Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [190,2,Mod(49,190)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(190, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("190.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 190 = 2 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 190.i (of order \(6\), 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: | \(1.51715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 20 x^{18} + 270 x^{16} - 1928 x^{14} + 9835 x^{12} - 29980 x^{10} + 66046 x^{8} - 89920 x^{6} + 85425 x^{4} - 34500 x^{2} + 10000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(-1.15118 - 0.664633i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 190.49 |
Dual form | 190.2.i.a.159.4 |
$q$-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 \(\left(\mathbb{Z}/190\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 1.15118 | + | 0.664633i | 0.664633 | + | 0.383726i | 0.794040 | − | 0.607866i | \(-0.207974\pi\) |
−0.129407 | + | 0.991592i | \(0.541307\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.866610 | − | 2.06131i | −0.387560 | − | 0.921845i | ||||
\(6\) | −0.664633 | − | 1.15118i | −0.271335 | − | 0.469966i | ||||
\(7\) | − | 2.32927i | − | 0.880379i | −0.897905 | − | 0.440190i | \(-0.854911\pi\) | ||
0.897905 | − | 0.440190i | \(-0.145089\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.616527 | − | 1.06786i | −0.205509 | − | 0.355952i | ||||
\(10\) | −0.280148 | + | 2.21845i | −0.0885905 | + | 0.701535i | ||||
\(11\) | 6.39380 | 1.92780 | 0.963901 | − | 0.266260i | \(-0.0857880\pi\) | ||||
0.963901 | + | 0.266260i | \(0.0857880\pi\) | |||||||
\(12\) | 1.32927i | 0.383726i | ||||||||
\(13\) | −0.743604 | + | 0.429320i | −0.206239 | + | 0.119072i | −0.599562 | − | 0.800328i | \(-0.704659\pi\) |
0.393324 | + | 0.919400i | \(0.371325\pi\) | |||||||
\(14\) | −1.16463 | + | 2.01720i | −0.311261 | + | 0.539120i | ||||
\(15\) | 0.372391 | − | 2.94891i | 0.0961508 | − | 0.761405i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 4.06176 | + | 2.34506i | 0.985122 | + | 0.568760i | 0.903813 | − | 0.427929i | \(-0.140757\pi\) |
0.0813093 | + | 0.996689i | \(0.474090\pi\) | |||||||
\(18\) | 1.23305i | 0.290634i | ||||||||
\(19\) | −3.75178 | + | 2.21903i | −0.860718 | + | 0.509081i | ||||
\(20\) | 1.35184 | − | 1.78116i | 0.302281 | − | 0.398279i | ||||
\(21\) | 1.54811 | − | 2.68140i | 0.337824 | − | 0.585129i | ||||
\(22\) | −5.53719 | − | 3.19690i | −1.18053 | − | 0.681581i | ||||
\(23\) | 3.00565 | − | 1.73531i | 0.626721 | − | 0.361838i | −0.152760 | − | 0.988263i | \(-0.548816\pi\) |
0.779481 | + | 0.626426i | \(0.215483\pi\) | |||||||
\(24\) | 0.664633 | − | 1.15118i | 0.135668 | − | 0.234983i | ||||
\(25\) | −3.49798 | + | 3.57270i | −0.699595 | + | 0.714540i | ||||
\(26\) | 0.858640 | 0.168393 | ||||||||
\(27\) | − | 5.62685i | − | 1.08289i | ||||||
\(28\) | 2.01720 | − | 1.16463i | 0.381216 | − | 0.220095i | ||||
\(29\) | −2.21048 | − | 3.82866i | −0.410476 | − | 0.710965i | 0.584466 | − | 0.811418i | \(-0.301304\pi\) |
−0.994942 | + | 0.100453i | \(0.967971\pi\) | |||||||
\(30\) | −1.79695 | + | 2.36763i | −0.328077 | + | 0.432269i | ||||
\(31\) | −8.25244 | −1.48218 | −0.741091 | − | 0.671405i | \(-0.765691\pi\) | ||||
−0.741091 | + | 0.671405i | \(0.765691\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 7.36040 | + | 4.24953i | 1.28128 | + | 0.739748i | ||||
\(34\) | −2.34506 | − | 4.06176i | −0.402174 | − | 0.696586i | ||||
\(35\) | −4.80133 | + | 2.01856i | −0.811573 | + | 0.341200i | ||||
\(36\) | 0.616527 | − | 1.06786i | 0.102754 | − | 0.177976i | ||||
\(37\) | 9.76821i | 1.60588i | 0.596057 | + | 0.802942i | \(0.296733\pi\) | ||||
−0.596057 | + | 0.802942i | \(0.703267\pi\) | |||||||
\(38\) | 4.35866 | − | 0.0458469i | 0.707068 | − | 0.00743735i | ||||
\(39\) | −1.14136 | −0.182764 | ||||||||
\(40\) | −2.06131 | + | 0.866610i | −0.325921 | + | 0.137023i | ||||
\(41\) | −1.84506 | + | 3.19574i | −0.288150 | + | 0.499090i | −0.973368 | − | 0.229248i | \(-0.926373\pi\) |
0.685218 | + | 0.728338i | \(0.259707\pi\) | |||||||
\(42\) | −2.68140 | + | 1.54811i | −0.413749 | + | 0.238878i | ||||
\(43\) | 6.17012 | + | 3.56232i | 0.940934 | + | 0.543249i | 0.890253 | − | 0.455466i | \(-0.150527\pi\) |
0.0506811 | + | 0.998715i | \(0.483861\pi\) | |||||||
\(44\) | 3.19690 | + | 5.53719i | 0.481951 | + | 0.834763i | ||||
\(45\) | −1.66689 | + | 2.19627i | −0.248485 | + | 0.327400i | ||||
\(46\) | −3.47063 | −0.511716 | ||||||||
\(47\) | −6.22992 | + | 3.59684i | −0.908727 | + | 0.524654i | −0.880021 | − | 0.474934i | \(-0.842472\pi\) |
−0.0287055 | + | 0.999588i | \(0.509138\pi\) | |||||||
\(48\) | −1.15118 | + | 0.664633i | −0.166158 | + | 0.0959315i | ||||
\(49\) | 1.57452 | 0.224932 | ||||||||
\(50\) | 4.81568 | − | 1.34506i | 0.681041 | − | 0.190220i | ||||
\(51\) | 3.11721 | + | 5.39916i | 0.436496 | + | 0.756033i | ||||
\(52\) | −0.743604 | − | 0.429320i | −0.103119 | − | 0.0595360i | ||||
\(53\) | 5.37446 | − | 3.10295i | 0.738239 | − | 0.426222i | −0.0831897 | − | 0.996534i | \(-0.526511\pi\) |
0.821429 | + | 0.570311i | \(0.193177\pi\) | |||||||
\(54\) | −2.81343 | + | 4.87300i | −0.382859 | + | 0.663131i | ||||
\(55\) | −5.54093 | − | 13.1796i | −0.747138 | − | 1.77713i | ||||
\(56\) | −2.32927 | −0.311261 | ||||||||
\(57\) | −5.79381 | + | 0.0609427i | −0.767409 | + | 0.00807206i | ||||
\(58\) | 4.42096i | 0.580500i | ||||||||
\(59\) | −3.09395 | + | 5.35888i | −0.402798 | + | 0.697667i | −0.994062 | − | 0.108811i | \(-0.965296\pi\) |
0.591264 | + | 0.806478i | \(0.298629\pi\) | |||||||
\(60\) | 2.74002 | − | 1.15195i | 0.353736 | − | 0.148717i | ||||
\(61\) | 4.01037 | + | 6.94616i | 0.513475 | + | 0.889365i | 0.999878 | + | 0.0156304i | \(0.00497553\pi\) |
−0.486403 | + | 0.873735i | \(0.661691\pi\) | |||||||
\(62\) | 7.14682 | + | 4.12622i | 0.907647 | + | 0.524030i | ||||
\(63\) | −2.48732 | + | 1.43605i | −0.313373 | + | 0.180926i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.52937 | + | 1.16074i | 0.189696 | + | 0.143973i | ||||
\(66\) | −4.24953 | − | 7.36040i | −0.523081 | − | 0.906002i | ||||
\(67\) | −4.24798 | + | 2.45257i | −0.518973 | + | 0.299629i | −0.736515 | − | 0.676422i | \(-0.763530\pi\) |
0.217541 | + | 0.976051i | \(0.430196\pi\) | |||||||
\(68\) | 4.69012i | 0.568760i | ||||||||
\(69\) | 4.61338 | 0.555386 | ||||||||
\(70\) | 5.16736 | + | 0.652538i | 0.617617 | + | 0.0779932i | ||||
\(71\) | −1.10005 | + | 1.90535i | −0.130552 | + | 0.226124i | −0.923890 | − | 0.382659i | \(-0.875008\pi\) |
0.793337 | + | 0.608782i | \(0.208342\pi\) | |||||||
\(72\) | −1.06786 | + | 0.616527i | −0.125848 | + | 0.0726584i | ||||
\(73\) | −4.03323 | − | 2.32859i | −0.472054 | − | 0.272540i | 0.245045 | − | 0.969512i | \(-0.421197\pi\) |
−0.717099 | + | 0.696971i | \(0.754531\pi\) | |||||||
\(74\) | 4.88411 | − | 8.45952i | 0.567766 | − | 0.983399i | ||||
\(75\) | −6.40132 | + | 1.78794i | −0.739161 | + | 0.206454i | ||||
\(76\) | −3.79763 | − | 2.13962i | −0.435618 | − | 0.245432i | ||||
\(77\) | − | 14.8928i | − | 1.69720i | ||||||
\(78\) | 0.988447 | + | 0.570680i | 0.111920 | + | 0.0646168i | ||||
\(79\) | 5.79153 | − | 10.0312i | 0.651598 | − | 1.12860i | −0.331137 | − | 0.943583i | \(-0.607432\pi\) |
0.982735 | − | 0.185018i | \(-0.0592344\pi\) | |||||||
\(80\) | 2.21845 | + | 0.280148i | 0.248030 | + | 0.0313215i | ||||
\(81\) | 1.89021 | − | 3.27394i | 0.210023 | − | 0.363771i | ||||
\(82\) | 3.19574 | − | 1.84506i | 0.352910 | − | 0.203753i | ||||
\(83\) | − | 6.07809i | − | 0.667157i | −0.942722 | − | 0.333579i | \(-0.891744\pi\) | ||
0.942722 | − | 0.333579i | \(-0.108256\pi\) | |||||||
\(84\) | 3.09621 | 0.337824 | ||||||||
\(85\) | 1.31393 | − | 10.4048i | 0.142515 | − | 1.12856i | ||||
\(86\) | −3.56232 | − | 6.17012i | −0.384135 | − | 0.665341i | ||||
\(87\) | − | 5.87663i | − | 0.630041i | ||||||
\(88\) | − | 6.39380i | − | 0.681581i | ||||||
\(89\) | 5.64947 | + | 9.78517i | 0.598843 | + | 1.03723i | 0.992992 | + | 0.118180i | \(0.0377059\pi\) |
−0.394149 | + | 0.919046i | \(0.628961\pi\) | |||||||
\(90\) | 2.54170 | − | 1.06858i | 0.267919 | − | 0.112638i | ||||
\(91\) | 1.00000 | + | 1.73205i | 0.104828 | + | 0.181568i | ||||
\(92\) | 3.00565 | + | 1.73531i | 0.313361 | + | 0.180919i | ||||
\(93\) | −9.50002 | − | 5.48484i | −0.985106 | − | 0.568751i | ||||
\(94\) | 7.19369 | 0.741972 | ||||||||
\(95\) | 7.82544 | + | 5.81055i | 0.802874 | + | 0.596149i | ||||
\(96\) | 1.32927 | 0.135668 | ||||||||
\(97\) | 9.82939 | + | 5.67500i | 0.998024 | + | 0.576209i | 0.907663 | − | 0.419700i | \(-0.137865\pi\) |
0.0903607 | + | 0.995909i | \(0.471198\pi\) | |||||||
\(98\) | −1.36358 | − | 0.787262i | −0.137742 | − | 0.0795254i | ||||
\(99\) | −3.94195 | − | 6.82766i | −0.396181 | − | 0.686205i | ||||
\(100\) | −4.84303 | − | 1.24299i | −0.484303 | − | 0.124299i | ||||
\(101\) | −1.11042 | − | 1.92331i | −0.110491 | − | 0.191377i | 0.805477 | − | 0.592627i | \(-0.201909\pi\) |
−0.915968 | + | 0.401250i | \(0.868576\pi\) | |||||||
\(102\) | − | 6.23441i | − | 0.617299i | ||||||
\(103\) | 3.26464i | 0.321675i | 0.986981 | + | 0.160837i | \(0.0514195\pi\) | ||||
−0.986981 | + | 0.160837i | \(0.948581\pi\) | |||||||
\(104\) | 0.429320 | + | 0.743604i | 0.0420983 | + | 0.0729164i | ||||
\(105\) | −6.86879 | − | 0.867396i | −0.670325 | − | 0.0846492i | ||||
\(106\) | −6.20589 | −0.602770 | ||||||||
\(107\) | − | 10.0000i | − | 0.966736i | −0.875417 | − | 0.483368i | \(-0.839413\pi\) | ||
0.875417 | − | 0.483368i | \(-0.160587\pi\) | |||||||
\(108\) | 4.87300 | − | 2.81343i | 0.468904 | − | 0.270722i | ||||
\(109\) | −1.51717 | + | 2.62782i | −0.145319 | + | 0.251699i | −0.929492 | − | 0.368843i | \(-0.879754\pi\) |
0.784173 | + | 0.620542i | \(0.213087\pi\) | |||||||
\(110\) | −1.79121 | + | 14.1843i | −0.170785 | + | 1.35242i | ||||
\(111\) | −6.49227 | + | 11.2449i | −0.616219 | + | 1.06732i | ||||
