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: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
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 | 58.17 | ||
Root | \(2.96307i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.4 |
$q$-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 | \(0.265538\pi\) | ||||
−0.671761 | + | 0.740768i | \(0.734462\pi\) | |||||||
\(3\) | 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 | \(-0.737858\pi\) | ||
0.679626 | − | 0.733559i | \(-0.262142\pi\) | |||||||
\(12\) | −8.27886 | −0.689905 | ||||||||
\(13\) | 14.1300i | 1.08692i | 0.839435 | + | 0.543460i | \(0.182886\pi\) | ||||
−0.839435 | + | 0.543460i | \(0.817114\pi\) | |||||||
\(14\) | 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 | \(-0.897296\pi\) | ||
0.948398 | − | 0.317084i | \(-0.102704\pi\) | |||||||
\(24\) | − | 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 | \(0.143927\pi\) | ||||
−0.899505 | + | 0.436910i | \(0.856073\pi\) | |||||||
\(32\) | − | 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 | \(-0.884740\pi\) | ||
0.935155 | − | 0.354238i | \(-0.115260\pi\) | |||||||
\(38\) | 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 | \(-0.797332\pi\) | ||
0.804063 | − | 0.594544i | \(-0.202668\pi\) | |||||||
\(44\) | 77.1379i | 1.75313i | ||||||||
\(45\) | 9.75266 | 0.216726 | ||||||||
\(46\) | 43.2190 | 0.939542 | ||||||||
\(47\) | 79.6198i | 1.69404i | 0.531563 | + | 0.847019i | \(0.321605\pi\) | ||||
−0.531563 | + | 0.847019i | \(0.678395\pi\) | |||||||
\(48\) | −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 | \(0.275183\pi\) | ||||
−0.649010 | + | 0.760780i | \(0.724817\pi\) | |||||||
\(62\) | −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 | \(-0.769321\pi\) | ||
0.748700 | − | 0.662909i | \(-0.230679\pi\) | |||||||
\(68\) | 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 | \(-0.904972\pi\) | ||
0.955767 | − | 0.294126i | \(-0.0950285\pi\) | |||||||
\(74\) | 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 | \(0.0248388\pi\) | ||||
−0.996957 | + | 0.0779542i | \(0.975161\pi\) | |||||||
\(84\) | −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 | \(-0.872468\pi\) | ||
0.920807 | − | 0.390019i | \(-0.127532\pi\) | |||||||
\(90\) | 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 | \(-0.825280\pi\) | ||
0.853099 | − | 0.521748i | \(-0.174720\pi\) | |||||||
\(98\) | 268.954i | 2.74443i | ||||||||
\(99\) | − | 48.4149i | − | 0.489039i | ||||||
\(100\) | 68.9808 | 0.689808 | ||||||||
\(101\) | 20.7851i | 0.205793i | 0.994692 | + | 0.102896i | \(0.0328110\pi\) | ||||
−0.994692 | + | 0.102896i | \(0.967189\pi\) | |||||||
\(102\) | − | 164.231i | − | 1.61011i | ||||||
\(103\) | 69.7688i | 0.677367i | 0.940900 | + | 0.338683i | \(0.109982\pi\) | ||||
−0.940900 | + | 0.338683i | \(0.890018\pi\) | |||||||
\(104\) | 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 | \(0.342565\pi\) | ||||
−0.474676 | + | 0.880160i | \(0.657435\pi\) | |||||||
\(110\) | 155.454 | 1.41322 | ||||||||
\(111\) | − | 45.4033i | − | 0.409039i | ||||||
\(112\) | −145.092 | −1.29547 | ||||||||
\(113\) | − | 83.6727i | − | 0.740467i | −0.928939 | − | 0.370233i | \(-0.879278\pi\) | ||
0.928939 | − | 0.370233i | \(-0.120722\pi\) | |||||||
\(114\) | 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 | \(0.121421\pi\) | ||||
−0.928123 | + | 0.372273i | \(0.878579\pi\) | |||||||
\(132\) | 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 | \(-0.995781\pi\) | ||
0.999912 | − | 0.0132529i | \(-0.00421865\pi\) | |||||||
\(150\) | − | 74.0664i | − | 0.493776i | ||||||
\(151\) | − | 57.9839i | − | 0.383999i | −0.981395 | − | 0.192000i | \(-0.938503\pi\) | ||
