Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 497.16 | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.g.683.16 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.00608872 | − | 1.73204i | 0.00351532 | − | 0.999994i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.02131 | − | 0.956187i | 0.903959 | − | 0.427620i | ||||
\(6\) | −1.22043 | − | 1.22904i | −0.498239 | − | 0.501755i | ||||
\(7\) | −1.11064 | − | 1.11064i | −0.419781 | − | 0.419781i | 0.465347 | − | 0.885128i | \(-0.345929\pi\) |
−0.885128 | + | 0.465347i | \(0.845929\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −2.99993 | − | 0.0210918i | −0.999975 | − | 0.00703060i | ||||
\(10\) | 0.753158 | − | 2.10541i | 0.238169 | − | 0.665789i | ||||
\(11\) | − | 2.70947i | − | 0.816936i | −0.912773 | − | 0.408468i | \(-0.866063\pi\) | ||
0.912773 | − | 0.408468i | \(-0.133937\pi\) | |||||||
\(12\) | −1.73204 | − | 0.00608872i | −0.499997 | − | 0.00175766i | ||||
\(13\) | 0.120439 | − | 0.120439i | 0.0334039 | − | 0.0334039i | −0.690208 | − | 0.723611i | \(-0.742481\pi\) |
0.723611 | + | 0.690208i | \(0.242481\pi\) | |||||||
\(14\) | −1.57068 | −0.419781 | ||||||||
\(15\) | −1.64385 | − | 3.50682i | −0.424440 | − | 0.905456i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.852346 | + | 0.852346i | −0.206724 | + | 0.206724i | −0.802874 | − | 0.596149i | \(-0.796697\pi\) |
0.596149 | + | 0.802874i | \(0.296697\pi\) | |||||||
\(18\) | −2.13618 | + | 2.10635i | −0.503503 | + | 0.496472i | ||||
\(19\) | 5.63716i | 1.29325i | 0.762807 | + | 0.646627i | \(0.223821\pi\) | ||||
−0.762807 | + | 0.646627i | \(0.776179\pi\) | |||||||
\(20\) | −0.956187 | − | 2.02131i | −0.213810 | − | 0.451979i | ||||
\(21\) | −1.93043 | + | 1.91690i | −0.421254 | + | 0.418303i | ||||
\(22\) | −1.91589 | − | 1.91589i | −0.408468 | − | 0.408468i | ||||
\(23\) | −6.00623 | − | 6.00623i | −1.25239 | − | 1.25239i | −0.954648 | − | 0.297738i | \(-0.903768\pi\) |
−0.297738 | − | 0.954648i | \(-0.596232\pi\) | |||||||
\(24\) | −1.22904 | + | 1.22043i | −0.250877 | + | 0.249120i | ||||
\(25\) | 3.17141 | − | 3.86551i | 0.634282 | − | 0.773101i | ||||
\(26\) | − | 0.170327i | − | 0.0334039i | ||||||
\(27\) | −0.0547976 | + | 5.19586i | −0.0105458 | + | 0.999944i | ||||
\(28\) | −1.11064 | + | 1.11064i | −0.209890 | + | 0.209890i | ||||
\(29\) | 9.37974 | 1.74177 | 0.870887 | − | 0.491483i | \(-0.163545\pi\) | ||||
0.870887 | + | 0.491483i | \(0.163545\pi\) | |||||||
\(30\) | −3.64207 | − | 1.31732i | −0.664948 | − | 0.240508i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −4.69291 | − | 0.0164972i | −0.816931 | − | 0.00287180i | ||||
\(34\) | 1.20540i | 0.206724i | ||||||||
\(35\) | −3.30692 | − | 1.18297i | −0.558971 | − | 0.199958i | ||||
\(36\) | −0.0210918 | + | 2.99993i | −0.00351530 | + | 0.499988i | ||||
\(37\) | 4.37896 | + | 4.37896i | 0.719897 | + | 0.719897i | 0.968584 | − | 0.248687i | \(-0.0799991\pi\) |
−0.248687 | + | 0.968584i | \(0.579999\pi\) | |||||||
\(38\) | 3.98607 | + | 3.98607i | 0.646627 | + | 0.646627i | ||||
\(39\) | −0.207872 | − | 0.209339i | −0.0332862 | − | 0.0335211i | ||||
\(40\) | −2.10541 | − | 0.753158i | −0.332895 | − | 0.119085i | ||||
\(41\) | − | 12.3602i | − | 1.93035i | −0.261611 | − | 0.965173i | \(-0.584254\pi\) | ||
0.261611 | − | 0.965173i | \(-0.415746\pi\) | |||||||
\(42\) | −0.00956340 | + | 2.72047i | −0.00147567 | + | 0.419778i | ||||
\(43\) | −6.77836 | + | 6.77836i | −1.03369 | + | 1.03369i | −0.0342777 | + | 0.999412i | \(0.510913\pi\) |
−0.999412 | + | 0.0342777i | \(0.989087\pi\) | |||||||
\(44\) | −2.70947 | −0.408468 | ||||||||
\(45\) | −6.08396 | + | 2.82586i | −0.906943 | + | 0.421254i | ||||
\(46\) | −8.49409 | −1.25239 | ||||||||
\(47\) | 1.75294 | − | 1.75294i | 0.255692 | − | 0.255692i | −0.567607 | − | 0.823299i | \(-0.692131\pi\) |
0.823299 | + | 0.567607i | \(0.192131\pi\) | |||||||
\(48\) | −0.00608872 | + | 1.73204i | −0.000878831 | + | 0.249998i | ||||
\(49\) | − | 4.53298i | − | 0.647568i | ||||||
\(50\) | −0.490799 | − | 4.97585i | −0.0694095 | − | 0.703692i | ||||
\(51\) | 1.47111 | + | 1.48149i | 0.205996 | + | 0.207450i | ||||
\(52\) | −0.120439 | − | 0.120439i | −0.0167019 | − | 0.0167019i | ||||
\(53\) | −0.0579639 | − | 0.0579639i | −0.00796195 | − | 0.00796195i | 0.703115 | − | 0.711077i | \(-0.251792\pi\) |
−0.711077 | + | 0.703115i | \(0.751792\pi\) | |||||||
\(54\) | 3.63528 | + | 3.71278i | 0.494699 | + | 0.505245i | ||||
\(55\) | −2.59076 | − | 5.47669i | −0.349338 | − | 0.738477i | ||||
\(56\) | 1.57068i | 0.209890i | ||||||||
\(57\) | 9.76379 | + | 0.0343231i | 1.29325 | + | 0.00454620i | ||||
\(58\) | 6.63248 | − | 6.63248i | 0.870887 | − | 0.870887i | ||||
\(59\) | −1.06847 | −0.139102 | −0.0695512 | − | 0.997578i | \(-0.522157\pi\) | ||||
−0.0695512 | + | 0.997578i | \(0.522157\pi\) | |||||||
\(60\) | −3.50682 | + | 1.64385i | −0.452728 | + | 0.212220i | ||||
\(61\) | 7.56989 | 0.969225 | 0.484612 | − | 0.874729i | \(-0.338961\pi\) | ||||
0.484612 | + | 0.874729i | \(0.338961\pi\) | |||||||
\(62\) | 0.707107 | − | 0.707107i | 0.0898027 | − | 0.0898027i | ||||
\(63\) | 3.30840 | + | 3.35525i | 0.416819 | + | 0.422722i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0.128283 | − | 0.358608i | 0.0159116 | − | 0.0444799i | ||||
\(66\) | −3.33006 | + | 3.30673i | −0.409902 | + | 0.407030i | ||||
\(67\) | 5.10127 | + | 5.10127i | 0.623219 | + | 0.623219i | 0.946353 | − | 0.323134i | \(-0.104737\pi\) |
−0.323134 | + | 0.946353i | \(0.604737\pi\) | |||||||
\(68\) | 0.852346 | + | 0.852346i | 0.103362 | + | 0.103362i | ||||
\(69\) | −10.4396 | + | 10.3665i | −1.25678 | + | 1.24798i | ||||
\(70\) | −3.17483 | + | 1.50186i | −0.379465 | + | 0.179507i | ||||
\(71\) | 15.7810i | 1.87286i | 0.350854 | + | 0.936430i | \(0.385891\pi\) | ||||
−0.350854 | + | 0.936430i | \(0.614109\pi\) | |||||||
\(72\) | 2.10635 | + | 2.13618i | 0.248236 | + | 0.251751i | ||||
\(73\) | −3.90256 | + | 3.90256i | −0.456760 | + | 0.456760i | −0.897590 | − | 0.440831i | \(-0.854684\pi\) |
0.440831 | + | 0.897590i | \(0.354684\pi\) | |||||||
\(74\) | 6.19279 | 0.719897 | ||||||||
\(75\) | −6.67590 | − | 5.51655i | −0.770867 | − | 0.636996i | ||||
\(76\) | 5.63716 | 0.646627 | ||||||||
\(77\) | −3.00924 | + | 3.00924i | −0.342934 | + | 0.342934i | ||||
\(78\) | −0.295013 | − | 0.00103707i | −0.0334037 | − | 0.000117425i | ||||
\(79\) | − | 7.85631i | − | 0.883904i | −0.897039 | − | 0.441952i | \(-0.854286\pi\) | ||
0.897039 | − | 0.441952i | \(-0.145714\pi\) | |||||||
\(80\) | −2.02131 | + | 0.956187i | −0.225990 | + | 0.106905i | ||||
\(81\) | 8.99911 | + | 0.126548i | 0.999901 | + | 0.0140609i | ||||
\(82\) | −8.74002 | − | 8.74002i | −0.965173 | − | 0.965173i | ||||
\(83\) | −8.60592 | − | 8.60592i | −0.944622 | − | 0.944622i | 0.0539231 | − | 0.998545i | \(-0.482827\pi\) |
−0.998545 | + | 0.0539231i | \(0.982827\pi\) | |||||||
\(84\) | 1.91690 | + | 1.93043i | 0.209151 | + | 0.210627i | ||||
\(85\) | −0.907855 | + | 2.53786i | −0.0984707 | + | 0.275270i | ||||
\(86\) | 9.58605i | 1.03369i | ||||||||
\(87\) | 0.0571106 | − | 16.2461i | 0.00612290 | − | 1.74176i | ||||
\(88\) | −1.91589 | + | 1.91589i | −0.204234 | + | 0.204234i | ||||
\(89\) | 5.43975 | 0.576612 | 0.288306 | − | 0.957538i | \(-0.406908\pi\) | ||||
0.288306 | + | 0.957538i | \(0.406908\pi\) | |||||||
\(90\) | −2.30382 | + | 6.30019i | −0.242844 | + | 0.664098i | ||||
\(91\) | −0.267529 | −0.0280446 | ||||||||
\(92\) | −6.00623 | + | 6.00623i | −0.626193 | + | 0.626193i | ||||
\(93\) | 0.00608872 | − | 1.73204i | 0.000631371 | − | 0.179604i | ||||
\(94\) | − | 2.47903i | − | 0.255692i | ||||||
\(95\) | 5.39018 | + | 11.3945i | 0.553021 | + | 1.16905i | ||||
\(96\) | 1.22043 | + | 1.22904i | 0.124560 | + | 0.125439i | ||||
\(97\) | −2.97219 | − | 2.97219i | −0.301780 | − | 0.301780i | 0.539930 | − | 0.841710i | \(-0.318451\pi\) |
−0.841710 | + | 0.539930i | \(0.818451\pi\) | |||||||
\(98\) | −3.20530 | − | 3.20530i | −0.323784 | − | 0.323784i | ||||
\(99\) | −0.0571477 | + | 8.12821i | −0.00574356 | + | 0.816916i | ||||
\(100\) | −3.86551 | − | 3.17141i | −0.386551 | − | 0.317141i | ||||
\(101\) | 11.9110i | 1.18519i | 0.805499 | + | 0.592597i | \(0.201897\pi\) | ||||
−0.805499 | + | 0.592597i | \(0.798103\pi\) | |||||||
\(102\) | 2.08780 | + | 0.00733933i | 0.206723 | + | 0.000726702i | ||||
\(103\) | 4.74787 | − | 4.74787i | 0.467822 | − | 0.467822i | −0.433386 | − | 0.901208i | \(-0.642681\pi\) |
0.901208 | + | 0.433386i | \(0.142681\pi\) | |||||||
\(104\) | −0.170327 | −0.0167019 | ||||||||
\(105\) | −2.06908 | + | 5.72051i | −0.201922 | + | 0.558265i | ||||
\(106\) | −0.0819733 | −0.00796195 | ||||||||
\(107\) | 11.4901 | − | 11.4901i | 1.11079 | − | 1.11079i | 0.117742 | − | 0.993044i | \(-0.462435\pi\) |
0.993044 | − | 0.117742i | \(-0.0375655\pi\) | |||||||
\(108\) | 5.19586 | + | 0.0547976i | 0.499972 | + | 0.00527290i | ||||
\(109\) | − | 4.28732i | − | 0.410651i | −0.978694 | − | 0.205326i | \(-0.934175\pi\) | ||
0.978694 | − | 0.205326i | \(-0.0658253\pi\) | |||||||
\(110\) | −5.70455 | − | 2.04066i | −0.543908 | − | 0.194569i | ||||
\(111\) | 7.61120 | − | 7.55787i | 0.722423 | − | 0.717362i | ||||
\(112\) | 1.11064 | + | 1.11064i | 0.104945 | + | 0.104945i | ||||
\(113\) | −5.16233 | − | 5.16233i | −0.485631 | − | 0.485631i | 0.421294 | − | 0.906924i | \(-0.361576\pi\) |
−0.906924 | + | 0.421294i | \(0.861576\pi\) | |||||||
\(114\) | 6.92831 | − | 6.87977i | 0.648896 | − | 0.644350i | ||||
\(115\) | −17.8836 | − | 6.39739i | −1.66765 | − | 0.596560i | ||||
\(116\) | − | 9.37974i | − | 0.870887i | ||||||
\(117\) | −0.363849 | + | 0.358769i | −0.0336379 | + | 0.0331682i | ||||
\(118\) | −0.755519 | + | 0.755519i | −0.0695512 | + | 0.0695512i | ||||
\(119\) | 1.89329 | 0.173558 | ||||||||