\(112\) | 2.01720 | + | 1.16463i | 0.190608 | + | 0.110047i | ||||
\(113\) | 4.97420i | 0.467933i | 0.972245 | + | 0.233966i | \(0.0751706\pi\) | ||||
−0.972245 | + | 0.233966i | \(0.924829\pi\) | |||||||
\(114\) | 5.04806 | + | 2.84413i | 0.472794 | + | 0.266377i | ||||
\(115\) | −6.18174 | − | 4.69173i | −0.576450 | − | 0.437506i | ||||
\(116\) | 2.21048 | − | 3.82866i | 0.205238 | − | 0.355482i | ||||
\(117\) | 0.916904 | + | 0.529375i | 0.0847678 | + | 0.0489407i | ||||
\(118\) | 5.35888 | − | 3.09395i | 0.493325 | − | 0.284821i | ||||
\(119\) | 5.46226 | − | 9.46092i | 0.500725 | − | 0.867281i | ||||
\(120\) | −2.94891 | − | 0.372391i | −0.269197 | − | 0.0339945i | ||||
\(121\) | 29.8806 | 2.71642 | ||||||||
\(122\) | − | 8.02074i | − | 0.726164i | ||||||
\(123\) | −4.24798 | + | 2.45257i | −0.383028 | + | 0.221141i | ||||
\(124\) | −4.12622 | − | 7.14682i | −0.370545 | − | 0.641803i | ||||
\(125\) | 10.3958 | + | 4.11427i | 0.929829 | + | 0.367991i | ||||
\(126\) | 2.87211 | 0.255868 | ||||||||
\(127\) | −12.3833 | + | 7.14949i | −1.09884 | + | 0.634415i | −0.935916 | − | 0.352224i | \(-0.885426\pi\) |
−0.162923 | + | 0.986639i | \(0.552092\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 4.73527 | + | 8.20172i | 0.416917 | + | 0.722121i | ||||
\(130\) | −0.744106 | − | 1.76992i | −0.0652624 | − | 0.155232i | ||||
\(131\) | −1.18947 | + | 2.06022i | −0.103924 | + | 0.180002i | −0.913298 | − | 0.407292i | \(-0.866473\pi\) |
0.809374 | + | 0.587294i | \(0.199807\pi\) | |||||||
\(132\) | 8.49905i | 0.739748i | ||||||||
\(133\) | 5.16872 | + | 8.73890i | 0.448185 | + | 0.757759i | ||||
\(134\) | 4.90515 | 0.423740 | ||||||||
\(135\) | −11.5987 | + | 4.87628i | −0.998255 | + | 0.419684i | ||||
\(136\) | 2.34506 | − | 4.06176i | 0.201087 | − | 0.348293i | ||||
\(137\) | −7.87364 | + | 4.54585i | −0.672690 | + | 0.388378i | −0.797095 | − | 0.603854i | \(-0.793631\pi\) |
0.124405 | + | 0.992232i | \(0.460298\pi\) | |||||||
\(138\) | −3.99531 | − | 2.30669i | −0.340103 | − | 0.196359i | ||||
\(139\) | −10.5329 | − | 18.2435i | −0.893389 | − | 1.54739i | −0.835786 | − | 0.549055i | \(-0.814988\pi\) |
−0.0576028 | − | 0.998340i | \(-0.518346\pi\) | |||||||
\(140\) | −4.14879 | − | 3.14879i | −0.350637 | − | 0.266122i | ||||
\(141\) | −9.56232 | −0.805293 | ||||||||
\(142\) | 1.90535 | − | 1.10005i | 0.159893 | − | 0.0923145i | ||||
\(143\) | −4.75445 | + | 2.74498i | −0.397587 | + | 0.229547i | ||||
\(144\) | 1.23305 | 0.102754 | ||||||||
\(145\) | −5.97643 | + | 7.87443i | −0.496315 | + | 0.653936i | ||||
\(146\) | 2.32859 | + | 4.03323i | 0.192715 | + | 0.333793i | ||||
\(147\) | 1.81256 | + | 1.04648i | 0.149497 | + | 0.0863122i | ||||
\(148\) | −8.45952 | + | 4.88411i | −0.695368 | + | 0.401471i | ||||
\(149\) | −3.17889 | + | 5.50600i | −0.260425 | + | 0.451069i | −0.966355 | − | 0.257212i | \(-0.917196\pi\) |
0.705930 | + | 0.708282i | \(0.250529\pi\) | |||||||
\(150\) | 6.43768 | + | 1.65226i | 0.525634 | + | 0.134906i | ||||
\(151\) | −3.05559 | −0.248660 | −0.124330 | − | 0.992241i | \(-0.539678\pi\) | ||||
−0.124330 | + | 0.992241i | \(0.539678\pi\) | |||||||
\(152\) | 2.21903 | + | 3.75178i | 0.179987 | + | 0.304310i | ||||
\(153\) | − | 5.78317i | − | 0.467541i | ||||||
\(154\) | −7.44642 | + | 12.8976i | −0.600050 | + | 1.03932i | ||||
\(155\) | 7.15164 | + | 17.0108i | 0.574434 | + | 1.36634i | ||||
\(156\) | −0.570680 | − | 0.988447i | −0.0456910 | − | 0.0791391i | ||||
\(157\) | 7.05180 | + | 4.07136i | 0.562795 | + | 0.324930i | 0.754267 | − | 0.656568i | \(-0.227993\pi\) |
−0.191472 | + | 0.981498i | \(0.561326\pi\) | |||||||
\(158\) | −10.0312 | + | 5.79153i | −0.798041 | + | 0.460749i | ||||
\(159\) | 8.24928 | 0.654210 | ||||||||
\(160\) | −1.78116 | − | 1.35184i | −0.140813 | − | 0.106872i | ||||
\(161\) | −4.04200 | − | 7.00096i | −0.318554 | − | 0.551753i | ||||
\(162\) | −3.27394 | + | 1.89021i | −0.257225 | + | 0.148509i | ||||
\(163\) | − | 13.4100i | − | 1.05035i | −0.850993 | − | 0.525177i | \(-0.823999\pi\) | ||
0.850993 | − | 0.525177i | \(-0.176001\pi\) | |||||||
\(164\) | −3.69012 | −0.288150 | ||||||||
\(165\) | 2.38099 | − | 18.8547i | 0.185360 | − | 1.46784i | ||||
\(166\) | −3.03905 | + | 5.26378i | −0.235876 | + | 0.408549i | ||||
\(167\) | 11.2450 | − | 6.49232i | 0.870166 | − | 0.502391i | 0.00276265 | − | 0.999996i | \(-0.499121\pi\) |
0.867403 | + | 0.497606i | \(0.165787\pi\) | |||||||
\(168\) | −2.68140 | − | 1.54811i | −0.206874 | − | 0.119439i | ||||
\(169\) | −6.13137 | + | 10.6198i | −0.471644 | + | 0.816911i | ||||
\(170\) | −6.34029 | + | 8.35385i | −0.486278 | + | 0.640711i | ||||
\(171\) | 4.68269 | + | 2.63827i | 0.358094 | + | 0.201754i | ||||
\(172\) | 7.12464i | 0.543249i | ||||||||
\(173\) | −1.83216 | − | 1.05780i | −0.139296 | − | 0.0804228i | 0.428732 | − | 0.903432i | \(-0.358960\pi\) |
−0.568029 | + | 0.823009i | \(0.692294\pi\) | |||||||
\(174\) | −2.93831 | + | 5.08931i | −0.222753 | + | 0.385819i | ||||
\(175\) | 8.32176 | + | 8.14771i | 0.629066 | + | 0.615909i | ||||
\(176\) | −3.19690 | + | 5.53719i | −0.240975 | + | 0.417381i | ||||
\(177\) | −7.12338 | + | 4.11268i | −0.535426 | + | 0.309128i | ||||
\(178\) | − | 11.2989i | − | 0.846892i | ||||||
\(179\) | 9.87938 | 0.738420 | 0.369210 | − | 0.929346i | \(-0.379628\pi\) | ||||
0.369210 | + | 0.929346i | \(0.379628\pi\) | |||||||
\(180\) | −2.73547 | − | 0.345437i | −0.203890 | − | 0.0257474i | ||||
\(181\) | −7.53974 | − | 13.0592i | −0.560425 | − | 0.970684i | −0.997459 | − | 0.0712395i | \(-0.977305\pi\) |
0.437034 | − | 0.899445i | \(-0.356029\pi\) | |||||||
\(182\) | − | 2.00000i | − | 0.148250i | ||||||
\(183\) | 10.6617i | 0.788135i | ||||||||
\(184\) | −1.73531 | − | 3.00565i | −0.127929 | − | 0.221579i | ||||
\(185\) | 20.1353 | − | 8.46523i | 1.48038 | − | 0.622376i | ||||
\(186\) | 5.48484 | + | 9.50002i | 0.402168 | + | 0.696575i | ||||
\(187\) | 25.9701 | + | 14.9938i | 1.89912 | + | 1.09646i | ||||
\(188\) | −6.22992 | − | 3.59684i | −0.454363 | − | 0.262327i | ||||
\(189\) | −13.1064 | −0.953352 | ||||||||
\(190\) | −3.87176 | − | 8.94480i | −0.280887 | − | 0.648924i | ||||
\(191\) | 8.84192 | 0.639779 | 0.319889 | − | 0.947455i | \(-0.396354\pi\) | ||||
0.319889 | + | 0.947455i | \(0.396354\pi\) | |||||||
\(192\) | −1.15118 | − | 0.664633i | −0.0830791 | − | 0.0479657i | ||||
\(193\) | −16.1885 | − | 9.34642i | −1.16527 | − | 0.672770i | −0.212710 | − | 0.977115i | \(-0.568229\pi\) |
−0.952562 | + | 0.304346i | \(0.901562\pi\) | |||||||
\(194\) | −5.67500 | − | 9.82939i | −0.407441 | − | 0.705709i | ||||
\(195\) | 0.989114 | + | 2.35269i | 0.0708319 | + | 0.168480i | ||||
\(196\) | 0.787262 | + | 1.36358i | 0.0562330 | + | 0.0973984i | ||||
\(197\) | − | 16.3169i | − | 1.16253i | −0.813713 | − | 0.581267i | \(-0.802557\pi\) | ||
0.813713 | − | 0.581267i | \(-0.197443\pi\) | |||||||
\(198\) | 7.88390i | 0.560284i | ||||||||
\(199\) | −1.57452 | − | 2.72715i | −0.111615 | − | 0.193323i | 0.804807 | − | 0.593537i | \(-0.202269\pi\) |
−0.916422 | + | 0.400214i | \(0.868936\pi\) | |||||||
\(200\) | 3.57270 | + | 3.49798i | 0.252628 | + | 0.247344i | ||||
\(201\) | −6.52024 | −0.459902 | ||||||||
\(202\) | 2.22085i | 0.156258i | ||||||||
\(203\) | −8.91797 | + | 5.14879i | −0.625919 | + | 0.361374i | ||||
\(204\) | −3.11721 | + | 5.39916i | −0.218248 | + | 0.378017i | ||||
\(205\) | 8.18634 | + | 1.03378i | 0.571759 | + | 0.0722022i | ||||
\(206\) | 1.63232 | − | 2.82726i | 0.113729 | − | 0.196985i | ||||
\(207\) | −3.70613 | − | 2.13973i | −0.257594 | − | 0.148722i | ||||
\(208\) | − | 0.858640i | − | 0.0595360i | ||||||
\(209\) | −23.9882 | + | 14.1881i | −1.65930 | + | 0.981408i | ||||
\(210\) | 5.51485 | + | 4.18558i | 0.380561 | + | 0.288833i | ||||
\(211\) | 3.95415 | − | 6.84879i | 0.272215 | − | 0.471490i | −0.697214 | − | 0.716863i | \(-0.745577\pi\) |
0.969429 | + | 0.245373i | \(0.0789104\pi\) | |||||||
\(212\) | 5.37446 | + | 3.10295i | 0.369119 | + | 0.213111i | ||||
\(213\) | −2.53272 | + | 1.46226i | −0.173539 | + | 0.100193i | ||||
\(214\) | −5.00000 | + | 8.66025i | −0.341793 | + | 0.592003i | ||||
\(215\) | 1.99595 | − | 15.8056i | 0.136123 | − | 1.07794i | ||||
\(216\) | −5.62685 | −0.382859 | ||||||||
\(217\) | 19.2221i | 1.30488i | ||||||||
\(218\) | 2.62782 | − | 1.51717i | 0.177978 | − | 0.102756i | ||||
\(219\) | −3.09531 | − | 5.36123i | −0.209162 | − | 0.362279i | ||||
\(220\) | 8.64339 | − | 11.3884i | 0.582737 | − | 0.767804i | ||||
\(221\) | −4.02712 | −0.270894 | ||||||||
\(222\) | 11.2449 | − | 6.49227i | 0.754711 | − | 0.435733i | ||||
\(223\) | 7.21336 | + | 4.16463i | 0.483042 | + | 0.278884i | 0.721683 | − | 0.692223i | \(-0.243369\pi\) |
−0.238641 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(224\) | −1.16463 | − | 2.01720i | −0.0778153 | − | 0.134780i | ||||
\(225\) | 5.97172 | + | 1.53267i | 0.398115 | + | 0.102178i | ||||
\(226\) | 2.48710 | − | 4.30778i | 0.165439 | − | 0.286549i | ||||
\(227\) | − | 11.3680i | − | 0.754523i | −0.926107 | − | 0.377261i | \(-0.876866\pi\) | ||
0.926107 | − | 0.377261i | \(-0.123134\pi\) | |||||||
\(228\) | −2.94968 | − | 4.98712i | −0.195348 | − | 0.330280i | ||||
\(229\) | 2.25560 | 0.149054 | 0.0745270 | − | 0.997219i | \(-0.476255\pi\) | ||||
0.0745270 | + | 0.997219i | \(0.476255\pi\) | |||||||
\(230\) | 3.00768 | + | 7.15403i | 0.198320 | + | 0.471722i | ||||
\(231\) | 9.89827 | − | 17.1443i | 0.651259 | − | 1.12801i | ||||
\(232\) | −3.82866 | + | 2.21048i | −0.251364 | + | 0.145125i | ||||
\(233\) | −13.8027 | − | 7.96900i | −0.904246 | − | 0.522067i | −0.0256705 | − | 0.999670i | \(-0.508172\pi\) |
−0.878575 | + | 0.477604i | \(0.841505\pi\) | |||||||
\(234\) | −0.529375 | − | 0.916904i | −0.0346063 | − | 0.0599399i | ||||
\(235\) | 12.8131 | + | 9.72471i | 0.835835 | + | 0.634370i | ||||
\(236\) | −6.18791 | −0.402798 | ||||||||
\(237\) | 13.3342 | − | 7.69848i | 0.866147 | − | 0.500070i | ||||
