Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.4 | ||
Root | \(-2.96307i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.17 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.96307i | − | 1.48154i | −0.671761 | − | 0.740768i | \(-0.734462\pi\) | ||
0.671761 | − | 0.740768i | \(-0.265538\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −4.77980 | −1.19495 | ||||||||
\(5\) | 3.25089 | 0.650178 | 0.325089 | − | 0.945683i | \(-0.394606\pi\) | ||||
0.325089 | + | 0.945683i | \(0.394606\pi\) | |||||||
\(6\) | − | 5.13219i | − | 0.855366i | ||||||
\(7\) | 11.8224 | 1.68891 | 0.844455 | − | 0.535626i | \(-0.179924\pi\) | ||||
0.844455 | + | 0.535626i | \(0.179924\pi\) | |||||||
\(8\) | 2.31061i | 0.288826i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 9.63262i | − | 0.963262i | ||||||
\(11\) | 16.1383i | 1.46712i | 0.679626 | + | 0.733559i | \(0.262142\pi\) | ||||
−0.679626 | + | 0.733559i | \(0.737858\pi\) | |||||||
\(12\) | −8.27886 | −0.689905 | ||||||||
\(13\) | − | 14.1300i | − | 1.08692i | −0.839435 | − | 0.543460i | \(-0.817114\pi\) | ||
0.839435 | − | 0.543460i | \(-0.182886\pi\) | |||||||
\(14\) | − | 35.0306i | − | 2.50218i | ||||||
\(15\) | 5.63070 | 0.375380 | ||||||||
\(16\) | −12.2727 | −0.767044 | ||||||||
\(17\) | −32.0002 | −1.88236 | −0.941182 | − | 0.337900i | \(-0.890283\pi\) | ||||
−0.941182 | + | 0.337900i | \(0.890283\pi\) | |||||||
\(18\) | − | 8.88922i | − | 0.493846i | ||||||
\(19\) | 14.7891 | 0.778372 | 0.389186 | − | 0.921159i | \(-0.372756\pi\) | ||||
0.389186 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(20\) | −15.5386 | −0.776930 | ||||||||
\(21\) | 20.4770 | 0.975093 | ||||||||
\(22\) | 47.8190 | 2.17359 | ||||||||
\(23\) | 14.5859i | 0.634168i | 0.948398 | + | 0.317084i | \(0.102704\pi\) | ||||
−0.948398 | + | 0.317084i | \(0.897296\pi\) | |||||||
\(24\) | 4.00209i | 0.166754i | ||||||||
\(25\) | −14.4317 | −0.577269 | ||||||||
\(26\) | −41.8681 | −1.61031 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −56.5086 | −2.01816 | ||||||||
\(29\) | −12.7940 | −0.441172 | −0.220586 | − | 0.975367i | \(-0.570797\pi\) | ||||
−0.220586 | + | 0.975367i | \(0.570797\pi\) | |||||||
\(30\) | − | 16.6842i | − | 0.556139i | ||||||
\(31\) | − | 27.0884i | − | 0.873821i | −0.899505 | − | 0.436910i | \(-0.856073\pi\) | ||
0.899505 | − | 0.436910i | \(-0.143927\pi\) | |||||||
\(32\) | 45.6074i | 1.42523i | ||||||||
\(33\) | 27.9523i | 0.847041i | ||||||||
\(34\) | 94.8189i | 2.78879i | ||||||||
\(35\) | 38.4332 | 1.09809 | ||||||||
\(36\) | −14.3394 | −0.398317 | ||||||||
\(37\) | 26.2136i | 0.708476i | 0.935155 | + | 0.354238i | \(0.115260\pi\) | ||||
−0.935155 | + | 0.354238i | \(0.884740\pi\) | |||||||
\(38\) | − | 43.8211i | − | 1.15319i | ||||||
\(39\) | − | 24.4738i | − | 0.627534i | ||||||
\(40\) | 7.51154i | 0.187788i | ||||||||
\(41\) | −37.3257 | −0.910383 | −0.455192 | − | 0.890394i | \(-0.650429\pi\) | ||||
−0.455192 | + | 0.890394i | \(0.650429\pi\) | |||||||
\(42\) | − | 60.6747i | − | 1.44464i | ||||||
\(43\) | 51.1308i | 1.18909i | 0.804063 | + | 0.594544i | \(0.202668\pi\) | ||||
−0.804063 | + | 0.594544i | \(0.797332\pi\) | |||||||
\(44\) | − | 77.1379i | − | 1.75313i | ||||||
\(45\) | 9.75266 | 0.216726 | ||||||||
\(46\) | 43.2190 | 0.939542 | ||||||||
\(47\) | − | 79.6198i | − | 1.69404i | −0.531563 | − | 0.847019i | \(-0.678395\pi\) | ||
0.531563 | − | 0.847019i | \(-0.321605\pi\) | |||||||
\(48\) | −21.2569 | −0.442853 | ||||||||
\(49\) | 90.7685 | 1.85242 | ||||||||
\(50\) | 42.7623i | 0.855245i | ||||||||
\(51\) | −55.4260 | −1.08678 | ||||||||
\(52\) | 67.5384i | 1.29882i | ||||||||
\(53\) | 86.2911 | 1.62813 | 0.814067 | − | 0.580770i | \(-0.197249\pi\) | ||||
0.814067 | + | 0.580770i | \(0.197249\pi\) | |||||||
\(54\) | − | 15.3966i | − | 0.285122i | ||||||
\(55\) | 52.4638i | 0.953887i | ||||||||
\(56\) | 27.3169i | 0.487802i | ||||||||
\(57\) | 25.6154 | 0.449393 | ||||||||
\(58\) | 37.9096i | 0.653613i | ||||||||
\(59\) | −18.5829 | + | 55.9971i | −0.314965 | + | 0.949103i | ||||
\(60\) | −26.9136 | −0.448561 | ||||||||
\(61\) | − | 92.8151i | − | 1.52156i | −0.649010 | − | 0.760780i | \(-0.724817\pi\) | ||
0.649010 | − | 0.760780i | \(-0.275183\pi\) | |||||||
\(62\) | −80.2651 | −1.29460 | ||||||||
\(63\) | 35.4671 | 0.562970 | ||||||||
\(64\) | 86.0471 | 1.34449 | ||||||||
\(65\) | − | 45.9349i | − | 0.706691i | ||||||
\(66\) | 82.8249 | 1.25492 | ||||||||
\(67\) | 88.8299i | 1.32582i | 0.748700 | + | 0.662909i | \(0.230679\pi\) | ||||
−0.748700 | + | 0.662909i | \(0.769321\pi\) | |||||||
\(68\) | 152.955 | 2.24933 | ||||||||
\(69\) | 25.2634i | 0.366137i | ||||||||
\(70\) | − | 113.880i | − | 1.62686i | ||||||
\(71\) | −13.4604 | −0.189583 | −0.0947916 | − | 0.995497i | \(-0.530218\pi\) | ||||
−0.0947916 | + | 0.995497i | \(0.530218\pi\) | |||||||
\(72\) | 6.93183i | 0.0962754i | ||||||||
\(73\) | 42.9424i | 0.588252i | 0.955767 | + | 0.294126i | \(0.0950285\pi\) | ||||
−0.955767 | + | 0.294126i | \(0.904972\pi\) | |||||||
\(74\) | 77.6729 | 1.04963 | ||||||||
\(75\) | −24.9965 | −0.333286 | ||||||||
\(76\) | −70.6888 | −0.930116 | ||||||||
\(77\) | 190.793i | 2.47783i | ||||||||
\(78\) | −72.5177 | −0.929714 | ||||||||
\(79\) | −1.74748 | −0.0221201 | −0.0110600 | − | 0.999939i | \(-0.503521\pi\) | ||||
−0.0110600 | + | 0.999939i | \(0.503521\pi\) | |||||||
\(80\) | −39.8972 | −0.498715 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 110.599i | 1.34877i | ||||||||
\(83\) | − | 12.9404i | − | 0.155908i | −0.996957 | − | 0.0779542i | \(-0.975161\pi\) | ||
0.996957 | − | 0.0779542i | \(-0.0248388\pi\) | |||||||
\(84\) | −97.8758 | −1.16519 | ||||||||
\(85\) | −104.029 | −1.22387 | ||||||||
\(86\) | 151.504 | 1.76168 | ||||||||
\(87\) | −22.1599 | −0.254711 | ||||||||
\(88\) | −37.2893 | −0.423742 | ||||||||
\(89\) | 69.4234i | 0.780038i | 0.920807 | + | 0.390019i | \(0.127532\pi\) | ||||
−0.920807 | + | 0.390019i | \(0.872468\pi\) | |||||||
\(90\) | − | 28.8979i | − | 0.321087i | ||||||
\(91\) | − | 167.050i | − | 1.83571i | ||||||
\(92\) | − | 69.7175i | − | 0.757799i | ||||||
\(93\) | − | 46.9186i | − | 0.504501i | ||||||
\(94\) | −235.919 | −2.50978 | ||||||||
\(95\) | 48.0776 | 0.506080 | ||||||||
\(96\) | 78.9942i | 0.822857i | ||||||||
\(97\) | 101.219i | 1.04350i | 0.853099 | + | 0.521748i | \(0.174720\pi\) | ||||
−0.853099 | + | 0.521748i | \(0.825280\pi\) | |||||||
\(98\) | − | 268.954i | − | 2.74443i | ||||||
\(99\) | 48.4149i | 0.489039i | ||||||||
\(100\) | 68.9808 | 0.689808 | ||||||||
\(101\) | − | 20.7851i | − | 0.205793i | −0.994692 | − | 0.102896i | \(-0.967189\pi\) | ||
0.994692 | − | 0.102896i | \(-0.0328110\pi\) | |||||||
\(102\) | 164.231i | 1.61011i | ||||||||
\(103\) | − | 69.7688i | − | 0.677367i | −0.940900 | − | 0.338683i | \(-0.890018\pi\) | ||
0.940900 | − | 0.338683i | \(-0.109982\pi\) | |||||||
\(104\) | 32.6488 | 0.313931 | ||||||||
\(105\) | 66.5683 | 0.633984 | ||||||||
\(106\) | − | 255.687i | − | 2.41214i | ||||||
\(107\) | −80.8718 | −0.755811 | −0.377906 | − | 0.925844i | \(-0.623356\pi\) | ||||
−0.377906 | + | 0.925844i | \(0.623356\pi\) | |||||||
\(108\) | −24.8366 | −0.229968 | ||||||||
\(109\) | − | 191.875i | − | 1.76032i | −0.474676 | − | 0.880160i | \(-0.657435\pi\) | ||
0.474676 | − | 0.880160i | \(-0.342565\pi\) | |||||||
\(110\) | 155.454 | 1.41322 | ||||||||
\(111\) | 45.4033i | 0.409039i | ||||||||
\(112\) | −145.092 | −1.29547 | ||||||||
