Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(49,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.j (of order \(6\), degree \(2\), 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.1731891456.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 9x^{6} + 65x^{4} - 144x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.3 | ||
Root | \(-2.21837 + 1.28078i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.349 |
Dual form | 950.2.j.f.49.3 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −2.21837 | + | 1.28078i | −1.28078 | + | 0.739457i | −0.976990 | − | 0.213284i | \(-0.931584\pi\) |
−0.303786 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.28078 | + | 2.21837i | −0.522875 | + | 0.905646i | ||||
\(7\) | − | 0.438447i | − | 0.165717i | −0.996561 | − | 0.0828587i | \(-0.973595\pi\) | ||
0.996561 | − | 0.0828587i | \(-0.0264050\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.78078 | − | 3.08440i | 0.593592 | − | 1.02813i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | 2.56155i | 0.739457i | ||||||||
\(13\) | 1.73205 | + | 1.00000i | 0.480384 | + | 0.277350i | 0.720577 | − | 0.693375i | \(-0.243877\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | −0.219224 | − | 0.379706i | −0.0585900 | − | 0.101481i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −4.43674 | + | 2.56155i | −1.07607 | + | 0.621268i | −0.929833 | − | 0.367982i | \(-0.880049\pi\) |
−0.146235 | + | 0.989250i | \(0.546715\pi\) | |||||||
\(18\) | − | 3.56155i | − | 0.839466i | ||||||
\(19\) | 2.50000 | − | 3.57071i | 0.573539 | − | 0.819178i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.561553 | + | 0.972638i | 0.122541 | + | 0.212247i | ||||
\(22\) | 0.866025 | − | 0.500000i | 0.184637 | − | 0.106600i | ||||
\(23\) | 4.05703 | + | 2.34233i | 0.845950 | + | 0.488409i | 0.859282 | − | 0.511502i | \(-0.170911\pi\) |
−0.0133324 | + | 0.999911i | \(0.504244\pi\) | |||||||
\(24\) | 1.28078 | + | 2.21837i | 0.261437 | + | 0.452823i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.43845i | 0.276829i | ||||||||
\(28\) | −0.379706 | − | 0.219224i | −0.0717578 | − | 0.0414294i | ||||
\(29\) | 1.00000 | − | 1.73205i | 0.185695 | − | 0.321634i | −0.758115 | − | 0.652121i | \(-0.773880\pi\) |
0.943811 | + | 0.330487i | \(0.107213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2462 | 1.84027 | 0.920137 | − | 0.391597i | \(-0.128077\pi\) | ||||
0.920137 | + | 0.391597i | \(0.128077\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −2.21837 | + | 1.28078i | −0.386169 | + | 0.222955i | ||||
\(34\) | −2.56155 | + | 4.43674i | −0.439303 | + | 0.760895i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.78078 | − | 3.08440i | −0.296796 | − | 0.514066i | ||||
\(37\) | 4.68466i | 0.770153i | 0.922885 | + | 0.385077i | \(0.125825\pi\) | ||||
−0.922885 | + | 0.385077i | \(0.874175\pi\) | |||||||
\(38\) | 0.379706 | − | 4.34233i | 0.0615965 | − | 0.704419i | ||||
\(39\) | −5.12311 | −0.820353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.06155 | + | 5.30277i | 0.478134 | + | 0.828153i | 0.999686 | − | 0.0250670i | \(-0.00797991\pi\) |
−0.521552 | + | 0.853220i | \(0.674647\pi\) | |||||||
\(42\) | 0.972638 | + | 0.561553i | 0.150081 | + | 0.0866495i | ||||
\(43\) | 2.70469 | − | 1.56155i | 0.412461 | − | 0.238135i | −0.279385 | − | 0.960179i | \(-0.590131\pi\) |
0.691847 | + | 0.722044i | \(0.256797\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.68466 | 0.690715 | ||||||||
\(47\) | 2.49146 | + | 1.43845i | 0.363417 | + | 0.209819i | 0.670579 | − | 0.741838i | \(-0.266046\pi\) |
−0.307161 | + | 0.951657i | \(0.599379\pi\) | |||||||
\(48\) | 2.21837 | + | 1.28078i | 0.320194 | + | 0.184864i | ||||
\(49\) | 6.80776 | 0.972538 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.56155 | − | 11.3649i | 0.918801 | − | 1.59141i | ||||
\(52\) | 1.73205 | − | 1.00000i | 0.240192 | − | 0.138675i | ||||
\(53\) | 6.54850 | + | 3.78078i | 0.899505 | + | 0.519330i | 0.877040 | − | 0.480418i | \(-0.159515\pi\) |
0.0224656 | + | 0.999748i | \(0.492848\pi\) | |||||||
\(54\) | 0.719224 | + | 1.24573i | 0.0978739 | + | 0.169523i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.438447 | −0.0585900 | ||||||||
\(57\) | −0.972638 | + | 11.1231i | −0.128829 | + | 1.47329i | ||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 7.28078 | + | 12.6107i | 0.947876 | + | 1.64177i | 0.749887 | + | 0.661566i | \(0.230108\pi\) |
0.197989 | + | 0.980204i | \(0.436559\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.56155 | + | 4.43674i | −0.327973 | + | 0.568066i | −0.982110 | − | 0.188310i | \(-0.939699\pi\) |
0.654136 | + | 0.756377i | \(0.273032\pi\) | |||||||
\(62\) | 8.87348 | − | 5.12311i | 1.12693 | − | 0.650635i | ||||
\(63\) | −1.35234 | − | 0.780776i | −0.170379 | − | 0.0983686i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.28078 | + | 2.21837i | −0.157653 | + | 0.273062i | ||||
\(67\) | 8.17394 | + | 4.71922i | 0.998605 | + | 0.576545i | 0.907835 | − | 0.419327i | \(-0.137734\pi\) |
0.0907698 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(68\) | 5.12311i | 0.621268i | ||||||||
\(69\) | −12.0000 | −1.44463 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.12311 | − | 14.0696i | −0.964035 | − | 1.66976i | −0.712185 | − | 0.701992i | \(-0.752294\pi\) |
−0.251850 | − | 0.967766i | \(-0.581039\pi\) | |||||||
\(72\) | −3.08440 | − | 1.78078i | −0.363499 | − | 0.209867i | ||||
\(73\) | −1.45896 | + | 0.842329i | −0.170758 | + | 0.0985872i | −0.582943 | − | 0.812513i | \(-0.698099\pi\) |
0.412185 | + | 0.911100i | \(0.364766\pi\) | |||||||
\(74\) | 2.34233 | + | 4.05703i | 0.272290 | + | 0.471621i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.84233 | − | 3.95042i | −0.211330 | − | 0.453144i | ||||
\(77\) | − | 0.438447i | − | 0.0499657i | ||||||
\(78\) | −4.43674 | + | 2.56155i | −0.502362 | + | 0.290039i | ||||
\(79\) | −5.56155 | − | 9.63289i | −0.625724 | − | 1.08379i | −0.988400 | − | 0.151870i | \(-0.951470\pi\) |
0.362677 | − | 0.931915i | \(-0.381863\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | + | 6.06218i | 0.388889 | + | 0.673575i | ||||
\(82\) | 5.30277 | + | 3.06155i | 0.585592 | + | 0.338092i | ||||
\(83\) | − | 10.8078i | − | 1.18631i | −0.805090 | − | 0.593153i | \(-0.797883\pi\) | ||
0.805090 | − | 0.593153i | \(-0.202117\pi\) | |||||||
\(84\) | 1.12311 | 0.122541 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.56155 | − | 2.70469i | 0.168387 | − | 0.291654i | ||||
\(87\) | 5.12311i | 0.549255i | ||||||||
\(88\) | − | 1.00000i | − | 0.106600i | ||||||
\(89\) | −1.34233 | + | 2.32498i | −0.142287 | + | 0.246448i | −0.928357 | − | 0.371689i | \(-0.878779\pi\) |
0.786071 | + | 0.618137i | \(0.212112\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.438447 | − | 0.759413i | 0.0459618 | − | 0.0796081i | ||||
\(92\) | 4.05703 | − | 2.34233i | 0.422975 | − | 0.244205i | ||||
\(93\) | −22.7299 | + | 13.1231i | −2.35698 | + | 1.36080i | ||||
\(94\) | 2.87689 | 0.296729 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.56155 | 0.261437 | ||||||||
\(97\) | −1.45896 | + | 0.842329i | −0.148135 | + | 0.0855256i | −0.572235 | − | 0.820089i | \(-0.693924\pi\) |
0.424101 | + | 0.905615i | \(0.360590\pi\) | |||||||
\(98\) | 5.89570 | − | 3.40388i | 0.595555 | − | 0.343844i | ||||
\(99\) | 1.78078 | − | 3.08440i | 0.178975 | − | 0.309993i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | + | 8.66025i | −0.497519 | + | 0.861727i | −0.999996 | − | 0.00286291i | \(-0.999089\pi\) |
0.502477 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(102\) | − | 13.1231i | − | 1.29938i | ||||||
\(103\) | − | 5.80776i | − | 0.572256i | −0.958191 | − | 0.286128i | \(-0.907632\pi\) | ||
0.958191 | − | 0.286128i | \(-0.0923683\pi\) | |||||||
\(104\) | 1.00000 | − | 1.73205i | 0.0980581 | − | 0.169842i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.56155 | 0.734443 | ||||||||
\(107\) | − | 2.24621i | − | 0.217149i | −0.994088 | − | 0.108575i | \(-0.965371\pi\) | ||
0.994088 | − | 0.108575i | \(-0.0346287\pi\) | |||||||
\(108\) | 1.24573 | + | 0.719224i | 0.119871 | + | 0.0692073i | ||||
\(109\) | −7.12311 | − | 12.3376i | −0.682270 | − | 1.18173i | −0.974286 | − | 0.225313i | \(-0.927660\pi\) |
0.292017 | − | 0.956413i | \(-0.405674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | − | 10.3923i | −0.569495 | − | 0.986394i | ||||
\(112\) | −0.379706 | + | 0.219224i | −0.0358789 | + | 0.0207147i | ||||
\(113\) | − | 16.8078i | − | 1.58114i | −0.612371 | − | 0.790571i | \(-0.709784\pi\) | ||
0.612371 | − | 0.790571i | \(-0.290216\pi\) | |||||||
\(114\) | 4.71922 | + | 10.1192i | 0.441996 | + | 0.947751i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.00000 | − | 1.73205i | −0.0928477 | − | 0.160817i | ||||
\(117\) | 6.16879 | − | 3.56155i | 0.570305 | − | 0.329266i | ||||
\(118\) | 12.6107 | + | 7.28078i | 1.16091 | + | 0.670250i | ||||
