Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(151,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.151 |
Dual form | 750.2.g.a.601.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | + | 0.951057i | 0.218508 | + | 0.672499i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.809017 | − | 0.587785i | −0.330280 | − | 0.239962i | ||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −0.809017 | − | 0.587785i | −0.286031 | − | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61803 | − | 4.97980i | −0.487856 | − | 1.50147i | −0.827802 | − | 0.561020i | \(-0.810409\pi\) |
0.339946 | − | 0.940445i | \(-0.389591\pi\) | |||||||
\(12\) | 0.309017 | − | 0.951057i | 0.0892055 | − | 0.274546i | ||||
\(13\) | 1.50000 | − | 4.61653i | 0.416025 | − | 1.28039i | −0.495306 | − | 0.868719i | \(-0.664944\pi\) |
0.911331 | − | 0.411675i | \(-0.135056\pi\) | |||||||
\(14\) | −0.618034 | − | 1.90211i | −0.165177 | − | 0.508361i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | 6.35410 | + | 4.61653i | 1.54110 | + | 1.11967i | 0.949644 | + | 0.313332i | \(0.101445\pi\) |
0.591452 | + | 0.806340i | \(0.298555\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.23607 | + | 1.62460i | 0.512989 | + | 0.372708i | 0.813956 | − | 0.580926i | \(-0.197309\pi\) |
−0.300967 | + | 0.953635i | \(0.597309\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.61803 | − | 1.17557i | 0.353084 | − | 0.256531i | ||||
\(22\) | 4.23607 | − | 3.07768i | 0.903133 | − | 0.656164i | ||||
\(23\) | −1.85410 | − | 5.70634i | −0.386607 | − | 1.18985i | −0.935308 | − | 0.353835i | \(-0.884877\pi\) |
0.548701 | − | 0.836019i | \(-0.315123\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.85410 | 0.951968 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 1.61803 | − | 1.17557i | 0.305780 | − | 0.222162i | ||||
\(29\) | 1.11803 | − | 0.812299i | 0.207614 | − | 0.150840i | −0.479120 | − | 0.877750i | \(-0.659044\pi\) |
0.686733 | + | 0.726909i | \(0.259044\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 2.17963i | −0.538816 | − | 0.391473i | 0.284829 | − | 0.958578i | \(-0.408063\pi\) |
−0.823645 | + | 0.567106i | \(0.808063\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 4.23607 | + | 3.07768i | 0.737405 | + | 0.535756i | ||||
\(34\) | −2.42705 | + | 7.46969i | −0.416236 | + | 1.28104i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | 0.663119 | − | 2.04087i | 0.109016 | − | 0.335517i | −0.881636 | − | 0.471930i | \(-0.843557\pi\) |
0.990652 | + | 0.136413i | \(0.0435575\pi\) | |||||||
\(38\) | −0.854102 | + | 2.62866i | −0.138554 | + | 0.426424i | ||||
\(39\) | 1.50000 | + | 4.61653i | 0.240192 | + | 0.739236i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.88197 | + | 5.79210i | −0.293914 | + | 0.904573i | 0.689670 | + | 0.724123i | \(0.257755\pi\) |
−0.983584 | + | 0.180450i | \(0.942245\pi\) | |||||||
\(42\) | 1.61803 | + | 1.17557i | 0.249668 | + | 0.181394i | ||||
\(43\) | 1.23607 | 0.188499 | 0.0942493 | − | 0.995549i | \(-0.469955\pi\) | ||||
0.0942493 | + | 0.995549i | \(0.469955\pi\) | |||||||
\(44\) | 4.23607 | + | 3.07768i | 0.638611 | + | 0.463978i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.85410 | − | 3.52671i | 0.715698 | − | 0.519985i | ||||
\(47\) | 3.85410 | − | 2.80017i | 0.562179 | − | 0.408447i | −0.270077 | − | 0.962839i | \(-0.587049\pi\) |
0.832256 | + | 0.554392i | \(0.187049\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.85410 | −1.09979 | ||||||||
\(52\) | 1.50000 | + | 4.61653i | 0.208013 | + | 0.640197i | ||||
\(53\) | 6.92705 | − | 5.03280i | 0.951504 | − | 0.691308i | 0.000341607 | − | 1.00000i | \(-0.499891\pi\) |
0.951162 | + | 0.308692i | \(0.0998913\pi\) | |||||||
\(54\) | −0.809017 | + | 0.587785i | −0.110093 | + | 0.0799874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.61803 | + | 1.17557i | 0.216219 | + | 0.157092i | ||||
\(57\) | −2.76393 | −0.366092 | ||||||||
\(58\) | 1.11803 | + | 0.812299i | 0.146805 | + | 0.106660i | ||||
\(59\) | 2.76393 | − | 8.50651i | 0.359833 | − | 1.10745i | −0.593320 | − | 0.804966i | \(-0.702183\pi\) |
0.953154 | − | 0.302487i | \(-0.0978167\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.73607 | − | 8.42075i | −0.350318 | − | 1.07817i | −0.958675 | − | 0.284504i | \(-0.908171\pi\) |
0.608357 | − | 0.793663i | \(-0.291829\pi\) | |||||||
\(62\) | 1.14590 | − | 3.52671i | 0.145529 | − | 0.447893i | ||||
\(63\) | −0.618034 | + | 1.90211i | −0.0778650 | + | 0.239644i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.61803 | + | 4.97980i | −0.199166 | + | 0.612971i | ||||
\(67\) | −7.85410 | − | 5.70634i | −0.959531 | − | 0.697140i | −0.00648944 | − | 0.999979i | \(-0.502066\pi\) |
−0.953042 | + | 0.302839i | \(0.902066\pi\) | |||||||
\(68\) | −7.85410 | −0.952450 | ||||||||
\(69\) | 4.85410 | + | 3.52671i | 0.584365 | + | 0.424566i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4721 | − | 8.33499i | 1.36149 | − | 0.989182i | 0.363144 | − | 0.931733i | \(-0.381703\pi\) |
0.998348 | − | 0.0574487i | \(-0.0182966\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | 0.972136 | + | 2.99193i | 0.113780 | + | 0.350179i | 0.991691 | − | 0.128646i | \(-0.0410631\pi\) |
−0.877911 | + | 0.478824i | \(0.841063\pi\) | |||||||
\(74\) | 2.14590 | 0.249456 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.76393 | −0.317045 | ||||||||
\(77\) | 3.23607 | + | 9.95959i | 0.368784 | + | 1.13500i | ||||
\(78\) | −3.92705 | + | 2.85317i | −0.444651 | + | 0.323058i | ||||
\(79\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −6.09017 | −0.672547 | ||||||||
\(83\) | 4.85410 | + | 3.52671i | 0.532807 | + | 0.387107i | 0.821407 | − | 0.570343i | \(-0.193190\pi\) |
−0.288600 | + | 0.957450i | \(0.593190\pi\) | |||||||
\(84\) | −0.618034 | + | 1.90211i | −0.0674330 | + | 0.207538i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.381966 | + | 1.17557i | 0.0411885 | + | 0.126765i | ||||
\(87\) | −0.427051 | + | 1.31433i | −0.0457847 | + | 0.140911i | ||||
\(88\) | −1.61803 | + | 4.97980i | −0.172483 | + | 0.530848i | ||||
\(89\) | 0.427051 | + | 1.31433i | 0.0452673 | + | 0.139318i | 0.971136 | − | 0.238528i | \(-0.0766648\pi\) |
−0.925868 | + | 0.377846i | \(0.876665\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | + | 9.23305i | −0.314485 | + | 0.967887i | ||||
\(92\) | 4.85410 | + | 3.52671i | 0.506075 | + | 0.367685i | ||||
\(93\) | 3.70820 | 0.384523 | ||||||||
\(94\) | 3.85410 | + | 2.80017i | 0.397520 | + | 0.288815i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.809017 | + | 0.587785i | −0.0825700 | + | 0.0599906i | ||||
\(97\) | −11.2082 | + | 8.14324i | −1.13802 | + | 0.826820i | −0.986842 | − | 0.161686i | \(-0.948307\pi\) |
−0.151178 | + | 0.988506i | \(0.548307\pi\) | |||||||
\(98\) | −0.927051 | − | 2.85317i | −0.0936463 | − | 0.288214i | ||||
\(99\) | −5.23607 | −0.526245 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.67376 | 0.166546 | 0.0832728 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832728 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(102\) | −2.42705 | − | 7.46969i | −0.240314 | − | 0.739610i | ||||
\(103\) | −1.85410 | + | 1.34708i | −0.182690 | + | 0.132732i | −0.675372 | − | 0.737478i | \(-0.736017\pi\) |
0.492682 | + | 0.870210i | \(0.336017\pi\) | |||||||
\(104\) | −3.92705 | + | 2.85317i | −0.385079 | + | 0.279776i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.92705 | + | 5.03280i | 0.672815 | + | 0.488828i | ||||
\(107\) | −10.9443 | −1.05802 | −0.529011 | − | 0.848615i | \(-0.677437\pi\) | ||||
−0.529011 | + | 0.848615i | \(0.677437\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 0.791796 | − | 2.43690i | 0.0758403 | − | 0.233412i | −0.905949 | − | 0.423388i | \(-0.860841\pi\) |
0.981789 | + | 0.189975i | \(0.0608408\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.663119 | + | 2.04087i | 0.0629405 | + | 0.193711i | ||||
\(112\) | −0.618034 | + | 1.90211i | −0.0583987 | + | 0.179733i | ||||
\(113\) | 3.57295 | − | 10.9964i | 0.336115 | − | 1.03445i | −0.630056 | − | 0.776550i | \(-0.716968\pi\) |
0.966170 | − | 0.257905i | \(-0.0830321\pi\) | |||||||
\(114\) | −0.854102 | − | 2.62866i | −0.0799940 | − | 0.246196i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.427051 | + | 1.31433i | −0.0396507 | + | 0.122032i | ||||
\(117\) | −3.92705 | − | 2.85317i | −0.363056 | − | 0.263776i | ||||
\(118\) | 8.94427 | 0.823387 | ||||||||
\(119\) | −12.7082 | − | 9.23305i | −1.16496 | − | 0.846392i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.2812 | + | 9.64932i | −1.20738 | + | 0.877211i | ||||
\(122\) | 7.16312 | − | 5.20431i | 0.648518 | − | 0.471176i | ||||
\(123\) | −1.88197 | − | 5.79210i | −0.169691 | − | 0.522256i | ||||
\(124\) | 3.70820 | 0.333007 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | −0.0901699 | − | 0.277515i | −0.00800129 | − | 0.0246254i | 0.946976 | − | 0.321304i | \(-0.104121\pi\) |
−0.954977 | + | 0.296678i | \(0.904121\pi\) | |||||||
\(128\) | −0.809017 | + | 0.587785i | −0.0715077 | + | 0.0519534i | ||||