\(113\) | 83.6727i | 0.740467i | 0.928939 | + | 0.370233i | \(0.120722\pi\) | ||||
−0.928939 | + | 0.370233i | \(0.879278\pi\) | |||||||
\(114\) | − | 75.9003i | − | 0.665792i | ||||||
\(115\) | 47.4170i | 0.412322i | ||||||||
\(116\) | 61.1528 | 0.527179 | ||||||||
\(117\) | − | 42.3899i | − | 0.362307i | ||||||
\(118\) | 165.924 | + | 55.0625i | 1.40613 | + | 0.466632i | ||||
\(119\) | −378.318 | −3.17914 | ||||||||
\(120\) | 13.0104i | 0.108420i | ||||||||
\(121\) | −139.445 | −1.15243 | ||||||||
\(122\) | −275.018 | −2.25425 | ||||||||
\(123\) | −64.6500 | −0.525610 | ||||||||
\(124\) | 129.477i | 1.04417i | ||||||||
\(125\) | −128.188 | −1.02551 | ||||||||
\(126\) | − | 105.092i | − | 0.834061i | ||||||
\(127\) | 67.6520 | 0.532693 | 0.266347 | − | 0.963877i | \(-0.414183\pi\) | ||||
0.266347 | + | 0.963877i | \(0.414183\pi\) | |||||||
\(128\) | − | 72.5345i | − | 0.566676i | ||||||
\(129\) | 88.5612i | 0.686521i | ||||||||
\(130\) | −136.109 | −1.04699 | ||||||||
\(131\) | − | 97.5354i | − | 0.744545i | −0.928123 | − | 0.372273i | \(-0.878579\pi\) | ||
0.928123 | − | 0.372273i | \(-0.121421\pi\) | |||||||
\(132\) | − | 133.607i | − | 1.01217i | ||||||
\(133\) | 174.842 | 1.31460 | ||||||||
\(134\) | 263.209 | 1.96425 | ||||||||
\(135\) | 16.8921 | 0.125127 | ||||||||
\(136\) | − | 73.9400i | − | 0.543676i | ||||||
\(137\) | −13.3827 | −0.0976840 | −0.0488420 | − | 0.998807i | \(-0.515553\pi\) | ||||
−0.0488420 | + | 0.998807i | \(0.515553\pi\) | |||||||
\(138\) | 74.8574 | 0.542445 | ||||||||
\(139\) | 78.8449 | 0.567230 | 0.283615 | − | 0.958938i | \(-0.408466\pi\) | ||||
0.283615 | + | 0.958938i | \(0.408466\pi\) | |||||||
\(140\) | −183.703 | −1.31217 | ||||||||
\(141\) | − | 137.905i | − | 0.978053i | ||||||
\(142\) | 39.8842i | 0.280874i | ||||||||
\(143\) | 228.034 | 1.59464 | ||||||||
\(144\) | −36.8181 | −0.255681 | ||||||||
\(145\) | −41.5919 | −0.286840 | ||||||||
\(146\) | 127.241 | 0.871516 | ||||||||
\(147\) | 157.216 | 1.06949 | ||||||||
\(148\) | − | 125.296i | − | 0.846594i | ||||||
\(149\) | 3.94936i | 0.0265058i | 0.999912 | + | 0.0132529i | \(0.00421865\pi\) | ||||
−0.999912 | + | 0.0132529i | \(0.995781\pi\) | |||||||
\(150\) | 74.0664i | 0.493776i | ||||||||
\(151\) | 57.9839i | 0.383999i | 0.981395 | + | 0.192000i | \(0.0614973\pi\) | ||||
−0.981395 | + | 0.192000i | \(0.938503\pi\) | |||||||
\(152\) | 34.1718i | 0.224814i | ||||||||
\(153\) | −96.0006 | −0.627455 | ||||||||
\(154\) | 565.334 | 3.67100 | ||||||||
\(155\) | − | 88.0615i | − | 0.568139i | ||||||
\(156\) | 116.980i | 0.749872i | ||||||||
\(157\) | 115.827i | 0.737751i | 0.929479 | + | 0.368876i | \(0.120257\pi\) | ||||
−0.929479 | + | 0.368876i | \(0.879743\pi\) | |||||||
\(158\) | 5.17792i | 0.0327717i | ||||||||
\(159\) | 149.461 | 0.940004 | ||||||||
\(160\) | 148.264i | 0.926652i | ||||||||
\(161\) | 172.439i | 1.07105i | ||||||||
\(162\) | − | 26.6677i | − | 0.164615i | ||||||
\(163\) | −249.112 | −1.52830 | −0.764149 | − | 0.645040i | \(-0.776841\pi\) | ||||
−0.764149 | + | 0.645040i | \(0.776841\pi\) | |||||||
\(164\) | 178.410 | 1.08786 | ||||||||
\(165\) | 90.8700i | 0.550727i | ||||||||
\(166\) | −38.3433 | −0.230984 | ||||||||
\(167\) | 50.4157 | 0.301890 | 0.150945 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150945 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(168\) | 47.3143i | 0.281633i | ||||||||
\(169\) | −30.6558 | −0.181395 | ||||||||
\(170\) | 308.246i | 1.81321i | ||||||||
\(171\) | 44.3672 | 0.259457 | ||||||||
\(172\) | − | 244.395i | − | 1.42090i | ||||||
\(173\) | − | 13.4190i | − | 0.0775665i | −0.999248 | − | 0.0387832i | \(-0.987652\pi\) | ||
0.999248 | − | 0.0387832i | \(-0.0123482\pi\) | |||||||
\(174\) | 65.6613i | 0.377364i | ||||||||
\(175\) | −170.617 | −0.974956 | ||||||||
\(176\) | − | 198.060i | − | 1.12534i | ||||||
\(177\) | −32.1866 | + | 96.9898i | −0.181845 | + | 0.547965i | ||||
\(178\) | 205.707 | 1.15565 | ||||||||
\(179\) | 103.685i | 0.579247i | 0.957141 | + | 0.289623i | \(0.0935300\pi\) | ||||
−0.957141 | + | 0.289623i | \(0.906470\pi\) | |||||||
\(180\) | −46.6158 | −0.258977 | ||||||||
\(181\) | 120.947 | 0.668214 | 0.334107 | − | 0.942535i | \(-0.391565\pi\) | ||||
0.334107 | + | 0.942535i | \(0.391565\pi\) | |||||||
\(182\) | −494.980 | −2.71967 | ||||||||
\(183\) | − | 160.760i | − | 0.878473i | ||||||
\(184\) | −33.7022 | −0.183164 | ||||||||
\(185\) | 85.2175i | 0.460635i | ||||||||
\(186\) | −139.023 | −0.747436 | ||||||||
\(187\) | − | 516.429i | − | 2.76165i | ||||||
\(188\) | 380.567i | 2.02429i | ||||||||
\(189\) | 61.4309 | 0.325031 | ||||||||
\(190\) | − | 142.457i | − | 0.749776i | ||||||
\(191\) | − | 226.707i | − | 1.18695i | −0.804854 | − | 0.593473i | \(-0.797756\pi\) | ||
0.804854 | − | 0.593473i | \(-0.202244\pi\) | |||||||
\(192\) | 149.038 | 0.776239 | ||||||||
\(193\) | 145.379 | 0.753261 | 0.376630 | − | 0.926364i | \(-0.377083\pi\) | ||||
0.376630 | + | 0.926364i | \(0.377083\pi\) | |||||||
\(194\) | 299.920 | 1.54598 | ||||||||
\(195\) | − | 79.5616i | − | 0.408008i | ||||||
\(196\) | −433.856 | −2.21355 | ||||||||
\(197\) | 95.2626 | 0.483567 | 0.241783 | − | 0.970330i | \(-0.422268\pi\) | ||||
0.241783 | + | 0.970330i | \(0.422268\pi\) | |||||||
\(198\) | 143.457 | 0.724530 | ||||||||
\(199\) | 119.091 | 0.598447 | 0.299224 | − | 0.954183i | \(-0.403272\pi\) | ||||
0.299224 | + | 0.954183i | \(0.403272\pi\) | |||||||
\(200\) | − | 33.3461i | − | 0.166731i | ||||||
\(201\) | 153.858i | 0.765462i | ||||||||
\(202\) | −61.5877 | −0.304890 | ||||||||
\(203\) | −151.255 | −0.745101 | ||||||||
\(204\) | 264.925 | 1.29865 | ||||||||
\(205\) | −121.342 | −0.591911 | ||||||||
\(206\) | −206.730 | −1.00354 | ||||||||
\(207\) | 43.7576i | 0.211389i | ||||||||
\(208\) | 173.413i | 0.833715i | ||||||||
\(209\) | 238.670i | 1.14196i | ||||||||
\(210\) | − | 197.247i | − | 0.939270i | ||||||
\(211\) | − | 129.974i | − | 0.615990i | −0.951388 | − | 0.307995i | \(-0.900342\pi\) | ||
0.951388 | − | 0.307995i | \(-0.0996581\pi\) | |||||||
\(212\) | −412.455 | −1.94554 | ||||||||
\(213\) | −23.3141 | −0.109456 | ||||||||
\(214\) | 239.629i | 1.11976i | ||||||||
\(215\) | 166.221i | 0.773119i | ||||||||
\(216\) | 12.0063i | 0.0555846i | ||||||||
\(217\) | − | 320.250i | − | 1.47581i | ||||||
\(218\) | −568.540 | −2.60798 | ||||||||
\(219\) | 74.3784i | 0.339627i | ||||||||
\(220\) | − | 250.767i | − | 1.13985i | ||||||
\(221\) | 452.161i | 2.04598i | ||||||||
\(222\) | 134.533 | 0.606006 | ||||||||
\(223\) | −21.6836 | −0.0972360 | −0.0486180 | − | 0.998817i | \(-0.515482\pi\) | ||||
−0.0486180 | + | 0.998817i | \(0.515482\pi\) | |||||||
\(224\) | 539.187i | 2.40709i | ||||||||
\(225\) | −43.2952 | −0.192423 | ||||||||
\(226\) | 247.928 | 1.09703 | ||||||||
\(227\) | − | 237.429i | − | 1.04594i | −0.852350 | − | 0.522972i | \(-0.824823\pi\) | ||
0.852350 | − | 0.522972i | \(-0.175177\pi\) | |||||||
\(228\) | −122.437 | −0.537003 | ||||||||
\(229\) | − | 203.447i | − | 0.888415i | −0.895924 | − | 0.444208i | \(-0.853485\pi\) | ||
0.895924 | − | 0.444208i | \(-0.146515\pi\) | |||||||
\(230\) | 140.500 | 0.610869 | ||||||||
\(231\) | 330.463i | 1.43058i | ||||||||
\(232\) | − | 29.5620i | − | 0.127422i | ||||||
\(233\) | − | 328.561i | − | 1.41013i | −0.709142 | − | 0.705066i | \(-0.750918\pi\) | ||
0.709142 | − | 0.705066i | \(-0.249082\pi\) | |||||||
\(234\) | −125.604 | −0.536771 | ||||||||
\(235\) | − | 258.835i | − | 1.10143i | ||||||
\(236\) | 88.8226 | − | 267.655i | 0.376367 | − | 1.13413i | ||||
