Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(100,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.j (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + 1005 x^{6} - 544 x^{5} + 811 x^{4} - 312 x^{3} + 195 x^{2} + 13 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.5 | ||
Root | \(0.379240 + 0.656863i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.100 |
Dual form | 273.2.j.b.172.5 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.379240 | + | 0.656863i | 0.268163 | + | 0.464472i | 0.968388 | − | 0.249451i | \(-0.0802500\pi\) |
−0.700224 | + | 0.713923i | \(0.746917\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.712354 | − | 1.23383i | 0.356177 | − | 0.616917i | ||||
\(5\) | −0.357869 | + | 0.619848i | −0.160044 | + | 0.277204i | −0.934884 | − | 0.354953i | \(-0.884497\pi\) |
0.774840 | + | 0.632157i | \(0.217830\pi\) | |||||||
\(6\) | −0.379240 | − | 0.656863i | −0.154824 | − | 0.268163i | ||||
\(7\) | −1.32176 | − | 2.29193i | −0.499577 | − | 0.866270i | ||||
\(8\) | 2.59757 | 0.918381 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.542874 | −0.171672 | ||||||||
\(11\) | 4.48772 | 1.35310 | 0.676549 | − | 0.736398i | \(-0.263475\pi\) | ||||
0.676549 | + | 0.736398i | \(0.263475\pi\) | |||||||
\(12\) | −0.712354 | + | 1.23383i | −0.205639 | + | 0.356177i | ||||
\(13\) | 3.26504 | − | 1.52954i | 0.905560 | − | 0.424217i | ||||
\(14\) | 1.00422 | − | 1.73741i | 0.268390 | − | 0.464341i | ||||
\(15\) | 0.357869 | − | 0.619848i | 0.0924015 | − | 0.160044i | ||||
\(16\) | −0.439604 | − | 0.761417i | −0.109901 | − | 0.190354i | ||||
\(17\) | 1.88727 | − | 3.26885i | 0.457730 | − | 0.792812i | −0.541110 | − | 0.840952i | \(-0.681996\pi\) |
0.998841 | + | 0.0481394i | \(0.0153292\pi\) | |||||||
\(18\) | 0.379240 | + | 0.656863i | 0.0893877 | + | 0.154824i | ||||
\(19\) | −5.92010 | −1.35816 | −0.679082 | − | 0.734062i | \(-0.737622\pi\) | ||||
−0.679082 | + | 0.734062i | \(0.737622\pi\) | |||||||
\(20\) | 0.509859 | + | 0.883102i | 0.114008 | + | 0.197468i | ||||
\(21\) | 1.32176 | + | 2.29193i | 0.288431 | + | 0.500141i | ||||
\(22\) | 1.70192 | + | 2.94782i | 0.362851 | + | 0.628477i | ||||
\(23\) | 0.465673 | + | 0.806569i | 0.0970995 | + | 0.168181i | 0.910483 | − | 0.413547i | \(-0.135710\pi\) |
−0.813383 | + | 0.581728i | \(0.802377\pi\) | |||||||
\(24\) | −2.59757 | −0.530227 | ||||||||
\(25\) | 2.24386 | + | 3.88648i | 0.448772 | + | 0.777296i | ||||
\(26\) | 2.24293 | + | 1.56463i | 0.439875 | + | 0.306848i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −3.76942 | − | 0.00184259i | −0.712354 | − | 0.000348216i | ||||
\(29\) | −1.12150 | + | 1.94250i | −0.208257 | + | 0.360713i | −0.951166 | − | 0.308681i | \(-0.900113\pi\) |
0.742908 | + | 0.669393i | \(0.233446\pi\) | |||||||
\(30\) | 0.542874 | 0.0991147 | ||||||||
\(31\) | 0.191136 | + | 0.331058i | 0.0343291 | + | 0.0594597i | 0.882679 | − | 0.469975i | \(-0.155737\pi\) |
−0.848350 | + | 0.529435i | \(0.822404\pi\) | |||||||
\(32\) | 2.93100 | − | 5.07665i | 0.518133 | − | 0.897433i | ||||
\(33\) | −4.48772 | −0.781211 | ||||||||
\(34\) | 2.86291 | 0.490986 | ||||||||
\(35\) | 1.89367 | 0.000925671i | 0.320088 | 0.000156467i | ||||||
\(36\) | 0.712354 | − | 1.23383i | 0.118726 | − | 0.205639i | ||||
\(37\) | 0.328723 | + | 0.569365i | 0.0540417 | + | 0.0936030i | 0.891781 | − | 0.452468i | \(-0.149456\pi\) |
−0.837739 | + | 0.546071i | \(0.816123\pi\) | |||||||
\(38\) | −2.24514 | − | 3.88870i | −0.364210 | − | 0.630830i | ||||
\(39\) | −3.26504 | + | 1.52954i | −0.522826 | + | 0.244922i | ||||
\(40\) | −0.929592 | + | 1.61010i | −0.146981 | + | 0.254579i | ||||
\(41\) | −2.29549 | + | 3.97591i | −0.358495 | + | 0.620932i | −0.987710 | − | 0.156300i | \(-0.950043\pi\) |
0.629214 | + | 0.777232i | \(0.283377\pi\) | |||||||
\(42\) | −1.00422 | + | 1.73741i | −0.154955 | + | 0.268088i | ||||
\(43\) | −2.50110 | − | 4.33202i | −0.381413 | − | 0.660627i | 0.609851 | − | 0.792516i | \(-0.291229\pi\) |
−0.991265 | + | 0.131889i | \(0.957896\pi\) | |||||||
\(44\) | 3.19684 | − | 5.53710i | 0.481942 | − | 0.834749i | ||||
\(45\) | −0.357869 | + | 0.619848i | −0.0533480 | + | 0.0924015i | ||||
\(46\) | −0.353203 | + | 0.611766i | −0.0520770 | + | 0.0902000i | ||||
\(47\) | −4.18536 | + | 7.24926i | −0.610498 | + | 1.05741i | 0.380659 | + | 0.924716i | \(0.375697\pi\) |
−0.991157 | + | 0.132698i | \(0.957636\pi\) | |||||||
\(48\) | 0.439604 | + | 0.761417i | 0.0634514 | + | 0.109901i | ||||
\(49\) | −3.50593 | + | 6.05875i | −0.500846 | + | 0.865536i | ||||
\(50\) | −1.70192 | + | 2.94782i | −0.240688 | + | 0.416884i | ||||
\(51\) | −1.88727 | + | 3.26885i | −0.264271 | + | 0.457730i | ||||
\(52\) | 0.438674 | − | 5.11809i | 0.0608332 | − | 0.709752i | ||||
\(53\) | −1.21338 | − | 2.10164i | −0.166671 | − | 0.288682i | 0.770577 | − | 0.637347i | \(-0.219968\pi\) |
−0.937247 | + | 0.348665i | \(0.886635\pi\) | |||||||
\(54\) | −0.379240 | − | 0.656863i | −0.0516080 | − | 0.0893877i | ||||
\(55\) | −1.60602 | + | 2.78170i | −0.216555 | + | 0.375085i | ||||
\(56\) | −3.43336 | − | 5.95347i | −0.458802 | − | 0.795565i | ||||
\(57\) | 5.92010 | 0.784137 | ||||||||
\(58\) | −1.70127 | −0.223388 | ||||||||
\(59\) | −2.80700 | + | 4.86187i | −0.365441 | + | 0.632962i | −0.988847 | − | 0.148937i | \(-0.952415\pi\) |
0.623406 | + | 0.781898i | \(0.285748\pi\) | |||||||
\(60\) | −0.509859 | − | 0.883102i | −0.0658225 | − | 0.114008i | ||||
\(61\) | 1.99378 | 0.255277 | 0.127639 | − | 0.991821i | \(-0.459260\pi\) | ||||
0.127639 | + | 0.991821i | \(0.459260\pi\) | |||||||
\(62\) | −0.144973 | + | 0.251101i | −0.0184116 | + | 0.0318898i | ||||
\(63\) | −1.32176 | − | 2.29193i | −0.166526 | − | 0.288757i | ||||
\(64\) | 2.68780 | 0.335975 | ||||||||
\(65\) | −0.220379 | + | 2.57121i | −0.0273347 | + | 0.318919i | ||||
\(66\) | −1.70192 | − | 2.94782i | −0.209492 | − | 0.362851i | ||||
\(67\) | −14.4655 | −1.76724 | −0.883618 | − | 0.468208i | \(-0.844900\pi\) | ||||
−0.883618 | + | 0.468208i | \(0.844900\pi\) | |||||||
\(68\) | −2.68881 | − | 4.65715i | −0.326066 | − | 0.564763i | ||||
\(69\) | −0.465673 | − | 0.806569i | −0.0560604 | − | 0.0970995i | ||||
\(70\) | 0.717546 | + | 1.24423i | 0.0857632 | + | 0.148714i | ||||
\(71\) | 2.14741 | + | 3.71943i | 0.254851 | + | 0.441415i | 0.964855 | − | 0.262783i | \(-0.0846402\pi\) |
−0.710004 | + | 0.704198i | \(0.751307\pi\) | |||||||
\(72\) | 2.59757 | 0.306127 | ||||||||
\(73\) | −1.34127 | − | 2.32315i | −0.156984 | − | 0.271905i | 0.776796 | − | 0.629753i | \(-0.216844\pi\) |
−0.933780 | + | 0.357848i | \(0.883511\pi\) | |||||||
\(74\) | −0.249330 | + | 0.431852i | −0.0289840 | + | 0.0502018i | ||||
\(75\) | −2.24386 | − | 3.88648i | −0.259099 | − | 0.448772i | ||||
\(76\) | −4.21721 | + | 7.30442i | −0.483747 | + | 0.837874i | ||||
\(77\) | −5.93167 | − | 10.2856i | −0.675976 | − | 1.17215i | ||||
\(78\) | −2.24293 | − | 1.56463i | −0.253962 | − | 0.177159i | ||||
\(79\) | 2.75173 | − | 4.76614i | 0.309594 | − | 0.536233i | −0.668679 | − | 0.743551i | \(-0.733140\pi\) |
0.978274 | + | 0.207318i | \(0.0664735\pi\) | |||||||
\(80\) | 0.629283 | 0.0703560 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.48217 | −0.384541 | ||||||||
\(83\) | 11.5302 | 1.26560 | 0.632800 | − | 0.774316i | \(-0.281906\pi\) | ||||
0.632800 | + | 0.774316i | \(0.281906\pi\) | |||||||
\(84\) | 3.76942 | + | 0.00184259i | 0.411278 | + | 0.000201043i | ||||
\(85\) | 1.35079 | + | 2.33964i | 0.146514 | + | 0.253770i | ||||
\(86\) | 1.89703 | − | 3.28575i | 0.204562 | − | 0.354312i | ||||
\(87\) | 1.12150 | − | 1.94250i | 0.120238 | − | 0.208257i | ||||
\(88\) | 11.6572 | 1.24266 | ||||||||
\(89\) | 6.05088 | + | 10.4804i | 0.641392 | + | 1.11092i | 0.985122 | + | 0.171856i | \(0.0549763\pi\) |
−0.343730 | + | 0.939069i | \(0.611690\pi\) | |||||||
\(90\) | −0.542874 | −0.0572239 | ||||||||
\(91\) | −7.82119 | − | 5.46159i | −0.819883 | − | 0.572531i | ||||
\(92\) | 1.32689 | 0.138338 | ||||||||
\(93\) | −0.191136 | − | 0.331058i | −0.0198199 | − | 0.0343291i | ||||
\(94\) | −6.34903 | −0.654852 | ||||||||
\(95\) | 2.11862 | − | 3.66956i | 0.217366 | − | 0.376489i | ||||
\(96\) | −2.93100 | + | 5.07665i | −0.299144 | + | 0.518133i | ||||
\(97\) | −1.79870 | − | 3.11544i | −0.182630 | − | 0.316325i | 0.760145 | − | 0.649753i | \(-0.225128\pi\) |
−0.942775 | + | 0.333429i | \(0.891794\pi\) | |||||||
\(98\) | −5.30936 | − | 0.00519069i | −0.536326 | − | 0.000524339i | ||||
\(99\) | 4.48772 | 0.451033 | ||||||||
\(100\) | 6.39369 | 0.639369 | ||||||||
\(101\) | 11.9792 | 1.19197 | 0.595986 | − | 0.802995i | \(-0.296761\pi\) | ||||
0.595986 | + | 0.802995i | \(0.296761\pi\) | |||||||
\(102\) | −2.86291 | −0.283471 | ||||||||
\(103\) | −1.54966 | + | 2.68409i | −0.152692 | + | 0.264471i | −0.932216 | − | 0.361901i | \(-0.882128\pi\) |
0.779524 | + | 0.626372i | \(0.215461\pi\) | |||||||
\(104\) | 8.48119 | − | 3.97308i | 0.831649 | − | 0.389593i | ||||
\(105\) | −1.89367 | 0.000925671i | −0.184803 | 9.03363e-5i | ||||||
\(106\) | 0.920325 | − | 1.59405i | 0.0893898 | − | 0.154828i | ||||
\(107\) | −5.59313 | − | 9.68758i | −0.540708 | − | 0.936534i | −0.998864 | − | 0.0476618i | \(-0.984823\pi\) |
0.458155 | − | 0.888872i | \(-0.348510\pi\) | |||||||
\(108\) | −0.712354 | + | 1.23383i | −0.0685463 | + | 0.118726i | ||||
\(109\) | 10.1906 | + | 17.6506i | 0.976082 | + | 1.69062i | 0.676316 | + | 0.736611i | \(0.263575\pi\) |
0.299766 | + | 0.954013i | \(0.403091\pi\) | |||||||
\(110\) | −2.43626 | −0.232289 | ||||||||
\(111\) | −0.328723 | − | 0.569365i | −0.0312010 | − | 0.0540417i | ||||
\(112\) | −1.16407 | + | 2.01395i | −0.109994 | + | 0.190300i | ||||
\(113\) | 8.55107 | + | 14.8109i | 0.804417 | + | 1.39329i | 0.916684 | + | 0.399613i | \(0.130856\pi\) |
−0.112266 | + | 0.993678i | \(0.535811\pi\) | |||||||
