Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (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: | \(8.86339462436\) |
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 | 253.5 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.b.487.5 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.23211 | + | 0.132937i | −0.998231 | + | 0.0594512i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | 1.47899 | − | 1.47899i | 0.559004 | − | 0.559004i | −0.370020 | − | 0.929024i | \(-0.620649\pi\) |
0.929024 | + | 0.370020i | \(0.120649\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −2.23211 | + | 0.132937i | −0.705856 | + | 0.0420383i | ||||
\(11\) | − | 1.15189i | − | 0.347307i | −0.984807 | − | 0.173653i | \(-0.944443\pi\) | ||
0.984807 | − | 0.173653i | \(-0.0555572\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −2.88999 | −0.801540 | −0.400770 | − | 0.916179i | \(-0.631257\pi\) | ||||
−0.400770 | + | 0.916179i | \(0.631257\pi\) | |||||||
\(14\) | 1.47899 | − | 1.47899i | 0.395276 | − | 0.395276i | ||||
\(15\) | 1.48434 | − | 1.67234i | 0.383255 | − | 0.431797i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 5.62089i | − | 1.36327i | −0.731694 | − | 0.681633i | \(-0.761270\pi\) | ||
0.731694 | − | 0.681633i | \(-0.238730\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −1.32254 | − | 1.32254i | −0.303412 | − | 0.303412i | 0.538935 | − | 0.842347i | \(-0.318827\pi\) |
−0.842347 | + | 0.538935i | \(0.818827\pi\) | |||||||
\(20\) | −2.23211 | + | 0.132937i | −0.499116 | + | 0.0297256i | ||||
\(21\) | 2.09160i | 0.456425i | ||||||||
\(22\) | − | 1.15189i | − | 0.245583i | ||||||
\(23\) | −2.70557 | −0.564151 | −0.282075 | − | 0.959392i | \(-0.591023\pi\) | ||||
−0.282075 | + | 0.959392i | \(0.591023\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 4.96466 | − | 0.593460i | 0.992931 | − | 0.118692i | ||||
\(26\) | −2.88999 | −0.566775 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1.47899 | − | 1.47899i | 0.279502 | − | 0.279502i | ||||
\(29\) | 6.59907 | − | 6.59907i | 1.22542 | − | 1.22542i | 0.259737 | − | 0.965679i | \(-0.416364\pi\) |
0.965679 | − | 0.259737i | \(-0.0836360\pi\) | |||||||
\(30\) | 1.48434 | − | 1.67234i | 0.271002 | − | 0.305327i | ||||
\(31\) | −0.920380 | − | 0.920380i | −0.165305 | − | 0.165305i | 0.619607 | − | 0.784912i | \(-0.287292\pi\) |
−0.784912 | + | 0.619607i | \(0.787292\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.814507 | + | 0.814507i | 0.141787 | + | 0.141787i | ||||
\(34\) | − | 5.62089i | − | 0.963975i | ||||||
\(35\) | −3.10465 | + | 3.49787i | −0.524782 | + | 0.591249i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −4.72726 | + | 3.82793i | −0.777157 | + | 0.629307i | ||||
\(38\) | −1.32254 | − | 1.32254i | −0.214544 | − | 0.214544i | ||||
\(39\) | 2.04353 | − | 2.04353i | 0.327227 | − | 0.327227i | ||||
\(40\) | −2.23211 | + | 0.132937i | −0.352928 | + | 0.0210192i | ||||
\(41\) | − | 6.84388i | − | 1.06883i | −0.845221 | − | 0.534417i | \(-0.820531\pi\) | ||
0.845221 | − | 0.534417i | \(-0.179469\pi\) | |||||||
\(42\) | 2.09160i | 0.322741i | ||||||||
\(43\) | 8.92633 | 1.36125 | 0.680626 | − | 0.732631i | \(-0.261708\pi\) | ||||
0.680626 | + | 0.732631i | \(0.261708\pi\) | |||||||
\(44\) | − | 1.15189i | − | 0.173653i | ||||||
\(45\) | 0.132937 | + | 2.23211i | 0.0198171 | + | 0.332744i | ||||
\(46\) | −2.70557 | −0.398915 | ||||||||
\(47\) | 5.84077 | − | 5.84077i | 0.851963 | − | 0.851963i | −0.138412 | − | 0.990375i | \(-0.544200\pi\) |
0.990375 | + | 0.138412i | \(0.0441997\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 2.62520i | 0.375029i | ||||||||
\(50\) | 4.96466 | − | 0.593460i | 0.702108 | − | 0.0839279i | ||||
\(51\) | 3.97457 | + | 3.97457i | 0.556551 | + | 0.556551i | ||||
\(52\) | −2.88999 | −0.400770 | ||||||||
\(53\) | −4.27233 | − | 4.27233i | −0.586850 | − | 0.586850i | 0.349927 | − | 0.936777i | \(-0.386206\pi\) |
−0.936777 | + | 0.349927i | \(0.886206\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 0.153128 | + | 2.57114i | 0.0206478 | + | 0.346692i | ||||
\(56\) | 1.47899 | − | 1.47899i | 0.197638 | − | 0.197638i | ||||
\(57\) | 1.87036 | 0.247735 | ||||||||
\(58\) | 6.59907 | − | 6.59907i | 0.866500 | − | 0.866500i | ||||
\(59\) | −7.37461 | − | 7.37461i | −0.960092 | − | 0.960092i | 0.0391416 | − | 0.999234i | \(-0.487538\pi\) |
−0.999234 | + | 0.0391416i | \(0.987538\pi\) | |||||||
\(60\) | 1.48434 | − | 1.67234i | 0.191628 | − | 0.215899i | ||||
\(61\) | 0.721634 | + | 0.721634i | 0.0923958 | + | 0.0923958i | 0.751794 | − | 0.659398i | \(-0.229189\pi\) |
−0.659398 | + | 0.751794i | \(0.729189\pi\) | |||||||
\(62\) | −0.920380 | − | 0.920380i | −0.116888 | − | 0.116888i | ||||
\(63\) | −1.47899 | − | 1.47899i | −0.186335 | − | 0.186335i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.45079 | − | 0.384187i | 0.800122 | − | 0.0476525i | ||||
\(66\) | 0.814507 | + | 0.814507i | 0.100259 | + | 0.100259i | ||||
\(67\) | −4.32408 | − | 4.32408i | −0.528271 | − | 0.528271i | 0.391786 | − | 0.920057i | \(-0.371857\pi\) |
−0.920057 | + | 0.391786i | \(0.871857\pi\) | |||||||
\(68\) | − | 5.62089i | − | 0.681633i | ||||||
\(69\) | 1.91313 | − | 1.91313i | 0.230314 | − | 0.230314i | ||||
\(70\) | −3.10465 | + | 3.49787i | −0.371077 | + | 0.418076i | ||||
\(71\) | −4.66092 | −0.553150 | −0.276575 | − | 0.960992i | \(-0.589199\pi\) | ||||
−0.276575 | + | 0.960992i | \(0.589199\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | 0.815358 | − | 0.815358i | 0.0954304 | − | 0.0954304i | −0.657780 | − | 0.753210i | \(-0.728504\pi\) |
0.753210 | + | 0.657780i | \(0.228504\pi\) | |||||||
\(74\) | −4.72726 | + | 3.82793i | −0.549533 | + | 0.444987i | ||||
\(75\) | −3.09090 | + | 3.93018i | −0.356907 | + | 0.453818i | ||||
\(76\) | −1.32254 | − | 1.32254i | −0.151706 | − | 0.151706i | ||||
\(77\) | −1.70362 | − | 1.70362i | −0.194146 | − | 0.194146i | ||||
\(78\) | 2.04353 | − | 2.04353i | 0.231385 | − | 0.231385i | ||||
\(79\) | 11.8987 | + | 11.8987i | 1.33871 | + | 1.33871i | 0.897309 | + | 0.441403i | \(0.145519\pi\) |
0.441403 | + | 0.897309i | \(0.354481\pi\) | |||||||
\(80\) | −2.23211 | + | 0.132937i | −0.249558 | + | 0.0148628i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | − | 6.84388i | − | 0.755780i | ||||||
\(83\) | −5.88898 | − | 5.88898i | −0.646399 | − | 0.646399i | 0.305722 | − | 0.952121i | \(-0.401102\pi\) |
−0.952121 | + | 0.305722i | \(0.901102\pi\) | |||||||
\(84\) | 2.09160i | 0.228212i | ||||||||
\(85\) | 0.747224 | + | 12.5465i | 0.0810478 | + | 1.36086i | ||||
\(86\) | 8.92633 | 0.962551 | ||||||||
\(87\) | 9.33249i | 1.00055i | ||||||||
\(88\) | − | 1.15189i | − | 0.122791i | ||||||
\(89\) | 6.87434 | − | 6.87434i | 0.728678 | − | 0.728678i | −0.241678 | − | 0.970356i | \(-0.577698\pi\) |
0.970356 | + | 0.241678i | \(0.0776978\pi\) | |||||||
\(90\) | 0.132937 | + | 2.23211i | 0.0140128 | + | 0.235285i | ||||
\(91\) | −4.27426 | + | 4.27426i | −0.448064 | + | 0.448064i | ||||
\(92\) | −2.70557 | −0.282075 | ||||||||
\(93\) | 1.30161 | 0.134971 | ||||||||
\(94\) | 5.84077 | − | 5.84077i | 0.602429 | − | 0.602429i | ||||
\(95\) | 3.12787 | + | 2.77625i | 0.320913 | + | 0.284837i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | − | 14.2915i | − | 1.45108i | −0.688181 | − | 0.725539i | \(-0.741590\pi\) | ||
0.688181 | − | 0.725539i | \(-0.258410\pi\) | |||||||
\(98\) | 2.62520i | 0.265186i | ||||||||
\(99\) | −1.15189 | −0.115769 | ||||||||
\(100\) | 4.96466 | − | 0.593460i | 0.496466 | − | 0.0593460i | ||||
\(101\) | 6.54373i | 0.651125i | 0.945520 | + | 0.325563i | \(0.105554\pi\) | ||||
−0.945520 | + | 0.325563i | \(0.894446\pi\) | |||||||
\(102\) | 3.97457 | + | 3.97457i | 0.393541 | + | 0.393541i | ||||
\(103\) | 2.35550i | 0.232094i | 0.993244 | + | 0.116047i | \(0.0370224\pi\) | ||||
−0.993244 | + | 0.116047i | \(0.962978\pi\) | |||||||
\(104\) | −2.88999 | −0.283387 | ||||||||
\(105\) | −0.278051 | − | 4.66869i | −0.0271350 | − | 0.455618i | ||||
\(106\) | −4.27233 | − | 4.27233i | −0.414965 | − | 0.414965i | ||||
\(107\) | −6.74914 | + | 6.74914i | −0.652464 | + | 0.652464i | −0.953586 | − | 0.301122i | \(-0.902639\pi\) |
0.301122 | + | 0.953586i | \(0.402639\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | −1.88769 | − | 1.88769i | −0.180808 | − | 0.180808i | 0.610900 | − | 0.791708i | \(-0.290808\pi\) |
−0.791708 | + | 0.610900i | \(0.790808\pi\) | |||||||
\(110\) | 0.153128 | + | 2.57114i | 0.0146002 | + | 0.245149i | ||||
\(111\) | 0.635924 | − | 6.04943i | 0.0603592 | − | 0.574186i | ||||
\(112\) | 1.47899 | − | 1.47899i | 0.139751 | − | 0.139751i | ||||
\(113\) | 17.4956i | 1.64585i | 0.568153 | + | 0.822923i | \(0.307658\pi\) | ||||
−0.568153 | + | 0.822923i | \(0.692342\pi\) | |||||||
\(114\) | 1.87036 | 0.175175 | ||||||||
\(115\) | 6.03914 | − | 0.359670i | 0.563153 | − | 0.0335394i | ||||
\(116\) | 6.59907 | − | 6.59907i | 0.612708 | − | 0.612708i | ||||
\(117\) | 2.88999i | 0.267180i | ||||||||
\(118\) | −7.37461 | − | 7.37461i | −0.678888 | − | 0.678888i | ||||
\(119\) | −8.31322 | − | 8.31322i | −0.762072 | − | 0.762072i | ||||
\(120\) | 1.48434 | − | 1.67234i | 0.135501 | − | 0.152663i | ||||
\(121\) | 9.67316 | 0.879378 | ||||||||
\(122\) | 0.721634 | + | 0.721634i | 0.0653337 | + | 0.0653337i | ||||