\(238\) | −9.46092 | + | 5.46226i | −0.613260 | + | 0.354066i | ||||
\(239\) | −6.63412 | −0.429126 | −0.214563 | − | 0.976710i | \(-0.568833\pi\) | ||||
−0.214563 | + | 0.976710i | \(0.568833\pi\) | |||||||
\(240\) | 2.36763 | + | 1.79695i | 0.152830 | + | 0.115993i | ||||
\(241\) | 11.0397 | + | 19.1213i | 0.711130 | + | 1.23171i | 0.964433 | + | 0.264326i | \(0.0851494\pi\) |
−0.253304 | + | 0.967387i | \(0.581517\pi\) | |||||||
\(242\) | −25.8774 | − | 14.9403i | −1.66346 | − | 0.960400i | ||||
\(243\) | −10.2671 | + | 5.92769i | −0.658632 | + | 0.380261i | ||||
\(244\) | −4.01037 | + | 6.94616i | −0.256738 | + | 0.444683i | ||||
\(245\) | −1.36450 | − | 3.24558i | −0.0871745 | − | 0.207352i | ||||
\(246\) | 4.90515 | 0.312741 | ||||||||
\(247\) | 1.83717 | − | 3.26080i | 0.116896 | − | 0.207480i | ||||
\(248\) | 8.25244i | 0.524030i | ||||||||
\(249\) | 4.03970 | − | 6.99696i | 0.256006 | − | 0.443415i | ||||
\(250\) | −6.94590 | − | 8.76096i | −0.439297 | − | 0.554092i | ||||
\(251\) | −4.72558 | − | 8.18494i | −0.298276 | − | 0.516629i | 0.677466 | − | 0.735554i | \(-0.263078\pi\) |
−0.975742 | + | 0.218926i | \(0.929745\pi\) | |||||||
\(252\) | −2.48732 | − | 1.43605i | −0.156686 | − | 0.0904630i | ||||
\(253\) | 19.2175 | − | 11.0952i | 1.20819 | − | 0.697552i | ||||
\(254\) | 14.2990 | 0.897198 | ||||||||
\(255\) | 8.42792 | − | 11.1045i | 0.527777 | − | 0.695390i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −23.1999 | + | 13.3945i | −1.44717 | + | 0.835524i | −0.998312 | − | 0.0580783i | \(-0.981503\pi\) |
−0.448859 | + | 0.893603i | \(0.648169\pi\) | |||||||
\(258\) | − | 9.47053i | − | 0.589610i | ||||||
\(259\) | 22.7528 | 1.41379 | ||||||||
\(260\) | −0.240546 | + | 1.90485i | −0.0149180 | + | 0.118134i | ||||
\(261\) | −2.72564 | + | 4.72095i | −0.168713 | + | 0.292219i | ||||
\(262\) | 2.06022 | − | 1.18947i | 0.127281 | − | 0.0734854i | ||||
\(263\) | 12.4598 | + | 7.19364i | 0.768301 | + | 0.443579i | 0.832268 | − | 0.554373i | \(-0.187042\pi\) |
−0.0639670 | + | 0.997952i | \(0.520375\pi\) | |||||||
\(264\) | 4.24953 | − | 7.36040i | 0.261540 | − | 0.453001i | ||||
\(265\) | −11.0537 | − | 8.38937i | −0.679022 | − | 0.515355i | ||||
\(266\) | −0.106790 | − | 10.1525i | −0.00654769 | − | 0.622488i | ||||
\(267\) | 15.0193i | 0.919166i | ||||||||
\(268\) | −4.24798 | − | 2.45257i | −0.259487 | − | 0.149815i | ||||
\(269\) | 6.44486 | − | 11.1628i | 0.392950 | − | 0.680609i | −0.599887 | − | 0.800085i | \(-0.704788\pi\) |
0.992837 | + | 0.119475i | \(0.0381212\pi\) | |||||||
\(270\) | 12.4829 | + | 1.57635i | 0.759684 | + | 0.0959336i | ||||
\(271\) | −10.0907 | + | 17.4776i | −0.612966 | + | 1.06169i | 0.377772 | + | 0.925899i | \(0.376690\pi\) |
−0.990738 | + | 0.135790i | \(0.956643\pi\) | |||||||
\(272\) | −4.06176 | + | 2.34506i | −0.246280 | + | 0.142190i | ||||
\(273\) | 2.65853i | 0.160902i | ||||||||
\(274\) | 9.09169 | 0.549249 | ||||||||
\(275\) | −22.3653 | + | 22.8431i | −1.34868 | + | 1.37749i | ||||
\(276\) | 2.30669 | + | 3.99531i | 0.138846 | + | 0.240489i | ||||
\(277\) | 7.40098i | 0.444682i | 0.974969 | + | 0.222341i | \(0.0713698\pi\) | ||||
−0.974969 | + | 0.222341i | \(0.928630\pi\) | |||||||
\(278\) | 21.0658i | 1.26344i | ||||||||
\(279\) | 5.08785 | + | 8.81242i | 0.304602 | + | 0.527586i | ||||
\(280\) | 2.01856 | + | 4.80133i | 0.120632 | + | 0.286934i | ||||
\(281\) | −1.36083 | − | 2.35703i | −0.0811805 | − | 0.140609i | 0.822577 | − | 0.568654i | \(-0.192536\pi\) |
−0.903757 | + | 0.428045i | \(0.859202\pi\) | |||||||
\(282\) | 8.28121 | + | 4.78116i | 0.493139 | + | 0.284714i | ||||
\(283\) | −17.7918 | − | 10.2721i | −1.05761 | − | 0.610613i | −0.132842 | − | 0.991137i | \(-0.542410\pi\) |
−0.924771 | + | 0.380524i | \(0.875744\pi\) | |||||||
\(284\) | −2.20011 | −0.130552 | ||||||||
\(285\) | 5.14660 | + | 11.8900i | 0.304858 | + | 0.704304i | ||||
\(286\) | 5.48997 | 0.324629 | ||||||||
\(287\) | 7.44372 | + | 4.29763i | 0.439389 | + | 0.253681i | ||||
\(288\) | −1.06786 | − | 0.616527i | −0.0629240 | − | 0.0363292i | ||||
\(289\) | 2.49860 | + | 4.32771i | 0.146977 | + | 0.254571i | ||||
\(290\) | 9.11296 | − | 3.83125i | 0.535131 | − | 0.224978i | ||||
\(291\) | 7.54358 | + | 13.0659i | 0.442213 | + | 0.765935i | ||||
\(292\) | − | 4.65717i | − | 0.272540i | ||||||
\(293\) | − | 26.7315i | − | 1.56167i | −0.624736 | − | 0.780836i | \(-0.714794\pi\) | ||
0.624736 | − | 0.780836i | \(-0.285206\pi\) | |||||||
\(294\) | −1.04648 | − | 1.81256i | −0.0610319 | − | 0.105710i | ||||
\(295\) | 13.7276 | + | 1.73353i | 0.799249 | + | 0.100930i | ||||
\(296\) | 9.76821 | 0.567766 | ||||||||
\(297\) | − | 35.9769i | − | 2.08759i | ||||||
\(298\) | 5.50600 | − | 3.17889i | 0.318954 | − | 0.184148i | ||||
\(299\) | −1.49001 | + | 2.58077i | −0.0861694 | + | 0.149250i | ||||
\(300\) | −4.74906 | − | 4.64974i | −0.274187 | − | 0.268453i | ||||
\(301\) | 8.29759 | − | 14.3718i | 0.478265 | − | 0.828379i | ||||
\(302\) | 2.64622 | + | 1.52779i | 0.152273 | + | 0.0879147i | ||||
\(303\) | − | 2.95210i | − | 0.169594i | ||||||
\(304\) | −0.0458469 | − | 4.35866i | −0.00262950 | − | 0.249986i | ||||
\(305\) | 10.8428 | − | 14.2862i | 0.620854 | − | 0.818026i | ||||
\(306\) | −2.89158 | + | 5.00837i | −0.165301 | + | 0.286310i | ||||
\(307\) | 11.0509 | + | 6.38026i | 0.630710 | + | 0.364141i | 0.781027 | − | 0.624497i | \(-0.214696\pi\) |
−0.150317 | + | 0.988638i | \(0.548029\pi\) | |||||||
\(308\) | 12.8976 | − | 7.44642i | 0.734908 | − | 0.424299i | ||||
\(309\) | −2.16979 | + | 3.75818i | −0.123435 | + | 0.213795i | ||||
\(310\) | 2.31190 | − | 18.3076i | 0.131307 | − | 1.03980i | ||||
\(311\) | −6.96646 | −0.395031 | −0.197516 | − | 0.980300i | \(-0.563287\pi\) | ||||
−0.197516 | + | 0.980300i | \(0.563287\pi\) | |||||||
\(312\) | 1.14136i | 0.0646168i | ||||||||
\(313\) | −22.6632 | + | 13.0846i | −1.28100 | + | 0.739585i | −0.977031 | − | 0.213097i | \(-0.931645\pi\) |
−0.303968 | + | 0.952682i | \(0.598312\pi\) | |||||||
\(314\) | −4.07136 | − | 7.05180i | −0.229760 | − | 0.397956i | ||||
\(315\) | 5.11569 | + | 3.88263i | 0.288236 | + | 0.218762i | ||||
\(316\) | 11.5831 | 0.651598 | ||||||||
\(317\) | 7.58413 | − | 4.37870i | 0.425967 | − | 0.245932i | −0.271660 | − | 0.962393i | \(-0.587573\pi\) |
0.697627 | + | 0.716461i | \(0.254239\pi\) | |||||||
\(318\) | −7.14408 | − | 4.12464i | −0.400620 | − | 0.231298i | ||||
\(319\) | −14.1334 | − | 24.4797i | −0.791316 | − | 1.37060i | ||||
\(320\) | 0.866610 | + | 2.06131i | 0.0484450 | + | 0.115231i | ||||
\(321\) | 6.64633 | − | 11.5118i | 0.370962 | − | 0.642525i | ||||
\(322\) | 8.08401i | 0.450504i | ||||||||
\(323\) | −20.4426 | + | 0.215028i | −1.13746 | + | 0.0119645i | ||||
\(324\) | 3.78042 | 0.210023 | ||||||||
\(325\) | 1.06728 | − | 4.15842i | 0.0592019 | − | 0.230668i | ||||
\(326\) | −6.70501 | + | 11.6134i | −0.371356 | + | 0.643208i | ||||
\(327\) | −3.49306 | + | 2.01672i | −0.193167 | + | 0.111525i | ||||
\(328\) | 3.19574 | + | 1.84506i | 0.176455 | + | 0.101876i | ||||
\(329\) | 8.37800 | + | 14.5111i | 0.461894 | + | 0.800024i | ||||
\(330\) | −11.4894 | + | 15.1382i | −0.632468 | + | 0.833329i | ||||
\(331\) | −9.34738 | −0.513779 | −0.256889 | − | 0.966441i | \(-0.582698\pi\) | ||||
−0.256889 | + | 0.966441i | \(0.582698\pi\) | |||||||
\(332\) | 5.26378 | − | 3.03905i | 0.288888 | − | 0.166789i | ||||
\(333\) | 10.4310 | − | 6.02237i | 0.571618 | − | 0.330024i | ||||
\(334\) | −12.9846 | −0.710488 | ||||||||
\(335\) | 8.73685 | + | 6.63097i | 0.477345 | + | 0.362289i | ||||
\(336\) | 1.54811 | + | 2.68140i | 0.0844561 | + | 0.146282i | ||||
\(337\) | −8.44159 | − | 4.87376i | −0.459843 | − | 0.265490i | 0.252135 | − | 0.967692i | \(-0.418867\pi\) |
−0.711978 | + | 0.702202i | \(0.752201\pi\) | |||||||
\(338\) | 10.6198 | − | 6.13137i | 0.577643 | − | 0.333502i | ||||
\(339\) | −3.30601 | + | 5.72618i | −0.179558 | + | 0.311003i | ||||
\(340\) | 9.66777 | − | 4.06450i | 0.524309 | − | 0.220429i | ||||
\(341\) | −52.7644 | −2.85735 | ||||||||
\(342\) | −2.73619 | − | 4.62615i | −0.147956 | − | 0.250154i | ||||
\(343\) | − | 19.9723i | − | 1.07840i | ||||||
\(344\) | 3.56232 | − | 6.17012i | 0.192067 | − | 0.332670i | ||||
\(345\) | −3.99800 | − | 9.50960i | −0.215245 | − | 0.511979i | ||||
\(346\) | 1.05780 | + | 1.83216i | 0.0568675 | + | 0.0984975i | ||||
\(347\) | −12.7853 | − | 7.38162i | −0.686353 | − | 0.396266i | 0.115891 | − | 0.993262i | \(-0.463028\pi\) |
−0.802244 | + | 0.596996i | \(0.796361\pi\) | |||||||
\(348\) | 5.08931 | − | 2.93831i | 0.272816 | − | 0.157510i | ||||
\(349\) | −14.8315 | −0.793913 | −0.396956 | − | 0.917837i | \(-0.629934\pi\) | ||||
−0.396956 | + | 0.917837i | \(0.629934\pi\) | |||||||
\(350\) | −3.13300 | − | 11.2170i | −0.167466 | − | 0.599574i | ||||
\(351\) | 2.41572 | + | 4.18415i | 0.128942 | + | 0.223333i | ||||
\(352\) | 5.53719 | − | 3.19690i | 0.295133 | − | 0.170395i | ||||
\(353\) | 26.8115i | 1.42703i | 0.700639 | + | 0.713516i | \(0.252898\pi\) | ||||
−0.700639 | + | 0.713516i | \(0.747102\pi\) | |||||||
\(354\) | 8.22537 | 0.437173 | ||||||||
\(355\) | 4.88083 | + | 0.616356i | 0.259048 | + | 0.0327128i | ||||
\(356\) | −5.64947 | + | 9.78517i | −0.299421 | + | 0.518613i | ||||
\(357\) | 12.5761 | − | 7.26080i | 0.665596 | − | 0.384282i | ||||
\(358\) | −8.55579 | − | 4.93969i | −0.452188 | − | 0.261071i | ||||
\(359\) | 0.197846 | − | 0.342680i | 0.0104419 | − | 0.0180859i | −0.860757 | − | 0.509016i | \(-0.830010\pi\) |
0.871199 | + | 0.490930i | \(0.163343\pi\) | |||||||
\(360\) | 2.19627 | + | 1.66689i | 0.115753 | + | 0.0878529i | ||||
\(361\) | 9.15178 | − | 16.6507i | 0.481673 | − | 0.876351i | ||||
\(362\) | 15.0795i | 0.792560i | ||||||||
\(363\) | 34.3979 | + | 19.8597i | 1.80542 | + | 1.04236i | ||||
\(364\) | −1.00000 | + | 1.73205i | −0.0524142 | + | 0.0907841i | ||||
\(365\) | −1.30470 | + | 10.3317i | −0.0682909 | + | 0.540786i | ||||
\(366\) | 5.33085 | − | 9.23330i | 0.278648 | − | 0.482632i | ||||