\(114\) | 2.24514 | + | 3.88870i | 0.210277 | + | 0.364210i | ||||
\(115\) | −0.666600 | −0.0621608 | ||||||||
\(116\) | 1.59781 | + | 2.76749i | 0.148353 | + | 0.256955i | ||||
\(117\) | 3.26504 | − | 1.52954i | 0.301853 | − | 0.141406i | ||||
\(118\) | −4.25811 | −0.391991 | ||||||||
\(119\) | −9.98650 | − | 0.00488165i | −0.915461 | − | 0.000447500i | ||||
\(120\) | 0.929592 | − | 1.61010i | 0.0848597 | − | 0.146981i | ||||
\(121\) | 9.13961 | 0.830874 | ||||||||
\(122\) | 0.756122 | + | 1.30964i | 0.0684560 | + | 0.118569i | ||||
\(123\) | 2.29549 | − | 3.97591i | 0.206977 | − | 0.358495i | ||||
\(124\) | 0.544627 | 0.0489089 | ||||||||
\(125\) | −6.79073 | −0.607381 | ||||||||
\(126\) | 1.00422 | − | 1.73741i | 0.0894634 | − | 0.154780i | ||||
\(127\) | 9.01920 | − | 15.6217i | 0.800325 | − | 1.38620i | −0.119077 | − | 0.992885i | \(-0.537994\pi\) |
0.919402 | − | 0.393318i | \(-0.128673\pi\) | |||||||
\(128\) | −4.84269 | − | 8.38778i | −0.428037 | − | 0.741382i | ||||
\(129\) | 2.50110 | + | 4.33202i | 0.220209 | + | 0.381413i | ||||
\(130\) | −1.77251 | + | 0.830345i | −0.155459 | + | 0.0728261i | ||||
\(131\) | −9.83728 | + | 17.0387i | −0.859487 | + | 1.48868i | 0.0129316 | + | 0.999916i | \(0.495884\pi\) |
−0.872419 | + | 0.488759i | \(0.837450\pi\) | |||||||
\(132\) | −3.19684 | + | 5.53710i | −0.278250 | + | 0.481942i | ||||
\(133\) | 7.82493 | + | 13.5685i | 0.678507 | + | 1.17654i | ||||
\(134\) | −5.48588 | − | 9.50182i | −0.473908 | − | 0.820832i | ||||
\(135\) | 0.357869 | − | 0.619848i | 0.0308005 | − | 0.0533480i | ||||
\(136\) | 4.90232 | − | 8.49107i | 0.420371 | − | 0.728104i | ||||
\(137\) | −9.64137 | + | 16.6993i | −0.823718 | + | 1.42672i | 0.0791773 | + | 0.996861i | \(0.474771\pi\) |
−0.902895 | + | 0.429861i | \(0.858563\pi\) | |||||||
\(138\) | 0.353203 | − | 0.611766i | 0.0300667 | − | 0.0520770i | ||||
\(139\) | −1.31388 | − | 2.27571i | −0.111442 | − | 0.193023i | 0.804910 | − | 0.593397i | \(-0.202214\pi\) |
−0.916352 | + | 0.400374i | \(0.868880\pi\) | |||||||
\(140\) | 1.35010 | − | 2.33581i | 0.114105 | − | 0.197412i | ||||
\(141\) | 4.18536 | − | 7.24926i | 0.352471 | − | 0.610498i | ||||
\(142\) | −1.62877 | + | 2.82111i | −0.136683 | + | 0.236743i | ||||
\(143\) | 14.6526 | − | 6.86413i | 1.22531 | − | 0.574007i | ||||
\(144\) | −0.439604 | − | 0.761417i | −0.0366337 | − | 0.0634514i | ||||
\(145\) | −0.802702 | − | 1.39032i | −0.0666607 | − | 0.115460i | ||||
\(146\) | 1.01733 | − | 1.76207i | 0.0841948 | − | 0.145830i | ||||
\(147\) | 3.50593 | − | 6.05875i | 0.289164 | − | 0.499718i | ||||
\(148\) | 0.936669 | 0.0769937 | ||||||||
\(149\) | −15.5896 | −1.27715 | −0.638573 | − | 0.769561i | \(-0.720475\pi\) | ||||
−0.638573 | + | 0.769561i | \(0.720475\pi\) | |||||||
\(150\) | 1.70192 | − | 2.94782i | 0.138961 | − | 0.240688i | ||||
\(151\) | 4.61134 | + | 7.98707i | 0.375265 | + | 0.649978i | 0.990367 | − | 0.138470i | \(-0.0442183\pi\) |
−0.615102 | + | 0.788448i | \(0.710885\pi\) | |||||||
\(152\) | −15.3779 | −1.24731 | ||||||||
\(153\) | 1.88727 | − | 3.26885i | 0.152577 | − | 0.264271i | ||||
\(154\) | 4.50668 | − | 7.79699i | 0.363158 | − | 0.628299i | ||||
\(155\) | −0.273607 | −0.0219767 | ||||||||
\(156\) | −0.438674 | + | 5.11809i | −0.0351221 | + | 0.409775i | ||||
\(157\) | −9.20539 | − | 15.9442i | −0.734670 | − | 1.27249i | −0.954868 | − | 0.297031i | \(-0.904003\pi\) |
0.220197 | − | 0.975455i | \(-0.429330\pi\) | |||||||
\(158\) | 4.17427 | 0.332087 | ||||||||
\(159\) | 1.21338 | + | 2.10164i | 0.0962273 | + | 0.166671i | ||||
\(160\) | 2.09783 | + | 3.63355i | 0.165848 | + | 0.287258i | ||||
\(161\) | 1.23310 | − | 2.13338i | 0.0971817 | − | 0.168134i | ||||
\(162\) | 0.379240 | + | 0.656863i | 0.0297959 | + | 0.0516080i | ||||
\(163\) | 11.1686 | 0.874793 | 0.437396 | − | 0.899269i | \(-0.355901\pi\) | ||||
0.437396 | + | 0.899269i | \(0.355901\pi\) | |||||||
\(164\) | 3.27040 | + | 5.66451i | 0.255376 | + | 0.442324i | ||||
\(165\) | 1.60602 | − | 2.78170i | 0.125028 | − | 0.216555i | ||||
\(166\) | 4.37270 | + | 7.57374i | 0.339387 | + | 0.587836i | ||||
\(167\) | 7.09719 | − | 12.2927i | 0.549197 | − | 0.951237i | −0.449133 | − | 0.893465i | \(-0.648267\pi\) |
0.998330 | − | 0.0577721i | \(-0.0183997\pi\) | |||||||
\(168\) | 3.43336 | + | 5.95347i | 0.264889 | + | 0.459320i | ||||
\(169\) | 8.32104 | − | 9.98801i | 0.640080 | − | 0.768309i | ||||
\(170\) | −1.02455 | + | 1.77457i | −0.0785794 | + | 0.136103i | ||||
\(171\) | −5.92010 | −0.452722 | ||||||||
\(172\) | −7.12666 | −0.543403 | ||||||||
\(173\) | 19.2725 | 1.46526 | 0.732630 | − | 0.680627i | \(-0.238293\pi\) | ||||
0.732630 | + | 0.680627i | \(0.238293\pi\) | |||||||
\(174\) | 1.70127 | 0.128973 | ||||||||
\(175\) | 5.94172 | − | 10.2798i | 0.449152 | − | 0.777076i | ||||
\(176\) | −1.97282 | − | 3.41702i | −0.148707 | − | 0.257568i | ||||
\(177\) | 2.80700 | − | 4.86187i | 0.210987 | − | 0.365441i | ||||
\(178\) | −4.58948 | + | 7.94921i | −0.343996 | + | 0.595818i | ||||
\(179\) | −11.2324 | −0.839553 | −0.419776 | − | 0.907628i | \(-0.637891\pi\) | ||||
−0.419776 | + | 0.907628i | \(0.637891\pi\) | |||||||
\(180\) | 0.509859 | + | 0.883102i | 0.0380027 | + | 0.0658225i | ||||
\(181\) | 2.43304 | 0.180846 | 0.0904232 | − | 0.995903i | \(-0.471178\pi\) | ||||
0.0904232 | + | 0.995903i | \(0.471178\pi\) | |||||||
\(182\) | 0.621412 | − | 7.20871i | 0.0460621 | − | 0.534345i | ||||
\(183\) | −1.99378 | −0.147385 | ||||||||
\(184\) | 1.20962 | + | 2.09512i | 0.0891743 | + | 0.154454i | ||||
\(185\) | −0.470560 | −0.0345962 | ||||||||
\(186\) | 0.144973 | − | 0.251101i | 0.0106299 | − | 0.0184116i | ||||
\(187\) | 8.46954 | − | 14.6697i | 0.619354 | − | 1.07275i | ||||
\(188\) | 5.96292 | + | 10.3281i | 0.434890 | + | 0.753252i | ||||
\(189\) | 1.32176 | + | 2.29193i | 0.0961436 | + | 0.166714i | ||||
\(190\) | 3.21387 | 0.233158 | ||||||||
\(191\) | −13.7391 | −0.994124 | −0.497062 | − | 0.867715i | \(-0.665588\pi\) | ||||
−0.497062 | + | 0.867715i | \(0.665588\pi\) | |||||||
\(192\) | −2.68780 | −0.193975 | ||||||||
\(193\) | −13.8673 | −0.998187 | −0.499094 | − | 0.866548i | \(-0.666334\pi\) | ||||
−0.499094 | + | 0.866548i | \(0.666334\pi\) | |||||||
\(194\) | 1.36428 | − | 2.36300i | 0.0979493 | − | 0.169653i | ||||
\(195\) | 0.220379 | − | 2.57121i | 0.0157817 | − | 0.184128i | ||||
\(196\) | 4.97803 | + | 8.64170i | 0.355574 | + | 0.617265i | ||||
\(197\) | −9.15733 | + | 15.8610i | −0.652433 | + | 1.13005i | 0.330098 | + | 0.943947i | \(0.392918\pi\) |
−0.982531 | + | 0.186100i | \(0.940415\pi\) | |||||||
\(198\) | 1.70192 | + | 2.94782i | 0.120950 | + | 0.209492i | ||||
\(199\) | 3.55862 | − | 6.16371i | 0.252264 | − | 0.436933i | −0.711885 | − | 0.702296i | \(-0.752158\pi\) |
0.964149 | + | 0.265363i | \(0.0854916\pi\) | |||||||
\(200\) | 5.82859 | + | 10.0954i | 0.412143 | + | 0.713853i | ||||
\(201\) | 14.4655 | 1.02031 | ||||||||
\(202\) | 4.54298 | + | 7.86867i | 0.319643 | + | 0.553638i | ||||
\(203\) | 5.93442 | + | 0.00290089i | 0.416515 | + | 0.000203603i | ||||
\(204\) | 2.68881 | + | 4.65715i | 0.188254 | + | 0.326066i | ||||
\(205\) | −1.64297 | − | 2.84571i | −0.114750 | − | 0.198753i | ||||
\(206\) | −2.35077 | −0.163786 | ||||||||
\(207\) | 0.465673 | + | 0.806569i | 0.0323665 | + | 0.0560604i | ||||
\(208\) | −2.59994 | − | 1.81367i | −0.180274 | − | 0.125755i | ||||
\(209\) | −26.5678 | −1.83773 | ||||||||
\(210\) | −0.717546 | − | 1.24423i | −0.0495154 | − | 0.0858601i | ||||
\(211\) | −5.95003 | + | 10.3058i | −0.409617 | + | 0.709478i | −0.994847 | − | 0.101390i | \(-0.967671\pi\) |
0.585230 | + | 0.810868i | \(0.301004\pi\) | |||||||
\(212\) | −3.45742 | −0.237457 | ||||||||
\(213\) | −2.14741 | − | 3.71943i | −0.147138 | − | 0.254851i | ||||
\(214\) | 4.24228 | − | 7.34784i | 0.289996 | − | 0.502288i | ||||
\(215\) | 3.58026 | 0.244172 | ||||||||
\(216\) | −2.59757 | −0.176742 | ||||||||
\(217\) | 0.506127 | − | 0.875649i | 0.0343581 | − | 0.0594429i | ||||
\(218\) | −7.72937 | + | 13.3877i | −0.523499 | + | 0.906726i | ||||
\(219\) | 1.34127 | + | 2.32315i | 0.0906349 | + | 0.156984i | ||||
\(220\) | 2.28810 | + | 3.96311i | 0.154264 | + | 0.267193i | ||||
\(221\) | 1.16220 | − | 13.5596i | 0.0781780 | − | 0.912117i | ||||
\(222\) | 0.249330 | − | 0.431852i | 0.0167339 | − | 0.0289840i | ||||
\(223\) | 11.9432 | − | 20.6863i | 0.799778 | − | 1.38526i | −0.119982 | − | 0.992776i | \(-0.538284\pi\) |
0.919760 | − | 0.392481i | \(-0.128383\pi\) | |||||||
\(224\) | −15.5094 | − | 0.00758139i | −1.03627 | − | 0.000506553i | ||||
\(225\) | 2.24386 | + | 3.88648i | 0.149591 | + | 0.259099i | ||||
\(226\) | −6.48582 | + | 11.2338i | −0.431430 | + | 0.747259i | ||||
\(227\) | −6.29391 | + | 10.9014i | −0.417741 | + | 0.723549i | −0.995712 | − | 0.0925083i | \(-0.970512\pi\) |
0.577971 | + | 0.816058i | \(0.303845\pi\) | |||||||
\(228\) | 4.21721 | − | 7.30442i | 0.279291 | − | 0.483747i | ||||
\(229\) | 7.66365 | − | 13.2738i | 0.506429 | − | 0.877160i | −0.493544 | − | 0.869721i | \(-0.664299\pi\) |
0.999972 | − | 0.00743905i | \(-0.00236795\pi\) | |||||||
\(230\) | −0.252801 | − | 0.437865i | −0.0166692 | − | 0.0288720i | ||||
\(231\) | 5.93167 | + | 10.2856i | 0.390275 | + | 0.676740i | ||||
\(232\) | −2.91318 | + | 5.04578i | −0.191260 | + | 0.331271i | ||||
\(233\) | 13.3343 | − | 23.0957i | 0.873559 | − | 1.51305i | 0.0152699 | − | 0.999883i | \(-0.495139\pi\) |
0.858289 | − | 0.513166i | \(-0.171527\pi\) | |||||||
\(234\) | 2.24293 | + | 1.56463i | 0.146625 | + | 0.102283i | ||||
\(235\) | −2.99563 | − | 5.18858i | −0.195413 | − | 0.338465i | ||||
\(236\) | 3.99916 | + | 6.92675i | 0.260323 | + | 0.450893i | ||||
\(237\) | −2.75173 | + | 4.76614i | −0.178744 | + | 0.309594i | ||||
\(238\) | −3.78407 | − | 6.56161i | −0.245285 | − | 0.425326i | ||||
