152i | −1.18885 | − | 1.18885i | −0.977384 | − | 0.211471i | \(-0.932175\pi\) |
−0.211471 | − | 0.977384i | \(-0.567825\pi\) | |||||||
\(138\) | 2.47384 | + | 4.10854i | 0.210588 | + | 0.349742i | ||||
\(139\) | 19.8141i | 1.68061i | 0.542116 | + | 0.840304i | \(0.317623\pi\) | ||||
−0.542116 | + | 0.840304i | \(0.682377\pi\) | |||||||
\(140\) | 0.317618 | + | 8.49282i | 0.0268436 | + | 0.717774i | ||||
\(141\) | 12.2247 | 1.02950 | ||||||||
\(142\) | −3.85572 | + | 3.85572i | −0.323565 | + | 0.323565i | ||||
\(143\) | 0.857953 | − | 0.857953i | 0.0717457 | − | 0.0717457i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −15.4418 | − | 14.3284i | −1.28237 | − | 1.18991i | ||||
\(146\) | 1.50154 | 0.124269 | ||||||||
\(147\) | −5.26496 | + | 5.26496i | −0.434247 | + | 0.434247i | ||||
\(148\) | −2.17130 | + | 2.17130i | −0.178480 | + | 0.178480i | ||||
\(149\) | 11.1431 | 0.912875 | 0.456438 | − | 0.889755i | \(-0.349125\pi\) | ||||
0.456438 | + | 0.889755i | \(0.349125\pi\) | |||||||
\(150\) | −0.373462 | − | 4.98603i | −0.0304930 | − | 0.407108i | ||||
\(151\) | 19.9653 | 1.62475 | 0.812375 | − | 0.583135i | \(-0.198174\pi\) | ||||
0.812375 | + | 0.583135i | \(0.198174\pi\) | |||||||
\(152\) | 3.68258 | + | 3.68258i | 0.298697 | + | 0.298697i | ||||
\(153\) | −4.95666 | + | 4.95666i | −0.400723 | + | 0.400723i | ||||
\(154\) | 1.53360i | 0.123581i | ||||||||
\(155\) | −5.07513 | + | 5.46948i | −0.407644 | + | 0.439319i | ||||
\(156\) | −3.00703 | −0.240755 | ||||||||
\(157\) | 2.44491 | + | 2.44491i | 0.195125 | + | 0.195125i | 0.797907 | − | 0.602781i | \(-0.205941\pi\) |
−0.602781 | + | 0.797907i | \(0.705941\pi\) | |||||||
\(158\) | −0.271221 | + | 0.271221i | −0.0215772 | + | 0.0215772i | ||||
\(159\) | 2.08749 | 0.165549 | ||||||||
\(160\) | −0.0835670 | − | 2.23451i | −0.00660655 | − | 0.176653i | ||||
\(161\) | −4.39331 | + | 17.6904i | −0.346242 | + | 1.39420i | ||||
\(162\) | −0.707107 | + | 0.707107i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 0.238521 | + | 0.238521i | 0.0186824 | + | 0.0186824i | 0.716386 | − | 0.697704i | \(-0.245795\pi\) |
−0.697704 | + | 0.716386i | \(0.745795\pi\) | |||||||
\(164\) | − | 5.69885i | − | 0.445006i | ||||||
\(165\) | −0.0337191 | − | 0.901617i | −0.00262502 | − | 0.0701908i | ||||
\(166\) | 17.4949i | 1.35787i | ||||||||
\(167\) | 6.43688 | − | 6.43688i | 0.498101 | − | 0.498101i | −0.412746 | − | 0.910846i | \(-0.635430\pi\) |
0.910846 | + | 0.412746i | \(0.135430\pi\) | |||||||
\(168\) | 2.68754 | − | 2.68754i | 0.207348 | − | 0.207348i | ||||
\(169\) | − | 3.95776i | − | 0.304443i | ||||||
\(170\) | −10.6615 | + | 11.4899i | −0.817698 | + | 0.881236i | ||||
\(171\) | − | 5.20795i | − | 0.398262i | ||||||
\(172\) | −2.56936 | − | 2.56936i | −0.195912 | − | 0.195912i | ||||
\(173\) | −5.89468 | − | 5.89468i | −0.448164 | − | 0.448164i | 0.446580 | − | 0.894744i | \(-0.352642\pi\) |
−0.894744 | + | 0.446580i | \(0.852642\pi\) | |||||||
\(174\) | 9.42076i | 0.714186i | ||||||||
\(175\) | 12.3965 | − | 14.4039i | 0.937086 | − | 1.08883i | ||||
\(176\) | − | 0.403497i | − | 0.0304147i | ||||||
\(177\) | 9.47547 | − | 9.47547i | 0.712220 | − | 0.712220i | ||||
\(178\) | −4.40639 | + | 4.40639i | −0.330273 | + | 0.330273i | ||||
\(179\) | − | 2.77575i | − | 0.207469i | −0.994605 | − | 0.103735i | \(-0.966921\pi\) | ||
0.994605 | − | 0.103735i | \(-0.0330792\pi\) | |||||||
\(180\) | −1.52094 | + | 1.63913i | −0.113364 | + | 0.122173i | ||||
\(181\) | − | 21.2640i | − | 1.58054i | −0.612760 | − | 0.790269i | \(-0.709941\pi\) | ||
0.612760 | − | 0.790269i | \(-0.290059\pi\) | |||||||
\(182\) | −8.08153 | − | 8.08153i | −0.599043 | − | 0.599043i | ||||
\(183\) | 5.31121 | − | 5.31121i | 0.392616 | − | 0.392616i | ||||
\(184\) | 1.15590 | − | 4.65445i | 0.0852143 | − | 0.343130i | ||||
\(185\) | 6.86145 | − | 0.256608i | 0.504464 | − | 0.0188662i | ||||
\(186\) | 3.33683 | 0.244668 | ||||||||
\(187\) | −2.00000 | + | 2.00000i | −0.146254 | + | 0.146254i | ||||
\(188\) | −8.64413 | − | 8.64413i | −0.630438 | − | 0.630438i | ||||
\(189\) | −3.80076 | −0.276465 | ||||||||
\(190\) | −0.435213 | − | 11.6372i | −0.0315737 | − | 0.844251i | ||||
\(191\) | 15.5937i | 1.12832i | 0.825666 | + | 0.564160i | \(0.190800\pi\) | ||||
−0.825666 | + | 0.564160i | \(0.809200\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −6.99660 | − | 6.99660i | −0.503626 | − | 0.503626i | 0.408937 | − | 0.912563i | \(-0.365900\pi\) |
−0.912563 | + | 0.408937i | \(0.865900\pi\) | |||||||
\(194\) | −11.6762 | −0.838301 | ||||||||
\(195\) | 4.92890 | + | 4.57353i | 0.352966 | + | 0.327517i | ||||
\(196\) | 7.44578 | 0.531841 | ||||||||
\(197\) | 4.96503 | − | 4.96503i | 0.353744 | − | 0.353744i | −0.507757 | − | 0.861501i | \(-0.669525\pi\) |
0.861501 | + | 0.507757i | \(0.169525\pi\) | |||||||
\(198\) | −0.285316 | + | 0.285316i | −0.0202765 | + | 0.0202765i | ||||
\(199\) | −13.2209 | −0.937202 | −0.468601 | − | 0.883410i | \(-0.655242\pi\) | ||||
−0.468601 | + | 0.883410i | \(0.655242\pi\) | |||||||
\(200\) | −3.26158 | + | 3.78974i | −0.230629 | + | 0.267975i | ||||
\(201\) | − | 6.51606i | − | 0.459608i | ||||||
\(202\) | −5.00944 | + | 5.00944i | −0.352463 | + | 0.352463i | ||||
\(203\) | −25.3187 | + | 25.3187i | −1.77702 | + | 1.77702i | ||||
\(204\) | 7.00978 | 0.490783 | ||||||||
\(205\) | −8.66763 | + | 9.34113i | −0.605374 | + | 0.652413i | ||||
\(206\) | − | 9.71622i | − | 0.676961i | ||||||
\(207\) | −4.10854 | + | 2.47384i | −0.285563 | + | 0.171944i | ||||
\(208\) | 2.12629 | + | 2.12629i | 0.147432 | + | 0.147432i | ||||
\(209\) | − | 2.10139i | − | 0.145356i | ||||||
\(210\) | −8.49282 | + | 0.317618i | −0.586060 | + | 0.0219177i | ||||
\(211\) | 14.3412 | 0.987286 | 0.493643 | − | 0.869665i | \(-0.335665\pi\) | ||||
0.493643 | + | 0.869665i | \(0.335665\pi\) | |||||||
\(212\) | −1.47608 | − | 1.47608i | −0.101377 | − | 0.101377i | ||||
\(213\) | −3.85572 | − | 3.85572i | −0.264189 | − | 0.264189i | ||||
\(214\) | 4.44997 | 0.304194 | ||||||||
\(215\) | 0.303651 | + | 8.11936i | 0.0207088 | + | 0.553736i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 8.96787 | + | 8.96787i | 0.608779 | + | 0.608779i | ||||
\(218\) | 8.97323 | − | 8.97323i | 0.607744 | − | 0.607744i | ||||
\(219\) | 1.50154i | 0.101465i | ||||||||
\(220\) | −0.613696 | + | 0.661382i | −0.0413754 | + | 0.0445904i | ||||
\(221\) | − | 21.0786i | − | 1.41790i | ||||||
\(222\) | −2.17130 | − | 2.17130i | −0.145728 | − | 0.145728i | ||||
\(223\) | −10.4795 | − | 10.4795i | −0.701757 | − | 0.701757i | 0.263030 | − | 0.964788i | \(-0.415278\pi\) |
−0.964788 | + | 0.263030i | \(0.915278\pi\) | |||||||
\(224\) | −3.80076 | −0.253949 | ||||||||
\(225\) | 4.98603 | − | 0.373462i | 0.332402 | − | 0.0248975i | ||||
\(226\) | − | 12.6784i | − | 0.843356i | ||||||
\(227\) | 0.390578 | + | 0.390578i | 0.0259236 | + | 0.0259236i | 0.719950 | − | 0.694026i | \(-0.244165\pi\) |
−0.694026 | + | 0.719950i | \(0.744165\pi\) | |||||||
\(228\) | −3.68258 | + | 3.68258i | −0.243885 | + | 0.243885i | ||||
\(229\) | 16.0170 | 1.05844 | 0.529218 | − | 0.848486i | \(-0.322485\pi\) | ||||
0.529218 | + | 0.848486i | \(0.322485\pi\) | |||||||
\(230\) | −8.97382 | + | 5.87116i | −0.591716 | + | 0.387133i | ||||
\(231\) | −1.53360 | −0.100903 | ||||||||
\(232\) | 6.66148 | − | 6.66148i | 0.437348 | − | 0.437348i | ||||
\(233\) | −13.0826 | − | 13.0826i | −0.857070 | − | 0.857070i | 0.133922 | − | 0.990992i | \(-0.457243\pi\) |
−0.990992 | + | 0.133922i | \(0.957243\pi\) | |||||||
\(234\) | − | 3.00703i | − | 0.196576i | ||||||
\(235\) | 1.02158 | + | 27.3161i | 0.0666404 | + | 1.78190i | ||||
\(236\) | −13.4003 | −0.872288 | ||||||||
\(237\) | −0.271221 | − | 0.271221i | −0.0176177 | − | 0.0176177i | ||||
\(238\) | 18.8391 | + | 18.8391i | 1.22116 | + | 1.22116i | ||||
\(239\) | 14.8384i | 0.959816i | 0.877319 | + | 0.479908i | \(0.159330\pi\) | ||||
−0.877319 | + | 0.479908i | \(0.840670\pi\) | |||||||
\(240\) | 2.23451 | − | 0.0835670i | 0.144237 | − | 0.00539423i | ||||
