Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(151,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.451 |
Dual form | 750.2.g.b.301.1 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.309017 | + | 0.951057i | −0.126156 | + | 0.388267i | ||||
\(7\) | −2.61803 | −0.989524 | −0.494762 | − | 0.869029i | \(-0.664745\pi\) | ||||
−0.494762 | + | 0.869029i | \(0.664745\pi\) | |||||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.92705 | − | 2.12663i | −0.882539 | − | 0.641202i | 0.0513829 | − | 0.998679i | \(-0.483637\pi\) |
−0.933922 | + | 0.357477i | \(0.883637\pi\) | |||||||
\(12\) | −0.809017 | + | 0.587785i | −0.233543 | + | 0.169679i | ||||
\(13\) | −5.23607 | + | 3.80423i | −1.45222 | + | 1.05510i | −0.466919 | + | 0.884300i | \(0.654636\pi\) |
−0.985305 | + | 0.170802i | \(0.945364\pi\) | |||||||
\(14\) | −2.11803 | − | 1.53884i | −0.566068 | − | 0.411273i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −0.381966 | + | 1.17557i | −0.0926404 | + | 0.285118i | −0.986632 | − | 0.162967i | \(-0.947894\pi\) |
0.893991 | + | 0.448085i | \(0.147894\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.76393 | + | 5.42882i | −0.404674 | + | 1.24546i | 0.516494 | + | 0.856291i | \(0.327237\pi\) |
−0.921167 | + | 0.389167i | \(0.872763\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.809017 | − | 2.48990i | −0.176542 | − | 0.543340i | ||||
\(22\) | −1.11803 | − | 3.44095i | −0.238366 | − | 0.733614i | ||||
\(23\) | 3.61803 | + | 2.62866i | 0.754412 | + | 0.548113i | 0.897191 | − | 0.441642i | \(-0.145604\pi\) |
−0.142779 | + | 0.989755i | \(0.545604\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.47214 | −1.26929 | ||||||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | −0.809017 | − | 2.48990i | −0.152890 | − | 0.470547i | ||||
\(29\) | 2.61803 | + | 8.05748i | 0.486157 | + | 1.49624i | 0.830299 | + | 0.557319i | \(0.188170\pi\) |
−0.344142 | + | 0.938918i | \(0.611830\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.04508 | − | 6.29412i | 0.367308 | − | 1.13046i | −0.581215 | − | 0.813750i | \(-0.697422\pi\) |
0.948523 | − | 0.316708i | \(-0.102578\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.11803 | − | 3.44095i | 0.194625 | − | 0.598993i | ||||
\(34\) | −1.00000 | + | 0.726543i | −0.171499 | + | 0.124601i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.809017 | − | 0.587785i | −0.134836 | − | 0.0979642i | ||||
\(37\) | 6.47214 | − | 4.70228i | 1.06401 | − | 0.773050i | 0.0891861 | − | 0.996015i | \(-0.471573\pi\) |
0.974827 | + | 0.222965i | \(0.0715734\pi\) | |||||||
\(38\) | −4.61803 | + | 3.35520i | −0.749144 | + | 0.544285i | ||||
\(39\) | −5.23607 | − | 3.80423i | −0.838442 | − | 0.609164i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.61803 | + | 3.35520i | −0.721216 | + | 0.523994i | −0.886772 | − | 0.462206i | \(-0.847058\pi\) |
0.165557 | + | 0.986200i | \(0.447058\pi\) | |||||||
\(42\) | 0.809017 | − | 2.48990i | 0.124834 | − | 0.384200i | ||||
\(43\) | 7.70820 | 1.17549 | 0.587745 | − | 0.809046i | \(-0.300016\pi\) | ||||
0.587745 | + | 0.809046i | \(0.300016\pi\) | |||||||
\(44\) | 1.11803 | − | 3.44095i | 0.168550 | − | 0.518743i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.38197 | + | 4.25325i | 0.203760 | + | 0.627108i | ||||
\(47\) | −0.527864 | − | 1.62460i | −0.0769969 | − | 0.236972i | 0.905149 | − | 0.425096i | \(-0.139759\pi\) |
−0.982145 | + | 0.188123i | \(0.939759\pi\) | |||||||
\(48\) | −0.809017 | − | 0.587785i | −0.116772 | − | 0.0848395i | ||||
\(49\) | −0.145898 | −0.0208426 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23607 | −0.173084 | ||||||||
\(52\) | −5.23607 | − | 3.80423i | −0.726112 | − | 0.527551i | ||||
\(53\) | 0.645898 | + | 1.98787i | 0.0887209 | + | 0.273055i | 0.985566 | − | 0.169289i | \(-0.0541471\pi\) |
−0.896846 | + | 0.442344i | \(0.854147\pi\) | |||||||
\(54\) | −0.309017 | − | 0.951057i | −0.0420519 | − | 0.129422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.809017 | − | 2.48990i | 0.108109 | − | 0.332727i | ||||
\(57\) | −5.70820 | −0.756070 | ||||||||
\(58\) | −2.61803 | + | 8.05748i | −0.343765 | + | 1.05800i | ||||
\(59\) | 2.92705 | − | 2.12663i | 0.381070 | − | 0.276863i | −0.380717 | − | 0.924692i | \(-0.624323\pi\) |
0.761786 | + | 0.647829i | \(0.224323\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.23607 | − | 1.62460i | −0.286299 | − | 0.208009i | 0.435361 | − | 0.900256i | \(-0.356621\pi\) |
−0.721660 | + | 0.692247i | \(0.756621\pi\) | |||||||
\(62\) | 5.35410 | − | 3.88998i | 0.679972 | − | 0.494028i | ||||
\(63\) | 2.11803 | − | 1.53884i | 0.266847 | − | 0.193876i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.92705 | − | 2.12663i | 0.360295 | − | 0.261770i | ||||
\(67\) | 0.472136 | − | 1.45309i | 0.0576806 | − | 0.177523i | −0.918065 | − | 0.396430i | \(-0.870249\pi\) |
0.975746 | + | 0.218907i | \(0.0702491\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | −1.38197 | + | 4.25325i | −0.166369 | + | 0.512032i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70820 | + | 5.25731i | 0.202727 | + | 0.623928i | 0.999799 | + | 0.0200445i | \(0.00638080\pi\) |
−0.797073 | + | 0.603884i | \(0.793619\pi\) | |||||||
\(72\) | −0.309017 | − | 0.951057i | −0.0364180 | − | 0.112083i | ||||
\(73\) | 2.85410 | + | 2.07363i | 0.334047 | + | 0.242700i | 0.742146 | − | 0.670238i | \(-0.233808\pi\) |
−0.408099 | + | 0.912938i | \(0.633808\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.70820 | −0.654776 | ||||||||
\(77\) | 7.66312 | + | 5.56758i | 0.873293 | + | 0.634485i | ||||
\(78\) | −2.00000 | − | 6.15537i | −0.226455 | − | 0.696958i | ||||
\(79\) | −1.73607 | − | 5.34307i | −0.195323 | − | 0.601142i | −0.999973 | − | 0.00739236i | \(-0.997647\pi\) |
0.804650 | − | 0.593750i | \(-0.202353\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | −5.70820 | −0.630366 | ||||||||
\(83\) | −0.663119 | + | 2.04087i | −0.0727868 | + | 0.224015i | −0.980831 | − | 0.194859i | \(-0.937575\pi\) |
0.908044 | + | 0.418874i | \(0.137575\pi\) | |||||||
\(84\) | 2.11803 | − | 1.53884i | 0.231096 | − | 0.167901i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.23607 | + | 4.53077i | 0.672453 | + | 0.488565i | ||||
\(87\) | −6.85410 | + | 4.97980i | −0.734837 | + | 0.533890i | ||||
\(88\) | 2.92705 | − | 2.12663i | 0.312025 | − | 0.226699i | ||||
\(89\) | −2.85410 | − | 2.07363i | −0.302534 | − | 0.219804i | 0.426152 | − | 0.904651i | \(-0.359869\pi\) |
−0.728686 | + | 0.684848i | \(0.759869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.7082 | − | 9.95959i | 1.43701 | − | 1.04405i | ||||
\(92\) | −1.38197 | + | 4.25325i | −0.144080 | + | 0.443432i | ||||
\(93\) | 6.61803 | 0.686258 | ||||||||
\(94\) | 0.527864 | − | 1.62460i | 0.0544450 | − | 0.167565i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.309017 | − | 0.951057i | −0.0315389 | − | 0.0970668i | ||||
\(97\) | 1.04508 | + | 3.21644i | 0.106112 | + | 0.326580i | 0.989990 | − | 0.141138i | \(-0.0450762\pi\) |
−0.883878 | + | 0.467718i | \(0.845076\pi\) | |||||||
\(98\) | −0.118034 | − | 0.0857567i | −0.0119232 | − | 0.00866274i | ||||
\(99\) | 3.61803 | 0.363626 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.38197 | 0.436022 | 0.218011 | − | 0.975946i | \(-0.430043\pi\) | ||||
0.218011 | + | 0.975946i | \(0.430043\pi\) | |||||||
\(102\) | −1.00000 | − | 0.726543i | −0.0990148 | − | 0.0719384i | ||||
\(103\) | −4.42705 | − | 13.6251i | −0.436210 | − | 1.34252i | −0.891841 | − | 0.452348i | \(-0.850586\pi\) |
0.455631 | − | 0.890169i | \(-0.349414\pi\) | |||||||
\(104\) | −2.00000 | − | 6.15537i | −0.196116 | − | 0.603583i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.645898 | + | 1.98787i | −0.0627352 | + | 0.193079i | ||||
\(107\) | 11.6180 | 1.12316 | 0.561579 | − | 0.827423i | \(-0.310194\pi\) | ||||
0.561579 | + | 0.827423i | \(0.310194\pi\) | |||||||
\(108\) | 0.309017 | − | 0.951057i | 0.0297352 | − | 0.0915155i | ||||
\(109\) | −13.9443 | + | 10.1311i | −1.33562 | + | 0.970384i | −0.336026 | + | 0.941853i | \(0.609083\pi\) |
−0.999593 | + | 0.0285313i | \(0.990917\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.47214 | + | 4.70228i | 0.614308 | + | 0.446321i | ||||
\(112\) | 2.11803 | − | 1.53884i | 0.200135 | − | 0.145407i | ||||
\(113\) | −15.5623 | + | 11.3067i | −1.46398 | + | 1.06364i | −0.481674 | + | 0.876350i | \(0.659971\pi\) |
−0.982304 | + | 0.187292i | \(0.940029\pi\) | |||||||
\(114\) | −4.61803 | − | 3.35520i | −0.432519 | − | 0.314243i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.85410 | + | 4.97980i | −0.636387 | + | 0.462363i | ||||
\(117\) | 2.00000 | − | 6.15537i | 0.184900 | − | 0.569064i | ||||
\(118\) | 3.61803 | 0.333067 | ||||||||
\(119\) | 1.00000 | − | 3.07768i | 0.0916698 | − | 0.282131i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.645898 | + | 1.98787i | 0.0587180 | + | 0.180715i | ||||
\(122\) | −0.854102 | − | 2.62866i | −0.0773268 | − | 0.237987i | ||||
\(123\) | −4.61803 | − | 3.35520i | −0.416394 | − | 0.302528i | ||||
\(124\) | 6.61803 | 0.594317 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.61803 | 0.233233 | ||||||||