\(237\) | −3.02673 | −0.0127710 | ||||||||
\(238\) | 1120.98i | 4.71002i | ||||||||
\(239\) | 206.816 | 0.865339 | 0.432669 | − | 0.901553i | \(-0.357572\pi\) | ||||
0.432669 | + | 0.901553i | \(0.357572\pi\) | |||||||
\(240\) | −69.1039 | −0.287933 | ||||||||
\(241\) | −138.114 | −0.573085 | −0.286543 | − | 0.958068i | \(-0.592506\pi\) | ||||
−0.286543 | + | 0.958068i | \(0.592506\pi\) | |||||||
\(242\) | 413.185i | 1.70737i | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 443.638i | 1.81819i | ||||||||
\(245\) | 295.078 | 1.20440 | ||||||||
\(246\) | 191.563i | 0.778710i | ||||||||
\(247\) | − | 208.969i | − | 0.846028i | ||||||
\(248\) | 62.5909 | 0.252382 | ||||||||
\(249\) | − | 22.4134i | − | 0.0900137i | ||||||
\(250\) | 379.831i | 1.51932i | ||||||||
\(251\) | 439.750 | 1.75199 | 0.875996 | − | 0.482319i | \(-0.160205\pi\) | ||||
0.875996 | + | 0.482319i | \(0.160205\pi\) | |||||||
\(252\) | −169.526 | −0.672722 | ||||||||
\(253\) | −235.391 | −0.930399 | ||||||||
\(254\) | − | 200.458i | − | 0.789204i | ||||||
\(255\) | −180.184 | −0.706602 | ||||||||
\(256\) | 129.263 | 0.504936 | ||||||||
\(257\) | 258.065 | 1.00414 | 0.502072 | − | 0.864826i | \(-0.332571\pi\) | ||||
0.502072 | + | 0.864826i | \(0.332571\pi\) | |||||||
\(258\) | 262.413 | 1.01711 | ||||||||
\(259\) | 309.907i | 1.19655i | ||||||||
\(260\) | 219.560i | 0.844461i | ||||||||
\(261\) | −38.3820 | −0.147057 | ||||||||
\(262\) | −289.005 | −1.10307 | ||||||||
\(263\) | −238.300 | −0.906084 | −0.453042 | − | 0.891489i | \(-0.649661\pi\) | ||||
−0.453042 | + | 0.891489i | \(0.649661\pi\) | |||||||
\(264\) | −64.5870 | −0.244648 | ||||||||
\(265\) | 280.523 | 1.05858 | ||||||||
\(266\) | − | 518.069i | − | 1.94763i | ||||||
\(267\) | 120.245i | 0.450355i | ||||||||
\(268\) | − | 424.589i | − | 1.58429i | ||||||
\(269\) | − | 320.536i | − | 1.19158i | −0.803138 | − | 0.595792i | \(-0.796838\pi\) | ||
0.803138 | − | 0.595792i | \(-0.203162\pi\) | |||||||
\(270\) | − | 50.0526i | − | 0.185380i | ||||||
\(271\) | −56.4111 | −0.208159 | −0.104079 | − | 0.994569i | \(-0.533190\pi\) | ||||
−0.104079 | + | 0.994569i | \(0.533190\pi\) | |||||||
\(272\) | 392.729 | 1.44386 | ||||||||
\(273\) | − | 289.339i | − | 1.05985i | ||||||
\(274\) | 39.6539i | 0.144722i | ||||||||
\(275\) | − | 232.904i | − | 0.846922i | ||||||
\(276\) | − | 120.754i | − | 0.437515i | ||||||
\(277\) | −238.376 | −0.860562 | −0.430281 | − | 0.902695i | \(-0.641585\pi\) | ||||
−0.430281 | + | 0.902695i | \(0.641585\pi\) | |||||||
\(278\) | − | 233.623i | − | 0.840372i | ||||||
\(279\) | − | 81.2653i | − | 0.291274i | ||||||
\(280\) | 88.8042i | 0.317158i | ||||||||
\(281\) | −161.899 | −0.576154 | −0.288077 | − | 0.957607i | \(-0.593016\pi\) | ||||
−0.288077 | + | 0.957607i | \(0.593016\pi\) | |||||||
\(282\) | −408.624 | −1.44902 | ||||||||
\(283\) | − | 411.702i | − | 1.45478i | −0.686226 | − | 0.727388i | \(-0.740734\pi\) | ||
0.686226 | − | 0.727388i | \(-0.259266\pi\) | |||||||
\(284\) | 64.3381 | 0.226542 | ||||||||
\(285\) | 83.2728 | 0.292185 | ||||||||
\(286\) | − | 675.680i | − | 2.36252i | ||||||
\(287\) | −441.278 | −1.53756 | ||||||||
\(288\) | 136.822i | 0.475077i | ||||||||
\(289\) | 735.012 | 2.54329 | ||||||||
\(290\) | 123.240i | 0.424965i | ||||||||
\(291\) | 175.317i | 0.602463i | ||||||||
\(292\) | − | 205.256i | − | 0.702932i | ||||||
\(293\) | 14.3590 | 0.0490069 | 0.0245034 | − | 0.999700i | \(-0.492200\pi\) | ||||
0.0245034 | + | 0.999700i | \(0.492200\pi\) | |||||||
\(294\) | − | 465.842i | − | 1.58450i | ||||||
\(295\) | −60.4110 | + | 182.040i | −0.204783 | + | 0.617086i | ||||
\(296\) | −60.5695 | −0.204627 | ||||||||
\(297\) | 83.8570i | 0.282347i | ||||||||
\(298\) | 11.7023 | 0.0392693 | ||||||||
\(299\) | 206.098 | 0.689290 | ||||||||
\(300\) | 119.478 | 0.398261 | ||||||||
\(301\) | 604.488i | 2.00826i | ||||||||
\(302\) | 171.811 | 0.568909 | ||||||||
\(303\) | − | 36.0008i | − | 0.118815i | ||||||
\(304\) | −181.502 | −0.597045 | ||||||||
\(305\) | − | 301.732i | − | 0.989284i | ||||||
\(306\) | 284.457i | 0.929597i | ||||||||
\(307\) | −200.292 | −0.652415 | −0.326208 | − | 0.945298i | \(-0.605771\pi\) | ||||
−0.326208 | + | 0.945298i | \(0.605771\pi\) | |||||||
\(308\) | − | 911.953i | − | 2.96089i | ||||||
\(309\) | − | 120.843i | − | 0.391078i | ||||||
\(310\) | −260.933 | −0.841718 | ||||||||
\(311\) | −175.394 | −0.563969 | −0.281984 | − | 0.959419i | \(-0.590993\pi\) | ||||
−0.281984 | + | 0.959419i | \(0.590993\pi\) | |||||||
\(312\) | 56.5494 | 0.181248 | ||||||||
\(313\) | − | 47.0884i | − | 0.150442i | −0.997167 | − | 0.0752210i | \(-0.976034\pi\) | ||
0.997167 | − | 0.0752210i | \(-0.0239662\pi\) | |||||||
\(314\) | 343.204 | 1.09301 | ||||||||
\(315\) | 115.300 | 0.366031 | ||||||||
\(316\) | 8.35263 | 0.0264324 | ||||||||
\(317\) | 204.197 | 0.644155 | 0.322077 | − | 0.946713i | \(-0.395619\pi\) | ||||
0.322077 | + | 0.946713i | \(0.395619\pi\) | |||||||
\(318\) | − | 442.863i | − | 1.39265i | ||||||
\(319\) | − | 206.473i | − | 0.647252i | ||||||
\(320\) | 279.730 | 0.874155 | ||||||||
\(321\) | −140.074 | −0.436368 | ||||||||
\(322\) | 510.951 | 1.58680 | ||||||||
\(323\) | −473.253 | −1.46518 | ||||||||
\(324\) | −43.0182 | −0.132772 | ||||||||
\(325\) | 203.920i | 0.627445i | ||||||||
\(326\) | 738.138i | 2.26423i | ||||||||
\(327\) | − | 332.337i | − | 1.01632i | ||||||
\(328\) | − | 86.2452i | − | 0.262943i | ||||||
\(329\) | − | 941.295i | − | 2.86108i | ||||||
\(330\) | 269.254 | 0.815922 | ||||||||
\(331\) | −540.983 | −1.63439 | −0.817195 | − | 0.576361i | \(-0.804472\pi\) | ||||
−0.817195 | + | 0.576361i | \(0.804472\pi\) | |||||||
\(332\) | 61.8525i | 0.186303i | ||||||||
\(333\) | 78.6409i | 0.236159i | ||||||||
\(334\) | − | 149.385i | − | 0.447261i | ||||||
\(335\) | 288.776i | 0.862018i | ||||||||
\(336\) | −251.307 | −0.747939 | ||||||||
\(337\) | 616.965i | 1.83076i | 0.402593 | + | 0.915379i | \(0.368109\pi\) | ||||
−0.402593 | + | 0.915379i | \(0.631891\pi\) | |||||||
\(338\) | 90.8355i | 0.268744i | ||||||||
\(339\) | 144.925i | 0.427509i | ||||||||
\(340\) | 497.238 | 1.46247 | ||||||||
\(341\) | 437.161 | 1.28200 | ||||||||
\(342\) | − | 131.463i | − | 0.384395i | ||||||
\(343\) | 493.803 | 1.43966 | ||||||||
\(344\) | −118.143 | −0.343440 | ||||||||
\(345\) | 82.1286i | 0.238054i | ||||||||
\(346\) | −39.7615 | −0.114918 | ||||||||
\(347\) | 47.1982i | 0.136018i | 0.997685 | + | 0.0680090i | \(0.0216647\pi\) | ||||
−0.997685 | + | 0.0680090i | \(0.978335\pi\) | |||||||
\(348\) | 105.920 | 0.304367 | ||||||||
\(349\) | 36.9208i | 0.105790i | 0.998600 | + | 0.0528952i | \(0.0168449\pi\) | ||||
−0.998600 | + | 0.0528952i | \(0.983155\pi\) | |||||||
\(350\) | 505.551i | 1.44443i | ||||||||
\(351\) | − | 73.4214i | − | 0.209178i | ||||||
\(352\) | −736.025 | −2.09098 | ||||||||
\(353\) | − | 83.2316i | − | 0.235784i | −0.993026 | − | 0.117892i | \(-0.962386\pi\) | ||
0.993026 | − | 0.117892i | \(-0.0376136\pi\) | |||||||
\(354\) | 287.388 | + | 95.3711i | 0.811830 | + | 0.269410i | ||||
\(355\) | −43.7583 | −0.123263 | ||||||||
\(356\) | − | 331.830i | − | 0.932107i | ||||||
\(357\) | −655.266 | −1.83548 | ||||||||
\(358\) | 307.227 | 0.858175 | ||||||||
\(359\) | 505.228 | 1.40732 | 0.703660 | − | 0.710537i | \(-0.251548\pi\) | ||||
0.703660 | + | 0.710537i | \(0.251548\pi\) | |||||||
\(360\) | 22.5346i | 0.0625961i | ||||||||
\(361\) | −142.284 | −0.394137 | ||||||||
