Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [190,2,Mod(11,190)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(190, base_ring=CyclotomicField(6))
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("190.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 190 = 2 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 190.e (of order \(3\), degree \(2\), 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: | \(1.51715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(1.28078 - 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 190.11 |
Dual form | 190.2.e.c.121.2 |
$q$-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 \(\left(\mathbb{Z}/190\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.28078 | − | 2.21837i | 0.739457 | − | 1.28078i | −0.213284 | − | 0.976990i | \(-0.568416\pi\) |
0.952740 | − | 0.303786i | \(-0.0982508\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −1.28078 | − | 2.21837i | −0.522875 | − | 0.905646i | ||||
\(7\) | 0.438447 | 0.165717 | 0.0828587 | − | 0.996561i | \(-0.473595\pi\) | ||||
0.0828587 | + | 0.996561i | \(0.473595\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.78078 | − | 3.08440i | −0.593592 | − | 1.02813i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 1.00000 | 0.301511 | 0.150756 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150756 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(12\) | −2.56155 | −0.739457 | ||||||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0.219224 | − | 0.379706i | 0.0585900 | − | 0.101481i | ||||
\(15\) | 1.28078 | + | 2.21837i | 0.330695 | + | 0.572781i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.56155 | + | 4.43674i | −0.621268 | + | 1.07607i | 0.367982 | + | 0.929833i | \(0.380049\pi\) |
−0.989250 | + | 0.146235i | \(0.953285\pi\) | |||||||
\(18\) | −3.56155 | −0.839466 | ||||||||
\(19\) | −2.50000 | − | 3.57071i | −0.573539 | − | 0.819178i | ||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.561553 | − | 0.972638i | 0.122541 | − | 0.212247i | ||||
\(22\) | 0.500000 | − | 0.866025i | 0.106600 | − | 0.184637i | ||||
\(23\) | 2.34233 | + | 4.05703i | 0.488409 | + | 0.845950i | 0.999911 | − | 0.0133324i | \(-0.00424395\pi\) |
−0.511502 | + | 0.859282i | \(0.670911\pi\) | |||||||
\(24\) | −1.28078 | + | 2.21837i | −0.261437 | + | 0.452823i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | −0.219224 | − | 0.379706i | −0.0414294 | − | 0.0717578i | ||||
\(29\) | −1.00000 | − | 1.73205i | −0.185695 | − | 0.321634i | 0.758115 | − | 0.652121i | \(-0.226120\pi\) |
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(30\) | 2.56155 | 0.467673 | ||||||||
\(31\) | 10.2462 | 1.84027 | 0.920137 | − | 0.391597i | \(-0.128077\pi\) | ||||
0.920137 | + | 0.391597i | \(0.128077\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 1.28078 | − | 2.21837i | 0.222955 | − | 0.386169i | ||||
\(34\) | 2.56155 | + | 4.43674i | 0.439303 | + | 0.760895i | ||||
\(35\) | −0.219224 | + | 0.379706i | −0.0370556 | + | 0.0641821i | ||||
\(36\) | −1.78078 | + | 3.08440i | −0.296796 | + | 0.514066i | ||||
\(37\) | −4.68466 | −0.770153 | −0.385077 | − | 0.922885i | \(-0.625825\pi\) | ||||
−0.385077 | + | 0.922885i | \(0.625825\pi\) | |||||||
\(38\) | −4.34233 | + | 0.379706i | −0.704419 | + | 0.0615965i | ||||
\(39\) | 5.12311 | 0.820353 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 3.06155 | − | 5.30277i | 0.478134 | − | 0.828153i | −0.521552 | − | 0.853220i | \(-0.674647\pi\) |
0.999686 | + | 0.0250670i | \(0.00797991\pi\) | |||||||
\(42\) | −0.561553 | − | 0.972638i | −0.0866495 | − | 0.150081i | ||||
\(43\) | −1.56155 | + | 2.70469i | −0.238135 | + | 0.412461i | −0.960179 | − | 0.279385i | \(-0.909869\pi\) |
0.722044 | + | 0.691847i | \(0.243203\pi\) | |||||||
\(44\) | −0.500000 | − | 0.866025i | −0.0753778 | − | 0.130558i | ||||
\(45\) | 3.56155 | 0.530925 | ||||||||
\(46\) | 4.68466 | 0.690715 | ||||||||
\(47\) | −1.43845 | − | 2.49146i | −0.209819 | − | 0.363417i | 0.741838 | − | 0.670579i | \(-0.233954\pi\) |
−0.951657 | + | 0.307161i | \(0.900621\pi\) | |||||||
\(48\) | 1.28078 | + | 2.21837i | 0.184864 | + | 0.320194i | ||||
\(49\) | −6.80776 | −0.972538 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 6.56155 | + | 11.3649i | 0.918801 | + | 1.59141i | ||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 3.78078 | + | 6.54850i | 0.519330 | + | 0.899505i | 0.999748 | + | 0.0224656i | \(0.00715162\pi\) |
−0.480418 | + | 0.877040i | \(0.659515\pi\) | |||||||
\(54\) | −0.719224 | + | 1.24573i | −0.0978739 | + | 0.169523i | ||||
\(55\) | −0.500000 | + | 0.866025i | −0.0674200 | + | 0.116775i | ||||
\(56\) | −0.438447 | −0.0585900 | ||||||||
\(57\) | −11.1231 | + | 0.972638i | −1.47329 | + | 0.128829i | ||||
\(58\) | −2.00000 | −0.262613 | ||||||||
\(59\) | −7.28078 | + | 12.6107i | −0.947876 | + | 1.64177i | −0.197989 | + | 0.980204i | \(0.563441\pi\) |
−0.749887 | + | 0.661566i | \(0.769892\pi\) | |||||||
\(60\) | 1.28078 | − | 2.21837i | 0.165348 | − | 0.286390i | ||||
\(61\) | −2.56155 | − | 4.43674i | −0.327973 | − | 0.568066i | 0.654136 | − | 0.756377i | \(-0.273032\pi\) |
−0.982110 | + | 0.188310i | \(0.939699\pi\) | |||||||
\(62\) | 5.12311 | − | 8.87348i | 0.650635 | − | 1.12693i | ||||
\(63\) | −0.780776 | − | 1.35234i | −0.0983686 | − | 0.170379i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | −1.28078 | − | 2.21837i | −0.157653 | − | 0.273062i | ||||
\(67\) | −4.71922 | − | 8.17394i | −0.576545 | − | 0.998605i | −0.995872 | − | 0.0907698i | \(-0.971067\pi\) |
0.419327 | − | 0.907835i | \(-0.362266\pi\) | |||||||
\(68\) | 5.12311 | 0.621268 | ||||||||
\(69\) | 12.0000 | 1.44463 | ||||||||
\(70\) | 0.219224 | + | 0.379706i | 0.0262022 | + | 0.0453836i | ||||
\(71\) | −8.12311 | + | 14.0696i | −0.964035 | + | 1.66976i | −0.251850 | + | 0.967766i | \(0.581039\pi\) |
−0.712185 | + | 0.701992i | \(0.752294\pi\) | |||||||
\(72\) | 1.78078 | + | 3.08440i | 0.209867 | + | 0.363499i | ||||
\(73\) | 0.842329 | − | 1.45896i | 0.0985872 | − | 0.170758i | −0.812513 | − | 0.582943i | \(-0.801901\pi\) |
0.911100 | + | 0.412185i | \(0.135234\pi\) | |||||||
\(74\) | −2.34233 | + | 4.05703i | −0.272290 | + | 0.471621i | ||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | −1.84233 | + | 3.95042i | −0.211330 | + | 0.453144i | ||||
\(77\) | 0.438447 | 0.0499657 | ||||||||
\(78\) | 2.56155 | − | 4.43674i | 0.290039 | − | 0.502362i | ||||
\(79\) | 5.56155 | − | 9.63289i | 0.625724 | − | 1.08379i | −0.362677 | − | 0.931915i | \(-0.618137\pi\) |
0.988400 | − | 0.151870i | \(-0.0485295\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | 3.50000 | − | 6.06218i | 0.388889 | − | 0.673575i | ||||
\(82\) | −3.06155 | − | 5.30277i | −0.338092 | − | 0.585592i | ||||
\(83\) | −10.8078 | −1.18631 | −0.593153 | − | 0.805090i | \(-0.702117\pi\) | ||||
−0.593153 | + | 0.805090i | \(0.702117\pi\) | |||||||
\(84\) | −1.12311 | −0.122541 | ||||||||
\(85\) | −2.56155 | − | 4.43674i | −0.277839 | − | 0.481232i | ||||
\(86\) | 1.56155 | + | 2.70469i | 0.168387 | + | 0.291654i | ||||
\(87\) | −5.12311 | −0.549255 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 1.34233 | + | 2.32498i | 0.142287 | + | 0.246448i | 0.928357 | − | 0.371689i | \(-0.121221\pi\) |
−0.786071 | + | 0.618137i | \(0.787888\pi\) | |||||||
\(90\) | 1.78078 | − | 3.08440i | 0.187710 | − | 0.325124i | ||||
\(91\) | 0.438447 | + | 0.759413i | 0.0459618 | + | 0.0796081i | ||||
\(92\) | 2.34233 | − | 4.05703i | 0.244205 | − | 0.422975i | ||||
\(93\) | 13.1231 | − | 22.7299i | 1.36080 | − | 2.35698i | ||||
\(94\) | −2.87689 | −0.296729 | ||||||||
\(95\) | 4.34233 | − | 0.379706i | 0.445514 | − | 0.0389571i | ||||
\(96\) | 2.56155 | 0.261437 | ||||||||
\(97\) | −0.842329 | + | 1.45896i | −0.0855256 | + | 0.148135i | −0.905615 | − | 0.424101i | \(-0.860590\pi\) |
0.820089 | + | 0.572235i | \(0.193924\pi\) | |||||||
\(98\) | −3.40388 | + | 5.89570i | −0.343844 | + | 0.595555i | ||||
\(99\) | −1.78078 | − | 3.08440i | −0.178975 | − | 0.309993i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | 13.1231 | 1.29938 | ||||||||
\(103\) | −5.80776 | −0.572256 | −0.286128 | − | 0.958191i | \(-0.592368\pi\) | ||||
−0.286128 | + | 0.958191i | \(0.592368\pi\) | |||||||
\(104\) | −1.00000 | − | 1.73205i | −0.0980581 | − | 0.169842i | ||||
\(105\) | 0.561553 | + | 0.972638i | 0.0548019 | + | 0.0949197i | ||||
\(106\) | 7.56155 | 0.734443 | ||||||||
\(107\) | 2.24621 | 0.217149 | 0.108575 | − | 0.994088i | \(-0.465371\pi\) | ||||
0.108575 | + | 0.994088i | \(0.465371\pi\) | |||||||
\(108\) | 0.719224 | + | 1.24573i | 0.0692073 | + | 0.119871i | ||||
\(109\) | 7.12311 | − | 12.3376i | 0.682270 | − | 1.18173i | −0.292017 | − | 0.956413i | \(-0.594326\pi\) |
0.974286 | − | 0.225313i | \(-0.0723404\pi\) | |||||||
\(110\) | 0.500000 | + | 0.866025i | 0.0476731 | + | 0.0825723i | ||||
\(111\) | −6.00000 | + | 10.3923i | −0.569495 | + | 0.986394i | ||||
\(112\) | −0.219224 | + | 0.379706i | −0.0207147 | + | 0.0358789i | ||||
\(113\) | −16.8078 | −1.58114 | −0.790571 | − | 0.612371i | \(-0.790216\pi\) | ||||
−0.790571 | + | 0.612371i | \(0.790216\pi\) | |||||||
\(114\) | −4.71922 | + | 10.1192i | −0.441996 | + | 0.947751i | ||||
\(115\) | −4.68466 | −0.436847 | ||||||||
\(116\) | −1.00000 | + | 1.73205i | −0.0928477 | + | 0.160817i | ||||
\(117\) | 3.56155 | − | 6.16879i | 0.329266 | − | 0.570305i | ||||
\(118\) | 7.28078 | + | 12.6107i | 0.670250 | + | 1.16091i | ||||
\(119\) | −1.12311 | + | 1.94528i | −0.102955 | + | 0.178323i | ||||
