Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(71,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.71");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.e (of order \(2\), degree \(1\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 34 x^{14} - 80 x^{13} + 97 x^{12} - 80 x^{11} + 498 x^{10} - 3288 x^{9} + \cdots + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 71.14 | ||
Root | \(-0.650833 + 2.92855i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.71 |
Dual form | 210.3.e.a.71.6 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | 0.650833 | − | 2.92855i | 0.216944 | − | 0.976184i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 4.14160 | + | 0.920417i | 0.690266 | + | 0.153403i | ||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −8.15283 | − | 3.81200i | −0.905870 | − | 0.423555i | ||||
\(10\) | 3.16228 | 0.316228 | ||||||||
\(11\) | − | 7.97556i | − | 0.725051i | −0.931974 | − | 0.362526i | \(-0.881915\pi\) | ||
0.931974 | − | 0.362526i | \(-0.118085\pi\) | |||||||
\(12\) | −1.30167 | + | 5.85710i | −0.108472 | + | 0.488092i | ||||
\(13\) | −5.79363 | −0.445664 | −0.222832 | − | 0.974857i | \(-0.571530\pi\) | ||||
−0.222832 | + | 0.974857i | \(0.571530\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | −6.54844 | − | 1.45531i | −0.436563 | − | 0.0970204i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 9.35782i | − | 0.550460i | −0.961378 | − | 0.275230i | \(-0.911246\pi\) | ||
0.961378 | − | 0.275230i | \(-0.0887541\pi\) | |||||||
\(18\) | 5.39098 | − | 11.5298i | 0.299499 | − | 0.640547i | ||||
\(19\) | −22.7979 | −1.19989 | −0.599946 | − | 0.800041i | \(-0.704811\pi\) | ||||
−0.599946 | + | 0.800041i | \(0.704811\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | −1.72194 | + | 7.74822i | −0.0819972 | + | 0.368963i | ||||
\(22\) | 11.2792 | 0.512689 | ||||||||
\(23\) | − | 34.9882i | − | 1.52123i | −0.649205 | − | 0.760613i | \(-0.724898\pi\) | ||
0.649205 | − | 0.760613i | \(-0.275102\pi\) | |||||||
\(24\) | −8.28320 | − | 1.84083i | −0.345133 | − | 0.0767014i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − | 8.19343i | − | 0.315132i | ||||||
\(27\) | −16.4698 | + | 21.3950i | −0.609991 | + | 0.792408i | ||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | − | 15.5858i | − | 0.537442i | −0.963218 | − | 0.268721i | \(-0.913399\pi\) | ||
0.963218 | − | 0.268721i | \(-0.0866010\pi\) | |||||||
\(30\) | 2.05811 | − | 9.26089i | 0.0686038 | − | 0.308696i | ||||
\(31\) | 25.5869 | 0.825384 | 0.412692 | − | 0.910871i | \(-0.364589\pi\) | ||||
0.412692 | + | 0.910871i | \(0.364589\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −23.3569 | − | 5.19076i | −0.707783 | − | 0.157296i | ||||
\(34\) | 13.2340 | 0.389234 | ||||||||
\(35\) | 5.91608i | 0.169031i | ||||||||
\(36\) | 16.3057 | + | 7.62399i | 0.452935 | + | 0.211778i | ||||
\(37\) | 38.4908 | 1.04029 | 0.520145 | − | 0.854078i | \(-0.325878\pi\) | ||||
0.520145 | + | 0.854078i | \(0.325878\pi\) | |||||||
\(38\) | − | 32.2412i | − | 0.848451i | ||||||
\(39\) | −3.77068 | + | 16.9669i | −0.0966842 | + | 0.435050i | ||||
\(40\) | −6.32456 | −0.158114 | ||||||||
\(41\) | 35.1062i | 0.856249i | 0.903720 | + | 0.428125i | \(0.140826\pi\) | ||||
−0.903720 | + | 0.428125i | \(0.859174\pi\) | |||||||
\(42\) | −10.9576 | − | 2.43519i | −0.260896 | − | 0.0579808i | ||||
\(43\) | 59.0951 | 1.37431 | 0.687153 | − | 0.726513i | \(-0.258860\pi\) | ||||
0.687153 | + | 0.726513i | \(0.258860\pi\) | |||||||
\(44\) | 15.9511i | 0.362526i | ||||||||
\(45\) | −8.52388 | + | 18.2303i | −0.189420 | + | 0.405118i | ||||
\(46\) | 49.4808 | 1.07567 | ||||||||
\(47\) | 1.03517i | 0.0220249i | 0.999939 | + | 0.0110124i | \(0.00350544\pi\) | ||||
−0.999939 | + | 0.0110124i | \(0.996495\pi\) | |||||||
\(48\) | 2.60333 | − | 11.7142i | 0.0542361 | − | 0.244046i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | − | 7.07107i | − | 0.141421i | ||||||
\(51\) | −27.4049 | − | 6.09038i | −0.537351 | − | 0.119419i | ||||
\(52\) | 11.5873 | 0.222832 | ||||||||
\(53\) | 41.5179i | 0.783357i | 0.920102 | + | 0.391679i | \(0.128105\pi\) | ||||
−0.920102 | + | 0.391679i | \(0.871895\pi\) | |||||||
\(54\) | −30.2571 | − | 23.2918i | −0.560317 | − | 0.431329i | ||||
\(55\) | −17.8339 | −0.324253 | ||||||||
\(56\) | 7.48331i | 0.133631i | ||||||||
\(57\) | −14.8377 | + | 66.7650i | −0.260310 | + | 1.17131i | ||||
\(58\) | 22.0417 | 0.380029 | ||||||||
\(59\) | − | 55.1602i | − | 0.934919i | −0.884014 | − | 0.467460i | \(-0.845169\pi\) | ||
0.884014 | − | 0.467460i | \(-0.154831\pi\) | |||||||
\(60\) | 13.0969 | + | 2.91061i | 0.218281 | + | 0.0485102i | ||||
\(61\) | −94.7726 | −1.55365 | −0.776824 | − | 0.629717i | \(-0.783171\pi\) | ||||
−0.776824 | + | 0.629717i | \(0.783171\pi\) | |||||||
\(62\) | 36.1853i | 0.583635i | ||||||||
\(63\) | 21.5704 | + | 10.0856i | 0.342387 | + | 0.160089i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 12.9549i | 0.199307i | ||||||||
\(66\) | 7.34084 | − | 33.0316i | 0.111225 | − | 0.500478i | ||||
\(67\) | 77.1064 | 1.15084 | 0.575421 | − | 0.817857i | \(-0.304838\pi\) | ||||
0.575421 | + | 0.817857i | \(0.304838\pi\) | |||||||
\(68\) | 18.7156i | 0.275230i | ||||||||
\(69\) | −102.465 | − | 22.7715i | −1.48500 | − | 0.330021i | ||||
\(70\) | −8.36660 | −0.119523 | ||||||||
\(71\) | − | 18.0046i | − | 0.253586i | −0.991929 | − | 0.126793i | \(-0.959532\pi\) | ||
0.991929 | − | 0.126793i | \(-0.0404684\pi\) | |||||||
\(72\) | −10.7820 | + | 23.0597i | −0.149749 | + | 0.320274i | ||||
\(73\) | 33.2022 | 0.454825 | 0.227412 | − | 0.973799i | \(-0.426973\pi\) | ||||
0.227412 | + | 0.973799i | \(0.426973\pi\) | |||||||
\(74\) | 54.4342i | 0.735597i | ||||||||
\(75\) | −3.25416 | + | 14.6428i | −0.0433889 | + | 0.195237i | ||||
\(76\) | 45.5959 | 0.599946 | ||||||||
\(77\) | 21.1014i | 0.274044i | ||||||||
\(78\) | −23.9949 | − | 5.33255i | −0.307627 | − | 0.0683660i | ||||
\(79\) | −54.9427 | −0.695478 | −0.347739 | − | 0.937591i | \(-0.613050\pi\) | ||||
−0.347739 | + | 0.937591i | \(0.613050\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 51.9374 | + | 62.1571i | 0.641202 | + | 0.767372i | ||||
\(82\) | −49.6477 | −0.605460 | ||||||||
\(83\) | 78.6593i | 0.947703i | 0.880605 | + | 0.473851i | \(0.157137\pi\) | ||||
−0.880605 | + | 0.473851i | \(0.842863\pi\) | |||||||
\(84\) | 3.44388 | − | 15.4964i | 0.0409986 | − | 0.184481i | ||||
\(85\) | −20.9247 | −0.246173 | ||||||||
\(86\) | 83.5731i | 0.971781i | ||||||||
\(87\) | −45.6439 | − | 10.1438i | −0.524643 | − | 0.116595i | ||||
\(88\) | −22.5583 | −0.256344 | ||||||||
\(89\) | 120.028i | 1.34863i | 0.738442 | + | 0.674317i | \(0.235562\pi\) | ||||
−0.738442 | + | 0.674317i | \(0.764438\pi\) | |||||||
\(90\) | −25.7815 | − | 12.0546i | −0.286461 | − | 0.133940i | ||||
\(91\) | 15.3285 | 0.168445 | ||||||||
\(92\) | 69.9764i | 0.760613i | ||||||||
\(93\) | 16.6528 | − | 74.9326i | 0.179062 | − | 0.805727i | ||||
\(94\) | −1.46395 | −0.0155739 | ||||||||
\(95\) | 50.9777i | 0.536608i | ||||||||
\(96\) | 16.5664 | + | 3.68167i | 0.172567 | + | 0.0383507i | ||||
\(97\) | 24.5127 | 0.252708 | 0.126354 | − | 0.991985i | \(-0.459672\pi\) | ||||
0.126354 | + | 0.991985i | \(0.459672\pi\) | |||||||
\(98\) | 9.89949i | 0.101015i | ||||||||
\(99\) | −30.4028 | + | 65.0234i | −0.307099 | + | 0.656802i | ||||
\(100\) | 10.0000 | 0.100000 | ||||||||
\(101\) | − | 158.695i | − | 1.57124i | −0.618709 | − | 0.785620i | \(-0.712344\pi\) | ||
0.618709 | − | 0.785620i | \(-0.287656\pi\) | |||||||
\(102\) | 8.61310 | − | 38.7563i | 0.0844421 | − | 0.379964i | ||||
\(103\) | 177.505 | 1.72335 | 0.861674 | − | 0.507461i | \(-0.169416\pi\) | ||||
0.861674 | + | 0.507461i | \(0.169416\pi\) | |||||||
\(104\) | 16.3869i | 0.157566i | ||||||||
\(105\) | 17.3255 | + | 3.85038i | 0.165005 | + | 0.0366703i | ||||
\(106\) | −58.7152 | −0.553917 | ||||||||
\(107\) | − | 210.992i | − | 1.97189i | −0.167064 | − | 0.985946i | \(-0.553429\pi\) | ||
0.167064 | − | 0.985946i | \(-0.446571\pi\) | |||||||
\(108\) | 32.9395 | − | 42.7900i | 0.304996 | − | 0.396204i | ||||
\(109\) | −98.5237 | −0.903887 | −0.451943 | − | 0.892047i | \(-0.649269\pi\) | ||||
−0.451943 | + | 0.892047i | \(0.649269\pi\) | |||||||
\(110\) | − | 25.2209i | − | 0.229281i | ||||||
\(111\) | 25.0511 | − | 112.722i | 0.225685 | − | 1.01552i | ||||
\(112\) | −10.5830 | −0.0944911 | ||||||||
\(113\) | 102.830i | 0.910000i | 0.890492 | + | 0.455000i | \(0.150361\pi\) | ||||
−0.890492 | + | 0.455000i | \(0.849639\pi\) | |||||||
\(114\) | −94.4199 | − | 20.9836i | −0.828245 | − | 0.184067i | ||||