\(127\) | 11.0172 | + | 8.00448i | 0.977620 | + | 0.710283i | 0.957176 | − | 0.289508i | \(-0.0934918\pi\) |
0.0204448 | + | 0.999791i | \(0.493492\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 2.38197 | + | 7.33094i | 0.209720 | + | 0.645453i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.52786 | + | 17.0130i | −0.482972 | + | 1.48643i | 0.351925 | + | 0.936028i | \(0.385527\pi\) |
−0.834897 | + | 0.550406i | \(0.814473\pi\) | |||||||
\(132\) | 3.61803 | 0.314909 | ||||||||
\(133\) | 4.61803 | − | 14.2128i | 0.400434 | − | 1.23241i | ||||
\(134\) | 1.23607 | − | 0.898056i | 0.106780 | − | 0.0775802i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | − | 0.726543i | −0.0857493 | − | 0.0623005i | ||||
\(137\) | −9.85410 | + | 7.15942i | −0.841893 | + | 0.611671i | −0.922899 | − | 0.385043i | \(-0.874187\pi\) |
0.0810060 | + | 0.996714i | \(0.474187\pi\) | |||||||
\(138\) | −3.61803 | + | 2.62866i | −0.307988 | + | 0.223766i | ||||
\(139\) | −8.47214 | − | 6.15537i | −0.718597 | − | 0.522091i | 0.167339 | − | 0.985899i | \(-0.446483\pi\) |
−0.885936 | + | 0.463808i | \(0.846483\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.38197 | − | 1.00406i | 0.116383 | − | 0.0845569i | ||||
\(142\) | −1.70820 | + | 5.25731i | −0.143349 | + | 0.441184i | ||||
\(143\) | 23.4164 | 1.95818 | ||||||||
\(144\) | 0.309017 | − | 0.951057i | 0.0257514 | − | 0.0792547i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.09017 | + | 3.35520i | 0.0902231 | + | 0.277678i | ||||
\(147\) | −0.0450850 | − | 0.138757i | −0.00371855 | − | 0.0114445i | ||||
\(148\) | 6.47214 | + | 4.70228i | 0.532006 | + | 0.386525i | ||||
\(149\) | 22.0902 | 1.80970 | 0.904849 | − | 0.425733i | \(-0.139984\pi\) | ||||
0.904849 | + | 0.425733i | \(0.139984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.3262 | 1.49137 | 0.745684 | − | 0.666300i | \(-0.232123\pi\) | ||||
0.745684 | + | 0.666300i | \(0.232123\pi\) | |||||||
\(152\) | −4.61803 | − | 3.35520i | −0.374572 | − | 0.272143i | ||||
\(153\) | −0.381966 | − | 1.17557i | −0.0308801 | − | 0.0950392i | ||||
\(154\) | 2.92705 | + | 9.00854i | 0.235868 | + | 0.725929i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 6.15537i | 0.160128 | − | 0.492824i | ||||
\(157\) | −8.65248 | −0.690543 | −0.345271 | − | 0.938503i | \(-0.612213\pi\) | ||||
−0.345271 | + | 0.938503i | \(0.612213\pi\) | |||||||
\(158\) | 1.73607 | − | 5.34307i | 0.138114 | − | 0.425072i | ||||
\(159\) | −1.69098 | + | 1.22857i | −0.134104 | + | 0.0974320i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.47214 | − | 6.88191i | −0.746509 | − | 0.542370i | ||||
\(162\) | 0.809017 | − | 0.587785i | 0.0635624 | − | 0.0461808i | ||||
\(163\) | −0.381966 | + | 0.277515i | −0.0299179 | + | 0.0217366i | −0.602644 | − | 0.798010i | \(-0.705886\pi\) |
0.572726 | + | 0.819747i | \(0.305886\pi\) | |||||||
\(164\) | −4.61803 | − | 3.35520i | −0.360608 | − | 0.261997i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.73607 | + | 1.26133i | −0.134745 | + | 0.0978980i | ||||
\(167\) | −3.61803 | + | 11.1352i | −0.279972 | + | 0.861665i | 0.707889 | + | 0.706324i | \(0.249648\pi\) |
−0.987861 | + | 0.155341i | \(0.950352\pi\) | |||||||
\(168\) | 2.61803 | 0.201986 | ||||||||
\(169\) | 8.92705 | − | 27.4746i | 0.686696 | − | 2.11343i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.76393 | − | 5.42882i | −0.134891 | − | 0.415153i | ||||
\(172\) | 2.38197 | + | 7.33094i | 0.181623 | + | 0.558979i | ||||
\(173\) | 4.11803 | + | 2.99193i | 0.313088 | + | 0.227472i | 0.733221 | − | 0.679991i | \(-0.238016\pi\) |
−0.420132 | + | 0.907463i | \(0.638016\pi\) | |||||||
\(174\) | −8.47214 | −0.642271 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.61803 | 0.272720 | ||||||||
\(177\) | 2.92705 | + | 2.12663i | 0.220011 | + | 0.159847i | ||||
\(178\) | −1.09017 | − | 3.35520i | −0.0817117 | − | 0.251483i | ||||
\(179\) | 3.04508 | + | 9.37181i | 0.227600 | + | 0.700482i | 0.998017 | + | 0.0629414i | \(0.0200481\pi\) |
−0.770417 | + | 0.637540i | \(0.779952\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.05573 | + | 6.32688i | −0.152801 | + | 0.470273i | −0.997931 | − | 0.0642869i | \(-0.979523\pi\) |
0.845130 | + | 0.534560i | \(0.179523\pi\) | |||||||
\(182\) | 16.9443 | 1.25599 | ||||||||
\(183\) | 0.854102 | − | 2.62866i | 0.0631370 | − | 0.194316i | ||||
\(184\) | −3.61803 | + | 2.62866i | −0.266725 | + | 0.193787i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.35410 | + | 3.88998i | 0.392582 | + | 0.285227i | ||||
\(187\) | 3.61803 | − | 2.62866i | 0.264577 | − | 0.192226i | ||||
\(188\) | 1.38197 | − | 1.00406i | 0.100790 | − | 0.0732284i | ||||
\(189\) | 2.11803 | + | 1.53884i | 0.154064 | + | 0.111934i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.47214 | + | 2.52265i | −0.251235 | + | 0.182533i | −0.706274 | − | 0.707939i | \(-0.749625\pi\) |
0.455039 | + | 0.890472i | \(0.349625\pi\) | |||||||
\(192\) | 0.309017 | − | 0.951057i | 0.0223014 | − | 0.0686366i | ||||
\(193\) | −17.8541 | −1.28517 | −0.642583 | − | 0.766216i | \(-0.722137\pi\) | ||||
−0.642583 | + | 0.766216i | \(0.722137\pi\) | |||||||
\(194\) | −1.04508 | + | 3.21644i | −0.0750327 | + | 0.230927i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.0450850 | − | 0.138757i | −0.00322036 | − | 0.00991123i | ||||
\(197\) | 5.28115 | + | 16.2537i | 0.376267 | + | 1.15803i | 0.942620 | + | 0.333867i | \(0.108354\pi\) |
−0.566354 | + | 0.824162i | \(0.691646\pi\) | |||||||
\(198\) | 2.92705 | + | 2.12663i | 0.208016 | + | 0.151133i | ||||
\(199\) | 19.5066 | 1.38278 | 0.691392 | − | 0.722480i | \(-0.256998\pi\) | ||||
0.691392 | + | 0.722480i | \(0.256998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.52786 | 0.107767 | ||||||||
\(202\) | 3.54508 | + | 2.57565i | 0.249431 | + | 0.181222i | ||||
\(203\) | −6.85410 | − | 21.0948i | −0.481064 | − | 1.48056i | ||||
\(204\) | −0.381966 | − | 1.17557i | −0.0267430 | − | 0.0823064i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.42705 | − | 13.6251i | 0.308447 | − | 0.949303i | ||||
\(207\) | −4.47214 | −0.310835 | ||||||||
\(208\) | 2.00000 | − | 6.15537i | 0.138675 | − | 0.426798i | ||||
\(209\) | 16.7082 | − | 12.1392i | 1.15573 | − | 0.839687i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.76393 | + | 2.00811i | 0.190277 | + | 0.138244i | 0.678845 | − | 0.734281i | \(-0.262481\pi\) |
−0.488568 | + | 0.872526i | \(0.662481\pi\) | |||||||
\(212\) | −1.69098 | + | 1.22857i | −0.116137 | + | 0.0843786i | ||||
\(213\) | −4.47214 | + | 3.24920i | −0.306426 | + | 0.222631i | ||||
\(214\) | 9.39919 | + | 6.82891i | 0.642515 | + | 0.466815i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.809017 | − | 0.587785i | 0.0550466 | − | 0.0399937i | ||||
\(217\) | −5.35410 | + | 16.4782i | −0.363460 | + | 1.11862i | ||||
\(218\) | −17.2361 | −1.16737 | ||||||||
\(219\) | −1.09017 | + | 3.35520i | −0.0736669 | + | 0.226723i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.47214 | − | 7.60845i | −0.166294 | − | 0.511800i | ||||
\(222\) | 2.47214 | + | 7.60845i | 0.165919 | + | 0.510646i | ||||
\(223\) | −6.54508 | − | 4.75528i | −0.438291 | − | 0.318437i | 0.346664 | − | 0.937989i | \(-0.387314\pi\) |
−0.784956 | + | 0.619552i | \(0.787314\pi\) | |||||||
\(224\) | 2.61803 | 0.174925 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.2361 | −1.27956 | ||||||||
\(227\) | −18.0172 | − | 13.0903i | −1.19584 | − | 0.868832i | −0.201975 | − | 0.979391i | \(-0.564736\pi\) |
−0.993870 | + | 0.110558i | \(0.964736\pi\) | |||||||
\(228\) | −1.76393 | − | 5.42882i | −0.116819 | − | 0.359533i | ||||
\(229\) | −1.70820 | − | 5.25731i | −0.112881 | − | 0.347413i | 0.878618 | − | 0.477525i | \(-0.158466\pi\) |
−0.991499 | + | 0.130113i | \(0.958466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.92705 | + | 9.00854i | −0.192586 | + | 0.592718i | ||||
\(232\) | −8.47214 | −0.556223 | ||||||||
\(233\) | −5.76393 | + | 17.7396i | −0.377608 | + | 1.16216i | 0.564095 | + | 0.825710i | \(0.309225\pi\) |
−0.941702 | + | 0.336447i | \(0.890775\pi\) | |||||||
\(234\) | 5.23607 | − | 3.80423i | 0.342292 | − | 0.248690i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.92705 | + | 2.12663i | 0.190535 | + | 0.138432i | ||||
\(237\) | 4.54508 | − | 3.30220i | 0.295235 | − | 0.214501i | ||||
\(238\) | 2.61803 | − | 1.90211i | 0.169702 | − | 0.123296i | ||||
\(239\) | −9.94427 | − | 7.22494i | −0.643241 | − | 0.467342i | 0.217721 | − | 0.976011i | \(-0.430138\pi\) |
−0.860962 | + | 0.508669i | \(0.830138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.73607 | + | 5.62058i | −0.498324 | + | 0.362054i | −0.808376 | − | 0.588666i | \(-0.799653\pi\) |
0.310052 | + | 0.950719i | \(0.399653\pi\) | |||||||
\(242\) | −0.645898 | + | 1.98787i | −0.0415199 | + | 0.127785i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.854102 | − | 2.62866i | 0.0546783 | − | 0.168282i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.76393 | − | 5.42882i | −0.112464 | − | 0.346129i | ||||
\(247\) | −11.4164 | − | 35.1361i | −0.726409 | − | 2.23566i | ||||
