Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(117,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.117");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.h (of order \(4\), 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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 117.2 | ||
Root | \(-1.28900 + 1.28900i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.117 |
Dual form | 370.2.h.e.253.2 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.28900 | − | 1.28900i | −0.744204 | − | 0.744204i | 0.229180 | − | 0.973384i | \(-0.426396\pi\) |
−0.973384 | + | 0.229180i | \(0.926396\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.63786 | − | 1.52231i | 0.732472 | − | 0.680797i | ||||
\(6\) | 1.28900 | + | 1.28900i | 0.526232 | + | 0.526232i | ||||
\(7\) | −3.01566 | − | 3.01566i | −1.13981 | − | 1.13981i | −0.988484 | − | 0.151328i | \(-0.951645\pi\) |
−0.151328 | − | 0.988484i | \(-0.548355\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.323040i | 0.107680i | ||||||||
\(10\) | −1.63786 | + | 1.52231i | −0.517936 | + | 0.481396i | ||||
\(11\) | 2.38854i | 0.720171i | 0.932919 | + | 0.360085i | \(0.117252\pi\) | ||||
−0.932919 | + | 0.360085i | \(0.882748\pi\) | |||||||
\(12\) | −1.28900 | − | 1.28900i | −0.372102 | − | 0.372102i | ||||
\(13\) | 1.44800 | 0.401602 | 0.200801 | − | 0.979632i | \(-0.435646\pi\) | ||||
0.200801 | + | 0.979632i | \(0.435646\pi\) | |||||||
\(14\) | 3.01566 | + | 3.01566i | 0.805969 | + | 0.805969i | ||||
\(15\) | −4.07345 | − | 0.148945i | −1.05176 | − | 0.0384573i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.09597i | − | 0.508347i | −0.967159 | − | 0.254173i | \(-0.918197\pi\) | ||
0.967159 | − | 0.254173i | \(-0.0818034\pi\) | |||||||
\(18\) | − | 0.323040i | − | 0.0761413i | ||||||
\(19\) | −2.46518 | + | 2.46518i | −0.565551 | + | 0.565551i | −0.930879 | − | 0.365328i | \(-0.880957\pi\) |
0.365328 | + | 0.930879i | \(0.380957\pi\) | |||||||
\(20\) | 1.63786 | − | 1.52231i | 0.366236 | − | 0.340398i | ||||
\(21\) | 7.77437i | 1.69651i | ||||||||
\(22\) | − | 2.38854i | − | 0.509238i | ||||||
\(23\) | −0.168727 | −0.0351820 | −0.0175910 | − | 0.999845i | \(-0.505600\pi\) | ||||
−0.0175910 | + | 0.999845i | \(0.505600\pi\) | |||||||
\(24\) | 1.28900 | + | 1.28900i | 0.263116 | + | 0.263116i | ||||
\(25\) | 0.365159 | − | 4.98665i | 0.0730318 | − | 0.997330i | ||||
\(26\) | −1.44800 | −0.283976 | ||||||||
\(27\) | −3.45060 | + | 3.45060i | −0.664068 | + | 0.664068i | ||||
\(28\) | −3.01566 | − | 3.01566i | −0.569906 | − | 0.569906i | ||||
\(29\) | −4.74797 | − | 4.74797i | −0.881676 | − | 0.881676i | 0.112029 | − | 0.993705i | \(-0.464265\pi\) |
−0.993705 | + | 0.112029i | \(0.964265\pi\) | |||||||
\(30\) | 4.07345 | + | 0.148945i | 0.743707 | + | 0.0271934i | ||||
\(31\) | −3.34342 | + | 3.34342i | −0.600496 | + | 0.600496i | −0.940444 | − | 0.339948i | \(-0.889590\pi\) |
0.339948 | + | 0.940444i | \(0.389590\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.07882 | − | 3.07882i | 0.535954 | − | 0.535954i | ||||
\(34\) | 2.09597i | 0.359456i | ||||||||
\(35\) | −9.52998 | − | 0.348461i | −1.61086 | − | 0.0589007i | ||||
\(36\) | 0.323040i | 0.0538401i | ||||||||
\(37\) | −1.89339 | + | 5.78058i | −0.311271 | + | 0.950321i | ||||
\(38\) | 2.46518 | − | 2.46518i | 0.399905 | − | 0.399905i | ||||
\(39\) | −1.86647 | − | 1.86647i | −0.298874 | − | 0.298874i | ||||
\(40\) | −1.63786 | + | 1.52231i | −0.258968 | + | 0.240698i | ||||
\(41\) | − | 6.22969i | − | 0.972913i | −0.873705 | − | 0.486457i | \(-0.838289\pi\) | ||
0.873705 | − | 0.486457i | \(-0.161711\pi\) | |||||||
\(42\) | − | 7.77437i | − | 1.19961i | ||||||
\(43\) | −3.07893 | −0.469532 | −0.234766 | − | 0.972052i | \(-0.575432\pi\) | ||||
−0.234766 | + | 0.972052i | \(0.575432\pi\) | |||||||
\(44\) | 2.38854i | 0.360085i | ||||||||
\(45\) | 0.491767 | + | 0.529094i | 0.0733083 | + | 0.0788727i | ||||
\(46\) | 0.168727 | 0.0248774 | ||||||||
\(47\) | −4.67540 | − | 4.67540i | −0.681978 | − | 0.681978i | 0.278468 | − | 0.960446i | \(-0.410173\pi\) |
−0.960446 | + | 0.278468i | \(0.910173\pi\) | |||||||
\(48\) | −1.28900 | − | 1.28900i | −0.186051 | − | 0.186051i | ||||
\(49\) | 11.1884i | 1.59834i | ||||||||
\(50\) | −0.365159 | + | 4.98665i | −0.0516413 | + | 0.705219i | ||||
\(51\) | −2.70170 | + | 2.70170i | −0.378314 | + | 0.378314i | ||||
\(52\) | 1.44800 | 0.200801 | ||||||||
\(53\) | −2.87955 | + | 2.87955i | −0.395537 | + | 0.395537i | −0.876656 | − | 0.481119i | \(-0.840231\pi\) |
0.481119 | + | 0.876656i | \(0.340231\pi\) | |||||||
\(54\) | 3.45060 | − | 3.45060i | 0.469567 | − | 0.469567i | ||||
\(55\) | 3.63609 | + | 3.91208i | 0.490290 | + | 0.527505i | ||||
\(56\) | 3.01566 | + | 3.01566i | 0.402984 | + | 0.402984i | ||||
\(57\) | 6.35524 | 0.841772 | ||||||||
\(58\) | 4.74797 | + | 4.74797i | 0.623439 | + | 0.623439i | ||||
\(59\) | 6.78438 | − | 6.78438i | 0.883251 | − | 0.883251i | −0.110612 | − | 0.993864i | \(-0.535281\pi\) |
0.993864 | + | 0.110612i | \(0.0352812\pi\) | |||||||
\(60\) | −4.07345 | − | 0.148945i | −0.525880 | − | 0.0192287i | ||||
\(61\) | 6.94487 | − | 6.94487i | 0.889199 | − | 0.889199i | −0.105247 | − | 0.994446i | \(-0.533563\pi\) |
0.994446 | + | 0.105247i | \(0.0335634\pi\) | |||||||
\(62\) | 3.34342 | − | 3.34342i | 0.424615 | − | 0.424615i | ||||
\(63\) | 0.974180 | − | 0.974180i | 0.122735 | − | 0.122735i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.37161 | − | 2.20430i | 0.294162 | − | 0.273409i | ||||
\(66\) | −3.07882 | + | 3.07882i | −0.378977 | + | 0.378977i | ||||
\(67\) | 7.89993 | − | 7.89993i | 0.965130 | − | 0.965130i | −0.0342818 | − | 0.999412i | \(-0.510914\pi\) |
0.999412 | + | 0.0342818i | \(0.0109144\pi\) | |||||||
\(68\) | − | 2.09597i | − | 0.254173i | ||||||
\(69\) | 0.217489 | + | 0.217489i | 0.0261826 | + | 0.0261826i | ||||
\(70\) | 9.52998 | + | 0.348461i | 1.13905 | + | 0.0416491i | ||||
\(71\) | 12.6621 | 1.50272 | 0.751358 | − | 0.659895i | \(-0.229399\pi\) | ||||
0.751358 | + | 0.659895i | \(0.229399\pi\) | |||||||
\(72\) | − | 0.323040i | − | 0.0380707i | ||||||
\(73\) | 4.83010 | + | 4.83010i | 0.565321 | + | 0.565321i | 0.930814 | − | 0.365493i | \(-0.119100\pi\) |
−0.365493 | + | 0.930814i | \(0.619100\pi\) | |||||||
\(74\) | 1.89339 | − | 5.78058i | 0.220102 | − | 0.671978i | ||||
\(75\) | −6.89848 | + | 5.95710i | −0.796568 | + | 0.687866i | ||||
\(76\) | −2.46518 | + | 2.46518i | −0.282776 | + | 0.282776i | ||||
\(77\) | 7.20301 | − | 7.20301i | 0.820859 | − | 0.820859i | ||||
\(78\) | 1.86647 | + | 1.86647i | 0.211336 | + | 0.211336i | ||||
\(79\) | −5.31500 | + | 5.31500i | −0.597984 | + | 0.597984i | −0.939776 | − | 0.341792i | \(-0.888966\pi\) |
0.341792 | + | 0.939776i | \(0.388966\pi\) | |||||||
\(80\) | 1.63786 | − | 1.52231i | 0.183118 | − | 0.170199i | ||||
\(81\) | 9.86477 | 1.09609 | ||||||||
\(82\) | 6.22969i | 0.687954i | ||||||||
\(83\) | 8.43313 | − | 8.43313i | 0.925657 | − | 0.925657i | −0.0717648 | − | 0.997422i | \(-0.522863\pi\) |
0.997422 | + | 0.0717648i | \(0.0228631\pi\) | |||||||
\(84\) | 7.77437i | 0.848253i | ||||||||
\(85\) | −3.19071 | − | 3.43290i | −0.346081 | − | 0.372350i | ||||
\(86\) | 3.07893 | 0.332009 | ||||||||
\(87\) | 12.2403i | 1.31229i | ||||||||
\(88\) | − | 2.38854i | − | 0.254619i | ||||||
\(89\) | −11.6295 | − | 11.6295i | −1.23273 | − | 1.23273i | −0.962912 | − | 0.269814i | \(-0.913038\pi\) |
−0.269814 | − | 0.962912i | \(-0.586962\pi\) | |||||||
\(90\) | −0.491767 | − | 0.529094i | −0.0518368 | − | 0.0557714i | ||||
\(91\) | −4.36667 | − | 4.36667i | −0.457751 | − | 0.457751i | ||||
\(92\) | −0.168727 | −0.0175910 | ||||||||
\(93\) | 8.61934 | 0.893784 | ||||||||
\(94\) | 4.67540 | + | 4.67540i | 0.482231 | + | 0.482231i | ||||
\(95\) | −0.284853 | + | 7.79038i | −0.0292253 | + | 0.799276i | ||||
\(96\) | 1.28900 | + | 1.28900i | 0.131558 | + | 0.131558i | ||||
\(97\) | 5.04296i | 0.512035i | 0.966672 | + | 0.256018i | \(0.0824105\pi\) | ||||
−0.966672 | + | 0.256018i | \(0.917589\pi\) | |||||||
\(98\) | − | 11.1884i | − | 1.13020i | ||||||
\(99\) | −0.771593 | −0.0775481 | ||||||||
\(100\) | 0.365159 | − | 4.98665i | 0.0365159 | − | 0.498665i | ||||
\(101\) | 11.7791i | 1.17207i | 0.810287 | + | 0.586033i | \(0.199311\pi\) | ||||
−0.810287 | + | 0.586033i | \(0.800689\pi\) | |||||||
\(102\) | 2.70170 | − | 2.70170i | 0.267508 | − | 0.267508i | ||||
\(103\) | 6.35592i | 0.626267i | 0.949709 | + | 0.313134i | \(0.101379\pi\) | ||||
−0.949709 | + | 0.313134i | \(0.898621\pi\) | |||||||
\(104\) | −1.44800 | −0.141988 | ||||||||
\(105\) | 11.8350 | + | 12.7333i | 1.15498 | + | 1.24264i | ||||
\(106\) | 2.87955 | − | 2.87955i | 0.279687 | − | 0.279687i | ||||
\(107\) | −7.29845 | − | 7.29845i | −0.705568 | − | 0.705568i | 0.260032 | − | 0.965600i | \(-0.416267\pi\) |
−0.965600 | + | 0.260032i | \(0.916267\pi\) | |||||||
\(108\) | −3.45060 | + | 3.45060i | −0.332034 | + | 0.332034i | ||||
\(109\) | −7.27809 | + | 7.27809i | −0.697114 | + | 0.697114i | −0.963787 | − | 0.266673i | \(-0.914076\pi\) |
0.266673 | + | 0.963787i | \(0.414076\pi\) | |||||||
\(110\) | −3.63609 | − | 3.91208i | −0.346687 | − | 0.373002i | ||||
\(111\) | 9.89174 | − | 5.01058i | 0.938883 | − | 0.475583i | ||||
\(112\) | −3.01566 | − | 3.01566i | −0.284953 | − | 0.284953i | ||||
\(113\) | − | 5.37412i | − | 0.505555i | −0.967524 | − | 0.252777i | \(-0.918656\pi\) | ||