\(120\) | −1.28078 | − | 2.21837i | −0.116918 | − | 0.202509i | ||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | −5.12311 | −0.463824 | ||||||||
\(123\) | −7.84233 | − | 13.5833i | −0.707119 | − | 1.22477i | ||||
\(124\) | −5.12311 | − | 8.87348i | −0.460068 | − | 0.796862i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.56155 | −0.139114 | ||||||||
\(127\) | 7.78078 | + | 13.4767i | 0.690432 | + | 1.19586i | 0.971696 | + | 0.236233i | \(0.0759130\pi\) |
−0.281264 | + | 0.959630i | \(0.590754\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | −1.00000 | + | 1.73205i | −0.0877058 | + | 0.151911i | ||||
\(131\) | 8.06155 | − | 13.9630i | 0.704341 | − | 1.21995i | −0.262588 | − | 0.964908i | \(-0.584576\pi\) |
0.966929 | − | 0.255046i | \(-0.0820908\pi\) | |||||||
\(132\) | −2.56155 | −0.222955 | ||||||||
\(133\) | −1.09612 | − | 1.56557i | −0.0950455 | − | 0.135752i | ||||
\(134\) | −9.43845 | −0.815358 | ||||||||
\(135\) | 0.719224 | − | 1.24573i | 0.0619009 | − | 0.107216i | ||||
\(136\) | 2.56155 | − | 4.43674i | 0.219651 | − | 0.380447i | ||||
\(137\) | 2.71922 | + | 4.70983i | 0.232319 | + | 0.402388i | 0.958490 | − | 0.285126i | \(-0.0920354\pi\) |
−0.726171 | + | 0.687514i | \(0.758702\pi\) | |||||||
\(138\) | 6.00000 | − | 10.3923i | 0.510754 | − | 0.884652i | ||||
\(139\) | −4.40388 | − | 7.62775i | −0.373532 | − | 0.646977i | 0.616574 | − | 0.787297i | \(-0.288520\pi\) |
−0.990106 | + | 0.140320i | \(0.955187\pi\) | |||||||
\(140\) | 0.438447 | 0.0370556 | ||||||||
\(141\) | −7.36932 | −0.620608 | ||||||||
\(142\) | 8.12311 | + | 14.0696i | 0.681676 | + | 1.18070i | ||||
\(143\) | 1.00000 | + | 1.73205i | 0.0836242 | + | 0.144841i | ||||
\(144\) | 3.56155 | 0.296796 | ||||||||
\(145\) | 2.00000 | 0.166091 | ||||||||
\(146\) | −0.842329 | − | 1.45896i | −0.0697117 | − | 0.120744i | ||||
\(147\) | −8.71922 | + | 15.1021i | −0.719149 | + | 1.24560i | ||||
\(148\) | 2.34233 | + | 4.05703i | 0.192538 | + | 0.333486i | ||||
\(149\) | −8.00000 | + | 13.8564i | −0.655386 | + | 1.13516i | 0.326411 | + | 0.945228i | \(0.394160\pi\) |
−0.981797 | + | 0.189933i | \(0.939173\pi\) | |||||||
\(150\) | −1.28078 | + | 2.21837i | −0.104575 | + | 0.181129i | ||||
\(151\) | 20.4924 | 1.66765 | 0.833825 | − | 0.552029i | \(-0.186146\pi\) | ||||
0.833825 | + | 0.552029i | \(0.186146\pi\) | |||||||
\(152\) | 2.50000 | + | 3.57071i | 0.202777 | + | 0.289623i | ||||
\(153\) | 18.2462 | 1.47512 | ||||||||
\(154\) | 0.219224 | − | 0.379706i | 0.0176655 | − | 0.0305976i | ||||
\(155\) | −5.12311 | + | 8.87348i | −0.411498 | + | 0.712735i | ||||
\(156\) | −2.56155 | − | 4.43674i | −0.205088 | − | 0.355223i | ||||
\(157\) | −1.21922 | + | 2.11176i | −0.0973046 | + | 0.168537i | −0.910568 | − | 0.413359i | \(-0.864355\pi\) |
0.813263 | + | 0.581896i | \(0.197689\pi\) | |||||||
\(158\) | −5.56155 | − | 9.63289i | −0.442453 | − | 0.766352i | ||||
\(159\) | 19.3693 | 1.53609 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.02699 | + | 1.77879i | 0.0809380 | + | 0.140189i | ||||
\(162\) | −3.50000 | − | 6.06218i | −0.274986 | − | 0.476290i | ||||
\(163\) | 17.0540 | 1.33577 | 0.667885 | − | 0.744264i | \(-0.267200\pi\) | ||||
0.667885 | + | 0.744264i | \(0.267200\pi\) | |||||||
\(164\) | −6.12311 | −0.478134 | ||||||||
\(165\) | 1.28078 | + | 2.21837i | 0.0997083 | + | 0.172700i | ||||
\(166\) | −5.40388 | + | 9.35980i | −0.419423 | + | 0.726461i | ||||
\(167\) | −0.342329 | − | 0.592932i | −0.0264902 | − | 0.0458824i | 0.852476 | − | 0.522766i | \(-0.175100\pi\) |
−0.878967 | + | 0.476883i | \(0.841766\pi\) | |||||||
\(168\) | −0.561553 | + | 0.972638i | −0.0433247 | + | 0.0750407i | ||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −5.12311 | −0.392924 | ||||||||
\(171\) | −6.56155 | + | 14.0696i | −0.501774 | + | 1.07593i | ||||
\(172\) | 3.12311 | 0.238135 | ||||||||
\(173\) | 2.90388 | − | 5.02967i | 0.220778 | − | 0.382399i | −0.734266 | − | 0.678861i | \(-0.762474\pi\) |
0.955044 | + | 0.296463i | \(0.0958070\pi\) | |||||||
\(174\) | −2.56155 | + | 4.43674i | −0.194191 | + | 0.336348i | ||||
\(175\) | −0.219224 | − | 0.379706i | −0.0165717 | − | 0.0287031i | ||||
\(176\) | −0.500000 | + | 0.866025i | −0.0376889 | + | 0.0652791i | ||||
\(177\) | 18.6501 | + | 32.3029i | 1.40183 | + | 2.42804i | ||||
\(178\) | 2.68466 | 0.201224 | ||||||||
\(179\) | 11.4924 | 0.858984 | 0.429492 | − | 0.903071i | \(-0.358693\pi\) | ||||
0.429492 | + | 0.903071i | \(0.358693\pi\) | |||||||
\(180\) | −1.78078 | − | 3.08440i | −0.132731 | − | 0.229897i | ||||
\(181\) | −10.6847 | − | 18.5064i | −0.794184 | − | 1.37557i | −0.923356 | − | 0.383945i | \(-0.874565\pi\) |
0.129171 | − | 0.991622i | \(-0.458768\pi\) | |||||||
\(182\) | 0.876894 | 0.0649997 | ||||||||
\(183\) | −13.1231 | −0.970088 | ||||||||
\(184\) | −2.34233 | − | 4.05703i | −0.172679 | − | 0.299088i | ||||
\(185\) | 2.34233 | − | 4.05703i | 0.172211 | − | 0.298279i | ||||
\(186\) | −13.1231 | − | 22.7299i | −0.962233 | − | 1.66664i | ||||
\(187\) | −2.56155 | + | 4.43674i | −0.187319 | + | 0.324447i | ||||
\(188\) | −1.43845 | + | 2.49146i | −0.104910 | + | 0.181709i | ||||
\(189\) | −0.630683 | −0.0458754 | ||||||||
\(190\) | 1.84233 | − | 3.95042i | 0.133657 | − | 0.286594i | ||||
\(191\) | −5.36932 | −0.388510 | −0.194255 | − | 0.980951i | \(-0.562229\pi\) | ||||
−0.194255 | + | 0.980951i | \(0.562229\pi\) | |||||||
\(192\) | 1.28078 | − | 2.21837i | 0.0924321 | − | 0.160097i | ||||
\(193\) | −12.8078 | + | 22.1837i | −0.921923 | + | 1.59682i | −0.125487 | + | 0.992095i | \(0.540049\pi\) |
−0.796436 | + | 0.604722i | \(0.793284\pi\) | |||||||
\(194\) | 0.842329 | + | 1.45896i | 0.0604757 | + | 0.104747i | ||||
\(195\) | −2.56155 | + | 4.43674i | −0.183437 | + | 0.317722i | ||||
\(196\) | 3.40388 | + | 5.89570i | 0.243134 | + | 0.421121i | ||||
\(197\) | 14.4384 | 1.02870 | 0.514348 | − | 0.857581i | \(-0.328034\pi\) | ||||
0.514348 | + | 0.857581i | \(0.328034\pi\) | |||||||
\(198\) | −3.56155 | −0.253109 | ||||||||
\(199\) | 1.43845 | + | 2.49146i | 0.101969 | + | 0.176615i | 0.912496 | − | 0.409086i | \(-0.134152\pi\) |
−0.810527 | + | 0.585701i | \(0.800819\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −24.1771 | −1.70532 | ||||||||
\(202\) | −10.0000 | −0.703598 | ||||||||
\(203\) | −0.438447 | − | 0.759413i | −0.0307730 | − | 0.0533003i | ||||
\(204\) | 6.56155 | − | 11.3649i | 0.459401 | − | 0.795705i | ||||
\(205\) | 3.06155 | + | 5.30277i | 0.213828 | + | 0.370361i | ||||
\(206\) | −2.90388 | + | 5.02967i | −0.202323 | + | 0.350434i | ||||
\(207\) | 8.34233 | − | 14.4493i | 0.579832 | − | 1.00430i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | −2.50000 | − | 3.57071i | −0.172929 | − | 0.246991i | ||||
\(210\) | 1.12311 | 0.0775017 | ||||||||
\(211\) | 1.65767 | − | 2.87117i | 0.114119 | − | 0.197659i | −0.803308 | − | 0.595563i | \(-0.796929\pi\) |
0.917427 | + | 0.397904i | \(0.130262\pi\) | |||||||
\(212\) | 3.78078 | − | 6.54850i | 0.259665 | − | 0.449753i | ||||
\(213\) | 20.8078 | + | 36.0401i | 1.42572 | + | 2.46943i | ||||
\(214\) | 1.12311 | − | 1.94528i | 0.0767739 | − | 0.132976i | ||||
\(215\) | −1.56155 | − | 2.70469i | −0.106497 | − | 0.184458i | ||||
\(216\) | 1.43845 | 0.0978739 | ||||||||
\(217\) | 4.49242 | 0.304966 | ||||||||
\(218\) | −7.12311 | − | 12.3376i | −0.482438 | − | 0.835606i | ||||
\(219\) | −2.15767 | − | 3.73720i | −0.145802 | − | 0.252536i | ||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −10.2462 | −0.689235 | ||||||||
\(222\) | 6.00000 | + | 10.3923i | 0.402694 | + | 0.697486i | ||||
\(223\) | −5.65767 | + | 9.79937i | −0.378866 | + | 0.656215i | −0.990897 | − | 0.134619i | \(-0.957019\pi\) |
0.612032 | + | 0.790833i | \(0.290352\pi\) | |||||||
\(224\) | 0.219224 | + | 0.379706i | 0.0146475 | + | 0.0253702i | ||||
\(225\) | −1.78078 | + | 3.08440i | −0.118718 | + | 0.205626i | ||||
\(226\) | −8.40388 | + | 14.5560i | −0.559018 | + | 0.968247i | ||||
\(227\) | 19.9309 | 1.32286 | 0.661429 | − | 0.750008i | \(-0.269950\pi\) | ||||
0.661429 | + | 0.750008i | \(0.269950\pi\) | |||||||
\(228\) | 6.40388 | + | 9.14657i | 0.424107 | + | 0.605747i | ||||
\(229\) | 12.8769 | 0.850929 | 0.425465 | − | 0.904975i | \(-0.360111\pi\) | ||||
0.425465 | + | 0.904975i | \(0.360111\pi\) | |||||||
\(230\) | −2.34233 | + | 4.05703i | −0.154449 | + | 0.267513i | ||||
\(231\) | 0.561553 | − | 0.972638i | 0.0369475 | − | 0.0639949i | ||||
\(232\) | 1.00000 | + | 1.73205i | 0.0656532 | + | 0.113715i | ||||
\(233\) | −1.15767 | + | 2.00514i | −0.0758415 | + | 0.131361i | −0.901452 | − | 0.432879i | \(-0.857498\pi\) |
0.825610 | + | 0.564241i | \(0.190831\pi\) | |||||||
\(234\) | −3.56155 | − | 6.16879i | −0.232826 | − | 0.403266i | ||||
\(235\) | 2.87689 | 0.187668 | ||||||||
\(236\) | 14.5616 | 0.947876 | ||||||||
\(237\) | −14.2462 | − | 24.6752i | −0.925391 | − | 1.60282i | ||||
\(238\) | 1.12311 | + | 1.94528i | 0.0728001 | + | 0.126094i | ||||
\(239\) | 18.2462 | 1.18025 | 0.590125 | − | 0.807312i | \(-0.299079\pi\) | ||||
0.590125 | + | 0.807312i | \(0.299079\pi\) | |||||||
\(240\) | −2.56155 | −0.165348 | ||||||||
\(241\) | 4.28078 | + | 7.41452i | 0.275749 | + | 0.477611i | 0.970324 | − | 0.241809i | \(-0.0777408\pi\) |
−0.694575 | + | 0.719421i | \(0.744407\pi\) | |||||||
\(242\) | −5.00000 | + | 8.66025i | −0.321412 | + | 0.556702i | ||||
\(243\) | −11.1231 | − | 19.2658i | −0.713548 | − | 1.23590i | ||||
\(244\) | −2.56155 | + | 4.43674i | −0.163987 | + | 0.284033i | ||||
\(245\) | 3.40388 | − | 5.89570i | 0.217466 | − | 0.376662i | ||||