\(119\) | 1.12311 | + | 1.94528i | 0.102955 | + | 0.178323i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 5.12311i | 0.463824i | ||||||||
\(123\) | −13.5833 | − | 7.84233i | −1.22477 | − | 0.707119i | ||||
\(124\) | 5.12311 | − | 8.87348i | 0.460068 | − | 0.796862i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.56155 | −0.139114 | ||||||||
\(127\) | −13.4767 | − | 7.78078i | −1.19586 | − | 0.690432i | −0.236233 | − | 0.971696i | \(-0.575913\pi\) |
−0.959630 | + | 0.281264i | \(0.909246\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −4.00000 | + | 6.92820i | −0.352180 | + | 0.609994i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.06155 | + | 13.9630i | 0.704341 | + | 1.21995i | 0.966929 | + | 0.255046i | \(0.0820908\pi\) |
−0.262588 | + | 0.964908i | \(0.584576\pi\) | |||||||
\(132\) | 2.56155i | 0.222955i | ||||||||
\(133\) | −1.56557 | − | 1.09612i | −0.135752 | − | 0.0950455i | ||||
\(134\) | 9.43845 | 0.815358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.56155 | + | 4.43674i | 0.219651 | + | 0.380447i | ||||
\(137\) | −4.70983 | − | 2.71922i | −0.402388 | − | 0.232319i | 0.285126 | − | 0.958490i | \(-0.407965\pi\) |
−0.687514 | + | 0.726171i | \(0.741298\pi\) | |||||||
\(138\) | −10.3923 | + | 6.00000i | −0.884652 | + | 0.510754i | ||||
\(139\) | 4.40388 | − | 7.62775i | 0.373532 | − | 0.646977i | −0.616574 | − | 0.787297i | \(-0.711480\pi\) |
0.990106 | + | 0.140320i | \(0.0448131\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.36932 | −0.620608 | ||||||||
\(142\) | −14.0696 | − | 8.12311i | −1.18070 | − | 0.681676i | ||||
\(143\) | 1.73205 | + | 1.00000i | 0.144841 | + | 0.0836242i | ||||
\(144\) | −3.56155 | −0.296796 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.842329 | + | 1.45896i | −0.0697117 | + | 0.120744i | ||||
\(147\) | −15.1021 | + | 8.71922i | −1.24560 | + | 0.719149i | ||||
\(148\) | 4.05703 | + | 2.34233i | 0.333486 | + | 0.192538i | ||||
\(149\) | 8.00000 | + | 13.8564i | 0.655386 | + | 1.13516i | 0.981797 | + | 0.189933i | \(0.0608272\pi\) |
−0.326411 | + | 0.945228i | \(0.605840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4924 | 1.66765 | 0.833825 | − | 0.552029i | \(-0.186146\pi\) | ||||
0.833825 | + | 0.552029i | \(0.186146\pi\) | |||||||
\(152\) | −3.57071 | − | 2.50000i | −0.289623 | − | 0.202777i | ||||
\(153\) | 18.2462i | 1.47512i | ||||||||
\(154\) | −0.219224 | − | 0.379706i | −0.0176655 | − | 0.0305976i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.56155 | + | 4.43674i | −0.205088 | + | 0.355223i | ||||
\(157\) | −2.11176 | + | 1.21922i | −0.168537 | + | 0.0973046i | −0.581896 | − | 0.813263i | \(-0.697689\pi\) |
0.413359 | + | 0.910568i | \(0.364355\pi\) | |||||||
\(158\) | −9.63289 | − | 5.56155i | −0.766352 | − | 0.442453i | ||||
\(159\) | −19.3693 | −1.53609 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.02699 | − | 1.77879i | 0.0809380 | − | 0.140189i | ||||
\(162\) | 6.06218 | + | 3.50000i | 0.476290 | + | 0.274986i | ||||
\(163\) | 17.0540i | 1.33577i | 0.744264 | + | 0.667885i | \(0.232800\pi\) | ||||
−0.744264 | + | 0.667885i | \(0.767200\pi\) | |||||||
\(164\) | 6.12311 | 0.478134 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.40388 | − | 9.35980i | −0.419423 | − | 0.726461i | ||||
\(167\) | 0.592932 | + | 0.342329i | 0.0458824 | + | 0.0264902i | 0.522766 | − | 0.852476i | \(-0.324900\pi\) |
−0.476883 | + | 0.878967i | \(0.658234\pi\) | |||||||
\(168\) | 0.972638 | − | 0.561553i | 0.0750407 | − | 0.0433247i | ||||
\(169\) | −4.50000 | − | 7.79423i | −0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.56155 | − | 14.0696i | −0.501774 | − | 1.07593i | ||||
\(172\) | − | 3.12311i | − | 0.238135i | ||||||
\(173\) | −5.02967 | + | 2.90388i | −0.382399 | + | 0.220778i | −0.678861 | − | 0.734266i | \(-0.737526\pi\) |
0.296463 | + | 0.955044i | \(0.404193\pi\) | |||||||
\(174\) | 2.56155 | + | 4.43674i | 0.194191 | + | 0.336348i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.500000 | − | 0.866025i | −0.0376889 | − | 0.0652791i | ||||
\(177\) | −32.3029 | − | 18.6501i | −2.42804 | − | 1.40183i | ||||
\(178\) | 2.68466i | 0.201224i | ||||||||
\(179\) | −11.4924 | −0.858984 | −0.429492 | − | 0.903071i | \(-0.641307\pi\) | ||||
−0.429492 | + | 0.903071i | \(0.641307\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6847 | + | 18.5064i | −0.794184 | + | 1.37557i | 0.129171 | + | 0.991622i | \(0.458768\pi\) |
−0.923356 | + | 0.383945i | \(0.874565\pi\) | |||||||
\(182\) | − | 0.876894i | − | 0.0649997i | ||||||
\(183\) | − | 13.1231i | − | 0.970088i | ||||||
\(184\) | 2.34233 | − | 4.05703i | 0.172679 | − | 0.299088i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −13.1231 | + | 22.7299i | −0.962233 | + | 1.66664i | ||||
\(187\) | −4.43674 | + | 2.56155i | −0.324447 | + | 0.187319i | ||||
\(188\) | 2.49146 | − | 1.43845i | 0.181709 | − | 0.104910i | ||||
\(189\) | 0.630683 | 0.0458754 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.36932 | −0.388510 | −0.194255 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194255 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(192\) | 2.21837 | − | 1.28078i | 0.160097 | − | 0.0924321i | ||||
\(193\) | 22.1837 | − | 12.8078i | 1.59682 | − | 0.921923i | 0.604722 | − | 0.796436i | \(-0.293284\pi\) |
0.992095 | − | 0.125487i | \(-0.0400492\pi\) | |||||||
\(194\) | −0.842329 | + | 1.45896i | −0.0604757 | + | 0.104747i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.40388 | − | 5.89570i | 0.243134 | − | 0.421121i | ||||
\(197\) | − | 14.4384i | − | 1.02870i | −0.857581 | − | 0.514348i | \(-0.828034\pi\) | ||
0.857581 | − | 0.514348i | \(-0.171966\pi\) | |||||||
\(198\) | − | 3.56155i | − | 0.253109i | ||||||
\(199\) | −1.43845 | + | 2.49146i | −0.101969 | + | 0.176615i | −0.912496 | − | 0.409086i | \(-0.865848\pi\) |
0.810527 | + | 0.585701i | \(0.199181\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24.1771 | −1.70532 | ||||||||
\(202\) | 10.0000i | 0.703598i | ||||||||
\(203\) | −0.759413 | − | 0.438447i | −0.0533003 | − | 0.0307730i | ||||
\(204\) | −6.56155 | − | 11.3649i | −0.459401 | − | 0.795705i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.90388 | − | 5.02967i | −0.202323 | − | 0.350434i | ||||
\(207\) | 14.4493 | − | 8.34233i | 1.00430 | − | 0.579832i | ||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | 2.50000 | − | 3.57071i | 0.172929 | − | 0.246991i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.65767 | + | 2.87117i | 0.114119 | + | 0.197659i | 0.917427 | − | 0.397904i | \(-0.130262\pi\) |
−0.803308 | + | 0.595563i | \(0.796929\pi\) | |||||||
\(212\) | 6.54850 | − | 3.78078i | 0.449753 | − | 0.259665i | ||||
\(213\) | 36.0401 | + | 20.8078i | 2.46943 | + | 1.42572i | ||||
\(214\) | −1.12311 | − | 1.94528i | −0.0767739 | − | 0.132976i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.43845 | 0.0978739 | ||||||||
\(217\) | − | 4.49242i | − | 0.304966i | ||||||
\(218\) | −12.3376 | − | 7.12311i | −0.835606 | − | 0.482438i | ||||
\(219\) | 2.15767 | − | 3.73720i | 0.145802 | − | 0.252536i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2462 | −0.689235 | ||||||||
\(222\) | −10.3923 | − | 6.00000i | −0.697486 | − | 0.402694i | ||||
\(223\) | 9.79937 | − | 5.65767i | 0.656215 | − | 0.378866i | −0.134619 | − | 0.990897i | \(-0.542981\pi\) |
0.790833 | + | 0.612032i | \(0.209648\pi\) | |||||||
\(224\) | −0.219224 | + | 0.379706i | −0.0146475 | + | 0.0253702i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.40388 | − | 14.5560i | −0.559018 | − | 0.968247i | ||||
\(227\) | − | 19.9309i | − | 1.32286i | −0.750008 | − | 0.661429i | \(-0.769950\pi\) | ||
0.750008 | − | 0.661429i | \(-0.230050\pi\) | |||||||
\(228\) | 9.14657 | + | 6.40388i | 0.605747 | + | 0.424107i | ||||
\(229\) | −12.8769 | −0.850929 | −0.425465 | − | 0.904975i | \(-0.639889\pi\) | ||||
−0.425465 | + | 0.904975i | \(0.639889\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.561553 | + | 0.972638i | 0.0369475 | + | 0.0639949i | ||||
\(232\) | −1.73205 | − | 1.00000i | −0.113715 | − | 0.0656532i | ||||
\(233\) | 2.00514 | − | 1.15767i | 0.131361 | − | 0.0758415i | −0.432879 | − | 0.901452i | \(-0.642502\pi\) |
0.564241 | + | 0.825610i | \(0.309169\pi\) | |||||||
\(234\) | 3.56155 | − | 6.16879i | 0.232826 | − | 0.403266i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 14.5616 | 0.947876 | ||||||||
\(237\) | 24.6752 | + | 14.2462i | 1.60282 | + | 0.925391i | ||||
\(238\) | 1.94528 | + | 1.12311i | 0.126094 | + | 0.0728001i | ||||
\(239\) | −18.2462 | −1.18025 | −0.590125 | − | 0.807312i | \(-0.700921\pi\) | ||||
−0.590125 | + | 0.807312i | \(0.700921\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.28078 | − | 7.41452i | 0.275749 | − | 0.477611i | −0.694575 | − | 0.719421i | \(-0.744407\pi\) |
0.970324 | + | 0.241809i | \(0.0777408\pi\) | |||||||