0.967524 | − | 0.252777i | \(-0.0813440\pi\) | |||||||
\(114\) | −6.35524 | −0.595222 | ||||||||
\(115\) | −0.276350 | + | 0.256854i | −0.0257698 | + | 0.0239518i | ||||
\(116\) | −4.74797 | − | 4.74797i | −0.440838 | − | 0.440838i | ||||
\(117\) | 0.467761i | 0.0432446i | ||||||||
\(118\) | −6.78438 | + | 6.78438i | −0.624553 | + | 0.624553i | ||||
\(119\) | −6.32073 | + | 6.32073i | −0.579420 | + | 0.579420i | ||||
\(120\) | 4.07345 | + | 0.148945i | 0.371854 | + | 0.0135967i | ||||
\(121\) | 5.29490 | 0.481354 | ||||||||
\(122\) | −6.94487 | + | 6.94487i | −0.628759 | + | 0.628759i | ||||
\(123\) | −8.03006 | + | 8.03006i | −0.724046 | + | 0.724046i | ||||
\(124\) | −3.34342 | + | 3.34342i | −0.300248 | + | 0.300248i | ||||
\(125\) | −6.99313 | − | 8.72331i | −0.625485 | − | 0.780236i | ||||
\(126\) | −0.974180 | + | 0.974180i | −0.0867868 | + | 0.0867868i | ||||
\(127\) | −11.7621 | − | 11.7621i | −1.04371 | − | 1.04371i | −0.999000 | − | 0.0447148i | \(-0.985762\pi\) |
−0.0447148 | − | 0.999000i | \(-0.514238\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.96873 | + | 3.96873i | 0.349428 | + | 0.349428i | ||||
\(130\) | −2.37161 | + | 2.20430i | −0.208004 | + | 0.193330i | ||||
\(131\) | 15.5939 | − | 15.5939i | 1.36245 | − | 1.36245i | 0.491657 | − | 0.870789i | \(-0.336391\pi\) |
0.870789 | − | 0.491657i | \(-0.163609\pi\) | |||||||
\(132\) | 3.07882 | − | 3.07882i | 0.267977 | − | 0.267977i | ||||
\(133\) | 14.8683 | 1.28924 | ||||||||
\(134\) | −7.89993 | + | 7.89993i | −0.682450 | + | 0.682450i | ||||
\(135\) | −0.398719 | + | 10.9045i | −0.0343162 | + | 0.938507i | ||||
\(136\) | 2.09597i | 0.179728i | ||||||||
\(137\) | 0.952787 | + | 0.952787i | 0.0814020 | + | 0.0814020i | 0.746635 | − | 0.665233i | \(-0.231668\pi\) |
−0.665233 | + | 0.746635i | \(0.731668\pi\) | |||||||
\(138\) | −0.217489 | − | 0.217489i | −0.0185139 | − | 0.0185139i | ||||
\(139\) | 8.19245 | 0.694874 | 0.347437 | − | 0.937703i | \(-0.387052\pi\) | ||||
0.347437 | + | 0.937703i | \(0.387052\pi\) | |||||||
\(140\) | −9.52998 | − | 0.348461i | −0.805431 | − | 0.0294503i | ||||
\(141\) | 12.0532i | 1.01506i | ||||||||
\(142\) | −12.6621 | −1.06258 | ||||||||
\(143\) | 3.45859i | 0.289222i | ||||||||
\(144\) | 0.323040i | 0.0269200i | ||||||||
\(145\) | −15.0044 | − | 0.548631i | −1.24605 | − | 0.0455613i | ||||
\(146\) | −4.83010 | − | 4.83010i | −0.399742 | − | 0.399742i | ||||
\(147\) | 14.4218 | − | 14.4218i | 1.18949 | − | 1.18949i | ||||
\(148\) | −1.89339 | + | 5.78058i | −0.155636 | + | 0.475161i | ||||
\(149\) | − | 22.8722i | − | 1.87377i | −0.349641 | − | 0.936884i | \(-0.613697\pi\) | ||
0.349641 | − | 0.936884i | \(-0.386303\pi\) | |||||||
\(150\) | 6.89848 | − | 5.95710i | 0.563258 | − | 0.486395i | ||||
\(151\) | − | 16.6501i | − | 1.35496i | −0.735539 | − | 0.677482i | \(-0.763071\pi\) | ||
0.735539 | − | 0.677482i | \(-0.236929\pi\) | |||||||
\(152\) | 2.46518 | − | 2.46518i | 0.199953 | − | 0.199953i | ||||
\(153\) | 0.677082 | 0.0547389 | ||||||||
\(154\) | −7.20301 | + | 7.20301i | −0.580435 | + | 0.580435i | ||||
\(155\) | −0.386334 | + | 10.5658i | −0.0310311 | + | 0.848663i | ||||
\(156\) | −1.86647 | − | 1.86647i | −0.149437 | − | 0.149437i | ||||
\(157\) | 10.1100 | + | 10.1100i | 0.806865 | + | 0.806865i | 0.984158 | − | 0.177293i | \(-0.0567341\pi\) |
−0.177293 | + | 0.984158i | \(0.556734\pi\) | |||||||
\(158\) | 5.31500 | − | 5.31500i | 0.422838 | − | 0.422838i | ||||
\(159\) | 7.42348 | 0.588721 | ||||||||
\(160\) | −1.63786 | + | 1.52231i | −0.129484 | + | 0.120349i | ||||
\(161\) | 0.508822 | + | 0.508822i | 0.0401008 | + | 0.0401008i | ||||
\(162\) | −9.86477 | −0.775049 | ||||||||
\(163\) | − | 1.81513i | − | 0.142172i | −0.997470 | − | 0.0710859i | \(-0.977354\pi\) | ||
0.997470 | − | 0.0710859i | \(-0.0226465\pi\) | |||||||
\(164\) | − | 6.22969i | − | 0.486457i | ||||||
\(165\) | 0.355759 | − | 9.72959i | 0.0276958 | − | 0.757447i | ||||
\(166\) | −8.43313 | + | 8.43313i | −0.654538 | + | 0.654538i | ||||
\(167\) | − | 16.2469i | − | 1.25722i | −0.777721 | − | 0.628610i | \(-0.783624\pi\) | ||
0.777721 | − | 0.628610i | \(-0.216376\pi\) | |||||||
\(168\) | − | 7.77437i | − | 0.599805i | ||||||
\(169\) | −10.9033 | −0.838716 | ||||||||
\(170\) | 3.19071 | + | 3.43290i | 0.244716 | + | 0.263291i | ||||
\(171\) | −0.796353 | − | 0.796353i | −0.0608986 | − | 0.0608986i | ||||
\(172\) | −3.07893 | −0.234766 | ||||||||
\(173\) | 12.0071 | + | 12.0071i | 0.912885 | + | 0.912885i | 0.996498 | − | 0.0836133i | \(-0.0266461\pi\) |
−0.0836133 | + | 0.996498i | \(0.526646\pi\) | |||||||
\(174\) | − | 12.2403i | − | 0.927932i | ||||||
\(175\) | −16.1392 | + | 13.9368i | −1.22001 | + | 1.05353i | ||||
\(176\) | 2.38854i | 0.180043i | ||||||||
\(177\) | −17.4901 | −1.31464 | ||||||||
\(178\) | 11.6295 | + | 11.6295i | 0.871669 | + | 0.871669i | ||||
\(179\) | 8.45867 | + | 8.45867i | 0.632231 | + | 0.632231i | 0.948627 | − | 0.316396i | \(-0.102473\pi\) |
−0.316396 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(180\) | 0.491767 | + | 0.529094i | 0.0366541 | + | 0.0394364i | ||||
\(181\) | 0.961200 | 0.0714454 | 0.0357227 | − | 0.999362i | \(-0.488627\pi\) | ||||
0.0357227 | + | 0.999362i | \(0.488627\pi\) | |||||||
\(182\) | 4.36667 | + | 4.36667i | 0.323679 | + | 0.323679i | ||||
\(183\) | −17.9039 | −1.32349 | ||||||||
\(184\) | 0.168727 | 0.0124387 | ||||||||
\(185\) | 5.69871 | + | 12.3501i | 0.418978 | + | 0.907997i | ||||
\(186\) | −8.61934 | −0.632000 | ||||||||
\(187\) | 5.00630 | 0.366097 | ||||||||
\(188\) | −4.67540 | − | 4.67540i | −0.340989 | − | 0.340989i | ||||
\(189\) | 20.8117 | 1.51383 | ||||||||
\(190\) | 0.284853 | − | 7.79038i | 0.0206654 | − | 0.565174i | ||||
\(191\) | 0.355141 | + | 0.355141i | 0.0256971 | + | 0.0256971i | 0.719839 | − | 0.694141i | \(-0.244216\pi\) |
−0.694141 | + | 0.719839i | \(0.744216\pi\) | |||||||
\(192\) | −1.28900 | − | 1.28900i | −0.0930255 | − | 0.0930255i | ||||
\(193\) | −7.33106 | −0.527701 | −0.263851 | − | 0.964564i | \(-0.584993\pi\) | ||||
−0.263851 | + | 0.964564i | \(0.584993\pi\) | |||||||
\(194\) | − | 5.04296i | − | 0.362064i | ||||||
\(195\) | −5.89835 | − | 0.215671i | −0.422389 | − | 0.0154445i | ||||
\(196\) | 11.1884i | 0.799171i | ||||||||
\(197\) | −8.20672 | − | 8.20672i | −0.584704 | − | 0.584704i | 0.351488 | − | 0.936192i | \(-0.385676\pi\) |
−0.936192 | + | 0.351488i | \(0.885676\pi\) | |||||||
\(198\) | 0.771593 | 0.0548348 | ||||||||
\(199\) | −0.480679 | − | 0.480679i | −0.0340744 | − | 0.0340744i | 0.689864 | − | 0.723939i | \(-0.257670\pi\) |
−0.723939 | + | 0.689864i | \(0.757670\pi\) | |||||||
\(200\) | −0.365159 | + | 4.98665i | −0.0258206 | + | 0.352609i | ||||
\(201\) | −20.3660 | −1.43651 | ||||||||
\(202\) | − | 11.7791i | − | 0.828776i | ||||||
\(203\) | 28.6365i | 2.00989i | ||||||||
\(204\) | −2.70170 | + | 2.70170i | −0.189157 | + | 0.189157i | ||||
\(205\) | −9.48350 | − | 10.2033i | −0.662356 | − | 0.712632i | ||||
\(206\) | − | 6.35592i | − | 0.442838i | ||||||
\(207\) | − | 0.0545055i | − | 0.00378840i | ||||||
\(208\) | 1.44800 | 0.100401 | ||||||||
\(209\) | −5.88817 | − | 5.88817i | −0.407293 | − | 0.407293i | ||||
\(210\) | −11.8350 | − | 12.7333i | −0.816691 | − | 0.878682i | ||||
\(211\) | −24.5328 | −1.68891 | −0.844453 | − | 0.535630i | \(-0.820074\pi\) | ||||
−0.844453 | + | 0.535630i | \(0.820074\pi\) | |||||||
\(212\) | −2.87955 | + | 2.87955i | −0.197768 | + | 0.197768i | ||||
\(213\) | −16.3215 | − | 16.3215i | −1.11833 | − | 1.11833i | ||||
\(214\) | 7.29845 | + | 7.29845i | 0.498912 | + | 0.498912i | ||||
\(215\) | −5.04284 | + | 4.68707i | −0.343919 | + | 0.319656i | ||||
\(216\) | 3.45060 | − | 3.45060i | 0.234784 | − | 0.234784i | ||||
\(217\) | 20.1652 | 1.36891 | ||||||||
\(218\) | 7.27809 | − | 7.27809i | 0.492934 | − | 0.492934i | ||||
\(219\) | − | 12.4520i | − | 0.841429i | ||||||
\(220\) | 3.63609 | + | 3.91208i | 0.245145 | + | 0.263753i | ||||
\(221\) | − | 3.03496i | − | 0.204153i | ||||||
\(222\) | −9.89174 | + | 5.01058i | −0.663890 | + | 0.336288i | ||||
\(223\) | 13.8026 | − | 13.8026i | 0.924289 | − | 0.924289i | −0.0730404 | − | 0.997329i | \(-0.523270\pi\) |
0.997329 | + | 0.0730404i | \(0.0232702\pi\) | |||||||
\(224\) | 3.01566 | + | 3.01566i | 0.201492 | + | 0.201492i | ||||
\(225\) | 1.61089 | + | 0.117961i | 0.107393 | + | 0.00786407i | ||||
\(226\) | 5.37412i | 0.357481i | ||||||||
\(227\) | 10.8328i | 0.718995i | 0.933146 | + | 0.359498i | \(0.117052\pi\) | ||||
−0.933146 | + | 0.359498i | \(0.882948\pi\) | |||||||
\(228\) | 6.35524 | 0.420886 | ||||||||
\(229\) | − | 17.5884i | − | 1.16227i | −0.813806 | − | 0.581136i | \(-0.802608\pi\) | ||
0.813806 | − | 0.581136i | \(-0.197392\pi\) | |||||||
\(230\) | 0.276350 | − | 0.256854i | 0.0182220 | − | 0.0169365i | ||||
\(231\) | −18.5694 | −1.22177 | ||||||||
\(232\) | 4.74797 | + | 4.74797i | 0.311720 | + | 0.311720i | ||||
\(233\) | −1.47378 | − | 1.47378i | −0.0965505 | − | 0.0965505i | 0.657182 | − | 0.753732i | \(-0.271748\pi\) |
−0.753732 | + | 0.657182i | \(0.771748\pi\) | |||||||
\(234\) | − | 0.467761i | − | 0.0305785i | ||||||
\(235\) | −14.7750 | − | 0.540245i | −0.963818 | − | 0.0352417i | ||||
\(236\) | 6.78438 | − | 6.78438i | 0.441626 | − | 0.441626i | ||||
\(237\) | 13.7021 | 0.890044 | ||||||||
\(238\) | 6.32073 | − | 6.32073i | 0.409712 | − | 0.409712i | ||||
\(239\) | −0.869275 | + | 0.869275i | −0.0562288 | + | 0.0562288i | −0.734662 | − | 0.678433i | \(-0.762659\pi\) |