\(115\) | −78.2360 | −0.680313 | ||||||||
\(116\) | 31.1717i | 0.268721i | ||||||||
\(117\) | 47.2345 | + | 22.0853i | 0.403713 | + | 0.188763i | ||||
\(118\) | 78.0084 | 0.661088 | ||||||||
\(119\) | 24.7585i | 0.208054i | ||||||||
\(120\) | −4.11623 | + | 18.5218i | −0.0343019 | + | 0.154348i | ||||
\(121\) | 57.3904 | 0.474301 | ||||||||
\(122\) | − | 134.029i | − | 1.09860i | ||||||
\(123\) | 102.810 | + | 22.8483i | 0.835857 | + | 0.185758i | ||||
\(124\) | −51.1738 | −0.412692 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −14.2632 | + | 30.5051i | −0.113200 | + | 0.242104i | ||||
\(127\) | 157.688 | 1.24164 | 0.620819 | − | 0.783954i | \(-0.286800\pi\) | ||||
0.620819 | + | 0.783954i | \(0.286800\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 38.4611 | − | 173.063i | 0.298148 | − | 1.34158i | ||||
\(130\) | −18.3211 | −0.140931 | ||||||||
\(131\) | − | 250.120i | − | 1.90932i | −0.297705 | − | 0.954658i | \(-0.596221\pi\) | ||
0.297705 | − | 0.954658i | \(-0.403779\pi\) | |||||||
\(132\) | 46.7137 | + | 10.3815i | 0.353892 | + | 0.0786479i | ||||
\(133\) | 60.3177 | 0.453516 | ||||||||
\(134\) | 109.045i | 0.813768i | ||||||||
\(135\) | 47.8407 | + | 36.8275i | 0.354376 | + | 0.272796i | ||||
\(136\) | −26.4679 | −0.194617 | ||||||||
\(137\) | − | 191.896i | − | 1.40070i | −0.713800 | − | 0.700350i | \(-0.753027\pi\) | ||
0.713800 | − | 0.700350i | \(-0.246973\pi\) | |||||||
\(138\) | 32.2037 | − | 144.907i | 0.233360 | − | 1.05005i | ||||
\(139\) | 21.4645 | 0.154421 | 0.0772103 | − | 0.997015i | \(-0.475399\pi\) | ||||
0.0772103 | + | 0.997015i | \(0.475399\pi\) | |||||||
\(140\) | − | 11.8322i | − | 0.0845154i | ||||||
\(141\) | 3.03155 | + | 0.673722i | 0.0215003 | + | 0.00477817i | ||||
\(142\) | 25.4624 | 0.179313 | ||||||||
\(143\) | 46.2074i | 0.323129i | ||||||||
\(144\) | −32.6113 | − | 15.2480i | −0.226468 | − | 0.105889i | ||||
\(145\) | −34.8510 | −0.240352 | ||||||||
\(146\) | 46.9550i | 0.321610i | ||||||||
\(147\) | 4.55583 | − | 20.4999i | 0.0309920 | − | 0.139455i | ||||
\(148\) | −76.9815 | −0.520145 | ||||||||
\(149\) | − | 66.8671i | − | 0.448772i | −0.974500 | − | 0.224386i | \(-0.927962\pi\) | ||
0.974500 | − | 0.224386i | \(-0.0720377\pi\) | |||||||
\(150\) | −20.7080 | − | 4.60208i | −0.138053 | − | 0.0306806i | ||||
\(151\) | −64.4712 | −0.426962 | −0.213481 | − | 0.976947i | \(-0.568480\pi\) | ||||
−0.213481 | + | 0.976947i | \(0.568480\pi\) | |||||||
\(152\) | 64.4823i | 0.424226i | ||||||||
\(153\) | −35.6720 | + | 76.2928i | −0.233150 | + | 0.498646i | ||||
\(154\) | −29.8418 | −0.193778 | ||||||||
\(155\) | − | 57.2141i | − | 0.369123i | ||||||
\(156\) | 7.54137 | − | 33.9339i | 0.0483421 | − | 0.217525i | ||||
\(157\) | −207.257 | −1.32011 | −0.660056 | − | 0.751217i | \(-0.729467\pi\) | ||||
−0.660056 | + | 0.751217i | \(0.729467\pi\) | |||||||
\(158\) | − | 77.7008i | − | 0.491777i | ||||||
\(159\) | 121.587 | + | 27.0212i | 0.764701 | + | 0.169945i | ||||
\(160\) | 12.6491 | 0.0790569 | ||||||||
\(161\) | 92.5701i | 0.574970i | ||||||||
\(162\) | −87.9035 | + | 73.4505i | −0.542614 | + | 0.453398i | ||||
\(163\) | 236.067 | 1.44826 | 0.724132 | − | 0.689662i | \(-0.242241\pi\) | ||||
0.724132 | + | 0.689662i | \(0.242241\pi\) | |||||||
\(164\) | − | 70.2124i | − | 0.428125i | ||||||
\(165\) | −11.6069 | + | 52.2275i | −0.0703448 | + | 0.316530i | ||||
\(166\) | −111.241 | −0.670127 | ||||||||
\(167\) | − | 109.647i | − | 0.656568i | −0.944579 | − | 0.328284i | \(-0.893530\pi\) | ||
0.944579 | − | 0.328284i | \(-0.106470\pi\) | |||||||
\(168\) | 21.9153 | + | 4.87039i | 0.130448 | + | 0.0289904i | ||||
\(169\) | −135.434 | −0.801384 | ||||||||
\(170\) | − | 29.5920i | − | 0.174071i | ||||||
\(171\) | 185.868 | + | 86.9057i | 1.08695 | + | 0.508220i | ||||
\(172\) | −118.190 | −0.687153 | ||||||||
\(173\) | − | 46.7105i | − | 0.270003i | −0.990845 | − | 0.135001i | \(-0.956896\pi\) | ||
0.990845 | − | 0.135001i | \(-0.0431039\pi\) | |||||||
\(174\) | 14.3455 | − | 64.5502i | 0.0824452 | − | 0.370978i | ||||
\(175\) | 13.2288 | 0.0755929 | ||||||||
\(176\) | − | 31.9023i | − | 0.181263i | ||||||
\(177\) | −161.540 | − | 35.9001i | −0.912653 | − | 0.202825i | ||||
\(178\) | −169.746 | −0.953629 | ||||||||
\(179\) | 293.828i | 1.64150i | 0.571289 | + | 0.820749i | \(0.306444\pi\) | ||||
−0.571289 | + | 0.820749i | \(0.693556\pi\) | |||||||
\(180\) | 17.0478 | − | 36.4606i | 0.0947098 | − | 0.202559i | ||||
\(181\) | −129.626 | −0.716168 | −0.358084 | − | 0.933689i | \(-0.616570\pi\) | ||||
−0.358084 | + | 0.933689i | \(0.616570\pi\) | |||||||
\(182\) | 21.6778i | 0.119109i | ||||||||
\(183\) | −61.6811 | + | 277.546i | −0.337055 | + | 1.51665i | ||||
\(184\) | −98.9616 | −0.537835 | ||||||||
\(185\) | − | 86.0680i | − | 0.465232i | ||||||
\(186\) | 105.971 | + | 23.5506i | 0.569735 | + | 0.126616i | ||||
\(187\) | −74.6339 | −0.399112 | ||||||||
\(188\) | − | 2.07034i | − | 0.0110124i | ||||||
\(189\) | 43.5749 | − | 56.6059i | 0.230555 | − | 0.299502i | ||||
\(190\) | −72.0934 | −0.379439 | ||||||||
\(191\) | − | 7.24400i | − | 0.0379267i | −0.999820 | − | 0.0189633i | \(-0.993963\pi\) | ||
0.999820 | − | 0.0189633i | \(-0.00603658\pi\) | |||||||
\(192\) | −5.20666 | + | 23.4284i | −0.0271180 | + | 0.122023i | ||||
\(193\) | −313.671 | −1.62524 | −0.812620 | − | 0.582793i | \(-0.801960\pi\) | ||||
−0.812620 | + | 0.582793i | \(0.801960\pi\) | |||||||
\(194\) | 34.6662i | 0.178692i | ||||||||
\(195\) | 37.9392 | + | 8.43150i | 0.194560 | + | 0.0432385i | ||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | − | 94.5137i | − | 0.479765i | −0.970802 | − | 0.239882i | \(-0.922891\pi\) | ||
0.970802 | − | 0.239882i | \(-0.0771089\pi\) | |||||||
\(198\) | −91.9570 | − | 42.9961i | −0.464429 | − | 0.217152i | ||||
\(199\) | −185.816 | −0.933747 | −0.466874 | − | 0.884324i | \(-0.654620\pi\) | ||||
−0.466874 | + | 0.884324i | \(0.654620\pi\) | |||||||
\(200\) | 14.1421i | 0.0707107i | ||||||||
\(201\) | 50.1834 | − | 225.810i | 0.249669 | − | 1.12343i | ||||
\(202\) | 224.429 | 1.11104 | ||||||||
\(203\) | 41.2362i | 0.203134i | ||||||||
\(204\) | 54.8098 | + | 12.1808i | 0.268675 | + | 0.0597096i | ||||
\(205\) | 78.4999 | 0.382926 | ||||||||
\(206\) | 251.030i | 1.21859i | ||||||||
\(207\) | −133.375 | + | 285.253i | −0.644323 | + | 1.37803i | ||||
\(208\) | −23.1745 | −0.111416 | ||||||||
\(209\) | 181.826i | 0.869983i | ||||||||
\(210\) | −5.44526 | + | 24.5020i | −0.0259298 | + | 0.116676i | ||||
\(211\) | 375.709 | 1.78061 | 0.890306 | − | 0.455363i | \(-0.150491\pi\) | ||||
0.890306 | + | 0.455363i | \(0.150491\pi\) | |||||||
\(212\) | − | 83.0359i | − | 0.391679i | ||||||
\(213\) | −52.7275 | − | 11.7180i | −0.247547 | − | 0.0550141i | ||||
\(214\) | 298.388 | 1.39434 | ||||||||
\(215\) | − | 132.141i | − | 0.614608i | ||||||
\(216\) | 60.5143 | + | 46.5835i | 0.280159 | + | 0.215664i | ||||
\(217\) | −67.6966 | −0.311966 | ||||||||
\(218\) | − | 139.334i | − | 0.639145i | ||||||
\(219\) | 21.6091 | − | 97.2344i | 0.0986717 | − | 0.443993i | ||||
\(220\) | 35.6678 | 0.162126 | ||||||||
\(221\) | 54.2158i | 0.245320i | ||||||||
\(222\) | 159.413 | + | 35.4275i | 0.718078 | + | 0.159584i | ||||
\(223\) | −19.6107 | −0.0879404 | −0.0439702 | − | 0.999033i | \(-0.514001\pi\) | ||||
−0.0439702 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 40.7642 | + | 19.0600i | 0.181174 | + | 0.0847110i | ||||
\(226\) | −145.424 | −0.643467 | ||||||||
\(227\) | − | 250.934i | − | 1.10543i | −0.833369 | − | 0.552717i | \(-0.813591\pi\) | ||
0.833369 | − | 0.552717i | \(-0.186409\pi\) | |||||||
\(228\) | 29.6753 | − | 133.530i | 0.130155 | − | 0.585657i | ||||
\(229\) | 296.680 | 1.29555 | 0.647773 | − | 0.761833i | \(-0.275701\pi\) | ||||
0.647773 | + | 0.761833i | \(0.275701\pi\) | |||||||
\(230\) | − | 110.642i | − | 0.481054i | ||||||
\(231\) | 61.7964 | + | 13.7335i | 0.267517 | + | 0.0594522i | ||||
\(232\) | −44.0834 | −0.190015 | ||||||||
\(233\) | 157.483i | 0.675891i | 0.941166 | + | 0.337946i | \(0.109732\pi\) | ||||
−0.941166 | + | 0.337946i | \(0.890268\pi\) | |||||||
\(234\) | −31.2333 | + | 66.7996i | −0.133476 | + | 0.285469i | ||||
\(235\) | 2.31471 | 0.00984983 | ||||||||
\(236\) | 110.320i | 0.467460i | ||||||||
\(237\) | −35.7586 | + | 160.903i | −0.150880 | + | 0.678914i | ||||
\(238\) | −35.0138 | −0.147117 | ||||||||
\(239\) | 78.7765i | 0.329609i | 0.986326 | + | 0.164804i | \(0.0526993\pi\) | ||||
−0.986326 | + | 0.164804i | \(0.947301\pi\) | |||||||
\(240\) | −26.1938 | − | 5.82123i | −0.109141 | − | 0.0242551i | ||||
