Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 553.23 | ||
Character | \(\chi\) | \(=\) | 690.553 |
Dual form | 690.3.k.b.277.23 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 3.24543 | − | 3.80358i | 0.649086 | − | 0.760715i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −6.75617 | + | 6.75617i | −0.965167 | + | 0.965167i | −0.999413 | − | 0.0342467i | \(-0.989097\pi\) |
0.0342467 | + | 0.999413i | \(0.489097\pi\) | |||||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0.558148 | + | 7.04900i | 0.0558148 | + | 0.704900i | ||||
\(11\) | 21.5756 | 1.96142 | 0.980708 | − | 0.195477i | \(-0.0626254\pi\) | ||||
0.980708 | + | 0.195477i | \(0.0626254\pi\) | |||||||
\(12\) | 2.44949 | − | 2.44949i | 0.204124 | − | 0.204124i | ||||
\(13\) | −1.08406 | − | 1.08406i | −0.0833889 | − | 0.0833889i | 0.664182 | − | 0.747571i | \(-0.268780\pi\) |
−0.747571 | + | 0.664182i | \(0.768780\pi\) | |||||||
\(14\) | − | 13.5123i | − | 0.965167i | ||||||
\(15\) | 8.63323 | − | 0.683589i | 0.575549 | − | 0.0455726i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 4.33966 | − | 4.33966i | 0.255274 | − | 0.255274i | −0.567855 | − | 0.823129i | \(-0.692226\pi\) |
0.823129 | + | 0.567855i | \(0.192226\pi\) | |||||||
\(18\) | −3.00000 | − | 3.00000i | −0.166667 | − | 0.166667i | ||||
\(19\) | − | 1.61010i | − | 0.0847420i | −0.999102 | − | 0.0423710i | \(-0.986509\pi\) | ||
0.999102 | − | 0.0423710i | \(-0.0134911\pi\) | |||||||
\(20\) | −7.60715 | − | 6.49086i | −0.380358 | − | 0.324543i | ||||
\(21\) | −16.5492 | −0.788055 | ||||||||
\(22\) | −21.5756 | + | 21.5756i | −0.980708 | + | 0.980708i | ||||
\(23\) | −3.39116 | − | 3.39116i | −0.147442 | − | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | −3.93439 | − | 24.6885i | −0.157376 | − | 0.987539i | ||||
\(26\) | 2.16811 | 0.0833889 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 13.5123 | + | 13.5123i | 0.482583 | + | 0.482583i | ||||
\(29\) | 10.6578i | 0.367509i | 0.982972 | + | 0.183754i | \(0.0588251\pi\) | ||||
−0.982972 | + | 0.183754i | \(0.941175\pi\) | |||||||
\(30\) | −7.94964 | + | 9.31682i | −0.264988 | + | 0.310561i | ||||
\(31\) | 21.7512 | 0.701653 | 0.350826 | − | 0.936441i | \(-0.385901\pi\) | ||||
0.350826 | + | 0.936441i | \(0.385901\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 26.4246 | + | 26.4246i | 0.800745 | + | 0.800745i | ||||
\(34\) | 8.67933i | 0.255274i | ||||||||
\(35\) | 3.77094 | + | 47.6243i | 0.107741 | + | 1.36069i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −18.5343 | + | 18.5343i | −0.500928 | + | 0.500928i | −0.911726 | − | 0.410798i | \(-0.865250\pi\) |
0.410798 | + | 0.911726i | \(0.365250\pi\) | |||||||
\(38\) | 1.61010 | + | 1.61010i | 0.0423710 | + | 0.0423710i | ||||
\(39\) | − | 2.65538i | − | 0.0680868i | ||||||
\(40\) | 14.0980 | − | 1.11630i | 0.352450 | − | 0.0279074i | ||||
\(41\) | 55.4586 | 1.35265 | 0.676325 | − | 0.736604i | \(-0.263572\pi\) | ||||
0.676325 | + | 0.736604i | \(0.263572\pi\) | |||||||
\(42\) | 16.5492 | − | 16.5492i | 0.394028 | − | 0.394028i | ||||
\(43\) | 45.1244 | + | 45.1244i | 1.04940 | + | 1.04940i | 0.998714 | + | 0.0506893i | \(0.0161418\pi\) |
0.0506893 | + | 0.998714i | \(0.483858\pi\) | |||||||
\(44\) | − | 43.1512i | − | 0.980708i | ||||||
\(45\) | 11.4107 | + | 9.73629i | 0.253572 | + | 0.216362i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −40.0209 | + | 40.0209i | −0.851509 | + | 0.851509i | −0.990319 | − | 0.138810i | \(-0.955672\pi\) |
0.138810 | + | 0.990319i | \(0.455672\pi\) | |||||||
\(48\) | −4.89898 | − | 4.89898i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 42.2916i | − | 0.863094i | ||||||
\(50\) | 28.6229 | + | 20.7541i | 0.572457 | + | 0.415082i | ||||
\(51\) | 10.6300 | 0.208431 | ||||||||
\(52\) | −2.16811 | + | 2.16811i | −0.0416945 | + | 0.0416945i | ||||
\(53\) | −22.8485 | − | 22.8485i | −0.431105 | − | 0.431105i | 0.457899 | − | 0.889004i | \(-0.348602\pi\) |
−0.889004 | + | 0.457899i | \(0.848602\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 70.0220 | − | 82.0644i | 1.27313 | − | 1.49208i | ||||
\(56\) | −27.0247 | −0.482583 | ||||||||
\(57\) | 1.97196 | − | 1.97196i | 0.0345958 | − | 0.0345958i | ||||
\(58\) | −10.6578 | − | 10.6578i | −0.183754 | − | 0.183754i | ||||
\(59\) | 45.0275i | 0.763178i | 0.924332 | + | 0.381589i | \(0.124623\pi\) | ||||
−0.924332 | + | 0.381589i | \(0.875377\pi\) | |||||||
\(60\) | −1.36718 | − | 17.2665i | −0.0227863 | − | 0.287774i | ||||
\(61\) | 106.893 | 1.75235 | 0.876174 | − | 0.481995i | \(-0.160088\pi\) | ||||
0.876174 | + | 0.481995i | \(0.160088\pi\) | |||||||
\(62\) | −21.7512 | + | 21.7512i | −0.350826 | + | 0.350826i | ||||
\(63\) | −20.2685 | − | 20.2685i | −0.321722 | − | 0.321722i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −7.64152 | + | 0.605064i | −0.117562 | + | 0.00930867i | ||||
\(66\) | −52.8492 | −0.800745 | ||||||||
\(67\) | 62.2296 | − | 62.2296i | 0.928800 | − | 0.928800i | −0.0688280 | − | 0.997629i | \(-0.521926\pi\) |
0.997629 | + | 0.0688280i | \(0.0219260\pi\) | |||||||
\(68\) | −8.67933 | − | 8.67933i | −0.127637 | − | 0.127637i | ||||
\(69\) | − | 8.30662i | − | 0.120386i | ||||||
\(70\) | −51.3952 | − | 43.8533i | −0.734217 | − | 0.626476i | ||||
\(71\) | 95.7602 | 1.34874 | 0.674368 | − | 0.738396i | \(-0.264416\pi\) | ||||
0.674368 | + | 0.738396i | \(0.264416\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.0833333 | + | 0.0833333i | ||||
\(73\) | −18.3047 | − | 18.3047i | −0.250749 | − | 0.250749i | 0.570529 | − | 0.821278i | \(-0.306738\pi\) |
−0.821278 | + | 0.570529i | \(0.806738\pi\) | |||||||
\(74\) | − | 37.0687i | − | 0.500928i | ||||||
\(75\) | 25.4185 | − | 35.0557i | 0.338913 | − | 0.467409i | ||||
\(76\) | −3.22020 | −0.0423710 | ||||||||
\(77\) | −145.768 | + | 145.768i | −1.89309 | + | 1.89309i | ||||
\(78\) | 2.65538 | + | 2.65538i | 0.0340434 | + | 0.0340434i | ||||
\(79\) | 74.1858i | 0.939061i | 0.882916 | + | 0.469530i | \(0.155577\pi\) | ||||
−0.882916 | + | 0.469530i | \(0.844423\pi\) | |||||||
\(80\) | −12.9817 | + | 15.2143i | −0.162271 | + | 0.190179i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −55.4586 | + | 55.4586i | −0.676325 | + | 0.676325i | ||||
\(83\) | 29.2294 | + | 29.2294i | 0.352162 | + | 0.352162i | 0.860913 | − | 0.508751i | \(-0.169893\pi\) |
−0.508751 | + | 0.860913i | \(0.669893\pi\) | |||||||
\(84\) | 33.0983i | 0.394028i | ||||||||
\(85\) | −2.42217 | − | 30.5903i | −0.0284962 | − | 0.359886i | ||||
\(86\) | −90.2487 | −1.04940 | ||||||||
\(87\) | −13.0530 | + | 13.0530i | −0.150035 | + | 0.150035i | ||||
\(88\) | 43.1512 | + | 43.1512i | 0.490354 | + | 0.490354i | ||||
\(89\) | 148.863i | 1.67261i | 0.548261 | + | 0.836307i | \(0.315290\pi\) | ||||
−0.548261 | + | 0.836307i | \(0.684710\pi\) | |||||||
\(90\) | −21.1470 | + | 1.67444i | −0.234967 | + | 0.0186049i | ||||
\(91\) | 14.6481 | 0.160968 | ||||||||
\(92\) | −6.78233 | + | 6.78233i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 26.6397 | + | 26.6397i | 0.286449 | + | 0.286449i | ||||
\(94\) | − | 80.0419i | − | 0.851509i | ||||||
\(95\) | −6.12413 | − | 5.22546i | −0.0644645 | − | 0.0550048i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −47.9480 | + | 47.9480i | −0.494309 | + | 0.494309i | −0.909661 | − | 0.415352i | \(-0.863659\pi\) |
0.415352 | + | 0.909661i | \(0.363659\pi\) | |||||||
\(98\) | 42.2916 | + | 42.2916i | 0.431547 | + | 0.431547i | ||||
\(99\) | 64.7268i | 0.653806i | ||||||||
\(100\) | −49.3769 | + | 7.86878i | −0.493769 | + | 0.0786878i | ||||
\(101\) | −148.987 | −1.47512 | −0.737558 | − | 0.675284i | \(-0.764021\pi\) | ||||
−0.737558 | + | 0.675284i | \(0.764021\pi\) | |||||||
\(102\) | −10.6300 | + | 10.6300i | −0.104215 | + | 0.104215i | ||||
\(103\) | 10.6269 | + | 10.6269i | 0.103174 | + | 0.103174i | 0.756809 | − | 0.653636i | \(-0.226757\pi\) |
−0.653636 | + | 0.756809i | \(0.726757\pi\) | |||||||
\(104\) | − | 4.33622i | − | 0.0416945i | ||||||
\(105\) | −53.7091 | + | 62.9460i | −0.511515 | + | 0.599486i | ||||
\(106\) | 45.6971 | 0.431105 | ||||||||
\(107\) | 65.2102 | − | 65.2102i | 0.609442 | − | 0.609442i | −0.333359 | − | 0.942800i | \(-0.608182\pi\) |
0.942800 | + | 0.333359i | \(0.108182\pi\) | |||||||
\(108\) | 7.34847 | + | 7.34847i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 64.0878i | 0.587962i | 0.955811 | + | 0.293981i | \(0.0949802\pi\) | ||||
−0.955811 | + | 0.293981i | \(0.905020\pi\) | |||||||
\(110\) | 12.0424 | + | 152.086i | 0.109476 | + | 1.38260i | ||||
\(111\) | −45.3997 | −0.409006 | ||||||||
\(112\) | 27.0247 | − | 27.0247i | 0.241292 | − | 0.241292i | ||||
\(113\) | −25.5020 | − | 25.5020i | −0.225682 | − | 0.225682i | 0.585204 | − | 0.810886i | \(-0.301014\pi\) |
−0.810886 | + | 0.585204i | \(0.801014\pi\) | |||||||
\(114\) | 3.94392i | 0.0345958i | ||||||||
\(115\) | −23.9043 | + | 1.89277i | −0.207864 | + | 0.0164589i | ||||
\(116\) | 21.3155 | 0.183754 | ||||||||
\(117\) | 3.25217 | − | 3.25217i | 0.0277963 | − | 0.0277963i | ||||
\(118\) | −45.0275 | − | 45.0275i | −0.381589 | − | 0.381589i | ||||
\(119\) | 58.6390i | 0.492764i | ||||||||
\(120\) | 18.6336 | + | 15.8993i | 0.155280 | + | 0.132494i | ||||
\(121\) | 344.506 | 2.84716 | ||||||||