0.981395 | − | 0.192000i | \(-0.0614973\pi\) | |||||||
\(152\) | − | 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 | \(-0.879743\pi\) | ||
0.929479 | − | 0.368876i | \(-0.120257\pi\) | |||||||
\(158\) | − | 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 | \(0.0123482\pi\) | ||||
−0.999248 | + | 0.0387832i | \(0.987652\pi\) | |||||||
\(174\) | − | 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 | \(-0.906470\pi\) | ||
0.957141 | − | 0.289623i | \(-0.0935300\pi\) | |||||||
\(180\) | −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 | \(0.202244\pi\) | ||||
−0.804854 | + | 0.593473i | \(0.797756\pi\) | |||||||
\(192\) | 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 | \(0.0996581\pi\) | ||||
−0.951388 | + | 0.307995i | \(0.900342\pi\) | |||||||
\(212\) | −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 | \(0.175177\pi\) | ||||
−0.852350 | + | 0.522972i | \(0.824823\pi\) | |||||||
\(228\) | −122.437 | −0.537003 | ||||||||
\(229\) | 203.447i | 0.888415i | 0.895924 | + | 0.444208i | \(0.146515\pi\) | ||||
−0.895924 | + | 0.444208i | \(0.853485\pi\) | |||||||
\(230\) | 140.500 | 0.610869 | ||||||||
\(231\) | − | 330.463i | − | 1.43058i | ||||||
\(232\) | 29.5620i | 0.127422i | ||||||||
\(233\) | 328.561i | 1.41013i | 0.709142 | + | 0.705066i | \(0.249082\pi\) | ||||
−0.709142 | + | 0.705066i | \(0.750918\pi\) | |||||||
\(234\) | −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 | \(0.203162\pi\) | ||||
−0.803138 | + | 0.595792i | \(0.796838\pi\) | |||||||
\(270\) | 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 | \(0.259266\pi\) | ||||
−0.686226 | + | 0.727388i | \(0.740734\pi\) | |||||||
\(284\) | 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 | \(0.0239662\pi\) | ||||
−0.997167 | + | 0.0752210i | \(0.976034\pi\) | |||||||
\(314\) | 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 | \(-0.631891\pi\) | ||
0.402593 | − | 0.915379i | \(-0.368109\pi\) | |||||||
\(338\) | − | 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 | \(-0.978335\pi\) | ||
0.997685 | − | 0.0680090i | \(-0.0216647\pi\) | |||||||
\(348\) | 105.920 | 0.304367 | ||||||||
\(349\) | − | 36.9208i | − | 0.105790i | −0.998600 | − | 0.0528952i | \(-0.983155\pi\) | ||
0.998600 | − | 0.0528952i | \(-0.0168449\pi\) | |||||||
\(350\) | − | 505.551i | − | 1.44443i | ||||||
\(351\) | 73.4214i | 0.209178i | ||||||||
\(352\) | −736.025 | −2.09098 | ||||||||
\(353\) | 83.2316i | 0.235784i | 0.993026 | + | 0.117892i | \(0.0376136\pi\) | ||||
−0.993026 | + | 0.117892i | \(0.962386\pi\) | |||||||
\(354\) | 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 | \(0.0213132\pi\) | ||||
−0.997759 | + | 0.0669075i | \(0.978687\pi\) | |||||||
\(368\) | 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 | \(-0.663791\pi\) | ||
0.492156 | − | 0.870507i | \(-0.336209\pi\) | |||||||
\(398\) | 352.875i | 0.886621i | ||||||||
\(399\) | 302.835 | 0.758985 | ||||||||
\(400\) | 177.116 | 0.442791 | ||||||||
\(401\) | 102.992i | 0.256838i | 0.991720 | + | 0.128419i | \(0.0409903\pi\) | ||||
−0.991720 | + | 0.128419i | \(0.959010\pi\) | |||||||
\(402\) | 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 | \(-0.656666\pi\) | ||
0.472549 | − | 0.881304i | \(-0.343334\pi\) | |||||||
\(410\) | − | 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 | \(-0.721740\pi\) | ||
0.641626 | − | 0.767018i | \(-0.278260\pi\) | |||||||
\(420\) | −318.183 | −0.757579 | ||||||||
\(421\) | 110.137i | 0.261607i | 0.991408 | + | 0.130804i | \(0.0417557\pi\) | ||||
−0.991408 | + | 0.130804i | \(0.958244\pi\) | |||||||
\(422\) | −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 | \(-0.921837\pi\) | ||