\(129\) | −1.00000 | + | 0.726543i | −0.0880451 | + | 0.0639685i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.618034 | + | 0.449028i | 0.0539979 | + | 0.0392318i | 0.614457 | − | 0.788950i | \(-0.289375\pi\) |
−0.560459 | + | 0.828182i | \(0.689375\pi\) | |||||||
\(132\) | −5.23607 | −0.455741 | ||||||||
\(133\) | −4.47214 | − | 3.24920i | −0.387783 | − | 0.281741i | ||||
\(134\) | 3.00000 | − | 9.23305i | 0.259161 | − | 0.797614i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.42705 | − | 7.46969i | −0.208118 | − | 0.640521i | ||||
\(137\) | 4.64590 | − | 14.2986i | 0.396926 | − | 1.22161i | −0.530526 | − | 0.847669i | \(-0.678005\pi\) |
0.927452 | − | 0.373943i | \(-0.121995\pi\) | |||||||
\(138\) | −1.85410 | + | 5.70634i | −0.157832 | + | 0.485756i | ||||
\(139\) | −4.14590 | − | 12.7598i | −0.351650 | − | 1.08227i | −0.957926 | − | 0.287014i | \(-0.907337\pi\) |
0.606276 | − | 0.795254i | \(-0.292663\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.47214 | + | 4.53077i | −0.123976 | + | 0.381560i | ||||
\(142\) | 11.4721 | + | 8.33499i | 0.962720 | + | 0.699457i | ||||
\(143\) | −25.4164 | −2.12543 | ||||||||
\(144\) | −0.809017 | − | 0.587785i | −0.0674181 | − | 0.0489821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.54508 | + | 1.84911i | −0.210633 | + | 0.153034i | ||||
\(147\) | 2.42705 | − | 1.76336i | 0.200180 | − | 0.145439i | ||||
\(148\) | 0.663119 | + | 2.04087i | 0.0545080 | + | 0.167759i | ||||
\(149\) | 7.03444 | 0.576284 | 0.288142 | − | 0.957588i | \(-0.406962\pi\) | ||||
0.288142 | + | 0.957588i | \(0.406962\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.94427 | −0.565117 | −0.282558 | − | 0.959250i | \(-0.591183\pi\) | ||||
−0.282558 | + | 0.959250i | \(0.591183\pi\) | |||||||
\(152\) | −0.854102 | − | 2.62866i | −0.0692768 | − | 0.213212i | ||||
\(153\) | 6.35410 | − | 4.61653i | 0.513699 | − | 0.373224i | ||||
\(154\) | −8.47214 | + | 6.15537i | −0.682704 | + | 0.496014i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.92705 | − | 2.85317i | −0.314416 | − | 0.228436i | ||||
\(157\) | −17.8541 | −1.42491 | −0.712456 | − | 0.701717i | \(-0.752417\pi\) | ||||
−0.712456 | + | 0.701717i | \(0.752417\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.64590 | + | 8.14324i | −0.209833 | + | 0.645801i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.70820 | + | 11.4127i | 0.292247 | + | 0.899445i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −6.32624 | + | 19.4702i | −0.495509 | + | 1.52502i | 0.320652 | + | 0.947197i | \(0.396098\pi\) |
−0.816162 | + | 0.577824i | \(0.803902\pi\) | |||||||
\(164\) | −1.88197 | − | 5.79210i | −0.146957 | − | 0.452287i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.85410 | + | 5.70634i | −0.143906 | + | 0.442898i | ||||
\(167\) | 5.23607 | + | 3.80423i | 0.405179 | + | 0.294380i | 0.771647 | − | 0.636051i | \(-0.219433\pi\) |
−0.366468 | + | 0.930431i | \(0.619433\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | −8.54508 | − | 6.20837i | −0.657314 | − | 0.477567i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.23607 | − | 1.62460i | 0.170996 | − | 0.124236i | ||||
\(172\) | −1.00000 | + | 0.726543i | −0.0762493 | + | 0.0553983i | ||||
\(173\) | 3.37132 | + | 10.3759i | 0.256317 | + | 0.788862i | 0.993567 | + | 0.113243i | \(0.0361238\pi\) |
−0.737250 | + | 0.675620i | \(0.763876\pi\) | |||||||
\(174\) | −1.38197 | −0.104767 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.23607 | −0.394683 | ||||||||
\(177\) | 2.76393 | + | 8.50651i | 0.207750 | + | 0.639388i | ||||
\(178\) | −1.11803 | + | 0.812299i | −0.0838002 | + | 0.0608844i | ||||
\(179\) | 3.09017 | − | 2.24514i | 0.230970 | − | 0.167810i | −0.466281 | − | 0.884637i | \(-0.654406\pi\) |
0.697251 | + | 0.716827i | \(0.254406\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.2082 | + | 11.7759i | 1.20475 | + | 0.875299i | 0.994743 | − | 0.102401i | \(-0.0326526\pi\) |
0.210003 | + | 0.977701i | \(0.432653\pi\) | |||||||
\(182\) | −9.70820 | −0.719620 | ||||||||
\(183\) | 7.16312 | + | 5.20431i | 0.529513 | + | 0.384714i | ||||
\(184\) | −1.85410 | + | 5.70634i | −0.136686 | + | 0.420677i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.14590 | + | 3.52671i | 0.0840213 | + | 0.258591i | ||||
\(187\) | 12.7082 | − | 39.1118i | 0.929316 | − | 2.86014i | ||||
\(188\) | −1.47214 | + | 4.53077i | −0.107367 | + | 0.330440i | ||||
\(189\) | −0.618034 | − | 1.90211i | −0.0449554 | − | 0.138358i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.236068 | + | 0.726543i | −0.0170813 | + | 0.0525708i | −0.959234 | − | 0.282614i | \(-0.908799\pi\) |
0.942153 | + | 0.335184i | \(0.108799\pi\) | |||||||
\(192\) | −0.809017 | − | 0.587785i | −0.0583858 | − | 0.0424197i | ||||
\(193\) | −2.38197 | −0.171458 | −0.0857288 | − | 0.996319i | \(-0.527322\pi\) | ||||
−0.0857288 | + | 0.996319i | \(0.527322\pi\) | |||||||
\(194\) | −11.2082 | − | 8.14324i | −0.804702 | − | 0.584650i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.42705 | − | 1.76336i | 0.173361 | − | 0.125954i | ||||
\(197\) | −10.7812 | + | 7.83297i | −0.768125 | + | 0.558076i | −0.901392 | − | 0.433005i | \(-0.857453\pi\) |
0.133266 | + | 0.991080i | \(0.457453\pi\) | |||||||
\(198\) | −1.61803 | − | 4.97980i | −0.114989 | − | 0.353899i | ||||
\(199\) | −6.18034 | −0.438113 | −0.219056 | − | 0.975712i | \(-0.570298\pi\) | ||||
−0.219056 | + | 0.975712i | \(0.570298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.70820 | 0.684764 | ||||||||
\(202\) | 0.517221 | + | 1.59184i | 0.0363915 | + | 0.112002i | ||||
\(203\) | −2.23607 | + | 1.62460i | −0.156941 | + | 0.114024i | ||||
\(204\) | 6.35410 | − | 4.61653i | 0.444876 | − | 0.323221i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.85410 | − | 1.34708i | −0.129181 | − | 0.0938558i | ||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | −3.92705 | − | 2.85317i | −0.272292 | − | 0.197832i | ||||
\(209\) | 4.47214 | − | 13.7638i | 0.309344 | − | 0.952063i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.47214 | − | 7.60845i | −0.170189 | − | 0.523787i | 0.829192 | − | 0.558963i | \(-0.188801\pi\) |
−0.999381 | + | 0.0351760i | \(0.988801\pi\) | |||||||
\(212\) | −2.64590 | + | 8.14324i | −0.181721 | + | 0.559280i | ||||
\(213\) | −4.38197 | + | 13.4863i | −0.300247 | + | 0.924066i | ||||
\(214\) | −3.38197 | − | 10.4086i | −0.231186 | − | 0.711519i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.309017 | − | 0.951057i | 0.0210259 | − | 0.0647112i | ||||
\(217\) | 6.00000 | + | 4.35926i | 0.407307 | + | 0.295926i | ||||
\(218\) | 2.56231 | 0.173541 | ||||||||
\(219\) | −2.54508 | − | 1.84911i | −0.171981 | − | 0.124951i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.8435 | − | 22.4091i | 2.07476 | − | 1.50740i | ||||
\(222\) | −1.73607 | + | 1.26133i | −0.116517 | + | 0.0846547i | ||||
\(223\) | 0.708204 | + | 2.17963i | 0.0474248 | + | 0.145959i | 0.971965 | − | 0.235127i | \(-0.0755505\pi\) |
−0.924540 | + | 0.381085i | \(0.875550\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.5623 | 0.769113 | ||||||||
\(227\) | 5.23607 | + | 16.1150i | 0.347530 | + | 1.06959i | 0.960215 | + | 0.279261i | \(0.0900893\pi\) |
−0.612685 | + | 0.790327i | \(0.709911\pi\) | |||||||
\(228\) | 2.23607 | − | 1.62460i | 0.148087 | − | 0.107592i | ||||
\(229\) | 19.6353 | − | 14.2658i | 1.29753 | − | 0.942714i | 0.297606 | − | 0.954689i | \(-0.403812\pi\) |
0.999928 | + | 0.0119751i | \(0.00381187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.47214 | − | 6.15537i | −0.557426 | − | 0.404993i | ||||
\(232\) | −1.38197 | −0.0907305 | ||||||||
\(233\) | −17.8713 | − | 12.9843i | −1.17079 | − | 0.850628i | −0.179686 | − | 0.983724i | \(-0.557508\pi\) |
−0.991103 | + | 0.133096i | \(0.957508\pi\) | |||||||
\(234\) | 1.50000 | − | 4.61653i | 0.0980581 | − | 0.301792i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.76393 | + | 8.50651i | 0.179917 | + | 0.553727i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.85410 | − | 14.9394i | 0.314645 | − | 0.968377i | ||||
\(239\) | 8.29180 | + | 25.5195i | 0.536352 | + | 1.65072i | 0.740710 | + | 0.671825i | \(0.234489\pi\) |
−0.204358 | + | 0.978896i | \(0.565511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.28115 | + | 13.1760i | −0.275773 | + | 0.848743i | 0.713240 | + | 0.700919i | \(0.247227\pi\) |
−0.989014 | + | 0.147824i | \(0.952773\pi\) | |||||||
\(242\) | −13.2812 | − | 9.64932i | −0.853745 | − | 0.620282i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 7.16312 | + | 5.20431i | 0.458572 | + | 0.333172i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.92705 | − | 3.57971i | 0.314137 | − | 0.228234i | ||||
\(247\) | 10.8541 | − | 7.88597i | 0.690630 | − | 0.501772i | ||||
\(248\) | 1.14590 | + | 3.52671i | 0.0727646 | + | 0.223946i | ||||
\(249\) | −6.00000 | −0.380235 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.4721 | −0.787234 | −0.393617 | − | 0.919274i | \(-0.628776\pi\) | ||||
−0.393617 | + | 0.919274i | \(0.628776\pi\) | |||||||
\(252\) | −0.618034 | − | 1.90211i | −0.0389325 | − | 0.119822i | ||||