\(241\) | − | 9.52147i | − | 0.613332i | −0.951817 | − | 0.306666i | \(-0.900787\pi\) | ||
0.951817 | − | 0.306666i | \(-0.0992135\pi\) | |||||||
\(242\) | 7.66305 | − | 7.66305i | 0.492600 | − | 0.492600i | ||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | −7.51118 | −0.480854 | ||||||||
\(245\) | −12.2046 | − | 11.3246i | −0.779721 | − | 0.723503i | ||||
\(246\) | 5.69885 | 0.363346 | ||||||||
\(247\) | 11.0736 | + | 11.0736i | 0.704598 | + | 0.704598i | ||||
\(248\) | −2.35950 | − | 2.35950i | −0.149828 | − | 0.149828i | ||||
\(249\) | −17.4949 | −1.10870 | ||||||||
\(250\) | 11.1101 | − | 1.25117i | 0.702665 | − | 0.0791310i | ||||
\(251\) | − | 2.75797i | − | 0.174082i | −0.996205 | − | 0.0870409i | \(-0.972259\pi\) | ||
0.996205 | − | 0.0870409i | \(-0.0277411\pi\) | |||||||
\(252\) | 2.68754 | + | 2.68754i | 0.169299 | + | 0.169299i | ||||
\(253\) | −1.65778 | + | 0.998189i | −0.104224 | + | 0.0627556i | ||||
\(254\) | 13.9199i | 0.873413i | ||||||||
\(255\) | −11.4899 | − | 10.6615i | −0.719526 | − | 0.667648i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.31593 | − | 4.31593i | 0.269220 | − | 0.269220i | −0.559566 | − | 0.828786i | \(-0.689032\pi\) |
0.828786 | + | 0.559566i | \(0.189032\pi\) | |||||||
\(258\) | 2.56936 | − | 2.56936i | 0.159961 | − | 0.159961i | ||||
\(259\) | − | 11.6709i | − | 0.725196i | ||||||
\(260\) | −0.251289 | − | 6.71923i | −0.0155843 | − | 0.416709i | ||||
\(261\) | −9.42076 | −0.583130 | ||||||||
\(262\) | −0.773709 | + | 0.773709i | −0.0477999 | + | 0.0477999i | ||||
\(263\) | −4.09411 | + | 4.09411i | −0.252453 | + | 0.252453i | −0.821976 | − | 0.569522i | \(-0.807128\pi\) |
0.569522 | + | 0.821976i | \(0.307128\pi\) | |||||||
\(264\) | 0.403497 | 0.0248335 | ||||||||
\(265\) | 0.174445 | + | 4.66451i | 0.0107161 | + | 0.286538i | ||||
\(266\) | −19.7942 | −1.21366 | ||||||||
\(267\) | −4.40639 | − | 4.40639i | −0.269667 | − | 0.269667i | ||||
\(268\) | −4.60755 | + | 4.60755i | −0.281451 | + | 0.281451i | ||||
\(269\) | 30.5379i | 1.86193i | 0.365111 | + | 0.930964i | \(0.381031\pi\) | ||||
−0.365111 | + | 0.930964i | \(0.618969\pi\) | |||||||
\(270\) | −1.63913 | − | 1.52094i | −0.0997540 | − | 0.0925617i | ||||
\(271\) | −14.3414 | −0.871178 | −0.435589 | − | 0.900146i | \(-0.643460\pi\) | ||||
−0.435589 | + | 0.900146i | \(0.643460\pi\) | |||||||
\(272\) | −4.95666 | − | 4.95666i | −0.300542 | − | 0.300542i | ||||
\(273\) | 8.08153 | − | 8.08153i | 0.489116 | − | 0.489116i | ||||
\(274\) | −19.6791 | −1.18885 | ||||||||
\(275\) | 2.01185 | − | 0.150691i | 0.121319 | − | 0.00908700i | ||||
\(276\) | 4.65445 | + | 1.15590i | 0.280165 | + | 0.0695772i | ||||
\(277\) | 2.49148 | − | 2.49148i | 0.149698 | − | 0.149698i | −0.628285 | − | 0.777983i | \(-0.716243\pi\) |
0.777983 | + | 0.628285i | \(0.216243\pi\) | |||||||
\(278\) | 14.0107 | + | 14.0107i | 0.840304 | + | 0.840304i | ||||
\(279\) | 3.33683i | 0.199771i | ||||||||
\(280\) | 6.22992 | + | 5.78074i | 0.372309 | + | 0.345465i | ||||
\(281\) | 24.3745i | 1.45406i | 0.686604 | + | 0.727031i | \(0.259100\pi\) | ||||
−0.686604 | + | 0.727031i | \(0.740900\pi\) | |||||||
\(282\) | 8.64413 | − | 8.64413i | 0.514751 | − | 0.514751i | ||||
\(283\) | −1.55632 | + | 1.55632i | −0.0925135 | + | 0.0925135i | −0.751849 | − | 0.659335i | \(-0.770838\pi\) |
0.659335 | + | 0.751849i | \(0.270838\pi\) | |||||||
\(284\) | 5.45281i | 0.323565i | ||||||||
\(285\) | 11.6372 | − | 0.435213i | 0.689328 | − | 0.0257798i | ||||
\(286\) | − | 1.21333i | − | 0.0717457i | ||||||
\(287\) | 15.3159 | + | 15.3159i | 0.904070 | + | 0.904070i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 32.1370i | 1.89041i | ||||||||
\(290\) | −21.0507 | + | 0.787264i | −1.23614 | + | 0.0462298i | ||||
\(291\) | − | 11.6762i | − | 0.684470i | ||||||
\(292\) | 1.06175 | − | 1.06175i | 0.0621343 | − | 0.0621343i | ||||
\(293\) | 16.6999 | − | 16.6999i | 0.975619 | − | 0.975619i | −0.0240909 | − | 0.999710i | \(-0.507669\pi\) |
0.999710 | + | 0.0240909i | \(0.00766911\pi\) | |||||||
\(294\) | 7.44578i | 0.434247i | ||||||||
\(295\) | 21.9648 | + | 20.3812i | 1.27884 | + | 1.18664i | ||||
\(296\) | 3.07068i | 0.178480i | ||||||||
\(297\) | −0.285316 | − | 0.285316i | −0.0165557 | − | 0.0165557i | ||||
\(298\) | 7.87934 | − | 7.87934i | 0.456438 | − | 0.456438i | ||||
\(299\) | 3.47584 | − | 13.9961i | 0.201013 | − | 0.809414i | ||||
\(300\) | −3.78974 | − | 3.26158i | −0.218800 | − | 0.188307i | ||||
\(301\) | 13.8105 | 0.796026 | ||||||||
\(302\) | 14.1176 | − | 14.1176i | 0.812375 | − | 0.812375i | ||||
\(303\) | −5.00944 | − | 5.00944i | −0.287785 | − | 0.287785i | ||||
\(304\) | 5.20795 | 0.298697 | ||||||||
\(305\) | 12.3118 | + | 11.4241i | 0.704970 | + | 0.654141i | ||||
\(306\) | 7.00978i | 0.400723i | ||||||||
\(307\) | 2.34796 | − | 2.34796i | 0.134005 | − | 0.134005i | −0.636923 | − | 0.770928i | \(-0.719793\pi\) |
0.770928 | + | 0.636923i | \(0.219793\pi\) | |||||||
\(308\) | 1.08442 | + | 1.08442i | 0.0617903 | + | 0.0617903i | ||||
\(309\) | 9.71622 | 0.552737 | ||||||||
\(310\) | 0.278849 | + | 7.45617i | 0.0158376 | + | 0.423482i | ||||
\(311\) | 12.8558 | 0.728988 | 0.364494 | − | 0.931206i | \(-0.381242\pi\) | ||||
0.364494 | + | 0.931206i | \(0.381242\pi\) | |||||||
\(312\) | −2.12629 | + | 2.12629i | −0.120378 | + | 0.120378i | ||||
\(313\) | 3.38173 | − | 3.38173i | 0.191147 | − | 0.191147i | −0.605045 | − | 0.796192i | \(-0.706845\pi\) |
0.796192 | + | 0.605045i | \(0.206845\pi\) | |||||||
\(314\) | 3.45763 | 0.195125 | ||||||||
\(315\) | −0.317618 | − | 8.49282i | −0.0178958 | − | 0.478516i | ||||
\(316\) | 0.383565i | 0.0215772i | ||||||||
\(317\) | 16.1019 | − | 16.1019i | 0.904375 | − | 0.904375i | −0.0914360 | − | 0.995811i | \(-0.529146\pi\) |
0.995811 | + | 0.0914360i | \(0.0291457\pi\) | |||||||
\(318\) | 1.47608 | − | 1.47608i | 0.0827743 | − | 0.0827743i | ||||
\(319\) | −3.80125 | −0.212829 | ||||||||
\(320\) | −1.63913 | − | 1.52094i | −0.0916299 | − | 0.0850233i | ||||
\(321\) | 4.44997i | 0.248373i | ||||||||
\(322\) | 9.40249 | + | 15.6156i | 0.523980 | + | 0.870222i | ||||
\(323\) | −25.8141 | − | 25.8141i | −1.43633 | − | 1.43633i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −9.80768 | + | 11.3959i | −0.544032 | + | 0.632128i | ||||
\(326\) | 0.337320 | 0.0186824 | ||||||||
\(327\) | 8.97323 | + | 8.97323i | 0.496221 | + | 0.496221i | ||||
\(328\) | −4.02970 | − | 4.02970i | −0.222503 | − | 0.222503i | ||||
\(329\) | 46.4630 | 2.56159 | ||||||||
\(330\) | −0.661382 | − | 0.613696i | −0.0364079 | − | 0.0337829i | ||||
\(331\) | 11.6757 | 0.641756 | 0.320878 | − | 0.947120i | \(-0.396022\pi\) | ||||
0.320878 | + | 0.947120i | \(0.396022\pi\) | |||||||
\(332\) | 12.3708 | + | 12.3708i | 0.678934 | + | 0.678934i | ||||
\(333\) | 2.17130 | − | 2.17130i | 0.118986 | − | 0.118986i | ||||
\(334\) | − | 9.10312i | − | 0.498101i | ||||||
\(335\) | 14.5602 | − | 0.544528i | 0.795508 | − | 0.0297507i | ||||
\(336\) | − | 3.80076i | − | 0.207348i | ||||||
\(337\) | 10.5109 | + | 10.5109i | 0.572567 | + | 0.572567i | 0.932845 | − | 0.360278i | \(-0.117318\pi\) |
−0.360278 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(338\) | −2.79856 | − | 2.79856i | −0.152221 | − | 0.152221i | ||||
\(339\) | 12.6784 | 0.688597 | ||||||||
\(340\) | 0.585786 | + | 15.6634i | 0.0317687 | + | 0.849467i | ||||
\(341\) | 1.34640i | 0.0729117i | ||||||||
\(342\) | −3.68258 | − | 3.68258i | −0.199131 | − | 0.199131i | ||||
\(343\) | −1.19805 | + | 1.19805i | −0.0646884 | + | 0.0646884i | ||||
\(344\) | −3.63363 | −0.195912 | ||||||||
\(345\) | −5.87116 | − | 8.97382i | −0.316093 | − | 0.483134i | ||||
\(346\) | −8.33634 | −0.448164 | ||||||||
\(347\) | −17.9614 | + | 17.9614i | −0.964218 | + | 0.964218i | −0.999382 | − | 0.0351639i | \(-0.988805\pi\) |
0.0351639 | + | 0.999382i | \(0.488805\pi\) | |||||||
\(348\) | 6.66148 | + | 6.66148i | 0.357093 | + | 0.357093i | ||||
\(349\) | − | 18.2166i | − | 0.975113i | −0.873092 | − | 0.487556i | \(-0.837888\pi\) | ||
0.873092 | − | 0.487556i | \(-0.162112\pi\) | |||||||