\(120\) | −1.31732 | + | 3.64207i | −0.120254 | + | 0.332474i | ||||
\(121\) | 3.65876 | 0.332615 | ||||||||
\(122\) | 5.35272 | − | 5.35272i | 0.484612 | − | 0.484612i | ||||
\(123\) | −21.4084 | − | 0.0752581i | −1.93033 | − | 0.00678579i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 2.71427 | − | 10.8459i | 0.242771 | − | 0.970084i | ||||
\(126\) | 4.71191 | + | 0.0331284i | 0.419771 | + | 0.00295131i | ||||
\(127\) | −1.14523 | − | 1.14523i | −0.101622 | − | 0.101622i | 0.654468 | − | 0.756090i | \(-0.272893\pi\) |
−0.756090 | + | 0.654468i | \(0.772893\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 11.6991 | + | 11.7817i | 1.03005 | + | 1.03732i | ||||
\(130\) | −0.162864 | − | 0.344284i | −0.0142842 | − | 0.0301957i | ||||
\(131\) | − | 2.05800i | − | 0.179809i | −0.995950 | − | 0.0899043i | \(-0.971344\pi\) | ||
0.995950 | − | 0.0899043i | \(-0.0286561\pi\) | |||||||
\(132\) | −0.0164972 | + | 4.69291i | −0.00143590 | + | 0.408466i | ||||
\(133\) | 6.26083 | − | 6.26083i | 0.542883 | − | 0.542883i | ||||
\(134\) | 7.21428 | 0.623219 | ||||||||
\(135\) | 4.85746 | + | 10.5549i | 0.418063 | + | 0.908418i | ||||
\(136\) | 1.20540 | 0.103362 | ||||||||
\(137\) | −9.93566 | + | 9.93566i | −0.848861 | + | 0.848861i | −0.989991 | − | 0.141130i | \(-0.954926\pi\) |
0.141130 | + | 0.989991i | \(0.454926\pi\) | |||||||
\(138\) | −0.0517181 | + | 14.7121i | −0.00440254 | + | 1.25238i | ||||
\(139\) | − | 6.17825i | − | 0.524032i | −0.965064 | − | 0.262016i | \(-0.915613\pi\) | ||
0.965064 | − | 0.262016i | \(-0.0843873\pi\) | |||||||
\(140\) | −1.18297 | + | 3.30692i | −0.0999789 | + | 0.279486i | ||||
\(141\) | −3.02548 | − | 3.04683i | −0.254792 | − | 0.256589i | ||||
\(142\) | 11.1589 | + | 11.1589i | 0.936430 | + | 0.936430i | ||||
\(143\) | −0.326327 | − | 0.326327i | −0.0272888 | − | 0.0272888i | ||||
\(144\) | 2.99993 | + | 0.0210918i | 0.249994 | + | 0.00175765i | ||||
\(145\) | 18.9594 | − | 8.96879i | 1.57449 | − | 0.744817i | ||||
\(146\) | 5.51905i | 0.456760i | ||||||||
\(147\) | −7.85130 | − | 0.0276000i | −0.647564 | − | 0.00227641i | ||||
\(148\) | 4.37896 | − | 4.37896i | 0.359948 | − | 0.359948i | ||||
\(149\) | 15.4668 | 1.26709 | 0.633544 | − | 0.773707i | \(-0.281600\pi\) | ||||
0.633544 | + | 0.773707i | \(0.281600\pi\) | |||||||
\(150\) | −8.62137 | + | 0.819788i | −0.703932 | + | 0.0669354i | ||||
\(151\) | −4.45159 | −0.362265 | −0.181132 | − | 0.983459i | \(-0.557976\pi\) | ||||
−0.181132 | + | 0.983459i | \(0.557976\pi\) | |||||||
\(152\) | 3.98607 | − | 3.98607i | 0.323313 | − | 0.323313i | ||||
\(153\) | 2.57495 | − | 2.53900i | 0.208172 | − | 0.205266i | ||||
\(154\) | 4.25570i | 0.342934i | ||||||||
\(155\) | 2.02131 | − | 0.956187i | 0.162356 | − | 0.0768028i | ||||
\(156\) | −0.209339 | + | 0.207872i | −0.0167605 | + | 0.0166431i | ||||
\(157\) | 5.72384 | + | 5.72384i | 0.456812 | + | 0.456812i | 0.897607 | − | 0.440796i | \(-0.145304\pi\) |
−0.440796 | + | 0.897607i | \(0.645304\pi\) | |||||||
\(158\) | −5.55525 | − | 5.55525i | −0.441952 | − | 0.441952i | ||||
\(159\) | −0.100749 | + | 0.100043i | −0.00798989 | + | 0.00793391i | ||||
\(160\) | −0.753158 | + | 2.10541i | −0.0595423 | + | 0.166447i | ||||
\(161\) | 13.3415i | 1.05146i | ||||||||
\(162\) | 6.45281 | − | 6.27385i | 0.506981 | − | 0.492920i | ||||
\(163\) | 14.2135 | − | 14.2135i | 1.11328 | − | 1.11328i | 0.120581 | − | 0.992704i | \(-0.461524\pi\) |
0.992704 | − | 0.120581i | \(-0.0384756\pi\) | |||||||
\(164\) | −12.3602 | −0.965173 | ||||||||
\(165\) | −9.50162 | + | 4.45396i | −0.739700 | + | 0.346740i | ||||
\(166\) | −12.1706 | −0.944622 | ||||||||
\(167\) | 8.59228 | − | 8.59228i | 0.664891 | − | 0.664891i | −0.291638 | − | 0.956529i | \(-0.594200\pi\) |
0.956529 | + | 0.291638i | \(0.0942003\pi\) | |||||||
\(168\) | 2.72047 | + | 0.00956340i | 0.209889 | + | 0.000737833i | ||||
\(169\) | 12.9710i | 0.997768i | ||||||||
\(170\) | 1.15259 | + | 2.43649i | 0.0883994 | + | 0.186870i | ||||
\(171\) | 0.118898 | − | 16.9111i | 0.00909235 | − | 1.29322i | ||||
\(172\) | 6.77836 | + | 6.77836i | 0.516845 | + | 0.516845i | ||||
\(173\) | 5.62788 | + | 5.62788i | 0.427879 | + | 0.427879i | 0.887905 | − | 0.460026i | \(-0.152160\pi\) |
−0.460026 | + | 0.887905i | \(0.652160\pi\) | |||||||
\(174\) | −11.4473 | − | 11.5281i | −0.867820 | − | 0.873943i | ||||
\(175\) | −7.81545 | + | 0.770887i | −0.590793 | + | 0.0582736i | ||||
\(176\) | 2.70947i | 0.204234i | ||||||||
\(177\) | −0.00650558 | + | 1.85063i | −0.000488990 | + | 0.139101i | ||||
\(178\) | 3.84648 | − | 3.84648i | 0.288306 | − | 0.288306i | ||||
\(179\) | 22.3130 | 1.66775 | 0.833876 | − | 0.551952i | \(-0.186117\pi\) | ||||
0.833876 | + | 0.551952i | \(0.186117\pi\) | |||||||
\(180\) | 2.82586 | + | 6.08396i | 0.210627 | + | 0.453471i | ||||
\(181\) | −12.4142 | −0.922742 | −0.461371 | − | 0.887207i | \(-0.652642\pi\) | ||||
−0.461371 | + | 0.887207i | \(0.652642\pi\) | |||||||
\(182\) | −0.189171 | + | 0.189171i | −0.0140223 | + | 0.0140223i | ||||
\(183\) | 0.0460909 | − | 13.1113i | 0.00340714 | − | 0.969219i | ||||
\(184\) | 8.49409i | 0.626193i | ||||||||
\(185\) | 13.0384 | + | 4.66414i | 0.958599 | + | 0.342915i | ||||
\(186\) | −1.22043 | − | 1.22904i | −0.0894864 | − | 0.0901178i | ||||
\(187\) | 2.30941 | + | 2.30941i | 0.168881 | + | 0.168881i | ||||
\(188\) | −1.75294 | − | 1.75294i | −0.127846 | − | 0.127846i | ||||
\(189\) | 5.83157 | − | 5.70985i | 0.424184 | − | 0.415331i | ||||
\(190\) | 11.8685 | + | 4.24567i | 0.861034 | + | 0.308013i | ||||
\(191\) | 12.7221i | 0.920537i | 0.887780 | + | 0.460268i | \(0.152247\pi\) | ||||
−0.887780 | + | 0.460268i | \(0.847753\pi\) | |||||||
\(192\) | 1.73204 | + | 0.00608872i | 0.124999 | + | 0.000439415i | ||||
\(193\) | 8.41038 | − | 8.41038i | 0.605393 | − | 0.605393i | −0.336346 | − | 0.941739i | \(-0.609191\pi\) |
0.941739 | + | 0.336346i | \(0.109191\pi\) | |||||||
\(194\) | −4.20331 | −0.301780 | ||||||||
\(195\) | −0.620343 | − | 0.224375i | −0.0444237 | − | 0.0160678i | ||||
\(196\) | −4.53298 | −0.323784 | ||||||||
\(197\) | 2.94410 | − | 2.94410i | 0.209759 | − | 0.209759i | −0.594406 | − | 0.804165i | \(-0.702613\pi\) |
0.804165 | + | 0.594406i | \(0.202613\pi\) | |||||||
\(198\) | 5.70711 | + | 5.78792i | 0.405586 | + | 0.411330i | ||||
\(199\) | − | 14.6680i | − | 1.03979i | −0.854231 | − | 0.519894i | \(-0.825971\pi\) | ||
0.854231 | − | 0.519894i | \(-0.174029\pi\) | |||||||
\(200\) | −4.97585 | + | 0.490799i | −0.351846 | + | 0.0347048i | ||||
\(201\) | 8.86666 | − | 8.80454i | 0.625406 | − | 0.621024i | ||||
\(202\) | 8.42238 | + | 8.42238i | 0.592597 | + | 0.592597i | ||||
\(203\) | −10.4175 | − | 10.4175i | −0.731163 | − | 0.731163i | ||||
\(204\) | 1.48149 | − | 1.47111i | 0.103725 | − | 0.102998i | ||||
\(205\) | −11.8187 | − | 24.9839i | −0.825455 | − | 1.74495i | ||||
\(206\) | − | 6.71451i | − | 0.467822i | ||||||
\(207\) | 17.8916 | + | 18.1449i | 1.24355 | + | 1.26116i | ||||
\(208\) | −0.120439 | + | 0.120439i | −0.00835097 | + | 0.00835097i | ||||
\(209\) | 15.2737 | 1.05651 | ||||||||
\(210\) | 2.58195 | + | 5.50807i | 0.178172 | + | 0.380093i | ||||
\(211\) | 18.9811 | 1.30671 | 0.653357 | − | 0.757050i | \(-0.273360\pi\) | ||||
0.653357 | + | 0.757050i | \(0.273360\pi\) | |||||||
\(212\) | −0.0579639 | + | 0.0579639i | −0.00398098 | + | 0.00398098i | ||||
\(213\) | 27.3333 | + | 0.0960861i | 1.87285 | + | 0.00658371i | ||||
\(214\) | − | 16.2494i | − | 1.11079i | ||||||
\(215\) | −7.21980 | + | 20.1826i | −0.492387 | + | 1.37644i | ||||
\(216\) | 3.71278 | − | 3.63528i | 0.252623 | − | 0.247350i | ||||
\(217\) | −1.11064 | − | 1.11064i | −0.0753949 | − | 0.0753949i | ||||
\(218\) | −3.03160 | − | 3.03160i | −0.205326 | − | 0.205326i | ||||
\(219\) | 6.73562 | + | 6.78314i | 0.455151 | + | 0.458362i | ||||
\(220\) | −5.47669 | + | 2.59076i | −0.369238 | + | 0.174669i | ||||
\(221\) | 0.205312i | 0.0138108i | ||||||||
\(222\) | 0.0377061 | − | 10.7262i | 0.00253067 | − | 0.719892i | ||||
\(223\) | 6.20254 | − | 6.20254i | 0.415352 | − | 0.415352i | −0.468246 | − | 0.883598i | \(-0.655114\pi\) |
0.883598 | + | 0.468246i | \(0.155114\pi\) | |||||||
\(224\) | 1.57068 | 0.104945 | ||||||||
\(225\) | −9.59553 | + | 11.5293i | −0.639702 | + | 0.768623i | ||||
\(226\) | −7.30063 | −0.485631 | ||||||||
\(227\) | −19.9921 | + | 19.9921i | −1.32692 | + | 1.32692i | −0.418875 | + | 0.908044i | \(0.637576\pi\) |
−0.908044 | + | 0.418875i | \(0.862424\pi\) | |||||||
\(228\) | 0.0343231 | − | 9.76379i | 0.00227310 | − | 0.646623i | ||||
\(229\) | 4.09903i | 0.270872i | 0.990786 | + | 0.135436i | \(0.0432435\pi\) | ||||
−0.990786 | + | 0.135436i | \(0.956757\pi\) | |||||||
\(230\) | −17.1692 | + | 8.12194i | −1.13210 | + | 0.535545i | ||||
\(231\) | 5.19380 | + | 5.23044i | 0.341727 | + | 0.344138i | ||||
\(232\) | −6.63248 | − | 6.63248i | −0.435443 | − | 0.435443i | ||||
\(233\) | 6.35559 | + | 6.35559i | 0.416369 | + | 0.416369i | 0.883950 | − | 0.467581i | \(-0.154874\pi\) |
−0.467581 | + | 0.883950i | \(0.654874\pi\) | |||||||
\(234\) | −0.00359250 | + | 0.510968i | −0.000234849 | + | 0.0334030i | ||||
\(235\) | 1.86710 | − | 5.21937i | 0.121796 | − | 0.340474i | ||||
\(236\) | 1.06847i | 0.0695512i | ||||||||
\(237\) | −13.6074 | − | 0.0478349i | −0.883898 | − | 0.00310721i | ||||
\(238\) | 1.33876 | − | 1.33876i | 0.0867789 | − | 0.0867789i | ||||
\(239\) | −20.9423 | −1.35465 | −0.677323 | − | 0.735686i | \(-0.736860\pi\) | ||||
−0.677323 | + | 0.735686i | \(0.736860\pi\) | |||||||
\(240\) | 1.64385 | + | 3.50682i | 0.106110 | + | 0.226364i | ||||
\(241\) | 23.1603 | 1.49189 | 0.745944 | − | 0.666008i | \(-0.231998\pi\) | ||||
0.745944 | + | 0.666008i | \(0.231998\pi\) | |||||||
\(242\) | 2.58714 | − | 2.58714i | 0.166307 | − | 0.166307i | ||||