\(241\) | −148.348 | −0.615553 | −0.307777 | − | 0.951459i | \(-0.599585\pi\) | ||||
−0.307777 | + | 0.951459i | \(0.599585\pi\) | |||||||
\(242\) | 81.1623i | 0.335381i | ||||||||
\(243\) | 215.833 | − | 111.647i | 0.888201 | − | 0.459454i | ||||
\(244\) | 189.545 | 0.776824 | ||||||||
\(245\) | − | 15.6525i | − | 0.0638877i | ||||||
\(246\) | −32.3124 | + | 145.396i | −0.131351 | + | 0.591040i | ||||
\(247\) | 132.083 | 0.534748 | ||||||||
\(248\) | − | 72.3707i | − | 0.291817i | ||||||
\(249\) | 230.358 | + | 51.1941i | 0.925132 | + | 0.205599i | ||||
\(250\) | −15.8114 | −0.0632456 | ||||||||
\(251\) | 223.217i | 0.889310i | 0.895702 | + | 0.444655i | \(0.146674\pi\) | ||||
−0.895702 | + | 0.444655i | \(0.853326\pi\) | |||||||
\(252\) | −43.1407 | − | 20.1712i | −0.171193 | − | 0.0800444i | ||||
\(253\) | −279.051 | −1.10297 | ||||||||
\(254\) | 223.004i | 0.877970i | ||||||||
\(255\) | −13.6185 | + | 61.2792i | −0.0534059 | + | 0.240310i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 359.930i | 1.40051i | 0.713894 | + | 0.700254i | \(0.246930\pi\) | ||||
−0.713894 | + | 0.700254i | \(0.753070\pi\) | |||||||
\(258\) | 244.748 | + | 54.3922i | 0.948637 | + | 0.210822i | ||||
\(259\) | −101.837 | −0.393193 | ||||||||
\(260\) | − | 25.9099i | − | 0.0996534i | ||||||
\(261\) | −59.4131 | + | 127.069i | −0.227637 | + | 0.486853i | ||||
\(262\) | 353.724 | 1.35009 | ||||||||
\(263\) | − | 228.402i | − | 0.868447i | −0.900805 | − | 0.434224i | \(-0.857023\pi\) | ||
0.900805 | − | 0.434224i | \(-0.142977\pi\) | |||||||
\(264\) | −14.6817 | + | 66.0632i | −0.0556124 | + | 0.250239i | ||||
\(265\) | 92.8369 | 0.350328 | ||||||||
\(266\) | 85.3021i | 0.320685i | ||||||||
\(267\) | 351.510 | + | 78.1185i | 1.31652 | + | 0.292579i | ||||
\(268\) | −154.213 | −0.575421 | ||||||||
\(269\) | − | 283.528i | − | 1.05401i | −0.849863 | − | 0.527003i | \(-0.823316\pi\) | ||
0.849863 | − | 0.527003i | \(-0.176684\pi\) | |||||||
\(270\) | −52.0820 | + | 67.6570i | −0.192896 | + | 0.250581i | ||||
\(271\) | −290.789 | −1.07302 | −0.536512 | − | 0.843893i | \(-0.680258\pi\) | ||||
−0.536512 | + | 0.843893i | \(0.680258\pi\) | |||||||
\(272\) | − | 37.4313i | − | 0.137615i | ||||||
\(273\) | 9.97629 | − | 44.8903i | 0.0365432 | − | 0.164433i | ||||
\(274\) | 271.382 | 0.990444 | ||||||||
\(275\) | 39.8778i | 0.145010i | ||||||||
\(276\) | 204.930 | + | 45.5430i | 0.742498 | + | 0.165011i | ||||
\(277\) | −267.470 | −0.965596 | −0.482798 | − | 0.875732i | \(-0.660379\pi\) | ||||
−0.482798 | + | 0.875732i | \(0.660379\pi\) | |||||||
\(278\) | 30.3553i | 0.109192i | ||||||||
\(279\) | −208.606 | − | 97.5372i | −0.747691 | − | 0.349596i | ||||
\(280\) | 16.7332 | 0.0597614 | ||||||||
\(281\) | − | 212.689i | − | 0.756900i | −0.925622 | − | 0.378450i | \(-0.876457\pi\) | ||
0.925622 | − | 0.378450i | \(-0.123543\pi\) | |||||||
\(282\) | −0.952787 | + | 4.28725i | −0.00337868 | + | 0.0152030i | ||||
\(283\) | −249.746 | −0.882496 | −0.441248 | − | 0.897385i | \(-0.645464\pi\) | ||||
−0.441248 | + | 0.897385i | \(0.645464\pi\) | |||||||
\(284\) | 36.0092i | 0.126793i | ||||||||
\(285\) | 149.291 | + | 33.1780i | 0.523828 | + | 0.116414i | ||||
\(286\) | −65.3472 | −0.228487 | ||||||||
\(287\) | − | 92.8823i | − | 0.323632i | ||||||
\(288\) | 21.5639 | − | 46.1194i | 0.0748747 | − | 0.160137i | ||||
\(289\) | 201.431 | 0.696993 | ||||||||
\(290\) | − | 49.2867i | − | 0.169954i | ||||||
\(291\) | 15.9537 | − | 71.7868i | 0.0548237 | − | 0.246690i | ||||
\(292\) | −66.4044 | −0.227412 | ||||||||
\(293\) | 312.196i | 1.06552i | 0.846268 | + | 0.532758i | \(0.178844\pi\) | ||||
−0.846268 | + | 0.532758i | \(0.821156\pi\) | |||||||
\(294\) | 28.9912 | + | 6.44292i | 0.0986095 | + | 0.0219147i | ||||
\(295\) | −123.342 | −0.418109 | ||||||||
\(296\) | − | 108.868i | − | 0.367798i | ||||||
\(297\) | 170.637 | + | 131.356i | 0.574537 | + | 0.442275i | ||||
\(298\) | 94.5643 | 0.317330 | ||||||||
\(299\) | 202.709i | 0.677955i | ||||||||
\(300\) | 6.50833 | − | 29.2855i | 0.0216944 | − | 0.0976184i | ||||
\(301\) | −156.351 | −0.519439 | ||||||||
\(302\) | − | 91.1760i | − | 0.301907i | ||||||
\(303\) | −464.748 | − | 103.284i | −1.53382 | − | 0.340872i | ||||
\(304\) | −91.1918 | −0.299973 | ||||||||
\(305\) | 211.918i | 0.694813i | ||||||||
\(306\) | −107.894 | − | 50.4478i | −0.352596 | − | 0.164862i | ||||
\(307\) | −155.259 | −0.505729 | −0.252864 | − | 0.967502i | \(-0.581373\pi\) | ||||
−0.252864 | + | 0.967502i | \(0.581373\pi\) | |||||||
\(308\) | − | 42.2027i | − | 0.137022i | ||||||
\(309\) | 115.526 | − | 519.832i | 0.373871 | − | 1.68231i | ||||
\(310\) | 80.9129 | 0.261009 | ||||||||
\(311\) | 338.149i | 1.08730i | 0.839313 | + | 0.543649i | \(0.182958\pi\) | ||||
−0.839313 | + | 0.543649i | \(0.817042\pi\) | |||||||
\(312\) | 47.9897 | + | 10.6651i | 0.153813 | + | 0.0341830i | ||||
\(313\) | 32.5551 | 0.104010 | 0.0520050 | − | 0.998647i | \(-0.483439\pi\) | ||||
0.0520050 | + | 0.998647i | \(0.483439\pi\) | |||||||
\(314\) | − | 293.106i | − | 0.933460i | ||||||
\(315\) | 22.5521 | − | 48.2328i | 0.0715939 | − | 0.153120i | ||||
\(316\) | 109.885 | 0.347739 | ||||||||
\(317\) | 156.813i | 0.494679i | 0.968929 | + | 0.247340i | \(0.0795563\pi\) | ||||
−0.968929 | + | 0.247340i | \(0.920444\pi\) | |||||||
\(318\) | −38.2138 | + | 171.951i | −0.120169 | + | 0.540725i | ||||
\(319\) | −124.306 | −0.389673 | ||||||||
\(320\) | 17.8885i | 0.0559017i | ||||||||
\(321\) | −617.902 | − | 137.321i | −1.92493 | − | 0.427791i | ||||
\(322\) | −130.914 | −0.406565 | ||||||||
\(323\) | 213.339i | 0.660493i | ||||||||
\(324\) | −103.875 | − | 124.314i | −0.320601 | − | 0.383686i | ||||
\(325\) | 28.9681 | 0.0891327 | ||||||||
\(326\) | 333.849i | 1.02408i | ||||||||
\(327\) | −64.1225 | + | 288.532i | −0.196093 | + | 0.882360i | ||||
\(328\) | 99.2954 | 0.302730 | ||||||||
\(329\) | − | 2.73880i | − | 0.00832462i | ||||||
\(330\) | −73.8609 | − | 16.4146i | −0.223821 | − | 0.0497413i | ||||
\(331\) | 62.7666 | 0.189627 | 0.0948136 | − | 0.995495i | \(-0.469775\pi\) | ||||
0.0948136 | + | 0.995495i | \(0.469775\pi\) | |||||||
\(332\) | − | 157.319i | − | 0.473851i | ||||||
\(333\) | −313.809 | − | 146.727i | −0.942369 | − | 0.440620i | ||||
\(334\) | 155.064 | 0.464263 | ||||||||
\(335\) | − | 172.415i | − | 0.514672i | ||||||
\(336\) | −6.88777 | + | 30.9929i | −0.0204993 | + | 0.0922407i | ||||
\(337\) | 429.763 | 1.27526 | 0.637631 | − | 0.770342i | \(-0.279914\pi\) | ||||
0.637631 | + | 0.770342i | \(0.279914\pi\) | |||||||
\(338\) | − | 191.532i | − | 0.566664i | ||||||
\(339\) | 301.143 | + | 66.9251i | 0.888327 | + | 0.197419i | ||||
\(340\) | 41.8495 | 0.123087 | ||||||||
\(341\) | − | 204.070i | − | 0.598446i | ||||||
\(342\) | −122.903 | + | 262.857i | −0.359366 | + | 0.768587i | ||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | − | 167.146i | − | 0.485890i | ||||||
\(345\) | −50.9186 | + | 229.118i | −0.147590 | + | 0.664111i | ||||
\(346\) | 66.0586 | 0.190921 | ||||||||
\(347\) | − | 611.203i | − | 1.76139i | −0.473683 | − | 0.880695i | \(-0.657076\pi\) | ||
0.473683 | − | 0.880695i | \(-0.342924\pi\) | |||||||
\(348\) | 91.2878 | + | 20.2875i | 0.262321 | + | 0.0582975i | ||||
\(349\) | −229.756 | −0.658327 | −0.329163 | − | 0.944273i | \(-0.606767\pi\) | ||||
−0.329163 | + | 0.944273i | \(0.606767\pi\) | |||||||
\(350\) | 18.7083i | 0.0534522i | ||||||||
\(351\) | 95.4197 | − | 123.955i | 0.271851 | − | 0.353148i | ||||
\(352\) | 45.1166 | 0.128172 | ||||||||
\(353\) | 434.601i | 1.23117i | 0.788072 | + | 0.615583i | \(0.211079\pi\) | ||||
−0.788072 | + | 0.615583i | \(0.788921\pi\) | |||||||
\(354\) | 50.7704 | − | 228.452i | 0.143419 | − | 0.645343i | ||||
\(355\) | −40.2596 | −0.113407 | ||||||||
\(356\) | − | 240.057i | − | 0.674317i | ||||||
\(357\) | 72.5065 | + | 16.1136i | 0.203099 | + | 0.0451362i | ||||
\(358\) | −415.536 | −1.16071 | ||||||||
\(359\) | 185.884i | 0.517782i | 0.965907 | + | 0.258891i | \(0.0833570\pi\) | ||||
−0.965907 | + | 0.258891i | \(0.916643\pi\) | |||||||
\(360\) | 51.5630 | + | 24.1092i | 0.143231 | + | 0.0669699i | ||||
\(361\) | 158.746 | 0.439740 | ||||||||
\(362\) | − | 183.320i | − | 0.506408i | ||||||
\(363\) | 37.3516 | − | 168.071i | 0.102897 | − | 0.463005i | ||||
\(364\) | −30.6570 | −0.0842225 | ||||||||
\(365\) | − | 74.2424i | − | 0.203404i | ||||||
\(366\) | −392.510 | − | 87.2303i | −1.07243 | − | 0.238334i | ||||
\(367\) | −418.446 | −1.14018 | −0.570090 | − | 0.821582i | \(-0.693092\pi\) | ||||
−0.570090 | + | 0.821582i | \(0.693092\pi\) | |||||||