\(246\) | −15.6847 | −1.00002 | ||||||||
\(247\) | 3.68466 | − | 7.90084i | 0.234449 | − | 0.502718i | ||||
\(248\) | −10.2462 | −0.650635 | ||||||||
\(249\) | −13.8423 | + | 23.9756i | −0.877222 | + | 1.51939i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −12.9654 | − | 22.4568i | −0.818371 | − | 1.41746i | −0.906882 | − | 0.421385i | \(-0.861544\pi\) |
0.0885109 | − | 0.996075i | \(-0.471789\pi\) | |||||||
\(252\) | −0.780776 | + | 1.35234i | −0.0491843 | + | 0.0851897i | ||||
\(253\) | 2.34233 | + | 4.05703i | 0.147261 | + | 0.255063i | ||||
\(254\) | 15.5616 | 0.976419 | ||||||||
\(255\) | −13.1231 | −0.821801 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.52699 | − | 11.3051i | −0.407142 | − | 0.705191i | 0.587426 | − | 0.809278i | \(-0.300141\pi\) |
−0.994568 | + | 0.104087i | \(0.966808\pi\) | |||||||
\(258\) | 8.00000 | 0.498058 | ||||||||
\(259\) | −2.05398 | −0.127628 | ||||||||
\(260\) | 1.00000 | + | 1.73205i | 0.0620174 | + | 0.107417i | ||||
\(261\) | −3.56155 | + | 6.16879i | −0.220455 | + | 0.381839i | ||||
\(262\) | −8.06155 | − | 13.9630i | −0.498044 | − | 0.862638i | ||||
\(263\) | 1.09612 | − | 1.89853i | 0.0675895 | − | 0.117068i | −0.830250 | − | 0.557391i | \(-0.811803\pi\) |
0.897840 | + | 0.440322i | \(0.145136\pi\) | |||||||
\(264\) | −1.28078 | + | 2.21837i | −0.0788263 | + | 0.136531i | ||||
\(265\) | −7.56155 | −0.464502 | ||||||||
\(266\) | −1.90388 | + | 0.166481i | −0.116734 | + | 0.0102076i | ||||
\(267\) | 6.87689 | 0.420859 | ||||||||
\(268\) | −4.71922 | + | 8.17394i | −0.288272 | + | 0.499303i | ||||
\(269\) | −2.00000 | + | 3.46410i | −0.121942 | + | 0.211210i | −0.920534 | − | 0.390664i | \(-0.872246\pi\) |
0.798591 | + | 0.601874i | \(0.205579\pi\) | |||||||
\(270\) | −0.719224 | − | 1.24573i | −0.0437706 | − | 0.0758128i | ||||
\(271\) | 4.12311 | − | 7.14143i | 0.250461 | − | 0.433811i | −0.713192 | − | 0.700969i | \(-0.752751\pi\) |
0.963653 | + | 0.267158i | \(0.0860845\pi\) | |||||||
\(272\) | −2.56155 | − | 4.43674i | −0.155317 | − | 0.269017i | ||||
\(273\) | 2.24621 | 0.135947 | ||||||||
\(274\) | 5.43845 | 0.328549 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | −6.00000 | − | 10.3923i | −0.361158 | − | 0.625543i | ||||
\(277\) | 4.24621 | 0.255130 | 0.127565 | − | 0.991830i | \(-0.459284\pi\) | ||||
0.127565 | + | 0.991830i | \(0.459284\pi\) | |||||||
\(278\) | −8.80776 | −0.528255 | ||||||||
\(279\) | −18.2462 | − | 31.6034i | −1.09237 | − | 1.89204i | ||||
\(280\) | 0.219224 | − | 0.379706i | 0.0131011 | − | 0.0226918i | ||||
\(281\) | −4.18466 | − | 7.24804i | −0.249636 | − | 0.432382i | 0.713789 | − | 0.700361i | \(-0.246978\pi\) |
−0.963425 | + | 0.267979i | \(0.913644\pi\) | |||||||
\(282\) | −3.68466 | + | 6.38202i | −0.219418 | + | 0.380043i | ||||
\(283\) | 9.71922 | − | 16.8342i | 0.577748 | − | 1.00069i | −0.417989 | − | 0.908452i | \(-0.637265\pi\) |
0.995737 | − | 0.0922367i | \(-0.0294016\pi\) | |||||||
\(284\) | 16.2462 | 0.964035 | ||||||||
\(285\) | 4.71922 | − | 10.1192i | 0.279543 | − | 0.599410i | ||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | 1.34233 | − | 2.32498i | 0.0792352 | − | 0.137239i | ||||
\(288\) | 1.78078 | − | 3.08440i | 0.104933 | − | 0.181750i | ||||
\(289\) | −4.62311 | − | 8.00745i | −0.271947 | − | 0.471027i | ||||
\(290\) | 1.00000 | − | 1.73205i | 0.0587220 | − | 0.101710i | ||||
\(291\) | 2.15767 | + | 3.73720i | 0.126485 | + | 0.219078i | ||||
\(292\) | −1.68466 | −0.0985872 | ||||||||
\(293\) | 23.5616 | 1.37648 | 0.688240 | − | 0.725483i | \(-0.258383\pi\) | ||||
0.688240 | + | 0.725483i | \(0.258383\pi\) | |||||||
\(294\) | 8.71922 | + | 15.1021i | 0.508515 | + | 0.880775i | ||||
\(295\) | −7.28078 | − | 12.6107i | −0.423903 | − | 0.734222i | ||||
\(296\) | 4.68466 | 0.272290 | ||||||||
\(297\) | −1.43845 | −0.0834672 | ||||||||
\(298\) | 8.00000 | + | 13.8564i | 0.463428 | + | 0.802680i | ||||
\(299\) | −4.68466 | + | 8.11407i | −0.270921 | + | 0.469249i | ||||
\(300\) | 1.28078 | + | 2.21837i | 0.0739457 | + | 0.128078i | ||||
\(301\) | −0.684658 | + | 1.18586i | −0.0394631 | + | 0.0683520i | ||||
\(302\) | 10.2462 | − | 17.7470i | 0.589603 | − | 1.02122i | ||||
\(303\) | −25.6155 | −1.47157 | ||||||||
\(304\) | 4.34233 | − | 0.379706i | 0.249050 | − | 0.0217777i | ||||
\(305\) | 5.12311 | 0.293348 | ||||||||
\(306\) | 9.12311 | − | 15.8017i | 0.521533 | − | 0.903322i | ||||
\(307\) | 11.9654 | − | 20.7247i | 0.682903 | − | 1.18282i | −0.291187 | − | 0.956666i | \(-0.594050\pi\) |
0.974091 | − | 0.226157i | \(-0.0726164\pi\) | |||||||
\(308\) | −0.219224 | − | 0.379706i | −0.0124914 | − | 0.0216358i | ||||
\(309\) | −7.43845 | + | 12.8838i | −0.423158 | + | 0.732932i | ||||
\(310\) | 5.12311 | + | 8.87348i | 0.290973 | + | 0.503980i | ||||
\(311\) | 4.00000 | 0.226819 | 0.113410 | − | 0.993548i | \(-0.463823\pi\) | ||||
0.113410 | + | 0.993548i | \(0.463823\pi\) | |||||||
\(312\) | −5.12311 | −0.290039 | ||||||||
\(313\) | −2.15767 | − | 3.73720i | −0.121959 | − | 0.211239i | 0.798581 | − | 0.601887i | \(-0.205584\pi\) |
−0.920540 | + | 0.390648i | \(0.872251\pi\) | |||||||
\(314\) | 1.21922 | + | 2.11176i | 0.0688048 | + | 0.119173i | ||||
\(315\) | 1.56155 | 0.0879835 | ||||||||
\(316\) | −11.1231 | −0.625724 | ||||||||
\(317\) | −9.34233 | − | 16.1814i | −0.524717 | − | 0.908837i | −0.999586 | − | 0.0287805i | \(-0.990838\pi\) |
0.474868 | − | 0.880057i | \(-0.342496\pi\) | |||||||
\(318\) | 9.68466 | − | 16.7743i | 0.543089 | − | 0.940657i | ||||
\(319\) | −1.00000 | − | 1.73205i | −0.0559893 | − | 0.0969762i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 2.87689 | − | 4.98293i | 0.160573 | − | 0.278120i | ||||
\(322\) | 2.05398 | 0.114464 | ||||||||
\(323\) | 22.2462 | − | 1.94528i | 1.23781 | − | 0.108238i | ||||
\(324\) | −7.00000 | −0.388889 | ||||||||
\(325\) | 1.00000 | − | 1.73205i | 0.0554700 | − | 0.0960769i | ||||
\(326\) | 8.52699 | − | 14.7692i | 0.472266 | − | 0.817989i | ||||
\(327\) | −18.2462 | − | 31.6034i | −1.00902 | − | 1.74767i | ||||
\(328\) | −3.06155 | + | 5.30277i | −0.169046 | + | 0.292796i | ||||
\(329\) | −0.630683 | − | 1.09238i | −0.0347707 | − | 0.0602246i | ||||
\(330\) | 2.56155 | 0.141009 | ||||||||
\(331\) | 23.4924 | 1.29126 | 0.645630 | − | 0.763650i | \(-0.276595\pi\) | ||||
0.645630 | + | 0.763650i | \(0.276595\pi\) | |||||||
\(332\) | 5.40388 | + | 9.35980i | 0.296577 | + | 0.513686i | ||||
\(333\) | 8.34233 | + | 14.4493i | 0.457157 | + | 0.791819i | ||||
\(334\) | −0.684658 | −0.0374628 | ||||||||
\(335\) | 9.43845 | 0.515677 | ||||||||
\(336\) | 0.561553 | + | 0.972638i | 0.0306352 | + | 0.0530618i | ||||
\(337\) | −10.5270 | + | 18.2333i | −0.573442 | + | 0.993230i | 0.422767 | + | 0.906238i | \(0.361059\pi\) |
−0.996209 | + | 0.0869917i | \(0.972275\pi\) | |||||||
\(338\) | −4.50000 | − | 7.79423i | −0.244768 | − | 0.423950i | ||||
\(339\) | −21.5270 | + | 37.2858i | −1.16919 | + | 2.02509i | ||||
\(340\) | −2.56155 | + | 4.43674i | −0.138920 | + | 0.240616i | ||||
\(341\) | 10.2462 | 0.554863 | ||||||||
\(342\) | 8.90388 | + | 12.7173i | 0.481467 | + | 0.687672i | ||||
\(343\) | −6.05398 | −0.326884 | ||||||||
\(344\) | 1.56155 | − | 2.70469i | 0.0841933 | − | 0.145827i | ||||
\(345\) | −6.00000 | + | 10.3923i | −0.323029 | + | 0.559503i | ||||
\(346\) | −2.90388 | − | 5.02967i | −0.156114 | − | 0.270397i | ||||
\(347\) | −0.842329 | + | 1.45896i | −0.0452186 | + | 0.0783209i | −0.887749 | − | 0.460328i | \(-0.847732\pi\) |
0.842530 | + | 0.538649i | \(0.181065\pi\) | |||||||
\(348\) | 2.56155 | + | 4.43674i | 0.137314 | + | 0.237834i | ||||
\(349\) | −14.2462 | −0.762582 | −0.381291 | − | 0.924455i | \(-0.624520\pi\) | ||||
−0.381291 | + | 0.924455i | \(0.624520\pi\) | |||||||
\(350\) | −0.438447 | −0.0234360 | ||||||||
\(351\) | −1.43845 | − | 2.49146i | −0.0767786 | − | 0.132984i | ||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 24.1771 | 1.28682 | 0.643408 | − | 0.765523i | \(-0.277520\pi\) | ||||
0.643408 | + | 0.765523i | \(0.277520\pi\) | |||||||
\(354\) | 37.3002 | 1.98248 | ||||||||
\(355\) | −8.12311 | − | 14.0696i | −0.431130 | − | 0.746739i | ||||
\(356\) | 1.34233 | − | 2.32498i | 0.0711433 | − | 0.123224i | ||||
\(357\) | 2.87689 | + | 4.98293i | 0.152261 | + | 0.263724i | ||||
\(358\) | 5.74621 | − | 9.95273i | 0.303697 | − | 0.526018i | ||||
\(359\) | −7.56155 | + | 13.0970i | −0.399083 | + | 0.691233i | −0.993613 | − | 0.112841i | \(-0.964005\pi\) |
0.594530 | + | 0.804074i | \(0.297338\pi\) | |||||||
\(360\) | −3.56155 | −0.187710 | ||||||||
\(361\) | −6.50000 | + | 17.8536i | −0.342105 | + | 0.939662i | ||||
\(362\) | −21.3693 | −1.12315 | ||||||||
\(363\) | −12.8078 | + | 22.1837i | −0.672233 | + | 1.16434i | ||||
\(364\) | 0.438447 | − | 0.759413i | 0.0229809 | − | 0.0398040i | ||||
\(365\) | 0.842329 | + | 1.45896i | 0.0440895 | + | 0.0763653i | ||||
\(366\) | −6.56155 | + | 11.3649i | −0.342978 | + | 0.594055i | ||||
\(367\) | 8.87689 | + | 15.3752i | 0.463370 | + | 0.802581i | 0.999126 | − | 0.0417921i | \(-0.0133067\pi\) |
−0.535756 | + | 0.844373i | \(0.679973\pi\) | |||||||
\(368\) | −4.68466 | −0.244205 | ||||||||
\(369\) | −21.8078 | −1.13527 | ||||||||
\(370\) | −2.34233 | − | 4.05703i | −0.121772 | − | 0.210915i | ||||
\(371\) | 1.65767 | + | 2.87117i | 0.0860620 | + | 0.149064i | ||||
\(372\) | −26.2462 | −1.36080 | ||||||||
\(373\) | −35.8078 | −1.85406 | −0.927028 | − | 0.374992i | \(-0.877645\pi\) | ||||
−0.927028 | + | 0.374992i | \(0.877645\pi\) | |||||||
