Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.5 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.28 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.21678i | − | 1.56750i | −0.621078 | − | 0.783749i | \(-0.713305\pi\) | ||
0.621078 | − | 0.783749i | \(-0.286695\pi\) | |||||||
\(3\) | −2.59178 | −1.49636 | −0.748182 | − | 0.663493i | \(-0.769073\pi\) | ||||
−0.748182 | + | 0.663493i | \(0.769073\pi\) | |||||||
\(4\) | −2.91410 | −1.45705 | ||||||||
\(5\) | 1.00571i | 0.449766i | 0.974386 | + | 0.224883i | \(0.0722001\pi\) | ||||
−0.974386 | + | 0.224883i | \(0.927800\pi\) | |||||||
\(6\) | 5.74540i | 2.34555i | ||||||||
\(7\) | 1.82096i | 0.688258i | 0.938922 | + | 0.344129i | \(0.111826\pi\) | ||||
−0.938922 | + | 0.344129i | \(0.888174\pi\) | |||||||
\(8\) | 2.02635i | 0.716423i | ||||||||
\(9\) | 3.71732 | 1.23911 | ||||||||
\(10\) | 2.22943 | 0.705008 | ||||||||
\(11\) | 2.73558i | 0.824810i | 0.911001 | + | 0.412405i | \(0.135311\pi\) | ||||
−0.911001 | + | 0.412405i | \(0.864689\pi\) | |||||||
\(12\) | 7.55270 | 2.18028 | ||||||||
\(13\) | 2.90778 | − | 2.13186i | 0.806472 | − | 0.591273i | ||||
\(14\) | 4.03666 | 1.07884 | ||||||||
\(15\) | − | 2.60657i | − | 0.673015i | ||||||
\(16\) | −1.33623 | −0.334057 | ||||||||
\(17\) | 2.66819 | 0.647131 | 0.323565 | − | 0.946206i | \(-0.395118\pi\) | ||||
0.323565 | + | 0.946206i | \(0.395118\pi\) | |||||||
\(18\) | − | 8.24047i | − | 1.94230i | ||||||
\(19\) | 2.04700i | 0.469614i | 0.972042 | + | 0.234807i | \(0.0754458\pi\) | ||||
−0.972042 | + | 0.234807i | \(0.924554\pi\) | |||||||
\(20\) | − | 2.93073i | − | 0.655332i | ||||||
\(21\) | − | 4.71953i | − | 1.02988i | ||||||
\(22\) | 6.06418 | 1.29289 | ||||||||
\(23\) | 1.36011 | 0.283603 | 0.141802 | − | 0.989895i | \(-0.454711\pi\) | ||||
0.141802 | + | 0.989895i | \(0.454711\pi\) | |||||||
\(24\) | − | 5.25186i | − | 1.07203i | ||||||
\(25\) | 3.98855 | 0.797710 | ||||||||
\(26\) | −4.72587 | − | 6.44589i | −0.926818 | − | 1.26414i | ||||
\(27\) | −1.85914 | −0.357792 | ||||||||
\(28\) | − | 5.30645i | − | 1.00283i | ||||||
\(29\) | −3.75197 | −0.696724 | −0.348362 | − | 0.937360i | \(-0.613262\pi\) | ||||
−0.348362 | + | 0.937360i | \(0.613262\pi\) | |||||||
\(30\) | −5.77819 | −1.05495 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | 7.01482i | 1.24006i | ||||||||
\(33\) | − | 7.09003i | − | 1.23422i | ||||||
\(34\) | − | 5.91478i | − | 1.01438i | ||||||
\(35\) | −1.83135 | −0.309555 | ||||||||
\(36\) | −10.8326 | −1.80544 | ||||||||
\(37\) | 5.04610i | 0.829573i | 0.909919 | + | 0.414787i | \(0.136144\pi\) | ||||
−0.909919 | + | 0.414787i | \(0.863856\pi\) | |||||||
\(38\) | 4.53774 | 0.736118 | ||||||||
\(39\) | −7.53631 | + | 5.52532i | −1.20678 | + | 0.884759i | ||||
\(40\) | −2.03792 | −0.322223 | ||||||||
\(41\) | − | 3.02730i | − | 0.472785i | −0.971658 | − | 0.236393i | \(-0.924035\pi\) | ||
0.971658 | − | 0.236393i | \(-0.0759652\pi\) | |||||||
\(42\) | −10.4621 | −1.61434 | ||||||||
\(43\) | 9.12211 | 1.39111 | 0.695554 | − | 0.718474i | \(-0.255159\pi\) | ||||
0.695554 | + | 0.718474i | \(0.255159\pi\) | |||||||
\(44\) | − | 7.97176i | − | 1.20179i | ||||||
\(45\) | 3.73854i | 0.557309i | ||||||||
\(46\) | − | 3.01506i | − | 0.444547i | ||||||
\(47\) | 7.62683i | 1.11249i | 0.831019 | + | 0.556244i | \(0.187758\pi\) | ||||
−0.831019 | + | 0.556244i | \(0.812242\pi\) | |||||||
\(48\) | 3.46321 | 0.499871 | ||||||||
\(49\) | 3.68411 | 0.526301 | ||||||||
\(50\) | − | 8.84173i | − | 1.25041i | ||||||
\(51\) | −6.91536 | −0.968343 | ||||||||
\(52\) | −8.47354 | + | 6.21246i | −1.17507 | + | 0.861513i | ||||
\(53\) | 5.26937 | 0.723804 | 0.361902 | − | 0.932216i | \(-0.382127\pi\) | ||||
0.361902 | + | 0.932216i | \(0.382127\pi\) | |||||||
\(54\) | 4.12130i | 0.560838i | ||||||||
\(55\) | −2.75120 | −0.370972 | ||||||||
\(56\) | −3.68990 | −0.493084 | ||||||||
\(57\) | − | 5.30537i | − | 0.702713i | ||||||
\(58\) | 8.31728i | 1.09211i | ||||||||
\(59\) | 2.66100i | 0.346433i | 0.984884 | + | 0.173216i | \(0.0554160\pi\) | ||||
−0.984884 | + | 0.173216i | \(0.944584\pi\) | |||||||
\(60\) | 7.59581i | 0.980615i | ||||||||
\(61\) | 7.14518 | 0.914847 | 0.457424 | − | 0.889249i | \(-0.348772\pi\) | ||||
0.457424 | + | 0.889249i | \(0.348772\pi\) | |||||||
\(62\) | −2.21678 | −0.281531 | ||||||||
\(63\) | 6.76909i | 0.852825i | ||||||||
\(64\) | 12.8778 | 1.60973 | ||||||||
\(65\) | 2.14403 | + | 2.92437i | 0.265935 | + | 0.362724i | ||||
\(66\) | −15.7170 | −1.93463 | ||||||||
\(67\) | 9.48459i | 1.15873i | 0.815069 | + | 0.579364i | \(0.196699\pi\) | ||||
−0.815069 | + | 0.579364i | \(0.803301\pi\) | |||||||
\(68\) | −7.77536 | −0.942901 | ||||||||
\(69\) | −3.52511 | −0.424374 | ||||||||
\(70\) | 4.05970i | 0.485227i | ||||||||
\(71\) | 4.99950i | 0.593331i | 0.954981 | + | 0.296665i | \(0.0958746\pi\) | ||||
−0.954981 | + | 0.296665i | \(0.904125\pi\) | |||||||
\(72\) | 7.53260i | 0.887725i | ||||||||
\(73\) | 4.50699i | 0.527503i | 0.964591 | + | 0.263751i | \(0.0849598\pi\) | ||||
−0.964591 | + | 0.263751i | \(0.915040\pi\) | |||||||
\(74\) | 11.1861 | 1.30035 | ||||||||
\(75\) | −10.3374 | −1.19367 | ||||||||
\(76\) | − | 5.96516i | − | 0.684250i | ||||||
\(77\) | −4.98139 | −0.567682 | ||||||||
\(78\) | 12.2484 | + | 16.7063i | 1.38686 | + | 1.89162i | ||||
\(79\) | −0.813843 | −0.0915645 | −0.0457822 | − | 0.998951i | \(-0.514578\pi\) | ||||
−0.0457822 | + | 0.998951i | \(0.514578\pi\) | |||||||
\(80\) | − | 1.34386i | − | 0.150248i | ||||||
\(81\) | −6.33348 | −0.703720 | ||||||||
\(82\) | −6.71086 | −0.741090 | ||||||||
\(83\) | − | 1.18611i | − | 0.130193i | −0.997879 | − | 0.0650963i | \(-0.979265\pi\) | ||
0.997879 | − | 0.0650963i | \(-0.0207355\pi\) | |||||||
\(84\) | 13.7532i | 1.50059i | ||||||||
\(85\) | 2.68342i | 0.291058i | ||||||||
\(86\) | − | 20.2217i | − | 2.18056i | ||||||
\(87\) | 9.72428 | 1.04255 | ||||||||
\(88\) | −5.54325 | −0.590913 | ||||||||
\(89\) | − | 16.2385i | − | 1.72128i | −0.509212 | − | 0.860641i | \(-0.670063\pi\) | ||
0.509212 | − | 0.860641i | \(-0.329937\pi\) | |||||||
\(90\) | 8.28751 | 0.873580 | ||||||||
\(91\) | 3.88204 | + | 5.29494i | 0.406948 | + | 0.555061i | ||||
\(92\) | −3.96350 | −0.413223 | ||||||||
\(93\) | 2.59178i | 0.268755i | ||||||||
\(94\) | 16.9070 | 1.74382 | ||||||||
\(95\) | −2.05868 | −0.211216 | ||||||||
\(96\) | − | 18.1809i | − | 1.85558i | ||||||
\(97\) | − | 3.69072i | − | 0.374736i | −0.982290 | − | 0.187368i | \(-0.940004\pi\) | ||
0.982290 | − | 0.187368i | \(-0.0599957\pi\) | |||||||
\(98\) | − | 8.16684i | − | 0.824976i | ||||||
\(99\) | 10.1690i | 1.02203i | ||||||||
\(100\) | −11.6230 | −1.16230 | ||||||||
\(101\) | −9.39142 | −0.934481 | −0.467241 | − | 0.884130i | \(-0.654752\pi\) | ||||
−0.467241 | + | 0.884130i | \(0.654752\pi\) | |||||||
\(102\) | 15.3298i | 1.51788i | ||||||||
\(103\) | 7.79135 | 0.767705 | 0.383852 | − | 0.923394i | \(-0.374597\pi\) | ||||
0.383852 | + | 0.923394i | \(0.374597\pi\) | |||||||
\(104\) | 4.31990 | + | 5.89217i | 0.423601 | + | 0.577775i | ||||
\(105\) | 4.74647 | 0.463208 | ||||||||
\(106\) | − | 11.6810i | − | 1.13456i | ||||||
\(107\) | −18.3141 | −1.77049 | −0.885245 | − | 0.465125i | \(-0.846009\pi\) | ||||
−0.885245 | + | 0.465125i | \(0.846009\pi\) | |||||||
\(108\) | 5.41772 | 0.521320 | ||||||||
\(109\) | 19.3010i | 1.84870i | 0.381542 | + | 0.924352i | \(0.375393\pi\) | ||||
−0.381542 | + | 0.924352i | \(0.624607\pi\) | |||||||
\(110\) | 6.09879i | 0.581497i | ||||||||
\(111\) | − | 13.0784i | − | 1.24134i | ||||||
\(112\) | − | 2.43322i | − | 0.229918i | ||||||
\(113\) | 1.71217 | 0.161067 | 0.0805335 | − | 0.996752i | \(-0.474338\pi\) | ||||