\(368\) | − | 139.953i | − | 0.380307i | ||||||
\(369\) | 133.825 | − | 286.215i | 0.362669 | − | 0.775651i | ||||
\(370\) | 121.718 | 0.328969 | ||||||||
\(371\) | − | 109.846i | − | 0.296081i | ||||||
\(372\) | −33.3056 | + | 149.865i | −0.0895312 | + | 0.402863i | ||||
\(373\) | 597.593 | 1.60213 | 0.801063 | − | 0.598581i | \(-0.204268\pi\) | ||||
0.801063 | + | 0.598581i | \(0.204268\pi\) | |||||||
\(374\) | − | 105.548i | − | 0.282215i | ||||||
\(375\) | 32.7422 | + | 7.27653i | 0.0873125 | + | 0.0194041i | ||||
\(376\) | 2.92790 | 0.00778697 | ||||||||
\(377\) | 90.2985i | 0.239519i | ||||||||
\(378\) | 80.0528 | + | 61.6242i | 0.211780 | + | 0.163027i | ||||
\(379\) | 563.466 | 1.48672 | 0.743358 | − | 0.668894i | \(-0.233232\pi\) | ||||
0.743358 | + | 0.668894i | \(0.233232\pi\) | |||||||
\(380\) | − | 101.955i | − | 0.268304i | ||||||
\(381\) | 102.629 | − | 461.797i | 0.269366 | − | 1.21207i | ||||
\(382\) | 10.2446 | 0.0268182 | ||||||||
\(383\) | − | 108.726i | − | 0.283881i | −0.989875 | − | 0.141940i | \(-0.954666\pi\) | ||
0.989875 | − | 0.141940i | \(-0.0453341\pi\) | |||||||
\(384\) | −33.1328 | − | 7.36333i | −0.0862833 | − | 0.0191753i | ||||
\(385\) | 47.1841 | 0.122556 | ||||||||
\(386\) | − | 443.598i | − | 1.14922i | ||||||
\(387\) | −481.793 | − | 225.270i | −1.24494 | − | 0.582094i | ||||
\(388\) | −49.0254 | −0.126354 | ||||||||
\(389\) | − | 128.348i | − | 0.329944i | −0.986298 | − | 0.164972i | \(-0.947247\pi\) | ||
0.986298 | − | 0.164972i | \(-0.0527534\pi\) | |||||||
\(390\) | −11.9239 | + | 53.6542i | −0.0305742 | + | 0.137575i | ||||
\(391\) | −327.414 | −0.837375 | ||||||||
\(392\) | − | 19.7990i | − | 0.0505076i | ||||||
\(393\) | −732.490 | − | 162.787i | −1.86384 | − | 0.414215i | ||||
\(394\) | 133.663 | 0.339245 | ||||||||
\(395\) | 122.856i | 0.311027i | ||||||||
\(396\) | 60.8056 | − | 130.047i | 0.153550 | − | 0.328401i | ||||
\(397\) | −165.453 | −0.416758 | −0.208379 | − | 0.978048i | \(-0.566819\pi\) | ||||
−0.208379 | + | 0.978048i | \(0.566819\pi\) | |||||||
\(398\) | − | 262.783i | − | 0.660259i | ||||||
\(399\) | 39.2567 | − | 176.643i | 0.0983878 | − | 0.442715i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 397.048i | 0.990144i | 0.868852 | + | 0.495072i | \(0.164858\pi\) | ||||
−0.868852 | + | 0.495072i | \(0.835142\pi\) | |||||||
\(402\) | 319.344 | + | 70.9700i | 0.794387 | + | 0.176542i | ||||
\(403\) | −148.241 | −0.367844 | ||||||||
\(404\) | 317.391i | 0.785620i | ||||||||
\(405\) | 138.988 | − | 116.135i | 0.343179 | − | 0.286754i | ||||
\(406\) | −58.3168 | −0.143638 | ||||||||
\(407\) | − | 306.985i | − | 0.754264i | ||||||
\(408\) | −17.2262 | + | 77.5127i | −0.0422211 | + | 0.189982i | ||||
\(409\) | 590.813 | 1.44453 | 0.722265 | − | 0.691616i | \(-0.243101\pi\) | ||||
0.722265 | + | 0.691616i | \(0.243101\pi\) | |||||||
\(410\) | 111.016i | 0.270770i | ||||||||
\(411\) | −561.977 | − | 124.892i | −1.36734 | − | 0.303874i | ||||
\(412\) | −355.010 | −0.861674 | ||||||||
\(413\) | 145.940i | 0.353366i | ||||||||
\(414\) | −403.409 | − | 188.621i | −0.974417 | − | 0.455605i | ||||
\(415\) | 175.888 | 0.423826 | ||||||||
\(416\) | − | 32.7737i | − | 0.0787829i | ||||||
\(417\) | 13.9698 | − | 62.8598i | 0.0335007 | − | 0.150743i | ||||
\(418\) | −257.141 | −0.615171 | ||||||||
\(419\) | − | 275.411i | − | 0.657305i | −0.944451 | − | 0.328653i | \(-0.893405\pi\) | ||
0.944451 | − | 0.328653i | \(-0.106595\pi\) | |||||||
\(420\) | −34.6511 | − | 7.70076i | −0.0825026 | − | 0.0183351i | ||||
\(421\) | 570.120 | 1.35420 | 0.677102 | − | 0.735890i | \(-0.263236\pi\) | ||||
0.677102 | + | 0.735890i | \(0.263236\pi\) | |||||||
\(422\) | 531.333i | 1.25908i | ||||||||
\(423\) | 3.94606 | − | 8.43956i | 0.00932875 | − | 0.0199517i | ||||
\(424\) | 117.430 | 0.276959 | ||||||||
\(425\) | 46.7891i | 0.110092i | ||||||||
\(426\) | 16.5718 | − | 74.5679i | 0.0389008 | − | 0.175042i | ||||
\(427\) | 250.745 | 0.587224 | ||||||||
\(428\) | 421.985i | 0.985946i | ||||||||
\(429\) | 135.321 | + | 30.0733i | 0.315433 | + | 0.0701010i | ||||
\(430\) | 186.875 | 0.434594 | ||||||||
\(431\) | − | 650.331i | − | 1.50889i | −0.656365 | − | 0.754444i | \(-0.727907\pi\) | ||
0.656365 | − | 0.754444i | \(-0.272093\pi\) | |||||||
\(432\) | −65.8790 | + | 85.5801i | −0.152498 | + | 0.198102i | ||||
\(433\) | 635.503 | 1.46767 | 0.733837 | − | 0.679325i | \(-0.237727\pi\) | ||||
0.733837 | + | 0.679325i | \(0.237727\pi\) | |||||||
\(434\) | − | 95.7374i | − | 0.220593i | ||||||
\(435\) | −22.6822 | + | 102.063i | −0.0521429 | + | 0.234627i | ||||
\(436\) | 197.047 | 0.451943 | ||||||||
\(437\) | 797.659i | 1.82531i | ||||||||
\(438\) | 137.510 | + | 30.5599i | 0.313950 | + | 0.0697714i | ||||
\(439\) | −341.898 | −0.778810 | −0.389405 | − | 0.921067i | \(-0.627319\pi\) | ||||
−0.389405 | + | 0.921067i | \(0.627319\pi\) | |||||||
\(440\) | 50.4419i | 0.114641i | ||||||||
\(441\) | −57.0698 | − | 26.6840i | −0.129410 | − | 0.0605079i | ||||
\(442\) | −76.6726 | −0.173468 | ||||||||
\(443\) | 254.231i | 0.573884i | 0.957948 | + | 0.286942i | \(0.0926387\pi\) | ||||
−0.957948 | + | 0.286942i | \(0.907361\pi\) | |||||||
\(444\) | −50.1021 | + | 225.444i | −0.112843 | + | 0.507758i | ||||
\(445\) | 268.392 | 0.603128 | ||||||||
\(446\) | − | 27.7337i | − | 0.0621833i | ||||||
\(447\) | −195.824 | − | 43.5193i | −0.438084 | − | 0.0973586i | ||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | 73.2691i | 0.163183i | 0.996666 | + | 0.0815915i | \(0.0260003\pi\) | ||||
−0.996666 | + | 0.0815915i | \(0.974000\pi\) | |||||||
\(450\) | −26.9549 | + | 57.6492i | −0.0598997 | + | 0.128109i | ||||
\(451\) | 279.992 | 0.620825 | ||||||||
\(452\) | − | 205.660i | − | 0.455000i | ||||||
\(453\) | −41.9600 | + | 188.807i | −0.0926269 | + | 0.416793i | ||||
\(454\) | 354.874 | 0.781660 | ||||||||
\(455\) | − | 34.2756i | − | 0.0753309i | ||||||
\(456\) | 188.840 | + | 41.9672i | 0.414122 | + | 0.0920334i | ||||
\(457\) | 201.124 | 0.440097 | 0.220049 | − | 0.975489i | \(-0.429378\pi\) | ||||
0.220049 | + | 0.975489i | \(0.429378\pi\) | |||||||
\(458\) | 419.569i | 0.916089i | ||||||||
\(459\) | 200.211 | + | 154.121i | 0.436189 | + | 0.335776i | ||||
\(460\) | 156.472 | 0.340157 | ||||||||
\(461\) | 500.367i | 1.08539i | 0.839929 | + | 0.542697i | \(0.182597\pi\) | ||||
−0.839929 | + | 0.542697i | \(0.817403\pi\) | |||||||
\(462\) | −19.4220 | + | 87.3933i | −0.0420391 | + | 0.189163i | ||||
\(463\) | −601.585 | −1.29932 | −0.649660 | − | 0.760225i | \(-0.725089\pi\) | ||||
−0.649660 | + | 0.760225i | \(0.725089\pi\) | |||||||
\(464\) | − | 62.3433i | − | 0.134361i | ||||||
\(465\) | −167.554 | − | 37.2368i | −0.360332 | − | 0.0800791i | ||||
\(466\) | −222.714 | −0.477927 | ||||||||
\(467\) | − | 271.025i | − | 0.580353i | −0.956973 | − | 0.290176i | \(-0.906286\pi\) | ||
0.956973 | − | 0.290176i | \(-0.0937140\pi\) | |||||||
\(468\) | −94.4690 | − | 44.1706i | −0.201857 | − | 0.0943816i | ||||
\(469\) | −204.004 | −0.434977 | ||||||||
\(470\) | 3.27349i | 0.00696488i | ||||||||
\(471\) | −134.890 | + | 606.964i | −0.286391 | + | 1.28867i | ||||
\(472\) | −156.017 | −0.330544 | ||||||||
\(473\) | − | 471.317i | − | 0.996442i | ||||||
\(474\) | −227.551 | − | 50.5702i | −0.480065 | − | 0.106688i | ||||
\(475\) | 113.990 | 0.239978 | ||||||||
\(476\) | − | 49.5170i | − | 0.104027i | ||||||
\(477\) | 158.266 | − | 338.489i | 0.331795 | − | 0.709620i | ||||
\(478\) | −111.407 | −0.233069 | ||||||||
\(479\) | 203.003i | 0.423807i | 0.977291 | + | 0.211903i | \(0.0679662\pi\) | ||||
−0.977291 | + | 0.211903i | \(0.932034\pi\) | |||||||
\(480\) | 8.23246 | − | 37.0436i | 0.0171510 | − | 0.0771741i | ||||
\(481\) | −223.001 | −0.463620 | ||||||||
\(482\) | − | 209.796i | − | 0.435262i | ||||||
\(483\) | 271.096 | + | 60.2477i | 0.561276 | + | 0.124736i | ||||
\(484\) | −114.781 | −0.237150 | ||||||||
\(485\) | − | 54.8121i | − | 0.113015i | ||||||
\(486\) | 157.893 | + | 305.234i | 0.324883 | + | 0.628053i | ||||
\(487\) | 795.875 | 1.63424 | 0.817120 | − | 0.576468i | \(-0.195569\pi\) | ||||
0.817120 | + | 0.576468i | \(0.195569\pi\) | |||||||
\(488\) | 268.057i | 0.549298i | ||||||||
\(489\) | 153.640 | − | 691.334i | 0.314193 | − | 1.41377i | ||||
\(490\) | 22.1359 | 0.0451754 | ||||||||
\(491\) | 41.1374i | 0.0837830i | 0.999122 | + | 0.0418915i | \(0.0133384\pi\) | ||||
−0.999122 | + | 0.0418915i | \(0.986662\pi\) | |||||||
\(492\) | −205.621 | − | 45.6966i | −0.417928 | − | 0.0928792i | ||||
\(493\) | −145.849 | −0.295841 | ||||||||
