Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(50,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("287.50");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.f (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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 50.18 | ||
Character | \(\chi\) | \(=\) | 287.50 |
Dual form | 287.2.f.a.155.3 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36496i | 1.67228i | 0.548519 | + | 0.836138i | \(0.315192\pi\) | ||||
−0.548519 | + | 0.836138i | \(0.684808\pi\) | |||||||
\(3\) | −0.345245 | − | 0.345245i | −0.199327 | − | 0.199327i | 0.600384 | − | 0.799712i | \(-0.295014\pi\) |
−0.799712 | + | 0.600384i | \(0.795014\pi\) | |||||||
\(4\) | −3.59302 | −1.79651 | ||||||||
\(5\) | − | 3.38746i | − | 1.51492i | −0.652882 | − | 0.757459i | \(-0.726440\pi\) | ||
0.652882 | − | 0.757459i | \(-0.273560\pi\) | |||||||
\(6\) | 0.816490 | − | 0.816490i | 0.333330 | − | 0.333330i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | − | 3.76741i | − | 1.33198i | ||||||
\(9\) | − | 2.76161i | − | 0.920537i | ||||||
\(10\) | 8.01120 | 2.53336 | ||||||||
\(11\) | −4.52500 | − | 4.52500i | −1.36434 | − | 1.36434i | −0.868300 | − | 0.496039i | \(-0.834787\pi\) |
−0.496039 | − | 0.868300i | \(-0.665213\pi\) | |||||||
\(12\) | 1.24047 | + | 1.24047i | 0.358093 | + | 0.358093i | ||||
\(13\) | 2.27384 | + | 2.27384i | 0.630648 | + | 0.630648i | 0.948231 | − | 0.317582i | \(-0.102871\pi\) |
−0.317582 | + | 0.948231i | \(0.602871\pi\) | |||||||
\(14\) | 1.67228 | − | 1.67228i | 0.446935 | − | 0.446935i | ||||
\(15\) | −1.16950 | + | 1.16950i | −0.301965 | + | 0.301965i | ||||
\(16\) | 1.72373 | 0.430933 | ||||||||
\(17\) | 1.60375 | − | 1.60375i | 0.388966 | − | 0.388966i | −0.485352 | − | 0.874319i | \(-0.661309\pi\) |
0.874319 | + | 0.485352i | \(0.161309\pi\) | |||||||
\(18\) | 6.53109 | 1.53939 | ||||||||
\(19\) | −1.78722 | + | 1.78722i | −0.410016 | + | 0.410016i | −0.881744 | − | 0.471728i | \(-0.843630\pi\) |
0.471728 | + | 0.881744i | \(0.343630\pi\) | |||||||
\(20\) | 12.1712i | 2.72156i | ||||||||
\(21\) | 0.488250i | 0.106545i | ||||||||
\(22\) | 10.7014 | − | 10.7014i | 2.28155 | − | 2.28155i | ||||
\(23\) | 2.09281 | 0.436382 | 0.218191 | − | 0.975906i | \(-0.429984\pi\) | ||||
0.218191 | + | 0.975906i | \(0.429984\pi\) | |||||||
\(24\) | −1.30068 | + | 1.30068i | −0.265500 | + | 0.265500i | ||||
\(25\) | −6.47489 | −1.29498 | ||||||||
\(26\) | −5.37752 | + | 5.37752i | −1.05462 | + | 1.05462i | ||||
\(27\) | −1.98917 | + | 1.98917i | −0.382816 | + | 0.382816i | ||||
\(28\) | 2.54065 | + | 2.54065i | 0.480137 | + | 0.480137i | ||||
\(29\) | 5.04961 | + | 5.04961i | 0.937690 | + | 0.937690i | 0.998169 | − | 0.0604796i | \(-0.0192630\pi\) |
−0.0604796 | + | 0.998169i | \(0.519263\pi\) | |||||||
\(30\) | −2.76583 | − | 2.76583i | −0.504968 | − | 0.504968i | ||||
\(31\) | −7.03888 | −1.26422 | −0.632110 | − | 0.774879i | \(-0.717811\pi\) | ||||
−0.632110 | + | 0.774879i | \(0.717811\pi\) | |||||||
\(32\) | − | 3.45827i | − | 0.611342i | ||||||
\(33\) | 3.12447i | 0.543900i | ||||||||
\(34\) | 3.79279 | + | 3.79279i | 0.650459 | + | 0.650459i | ||||
\(35\) | −2.39530 | + | 2.39530i | −0.404879 | + | 0.404879i | ||||
\(36\) | 9.92251i | 1.65375i | ||||||||
\(37\) | −1.49096 | −0.245113 | −0.122557 | − | 0.992462i | \(-0.539109\pi\) | ||||
−0.122557 | + | 0.992462i | \(0.539109\pi\) | |||||||
\(38\) | −4.22669 | − | 4.22669i | −0.685660 | − | 0.685660i | ||||
\(39\) | − | 1.57006i | − | 0.251411i | ||||||
\(40\) | −12.7620 | −2.01784 | ||||||||
\(41\) | 6.37022 | − | 0.648351i | 0.994860 | − | 0.101255i | ||||
\(42\) | −1.15469 | −0.178173 | ||||||||
\(43\) | − | 8.39742i | − | 1.28059i | −0.768127 | − | 0.640297i | \(-0.778811\pi\) | ||
0.768127 | − | 0.640297i | \(-0.221189\pi\) | |||||||
\(44\) | 16.2584 | + | 16.2584i | 2.45105 | + | 2.45105i | ||||
\(45\) | −9.35485 | −1.39454 | ||||||||
\(46\) | 4.94941i | 0.729751i | ||||||||
\(47\) | 3.22472 | − | 3.22472i | 0.470373 | − | 0.470373i | −0.431662 | − | 0.902035i | \(-0.642073\pi\) |
0.902035 | + | 0.431662i | \(0.142073\pi\) | |||||||
\(48\) | −0.595110 | − | 0.595110i | −0.0858967 | − | 0.0858967i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | − | 15.3128i | − | 2.16556i | ||||||
\(51\) | −1.10737 | −0.155063 | ||||||||
\(52\) | −8.16993 | − | 8.16993i | −1.13296 | − | 1.13296i | ||||
\(53\) | 2.69379 | + | 2.69379i | 0.370021 | + | 0.370021i | 0.867485 | − | 0.497464i | \(-0.165735\pi\) |
−0.497464 | + | 0.867485i | \(0.665735\pi\) | |||||||
\(54\) | −4.70430 | − | 4.70430i | −0.640174 | − | 0.640174i | ||||
\(55\) | −15.3283 | + | 15.3283i | −2.06686 | + | 2.06686i | ||||
\(56\) | −2.66396 | + | 2.66396i | −0.355987 | + | 0.355987i | ||||
\(57\) | 1.23406 | 0.163455 | ||||||||
\(58\) | −11.9421 | + | 11.9421i | −1.56808 | + | 1.56808i | ||||
\(59\) | 11.1417 | 1.45052 | 0.725261 | − | 0.688474i | \(-0.241719\pi\) | ||||
0.725261 | + | 0.688474i | \(0.241719\pi\) | |||||||
\(60\) | 4.20205 | − | 4.20205i | 0.542482 | − | 0.542482i | ||||
\(61\) | − | 3.84534i | − | 0.492346i | −0.969226 | − | 0.246173i | \(-0.920827\pi\) | ||
0.969226 | − | 0.246173i | \(-0.0791731\pi\) | |||||||
\(62\) | − | 16.6466i | − | 2.11413i | ||||||
\(63\) | −1.95275 | + | 1.95275i | −0.246024 | + | 0.246024i | ||||
\(64\) | 11.6261 | 1.45327 | ||||||||
\(65\) | 7.70253 | − | 7.70253i | 0.955381 | − | 0.955381i | ||||
\(66\) | −7.38923 | −0.909552 | ||||||||
\(67\) | 8.06125 | − | 8.06125i | 0.984838 | − | 0.984838i | −0.0150487 | − | 0.999887i | \(-0.504790\pi\) |
0.999887 | + | 0.0150487i | \(0.00479032\pi\) | |||||||
\(68\) | −5.76229 | + | 5.76229i | −0.698781 | + | 0.698781i | ||||
\(69\) | −0.722533 | − | 0.722533i | −0.0869828 | − | 0.0869828i | ||||
\(70\) | −5.66477 | − | 5.66477i | −0.677070 | − | 0.677070i | ||||
\(71\) | −6.19373 | − | 6.19373i | −0.735060 | − | 0.735060i | 0.236557 | − | 0.971618i | \(-0.423981\pi\) |
−0.971618 | + | 0.236557i | \(0.923981\pi\) | |||||||
\(72\) | −10.4041 | −1.22614 | ||||||||
\(73\) | 0.337794i | 0.0395358i | 0.999805 | + | 0.0197679i | \(0.00629273\pi\) | ||||
−0.999805 | + | 0.0197679i | \(0.993707\pi\) | |||||||
\(74\) | − | 3.52607i | − | 0.409897i | ||||||
\(75\) | 2.23542 | + | 2.23542i | 0.258125 | + | 0.258125i | ||||
\(76\) | 6.42150 | − | 6.42150i | 0.736596 | − | 0.736596i | ||||
\(77\) | 6.39932i | 0.729270i | ||||||||
\(78\) | 3.71313 | 0.420429 | ||||||||
\(79\) | −6.02318 | − | 6.02318i | −0.677661 | − | 0.677661i | 0.281810 | − | 0.959470i | \(-0.409065\pi\) |
−0.959470 | + | 0.281810i | \(0.909065\pi\) | |||||||
\(80\) | − | 5.83907i | − | 0.652828i | ||||||
\(81\) | −6.91133 | −0.767926 | ||||||||
\(82\) | 1.53332 | + | 15.0653i | 0.169327 | + | 1.66368i | ||||
\(83\) | 8.24654 | 0.905175 | 0.452588 | − | 0.891720i | \(-0.350501\pi\) | ||||
0.452588 | + | 0.891720i | \(0.350501\pi\) | |||||||
\(84\) | − | 1.75429i | − | 0.191409i | ||||||
\(85\) | −5.43263 | − | 5.43263i | −0.589252 | − | 0.589252i | ||||
\(86\) | 19.8595 | 2.14151 | ||||||||
\(87\) | − | 3.48671i | − | 0.373815i | ||||||
\(88\) | −17.0475 | + | 17.0475i | −1.81727 | + | 1.81727i | ||||
\(89\) | 7.27755 | + | 7.27755i | 0.771419 | + | 0.771419i | 0.978355 | − | 0.206936i | \(-0.0663491\pi\) |
−0.206936 | + | 0.978355i | \(0.566349\pi\) | |||||||
\(90\) | − | 22.1238i | − | 2.33205i | ||||||
\(91\) | − | 3.21569i | − | 0.337096i | ||||||
\(92\) | −7.51951 | −0.783963 | ||||||||
\(93\) | 2.43014 | + | 2.43014i | 0.251994 | + | 0.251994i | ||||
\(94\) | 7.62632 | + | 7.62632i | 0.786594 | + | 0.786594i | ||||
\(95\) | 6.05413 | + | 6.05413i | 0.621140 | + | 0.621140i | ||||
\(96\) | −1.19395 | + | 1.19395i | −0.121857 | + | 0.121857i | ||||
\(97\) | −3.77195 | + | 3.77195i | −0.382983 | + | 0.382983i | −0.872176 | − | 0.489193i | \(-0.837292\pi\) |
0.489193 | + | 0.872176i | \(0.337292\pi\) | |||||||
\(98\) | −2.36496 | −0.238897 | ||||||||
\(99\) | −12.4963 | + | 12.4963i | −1.25593 | + | 1.25593i | ||||
\(100\) | 23.2644 | 2.32644 | ||||||||
\(101\) | −5.69636 | + | 5.69636i | −0.566809 | + | 0.566809i | −0.931233 | − | 0.364424i | \(-0.881266\pi\) |
0.364424 | + | 0.931233i | \(0.381266\pi\) | |||||||
\(102\) | − | 2.61889i | − | 0.259308i | ||||||
\(103\) | 17.2056i | 1.69532i | 0.530543 | + | 0.847658i | \(0.321988\pi\) | ||||
−0.530543 | + | 0.847658i | \(0.678012\pi\) | |||||||
\(104\) | 8.56647 | − | 8.56647i | 0.840012 | − | 0.840012i | ||||
\(105\) | 1.65393 | 0.161407 | ||||||||
\(106\) | −6.37070 | + | 6.37070i | −0.618777 | + | 0.618777i | ||||
\(107\) | −13.1102 | −1.26741 | −0.633704 | − | 0.773575i | \(-0.718466\pi\) | ||||
−0.633704 | + | 0.773575i | \(0.718466\pi\) | |||||||
\(108\) | 7.14711 | − | 7.14711i | 0.687731 | − | 0.687731i | ||||
\(109\) | 7.54601 | − | 7.54601i | 0.722776 | − | 0.722776i | −0.246394 | − | 0.969170i | \(-0.579246\pi\) |
0.969170 | + | 0.246394i | \(0.0792456\pi\) | |||||||
\(110\) | −36.2507 | − | 36.2507i | −3.45637 | − | 3.45637i | ||||
\(111\) | 0.514748 | + | 0.514748i | 0.0488577 | + | 0.0488577i | ||||