\(253\) | −25.4164 | + | 18.4661i | −1.59792 | + | 1.16095i | ||||
\(254\) | 0.236068 | − | 0.171513i | 0.0148122 | − | 0.0107617i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 11.6180 | 0.724713 | 0.362357 | − | 0.932040i | \(-0.381972\pi\) | ||||
0.362357 | + | 0.932040i | \(0.381972\pi\) | |||||||
\(258\) | −1.00000 | − | 0.726543i | −0.0622573 | − | 0.0452326i | ||||
\(259\) | −1.32624 | + | 4.08174i | −0.0824084 | + | 0.253627i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.427051 | − | 1.31433i | −0.0264338 | − | 0.0813548i | ||||
\(262\) | −0.236068 | + | 0.726543i | −0.0145843 | + | 0.0448859i | ||||
\(263\) | −0.145898 | + | 0.449028i | −0.00899646 | + | 0.0276883i | −0.955454 | − | 0.295140i | \(-0.904634\pi\) |
0.946458 | + | 0.322828i | \(0.104634\pi\) | |||||||
\(264\) | −1.61803 | − | 4.97980i | −0.0995831 | − | 0.306485i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.70820 | − | 5.25731i | 0.104737 | − | 0.322346i | ||||
\(267\) | −1.11803 | − | 0.812299i | −0.0684226 | − | 0.0497119i | ||||
\(268\) | 9.70820 | 0.593023 | ||||||||
\(269\) | 1.54508 | + | 1.12257i | 0.0942055 | + | 0.0684443i | 0.633891 | − | 0.773422i | \(-0.281457\pi\) |
−0.539685 | + | 0.841867i | \(0.681457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.7984 | + | 16.5640i | −1.38490 | + | 1.00619i | −0.388500 | + | 0.921449i | \(0.627007\pi\) |
−0.996403 | + | 0.0847417i | \(0.972993\pi\) | |||||||
\(272\) | 6.35410 | − | 4.61653i | 0.385274 | − | 0.279918i | ||||
\(273\) | −3.00000 | − | 9.23305i | −0.181568 | − | 0.558810i | ||||
\(274\) | 15.0344 | 0.908264 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 6.84346 | + | 21.0620i | 0.411184 | + | 1.26549i | 0.915620 | + | 0.402044i | \(0.131700\pi\) |
−0.504437 | + | 0.863449i | \(0.668300\pi\) | |||||||
\(278\) | 10.8541 | − | 7.88597i | 0.650986 | − | 0.472969i | ||||
\(279\) | −3.00000 | + | 2.17963i | −0.179605 | + | 0.130491i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.92705 | + | 3.57971i | 0.293923 | + | 0.213548i | 0.724968 | − | 0.688783i | \(-0.241855\pi\) |
−0.431044 | + | 0.902331i | \(0.641855\pi\) | |||||||
\(282\) | −4.76393 | −0.283688 | ||||||||
\(283\) | 2.61803 | + | 1.90211i | 0.155626 | + | 0.113069i | 0.662873 | − | 0.748732i | \(-0.269337\pi\) |
−0.507247 | + | 0.861801i | \(0.669337\pi\) | |||||||
\(284\) | −4.38197 | + | 13.4863i | −0.260022 | + | 0.800265i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.85410 | − | 24.1724i | −0.464423 | − | 1.42935i | ||||
\(287\) | 3.76393 | − | 11.5842i | 0.222178 | − | 0.683793i | ||||
\(288\) | 0.309017 | − | 0.951057i | 0.0182090 | − | 0.0560415i | ||||
\(289\) | 13.8090 | + | 42.4998i | 0.812295 | + | 2.49999i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.28115 | − | 13.1760i | 0.250966 | − | 0.772393i | ||||
\(292\) | −2.54508 | − | 1.84911i | −0.148940 | − | 0.108211i | ||||
\(293\) | 28.7984 | 1.68242 | 0.841209 | − | 0.540709i | \(-0.181844\pi\) | ||||
0.841209 | + | 0.540709i | \(0.181844\pi\) | |||||||
\(294\) | 2.42705 | + | 1.76336i | 0.141548 | + | 0.102841i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.73607 | + | 1.26133i | −0.100907 | + | 0.0733132i | ||||
\(297\) | 4.23607 | − | 3.07768i | 0.245802 | − | 0.178585i | ||||
\(298\) | 2.17376 | + | 6.69015i | 0.125923 | + | 0.387550i | ||||
\(299\) | −29.1246 | −1.68432 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.47214 | −0.142492 | ||||||||
\(302\) | −2.14590 | − | 6.60440i | −0.123483 | − | 0.380040i | ||||
\(303\) | −1.35410 | + | 0.983813i | −0.0777911 | + | 0.0565186i | ||||
\(304\) | 2.23607 | − | 1.62460i | 0.128247 | − | 0.0931771i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.35410 | + | 4.61653i | 0.363240 | + | 0.263909i | ||||
\(307\) | 16.2918 | 0.929822 | 0.464911 | − | 0.885357i | \(-0.346086\pi\) | ||||
0.464911 | + | 0.885357i | \(0.346086\pi\) | |||||||
\(308\) | −8.47214 | − | 6.15537i | −0.482745 | − | 0.350735i | ||||
\(309\) | 0.708204 | − | 2.17963i | 0.0402883 | − | 0.123995i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.76393 | − | 17.7396i | −0.326843 | − | 1.00592i | −0.970602 | − | 0.240690i | \(-0.922626\pi\) |
0.643759 | − | 0.765228i | \(-0.277374\pi\) | |||||||
\(312\) | 1.50000 | − | 4.61653i | 0.0849208 | − | 0.261359i | ||||
\(313\) | 8.14590 | − | 25.0705i | 0.460433 | − | 1.41707i | −0.404203 | − | 0.914669i | \(-0.632451\pi\) |
0.864636 | − | 0.502399i | \(-0.167549\pi\) | |||||||
\(314\) | −5.51722 | − | 16.9803i | −0.311355 | − | 0.958252i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.61803 | − | 4.08174i | −0.315540 | − | 0.229253i | 0.418730 | − | 0.908111i | \(-0.362475\pi\) |
−0.734270 | + | 0.678857i | \(0.762475\pi\) | |||||||
\(318\) | −8.56231 | −0.480150 | ||||||||
\(319\) | −5.85410 | − | 4.25325i | −0.327767 | − | 0.238137i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.85410 | − | 6.43288i | 0.494188 | − | 0.359048i | ||||
\(322\) | −9.70820 | + | 7.05342i | −0.541017 | + | 0.393072i | ||||
\(323\) | 6.70820 | + | 20.6457i | 0.373254 | + | 1.14876i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.4721 | −1.13385 | ||||||||
\(327\) | 0.791796 | + | 2.43690i | 0.0437864 | + | 0.134761i | ||||
\(328\) | 4.92705 | − | 3.57971i | 0.272051 | − | 0.197657i | ||||
\(329\) | −7.70820 | + | 5.60034i | −0.424967 | + | 0.308757i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2705 | + | 19.0866i | 1.44396 | + | 1.04910i | 0.987197 | + | 0.159507i | \(0.0509906\pi\) |
0.456761 | + | 0.889589i | \(0.349009\pi\) | |||||||
\(332\) | −6.00000 | −0.329293 | ||||||||
\(333\) | −1.73607 | − | 1.26133i | −0.0951359 | − | 0.0691203i | ||||
\(334\) | −2.00000 | + | 6.15537i | −0.109435 | + | 0.336807i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.618034 | − | 1.90211i | −0.0337165 | − | 0.103769i | ||||
\(337\) | −8.90983 | + | 27.4216i | −0.485349 | + | 1.49375i | 0.346125 | + | 0.938188i | \(0.387497\pi\) |
−0.831474 | + | 0.555563i | \(0.812503\pi\) | |||||||
\(338\) | 3.26393 | − | 10.0453i | 0.177534 | − | 0.546395i | ||||
\(339\) | 3.57295 | + | 10.9964i | 0.194056 | + | 0.597243i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | + | 18.4661i | −0.324918 | + | 0.999995i | ||||
\(342\) | 2.23607 | + | 1.62460i | 0.120913 | + | 0.0878482i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | −1.00000 | − | 0.726543i | −0.0539164 | − | 0.0391725i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.82624 | + | 6.41264i | −0.474501 | + | 0.344746i | ||||
\(347\) | −4.23607 | + | 3.07768i | −0.227404 | + | 0.165219i | −0.695653 | − | 0.718378i | \(-0.744885\pi\) |
0.468249 | + | 0.883596i | \(0.344885\pi\) | |||||||
\(348\) | −0.427051 | − | 1.31433i | −0.0228923 | − | 0.0704554i | ||||
\(349\) | 14.7984 | 0.792139 | 0.396069 | − | 0.918221i | \(-0.370374\pi\) | ||||
0.396069 | + | 0.918221i | \(0.370374\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.85410 | 0.259093 | ||||||||
\(352\) | −1.61803 | − | 4.97980i | −0.0862415 | − | 0.265424i | ||||
\(353\) | 16.5623 | − | 12.0332i | 0.881523 | − | 0.640464i | −0.0521313 | − | 0.998640i | \(-0.516601\pi\) |
0.933654 | + | 0.358177i | \(0.116601\pi\) | |||||||
\(354\) | −7.23607 | + | 5.25731i | −0.384593 | + | 0.279423i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.11803 | − | 0.812299i | −0.0592557 | − | 0.0430518i | ||||
\(357\) | 15.7082 | 0.831366 | ||||||||
\(358\) | 3.09017 | + | 2.24514i | 0.163321 | + | 0.118659i | ||||
\(359\) | −8.61803 | + | 26.5236i | −0.454842 | + | 1.39986i | 0.416478 | + | 0.909146i | \(0.363264\pi\) |
−0.871320 | + | 0.490715i | \(0.836736\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.51064 | − | 10.8046i | −0.184771 | − | 0.568666i | ||||
\(362\) | −6.19098 | + | 19.0539i | −0.325391 | + | 1.00145i | ||||
\(363\) | 5.07295 | − | 15.6129i | 0.266261 | − | 0.819466i | ||||
\(364\) | −3.00000 | − | 9.23305i | −0.157243 | − | 0.483943i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.73607 | + | 8.42075i | −0.143017 | + | 0.440160i | ||||
\(367\) | −10.0902 | − | 7.33094i | −0.526703 | − | 0.382672i | 0.292420 | − | 0.956290i | \(-0.405539\pi\) |
−0.819123 | + | 0.573618i | \(0.805539\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 4.92705 | + | 3.57971i | 0.256492 | + | 0.186352i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8541 | + | 10.0656i | −0.719269 | + | 0.522580i | ||||
\(372\) | −3.00000 | + | 2.17963i | −0.155543 | + | 0.113008i | ||||
\(373\) | −0.798374 | − | 2.45714i | −0.0413382 | − | 0.127226i | 0.928258 | − | 0.371938i | \(-0.121307\pi\) |
−0.969596 | + | 0.244712i | \(0.921307\pi\) | |||||||
\(374\) | 41.1246 | 2.12650 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.76393 | −0.245681 | ||||||||
\(377\) | −2.07295 | − | 6.37988i | −0.106762 | − | 0.328581i | ||||
\(378\) | 1.61803 | − | 1.17557i | 0.0832227 | − | 0.0604648i | ||||
\(379\) | 2.76393 | − | 2.00811i | 0.141974 | − | 0.103150i | −0.514531 | − | 0.857472i | \(-0.672034\pi\) |