\(122\) | −106.893 | + | 106.893i | −0.876174 | + | 0.876174i | ||||
\(123\) | 67.9227 | + | 67.9227i | 0.552217 | + | 0.552217i | ||||
\(124\) | − | 43.5025i | − | 0.350826i | ||||||
\(125\) | −106.673 | − | 65.1599i | −0.853386 | − | 0.521279i | ||||
\(126\) | 40.5370 | 0.321722 | ||||||||
\(127\) | 45.7519 | − | 45.7519i | 0.360251 | − | 0.360251i | −0.503654 | − | 0.863905i | \(-0.668011\pi\) |
0.863905 | + | 0.503654i | \(0.168011\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 110.532i | 0.856835i | ||||||||
\(130\) | 7.03645 | − | 8.24658i | 0.0541266 | − | 0.0634352i | ||||
\(131\) | 72.3213 | 0.552071 | 0.276035 | − | 0.961147i | \(-0.410979\pi\) | ||||
0.276035 | + | 0.961147i | \(0.410979\pi\) | |||||||
\(132\) | 52.8492 | − | 52.8492i | 0.400373 | − | 0.400373i | ||||
\(133\) | 10.8781 | + | 10.8781i | 0.0817902 | + | 0.0817902i | ||||
\(134\) | 124.459i | 0.928800i | ||||||||
\(135\) | 2.05077 | + | 25.8997i | 0.0151909 | + | 0.191850i | ||||
\(136\) | 17.3587 | 0.127637 | ||||||||
\(137\) | −176.166 | + | 176.166i | −1.28588 | + | 1.28588i | −0.348621 | + | 0.937264i | \(0.613350\pi\) |
−0.937264 | + | 0.348621i | \(0.886650\pi\) | |||||||
\(138\) | 8.30662 | + | 8.30662i | 0.0601929 | + | 0.0601929i | ||||
\(139\) | − | 113.493i | − | 0.816494i | −0.912871 | − | 0.408247i | \(-0.866140\pi\) | ||
0.912871 | − | 0.408247i | \(-0.133860\pi\) | |||||||
\(140\) | 95.2485 | − | 7.54188i | 0.680346 | − | 0.0538706i | ||||
\(141\) | −98.0309 | −0.695254 | ||||||||
\(142\) | −95.7602 | + | 95.7602i | −0.674368 | + | 0.674368i | ||||
\(143\) | −23.3891 | − | 23.3891i | −0.163560 | − | 0.163560i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 40.5376 | + | 34.5890i | 0.279570 | + | 0.238545i | ||||
\(146\) | 36.6093 | 0.250749 | ||||||||
\(147\) | 51.7964 | − | 51.7964i | 0.352356 | − | 0.352356i | ||||
\(148\) | 37.0687 | + | 37.0687i | 0.250464 | + | 0.250464i | ||||
\(149\) | − | 221.934i | − | 1.48949i | −0.667349 | − | 0.744745i | \(-0.732571\pi\) | ||
0.667349 | − | 0.744745i | \(-0.267429\pi\) | |||||||
\(150\) | 9.63725 | + | 60.4742i | 0.0642483 | + | 0.403161i | ||||
\(151\) | −180.400 | −1.19470 | −0.597350 | − | 0.801981i | \(-0.703780\pi\) | ||||
−0.597350 | + | 0.801981i | \(0.703780\pi\) | |||||||
\(152\) | 3.22020 | − | 3.22020i | 0.0211855 | − | 0.0211855i | ||||
\(153\) | 13.0190 | + | 13.0190i | 0.0850914 | + | 0.0850914i | ||||
\(154\) | − | 291.536i | − | 1.89309i | ||||||
\(155\) | 70.5921 | − | 82.7325i | 0.455433 | − | 0.533758i | ||||
\(156\) | −5.31077 | −0.0340434 | ||||||||
\(157\) | 12.4596 | − | 12.4596i | 0.0793604 | − | 0.0793604i | −0.666312 | − | 0.745673i | \(-0.732128\pi\) |
0.745673 | + | 0.666312i | \(0.232128\pi\) | |||||||
\(158\) | −74.1858 | − | 74.1858i | −0.469530 | − | 0.469530i | ||||
\(159\) | − | 55.9673i | − | 0.351995i | ||||||
\(160\) | −2.23259 | − | 28.1960i | −0.0139537 | − | 0.176225i | ||||
\(161\) | 45.8226 | 0.284612 | ||||||||
\(162\) | 9.00000 | − | 9.00000i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | −117.984 | − | 117.984i | −0.723827 | − | 0.723827i | 0.245556 | − | 0.969382i | \(-0.421030\pi\) |
−0.969382 | + | 0.245556i | \(0.921030\pi\) | |||||||
\(164\) | − | 110.917i | − | 0.676325i | ||||||
\(165\) | 186.267 | − | 14.7488i | 1.12889 | − | 0.0893869i | ||||
\(166\) | −58.4589 | −0.352162 | ||||||||
\(167\) | 158.202 | − | 158.202i | 0.947318 | − | 0.947318i | −0.0513618 | − | 0.998680i | \(-0.516356\pi\) |
0.998680 | + | 0.0513618i | \(0.0163562\pi\) | |||||||
\(168\) | −33.0983 | − | 33.0983i | −0.197014 | − | 0.197014i | ||||
\(169\) | − | 166.650i | − | 0.986093i | ||||||
\(170\) | 33.0125 | + | 28.1681i | 0.194191 | + | 0.165695i | ||||
\(171\) | 4.83029 | 0.0282473 | ||||||||
\(172\) | 90.2487 | − | 90.2487i | 0.524702 | − | 0.524702i | ||||
\(173\) | −45.6033 | − | 45.6033i | −0.263603 | − | 0.263603i | 0.562913 | − | 0.826516i | \(-0.309681\pi\) |
−0.826516 | + | 0.562913i | \(0.809681\pi\) | |||||||
\(174\) | − | 26.1061i | − | 0.150035i | ||||||
\(175\) | 193.381 | + | 140.218i | 1.10503 | + | 0.801246i | ||||
\(176\) | −86.3023 | −0.490354 | ||||||||
\(177\) | −55.1472 | + | 55.1472i | −0.311566 | + | 0.311566i | ||||
\(178\) | −148.863 | − | 148.863i | −0.836307 | − | 0.836307i | ||||
\(179\) | − | 111.478i | − | 0.622781i | −0.950282 | − | 0.311391i | \(-0.899205\pi\) | ||
0.950282 | − | 0.311391i | \(-0.100795\pi\) | |||||||
\(180\) | 19.4726 | − | 22.8215i | 0.108181 | − | 0.126786i | ||||
\(181\) | −247.255 | −1.36605 | −0.683025 | − | 0.730395i | \(-0.739336\pi\) | ||||
−0.683025 | + | 0.730395i | \(0.739336\pi\) | |||||||
\(182\) | −14.6481 | + | 14.6481i | −0.0804842 | + | 0.0804842i | ||||
\(183\) | 130.917 | + | 130.917i | 0.715393 | + | 0.715393i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | 10.3449 | + | 130.649i | 0.0559184 | + | 0.706209i | ||||
\(186\) | −53.2794 | −0.286449 | ||||||||
\(187\) | 93.6308 | − | 93.6308i | 0.500699 | − | 0.500699i | ||||
\(188\) | 80.0419 | + | 80.0419i | 0.425755 | + | 0.425755i | ||||
\(189\) | − | 49.6475i | − | 0.262685i | ||||||
\(190\) | 11.3496 | − | 0.898673i | 0.0597347 | − | 0.00472986i | ||||
\(191\) | −113.944 | −0.596567 | −0.298283 | − | 0.954477i | \(-0.596414\pi\) | ||||
−0.298283 | + | 0.954477i | \(0.596414\pi\) | |||||||
\(192\) | −9.79796 | + | 9.79796i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −39.6216 | − | 39.6216i | −0.205293 | − | 0.205293i | 0.596970 | − | 0.802263i | \(-0.296371\pi\) |
−0.802263 | + | 0.596970i | \(0.796371\pi\) | |||||||
\(194\) | − | 95.8960i | − | 0.494309i | ||||||
\(195\) | −10.1000 | − | 8.61786i | −0.0517946 | − | 0.0441941i | ||||
\(196\) | −84.5832 | −0.431547 | ||||||||
\(197\) | −167.861 | + | 167.861i | −0.852085 | + | 0.852085i | −0.990390 | − | 0.138304i | \(-0.955835\pi\) |
0.138304 | + | 0.990390i | \(0.455835\pi\) | |||||||
\(198\) | −64.7268 | − | 64.7268i | −0.326903 | − | 0.326903i | ||||
\(199\) | − | 177.527i | − | 0.892094i | −0.895009 | − | 0.446047i | \(-0.852831\pi\) | ||
0.895009 | − | 0.446047i | \(-0.147169\pi\) | |||||||
\(200\) | 41.5082 | − | 57.2457i | 0.207541 | − | 0.286229i | ||||
\(201\) | 152.431 | 0.758362 | ||||||||
\(202\) | 148.987 | − | 148.987i | 0.737558 | − | 0.737558i | ||||
\(203\) | −72.0056 | − | 72.0056i | −0.354707 | − | 0.354707i | ||||
\(204\) | − | 21.2599i | − | 0.104215i | ||||||
\(205\) | 179.987 | − | 210.941i | 0.877985 | − | 1.02898i | ||||
\(206\) | −21.2538 | −0.103174 | ||||||||
\(207\) | 10.1735 | − | 10.1735i | 0.0491473 | − | 0.0491473i | ||||
\(208\) | 4.33622 | + | 4.33622i | 0.0208472 | + | 0.0208472i | ||||
\(209\) | − | 34.7388i | − | 0.166214i | ||||||
\(210\) | −9.23688 | − | 116.655i | −0.0439852 | − | 0.555501i | ||||
\(211\) | −236.548 | −1.12108 | −0.560541 | − | 0.828127i | \(-0.689407\pi\) | ||||
−0.560541 | + | 0.828127i | \(0.689407\pi\) | |||||||
\(212\) | −45.6971 | + | 45.6971i | −0.215552 | + | 0.215552i | ||||
\(213\) | 117.282 | + | 117.282i | 0.550619 | + | 0.550619i | ||||
\(214\) | 130.420i | 0.609442i | ||||||||
\(215\) | 318.082 | − | 25.1861i | 1.47945 | − | 0.117145i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −146.955 | + | 146.955i | −0.677212 | + | 0.677212i | ||||
\(218\) | −64.0878 | − | 64.0878i | −0.293981 | − | 0.293981i | ||||
\(219\) | − | 44.8371i | − | 0.204736i | ||||||
\(220\) | −164.129 | − | 140.044i | −0.746040 | − | 0.636564i | ||||
\(221\) | −9.40887 | −0.0425741 | ||||||||
\(222\) | 45.3997 | − | 45.3997i | 0.204503 | − | 0.204503i | ||||
\(223\) | 274.188 | + | 274.188i | 1.22954 | + | 1.22954i | 0.964137 | + | 0.265405i | \(0.0855055\pi\) |
0.265405 | + | 0.964137i | \(0.414494\pi\) | |||||||
\(224\) | 54.0493i | 0.241292i | ||||||||
\(225\) | 74.0654 | − | 11.8032i | 0.329180 | − | 0.0524585i | ||||
\(226\) | 51.0041 | 0.225682 | ||||||||
\(227\) | −61.8993 | + | 61.8993i | −0.272684 | + | 0.272684i | −0.830180 | − | 0.557496i | \(-0.811762\pi\) |
0.557496 | + | 0.830180i | \(0.311762\pi\) | |||||||
\(228\) | −3.94392 | − | 3.94392i | −0.0172979 | − | 0.0172979i | ||||
\(229\) | − | 421.368i | − | 1.84003i | −0.391878 | − | 0.920017i | \(-0.628174\pi\) | ||
0.391878 | − | 0.920017i | \(-0.371826\pi\) | |||||||
\(230\) | 22.0116 | − | 25.7971i | 0.0957025 | − | 0.112161i | ||||
\(231\) | −357.058 | −1.54570 | ||||||||
\(232\) | −21.3155 | + | 21.3155i | −0.0918772 | + | 0.0918772i | ||||
\(233\) | 225.024 | + | 225.024i | 0.965768 | + | 0.965768i | 0.999433 | − | 0.0336653i | \(-0.0107180\pi\) |
−0.0336653 | + | 0.999433i | \(0.510718\pi\) | |||||||
\(234\) | 6.50434i | 0.0277963i | ||||||||
\(235\) | 22.3376 | + | 282.108i | 0.0950536 | + | 1.20046i | ||||
\(236\) | 90.0550 | 0.381589 | ||||||||
\(237\) | −90.8587 | + | 90.8587i | −0.383370 | + | 0.383370i | ||||
\(238\) | −58.6390 | − | 58.6390i | −0.246382 | − | 0.246382i | ||||
\(239\) | − | 222.316i | − | 0.930193i | −0.885260 | − | 0.465096i | \(-0.846020\pi\) | ||
0.885260 | − | 0.465096i | \(-0.153980\pi\) | |||||||
\(240\) | −34.5329 | + | 2.73436i | −0.143887 | + | 0.0113932i | ||||
\(241\) | 37.5718 | 0.155900 | 0.0779498 | − | 0.996957i | \(-0.475163\pi\) | ||||
0.0779498 | + | 0.996957i | \(0.475163\pi\) | |||||||