\(248\) | 5.35410 | + | 3.88998i | 0.339986 | + | 0.247014i | ||||
\(249\) | −2.14590 | −0.135991 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5623 | 0.856045 | 0.428023 | − | 0.903768i | \(-0.359210\pi\) | ||||
0.428023 | + | 0.903768i | \(0.359210\pi\) | |||||||
\(252\) | 2.11803 | + | 1.53884i | 0.133424 | + | 0.0969379i | ||||
\(253\) | −5.00000 | − | 15.3884i | −0.314347 | − | 0.967462i | ||||
\(254\) | 4.20820 | + | 12.9515i | 0.264046 | + | 0.812651i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | −2.38197 | + | 7.33094i | −0.148295 | + | 0.456404i | ||||
\(259\) | −16.9443 | + | 12.3107i | −1.05287 | + | 0.764952i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.85410 | − | 4.97980i | −0.424258 | − | 0.308242i | ||||
\(262\) | −14.4721 | + | 10.5146i | −0.894092 | + | 0.649596i | ||||
\(263\) | −9.47214 | + | 6.88191i | −0.584077 | + | 0.424357i | −0.840192 | − | 0.542290i | \(-0.817558\pi\) |
0.256115 | + | 0.966646i | \(0.417558\pi\) | |||||||
\(264\) | 2.92705 | + | 2.12663i | 0.180148 | + | 0.130885i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 12.0902 | − | 8.78402i | 0.741296 | − | 0.538583i | ||||
\(267\) | 1.09017 | − | 3.35520i | 0.0667173 | − | 0.205335i | ||||
\(268\) | 1.52786 | 0.0933292 | ||||||||
\(269\) | −2.80902 | + | 8.64527i | −0.171269 | + | 0.527111i | −0.999443 | − | 0.0333590i | \(-0.989380\pi\) |
0.828175 | + | 0.560470i | \(0.189380\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.57295 | − | 17.1518i | −0.338533 | − | 1.04190i | −0.964956 | − | 0.262413i | \(-0.915482\pi\) |
0.626423 | − | 0.779483i | \(-0.284518\pi\) | |||||||
\(272\) | −0.381966 | − | 1.17557i | −0.0231601 | − | 0.0712794i | ||||
\(273\) | 13.7082 | + | 9.95959i | 0.829658 | + | 0.602782i | ||||
\(274\) | −12.1803 | −0.735841 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | 13.7082 | + | 9.95959i | 0.823646 | + | 0.598414i | 0.917755 | − | 0.397148i | \(-0.130000\pi\) |
−0.0941084 | + | 0.995562i | \(0.530000\pi\) | |||||||
\(278\) | −3.23607 | − | 9.95959i | −0.194086 | − | 0.597337i | ||||
\(279\) | 2.04508 | + | 6.29412i | 0.122436 | + | 0.376819i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.81966 | − | 5.60034i | 0.108552 | − | 0.334088i | −0.881996 | − | 0.471257i | \(-0.843800\pi\) |
0.990548 | + | 0.137169i | \(0.0438004\pi\) | |||||||
\(282\) | 1.70820 | 0.101722 | ||||||||
\(283\) | −1.41641 | + | 4.35926i | −0.0841967 | + | 0.259131i | −0.984288 | − | 0.176571i | \(-0.943500\pi\) |
0.900091 | + | 0.435701i | \(0.143500\pi\) | |||||||
\(284\) | −4.47214 | + | 3.24920i | −0.265372 | + | 0.192804i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.9443 | + | 13.7638i | 1.12020 | + | 0.813872i | ||||
\(287\) | 12.0902 | − | 8.78402i | 0.713660 | − | 0.518504i | ||||
\(288\) | 0.809017 | − | 0.587785i | 0.0476718 | − | 0.0346356i | ||||
\(289\) | 12.5172 | + | 9.09429i | 0.736307 | + | 0.534958i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.73607 | + | 1.98787i | −0.160391 | + | 0.116531i | ||||
\(292\) | −1.09017 | + | 3.35520i | −0.0637974 | + | 0.196348i | ||||
\(293\) | 22.0902 | 1.29052 | 0.645261 | − | 0.763962i | \(-0.276749\pi\) | ||||
0.645261 | + | 0.763962i | \(0.276749\pi\) | |||||||
\(294\) | 0.0450850 | − | 0.138757i | 0.00262941 | − | 0.00809249i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.47214 | + | 7.60845i | 0.143690 | + | 0.442232i | ||||
\(297\) | 1.11803 | + | 3.44095i | 0.0648749 | + | 0.199664i | ||||
\(298\) | 17.8713 | + | 12.9843i | 1.03526 | + | 0.752159i | ||||
\(299\) | −28.9443 | −1.67389 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.1803 | −1.16318 | ||||||||
\(302\) | 14.8262 | + | 10.7719i | 0.853154 | + | 0.619853i | ||||
\(303\) | 1.35410 | + | 4.16750i | 0.0777911 | + | 0.239416i | ||||
\(304\) | −1.76393 | − | 5.42882i | −0.101168 | − | 0.311364i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.381966 | − | 1.17557i | 0.0218355 | − | 0.0672029i | ||||
\(307\) | −10.0000 | −0.570730 | −0.285365 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285365 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(308\) | −2.92705 | + | 9.00854i | −0.166784 | + | 0.513309i | ||||
\(309\) | 11.5902 | − | 8.42075i | 0.659342 | − | 0.479040i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.854102 | + | 0.620541i | 0.0484317 | + | 0.0351877i | 0.611738 | − | 0.791061i | \(-0.290471\pi\) |
−0.563306 | + | 0.826248i | \(0.690471\pi\) | |||||||
\(312\) | 5.23607 | − | 3.80423i | 0.296434 | − | 0.215372i | ||||
\(313\) | −13.1631 | + | 9.56357i | −0.744023 | + | 0.540565i | −0.893969 | − | 0.448130i | \(-0.852090\pi\) |
0.149945 | + | 0.988694i | \(0.452090\pi\) | |||||||
\(314\) | −7.00000 | − | 5.08580i | −0.395033 | − | 0.287008i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.54508 | − | 3.30220i | 0.255681 | − | 0.185763i | ||||
\(317\) | 6.35410 | − | 19.5559i | 0.356882 | − | 1.09837i | −0.598028 | − | 0.801475i | \(-0.704049\pi\) |
0.954910 | − | 0.296895i | \(-0.0959510\pi\) | |||||||
\(318\) | −2.09017 | −0.117211 | ||||||||
\(319\) | 9.47214 | − | 29.1522i | 0.530338 | − | 1.63221i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.59017 | + | 11.0494i | 0.200384 | + | 0.616718i | ||||
\(322\) | −3.61803 | − | 11.1352i | −0.201625 | − | 0.620538i | ||||
\(323\) | −5.70820 | − | 4.14725i | −0.317613 | − | 0.230759i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.472136 | −0.0261492 | ||||||||
\(327\) | −13.9443 | − | 10.1311i | −0.771120 | − | 0.560251i | ||||
\(328\) | −1.76393 | − | 5.42882i | −0.0973969 | − | 0.299757i | ||||
\(329\) | 1.38197 | + | 4.25325i | 0.0761903 | + | 0.234489i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.56231 | + | 17.1190i | −0.305732 | + | 0.940946i | 0.673671 | + | 0.739031i | \(0.264716\pi\) |
−0.979403 | + | 0.201915i | \(0.935284\pi\) | |||||||
\(332\) | −2.14590 | −0.117771 | ||||||||
\(333\) | −2.47214 | + | 7.60845i | −0.135472 | + | 0.416941i | ||||
\(334\) | −9.47214 | + | 6.88191i | −0.518292 | + | 0.376561i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.11803 | + | 1.53884i | 0.115548 | + | 0.0839507i | ||||
\(337\) | 0.736068 | − | 0.534785i | 0.0400962 | − | 0.0291316i | −0.567557 | − | 0.823334i | \(-0.692111\pi\) |
0.607653 | + | 0.794203i | \(0.292111\pi\) | |||||||
\(338\) | 23.3713 | − | 16.9803i | 1.27123 | − | 0.923604i | ||||
\(339\) | −15.5623 | − | 11.3067i | −0.845228 | − | 0.614094i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.3713 | + | 14.0741i | −1.04902 | + | 0.762155i | ||||
\(342\) | 1.76393 | − | 5.42882i | 0.0953825 | − | 0.293557i | ||||
\(343\) | 18.7082 | 1.01015 | ||||||||
\(344\) | −2.38197 | + | 7.33094i | −0.128427 | + | 0.395258i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.57295 | + | 4.84104i | 0.0845623 | + | 0.260256i | ||||
\(347\) | −6.35410 | − | 19.5559i | −0.341106 | − | 1.04982i | −0.963636 | − | 0.267220i | \(-0.913895\pi\) |
0.622529 | − | 0.782596i | \(-0.286105\pi\) | |||||||
\(348\) | −6.85410 | − | 4.97980i | −0.367418 | − | 0.266945i | ||||
\(349\) | −27.8885 | −1.49284 | −0.746420 | − | 0.665475i | \(-0.768229\pi\) | ||||
−0.746420 | + | 0.665475i | \(0.768229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.47214 | 0.345457 | ||||||||
\(352\) | 2.92705 | + | 2.12663i | 0.156012 | + | 0.113350i | ||||
\(353\) | 4.09017 | + | 12.5882i | 0.217698 | + | 0.670005i | 0.998951 | + | 0.0457907i | \(0.0145807\pi\) |
−0.781253 | + | 0.624214i | \(0.785419\pi\) | |||||||
\(354\) | 1.11803 | + | 3.44095i | 0.0594228 | + | 0.182885i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.09017 | − | 3.35520i | 0.0577789 | − | 0.177825i | ||||
\(357\) | 3.23607 | 0.171271 | ||||||||
\(358\) | −3.04508 | + | 9.37181i | −0.160938 | + | 0.495315i | ||||
\(359\) | −17.9443 | + | 13.0373i | −0.947062 | + | 0.688081i | −0.950110 | − | 0.311914i | \(-0.899030\pi\) |
0.00304782 | + | 0.999995i | \(0.499030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.9894 | − | 7.98424i | −0.578387 | − | 0.420223i | ||||
\(362\) | −5.38197 | + | 3.91023i | −0.282870 | + | 0.205517i | ||||
\(363\) | −1.69098 | + | 1.22857i | −0.0887536 | + | 0.0644833i | ||||
\(364\) | 13.7082 | + | 9.95959i | 0.718505 | + | 0.522025i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.23607 | − | 1.62460i | 0.116881 | − | 0.0849191i | ||||
\(367\) | 9.46149 | − | 29.1195i | 0.493886 | − | 1.52002i | −0.324800 | − | 0.945783i | \(-0.605297\pi\) |
0.818686 | − | 0.574242i | \(-0.194703\pi\) | |||||||
\(368\) | −4.47214 | −0.233126 | ||||||||
\(369\) | 1.76393 | − | 5.42882i | 0.0918266 | − | 0.282613i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.69098 | − | 5.20431i | −0.0877915 | − | 0.270194i | ||||
\(372\) | 2.04508 | + | 6.29412i | 0.106033 | + | 0.326335i | ||||
\(373\) | −9.32624 | − | 6.77591i | −0.482894 | − | 0.350843i | 0.319551 | − | 0.947569i | \(-0.396468\pi\) |
−0.802445 | + | 0.596726i | \(0.796468\pi\) | |||||||
\(374\) | 4.47214 | 0.231249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.70820 | 0.0880939 | ||||||||
\(377\) | −44.3607 | − | 32.2299i | −2.28469 | − | 1.65993i | ||||