0.0805335 | + | 0.996752i | \(0.474338\pi\) | |||||||
\(114\) | −11.7608 | −1.10150 | ||||||||
\(115\) | 1.36788i | 0.127555i | ||||||||
\(116\) | 10.9336 | 1.01516 | ||||||||
\(117\) | 10.8091 | − | 7.92482i | 0.999305 | − | 0.732650i | ||||
\(118\) | 5.89884 | 0.543032 | ||||||||
\(119\) | 4.85866i | 0.445393i | ||||||||
\(120\) | 5.28183 | 0.482163 | ||||||||
\(121\) | 3.51658 | 0.319689 | ||||||||
\(122\) | − | 15.8393i | − | 1.43402i | ||||||
\(123\) | 7.84610i | 0.707459i | ||||||||
\(124\) | 2.91410i | 0.261694i | ||||||||
\(125\) | 9.03986i | 0.808550i | ||||||||
\(126\) | 15.0056 | 1.33680 | ||||||||
\(127\) | 16.9909 | 1.50770 | 0.753849 | − | 0.657048i | \(-0.228195\pi\) | ||||
0.753849 | + | 0.657048i | \(0.228195\pi\) | |||||||
\(128\) | − | 14.5176i | − | 1.28319i | ||||||
\(129\) | −23.6425 | −2.08161 | ||||||||
\(130\) | 6.48268 | − | 4.75284i | 0.568569 | − | 0.416852i | ||||
\(131\) | −12.4908 | −1.09133 | −0.545663 | − | 0.838005i | \(-0.683722\pi\) | ||||
−0.545663 | + | 0.838005i | \(0.683722\pi\) | |||||||
\(132\) | 20.6610i | 1.79831i | ||||||||
\(133\) | −3.72750 | −0.323215 | ||||||||
\(134\) | 21.0252 | 1.81630 | ||||||||
\(135\) | − | 1.86975i | − | 0.160923i | ||||||
\(136\) | 5.40669i | 0.463619i | ||||||||
\(137\) | 3.57641i | 0.305553i | 0.988261 | + | 0.152777i | \(0.0488215\pi\) | ||||
−0.988261 | + | 0.152777i | \(0.951179\pi\) | |||||||
\(138\) | 7.81438i | 0.665205i | ||||||||
\(139\) | −17.1808 | −1.45725 | −0.728627 | − | 0.684911i | \(-0.759841\pi\) | ||||
−0.728627 | + | 0.684911i | \(0.759841\pi\) | |||||||
\(140\) | 5.33675 | 0.451037 | ||||||||
\(141\) | − | 19.7671i | − | 1.66469i | ||||||
\(142\) | 11.0828 | 0.930045 | ||||||||
\(143\) | 5.83189 | + | 7.95446i | 0.487687 | + | 0.665186i | ||||
\(144\) | −4.96719 | −0.413933 | ||||||||
\(145\) | − | 3.77339i | − | 0.313363i | ||||||
\(146\) | 9.99098 | 0.826859 | ||||||||
\(147\) | −9.54839 | −0.787538 | ||||||||
\(148\) | − | 14.7048i | − | 1.20873i | ||||||
\(149\) | − | 9.50590i | − | 0.778754i | −0.921078 | − | 0.389377i | \(-0.872690\pi\) | ||
0.921078 | − | 0.389377i | \(-0.127310\pi\) | |||||||
\(150\) | 22.9158i | 1.87107i | ||||||||
\(151\) | − | 0.701427i | − | 0.0570814i | −0.999593 | − | 0.0285407i | \(-0.990914\pi\) | ||
0.999593 | − | 0.0285407i | \(-0.00908601\pi\) | |||||||
\(152\) | −4.14794 | −0.336442 | ||||||||
\(153\) | 9.91851 | 0.801864 | ||||||||
\(154\) | 11.0426i | 0.889840i | ||||||||
\(155\) | 1.00571 | 0.0807804 | ||||||||
\(156\) | 21.9616 | − | 16.1013i | 1.75833 | − | 1.28914i | ||||
\(157\) | −19.7650 | −1.57742 | −0.788710 | − | 0.614765i | \(-0.789251\pi\) | ||||
−0.788710 | + | 0.614765i | \(0.789251\pi\) | |||||||
\(158\) | 1.80411i | 0.143527i | ||||||||
\(159\) | −13.6571 | −1.08307 | ||||||||
\(160\) | −7.05487 | −0.557736 | ||||||||
\(161\) | 2.47671i | 0.195192i | ||||||||
\(162\) | 14.0399i | 1.10308i | ||||||||
\(163\) | 12.0409i | 0.943115i | 0.881835 | + | 0.471557i | \(0.156308\pi\) | ||||
−0.881835 | + | 0.471557i | \(0.843692\pi\) | |||||||
\(164\) | 8.82186i | 0.688872i | ||||||||
\(165\) | 7.13050 | 0.555109 | ||||||||
\(166\) | −2.62934 | −0.204077 | ||||||||
\(167\) | − | 20.4561i | − | 1.58294i | −0.611205 | − | 0.791472i | \(-0.709315\pi\) | ||
0.611205 | − | 0.791472i | \(-0.290685\pi\) | |||||||
\(168\) | 9.56342 | 0.737834 | ||||||||
\(169\) | 3.91031 | − | 12.3980i | 0.300793 | − | 0.953689i | ||||
\(170\) | 5.94854 | 0.456232 | ||||||||
\(171\) | 7.60935i | 0.581902i | ||||||||
\(172\) | −26.5827 | −2.02691 | ||||||||
\(173\) | 6.97691 | 0.530445 | 0.265222 | − | 0.964187i | \(-0.414555\pi\) | ||||
0.265222 | + | 0.964187i | \(0.414555\pi\) | |||||||
\(174\) | − | 21.5566i | − | 1.63420i | ||||||
\(175\) | 7.26299i | 0.549030i | ||||||||
\(176\) | − | 3.65537i | − | 0.275534i | ||||||
\(177\) | − | 6.89672i | − | 0.518389i | ||||||
\(178\) | −35.9972 | −2.69811 | ||||||||
\(179\) | 8.92044 | 0.666745 | 0.333372 | − | 0.942795i | \(-0.391813\pi\) | ||||
0.333372 | + | 0.942795i | \(0.391813\pi\) | |||||||
\(180\) | − | 10.8945i | − | 0.812026i | ||||||
\(181\) | −10.7089 | −0.795988 | −0.397994 | − | 0.917388i | \(-0.630293\pi\) | ||||
−0.397994 | + | 0.917388i | \(0.630293\pi\) | |||||||
\(182\) | 11.7377 | − | 8.60561i | 0.870056 | − | 0.637890i | ||||
\(183\) | −18.5187 | −1.36894 | ||||||||
\(184\) | 2.75606i | 0.203180i | ||||||||
\(185\) | −5.07490 | −0.373114 | ||||||||
\(186\) | 5.74540 | 0.421273 | ||||||||
\(187\) | 7.29905i | 0.533760i | ||||||||
\(188\) | − | 22.2253i | − | 1.62095i | ||||||
\(189\) | − | 3.38542i | − | 0.246253i | ||||||
\(190\) | 4.56364i | 0.331081i | ||||||||
\(191\) | −18.3129 | −1.32507 | −0.662537 | − | 0.749029i | \(-0.730520\pi\) | ||||
−0.662537 | + | 0.749029i | \(0.730520\pi\) | |||||||
\(192\) | −33.3765 | −2.40874 | ||||||||
\(193\) | − | 5.31567i | − | 0.382630i | −0.981529 | − | 0.191315i | \(-0.938725\pi\) | ||
0.981529 | − | 0.191315i | \(-0.0612753\pi\) | |||||||
\(194\) | −8.18151 | −0.587398 | ||||||||
\(195\) | −5.55686 | − | 7.57933i | −0.397935 | − | 0.542767i | ||||
\(196\) | −10.7358 | −0.766846 | ||||||||
\(197\) | 6.99284i | 0.498219i | 0.968475 | + | 0.249109i | \(0.0801379\pi\) | ||||
−0.968475 | + | 0.249109i | \(0.919862\pi\) | |||||||
\(198\) | 22.5425 | 1.60203 | ||||||||
\(199\) | −4.55657 | −0.323007 | −0.161503 | − | 0.986872i | \(-0.551634\pi\) | ||||
−0.161503 | + | 0.986872i | \(0.551634\pi\) | |||||||
\(200\) | 8.08220i | 0.571498i | ||||||||
\(201\) | − | 24.5820i | − | 1.73388i | ||||||
\(202\) | 20.8187i | 1.46480i | ||||||||
\(203\) | − | 6.83219i | − | 0.479526i | ||||||
\(204\) | 20.1520 | 1.41092 | ||||||||
\(205\) | 3.04458 | 0.212643 | ||||||||
\(206\) | − | 17.2717i | − | 1.20338i | ||||||
\(207\) | 5.05597 | 0.351415 | ||||||||
\(208\) | −3.88545 | + | 2.84866i | −0.269408 | + | 0.197519i | ||||
\(209\) | −5.59974 | −0.387342 | ||||||||
\(210\) | − | 10.5219i | − | 0.726077i | ||||||
\(211\) | 17.7764 | 1.22378 | 0.611889 | − | 0.790944i | \(-0.290410\pi\) | ||||
0.611889 | + | 0.790944i | \(0.290410\pi\) | |||||||
\(212\) | −15.3555 | −1.05462 | ||||||||
\(213\) | − | 12.9576i | − | 0.887839i | ||||||
\(214\) | 40.5983i | 2.77524i | ||||||||
\(215\) | 9.17418i | 0.625674i | ||||||||
\(216\) | − | 3.76727i | − | 0.256330i | ||||||
\(217\) | 1.82096 | 0.123615 | ||||||||
\(218\) | 42.7861 | 2.89784 | ||||||||
\(219\) | − | 11.6811i | − | 0.789336i | ||||||
\(220\) | 8.01726 | 0.540524 | ||||||||
\(221\) | 7.75849 | − | 5.68821i | 0.521893 | − | 0.382631i | ||||
\(222\) | −28.9918 | −1.94580 | ||||||||
\(223\) | − | 28.1562i | − | 1.88548i | −0.333532 | − | 0.942739i | \(-0.608240\pi\) | ||
0.333532 | − | 0.942739i | \(-0.391760\pi\) | |||||||
\(224\) | −12.7737 | −0.853479 | ||||||||
\(225\) | 14.8267 | 0.988448 | ||||||||
\(226\) | − | 3.79549i | − | 0.252472i | ||||||
\(227\) | − | 10.2989i | − | 0.683561i | −0.939780 | − | 0.341781i | \(-0.888970\pi\) | ||
0.939780 | − | 0.341781i | \(-0.111030\pi\) | |||||||
\(228\) | 15.4604i | 1.02389i | ||||||||
\(229\) | − | 11.7672i | − | 0.777601i | −0.921322 | − | 0.388800i | \(-0.872890\pi\) | ||
0.921322 | − | 0.388800i | \(-0.127110\pi\) | |||||||
\(230\) | 3.03228 | 0.199942 | ||||||||
\(231\) | 12.9107 | 0.849459 | ||||||||
\(232\) | − | 7.60281i | − | 0.499149i | ||||||
\(233\) | 15.0623 | 0.986765 | 0.493382 | − | 0.869813i | \(-0.335760\pi\) | ||||
0.493382 | + | 0.869813i | \(0.335760\pi\) | |||||||
\(234\) | −17.5676 | − | 23.9614i | −1.14843 | − | 1.56641i | ||||
\(235\) | −7.67036 | −0.500359 | ||||||||
\(236\) | − | 7.75441i | − | 0.504769i | ||||||
\(237\) | 2.10930 | 0.137014 | ||||||||