\(374\) | 2.56155 | + | 4.43674i | 0.132455 | + | 0.229418i | ||||
\(375\) | 1.28078 | − | 2.21837i | 0.0661390 | − | 0.114556i | ||||
\(376\) | 1.43845 | + | 2.49146i | 0.0741822 | + | 0.128487i | ||||
\(377\) | 2.00000 | − | 3.46410i | 0.103005 | − | 0.178410i | ||||
\(378\) | −0.315342 | + | 0.546188i | −0.0162194 | + | 0.0280929i | ||||
\(379\) | −0.492423 | −0.0252940 | −0.0126470 | − | 0.999920i | \(-0.504026\pi\) | ||||
−0.0126470 | + | 0.999920i | \(0.504026\pi\) | |||||||
\(380\) | −2.50000 | − | 3.57071i | −0.128247 | − | 0.183174i | ||||
\(381\) | 39.8617 | 2.04218 | ||||||||
\(382\) | −2.68466 | + | 4.64996i | −0.137359 | + | 0.237913i | ||||
\(383\) | −2.56155 | + | 4.43674i | −0.130889 | + | 0.226707i | −0.924020 | − | 0.382345i | \(-0.875117\pi\) |
0.793130 | + | 0.609052i | \(0.208450\pi\) | |||||||
\(384\) | −1.28078 | − | 2.21837i | −0.0653593 | − | 0.113206i | ||||
\(385\) | −0.219224 | + | 0.379706i | −0.0111727 | + | 0.0193516i | ||||
\(386\) | 12.8078 | + | 22.1837i | 0.651898 | + | 1.12912i | ||||
\(387\) | 11.1231 | 0.565419 | ||||||||
\(388\) | 1.68466 | 0.0855256 | ||||||||
\(389\) | 9.56155 | + | 16.5611i | 0.484790 | + | 0.839681i | 0.999847 | − | 0.0174749i | \(-0.00556271\pi\) |
−0.515057 | + | 0.857156i | \(0.672229\pi\) | |||||||
\(390\) | 2.56155 | + | 4.43674i | 0.129709 | + | 0.224663i | ||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | 6.80776 | 0.343844 | ||||||||
\(393\) | −20.6501 | − | 35.7670i | −1.04166 | − | 1.80421i | ||||
\(394\) | 7.21922 | − | 12.5041i | 0.363699 | − | 0.629946i | ||||
\(395\) | 5.56155 | + | 9.63289i | 0.279832 | + | 0.484683i | ||||
\(396\) | −1.78078 | + | 3.08440i | −0.0894874 | + | 0.154997i | ||||
\(397\) | −14.1501 | + | 24.5087i | −0.710173 | + | 1.23006i | 0.254619 | + | 0.967041i | \(0.418050\pi\) |
−0.964792 | + | 0.263014i | \(0.915283\pi\) | |||||||
\(398\) | 2.87689 | 0.144206 | ||||||||
\(399\) | −4.87689 | + | 0.426450i | −0.244150 | + | 0.0213492i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −13.9654 | + | 24.1888i | −0.697401 | + | 1.20793i | 0.271964 | + | 0.962307i | \(0.412327\pi\) |
−0.969365 | + | 0.245626i | \(0.921007\pi\) | |||||||
\(402\) | −12.0885 | + | 20.9380i | −0.602922 | + | 1.04429i | ||||
\(403\) | 10.2462 | + | 17.7470i | 0.510400 | + | 0.884039i | ||||
\(404\) | −5.00000 | + | 8.66025i | −0.248759 | + | 0.430864i | ||||
\(405\) | 3.50000 | + | 6.06218i | 0.173916 | + | 0.301232i | ||||
\(406\) | −0.876894 | −0.0435195 | ||||||||
\(407\) | −4.68466 | −0.232210 | ||||||||
\(408\) | −6.56155 | − | 11.3649i | −0.324845 | − | 0.562649i | ||||
\(409\) | −10.5000 | − | 18.1865i | −0.519192 | − | 0.899266i | −0.999751 | − | 0.0223042i | \(-0.992900\pi\) |
0.480560 | − | 0.876962i | \(-0.340434\pi\) | |||||||
\(410\) | 6.12311 | 0.302399 | ||||||||
\(411\) | 13.9309 | 0.687159 | ||||||||
\(412\) | 2.90388 | + | 5.02967i | 0.143064 | + | 0.247794i | ||||
\(413\) | −3.19224 | + | 5.52911i | −0.157080 | + | 0.272070i | ||||
\(414\) | −8.34233 | − | 14.4493i | −0.410003 | − | 0.710146i | ||||
\(415\) | 5.40388 | − | 9.35980i | 0.265266 | − | 0.459454i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | −22.5616 | −1.10484 | ||||||||
\(418\) | −4.34233 | + | 0.379706i | −0.212390 | + | 0.0185720i | ||||
\(419\) | −17.5616 | −0.857938 | −0.428969 | − | 0.903319i | \(-0.641123\pi\) | ||||
−0.428969 | + | 0.903319i | \(0.641123\pi\) | |||||||
\(420\) | 0.561553 | − | 0.972638i | 0.0274010 | − | 0.0474599i | ||||
\(421\) | −16.2462 | + | 28.1393i | −0.791792 | + | 1.37142i | 0.133065 | + | 0.991107i | \(0.457518\pi\) |
−0.924856 | + | 0.380316i | \(0.875815\pi\) | |||||||
\(422\) | −1.65767 | − | 2.87117i | −0.0806942 | − | 0.139766i | ||||
\(423\) | −5.12311 | + | 8.87348i | −0.249094 | + | 0.431443i | ||||
\(424\) | −3.78078 | − | 6.54850i | −0.183611 | − | 0.318023i | ||||
\(425\) | 5.12311 | 0.248507 | ||||||||
\(426\) | 41.6155 | 2.01628 | ||||||||
\(427\) | −1.12311 | − | 1.94528i | −0.0543509 | − | 0.0941385i | ||||
\(428\) | −1.12311 | − | 1.94528i | −0.0542874 | − | 0.0940285i | ||||
\(429\) | 5.12311 | 0.247346 | ||||||||
\(430\) | −3.12311 | −0.150610 | ||||||||
\(431\) | 3.68466 | + | 6.38202i | 0.177484 | + | 0.307411i | 0.941018 | − | 0.338356i | \(-0.109871\pi\) |
−0.763534 | + | 0.645767i | \(0.776538\pi\) | |||||||
\(432\) | 0.719224 | − | 1.24573i | 0.0346037 | − | 0.0599353i | ||||
\(433\) | 18.3693 | + | 31.8166i | 0.882773 | + | 1.52901i | 0.848245 | + | 0.529604i | \(0.177659\pi\) |
0.0345280 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(434\) | 2.24621 | − | 3.89055i | 0.107822 | − | 0.186752i | ||||
\(435\) | 2.56155 | − | 4.43674i | 0.122817 | − | 0.212725i | ||||
\(436\) | −14.2462 | −0.682270 | ||||||||
\(437\) | 8.63068 | − | 18.5064i | 0.412862 | − | 0.885280i | ||||
\(438\) | −4.31534 | −0.206195 | ||||||||
\(439\) | 8.24621 | − | 14.2829i | 0.393570 | − | 0.681684i | −0.599347 | − | 0.800489i | \(-0.704573\pi\) |
0.992918 | + | 0.118806i | \(0.0379065\pi\) | |||||||
\(440\) | 0.500000 | − | 0.866025i | 0.0238366 | − | 0.0412861i | ||||
\(441\) | 12.1231 | + | 20.9978i | 0.577291 | + | 0.999897i | ||||
\(442\) | −5.12311 | + | 8.87348i | −0.243681 | + | 0.422068i | ||||
\(443\) | −16.9654 | − | 29.3850i | −0.806052 | − | 1.39612i | −0.915578 | − | 0.402139i | \(-0.868267\pi\) |
0.109526 | − | 0.993984i | \(-0.465067\pi\) | |||||||
\(444\) | 12.0000 | 0.569495 | ||||||||
\(445\) | −2.68466 | −0.127265 | ||||||||
\(446\) | 5.65767 | + | 9.79937i | 0.267898 | + | 0.464014i | ||||
\(447\) | 20.4924 | + | 35.4939i | 0.969258 | + | 1.67880i | ||||
\(448\) | 0.438447 | 0.0207147 | ||||||||
\(449\) | 29.0000 | 1.36859 | 0.684297 | − | 0.729203i | \(-0.260109\pi\) | ||||
0.684297 | + | 0.729203i | \(0.260109\pi\) | |||||||
\(450\) | 1.78078 | + | 3.08440i | 0.0839466 | + | 0.145400i | ||||
\(451\) | 3.06155 | − | 5.30277i | 0.144163 | − | 0.249697i | ||||
\(452\) | 8.40388 | + | 14.5560i | 0.395285 | + | 0.684654i | ||||
\(453\) | 26.2462 | − | 45.4598i | 1.23315 | − | 2.13589i | ||||
\(454\) | 9.96543 | − | 17.2606i | 0.467701 | − | 0.810082i | ||||
\(455\) | −0.876894 | −0.0411094 | ||||||||
\(456\) | 11.1231 | − | 0.972638i | 0.520887 | − | 0.0455479i | ||||
\(457\) | 7.05398 | 0.329971 | 0.164986 | − | 0.986296i | \(-0.447242\pi\) | ||||
0.164986 | + | 0.986296i | \(0.447242\pi\) | |||||||
\(458\) | 6.43845 | − | 11.1517i | 0.300849 | − | 0.521086i | ||||
\(459\) | 3.68466 | − | 6.38202i | 0.171985 | − | 0.297887i | ||||
\(460\) | 2.34233 | + | 4.05703i | 0.109212 | + | 0.189160i | ||||
\(461\) | 19.4924 | − | 33.7619i | 0.907853 | − | 1.57245i | 0.0908110 | − | 0.995868i | \(-0.471054\pi\) |
0.817042 | − | 0.576579i | \(-0.195613\pi\) | |||||||
\(462\) | −0.561553 | − | 0.972638i | −0.0261258 | − | 0.0452512i | ||||
\(463\) | −19.5616 | −0.909102 | −0.454551 | − | 0.890721i | \(-0.650200\pi\) | ||||
−0.454551 | + | 0.890721i | \(0.650200\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | 13.1231 | + | 22.7299i | 0.608569 | + | 1.05407i | ||||
\(466\) | 1.15767 | + | 2.00514i | 0.0536281 | + | 0.0928865i | ||||
\(467\) | 16.5616 | 0.766377 | 0.383189 | − | 0.923670i | \(-0.374826\pi\) | ||||
0.383189 | + | 0.923670i | \(0.374826\pi\) | |||||||
\(468\) | −7.12311 | −0.329266 | ||||||||
\(469\) | −2.06913 | − | 3.58384i | −0.0955436 | − | 0.165486i | ||||
\(470\) | 1.43845 | − | 2.49146i | 0.0663506 | − | 0.114923i | ||||
\(471\) | 3.12311 | + | 5.40938i | 0.143905 | + | 0.249251i | ||||
\(472\) | 7.28078 | − | 12.6107i | 0.335125 | − | 0.580453i | ||||
\(473\) | −1.56155 | + | 2.70469i | −0.0718003 | + | 0.124362i | ||||
\(474\) | −28.4924 | −1.30870 | ||||||||
\(475\) | −1.84233 | + | 3.95042i | −0.0845319 | + | 0.181258i | ||||
\(476\) | 2.24621 | 0.102955 | ||||||||
\(477\) | 13.4654 | − | 23.3228i | 0.616540 | − | 1.06788i | ||||
\(478\) | 9.12311 | − | 15.8017i | 0.417281 | − | 0.722752i | ||||
\(479\) | −14.6847 | − | 25.4346i | −0.670959 | − | 1.16214i | −0.977632 | − | 0.210321i | \(-0.932549\pi\) |
0.306673 | − | 0.951815i | \(-0.400784\pi\) | |||||||
\(480\) | −1.28078 | + | 2.21837i | −0.0584592 | + | 0.101254i | ||||
\(481\) | −4.68466 | − | 8.11407i | −0.213602 | − | 0.369970i | ||||
\(482\) | 8.56155 | 0.389968 | ||||||||
\(483\) | 5.26137 | 0.239400 | ||||||||
\(484\) | 5.00000 | + | 8.66025i | 0.227273 | + | 0.393648i | ||||
\(485\) | −0.842329 | − | 1.45896i | −0.0382482 | − | 0.0662478i | ||||
\(486\) | −22.2462 | −1.00911 | ||||||||
\(487\) | −6.93087 | −0.314068 | −0.157034 | − | 0.987593i | \(-0.550193\pi\) | ||||
−0.157034 | + | 0.987593i | \(0.550193\pi\) | |||||||
\(488\) | 2.56155 | + | 4.43674i | 0.115956 | + | 0.200842i | ||||
\(489\) | 21.8423 | − | 37.8320i | 0.987744 | − | 1.71082i | ||||
\(490\) | −3.40388 | − | 5.89570i | −0.153772 | − | 0.266340i | ||||
\(491\) | 4.58854 | − | 7.94759i | 0.207078 | − | 0.358670i | −0.743715 | − | 0.668497i | \(-0.766938\pi\) |
0.950793 | + | 0.309827i | \(0.100271\pi\) | |||||||
\(492\) | −7.84233 | + | 13.5833i | −0.353560 | + | 0.612383i | ||||
\(493\) | 10.2462 | 0.461466 | ||||||||
\(494\) | −5.00000 | − | 7.14143i | −0.224961 | − | 0.321308i | ||||
\(495\) | 3.56155 | 0.160080 | ||||||||
\(496\) | −5.12311 | + | 8.87348i | −0.230034 | + | 0.398431i | ||||
\(497\) | −3.56155 | + | 6.16879i | −0.159757 | + | 0.276708i | ||||
\(498\) | 13.8423 | + | 23.9756i | 0.620290 | + | 1.07437i | ||||
\(499\) | −14.5000 | + | 25.1147i | −0.649109 | + | 1.12429i | 0.334227 | + | 0.942493i | \(0.391525\pi\) |
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −1.75379 | −0.0783535 | ||||||||