\(378\) | 0.809017 | + | 2.48990i | 0.0416113 | + | 0.128067i | ||||
\(379\) | −6.23607 | − | 19.1926i | −0.320325 | − | 0.985860i | −0.973507 | − | 0.228658i | \(-0.926566\pi\) |
0.653181 | − | 0.757201i | \(-0.273434\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.20820 | + | 12.9515i | −0.215593 | + | 0.663526i | ||||
\(382\) | −4.29180 | −0.219587 | ||||||||
\(383\) | 6.18034 | − | 19.0211i | 0.315801 | − | 0.971934i | −0.659623 | − | 0.751597i | \(-0.729284\pi\) |
0.975424 | − | 0.220338i | \(-0.0707160\pi\) | |||||||
\(384\) | 0.809017 | − | 0.587785i | 0.0412850 | − | 0.0299953i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.4443 | − | 10.4944i | −0.735194 | − | 0.534150i | ||||
\(387\) | −6.23607 | + | 4.53077i | −0.316997 | + | 0.230312i | ||||
\(388\) | −2.73607 | + | 1.98787i | −0.138903 | + | 0.100919i | ||||
\(389\) | 10.0172 | + | 7.27794i | 0.507893 | + | 0.369006i | 0.812024 | − | 0.583624i | \(-0.198366\pi\) |
−0.304131 | + | 0.952630i | \(0.598366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.47214 | + | 3.24920i | −0.226166 | + | 0.164319i | ||||
\(392\) | 0.0450850 | − | 0.138757i | 0.00227713 | − | 0.00700830i | ||||
\(393\) | −17.8885 | −0.902358 | ||||||||
\(394\) | −5.28115 | + | 16.2537i | −0.266061 | + | 0.818850i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.11803 | + | 3.44095i | 0.0561833 | + | 0.172914i | ||||
\(397\) | 9.50658 | + | 29.2582i | 0.477121 | + | 1.46843i | 0.843075 | + | 0.537796i | \(0.180743\pi\) |
−0.365954 | + | 0.930633i | \(0.619257\pi\) | |||||||
\(398\) | 15.7812 | + | 11.4657i | 0.791038 | + | 0.574723i | ||||
\(399\) | 14.9443 | 0.748149 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.7082 | 1.28381 | 0.641903 | − | 0.766786i | \(-0.278145\pi\) | ||||
0.641903 | + | 0.766786i | \(0.278145\pi\) | |||||||
\(402\) | 1.23607 | + | 0.898056i | 0.0616495 | + | 0.0447910i | ||||
\(403\) | 13.2361 | + | 40.7364i | 0.659336 | + | 2.02923i | ||||
\(404\) | 1.35410 | + | 4.16750i | 0.0673691 | + | 0.207341i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.85410 | − | 21.0948i | 0.340163 | − | 1.04692i | ||||
\(407\) | −28.9443 | −1.43471 | ||||||||
\(408\) | 0.381966 | − | 1.17557i | 0.0189101 | − | 0.0581994i | ||||
\(409\) | −4.69098 | + | 3.40820i | −0.231954 | + | 0.168525i | −0.697691 | − | 0.716399i | \(-0.745789\pi\) |
0.465737 | + | 0.884923i | \(0.345789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.85410 | − | 7.15942i | −0.486067 | − | 0.353148i | ||||
\(412\) | 11.5902 | − | 8.42075i | 0.571007 | − | 0.414861i | ||||
\(413\) | −7.66312 | + | 5.56758i | −0.377077 | + | 0.273963i | ||||
\(414\) | −3.61803 | − | 2.62866i | −0.177817 | − | 0.129191i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.23607 | − | 3.80423i | 0.256719 | − | 0.186518i | ||||
\(417\) | 3.23607 | − | 9.95959i | 0.158471 | − | 0.487723i | ||||
\(418\) | 20.6525 | 1.01015 | ||||||||
\(419\) | −0.954915 | + | 2.93893i | −0.0466507 | + | 0.143576i | −0.971669 | − | 0.236347i | \(-0.924050\pi\) |
0.925018 | + | 0.379923i | \(0.124050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.03444 | − | 21.6498i | −0.342838 | − | 1.05515i | −0.962731 | − | 0.270460i | \(-0.912824\pi\) |
0.619893 | − | 0.784686i | \(-0.287176\pi\) | |||||||
\(422\) | 1.05573 | + | 3.24920i | 0.0513920 | + | 0.158168i | ||||
\(423\) | 1.38197 | + | 1.00406i | 0.0671935 | + | 0.0488189i | ||||
\(424\) | −2.09017 | −0.101508 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.52786 | −0.267826 | ||||||||
\(427\) | 5.85410 | + | 4.25325i | 0.283300 | + | 0.205829i | ||||
\(428\) | 3.59017 | + | 11.0494i | 0.173537 | + | 0.534093i | ||||
\(429\) | 7.23607 | + | 22.2703i | 0.349361 | + | 1.07522i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.20163 | − | 16.0090i | 0.250554 | − | 0.771124i | −0.744120 | − | 0.668046i | \(-0.767131\pi\) |
0.994673 | − | 0.103078i | \(-0.0328692\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −4.79180 | + | 14.7476i | −0.230279 | + | 0.708726i | 0.767434 | + | 0.641128i | \(0.221533\pi\) |
−0.997713 | + | 0.0675976i | \(0.978467\pi\) | |||||||
\(434\) | −14.0172 | + | 10.1841i | −0.672848 | + | 0.488853i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.9443 | − | 10.1311i | −0.667810 | − | 0.485192i | ||||
\(437\) | −20.6525 | + | 15.0049i | −0.987942 | + | 0.717782i | ||||
\(438\) | −2.85410 | + | 2.07363i | −0.136374 | + | 0.0990817i | ||||
\(439\) | 19.0172 | + | 13.8168i | 0.907642 | + | 0.659441i | 0.940418 | − | 0.340022i | \(-0.110434\pi\) |
−0.0327751 | + | 0.999463i | \(0.510434\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.118034 | − | 0.0857567i | 0.00562067 | − | 0.00408365i | ||||
\(442\) | 2.47214 | − | 7.60845i | 0.117588 | − | 0.361897i | ||||
\(443\) | −16.6180 | −0.789547 | −0.394773 | − | 0.918779i | \(-0.629177\pi\) | ||||
−0.394773 | + | 0.918779i | \(0.629177\pi\) | |||||||
\(444\) | −2.47214 | + | 7.60845i | −0.117322 | + | 0.361081i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.50000 | − | 7.69421i | −0.118378 | − | 0.364331i | ||||
\(447\) | 6.82624 | + | 21.0090i | 0.322870 | + | 0.993692i | ||||
\(448\) | 2.11803 | + | 1.53884i | 0.100068 | + | 0.0727034i | ||||
\(449\) | −27.7082 | −1.30763 | −0.653815 | − | 0.756654i | \(-0.726833\pi\) | ||||
−0.653815 | + | 0.756654i | \(0.726833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6525 | 0.972487 | ||||||||
\(452\) | −15.5623 | − | 11.3067i | −0.731989 | − | 0.531821i | ||||
\(453\) | 5.66312 | + | 17.4293i | 0.266077 | + | 0.818899i | ||||
\(454\) | −6.88197 | − | 21.1805i | −0.322987 | − | 0.994051i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.76393 | − | 5.42882i | 0.0826037 | − | 0.254228i | ||||
\(457\) | 4.09017 | 0.191330 | 0.0956650 | − | 0.995414i | \(-0.469502\pi\) | ||||
0.0956650 | + | 0.995414i | \(0.469502\pi\) | |||||||
\(458\) | 1.70820 | − | 5.25731i | 0.0798191 | − | 0.245658i | ||||
\(459\) | 1.00000 | − | 0.726543i | 0.0466760 | − | 0.0339121i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.11803 | − | 4.44501i | −0.284945 | − | 0.207025i | 0.436126 | − | 0.899885i | \(-0.356350\pi\) |
−0.721072 | + | 0.692861i | \(0.756350\pi\) | |||||||
\(462\) | −7.66312 | + | 5.56758i | −0.356521 | + | 0.259027i | ||||
\(463\) | −18.4721 | + | 13.4208i | −0.858473 | + | 0.623717i | −0.927469 | − | 0.373900i | \(-0.878020\pi\) |
0.0689961 | + | 0.997617i | \(0.478020\pi\) | |||||||
\(464\) | −6.85410 | − | 4.97980i | −0.318194 | − | 0.231181i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.0902 | + | 10.9637i | −0.699039 | + | 0.507881i | ||||
\(467\) | −3.29837 | + | 10.1514i | −0.152631 | + | 0.469749i | −0.997913 | − | 0.0645710i | \(-0.979432\pi\) |
0.845283 | + | 0.534320i | \(0.179432\pi\) | |||||||
\(468\) | 6.47214 | 0.299175 | ||||||||
\(469\) | −1.23607 | + | 3.80423i | −0.0570763 | + | 0.175663i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.67376 | − | 8.22899i | −0.123200 | − | 0.379172i | ||||
\(472\) | 1.11803 | + | 3.44095i | 0.0514617 | + | 0.158383i | ||||
\(473\) | −22.5623 | − | 16.3925i | −1.03742 | − | 0.753727i | ||||
\(474\) | 5.61803 | 0.258045 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.23607 | 0.148325 | ||||||||
\(477\) | −1.69098 | − | 1.22857i | −0.0774248 | − | 0.0562524i | ||||
\(478\) | −3.79837 | − | 11.6902i | −0.173734 | − | 0.534697i | ||||
\(479\) | −9.00000 | − | 27.6992i | −0.411220 | − | 1.26561i | −0.915588 | − | 0.402117i | \(-0.868274\pi\) |
0.504368 | − | 0.863489i | \(-0.331726\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | + | 49.2429i | −0.729537 | + | 2.24528i | ||||
\(482\) | −9.56231 | −0.435551 | ||||||||
\(483\) | 3.61803 | − | 11.1352i | 0.164626 | − | 0.506667i | ||||
\(484\) | −1.69098 | + | 1.22857i | −0.0768629 | + | 0.0558441i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.809017 | + | 0.587785i | 0.0366978 | + | 0.0266625i | ||||
\(487\) | 14.3992 | − | 10.4616i | 0.652489 | − | 0.474061i | −0.211629 | − | 0.977350i | \(-0.567877\pi\) |
0.864118 | + | 0.503289i | \(0.167877\pi\) | |||||||
\(488\) | 2.23607 | − | 1.62460i | 0.101222 | − | 0.0735421i | ||||
\(489\) | −0.381966 | − | 0.277515i | −0.0172731 | − | 0.0125496i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.4443 | − | 14.8536i | 0.922637 | − | 0.670335i | −0.0215419 | − | 0.999768i | \(-0.506858\pi\) |
0.944179 | + | 0.329433i | \(0.106858\pi\) | |||||||
\(492\) | 1.76393 | − | 5.42882i | 0.0795242 | − | 0.244750i | ||||
\(493\) | −10.4721 | −0.471641 | ||||||||
\(494\) | 11.4164 | − | 35.1361i | 0.513648 | − | 1.58085i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.04508 | + | 6.29412i | 0.0918270 | + | 0.282615i | ||||
\(497\) | −4.47214 | − | 13.7638i | −0.200603 | − | 0.617392i | ||||
\(498\) | −1.73607 | − | 1.26133i | −0.0777951 | − | 0.0565214i | ||||
\(499\) | 35.5967 | 1.59353 | 0.796765 | − | 0.604290i | \(-0.206543\pi\) | ||||
0.796765 | + | 0.604290i | \(0.206543\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.7082 | −0.523084 | ||||||||
\(502\) | 10.9721 | + | 7.97172i | 0.489710 | + | 0.355795i | ||||