0.678433 | + | 0.734662i | \(0.262659\pi\) | |||||||
\(240\) | −4.07345 | − | 0.148945i | −0.262940 | − | 0.00961433i | ||||
\(241\) | 7.39427 | + | 7.39427i | 0.476307 | + | 0.476307i | 0.903948 | − | 0.427642i | \(-0.140655\pi\) |
−0.427642 | + | 0.903948i | \(0.640655\pi\) | |||||||
\(242\) | −5.29490 | −0.340369 | ||||||||
\(243\) | −2.36388 | − | 2.36388i | −0.151643 | − | 0.151643i | ||||
\(244\) | 6.94487 | − | 6.94487i | 0.444599 | − | 0.444599i | ||||
\(245\) | 17.0322 | + | 18.3250i | 1.08815 | + | 1.17074i | ||||
\(246\) | 8.03006 | − | 8.03006i | 0.511978 | − | 0.511978i | ||||
\(247\) | −3.56958 | + | 3.56958i | −0.227127 | + | 0.227127i | ||||
\(248\) | 3.34342 | − | 3.34342i | 0.212307 | − | 0.212307i | ||||
\(249\) | −21.7406 | −1.37776 | ||||||||
\(250\) | 6.99313 | + | 8.72331i | 0.442285 | + | 0.551710i | ||||
\(251\) | 15.8249 | − | 15.8249i | 0.998857 | − | 0.998857i | −0.00114211 | − | 0.999999i | \(-0.500364\pi\) |
0.999999 | + | 0.00114211i | \(0.000363545\pi\) | |||||||
\(252\) | 0.974180 | − | 0.974180i | 0.0613675 | − | 0.0613675i | ||||
\(253\) | − | 0.403010i | − | 0.0253370i | ||||||
\(254\) | 11.7621 | + | 11.7621i | 0.738018 | + | 0.738018i | ||||
\(255\) | −0.312183 | + | 8.53783i | −0.0195497 | + | 0.534660i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.1629i | 1.44486i | 0.691443 | + | 0.722431i | \(0.256975\pi\) | ||||
−0.691443 | + | 0.722431i | \(0.743025\pi\) | |||||||
\(258\) | −3.96873 | − | 3.96873i | −0.247083 | − | 0.247083i | ||||
\(259\) | 23.1421 | − | 11.7224i | 1.43798 | − | 0.728396i | ||||
\(260\) | 2.37161 | − | 2.20430i | 0.147081 | − | 0.136705i | ||||
\(261\) | 1.53379 | − | 1.53379i | 0.0949390 | − | 0.0949390i | ||||
\(262\) | −15.5939 | + | 15.5939i | −0.963395 | + | 0.963395i | ||||
\(263\) | −12.7777 | − | 12.7777i | −0.787909 | − | 0.787909i | 0.193242 | − | 0.981151i | \(-0.438100\pi\) |
−0.981151 | + | 0.193242i | \(0.938100\pi\) | |||||||
\(264\) | −3.07882 | + | 3.07882i | −0.189488 | + | 0.189488i | ||||
\(265\) | −0.332734 | + | 9.09986i | −0.0204397 | + | 0.559000i | ||||
\(266\) | −14.8683 | −0.911634 | ||||||||
\(267\) | 29.9809i | 1.83480i | ||||||||
\(268\) | 7.89993 | − | 7.89993i | 0.482565 | − | 0.482565i | ||||
\(269\) | 5.62728i | 0.343101i | 0.985175 | + | 0.171551i | \(0.0548777\pi\) | ||||
−0.985175 | + | 0.171551i | \(0.945122\pi\) | |||||||
\(270\) | 0.398719 | − | 10.9045i | 0.0242652 | − | 0.663625i | ||||
\(271\) | −21.2992 | −1.29384 | −0.646919 | − | 0.762559i | \(-0.723943\pi\) | ||||
−0.646919 | + | 0.762559i | \(0.723943\pi\) | |||||||
\(272\) | − | 2.09597i | − | 0.127087i | ||||||
\(273\) | 11.2573i | 0.681320i | ||||||||
\(274\) | −0.952787 | − | 0.952787i | −0.0575599 | − | 0.0575599i | ||||
\(275\) | 11.9108 | + | 0.872195i | 0.718247 | + | 0.0525953i | ||||
\(276\) | 0.217489 | + | 0.217489i | 0.0130913 | + | 0.0130913i | ||||
\(277\) | 24.8652 | 1.49401 | 0.747003 | − | 0.664821i | \(-0.231492\pi\) | ||||
0.747003 | + | 0.664821i | \(0.231492\pi\) | |||||||
\(278\) | −8.19245 | −0.491350 | ||||||||
\(279\) | −1.08006 | − | 1.08006i | −0.0646615 | − | 0.0646615i | ||||
\(280\) | 9.52998 | + | 0.348461i | 0.569525 | + | 0.0208245i | ||||
\(281\) | 0.925329 | + | 0.925329i | 0.0552005 | + | 0.0552005i | 0.734168 | − | 0.678968i | \(-0.237572\pi\) |
−0.678968 | + | 0.734168i | \(0.737572\pi\) | |||||||
\(282\) | − | 12.0532i | − | 0.717757i | ||||||
\(283\) | 0.300587i | 0.0178681i | 0.999960 | + | 0.00893403i | \(0.00284383\pi\) | ||||
−0.999960 | + | 0.00893403i | \(0.997156\pi\) | |||||||
\(284\) | 12.6621 | 0.751358 | ||||||||
\(285\) | 10.4090 | − | 9.67462i | 0.616574 | − | 0.573075i | ||||
\(286\) | − | 3.45859i | − | 0.204511i | ||||||
\(287\) | −18.7866 | + | 18.7866i | −1.10894 | + | 1.10894i | ||||
\(288\) | − | 0.323040i | − | 0.0190353i | ||||||
\(289\) | 12.6069 | 0.741583 | ||||||||
\(290\) | 15.0044 | + | 0.548631i | 0.881087 | + | 0.0322167i | ||||
\(291\) | 6.50038 | − | 6.50038i | 0.381059 | − | 0.381059i | ||||
\(292\) | 4.83010 | + | 4.83010i | 0.282660 | + | 0.282660i | ||||
\(293\) | −22.4364 | + | 22.4364i | −1.31075 | + | 1.31075i | −0.389881 | + | 0.920865i | \(0.627484\pi\) |
−0.920865 | + | 0.389881i | \(0.872516\pi\) | |||||||
\(294\) | −14.4218 | + | 14.4218i | −0.841099 | + | 0.841099i | ||||
\(295\) | 0.783939 | − | 21.4398i | 0.0456427 | − | 1.24827i | ||||
\(296\) | 1.89339 | − | 5.78058i | 0.110051 | − | 0.335989i | ||||
\(297\) | −8.24188 | − | 8.24188i | −0.478242 | − | 0.478242i | ||||
\(298\) | 22.8722i | 1.32495i | ||||||||
\(299\) | −0.244316 | −0.0141291 | ||||||||
\(300\) | −6.89848 | + | 5.95710i | −0.398284 | + | 0.343933i | ||||
\(301\) | 9.28499 | + | 9.28499i | 0.535178 | + | 0.535178i | ||||
\(302\) | 16.6501i | 0.958104i | ||||||||
\(303\) | 15.1833 | − | 15.1833i | 0.872257 | − | 0.872257i | ||||
\(304\) | −2.46518 | + | 2.46518i | −0.141388 | + | 0.141388i | ||||
\(305\) | 0.802483 | − | 21.9469i | 0.0459500 | − | 1.25668i | ||||
\(306\) | −0.677082 | −0.0387062 | ||||||||
\(307\) | −2.94724 | + | 2.94724i | −0.168208 | + | 0.168208i | −0.786191 | − | 0.617983i | \(-0.787950\pi\) |
0.617983 | + | 0.786191i | \(0.287950\pi\) | |||||||
\(308\) | 7.20301 | − | 7.20301i | 0.410430 | − | 0.410430i | ||||
\(309\) | 8.19278 | − | 8.19278i | 0.466071 | − | 0.466071i | ||||
\(310\) | 0.386334 | − | 10.5658i | 0.0219423 | − | 0.600095i | ||||
\(311\) | −12.0863 | + | 12.0863i | −0.685353 | + | 0.685353i | −0.961201 | − | 0.275848i | \(-0.911041\pi\) |
0.275848 | + | 0.961201i | \(0.411041\pi\) | |||||||
\(312\) | 1.86647 | + | 1.86647i | 0.105668 | + | 0.105668i | ||||
\(313\) | 2.00477 | 0.113316 | 0.0566582 | − | 0.998394i | \(-0.481955\pi\) | ||||
0.0566582 | + | 0.998394i | \(0.481955\pi\) | |||||||
\(314\) | −10.1100 | − | 10.1100i | −0.570540 | − | 0.570540i | ||||
\(315\) | 0.112567 | − | 3.07857i | 0.00634243 | − | 0.173458i | ||||
\(316\) | −5.31500 | + | 5.31500i | −0.298992 | + | 0.298992i | ||||
\(317\) | −7.28840 | + | 7.28840i | −0.409357 | + | 0.409357i | −0.881514 | − | 0.472157i | \(-0.843475\pi\) |
0.472157 | + | 0.881514i | \(0.343475\pi\) | |||||||
\(318\) | −7.42348 | −0.416288 | ||||||||
\(319\) | 11.3407 | − | 11.3407i | 0.634957 | − | 0.634957i | ||||
\(320\) | 1.63786 | − | 1.52231i | 0.0915591 | − | 0.0850996i | ||||
\(321\) | 18.8154i | 1.05017i | ||||||||
\(322\) | −0.508822 | − | 0.508822i | −0.0283556 | − | 0.0283556i | ||||
\(323\) | 5.16694 | + | 5.16694i | 0.287496 | + | 0.287496i | ||||
\(324\) | 9.86477 | 0.548043 | ||||||||
\(325\) | 0.528749 | − | 7.22065i | 0.0293297 | − | 0.400530i | ||||
\(326\) | 1.81513i | 0.100531i | ||||||||
\(327\) | 18.7629 | 1.03759 | ||||||||
\(328\) | 6.22969i | 0.343977i | ||||||||
\(329\) | 28.1988i | 1.55465i | ||||||||
\(330\) | −0.355759 | + | 9.72959i | −0.0195839 | + | 0.535596i | ||||
\(331\) | −0.839383 | − | 0.839383i | −0.0461367 | − | 0.0461367i | 0.683662 | − | 0.729799i | \(-0.260386\pi\) |
−0.729799 | + | 0.683662i | \(0.760386\pi\) | |||||||
\(332\) | 8.43313 | − | 8.43313i | 0.462828 | − | 0.462828i | ||||
\(333\) | −1.86736 | − | 0.611642i | −0.102331 | − | 0.0335178i | ||||
\(334\) | 16.2469i | 0.888988i | ||||||||
\(335\) | 0.912841 | − | 24.9651i | 0.0498739 | − | 1.36399i | ||||
\(336\) | 7.77437i | 0.424127i | ||||||||
\(337\) | 7.69155 | − | 7.69155i | 0.418986 | − | 0.418986i | −0.465868 | − | 0.884854i | \(-0.654258\pi\) |
0.884854 | + | 0.465868i | \(0.154258\pi\) | |||||||
\(338\) | 10.9033 | 0.593062 | ||||||||
\(339\) | −6.92724 | + | 6.92724i | −0.376236 | + | 0.376236i | ||||
\(340\) | −3.19071 | − | 3.43290i | −0.173040 | − | 0.186175i | ||||
\(341\) | −7.98588 | − | 7.98588i | −0.432460 | − | 0.432460i | ||||
\(342\) | 0.796353 | + | 0.796353i | 0.0430618 | + | 0.0430618i | ||||
\(343\) | 12.6308 | − | 12.6308i | 0.681998 | − | 0.681998i | ||||
\(344\) | 3.07893 | 0.166005 | ||||||||
\(345\) | 0.687300 | + | 0.0251309i | 0.0370030 | + | 0.00135300i | ||||
\(346\) | −12.0071 | − | 12.0071i | −0.645507 | − | 0.645507i | ||||
\(347\) | 21.8436 | 1.17263 | 0.586313 | − | 0.810085i | \(-0.300579\pi\) | ||||
0.586313 | + | 0.810085i | \(0.300579\pi\) | |||||||
\(348\) | 12.2403i | 0.656147i | ||||||||
\(349\) | 4.00432i | 0.214346i | 0.994240 | + | 0.107173i | \(0.0341799\pi\) | ||||
−0.994240 | + | 0.107173i | \(0.965820\pi\) | |||||||
\(350\) | 16.1392 | − | 13.9368i | 0.862678 | − | 0.744955i | ||||
\(351\) | −4.99646 | + | 4.99646i | −0.266691 | + | 0.266691i | ||||
\(352\) | − | 2.38854i | − | 0.127309i | ||||||
\(353\) | 11.1747i | 0.594769i | 0.954758 | + | 0.297384i | \(0.0961143\pi\) | ||||
−0.954758 | + | 0.297384i | \(0.903886\pi\) | |||||||
\(354\) | 17.4901 | 0.929590 | ||||||||
\(355\) | 20.7387 | − | 19.2756i | 1.10070 | − | 1.02304i | ||||
\(356\) | −11.6295 | − | 11.6295i | −0.616363 | − | 0.616363i | ||||
\(357\) | 16.2948 | 0.862414 | ||||||||
\(358\) | −8.45867 | − | 8.45867i | −0.447055 | − | 0.447055i | ||||
\(359\) | − | 19.4341i | − | 1.02570i | −0.858480 | − | 0.512848i | \(-0.828591\pi\) | ||
0.858480 | − | 0.512848i | \(-0.171409\pi\) | |||||||
\(360\) | −0.491767 | − | 0.529094i | −0.0259184 | − | 0.0278857i | ||||
\(361\) | 6.84576i | 0.360303i | ||||||||
\(362\) | −0.961200 | −0.0505196 | ||||||||
\(363\) | −6.82512 | − | 6.82512i | −0.358226 | − | 0.358226i | ||||
\(364\) | −4.36667 | − | 4.36667i | −0.228875 | − | 0.228875i | ||||