\(239\) | −14.5891 | −0.943693 | −0.471846 | − | 0.881681i | \(-0.656412\pi\) | ||||
−0.471846 | + | 0.881681i | \(0.656412\pi\) | |||||||
\(240\) | −0.629283 | −0.0406201 | ||||||||
\(241\) | −6.44615 | + | 11.1651i | −0.415233 | + | 0.719204i | −0.995453 | − | 0.0952555i | \(-0.969633\pi\) |
0.580220 | + | 0.814460i | \(0.302967\pi\) | |||||||
\(242\) | 3.46611 | + | 6.00347i | 0.222810 | + | 0.385918i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.42028 | − | 2.45999i | 0.0909240 | − | 0.157485i | ||||
\(245\) | −2.50084 | − | 4.34138i | −0.159773 | − | 0.277361i | ||||
\(246\) | 3.48217 | 0.222015 | ||||||||
\(247\) | −19.3294 | + | 9.05501i | −1.22990 | + | 0.576157i | ||||
\(248\) | 0.496490 | + | 0.859947i | 0.0315272 | + | 0.0546067i | ||||
\(249\) | −11.5302 | −0.730694 | ||||||||
\(250\) | −2.57532 | − | 4.46058i | −0.162877 | − | 0.282112i | ||||
\(251\) | −12.0203 | − | 20.8198i | −0.758717 | − | 1.31414i | −0.943505 | − | 0.331359i | \(-0.892493\pi\) |
0.184787 | − | 0.982779i | \(-0.440840\pi\) | |||||||
\(252\) | −3.76942 | − | 0.00184259i | −0.237451 | − | 0.000116072i | ||||
\(253\) | 2.08981 | + | 3.61965i | 0.131385 | + | 0.227566i | ||||
\(254\) | 13.6818 | 0.858471 | ||||||||
\(255\) | −1.35079 | − | 2.33964i | −0.0845899 | − | 0.146514i | ||||
\(256\) | 6.36088 | − | 11.0174i | 0.397555 | − | 0.688586i | ||||
\(257\) | −9.35724 | − | 16.2072i | −0.583689 | − | 1.01098i | −0.995038 | − | 0.0995004i | \(-0.968276\pi\) |
0.411349 | − | 0.911478i | \(-0.365058\pi\) | |||||||
\(258\) | −1.89703 | + | 3.28575i | −0.118104 | + | 0.204562i | ||||
\(259\) | 0.870456 | − | 1.50597i | 0.0540875 | − | 0.0935766i | ||||
\(260\) | 3.01545 | + | 2.10352i | 0.187010 | + | 0.130455i | ||||
\(261\) | −1.12150 | + | 1.94250i | −0.0694192 | + | 0.120238i | ||||
\(262\) | −14.9228 | −0.921931 | ||||||||
\(263\) | −9.37129 | −0.577859 | −0.288929 | − | 0.957350i | \(-0.593299\pi\) | ||||
−0.288929 | + | 0.957350i | \(0.593299\pi\) | |||||||
\(264\) | −11.6572 | −0.717450 | ||||||||
\(265\) | 1.73693 | 0.106699 | ||||||||
\(266\) | −5.94511 | + | 10.2856i | −0.364518 | + | 0.630652i | ||||
\(267\) | −6.05088 | − | 10.4804i | −0.370308 | − | 0.641392i | ||||
\(268\) | −10.3045 | + | 17.8480i | −0.629449 | + | 1.09024i | ||||
\(269\) | −6.07464 | + | 10.5216i | −0.370377 | + | 0.641512i | −0.989624 | − | 0.143685i | \(-0.954105\pi\) |
0.619246 | + | 0.785197i | \(0.287438\pi\) | |||||||
\(270\) | 0.542874 | 0.0330382 | ||||||||
\(271\) | 7.32926 | + | 12.6946i | 0.445221 | + | 0.771145i | 0.998068 | − | 0.0621380i | \(-0.0197919\pi\) |
−0.552847 | + | 0.833283i | \(0.686459\pi\) | |||||||
\(272\) | −3.31861 | −0.201220 | ||||||||
\(273\) | 7.82119 | + | 5.46159i | 0.473360 | + | 0.330551i | ||||
\(274\) | −14.6256 | −0.883563 | ||||||||
\(275\) | 10.0698 | + | 17.4414i | 0.607232 | + | 1.05176i | ||||
\(276\) | −1.32689 | −0.0798697 | ||||||||
\(277\) | 2.51608 | − | 4.35797i | 0.151176 | − | 0.261845i | −0.780484 | − | 0.625176i | \(-0.785027\pi\) |
0.931660 | + | 0.363331i | \(0.118361\pi\) | |||||||
\(278\) | 0.996555 | − | 1.72608i | 0.0597694 | − | 0.103524i | ||||
\(279\) | 0.191136 | + | 0.331058i | 0.0114430 | + | 0.0198199i | ||||
\(280\) | 4.91894 | + | 0.00240450i | 0.293963 | + | 0.000143696i | ||||
\(281\) | 0.854888 | 0.0509984 | 0.0254992 | − | 0.999675i | \(-0.491882\pi\) | ||||
0.0254992 | + | 0.999675i | \(0.491882\pi\) | |||||||
\(282\) | 6.34903 | 0.378079 | ||||||||
\(283\) | −31.2774 | −1.85925 | −0.929625 | − | 0.368506i | \(-0.879869\pi\) | ||||
−0.929625 | + | 0.368506i | \(0.879869\pi\) | |||||||
\(284\) | 6.11888 | 0.363088 | ||||||||
\(285\) | −2.11862 | + | 3.66956i | −0.125496 | + | 0.217366i | ||||
\(286\) | 10.0656 | + | 7.02160i | 0.595194 | + | 0.415196i | ||||
\(287\) | 12.1466 | + | 0.00593756i | 0.716991 | + | 0.000350483i | ||||
\(288\) | 2.93100 | − | 5.07665i | 0.172711 | − | 0.299144i | ||||
\(289\) | 1.37642 | + | 2.38403i | 0.0809657 | + | 0.140237i | ||||
\(290\) | 0.608833 | − | 1.05453i | 0.0357519 | − | 0.0619241i | ||||
\(291\) | 1.79870 | + | 3.11544i | 0.105442 | + | 0.182630i | ||||
\(292\) | −3.82185 | −0.223657 | ||||||||
\(293\) | 0.339044 | + | 0.587241i | 0.0198071 | + | 0.0343070i | 0.875759 | − | 0.482748i | \(-0.160361\pi\) |
−0.855952 | + | 0.517055i | \(0.827028\pi\) | |||||||
\(294\) | 5.30936 | + | 0.00519069i | 0.309648 | + | 0.000302727i | ||||
\(295\) | −2.00908 | − | 3.47983i | −0.116973 | − | 0.202603i | ||||
\(296\) | 0.853882 | + | 1.47897i | 0.0496309 | + | 0.0859632i | ||||
\(297\) | −4.48772 | −0.260404 | ||||||||
\(298\) | −5.91219 | − | 10.2402i | −0.342484 | − | 0.593199i | ||||
\(299\) | 2.75412 | + | 1.92122i | 0.159275 | + | 0.111107i | ||||
\(300\) | −6.39369 | −0.369140 | ||||||||
\(301\) | −6.62288 | + | 11.4582i | −0.381736 | + | 0.660441i | ||||
\(302\) | −3.49761 | + | 6.05803i | −0.201265 | + | 0.348601i | ||||
\(303\) | −11.9792 | −0.688185 | ||||||||
\(304\) | 2.60250 | + | 4.50766i | 0.149264 | + | 0.258532i | ||||
\(305\) | −0.713513 | + | 1.23584i | −0.0408556 | + | 0.0707640i | ||||
\(306\) | 2.86291 | 0.163662 | ||||||||
\(307\) | −27.2103 | −1.55297 | −0.776487 | − | 0.630134i | \(-0.783000\pi\) | ||||
−0.776487 | + | 0.630134i | \(0.783000\pi\) | |||||||
\(308\) | −16.9161 | − | 0.00826901i | −0.963885 | − | 0.000471171i | ||||
\(309\) | 1.54966 | − | 2.68409i | 0.0881569 | − | 0.152692i | ||||
\(310\) | −0.103763 | − | 0.179722i | −0.00589333 | − | 0.0102076i | ||||
\(311\) | 7.06426 | + | 12.2357i | 0.400577 | + | 0.693821i | 0.993796 | − | 0.111221i | \(-0.0354762\pi\) |
−0.593218 | + | 0.805042i | \(0.702143\pi\) | |||||||
\(312\) | −8.48119 | + | 3.97308i | −0.480153 | + | 0.224932i | ||||
\(313\) | 9.84907 | − | 17.0591i | 0.556703 | − | 0.964237i | −0.441066 | − | 0.897475i | \(-0.645400\pi\) |
0.997769 | − | 0.0667627i | \(-0.0212670\pi\) | |||||||
\(314\) | 6.98211 | − | 12.0934i | 0.394023 | − | 0.682468i | ||||
\(315\) | 1.89367 | 0.000925671i | 0.106696 | 5.21557e-5i | ||||||
\(316\) | −3.92042 | − | 6.79036i | −0.220541 | − | 0.381988i | ||||
\(317\) | −7.83931 | + | 13.5781i | −0.440299 | + | 0.762621i | −0.997711 | − | 0.0676152i | \(-0.978461\pi\) |
0.557412 | + | 0.830236i | \(0.311794\pi\) | |||||||
\(318\) | −0.920325 | + | 1.59405i | −0.0516092 | + | 0.0893898i | ||||
\(319\) | −5.03298 | + | 8.71738i | −0.281793 | + | 0.488079i | ||||
\(320\) | −0.961881 | + | 1.66603i | −0.0537708 | + | 0.0931338i | ||||
\(321\) | 5.59313 | + | 9.68758i | 0.312178 | + | 0.540708i | ||||
\(322\) | 1.86898 | 0.000913602i | 0.104154 | 5.09131e-5i | ||||||
\(323\) | −11.1728 | + | 19.3519i | −0.621673 | + | 1.07677i | ||||
\(324\) | 0.712354 | − | 1.23383i | 0.0395752 | − | 0.0685463i | ||||
\(325\) | 13.2708 | + | 9.25746i | 0.736132 | + | 0.513511i | ||||
\(326\) | 4.23558 | + | 7.33625i | 0.234587 | + | 0.406317i | ||||
\(327\) | −10.1906 | − | 17.6506i | −0.563541 | − | 0.976082i | ||||
\(328\) | −5.96270 | + | 10.3277i | −0.329235 | + | 0.570252i | ||||
\(329\) | 22.1469 | + | 0.0108259i | 1.22100 | + | 0.000596853i | ||||
\(330\) | 2.43626 | 0.134112 | ||||||||
\(331\) | 14.4236 | 0.792793 | 0.396396 | − | 0.918079i | \(-0.370261\pi\) | ||||
0.396396 | + | 0.918079i | \(0.370261\pi\) | |||||||
\(332\) | 8.21355 | − | 14.2263i | 0.450777 | − | 0.780769i | ||||
\(333\) | 0.328723 | + | 0.569365i | 0.0180139 | + | 0.0312010i | ||||
\(334\) | 10.7662 | 0.589098 | ||||||||
\(335\) | 5.17674 | − | 8.96638i | 0.282836 | − | 0.489886i | ||||
\(336\) | 1.16407 | − | 2.01395i | 0.0635051 | − | 0.109870i | ||||
\(337\) | 14.4299 | 0.786049 | 0.393025 | − | 0.919528i | \(-0.371429\pi\) | ||||
0.393025 | + | 0.919528i | \(0.371429\pi\) | |||||||
\(338\) | 9.71643 | + | 1.67793i | 0.528504 | + | 0.0912672i | ||||
\(339\) | −8.55107 | − | 14.8109i | −0.464431 | − | 0.804417i | ||||
\(340\) | 3.84897 | 0.208740 | ||||||||
\(341\) | 0.857766 | + | 1.48569i | 0.0464506 | + | 0.0804548i | ||||
\(342\) | −2.24514 | − | 3.88870i | −0.121403 | − | 0.210277i | ||||
\(343\) | 18.5202 | + | 0.0271595i | 0.999999 | + | 0.00146647i | ||||
\(344\) | −6.49678 | − | 11.2527i | −0.350283 | − | 0.606707i | ||||
\(345\) | 0.666600 | 0.0358885 | ||||||||
\(346\) | 7.30890 | + | 12.6594i | 0.392929 | + | 0.680573i | ||||
\(347\) | 2.33434 | − | 4.04319i | 0.125314 | − | 0.217050i | −0.796542 | − | 0.604584i | \(-0.793340\pi\) |
0.921856 | + | 0.387534i | \(0.126673\pi\) | |||||||
\(348\) | −1.59781 | − | 2.76749i | −0.0856517 | − | 0.148353i | ||||
\(349\) | 2.06807 | − | 3.58201i | 0.110701 | − | 0.191740i | −0.805352 | − | 0.592797i | \(-0.798024\pi\) |
0.916053 | + | 0.401057i | \(0.131357\pi\) | |||||||
\(350\) | 9.00573 | + | 0.00440222i | 0.481376 | + | 0.000235309i | ||||
\(351\) | −3.26504 | + | 1.52954i | −0.174275 | + | 0.0816406i | ||||
\(352\) | 13.1535 | − | 22.7826i | 0.701085 | − | 1.21431i | ||||
\(353\) | 35.7899 | 1.90491 | 0.952453 | − | 0.304684i | \(-0.0985509\pi\) | ||||
0.952453 | + | 0.304684i | \(0.0985509\pi\) | |||||||
\(354\) | 4.25811 | 0.226316 | ||||||||
\(355\) | −3.07397 | −0.163150 | ||||||||
\(356\) | 17.2415 | 0.913797 | ||||||||
\(357\) | 9.98650 | + | 0.00488165i | 0.528541 | + | 0.000258364i | ||||
\(358\) | −4.25979 | − | 7.37818i | −0.225137 | − | 0.389949i | ||||
\(359\) | 12.6381 | − | 21.8899i | 0.667014 | − | 1.15530i | −0.311721 | − | 0.950174i | \(-0.600905\pi\) |
0.978735 | − | 0.205129i | \(-0.0657614\pi\) | |||||||
\(360\) | −0.929592 | + | 1.61010i | −0.0489938 | + | 0.0848597i | ||||
\(361\) | 16.0476 | 0.844611 | ||||||||
\(362\) | 0.922706 | + | 1.59817i | 0.0484964 | + | 0.0839982i | ||||
\(363\) | −9.13961 | −0.479705 | ||||||||
\(364\) | −12.3102 | + | 5.75945i | −0.645227 | + | 0.301877i | ||||
\(365\) | 1.92000 | 0.100498 | ||||||||
\(366\) | −0.756122 | − | 1.30964i | −0.0395231 | − | 0.0684560i | ||||