\(242\) | −8.66025 | + | 5.00000i | −0.556702 | + | 0.321412i | ||||
\(243\) | −19.2658 | − | 11.1231i | −1.23590 | − | 0.713548i | ||||
\(244\) | 2.56155 | + | 4.43674i | 0.163987 | + | 0.284033i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.6847 | −1.00002 | ||||||||
\(247\) | 7.90084 | − | 3.68466i | 0.502718 | − | 0.234449i | ||||
\(248\) | − | 10.2462i | − | 0.650635i | ||||||
\(249\) | 13.8423 | + | 23.9756i | 0.877222 | + | 1.51939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.9654 | + | 22.4568i | −0.818371 | + | 1.41746i | 0.0885109 | + | 0.996075i | \(0.471789\pi\) |
−0.906882 | + | 0.421385i | \(0.861544\pi\) | |||||||
\(252\) | −1.35234 | + | 0.780776i | −0.0851897 | + | 0.0491843i | ||||
\(253\) | 4.05703 | + | 2.34233i | 0.255063 | + | 0.147261i | ||||
\(254\) | −15.5616 | −0.976419 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 11.3051 | + | 6.52699i | 0.705191 | + | 0.407142i | 0.809278 | − | 0.587426i | \(-0.199859\pi\) |
−0.104087 | + | 0.994568i | \(0.533192\pi\) | |||||||
\(258\) | 8.00000i | 0.498058i | ||||||||
\(259\) | 2.05398 | 0.127628 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.56155 | − | 6.16879i | −0.220455 | − | 0.381839i | ||||
\(262\) | 13.9630 | + | 8.06155i | 0.862638 | + | 0.498044i | ||||
\(263\) | −1.89853 | + | 1.09612i | −0.117068 | + | 0.0675895i | −0.557391 | − | 0.830250i | \(-0.688197\pi\) |
0.440322 | + | 0.897840i | \(0.354864\pi\) | |||||||
\(264\) | 1.28078 | + | 2.21837i | 0.0788263 | + | 0.136531i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.90388 | − | 0.166481i | −0.116734 | − | 0.0102076i | ||||
\(267\) | − | 6.87689i | − | 0.420859i | ||||||
\(268\) | 8.17394 | − | 4.71922i | 0.499303 | − | 0.288272i | ||||
\(269\) | 2.00000 | + | 3.46410i | 0.121942 | + | 0.211210i | 0.920534 | − | 0.390664i | \(-0.127754\pi\) |
−0.798591 | + | 0.601874i | \(0.794421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.12311 | + | 7.14143i | 0.250461 | + | 0.433811i | 0.963653 | − | 0.267158i | \(-0.0860845\pi\) |
−0.713192 | + | 0.700969i | \(0.752751\pi\) | |||||||
\(272\) | 4.43674 | + | 2.56155i | 0.269017 | + | 0.155317i | ||||
\(273\) | 2.24621i | 0.135947i | ||||||||
\(274\) | −5.43845 | −0.328549 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | − | 4.24621i | − | 0.255130i | −0.991830 | − | 0.127565i | \(-0.959284\pi\) | ||
0.991830 | − | 0.127565i | \(-0.0407162\pi\) | |||||||
\(278\) | − | 8.80776i | − | 0.528255i | ||||||
\(279\) | 18.2462 | − | 31.6034i | 1.09237 | − | 1.89204i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.18466 | + | 7.24804i | −0.249636 | + | 0.432382i | −0.963425 | − | 0.267979i | \(-0.913644\pi\) |
0.713789 | + | 0.700361i | \(0.246978\pi\) | |||||||
\(282\) | −6.38202 | + | 3.68466i | −0.380043 | + | 0.219418i | ||||
\(283\) | −16.8342 | + | 9.71922i | −1.00069 | + | 0.577748i | −0.908452 | − | 0.417989i | \(-0.862735\pi\) |
−0.0922367 | + | 0.995737i | \(0.529402\pi\) | |||||||
\(284\) | −16.2462 | −0.964035 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 2.32498 | − | 1.34233i | 0.137239 | − | 0.0792352i | ||||
\(288\) | −3.08440 | + | 1.78078i | −0.181750 | + | 0.104933i | ||||
\(289\) | 4.62311 | − | 8.00745i | 0.271947 | − | 0.471027i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.15767 | − | 3.73720i | 0.126485 | − | 0.219078i | ||||
\(292\) | 1.68466i | 0.0985872i | ||||||||
\(293\) | 23.5616i | 1.37648i | 0.725483 | + | 0.688240i | \(0.241617\pi\) | ||||
−0.725483 | + | 0.688240i | \(0.758383\pi\) | |||||||
\(294\) | −8.71922 | + | 15.1021i | −0.508515 | + | 0.880775i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.68466 | 0.272290 | ||||||||
\(297\) | 1.43845i | 0.0834672i | ||||||||
\(298\) | 13.8564 | + | 8.00000i | 0.802680 | + | 0.463428i | ||||
\(299\) | 4.68466 | + | 8.11407i | 0.270921 | + | 0.469249i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.684658 | − | 1.18586i | −0.0394631 | − | 0.0683520i | ||||
\(302\) | 17.7470 | − | 10.2462i | 1.02122 | − | 0.589603i | ||||
\(303\) | − | 25.6155i | − | 1.47157i | ||||||
\(304\) | −4.34233 | − | 0.379706i | −0.249050 | − | 0.0217777i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 9.12311 | + | 15.8017i | 0.521533 | + | 0.903322i | ||||
\(307\) | 20.7247 | − | 11.9654i | 1.18282 | − | 0.682903i | 0.226157 | − | 0.974091i | \(-0.427384\pi\) |
0.956666 | + | 0.291187i | \(0.0940503\pi\) | |||||||
\(308\) | −0.379706 | − | 0.219224i | −0.0216358 | − | 0.0124914i | ||||
\(309\) | 7.43845 | + | 12.8838i | 0.423158 | + | 0.732932i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | 5.12311i | 0.290039i | ||||||||
\(313\) | −3.73720 | − | 2.15767i | −0.211239 | − | 0.121959i | 0.390648 | − | 0.920540i | \(-0.372251\pi\) |
−0.601887 | + | 0.798581i | \(0.705584\pi\) | |||||||
\(314\) | −1.21922 | + | 2.11176i | −0.0688048 | + | 0.119173i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.1231 | −0.625724 | ||||||||
\(317\) | 16.1814 | + | 9.34233i | 0.908837 | + | 0.524717i | 0.880057 | − | 0.474868i | \(-0.157504\pi\) |
0.0287805 | + | 0.999586i | \(0.490838\pi\) | |||||||
\(318\) | −16.7743 | + | 9.68466i | −0.940657 | + | 0.543089i | ||||
\(319\) | 1.00000 | − | 1.73205i | 0.0559893 | − | 0.0969762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.87689 | + | 4.98293i | 0.160573 | + | 0.278120i | ||||
\(322\) | − | 2.05398i | − | 0.114464i | ||||||
\(323\) | −1.94528 | + | 22.2462i | −0.108238 | + | 1.23781i | ||||
\(324\) | 7.00000 | 0.388889 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.52699 | + | 14.7692i | 0.472266 | + | 0.817989i | ||||
\(327\) | 31.6034 | + | 18.2462i | 1.74767 | + | 1.00902i | ||||
\(328\) | 5.30277 | − | 3.06155i | 0.292796 | − | 0.169046i | ||||
\(329\) | 0.630683 | − | 1.09238i | 0.0347707 | − | 0.0602246i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.4924 | 1.29126 | 0.645630 | − | 0.763650i | \(-0.276595\pi\) | ||||
0.645630 | + | 0.763650i | \(0.276595\pi\) | |||||||
\(332\) | −9.35980 | − | 5.40388i | −0.513686 | − | 0.296577i | ||||
\(333\) | 14.4493 | + | 8.34233i | 0.791819 | + | 0.457157i | ||||
\(334\) | 0.684658 | 0.0374628 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.561553 | − | 0.972638i | 0.0306352 | − | 0.0530618i | ||||
\(337\) | −18.2333 | + | 10.5270i | −0.993230 | + | 0.573442i | −0.906238 | − | 0.422767i | \(-0.861059\pi\) |
−0.0869917 | + | 0.996209i | \(0.527725\pi\) | |||||||
\(338\) | −7.79423 | − | 4.50000i | −0.423950 | − | 0.244768i | ||||
\(339\) | 21.5270 | + | 37.2858i | 1.16919 | + | 2.02509i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2462 | 0.554863 | ||||||||
\(342\) | −12.7173 | − | 8.90388i | −0.687672 | − | 0.481467i | ||||
\(343\) | − | 6.05398i | − | 0.326884i | ||||||
\(344\) | −1.56155 | − | 2.70469i | −0.0841933 | − | 0.145827i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.90388 | + | 5.02967i | −0.156114 | + | 0.270397i | ||||
\(347\) | −1.45896 | + | 0.842329i | −0.0783209 | + | 0.0452186i | −0.538649 | − | 0.842530i | \(-0.681065\pi\) |
0.460328 | + | 0.887749i | \(0.347732\pi\) | |||||||
\(348\) | 4.43674 | + | 2.56155i | 0.237834 | + | 0.137314i | ||||
\(349\) | 14.2462 | 0.762582 | 0.381291 | − | 0.924455i | \(-0.375480\pi\) | ||||
0.381291 | + | 0.924455i | \(0.375480\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.43845 | + | 2.49146i | −0.0767786 | + | 0.132984i | ||||
\(352\) | −0.866025 | − | 0.500000i | −0.0461593 | − | 0.0266501i | ||||
\(353\) | 24.1771i | 1.28682i | 0.765523 | + | 0.643408i | \(0.222480\pi\) | ||||
−0.765523 | + | 0.643408i | \(0.777520\pi\) | |||||||
\(354\) | −37.3002 | −1.98248 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.34233 | + | 2.32498i | 0.0711433 | + | 0.123224i | ||||
\(357\) | −4.98293 | − | 2.87689i | −0.263724 | − | 0.152261i | ||||
\(358\) | −9.95273 | + | 5.74621i | −0.526018 | + | 0.303697i | ||||
\(359\) | 7.56155 | + | 13.0970i | 0.399083 | + | 0.691233i | 0.993613 | − | 0.112841i | \(-0.0359950\pi\) |
−0.594530 | + | 0.804074i | \(0.702662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.50000 | − | 17.8536i | −0.342105 | − | 0.939662i | ||||
\(362\) | 21.3693i | 1.12315i | ||||||||
\(363\) | 22.1837 | − | 12.8078i | 1.16434 | − | 0.672233i | ||||
\(364\) | −0.438447 | − | 0.759413i | −0.0229809 | − | 0.0398040i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.56155 | − | 11.3649i | −0.342978 | − | 0.594055i | ||||
\(367\) | −15.3752 | − | 8.87689i | −0.802581 | − | 0.463370i | 0.0417921 | − | 0.999126i | \(-0.486693\pi\) |
−0.844373 | + | 0.535756i | \(0.820027\pi\) | |||||||
\(368\) | − | 4.68466i | − | 0.244205i | ||||||
\(369\) | 21.8078 | 1.13527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.65767 | − | 2.87117i | 0.0860620 | − | 0.149064i | ||||
\(372\) | 26.2462i | 1.36080i | ||||||||
\(373\) | − | 35.8078i | − | 1.85406i | −0.374992 | − | 0.927028i | \(-0.622355\pi\) | ||
0.374992 | − | 0.927028i | \(-0.377645\pi\) | |||||||