\(123\) | 4.83935 | + | 4.83935i | 0.436350 | + | 0.436350i | ||||
\(124\) | −0.920380 | − | 0.920380i | −0.0826526 | − | 0.0826526i | ||||
\(125\) | −11.0028 | + | 1.98466i | −0.984118 | + | 0.177513i | ||||
\(126\) | −1.47899 | − | 1.47899i | −0.131759 | − | 0.131759i | ||||
\(127\) | 0.311708 | − | 0.311708i | 0.0276596 | − | 0.0276596i | −0.693142 | − | 0.720801i | \(-0.743774\pi\) |
0.720801 | + | 0.693142i | \(0.243774\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −6.31187 | + | 6.31187i | −0.555729 | + | 0.555729i | ||||
\(130\) | 6.45079 | − | 0.384187i | 0.565772 | − | 0.0336954i | ||||
\(131\) | 12.4801 | + | 12.4801i | 1.09039 | + | 1.09039i | 0.995486 | + | 0.0949069i | \(0.0302553\pi\) |
0.0949069 | + | 0.995486i | \(0.469745\pi\) | |||||||
\(132\) | 0.814507 | + | 0.814507i | 0.0708937 | + | 0.0708937i | ||||
\(133\) | −3.91204 | −0.339217 | ||||||||
\(134\) | −4.32408 | − | 4.32408i | −0.373544 | − | 0.373544i | ||||
\(135\) | −1.67234 | − | 1.48434i | −0.143932 | − | 0.127752i | ||||
\(136\) | − | 5.62089i | − | 0.481988i | ||||||
\(137\) | −11.8735 | + | 11.8735i | −1.01442 | + | 1.01442i | −0.0145281 | + | 0.999894i | \(0.504625\pi\) |
−0.999894 | + | 0.0145281i | \(0.995375\pi\) | |||||||
\(138\) | 1.91313 | − | 1.91313i | 0.162856 | − | 0.162856i | ||||
\(139\) | −15.6010 | −1.32326 | −0.661629 | − | 0.749832i | \(-0.730134\pi\) | ||||
−0.661629 | + | 0.749832i | \(0.730134\pi\) | |||||||
\(140\) | −3.10465 | + | 3.49787i | −0.262391 | + | 0.295624i | ||||
\(141\) | 8.26009i | 0.695625i | ||||||||
\(142\) | −4.66092 | −0.391136 | ||||||||
\(143\) | 3.32894i | 0.278380i | ||||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −13.8526 | + | 15.6071i | −1.15040 | + | 1.29610i | ||||
\(146\) | 0.815358 | − | 0.815358i | 0.0674795 | − | 0.0674795i | ||||
\(147\) | −1.85630 | − | 1.85630i | −0.153105 | − | 0.153105i | ||||
\(148\) | −4.72726 | + | 3.82793i | −0.388578 | + | 0.314654i | ||||
\(149\) | 4.64148i | 0.380245i | 0.981760 | + | 0.190122i | \(0.0608885\pi\) | ||||
−0.981760 | + | 0.190122i | \(0.939111\pi\) | |||||||
\(150\) | −3.09090 | + | 3.93018i | −0.252371 | + | 0.320898i | ||||
\(151\) | 14.5106i | 1.18086i | 0.807090 | + | 0.590429i | \(0.201041\pi\) | ||||
−0.807090 | + | 0.590429i | \(0.798959\pi\) | |||||||
\(152\) | −1.32254 | − | 1.32254i | −0.107272 | − | 0.107272i | ||||
\(153\) | −5.62089 | −0.454422 | ||||||||
\(154\) | −1.70362 | − | 1.70362i | −0.137282 | − | 0.137282i | ||||
\(155\) | 2.17675 | + | 1.93204i | 0.174840 | + | 0.155185i | ||||
\(156\) | 2.04353 | − | 2.04353i | 0.163614 | − | 0.163614i | ||||
\(157\) | −13.1125 | + | 13.1125i | −1.04649 | + | 1.04649i | −0.0476223 | + | 0.998865i | \(0.515164\pi\) |
−0.998865 | + | 0.0476223i | \(0.984836\pi\) | |||||||
\(158\) | 11.8987 | + | 11.8987i | 0.946612 | + | 0.946612i | ||||
\(159\) | 6.04199 | 0.479161 | ||||||||
\(160\) | −2.23211 | + | 0.132937i | −0.176464 | + | 0.0105096i | ||||
\(161\) | −4.00150 | + | 4.00150i | −0.315363 | + | 0.315363i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | − | 8.81029i | − | 0.690076i | −0.938589 | − | 0.345038i | \(-0.887866\pi\) | ||
0.938589 | − | 0.345038i | \(-0.112134\pi\) | |||||||
\(164\) | − | 6.84388i | − | 0.534417i | ||||||
\(165\) | −1.92635 | − | 1.70979i | −0.149966 | − | 0.133107i | ||||
\(166\) | −5.88898 | − | 5.88898i | −0.457073 | − | 0.457073i | ||||
\(167\) | − | 13.2859i | − | 1.02809i | −0.857763 | − | 0.514046i | \(-0.828146\pi\) | ||
0.857763 | − | 0.514046i | \(-0.171854\pi\) | |||||||
\(168\) | 2.09160i | 0.161371i | ||||||||
\(169\) | −4.64793 | −0.357533 | ||||||||
\(170\) | 0.747224 | + | 12.5465i | 0.0573094 | + | 0.962270i | ||||
\(171\) | −1.32254 | + | 1.32254i | −0.101137 | + | 0.101137i | ||||
\(172\) | 8.92633 | 0.680626 | ||||||||
\(173\) | −16.3729 | + | 16.3729i | −1.24481 | + | 1.24481i | −0.286822 | + | 0.957984i | \(0.592599\pi\) |
−0.957984 | + | 0.286822i | \(0.907401\pi\) | |||||||
\(174\) | 9.33249i | 0.707495i | ||||||||
\(175\) | 6.46494 | − | 8.22037i | 0.488703 | − | 0.621402i | ||||
\(176\) | − | 1.15189i | − | 0.0868267i | ||||||
\(177\) | 10.4293 | 0.783912 | ||||||||
\(178\) | 6.87434 | − | 6.87434i | 0.515253 | − | 0.515253i | ||||
\(179\) | 6.39446 | − | 6.39446i | 0.477945 | − | 0.477945i | −0.426529 | − | 0.904474i | \(-0.640264\pi\) |
0.904474 | + | 0.426529i | \(0.140264\pi\) | |||||||
\(180\) | 0.132937 | + | 2.23211i | 0.00990853 | + | 0.166372i | ||||
\(181\) | 7.94042 | 0.590206 | 0.295103 | − | 0.955465i | \(-0.404646\pi\) | ||||
0.295103 | + | 0.955465i | \(0.404646\pi\) | |||||||
\(182\) | −4.27426 | + | 4.27426i | −0.316829 | + | 0.316829i | ||||
\(183\) | −1.02055 | −0.0754409 | ||||||||
\(184\) | −2.70557 | −0.199457 | ||||||||
\(185\) | 10.0429 | − | 9.17279i | 0.738369 | − | 0.674397i | ||||
\(186\) | 1.30161 | 0.0954390 | ||||||||
\(187\) | −6.47463 | −0.473472 | ||||||||
\(188\) | 5.84077 | − | 5.84077i | 0.425982 | − | 0.425982i | ||||
\(189\) | 2.09160 | 0.152142 | ||||||||
\(190\) | 3.12787 | + | 2.77625i | 0.226920 | + | 0.201410i | ||||
\(191\) | 17.8463 | − | 17.8463i | 1.29131 | − | 1.29131i | 0.357332 | − | 0.933977i | \(-0.383686\pi\) |
0.933977 | − | 0.357332i | \(-0.116314\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 5.07031 | 0.364969 | 0.182485 | − | 0.983209i | \(-0.441586\pi\) | ||||
0.182485 | + | 0.983209i | \(0.441586\pi\) | |||||||
\(194\) | − | 14.2915i | − | 1.02607i | ||||||
\(195\) | −4.28974 | + | 4.83306i | −0.307195 | + | 0.346103i | ||||
\(196\) | 2.62520i | 0.187514i | ||||||||
\(197\) | −11.3573 | + | 11.3573i | −0.809177 | + | 0.809177i | −0.984509 | − | 0.175332i | \(-0.943900\pi\) |
0.175332 | + | 0.984509i | \(0.443900\pi\) | |||||||
\(198\) | −1.15189 | −0.0818610 | ||||||||
\(199\) | 12.7174 | − | 12.7174i | 0.901511 | − | 0.901511i | −0.0940562 | − | 0.995567i | \(-0.529983\pi\) |
0.995567 | + | 0.0940562i | \(0.0299833\pi\) | |||||||
\(200\) | 4.96466 | − | 0.593460i | 0.351054 | − | 0.0419640i | ||||
\(201\) | 6.11518 | 0.431331 | ||||||||
\(202\) | 6.54373i | 0.460415i | ||||||||
\(203\) | − | 19.5199i | − | 1.37003i | ||||||
\(204\) | 3.97457 | + | 3.97457i | 0.278276 | + | 0.278276i | ||||
\(205\) | 0.909804 | + | 15.2763i | 0.0635435 | + | 1.06694i | ||||
\(206\) | 2.35550i | 0.164116i | ||||||||
\(207\) | 2.70557i | 0.188050i | ||||||||
\(208\) | −2.88999 | −0.200385 | ||||||||
\(209\) | −1.52342 | + | 1.52342i | −0.105377 | + | 0.105377i | ||||
\(210\) | −0.278051 | − | 4.66869i | −0.0191873 | − | 0.322170i | ||||
\(211\) | 21.8632 | 1.50512 | 0.752562 | − | 0.658521i | \(-0.228818\pi\) | ||||
0.752562 | + | 0.658521i | \(0.228818\pi\) | |||||||
\(212\) | −4.27233 | − | 4.27233i | −0.293425 | − | 0.293425i | ||||
\(213\) | 3.29577 | − | 3.29577i | 0.225823 | − | 0.225823i | ||||
\(214\) | −6.74914 | + | 6.74914i | −0.461361 | + | 0.461361i | ||||
\(215\) | −19.9246 | + | 1.18664i | −1.35885 | + | 0.0809281i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | −2.72246 | −0.184813 | ||||||||
\(218\) | −1.88769 | − | 1.88769i | −0.127851 | − | 0.127851i | ||||
\(219\) | 1.15309i | 0.0779186i | ||||||||
\(220\) | 0.153128 | + | 2.57114i | 0.0103239 | + | 0.173346i | ||||
\(221\) | 16.2443i | 1.09271i | ||||||||
\(222\) | 0.635924 | − | 6.04943i | 0.0426804 | − | 0.406011i | ||||
\(223\) | −9.79908 | − | 9.79908i | −0.656195 | − | 0.656195i | 0.298283 | − | 0.954478i | \(-0.403586\pi\) |
−0.954478 | + | 0.298283i | \(0.903586\pi\) | |||||||
\(224\) | 1.47899 | − | 1.47899i | 0.0988189 | − | 0.0988189i | ||||
\(225\) | −0.593460 | − | 4.96466i | −0.0395640 | − | 0.330977i | ||||
\(226\) | 17.4956i | 1.16379i | ||||||||
\(227\) | − | 12.4848i | − | 0.828645i | −0.910130 | − | 0.414322i | \(-0.864019\pi\) | ||
0.910130 | − | 0.414322i | \(-0.135981\pi\) | |||||||
\(228\) | 1.87036 | 0.123867 | ||||||||
\(229\) | 4.90899i | 0.324395i | 0.986758 | + | 0.162197i | \(0.0518582\pi\) | ||||
−0.986758 | + | 0.162197i | \(0.948142\pi\) | |||||||
\(230\) | 6.03914 | − | 0.359670i | 0.398209 | − | 0.0237160i | ||||
\(231\) | 2.40929 | 0.158519 | ||||||||
\(232\) | 6.59907 | − | 6.59907i | 0.433250 | − | 0.433250i | ||||
\(233\) | −6.62951 | + | 6.62951i | −0.434313 | + | 0.434313i | −0.890093 | − | 0.455779i | \(-0.849361\pi\) |
0.455779 | + | 0.890093i | \(0.349361\pi\) | |||||||
\(234\) | 2.88999i | 0.188925i | ||||||||
\(235\) | −12.2608 | + | 13.8137i | −0.799806 | + | 0.901106i | ||||
\(236\) | −7.37461 | − | 7.37461i | −0.480046 | − | 0.480046i | ||||
\(237\) | −16.8273 | −1.09305 | ||||||||
\(238\) | −8.31322 | − | 8.31322i | −0.538866 | − | 0.538866i | ||||
\(239\) | −14.4055 | − | 14.4055i | −0.931817 | − | 0.931817i | 0.0660028 | − | 0.997819i | \(-0.478975\pi\) |
−0.997819 | + | 0.0660028i | \(0.978975\pi\) | |||||||
\(240\) | 1.48434 | − | 1.67234i | 0.0958138 | − | 0.107949i | ||||
\(241\) | −5.83291 | + | 5.83291i | −0.375731 | + | 0.375731i | −0.869559 | − | 0.493829i | \(-0.835597\pi\) |
0.493829 | + | 0.869559i | \(0.335597\pi\) | |||||||
\(242\) | 9.67316 | 0.621814 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0.721634 | + | 0.721634i | 0.0461979 | + | 0.0461979i | ||||
\(245\) | −0.348986 | − | 5.85975i | −0.0222959 | − | 0.374366i | ||||
\(246\) | 4.83935 | + | 4.83935i | 0.308546 | + | 0.308546i | ||||