\(242\) | −344.506 | + | 344.506i | −1.42358 | + | 1.42358i | ||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | − | 213.787i | − | 0.876174i | ||||||
\(245\) | −160.859 | − | 137.254i | −0.656568 | − | 0.560222i | ||||
\(246\) | −135.845 | −0.552217 | ||||||||
\(247\) | −1.74544 | + | 1.74544i | −0.00706654 | + | 0.00706654i | ||||
\(248\) | 43.5025 | + | 43.5025i | 0.175413 | + | 0.175413i | ||||
\(249\) | 71.5972i | 0.287539i | ||||||||
\(250\) | 171.833 | − | 41.5134i | 0.687333 | − | 0.166053i | ||||
\(251\) | 117.012 | 0.466183 | 0.233091 | − | 0.972455i | \(-0.425116\pi\) | ||||
0.233091 | + | 0.972455i | \(0.425116\pi\) | |||||||
\(252\) | −40.5370 | + | 40.5370i | −0.160861 | + | 0.160861i | ||||
\(253\) | −73.1664 | − | 73.1664i | −0.289195 | − | 0.289195i | ||||
\(254\) | 91.5037i | 0.360251i | ||||||||
\(255\) | 34.4988 | − | 40.4319i | 0.135289 | − | 0.158556i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 255.718 | − | 255.718i | 0.995013 | − | 0.995013i | −0.00497439 | − | 0.999988i | \(-0.501583\pi\) |
0.999988 | + | 0.00497439i | \(0.00158340\pi\) | |||||||
\(258\) | −110.532 | − | 110.532i | −0.428417 | − | 0.428417i | ||||
\(259\) | − | 250.442i | − | 0.966958i | ||||||
\(260\) | 1.21013 | + | 15.2830i | 0.00465434 | + | 0.0587809i | ||||
\(261\) | −31.9733 | −0.122503 | ||||||||
\(262\) | −72.3213 | + | 72.3213i | −0.276035 | + | 0.276035i | ||||
\(263\) | 97.8083 | + | 97.8083i | 0.371895 | + | 0.371895i | 0.868167 | − | 0.496272i | \(-0.165298\pi\) |
−0.496272 | + | 0.868167i | \(0.665298\pi\) | |||||||
\(264\) | 105.698i | 0.400373i | ||||||||
\(265\) | −161.060 | + | 12.7529i | −0.607772 | + | 0.0481241i | ||||
\(266\) | −21.7562 | −0.0817902 | ||||||||
\(267\) | −182.319 | + | 182.319i | −0.682842 | + | 0.682842i | ||||
\(268\) | −124.459 | − | 124.459i | −0.464400 | − | 0.464400i | ||||
\(269\) | − | 247.337i | − | 0.919469i | −0.888057 | − | 0.459734i | \(-0.847945\pi\) | ||
0.888057 | − | 0.459734i | \(-0.152055\pi\) | |||||||
\(270\) | −27.9505 | − | 23.8489i | −0.103520 | − | 0.0883294i | ||||
\(271\) | −174.097 | −0.642424 | −0.321212 | − | 0.947007i | \(-0.604090\pi\) | ||||
−0.321212 | + | 0.947007i | \(0.604090\pi\) | |||||||
\(272\) | −17.3587 | + | 17.3587i | −0.0638186 | + | 0.0638186i | ||||
\(273\) | 17.9402 | + | 17.9402i | 0.0657151 | + | 0.0657151i | ||||
\(274\) | − | 352.332i | − | 1.28588i | ||||||
\(275\) | −84.8867 | − | 532.668i | −0.308679 | − | 1.93698i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 66.2186 | − | 66.2186i | 0.239056 | − | 0.239056i | −0.577403 | − | 0.816459i | \(-0.695934\pi\) |
0.816459 | + | 0.577403i | \(0.195934\pi\) | |||||||
\(278\) | 113.493 | + | 113.493i | 0.408247 | + | 0.408247i | ||||
\(279\) | 65.2537i | 0.233884i | ||||||||
\(280\) | −87.7066 | + | 102.790i | −0.313238 | + | 0.367109i | ||||
\(281\) | 90.6244 | 0.322507 | 0.161253 | − | 0.986913i | \(-0.448446\pi\) | ||||
0.161253 | + | 0.986913i | \(0.448446\pi\) | |||||||
\(282\) | 98.0309 | − | 98.0309i | 0.347627 | − | 0.347627i | ||||
\(283\) | −351.544 | − | 351.544i | −1.24221 | − | 1.24221i | −0.959084 | − | 0.283121i | \(-0.908630\pi\) |
−0.283121 | − | 0.959084i | \(-0.591370\pi\) | |||||||
\(284\) | − | 191.520i | − | 0.674368i | ||||||
\(285\) | −1.10065 | − | 13.9004i | −0.00386191 | − | 0.0487732i | ||||
\(286\) | 46.7783 | 0.163560 | ||||||||
\(287\) | −374.688 | + | 374.688i | −1.30553 | + | 1.30553i | ||||
\(288\) | 12.0000 | + | 12.0000i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 251.335i | 0.869670i | ||||||||
\(290\) | −75.1266 | + | 5.94860i | −0.259057 | + | 0.0205124i | ||||
\(291\) | −117.448 | −0.403602 | ||||||||
\(292\) | −36.6093 | + | 36.6093i | −0.125374 | + | 0.125374i | ||||
\(293\) | 40.2972 | + | 40.2972i | 0.137533 | + | 0.137533i | 0.772522 | − | 0.634988i | \(-0.218995\pi\) |
−0.634988 | + | 0.772522i | \(0.718995\pi\) | |||||||
\(294\) | 103.593i | 0.352356i | ||||||||
\(295\) | 171.266 | + | 146.134i | 0.580561 | + | 0.495368i | ||||
\(296\) | −74.1374 | −0.250464 | ||||||||
\(297\) | −79.2738 | + | 79.2738i | −0.266915 | + | 0.266915i | ||||
\(298\) | 221.934 | + | 221.934i | 0.744745 | + | 0.744745i | ||||
\(299\) | 7.35242i | 0.0245900i | ||||||||
\(300\) | −70.1114 | − | 50.8369i | −0.233705 | − | 0.169456i | ||||
\(301\) | −609.735 | −2.02570 | ||||||||
\(302\) | 180.400 | − | 180.400i | 0.597350 | − | 0.597350i | ||||
\(303\) | −182.471 | − | 182.471i | −0.602213 | − | 0.602213i | ||||
\(304\) | 6.44039i | 0.0211855i | ||||||||
\(305\) | 346.914 | − | 406.577i | 1.13742 | − | 1.33304i | ||||
\(306\) | −26.0380 | −0.0850914 | ||||||||
\(307\) | 230.119 | − | 230.119i | 0.749575 | − | 0.749575i | −0.224825 | − | 0.974399i | \(-0.572181\pi\) |
0.974399 | + | 0.224825i | \(0.0721809\pi\) | |||||||
\(308\) | 291.536 | + | 291.536i | 0.946547 | + | 0.946547i | ||||
\(309\) | 26.0304i | 0.0842409i | ||||||||
\(310\) | 12.1404 | + | 153.325i | 0.0391626 | + | 0.494595i | ||||
\(311\) | −350.808 | −1.12800 | −0.564000 | − | 0.825775i | \(-0.690738\pi\) | ||||
−0.564000 | + | 0.825775i | \(0.690738\pi\) | |||||||
\(312\) | 5.31077 | − | 5.31077i | 0.0170217 | − | 0.0170217i | ||||
\(313\) | 299.963 | + | 299.963i | 0.958348 | + | 0.958348i | 0.999167 | − | 0.0408185i | \(-0.0129965\pi\) |
−0.0408185 | + | 0.999167i | \(0.512997\pi\) | |||||||
\(314\) | 24.9192i | 0.0793604i | ||||||||
\(315\) | −142.873 | + | 11.3128i | −0.453564 | + | 0.0359137i | ||||
\(316\) | 148.372 | 0.469530 | ||||||||
\(317\) | −270.830 | + | 270.830i | −0.854353 | + | 0.854353i | −0.990666 | − | 0.136313i | \(-0.956475\pi\) |
0.136313 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(318\) | 55.9673 | + | 55.9673i | 0.175998 | + | 0.175998i | ||||
\(319\) | 229.947i | 0.720838i | ||||||||
\(320\) | 30.4286 | + | 25.9634i | 0.0950894 | + | 0.0811357i | ||||
\(321\) | 159.732 | 0.497607 | ||||||||
\(322\) | −45.8226 | + | 45.8226i | −0.142306 | + | 0.142306i | ||||
\(323\) | −6.98728 | − | 6.98728i | −0.0216325 | − | 0.0216325i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | −22.4986 | + | 31.0288i | −0.0692264 | + | 0.0954732i | ||||
\(326\) | 235.967 | 0.723827 | ||||||||
\(327\) | −78.4912 | + | 78.4912i | −0.240034 | + | 0.240034i | ||||
\(328\) | 110.917 | + | 110.917i | 0.338162 | + | 0.338162i | ||||
\(329\) | − | 540.776i | − | 1.64370i | ||||||
\(330\) | −171.518 | + | 201.016i | −0.519752 | + | 0.609139i | ||||
\(331\) | −331.091 | −1.00028 | −0.500138 | − | 0.865946i | \(-0.666717\pi\) | ||||
−0.500138 | + | 0.865946i | \(0.666717\pi\) | |||||||
\(332\) | 58.4589 | − | 58.4589i | 0.176081 | − | 0.176081i | ||||
\(333\) | −55.6030 | − | 55.6030i | −0.166976 | − | 0.166976i | ||||
\(334\) | 316.404i | 0.947318i | ||||||||
\(335\) | −34.7334 | − | 438.657i | −0.103682 | − | 1.30942i | ||||
\(336\) | 66.1966 | 0.197014 | ||||||||
\(337\) | 353.159 | − | 353.159i | 1.04795 | − | 1.04795i | 0.0491601 | − | 0.998791i | \(-0.484346\pi\) |
0.998791 | − | 0.0491601i | \(-0.0156545\pi\) | |||||||
\(338\) | 166.650 | + | 166.650i | 0.493046 | + | 0.493046i | ||||
\(339\) | − | 62.4670i | − | 0.184268i | ||||||
\(340\) | −61.1806 | + | 4.84435i | −0.179943 | + | 0.0142481i | ||||
\(341\) | 469.296 | 1.37623 | ||||||||
\(342\) | −4.83029 | + | 4.83029i | −0.0141237 | + | 0.0141237i | ||||
\(343\) | −45.3232 | − | 45.3232i | −0.132138 | − | 0.132138i | ||||
\(344\) | 180.497i | 0.524702i | ||||||||
\(345\) | −31.5949 | − | 26.9586i | −0.0915794 | − | 0.0781407i | ||||
\(346\) | 91.2066 | 0.263603 | ||||||||
\(347\) | −60.6618 | + | 60.6618i | −0.174818 | + | 0.174818i | −0.789092 | − | 0.614274i | \(-0.789449\pi\) |
0.614274 | + | 0.789092i | \(0.289449\pi\) | |||||||
\(348\) | 26.1061 | + | 26.1061i | 0.0750174 | + | 0.0750174i | ||||
\(349\) | − | 185.071i | − | 0.530288i | −0.964209 | − | 0.265144i | \(-0.914580\pi\) | ||
0.964209 | − | 0.265144i | \(-0.0854195\pi\) | |||||||
\(350\) | −333.599 | + | 53.1628i | −0.953140 | + | 0.151894i | ||||
\(351\) | 7.96615 | 0.0226956 | ||||||||
\(352\) | 86.3023 | − | 86.3023i | 0.245177 | − | 0.245177i | ||||
\(353\) | −383.652 | − | 383.652i | −1.08683 | − | 1.08683i | −0.995853 | − | 0.0909792i | \(-0.971000\pi\) |
−0.0909792 | − | 0.995853i | \(-0.529000\pi\) | |||||||
\(354\) | − | 110.294i | − | 0.311566i | ||||||
\(355\) | 310.783 | − | 364.231i | 0.875445 | − | 1.02600i | ||||
\(356\) | 297.725 | 0.836307 | ||||||||
\(357\) | −71.8178 | + | 71.8178i | −0.201170 | + | 0.201170i | ||||
\(358\) | 111.478 | + | 111.478i | 0.311391 | + | 0.311391i | ||||
\(359\) | 7.62023i | 0.0212263i | 0.999944 | + | 0.0106131i | \(0.00337833\pi\) | ||||
−0.999944 | + | 0.0106131i | \(0.996622\pi\) | |||||||
\(360\) | 3.34889 | + | 42.2940i | 0.00930247 | + | 0.117483i | ||||
\(361\) | 358.408 | 0.992819 | ||||||||
\(362\) | 247.255 | − | 247.255i | 0.683025 | − | 0.683025i | ||||
\(363\) | 421.932 | + | 421.932i | 1.16235 | + | 1.16235i | ||||
\(364\) | − | 29.2963i | − | 0.0804842i | ||||||
\(365\) | −129.030 | + | 10.2167i | −0.353506 | + | 0.0279910i | ||||
\(366\) | −261.834 | −0.715393 | ||||||||
\(367\) | 2.44002 | − | 2.44002i | 0.00664855 | − | 0.00664855i | −0.703775 | − | 0.710423i | \(-0.748504\pi\) |
0.710423 | + | 0.703775i | \(0.248504\pi\) | |||||||