\(374\) | −2.56155 | + | 4.43674i | −0.132455 | + | 0.229418i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.43845 | − | 2.49146i | 0.0741822 | − | 0.128487i | ||||
\(377\) | 3.46410 | − | 2.00000i | 0.178410 | − | 0.103005i | ||||
\(378\) | 0.546188 | − | 0.315342i | 0.0280929 | − | 0.0162194i | ||||
\(379\) | 0.492423 | 0.0252940 | 0.0126470 | − | 0.999920i | \(-0.495974\pi\) | ||||
0.0126470 | + | 0.999920i | \(0.495974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.8617 | 2.04218 | ||||||||
\(382\) | −4.64996 | + | 2.68466i | −0.237913 | + | 0.137359i | ||||
\(383\) | 4.43674 | − | 2.56155i | 0.226707 | − | 0.130889i | −0.382345 | − | 0.924020i | \(-0.624883\pi\) |
0.609052 | + | 0.793130i | \(0.291550\pi\) | |||||||
\(384\) | 1.28078 | − | 2.21837i | 0.0653593 | − | 0.113206i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.8078 | − | 22.1837i | 0.651898 | − | 1.12912i | ||||
\(387\) | − | 11.1231i | − | 0.565419i | ||||||
\(388\) | 1.68466i | 0.0855256i | ||||||||
\(389\) | −9.56155 | + | 16.5611i | −0.484790 | + | 0.839681i | −0.999847 | − | 0.0174749i | \(-0.994437\pi\) |
0.515057 | + | 0.857156i | \(0.327771\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | − | 6.80776i | − | 0.343844i | ||||||
\(393\) | −35.7670 | − | 20.6501i | −1.80421 | − | 1.04166i | ||||
\(394\) | −7.21922 | − | 12.5041i | −0.363699 | − | 0.629946i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.78078 | − | 3.08440i | −0.0894874 | − | 0.154997i | ||||
\(397\) | −24.5087 | + | 14.1501i | −1.23006 | + | 0.710173i | −0.967041 | − | 0.254619i | \(-0.918050\pi\) |
−0.263014 | + | 0.964792i | \(0.584717\pi\) | |||||||
\(398\) | 2.87689i | 0.144206i | ||||||||
\(399\) | 4.87689 | + | 0.426450i | 0.244150 | + | 0.0213492i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.9654 | − | 24.1888i | −0.697401 | − | 1.20793i | −0.969365 | − | 0.245626i | \(-0.921007\pi\) |
0.271964 | − | 0.962307i | \(-0.412327\pi\) | |||||||
\(402\) | −20.9380 | + | 12.0885i | −1.04429 | + | 0.602922i | ||||
\(403\) | 17.7470 | + | 10.2462i | 0.884039 | + | 0.510400i | ||||
\(404\) | 5.00000 | + | 8.66025i | 0.248759 | + | 0.430864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.876894 | −0.0435195 | ||||||||
\(407\) | 4.68466i | 0.232210i | ||||||||
\(408\) | −11.3649 | − | 6.56155i | −0.562649 | − | 0.324845i | ||||
\(409\) | 10.5000 | − | 18.1865i | 0.519192 | − | 0.899266i | −0.480560 | − | 0.876962i | \(-0.659566\pi\) |
0.999751 | − | 0.0223042i | \(-0.00710022\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.9309 | 0.687159 | ||||||||
\(412\) | −5.02967 | − | 2.90388i | −0.247794 | − | 0.143064i | ||||
\(413\) | 5.52911 | − | 3.19224i | 0.272070 | − | 0.157080i | ||||
\(414\) | 8.34233 | − | 14.4493i | 0.410003 | − | 0.710146i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.00000 | − | 1.73205i | −0.0490290 | − | 0.0849208i | ||||
\(417\) | 22.5616i | 1.10484i | ||||||||
\(418\) | 0.379706 | − | 4.34233i | 0.0185720 | − | 0.212390i | ||||
\(419\) | 17.5616 | 0.857938 | 0.428969 | − | 0.903319i | \(-0.358877\pi\) | ||||
0.428969 | + | 0.903319i | \(0.358877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2462 | − | 28.1393i | −0.791792 | − | 1.37142i | −0.924856 | − | 0.380316i | \(-0.875815\pi\) |
0.133065 | − | 0.991107i | \(-0.457518\pi\) | |||||||
\(422\) | 2.87117 | + | 1.65767i | 0.139766 | + | 0.0806942i | ||||
\(423\) | 8.87348 | − | 5.12311i | 0.431443 | − | 0.249094i | ||||
\(424\) | 3.78078 | − | 6.54850i | 0.183611 | − | 0.318023i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 41.6155 | 2.01628 | ||||||||
\(427\) | 1.94528 | + | 1.12311i | 0.0941385 | + | 0.0543509i | ||||
\(428\) | −1.94528 | − | 1.12311i | −0.0940285 | − | 0.0542874i | ||||
\(429\) | −5.12311 | −0.247346 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.68466 | − | 6.38202i | 0.177484 | − | 0.307411i | −0.763534 | − | 0.645767i | \(-0.776538\pi\) |
0.941018 | + | 0.338356i | \(0.109871\pi\) | |||||||
\(432\) | 1.24573 | − | 0.719224i | 0.0599353 | − | 0.0346037i | ||||
\(433\) | 31.8166 | + | 18.3693i | 1.52901 | + | 0.882773i | 0.999404 | + | 0.0345280i | \(0.0109928\pi\) |
0.529604 | + | 0.848245i | \(0.322341\pi\) | |||||||
\(434\) | −2.24621 | − | 3.89055i | −0.107822 | − | 0.186752i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.2462 | −0.682270 | ||||||||
\(437\) | 18.5064 | − | 8.63068i | 0.885280 | − | 0.412862i | ||||
\(438\) | − | 4.31534i | − | 0.206195i | ||||||
\(439\) | −8.24621 | − | 14.2829i | −0.393570 | − | 0.681684i | 0.599347 | − | 0.800489i | \(-0.295427\pi\) |
−0.992918 | + | 0.118806i | \(0.962094\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.1231 | − | 20.9978i | 0.577291 | − | 0.999897i | ||||
\(442\) | −8.87348 | + | 5.12311i | −0.422068 | + | 0.243681i | ||||
\(443\) | −29.3850 | − | 16.9654i | −1.39612 | − | 0.806052i | −0.402139 | − | 0.915578i | \(-0.631733\pi\) |
−0.993984 | + | 0.109526i | \(0.965067\pi\) | |||||||
\(444\) | −12.0000 | −0.569495 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.65767 | − | 9.79937i | 0.267898 | − | 0.464014i | ||||
\(447\) | −35.4939 | − | 20.4924i | −1.67880 | − | 0.969258i | ||||
\(448\) | 0.438447i | 0.0207147i | ||||||||
\(449\) | −29.0000 | −1.36859 | −0.684297 | − | 0.729203i | \(-0.739891\pi\) | ||||
−0.684297 | + | 0.729203i | \(0.739891\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.06155 | + | 5.30277i | 0.144163 | + | 0.249697i | ||||
\(452\) | −14.5560 | − | 8.40388i | −0.684654 | − | 0.395285i | ||||
\(453\) | −45.4598 | + | 26.2462i | −2.13589 | + | 1.23315i | ||||
\(454\) | −9.96543 | − | 17.2606i | −0.467701 | − | 0.810082i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 11.1231 | + | 0.972638i | 0.520887 | + | 0.0455479i | ||||
\(457\) | − | 7.05398i | − | 0.329971i | −0.986296 | − | 0.164986i | \(-0.947242\pi\) | ||
0.986296 | − | 0.164986i | \(-0.0527577\pi\) | |||||||
\(458\) | −11.1517 | + | 6.43845i | −0.521086 | + | 0.300849i | ||||
\(459\) | −3.68466 | − | 6.38202i | −0.171985 | − | 0.297887i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4924 | + | 33.7619i | 0.907853 | + | 1.57245i | 0.817042 | + | 0.576579i | \(0.195613\pi\) |
0.0908110 | + | 0.995868i | \(0.471054\pi\) | |||||||
\(462\) | 0.972638 | + | 0.561553i | 0.0452512 | + | 0.0261258i | ||||
\(463\) | − | 19.5616i | − | 0.909102i | −0.890721 | − | 0.454551i | \(-0.849800\pi\) | ||
0.890721 | − | 0.454551i | \(-0.150200\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.15767 | − | 2.00514i | 0.0536281 | − | 0.0928865i | ||||
\(467\) | − | 16.5616i | − | 0.766377i | −0.923670 | − | 0.383189i | \(-0.874826\pi\) | ||
0.923670 | − | 0.383189i | \(-0.125174\pi\) | |||||||
\(468\) | − | 7.12311i | − | 0.329266i | ||||||
\(469\) | 2.06913 | − | 3.58384i | 0.0955436 | − | 0.165486i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.12311 | − | 5.40938i | 0.143905 | − | 0.249251i | ||||
\(472\) | 12.6107 | − | 7.28078i | 0.580453 | − | 0.335125i | ||||
\(473\) | 2.70469 | − | 1.56155i | 0.124362 | − | 0.0718003i | ||||
\(474\) | 28.4924 | 1.30870 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.24621 | 0.102955 | ||||||||
\(477\) | 23.3228 | − | 13.4654i | 1.06788 | − | 0.616540i | ||||
\(478\) | −15.8017 | + | 9.12311i | −0.722752 | + | 0.417281i | ||||
\(479\) | 14.6847 | − | 25.4346i | 0.670959 | − | 1.16214i | −0.306673 | − | 0.951815i | \(-0.599216\pi\) |
0.977632 | − | 0.210321i | \(-0.0674508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.68466 | + | 8.11407i | −0.213602 | + | 0.369970i | ||||
\(482\) | − | 8.56155i | − | 0.389968i | ||||||
\(483\) | 5.26137i | 0.239400i | ||||||||
\(484\) | −5.00000 | + | 8.66025i | −0.227273 | + | 0.393648i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.2462 | −1.00911 | ||||||||
\(487\) | 6.93087i | 0.314068i | 0.987593 | + | 0.157034i | \(0.0501932\pi\) | ||||
−0.987593 | + | 0.157034i | \(0.949807\pi\) | |||||||
\(488\) | 4.43674 | + | 2.56155i | 0.200842 | + | 0.115956i | ||||
\(489\) | −21.8423 | − | 37.8320i | −0.987744 | − | 1.71082i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.58854 | + | 7.94759i | 0.207078 | + | 0.358670i | 0.950793 | − | 0.309827i | \(-0.100271\pi\) |
−0.743715 | + | 0.668497i | \(0.766938\pi\) | |||||||
\(492\) | −13.5833 | + | 7.84233i | −0.612383 | + | 0.353560i | ||||
\(493\) | 10.2462i | 0.461466i | ||||||||
\(494\) | 5.00000 | − | 7.14143i | 0.224961 | − | 0.321308i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.12311 | − | 8.87348i | −0.230034 | − | 0.398431i | ||||
\(497\) | −6.16879 | + | 3.56155i | −0.276708 | + | 0.159757i | ||||
\(498\) | 23.9756 | + | 13.8423i | 1.07437 | + | 0.620290i | ||||
\(499\) | 14.5000 | + | 25.1147i | 0.649109 | + | 1.12429i | 0.983336 | + | 0.181797i | \(0.0581915\pi\) |
−0.334227 | + | 0.942493i | \(0.608475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.75379 | −0.0783535 | ||||||||