\(350\) | −1.41944 | − | 18.9507i | −0.0758722 | − | 1.01296i | ||||
\(351\) | 3.00703 | 0.160504 | ||||||||
\(352\) | −0.285316 | − | 0.285316i | −0.0152074 | − | 0.0152074i | ||||
\(353\) | −13.3386 | − | 13.3386i | −0.709942 | − | 0.709942i | 0.256581 | − | 0.966523i | \(-0.417404\pi\) |
−0.966523 | + | 0.256581i | \(0.917404\pi\) | |||||||
\(354\) | − | 13.4003i | − | 0.712220i | ||||||
\(355\) | 8.29342 | − | 8.93784i | 0.440169 | − | 0.474371i | ||||
\(356\) | 6.23158i | 0.330273i | ||||||||
\(357\) | −18.8391 | + | 18.8391i | −0.997070 | + | 0.997070i | ||||
\(358\) | −1.96275 | − | 1.96275i | −0.103735 | − | 0.103735i | ||||
\(359\) | 23.6679 | 1.24915 | 0.624573 | − | 0.780967i | \(-0.285273\pi\) | ||||
0.624573 | + | 0.780967i | \(0.285273\pi\) | |||||||
\(360\) | 0.0835670 | + | 2.23451i | 0.00440437 | + | 0.117769i | ||||
\(361\) | 8.12277 | 0.427514 | ||||||||
\(362\) | −15.0359 | − | 15.0359i | −0.790269 | − | 0.790269i | ||||
\(363\) | 7.66305 | + | 7.66305i | 0.402206 | + | 0.402206i | ||||
\(364\) | −11.4290 | −0.599043 | ||||||||
\(365\) | −3.35521 | + | 0.125479i | −0.175620 | + | 0.00656789i | ||||
\(366\) | − | 7.51118i | − | 0.392616i | ||||||
\(367\) | 1.82999 | + | 1.82999i | 0.0955248 | + | 0.0955248i | 0.753254 | − | 0.657729i | \(-0.228483\pi\) |
−0.657729 | + | 0.753254i | \(0.728483\pi\) | |||||||
\(368\) | −2.47384 | − | 4.10854i | −0.128958 | − | 0.214172i | ||||
\(369\) | 5.69885i | 0.296670i | ||||||||
\(370\) | 4.67033 | − | 5.03323i | 0.242799 | − | 0.261665i | ||||
\(371\) | 7.93404 | 0.411915 | ||||||||
\(372\) | 2.35950 | − | 2.35950i | 0.122334 | − | 0.122334i | ||||
\(373\) | −4.97536 | + | 4.97536i | −0.257615 | + | 0.257615i | −0.824083 | − | 0.566469i | \(-0.808309\pi\) |
0.566469 | + | 0.824083i | \(0.308309\pi\) | |||||||
\(374\) | 2.82843i | 0.146254i | ||||||||
\(375\) | 1.25117 | + | 11.1101i | 0.0646102 | + | 0.573724i | ||||
\(376\) | −12.2247 | −0.630438 | ||||||||
\(377\) | 20.0313 | − | 20.0313i | 1.03166 | − | 1.03166i | ||||
\(378\) | −2.68754 | + | 2.68754i | −0.138232 | + | 0.138232i | ||||
\(379\) | 3.53426 | 0.181543 | 0.0907714 | − | 0.995872i | \(-0.471067\pi\) | ||||
0.0907714 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(380\) | −8.53649 | − | 7.92100i | −0.437912 | − | 0.406339i | ||||
\(381\) | −13.9199 | −0.713138 | ||||||||
\(382\) | 11.0264 | + | 11.0264i | 0.564160 | + | 0.564160i | ||||
\(383\) | −13.8129 | + | 13.8129i | −0.705805 | + | 0.705805i | −0.965650 | − | 0.259845i | \(-0.916329\pi\) |
0.259845 | + | 0.965650i | \(0.416329\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −0.128158 | − | 3.42683i | −0.00653154 | − | 0.174647i | ||||
\(386\) | −9.89468 | −0.503626 | ||||||||
\(387\) | 2.56936 | + | 2.56936i | 0.130608 | + | 0.130608i | ||||
\(388\) | −8.25631 | + | 8.25631i | −0.419150 | + | 0.419150i | ||||
\(389\) | 6.63285 | 0.336299 | 0.168149 | − | 0.985762i | \(-0.446221\pi\) | ||||
0.168149 | + | 0.985762i | \(0.446221\pi\) | |||||||
\(390\) | 6.71923 | − | 0.251289i | 0.340242 | − | 0.0127245i | ||||
\(391\) | −8.10263 | + | 32.6267i | −0.409768 | + | 1.65000i | ||||
\(392\) | 5.26496 | − | 5.26496i | 0.265921 | − | 0.265921i | ||||
\(393\) | −0.773709 | − | 0.773709i | −0.0390284 | − | 0.0390284i | ||||
\(394\) | − | 7.02162i | − | 0.353744i | ||||||
\(395\) | 0.583380 | − | 0.628711i | 0.0293530 | − | 0.0316339i | ||||
\(396\) | 0.403497i | 0.0202765i | ||||||||
\(397\) | −6.61498 | + | 6.61498i | −0.331996 | + | 0.331996i | −0.853344 | − | 0.521348i | \(-0.825429\pi\) |
0.521348 | + | 0.853344i | \(0.325429\pi\) | |||||||
\(398\) | −9.34856 | + | 9.34856i | −0.468601 | + | 0.468601i | ||||
\(399\) | − | 19.7942i | − | 0.990948i | ||||||
\(400\) | 0.373462 | + | 4.98603i | 0.0186731 | + | 0.249302i | ||||
\(401\) | 9.81654i | 0.490215i | 0.969496 | + | 0.245107i | \(0.0788232\pi\) | ||||
−0.969496 | + | 0.245107i | \(0.921177\pi\) | |||||||
\(402\) | −4.60755 | − | 4.60755i | −0.229804 | − | 0.229804i | ||||
\(403\) | −7.09508 | − | 7.09508i | −0.353431 | − | 0.353431i | ||||
\(404\) | 7.08442i | 0.352463i | ||||||||
\(405\) | 1.52094 | − | 1.63913i | 0.0755763 | − | 0.0814488i | ||||
\(406\) | 35.8060i | 1.77702i | ||||||||
\(407\) | 0.876113 | − | 0.876113i | 0.0434273 | − | 0.0434273i | ||||
\(408\) | 4.95666 | − | 4.95666i | 0.245391 | − | 0.245391i | ||||
\(409\) | 1.62998i | 0.0805974i | 0.999188 | + | 0.0402987i | \(0.0128309\pi\) | ||||
−0.999188 | + | 0.0402987i | \(0.987169\pi\) | |||||||
\(410\) | 0.476236 | + | 12.7341i | 0.0235196 | + | 0.628893i | ||||
\(411\) | − | 19.6791i | − | 0.970696i | ||||||
\(412\) | −6.87041 | − | 6.87041i | −0.338481 | − | 0.338481i | ||||
\(413\) | 36.0140 | − | 36.0140i | 1.77213 | − | 1.77213i | ||||
\(414\) | −1.15590 | + | 4.65445i | −0.0568096 | + | 0.228754i | ||||
\(415\) | −1.46200 | − | 39.0925i | −0.0717666 | − | 1.91897i | ||||
\(416\) | 3.00703 | 0.147432 | ||||||||
\(417\) | −14.0107 | + | 14.0107i | −0.686105 | + | 0.686105i | ||||
\(418\) | −1.48591 | − | 1.48591i | −0.0726782 | − | 0.0726782i | ||||
\(419\) | −11.2744 | −0.550791 | −0.275395 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275395 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(420\) | −5.78074 | + | 6.22992i | −0.282071 | + | 0.303989i | ||||
\(421\) | 16.1033i | 0.784825i | 0.919789 | + | 0.392412i | \(0.128359\pi\) | ||||
−0.919789 | + | 0.392412i | \(0.871641\pi\) | |||||||
\(422\) | 10.1407 | − | 10.1407i | 0.493643 | − | 0.493643i | ||||
\(423\) | 8.64413 | + | 8.64413i | 0.420292 | + | 0.420292i | ||||
\(424\) | −2.08749 | −0.101377 | ||||||||
\(425\) | 22.8630 | − | 26.5652i | 1.10902 | − | 1.28860i | ||||
\(426\) | −5.45281 | −0.264189 | ||||||||
\(427\) | 20.1866 | − | 20.1866i | 0.976899 | − | 0.976899i | ||||
\(428\) | 3.14660 | − | 3.14660i | 0.152097 | − | 0.152097i | ||||
\(429\) | 1.21333 | 0.0585801 | ||||||||
\(430\) | 5.95597 | + | 5.52654i | 0.287222 | + | 0.266513i | ||||
\(431\) | 37.5672i | 1.80955i | 0.425894 | + | 0.904773i | \(0.359960\pi\) | ||||
−0.425894 | + | 0.904773i | \(0.640040\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −19.4771 | + | 19.4771i | −0.936012 | + | 0.936012i | −0.998072 | − | 0.0620607i | \(-0.980233\pi\) |
0.0620607 | + | 0.998072i | \(0.480233\pi\) | |||||||
\(434\) | 12.6825 | 0.608779 | ||||||||
\(435\) | −0.787264 | − | 21.0507i | −0.0377464 | − | 1.00931i | ||||
\(436\) | − | 12.6901i | − | 0.607744i | ||||||
\(437\) | −12.8837 | − | 21.3971i | −0.616309 | − | 1.02356i | ||||
\(438\) | 1.06175 | + | 1.06175i | 0.0507324 | + | 0.0507324i | ||||
\(439\) | 27.5197i | 1.31344i | 0.754133 | + | 0.656721i | \(0.228057\pi\) | ||||
−0.754133 | + | 0.656721i | \(0.771943\pi\) | |||||||
\(440\) | 0.0337191 | + | 0.901617i | 0.00160749 | + | 0.0429829i | ||||
\(441\) | −7.44578 | −0.354561 | ||||||||
\(442\) | −14.9048 | − | 14.9048i | −0.708951 | − | 0.708951i | ||||
\(443\) | 21.8369 | + | 21.8369i | 1.03750 | + | 1.03750i | 0.999269 | + | 0.0382321i | \(0.0121726\pi\) |
0.0382321 | + | 0.999269i | \(0.487827\pi\) | |||||||
\(444\) | −3.07068 | −0.145728 | ||||||||
\(445\) | 9.47788 | − | 10.2143i | 0.449295 | − | 0.484206i | ||||
\(446\) | −14.8202 | −0.701757 | ||||||||
\(447\) | 7.87934 | + | 7.87934i | 0.372680 | + | 0.372680i | ||||
\(448\) | −2.68754 | + | 2.68754i | −0.126974 | + | 0.126974i | ||||
\(449\) | − | 3.81966i | − | 0.180261i | −0.995930 | − | 0.0901306i | \(-0.971272\pi\) | ||
0.995930 | − | 0.0901306i | \(-0.0287284\pi\) | |||||||
\(450\) | 3.26158 | − | 3.78974i | 0.153752 | − | 0.178650i | ||||
\(451\) | 2.29947i | 0.108278i | ||||||||
\(452\) | −8.96499 | − | 8.96499i | −0.421678 | − | 0.421678i | ||||
\(453\) | 14.1176 | + | 14.1176i | 0.663301 | + | 0.663301i | ||||
\(454\) | 0.552361 | 0.0259236 | ||||||||
\(455\) | 18.7336 | + | 17.3829i | 0.878244 | + | 0.814922i | ||||
\(456\) | 5.20795i | 0.243885i | ||||||||
\(457\) | −19.1698 | − | 19.1698i | −0.896726 | − | 0.896726i | 0.0984194 | − | 0.995145i | \(-0.468621\pi\) |