\(362\) | − | 358.374i | − | 0.989983i | ||||||
\(363\) | −241.525 | −0.665359 | ||||||||
\(364\) | 798.464i | 2.19358i | ||||||||
\(365\) | 139.601i | 0.382468i | ||||||||
\(366\) | −476.345 | −1.30149 | ||||||||
\(367\) | − | 49.1101i | − | 0.133815i | −0.997759 | − | 0.0669075i | \(-0.978687\pi\) | ||
0.997759 | − | 0.0669075i | \(-0.0213132\pi\) | |||||||
\(368\) | − | 179.008i | − | 0.486434i | ||||||
\(369\) | −111.977 | −0.303461 | ||||||||
\(370\) | 252.506 | 0.682448 | ||||||||
\(371\) | 1020.17 | 2.74977 | ||||||||
\(372\) | 224.261i | 0.602853i | ||||||||
\(373\) | −583.281 | −1.56376 | −0.781879 | − | 0.623431i | \(-0.785738\pi\) | ||||
−0.781879 | + | 0.623431i | \(0.785738\pi\) | |||||||
\(374\) | −1530.22 | −4.09149 | ||||||||
\(375\) | −222.028 | −0.592076 | ||||||||
\(376\) | 183.970 | 0.489283 | ||||||||
\(377\) | 180.779i | 0.479519i | ||||||||
\(378\) | − | 182.024i | − | 0.481545i | ||||||
\(379\) | 161.645 | 0.426504 | 0.213252 | − | 0.976997i | \(-0.431594\pi\) | ||||
0.213252 | + | 0.976997i | \(0.431594\pi\) | |||||||
\(380\) | −229.801 | −0.604740 | ||||||||
\(381\) | 117.177 | 0.307550 | ||||||||
\(382\) | −671.749 | −1.75851 | ||||||||
\(383\) | −167.234 | −0.436642 | −0.218321 | − | 0.975877i | \(-0.570058\pi\) | ||||
−0.218321 | + | 0.975877i | \(0.570058\pi\) | |||||||
\(384\) | − | 125.633i | − | 0.327170i | ||||||
\(385\) | 620.247i | 1.61103i | ||||||||
\(386\) | − | 430.770i | − | 1.11598i | ||||||
\(387\) | 153.392i | 0.396363i | ||||||||
\(388\) | − | 483.808i | − | 1.24693i | ||||||
\(389\) | −327.884 | −0.842889 | −0.421445 | − | 0.906854i | \(-0.638477\pi\) | ||||
−0.421445 | + | 0.906854i | \(0.638477\pi\) | |||||||
\(390\) | −235.747 | −0.604479 | ||||||||
\(391\) | − | 466.750i | − | 1.19373i | ||||||
\(392\) | 209.731i | 0.535027i | ||||||||
\(393\) | − | 168.936i | − | 0.429863i | ||||||
\(394\) | − | 282.270i | − | 0.716421i | ||||||
\(395\) | −5.68088 | −0.0143820 | ||||||||
\(396\) | − | 231.414i | − | 0.584378i | ||||||
\(397\) | 691.182i | 1.74101i | 0.492156 | + | 0.870507i | \(0.336209\pi\) | ||||
−0.492156 | + | 0.870507i | \(0.663791\pi\) | |||||||
\(398\) | − | 352.875i | − | 0.886621i | ||||||
\(399\) | 302.835 | 0.758985 | ||||||||
\(400\) | 177.116 | 0.442791 | ||||||||
\(401\) | − | 102.992i | − | 0.256838i | −0.991720 | − | 0.128419i | \(-0.959010\pi\) | ||
0.991720 | − | 0.128419i | \(-0.0409903\pi\) | |||||||
\(402\) | 455.892 | 1.13406 | ||||||||
\(403\) | −382.759 | −0.949774 | ||||||||
\(404\) | 99.3485i | 0.245912i | ||||||||
\(405\) | 29.2580 | 0.0722420 | ||||||||
\(406\) | 448.181i | 1.10389i | ||||||||
\(407\) | −423.043 | −1.03942 | ||||||||
\(408\) | − | 128.068i | − | 0.313892i | ||||||
\(409\) | 720.907i | 1.76261i | 0.472549 | + | 0.881304i | \(0.343334\pi\) | ||||
−0.472549 | + | 0.881304i | \(0.656666\pi\) | |||||||
\(410\) | 359.544i | 0.876937i | ||||||||
\(411\) | −23.1795 | −0.0563979 | ||||||||
\(412\) | 333.481i | 0.809420i | ||||||||
\(413\) | −219.694 | + | 662.019i | −0.531947 | + | 1.60295i | ||||
\(414\) | 129.657 | 0.313181 | ||||||||
\(415\) | − | 42.0678i | − | 0.101368i | ||||||
\(416\) | 644.430 | 1.54911 | ||||||||
\(417\) | 136.563 | 0.327490 | ||||||||
\(418\) | 707.198 | 1.69186 | ||||||||
\(419\) | 642.761i | 1.53404i | 0.641626 | + | 0.767018i | \(0.278260\pi\) | ||||
−0.641626 | + | 0.767018i | \(0.721740\pi\) | |||||||
\(420\) | −318.183 | −0.757579 | ||||||||
\(421\) | − | 110.137i | − | 0.261607i | −0.991408 | − | 0.130804i | \(-0.958244\pi\) | ||
0.991408 | − | 0.130804i | \(-0.0417557\pi\) | |||||||
\(422\) | −385.122 | −0.912612 | ||||||||
\(423\) | − | 238.859i | − | 0.564679i | ||||||
\(424\) | 199.385i | 0.470248i | ||||||||
\(425\) | 461.818 | 1.08663 | ||||||||
\(426\) | 69.0814i | 0.162163i | ||||||||
\(427\) | − | 1097.29i | − | 2.56978i | ||||||
\(428\) | 386.551 | 0.903157 | ||||||||
\(429\) | 394.966 | 0.920666 | ||||||||
\(430\) | 492.524 | 1.14540 | ||||||||
\(431\) | 209.550i | 0.486194i | 0.970002 | + | 0.243097i | \(0.0781633\pi\) | ||||
−0.970002 | + | 0.243097i | \(0.921837\pi\) | |||||||
\(432\) | −63.7708 | −0.147618 | ||||||||
\(433\) | −24.0985 | −0.0556548 | −0.0278274 | − | 0.999613i | \(-0.508859\pi\) | ||||
−0.0278274 | + | 0.999613i | \(0.508859\pi\) | |||||||
\(434\) | −948.923 | −2.18646 | ||||||||
\(435\) | −72.0392 | −0.165607 | ||||||||
\(436\) | 917.124i | 2.10350i | ||||||||
\(437\) | 215.711i | 0.493618i | ||||||||
\(438\) | 220.389 | 0.503170 | ||||||||
\(439\) | −552.406 | −1.25833 | −0.629164 | − | 0.777273i | \(-0.716603\pi\) | ||||
−0.629164 | + | 0.777273i | \(0.716603\pi\) | |||||||
\(440\) | −121.223 | −0.275508 | ||||||||
\(441\) | 272.306 | 0.617473 | ||||||||
\(442\) | 1339.79 | 3.03119 | ||||||||
\(443\) | − | 406.654i | − | 0.917955i | −0.888448 | − | 0.458977i | \(-0.848216\pi\) | ||
0.888448 | − | 0.458977i | \(-0.151784\pi\) | |||||||
\(444\) | − | 217.019i | − | 0.488781i | ||||||
\(445\) | 225.688i | 0.507163i | ||||||||
\(446\) | 64.2502i | 0.144059i | ||||||||
\(447\) | 6.84050i | 0.0153031i | ||||||||
\(448\) | 1017.28 | 2.27072 | ||||||||
\(449\) | −107.442 | −0.239292 | −0.119646 | − | 0.992817i | \(-0.538176\pi\) | ||||
−0.119646 | + | 0.992817i | \(0.538176\pi\) | |||||||
\(450\) | 128.287i | 0.285082i | ||||||||
\(451\) | − | 602.373i | − | 1.33564i | ||||||
\(452\) | − | 399.939i | − | 0.884821i | ||||||
\(453\) | 100.431i | 0.221702i | ||||||||
\(454\) | −703.521 | −1.54961 | ||||||||
\(455\) | − | 543.060i | − | 1.19354i | ||||||
\(456\) | 59.1872i | 0.129797i | ||||||||
\(457\) | − | 145.963i | − | 0.319393i | −0.987166 | − | 0.159697i | \(-0.948948\pi\) | ||
0.987166 | − | 0.159697i | \(-0.0510516\pi\) | |||||||
\(458\) | −602.829 | −1.31622 | ||||||||
\(459\) | −166.278 | −0.362261 | ||||||||
\(460\) | − | 226.644i | − | 0.492704i | ||||||
\(461\) | −194.199 | −0.421255 | −0.210628 | − | 0.977566i | \(-0.567551\pi\) | ||||
−0.210628 | + | 0.977566i | \(0.567551\pi\) | |||||||
\(462\) | 979.186 | 2.11945 | ||||||||
\(463\) | 40.1621i | 0.0867433i | 0.999059 | + | 0.0433716i | \(0.0138100\pi\) | ||||
−0.999059 | + | 0.0433716i | \(0.986190\pi\) | |||||||
\(464\) | 157.017 | 0.338399 | ||||||||
\(465\) | − | 152.527i | − | 0.328015i | ||||||
\(466\) | −973.549 | −2.08916 | ||||||||
\(467\) | 316.774i | 0.678316i | 0.940729 | + | 0.339158i | \(0.110142\pi\) | ||||
−0.940729 | + | 0.339158i | \(0.889858\pi\) | |||||||
\(468\) | 202.615i | 0.432939i | ||||||||
\(469\) | 1050.18i | 2.23919i | ||||||||
\(470\) | −766.947 | −1.63180 | ||||||||
\(471\) | 200.618i | 0.425941i | ||||||||
\(472\) | −129.387 | − | 42.9379i | −0.274126 | − | 0.0909701i | ||||
\(473\) | −825.164 | −1.74453 | ||||||||
\(474\) | 8.96843i | 0.0189207i | ||||||||
\(475\) | −213.432 | −0.449330 | ||||||||
\(476\) | 1808.29 | 3.79892 | ||||||||
\(477\) | 258.873 | 0.542712 | ||||||||
\(478\) | − | 612.811i | − | 1.28203i | ||||||
\(479\) | 124.453 | 0.259818 | 0.129909 | − | 0.991526i | \(-0.458532\pi\) | ||||
0.129909 | + | 0.991526i | \(0.458532\pi\) | |||||||
\(480\) | 256.801i | 0.535003i | ||||||||
\(481\) | 370.397 | 0.770057 | ||||||||
\(482\) | 409.240i | 0.849047i | ||||||||
\(483\) | 298.674i | 0.618372i | ||||||||
\(484\) | 666.518 | 1.37710 | ||||||||
\(485\) | 329.052i | 0.678458i | ||||||||
\(486\) | − | 46.1897i | − | 0.0950406i | ||||||
\(487\) | 97.3968 | 0.199993 | 0.0999967 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999967 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(488\) | 214.460 | 0.439466 | ||||||||