\(367\) | 35.3997 | 1.84785 | 0.923925 | − | 0.382573i | \(-0.124962\pi\) | ||||
0.923925 | + | 0.382573i | \(0.124962\pi\) | |||||||
\(368\) | 0.409423 | − | 0.709142i | 0.0213427 | − | 0.0369666i | ||||
\(369\) | −2.29549 | + | 3.97591i | −0.119498 | + | 0.206977i | ||||
\(370\) | −0.178455 | − | 0.309093i | −0.00927744 | − | 0.0160690i | ||||
\(371\) | −3.21302 | + | 5.55884i | −0.166812 | + | 0.288600i | ||||
\(372\) | −0.544627 | −0.0282376 | ||||||||
\(373\) | −32.7804 | −1.69730 | −0.848652 | − | 0.528951i | \(-0.822586\pi\) | ||||
−0.848652 | + | 0.528951i | \(0.822586\pi\) | |||||||
\(374\) | 12.8480 | 0.664352 | ||||||||
\(375\) | 6.79073 | 0.350672 | ||||||||
\(376\) | −10.8718 | + | 18.8305i | −0.560669 | + | 0.971108i | ||||
\(377\) | −0.690631 | + | 8.05771i | −0.0355693 | + | 0.414993i | ||||
\(378\) | −1.00422 | + | 1.73741i | −0.0516517 | + | 0.0893625i | ||||
\(379\) | −6.04308 | + | 10.4669i | −0.310412 | + | 0.537650i | −0.978452 | − | 0.206476i | \(-0.933800\pi\) |
0.668039 | + | 0.744126i | \(0.267134\pi\) | |||||||
\(380\) | −3.01842 | − | 5.22806i | −0.154842 | − | 0.268194i | ||||
\(381\) | −9.01920 | + | 15.6217i | −0.462068 | + | 0.800325i | ||||
\(382\) | −5.21040 | − | 9.02468i | −0.266587 | − | 0.461743i | ||||
\(383\) | −0.512172 | −0.0261708 | −0.0130854 | − | 0.999914i | \(-0.504165\pi\) | ||||
−0.0130854 | + | 0.999914i | \(0.504165\pi\) | |||||||
\(384\) | 4.84269 | + | 8.38778i | 0.247127 | + | 0.428037i | ||||
\(385\) | 8.49824 | + | 0.00415415i | 0.433110 | + | 0.000211715i | ||||
\(386\) | −5.25902 | − | 9.10889i | −0.267677 | − | 0.463630i | ||||
\(387\) | −2.50110 | − | 4.33202i | −0.127138 | − | 0.220209i | ||||
\(388\) | −5.12524 | −0.260195 | ||||||||
\(389\) | −17.7577 | − | 30.7573i | −0.900353 | − | 1.55946i | −0.827037 | − | 0.562148i | \(-0.809975\pi\) |
−0.0733162 | − | 0.997309i | \(-0.523358\pi\) | |||||||
\(390\) | 1.77251 | − | 0.830345i | 0.0897544 | − | 0.0420462i | ||||
\(391\) | 3.51540 | 0.177781 | ||||||||
\(392\) | −9.10690 | + | 15.7381i | −0.459968 | + | 0.794892i | ||||
\(393\) | 9.83728 | − | 17.0387i | 0.496225 | − | 0.859487i | ||||
\(394\) | −13.8913 | −0.699834 | ||||||||
\(395\) | 1.96952 | + | 3.41131i | 0.0990974 | + | 0.171642i | ||||
\(396\) | 3.19684 | − | 5.53710i | 0.160647 | − | 0.278250i | ||||
\(397\) | −8.29730 | −0.416430 | −0.208215 | − | 0.978083i | \(-0.566765\pi\) | ||||
−0.208215 | + | 0.978083i | \(0.566765\pi\) | |||||||
\(398\) | 5.39828 | 0.270591 | ||||||||
\(399\) | −7.82493 | − | 13.5685i | −0.391736 | − | 0.679274i | ||||
\(400\) | 1.97282 | − | 3.41702i | 0.0986410 | − | 0.170851i | ||||
\(401\) | −6.96021 | − | 12.0554i | −0.347576 | − | 0.602019i | 0.638242 | − | 0.769836i | \(-0.279662\pi\) |
−0.985818 | + | 0.167816i | \(0.946329\pi\) | |||||||
\(402\) | 5.48588 | + | 9.50182i | 0.273611 | + | 0.473908i | ||||
\(403\) | 1.13043 | + | 0.788568i | 0.0563109 | + | 0.0392814i | ||||
\(404\) | 8.53341 | − | 14.7803i | 0.424553 | − | 0.735347i | ||||
\(405\) | −0.357869 | + | 0.619848i | −0.0177827 | + | 0.0308005i | ||||
\(406\) | 2.24867 | + | 3.89920i | 0.111599 | + | 0.193514i | ||||
\(407\) | 1.47522 | + | 2.55515i | 0.0731238 | + | 0.126654i | ||||
\(408\) | −4.90232 | + | 8.49107i | −0.242701 | + | 0.420371i | ||||
\(409\) | 2.45871 | − | 4.25862i | 0.121576 | − | 0.210575i | −0.798814 | − | 0.601579i | \(-0.794539\pi\) |
0.920389 | + | 0.391004i | \(0.127872\pi\) | |||||||
\(410\) | 1.24616 | − | 2.15841i | 0.0615435 | − | 0.106597i | ||||
\(411\) | 9.64137 | − | 16.6993i | 0.475574 | − | 0.823718i | ||||
\(412\) | 2.20781 | + | 3.82404i | 0.108771 | + | 0.188397i | ||||
\(413\) | 14.8533 | + | 0.00726064i | 0.730881 | + | 0.000357273i | ||||
\(414\) | −0.353203 | + | 0.611766i | −0.0173590 | + | 0.0300667i | ||||
\(415\) | −4.12629 | + | 7.14694i | −0.202552 | + | 0.350830i | ||||
\(416\) | 1.80494 | − | 21.0586i | 0.0884945 | − | 1.03248i | ||||
\(417\) | 1.31388 | + | 2.27571i | 0.0643412 | + | 0.111442i | ||||
\(418\) | −10.0756 | − | 17.4514i | −0.492812 | − | 0.853575i | ||||
\(419\) | 4.85147 | − | 8.40299i | 0.237010 | − | 0.410513i | −0.722845 | − | 0.691010i | \(-0.757166\pi\) |
0.959855 | + | 0.280497i | \(0.0904993\pi\) | |||||||
\(420\) | −1.35010 | + | 2.33581i | −0.0658783 | + | 0.113976i | ||||
\(421\) | −15.2944 | −0.745405 | −0.372702 | − | 0.927951i | \(-0.621569\pi\) | ||||
−0.372702 | + | 0.927951i | \(0.621569\pi\) | |||||||
\(422\) | −9.02596 | −0.439377 | ||||||||
\(423\) | −4.18536 | + | 7.24926i | −0.203499 | + | 0.352471i | ||||
\(424\) | −3.15184 | − | 5.45915i | −0.153067 | − | 0.265120i | ||||
\(425\) | 16.9391 | 0.821666 | ||||||||
\(426\) | 1.62877 | − | 2.82111i | 0.0789142 | − | 0.136683i | ||||
\(427\) | −2.63529 | − | 4.56961i | −0.127531 | − | 0.221139i | ||||
\(428\) | −15.9371 | −0.770351 | ||||||||
\(429\) | −14.6526 | + | 6.86413i | −0.707434 | + | 0.331403i | ||||
\(430\) | 1.35778 | + | 2.35174i | 0.0654779 | + | 0.113411i | ||||
\(431\) | 32.6580 | 1.57308 | 0.786541 | − | 0.617538i | \(-0.211870\pi\) | ||||
0.786541 | + | 0.617538i | \(0.211870\pi\) | |||||||
\(432\) | 0.439604 | + | 0.761417i | 0.0211505 | + | 0.0366337i | ||||
\(433\) | 9.28189 | + | 16.0767i | 0.446059 | + | 0.772597i | 0.998125 | − | 0.0612034i | \(-0.0194938\pi\) |
−0.552066 | + | 0.833800i | \(0.686160\pi\) | |||||||
\(434\) | 0.767125 | 0.000374990i | 0.0368232 | 1.80001e-5i | ||||||
\(435\) | 0.802702 | + | 1.39032i | 0.0384866 | + | 0.0666607i | ||||
\(436\) | 29.0372 | 1.39063 | ||||||||
\(437\) | −2.75683 | − | 4.77497i | −0.131877 | − | 0.228418i | ||||
\(438\) | −1.01733 | + | 1.76207i | −0.0486099 | + | 0.0841948i | ||||
\(439\) | −4.72738 | − | 8.18806i | −0.225625 | − | 0.390795i | 0.730881 | − | 0.682504i | \(-0.239109\pi\) |
−0.956507 | + | 0.291710i | \(0.905776\pi\) | |||||||
\(440\) | −4.17175 | + | 7.22568i | −0.198880 | + | 0.344471i | ||||
\(441\) | −3.50593 | + | 6.05875i | −0.166949 | + | 0.288512i | ||||
\(442\) | 9.34755 | − | 4.37893i | 0.444617 | − | 0.208285i | ||||
\(443\) | −3.71593 | + | 6.43618i | −0.176549 | + | 0.305792i | −0.940696 | − | 0.339250i | \(-0.889827\pi\) |
0.764147 | + | 0.645042i | \(0.223160\pi\) | |||||||
\(444\) | −0.936669 | −0.0444523 | ||||||||
\(445\) | −8.66170 | −0.410604 | ||||||||
\(446\) | 18.1174 | 0.857885 | ||||||||
\(447\) | 15.5896 | 0.737361 | ||||||||
\(448\) | −3.55261 | − | 6.16026i | −0.167845 | − | 0.291045i | ||||
\(449\) | −9.42362 | − | 16.3222i | −0.444728 | − | 0.770291i | 0.553305 | − | 0.832979i | \(-0.313366\pi\) |
−0.998033 | + | 0.0626872i | \(0.980033\pi\) | |||||||
\(450\) | −1.70192 | + | 2.94782i | −0.0802294 | + | 0.138961i | ||||
\(451\) | −10.3015 | + | 17.8427i | −0.485079 | + | 0.840182i | ||||
\(452\) | 24.3656 | 1.14606 | ||||||||
\(453\) | −4.61134 | − | 7.98707i | −0.216659 | − | 0.375265i | ||||
\(454\) | −9.54761 | −0.448092 | ||||||||
\(455\) | 6.18432 | − | 2.89341i | 0.289925 | − | 0.135645i | ||||
\(456\) | 15.3779 | 0.720136 | ||||||||
\(457\) | 3.40003 | + | 5.88903i | 0.159047 | + | 0.275477i | 0.934525 | − | 0.355897i | \(-0.115825\pi\) |
−0.775478 | + | 0.631374i | \(0.782491\pi\) | |||||||
\(458\) | 11.6255 | 0.543222 | ||||||||
\(459\) | −1.88727 | + | 3.26885i | −0.0880903 | + | 0.152577i | ||||
\(460\) | −0.474855 | + | 0.822473i | −0.0221402 | + | 0.0383480i | ||||
\(461\) | −4.80595 | − | 8.32415i | −0.223836 | − | 0.387694i | 0.732134 | − | 0.681161i | \(-0.238525\pi\) |
−0.955969 | + | 0.293466i | \(0.905191\pi\) | |||||||
\(462\) | −4.50668 | + | 7.79699i | −0.209670 | + | 0.362749i | ||||
\(463\) | −23.4929 | −1.09181 | −0.545905 | − | 0.837847i | \(-0.683814\pi\) | ||||
−0.545905 | + | 0.837847i | \(0.683814\pi\) | |||||||
\(464\) | 1.97207 | 0.0915508 | ||||||||
\(465\) | 0.273607 | 0.0126882 | ||||||||
\(466\) | 20.2276 | 0.937026 | ||||||||
\(467\) | 7.24654 | − | 12.5514i | 0.335330 | − | 0.580808i | −0.648218 | − | 0.761455i | \(-0.724486\pi\) |
0.983548 | + | 0.180646i | \(0.0578189\pi\) | |||||||
\(468\) | 0.438674 | − | 5.11809i | 0.0202777 | − | 0.236584i | ||||
\(469\) | 19.1198 | + | 33.1539i | 0.882870 | + | 1.53090i | ||||
\(470\) | 2.27212 | − | 3.93543i | 0.104805 | − | 0.181528i | ||||
\(471\) | 9.20539 | + | 15.9442i | 0.424162 | + | 0.734670i | ||||
\(472\) | −7.29139 | + | 12.6291i | −0.335614 | + | 0.581300i | ||||
\(473\) | −11.2242 | − | 19.4409i | −0.516090 | − | 0.893894i | ||||
\(474\) | −4.17427 | −0.191731 | ||||||||
\(475\) | −13.2839 | − | 23.0083i | −0.609506 | − | 1.05570i | ||||
\(476\) | −7.11994 | + | 12.3182i | −0.326342 | + | 0.564604i | ||||
\(477\) | −1.21338 | − | 2.10164i | −0.0555569 | − | 0.0962273i | ||||
\(478\) | −5.53279 | − | 9.58307i | −0.253064 | − | 0.438319i | ||||
\(479\) | 14.5134 | 0.663134 | 0.331567 | − | 0.943432i | \(-0.392423\pi\) | ||||
0.331567 | + | 0.943432i | \(0.392423\pi\) | |||||||
\(480\) | −2.09783 | − | 3.63355i | −0.0957525 | − | 0.165848i | ||||
\(481\) | 1.94416 | + | 1.35621i | 0.0886461 | + | 0.0618378i | ||||
\(482\) | −9.77855 | −0.445401 | ||||||||
\(483\) | −1.23310 | + | 2.13338i | −0.0561079 | + | 0.0970720i | ||||
\(484\) | 6.51064 | − | 11.2768i | 0.295938 | − | 0.512580i | ||||
\(485\) | 2.57480 | 0.116915 | ||||||||
\(486\) | −0.379240 | − | 0.656863i | −0.0172027 | − | 0.0297959i | ||||
\(487\) | −11.6964 | + | 20.2587i | −0.530013 | + | 0.918009i | 0.469374 | + | 0.882999i | \(0.344480\pi\) |
−0.999387 | + | 0.0350099i | \(0.988854\pi\) | |||||||
\(488\) | 5.17899 | 0.234442 | ||||||||
\(489\) | −11.1686 | −0.505062 | ||||||||
\(490\) | 1.90327 | − | 3.28914i | 0.0859812 | − | 0.148588i | ||||
\(491\) | 0.786824 | − | 1.36282i | 0.0355089 | − | 0.0615032i | −0.847725 | − | 0.530436i | \(-0.822028\pi\) |
0.883234 | + | 0.468933i | \(0.155361\pi\) | |||||||
\(492\) | −3.27040 | − | 5.66451i | −0.147441 | − | 0.255376i | ||||