−0.995145 | + | 0.0984194i | \(0.968621\pi\) | |||||||
\(458\) | 11.3258 | − | 11.3258i | 0.529218 | − | 0.529218i | ||||
\(459\) | −7.00978 | −0.327189 | ||||||||
\(460\) | −2.19392 | + | 10.4970i | −0.102292 | + | 0.489425i | ||||
\(461\) | −23.5334 | −1.09606 | −0.548029 | − | 0.836459i | \(-0.684622\pi\) | ||||
−0.548029 | + | 0.836459i | \(0.684622\pi\) | |||||||
\(462\) | −1.08442 | + | 1.08442i | −0.0504516 | + | 0.0504516i | ||||
\(463\) | 20.0945 | + | 20.0945i | 0.933869 | + | 0.933869i | 0.997945 | − | 0.0640760i | \(-0.0204100\pi\) |
−0.0640760 | + | 0.997945i | \(0.520410\pi\) | |||||||
\(464\) | − | 9.42076i | − | 0.437348i | ||||||
\(465\) | −7.45617 | + | 0.278849i | −0.345771 | + | 0.0129313i | ||||
\(466\) | −18.5016 | −0.857070 | ||||||||
\(467\) | −8.34291 | − | 8.34291i | −0.386064 | − | 0.386064i | 0.487217 | − | 0.873281i | \(-0.338012\pi\) |
−0.873281 | + | 0.487217i | \(0.838012\pi\) | |||||||
\(468\) | −2.12629 | − | 2.12629i | −0.0982879 | − | 0.0982879i | ||||
\(469\) | − | 24.7660i | − | 1.14359i | ||||||
\(470\) | 20.0377 | + | 18.5930i | 0.924272 | + | 0.857631i | ||||
\(471\) | 3.45763i | 0.159319i | ||||||||
\(472\) | −9.47547 | + | 9.47547i | −0.436144 | + | 0.436144i | ||||
\(473\) | 1.03673 | + | 1.03673i | 0.0476689 | + | 0.0476689i | ||||
\(474\) | −0.383565 | −0.0176177 | ||||||||
\(475\) | 1.94497 | + | 25.9670i | 0.0892414 | + | 1.19145i | ||||
\(476\) | 26.6425 | 1.22116 | ||||||||
\(477\) | 1.47608 | + | 1.47608i | 0.0675849 | + | 0.0675849i | ||||
\(478\) | 10.4923 | + | 10.4923i | 0.479908 | + | 0.479908i | ||||
\(479\) | −21.0887 | −0.963565 | −0.481783 | − | 0.876291i | \(-0.660011\pi\) | ||||
−0.481783 | + | 0.876291i | \(0.660011\pi\) | |||||||
\(480\) | 1.52094 | − | 1.63913i | 0.0694213 | − | 0.0748155i | ||||
\(481\) | 9.23364i | 0.421018i | ||||||||
\(482\) | −6.73270 | − | 6.73270i | −0.306666 | − | 0.306666i | ||||
\(483\) | −15.6156 | + | 9.40249i | −0.710533 | + | 0.427828i | ||||
\(484\) | − | 10.8372i | − | 0.492600i | ||||||
\(485\) | 26.0905 | − | 0.975743i | 1.18471 | − | 0.0443062i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −0.859666 | + | 0.859666i | −0.0389552 | + | 0.0389552i | −0.726316 | − | 0.687361i | \(-0.758769\pi\) |
0.687361 | + | 0.726316i | \(0.258769\pi\) | |||||||
\(488\) | −5.31121 | + | 5.31121i | −0.240427 | + | 0.240427i | ||||
\(489\) | 0.337320i | 0.0152541i | ||||||||
\(490\) | −16.6376 | + | 0.622221i | −0.751612 | + | 0.0281091i | ||||
\(491\) | −27.6182 | −1.24639 | −0.623197 | − | 0.782065i | \(-0.714166\pi\) | ||||
−0.623197 | + | 0.782065i | \(0.714166\pi\) | |||||||
\(492\) | 4.02970 | − | 4.02970i | 0.181673 | − | 0.181673i | ||||
\(493\) | −46.6955 | + | 46.6955i | −2.10306 | + | 2.10306i | ||||
\(494\) | 15.6605 | 0.704598 | ||||||||
\(495\) | 0.613696 | − | 0.661382i | 0.0275836 | − | 0.0297269i | ||||
\(496\) | −3.33683 | −0.149828 | ||||||||
\(497\) | −14.6547 | − | 14.6547i | −0.657351 | − | 0.657351i | ||||
\(498\) | −12.3708 | + | 12.3708i | −0.554348 | + | 0.554348i | ||||
\(499\) | − | 18.6771i | − | 0.836101i | −0.908424 | − | 0.418051i | \(-0.862713\pi\) | ||
0.908424 | − | 0.418051i | \(-0.137287\pi\) | |||||||
\(500\) | 6.97132 | − | 8.74075i | 0.311767 | − | 0.390898i | ||||
\(501\) | 9.10312 | 0.406697 | ||||||||
\(502\) | −1.95018 | − | 1.95018i | −0.0870409 | − | 0.0870409i | ||||
\(503\) | 2.24840 | − | 2.24840i | 0.100251 | − | 0.100251i | −0.655202 | − | 0.755453i | \(-0.727417\pi\) |
0.755453 | + | 0.655202i | \(0.227417\pi\) | |||||||
\(504\) | 3.80076 | 0.169299 | ||||||||
\(505\) | 10.7750 | − | 11.6122i | 0.479481 | − | 0.516738i | ||||
\(506\) | −0.466404 | + | 1.87806i | −0.0207342 | + | 0.0834898i | ||||
\(507\) | 2.79856 | − | 2.79856i | 0.124288 | − | 0.124288i | ||||
\(508\) | 9.84286 | + | 9.84286i | 0.436706 | + | 0.436706i | ||||
\(509\) | 10.9101i | 0.483582i | 0.970328 | + | 0.241791i | \(0.0777348\pi\) | ||||
−0.970328 | + | 0.241791i | \(0.922265\pi\) | |||||||
\(510\) | −15.6634 | + | 0.585786i | −0.693587 | + | 0.0259391i | ||||
\(511\) | 5.70700i | 0.252463i | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 3.68258 | − | 3.68258i | 0.162590 | − | 0.162590i | ||||
\(514\) | − | 6.10364i | − | 0.269220i | ||||||
\(515\) | 0.811956 | + | 21.7110i | 0.0357790 | + | 0.956699i | ||||
\(516\) | − | 3.63363i | − | 0.159961i | ||||||
\(517\) | 3.48788 | + | 3.48788i | 0.153397 | + | 0.153397i | ||||
\(518\) | −8.25259 | − | 8.25259i | −0.362598 | − | 0.362598i | ||||
\(519\) | − | 8.33634i | − | 0.365925i | ||||||
\(520\) | −4.92890 | − | 4.57353i | −0.216147 | − | 0.200562i | ||||
\(521\) | − | 31.7519i | − | 1.39108i | −0.718489 | − | 0.695539i | \(-0.755166\pi\) | ||
0.718489 | − | 0.695539i | \(-0.244834\pi\) | |||||||
\(522\) | −6.66148 | + | 6.66148i | −0.291565 | + | 0.291565i | ||||
\(523\) | 17.6479 | − | 17.6479i | 0.771687 | − | 0.771687i | −0.206714 | − | 0.978401i | \(-0.566277\pi\) |
0.978401 | + | 0.206714i | \(0.0662771\pi\) | |||||||
\(524\) | 1.09419i | 0.0477999i | ||||||||
\(525\) | 18.9507 | − | 1.41944i | 0.827077 | − | 0.0619494i | ||||
\(526\) | 5.78994i | 0.252453i | ||||||||
\(527\) | 16.5395 | + | 16.5395i | 0.720474 | + | 0.720474i | ||||
\(528\) | 0.285316 | − | 0.285316i | 0.0124168 | − | 0.0124168i | ||||
\(529\) | −10.7602 | + | 20.3278i | −0.467834 | + | 0.883816i | ||||
\(530\) | 3.42165 | + | 3.17495i | 0.148627 | + | 0.137911i | ||||
\(531\) | 13.4003 | 0.581525 | ||||||||
\(532\) | −13.9966 | + | 13.9966i | −0.606829 | + | 0.606829i | ||||
\(533\) | −12.1174 | − | 12.1174i | −0.524864 | − | 0.524864i | ||||
\(534\) | −6.23158 | −0.269667 | ||||||||
\(535\) | −9.94348 | + | 0.371871i | −0.429894 | + | 0.0160774i | ||||
\(536\) | 6.51606i | 0.281451i | ||||||||
\(537\) | 1.96275 | − | 1.96275i | 0.0846989 | − | 0.0846989i | ||||
\(538\) | 21.5936 | + | 21.5936i | 0.930964 | + | 0.930964i | ||||
\(539\) | −3.00435 | −0.129407 | ||||||||
\(540\) | −2.23451 | + | 0.0835670i | −0.0961578 | + | 0.00359615i | ||||
\(541\) | 33.4617 | 1.43863 | 0.719315 | − | 0.694684i | \(-0.244456\pi\) | ||||
0.719315 | + | 0.694684i | \(0.244456\pi\) | |||||||
\(542\) | −10.1409 | + | 10.1409i | −0.435589 | + | 0.435589i | ||||
\(543\) | 15.0359 | − | 15.0359i | 0.645252 | − | 0.645252i | ||||
\(544\) | −7.00978 | −0.300542 | ||||||||
\(545\) | −19.3009 | + | 20.8006i | −0.826758 | + | 0.890999i | ||||
\(546\) | − | 11.4290i | − | 0.489116i | ||||||
\(547\) | −12.8216 | + | 12.8216i | −0.548213 | + | 0.548213i | −0.925924 | − | 0.377711i | \(-0.876711\pi\) |
0.377711 | + | 0.925924i | \(0.376711\pi\) | |||||||
\(548\) | −13.9152 | + | 13.9152i | −0.594427 | + | 0.594427i | ||||
\(549\) | 7.51118 | 0.320569 | ||||||||
\(550\) | 1.31604 | − | 1.52915i | 0.0561161 | − | 0.0652031i | ||||
\(551\) | − | 49.0629i | − | 2.09015i | ||||||
\(552\) | 4.10854 | − | 2.47384i | 0.174871 | − | 0.105294i | ||||
\(553\) | −1.03085 | − | 1.03085i | −0.0438361 | − | 0.0438361i | ||||
\(554\) | − | 3.52348i | − | 0.149698i | ||||||
\(555\) | 5.03323 | + | 4.67033i | 0.213649 | + | 0.198245i | ||||
\(556\) | 19.8141 | 0.840304 | ||||||||
\(557\) | 14.8590 | + | 14.8590i | 0.629594 | + | 0.629594i | 0.947966 | − | 0.318372i | \(-0.103136\pi\) |
−0.318372 | + | 0.947966i | \(0.603136\pi\) | |||||||
\(558\) | 2.35950 | + | 2.35950i | 0.0998854 | + | 0.0998854i | ||||
\(559\) | −10.9264 | −0.462139 | ||||||||
\(560\) | 8.49282 | − | 0.317618i | 0.358887 | − | 0.0134218i | ||||
\(561\) | −2.82843 | −0.119416 | ||||||||
\(562\) | 17.2354 | + | 17.2354i | 0.727031 | + | 0.727031i | ||||
\(563\) | 2.14137 | − | 2.14137i | 0.0902478 | − | 0.0902478i | −0.660542 | − | 0.750789i | \(-0.729673\pi\) |
0.750789 | + | 0.660542i | \(0.229673\pi\) | |||||||
\(564\) | − | 12.2247i | − | 0.514751i | ||||||
\(565\) | 1.05950 | + | 28.3300i | 0.0445734 | + | 1.19185i | ||||
\(566\) | 2.20097i | 0.0925135i | ||||||||
\(567\) | −2.68754 | − | 2.68754i | −0.112866 | − | 0.112866i | ||||
\(568\) | 3.85572 | + | 3.85572i | 0.161782 | + | 0.161782i | ||||