\(112\) | −1.21886 | − | 1.21886i | −0.115172 | − | 0.115172i | ||||
\(113\) | −11.7968 | −1.10975 | −0.554876 | − | 0.831933i | \(-0.687234\pi\) | ||||
−0.554876 | + | 0.831933i | \(0.687234\pi\) | |||||||
\(114\) | 2.91849i | 0.273341i | ||||||||
\(115\) | − | 7.08932i | − | 0.661083i | ||||||
\(116\) | −18.1433 | − | 18.1433i | −1.68457 | − | 1.68457i | ||||
\(117\) | 6.27945 | − | 6.27945i | 0.580535 | − | 0.580535i | ||||
\(118\) | 26.3495i | 2.42567i | ||||||||
\(119\) | −2.26804 | −0.207911 | ||||||||
\(120\) | 4.40601 | + | 4.40601i | 0.402211 | + | 0.402211i | ||||
\(121\) | 29.9513i | 2.72284i | ||||||||
\(122\) | 9.09407 | 0.823338 | ||||||||
\(123\) | −2.42313 | − | 1.97545i | −0.218486 | − | 0.178120i | ||||
\(124\) | 25.2908 | 2.27118 | ||||||||
\(125\) | 4.99614i | 0.446868i | ||||||||
\(126\) | −4.61818 | − | 4.61818i | −0.411420 | − | 0.411420i | ||||
\(127\) | 2.37889 | 0.211092 | 0.105546 | − | 0.994414i | \(-0.466341\pi\) | ||||
0.105546 | + | 0.994414i | \(0.466341\pi\) | |||||||
\(128\) | 20.5787i | 1.81892i | ||||||||
\(129\) | −2.89917 | + | 2.89917i | −0.255257 | + | 0.255257i | ||||
\(130\) | 18.2161 | + | 18.2161i | 1.59766 | + | 1.59766i | ||||
\(131\) | − | 3.83173i | − | 0.334779i | −0.985891 | − | 0.167390i | \(-0.946466\pi\) | ||
0.985891 | − | 0.167390i | \(-0.0535338\pi\) | |||||||
\(132\) | − | 11.2263i | − | 0.977121i | ||||||
\(133\) | 2.52751 | 0.219163 | ||||||||
\(134\) | 19.0645 | + | 19.0645i | 1.64692 | + | 1.64692i | ||||
\(135\) | 6.73823 | + | 6.73823i | 0.579935 | + | 0.579935i | ||||
\(136\) | −6.04198 | − | 6.04198i | −0.518096 | − | 0.518096i | ||||
\(137\) | 2.57611 | − | 2.57611i | 0.220092 | − | 0.220092i | −0.588445 | − | 0.808537i | \(-0.700260\pi\) |
0.808537 | + | 0.588445i | \(0.200260\pi\) | |||||||
\(138\) | 1.70876 | − | 1.70876i | 0.145459 | − | 0.145459i | ||||
\(139\) | −9.28683 | −0.787698 | −0.393849 | − | 0.919175i | \(-0.628857\pi\) | ||||
−0.393849 | + | 0.919175i | \(0.628857\pi\) | |||||||
\(140\) | 8.60634 | − | 8.60634i | 0.727368 | − | 0.727368i | ||||
\(141\) | −2.22664 | −0.187517 | ||||||||
\(142\) | 14.6479 | − | 14.6479i | 1.22922 | − | 1.22922i | ||||
\(143\) | − | 20.5782i | − | 1.72084i | ||||||
\(144\) | − | 4.76028i | − | 0.396690i | ||||||
\(145\) | 17.1054 | − | 17.1054i | 1.42052 | − | 1.42052i | ||||
\(146\) | −0.798868 | −0.0661148 | ||||||||
\(147\) | 0.345245 | − | 0.345245i | 0.0284753 | − | 0.0284753i | ||||
\(148\) | 5.35706 | 0.440348 | ||||||||
\(149\) | 12.4251 | − | 12.4251i | 1.01790 | − | 1.01790i | 0.0180632 | − | 0.999837i | \(-0.494250\pi\) |
0.999837 | − | 0.0180632i | \(-0.00575001\pi\) | |||||||
\(150\) | −5.28668 | + | 5.28668i | −0.431656 | + | 0.431656i | ||||
\(151\) | 13.4116 | + | 13.4116i | 1.09142 | + | 1.09142i | 0.995377 | + | 0.0960425i | \(0.0306185\pi\) |
0.0960425 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(152\) | 6.73318 | + | 6.73318i | 0.546133 | + | 0.546133i | ||||
\(153\) | −4.42893 | − | 4.42893i | −0.358058 | − | 0.358058i | ||||
\(154\) | −15.1341 | −1.21954 | ||||||||
\(155\) | 23.8439i | 1.91519i | ||||||||
\(156\) | 5.64125i | 0.451662i | ||||||||
\(157\) | 10.4505 | + | 10.4505i | 0.834044 | + | 0.834044i | 0.988067 | − | 0.154023i | \(-0.0492230\pi\) |
−0.154023 | + | 0.988067i | \(0.549223\pi\) | |||||||
\(158\) | 14.2446 | − | 14.2446i | 1.13324 | − | 1.13324i | ||||
\(159\) | − | 1.86004i | − | 0.147511i | ||||||
\(160\) | −11.7148 | −0.926134 | ||||||||
\(161\) | −1.47984 | − | 1.47984i | −0.116628 | − | 0.116628i | ||||
\(162\) | − | 16.3450i | − | 1.28418i | ||||||
\(163\) | 2.73606 | 0.214305 | 0.107152 | − | 0.994243i | \(-0.465827\pi\) | ||||
0.107152 | + | 0.994243i | \(0.465827\pi\) | |||||||
\(164\) | −22.8883 | + | 2.32954i | −1.78727 | + | 0.181906i | ||||
\(165\) | 10.5840 | 0.823965 | ||||||||
\(166\) | 19.5027i | 1.51370i | ||||||||
\(167\) | 14.1570 | + | 14.1570i | 1.09550 | + | 1.09550i | 0.994930 | + | 0.100571i | \(0.0320670\pi\) |
0.100571 | + | 0.994930i | \(0.467933\pi\) | |||||||
\(168\) | 1.83944 | 0.141916 | ||||||||
\(169\) | − | 2.65935i | − | 0.204565i | ||||||
\(170\) | 12.8479 | − | 12.8479i | 0.985392 | − | 0.985392i | ||||
\(171\) | 4.93560 | + | 4.93560i | 0.377435 | + | 0.377435i | ||||
\(172\) | 30.1721i | 2.30060i | ||||||||
\(173\) | − | 22.2778i | − | 1.69375i | −0.531791 | − | 0.846875i | \(-0.678481\pi\) | ||
0.531791 | − | 0.846875i | \(-0.321519\pi\) | |||||||
\(174\) | 8.24591 | 0.625121 | ||||||||
\(175\) | 4.57844 | + | 4.57844i | 0.346098 | + | 0.346098i | ||||
\(176\) | −7.79989 | − | 7.79989i | −0.587939 | − | 0.587939i | ||||
\(177\) | −3.84661 | − | 3.84661i | −0.289129 | − | 0.289129i | ||||
\(178\) | −17.2111 | + | 17.2111i | −1.29003 | + | 1.29003i | ||||
\(179\) | 0.620825 | − | 0.620825i | 0.0464026 | − | 0.0464026i | −0.683525 | − | 0.729927i | \(-0.739554\pi\) |
0.729927 | + | 0.683525i | \(0.239554\pi\) | |||||||
\(180\) | 33.6121 | 2.50530 | ||||||||
\(181\) | 13.5643 | − | 13.5643i | 1.00822 | − | 1.00822i | 0.00825740 | − | 0.999966i | \(-0.497372\pi\) |
0.999966 | − | 0.00825740i | \(-0.00262844\pi\) | |||||||
\(182\) | 7.60496 | 0.563717 | ||||||||
\(183\) | −1.32759 | + | 1.32759i | −0.0981380 | + | 0.0981380i | ||||
\(184\) | − | 7.88449i | − | 0.581252i | ||||||
\(185\) | 5.05058i | 0.371326i | ||||||||
\(186\) | −5.74717 | + | 5.74717i | −0.421403 | + | 0.421403i | ||||
\(187\) | −14.5139 | −1.06136 | ||||||||
\(188\) | −11.5865 | + | 11.5865i | −0.845030 | + | 0.845030i | ||||
\(189\) | 2.81311 | 0.204624 | ||||||||
\(190\) | −14.3177 | + | 14.3177i | −1.03872 | + | 1.03872i | ||||
\(191\) | 3.81740 | − | 3.81740i | 0.276218 | − | 0.276218i | −0.555379 | − | 0.831597i | \(-0.687427\pi\) |
0.831597 | + | 0.555379i | \(0.187427\pi\) | |||||||
\(192\) | −4.01387 | − | 4.01387i | −0.289676 | − | 0.289676i | ||||
\(193\) | −11.6632 | − | 11.6632i | −0.839535 | − | 0.839535i | 0.149263 | − | 0.988798i | \(-0.452310\pi\) |
−0.988798 | + | 0.149263i | \(0.952310\pi\) | |||||||
\(194\) | −8.92049 | − | 8.92049i | −0.640454 | − | 0.640454i | ||||
\(195\) | −5.31852 | −0.380867 | ||||||||
\(196\) | − | 3.59302i | − | 0.256644i | ||||||
\(197\) | − | 12.8279i | − | 0.913953i | −0.889479 | − | 0.456976i | \(-0.848932\pi\) | ||
0.889479 | − | 0.456976i | \(-0.151068\pi\) | |||||||
\(198\) | −29.5532 | − | 29.5532i | −2.10025 | − | 2.10025i | ||||
\(199\) | −16.0847 | + | 16.0847i | −1.14022 | + | 1.14022i | −0.151807 | + | 0.988410i | \(0.548509\pi\) |
−0.988410 | + | 0.151807i | \(0.951491\pi\) | |||||||
\(200\) | 24.3936i | 1.72489i | ||||||||
\(201\) | −5.56621 | −0.392610 | ||||||||
\(202\) | −13.4716 | − | 13.4716i | −0.947862 | − | 0.947862i | ||||
\(203\) | − | 7.14123i | − | 0.501216i | ||||||
\(204\) | 3.97881 | 0.278572 | ||||||||
\(205\) | −2.19626 | − | 21.5789i | −0.153394 | − | 1.50713i | ||||
\(206\) | −40.6904 | −2.83504 | ||||||||
\(207\) | − | 5.77954i | − | 0.401706i | ||||||
\(208\) | 3.91948 | + | 3.91948i | 0.271767 | + | 0.271767i | ||||
\(209\) | 16.1743 | 1.11880 | ||||||||
\(210\) | 3.91147i | 0.269917i | ||||||||
\(211\) | −6.58885 | + | 6.58885i | −0.453595 | + | 0.453595i | −0.896546 | − | 0.442951i | \(-0.853932\pi\) |
0.442951 | + | 0.896546i | \(0.353932\pi\) | |||||||
\(212\) | −9.67884 | − | 9.67884i | −0.664746 | − | 0.664746i | ||||
\(213\) | 4.27671i | 0.293035i | ||||||||
\(214\) | − | 31.0050i | − | 2.11946i | ||||||
\(215\) | −28.4459 | −1.94000 | ||||||||
\(216\) | 7.49402 | + | 7.49402i | 0.509903 | + | 0.509903i | ||||
\(217\) | 4.97724 | + | 4.97724i | 0.337877 | + | 0.337877i | ||||
\(218\) | 17.8460 | + | 17.8460i | 1.20868 | + | 1.20868i | ||||
\(219\) | 0.116622 | − | 0.116622i | 0.00788057 | − | 0.00788057i | ||||
\(220\) | 55.0747 | − | 55.0747i | 3.71314 | − | 3.71314i | ||||
\(221\) | 7.29332 | 0.490602 | ||||||||
\(222\) | −1.21736 | + | 1.21736i | −0.0817037 | + | 0.0817037i | ||||
\(223\) | −11.6325 | −0.778967 | −0.389483 | − | 0.921033i | \(-0.627346\pi\) | ||||
−0.389483 | + | 0.921033i | \(0.627346\pi\) | |||||||
\(224\) | −2.44537 | + | 2.44537i | −0.163388 | + | 0.163388i | ||||
\(225\) | 17.8811i | 1.19208i | ||||||||
\(226\) | − | 27.8990i | − | 1.85581i | ||||||
\(227\) | 1.05806 | − | 1.05806i | 0.0702258 | − | 0.0702258i | −0.671122 | − | 0.741347i | \(-0.734187\pi\) |
0.741347 | + | 0.671122i | \(0.234187\pi\) | |||||||
\(228\) | −4.43398 | −0.293648 | ||||||||
\(229\) | 14.7703 | − | 14.7703i | 0.976047 | − | 0.976047i | −0.0236727 | − | 0.999720i | \(-0.507536\pi\) |
0.999720 | + | 0.0236727i | \(0.00753597\pi\) | |||||||
\(230\) | 16.7659 | 1.10551 | ||||||||
\(231\) | 2.20933 | − | 2.20933i | 0.145363 | − | 0.145363i | ||||
\(232\) | 19.0240 | − | 19.0240i | 1.24899 | − | 1.24899i | ||||
\(233\) | 3.21122 | + | 3.21122i | 0.210374 | + | 0.210374i | 0.804426 | − | 0.594052i | \(-0.202473\pi\) |
−0.594052 | + | 0.804426i | \(0.702473\pi\) | |||||||
\(234\) | 14.8506 | + | 14.8506i | 0.970815 | + | 0.970815i | ||||