\(243\) | 0.273979 | − | 15.5860i | 0.0175757 | − | 0.999846i | ||||
\(244\) | − | 7.56989i | − | 0.484612i | ||||||
\(245\) | −4.33437 | − | 9.16256i | −0.276913 | − | 0.585375i | ||||
\(246\) | −15.1913 | + | 15.0848i | −0.968560 | + | 0.961774i | ||||
\(247\) | 0.678936 | + | 0.678936i | 0.0431997 | + | 0.0431997i | ||||
\(248\) | −0.707107 | − | 0.707107i | −0.0449013 | − | 0.0449013i | ||||
\(249\) | −14.9582 | + | 14.8534i | −0.947937 | + | 0.941296i | ||||
\(250\) | −5.74991 | − | 9.58846i | −0.363656 | − | 0.606427i | ||||
\(251\) | 30.2525i | 1.90952i | 0.297373 | + | 0.954761i | \(0.403890\pi\) | ||||
−0.297373 | + | 0.954761i | \(0.596110\pi\) | |||||||
\(252\) | 3.35525 | − | 3.30840i | 0.211361 | − | 0.208410i | ||||
\(253\) | −16.2737 | + | 16.2737i | −1.02312 | + | 1.02312i | ||||
\(254\) | −1.61959 | −0.101622 | ||||||||
\(255\) | 4.39015 | + | 1.58789i | 0.274922 | + | 0.0994378i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.86596 | + | 4.86596i | −0.303531 | + | 0.303531i | −0.842393 | − | 0.538863i | \(-0.818854\pi\) |
0.538863 | + | 0.842393i | \(0.318854\pi\) | |||||||
\(258\) | 16.6034 | + | 0.0583667i | 1.03368 | + | 0.00363375i | ||||
\(259\) | − | 9.72686i | − | 0.604398i | ||||||
\(260\) | −0.358608 | − | 0.128283i | −0.0222399 | − | 0.00795578i | ||||
\(261\) | −28.1385 | − | 0.197836i | −1.74173 | − | 0.0122457i | ||||
\(262\) | −1.45523 | − | 1.45523i | −0.0899043 | − | 0.0899043i | ||||
\(263\) | −16.9917 | − | 16.9917i | −1.04775 | − | 1.04775i | −0.998801 | − | 0.0489530i | \(-0.984412\pi\) |
−0.0489530 | − | 0.998801i | \(-0.515588\pi\) | |||||||
\(264\) | 3.30673 | + | 3.33006i | 0.203515 | + | 0.204951i | ||||
\(265\) | −0.172587 | − | 0.0617388i | −0.0106020 | − | 0.00379259i | ||||
\(266\) | − | 8.85415i | − | 0.542883i | ||||||
\(267\) | 0.0331211 | − | 9.42186i | 0.00202698 | − | 0.576609i | ||||
\(268\) | 5.10127 | − | 5.10127i | 0.311609 | − | 0.311609i | ||||
\(269\) | 1.95810 | 0.119387 | 0.0596936 | − | 0.998217i | \(-0.480988\pi\) | ||||
0.0596936 | + | 0.998217i | \(0.480988\pi\) | |||||||
\(270\) | 10.8982 | + | 4.02868i | 0.663241 | + | 0.245177i | ||||
\(271\) | −5.58554 | −0.339298 | −0.169649 | − | 0.985505i | \(-0.554263\pi\) | ||||
−0.169649 | + | 0.985505i | \(0.554263\pi\) | |||||||
\(272\) | 0.852346 | − | 0.852346i | 0.0516811 | − | 0.0516811i | ||||
\(273\) | −0.00162891 | + | 0.463370i | −9.85859e−5 | + | 0.0280444i | ||||
\(274\) | 14.0512i | 0.848861i | ||||||||
\(275\) | −10.4735 | − | 8.59285i | −0.631575 | − | 0.518168i | ||||
\(276\) | 10.3665 | + | 10.4396i | 0.623988 | + | 0.628390i | ||||
\(277\) | −4.89103 | − | 4.89103i | −0.293874 | − | 0.293874i | 0.544735 | − | 0.838608i | \(-0.316630\pi\) |
−0.838608 | + | 0.544735i | \(0.816630\pi\) | |||||||
\(278\) | −4.36868 | − | 4.36868i | −0.262016 | − | 0.262016i | ||||
\(279\) | −2.99993 | − | 0.0210918i | −0.179601 | − | 0.00126273i | ||||
\(280\) | 1.50186 | + | 3.17483i | 0.0897533 | + | 0.189732i | ||||
\(281\) | 4.05643i | 0.241987i | 0.992653 | + | 0.120993i | \(0.0386080\pi\) | ||||
−0.992653 | + | 0.120993i | \(0.961392\pi\) | |||||||
\(282\) | −4.29377 | − | 0.0150941i | −0.255690 | − | 0.000898840i | ||||
\(283\) | 7.09487 | − | 7.09487i | 0.421746 | − | 0.421746i | −0.464058 | − | 0.885805i | \(-0.653607\pi\) |
0.885805 | + | 0.464058i | \(0.153607\pi\) | |||||||
\(284\) | 15.7810 | 0.936430 | ||||||||
\(285\) | 19.7685 | − | 9.26663i | 1.17098 | − | 0.548908i | ||||
\(286\) | −0.461496 | −0.0272888 | ||||||||
\(287\) | −13.7277 | + | 13.7277i | −0.810323 | + | 0.810323i | ||||
\(288\) | 2.13618 | − | 2.10635i | 0.125876 | − | 0.124118i | ||||
\(289\) | 15.5470i | 0.914530i | ||||||||
\(290\) | 7.06442 | − | 19.7482i | 0.414837 | − | 1.15965i | ||||
\(291\) | −5.16605 | + | 5.12986i | −0.302839 | + | 0.300718i | ||||
\(292\) | 3.90256 | + | 3.90256i | 0.228380 | + | 0.228380i | ||||
\(293\) | −13.6690 | − | 13.6690i | −0.798554 | − | 0.798554i | 0.184314 | − | 0.982867i | \(-0.440994\pi\) |
−0.982867 | + | 0.184314i | \(0.940994\pi\) | |||||||
\(294\) | −5.57122 | + | 5.53219i | −0.324920 | + | 0.322644i | ||||
\(295\) | −2.15970 | + | 1.02165i | −0.125743 | + | 0.0594829i | ||||
\(296\) | − | 6.19279i | − | 0.359948i | ||||||
\(297\) | 14.0780 | + | 0.148472i | 0.816891 | + | 0.00861524i | ||||
\(298\) | 10.9367 | − | 10.9367i | 0.633544 | − | 0.633544i | ||||
\(299\) | −1.44677 | −0.0836691 | ||||||||
\(300\) | −5.51655 | + | 6.67590i | −0.318498 | + | 0.385433i | ||||
\(301\) | 15.0566 | 0.867847 | ||||||||
\(302\) | −3.14775 | + | 3.14775i | −0.181132 | + | 0.181132i | ||||
\(303\) | 20.6304 | + | 0.0725230i | 1.18519 | + | 0.00416634i | ||||
\(304\) | − | 5.63716i | − | 0.323313i | ||||||
\(305\) | 15.3011 | − | 7.23823i | 0.876139 | − | 0.414460i | ||||
\(306\) | 0.0254240 | − | 3.61611i | 0.00145340 | − | 0.206719i | ||||
\(307\) | 6.23253 | + | 6.23253i | 0.355709 | + | 0.355709i | 0.862229 | − | 0.506519i | \(-0.169068\pi\) |
−0.506519 | + | 0.862229i | \(0.669068\pi\) | |||||||
\(308\) | 3.00924 | + | 3.00924i | 0.171467 | + | 0.171467i | ||||
\(309\) | −8.19460 | − | 8.25242i | −0.466175 | − | 0.469464i | ||||
\(310\) | 0.753158 | − | 2.10541i | 0.0427765 | − | 0.119579i | ||||
\(311\) | 30.1255i | 1.70826i | 0.520061 | + | 0.854129i | \(0.325909\pi\) | ||||
−0.520061 | + | 0.854129i | \(0.674091\pi\) | |||||||
\(312\) | −0.00103707 | + | 0.295013i | −5.87127e−5 | + | 0.0167018i | ||||
\(313\) | −11.1395 | + | 11.1395i | −0.629641 | + | 0.629641i | −0.947978 | − | 0.318337i | \(-0.896876\pi\) |
0.318337 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(314\) | 8.09473 | 0.456812 | ||||||||
\(315\) | 9.89556 | + | 3.61856i | 0.557552 | + | 0.203883i | ||||
\(316\) | −7.85631 | −0.441952 | ||||||||
\(317\) | 12.6989 | − | 12.6989i | 0.713244 | − | 0.713244i | −0.253969 | − | 0.967212i | \(-0.581736\pi\) |
0.967212 | + | 0.253969i | \(0.0817361\pi\) | |||||||
\(318\) | −0.000499112 | 0.141981i | −2.79888e−5 | 0.00796190i | ||||||
\(319\) | − | 25.4141i | − | 1.42292i | ||||||
\(320\) | 0.956187 | + | 2.02131i | 0.0534525 | + | 0.112995i | ||||
\(321\) | −19.8313 | − | 19.9712i | −1.10687 | − | 1.11468i | ||||
\(322\) | 9.43384 | + | 9.43384i | 0.525728 | + | 0.525728i | ||||
\(323\) | −4.80481 | − | 4.80481i | −0.267347 | − | 0.267347i | ||||
\(324\) | 0.126548 | − | 8.99911i | 0.00703043 | − | 0.499951i | ||||
\(325\) | −0.0835964 | − | 0.847522i | −0.00463709 | − | 0.0470121i | ||||
\(326\) | − | 20.1009i | − | 1.11328i | ||||||
\(327\) | −7.42582 | − | 0.0261043i | −0.410649 | − | 0.00144357i | ||||
\(328\) | −8.74002 | + | 8.74002i | −0.482587 | + | 0.482587i | ||||
\(329\) | −3.89375 | −0.214669 | ||||||||
\(330\) | −3.56924 | + | 9.86808i | −0.196480 | + | 0.543220i | ||||
\(331\) | −33.5872 | −1.84612 | −0.923060 | − | 0.384656i | \(-0.874320\pi\) | ||||
−0.923060 | + | 0.384656i | \(0.874320\pi\) | |||||||
\(332\) | −8.60592 | + | 8.60592i | −0.472311 | + | 0.472311i | ||||
\(333\) | −13.0442 | − | 13.2289i | −0.714818 | − | 0.724940i | ||||
\(334\) | − | 12.1513i | − | 0.664891i | ||||||
\(335\) | 15.1890 | + | 5.43349i | 0.829865 | + | 0.296863i | ||||
\(336\) | 1.93043 | − | 1.91690i | 0.105313 | − | 0.104576i | ||||
\(337\) | −4.79406 | − | 4.79406i | −0.261149 | − | 0.261149i | 0.564372 | − | 0.825521i | \(-0.309118\pi\) |
−0.825521 | + | 0.564372i | \(0.809118\pi\) | |||||||
\(338\) | 9.17187 | + | 9.17187i | 0.498884 | + | 0.498884i | ||||
\(339\) | −8.97279 | + | 8.90992i | −0.487335 | + | 0.483921i | ||||
\(340\) | 2.53786 | + | 0.907855i | 0.137635 | + | 0.0492354i | ||||
\(341\) | − | 2.70947i | − | 0.146726i | ||||||
\(342\) | −11.8739 | − | 12.0420i | −0.642065 | − | 0.651157i | ||||
\(343\) | −12.8089 | + | 12.8089i | −0.691618 | + | 0.691618i | ||||
\(344\) | 9.58605 | 0.516845 | ||||||||
\(345\) | −11.1894 | + | 30.9361i | −0.602418 | + | 1.66554i | ||||
\(346\) | 7.95902 | 0.427879 | ||||||||
\(347\) | −16.6890 | + | 16.6890i | −0.895910 | + | 0.895910i | −0.995071 | − | 0.0991609i | \(-0.968384\pi\) |
0.0991609 | + | 0.995071i | \(0.468384\pi\) | |||||||
\(348\) | −16.2461 | − | 0.0571106i | −0.870882 | − | 0.00306145i | ||||
\(349\) | 19.9193i | 1.06626i | 0.846034 | + | 0.533129i | \(0.178984\pi\) | ||||
−0.846034 | + | 0.533129i | \(0.821016\pi\) | |||||||
\(350\) | −4.98126 | + | 6.07146i | −0.266260 | + | 0.324533i | ||||
\(351\) | 0.619187 | + | 0.632386i | 0.0330497 | + | 0.0337543i | ||||
\(352\) | 1.91589 | + | 1.91589i | 0.102117 | + | 0.102117i | ||||
\(353\) | 14.1451 | + | 14.1451i | 0.752867 | + | 0.752867i | 0.975013 | − | 0.222147i | \(-0.0713064\pi\) |
−0.222147 | + | 0.975013i | \(0.571306\pi\) | |||||||
\(354\) | 1.30399 | + | 1.31319i | 0.0693063 | + | 0.0697952i | ||||
\(355\) | 15.0896 | + | 31.8983i | 0.800872 | + | 1.69299i | ||||
\(356\) | − | 5.43975i | − | 0.288306i | ||||||
\(357\) | 0.0115277 | − | 3.27926i | 0.000610112 | − | 0.173557i | ||||
\(358\) | 15.7777 | − | 15.7777i | 0.833876 | − | 0.833876i | ||||
\(359\) | 8.32324 | 0.439284 | 0.219642 | − | 0.975581i | \(-0.429511\pi\) | ||||
0.219642 | + | 0.975581i | \(0.429511\pi\) | |||||||
\(360\) | 6.30019 | + | 2.30382i | 0.332049 | + | 0.121422i | ||||
\(361\) | −12.7776 | −0.672504 | ||||||||
\(362\) | −8.77818 | + | 8.77818i | −0.461371 | + | 0.461371i | ||||
\(363\) | 0.0222772 | − | 6.33712i | 0.00116925 | − | 0.332613i | ||||
\(364\) | 0.267529i | 0.0140223i | ||||||||
\(365\) | −4.15671 | + | 11.6199i | −0.217572 | + | 0.608211i | ||||
\(366\) | −9.23853 | − | 9.30371i | −0.482906 | − | 0.486313i | ||||
\(367\) | 1.16292 | + | 1.16292i | 0.0607039 | + | 0.0607039i | 0.736807 | − | 0.676103i | \(-0.236333\pi\) |
−0.676103 | + | 0.736807i | \(0.736333\pi\) | |||||||
\(368\) | 6.00623 | + | 6.00623i | 0.313096 | + | 0.313096i | ||||