\(569\) | −44.6987 | −1.87387 | −0.936934 | − | 0.349506i | \(-0.886350\pi\) | ||||
−0.936934 | + | 0.349506i | \(0.886350\pi\) | |||||||
\(570\) | 7.92100 | − | 8.53649i | 0.331774 | − | 0.357554i | ||||
\(571\) | 26.7672i | 1.12017i | 0.828435 | + | 0.560085i | \(0.189232\pi\) | ||||
−0.828435 | + | 0.560085i | \(0.810768\pi\) | |||||||
\(572\) | −0.857953 | − | 0.857953i | −0.0358728 | − | 0.0358728i | ||||
\(573\) | −11.0264 | + | 11.0264i | −0.460635 | + | 0.460635i | ||||
\(574\) | 21.6600 | 0.904070 | ||||||||
\(575\) | 19.5614 | − | 13.8691i | 0.815768 | − | 0.578380i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | −14.2226 | + | 14.2226i | −0.592095 | + | 0.592095i | −0.938197 | − | 0.346102i | \(-0.887505\pi\) |
0.346102 | + | 0.938197i | \(0.387505\pi\) | |||||||
\(578\) | 22.7243 | + | 22.7243i | 0.945207 | + | 0.945207i | ||||
\(579\) | − | 9.89468i | − | 0.411209i | ||||||
\(580\) | −14.3284 | + | 15.4418i | −0.594956 | + | 0.641186i | ||||
\(581\) | −66.4940 | −2.75863 | ||||||||
\(582\) | −8.25631 | − | 8.25631i | −0.342235 | − | 0.342235i | ||||
\(583\) | 0.595593 | + | 0.595593i | 0.0246669 | + | 0.0246669i | ||||
\(584\) | − | 1.50154i | − | 0.0621343i | ||||||
\(585\) | 0.251289 | + | 6.71923i | 0.0103895 | + | 0.277806i | ||||
\(586\) | − | 23.6172i | − | 0.975619i | ||||||
\(587\) | −7.01819 | + | 7.01819i | −0.289672 | + | 0.289672i | −0.836950 | − | 0.547279i | \(-0.815664\pi\) |
0.547279 | + | 0.836950i | \(0.315664\pi\) | |||||||
\(588\) | 5.26496 | + | 5.26496i | 0.217123 | + | 0.217123i | ||||
\(589\) | −17.3781 | −0.716050 | ||||||||
\(590\) | 29.9431 | − | 1.11983i | 1.23274 | − | 0.0461025i | ||||
\(591\) | 7.02162 | 0.288831 | ||||||||
\(592\) | 2.17130 | + | 2.17130i | 0.0892398 | + | 0.0892398i | ||||
\(593\) | −22.3974 | − | 22.3974i | −0.919752 | − | 0.919752i | 0.0772588 | − | 0.997011i | \(-0.475383\pi\) |
−0.997011 | + | 0.0772588i | \(0.975383\pi\) | |||||||
\(594\) | −0.403497 | −0.0165557 | ||||||||
\(595\) | −43.6704 | − | 40.5217i | −1.79031 | − | 1.66123i | ||||
\(596\) | − | 11.1431i | − | 0.456438i | ||||||
\(597\) | −9.34856 | − | 9.34856i | −0.382611 | − | 0.382611i | ||||
\(598\) | −7.43893 | − | 12.3545i | −0.304201 | − | 0.505214i | ||||
\(599\) | − | 2.54190i | − | 0.103859i | −0.998651 | − | 0.0519296i | \(-0.983463\pi\) | ||
0.998651 | − | 0.0519296i | \(-0.0165371\pi\) | |||||||
\(600\) | −4.98603 | + | 0.373462i | −0.203554 | + | 0.0152465i | ||||
\(601\) | −15.8155 | −0.645130 | −0.322565 | − | 0.946547i | \(-0.604545\pi\) | ||||
−0.322565 | + | 0.946547i | \(0.604545\pi\) | |||||||
\(602\) | 9.76553 | − | 9.76553i | 0.398013 | − | 0.398013i | ||||
\(603\) | 4.60755 | − | 4.60755i | 0.187634 | − | 0.187634i | ||||
\(604\) | − | 19.9653i | − | 0.812375i | ||||||
\(605\) | −16.4828 | + | 17.7635i | −0.670119 | + | 0.722189i | ||||
\(606\) | −7.08442 | −0.287785 | ||||||||
\(607\) | −3.60929 | + | 3.60929i | −0.146497 | + | 0.146497i | −0.776551 | − | 0.630054i | \(-0.783033\pi\) |
0.630054 | + | 0.776551i | \(0.283033\pi\) | |||||||
\(608\) | 3.68258 | − | 3.68258i | 0.149348 | − | 0.149348i | ||||
\(609\) | −35.8060 | −1.45093 | ||||||||
\(610\) | 16.7838 | − | 0.627687i | 0.679556 | − | 0.0254143i | ||||
\(611\) | −36.7599 | −1.48715 | ||||||||
\(612\) | 4.95666 | + | 4.95666i | 0.200361 | + | 0.200361i | ||||
\(613\) | 14.0673 | − | 14.0673i | 0.568173 | − | 0.568173i | −0.363444 | − | 0.931616i | \(-0.618399\pi\) |
0.931616 | + | 0.363444i | \(0.118399\pi\) | |||||||
\(614\) | − | 3.32051i | − | 0.134005i | ||||||
\(615\) | −12.7341 | + | 0.476236i | −0.513489 | + | 0.0192037i | ||||
\(616\) | 1.53360 | 0.0617903 | ||||||||
\(617\) | 31.3443 | + | 31.3443i | 1.26187 | + | 1.26187i | 0.950185 | + | 0.311688i | \(0.100894\pi\) |
0.311688 | + | 0.950185i | \(0.399106\pi\) | |||||||
\(618\) | 6.87041 | − | 6.87041i | 0.276368 | − | 0.276368i | ||||
\(619\) | −20.0495 | −0.805857 | −0.402928 | − | 0.915232i | \(-0.632008\pi\) | ||||
−0.402928 | + | 0.915232i | \(0.632008\pi\) | |||||||
\(620\) | 5.46948 | + | 5.07513i | 0.219660 | + | 0.203822i | ||||
\(621\) | −4.65445 | − | 1.15590i | −0.186777 | − | 0.0463848i | ||||
\(622\) | 9.09045 | − | 9.09045i | 0.364494 | − | 0.364494i | ||||
\(623\) | −16.7476 | − | 16.7476i | −0.670980 | − | 0.670980i | ||||
\(624\) | 3.00703i | 0.120378i | ||||||||
\(625\) | −24.7211 | + | 3.72419i | −0.988842 | + | 0.148967i | ||||
\(626\) | − | 4.78249i | − | 0.191147i | ||||||
\(627\) | 1.48591 | − | 1.48591i | 0.0593415 | − | 0.0593415i | ||||
\(628\) | 2.44491 | − | 2.44491i | 0.0975627 | − | 0.0975627i | ||||
\(629\) | − | 21.5248i | − | 0.858250i | ||||||
\(630\) | −6.22992 | − | 5.78074i | −0.248206 | − | 0.230310i | ||||
\(631\) | − | 13.0006i | − | 0.517544i | −0.965938 | − | 0.258772i | \(-0.916682\pi\) | ||
0.965938 | − | 0.258772i | \(-0.0833178\pi\) | |||||||
\(632\) | 0.271221 | + | 0.271221i | 0.0107886 | + | 0.0107886i | ||||
\(633\) | 10.1407 | + | 10.1407i | 0.403058 | + | 0.403058i | ||||
\(634\) | − | 22.7716i | − | 0.904375i | ||||||
\(635\) | −1.16324 | − | 31.1041i | −0.0461620 | − | 1.23433i | ||||
\(636\) | − | 2.08749i | − | 0.0827743i | ||||||
\(637\) | 15.8319 | − | 15.8319i | 0.627283 | − | 0.627283i | ||||
\(638\) | −2.68789 | + | 2.68789i | −0.106415 | + | 0.106415i | ||||
\(639\) | − | 5.45281i | − | 0.215710i | ||||||
\(640\) | −2.23451 | + | 0.0835670i | −0.0883266 | + | 0.00330328i | ||||
\(641\) | − | 14.0108i | − | 0.553393i | −0.960957 | − | 0.276696i | \(-0.910760\pi\) | ||
0.960957 | − | 0.276696i | \(-0.0892396\pi\) | |||||||
\(642\) | 3.14660 | + | 3.14660i | 0.124187 | + | 0.124187i | ||||
\(643\) | −10.2908 | + | 10.2908i | −0.405829 | + | 0.405829i | −0.880281 | − | 0.474452i | \(-0.842646\pi\) |
0.474452 | + | 0.880281i | \(0.342646\pi\) | |||||||
\(644\) | 17.6904 | + | 4.39331i | 0.697101 | + | 0.173121i | ||||
\(645\) | −5.52654 | + | 5.95597i | −0.217607 | + | 0.234516i | ||||
\(646\) | −36.5066 | −1.43633 | ||||||||
\(647\) | −11.8108 | + | 11.8108i | −0.464329 | + | 0.464329i | −0.900071 | − | 0.435743i | \(-0.856486\pi\) |
0.435743 | + | 0.900071i | \(0.356486\pi\) | |||||||
\(648\) | 0.707107 | + | 0.707107i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | 5.40700 | 0.212243 | ||||||||
\(650\) | 1.12301 | + | 14.9932i | 0.0440482 | + | 0.588080i | ||||
\(651\) | 12.6825i | 0.497066i | ||||||||
\(652\) | 0.238521 | − | 0.238521i | 0.00934121 | − | 0.00934121i | ||||
\(653\) | −7.33870 | − | 7.33870i | −0.287185 | − | 0.287185i | 0.548781 | − | 0.835966i | \(-0.315092\pi\) |
−0.835966 | + | 0.548781i | \(0.815092\pi\) | |||||||
\(654\) | 12.6901 | 0.496221 | ||||||||
\(655\) | 1.66420 | − | 1.79351i | 0.0650257 | − | 0.0700784i | ||||
\(656\) | −5.69885 | −0.222503 | ||||||||
\(657\) | −1.06175 | + | 1.06175i | −0.0414229 | + | 0.0414229i | ||||
\(658\) | 32.8543 | − | 32.8543i | 1.28079 | − | 1.28079i | ||||
\(659\) | −29.6115 | −1.15350 | −0.576750 | − | 0.816921i | \(-0.695679\pi\) | ||||
−0.576750 | + | 0.816921i | \(0.695679\pi\) | |||||||
\(660\) | −0.901617 | + | 0.0337191i | −0.0350954 | + | 0.00131251i | ||||
\(661\) | 0.177775i | 0.00691465i | 0.999994 | + | 0.00345732i | \(0.00110050\pi\) | ||||
−0.999994 | + | 0.00345732i | \(0.998899\pi\) | |||||||
\(662\) | 8.25599 | − | 8.25599i | 0.320878 | − | 0.320878i | ||||
\(663\) | 14.9048 | − | 14.9048i | 0.578856 | − | 0.578856i | ||||
\(664\) | 17.4949 | 0.678934 | ||||||||
\(665\) | 44.2302 | − | 1.65414i | 1.71517 | − | 0.0641448i | ||||
\(666\) | − | 3.07068i | − | 0.118986i | ||||||
\(667\) | −38.7055 | + | 23.3055i | −1.49868 | + | 0.902392i | ||||
\(668\) | −6.43688 | − | 6.43688i | −0.249050 | − | 0.249050i | ||||
\(669\) | − | 14.8202i | − | 0.572982i | ||||||
\(670\) | 9.91057 | − | 10.6806i | 0.382879 | − | 0.412629i | ||||
\(671\) | 3.03074 | 0.117000 | ||||||||
\(672\) | −2.68754 | − | 2.68754i | −0.103674 | − | 0.103674i | ||||
\(673\) | 3.91098 | + | 3.91098i | 0.150757 | + | 0.150757i | 0.778456 | − | 0.627699i | \(-0.216003\pi\) |
−0.627699 | + | 0.778456i | \(0.716003\pi\) | |||||||