\(502\) | 25.9309i | 1.15735i | ||||||||
\(503\) | −23.7493 | − | 13.7116i | −1.05893 | − | 0.611372i | −0.133792 | − | 0.991009i | \(-0.542715\pi\) |
−0.925135 | + | 0.379637i | \(0.876049\pi\) | |||||||
\(504\) | −0.780776 | + | 1.35234i | −0.0347785 | + | 0.0602382i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.68466 | 0.208258 | ||||||||
\(507\) | 19.9653 | + | 11.5270i | 0.886691 | + | 0.511931i | ||||
\(508\) | −13.4767 | + | 7.78078i | −0.597932 | + | 0.345216i | ||||
\(509\) | −0.438447 | + | 0.759413i | −0.0194338 | + | 0.0336604i | −0.875579 | − | 0.483075i | \(-0.839520\pi\) |
0.856145 | + | 0.516736i | \(0.172853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.369317 | + | 0.639676i | 0.0163376 | + | 0.0282976i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.13628 | + | 3.59612i | 0.226772 | + | 0.158772i | ||||
\(514\) | 13.0540 | 0.575786 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.00000 | + | 6.92820i | 0.176090 | + | 0.304997i | ||||
\(517\) | 2.49146 | + | 1.43845i | 0.109574 | + | 0.0632628i | ||||
\(518\) | 1.77879 | − | 1.02699i | 0.0781558 | − | 0.0451232i | ||||
\(519\) | 7.43845 | − | 12.8838i | 0.326512 | − | 0.565535i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.8078 | −0.999226 | −0.499613 | − | 0.866249i | \(-0.666524\pi\) | ||||
−0.499613 | + | 0.866249i | \(0.666524\pi\) | |||||||
\(522\) | −6.16879 | − | 3.56155i | −0.270001 | − | 0.155885i | ||||
\(523\) | −12.6705 | − | 7.31534i | −0.554044 | − | 0.319878i | 0.196707 | − | 0.980462i | \(-0.436975\pi\) |
−0.750752 | + | 0.660585i | \(0.770308\pi\) | |||||||
\(524\) | 16.1231 | 0.704341 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.09612 | + | 1.89853i | −0.0477930 | + | 0.0827799i | ||||
\(527\) | −45.4598 | + | 26.2462i | −1.98026 | + | 1.14330i | ||||
\(528\) | 2.21837 | + | 1.28078i | 0.0965422 | + | 0.0557386i | ||||
\(529\) | −0.526988 | − | 0.912769i | −0.0229125 | − | 0.0396856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 51.8617 | 2.25061 | ||||||||
\(532\) | −1.73205 | + | 0.807764i | −0.0750939 | + | 0.0350210i | ||||
\(533\) | 12.2462i | 0.530442i | ||||||||
\(534\) | −3.43845 | − | 5.95557i | −0.148796 | − | 0.257723i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.71922 | − | 8.17394i | 0.203839 | − | 0.353060i | ||||
\(537\) | 25.4944 | − | 14.7192i | 1.10017 | − | 0.635181i | ||||
\(538\) | 3.46410 | + | 2.00000i | 0.149348 | + | 0.0862261i | ||||
\(539\) | 6.80776 | 0.293231 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2462 | − | 24.6752i | 0.612492 | − | 1.06087i | −0.378326 | − | 0.925672i | \(-0.623500\pi\) |
0.990819 | − | 0.135196i | \(-0.0431664\pi\) | |||||||
\(542\) | 7.14143 | + | 4.12311i | 0.306751 | + | 0.177103i | ||||
\(543\) | − | 54.7386i | − | 2.34906i | ||||||
\(544\) | 5.12311 | 0.219651 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.12311 | + | 1.94528i | 0.0480645 | + | 0.0832501i | ||||
\(547\) | −4.22351 | − | 2.43845i | −0.180584 | − | 0.104260i | 0.406983 | − | 0.913436i | \(-0.366581\pi\) |
−0.587567 | + | 0.809175i | \(0.699914\pi\) | |||||||
\(548\) | −4.70983 | + | 2.71922i | −0.201194 | + | 0.116159i | ||||
\(549\) | 9.12311 | + | 15.8017i | 0.389365 | + | 0.674399i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.68466 | − | 7.90084i | −0.156972 | − | 0.336587i | ||||
\(552\) | 12.0000i | 0.510754i | ||||||||
\(553\) | −4.22351 | + | 2.43845i | −0.179602 | + | 0.103693i | ||||
\(554\) | −2.12311 | − | 3.67733i | −0.0902021 | − | 0.156235i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.40388 | − | 7.62775i | −0.186766 | − | 0.323489i | ||||
\(557\) | 36.0868 | + | 20.8348i | 1.52905 | + | 0.882797i | 0.999402 | + | 0.0345785i | \(0.0110089\pi\) |
0.529647 | + | 0.848218i | \(0.322324\pi\) | |||||||
\(558\) | − | 36.4924i | − | 1.54485i | ||||||
\(559\) | 6.24621 | 0.264187 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.56155 | − | 11.3649i | 0.277029 | − | 0.479828i | ||||
\(562\) | 8.36932i | 0.353038i | ||||||||
\(563\) | 21.3002i | 0.897696i | 0.893608 | + | 0.448848i | \(0.148166\pi\) | ||||
−0.893608 | + | 0.448848i | \(0.851834\pi\) | |||||||
\(564\) | −3.68466 | + | 6.38202i | −0.155152 | + | 0.268731i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.71922 | + | 16.8342i | −0.408529 | + | 0.707594i | ||||
\(567\) | 2.65794 | − | 1.53457i | 0.111623 | − | 0.0644457i | ||||
\(568\) | −14.0696 | + | 8.12311i | −0.590349 | + | 0.340838i | ||||
\(569\) | 11.1771 | 0.468568 | 0.234284 | − | 0.972168i | \(-0.424726\pi\) | ||||
0.234284 | + | 0.972168i | \(0.424726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.80776 | −0.201199 | −0.100599 | − | 0.994927i | \(-0.532076\pi\) | ||||
−0.100599 | + | 0.994927i | \(0.532076\pi\) | |||||||
\(572\) | 1.73205 | − | 1.00000i | 0.0724207 | − | 0.0418121i | ||||
\(573\) | 11.9111 | − | 6.87689i | 0.497595 | − | 0.287286i | ||||
\(574\) | 1.34233 | − | 2.32498i | 0.0560277 | − | 0.0970429i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.78078 | + | 3.08440i | −0.0741990 | + | 0.128516i | ||||
\(577\) | 16.3153i | 0.679217i | 0.940567 | + | 0.339608i | \(0.110295\pi\) | ||||
−0.940567 | + | 0.339608i | \(0.889705\pi\) | |||||||
\(578\) | − | 9.24621i | − | 0.384592i | ||||||
\(579\) | −32.8078 | + | 56.8247i | −1.36344 | + | 2.36155i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.73863 | −0.196592 | ||||||||
\(582\) | − | 4.31534i | − | 0.178877i | ||||||
\(583\) | 6.54850 | + | 3.78078i | 0.271211 | + | 0.156584i | ||||
\(584\) | 0.842329 | + | 1.45896i | 0.0348558 | + | 0.0603721i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.7808 | + | 20.4049i | 0.486659 | + | 0.842919i | ||||
\(587\) | −23.1563 | + | 13.3693i | −0.955764 | + | 0.551811i | −0.894867 | − | 0.446333i | \(-0.852730\pi\) |
−0.0608975 | + | 0.998144i | \(0.519396\pi\) | |||||||
\(588\) | 17.4384i | 0.719149i | ||||||||
\(589\) | 25.6155 | − | 36.5863i | 1.05547 | − | 1.50751i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.4924 | + | 32.0298i | 0.760677 | + | 1.31753i | ||||
\(592\) | 4.05703 | − | 2.34233i | 0.166743 | − | 0.0962691i | ||||
\(593\) | −22.1238 | − | 12.7732i | −0.908517 | − | 0.524532i | −0.0285632 | − | 0.999592i | \(-0.509093\pi\) |
−0.879954 | + | 0.475060i | \(0.842427\pi\) | |||||||
\(594\) | 0.719224 | + | 1.24573i | 0.0295101 | + | 0.0511130i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 16.0000 | 0.655386 | ||||||||
\(597\) | − | 7.36932i | − | 0.301606i | ||||||
\(598\) | 8.11407 | + | 4.68466i | 0.331809 | + | 0.191570i | ||||
\(599\) | −16.2462 | + | 28.1393i | −0.663802 | + | 1.14974i | 0.315806 | + | 0.948824i | \(0.397725\pi\) |
−0.979609 | + | 0.200915i | \(0.935608\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.6307 | −0.474425 | −0.237213 | − | 0.971458i | \(-0.576234\pi\) | ||||
−0.237213 | + | 0.971458i | \(0.576234\pi\) | |||||||
\(602\) | −1.18586 | − | 0.684658i | −0.0483322 | − | 0.0279046i | ||||
\(603\) | 29.1119 | − | 16.8078i | 1.18553 | − | 0.684465i | ||||
\(604\) | 10.2462 | − | 17.7470i | 0.416912 | − | 0.722113i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.8078 | − | 22.1837i | −0.520280 | − | 0.901151i | ||||
\(607\) | − | 10.1922i | − | 0.413690i | −0.978374 | − | 0.206845i | \(-0.933680\pi\) | ||
0.978374 | − | 0.206845i | \(-0.0663196\pi\) | |||||||
\(608\) | −3.95042 | + | 1.84233i | −0.160211 | + | 0.0747163i | ||||
\(609\) | 2.24621 | 0.0910211 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.87689 | + | 4.98293i | 0.116387 | + | 0.201588i | ||||
\(612\) | 15.8017 | + | 9.12311i | 0.638745 | + | 0.368780i | ||||
\(613\) | 26.5737 | − | 15.3423i | 1.07330 | − | 0.619671i | 0.144220 | − | 0.989546i | \(-0.453933\pi\) |
0.929082 | + | 0.369875i | \(0.120599\pi\) | |||||||
\(614\) | 11.9654 | − | 20.7247i | 0.482886 | − | 0.836382i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.438447 | −0.0176655 | ||||||||
\(617\) | 6.22866 | + | 3.59612i | 0.250756 | + | 0.144774i | 0.620111 | − | 0.784514i | \(-0.287088\pi\) |
−0.369354 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(618\) | 12.8838 | + | 7.43845i | 0.518261 | + | 0.299218i | ||||
\(619\) | −26.0540 | −1.04720 | −0.523599 | − | 0.851965i | \(-0.675411\pi\) | ||||
−0.523599 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.36932 | + | 5.83583i | −0.135206 | + | 0.234184i | ||||
\(622\) | 3.46410 | − | 2.00000i | 0.138898 | − | 0.0801927i | ||||
\(623\) | 1.01938 | + | 0.588540i | 0.0408407 | + | 0.0235794i | ||||
\(624\) | 2.56155 | + | 4.43674i | 0.102544 | + | 0.177612i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.31534 | −0.172476 | ||||||||
\(627\) | −0.972638 | + | 11.1231i | −0.0388434 | + | 0.444214i | ||||
\(628\) | 2.43845i | 0.0973046i | ||||||||