\(247\) | 3.82214 | + | 3.82214i | 0.243197 | + | 0.243197i | ||||
\(248\) | −0.920380 | − | 0.920380i | −0.0584442 | − | 0.0584442i | ||||
\(249\) | 8.32827 | 0.527783 | ||||||||
\(250\) | −11.0028 | + | 1.98466i | −0.695877 | + | 0.125521i | ||||
\(251\) | 12.0063 | + | 12.0063i | 0.757830 | + | 0.757830i | 0.975927 | − | 0.218097i | \(-0.0699848\pi\) |
−0.218097 | + | 0.975927i | \(0.569985\pi\) | |||||||
\(252\) | −1.47899 | − | 1.47899i | −0.0931673 | − | 0.0931673i | ||||
\(253\) | 3.11651i | 0.195933i | ||||||||
\(254\) | 0.311708 | − | 0.311708i | 0.0195583 | − | 0.0195583i | ||||
\(255\) | −9.40006 | − | 8.34333i | −0.588655 | − | 0.522479i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 8.79481i | − | 0.548605i | −0.961643 | − | 0.274303i | \(-0.911553\pi\) | ||
0.961643 | − | 0.274303i | \(-0.0884470\pi\) | |||||||
\(258\) | −6.31187 | + | 6.31187i | −0.392960 | + | 0.392960i | ||||
\(259\) | −1.33010 | + | 12.6530i | −0.0826483 | + | 0.786219i | ||||
\(260\) | 6.45079 | − | 0.384187i | 0.400061 | − | 0.0238262i | ||||
\(261\) | −6.59907 | − | 6.59907i | −0.408472 | − | 0.408472i | ||||
\(262\) | 12.4801 | + | 12.4801i | 0.771024 | + | 0.771024i | ||||
\(263\) | 4.85857 | − | 4.85857i | 0.299592 | − | 0.299592i | −0.541262 | − | 0.840854i | \(-0.682053\pi\) |
0.840854 | + | 0.541262i | \(0.182053\pi\) | |||||||
\(264\) | 0.814507 | + | 0.814507i | 0.0501294 | + | 0.0501294i | ||||
\(265\) | 10.1043 | + | 8.96837i | 0.620701 | + | 0.550923i | ||||
\(266\) | −3.91204 | −0.239862 | ||||||||
\(267\) | 9.72178i | 0.594963i | ||||||||
\(268\) | −4.32408 | − | 4.32408i | −0.264135 | − | 0.264135i | ||||
\(269\) | 10.8073i | 0.658933i | 0.944167 | + | 0.329466i | \(0.106869\pi\) | ||||
−0.944167 | + | 0.329466i | \(0.893131\pi\) | |||||||
\(270\) | −1.67234 | − | 1.48434i | −0.101776 | − | 0.0903342i | ||||
\(271\) | 20.9907 | 1.27509 | 0.637547 | − | 0.770411i | \(-0.279949\pi\) | ||||
0.637547 | + | 0.770411i | \(0.279949\pi\) | |||||||
\(272\) | − | 5.62089i | − | 0.340817i | ||||||
\(273\) | − | 6.04472i | − | 0.365843i | ||||||
\(274\) | −11.8735 | + | 11.8735i | −0.717305 | + | 0.717305i | ||||
\(275\) | −0.683599 | − | 5.71872i | −0.0412225 | − | 0.344852i | ||||
\(276\) | 1.91313 | − | 1.91313i | 0.115157 | − | 0.115157i | ||||
\(277\) | −2.34619 | −0.140969 | −0.0704844 | − | 0.997513i | \(-0.522455\pi\) | ||||
−0.0704844 | + | 0.997513i | \(0.522455\pi\) | |||||||
\(278\) | −15.6010 | −0.935684 | ||||||||
\(279\) | −0.920380 | + | 0.920380i | −0.0551017 | + | 0.0551017i | ||||
\(280\) | −3.10465 | + | 3.49787i | −0.185538 | + | 0.209038i | ||||
\(281\) | 12.4830 | − | 12.4830i | 0.744674 | − | 0.744674i | −0.228800 | − | 0.973474i | \(-0.573480\pi\) |
0.973474 | + | 0.228800i | \(0.0734800\pi\) | |||||||
\(282\) | 8.26009i | 0.491881i | ||||||||
\(283\) | 4.16867i | 0.247802i | 0.992295 | + | 0.123901i | \(0.0395405\pi\) | ||||
−0.992295 | + | 0.123901i | \(0.960460\pi\) | |||||||
\(284\) | −4.66092 | −0.276575 | ||||||||
\(285\) | −4.17484 | + | 0.248639i | −0.247296 | + | 0.0147281i | ||||
\(286\) | 3.32894i | 0.196845i | ||||||||
\(287\) | −10.1220 | − | 10.1220i | −0.597483 | − | 0.597483i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −14.5944 | −0.858496 | ||||||||
\(290\) | −13.8526 | + | 15.6071i | −0.813453 | + | 0.916482i | ||||
\(291\) | 10.1056 | + | 10.1056i | 0.592400 | + | 0.592400i | ||||
\(292\) | 0.815358 | − | 0.815358i | 0.0477152 | − | 0.0477152i | ||||
\(293\) | 3.92862 | + | 3.92862i | 0.229513 | + | 0.229513i | 0.812489 | − | 0.582976i | \(-0.198112\pi\) |
−0.582976 | + | 0.812489i | \(0.698112\pi\) | |||||||
\(294\) | −1.85630 | − | 1.85630i | −0.108262 | − | 0.108262i | ||||
\(295\) | 17.4413 | + | 15.4806i | 1.01547 | + | 0.901315i | ||||
\(296\) | −4.72726 | + | 3.82793i | −0.274766 | + | 0.222494i | ||||
\(297\) | 0.814507 | − | 0.814507i | 0.0472625 | − | 0.0472625i | ||||
\(298\) | 4.64148i | 0.268874i | ||||||||
\(299\) | 7.81909 | 0.452190 | ||||||||
\(300\) | −3.09090 | + | 3.93018i | −0.178453 | + | 0.226909i | ||||
\(301\) | 13.2019 | − | 13.2019i | 0.760946 | − | 0.760946i | ||||
\(302\) | 14.5106i | 0.834993i | ||||||||
\(303\) | −4.62711 | − | 4.62711i | −0.265821 | − | 0.265821i | ||||
\(304\) | −1.32254 | − | 1.32254i | −0.0758529 | − | 0.0758529i | ||||
\(305\) | −1.70670 | − | 1.51484i | −0.0977254 | − | 0.0867394i | ||||
\(306\) | −5.62089 | −0.321325 | ||||||||
\(307\) | −0.507816 | − | 0.507816i | −0.0289826 | − | 0.0289826i | 0.692467 | − | 0.721450i | \(-0.256524\pi\) |
−0.721450 | + | 0.692467i | \(0.756524\pi\) | |||||||
\(308\) | −1.70362 | − | 1.70362i | −0.0970729 | − | 0.0970729i | ||||
\(309\) | −1.66559 | − | 1.66559i | −0.0947522 | − | 0.0947522i | ||||
\(310\) | 2.17675 | + | 1.93204i | 0.123631 | + | 0.109733i | ||||
\(311\) | −0.433905 | − | 0.433905i | −0.0246045 | − | 0.0246045i | 0.694697 | − | 0.719302i | \(-0.255538\pi\) |
−0.719302 | + | 0.694697i | \(0.755538\pi\) | |||||||
\(312\) | 2.04353 | − | 2.04353i | 0.115692 | − | 0.115692i | ||||
\(313\) | 18.8073 | 1.06305 | 0.531526 | − | 0.847042i | \(-0.321619\pi\) | ||||
0.531526 | + | 0.847042i | \(0.321619\pi\) | |||||||
\(314\) | −13.1125 | + | 13.1125i | −0.739979 | + | 0.739979i | ||||
\(315\) | 3.49787 | + | 3.10465i | 0.197083 | + | 0.174927i | ||||
\(316\) | 11.8987 | + | 11.8987i | 0.669356 | + | 0.669356i | ||||
\(317\) | 11.5222 | + | 11.5222i | 0.647149 | + | 0.647149i | 0.952303 | − | 0.305154i | \(-0.0987080\pi\) |
−0.305154 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(318\) | 6.04199 | 0.338818 | ||||||||
\(319\) | −7.60138 | − | 7.60138i | −0.425596 | − | 0.425596i | ||||
\(320\) | −2.23211 | + | 0.132937i | −0.124779 | + | 0.00743140i | ||||
\(321\) | − | 9.54472i | − | 0.532734i | ||||||
\(322\) | −4.00150 | + | 4.00150i | −0.222995 | + | 0.222995i | ||||
\(323\) | −7.43386 | + | 7.43386i | −0.413631 | + | 0.413631i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −14.3478 | + | 1.71510i | −0.795874 | + | 0.0951364i | ||||
\(326\) | − | 8.81029i | − | 0.487957i | ||||||
\(327\) | 2.66960 | 0.147629 | ||||||||
\(328\) | − | 6.84388i | − | 0.377890i | ||||||
\(329\) | − | 17.2768i | − | 0.952502i | ||||||
\(330\) | −1.92635 | − | 1.70979i | −0.106042 | − | 0.0941210i | ||||
\(331\) | −7.39172 | + | 7.39172i | −0.406286 | + | 0.406286i | −0.880441 | − | 0.474155i | \(-0.842753\pi\) |
0.474155 | + | 0.880441i | \(0.342753\pi\) | |||||||
\(332\) | −5.88898 | − | 5.88898i | −0.323199 | − | 0.323199i | ||||
\(333\) | 3.82793 | + | 4.72726i | 0.209769 | + | 0.259052i | ||||
\(334\) | − | 13.2859i | − | 0.726971i | ||||||
\(335\) | 10.2267 | + | 9.07701i | 0.558743 | + | 0.495930i | ||||
\(336\) | 2.09160i | 0.114106i | ||||||||
\(337\) | −4.90709 | − | 4.90709i | −0.267306 | − | 0.267306i | 0.560708 | − | 0.828014i | \(-0.310529\pi\) |
−0.828014 | + | 0.560708i | \(0.810529\pi\) | |||||||
\(338\) | −4.64793 | −0.252814 | ||||||||
\(339\) | −12.3712 | − | 12.3712i | −0.671914 | − | 0.671914i | ||||
\(340\) | 0.747224 | + | 12.5465i | 0.0405239 | + | 0.680428i | ||||
\(341\) | −1.06017 | + | 1.06017i | −0.0574116 | + | 0.0574116i | ||||
\(342\) | −1.32254 | + | 1.32254i | −0.0715148 | + | 0.0715148i | ||||
\(343\) | 14.2355 | + | 14.2355i | 0.768647 | + | 0.768647i | ||||
\(344\) | 8.92633 | 0.481276 | ||||||||
\(345\) | −4.01599 | + | 4.52464i | −0.216214 | + | 0.243599i | ||||
\(346\) | −16.3729 | + | 16.3729i | −0.880211 | + | 0.880211i | ||||
\(347\) | 5.47655 | 0.293997 | 0.146998 | − | 0.989137i | \(-0.453039\pi\) | ||||
0.146998 | + | 0.989137i | \(0.453039\pi\) | |||||||
\(348\) | 9.33249i | 0.500274i | ||||||||
\(349\) | 17.9938i | 0.963188i | 0.876394 | + | 0.481594i | \(0.159942\pi\) | ||||
−0.876394 | + | 0.481594i | \(0.840058\pi\) | |||||||
\(350\) | 6.46494 | − | 8.22037i | 0.345565 | − | 0.439397i | ||||
\(351\) | −2.04353 | − | 2.04353i | −0.109076 | − | 0.109076i | ||||
\(352\) | − | 1.15189i | − | 0.0613957i | ||||||
\(353\) | 0.511524i | 0.0272257i | 0.999907 | + | 0.0136128i | \(0.00433324\pi\) | ||||
−0.999907 | + | 0.0136128i | \(0.995667\pi\) | |||||||
\(354\) | 10.4293 | 0.554309 | ||||||||
\(355\) | 10.4037 | − | 0.619609i | 0.552172 | − | 0.0328854i | ||||
\(356\) | 6.87434 | − | 6.87434i | 0.364339 | − | 0.364339i | ||||
\(357\) | 11.7567 | 0.622229 | ||||||||
\(358\) | 6.39446 | − | 6.39446i | 0.337958 | − | 0.337958i | ||||
\(359\) | − | 30.4736i | − | 1.60833i | −0.594403 | − | 0.804167i | \(-0.702612\pi\) | ||
0.594403 | − | 0.804167i | \(-0.297388\pi\) | |||||||
\(360\) | 0.132937 | + | 2.23211i | 0.00700639 | + | 0.117643i | ||||
\(361\) | − | 15.5018i | − | 0.815883i | ||||||
\(362\) | 7.94042 | 0.417339 | ||||||||
\(363\) | −6.83996 | + | 6.83996i | −0.359005 | + | 0.359005i | ||||
\(364\) | −4.27426 | + | 4.27426i | −0.224032 | + | 0.224032i | ||||
\(365\) | −1.71158 | + | 1.92836i | −0.0895882 | + | 0.100935i | ||||
\(366\) | −1.02055 | −0.0533448 | ||||||||
\(367\) | 1.10113 | − | 1.10113i | 0.0574786 | − | 0.0574786i | −0.677783 | − | 0.735262i | \(-0.737059\pi\) |
0.735262 | + | 0.677783i | \(0.237059\pi\) | |||||||
\(368\) | −2.70557 | −0.141038 | ||||||||
\(369\) | −6.84388 | −0.356278 | ||||||||
\(370\) | 10.0429 | − | 9.17279i | 0.522106 | − | 0.476871i | ||||