\(674\) | 14.8647 | 0.572567 | ||||||||
\(675\) | 3.78974 | + | 3.26158i | 0.145867 | + | 0.125538i | ||||
\(676\) | −3.95776 | −0.152221 | ||||||||
\(677\) | −31.1105 | − | 31.1105i | −1.19567 | − | 1.19567i | −0.975450 | − | 0.220223i | \(-0.929322\pi\) |
−0.220223 | − | 0.975450i | \(-0.570678\pi\) | |||||||
\(678\) | 8.96499 | − | 8.96499i | 0.344299 | − | 0.344299i | ||||
\(679\) | − | 44.3784i | − | 1.70309i | ||||||
\(680\) | 11.4899 | + | 10.6615i | 0.440618 | + | 0.408849i | ||||
\(681\) | 0.552361i | 0.0211665i | ||||||||
\(682\) | 0.952050 | + | 0.952050i | 0.0364559 | + | 0.0364559i | ||||
\(683\) | 27.1997 | + | 27.1997i | 1.04077 | + | 1.04077i | 0.999133 | + | 0.0416348i | \(0.0132566\pi\) |
0.0416348 | + | 0.999133i | \(0.486743\pi\) | |||||||
\(684\) | −5.20795 | −0.199131 | ||||||||
\(685\) | 43.9730 | − | 1.64452i | 1.68012 | − | 0.0628339i | ||||
\(686\) | 1.69429i | 0.0646884i | ||||||||
\(687\) | 11.3258 | + | 11.3258i | 0.432104 | + | 0.432104i | ||||
\(688\) | −2.56936 | + | 2.56936i | −0.0979560 | + | 0.0979560i | ||||
\(689\) | −6.27715 | −0.239140 | ||||||||
\(690\) | −10.4970 | − | 2.19392i | −0.399613 | − | 0.0835209i | ||||
\(691\) | 31.8947 | 1.21333 | 0.606666 | − | 0.794957i | \(-0.292507\pi\) | ||||
0.606666 | + | 0.794957i | \(0.292507\pi\) | |||||||
\(692\) | −5.89468 | + | 5.89468i | −0.224082 | + | 0.224082i | ||||
\(693\) | −1.08442 | − | 1.08442i | −0.0411936 | − | 0.0411936i | ||||
\(694\) | 25.4012i | 0.964218i | ||||||||
\(695\) | −32.4777 | − | 30.1361i | −1.23195 | − | 1.14313i | ||||
\(696\) | 9.42076 | 0.357093 | ||||||||
\(697\) | 28.2473 | + | 28.2473i | 1.06994 | + | 1.06994i | ||||
\(698\) | −12.8811 | − | 12.8811i | −0.487556 | − | 0.487556i | ||||
\(699\) | − | 18.5016i | − | 0.699795i | ||||||
\(700\) | −14.4039 | − | 12.3965i | −0.544415 | − | 0.468543i | ||||
\(701\) | − | 39.2405i | − | 1.48209i | −0.671454 | − | 0.741046i | \(-0.734330\pi\) | ||
0.671454 | − | 0.741046i | \(-0.265670\pi\) | |||||||
\(702\) | 2.12629 | − | 2.12629i | 0.0802518 | − | 0.0802518i | ||||
\(703\) | 11.3080 | + | 11.3080i | 0.426490 | + | 0.426490i | ||||
\(704\) | −0.403497 | −0.0152074 | ||||||||
\(705\) | −18.5930 | + | 20.0377i | −0.700253 | + | 0.754665i | ||||
\(706\) | −18.8636 | −0.709942 | ||||||||
\(707\) | −19.0397 | − | 19.0397i | −0.716061 | − | 0.716061i | ||||
\(708\) | −9.47547 | − | 9.47547i | −0.356110 | − | 0.356110i | ||||
\(709\) | 19.6493 | 0.737944 | 0.368972 | − | 0.929440i | \(-0.379710\pi\) | ||||
0.368972 | + | 0.929440i | \(0.379710\pi\) | |||||||
\(710\) | −0.455675 | − | 12.1843i | −0.0171012 | − | 0.457270i | ||||
\(711\) | − | 0.383565i | − | 0.0143848i | ||||||
\(712\) | 4.40639 | + | 4.40639i | 0.165137 | + | 0.165137i | ||||
\(713\) | 8.25480 | + | 13.7095i | 0.309145 | + | 0.513425i | ||||
\(714\) | 26.6425i | 0.997070i | ||||||||
\(715\) | 0.101394 | + | 2.71119i | 0.00379193 | + | 0.101393i | ||||
\(716\) | −2.77575 | −0.103735 | ||||||||
\(717\) | −10.4923 | + | 10.4923i | −0.391843 | + | 0.391843i | ||||
\(718\) | 16.7358 | − | 16.7358i | 0.624573 | − | 0.624573i | ||||
\(719\) | − | 42.4908i | − | 1.58464i | −0.610105 | − | 0.792321i | \(-0.708873\pi\) | ||
0.610105 | − | 0.792321i | \(-0.291127\pi\) | |||||||
\(720\) | 1.63913 | + | 1.52094i | 0.0610866 | + | 0.0566822i | ||||
\(721\) | 36.9290 | 1.37531 | ||||||||
\(722\) | 5.74366 | − | 5.74366i | 0.213757 | − | 0.213757i | ||||
\(723\) | 6.73270 | − | 6.73270i | 0.250392 | − | 0.250392i | ||||
\(724\) | −21.2640 | −0.790269 | ||||||||
\(725\) | 46.9722 | − | 3.51829i | 1.74450 | − | 0.130666i | ||||
\(726\) | 10.8372 | 0.402206 | ||||||||
\(727\) | −28.3443 | − | 28.3443i | −1.05123 | − | 1.05123i | −0.998615 | − | 0.0526167i | \(-0.983244\pi\) |
−0.0526167 | − | 0.998615i | \(-0.516756\pi\) | |||||||
\(728\) | −8.08153 | + | 8.08153i | −0.299521 | + | 0.299521i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −2.28376 | + | 2.46122i | −0.0845258 | + | 0.0910937i | ||||
\(731\) | 25.4709 | 0.942076 | ||||||||
\(732\) | −5.31121 | − | 5.31121i | −0.196308 | − | 0.196308i | ||||
\(733\) | 35.1881 | − | 35.1881i | 1.29970 | − | 1.29970i | 0.371114 | − | 0.928587i | \(-0.378976\pi\) |
0.928587 | − | 0.371114i | \(-0.121024\pi\) | |||||||
\(734\) | 2.58800 | 0.0955248 | ||||||||
\(735\) | −0.622221 | − | 16.6376i | −0.0229510 | − | 0.613688i | ||||
\(736\) | −4.65445 | − | 1.15590i | −0.171565 | − | 0.0426072i | ||||
\(737\) | 1.85913 | − | 1.85913i | 0.0684821 | − | 0.0684821i | ||||
\(738\) | 4.02970 | + | 4.02970i | 0.148335 | + | 0.148335i | ||||
\(739\) | 7.24476i | 0.266503i | 0.991082 | + | 0.133251i | \(0.0425417\pi\) | ||||
−0.991082 | + | 0.133251i | \(0.957458\pi\) | |||||||
\(740\) | −0.256608 | − | 6.86145i | −0.00943308 | − | 0.252232i | ||||
\(741\) | 15.6605i | 0.575302i | ||||||||
\(742\) | 5.61022 | − | 5.61022i | 0.205957 | − | 0.205957i | ||||
\(743\) | 38.2888 | − | 38.2888i | 1.40468 | − | 1.40468i | 0.620370 | − | 0.784309i | \(-0.286983\pi\) |
0.784309 | − | 0.620370i | \(-0.213017\pi\) | |||||||
\(744\) | − | 3.33683i | − | 0.122334i | ||||||
\(745\) | −16.9480 | + | 18.2649i | −0.620926 | + | 0.669173i | ||||
\(746\) | 7.03623i | 0.257615i | ||||||||
\(747\) | −12.3708 | − | 12.3708i | −0.452623 | − | 0.452623i | ||||
\(748\) | 2.00000 | + | 2.00000i | 0.0731272 | + | 0.0731272i | ||||
\(749\) | 16.9133i | 0.617997i | ||||||||
\(750\) | 8.74075 | + | 6.97132i | 0.319167 | + | 0.254557i | ||||
\(751\) | − | 24.3210i | − | 0.887484i | −0.896155 | − | 0.443742i | \(-0.853651\pi\) | ||
0.896155 | − | 0.443742i | \(-0.146349\pi\) | |||||||
\(752\) | −8.64413 | + | 8.64413i | −0.315219 | + | 0.315219i | ||||
\(753\) | 1.95018 | − | 1.95018i | 0.0710686 | − | 0.0710686i | ||||
\(754\) | − | 28.3285i | − | 1.03166i | ||||||
\(755\) | −30.3660 | + | 32.7256i | −1.10513 | + | 1.19101i | ||||
\(756\) | 3.80076i | 0.138232i | ||||||||
\(757\) | −26.9257 | − | 26.9257i | −0.978630 | − | 0.978630i | 0.0211465 | − | 0.999776i | \(-0.493268\pi\) |
−0.999776 | + | 0.0211465i | \(0.993268\pi\) | |||||||
\(758\) | 2.49910 | − | 2.49910i | 0.0907714 | − | 0.0907714i | ||||
\(759\) | −1.87806 | − | 0.466404i | −0.0681691 | − | 0.0169294i | ||||
\(760\) | −11.6372 | + | 0.435213i | −0.422126 | + | 0.0157868i | ||||
\(761\) | −6.15795 | −0.223226 | −0.111613 | − | 0.993752i | \(-0.535602\pi\) | ||||
−0.111613 | + | 0.993752i | \(0.535602\pi\) | |||||||
\(762\) | −9.84286 | + | 9.84286i | −0.356569 | + | 0.356569i | ||||
\(763\) | 34.1051 | + | 34.1051i | 1.23469 | + | 1.23469i | ||||
\(764\) | 15.5937 | 0.564160 | ||||||||
\(765\) | −0.585786 | − | 15.6634i | −0.0211792 | − | 0.566311i | ||||
\(766\) | 19.5344i | 0.705805i | ||||||||
\(767\) | −28.4931 | + | 28.4931i | −1.02882 | + | 1.02882i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | −23.1519 | −0.834877 | −0.417439 | − | 0.908705i | \(-0.637072\pi\) | ||||
−0.417439 | + | 0.908705i | \(0.637072\pi\) | |||||||
\(770\) | −2.51376 | − | 2.33251i | −0.0905895 | − | 0.0840579i | ||||
\(771\) | 6.10364 | 0.219817 | ||||||||
\(772\) | −6.99660 | + | 6.99660i | −0.251813 | + | 0.251813i | ||||
\(773\) | −7.51233 | + | 7.51233i | −0.270200 | + | 0.270200i | −0.829181 | − | 0.558981i | \(-0.811193\pi\) |
0.558981 | + | 0.829181i | \(0.311193\pi\) | |||||||
\(774\) | 3.63363 | 0.130608 | ||||||||
\(775\) | −1.24618 | − | 16.6375i | −0.0447641 | − | 0.597638i | ||||
\(776\) | 11.6762i | 0.419150i | ||||||||
\(777\) | 8.25259 | − | 8.25259i | 0.296060 | − | 0.296060i | ||||
\(778\) | 4.69013 | − | 4.69013i | 0.168149 | − | 0.168149i | ||||
\(779\) | −29.6794 | −1.06337 | ||||||||
\(780\) | 4.57353 | − | 4.92890i | 0.163759 | − | 0.176483i | ||||
\(781\) | − | 2.20019i | − | 0.0787291i | ||||||
\(782\) | 17.3411 | + | 28.8000i | 0.620117 | + | 1.02988i | ||||
\(783\) | −6.66148 | − | 6.66148i | −0.238062 | − | 0.238062i | ||||
\(784\) | − | 7.44578i | − | 0.265921i | ||||||
\(785\) | −7.72610 | + | 0.288944i | −0.275756 | + | 0.0103128i | ||||
\(786\) | −1.09419 | −0.0390284 | ||||||||