\(367\) | −6.04879 | + | 3.49227i | −0.315744 | + | 0.182295i | −0.649494 | − | 0.760367i | \(-0.725019\pi\) |
0.333750 | + | 0.942662i | \(0.391686\pi\) | |||||||
\(368\) | 3.47063i | 0.180919i | ||||||||
\(369\) | 4.55011 | 0.236870 | ||||||||
\(370\) | −21.6703 | − | 2.73654i | −1.12658 | − | 0.142266i | ||||
\(371\) | −7.22758 | − | 12.5185i | −0.375237 | − | 0.649930i | ||||
\(372\) | − | 10.9697i | − | 0.568751i | ||||||
\(373\) | 2.52621i | 0.130802i | 0.997859 | + | 0.0654012i | \(0.0208327\pi\) | ||||
−0.997859 | + | 0.0654012i | \(0.979167\pi\) | |||||||
\(374\) | −14.9938 | − | 25.9701i | −0.775313 | − | 1.34288i | ||||
\(375\) | 9.23294 | + | 11.6456i | 0.476787 | + | 0.601379i | ||||
\(376\) | 3.59684 | + | 6.22992i | 0.185493 | + | 0.321283i | ||||
\(377\) | 3.28744 | + | 1.89801i | 0.169312 | + | 0.0977523i | ||||
\(378\) | 11.3505 | + | 6.55321i | 0.583807 | + | 0.337061i | ||||
\(379\) | 29.3075 | 1.50543 | 0.752713 | − | 0.658349i | \(-0.228745\pi\) | ||||
0.752713 | + | 0.658349i | \(0.228745\pi\) | |||||||
\(380\) | −1.11936 | + | 9.68231i | −0.0574219 | + | 0.496692i | ||||
\(381\) | −19.0071 | −0.973765 | ||||||||
\(382\) | −7.65733 | − | 4.42096i | −0.391783 | − | 0.226196i | ||||
\(383\) | −5.39911 | − | 3.11717i | −0.275881 | − | 0.159280i | 0.355676 | − | 0.934609i | \(-0.384251\pi\) |
−0.631557 | + | 0.775329i | \(0.717584\pi\) | |||||||
\(384\) | 0.664633 | + | 1.15118i | 0.0339169 | + | 0.0587458i | ||||
\(385\) | −30.6987 | + | 12.9063i | −1.56455 | + | 0.657765i | ||||
\(386\) | 9.34642 | + | 16.1885i | 0.475720 | + | 0.823971i | ||||
\(387\) | − | 8.78506i | − | 0.446570i | ||||||
\(388\) | 11.3500i | 0.576209i | ||||||||
\(389\) | 13.2183 | + | 22.8947i | 0.670193 | + | 1.16081i | 0.977849 | + | 0.209311i | \(0.0671220\pi\) |
−0.307656 | + | 0.951498i | \(0.599545\pi\) | |||||||
\(390\) | 0.319749 | − | 2.53205i | 0.0161911 | − | 0.128215i | ||||
\(391\) | 16.2776 | 0.823196 | ||||||||
\(392\) | − | 1.57452i | − | 0.0795254i | ||||||
\(393\) | −2.73857 | + | 1.58112i | −0.138143 | + | 0.0797567i | ||||
\(394\) | −8.15847 | + | 14.1309i | −0.411018 | + | 0.711903i | ||||
\(395\) | −25.6964 | − | 3.24497i | −1.29293 | − | 0.163272i | ||||
\(396\) | 3.94195 | − | 6.82766i | 0.198090 | − | 0.343103i | ||||
\(397\) | −7.56171 | − | 4.36575i | −0.379511 | − | 0.219111i | 0.298094 | − | 0.954536i | \(-0.403649\pi\) |
−0.677606 | + | 0.735426i | \(0.736982\pi\) | |||||||
\(398\) | 3.14905i | 0.157847i | ||||||||
\(399\) | 0.141952 | + | 13.4953i | 0.00710648 | + | 0.675611i | ||||
\(400\) | −1.34506 | − | 4.81568i | −0.0672530 | − | 0.240784i | ||||
\(401\) | 1.58356 | − | 2.74281i | 0.0790794 | − | 0.136969i | −0.823774 | − | 0.566919i | \(-0.808135\pi\) |
0.902853 | + | 0.429949i | \(0.141469\pi\) | |||||||
\(402\) | 5.64669 | + | 3.26012i | 0.281631 | + | 0.162600i | ||||
\(403\) | 6.13654 | − | 3.54294i | 0.305683 | − | 0.176486i | ||||
\(404\) | 1.11042 | − | 1.92331i | 0.0552457 | − | 0.0956884i | ||||
\(405\) | −8.38666 | − | 1.05907i | −0.416737 | − | 0.0526258i | ||||
\(406\) | 10.2976 | 0.511061 | ||||||||
\(407\) | 62.4560i | 3.09583i | ||||||||
\(408\) | 5.39916 | − | 3.11721i | 0.267298 | − | 0.154325i | ||||
\(409\) | 8.54431 | + | 14.7992i | 0.422489 | + | 0.731773i | 0.996182 | − | 0.0872978i | \(-0.0278232\pi\) |
−0.573693 | + | 0.819070i | \(0.694490\pi\) | |||||||
\(410\) | −6.57269 | − | 4.98845i | −0.324602 | − | 0.246362i | ||||
\(411\) | −12.0853 | −0.596123 | ||||||||
\(412\) | −2.82726 | + | 1.63232i | −0.139289 | + | 0.0804187i | ||||
\(413\) | 12.4823 | + | 7.20664i | 0.614212 | + | 0.354615i | ||||
\(414\) | 2.13973 | + | 3.70613i | 0.105162 | + | 0.182146i | ||||
\(415\) | −12.5288 | + | 5.26733i | −0.615016 | + | 0.258563i | ||||
\(416\) | −0.429320 | + | 0.743604i | −0.0210491 | + | 0.0364582i | ||||
\(417\) | − | 28.0020i | − | 1.37127i | ||||||
\(418\) | 27.8684 | − | 0.293136i | 1.36309 | − | 0.0143378i | ||||
\(419\) | −7.80296 | −0.381200 | −0.190600 | − | 0.981668i | \(-0.561043\pi\) | ||||
−0.190600 | + | 0.981668i | \(0.561043\pi\) | |||||||
\(420\) | −2.68321 | − | 6.38224i | −0.130927 | − | 0.311422i | ||||
\(421\) | −16.9845 | + | 29.4180i | −0.827773 | + | 1.43374i | 0.0720091 | + | 0.997404i | \(0.477059\pi\) |
−0.899782 | + | 0.436340i | \(0.856274\pi\) | |||||||
\(422\) | −6.84879 | + | 3.95415i | −0.333394 | + | 0.192485i | ||||
\(423\) | 7.68182 | + | 4.43510i | 0.373503 | + | 0.215642i | ||||
\(424\) | −3.10295 | − | 5.37446i | −0.150692 | − | 0.261007i | ||||
\(425\) | −22.5861 | + | 6.30849i | −1.09559 | + | 0.306007i | ||||
\(426\) | 2.92453 | 0.141694 | ||||||||
\(427\) | 16.1795 | − | 9.34122i | 0.782979 | − | 0.452053i | ||||
\(428\) | 8.66025 | − | 5.00000i | 0.418609 | − | 0.241684i | ||||
\(429\) | −7.29763 | −0.352333 | ||||||||
\(430\) | −9.63137 | + | 12.6901i | −0.464466 | + | 0.611972i | ||||
\(431\) | −9.07565 | − | 15.7195i | −0.437158 | − | 0.757181i | 0.560311 | − | 0.828283i | \(-0.310682\pi\) |
−0.997469 | + | 0.0711019i | \(0.977348\pi\) | |||||||
\(432\) | 4.87300 | + | 2.81343i | 0.234452 | + | 0.135361i | ||||
\(433\) | −0.272199 | + | 0.157154i | −0.0130810 | + | 0.00755234i | −0.506526 | − | 0.862225i | \(-0.669071\pi\) |
0.493445 | + | 0.869777i | \(0.335737\pi\) | |||||||
\(434\) | 9.61106 | − | 16.6468i | 0.461346 | − | 0.799074i | ||||
\(435\) | −12.1135 | + | 5.09274i | −0.580800 | + | 0.244178i | ||||
\(436\) | −3.03434 | −0.145319 | ||||||||
\(437\) | −7.42583 | + | 13.1802i | −0.355226 | + | 0.630492i | ||||
\(438\) | 6.19062i | 0.295799i | ||||||||
\(439\) | 4.33220 | − | 7.50359i | 0.206765 | − | 0.358127i | −0.743929 | − | 0.668259i | \(-0.767040\pi\) |
0.950694 | + | 0.310132i | \(0.100373\pi\) | |||||||
\(440\) | −13.1796 | + | 5.54093i | −0.628312 | + | 0.264153i | ||||
\(441\) | −0.970736 | − | 1.68136i | −0.0462255 | − | 0.0800650i | ||||
\(442\) | 3.48759 | + | 2.01356i | 0.165888 | + | 0.0957753i | ||||
\(443\) | 3.36744 | − | 1.94419i | 0.159992 | − | 0.0923714i | −0.417866 | − | 0.908509i | \(-0.637222\pi\) |
0.577858 | + | 0.816137i | \(0.303889\pi\) | |||||||
\(444\) | −12.9845 | −0.616219 | ||||||||
\(445\) | 15.2744 | − | 20.1252i | 0.724074 | − | 0.954027i | ||||
\(446\) | −4.16463 | − | 7.21336i | −0.197201 | − | 0.341562i | ||||
\(447\) | −7.31894 | + | 4.22559i | −0.346174 | + | 0.199864i | ||||
\(448\) | 2.32927i | 0.110047i | ||||||||
\(449\) | −32.9375 | −1.55442 | −0.777208 | − | 0.629243i | \(-0.783365\pi\) | ||||
−0.777208 | + | 0.629243i | \(0.783365\pi\) | |||||||
\(450\) | −4.40533 | − | 4.31319i | −0.207669 | − | 0.203326i | ||||
\(451\) | −11.7969 | + | 20.4329i | −0.555496 | + | 0.962147i | ||||
\(452\) | −4.30778 | + | 2.48710i | −0.202621 | + | 0.116983i | ||||
\(453\) | −3.51752 | − | 2.03084i | −0.165268 | − | 0.0954174i | ||||
\(454\) | −5.68402 | + | 9.84500i | −0.266764 | + | 0.462049i | ||||
\(455\) | 2.70368 | − | 3.56232i | 0.126750 | − | 0.167004i | ||||
\(456\) | 0.0609427 | + | 5.79381i | 0.00285390 | + | 0.271320i | ||||
\(457\) | 1.22533i | 0.0573184i | 0.999589 | + | 0.0286592i | \(0.00912376\pi\) | ||||
−0.999589 | + | 0.0286592i | \(0.990876\pi\) | |||||||
\(458\) | −1.95341 | − | 1.12780i | −0.0912766 | − | 0.0526986i | ||||
\(459\) | 13.1953 | − | 22.8549i | 0.615904 | − | 1.06678i | ||||
\(460\) | 0.972288 | − | 7.69941i | 0.0453331 | − | 0.358987i | ||||
\(461\) | 19.5927 | − | 33.9356i | 0.912524 | − | 1.58054i | 0.102038 | − | 0.994781i | \(-0.467464\pi\) |
0.810486 | − | 0.585758i | \(-0.199203\pi\) | |||||||
\(462\) | −17.1443 | + | 9.89827i | −0.797626 | + | 0.460509i | ||||
\(463\) | 32.5754i | 1.51391i | 0.653469 | + | 0.756953i | \(0.273313\pi\) | ||||
−0.653469 | + | 0.756953i | \(0.726687\pi\) | |||||||
\(464\) | 4.42096 | 0.205238 | ||||||||
\(465\) | −3.07313 | + | 24.3357i | −0.142513 | + | 1.12854i | ||||
\(466\) | 7.96900 | + | 13.8027i | 0.369157 | + | 0.639398i | ||||
\(467\) | − | 16.9079i | − | 0.782406i | −0.920304 | − | 0.391203i | \(-0.872059\pi\) | ||
0.920304 | − | 0.391203i | \(-0.127941\pi\) | |||||||
\(468\) | 1.05875i | 0.0489407i | ||||||||
\(469\) | 5.71269 | + | 9.89467i | 0.263788 | + | 0.456894i | ||||
\(470\) | −6.23412 | − | 14.8284i | −0.287558 | − | 0.683983i | ||||
\(471\) | 5.41192 | + | 9.37371i | 0.249368 | + | 0.431918i | ||||
\(472\) | 5.35888 | + | 3.09395i | 0.246663 | + | 0.142411i | ||||
\(473\) | 39.4505 | + | 22.7767i | 1.81394 | + | 1.04728i | ||||
\(474\) | −15.3970 | −0.707206 | ||||||||
\(475\) | 5.19572 | − | 21.1661i | 0.238396 | − | 0.971168i | ||||
\(476\) | 10.9245 | 0.500725 | ||||||||
\(477\) | −6.62700 | − | 3.82610i | −0.303429 | − | 0.175185i | ||||
\(478\) | 5.74532 | + | 3.31706i | 0.262785 | + | 0.151719i | ||||
\(479\) | 1.82570 | + | 3.16220i | 0.0834181 | + | 0.144484i | 0.904716 | − | 0.426015i | \(-0.140083\pi\) |
−0.821298 | + | 0.570500i | \(0.806750\pi\) | |||||||
\(480\) | −1.15195 | − | 2.74002i | −0.0525793 | − | 0.125064i | ||||
\(481\) | −4.19369 | − | 7.26368i | −0.191216 | − | 0.331195i | ||||
\(482\) | − | 22.0794i | − | 1.00569i | ||||||
\(483\) | − | 10.7458i | − | 0.488950i | ||||||
\(484\) | 14.9403 | + | 25.8774i | 0.679106 | + | 1.17625i | ||||
\(485\) | 3.17968 | − | 25.1794i | 0.144382 | − | 1.14334i | ||||
\(486\) | 11.8554 | 0.537771 | ||||||||
\(487\) | − | 13.7416i | − | 0.622691i | −0.950297 | − | 0.311346i | \(-0.899220\pi\) | ||
0.950297 | − | 0.311346i | \(-0.100780\pi\) | |||||||
\(488\) | 6.94616 | − | 4.01037i | 0.314438 | − | 0.181541i | ||||
\(489\) | 8.91274 | − | 15.4373i | 0.403048 | − | 0.698099i | ||||
\(490\) | −0.441099 | + | 3.49300i | −0.0199268 | + | 0.157798i | ||||
\(491\) | 17.3839 | − | 30.1098i | 0.784525 | − | 1.35884i | −0.144758 | − | 0.989467i | \(-0.546240\pi\) |
0.929283 | − | 0.369369i | \(-0.120426\pi\) | |||||||
\(492\) | −4.24798 | − | 2.45257i | −0.191514 | − | 0.110571i | ||||
\(493\) | − | 20.7348i | − | 0.933849i | ||||||