\(369\) | −0.260700 | + | 37.0798i | −0.0135715 | + | 1.93030i | ||||
\(370\) | 12.5176 | − | 5.92146i | 0.650757 | − | 0.307842i | ||||
\(371\) | 0.128754i | 0.00668455i | ||||||||
\(372\) | −1.73204 | − | 0.00608872i | −0.0898021 | − | 0.000315685i | ||||
\(373\) | −4.28033 | + | 4.28033i | −0.221627 | + | 0.221627i | −0.809183 | − | 0.587556i | \(-0.800090\pi\) |
0.587556 | + | 0.809183i | \(0.300090\pi\) | |||||||
\(374\) | 3.26599 | 0.168881 | ||||||||
\(375\) | −18.7689 | − | 4.76726i | −0.969224 | − | 0.246180i | ||||
\(376\) | −2.47903 | −0.127846 | ||||||||
\(377\) | 1.12969 | − | 1.12969i | 0.0581820 | − | 0.0581820i | ||||
\(378\) | 0.0860692 | − | 8.16102i | 0.00442692 | − | 0.419758i | ||||
\(379\) | 12.4876i | 0.641444i | 0.947173 | + | 0.320722i | \(0.103926\pi\) | ||||
−0.947173 | + | 0.320722i | \(0.896074\pi\) | |||||||
\(380\) | 11.3945 | − | 5.39018i | 0.584524 | − | 0.276510i | ||||
\(381\) | −1.99055 | + | 1.97660i | −0.101979 | + | 0.101264i | ||||
\(382\) | 8.99586 | + | 8.99586i | 0.460268 | + | 0.460268i | ||||
\(383\) | 1.59874 | + | 1.59874i | 0.0816916 | + | 0.0816916i | 0.746772 | − | 0.665080i | \(-0.231603\pi\) |
−0.665080 | + | 0.746772i | \(0.731603\pi\) | |||||||
\(384\) | 1.22904 | − | 1.22043i | 0.0627193 | − | 0.0622799i | ||||
\(385\) | −3.20521 | + | 8.96000i | −0.163353 | + | 0.456644i | ||||
\(386\) | − | 11.8941i | − | 0.605393i | ||||||
\(387\) | 20.4775 | − | 20.1916i | 1.04093 | − | 1.02640i | ||||
\(388\) | −2.97219 | + | 2.97219i | −0.150890 | + | 0.150890i | ||||
\(389\) | 6.21736 | 0.315233 | 0.157616 | − | 0.987500i | \(-0.449619\pi\) | ||||
0.157616 | + | 0.987500i | \(0.449619\pi\) | |||||||
\(390\) | −0.597305 | + | 0.279992i | −0.0302457 | + | 0.0141779i | ||||
\(391\) | 10.2388 | 0.517797 | ||||||||
\(392\) | −3.20530 | + | 3.20530i | −0.161892 | + | 0.161892i | ||||
\(393\) | −3.56454 | − | 0.0125306i | −0.179807 | − | 0.000632085i | ||||
\(394\) | − | 4.16359i | − | 0.209759i | ||||||
\(395\) | −7.51210 | − | 15.8801i | −0.377975 | − | 0.799013i | ||||
\(396\) | 8.12821 | + | 0.0571477i | 0.408458 | + | 0.00287178i | ||||
\(397\) | 15.0580 | + | 15.0580i | 0.755741 | + | 0.755741i | 0.975544 | − | 0.219803i | \(-0.0705416\pi\) |
−0.219803 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(398\) | −10.3719 | − | 10.3719i | −0.519894 | − | 0.519894i | ||||
\(399\) | −10.8059 | − | 10.8821i | −0.540971 | − | 0.544788i | ||||
\(400\) | −3.17141 | + | 3.86551i | −0.158571 | + | 0.193275i | ||||
\(401\) | − | 3.70278i | − | 0.184908i | −0.995717 | − | 0.0924540i | \(-0.970529\pi\) | ||
0.995717 | − | 0.0924540i | \(-0.0294711\pi\) | |||||||
\(402\) | 0.0439257 | − | 12.4954i | 0.00219082 | − | 0.623215i | ||||
\(403\) | 0.120439 | − | 0.120439i | 0.00599951 | − | 0.00599951i | ||||
\(404\) | 11.9110 | 0.592597 | ||||||||
\(405\) | 18.3110 | − | 8.34904i | 0.909882 | − | 0.414867i | ||||
\(406\) | −14.7325 | −0.731163 | ||||||||
\(407\) | 11.8647 | − | 11.8647i | 0.588110 | − | 0.588110i | ||||
\(408\) | 0.00733933 | − | 2.08780i | 0.000363351 | − | 0.103361i | ||||
\(409\) | − | 11.8101i | − | 0.583970i | −0.956423 | − | 0.291985i | \(-0.905684\pi\) | ||
0.956423 | − | 0.291985i | \(-0.0943157\pi\) | |||||||
\(410\) | −26.0234 | − | 9.30922i | −1.28520 | − | 0.459749i | ||||
\(411\) | 17.1485 | + | 17.2695i | 0.845872 | + | 0.851840i | ||||
\(412\) | −4.74787 | − | 4.74787i | −0.233911 | − | 0.233911i | ||||
\(413\) | 1.18668 | + | 1.18668i | 0.0583925 | + | 0.0583925i | ||||
\(414\) | 25.4817 | + | 0.179156i | 1.25235 | + | 0.00880503i | ||||
\(415\) | −25.6241 | − | 9.16638i | −1.25784 | − | 0.449960i | ||||
\(416\) | 0.170327i | 0.00835097i | ||||||||
\(417\) | −10.7010 | − | 0.0376176i | −0.524029 | − | 0.00184214i | ||||
\(418\) | 10.8002 | − | 10.8002i | 0.528253 | − | 0.528253i | ||||
\(419\) | −4.51774 | −0.220706 | −0.110353 | − | 0.993892i | \(-0.535198\pi\) | ||||
−0.110353 | + | 0.993892i | \(0.535198\pi\) | |||||||
\(420\) | 5.72051 | + | 2.06908i | 0.279132 | + | 0.100961i | ||||
\(421\) | −34.9059 | −1.70121 | −0.850604 | − | 0.525807i | \(-0.823763\pi\) | ||||
−0.850604 | + | 0.525807i | \(0.823763\pi\) | |||||||
\(422\) | 13.4217 | − | 13.4217i | 0.653357 | − | 0.653357i | ||||
\(423\) | −5.29565 | + | 5.22170i | −0.257483 | + | 0.253888i | ||||
\(424\) | 0.0819733i | 0.00398098i | ||||||||
\(425\) | 0.591609 | + | 5.99789i | 0.0286973 | + | 0.290940i | ||||
\(426\) | 19.3955 | − | 19.2596i | 0.939716 | − | 0.933133i | ||||
\(427\) | −8.40739 | − | 8.40739i | −0.406862 | − | 0.406862i | ||||
\(428\) | −11.4901 | − | 11.4901i | −0.555393 | − | 0.555393i | ||||
\(429\) | −0.567198 | + | 0.563225i | −0.0273846 | + | 0.0271927i | ||||
\(430\) | 9.16606 | + | 19.3764i | 0.442026 | + | 0.934413i | ||||
\(431\) | − | 7.18868i | − | 0.346267i | −0.984898 | − | 0.173133i | \(-0.944611\pi\) | ||
0.984898 | − | 0.173133i | \(-0.0553892\pi\) | |||||||
\(432\) | 0.0547976 | − | 5.19586i | 0.00263645 | − | 0.249986i | ||||
\(433\) | −2.70121 | + | 2.70121i | −0.129812 | + | 0.129812i | −0.769028 | − | 0.639216i | \(-0.779259\pi\) |
0.639216 | + | 0.769028i | \(0.279259\pi\) | |||||||
\(434\) | −1.57068 | −0.0753949 | ||||||||
\(435\) | −15.4189 | − | 32.8930i | −0.739278 | − | 1.57710i | ||||
\(436\) | −4.28732 | −0.205326 | ||||||||
\(437\) | 33.8581 | − | 33.8581i | 1.61965 | − | 1.61965i | ||||
\(438\) | 9.55921 | + | 0.0336039i | 0.456757 | + | 0.00160566i | ||||
\(439\) | 13.5187i | 0.645211i | 0.946533 | + | 0.322606i | \(0.104559\pi\) | ||||
−0.946533 | + | 0.322606i | \(0.895441\pi\) | |||||||
\(440\) | −2.04066 | + | 5.70455i | −0.0972846 | + | 0.271954i | ||||
\(441\) | −0.0956087 | + | 13.5986i | −0.00455279 | + | 0.647552i | ||||
\(442\) | 0.145177 | + | 0.145177i | 0.00690539 | + | 0.00690539i | ||||
\(443\) | 5.99533 | + | 5.99533i | 0.284847 | + | 0.284847i | 0.835038 | − | 0.550192i | \(-0.185445\pi\) |
−0.550192 | + | 0.835038i | \(0.685445\pi\) | |||||||
\(444\) | −7.55787 | − | 7.61120i | −0.358681 | − | 0.361212i | ||||
\(445\) | 10.9954 | − | 5.20142i | 0.521233 | − | 0.246571i | ||||
\(446\) | − | 8.77171i | − | 0.415352i | ||||||
\(447\) | 0.0941728 | − | 26.7891i | 0.00445422 | − | 1.26708i | ||||
\(448\) | 1.11064 | − | 1.11064i | 0.0524726 | − | 0.0524726i | ||||
\(449\) | −6.91133 | −0.326166 | −0.163083 | − | 0.986612i | \(-0.552144\pi\) | ||||
−0.163083 | + | 0.986612i | \(0.552144\pi\) | |||||||
\(450\) | 1.36741 | + | 14.9375i | 0.0644604 | + | 0.704163i | ||||
\(451\) | −33.4897 | −1.57697 | ||||||||
\(452\) | −5.16233 | + | 5.16233i | −0.242815 | + | 0.242815i | ||||
\(453\) | −0.0271045 | + | 7.71032i | −0.00127348 | + | 0.362263i | ||||
\(454\) | 28.2730i | 1.32692i | ||||||||
\(455\) | −0.540759 | + | 0.255807i | −0.0253512 | + | 0.0119924i | ||||
\(456\) | −6.87977 | − | 6.92831i | −0.322175 | − | 0.324448i | ||||
\(457\) | −7.97308 | − | 7.97308i | −0.372965 | − | 0.372965i | 0.495591 | − | 0.868556i | \(-0.334951\pi\) |
−0.868556 | + | 0.495591i | \(0.834951\pi\) | |||||||
\(458\) | 2.89845 | + | 2.89845i | 0.135436 | + | 0.135436i | ||||
\(459\) | −4.38197 | − | 4.47538i | −0.204533 | − | 0.208893i | ||||
\(460\) | −6.39739 | + | 17.8836i | −0.298280 | + | 0.833825i | ||||
\(461\) | 19.9386i | 0.928632i | 0.885670 | + | 0.464316i | \(0.153700\pi\) | ||||
−0.885670 | + | 0.464316i | \(0.846300\pi\) | |||||||
\(462\) | 7.37105 | + | 0.0259118i | 0.342932 | + | 0.00120552i | ||||
\(463\) | 5.79569 | − | 5.79569i | 0.269348 | − | 0.269348i | −0.559489 | − | 0.828838i | \(-0.689003\pi\) |
0.828838 | + | 0.559489i | \(0.189003\pi\) | |||||||
\(464\) | −9.37974 | −0.435443 | ||||||||
\(465\) | −1.64385 | − | 3.50682i | −0.0762316 | − | 0.162625i | ||||
\(466\) | 8.98817 | 0.416369 | ||||||||
\(467\) | −17.5385 | + | 17.5385i | −0.811584 | + | 0.811584i | −0.984871 | − | 0.173288i | \(-0.944561\pi\) |
0.173288 | + | 0.984871i | \(0.444561\pi\) | |||||||
\(468\) | 0.358769 | + | 0.363849i | 0.0165841 | + | 0.0168189i | ||||
\(469\) | − | 11.3313i | − | 0.523231i | ||||||
\(470\) | −2.37041 | − | 5.01089i | −0.109339 | − | 0.231135i | ||||
\(471\) | 9.94876 | − | 9.87906i | 0.458415 | − | 0.455203i | ||||
\(472\) | 0.755519 | + | 0.755519i | 0.0347756 | + | 0.0347756i | ||||
\(473\) | 18.3658 | + | 18.3658i | 0.844459 | + | 0.844459i | ||||
\(474\) | −9.65574 | + | 9.58809i | −0.443503 | + | 0.440396i | ||||
\(475\) | 21.7905 | + | 17.8778i | 0.999816 | + | 0.820288i | ||||
\(476\) | − | 1.89329i | − | 0.0867789i | ||||||
\(477\) | 0.172665 | + | 0.175110i | 0.00790578 | + | 0.00801773i | ||||
\(478\) | −14.8085 | + | 14.8085i | −0.677323 | + | 0.677323i | ||||
\(479\) | −12.9831 | −0.593212 | −0.296606 | − | 0.955000i | \(-0.595855\pi\) | ||||
−0.296606 | + | 0.955000i | \(0.595855\pi\) | |||||||
\(480\) | 3.64207 | + | 1.31732i | 0.166237 | + | 0.0601271i | ||||
\(481\) | 1.05480 | 0.0480947 | ||||||||
\(482\) | 16.3768 | − | 16.3768i | 0.745944 | − | 0.745944i | ||||
\(483\) | 23.1080 | + | 0.0812325i | 1.05145 | + | 0.00369620i | ||||
\(484\) | − | 3.65876i | − | 0.166307i | ||||||
\(485\) | −8.84970 | − | 3.16576i | −0.401844 | − | 0.143750i | ||||
\(486\) | −10.8273 | − | 11.2147i | −0.491135 | − | 0.508711i | ||||
\(487\) | −4.06854 | − | 4.06854i | −0.184363 | − | 0.184363i | 0.608891 | − | 0.793254i | \(-0.291615\pi\) |
−0.793254 | + | 0.608891i | \(0.791615\pi\) | |||||||
\(488\) | −5.35272 | − | 5.35272i | −0.242306 | − | 0.242306i | ||||
\(489\) | −24.5317 | − | 24.7048i | −1.10936 | − | 1.11719i | ||||
\(490\) | −9.54378 | − | 3.41405i | −0.431144 | − | 0.154231i | ||||
\(491\) | − | 40.3334i | − | 1.82022i | −0.414367 | − | 0.910110i | \(-0.635997\pi\) | ||
0.414367 | − | 0.910110i | \(-0.364003\pi\) | |||||||
\(492\) | −0.0752581 | + | 21.4084i | −0.00339290 | + | 0.965167i | ||||