0.656505 | + | 0.754322i | \(0.272034\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.236068 | + | 0.171513i | 0.0120941 | + | 0.00878690i | ||||
\(382\) | −0.763932 | −0.0390862 | ||||||||
\(383\) | 16.5623 | + | 12.0332i | 0.846294 | + | 0.614869i | 0.924122 | − | 0.382098i | \(-0.124798\pi\) |
−0.0778275 | + | 0.996967i | \(0.524798\pi\) | |||||||
\(384\) | 0.309017 | − | 0.951057i | 0.0157695 | − | 0.0485334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.736068 | − | 2.26538i | −0.0374649 | − | 0.115305i | ||||
\(387\) | 0.381966 | − | 1.17557i | 0.0194164 | − | 0.0597576i | ||||
\(388\) | 4.28115 | − | 13.1760i | 0.217343 | − | 0.668912i | ||||
\(389\) | 4.93769 | + | 15.1967i | 0.250351 | + | 0.770501i | 0.994710 | + | 0.102722i | \(0.0327551\pi\) |
−0.744359 | + | 0.667780i | \(0.767245\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5623 | − | 44.8182i | 0.736447 | − | 2.26655i | ||||
\(392\) | 2.42705 | + | 1.76336i | 0.122585 | + | 0.0890629i | ||||
\(393\) | −0.763932 | −0.0385353 | ||||||||
\(394\) | −10.7812 | − | 7.83297i | −0.543147 | − | 0.394619i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.23607 | − | 3.07768i | 0.212870 | − | 0.154659i | ||||
\(397\) | 23.3262 | − | 16.9475i | 1.17071 | − | 0.850571i | 0.179617 | − | 0.983737i | \(-0.442514\pi\) |
0.991094 | + | 0.133166i | \(0.0425143\pi\) | |||||||
\(398\) | −1.90983 | − | 5.87785i | −0.0957311 | − | 0.294630i | ||||
\(399\) | 5.52786 | 0.276739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.0902 | −1.30288 | −0.651440 | − | 0.758700i | \(-0.725835\pi\) | ||||
−0.651440 | + | 0.758700i | \(0.725835\pi\) | |||||||
\(402\) | 3.00000 | + | 9.23305i | 0.149626 | + | 0.460503i | ||||
\(403\) | −14.5623 | + | 10.5801i | −0.725400 | + | 0.527034i | ||||
\(404\) | −1.35410 | + | 0.983813i | −0.0673691 | + | 0.0489465i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.23607 | − | 1.62460i | −0.110974 | − | 0.0806275i | ||||
\(407\) | −11.2361 | −0.556951 | ||||||||
\(408\) | 6.35410 | + | 4.61653i | 0.314575 | + | 0.228552i | ||||
\(409\) | 6.48278 | − | 19.9519i | 0.320553 | − | 0.986560i | −0.652855 | − | 0.757483i | \(-0.726429\pi\) |
0.973408 | − | 0.229077i | \(-0.0735709\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.64590 | + | 14.2986i | 0.229165 | + | 0.705298i | ||||
\(412\) | 0.708204 | − | 2.17963i | 0.0348907 | − | 0.107383i | ||||
\(413\) | −5.52786 | + | 17.0130i | −0.272008 | + | 0.837156i | ||||
\(414\) | −1.85410 | − | 5.70634i | −0.0911241 | − | 0.280451i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.50000 | − | 4.61653i | 0.0735436 | − | 0.226344i | ||||
\(417\) | 10.8541 | + | 7.88597i | 0.531528 | + | 0.386177i | ||||
\(418\) | 14.4721 | 0.707855 | ||||||||
\(419\) | 30.6525 | + | 22.2703i | 1.49747 | + | 1.08798i | 0.971375 | + | 0.237552i | \(0.0763450\pi\) |
0.526097 | + | 0.850425i | \(0.323655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.97214 | − | 6.51864i | 0.437275 | − | 0.317699i | −0.347276 | − | 0.937763i | \(-0.612893\pi\) |
0.784551 | + | 0.620064i | \(0.212893\pi\) | |||||||
\(422\) | 6.47214 | − | 4.70228i | 0.315059 | − | 0.228904i | ||||
\(423\) | −1.47214 | − | 4.53077i | −0.0715777 | − | 0.220294i | ||||
\(424\) | −8.56231 | −0.415822 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.1803 | −0.687040 | ||||||||
\(427\) | 5.47214 | + | 16.8415i | 0.264815 | + | 0.815017i | ||||
\(428\) | 8.85410 | − | 6.43288i | 0.427979 | − | 0.310945i | ||||
\(429\) | 20.5623 | − | 14.9394i | 0.992757 | − | 0.721281i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 2.17963i | −0.144505 | − | 0.104989i | 0.513184 | − | 0.858279i | \(-0.328466\pi\) |
−0.657689 | + | 0.753290i | \(0.728466\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −18.7254 | − | 13.6048i | −0.899886 | − | 0.653806i | 0.0385504 | − | 0.999257i | \(-0.487726\pi\) |
−0.938437 | + | 0.345451i | \(0.887726\pi\) | |||||||
\(434\) | −2.29180 | + | 7.05342i | −0.110010 | + | 0.338575i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.791796 | + | 2.43690i | 0.0379202 | + | 0.116706i | ||||
\(437\) | 5.12461 | − | 15.7719i | 0.245143 | − | 0.754474i | ||||
\(438\) | 0.972136 | − | 2.99193i | 0.0464505 | − | 0.142960i | ||||
\(439\) | −7.76393 | − | 23.8949i | −0.370552 | − | 1.14044i | −0.946431 | − | 0.322907i | \(-0.895340\pi\) |
0.575878 | − | 0.817535i | \(-0.304660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.927051 | + | 2.85317i | −0.0441453 | + | 0.135865i | ||||
\(442\) | 30.8435 | + | 22.4091i | 1.46707 | + | 1.06589i | ||||
\(443\) | −30.0689 | −1.42862 | −0.714308 | − | 0.699832i | \(-0.753258\pi\) | ||||
−0.714308 | + | 0.699832i | \(0.753258\pi\) | |||||||
\(444\) | −1.73607 | − | 1.26133i | −0.0823901 | − | 0.0598599i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.85410 | + | 1.34708i | −0.0877943 | + | 0.0637863i | ||||
\(447\) | −5.69098 | + | 4.13474i | −0.269174 | + | 0.195567i | ||||
\(448\) | −0.618034 | − | 1.90211i | −0.0291994 | − | 0.0898664i | ||||
\(449\) | 4.79837 | 0.226449 | 0.113225 | − | 0.993569i | \(-0.463882\pi\) | ||||
0.113225 | + | 0.993569i | \(0.463882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.8885 | 1.50157 | ||||||||
\(452\) | 3.57295 | + | 10.9964i | 0.168057 | + | 0.517227i | ||||
\(453\) | 5.61803 | − | 4.08174i | 0.263958 | − | 0.191777i | ||||
\(454\) | −13.7082 | + | 9.95959i | −0.643358 | + | 0.467427i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.23607 | + | 1.62460i | 0.104713 | + | 0.0760788i | ||||
\(457\) | 12.4721 | 0.583422 | 0.291711 | − | 0.956507i | \(-0.405775\pi\) | ||||
0.291711 | + | 0.956507i | \(0.405775\pi\) | |||||||
\(458\) | 19.6353 | + | 14.2658i | 0.917495 | + | 0.666599i | ||||
\(459\) | −2.42705 | + | 7.46969i | −0.113285 | + | 0.348655i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.75329 | + | 23.8622i | 0.361107 | + | 1.11137i | 0.952383 | + | 0.304903i | \(0.0986241\pi\) |
−0.591277 | + | 0.806469i | \(0.701376\pi\) | |||||||
\(462\) | 3.23607 | − | 9.95959i | 0.150556 | − | 0.463362i | ||||
\(463\) | 3.79837 | − | 11.6902i | 0.176525 | − | 0.543289i | −0.823174 | − | 0.567789i | \(-0.807799\pi\) |
0.999700 | + | 0.0244992i | \(0.00779912\pi\) | |||||||
\(464\) | −0.427051 | − | 1.31433i | −0.0198253 | − | 0.0610161i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.82624 | − | 21.0090i | 0.316219 | − | 0.973223i | ||||
\(467\) | 12.7984 | + | 9.29856i | 0.592238 | + | 0.430286i | 0.843115 | − | 0.537733i | \(-0.180719\pi\) |
−0.250877 | + | 0.968019i | \(0.580719\pi\) | |||||||
\(468\) | 4.85410 | 0.224381 | ||||||||
\(469\) | 15.7082 | + | 11.4127i | 0.725337 | + | 0.526989i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4443 | − | 10.4944i | 0.665557 | − | 0.483555i | ||||
\(472\) | −7.23607 | + | 5.25731i | −0.333067 | + | 0.241987i | ||||
\(473\) | −2.00000 | − | 6.15537i | −0.0919601 | − | 0.283024i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 15.7082 | 0.719984 | ||||||||
\(477\) | −2.64590 | − | 8.14324i | −0.121147 | − | 0.372853i | ||||
\(478\) | −21.7082 | + | 15.7719i | −0.992910 | + | 0.721391i | ||||
\(479\) | −3.61803 | + | 2.62866i | −0.165312 | + | 0.120106i | −0.667366 | − | 0.744730i | \(-0.732578\pi\) |
0.502053 | + | 0.864837i | \(0.332578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.42705 | − | 6.12261i | −0.384240 | − | 0.279167i | ||||
\(482\) | −13.8541 | −0.631037 | ||||||||
\(483\) | −9.70820 | − | 7.05342i | −0.441739 | − | 0.320942i | ||||
\(484\) | 5.07295 | − | 15.6129i | 0.230589 | − | 0.709679i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.309017 | + | 0.951057i | 0.0140173 | + | 0.0431408i | ||||
\(487\) | −3.18034 | + | 9.78808i | −0.144115 | + | 0.443540i | −0.996896 | − | 0.0787282i | \(-0.974914\pi\) |
0.852781 | + | 0.522268i | \(0.174914\pi\) | |||||||
\(488\) | −2.73607 | + | 8.42075i | −0.123856 | + | 0.381190i | ||||
\(489\) | −6.32624 | − | 19.4702i | −0.286082 | − | 0.880471i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.23607 | − | 28.4257i | 0.416818 | − | 1.28283i | −0.493797 | − | 0.869577i | \(-0.664391\pi\) |
0.910615 | − | 0.413256i | \(-0.135609\pi\) | |||||||
\(492\) | 4.92705 | + | 3.57971i | 0.222129 | + | 0.161386i | ||||
\(493\) | 10.8541 | 0.488844 | ||||||||
\(494\) | 10.8541 | + | 7.88597i | 0.488349 | + | 0.354806i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.00000 | + | 2.17963i | −0.134704 | + | 0.0978682i | ||||
\(497\) | −22.9443 | + | 16.6700i | −1.02919 | + | 0.747751i | ||||
\(498\) | −1.85410 | − | 5.70634i | −0.0830843 | − | 0.255707i | ||||
\(499\) | −33.4164 | −1.49592 | −0.747962 | − | 0.663742i | \(-0.768967\pi\) | ||||
−0.747962 | + | 0.663742i | \(0.768967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.47214 | −0.289154 | ||||||||
\(502\) | −3.85410 | − | 11.8617i | −0.172017 | − | 0.529414i | ||||
\(503\) | 17.4164 | − | 12.6538i | 0.776559 | − | 0.564203i | −0.127385 | − | 0.991853i | \(-0.540658\pi\) |
0.903944 | + | 0.427650i | \(0.140658\pi\) | |||||||