\(494\) | −3.22143 | + | 1.90535i | −0.144939 | + | 0.0857258i | ||||
\(495\) | −10.6578 | + | 14.0425i | −0.479031 | + | 0.631163i | ||||
\(496\) | 4.12622 | − | 7.14682i | 0.185273 | − | 0.320902i | ||||
\(497\) | 4.43807 | + | 2.56232i | 0.199075 | + | 0.114936i | ||||
\(498\) | −6.99696 | + | 4.03970i | −0.313541 | + | 0.181023i | ||||
\(499\) | 8.31410 | − | 14.4005i | 0.372190 | − | 0.644653i | −0.617712 | − | 0.786405i | \(-0.711940\pi\) |
0.989902 | + | 0.141752i | \(0.0452735\pi\) | |||||||
\(500\) | 1.63484 | + | 11.0602i | 0.0731124 | + | 0.494626i | ||||
\(501\) | 17.2600 | 0.771121 | ||||||||
\(502\) | 9.45115i | 0.421825i | ||||||||
\(503\) | −4.12176 | + | 2.37970i | −0.183780 | + | 0.106106i | −0.589068 | − | 0.808084i | \(-0.700505\pi\) |
0.405287 | + | 0.914189i | \(0.367171\pi\) | |||||||
\(504\) | 1.43605 | + | 2.48732i | 0.0639670 | + | 0.110794i | ||||
\(505\) | −3.00223 | + | 3.95569i | −0.133598 | + | 0.176026i | ||||
\(506\) | −22.1905 | −0.986487 | ||||||||
\(507\) | −14.1166 | + | 8.15022i | −0.626940 | + | 0.361964i | ||||
\(508\) | −12.3833 | − | 7.14949i | −0.549419 | − | 0.317207i | ||||
\(509\) | −1.41576 | − | 2.45217i | −0.0627524 | − | 0.108690i | 0.832942 | − | 0.553360i | \(-0.186655\pi\) |
−0.895695 | + | 0.444669i | \(0.853321\pi\) | |||||||
\(510\) | −12.8510 | + | 5.40280i | −0.569053 | + | 0.239240i | ||||
\(511\) | −5.42390 | + | 9.39446i | −0.239939 | + | 0.415587i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 12.4862 | + | 21.1107i | 0.551278 | + | 0.932062i | ||||
\(514\) | 26.7890 | 1.18161 | ||||||||
\(515\) | 6.72943 | − | 2.82917i | 0.296534 | − | 0.124668i | ||||
\(516\) | −4.73527 | + | 8.20172i | −0.208459 | + | 0.361061i | ||||
\(517\) | −39.8328 | + | 22.9975i | −1.75185 | + | 1.01143i | ||||
\(518\) | −19.7045 | − | 11.3764i | −0.865764 | − | 0.499849i | ||||
\(519\) | −1.40609 | − | 2.43542i | −0.0617206 | − | 0.106903i | ||||
\(520\) | 1.16074 | − | 1.52937i | 0.0509020 | − | 0.0670675i | ||||
\(521\) | 4.92317 | 0.215688 | 0.107844 | − | 0.994168i | \(-0.465605\pi\) | ||||
0.107844 | + | 0.994168i | \(0.465605\pi\) | |||||||
\(522\) | 4.72095 | − | 2.72564i | 0.206630 | − | 0.119298i | ||||
\(523\) | 25.0190 | − | 14.4447i | 1.09400 | − | 0.631624i | 0.159365 | − | 0.987220i | \(-0.449055\pi\) |
0.934640 | + | 0.355596i | \(0.115722\pi\) | |||||||
\(524\) | −2.37893 | −0.103924 | ||||||||
\(525\) | 4.16459 | + | 14.9104i | 0.181757 | + | 0.650742i | ||||
\(526\) | −7.19364 | − | 12.4598i | −0.313658 | − | 0.543271i | ||||
\(527\) | −33.5194 | − | 19.3525i | −1.46013 | − | 0.843006i | ||||
\(528\) | −7.36040 | + | 4.24953i | −0.320320 | + | 0.184937i | ||||
\(529\) | −5.47738 | + | 9.48710i | −0.238147 | + | 0.412483i | ||||
\(530\) | 5.37809 | + | 12.7923i | 0.233609 | + | 0.555660i | ||||
\(531\) | 7.63002 | 0.331115 | ||||||||
\(532\) | −4.98375 | + | 8.84569i | −0.216073 | + | 0.383509i | ||||
\(533\) | − | 3.16848i | − | 0.137242i | ||||||
\(534\) | 7.50965 | − | 13.0071i | 0.324974 | − | 0.562872i | ||||
\(535\) | −20.6131 | + | 8.66610i | −0.891181 | + | 0.374668i | ||||
\(536\) | 2.45257 | + | 4.24798i | 0.105935 | + | 0.183485i | ||||
\(537\) | 11.3729 | + | 6.56616i | 0.490778 | + | 0.283351i | ||||
\(538\) | −11.1628 | + | 6.44486i | −0.481264 | + | 0.277858i | ||||
\(539\) | 10.0672 | 0.433624 | ||||||||
\(540\) | −10.0223 | − | 7.60660i | −0.431292 | − | 0.327336i | ||||
\(541\) | −2.30730 | − | 3.99637i | −0.0991987 | − | 0.171817i | 0.812154 | − | 0.583442i | \(-0.198295\pi\) |
−0.911353 | + | 0.411625i | \(0.864961\pi\) | |||||||
\(542\) | 17.4776 | − | 10.0907i | 0.750727 | − | 0.433433i | ||||
\(543\) | − | 20.0446i | − | 0.860198i | ||||||
\(544\) | 4.69012 | 0.201087 | ||||||||
\(545\) | 6.73153 | + | 0.850064i | 0.288347 | + | 0.0364127i | ||||
\(546\) | 1.32927 | − | 2.30235i | 0.0568873 | − | 0.0985317i | ||||
\(547\) | 21.0552 | − | 12.1562i | 0.900255 | − | 0.519763i | 0.0229724 | − | 0.999736i | \(-0.492687\pi\) |
0.877283 | + | 0.479973i | \(0.159354\pi\) | |||||||
\(548\) | −7.87364 | − | 4.54585i | −0.336345 | − | 0.194189i | ||||
\(549\) | 4.94500 | − | 8.56500i | 0.211048 | − | 0.365545i | ||||
\(550\) | 30.7905 | − | 8.60004i | 1.31291 | − | 0.366707i | ||||
\(551\) | 16.7892 | + | 9.45919i | 0.715243 | + | 0.402975i | ||||
\(552\) | − | 4.61338i | − | 0.196359i | ||||||
\(553\) | −23.3654 | − | 13.4900i | −0.993597 | − | 0.573654i | ||||
\(554\) | 3.70049 | − | 6.40943i | 0.157219 | − | 0.272311i | ||||
\(555\) | 28.8056 | + | 3.63759i | 1.22273 | + | 0.154407i | ||||
\(556\) | 10.5329 | − | 18.2435i | 0.446694 | − | 0.773697i | ||||
\(557\) | 21.1577 | − | 12.2154i | 0.896479 | − | 0.517582i | 0.0204227 | − | 0.999791i | \(-0.493499\pi\) |
0.876056 | + | 0.482209i | \(0.160165\pi\) | |||||||
\(558\) | − | 10.1757i | − | 0.430772i | ||||||
\(559\) | −6.11750 | −0.258743 | ||||||||
\(560\) | 0.652538 | − | 5.16736i | 0.0275748 | − | 0.218361i | ||||
\(561\) | 19.9308 | + | 34.5211i | 0.841478 | + | 1.45748i | ||||
\(562\) | 2.72167i | 0.114807i | ||||||||
\(563\) | 19.7981i | 0.834390i | 0.908817 | + | 0.417195i | \(0.136987\pi\) | ||||
−0.908817 | + | 0.417195i | \(0.863013\pi\) | |||||||
\(564\) | −4.78116 | − | 8.28121i | −0.201323 | − | 0.348702i | ||||
\(565\) | 10.2533 | − | 4.31069i | 0.431361 | − | 0.181352i | ||||
\(566\) | 10.2721 | + | 17.7918i | 0.431769 | + | 0.747845i | ||||
\(567\) | −7.62587 | − | 4.40280i | −0.320256 | − | 0.184900i | ||||
\(568\) | 1.90535 | + | 1.10005i | 0.0799467 | + | 0.0461573i | ||||
\(569\) | 39.9935 | 1.67662 | 0.838308 | − | 0.545197i | \(-0.183545\pi\) | ||||
0.838308 | + | 0.545197i | \(0.183545\pi\) | |||||||
\(570\) | 1.48792 | − | 12.8704i | 0.0623223 | − | 0.539080i | ||||
\(571\) | −30.3255 | −1.26908 | −0.634542 | − | 0.772889i | \(-0.718811\pi\) | ||||
−0.634542 | + | 0.772889i | \(0.718811\pi\) | |||||||
\(572\) | −4.75445 | − | 2.74498i | −0.198794 | − | 0.114774i | ||||
\(573\) | 10.1786 | + | 5.87663i | 0.425218 | + | 0.245500i | ||||
\(574\) | −4.29763 | − | 7.44372i | −0.179380 | − | 0.310695i | ||||
\(575\) | −4.31394 | + | 16.8084i | −0.179904 | + | 0.700957i | ||||
\(576\) | 0.616527 | + | 1.06786i | 0.0256886 | + | 0.0444940i | ||||
\(577\) | 31.8330i | 1.32523i | 0.748962 | + | 0.662613i | \(0.230552\pi\) | ||||
−0.748962 | + | 0.662613i | \(0.769448\pi\) | |||||||
\(578\) | − | 4.99721i | − | 0.207856i | ||||||
\(579\) | −12.4239 | − | 21.5188i | −0.516318 | − | 0.894289i | ||||
\(580\) | −9.80767 | − | 1.23852i | −0.407241 | − | 0.0514268i | ||||
\(581\) | −14.1575 | −0.587352 | ||||||||
\(582\) | − | 15.0872i | − | 0.625383i | ||||||
\(583\) | 34.3632 | − | 19.8396i | 1.42318 | − | 0.821673i | ||||
\(584\) | −2.32859 | + | 4.03323i | −0.0963576 | + | 0.166896i | ||||
\(585\) | 0.296606 | − | 2.34878i | 0.0122632 | − | 0.0971102i | ||||
\(586\) | −13.3658 | + | 23.1502i | −0.552134 | + | 0.956324i | ||||
\(587\) | −0.919322 | − | 0.530771i | −0.0379445 | − | 0.0219073i | 0.480908 | − | 0.876771i | \(-0.340307\pi\) |
−0.518852 | + | 0.854864i | \(0.673641\pi\) | |||||||
\(588\) | 2.09296i | 0.0863122i | ||||||||
\(589\) | 30.9614 | − | 18.3124i | 1.27574 | − | 0.754551i | ||||
\(590\) | −11.0216 | − | 8.36506i | −0.453754 | − | 0.344384i | ||||
\(591\) | 10.8448 | − | 18.7837i | 0.446094 | − | 0.772657i | ||||
\(592\) | −8.45952 | − | 4.88411i | −0.347684 | − | 0.200736i | ||||
\(593\) | 32.5188 | − | 18.7747i | 1.33539 | − | 0.770985i | 0.349266 | − | 0.937024i | \(-0.386431\pi\) |
0.986119 | + | 0.166039i | \(0.0530976\pi\) | |||||||
\(594\) | −17.9885 | + | 31.1570i | −0.738076 | + | 1.27839i | ||||
\(595\) | −24.2355 | − | 3.06048i | −0.993559 | − | 0.125468i | ||||
\(596\) | −6.35778 | −0.260425 | ||||||||
\(597\) | − | 4.18592i | − | 0.171318i | ||||||
\(598\) | 2.58077 | − | 1.49001i | 0.105536 | − | 0.0609310i | ||||
\(599\) | −5.02165 | − | 8.69775i | −0.205179 | − | 0.355380i | 0.745011 | − | 0.667052i | \(-0.232444\pi\) |
−0.950190 | + | 0.311672i | \(0.899111\pi\) | |||||||
\(600\) | 1.78794 | + | 6.40132i | 0.0729924 | + | 0.261333i | ||||
\(601\) | 7.56630 | 0.308636 | 0.154318 | − | 0.988021i | \(-0.450682\pi\) | ||||
0.154318 | + | 0.988021i | \(0.450682\pi\) | |||||||
\(602\) | −14.3718 | + | 8.29759i | −0.585753 | + | 0.338184i | ||||
\(603\) | 5.23799 | + | 3.02415i | 0.213307 | + | 0.123153i | ||||
\(604\) | −1.52779 | − | 2.64622i | −0.0621651 | − | 0.107673i | ||||
\(605\) | −25.8949 | − | 61.5932i | −1.05278 | − | 2.50412i | ||||
\(606\) | −1.47605 | + | 2.55659i | −0.0599604 | + | 0.103854i | ||||
\(607\) | 30.8174i | 1.25084i | 0.780288 | + | 0.625420i | \(0.215072\pi\) | ||||
−0.780288 | + | 0.625420i | \(0.784928\pi\) | |||||||
\(608\) | −2.13962 | + | 3.79763i | −0.0867732 | + | 0.154014i | ||||
\(609\) | −13.6882 | −0.554675 | ||||||||
\(610\) | −16.5332 | + | 6.95085i | −0.669410 | + | 0.281432i | ||||
\(611\) | 3.08839 | − | 5.34925i | 0.124943 | − | 0.216408i | ||||
\(612\) | 5.00837 | − | 2.89158i | 0.202451 | − | 0.116885i | ||||
\(613\) | 16.2208 | + | 9.36510i | 0.655153 | + | 0.378253i | 0.790428 | − | 0.612555i | \(-0.209858\pi\) |
−0.135275 | + | 0.990808i | \(0.543192\pi\) | |||||||
\(614\) | −6.38026 | − | 11.0509i | −0.257486 | − | 0.445980i | ||||
\(615\) | 8.73685 | + | 6.63097i | 0.352304 | + | 0.267387i | ||||
\(616\) | −14.8928 | −0.600050 | ||||||||
\(617\) | 40.1386 | − | 23.1741i | 1.61592 | − | 0.932952i | 0.627960 | − | 0.778245i | \(-0.283890\pi\) |
0.987960 | − | 0.154707i | \(-0.0494434\pi\) | |||||||
\(618\) | 3.75818 | − | 2.16979i | 0.151176 | − | 0.0872816i | ||||
\(619\) | −11.5591 | −0.464600 | −0.232300 | − | 0.972644i | \(-0.574625\pi\) | ||||
−0.232300 | + | 0.972644i | \(0.574625\pi\) | |||||||
\(620\) | −11.1560 | + | 14.6989i | −0.448035 | + | 0.590322i | ||||
\(621\) | −9.76435 | − | 16.9123i | −0.391830 | − | 0.678669i | ||||
\(622\) | 6.03313 | + | 3.48323i | 0.241906 | + | 0.139665i | ||||