\(493\) | 4.23315 | + | 7.33203i | 0.190652 | + | 0.330218i | ||||
\(494\) | −13.2784 | − | 9.26275i | −0.597423 | − | 0.416751i | ||||
\(495\) | −1.60602 | + | 2.78170i | −0.0721851 | + | 0.125028i | ||||
\(496\) | 0.168049 | − | 0.291069i | 0.00754560 | − | 0.0130694i | ||||
\(497\) | 5.68633 | − | 9.83791i | 0.255067 | − | 0.441291i | ||||
\(498\) | −4.37270 | − | 7.57374i | −0.195945 | − | 0.339387i | ||||
\(499\) | −7.86689 | + | 13.6259i | −0.352170 | + | 0.609977i | −0.986629 | − | 0.162980i | \(-0.947890\pi\) |
0.634459 | + | 0.772956i | \(0.281223\pi\) | |||||||
\(500\) | −4.83740 | + | 8.37862i | −0.216335 | + | 0.374703i | ||||
\(501\) | −7.09719 | + | 12.2927i | −0.317079 | + | 0.549197i | ||||
\(502\) | 9.11719 | − | 15.7914i | 0.406920 | − | 0.704807i | ||||
\(503\) | 17.7055 | + | 30.6668i | 0.789447 | + | 1.36736i | 0.926306 | + | 0.376773i | \(0.122966\pi\) |
−0.136858 | + | 0.990591i | \(0.543701\pi\) | |||||||
\(504\) | −3.43336 | − | 5.95347i | −0.152934 | − | 0.265188i | ||||
\(505\) | −4.28698 | + | 7.42526i | −0.190768 | + | 0.330420i | ||||
\(506\) | −1.58508 | + | 2.74543i | −0.0704653 | + | 0.122049i | ||||
\(507\) | −8.32104 | + | 9.98801i | −0.369550 | + | 0.443583i | ||||
\(508\) | −12.8497 | − | 22.2564i | −0.570115 | − | 0.987467i | ||||
\(509\) | 5.20477 | + | 9.01493i | 0.230697 | + | 0.399580i | 0.958014 | − | 0.286723i | \(-0.0925659\pi\) |
−0.727316 | + | 0.686303i | \(0.759233\pi\) | |||||||
\(510\) | 1.02455 | − | 1.77457i | 0.0453678 | − | 0.0785794i | ||||
\(511\) | −3.55168 | + | 6.14475i | −0.157117 | + | 0.271828i | ||||
\(512\) | −9.72154 | −0.429635 | ||||||||
\(513\) | 5.92010 | 0.261379 | ||||||||
\(514\) | 7.09728 | − | 12.2929i | 0.313048 | − | 0.542214i | ||||
\(515\) | −1.10915 | − | 1.92110i | −0.0488750 | − | 0.0846540i | ||||
\(516\) | 7.12666 | 0.313734 | ||||||||
\(517\) | −18.7827 | + | 32.5326i | −0.826063 | + | 1.43078i | ||||
\(518\) | 1.31933 | 0.000644921i | 0.0579680 | 2.83362e-5i | ||||||
\(519\) | −19.2725 | −0.845968 | ||||||||
\(520\) | −0.572451 | + | 6.67889i | −0.0251037 | + | 0.292889i | ||||
\(521\) | −0.513222 | − | 0.888926i | −0.0224847 | − | 0.0389446i | 0.854564 | − | 0.519346i | \(-0.173824\pi\) |
−0.877049 | + | 0.480401i | \(0.840491\pi\) | |||||||
\(522\) | −1.70127 | −0.0744627 | ||||||||
\(523\) | 9.02138 | + | 15.6255i | 0.394477 | + | 0.683255i | 0.993034 | − | 0.117826i | \(-0.0375924\pi\) |
−0.598557 | + | 0.801080i | \(0.704259\pi\) | |||||||
\(524\) | 14.0153 | + | 24.2751i | 0.612259 | + | 1.06046i | ||||
\(525\) | −5.94172 | + | 10.2798i | −0.259318 | + | 0.448645i | ||||
\(526\) | −3.55397 | − | 6.15566i | −0.154960 | − | 0.268399i | ||||
\(527\) | 1.44290 | 0.0628539 | ||||||||
\(528\) | 1.97282 | + | 3.41702i | 0.0858559 | + | 0.148707i | ||||
\(529\) | 11.0663 | − | 19.1674i | 0.481143 | − | 0.833365i | ||||
\(530\) | 0.658712 | + | 1.14092i | 0.0286126 | + | 0.0495585i | ||||
\(531\) | −2.80700 | + | 4.86187i | −0.121814 | + | 0.210987i | ||||
\(532\) | 22.3154 | + | 0.0109083i | 0.967494 | + | 0.000472935i | ||||
\(533\) | −1.41359 | + | 16.4926i | −0.0612292 | + | 0.714372i | ||||
\(534\) | 4.58948 | − | 7.94921i | 0.198606 | − | 0.343996i | ||||
\(535\) | 8.00644 | 0.346148 | ||||||||
\(536\) | −37.5751 | −1.62300 | ||||||||
\(537\) | 11.2324 | 0.484716 | ||||||||
\(538\) | −9.21499 | −0.397286 | ||||||||
\(539\) | −15.7336 | + | 27.1900i | −0.677694 | + | 1.17116i | ||||
\(540\) | −0.509859 | − | 0.883102i | −0.0219408 | − | 0.0380027i | ||||
\(541\) | 16.7318 | − | 28.9803i | 0.719355 | − | 1.24596i | −0.241900 | − | 0.970301i | \(-0.577771\pi\) |
0.961256 | − | 0.275659i | \(-0.0888960\pi\) | |||||||
\(542\) | −5.55910 | + | 9.62864i | −0.238784 | + | 0.413585i | ||||
\(543\) | −2.43304 | −0.104412 | ||||||||
\(544\) | −11.0632 | − | 19.1620i | −0.474331 | − | 0.821565i | ||||
\(545\) | −14.5876 | −0.624865 | ||||||||
\(546\) | −0.621412 | + | 7.20871i | −0.0265940 | + | 0.308504i | ||||
\(547\) | 30.7718 | 1.31571 | 0.657853 | − | 0.753146i | \(-0.271465\pi\) | ||||
0.657853 | + | 0.753146i | \(0.271465\pi\) | |||||||
\(548\) | 13.7361 | + | 23.7917i | 0.586779 | + | 1.01633i | ||||
\(549\) | 1.99378 | 0.0850925 | ||||||||
\(550\) | −7.63775 | + | 13.2290i | −0.325675 | + | 0.564085i | ||||
\(551\) | 6.63940 | − | 11.4998i | 0.282848 | − | 0.489907i | ||||
\(552\) | −1.20962 | − | 2.09512i | −0.0514848 | − | 0.0891743i | ||||
\(553\) | −14.5608 | − | 0.00711768i | −0.619188 | − | 0.000302675i | ||||
\(554\) | 3.81679 | 0.162160 | ||||||||
\(555\) | 0.470560 | 0.0199741 | ||||||||
\(556\) | −3.74380 | −0.158773 | ||||||||
\(557\) | 15.6343 | 0.662446 | 0.331223 | − | 0.943553i | \(-0.392539\pi\) | ||||
0.331223 | + | 0.943553i | \(0.392539\pi\) | |||||||
\(558\) | −0.144973 | + | 0.251101i | −0.00613720 | + | 0.0106299i | ||||
\(559\) | −14.7922 | − | 10.3187i | −0.625642 | − | 0.436436i | ||||
\(560\) | −0.831759 | − | 1.44228i | −0.0351482 | − | 0.0609473i | ||||
\(561\) | −8.46954 | + | 14.6697i | −0.357584 | + | 0.619354i | ||||
\(562\) | 0.324208 | + | 0.561545i | 0.0136759 | + | 0.0236873i | ||||
\(563\) | −16.7621 | + | 29.0328i | −0.706438 | + | 1.22359i | 0.259733 | + | 0.965681i | \(0.416366\pi\) |
−0.966170 | + | 0.257905i | \(0.916968\pi\) | |||||||
\(564\) | −5.96292 | − | 10.3281i | −0.251084 | − | 0.434890i | ||||
\(565\) | −12.2407 | −0.514969 | ||||||||
\(566\) | −11.8617 | − | 20.5450i | −0.498583 | − | 0.863570i | ||||
\(567\) | −1.32176 | − | 2.29193i | −0.0555085 | − | 0.0962522i | ||||
\(568\) | 5.57806 | + | 9.66149i | 0.234050 | + | 0.405387i | ||||
\(569\) | −10.6031 | − | 18.3651i | −0.444504 | − | 0.769903i | 0.553514 | − | 0.832840i | \(-0.313287\pi\) |
−0.998018 | + | 0.0629368i | \(0.979953\pi\) | |||||||
\(570\) | −3.21387 | −0.134614 | ||||||||
\(571\) | −0.869647 | − | 1.50627i | −0.0363936 | − | 0.0630356i | 0.847255 | − | 0.531187i | \(-0.178254\pi\) |
−0.883648 | + | 0.468151i | \(0.844920\pi\) | |||||||
\(572\) | 1.96865 | − | 22.9686i | 0.0823133 | − | 0.960364i | ||||
\(573\) | 13.7391 | 0.573958 | ||||||||
\(574\) | 4.60258 | + | 7.98090i | 0.192108 | + | 0.333116i | ||||
\(575\) | −2.08981 | + | 3.61965i | −0.0871510 | + | 0.150950i | ||||
\(576\) | 2.68780 | 0.111992 | ||||||||
\(577\) | −2.83193 | − | 4.90504i | −0.117895 | − | 0.204199i | 0.801039 | − | 0.598613i | \(-0.204281\pi\) |
−0.918933 | + | 0.394413i | \(0.870948\pi\) | |||||||
\(578\) | −1.04399 | + | 1.80824i | −0.0434241 | + | 0.0752127i | ||||
\(579\) | 13.8673 | 0.576304 | ||||||||
\(580\) | −2.28723 | −0.0949721 | ||||||||
\(581\) | −15.2401 | − | 26.4264i | −0.632264 | − | 1.09635i | ||||
\(582\) | −1.36428 | + | 2.36300i | −0.0565511 | + | 0.0979493i | ||||
\(583\) | −5.44531 | − | 9.43155i | −0.225522 | − | 0.390615i | ||||
\(584\) | −3.48406 | − | 6.03456i | −0.144171 | − | 0.249712i | ||||
\(585\) | −0.220379 | + | 2.57121i | −0.00911157 | + | 0.106306i | ||||
\(586\) | −0.257158 | + | 0.445411i | −0.0106231 | + | 0.0183997i | ||||
\(587\) | 8.06910 | − | 13.9761i | 0.333047 | − | 0.576855i | −0.650060 | − | 0.759882i | \(-0.725256\pi\) |
0.983108 | + | 0.183028i | \(0.0585898\pi\) | |||||||
\(588\) | −4.97803 | − | 8.64170i | −0.205291 | − | 0.356378i | ||||
\(589\) | −1.13155 | − | 1.95990i | −0.0466246 | − | 0.0807561i | ||||
\(590\) | 1.52385 | − | 2.63938i | 0.0627358 | − | 0.108662i | ||||
\(591\) | 9.15733 | − | 15.8610i | 0.376682 | − | 0.652433i | ||||
\(592\) | 0.289016 | − | 0.500590i | 0.0118785 | − | 0.0205741i | ||||
\(593\) | −21.1595 | + | 36.6493i | −0.868917 | + | 1.50501i | −0.00581233 | + | 0.999983i | \(0.501850\pi\) |
−0.863105 | + | 0.505025i | \(0.831483\pi\) | |||||||
\(594\) | −1.70192 | − | 2.94782i | −0.0698307 | − | 0.120950i | ||||
\(595\) | 3.57689 | − | 6.18836i | 0.146638 | − | 0.253698i | ||||
\(596\) | −11.1053 | + | 19.2349i | −0.454890 | + | 0.787893i | ||||
\(597\) | −3.55862 | + | 6.16371i | −0.145644 | + | 0.252264i | ||||
\(598\) | −0.217506 | + | 2.53768i | −0.00889448 | + | 0.103774i | ||||
\(599\) | 22.9026 | + | 39.6685i | 0.935776 | + | 1.62081i | 0.773244 | + | 0.634108i | \(0.218633\pi\) |
0.162532 | + | 0.986703i | \(0.448034\pi\) | |||||||
\(600\) | −5.82859 | − | 10.0954i | −0.237951 | − | 0.412143i | ||||
\(601\) | 6.27579 | − | 10.8700i | 0.255995 | − | 0.443396i | −0.709170 | − | 0.705037i | \(-0.750930\pi\) |
0.965165 | + | 0.261641i | \(0.0842637\pi\) | |||||||
\(602\) | −10.0381 | − | 0.00490689i | −0.409124 | − | 0.000199990i | ||||
\(603\) | −14.4655 | −0.589079 | ||||||||
\(604\) | 13.1396 | 0.534643 | ||||||||
\(605\) | −3.27079 | + | 5.66517i | −0.132976 | + | 0.230322i | ||||
\(606\) | −4.54298 | − | 7.86867i | −0.184546 | − | 0.319643i | ||||
\(607\) | 34.4923 | 1.40000 | 0.700000 | − | 0.714143i | \(-0.253183\pi\) | ||||
0.700000 | + | 0.714143i | \(0.253183\pi\) | |||||||
\(608\) | −17.3518 | + | 30.0543i | −0.703710 | + | 1.21886i | ||||
\(609\) | −5.93442 | − | 0.00290089i | −0.240475 | − | 0.000117550i | ||||
\(610\) | −1.08237 | −0.0438239 | ||||||||
\(611\) | −2.57739 | + | 30.0708i | −0.104270 | + | 1.21654i | ||||
\(612\) | −2.68881 | − | 4.65715i | −0.108689 | − | 0.188254i | ||||
\(613\) | −34.1674 | −1.38001 | −0.690003 | − | 0.723806i | \(-0.742391\pi\) | ||||
−0.690003 | + | 0.723806i | \(0.742391\pi\) | |||||||
\(614\) | −10.3192 | − | 17.8734i | −0.416450 | − | 0.721313i | ||||
\(615\) | 1.64297 | + | 2.84571i | 0.0662510 | + | 0.114750i | ||||
\(616\) | −15.4079 | − | 26.7175i | −0.620803 | − | 1.07648i | ||||
\(617\) | −18.4048 | − | 31.8781i | −0.740950 | − | 1.28336i | −0.952063 | − | 0.305902i | \(-0.901042\pi\) |
0.211113 | − | 0.977462i | \(-0.432291\pi\) | |||||||
\(618\) | 2.35077 | 0.0945618 | ||||||||
\(619\) | −17.9351 | − | 31.0644i | −0.720871 | − | 1.24858i | −0.960651 | − | 0.277758i | \(-0.910409\pi\) |
0.239780 | − | 0.970827i | \(-0.422925\pi\) | |||||||