\(365\) | 15.2639 | + | 0.558121i | 0.798951 | + | 0.0292134i | ||||
\(366\) | 17.9039 | 0.935850 | ||||||||
\(367\) | 10.2957 | + | 10.2957i | 0.537430 | + | 0.537430i | 0.922773 | − | 0.385343i | \(-0.125917\pi\) |
−0.385343 | + | 0.922773i | \(0.625917\pi\) | |||||||
\(368\) | −0.168727 | −0.00879549 | ||||||||
\(369\) | 2.01244 | 0.104763 | ||||||||
\(370\) | −5.69871 | − | 12.3501i | −0.296262 | − | 0.642051i | ||||
\(371\) | 17.3675 | 0.901675 | ||||||||
\(372\) | 8.61934 | 0.446892 | ||||||||
\(373\) | −23.2626 | − | 23.2626i | −1.20449 | − | 1.20449i | −0.972786 | − | 0.231704i | \(-0.925570\pi\) |
−0.231704 | − | 0.972786i | \(-0.574430\pi\) | |||||||
\(374\) | −5.00630 | −0.258869 | ||||||||
\(375\) | −2.23019 | + | 20.2585i | −0.115167 | + | 1.04614i | ||||
\(376\) | 4.67540 | + | 4.67540i | 0.241115 | + | 0.241115i | ||||
\(377\) | −6.87505 | − | 6.87505i | −0.354083 | − | 0.354083i | ||||
\(378\) | −20.8117 | −1.07044 | ||||||||
\(379\) | 11.6263i | 0.597203i | 0.954378 | + | 0.298602i | \(0.0965202\pi\) | ||||
−0.954378 | + | 0.298602i | \(0.903480\pi\) | |||||||
\(380\) | −0.284853 | + | 7.79038i | −0.0146127 | + | 0.399638i | ||||
\(381\) | 30.3226i | 1.55347i | ||||||||
\(382\) | −0.355141 | − | 0.355141i | −0.0181706 | − | 0.0181706i | ||||
\(383\) | 8.97694 | 0.458700 | 0.229350 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229350 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(384\) | 1.28900 | + | 1.28900i | 0.0657790 | + | 0.0657790i | ||||
\(385\) | 0.832312 | − | 22.7627i | 0.0424185 | − | 1.16009i | ||||
\(386\) | 7.33106 | 0.373141 | ||||||||
\(387\) | − | 0.994617i | − | 0.0505592i | ||||||
\(388\) | 5.04296i | 0.256018i | ||||||||
\(389\) | 14.6826 | − | 14.6826i | 0.744440 | − | 0.744440i | −0.228989 | − | 0.973429i | \(-0.573542\pi\) |
0.973429 | + | 0.228989i | \(0.0735420\pi\) | |||||||
\(390\) | 5.89835 | + | 0.215671i | 0.298674 | + | 0.0109209i | ||||
\(391\) | 0.353646i | 0.0178846i | ||||||||
\(392\) | − | 11.1884i | − | 0.565100i | ||||||
\(393\) | −40.2011 | −2.02788 | ||||||||
\(394\) | 8.20672 | + | 8.20672i | 0.413448 | + | 0.413448i | ||||
\(395\) | −0.614151 | + | 16.7963i | −0.0309013 | + | 0.845112i | ||||
\(396\) | −0.771593 | −0.0387740 | ||||||||
\(397\) | 0.327150 | − | 0.327150i | 0.0164192 | − | 0.0164192i | −0.698850 | − | 0.715269i | \(-0.746304\pi\) |
0.715269 | + | 0.698850i | \(0.246304\pi\) | |||||||
\(398\) | 0.480679 | + | 0.480679i | 0.0240943 | + | 0.0240943i | ||||
\(399\) | −19.1652 | − | 19.1652i | −0.959461 | − | 0.959461i | ||||
\(400\) | 0.365159 | − | 4.98665i | 0.0182579 | − | 0.249332i | ||||
\(401\) | 19.1836 | − | 19.1836i | 0.957985 | − | 0.957985i | −0.0411677 | − | 0.999152i | \(-0.513108\pi\) |
0.999152 | + | 0.0411677i | \(0.0131078\pi\) | |||||||
\(402\) | 20.3660 | 1.01576 | ||||||||
\(403\) | −4.84126 | + | 4.84126i | −0.241161 | + | 0.241161i | ||||
\(404\) | 11.7791i | 0.586033i | ||||||||
\(405\) | 16.1571 | − | 15.0172i | 0.802852 | − | 0.746211i | ||||
\(406\) | − | 28.6365i | − | 1.42121i | ||||||
\(407\) | −13.8071 | − | 4.52243i | −0.684393 | − | 0.224169i | ||||
\(408\) | 2.70170 | − | 2.70170i | 0.133754 | − | 0.133754i | ||||
\(409\) | 9.30031 | + | 9.30031i | 0.459871 | + | 0.459871i | 0.898613 | − | 0.438742i | \(-0.144576\pi\) |
−0.438742 | + | 0.898613i | \(0.644576\pi\) | |||||||
\(410\) | 9.48350 | + | 10.2033i | 0.468357 | + | 0.503907i | ||||
\(411\) | − | 2.45628i | − | 0.121160i | ||||||
\(412\) | 6.35592i | 0.313134i | ||||||||
\(413\) | −40.9188 | −2.01348 | ||||||||
\(414\) | 0.0545055i | 0.00267880i | ||||||||
\(415\) | 0.974453 | − | 26.6501i | 0.0478340 | − | 1.30820i | ||||
\(416\) | −1.44800 | −0.0709939 | ||||||||
\(417\) | −10.5601 | − | 10.5601i | −0.517128 | − | 0.517128i | ||||
\(418\) | 5.88817 | + | 5.88817i | 0.288000 | + | 0.288000i | ||||
\(419\) | − | 11.9651i | − | 0.584532i | −0.956337 | − | 0.292266i | \(-0.905591\pi\) | ||
0.956337 | − | 0.292266i | \(-0.0944093\pi\) | |||||||
\(420\) | 11.8350 | + | 12.7333i | 0.577488 | + | 0.621322i | ||||
\(421\) | 17.5941 | − | 17.5941i | 0.857482 | − | 0.857482i | −0.133559 | − | 0.991041i | \(-0.542641\pi\) |
0.991041 | + | 0.133559i | \(0.0426405\pi\) | |||||||
\(422\) | 24.5328 | 1.19424 | ||||||||
\(423\) | 1.51034 | − | 1.51034i | 0.0734354 | − | 0.0734354i | ||||
\(424\) | 2.87955 | − | 2.87955i | 0.139843 | − | 0.139843i | ||||
\(425\) | −10.4519 | − | 0.765361i | −0.506990 | − | 0.0371255i | ||||
\(426\) | 16.3215 | + | 16.3215i | 0.790777 | + | 0.790777i | ||||
\(427\) | −41.8867 | −2.02704 | ||||||||
\(428\) | −7.29845 | − | 7.29845i | −0.352784 | − | 0.352784i | ||||
\(429\) | 4.45812 | − | 4.45812i | 0.215240 | − | 0.215240i | ||||
\(430\) | 5.04284 | − | 4.68707i | 0.243187 | − | 0.226031i | ||||
\(431\) | −9.36769 | + | 9.36769i | −0.451226 | + | 0.451226i | −0.895761 | − | 0.444536i | \(-0.853369\pi\) |
0.444536 | + | 0.895761i | \(0.353369\pi\) | |||||||
\(432\) | −3.45060 | + | 3.45060i | −0.166017 | + | 0.166017i | ||||
\(433\) | 11.6303 | − | 11.6303i | 0.558916 | − | 0.558916i | −0.370083 | − | 0.928999i | \(-0.620671\pi\) |
0.928999 | + | 0.370083i | \(0.120671\pi\) | |||||||
\(434\) | −20.1652 | −0.967962 | ||||||||
\(435\) | 18.6335 | + | 20.0478i | 0.893406 | + | 0.961219i | ||||
\(436\) | −7.27809 | + | 7.27809i | −0.348557 | + | 0.348557i | ||||
\(437\) | 0.415942 | − | 0.415942i | 0.0198972 | − | 0.0198972i | ||||
\(438\) | 12.4520i | 0.594980i | ||||||||
\(439\) | 16.3753 | + | 16.3753i | 0.781552 | + | 0.781552i | 0.980093 | − | 0.198540i | \(-0.0636201\pi\) |
−0.198540 | + | 0.980093i | \(0.563620\pi\) | |||||||
\(440\) | −3.63609 | − | 3.91208i | −0.173344 | − | 0.186501i | ||||
\(441\) | −3.61430 | −0.172110 | ||||||||
\(442\) | 3.03496i | 0.144358i | ||||||||
\(443\) | 18.4976 | + | 18.4976i | 0.878850 | + | 0.878850i | 0.993416 | − | 0.114566i | \(-0.0365477\pi\) |
−0.114566 | + | 0.993416i | \(0.536548\pi\) | |||||||
\(444\) | 9.89174 | − | 5.01058i | 0.469441 | − | 0.237792i | ||||
\(445\) | −36.7512 | − | 1.34380i | −1.74217 | − | 0.0637021i | ||||
\(446\) | −13.8026 | + | 13.8026i | −0.653571 | + | 0.653571i | ||||
\(447\) | −29.4823 | + | 29.4823i | −1.39447 | + | 1.39447i | ||||
\(448\) | −3.01566 | − | 3.01566i | −0.142477 | − | 0.142477i | ||||
\(449\) | −28.1954 | + | 28.1954i | −1.33062 | + | 1.33062i | −0.425808 | + | 0.904814i | \(0.640010\pi\) |
−0.904814 | + | 0.425808i | \(0.859990\pi\) | |||||||
\(450\) | −1.61089 | − | 0.117961i | −0.0759380 | − | 0.00556074i | ||||
\(451\) | 14.8798 | 0.700664 | ||||||||
\(452\) | − | 5.37412i | − | 0.252777i | ||||||
\(453\) | −21.4619 | + | 21.4619i | −1.00837 | + | 1.00837i | ||||
\(454\) | − | 10.8328i | − | 0.508406i | ||||||
\(455\) | −13.7994 | − | 0.504570i | −0.646925 | − | 0.0236546i | ||||
\(456\) | −6.35524 | −0.297611 | ||||||||
\(457\) | 30.7275i | 1.43737i | 0.695334 | + | 0.718687i | \(0.255256\pi\) | ||||
−0.695334 | + | 0.718687i | \(0.744744\pi\) | |||||||
\(458\) | 17.5884i | 0.821851i | ||||||||
\(459\) | 7.23235 | + | 7.23235i | 0.337577 | + | 0.337577i | ||||
\(460\) | −0.276350 | + | 0.256854i | −0.0128849 | + | 0.0119759i | ||||
\(461\) | −9.22827 | − | 9.22827i | −0.429804 | − | 0.429804i | 0.458758 | − | 0.888561i | \(-0.348295\pi\) |
−0.888561 | + | 0.458758i | \(0.848295\pi\) | |||||||
\(462\) | 18.5694 | 0.863925 | ||||||||
\(463\) | 13.6064 | 0.632343 | 0.316172 | − | 0.948702i | \(-0.397602\pi\) | ||||
0.316172 | + | 0.948702i | \(0.397602\pi\) | |||||||
\(464\) | −4.74797 | − | 4.74797i | −0.220419 | − | 0.220419i | ||||
\(465\) | 14.1173 | − | 13.1213i | 0.654672 | − | 0.608485i | ||||
\(466\) | 1.47378 | + | 1.47378i | 0.0682715 | + | 0.0682715i | ||||
\(467\) | − | 19.5369i | − | 0.904059i | −0.892003 | − | 0.452030i | \(-0.850700\pi\) | ||
0.892003 | − | 0.452030i | \(-0.149300\pi\) | |||||||
\(468\) | 0.467761i | 0.0216223i | ||||||||
\(469\) | −47.6470 | −2.20013 | ||||||||
\(470\) | 14.7750 | + | 0.540245i | 0.681522 | + | 0.0249197i | ||||
\(471\) | − | 26.0635i | − | 1.20094i | ||||||
\(472\) | −6.78438 | + | 6.78438i | −0.312277 | + | 0.312277i | ||||
\(473\) | − | 7.35412i | − | 0.338143i | ||||||
\(474\) | −13.7021 | −0.629356 | ||||||||
\(475\) | 11.3928 | + | 13.1932i | 0.522738 | + | 0.605344i | ||||
\(476\) | −6.32073 | + | 6.32073i | −0.289710 | + | 0.289710i | ||||
\(477\) | −0.930212 | − | 0.930212i | −0.0425915 | − | 0.0425915i | ||||
\(478\) | 0.869275 | − | 0.869275i | 0.0397597 | − | 0.0397597i | ||||
\(479\) | −25.1547 | + | 25.1547i | −1.14935 | + | 1.14935i | −0.162667 | + | 0.986681i | \(0.552010\pi\) |
−0.986681 | + | 0.162667i | \(0.947990\pi\) | |||||||
\(480\) | 4.07345 | + | 0.148945i | 0.185927 | + | 0.00679836i | ||||
\(481\) | −2.74162 | + | 8.37026i | −0.125007 | + | 0.381651i | ||||
\(482\) | −7.39427 | − | 7.39427i | −0.336800 | − | 0.336800i | ||||
\(483\) | − | 1.31174i | − | 0.0596864i | ||||||
\(484\) | 5.29490 | 0.240677 | ||||||||
\(485\) | 7.67694 | + | 8.25966i | 0.348592 | + | 0.375052i | ||||
\(486\) | 2.36388 | + | 2.36388i | 0.107228 | + | 0.107228i | ||||
\(487\) | 41.5088i | 1.88094i | 0.339873 | + | 0.940471i | \(0.389616\pi\) | ||||
−0.339873 | + | 0.940471i | \(0.610384\pi\) | |||||||
\(488\) | −6.94487 | + | 6.94487i | −0.314379 | + | 0.314379i | ||||
\(489\) | −2.33970 | + | 2.33970i | −0.105805 | + | 0.105805i | ||||
\(490\) | −17.0322 | − | 18.3250i | −0.769436 | − | 0.827840i | ||||