\(493\) | −7.99478 | + | 7.99478i | −0.360067 | + | 0.360067i | ||||
\(494\) | 0.960160 | 0.0431997 | ||||||||
\(495\) | 7.65658 | + | 16.4843i | 0.344138 | + | 0.740915i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 17.5269 | − | 17.5269i | 0.786191 | − | 0.786191i | ||||
\(498\) | −0.0741034 | + | 21.0800i | −0.00332065 | + | 0.944616i | ||||
\(499\) | 33.6843i | 1.50791i | 0.656924 | + | 0.753957i | \(0.271857\pi\) | ||||
−0.656924 | + | 0.753957i | \(0.728143\pi\) | |||||||
\(500\) | −10.8459 | − | 2.71427i | −0.485042 | − | 0.121386i | ||||
\(501\) | −14.8299 | − | 14.9345i | −0.662549 | − | 0.667224i | ||||
\(502\) | 21.3918 | + | 21.3918i | 0.954761 | + | 0.954761i | ||||
\(503\) | −24.9786 | − | 24.9786i | −1.11374 | − | 1.11374i | −0.992640 | − | 0.121099i | \(-0.961358\pi\) |
−0.121099 | − | 0.992640i | \(-0.538642\pi\) | |||||||
\(504\) | 0.0331284 | − | 4.71191i | 0.00147566 | − | 0.209885i | ||||
\(505\) | 11.3892 | + | 24.0760i | 0.506812 | + | 1.07137i | ||||
\(506\) | 23.0145i | 1.02312i | ||||||||
\(507\) | 22.4663 | + | 0.0789767i | 0.997762 | + | 0.00350748i | ||||
\(508\) | −1.14523 | + | 1.14523i | −0.0508112 | + | 0.0508112i | ||||
\(509\) | −23.8231 | −1.05594 | −0.527970 | − | 0.849263i | \(-0.677047\pi\) | ||||
−0.527970 | + | 0.849263i | \(0.677047\pi\) | |||||||
\(510\) | 4.22711 | − | 1.98149i | 0.187180 | − | 0.0877419i | ||||
\(511\) | 8.66864 | 0.383478 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −29.2899 | − | 0.308903i | −1.29318 | − | 0.0136384i | ||||
\(514\) | 6.88151i | 0.303531i | ||||||||
\(515\) | 5.05708 | − | 14.1368i | 0.222842 | − | 0.622942i | ||||
\(516\) | 11.7817 | − | 11.6991i | 0.518659 | − | 0.515025i | ||||
\(517\) | −4.74953 | − | 4.74953i | −0.208884 | − | 0.208884i | ||||
\(518\) | −6.87793 | − | 6.87793i | −0.302199 | − | 0.302199i | ||||
\(519\) | 9.78197 | − | 9.71344i | 0.429381 | − | 0.426373i | ||||
\(520\) | −0.344284 | + | 0.162864i | −0.0150979 | + | 0.00714208i | ||||
\(521\) | − | 21.7076i | − | 0.951027i | −0.879708 | − | 0.475514i | \(-0.842262\pi\) | ||
0.879708 | − | 0.475514i | \(-0.157738\pi\) | |||||||
\(522\) | −20.0368 | + | 19.7570i | −0.876988 | + | 0.864743i | ||||
\(523\) | 3.85110 | − | 3.85110i | 0.168397 | − | 0.168397i | −0.617878 | − | 0.786274i | \(-0.712007\pi\) |
0.786274 | + | 0.617878i | \(0.212007\pi\) | |||||||
\(524\) | −2.05800 | −0.0899043 | ||||||||
\(525\) | 1.28762 | + | 13.5414i | 0.0561964 | + | 0.590994i | ||||
\(526\) | −24.0299 | −1.04775 | ||||||||
\(527\) | −0.852346 | + | 0.852346i | −0.0371288 | + | 0.0371288i | ||||
\(528\) | 4.69291 | + | 0.0164972i | 0.204233 | + | 0.000717949i | ||||
\(529\) | 49.1496i | 2.13694i | ||||||||
\(530\) | −0.165694 | + | 0.0783818i | −0.00719727 | + | 0.00340469i | ||||
\(531\) | 3.20532 | + | 0.0225359i | 0.139099 | + | 0.000977973i | ||||
\(532\) | −6.26083 | − | 6.26083i | −0.271442 | − | 0.271442i | ||||
\(533\) | −1.48866 | − | 1.48866i | −0.0644810 | − | 0.0644810i | ||||
\(534\) | −6.63884 | − | 6.68568i | −0.287291 | − | 0.289318i | ||||
\(535\) | 12.2384 | − | 34.2117i | 0.529110 | − | 1.47910i | ||||
\(536\) | − | 7.21428i | − | 0.311609i | ||||||
\(537\) | 0.135858 | − | 38.6470i | 0.00586269 | − | 1.66774i | ||||
\(538\) | 1.38458 | − | 1.38458i | 0.0596936 | − | 0.0596936i | ||||
\(539\) | −12.2820 | −0.529022 | ||||||||
\(540\) | 10.5549 | − | 4.85746i | 0.454209 | − | 0.209032i | ||||
\(541\) | −29.0743 | −1.25000 | −0.625000 | − | 0.780625i | \(-0.714901\pi\) | ||||
−0.625000 | + | 0.780625i | \(0.714901\pi\) | |||||||
\(542\) | −3.94958 | + | 3.94958i | −0.169649 | + | 0.169649i | ||||
\(543\) | −0.0755867 | + | 21.5019i | −0.00324374 | + | 0.922736i | ||||
\(544\) | − | 1.20540i | − | 0.0516811i | ||||||
\(545\) | −4.09948 | − | 8.66602i | −0.175603 | − | 0.371212i | ||||
\(546\) | 0.326500 | + | 0.328804i | 0.0139729 | + | 0.0140715i | ||||
\(547\) | 3.34876 | + | 3.34876i | 0.143183 | + | 0.143183i | 0.775065 | − | 0.631882i | \(-0.217717\pi\) |
−0.631882 | + | 0.775065i | \(0.717717\pi\) | |||||||
\(548\) | 9.93566 | + | 9.93566i | 0.424431 | + | 0.424431i | ||||
\(549\) | −22.7091 | − | 0.159663i | −0.969201 | − | 0.00681423i | ||||
\(550\) | −13.4819 | + | 1.32981i | −0.574872 | + | 0.0567032i | ||||
\(551\) | 52.8751i | 2.25256i | ||||||||
\(552\) | 14.7121 | + | 0.0517181i | 0.626189 | + | 0.00220127i | ||||
\(553\) | −8.72550 | + | 8.72550i | −0.371046 | + | 0.371046i | ||||
\(554\) | −6.91697 | −0.293874 | ||||||||
\(555\) | 8.15787 | − | 22.5546i | 0.346282 | − | 0.957388i | ||||
\(556\) | −6.17825 | −0.262016 | ||||||||
\(557\) | −30.4377 | + | 30.4377i | −1.28969 | + | 1.28969i | −0.354709 | + | 0.934977i | \(0.615420\pi\) |
−0.934977 | + | 0.354709i | \(0.884580\pi\) | |||||||
\(558\) | −2.13618 | + | 2.10635i | −0.0904318 | + | 0.0891691i | ||||
\(559\) | 1.63276i | 0.0690585i | ||||||||
\(560\) | 3.30692 | + | 1.18297i | 0.139743 | + | 0.0499895i | ||||
\(561\) | 4.01405 | − | 3.98592i | 0.169473 | − | 0.168286i | ||||
\(562\) | 2.86833 | + | 2.86833i | 0.120993 | + | 0.120993i | ||||
\(563\) | 8.90858 | + | 8.90858i | 0.375452 | + | 0.375452i | 0.869458 | − | 0.494006i | \(-0.164468\pi\) |
−0.494006 | + | 0.869458i | \(0.664468\pi\) | |||||||
\(564\) | −3.04683 | + | 3.02548i | −0.128295 | + | 0.127396i | ||||
\(565\) | −15.3708 | − | 5.49853i | −0.646656 | − | 0.231325i | ||||
\(566\) | − | 10.0337i | − | 0.421746i | ||||||
\(567\) | −9.85419 | − | 10.1353i | −0.413837 | − | 0.425642i | ||||
\(568\) | 11.1589 | − | 11.1589i | 0.468215 | − | 0.468215i | ||||
\(569\) | 0.145735 | 0.00610954 | 0.00305477 | − | 0.999995i | \(-0.499028\pi\) | ||||
0.00305477 | + | 0.999995i | \(0.499028\pi\) | |||||||
\(570\) | 7.42594 | − | 20.5309i | 0.311038 | − | 0.859946i | ||||
\(571\) | 34.5504 | 1.44589 | 0.722946 | − | 0.690905i | \(-0.242788\pi\) | ||||
0.722946 | + | 0.690905i | \(0.242788\pi\) | |||||||
\(572\) | −0.326327 | + | 0.326327i | −0.0136444 | + | 0.0136444i | ||||
\(573\) | 22.0351 | + | 0.0774611i | 0.920531 | + | 0.00323598i | ||||
\(574\) | 19.4139i | 0.810323i | ||||||||
\(575\) | −42.2654 | + | 4.16890i | −1.76259 | + | 0.173855i | ||||
\(576\) | 0.0210918 | − | 2.99993i | 0.000878825 | − | 0.124997i | ||||
\(577\) | 20.0214 | + | 20.0214i | 0.833502 | + | 0.833502i | 0.987994 | − | 0.154492i | \(-0.0493740\pi\) |
−0.154492 | + | 0.987994i | \(0.549374\pi\) | |||||||
\(578\) | 10.9934 | + | 10.9934i | 0.457265 | + | 0.457265i | ||||
\(579\) | −14.5159 | − | 14.6183i | −0.603261 | − | 0.607517i | ||||
\(580\) | −8.96879 | − | 18.9594i | −0.372409 | − | 0.787246i | ||||
\(581\) | 19.1161i | 0.793068i | ||||||||
\(582\) | −0.0255928 | + | 7.28031i | −0.00106086 | + | 0.301779i | ||||
\(583\) | −0.157051 | + | 0.157051i | −0.00650441 | + | 0.00650441i | ||||
\(584\) | 5.51905 | 0.228380 | ||||||||
\(585\) | −0.392403 | + | 1.07309i | −0.0162239 | + | 0.0443669i | ||||
\(586\) | −19.3309 | −0.798554 | ||||||||
\(587\) | 0.473651 | − | 0.473651i | 0.0195497 | − | 0.0195497i | −0.697264 | − | 0.716814i | \(-0.745600\pi\) |
0.716814 | + | 0.697264i | \(0.245600\pi\) | |||||||
\(588\) | −0.0276000 | + | 7.85130i | −0.00113821 | + | 0.323782i | ||||
\(589\) | 5.63716i | 0.232275i | ||||||||
\(590\) | −0.804723 | + | 2.24956i | −0.0331299 | + | 0.0926129i | ||||
\(591\) | −5.08138 | − | 5.11723i | −0.209020 | − | 0.210495i | ||||
\(592\) | −4.37896 | − | 4.37896i | −0.179974 | − | 0.179974i | ||||
\(593\) | 20.6378 | + | 20.6378i | 0.847492 | + | 0.847492i | 0.989820 | − | 0.142328i | \(-0.0454587\pi\) |
−0.142328 | + | 0.989820i | \(0.545459\pi\) | |||||||
\(594\) | 10.0597 | − | 9.84970i | 0.412753 | − | 0.404138i | ||||
\(595\) | 3.82693 | − | 1.81034i | 0.156889 | − | 0.0742167i | ||||
\(596\) | − | 15.4668i | − | 0.633544i | ||||||
\(597\) | −25.4056 | − | 0.0893094i | −1.03978 | − | 0.00365519i | ||||
\(598\) | −1.02302 | + | 1.02302i | −0.0418345 | + | 0.0418345i | ||||
\(599\) | 5.59941 | 0.228786 | 0.114393 | − | 0.993436i | \(-0.463508\pi\) | ||||
0.114393 | + | 0.993436i | \(0.463508\pi\) | |||||||
\(600\) | 0.819788 | + | 8.62137i | 0.0334677 | + | 0.351966i | ||||
\(601\) | −27.3476 | −1.11553 | −0.557766 | − | 0.829998i | \(-0.688341\pi\) | ||||
−0.557766 | + | 0.829998i | \(0.688341\pi\) | |||||||
\(602\) | 10.6466 | − | 10.6466i | 0.433923 | − | 0.433923i | ||||
\(603\) | −15.1958 | − | 15.4110i | −0.618822 | − | 0.627585i | ||||
\(604\) | 4.45159i | 0.181132i | ||||||||
\(605\) | 7.39551 | − | 3.49846i | 0.300670 | − | 0.142233i | ||||
\(606\) | 14.6392 | − | 14.5366i | 0.594676 | − | 0.590510i | ||||
\(607\) | 6.88434 | + | 6.88434i | 0.279427 | + | 0.279427i | 0.832880 | − | 0.553453i | \(-0.186690\pi\) |
−0.553453 | + | 0.832880i | \(0.686690\pi\) | |||||||
\(608\) | −3.98607 | − | 3.98607i | −0.161657 | − | 0.161657i | ||||
\(609\) | −18.1069 | + | 17.9801i | −0.733729 | + | 0.728589i | ||||
\(610\) | 5.70132 | − | 15.9377i | 0.230840 | − | 0.645299i | ||||
\(611\) | − | 0.422245i | − | 0.0170822i | ||||||
\(612\) | −2.53900 | − | 2.57495i | −0.102633 | − | 0.104086i | ||||
\(613\) | −13.6123 | + | 13.6123i | −0.549794 | + | 0.549794i | −0.926381 | − | 0.376587i | \(-0.877098\pi\) |
0.376587 | + | 0.926381i | \(0.377098\pi\) | |||||||
\(614\) | 8.81412 | 0.355709 | ||||||||
\(615\) | −43.3451 | + | 20.3184i | −1.74784 | + | 0.819315i | ||||
\(616\) | 4.25570 | 0.171467 | ||||||||
\(617\) | 7.85935 | − | 7.85935i | 0.316406 | − | 0.316406i | −0.530979 | − | 0.847385i | \(-0.678176\pi\) |
0.847385 | + | 0.530979i | \(0.178176\pi\) | |||||||
\(618\) | −11.6298 | − | 0.0408827i | −0.467819 | − | 0.00164455i | ||||
\(619\) | − | 17.0857i | − | 0.686733i | −0.939202 | − | 0.343366i | \(-0.888433\pi\) | ||
0.939202 | − | 0.343366i | \(-0.111567\pi\) | |||||||
\(620\) | −0.956187 | − | 2.02131i | −0.0384014 | − | 0.0811779i | ||||