\(238\) | 10.7706 | 0.698152 | ||||||||
\(239\) | 4.17457i | 0.270030i | 0.990844 | + | 0.135015i | \(0.0431083\pi\) | ||||
−0.990844 | + | 0.135015i | \(0.956892\pi\) | |||||||
\(240\) | 3.48298i | 0.224825i | ||||||||
\(241\) | 17.7274i | 1.14192i | 0.820978 | + | 0.570960i | \(0.193429\pi\) | ||||
−0.820978 | + | 0.570960i | \(0.806571\pi\) | |||||||
\(242\) | − | 7.79548i | − | 0.501112i | ||||||
\(243\) | 21.9924 | 1.41081 | ||||||||
\(244\) | −20.8218 | −1.33298 | ||||||||
\(245\) | 3.70514i | 0.236713i | ||||||||
\(246\) | 17.3931 | 1.10894 | ||||||||
\(247\) | 4.36392 | + | 5.95221i | 0.277670 | + | 0.378730i | ||||
\(248\) | 2.02635 | 0.128673 | ||||||||
\(249\) | 3.07414i | 0.194816i | ||||||||
\(250\) | 20.0393 | 1.26740 | ||||||||
\(251\) | 1.71621 | 0.108326 | 0.0541632 | − | 0.998532i | \(-0.482751\pi\) | ||||
0.0541632 | + | 0.998532i | \(0.482751\pi\) | |||||||
\(252\) | − | 19.7258i | − | 1.24261i | ||||||
\(253\) | 3.72070i | 0.233918i | ||||||||
\(254\) | − | 37.6650i | − | 2.36331i | ||||||
\(255\) | − | 6.95483i | − | 0.435528i | ||||||
\(256\) | −6.42669 | −0.401668 | ||||||||
\(257\) | 17.8955 | 1.11629 | 0.558147 | − | 0.829742i | \(-0.311513\pi\) | ||||
0.558147 | + | 0.829742i | \(0.311513\pi\) | |||||||
\(258\) | 52.4101i | 3.26291i | ||||||||
\(259\) | −9.18874 | −0.570961 | ||||||||
\(260\) | −6.24792 | − | 8.52191i | −0.387480 | − | 0.528507i | ||||
\(261\) | −13.9473 | −0.863315 | ||||||||
\(262\) | 27.6893i | 1.71065i | ||||||||
\(263\) | −0.133456 | −0.00822927 | −0.00411463 | − | 0.999992i | \(-0.501310\pi\) | ||||
−0.00411463 | + | 0.999992i | \(0.501310\pi\) | |||||||
\(264\) | 14.3669 | 0.884221 | ||||||||
\(265\) | 5.29945i | 0.325543i | ||||||||
\(266\) | 8.26304i | 0.506639i | ||||||||
\(267\) | 42.0867i | 2.57567i | ||||||||
\(268\) | − | 27.6390i | − | 1.68832i | ||||||
\(269\) | 24.3960 | 1.48745 | 0.743725 | − | 0.668485i | \(-0.233057\pi\) | ||||
0.743725 | + | 0.668485i | \(0.233057\pi\) | |||||||
\(270\) | −4.14482 | −0.252246 | ||||||||
\(271\) | 3.25829i | 0.197927i | 0.995091 | + | 0.0989635i | \(0.0315527\pi\) | ||||
−0.995091 | + | 0.0989635i | \(0.968447\pi\) | |||||||
\(272\) | −3.56531 | −0.216179 | ||||||||
\(273\) | −10.0614 | − | 13.7233i | −0.608943 | − | 0.830573i | ||||
\(274\) | 7.92809 | 0.478954 | ||||||||
\(275\) | 10.9110i | 0.657959i | ||||||||
\(276\) | 10.2725 | 0.618333 | ||||||||
\(277\) | 10.6944 | 0.642563 | 0.321282 | − | 0.946984i | \(-0.395886\pi\) | ||||
0.321282 | + | 0.946984i | \(0.395886\pi\) | |||||||
\(278\) | 38.0859i | 2.28424i | ||||||||
\(279\) | − | 3.71732i | − | 0.222550i | ||||||
\(280\) | − | 3.71097i | − | 0.221773i | ||||||
\(281\) | 0.279634i | 0.0166816i | 0.999965 | + | 0.00834078i | \(0.00265498\pi\) | ||||
−0.999965 | + | 0.00834078i | \(0.997345\pi\) | |||||||
\(282\) | −43.8191 | −2.60939 | ||||||||
\(283\) | 8.05685 | 0.478930 | 0.239465 | − | 0.970905i | \(-0.423028\pi\) | ||||
0.239465 | + | 0.970905i | \(0.423028\pi\) | |||||||
\(284\) | − | 14.5690i | − | 0.864512i | ||||||
\(285\) | 5.33565 | 0.316057 | ||||||||
\(286\) | 17.6333 | − | 12.9280i | 1.04268 | − | 0.764449i | ||||
\(287\) | 5.51260 | 0.325398 | ||||||||
\(288\) | 26.0764i | 1.53656i | ||||||||
\(289\) | −9.88077 | −0.581222 | ||||||||
\(290\) | −8.36476 | −0.491196 | ||||||||
\(291\) | 9.56554i | 0.560742i | ||||||||
\(292\) | − | 13.1338i | − | 0.768597i | ||||||
\(293\) | − | 23.0395i | − | 1.34598i | −0.739650 | − | 0.672992i | \(-0.765009\pi\) | ||
0.739650 | − | 0.672992i | \(-0.234991\pi\) | |||||||
\(294\) | 21.1667i | 1.23446i | ||||||||
\(295\) | −2.67619 | −0.155814 | ||||||||
\(296\) | −10.2252 | −0.594326 | ||||||||
\(297\) | − | 5.08583i | − | 0.295110i | ||||||
\(298\) | −21.0725 | −1.22070 | ||||||||
\(299\) | 3.95490 | − | 2.89957i | 0.228718 | − | 0.167687i | ||||
\(300\) | 30.1243 | 1.73923 | ||||||||
\(301\) | 16.6110i | 0.957441i | ||||||||
\(302\) | −1.55491 | −0.0894749 | ||||||||
\(303\) | 24.3405 | 1.39832 | ||||||||
\(304\) | − | 2.73526i | − | 0.156878i | ||||||
\(305\) | 7.18597i | 0.411468i | ||||||||
\(306\) | − | 21.9871i | − | 1.25692i | ||||||
\(307\) | 31.6411i | 1.80585i | 0.429796 | + | 0.902926i | \(0.358585\pi\) | ||||
−0.429796 | + | 0.902926i | \(0.641415\pi\) | |||||||
\(308\) | 14.5162 | 0.827140 | ||||||||
\(309\) | −20.1935 | −1.14877 | ||||||||
\(310\) | − | 2.22943i | − | 0.126623i | ||||||
\(311\) | −30.7261 | −1.74232 | −0.871158 | − | 0.491003i | \(-0.836630\pi\) | ||||
−0.871158 | + | 0.491003i | \(0.836630\pi\) | |||||||
\(312\) | −11.1962 | − | 15.2712i | −0.633862 | − | 0.864562i | ||||
\(313\) | 33.4766 | 1.89221 | 0.946105 | − | 0.323860i | \(-0.104981\pi\) | ||||
0.946105 | + | 0.323860i | \(0.104981\pi\) | |||||||
\(314\) | 43.8146i | 2.47260i | ||||||||
\(315\) | −6.80773 | −0.383572 | ||||||||
\(316\) | 2.37162 | 0.133414 | ||||||||
\(317\) | 6.42234i | 0.360714i | 0.983601 | + | 0.180357i | \(0.0577254\pi\) | ||||
−0.983601 | + | 0.180357i | \(0.942275\pi\) | |||||||
\(318\) | 30.2746i | 1.69772i | ||||||||
\(319\) | − | 10.2638i | − | 0.574664i | ||||||
\(320\) | 12.9513i | 0.724002i | ||||||||
\(321\) | 47.4661 | 2.64930 | ||||||||
\(322\) | 5.49031 | 0.305963 | ||||||||
\(323\) | 5.46178i | 0.303901i | ||||||||
\(324\) | 18.4564 | 1.02536 | ||||||||
\(325\) | 11.5978 | − | 8.50305i | 0.643331 | − | 0.471664i | ||||
\(326\) | 26.6920 | 1.47833 | ||||||||
\(327\) | − | 50.0240i | − | 2.76633i | ||||||
\(328\) | 6.13438 | 0.338714 | ||||||||
\(329\) | −13.8881 | −0.765678 | ||||||||
\(330\) | − | 15.8067i | − | 0.870132i | ||||||
\(331\) | − | 33.3045i | − | 1.83058i | −0.402792 | − | 0.915291i | \(-0.631960\pi\) | ||
0.402792 | − | 0.915291i | \(-0.368040\pi\) | |||||||
\(332\) | 3.45644i | 0.189697i | ||||||||
\(333\) | 18.7580i | 1.02793i | ||||||||
\(334\) | −45.3467 | −2.48126 | ||||||||
\(335\) | −9.53874 | −0.521157 | ||||||||
\(336\) | 6.30637i | 0.344040i | ||||||||
\(337\) | −0.475146 | −0.0258829 | −0.0129414 | − | 0.999916i | \(-0.504120\pi\) | ||||
−0.0129414 | + | 0.999916i | \(0.504120\pi\) | |||||||
\(338\) | −27.4835 | − | 8.66829i | −1.49491 | − | 0.471493i | ||||
\(339\) | −4.43755 | −0.241015 | ||||||||
\(340\) | − | 7.81975i | − | 0.424085i | ||||||
\(341\) | 2.73558 | 0.148140 | ||||||||
\(342\) | 16.8682 | 0.912130 | ||||||||
\(343\) | 19.4553i | 1.05049i | ||||||||
\(344\) | 18.4846i | 0.996622i | ||||||||
\(345\) | − | 3.54523i | − | 0.190869i | ||||||
\(346\) | − | 15.4663i | − | 0.831471i | ||||||
\(347\) | 12.3110 | 0.660887 | 0.330443 | − | 0.943826i | \(-0.392802\pi\) | ||||
0.330443 | + | 0.943826i | \(0.392802\pi\) | |||||||
\(348\) | −28.3375 | −1.51905 | ||||||||
\(349\) | − | 34.9537i | − | 1.87103i | −0.353289 | − | 0.935514i | \(-0.614937\pi\) | ||
0.353289 | − | 0.935514i | \(-0.385063\pi\) | |||||||
\(350\) | 16.1004 | 0.860604 | ||||||||
\(351\) | −5.40596 | + | 3.96343i | −0.288549 | + | 0.211552i | ||||
\(352\) | −19.1896 | −1.02281 | ||||||||
\(353\) | 10.5811i | 0.563177i | 0.959535 | + | 0.281589i | \(0.0908614\pi\) | ||||
−0.959535 | + | 0.281589i | \(0.909139\pi\) | |||||||
\(354\) | −15.2885 | −0.812574 | ||||||||
\(355\) | −5.02803 | −0.266860 | ||||||||
\(356\) | 47.3207i | 2.50799i | ||||||||
\(357\) | − | 12.5926i | − | 0.666470i | ||||||
\(358\) | − | 19.7746i | − | 1.04512i | ||||||
\(359\) | 16.8943i | 0.891646i | 0.895121 | + | 0.445823i | \(0.147089\pi\) | ||||
−0.895121 | + | 0.445823i | \(0.852911\pi\) | |||||||
\(360\) | −7.57560 | −0.399269 | ||||||||
\(361\) | 14.8098 | 0.779463 | ||||||||
\(362\) | 23.7393i | 1.24771i | ||||||||
\(363\) | −9.11421 | −0.478372 | ||||||||