\(494\) | 186.793i | 0.378124i | ||||||||
\(495\) | 145.397 | + | 67.9828i | 0.293731 | + | 0.137339i | ||||
\(496\) | 102.348 | 0.206346 | ||||||||
\(497\) | 47.6357i | 0.0958466i | ||||||||
\(498\) | −72.3994 | + | 325.775i | −0.145380 | + | 0.654167i | ||||
\(499\) | 590.508 | 1.18338 | 0.591692 | − | 0.806164i | \(-0.298460\pi\) | ||||
0.591692 | + | 0.806164i | \(0.298460\pi\) | |||||||
\(500\) | − | 22.3607i | − | 0.0447214i | ||||||
\(501\) | −321.106 | − | 71.3618i | −0.640931 | − | 0.142439i | ||||
\(502\) | −315.676 | −0.628837 | ||||||||
\(503\) | − | 276.575i | − | 0.549850i | −0.961466 | − | 0.274925i | \(-0.911347\pi\) | ||
0.961466 | − | 0.274925i | \(-0.0886531\pi\) | |||||||
\(504\) | 28.5264 | − | 61.0102i | 0.0565999 | − | 0.121052i | ||||
\(505\) | −354.854 | −0.702680 | ||||||||
\(506\) | − | 394.637i | − | 0.779916i | ||||||
\(507\) | −88.1448 | + | 396.625i | −0.173856 | + | 0.782298i | ||||
\(508\) | −315.376 | −0.620819 | ||||||||
\(509\) | 311.610i | 0.612201i | 0.951999 | + | 0.306100i | \(0.0990243\pi\) | ||||
−0.951999 | + | 0.306100i | \(0.900976\pi\) | |||||||
\(510\) | −86.6618 | − | 19.2595i | −0.169925 | − | 0.0377637i | ||||
\(511\) | −87.8448 | −0.171908 | ||||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 375.477 | − | 487.762i | 0.731923 | − | 0.950804i | ||||
\(514\) | −509.019 | −0.990309 | ||||||||
\(515\) | − | 396.913i | − | 0.770705i | ||||||
\(516\) | −76.9221 | + | 346.126i | −0.149074 | + | 0.670788i | ||||
\(517\) | 8.25606 | 0.0159692 | ||||||||
\(518\) | − | 144.019i | − | 0.278029i | ||||||
\(519\) | −136.794 | − | 30.4007i | −0.263572 | − | 0.0585756i | ||||
\(520\) | 36.6421 | 0.0704656 | ||||||||
\(521\) | 435.399i | 0.835698i | 0.908516 | + | 0.417849i | \(0.137216\pi\) | ||||
−0.908516 | + | 0.417849i | \(0.862784\pi\) | |||||||
\(522\) | −179.702 | − | 84.0229i | −0.344257 | − | 0.160963i | ||||
\(523\) | 619.746 | 1.18498 | 0.592491 | − | 0.805577i | \(-0.298144\pi\) | ||||
0.592491 | + | 0.805577i | \(0.298144\pi\) | |||||||
\(524\) | 500.241i | 0.954658i | ||||||||
\(525\) | 8.60971 | − | 38.7411i | 0.0163994 | − | 0.0737926i | ||||
\(526\) | 323.009 | 0.614085 | ||||||||
\(527\) | − | 239.438i | − | 0.454341i | ||||||
\(528\) | −93.4274 | − | 20.7630i | −0.176946 | − | 0.0393239i | ||||
\(529\) | −695.175 | −1.31413 | ||||||||
\(530\) | 131.291i | 0.247719i | ||||||||
\(531\) | −210.271 | + | 449.712i | −0.395990 | + | 0.846916i | ||||
\(532\) | −120.635 | −0.226758 | ||||||||
\(533\) | − | 203.392i | − | 0.381599i | ||||||
\(534\) | −110.476 | + | 497.110i | −0.206884 | + | 0.930917i | ||||
\(535\) | −471.793 | −0.881857 | ||||||||
\(536\) | − | 218.090i | − | 0.406884i | ||||||
\(537\) | 860.491 | + | 191.233i | 1.60240 | + | 0.356114i | ||||
\(538\) | 400.969 | 0.745295 | ||||||||
\(539\) | − | 55.8289i | − | 0.103579i | ||||||
\(540\) | −95.6814 | − | 73.6550i | −0.177188 | − | 0.136398i | ||||
\(541\) | 709.366 | 1.31121 | 0.655606 | − | 0.755103i | \(-0.272413\pi\) | ||||
0.655606 | + | 0.755103i | \(0.272413\pi\) | |||||||
\(542\) | − | 411.238i | − | 0.758742i | ||||||
\(543\) | −84.3652 | + | 379.618i | −0.155369 | + | 0.699112i | ||||
\(544\) | 52.9359 | 0.0973086 | ||||||||
\(545\) | 220.306i | 0.404231i | ||||||||
\(546\) | 63.4845 | + | 14.1086i | 0.116272 | + | 0.0258399i | ||||
\(547\) | −306.448 | −0.560234 | −0.280117 | − | 0.959966i | \(-0.590373\pi\) | ||||
−0.280117 | + | 0.959966i | \(0.590373\pi\) | |||||||
\(548\) | 383.792i | 0.700350i | ||||||||
\(549\) | 772.665 | + | 361.273i | 1.40740 | + | 0.658056i | ||||
\(550\) | −56.3958 | −0.102538 | ||||||||
\(551\) | 355.325i | 0.644873i | ||||||||
\(552\) | −64.4075 | + | 289.814i | −0.116680 | + | 0.525026i | ||||
\(553\) | 145.365 | 0.262866 | ||||||||
\(554\) | − | 378.260i | − | 0.682780i | ||||||
\(555\) | −252.054 | − | 56.0159i | −0.454152 | − | 0.100929i | ||||
\(556\) | −42.9289 | −0.0772103 | ||||||||
\(557\) | 259.701i | 0.466250i | 0.972447 | + | 0.233125i | \(0.0748951\pi\) | ||||
−0.972447 | + | 0.233125i | \(0.925105\pi\) | |||||||
\(558\) | 137.938 | − | 295.013i | 0.247201 | − | 0.528697i | ||||
\(559\) | −342.375 | −0.612478 | ||||||||
\(560\) | 23.6643i | 0.0422577i | ||||||||
\(561\) | −48.5742 | + | 218.569i | −0.0865851 | + | 0.389607i | ||||
\(562\) | 300.787 | 0.535209 | ||||||||
\(563\) | 1066.78i | 1.89481i | 0.320032 | + | 0.947407i | \(0.396306\pi\) | ||||
−0.320032 | + | 0.947407i | \(0.603694\pi\) | |||||||
\(564\) | −6.06309 | − | 1.34744i | −0.0107502 | − | 0.00238909i | ||||
\(565\) | 229.935 | 0.406964 | ||||||||
\(566\) | − | 353.195i | − | 0.624019i | ||||||
\(567\) | −137.413 | − | 164.452i | −0.242352 | − | 0.290039i | ||||
\(568\) | −50.9248 | −0.0896563 | ||||||||
\(569\) | − | 294.913i | − | 0.518301i | −0.965837 | − | 0.259150i | \(-0.916557\pi\) | ||
0.965837 | − | 0.259150i | \(-0.0834425\pi\) | |||||||
\(570\) | −46.9208 | + | 211.129i | −0.0823171 | + | 0.370402i | ||||
\(571\) | 183.465 | 0.321304 | 0.160652 | − | 0.987011i | \(-0.448640\pi\) | ||||
0.160652 | + | 0.987011i | \(0.448640\pi\) | |||||||
\(572\) | − | 92.4149i | − | 0.161564i | ||||||
\(573\) | −21.2144 | − | 4.71463i | −0.0370234 | − | 0.00822798i | ||||
\(574\) | 131.355 | 0.228842 | ||||||||
\(575\) | 174.941i | 0.304245i | ||||||||
\(576\) | 65.2227 | + | 30.4960i | 0.113234 | + | 0.0529444i | ||||
\(577\) | 740.634 | 1.28359 | 0.641797 | − | 0.766874i | \(-0.278189\pi\) | ||||
0.641797 | + | 0.766874i | \(0.278189\pi\) | |||||||
\(578\) | 284.867i | 0.492849i | ||||||||
\(579\) | −204.148 | + | 918.603i | −0.352587 | + | 1.58653i | ||||
\(580\) | 69.7020 | 0.120176 | ||||||||
\(581\) | − | 208.113i | − | 0.358198i | ||||||
\(582\) | 101.522 | + | 22.5619i | 0.174436 | + | 0.0387662i | ||||
\(583\) | 331.129 | 0.567974 | ||||||||
\(584\) | − | 93.9101i | − | 0.160805i | ||||||
\(585\) | 49.3842 | − | 105.619i | 0.0844174 | − | 0.180546i | ||||
\(586\) | −441.512 | −0.753433 | ||||||||
\(587\) | − | 694.040i | − | 1.18235i | −0.806543 | − | 0.591175i | \(-0.798664\pi\) | ||
0.806543 | − | 0.591175i | \(-0.201336\pi\) | |||||||
\(588\) | −9.11166 | + | 40.9997i | −0.0154960 | + | 0.0697274i | ||||
\(589\) | −583.329 | −0.990371 | ||||||||
\(590\) | − | 174.432i | − | 0.295647i | ||||||
\(591\) | −276.788 | − | 61.5126i | −0.468339 | − | 0.104082i | ||||
\(592\) | 153.963 | 0.260073 | ||||||||
\(593\) | − | 428.653i | − | 0.722855i | −0.932400 | − | 0.361427i | \(-0.882290\pi\) | ||
0.932400 | − | 0.361427i | \(-0.117710\pi\) | |||||||
\(594\) | −185.765 | + | 241.318i | −0.312736 | + | 0.406259i | ||||
\(595\) | 55.3616 | 0.0930448 | ||||||||
\(596\) | 133.734i | 0.224386i | ||||||||
\(597\) | −120.935 | + | 544.171i | −0.202571 | + | 0.911509i | ||||
\(598\) | −286.673 | −0.479387 | ||||||||
\(599\) | 1068.82i | 1.78433i | 0.451705 | + | 0.892167i | \(0.350816\pi\) | ||||
−0.451705 | + | 0.892167i | \(0.649184\pi\) | |||||||
\(600\) | 41.4160 | + | 9.20417i | 0.0690266 | + | 0.0153403i | ||||
\(601\) | 259.767 | 0.432224 | 0.216112 | − | 0.976369i | \(-0.430662\pi\) | ||||
0.216112 | + | 0.976369i | \(0.430662\pi\) | |||||||
\(602\) | − | 221.114i | − | 0.367299i | ||||||
\(603\) | −628.636 | − | 293.929i | −1.04251 | − | 0.487445i | ||||
\(604\) | 128.942 | 0.213481 | ||||||||
\(605\) | − | 128.329i | − | 0.212114i | ||||||
\(606\) | 146.066 | − | 657.252i | 0.241033 | − | 1.08457i | ||||
\(607\) | −1147.06 | −1.88972 | −0.944858 | − | 0.327479i | \(-0.893801\pi\) | ||||
−0.944858 | + | 0.327479i | \(0.893801\pi\) | |||||||
\(608\) | − | 128.965i | − | 0.212113i | ||||||
\(609\) | 120.762 | + | 26.8379i | 0.198296 | + | 0.0440688i | ||||
\(610\) | −299.697 | −0.491307 | ||||||||
\(611\) | − | 5.99739i | − | 0.00981569i | ||||||
\(612\) | 71.3440 | − | 152.586i | 0.116575 | − | 0.249323i | ||||
\(613\) | −166.678 | −0.271905 | −0.135952 | − | 0.990715i | \(-0.543409\pi\) | ||||
−0.135952 | + | 0.990715i | \(0.543409\pi\) | |||||||
\(614\) | − | 219.569i | − | 0.357604i | ||||||
\(615\) | 51.0903 | − | 229.891i | 0.0830737 | − | 0.373807i | ||||
\(616\) | 59.6837 | 0.0968890 | ||||||||
\(617\) | 319.900i | 0.518477i | 0.965813 | + | 0.259238i | \(0.0834716\pi\) | ||||
−0.965813 | + | 0.259238i | \(0.916528\pi\) | |||||||
\(618\) | 735.154 | + | 163.379i | 1.18957 | + | 0.264367i | ||||
\(619\) | −917.131 | −1.48163 | −0.740817 | − | 0.671707i | \(-0.765561\pi\) | ||||
−0.740817 | + | 0.671707i | \(0.765561\pi\) | |||||||
\(620\) | 114.428i | 0.184561i | ||||||||
\(621\) | 748.574 | + | 576.247i | 1.20543 | + | 0.927935i | ||||