\(368\) | 13.5647 | + | 13.5647i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 166.376i | 0.450883i | ||||||||
\(370\) | −140.994 | − | 120.304i | −0.381064 | − | 0.325145i | ||||
\(371\) | 308.737 | 0.832176 | ||||||||
\(372\) | 53.2794 | − | 53.2794i | 0.143224 | − | 0.143224i | ||||
\(373\) | −355.285 | − | 355.285i | −0.952507 | − | 0.952507i | 0.0464155 | − | 0.998922i | \(-0.485220\pi\) |
−0.998922 | + | 0.0464155i | \(0.985220\pi\) | |||||||
\(374\) | 187.262i | 0.500699i | ||||||||
\(375\) | −50.8433 | − | 210.452i | −0.135582 | − | 0.561205i | ||||
\(376\) | −160.084 | −0.425755 | ||||||||
\(377\) | 11.5536 | − | 11.5536i | 0.0306462 | − | 0.0306462i | ||||
\(378\) | 49.6475 | + | 49.6475i | 0.131343 | + | 0.131343i | ||||
\(379\) | − | 175.743i | − | 0.463703i | −0.972751 | − | 0.231851i | \(-0.925522\pi\) | ||
0.972751 | − | 0.231851i | \(-0.0744783\pi\) | |||||||
\(380\) | −10.4509 | + | 12.2483i | −0.0275024 | + | 0.0322323i | ||||
\(381\) | 112.069 | 0.294144 | ||||||||
\(382\) | 113.944 | − | 113.944i | 0.298283 | − | 0.298283i | ||||
\(383\) | 154.583 | + | 154.583i | 0.403610 | + | 0.403610i | 0.879503 | − | 0.475893i | \(-0.157875\pi\) |
−0.475893 | + | 0.879503i | \(0.657875\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 81.3603 | + | 1027.52i | 0.211325 | + | 2.66889i | ||||
\(386\) | 79.2432 | 0.205293 | ||||||||
\(387\) | −135.373 | + | 135.373i | −0.349801 | + | 0.349801i | ||||
\(388\) | 95.8960 | + | 95.8960i | 0.247155 | + | 0.247155i | ||||
\(389\) | 744.952i | 1.91504i | 0.288362 | + | 0.957522i | \(0.406889\pi\) | ||||
−0.288362 | + | 0.957522i | \(0.593111\pi\) | |||||||
\(390\) | 18.7178 | − | 1.48210i | 0.0479944 | − | 0.00380025i | ||||
\(391\) | −29.4330 | −0.0752763 | ||||||||
\(392\) | 84.5832 | − | 84.5832i | 0.215773 | − | 0.215773i | ||||
\(393\) | 88.5751 | + | 88.5751i | 0.225382 | + | 0.225382i | ||||
\(394\) | − | 335.722i | − | 0.852085i | ||||||
\(395\) | 282.171 | + | 240.765i | 0.714358 | + | 0.609531i | ||||
\(396\) | 129.454 | 0.326903 | ||||||||
\(397\) | −71.7915 | + | 71.7915i | −0.180835 | + | 0.180835i | −0.791720 | − | 0.610885i | \(-0.790814\pi\) |
0.610885 | + | 0.791720i | \(0.290814\pi\) | |||||||
\(398\) | 177.527 | + | 177.527i | 0.446047 | + | 0.446047i | ||||
\(399\) | 26.6458i | 0.0667814i | ||||||||
\(400\) | 15.7376 | + | 98.7539i | 0.0393439 | + | 0.246885i | ||||
\(401\) | −460.952 | −1.14951 | −0.574754 | − | 0.818327i | \(-0.694902\pi\) | ||||
−0.574754 | + | 0.818327i | \(0.694902\pi\) | |||||||
\(402\) | −152.431 | + | 152.431i | −0.379181 | + | 0.379181i | ||||
\(403\) | −23.5796 | − | 23.5796i | −0.0585101 | − | 0.0585101i | ||||
\(404\) | 297.973i | 0.737558i | ||||||||
\(405\) | −29.2089 | + | 34.2322i | −0.0721206 | + | 0.0845239i | ||||
\(406\) | 144.011 | 0.354707 | ||||||||
\(407\) | −399.889 | + | 399.889i | −0.982529 | + | 0.982529i | ||||
\(408\) | 21.2599 | + | 21.2599i | 0.0521076 | + | 0.0521076i | ||||
\(409\) | 24.4609i | 0.0598066i | 0.999553 | + | 0.0299033i | \(0.00951993\pi\) | ||||
−0.999553 | + | 0.0299033i | \(0.990480\pi\) | |||||||
\(410\) | 30.9541 | + | 390.928i | 0.0754979 | + | 0.953483i | ||||
\(411\) | −431.517 | −1.04992 | ||||||||
\(412\) | 21.2538 | − | 21.2538i | 0.0515868 | − | 0.0515868i | ||||
\(413\) | −304.213 | − | 304.213i | −0.736594 | − | 0.736594i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 206.039 | − | 16.3144i | 0.496478 | − | 0.0393117i | ||||
\(416\) | −8.67245 | −0.0208472 | ||||||||
\(417\) | 139.000 | − | 139.000i | 0.333332 | − | 0.333332i | ||||
\(418\) | 34.7388 | + | 34.7388i | 0.0831072 | + | 0.0831072i | ||||
\(419\) | − | 671.275i | − | 1.60209i | −0.598605 | − | 0.801045i | \(-0.704278\pi\) | ||
0.598605 | − | 0.801045i | \(-0.295722\pi\) | |||||||
\(420\) | 125.892 | + | 107.418i | 0.299743 | + | 0.255758i | ||||
\(421\) | 386.936 | 0.919089 | 0.459544 | − | 0.888155i | \(-0.348013\pi\) | ||||
0.459544 | + | 0.888155i | \(0.348013\pi\) | |||||||
\(422\) | 236.548 | − | 236.548i | 0.560541 | − | 0.560541i | ||||
\(423\) | −120.063 | − | 120.063i | −0.283836 | − | 0.283836i | ||||
\(424\) | − | 91.3942i | − | 0.215552i | ||||||
\(425\) | −124.214 | − | 90.0657i | −0.292267 | − | 0.211919i | ||||
\(426\) | −234.564 | −0.550619 | ||||||||
\(427\) | −722.189 | + | 722.189i | −1.69131 | + | 1.69131i | ||||
\(428\) | −130.420 | − | 130.420i | −0.304721 | − | 0.304721i | ||||
\(429\) | − | 57.2915i | − | 0.133547i | ||||||
\(430\) | −292.896 | + | 343.268i | −0.681153 | + | 0.798298i | ||||
\(431\) | −238.331 | −0.552973 | −0.276487 | − | 0.961018i | \(-0.589170\pi\) | ||||
−0.276487 | + | 0.961018i | \(0.589170\pi\) | |||||||
\(432\) | 14.6969 | − | 14.6969i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −178.331 | − | 178.331i | −0.411851 | − | 0.411851i | 0.470532 | − | 0.882383i | \(-0.344062\pi\) |
−0.882383 | + | 0.470532i | \(0.844062\pi\) | |||||||
\(434\) | − | 293.910i | − | 0.677212i | ||||||
\(435\) | 7.28552 | + | 92.0109i | 0.0167483 | + | 0.211519i | ||||
\(436\) | 128.176 | 0.293981 | ||||||||
\(437\) | −5.46011 | + | 5.46011i | −0.0124945 | + | 0.0124945i | ||||
\(438\) | 44.8371 | + | 44.8371i | 0.102368 | + | 0.102368i | ||||
\(439\) | 739.579i | 1.68469i | 0.538938 | + | 0.842345i | \(0.318826\pi\) | ||||
−0.538938 | + | 0.842345i | \(0.681174\pi\) | |||||||
\(440\) | 304.173 | − | 24.0847i | 0.691302 | − | 0.0547381i | ||||
\(441\) | 126.875 | 0.287698 | ||||||||
\(442\) | 9.40887 | − | 9.40887i | 0.0212870 | − | 0.0212870i | ||||
\(443\) | 180.225 | + | 180.225i | 0.406828 | + | 0.406828i | 0.880631 | − | 0.473803i | \(-0.157119\pi\) |
−0.473803 | + | 0.880631i | \(0.657119\pi\) | |||||||
\(444\) | 90.7993i | 0.204503i | ||||||||
\(445\) | 566.211 | + | 483.123i | 1.27238 | + | 1.08567i | ||||
\(446\) | −548.376 | −1.22954 | ||||||||
\(447\) | 271.812 | − | 271.812i | 0.608082 | − | 0.608082i | ||||
\(448\) | −54.0493 | − | 54.0493i | −0.120646 | − | 0.120646i | ||||
\(449\) | 798.750i | 1.77895i | 0.456981 | + | 0.889476i | \(0.348931\pi\) | ||||
−0.456981 | + | 0.889476i | \(0.651069\pi\) | |||||||
\(450\) | −62.2622 | + | 85.8686i | −0.138361 | + | 0.190819i | ||||
\(451\) | 1196.55 | 2.65311 | ||||||||
\(452\) | −51.0041 | + | 51.0041i | −0.112841 | + | 0.112841i | ||||
\(453\) | −220.944 | − | 220.944i | −0.487734 | − | 0.487734i | ||||
\(454\) | − | 123.799i | − | 0.272684i | ||||||
\(455\) | 47.5394 | − | 55.7153i | 0.104482 | − | 0.122451i | ||||
\(456\) | 7.88784 | 0.0172979 | ||||||||
\(457\) | −217.052 | + | 217.052i | −0.474950 | + | 0.474950i | −0.903512 | − | 0.428562i | \(-0.859020\pi\) |
0.428562 | + | 0.903512i | \(0.359020\pi\) | |||||||
\(458\) | 421.368 | + | 421.368i | 0.920017 | + | 0.920017i | ||||
\(459\) | 31.8899i | 0.0694769i | ||||||||
\(460\) | 3.78554 | + | 47.8087i | 0.00822945 | + | 0.103932i | ||||
\(461\) | −297.784 | −0.645952 | −0.322976 | − | 0.946407i | \(-0.604683\pi\) | ||||
−0.322976 | + | 0.946407i | \(0.604683\pi\) | |||||||
\(462\) | 357.058 | − | 357.058i | 0.772852 | − | 0.772852i | ||||
\(463\) | 126.175 | + | 126.175i | 0.272517 | + | 0.272517i | 0.830113 | − | 0.557596i | \(-0.188276\pi\) |
−0.557596 | + | 0.830113i | \(0.688276\pi\) | |||||||
\(464\) | − | 42.6310i | − | 0.0918772i | ||||||
\(465\) | 187.783 | − | 14.8689i | 0.403835 | − | 0.0319761i | ||||
\(466\) | −450.048 | −0.965768 | ||||||||
\(467\) | 372.155 | − | 372.155i | 0.796905 | − | 0.796905i | −0.185701 | − | 0.982606i | \(-0.559456\pi\) |
0.982606 | + | 0.185701i | \(0.0594556\pi\) | |||||||
\(468\) | −6.50434 | − | 6.50434i | −0.0138982 | − | 0.0138982i | ||||
\(469\) | 840.868i | 1.79289i | ||||||||
\(470\) | −304.445 | − | 259.770i | −0.647756 | − | 0.552702i | ||||
\(471\) | 30.5196 | 0.0647975 | ||||||||
\(472\) | −90.0550 | + | 90.0550i | −0.190794 | + | 0.190794i | ||||
\(473\) | 973.584 | + | 973.584i | 2.05832 | + | 2.05832i | ||||
\(474\) | − | 181.717i | − | 0.383370i | ||||||
\(475\) | −39.7509 | + | 6.33475i | −0.0836860 | + | 0.0133363i | ||||
\(476\) | 117.278 | 0.246382 | ||||||||
\(477\) | 68.5456 | − | 68.5456i | 0.143702 | − | 0.143702i | ||||
\(478\) | 222.316 | + | 222.316i | 0.465096 | + | 0.465096i | ||||
\(479\) | − | 149.254i | − | 0.311594i | −0.987789 | − | 0.155797i | \(-0.950205\pi\) | ||
0.987789 | − | 0.155797i | \(-0.0497946\pi\) | |||||||
\(480\) | 31.7986 | − | 37.2673i | 0.0662470 | − | 0.0776402i | ||||
\(481\) | 40.1845 | 0.0835437 | ||||||||
\(482\) | −37.5718 | + | 37.5718i | −0.0779498 | + | 0.0779498i | ||||
\(483\) | 56.1209 | + | 56.1209i | 0.116192 | + | 0.116192i | ||||
\(484\) | − | 689.012i | − | 1.42358i | ||||||
\(485\) | 26.7621 | + | 337.986i | 0.0551796 | + | 0.696878i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −63.4861 | + | 63.4861i | −0.130362 | + | 0.130362i | −0.769277 | − | 0.638915i | \(-0.779383\pi\) |
0.638915 | + | 0.769277i | \(0.279383\pi\) | |||||||
\(488\) | 213.787 | + | 213.787i | 0.438087 | + | 0.438087i | ||||
\(489\) | − | 289.000i | − | 0.591002i | ||||||
\(490\) | 298.114 | − | 23.6050i | 0.608395 | − | 0.0481734i | ||||
\(491\) | −574.263 | −1.16958 | −0.584789 | − | 0.811186i | \(-0.698823\pi\) | ||||
−0.584789 | + | 0.811186i | \(0.698823\pi\) | |||||||
\(492\) | 135.845 | − | 135.845i | 0.276108 | − | 0.276108i | ||||