\(621\) | 31.5367 | − | 30.8784i | 1.26552 | − | 1.23911i | ||||
\(622\) | 21.3019 | + | 21.3019i | 0.854129 | + | 0.854129i | ||||
\(623\) | −6.04158 | − | 6.04158i | −0.242051 | − | 0.242051i | ||||
\(624\) | 0.207872 | + | 0.209339i | 0.00832156 | + | 0.00838027i | ||||
\(625\) | −4.88429 | − | 24.5182i | −0.195372 | − | 0.980729i | ||||
\(626\) | 15.7536i | 0.629641i | ||||||||
\(627\) | 0.0929974 | − | 26.4547i | 0.00371396 | − | 1.05650i | ||||
\(628\) | 5.72384 | − | 5.72384i | 0.228406 | − | 0.228406i | ||||
\(629\) | −7.46478 | −0.297640 | ||||||||
\(630\) | 9.55593 | − | 4.43851i | 0.380717 | − | 0.176834i | ||||
\(631\) | 25.6532 | 1.02124 | 0.510619 | − | 0.859807i | \(-0.329416\pi\) | ||||
0.510619 | + | 0.859807i | \(0.329416\pi\) | |||||||
\(632\) | −5.55525 | + | 5.55525i | −0.220976 | + | 0.220976i | ||||
\(633\) | 0.115571 | − | 32.8761i | 0.00459352 | − | 1.30671i | ||||
\(634\) | − | 17.9590i | − | 0.713244i | ||||||
\(635\) | −3.40991 | − | 1.21981i | −0.135318 | − | 0.0484066i | ||||
\(636\) | 0.100043 | + | 0.100749i | 0.00396696 | + | 0.00399495i | ||||
\(637\) | −0.545949 | − | 0.545949i | −0.0216313 | − | 0.0216313i | ||||
\(638\) | −17.9705 | − | 17.9705i | −0.711459 | − | 0.711459i | ||||
\(639\) | 0.332850 | − | 47.3418i | 0.0131673 | − | 1.87281i | ||||
\(640\) | 2.10541 | + | 0.753158i | 0.0832237 | + | 0.0297712i | ||||
\(641\) | 16.1733i | 0.638807i | 0.947619 | + | 0.319404i | \(0.103483\pi\) | ||||
−0.947619 | + | 0.319404i | \(0.896517\pi\) | |||||||
\(642\) | −28.1446 | − | 0.0989380i | −1.11078 | − | 0.00390477i | ||||
\(643\) | −17.2738 | + | 17.2738i | −0.681213 | + | 0.681213i | −0.960274 | − | 0.279060i | \(-0.909977\pi\) |
0.279060 | + | 0.960274i | \(0.409977\pi\) | |||||||
\(644\) | 13.3415 | 0.525728 | ||||||||
\(645\) | 34.9131 | + | 12.6279i | 1.37470 | + | 0.497222i | ||||
\(646\) | −6.79503 | −0.267347 | ||||||||
\(647\) | −27.3602 | + | 27.3602i | −1.07564 | + | 1.07564i | −0.0787470 | + | 0.996895i | \(0.525092\pi\) |
−0.996895 | + | 0.0787470i | \(0.974908\pi\) | |||||||
\(648\) | −6.27385 | − | 6.45281i | −0.246460 | − | 0.253490i | ||||
\(649\) | 2.89498i | 0.113638i | ||||||||
\(650\) | −0.658400 | − | 0.540177i | −0.0258246 | − | 0.0211875i | ||||
\(651\) | −1.93043 | + | 1.91690i | −0.0756594 | + | 0.0751294i | ||||
\(652\) | −14.2135 | − | 14.2135i | −0.556642 | − | 0.556642i | ||||
\(653\) | 28.0015 | + | 28.0015i | 1.09578 | + | 1.09578i | 0.994898 | + | 0.100884i | \(0.0321672\pi\) |
0.100884 | + | 0.994898i | \(0.467833\pi\) | |||||||
\(654\) | −5.26930 | + | 5.23239i | −0.206046 | + | 0.204603i | ||||
\(655\) | −1.96784 | − | 4.15987i | −0.0768897 | − | 0.162539i | ||||
\(656\) | 12.3602i | 0.482587i | ||||||||
\(657\) | 11.7897 | − | 11.6251i | 0.459960 | − | 0.453537i | ||||
\(658\) | −2.75329 | + | 2.75329i | −0.107335 | + | 0.107335i | ||||
\(659\) | 25.8325 | 1.00629 | 0.503145 | − | 0.864202i | \(-0.332176\pi\) | ||||
0.503145 | + | 0.864202i | \(0.332176\pi\) | |||||||
\(660\) | 4.45396 | + | 9.50162i | 0.173370 | + | 0.369850i | ||||
\(661\) | 9.74125 | 0.378891 | 0.189445 | − | 0.981891i | \(-0.439331\pi\) | ||||
0.189445 | + | 0.981891i | \(0.439331\pi\) | |||||||
\(662\) | −23.7497 | + | 23.7497i | −0.923060 | + | 0.923060i | ||||
\(663\) | 0.355609 | + | 0.00125009i | 0.0138107 | + | 4.85493e-5i | ||||
\(664\) | 12.1706i | 0.472311i | ||||||||
\(665\) | 6.66857 | − | 18.6416i | 0.258596 | − | 0.722891i | ||||
\(666\) | −18.5779 | − | 0.130617i | −0.719879 | − | 0.00506131i | ||||
\(667\) | −56.3369 | − | 56.3369i | −2.18137 | − | 2.18137i | ||||
\(668\) | −8.59228 | − | 8.59228i | −0.332445 | − | 0.332445i | ||||
\(669\) | −10.7053 | − | 10.7808i | −0.413890 | − | 0.416810i | ||||
\(670\) | 14.5823 | − | 6.89820i | 0.563364 | − | 0.266501i | ||||
\(671\) | − | 20.5104i | − | 0.791795i | ||||||
\(672\) | 0.00956340 | − | 2.72047i | 0.000368916 | − | 0.104945i | ||||
\(673\) | −28.8522 | + | 28.8522i | −1.11217 | + | 1.11217i | −0.119314 | + | 0.992857i | \(0.538070\pi\) |
−0.992857 | + | 0.119314i | \(0.961930\pi\) | |||||||
\(674\) | −6.77982 | −0.261149 | ||||||||
\(675\) | 19.9109 | + | 16.6900i | 0.766369 | + | 0.642400i | ||||
\(676\) | 12.9710 | 0.498884 | ||||||||
\(677\) | 15.0187 | − | 15.0187i | 0.577215 | − | 0.577215i | −0.356920 | − | 0.934135i | \(-0.616173\pi\) |
0.934135 | + | 0.356920i | \(0.116173\pi\) | |||||||
\(678\) | −0.0444515 | + | 12.6450i | −0.00170715 | + | 0.485628i | ||||
\(679\) | 6.60205i | 0.253363i | ||||||||
\(680\) | 2.43649 | − | 1.15259i | 0.0934351 | − | 0.0441997i | ||||
\(681\) | 34.5053 | + | 34.7488i | 1.32225 | + | 1.33158i | ||||
\(682\) | −1.91589 | − | 1.91589i | −0.0733631 | − | 0.0733631i | ||||
\(683\) | −9.36926 | − | 9.36926i | −0.358505 | − | 0.358505i | 0.504757 | − | 0.863262i | \(-0.331582\pi\) |
−0.863262 | + | 0.504757i | \(0.831582\pi\) | |||||||
\(684\) | −16.9111 | − | 0.118898i | −0.646611 | − | 0.00454618i | ||||
\(685\) | −10.5827 | + | 29.5834i | −0.404345 | + | 1.13033i | ||||
\(686\) | 18.1146i | 0.691618i | ||||||||
\(687\) | 7.09969 | + | 0.0249579i | 0.270870 | + | 0.000952202i | ||||
\(688\) | 6.77836 | − | 6.77836i | 0.258423 | − | 0.258423i | ||||
\(689\) | −0.0139623 | −0.000531920 | ||||||||
\(690\) | 13.9630 | + | 29.7872i | 0.531562 | + | 1.13398i | ||||
\(691\) | 13.5136 | 0.514081 | 0.257040 | − | 0.966401i | \(-0.417253\pi\) | ||||
0.257040 | + | 0.966401i | \(0.417253\pi\) | |||||||
\(692\) | 5.62788 | − | 5.62788i | 0.213940 | − | 0.213940i | ||||
\(693\) | 9.09096 | − | 8.96402i | 0.345337 | − | 0.340515i | ||||
\(694\) | 23.6018i | 0.895910i | ||||||||
\(695\) | −5.90756 | − | 12.4882i | −0.224087 | − | 0.473703i | ||||
\(696\) | −11.5281 | + | 11.4473i | −0.436972 | + | 0.433910i | ||||
\(697\) | 10.5352 | + | 10.5352i | 0.399049 | + | 0.399049i | ||||
\(698\) | 14.0851 | + | 14.0851i | 0.533129 | + | 0.533129i | ||||
\(699\) | 11.0468 | − | 10.9694i | 0.417830 | − | 0.414903i | ||||
\(700\) | 0.770887 | + | 7.81545i | 0.0291368 | + | 0.295396i | ||||
\(701\) | − | 13.1874i | − | 0.498083i | −0.968493 | − | 0.249041i | \(-0.919884\pi\) | ||
0.968493 | − | 0.249041i | \(-0.0801155\pi\) | |||||||
\(702\) | 0.884996 | + | 0.00933350i | 0.0334020 | + | 0.000352270i | ||||
\(703\) | −24.6849 | + | 24.6849i | −0.931009 | + | 0.931009i | ||||
\(704\) | 2.70947 | 0.102117 | ||||||||
\(705\) | −9.02878 | − | 3.26567i | −0.340044 | − | 0.122992i | ||||
\(706\) | 20.0042 | 0.752867 | ||||||||
\(707\) | 13.2288 | − | 13.2288i | 0.497522 | − | 0.497522i | ||||
\(708\) | 1.85063 | + | 0.00650558i | 0.0695507 | + | 0.000244495i | ||||
\(709\) | − | 31.6160i | − | 1.18736i | −0.804700 | − | 0.593681i | \(-0.797674\pi\) | ||
0.804700 | − | 0.593681i | \(-0.202326\pi\) | |||||||
\(710\) | 33.2255 | + | 11.8856i | 1.24693 | + | 0.446058i | ||||
\(711\) | −0.165704 | + | 23.5683i | −0.00621438 | + | 0.883882i | ||||
\(712\) | −3.84648 | − | 3.84648i | −0.144153 | − | 0.144153i | ||||
\(713\) | −6.00623 | − | 6.00623i | −0.224935 | − | 0.224935i | ||||
\(714\) | −2.31063 | − | 2.32694i | −0.0864733 | − | 0.0870834i | ||||
\(715\) | −0.971639 | − | 0.347579i | −0.0363372 | − | 0.0129987i | ||||
\(716\) | − | 22.3130i | − | 0.833876i | ||||||
\(717\) | −0.127512 | + | 36.2729i | −0.00476202 | + | 1.35464i | ||||
\(718\) | 5.88542 | − | 5.88542i | 0.219642 | − | 0.219642i | ||||
\(719\) | 13.1043 | 0.488708 | 0.244354 | − | 0.969686i | \(-0.421424\pi\) | ||||
0.244354 | + | 0.969686i | \(0.421424\pi\) | |||||||
\(720\) | 6.08396 | − | 2.82586i | 0.226736 | − | 0.105313i | ||||
\(721\) | −10.5463 | −0.392765 | ||||||||
\(722\) | −9.03512 | + | 9.03512i | −0.336252 | + | 0.336252i | ||||
\(723\) | 0.141017 | − | 40.1146i | 0.00524447 | − | 1.49188i | ||||
\(724\) | 12.4142i | 0.461371i | ||||||||
\(725\) | 29.7470 | − | 36.2575i | 1.10478 | − | 1.34657i | ||||
\(726\) | −4.46527 | − | 4.49678i | −0.165722 | − | 0.166891i | ||||
\(727\) | 0.608842 | + | 0.608842i | 0.0225807 | + | 0.0225807i | 0.718307 | − | 0.695726i | \(-0.244917\pi\) |
−0.695726 | + | 0.718307i | \(0.744917\pi\) | |||||||
\(728\) | 0.189171 | + | 0.189171i | 0.00701115 | + | 0.00701115i | ||||
\(729\) | −26.9940 | − | 0.569441i | −0.999778 | − | 0.0210904i | ||||
\(730\) | 5.27724 | + | 11.1557i | 0.195319 | + | 0.412892i | ||||
\(731\) | − | 11.5550i | − | 0.427378i | ||||||
\(732\) | −13.1113 | − | 0.0460909i | −0.484609 | − | 0.00170357i | ||||
\(733\) | −16.4184 | + | 16.4184i | −0.606426 | + | 0.606426i | −0.942010 | − | 0.335584i | \(-0.891066\pi\) |
0.335584 | + | 0.942010i | \(0.391066\pi\) | |||||||
\(734\) | 1.64462 | 0.0607039 | ||||||||
\(735\) | −15.8963 | + | 7.45152i | −0.586345 | + | 0.274853i | ||||
\(736\) | 8.49409 | 0.313096 | ||||||||
\(737\) | 13.8217 | − | 13.8217i | 0.509130 | − | 0.509130i | ||||
\(738\) | 26.0351 | + | 26.4037i | 0.958364 | + | 0.971935i | ||||
\(739\) | − | 35.9006i | − | 1.32062i | −0.750991 | − | 0.660312i | \(-0.770424\pi\) | ||
0.750991 | − | 0.660312i | \(-0.229576\pi\) | |||||||
\(740\) | 4.66414 | − | 13.0384i | 0.171457 | − | 0.479300i | ||||
\(741\) | 1.18008 | − | 1.17181i | 0.0433513 | − | 0.0430475i | ||||
\(742\) | 0.0910425 | + | 0.0910425i | 0.00334227 | + | 0.00334227i | ||||
\(743\) | 1.93927 | + | 1.93927i | 0.0711450 | + | 0.0711450i | 0.741784 | − | 0.670639i | \(-0.233980\pi\) |
−0.670639 | + | 0.741784i | \(0.733980\pi\) | |||||||
\(744\) | −1.22904 | + | 1.22043i | −0.0450589 | + | 0.0447432i | ||||
\(745\) | 31.2632 | − | 14.7891i | 1.14539 | − | 0.541832i | ||||
\(746\) | 6.05331i | 0.221627i | ||||||||
\(747\) | 25.6356 | + | 25.9986i | 0.937957 | + | 0.951240i | ||||
\(748\) | 2.30941 | − | 2.30941i | 0.0844403 | − | 0.0844403i | ||||
\(749\) | −25.5225 | −0.932573 | ||||||||