\(235\) | −10.9236 | − | 10.9236i | −0.712577 | − | 0.712577i | ||||
\(236\) | −40.0322 | −2.60587 | ||||||||
\(237\) | 4.15895i | 0.270153i | ||||||||
\(238\) | − | 5.36382i | − | 0.347685i | ||||||
\(239\) | 7.46058 | + | 7.46058i | 0.482585 | + | 0.482585i | 0.905956 | − | 0.423371i | \(-0.139153\pi\) |
−0.423371 | + | 0.905956i | \(0.639153\pi\) | |||||||
\(240\) | −2.01591 | + | 2.01591i | −0.130127 | + | 0.130127i | ||||
\(241\) | 18.7378i | 1.20701i | 0.797361 | + | 0.603503i | \(0.206229\pi\) | ||||
−0.797361 | + | 0.603503i | \(0.793771\pi\) | |||||||
\(242\) | −70.8335 | −4.55335 | ||||||||
\(243\) | 8.35361 | + | 8.35361i | 0.535884 | + | 0.535884i | ||||
\(244\) | 13.8164i | 0.884503i | ||||||||
\(245\) | 3.38746 | 0.216417 | ||||||||
\(246\) | 4.67184 | − | 5.73059i | 0.297866 | − | 0.365369i | ||||
\(247\) | −8.12767 | −0.517151 | ||||||||
\(248\) | 26.5184i | 1.68392i | ||||||||
\(249\) | −2.84708 | − | 2.84708i | −0.180426 | − | 0.180426i | ||||
\(250\) | −11.8156 | −0.747287 | ||||||||
\(251\) | − | 9.37994i | − | 0.592057i | −0.955179 | − | 0.296028i | \(-0.904338\pi\) | ||
0.955179 | − | 0.296028i | \(-0.0956623\pi\) | |||||||
\(252\) | 7.01628 | − | 7.01628i | 0.441984 | − | 0.441984i | ||||
\(253\) | −9.46998 | − | 9.46998i | −0.595373 | − | 0.595373i | ||||
\(254\) | 5.62596i | 0.353004i | ||||||||
\(255\) | 3.75118i | 0.234908i | ||||||||
\(256\) | −25.4155 | −1.58847 | ||||||||
\(257\) | −3.54473 | − | 3.54473i | −0.221114 | − | 0.221114i | 0.587853 | − | 0.808967i | \(-0.299973\pi\) |
−0.808967 | + | 0.587853i | \(0.799973\pi\) | |||||||
\(258\) | −6.85640 | − | 6.85640i | −0.426861 | − | 0.426861i | ||||
\(259\) | 1.05427 | + | 1.05427i | 0.0655092 | + | 0.0655092i | ||||
\(260\) | −27.6753 | + | 27.6753i | −1.71635 | + | 1.71635i | ||||
\(261\) | 13.9451 | − | 13.9451i | 0.863178 | − | 0.863178i | ||||
\(262\) | 9.06186 | 0.559844 | ||||||||
\(263\) | −1.21091 | + | 1.21091i | −0.0746679 | + | 0.0746679i | −0.743454 | − | 0.668787i | \(-0.766814\pi\) |
0.668787 | + | 0.743454i | \(0.266814\pi\) | |||||||
\(264\) | 11.7712 | 0.724465 | ||||||||
\(265\) | 9.12512 | − | 9.12512i | 0.560552 | − | 0.560552i | ||||
\(266\) | 5.97744i | 0.366500i | ||||||||
\(267\) | − | 5.02508i | − | 0.307530i | ||||||
\(268\) | −28.9642 | + | 28.9642i | −1.76927 | + | 1.76927i | ||||
\(269\) | −13.9173 | −0.848555 | −0.424277 | − | 0.905532i | \(-0.639472\pi\) | ||||
−0.424277 | + | 0.905532i | \(0.639472\pi\) | |||||||
\(270\) | −15.9356 | + | 15.9356i | −0.969811 | + | 0.969811i | ||||
\(271\) | 26.4290 | 1.60545 | 0.802724 | − | 0.596351i | \(-0.203383\pi\) | ||||
0.802724 | + | 0.596351i | \(0.203383\pi\) | |||||||
\(272\) | 2.76443 | − | 2.76443i | 0.167618 | − | 0.167618i | ||||
\(273\) | −1.11020 | + | 1.11020i | −0.0671924 | + | 0.0671924i | ||||
\(274\) | 6.09238 | + | 6.09238i | 0.368054 | + | 0.368054i | ||||
\(275\) | 29.2989 | + | 29.2989i | 1.76679 | + | 1.76679i | ||||
\(276\) | 2.59607 | + | 2.59607i | 0.156265 | + | 0.156265i | ||||
\(277\) | −14.9441 | −0.897903 | −0.448952 | − | 0.893556i | \(-0.648202\pi\) | ||||
−0.448952 | + | 0.893556i | \(0.648202\pi\) | |||||||
\(278\) | − | 21.9629i | − | 1.31725i | ||||||
\(279\) | 19.4387i | 1.16376i | ||||||||
\(280\) | 9.02407 | + | 9.02407i | 0.539291 | + | 0.539291i | ||||
\(281\) | −4.51235 | + | 4.51235i | −0.269184 | + | 0.269184i | −0.828772 | − | 0.559587i | \(-0.810960\pi\) |
0.559587 | + | 0.828772i | \(0.310960\pi\) | |||||||
\(282\) | − | 5.26590i | − | 0.313580i | ||||||
\(283\) | 1.27954 | 0.0760606 | 0.0380303 | − | 0.999277i | \(-0.487892\pi\) | ||||
0.0380303 | + | 0.999277i | \(0.487892\pi\) | |||||||
\(284\) | 22.2542 | + | 22.2542i | 1.32054 | + | 1.32054i | ||||
\(285\) | − | 4.18032i | − | 0.247621i | ||||||
\(286\) | 48.6666 | 2.87771 | ||||||||
\(287\) | −4.96288 | − | 4.04597i | −0.292949 | − | 0.238826i | ||||
\(288\) | −9.55041 | −0.562763 | ||||||||
\(289\) | 11.8560i | 0.697411i | ||||||||
\(290\) | 40.4534 | + | 40.4534i | 2.37551 | + | 2.37551i | ||||
\(291\) | 2.60449 | 0.152678 | ||||||||
\(292\) | − | 1.21370i | − | 0.0710264i | ||||||
\(293\) | 9.79823 | − | 9.79823i | 0.572419 | − | 0.572419i | −0.360385 | − | 0.932804i | \(-0.617355\pi\) |
0.932804 | + | 0.360385i | \(0.117355\pi\) | |||||||
\(294\) | 0.816490 | + | 0.816490i | 0.0476186 | + | 0.0476186i | ||||
\(295\) | − | 37.7420i | − | 2.19742i | ||||||
\(296\) | 5.61708i | 0.326486i | ||||||||
\(297\) | 18.0020 | 1.04458 | ||||||||
\(298\) | 29.3847 | + | 29.3847i | 1.70221 | + | 1.70221i | ||||
\(299\) | 4.75871 | + | 4.75871i | 0.275203 | + | 0.275203i | ||||
\(300\) | −8.03192 | − | 8.03192i | −0.463723 | − | 0.463723i | ||||
\(301\) | −5.93787 | + | 5.93787i | −0.342253 | + | 0.342253i | ||||
\(302\) | −31.7178 | + | 31.7178i | −1.82516 | + | 1.82516i | ||||
\(303\) | 3.93328 | 0.225961 | ||||||||
\(304\) | −3.08068 | + | 3.08068i | −0.176689 | + | 0.176689i | ||||
\(305\) | −13.0259 | −0.745864 | ||||||||
\(306\) | 10.4742 | − | 10.4742i | 0.598771 | − | 0.598771i | ||||
\(307\) | − | 15.9502i | − | 0.910328i | −0.890408 | − | 0.455164i | \(-0.849581\pi\) | ||
0.890408 | − | 0.455164i | \(-0.150419\pi\) | |||||||
\(308\) | − | 22.9929i | − | 1.31014i | ||||||
\(309\) | 5.94014 | − | 5.94014i | 0.337923 | − | 0.337923i | ||||
\(310\) | −56.3898 | −3.20273 | ||||||||
\(311\) | 1.31932 | − | 1.31932i | 0.0748115 | − | 0.0748115i | −0.668711 | − | 0.743522i | \(-0.733154\pi\) |
0.743522 | + | 0.668711i | \(0.233154\pi\) | |||||||
\(312\) | −5.91507 | −0.334875 | ||||||||
\(313\) | −2.61177 | + | 2.61177i | −0.147626 | + | 0.147626i | −0.777057 | − | 0.629431i | \(-0.783288\pi\) |
0.629431 | + | 0.777057i | \(0.283288\pi\) | |||||||
\(314\) | −24.7151 | + | 24.7151i | −1.39475 | + | 1.39475i | ||||
\(315\) | 6.61488 | + | 6.61488i | 0.372706 | + | 0.372706i | ||||
\(316\) | 21.6414 | + | 21.6414i | 1.21742 | + | 1.21742i | ||||
\(317\) | −8.17711 | − | 8.17711i | −0.459272 | − | 0.459272i | 0.439144 | − | 0.898416i | \(-0.355282\pi\) |
−0.898416 | + | 0.439144i | \(0.855282\pi\) | |||||||
\(318\) | 4.39891 | 0.246679 | ||||||||
\(319\) | − | 45.6990i | − | 2.55865i | ||||||
\(320\) | − | 39.3831i | − | 2.20158i | ||||||
\(321\) | 4.52622 | + | 4.52622i | 0.252629 | + | 0.252629i | ||||
\(322\) | 3.49976 | − | 3.49976i | 0.195034 | − | 0.195034i | ||||
\(323\) | 5.73249i | 0.318964i | ||||||||
\(324\) | 24.8325 | 1.37959 | ||||||||
\(325\) | −14.7228 | − | 14.7228i | −0.816676 | − | 0.816676i | ||||
\(326\) | 6.47067i | 0.358377i | ||||||||
\(327\) | −5.21044 | −0.288138 | ||||||||
\(328\) | −2.44261 | − | 23.9992i | −0.134870 | − | 1.32514i | ||||
\(329\) | −4.56044 | −0.251425 | ||||||||
\(330\) | 25.0307i | 1.37790i | ||||||||
\(331\) | −5.68372 | − | 5.68372i | −0.312405 | − | 0.312405i | 0.533435 | − | 0.845841i | \(-0.320901\pi\) |
−0.845841 | + | 0.533435i | \(0.820901\pi\) | |||||||
\(332\) | −29.6299 | −1.62615 | ||||||||
\(333\) | 4.11747i | 0.225636i | ||||||||
\(334\) | −33.4807 | + | 33.4807i | −1.83198 | + | 1.83198i | ||||
\(335\) | −27.3072 | − | 27.3072i | −1.49195 | − | 1.49195i | ||||
\(336\) | 0.841613i | 0.0459137i | ||||||||
\(337\) | − | 26.9418i | − | 1.46761i | −0.679359 | − | 0.733806i | \(-0.737742\pi\) | ||
0.679359 | − | 0.733806i | \(-0.262258\pi\) | |||||||
\(338\) | 6.28924 | 0.342090 | ||||||||
\(339\) | 4.07279 | + | 4.07279i | 0.221204 | + | 0.221204i | ||||
\(340\) | 19.5195 | + | 19.5195i | 1.05860 | + | 1.05860i | ||||
\(341\) | 31.8509 | + | 31.8509i | 1.72483 | + | 1.72483i | ||||
\(342\) | −11.6725 | + | 11.6725i | −0.631175 | + | 0.631175i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −31.6365 | −1.70573 | ||||||||
\(345\) | −2.44755 | + | 2.44755i | −0.131772 | + | 0.131772i | ||||
\(346\) | 52.6860 | 2.83242 | ||||||||
\(347\) | 21.5790 | − | 21.5790i | 1.15842 | − | 1.15842i | 0.173609 | − | 0.984815i | \(-0.444457\pi\) |
0.984815 | − | 0.173609i | \(-0.0555430\pi\) | |||||||
\(348\) | 12.5278i | 0.671561i | ||||||||
\(349\) | 11.3453i | 0.607298i | 0.952784 | + | 0.303649i | \(0.0982051\pi\) | ||||
−0.952784 | + | 0.303649i | \(0.901795\pi\) | |||||||
\(350\) | −10.8278 | + | 10.8278i | −0.578771 | + | 0.578771i | ||||
\(351\) | −9.04608 | −0.482844 | ||||||||
\(352\) | −15.6487 | + | 15.6487i | −0.834079 | + | 0.834079i | ||||
\(353\) | −11.8800 | −0.632308 | −0.316154 | − | 0.948708i | \(-0.602392\pi\) | ||||
−0.316154 | + | 0.948708i | \(0.602392\pi\) | |||||||
\(354\) | 9.09705 | − | 9.09705i | 0.483503 | − | 0.483503i | ||||
\(355\) | −20.9810 | + | 20.9810i | −1.11356 | + | 1.11356i | ||||
\(356\) | −26.1484 | − | 26.1484i | −1.38586 | − | 1.38586i | ||||
\(357\) | 0.783031 | + | 0.783031i | 0.0414424 | + | 0.0414424i | ||||
\(358\) | 1.46822 | + | 1.46822i | 0.0775980 | + | 0.0775980i | ||||
\(359\) | 11.8506 | 0.625452 | 0.312726 | − | 0.949843i | \(-0.398758\pi\) | ||||
0.312726 | + | 0.949843i | \(0.398758\pi\) | |||||||
\(360\) | 35.2436i | 1.85750i | ||||||||
\(361\) | 12.6117i | 0.663774i | ||||||||
\(362\) | 32.0789 | + | 32.0789i | 1.68603 | + | 1.68603i | ||||