\(489\) | −431.475 | −0.882363 | ||||||||
\(490\) | − | 874.339i | − | 1.78436i | ||||||
\(491\) | 548.845 | 1.11781 | 0.558905 | − | 0.829231i | \(-0.311221\pi\) | ||||
0.558905 | + | 0.829231i | \(0.311221\pi\) | |||||||
\(492\) | 309.014 | 0.628078 | ||||||||
\(493\) | 409.410 | 0.830447 | ||||||||
\(494\) | −619.190 | −1.25342 | ||||||||
\(495\) | 157.391i | 0.317962i | ||||||||
\(496\) | 332.448i | 0.670259i | ||||||||
\(497\) | −159.134 | −0.320189 | ||||||||
\(498\) | −66.4126 | −0.133359 | ||||||||
\(499\) | −184.851 | −0.370443 | −0.185221 | − | 0.982697i | \(-0.559300\pi\) | ||||
−0.185221 | + | 0.982697i | \(0.559300\pi\) | |||||||
\(500\) | 612.714 | 1.22543 | ||||||||
\(501\) | 87.3225 | 0.174296 | ||||||||
\(502\) | − | 1303.01i | − | 2.59564i | ||||||
\(503\) | − | 244.747i | − | 0.486574i | −0.969954 | − | 0.243287i | \(-0.921774\pi\) | ||
0.969954 | − | 0.243287i | \(-0.0782256\pi\) | |||||||
\(504\) | 81.9507i | 0.162601i | ||||||||
\(505\) | − | 67.5699i | − | 0.133802i | ||||||
\(506\) | 697.480i | 1.37842i | ||||||||
\(507\) | −53.0975 | −0.104729 | ||||||||
\(508\) | −323.363 | −0.636542 | ||||||||
\(509\) | 66.3400i | 0.130334i | 0.997874 | + | 0.0651670i | \(0.0207580\pi\) | ||||
−0.997874 | + | 0.0651670i | \(0.979242\pi\) | |||||||
\(510\) | 533.897i | 1.04686i | ||||||||
\(511\) | 507.681i | 0.993504i | ||||||||
\(512\) | − | 673.155i | − | 1.31476i | ||||||
\(513\) | 76.8462 | 0.149798 | ||||||||
\(514\) | − | 764.666i | − | 1.48768i | ||||||
\(515\) | − | 226.810i | − | 0.440409i | ||||||
\(516\) | − | 423.305i | − | 0.820358i | ||||||
\(517\) | 1284.93 | 2.48535 | ||||||||
\(518\) | 918.278 | 1.77274 | ||||||||
\(519\) | − | 23.2424i | − | 0.0447830i | ||||||
\(520\) | 106.138 | 0.204111 | ||||||||
\(521\) | −762.537 | −1.46360 | −0.731802 | − | 0.681518i | \(-0.761320\pi\) | ||||
−0.731802 | + | 0.681518i | \(0.761320\pi\) | |||||||
\(522\) | 113.729i | 0.217871i | ||||||||
\(523\) | 402.292 | 0.769201 | 0.384600 | − | 0.923083i | \(-0.374339\pi\) | ||||
0.384600 | + | 0.923083i | \(0.374339\pi\) | |||||||
\(524\) | 466.200i | 0.889694i | ||||||||
\(525\) | −295.518 | −0.562891 | ||||||||
\(526\) | 706.100i | 1.34240i | ||||||||
\(527\) | 866.835i | 1.64485i | ||||||||
\(528\) | − | 343.051i | − | 0.649717i | ||||||
\(529\) | 316.253 | 0.597831 | ||||||||
\(530\) | − | 831.210i | − | 1.56832i | ||||||
\(531\) | −55.7487 | + | 167.991i | −0.104988 | + | 0.316368i | ||||
\(532\) | −835.709 | −1.57088 | ||||||||
\(533\) | 527.411i | 0.989514i | ||||||||
\(534\) | 356.294 | 0.667218 | ||||||||
\(535\) | −262.905 | −0.491411 | ||||||||
\(536\) | −205.251 | −0.382931 | ||||||||
\(537\) | 179.588i | 0.334428i | ||||||||
\(538\) | −949.773 | −1.76538 | ||||||||
\(539\) | 1464.85i | 2.71772i | ||||||||
\(540\) | −80.7409 | −0.149520 | ||||||||
\(541\) | − | 479.860i | − | 0.886987i | −0.896278 | − | 0.443494i | \(-0.853739\pi\) | ||
0.896278 | − | 0.443494i | \(-0.146261\pi\) | |||||||
\(542\) | 167.150i | 0.308395i | ||||||||
\(543\) | 209.486 | 0.385793 | ||||||||
\(544\) | − | 1459.44i | − | 2.68280i | ||||||
\(545\) | − | 623.764i | − | 1.14452i | ||||||
\(546\) | −857.331 | −1.57020 | ||||||||
\(547\) | 670.600 | 1.22596 | 0.612980 | − | 0.790098i | \(-0.289971\pi\) | ||||
0.612980 | + | 0.790098i | \(0.289971\pi\) | |||||||
\(548\) | 63.9667 | 0.116728 | ||||||||
\(549\) | − | 278.445i | − | 0.507186i | ||||||
\(550\) | −690.110 | −1.25475 | ||||||||
\(551\) | −189.211 | −0.343396 | ||||||||
\(552\) | −58.3740 | −0.105750 | ||||||||
\(553\) | −20.6594 | −0.0373588 | ||||||||
\(554\) | 706.324i | 1.27495i | ||||||||
\(555\) | 147.601i | 0.265948i | ||||||||
\(556\) | −376.863 | −0.677812 | ||||||||
\(557\) | 719.857 | 1.29238 | 0.646191 | − | 0.763176i | \(-0.276361\pi\) | ||||
0.646191 | + | 0.763176i | \(0.276361\pi\) | |||||||
\(558\) | −240.795 | −0.431533 | ||||||||
\(559\) | 722.476 | 1.29244 | ||||||||
\(560\) | −471.679 | −0.842284 | ||||||||
\(561\) | − | 894.480i | − | 1.59444i | ||||||
\(562\) | 479.719i | 0.853593i | ||||||||
\(563\) | − | 622.327i | − | 1.10538i | −0.833388 | − | 0.552688i | \(-0.813602\pi\) | ||
0.833388 | − | 0.552688i | \(-0.186398\pi\) | |||||||
\(564\) | 659.161i | 1.16872i | ||||||||
\(565\) | 272.011i | 0.481435i | ||||||||
\(566\) | −1219.90 | −2.15530 | ||||||||
\(567\) | 106.401 | 0.187657 | ||||||||
\(568\) | − | 31.1017i | − | 0.0547566i | ||||||
\(569\) | − | 540.853i | − | 0.950532i | −0.879842 | − | 0.475266i | \(-0.842352\pi\) | ||
0.879842 | − | 0.475266i | \(-0.157648\pi\) | |||||||
\(570\) | − | 246.743i | − | 0.432883i | ||||||
\(571\) | − | 783.357i | − | 1.37190i | −0.727647 | − | 0.685952i | \(-0.759386\pi\) | ||
0.727647 | − | 0.685952i | \(-0.240614\pi\) | |||||||
\(572\) | −1089.96 | −1.90552 | ||||||||
\(573\) | − | 392.668i | − | 0.685284i | ||||||
\(574\) | 1307.54i | 2.27794i | ||||||||
\(575\) | − | 210.499i | − | 0.366085i | ||||||
\(576\) | 258.141 | 0.448162 | ||||||||
\(577\) | −1080.41 | −1.87246 | −0.936229 | − | 0.351390i | \(-0.885709\pi\) | ||||
−0.936229 | + | 0.351390i | \(0.885709\pi\) | |||||||
\(578\) | − | 2177.89i | − | 3.76798i | ||||||
\(579\) | 251.804 | 0.434895 | ||||||||
\(580\) | 198.801 | 0.342760 | ||||||||
\(581\) | − | 152.986i | − | 0.263315i | ||||||
\(582\) | 519.476 | 0.892571 | ||||||||
\(583\) | 1392.59i | 2.38867i | ||||||||
\(584\) | −99.2231 | −0.169903 | ||||||||
\(585\) | − | 137.805i | − | 0.235564i | ||||||
\(586\) | − | 42.5468i | − | 0.0726055i | ||||||
\(587\) | − | 817.508i | − | 1.39269i | −0.717708 | − | 0.696344i | \(-0.754809\pi\) | ||
0.717708 | − | 0.696344i | \(-0.245191\pi\) | |||||||
\(588\) | −751.460 | −1.27799 | ||||||||
\(589\) | − | 400.613i | − | 0.680158i | ||||||
\(590\) | 539.399 | + | 179.002i | 0.914235 | + | 0.303393i | ||||
\(591\) | 165.000 | 0.279187 | ||||||||
\(592\) | − | 321.712i | − | 0.543432i | ||||||
\(593\) | 1049.16 | 1.76924 | 0.884621 | − | 0.466310i | \(-0.154417\pi\) | ||||
0.884621 | + | 0.466310i | \(0.154417\pi\) | |||||||
\(594\) | 248.475 | 0.418307 | ||||||||
\(595\) | −1229.87 | −2.06701 | ||||||||
\(596\) | − | 18.8772i | − | 0.0316731i | ||||||
\(597\) | 206.272 | 0.345514 | ||||||||
\(598\) | − | 610.682i | − | 1.02121i | ||||||
\(599\) | −209.961 | −0.350520 | −0.175260 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175260 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(600\) | − | 57.7571i | − | 0.0962619i | ||||||
\(601\) | 60.2370i | 0.100228i | 0.998744 | + | 0.0501139i | \(0.0159584\pi\) | ||||
−0.998744 | + | 0.0501139i | \(0.984042\pi\) | |||||||
\(602\) | 1791.14 | 2.97532 | ||||||||
\(603\) | 266.490i | 0.441940i | ||||||||
\(604\) | − | 277.152i | − | 0.458860i | ||||||
\(605\) | −453.319 | −0.749287 | ||||||||
\(606\) | −106.673 | −0.176028 | ||||||||
\(607\) | 839.696 | 1.38335 | 0.691677 | − | 0.722207i | \(-0.256872\pi\) | ||||
0.691677 | + | 0.722207i | \(0.256872\pi\) | |||||||
\(608\) | 674.490i | 1.10936i | ||||||||
\(609\) | −261.982 | −0.430184 | ||||||||
\(610\) | −894.053 | −1.46566 | ||||||||
\(611\) | −1125.02 | −1.84128 | ||||||||
\(612\) | 458.864 | 0.749777 | ||||||||
\(613\) | 14.7095i | 0.0239960i | 0.999928 | + | 0.0119980i | \(0.00381917\pi\) | ||||
−0.999928 | + | 0.0119980i | \(0.996181\pi\) | |||||||
\(614\) | 593.478i | 0.966577i | ||||||||
\(615\) | −210.170 | −0.341740 | ||||||||
\(616\) | −440.848 | −0.715663 | ||||||||