\(504\) | 1.61803 | − | 1.17557i | 0.0720730 | − | 0.0523641i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −25.4164 | − | 18.4661i | −1.12990 | − | 0.820918i | ||||
\(507\) | 10.5623 | 0.469088 | ||||||||
\(508\) | 0.236068 | + | 0.171513i | 0.0104738 | + | 0.00760968i | ||||
\(509\) | −4.24671 | + | 13.0700i | −0.188232 | + | 0.579319i | −0.999989 | − | 0.00467647i | \(-0.998511\pi\) |
0.811757 | + | 0.583995i | \(0.198511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.94427 | − | 5.98385i | −0.0860095 | − | 0.264710i | ||||
\(512\) | 0.309017 | − | 0.951057i | 0.0136568 | − | 0.0420312i | ||||
\(513\) | −0.854102 | + | 2.62866i | −0.0377095 | + | 0.116058i | ||||
\(514\) | 3.59017 | + | 11.0494i | 0.158356 | + | 0.487368i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.381966 | − | 1.17557i | 0.0168151 | − | 0.0517516i | ||||
\(517\) | −20.1803 | − | 14.6619i | −0.887530 | − | 0.644829i | ||||
\(518\) | −4.29180 | −0.188571 | ||||||||
\(519\) | −8.82624 | − | 6.41264i | −0.387429 | − | 0.281484i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.07295 | + | 3.68571i | −0.222250 | + | 0.161474i | −0.693339 | − | 0.720612i | \(-0.743861\pi\) |
0.471089 | + | 0.882086i | \(0.343861\pi\) | |||||||
\(522\) | 1.11803 | − | 0.812299i | 0.0489350 | − | 0.0355534i | ||||
\(523\) | 0.708204 | + | 2.17963i | 0.0309676 | + | 0.0953085i | 0.965346 | − | 0.260975i | \(-0.0840439\pi\) |
−0.934378 | + | 0.356283i | \(0.884044\pi\) | |||||||
\(524\) | −0.763932 | −0.0333725 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.472136 | −0.0205861 | ||||||||
\(527\) | −9.00000 | − | 27.6992i | −0.392046 | − | 1.20659i | ||||
\(528\) | 4.23607 | − | 3.07768i | 0.184351 | − | 0.133939i | ||||
\(529\) | −10.5172 | + | 7.64121i | −0.457270 | + | 0.332226i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.23607 | − | 5.25731i | −0.314019 | − | 0.228148i | ||||
\(532\) | 5.52786 | 0.239663 | ||||||||
\(533\) | 23.9164 | + | 17.3763i | 1.03593 | + | 0.752651i | ||||
\(534\) | 0.427051 | − | 1.31433i | 0.0184803 | − | 0.0568765i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.00000 | + | 9.23305i | 0.129580 | + | 0.398807i | ||||
\(537\) | −1.18034 | + | 3.63271i | −0.0509354 | + | 0.156763i | ||||
\(538\) | −0.590170 | + | 1.81636i | −0.0254440 | + | 0.0783087i | ||||
\(539\) | 4.85410 | + | 14.9394i | 0.209081 | + | 0.643485i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.57295 | − | 20.2295i | 0.282593 | − | 0.869732i | −0.704517 | − | 0.709688i | \(-0.748836\pi\) |
0.987110 | − | 0.160045i | \(-0.0511639\pi\) | |||||||
\(542\) | −22.7984 | − | 16.5640i | −0.979274 | − | 0.711484i | ||||
\(543\) | −20.0344 | −0.859760 | ||||||||
\(544\) | 6.35410 | + | 4.61653i | 0.272430 | + | 0.197932i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 7.85410 | − | 5.70634i | 0.336125 | − | 0.244209i | ||||
\(547\) | 1.61803 | − | 1.17557i | 0.0691821 | − | 0.0502638i | −0.552657 | − | 0.833409i | \(-0.686386\pi\) |
0.621839 | + | 0.783145i | \(0.286386\pi\) | |||||||
\(548\) | 4.64590 | + | 14.2986i | 0.198463 | + | 0.610806i | ||||
\(549\) | −8.85410 | −0.377884 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.81966 | 0.162723 | ||||||||
\(552\) | −1.85410 | − | 5.70634i | −0.0789158 | − | 0.242878i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −17.9164 | + | 13.0170i | −0.761195 | + | 0.553041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.8541 | + | 7.88597i | 0.460316 | + | 0.334439i | ||||
\(557\) | 27.2705 | 1.15549 | 0.577744 | − | 0.816218i | \(-0.303933\pi\) | ||||
0.577744 | + | 0.816218i | \(0.303933\pi\) | |||||||
\(558\) | −3.00000 | − | 2.17963i | −0.127000 | − | 0.0922710i | ||||
\(559\) | 1.85410 | − | 5.70634i | 0.0784202 | − | 0.241352i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.7082 | + | 39.1118i | 0.536541 | + | 1.65130i | ||||
\(562\) | −1.88197 | + | 5.79210i | −0.0793859 | + | 0.244325i | ||||
\(563\) | −3.23607 | + | 9.95959i | −0.136384 | + | 0.419747i | −0.995803 | − | 0.0915256i | \(-0.970826\pi\) |
0.859419 | + | 0.511272i | \(0.170826\pi\) | |||||||
\(564\) | −1.47214 | − | 4.53077i | −0.0619881 | − | 0.190780i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.00000 | + | 3.07768i | −0.0420331 | + | 0.129365i | ||||
\(567\) | 1.61803 | + | 1.17557i | 0.0679510 | + | 0.0493693i | ||||
\(568\) | −14.1803 | −0.594994 | ||||||||
\(569\) | −17.2984 | − | 12.5680i | −0.725186 | − | 0.526878i | 0.162851 | − | 0.986651i | \(-0.447931\pi\) |
−0.888037 | + | 0.459772i | \(0.847931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.2705 | + | 19.8132i | −1.14124 | + | 0.829156i | −0.987291 | − | 0.158924i | \(-0.949198\pi\) |
−0.153944 | + | 0.988080i | \(0.549198\pi\) | |||||||
\(572\) | 20.5623 | − | 14.9394i | 0.859753 | − | 0.624647i | ||||
\(573\) | −0.236068 | − | 0.726543i | −0.00986188 | − | 0.0303517i | ||||
\(574\) | 12.1803 | 0.508398 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.90983 | − | 27.4216i | −0.370921 | − | 1.14158i | −0.946190 | − | 0.323613i | \(-0.895102\pi\) |
0.575268 | − | 0.817965i | \(-0.304898\pi\) | |||||||
\(578\) | −36.1525 | + | 26.2663i | −1.50374 | + | 1.09253i | ||||
\(579\) | 1.92705 | − | 1.40008i | 0.0800855 | − | 0.0581855i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.70820 | − | 7.05342i | −0.402764 | − | 0.292625i | ||||
\(582\) | 13.8541 | 0.574271 | ||||||||
\(583\) | −36.2705 | − | 26.3521i | −1.50217 | − | 1.09139i | ||||
\(584\) | 0.972136 | − | 2.99193i | 0.0402273 | − | 0.123807i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.89919 | + | 27.3889i | 0.367622 | + | 1.13142i | ||||
\(587\) | 4.90983 | − | 15.1109i | 0.202650 | − | 0.623694i | −0.797151 | − | 0.603780i | \(-0.793661\pi\) |
0.999802 | − | 0.0199141i | \(-0.00633929\pi\) | |||||||
\(588\) | −0.927051 | + | 2.85317i | −0.0382309 | + | 0.117663i | ||||
\(589\) | −3.16718 | − | 9.74759i | −0.130502 | − | 0.401642i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.11803 | − | 12.6740i | 0.169393 | − | 0.521339i | ||||
\(592\) | −1.73607 | − | 1.26133i | −0.0713520 | − | 0.0518402i | ||||
\(593\) | 6.03444 | 0.247805 | 0.123902 | − | 0.992294i | \(-0.460459\pi\) | ||||
0.123902 | + | 0.992294i | \(0.460459\pi\) | |||||||
\(594\) | 4.23607 | + | 3.07768i | 0.173808 | + | 0.126279i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.69098 | + | 4.13474i | −0.233112 | + | 0.169366i | ||||
\(597\) | 5.00000 | − | 3.63271i | 0.204636 | − | 0.148677i | ||||
\(598\) | −9.00000 | − | 27.6992i | −0.368037 | − | 1.13270i | ||||
\(599\) | 1.05573 | 0.0431359 | 0.0215679 | − | 0.999767i | \(-0.493134\pi\) | ||||
0.0215679 | + | 0.999767i | \(0.493134\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.32624 | 0.298843 | 0.149422 | − | 0.988774i | \(-0.452259\pi\) | ||||
0.149422 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(602\) | −0.763932 | − | 2.35114i | −0.0311355 | − | 0.0958254i | ||||
\(603\) | −7.85410 | + | 5.70634i | −0.319844 | + | 0.232380i | ||||
\(604\) | 5.61803 | − | 4.08174i | 0.228595 | − | 0.166084i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.35410 | − | 0.983813i | −0.0550066 | − | 0.0399647i | ||||
\(607\) | 1.81966 | 0.0738577 | 0.0369289 | − | 0.999318i | \(-0.488243\pi\) | ||||
0.0369289 | + | 0.999318i | \(0.488243\pi\) | |||||||
\(608\) | 2.23607 | + | 1.62460i | 0.0906845 | + | 0.0658862i | ||||
\(609\) | 0.854102 | − | 2.62866i | 0.0346100 | − | 0.106518i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.14590 | − | 21.9928i | −0.289092 | − | 0.889734i | ||||
\(612\) | −2.42705 | + | 7.46969i | −0.0981077 | + | 0.301945i | ||||
\(613\) | 6.66312 | − | 20.5070i | 0.269121 | − | 0.828269i | −0.721594 | − | 0.692316i | \(-0.756590\pi\) |
0.990715 | − | 0.135953i | \(-0.0434096\pi\) | |||||||
\(614\) | 5.03444 | + | 15.4944i | 0.203174 | + | 0.625304i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.23607 | − | 9.95959i | 0.130385 | − | 0.401283i | ||||
\(617\) | 6.78115 | + | 4.92680i | 0.272999 | + | 0.198345i | 0.715858 | − | 0.698246i | \(-0.246036\pi\) |
−0.442859 | + | 0.896591i | \(0.646036\pi\) | |||||||
\(618\) | 2.29180 | 0.0921896 | ||||||||
\(619\) | −2.76393 | − | 2.00811i | −0.111092 | − | 0.0807129i | 0.530852 | − | 0.847464i | \(-0.321872\pi\) |
−0.641944 | + | 0.766751i | \(0.721872\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.85410 | − | 3.52671i | 0.194788 | − | 0.141522i | ||||
\(622\) | 15.0902 | − | 10.9637i | 0.605061 | − | 0.439602i | ||||
\(623\) | −0.854102 | − | 2.62866i | −0.0342189 | − | 0.105315i | ||||
\(624\) | 4.85410 | 0.194320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.3607 | 1.05358 | ||||||||
\(627\) | 4.47214 | + | 13.7638i | 0.178600 | + | 0.549674i | ||||
\(628\) | 14.4443 | − | 10.4944i | 0.576389 | − | 0.418771i | ||||
\(629\) | 13.6353 | − | 9.90659i | 0.543673 | − | 0.395002i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.8885 | + | 25.3480i | 1.38889 | + | 1.00909i | 0.995986 | + | 0.0895093i | \(0.0285299\pi\) |