\(363\) | 10.3405 | − | 10.3405i | 0.542737 | − | 0.542737i | ||||
\(364\) | 11.5540i | 0.605595i | ||||||||
\(365\) | 1.14426 | 0.0598935 | ||||||||
\(366\) | −3.13968 | − | 3.13968i | −0.164114 | − | 0.164114i | ||||
\(367\) | − | 0.112635i | − | 0.00587948i | −0.999996 | − | 0.00293974i | \(-0.999064\pi\) | ||
0.999996 | − | 0.00293974i | \(-0.000935750\pi\) | |||||||
\(368\) | 3.60745 | 0.188051 | ||||||||
\(369\) | −1.79049 | − | 17.5921i | −0.0932094 | − | 0.915806i | ||||
\(370\) | −11.9444 | −0.620960 | ||||||||
\(371\) | − | 3.80960i | − | 0.197785i | ||||||
\(372\) | −8.73153 | − | 8.73153i | −0.452709 | − | 0.452709i | ||||
\(373\) | −7.31055 | −0.378526 | −0.189263 | − | 0.981926i | \(-0.560610\pi\) | ||||
−0.189263 | + | 0.981926i | \(0.560610\pi\) | |||||||
\(374\) | − | 34.3248i | − | 1.77489i | ||||||
\(375\) | 1.72489 | − | 1.72489i | 0.0890731 | − | 0.0890731i | ||||
\(376\) | −12.1488 | − | 12.1488i | −0.626529 | − | 0.626529i | ||||
\(377\) | 22.9640i | 1.18271i | ||||||||
\(378\) | 6.65288i | 0.342187i | ||||||||
\(379\) | −12.5411 | −0.644194 | −0.322097 | − | 0.946707i | \(-0.604388\pi\) | ||||
−0.322097 | + | 0.946707i | \(0.604388\pi\) | |||||||
\(380\) | −21.7526 | − | 21.7526i | −1.11588 | − | 1.11588i | ||||
\(381\) | −0.821299 | − | 0.821299i | −0.0420764 | − | 0.0420764i | ||||
\(382\) | 9.02799 | + | 9.02799i | 0.461912 | + | 0.461912i | ||||
\(383\) | 17.0533 | − | 17.0533i | 0.871382 | − | 0.871382i | −0.121241 | − | 0.992623i | \(-0.538687\pi\) |
0.992623 | + | 0.121241i | \(0.0386873\pi\) | |||||||
\(384\) | 7.10471 | − | 7.10471i | 0.362561 | − | 0.362561i | ||||
\(385\) | 21.6774 | 1.10478 | ||||||||
\(386\) | 27.5829 | − | 27.5829i | 1.40393 | − | 1.40393i | ||||
\(387\) | −23.1904 | −1.17883 | ||||||||
\(388\) | 13.5527 | − | 13.5527i | 0.688033 | − | 0.688033i | ||||
\(389\) | − | 9.88763i | − | 0.501323i | −0.968075 | − | 0.250661i | \(-0.919352\pi\) | ||
0.968075 | − | 0.250661i | \(-0.0806481\pi\) | |||||||
\(390\) | − | 12.5781i | − | 0.636915i | ||||||
\(391\) | 3.35634 | − | 3.35634i | 0.169738 | − | 0.169738i | ||||
\(392\) | 3.76741 | 0.190283 | ||||||||
\(393\) | −1.32288 | + | 1.32288i | −0.0667307 | + | 0.0667307i | ||||
\(394\) | 30.3375 | 1.52838 | ||||||||
\(395\) | −20.4033 | + | 20.4033i | −1.02660 | + | 1.02660i | ||||
\(396\) | 44.8994 | − | 44.8994i | 2.25628 | − | 2.25628i | ||||
\(397\) | 15.9964 | + | 15.9964i | 0.802837 | + | 0.802837i | 0.983538 | − | 0.180701i | \(-0.0578367\pi\) |
−0.180701 | + | 0.983538i | \(0.557837\pi\) | |||||||
\(398\) | −38.0397 | − | 38.0397i | −1.90676 | − | 1.90676i | ||||
\(399\) | −0.872609 | − | 0.872609i | −0.0436851 | − | 0.0436851i | ||||
\(400\) | −11.1610 | −0.558049 | ||||||||
\(401\) | 13.3023i | 0.664286i | 0.943229 | + | 0.332143i | \(0.107772\pi\) | ||||
−0.943229 | + | 0.332143i | \(0.892228\pi\) | |||||||
\(402\) | − | 13.1638i | − | 0.656553i | ||||||
\(403\) | −16.0053 | − | 16.0053i | −0.797278 | − | 0.797278i | ||||
\(404\) | 20.4671 | − | 20.4671i | 1.01828 | − | 1.01828i | ||||
\(405\) | 23.4119i | 1.16335i | ||||||||
\(406\) | 16.8887 | 0.838172 | ||||||||
\(407\) | 6.74662 | + | 6.74662i | 0.334417 | + | 0.334417i | ||||
\(408\) | 4.17193i | 0.206541i | ||||||||
\(409\) | −10.0331 | −0.496105 | −0.248053 | − | 0.968747i | \(-0.579791\pi\) | ||||
−0.248053 | + | 0.968747i | \(0.579791\pi\) | |||||||
\(410\) | 51.0330 | − | 5.19407i | 2.52034 | − | 0.256517i | ||||
\(411\) | −1.77878 | −0.0877406 | ||||||||
\(412\) | − | 61.8199i | − | 3.04565i | ||||||
\(413\) | −7.87835 | − | 7.87835i | −0.387668 | − | 0.387668i | ||||
\(414\) | 13.6683 | 0.671763 | ||||||||
\(415\) | − | 27.9348i | − | 1.37127i | ||||||
\(416\) | 7.86355 | − | 7.86355i | 0.385542 | − | 0.385542i | ||||
\(417\) | 3.20623 | + | 3.20623i | 0.157010 | + | 0.157010i | ||||
\(418\) | 38.2515i | 1.87094i | ||||||||
\(419\) | 38.0389i | 1.85832i | 0.369676 | + | 0.929161i | \(0.379469\pi\) | ||||
−0.369676 | + | 0.929161i | \(0.620531\pi\) | |||||||
\(420\) | −5.94259 | −0.289969 | ||||||||
\(421\) | 6.25574 | + | 6.25574i | 0.304886 | + | 0.304886i | 0.842922 | − | 0.538036i | \(-0.180833\pi\) |
−0.538036 | + | 0.842922i | \(0.680833\pi\) | |||||||
\(422\) | −15.5823 | − | 15.5823i | −0.758536 | − | 0.758536i | ||||
\(423\) | −8.90542 | − | 8.90542i | −0.432996 | − | 0.432996i | ||||
\(424\) | 10.1486 | − | 10.1486i | 0.492861 | − | 0.492861i | ||||
\(425\) | −10.3841 | + | 10.3841i | −0.503703 | + | 0.503703i | ||||
\(426\) | −10.1142 | −0.490036 | ||||||||
\(427\) | −2.71907 | + | 2.71907i | −0.131585 | + | 0.131585i | ||||
\(428\) | 47.1051 | 2.27691 | ||||||||
\(429\) | −7.10453 | + | 7.10453i | −0.343010 | + | 0.343010i | ||||
\(430\) | − | 67.2734i | − | 3.24421i | ||||||
\(431\) | 24.9643i | 1.20249i | 0.799066 | + | 0.601243i | \(0.205328\pi\) | ||||
−0.799066 | + | 0.601243i | \(0.794672\pi\) | |||||||
\(432\) | −3.42879 | + | 3.42879i | −0.164968 | + | 0.164968i | ||||
\(433\) | 31.2296 | 1.50080 | 0.750400 | − | 0.660984i | \(-0.229861\pi\) | ||||
0.750400 | + | 0.660984i | \(0.229861\pi\) | |||||||
\(434\) | −11.7710 | + | 11.7710i | −0.565024 | + | 0.565024i | ||||
\(435\) | −11.8111 | −0.566299 | ||||||||
\(436\) | −27.1129 | + | 27.1129i | −1.29847 | + | 1.29847i | ||||
\(437\) | −3.74031 | + | 3.74031i | −0.178923 | + | 0.178923i | ||||
\(438\) | 0.275805 | + | 0.275805i | 0.0131785 | + | 0.0131785i | ||||
\(439\) | 1.37084 | + | 1.37084i | 0.0654266 | + | 0.0654266i | 0.739063 | − | 0.673636i | \(-0.235269\pi\) |
−0.673636 | + | 0.739063i | \(0.735269\pi\) | |||||||
\(440\) | 57.7479 | + | 57.7479i | 2.75302 | + | 2.75302i | ||||
\(441\) | 2.76161 | 0.131505 | ||||||||
\(442\) | 17.2484i | 0.820421i | ||||||||
\(443\) | − | 14.0283i | − | 0.666503i | −0.942838 | − | 0.333251i | \(-0.891854\pi\) | ||
0.942838 | − | 0.333251i | \(-0.108146\pi\) | |||||||
\(444\) | −1.84950 | − | 1.84950i | −0.0877733 | − | 0.0877733i | ||||
\(445\) | 24.6524 | − | 24.6524i | 1.16864 | − | 1.16864i | ||||
\(446\) | − | 27.5102i | − | 1.30265i | ||||||
\(447\) | −8.57938 | −0.405791 | ||||||||
\(448\) | −8.22092 | − | 8.22092i | −0.388402 | − | 0.388402i | ||||
\(449\) | − | 19.4083i | − | 0.915937i | −0.888969 | − | 0.457968i | \(-0.848577\pi\) | ||
0.888969 | − | 0.457968i | \(-0.151423\pi\) | |||||||
\(450\) | −42.2881 | −1.99348 | ||||||||
\(451\) | −31.7590 | − | 25.8914i | −1.49547 | − | 1.21918i | ||||
\(452\) | 42.3862 | 1.99368 | ||||||||
\(453\) | − | 9.26057i | − | 0.435100i | ||||||
\(454\) | 2.50226 | + | 2.50226i | 0.117437 | + | 0.117437i | ||||
\(455\) | −10.8930 | −0.510673 | ||||||||
\(456\) | − | 4.64920i | − | 0.217719i | ||||||
\(457\) | −7.73063 | + | 7.73063i | −0.361624 | + | 0.361624i | −0.864410 | − | 0.502787i | \(-0.832308\pi\) |
0.502787 | + | 0.864410i | \(0.332308\pi\) | |||||||
\(458\) | 34.9310 | + | 34.9310i | 1.63222 | + | 1.63222i | ||||
\(459\) | 6.38025i | 0.297805i | ||||||||
\(460\) | 25.4720i | 1.18764i | ||||||||
\(461\) | −6.71449 | −0.312725 | −0.156362 | − | 0.987700i | \(-0.549977\pi\) | ||||
−0.156362 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(462\) | 5.22498 | + | 5.22498i | 0.243088 | + | 0.243088i | ||||
\(463\) | −1.67116 | − | 1.67116i | −0.0776654 | − | 0.0776654i | 0.667207 | − | 0.744872i | \(-0.267490\pi\) |
−0.744872 | + | 0.667207i | \(0.767490\pi\) | |||||||
\(464\) | 8.70418 | + | 8.70418i | 0.404081 | + | 0.404081i | ||||
\(465\) | 8.23200 | − | 8.23200i | 0.381750 | − | 0.381750i | ||||
\(466\) | −7.59440 | + | 7.59440i | −0.351804 | + | 0.351804i | ||||
\(467\) | 16.5906 | 0.767720 | 0.383860 | − | 0.923391i | \(-0.374594\pi\) | ||||
0.383860 | + | 0.923391i | \(0.374594\pi\) | |||||||
\(468\) | −22.5622 | + | 22.5622i | −1.04294 | + | 1.04294i | ||||
\(469\) | −11.4003 | −0.526418 | ||||||||
\(470\) | 25.8338 | − | 25.8338i | 1.19163 | − | 1.19163i | ||||
\(471\) | − | 7.21600i | − | 0.332496i | ||||||
\(472\) | − | 41.9753i | − | 1.93207i | ||||||
\(473\) | −37.9983 | + | 37.9983i | −1.74716 | + | 1.74716i | ||||
\(474\) | −9.83573 | −0.451770 | ||||||||
\(475\) | 11.5720 | − | 11.5720i | 0.530961 | − | 0.530961i | ||||
\(476\) | 8.14911 | 0.373514 | ||||||||
\(477\) | 7.43921 | − | 7.43921i | 0.340618 | − | 0.340618i | ||||
\(478\) | −17.6439 | + | 17.6439i | −0.807015 | + | 0.807015i | ||||
\(479\) | −12.8402 | − | 12.8402i | −0.586683 | − | 0.586683i | 0.350048 | − | 0.936732i | \(-0.386165\pi\) |
−0.936732 | + | 0.350048i | \(0.886165\pi\) | |||||||
\(480\) | 4.04447 | + | 4.04447i | 0.184604 | + | 0.184604i | ||||
\(481\) | −3.39021 | − | 3.39021i | −0.154580 | − | 0.154580i | ||||
\(482\) | −44.3140 | −2.01845 | ||||||||
\(483\) | 1.02182i | 0.0464943i | ||||||||
\(484\) | − | 107.615i | − | 4.89161i | ||||||
\(485\) | 12.7773 | + | 12.7773i | 0.580189 | + | 0.580189i | ||||
\(486\) | −19.7559 | + | 19.7559i | −0.896147 | + | 0.896147i | ||||
\(487\) | 31.7450i | 1.43850i | 0.694750 | + | 0.719251i | \(0.255515\pi\) | ||||
−0.694750 | + | 0.719251i | \(0.744485\pi\) | |||||||