\(617\) | −126.319 | −0.204730 | −0.102365 | − | 0.994747i | \(-0.532641\pi\) | ||||
−0.102365 | + | 0.994747i | \(0.532641\pi\) | |||||||
\(618\) | −358.067 | −0.579396 | ||||||||
\(619\) | −957.437 | −1.54675 | −0.773374 | − | 0.633950i | \(-0.781432\pi\) | ||||
−0.773374 | + | 0.633950i | \(0.781432\pi\) | |||||||
\(620\) | 420.917i | 0.678898i | ||||||||
\(621\) | 75.7903i | 0.122046i | ||||||||
\(622\) | 519.706i | 0.835540i | ||||||||
\(623\) | 820.749i | 1.31741i | ||||||||
\(624\) | 300.360i | 0.481346i | ||||||||
\(625\) | −55.9320 | −0.0894912 | ||||||||
\(626\) | −139.526 | −0.222885 | ||||||||
\(627\) | 413.389i | 0.659313i | ||||||||
\(628\) | − | 553.630i | − | 0.881576i | ||||||
\(629\) | − | 838.841i | − | 1.33361i | ||||||
\(630\) | − | 341.641i | − | 0.542288i | ||||||
\(631\) | 854.136 | 1.35362 | 0.676811 | − | 0.736157i | \(-0.263361\pi\) | ||||
0.676811 | + | 0.736157i | \(0.263361\pi\) | |||||||
\(632\) | − | 4.03776i | − | 0.00638886i | ||||||
\(633\) | − | 225.122i | − | 0.355642i | ||||||
\(634\) | − | 605.051i | − | 0.954339i | ||||||
\(635\) | 219.929 | 0.346345 | ||||||||
\(636\) | −714.392 | −1.12326 | ||||||||
\(637\) | − | 1282.56i | − | 2.01343i | ||||||
\(638\) | −611.796 | −0.958927 | ||||||||
\(639\) | −40.3812 | −0.0631944 | ||||||||
\(640\) | − | 235.801i | − | 0.368440i | ||||||
\(641\) | −196.567 | −0.306657 | −0.153329 | − | 0.988175i | \(-0.548999\pi\) | ||||
−0.153329 | + | 0.988175i | \(0.548999\pi\) | |||||||
\(642\) | 415.050i | 0.646495i | ||||||||
\(643\) | −185.202 | −0.288028 | −0.144014 | − | 0.989576i | \(-0.546001\pi\) | ||||
−0.144014 | + | 0.989576i | \(0.546001\pi\) | |||||||
\(644\) | − | 824.226i | − | 1.27985i | ||||||
\(645\) | 287.902i | 0.446360i | ||||||||
\(646\) | 1402.28i | 2.17072i | ||||||||
\(647\) | 103.318 | 0.159688 | 0.0798440 | − | 0.996807i | \(-0.474558\pi\) | ||||
0.0798440 | + | 0.996807i | \(0.474558\pi\) | |||||||
\(648\) | 20.7955i | 0.0320918i | ||||||||
\(649\) | −903.698 | − | 299.897i | −1.39245 | − | 0.462090i | ||||
\(650\) | 604.229 | 0.929583 | ||||||||
\(651\) | − | 554.689i | − | 0.852057i | ||||||
\(652\) | 1190.71 | 1.82624 | ||||||||
\(653\) | −387.091 | −0.592789 | −0.296394 | − | 0.955066i | \(-0.595784\pi\) | ||||
−0.296394 | + | 0.955066i | \(0.595784\pi\) | |||||||
\(654\) | −984.739 | −1.50572 | ||||||||
\(655\) | − | 317.077i | − | 0.484086i | ||||||
\(656\) | 458.087 | 0.698304 | ||||||||
\(657\) | 128.827i | 0.196084i | ||||||||
\(658\) | −2789.12 | −4.23879 | ||||||||
\(659\) | 388.451i | 0.589456i | 0.955581 | + | 0.294728i | \(0.0952290\pi\) | ||||
−0.955581 | + | 0.294728i | \(0.904771\pi\) | |||||||
\(660\) | − | 434.340i | − | 0.658092i | ||||||
\(661\) | 699.132 | 1.05769 | 0.528844 | − | 0.848719i | \(-0.322626\pi\) | ||||
0.528844 | + | 0.848719i | \(0.322626\pi\) | |||||||
\(662\) | 1602.97i | 2.42141i | ||||||||
\(663\) | 783.167i | 1.18125i | ||||||||
\(664\) | 29.9002 | 0.0450304 | ||||||||
\(665\) | 568.391 | 0.854724 | ||||||||
\(666\) | 233.019 | 0.349878 | ||||||||
\(667\) | − | 186.611i | − | 0.279777i | ||||||
\(668\) | −240.977 | −0.360744 | ||||||||
\(669\) | −37.5572 | −0.0561392 | ||||||||
\(670\) | 855.664 | 1.27711 | ||||||||
\(671\) | 1497.88 | 2.23231 | ||||||||
\(672\) | 933.900i | 1.38973i | ||||||||
\(673\) | 982.617i | 1.46005i | 0.683418 | + | 0.730027i | \(0.260493\pi\) | ||||
−0.683418 | + | 0.730027i | \(0.739507\pi\) | |||||||
\(674\) | 1828.11 | 2.71233 | ||||||||
\(675\) | −74.9895 | −0.111095 | ||||||||
\(676\) | 146.529 | 0.216759 | ||||||||
\(677\) | −176.203 | −0.260270 | −0.130135 | − | 0.991496i | \(-0.541541\pi\) | ||||
−0.130135 | + | 0.991496i | \(0.541541\pi\) | |||||||
\(678\) | 429.425 | 0.633370 | ||||||||
\(679\) | 1196.65i | 1.76237i | ||||||||
\(680\) | − | 240.371i | − | 0.353486i | ||||||
\(681\) | − | 411.240i | − | 0.603876i | ||||||
\(682\) | − | 1295.34i | − | 1.89933i | ||||||
\(683\) | 793.332i | 1.16154i | 0.814068 | + | 0.580770i | \(0.197248\pi\) | ||||
−0.814068 | + | 0.580770i | \(0.802752\pi\) | |||||||
\(684\) | −212.066 | −0.310039 | ||||||||
\(685\) | −43.5057 | −0.0635120 | ||||||||
\(686\) | − | 1463.17i | − | 2.13291i | ||||||
\(687\) | − | 352.381i | − | 0.512927i | ||||||
\(688\) | − | 627.513i | − | 0.912083i | ||||||
\(689\) | − | 1219.29i | − | 1.76965i | ||||||
\(690\) | 243.353 | 0.352686 | ||||||||
\(691\) | − | 977.811i | − | 1.41507i | −0.706680 | − | 0.707533i | \(-0.749808\pi\) | ||
0.706680 | − | 0.707533i | \(-0.250192\pi\) | |||||||
\(692\) | 64.1402i | 0.0926881i | ||||||||
\(693\) | 572.379i | 0.825944i | ||||||||
\(694\) | 139.852 | 0.201516 | ||||||||
\(695\) | 256.316 | 0.368800 | ||||||||
\(696\) | − | 51.2028i | − | 0.0735672i | ||||||
\(697\) | 1194.43 | 1.71367 | ||||||||
\(698\) | 109.399 | 0.156732 | ||||||||
\(699\) | − | 569.084i | − | 0.814140i | ||||||
\(700\) | 815.517 | 1.16502 | ||||||||
\(701\) | − | 940.284i | − | 1.34135i | −0.741753 | − | 0.670674i | \(-0.766005\pi\) | ||
0.741753 | − | 0.670674i | \(-0.233995\pi\) | |||||||
\(702\) | −217.553 | −0.309905 | ||||||||
\(703\) | 387.675i | 0.551458i | ||||||||
\(704\) | 1388.65i | 1.97252i | ||||||||
\(705\) | − | 448.315i | − | 0.635908i | ||||||
\(706\) | −246.621 | −0.349322 | ||||||||
\(707\) | − | 245.729i | − | 0.347566i | ||||||
\(708\) | 153.845 | − | 463.592i | 0.217296 | − | 0.654791i | ||||
\(709\) | 1249.95 | 1.76298 | 0.881488 | − | 0.472207i | \(-0.156542\pi\) | ||||
0.881488 | + | 0.472207i | \(0.156542\pi\) | |||||||
\(710\) | 129.659i | 0.182618i | ||||||||
\(711\) | −5.24245 | −0.00737335 | ||||||||
\(712\) | −160.410 | −0.225296 | ||||||||
\(713\) | 395.108 | 0.554149 | ||||||||
\(714\) | 1941.60i | 2.71933i | ||||||||
\(715\) | 741.311 | 1.03680 | ||||||||
\(716\) | − | 495.595i | − | 0.692171i | ||||||
\(717\) | 358.216 | 0.499603 | ||||||||
\(718\) | − | 1497.03i | − | 2.08500i | ||||||
\(719\) | 711.393i | 0.989420i | 0.869058 | + | 0.494710i | \(0.164726\pi\) | ||||
−0.869058 | + | 0.494710i | \(0.835274\pi\) | |||||||
\(720\) | −119.692 | −0.166238 | ||||||||
\(721\) | − | 824.832i | − | 1.14401i | ||||||
\(722\) | 421.597i | 0.583929i | ||||||||
\(723\) | −239.220 | −0.330871 | ||||||||
\(724\) | −578.101 | −0.798483 | ||||||||
\(725\) | 184.640 | 0.254675 | ||||||||
\(726\) | 715.657i | 0.985753i | ||||||||
\(727\) | −729.102 | −1.00289 | −0.501446 | − | 0.865189i | \(-0.667198\pi\) | ||||
−0.501446 | + | 0.865189i | \(0.667198\pi\) | |||||||
\(728\) | 385.987 | 0.530202 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 413.647 | 0.566640 | ||||||||
\(731\) | − | 1636.20i | − | 2.23830i | ||||||
\(732\) | 768.403i | 1.04973i | ||||||||
\(733\) | −1330.92 | −1.81572 | −0.907861 | − | 0.419271i | \(-0.862286\pi\) | ||||
−0.907861 | + | 0.419271i | \(0.862286\pi\) | |||||||
\(734\) | −145.517 | −0.198252 | ||||||||
\(735\) | 511.091 | 0.695361 | ||||||||
\(736\) | −665.222 | −0.903835 | ||||||||
\(737\) | −1433.56 | −1.94513 | ||||||||
\(738\) | 331.796i | 0.449589i | ||||||||
\(739\) | 1212.71i | 1.64101i | 0.571640 | + | 0.820505i | \(0.306307\pi\) | ||||
−0.571640 | + | 0.820505i | \(0.693693\pi\) | |||||||
\(740\) | − | 407.323i | − | 0.550436i | ||||||
\(741\) | − | 361.945i | − | 0.488454i | ||||||
\(742\) | − | 3022.83i | − | 4.07389i | ||||||
\(743\) | 1031.43 | 1.38820 | 0.694100 | − | 0.719878i | \(-0.255802\pi\) | ||||
0.694100 | + | 0.719878i | \(0.255802\pi\) | |||||||
\(744\) | 108.411 | 0.145713 | ||||||||
\(745\) | 12.8389i | 0.0172335i | ||||||||