\(493\) | 46.2511 | + | 46.2511i | 0.0938155 | + | 0.0938155i | ||||
\(494\) | − | 3.49087i | − | 0.00706654i | ||||||
\(495\) | 246.193 | + | 210.066i | 0.497360 | + | 0.424376i | ||||
\(496\) | −87.0049 | −0.175413 | ||||||||
\(497\) | −646.972 | + | 646.972i | −1.30175 | + | 1.30175i | ||||
\(498\) | −71.5972 | − | 71.5972i | −0.143770 | − | 0.143770i | ||||
\(499\) | − | 138.028i | − | 0.276609i | −0.990390 | − | 0.138305i | \(-0.955835\pi\) | ||
0.990390 | − | 0.138305i | \(-0.0441653\pi\) | |||||||
\(500\) | −130.320 | + | 213.347i | −0.260640 | + | 0.426693i | ||||
\(501\) | 387.515 | 0.773482 | ||||||||
\(502\) | −117.012 | + | 117.012i | −0.233091 | + | 0.233091i | ||||
\(503\) | −148.954 | − | 148.954i | −0.296131 | − | 0.296131i | 0.543365 | − | 0.839496i | \(-0.317150\pi\) |
−0.839496 | + | 0.543365i | \(0.817150\pi\) | |||||||
\(504\) | − | 81.0740i | − | 0.160861i | ||||||
\(505\) | −483.526 | + | 566.682i | −0.957476 | + | 1.12214i | ||||
\(506\) | 146.333 | 0.289195 | ||||||||
\(507\) | 204.103 | − | 204.103i | 0.402571 | − | 0.402571i | ||||
\(508\) | −91.5037 | − | 91.5037i | −0.180125 | − | 0.180125i | ||||
\(509\) | 584.754i | 1.14883i | 0.818564 | + | 0.574415i | \(0.194770\pi\) | ||||
−0.818564 | + | 0.574415i | \(0.805230\pi\) | |||||||
\(510\) | 5.93309 | + | 74.9306i | 0.0116335 | + | 0.146923i | ||||
\(511\) | 247.339 | 0.484029 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.91588 | + | 5.91588i | 0.0115319 | + | 0.0115319i | ||||
\(514\) | 511.437i | 0.995013i | ||||||||
\(515\) | 74.9090 | − | 5.93138i | 0.145454 | − | 0.0115172i | ||||
\(516\) | 221.063 | 0.428417 | ||||||||
\(517\) | −863.475 | + | 863.475i | −1.67016 | + | 1.67016i | ||||
\(518\) | 250.442 | + | 250.442i | 0.483479 | + | 0.483479i | ||||
\(519\) | − | 111.705i | − | 0.215231i | ||||||
\(520\) | −16.4932 | − | 14.0729i | −0.0317176 | − | 0.0270633i | ||||
\(521\) | −655.891 | −1.25891 | −0.629454 | − | 0.777038i | \(-0.716721\pi\) | ||||
−0.629454 | + | 0.777038i | \(0.716721\pi\) | |||||||
\(522\) | 31.9733 | − | 31.9733i | 0.0612515 | − | 0.0612515i | ||||
\(523\) | −133.671 | − | 133.671i | −0.255584 | − | 0.255584i | 0.567671 | − | 0.823255i | \(-0.307845\pi\) |
−0.823255 | + | 0.567671i | \(0.807845\pi\) | |||||||
\(524\) | − | 144.643i | − | 0.276035i | ||||||
\(525\) | 65.1108 | + | 408.573i | 0.124021 | + | 0.778235i | ||||
\(526\) | −195.617 | −0.371895 | ||||||||
\(527\) | 94.3930 | − | 94.3930i | 0.179114 | − | 0.179114i | ||||
\(528\) | −105.698 | − | 105.698i | −0.200186 | − | 0.200186i | ||||
\(529\) | 23.0000i | 0.0434783i | ||||||||
\(530\) | 148.307 | − | 173.812i | 0.279824 | − | 0.327948i | ||||
\(531\) | −135.083 | −0.254393 | ||||||||
\(532\) | 21.7562 | − | 21.7562i | 0.0408951 | − | 0.0408951i | ||||
\(533\) | −60.1203 | − | 60.1203i | −0.112796 | − | 0.112796i | ||||
\(534\) | − | 364.638i | − | 0.682842i | ||||||
\(535\) | −36.3970 | − | 459.667i | −0.0680317 | − | 0.859191i | ||||
\(536\) | 248.919 | 0.464400 | ||||||||
\(537\) | 136.532 | − | 136.532i | 0.254249 | − | 0.254249i | ||||
\(538\) | 247.337 | + | 247.337i | 0.459734 | + | 0.459734i | ||||
\(539\) | − | 912.466i | − | 1.69289i | ||||||
\(540\) | 51.7994 | − | 4.10153i | 0.0959248 | − | 0.00759543i | ||||
\(541\) | −121.373 | −0.224349 | −0.112174 | − | 0.993689i | \(-0.535782\pi\) | ||||
−0.112174 | + | 0.993689i | \(0.535782\pi\) | |||||||
\(542\) | 174.097 | − | 174.097i | 0.321212 | − | 0.321212i | ||||
\(543\) | −302.824 | − | 302.824i | −0.557688 | − | 0.557688i | ||||
\(544\) | − | 34.7173i | − | 0.0638186i | ||||||
\(545\) | 243.763 | + | 207.992i | 0.447272 | + | 0.381638i | ||||
\(546\) | −35.8804 | −0.0657151 | ||||||||
\(547\) | 529.758 | − | 529.758i | 0.968480 | − | 0.968480i | −0.0310385 | − | 0.999518i | \(-0.509881\pi\) |
0.999518 | + | 0.0310385i | \(0.00988143\pi\) | |||||||
\(548\) | 352.332 | + | 352.332i | 0.642942 | + | 0.642942i | ||||
\(549\) | 320.680i | 0.584116i | ||||||||
\(550\) | 617.555 | + | 447.781i | 1.12283 | + | 0.814148i | ||||
\(551\) | 17.1600 | 0.0311434 | ||||||||
\(552\) | 16.6132 | − | 16.6132i | 0.0300965 | − | 0.0300965i | ||||
\(553\) | −501.212 | − | 501.212i | −0.906350 | − | 0.906350i | ||||
\(554\) | 132.437i | 0.239056i | ||||||||
\(555\) | −147.341 | + | 172.681i | −0.265480 | + | 0.311137i | ||||
\(556\) | −226.985 | −0.408247 | ||||||||
\(557\) | 360.364 | − | 360.364i | 0.646973 | − | 0.646973i | −0.305288 | − | 0.952260i | \(-0.598753\pi\) |
0.952260 | + | 0.305288i | \(0.0987526\pi\) | |||||||
\(558\) | −65.2537 | − | 65.2537i | −0.116942 | − | 0.116942i | ||||
\(559\) | − | 97.8347i | − | 0.175017i | ||||||
\(560\) | −15.0838 | − | 190.497i | −0.0269353 | − | 0.340173i | ||||
\(561\) | 229.348 | 0.408819 | ||||||||
\(562\) | −90.6244 | + | 90.6244i | −0.161253 | + | 0.161253i | ||||
\(563\) | 190.104 | + | 190.104i | 0.337662 | + | 0.337662i | 0.855487 | − | 0.517825i | \(-0.173258\pi\) |
−0.517825 | + | 0.855487i | \(0.673258\pi\) | |||||||
\(564\) | 196.062i | 0.347627i | ||||||||
\(565\) | −179.764 | + | 14.2339i | −0.318166 | + | 0.0251928i | ||||
\(566\) | 703.088 | 1.24221 | ||||||||
\(567\) | 60.8055 | − | 60.8055i | 0.107241 | − | 0.107241i | ||||
\(568\) | 191.520 | + | 191.520i | 0.337184 | + | 0.337184i | ||||
\(569\) | − | 547.652i | − | 0.962481i | −0.876589 | − | 0.481241i | \(-0.840186\pi\) | ||
0.876589 | − | 0.481241i | \(-0.159814\pi\) | |||||||
\(570\) | 15.0010 | + | 12.7997i | 0.0263175 | + | 0.0224556i | ||||
\(571\) | −827.747 | −1.44964 | −0.724822 | − | 0.688936i | \(-0.758078\pi\) | ||||
−0.724822 | + | 0.688936i | \(0.758078\pi\) | |||||||
\(572\) | −46.7783 | + | 46.7783i | −0.0817802 | + | 0.0817802i | ||||
\(573\) | −139.553 | − | 139.553i | −0.243547 | − | 0.243547i | ||||
\(574\) | − | 749.376i | − | 1.30553i | ||||||
\(575\) | −70.3805 | + | 97.0648i | −0.122401 | + | 0.168808i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 14.5416 | − | 14.5416i | 0.0252021 | − | 0.0252021i | −0.694393 | − | 0.719596i | \(-0.744327\pi\) |
0.719596 | + | 0.694393i | \(0.244327\pi\) | |||||||
\(578\) | −251.335 | − | 251.335i | −0.434835 | − | 0.434835i | ||||
\(579\) | − | 97.0527i | − | 0.167621i | ||||||
\(580\) | 69.1779 | − | 81.0752i | 0.119272 | − | 0.139785i | ||||
\(581\) | −394.958 | −0.679790 | ||||||||
\(582\) | 117.448 | − | 117.448i | 0.201801 | − | 0.201801i | ||||
\(583\) | −492.971 | − | 492.971i | −0.845576 | − | 0.845576i | ||||
\(584\) | − | 73.2187i | − | 0.125374i | ||||||
\(585\) | −1.81519 | − | 22.9245i | −0.00310289 | − | 0.0391873i | ||||
\(586\) | −80.5945 | −0.137533 | ||||||||
\(587\) | 86.3579 | − | 86.3579i | 0.147117 | − | 0.147117i | −0.629712 | − | 0.776829i | \(-0.716827\pi\) |
0.776829 | + | 0.629712i | \(0.216827\pi\) | |||||||
\(588\) | −103.593 | − | 103.593i | −0.176178 | − | 0.176178i | ||||
\(589\) | − | 35.0216i | − | 0.0594595i | ||||||
\(590\) | −317.399 | + | 25.1320i | −0.537965 | + | 0.0425966i | ||||
\(591\) | −411.173 | −0.695725 | ||||||||
\(592\) | 74.1374 | − | 74.1374i | 0.125232 | − | 0.125232i | ||||
\(593\) | −464.807 | − | 464.807i | −0.783823 | − | 0.783823i | 0.196651 | − | 0.980474i | \(-0.436993\pi\) |
−0.980474 | + | 0.196651i | \(0.936993\pi\) | |||||||
\(594\) | − | 158.548i | − | 0.266915i | ||||||
\(595\) | 223.038 | + | 190.309i | 0.374853 | + | 0.319846i | ||||
\(596\) | −443.868 | −0.744745 | ||||||||
\(597\) | 217.425 | − | 217.425i | 0.364196 | − | 0.364196i | ||||
\(598\) | −7.35242 | − | 7.35242i | −0.0122950 | − | 0.0122950i | ||||
\(599\) | − | 573.997i | − | 0.958259i | −0.877744 | − | 0.479130i | \(-0.840952\pi\) | ||
0.877744 | − | 0.479130i | \(-0.159048\pi\) | |||||||
\(600\) | 120.948 | − | 19.2745i | 0.201581 | − | 0.0321242i | ||||
\(601\) | −141.986 | −0.236250 | −0.118125 | − | 0.992999i | \(-0.537688\pi\) | ||||
−0.118125 | + | 0.992999i | \(0.537688\pi\) | |||||||
\(602\) | 609.735 | − | 609.735i | 1.01285 | − | 1.01285i | ||||
\(603\) | 186.689 | + | 186.689i | 0.309600 | + | 0.309600i | ||||
\(604\) | 360.799i | 0.597350i | ||||||||
\(605\) | 1118.07 | − | 1310.35i | 1.84805 | − | 2.16587i | ||||
\(606\) | 364.941 | 0.602213 | ||||||||
\(607\) | 369.871 | − | 369.871i | 0.609342 | − | 0.609342i | −0.333432 | − | 0.942774i | \(-0.608207\pi\) |
0.942774 | + | 0.333432i | \(0.108207\pi\) | |||||||
\(608\) | −6.44039 | − | 6.44039i | −0.0105928 | − | 0.0105928i | ||||
\(609\) | − | 176.377i | − | 0.289617i | ||||||
\(610\) | 59.6623 | + | 753.491i | 0.0978070 | + | 1.23523i | ||||
\(611\) | 86.7698 | 0.142013 | ||||||||
\(612\) | 26.0380 | − | 26.0380i | 0.0425457 | − | 0.0425457i | ||||
\(613\) | −196.795 | − | 196.795i | −0.321036 | − | 0.321036i | 0.528129 | − | 0.849164i | \(-0.322894\pi\) |
−0.849164 | + | 0.528129i | \(0.822894\pi\) | |||||||
\(614\) | 460.239i | 0.749575i | ||||||||
\(615\) | 478.787 | − | 37.9109i | 0.778516 | − | 0.0616438i | ||||
\(616\) | −583.073 | −0.946547 | ||||||||
\(617\) | −323.009 | + | 323.009i | −0.523516 | + | 0.523516i | −0.918631 | − | 0.395116i | \(-0.870705\pi\) |
0.395116 | + | 0.918631i | \(0.370705\pi\) | |||||||
\(618\) | −26.0304 | − | 26.0304i | −0.0421205 | − | 0.0421205i | ||||
\(619\) | 326.754i | 0.527874i | 0.964540 | + | 0.263937i | \(0.0850211\pi\) | ||||