\(503\) | −7.38197 | − | 22.7194i | −0.329146 | − | 1.01301i | −0.969534 | − | 0.244955i | \(-0.921227\pi\) |
0.640389 | − | 0.768051i | \(-0.278773\pi\) | |||||||
\(504\) | 0.809017 | + | 2.48990i | 0.0360365 | + | 0.110909i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.00000 | − | 15.3884i | 0.222277 | − | 0.684099i | ||||
\(507\) | 28.8885 | 1.28299 | ||||||||
\(508\) | −4.20820 | + | 12.9515i | −0.186709 | + | 0.574631i | ||||
\(509\) | 14.1631 | − | 10.2901i | 0.627769 | − | 0.456101i | −0.227857 | − | 0.973694i | \(-0.573172\pi\) |
0.855627 | + | 0.517593i | \(0.173172\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.47214 | − | 5.42882i | −0.330548 | − | 0.240157i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | 4.61803 | − | 3.35520i | 0.203891 | − | 0.148136i | ||||
\(514\) | 17.7984 | + | 12.9313i | 0.785053 | + | 0.570374i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.23607 | + | 4.53077i | −0.274528 | + | 0.199456i | ||||
\(517\) | −1.90983 | + | 5.87785i | −0.0839942 | + | 0.258508i | ||||
\(518\) | −20.9443 | −0.920238 | ||||||||
\(519\) | −1.57295 | + | 4.84104i | −0.0690448 | + | 0.212498i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.38197 | + | 13.4863i | 0.191977 | + | 0.590846i | 0.999999 | + | 0.00169226i | \(0.000538663\pi\) |
−0.808021 | + | 0.589153i | \(0.799461\pi\) | |||||||
\(522\) | −2.61803 | − | 8.05748i | −0.114588 | − | 0.352666i | ||||
\(523\) | 8.94427 | + | 6.49839i | 0.391106 | + | 0.284155i | 0.765908 | − | 0.642950i | \(-0.222290\pi\) |
−0.374803 | + | 0.927105i | \(0.622290\pi\) | |||||||
\(524\) | −17.8885 | −0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.7082 | −0.510502 | ||||||||
\(527\) | 6.61803 | + | 4.80828i | 0.288286 | + | 0.209452i | ||||
\(528\) | 1.11803 | + | 3.44095i | 0.0486562 | + | 0.149748i | ||||
\(529\) | −0.927051 | − | 2.85317i | −0.0403066 | − | 0.124051i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.11803 | + | 3.44095i | −0.0485185 | + | 0.149325i | ||||
\(532\) | 14.9443 | 0.647916 | ||||||||
\(533\) | 11.4164 | − | 35.1361i | 0.494500 | − | 1.52191i | ||||
\(534\) | 2.85410 | − | 2.07363i | 0.123509 | − | 0.0897346i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.23607 | + | 0.898056i | 0.0533900 | + | 0.0387901i | ||||
\(537\) | −7.97214 | + | 5.79210i | −0.344023 | + | 0.249947i | ||||
\(538\) | −7.35410 | + | 5.34307i | −0.317058 | + | 0.230356i | ||||
\(539\) | 0.427051 | + | 0.310271i | 0.0183944 | + | 0.0133643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.1803 | − | 15.3884i | 0.910614 | − | 0.661600i | −0.0305561 | − | 0.999533i | \(-0.509728\pi\) |
0.941170 | + | 0.337933i | \(0.109728\pi\) | |||||||
\(542\) | 5.57295 | − | 17.1518i | 0.239379 | − | 0.736732i | ||||
\(543\) | −6.65248 | −0.285485 | ||||||||
\(544\) | 0.381966 | − | 1.17557i | 0.0163767 | − | 0.0504022i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.23607 | + | 16.1150i | 0.224083 | + | 0.689657i | ||||
\(547\) | −3.00000 | − | 9.23305i | −0.128271 | − | 0.394777i | 0.866212 | − | 0.499677i | \(-0.166548\pi\) |
−0.994483 | + | 0.104900i | \(0.966548\pi\) | |||||||
\(548\) | −9.85410 | − | 7.15942i | −0.420946 | − | 0.305835i | ||||
\(549\) | 2.76393 | 0.117962 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −48.3607 | −2.06023 | ||||||||
\(552\) | −3.61803 | − | 2.62866i | −0.153994 | − | 0.111883i | ||||
\(553\) | 4.54508 | + | 13.9883i | 0.193277 | + | 0.594844i | ||||
\(554\) | 5.23607 | + | 16.1150i | 0.222459 | + | 0.684659i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.23607 | − | 9.95959i | 0.137240 | − | 0.422381i | ||||
\(557\) | 18.3262 | 0.776508 | 0.388254 | − | 0.921552i | \(-0.373078\pi\) | ||||
0.388254 | + | 0.921552i | \(0.373078\pi\) | |||||||
\(558\) | −2.04508 | + | 6.29412i | −0.0865754 | + | 0.266452i | ||||
\(559\) | −40.3607 | + | 29.3238i | −1.70707 | + | 1.24026i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.61803 | + | 2.62866i | 0.152754 | + | 0.110982i | ||||
\(562\) | 4.76393 | − | 3.46120i | 0.200954 | − | 0.146002i | ||||
\(563\) | 17.2082 | − | 12.5025i | 0.725239 | − | 0.526917i | −0.162815 | − | 0.986657i | \(-0.552057\pi\) |
0.888054 | + | 0.459739i | \(0.152057\pi\) | |||||||
\(564\) | 1.38197 | + | 1.00406i | 0.0581913 | + | 0.0422784i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.70820 | + | 2.69417i | −0.155867 | + | 0.113244i | ||||
\(567\) | −0.809017 | + | 2.48990i | −0.0339755 | + | 0.104566i | ||||
\(568\) | −5.52786 | −0.231944 | ||||||||
\(569\) | −8.58359 | + | 26.4176i | −0.359843 | + | 1.10748i | 0.593305 | + | 0.804978i | \(0.297823\pi\) |
−0.953148 | + | 0.302505i | \(0.902177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.43769 | + | 7.50245i | 0.102014 | + | 0.313968i | 0.989018 | − | 0.147794i | \(-0.0472174\pi\) |
−0.887004 | + | 0.461762i | \(0.847217\pi\) | |||||||
\(572\) | 7.23607 | + | 22.2703i | 0.302555 | + | 0.931169i | ||||
\(573\) | −3.47214 | − | 2.52265i | −0.145051 | − | 0.105385i | ||||
\(574\) | 14.9443 | 0.623762 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 7.26393 | + | 5.27756i | 0.302401 | + | 0.219708i | 0.728629 | − | 0.684908i | \(-0.240158\pi\) |
−0.426228 | + | 0.904616i | \(0.640158\pi\) | |||||||
\(578\) | 4.78115 | + | 14.7149i | 0.198870 | + | 0.612058i | ||||
\(579\) | −5.51722 | − | 16.9803i | −0.229288 | − | 0.705676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.73607 | − | 5.34307i | 0.0720242 | − | 0.221668i | ||||
\(582\) | −3.38197 | −0.140187 | ||||||||
\(583\) | 2.33688 | − | 7.19218i | 0.0967837 | − | 0.297870i | ||||
\(584\) | −2.85410 | + | 2.07363i | −0.118104 | + | 0.0858073i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.8713 | + | 12.9843i | 0.738258 | + | 0.536376i | ||||
\(587\) | −0.781153 | + | 0.567541i | −0.0322416 | + | 0.0234249i | −0.603789 | − | 0.797144i | \(-0.706343\pi\) |
0.571548 | + | 0.820569i | \(0.306343\pi\) | |||||||
\(588\) | 0.118034 | − | 0.0857567i | 0.00486764 | − | 0.00353655i | ||||
\(589\) | 30.5623 | + | 22.2048i | 1.25930 | + | 0.914933i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.8262 | + | 10.0453i | −0.568735 | + | 0.413210i | ||||
\(592\) | −2.47214 | + | 7.60845i | −0.101604 | + | 0.312705i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | −1.11803 | + | 3.44095i | −0.0458735 | + | 0.141184i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.82624 | + | 21.0090i | 0.279614 | + | 0.860562i | ||||
\(597\) | 6.02786 | + | 18.5519i | 0.246704 | + | 0.759277i | ||||
\(598\) | −23.4164 | − | 17.0130i | −0.957568 | − | 0.695714i | ||||
\(599\) | 0.472136 | 0.0192910 | 0.00964548 | − | 0.999953i | \(-0.496930\pi\) | ||||
0.00964548 | + | 0.999953i | \(0.496930\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.72949 | −0.315292 | −0.157646 | − | 0.987496i | \(-0.550391\pi\) | ||||
−0.157646 | + | 0.987496i | \(0.550391\pi\) | |||||||
\(602\) | −16.3262 | − | 11.8617i | −0.665408 | − | 0.483447i | ||||
\(603\) | 0.472136 | + | 1.45309i | 0.0192269 | + | 0.0591742i | ||||
\(604\) | 5.66312 | + | 17.4293i | 0.230429 | + | 0.709188i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.35410 | + | 4.16750i | −0.0550066 | + | 0.169293i | ||||
\(607\) | −6.56231 | −0.266356 | −0.133178 | − | 0.991092i | \(-0.542518\pi\) | ||||
−0.133178 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(608\) | 1.76393 | − | 5.42882i | 0.0715369 | − | 0.220168i | ||||
\(609\) | 17.9443 | − | 13.0373i | 0.727139 | − | 0.528297i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.94427 | + | 6.49839i | 0.361847 | + | 0.262897i | ||||
\(612\) | 1.00000 | − | 0.726543i | 0.0404226 | − | 0.0293687i | ||||
\(613\) | 39.0344 | − | 28.3602i | 1.57659 | − | 1.14546i | 0.656105 | − | 0.754669i | \(-0.272203\pi\) |
0.920481 | − | 0.390788i | \(-0.127797\pi\) | |||||||
\(614\) | −8.09017 | − | 5.87785i | −0.326493 | − | 0.237211i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.66312 | + | 5.56758i | −0.308756 | + | 0.224324i | ||||
\(617\) | −0.652476 | + | 2.00811i | −0.0262677 | + | 0.0808436i | −0.963331 | − | 0.268316i | \(-0.913533\pi\) |
0.937063 | + | 0.349160i | \(0.113533\pi\) | |||||||
\(618\) | 14.3262 | 0.576286 | ||||||||
\(619\) | −2.90983 | + | 8.95554i | −0.116956 | + | 0.359953i | −0.992350 | − | 0.123457i | \(-0.960602\pi\) |
0.875394 | + | 0.483410i | \(0.160602\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38197 | − | 4.25325i | −0.0554564 | − | 0.170677i | ||||
\(622\) | 0.326238 | + | 1.00406i | 0.0130809 | + | 0.0402590i | ||||
\(623\) | 7.47214 | + | 5.42882i | 0.299365 | + | 0.217501i | ||||
\(624\) | 6.47214 | 0.259093 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.2705 | −0.650300 | ||||||||
\(627\) | 16.7082 | + | 12.1392i | 0.667261 | + | 0.484794i | ||||
\(628\) | −2.67376 | − | 8.22899i | −0.106695 | − | 0.328373i | ||||
\(629\) | 3.05573 | + | 9.40456i | 0.121840 | + | 0.374985i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.3607 | − | 44.1976i | 0.571690 | − | 1.75948i | −0.0754947 | − | 0.997146i | \(-0.524054\pi\) |
0.647184 | − | 0.762334i | \(-0.275946\pi\) | |||||||