\(502\) | −25.9309 | −1.15735 | ||||||||
\(503\) | −13.7116 | − | 23.7493i | −0.611372 | − | 1.05893i | −0.991009 | − | 0.133792i | \(-0.957285\pi\) |
0.379637 | − | 0.925135i | \(-0.376049\pi\) | |||||||
\(504\) | 0.780776 | + | 1.35234i | 0.0347785 | + | 0.0602382i | ||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 4.68466 | 0.208258 | ||||||||
\(507\) | −11.5270 | − | 19.9653i | −0.511931 | − | 0.886691i | ||||
\(508\) | 7.78078 | − | 13.4767i | 0.345216 | − | 0.597932i | ||||
\(509\) | 0.438447 | + | 0.759413i | 0.0194338 | + | 0.0336604i | 0.875579 | − | 0.483075i | \(-0.160480\pi\) |
−0.856145 | + | 0.516736i | \(0.827147\pi\) | |||||||
\(510\) | −6.56155 | + | 11.3649i | −0.290550 | + | 0.503248i | ||||
\(511\) | 0.369317 | − | 0.639676i | 0.0163376 | − | 0.0282976i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.59612 | + | 5.13628i | 0.158772 | + | 0.226772i | ||||
\(514\) | −13.0540 | −0.575786 | ||||||||
\(515\) | 2.90388 | − | 5.02967i | 0.127960 | − | 0.221634i | ||||
\(516\) | 4.00000 | − | 6.92820i | 0.176090 | − | 0.304997i | ||||
\(517\) | −1.43845 | − | 2.49146i | −0.0632628 | − | 0.109574i | ||||
\(518\) | −1.02699 | + | 1.77879i | −0.0451232 | + | 0.0781558i | ||||
\(519\) | −7.43845 | − | 12.8838i | −0.326512 | − | 0.565535i | ||||
\(520\) | 2.00000 | 0.0877058 | ||||||||
\(521\) | −22.8078 | −0.999226 | −0.499613 | − | 0.866249i | \(-0.666524\pi\) | ||||
−0.499613 | + | 0.866249i | \(0.666524\pi\) | |||||||
\(522\) | 3.56155 | + | 6.16879i | 0.155885 | + | 0.270001i | ||||
\(523\) | −7.31534 | − | 12.6705i | −0.319878 | − | 0.554044i | 0.660585 | − | 0.750752i | \(-0.270308\pi\) |
−0.980462 | + | 0.196707i | \(0.936975\pi\) | |||||||
\(524\) | −16.1231 | −0.704341 | ||||||||
\(525\) | −1.12311 | −0.0490163 | ||||||||
\(526\) | −1.09612 | − | 1.89853i | −0.0477930 | − | 0.0827799i | ||||
\(527\) | −26.2462 | + | 45.4598i | −1.14330 | + | 1.98026i | ||||
\(528\) | 1.28078 | + | 2.21837i | 0.0557386 | + | 0.0965422i | ||||
\(529\) | 0.526988 | − | 0.912769i | 0.0229125 | − | 0.0396856i | ||||
\(530\) | −3.78078 | + | 6.54850i | −0.164226 | + | 0.284449i | ||||
\(531\) | 51.8617 | 2.25061 | ||||||||
\(532\) | −0.807764 | + | 1.73205i | −0.0350210 | + | 0.0750939i | ||||
\(533\) | 12.2462 | 0.530442 | ||||||||
\(534\) | 3.43845 | − | 5.95557i | 0.148796 | − | 0.257723i | ||||
\(535\) | −1.12311 | + | 1.94528i | −0.0485561 | + | 0.0841016i | ||||
\(536\) | 4.71922 | + | 8.17394i | 0.203839 | + | 0.353060i | ||||
\(537\) | 14.7192 | − | 25.4944i | 0.635181 | − | 1.10017i | ||||
\(538\) | 2.00000 | + | 3.46410i | 0.0862261 | + | 0.149348i | ||||
\(539\) | −6.80776 | −0.293231 | ||||||||
\(540\) | −1.43845 | −0.0619009 | ||||||||
\(541\) | 14.2462 | + | 24.6752i | 0.612492 | + | 1.06087i | 0.990819 | + | 0.135196i | \(0.0431664\pi\) |
−0.378326 | + | 0.925672i | \(0.623500\pi\) | |||||||
\(542\) | −4.12311 | − | 7.14143i | −0.177103 | − | 0.306751i | ||||
\(543\) | −54.7386 | −2.34906 | ||||||||
\(544\) | −5.12311 | −0.219651 | ||||||||
\(545\) | 7.12311 | + | 12.3376i | 0.305120 | + | 0.528484i | ||||
\(546\) | 1.12311 | − | 1.94528i | 0.0480645 | − | 0.0832501i | ||||
\(547\) | 2.43845 | + | 4.22351i | 0.104260 | + | 0.180584i | 0.913436 | − | 0.406983i | \(-0.133419\pi\) |
−0.809175 | + | 0.587567i | \(0.800086\pi\) | |||||||
\(548\) | 2.71922 | − | 4.70983i | 0.116159 | − | 0.201194i | ||||
\(549\) | −9.12311 | + | 15.8017i | −0.389365 | + | 0.674399i | ||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −3.68466 | + | 7.90084i | −0.156972 | + | 0.336587i | ||||
\(552\) | −12.0000 | −0.510754 | ||||||||
\(553\) | 2.43845 | − | 4.22351i | 0.103693 | − | 0.179602i | ||||
\(554\) | 2.12311 | − | 3.67733i | 0.0902021 | − | 0.156235i | ||||
\(555\) | −6.00000 | − | 10.3923i | −0.254686 | − | 0.441129i | ||||
\(556\) | −4.40388 | + | 7.62775i | −0.186766 | + | 0.323489i | ||||
\(557\) | −20.8348 | − | 36.0868i | −0.882797 | − | 1.52905i | −0.848218 | − | 0.529647i | \(-0.822324\pi\) |
−0.0345785 | − | 0.999402i | \(-0.511009\pi\) | |||||||
\(558\) | −36.4924 | −1.54485 | ||||||||
\(559\) | −6.24621 | −0.264187 | ||||||||
\(560\) | −0.219224 | − | 0.379706i | −0.00926389 | − | 0.0160455i | ||||
\(561\) | 6.56155 | + | 11.3649i | 0.277029 | + | 0.479828i | ||||
\(562\) | −8.36932 | −0.353038 | ||||||||
\(563\) | 21.3002 | 0.897696 | 0.448848 | − | 0.893608i | \(-0.351834\pi\) | ||||
0.448848 | + | 0.893608i | \(0.351834\pi\) | |||||||
\(564\) | 3.68466 | + | 6.38202i | 0.155152 | + | 0.268731i | ||||
\(565\) | 8.40388 | − | 14.5560i | 0.353554 | − | 0.612373i | ||||
\(566\) | −9.71922 | − | 16.8342i | −0.408529 | − | 0.707594i | ||||
\(567\) | 1.53457 | − | 2.65794i | 0.0644457 | − | 0.111623i | ||||
\(568\) | 8.12311 | − | 14.0696i | 0.340838 | − | 0.590349i | ||||
\(569\) | −11.1771 | −0.468568 | −0.234284 | − | 0.972168i | \(-0.575274\pi\) | ||||
−0.234284 | + | 0.972168i | \(0.575274\pi\) | |||||||
\(570\) | −6.40388 | − | 9.14657i | −0.268229 | − | 0.383108i | ||||
\(571\) | −4.80776 | −0.201199 | −0.100599 | − | 0.994927i | \(-0.532076\pi\) | ||||
−0.100599 | + | 0.994927i | \(0.532076\pi\) | |||||||
\(572\) | 1.00000 | − | 1.73205i | 0.0418121 | − | 0.0724207i | ||||
\(573\) | −6.87689 | + | 11.9111i | −0.287286 | + | 0.497595i | ||||
\(574\) | −1.34233 | − | 2.32498i | −0.0560277 | − | 0.0970429i | ||||
\(575\) | 2.34233 | − | 4.05703i | 0.0976819 | − | 0.169190i | ||||
\(576\) | −1.78078 | − | 3.08440i | −0.0741990 | − | 0.128516i | ||||
\(577\) | −16.3153 | −0.679217 | −0.339608 | − | 0.940567i | \(-0.610295\pi\) | ||||
−0.339608 | + | 0.940567i | \(0.610295\pi\) | |||||||
\(578\) | −9.24621 | −0.384592 | ||||||||
\(579\) | 32.8078 | + | 56.8247i | 1.36344 | + | 2.36155i | ||||
\(580\) | −1.00000 | − | 1.73205i | −0.0415227 | − | 0.0719195i | ||||
\(581\) | −4.73863 | −0.196592 | ||||||||
\(582\) | 4.31534 | 0.178877 | ||||||||
\(583\) | 3.78078 | + | 6.54850i | 0.156584 | + | 0.271211i | ||||
\(584\) | −0.842329 | + | 1.45896i | −0.0348558 | + | 0.0603721i | ||||
\(585\) | 3.56155 | + | 6.16879i | 0.147252 | + | 0.255048i | ||||
\(586\) | 11.7808 | − | 20.4049i | 0.486659 | − | 0.842919i | ||||
\(587\) | −13.3693 | + | 23.1563i | −0.551811 | + | 0.955764i | 0.446333 | + | 0.894867i | \(0.352730\pi\) |
−0.998144 | + | 0.0608975i | \(0.980604\pi\) | |||||||
\(588\) | 17.4384 | 0.719149 | ||||||||
\(589\) | −25.6155 | − | 36.5863i | −1.05547 | − | 1.50751i | ||||
\(590\) | −14.5616 | −0.599490 | ||||||||
\(591\) | 18.4924 | − | 32.0298i | 0.760677 | − | 1.31753i | ||||
\(592\) | 2.34233 | − | 4.05703i | 0.0962691 | − | 0.166743i | ||||
\(593\) | −12.7732 | − | 22.1238i | −0.524532 | − | 0.908517i | −0.999592 | − | 0.0285632i | \(-0.990907\pi\) |
0.475060 | − | 0.879954i | \(-0.342427\pi\) | |||||||
\(594\) | −0.719224 | + | 1.24573i | −0.0295101 | + | 0.0511130i | ||||
\(595\) | −1.12311 | − | 1.94528i | −0.0460428 | − | 0.0797485i | ||||
\(596\) | 16.0000 | 0.655386 | ||||||||
\(597\) | 7.36932 | 0.301606 | ||||||||
\(598\) | 4.68466 | + | 8.11407i | 0.191570 | + | 0.331809i | ||||
\(599\) | 16.2462 | + | 28.1393i | 0.663802 | + | 1.14974i | 0.979609 | + | 0.200915i | \(0.0643917\pi\) |
−0.315806 | + | 0.948824i | \(0.602275\pi\) | |||||||
\(600\) | 2.56155 | 0.104575 | ||||||||
\(601\) | −11.6307 | −0.474425 | −0.237213 | − | 0.971458i | \(-0.576234\pi\) | ||||
−0.237213 | + | 0.971458i | \(0.576234\pi\) | |||||||
\(602\) | 0.684658 | + | 1.18586i | 0.0279046 | + | 0.0483322i | ||||
\(603\) | −16.8078 | + | 29.1119i | −0.684465 | + | 1.18553i | ||||
\(604\) | −10.2462 | − | 17.7470i | −0.416912 | − | 0.722113i | ||||
\(605\) | 5.00000 | − | 8.66025i | 0.203279 | − | 0.352089i | ||||
\(606\) | −12.8078 | + | 22.1837i | −0.520280 | + | 0.901151i | ||||
\(607\) | 10.1922 | 0.413690 | 0.206845 | − | 0.978374i | \(-0.433680\pi\) | ||||
0.206845 | + | 0.978374i | \(0.433680\pi\) | |||||||
\(608\) | 1.84233 | − | 3.95042i | 0.0747163 | − | 0.160211i | ||||
\(609\) | −2.24621 | −0.0910211 | ||||||||
\(610\) | 2.56155 | − | 4.43674i | 0.103714 | − | 0.179638i | ||||
\(611\) | 2.87689 | − | 4.98293i | 0.116387 | − | 0.201588i | ||||
\(612\) | −9.12311 | − | 15.8017i | −0.368780 | − | 0.638745i | ||||
\(613\) | −15.3423 | + | 26.5737i | −0.619671 | + | 1.07330i | 0.369875 | + | 0.929082i | \(0.379401\pi\) |
−0.989546 | + | 0.144220i | \(0.953933\pi\) | |||||||
\(614\) | −11.9654 | − | 20.7247i | −0.482886 | − | 0.836382i | ||||
\(615\) | 15.6847 | 0.632466 | ||||||||
\(616\) | −0.438447 | −0.0176655 | ||||||||
\(617\) | −3.59612 | − | 6.22866i | −0.144774 | − | 0.250756i | 0.784514 | − | 0.620111i | \(-0.212912\pi\) |
−0.929289 | + | 0.369354i | \(0.879579\pi\) | |||||||
\(618\) | 7.43845 | + | 12.8838i | 0.299218 | + | 0.518261i | ||||
\(619\) | 26.0540 | 1.04720 | 0.523599 | − | 0.851965i | \(-0.324589\pi\) | ||||
0.523599 | + | 0.851965i | \(0.324589\pi\) | |||||||
\(620\) | 10.2462 | 0.411498 | ||||||||
\(621\) | −3.36932 | − | 5.83583i | −0.135206 | − | 0.234184i | ||||
\(622\) | 2.00000 | − | 3.46410i | 0.0801927 | − | 0.138898i | ||||
\(623\) | 0.588540 | + | 1.01938i | 0.0235794 | + | 0.0408407i | ||||
\(624\) | −2.56155 | + | 4.43674i | −0.102544 | + | 0.177612i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4.31534 | −0.172476 | ||||||||
\(627\) | −11.1231 | + | 0.972638i | −0.444214 | + | 0.0388434i | ||||
\(628\) | 2.43845 | 0.0973046 | ||||||||
\(629\) | 12.0000 | − | 20.7846i | 0.478471 | − | 0.828737i | ||||