−0.964540 | + | 0.263937i | \(0.914979\pi\) | |||||||
\(620\) | −165.465 | − | 141.184i | −0.266879 | − | 0.227716i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | 350.808 | − | 350.808i | 0.564000 | − | 0.564000i | ||||
\(623\) | −1005.74 | − | 1005.74i | −1.61435 | − | 1.61435i | ||||
\(624\) | 10.6215i | 0.0170217i | ||||||||
\(625\) | −594.041 | + | 194.268i | −0.950466 | + | 0.310829i | ||||
\(626\) | −599.926 | −0.958348 | ||||||||
\(627\) | 42.5462 | − | 42.5462i | 0.0678567 | − | 0.0678567i | ||||
\(628\) | −24.9192 | − | 24.9192i | −0.0396802 | − | 0.0396802i | ||||
\(629\) | 160.866i | 0.255748i | ||||||||
\(630\) | 131.560 | − | 154.186i | 0.208825 | − | 0.244739i | ||||
\(631\) | 818.531 | 1.29720 | 0.648598 | − | 0.761131i | \(-0.275356\pi\) | ||||
0.648598 | + | 0.761131i | \(0.275356\pi\) | |||||||
\(632\) | −148.372 | + | 148.372i | −0.234765 | + | 0.234765i | ||||
\(633\) | −289.711 | − | 289.711i | −0.457680 | − | 0.457680i | ||||
\(634\) | − | 541.660i | − | 0.854353i | ||||||
\(635\) | −25.5363 | − | 322.505i | −0.0402147 | − | 0.507882i | ||||
\(636\) | −111.935 | −0.175998 | ||||||||
\(637\) | −45.8464 | + | 45.8464i | −0.0719724 | + | 0.0719724i | ||||
\(638\) | −229.947 | − | 229.947i | −0.360419 | − | 0.360419i | ||||
\(639\) | 287.281i | 0.449579i | ||||||||
\(640\) | −56.3920 | + | 4.46519i | −0.0881126 | + | 0.00697685i | ||||
\(641\) | −1117.35 | −1.74314 | −0.871570 | − | 0.490271i | \(-0.836898\pi\) | ||||
−0.871570 | + | 0.490271i | \(0.836898\pi\) | |||||||
\(642\) | −159.732 | + | 159.732i | −0.248803 | + | 0.248803i | ||||
\(643\) | −374.672 | − | 374.672i | −0.582694 | − | 0.582694i | 0.352949 | − | 0.935643i | \(-0.385179\pi\) |
−0.935643 | + | 0.352949i | \(0.885179\pi\) | |||||||
\(644\) | − | 91.6451i | − | 0.142306i | ||||||
\(645\) | 420.416 | + | 358.723i | 0.651807 | + | 0.556159i | ||||
\(646\) | 13.9746 | 0.0216325 | ||||||||
\(647\) | −706.633 | + | 706.633i | −1.09217 | + | 1.09217i | −0.0968710 | + | 0.995297i | \(0.530883\pi\) |
−0.995297 | + | 0.0968710i | \(0.969117\pi\) | |||||||
\(648\) | −18.0000 | − | 18.0000i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 971.495i | 1.49691i | ||||||||
\(650\) | −8.53020 | − | 53.5274i | −0.0131234 | − | 0.0823498i | ||||
\(651\) | −359.965 | −0.552941 | ||||||||
\(652\) | −235.967 | + | 235.967i | −0.361913 | + | 0.361913i | ||||
\(653\) | 845.591 | + | 845.591i | 1.29493 | + | 1.29493i | 0.931697 | + | 0.363236i | \(0.118328\pi\) |
0.363236 | + | 0.931697i | \(0.381672\pi\) | |||||||
\(654\) | − | 156.982i | − | 0.240034i | ||||||
\(655\) | 234.714 | − | 275.080i | 0.358341 | − | 0.419969i | ||||
\(656\) | −221.835 | −0.338162 | ||||||||
\(657\) | 54.9140 | − | 54.9140i | 0.0835829 | − | 0.0835829i | ||||
\(658\) | 540.776 | + | 540.776i | 0.821848 | + | 0.821848i | ||||
\(659\) | − | 1313.34i | − | 1.99293i | −0.0840117 | − | 0.996465i | \(-0.526773\pi\) | ||
0.0840117 | − | 0.996465i | \(-0.473227\pi\) | |||||||
\(660\) | −29.4977 | − | 372.534i | −0.0446934 | − | 0.564446i | ||||
\(661\) | −706.286 | −1.06851 | −0.534255 | − | 0.845323i | \(-0.679408\pi\) | ||||
−0.534255 | + | 0.845323i | \(0.679408\pi\) | |||||||
\(662\) | 331.091 | − | 331.091i | 0.500138 | − | 0.500138i | ||||
\(663\) | −11.5235 | − | 11.5235i | −0.0173808 | − | 0.0173808i | ||||
\(664\) | 116.918i | 0.176081i | ||||||||
\(665\) | 76.6797 | − | 6.07159i | 0.115308 | − | 0.00913021i | ||||
\(666\) | 111.206 | 0.166976 | ||||||||
\(667\) | 36.1422 | − | 36.1422i | 0.0541862 | − | 0.0541862i | ||||
\(668\) | −316.404 | − | 316.404i | −0.473659 | − | 0.473659i | ||||
\(669\) | 671.620i | 1.00392i | ||||||||
\(670\) | 473.390 | + | 403.924i | 0.706553 | + | 0.602871i | ||||
\(671\) | 2306.28 | 3.43709 | ||||||||
\(672\) | −66.1966 | + | 66.1966i | −0.0985069 | + | 0.0985069i | ||||
\(673\) | 99.1229 | + | 99.1229i | 0.147285 | + | 0.147285i | 0.776904 | − | 0.629619i | \(-0.216789\pi\) |
−0.629619 | + | 0.776904i | \(0.716789\pi\) | |||||||
\(674\) | 706.319i | 1.04795i | ||||||||
\(675\) | 105.167 | + | 76.2554i | 0.155803 | + | 0.112971i | ||||
\(676\) | −333.299 | −0.493046 | ||||||||
\(677\) | −616.977 | + | 616.977i | −0.911339 | + | 0.911339i | −0.996378 | − | 0.0850382i | \(-0.972899\pi\) |
0.0850382 | + | 0.996378i | \(0.472899\pi\) | |||||||
\(678\) | 62.4670 | + | 62.4670i | 0.0921342 | + | 0.0921342i | ||||
\(679\) | − | 647.890i | − | 0.954182i | ||||||
\(680\) | 56.3363 | − | 66.0250i | 0.0828474 | − | 0.0970955i | ||||
\(681\) | −151.622 | −0.222646 | ||||||||
\(682\) | −469.296 | + | 469.296i | −0.688117 | + | 0.688117i | ||||
\(683\) | 229.053 | + | 229.053i | 0.335363 | + | 0.335363i | 0.854619 | − | 0.519256i | \(-0.173791\pi\) |
−0.519256 | + | 0.854619i | \(0.673791\pi\) | |||||||
\(684\) | − | 9.66059i | − | 0.0141237i | ||||||
\(685\) | 98.3268 | + | 1241.80i | 0.143543 | + | 1.81284i | ||||
\(686\) | 90.6463 | 0.132138 | ||||||||
\(687\) | 516.068 | − | 516.068i | 0.751191 | − | 0.751191i | ||||
\(688\) | −180.497 | − | 180.497i | −0.262351 | − | 0.262351i | ||||
\(689\) | 49.5382i | 0.0718987i | ||||||||
\(690\) | 58.5534 | − | 4.63633i | 0.0848600 | − | 0.00671931i | ||||
\(691\) | 609.437 | 0.881964 | 0.440982 | − | 0.897516i | \(-0.354630\pi\) | ||||
0.440982 | + | 0.897516i | \(0.354630\pi\) | |||||||
\(692\) | −91.2066 | + | 91.2066i | −0.131801 | + | 0.131801i | ||||
\(693\) | −437.305 | − | 437.305i | −0.631031 | − | 0.631031i | ||||
\(694\) | − | 121.324i | − | 0.174818i | ||||||
\(695\) | −431.678 | − | 368.332i | −0.621120 | − | 0.529975i | ||||
\(696\) | −52.2121 | −0.0750174 | ||||||||
\(697\) | 240.672 | − | 240.672i | 0.345297 | − | 0.345297i | ||||
\(698\) | 185.071 | + | 185.071i | 0.265144 | + | 0.265144i | ||||
\(699\) | 551.194i | 0.788546i | ||||||||
\(700\) | 280.436 | − | 386.762i | 0.400623 | − | 0.552517i | ||||
\(701\) | −827.352 | −1.18025 | −0.590123 | − | 0.807313i | \(-0.700921\pi\) | ||||
−0.590123 | + | 0.807313i | \(0.700921\pi\) | |||||||
\(702\) | −7.96615 | + | 7.96615i | −0.0113478 | + | 0.0113478i | ||||
\(703\) | 29.8421 | + | 29.8421i | 0.0424497 | + | 0.0424497i | ||||
\(704\) | 172.605i | 0.245177i | ||||||||
\(705\) | −318.152 | + | 372.868i | −0.451280 | + | 0.528891i | ||||
\(706\) | 767.303 | 1.08683 | ||||||||
\(707\) | 1006.58 | − | 1006.58i | 1.42373 | − | 1.42373i | ||||
\(708\) | 110.294 | + | 110.294i | 0.155783 | + | 0.155783i | ||||
\(709\) | 339.906i | 0.479416i | 0.970845 | + | 0.239708i | \(0.0770518\pi\) | ||||
−0.970845 | + | 0.239708i | \(0.922948\pi\) | |||||||
\(710\) | 53.4484 | + | 675.014i | 0.0752794 | + | 0.950724i | ||||
\(711\) | −222.557 | −0.313020 | ||||||||
\(712\) | −297.725 | + | 297.725i | −0.418154 | + | 0.418154i | ||||
\(713\) | −73.7620 | − | 73.7620i | −0.103453 | − | 0.103453i | ||||
\(714\) | − | 143.636i | − | 0.201170i | ||||||
\(715\) | −164.870 | + | 13.0546i | −0.230588 | + | 0.0182582i | ||||
\(716\) | −222.956 | −0.311391 | ||||||||
\(717\) | 272.280 | − | 272.280i | 0.379750 | − | 0.379750i | ||||
\(718\) | −7.62023 | − | 7.62023i | −0.0106131 | − | 0.0106131i | ||||
\(719\) | 114.840i | 0.159722i | 0.996806 | + | 0.0798610i | \(0.0254476\pi\) | ||||
−0.996806 | + | 0.0798610i | \(0.974552\pi\) | |||||||
\(720\) | −45.6429 | − | 38.9451i | −0.0633929 | − | 0.0540905i | ||||
\(721\) | −143.594 | −0.199160 | ||||||||
\(722\) | −358.408 | + | 358.408i | −0.496409 | + | 0.496409i | ||||
\(723\) | 46.0159 | + | 46.0159i | 0.0636457 | + | 0.0636457i | ||||
\(724\) | 494.510i | 0.683025i | ||||||||
\(725\) | 263.124 | − | 41.9317i | 0.362929 | − | 0.0578369i | ||||
\(726\) | −843.863 | −1.16235 | ||||||||
\(727\) | −48.1716 | + | 48.1716i | −0.0662609 | + | 0.0662609i | −0.739461 | − | 0.673200i | \(-0.764919\pi\) |
0.673200 | + | 0.739461i | \(0.264919\pi\) | |||||||
\(728\) | 29.2963 | + | 29.2963i | 0.0402421 | + | 0.0402421i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 118.813 | − | 139.246i | 0.162757 | − | 0.190748i | ||||
\(731\) | 391.649 | 0.535772 | ||||||||
\(732\) | 261.834 | − | 261.834i | 0.357697 | − | 0.357697i | ||||
\(733\) | −171.334 | − | 171.334i | −0.233743 | − | 0.233743i | 0.580510 | − | 0.814253i | \(-0.302853\pi\) |
−0.814253 | + | 0.580510i | \(0.802853\pi\) | |||||||
\(734\) | 4.88004i | 0.00664855i | ||||||||
\(735\) | −28.9101 | − | 365.113i | −0.0393334 | − | 0.496753i | ||||
\(736\) | −27.1293 | −0.0368605 | ||||||||
\(737\) | 1342.64 | − | 1342.64i | 1.82176 | − | 1.82176i | ||||
\(738\) | −166.376 | − | 166.376i | −0.225442 | − | 0.225442i | ||||
\(739\) | 285.604i | 0.386474i | 0.981152 | + | 0.193237i | \(0.0618986\pi\) | ||||
−0.981152 | + | 0.193237i | \(0.938101\pi\) | |||||||
\(740\) | 261.297 | − | 20.6898i | 0.353104 | − | 0.0279592i | ||||
\(741\) | −4.27543 | −0.00576981 | ||||||||
\(742\) | −308.737 | + | 308.737i | −0.416088 | + | 0.416088i | ||||
\(743\) | 38.7694 | + | 38.7694i | 0.0521796 | + | 0.0521796i | 0.732715 | − | 0.680536i | \(-0.238253\pi\) |
−0.680536 | + | 0.732715i | \(0.738253\pi\) | |||||||
\(744\) | 106.559i | 0.143224i | ||||||||
\(745\) | −844.143 | − | 720.271i | −1.13308 | − | 0.966806i | ||||
\(746\) | 710.570 | 0.952507 | ||||||||
\(747\) | −87.6883 | + | 87.6883i | −0.117387 | + | 0.117387i | ||||