\(622\) | −478.216 | −0.768835 | ||||||||
\(623\) | − | 317.565i | − | 0.509736i | ||||||
\(624\) | −15.0827 | + | 67.8678i | −0.0241710 | + | 0.108762i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 46.0399i | 0.0735461i | ||||||||
\(627\) | 532.488 | + | 118.339i | 0.849263 | + | 0.188738i | ||||
\(628\) | 414.515 | 0.660056 | ||||||||
\(629\) | − | 360.190i | − | 0.572639i | ||||||
\(630\) | 68.2115 | + | 31.8934i | 0.108272 | + | 0.0506245i | ||||
\(631\) | 695.889 | 1.10283 | 0.551417 | − | 0.834229i | \(-0.314087\pi\) | ||||
0.551417 | + | 0.834229i | \(0.314087\pi\) | |||||||
\(632\) | 155.402i | 0.245889i | ||||||||
\(633\) | 244.524 | − | 1100.28i | 0.386294 | − | 1.73820i | ||||
\(634\) | −221.767 | −0.349791 | ||||||||
\(635\) | − | 352.601i | − | 0.555277i | ||||||
\(636\) | −243.175 | − | 54.0425i | −0.382350 | − | 0.0849725i | ||||
\(637\) | −40.5554 | −0.0636662 | ||||||||
\(638\) | − | 175.795i | − | 0.275541i | ||||||
\(639\) | −68.6335 | + | 146.789i | −0.107408 | + | 0.229716i | ||||
\(640\) | −25.2982 | −0.0395285 | ||||||||
\(641\) | − | 75.7558i | − | 0.118184i | −0.998253 | − | 0.0590919i | \(-0.981180\pi\) | ||
0.998253 | − | 0.0590919i | \(-0.0188205\pi\) | |||||||
\(642\) | 194.201 | − | 873.846i | 0.302494 | − | 1.36113i | ||||
\(643\) | 1173.40 | 1.82488 | 0.912438 | − | 0.409215i | \(-0.134197\pi\) | ||||
0.912438 | + | 0.409215i | \(0.134197\pi\) | |||||||
\(644\) | − | 185.140i | − | 0.287485i | ||||||
\(645\) | −386.981 | − | 86.0016i | −0.599971 | − | 0.133336i | ||||
\(646\) | −301.707 | −0.467039 | ||||||||
\(647\) | 322.830i | 0.498964i | 0.968379 | + | 0.249482i | \(0.0802603\pi\) | ||||
−0.968379 | + | 0.249482i | \(0.919740\pi\) | |||||||
\(648\) | 175.807 | − | 146.901i | 0.271307 | − | 0.226699i | ||||
\(649\) | −439.934 | −0.677864 | ||||||||
\(650\) | 40.9671i | 0.0630264i | ||||||||
\(651\) | −44.0592 | + | 198.253i | −0.0676792 | + | 0.304536i | ||||
\(652\) | −472.134 | −0.724132 | ||||||||
\(653\) | − | 1056.82i | − | 1.61841i | −0.587526 | − | 0.809206i | \(-0.699898\pi\) | ||
0.587526 | − | 0.809206i | \(-0.300102\pi\) | |||||||
\(654\) | −408.045 | − | 90.6828i | −0.623923 | − | 0.138659i | ||||
\(655\) | −559.286 | −0.853872 | ||||||||
\(656\) | 140.425i | 0.214062i | ||||||||
\(657\) | −270.692 | − | 126.567i | −0.412012 | − | 0.192643i | ||||
\(658\) | 3.87325 | 0.00588640 | ||||||||
\(659\) | 808.670i | 1.22712i | 0.789649 | + | 0.613559i | \(0.210263\pi\) | ||||
−0.789649 | + | 0.613559i | \(0.789737\pi\) | |||||||
\(660\) | 23.2138 | − | 104.455i | 0.0351724 | − | 0.158265i | ||||
\(661\) | 1068.86 | 1.61703 | 0.808515 | − | 0.588476i | \(-0.200272\pi\) | ||||
0.808515 | + | 0.588476i | \(0.200272\pi\) | |||||||
\(662\) | 88.7654i | 0.134087i | ||||||||
\(663\) | 158.774 | + | 35.2854i | 0.239478 | + | 0.0532208i | ||||
\(664\) | 222.482 | 0.335064 | ||||||||
\(665\) | − | 134.874i | − | 0.202819i | ||||||
\(666\) | 207.503 | − | 443.793i | 0.311566 | − | 0.666355i | ||||
\(667\) | −545.320 | −0.817572 | ||||||||
\(668\) | 219.294i | 0.328284i | ||||||||
\(669\) | −12.7633 | + | 57.4310i | −0.0190782 | + | 0.0858460i | ||||
\(670\) | 243.832 | 0.363928 | ||||||||
\(671\) | 755.865i | 1.12647i | ||||||||
\(672\) | −43.8306 | − | 9.74078i | −0.0652240 | − | 0.0144952i | ||||
\(673\) | −1159.59 | −1.72302 | −0.861508 | − | 0.507744i | \(-0.830479\pi\) | ||||
−0.861508 | + | 0.507744i | \(0.830479\pi\) | |||||||
\(674\) | 607.777i | 0.901747i | ||||||||
\(675\) | 82.3488 | − | 106.975i | 0.121998 | − | 0.158482i | ||||
\(676\) | 270.868 | 0.400692 | ||||||||
\(677\) | − | 202.423i | − | 0.298999i | −0.988762 | − | 0.149500i | \(-0.952234\pi\) | ||
0.988762 | − | 0.149500i | \(-0.0477663\pi\) | |||||||
\(678\) | −94.6464 | + | 425.880i | −0.139596 | + | 0.628142i | ||||
\(679\) | −64.8546 | −0.0955148 | ||||||||
\(680\) | 59.1841i | 0.0870354i | ||||||||
\(681\) | −734.872 | − | 163.316i | −1.07911 | − | 0.239818i | ||||
\(682\) | 288.599 | 0.423165 | ||||||||
\(683\) | − | 432.740i | − | 0.633587i | −0.948494 | − | 0.316794i | \(-0.897394\pi\) | ||
0.948494 | − | 0.316794i | \(-0.102606\pi\) | |||||||
\(684\) | −371.736 | − | 173.811i | −0.543473 | − | 0.254110i | ||||
\(685\) | −429.092 | −0.626412 | ||||||||
\(686\) | − | 26.1916i | − | 0.0381802i | ||||||
\(687\) | 193.089 | − | 868.843i | 0.281061 | − | 1.26469i | ||||
\(688\) | 236.381 | 0.343576 | ||||||||
\(689\) | − | 240.539i | − | 0.349114i | ||||||
\(690\) | −324.022 | − | 72.0097i | −0.469597 | − | 0.104362i | ||||
\(691\) | −507.481 | −0.734415 | −0.367208 | − | 0.930139i | \(-0.619686\pi\) | ||||
−0.367208 | + | 0.930139i | \(0.619686\pi\) | |||||||
\(692\) | 93.4210i | 0.135001i | ||||||||
\(693\) | 80.4383 | − | 172.036i | 0.116073 | − | 0.248248i | ||||
\(694\) | 864.371 | 1.24549 | ||||||||
\(695\) | − | 47.9960i | − | 0.0690590i | ||||||
\(696\) | −28.6909 | + | 129.100i | −0.0412226 | + | 0.185489i | ||||
\(697\) | 328.518 | 0.471331 | ||||||||
\(698\) | − | 324.924i | − | 0.465507i | ||||||
\(699\) | 461.196 | + | 102.495i | 0.659794 | + | 0.146631i | ||||
\(700\) | −26.4575 | −0.0377964 | ||||||||
\(701\) | − | 465.228i | − | 0.663663i | −0.943339 | − | 0.331831i | \(-0.892333\pi\) | ||
0.943339 | − | 0.331831i | \(-0.107667\pi\) | |||||||
\(702\) | 175.299 | + | 134.944i | 0.249713 | + | 0.192228i | ||||
\(703\) | −877.510 | −1.24824 | ||||||||
\(704\) | 63.8045i | 0.0906314i | ||||||||
\(705\) | 1.50649 | − | 6.77875i | 0.00213686 | − | 0.00961524i | ||||
\(706\) | −614.619 | −0.870566 | ||||||||
\(707\) | 419.868i | 0.593873i | ||||||||
\(708\) | 323.079 | + | 71.8002i | 0.456327 | + | 0.101413i | ||||
\(709\) | −902.795 | −1.27334 | −0.636668 | − | 0.771138i | \(-0.719688\pi\) | ||||
−0.636668 | + | 0.771138i | \(0.719688\pi\) | |||||||
\(710\) | − | 56.9356i | − | 0.0801910i | ||||||
\(711\) | 447.939 | + | 209.442i | 0.630013 | + | 0.294573i | ||||
\(712\) | 339.492 | 0.476814 | ||||||||
\(713\) | − | 895.240i | − | 1.25560i | ||||||
\(714\) | −22.7881 | + | 102.540i | −0.0319161 | + | 0.143613i | ||||
\(715\) | 103.323 | 0.144508 | ||||||||
\(716\) | − | 587.656i | − | 0.820749i | ||||||
\(717\) | 230.701 | + | 51.2703i | 0.321759 | + | 0.0715067i | ||||
\(718\) | −262.879 | −0.366127 | ||||||||
\(719\) | − | 1105.81i | − | 1.53798i | −0.639262 | − | 0.768989i | \(-0.720760\pi\) | ||
0.639262 | − | 0.768989i | \(-0.279240\pi\) | |||||||
\(720\) | −34.0955 | + | 72.9212i | −0.0473549 | + | 0.101279i | ||||
\(721\) | −469.634 | −0.651365 | ||||||||
\(722\) | 224.501i | 0.310943i | ||||||||
\(723\) | −96.5500 | + | 434.446i | −0.133541 | + | 0.600893i | ||||
\(724\) | 259.253 | 0.358084 | ||||||||
\(725\) | 77.9292i | 0.107488i | ||||||||
\(726\) | 237.688 | + | 52.8231i | 0.327394 | + | 0.0727591i | ||||
\(727\) | −215.564 | −0.296512 | −0.148256 | − | 0.988949i | \(-0.547366\pi\) | ||||
−0.148256 | + | 0.988949i | \(0.547366\pi\) | |||||||
\(728\) | − | 43.3555i | − | 0.0595543i | ||||||
\(729\) | −186.494 | − | 704.742i | −0.255822 | − | 0.966724i | ||||
\(730\) | 104.995 | 0.143828 | ||||||||
\(731\) | − | 553.002i | − | 0.756501i | ||||||
\(732\) | 123.362 | − | 555.093i | 0.168528 | − | 0.758323i | ||||
\(733\) | 1068.10 | 1.45716 | 0.728578 | − | 0.684963i | \(-0.240181\pi\) | ||||
0.728578 | + | 0.684963i | \(0.240181\pi\) | |||||||
\(734\) | − | 591.772i | − | 0.806229i | ||||||
\(735\) | −45.8391 | − | 10.1871i | −0.0623661 | − | 0.0138601i | ||||
\(736\) | 197.923 | 0.268917 | ||||||||
\(737\) | − | 614.967i | − | 0.834419i | ||||||
\(738\) | 404.769 | + | 189.257i | 0.548468 | + | 0.256446i | ||||
\(739\) | −156.720 | −0.212071 | −0.106035 | − | 0.994362i | \(-0.533816\pi\) | ||||
−0.106035 | + | 0.994362i | \(0.533816\pi\) | |||||||
\(740\) | 172.136i | 0.232616i | ||||||||
\(741\) | 85.9638 | − | 386.811i | 0.116011 | − | 0.522012i | ||||
\(742\) | 155.346 | 0.209361 | ||||||||
\(743\) | − | 423.464i | − | 0.569938i | −0.958537 | − | 0.284969i | \(-0.908017\pi\) | ||
0.958537 | − | 0.284969i | \(-0.0919834\pi\) | |||||||
\(744\) | −211.941 | − | 47.1012i | −0.284867 | − | 0.0633081i | ||||
\(745\) | −149.519 | −0.200697 | ||||||||
\(746\) | 845.124i | 1.13287i | ||||||||
\(747\) | 299.849 | − | 641.296i | 0.401404 | − | 0.858496i | ||||
\(748\) | 149.268 | 0.199556 | ||||||||
\(749\) | 558.234i | 0.745305i | ||||||||
\(750\) | −10.2906 | + | 46.3045i | −0.0137208 | + | 0.0617393i | ||||
\(751\) | −1305.05 | −1.73776 | −0.868878 | − | 0.495026i | \(-0.835158\pi\) | ||||
−0.868878 | + | 0.495026i | \(0.835158\pi\) | |||||||
\(752\) | 4.14068i | 0.00550622i | ||||||||