\(630\) | 0.780776 | − | 1.35234i | 0.0311069 | − | 0.0538787i | ||||
\(631\) | −2.12311 | − | 3.67733i | −0.0845195 | − | 0.146392i | 0.820667 | − | 0.571407i | \(-0.193602\pi\) |
−0.905186 | + | 0.425015i | \(0.860269\pi\) | |||||||
\(632\) | −5.56155 | + | 9.63289i | −0.221227 | + | 0.383176i | ||||
\(633\) | −4.24621 | − | 7.35465i | −0.168772 | − | 0.292321i | ||||
\(634\) | −18.6847 | −0.742063 | ||||||||
\(635\) | −15.5616 | −0.617541 | ||||||||
\(636\) | −9.68466 | − | 16.7743i | −0.384022 | − | 0.665145i | ||||
\(637\) | −6.80776 | − | 11.7914i | −0.269733 | − | 0.467192i | ||||
\(638\) | −2.00000 | −0.0791808 | ||||||||
\(639\) | 57.8617 | 2.28898 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −3.71922 | + | 6.44188i | −0.146900 | + | 0.254439i | −0.930080 | − | 0.367356i | \(-0.880263\pi\) |
0.783180 | + | 0.621795i | \(0.213596\pi\) | |||||||
\(642\) | −2.87689 | − | 4.98293i | −0.113542 | − | 0.196660i | ||||
\(643\) | 11.2808 | − | 19.5389i | 0.444870 | − | 0.770538i | −0.553173 | − | 0.833067i | \(-0.686583\pi\) |
0.998043 | + | 0.0625284i | \(0.0199164\pi\) | |||||||
\(644\) | 1.02699 | − | 1.77879i | 0.0404690 | − | 0.0700943i | ||||
\(645\) | −8.00000 | −0.315000 | ||||||||
\(646\) | 9.43845 | − | 20.2384i | 0.371351 | − | 0.796270i | ||||
\(647\) | 3.17708 | 0.124904 | 0.0624520 | − | 0.998048i | \(-0.480108\pi\) | ||||
0.0624520 | + | 0.998048i | \(0.480108\pi\) | |||||||
\(648\) | −3.50000 | + | 6.06218i | −0.137493 | + | 0.238145i | ||||
\(649\) | −7.28078 | + | 12.6107i | −0.285795 | + | 0.495012i | ||||
\(650\) | −1.00000 | − | 1.73205i | −0.0392232 | − | 0.0679366i | ||||
\(651\) | 5.75379 | − | 9.96585i | 0.225509 | − | 0.390593i | ||||
\(652\) | −8.52699 | − | 14.7692i | −0.333943 | − | 0.578406i | ||||
\(653\) | −5.06913 | −0.198370 | −0.0991852 | − | 0.995069i | \(-0.531624\pi\) | ||||
−0.0991852 | + | 0.995069i | \(0.531624\pi\) | |||||||
\(654\) | −36.4924 | −1.42697 | ||||||||
\(655\) | 8.06155 | + | 13.9630i | 0.314991 | + | 0.545580i | ||||
\(656\) | 3.06155 | + | 5.30277i | 0.119534 | + | 0.207038i | ||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −1.26137 | −0.0491732 | ||||||||
\(659\) | −9.46543 | − | 16.3946i | −0.368721 | − | 0.638643i | 0.620645 | − | 0.784092i | \(-0.286871\pi\) |
−0.989366 | + | 0.145448i | \(0.953538\pi\) | |||||||
\(660\) | 1.28078 | − | 2.21837i | 0.0498542 | − | 0.0863499i | ||||
\(661\) | 19.9309 | + | 34.5213i | 0.775221 | + | 1.34272i | 0.934670 | + | 0.355516i | \(0.115695\pi\) |
−0.159449 | + | 0.987206i | \(0.550972\pi\) | |||||||
\(662\) | 11.7462 | − | 20.3450i | 0.456529 | − | 0.790732i | ||||
\(663\) | −13.1231 | + | 22.7299i | −0.509659 | + | 0.882756i | ||||
\(664\) | 10.8078 | 0.419423 | ||||||||
\(665\) | 1.90388 | − | 0.166481i | 0.0738294 | − | 0.00645586i | ||||
\(666\) | 16.6847 | 0.646517 | ||||||||
\(667\) | 4.68466 | − | 8.11407i | 0.181391 | − | 0.314178i | ||||
\(668\) | −0.342329 | + | 0.592932i | −0.0132451 | + | 0.0229412i | ||||
\(669\) | 14.4924 | + | 25.1016i | 0.560309 | + | 0.970484i | ||||
\(670\) | 4.71922 | − | 8.17394i | 0.182320 | − | 0.315787i | ||||
\(671\) | −2.56155 | − | 4.43674i | −0.0988876 | − | 0.171278i | ||||
\(672\) | 1.12311 | 0.0433247 | ||||||||
\(673\) | 46.1080 | 1.77733 | 0.888665 | − | 0.458556i | \(-0.151633\pi\) | ||||
0.888665 | + | 0.458556i | \(0.151633\pi\) | |||||||
\(674\) | 10.5270 | + | 18.2333i | 0.405484 | + | 0.702320i | ||||
\(675\) | 0.719224 | + | 1.24573i | 0.0276829 | + | 0.0479482i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −23.1771 | −0.890768 | −0.445384 | − | 0.895340i | \(-0.646933\pi\) | ||||
−0.445384 | + | 0.895340i | \(0.646933\pi\) | |||||||
\(678\) | 21.5270 | + | 37.2858i | 0.826739 | + | 1.43195i | ||||
\(679\) | −0.369317 | + | 0.639676i | −0.0141731 | + | 0.0245485i | ||||
\(680\) | 2.56155 | + | 4.43674i | 0.0982311 | + | 0.170141i | ||||
\(681\) | 25.5270 | − | 44.2140i | 0.978196 | − | 1.69429i | ||||
\(682\) | 5.12311 | − | 8.87348i | 0.196174 | − | 0.339783i | ||||
\(683\) | 28.0000 | 1.07139 | 0.535695 | − | 0.844411i | \(-0.320050\pi\) | ||||
0.535695 | + | 0.844411i | \(0.320050\pi\) | |||||||
\(684\) | 15.4654 | − | 1.35234i | 0.591336 | − | 0.0517082i | ||||
\(685\) | −5.43845 | −0.207792 | ||||||||
\(686\) | −3.02699 | + | 5.24290i | −0.115571 | + | 0.200175i | ||||
\(687\) | 16.4924 | − | 28.5657i | 0.629225 | − | 1.08985i | ||||
\(688\) | −1.56155 | − | 2.70469i | −0.0595336 | − | 0.103115i | ||||
\(689\) | −7.56155 | + | 13.0970i | −0.288072 | + | 0.498956i | ||||
\(690\) | 6.00000 | + | 10.3923i | 0.228416 | + | 0.395628i | ||||
\(691\) | −21.0691 | −0.801507 | −0.400754 | − | 0.916186i | \(-0.631252\pi\) | ||||
−0.400754 | + | 0.916186i | \(0.631252\pi\) | |||||||
\(692\) | −5.80776 | −0.220778 | ||||||||
\(693\) | −0.780776 | − | 1.35234i | −0.0296592 | − | 0.0513713i | ||||
\(694\) | 0.842329 | + | 1.45896i | 0.0319744 | + | 0.0553813i | ||||
\(695\) | 8.80776 | 0.334098 | ||||||||
\(696\) | 5.12311 | 0.194191 | ||||||||
\(697\) | 15.6847 | + | 27.1666i | 0.594099 | + | 1.02901i | ||||
\(698\) | −7.12311 | + | 12.3376i | −0.269614 | + | 0.466984i | ||||
\(699\) | 2.96543 | + | 5.13628i | 0.112163 | + | 0.194272i | ||||
\(700\) | −0.219224 | + | 0.379706i | −0.00828587 | + | 0.0143516i | ||||
\(701\) | −3.24621 | + | 5.62260i | −0.122608 | + | 0.212363i | −0.920795 | − | 0.390046i | \(-0.872459\pi\) |
0.798188 | + | 0.602409i | \(0.205792\pi\) | |||||||
\(702\) | −2.87689 | −0.108581 | ||||||||
\(703\) | 11.7116 | + | 16.7276i | 0.441713 | + | 0.630892i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 3.68466 | − | 6.38202i | 0.138772 | − | 0.240361i | ||||
\(706\) | 12.0885 | − | 20.9380i | 0.454958 | − | 0.788011i | ||||
\(707\) | −2.19224 | − | 3.79706i | −0.0824475 | − | 0.142803i | ||||
\(708\) | 18.6501 | − | 32.3029i | 0.700913 | − | 1.21402i | ||||
\(709\) | 20.0000 | + | 34.6410i | 0.751116 | + | 1.30097i | 0.947282 | + | 0.320400i | \(0.103817\pi\) |
−0.196167 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(710\) | −16.2462 | −0.609709 | ||||||||
\(711\) | −39.6155 | −1.48570 | ||||||||
\(712\) | −1.34233 | − | 2.32498i | −0.0503059 | − | 0.0871324i | ||||
\(713\) | 24.0000 | + | 41.5692i | 0.898807 | + | 1.55678i | ||||
\(714\) | 5.75379 | 0.215330 | ||||||||
\(715\) | −2.00000 | −0.0747958 | ||||||||
\(716\) | −5.74621 | − | 9.95273i | −0.214746 | − | 0.371951i | ||||
\(717\) | 23.3693 | − | 40.4768i | 0.872743 | − | 1.51164i | ||||
\(718\) | 7.56155 | + | 13.0970i | 0.282195 | + | 0.488775i | ||||
\(719\) | −7.43845 | + | 12.8838i | −0.277407 | + | 0.480483i | −0.970740 | − | 0.240134i | \(-0.922808\pi\) |
0.693332 | + | 0.720618i | \(0.256142\pi\) | |||||||
\(720\) | −1.78078 | + | 3.08440i | −0.0663656 | + | 0.114949i | ||||
\(721\) | −2.54640 | −0.0948328 | ||||||||
\(722\) | 12.2116 | + | 14.5560i | 0.454470 | + | 0.541716i | ||||
\(723\) | 21.9309 | 0.815618 | ||||||||
\(724\) | −10.6847 | + | 18.5064i | −0.397092 | + | 0.687784i | ||||
\(725\) | −1.00000 | + | 1.73205i | −0.0371391 | + | 0.0643268i | ||||
\(726\) | 12.8078 | + | 22.1837i | 0.475341 | + | 0.823314i | ||||
\(727\) | 4.00000 | − | 6.92820i | 0.148352 | − | 0.256953i | −0.782267 | − | 0.622944i | \(-0.785937\pi\) |
0.930618 | + | 0.365991i | \(0.119270\pi\) | |||||||
\(728\) | −0.438447 | − | 0.759413i | −0.0162499 | − | 0.0281457i | ||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 1.68466 | 0.0623520 | ||||||||
\(731\) | −8.00000 | − | 13.8564i | −0.295891 | − | 0.512498i | ||||
\(732\) | 6.56155 | + | 11.3649i | 0.242522 | + | 0.420060i | ||||
\(733\) | −26.9309 | −0.994714 | −0.497357 | − | 0.867546i | \(-0.665696\pi\) | ||||
−0.497357 | + | 0.867546i | \(0.665696\pi\) | |||||||
\(734\) | 17.7538 | 0.655304 | ||||||||
\(735\) | −8.71922 | − | 15.1021i | −0.321613 | − | 0.557051i | ||||
\(736\) | −2.34233 | + | 4.05703i | −0.0863394 | + | 0.149544i | ||||
\(737\) | −4.71922 | − | 8.17394i | −0.173835 | − | 0.301091i | ||||
\(738\) | −10.9039 | + | 18.8861i | −0.401377 | + | 0.695206i | ||||
\(739\) | −9.37689 | + | 16.2413i | −0.344935 | + | 0.597444i | −0.985342 | − | 0.170591i | \(-0.945432\pi\) |
0.640407 | + | 0.768036i | \(0.278766\pi\) | |||||||
\(740\) | −4.68466 | −0.172211 | ||||||||
\(741\) | −12.8078 | − | 18.2931i | −0.470505 | − | 0.672016i | ||||
\(742\) | 3.31534 | 0.121710 | ||||||||
\(743\) | 9.21922 | − | 15.9682i | 0.338221 | − | 0.585815i | −0.645878 | − | 0.763441i | \(-0.723508\pi\) |
0.984098 | + | 0.177626i | \(0.0568417\pi\) | |||||||
\(744\) | −13.1231 | + | 22.7299i | −0.481116 | + | 0.833318i | ||||
\(745\) | −8.00000 | − | 13.8564i | −0.293097 | − | 0.507659i | ||||
\(746\) | −17.9039 | + | 31.0104i | −0.655508 | + | 1.13537i | ||||
\(747\) | 19.2462 | + | 33.3354i | 0.704182 | + | 1.21968i | ||||
\(748\) | 5.12311 | 0.187319 | ||||||||
\(749\) | 0.984845 | 0.0359855 | ||||||||
\(750\) | −1.28078 | − | 2.21837i | −0.0467673 | − | 0.0810034i | ||||
\(751\) | 17.4384 | + | 30.2043i | 0.636338 | + | 1.10217i | 0.986230 | + | 0.165380i | \(0.0528849\pi\) |
−0.349892 | + | 0.936790i | \(0.613782\pi\) | |||||||
\(752\) | 2.87689 | 0.104910 | ||||||||
\(753\) | −66.4233 | −2.42060 | ||||||||
\(754\) | −2.00000 | − | 3.46410i | −0.0728357 | − | 0.126155i | ||||
\(755\) | −10.2462 | + | 17.7470i | −0.372898 | + | 0.645878i | ||||
\(756\) | 0.315342 | + | 0.546188i | 0.0114689 | + | 0.0198647i | ||||
\(757\) | 9.78078 | − | 16.9408i | 0.355488 | − | 0.615724i | −0.631713 | − | 0.775202i | \(-0.717648\pi\) |