\(750\) | −16.6426 | + | 9.90069i | −0.607702 | + | 0.361522i | ||||
\(751\) | −3.28109 | −0.119729 | −0.0598643 | − | 0.998207i | \(-0.519067\pi\) | ||||
−0.0598643 | + | 0.998207i | \(0.519067\pi\) | |||||||
\(752\) | −1.75294 | + | 1.75294i | −0.0639230 | + | 0.0639230i | ||||
\(753\) | 52.3986 | + | 0.184199i | 1.90951 | + | 0.00671259i | ||||
\(754\) | − | 1.59762i | − | 0.0581820i | ||||||
\(755\) | −8.99805 | + | 4.25655i | −0.327472 | + | 0.154912i | ||||
\(756\) | −5.70985 | − | 5.83157i | −0.207665 | − | 0.212092i | ||||
\(757\) | −13.7472 | − | 13.7472i | −0.499650 | − | 0.499650i | 0.411679 | − | 0.911329i | \(-0.364942\pi\) |
−0.911329 | + | 0.411679i | \(0.864942\pi\) | |||||||
\(758\) | 8.83005 | + | 8.83005i | 0.320722 | + | 0.320722i | ||||
\(759\) | 28.0876 | + | 28.2858i | 1.01952 | + | 1.02671i | ||||
\(760\) | 4.24567 | − | 11.8685i | 0.154007 | − | 0.430517i | ||||
\(761\) | 11.9167i | 0.431981i | 0.976395 | + | 0.215991i | \(0.0692981\pi\) | ||||
−0.976395 | + | 0.215991i | \(0.930702\pi\) | |||||||
\(762\) | −0.00986125 | + | 2.80520i | −0.000357235 | + | 0.101622i | ||||
\(763\) | −4.76166 | + | 4.76166i | −0.172384 | + | 0.172384i | ||||
\(764\) | 12.7221 | 0.460268 | ||||||||
\(765\) | 2.77703 | − | 7.59424i | 0.100404 | − | 0.274570i | ||||
\(766\) | 2.26095 | 0.0816916 | ||||||||
\(767\) | −0.128685 | + | 0.128685i | −0.00464656 | + | 0.00464656i | ||||
\(768\) | 0.00608872 | − | 1.73204i | 0.000219708 | − | 0.0624996i | ||||
\(769\) | − | 6.78944i | − | 0.244834i | −0.992479 | − | 0.122417i | \(-0.960936\pi\) | ||
0.992479 | − | 0.122417i | \(-0.0390645\pi\) | |||||||
\(770\) | 4.06925 | + | 8.60211i | 0.146646 | + | 0.309998i | ||||
\(771\) | 8.39842 | + | 8.45767i | 0.302462 | + | 0.304596i | ||||
\(772\) | −8.41038 | − | 8.41038i | −0.302696 | − | 0.302696i | ||||
\(773\) | −2.30473 | − | 2.30473i | −0.0828952 | − | 0.0828952i | 0.664443 | − | 0.747339i | \(-0.268669\pi\) |
−0.747339 | + | 0.664443i | \(0.768669\pi\) | |||||||
\(774\) | 0.202187 | − | 28.7574i | 0.00726746 | − | 1.03366i | ||||
\(775\) | 3.17141 | − | 3.86551i | 0.113920 | − | 0.138853i | ||||
\(776\) | 4.20331i | 0.150890i | ||||||||
\(777\) | −16.8473 | − | 0.0592241i | −0.604394 | − | 0.00212465i | ||||
\(778\) | 4.39634 | − | 4.39634i | 0.157616 | − | 0.157616i | ||||
\(779\) | 69.6767 | 2.49643 | ||||||||
\(780\) | −0.224375 | + | 0.620343i | −0.00803391 | + | 0.0222118i | ||||
\(781\) | 42.7582 | 1.53001 | ||||||||
\(782\) | 7.23990 | − | 7.23990i | 0.258898 | − | 0.258898i | ||||
\(783\) | −0.513987 | + | 48.7358i | −0.0183684 | + | 1.74168i | ||||
\(784\) | 4.53298i | 0.161892i | ||||||||
\(785\) | 17.0427 | + | 6.09660i | 0.608281 | + | 0.217597i | ||||
\(786\) | −2.52937 | + | 2.51165i | −0.0902198 | + | 0.0895877i | ||||
\(787\) | 38.2415 | + | 38.2415i | 1.36316 | + | 1.36316i | 0.869856 | + | 0.493305i | \(0.164211\pi\) |
0.493305 | + | 0.869856i | \(0.335789\pi\) | |||||||
\(788\) | −2.94410 | − | 2.94410i | −0.104879 | − | 0.104879i | ||||
\(789\) | −29.5338 | + | 29.3269i | −1.05143 | + | 1.04406i | ||||
\(790\) | −16.5408 | − | 5.91704i | −0.588494 | − | 0.210519i | ||||
\(791\) | 11.4669i | 0.407717i | ||||||||
\(792\) | 5.78792 | − | 5.70711i | 0.205665 | − | 0.202793i | ||||
\(793\) | 0.911712 | − | 0.911712i | 0.0323759 | − | 0.0323759i | ||||
\(794\) | 21.2953 | 0.755741 | ||||||||
\(795\) | −0.107985 | + | 0.298552i | −0.00382983 | + | 0.0105886i | ||||
\(796\) | −14.6680 | −0.519894 | ||||||||
\(797\) | −26.9645 | + | 26.9645i | −0.955132 | + | 0.955132i | −0.999036 | − | 0.0439037i | \(-0.986021\pi\) |
0.0439037 | + | 0.999036i | \(0.486021\pi\) | |||||||
\(798\) | −15.3358 | − | 0.0539105i | −0.542880 | − | 0.00190841i | ||||
\(799\) | 2.98821i | 0.105715i | ||||||||
\(800\) | 0.490799 | + | 4.97585i | 0.0173524 | + | 0.175923i | ||||
\(801\) | −16.3188 | − | 0.114734i | −0.576598 | − | 0.00405393i | ||||
\(802\) | −2.61826 | − | 2.61826i | −0.0924540 | − | 0.0924540i | ||||
\(803\) | 10.5739 | + | 10.5739i | 0.373144 | + | 0.373144i | ||||
\(804\) | −8.80454 | − | 8.86666i | −0.310512 | − | 0.312703i | ||||
\(805\) | 12.7569 | + | 26.9673i | 0.449623 | + | 0.950472i | ||||
\(806\) | − | 0.170327i | − | 0.00599951i | ||||||
\(807\) | 0.0119223 | − | 3.39150i | 0.000419684 | − | 0.119386i | ||||
\(808\) | 8.42238 | − | 8.42238i | 0.296298 | − | 0.296298i | ||||
\(809\) | −10.1513 | −0.356900 | −0.178450 | − | 0.983949i | \(-0.557108\pi\) | ||||
−0.178450 | + | 0.983949i | \(0.557108\pi\) | |||||||
\(810\) | 7.04418 | − | 18.8515i | 0.247507 | − | 0.662375i | ||||
\(811\) | 38.3970 | 1.34830 | 0.674151 | − | 0.738594i | \(-0.264510\pi\) | ||||
0.674151 | + | 0.738594i | \(0.264510\pi\) | |||||||
\(812\) | −10.4175 | + | 10.4175i | −0.365582 | + | 0.365582i | ||||
\(813\) | −0.0340088 | + | 9.67439i | −0.00119274 | + | 0.339296i | ||||
\(814\) | − | 16.7792i | − | 0.588110i | ||||||
\(815\) | 15.1391 | − | 42.3206i | 0.530300 | − | 1.48243i | ||||
\(816\) | −1.47111 | − | 1.48149i | −0.0514991 | − | 0.0518624i | ||||
\(817\) | −38.2107 | − | 38.2107i | −1.33682 | − | 1.33682i | ||||
\(818\) | −8.35097 | − | 8.35097i | −0.291985 | − | 0.291985i | ||||
\(819\) | 0.802566 | + | 0.00564266i | 0.0280439 | + | 0.000197170i | ||||
\(820\) | −24.9839 | + | 11.8187i | −0.872477 | + | 0.412727i | ||||
\(821\) | 0.682885i | 0.0238329i | 0.999929 | + | 0.0119164i | \(0.00379321\pi\) | ||||
−0.999929 | + | 0.0119164i | \(0.996207\pi\) | |||||||
\(822\) | 24.3372 | + | 0.0855535i | 0.848856 | + | 0.00298402i | ||||
\(823\) | −4.32786 | + | 4.32786i | −0.150860 | + | 0.150860i | −0.778502 | − | 0.627642i | \(-0.784020\pi\) |
0.627642 | + | 0.778502i | \(0.284020\pi\) | |||||||
\(824\) | −6.71451 | −0.233911 | ||||||||
\(825\) | −14.9469 | + | 18.0882i | −0.520385 | + | 0.629749i | ||||
\(826\) | 1.67821 | 0.0583925 | ||||||||
\(827\) | 12.3055 | − | 12.3055i | 0.427903 | − | 0.427903i | −0.460010 | − | 0.887914i | \(-0.652154\pi\) |
0.887914 | + | 0.460010i | \(0.152154\pi\) | |||||||
\(828\) | 18.1449 | − | 17.8916i | 0.630580 | − | 0.621775i | ||||
\(829\) | 48.9864i | 1.70137i | 0.525678 | + | 0.850684i | \(0.323812\pi\) | ||||
−0.525678 | + | 0.850684i | \(0.676188\pi\) | |||||||
\(830\) | −24.6006 | + | 11.6374i | −0.853899 | + | 0.403939i | ||||
\(831\) | −8.50125 | + | 8.44169i | −0.294905 | + | 0.292839i | ||||
\(832\) | 0.120439 | + | 0.120439i | 0.00417548 | + | 0.00417548i | ||||
\(833\) | 3.86366 | + | 3.86366i | 0.133868 | + | 0.133868i | ||||
\(834\) | −7.59333 | + | 7.54013i | −0.262936 | + | 0.261093i | ||||
\(835\) | 9.15186 | − | 25.5835i | 0.316713 | − | 0.885354i | ||||
\(836\) | − | 15.2737i | − | 0.528253i | ||||||
\(837\) | −0.0547976 | + | 5.19586i | −0.00189408 | + | 0.179595i | ||||
\(838\) | −3.19452 | + | 3.19452i | −0.110353 | + | 0.110353i | ||||
\(839\) | −20.1390 | −0.695274 | −0.347637 | − | 0.937629i | \(-0.613016\pi\) | ||||
−0.347637 | + | 0.937629i | \(0.613016\pi\) | |||||||
\(840\) | 5.50807 | − | 2.58195i | 0.190047 | − | 0.0890858i | ||||
\(841\) | 58.9795 | 2.03378 | ||||||||
\(842\) | −24.6822 | + | 24.6822i | −0.850604 | + | 0.850604i | ||||
\(843\) | 7.02591 | + | 0.0246985i | 0.241985 | + | 0.000850661i | ||||
\(844\) | − | 18.9811i | − | 0.653357i | ||||||
\(845\) | 12.4027 | + | 26.2184i | 0.426666 | + | 0.901941i | ||||
\(846\) | −0.0522871 | + | 7.43689i | −0.00179767 | + | 0.255686i | ||||
\(847\) | −4.06355 | − | 4.06355i | −0.139625 | − | 0.139625i | ||||
\(848\) | 0.0579639 | + | 0.0579639i | 0.00199049 | + | 0.00199049i | ||||
\(849\) | −12.2454 | − | 12.3318i | −0.420261 | − | 0.423226i | ||||
\(850\) | 4.65948 | + | 3.82282i | 0.159819 | + | 0.131122i | ||||
\(851\) | − | 52.6021i | − | 1.80318i | ||||||
\(852\) | 0.0960861 | − | 27.3333i | 0.00329185 | − | 0.936424i | ||||
\(853\) | 11.7571 | − | 11.7571i | 0.402557 | − | 0.402557i | −0.476576 | − | 0.879133i | \(-0.658122\pi\) |
0.879133 | + | 0.476576i | \(0.158122\pi\) | |||||||
\(854\) | −11.8898 | −0.406862 | ||||||||
\(855\) | −15.9298 | − | 34.2962i | −0.544788 | − | 1.17291i | ||||
\(856\) | −16.2494 | −0.555393 | ||||||||
\(857\) | 28.6796 | − | 28.6796i | 0.979676 | − | 0.979676i | −0.0201218 | − | 0.999798i | \(-0.506405\pi\) |
0.999798 | + | 0.0201218i | \(0.00640539\pi\) | |||||||
\(858\) | −0.00280992 | + | 0.799330i | −9.59291e−5 | + | 0.0272887i | ||||
\(859\) | − | 21.3434i | − | 0.728226i | −0.931355 | − | 0.364113i | \(-0.881372\pi\) | ||
0.931355 | − | 0.364113i | \(-0.118628\pi\) | |||||||
\(860\) | 20.1826 | + | 7.21980i | 0.688220 | + | 0.246193i | ||||
\(861\) | 23.6934 | + | 23.8606i | 0.807469 | + | 0.813166i | ||||
\(862\) | −5.08317 | − | 5.08317i | −0.173133 | − | 0.173133i | ||||
\(863\) | −24.1749 | − | 24.1749i | −0.822923 | − | 0.822923i | 0.163603 | − | 0.986526i | \(-0.447688\pi\) |
−0.986526 | + | 0.163603i | \(0.947688\pi\) | |||||||
\(864\) | −3.63528 | − | 3.71278i | −0.123675 | − | 0.126311i | ||||
\(865\) | 16.7570 | + | 5.99439i | 0.569755 | + | 0.203816i | ||||
\(866\) | 3.82009i | 0.129812i | ||||||||
\(867\) | 26.9281 | + | 0.0946614i | 0.914525 | + | 0.00321487i | ||||
\(868\) | −1.11064 | + | 1.11064i | −0.0376974 | + | 0.0376974i | ||||
\(869\) | −21.2864 | −0.722093 | ||||||||
\(870\) | −34.1617 | − | 12.3561i | −1.15819 | − | 0.418911i | ||||
\(871\) | 1.22879 | 0.0416358 | ||||||||
\(872\) | −3.03160 | + | 3.03160i | −0.102663 | + | 0.102663i | ||||
\(873\) | 8.85367 | + | 8.97904i | 0.299651 | + | 0.303895i | ||||
\(874\) | − | 47.8826i | − | 1.61965i | ||||||
\(875\) | −15.0604 | + | 9.03124i | −0.509133 | + | 0.305312i | ||||
\(876\) | 6.78314 | − | 6.73562i | 0.229181 | − | 0.227576i | ||||
\(877\) | 27.7279 | + | 27.7279i | 0.936304 | + | 0.936304i | 0.998089 | − | 0.0617854i | \(-0.0196794\pi\) |