\(629\) | −12.0000 | − | 20.7846i | −0.478471 | − | 0.828737i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.12311 | + | 3.67733i | −0.0845195 | + | 0.146392i | −0.905186 | − | 0.425015i | \(-0.860269\pi\) |
0.820667 | + | 0.571407i | \(0.193602\pi\) | |||||||
\(632\) | −9.63289 | + | 5.56155i | −0.383176 | + | 0.221227i | ||||
\(633\) | −7.35465 | − | 4.24621i | −0.292321 | − | 0.168772i | ||||
\(634\) | 18.6847 | 0.742063 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −9.68466 | + | 16.7743i | −0.384022 | + | 0.665145i | ||||
\(637\) | 11.7914 | + | 6.80776i | 0.467192 | + | 0.269733i | ||||
\(638\) | − | 2.00000i | − | 0.0791808i | ||||||
\(639\) | −57.8617 | −2.28898 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.71922 | − | 6.44188i | −0.146900 | − | 0.254439i | 0.783180 | − | 0.621795i | \(-0.213596\pi\) |
−0.930080 | + | 0.367356i | \(0.880263\pi\) | |||||||
\(642\) | 4.98293 | + | 2.87689i | 0.196660 | + | 0.113542i | ||||
\(643\) | −19.5389 | + | 11.2808i | −0.770538 | + | 0.444870i | −0.833067 | − | 0.553173i | \(-0.813417\pi\) |
0.0625284 | + | 0.998043i | \(0.480084\pi\) | |||||||
\(644\) | −1.02699 | − | 1.77879i | −0.0404690 | − | 0.0700943i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.43845 | + | 20.2384i | 0.371351 | + | 0.796270i | ||||
\(647\) | − | 3.17708i | − | 0.124904i | −0.998048 | − | 0.0624520i | \(-0.980108\pi\) | ||
0.998048 | − | 0.0624520i | \(-0.0198920\pi\) | |||||||
\(648\) | 6.06218 | − | 3.50000i | 0.238145 | − | 0.137493i | ||||
\(649\) | 7.28078 | + | 12.6107i | 0.285795 | + | 0.495012i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.75379 | + | 9.96585i | 0.225509 | + | 0.390593i | ||||
\(652\) | 14.7692 | + | 8.52699i | 0.578406 | + | 0.333943i | ||||
\(653\) | − | 5.06913i | − | 0.198370i | −0.995069 | − | 0.0991852i | \(-0.968376\pi\) | ||
0.995069 | − | 0.0991852i | \(-0.0316236\pi\) | |||||||
\(654\) | 36.4924 | 1.42697 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.06155 | − | 5.30277i | 0.119534 | − | 0.207038i | ||||
\(657\) | 6.00000i | 0.234082i | ||||||||
\(658\) | − | 1.26137i | − | 0.0491732i | ||||||
\(659\) | 9.46543 | − | 16.3946i | 0.368721 | − | 0.638643i | −0.620645 | − | 0.784092i | \(-0.713129\pi\) |
0.989366 | + | 0.145448i | \(0.0464624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.9309 | − | 34.5213i | 0.775221 | − | 1.34272i | −0.159449 | − | 0.987206i | \(-0.550972\pi\) |
0.934670 | − | 0.355516i | \(-0.115695\pi\) | |||||||
\(662\) | 20.3450 | − | 11.7462i | 0.790732 | − | 0.456529i | ||||
\(663\) | 22.7299 | − | 13.1231i | 0.882756 | − | 0.509659i | ||||
\(664\) | −10.8078 | −0.419423 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16.6847 | 0.646517 | ||||||||
\(667\) | 8.11407 | − | 4.68466i | 0.314178 | − | 0.181391i | ||||
\(668\) | 0.592932 | − | 0.342329i | 0.0229412 | − | 0.0132451i | ||||
\(669\) | −14.4924 | + | 25.1016i | −0.560309 | + | 0.970484i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.56155 | + | 4.43674i | −0.0988876 | + | 0.171278i | ||||
\(672\) | − | 1.12311i | − | 0.0433247i | ||||||
\(673\) | 46.1080i | 1.77733i | 0.458556 | + | 0.888665i | \(0.348367\pi\) | ||||
−0.458556 | + | 0.888665i | \(0.651633\pi\) | |||||||
\(674\) | −10.5270 | + | 18.2333i | −0.405484 | + | 0.702320i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 23.1771i | 0.890768i | 0.895340 | + | 0.445384i | \(0.146933\pi\) | ||||
−0.895340 | + | 0.445384i | \(0.853067\pi\) | |||||||
\(678\) | 37.2858 | + | 21.5270i | 1.43195 | + | 0.826739i | ||||
\(679\) | 0.369317 | + | 0.639676i | 0.0141731 | + | 0.0245485i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25.5270 | + | 44.2140i | 0.978196 | + | 1.69429i | ||||
\(682\) | 8.87348 | − | 5.12311i | 0.339783 | − | 0.196174i | ||||
\(683\) | 28.0000i | 1.07139i | 0.844411 | + | 0.535695i | \(0.179950\pi\) | ||||
−0.844411 | + | 0.535695i | \(0.820050\pi\) | |||||||
\(684\) | −15.4654 | − | 1.35234i | −0.591336 | − | 0.0517082i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.02699 | − | 5.24290i | −0.115571 | − | 0.200175i | ||||
\(687\) | 28.5657 | − | 16.4924i | 1.08985 | − | 0.629225i | ||||
\(688\) | −2.70469 | − | 1.56155i | −0.103115 | − | 0.0595336i | ||||
\(689\) | 7.56155 | + | 13.0970i | 0.288072 | + | 0.498956i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.0691 | −0.801507 | −0.400754 | − | 0.916186i | \(-0.631252\pi\) | ||||
−0.400754 | + | 0.916186i | \(0.631252\pi\) | |||||||
\(692\) | 5.80776i | 0.220778i | ||||||||
\(693\) | −1.35234 | − | 0.780776i | −0.0513713 | − | 0.0296592i | ||||
\(694\) | −0.842329 | + | 1.45896i | −0.0319744 | + | 0.0553813i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.12311 | 0.194191 | ||||||||
\(697\) | −27.1666 | − | 15.6847i | −1.02901 | − | 0.594099i | ||||
\(698\) | 12.3376 | − | 7.12311i | 0.466984 | − | 0.269614i | ||||
\(699\) | −2.96543 | + | 5.13628i | −0.112163 | + | 0.194272i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.24621 | − | 5.62260i | −0.122608 | − | 0.212363i | 0.798188 | − | 0.602409i | \(-0.205792\pi\) |
−0.920795 | + | 0.390046i | \(0.872459\pi\) | |||||||
\(702\) | 2.87689i | 0.108581i | ||||||||
\(703\) | 16.7276 | + | 11.7116i | 0.630892 | + | 0.441713i | ||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0885 | + | 20.9380i | 0.454958 | + | 0.788011i | ||||
\(707\) | 3.79706 | + | 2.19224i | 0.142803 | + | 0.0824475i | ||||
\(708\) | −32.3029 | + | 18.6501i | −1.21402 | + | 0.700913i | ||||
\(709\) | −20.0000 | + | 34.6410i | −0.751116 | + | 1.30097i | 0.196167 | + | 0.980571i | \(0.437151\pi\) |
−0.947282 | + | 0.320400i | \(0.896183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.6155 | −1.48570 | ||||||||
\(712\) | 2.32498 | + | 1.34233i | 0.0871324 | + | 0.0503059i | ||||
\(713\) | 41.5692 | + | 24.0000i | 1.55678 | + | 0.898807i | ||||
\(714\) | −5.75379 | −0.215330 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.74621 | + | 9.95273i | −0.214746 | + | 0.371951i | ||||
\(717\) | 40.4768 | − | 23.3693i | 1.51164 | − | 0.872743i | ||||
\(718\) | 13.0970 | + | 7.56155i | 0.488775 | + | 0.282195i | ||||
\(719\) | 7.43845 | + | 12.8838i | 0.277407 | + | 0.480483i | 0.970740 | − | 0.240134i | \(-0.0771915\pi\) |
−0.693332 | + | 0.720618i | \(0.743858\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.54640 | −0.0948328 | ||||||||
\(722\) | −14.5560 | − | 12.2116i | −0.541716 | − | 0.454470i | ||||
\(723\) | 21.9309i | 0.815618i | ||||||||
\(724\) | 10.6847 | + | 18.5064i | 0.397092 | + | 0.687784i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.8078 | − | 22.1837i | 0.475341 | − | 0.823314i | ||||
\(727\) | 6.92820 | − | 4.00000i | 0.256953 | − | 0.148352i | −0.365991 | − | 0.930618i | \(-0.619270\pi\) |
0.622944 | + | 0.782267i | \(0.285937\pi\) | |||||||
\(728\) | −0.759413 | − | 0.438447i | −0.0281457 | − | 0.0162499i | ||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | + | 13.8564i | −0.295891 | + | 0.512498i | ||||
\(732\) | −11.3649 | − | 6.56155i | −0.420060 | − | 0.242522i | ||||
\(733\) | − | 26.9309i | − | 0.994714i | −0.867546 | − | 0.497357i | \(-0.834304\pi\) | ||
0.867546 | − | 0.497357i | \(-0.165696\pi\) | |||||||
\(734\) | −17.7538 | −0.655304 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.34233 | − | 4.05703i | −0.0863394 | − | 0.149544i | ||||
\(737\) | 8.17394 | + | 4.71922i | 0.301091 | + | 0.173835i | ||||
\(738\) | 18.8861 | − | 10.9039i | 0.695206 | − | 0.401377i | ||||
\(739\) | 9.37689 | + | 16.2413i | 0.344935 | + | 0.597444i | 0.985342 | − | 0.170591i | \(-0.0545677\pi\) |
−0.640407 | + | 0.768036i | \(0.721234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.8078 | + | 18.2931i | −0.470505 | + | 0.672016i | ||||
\(742\) | − | 3.31534i | − | 0.121710i | ||||||
\(743\) | −15.9682 | + | 9.21922i | −0.585815 | + | 0.338221i | −0.763441 | − | 0.645878i | \(-0.776492\pi\) |
0.177626 | + | 0.984098i | \(0.443158\pi\) | |||||||
\(744\) | 13.1231 | + | 22.7299i | 0.481116 | + | 0.833318i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.9039 | − | 31.0104i | −0.655508 | − | 1.13537i | ||||
\(747\) | −33.3354 | − | 19.2462i | −1.21968 | − | 0.704182i | ||||
\(748\) | 5.12311i | 0.187319i | ||||||||
\(749\) | −0.984845 | −0.0359855 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.4384 | − | 30.2043i | 0.636338 | − | 1.10217i | −0.349892 | − | 0.936790i | \(-0.613782\pi\) |
0.986230 | − | 0.165380i | \(-0.0528849\pi\) | |||||||
\(752\) | − | 2.87689i | − | 0.104910i | ||||||
\(753\) | − | 66.4233i | − | 2.42060i | ||||||
\(754\) | 2.00000 | − | 3.46410i | 0.0728357 | − | 0.126155i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.315342 | − | 0.546188i | 0.0114689 | − | 0.0198647i | ||||
\(757\) | 16.9408 | − | 9.78078i | 0.615724 | − | 0.355488i | −0.159478 | − | 0.987201i | \(-0.550981\pi\) |
0.775202 | + | 0.631713i | \(0.217648\pi\) | |||||||