\(364\) | −11.3126 | − | 15.4300i | −0.592943 | − | 0.808751i | ||||
\(365\) | −4.53271 | −0.237253 | ||||||||
\(366\) | 41.0519i | 2.14582i | ||||||||
\(367\) | −10.0627 | −0.525270 | −0.262635 | − | 0.964895i | \(-0.584592\pi\) | ||||
−0.262635 | + | 0.964895i | \(0.584592\pi\) | |||||||
\(368\) | −1.81742 | −0.0947396 | ||||||||
\(369\) | − | 11.2535i | − | 0.585832i | ||||||
\(370\) | 11.2499i | 0.584856i | ||||||||
\(371\) | 9.59531i | 0.498164i | ||||||||
\(372\) | − | 7.55270i | − | 0.391589i | ||||||
\(373\) | −21.3532 | −1.10563 | −0.552814 | − | 0.833305i | \(-0.686446\pi\) | ||||
−0.552814 | + | 0.833305i | \(0.686446\pi\) | |||||||
\(374\) | 16.1804 | 0.836667 | ||||||||
\(375\) | − | 23.4293i | − | 1.20989i | ||||||
\(376\) | −15.4546 | −0.797012 | ||||||||
\(377\) | −10.9099 | + | 7.99869i | −0.561888 | + | 0.411954i | ||||
\(378\) | −7.50472 | −0.386001 | ||||||||
\(379\) | − | 14.8171i | − | 0.761101i | −0.924760 | − | 0.380551i | \(-0.875735\pi\) | ||
0.924760 | − | 0.380551i | \(-0.124265\pi\) | |||||||
\(380\) | 5.99921 | 0.307753 | ||||||||
\(381\) | −44.0366 | −2.25607 | ||||||||
\(382\) | 40.5956i | 2.07705i | ||||||||
\(383\) | − | 36.9845i | − | 1.88982i | −0.327333 | − | 0.944909i | \(-0.606150\pi\) | ||
0.327333 | − | 0.944909i | \(-0.393850\pi\) | |||||||
\(384\) | 37.6265i | 1.92012i | ||||||||
\(385\) | − | 5.00982i | − | 0.255324i | ||||||
\(386\) | −11.7837 | −0.599772 | ||||||||
\(387\) | 33.9098 | 1.72373 | ||||||||
\(388\) | 10.7551i | 0.546009i | ||||||||
\(389\) | −4.01436 | −0.203536 | −0.101768 | − | 0.994808i | \(-0.532450\pi\) | ||||
−0.101768 | + | 0.994808i | \(0.532450\pi\) | |||||||
\(390\) | −16.8017 | + | 12.3183i | −0.850786 | + | 0.623762i | ||||
\(391\) | 3.62904 | 0.183528 | ||||||||
\(392\) | 7.46529i | 0.377054i | ||||||||
\(393\) | 32.3734 | 1.63302 | ||||||||
\(394\) | 15.5016 | 0.780957 | ||||||||
\(395\) | − | 0.818488i | − | 0.0411826i | ||||||
\(396\) | − | 29.6336i | − | 1.48914i | ||||||
\(397\) | 19.4208i | 0.974702i | 0.873206 | + | 0.487351i | \(0.162037\pi\) | ||||
−0.873206 | + | 0.487351i | \(0.837963\pi\) | |||||||
\(398\) | 10.1009i | 0.506312i | ||||||||
\(399\) | 9.66086 | 0.483648 | ||||||||
\(400\) | −5.32962 | −0.266481 | ||||||||
\(401\) | − | 3.27194i | − | 0.163393i | −0.996657 | − | 0.0816965i | \(-0.973966\pi\) | ||
0.996657 | − | 0.0816965i | \(-0.0260338\pi\) | |||||||
\(402\) | −54.4928 | −2.71785 | ||||||||
\(403\) | −2.13186 | − | 2.90778i | −0.106196 | − | 0.144847i | ||||
\(404\) | 27.3675 | 1.36159 | ||||||||
\(405\) | − | 6.36964i | − | 0.316510i | ||||||
\(406\) | −15.1454 | −0.751655 | ||||||||
\(407\) | −13.8040 | −0.684240 | ||||||||
\(408\) | − | 14.0129i | − | 0.693744i | ||||||
\(409\) | 13.7956i | 0.682149i | 0.940036 | + | 0.341075i | \(0.110791\pi\) | ||||
−0.940036 | + | 0.341075i | \(0.889209\pi\) | |||||||
\(410\) | − | 6.74916i | − | 0.333317i | ||||||
\(411\) | − | 9.26926i | − | 0.457219i | ||||||
\(412\) | −22.7048 | −1.11858 | ||||||||
\(413\) | −4.84557 | −0.238435 | ||||||||
\(414\) | − | 11.2080i | − | 0.550841i | ||||||
\(415\) | 1.19288 | 0.0585562 | ||||||||
\(416\) | 14.9546 | + | 20.3975i | 0.733212 | + | 1.00007i | ||||
\(417\) | 44.5287 | 2.18058 | ||||||||
\(418\) | 12.4134i | 0.607157i | ||||||||
\(419\) | −28.8551 | −1.40967 | −0.704833 | − | 0.709374i | \(-0.748978\pi\) | ||||
−0.704833 | + | 0.709374i | \(0.748978\pi\) | |||||||
\(420\) | −13.8317 | −0.674916 | ||||||||
\(421\) | 14.0841i | 0.686417i | 0.939259 | + | 0.343209i | \(0.111514\pi\) | ||||
−0.939259 | + | 0.343209i | \(0.888486\pi\) | |||||||
\(422\) | − | 39.4063i | − | 1.91827i | ||||||
\(423\) | 28.3514i | 1.37849i | ||||||||
\(424\) | 10.6776i | 0.518550i | ||||||||
\(425\) | 10.6422 | 0.516223 | ||||||||
\(426\) | −28.7241 | −1.39169 | ||||||||
\(427\) | 13.0111i | 0.629651i | ||||||||
\(428\) | 53.3691 | 2.57969 | ||||||||
\(429\) | −15.1150 | − | 20.6162i | −0.729758 | − | 0.995360i | ||||
\(430\) | 20.3371 | 0.980742 | ||||||||
\(431\) | 21.1516i | 1.01884i | 0.860519 | + | 0.509419i | \(0.170139\pi\) | ||||
−0.860519 | + | 0.509419i | \(0.829861\pi\) | |||||||
\(432\) | 2.48424 | 0.119523 | ||||||||
\(433\) | −32.6610 | −1.56959 | −0.784795 | − | 0.619756i | \(-0.787232\pi\) | ||||
−0.784795 | + | 0.619756i | \(0.787232\pi\) | |||||||
\(434\) | − | 4.03666i | − | 0.193766i | ||||||
\(435\) | 9.77979i | 0.468905i | ||||||||
\(436\) | − | 56.2451i | − | 2.69365i | ||||||
\(437\) | 2.78415i | 0.133184i | ||||||||
\(438\) | −25.8944 | −1.23728 | ||||||||
\(439\) | 28.3889 | 1.35493 | 0.677463 | − | 0.735557i | \(-0.263079\pi\) | ||||
0.677463 | + | 0.735557i | \(0.263079\pi\) | |||||||
\(440\) | − | 5.57490i | − | 0.265773i | ||||||
\(441\) | 13.6950 | 0.652143 | ||||||||
\(442\) | −12.6095 | − | 17.1988i | −0.599773 | − | 0.818065i | ||||
\(443\) | 34.5066 | 1.63946 | 0.819729 | − | 0.572751i | \(-0.194124\pi\) | ||||
0.819729 | + | 0.572751i | \(0.194124\pi\) | |||||||
\(444\) | 38.1117i | 1.80870i | ||||||||
\(445\) | 16.3312 | 0.774175 | ||||||||
\(446\) | −62.4160 | −2.95548 | ||||||||
\(447\) | 24.6372i | 1.16530i | ||||||||
\(448\) | 23.4500i | 1.10791i | ||||||||
\(449\) | − | 8.05040i | − | 0.379922i | −0.981792 | − | 0.189961i | \(-0.939164\pi\) | ||
0.981792 | − | 0.189961i | \(-0.0608362\pi\) | |||||||
\(450\) | − | 32.8675i | − | 1.54939i | ||||||
\(451\) | 8.28144 | 0.389958 | ||||||||
\(452\) | −4.98942 | −0.234682 | ||||||||
\(453\) | 1.81795i | 0.0854145i | ||||||||
\(454\) | −22.8303 | −1.07148 | ||||||||
\(455\) | −5.32517 | + | 3.90420i | −0.249648 | + | 0.183032i | ||||
\(456\) | 10.7505 | 0.503440 | ||||||||
\(457\) | − | 1.80609i | − | 0.0844853i | −0.999107 | − | 0.0422427i | \(-0.986550\pi\) | ||
0.999107 | − | 0.0422427i | \(-0.0134503\pi\) | |||||||
\(458\) | −26.0853 | −1.21889 | ||||||||
\(459\) | −4.96053 | −0.231538 | ||||||||
\(460\) | − | 3.98613i | − | 0.185854i | ||||||
\(461\) | 31.7743i | 1.47988i | 0.672675 | + | 0.739938i | \(0.265145\pi\) | ||||
−0.672675 | + | 0.739938i | \(0.734855\pi\) | |||||||
\(462\) | − | 28.6200i | − | 1.33152i | ||||||
\(463\) | − | 38.5673i | − | 1.79237i | −0.443677 | − | 0.896187i | \(-0.646326\pi\) | ||
0.443677 | − | 0.896187i | \(-0.353674\pi\) | |||||||
\(464\) | 5.01349 | 0.232745 | ||||||||
\(465\) | −2.60657 | −0.120877 | ||||||||
\(466\) | − | 33.3898i | − | 1.54675i | ||||||
\(467\) | −32.7853 | −1.51712 | −0.758561 | − | 0.651602i | \(-0.774097\pi\) | ||||
−0.758561 | + | 0.651602i | \(0.774097\pi\) | |||||||
\(468\) | −31.4989 | + | 23.0937i | −1.45604 | + | 1.06751i | ||||
\(469\) | −17.2711 | −0.797504 | ||||||||
\(470\) | 17.0035i | 0.784312i | ||||||||
\(471\) | 51.2266 | 2.36040 | ||||||||
\(472\) | −5.39212 | −0.248192 | ||||||||
\(473\) | 24.9543i | 1.14740i | ||||||||
\(474\) | − | 4.67585i | − | 0.214769i | ||||||
\(475\) | 8.16456i | 0.374616i | ||||||||
\(476\) | − | 14.1586i | − | 0.648959i | ||||||
\(477\) | 19.5880 | 0.896871 | ||||||||
\(478\) | 9.25409 | 0.423272 | ||||||||
\(479\) | − | 31.2073i | − | 1.42590i | −0.701217 | − | 0.712948i | \(-0.747359\pi\) | ||
0.701217 | − | 0.712948i | \(-0.252641\pi\) | |||||||
\(480\) | 18.2847 | 0.834577 | ||||||||
\(481\) | 10.7576 | + | 14.6729i | 0.490504 | + | 0.669028i | ||||
\(482\) | 39.2976 | 1.78996 | ||||||||
\(483\) | − | 6.41908i | − | 0.292078i | ||||||
\(484\) | −10.2477 | −0.465803 | ||||||||
\(485\) | 3.71179 | 0.168544 | ||||||||
\(486\) | − | 48.7523i | − | 2.21145i | ||||||
\(487\) | 0.361759i | 0.0163929i | 0.999966 | + | 0.00819643i | \(0.00260903\pi\) | ||||
−0.999966 | + | 0.00819643i | \(0.997391\pi\) | |||||||
\(488\) | 14.4787i | 0.655418i | ||||||||