\(753\) | 653.702 | + | 145.277i | 0.868130 | + | 0.192931i | ||||
\(754\) | −127.701 | −0.169365 | ||||||||
\(755\) | 144.162i | 0.190943i | ||||||||
\(756\) | −87.1498 | + | 113.212i | −0.115277 | + | 0.149751i | ||||
\(757\) | 59.6912 | 0.0788523 | 0.0394261 | − | 0.999222i | \(-0.487447\pi\) | ||||
0.0394261 | + | 0.999222i | \(0.487447\pi\) | |||||||
\(758\) | 796.861i | 1.05127i | ||||||||
\(759\) | −181.615 | + | 817.214i | −0.239282 | + | 1.07670i | ||||
\(760\) | 144.187 | 0.189720 | ||||||||
\(761\) | 899.617i | 1.18215i | 0.806616 | + | 0.591075i | \(0.201296\pi\) | ||||
−0.806616 | + | 0.591075i | \(0.798704\pi\) | |||||||
\(762\) | 653.080 | + | 145.139i | 0.857060 | + | 0.190471i | ||||
\(763\) | 260.669 | 0.341637 | ||||||||
\(764\) | 14.4880i | 0.0189633i | ||||||||
\(765\) | 170.596 | + | 79.7650i | 0.223001 | + | 0.104268i | ||||
\(766\) | 153.762 | 0.200734 | ||||||||
\(767\) | 319.578i | 0.416660i | ||||||||
\(768\) | 10.4133 | − | 46.8568i | 0.0135590 | − | 0.0610115i | ||||
\(769\) | −268.385 | −0.349005 | −0.174503 | − | 0.984657i | \(-0.555832\pi\) | ||||
−0.174503 | + | 0.984657i | \(0.555832\pi\) | |||||||
\(770\) | 66.7284i | 0.0866602i | ||||||||
\(771\) | 1054.08 | + | 234.255i | 1.36715 | + | 0.303832i | ||||
\(772\) | 627.343 | 0.812620 | ||||||||
\(773\) | 80.8488i | 0.104591i | 0.998632 | + | 0.0522955i | \(0.0166538\pi\) | ||||
−0.998632 | + | 0.0522955i | \(0.983346\pi\) | |||||||
\(774\) | 318.581 | − | 681.358i | 0.411603 | − | 0.880307i | ||||
\(775\) | −127.935 | −0.165077 | ||||||||
\(776\) | − | 69.3324i | − | 0.0893459i | ||||||
\(777\) | −66.2789 | + | 298.235i | −0.0853010 | + | 0.383829i | ||||
\(778\) | 181.512 | 0.233306 | ||||||||
\(779\) | − | 800.350i | − | 1.02741i | ||||||
\(780\) | −75.8785 | − | 16.8630i | −0.0972801 | − | 0.0216192i | ||||
\(781\) | −143.597 | −0.183863 | ||||||||
\(782\) | − | 463.033i | − | 0.592113i | ||||||
\(783\) | 333.459 | + | 256.695i | 0.425874 | + | 0.327835i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 463.442i | 0.590372i | ||||||||
\(786\) | 230.215 | − | 1035.90i | 0.292894 | − | 1.31794i | ||||
\(787\) | 592.703 | 0.753117 | 0.376559 | − | 0.926393i | \(-0.377107\pi\) | ||||
0.376559 | + | 0.926393i | \(0.377107\pi\) | |||||||
\(788\) | 189.027i | 0.239882i | ||||||||
\(789\) | −668.886 | − | 148.651i | −0.847764 | − | 0.188405i | ||||
\(790\) | −173.744 | −0.219929 | ||||||||
\(791\) | − | 272.062i | − | 0.343948i | ||||||
\(792\) | 183.914 | + | 85.9922i | 0.232215 | + | 0.108576i | ||||
\(793\) | 549.077 | 0.692405 | ||||||||
\(794\) | − | 233.986i | − | 0.294693i | ||||||
\(795\) | 60.4213 | − | 271.878i | 0.0760017 | − | 0.341985i | ||||
\(796\) | 371.632 | 0.466874 | ||||||||
\(797\) | 463.874i | 0.582025i | 0.956719 | + | 0.291012i | \(0.0939921\pi\) | ||||
−0.956719 | + | 0.291012i | \(0.906008\pi\) | |||||||
\(798\) | 249.812 | + | 55.5174i | 0.313047 | + | 0.0695707i | ||||
\(799\) | 9.68693 | 0.0121238 | ||||||||
\(800\) | − | 28.2843i | − | 0.0353553i | ||||||
\(801\) | 457.548 | − | 978.572i | 0.571221 | − | 1.22169i | ||||
\(802\) | −561.510 | −0.700138 | ||||||||
\(803\) | − | 264.806i | − | 0.329771i | ||||||
\(804\) | −100.367 | + | 451.620i | −0.124834 | + | 0.561717i | ||||
\(805\) | 206.993 | 0.257134 | ||||||||
\(806\) | − | 209.644i | − | 0.260105i | ||||||
\(807\) | −830.326 | − | 184.529i | −1.02890 | − | 0.228661i | ||||
\(808\) | −448.858 | −0.555518 | ||||||||
\(809\) | − | 454.905i | − | 0.562305i | −0.959663 | − | 0.281152i | \(-0.909283\pi\) | ||
0.959663 | − | 0.281152i | \(-0.0907166\pi\) | |||||||
\(810\) | 164.240 | + | 196.558i | 0.202766 | + | 0.242664i | ||||
\(811\) | 349.822 | 0.431346 | 0.215673 | − | 0.976466i | \(-0.430805\pi\) | ||||
0.215673 | + | 0.976466i | \(0.430805\pi\) | |||||||
\(812\) | − | 82.4725i | − | 0.101567i | ||||||
\(813\) | −189.255 | + | 851.591i | −0.232786 | + | 1.04747i | ||||
\(814\) | 434.143 | 0.533345 | ||||||||
\(815\) | − | 527.862i | − | 0.647683i | ||||||
\(816\) | −109.620 | − | 24.3615i | −0.134338 | − | 0.0298548i | ||||
\(817\) | −1347.25 | −1.64902 | ||||||||
\(818\) | 835.536i | 1.02144i | ||||||||
\(819\) | −124.971 | − | 58.4322i | −0.152589 | − | 0.0713458i | ||||
\(820\) | −157.000 | −0.191463 | ||||||||
\(821\) | 779.459i | 0.949402i | 0.880147 | + | 0.474701i | \(0.157444\pi\) | ||||
−0.880147 | + | 0.474701i | \(0.842556\pi\) | |||||||
\(822\) | 176.624 | − | 794.755i | 0.214871 | − | 0.966856i | ||||
\(823\) | −931.372 | −1.13168 | −0.565839 | − | 0.824516i | \(-0.691448\pi\) | ||||
−0.565839 | + | 0.824516i | \(0.691448\pi\) | |||||||
\(824\) | − | 502.060i | − | 0.609296i | ||||||
\(825\) | 116.784 | + | 25.9538i | 0.141557 | + | 0.0314591i | ||||
\(826\) | −206.391 | −0.249868 | ||||||||
\(827\) | − | 197.854i | − | 0.239243i | −0.992820 | − | 0.119621i | \(-0.961832\pi\) | ||
0.992820 | − | 0.119621i | \(-0.0381681\pi\) | |||||||
\(828\) | 266.750 | − | 570.506i | 0.322162 | − | 0.689017i | ||||
\(829\) | −767.502 | −0.925816 | −0.462908 | − | 0.886406i | \(-0.653194\pi\) | ||||
−0.462908 | + | 0.886406i | \(0.653194\pi\) | |||||||
\(830\) | 248.743i | 0.299690i | ||||||||
\(831\) | −174.078 | + | 783.300i | −0.209481 | + | 0.942599i | ||||
\(832\) | 46.3490 | 0.0557080 | ||||||||
\(833\) | − | 65.5048i | − | 0.0786372i | ||||||
\(834\) | 88.8972 | + | 19.7563i | 0.106591 | + | 0.0236886i | ||||
\(835\) | −245.178 | −0.293626 | ||||||||
\(836\) | − | 363.653i | − | 0.434991i | ||||||
\(837\) | −421.410 | + | 547.432i | −0.503477 | + | 0.654041i | ||||
\(838\) | 389.490 | 0.464785 | ||||||||
\(839\) | 789.441i | 0.940931i | 0.882418 | + | 0.470466i | \(0.155914\pi\) | ||||
−0.882418 | + | 0.470466i | \(0.844086\pi\) | |||||||
\(840\) | 10.8905 | − | 49.0040i | 0.0129649 | − | 0.0583382i | ||||
\(841\) | 598.082 | 0.711156 | ||||||||
\(842\) | 806.271i | 0.957566i | ||||||||
\(843\) | −622.870 | − | 138.425i | −0.738874 | − | 0.164205i | ||||
\(844\) | −751.418 | −0.890306 | ||||||||
\(845\) | 302.839i | 0.358390i | ||||||||
\(846\) | 11.9353 | + | 5.58057i | 0.0141080 | + | 0.00659642i | ||||
\(847\) | −151.841 | −0.179269 | ||||||||
\(848\) | 166.072i | 0.195839i | ||||||||
\(849\) | −162.543 | + | 731.395i | −0.191452 | + | 0.861478i | ||||
\(850\) | −66.1698 | −0.0778468 | ||||||||
\(851\) | − | 1346.72i | − | 1.58252i | ||||||
\(852\) | 105.455 | + | 23.4360i | 0.123773 | + | 0.0275070i | ||||
\(853\) | −167.784 | −0.196699 | −0.0983493 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983493 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(854\) | 354.606i | 0.415230i | ||||||||
\(855\) | 194.327 | − | 415.613i | 0.227283 | − | 0.486097i | ||||
\(856\) | −596.777 | −0.697169 | ||||||||
\(857\) | 873.473i | 1.01922i | 0.860405 | + | 0.509611i | \(0.170211\pi\) | ||||
−0.860405 | + | 0.509611i | \(0.829789\pi\) | |||||||
\(858\) | −42.5301 | + | 191.373i | −0.0495689 | + | 0.223045i | ||||
\(859\) | 480.534 | 0.559411 | 0.279705 | − | 0.960086i | \(-0.409763\pi\) | ||||
0.279705 | + | 0.960086i | \(0.409763\pi\) | |||||||
\(860\) | 264.282i | 0.307304i | ||||||||
\(861\) | −272.011 | − | 60.4509i | −0.315924 | − | 0.0702101i | ||||
\(862\) | 919.706 | 1.06694 | ||||||||
\(863\) | 263.159i | 0.304936i | 0.988308 | + | 0.152468i | \(0.0487220\pi\) | ||||
−0.988308 | + | 0.152468i | \(0.951278\pi\) | |||||||
\(864\) | −121.029 | − | 93.1670i | −0.140079 | − | 0.107832i | ||||
\(865\) | −104.448 | −0.120749 | ||||||||
\(866\) | 898.737i | 1.03780i | ||||||||
\(867\) | 131.098 | − | 589.901i | 0.151209 | − | 0.680394i | ||||
\(868\) | 135.393 | 0.155983 | ||||||||
\(869\) | 438.199i | 0.504257i | ||||||||
\(870\) | −144.339 | − | 32.0774i | −0.165907 | − | 0.0368706i | ||||
\(871\) | −446.726 | −0.512888 | ||||||||
\(872\) | 278.667i | 0.319572i | ||||||||
\(873\) | −199.848 | − | 93.4424i | −0.228921 | − | 0.107036i | ||||
\(874\) | −1128.06 | −1.29069 | ||||||||
\(875\) | − | 29.5804i | − | 0.0338062i | ||||||
\(876\) | −43.2182 | + | 194.469i | −0.0493358 | + | 0.221996i | ||||
\(877\) | −982.305 | −1.12007 | −0.560037 | − | 0.828468i | \(-0.689213\pi\) | ||||
−0.560037 | + | 0.828468i | \(0.689213\pi\) | |||||||
\(878\) | − | 483.517i | − | 0.550702i | ||||||
\(879\) | 914.282 | + | 203.187i | 1.04014 | + | 0.231158i | ||||
\(880\) | −71.3356 | −0.0810632 | ||||||||
\(881\) | − | 651.840i | − | 0.739886i | −0.929054 | − | 0.369943i | \(-0.879377\pi\) | ||
0.929054 | − | 0.369943i | \(-0.120623\pi\) | |||||||
\(882\) | 37.7368 | − | 80.7089i | 0.0427855 | − | 0.0915067i | ||||