\(758\) | 0.426450 | − | 0.246211i | 0.0154894 | − | 0.00894280i | ||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −51.9848 | −1.88445 | −0.942225 | − | 0.334982i | \(-0.891270\pi\) | ||||
−0.942225 | + | 0.334982i | \(0.891270\pi\) | |||||||
\(762\) | 34.5213 | − | 19.9309i | 1.25057 | − | 0.722019i | ||||
\(763\) | −5.40938 | + | 3.12311i | −0.195833 | + | 0.113064i | ||||
\(764\) | −2.68466 | + | 4.64996i | −0.0971275 | + | 0.168230i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.56155 | − | 4.43674i | 0.0925527 | − | 0.160306i | ||||
\(767\) | 29.1231i | 1.05157i | ||||||||
\(768\) | − | 2.56155i | − | 0.0924321i | ||||||
\(769\) | 13.2462 | − | 22.9431i | 0.477671 | − | 0.827350i | −0.522002 | − | 0.852944i | \(-0.674815\pi\) |
0.999672 | + | 0.0255946i | \(0.00814792\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.4384 | −1.20426 | ||||||||
\(772\) | − | 25.6155i | − | 0.921923i | ||||||
\(773\) | 12.3843 | + | 7.15009i | 0.445433 | + | 0.257171i | 0.705900 | − | 0.708312i | \(-0.250543\pi\) |
−0.260466 | + | 0.965483i | \(0.583876\pi\) | |||||||
\(774\) | −5.56155 | − | 9.63289i | −0.199906 | − | 0.346247i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.842329 | + | 1.45896i | 0.0302379 | + | 0.0523735i | ||||
\(777\) | −4.55648 | + | 2.63068i | −0.163463 | + | 0.0943752i | ||||
\(778\) | 19.1231i | 0.685597i | ||||||||
\(779\) | 26.5885 | + | 2.32498i | 0.952633 | + | 0.0833011i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.12311 | − | 14.0696i | −0.290668 | − | 0.503451i | ||||
\(782\) | −20.7846 | + | 12.0000i | −0.743256 | + | 0.429119i | ||||
\(783\) | 2.49146 | + | 1.43845i | 0.0890376 | + | 0.0514059i | ||||
\(784\) | −3.40388 | − | 5.89570i | −0.121567 | − | 0.210561i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −41.3002 | −1.47313 | ||||||||
\(787\) | − | 8.56155i | − | 0.305186i | −0.988289 | − | 0.152593i | \(-0.951238\pi\) | ||
0.988289 | − | 0.152593i | \(-0.0487624\pi\) | |||||||
\(788\) | −12.5041 | − | 7.21922i | −0.445439 | − | 0.257174i | ||||
\(789\) | 2.80776 | − | 4.86319i | 0.0999590 | − | 0.173134i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.36932 | −0.262023 | ||||||||
\(792\) | −3.08440 | − | 1.78078i | −0.109599 | − | 0.0632771i | ||||
\(793\) | −8.87348 | + | 5.12311i | −0.315106 | + | 0.181927i | ||||
\(794\) | −14.1501 | + | 24.5087i | −0.502168 | + | 0.869781i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.43845 | + | 2.49146i | 0.0509844 | + | 0.0883076i | ||||
\(797\) | 4.19224i | 0.148497i | 0.997240 | + | 0.0742483i | \(0.0236557\pi\) | ||||
−0.997240 | + | 0.0742483i | \(0.976344\pi\) | |||||||
\(798\) | 4.43674 | − | 2.06913i | 0.157059 | − | 0.0732464i | ||||
\(799\) | −14.7386 | −0.521415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.78078 | + | 8.28055i | 0.168920 | + | 0.292579i | ||||
\(802\) | −24.1888 | − | 13.9654i | −0.854138 | − | 0.493137i | ||||
\(803\) | −1.45896 | + | 0.842329i | −0.0514855 | + | 0.0297252i | ||||
\(804\) | −12.0885 | + | 20.9380i | −0.426330 | + | 0.738425i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 20.4924 | 0.721815 | ||||||||
\(807\) | −8.87348 | − | 5.12311i | −0.312361 | − | 0.180342i | ||||
\(808\) | 8.66025 | + | 5.00000i | 0.304667 | + | 0.175899i | ||||
\(809\) | −23.4384 | −0.824052 | −0.412026 | − | 0.911172i | \(-0.635179\pi\) | ||||
−0.412026 | + | 0.911172i | \(0.635179\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.58854 | − | 7.94759i | 0.161125 | − | 0.279077i | −0.774147 | − | 0.633006i | \(-0.781821\pi\) |
0.935273 | + | 0.353928i | \(0.115154\pi\) | |||||||
\(812\) | −0.759413 | + | 0.438447i | −0.0266502 | + | 0.0153865i | ||||
\(813\) | −18.2931 | − | 10.5616i | −0.641569 | − | 0.370410i | ||||
\(814\) | 2.34233 | + | 4.05703i | 0.0820986 | + | 0.142199i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.1231 | −0.459401 | ||||||||
\(817\) | 1.18586 | − | 13.5616i | 0.0414881 | − | 0.474459i | ||||
\(818\) | − | 21.0000i | − | 0.734248i | ||||||
\(819\) | −1.56155 | − | 2.70469i | −0.0545651 | − | 0.0945095i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.00000 | − | 12.1244i | 0.244302 | − | 0.423143i | −0.717633 | − | 0.696421i | \(-0.754775\pi\) |
0.961935 | + | 0.273278i | \(0.0881079\pi\) | |||||||
\(822\) | 12.0645 | − | 6.96543i | 0.420797 | − | 0.242947i | ||||
\(823\) | 23.5360 | + | 13.5885i | 0.820415 | + | 0.473667i | 0.850560 | − | 0.525879i | \(-0.176263\pi\) |
−0.0301446 | + | 0.999546i | \(0.509597\pi\) | |||||||
\(824\) | −5.80776 | −0.202323 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.19224 | − | 5.52911i | 0.111072 | − | 0.192383i | ||||
\(827\) | −27.6529 | − | 15.9654i | −0.961587 | − | 0.555173i | −0.0649260 | − | 0.997890i | \(-0.520681\pi\) |
−0.896661 | + | 0.442718i | \(0.854014\pi\) | |||||||
\(828\) | − | 16.6847i | − | 0.579832i | ||||||
\(829\) | −26.7386 | −0.928671 | −0.464336 | − | 0.885659i | \(-0.653707\pi\) | ||||
−0.464336 | + | 0.885659i | \(0.653707\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.43845 | + | 9.41967i | 0.188658 | + | 0.326765i | ||||
\(832\) | −1.73205 | − | 1.00000i | −0.0600481 | − | 0.0346688i | ||||
\(833\) | −30.2043 | + | 17.4384i | −1.04652 | + | 0.604206i | ||||
\(834\) | 11.2808 | + | 19.5389i | 0.390621 | + | 0.676576i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.84233 | − | 3.95042i | −0.0637183 | − | 0.136628i | ||||
\(837\) | 14.7386i | 0.509442i | ||||||||
\(838\) | 15.2088 | − | 8.78078i | 0.525378 | − | 0.303327i | ||||
\(839\) | 1.24621 | + | 2.15850i | 0.0430240 | + | 0.0745197i | 0.886735 | − | 0.462277i | \(-0.152967\pi\) |
−0.843712 | + | 0.536797i | \(0.819634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | −28.1393 | − | 16.2462i | −0.969743 | − | 0.559881i | ||||
\(843\) | − | 21.4384i | − | 0.738379i | ||||||
\(844\) | 3.31534 | 0.114119 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.12311 | − | 8.87348i | 0.176136 | − | 0.305077i | ||||
\(847\) | 4.38447i | 0.150652i | ||||||||
\(848\) | − | 7.56155i | − | 0.259665i | ||||||
\(849\) | 24.8963 | − | 43.1217i | 0.854439 | − | 1.47993i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.9730 | + | 19.0058i | −0.376150 | + | 0.651511i | ||||
\(852\) | 36.0401 | − | 20.8078i | 1.23471 | − | 0.712862i | ||||
\(853\) | 0.639676 | − | 0.369317i | 0.0219021 | − | 0.0126452i | −0.489009 | − | 0.872279i | \(-0.662641\pi\) |
0.510911 | + | 0.859634i | \(0.329308\pi\) | |||||||
\(854\) | 2.24621 | 0.0768638 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.24621 | −0.0767739 | ||||||||
\(857\) | −25.8012 | + | 14.8963i | −0.881351 | + | 0.508848i | −0.871104 | − | 0.491099i | \(-0.836595\pi\) |
−0.0102472 | + | 0.999947i | \(0.503262\pi\) | |||||||
\(858\) | −4.43674 | + | 2.56155i | −0.151468 | + | 0.0874500i | ||||
\(859\) | 23.7462 | − | 41.1296i | 0.810210 | − | 1.40333i | −0.102506 | − | 0.994732i | \(-0.532686\pi\) |
0.912717 | − | 0.408593i | \(-0.133980\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.43845 | + | 5.95557i | −0.117182 | + | 0.202965i | ||||
\(862\) | − | 7.36932i | − | 0.251000i | ||||||
\(863\) | 52.3002i | 1.78032i | 0.455649 | + | 0.890160i | \(0.349407\pi\) | ||||
−0.455649 | + | 0.890160i | \(0.650593\pi\) | |||||||
\(864\) | 0.719224 | − | 1.24573i | 0.0244685 | − | 0.0423807i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.7386 | 1.24843 | ||||||||
\(867\) | 23.6847i | 0.804373i | ||||||||
\(868\) | −3.89055 | − | 2.24621i | −0.132054 | − | 0.0762414i | ||||
\(869\) | −5.56155 | − | 9.63289i | −0.188663 | − | 0.326773i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.43845 | + | 16.3479i | 0.319810 | + | 0.553926i | ||||
\(872\) | −12.3376 | + | 7.12311i | −0.417803 | + | 0.241219i | ||||
\(873\) | 6.00000i | 0.203069i | ||||||||
\(874\) | 11.7116 | − | 16.7276i | 0.396152 | − | 0.565819i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.15767 | − | 3.73720i | −0.0729009 | − | 0.126268i | ||||
\(877\) | −15.4220 | + | 8.90388i | −0.520763 | + | 0.300663i | −0.737247 | − | 0.675623i | \(-0.763875\pi\) |
0.216484 | + | 0.976286i | \(0.430541\pi\) | |||||||
\(878\) | −14.2829 | − | 8.24621i | −0.482023 | − | 0.278296i | ||||
\(879\) | −30.1771 | − | 52.2682i | −1.01785 | − | 1.76296i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.1231 | −0.812728 | −0.406364 | − | 0.913711i | \(-0.633204\pi\) | ||||
−0.406364 | + | 0.913711i | \(0.633204\pi\) | |||||||
\(882\) | − | 24.2462i | − | 0.816412i | ||||||
\(883\) | 7.62775 | + | 4.40388i | 0.256694 | + | 0.148202i | 0.622826 | − | 0.782361i | \(-0.285985\pi\) |
−0.366131 | + | 0.930563i | \(0.619318\pi\) | |||||||
\(884\) | −5.12311 | + | 8.87348i | −0.172309 | + | 0.298447i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −33.9309 | −1.13993 | ||||||||
\(887\) | −22.7299 | − | 13.1231i | −0.763195 | − | 0.440631i | 0.0672468 | − | 0.997736i | \(-0.478579\pi\) |
−0.830442 | + | 0.557106i | \(0.811912\pi\) | |||||||