\(488\) | −14.4870 | −0.655795 | ||||||||
\(489\) | −0.944612 | − | 0.944612i | −0.0427168 | − | 0.0427168i | ||||
\(490\) | 8.01120i | 0.361909i | ||||||||
\(491\) | −22.1790 | −1.00092 | −0.500461 | − | 0.865759i | \(-0.666836\pi\) | ||||
−0.500461 | + | 0.865759i | \(0.666836\pi\) | |||||||
\(492\) | 8.70633 | + | 7.09781i | 0.392512 | + | 0.319994i | ||||
\(493\) | 16.1966 | 0.729459 | ||||||||
\(494\) | − | 19.2216i | − | 0.864820i | ||||||
\(495\) | 42.3307 | + | 42.3307i | 1.90262 | + | 1.90262i | ||||
\(496\) | −12.1331 | −0.544794 | ||||||||
\(497\) | 8.75925i | 0.392906i | ||||||||
\(498\) | 6.73321 | − | 6.73321i | 0.301722 | − | 0.301722i | ||||
\(499\) | 15.4353 | + | 15.4353i | 0.690977 | + | 0.690977i | 0.962447 | − | 0.271470i | \(-0.0875097\pi\) |
−0.271470 | + | 0.962447i | \(0.587510\pi\) | |||||||
\(500\) | − | 17.9512i | − | 0.802802i | ||||||
\(501\) | − | 9.77527i | − | 0.436727i | ||||||
\(502\) | 22.1831 | 0.990082 | ||||||||
\(503\) | 20.2826 | + | 20.2826i | 0.904356 | + | 0.904356i | 0.995809 | − | 0.0914529i | \(-0.0291511\pi\) |
−0.0914529 | + | 0.995809i | \(0.529151\pi\) | |||||||
\(504\) | 7.35683 | + | 7.35683i | 0.327699 | + | 0.327699i | ||||
\(505\) | 19.2962 | + | 19.2962i | 0.858670 | + | 0.858670i | ||||
\(506\) | 22.3961 | − | 22.3961i | 0.995628 | − | 0.995628i | ||||
\(507\) | −0.918127 | + | 0.918127i | −0.0407754 | + | 0.0407754i | ||||
\(508\) | −8.54738 | −0.379229 | ||||||||
\(509\) | −5.12520 | + | 5.12520i | −0.227171 | + | 0.227171i | −0.811510 | − | 0.584339i | \(-0.801354\pi\) |
0.584339 | + | 0.811510i | \(0.301354\pi\) | |||||||
\(510\) | −8.87138 | −0.392831 | ||||||||
\(511\) | 0.238857 | − | 0.238857i | 0.0105664 | − | 0.0105664i | ||||
\(512\) | − | 18.9492i | − | 0.837442i | ||||||
\(513\) | − | 7.11015i | − | 0.313921i | ||||||
\(514\) | 8.38313 | − | 8.38313i | 0.369764 | − | 0.369764i | ||||
\(515\) | 58.2832 | 2.56827 | ||||||||
\(516\) | 10.4168 | − | 10.4168i | 0.458572 | − | 0.458572i | ||||
\(517\) | −29.1837 | −1.28350 | ||||||||
\(518\) | −2.49330 | + | 2.49330i | −0.109550 | + | 0.109550i | ||||
\(519\) | −7.69131 | + | 7.69131i | −0.337611 | + | 0.337611i | ||||
\(520\) | −29.0186 | − | 29.0186i | −1.27255 | − | 1.27255i | ||||
\(521\) | −12.4076 | − | 12.4076i | −0.543586 | − | 0.543586i | 0.380992 | − | 0.924578i | \(-0.375583\pi\) |
−0.924578 | + | 0.380992i | \(0.875583\pi\) | |||||||
\(522\) | 32.9795 | + | 32.9795i | 1.44347 | + | 1.44347i | ||||
\(523\) | −7.87303 | −0.344264 | −0.172132 | − | 0.985074i | \(-0.555065\pi\) | ||||
−0.172132 | + | 0.985074i | \(0.555065\pi\) | |||||||
\(524\) | 13.7675i | 0.601434i | ||||||||
\(525\) | − | 3.16137i | − | 0.137973i | ||||||
\(526\) | −2.86375 | − | 2.86375i | −0.124865 | − | 0.124865i | ||||
\(527\) | −11.2886 | + | 11.2886i | −0.491739 | + | 0.491739i | ||||
\(528\) | 5.38575i | 0.234385i | ||||||||
\(529\) | −18.6201 | −0.809571 | ||||||||
\(530\) | 21.5805 | + | 21.5805i | 0.937397 | + | 0.937397i | ||||
\(531\) | − | 30.7690i | − | 1.33526i | ||||||
\(532\) | −9.08137 | −0.393727 | ||||||||
\(533\) | 15.9591 | + | 13.0106i | 0.691264 | + | 0.563551i | ||||
\(534\) | 11.8841 | 0.514275 | ||||||||
\(535\) | 44.4102i | 1.92002i | ||||||||
\(536\) | −30.3700 | − | 30.3700i | −1.31179 | − | 1.31179i | ||||
\(537\) | −0.428674 | −0.0184986 | ||||||||
\(538\) | − | 32.9139i | − | 1.41902i | ||||||
\(539\) | 4.52500 | − | 4.52500i | 0.194906 | − | 0.194906i | ||||
\(540\) | −24.2106 | − | 24.2106i | −1.04186 | − | 1.04186i | ||||
\(541\) | 20.9792i | 0.901967i | 0.892532 | + | 0.450983i | \(0.148927\pi\) | ||||
−0.892532 | + | 0.450983i | \(0.851073\pi\) | |||||||
\(542\) | 62.5034i | 2.68475i | ||||||||
\(543\) | −9.36599 | −0.401933 | ||||||||
\(544\) | −5.54620 | − | 5.54620i | −0.237791 | − | 0.237791i | ||||
\(545\) | −25.5618 | − | 25.5618i | −1.09495 | − | 1.09495i | ||||
\(546\) | −2.62558 | − | 2.62558i | −0.112364 | − | 0.112364i | ||||
\(547\) | 2.82793 | − | 2.82793i | 0.120914 | − | 0.120914i | −0.644061 | − | 0.764974i | \(-0.722752\pi\) |
0.764974 | + | 0.644061i | \(0.222752\pi\) | |||||||
\(548\) | −9.25599 | + | 9.25599i | −0.395396 | + | 0.395396i | ||||
\(549\) | −10.6193 | −0.453223 | ||||||||
\(550\) | −69.2906 | + | 69.2906i | −2.95456 | + | 2.95456i | ||||
\(551\) | −18.0495 | −0.768935 | ||||||||
\(552\) | −2.72208 | + | 2.72208i | −0.115859 | + | 0.115859i | ||||
\(553\) | 8.51806i | 0.362225i | ||||||||
\(554\) | − | 35.3421i | − | 1.50154i | ||||||
\(555\) | 1.74369 | − | 1.74369i | 0.0740155 | − | 0.0740155i | ||||
\(556\) | 33.3677 | 1.41511 | ||||||||
\(557\) | 4.53365 | − | 4.53365i | 0.192097 | − | 0.192097i | −0.604505 | − | 0.796602i | \(-0.706629\pi\) |
0.796602 | + | 0.604505i | \(0.206629\pi\) | |||||||
\(558\) | −45.9716 | −1.94613 | ||||||||
\(559\) | 19.0943 | − | 19.0943i | 0.807605 | − | 0.807605i | ||||
\(560\) | −4.12885 | + | 4.12885i | −0.174476 | + | 0.174476i | ||||
\(561\) | 5.01086 | + | 5.01086i | 0.211559 | + | 0.211559i | ||||
\(562\) | −10.6715 | − | 10.6715i | −0.450151 | − | 0.450151i | ||||
\(563\) | −7.17733 | − | 7.17733i | −0.302488 | − | 0.302488i | 0.539498 | − | 0.841987i | \(-0.318614\pi\) |
−0.841987 | + | 0.539498i | \(0.818614\pi\) | |||||||
\(564\) | 8.00034 | 0.336875 | ||||||||
\(565\) | 39.9613i | 1.68118i | ||||||||
\(566\) | 3.02605i | 0.127194i | ||||||||
\(567\) | 4.88705 | + | 4.88705i | 0.205237 | + | 0.205237i | ||||
\(568\) | −23.3343 | + | 23.3343i | −0.979087 | + | 0.979087i | ||||
\(569\) | − | 7.20779i | − | 0.302166i | −0.988521 | − | 0.151083i | \(-0.951724\pi\) | ||
0.988521 | − | 0.151083i | \(-0.0482761\pi\) | |||||||
\(570\) | 9.88626 | 0.414090 | ||||||||
\(571\) | 23.6673 | + | 23.6673i | 0.990447 | + | 0.990447i | 0.999955 | − | 0.00950800i | \(-0.00302654\pi\) |
−0.00950800 | + | 0.999955i | \(0.503027\pi\) | |||||||
\(572\) | 73.9379i | 3.09150i | ||||||||
\(573\) | −2.63588 | −0.110116 | ||||||||
\(574\) | 9.56854 | − | 11.7370i | 0.399383 | − | 0.489892i | ||||
\(575\) | −13.5507 | −0.565105 | ||||||||
\(576\) | − | 32.1069i | − | 1.33779i | ||||||
\(577\) | 24.2356 | + | 24.2356i | 1.00894 | + | 1.00894i | 0.999960 | + | 0.00898091i | \(0.00285875\pi\) |
0.00898091 | + | 0.999960i | \(0.497141\pi\) | |||||||
\(578\) | −28.0389 | −1.16626 | ||||||||
\(579\) | 8.05332i | 0.334685i | ||||||||
\(580\) | −61.4599 | + | 61.4599i | −2.55198 | + | 2.55198i | ||||
\(581\) | −5.83118 | − | 5.83118i | −0.241918 | − | 0.241918i | ||||
\(582\) | 6.15951i | 0.255320i | ||||||||
\(583\) | − | 24.3788i | − | 1.00967i | ||||||
\(584\) | 1.27261 | 0.0526610 | ||||||||
\(585\) | −21.2714 | − | 21.2714i | −0.879464 | − | 0.879464i | ||||
\(586\) | 23.1724 | + | 23.1724i | 0.957242 | + | 0.957242i | ||||
\(587\) | 13.7688 | + | 13.7688i | 0.568301 | + | 0.568301i | 0.931652 | − | 0.363351i | \(-0.118368\pi\) |
−0.363351 | + | 0.931652i | \(0.618368\pi\) | |||||||
\(588\) | −1.24047 | + | 1.24047i | −0.0511562 | + | 0.0511562i | ||||
\(589\) | 12.5800 | − | 12.5800i | 0.518350 | − | 0.518350i | ||||
\(590\) | 89.2581 | 3.67470 | ||||||||
\(591\) | −4.42878 | + | 4.42878i | −0.182176 | + | 0.182176i | ||||
\(592\) | −2.57002 | −0.105627 | ||||||||
\(593\) | −28.3190 | + | 28.3190i | −1.16292 | + | 1.16292i | −0.179091 | + | 0.983833i | \(0.557316\pi\) |
−0.983833 | + | 0.179091i | \(0.942684\pi\) | |||||||
\(594\) | 42.5739i | 1.74683i | ||||||||
\(595\) | 7.68291i | 0.314968i | ||||||||
\(596\) | −44.6434 | + | 44.6434i | −1.82867 | + | 1.82867i | ||||
\(597\) | 11.1064 | 0.454553 | ||||||||
\(598\) | −11.2541 | + | 11.2541i | −0.460216 | + | 0.460216i | ||||
\(599\) | 15.7542 | 0.643699 | 0.321850 | − | 0.946791i | \(-0.395695\pi\) | ||||
0.321850 | + | 0.946791i | \(0.395695\pi\) | |||||||
\(600\) | 8.42177 | − | 8.42177i | 0.343817 | − | 0.343817i | ||||
\(601\) | −27.4544 | + | 27.4544i | −1.11989 | + | 1.11989i | −0.128131 | + | 0.991757i | \(0.540898\pi\) |
−0.991757 | + | 0.128131i | \(0.959102\pi\) | |||||||
\(602\) | −14.0428 | − | 14.0428i | −0.572342 | − | 0.572342i | ||||
\(603\) | −22.2620 | − | 22.2620i | −0.906580 | − | 0.906580i | ||||
\(604\) | −48.1881 | − | 48.1881i | −1.96074 | − | 1.96074i | ||||
\(605\) | 101.459 | 4.12489 | ||||||||
\(606\) | 9.30204i | 0.377870i | ||||||||
\(607\) | 2.17266i | 0.0881857i | 0.999027 | + | 0.0440928i | \(0.0140397\pi\) | ||||
−0.999027 | + | 0.0440928i | \(0.985960\pi\) | |||||||
\(608\) | 6.18069 | + | 6.18069i | 0.250660 | + | 0.250660i | ||||
\(609\) | −2.46548 | + | 2.46548i | −0.0999061 | + | 0.0999061i | ||||
\(610\) | − | 30.8058i | − | 1.24729i | ||||||
\(611\) | 14.6650 | 0.593281 | ||||||||
\(612\) | 15.9132 | + | 15.9132i | 0.643254 | + | 0.643254i | ||||
\(613\) | 2.17153i | 0.0877073i | 0.999038 | + | 0.0438536i | \(0.0139635\pi\) | ||||
−0.999038 | + | 0.0438536i | \(0.986036\pi\) | |||||||
\(614\) | 37.7216 | 1.52232 | ||||||||
\(615\) | −6.69175 | + | 8.20824i | −0.269837 | + | 0.330988i | ||||
\(616\) | 24.1089 | 0.971374 | ||||||||