0.392905 | + | 0.919579i | \(0.371470\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.47214 | + | 4.70228i | 0.257244 | + | 0.186899i | ||||
\(634\) | 2.14590 | − | 6.60440i | 0.0852245 | − | 0.262294i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.64590 | − | 8.14324i | −0.104917 | − | 0.322900i | ||||
\(637\) | −4.50000 | + | 13.8496i | −0.178296 | + | 0.548740i | ||||
\(638\) | 2.23607 | − | 6.88191i | 0.0885268 | − | 0.272457i | ||||
\(639\) | −4.38197 | − | 13.4863i | −0.173348 | − | 0.533510i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.32624 | + | 25.6255i | −0.328867 | + | 1.01215i | 0.640798 | + | 0.767709i | \(0.278603\pi\) |
−0.969665 | + | 0.244438i | \(0.921397\pi\) | |||||||
\(642\) | 8.85410 | + | 6.43288i | 0.349444 | + | 0.253886i | ||||
\(643\) | 39.7771 | 1.56866 | 0.784328 | − | 0.620347i | \(-0.213008\pi\) | ||||
0.784328 | + | 0.620347i | \(0.213008\pi\) | |||||||
\(644\) | −9.70820 | − | 7.05342i | −0.382557 | − | 0.277944i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.5623 | + | 12.7598i | −0.690980 | + | 0.502026i | ||||
\(647\) | −29.0344 | + | 21.0948i | −1.14146 | + | 0.829320i | −0.987322 | − | 0.158729i | \(-0.949261\pi\) |
−0.154139 | + | 0.988049i | \(0.549261\pi\) | |||||||
\(648\) | 0.309017 | + | 0.951057i | 0.0121393 | + | 0.0373610i | ||||
\(649\) | −46.8328 | −1.83835 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.41641 | −0.290672 | ||||||||
\(652\) | −6.32624 | − | 19.4702i | −0.247755 | − | 0.762510i | ||||
\(653\) | −26.0623 | + | 18.9354i | −1.01990 | + | 0.740998i | −0.966262 | − | 0.257562i | \(-0.917081\pi\) |
−0.0536351 | + | 0.998561i | \(0.517081\pi\) | |||||||
\(654\) | −2.07295 | + | 1.50609i | −0.0810587 | + | 0.0588926i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.92705 | + | 3.57971i | 0.192369 | + | 0.139764i | ||||
\(657\) | 3.14590 | 0.122733 | ||||||||
\(658\) | −7.70820 | − | 5.60034i | −0.300497 | − | 0.218324i | ||||
\(659\) | 12.0344 | − | 37.0382i | 0.468795 | − | 1.44280i | −0.385351 | − | 0.922770i | \(-0.625920\pi\) |
0.854146 | − | 0.520033i | \(-0.174080\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.27051 | − | 22.3763i | −0.282790 | − | 0.870338i | −0.987052 | − | 0.160398i | \(-0.948722\pi\) |
0.704262 | − | 0.709940i | \(-0.251278\pi\) | |||||||
\(662\) | −10.0344 | + | 30.8828i | −0.390000 | + | 1.20030i | ||||
\(663\) | −11.7812 | + | 36.2587i | −0.457542 | + | 1.40817i | ||||
\(664\) | −1.85410 | − | 5.70634i | −0.0719531 | − | 0.221449i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.663119 | − | 2.04087i | 0.0256953 | − | 0.0790821i | ||||
\(667\) | −6.70820 | − | 4.87380i | −0.259743 | − | 0.188714i | ||||
\(668\) | −6.47214 | −0.250414 | ||||||||
\(669\) | −1.85410 | − | 1.34708i | −0.0716837 | − | 0.0520813i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −37.5066 | + | 27.2501i | −1.44793 | + | 1.05198i | ||||
\(672\) | 1.61803 | − | 1.17557i | 0.0624170 | − | 0.0453486i | ||||
\(673\) | 5.80902 | + | 17.8783i | 0.223921 | + | 0.689158i | 0.998399 | + | 0.0565578i | \(0.0180125\pi\) |
−0.774478 | + | 0.632601i | \(0.781987\pi\) | |||||||
\(674\) | −28.8328 | −1.11060 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5623 | 0.406243 | ||||||||
\(677\) | −11.2705 | − | 34.6871i | −0.433161 | − | 1.33313i | −0.894960 | − | 0.446147i | \(-0.852796\pi\) |
0.461799 | − | 0.886985i | \(-0.347204\pi\) | |||||||
\(678\) | −9.35410 | + | 6.79615i | −0.359242 | + | 0.261005i | ||||
\(679\) | 22.4164 | − | 16.2865i | 0.860263 | − | 0.625017i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.7082 | − | 9.95959i | −0.525300 | − | 0.381652i | ||||
\(682\) | −19.4164 | −0.743493 | ||||||||
\(683\) | 15.7082 | + | 11.4127i | 0.601058 | + | 0.436694i | 0.846254 | − | 0.532779i | \(-0.178852\pi\) |
−0.245196 | + | 0.969473i | \(0.578852\pi\) | |||||||
\(684\) | −0.854102 | + | 2.62866i | −0.0326574 | + | 0.100509i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.18034 | + | 19.0211i | 0.235966 | + | 0.726230i | ||||
\(687\) | −7.50000 | + | 23.0826i | −0.286143 | + | 0.880657i | ||||
\(688\) | 0.381966 | − | 1.17557i | 0.0145623 | − | 0.0448182i | ||||
\(689\) | −12.8435 | − | 39.5281i | −0.489297 | − | 1.50590i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.47214 | + | 22.9969i | −0.284253 | + | 0.874842i | 0.702368 | + | 0.711814i | \(0.252126\pi\) |
−0.986621 | + | 0.163028i | \(0.947874\pi\) | |||||||
\(692\) | −8.82624 | − | 6.41264i | −0.335523 | − | 0.243772i | ||||
\(693\) | 10.4721 | 0.397804 | ||||||||
\(694\) | −4.23607 | − | 3.07768i | −0.160799 | − | 0.116827i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.11803 | − | 0.812299i | 0.0423790 | − | 0.0307901i | ||||
\(697\) | −38.6976 | + | 28.1154i | −1.46577 | + | 1.06495i | ||||
\(698\) | 4.57295 | + | 14.0741i | 0.173089 | + | 0.532712i | ||||
\(699\) | 22.0902 | 0.835527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.1591 | −0.761397 | −0.380698 | − | 0.924699i | \(-0.624316\pi\) | ||||
−0.380698 | + | 0.924699i | \(0.624316\pi\) | |||||||
\(702\) | 1.50000 | + | 4.61653i | 0.0566139 | + | 0.174240i | ||||
\(703\) | 4.79837 | − | 3.48622i | 0.180974 | − | 0.131485i | ||||
\(704\) | 4.23607 | − | 3.07768i | 0.159653 | − | 0.115995i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.5623 | + | 12.0332i | 0.623331 | + | 0.452876i | ||||
\(707\) | −3.34752 | −0.125897 | ||||||||
\(708\) | −7.23607 | − | 5.25731i | −0.271948 | − | 0.197582i | ||||
\(709\) | −9.20820 | + | 28.3399i | −0.345821 | + | 1.06433i | 0.615321 | + | 0.788276i | \(0.289026\pi\) |
−0.961143 | + | 0.276052i | \(0.910974\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.427051 | − | 1.31433i | 0.0160044 | − | 0.0492565i | ||||
\(713\) | −6.87539 | + | 21.1603i | −0.257485 | + | 0.792458i | ||||
\(714\) | 4.85410 | + | 14.9394i | 0.181660 | + | 0.559093i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.18034 | + | 3.63271i | −0.0441114 | + | 0.135761i | ||||
\(717\) | −21.7082 | − | 15.7719i | −0.810708 | − | 0.589014i | ||||
\(718\) | −27.8885 | −1.04079 | ||||||||
\(719\) | −18.0902 | − | 13.1433i | −0.674649 | − | 0.490162i | 0.196929 | − | 0.980418i | \(-0.436903\pi\) |
−0.871578 | + | 0.490256i | \(0.836903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.70820 | − | 2.69417i | 0.138101 | − | 0.100336i | ||||
\(722\) | 9.19098 | − | 6.67764i | 0.342053 | − | 0.248516i | ||||
\(723\) | −4.28115 | − | 13.1760i | −0.159218 | − | 0.490022i | ||||
\(724\) | −20.0344 | −0.744574 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 16.4164 | 0.609270 | ||||||||
\(727\) | −3.18034 | − | 9.78808i | −0.117952 | − | 0.363020i | 0.874599 | − | 0.484847i | \(-0.161125\pi\) |
−0.992551 | + | 0.121827i | \(0.961125\pi\) | |||||||
\(728\) | 7.85410 | − | 5.70634i | 0.291092 | − | 0.211491i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.85410 | + | 5.70634i | 0.290494 | + | 0.211057i | ||||
\(732\) | −8.85410 | −0.327257 | ||||||||
\(733\) | −5.14590 | − | 3.73871i | −0.190068 | − | 0.138093i | 0.488682 | − | 0.872462i | \(-0.337478\pi\) |
−0.678750 | + | 0.734370i | \(0.737478\pi\) | |||||||
\(734\) | 3.85410 | − | 11.8617i | 0.142257 | − | 0.437824i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.85410 | − | 5.70634i | −0.0683431 | − | 0.210338i | ||||
\(737\) | −15.7082 | + | 48.3449i | −0.578619 | + | 1.78081i | ||||
\(738\) | −1.88197 | + | 5.79210i | −0.0692761 | + | 0.213210i | ||||
\(739\) | 2.56231 | + | 7.88597i | 0.0942559 | + | 0.290090i | 0.987059 | − | 0.160357i | \(-0.0512646\pi\) |
−0.892803 | + | 0.450447i | \(0.851265\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.14590 | + | 12.7598i | −0.152303 | + | 0.468742i | ||||
\(742\) | −13.8541 | − | 10.0656i | −0.508600 | − | 0.369520i | ||||
\(743\) | −6.65248 | −0.244056 | −0.122028 | − | 0.992527i | \(-0.538940\pi\) | ||||
−0.122028 | + | 0.992527i | \(0.538940\pi\) | |||||||
\(744\) | −3.00000 | − | 2.17963i | −0.109985 | − | 0.0799090i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.09017 | − | 1.51860i | 0.0765266 | − | 0.0555998i | ||||
\(747\) | 4.85410 | − | 3.52671i | 0.177602 | − | 0.129036i | ||||
\(748\) | 12.7082 | + | 39.1118i | 0.464658 | + | 1.43007i | ||||
\(749\) | 21.8885 | 0.799790 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7639 | 0.538744 | 0.269372 | − | 0.963036i | \(-0.413184\pi\) | ||||
0.269372 | + | 0.963036i | \(0.413184\pi\) | |||||||
\(752\) | −1.47214 | − | 4.53077i | −0.0536833 | − | 0.165220i | ||||
\(753\) | 10.0902 | − | 7.33094i | 0.367706 | − | 0.267154i | ||||
\(754\) | 5.42705 | − | 3.94298i | 0.197642 | − | 0.143595i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.61803 | + | 1.17557i | 0.0588473 | + | 0.0427551i | ||||
\(757\) | 28.8541 | 1.04872 | 0.524360 | − | 0.851497i | \(-0.324305\pi\) | ||||
0.524360 | + | 0.851497i | \(0.324305\pi\) | |||||||
\(758\) | 2.76393 | + | 2.00811i | 0.100391 | + | 0.0729380i | ||||
\(759\) | 9.70820 | − | 29.8788i | 0.352385 | − | 1.08453i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.46556 | + | 22.9766i | 0.270626 | + | 0.832902i | 0.990344 | + | 0.138635i | \(0.0442714\pi\) |