\(748\) | −187.262 | − | 187.262i | −0.250350 | − | 0.250350i | ||||
\(749\) | 881.143i | 1.17643i | ||||||||
\(750\) | 261.295 | + | 159.609i | 0.348393 | + | 0.212811i | ||||
\(751\) | −98.0276 | −0.130529 | −0.0652647 | − | 0.997868i | \(-0.520789\pi\) | ||||
−0.0652647 | + | 0.997868i | \(0.520789\pi\) | |||||||
\(752\) | 160.084 | − | 160.084i | 0.212877 | − | 0.212877i | ||||
\(753\) | 143.310 | + | 143.310i | 0.190318 | + | 0.190318i | ||||
\(754\) | 23.1072i | 0.0306462i | ||||||||
\(755\) | −585.474 | + | 686.164i | −0.775462 | + | 0.908826i | ||||
\(756\) | −99.2950 | −0.131343 | ||||||||
\(757\) | 371.185 | − | 371.185i | 0.490336 | − | 0.490336i | −0.418076 | − | 0.908412i | \(-0.637295\pi\) |
0.908412 | + | 0.418076i | \(0.137295\pi\) | |||||||
\(758\) | 175.743 | + | 175.743i | 0.231851 | + | 0.231851i | ||||
\(759\) | − | 179.220i | − | 0.236127i | ||||||
\(760\) | −1.79735 | − | 22.6992i | −0.00236493 | − | 0.0298673i | ||||
\(761\) | 15.1023 | 0.0198453 | 0.00992264 | − | 0.999951i | \(-0.496841\pi\) | ||||
0.00992264 | + | 0.999951i | \(0.496841\pi\) | |||||||
\(762\) | −112.069 | + | 112.069i | −0.147072 | + | 0.147072i | ||||
\(763\) | −432.988 | − | 432.988i | −0.567481 | − | 0.567481i | ||||
\(764\) | 227.888i | 0.298283i | ||||||||
\(765\) | 91.7709 | − | 7.26652i | 0.119962 | − | 0.00949872i | ||||
\(766\) | −309.165 | −0.403610 | ||||||||
\(767\) | 48.8123 | − | 48.8123i | 0.0636406 | − | 0.0636406i | ||||
\(768\) | 19.5959 | + | 19.5959i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | 69.2758i | 0.0900855i | 0.998985 | + | 0.0450428i | \(0.0143424\pi\) | ||||
−0.998985 | + | 0.0450428i | \(0.985658\pi\) | |||||||
\(770\) | −1108.88 | − | 946.161i | −1.44011 | − | 1.22878i | ||||
\(771\) | 626.380 | 0.812425 | ||||||||
\(772\) | −79.2432 | + | 79.2432i | −0.102647 | + | 0.102647i | ||||
\(773\) | −741.092 | − | 741.092i | −0.958722 | − | 0.958722i | 0.0404588 | − | 0.999181i | \(-0.487118\pi\) |
−0.999181 | + | 0.0404588i | \(0.987118\pi\) | |||||||
\(774\) | − | 270.746i | − | 0.349801i | ||||||
\(775\) | −85.5778 | − | 537.005i | −0.110423 | − | 0.692909i | ||||
\(776\) | −191.792 | −0.247155 | ||||||||
\(777\) | 306.728 | − | 306.728i | 0.394759 | − | 0.394759i | ||||
\(778\) | −744.952 | − | 744.952i | −0.957522 | − | 0.957522i | ||||
\(779\) | − | 89.2938i | − | 0.114626i | ||||||
\(780\) | −17.2357 | + | 20.1999i | −0.0220971 | + | 0.0258973i | ||||
\(781\) | 2066.08 | 2.64543 | ||||||||
\(782\) | 29.4330 | − | 29.4330i | 0.0376381 | − | 0.0376381i | ||||
\(783\) | −39.1591 | − | 39.1591i | −0.0500116 | − | 0.0500116i | ||||
\(784\) | 169.166i | 0.215773i | ||||||||
\(785\) | −6.95429 | − | 87.8277i | −0.00885897 | − | 0.111882i | ||||
\(786\) | −177.150 | −0.225382 | ||||||||
\(787\) | −249.487 | + | 249.487i | −0.317010 | + | 0.317010i | −0.847618 | − | 0.530608i | \(-0.821964\pi\) |
0.530608 | + | 0.847618i | \(0.321964\pi\) | |||||||
\(788\) | 335.722 | + | 335.722i | 0.426043 | + | 0.426043i | ||||
\(789\) | 239.580i | 0.303651i | ||||||||
\(790\) | −522.936 | + | 41.4067i | −0.661944 | + | 0.0524135i | ||||
\(791\) | 344.592 | 0.435641 | ||||||||
\(792\) | −129.454 | + | 129.454i | −0.163451 | + | 0.163451i | ||||
\(793\) | −115.878 | − | 115.878i | −0.146126 | − | 0.146126i | ||||
\(794\) | − | 143.583i | − | 0.180835i | ||||||
\(795\) | −212.876 | − | 181.638i | −0.267768 | − | 0.228475i | ||||
\(796\) | −355.054 | −0.446047 | ||||||||
\(797\) | −708.670 | + | 708.670i | −0.889172 | + | 0.889172i | −0.994444 | − | 0.105271i | \(-0.966429\pi\) |
0.105271 | + | 0.994444i | \(0.466429\pi\) | |||||||
\(798\) | −26.6458 | − | 26.6458i | −0.0333907 | − | 0.0333907i | ||||
\(799\) | 347.355i | 0.434737i | ||||||||
\(800\) | −114.491 | − | 83.0163i | −0.143114 | − | 0.103770i | ||||
\(801\) | −446.588 | −0.557538 | ||||||||
\(802\) | 460.952 | − | 460.952i | 0.574754 | − | 0.574754i | ||||
\(803\) | −394.934 | − | 394.934i | −0.491823 | − | 0.491823i | ||||
\(804\) | − | 304.862i | − | 0.379181i | ||||||
\(805\) | 148.714 | − | 174.290i | 0.184738 | − | 0.216509i | ||||
\(806\) | 47.1591 | 0.0585101 | ||||||||
\(807\) | 302.925 | − | 302.925i | 0.375371 | − | 0.375371i | ||||
\(808\) | −297.973 | − | 297.973i | −0.368779 | − | 0.368779i | ||||
\(809\) | − | 48.4853i | − | 0.0599324i | −0.999551 | − | 0.0299662i | \(-0.990460\pi\) | ||
0.999551 | − | 0.0299662i | \(-0.00953997\pi\) | |||||||
\(810\) | −5.02333 | − | 63.4410i | −0.00620165 | − | 0.0783223i | ||||
\(811\) | 823.080 | 1.01490 | 0.507448 | − | 0.861682i | \(-0.330589\pi\) | ||||
0.507448 | + | 0.861682i | \(0.330589\pi\) | |||||||
\(812\) | −144.011 | + | 144.011i | −0.177354 | + | 0.177354i | ||||
\(813\) | −213.224 | − | 213.224i | −0.262269 | − | 0.262269i | ||||
\(814\) | − | 799.778i | − | 0.982529i | ||||||
\(815\) | −831.668 | + | 65.8524i | −1.02045 | + | 0.0808005i | ||||
\(816\) | −42.5198 | −0.0521076 | ||||||||
\(817\) | 72.6547 | − | 72.6547i | 0.0889286 | − | 0.0889286i | ||||
\(818\) | −24.4609 | − | 24.4609i | −0.0299033 | − | 0.0299033i | ||||
\(819\) | 43.9444i | 0.0536561i | ||||||||
\(820\) | −421.882 | − | 359.974i | −0.514491 | − | 0.438993i | ||||
\(821\) | 1372.41 | 1.67164 | 0.835818 | − | 0.549007i | \(-0.184994\pi\) | ||||
0.835818 | + | 0.549007i | \(0.184994\pi\) | |||||||
\(822\) | 431.517 | − | 431.517i | 0.524960 | − | 0.524960i | ||||
\(823\) | 719.853 | + | 719.853i | 0.874669 | + | 0.874669i | 0.992977 | − | 0.118308i | \(-0.0377469\pi\) |
−0.118308 | + | 0.992977i | \(0.537747\pi\) | |||||||
\(824\) | 42.5075i | 0.0515868i | ||||||||
\(825\) | 548.418 | − | 756.347i | 0.664749 | − | 0.916784i | ||||
\(826\) | 608.427 | 0.736594 | ||||||||
\(827\) | −299.280 | + | 299.280i | −0.361886 | + | 0.361886i | −0.864507 | − | 0.502621i | \(-0.832369\pi\) |
0.502621 | + | 0.864507i | \(0.332369\pi\) | |||||||
\(828\) | −20.3470 | − | 20.3470i | −0.0245737 | − | 0.0245737i | ||||
\(829\) | − | 1071.91i | − | 1.29302i | −0.762905 | − | 0.646510i | \(-0.776228\pi\) | ||
0.762905 | − | 0.646510i | \(-0.223772\pi\) | |||||||
\(830\) | −189.724 | + | 222.353i | −0.228583 | + | 0.267895i | ||||
\(831\) | 162.202 | 0.195189 | ||||||||
\(832\) | 8.67245 | − | 8.67245i | 0.0104236 | − | 0.0104236i | ||||
\(833\) | −183.531 | − | 183.531i | −0.220326 | − | 0.220326i | ||||
\(834\) | 277.999i | 0.333332i | ||||||||
\(835\) | −88.3002 | − | 1115.17i | −0.105749 | − | 1.33553i | ||||
\(836\) | −69.4776 | −0.0831072 | ||||||||
\(837\) | −79.9191 | + | 79.9191i | −0.0954828 | + | 0.0954828i | ||||
\(838\) | 671.275 | + | 671.275i | 0.801045 | + | 0.801045i | ||||
\(839\) | − | 383.200i | − | 0.456734i | −0.973575 | − | 0.228367i | \(-0.926661\pi\) | ||
0.973575 | − | 0.228367i | \(-0.0733387\pi\) | |||||||
\(840\) | −233.310 | + | 18.4738i | −0.277750 | + | 0.0219926i | ||||
\(841\) | 727.412 | 0.864937 | ||||||||
\(842\) | −386.936 | + | 386.936i | −0.459544 | + | 0.459544i | ||||
\(843\) | 110.992 | + | 110.992i | 0.131663 | + | 0.131663i | ||||
\(844\) | 473.097i | 0.560541i | ||||||||
\(845\) | −633.865 | − | 540.849i | −0.750136 | − | 0.640059i | ||||
\(846\) | 240.126 | 0.283836 | ||||||||
\(847\) | −2327.54 | + | 2327.54i | −2.74798 | + | 2.74798i | ||||
\(848\) | 91.3942 | + | 91.3942i | 0.107776 | + | 0.107776i | ||||
\(849\) | − | 861.104i | − | 1.01426i | ||||||
\(850\) | 214.279 | − | 34.1478i | 0.252093 | − | 0.0401739i | ||||
\(851\) | 125.706 | 0.147716 | ||||||||
\(852\) | 234.564 | − | 234.564i | 0.275310 | − | 0.275310i | ||||
\(853\) | −651.300 | − | 651.300i | −0.763540 | − | 0.763540i | 0.213420 | − | 0.976960i | \(-0.431540\pi\) |
−0.976960 | + | 0.213420i | \(0.931540\pi\) | |||||||
\(854\) | − | 1444.38i | − | 1.69131i | ||||||
\(855\) | 15.6764 | − | 18.3724i | 0.0183349 | − | 0.0214882i | ||||
\(856\) | 260.841 | 0.304721 | ||||||||
\(857\) | −205.089 | + | 205.089i | −0.239311 | + | 0.239311i | −0.816565 | − | 0.577254i | \(-0.804124\pi\) |
0.577254 | + | 0.816565i | \(0.304124\pi\) | |||||||
\(858\) | 57.2915 | + | 57.2915i | 0.0667733 | + | 0.0667733i | ||||
\(859\) | 1544.42i | 1.79793i | 0.438021 | + | 0.898965i | \(0.355680\pi\) | ||||
−0.438021 | + | 0.898965i | \(0.644320\pi\) | |||||||
\(860\) | −50.3722 | − | 636.164i | −0.0585723 | − | 0.739725i | ||||
\(861\) | −917.794 | −1.06596 | ||||||||
\(862\) | 238.331 | − | 238.331i | 0.276487 | − | 0.276487i | ||||
\(863\) | 284.031 | + | 284.031i | 0.329121 | + | 0.329121i | 0.852252 | − | 0.523131i | \(-0.175236\pi\) |
−0.523131 | + | 0.852252i | \(0.675236\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | −321.458 | + | 25.4534i | −0.371628 | + | 0.0294259i | ||||
\(866\) | 356.663 | 0.411851 | ||||||||
\(867\) | −307.821 | + | 307.821i | −0.355041 | + | 0.355041i | ||||
\(868\) | 293.910 | + | 293.910i | 0.338606 | + | 0.338606i | ||||
\(869\) | 1600.60i | 1.84189i | ||||||||
\(870\) | −99.2964 | − | 84.7253i | −0.114134 | − | 0.0973854i | ||||
\(871\) | −134.921 | −0.154903 | ||||||||
\(872\) | −128.176 | + | 128.176i | −0.146990 | + | 0.146990i | ||||
\(873\) | −143.844 | − | 143.844i | −0.164770 | − | 0.164770i | ||||
\(874\) | − | 10.9202i | − | 0.0124945i | ||||||
\(875\) | 1160.93 | − | 280.471i | 1.32678 | − | 0.320538i | ||||