\(617\) | − | 35.5485i | − | 1.43113i | −0.698548 | − | 0.715564i | \(-0.746170\pi\) | ||
0.698548 | − | 0.715564i | \(-0.253830\pi\) | |||||||
\(618\) | 14.0482 | + | 14.0482i | 0.565101 | + | 0.565101i | ||||
\(619\) | −0.332688 | −0.0133719 | −0.00668593 | − | 0.999978i | \(-0.502128\pi\) | ||||
−0.00668593 | + | 0.999978i | \(0.502128\pi\) | |||||||
\(620\) | − | 85.6716i | − | 3.44066i | ||||||
\(621\) | −4.16296 | + | 4.16296i | −0.167054 | + | 0.167054i | ||||
\(622\) | 3.12012 | + | 3.12012i | 0.125106 | + | 0.125106i | ||||
\(623\) | − | 10.2920i | − | 0.412341i | ||||||
\(624\) | − | 2.70636i | − | 0.108341i | ||||||
\(625\) | −15.4502 | −0.618009 | ||||||||
\(626\) | −6.17672 | − | 6.17672i | −0.246871 | − | 0.246871i | ||||
\(627\) | −5.58411 | − | 5.58411i | −0.223008 | − | 0.223008i | ||||
\(628\) | −37.5490 | − | 37.5490i | −1.49837 | − | 1.49837i | ||||
\(629\) | −2.39113 | + | 2.39113i | −0.0953407 | + | 0.0953407i | ||||
\(630\) | −15.6439 | + | 15.6439i | −0.623268 | + | 0.623268i | ||||
\(631\) | −10.0432 | −0.399814 | −0.199907 | − | 0.979815i | \(-0.564064\pi\) | ||||
−0.199907 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(632\) | −22.6918 | + | 22.6918i | −0.902631 | + | 0.902631i | ||||
\(633\) | 4.54953 | 0.180828 | ||||||||
\(634\) | 19.3385 | − | 19.3385i | 0.768030 | − | 0.768030i | ||||
\(635\) | − | 8.05839i | − | 0.319787i | ||||||
\(636\) | 6.68315i | 0.265004i | ||||||||
\(637\) | −2.27384 | + | 2.27384i | −0.0900926 | + | 0.0900926i | ||||
\(638\) | 108.076 | 4.27878 | ||||||||
\(639\) | −17.1047 | + | 17.1047i | −0.676650 | + | 0.676650i | ||||
\(640\) | 69.7097 | 2.75552 | ||||||||
\(641\) | −32.6859 | + | 32.6859i | −1.29101 | + | 1.29101i | −0.356854 | + | 0.934160i | \(0.616151\pi\) |
−0.934160 | + | 0.356854i | \(0.883849\pi\) | |||||||
\(642\) | −10.7043 | + | 10.7043i | −0.422466 | + | 0.422466i | ||||
\(643\) | 5.54903 | + | 5.54903i | 0.218833 | + | 0.218833i | 0.808006 | − | 0.589174i | \(-0.200547\pi\) |
−0.589174 | + | 0.808006i | \(0.700547\pi\) | |||||||
\(644\) | 5.31710 | + | 5.31710i | 0.209523 | + | 0.209523i | ||||
\(645\) | 9.82082 | + | 9.82082i | 0.386694 | + | 0.386694i | ||||
\(646\) | −13.5571 | −0.533397 | ||||||||
\(647\) | − | 40.0890i | − | 1.57606i | −0.615637 | − | 0.788030i | \(-0.711101\pi\) | ||
0.615637 | − | 0.788030i | \(-0.288899\pi\) | |||||||
\(648\) | 26.0378i | 1.02286i | ||||||||
\(649\) | −50.4161 | − | 50.4161i | −1.97900 | − | 1.97900i | ||||
\(650\) | 34.8189 | − | 34.8189i | 1.36571 | − | 1.36571i | ||||
\(651\) | − | 3.43674i | − | 0.134696i | ||||||
\(652\) | −9.83072 | −0.385001 | ||||||||
\(653\) | −0.757485 | − | 0.757485i | −0.0296427 | − | 0.0296427i | 0.692130 | − | 0.721773i | \(-0.256672\pi\) |
−0.721773 | + | 0.692130i | \(0.756672\pi\) | |||||||
\(654\) | − | 12.3225i | − | 0.481847i | ||||||
\(655\) | −12.9798 | −0.507164 | ||||||||
\(656\) | 10.9805 | − | 1.11758i | 0.428718 | − | 0.0436343i | ||||
\(657\) | 0.932856 | 0.0363942 | ||||||||
\(658\) | − | 10.7852i | − | 0.420452i | ||||||
\(659\) | 11.5728 | + | 11.5728i | 0.450812 | + | 0.450812i | 0.895624 | − | 0.444812i | \(-0.146730\pi\) |
−0.444812 | + | 0.895624i | \(0.646730\pi\) | |||||||
\(660\) | −38.0286 | −1.48026 | ||||||||
\(661\) | − | 0.349292i | − | 0.0135859i | −0.999977 | − | 0.00679294i | \(-0.997838\pi\) | ||
0.999977 | − | 0.00679294i | \(-0.00216228\pi\) | |||||||
\(662\) | 13.4417 | − | 13.4417i | 0.522428 | − | 0.522428i | ||||
\(663\) | −2.51798 | − | 2.51798i | −0.0977903 | − | 0.0977903i | ||||
\(664\) | − | 31.0681i | − | 1.20568i | ||||||
\(665\) | − | 8.56183i | − | 0.332014i | ||||||
\(666\) | −9.73762 | −0.377325 | ||||||||
\(667\) | 10.5679 | + | 10.5679i | 0.409191 | + | 0.409191i | ||||
\(668\) | −50.8663 | − | 50.8663i | −1.96808 | − | 1.96808i | ||||
\(669\) | 4.01605 | + | 4.01605i | 0.155269 | + | 0.155269i | ||||
\(670\) | 64.5802 | − | 64.5802i | 2.49495 | − | 2.49495i | ||||
\(671\) | −17.4002 | + | 17.4002i | −0.671727 | + | 0.671727i | ||||
\(672\) | 1.68850 | 0.0651355 | ||||||||
\(673\) | 5.03945 | − | 5.03945i | 0.194257 | − | 0.194257i | −0.603276 | − | 0.797533i | \(-0.706138\pi\) |
0.797533 | + | 0.603276i | \(0.206138\pi\) | |||||||
\(674\) | 63.7161 | 2.45425 | ||||||||
\(675\) | 12.8797 | − | 12.8797i | 0.495738 | − | 0.495738i | ||||
\(676\) | 9.55508i | 0.367503i | ||||||||
\(677\) | − | 50.4366i | − | 1.93844i | −0.246201 | − | 0.969219i | \(-0.579182\pi\) | ||
0.246201 | − | 0.969219i | \(-0.420818\pi\) | |||||||
\(678\) | −9.63198 | + | 9.63198i | −0.369914 | + | 0.369914i | ||||
\(679\) | 5.33434 | 0.204713 | ||||||||
\(680\) | −20.4670 | + | 20.4670i | −0.784873 | + | 0.784873i | ||||
\(681\) | −0.730579 | −0.0279958 | ||||||||
\(682\) | −75.3261 | + | 75.3261i | −2.88438 | + | 2.88438i | ||||
\(683\) | −2.68737 | + | 2.68737i | −0.102829 | + | 0.102829i | −0.756650 | − | 0.653820i | \(-0.773165\pi\) |
0.653820 | + | 0.756650i | \(0.273165\pi\) | |||||||
\(684\) | −17.7337 | − | 17.7337i | −0.678064 | − | 0.678064i | ||||
\(685\) | −8.72646 | − | 8.72646i | −0.333421 | − | 0.333421i | ||||
\(686\) | 1.67228 | + | 1.67228i | 0.0638478 | + | 0.0638478i | ||||
\(687\) | −10.1987 | −0.389106 | ||||||||
\(688\) | − | 14.4749i | − | 0.551850i | ||||||
\(689\) | 12.2505i | 0.466706i | ||||||||
\(690\) | −5.78836 | − | 5.78836i | −0.220359 | − | 0.220359i | ||||
\(691\) | −19.6831 | + | 19.6831i | −0.748780 | + | 0.748780i | −0.974250 | − | 0.225470i | \(-0.927608\pi\) |
0.225470 | + | 0.974250i | \(0.427608\pi\) | |||||||
\(692\) | 80.0445i | 3.04284i | ||||||||
\(693\) | 17.6724 | 0.671320 | ||||||||
\(694\) | 51.0335 | + | 51.0335i | 1.93720 | + | 1.93720i | ||||
\(695\) | 31.4588i | 1.19330i | ||||||||
\(696\) | −13.1359 | −0.497914 | ||||||||
\(697\) | 9.17643 | − | 11.2560i | 0.347582 | − | 0.426352i | ||||
\(698\) | −26.8311 | −1.01557 | ||||||||
\(699\) | − | 2.21732i | − | 0.0838667i | ||||||
\(700\) | −16.4504 | − | 16.4504i | −0.621767 | − | 0.621767i | ||||
\(701\) | −23.2918 | −0.879720 | −0.439860 | − | 0.898066i | \(-0.644972\pi\) | ||||
−0.439860 | + | 0.898066i | \(0.644972\pi\) | |||||||
\(702\) | − | 21.3936i | − | 0.807449i | ||||||
\(703\) | 2.66468 | − | 2.66468i | 0.100500 | − | 0.100500i | ||||
\(704\) | −52.6083 | − | 52.6083i | −1.98275 | − | 1.98275i | ||||
\(705\) | 7.54264i | 0.284072i | ||||||||
\(706\) | − | 28.0956i | − | 1.05739i | ||||||
\(707\) | 8.05587 | 0.302972 | ||||||||
\(708\) | 13.8209 | + | 13.8209i | 0.519422 | + | 0.519422i | ||||
\(709\) | 29.6639 | + | 29.6639i | 1.11405 | + | 1.11405i | 0.992597 | + | 0.121453i | \(0.0387553\pi\) |
0.121453 | + | 0.992597i | \(0.461245\pi\) | |||||||
\(710\) | −49.6192 | − | 49.6192i | −1.86217 | − | 1.86217i | ||||
\(711\) | −16.6337 | + | 16.6337i | −0.623812 | + | 0.623812i | ||||
\(712\) | 27.4175 | − | 27.4175i | 1.02752 | − | 1.02752i | ||||
\(713\) | −14.7311 | −0.551682 | ||||||||
\(714\) | −1.85183 | + | 1.85183i | −0.0693031 | + | 0.0693031i | ||||
\(715\) | −69.7079 | −2.60693 | ||||||||
\(716\) | −2.23063 | + | 2.23063i | −0.0833627 | + | 0.0833627i | ||||
\(717\) | − | 5.15146i | − | 0.192385i | ||||||
\(718\) | 28.0262i | 1.04593i | ||||||||
\(719\) | 11.2635 | − | 11.2635i | 0.420056 | − | 0.420056i | −0.465167 | − | 0.885223i | \(-0.654006\pi\) |
0.885223 | + | 0.465167i | \(0.154006\pi\) | |||||||
\(720\) | −16.1253 | −0.600953 | ||||||||
\(721\) | 12.1662 | − | 12.1662i | 0.453092 | − | 0.453092i | ||||
\(722\) | −29.8261 | −1.11001 | ||||||||
\(723\) | 6.46913 | − | 6.46913i | 0.240589 | − | 0.240589i | ||||
\(724\) | −48.7366 | + | 48.7366i | −1.81128 | + | 1.81128i | ||||
\(725\) | −32.6957 | − | 32.6957i | −1.21429 | − | 1.21429i | ||||
\(726\) | 24.4549 | + | 24.4549i | 0.907607 | + | 0.907607i | ||||
\(727\) | 20.7669 | + | 20.7669i | 0.770203 | + | 0.770203i | 0.978142 | − | 0.207939i | \(-0.0666756\pi\) |
−0.207939 | + | 0.978142i | \(0.566676\pi\) | |||||||
\(728\) | −12.1148 | −0.449005 | ||||||||
\(729\) | 14.9659i | 0.554293i | ||||||||
\(730\) | 2.70613i | 0.100159i | ||||||||
\(731\) | −13.4673 | − | 13.4673i | −0.498108 | − | 0.498108i | ||||
\(732\) | 4.77004 | − | 4.77004i | 0.176306 | − | 0.176306i | ||||
\(733\) | − | 23.5888i | − | 0.871271i | −0.900123 | − | 0.435636i | \(-0.856524\pi\) | ||
0.900123 | − | 0.435636i | \(-0.143476\pi\) | |||||||
\(734\) | 0.266376 | 0.00983212 | ||||||||
\(735\) | −1.16950 | − | 1.16950i | −0.0431378 | − | 0.0431378i | ||||
\(736\) | − | 7.23752i | − | 0.266779i | ||||||
\(737\) | −72.9543 | −2.68731 | ||||||||
\(738\) | 41.6044 | − | 4.23444i | 1.53148 | − | 0.155872i | ||||
\(739\) | −3.86485 | −0.142171 | −0.0710854 | − | 0.997470i | \(-0.522646\pi\) | ||||
−0.0710854 | + | 0.997470i | \(0.522646\pi\) | |||||||
\(740\) | − | 18.1468i | − | 0.667091i | ||||||
\(741\) | 2.80604 | + | 2.80604i | 0.103082 | + | 0.103082i | ||||
\(742\) | 9.00953 | 0.330750 | ||||||||
\(743\) | − | 53.8393i | − | 1.97517i | −0.157074 | − | 0.987587i | \(-0.550206\pi\) | ||
0.157074 | − | 0.987587i | \(-0.449794\pi\) | |||||||