\(632\) | 5.61803 | 0.223473 | ||||||||
\(633\) | −1.05573 | + | 3.24920i | −0.0419614 | + | 0.129144i | ||||
\(634\) | 16.6353 | − | 12.0862i | 0.660670 | − | 0.480005i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.69098 | − | 1.22857i | −0.0670518 | − | 0.0487160i | ||||
\(637\) | 0.763932 | − | 0.555029i | 0.0302681 | − | 0.0219911i | ||||
\(638\) | 24.7984 | − | 18.0171i | 0.981777 | − | 0.713303i | ||||
\(639\) | −4.47214 | − | 3.24920i | −0.176915 | − | 0.128536i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1803 | − | 8.12299i | 0.441597 | − | 0.320839i | −0.344672 | − | 0.938723i | \(-0.612010\pi\) |
0.786269 | + | 0.617884i | \(0.212010\pi\) | |||||||
\(642\) | −3.59017 | + | 11.0494i | −0.141693 | + | 0.436085i | ||||
\(643\) | −21.8885 | −0.863200 | −0.431600 | − | 0.902065i | \(-0.642051\pi\) | ||||
−0.431600 | + | 0.902065i | \(0.642051\pi\) | |||||||
\(644\) | 3.61803 | − | 11.1352i | 0.142571 | − | 0.438787i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.18034 | − | 6.71040i | −0.0857843 | − | 0.264017i | ||||
\(647\) | 7.09017 | + | 21.8213i | 0.278743 | + | 0.857884i | 0.988205 | + | 0.153139i | \(0.0489383\pi\) |
−0.709461 | + | 0.704744i | \(0.751062\pi\) | |||||||
\(648\) | 0.809017 | + | 0.587785i | 0.0317812 | + | 0.0230904i | ||||
\(649\) | −13.0902 | −0.513834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.3262 | −0.679069 | ||||||||
\(652\) | −0.381966 | − | 0.277515i | −0.0149589 | − | 0.0108683i | ||||
\(653\) | 1.19098 | + | 3.66547i | 0.0466068 | + | 0.143441i | 0.971652 | − | 0.236417i | \(-0.0759730\pi\) |
−0.925045 | + | 0.379858i | \(0.875973\pi\) | |||||||
\(654\) | −5.32624 | − | 16.3925i | −0.208272 | − | 0.640996i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.76393 | − | 5.42882i | 0.0688700 | − | 0.211960i | ||||
\(657\) | −3.52786 | −0.137635 | ||||||||
\(658\) | −1.38197 | + | 4.25325i | −0.0538746 | + | 0.165809i | ||||
\(659\) | 16.6803 | − | 12.1190i | 0.649774 | − | 0.472088i | −0.213420 | − | 0.976960i | \(-0.568460\pi\) |
0.863194 | + | 0.504872i | \(0.168460\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.6525 | + | 17.9111i | 0.958870 | + | 0.696660i | 0.952888 | − | 0.303322i | \(-0.0980958\pi\) |
0.00598211 | + | 0.999982i | \(0.498096\pi\) | |||||||
\(662\) | −14.5623 | + | 10.5801i | −0.565980 | + | 0.411209i | ||||
\(663\) | 6.47214 | − | 4.70228i | 0.251357 | − | 0.182622i | ||||
\(664\) | −1.73607 | − | 1.26133i | −0.0673725 | − | 0.0489490i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.47214 | + | 4.70228i | −0.250790 | + | 0.182210i | ||||
\(667\) | −11.7082 | + | 36.0341i | −0.453343 | + | 1.39525i | ||||
\(668\) | −11.7082 | −0.453004 | ||||||||
\(669\) | 2.50000 | − | 7.69421i | 0.0966556 | − | 0.297475i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.09017 | + | 9.51057i | 0.119295 | + | 0.367151i | ||||
\(672\) | 0.809017 | + | 2.48990i | 0.0312085 | + | 0.0960499i | ||||
\(673\) | −25.4443 | − | 18.4863i | −0.980805 | − | 0.712596i | −0.0229163 | − | 0.999737i | \(-0.507295\pi\) |
−0.957888 | + | 0.287141i | \(0.907295\pi\) | |||||||
\(674\) | 0.909830 | 0.0350453 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 28.8885 | 1.11110 | ||||||||
\(677\) | 23.5344 | + | 17.0988i | 0.904502 | + | 0.657159i | 0.939618 | − | 0.342224i | \(-0.111180\pi\) |
−0.0351163 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(678\) | −5.94427 | − | 18.2946i | −0.228288 | − | 0.702599i | ||||
\(679\) | −2.73607 | − | 8.42075i | −0.105001 | − | 0.323159i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.88197 | − | 21.1805i | 0.263718 | − | 0.811639i | ||||
\(682\) | −23.9443 | −0.916874 | ||||||||
\(683\) | −10.3541 | + | 31.8666i | −0.396189 | + | 1.21934i | 0.531843 | + | 0.846843i | \(0.321500\pi\) |
−0.928032 | + | 0.372501i | \(0.878500\pi\) | |||||||
\(684\) | 4.61803 | − | 3.35520i | 0.176575 | − | 0.128289i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 15.1353 | + | 10.9964i | 0.577867 | + | 0.419845i | ||||
\(687\) | 4.47214 | − | 3.24920i | 0.170623 | − | 0.123965i | ||||
\(688\) | −6.23607 | + | 4.53077i | −0.237748 | + | 0.172734i | ||||
\(689\) | −10.9443 | − | 7.95148i | −0.416944 | − | 0.302927i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.09017 | + | 6.60440i | −0.345806 | + | 0.251243i | −0.747108 | − | 0.664703i | \(-0.768558\pi\) |
0.401301 | + | 0.915946i | \(0.368558\pi\) | |||||||
\(692\) | −1.57295 | + | 4.84104i | −0.0597945 | + | 0.184029i | ||||
\(693\) | −9.47214 | −0.359817 | ||||||||
\(694\) | 6.35410 | − | 19.5559i | 0.241198 | − | 0.742332i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.61803 | − | 8.05748i | −0.0992363 | − | 0.305418i | ||||
\(697\) | −2.18034 | − | 6.71040i | −0.0825863 | − | 0.254174i | ||||
\(698\) | −22.5623 | − | 16.3925i | −0.853996 | − | 0.620464i | ||||
\(699\) | −18.6525 | −0.705501 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.8328 | 1.54223 | 0.771117 | − | 0.636693i | \(-0.219698\pi\) | ||||
0.771117 | + | 0.636693i | \(0.219698\pi\) | |||||||
\(702\) | 5.23607 | + | 3.80423i | 0.197623 | + | 0.143581i | ||||
\(703\) | 14.1115 | + | 43.4306i | 0.532224 | + | 1.63802i | ||||
\(704\) | 1.11803 | + | 3.44095i | 0.0421375 | + | 0.129686i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.09017 | + | 12.5882i | −0.153936 | + | 0.473765i | ||||
\(707\) | −11.4721 | −0.431454 | ||||||||
\(708\) | −1.11803 | + | 3.44095i | −0.0420183 | + | 0.129319i | ||||
\(709\) | 35.3607 | − | 25.6910i | 1.32800 | − | 0.964847i | 0.328203 | − | 0.944607i | \(-0.393557\pi\) |
0.999795 | − | 0.0202400i | \(-0.00644302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.54508 | + | 3.30220i | 0.170454 | + | 0.123842i | ||||
\(712\) | 2.85410 | − | 2.07363i | 0.106962 | − | 0.0777124i | ||||
\(713\) | 23.9443 | − | 17.3965i | 0.896720 | − | 0.651505i | ||||
\(714\) | 2.61803 | + | 1.90211i | 0.0979775 | + | 0.0711848i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.97214 | + | 5.79210i | −0.297933 | + | 0.216461i | ||||
\(717\) | 3.79837 | − | 11.6902i | 0.141853 | − | 0.436578i | ||||
\(718\) | −22.1803 | −0.827763 | ||||||||
\(719\) | −5.12461 | + | 15.7719i | −0.191116 | + | 0.588194i | 0.808884 | + | 0.587968i | \(0.200072\pi\) |
−1.00000 | 0.000225882i | \(0.999928\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.5902 | + | 35.6709i | 0.431640 | + | 1.32845i | ||||
\(722\) | −4.19756 | − | 12.9188i | −0.156217 | − | 0.480787i | ||||
\(723\) | −7.73607 | − | 5.62058i | −0.287707 | − | 0.209032i | ||||
\(724\) | −6.65248 | −0.247237 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.09017 | −0.0775735 | ||||||||
\(727\) | −6.94427 | − | 5.04531i | −0.257549 | − | 0.187120i | 0.451517 | − | 0.892263i | \(-0.350883\pi\) |
−0.709066 | + | 0.705142i | \(0.750883\pi\) | |||||||
\(728\) | 5.23607 | + | 16.1150i | 0.194062 | + | 0.597260i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.94427 | + | 9.06154i | −0.108898 | + | 0.335153i | ||||
\(732\) | 2.76393 | 0.102158 | ||||||||
\(733\) | 11.0902 | − | 34.1320i | 0.409625 | − | 1.26070i | −0.507346 | − | 0.861742i | \(-0.669374\pi\) |
0.916971 | − | 0.398953i | \(-0.130626\pi\) | |||||||
\(734\) | 24.7705 | − | 17.9968i | 0.914296 | − | 0.664275i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.61803 | − | 2.62866i | −0.133363 | − | 0.0968935i | ||||
\(737\) | −4.47214 | + | 3.24920i | −0.164733 | + | 0.119686i | ||||
\(738\) | 4.61803 | − | 3.35520i | 0.169992 | − | 0.123507i | ||||
\(739\) | 38.9787 | + | 28.3197i | 1.43386 | + | 1.04176i | 0.989283 | + | 0.146014i | \(0.0466444\pi\) |
0.444573 | + | 0.895743i | \(0.353356\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.8885 | − | 21.7153i | 1.09798 | − | 0.797731i | ||||
\(742\) | 1.69098 | − | 5.20431i | 0.0620779 | − | 0.191056i | ||||
\(743\) | 39.0132 | 1.43125 | 0.715627 | − | 0.698483i | \(-0.246141\pi\) | ||||
0.715627 | + | 0.698483i | \(0.246141\pi\) | |||||||
\(744\) | −2.04508 | + | 6.29412i | −0.0749765 | + | 0.230754i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.56231 | − | 10.9637i | −0.130425 | − | 0.401408i | ||||
\(747\) | −0.663119 | − | 2.04087i | −0.0242623 | − | 0.0746715i | ||||
\(748\) | 3.61803 | + | 2.62866i | 0.132288 | + | 0.0961132i | ||||
\(749\) | −30.4164 | −1.11139 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24.7984 | 0.904906 | 0.452453 | − | 0.891788i | \(-0.350549\pi\) | ||||
0.452453 | + | 0.891788i | \(0.350549\pi\) | |||||||
\(752\) | 1.38197 | + | 1.00406i | 0.0503951 | + | 0.0366142i | ||||
\(753\) | 4.19098 | + | 12.8985i | 0.152728 | + | 0.470048i | ||||
\(754\) | −16.9443 | − | 52.1491i | −0.617074 | − | 1.89916i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.809017 | + | 2.48990i | −0.0294237 | + | 0.0905567i | ||||
\(757\) | 17.1246 | 0.622405 | 0.311202 | − | 0.950344i | \(-0.399268\pi\) | ||||
0.311202 | + | 0.950344i | \(0.399268\pi\) | |||||||
\(758\) | 6.23607 | − | 19.1926i | 0.226504 | − | 0.697108i | ||||
\(759\) | 13.0902 | − | 9.51057i | 0.475143 | − | 0.345212i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.14590 | − | 0.832544i | −0.0415388 | − | 0.0301797i | 0.566822 | − | 0.823840i | \(-0.308173\pi\) |