\(787\) | −8.97134 | − | 8.97134i | −0.319794 | − | 0.319794i | 0.528894 | − | 0.848688i | \(-0.322607\pi\) |
−0.848688 | + | 0.528894i | \(0.822607\pi\) | |||||||
\(788\) | −4.96503 | − | 4.96503i | −0.176872 | − | 0.176872i | ||||
\(789\) | −5.78994 | −0.206127 | ||||||||
\(790\) | −0.0320534 | − | 0.857078i | −0.00114041 | − | 0.0304935i | ||||
\(791\) | 48.1876 | 1.71335 | ||||||||
\(792\) | 0.285316 | + | 0.285316i | 0.0101382 | + | 0.0101382i | ||||
\(793\) | −15.9710 | + | 15.9710i | −0.567146 | + | 0.567146i | ||||
\(794\) | 9.35499i | 0.331996i | ||||||||
\(795\) | −3.17495 | + | 3.42165i | −0.112604 | + | 0.121354i | ||||
\(796\) | 13.2209i | 0.468601i | ||||||||
\(797\) | 10.1932 | + | 10.1932i | 0.361061 | + | 0.361061i | 0.864204 | − | 0.503142i | \(-0.167823\pi\) |
−0.503142 | + | 0.864204i | \(0.667823\pi\) | |||||||
\(798\) | −13.9966 | − | 13.9966i | −0.495474 | − | 0.495474i | ||||
\(799\) | 85.6921 | 3.03157 | ||||||||
\(800\) | 3.78974 | + | 3.26158i | 0.133987 | + | 0.115314i | ||||
\(801\) | − | 6.23158i | − | 0.220182i | ||||||
\(802\) | 6.94134 | + | 6.94134i | 0.245107 | + | 0.245107i | ||||
\(803\) | −0.428414 | + | 0.428414i | −0.0151184 | + | 0.0151184i | ||||
\(804\) | −6.51606 | −0.229804 | ||||||||
\(805\) | −22.3149 | − | 34.1073i | −0.786496 | − | 1.20213i | ||||
\(806\) | −10.0340 | −0.353431 | ||||||||
\(807\) | −21.5936 | + | 21.5936i | −0.760129 | + | 0.760129i | ||||
\(808\) | 5.00944 | + | 5.00944i | 0.176231 | + | 0.176231i | ||||
\(809\) | − | 20.1026i | − | 0.706771i | −0.935478 | − | 0.353385i | \(-0.885030\pi\) | ||
0.935478 | − | 0.353385i | \(-0.114970\pi\) | |||||||
\(810\) | −0.0835670 | − | 2.23451i | −0.00293625 | − | 0.0785125i | ||||
\(811\) | −48.2332 | −1.69370 | −0.846849 | − | 0.531833i | \(-0.821503\pi\) | ||||
−0.846849 | + | 0.531833i | \(0.821503\pi\) | |||||||
\(812\) | 25.3187 | + | 25.3187i | 0.888512 | + | 0.888512i | ||||
\(813\) | −10.1409 | − | 10.1409i | −0.355657 | − | 0.355657i | ||||
\(814\) | − | 1.23901i | − | 0.0434273i | ||||||
\(815\) | −0.753743 | + | 0.0281888i | −0.0264025 | + | 0.000987411i | ||||
\(816\) | − | 7.00978i | − | 0.245391i | ||||||
\(817\) | −13.3811 | + | 13.3811i | −0.468146 | + | 0.468146i | ||||
\(818\) | 1.15257 | + | 1.15257i | 0.0402987 | + | 0.0402987i | ||||
\(819\) | 11.4290 | 0.399362 | ||||||||
\(820\) | 9.34113 | + | 8.66763i | 0.326207 | + | 0.302687i | ||||
\(821\) | −12.0371 | −0.420098 | −0.210049 | − | 0.977691i | \(-0.567362\pi\) | ||||
−0.210049 | + | 0.977691i | \(0.567362\pi\) | |||||||
\(822\) | −13.9152 | − | 13.9152i | −0.485348 | − | 0.485348i | ||||
\(823\) | −25.7663 | − | 25.7663i | −0.898157 | − | 0.898157i | 0.0971160 | − | 0.995273i | \(-0.469038\pi\) |
−0.995273 | + | 0.0971160i | \(0.969038\pi\) | |||||||
\(824\) | −9.71622 | −0.338481 | ||||||||
\(825\) | 1.52915 | + | 1.31604i | 0.0532381 | + | 0.0458186i | ||||
\(826\) | − | 50.9315i | − | 1.77213i | ||||||
\(827\) | −7.09270 | − | 7.09270i | −0.246637 | − | 0.246637i | 0.572952 | − | 0.819589i | \(-0.305798\pi\) |
−0.819589 | + | 0.572952i | \(0.805798\pi\) | |||||||
\(828\) | 2.47384 | + | 4.10854i | 0.0859720 | + | 0.142782i | ||||
\(829\) | 18.4503i | 0.640807i | 0.947281 | + | 0.320403i | \(0.103818\pi\) | ||||
−0.947281 | + | 0.320403i | \(0.896182\pi\) | |||||||
\(830\) | −28.6764 | − | 26.6088i | −0.995371 | − | 0.923604i | ||||
\(831\) | 3.52348 | 0.122228 | ||||||||
\(832\) | 2.12629 | − | 2.12629i | 0.0737160 | − | 0.0737160i | ||||
\(833\) | −36.9062 | + | 36.9062i | −1.27872 | + | 1.27872i | ||||
\(834\) | 19.8141i | 0.686105i | ||||||||
\(835\) | 0.760721 | + | 20.3410i | 0.0263258 | + | 0.703929i | ||||
\(836\) | −2.10139 | −0.0726782 | ||||||||
\(837\) | −2.35950 | + | 2.35950i | −0.0815561 | + | 0.0815561i | ||||
\(838\) | −7.97221 | + | 7.97221i | −0.275395 | + | 0.275395i | ||||
\(839\) | −8.78459 | −0.303278 | −0.151639 | − | 0.988436i | \(-0.548455\pi\) | ||||
−0.151639 | + | 0.988436i | \(0.548455\pi\) | |||||||
\(840\) | 0.317618 | + | 8.49282i | 0.0109589 | + | 0.293030i | ||||
\(841\) | −59.7506 | −2.06037 | ||||||||
\(842\) | 11.3867 | + | 11.3867i | 0.392412 | + | 0.392412i | ||||
\(843\) | −17.2354 | + | 17.2354i | −0.593619 | + | 0.593619i | ||||
\(844\) | − | 14.3412i | − | 0.493643i | ||||||
\(845\) | 6.48726 | + | 6.01952i | 0.223168 | + | 0.207078i | ||||
\(846\) | 12.2247 | 0.420292 | ||||||||
\(847\) | 29.1254 | + | 29.1254i | 1.00076 | + | 1.00076i | ||||
\(848\) | −1.47608 | + | 1.47608i | −0.0506887 | + | 0.0506887i | ||||
\(849\) | −2.20097 | −0.0755370 | ||||||||
\(850\) | −2.61789 | − | 34.9510i | −0.0897928 | − | 1.19881i | ||||
\(851\) | 3.54941 | − | 14.2923i | 0.121672 | − | 0.489935i | ||||
\(852\) | −3.85572 | + | 3.85572i | −0.132095 | + | 0.132095i | ||||
\(853\) | 24.3103 | + | 24.3103i | 0.832367 | + | 0.832367i | 0.987840 | − | 0.155473i | \(-0.0496901\pi\) |
−0.155473 | + | 0.987840i | \(0.549690\pi\) | |||||||
\(854\) | − | 28.5482i | − | 0.976899i | ||||||
\(855\) | 8.53649 | + | 7.92100i | 0.291942 | + | 0.270893i | ||||
\(856\) | − | 4.44997i | − | 0.152097i | ||||||
\(857\) | −0.739435 | + | 0.739435i | −0.0252586 | + | 0.0252586i | −0.719623 | − | 0.694365i | \(-0.755685\pi\) |
0.694365 | + | 0.719623i | \(0.255685\pi\) | |||||||
\(858\) | 0.857953 | − | 0.857953i | 0.0292900 | − | 0.0292900i | ||||
\(859\) | 30.8003i | 1.05089i | 0.850827 | + | 0.525446i | \(0.176101\pi\) | ||||
−0.850827 | + | 0.525446i | \(0.823899\pi\) | |||||||
\(860\) | 8.11936 | − | 0.303651i | 0.276868 | − | 0.0103544i | ||||
\(861\) | 21.6600i | 0.738170i | ||||||||
\(862\) | 26.5640 | + | 26.5640i | 0.904773 | + | 0.904773i | ||||
\(863\) | 13.3147 | + | 13.3147i | 0.453238 | + | 0.453238i | 0.896428 | − | 0.443190i | \(-0.146153\pi\) |
−0.443190 | + | 0.896428i | \(0.646153\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 18.6276 | − | 0.696643i | 0.633357 | − | 0.0236866i | ||||
\(866\) | 27.5448i | 0.936012i | ||||||||
\(867\) | −22.7243 | + | 22.7243i | −0.771758 | + | 0.771758i | ||||
\(868\) | 8.96787 | − | 8.96787i | 0.304389 | − | 0.304389i | ||||
\(869\) | − | 0.154767i | − | 0.00525012i | ||||||
\(870\) | −15.4418 | − | 14.3284i | −0.523526 | − | 0.485780i | ||||
\(871\) | 19.5940i | 0.663918i | ||||||||
\(872\) | −8.97323 | − | 8.97323i | −0.303872 | − | 0.303872i | ||||
\(873\) | 8.25631 | − | 8.25631i | 0.279434 | − | 0.279434i | ||||
\(874\) | −24.2401 | − | 6.01989i | −0.819935 | − | 0.203626i | ||||
\(875\) | 4.75540 | + | 42.2269i | 0.160762 | + | 1.42753i | ||||
\(876\) | 1.50154 | 0.0507324 | ||||||||
\(877\) | 28.5210 | − | 28.5210i | 0.963087 | − | 0.963087i | −0.0362555 | − | 0.999343i | \(-0.511543\pi\) |
0.999343 | + | 0.0362555i | \(0.0115430\pi\) | |||||||
\(878\) | 19.4594 | + | 19.4594i | 0.656721 | + | 0.656721i | ||||
\(879\) | 23.6172 | 0.796589 | ||||||||
\(880\) | 0.661382 | + | 0.613696i | 0.0222952 | + | 0.0206877i | ||||
\(881\) | 13.8180i | 0.465540i | 0.972532 | + | 0.232770i | \(0.0747789\pi\) | ||||
−0.972532 | + | 0.232770i | \(0.925221\pi\) | |||||||
\(882\) | −5.26496 | + | 5.26496i | −0.177280 | + | 0.177280i | ||||
\(883\) | −36.0797 | − | 36.0797i | −1.21418 | − | 1.21418i | −0.969639 | − | 0.244539i | \(-0.921363\pi\) |
−0.244539 | − | 0.969639i | \(-0.578637\pi\) | |||||||
\(884\) | −21.0786 | −0.708951 | ||||||||
\(885\) | 1.11983 | + | 29.9431i | 0.0376426 | + | 1.00653i | ||||
\(886\) | 30.8820 | 1.03750 | ||||||||
\(887\) | −0.653908 | + | 0.653908i | −0.0219561 | + | 0.0219561i | −0.718000 | − | 0.696044i | \(-0.754942\pi\) |
0.696044 | + | 0.718000i | \(0.254942\pi\) | |||||||
\(888\) | −2.17130 | + | 2.17130i | −0.0728640 | + | 0.0728640i | ||||
\(889\) | −52.9062 | −1.77442 | ||||||||
\(890\) | −0.520755 | − | 13.9245i | −0.0174557 | − | 0.466750i | ||||
\(891\) | − | 0.403497i | − | 0.0135177i | ||||||
\(892\) | −10.4795 | + | 10.4795i | −0.350879 | + | 0.350879i | ||||
\(893\) | −45.0182 | + | 45.0182i | −1.50648 | + | 1.50648i | ||||
\(894\) | 11.1431 | 0.372680 | ||||||||