\(371\) | −12.6374 | −0.656103 | ||||||||
\(372\) | 1.30161 | 0.0674856 | ||||||||
\(373\) | 13.3085 | − | 13.3085i | 0.689088 | − | 0.689088i | −0.272943 | − | 0.962030i | \(-0.587997\pi\) |
0.962030 | + | 0.272943i | \(0.0879969\pi\) | |||||||
\(374\) | −6.47463 | −0.334795 | ||||||||
\(375\) | 6.37678 | − | 9.18350i | 0.329295 | − | 0.474234i | ||||
\(376\) | 5.84077 | − | 5.84077i | 0.301214 | − | 0.301214i | ||||
\(377\) | −19.0713 | + | 19.0713i | −0.982221 | + | 0.982221i | ||||
\(378\) | 2.09160 | 0.107580 | ||||||||
\(379\) | − | 31.3641i | − | 1.61107i | −0.592551 | − | 0.805533i | \(-0.701879\pi\) | ||
0.592551 | − | 0.805533i | \(-0.298121\pi\) | |||||||
\(380\) | 3.12787 | + | 2.77625i | 0.160457 | + | 0.142418i | ||||
\(381\) | 0.440822i | 0.0225840i | ||||||||
\(382\) | 17.8463 | − | 17.8463i | 0.913094 | − | 0.913094i | ||||
\(383\) | 7.04860 | 0.360167 | 0.180083 | − | 0.983651i | \(-0.442363\pi\) | ||||
0.180083 | + | 0.983651i | \(0.442363\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 4.02915 | + | 3.57621i | 0.205345 | + | 0.182260i | ||||
\(386\) | 5.07031 | 0.258072 | ||||||||
\(387\) | − | 8.92633i | − | 0.453751i | ||||||
\(388\) | − | 14.2915i | − | 0.725539i | ||||||
\(389\) | 18.3786 | + | 18.3786i | 0.931831 | + | 0.931831i | 0.997820 | − | 0.0659891i | \(-0.0210202\pi\) |
−0.0659891 | + | 0.997820i | \(0.521020\pi\) | |||||||
\(390\) | −4.28974 | + | 4.83306i | −0.217219 | + | 0.244732i | ||||
\(391\) | 15.2077i | 0.769088i | ||||||||
\(392\) | 2.62520i | 0.132593i | ||||||||
\(393\) | −17.6496 | −0.890302 | ||||||||
\(394\) | −11.3573 | + | 11.3573i | −0.572175 | + | 0.572175i | ||||
\(395\) | −28.1411 | − | 24.9775i | −1.41593 | − | 1.25676i | ||||
\(396\) | −1.15189 | −0.0578845 | ||||||||
\(397\) | 11.4488 | + | 11.4488i | 0.574601 | + | 0.574601i | 0.933411 | − | 0.358810i | \(-0.116817\pi\) |
−0.358810 | + | 0.933411i | \(0.616817\pi\) | |||||||
\(398\) | 12.7174 | − | 12.7174i | 0.637464 | − | 0.637464i | ||||
\(399\) | 2.76623 | − | 2.76623i | 0.138485 | − | 0.138485i | ||||
\(400\) | 4.96466 | − | 0.593460i | 0.248233 | − | 0.0296730i | ||||
\(401\) | −14.1357 | − | 14.1357i | −0.705906 | − | 0.705906i | 0.259766 | − | 0.965672i | \(-0.416355\pi\) |
−0.965672 | + | 0.259766i | \(0.916355\pi\) | |||||||
\(402\) | 6.11518 | 0.304997 | ||||||||
\(403\) | 2.65989 | + | 2.65989i | 0.132499 | + | 0.132499i | ||||
\(404\) | 6.54373i | 0.325563i | ||||||||
\(405\) | 2.23211 | − | 0.132937i | 0.110915 | − | 0.00660568i | ||||
\(406\) | − | 19.5199i | − | 0.968754i | ||||||
\(407\) | 4.40934 | + | 5.44526i | 0.218563 | + | 0.269912i | ||||
\(408\) | 3.97457 | + | 3.97457i | 0.196771 | + | 0.196771i | ||||
\(409\) | −20.4751 | + | 20.4751i | −1.01243 | + | 1.01243i | −0.0125077 | + | 0.999922i | \(0.503981\pi\) |
−0.999922 | + | 0.0125077i | \(0.996019\pi\) | |||||||
\(410\) | 0.909804 | + | 15.2763i | 0.0449320 | + | 0.754443i | ||||
\(411\) | − | 16.7917i | − | 0.828273i | ||||||
\(412\) | 2.35550i | 0.116047i | ||||||||
\(413\) | −21.8139 | −1.07339 | ||||||||
\(414\) | 2.70557i | 0.132972i | ||||||||
\(415\) | 13.9277 | + | 12.3620i | 0.683685 | + | 0.606826i | ||||
\(416\) | −2.88999 | −0.141694 | ||||||||
\(417\) | 11.0316 | − | 11.0316i | 0.540218 | − | 0.540218i | ||||
\(418\) | −1.52342 | + | 1.52342i | −0.0745127 | + | 0.0745127i | ||||
\(419\) | − | 16.7209i | − | 0.816870i | −0.912787 | − | 0.408435i | \(-0.866075\pi\) | ||
0.912787 | − | 0.408435i | \(-0.133925\pi\) | |||||||
\(420\) | −0.278051 | − | 4.66869i | −0.0135675 | − | 0.227809i | ||||
\(421\) | 22.8919 | + | 22.8919i | 1.11569 | + | 1.11569i | 0.992367 | + | 0.123318i | \(0.0393535\pi\) |
0.123318 | + | 0.992367i | \(0.460647\pi\) | |||||||
\(422\) | 21.8632 | 1.06428 | ||||||||
\(423\) | −5.84077 | − | 5.84077i | −0.283988 | − | 0.283988i | ||||
\(424\) | −4.27233 | − | 4.27233i | −0.207483 | − | 0.207483i | ||||
\(425\) | −3.33578 | − | 27.9058i | −0.161809 | − | 1.35363i | ||||
\(426\) | 3.29577 | − | 3.29577i | 0.159681 | − | 0.159681i | ||||
\(427\) | 2.13457 | 0.103299 | ||||||||
\(428\) | −6.74914 | + | 6.74914i | −0.326232 | + | 0.326232i | ||||
\(429\) | −2.35392 | − | 2.35392i | −0.113648 | − | 0.113648i | ||||
\(430\) | −19.9246 | + | 1.18664i | −0.960849 | + | 0.0572248i | ||||
\(431\) | −5.61789 | − | 5.61789i | −0.270604 | − | 0.270604i | 0.558739 | − | 0.829343i | \(-0.311285\pi\) |
−0.829343 | + | 0.558739i | \(0.811285\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 4.80295 | + | 4.80295i | 0.230815 | + | 0.230815i | 0.813033 | − | 0.582218i | \(-0.197815\pi\) |
−0.582218 | + | 0.813033i | \(0.697815\pi\) | |||||||
\(434\) | −2.72246 | −0.130682 | ||||||||
\(435\) | −1.24063 | − | 20.8312i | −0.0594838 | − | 0.998779i | ||||
\(436\) | −1.88769 | − | 1.88769i | −0.0904041 | − | 0.0904041i | ||||
\(437\) | 3.57823 | + | 3.57823i | 0.171170 | + | 0.171170i | ||||
\(438\) | 1.15309i | 0.0550968i | ||||||||
\(439\) | 7.82626 | − | 7.82626i | 0.373527 | − | 0.373527i | −0.495233 | − | 0.868760i | \(-0.664917\pi\) |
0.868760 | + | 0.495233i | \(0.164917\pi\) | |||||||
\(440\) | 0.153128 | + | 2.57114i | 0.00730010 | + | 0.122574i | ||||
\(441\) | 2.62520 | 0.125010 | ||||||||
\(442\) | 16.2443i | 0.772665i | ||||||||
\(443\) | 13.6322 | − | 13.6322i | 0.647683 | − | 0.647683i | −0.304749 | − | 0.952433i | \(-0.598573\pi\) |
0.952433 | + | 0.304749i | \(0.0985727\pi\) | |||||||
\(444\) | 0.635924 | − | 6.04943i | 0.0301796 | − | 0.287093i | ||||
\(445\) | −14.4304 | + | 16.2582i | −0.684069 | + | 0.770710i | ||||
\(446\) | −9.79908 | − | 9.79908i | −0.464000 | − | 0.464000i | ||||
\(447\) | −3.28202 | − | 3.28202i | −0.155234 | − | 0.155234i | ||||
\(448\) | 1.47899 | − | 1.47899i | 0.0698755 | − | 0.0698755i | ||||
\(449\) | 16.5631 | + | 16.5631i | 0.781661 | + | 0.781661i | 0.980111 | − | 0.198450i | \(-0.0635909\pi\) |
−0.198450 | + | 0.980111i | \(0.563591\pi\) | |||||||
\(450\) | −0.593460 | − | 4.96466i | −0.0279760 | − | 0.234036i | ||||
\(451\) | −7.88337 | −0.371214 | ||||||||
\(452\) | 17.4956i | 0.822923i | ||||||||
\(453\) | −10.2606 | − | 10.2606i | −0.482083 | − | 0.482083i | ||||
\(454\) | − | 12.4848i | − | 0.585940i | ||||||
\(455\) | 8.97242 | − | 10.1088i | 0.420634 | − | 0.473910i | ||||
\(456\) | 1.87036 | 0.0875874 | ||||||||
\(457\) | 15.3145i | 0.716381i | 0.933649 | + | 0.358191i | \(0.116606\pi\) | ||||
−0.933649 | + | 0.358191i | \(0.883394\pi\) | |||||||
\(458\) | 4.90899i | 0.229382i | ||||||||
\(459\) | 3.97457 | − | 3.97457i | 0.185517 | − | 0.185517i | ||||
\(460\) | 6.03914 | − | 0.359670i | 0.281576 | − | 0.0167697i | ||||
\(461\) | 25.8489 | − | 25.8489i | 1.20390 | − | 1.20390i | 0.230933 | − | 0.972970i | \(-0.425822\pi\) |
0.972970 | − | 0.230933i | \(-0.0741777\pi\) | |||||||
\(462\) | 2.40929 | 0.112090 | ||||||||
\(463\) | 23.9015 | 1.11080 | 0.555399 | − | 0.831584i | \(-0.312565\pi\) | ||||
0.555399 | + | 0.831584i | \(0.312565\pi\) | |||||||
\(464\) | 6.59907 | − | 6.59907i | 0.306354 | − | 0.306354i | ||||
\(465\) | −2.90535 | + | 0.173033i | −0.134732 | + | 0.00802419i | ||||
\(466\) | −6.62951 | + | 6.62951i | −0.307106 | + | 0.307106i | ||||
\(467\) | − | 7.54639i | − | 0.349205i | −0.984639 | − | 0.174603i | \(-0.944136\pi\) | ||
0.984639 | − | 0.174603i | \(-0.0558641\pi\) | |||||||
\(468\) | 2.88999i | 0.133590i | ||||||||
\(469\) | −12.7905 | −0.590611 | ||||||||
\(470\) | −12.2608 | + | 13.8137i | −0.565548 | + | 0.637179i | ||||
\(471\) | − | 18.5438i | − | 0.854454i | ||||||
\(472\) | −7.37461 | − | 7.37461i | −0.339444 | − | 0.339444i | ||||
\(473\) | − | 10.2821i | − | 0.472772i | ||||||
\(474\) | −16.8273 | −0.772906 | ||||||||
\(475\) | −7.35084 | − | 5.78108i | −0.337279 | − | 0.265254i | ||||
\(476\) | −8.31322 | − | 8.31322i | −0.381036 | − | 0.381036i | ||||
\(477\) | −4.27233 | + | 4.27233i | −0.195617 | + | 0.195617i | ||||
\(478\) | −14.4055 | − | 14.4055i | −0.658894 | − | 0.658894i | ||||
\(479\) | 24.1200 | + | 24.1200i | 1.10207 | + | 1.10207i | 0.994160 | + | 0.107912i | \(0.0344165\pi\) |
0.107912 | + | 0.994160i | \(0.465583\pi\) | |||||||
\(480\) | 1.48434 | − | 1.67234i | 0.0677506 | − | 0.0763317i | ||||
\(481\) | 13.6618 | − | 11.0627i | 0.622922 | − | 0.504415i | ||||
\(482\) | −5.83291 | + | 5.83291i | −0.265682 | + | 0.265682i | ||||
\(483\) | − | 5.65898i | − | 0.257492i | ||||||
\(484\) | 9.67316 | 0.439689 | ||||||||
\(485\) | 1.89986 | + | 31.9002i | 0.0862683 | + | 1.44851i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | 1.74655i | 0.0791437i | 0.999217 | + | 0.0395719i | \(0.0125994\pi\) | ||||
−0.999217 | + | 0.0395719i | \(0.987401\pi\) | |||||||
\(488\) | 0.721634 | + | 0.721634i | 0.0326669 | + | 0.0326669i | ||||
\(489\) | 6.22982 | + | 6.22982i | 0.281722 | + | 0.281722i | ||||
\(490\) | −0.348986 | − | 5.85975i | −0.0157656 | − | 0.264716i | ||||
\(491\) | −6.46050 | −0.291558 | −0.145779 | − | 0.989317i | \(-0.546569\pi\) | ||||
−0.145779 | + | 0.989317i | \(0.546569\pi\) | |||||||
\(492\) | 4.83935 | + | 4.83935i | 0.218175 | + | 0.218175i | ||||
\(493\) | −37.0927 | − | 37.0927i | −1.67057 | − | 1.67057i | ||||
\(494\) | 3.82214 | + | 3.82214i | 0.171966 | + | 0.171966i | ||||
\(495\) | 2.57114 | − | 0.153128i | 0.115564 | − | 0.00688260i | ||||