0.987201 | + | 0.159478i | \(0.0509812\pi\) | |||||||
\(758\) | −0.246211 | + | 0.426450i | −0.00894280 | + | 0.0154894i | ||||
\(759\) | 12.0000 | 0.435572 | ||||||||
\(760\) | −4.34233 | + | 0.379706i | −0.157513 | + | 0.0137734i | ||||
\(761\) | −51.9848 | −1.88445 | −0.942225 | − | 0.334982i | \(-0.891270\pi\) | ||||
−0.942225 | + | 0.334982i | \(0.891270\pi\) | |||||||
\(762\) | 19.9309 | − | 34.5213i | 0.722019 | − | 1.25057i | ||||
\(763\) | 3.12311 | − | 5.40938i | 0.113064 | − | 0.195833i | ||||
\(764\) | 2.68466 | + | 4.64996i | 0.0971275 | + | 0.168230i | ||||
\(765\) | −9.12311 | + | 15.8017i | −0.329847 | + | 0.571311i | ||||
\(766\) | 2.56155 | + | 4.43674i | 0.0925527 | + | 0.160306i | ||||
\(767\) | −29.1231 | −1.05157 | ||||||||
\(768\) | −2.56155 | −0.0924321 | ||||||||
\(769\) | −13.2462 | − | 22.9431i | −0.477671 | − | 0.827350i | 0.522002 | − | 0.852944i | \(-0.325185\pi\) |
−0.999672 | + | 0.0255946i | \(0.991852\pi\) | |||||||
\(770\) | 0.219224 | + | 0.379706i | 0.00790027 | + | 0.0136837i | ||||
\(771\) | −33.4384 | −1.20426 | ||||||||
\(772\) | 25.6155 | 0.921923 | ||||||||
\(773\) | 7.15009 | + | 12.3843i | 0.257171 | + | 0.445433i | 0.965483 | − | 0.260466i | \(-0.0838763\pi\) |
−0.708312 | + | 0.705900i | \(0.750543\pi\) | |||||||
\(774\) | 5.56155 | − | 9.63289i | 0.199906 | − | 0.346247i | ||||
\(775\) | −5.12311 | − | 8.87348i | −0.184027 | − | 0.318745i | ||||
\(776\) | 0.842329 | − | 1.45896i | 0.0302379 | − | 0.0523735i | ||||
\(777\) | −2.63068 | + | 4.55648i | −0.0943752 | + | 0.163463i | ||||
\(778\) | 19.1231 | 0.685597 | ||||||||
\(779\) | −26.5885 | + | 2.32498i | −0.952633 | + | 0.0833011i | ||||
\(780\) | 5.12311 | 0.183437 | ||||||||
\(781\) | −8.12311 | + | 14.0696i | −0.290668 | + | 0.503451i | ||||
\(782\) | −12.0000 | + | 20.7846i | −0.429119 | + | 0.743256i | ||||
\(783\) | 1.43845 | + | 2.49146i | 0.0514059 | + | 0.0890376i | ||||
\(784\) | 3.40388 | − | 5.89570i | 0.121567 | − | 0.210561i | ||||
\(785\) | −1.21922 | − | 2.11176i | −0.0435160 | − | 0.0753718i | ||||
\(786\) | −41.3002 | −1.47313 | ||||||||
\(787\) | 8.56155 | 0.305186 | 0.152593 | − | 0.988289i | \(-0.451238\pi\) | ||||
0.152593 | + | 0.988289i | \(0.451238\pi\) | |||||||
\(788\) | −7.21922 | − | 12.5041i | −0.257174 | − | 0.445439i | ||||
\(789\) | −2.80776 | − | 4.86319i | −0.0999590 | − | 0.173134i | ||||
\(790\) | 11.1231 | 0.395742 | ||||||||
\(791\) | −7.36932 | −0.262023 | ||||||||
\(792\) | 1.78078 | + | 3.08440i | 0.0632771 | + | 0.109599i | ||||
\(793\) | 5.12311 | − | 8.87348i | 0.181927 | − | 0.315106i | ||||
\(794\) | 14.1501 | + | 24.5087i | 0.502168 | + | 0.869781i | ||||
\(795\) | −9.68466 | + | 16.7743i | −0.343479 | + | 0.594924i | ||||
\(796\) | 1.43845 | − | 2.49146i | 0.0509844 | − | 0.0883076i | ||||
\(797\) | −4.19224 | −0.148497 | −0.0742483 | − | 0.997240i | \(-0.523656\pi\) | ||||
−0.0742483 | + | 0.997240i | \(0.523656\pi\) | |||||||
\(798\) | −2.06913 | + | 4.43674i | −0.0732464 | + | 0.157059i | ||||
\(799\) | 14.7386 | 0.521415 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 4.78078 | − | 8.28055i | 0.168920 | − | 0.292579i | ||||
\(802\) | 13.9654 | + | 24.1888i | 0.493137 | + | 0.854138i | ||||
\(803\) | 0.842329 | − | 1.45896i | 0.0297252 | − | 0.0514855i | ||||
\(804\) | 12.0885 | + | 20.9380i | 0.426330 | + | 0.738425i | ||||
\(805\) | −2.05398 | −0.0723931 | ||||||||
\(806\) | 20.4924 | 0.721815 | ||||||||
\(807\) | 5.12311 | + | 8.87348i | 0.180342 | + | 0.312361i | ||||
\(808\) | 5.00000 | + | 8.66025i | 0.175899 | + | 0.304667i | ||||
\(809\) | 23.4384 | 0.824052 | 0.412026 | − | 0.911172i | \(-0.364821\pi\) | ||||
0.412026 | + | 0.911172i | \(0.364821\pi\) | |||||||
\(810\) | 7.00000 | 0.245955 | ||||||||
\(811\) | 4.58854 | + | 7.94759i | 0.161125 | + | 0.279077i | 0.935273 | − | 0.353928i | \(-0.115154\pi\) |
−0.774147 | + | 0.633006i | \(0.781821\pi\) | |||||||
\(812\) | −0.438447 | + | 0.759413i | −0.0153865 | + | 0.0266502i | ||||
\(813\) | −10.5616 | − | 18.2931i | −0.370410 | − | 0.641569i | ||||
\(814\) | −2.34233 | + | 4.05703i | −0.0820986 | + | 0.142199i | ||||
\(815\) | −8.52699 | + | 14.7692i | −0.298687 | + | 0.517342i | ||||
\(816\) | −13.1231 | −0.459401 | ||||||||
\(817\) | 13.5616 | − | 1.18586i | 0.474459 | − | 0.0414881i | ||||
\(818\) | −21.0000 | −0.734248 | ||||||||
\(819\) | 1.56155 | − | 2.70469i | 0.0545651 | − | 0.0945095i | ||||
\(820\) | 3.06155 | − | 5.30277i | 0.106914 | − | 0.185181i | ||||
\(821\) | 7.00000 | + | 12.1244i | 0.244302 | + | 0.423143i | 0.961935 | − | 0.273278i | \(-0.0881079\pi\) |
−0.717633 | + | 0.696421i | \(0.754775\pi\) | |||||||
\(822\) | 6.96543 | − | 12.0645i | 0.242947 | − | 0.420797i | ||||
\(823\) | 13.5885 | + | 23.5360i | 0.473667 | + | 0.820415i | 0.999546 | − | 0.0301446i | \(-0.00959679\pi\) |
−0.525879 | + | 0.850560i | \(0.676263\pi\) | |||||||
\(824\) | 5.80776 | 0.202323 | ||||||||
\(825\) | −2.56155 | −0.0891818 | ||||||||
\(826\) | 3.19224 | + | 5.52911i | 0.111072 | + | 0.192383i | ||||
\(827\) | 15.9654 | + | 27.6529i | 0.555173 | + | 0.961587i | 0.997890 | + | 0.0649260i | \(0.0206811\pi\) |
−0.442718 | + | 0.896661i | \(0.645986\pi\) | |||||||
\(828\) | −16.6847 | −0.579832 | ||||||||
\(829\) | 26.7386 | 0.928671 | 0.464336 | − | 0.885659i | \(-0.346293\pi\) | ||||
0.464336 | + | 0.885659i | \(0.346293\pi\) | |||||||
\(830\) | −5.40388 | − | 9.35980i | −0.187571 | − | 0.324883i | ||||
\(831\) | 5.43845 | − | 9.41967i | 0.188658 | − | 0.326765i | ||||
\(832\) | 1.00000 | + | 1.73205i | 0.0346688 | + | 0.0600481i | ||||
\(833\) | 17.4384 | − | 30.2043i | 0.604206 | − | 1.04652i | ||||
\(834\) | −11.2808 | + | 19.5389i | −0.390621 | + | 0.676576i | ||||
\(835\) | 0.684658 | 0.0236936 | ||||||||
\(836\) | −1.84233 | + | 3.95042i | −0.0637183 | + | 0.136628i | ||||
\(837\) | −14.7386 | −0.509442 | ||||||||
\(838\) | −8.78078 | + | 15.2088i | −0.303327 | + | 0.525378i | ||||
\(839\) | −1.24621 | + | 2.15850i | −0.0430240 | + | 0.0745197i | −0.886735 | − | 0.462277i | \(-0.847033\pi\) |
0.843712 | + | 0.536797i | \(0.180366\pi\) | |||||||
\(840\) | −0.561553 | − | 0.972638i | −0.0193754 | − | 0.0335592i | ||||
\(841\) | 12.5000 | − | 21.6506i | 0.431034 | − | 0.746574i | ||||
\(842\) | 16.2462 | + | 28.1393i | 0.559881 | + | 0.969743i | ||||
\(843\) | −21.4384 | −0.738379 | ||||||||
\(844\) | −3.31534 | −0.114119 | ||||||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 5.12311 | + | 8.87348i | 0.176136 | + | 0.305077i | ||||
\(847\) | −4.38447 | −0.150652 | ||||||||
\(848\) | −7.56155 | −0.259665 | ||||||||
\(849\) | −24.8963 | − | 43.1217i | −0.854439 | − | 1.47993i | ||||
\(850\) | 2.56155 | − | 4.43674i | 0.0878605 | − | 0.152179i | ||||
\(851\) | −10.9730 | − | 19.0058i | −0.376150 | − | 0.651511i | ||||
\(852\) | 20.8078 | − | 36.0401i | 0.712862 | − | 1.23471i | ||||
\(853\) | −0.369317 | + | 0.639676i | −0.0126452 | + | 0.0219021i | −0.872279 | − | 0.489009i | \(-0.837359\pi\) |
0.859634 | + | 0.510911i | \(0.170692\pi\) | |||||||
\(854\) | −2.24621 | −0.0768638 | ||||||||
\(855\) | −8.90388 | − | 12.7173i | −0.304506 | − | 0.434922i | ||||
\(856\) | −2.24621 | −0.0767739 | ||||||||
\(857\) | −14.8963 | + | 25.8012i | −0.508848 | + | 0.881351i | 0.491099 | + | 0.871104i | \(0.336595\pi\) |
−0.999947 | + | 0.0102472i | \(0.996738\pi\) | |||||||
\(858\) | 2.56155 | − | 4.43674i | 0.0874500 | − | 0.151468i | ||||
\(859\) | −23.7462 | − | 41.1296i | −0.810210 | − | 1.40333i | −0.912717 | − | 0.408593i | \(-0.866020\pi\) |
0.102506 | − | 0.994732i | \(-0.467314\pi\) | |||||||
\(860\) | −1.56155 | + | 2.70469i | −0.0532485 | + | 0.0922291i | ||||
\(861\) | −3.43845 | − | 5.95557i | −0.117182 | − | 0.202965i | ||||
\(862\) | 7.36932 | 0.251000 | ||||||||
\(863\) | 52.3002 | 1.78032 | 0.890160 | − | 0.455649i | \(-0.150593\pi\) | ||||
0.890160 | + | 0.455649i | \(0.150593\pi\) | |||||||
\(864\) | −0.719224 | − | 1.24573i | −0.0244685 | − | 0.0423807i | ||||
\(865\) | 2.90388 | + | 5.02967i | 0.0987350 | + | 0.171014i | ||||
\(866\) | 36.7386 | 1.24843 | ||||||||
\(867\) | −23.6847 | −0.804373 | ||||||||
\(868\) | −2.24621 | − | 3.89055i | −0.0762414 | − | 0.132054i | ||||
\(869\) | 5.56155 | − | 9.63289i | 0.188663 | − | 0.326773i | ||||
\(870\) | −2.56155 | − | 4.43674i | −0.0868448 | − | 0.150420i | ||||
\(871\) | 9.43845 | − | 16.3479i | 0.319810 | − | 0.553926i | ||||
\(872\) | −7.12311 | + | 12.3376i | −0.241219 | + | 0.417803i | ||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | −11.7116 | − | 16.7276i | −0.396152 | − | 0.565819i | ||||
\(875\) | 0.438447 | 0.0148222 | ||||||||
\(876\) | −2.15767 | + | 3.73720i | −0.0729009 | + | 0.126268i | ||||
\(877\) | −8.90388 | + | 15.4220i | −0.300663 | + | 0.520763i | −0.976286 | − | 0.216484i | \(-0.930541\pi\) |
0.675623 | + | 0.737247i | \(0.263875\pi\) | |||||||
\(878\) | −8.24621 | − | 14.2829i | −0.278296 | − | 0.482023i | ||||
\(879\) | 30.1771 | − | 52.2682i | 1.01785 | − | 1.76296i | ||||
\(880\) | −0.500000 | − | 0.866025i | −0.0168550 | − | 0.0291937i | ||||
\(881\) | −24.1231 | −0.812728 | −0.406364 | − | 0.913711i | \(-0.633204\pi\) | ||||
−0.406364 | + | 0.913711i | \(0.633204\pi\) | |||||||
\(882\) | 24.2462 | 0.816412 | ||||||||
\(883\) | 4.40388 | + | 7.62775i | 0.148202 | + | 0.256694i | 0.930563 | − | 0.366131i | \(-0.119318\pi\) |
−0.782361 | + | 0.622826i | \(0.785985\pi\) | |||||||
\(884\) | 5.12311 | + | 8.87348i | 0.172309 | + | 0.298447i | ||||
\(885\) | −37.3002 | −1.25383 | ||||||||
\(886\) | −33.9309 | −1.13993 | ||||||||