\(620\) | −0.194905 | + | 0.337586i | −0.00782758 | + | 0.0135578i | ||||
\(621\) | −0.465673 | − | 0.806569i | −0.0186868 | − | 0.0323665i | ||||
\(622\) | −5.35810 | + | 9.28050i | −0.214840 | + | 0.372114i | ||||
\(623\) | 16.0227 | − | 27.7208i | 0.641935 | − | 1.11061i | ||||
\(624\) | 2.59994 | + | 1.81367i | 0.104081 | + | 0.0726049i | ||||
\(625\) | −8.78910 | + | 15.2232i | −0.351564 | + | 0.608927i | ||||
\(626\) | 14.9407 | 0.597149 | ||||||||
\(627\) | 26.5678 | 1.06101 | ||||||||
\(628\) | −26.2300 | −1.04669 | ||||||||
\(629\) | 2.48156 | 0.0989462 | ||||||||
\(630\) | 0.717546 | + | 1.24423i | 0.0285877 | + | 0.0495713i | ||||
\(631\) | −9.93368 | − | 17.2056i | −0.395453 | − | 0.684945i | 0.597706 | − | 0.801716i | \(-0.296079\pi\) |
−0.993159 | + | 0.116770i | \(0.962746\pi\) | |||||||
\(632\) | 7.14783 | − | 12.3804i | 0.284325 | − | 0.492466i | ||||
\(633\) | 5.95003 | − | 10.3058i | 0.236493 | − | 0.409617i | ||||
\(634\) | −11.8919 | −0.472288 | ||||||||
\(635\) | 6.45539 | + | 11.1811i | 0.256174 | + | 0.443707i | ||||
\(636\) | 3.45742 | 0.137096 | ||||||||
\(637\) | −2.17992 | + | 25.1445i | −0.0863715 | + | 0.996263i | ||||
\(638\) | −7.63483 | −0.302266 | ||||||||
\(639\) | 2.14741 | + | 3.71943i | 0.0849504 | + | 0.147138i | ||||
\(640\) | 6.93220 | 0.274019 | ||||||||
\(641\) | 1.27505 | − | 2.20844i | 0.0503613 | − | 0.0872282i | −0.839746 | − | 0.542980i | \(-0.817296\pi\) |
0.890107 | + | 0.455751i | \(0.150629\pi\) | |||||||
\(642\) | −4.24228 | + | 7.34784i | −0.167429 | + | 0.289996i | ||||
\(643\) | 7.23729 | + | 12.5354i | 0.285411 | + | 0.494346i | 0.972709 | − | 0.232029i | \(-0.0745366\pi\) |
−0.687298 | + | 0.726376i | \(0.741203\pi\) | |||||||
\(644\) | −1.75383 | − | 3.04116i | −0.0691106 | − | 0.119838i | ||||
\(645\) | −3.58026 | −0.140973 | ||||||||
\(646\) | −16.9488 | −0.666840 | ||||||||
\(647\) | −31.6619 | −1.24476 | −0.622379 | − | 0.782716i | \(-0.713834\pi\) | ||||
−0.622379 | + | 0.782716i | \(0.713834\pi\) | |||||||
\(648\) | 2.59757 | 0.102042 | ||||||||
\(649\) | −12.5970 | + | 21.8187i | −0.494477 | + | 0.856459i | ||||
\(650\) | −1.04806 | + | 12.2279i | −0.0411083 | + | 0.479618i | ||||
\(651\) | −0.506127 | + | 0.875649i | −0.0198367 | + | 0.0343194i | ||||
\(652\) | 7.95600 | − | 13.7802i | 0.311581 | − | 0.539674i | ||||
\(653\) | −3.52992 | − | 6.11399i | −0.138136 | − | 0.239259i | 0.788655 | − | 0.614836i | \(-0.210778\pi\) |
−0.926791 | + | 0.375577i | \(0.877445\pi\) | |||||||
\(654\) | 7.72937 | − | 13.3877i | 0.302242 | − | 0.523499i | ||||
\(655\) | −7.04092 | − | 12.1952i | −0.275112 | − | 0.476507i | ||||
\(656\) | 4.03643 | 0.157596 | ||||||||
\(657\) | −1.34127 | − | 2.32315i | −0.0523281 | − | 0.0906349i | ||||
\(658\) | 8.39186 | + | 14.5516i | 0.327149 | + | 0.567279i | ||||
\(659\) | 6.73098 | + | 11.6584i | 0.262202 | + | 0.454147i | 0.966827 | − | 0.255433i | \(-0.0822181\pi\) |
−0.704625 | + | 0.709580i | \(0.748885\pi\) | |||||||
\(660\) | −2.28810 | − | 3.96311i | −0.0890644 | − | 0.154264i | ||||
\(661\) | 4.13958 | 0.161011 | 0.0805054 | − | 0.996754i | \(-0.474347\pi\) | ||||
0.0805054 | + | 0.996754i | \(0.474347\pi\) | |||||||
\(662\) | 5.47001 | + | 9.47433i | 0.212598 | + | 0.368230i | ||||
\(663\) | −1.16220 | + | 13.5596i | −0.0451361 | + | 0.526611i | ||||
\(664\) | 29.9504 | 1.16230 | ||||||||
\(665\) | −11.2107 | − | 0.00548007i | −0.434732 | − | 0.000212508i | ||||
\(666\) | −0.249330 | + | 0.431852i | −0.00966134 | + | 0.0167339i | ||||
\(667\) | −2.08901 | −0.0808868 | ||||||||
\(668\) | −10.1114 | − | 17.5135i | −0.391223 | − | 0.677617i | ||||
\(669\) | −11.9432 | + | 20.6863i | −0.461752 | + | 0.799778i | ||||
\(670\) | 7.85291 | 0.303384 | ||||||||
\(671\) | 8.94753 | 0.345415 | ||||||||
\(672\) | 15.5094 | + | 0.00758139i | 0.598289 | + | 0.000292458i | ||||
\(673\) | −3.09545 | + | 5.36148i | −0.119321 | + | 0.206670i | −0.919499 | − | 0.393093i | \(-0.871405\pi\) |
0.800178 | + | 0.599763i | \(0.204738\pi\) | |||||||
\(674\) | 5.47241 | + | 9.47850i | 0.210790 | + | 0.365098i | ||||
\(675\) | −2.24386 | − | 3.88648i | −0.0863662 | − | 0.149591i | ||||
\(676\) | −6.39602 | − | 17.3818i | −0.246001 | − | 0.668530i | ||||
\(677\) | 8.44416 | − | 14.6257i | 0.324535 | − | 0.562112i | −0.656883 | − | 0.753993i | \(-0.728125\pi\) |
0.981418 | + | 0.191881i | \(0.0614587\pi\) | |||||||
\(678\) | 6.48582 | − | 11.2338i | 0.249086 | − | 0.431430i | ||||
\(679\) | −4.76294 | + | 8.24034i | −0.182785 | + | 0.316235i | ||||
\(680\) | 3.50878 | + | 6.07739i | 0.134556 | + | 0.233057i | ||||
\(681\) | 6.29391 | − | 10.9014i | 0.241183 | − | 0.417741i | ||||
\(682\) | −0.650598 | + | 1.12687i | −0.0249127 | + | 0.0431501i | ||||
\(683\) | −6.68862 | + | 11.5850i | −0.255933 | + | 0.443289i | −0.965149 | − | 0.261703i | \(-0.915716\pi\) |
0.709215 | + | 0.704992i | \(0.249049\pi\) | |||||||
\(684\) | −4.21721 | + | 7.30442i | −0.161249 | + | 0.279291i | ||||
\(685\) | −6.90070 | − | 11.9524i | −0.263662 | − | 0.456676i | ||||
\(686\) | 7.00578 | + | 12.1756i | 0.267482 | + | 0.464865i | ||||
\(687\) | −7.66365 | + | 13.2738i | −0.292387 | + | 0.506429i | ||||
\(688\) | −2.19898 | + | 3.80875i | −0.0838354 | + | 0.145207i | ||||
\(689\) | −7.17627 | − | 5.00603i | −0.273394 | − | 0.190714i | ||||
\(690\) | 0.252801 | + | 0.437865i | 0.00962398 | + | 0.0166692i | ||||
\(691\) | −4.90190 | − | 8.49034i | −0.186477 | − | 0.322988i | 0.757596 | − | 0.652723i | \(-0.226374\pi\) |
−0.944073 | + | 0.329736i | \(0.893040\pi\) | |||||||
\(692\) | 13.7288 | − | 23.7790i | 0.521892 | − | 0.903943i | ||||
\(693\) | −5.93167 | − | 10.2856i | −0.225325 | − | 0.390716i | ||||
\(694\) | 3.54110 | 0.134418 | ||||||||
\(695\) | 1.88079 | 0.0713426 | ||||||||
\(696\) | 2.91318 | − | 5.04578i | 0.110424 | − | 0.191260i | ||||
\(697\) | 8.66443 | + | 15.0072i | 0.328189 | + | 0.568439i | ||||
\(698\) | 3.13718 | 0.118744 | ||||||||
\(699\) | −13.3343 | + | 23.0957i | −0.504350 | + | 0.873559i | ||||
\(700\) | −8.45089 | − | 14.6539i | −0.319414 | − | 0.553866i | ||||
\(701\) | 35.6715 | 1.34729 | 0.673647 | − | 0.739054i | \(-0.264727\pi\) | ||||
0.673647 | + | 0.739054i | \(0.264727\pi\) | |||||||
\(702\) | −2.24293 | − | 1.56463i | −0.0846540 | − | 0.0590530i | ||||
\(703\) | −1.94607 | − | 3.37070i | −0.0733976 | − | 0.127128i | ||||
\(704\) | 12.0621 | 0.454607 | ||||||||
\(705\) | 2.99563 | + | 5.18858i | 0.112822 | + | 0.195413i | ||||
\(706\) | 13.5730 | + | 23.5091i | 0.510826 | + | 0.884777i | ||||
\(707\) | −15.8335 | − | 27.4555i | −0.595481 | − | 1.03257i | ||||
\(708\) | −3.99916 | − | 6.92675i | −0.150298 | − | 0.260323i | ||||
\(709\) | 31.7496 | 1.19238 | 0.596191 | − | 0.802842i | \(-0.296680\pi\) | ||||
0.596191 | + | 0.802842i | \(0.296680\pi\) | |||||||
\(710\) | −1.16577 | − | 2.01918i | −0.0437507 | − | 0.0757785i | ||||
\(711\) | 2.75173 | − | 4.76614i | 0.103198 | − | 0.178744i | ||||
\(712\) | 15.7176 | + | 27.2237i | 0.589043 | + | 1.02025i | ||||
\(713\) | −0.178014 | + | 0.308329i | −0.00666667 | + | 0.0115470i | ||||
\(714\) | 3.78407 | + | 6.56161i | 0.141615 | + | 0.245562i | ||||
\(715\) | −0.989000 | + | 11.5388i | −0.0369865 | + | 0.431528i | ||||
\(716\) | −8.00148 | + | 13.8590i | −0.299029 | + | 0.517934i | ||||
\(717\) | 14.5891 | 0.544841 | ||||||||
\(718\) | 19.1715 | 0.715475 | ||||||||
\(719\) | −6.98125 | −0.260357 | −0.130178 | − | 0.991491i | \(-0.541555\pi\) | ||||
−0.130178 | + | 0.991491i | \(0.541555\pi\) | |||||||
\(720\) | 0.629283 | 0.0234520 | ||||||||
\(721\) | 8.20002 | + | 0.00400837i | 0.305385 | + | 0.000149280i | ||||
\(722\) | 6.08590 | + | 10.5411i | 0.226494 | + | 0.392299i | ||||
\(723\) | 6.44615 | − | 11.1651i | 0.239735 | − | 0.415233i | ||||
\(724\) | 1.73319 | − | 3.00197i | 0.0644133 | − | 0.111567i | ||||
\(725\) | −10.0660 | −0.373840 | ||||||||
\(726\) | −3.46611 | − | 6.00347i | −0.128639 | − | 0.222810i | ||||
\(727\) | −2.58607 | −0.0959121 | −0.0479561 | − | 0.998849i | \(-0.515271\pi\) | ||||
−0.0479561 | + | 0.998849i | \(0.515271\pi\) | |||||||
\(728\) | −20.3161 | − | 14.1869i | −0.752965 | − | 0.525801i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.728142 | + | 1.26118i | 0.0269498 | + | 0.0466783i | ||||
\(731\) | −18.8810 | −0.698338 | ||||||||
\(732\) | −1.42028 | + | 2.45999i | −0.0524950 | + | 0.0909240i | ||||
\(733\) | 6.30712 | − | 10.9243i | 0.232959 | − | 0.403497i | −0.725719 | − | 0.687992i | \(-0.758493\pi\) |
0.958678 | + | 0.284495i | \(0.0918259\pi\) | |||||||
\(734\) | 13.4250 | + | 23.2528i | 0.495526 | + | 0.858276i | ||||
\(735\) | 2.50084 | + | 4.34138i | 0.0922450 | + | 0.160134i | ||||
\(736\) | 5.45955 | 0.201242 | ||||||||
\(737\) | −64.9169 | −2.39124 | ||||||||
\(738\) | −3.48217 | −0.128180 | ||||||||
\(739\) | 2.94077 | 0.108178 | 0.0540889 | − | 0.998536i | \(-0.482775\pi\) | ||||
0.0540889 | + | 0.998536i | \(0.482775\pi\) | |||||||
\(740\) | −0.335205 | + | 0.580592i | −0.0123224 | + | 0.0213430i | ||||
\(741\) | 19.3294 | − | 9.05501i | 0.710083 | − | 0.332644i | ||||
\(742\) | −4.86990 | − | 0.00238053i | −0.178780 | − | 8.73920e-5i | ||||
\(743\) | 20.5461 | − | 35.5869i | 0.753763 | − | 1.30556i | −0.192224 | − | 0.981351i | \(-0.561570\pi\) |
0.945987 | − | 0.324205i | \(-0.105097\pi\) | |||||||
\(744\) | −0.496490 | − | 0.859947i | −0.0182022 | − | 0.0315272i | ||||
\(745\) | 5.57903 | − | 9.66316i | 0.204400 | − | 0.354031i | ||||
\(746\) | −12.4316 | − | 21.5322i | −0.455155 | − | 0.788351i | ||||
\(747\) | 11.5302 | 0.421866 | ||||||||
\(748\) | −12.0666 | − | 20.9000i | −0.441199 | − | 0.764180i | ||||
\(749\) | −14.8106 | + | 25.6237i | −0.541166 | + | 0.936270i | ||||
\(750\) | 2.57532 | + | 4.46058i | 0.0940372 | + | 0.162877i | ||||
\(751\) | 15.2160 | + | 26.3549i | 0.555241 | + | 0.961705i | 0.997885 | + | 0.0650079i | \(0.0207073\pi\) |