\(489\) | − | 31.2073i | − | 1.41124i | ||||||
\(490\) | 8.21346 | 0.371046 | ||||||||
\(491\) | −40.0199 | −1.80607 | −0.903036 | − | 0.429565i | \(-0.858667\pi\) | ||||
−0.903036 | + | 0.429565i | \(0.858667\pi\) | |||||||
\(492\) | − | 22.8643i | − | 1.03080i | ||||||
\(493\) | −10.0110 | −0.450871 | ||||||||
\(494\) | 13.1947 | − | 9.67384i | 0.593659 | − | 0.435247i | ||||
\(495\) | −10.2271 | −0.459674 | ||||||||
\(496\) | 1.33623i | 0.0599984i | ||||||||
\(497\) | −9.10388 | −0.408365 | ||||||||
\(498\) | 6.81468 | 0.305373 | ||||||||
\(499\) | − | 25.3343i | − | 1.13412i | −0.823677 | − | 0.567060i | \(-0.808081\pi\) | ||
0.823677 | − | 0.567060i | \(-0.191919\pi\) | |||||||
\(500\) | − | 26.3430i | − | 1.17810i | ||||||
\(501\) | 53.0178i | 2.36866i | ||||||||
\(502\) | − | 3.80446i | − | 0.169801i | ||||||
\(503\) | −26.7858 | −1.19432 | −0.597159 | − | 0.802123i | \(-0.703704\pi\) | ||||
−0.597159 | + | 0.802123i | \(0.703704\pi\) | |||||||
\(504\) | −13.7166 | −0.610984 | ||||||||
\(505\) | − | 9.44503i | − | 0.420298i | ||||||
\(506\) | 8.24796 | 0.366667 | ||||||||
\(507\) | −10.1347 | + | 32.1328i | −0.450097 | + | 1.42707i | ||||
\(508\) | −49.5131 | −2.19679 | ||||||||
\(509\) | 37.9869i | 1.68374i | 0.539680 | + | 0.841870i | \(0.318545\pi\) | ||||
−0.539680 | + | 0.841870i | \(0.681455\pi\) | |||||||
\(510\) | −15.4173 | −0.682690 | ||||||||
\(511\) | −8.20704 | −0.363058 | ||||||||
\(512\) | − | 14.7887i | − | 0.653576i | ||||||
\(513\) | − | 3.80566i | − | 0.168024i | ||||||
\(514\) | − | 39.6704i | − | 1.74979i | ||||||
\(515\) | 7.83583i | 0.345288i | ||||||||
\(516\) | 68.8965 | 3.03300 | ||||||||
\(517\) | −20.8638 | −0.917590 | ||||||||
\(518\) | 20.3694i | 0.894979i | ||||||||
\(519\) | −18.0826 | −0.793739 | ||||||||
\(520\) | −5.92581 | + | 4.34456i | −0.259864 | + | 0.190522i | ||||
\(521\) | −8.49756 | −0.372285 | −0.186143 | − | 0.982523i | \(-0.559599\pi\) | ||||
−0.186143 | + | 0.982523i | \(0.559599\pi\) | |||||||
\(522\) | 30.9180i | 1.35324i | ||||||||
\(523\) | 16.0250 | 0.700722 | 0.350361 | − | 0.936615i | \(-0.386059\pi\) | ||||
0.350361 | + | 0.936615i | \(0.386059\pi\) | |||||||
\(524\) | 36.3994 | 1.59012 | ||||||||
\(525\) | − | 18.8241i | − | 0.821550i | ||||||
\(526\) | 0.295843i | 0.0128994i | ||||||||
\(527\) | − | 2.66819i | − | 0.116228i | ||||||
\(528\) | 9.47390i | 0.412299i | ||||||||
\(529\) | −21.1501 | −0.919569 | ||||||||
\(530\) | 11.7477 | 0.510288 | ||||||||
\(531\) | 9.89179i | 0.429267i | ||||||||
\(532\) | 10.8623 | 0.470941 | ||||||||
\(533\) | −6.45380 | − | 8.80272i | −0.279545 | − | 0.381288i | ||||
\(534\) | 93.2969 | 4.03735 | ||||||||
\(535\) | − | 18.4186i | − | 0.796307i | ||||||
\(536\) | −19.2191 | −0.830139 | ||||||||
\(537\) | −23.1198 | −0.997694 | ||||||||
\(538\) | − | 54.0805i | − | 2.33158i | ||||||
\(539\) | 10.0782i | 0.434098i | ||||||||
\(540\) | 5.44864i | 0.234472i | ||||||||
\(541\) | 26.8172i | 1.15296i | 0.817111 | + | 0.576481i | \(0.195575\pi\) | ||||
−0.817111 | + | 0.576481i | \(0.804425\pi\) | |||||||
\(542\) | 7.22290 | 0.310250 | ||||||||
\(543\) | 27.7552 | 1.19109 | ||||||||
\(544\) | 18.7169i | 0.802479i | ||||||||
\(545\) | −19.4112 | −0.831485 | ||||||||
\(546\) | −30.4215 | + | 22.3038i | −1.30192 | + | 0.954516i | ||||
\(547\) | 0.552928 | 0.0236415 | 0.0118207 | − | 0.999930i | \(-0.496237\pi\) | ||||
0.0118207 | + | 0.999930i | \(0.496237\pi\) | |||||||
\(548\) | − | 10.4220i | − | 0.445206i | ||||||
\(549\) | 26.5609 | 1.13359 | ||||||||
\(550\) | 24.1873 | 1.03135 | ||||||||
\(551\) | − | 7.68028i | − | 0.327191i | ||||||
\(552\) | − | 7.14311i | − | 0.304031i | ||||||
\(553\) | − | 1.48197i | − | 0.0630200i | ||||||
\(554\) | − | 23.7071i | − | 1.00722i | ||||||
\(555\) | 13.1530 | 0.558315 | ||||||||
\(556\) | 50.0664 | 2.12329 | ||||||||
\(557\) | 15.0526i | 0.637797i | 0.947789 | + | 0.318899i | \(0.103313\pi\) | ||||
−0.947789 | + | 0.318899i | \(0.896687\pi\) | |||||||
\(558\) | −8.24047 | −0.348847 | ||||||||
\(559\) | 26.5250 | − | 19.4471i | 1.12189 | − | 0.822524i | ||||
\(560\) | 2.44711 | 0.103409 | ||||||||
\(561\) | − | 18.9175i | − | 0.798699i | ||||||
\(562\) | 0.619886 | 0.0261483 | ||||||||
\(563\) | −1.95269 | −0.0822963 | −0.0411481 | − | 0.999153i | \(-0.513102\pi\) | ||||
−0.0411481 | + | 0.999153i | \(0.513102\pi\) | |||||||
\(564\) | 57.6031i | 2.42553i | ||||||||
\(565\) | 1.72194i | 0.0724425i | ||||||||
\(566\) | − | 17.8602i | − | 0.750721i | ||||||
\(567\) | − | 11.5330i | − | 0.484341i | ||||||
\(568\) | −10.1307 | −0.425076 | ||||||||
\(569\) | −10.6879 | −0.448062 | −0.224031 | − | 0.974582i | \(-0.571922\pi\) | ||||
−0.224031 | + | 0.974582i | \(0.571922\pi\) | |||||||
\(570\) | − | 11.8280i | − | 0.495418i | ||||||
\(571\) | −11.1927 | −0.468401 | −0.234201 | − | 0.972188i | \(-0.575247\pi\) | ||||
−0.234201 | + | 0.972188i | \(0.575247\pi\) | |||||||
\(572\) | −16.9947 | − | 23.1801i | −0.710584 | − | 0.969208i | ||||
\(573\) | 47.4630 | 1.98279 | ||||||||
\(574\) | − | 12.2202i | − | 0.510061i | ||||||
\(575\) | 5.42488 | 0.226233 | ||||||||
\(576\) | 47.8711 | 1.99463 | ||||||||
\(577\) | − | 38.1339i | − | 1.58753i | −0.608222 | − | 0.793767i | \(-0.708117\pi\) | ||
0.608222 | − | 0.793767i | \(-0.291883\pi\) | |||||||
\(578\) | 21.9035i | 0.911064i | ||||||||
\(579\) | 13.7770i | 0.572554i | ||||||||
\(580\) | 10.9960i | 0.456585i | ||||||||
\(581\) | 2.15986 | 0.0896061 | ||||||||
\(582\) | 21.2047 | 0.878962 | ||||||||
\(583\) | 14.4148i | 0.597000i | ||||||||
\(584\) | −9.13273 | −0.377915 | ||||||||
\(585\) | 7.97006 | + | 10.8708i | 0.329521 | + | 0.449454i | ||||
\(586\) | −51.0735 | −2.10983 | ||||||||
\(587\) | 5.26098i | 0.217144i | 0.994089 | + | 0.108572i | \(0.0346278\pi\) | ||||
−0.994089 | + | 0.108572i | \(0.965372\pi\) | |||||||
\(588\) | 27.8250 | 1.14748 | ||||||||
\(589\) | 2.04700 | 0.0843451 | ||||||||
\(590\) | 5.93251i | 0.244238i | ||||||||
\(591\) | − | 18.1239i | − | 0.745517i | ||||||
\(592\) | − | 6.74274i | − | 0.277125i | ||||||
\(593\) | − | 25.9148i | − | 1.06419i | −0.846684 | − | 0.532096i | \(-0.821405\pi\) | ||
0.846684 | − | 0.532096i | \(-0.178595\pi\) | |||||||
\(594\) | −11.2742 | −0.462584 | ||||||||
\(595\) | −4.88640 | −0.200323 | ||||||||
\(596\) | 27.7011i | 1.13468i | ||||||||
\(597\) | 11.8096 | 0.483336 | ||||||||
\(598\) | −6.42771 | − | 8.76713i | −0.262848 | − | 0.358515i | ||||
\(599\) | 41.6832 | 1.70313 | 0.851564 | − | 0.524250i | \(-0.175654\pi\) | ||||
0.851564 | + | 0.524250i | \(0.175654\pi\) | |||||||
\(600\) | − | 20.9473i | − | 0.855170i | ||||||
\(601\) | 21.5712 | 0.879908 | 0.439954 | − | 0.898020i | \(-0.354995\pi\) | ||||
0.439954 | + | 0.898020i | \(0.354995\pi\) | |||||||
\(602\) | 36.8228 | 1.50079 | ||||||||
\(603\) | 35.2573i | 1.43579i | ||||||||
\(604\) | 2.04403i | 0.0831703i | ||||||||
\(605\) | 3.53666i | 0.143786i | ||||||||
\(606\) | − | 53.9574i | − | 2.19187i | ||||||
\(607\) | 34.8299 | 1.41370 | 0.706851 | − | 0.707362i | \(-0.250115\pi\) | ||||
0.706851 | + | 0.707362i | \(0.250115\pi\) | |||||||
\(608\) | −14.3593 | −0.582348 | ||||||||
\(609\) | 17.7075i | 0.717545i | ||||||||
\(610\) | 15.9297 | 0.644974 | ||||||||
\(611\) | 16.2594 | + | 22.1771i | 0.657783 | + | 0.897190i | ||||
\(612\) | −28.9035 | −1.16836 | ||||||||
\(613\) | − | 19.2039i | − | 0.775639i | −0.921735 | − | 0.387819i | \(-0.873228\pi\) | ||
0.921735 | − | 0.387819i | \(-0.126772\pi\) | |||||||
\(614\) | 70.1412 | 2.83067 | ||||||||
\(615\) | −7.89089 | −0.318191 | ||||||||
\(616\) | − | 10.0940i | − | 0.406700i | ||||||
\(617\) | 13.1172i | 0.528079i | 0.964512 | + | 0.264040i | \(0.0850550\pi\) | ||||