\(746\) | 1728.31i | 2.31676i | ||||||||
\(747\) | − | 38.8212i | − | 0.0519695i | ||||||
\(748\) | 2468.43i | 3.30003i | ||||||||
\(749\) | −956.096 | −1.27650 | ||||||||
\(750\) | 657.886i | 0.877182i | ||||||||
\(751\) | 673.571i | 0.896899i | 0.893808 | + | 0.448450i | \(0.148024\pi\) | ||||
−0.893808 | + | 0.448450i | \(0.851976\pi\) | |||||||
\(752\) | 977.149i | 1.29940i | ||||||||
\(753\) | 761.669 | 1.01151 | ||||||||
\(754\) | 535.661 | 0.710425 | ||||||||
\(755\) | 188.499i | 0.249668i | ||||||||
\(756\) | −293.627 | −0.388396 | ||||||||
\(757\) | −142.288 | −0.187962 | −0.0939812 | − | 0.995574i | \(-0.529959\pi\) | ||||
−0.0939812 | + | 0.995574i | \(0.529959\pi\) | |||||||
\(758\) | − | 478.966i | − | 0.631881i | ||||||
\(759\) | −407.709 | −0.537166 | ||||||||
\(760\) | 111.089i | 0.146169i | ||||||||
\(761\) | 585.282 | 0.769096 | 0.384548 | − | 0.923105i | \(-0.374357\pi\) | ||||
0.384548 | + | 0.923105i | \(0.374357\pi\) | |||||||
\(762\) | − | 347.203i | − | 0.455647i | ||||||
\(763\) | − | 2268.42i | − | 2.97302i | ||||||
\(764\) | 1083.61i | 1.41834i | ||||||||
\(765\) | −312.087 | −0.407957 | ||||||||
\(766\) | 495.526i | 0.646901i | ||||||||
\(767\) | 791.237 | + | 262.576i | 1.03160 | + | 0.342341i | ||||
\(768\) | 223.891 | 0.291525 | ||||||||
\(769\) | − | 545.480i | − | 0.709337i | −0.934992 | − | 0.354668i | \(-0.884594\pi\) | ||
0.934992 | − | 0.354668i | \(-0.115406\pi\) | |||||||
\(770\) | 1837.84 | 2.38680 | ||||||||
\(771\) | 446.982 | 0.579743 | ||||||||
\(772\) | −694.885 | −0.900110 | ||||||||
\(773\) | − | 119.861i | − | 0.155060i | −0.996990 | − | 0.0775299i | \(-0.975297\pi\) | ||
0.996990 | − | 0.0775299i | \(-0.0247033\pi\) | |||||||
\(774\) | 454.513 | 0.587226 | ||||||||
\(775\) | 390.933i | 0.504430i | ||||||||
\(776\) | −233.878 | −0.301389 | ||||||||
\(777\) | 536.775i | 0.690830i | ||||||||
\(778\) | 971.544i | 1.24877i | ||||||||
\(779\) | −552.012 | −0.708617 | ||||||||
\(780\) | 380.289i | 0.487550i | ||||||||
\(781\) | − | 217.228i | − | 0.278141i | ||||||
\(782\) | −1383.01 | −1.76856 | ||||||||
\(783\) | −66.4796 | −0.0849037 | ||||||||
\(784\) | −1113.97 | −1.42089 | ||||||||
\(785\) | 376.540i | 0.479669i | ||||||||
\(786\) | −500.570 | −0.636858 | ||||||||
\(787\) | 1312.72 | 1.66800 | 0.834001 | − | 0.551763i | \(-0.186045\pi\) | ||||
0.834001 | + | 0.551763i | \(0.186045\pi\) | |||||||
\(788\) | −455.336 | −0.577838 | ||||||||
\(789\) | −412.748 | −0.523128 | ||||||||
\(790\) | 16.8329i | 0.0213074i | ||||||||
\(791\) | 989.210i | 1.25058i | ||||||||
\(792\) | −111.868 | −0.141247 | ||||||||
\(793\) | −1311.47 | −1.65381 | ||||||||
\(794\) | 2048.02 | 2.57938 | ||||||||
\(795\) | 485.880 | 0.611170 | ||||||||
\(796\) | −569.231 | −0.715115 | ||||||||
\(797\) | − | 960.105i | − | 1.20465i | −0.798251 | − | 0.602324i | \(-0.794241\pi\) | ||
0.798251 | − | 0.602324i | \(-0.205759\pi\) | |||||||
\(798\) | − | 897.322i | − | 1.12446i | ||||||
\(799\) | 2547.85i | 3.18879i | ||||||||
\(800\) | − | 658.193i | − | 0.822741i | ||||||
\(801\) | 208.270i | 0.260013i | ||||||||
\(802\) | −305.173 | −0.380516 | ||||||||
\(803\) | −693.017 | −0.863035 | ||||||||
\(804\) | − | 735.410i | − | 0.914689i | ||||||
\(805\) | 560.581i | 0.696374i | ||||||||
\(806\) | 1134.14i | 1.40712i | ||||||||
\(807\) | − | 555.185i | − | 0.687962i | ||||||
\(808\) | 48.0262 | 0.0594384 | ||||||||
\(809\) | 1323.21i | 1.63562i | 0.575491 | + | 0.817808i | \(0.304811\pi\) | ||||
−0.575491 | + | 0.817808i | \(0.695189\pi\) | |||||||
\(810\) | − | 86.6936i | − | 0.107029i | ||||||
\(811\) | 1050.46i | 1.29526i | 0.761954 | + | 0.647631i | \(0.224240\pi\) | ||||
−0.761954 | + | 0.647631i | \(0.775760\pi\) | |||||||
\(812\) | 722.971 | 0.890359 | ||||||||
\(813\) | −97.7069 | −0.120181 | ||||||||
\(814\) | 1253.51i | 1.53994i | ||||||||
\(815\) | −809.837 | −0.993665 | ||||||||
\(816\) | 680.226 | 0.833610 | ||||||||
\(817\) | 756.177i | 0.925553i | ||||||||
\(818\) | 2136.10 | 2.61137 | ||||||||
\(819\) | − | 501.149i | − | 0.611904i | ||||||
\(820\) | 579.989 | 0.707304 | ||||||||
\(821\) | − | 627.425i | − | 0.764220i | −0.924117 | − | 0.382110i | \(-0.875197\pi\) | ||
0.924117 | − | 0.382110i | \(-0.124803\pi\) | |||||||
\(822\) | 68.6827i | 0.0835555i | ||||||||
\(823\) | 579.065i | 0.703602i | 0.936075 | + | 0.351801i | \(0.114431\pi\) | ||||
−0.936075 | + | 0.351801i | \(0.885569\pi\) | |||||||
\(824\) | 161.208 | 0.195641 | ||||||||
\(825\) | − | 403.401i | − | 0.488971i | ||||||
\(826\) | 1961.61 | + | 650.970i | 2.37483 | + | 0.788099i | ||||
\(827\) | −884.953 | −1.07008 | −0.535038 | − | 0.844828i | \(-0.679703\pi\) | ||||
−0.535038 | + | 0.844828i | \(0.679703\pi\) | |||||||
\(828\) | − | 209.153i | − | 0.252600i | ||||||
\(829\) | 749.807 | 0.904472 | 0.452236 | − | 0.891898i | \(-0.350627\pi\) | ||||
0.452236 | + | 0.891898i | \(0.350627\pi\) | |||||||
\(830\) | −124.650 | −0.150181 | ||||||||
\(831\) | −412.879 | −0.496846 | ||||||||
\(832\) | − | 1215.84i | − | 1.46135i | ||||||
\(833\) | −2904.61 | −3.48693 | ||||||||
\(834\) | − | 404.647i | − | 0.485189i | ||||||
\(835\) | 163.896 | 0.196282 | ||||||||
\(836\) | − | 1140.80i | − | 1.36459i | ||||||
\(837\) | − | 140.756i | − | 0.168167i | ||||||
\(838\) | 1904.55 | 2.27273 | ||||||||
\(839\) | − | 831.080i | − | 0.990560i | −0.868733 | − | 0.495280i | \(-0.835066\pi\) | ||
0.868733 | − | 0.495280i | \(-0.164934\pi\) | |||||||
\(840\) | 153.813i | 0.183111i | ||||||||
\(841\) | −677.314 | −0.805367 | ||||||||
\(842\) | −326.343 | −0.387581 | ||||||||
\(843\) | −280.418 | −0.332643 | ||||||||
\(844\) | 621.250i | 0.736078i | ||||||||
\(845\) | −99.6587 | −0.117939 | ||||||||
\(846\) | −707.757 | −0.836593 | ||||||||
\(847\) | −1648.57 | −1.94636 | ||||||||
\(848\) | −1059.03 | −1.24885 | ||||||||
\(849\) | − | 713.088i | − | 0.839915i | ||||||
\(850\) | − | 1368.40i | − | 1.60988i | ||||||
\(851\) | −382.348 | −0.449293 | ||||||||
\(852\) | 111.437 | 0.130794 | ||||||||
\(853\) | 380.422 | 0.445981 | 0.222991 | − | 0.974821i | \(-0.428418\pi\) | ||||
0.222991 | + | 0.974821i | \(0.428418\pi\) | |||||||
\(854\) | −3251.37 | −3.80722 | ||||||||
\(855\) | 144.233 | 0.168693 | ||||||||
\(856\) | − | 186.863i | − | 0.218298i | ||||||
\(857\) | 1111.73i | 1.29724i | 0.761114 | + | 0.648619i | \(0.224653\pi\) | ||||
−0.761114 | + | 0.648619i | \(0.775347\pi\) | |||||||
\(858\) | − | 1170.31i | − | 1.36400i | ||||||
\(859\) | − | 188.285i | − | 0.219191i | −0.993976 | − | 0.109596i | \(-0.965044\pi\) | ||
0.993976 | − | 0.109596i | \(-0.0349556\pi\) | |||||||
\(860\) | − | 794.501i | − | 0.923839i | ||||||
\(861\) | −764.317 | −0.887708 | ||||||||
\(862\) | 620.911 | 0.720314 | ||||||||
\(863\) | 1545.16i | 1.79045i | 0.445616 | + | 0.895224i | \(0.352985\pi\) | ||||
−0.445616 | + | 0.895224i | \(0.647015\pi\) | |||||||
\(864\) | 236.983i | 0.274286i | ||||||||
\(865\) | − | 43.6237i | − | 0.0504320i | ||||||
\(866\) | 71.4057i | 0.0824546i | ||||||||
\(867\) | 1273.08 | 1.46837 | ||||||||
\(868\) | 1530.73i | 1.76351i | ||||||||
\(869\) | − | 28.2014i | − | 0.0324527i | ||||||
\(870\) | 213.457i | 0.245353i | ||||||||
\(871\) | 1255.16 | 1.44106 | ||||||||
\(872\) | 443.348 | 0.508427 | ||||||||
\(873\) | 303.657i | 0.347832i | ||||||||
\(874\) | 639.168 | 0.731313 | ||||||||
\(875\) | −1515.49 | −1.73199 | ||||||||
\(876\) | − | 355.514i | − | 0.405838i | ||||||
\(877\) | 1640.14 | 1.87017 | 0.935083 | − | 0.354429i | \(-0.115325\pi\) | ||||