−0.442644 | + | 0.896698i | \(0.645959\pi\) | |||||||
\(752\) | 7.35961 | 0.268377 | ||||||||
\(753\) | 12.0203 | + | 20.8198i | 0.438046 | + | 0.758717i | ||||
\(754\) | −5.55473 | + | 2.60216i | −0.202291 | + | 0.0947650i | ||||
\(755\) | −6.60102 | −0.240236 | ||||||||
\(756\) | 3.76942 | + | 0.00184259i | 0.137093 | + | 6.70143e-5i | ||||
\(757\) | 15.7459 | − | 27.2726i | 0.572293 | − | 0.991241i | −0.424037 | − | 0.905645i | \(-0.639387\pi\) |
0.996330 | − | 0.0855959i | \(-0.0272794\pi\) | |||||||
\(758\) | −9.16711 | −0.332965 | ||||||||
\(759\) | −2.08981 | − | 3.61965i | −0.0758552 | − | 0.131385i | ||||
\(760\) | 5.50328 | − | 9.53196i | 0.199625 | − | 0.345760i | ||||
\(761\) | −44.1732 | −1.60128 | −0.800638 | − | 0.599148i | \(-0.795506\pi\) | ||||
−0.800638 | + | 0.599148i | \(0.795506\pi\) | |||||||
\(762\) | −13.6818 | −0.495638 | ||||||||
\(763\) | 26.9846 | − | 46.6860i | 0.976909 | − | 1.69015i | ||||
\(764\) | −9.78707 | + | 16.9517i | −0.354084 | + | 0.613291i | ||||
\(765\) | 1.35079 | + | 2.33964i | 0.0488380 | + | 0.0845899i | ||||
\(766\) | −0.194236 | − | 0.336427i | −0.00701804 | − | 0.0121556i | ||||
\(767\) | −1.72858 | + | 20.1676i | −0.0624154 | + | 0.728211i | ||||
\(768\) | −6.36088 | + | 11.0174i | −0.229529 | + | 0.397555i | ||||
\(769\) | 25.4717 | − | 44.1182i | 0.918532 | − | 1.59094i | 0.116887 | − | 0.993145i | \(-0.462709\pi\) |
0.801646 | − | 0.597799i | \(-0.203958\pi\) | |||||||
\(770\) | 3.22014 | + | 5.58376i | 0.116046 | + | 0.201225i | ||||
\(771\) | 9.35724 | + | 16.2072i | 0.336993 | + | 0.583689i | ||||
\(772\) | −9.87840 | + | 17.1099i | −0.355531 | + | 0.615798i | ||||
\(773\) | 2.87103 | − | 4.97278i | 0.103264 | − | 0.178858i | −0.809764 | − | 0.586756i | \(-0.800405\pi\) |
0.913028 | + | 0.407898i | \(0.133738\pi\) | |||||||
\(774\) | 1.89703 | − | 3.28575i | 0.0681874 | − | 0.118104i | ||||
\(775\) | −0.857766 | + | 1.48569i | −0.0308119 | + | 0.0533677i | ||||
\(776\) | −4.67225 | − | 8.09257i | −0.167724 | − | 0.290506i | ||||
\(777\) | −0.870456 | + | 1.50597i | −0.0312274 | + | 0.0540265i | ||||
\(778\) | 13.4689 | − | 23.3288i | 0.482883 | − | 0.836378i | ||||
\(779\) | 13.5895 | − | 23.5378i | 0.486896 | − | 0.843328i | ||||
\(780\) | −3.01545 | − | 2.10352i | −0.107970 | − | 0.0753181i | ||||
\(781\) | 9.63699 | + | 16.6918i | 0.344839 | + | 0.597278i | ||||
\(782\) | 1.33318 | + | 2.30914i | 0.0476745 | + | 0.0825746i | ||||
\(783\) | 1.12150 | − | 1.94250i | 0.0400792 | − | 0.0694192i | ||||
\(784\) | 6.15445 | + | 0.00601690i | 0.219802 | + | 0.000214889i | ||||
\(785\) | 13.1773 | 0.470318 | ||||||||
\(786\) | 14.9228 | 0.532277 | ||||||||
\(787\) | −15.0412 | + | 26.0521i | −0.536160 | + | 0.928656i | 0.462946 | + | 0.886386i | \(0.346792\pi\) |
−0.999106 | + | 0.0422699i | \(0.986541\pi\) | |||||||
\(788\) | 13.0465 | + | 22.5972i | 0.464763 | + | 0.804993i | ||||
\(789\) | 9.37129 | 0.333627 | ||||||||
\(790\) | −1.49384 | + | 2.58741i | −0.0531486 | + | 0.0920560i | ||||
\(791\) | 22.6432 | − | 39.1749i | 0.805098 | − | 1.39290i | ||||
\(792\) | 11.6572 | 0.414220 | ||||||||
\(793\) | 6.50978 | − | 3.04956i | 0.231169 | − | 0.108293i | ||||
\(794\) | −3.14667 | − | 5.45019i | −0.111671 | − | 0.193420i | ||||
\(795\) | −1.73693 | −0.0616024 | ||||||||
\(796\) | −5.06999 | − | 8.78148i | −0.179701 | − | 0.311251i | ||||
\(797\) | −4.03274 | − | 6.98491i | −0.142847 | − | 0.247418i | 0.785721 | − | 0.618581i | \(-0.212292\pi\) |
−0.928568 | + | 0.371163i | \(0.878959\pi\) | |||||||
\(798\) | 5.94511 | − | 10.2856i | 0.210455 | − | 0.364107i | ||||
\(799\) | 15.7978 | + | 27.3626i | 0.558887 | + | 0.968020i | ||||
\(800\) | 26.3070 | 0.930094 | ||||||||
\(801\) | 6.05088 | + | 10.4804i | 0.213797 | + | 0.370308i | ||||
\(802\) | 5.27918 | − | 9.14380i | 0.186414 | − | 0.322879i | ||||
\(803\) | −6.01926 | − | 10.4257i | −0.212415 | − | 0.367914i | ||||
\(804\) | 10.3045 | − | 17.8480i | 0.363412 | − | 0.629449i | ||||
\(805\) | 0.881082 | + | 1.52780i | 0.0310541 | + | 0.0538480i | ||||
\(806\) | −0.0892758 | + | 1.04160i | −0.00314461 | + | 0.0366887i | ||||
\(807\) | 6.07464 | − | 10.5216i | 0.213837 | − | 0.370377i | ||||
\(808\) | 31.1168 | 1.09468 | ||||||||
\(809\) | −18.5185 | −0.651077 | −0.325538 | − | 0.945529i | \(-0.605546\pi\) | ||||
−0.325538 | + | 0.945529i | \(0.605546\pi\) | |||||||
\(810\) | −0.542874 | −0.0190746 | ||||||||
\(811\) | 20.3264 | 0.713755 | 0.356878 | − | 0.934151i | \(-0.383841\pi\) | ||||
0.356878 | + | 0.934151i | \(0.383841\pi\) | |||||||
\(812\) | 4.23099 | − | 7.32002i | 0.148479 | − | 0.256882i | ||||
\(813\) | −7.32926 | − | 12.6946i | −0.257048 | − | 0.445221i | ||||
\(814\) | −1.11892 | + | 1.93803i | −0.0392182 | + | 0.0679279i | ||||
\(815\) | −3.99690 | + | 6.92284i | −0.140005 | + | 0.242496i | ||||
\(816\) | 3.31861 | 0.116175 | ||||||||
\(817\) | 14.8067 | + | 25.6460i | 0.518022 | + | 0.897241i | ||||
\(818\) | 3.72977 | 0.130408 | ||||||||
\(819\) | −7.82119 | − | 5.46159i | −0.273294 | − | 0.190844i | ||||
\(820\) | −4.68151 | −0.163485 | ||||||||
\(821\) | 1.20362 | + | 2.08473i | 0.0420067 | + | 0.0727577i | 0.886264 | − | 0.463180i | \(-0.153292\pi\) |
−0.844258 | + | 0.535938i | \(0.819958\pi\) | |||||||
\(822\) | 14.6256 | 0.510126 | ||||||||
\(823\) | 15.3210 | − | 26.5368i | 0.534057 | − | 0.925013i | −0.465152 | − | 0.885231i | \(-0.654000\pi\) |
0.999208 | − | 0.0397824i | \(-0.0126665\pi\) | |||||||
\(824\) | −4.02535 | + | 6.97211i | −0.140230 | + | 0.242885i | ||||
\(825\) | −10.0698 | − | 17.4414i | −0.350586 | − | 0.607232i | ||||
\(826\) | 5.62818 | + | 9.75931i | 0.195829 | + | 0.339570i | ||||
\(827\) | 3.92281 | 0.136409 | 0.0682047 | − | 0.997671i | \(-0.478273\pi\) | ||||
0.0682047 | + | 0.997671i | \(0.478273\pi\) | |||||||
\(828\) | 1.32689 | 0.0461128 | ||||||||
\(829\) | 10.6484 | 0.369834 | 0.184917 | − | 0.982754i | \(-0.440798\pi\) | ||||
0.184917 | + | 0.982754i | \(0.440798\pi\) | |||||||
\(830\) | −6.25942 | −0.217268 | ||||||||
\(831\) | −2.51608 | + | 4.35797i | −0.0872817 | + | 0.151176i | ||||
\(832\) | 8.77579 | − | 4.11109i | 0.304246 | − | 0.142526i | ||||
\(833\) | 13.1885 | + | 22.8948i | 0.456955 | + | 0.793259i | ||||
\(834\) | −0.996555 | + | 1.72608i | −0.0345079 | + | 0.0597694i | ||||
\(835\) | 5.07973 | + | 8.79836i | 0.175791 | + | 0.304480i | ||||
\(836\) | −18.9256 | + | 32.7802i | −0.654557 | + | 1.13373i | ||||
\(837\) | −0.191136 | − | 0.331058i | −0.00660664 | − | 0.0114430i | ||||
\(838\) | 7.35948 | 0.254229 | ||||||||
\(839\) | −13.8289 | − | 23.9523i | −0.477426 | − | 0.826925i | 0.522240 | − | 0.852799i | \(-0.325097\pi\) |
−0.999665 | + | 0.0258735i | \(0.991763\pi\) | |||||||
\(840\) | −4.91894 | − | 0.00240450i | −0.169719 | − | 8.29631e-5i | ||||
\(841\) | 11.9845 | + | 20.7577i | 0.413258 | + | 0.715783i | ||||
\(842\) | −5.80026 | − | 10.0463i | −0.199890 | − | 0.346220i | ||||
\(843\) | −0.854888 | −0.0294439 | ||||||||
\(844\) | 8.47706 | + | 14.6827i | 0.291792 | + | 0.505399i | ||||
\(845\) | 3.21320 | + | 8.73218i | 0.110538 | + | 0.300396i | ||||
\(846\) | −6.34903 | −0.218284 | ||||||||
\(847\) | −12.0803 | − | 20.9474i | −0.415085 | − | 0.719761i | ||||
\(848\) | −1.06681 | + | 1.84778i | −0.0366345 | + | 0.0634529i | ||||
\(849\) | 31.2774 | 1.07344 | ||||||||
\(850\) | 6.42398 | + | 11.1267i | 0.220341 | + | 0.381641i | ||||
\(851\) | −0.306155 | + | 0.530275i | −0.0104948 | + | 0.0181776i | ||||
\(852\) | −6.11888 | −0.209629 | ||||||||
\(853\) | −8.76490 | −0.300105 | −0.150052 | − | 0.988678i | \(-0.547944\pi\) | ||||
−0.150052 | + | 0.988678i | \(0.547944\pi\) | |||||||
\(854\) | 2.00220 | − | 3.46401i | 0.0685140 | − | 0.118536i | ||||
\(855\) | 2.11862 | − | 3.66956i | 0.0724554 | − | 0.125496i | ||||
\(856\) | −14.5286 | − | 25.1642i | −0.496576 | − | 0.860095i | ||||
\(857\) | −12.9737 | − | 22.4711i | −0.443173 | − | 0.767598i | 0.554750 | − | 0.832017i | \(-0.312814\pi\) |
−0.997923 | + | 0.0644193i | \(0.979480\pi\) | |||||||
\(858\) | −10.0656 | − | 7.02160i | −0.343636 | − | 0.239713i | ||||
\(859\) | −27.8958 | + | 48.3170i | −0.951793 | + | 1.64855i | −0.210251 | + | 0.977648i | \(0.567428\pi\) |
−0.741542 | + | 0.670906i | \(0.765905\pi\) | |||||||
\(860\) | 2.55041 | − | 4.41744i | 0.0869684 | − | 0.150634i | ||||
\(861\) | −12.1466 | − | 0.00593756i | −0.413955 | − | 0.000202351i | ||||
\(862\) | 12.3852 | + | 21.4518i | 0.421843 | + | 0.730653i | ||||
\(863\) | −5.86854 | + | 10.1646i | −0.199767 | + | 0.346007i | −0.948453 | − | 0.316918i | \(-0.897352\pi\) |
0.748686 | + | 0.662925i | \(0.230685\pi\) | |||||||
\(864\) | −2.93100 | + | 5.07665i | −0.0997148 | + | 0.172711i | ||||
\(865\) | −6.89703 | + | 11.9460i | −0.234506 | + | 0.406176i | ||||
\(866\) | −7.04013 | + | 12.1939i | −0.239233 | + | 0.414364i | ||||
\(867\) | −1.37642 | − | 2.38403i | −0.0467456 | − | 0.0809657i | ||||
\(868\) | −0.719863 | − | 1.24825i | −0.0244338 | − | 0.0423683i | ||||
\(869\) | 12.3490 | − | 21.3891i | 0.418911 | − | 0.725576i | ||||
\(870\) | −0.608833 | + | 1.05453i | −0.0206414 | + | 0.0357519i | ||||
\(871\) | −47.2303 | + | 22.1254i | −1.60034 | + | 0.749692i | ||||
\(872\) | 26.4708 | + | 45.8488i | 0.896415 | + | 1.55264i | ||||
\(873\) | −1.79870 | − | 3.11544i | −0.0608767 | − | 0.105442i | ||||
\(874\) | 2.09100 | − | 3.62172i | 0.0707292 | − | 0.122506i | ||||
\(875\) | 8.97568 | + | 15.5639i | 0.303433 | + | 0.526156i | ||||
\(876\) | 3.82185 | 0.129128 | ||||||||
\(877\) | −10.9556 | −0.369943 | −0.184972 | − | 0.982744i | \(-0.559219\pi\) | ||||
−0.184972 | + | 0.982744i | \(0.559219\pi\) | |||||||
\(878\) | 3.58562 | − | 6.21048i | 0.121009 | − | 0.209594i | ||||
\(879\) | −0.339044 | − | 0.587241i | −0.0114357 | − | 0.0198071i | ||||
\(880\) | 2.82405 | 0.0951986 | ||||||||