−0.608361 | + | 0.793661i | \(0.708173\pi\) | |||||||
\(762\) | −11.0172 | + | 8.00448i | −0.399112 | + | 0.289972i | ||||
\(763\) | 36.5066 | − | 26.5236i | 1.32163 | − | 0.960218i | ||||
\(764\) | −3.47214 | − | 2.52265i | −0.125617 | − | 0.0912664i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.1803 | − | 11.7557i | 0.584619 | − | 0.424751i | ||||
\(767\) | −7.23607 | + | 22.2703i | −0.261279 | + | 0.804135i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 7.62868 | − | 23.4787i | 0.275097 | − | 0.846662i | −0.714097 | − | 0.700047i | \(-0.753162\pi\) |
0.989194 | − | 0.146615i | \(-0.0468377\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.79837 | + | 20.9232i | 0.244837 | + | 0.753532i | ||||
\(772\) | −5.51722 | − | 16.9803i | −0.198569 | − | 0.611133i | ||||
\(773\) | −0.927051 | − | 0.673542i | −0.0333437 | − | 0.0242256i | 0.570989 | − | 0.820958i | \(-0.306560\pi\) |
−0.604332 | + | 0.796732i | \(0.706560\pi\) | |||||||
\(774\) | −7.70820 | −0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.38197 | −0.121406 | ||||||||
\(777\) | −16.9443 | − | 12.3107i | −0.607872 | − | 0.441645i | ||||
\(778\) | 3.82624 | + | 11.7759i | 0.137177 | + | 0.422188i | ||||
\(779\) | −10.0689 | − | 30.9888i | −0.360755 | − | 1.11029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.18034 | − | 19.0211i | 0.221150 | − | 0.680630i | ||||
\(782\) | −5.52786 | −0.197676 | ||||||||
\(783\) | 2.61803 | − | 8.05748i | 0.0935609 | − | 0.287951i | ||||
\(784\) | 0.118034 | − | 0.0857567i | 0.00421550 | − | 0.00306274i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.4721 | − | 10.5146i | −0.516204 | − | 0.375044i | ||||
\(787\) | 22.7082 | − | 16.4985i | 0.809460 | − | 0.588107i | −0.104214 | − | 0.994555i | \(-0.533233\pi\) |
0.913674 | + | 0.406448i | \(0.133233\pi\) | |||||||
\(788\) | −13.8262 | + | 10.0453i | −0.492539 | + | 0.357851i | ||||
\(789\) | −9.47214 | − | 6.88191i | −0.337217 | − | 0.245002i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.7426 | − | 29.6013i | 1.44864 | − | 1.05250i | ||||
\(792\) | −1.11803 | + | 3.44095i | −0.0397276 | + | 0.122269i | ||||
\(793\) | 17.8885 | 0.635241 | ||||||||
\(794\) | −9.50658 | + | 29.2582i | −0.337376 | + | 1.03834i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.02786 | + | 18.5519i | 0.213652 | + | 0.657553i | ||||
\(797\) | −0.465558 | − | 1.43284i | −0.0164909 | − | 0.0507538i | 0.942472 | − | 0.334284i | \(-0.108494\pi\) |
−0.958963 | + | 0.283530i | \(0.908494\pi\) | |||||||
\(798\) | 12.0902 | + | 8.78402i | 0.427987 | + | 0.310951i | ||||
\(799\) | 2.11146 | 0.0746979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.52786 | 0.124651 | ||||||||
\(802\) | 20.7984 | + | 15.1109i | 0.734416 | + | 0.533585i | ||||
\(803\) | −3.94427 | − | 12.1392i | −0.139190 | − | 0.428384i | ||||
\(804\) | 0.472136 | + | 1.45309i | 0.0166510 | + | 0.0512464i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.2361 | + | 40.7364i | −0.466221 | + | 1.43488i | ||||
\(807\) | −9.09017 | −0.319989 | ||||||||
\(808\) | −1.35410 | + | 4.16750i | −0.0476371 | + | 0.146612i | ||||
\(809\) | 24.9443 | − | 18.1231i | 0.876994 | − | 0.637173i | −0.0554606 | − | 0.998461i | \(-0.517663\pi\) |
0.932454 | + | 0.361288i | \(0.117663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.61803 | + | 3.35520i | 0.162161 | + | 0.117817i | 0.665906 | − | 0.746035i | \(-0.268045\pi\) |
−0.503745 | + | 0.863852i | \(0.668045\pi\) | |||||||
\(812\) | 17.9443 | − | 13.0373i | 0.629720 | − | 0.457519i | ||||
\(813\) | 14.5902 | − | 10.6004i | 0.511700 | − | 0.371772i | ||||
\(814\) | −23.4164 | − | 17.0130i | −0.820745 | − | 0.596306i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | − | 0.726543i | 0.0350070 | − | 0.0254341i | ||||
\(817\) | −13.5967 | + | 41.8465i | −0.475690 | + | 1.46402i | ||||
\(818\) | −5.79837 | −0.202735 | ||||||||
\(819\) | −5.23607 | + | 16.1150i | −0.182963 | + | 0.563102i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.9336 | − | 42.8833i | −0.486287 | − | 1.49664i | −0.830108 | − | 0.557602i | \(-0.811721\pi\) |
0.343821 | − | 0.939035i | \(-0.388279\pi\) | |||||||
\(822\) | −3.76393 | − | 11.5842i | −0.131282 | − | 0.404045i | ||||
\(823\) | 2.39919 | + | 1.74311i | 0.0836304 | + | 0.0607610i | 0.628815 | − | 0.777555i | \(-0.283540\pi\) |
−0.545184 | + | 0.838316i | \(0.683540\pi\) | |||||||
\(824\) | 14.3262 | 0.499078 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.47214 | −0.329578 | ||||||||
\(827\) | 35.6803 | + | 25.9233i | 1.24073 | + | 0.901441i | 0.997647 | − | 0.0685652i | \(-0.0218421\pi\) |
0.243080 | + | 0.970006i | \(0.421842\pi\) | |||||||
\(828\) | −1.38197 | − | 4.25325i | −0.0480266 | − | 0.147811i | ||||
\(829\) | 8.00000 | + | 24.6215i | 0.277851 | + | 0.855139i | 0.988451 | + | 0.151542i | \(0.0484239\pi\) |
−0.710599 | + | 0.703597i | \(0.751576\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.23607 | + | 16.1150i | −0.181637 | + | 0.559022i | ||||
\(832\) | 6.47214 | 0.224381 | ||||||||
\(833\) | 0.0557281 | − | 0.171513i | 0.00193086 | − | 0.00594259i | ||||
\(834\) | 8.47214 | − | 6.15537i | 0.293366 | − | 0.213143i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.7082 | + | 12.1392i | 0.577865 | + | 0.419844i | ||||
\(837\) | −5.35410 | + | 3.88998i | −0.185065 | + | 0.134457i | ||||
\(838\) | −2.50000 | + | 1.81636i | −0.0863611 | + | 0.0627450i | ||||
\(839\) | −5.14590 | − | 3.73871i | −0.177656 | − | 0.129075i | 0.495403 | − | 0.868663i | \(-0.335020\pi\) |
−0.673060 | + | 0.739588i | \(0.735020\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.6074 | + | 25.1437i | −1.19336 | + | 0.867026i | ||||
\(842\) | 7.03444 | − | 21.6498i | 0.242423 | − | 0.746101i | ||||
\(843\) | 5.88854 | 0.202812 | ||||||||
\(844\) | −1.05573 | + | 3.24920i | −0.0363397 | + | 0.111842i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.527864 | + | 1.62460i | 0.0181483 | + | 0.0558548i | ||||
\(847\) | −1.69098 | − | 5.20431i | −0.0581029 | − | 0.178822i | ||||
\(848\) | −1.69098 | − | 1.22857i | −0.0580686 | − | 0.0421893i | ||||
\(849\) | −4.58359 | −0.157308 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.7771 | 1.22642 | ||||||||
\(852\) | −4.47214 | − | 3.24920i | −0.153213 | − | 0.111316i | ||||
\(853\) | 13.4721 | + | 41.4630i | 0.461277 | + | 1.41967i | 0.863605 | + | 0.504169i | \(0.168201\pi\) |
−0.402328 | + | 0.915496i | \(0.631799\pi\) | |||||||
\(854\) | 2.23607 | + | 6.88191i | 0.0765167 | + | 0.235494i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.59017 | + | 11.0494i | −0.122709 | + | 0.377661i | ||||
\(857\) | 16.0689 | 0.548903 | 0.274451 | − | 0.961601i | \(-0.411504\pi\) | ||||
0.274451 | + | 0.961601i | \(0.411504\pi\) | |||||||
\(858\) | −7.23607 | + | 22.2703i | −0.247035 | + | 0.760296i | ||||
\(859\) | 1.85410 | − | 1.34708i | 0.0632611 | − | 0.0459619i | −0.555705 | − | 0.831379i | \(-0.687552\pi\) |
0.618966 | + | 0.785417i | \(0.287552\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.0902 | + | 8.78402i | 0.412032 | + | 0.299359i | ||||
\(862\) | 13.6180 | − | 9.89408i | 0.463832 | − | 0.336994i | ||||
\(863\) | −8.23607 | + | 5.98385i | −0.280359 | + | 0.203693i | −0.719074 | − | 0.694934i | \(-0.755434\pi\) |
0.438715 | + | 0.898626i | \(0.355434\pi\) | |||||||
\(864\) | 0.809017 | + | 0.587785i | 0.0275233 | + | 0.0199969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12.5451 | + | 9.11454i | −0.426299 | + | 0.309725i | ||||
\(867\) | −4.78115 | + | 14.7149i | −0.162376 | + | 0.499743i | ||||
\(868\) | −17.3262 | −0.588091 | ||||||||
\(869\) | −6.28115 | + | 19.3314i | −0.213074 | + | 0.655773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.05573 | + | 9.40456i | 0.103539 | + | 0.318661i | ||||
\(872\) | −5.32624 | − | 16.3925i | −0.180369 | − | 0.555119i | ||||
\(873\) | −2.73607 | − | 1.98787i | −0.0926019 | − | 0.0672792i | ||||
\(874\) | −25.5279 | −0.863493 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.52786 | −0.119195 | ||||||||
\(877\) | −30.0344 | − | 21.8213i | −1.01419 | − | 0.736853i | −0.0491070 | − | 0.998794i | \(-0.515638\pi\) |
−0.965084 | + | 0.261941i | \(0.915638\pi\) | |||||||
\(878\) | 7.26393 | + | 22.3561i | 0.245146 | + | 0.754481i | ||||
\(879\) | 6.82624 | + | 21.0090i | 0.230243 | + | 0.708616i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.29180 | + | 22.4418i | −0.245667 | + | 0.756085i | 0.749859 | + | 0.661597i | \(0.230121\pi\) |
−0.995526 | + | 0.0944874i | \(0.969879\pi\) | |||||||
\(882\) | 0.145898 | 0.00491264 | ||||||||
\(883\) | 9.29180 | − | 28.5972i | 0.312694 | − | 0.962373i | −0.663999 | − | 0.747733i | \(-0.731142\pi\) |
0.976693 | − | 0.214640i | \(-0.0688577\pi\) | |||||||
\(884\) | 6.47214 | − | 4.70228i | 0.217681 | − | 0.158155i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.4443 | − | 9.76784i | −0.451669 | − | 0.328157i | ||||
\(887\) | 18.9443 | − | 13.7638i | 0.636086 | − | 0.462144i | −0.222417 | − | 0.974952i | \(-0.571395\pi\) |
0.858503 | + | 0.512808i | \(0.171395\pi\) | |||||||