−0.719717 | + | 0.694267i | \(0.755729\pi\) | |||||||
\(762\) | −0.0901699 | + | 0.277515i | −0.00326651 | + | 0.0100533i | ||||
\(763\) | −1.58359 | + | 4.87380i | −0.0573299 | + | 0.176443i | ||||
\(764\) | −0.236068 | − | 0.726543i | −0.00854064 | − | 0.0262854i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.32624 | + | 19.4702i | −0.228576 | + | 0.703485i | ||||
\(767\) | −35.1246 | − | 25.5195i | −1.26828 | − | 0.921457i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 1.90983 | + | 1.38757i | 0.0688702 | + | 0.0500372i | 0.621688 | − | 0.783265i | \(-0.286447\pi\) |
−0.552817 | + | 0.833302i | \(0.686447\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.39919 | + | 6.82891i | −0.338503 | + | 0.245937i | ||||
\(772\) | 1.92705 | − | 1.40008i | 0.0693561 | − | 0.0503901i | ||||
\(773\) | −4.35410 | − | 13.4005i | −0.156606 | − | 0.481984i | 0.841714 | − | 0.539924i | \(-0.181547\pi\) |
−0.998320 | + | 0.0579395i | \(0.981547\pi\) | |||||||
\(774\) | 1.23607 | 0.0444295 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.8541 | 0.497333 | ||||||||
\(777\) | −1.32624 | − | 4.08174i | −0.0475785 | − | 0.146432i | ||||
\(778\) | −12.9271 | + | 9.39205i | −0.463457 | + | 0.336721i | ||||
\(779\) | −13.6180 | + | 9.89408i | −0.487917 | + | 0.354492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.0689 | − | 43.6426i | −2.14943 | − | 1.56165i | ||||
\(782\) | 47.1246 | 1.68517 | ||||||||
\(783\) | 1.11803 | + | 0.812299i | 0.0399553 | + | 0.0290292i | ||||
\(784\) | −0.927051 | + | 2.85317i | −0.0331090 | + | 0.101899i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.236068 | − | 0.726543i | −0.00842027 | − | 0.0259149i | ||||
\(787\) | −9.43769 | + | 29.0462i | −0.336417 | + | 1.03539i | 0.629602 | + | 0.776918i | \(0.283218\pi\) |
−0.966020 | + | 0.258469i | \(0.916782\pi\) | |||||||
\(788\) | 4.11803 | − | 12.6740i | 0.146699 | − | 0.451493i | ||||
\(789\) | −0.145898 | − | 0.449028i | −0.00519411 | − | 0.0159858i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.14590 | + | 21.9928i | −0.254079 | + | 0.781974i | ||||
\(792\) | 4.23607 | + | 3.07768i | 0.150522 | + | 0.109361i | ||||
\(793\) | −42.9787 | −1.52622 | ||||||||
\(794\) | 23.3262 | + | 16.9475i | 0.827817 | + | 0.601444i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.00000 | − | 3.63271i | 0.177220 | − | 0.128758i | ||||
\(797\) | −10.7812 | + | 7.83297i | −0.381888 | + | 0.277458i | −0.762123 | − | 0.647432i | \(-0.775843\pi\) |
0.380235 | + | 0.924890i | \(0.375843\pi\) | |||||||
\(798\) | 1.70820 | + | 5.25731i | 0.0604698 | + | 0.186107i | ||||
\(799\) | 37.4164 | 1.32370 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.38197 | 0.0488294 | ||||||||
\(802\) | −8.06231 | − | 24.8132i | −0.284690 | − | 0.876185i | ||||
\(803\) | 13.3262 | − | 9.68208i | 0.470273 | − | 0.341673i | ||||
\(804\) | −7.85410 | + | 5.70634i | −0.276993 | + | 0.201247i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.5623 | − | 10.5801i | −0.512935 | − | 0.372669i | ||||
\(807\) | −1.90983 | −0.0672292 | ||||||||
\(808\) | −1.35410 | − | 0.983813i | −0.0476371 | − | 0.0346104i | ||||
\(809\) | 2.53851 | − | 7.81272i | 0.0892492 | − | 0.274681i | −0.896463 | − | 0.443118i | \(-0.853872\pi\) |
0.985712 | + | 0.168438i | \(0.0538722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.18034 | + | 9.78808i | 0.111677 | + | 0.343706i | 0.991239 | − | 0.132077i | \(-0.0421647\pi\) |
−0.879563 | + | 0.475783i | \(0.842165\pi\) | |||||||
\(812\) | 0.854102 | − | 2.62866i | 0.0299731 | − | 0.0922477i | ||||
\(813\) | 8.70820 | − | 26.8011i | 0.305410 | − | 0.939955i | ||||
\(814\) | −3.47214 | − | 10.6861i | −0.121698 | − | 0.374549i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.42705 | + | 7.46969i | −0.0849638 | + | 0.261492i | ||||
\(817\) | 2.76393 | + | 2.00811i | 0.0966977 | + | 0.0702550i | ||||
\(818\) | 20.9787 | 0.733504 | ||||||||
\(819\) | 7.85410 | + | 5.70634i | 0.274445 | + | 0.199396i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 36.2705 | − | 26.3521i | 1.26585 | − | 0.919694i | 0.266820 | − | 0.963746i | \(-0.414027\pi\) |
0.999029 | + | 0.0440528i | \(0.0140270\pi\) | |||||||
\(822\) | −12.1631 | + | 8.83702i | −0.424237 | + | 0.308227i | ||||
\(823\) | 7.29180 | + | 22.4418i | 0.254176 | + | 0.782273i | 0.993991 | + | 0.109463i | \(0.0349131\pi\) |
−0.739815 | + | 0.672811i | \(0.765087\pi\) | |||||||
\(824\) | 2.29180 | 0.0798385 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.8885 | −0.622422 | ||||||||
\(827\) | −4.56231 | − | 14.0413i | −0.158647 | − | 0.488265i | 0.839865 | − | 0.542795i | \(-0.182634\pi\) |
−0.998512 | + | 0.0545300i | \(0.982634\pi\) | |||||||
\(828\) | 4.85410 | − | 3.52671i | 0.168692 | − | 0.122562i | ||||
\(829\) | −31.6697 | + | 23.0094i | −1.09993 | + | 0.799149i | −0.981049 | − | 0.193759i | \(-0.937932\pi\) |
−0.118885 | + | 0.992908i | \(0.537932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.9164 | − | 13.0170i | −0.621513 | − | 0.451556i | ||||
\(832\) | 4.85410 | 0.168286 | ||||||||
\(833\) | −19.0623 | − | 13.8496i | −0.660470 | − | 0.479859i | ||||
\(834\) | −4.14590 | + | 12.7598i | −0.143561 | + | 0.441834i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.47214 | + | 13.7638i | 0.154672 | + | 0.476032i | ||||
\(837\) | 1.14590 | − | 3.52671i | 0.0396080 | − | 0.121901i | ||||
\(838\) | −11.7082 | + | 36.0341i | −0.404453 | + | 1.24478i | ||||
\(839\) | −1.58359 | − | 4.87380i | −0.0546717 | − | 0.168262i | 0.919992 | − | 0.391937i | \(-0.128195\pi\) |
−0.974664 | + | 0.223674i | \(0.928195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.37132 | + | 25.7643i | −0.288666 | + | 0.888424i | ||||
\(842\) | 8.97214 | + | 6.51864i | 0.309200 | + | 0.224647i | ||||
\(843\) | −6.09017 | −0.209757 | ||||||||
\(844\) | 6.47214 | + | 4.70228i | 0.222780 | + | 0.161859i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.85410 | − | 2.80017i | 0.132507 | − | 0.0962718i | ||||
\(847\) | 26.5623 | − | 19.2986i | 0.912692 | − | 0.663109i | ||||
\(848\) | −2.64590 | − | 8.14324i | −0.0908605 | − | 0.279640i | ||||
\(849\) | −3.23607 | −0.111062 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.8754 | −0.441363 | ||||||||
\(852\) | −4.38197 | − | 13.4863i | −0.150124 | − | 0.462033i | ||||
\(853\) | 13.3090 | − | 9.66957i | 0.455692 | − | 0.331080i | −0.336147 | − | 0.941810i | \(-0.609124\pi\) |
0.791839 | + | 0.610730i | \(0.209124\pi\) | |||||||
\(854\) | −14.3262 | + | 10.4086i | −0.490234 | + | 0.356176i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.85410 | + | 6.43288i | 0.302627 | + | 0.219871i | ||||
\(857\) | −23.3050 | −0.796082 | −0.398041 | − | 0.917368i | \(-0.630310\pi\) | ||||
−0.398041 | + | 0.917368i | \(0.630310\pi\) | |||||||
\(858\) | 20.5623 | + | 14.9394i | 0.701986 | + | 0.510022i | ||||
\(859\) | 14.0689 | − | 43.2996i | 0.480024 | − | 1.47736i | −0.359036 | − | 0.933324i | \(-0.616894\pi\) |
0.839060 | − | 0.544039i | \(-0.183106\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.76393 | + | 11.5842i | 0.128274 | + | 0.394788i | ||||
\(862\) | 1.14590 | − | 3.52671i | 0.0390294 | − | 0.120120i | ||||
\(863\) | −3.76393 | + | 11.5842i | −0.128126 | + | 0.394330i | −0.994458 | − | 0.105138i | \(-0.966471\pi\) |
0.866332 | + | 0.499469i | \(0.166471\pi\) | |||||||
\(864\) | 0.309017 | + | 0.951057i | 0.0105130 | + | 0.0323556i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7.15248 | − | 22.0131i | 0.243051 | − | 0.748034i | ||||
\(867\) | −36.1525 | − | 26.2663i | −1.22780 | − | 0.892051i | ||||
\(868\) | −7.41641 | −0.251729 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.1246 | + | 27.6992i | −1.29180 | + | 0.938550i | ||||
\(872\) | −2.07295 | + | 1.50609i | −0.0701989 | + | 0.0510025i | ||||
\(873\) | 4.28115 | + | 13.1760i | 0.144895 | + | 0.445941i | ||||
\(874\) | 16.5836 | 0.560948 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.14590 | 0.106290 | ||||||||
\(877\) | −5.55573 | − | 17.0988i | −0.187604 | − | 0.577385i | 0.812380 | − | 0.583129i | \(-0.198172\pi\) |
−0.999984 | + | 0.00574402i | \(0.998172\pi\) | |||||||
\(878\) | 20.3262 | − | 14.7679i | 0.685977 | − | 0.498392i | ||||
\(879\) | −23.2984 | + | 16.9273i | −0.785835 | + | 0.570942i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.7984 | − | 27.4621i | −1.27346 | − | 0.925223i | −0.274125 | − | 0.961694i | \(-0.588388\pi\) |
−0.999335 | + | 0.0364716i | \(0.988388\pi\) | |||||||
\(882\) | −3.00000 | −0.101015 | ||||||||
\(883\) | 34.1246 | + | 24.7930i | 1.14838 | + | 0.834350i | 0.988265 | − | 0.152747i | \(-0.0488121\pi\) |
0.160119 | + | 0.987098i | \(0.448812\pi\) | |||||||
\(884\) | −11.7812 | + | 36.2587i | −0.396243 | + | 1.21951i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.29180 | − | 28.5972i | −0.312164 | − | 0.960742i | ||||
\(887\) | −7.97871 | + | 24.5560i | −0.267899 | + | 0.824508i | 0.723112 | + | 0.690730i | \(0.242711\pi\) |
−0.991011 | + | 0.133778i | \(0.957289\pi\) | |||||||