\(881\) | −0.925967 | + | 1.60382i | −0.0311966 | + | 0.0540341i | −0.881202 | − | 0.472740i | \(-0.843265\pi\) |
0.850006 | + | 0.526774i | \(0.176598\pi\) | |||||||
\(882\) | −5.30936 | − | 0.00519069i | −0.178775 | − | 0.000174780i | ||||
\(883\) | −50.8664 | −1.71179 | −0.855896 | − | 0.517149i | \(-0.826993\pi\) | ||||
−0.855896 | + | 0.517149i | \(0.826993\pi\) | |||||||
\(884\) | −15.9024 | − | 11.0932i | −0.534855 | − | 0.373104i | ||||
\(885\) | 2.00908 | + | 3.47983i | 0.0675345 | + | 0.116973i | ||||
\(886\) | −5.63692 | −0.189376 | ||||||||
\(887\) | 10.5435 | + | 18.2619i | 0.354016 | + | 0.613174i | 0.986949 | − | 0.161033i | \(-0.0514824\pi\) |
−0.632933 | + | 0.774207i | \(0.718149\pi\) | |||||||
\(888\) | −0.853882 | − | 1.47897i | −0.0286544 | − | 0.0496309i | ||||
\(889\) | −47.7251 | − | 0.0233292i | −1.60065 | − | 0.000782437i | ||||
\(890\) | −3.28487 | − | 5.68955i | −0.110109 | − | 0.190714i | ||||
\(891\) | 4.48772 | 0.150344 | ||||||||
\(892\) | −17.0156 | − | 29.4719i | −0.569725 | − | 0.986793i | ||||
\(893\) | 24.7778 | − | 42.9164i | 0.829157 | − | 1.43614i | ||||
\(894\) | 5.91219 | + | 10.2402i | 0.197733 | + | 0.342484i | ||||
\(895\) | 4.01975 | − | 6.96241i | 0.134365 | − | 0.232728i | ||||
\(896\) | −12.8234 | + | 22.1857i | −0.428399 | + | 0.741173i | ||||
\(897\) | −2.75412 | − | 1.92122i | −0.0919573 | − | 0.0641476i | ||||
\(898\) | 7.14763 | − | 12.3801i | 0.238519 | − | 0.413128i | ||||
\(899\) | −0.857438 | −0.0285972 | ||||||||
\(900\) | 6.39369 | 0.213123 | ||||||||
\(901\) | −9.15991 | −0.305161 | ||||||||
\(902\) | −15.6270 | −0.520322 | ||||||||
\(903\) | 6.62288 | − | 11.4582i | 0.220396 | − | 0.381306i | ||||
\(904\) | 22.2120 | + | 38.4724i | 0.738761 | + | 1.27957i | ||||
\(905\) | −0.870711 | + | 1.50812i | −0.0289434 | + | 0.0501314i | ||||
\(906\) | 3.49761 | − | 6.05803i | 0.116200 | − | 0.201265i | ||||
\(907\) | −10.2256 | −0.339537 | −0.169768 | − | 0.985484i | \(-0.554302\pi\) | ||||
−0.169768 | + | 0.985484i | \(0.554302\pi\) | |||||||
\(908\) | 8.96698 | + | 15.5313i | 0.297580 | + | 0.515423i | ||||
\(909\) | 11.9792 | 0.397324 | ||||||||
\(910\) | 4.24592 | + | 2.96496i | 0.140751 | + | 0.0982873i | ||||
\(911\) | 35.4885 | 1.17578 | 0.587892 | − | 0.808939i | \(-0.299958\pi\) | ||||
0.587892 | + | 0.808939i | \(0.299958\pi\) | |||||||
\(912\) | −2.60250 | − | 4.50766i | −0.0861774 | − | 0.149264i | ||||
\(913\) | 51.7441 | 1.71248 | ||||||||
\(914\) | −2.57886 | + | 4.46671i | −0.0853010 | + | 0.147746i | ||||
\(915\) | 0.713513 | − | 1.23584i | 0.0235880 | − | 0.0408556i | ||||
\(916\) | −10.9185 | − | 18.9113i | −0.360756 | − | 0.624848i | ||||
\(917\) | 52.0540 | + | 0.0254453i | 1.71897 | + | 0.000840277i | ||||
\(918\) | −2.86291 | −0.0944903 | ||||||||
\(919\) | 2.99682 | 0.0988560 | 0.0494280 | − | 0.998778i | \(-0.484260\pi\) | ||||
0.0494280 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(920\) | −1.73154 | −0.0570872 | ||||||||
\(921\) | 27.2103 | 0.896610 | ||||||||
\(922\) | 3.64522 | − | 6.31371i | 0.120049 | − | 0.207931i | ||||
\(923\) | 12.7004 | + | 8.85956i | 0.418039 | + | 0.291616i | ||||
\(924\) | 16.9161 | + | 0.00826901i | 0.556499 | + | 0.000272031i | ||||
\(925\) | −1.47522 | + | 2.55515i | −0.0485048 | + | 0.0840128i | ||||
\(926\) | −8.90946 | − | 15.4316i | −0.292783 | − | 0.507115i | ||||
\(927\) | −1.54966 | + | 2.68409i | −0.0508974 | + | 0.0881569i | ||||
\(928\) | 6.57425 | + | 11.3869i | 0.215810 | + | 0.373794i | ||||
\(929\) | −59.8495 | −1.96360 | −0.981800 | − | 0.189918i | \(-0.939178\pi\) | ||||
−0.981800 | + | 0.189918i | \(0.939178\pi\) | |||||||
\(930\) | 0.103763 | + | 0.179722i | 0.00340252 | + | 0.00589333i | ||||
\(931\) | 20.7554 | − | 35.8684i | 0.680232 | − | 1.17554i | ||||
\(932\) | −18.9975 | − | 32.9046i | −0.622283 | − | 1.07783i | ||||
\(933\) | −7.06426 | − | 12.2357i | −0.231274 | − | 0.400577i | ||||
\(934\) | 10.9927 | 0.359693 | ||||||||
\(935\) | 6.06198 | + | 10.4997i | 0.198248 | + | 0.343375i | ||||
\(936\) | 8.48119 | − | 3.97308i | 0.277216 | − | 0.129864i | ||||
\(937\) | −60.1408 | −1.96471 | −0.982357 | − | 0.187015i | \(-0.940119\pi\) | ||||
−0.982357 | + | 0.187015i | \(0.940119\pi\) | |||||||
\(938\) | −14.5266 | + | 25.1324i | −0.474309 | + | 0.820601i | ||||
\(939\) | −9.84907 | + | 17.0591i | −0.321412 | + | 0.556703i | ||||
\(940\) | −8.53578 | −0.278407 | ||||||||
\(941\) | −0.964242 | − | 1.67012i | −0.0314334 | − | 0.0544443i | 0.849881 | − | 0.526975i | \(-0.176674\pi\) |
−0.881314 | + | 0.472531i | \(0.843341\pi\) | |||||||
\(942\) | −6.98211 | + | 12.0934i | −0.227489 | + | 0.394023i | ||||
\(943\) | −4.27579 | −0.139239 | ||||||||
\(944\) | 4.93588 | 0.160649 | ||||||||
\(945\) | −1.89367 | 0.000925671i | −0.0616010 | 3.01121e-5i | ||||||
\(946\) | 8.51334 | − | 14.7455i | 0.276793 | − | 0.479419i | ||||
\(947\) | 0.341387 | + | 0.591300i | 0.0110936 | + | 0.0192147i | 0.871519 | − | 0.490362i | \(-0.163135\pi\) |
−0.860425 | + | 0.509577i | \(0.829802\pi\) | |||||||
\(948\) | 3.92042 | + | 6.79036i | 0.127329 | + | 0.220541i | ||||
\(949\) | −7.93267 | − | 5.53368i | −0.257505 | − | 0.179631i | ||||
\(950\) | 10.0756 | − | 17.4514i | 0.326894 | − | 0.566197i | ||||
\(951\) | 7.83931 | − | 13.5781i | 0.254207 | − | 0.440299i | ||||
\(952\) | −25.9407 | − | 0.0126804i | −0.840741 | − | 0.000410975i | ||||
\(953\) | 16.6889 | + | 28.9060i | 0.540606 | + | 0.936358i | 0.998869 | + | 0.0475411i | \(0.0151385\pi\) |
−0.458263 | + | 0.888817i | \(0.651528\pi\) | |||||||
\(954\) | 0.920325 | − | 1.59405i | 0.0297966 | − | 0.0516092i | ||||
\(955\) | 4.91679 | − | 8.51613i | 0.159104 | − | 0.275575i | ||||
\(956\) | −10.3926 | + | 18.0006i | −0.336122 | + | 0.582180i | ||||
\(957\) | 5.03298 | − | 8.71738i | 0.162693 | − | 0.281793i | ||||
\(958\) | 5.50406 | + | 9.53332i | 0.177828 | + | 0.308008i | ||||
\(959\) | 51.0173 | + | 0.0249385i | 1.64744 | + | 0.000805308i | ||||
\(960\) | 0.961881 | − | 1.66603i | 0.0310446 | − | 0.0537708i | ||||
\(961\) | 15.4269 | − | 26.7202i | 0.497643 | − | 0.861943i | ||||
\(962\) | −0.153540 | + | 1.79138i | −0.00495032 | + | 0.0577563i | ||||
\(963\) | −5.59313 | − | 9.68758i | −0.180236 | − | 0.312178i | ||||
\(964\) | 9.18387 | + | 15.9069i | 0.295793 | + | 0.512328i | ||||
\(965\) | 4.96267 | − | 8.59559i | 0.159754 | − | 0.276702i | ||||
\(966\) | −1.86898 | 0.000913602i | −0.0601333 | 2.93947e-5i | ||||||
\(967\) | −4.60355 | −0.148040 | −0.0740201 | − | 0.997257i | \(-0.523583\pi\) | ||||
−0.0740201 | + | 0.997257i | \(0.523583\pi\) | |||||||
\(968\) | 23.7408 | 0.763059 | ||||||||
\(969\) | 11.1728 | − | 19.3519i | 0.358923 | − | 0.621673i | ||||
\(970\) | 0.976465 | + | 1.69129i | 0.0313524 | + | 0.0543040i | ||||
\(971\) | −2.13297 | −0.0684503 | −0.0342251 | − | 0.999414i | \(-0.510896\pi\) | ||||
−0.0342251 | + | 0.999414i | \(0.510896\pi\) | |||||||
\(972\) | −0.712354 | + | 1.23383i | −0.0228488 | + | 0.0395752i | ||||
\(973\) | −3.47915 | + | 6.01927i | −0.111537 | + | 0.192969i | ||||
\(974\) | −17.7429 | −0.568520 | ||||||||
\(975\) | −13.2708 | − | 9.25746i | −0.425006 | − | 0.296476i | ||||
\(976\) | −0.876474 | − | 1.51810i | −0.0280553 | − | 0.0485931i | ||||
\(977\) | −36.3686 | −1.16354 | −0.581768 | − | 0.813355i | \(-0.697639\pi\) | ||||
−0.581768 | + | 0.813355i | \(0.697639\pi\) | |||||||
\(978\) | −4.23558 | − | 7.33625i | −0.135439 | − | 0.234587i | ||||
\(979\) | 27.1547 | + | 47.0333i | 0.867867 | + | 1.50319i | ||||
\(980\) | −7.13803 | − | 0.00697849i | −0.228016 | − | 0.000222920i | ||||
\(981\) | 10.1906 | + | 17.6506i | 0.325361 | + | 0.563541i | ||||
\(982\) | 1.19358 | 0.0380887 | ||||||||
\(983\) | −10.0001 | − | 17.3207i | −0.318954 | − | 0.552444i | 0.661316 | − | 0.750107i | \(-0.269998\pi\) |
−0.980270 | + | 0.197663i | \(0.936665\pi\) | |||||||
\(984\) | 5.96270 | − | 10.3277i | 0.190084 | − | 0.329235i | ||||
\(985\) | −6.55426 | − | 11.3523i | −0.208836 | − | 0.361715i | ||||
\(986\) | −3.21076 | + | 5.56120i | −0.102251 | + | 0.177105i | ||||
\(987\) | −22.1469 | − | 0.0108259i | −0.704942 | − | 0.000344593i | ||||
\(988\) | −2.59700 | + | 30.2996i | −0.0826215 | + | 0.963960i | ||||
\(989\) | 2.32938 | − | 4.03461i | 0.0740701 | − | 0.128293i | ||||
\(990\) | −2.43626 | −0.0774295 | ||||||||
\(991\) | 20.8006 | 0.660754 | 0.330377 | − | 0.943849i | \(-0.392824\pi\) | ||||
0.330377 | + | 0.943849i | \(0.392824\pi\) | |||||||
\(992\) | 2.24088 | 0.0711482 | ||||||||
\(993\) | −14.4236 | −0.457719 | ||||||||
\(994\) | 8.61865 | + | 0.00421301i | 0.273367 | + | 0.000133629i | ||||
\(995\) | 2.54704 | + | 4.41160i | 0.0807466 | + | 0.139857i | ||||
\(996\) | −8.21355 | + | 14.2263i | −0.260256 | + | 0.450777i | ||||
\(997\) | 11.0553 | − | 19.1483i | 0.350124 | − | 0.606433i | −0.636147 | − | 0.771568i | \(-0.719473\pi\) |
0.986271 | + | 0.165135i | \(0.0528060\pi\) | |||||||
\(998\) | −11.9338 | −0.377756 | ||||||||
\(999\) | −0.328723 | − | 0.569365i | −0.0104003 | − | 0.0180139i |
(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 | 273.2.j.b.100.5 | ✓ | 16 | |
3.2 | odd | 2 | 819.2.n.e.100.4 | 16 | |||
7.4 | even | 3 | 273.2.l.b.256.4 | yes | 16 | ||
13.3 | even | 3 | 273.2.l.b.16.4 | yes | 16 | ||
21.11 | odd | 6 | 819.2.s.e.802.5 | 16 | |||
39.29 | odd | 6 | 819.2.s.e.289.5 | 16 | |||
91.81 | even | 3 | inner | 273.2.j.b.172.5 | yes | 16 | |
273.263 | odd | 6 | 819.2.n.e.172.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.b.100.5 | ✓ | 16 | 1.1 | even | 1 | trivial | |
273.2.j.b.172.5 | yes | 16 | 91.81 | even | 3 | inner | |
273.2.l.b.16.4 | yes | 16 | 13.3 | even | 3 | ||
273.2.l.b.256.4 | yes | 16 | 7.4 | even | 3 | ||
819.2.n.e.100.4 | 16 | 3.2 | odd | 2 | |||
819.2.n.e.172.4 | 16 | 273.263 | odd | 6 | |||
819.2.s.e.289.5 | 16 | 39.29 | odd | 6 | |||
819.2.s.e.802.5 | 16 | 21.11 | odd | 6 |