\(491\) | −24.6515 | −1.11250 | −0.556252 | − | 0.831013i | \(-0.687761\pi\) | ||||
−0.556252 | + | 0.831013i | \(0.687761\pi\) | |||||||
\(492\) | −8.03006 | + | 8.03006i | −0.362023 | + | 0.362023i | ||||
\(493\) | −9.95160 | + | 9.95160i | −0.448197 | + | 0.448197i | ||||
\(494\) | 3.56958 | − | 3.56958i | 0.160603 | − | 0.160603i | ||||
\(495\) | −1.26376 | + | 1.17460i | −0.0568018 | + | 0.0527945i | ||||
\(496\) | −3.34342 | + | 3.34342i | −0.150124 | + | 0.150124i | ||||
\(497\) | −38.1846 | − | 38.1846i | −1.71281 | − | 1.71281i | ||||
\(498\) | 21.7406 | 0.974220 | ||||||||
\(499\) | −16.8585 | − | 16.8585i | −0.754689 | − | 0.754689i | 0.220662 | − | 0.975350i | \(-0.429178\pi\) |
−0.975350 | + | 0.220662i | \(0.929178\pi\) | |||||||
\(500\) | −6.99313 | − | 8.72331i | −0.312742 | − | 0.390118i | ||||
\(501\) | −20.9422 | + | 20.9422i | −0.935628 | + | 0.935628i | ||||
\(502\) | −15.8249 | + | 15.8249i | −0.706299 | + | 0.706299i | ||||
\(503\) | −14.5276 | −0.647755 | −0.323877 | − | 0.946099i | \(-0.604987\pi\) | ||||
−0.323877 | + | 0.946099i | \(0.604987\pi\) | |||||||
\(504\) | −0.974180 | + | 0.974180i | −0.0433934 | + | 0.0433934i | ||||
\(505\) | 17.9314 | + | 19.2925i | 0.797939 | + | 0.858506i | ||||
\(506\) | 0.403010i | 0.0179160i | ||||||||
\(507\) | 14.0544 | + | 14.0544i | 0.624176 | + | 0.624176i | ||||
\(508\) | −11.7621 | − | 11.7621i | −0.521857 | − | 0.521857i | ||||
\(509\) | 38.8001 | 1.71978 | 0.859892 | − | 0.510476i | \(-0.170531\pi\) | ||||
0.859892 | + | 0.510476i | \(0.170531\pi\) | |||||||
\(510\) | 0.312183 | − | 8.53783i | 0.0138237 | − | 0.378061i | ||||
\(511\) | − | 29.1319i | − | 1.28872i | ||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 17.0127i | − | 0.751129i | ||||||
\(514\) | − | 23.1629i | − | 1.02167i | ||||||
\(515\) | 9.67567 | + | 10.4101i | 0.426361 | + | 0.458724i | ||||
\(516\) | 3.96873 | + | 3.96873i | 0.174714 | + | 0.174714i | ||||
\(517\) | 11.1674 | − | 11.1674i | 0.491140 | − | 0.491140i | ||||
\(518\) | −23.1421 | + | 11.7224i | −1.01680 | + | 0.515054i | ||||
\(519\) | − | 30.9544i | − | 1.35875i | ||||||
\(520\) | −2.37161 | + | 2.20430i | −0.104002 | + | 0.0966648i | ||||
\(521\) | 1.46992i | 0.0643983i | 0.999481 | + | 0.0321991i | \(0.0102511\pi\) | ||||
−0.999481 | + | 0.0321991i | \(0.989749\pi\) | |||||||
\(522\) | −1.53379 | + | 1.53379i | −0.0671320 | + | 0.0671320i | ||||
\(523\) | 37.4377 | 1.63704 | 0.818519 | − | 0.574479i | \(-0.194795\pi\) | ||||
0.818519 | + | 0.574479i | \(0.194795\pi\) | |||||||
\(524\) | 15.5939 | − | 15.5939i | 0.681223 | − | 0.681223i | ||||
\(525\) | 38.7680 | + | 2.83888i | 1.69198 | + | 0.123899i | ||||
\(526\) | 12.7777 | + | 12.7777i | 0.557136 | + | 0.557136i | ||||
\(527\) | 7.00770 | + | 7.00770i | 0.305260 | + | 0.305260i | ||||
\(528\) | 3.07882 | − | 3.07882i | 0.133989 | − | 0.133989i | ||||
\(529\) | −22.9715 | −0.998762 | ||||||||
\(530\) | 0.332734 | − | 9.09986i | 0.0144530 | − | 0.395273i | ||||
\(531\) | 2.19163 | + | 2.19163i | 0.0951086 | + | 0.0951086i | ||||
\(532\) | 14.8683 | 0.644622 | ||||||||
\(533\) | − | 9.02057i | − | 0.390724i | ||||||
\(534\) | − | 29.9809i | − | 1.29740i | ||||||
\(535\) | −23.0643 | − | 0.843340i | −0.997157 | − | 0.0364608i | ||||
\(536\) | −7.89993 | + | 7.89993i | −0.341225 | + | 0.341225i | ||||
\(537\) | − | 21.8065i | − | 0.941018i | ||||||
\(538\) | − | 5.62728i | − | 0.242609i | ||||||
\(539\) | −26.7239 | −1.15108 | ||||||||
\(540\) | −0.398719 | + | 10.9045i | −0.0171581 | + | 0.469254i | ||||
\(541\) | 1.13614 | + | 1.13614i | 0.0488465 | + | 0.0488465i | 0.731108 | − | 0.682262i | \(-0.239003\pi\) |
−0.682262 | + | 0.731108i | \(0.739003\pi\) | |||||||
\(542\) | 21.2992 | 0.914881 | ||||||||
\(543\) | −1.23899 | − | 1.23899i | −0.0531700 | − | 0.0531700i | ||||
\(544\) | 2.09597i | 0.0898639i | ||||||||
\(545\) | −0.840987 | + | 23.0000i | −0.0360239 | + | 0.985210i | ||||
\(546\) | − | 11.2573i | − | 0.481766i | ||||||
\(547\) | 41.4457 | 1.77209 | 0.886045 | − | 0.463599i | \(-0.153442\pi\) | ||||
0.886045 | + | 0.463599i | \(0.153442\pi\) | |||||||
\(548\) | 0.952787 | + | 0.952787i | 0.0407010 | + | 0.0407010i | ||||
\(549\) | 2.24347 | + | 2.24347i | 0.0957490 | + | 0.0957490i | ||||
\(550\) | −11.9108 | − | 0.872195i | −0.507878 | − | 0.0371905i | ||||
\(551\) | 23.4092 | 0.997266 | ||||||||
\(552\) | −0.217489 | − | 0.217489i | −0.00925694 | − | 0.00925694i | ||||
\(553\) | 32.0564 | 1.36318 | ||||||||
\(554\) | −24.8652 | −1.05642 | ||||||||
\(555\) | 8.57362 | − | 23.2649i | 0.363930 | − | 0.987540i | ||||
\(556\) | 8.19245 | 0.347437 | ||||||||
\(557\) | 24.9812 | 1.05849 | 0.529244 | − | 0.848470i | \(-0.322476\pi\) | ||||
0.529244 | + | 0.848470i | \(0.322476\pi\) | |||||||
\(558\) | 1.08006 | + | 1.08006i | 0.0457226 | + | 0.0457226i | ||||
\(559\) | −4.45827 | −0.188565 | ||||||||
\(560\) | −9.52998 | − | 0.348461i | −0.402715 | − | 0.0147252i | ||||
\(561\) | −6.45311 | − | 6.45311i | −0.272451 | − | 0.272451i | ||||
\(562\) | −0.925329 | − | 0.925329i | −0.0390326 | − | 0.0390326i | ||||
\(563\) | 36.8702 | 1.55389 | 0.776946 | − | 0.629567i | \(-0.216768\pi\) | ||||
0.776946 | + | 0.629567i | \(0.216768\pi\) | |||||||
\(564\) | 12.0532i | 0.507531i | ||||||||
\(565\) | −8.18106 | − | 8.80205i | −0.344180 | − | 0.370305i | ||||
\(566\) | − | 0.300587i | − | 0.0126346i | ||||||
\(567\) | −29.7488 | − | 29.7488i | −1.24933 | − | 1.24933i | ||||
\(568\) | −12.6621 | −0.531290 | ||||||||
\(569\) | −9.95317 | − | 9.95317i | −0.417259 | − | 0.417259i | 0.466999 | − | 0.884258i | \(-0.345335\pi\) |
−0.884258 | + | 0.466999i | \(0.845335\pi\) | |||||||
\(570\) | −10.4090 | + | 9.67462i | −0.435984 | + | 0.405225i | ||||
\(571\) | 13.1507 | 0.550340 | 0.275170 | − | 0.961396i | \(-0.411266\pi\) | ||||
0.275170 | + | 0.961396i | \(0.411266\pi\) | |||||||
\(572\) | 3.45859i | 0.144611i | ||||||||
\(573\) | − | 0.915554i | − | 0.0382478i | ||||||
\(574\) | 18.7866 | − | 18.7866i | 0.784138 | − | 0.784138i | ||||
\(575\) | −0.0616121 | + | 0.841381i | −0.00256940 | + | 0.0350880i | ||||
\(576\) | 0.323040i | 0.0134600i | ||||||||
\(577\) | − | 4.76642i | − | 0.198429i | −0.995066 | − | 0.0992144i | \(-0.968367\pi\) | ||
0.995066 | − | 0.0992144i | \(-0.0316330\pi\) | |||||||
\(578\) | −12.6069 | −0.524379 | ||||||||
\(579\) | 9.44973 | + | 9.44973i | 0.392718 | + | 0.392718i | ||||
\(580\) | −15.0044 | − | 0.548631i | −0.623023 | − | 0.0227806i | ||||
\(581\) | −50.8629 | −2.11015 | ||||||||
\(582\) | −6.50038 | + | 6.50038i | −0.269449 | + | 0.269449i | ||||
\(583\) | −6.87791 | − | 6.87791i | −0.284854 | − | 0.284854i | ||||
\(584\) | −4.83010 | − | 4.83010i | −0.199871 | − | 0.199871i | ||||
\(585\) | 0.712077 | + | 0.766127i | 0.0294408 | + | 0.0316755i | ||||
\(586\) | 22.4364 | − | 22.4364i | 0.926837 | − | 0.926837i | ||||
\(587\) | −1.56926 | −0.0647702 | −0.0323851 | − | 0.999475i | \(-0.510310\pi\) | ||||
−0.0323851 | + | 0.999475i | \(0.510310\pi\) | |||||||
\(588\) | 14.4218 | − | 14.4218i | 0.594747 | − | 0.594747i | ||||
\(589\) | − | 16.4843i | − | 0.679223i | ||||||
\(590\) | −0.783939 | + | 21.4398i | −0.0322743 | + | 0.882661i | ||||
\(591\) | 21.1569i | 0.870279i | ||||||||
\(592\) | −1.89339 | + | 5.78058i | −0.0778179 | + | 0.237580i | ||||
\(593\) | 9.67923 | − | 9.67923i | 0.397478 | − | 0.397478i | −0.479864 | − | 0.877343i | \(-0.659314\pi\) |
0.877343 | + | 0.479864i | \(0.159314\pi\) | |||||||
\(594\) | 8.24188 | + | 8.24188i | 0.338168 | + | 0.338168i | ||||
\(595\) | −0.730363 | + | 19.9745i | −0.0299420 | + | 0.818876i | ||||
\(596\) | − | 22.8722i | − | 0.936884i | ||||||
\(597\) | 1.23919i | 0.0507167i | ||||||||
\(598\) | 0.244316 | 0.00999082 | ||||||||
\(599\) | 43.4898i | 1.77694i | 0.458931 | + | 0.888472i | \(0.348232\pi\) | ||||
−0.458931 | + | 0.888472i | \(0.651768\pi\) | |||||||
\(600\) | 6.89848 | − | 5.95710i | 0.281629 | − | 0.243198i | ||||
\(601\) | −46.6191 | −1.90163 | −0.950817 | − | 0.309754i | \(-0.899753\pi\) | ||||
−0.950817 | + | 0.309754i | \(0.899753\pi\) | |||||||
\(602\) | −9.28499 | − | 9.28499i | −0.378428 | − | 0.378428i | ||||
\(603\) | 2.55200 | + | 2.55200i | 0.103925 | + | 0.103925i | ||||
\(604\) | − | 16.6501i | − | 0.677482i | ||||||
\(605\) | 8.67229 | − | 8.06046i | 0.352579 | − | 0.327704i | ||||
\(606\) | −15.1833 | + | 15.1833i | −0.616779 | + | 0.616779i | ||||
\(607\) | −11.8472 | −0.480862 | −0.240431 | − | 0.970666i | \(-0.577289\pi\) | ||||
−0.240431 | + | 0.970666i | \(0.577289\pi\) | |||||||
\(608\) | 2.46518 | − | 2.46518i | 0.0999763 | − | 0.0999763i | ||||
\(609\) | 36.9125 | − | 36.9125i | 1.49577 | − | 1.49577i | ||||
\(610\) | −0.802483 | + | 21.9469i | −0.0324916 | + | 0.888605i | ||||
\(611\) | −6.76997 | − | 6.76997i | −0.273884 | − | 0.273884i | ||||
\(612\) | 0.677082 | 0.0273694 | ||||||||
\(613\) | −32.8563 | − | 32.8563i | −1.32705 | − | 1.32705i | −0.907930 | − | 0.419122i | \(-0.862338\pi\) |
−0.419122 | − | 0.907930i | \(-0.637662\pi\) | |||||||
\(614\) | 2.94724 | − | 2.94724i | 0.118941 | − | 0.118941i | ||||
\(615\) | −0.927878 | + | 25.3763i | −0.0374156 | + | 1.02327i | ||||
\(616\) | −7.20301 | + | 7.20301i | −0.290218 | + | 0.290218i | ||||
\(617\) | 7.41696 | − | 7.41696i | 0.298595 | − | 0.298595i | −0.541868 | − | 0.840464i | \(-0.682283\pi\) |
0.840464 | + | 0.541868i | \(0.182283\pi\) | |||||||