\(888\) | −10.3923 | + | 6.00000i | −0.348743 | + | 0.201347i | ||||
\(889\) | −3.41146 | + | 5.90882i | −0.114417 | + | 0.198176i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.50000 | + | 6.06218i | 0.117254 | + | 0.203091i | ||||
\(892\) | − | 11.3153i | − | 0.378866i | ||||||
\(893\) | 11.3649 | − | 5.30019i | 0.380313 | − | 0.177364i | ||||
\(894\) | −40.9848 | −1.37074 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.219224 | + | 0.379706i | 0.00732375 | + | 0.0126851i | ||||
\(897\) | −20.7846 | − | 12.0000i | −0.693978 | − | 0.400668i | ||||
\(898\) | −25.1147 | + | 14.5000i | −0.838090 | + | 0.483871i | ||||
\(899\) | 10.2462 | − | 17.7470i | 0.341730 | − | 0.591894i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.7386 | −1.29057 | ||||||||
\(902\) | 5.30277 | + | 3.06155i | 0.176563 | + | 0.101939i | ||||
\(903\) | 3.03765 | + | 1.75379i | 0.101087 | + | 0.0583624i | ||||
\(904\) | −16.8078 | −0.559018 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −26.2462 | + | 45.4598i | −0.871972 | + | 1.51030i | ||||
\(907\) | 43.4546 | − | 25.0885i | 1.44289 | − | 0.833051i | 0.444846 | − | 0.895607i | \(-0.353259\pi\) |
0.998041 | + | 0.0625559i | \(0.0199252\pi\) | |||||||
\(908\) | −17.2606 | − | 9.96543i | −0.572814 | − | 0.330715i | ||||
\(909\) | 17.8078 | + | 30.8440i | 0.590646 | + | 1.02303i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3845 | 0.410316 | 0.205158 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205158 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(912\) | 10.1192 | − | 4.71922i | 0.335081 | − | 0.156269i | ||||
\(913\) | − | 10.8078i | − | 0.357685i | ||||||
\(914\) | −3.52699 | − | 6.10892i | −0.116662 | − | 0.202065i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.43845 | + | 11.1517i | −0.212732 | + | 0.368463i | ||||
\(917\) | 6.12205 | − | 3.53457i | 0.202168 | − | 0.116722i | ||||
\(918\) | −6.38202 | − | 3.68466i | −0.210638 | − | 0.121612i | ||||
\(919\) | −20.2462 | −0.667861 | −0.333930 | − | 0.942598i | \(-0.608375\pi\) | ||||
−0.333930 | + | 0.942598i | \(0.608375\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.6501 | + | 53.0875i | −1.00995 | + | 1.74929i | ||||
\(922\) | 33.7619 | + | 19.4924i | 1.11189 | + | 0.641949i | ||||
\(923\) | − | 32.4924i | − | 1.06950i | ||||||
\(924\) | 1.12311 | 0.0369475 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.78078 | − | 16.9408i | −0.321416 | − | 0.556709i | ||||
\(927\) | −17.9134 | − | 10.3423i | −0.588355 | − | 0.339687i | ||||
\(928\) | −1.73205 | + | 1.00000i | −0.0568574 | + | 0.0328266i | ||||
\(929\) | −17.9924 | − | 31.1638i | −0.590312 | − | 1.02245i | −0.994190 | − | 0.107638i | \(-0.965671\pi\) |
0.403878 | − | 0.914813i | \(-0.367662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.0194 | − | 24.3086i | 0.557789 | − | 0.796682i | ||||
\(932\) | − | 2.31534i | − | 0.0758415i | ||||||
\(933\) | −8.87348 | + | 5.12311i | −0.290505 | + | 0.167723i | ||||
\(934\) | −8.28078 | − | 14.3427i | −0.270955 | − | 0.469308i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.56155 | − | 6.16879i | −0.116413 | − | 0.201633i | ||||
\(937\) | −43.4546 | − | 25.0885i | −1.41960 | − | 0.819607i | −0.423337 | − | 0.905972i | \(-0.639141\pi\) |
−0.996264 | + | 0.0863653i | \(0.972475\pi\) | |||||||
\(938\) | − | 4.13826i | − | 0.135119i | ||||||
\(939\) | 11.0540 | 0.360733 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.12311 | − | 14.0696i | 0.264806 | − | 0.458657i | −0.702707 | − | 0.711479i | \(-0.748026\pi\) |
0.967513 | + | 0.252822i | \(0.0813589\pi\) | |||||||
\(942\) | − | 6.24621i | − | 0.203513i | ||||||
\(943\) | 28.6847i | 0.934101i | ||||||||
\(944\) | 7.28078 | − | 12.6107i | 0.236969 | − | 0.410442i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.56155 | − | 2.70469i | 0.0507705 | − | 0.0879370i | ||||
\(947\) | −48.9239 | + | 28.2462i | −1.58981 | + | 0.917879i | −0.596475 | + | 0.802631i | \(0.703433\pi\) |
−0.993337 | + | 0.115247i | \(0.963234\pi\) | |||||||
\(948\) | 24.6752 | − | 14.2462i | 0.801412 | − | 0.462695i | ||||
\(949\) | −3.36932 | −0.109373 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.8617 | −1.55202 | ||||||||
\(952\) | 1.94528 | − | 1.12311i | 0.0630468 | − | 0.0364001i | ||||
\(953\) | −13.5833 | + | 7.84233i | −0.440007 | + | 0.254038i | −0.703600 | − | 0.710596i | \(-0.748425\pi\) |
0.263594 | + | 0.964634i | \(0.415092\pi\) | |||||||
\(954\) | 13.4654 | − | 23.3228i | 0.435960 | − | 0.755104i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.12311 | + | 15.8017i | −0.295062 | + | 0.511063i | ||||
\(957\) | 5.12311i | 0.165606i | ||||||||
\(958\) | − | 29.3693i | − | 0.948880i | ||||||
\(959\) | −1.19224 | + | 2.06501i | −0.0384993 | + | 0.0666828i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | 9.36932i | 0.302079i | ||||||||
\(963\) | −6.92820 | − | 4.00000i | −0.223258 | − | 0.128898i | ||||
\(964\) | −4.28078 | − | 7.41452i | −0.137875 | − | 0.238806i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.63068 | + | 4.55648i | 0.0846408 | + | 0.146602i | ||||
\(967\) | −25.2213 | + | 14.5616i | −0.811064 | + | 0.468268i | −0.847325 | − | 0.531074i | \(-0.821788\pi\) |
0.0362613 | + | 0.999342i | \(0.488455\pi\) | |||||||
\(968\) | 10.0000i | 0.321412i | ||||||||
\(969\) | −24.1771 | − | 51.8418i | −0.776680 | − | 1.66540i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.96543 | − | 15.5286i | −0.287714 | − | 0.498336i | 0.685549 | − | 0.728026i | \(-0.259562\pi\) |
−0.973264 | + | 0.229690i | \(0.926229\pi\) | |||||||
\(972\) | −19.2658 | + | 11.1231i | −0.617950 | + | 0.356774i | ||||
\(973\) | −3.34436 | − | 1.93087i | −0.107215 | − | 0.0619008i | ||||
\(974\) | 3.46543 | + | 6.00231i | 0.111040 | + | 0.192326i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.12311 | 0.163987 | ||||||||
\(977\) | 30.3153i | 0.969874i | 0.874549 | + | 0.484937i | \(0.161157\pi\) | ||||
−0.874549 | + | 0.484937i | \(0.838843\pi\) | |||||||
\(978\) | −37.8320 | − | 21.8423i | −1.20973 | − | 0.698441i | ||||
\(979\) | −1.34233 | + | 2.32498i | −0.0429010 | + | 0.0743068i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −50.7386 | −1.61996 | ||||||||
\(982\) | 7.94759 | + | 4.58854i | 0.253618 | + | 0.146426i | ||||
\(983\) | 35.9934 | − | 20.7808i | 1.14801 | − | 0.662804i | 0.199608 | − | 0.979876i | \(-0.436033\pi\) |
0.948401 | + | 0.317072i | \(0.102700\pi\) | |||||||
\(984\) | −7.84233 | + | 13.5833i | −0.250004 | + | 0.433020i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.12311 | + | 8.87348i | 0.163153 | + | 0.282589i | ||||
\(987\) | 3.23106i | 0.102846i | ||||||||
\(988\) | 0.759413 | − | 8.68466i | 0.0241601 | − | 0.276296i | ||||
\(989\) | 14.6307 | 0.465229 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.19224 | + | 7.26117i | 0.133171 | + | 0.230659i | 0.924897 | − | 0.380217i | \(-0.124151\pi\) |
−0.791726 | + | 0.610876i | \(0.790817\pi\) | |||||||
\(992\) | −8.87348 | − | 5.12311i | −0.281733 | − | 0.162659i | ||||
\(993\) | −52.1149 | + | 30.0885i | −1.65382 | + | 0.954831i | ||||
\(994\) | −3.56155 | + | 6.16879i | −0.112966 | + | 0.195662i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 27.6847 | 0.877222 | ||||||||
\(997\) | −2.32498 | − | 1.34233i | −0.0736329 | − | 0.0425120i | 0.462732 | − | 0.886498i | \(-0.346869\pi\) |
−0.536364 | + | 0.843986i | \(0.680203\pi\) | |||||||
\(998\) | 25.1147 | + | 14.5000i | 0.794993 | + | 0.458989i | ||||
\(999\) | −6.73863 | −0.213201 |
(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 | 950.2.j.f.349.3 | 8 | ||
5.2 | odd | 4 | 190.2.e.c.121.2 | yes | 4 | ||
5.3 | odd | 4 | 950.2.e.h.501.1 | 4 | |||
5.4 | even | 2 | inner | 950.2.j.f.349.2 | 8 | ||
15.2 | even | 4 | 1710.2.l.m.1261.1 | 4 | |||
19.11 | even | 3 | inner | 950.2.j.f.49.2 | 8 | ||
20.7 | even | 4 | 1520.2.q.h.881.1 | 4 | |||
95.7 | odd | 12 | 3610.2.a.k.1.1 | 2 | |||
95.12 | even | 12 | 3610.2.a.u.1.2 | 2 | |||
95.49 | even | 6 | inner | 950.2.j.f.49.3 | 8 | ||
95.68 | odd | 12 | 950.2.e.h.201.1 | 4 | |||
95.87 | odd | 12 | 190.2.e.c.11.2 | ✓ | 4 | ||
285.182 | even | 12 | 1710.2.l.m.1531.1 | 4 | |||
380.87 | even | 12 | 1520.2.q.h.961.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.e.c.11.2 | ✓ | 4 | 95.87 | odd | 12 | ||
190.2.e.c.121.2 | yes | 4 | 5.2 | odd | 4 | ||
950.2.e.h.201.1 | 4 | 95.68 | odd | 12 | |||
950.2.e.h.501.1 | 4 | 5.3 | odd | 4 | |||
950.2.j.f.49.2 | 8 | 19.11 | even | 3 | inner | ||
950.2.j.f.49.3 | 8 | 95.49 | even | 6 | inner | ||
950.2.j.f.349.2 | 8 | 5.4 | even | 2 | inner | ||
950.2.j.f.349.3 | 8 | 1.1 | even | 1 | trivial | ||
1520.2.q.h.881.1 | 4 | 20.7 | even | 4 | |||
1520.2.q.h.961.1 | 4 | 380.87 | even | 12 | |||
1710.2.l.m.1261.1 | 4 | 15.2 | even | 4 | |||
1710.2.l.m.1531.1 | 4 | 285.182 | even | 12 | |||
3610.2.a.k.1.1 | 2 | 95.7 | odd | 12 | |||
3610.2.a.u.1.2 | 2 | 95.12 | even | 12 |