\(888\) | −6.47214 | + | 4.70228i | −0.217191 | + | 0.157798i | ||||
\(889\) | −28.8435 | − | 20.9560i | −0.967379 | − | 0.702842i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.92705 | + | 2.12663i | −0.0980599 | + | 0.0712447i | ||||
\(892\) | 2.50000 | − | 7.69421i | 0.0837062 | − | 0.257621i | ||||
\(893\) | 9.75078 | 0.326297 | ||||||||
\(894\) | −6.82624 | + | 21.0090i | −0.228304 | + | 0.702646i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.809017 | + | 2.48990i | 0.0270274 | + | 0.0831817i | ||||
\(897\) | −8.94427 | − | 27.5276i | −0.298641 | − | 0.919121i | ||||
\(898\) | −22.4164 | − | 16.2865i | −0.748045 | − | 0.543487i | ||||
\(899\) | 56.0689 | 1.87000 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.58359 | −0.0860719 | ||||||||
\(902\) | 16.7082 | + | 12.1392i | 0.556322 | + | 0.404192i | ||||
\(903\) | −6.23607 | − | 19.1926i | −0.207523 | − | 0.638691i | ||||
\(904\) | −5.94427 | − | 18.2946i | −0.197704 | − | 0.608469i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.66312 | + | 17.4293i | −0.188145 | + | 0.579049i | ||||
\(907\) | −30.4721 | −1.01181 | −0.505905 | − | 0.862589i | \(-0.668841\pi\) | ||||
−0.505905 | + | 0.862589i | \(0.668841\pi\) | |||||||
\(908\) | 6.88197 | − | 21.1805i | 0.228386 | − | 0.702900i | ||||
\(909\) | −3.54508 | + | 2.57565i | −0.117583 | + | 0.0854291i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.7082 | − | 10.6861i | −0.487305 | − | 0.354047i | 0.316842 | − | 0.948478i | \(-0.397377\pi\) |
−0.804147 | + | 0.594431i | \(0.797377\pi\) | |||||||
\(912\) | 4.61803 | − | 3.35520i | 0.152918 | − | 0.111102i | ||||
\(913\) | 6.28115 | − | 4.56352i | 0.207876 | − | 0.151031i | ||||
\(914\) | 3.30902 | + | 2.40414i | 0.109453 | + | 0.0795219i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.47214 | − | 3.24920i | 0.147764 | − | 0.107356i | ||||
\(917\) | 14.4721 | − | 44.5407i | 0.477912 | − | 1.47086i | ||||
\(918\) | 1.23607 | 0.0407963 | ||||||||
\(919\) | −12.5836 | + | 38.7283i | −0.415094 | + | 1.27753i | 0.497072 | + | 0.867709i | \(0.334408\pi\) |
−0.912166 | + | 0.409820i | \(0.865592\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.09017 | − | 9.51057i | −0.101825 | − | 0.313384i | ||||
\(922\) | −2.33688 | − | 7.19218i | −0.0769611 | − | 0.236862i | ||||
\(923\) | −28.9443 | − | 21.0292i | −0.952712 | − | 0.692186i | ||||
\(924\) | −9.47214 | −0.311610 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.8328 | −0.750333 | ||||||||
\(927\) | 11.5902 | + | 8.42075i | 0.380671 | + | 0.276574i | ||||
\(928\) | −2.61803 | − | 8.05748i | −0.0859412 | − | 0.264500i | ||||
\(929\) | −5.87539 | − | 18.0826i | −0.192765 | − | 0.593270i | −0.999995 | − | 0.00303360i | \(-0.999034\pi\) |
0.807230 | − | 0.590237i | \(-0.200966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.257354 | − | 0.792055i | 0.00843444 | − | 0.0259585i | ||||
\(932\) | −18.6525 | −0.610982 | ||||||||
\(933\) | −0.326238 | + | 1.00406i | −0.0106806 | + | 0.0328714i | ||||
\(934\) | −8.63525 | + | 6.27388i | −0.282554 | + | 0.205288i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.23607 | + | 3.80423i | 0.171146 | + | 0.124345i | ||||
\(937\) | −7.02786 | + | 5.10604i | −0.229590 | + | 0.166807i | −0.696633 | − | 0.717428i | \(-0.745319\pi\) |
0.467043 | + | 0.884235i | \(0.345319\pi\) | |||||||
\(938\) | −3.23607 | + | 2.35114i | −0.105661 | + | 0.0767675i | ||||
\(939\) | −13.1631 | − | 9.56357i | −0.429562 | − | 0.312095i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.59017 | − | 2.60841i | 0.117036 | − | 0.0850318i | −0.527728 | − | 0.849414i | \(-0.676956\pi\) |
0.644764 | + | 0.764382i | \(0.276956\pi\) | |||||||
\(942\) | 2.67376 | − | 8.22899i | 0.0871159 | − | 0.268115i | ||||
\(943\) | −25.5279 | −0.831302 | ||||||||
\(944\) | −1.11803 | + | 3.44095i | −0.0363889 | + | 0.111994i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.61803 | − | 26.5236i | −0.280196 | − | 0.862356i | ||||
\(947\) | 10.3713 | + | 31.9196i | 0.337023 | + | 1.03725i | 0.965717 | + | 0.259597i | \(0.0835897\pi\) |
−0.628694 | + | 0.777652i | \(0.716410\pi\) | |||||||
\(948\) | 4.54508 | + | 3.30220i | 0.147617 | + | 0.107250i | ||||
\(949\) | −22.8328 | −0.741185 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 20.5623 | 0.666778 | ||||||||
\(952\) | 2.61803 | + | 1.90211i | 0.0848510 | + | 0.0616478i | ||||
\(953\) | −1.63932 | − | 5.04531i | −0.0531028 | − | 0.163434i | 0.920988 | − | 0.389591i | \(-0.127384\pi\) |
−0.974091 | + | 0.226157i | \(0.927384\pi\) | |||||||
\(954\) | −0.645898 | − | 1.98787i | −0.0209117 | − | 0.0643597i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.79837 | − | 11.6902i | 0.122848 | − | 0.378088i | ||||
\(957\) | 30.6525 | 0.990854 | ||||||||
\(958\) | 9.00000 | − | 27.6992i | 0.290777 | − | 0.894919i | ||||
\(959\) | 25.7984 | − | 18.7436i | 0.833073 | − | 0.605263i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.3541 | − | 7.52270i | −0.334003 | − | 0.242668i | ||||
\(962\) | −41.8885 | + | 30.4338i | −1.35054 | + | 0.981225i | ||||
\(963\) | −9.39919 | + | 6.82891i | −0.302885 | + | 0.220059i | ||||
\(964\) | −7.73607 | − | 5.62058i | −0.249162 | − | 0.181027i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.47214 | − | 6.88191i | 0.304761 | − | 0.221422i | ||||
\(967\) | −3.37132 | + | 10.3759i | −0.108414 | + | 0.333665i | −0.990517 | − | 0.137393i | \(-0.956128\pi\) |
0.882102 | + | 0.471058i | \(0.156128\pi\) | |||||||
\(968\) | −2.09017 | −0.0671806 | ||||||||
\(969\) | 2.18034 | − | 6.71040i | 0.0700426 | − | 0.215569i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.39261 | − | 13.5191i | −0.140966 | − | 0.433847i | 0.855505 | − | 0.517795i | \(-0.173247\pi\) |
−0.996470 | + | 0.0839479i | \(0.973247\pi\) | |||||||
\(972\) | 0.309017 | + | 0.951057i | 0.00991172 | + | 0.0305052i | ||||
\(973\) | 22.1803 | + | 16.1150i | 0.711069 | + | 0.516622i | ||||
\(974\) | 17.7984 | 0.570297 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.76393 | 0.0884713 | ||||||||
\(977\) | −0.618034 | − | 0.449028i | −0.0197727 | − | 0.0143657i | 0.577855 | − | 0.816139i | \(-0.303890\pi\) |
−0.597628 | + | 0.801774i | \(0.703890\pi\) | |||||||
\(978\) | −0.145898 | − | 0.449028i | −0.00466530 | − | 0.0143583i | ||||
\(979\) | 3.94427 | + | 12.1392i | 0.126059 | + | 0.387971i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.32624 | − | 16.3925i | 0.170054 | − | 0.523371i | ||||
\(982\) | 25.2705 | 0.806414 | ||||||||
\(983\) | −12.4164 | + | 38.2138i | −0.396022 | + | 1.21883i | 0.532141 | + | 0.846656i | \(0.321388\pi\) |
−0.928163 | + | 0.372174i | \(0.878612\pi\) | |||||||
\(984\) | 4.61803 | − | 3.35520i | 0.147218 | − | 0.106960i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.47214 | − | 6.15537i | −0.269808 | − | 0.196027i | ||||
\(987\) | −3.61803 | + | 2.62866i | −0.115163 | + | 0.0836710i | ||||
\(988\) | 29.8885 | − | 21.7153i | 0.950881 | − | 0.690856i | ||||
\(989\) | 27.8885 | + | 20.2622i | 0.886804 | + | 0.644301i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8262 | + | 17.3108i | −0.756865 | + | 0.549895i | −0.897947 | − | 0.440103i | \(-0.854942\pi\) |
0.141082 | + | 0.989998i | \(0.454942\pi\) | |||||||
\(992\) | −2.04508 | + | 6.29412i | −0.0649315 | + | 0.199839i | ||||
\(993\) | −18.0000 | −0.571213 | ||||||||
\(994\) | 4.47214 | − | 13.7638i | 0.141848 | − | 0.436562i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.663119 | − | 2.04087i | −0.0210117 | − | 0.0646675i | ||||
\(997\) | 1.72949 | + | 5.32282i | 0.0547735 | + | 0.168576i | 0.974701 | − | 0.223513i | \(-0.0717526\pi\) |
−0.919927 | + | 0.392089i | \(0.871753\pi\) | |||||||
\(998\) | 28.7984 | + | 20.9232i | 0.911597 | + | 0.662314i | ||||
\(999\) | −8.00000 | −0.253109 |
(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 | 750.2.g.b.451.1 | 4 | ||
5.2 | odd | 4 | 750.2.h.b.49.1 | 8 | |||
5.3 | odd | 4 | 750.2.h.b.49.2 | 8 | |||
5.4 | even | 2 | 150.2.g.a.91.1 | yes | 4 | ||
15.14 | odd | 2 | 450.2.h.c.91.1 | 4 | |||
25.2 | odd | 20 | 750.2.h.b.199.2 | 8 | |||
25.6 | even | 5 | 3750.2.a.d.1.1 | 2 | |||
25.8 | odd | 20 | 3750.2.c.b.1249.4 | 4 | |||
25.11 | even | 5 | inner | 750.2.g.b.301.1 | 4 | ||
25.14 | even | 10 | 150.2.g.a.61.1 | ✓ | 4 | ||
25.17 | odd | 20 | 3750.2.c.b.1249.1 | 4 | |||
25.19 | even | 10 | 3750.2.a.f.1.2 | 2 | |||
25.23 | odd | 20 | 750.2.h.b.199.1 | 8 | |||
75.14 | odd | 10 | 450.2.h.c.361.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.61.1 | ✓ | 4 | 25.14 | even | 10 | ||
150.2.g.a.91.1 | yes | 4 | 5.4 | even | 2 | ||
450.2.h.c.91.1 | 4 | 15.14 | odd | 2 | |||
450.2.h.c.361.1 | 4 | 75.14 | odd | 10 | |||
750.2.g.b.301.1 | 4 | 25.11 | even | 5 | inner | ||
750.2.g.b.451.1 | 4 | 1.1 | even | 1 | trivial | ||
750.2.h.b.49.1 | 8 | 5.2 | odd | 4 | |||
750.2.h.b.49.2 | 8 | 5.3 | odd | 4 | |||
750.2.h.b.199.1 | 8 | 25.23 | odd | 20 | |||
750.2.h.b.199.2 | 8 | 25.2 | odd | 20 | |||
3750.2.a.d.1.1 | 2 | 25.6 | even | 5 | |||
3750.2.a.f.1.2 | 2 | 25.19 | even | 10 | |||
3750.2.c.b.1249.1 | 4 | 25.17 | odd | 20 | |||
3750.2.c.b.1249.4 | 4 | 25.8 | odd | 20 |