\(623\) | 22.7923 | − | 13.1591i | 0.913153 | − | 0.527209i | ||||
\(624\) | 0.570680 | − | 0.988447i | 0.0228455 | − | 0.0395695i | ||||
\(625\) | −0.528335 | − | 24.9944i | −0.0211334 | − | 0.999777i | ||||
\(626\) | 26.1692 | 1.04593 | ||||||||
\(627\) | −37.0445 | + | 0.389655i | −1.47941 | + | 0.0155613i | ||||
\(628\) | 8.14272i | 0.324930i | ||||||||
\(629\) | −22.9070 | + | 39.6761i | −0.913363 | + | 1.58199i | ||||
\(630\) | −2.48900 | − | 5.92030i | −0.0991641 | − | 0.235870i | ||||
\(631\) | −22.4567 | − | 38.8962i | −0.893989 | − | 1.54843i | −0.835051 | − | 0.550173i | \(-0.814562\pi\) |
−0.0589383 | − | 0.998262i | \(-0.518772\pi\) | |||||||
\(632\) | −10.0312 | − | 5.79153i | −0.399021 | − | 0.230375i | ||||
\(633\) | 9.10386 | − | 5.25612i | 0.361846 | − | 0.208912i | ||||
\(634\) | −8.75740 | −0.347801 | ||||||||
\(635\) | 25.4688 | + | 19.3299i | 1.01070 | + | 0.767085i | ||||
\(636\) | 4.12464 | + | 7.14408i | 0.163553 | + | 0.283281i | ||||
\(637\) | −1.17082 | + | 0.675974i | −0.0463897 | + | 0.0267831i | ||||
\(638\) | 28.2667i | 1.11909i | ||||||||
\(639\) | 2.71285 | 0.107319 | ||||||||
\(640\) | 0.280148 | − | 2.21845i | 0.0110738 | − | 0.0876919i | ||||
\(641\) | 17.3522 | − | 30.0549i | 0.685371 | − | 1.18710i | −0.287949 | − | 0.957646i | \(-0.592973\pi\) |
0.973320 | − | 0.229451i | \(-0.0736932\pi\) | |||||||
\(642\) | −11.5118 | + | 6.64633i | −0.454333 | + | 0.262310i | ||||
\(643\) | −32.4734 | − | 18.7485i | −1.28062 | − | 0.739369i | −0.303662 | − | 0.952780i | \(-0.598209\pi\) |
−0.976963 | + | 0.213411i | \(0.931543\pi\) | |||||||
\(644\) | 4.04200 | − | 7.00096i | 0.159277 | − | 0.275876i | ||||
\(645\) | 12.8026 | − | 16.8685i | 0.504104 | − | 0.664198i | ||||
\(646\) | 17.8113 | + | 10.0351i | 0.700778 | + | 0.394825i | ||||
\(647\) | − | 22.6592i | − | 0.890823i | −0.895326 | − | 0.445412i | \(-0.853057\pi\) | ||
0.895326 | − | 0.445412i | \(-0.146943\pi\) | |||||||
\(648\) | −3.27394 | − | 1.89021i | −0.128612 | − | 0.0742544i | ||||
\(649\) | −19.7821 | + | 34.2636i | −0.776516 | + | 1.34496i | ||||
\(650\) | −3.00350 | + | 3.06766i | −0.117807 | + | 0.120324i | ||||
\(651\) | −12.7756 | + | 22.1281i | −0.500717 | + | 0.867267i | ||||
\(652\) | 11.6134 | − | 6.70501i | 0.454817 | − | 0.262588i | ||||
\(653\) | 17.7667i | 0.695266i | 0.937631 | + | 0.347633i | \(0.113014\pi\) | ||||
−0.937631 | + | 0.347633i | \(0.886986\pi\) | |||||||
\(654\) | 4.03344 | 0.157720 | ||||||||
\(655\) | 5.27754 | + | 0.666452i | 0.206211 | + | 0.0260404i | ||||
\(656\) | −1.84506 | − | 3.19574i | −0.0720375 | − | 0.124773i | ||||
\(657\) | 5.74255i | 0.224038i | ||||||||
\(658\) | − | 16.7560i | − | 0.653217i | ||||||
\(659\) | 0.991869 | + | 1.71797i | 0.0386377 | + | 0.0669225i | 0.884698 | − | 0.466165i | \(-0.154365\pi\) |
−0.846060 | + | 0.533088i | \(0.821031\pi\) | |||||||
\(660\) | 17.5192 | − | 7.36536i | 0.681932 | − | 0.286696i | ||||
\(661\) | −13.1253 | − | 22.7337i | −0.510515 | − | 0.884237i | −0.999926 | − | 0.0121841i | \(-0.996122\pi\) |
0.489411 | − | 0.872053i | \(-0.337212\pi\) | |||||||
\(662\) | 8.09507 | + | 4.67369i | 0.314624 | + | 0.181648i | ||||
\(663\) | −4.63593 | − | 2.67656i | −0.180045 | − | 0.103949i | ||||
\(664\) | −6.07809 | −0.235876 | ||||||||
\(665\) | 13.5343 | − | 18.2275i | 0.524838 | − | 0.706833i | ||||
\(666\) | −12.0447 | −0.466724 | ||||||||
\(667\) | −13.2879 | − | 7.67175i | −0.514508 | − | 0.297051i | ||||
\(668\) | 11.2450 | + | 6.49232i | 0.435083 | + | 0.251195i | ||||
\(669\) | 5.53590 | + | 9.58846i | 0.214030 | + | 0.370711i | ||||
\(670\) | −4.25085 | − | 10.1110i | −0.164225 | − | 0.390622i | ||||
\(671\) | 25.6415 | + | 44.4124i | 0.989879 | + | 1.71452i | ||||
\(672\) | − | 3.09621i | − | 0.119439i | ||||||
\(673\) | 16.0432i | 0.618418i | 0.950994 | + | 0.309209i | \(0.100064\pi\) | ||||
−0.950994 | + | 0.309209i | \(0.899936\pi\) | |||||||
\(674\) | 4.87376 | + | 8.44159i | 0.187730 | + | 0.325158i | ||||
\(675\) | 20.1030 | + | 19.6826i | 0.773766 | + | 0.757583i | ||||
\(676\) | −12.2627 | −0.471644 | ||||||||
\(677\) | − | 48.5483i | − | 1.86586i | −0.360056 | − | 0.932931i | \(-0.617243\pi\) | ||
0.360056 | − | 0.932931i | \(-0.382757\pi\) | |||||||
\(678\) | 5.72618 | − | 3.30601i | 0.219913 | − | 0.126967i | ||||
\(679\) | 13.2186 | − | 22.8953i | 0.507283 | − | 0.878640i | ||||
\(680\) | −10.4048 | − | 1.31393i | −0.399005 | − | 0.0503868i | ||||
\(681\) | 7.55556 | − | 13.0866i | 0.289530 | − | 0.501480i | ||||
\(682\) | 45.6953 | + | 26.3822i | 1.74976 | + | 1.01023i | ||||
\(683\) | 13.3802i | 0.511981i | 0.966679 | + | 0.255990i | \(0.0824015\pi\) | ||||
−0.966679 | + | 0.255990i | \(0.917598\pi\) | |||||||
\(684\) | 0.0565317 | + | 5.37446i | 0.00216155 | + | 0.205498i | ||||
\(685\) | 16.1938 | + | 12.2905i | 0.618732 | + | 0.469596i | ||||
\(686\) | −9.98617 | + | 17.2966i | −0.381274 | + | 0.660385i | ||||
\(687\) | 2.59659 | + | 1.49914i | 0.0990662 | + | 0.0571959i | ||||
\(688\) | −6.17012 | + | 3.56232i | −0.235234 | + | 0.135812i | ||||
\(689\) | −2.66431 | + | 4.61473i | −0.101502 | + | 0.175807i | ||||
\(690\) | −1.29243 | + | 10.2346i | −0.0492019 | + | 0.389623i | ||||
\(691\) | −25.8354 | −0.982825 | −0.491413 | − | 0.870927i | \(-0.663519\pi\) | ||||
−0.491413 | + | 0.870927i | \(0.663519\pi\) | |||||||
\(692\) | − | 2.11559i | − | 0.0804228i | ||||||
\(693\) | −15.9034 | + | 9.18184i | −0.604121 | + | 0.348789i | ||||
\(694\) | 7.38162 | + | 12.7853i | 0.280202 | + | 0.485325i | ||||
\(695\) | −28.4776 | + | 37.5215i | −1.08022 | + | 1.42327i | ||||
\(696\) | −5.87663 | −0.222753 | ||||||||
\(697\) | −14.9884 | + | 8.65354i | −0.567725 | + | 0.327776i | ||||
\(698\) | 12.8445 | + | 7.41576i | 0.486170 | + | 0.280691i | ||||
\(699\) | −10.5929 | − | 18.3475i | −0.400661 | − | 0.693965i | ||||
\(700\) | −2.89525 | + | 11.2807i | −0.109430 | + | 0.426371i | ||||
\(701\) | −24.6167 | + | 42.6373i | −0.929758 | + | 1.61039i | −0.146034 | + | 0.989280i | \(0.546651\pi\) |
−0.783724 | + | 0.621109i | \(0.786682\pi\) | |||||||
\(702\) | − | 4.83144i | − | 0.182351i | ||||||
\(703\) | −21.6760 | − | 36.6482i | −0.817525 | − | 1.38221i | ||||
\(704\) | −6.39380 | −0.240975 | ||||||||
\(705\) | 8.28680 | + | 19.7109i | 0.312099 | + | 0.742355i | ||||
\(706\) | 13.4058 | − | 23.2194i | 0.504532 | − | 0.873875i | ||||
\(707\) | −4.47990 | + | 2.58647i | −0.168484 | + | 0.0972744i | ||||
\(708\) | −7.12338 | − | 4.11268i | −0.267713 | − | 0.154564i | ||||
\(709\) | 5.44796 | + | 9.43614i | 0.204602 | + | 0.354382i | 0.950006 | − | 0.312232i | \(-0.101077\pi\) |
−0.745404 | + | 0.666613i | \(0.767743\pi\) | |||||||
\(710\) | −3.91875 | − | 2.97420i | −0.147068 | − | 0.111620i | ||||
\(711\) | −14.2825 | −0.535637 | ||||||||
\(712\) | 9.78517 | − | 5.64947i | 0.366715 | − | 0.211723i | ||||
\(713\) | −24.8039 | + | 14.3206i | −0.928915 | + | 0.536309i | ||||
\(714\) | −14.5216 | −0.543457 | ||||||||
\(715\) | 9.77851 | + | 7.42156i | 0.365696 | + | 0.277551i | ||||
\(716\) | 4.93969 | + | 8.55579i | 0.184605 | + | 0.319745i | ||||
\(717\) | −7.63705 | − | 4.40925i | −0.285211 | − | 0.164667i | ||||
\(718\) | −0.342680 | + | 0.197846i | −0.0127887 | + | 0.00738355i | ||||
\(719\) | −16.9141 | + | 29.2961i | −0.630789 | + | 1.09256i | 0.356602 | + | 0.934257i | \(0.383935\pi\) |
−0.987391 | + | 0.158302i | \(0.949398\pi\) | |||||||
\(720\) | −1.06858 | − | 2.54170i | −0.0398235 | − | 0.0947237i | ||||
\(721\) | 7.60422 | 0.283196 | ||||||||
\(722\) | −16.2510 | + | 9.84402i | −0.604800 | + | 0.366356i | ||||
\(723\) | 29.3494i | 1.09152i | ||||||||
\(724\) | 7.53974 | − | 13.0592i | 0.280212 | − | 0.485342i | ||||
\(725\) | 21.4109 | + | 5.49519i | 0.795179 | + | 0.204086i | ||||
\(726\) | −19.8597 | − | 34.3979i | −0.737061 | − | 1.27663i | ||||
\(727\) | 44.1108 | + | 25.4674i | 1.63598 | + | 0.944533i | 0.982198 | + | 0.187848i | \(0.0601513\pi\) |
0.653780 | + | 0.756684i | \(0.273182\pi\) | |||||||
\(728\) | 1.73205 | − | 1.00000i | 0.0641941 | − | 0.0370625i | ||||
\(729\) | −27.1002 | −1.00371 | ||||||||
\(730\) | 6.29575 | − | 8.29517i | 0.233016 | − | 0.307018i | ||||
\(731\) | 16.7077 | + | 28.9386i | 0.617957 | + | 1.07033i | ||||
\(732\) | −9.23330 | + | 5.33085i | −0.341272 | + | 0.197034i | ||||
\(733\) | 30.8270i | 1.13862i | 0.822123 | + | 0.569310i | \(0.192790\pi\) | ||||
−0.822123 | + | 0.569310i | \(0.807210\pi\) | |||||||
\(734\) | 6.98454 | 0.257804 | ||||||||
\(735\) | 0.586338 | − | 4.64312i | 0.0216274 | − | 0.171264i | ||||
\(736\) | 1.73531 | − | 3.00565i | 0.0639645 | − | 0.110790i | ||||
\(737\) | −27.1607 | + | 15.6813i | −1.00048 | + | 0.577626i | ||||
\(738\) | −3.94052 | − | 2.27506i | −0.145052 | − | 0.0837460i | ||||
\(739\) | −18.8645 | + | 32.6742i | −0.693941 | + | 1.20194i | 0.276596 | + | 0.960986i | \(0.410794\pi\) |
−0.970536 | + | 0.240954i | \(0.922540\pi\) | |||||||
\(740\) | 17.3987 | + | 13.2051i | 0.639591 | + | 0.485428i | ||||
\(741\) | 4.28214 | − | 2.53272i | 0.157308 | − | 0.0930417i | ||||
\(742\) | 14.4552i | 0.530666i | ||||||||
\(743\) | −28.4038 | − | 16.3990i | −1.04204 | − | 0.601619i | −0.121626 | − | 0.992576i | \(-0.538811\pi\) |
−0.920409 | + | 0.390957i | \(0.872144\pi\) | |||||||
\(744\) | −5.48484 | + | 9.50002i | −0.201084 | + | 0.348288i | ||||
\(745\) | 14.1044 | + | 1.78112i | 0.516746 | + | 0.0652551i | ||||
\(746\) | 1.26311 | − | 2.18777i | 0.0462456 | − | 0.0800998i | ||||
\(747\) | −6.49053 | + | 3.74731i | −0.237476 | + | 0.137107i | ||||
\(748\) | 29.9877i | 1.09646i | ||||||||
\(749\) | −23.2927 | −0.851095 | ||||||||
\(750\) | −2.17314 | − | 14.7019i | −0.0793518 | − | 0.536837i | ||||
\(751\) | −2.19685 | − | 3.80505i | −0.0801641 | − | 0.138848i | 0.823156 | − | 0.567815i | \(-0.192211\pi\) |
−0.903320 | + | 0.428967i | \(0.858878\pi\) | |||||||
\(752\) | − | 7.19369i | − | 0.262327i | ||||||
\(753\) | − | 12.5631i | − | 0.457824i | ||||||