\(618\) | −8.19278 | + | 8.19278i | −0.329562 | + | 0.329562i | ||||
\(619\) | −4.51948 | −0.181653 | −0.0908266 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908266 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(620\) | −0.386334 | + | 10.5658i | −0.0155155 | + | 0.424331i | ||||
\(621\) | 0.582209 | − | 0.582209i | 0.0233632 | − | 0.0233632i | ||||
\(622\) | 12.0863 | − | 12.0863i | 0.484618 | − | 0.484618i | ||||
\(623\) | 70.1413i | 2.81015i | ||||||||
\(624\) | −1.86647 | − | 1.86647i | −0.0747185 | − | 0.0747185i | ||||
\(625\) | −24.7333 | − | 3.64184i | −0.989333 | − | 0.145673i | ||||
\(626\) | −2.00477 | −0.0801267 | ||||||||
\(627\) | 15.1797i | 0.606219i | ||||||||
\(628\) | 10.1100 | + | 10.1100i | 0.403432 | + | 0.403432i | ||||
\(629\) | 12.1159 | + | 3.96849i | 0.483093 | + | 0.158234i | ||||
\(630\) | −0.112567 | + | 3.07857i | −0.00448478 | + | 0.122653i | ||||
\(631\) | −5.79579 | + | 5.79579i | −0.230727 | + | 0.230727i | −0.812996 | − | 0.582269i | \(-0.802165\pi\) |
0.582269 | + | 0.812996i | \(0.302165\pi\) | |||||||
\(632\) | 5.31500 | − | 5.31500i | 0.211419 | − | 0.211419i | ||||
\(633\) | 31.6227 | + | 31.6227i | 1.25689 | + | 1.25689i | ||||
\(634\) | 7.28840 | − | 7.28840i | 0.289459 | − | 0.289459i | ||||
\(635\) | −37.1701 | − | 1.35911i | −1.47505 | − | 0.0539348i | ||||
\(636\) | 7.42348 | 0.294360 | ||||||||
\(637\) | 16.2008i | 0.641898i | ||||||||
\(638\) | −11.3407 | + | 11.3407i | −0.448983 | + | 0.448983i | ||||
\(639\) | 4.09037i | 0.161813i | ||||||||
\(640\) | −1.63786 | + | 1.52231i | −0.0647420 | + | 0.0601745i | ||||
\(641\) | 34.7174 | 1.37125 | 0.685627 | − | 0.727953i | \(-0.259528\pi\) | ||||
0.685627 | + | 0.727953i | \(0.259528\pi\) | |||||||
\(642\) | − | 18.8154i | − | 0.742585i | ||||||
\(643\) | 39.5100i | 1.55812i | 0.626949 | + | 0.779060i | \(0.284303\pi\) | ||||
−0.626949 | + | 0.779060i | \(0.715697\pi\) | |||||||
\(644\) | 0.508822 | + | 0.508822i | 0.0200504 | + | 0.0200504i | ||||
\(645\) | 12.5419 | + | 0.458589i | 0.493835 | + | 0.0180569i | ||||
\(646\) | −5.16694 | − | 5.16694i | −0.203291 | − | 0.203291i | ||||
\(647\) | −4.05796 | −0.159535 | −0.0797675 | − | 0.996813i | \(-0.525418\pi\) | ||||
−0.0797675 | + | 0.996813i | \(0.525418\pi\) | |||||||
\(648\) | −9.86477 | −0.387525 | ||||||||
\(649\) | 16.2047 | + | 16.2047i | 0.636092 | + | 0.636092i | ||||
\(650\) | −0.528749 | + | 7.22065i | −0.0207392 | + | 0.283217i | ||||
\(651\) | −25.9930 | − | 25.9930i | −1.01875 | − | 1.01875i | ||||
\(652\) | − | 1.81513i | − | 0.0710859i | ||||||
\(653\) | − | 27.8245i | − | 1.08886i | −0.838807 | − | 0.544429i | \(-0.816747\pi\) | ||
0.838807 | − | 0.544429i | \(-0.183253\pi\) | |||||||
\(654\) | −18.7629 | −0.733688 | ||||||||
\(655\) | 1.80188 | − | 49.2793i | 0.0704054 | − | 1.92550i | ||||
\(656\) | − | 6.22969i | − | 0.243228i | ||||||
\(657\) | −1.56032 | + | 1.56032i | −0.0608738 | + | 0.0608738i | ||||
\(658\) | − | 28.1988i | − | 1.09931i | ||||||
\(659\) | 34.5284 | 1.34503 | 0.672517 | − | 0.740082i | \(-0.265213\pi\) | ||||
0.672517 | + | 0.740082i | \(0.265213\pi\) | |||||||
\(660\) | 0.355759 | − | 9.72959i | 0.0138479 | − | 0.378724i | ||||
\(661\) | −28.4737 | + | 28.4737i | −1.10750 | + | 1.10750i | −0.114022 | + | 0.993478i | \(0.536373\pi\) |
−0.993478 | + | 0.114022i | \(0.963627\pi\) | |||||||
\(662\) | 0.839383 | + | 0.839383i | 0.0326236 | + | 0.0326236i | ||||
\(663\) | −3.91206 | + | 3.91206i | −0.151932 | + | 0.151932i | ||||
\(664\) | −8.43313 | + | 8.43313i | −0.327269 | + | 0.327269i | ||||
\(665\) | 24.3522 | − | 22.6341i | 0.944336 | − | 0.877713i | ||||
\(666\) | 1.86736 | + | 0.611642i | 0.0723587 | + | 0.0237006i | ||||
\(667\) | 0.801110 | + | 0.801110i | 0.0310191 | + | 0.0310191i | ||||
\(668\) | − | 16.2469i | − | 0.628610i | ||||||
\(669\) | −35.5830 | −1.37572 | ||||||||
\(670\) | −0.912841 | + | 24.9651i | −0.0352661 | + | 0.964486i | ||||
\(671\) | 16.5881 | + | 16.5881i | 0.640375 | + | 0.640375i | ||||
\(672\) | − | 7.77437i | − | 0.299903i | ||||||
\(673\) | 7.80123 | − | 7.80123i | 0.300715 | − | 0.300715i | −0.540578 | − | 0.841294i | \(-0.681795\pi\) |
0.841294 | + | 0.540578i | \(0.181795\pi\) | |||||||
\(674\) | −7.69155 | + | 7.69155i | −0.296268 | + | 0.296268i | ||||
\(675\) | 15.9469 | + | 18.4669i | 0.613797 | + | 0.710793i | ||||
\(676\) | −10.9033 | −0.419358 | ||||||||
\(677\) | 27.1256 | − | 27.1256i | 1.04252 | − | 1.04252i | 0.0434658 | − | 0.999055i | \(-0.486160\pi\) |
0.999055 | − | 0.0434658i | \(-0.0138400\pi\) | |||||||
\(678\) | 6.92724 | − | 6.92724i | 0.266039 | − | 0.266039i | ||||
\(679\) | 15.2079 | − | 15.2079i | 0.583624 | − | 0.583624i | ||||
\(680\) | 3.19071 | + | 3.43290i | 0.122358 | + | 0.131646i | ||||
\(681\) | 13.9634 | − | 13.9634i | 0.535079 | − | 0.535079i | ||||
\(682\) | 7.98588 | + | 7.98588i | 0.305795 | + | 0.305795i | ||||
\(683\) | −5.91525 | −0.226341 | −0.113170 | − | 0.993576i | \(-0.536101\pi\) | ||||
−0.113170 | + | 0.993576i | \(0.536101\pi\) | |||||||
\(684\) | −0.796353 | − | 0.796353i | −0.0304493 | − | 0.0304493i | ||||
\(685\) | 3.01096 | + | 0.110095i | 0.115043 | + | 0.00420651i | ||||
\(686\) | −12.6308 | + | 12.6308i | −0.482246 | + | 0.482246i | ||||
\(687\) | −22.6714 | + | 22.6714i | −0.864968 | + | 0.864968i | ||||
\(688\) | −3.07893 | −0.117383 | ||||||||
\(689\) | −4.16958 | + | 4.16958i | −0.158848 | + | 0.158848i | ||||
\(690\) | −0.687300 | − | 0.0251309i | −0.0261651 | − | 0.000956718i | ||||
\(691\) | 8.32303i | 0.316623i | 0.987389 | + | 0.158312i | \(0.0506050\pi\) | ||||
−0.987389 | + | 0.158312i | \(0.949395\pi\) | |||||||
\(692\) | 12.0071 | + | 12.0071i | 0.456442 | + | 0.456442i | ||||
\(693\) | 2.32686 | + | 2.32686i | 0.0883902 | + | 0.0883902i | ||||
\(694\) | −21.8436 | −0.829171 | ||||||||
\(695\) | 13.4181 | − | 12.4714i | 0.508976 | − | 0.473068i | ||||
\(696\) | − | 12.2403i | − | 0.463966i | ||||||
\(697\) | −13.0572 | −0.494578 | ||||||||
\(698\) | − | 4.00432i | − | 0.151566i | ||||||
\(699\) | 3.79940i | 0.143707i | ||||||||
\(700\) | −16.1392 | + | 13.9368i | −0.610005 | + | 0.526763i | ||||
\(701\) | 15.3758 | + | 15.3758i | 0.580737 | + | 0.580737i | 0.935106 | − | 0.354369i | \(-0.115304\pi\) |
−0.354369 | + | 0.935106i | \(0.615304\pi\) | |||||||
\(702\) | 4.99646 | − | 4.99646i | 0.188579 | − | 0.188579i | ||||
\(703\) | −9.58262 | − | 18.9177i | −0.361415 | − | 0.713495i | ||||
\(704\) | 2.38854i | 0.0900213i | ||||||||
\(705\) | 18.3487 | + | 19.7414i | 0.691050 | + | 0.743504i | ||||
\(706\) | − | 11.1747i | − | 0.420565i | ||||||
\(707\) | 35.5218 | − | 35.5218i | 1.33594 | − | 1.33594i | ||||
\(708\) | −17.4901 | −0.657319 | ||||||||
\(709\) | −18.0591 | + | 18.0591i | −0.678223 | + | 0.678223i | −0.959598 | − | 0.281375i | \(-0.909210\pi\) |
0.281375 | + | 0.959598i | \(0.409210\pi\) | |||||||
\(710\) | −20.7387 | + | 19.2756i | −0.778311 | + | 0.723401i | ||||
\(711\) | −1.71696 | − | 1.71696i | −0.0643910 | − | 0.0643910i | ||||
\(712\) | 11.6295 | + | 11.6295i | 0.435835 | + | 0.435835i | ||||
\(713\) | 0.564125 | − | 0.564125i | 0.0211266 | − | 0.0211266i | ||||
\(714\) | −16.2948 | −0.609819 | ||||||||
\(715\) | 5.26504 | + | 5.66468i | 0.196901 | + | 0.211847i | ||||
\(716\) | 8.45867 | + | 8.45867i | 0.316115 | + | 0.316115i | ||||
\(717\) | 2.24099 | 0.0836914 | ||||||||
\(718\) | 19.4341i | 0.725276i | ||||||||
\(719\) | 18.4885i | 0.689505i | 0.938694 | + | 0.344752i | \(0.112037\pi\) | ||||
−0.938694 | + | 0.344752i | \(0.887963\pi\) | |||||||
\(720\) | 0.491767 | + | 0.529094i | 0.0183271 | + | 0.0197182i | ||||
\(721\) | 19.1673 | − | 19.1673i | 0.713827 | − | 0.713827i | ||||
\(722\) | − | 6.84576i | − | 0.254773i | ||||||
\(723\) | − | 19.0624i | − | 0.708939i | ||||||
\(724\) | 0.961200 | 0.0357227 | ||||||||
\(725\) | −25.4102 | + | 21.9427i | −0.943712 | + | 0.814931i | ||||
\(726\) | 6.82512 | + | 6.82512i | 0.253304 | + | 0.253304i | ||||
\(727\) | −0.154078 | −0.00571445 | −0.00285722 | − | 0.999996i | \(-0.500909\pi\) | ||||
−0.00285722 | + | 0.999996i | \(0.500909\pi\) | |||||||
\(728\) | 4.36667 | + | 4.36667i | 0.161839 | + | 0.161839i | ||||
\(729\) | − | 23.5002i | − | 0.870378i | ||||||
\(730\) | −15.2639 | − | 0.558121i | −0.564943 | − | 0.0206570i | ||||
\(731\) | 6.45333i | 0.238685i | ||||||||
\(732\) | −17.9039 | −0.661746 | ||||||||
\(733\) | −26.0288 | − | 26.0288i | −0.961397 | − | 0.961397i | 0.0378850 | − | 0.999282i | \(-0.487938\pi\) |
−0.999282 | + | 0.0378850i | \(0.987938\pi\) | |||||||
\(734\) | −10.2957 | − | 10.2957i | −0.380020 | − | 0.380020i | ||||
\(735\) | 1.66645 | − | 45.5754i | 0.0614680 | − | 1.68107i | ||||
\(736\) | 0.168727 | 0.00621935 | ||||||||
\(737\) | 18.8693 | + | 18.8693i | 0.695059 | + | 0.695059i | ||||
\(738\) | −2.01244 | −0.0740789 | ||||||||
\(739\) | 36.2429 | 1.33322 | 0.666608 | − | 0.745408i | \(-0.267745\pi\) | ||||
0.666608 | + | 0.745408i | \(0.267745\pi\) | |||||||
\(740\) | 5.69871 | + | 12.3501i | 0.209489 | + | 0.453998i | ||||
\(741\) | 9.20236 | 0.338057 | ||||||||
\(742\) | −17.3675 | −0.637581 | ||||||||
\(743\) | −7.38988 | − | 7.38988i | −0.271109 | − | 0.271109i | 0.558438 | − | 0.829546i | \(-0.311401\pi\) |
−0.829546 | + | 0.558438i | \(0.811401\pi\) | |||||||
\(744\) | −8.61934 | −0.316000 | ||||||||
\(745\) | −34.8186 | − | 37.4615i | −1.27565 | − | 1.37248i | ||||
\(746\) | 23.2626 | + | 23.2626i | 0.851704 | + | 0.851704i | ||||