−0.964512 | + | 0.264040i | \(0.914945\pi\) | |||||||
\(618\) | 44.7644i | 1.80069i | ||||||||
\(619\) | 7.80176i | 0.313579i | 0.987632 | + | 0.156790i | \(0.0501145\pi\) | ||||
−0.987632 | + | 0.156790i | \(0.949886\pi\) | |||||||
\(620\) | −2.93073 | −0.117701 | ||||||||
\(621\) | −2.52864 | −0.101471 | ||||||||
\(622\) | 68.1128i | 2.73108i | ||||||||
\(623\) | 29.5697 | 1.18469 | ||||||||
\(624\) | 10.0702 | − | 7.38309i | 0.403132 | − | 0.295560i | ||||
\(625\) | 10.8513 | 0.434052 | ||||||||
\(626\) | − | 74.2102i | − | 2.96603i | ||||||
\(627\) | 14.5133 | 0.579605 | ||||||||
\(628\) | 57.5972 | 2.29838 | ||||||||
\(629\) | 13.4639i | 0.536842i | ||||||||
\(630\) | 15.0912i | 0.601249i | ||||||||
\(631\) | 4.02885i | 0.160386i | 0.996779 | + | 0.0801930i | \(0.0255537\pi\) | ||||
−0.996779 | + | 0.0801930i | \(0.974446\pi\) | |||||||
\(632\) | − | 1.64913i | − | 0.0655989i | ||||||
\(633\) | −46.0725 | −1.83122 | ||||||||
\(634\) | 14.2369 | 0.565419 | ||||||||
\(635\) | 17.0879i | 0.678112i | ||||||||
\(636\) | 39.7980 | 1.57809 | ||||||||
\(637\) | 10.7126 | − | 7.85401i | 0.424447 | − | 0.311187i | ||||
\(638\) | −22.7526 | −0.900785 | ||||||||
\(639\) | 18.5847i | 0.735201i | ||||||||
\(640\) | 14.6005 | 0.577136 | ||||||||
\(641\) | −2.73730 | −0.108117 | −0.0540584 | − | 0.998538i | \(-0.517216\pi\) | ||||
−0.0540584 | + | 0.998538i | \(0.517216\pi\) | |||||||
\(642\) | − | 105.222i | − | 4.15277i | ||||||
\(643\) | − | 7.54898i | − | 0.297703i | −0.988860 | − | 0.148851i | \(-0.952442\pi\) | ||
0.988860 | − | 0.148851i | \(-0.0475576\pi\) | |||||||
\(644\) | − | 7.21737i | − | 0.284404i | ||||||
\(645\) | − | 23.7774i | − | 0.936236i | ||||||
\(646\) | 12.1075 | 0.476365 | ||||||||
\(647\) | −9.51543 | −0.374090 | −0.187045 | − | 0.982351i | \(-0.559891\pi\) | ||||
−0.187045 | + | 0.982351i | \(0.559891\pi\) | |||||||
\(648\) | − | 12.8339i | − | 0.504162i | ||||||
\(649\) | −7.27939 | −0.285741 | ||||||||
\(650\) | −18.8494 | − | 25.7098i | −0.739332 | − | 1.00842i | ||||
\(651\) | −4.71953 | −0.184973 | ||||||||
\(652\) | − | 35.0883i | − | 1.37416i | ||||||
\(653\) | −15.6207 | −0.611286 | −0.305643 | − | 0.952146i | \(-0.598871\pi\) | ||||
−0.305643 | + | 0.952146i | \(0.598871\pi\) | |||||||
\(654\) | −110.892 | −4.33622 | ||||||||
\(655\) | − | 12.5621i | − | 0.490842i | ||||||
\(656\) | 4.04517i | 0.157937i | ||||||||
\(657\) | 16.7539i | 0.653632i | ||||||||
\(658\) | 30.7869i | 1.20020i | ||||||||
\(659\) | 5.25385 | 0.204661 | 0.102330 | − | 0.994750i | \(-0.467370\pi\) | ||||
0.102330 | + | 0.994750i | \(0.467370\pi\) | |||||||
\(660\) | −20.7790 | −0.808821 | ||||||||
\(661\) | − | 27.8552i | − | 1.08344i | −0.840558 | − | 0.541721i | \(-0.817773\pi\) | ||
0.840558 | − | 0.541721i | \(-0.182227\pi\) | |||||||
\(662\) | −73.8287 | −2.86943 | ||||||||
\(663\) | −20.1083 | + | 14.7426i | −0.780942 | + | 0.572555i | ||||
\(664\) | 2.40348 | 0.0932730 | ||||||||
\(665\) | − | 3.74878i | − | 0.145371i | ||||||
\(666\) | 41.5822 | 1.61128 | ||||||||
\(667\) | −5.10310 | −0.197593 | ||||||||
\(668\) | 59.6112i | 2.30643i | ||||||||
\(669\) | 72.9746i | 2.82136i | ||||||||
\(670\) | 21.1452i | 0.816912i | ||||||||
\(671\) | 19.5463i | 0.754575i | ||||||||
\(672\) | 33.1066 | 1.27712 | ||||||||
\(673\) | −36.1550 | −1.39367 | −0.696837 | − | 0.717229i | \(-0.745410\pi\) | ||||
−0.696837 | + | 0.717229i | \(0.745410\pi\) | |||||||
\(674\) | 1.05329i | 0.0405713i | ||||||||
\(675\) | −7.41527 | −0.285414 | ||||||||
\(676\) | −11.3950 | + | 36.1289i | −0.438271 | + | 1.38957i | ||||
\(677\) | −27.9179 | −1.07297 | −0.536487 | − | 0.843909i | \(-0.680249\pi\) | ||||
−0.536487 | + | 0.843909i | \(0.680249\pi\) | |||||||
\(678\) | 9.83707i | 0.377790i | ||||||||
\(679\) | 6.72066 | 0.257915 | ||||||||
\(680\) | −5.43755 | −0.208520 | ||||||||
\(681\) | 26.6924i | 1.02286i | ||||||||
\(682\) | − | 6.06418i | − | 0.232209i | ||||||
\(683\) | − | 37.1396i | − | 1.42111i | −0.703642 | − | 0.710554i | \(-0.748444\pi\) | ||
0.703642 | − | 0.710554i | \(-0.251556\pi\) | |||||||
\(684\) | − | 22.1744i | − | 0.847859i | ||||||
\(685\) | −3.59682 | −0.137428 | ||||||||
\(686\) | 43.1281 | 1.64664 | ||||||||
\(687\) | 30.4981i | 1.16357i | ||||||||
\(688\) | −12.1892 | −0.464710 | ||||||||
\(689\) | 15.3222 | − | 11.2336i | 0.583728 | − | 0.427965i | ||||
\(690\) | −7.85899 | −0.299187 | ||||||||
\(691\) | − | 40.0257i | − | 1.52265i | −0.648371 | − | 0.761324i | \(-0.724549\pi\) | ||
0.648371 | − | 0.761324i | \(-0.275451\pi\) | |||||||
\(692\) | −20.3314 | −0.772884 | ||||||||
\(693\) | −18.5174 | −0.703419 | ||||||||
\(694\) | − | 27.2906i | − | 1.03594i | ||||||
\(695\) | − | 17.2788i | − | 0.655424i | ||||||
\(696\) | 19.7048i | 0.746909i | ||||||||
\(697\) | − | 8.07742i | − | 0.305954i | ||||||
\(698\) | −77.4845 | −2.93283 | ||||||||
\(699\) | −39.0382 | −1.47656 | ||||||||
\(700\) | − | 21.1651i | − | 0.799964i | ||||||
\(701\) | −30.3361 | −1.14578 | −0.572890 | − | 0.819632i | \(-0.694178\pi\) | ||||
−0.572890 | + | 0.819632i | \(0.694178\pi\) | |||||||
\(702\) | 8.78604 | + | 11.9838i | 0.331608 | + | 0.452300i | ||||
\(703\) | −10.3294 | −0.389579 | ||||||||
\(704\) | 35.2284i | 1.32772i | ||||||||
\(705\) | 19.8799 | 0.748720 | ||||||||
\(706\) | 23.4560 | 0.882779 | ||||||||
\(707\) | − | 17.1014i | − | 0.643164i | ||||||
\(708\) | 20.0977i | 0.755319i | ||||||||
\(709\) | − | 4.72511i | − | 0.177455i | −0.996056 | − | 0.0887276i | \(-0.971720\pi\) | ||
0.996056 | − | 0.0887276i | \(-0.0282801\pi\) | |||||||
\(710\) | 11.1460i | 0.418303i | ||||||||
\(711\) | −3.02532 | −0.113458 | ||||||||
\(712\) | 32.9050 | 1.23317 | ||||||||
\(713\) | − | 1.36011i | − | 0.0509366i | ||||||
\(714\) | −27.9149 | −1.04469 | ||||||||
\(715\) | −7.99987 | + | 5.86518i | −0.299178 | + | 0.219345i | ||||
\(716\) | −25.9950 | −0.971480 | ||||||||
\(717\) | − | 10.8196i | − | 0.404064i | ||||||
\(718\) | 37.4509 | 1.39765 | ||||||||
\(719\) | −0.620833 | −0.0231532 | −0.0115766 | − | 0.999933i | \(-0.503685\pi\) | ||||
−0.0115766 | + | 0.999933i | \(0.503685\pi\) | |||||||
\(720\) | − | 4.99555i | − | 0.186173i | ||||||
\(721\) | 14.1877i | 0.528379i | ||||||||
\(722\) | − | 32.8300i | − | 1.22181i | ||||||
\(723\) | − | 45.9454i | − | 1.70873i | ||||||
\(724\) | 31.2068 | 1.15979 | ||||||||
\(725\) | −14.9649 | −0.555783 | ||||||||
\(726\) | 20.2042i | 0.749847i | ||||||||
\(727\) | 5.87302 | 0.217818 | 0.108909 | − | 0.994052i | \(-0.465264\pi\) | ||||
0.108909 | + | 0.994052i | \(0.465264\pi\) | |||||||
\(728\) | −10.7294 | + | 7.86637i | −0.397658 | + | 0.291547i | ||||
\(729\) | −37.9990 | −1.40737 | ||||||||
\(730\) | 10.0480i | 0.371894i | ||||||||
\(731\) | 24.3395 | 0.900229 | ||||||||
\(732\) | 53.9654 | 1.99462 | ||||||||
\(733\) | 37.4352i | 1.38270i | 0.722520 | + | 0.691350i | \(0.242984\pi\) | ||||
−0.722520 | + | 0.691350i | \(0.757016\pi\) | |||||||
\(734\) | 22.3068i | 0.823360i | ||||||||
\(735\) | − | 9.60290i | − | 0.354208i | ||||||
\(736\) | 9.54095i | 0.351684i | ||||||||
\(737\) | −25.9459 | −0.955730 | ||||||||
\(738\) | −24.9464 | −0.918290 | ||||||||
\(739\) | 2.78103i | 0.102302i | 0.998691 | + | 0.0511509i | \(0.0162890\pi\) | ||||
−0.998691 | + | 0.0511509i | \(0.983711\pi\) | |||||||
\(740\) | 14.7888 | 0.543646 | ||||||||
\(741\) | −11.3103 | − | 15.4268i | −0.415495 | − | 0.566719i | ||||
\(742\) | 21.2707 | 0.780871 | ||||||||
\(743\) | − | 18.4482i | − | 0.676799i | −0.941003 | − | 0.338399i | \(-0.890115\pi\) | ||
0.941003 | − | 0.338399i | \(-0.109885\pi\) | |||||||
\(744\) | −5.25186 | −0.192542 | ||||||||
\(745\) | 9.56017 | 0.350257 | ||||||||