\(888\) | 0.663119 | − | 2.04087i | 0.0222528 | − | 0.0684871i | ||||
\(889\) | 0.180340 | + | 0.555029i | 0.00604841 | + | 0.0186151i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.61803 | + | 4.97980i | −0.0542062 | + | 0.166829i | ||||
\(892\) | −1.85410 | − | 1.34708i | −0.0620799 | − | 0.0451037i | ||||
\(893\) | 13.1672 | 0.440623 | ||||||||
\(894\) | −5.69098 | − | 4.13474i | −0.190335 | − | 0.138286i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.61803 | − | 1.17557i | 0.0540547 | − | 0.0392731i | ||||
\(897\) | 23.5623 | − | 17.1190i | 0.786722 | − | 0.571587i | ||||
\(898\) | 1.48278 | + | 4.56352i | 0.0494810 | + | 0.152287i | ||||
\(899\) | −5.12461 | −0.170915 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.2492 | 2.24040 | ||||||||
\(902\) | 9.85410 | + | 30.3278i | 0.328106 | + | 1.00981i | ||||
\(903\) | 2.00000 | − | 1.45309i | 0.0665558 | − | 0.0483556i | ||||
\(904\) | −9.35410 | + | 6.79615i | −0.311113 | + | 0.226037i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 5.61803 | + | 4.08174i | 0.186647 | + | 0.135607i | ||||
\(907\) | −20.2918 | −0.673778 | −0.336889 | − | 0.941544i | \(-0.609375\pi\) | ||||
−0.336889 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(908\) | −13.7082 | − | 9.95959i | −0.454923 | − | 0.330521i | ||||
\(909\) | 0.517221 | − | 1.59184i | 0.0171551 | − | 0.0527981i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.3262 | + | 53.3247i | 0.574044 | + | 1.76673i | 0.639412 | + | 0.768864i | \(0.279178\pi\) |
−0.0653683 | + | 0.997861i | \(0.520822\pi\) | |||||||
\(912\) | −0.854102 | + | 2.62866i | −0.0282821 | + | 0.0870435i | ||||
\(913\) | 9.70820 | − | 29.8788i | 0.321295 | − | 0.988843i | ||||
\(914\) | 3.85410 | + | 11.8617i | 0.127482 | + | 0.392350i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.50000 | + | 23.0826i | −0.247807 | + | 0.762671i | ||||
\(917\) | −1.23607 | − | 0.898056i | −0.0408186 | − | 0.0296564i | ||||
\(918\) | −7.85410 | −0.259224 | ||||||||
\(919\) | 0.854102 | + | 0.620541i | 0.0281742 | + | 0.0204698i | 0.601783 | − | 0.798659i | \(-0.294457\pi\) |
−0.573609 | + | 0.819129i | \(0.694457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.1803 | + | 9.57608i | −0.434307 | + | 0.315542i | ||||
\(922\) | −20.2984 | + | 14.7476i | −0.668491 | + | 0.485687i | ||||
\(923\) | −21.2705 | − | 65.4639i | −0.700127 | − | 2.15477i | ||||
\(924\) | 10.4721 | 0.344508 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 12.2918 | 0.403933 | ||||||||
\(927\) | 0.708204 | + | 2.17963i | 0.0232605 | + | 0.0715884i | ||||
\(928\) | 1.11803 | − | 0.812299i | 0.0367013 | − | 0.0266650i | ||||
\(929\) | 25.0623 | − | 18.2088i | 0.822268 | − | 0.597412i | −0.0950935 | − | 0.995468i | \(-0.530315\pi\) |
0.917361 | + | 0.398056i | \(0.130315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.70820 | − | 4.87380i | −0.219853 | − | 0.159732i | ||||
\(932\) | 22.0902 | 0.723588 | ||||||||
\(933\) | 15.0902 | + | 10.9637i | 0.494030 | + | 0.358934i | ||||
\(934\) | −4.88854 | + | 15.0454i | −0.159958 | + | 0.492300i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.50000 | + | 4.61653i | 0.0490290 | + | 0.150896i | ||||
\(937\) | −10.8435 | + | 33.3727i | −0.354240 | + | 1.09024i | 0.602208 | + | 0.798339i | \(0.294288\pi\) |
−0.956449 | + | 0.291901i | \(0.905712\pi\) | |||||||
\(938\) | −6.00000 | + | 18.4661i | −0.195907 | + | 0.602940i | ||||
\(939\) | 8.14590 | + | 25.0705i | 0.265831 | + | 0.818145i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.69756 | − | 20.6130i | 0.218334 | − | 0.671964i | −0.780566 | − | 0.625074i | \(-0.785069\pi\) |
0.998900 | − | 0.0468901i | \(-0.0149311\pi\) | |||||||
\(942\) | 14.4443 | + | 10.4944i | 0.470620 | + | 0.341925i | ||||
\(943\) | 36.5410 | 1.18994 | ||||||||
\(944\) | −7.23607 | − | 5.25731i | −0.235514 | − | 0.171111i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.23607 | − | 3.80423i | 0.170239 | − | 0.123686i | ||||
\(947\) | 8.85410 | − | 6.43288i | 0.287720 | − | 0.209041i | −0.434558 | − | 0.900644i | \(-0.643095\pi\) |
0.722278 | + | 0.691603i | \(0.243095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.2705 | 0.495702 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.94427 | 0.225183 | ||||||||
\(952\) | 4.85410 | + | 14.9394i | 0.157322 | + | 0.484188i | ||||
\(953\) | −26.5902 | + | 19.3189i | −0.861340 | + | 0.625800i | −0.928249 | − | 0.371959i | \(-0.878686\pi\) |
0.0669091 | + | 0.997759i | \(0.478686\pi\) | |||||||
\(954\) | 6.92705 | − | 5.03280i | 0.224272 | − | 0.162943i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.7082 | − | 15.7719i | −0.702093 | − | 0.510101i | ||||
\(957\) | 7.23607 | 0.233909 | ||||||||
\(958\) | −3.61803 | − | 2.62866i | −0.116893 | − | 0.0849280i | ||||
\(959\) | −9.29180 | + | 28.5972i | −0.300048 | + | 0.923452i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.33030 | − | 16.4050i | −0.171945 | − | 0.529193i | ||||
\(962\) | 3.21885 | − | 9.90659i | 0.103780 | − | 0.319401i | ||||
\(963\) | −3.38197 | + | 10.4086i | −0.108982 | + | 0.335413i | ||||
\(964\) | −4.28115 | − | 13.1760i | −0.137887 | − | 0.424371i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.70820 | − | 11.4127i | 0.119310 | − | 0.367197i | ||||
\(967\) | 33.1246 | + | 24.0664i | 1.06522 | + | 0.773925i | 0.975046 | − | 0.222002i | \(-0.0712591\pi\) |
0.0901695 | + | 0.995926i | \(0.471259\pi\) | |||||||
\(968\) | 16.4164 | 0.527643 | ||||||||
\(969\) | −17.5623 | − | 12.7598i | −0.564183 | − | 0.409903i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.3262 | − | 19.8537i | 0.876941 | − | 0.637135i | −0.0554996 | − | 0.998459i | \(-0.517675\pi\) |
0.932440 | + | 0.361324i | \(0.117675\pi\) | |||||||
\(972\) | −0.809017 | + | 0.587785i | −0.0259492 | + | 0.0188532i | ||||
\(973\) | 8.29180 | + | 25.5195i | 0.265823 | + | 0.818118i | ||||
\(974\) | −10.2918 | −0.329770 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.85410 | −0.283413 | ||||||||
\(977\) | 6.35410 | + | 19.5559i | 0.203286 | + | 0.625649i | 0.999779 | + | 0.0210023i | \(0.00668574\pi\) |
−0.796494 | + | 0.604647i | \(0.793314\pi\) | |||||||
\(978\) | 16.5623 | − | 12.0332i | 0.529604 | − | 0.384780i | ||||
\(979\) | 5.85410 | − | 4.25325i | 0.187098 | − | 0.135935i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.07295 | − | 1.50609i | −0.0661842 | − | 0.0480856i | ||||
\(982\) | 29.8885 | 0.953782 | ||||||||
\(983\) | −34.4164 | − | 25.0050i | −1.09771 | − | 0.797535i | −0.117028 | − | 0.993129i | \(-0.537337\pi\) |
−0.980685 | + | 0.195594i | \(0.937337\pi\) | |||||||
\(984\) | −1.88197 | + | 5.79210i | −0.0599949 | + | 0.184645i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.35410 | + | 10.3229i | 0.106816 | + | 0.328747i | ||||
\(987\) | 2.94427 | − | 9.06154i | 0.0937172 | − | 0.288432i | ||||
\(988\) | −4.14590 | + | 12.7598i | −0.131899 | + | 0.405942i | ||||
\(989\) | −2.29180 | − | 7.05342i | −0.0728749 | − | 0.224286i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7082 | − | 57.5779i | 0.594286 | − | 1.82902i | 0.0360356 | − | 0.999351i | \(-0.488527\pi\) |
0.558250 | − | 0.829673i | \(-0.311473\pi\) | |||||||
\(992\) | −3.00000 | − | 2.17963i | −0.0952501 | − | 0.0692032i | ||||
\(993\) | −32.4721 | −1.03047 | ||||||||
\(994\) | −22.9443 | − | 16.6700i | −0.727748 | − | 0.528740i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.85410 | − | 3.52671i | 0.153808 | − | 0.111748i | ||||
\(997\) | −1.14590 | + | 0.832544i | −0.0362910 | + | 0.0263669i | −0.605783 | − | 0.795630i | \(-0.707140\pi\) |
0.569492 | + | 0.821997i | \(0.307140\pi\) | |||||||
\(998\) | −10.3262 | − | 31.7809i | −0.326871 | − | 1.00601i | ||||
\(999\) | 2.14590 | 0.0678932 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 750.2.g.a.151.1 | 4 | ||
5.2 | odd | 4 | 750.2.h.a.349.1 | 8 | |||
5.3 | odd | 4 | 750.2.h.a.349.2 | 8 | |||
5.4 | even | 2 | 150.2.g.b.31.1 | ✓ | 4 | ||
15.14 | odd | 2 | 450.2.h.b.181.1 | 4 | |||
25.2 | odd | 20 | 3750.2.c.c.1249.3 | 4 | |||
25.3 | odd | 20 | 750.2.h.a.649.1 | 8 | |||
25.4 | even | 10 | 150.2.g.b.121.1 | yes | 4 | ||
25.11 | even | 5 | 3750.2.a.g.1.1 | 2 | |||
25.14 | even | 10 | 3750.2.a.b.1.1 | 2 | |||
25.21 | even | 5 | inner | 750.2.g.a.601.1 | 4 | ||
25.22 | odd | 20 | 750.2.h.a.649.2 | 8 | |||
25.23 | odd | 20 | 3750.2.c.c.1249.1 | 4 | |||
75.29 | odd | 10 | 450.2.h.b.271.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.b.31.1 | ✓ | 4 | 5.4 | even | 2 | ||
150.2.g.b.121.1 | yes | 4 | 25.4 | even | 10 | ||
450.2.h.b.181.1 | 4 | 15.14 | odd | 2 | |||
450.2.h.b.271.1 | 4 | 75.29 | odd | 10 | |||
750.2.g.a.151.1 | 4 | 1.1 | even | 1 | trivial | ||
750.2.g.a.601.1 | 4 | 25.21 | even | 5 | inner | ||
750.2.h.a.349.1 | 8 | 5.2 | odd | 4 | |||
750.2.h.a.349.2 | 8 | 5.3 | odd | 4 | |||
750.2.h.a.649.1 | 8 | 25.3 | odd | 20 | |||
750.2.h.a.649.2 | 8 | 25.22 | odd | 20 | |||
3750.2.a.b.1.1 | 2 | 25.14 | even | 10 | |||
3750.2.a.g.1.1 | 2 | 25.11 | even | 5 | |||
3750.2.c.c.1249.1 | 4 | 25.23 | odd | 20 | |||
3750.2.c.c.1249.3 | 4 | 25.2 | odd | 20 |