−0.0617854 | + | 0.998089i | \(0.519679\pi\) | |||||||
\(878\) | 9.55915 | + | 9.55915i | 0.322606 | + | 0.322606i | ||||
\(879\) | −23.7585 | + | 23.5921i | −0.801356 | + | 0.795742i | ||||
\(880\) | 2.59076 | + | 5.47669i | 0.0873346 | + | 0.184619i | ||||
\(881\) | − | 13.2873i | − | 0.447662i | −0.974628 | − | 0.223831i | \(-0.928144\pi\) | ||
0.974628 | − | 0.223831i | \(-0.0718563\pi\) | |||||||
\(882\) | 9.54805 | + | 9.68326i | 0.321500 | + | 0.326052i | ||||
\(883\) | 17.6127 | − | 17.6127i | 0.592714 | − | 0.592714i | −0.345650 | − | 0.938364i | \(-0.612342\pi\) |
0.938364 | + | 0.345650i | \(0.112342\pi\) | |||||||
\(884\) | 0.205312 | 0.00690539 | ||||||||
\(885\) | 1.75639 | + | 3.74691i | 0.0590405 | + | 0.125951i | ||||
\(886\) | 8.47867 | 0.284847 | ||||||||
\(887\) | −19.7879 | + | 19.7879i | −0.664413 | + | 0.664413i | −0.956417 | − | 0.292004i | \(-0.905678\pi\) |
0.292004 | + | 0.956417i | \(0.405678\pi\) | |||||||
\(888\) | −10.7262 | − | 0.0377061i | −0.359946 | − | 0.00126533i | ||||
\(889\) | 2.54386i | 0.0853182i | ||||||||
\(890\) | 4.09699 | − | 11.4529i | 0.137331 | − | 0.383902i | ||||
\(891\) | 0.342877 | − | 24.3828i | 0.0114868 | − | 0.816856i | ||||
\(892\) | −6.20254 | − | 6.20254i | −0.207676 | − | 0.207676i | ||||
\(893\) | 9.88158 | + | 9.88158i | 0.330674 | + | 0.330674i | ||||
\(894\) | −18.8761 | − | 19.0093i | −0.631313 | − | 0.635767i | ||||
\(895\) | 45.1016 | − | 21.3354i | 1.50758 | − | 0.713164i | ||||
\(896\) | − | 1.57068i | − | 0.0524726i | ||||||
\(897\) | −0.00880899 | + | 2.50587i | −0.000294124 | + | 0.0836685i | ||||
\(898\) | −4.88705 | + | 4.88705i | −0.163083 | + | 0.163083i | ||||
\(899\) | 9.37974 | 0.312832 | ||||||||
\(900\) | 11.5293 | + | 9.59553i | 0.384311 | + | 0.319851i | ||||
\(901\) | 0.0988105 | 0.00329186 | ||||||||
\(902\) | −23.6808 | + | 23.6808i | −0.788485 | + | 0.788485i | ||||
\(903\) | 0.0916752 | − | 26.0786i | 0.00305076 | − | 0.867841i | ||||
\(904\) | 7.30063i | 0.242815i | ||||||||
\(905\) | −25.0930 | + | 11.8703i | −0.834120 | + | 0.394583i | ||||
\(906\) | 5.43286 | + | 5.47119i | 0.180495 | + | 0.181768i | ||||
\(907\) | 7.84127 | + | 7.84127i | 0.260365 | + | 0.260365i | 0.825202 | − | 0.564837i | \(-0.191061\pi\) |
−0.564837 | + | 0.825202i | \(0.691061\pi\) | |||||||
\(908\) | 19.9921 | + | 19.9921i | 0.663459 | + | 0.663459i | ||||
\(909\) | 0.251226 | − | 35.7323i | 0.00833262 | − | 1.18516i | ||||
\(910\) | −0.201491 | + | 0.563257i | −0.00667937 | + | 0.0186718i | ||||
\(911\) | 22.3664i | 0.741031i | 0.928826 | + | 0.370515i | \(0.120819\pi\) | ||||
−0.928826 | + | 0.370515i | \(0.879181\pi\) | |||||||
\(912\) | −9.76379 | − | 0.0343231i | −0.323311 | − | 0.00113655i | ||||
\(913\) | −23.3175 | + | 23.3175i | −0.771696 | + | 0.771696i | ||||
\(914\) | −11.2756 | −0.372965 | ||||||||
\(915\) | −12.4437 | − | 26.5462i | −0.411377 | − | 0.877591i | ||||
\(916\) | 4.09903 | 0.135436 | ||||||||
\(917\) | −2.28569 | + | 2.28569i | −0.0754802 | + | 0.0754802i | ||||
\(918\) | −6.26309 | − | 0.0660529i | −0.206713 | − | 0.00218007i | ||||
\(919\) | − | 17.0089i | − | 0.561071i | −0.959844 | − | 0.280535i | \(-0.909488\pi\) | ||
0.959844 | − | 0.280535i | \(-0.0905120\pi\) | |||||||
\(920\) | 8.12194 | + | 17.1692i | 0.267773 | + | 0.566052i | ||||
\(921\) | 10.8329 | − | 10.7570i | 0.356957 | − | 0.354456i | ||||
\(922\) | 14.0987 | + | 14.0987i | 0.464316 | + | 0.464316i | ||||
\(923\) | 1.90065 | + | 1.90065i | 0.0625608 | + | 0.0625608i | ||||
\(924\) | 5.23044 | − | 5.19380i | 0.172069 | − | 0.170863i | ||||
\(925\) | 30.8144 | − | 3.03942i | 1.01317 | − | 0.0999354i | ||||
\(926\) | − | 8.19634i | − | 0.269348i | ||||||
\(927\) | −14.3434 | + | 14.1431i | −0.471099 | + | 0.464521i | ||||
\(928\) | −6.63248 | + | 6.63248i | −0.217722 | + | 0.217722i | ||||
\(929\) | 52.5241 | 1.72326 | 0.861630 | − | 0.507537i | \(-0.169444\pi\) | ||||
0.861630 | + | 0.507537i | \(0.169444\pi\) | |||||||
\(930\) | −3.64207 | − | 1.31732i | −0.119428 | − | 0.0431966i | ||||
\(931\) | 25.5531 | 0.837470 | ||||||||
\(932\) | 6.35559 | − | 6.35559i | 0.208184 | − | 0.208184i | ||||
\(933\) | 52.1785 | + | 0.183425i | 1.70825 | + | 0.00600508i | ||||
\(934\) | 24.8031i | 0.811584i | ||||||||
\(935\) | 6.87626 | + | 2.45981i | 0.224878 | + | 0.0804443i | ||||
\(936\) | 0.510968 | + | 0.00359250i | 0.0167015 | + | 0.000117425i | ||||
\(937\) | −6.40958 | − | 6.40958i | −0.209392 | − | 0.209392i | 0.594617 | − | 0.804009i | \(-0.297304\pi\) |
−0.804009 | + | 0.594617i | \(0.797304\pi\) | |||||||
\(938\) | −8.01244 | − | 8.01244i | −0.261615 | − | 0.261615i | ||||
\(939\) | 19.2262 | + | 19.3618i | 0.627423 | + | 0.631850i | ||||
\(940\) | −5.21937 | − | 1.86710i | −0.170237 | − | 0.0608980i | ||||
\(941\) | − | 16.6319i | − | 0.542183i | −0.962554 | − | 0.271091i | \(-0.912615\pi\) | ||
0.962554 | − | 0.271091i | \(-0.0873846\pi\) | |||||||
\(942\) | 0.0492865 | − | 14.0204i | 0.00160584 | − | 0.456809i | ||||
\(943\) | −74.2385 | + | 74.2385i | −2.41754 | + | 2.41754i | ||||
\(944\) | 1.06847 | 0.0347756 | ||||||||
\(945\) | 6.32774 | − | 17.1175i | 0.205842 | − | 0.556831i | ||||
\(946\) | 25.9731 | 0.844459 | ||||||||
\(947\) | 1.14638 | − | 1.14638i | 0.0372524 | − | 0.0372524i | −0.688235 | − | 0.725488i | \(-0.741614\pi\) |
0.725488 | + | 0.688235i | \(0.241614\pi\) | |||||||
\(948\) | −0.0478349 | + | 13.6074i | −0.00155360 | + | 0.441949i | ||||
\(949\) | 0.940042i | 0.0305151i | ||||||||
\(950\) | 28.0497 | − | 2.76672i | 0.910052 | − | 0.0897641i | ||||
\(951\) | −21.9178 | − | 22.0724i | −0.710732 | − | 0.715746i | ||||
\(952\) | −1.33876 | − | 1.33876i | −0.0433894 | − | 0.0433894i | ||||
\(953\) | −21.7711 | − | 21.7711i | −0.705233 | − | 0.705233i | 0.260296 | − | 0.965529i | \(-0.416180\pi\) |
−0.965529 | + | 0.260296i | \(0.916180\pi\) | |||||||
\(954\) | 0.245914 | + | 0.00172897i | 0.00796175 | + | 5.59773e-5i | ||||
\(955\) | 12.1647 | + | 25.7153i | 0.393640 | + | 0.832127i | ||||
\(956\) | 20.9423i | 0.677323i | ||||||||
\(957\) | −44.0183 | − | 0.154740i | −1.42291 | − | 0.00500202i | ||||
\(958\) | −9.18043 | + | 9.18043i | −0.296606 | + | 0.296606i | ||||
\(959\) | 22.0698 | 0.712671 | ||||||||
\(960\) | 3.50682 | − | 1.64385i | 0.113182 | − | 0.0530549i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0.745855 | − | 0.745855i | 0.0240473 | − | 0.0240473i | ||||
\(963\) | −34.7117 | + | 34.2270i | −1.11857 | + | 1.10295i | ||||
\(964\) | − | 23.1603i | − | 0.745944i | ||||||
\(965\) | 8.95811 | − | 25.0419i | 0.288372 | − | 0.806128i | ||||
\(966\) | 16.3972 | − | 16.2824i | 0.527572 | − | 0.523876i | ||||
\(967\) | −22.4276 | − | 22.4276i | −0.721222 | − | 0.721222i | 0.247632 | − | 0.968854i | \(-0.420348\pi\) |
−0.968854 | + | 0.247632i | \(0.920348\pi\) | |||||||
\(968\) | −2.58714 | − | 2.58714i | −0.0831537 | − | 0.0831537i | ||||
\(969\) | −8.35138 | + | 8.29287i | −0.268285 | + | 0.266405i | ||||
\(970\) | −8.49621 | + | 4.01916i | −0.272797 | + | 0.129047i | ||||
\(971\) | 42.8935i | 1.37652i | 0.725466 | + | 0.688258i | \(0.241624\pi\) | ||||
−0.725466 | + | 0.688258i | \(0.758376\pi\) | |||||||
\(972\) | −15.5860 | − | 0.273979i | −0.499923 | − | 0.00878787i | ||||
\(973\) | −6.86178 | + | 6.86178i | −0.219979 | + | 0.219979i | ||||
\(974\) | −5.75378 | −0.184363 | ||||||||
\(975\) | −1.46845 | + | 0.139632i | −0.0470281 | + | 0.00447180i | ||||
\(976\) | −7.56989 | −0.242306 | ||||||||
\(977\) | 11.0944 | − | 11.0944i | 0.354942 | − | 0.354942i | −0.507003 | − | 0.861945i | \(-0.669247\pi\) |
0.861945 | + | 0.507003i | \(0.169247\pi\) | |||||||
\(978\) | −34.8155 | − | 0.122389i | −1.11328 | − | 0.00391355i | ||||
\(979\) | − | 14.7388i | − | 0.471055i | ||||||
\(980\) | −9.16256 | + | 4.33437i | −0.292687 | + | 0.138456i | ||||
\(981\) | −0.0904274 | + | 12.8617i | −0.00288713 | + | 0.410641i | ||||
\(982\) | −28.5200 | − | 28.5200i | −0.910110 | − | 0.910110i | ||||
\(983\) | −1.92745 | − | 1.92745i | −0.0614760 | − | 0.0614760i | 0.675700 | − | 0.737176i | \(-0.263841\pi\) |
−0.737176 | + | 0.675700i | \(0.763841\pi\) | |||||||
\(984\) | 15.0848 | + | 15.1913i | 0.480887 | + | 0.484280i | ||||
\(985\) | 3.13584 | − | 8.76607i | 0.0999162 | − | 0.279310i | ||||
\(986\) | 11.3063i | 0.360067i | ||||||||
\(987\) | −0.0237079 | + | 6.74412i | −0.000754632 | + | 0.214668i | ||||
\(988\) | 0.678936 | − | 0.678936i | 0.0215998 | − | 0.0215998i | ||||
\(989\) | 81.4248 | 2.58916 | ||||||||
\(990\) | 17.0702 | + | 6.24215i | 0.542526 | + | 0.198388i | ||||
\(991\) | 17.1483 | 0.544735 | 0.272368 | − | 0.962193i | \(-0.412193\pi\) | ||||
0.272368 | + | 0.962193i | \(0.412193\pi\) | |||||||
\(992\) | −0.707107 | + | 0.707107i | −0.0224507 | + | 0.0224507i | ||||
\(993\) | −0.204503 | + | 58.1744i | −0.00648971 | + | 1.84611i | ||||
\(994\) | − | 24.7868i | − | 0.786191i | ||||||
\(995\) | −14.0254 | − | 29.6487i | −0.444634 | − | 0.939926i | ||||
\(996\) | 14.8534 | + | 14.9582i | 0.470648 | + | 0.473968i | ||||
\(997\) | −17.9033 | − | 17.9033i | −0.567002 | − | 0.567002i | 0.364285 | − | 0.931287i | \(-0.381313\pi\) |
−0.931287 | + | 0.364285i | \(0.881313\pi\) | |||||||
\(998\) | 23.8184 | + | 23.8184i | 0.753957 | + | 0.753957i | ||||
\(999\) | −22.9924 | + | 22.5125i | −0.727449 | + | 0.712265i |
(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 | 930.2.j.g.497.16 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.j.g.497.10 | ✓ | 40 | |
5.3 | odd | 4 | inner | 930.2.j.g.683.10 | yes | 40 | |
15.8 | even | 4 | inner | 930.2.j.g.683.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.g.497.10 | ✓ | 40 | 3.2 | odd | 2 | inner | |
930.2.j.g.497.16 | yes | 40 | 1.1 | even | 1 | trivial | |
930.2.j.g.683.10 | yes | 40 | 5.3 | odd | 4 | inner | |
930.2.j.g.683.16 | yes | 40 | 15.8 | even | 4 | inner |