\(883\) | 811.043 | 0.918509 | 0.459254 | − | 0.888305i | \(-0.348117\pi\) | ||||
0.459254 | + | 0.888305i | \(0.348117\pi\) | |||||||
\(884\) | − | 108.432i | − | 0.122660i | ||||||
\(885\) | −80.2751 | + | 361.214i | −0.0907063 | + | 0.408151i | ||||
\(886\) | −359.536 | −0.405797 | ||||||||
\(887\) | 795.521i | 0.896867i | 0.893816 | + | 0.448433i | \(0.148018\pi\) | ||||
−0.893816 | + | 0.448433i | \(0.851982\pi\) | |||||||
\(888\) | −318.826 | − | 70.8551i | −0.359039 | − | 0.0797918i | ||||
\(889\) | −417.203 | −0.469295 | ||||||||
\(890\) | 379.563i | 0.426476i | ||||||||
\(891\) | 495.738 | − | 414.230i | 0.556384 | − | 0.464904i | ||||
\(892\) | 39.2214 | 0.0439702 | ||||||||
\(893\) | − | 23.5997i | − | 0.0264275i | ||||||
\(894\) | 61.5456 | − | 276.937i | 0.0688429 | − | 0.309772i | ||||
\(895\) | 657.020 | 0.734100 | ||||||||
\(896\) | 29.9333i | 0.0334077i | ||||||||
\(897\) | 593.643 | + | 131.929i | 0.661809 | + | 0.147079i | ||||
\(898\) | −103.618 | −0.115388 | ||||||||
\(899\) | − | 398.793i | − | 0.443596i | ||||||
\(900\) | −81.5283 | − | 38.1200i | −0.0905870 | − | 0.0423555i | ||||
\(901\) | 388.518 | 0.431207 | ||||||||
\(902\) | 395.968i | 0.438989i | ||||||||
\(903\) | −101.758 | + | 457.882i | −0.112689 | + | 0.507068i | ||||
\(904\) | 290.847 | 0.321733 | ||||||||
\(905\) | 289.854i | 0.320280i | ||||||||
\(906\) | −267.014 | − | 59.3404i | −0.294717 | − | 0.0654971i | ||||
\(907\) | 855.003 | 0.942672 | 0.471336 | − | 0.881954i | \(-0.343772\pi\) | ||||
0.471336 | + | 0.881954i | \(0.343772\pi\) | |||||||
\(908\) | 501.867i | 0.552717i | ||||||||
\(909\) | −604.946 | + | 1293.82i | −0.665507 | + | 1.42334i | ||||
\(910\) | 48.4730 | 0.0532670 | ||||||||
\(911\) | 1234.06i | 1.35462i | 0.735696 | + | 0.677312i | \(0.236855\pi\) | ||||
−0.735696 | + | 0.677312i | \(0.763145\pi\) | |||||||
\(912\) | −59.3506 | + | 267.060i | −0.0650774 | + | 0.292829i | ||||
\(913\) | 627.352 | 0.687133 | ||||||||
\(914\) | 284.433i | 0.311196i | ||||||||
\(915\) | 620.613 | + | 137.923i | 0.678265 | + | 0.150736i | ||||
\(916\) | −593.360 | −0.647773 | ||||||||
\(917\) | 661.756i | 0.721653i | ||||||||
\(918\) | −217.960 | + | 283.141i | −0.237429 | + | 0.308432i | ||||
\(919\) | −1390.69 | −1.51326 | −0.756632 | − | 0.653842i | \(-0.773156\pi\) | ||||
−0.756632 | + | 0.653842i | \(0.773156\pi\) | |||||||
\(920\) | 221.285i | 0.240527i | ||||||||
\(921\) | −101.048 | + | 454.683i | −0.109715 | + | 0.493684i | ||||
\(922\) | −707.625 | −0.767490 | ||||||||
\(923\) | 104.312i | 0.113014i | ||||||||
\(924\) | −123.593 | − | 27.4669i | −0.133758 | − | 0.0297261i | ||||
\(925\) | −192.454 | −0.208058 | ||||||||
\(926\) | − | 850.770i | − | 0.918758i | ||||||
\(927\) | −1447.17 | − | 676.648i | −1.56113 | − | 0.729933i | ||||
\(928\) | 88.1668 | 0.0950073 | ||||||||
\(929\) | − | 934.368i | − | 1.00578i | −0.864351 | − | 0.502889i | \(-0.832270\pi\) | ||
0.864351 | − | 0.502889i | \(-0.167730\pi\) | |||||||
\(930\) | 52.6608 | − | 236.958i | 0.0566245 | − | 0.254793i | ||||
\(931\) | −159.586 | −0.171413 | ||||||||
\(932\) | − | 314.965i | − | 0.337946i | ||||||
\(933\) | 990.288 | + | 220.079i | 1.06140 | + | 0.235883i | ||||
\(934\) | 383.287 | 0.410372 | ||||||||
\(935\) | 166.887i | 0.178488i | ||||||||
\(936\) | 62.4666 | − | 133.599i | 0.0667378 | − | 0.142734i | ||||
\(937\) | 229.679 | 0.245122 | 0.122561 | − | 0.992461i | \(-0.460889\pi\) | ||||
0.122561 | + | 0.992461i | \(0.460889\pi\) | |||||||
\(938\) | − | 288.506i | − | 0.307575i | ||||||
\(939\) | 21.1879 | − | 95.3393i | 0.0225644 | − | 0.101533i | ||||
\(940\) | −4.62942 | −0.00492491 | ||||||||
\(941\) | − | 688.683i | − | 0.731863i | −0.930642 | − | 0.365932i | \(-0.880750\pi\) | ||
0.930642 | − | 0.365932i | \(-0.119250\pi\) | |||||||
\(942\) | −858.377 | − | 190.763i | −0.911228 | − | 0.202509i | ||||
\(943\) | 1228.30 | 1.30255 | ||||||||
\(944\) | − | 220.641i | − | 0.233730i | ||||||
\(945\) | −126.575 | − | 97.4364i | −0.133941 | − | 0.103107i | ||||
\(946\) | 666.543 | 0.704591 | ||||||||
\(947\) | 897.803i | 0.948049i | 0.880512 | + | 0.474025i | \(0.157199\pi\) | ||||
−0.880512 | + | 0.474025i | \(0.842801\pi\) | |||||||
\(948\) | 71.5171 | − | 321.805i | 0.0754400 | − | 0.339457i | ||||
\(949\) | −192.361 | −0.202699 | ||||||||
\(950\) | 161.206i | 0.169690i | ||||||||
\(951\) | 459.236 | + | 102.059i | 0.482898 | + | 0.107318i | ||||
\(952\) | 70.0275 | 0.0735584 | ||||||||
\(953\) | 809.558i | 0.849483i | 0.905315 | + | 0.424742i | \(0.139635\pi\) | ||||
−0.905315 | + | 0.424742i | \(0.860365\pi\) | |||||||
\(954\) | 478.695 | + | 223.822i | 0.501777 | + | 0.234614i | ||||
\(955\) | −16.1981 | −0.0169613 | ||||||||
\(956\) | − | 157.553i | − | 0.164804i | ||||||
\(957\) | −80.9023 | + | 364.036i | −0.0845374 | + | 0.380393i | ||||
\(958\) | −287.090 | −0.299677 | ||||||||
\(959\) | 507.709i | 0.529415i | ||||||||
\(960\) | 52.3875 | + | 11.6425i | 0.0545703 | + | 0.0121276i | ||||
\(961\) | −306.310 | −0.318741 | ||||||||
\(962\) | − | 315.371i | − | 0.327829i | ||||||
\(963\) | −804.302 | + | 1720.19i | −0.835205 | + | 1.78628i | ||||
\(964\) | 296.697 | 0.307777 | ||||||||
\(965\) | 701.391i | 0.726830i | ||||||||
\(966\) | −85.2031 | + | 383.388i | −0.0882019 | + | 0.396882i | ||||
\(967\) | 952.817 | 0.985333 | 0.492667 | − | 0.870218i | \(-0.336022\pi\) | ||||
0.492667 | + | 0.870218i | \(0.336022\pi\) | |||||||
\(968\) | − | 162.325i | − | 0.167691i | ||||||
\(969\) | 624.775 | + | 138.848i | 0.644762 | + | 0.143290i | ||||
\(970\) | 77.5160 | 0.0799134 | ||||||||
\(971\) | − | 755.094i | − | 0.777646i | −0.921313 | − | 0.388823i | \(-0.872882\pi\) | ||
0.921313 | − | 0.388823i | \(-0.127118\pi\) | |||||||
\(972\) | −431.666 | + | 223.295i | −0.444101 | + | 0.229727i | ||||
\(973\) | −56.7897 | −0.0583655 | ||||||||
\(974\) | 1125.54i | 1.15558i | ||||||||
\(975\) | 18.8534 | − | 84.8347i | 0.0193368 | − | 0.0870099i | ||||
\(976\) | −379.090 | −0.388412 | ||||||||
\(977\) | 1865.83i | 1.90975i | 0.297006 | + | 0.954876i | \(0.404012\pi\) | ||||
−0.297006 | + | 0.954876i | \(0.595988\pi\) | |||||||
\(978\) | 977.694 | + | 217.280i | 0.999687 | + | 0.222168i | ||||
\(979\) | 957.295 | 0.977829 | ||||||||
\(980\) | 31.3050i | 0.0319438i | ||||||||
\(981\) | 803.247 | + | 375.572i | 0.818804 | + | 0.382846i | ||||
\(982\) | −58.1771 | −0.0592435 | ||||||||
\(983\) | − | 1469.42i | − | 1.49483i | −0.664356 | − | 0.747417i | \(-0.731294\pi\) | ||
0.664356 | − | 0.747417i | \(-0.268706\pi\) | |||||||
\(984\) | 64.6247 | − | 290.792i | 0.0656755 | − | 0.295520i | ||||
\(985\) | −211.339 | −0.214557 | ||||||||
\(986\) | − | 206.262i | − | 0.209191i | ||||||
\(987\) | −8.02072 | − | 1.78250i | −0.00812636 | − | 0.00180598i | ||||
\(988\) | −264.166 | −0.267374 | ||||||||
\(989\) | − | 2067.63i | − | 2.09063i | ||||||
\(990\) | −96.1422 | + | 205.622i | −0.0971133 | + | 0.207699i | ||||
\(991\) | 1075.76 | 1.08553 | 0.542764 | − | 0.839885i | \(-0.317378\pi\) | ||||
0.542764 | + | 0.839885i | \(0.317378\pi\) | |||||||
\(992\) | 144.741i | 0.145909i | ||||||||
\(993\) | 40.8506 | − | 183.815i | 0.0411385 | − | 0.185111i | ||||
\(994\) | −67.3671 | −0.0677738 | ||||||||
\(995\) | 415.497i | 0.417585i | ||||||||
\(996\) | −460.716 | − | 102.388i | −0.462566 | − | 0.102799i | ||||
\(997\) | 1114.55 | 1.11791 | 0.558953 | − | 0.829199i | \(-0.311203\pi\) | ||||
0.558953 | + | 0.829199i | \(0.311203\pi\) | |||||||
\(998\) | 835.105i | 0.836779i | ||||||||
\(999\) | −633.934 | + | 823.511i | −0.634568 | + | 0.824335i |
(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 | 210.3.e.a.71.14 | yes | 16 | |
3.2 | odd | 2 | inner | 210.3.e.a.71.6 | ✓ | 16 | |
4.3 | odd | 2 | 1680.3.l.c.1121.6 | 16 | |||
5.2 | odd | 4 | 1050.3.c.c.449.1 | 32 | |||
5.3 | odd | 4 | 1050.3.c.c.449.32 | 32 | |||
5.4 | even | 2 | 1050.3.e.d.701.3 | 16 | |||
12.11 | even | 2 | 1680.3.l.c.1121.5 | 16 | |||
15.2 | even | 4 | 1050.3.c.c.449.31 | 32 | |||
15.8 | even | 4 | 1050.3.c.c.449.2 | 32 | |||
15.14 | odd | 2 | 1050.3.e.d.701.11 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.e.a.71.6 | ✓ | 16 | 3.2 | odd | 2 | inner | |
210.3.e.a.71.14 | yes | 16 | 1.1 | even | 1 | trivial | |
1050.3.c.c.449.1 | 32 | 5.2 | odd | 4 | |||
1050.3.c.c.449.2 | 32 | 15.8 | even | 4 | |||
1050.3.c.c.449.31 | 32 | 15.2 | even | 4 | |||
1050.3.c.c.449.32 | 32 | 5.3 | odd | 4 | |||
1050.3.e.d.701.3 | 16 | 5.4 | even | 2 | |||
1050.3.e.d.701.11 | 16 | 15.14 | odd | 2 | |||
1680.3.l.c.1121.5 | 16 | 12.11 | even | 2 | |||
1680.3.l.c.1121.6 | 16 | 4.3 | odd | 2 |