0.970002 | − | 0.243097i | \(-0.0781633\pi\) | |||||||
\(432\) | −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 | \(0.151784\pi\) | ||||
−0.888448 | + | 0.458977i | \(0.848216\pi\) | |||||||
\(444\) | 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 | \(0.0510516\pi\) | ||||
−0.987166 | + | 0.159697i | \(0.948948\pi\) | |||||||
\(458\) | −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 | \(-0.986190\pi\) | ||
0.999059 | − | 0.0433716i | \(-0.0138100\pi\) | |||||||
\(464\) | 157.017 | 0.338399 | ||||||||
\(465\) | 152.527i | 0.328015i | ||||||||
\(466\) | −973.549 | −2.08916 | ||||||||
\(467\) | − | 316.774i | − | 0.678316i | −0.940729 | − | 0.339158i | \(-0.889858\pi\) | ||
0.940729 | − | 0.339158i | \(-0.110142\pi\) | |||||||
\(468\) | − | 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 | \(0.0782256\pi\) | ||||
−0.969954 | + | 0.243287i | \(0.921774\pi\) | |||||||
\(504\) | − | 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 | \(-0.979242\pi\) | ||
0.997874 | − | 0.0651670i | \(-0.0207580\pi\) | |||||||
\(510\) | − | 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 | \(0.146261\pi\) | ||||
−0.896278 | + | 0.443494i | \(0.853739\pi\) | |||||||
\(542\) | − | 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 | \(0.186398\pi\) | ||||
−0.833388 | + | 0.552688i | \(0.813602\pi\) | |||||||
\(564\) | − | 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 | \(0.157648\pi\) | ||||
−0.879842 | + | 0.475266i | \(0.842352\pi\) | |||||||
\(570\) | 246.743i | 0.432883i | ||||||||
\(571\) | 783.357i | 1.37190i | 0.727647 | + | 0.685952i | \(0.240614\pi\) | ||||
−0.727647 | + | 0.685952i | \(0.759386\pi\) | |||||||
\(572\) | −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 | \(0.245191\pi\) | ||||
−0.717708 | + | 0.696344i | \(0.754809\pi\) | |||||||
\(588\) | −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 | \(-0.984042\pi\) | ||
0.998744 | − | 0.0501139i | \(-0.0159584\pi\) | |||||||
\(602\) | 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 | \(-0.996181\pi\) | ||
0.999928 | − | 0.0119980i | \(-0.00381917\pi\) | |||||||
\(614\) | − | 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 | \(-0.904771\pi\) | ||
0.955581 | − | 0.294728i | \(-0.0952290\pi\) | |||||||
\(660\) | 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 | \(-0.739507\pi\) | ||
0.683418 | − | 0.730027i | \(-0.260493\pi\) | |||||||
\(674\) | 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 | \(-0.802752\pi\) | ||
0.814068 | − | 0.580770i | \(-0.197248\pi\) | |||||||
\(684\) | −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 | \(0.250192\pi\) | ||||
−0.706680 | + | 0.707533i | \(0.749808\pi\) | |||||||
\(692\) | − | 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 | \(0.233995\pi\) | ||||
−0.741753 | + | 0.670674i | \(0.766005\pi\) | |||||||
\(702\) | −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 | \(-0.835274\pi\) | ||
0.869058 | − | 0.494710i | \(-0.164726\pi\) | |||||||
\(720\) | −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 | \(-0.693693\pi\) | ||
0.571640 | − | 0.820505i | \(-0.306307\pi\) | |||||||
\(740\) | 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 | \(-0.851976\pi\) | ||
0.893808 | − | 0.448450i | \(-0.148024\pi\) | |||||||
\(752\) | − | 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 | \(0.115406\pi\) | ||||
−0.934992 | + | 0.354668i | \(0.884594\pi\) | |||||||
\(770\) | 1837.84 | 2.38680 | ||||||||
\(771\) | 446.982 | 0.579743 | ||||||||
\(772\) | −694.885 | −0.900110 | ||||||||
\(773\) | 119.861i | 0.155060i | 0.996990 | + | 0.0775299i | \(0.0247033\pi\) | ||||