\(744\) | 9.15534 | − | 9.15534i | 0.335651 | − | 0.335651i | ||||
\(745\) | −42.0894 | − | 42.0894i | −1.54204 | − | 1.54204i | ||||
\(746\) | − | 17.2891i | − | 0.633000i | ||||||
\(747\) | − | 22.7737i | − | 0.833248i | ||||||
\(748\) | 52.1488 | 1.90675 | ||||||||
\(749\) | 9.27029 | + | 9.27029i | 0.338729 | + | 0.338729i | ||||
\(750\) | 4.07929 | + | 4.07929i | 0.148955 | + | 0.148955i | ||||
\(751\) | −25.5321 | − | 25.5321i | −0.931679 | − | 0.931679i | 0.0661315 | − | 0.997811i | \(-0.478934\pi\) |
−0.997811 | + | 0.0661315i | \(0.978934\pi\) | |||||||
\(752\) | 5.55855 | − | 5.55855i | 0.202699 | − | 0.202699i | ||||
\(753\) | −3.23838 | + | 3.23838i | −0.118013 | + | 0.118013i | ||||
\(754\) | −54.3088 | −1.97781 | ||||||||
\(755\) | 45.4312 | − | 45.4312i | 1.65341 | − | 1.65341i | ||||
\(756\) | −10.1075 | −0.367608 | ||||||||
\(757\) | −24.4734 | + | 24.4734i | −0.889499 | + | 0.889499i | −0.994475 | − | 0.104975i | \(-0.966524\pi\) |
0.104975 | + | 0.994475i | \(0.466524\pi\) | |||||||
\(758\) | − | 29.6592i | − | 1.07727i | ||||||
\(759\) | 6.53893i | 0.237348i | ||||||||
\(760\) | 22.8084 | − | 22.8084i | 0.827347 | − | 0.827347i | ||||
\(761\) | −49.6878 | −1.80118 | −0.900591 | − | 0.434668i | \(-0.856866\pi\) | ||||
−0.900591 | + | 0.434668i | \(0.856866\pi\) | |||||||
\(762\) | 1.94234 | − | 1.94234i | 0.0703634 | − | 0.0703634i | ||||
\(763\) | −10.6717 | −0.386340 | ||||||||
\(764\) | −13.7160 | + | 13.7160i | −0.496227 | + | 0.496227i | ||||
\(765\) | −15.0028 | + | 15.0028i | −0.542428 | + | 0.542428i | ||||
\(766\) | 40.3303 | + | 40.3303i | 1.45719 | + | 1.45719i | ||||
\(767\) | 25.3343 | + | 25.3343i | 0.914769 | + | 0.914769i | ||||
\(768\) | 8.77459 | + | 8.77459i | 0.316626 | + | 0.316626i | ||||
\(769\) | 41.4266 | 1.49388 | 0.746941 | − | 0.664890i | \(-0.231522\pi\) | ||||
0.746941 | + | 0.664890i | \(0.231522\pi\) | |||||||
\(770\) | 51.2662i | 1.84751i | ||||||||
\(771\) | 2.44760i | 0.0881482i | ||||||||
\(772\) | 41.9060 | + | 41.9060i | 1.50823 | + | 1.50823i | ||||
\(773\) | 8.72433 | − | 8.72433i | 0.313792 | − | 0.313792i | −0.532584 | − | 0.846377i | \(-0.678779\pi\) |
0.846377 | + | 0.532584i | \(0.178779\pi\) | |||||||
\(774\) | − | 54.8443i | − | 1.97134i | ||||||
\(775\) | 45.5760 | 1.63714 | ||||||||
\(776\) | 14.2105 | + | 14.2105i | 0.510127 | + | 0.510127i | ||||
\(777\) | − | 0.727964i | − | 0.0261156i | ||||||
\(778\) | 23.3838 | 0.838351 | ||||||||
\(779\) | −10.2262 | + | 12.5437i | −0.366392 | + | 0.449425i | ||||
\(780\) | 19.1095 | 0.684231 | ||||||||
\(781\) | 56.0533i | 2.00574i | ||||||||
\(782\) | 7.93761 | + | 7.93761i | 0.283848 | + | 0.283848i | ||||
\(783\) | −20.0891 | −0.717925 | ||||||||
\(784\) | 1.72373i | 0.0615619i | ||||||||
\(785\) | 35.4008 | − | 35.4008i | 1.26351 | − | 1.26351i | ||||
\(786\) | −3.12856 | − | 3.12856i | −0.111592 | − | 0.111592i | ||||
\(787\) | 29.1445i | 1.03889i | 0.854504 | + | 0.519445i | \(0.173861\pi\) | ||||
−0.854504 | + | 0.519445i | \(0.826139\pi\) | |||||||
\(788\) | 46.0910i | 1.64192i | ||||||||
\(789\) | 0.836121 | 0.0297667 | ||||||||
\(790\) | −48.2529 | − | 48.2529i | −1.71676 | − | 1.71676i | ||||
\(791\) | 8.34161 | + | 8.34161i | 0.296594 | + | 0.296594i | ||||
\(792\) | 47.0787 | + | 47.0787i | 1.67287 | + | 1.67287i | ||||
\(793\) | 8.74368 | − | 8.74368i | 0.310497 | − | 0.310497i | ||||
\(794\) | −37.8308 | + | 37.8308i | −1.34257 | + | 1.34257i | ||||
\(795\) | −6.30081 | −0.223467 | ||||||||
\(796\) | 57.7927 | − | 57.7927i | 2.04841 | − | 2.04841i | ||||
\(797\) | 30.3753 | 1.07595 | 0.537974 | − | 0.842961i | \(-0.319190\pi\) | ||||
0.537974 | + | 0.842961i | \(0.319190\pi\) | |||||||
\(798\) | 2.06368 | − | 2.06368i | 0.0730536 | − | 0.0730536i | ||||
\(799\) | − | 10.3433i | − | 0.365919i | ||||||
\(800\) | 22.3920i | 0.791675i | ||||||||
\(801\) | 20.0978 | − | 20.0978i | 0.710120 | − | 0.710120i | ||||
\(802\) | −31.4594 | −1.11087 | ||||||||
\(803\) | 1.52852 | − | 1.52852i | 0.0539403 | − | 0.0539403i | ||||
\(804\) | 19.9995 | 0.705328 | ||||||||
\(805\) | −5.01291 | + | 5.01291i | −0.176682 | + | 0.176682i | ||||
\(806\) | 37.8517 | − | 37.8517i | 1.33327 | − | 1.33327i | ||||
\(807\) | 4.80489 | + | 4.80489i | 0.169140 | + | 0.169140i | ||||
\(808\) | 21.4606 | + | 21.4606i | 0.754980 | + | 0.754980i | ||||
\(809\) | 19.6017 | + | 19.6017i | 0.689161 | + | 0.689161i | 0.962046 | − | 0.272886i | \(-0.0879781\pi\) |
−0.272886 | + | 0.962046i | \(0.587978\pi\) | |||||||
\(810\) | −55.3680 | −1.94543 | ||||||||
\(811\) | − | 48.0748i | − | 1.68813i | −0.536238 | − | 0.844067i | \(-0.680155\pi\) | ||
0.536238 | − | 0.844067i | \(-0.319845\pi\) | |||||||
\(812\) | 25.6586i | 0.900439i | ||||||||
\(813\) | −9.12449 | − | 9.12449i | −0.320010 | − | 0.320010i | ||||
\(814\) | −15.9555 | + | 15.9555i | −0.559238 | + | 0.559238i | ||||
\(815\) | − | 9.26830i | − | 0.324655i | ||||||
\(816\) | −1.90881 | −0.0668218 | ||||||||
\(817\) | 15.0080 | + | 15.0080i | 0.525064 | + | 0.525064i | ||||
\(818\) | − | 23.7279i | − | 0.829625i | ||||||
\(819\) | −8.88048 | −0.310309 | ||||||||
\(820\) | 7.89121 | + | 77.5332i | 0.275573 | + | 2.70758i | ||||
\(821\) | −22.6320 | −0.789863 | −0.394931 | − | 0.918711i | \(-0.629232\pi\) | ||||
−0.394931 | + | 0.918711i | \(0.629232\pi\) | |||||||
\(822\) | − | 4.20673i | − | 0.146727i | ||||||
\(823\) | 6.69343 | + | 6.69343i | 0.233318 | + | 0.233318i | 0.814076 | − | 0.580758i | \(-0.197244\pi\) |
−0.580758 | + | 0.814076i | \(0.697244\pi\) | |||||||
\(824\) | 64.8205 | 2.25813 | ||||||||
\(825\) | − | 20.2306i | − | 0.704339i | ||||||
\(826\) | 18.6319 | − | 18.6319i | 0.648288 | − | 0.648288i | ||||
\(827\) | 30.5431 | + | 30.5431i | 1.06209 | + | 1.06209i | 0.997940 | + | 0.0641464i | \(0.0204325\pi\) |
0.0641464 | + | 0.997940i | \(0.479568\pi\) | |||||||
\(828\) | 20.7660i | 0.721667i | ||||||||
\(829\) | − | 45.0033i | − | 1.56303i | −0.623887 | − | 0.781515i | \(-0.714447\pi\) | ||
0.623887 | − | 0.781515i | \(-0.285553\pi\) | |||||||
\(830\) | 66.0646 | 2.29314 | ||||||||
\(831\) | 5.15938 | + | 5.15938i | 0.178977 | + | 0.178977i | ||||
\(832\) | 26.4359 | + | 26.4359i | 0.916500 | + | 0.916500i | ||||
\(833\) | 1.60375 | + | 1.60375i | 0.0555666 | + | 0.0555666i | ||||
\(834\) | −7.58260 | + | 7.58260i | −0.262564 | + | 0.262564i | ||||
\(835\) | 47.9563 | − | 47.9563i | 1.65960 | − | 1.65960i | ||||
\(836\) | −58.1146 | −2.00994 | ||||||||
\(837\) | 14.0015 | − | 14.0015i | 0.483963 | − | 0.483963i | ||||
\(838\) | −89.9603 | −3.10763 | ||||||||
\(839\) | −26.5463 | + | 26.5463i | −0.916480 | + | 0.916480i | −0.996771 | − | 0.0802918i | \(-0.974415\pi\) |
0.0802918 | + | 0.996771i | \(0.474415\pi\) | |||||||
\(840\) | − | 6.23103i | − | 0.214991i | ||||||
\(841\) | 21.9972i | 0.758524i | ||||||||
\(842\) | −14.7946 | + | 14.7946i | −0.509854 | + | 0.509854i | ||||
\(843\) | 3.11574 | 0.107312 | ||||||||
\(844\) | 23.6738 | − | 23.6738i | 0.814887 | − | 0.814887i | ||||
\(845\) | −9.00844 | −0.309900 | ||||||||
\(846\) | 21.0609 | − | 21.0609i | 0.724089 | − | 0.724089i | ||||
\(847\) | 21.1788 | − | 21.1788i | 0.727711 | − | 0.727711i | ||||
\(848\) | 4.64338 | + | 4.64338i | 0.159454 | + | 0.159454i | ||||
\(849\) | −0.441754 | − | 0.441754i | −0.0151610 | − | 0.0151610i | ||||
\(850\) | −24.5579 | − | 24.5579i | −0.842330 | − | 0.842330i | ||||
\(851\) | −3.12031 | −0.106963 | ||||||||
\(852\) | − | 15.3663i | − | 0.526440i | ||||||
\(853\) | 7.89965i | 0.270479i | 0.990813 | + | 0.135239i | \(0.0431804\pi\) | ||||
−0.990813 | + | 0.135239i | \(0.956820\pi\) | |||||||
\(854\) | −6.43048 | − | 6.43048i | −0.220046 | − | 0.220046i | ||||
\(855\) | 16.7191 | − | 16.7191i | 0.571783 | − | 0.571783i | ||||
\(856\) | 49.3914i | 1.68816i | ||||||||
\(857\) | 54.5233 | 1.86248 | 0.931240 | − | 0.364406i | \(-0.118728\pi\) | ||||
0.931240 | + | 0.364406i | \(0.118728\pi\) | |||||||
\(858\) | −16.8019 | − | 16.8019i | −0.573607 | − | 0.573607i | ||||
\(859\) | 11.2917i | 0.385267i | 0.981271 | + | 0.192633i | \(0.0617028\pi\) | ||||
−0.981271 | + | 0.192633i | \(0.938297\pi\) | |||||||
\(860\) | 102.207 | 3.48522 | ||||||||
\(861\) | 0.316558 | + | 3.11026i | 0.0107883 | + | 0.105997i | ||||
\(862\) | −59.0394 | −2.01089 | ||||||||
\(863\) | − | 0.277647i | − | 0.00945121i | −0.999989 | − | 0.00472560i | \(-0.998496\pi\) | ||
0.999989 | − | 0.00472560i | \(-0.00150421\pi\) | |||||||
\(864\) | 6.87909 | + | 6.87909i | 0.234031 | + | 0.234031i | ||||
\(865\) | −75.4652 | −2.56589 | ||||||||
\(866\) | 73.8567i | 2.50975i | ||||||||
\(867\) | 4.09322 | − | 4.09322i | 0.139013 | − | 0.139013i | ||||
\(868\) | −17.8833 | − | 17.8833i | −0.606999 | − | 0.606999i | ||||
\(869\) | 54.5098i | 1.84912i | ||||||||
\(870\) | − | 27.9327i | − | 0.947008i | ||||||
\(871\) | 36.6599 | 1.24217 | ||||||||
\(872\) | −28.4289 | − | 28.4289i | −0.962725 | − | 0.962725i | ||||
\(873\) | 10.4167 | + | 10.4167i | 0.352550 | + | 0.352550i | ||||
\(874\) | −8.84567 | − | 8.84567i | −0.299209 | − | 0.299209i | ||||