\(496\) | −0.920380 | − | 0.920380i | −0.0413263 | − | 0.0413263i | ||||
\(497\) | −6.89344 | + | 6.89344i | −0.309213 | + | 0.309213i | ||||
\(498\) | 8.32827 | 0.373199 | ||||||||
\(499\) | 11.4622 | − | 11.4622i | 0.513120 | − | 0.513120i | −0.402361 | − | 0.915481i | \(-0.631810\pi\) |
0.915481 | + | 0.402361i | \(0.131810\pi\) | |||||||
\(500\) | −11.0028 | + | 1.98466i | −0.492059 | + | 0.0887565i | ||||
\(501\) | 9.39453 | + | 9.39453i | 0.419717 | + | 0.419717i | ||||
\(502\) | 12.0063 | + | 12.0063i | 0.535867 | + | 0.535867i | ||||
\(503\) | 14.2394 | 0.634904 | 0.317452 | − | 0.948274i | \(-0.397173\pi\) | ||||
0.317452 | + | 0.948274i | \(0.397173\pi\) | |||||||
\(504\) | −1.47899 | − | 1.47899i | −0.0658793 | − | 0.0658793i | ||||
\(505\) | −0.869903 | − | 14.6063i | −0.0387102 | − | 0.649974i | ||||
\(506\) | 3.11651i | 0.138546i | ||||||||
\(507\) | 3.28658 | − | 3.28658i | 0.145962 | − | 0.145962i | ||||
\(508\) | 0.311708 | − | 0.311708i | 0.0138298 | − | 0.0138298i | ||||
\(509\) | 42.1660 | 1.86897 | 0.934487 | − | 0.355997i | \(-0.115859\pi\) | ||||
0.934487 | + | 0.355997i | \(0.115859\pi\) | |||||||
\(510\) | −9.40006 | − | 8.34333i | −0.416242 | − | 0.369449i | ||||
\(511\) | − | 2.41180i | − | 0.106692i | ||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | − | 1.87036i | − | 0.0825782i | ||||||
\(514\) | − | 8.79481i | − | 0.387923i | ||||||
\(515\) | −0.313133 | − | 5.25775i | −0.0137983 | − | 0.231684i | ||||
\(516\) | −6.31187 | + | 6.31187i | −0.277865 | + | 0.277865i | ||||
\(517\) | −6.72790 | − | 6.72790i | −0.295893 | − | 0.295893i | ||||
\(518\) | −1.33010 | + | 12.6530i | −0.0584412 | + | 0.555941i | ||||
\(519\) | − | 23.1547i | − | 1.01638i | ||||||
\(520\) | 6.45079 | − | 0.384187i | 0.282886 | − | 0.0168477i | ||||
\(521\) | − | 8.55702i | − | 0.374890i | −0.982275 | − | 0.187445i | \(-0.939979\pi\) | ||
0.982275 | − | 0.187445i | \(-0.0600206\pi\) | |||||||
\(522\) | −6.59907 | − | 6.59907i | −0.288833 | − | 0.288833i | ||||
\(523\) | −16.9569 | −0.741473 | −0.370737 | − | 0.928738i | \(-0.620895\pi\) | ||||
−0.370737 | + | 0.928738i | \(0.620895\pi\) | |||||||
\(524\) | 12.4801 | + | 12.4801i | 0.545197 | + | 0.545197i | ||||
\(525\) | 1.24128 | + | 10.3841i | 0.0541740 | + | 0.453198i | ||||
\(526\) | 4.85857 | − | 4.85857i | 0.211844 | − | 0.211844i | ||||
\(527\) | −5.17336 | + | 5.17336i | −0.225355 | + | 0.225355i | ||||
\(528\) | 0.814507 | + | 0.814507i | 0.0354469 | + | 0.0354469i | ||||
\(529\) | −15.6799 | −0.681734 | ||||||||
\(530\) | 10.1043 | + | 8.96837i | 0.438902 | + | 0.389561i | ||||
\(531\) | −7.37461 | + | 7.37461i | −0.320031 | + | 0.320031i | ||||
\(532\) | −3.91204 | −0.169608 | ||||||||
\(533\) | 19.7788i | 0.856714i | ||||||||
\(534\) | 9.72178i | 0.420703i | ||||||||
\(535\) | 14.1676 | − | 15.9620i | 0.612520 | − | 0.690099i | ||||
\(536\) | −4.32408 | − | 4.32408i | −0.186772 | − | 0.186772i | ||||
\(537\) | 9.04314i | 0.390240i | ||||||||
\(538\) | 10.8073i | 0.465936i | ||||||||
\(539\) | 3.02394 | 0.130250 | ||||||||
\(540\) | −1.67234 | − | 1.48434i | −0.0719662 | − | 0.0638759i | ||||
\(541\) | 0.972918 | − | 0.972918i | 0.0418290 | − | 0.0418290i | −0.685883 | − | 0.727712i | \(-0.740584\pi\) |
0.727712 | + | 0.685883i | \(0.240584\pi\) | |||||||
\(542\) | 20.9907 | 0.901628 | ||||||||
\(543\) | −5.61472 | + | 5.61472i | −0.240951 | + | 0.240951i | ||||
\(544\) | − | 5.62089i | − | 0.240994i | ||||||
\(545\) | 4.46449 | + | 3.96260i | 0.191238 | + | 0.169739i | ||||
\(546\) | − | 6.04472i | − | 0.258690i | ||||||
\(547\) | −3.68086 | −0.157382 | −0.0786911 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786911 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(548\) | −11.8735 | + | 11.8735i | −0.507211 | + | 0.507211i | ||||
\(549\) | 0.721634 | − | 0.721634i | 0.0307986 | − | 0.0307986i | ||||
\(550\) | −0.683599 | − | 5.71872i | −0.0291487 | − | 0.243847i | ||||
\(551\) | −17.4551 | −0.743611 | ||||||||
\(552\) | 1.91313 | − | 1.91313i | 0.0814282 | − | 0.0814282i | ||||
\(553\) | 35.1961 | 1.49669 | ||||||||
\(554\) | −2.34619 | −0.0996800 | ||||||||
\(555\) | −0.615261 | + | 13.5875i | −0.0261164 | + | 0.576759i | ||||
\(556\) | −15.6010 | −0.661629 | ||||||||
\(557\) | −33.5711 | −1.42245 | −0.711227 | − | 0.702963i | \(-0.751860\pi\) | ||||
−0.711227 | + | 0.702963i | \(0.751860\pi\) | |||||||
\(558\) | −0.920380 | + | 0.920380i | −0.0389628 | + | 0.0389628i | ||||
\(559\) | −25.7970 | −1.09110 | ||||||||
\(560\) | −3.10465 | + | 3.49787i | −0.131195 | + | 0.147812i | ||||
\(561\) | 4.57825 | − | 4.57825i | 0.193294 | − | 0.193294i | ||||
\(562\) | 12.4830 | − | 12.4830i | 0.526564 | − | 0.526564i | ||||
\(563\) | −15.1872 | −0.640063 | −0.320031 | − | 0.947407i | \(-0.603693\pi\) | ||||
−0.320031 | + | 0.947407i | \(0.603693\pi\) | |||||||
\(564\) | 8.26009i | 0.347813i | ||||||||
\(565\) | −2.32581 | − | 39.0521i | −0.0978475 | − | 1.64294i | ||||
\(566\) | 4.16867i | 0.175222i | ||||||||
\(567\) | −1.47899 | + | 1.47899i | −0.0621116 | + | 0.0621116i | ||||
\(568\) | −4.66092 | −0.195568 | ||||||||
\(569\) | 23.9696 | − | 23.9696i | 1.00486 | − | 1.00486i | 0.00486775 | − | 0.999988i | \(-0.498451\pi\) |
0.999988 | − | 0.00486775i | \(-0.00154946\pi\) | |||||||
\(570\) | −4.17484 | + | 0.248639i | −0.174865 | + | 0.0104143i | ||||
\(571\) | −8.62869 | −0.361100 | −0.180550 | − | 0.983566i | \(-0.557788\pi\) | ||||
−0.180550 | + | 0.983566i | \(0.557788\pi\) | |||||||
\(572\) | 3.32894i | 0.139190i | ||||||||
\(573\) | 25.2384i | 1.05435i | ||||||||
\(574\) | −10.1220 | − | 10.1220i | −0.422484 | − | 0.422484i | ||||
\(575\) | −13.4322 | + | 1.60565i | −0.560163 | + | 0.0669602i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 14.2646i | − | 0.593842i | −0.954902 | − | 0.296921i | \(-0.904040\pi\) | ||
0.954902 | − | 0.296921i | \(-0.0959599\pi\) | |||||||
\(578\) | −14.5944 | −0.607049 | ||||||||
\(579\) | −3.58525 | + | 3.58525i | −0.148998 | + | 0.148998i | ||||
\(580\) | −13.8526 | + | 15.6071i | −0.575198 | + | 0.648051i | ||||
\(581\) | −17.4194 | −0.722679 | ||||||||
\(582\) | 10.1056 | + | 10.1056i | 0.418890 | + | 0.418890i | ||||
\(583\) | −4.92124 | + | 4.92124i | −0.203817 | + | 0.203817i | ||||
\(584\) | 0.815358 | − | 0.815358i | 0.0337397 | − | 0.0337397i | ||||
\(585\) | −0.384187 | − | 6.45079i | −0.0158842 | − | 0.266707i | ||||
\(586\) | 3.92862 | + | 3.92862i | 0.162290 | + | 0.162290i | ||||
\(587\) | −22.1077 | −0.912481 | −0.456241 | − | 0.889856i | \(-0.650804\pi\) | ||||
−0.456241 | + | 0.889856i | \(0.650804\pi\) | |||||||
\(588\) | −1.85630 | − | 1.85630i | −0.0765525 | − | 0.0765525i | ||||
\(589\) | 2.43448i | 0.100311i | ||||||||
\(590\) | 17.4413 | + | 15.4806i | 0.718047 | + | 0.637326i | ||||
\(591\) | − | 16.0617i | − | 0.660691i | ||||||
\(592\) | −4.72726 | + | 3.82793i | −0.194289 | + | 0.157327i | ||||
\(593\) | −4.52142 | − | 4.52142i | −0.185672 | − | 0.185672i | 0.608150 | − | 0.793822i | \(-0.291912\pi\) |
−0.793822 | + | 0.608150i | \(0.791912\pi\) | |||||||
\(594\) | 0.814507 | − | 0.814507i | 0.0334196 | − | 0.0334196i | ||||
\(595\) | 19.6612 | + | 17.4509i | 0.806030 | + | 0.715418i | ||||
\(596\) | 4.64148i | 0.190122i | ||||||||
\(597\) | 17.9851i | 0.736080i | ||||||||
\(598\) | 7.81909 | 0.319746 | ||||||||
\(599\) | 2.38790i | 0.0975668i | 0.998809 | + | 0.0487834i | \(0.0155344\pi\) | ||||
−0.998809 | + | 0.0487834i | \(0.984466\pi\) | |||||||
\(600\) | −3.09090 | + | 3.93018i | −0.126186 | + | 0.160449i | ||||
\(601\) | −25.0314 | −1.02105 | −0.510526 | − | 0.859862i | \(-0.670549\pi\) | ||||
−0.510526 | + | 0.859862i | \(0.670549\pi\) | |||||||
\(602\) | 13.2019 | − | 13.2019i | 0.538070 | − | 0.538070i | ||||
\(603\) | −4.32408 | + | 4.32408i | −0.176090 | + | 0.176090i | ||||
\(604\) | 14.5106i | 0.590429i | ||||||||
\(605\) | −21.5916 | + | 1.28592i | −0.877823 | + | 0.0522800i | ||||
\(606\) | −4.62711 | − | 4.62711i | −0.187964 | − | 0.187964i | ||||
\(607\) | 3.19973 | 0.129873 | 0.0649365 | − | 0.997889i | \(-0.479316\pi\) | ||||
0.0649365 | + | 0.997889i | \(0.479316\pi\) | |||||||
\(608\) | −1.32254 | − | 1.32254i | −0.0536361 | − | 0.0536361i | ||||
\(609\) | 13.8026 | + | 13.8026i | 0.559311 | + | 0.559311i | ||||
\(610\) | −1.70670 | − | 1.51484i | −0.0691023 | − | 0.0613340i | ||||
\(611\) | −16.8798 | + | 16.8798i | −0.682883 | + | 0.682883i | ||||
\(612\) | −5.62089 | −0.227211 | ||||||||
\(613\) | 4.03461 | − | 4.03461i | 0.162956 | − | 0.162956i | −0.620919 | − | 0.783875i | \(-0.713240\pi\) |
0.783875 | + | 0.620919i | \(0.213240\pi\) | |||||||
\(614\) | −0.507816 | − | 0.507816i | −0.0204938 | − | 0.0204938i | ||||
\(615\) | −11.4453 | − | 10.1587i | −0.461520 | − | 0.409637i | ||||
\(616\) | −1.70362 | − | 1.70362i | −0.0686409 | − | 0.0686409i | ||||
\(617\) | 0.467215 | + | 0.467215i | 0.0188094 | + | 0.0188094i | 0.716449 | − | 0.697640i | \(-0.245766\pi\) |
−0.697640 | + | 0.716449i | \(0.745766\pi\) | |||||||
\(618\) | −1.66559 | − | 1.66559i | −0.0669999 | − | 0.0669999i | ||||
\(619\) | 19.5482 | 0.785707 | 0.392853 | − | 0.919601i | \(-0.371488\pi\) | ||||
0.392853 | + | 0.919601i | \(0.371488\pi\) | |||||||
\(620\) | 2.17675 | + | 1.93204i | 0.0874202 | + | 0.0775926i | ||||
\(621\) | −1.91313 | − | 1.91313i | −0.0767712 | − | 0.0767712i | ||||