\(747\) | 2.72424 | + | 2.72424i | 0.0996748 | + | 0.0996748i | ||||
\(748\) | 5.00630 | 0.183048 | ||||||||
\(749\) | 44.0193i | 1.60843i | ||||||||
\(750\) | 2.23019 | − | 20.2585i | 0.0814351 | − | 0.739735i | ||||
\(751\) | − | 18.3541i | − | 0.669749i | −0.942263 | − | 0.334874i | \(-0.891306\pi\) | ||
0.942263 | − | 0.334874i | \(-0.108694\pi\) | |||||||
\(752\) | −4.67540 | − | 4.67540i | −0.170494 | − | 0.170494i | ||||
\(753\) | −40.7965 | −1.48671 | ||||||||
\(754\) | 6.87505 | + | 6.87505i | 0.250374 | + | 0.250374i | ||||
\(755\) | −25.3465 | − | 27.2705i | −0.922455 | − | 0.992474i | ||||
\(756\) | 20.8117 | 0.756913 | ||||||||
\(757\) | 7.26929i | 0.264207i | 0.991236 | + | 0.132104i | \(0.0421731\pi\) | ||||
−0.991236 | + | 0.132104i | \(0.957827\pi\) | |||||||
\(758\) | − | 11.6263i | − | 0.422287i | ||||||
\(759\) | −0.519480 | + | 0.519480i | −0.0188559 | + | 0.0188559i | ||||
\(760\) | 0.284853 | − | 7.79038i | 0.0103327 | − | 0.282587i | ||||
\(761\) | − | 19.7277i | − | 0.715127i | −0.933889 | − | 0.357564i | \(-0.883608\pi\) | ||
0.933889 | − | 0.357564i | \(-0.116392\pi\) | |||||||
\(762\) | − | 30.3226i | − | 1.09847i | ||||||
\(763\) | 43.8965 | 1.58916 | ||||||||
\(764\) | 0.355141 | + | 0.355141i | 0.0128486 | + | 0.0128486i | ||||
\(765\) | 1.10896 | − | 1.03073i | 0.0400947 | − | 0.0372660i | ||||
\(766\) | −8.97694 | −0.324350 | ||||||||
\(767\) | 9.82377 | − | 9.82377i | 0.354716 | − | 0.354716i | ||||
\(768\) | −1.28900 | − | 1.28900i | −0.0465128 | − | 0.0465128i | ||||
\(769\) | −22.1613 | − | 22.1613i | −0.799158 | − | 0.799158i | 0.183805 | − | 0.982963i | \(-0.441159\pi\) |
−0.982963 | + | 0.183805i | \(0.941159\pi\) | |||||||
\(770\) | −0.832312 | + | 22.7627i | −0.0299944 | + | 0.820311i | ||||
\(771\) | 29.8570 | − | 29.8570i | 1.07527 | − | 1.07527i | ||||
\(772\) | −7.33106 | −0.263851 | ||||||||
\(773\) | −30.0504 | + | 30.0504i | −1.08084 | + | 1.08084i | −0.0844052 | + | 0.996432i | \(0.526899\pi\) |
−0.996432 | + | 0.0844052i | \(0.973101\pi\) | |||||||
\(774\) | 0.994617i | 0.0357508i | ||||||||
\(775\) | 15.4516 | + | 17.8933i | 0.555037 | + | 0.642748i | ||||
\(776\) | − | 5.04296i | − | 0.181032i | ||||||
\(777\) | −44.9403 | − | 14.7199i | −1.61223 | − | 0.528074i | ||||
\(778\) | −14.6826 | + | 14.6826i | −0.526398 | + | 0.526398i | ||||
\(779\) | 15.3573 | + | 15.3573i | 0.550232 | + | 0.550232i | ||||
\(780\) | −5.89835 | − | 0.215671i | −0.211195 | − | 0.00772227i | ||||
\(781\) | 30.2439i | 1.08221i | ||||||||
\(782\) | − | 0.353646i | − | 0.0126464i | ||||||
\(783\) | 32.7667 | 1.17099 | ||||||||
\(784\) | 11.1884i | 0.399586i | ||||||||
\(785\) | 31.9492 | + | 1.16821i | 1.14032 | + | 0.0416954i | ||||
\(786\) | 40.2011 | 1.43393 | ||||||||
\(787\) | 22.2914 | + | 22.2914i | 0.794603 | + | 0.794603i | 0.982239 | − | 0.187636i | \(-0.0600825\pi\) |
−0.187636 | + | 0.982239i | \(0.560083\pi\) | |||||||
\(788\) | −8.20672 | − | 8.20672i | −0.292352 | − | 0.292352i | ||||
\(789\) | 32.9410i | 1.17273i | ||||||||
\(790\) | 0.614151 | − | 16.7963i | 0.0218505 | − | 0.597584i | ||||
\(791\) | −16.2065 | + | 16.2065i | −0.576237 | + | 0.576237i | ||||
\(792\) | 0.771593 | 0.0274174 | ||||||||
\(793\) | 10.0561 | − | 10.0561i | 0.357104 | − | 0.357104i | ||||
\(794\) | −0.327150 | + | 0.327150i | −0.0116101 | + | 0.0116101i | ||||
\(795\) | 12.1586 | − | 11.3008i | 0.431222 | − | 0.400799i | ||||
\(796\) | −0.480679 | − | 0.480679i | −0.0170372 | − | 0.0170372i | ||||
\(797\) | 17.6688 | 0.625862 | 0.312931 | − | 0.949776i | \(-0.398689\pi\) | ||||
0.312931 | + | 0.949776i | \(0.398689\pi\) | |||||||
\(798\) | 19.1652 | + | 19.1652i | 0.678442 | + | 0.678442i | ||||
\(799\) | −9.79950 | + | 9.79950i | −0.346681 | + | 0.346681i | ||||
\(800\) | −0.365159 | + | 4.98665i | −0.0129103 | + | 0.176305i | ||||
\(801\) | 3.75680 | − | 3.75680i | 0.132740 | − | 0.132740i | ||||
\(802\) | −19.1836 | + | 19.1836i | −0.677397 | + | 0.677397i | ||||
\(803\) | −11.5369 | + | 11.5369i | −0.407128 | + | 0.407128i | ||||
\(804\) | −20.3660 | −0.718254 | ||||||||
\(805\) | 1.60796 | + | 0.0587947i | 0.0566733 | + | 0.00207224i | ||||
\(806\) | 4.84126 | − | 4.84126i | 0.170526 | − | 0.170526i | ||||
\(807\) | 7.25356 | − | 7.25356i | 0.255337 | − | 0.255337i | ||||
\(808\) | − | 11.7791i | − | 0.414388i | ||||||
\(809\) | 16.5367 | + | 16.5367i | 0.581399 | + | 0.581399i | 0.935288 | − | 0.353888i | \(-0.115141\pi\) |
−0.353888 | + | 0.935288i | \(0.615141\pi\) | |||||||
\(810\) | −16.1571 | + | 15.0172i | −0.567702 | + | 0.527651i | ||||
\(811\) | 40.9951 | 1.43953 | 0.719767 | − | 0.694216i | \(-0.244249\pi\) | ||||
0.719767 | + | 0.694216i | \(0.244249\pi\) | |||||||
\(812\) | 28.6365i | 1.00495i | ||||||||
\(813\) | 27.4547 | + | 27.4547i | 0.962879 | + | 0.962879i | ||||
\(814\) | 13.8071 | + | 4.52243i | 0.483939 | + | 0.158511i | ||||
\(815\) | −2.76318 | − | 2.97292i | −0.0967901 | − | 0.104137i | ||||
\(816\) | −2.70170 | + | 2.70170i | −0.0945785 | + | 0.0945785i | ||||
\(817\) | 7.59011 | − | 7.59011i | 0.265544 | − | 0.265544i | ||||
\(818\) | −9.30031 | − | 9.30031i | −0.325178 | − | 0.325178i | ||||
\(819\) | 1.41061 | − | 1.41061i | 0.0492907 | − | 0.0492907i | ||||
\(820\) | −9.48350 | − | 10.2033i | −0.331178 | − | 0.356316i | ||||
\(821\) | −15.0113 | −0.523897 | −0.261948 | − | 0.965082i | \(-0.584365\pi\) | ||||
−0.261948 | + | 0.965082i | \(0.584365\pi\) | |||||||
\(822\) | 2.45628i | 0.0856727i | ||||||||
\(823\) | 34.4033 | − | 34.4033i | 1.19922 | − | 1.19922i | 0.224826 | − | 0.974399i | \(-0.427819\pi\) |
0.974399 | − | 0.224826i | \(-0.0721814\pi\) | |||||||
\(824\) | − | 6.35592i | − | 0.221419i | ||||||
\(825\) | −14.2287 | − | 16.4773i | −0.495381 | − | 0.573665i | ||||
\(826\) | 40.9188 | 1.42375 | ||||||||
\(827\) | − | 2.14845i | − | 0.0747090i | −0.999302 | − | 0.0373545i | \(-0.988107\pi\) | ||
0.999302 | − | 0.0373545i | \(-0.0118931\pi\) | |||||||
\(828\) | − | 0.0545055i | − | 0.00189420i | ||||||
\(829\) | 18.9396 | + | 18.9396i | 0.657800 | + | 0.657800i | 0.954859 | − | 0.297059i | \(-0.0960057\pi\) |
−0.297059 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(830\) | −0.974453 | + | 26.6501i | −0.0338238 | + | 0.925039i | ||||
\(831\) | −32.0512 | − | 32.0512i | −1.11185 | − | 1.11185i | ||||
\(832\) | 1.44800 | 0.0502003 | ||||||||
\(833\) | 23.4505 | 0.812513 | ||||||||
\(834\) | 10.5601 | + | 10.5601i | 0.365665 | + | 0.365665i | ||||
\(835\) | −24.7327 | − | 26.6100i | −0.855911 | − | 0.920878i | ||||
\(836\) | −5.88817 | − | 5.88817i | −0.203647 | − | 0.203647i | ||||
\(837\) | − | 23.0736i | − | 0.797541i | ||||||
\(838\) | 11.9651i | 0.413327i | ||||||||
\(839\) | 26.3122 | 0.908399 | 0.454200 | − | 0.890900i | \(-0.349925\pi\) | ||||
0.454200 | + | 0.890900i | \(0.349925\pi\) | |||||||
\(840\) | −11.8350 | − | 12.7333i | −0.408346 | − | 0.439341i | ||||
\(841\) | 16.0865i | 0.554705i | ||||||||
\(842\) | −17.5941 | + | 17.5941i | −0.606331 | + | 0.606331i | ||||
\(843\) | − | 2.38550i | − | 0.0821609i | ||||||
\(844\) | −24.5328 | −0.844453 | ||||||||
\(845\) | −17.8581 | + | 16.5982i | −0.614336 | + | 0.570995i | ||||
\(846\) | −1.51034 | + | 1.51034i | −0.0519267 | + | 0.0519267i | ||||
\(847\) | −15.9676 | − | 15.9676i | −0.548653 | − | 0.548653i | ||||
\(848\) | −2.87955 | + | 2.87955i | −0.0988842 | + | 0.0988842i | ||||
\(849\) | 0.387457 | − | 0.387457i | 0.0132975 | − | 0.0132975i | ||||
\(850\) | 10.4519 | + | 0.765361i | 0.358496 | + | 0.0262517i | ||||
\(851\) | 0.319466 | − | 0.975338i | 0.0109511 | − | 0.0334342i | ||||
\(852\) | −16.3215 | − | 16.3215i | −0.559164 | − | 0.559164i | ||||
\(853\) | 29.3440i | 1.00472i | 0.864658 | + | 0.502360i | \(0.167535\pi\) | ||||
−0.864658 | + | 0.502360i | \(0.832465\pi\) | |||||||
\(854\) | 41.8867 | 1.43333 | ||||||||
\(855\) | −2.51661 | − | 0.0920190i | −0.0860662 | − | 0.00314698i | ||||
\(856\) | 7.29845 | + | 7.29845i | 0.249456 | + | 0.249456i | ||||
\(857\) | 16.7643i | 0.572658i | 0.958131 | + | 0.286329i | \(0.0924350\pi\) | ||||
−0.958131 | + | 0.286329i | \(0.907565\pi\) | |||||||
\(858\) | −4.45812 | + | 4.45812i | −0.152198 | + | 0.152198i | ||||
\(859\) | −22.7459 | + | 22.7459i | −0.776081 | + | 0.776081i | −0.979162 | − | 0.203081i | \(-0.934905\pi\) |
0.203081 | + | 0.979162i | \(0.434905\pi\) | |||||||
\(860\) | −5.04284 | + | 4.68707i | −0.171960 | + | 0.159828i | ||||
\(861\) | 48.4319 | 1.65055 | ||||||||
\(862\) | 9.36769 | − | 9.36769i | 0.319065 | − | 0.319065i | ||||
\(863\) | 16.6468 | − | 16.6468i | 0.566664 | − | 0.566664i | −0.364528 | − | 0.931192i | \(-0.618770\pi\) |
0.931192 | + | 0.364528i | \(0.118770\pi\) | |||||||
\(864\) | 3.45060 | − | 3.45060i | 0.117392 | − | 0.117392i | ||||
\(865\) | 37.9445 | + | 1.38743i | 1.29015 | + | 0.0471740i | ||||
\(866\) | −11.6303 | + | 11.6303i | −0.395214 | + | 0.395214i | ||||
\(867\) | −16.2503 | − | 16.2503i | −0.551890 | − | 0.551890i | ||||
\(868\) | 20.1652 | 0.684453 | ||||||||
\(869\) | −12.6951 | − | 12.6951i | −0.430650 | − | 0.430650i | ||||
\(870\) | −18.6335 | − | 20.0478i | −0.631733 | − | 0.679685i | ||||
\(871\) | 11.4391 | − | 11.4391i | 0.387598 | − | 0.387598i | ||||
\(872\) | 7.27809 | − | 7.27809i | 0.246467 | − | 0.246467i | ||||
\(873\) | −1.62908 | −0.0551360 | ||||||||
\(874\) | −0.415942 | + | 0.415942i | −0.0140694 | + | 0.0140694i | ||||
\(875\) | −5.21761 | + | 47.3954i | −0.176387 | + | 1.60226i | ||||