0.935083 | + | 0.354429i | \(0.115325\pi\) | |||||||
\(878\) | 1636.82i | 1.86426i | ||||||||
\(879\) | 24.8705 | 0.0282941 | ||||||||
\(880\) | − | 643.872i | − | 0.731673i | ||||||
\(881\) | − | 1656.83i | − | 1.88063i | −0.340306 | − | 0.940315i | \(-0.610531\pi\) | ||
0.340306 | − | 0.940315i | \(-0.389469\pi\) | |||||||
\(882\) | − | 806.861i | − | 0.914809i | ||||||
\(883\) | −210.287 | −0.238151 | −0.119075 | − | 0.992885i | \(-0.537993\pi\) | ||||
−0.119075 | + | 0.992885i | \(0.537993\pi\) | |||||||
\(884\) | − | 2161.24i | − | 2.44484i | ||||||
\(885\) | −104.635 | + | 315.303i | −0.118231 | + | 0.356275i | ||||
\(886\) | −1204.95 | −1.35998 | ||||||||
\(887\) | 782.513i | 0.882202i | 0.897457 | + | 0.441101i | \(0.145412\pi\) | ||||
−0.897457 | + | 0.441101i | \(0.854588\pi\) | |||||||
\(888\) | −104.909 | −0.118141 | ||||||||
\(889\) | 799.807 | 0.899671 | ||||||||
\(890\) | 668.729 | 0.751381 | ||||||||
\(891\) | 145.245i | 0.163013i | ||||||||
\(892\) | 103.643 | 0.116192 | ||||||||
\(893\) | − | 1177.50i | − | 1.31859i | ||||||
\(894\) | 20.2689 | 0.0226721 | ||||||||
\(895\) | 337.069i | 0.376613i | ||||||||
\(896\) | − | 857.530i | − | 0.957064i | ||||||
\(897\) | 356.971 | 0.397962 | ||||||||
\(898\) | 318.359i | 0.354520i | ||||||||
\(899\) | 346.570i | 0.385506i | ||||||||
\(900\) | 206.942 | 0.229936 | ||||||||
\(901\) | −2761.33 | −3.06474 | ||||||||
\(902\) | −1784.88 | −1.97880 | ||||||||
\(903\) | 1047.00i | 1.15947i | ||||||||
\(904\) | −193.335 | −0.213866 | ||||||||
\(905\) | 393.184 | 0.434458 | ||||||||
\(906\) | 297.585 | 0.328460 | ||||||||
\(907\) | 82.0657 | 0.0904803 | 0.0452402 | − | 0.998976i | \(-0.485595\pi\) | ||||
0.0452402 | + | 0.998976i | \(0.485595\pi\) | |||||||
\(908\) | 1134.87i | 1.24985i | ||||||||
\(909\) | − | 62.3552i | − | 0.0685976i | ||||||
\(910\) | −1609.13 | −1.76827 | ||||||||
\(911\) | −879.346 | −0.965253 | −0.482627 | − | 0.875826i | \(-0.660317\pi\) | ||||
−0.482627 | + | 0.875826i | \(0.660317\pi\) | |||||||
\(912\) | −314.370 | −0.344704 | ||||||||
\(913\) | 208.836 | 0.228736 | ||||||||
\(914\) | −432.498 | −0.473192 | ||||||||
\(915\) | − | 522.614i | − | 0.571163i | ||||||
\(916\) | 972.437i | 1.06161i | ||||||||
\(917\) | − | 1153.10i | − | 1.25747i | ||||||
\(918\) | 492.693i | 0.536703i | ||||||||
\(919\) | − | 1122.64i | − | 1.22159i | −0.791789 | − | 0.610794i | \(-0.790850\pi\) | ||
0.791789 | − | 0.610794i | \(-0.209150\pi\) | |||||||
\(920\) | −109.562 | −0.119089 | ||||||||
\(921\) | −346.915 | −0.376672 | ||||||||
\(922\) | 575.425i | 0.624105i | ||||||||
\(923\) | 190.195i | 0.206062i | ||||||||
\(924\) | − | 1579.55i | − | 1.70947i | ||||||
\(925\) | − | 378.308i | − | 0.408981i | ||||||
\(926\) | 119.003 | 0.128513 | ||||||||
\(927\) | − | 209.306i | − | 0.225789i | ||||||
\(928\) | − | 583.500i | − | 0.628772i | ||||||
\(929\) | − | 386.165i | − | 0.415678i | −0.978163 | − | 0.207839i | \(-0.933357\pi\) | ||
0.978163 | − | 0.207839i | \(-0.0666431\pi\) | |||||||
\(930\) | −451.949 | −0.485966 | ||||||||
\(931\) | 1342.38 | 1.44187 | ||||||||
\(932\) | 1570.45i | 1.68504i | ||||||||
\(933\) | −303.792 | −0.325607 | ||||||||
\(934\) | 938.623 | 1.00495 | ||||||||
\(935\) | − | 1678.85i | − | 1.79556i | ||||||
\(936\) | 97.9465 | 0.104644 | ||||||||
\(937\) | 37.2676i | 0.0397733i | 0.999802 | + | 0.0198867i | \(0.00633054\pi\) | ||||
−0.999802 | + | 0.0198867i | \(0.993669\pi\) | |||||||
\(938\) | 3111.76 | 3.31744 | ||||||||
\(939\) | − | 81.5594i | − | 0.0868578i | ||||||
\(940\) | 1237.18i | 1.31615i | ||||||||
\(941\) | − | 706.531i | − | 0.750830i | −0.926857 | − | 0.375415i | \(-0.877500\pi\) | ||
0.926857 | − | 0.375415i | \(-0.122500\pi\) | |||||||
\(942\) | 594.446 | 0.631047 | ||||||||
\(943\) | − | 544.427i | − | 0.577336i | ||||||
\(944\) | 228.063 | − | 687.236i | 0.241592 | − | 0.728004i | ||||
\(945\) | 199.705 | 0.211328 | ||||||||
\(946\) | 2445.02i | 2.58459i | ||||||||
\(947\) | 15.8695 | 0.0167577 | 0.00837883 | − | 0.999965i | \(-0.497333\pi\) | ||||
0.00837883 | + | 0.999965i | \(0.497333\pi\) | |||||||
\(948\) | 14.4672 | 0.0152607 | ||||||||
\(949\) | 606.774 | 0.639383 | ||||||||
\(950\) | 632.414i | 0.665699i | ||||||||
\(951\) | 353.680 | 0.371903 | ||||||||
\(952\) | − | 874.146i | − | 0.918221i | ||||||
\(953\) | −473.228 | −0.496567 | −0.248283 | − | 0.968687i | \(-0.579866\pi\) | ||||
−0.248283 | + | 0.968687i | \(0.579866\pi\) | |||||||
\(954\) | − | 767.061i | − | 0.804047i | ||||||
\(955\) | − | 736.999i | − | 0.771726i | ||||||
\(956\) | −988.539 | −1.03404 | ||||||||
\(957\) | − | 357.622i | − | 0.373691i | ||||||
\(958\) | − | 368.762i | − | 0.384929i | ||||||
\(959\) | −158.215 | −0.164980 | ||||||||
\(960\) | 484.506 | 0.504693 | ||||||||
\(961\) | 227.216 | 0.236437 | ||||||||
\(962\) | − | 1097.51i | − | 1.14087i | ||||||
\(963\) | −242.615 | −0.251937 | ||||||||
\(964\) | 660.155 | 0.684808 | ||||||||
\(965\) | 472.612 | 0.489753 | ||||||||
\(966\) | 884.992 | 0.916141 | ||||||||
\(967\) | − | 587.252i | − | 0.607292i | −0.952785 | − | 0.303646i | \(-0.901796\pi\) | ||
0.952785 | − | 0.303646i | \(-0.0982040\pi\) | |||||||
\(968\) | − | 322.202i | − | 0.332854i | ||||||
\(969\) | −819.698 | −0.845922 | ||||||||
\(970\) | 975.006 | 1.00516 | ||||||||
\(971\) | 1259.85 | 1.29748 | 0.648738 | − | 0.761012i | \(-0.275297\pi\) | ||||
0.648738 | + | 0.761012i | \(0.275297\pi\) | |||||||
\(972\) | −74.5097 | −0.0766561 | ||||||||
\(973\) | 932.134 | 0.958000 | ||||||||
\(974\) | − | 288.594i | − | 0.296298i | ||||||
\(975\) | 353.199i | 0.362256i | ||||||||
\(976\) | 1139.09i | 1.16710i | ||||||||
\(977\) | 307.843i | 0.315090i | 0.987512 | + | 0.157545i | \(0.0503580\pi\) | ||||
−0.987512 | + | 0.157545i | \(0.949642\pi\) | |||||||
\(978\) | 1278.49i | 1.30725i | ||||||||
\(979\) | −1120.38 | −1.14441 | ||||||||
\(980\) | −1410.42 | −1.43920 | ||||||||
\(981\) | − | 575.625i | − | 0.586774i | ||||||
\(982\) | − | 1626.27i | − | 1.65608i | ||||||
\(983\) | 421.899i | 0.429195i | 0.976703 | + | 0.214597i | \(0.0688439\pi\) | ||||
−0.976703 | + | 0.214597i | \(0.931156\pi\) | |||||||
\(984\) | − | 149.381i | − | 0.151810i | ||||||
\(985\) | 309.688 | 0.314404 | ||||||||
\(986\) | − | 1213.11i | − | 1.23034i | ||||||
\(987\) | − | 1630.37i | − | 1.65184i | ||||||
\(988\) | 998.830i | 1.01096i | ||||||||
\(989\) | −745.787 | −0.754082 | ||||||||
\(990\) | 466.362 | 0.471073 | ||||||||
\(991\) | − | 1003.50i | − | 1.01261i | −0.862354 | − | 0.506306i | \(-0.831011\pi\) | ||
0.862354 | − | 0.506306i | \(-0.168989\pi\) | |||||||
\(992\) | 1235.43 | 1.24540 | ||||||||
\(993\) | −937.011 | −0.943616 | ||||||||
\(994\) | 471.525i | 0.474372i | ||||||||
\(995\) | 387.151 | 0.389097 | ||||||||
\(996\) | 107.132i | 0.107562i | ||||||||
\(997\) | −1320.45 | −1.32443 | −0.662214 | − | 0.749315i | \(-0.730383\pi\) | ||||
−0.662214 | + | 0.749315i | \(0.730383\pi\) | |||||||
\(998\) | 547.727i | 0.548825i | ||||||||
\(999\) | 136.210i | 0.136346i |
(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 | 177.3.c.a.58.4 | ✓ | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.17 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.17 | yes | 20 | |
177.176 | even | 2 | 531.3.c.c.235.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
177.3.c.a.58.17 | yes | 20 | 59.58 | odd | 2 | inner | |
531.3.c.c.235.4 | 20 | 177.176 | even | 2 | |||
531.3.c.c.235.17 | 20 | 3.2 | odd | 2 |