\(622\) | −0.433905 | − | 0.433905i | −0.0173980 | − | 0.0173980i | ||||
\(623\) | − | 20.3341i | − | 0.814668i | ||||||
\(624\) | 2.04353 | − | 2.04353i | 0.0818069 | − | 0.0818069i | ||||
\(625\) | 24.2956 | − | 5.89265i | 0.971824 | − | 0.235706i | ||||
\(626\) | 18.8073 | 0.751691 | ||||||||
\(627\) | − | 2.15444i | − | 0.0860399i | ||||||
\(628\) | −13.1125 | + | 13.1125i | −0.523244 | + | 0.523244i | ||||
\(629\) | 21.5164 | + | 26.5714i | 0.857914 | + | 1.05947i | ||||
\(630\) | 3.49787 | + | 3.10465i | 0.139359 | + | 0.123692i | ||||
\(631\) | 23.3820 | + | 23.3820i | 0.930821 | + | 0.930821i | 0.997757 | − | 0.0669364i | \(-0.0213224\pi\) |
−0.0669364 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(632\) | 11.8987 | + | 11.8987i | 0.473306 | + | 0.473306i | ||||
\(633\) | −15.4596 | + | 15.4596i | −0.614465 | + | 0.614465i | ||||
\(634\) | 11.5222 | + | 11.5222i | 0.457603 | + | 0.457603i | ||||
\(635\) | −0.654330 | + | 0.737205i | −0.0259663 | + | 0.0292551i | ||||
\(636\) | 6.04199 | 0.239580 | ||||||||
\(637\) | − | 7.58682i | − | 0.300601i | ||||||
\(638\) | −7.60138 | − | 7.60138i | −0.300941 | − | 0.300941i | ||||
\(639\) | 4.66092i | 0.184383i | ||||||||
\(640\) | −2.23211 | + | 0.132937i | −0.0882320 | + | 0.00525479i | ||||
\(641\) | 22.8783 | 0.903637 | 0.451818 | − | 0.892110i | \(-0.350775\pi\) | ||||
0.451818 | + | 0.892110i | \(0.350775\pi\) | |||||||
\(642\) | − | 9.54472i | − | 0.376700i | ||||||
\(643\) | − | 20.4157i | − | 0.805118i | −0.915394 | − | 0.402559i | \(-0.868121\pi\) | ||
0.915394 | − | 0.402559i | \(-0.131879\pi\) | |||||||
\(644\) | −4.00150 | + | 4.00150i | −0.157681 | + | 0.157681i | ||||
\(645\) | 13.2497 | − | 14.9279i | 0.521707 | − | 0.587785i | ||||
\(646\) | −7.43386 | + | 7.43386i | −0.292481 | + | 0.292481i | ||||
\(647\) | −11.4754 | −0.451143 | −0.225572 | − | 0.974227i | \(-0.572425\pi\) | ||||
−0.225572 | + | 0.974227i | \(0.572425\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −8.49471 | + | 8.49471i | −0.333446 | + | 0.333446i | ||||
\(650\) | −14.3478 | + | 1.71510i | −0.562768 | + | 0.0672716i | ||||
\(651\) | 1.92507 | − | 1.92507i | 0.0754494 | − | 0.0754494i | ||||
\(652\) | − | 8.81029i | − | 0.345038i | ||||||
\(653\) | 20.2423i | 0.792144i | 0.918219 | + | 0.396072i | \(0.129627\pi\) | ||||
−0.918219 | + | 0.396072i | \(0.870373\pi\) | |||||||
\(654\) | 2.66960 | 0.104390 | ||||||||
\(655\) | −29.5161 | − | 26.1980i | −1.15329 | − | 1.02364i | ||||
\(656\) | − | 6.84388i | − | 0.267209i | ||||||
\(657\) | −0.815358 | − | 0.815358i | −0.0318101 | − | 0.0318101i | ||||
\(658\) | − | 17.2768i | − | 0.673520i | ||||||
\(659\) | 25.5001 | 0.993341 | 0.496671 | − | 0.867939i | \(-0.334556\pi\) | ||||
0.496671 | + | 0.867939i | \(0.334556\pi\) | |||||||
\(660\) | −1.92635 | − | 1.70979i | −0.0749830 | − | 0.0665536i | ||||
\(661\) | −20.7117 | − | 20.7117i | −0.805592 | − | 0.805592i | 0.178372 | − | 0.983963i | \(-0.442917\pi\) |
−0.983963 | + | 0.178372i | \(0.942917\pi\) | |||||||
\(662\) | −7.39172 | + | 7.39172i | −0.287287 | + | 0.287287i | ||||
\(663\) | −11.4865 | − | 11.4865i | −0.446098 | − | 0.446098i | ||||
\(664\) | −5.88898 | − | 5.88898i | −0.228537 | − | 0.228537i | ||||
\(665\) | 8.73211 | − | 0.520054i | 0.338617 | − | 0.0201668i | ||||
\(666\) | 3.82793 | + | 4.72726i | 0.148329 | + | 0.183178i | ||||
\(667\) | −17.8543 | + | 17.8543i | −0.691320 | + | 0.691320i | ||||
\(668\) | − | 13.2859i | − | 0.514046i | ||||||
\(669\) | 13.8580 | 0.535781 | ||||||||
\(670\) | 10.2267 | + | 9.07701i | 0.395091 | + | 0.350676i | ||||
\(671\) | 0.831241 | − | 0.831241i | 0.0320897 | − | 0.0320897i | ||||
\(672\) | 2.09160i | 0.0806853i | ||||||||
\(673\) | −28.3498 | − | 28.3498i | −1.09280 | − | 1.09280i | −0.995228 | − | 0.0975766i | \(-0.968891\pi\) |
−0.0975766 | − | 0.995228i | \(-0.531109\pi\) | |||||||
\(674\) | −4.90709 | − | 4.90709i | −0.189014 | − | 0.189014i | ||||
\(675\) | 3.93018 | + | 3.09090i | 0.151273 | + | 0.118969i | ||||
\(676\) | −4.64793 | −0.178767 | ||||||||
\(677\) | 7.07539 | + | 7.07539i | 0.271929 | + | 0.271929i | 0.829876 | − | 0.557947i | \(-0.188411\pi\) |
−0.557947 | + | 0.829876i | \(0.688411\pi\) | |||||||
\(678\) | −12.3712 | − | 12.3712i | −0.475115 | − | 0.475115i | ||||
\(679\) | −21.1369 | − | 21.1369i | −0.811159 | − | 0.811159i | ||||
\(680\) | 0.747224 | + | 12.5465i | 0.0286547 | + | 0.481135i | ||||
\(681\) | 8.82808 | + | 8.82808i | 0.338293 | + | 0.338293i | ||||
\(682\) | −1.06017 | + | 1.06017i | −0.0405961 | + | 0.0405961i | ||||
\(683\) | 27.8779 | 1.06672 | 0.533359 | − | 0.845889i | \(-0.320930\pi\) | ||||
0.533359 | + | 0.845889i | \(0.320930\pi\) | |||||||
\(684\) | −1.32254 | + | 1.32254i | −0.0505686 | + | 0.0505686i | ||||
\(685\) | 24.9246 | − | 28.0814i | 0.952320 | − | 1.07294i | ||||
\(686\) | 14.2355 | + | 14.2355i | 0.543515 | + | 0.543515i | ||||
\(687\) | −3.47118 | − | 3.47118i | −0.132434 | − | 0.132434i | ||||
\(688\) | 8.92633 | 0.340313 | ||||||||
\(689\) | 12.3470 | + | 12.3470i | 0.470384 | + | 0.470384i | ||||
\(690\) | −4.01599 | + | 4.52464i | −0.152886 | + | 0.172250i | ||||
\(691\) | 36.3085i | 1.38124i | 0.723218 | + | 0.690619i | \(0.242662\pi\) | ||||
−0.723218 | + | 0.690619i | \(0.757338\pi\) | |||||||
\(692\) | −16.3729 | + | 16.3729i | −0.622403 | + | 0.622403i | ||||
\(693\) | −1.70362 | + | 1.70362i | −0.0647153 | + | 0.0647153i | ||||
\(694\) | 5.47655 | 0.207887 | ||||||||
\(695\) | 34.8231 | − | 2.07394i | 1.32092 | − | 0.0786692i | ||||
\(696\) | 9.33249i | 0.353747i | ||||||||
\(697\) | −38.4687 | −1.45711 | ||||||||
\(698\) | 17.9938i | 0.681077i | ||||||||
\(699\) | − | 9.37554i | − | 0.354615i | ||||||
\(700\) | 6.46494 | − | 8.22037i | 0.244352 | − | 0.310701i | ||||
\(701\) | −26.0059 | + | 26.0059i | −0.982229 | + | 0.982229i | −0.999845 | − | 0.0176154i | \(-0.994393\pi\) |
0.0176154 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(702\) | −2.04353 | − | 2.04353i | −0.0771282 | − | 0.0771282i | ||||
\(703\) | 11.3146 | + | 1.18940i | 0.426738 | + | 0.0448592i | ||||
\(704\) | − | 1.15189i | − | 0.0434133i | ||||||
\(705\) | −1.09807 | − | 18.4375i | −0.0413557 | − | 0.694395i | ||||
\(706\) | 0.511524i | 0.0192515i | ||||||||
\(707\) | 9.67808 | + | 9.67808i | 0.363982 | + | 0.363982i | ||||
\(708\) | 10.4293 | 0.391956 | ||||||||
\(709\) | −1.61126 | − | 1.61126i | −0.0605121 | − | 0.0605121i | 0.676203 | − | 0.736715i | \(-0.263624\pi\) |
−0.736715 | + | 0.676203i | \(0.763624\pi\) | |||||||
\(710\) | 10.4037 | − | 0.619609i | 0.390444 | − | 0.0232535i | ||||
\(711\) | 11.8987 | − | 11.8987i | 0.446237 | − | 0.446237i | ||||
\(712\) | 6.87434 | − | 6.87434i | 0.257627 | − | 0.257627i | ||||
\(713\) | 2.49016 | + | 2.49016i | 0.0932571 | + | 0.0932571i | ||||
\(714\) | 11.7567 | 0.439982 | ||||||||
\(715\) | −0.442539 | − | 7.43058i | −0.0165500 | − | 0.277888i | ||||
\(716\) | 6.39446 | − | 6.39446i | 0.238972 | − | 0.238972i | ||||
\(717\) | 20.3725 | 0.760825 | ||||||||
\(718\) | − | 30.4736i | − | 1.13726i | ||||||
\(719\) | − | 13.7328i | − | 0.512145i | −0.966658 | − | 0.256073i | \(-0.917571\pi\) | ||
0.966658 | − | 0.256073i | \(-0.0824286\pi\) | |||||||
\(720\) | 0.132937 | + | 2.23211i | 0.00495426 | + | 0.0831859i | ||||
\(721\) | 3.48375 | + | 3.48375i | 0.129742 | + | 0.129742i | ||||
\(722\) | − | 15.5018i | − | 0.576916i | ||||||
\(723\) | − | 8.24898i | − | 0.306783i | ||||||
\(724\) | 7.94042 | 0.295103 | ||||||||
\(725\) | 28.8458 | − | 36.6784i | 1.07131 | − | 1.36220i | ||||
\(726\) | −6.83996 | + | 6.83996i | −0.253855 | + | 0.253855i | ||||
\(727\) | −30.8968 | −1.14590 | −0.572949 | − | 0.819591i | \(-0.694201\pi\) | ||||
−0.572949 | + | 0.819591i | \(0.694201\pi\) | |||||||
\(728\) | −4.27426 | + | 4.27426i | −0.158415 | + | 0.158415i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −1.71158 | + | 1.92836i | −0.0633484 | + | 0.0713719i | ||||
\(731\) | − | 50.1740i | − | 1.85575i | ||||||
\(732\) | −1.02055 | −0.0377204 | ||||||||
\(733\) | 33.6973 | − | 33.6973i | 1.24464 | − | 1.24464i | 0.286581 | − | 0.958056i | \(-0.407481\pi\) |
0.958056 | − | 0.286581i | \(-0.0925187\pi\) | |||||||
\(734\) | 1.10113 | − | 1.10113i | 0.0406435 | − | 0.0406435i | ||||
\(735\) | 4.39024 | + | 3.89670i | 0.161936 | + | 0.143732i | ||||
\(736\) | −2.70557 | −0.0997287 | ||||||||
\(737\) | −4.98085 | + | 4.98085i | −0.183472 | + | 0.183472i | ||||
\(738\) | −6.84388 | −0.251927 | ||||||||
\(739\) | 8.47618 | 0.311801 | 0.155901 | − | 0.987773i | \(-0.450172\pi\) | ||||
0.155901 | + | 0.987773i | \(0.450172\pi\) | |||||||
\(740\) | 10.0429 | − | 9.17279i | 0.369184 | − | 0.337199i | ||||
\(741\) | −5.40532 | −0.198569 | ||||||||
\(742\) | −12.6374 | −0.463935 | ||||||||
\(743\) | −25.8387 | + | 25.8387i | −0.947932 | + | 0.947932i | −0.998710 | − | 0.0507782i | \(-0.983830\pi\) |
0.0507782 | + | 0.998710i | \(0.483830\pi\) | |||||||
\(744\) | 1.30161 | 0.0477195 | ||||||||
\(745\) | −0.617024 | − | 10.3603i | −0.0226060 | − | 0.379572i | ||||
\(746\) | 13.3085 | − | 13.3085i | 0.487259 | − | 0.487259i | ||||
\(747\) | −5.88898 | + | 5.88898i | −0.215466 | + | 0.215466i | ||||
\(748\) | −6.47463 | −0.236736 | ||||||||
\(749\) | 19.9637i | 0.729459i | ||||||||