\(887\) | 13.1231 | + | 22.7299i | 0.440631 | + | 0.763195i | 0.997736 | − | 0.0672468i | \(-0.0214215\pi\) |
−0.557106 | + | 0.830442i | \(0.688088\pi\) | |||||||
\(888\) | 6.00000 | − | 10.3923i | 0.201347 | − | 0.348743i | ||||
\(889\) | 3.41146 | + | 5.90882i | 0.114417 | + | 0.198176i | ||||
\(890\) | −1.34233 | + | 2.32498i | −0.0449950 | + | 0.0779336i | ||||
\(891\) | 3.50000 | − | 6.06218i | 0.117254 | − | 0.203091i | ||||
\(892\) | 11.3153 | 0.378866 | ||||||||
\(893\) | −5.30019 | + | 11.3649i | −0.177364 | + | 0.380313i | ||||
\(894\) | 40.9848 | 1.37074 | ||||||||
\(895\) | −5.74621 | + | 9.95273i | −0.192075 | + | 0.332683i | ||||
\(896\) | 0.219224 | − | 0.379706i | 0.00732375 | − | 0.0126851i | ||||
\(897\) | 12.0000 | + | 20.7846i | 0.400668 | + | 0.693978i | ||||
\(898\) | 14.5000 | − | 25.1147i | 0.483871 | − | 0.838090i | ||||
\(899\) | −10.2462 | − | 17.7470i | −0.341730 | − | 0.591894i | ||||
\(900\) | 3.56155 | 0.118718 | ||||||||
\(901\) | −38.7386 | −1.29057 | ||||||||
\(902\) | −3.06155 | − | 5.30277i | −0.101939 | − | 0.176563i | ||||
\(903\) | 1.75379 | + | 3.03765i | 0.0583624 | + | 0.101087i | ||||
\(904\) | 16.8078 | 0.559018 | ||||||||
\(905\) | 21.3693 | 0.710340 | ||||||||
\(906\) | −26.2462 | − | 45.4598i | −0.871972 | − | 1.51030i | ||||
\(907\) | 25.0885 | − | 43.4546i | 0.833051 | − | 1.44289i | −0.0625559 | − | 0.998041i | \(-0.519925\pi\) |
0.895607 | − | 0.444846i | \(-0.146741\pi\) | |||||||
\(908\) | −9.96543 | − | 17.2606i | −0.330715 | − | 0.572814i | ||||
\(909\) | −17.8078 | + | 30.8440i | −0.590646 | + | 1.02303i | ||||
\(910\) | −0.438447 | + | 0.759413i | −0.0145344 | + | 0.0251743i | ||||
\(911\) | 12.3845 | 0.410316 | 0.205158 | − | 0.978729i | \(-0.434229\pi\) | ||||
0.205158 | + | 0.978729i | \(0.434229\pi\) | |||||||
\(912\) | 4.71922 | − | 10.1192i | 0.156269 | − | 0.335081i | ||||
\(913\) | −10.8078 | −0.357685 | ||||||||
\(914\) | 3.52699 | − | 6.10892i | 0.116662 | − | 0.202065i | ||||
\(915\) | 6.56155 | − | 11.3649i | 0.216918 | − | 0.375713i | ||||
\(916\) | −6.43845 | − | 11.1517i | −0.212732 | − | 0.368463i | ||||
\(917\) | 3.53457 | − | 6.12205i | 0.116722 | − | 0.202168i | ||||
\(918\) | −3.68466 | − | 6.38202i | −0.121612 | − | 0.210638i | ||||
\(919\) | 20.2462 | 0.667861 | 0.333930 | − | 0.942598i | \(-0.391625\pi\) | ||||
0.333930 | + | 0.942598i | \(0.391625\pi\) | |||||||
\(920\) | 4.68466 | 0.154449 | ||||||||
\(921\) | −30.6501 | − | 53.0875i | −1.00995 | − | 1.74929i | ||||
\(922\) | −19.4924 | − | 33.7619i | −0.641949 | − | 1.11189i | ||||
\(923\) | −32.4924 | −1.06950 | ||||||||
\(924\) | −1.12311 | −0.0369475 | ||||||||
\(925\) | 2.34233 | + | 4.05703i | 0.0770153 | + | 0.133394i | ||||
\(926\) | −9.78078 | + | 16.9408i | −0.321416 | + | 0.556709i | ||||
\(927\) | 10.3423 | + | 17.9134i | 0.339687 | + | 0.588355i | ||||
\(928\) | 1.00000 | − | 1.73205i | 0.0328266 | − | 0.0568574i | ||||
\(929\) | 17.9924 | − | 31.1638i | 0.590312 | − | 1.02245i | −0.403878 | − | 0.914813i | \(-0.632338\pi\) |
0.994190 | − | 0.107638i | \(-0.0343287\pi\) | |||||||
\(930\) | 26.2462 | 0.860647 | ||||||||
\(931\) | 17.0194 | + | 24.3086i | 0.557789 | + | 0.796682i | ||||
\(932\) | 2.31534 | 0.0758415 | ||||||||
\(933\) | 5.12311 | − | 8.87348i | 0.167723 | − | 0.290505i | ||||
\(934\) | 8.28078 | − | 14.3427i | 0.270955 | − | 0.469308i | ||||
\(935\) | −2.56155 | − | 4.43674i | −0.0837717 | − | 0.145097i | ||||
\(936\) | −3.56155 | + | 6.16879i | −0.116413 | + | 0.201633i | ||||
\(937\) | 25.0885 | + | 43.4546i | 0.819607 | + | 1.41960i | 0.905972 | + | 0.423337i | \(0.139141\pi\) |
−0.0863653 | + | 0.996264i | \(0.527525\pi\) | |||||||
\(938\) | −4.13826 | −0.135119 | ||||||||
\(939\) | −11.0540 | −0.360733 | ||||||||
\(940\) | −1.43845 | − | 2.49146i | −0.0469170 | − | 0.0812626i | ||||
\(941\) | 8.12311 | + | 14.0696i | 0.264806 | + | 0.458657i | 0.967513 | − | 0.252822i | \(-0.0813589\pi\) |
−0.702707 | + | 0.711479i | \(0.748026\pi\) | |||||||
\(942\) | 6.24621 | 0.203513 | ||||||||
\(943\) | 28.6847 | 0.934101 | ||||||||
\(944\) | −7.28078 | − | 12.6107i | −0.236969 | − | 0.410442i | ||||
\(945\) | 0.315342 | − | 0.546188i | 0.0102581 | − | 0.0177675i | ||||
\(946\) | 1.56155 | + | 2.70469i | 0.0507705 | + | 0.0879370i | ||||
\(947\) | −28.2462 | + | 48.9239i | −0.917879 | + | 1.58981i | −0.115247 | + | 0.993337i | \(0.536766\pi\) |
−0.802631 | + | 0.596475i | \(0.796567\pi\) | |||||||
\(948\) | −14.2462 | + | 24.6752i | −0.462695 | + | 0.801412i | ||||
\(949\) | 3.36932 | 0.109373 | ||||||||
\(950\) | 2.50000 | + | 3.57071i | 0.0811107 | + | 0.115849i | ||||
\(951\) | −47.8617 | −1.55202 | ||||||||
\(952\) | 1.12311 | − | 1.94528i | 0.0364001 | − | 0.0630468i | ||||
\(953\) | 7.84233 | − | 13.5833i | 0.254038 | − | 0.440007i | −0.710596 | − | 0.703600i | \(-0.751575\pi\) |
0.964634 | + | 0.263594i | \(0.0849078\pi\) | |||||||
\(954\) | −13.4654 | − | 23.3228i | −0.435960 | − | 0.755104i | ||||
\(955\) | 2.68466 | − | 4.64996i | 0.0868735 | − | 0.150469i | ||||
\(956\) | −9.12311 | − | 15.8017i | −0.295062 | − | 0.511063i | ||||
\(957\) | −5.12311 | −0.165606 | ||||||||
\(958\) | −29.3693 | −0.948880 | ||||||||
\(959\) | 1.19224 | + | 2.06501i | 0.0384993 | + | 0.0666828i | ||||
\(960\) | 1.28078 | + | 2.21837i | 0.0413369 | + | 0.0715976i | ||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | −9.36932 | −0.302079 | ||||||||
\(963\) | −4.00000 | − | 6.92820i | −0.128898 | − | 0.223258i | ||||
\(964\) | 4.28078 | − | 7.41452i | 0.137875 | − | 0.238806i | ||||
\(965\) | −12.8078 | − | 22.1837i | −0.412297 | − | 0.714119i | ||||
\(966\) | 2.63068 | − | 4.55648i | 0.0846408 | − | 0.146602i | ||||
\(967\) | −14.5616 | + | 25.2213i | −0.468268 | + | 0.811064i | −0.999342 | − | 0.0362613i | \(-0.988455\pi\) |
0.531074 | + | 0.847325i | \(0.321788\pi\) | |||||||
\(968\) | 10.0000 | 0.321412 | ||||||||
\(969\) | 24.1771 | − | 51.8418i | 0.776680 | − | 1.66540i | ||||
\(970\) | −1.68466 | −0.0540911 | ||||||||
\(971\) | −8.96543 | + | 15.5286i | −0.287714 | + | 0.498336i | −0.973264 | − | 0.229690i | \(-0.926229\pi\) |
0.685549 | + | 0.728026i | \(0.259562\pi\) | |||||||
\(972\) | −11.1231 | + | 19.2658i | −0.356774 | + | 0.617950i | ||||
\(973\) | −1.93087 | − | 3.34436i | −0.0619008 | − | 0.107215i | ||||
\(974\) | −3.46543 | + | 6.00231i | −0.111040 | + | 0.192326i | ||||
\(975\) | −2.56155 | − | 4.43674i | −0.0820353 | − | 0.142089i | ||||
\(976\) | 5.12311 | 0.163987 | ||||||||
\(977\) | −30.3153 | −0.969874 | −0.484937 | − | 0.874549i | \(-0.661157\pi\) | ||||
−0.484937 | + | 0.874549i | \(0.661157\pi\) | |||||||
\(978\) | −21.8423 | − | 37.8320i | −0.698441 | − | 1.20973i | ||||
\(979\) | 1.34233 | + | 2.32498i | 0.0429010 | + | 0.0743068i | ||||
\(980\) | −6.80776 | −0.217466 | ||||||||
\(981\) | −50.7386 | −1.61996 | ||||||||
\(982\) | −4.58854 | − | 7.94759i | −0.146426 | − | 0.253618i | ||||
\(983\) | −20.7808 | + | 35.9934i | −0.662804 | + | 1.14801i | 0.317072 | + | 0.948401i | \(0.397300\pi\) |
−0.979876 | + | 0.199608i | \(0.936033\pi\) | |||||||
\(984\) | 7.84233 | + | 13.5833i | 0.250004 | + | 0.433020i | ||||
\(985\) | −7.21922 | + | 12.5041i | −0.230024 | + | 0.398413i | ||||
\(986\) | 5.12311 | − | 8.87348i | 0.163153 | − | 0.282589i | ||||
\(987\) | −3.23106 | −0.102846 | ||||||||
\(988\) | −8.68466 | + | 0.759413i | −0.276296 | + | 0.0241601i | ||||
\(989\) | −14.6307 | −0.465229 | ||||||||
\(990\) | 1.78078 | − | 3.08440i | 0.0565968 | − | 0.0980285i | ||||
\(991\) | 4.19224 | − | 7.26117i | 0.133171 | − | 0.230659i | −0.791726 | − | 0.610876i | \(-0.790817\pi\) |
0.924897 | + | 0.380217i | \(0.124151\pi\) | |||||||
\(992\) | 5.12311 | + | 8.87348i | 0.162659 | + | 0.281733i | ||||
\(993\) | 30.0885 | − | 52.1149i | 0.954831 | − | 1.65382i | ||||
\(994\) | 3.56155 | + | 6.16879i | 0.112966 | + | 0.195662i | ||||
\(995\) | −2.87689 | −0.0912037 | ||||||||
\(996\) | 27.6847 | 0.877222 | ||||||||
\(997\) | 1.34233 | + | 2.32498i | 0.0425120 | + | 0.0736329i | 0.886498 | − | 0.462732i | \(-0.153131\pi\) |
−0.843986 | + | 0.536364i | \(0.819797\pi\) | |||||||
\(998\) | 14.5000 | + | 25.1147i | 0.458989 | + | 0.794993i | ||||
\(999\) | 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 | 190.2.e.c.11.2 | ✓ | 4 | |
3.2 | odd | 2 | 1710.2.l.m.1531.1 | 4 | |||
4.3 | odd | 2 | 1520.2.q.h.961.1 | 4 | |||
5.2 | odd | 4 | 950.2.j.f.49.3 | 8 | |||
5.3 | odd | 4 | 950.2.j.f.49.2 | 8 | |||
5.4 | even | 2 | 950.2.e.h.201.1 | 4 | |||
19.7 | even | 3 | inner | 190.2.e.c.121.2 | yes | 4 | |
19.8 | odd | 6 | 3610.2.a.u.1.2 | 2 | |||
19.11 | even | 3 | 3610.2.a.k.1.1 | 2 | |||
57.26 | odd | 6 | 1710.2.l.m.1261.1 | 4 | |||
76.7 | odd | 6 | 1520.2.q.h.881.1 | 4 | |||
95.7 | odd | 12 | 950.2.j.f.349.2 | 8 | |||
95.64 | even | 6 | 950.2.e.h.501.1 | 4 | |||
95.83 | odd | 12 | 950.2.j.f.349.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.e.c.11.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
190.2.e.c.121.2 | yes | 4 | 19.7 | even | 3 | inner | |
950.2.e.h.201.1 | 4 | 5.4 | even | 2 | |||
950.2.e.h.501.1 | 4 | 95.64 | even | 6 | |||
950.2.j.f.49.2 | 8 | 5.3 | odd | 4 | |||
950.2.j.f.49.3 | 8 | 5.2 | odd | 4 | |||
950.2.j.f.349.2 | 8 | 95.7 | odd | 12 | |||
950.2.j.f.349.3 | 8 | 95.83 | odd | 12 | |||
1520.2.q.h.881.1 | 4 | 76.7 | odd | 6 | |||
1520.2.q.h.961.1 | 4 | 4.3 | odd | 2 | |||
1710.2.l.m.1261.1 | 4 | 57.26 | odd | 6 | |||
1710.2.l.m.1531.1 | 4 | 3.2 | odd | 2 | |||
3610.2.a.k.1.1 | 2 | 19.11 | even | 3 | |||
3610.2.a.u.1.2 | 2 | 19.8 | odd | 6 |