\(875\) | 3.53280 | − | 3.53280i | 0.119431 | − | 0.119431i | ||||
\(876\) | −0.419024 | + | 0.419024i | −0.0141575 | + | 0.0141575i | ||||
\(877\) | 46.4874 | 1.56977 | 0.784884 | − | 0.619642i | \(-0.212722\pi\) | ||||
0.784884 | + | 0.619642i | \(0.212722\pi\) | |||||||
\(878\) | −3.24197 | + | 3.24197i | −0.109411 | + | 0.109411i | ||||
\(879\) | −6.76558 | −0.228197 | ||||||||
\(880\) | −26.4218 | + | 26.4218i | −0.890679 | + | 0.890679i | ||||
\(881\) | 11.4935i | 0.387225i | 0.981078 | + | 0.193613i | \(0.0620205\pi\) | ||||
−0.981078 | + | 0.193613i | \(0.937980\pi\) | |||||||
\(882\) | 6.53109i | 0.219913i | ||||||||
\(883\) | −9.33299 | + | 9.33299i | −0.314080 | + | 0.314080i | −0.846488 | − | 0.532408i | \(-0.821287\pi\) |
0.532408 | + | 0.846488i | \(0.321287\pi\) | |||||||
\(884\) | −26.2050 | −0.881370 | ||||||||
\(885\) | −13.0302 | + | 13.0302i | −0.438006 | + | 0.438006i | ||||
\(886\) | 33.1762 | 1.11458 | ||||||||
\(887\) | −20.2074 | + | 20.2074i | −0.678499 | + | 0.678499i | −0.959660 | − | 0.281162i | \(-0.909280\pi\) |
0.281162 | + | 0.959660i | \(0.409280\pi\) | |||||||
\(888\) | 1.93927 | − | 1.93927i | 0.0650776 | − | 0.0650776i | ||||
\(889\) | −1.68213 | − | 1.68213i | −0.0564167 | − | 0.0564167i | ||||
\(890\) | 58.3019 | + | 58.3019i | 1.95428 | + | 1.95428i | ||||
\(891\) | 31.2738 | + | 31.2738i | 1.04771 | + | 1.04771i | ||||
\(892\) | 41.7956 | 1.39942 | ||||||||
\(893\) | 11.5265i | 0.385721i | ||||||||
\(894\) | − | 20.2899i | − | 0.678594i | ||||||
\(895\) | −2.10302 | − | 2.10302i | −0.0702962 | − | 0.0702962i | ||||
\(896\) | 14.5514 | − | 14.5514i | 0.486127 | − | 0.486127i | ||||
\(897\) | − | 3.28584i | − | 0.109711i | ||||||
\(898\) | 45.8999 | 1.53170 | ||||||||
\(899\) | −35.5436 | − | 35.5436i | −1.18545 | − | 1.18545i | ||||
\(900\) | − | 64.2472i | − | 2.14157i | ||||||
\(901\) | 8.64033 | 0.287851 | ||||||||
\(902\) | 61.2321 | − | 75.1087i | 2.03881 | − | 2.50085i | ||||
\(903\) | 4.10004 | 0.136441 | ||||||||
\(904\) | 44.4435i | 1.47817i | ||||||||
\(905\) | −45.9484 | − | 45.9484i | −1.52738 | − | 1.52738i | ||||
\(906\) | 21.9008 | 0.727607 | ||||||||
\(907\) | 17.6975i | 0.587637i | 0.955861 | + | 0.293818i | \(0.0949261\pi\) | ||||
−0.955861 | + | 0.293818i | \(0.905074\pi\) | |||||||
\(908\) | −3.80162 | + | 3.80162i | −0.126161 | + | 0.126161i | ||||
\(909\) | 15.7311 | + | 15.7311i | 0.521769 | + | 0.521769i | ||||
\(910\) | − | 25.7615i | − | 0.853986i | ||||||
\(911\) | 13.1925i | 0.437087i | 0.975827 | + | 0.218544i | \(0.0701306\pi\) | ||||
−0.975827 | + | 0.218544i | \(0.929869\pi\) | |||||||
\(912\) | 2.12718 | 0.0704380 | ||||||||
\(913\) | −37.3156 | − | 37.3156i | −1.23497 | − | 1.23497i | ||||
\(914\) | −18.2826 | − | 18.2826i | −0.604735 | − | 0.604735i | ||||
\(915\) | 4.49715 | + | 4.49715i | 0.148671 | + | 0.148671i | ||||
\(916\) | −53.0698 | + | 53.0698i | −1.75348 | + | 1.75348i | ||||
\(917\) | −2.70944 | + | 2.70944i | −0.0894736 | + | 0.0894736i | ||||
\(918\) | −15.0890 | −0.498012 | ||||||||
\(919\) | 30.6508 | − | 30.6508i | 1.01108 | − | 1.01108i | 0.0111379 | − | 0.999938i | \(-0.496455\pi\) |
0.999938 | − | 0.0111379i | \(-0.00354538\pi\) | |||||||
\(920\) | −26.7084 | −0.880550 | ||||||||
\(921\) | −5.50674 | + | 5.50674i | −0.181453 | + | 0.181453i | ||||
\(922\) | − | 15.8795i | − | 0.522963i | ||||||
\(923\) | − | 28.1670i | − | 0.927129i | ||||||
\(924\) | −7.93817 | + | 7.93817i | −0.261147 | + | 0.261147i | ||||
\(925\) | 9.65383 | 0.317416 | ||||||||
\(926\) | 3.95222 | − | 3.95222i | 0.129878 | − | 0.129878i | ||||
\(927\) | 47.5151 | 1.56060 | ||||||||
\(928\) | 17.4630 | − | 17.4630i | 0.573250 | − | 0.573250i | ||||
\(929\) | 12.3559 | − | 12.3559i | 0.405383 | − | 0.405383i | −0.474742 | − | 0.880125i | \(-0.657459\pi\) |
0.880125 | + | 0.474742i | \(0.157459\pi\) | |||||||
\(930\) | 19.4683 | + | 19.4683i | 0.638391 | + | 0.638391i | ||||
\(931\) | −1.78722 | − | 1.78722i | −0.0585737 | − | 0.0585737i | ||||
\(932\) | −11.5380 | − | 11.5380i | −0.377939 | − | 0.377939i | ||||
\(933\) | −0.910975 | −0.0298240 | ||||||||
\(934\) | 39.2360i | 1.28384i | ||||||||
\(935\) | 49.1654i | 1.60788i | ||||||||
\(936\) | −23.6573 | − | 23.6573i | −0.773262 | − | 0.773262i | ||||
\(937\) | 15.8474 | − | 15.8474i | 0.517712 | − | 0.517712i | −0.399167 | − | 0.916878i | \(-0.630701\pi\) |
0.916878 | + | 0.399167i | \(0.130701\pi\) | |||||||
\(938\) | − | 26.9613i | − | 0.880317i | ||||||
\(939\) | 1.80340 | 0.0588518 | ||||||||
\(940\) | 39.2487 | + | 39.2487i | 1.28015 | + | 1.28015i | ||||
\(941\) | 43.2082i | 1.40855i | 0.709929 | + | 0.704274i | \(0.248727\pi\) | ||||
−0.709929 | + | 0.704274i | \(0.751273\pi\) | |||||||
\(942\) | 17.0655 | 0.556025 | ||||||||
\(943\) | 13.3317 | − | 1.35688i | 0.434139 | − | 0.0441860i | ||||
\(944\) | 19.2052 | 0.625078 | ||||||||
\(945\) | − | 9.52930i | − | 0.309988i | ||||||
\(946\) | −89.8644 | − | 89.8644i | −2.92174 | − | 2.92174i | ||||
\(947\) | 6.19364 | 0.201266 | 0.100633 | − | 0.994924i | \(-0.467913\pi\) | ||||
0.100633 | + | 0.994924i | \(0.467913\pi\) | |||||||
\(948\) | − | 14.9432i | − | 0.485331i | ||||||
\(949\) | −0.768088 | + | 0.768088i | −0.0249332 | + | 0.0249332i | ||||
\(950\) | 27.3674 | + | 27.3674i | 0.887914 | + | 0.887914i | ||||
\(951\) | 5.64621i | 0.183091i | ||||||||
\(952\) | 8.54465i | 0.276934i | ||||||||
\(953\) | −10.6028 | −0.343457 | −0.171729 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171729 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(954\) | 17.5934 | + | 17.5934i | 0.569608 | + | 0.569608i | ||||
\(955\) | −12.9313 | − | 12.9313i | −0.418447 | − | 0.418447i | ||||
\(956\) | −26.8060 | − | 26.8060i | −0.866967 | − | 0.866967i | ||||
\(957\) | −15.7774 | + | 15.7774i | −0.510010 | + | 0.510010i | ||||
\(958\) | 30.3665 | − | 30.3665i | 0.981097 | − | 0.981097i | ||||
\(959\) | −3.64317 | −0.117644 | ||||||||
\(960\) | −13.5968 | + | 13.5968i | −0.438835 | + | 0.438835i | ||||
\(961\) | 18.5458 | 0.598252 | ||||||||
\(962\) | 8.01769 | − | 8.01769i | 0.258501 | − | 0.258501i | ||||
\(963\) | 36.2052i | 1.16670i | ||||||||
\(964\) | − | 67.3251i | − | 2.16840i | ||||||
\(965\) | −39.5086 | + | 39.5086i | −1.27183 | + | 1.27183i | ||||
\(966\) | −2.41655 | −0.0777513 | ||||||||
\(967\) | 16.4960 | − | 16.4960i | 0.530476 | − | 0.530476i | −0.390238 | − | 0.920714i | \(-0.627607\pi\) |
0.920714 | + | 0.390238i | \(0.127607\pi\) | |||||||
\(968\) | 112.839 | 3.62678 | ||||||||
\(969\) | 1.97911 | − | 1.97911i | 0.0635783 | − | 0.0635783i | ||||
\(970\) | −30.2178 | + | 30.2178i | −0.970236 | + | 0.970236i | ||||
\(971\) | −2.19274 | − | 2.19274i | −0.0703684 | − | 0.0703684i | 0.671047 | − | 0.741415i | \(-0.265845\pi\) |
−0.741415 | + | 0.671047i | \(0.765845\pi\) | |||||||
\(972\) | −30.0147 | − | 30.0147i | −0.962720 | − | 0.962720i | ||||
\(973\) | 6.56678 | + | 6.56678i | 0.210521 | + | 0.210521i | ||||
\(974\) | −75.0755 | −2.40557 | ||||||||
\(975\) | 10.1660i | 0.325572i | ||||||||
\(976\) | − | 6.62834i | − | 0.212168i | ||||||
\(977\) | −13.4743 | − | 13.4743i | −0.431082 | − | 0.431082i | 0.457914 | − | 0.888996i | \(-0.348597\pi\) |
−0.888996 | + | 0.457914i | \(0.848597\pi\) | |||||||
\(978\) | 2.23397 | − | 2.23397i | 0.0714344 | − | 0.0714344i | ||||
\(979\) | − | 65.8618i | − | 2.10495i | ||||||
\(980\) | −12.1712 | −0.388795 | ||||||||
\(981\) | −20.8391 | − | 20.8391i | −0.665342 | − | 0.665342i | ||||
\(982\) | − | 52.4523i | − | 1.67382i | ||||||
\(983\) | −3.89718 | −0.124301 | −0.0621504 | − | 0.998067i | \(-0.519796\pi\) | ||||
−0.0621504 | + | 0.998067i | \(0.519796\pi\) | |||||||
\(984\) | −7.44232 | + | 9.12891i | −0.237252 | + | 0.291019i | ||||
\(985\) | −43.4541 | −1.38456 | ||||||||
\(986\) | 38.3043i | 1.21986i | ||||||||
\(987\) | 1.57447 | + | 1.57447i | 0.0501159 | + | 0.0501159i | ||||
\(988\) | 29.2029 | 0.929067 | ||||||||
\(989\) | − | 17.5742i | − | 0.558828i | ||||||
\(990\) | −100.110 | + | 100.110i | −3.18171 | + | 3.18171i | ||||
\(991\) | −1.83130 | − | 1.83130i | −0.0581732 | − | 0.0581732i | 0.677422 | − | 0.735595i | \(-0.263097\pi\) |
−0.735595 | + | 0.677422i | \(0.763097\pi\) | |||||||
\(992\) | 24.3424i | 0.772871i | ||||||||
\(993\) | 3.92455i | 0.124542i | ||||||||
\(994\) | −20.7152 | −0.657048 | ||||||||
\(995\) | 54.4864 | + | 54.4864i | 1.72734 | + | 1.72734i | ||||
\(996\) | 10.2296 | + | 10.2296i | 0.324137 | + | 0.324137i | ||||
\(997\) | 19.4793 | + | 19.4793i | 0.616915 | + | 0.616915i | 0.944739 | − | 0.327824i | \(-0.106315\pi\) |
−0.327824 | + | 0.944739i | \(0.606315\pi\) | |||||||
\(998\) | −36.5037 | + | 36.5037i | −1.15550 | + | 1.15550i | ||||
\(999\) | 2.96578 | − | 2.96578i | 0.0938331 | − | 0.0938331i |
(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 | 287.2.f.a.50.18 | ✓ | 40 | |
41.32 | even | 4 | inner | 287.2.f.a.155.3 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.f.a.50.18 | ✓ | 40 | 1.1 | even | 1 | trivial | |
287.2.f.a.155.3 | yes | 40 | 41.32 | even | 4 | inner |