\(750\) | 6.37678 | − | 9.18350i | 0.232847 | − | 0.335334i | ||||
\(751\) | 5.27898i | 0.192633i | 0.995351 | + | 0.0963163i | \(0.0307060\pi\) | ||||
−0.995351 | + | 0.0963163i | \(0.969294\pi\) | |||||||
\(752\) | 5.84077 | − | 5.84077i | 0.212991 | − | 0.212991i | ||||
\(753\) | −16.9795 | −0.618766 | ||||||||
\(754\) | −19.0713 | + | 19.0713i | −0.694535 | + | 0.694535i | ||||
\(755\) | −1.92900 | − | 32.3894i | −0.0702034 | − | 1.17877i | ||||
\(756\) | 2.09160 | 0.0760708 | ||||||||
\(757\) | − | 16.2149i | − | 0.589340i | −0.955599 | − | 0.294670i | \(-0.904790\pi\) | ||
0.955599 | − | 0.294670i | \(-0.0952097\pi\) | |||||||
\(758\) | − | 31.3641i | − | 1.13920i | ||||||
\(759\) | −2.20371 | − | 2.20371i | −0.0799895 | − | 0.0799895i | ||||
\(760\) | 3.12787 | + | 2.77625i | 0.113460 | + | 0.100705i | ||||
\(761\) | − | 10.2102i | − | 0.370118i | −0.982727 | − | 0.185059i | \(-0.940752\pi\) | ||
0.982727 | − | 0.185059i | \(-0.0592476\pi\) | |||||||
\(762\) | 0.440822i | 0.0159693i | ||||||||
\(763\) | −5.58374 | −0.202145 | ||||||||
\(764\) | 17.8463 | − | 17.8463i | 0.645655 | − | 0.645655i | ||||
\(765\) | 12.5465 | − | 0.747224i | 0.453618 | − | 0.0270159i | ||||
\(766\) | 7.04860 | 0.254676 | ||||||||
\(767\) | 21.3126 | + | 21.3126i | 0.769552 | + | 0.769552i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 0.152750 | − | 0.152750i | 0.00550832 | − | 0.00550832i | −0.704347 | − | 0.709856i | \(-0.748760\pi\) |
0.709856 | + | 0.704347i | \(0.248760\pi\) | |||||||
\(770\) | 4.02915 | + | 3.57621i | 0.145201 | + | 0.128877i | ||||
\(771\) | 6.21887 | + | 6.21887i | 0.223967 | + | 0.223967i | ||||
\(772\) | 5.07031 | 0.182485 | ||||||||
\(773\) | 11.9977 | + | 11.9977i | 0.431529 | + | 0.431529i | 0.889148 | − | 0.457619i | \(-0.151298\pi\) |
−0.457619 | + | 0.889148i | \(0.651298\pi\) | |||||||
\(774\) | − | 8.92633i | − | 0.320850i | ||||||
\(775\) | −5.11558 | − | 4.02316i | −0.183757 | − | 0.144516i | ||||
\(776\) | − | 14.2915i | − | 0.513034i | ||||||
\(777\) | −8.00650 | − | 9.88754i | −0.287232 | − | 0.354714i | ||||
\(778\) | 18.3786 | + | 18.3786i | 0.658904 | + | 0.658904i | ||||
\(779\) | −9.05131 | + | 9.05131i | −0.324297 | + | 0.324297i | ||||
\(780\) | −4.28974 | + | 4.83306i | −0.153597 | + | 0.173051i | ||||
\(781\) | 5.36885i | 0.192113i | ||||||||
\(782\) | 15.2077i | 0.543827i | ||||||||
\(783\) | 9.33249 | 0.333516 | ||||||||
\(784\) | 2.62520i | 0.0937572i | ||||||||
\(785\) | 27.5253 | − | 31.0116i | 0.982422 | − | 1.10685i | ||||
\(786\) | −17.6496 | −0.629539 | ||||||||
\(787\) | 4.08657 | − | 4.08657i | 0.145670 | − | 0.145670i | −0.630510 | − | 0.776181i | \(-0.717154\pi\) |
0.776181 | + | 0.630510i | \(0.217154\pi\) | |||||||
\(788\) | −11.3573 | + | 11.3573i | −0.404589 | + | 0.404589i | ||||
\(789\) | 6.87106i | 0.244616i | ||||||||
\(790\) | −28.1411 | − | 24.9775i | −1.00122 | − | 0.888661i | ||||
\(791\) | 25.8757 | + | 25.8757i | 0.920035 | + | 0.920035i | ||||
\(792\) | −1.15189 | −0.0409305 | ||||||||
\(793\) | −2.08552 | − | 2.08552i | −0.0740590 | − | 0.0740590i | ||||
\(794\) | 11.4488 | + | 11.4488i | 0.406304 | + | 0.406304i | ||||
\(795\) | −13.4864 | + | 0.803203i | −0.478313 | + | 0.0284867i | ||||
\(796\) | 12.7174 | − | 12.7174i | 0.450755 | − | 0.450755i | ||||
\(797\) | 17.9557 | 0.636024 | 0.318012 | − | 0.948087i | \(-0.396985\pi\) | ||||
0.318012 | + | 0.948087i | \(0.396985\pi\) | |||||||
\(798\) | 2.76623 | − | 2.76623i | 0.0979234 | − | 0.0979234i | ||||
\(799\) | −32.8303 | − | 32.8303i | −1.16145 | − | 1.16145i | ||||
\(800\) | 4.96466 | − | 0.593460i | 0.175527 | − | 0.0209820i | ||||
\(801\) | −6.87434 | − | 6.87434i | −0.242893 | − | 0.242893i | ||||
\(802\) | −14.1357 | − | 14.1357i | −0.499151 | − | 0.499151i | ||||
\(803\) | −0.939199 | − | 0.939199i | −0.0331436 | − | 0.0331436i | ||||
\(804\) | 6.11518 | 0.215666 | ||||||||
\(805\) | 8.39986 | − | 9.46375i | 0.296056 | − | 0.333553i | ||||
\(806\) | 2.65989 | + | 2.65989i | 0.0936908 | + | 0.0936908i | ||||
\(807\) | −7.64191 | − | 7.64191i | −0.269008 | − | 0.269008i | ||||
\(808\) | 6.54373i | 0.230208i | ||||||||
\(809\) | −5.66008 | + | 5.66008i | −0.198998 | + | 0.198998i | −0.799570 | − | 0.600572i | \(-0.794939\pi\) |
0.600572 | + | 0.799570i | \(0.294939\pi\) | |||||||
\(810\) | 2.23211 | − | 0.132937i | 0.0784285 | − | 0.00467092i | ||||
\(811\) | 33.9490 | 1.19211 | 0.596054 | − | 0.802944i | \(-0.296734\pi\) | ||||
0.596054 | + | 0.802944i | \(0.296734\pi\) | |||||||
\(812\) | − | 19.5199i | − | 0.685013i | ||||||
\(813\) | −14.8427 | + | 14.8427i | −0.520555 | + | 0.520555i | ||||
\(814\) | 4.40934 | + | 5.44526i | 0.154547 | + | 0.190856i | ||||
\(815\) | 1.17121 | + | 19.6656i | 0.0410258 | + | 0.688855i | ||||
\(816\) | 3.97457 | + | 3.97457i | 0.139138 | + | 0.139138i | ||||
\(817\) | −11.8054 | − | 11.8054i | −0.413020 | − | 0.413020i | ||||
\(818\) | −20.4751 | + | 20.4751i | −0.715896 | + | 0.715896i | ||||
\(819\) | 4.27426 | + | 4.27426i | 0.149355 | + | 0.149355i | ||||
\(820\) | 0.909804 | + | 15.2763i | 0.0317717 | + | 0.533472i | ||||
\(821\) | −17.9270 | −0.625658 | −0.312829 | − | 0.949810i | \(-0.601277\pi\) | ||||
−0.312829 | + | 0.949810i | \(0.601277\pi\) | |||||||
\(822\) | − | 16.7917i | − | 0.585677i | ||||||
\(823\) | 12.8847 | + | 12.8847i | 0.449132 | + | 0.449132i | 0.895066 | − | 0.445934i | \(-0.147128\pi\) |
−0.445934 | + | 0.895066i | \(0.647128\pi\) | |||||||
\(824\) | 2.35550i | 0.0820578i | ||||||||
\(825\) | 4.52712 | + | 3.56037i | 0.157614 | + | 0.123956i | ||||
\(826\) | −21.8139 | −0.759002 | ||||||||
\(827\) | − | 24.0587i | − | 0.836605i | −0.908308 | − | 0.418302i | \(-0.862625\pi\) | ||
0.908308 | − | 0.418302i | \(-0.137375\pi\) | |||||||
\(828\) | 2.70557i | 0.0940251i | ||||||||
\(829\) | −6.84774 | + | 6.84774i | −0.237832 | + | 0.237832i | −0.815952 | − | 0.578120i | \(-0.803787\pi\) |
0.578120 | + | 0.815952i | \(0.303787\pi\) | |||||||
\(830\) | 13.9277 | + | 12.3620i | 0.483438 | + | 0.429091i | ||||
\(831\) | 1.65901 | − | 1.65901i | 0.0575503 | − | 0.0575503i | ||||
\(832\) | −2.88999 | −0.100193 | ||||||||
\(833\) | 14.7560 | 0.511265 | ||||||||
\(834\) | 11.0316 | − | 11.0316i | 0.381991 | − | 0.381991i | ||||
\(835\) | 1.76618 | + | 29.6556i | 0.0611213 | + | 1.02627i | ||||
\(836\) | −1.52342 | + | 1.52342i | −0.0526885 | + | 0.0526885i | ||||
\(837\) | − | 1.30161i | − | 0.0449904i | ||||||
\(838\) | − | 16.7209i | − | 0.577614i | ||||||
\(839\) | −33.9557 | −1.17228 | −0.586140 | − | 0.810210i | \(-0.699353\pi\) | ||||
−0.586140 | + | 0.810210i | \(0.699353\pi\) | |||||||
\(840\) | −0.278051 | − | 4.66869i | −0.00959367 | − | 0.161085i | ||||
\(841\) | − | 58.0955i | − | 2.00329i | ||||||
\(842\) | 22.8919 | + | 22.8919i | 0.788909 | + | 0.788909i | ||||
\(843\) | 17.6536i | 0.608024i | ||||||||
\(844\) | 21.8632 | 0.752562 | ||||||||
\(845\) | 10.3747 | − | 0.617882i | 0.356901 | − | 0.0212558i | ||||
\(846\) | −5.84077 | − | 5.84077i | −0.200810 | − | 0.200810i | ||||
\(847\) | 14.3065 | − | 14.3065i | 0.491576 | − | 0.491576i | ||||
\(848\) | −4.27233 | − | 4.27233i | −0.146712 | − | 0.146712i | ||||
\(849\) | −2.94770 | − | 2.94770i | −0.101165 | − | 0.101165i | ||||
\(850\) | −3.33578 | − | 27.9058i | −0.114416 | − | 0.957161i | ||||
\(851\) | 12.7899 | − | 10.3567i | 0.438433 | − | 0.355024i | ||||
\(852\) | 3.29577 | − | 3.29577i | 0.112911 | − | 0.112911i | ||||
\(853\) | 31.3903i | 1.07478i | 0.843333 | + | 0.537391i | \(0.180590\pi\) | ||||
−0.843333 | + | 0.537391i | \(0.819410\pi\) | |||||||
\(854\) | 2.13457 | 0.0730436 | ||||||||
\(855\) | 2.77625 | − | 3.12787i | 0.0949456 | − | 0.106971i | ||||
\(856\) | −6.74914 | + | 6.74914i | −0.230681 | + | 0.230681i | ||||
\(857\) | − | 8.66191i | − | 0.295885i | −0.988996 | − | 0.147943i | \(-0.952735\pi\) | ||
0.988996 | − | 0.147943i | \(-0.0472651\pi\) | |||||||
\(858\) | −2.35392 | − | 2.35392i | −0.0803615 | − | 0.0803615i | ||||
\(859\) | 17.7807 | + | 17.7807i | 0.606669 | + | 0.606669i | 0.942074 | − | 0.335405i | \(-0.108873\pi\) |
−0.335405 | + | 0.942074i | \(0.608873\pi\) | |||||||
\(860\) | −19.9246 | + | 1.18664i | −0.679423 | + | 0.0404640i | ||||
\(861\) | 14.3147 | 0.487843 | ||||||||
\(862\) | −5.61789 | − | 5.61789i | −0.191346 | − | 0.191346i | ||||
\(863\) | 17.8599 | + | 17.8599i | 0.607959 | + | 0.607959i | 0.942412 | − | 0.334454i | \(-0.108552\pi\) |
−0.334454 | + | 0.942412i | \(0.608552\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 34.3695 | − | 38.7227i | 1.16860 | − | 1.31661i | ||||
\(866\) | 4.80295 | + | 4.80295i | 0.163211 | + | 0.163211i | ||||
\(867\) | 10.3198 | − | 10.3198i | 0.350480 | − | 0.350480i | ||||
\(868\) | −2.72246 | −0.0924063 | ||||||||
\(869\) | 13.7060 | − | 13.7060i | 0.464944 | − | 0.464944i | ||||
\(870\) | −1.24063 | − | 20.8312i | −0.0420614 | − | 0.706243i | ||||
\(871\) | 12.4966 | + | 12.4966i | 0.423430 | + | 0.423430i | ||||
\(872\) | −1.88769 | − | 1.88769i | −0.0639254 | − | 0.0639254i | ||||
\(873\) | −14.2915 | −0.483693 | ||||||||
\(874\) | 3.57823 | + | 3.57823i | 0.121035 | + | 0.121035i | ||||
\(875\) | −13.3377 | + | 19.2082i | −0.450896 | + | 0.649357i | ||||
\(876\) | 1.15309i | 0.0389593i | ||||||||
\(877\) | 22.3059 | − | 22.3059i | 0.753218 | − | 0.753218i | −0.221860 | − | 0.975078i | \(-0.571213\pi\) |