\(754\) | −1.89801 | − | 3.28744i | −0.0691213 | − | 0.119722i | ||||
\(755\) | 2.64800 | + | 6.29851i | 0.0963707 | + | 0.229226i | ||||
\(756\) | −6.55321 | − | 11.3505i | −0.238338 | − | 0.412814i | ||||
\(757\) | 44.1472 | + | 25.4884i | 1.60456 | + | 0.926391i | 0.990560 | + | 0.137082i | \(0.0437725\pi\) |
0.613997 | + | 0.789309i | \(0.289561\pi\) | |||||||
\(758\) | −25.3811 | − | 14.6538i | −0.921881 | − | 0.532248i | ||||
\(759\) | 29.4970 | 1.07067 | ||||||||
\(760\) | 5.81055 | − | 7.82544i | 0.210771 | − | 0.283859i | ||||
\(761\) | 10.5364 | 0.381945 | 0.190973 | − | 0.981595i | \(-0.438836\pi\) | ||||
0.190973 | + | 0.981595i | \(0.438836\pi\) | |||||||
\(762\) | 16.4607 | + | 9.50357i | 0.596307 | + | 0.344278i | ||||
\(763\) | 6.12088 | + | 3.53389i | 0.221591 | + | 0.127935i | ||||
\(764\) | 4.42096 | + | 7.65733i | 0.159945 | + | 0.277032i | ||||
\(765\) | −11.9209 | + | 5.01175i | −0.431001 | + | 0.181200i | ||||
\(766\) | 3.11717 | + | 5.39911i | 0.112628 | + | 0.195078i | ||||
\(767\) | − | 5.31318i | − | 0.191848i | ||||||
\(768\) | − | 1.32927i | − | 0.0479657i | ||||||
\(769\) | −22.2243 | − | 38.4936i | −0.801429 | − | 1.38812i | −0.918676 | − | 0.395013i | \(-0.870740\pi\) |
0.117246 | − | 0.993103i | \(-0.462593\pi\) | |||||||
\(770\) | 33.0390 | + | 4.17220i | 1.19064 | + | 0.150356i | ||||
\(771\) | −35.6096 | −1.28245 | ||||||||
\(772\) | − | 18.6928i | − | 0.672770i | ||||||
\(773\) | −40.1667 | + | 23.1902i | −1.44469 | + | 0.834095i | −0.998158 | − | 0.0606710i | \(-0.980676\pi\) |
−0.446536 | + | 0.894766i | \(0.647343\pi\) | |||||||
\(774\) | −4.39253 | + | 7.60809i | −0.157886 | + | 0.273467i | ||||
\(775\) | 28.8668 | − | 29.4835i | 1.03693 | − | 1.05908i | ||||
\(776\) | 5.67500 | − | 9.82939i | 0.203721 | − | 0.352855i | ||||
\(777\) | 26.1925 | + | 15.1222i | 0.939649 | + | 0.542507i | ||||
\(778\) | − | 26.4365i | − | 0.947796i | ||||||
\(779\) | −0.169181 | − | 16.0840i | −0.00606152 | − | 0.576268i | ||||
\(780\) | −1.54294 | + | 2.03294i | −0.0552460 | + | 0.0727911i | ||||
\(781\) | −7.03353 | + | 12.1824i | −0.251679 | + | 0.435921i | ||||
\(782\) | −14.0969 | − | 8.13882i | −0.504102 | − | 0.291044i | ||||
\(783\) | −21.5433 | + | 12.4380i | −0.769895 | + | 0.444499i | ||||
\(784\) | −0.787262 | + | 1.36358i | −0.0281165 | + | 0.0486992i | ||||
\(785\) | 2.28116 | − | 18.0642i | 0.0814182 | − | 0.644739i | ||||
\(786\) | 3.16223 | 0.112793 | ||||||||
\(787\) | − | 13.6958i | − | 0.488204i | −0.969750 | − | 0.244102i | \(-0.921507\pi\) | ||
0.969750 | − | 0.244102i | \(-0.0784932\pi\) | |||||||
\(788\) | 14.1309 | − | 8.15847i | 0.503392 | − | 0.290633i | ||||
\(789\) | 9.56226 | + | 16.5623i | 0.340425 | + | 0.589634i | ||||
\(790\) | 20.6313 | + | 15.6584i | 0.734028 | + | 0.557102i | ||||
\(791\) | 11.5862 | 0.411959 | ||||||||
\(792\) | −6.82766 | + | 3.94195i | −0.242610 | + | 0.140071i | ||||
\(793\) | −5.96425 | − | 3.44346i | −0.211797 | − | 0.122281i | ||||
\(794\) | 4.36575 | + | 7.56171i | 0.154935 | + | 0.268355i | ||||
\(795\) | −7.14890 | − | 17.0043i | −0.253545 | − | 0.603080i | ||||
\(796\) | 1.57452 | − | 2.72715i | 0.0558075 | − | 0.0966614i | ||||
\(797\) | 30.5751i | 1.08303i | 0.840692 | + | 0.541513i | \(0.182148\pi\) | ||||
−0.840692 | + | 0.541513i | \(0.817852\pi\) | |||||||
\(798\) | 6.62473 | − | 11.7583i | 0.234513 | − | 0.416238i | ||||
\(799\) | −33.7392 | −1.19361 | ||||||||
\(800\) | −1.24299 | + | 4.84303i | −0.0439462 | + | 0.171227i | ||||
\(801\) | 6.96610 | − | 12.0656i | 0.246135 | − | 0.426319i | ||||
\(802\) | −2.74281 | + | 1.58356i | −0.0968520 | + | 0.0559175i | ||||
\(803\) | −25.7877 | − | 14.8885i | −0.910027 | − | 0.525404i | ||||
\(804\) | −3.26012 | − | 5.64669i | −0.114976 | − | 0.199144i | ||||
\(805\) | −10.9283 | + | 14.3989i | −0.385171 | + | 0.507495i | ||||
\(806\) | −7.08587 | −0.249589 | ||||||||
\(807\) | 14.8384 | − | 8.56693i | 0.522335 | − | 0.301570i | ||||
\(808\) | −1.92331 | + | 1.11042i | −0.0676619 | + | 0.0390646i | ||||
\(809\) | 27.5436 | 0.968381 | 0.484191 | − | 0.874963i | \(-0.339114\pi\) | ||||
0.484191 | + | 0.874963i | \(0.339114\pi\) | |||||||
\(810\) | 6.73352 | + | 5.11052i | 0.236592 | + | 0.179565i | ||||
\(811\) | 9.07845 | + | 15.7243i | 0.318787 | + | 0.552156i | 0.980235 | − | 0.197835i | \(-0.0633911\pi\) |
−0.661448 | + | 0.749991i | \(0.730058\pi\) | |||||||
\(812\) | −8.91797 | − | 5.14879i | −0.312959 | − | 0.180687i | ||||
\(813\) | −23.2324 | + | 13.4132i | −0.814795 | + | 0.470422i | ||||
\(814\) | 31.2280 | − | 54.0885i | 1.09454 | − | 1.89580i | ||||
\(815\) | −27.6422 | + | 11.6213i | −0.968263 | + | 0.407075i | ||||
\(816\) | −6.23441 | −0.218248 | ||||||||
\(817\) | −31.0539 | + | 0.326643i | −1.08644 | + | 0.0114278i | ||||
\(818\) | − | 17.0886i | − | 0.597490i | ||||||
\(819\) | 1.23305 | − | 2.13571i | 0.0430864 | − | 0.0746278i | ||||
\(820\) | 3.19789 | + | 7.60647i | 0.111675 | + | 0.265629i | ||||
\(821\) | 12.2072 | + | 21.1436i | 0.426036 | + | 0.737916i | 0.996517 | − | 0.0833952i | \(-0.0265764\pi\) |
−0.570481 | + | 0.821311i | \(0.693243\pi\) | |||||||
\(822\) | 10.4662 | + | 6.04264i | 0.365049 | + | 0.210761i | ||||
\(823\) | −9.74999 | + | 5.62916i | −0.339863 | + | 0.196220i | −0.660212 | − | 0.751080i | \(-0.729533\pi\) |
0.320348 | + | 0.947300i | \(0.396200\pi\) | |||||||
\(824\) | 3.26464 | 0.113729 | ||||||||
\(825\) | −40.9288 | + | 11.4317i | −1.42496 | + | 0.398002i | ||||
\(826\) | −7.20664 | − | 12.4823i | −0.250751 | − | 0.434313i | ||||
\(827\) | 46.9696 | − | 27.1179i | 1.63329 | − | 0.942983i | 0.650227 | − | 0.759740i | \(-0.274674\pi\) |
0.983068 | − | 0.183243i | \(-0.0586595\pi\) | |||||||
\(828\) | − | 4.27947i | − | 0.148722i | ||||||
\(829\) | −1.30919 | −0.0454701 | −0.0227350 | − | 0.999742i | \(-0.507237\pi\) | ||||
−0.0227350 | + | 0.999742i | \(0.507237\pi\) | |||||||
\(830\) | 13.4839 | + | 1.70276i | 0.468034 | + | 0.0591038i | ||||
\(831\) | −4.91893 | + | 8.51984i | −0.170636 | + | 0.295550i | ||||
\(832\) | 0.743604 | − | 0.429320i | 0.0257798 | − | 0.0148840i | ||||
\(833\) | 6.39534 | + | 3.69235i | 0.221585 | + | 0.127932i | ||||
\(834\) | −14.0010 | + | 24.2505i | −0.484816 | + | 0.839725i | ||||
\(835\) | −23.1277 | − | 17.5531i | −0.800367 | − | 0.607452i | ||||
\(836\) | −24.2813 | − | 13.6803i | −0.839786 | − | 0.473144i | ||||
\(837\) | 46.4352i | 1.60504i | ||||||||
\(838\) | 6.75756 | + | 3.90148i | 0.233436 | + | 0.134774i | ||||
\(839\) | −14.7642 | + | 25.5723i | −0.509716 | + | 0.882854i | 0.490220 | + | 0.871598i | \(0.336916\pi\) |
−0.999937 | + | 0.0112559i | \(0.996417\pi\) | |||||||
\(840\) | −0.867396 | + | 6.86879i | −0.0299280 | + | 0.236996i | ||||
\(841\) | 4.72756 | − | 8.18837i | 0.163019 | − | 0.282358i | ||||
\(842\) | 29.4180 | − | 16.9845i | 1.01381 | − | 0.585324i | ||||
\(843\) | − | 3.61782i | − | 0.124604i | ||||||
\(844\) | 7.90831 | 0.272215 | ||||||||
\(845\) | 27.2043 | + | 3.43538i | 0.935855 | + | 0.118181i | ||||
\(846\) | −4.43510 | − | 7.68182i | −0.152482 | − | 0.264107i | ||||
\(847\) | − | 69.5999i | − | 2.39148i | ||||||
\(848\) | 6.20589i | 0.213111i | ||||||||
\(849\) | −13.6543 | − | 23.6500i | −0.468616 | − | 0.811667i | ||||
\(850\) | 22.7144 | + | 5.82976i | 0.779098 | + | 0.199959i | ||||
\(851\) | 16.9509 | + | 29.3598i | 0.581069 | + | 1.00644i | ||||
\(852\) | −2.53272 | − | 1.46226i | −0.0867694 | − | 0.0500964i | ||||
\(853\) | −7.28928 | − | 4.20847i | −0.249580 | − | 0.144095i | 0.369992 | − | 0.929035i | \(-0.379361\pi\) |
−0.619572 | + | 0.784940i | \(0.712694\pi\) | |||||||
\(854\) | −18.6824 | −0.639300 | ||||||||
\(855\) | 1.38023 | − | 11.9388i | 0.0472029 | − | 0.408299i | ||||
\(856\) | −10.0000 | −0.341793 | ||||||||
\(857\) | 11.8141 | + | 6.82088i | 0.403562 | + | 0.232997i | 0.688020 | − | 0.725692i | \(-0.258480\pi\) |
−0.284458 | + | 0.958689i | \(0.591813\pi\) | |||||||
\(858\) | 6.31993 | + | 3.64881i | 0.215759 | + | 0.124568i | ||||
\(859\) | −7.70524 | − | 13.3459i | −0.262899 | − | 0.455355i | 0.704112 | − | 0.710089i | \(-0.251345\pi\) |
−0.967011 | + | 0.254734i | \(0.918012\pi\) | |||||||
\(860\) | 14.6861 | − | 6.17428i | 0.500791 | − | 0.210541i | ||||
\(861\) | 5.71269 | + | 9.89467i | 0.194688 | + | 0.337210i | ||||
\(862\) | 18.1513i | 0.618235i | ||||||||
\(863\) | − | 45.4425i | − | 1.54688i | −0.633869 | − | 0.773440i | \(-0.718534\pi\) | ||
0.633869 | − | 0.773440i | \(-0.281466\pi\) | |||||||
\(864\) | −2.81343 | − | 4.87300i | −0.0957147 | − | 0.165783i | ||||
\(865\) | −0.592679 | + | 4.69334i | −0.0201517 | + | 0.159578i | ||||
\(866\) | 0.314308 | 0.0106806 | ||||||||
\(867\) | 6.64261i | 0.225595i | ||||||||
\(868\) | −16.6468 | + | 9.61106i | −0.565031 | + | 0.326221i | ||||
\(869\) | 37.0299 | − | 64.1376i | 1.25615 | − | 2.17572i | ||||
\(870\) | 13.0370 | + | 1.64632i | 0.441996 | + | 0.0558156i | ||||
\(871\) | 2.10588 | − | 3.64749i | 0.0713549 | − | 0.123590i | ||||
\(872\) | 2.62782 | + | 1.51717i | 0.0889891 | + | 0.0513779i | ||||
\(873\) | − | 13.9952i | − | 0.473665i | ||||||
\(874\) | 13.0210 | − | 7.70143i | 0.440443 | − | 0.260505i | ||||
\(875\) | 9.58322 | − | 24.2146i | 0.323972 | − | 0.818603i | ||||
\(876\) | 3.09531 | − | 5.36123i | 0.104581 | − | 0.181139i | ||||
\(877\) | −32.3964 | − | 18.7041i | −1.09395 | − | 0.631591i | −0.159323 | − | 0.987226i | \(-0.550931\pi\) |
−0.934625 | + | 0.355635i | \(0.884265\pi\) | |||||||
\(878\) | −7.50359 | + | 4.33220i | −0.253234 | + | 0.146205i | ||||
\(879\) | 17.7666 | − | 30.7727i | 0.599254 | − | 1.03794i | ||||
\(880\) | 14.1843 | + | 1.79121i | 0.478153 | + | 0.0603816i | ||||
\(881\) | 3.04062 | 0.102441 | 0.0512206 | − | 0.998687i | \(-0.483689\pi\) | ||||
0.0512206 | + | 0.998687i | \(0.483689\pi\) | |||||||
\(882\) | 1.94147i | 0.0653728i | ||||||||
\(883\) | −7.05837 | + | 4.07515i | −0.237533 | + | 0.137140i | −0.614042 | − | 0.789273i | \(-0.710458\pi\) |