\(746\) | 47.3353i | 1.73307i | ||||||||
\(747\) | − | 4.40916i | − | 0.161323i | ||||||
\(748\) | − | 21.2702i | − | 0.777714i | ||||||
\(749\) | − | 33.3492i | − | 1.21855i | ||||||
\(750\) | −51.9376 | −1.89649 | ||||||||
\(751\) | 34.9474 | 1.27525 | 0.637624 | − | 0.770348i | \(-0.279917\pi\) | ||||
0.637624 | + | 0.770348i | \(0.279917\pi\) | |||||||
\(752\) | − | 10.1912i | − | 0.371634i | ||||||
\(753\) | −4.44805 | −0.162096 | ||||||||
\(754\) | 17.7313 | + | 24.1848i | 0.645736 | + | 0.880758i | ||||
\(755\) | 0.705431 | 0.0256733 | ||||||||
\(756\) | 9.86544i | 0.358803i | ||||||||
\(757\) | 40.5867 | 1.47515 | 0.737574 | − | 0.675266i | \(-0.235971\pi\) | ||||
0.737574 | + | 0.675266i | \(0.235971\pi\) | |||||||
\(758\) | −32.8461 | −1.19302 | ||||||||
\(759\) | − | 9.64324i | − | 0.350027i | ||||||
\(760\) | − | 4.17162i | − | 0.151320i | ||||||
\(761\) | − | 35.5111i | − | 1.28728i | −0.765330 | − | 0.643638i | \(-0.777424\pi\) | ||
0.765330 | − | 0.643638i | \(-0.222576\pi\) | |||||||
\(762\) | 97.6194i | 3.53638i | ||||||||
\(763\) | −35.1464 | −1.27238 | ||||||||
\(764\) | 53.3655 | 1.93070 | ||||||||
\(765\) | 9.97513i | 0.360652i | ||||||||
\(766\) | −81.9863 | −2.96229 | ||||||||
\(767\) | 5.67289 | + | 7.73759i | 0.204836 | + | 0.279388i | ||||
\(768\) | 16.6566 | 0.601042 | ||||||||
\(769\) | 5.42518i | 0.195637i | 0.995204 | + | 0.0978186i | \(0.0311865\pi\) | ||||
−0.995204 | + | 0.0978186i | \(0.968814\pi\) | |||||||
\(770\) | −11.1057 | −0.400220 | ||||||||
\(771\) | −46.3813 | −1.67038 | ||||||||
\(772\) | 15.4904i | 0.557511i | ||||||||
\(773\) | − | 16.2454i | − | 0.584305i | −0.956372 | − | 0.292152i | \(-0.905629\pi\) | ||
0.956372 | − | 0.292152i | \(-0.0943715\pi\) | |||||||
\(774\) | − | 75.1705i | − | 2.70195i | ||||||
\(775\) | − | 3.98855i | − | 0.143273i | ||||||
\(776\) | 7.47870 | 0.268470 | ||||||||
\(777\) | 23.8152 | 0.854365 | ||||||||
\(778\) | 8.89893i | 0.319042i | ||||||||
\(779\) | 6.19689 | 0.222027 | ||||||||
\(780\) | 16.1932 | + | 22.0869i | 0.579811 | + | 0.790839i | ||||
\(781\) | −13.6765 | −0.489385 | ||||||||
\(782\) | − | 8.04476i | − | 0.287680i | ||||||
\(783\) | 6.97544 | 0.249282 | ||||||||
\(784\) | −4.92281 | −0.175815 | ||||||||
\(785\) | − | 19.8779i | − | 0.709471i | ||||||
\(786\) | − | 71.7646i | − | 2.55976i | ||||||
\(787\) | − | 6.94525i | − | 0.247572i | −0.992309 | − | 0.123786i | \(-0.960496\pi\) | ||
0.992309 | − | 0.123786i | \(-0.0395036\pi\) | |||||||
\(788\) | − | 20.3778i | − | 0.725929i | ||||||
\(789\) | 0.345889 | 0.0123140 | ||||||||
\(790\) | −1.81441 | −0.0645537 | ||||||||
\(791\) | 3.11778i | 0.110856i | ||||||||
\(792\) | −20.6061 | −0.732204 | ||||||||
\(793\) | 20.7766 | − | 15.2326i | 0.737798 | − | 0.540924i | ||||
\(794\) | 43.0516 | 1.52784 | ||||||||
\(795\) | − | 13.7350i | − | 0.487131i | ||||||
\(796\) | 13.2783 | 0.470637 | ||||||||
\(797\) | −2.95087 | −0.104525 | −0.0522626 | − | 0.998633i | \(-0.516643\pi\) | ||||
−0.0522626 | + | 0.998633i | \(0.516643\pi\) | |||||||
\(798\) | − | 21.4160i | − | 0.758117i | ||||||
\(799\) | 20.3498i | 0.719925i | ||||||||
\(800\) | 27.9790i | 0.989206i | ||||||||
\(801\) | − | 60.3639i | − | 2.13285i | ||||||
\(802\) | −7.25317 | −0.256118 | ||||||||
\(803\) | −12.3292 | −0.435089 | ||||||||
\(804\) | 71.6343i | 2.52635i | ||||||||
\(805\) | −2.49085 | −0.0877908 | ||||||||
\(806\) | −6.44589 | + | 4.72587i | −0.227047 | + | 0.166462i | ||||
\(807\) | −63.2291 | −2.22577 | ||||||||
\(808\) | − | 19.0303i | − | 0.669484i | ||||||
\(809\) | −35.5675 | −1.25049 | −0.625243 | − | 0.780430i | \(-0.715000\pi\) | ||||
−0.625243 | + | 0.780430i | \(0.715000\pi\) | |||||||
\(810\) | −14.1201 | −0.496128 | ||||||||
\(811\) | − | 20.4375i | − | 0.717659i | −0.933403 | − | 0.358830i | \(-0.883176\pi\) | ||
0.933403 | − | 0.358830i | \(-0.116824\pi\) | |||||||
\(812\) | 19.9097i | 0.698692i | ||||||||
\(813\) | − | 8.44477i | − | 0.296171i | ||||||
\(814\) | 30.6004i | 1.07254i | ||||||||
\(815\) | −12.1096 | −0.424181 | ||||||||
\(816\) | 9.24050 | 0.323482 | ||||||||
\(817\) | 18.6729i | 0.653284i | ||||||||
\(818\) | 30.5818 | 1.06927 | ||||||||
\(819\) | 14.4308 | + | 19.6830i | 0.504252 | + | 0.687780i | ||||
\(820\) | −8.87222 | −0.309831 | ||||||||
\(821\) | 35.8194i | 1.25011i | 0.780582 | + | 0.625053i | \(0.214923\pi\) | ||||
−0.780582 | + | 0.625053i | \(0.785077\pi\) | |||||||
\(822\) | −20.5479 | −0.716689 | ||||||||
\(823\) | −7.45012 | −0.259695 | −0.129848 | − | 0.991534i | \(-0.541449\pi\) | ||||
−0.129848 | + | 0.991534i | \(0.541449\pi\) | |||||||
\(824\) | 15.7880i | 0.550002i | ||||||||
\(825\) | − | 28.2789i | − | 0.984546i | ||||||
\(826\) | 10.7415i | 0.373746i | ||||||||
\(827\) | 11.2580i | 0.391478i | 0.980656 | + | 0.195739i | \(0.0627105\pi\) | ||||
−0.980656 | + | 0.195739i | \(0.937290\pi\) | |||||||
\(828\) | −14.7336 | −0.512028 | ||||||||
\(829\) | −35.2422 | −1.22401 | −0.612006 | − | 0.790853i | \(-0.709637\pi\) | ||||
−0.612006 | + | 0.790853i | \(0.709637\pi\) | |||||||
\(830\) | − | 2.64435i | − | 0.0917868i | ||||||
\(831\) | −27.7175 | −0.961509 | ||||||||
\(832\) | 37.4459 | − | 27.4538i | 1.29820 | − | 0.951789i | ||||
\(833\) | 9.82989 | 0.340586 | ||||||||
\(834\) | − | 98.7103i | − | 3.41806i | ||||||
\(835\) | 20.5729 | 0.711955 | ||||||||
\(836\) | 16.3182 | 0.564376 | ||||||||
\(837\) | 1.85914i | 0.0642613i | ||||||||
\(838\) | 63.9654i | 2.20965i | ||||||||
\(839\) | − | 43.3244i | − | 1.49572i | −0.663854 | − | 0.747862i | \(-0.731080\pi\) | ||
0.663854 | − | 0.747862i | \(-0.268920\pi\) | |||||||
\(840\) | 9.61801i | 0.331853i | ||||||||
\(841\) | −14.9227 | −0.514576 | ||||||||
\(842\) | 31.2213 | 1.07596 | ||||||||
\(843\) | − | 0.724749i | − | 0.0249617i | ||||||
\(844\) | −51.8022 | −1.78311 | ||||||||
\(845\) | 12.4687 | + | 3.93264i | 0.428937 | + | 0.135287i | ||||
\(846\) | 62.8487 | 2.16078 | ||||||||
\(847\) | 6.40355i | 0.220029i | ||||||||
\(848\) | −7.04109 | −0.241792 | ||||||||
\(849\) | −20.8816 | −0.716654 | ||||||||
\(850\) | − | 23.5914i | − | 0.809178i | ||||||
\(851\) | 6.86326i | 0.235270i | ||||||||
\(852\) | 37.7597i | 1.29363i | ||||||||
\(853\) | 19.0628i | 0.652699i | 0.945249 | + | 0.326350i | \(0.105819\pi\) | ||||
−0.945249 | + | 0.326350i | \(0.894181\pi\) | |||||||
\(854\) | 28.8427 | 0.986976 | ||||||||
\(855\) | −7.65279 | −0.261720 | ||||||||
\(856\) | − | 37.1108i | − | 1.26842i | ||||||
\(857\) | 28.1693 | 0.962247 | 0.481123 | − | 0.876653i | \(-0.340229\pi\) | ||||
0.481123 | + | 0.876653i | \(0.340229\pi\) | |||||||
\(858\) | −45.7015 | + | 33.5065i | −1.56022 | + | 1.14389i | ||||
\(859\) | −19.7322 | −0.673254 | −0.336627 | − | 0.941638i | \(-0.609286\pi\) | ||||
−0.336627 | + | 0.941638i | \(0.609286\pi\) | |||||||
\(860\) | − | 26.7345i | − | 0.911637i | ||||||
\(861\) | −14.2874 | −0.486915 | ||||||||
\(862\) | 46.8884 | 1.59702 | ||||||||
\(863\) | − | 6.48496i | − | 0.220751i | −0.993890 | − | 0.110375i | \(-0.964795\pi\) | ||
0.993890 | − | 0.110375i | \(-0.0352053\pi\) | |||||||
\(864\) | − | 13.0415i | − | 0.443682i | ||||||
\(865\) | 7.01674i | 0.238576i | ||||||||
\(866\) | 72.4022i | 2.46033i | ||||||||
\(867\) | 25.6088 | 0.869720 | ||||||||
\(868\) | −5.30645 | −0.180113 | ||||||||
\(869\) | − | 2.22633i | − | 0.0755232i | ||||||
\(870\) | 21.6796 | 0.735008 | ||||||||
\(871\) | 20.2199 | + | 27.5791i | 0.685124 | + | 0.934481i | ||||
\(872\) | −39.1107 | −1.32445 | ||||||||
\(873\) | − | 13.7196i | − | 0.464338i | ||||||
\(874\) | 6.17183 | 0.208765 | ||||||||
\(875\) | −16.4612 | −0.556491 | ||||||||
\(876\) | 34.0399i | 1.15010i | ||||||||