\(876\) | − | 12.4520i | − | 0.420714i | ||||||
\(877\) | −26.6229 | − | 26.6229i | −0.898990 | − | 0.898990i | 0.0963568 | − | 0.995347i | \(-0.469281\pi\) |
−0.995347 | + | 0.0963568i | \(0.969281\pi\) | |||||||
\(878\) | −16.3753 | − | 16.3753i | −0.552641 | − | 0.552641i | ||||
\(879\) | 57.8409 | 1.95093 | ||||||||
\(880\) | 3.63609 | + | 3.91208i | 0.122572 | + | 0.131876i | ||||
\(881\) | 30.3341i | 1.02198i | 0.859587 | + | 0.510990i | \(0.170721\pi\) | ||||
−0.859587 | + | 0.510990i | \(0.829279\pi\) | |||||||
\(882\) | 3.61430 | 0.121700 | ||||||||
\(883\) | − | 31.6440i | − | 1.06491i | −0.846459 | − | 0.532453i | \(-0.821270\pi\) | ||
0.846459 | − | 0.532453i | \(-0.178730\pi\) | |||||||
\(884\) | − | 3.03496i | − | 0.102077i | ||||||
\(885\) | −28.6464 | + | 26.6254i | −0.962937 | + | 0.895002i | ||||
\(886\) | −18.4976 | − | 18.4976i | −0.621441 | − | 0.621441i | ||||
\(887\) | −6.61467 | + | 6.61467i | −0.222099 | + | 0.222099i | −0.809382 | − | 0.587283i | \(-0.800198\pi\) |
0.587283 | + | 0.809382i | \(0.300198\pi\) | |||||||
\(888\) | −9.89174 | + | 5.01058i | −0.331945 | + | 0.168144i | ||||
\(889\) | 70.9408i | 2.37928i | ||||||||
\(890\) | 36.7512 | + | 1.34380i | 1.23190 | + | 0.0450442i | ||||
\(891\) | 23.5623i | 0.789368i | ||||||||
\(892\) | 13.8026 | − | 13.8026i | 0.462144 | − | 0.462144i | ||||
\(893\) | 23.0514 | 0.771387 | ||||||||
\(894\) | 29.4823 | − | 29.4823i | 0.986036 | − | 0.986036i | ||||
\(895\) | 26.7308 | + | 0.977404i | 0.893512 | + | 0.0326710i | ||||
\(896\) | 3.01566 | + | 3.01566i | 0.100746 | + | 0.100746i | ||||
\(897\) | 0.314923 | + | 0.314923i | 0.0105150 | + | 0.0105150i | ||||
\(898\) | 28.1954 | − | 28.1954i | 0.940891 | − | 0.940891i | ||||
\(899\) | 31.7489 | 1.05889 | ||||||||
\(900\) | 1.61089 | + | 0.117961i | 0.0536963 | + | 0.00393203i | ||||
\(901\) | 6.03545 | + | 6.03545i | 0.201070 | + | 0.201070i | ||||
\(902\) | −14.8798 | −0.495444 | ||||||||
\(903\) | − | 23.9367i | − | 0.796563i | ||||||
\(904\) | 5.37412i | 0.178741i | ||||||||
\(905\) | 1.57431 | − | 1.46324i | 0.0523318 | − | 0.0486398i | ||||
\(906\) | 21.4619 | − | 21.4619i | 0.713025 | − | 0.713025i | ||||
\(907\) | 41.6369i | 1.38253i | 0.722602 | + | 0.691265i | \(0.242946\pi\) | ||||
−0.722602 | + | 0.691265i | \(0.757054\pi\) | |||||||
\(908\) | 10.8328i | 0.359498i | ||||||||
\(909\) | −3.80513 | −0.126208 | ||||||||
\(910\) | 13.7994 | + | 0.504570i | 0.457445 | + | 0.0167263i | ||||
\(911\) | 5.98425 | + | 5.98425i | 0.198267 | + | 0.198267i | 0.799257 | − | 0.600990i | \(-0.205227\pi\) |
−0.600990 | + | 0.799257i | \(0.705227\pi\) | |||||||
\(912\) | 6.35524 | 0.210443 | ||||||||
\(913\) | 20.1428 | + | 20.1428i | 0.666631 | + | 0.666631i | ||||
\(914\) | − | 30.7275i | − | 1.01638i | ||||||
\(915\) | −29.3240 | + | 27.2552i | −0.969421 | + | 0.901029i | ||||
\(916\) | − | 17.5884i | − | 0.581136i | ||||||
\(917\) | −94.0518 | −3.10586 | ||||||||
\(918\) | −7.23235 | − | 7.23235i | −0.238703 | − | 0.238703i | ||||
\(919\) | −12.1528 | − | 12.1528i | −0.400885 | − | 0.400885i | 0.477660 | − | 0.878545i | \(-0.341485\pi\) |
−0.878545 | + | 0.477660i | \(0.841485\pi\) | |||||||
\(920\) | 0.276350 | − | 0.256854i | 0.00911101 | − | 0.00846823i | ||||
\(921\) | 7.59798 | 0.250362 | ||||||||
\(922\) | 9.22827 | + | 9.22827i | 0.303917 | + | 0.303917i | ||||
\(923\) | 18.3347 | 0.603494 | ||||||||
\(924\) | −18.5694 | −0.610887 | ||||||||
\(925\) | 28.1343 | + | 11.5525i | 0.925051 | + | 0.379844i | ||||
\(926\) | −13.6064 | −0.447134 | ||||||||
\(927\) | −2.05322 | −0.0674366 | ||||||||
\(928\) | 4.74797 | + | 4.74797i | 0.155860 | + | 0.155860i | ||||
\(929\) | −11.0600 | −0.362867 | −0.181434 | − | 0.983403i | \(-0.558074\pi\) | ||||
−0.181434 | + | 0.983403i | \(0.558074\pi\) | |||||||
\(930\) | −14.1173 | + | 13.1213i | −0.462923 | + | 0.430264i | ||||
\(931\) | −27.5814 | − | 27.5814i | −0.903945 | − | 0.903945i | ||||
\(932\) | −1.47378 | − | 1.47378i | −0.0482753 | − | 0.0482753i | ||||
\(933\) | 31.1586 | 1.02009 | ||||||||
\(934\) | 19.5369i | 0.639267i | ||||||||
\(935\) | 8.19960 | − | 7.62112i | 0.268156 | − | 0.249237i | ||||
\(936\) | − | 0.467761i | − | 0.0152893i | ||||||
\(937\) | 15.6788 | + | 15.6788i | 0.512205 | + | 0.512205i | 0.915202 | − | 0.402997i | \(-0.132031\pi\) |
−0.402997 | + | 0.915202i | \(0.632031\pi\) | |||||||
\(938\) | 47.6470 | 1.55573 | ||||||||
\(939\) | −2.58415 | − | 2.58415i | −0.0843305 | − | 0.0843305i | ||||
\(940\) | −14.7750 | − | 0.540245i | −0.481909 | − | 0.0176209i | ||||
\(941\) | −18.6061 | −0.606540 | −0.303270 | − | 0.952905i | \(-0.598078\pi\) | ||||
−0.303270 | + | 0.952905i | \(0.598078\pi\) | |||||||
\(942\) | 26.0635i | 0.849196i | ||||||||
\(943\) | 1.05111i | 0.0342290i | ||||||||
\(944\) | 6.78438 | − | 6.78438i | 0.220813 | − | 0.220813i | ||||
\(945\) | 34.0866 | − | 31.6818i | 1.10884 | − | 1.03061i | ||||
\(946\) | 7.35412i | 0.239103i | ||||||||
\(947\) | 1.38953i | 0.0451536i | 0.999745 | + | 0.0225768i | \(0.00718702\pi\) | ||||
−0.999745 | + | 0.0225768i | \(0.992813\pi\) | |||||||
\(948\) | 13.7021 | 0.445022 | ||||||||
\(949\) | 6.99398 | + | 6.99398i | 0.227034 | + | 0.227034i | ||||
\(950\) | −11.3928 | − | 13.1932i | −0.369632 | − | 0.428043i | ||||
\(951\) | 18.7895 | 0.609291 | ||||||||
\(952\) | 6.32073 | − | 6.32073i | 0.204856 | − | 0.204856i | ||||
\(953\) | −24.4066 | − | 24.4066i | −0.790606 | − | 0.790606i | 0.190987 | − | 0.981593i | \(-0.438831\pi\) |
−0.981593 | + | 0.190987i | \(0.938831\pi\) | |||||||
\(954\) | 0.930212 | + | 0.930212i | 0.0301167 | + | 0.0301167i | ||||
\(955\) | 1.12231 | + | 0.0410368i | 0.0363170 | + | 0.00132792i | ||||
\(956\) | −0.869275 | + | 0.869275i | −0.0281144 | + | 0.0281144i | ||||
\(957\) | −29.2363 | −0.945076 | ||||||||
\(958\) | 25.1547 | − | 25.1547i | 0.812712 | − | 0.812712i | ||||
\(959\) | − | 5.74656i | − | 0.185566i | ||||||
\(960\) | −4.07345 | − | 0.148945i | −0.131470 | − | 0.00480717i | ||||
\(961\) | 8.64307i | 0.278809i | ||||||||
\(962\) | 2.74162 | − | 8.37026i | 0.0883935 | − | 0.269868i | ||||
\(963\) | 2.35769 | − | 2.35769i | 0.0759756 | − | 0.0759756i | ||||
\(964\) | 7.39427 | + | 7.39427i | 0.238153 | + | 0.238153i | ||||
\(965\) | −12.0072 | + | 11.1601i | −0.386527 | + | 0.359257i | ||||
\(966\) | 1.31174i | 0.0422047i | ||||||||
\(967\) | − | 32.8029i | − | 1.05487i | −0.849596 | − | 0.527434i | \(-0.823154\pi\) | ||
0.849596 | − | 0.527434i | \(-0.176846\pi\) | |||||||
\(968\) | −5.29490 | −0.170184 | ||||||||
\(969\) | − | 13.3204i | − | 0.427912i | ||||||
\(970\) | −7.67694 | − | 8.25966i | −0.246492 | − | 0.265202i | ||||
\(971\) | 19.3196 | 0.619995 | 0.309998 | − | 0.950737i | \(-0.399672\pi\) | ||||
0.309998 | + | 0.950737i | \(0.399672\pi\) | |||||||
\(972\) | −2.36388 | − | 2.36388i | −0.0758215 | − | 0.0758215i | ||||
\(973\) | −24.7056 | − | 24.7056i | −0.792026 | − | 0.792026i | ||||
\(974\) | − | 41.5088i | − | 1.33003i | ||||||
\(975\) | −9.98897 | + | 8.62586i | −0.319903 | + | 0.276249i | ||||
\(976\) | 6.94487 | − | 6.94487i | 0.222300 | − | 0.222300i | ||||
\(977\) | −14.6717 | −0.469391 | −0.234695 | − | 0.972069i | \(-0.575409\pi\) | ||||
−0.234695 | + | 0.972069i | \(0.575409\pi\) | |||||||
\(978\) | 2.33970 | − | 2.33970i | 0.0748154 | − | 0.0748154i | ||||
\(979\) | 27.7775 | − | 27.7775i | 0.887773 | − | 0.887773i | ||||
\(980\) | 17.0322 | + | 18.3250i | 0.544073 | + | 0.585371i | ||||
\(981\) | −2.35112 | − | 2.35112i | −0.0750653 | − | 0.0750653i | ||||
\(982\) | 24.6515 | 0.786659 | ||||||||
\(983\) | −26.7565 | − | 26.7565i | −0.853400 | − | 0.853400i | 0.137150 | − | 0.990550i | \(-0.456206\pi\) |
−0.990550 | + | 0.137150i | \(0.956206\pi\) | |||||||
\(984\) | 8.03006 | − | 8.03006i | 0.255989 | − | 0.255989i | ||||
\(985\) | −25.9346 | − | 0.948291i | −0.826345 | − | 0.0302150i | ||||
\(986\) | 9.95160 | − | 9.95160i | 0.316923 | − | 0.316923i | ||||
\(987\) | 36.3483 | − | 36.3483i | 1.15698 | − | 1.15698i | ||||
\(988\) | −3.56958 | + | 3.56958i | −0.113563 | + | 0.113563i | ||||
\(989\) | 0.519497 | 0.0165190 | ||||||||
\(990\) | 1.26376 | − | 1.17460i | 0.0401649 | − | 0.0373313i | ||||
\(991\) | −22.3239 | + | 22.3239i | −0.709143 | + | 0.709143i | −0.966355 | − | 0.257212i | \(-0.917196\pi\) |
0.257212 | + | 0.966355i | \(0.417196\pi\) | |||||||
\(992\) | 3.34342 | − | 3.34342i | 0.106154 | − | 0.106154i | ||||
\(993\) | 2.16393i | 0.0686702i | ||||||||
\(994\) | 38.1846 | + | 38.1846i | 1.21114 | + | 1.21114i | ||||
\(995\) | −1.51903 | − | 0.0555427i | −0.0481564 | − | 0.00176082i | ||||
\(996\) | −21.7406 | −0.688878 | ||||||||
\(997\) | − | 46.0799i | − | 1.45936i | −0.683787 | − | 0.729682i | \(-0.739668\pi\) | ||
0.683787 | − | 0.729682i | \(-0.260332\pi\) | |||||||
\(998\) | 16.8585 | + | 16.8585i | 0.533645 | + | 0.533645i | ||||
\(999\) | −13.4131 | − | 26.4798i | −0.424373 | − | 0.837784i |
(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 | 370.2.h.e.117.2 | yes | 20 | |
5.3 | odd | 4 | 370.2.g.e.43.9 | ✓ | 20 | ||
37.31 | odd | 4 | 370.2.g.e.327.9 | yes | 20 | ||
185.68 | even | 4 | inner | 370.2.h.e.253.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.g.e.43.9 | ✓ | 20 | 5.3 | odd | 4 | ||
370.2.g.e.327.9 | yes | 20 | 37.31 | odd | 4 | ||
370.2.h.e.117.2 | yes | 20 | 1.1 | even | 1 | trivial | |
370.2.h.e.253.2 | yes | 20 | 185.68 | even | 4 | inner |