0.376509 | + | 0.926413i | \(0.377124\pi\) | |||||||
\(884\) | −2.01356 | − | 3.48759i | −0.0677234 | − | 0.117300i | ||||
\(885\) | 14.6507 | + | 11.1194i | 0.492478 | + | 0.373774i | ||||
\(886\) | −3.88838 | −0.130633 | ||||||||
\(887\) | −39.9704 | + | 23.0769i | −1.34207 | + | 0.774847i | −0.987112 | − | 0.160034i | \(-0.948840\pi\) |
−0.354963 | + | 0.934881i | \(0.615506\pi\) | |||||||
\(888\) | 11.2449 | + | 6.49227i | 0.377356 | + | 0.217866i | ||||
\(889\) | 16.6531 | + | 28.8439i | 0.558526 | + | 0.967395i | ||||
\(890\) | −23.2906 | + | 9.79177i | −0.780702 | + | 0.328221i | ||||
\(891\) | 12.0856 | − | 20.9329i | 0.404883 | − | 0.701278i | ||||
\(892\) | 8.32927i | 0.278884i | ||||||||
\(893\) | 15.3918 | − | 27.3190i | 0.515067 | − | 0.914195i | ||||
\(894\) | 8.45118 | 0.282650 | ||||||||
\(895\) | −8.56157 | − | 20.3644i | −0.286182 | − | 0.680708i | ||||
\(896\) | 1.16463 | − | 2.01720i | 0.0389076 | − | 0.0673900i | ||||
\(897\) | −3.43053 | + | 1.98062i | −0.114542 | + | 0.0661309i | ||||
\(898\) | 28.5247 | + | 16.4687i | 0.951882 | + | 0.549569i | ||||
\(899\) | 18.2418 | + | 31.5958i | 0.608400 | + | 1.05378i | ||||
\(900\) | 1.65853 | + | 5.93800i | 0.0552843 | + | 0.197933i | ||||
\(901\) | 29.1064 | 0.969674 | ||||||||
\(902\) | 20.4329 | − | 11.7969i | 0.680341 | − | 0.392795i | ||||
\(903\) | 19.1040 | − | 11.0297i | 0.635741 | − | 0.367045i | ||||
\(904\) | 4.97420 | 0.165439 | ||||||||
\(905\) | −20.3851 | + | 26.8590i | −0.677622 | + | 0.892823i | ||||
\(906\) | 2.03084 | + | 3.51752i | 0.0674703 | + | 0.116862i | ||||
\(907\) | −27.0823 | − | 15.6360i | −0.899252 | − | 0.519184i | −0.0222948 | − | 0.999751i | \(-0.507097\pi\) |
−0.876958 | + | 0.480568i | \(0.840431\pi\) | |||||||
\(908\) | 9.84500 | − | 5.68402i | 0.326718 | − | 0.188631i | ||||
\(909\) | −1.36921 | + | 2.37155i | −0.0454140 | + | 0.0786593i | ||||
\(910\) | −4.12261 | + | 1.73322i | −0.136663 | + | 0.0574557i | ||||
\(911\) | 40.3430 | 1.33662 | 0.668312 | − | 0.743881i | \(-0.267017\pi\) | ||||
0.668312 | + | 0.743881i | \(0.267017\pi\) | |||||||
\(912\) | 2.84413 | − | 5.04806i | 0.0941785 | − | 0.167158i | ||||
\(913\) | − | 38.8621i | − | 1.28615i | ||||||
\(914\) | 0.612664 | − | 1.06116i | 0.0202651 | − | 0.0351002i | ||||
\(915\) | 21.9770 | − | 9.23952i | 0.726538 | − | 0.305449i | ||||
\(916\) | 1.12780 | + | 1.95341i | 0.0372635 | + | 0.0645423i | ||||
\(917\) | 4.79879 | + | 2.77058i | 0.158470 | + | 0.0914927i | ||||
\(918\) | −22.8549 | + | 13.1953i | −0.754325 | + | 0.435510i | ||||
\(919\) | −33.5859 | −1.10790 | −0.553948 | − | 0.832552i | \(-0.686879\pi\) | ||||
−0.553948 | + | 0.832552i | \(0.686879\pi\) | |||||||
\(920\) | −4.69173 | + | 6.18174i | −0.154682 | + | 0.203806i | ||||
\(921\) | 8.48106 | + | 14.6896i | 0.279460 | + | 0.484040i | ||||
\(922\) | −33.9356 | + | 19.5927i | −1.11761 | + | 0.645252i | ||||
\(923\) | − | 1.88910i | − | 0.0621805i | ||||||
\(924\) | 19.7965 | 0.651259 | ||||||||
\(925\) | −34.8989 | − | 34.1690i | −1.14747 | − | 1.12347i | ||||
\(926\) | 16.2877 | − | 28.2111i | 0.535247 | − | 0.927075i | ||||
\(927\) | 3.48617 | − | 2.01274i | 0.114501 | − | 0.0661070i | ||||
\(928\) | −3.82866 | − | 2.21048i | −0.125682 | − | 0.0725625i | ||||
\(929\) | 4.06819 | − | 7.04632i | 0.133473 | − | 0.231182i | −0.791540 | − | 0.611117i | \(-0.790720\pi\) |
0.925013 | + | 0.379935i | \(0.124054\pi\) | |||||||
\(930\) | 14.8292 | − | 19.5387i | 0.486270 | − | 0.640701i | ||||
\(931\) | −5.90727 | + | 3.49392i | −0.193603 | + | 0.114509i | ||||
\(932\) | − | 15.9380i | − | 0.522067i | ||||||
\(933\) | −8.01963 | − | 4.63013i | −0.262551 | − | 0.151584i | ||||
\(934\) | −8.45397 | + | 14.6427i | −0.276622 | + | 0.479124i | ||||
\(935\) | 8.40098 | − | 66.5261i | 0.274741 | − | 2.17564i | ||||
\(936\) | 0.529375 | − | 0.916904i | 0.0173032 | − | 0.0299699i | ||||
\(937\) | 12.6488 | − | 7.30278i | 0.413218 | − | 0.238571i | −0.278953 | − | 0.960305i | \(-0.589988\pi\) |
0.692171 | + | 0.721733i | \(0.256654\pi\) | |||||||
\(938\) | − | 11.4254i | − | 0.373052i | ||||||
\(939\) | −34.7858 | −1.13519 | ||||||||
\(940\) | −2.01530 | + | 15.9588i | −0.0657317 | + | 0.520520i | ||||
\(941\) | 9.92629 | + | 17.1928i | 0.323588 | + | 0.560471i | 0.981226 | − | 0.192864i | \(-0.0617775\pi\) |
−0.657638 | + | 0.753334i | \(0.728444\pi\) | |||||||
\(942\) | − | 10.8238i | − | 0.352659i | ||||||
\(943\) | 12.8070i | 0.417054i | ||||||||
\(944\) | −3.09395 | − | 5.35888i | −0.100700 | − | 0.174417i | ||||
\(945\) | 11.3582 | + | 27.0164i | 0.369481 | + | 0.878843i | ||||
\(946\) | −22.7767 | − | 39.4505i | −0.740536 | − | 1.28265i | ||||
\(947\) | 18.9171 | + | 10.9218i | 0.614724 | + | 0.354911i | 0.774812 | − | 0.632191i | \(-0.217844\pi\) |
−0.160088 | + | 0.987103i | \(0.551178\pi\) | |||||||
\(948\) | 13.3342 | + | 7.69848i | 0.433073 | + | 0.250035i | ||||
\(949\) | 3.99883 | 0.129808 | ||||||||
\(950\) | −15.0827 | + | 15.7325i | −0.489347 | + | 0.510431i | ||||
\(951\) | 11.6409 | 0.377482 | ||||||||
\(952\) | −9.46092 | − | 5.46226i | −0.306630 | − | 0.177033i | ||||
\(953\) | 4.76776 | + | 2.75267i | 0.154443 | + | 0.0891676i | 0.575230 | − | 0.817992i | \(-0.304913\pi\) |
−0.420787 | + | 0.907160i | \(0.638246\pi\) | |||||||
\(954\) | 3.82610 | + | 6.62700i | 0.123875 | + | 0.214557i | ||||
\(955\) | −7.66249 | − | 18.2259i | −0.247952 | − | 0.589777i | ||||
\(956\) | −3.31706 | − | 5.74532i | −0.107281 | − | 0.185817i | ||||
\(957\) | − | 37.5740i | − | 1.21459i | ||||||
\(958\) | − | 3.65139i | − | 0.117971i | ||||||
\(959\) | 10.5885 | + | 18.3398i | 0.341920 | + | 0.592223i | ||||
\(960\) | −0.372391 | + | 2.94891i | −0.0120189 | + | 0.0951756i | ||||
\(961\) | 37.1027 | 1.19686 | ||||||||
\(962\) | 8.38738i | 0.270420i | ||||||||
\(963\) | −10.6786 | + | 6.16527i | −0.344112 | + | 0.198673i | ||||
\(964\) | −11.0397 | + | 19.1213i | −0.355565 | + | 0.615856i | ||||
\(965\) | −5.23675 | + | 41.4691i | −0.168577 | + | 1.33494i | ||||
\(966\) | −5.37289 | + | 9.30613i | −0.172870 | + | 0.299420i | ||||
\(967\) | 49.1371 | + | 28.3693i | 1.58014 | + | 0.912295i | 0.994837 | + | 0.101481i | \(0.0323582\pi\) |
0.585304 | + | 0.810814i | \(0.300975\pi\) | |||||||
\(968\) | − | 29.8806i | − | 0.960400i | ||||||
\(969\) | −23.6760 | − | 13.3393i | −0.760583 | − | 0.428520i | ||||
\(970\) | −15.3434 | + | 20.2162i | −0.492646 | + | 0.649102i | ||||
\(971\) | 7.20815 | − | 12.4849i | 0.231321 | − | 0.400659i | −0.726876 | − | 0.686768i | \(-0.759029\pi\) |
0.958197 | + | 0.286109i | \(0.0923620\pi\) | |||||||
\(972\) | −10.2671 | − | 5.92769i | −0.329316 | − | 0.190131i | ||||
\(973\) | −42.4940 | + | 24.5339i | −1.36229 | + | 0.786521i | ||||
\(974\) | −6.87080 | + | 11.9006i | −0.220155 | + | 0.381319i | ||||
\(975\) | 3.99245 | − | 4.07773i | 0.127861 | − | 0.130592i | ||||
\(976\) | −8.02074 | −0.256738 | ||||||||
\(977\) | − | 31.9776i | − | 1.02305i | −0.859267 | − | 0.511527i | \(-0.829080\pi\) | ||
0.859267 | − | 0.511527i | \(-0.170920\pi\) | |||||||
\(978\) | −15.4373 | + | 8.91274i | −0.493631 | + | 0.284998i | ||||
\(979\) | 36.1216 | + | 62.5644i | 1.15445 | + | 1.99957i | ||||
\(980\) | 2.12850 | − | 2.80448i | 0.0679925 | − | 0.0895858i | ||||
\(981\) | 3.74151 | 0.119457 | ||||||||
\(982\) | −30.1098 | + | 17.3839i | −0.960842 | + | 0.554743i | ||||
\(983\) | −13.1917 | − | 7.61623i | −0.420750 | − | 0.242920i | 0.274648 | − | 0.961545i | \(-0.411439\pi\) |
−0.695398 | + | 0.718625i | \(0.744772\pi\) | |||||||
\(984\) | 2.45257 | + | 4.24798i | 0.0781852 | + | 0.135421i | ||||
\(985\) | −33.6342 | + | 14.1404i | −1.07167 | + | 0.450551i | ||||
\(986\) | −10.3674 | + | 17.9569i | −0.330166 | + | 0.571864i | ||||
\(987\) | 22.2732i | 0.708963i | ||||||||
\(988\) | 3.74252 | − | 0.0393660i | 0.119065 | − | 0.00125240i | ||||
\(989\) | 24.7270 | 0.786271 | ||||||||
\(990\) | 16.2511 | − | 6.83226i | 0.516495 | − | 0.217144i | ||||
\(991\) | 8.16214 | − | 14.1372i | 0.259279 | − | 0.449084i | −0.706770 | − | 0.707443i | \(-0.749848\pi\) |
0.966049 | + | 0.258359i | \(0.0831818\pi\) | |||||||
\(992\) | −7.14682 | + | 4.12622i | −0.226912 | + | 0.131008i | ||||
\(993\) | −10.7605 | − | 6.21258i | −0.341474 | − | 0.197150i | ||||
\(994\) | −2.56232 | − | 4.43807i | −0.0812718 | − | 0.140767i | ||||
\(995\) | −4.25701 | + | 5.60896i | −0.134956 | + | 0.177816i | ||||
\(996\) | 8.07940 | 0.256006 | ||||||||
\(997\) | 19.2635 | − | 11.1218i | 0.610081 | − | 0.352230i | −0.162916 | − | 0.986640i | \(-0.552090\pi\) |
0.772997 | + | 0.634410i | \(0.218757\pi\) | |||||||
\(998\) | −14.4005 | + | 8.31410i | −0.455838 | + | 0.263178i | ||||
\(999\) | 54.9643 | 1.73899 |
(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 | 190.2.i.a.49.4 | ✓ | 20 | |
3.2 | odd | 2 | 1710.2.t.d.1189.9 | 20 | |||
5.2 | odd | 4 | 950.2.e.o.201.4 | 10 | |||
5.3 | odd | 4 | 950.2.e.n.201.2 | 10 | |||
5.4 | even | 2 | inner | 190.2.i.a.49.7 | yes | 20 | |
15.14 | odd | 2 | 1710.2.t.d.1189.1 | 20 | |||
19.7 | even | 3 | inner | 190.2.i.a.159.7 | yes | 20 | |
57.26 | odd | 6 | 1710.2.t.d.919.1 | 20 | |||
95.7 | odd | 12 | 950.2.e.o.501.4 | 10 | |||
95.64 | even | 6 | inner | 190.2.i.a.159.4 | yes | 20 | |
95.83 | odd | 12 | 950.2.e.n.501.2 | 10 | |||
285.254 | odd | 6 | 1710.2.t.d.919.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.i.a.49.4 | ✓ | 20 | 1.1 | even | 1 | trivial | |
190.2.i.a.49.7 | yes | 20 | 5.4 | even | 2 | inner | |
190.2.i.a.159.4 | yes | 20 | 95.64 | even | 6 | inner | |
190.2.i.a.159.7 | yes | 20 | 19.7 | even | 3 | inner | |
950.2.e.n.201.2 | 10 | 5.3 | odd | 4 | |||
950.2.e.n.501.2 | 10 | 95.83 | odd | 12 | |||
950.2.e.o.201.4 | 10 | 5.2 | odd | 4 | |||
950.2.e.o.501.4 | 10 | 95.7 | odd | 12 | |||
1710.2.t.d.919.1 | 20 | 57.26 | odd | 6 | |||
1710.2.t.d.919.9 | 20 | 285.254 | odd | 6 | |||
1710.2.t.d.1189.1 | 20 | 15.14 | odd | 2 | |||
1710.2.t.d.1189.9 | 20 | 3.2 | odd | 2 |