\(876\) | −89.6742 | −0.102368 | ||||||||
\(877\) | 1226.80 | − | 1226.80i | 1.39885 | − | 1.39885i | 0.595498 | − | 0.803357i | \(-0.296955\pi\) |
0.803357 | − | 0.595498i | \(-0.203045\pi\) | |||||||
\(878\) | −739.579 | − | 739.579i | −0.842345 | − | 0.842345i | ||||
\(879\) | 98.7076i | 0.112295i | ||||||||
\(880\) | −280.088 | + | 328.258i | −0.318282 | + | 0.373020i | ||||
\(881\) | 1011.62 | 1.14827 | 0.574133 | − | 0.818762i | \(-0.305339\pi\) | ||||
0.574133 | + | 0.818762i | \(0.305339\pi\) | |||||||
\(882\) | −126.875 | + | 126.875i | −0.143849 | + | 0.143849i | ||||
\(883\) | 577.715 | + | 577.715i | 0.654264 | + | 0.654264i | 0.954017 | − | 0.299753i | \(-0.0969042\pi\) |
−0.299753 | + | 0.954017i | \(0.596904\pi\) | |||||||
\(884\) | 18.8177i | 0.0212870i | ||||||||
\(885\) | 30.7803 | + | 388.733i | 0.0347800 | + | 0.439246i | ||||
\(886\) | −360.450 | −0.406828 | ||||||||
\(887\) | −403.325 | + | 403.325i | −0.454707 | + | 0.454707i | −0.896913 | − | 0.442206i | \(-0.854196\pi\) |
0.442206 | + | 0.896913i | \(0.354196\pi\) | |||||||
\(888\) | −90.7993 | − | 90.7993i | −0.102252 | − | 0.102252i | ||||
\(889\) | 618.214i | 0.695404i | ||||||||
\(890\) | −1049.33 | + | 83.0874i | −1.17903 | + | 0.0933567i | ||||
\(891\) | −194.180 | −0.217935 | ||||||||
\(892\) | 548.376 | − | 548.376i | 0.614771 | − | 0.614771i | ||||
\(893\) | 64.4376 | + | 64.4376i | 0.0721586 | + | 0.0721586i | ||||
\(894\) | 543.625i | 0.608082i | ||||||||
\(895\) | −424.015 | − | 361.793i | −0.473759 | − | 0.404238i | ||||
\(896\) | 108.099 | 0.120646 | ||||||||
\(897\) | −9.00484 | + | 9.00484i | −0.0100388 | + | 0.0100388i | ||||
\(898\) | −798.750 | − | 798.750i | −0.889476 | − | 0.889476i | ||||
\(899\) | 231.819i | 0.257863i | ||||||||
\(900\) | −23.6063 | − | 148.131i | −0.0262293 | − | 0.164590i | ||||
\(901\) | −198.310 | −0.220100 | ||||||||
\(902\) | −1196.55 | + | 1196.55i | −1.32655 | + | 1.32655i | ||||
\(903\) | −746.770 | − | 746.770i | −0.826988 | − | 0.826988i | ||||
\(904\) | − | 102.008i | − | 0.112841i | ||||||
\(905\) | −802.448 | + | 940.453i | −0.886683 | + | 1.03918i | ||||
\(906\) | 441.887 | 0.487734 | ||||||||
\(907\) | 633.280 | − | 633.280i | 0.698214 | − | 0.698214i | −0.265811 | − | 0.964025i | \(-0.585640\pi\) |
0.964025 | + | 0.265811i | \(0.0856398\pi\) | |||||||
\(908\) | 123.799 | + | 123.799i | 0.136342 | + | 0.136342i | ||||
\(909\) | − | 446.960i | − | 0.491705i | ||||||
\(910\) | 8.17582 | + | 103.255i | 0.00898442 | + | 0.113467i | ||||
\(911\) | −8.24514 | −0.00905065 | −0.00452533 | − | 0.999990i | \(-0.501440\pi\) | ||||
−0.00452533 | + | 0.999990i | \(0.501440\pi\) | |||||||
\(912\) | −7.88784 | + | 7.88784i | −0.00864895 | + | 0.00864895i | ||||
\(913\) | 630.642 | + | 630.642i | 0.690736 | + | 0.690736i | ||||
\(914\) | − | 434.104i | − | 0.474950i | ||||||
\(915\) | 922.834 | − | 73.0711i | 1.00856 | − | 0.0798591i | ||||
\(916\) | −842.736 | −0.920017 | ||||||||
\(917\) | −488.615 | + | 488.615i | −0.532840 | + | 0.532840i | ||||
\(918\) | −31.8899 | − | 31.8899i | −0.0347384 | − | 0.0347384i | ||||
\(919\) | 297.033i | 0.323213i | 0.986855 | + | 0.161607i | \(0.0516676\pi\) | ||||
−0.986855 | + | 0.161607i | \(0.948332\pi\) | |||||||
\(920\) | −51.5942 | − | 44.0231i | −0.0560807 | − | 0.0478512i | ||||
\(921\) | 563.675 | 0.612025 | ||||||||
\(922\) | 297.784 | − | 297.784i | 0.322976 | − | 0.322976i | ||||
\(923\) | −103.809 | − | 103.809i | −0.112470 | − | 0.112470i | ||||
\(924\) | 714.116i | 0.772852i | ||||||||
\(925\) | 530.506 | + | 384.663i | 0.573520 | + | 0.415852i | ||||
\(926\) | −252.351 | −0.272517 | ||||||||
\(927\) | −31.8807 | + | 31.8807i | −0.0343912 | + | 0.0343912i | ||||
\(928\) | 42.6310 | + | 42.6310i | 0.0459386 | + | 0.0459386i | ||||
\(929\) | 642.952i | 0.692091i | 0.938218 | + | 0.346045i | \(0.112476\pi\) | ||||
−0.938218 | + | 0.346045i | \(0.887524\pi\) | |||||||
\(930\) | −172.915 | + | 202.652i | −0.185930 | + | 0.217906i | ||||
\(931\) | −68.0936 | −0.0731403 | ||||||||
\(932\) | 450.048 | − | 450.048i | 0.482884 | − | 0.482884i | ||||
\(933\) | −429.650 | − | 429.650i | −0.460504 | − | 0.460504i | ||||
\(934\) | 744.310i | 0.796905i | ||||||||
\(935\) | −52.2598 | − | 660.004i | −0.0558929 | − | 0.705886i | ||||
\(936\) | 13.0087 | 0.0138982 | ||||||||
\(937\) | 1255.14 | − | 1255.14i | 1.33953 | − | 1.33953i | 0.443021 | − | 0.896511i | \(-0.353907\pi\) |
0.896511 | − | 0.443021i | \(-0.146093\pi\) | |||||||
\(938\) | −840.868 | − | 840.868i | −0.896447 | − | 0.896447i | ||||
\(939\) | 734.756i | 0.782488i | ||||||||
\(940\) | 564.215 | − | 44.6752i | 0.600229 | − | 0.0475268i | ||||
\(941\) | 898.683 | 0.955030 | 0.477515 | − | 0.878624i | \(-0.341538\pi\) | ||||
0.477515 | + | 0.878624i | \(0.341538\pi\) | |||||||
\(942\) | −30.5196 | + | 30.5196i | −0.0323987 | + | 0.0323987i | ||||
\(943\) | −188.069 | − | 188.069i | −0.199437 | − | 0.199437i | ||||
\(944\) | − | 180.110i | − | 0.190794i | ||||||
\(945\) | −188.838 | − | 161.127i | −0.199829 | − | 0.170505i | ||||
\(946\) | −1947.17 | −2.05832 | ||||||||
\(947\) | −908.004 | + | 908.004i | −0.958822 | + | 0.958822i | −0.999185 | − | 0.0403634i | \(-0.987148\pi\) |
0.0403634 | + | 0.999185i | \(0.487148\pi\) | |||||||
\(948\) | 181.717 | + | 181.717i | 0.191685 | + | 0.191685i | ||||
\(949\) | 39.6866i | 0.0418193i | ||||||||
\(950\) | 33.4161 | − | 46.0856i | 0.0351749 | − | 0.0485112i | ||||
\(951\) | −663.395 | −0.697576 | ||||||||
\(952\) | −117.278 | + | 117.278i | −0.123191 | + | 0.123191i | ||||
\(953\) | −550.047 | − | 550.047i | −0.577174 | − | 0.577174i | 0.356949 | − | 0.934124i | \(-0.383817\pi\) |
−0.934124 | + | 0.356949i | \(0.883817\pi\) | |||||||
\(954\) | 137.091i | 0.143702i | ||||||||
\(955\) | −369.798 | + | 433.396i | −0.387223 | + | 0.453817i | ||||
\(956\) | −444.632 | −0.465096 | ||||||||
\(957\) | −281.627 | + | 281.627i | −0.294281 | + | 0.294281i | ||||
\(958\) | 149.254 | + | 149.254i | 0.155797 | + | 0.155797i | ||||
\(959\) | − | 2380.42i | − | 2.48219i | ||||||
\(960\) | 5.46871 | + | 69.0659i | 0.00569658 | + | 0.0719436i | ||||
\(961\) | −487.884 | −0.507683 | ||||||||
\(962\) | −40.1845 | + | 40.1845i | −0.0417718 | + | 0.0417718i | ||||
\(963\) | 195.631 | + | 195.631i | 0.203147 | + | 0.203147i | ||||
\(964\) | − | 75.1436i | − | 0.0779498i | ||||||
\(965\) | −279.293 | + | 22.1147i | −0.289423 | + | 0.0229168i | ||||
\(966\) | −112.242 | −0.116192 | ||||||||
\(967\) | −764.523 | + | 764.523i | −0.790614 | + | 0.790614i | −0.981594 | − | 0.190980i | \(-0.938833\pi\) |
0.190980 | + | 0.981594i | \(0.438833\pi\) | |||||||
\(968\) | 689.012 | + | 689.012i | 0.711789 | + | 0.711789i | ||||
\(969\) | − | 17.1153i | − | 0.0176628i | ||||||
\(970\) | −364.748 | − | 311.224i | −0.376029 | − | 0.320849i | ||||
\(971\) | 1638.75 | 1.68769 | 0.843846 | − | 0.536585i | \(-0.180286\pi\) | ||||
0.843846 | + | 0.536585i | \(0.180286\pi\) | |||||||
\(972\) | −22.0454 | + | 22.0454i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 766.775 | + | 766.775i | 0.788053 | + | 0.788053i | ||||
\(974\) | − | 126.972i | − | 0.130362i | ||||||
\(975\) | −65.5574 | + | 10.4473i | −0.0672383 | + | 0.0107152i | ||||
\(976\) | −427.573 | −0.438087 | ||||||||
\(977\) | −30.1707 | + | 30.1707i | −0.0308810 | + | 0.0308810i | −0.722379 | − | 0.691498i | \(-0.756951\pi\) |
0.691498 | + | 0.722379i | \(0.256951\pi\) | |||||||
\(978\) | 289.000 | + | 289.000i | 0.295501 | + | 0.295501i | ||||
\(979\) | 3211.80i | 3.28069i | ||||||||
\(980\) | −274.509 | + | 321.719i | −0.280111 | + | 0.328284i | ||||
\(981\) | −192.264 | −0.195987 | ||||||||
\(982\) | 574.263 | − | 574.263i | 0.584789 | − | 0.584789i | ||||
\(983\) | −451.884 | − | 451.884i | −0.459699 | − | 0.459699i | 0.438858 | − | 0.898557i | \(-0.355383\pi\) |
−0.898557 | + | 0.438858i | \(0.855383\pi\) | |||||||
\(984\) | 271.691i | 0.276108i | ||||||||
\(985\) | 93.6912 | + | 1183.25i | 0.0951180 | + | 1.20127i | ||||
\(986\) | −92.5021 | −0.0938155 | ||||||||
\(987\) | 662.313 | − | 662.313i | 0.671036 | − | 0.671036i | ||||
\(988\) | 3.49087 | + | 3.49087i | 0.00353327 | + | 0.00353327i | ||||
\(989\) | − | 306.048i | − | 0.309452i | ||||||
\(990\) | −456.259 | + | 36.1271i | −0.460868 | + | 0.0364920i | ||||
\(991\) | −542.646 | −0.547575 | −0.273787 | − | 0.961790i | \(-0.588276\pi\) | ||||
−0.273787 | + | 0.961790i | \(0.588276\pi\) | |||||||
\(992\) | 87.0049 | − | 87.0049i | 0.0877066 | − | 0.0877066i | ||||
\(993\) | −405.502 | − | 405.502i | −0.408361 | − | 0.408361i | ||||
\(994\) | − | 1293.94i | − | 1.30175i | ||||||
\(995\) | −675.237 | − | 576.150i | −0.678630 | − | 0.579046i | ||||
\(996\) | 143.194 | 0.143770 | ||||||||
\(997\) | −456.492 | + | 456.492i | −0.457865 | + | 0.457865i | −0.897954 | − | 0.440089i | \(-0.854947\pi\) |
0.440089 | + | 0.897954i | \(0.354947\pi\) | |||||||
\(998\) | 138.028 | + | 138.028i | 0.138305 | + | 0.138305i | ||||
\(999\) | − | 136.199i | − | 0.136335i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 690.3.k.b.553.23 | yes | 48 | |
5.2 | odd | 4 | inner | 690.3.k.b.277.23 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.23 | ✓ | 48 | 5.2 | odd | 4 | inner | |
690.3.k.b.553.23 | yes | 48 | 1.1 | even | 1 | trivial |