0.975078 | + | 0.221860i | \(0.0712129\pi\) | |||||||
\(878\) | 7.82626 | − | 7.82626i | 0.264123 | − | 0.264123i | ||||
\(879\) | −5.55591 | −0.187396 | ||||||||
\(880\) | 0.153128 | + | 2.57114i | 0.00516195 | + | 0.0866731i | ||||
\(881\) | 50.8644i | 1.71367i | 0.515594 | + | 0.856833i | \(0.327571\pi\) | ||||
−0.515594 | + | 0.856833i | \(0.672429\pi\) | |||||||
\(882\) | 2.62520 | 0.0883952 | ||||||||
\(883\) | − | 31.8341i | − | 1.07130i | −0.844439 | − | 0.535652i | \(-0.820066\pi\) | ||
0.844439 | − | 0.535652i | \(-0.179934\pi\) | |||||||
\(884\) | 16.2443i | 0.546357i | ||||||||
\(885\) | −23.2793 | + | 1.38643i | −0.782525 | + | 0.0466045i | ||||
\(886\) | 13.6322 | − | 13.6322i | 0.457981 | − | 0.457981i | ||||
\(887\) | 23.7032 | + | 23.7032i | 0.795875 | + | 0.795875i | 0.982442 | − | 0.186567i | \(-0.0597362\pi\) |
−0.186567 | + | 0.982442i | \(0.559736\pi\) | |||||||
\(888\) | 0.635924 | − | 6.04943i | 0.0213402 | − | 0.203006i | ||||
\(889\) | − | 0.922024i | − | 0.0309237i | ||||||
\(890\) | −14.4304 | + | 16.2582i | −0.483710 | + | 0.544975i | ||||
\(891\) | 1.15189i | 0.0385896i | ||||||||
\(892\) | −9.79908 | − | 9.79908i | −0.328098 | − | 0.328098i | ||||
\(893\) | −15.4493 | −0.516991 | ||||||||
\(894\) | −3.28202 | − | 3.28202i | −0.109767 | − | 0.109767i | ||||
\(895\) | −13.4231 | + | 15.1232i | −0.448685 | + | 0.505514i | ||||
\(896\) | 1.47899 | − | 1.47899i | 0.0494094 | − | 0.0494094i | ||||
\(897\) | −5.52893 | + | 5.52893i | −0.184606 | + | 0.184606i | ||||
\(898\) | 16.5631 | + | 16.5631i | 0.552717 | + | 0.552717i | ||||
\(899\) | −12.1473 | −0.405135 | ||||||||
\(900\) | −0.593460 | − | 4.96466i | −0.0197820 | − | 0.165489i | ||||
\(901\) | −24.0143 | + | 24.0143i | −0.800033 | + | 0.800033i | ||||
\(902\) | −7.88337 | −0.262488 | ||||||||
\(903\) | 18.6703i | 0.621310i | ||||||||
\(904\) | 17.4956i | 0.581895i | ||||||||
\(905\) | −17.7239 | + | 1.05557i | −0.589163 | + | 0.0350885i | ||||
\(906\) | −10.2606 | − | 10.2606i | −0.340884 | − | 0.340884i | ||||
\(907\) | − | 21.5811i | − | 0.716589i | −0.933609 | − | 0.358294i | \(-0.883358\pi\) | ||
0.933609 | − | 0.358294i | \(-0.116642\pi\) | |||||||
\(908\) | − | 12.4848i | − | 0.414322i | ||||||
\(909\) | 6.54373 | 0.217042 | ||||||||
\(910\) | 8.97242 | − | 10.1088i | 0.297433 | − | 0.335105i | ||||
\(911\) | −38.1307 | + | 38.1307i | −1.26332 | + | 1.26332i | −0.313853 | + | 0.949471i | \(0.601620\pi\) |
−0.949471 | + | 0.313853i | \(0.898380\pi\) | |||||||
\(912\) | 1.87036 | 0.0619337 | ||||||||
\(913\) | −6.78343 | + | 6.78343i | −0.224499 | + | 0.224499i | ||||
\(914\) | 15.3145i | 0.506558i | ||||||||
\(915\) | 2.27797 | − | 0.135668i | 0.0753074 | − | 0.00448505i | ||||
\(916\) | 4.90899i | 0.162197i | ||||||||
\(917\) | 36.9158 | 1.21907 | ||||||||
\(918\) | 3.97457 | − | 3.97457i | 0.131180 | − | 0.131180i | ||||
\(919\) | −4.29529 | + | 4.29529i | −0.141688 | + | 0.141688i | −0.774393 | − | 0.632705i | \(-0.781945\pi\) |
0.632705 | + | 0.774393i | \(0.281945\pi\) | |||||||
\(920\) | 6.03914 | − | 0.359670i | 0.199105 | − | 0.0118580i | ||||
\(921\) | 0.718161 | 0.0236642 | ||||||||
\(922\) | 25.8489 | − | 25.8489i | 0.851287 | − | 0.851287i | ||||
\(923\) | 13.4700 | 0.443372 | ||||||||
\(924\) | 2.40929 | 0.0792597 | ||||||||
\(925\) | −21.1975 | + | 21.8098i | −0.696969 | + | 0.717101i | ||||
\(926\) | 23.9015 | 0.785454 | ||||||||
\(927\) | 2.35550 | 0.0773648 | ||||||||
\(928\) | 6.59907 | − | 6.59907i | 0.216625 | − | 0.216625i | ||||
\(929\) | −1.53246 | −0.0502783 | −0.0251392 | − | 0.999684i | \(-0.508003\pi\) | ||||
−0.0251392 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(930\) | −2.90535 | + | 0.173033i | −0.0952702 | + | 0.00567396i | ||||
\(931\) | 3.47194 | − | 3.47194i | 0.113788 | − | 0.113788i | ||||
\(932\) | −6.62951 | + | 6.62951i | −0.217157 | + | 0.217157i | ||||
\(933\) | 0.613635 | 0.0200895 | ||||||||
\(934\) | − | 7.54639i | − | 0.246925i | ||||||
\(935\) | 14.4521 | − | 0.860717i | 0.472634 | − | 0.0281485i | ||||
\(936\) | 2.88999i | 0.0944624i | ||||||||
\(937\) | −39.9671 | + | 39.9671i | −1.30567 | + | 1.30567i | −0.381156 | + | 0.924511i | \(0.624474\pi\) |
−0.924511 | + | 0.381156i | \(0.875526\pi\) | |||||||
\(938\) | −12.7905 | −0.417625 | ||||||||
\(939\) | −13.2988 | + | 13.2988i | −0.433989 | + | 0.433989i | ||||
\(940\) | −12.2608 | + | 13.8137i | −0.399903 | + | 0.450553i | ||||
\(941\) | −46.4990 | −1.51582 | −0.757911 | − | 0.652358i | \(-0.773780\pi\) | ||||
−0.757911 | + | 0.652358i | \(0.773780\pi\) | |||||||
\(942\) | − | 18.5438i | − | 0.604190i | ||||||
\(943\) | 18.5166i | 0.602984i | ||||||||
\(944\) | −7.37461 | − | 7.37461i | −0.240023 | − | 0.240023i | ||||
\(945\) | −4.66869 | + | 0.278051i | −0.151873 | + | 0.00904500i | ||||
\(946\) | − | 10.2821i | − | 0.334301i | ||||||
\(947\) | 30.4143i | 0.988331i | 0.869368 | + | 0.494166i | \(0.164526\pi\) | ||||
−0.869368 | + | 0.494166i | \(0.835474\pi\) | |||||||
\(948\) | −16.8273 | −0.546527 | ||||||||
\(949\) | −2.35638 | + | 2.35638i | −0.0764913 | + | 0.0764913i | ||||
\(950\) | −7.35084 | − | 5.78108i | −0.238493 | − | 0.187563i | ||||
\(951\) | −16.2948 | −0.528395 | ||||||||
\(952\) | −8.31322 | − | 8.31322i | −0.269433 | − | 0.269433i | ||||
\(953\) | 18.5452 | − | 18.5452i | 0.600738 | − | 0.600738i | −0.339770 | − | 0.940509i | \(-0.610349\pi\) |
0.940509 | + | 0.339770i | \(0.110349\pi\) | |||||||
\(954\) | −4.27233 | + | 4.27233i | −0.138322 | + | 0.138322i | ||||
\(955\) | −37.4624 | + | 42.2073i | −1.21226 | + | 1.36580i | ||||
\(956\) | −14.4055 | − | 14.4055i | −0.465908 | − | 0.465908i | ||||
\(957\) | 10.7500 | 0.347497 | ||||||||
\(958\) | 24.1200 | + | 24.1200i | 0.779283 | + | 0.779283i | ||||
\(959\) | 35.1215i | 1.13413i | ||||||||
\(960\) | 1.48434 | − | 1.67234i | 0.0479069 | − | 0.0539746i | ||||
\(961\) | − | 29.3058i | − | 0.945348i | ||||||
\(962\) | 13.6618 | − | 11.0627i | 0.440473 | − | 0.356675i | ||||
\(963\) | 6.74914 | + | 6.74914i | 0.217488 | + | 0.217488i | ||||
\(964\) | −5.83291 | + | 5.83291i | −0.187865 | + | 0.187865i | ||||
\(965\) | −11.3175 | + | 0.674031i | −0.364324 | + | 0.0216978i | ||||
\(966\) | − | 5.65898i | − | 0.182075i | ||||||
\(967\) | − | 38.3059i | − | 1.23183i | −0.787811 | − | 0.615917i | \(-0.788786\pi\) | ||
0.787811 | − | 0.615917i | \(-0.211214\pi\) | |||||||
\(968\) | 9.67316 | 0.310907 | ||||||||
\(969\) | − | 10.5131i | − | 0.337728i | ||||||
\(970\) | 1.89986 | + | 31.9002i | 0.0610009 | + | 1.02425i | ||||
\(971\) | −42.4464 | −1.36217 | −0.681084 | − | 0.732205i | \(-0.738491\pi\) | ||||
−0.681084 | + | 0.732205i | \(0.738491\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −23.0736 | + | 23.0736i | −0.739706 | + | 0.739706i | ||||
\(974\) | 1.74655i | 0.0559631i | ||||||||
\(975\) | 8.93269 | − | 11.3582i | 0.286075 | − | 0.363754i | ||||
\(976\) | 0.721634 | + | 0.721634i | 0.0230990 | + | 0.0230990i | ||||
\(977\) | −2.92825 | −0.0936831 | −0.0468415 | − | 0.998902i | \(-0.514916\pi\) | ||||
−0.0468415 | + | 0.998902i | \(0.514916\pi\) | |||||||
\(978\) | 6.22982 | + | 6.22982i | 0.199208 | + | 0.199208i | ||||
\(979\) | −7.91846 | − | 7.91846i | −0.253075 | − | 0.253075i | ||||
\(980\) | −0.348986 | − | 5.85975i | −0.0111480 | − | 0.187183i | ||||
\(981\) | −1.88769 | + | 1.88769i | −0.0602694 | + | 0.0602694i | ||||
\(982\) | −6.46050 | −0.206163 | ||||||||
\(983\) | 22.1302 | − | 22.1302i | 0.705843 | − | 0.705843i | −0.259816 | − | 0.965658i | \(-0.583662\pi\) |
0.965658 | + | 0.259816i | \(0.0836618\pi\) | |||||||
\(984\) | 4.83935 | + | 4.83935i | 0.154273 | + | 0.154273i | ||||
\(985\) | 23.8411 | − | 26.8607i | 0.759640 | − | 0.855853i | ||||
\(986\) | −37.0927 | − | 37.0927i | −1.18127 | − | 1.18127i | ||||
\(987\) | 12.2166 | + | 12.2166i | 0.388857 | + | 0.388857i | ||||
\(988\) | 3.82214 | + | 3.82214i | 0.121598 | + | 0.121598i | ||||
\(989\) | −24.1508 | −0.767952 | ||||||||
\(990\) | 2.57114 | − | 0.153128i | 0.0817162 | − | 0.00486673i | ||||
\(991\) | 12.2981 | + | 12.2981i | 0.390663 | + | 0.390663i | 0.874924 | − | 0.484261i | \(-0.160911\pi\) |
−0.484261 | + | 0.874924i | \(0.660911\pi\) | |||||||
\(992\) | −0.920380 | − | 0.920380i | −0.0292221 | − | 0.0292221i | ||||
\(993\) | − | 10.4535i | − | 0.331731i | ||||||
\(994\) | −6.89344 | + | 6.89344i | −0.218647 | + | 0.218647i | ||||
\(995\) | −26.6960 | + | 30.0772i | −0.846320 | + | 0.953512i | ||||
\(996\) | 8.32827 | 0.263891 | ||||||||
\(997\) | − | 12.8502i | − | 0.406971i | −0.979078 | − | 0.203485i | \(-0.934773\pi\) | ||
0.979078 | − | 0.203485i | \(-0.0652269\pi\) | |||||||
\(998\) | 11.4622 | − | 11.4622i | 0.362830 | − | 0.362830i | ||||
\(999\) | −6.04943 | − | 0.635924i | −0.191395 | − | 0.0201197i |
(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 | 1110.2.o.b.253.5 | yes | 40 | |
5.2 | odd | 4 | 1110.2.l.b.697.16 | yes | 40 | ||
37.6 | odd | 4 | 1110.2.l.b.43.16 | ✓ | 40 | ||
185.117 | even | 4 | inner | 1110.2.o.b.487.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.16 | ✓ | 40 | 37.6 | odd | 4 | ||
1110.2.l.b.697.16 | yes | 40 | 5.2 | odd | 4 | ||
1110.2.o.b.253.5 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.o.b.487.5 | yes | 40 | 185.117 | even | 4 | inner |