\(877\) | − | 19.0913i | − | 0.644666i | −0.946626 | − | 0.322333i | \(-0.895533\pi\) | ||
0.946626 | − | 0.322333i | \(-0.104467\pi\) | |||||||
\(878\) | − | 62.9318i | − | 2.12384i | ||||||
\(879\) | 59.7134i | 2.01408i | ||||||||
\(880\) | 3.67623 | 0.123926 | ||||||||
\(881\) | 2.46976 | 0.0832082 | 0.0416041 | − | 0.999134i | \(-0.486753\pi\) | ||||
0.0416041 | + | 0.999134i | \(0.486753\pi\) | |||||||
\(882\) | − | 30.3588i | − | 1.02223i | ||||||
\(883\) | 19.1170 | 0.643338 | 0.321669 | − | 0.946852i | \(-0.395756\pi\) | ||||
0.321669 | + | 0.946852i | \(0.395756\pi\) | |||||||
\(884\) | −22.6090 | + | 16.5760i | −0.760423 | + | 0.557512i | ||||
\(885\) | 6.93609 | 0.233154 | ||||||||
\(886\) | − | 76.4934i | − | 2.56985i | ||||||
\(887\) | 23.3018 | 0.782399 | 0.391199 | − | 0.920306i | \(-0.372060\pi\) | ||||
0.391199 | + | 0.920306i | \(0.372060\pi\) | |||||||
\(888\) | 26.5014 | 0.889328 | ||||||||
\(889\) | 30.9397i | 1.03769i | ||||||||
\(890\) | − | 36.2027i | − | 1.21352i | ||||||
\(891\) | − | 17.3258i | − | 0.580435i | ||||||
\(892\) | 82.0499i | 2.74723i | ||||||||
\(893\) | −15.6121 | −0.522439 | ||||||||
\(894\) | 54.6152 | 1.82660 | ||||||||
\(895\) | 8.97136i | 0.299880i | ||||||||
\(896\) | 26.4360 | 0.883166 | ||||||||
\(897\) | −10.2502 | + | 7.51506i | −0.342245 | + | 0.250920i | ||||
\(898\) | −17.8459 | −0.595527 | ||||||||
\(899\) | 3.75197i | 0.125135i | ||||||||
\(900\) | −43.2065 | −1.44022 | ||||||||
\(901\) | 14.0597 | 0.468396 | ||||||||
\(902\) | − | 18.3581i | − | 0.611258i | ||||||
\(903\) | − | 43.0520i | − | 1.43268i | ||||||
\(904\) | 3.46945i | 0.115392i | ||||||||
\(905\) | − | 10.7700i | − | 0.358009i | ||||||
\(906\) | 4.02998 | 0.133887 | ||||||||
\(907\) | 2.87726 | 0.0955379 | 0.0477689 | − | 0.998858i | \(-0.484789\pi\) | ||||
0.0477689 | + | 0.998858i | \(0.484789\pi\) | |||||||
\(908\) | 30.0120i | 0.995982i | ||||||||
\(909\) | −34.9109 | −1.15792 | ||||||||
\(910\) | 8.65473 | + | 11.8047i | 0.286902 | + | 0.391322i | ||||
\(911\) | −48.4102 | −1.60390 | −0.801951 | − | 0.597390i | \(-0.796204\pi\) | ||||
−0.801951 | + | 0.597390i | \(0.796204\pi\) | |||||||
\(912\) | 7.08919i | 0.234746i | ||||||||
\(913\) | 3.24471 | 0.107384 | ||||||||
\(914\) | −4.00370 | −0.132431 | ||||||||
\(915\) | − | 18.6245i | − | 0.615705i | ||||||
\(916\) | 34.2909i | 1.13300i | ||||||||
\(917\) | − | 22.7452i | − | 0.751114i | ||||||
\(918\) | 10.9964i | 0.362935i | ||||||||
\(919\) | −29.7821 | −0.982419 | −0.491210 | − | 0.871041i | \(-0.663445\pi\) | ||||
−0.491210 | + | 0.871041i | \(0.663445\pi\) | |||||||
\(920\) | −2.77180 | −0.0913835 | ||||||||
\(921\) | − | 82.0067i | − | 2.70221i | ||||||
\(922\) | 70.4365 | 2.31970 | ||||||||
\(923\) | 10.6582 | + | 14.5374i | 0.350820 | + | 0.478505i | ||||
\(924\) | −37.6229 | −1.23770 | ||||||||
\(925\) | 20.1266i | 0.661759i | ||||||||
\(926\) | −85.4950 | −2.80954 | ||||||||
\(927\) | 28.9630 | 0.951268 | ||||||||
\(928\) | − | 26.3194i | − | 0.863977i | ||||||
\(929\) | 54.5572i | 1.78996i | 0.446103 | + | 0.894982i | \(0.352812\pi\) | ||||
−0.446103 | + | 0.894982i | \(0.647188\pi\) | |||||||
\(930\) | 5.77819i | 0.189474i | ||||||||
\(931\) | 7.54136i | 0.247158i | ||||||||
\(932\) | −43.8931 | −1.43776 | ||||||||
\(933\) | 79.6352 | 2.60714 | ||||||||
\(934\) | 72.6777i | 2.37809i | ||||||||
\(935\) | −7.34072 | −0.240067 | ||||||||
\(936\) | 16.0585 | + | 21.9031i | 0.524888 | + | 0.715925i | ||||
\(937\) | 31.8081 | 1.03912 | 0.519562 | − | 0.854433i | \(-0.326095\pi\) | ||||
0.519562 | + | 0.854433i | \(0.326095\pi\) | |||||||
\(938\) | 38.2861i | 1.25008i | ||||||||
\(939\) | −86.7640 | −2.83144 | ||||||||
\(940\) | 22.3522 | 0.729048 | ||||||||
\(941\) | − | 30.6060i | − | 0.997726i | −0.866681 | − | 0.498863i | \(-0.833751\pi\) | ||
0.866681 | − | 0.498863i | \(-0.166249\pi\) | |||||||
\(942\) | − | 113.558i | − | 3.69992i | ||||||
\(943\) | − | 4.11747i | − | 0.134083i | ||||||
\(944\) | − | 3.55570i | − | 0.115728i | ||||||
\(945\) | 3.40474 | 0.110756 | ||||||||
\(946\) | 55.3181 | 1.79855 | ||||||||
\(947\) | 24.4062i | 0.793094i | 0.918014 | + | 0.396547i | \(0.129792\pi\) | ||||
−0.918014 | + | 0.396547i | \(0.870208\pi\) | |||||||
\(948\) | −6.14671 | −0.199636 | ||||||||
\(949\) | 9.60828 | + | 13.1053i | 0.311898 | + | 0.425416i | ||||
\(950\) | 18.0990 | 0.587209 | ||||||||
\(951\) | − | 16.6453i | − | 0.539760i | ||||||
\(952\) | −9.84536 | −0.319090 | ||||||||
\(953\) | 22.7737 | 0.737712 | 0.368856 | − | 0.929487i | \(-0.379750\pi\) | ||||
0.368856 | + | 0.929487i | \(0.379750\pi\) | |||||||
\(954\) | − | 43.4221i | − | 1.40584i | ||||||
\(955\) | − | 18.4174i | − | 0.595974i | ||||||
\(956\) | − | 12.1651i | − | 0.393448i | ||||||
\(957\) | 26.6016i | 0.859907i | ||||||||
\(958\) | −69.1796 | −2.23509 | ||||||||
\(959\) | −6.51249 | −0.210299 | ||||||||
\(960\) | − | 33.5670i | − | 1.08337i | ||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 32.5266 | − | 23.8472i | 1.04870 | − | 0.768864i | ||||
\(963\) | −68.0794 | −2.19383 | ||||||||
\(964\) | − | 51.6593i | − | 1.66383i | ||||||
\(965\) | 5.34601 | 0.172094 | ||||||||
\(966\) | −14.2297 | −0.457832 | ||||||||
\(967\) | 48.8154i | 1.56980i | 0.619623 | + | 0.784899i | \(0.287285\pi\) | ||||
−0.619623 | + | 0.784899i | \(0.712715\pi\) | |||||||
\(968\) | 7.12583i | 0.229033i | ||||||||
\(969\) | − | 14.1557i | − | 0.454747i | ||||||
\(970\) | − | 8.22821i | − | 0.264192i | ||||||
\(971\) | 50.6775 | 1.62632 | 0.813160 | − | 0.582041i | \(-0.197746\pi\) | ||||
0.813160 | + | 0.582041i | \(0.197746\pi\) | |||||||
\(972\) | −64.0881 | −2.05563 | ||||||||
\(973\) | − | 31.2855i | − | 1.00297i | ||||||
\(974\) | 0.801939 | 0.0256958 | ||||||||
\(975\) | −30.0590 | + | 22.0380i | −0.962657 | + | 0.705782i | ||||
\(976\) | −9.54760 | −0.305611 | ||||||||
\(977\) | 51.8306i | 1.65821i | 0.559094 | + | 0.829105i | \(0.311149\pi\) | ||||
−0.559094 | + | 0.829105i | \(0.688851\pi\) | |||||||
\(978\) | −69.1797 | −2.21212 | ||||||||
\(979\) | 44.4219 | 1.41973 | ||||||||
\(980\) | − | 10.7971i | − | 0.344902i | ||||||
\(981\) | 71.7481i | 2.29074i | ||||||||
\(982\) | 88.7151i | 2.83101i | ||||||||
\(983\) | − | 12.0939i | − | 0.385736i | −0.981225 | − | 0.192868i | \(-0.938221\pi\) | ||
0.981225 | − | 0.192868i | \(-0.0617789\pi\) | |||||||
\(984\) | −15.8990 | −0.506840 | ||||||||
\(985\) | −7.03275 | −0.224082 | ||||||||
\(986\) | 22.1921i | 0.706740i | ||||||||
\(987\) | 35.9950 | 1.14573 | ||||||||
\(988\) | −12.7169 | − | 17.3453i | −0.404578 | − | 0.551828i | ||||
\(989\) | 12.4071 | 0.394522 | ||||||||
\(990\) | 22.6712i | 0.720537i | ||||||||
\(991\) | 49.4882 | 1.57204 | 0.786022 | − | 0.618199i | \(-0.212137\pi\) | ||||
0.786022 | + | 0.618199i | \(0.212137\pi\) | |||||||
\(992\) | 7.01482 | 0.222721 | ||||||||
\(993\) | 86.3180i | 2.73922i | ||||||||
\(994\) | 20.1813i | 0.640111i | ||||||||
\(995\) | − | 4.58258i | − | 0.145278i | ||||||
\(996\) | − | 8.95834i | − | 0.283856i | ||||||
\(997\) | −9.06621 | −0.287130 | −0.143565 | − | 0.989641i | \(-0.545857\pi\) | ||||
−0.143565 | + | 0.989641i | \(0.545857\pi\) | |||||||
\(998\) | −56.1605 | −1.77773 | ||||||||
\(999\) | − | 9.38140i | − | 0.296814i |
(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 | 403.2.c.b.311.5 | ✓ | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.2 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.15 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.28 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
403.2.c.b.311.28 | yes | 32 | 13.12 | even | 2 | inner | |
5239.2.a.k.1.15 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.2 | 16 | 13.5 | odd | 4 |