−0.996990 | + | 0.0775299i | \(0.975297\pi\) | |||||||
\(774\) | 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 | \(0.205759\pi\) | ||||
−0.798251 | + | 0.602324i | \(0.794241\pi\) | |||||||
\(798\) | 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 | \(-0.695189\pi\) | ||
0.575491 | − | 0.817808i | \(-0.304811\pi\) | |||||||
\(810\) | 86.6936i | 0.107029i | ||||||||
\(811\) | − | 1050.46i | − | 1.29526i | −0.761954 | − | 0.647631i | \(-0.775760\pi\) | ||
0.761954 | − | 0.647631i | \(-0.224240\pi\) | |||||||
\(812\) | 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 | \(0.124803\pi\) | ||||
−0.924117 | + | 0.382110i | \(0.875197\pi\) | |||||||
\(822\) | − | 68.6827i | − | 0.0835555i | ||||||
\(823\) | − | 579.065i | − | 0.703602i | −0.936075 | − | 0.351801i | \(-0.885569\pi\) | ||
0.936075 | − | 0.351801i | \(-0.114431\pi\) | |||||||
\(824\) | 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 | \(0.164934\pi\) | ||||
−0.868733 | + | 0.495280i | \(0.835066\pi\) | |||||||
\(840\) | − | 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 | \(-0.775347\pi\) | ||
0.761114 | − | 0.648619i | \(-0.224653\pi\) | |||||||
\(858\) | 1170.31i | 1.36400i | ||||||||
\(859\) | 188.285i | 0.219191i | 0.993976 | + | 0.109596i | \(0.0349556\pi\) | ||||
−0.993976 | + | 0.109596i | \(0.965044\pi\) | |||||||
\(860\) | 794.501i | 0.923839i | ||||||||
\(861\) | −764.317 | −0.887708 | ||||||||
\(862\) | 620.911 | 0.720314 | ||||||||
\(863\) | − | 1545.16i | − | 1.79045i | −0.445616 | − | 0.895224i | \(-0.647015\pi\) | ||
0.445616 | − | 0.895224i | \(-0.352985\pi\) | |||||||
\(864\) | − | 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 | \(0.389469\pi\) | ||||
−0.340306 | + | 0.940315i | \(0.610531\pi\) | |||||||
\(882\) | 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 | \(-0.854588\pi\) | ||
0.897457 | − | 0.441101i | \(-0.145412\pi\) | |||||||
\(888\) | −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 | \(0.209150\pi\) | ||||
−0.791789 | + | 0.610794i | \(0.790850\pi\) | |||||||
\(920\) | −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 | \(0.0666431\pi\) | ||||
−0.978163 | + | 0.207839i | \(0.933357\pi\) | |||||||
\(930\) | −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 | \(-0.993669\pi\) | ||
0.999802 | − | 0.0198867i | \(-0.00633054\pi\) | |||||||
\(938\) | 3111.76 | 3.31744 | ||||||||
\(939\) | 81.5594i | 0.0868578i | ||||||||
\(940\) | − | 1237.18i | − | 1.31615i | ||||||
\(941\) | 706.531i | 0.750830i | 0.926857 | + | 0.375415i | \(0.122500\pi\) | ||||
−0.926857 | + | 0.375415i | \(0.877500\pi\) | |||||||
\(942\) | 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 | \(0.0982040\pi\) | ||||
−0.952785 | + | 0.303646i | \(0.901796\pi\) | |||||||
\(968\) | 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 | \(-0.949642\pi\) | ||
0.987512 | − | 0.157545i | \(-0.0503580\pi\) | |||||||
\(978\) | − | 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 | \(-0.931156\pi\) | ||
0.976703 | − | 0.214597i | \(-0.0688439\pi\) | |||||||
\(984\) | 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 | \(0.168989\pi\) | ||||
−0.862354 | + | 0.506306i | \(0.831011\pi\) | |||||||
\(992\) | 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.58.17 | yes | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.4 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.4 | ✓ | 20 | |
177.176 | even | 2 | 531.3.c.c.235.17 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.4 | ✓ | 20 | 59.58 | odd | 2 | inner | |
177.3.c.a.58.17 | yes | 20 | 1.1 | even | 1 | trivial | |
531.3.c.c.235.4 | 20 | 3.2 | odd | 2 | |||
531.3.c.c.235.17 | 20 | 177.176 | even | 2 |