\(895\) | 4.54980 | + | 4.22175i | 0.152083 | + | 0.141118i | ||||
\(896\) | 3.80076i | 0.126974i | ||||||||
\(897\) | 12.3545 | − | 7.43893i | 0.412505 | − | 0.248379i | ||||
\(898\) | −2.70091 | − | 2.70091i | −0.0901306 | − | 0.0901306i | ||||
\(899\) | 31.4355i | 1.04843i | ||||||||
\(900\) | −0.373462 | − | 4.98603i | −0.0124487 | − | 0.166201i | ||||
\(901\) | 14.6328 | 0.487490 | ||||||||
\(902\) | 1.62597 | + | 1.62597i | 0.0541389 | + | 0.0541389i | ||||
\(903\) | 9.76553 | + | 9.76553i | 0.324976 | + | 0.324976i | ||||
\(904\) | −12.6784 | −0.421678 | ||||||||
\(905\) | 34.8543 | + | 32.3413i | 1.15860 | + | 1.07506i | ||||
\(906\) | 19.9653 | 0.663301 | ||||||||
\(907\) | −5.71177 | − | 5.71177i | −0.189656 | − | 0.189656i | 0.605891 | − | 0.795547i | \(-0.292817\pi\) |
−0.795547 | + | 0.605891i | \(0.792817\pi\) | |||||||
\(908\) | 0.390578 | − | 0.390578i | 0.0129618 | − | 0.0129618i | ||||
\(909\) | − | 7.08442i | − | 0.234975i | ||||||
\(910\) | 25.5382 | − | 0.955088i | 0.846583 | − | 0.0316609i | ||||
\(911\) | − | 40.5977i | − | 1.34506i | −0.740069 | − | 0.672531i | \(-0.765207\pi\) | ||
0.740069 | − | 0.672531i | \(-0.234793\pi\) | |||||||
\(912\) | 3.68258 | + | 3.68258i | 0.121942 | + | 0.121942i | ||||
\(913\) | −4.99157 | − | 4.99157i | −0.165197 | − | 0.165197i | ||||
\(914\) | −27.1102 | −0.896726 | ||||||||
\(915\) | 0.627687 | + | 16.7838i | 0.0207507 | + | 0.554855i | ||||
\(916\) | − | 16.0170i | − | 0.529218i | ||||||
\(917\) | −2.94068 | − | 2.94068i | −0.0971098 | − | 0.0971098i | ||||
\(918\) | −4.95666 | + | 4.95666i | −0.163594 | + | 0.163594i | ||||
\(919\) | 48.2150 | 1.59047 | 0.795233 | − | 0.606304i | \(-0.207349\pi\) | ||||
0.795233 | + | 0.606304i | \(0.207349\pi\) | |||||||
\(920\) | 5.87116 | + | 8.97382i | 0.193566 | + | 0.295858i | ||||
\(921\) | 3.32051 | 0.109415 | ||||||||
\(922\) | −16.6406 | + | 16.6406i | −0.548029 | + | 0.548029i | ||||
\(923\) | 11.5943 | + | 11.5943i | 0.381630 | + | 0.381630i | ||||
\(924\) | 1.53360i | 0.0504516i | ||||||||
\(925\) | −10.0153 | + | 11.6371i | −0.329300 | + | 0.382624i | ||||
\(926\) | 28.4179 | 0.933869 | ||||||||
\(927\) | 6.87041 | + | 6.87041i | 0.225654 | + | 0.225654i | ||||
\(928\) | −6.66148 | − | 6.66148i | −0.218674 | − | 0.218674i | ||||
\(929\) | − | 11.6567i | − | 0.382444i | −0.981547 | − | 0.191222i | \(-0.938755\pi\) | ||
0.981547 | − | 0.191222i | \(-0.0612451\pi\) | |||||||
\(930\) | −5.07513 | + | 5.46948i | −0.166420 | + | 0.179351i | ||||
\(931\) | − | 38.7773i | − | 1.27087i | ||||||
\(932\) | −13.0826 | + | 13.0826i | −0.428535 | + | 0.428535i | ||||
\(933\) | 9.09045 | + | 9.09045i | 0.297608 | + | 0.297608i | ||||
\(934\) | −11.7987 | −0.386064 | ||||||||
\(935\) | −0.236363 | − | 6.32014i | −0.00772990 | − | 0.206691i | ||||
\(936\) | −3.00703 | −0.0982879 | ||||||||
\(937\) | −17.6289 | − | 17.6289i | −0.575910 | − | 0.575910i | 0.357864 | − | 0.933774i | \(-0.383505\pi\) |
−0.933774 | + | 0.357864i | \(0.883505\pi\) | |||||||
\(938\) | −17.5122 | − | 17.5122i | −0.571794 | − | 0.571794i | ||||
\(939\) | 4.78249 | 0.156071 | ||||||||
\(940\) | 27.3161 | − | 1.02158i | 0.890952 | − | 0.0333202i | ||||
\(941\) | − | 27.4365i | − | 0.894403i | −0.894433 | − | 0.447202i | \(-0.852421\pi\) | ||
0.894433 | − | 0.447202i | \(-0.147579\pi\) | |||||||
\(942\) | 2.44491 | + | 2.44491i | 0.0796596 | + | 0.0796596i | ||||
\(943\) | 14.0981 | + | 23.4140i | 0.459097 | + | 0.762463i | ||||
\(944\) | 13.4003i | 0.436144i | ||||||||
\(945\) | 5.78074 | − | 6.22992i | 0.188048 | − | 0.202659i | ||||
\(946\) | 1.46616 | 0.0476689 | ||||||||
\(947\) | −15.9301 | + | 15.9301i | −0.517658 | + | 0.517658i | −0.916862 | − | 0.399204i | \(-0.869286\pi\) |
0.399204 | + | 0.916862i | \(0.369286\pi\) | |||||||
\(948\) | −0.271221 | + | 0.271221i | −0.00880886 | + | 0.00880886i | ||||
\(949\) | − | 4.51519i | − | 0.146569i | ||||||
\(950\) | 19.7368 | + | 16.9862i | 0.640345 | + | 0.551104i | ||||
\(951\) | 22.7716 | 0.738419 | ||||||||
\(952\) | 18.8391 | − | 18.8391i | 0.610578 | − | 0.610578i | ||||
\(953\) | 2.64543 | − | 2.64543i | 0.0856937 | − | 0.0856937i | −0.662961 | − | 0.748654i | \(-0.730700\pi\) |
0.748654 | + | 0.662961i | \(0.230700\pi\) | |||||||
\(954\) | 2.08749 | 0.0675849 | ||||||||
\(955\) | −25.5600 | − | 23.7171i | −0.827102 | − | 0.767468i | ||||
\(956\) | 14.8384 | 0.479908 | ||||||||
\(957\) | −2.68789 | − | 2.68789i | −0.0868871 | − | 0.0868871i | ||||
\(958\) | −14.9119 | + | 14.9119i | −0.481783 | + | 0.481783i | ||||
\(959\) | − | 74.7954i | − | 2.41527i | ||||||
\(960\) | −0.0835670 | − | 2.23451i | −0.00269711 | − | 0.0721184i | ||||
\(961\) | −19.8656 | −0.640825 | ||||||||
\(962\) | 6.52917 | + | 6.52917i | 0.210509 | + | 0.210509i | ||||
\(963\) | −3.14660 | + | 3.14660i | −0.101398 | + | 0.101398i | ||||
\(964\) | −9.52147 | −0.306666 | ||||||||
\(965\) | 22.1097 | − | 0.826869i | 0.711737 | − | 0.0266179i | ||||
\(966\) | −4.39331 | + | 17.6904i | −0.141353 | + | 0.569181i | ||||
\(967\) | −15.6966 | + | 15.6966i | −0.504768 | + | 0.504768i | −0.912916 | − | 0.408148i | \(-0.866175\pi\) |
0.408148 | + | 0.912916i | \(0.366175\pi\) | |||||||
\(968\) | −7.66305 | − | 7.66305i | −0.246300 | − | 0.246300i | ||||
\(969\) | − | 36.5066i | − | 1.17276i | ||||||
\(970\) | 17.7588 | − | 19.1387i | 0.570201 | − | 0.614507i | ||||
\(971\) | 25.6347i | 0.822656i | 0.911487 | + | 0.411328i | \(0.134935\pi\) | ||||
−0.911487 | + | 0.411328i | \(0.865065\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | −53.2512 | + | 53.2512i | −1.70715 | + | 1.70715i | ||||
\(974\) | 1.21575i | 0.0389552i | ||||||||
\(975\) | −14.9932 | + | 1.12301i | −0.480166 | + | 0.0359652i | ||||
\(976\) | 7.51118i | 0.240427i | ||||||||
\(977\) | 7.40750 | + | 7.40750i | 0.236987 | + | 0.236987i | 0.815601 | − | 0.578614i | \(-0.196406\pi\) |
−0.578614 | + | 0.815601i | \(0.696406\pi\) | |||||||
\(978\) | 0.238521 | + | 0.238521i | 0.00762706 | + | 0.00762706i | ||||
\(979\) | − | 2.51443i | − | 0.0803614i | ||||||
\(980\) | −11.3246 | + | 12.2046i | −0.361751 | + | 0.389860i | ||||
\(981\) | 12.6901i | 0.405162i | ||||||||
\(982\) | −19.5290 | + | 19.5290i | −0.623197 | + | 0.623197i | ||||
\(983\) | −13.6949 | + | 13.6949i | −0.436800 | + | 0.436800i | −0.890933 | − | 0.454134i | \(-0.849949\pi\) |
0.454134 | + | 0.890933i | \(0.349949\pi\) | |||||||
\(984\) | − | 5.69885i | − | 0.181673i | ||||||
\(985\) | 0.586776 | + | 15.6898i | 0.0186962 | + | 0.499920i | ||||
\(986\) | 66.0374i | 2.10306i | ||||||||
\(987\) | 32.8543 | + | 32.8543i | 1.04576 | + | 1.04576i | ||||
\(988\) | 11.0736 | − | 11.0736i | 0.352299 | − | 0.352299i | ||||
\(989\) | 16.9125 | + | 4.20012i | 0.537787 | + | 0.133556i | ||||
\(990\) | −0.0337191 | − | 0.901617i | −0.00107166 | − | 0.0286553i | ||||
\(991\) | −5.10343 | −0.162116 | −0.0810578 | − | 0.996709i | \(-0.525830\pi\) | ||||
−0.0810578 | + | 0.996709i | \(0.525830\pi\) | |||||||
\(992\) | −2.35950 | + | 2.35950i | −0.0749140 | + | 0.0749140i | ||||
\(993\) | 8.25599 | + | 8.25599i | 0.261996 | + | 0.261996i | ||||
\(994\) | −20.7248 | −0.657351 | ||||||||
\(995\) | 20.1082 | − | 21.6706i | 0.637472 | − | 0.687005i | ||||
\(996\) | 17.4949i | 0.554348i | ||||||||
\(997\) | 14.7859 | − | 14.7859i | 0.468274 | − | 0.468274i | −0.433081 | − | 0.901355i | \(-0.642574\pi\) |
0.901355 | + | 0.433081i | \(0.142574\pi\) | |||||||
\(998\) | −13.2067 | − | 13.2067i | −0.418051 | − | 0.418051i | ||||
\(999\) | 3.07068 | 0.0971520 |
(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 | 690.2.j.b.643.8 | yes | 24 | |
5.2 | odd | 4 | inner | 690.2.j.b.367.11 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.b.643.11 | yes | 24 | |
115.22 | even | 4 | inner | 690.2.j.b.367.8 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.b.367.8 | ✓ | 24 | 115.22 | even | 4 | inner | |
690.2.j.b.367.11 | yes | 24 | 5.2 | odd | 4 | inner | |
690.2.j.b.643.8 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.b.643.11 | yes | 24 | 23.22 | odd | 2 | inner |