Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(253,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.o (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 253.5 | ||
Character | \(\chi\) | \(=\) | 1110.253 |
Dual form | 1110.2.o.a.487.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.63524 | + | 1.52512i | 0.731300 | + | 0.682056i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | 1.84299 | − | 1.84299i | 0.696583 | − | 0.696583i | −0.267089 | − | 0.963672i | \(-0.586062\pi\) |
0.963672 | + | 0.267089i | \(0.0860617\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.63524 | − | 1.52512i | −0.517107 | − | 0.482286i | ||||
\(11\) | 3.01042i | 0.907674i | 0.891085 | + | 0.453837i | \(0.149945\pi\) | ||||
−0.891085 | + | 0.453837i | \(0.850055\pi\) | |||||||
\(12\) | −0.707107 | + | 0.707107i | −0.204124 | + | 0.204124i | ||||
\(13\) | −1.82067 | −0.504963 | −0.252481 | − | 0.967602i | \(-0.581247\pi\) | ||||
−0.252481 | + | 0.967602i | \(0.581247\pi\) | |||||||
\(14\) | −1.84299 | + | 1.84299i | −0.492559 | + | 0.492559i | ||||
\(15\) | −2.23471 | + | 0.0778616i | −0.577000 | + | 0.0201038i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.42248i | 1.31515i | 0.753391 | + | 0.657573i | \(0.228417\pi\) | ||||
−0.753391 | + | 0.657573i | \(0.771583\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0.509592 | + | 0.509592i | 0.116909 | + | 0.116909i | 0.763141 | − | 0.646232i | \(-0.223656\pi\) |
−0.646232 | + | 0.763141i | \(0.723656\pi\) | |||||||
\(20\) | 1.63524 | + | 1.52512i | 0.365650 | + | 0.341028i | ||||
\(21\) | 2.60638i | 0.568758i | ||||||||
\(22\) | − | 3.01042i | − | 0.641823i | ||||||
\(23\) | −0.0216604 | −0.00451651 | −0.00225825 | − | 0.999997i | \(-0.500719\pi\) | ||||
−0.00225825 | + | 0.999997i | \(0.500719\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | 0.347996 | + | 4.98788i | 0.0695993 | + | 0.997575i | ||||
\(26\) | 1.82067 | 0.357063 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1.84299 | − | 1.84299i | 0.348292 | − | 0.348292i | ||||
\(29\) | 4.67832 | − | 4.67832i | 0.868742 | − | 0.868742i | −0.123591 | − | 0.992333i | \(-0.539441\pi\) |
0.992333 | + | 0.123591i | \(0.0394412\pi\) | |||||||
\(30\) | 2.23471 | − | 0.0778616i | 0.408001 | − | 0.0142155i | ||||
\(31\) | 1.55104 | + | 1.55104i | 0.278574 | + | 0.278574i | 0.832540 | − | 0.553965i | \(-0.186886\pi\) |
−0.553965 | + | 0.832540i | \(0.686886\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.12868 | − | 2.12868i | −0.370556 | − | 0.370556i | ||||
\(34\) | − | 5.42248i | − | 0.929948i | ||||||
\(35\) | 5.82450 | − | 0.202937i | 0.984520 | − | 0.0343025i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 2.27285 | − | 5.64218i | 0.373655 | − | 0.927568i | ||||
\(38\) | −0.509592 | − | 0.509592i | −0.0826668 | − | 0.0826668i | ||||
\(39\) | 1.28741 | − | 1.28741i | 0.206150 | − | 0.206150i | ||||
\(40\) | −1.63524 | − | 1.52512i | −0.258554 | − | 0.241143i | ||||
\(41\) | 6.35587i | 0.992619i | 0.868146 | + | 0.496310i | \(0.165312\pi\) | ||||
−0.868146 | + | 0.496310i | \(0.834688\pi\) | |||||||
\(42\) | − | 2.60638i | − | 0.402173i | ||||||
\(43\) | −7.86706 | −1.19972 | −0.599858 | − | 0.800107i | \(-0.704776\pi\) | ||||
−0.599858 | + | 0.800107i | \(0.704776\pi\) | |||||||
\(44\) | 3.01042i | 0.453837i | ||||||||
\(45\) | 1.52512 | − | 1.63524i | 0.227352 | − | 0.243767i | ||||
\(46\) | 0.0216604 | 0.00319365 | ||||||||
\(47\) | −0.176174 | + | 0.176174i | −0.0256976 | + | 0.0256976i | −0.719839 | − | 0.694141i | \(-0.755784\pi\) |
0.694141 | + | 0.719839i | \(0.255784\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 0.206804i | 0.0295435i | ||||||||
\(50\) | −0.347996 | − | 4.98788i | −0.0492141 | − | 0.705392i | ||||
\(51\) | −3.83427 | − | 3.83427i | −0.536906 | − | 0.536906i | ||||
\(52\) | −1.82067 | −0.252481 | ||||||||
\(53\) | 2.05089 | + | 2.05089i | 0.281711 | + | 0.281711i | 0.833791 | − | 0.552080i | \(-0.186166\pi\) |
−0.552080 | + | 0.833791i | \(0.686166\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | −4.59126 | + | 4.92274i | −0.619085 | + | 0.663782i | ||||
\(56\) | −1.84299 | + | 1.84299i | −0.246279 | + | 0.246279i | ||||
\(57\) | −0.720673 | −0.0954554 | ||||||||
\(58\) | −4.67832 | + | 4.67832i | −0.614293 | + | 0.614293i | ||||
\(59\) | 2.84934 | + | 2.84934i | 0.370952 | + | 0.370952i | 0.867824 | − | 0.496872i | \(-0.165518\pi\) |
−0.496872 | + | 0.867824i | \(0.665518\pi\) | |||||||
\(60\) | −2.23471 | + | 0.0778616i | −0.288500 | + | 0.0100519i | ||||
\(61\) | 4.51718 | + | 4.51718i | 0.578366 | + | 0.578366i | 0.934453 | − | 0.356087i | \(-0.115889\pi\) |
−0.356087 | + | 0.934453i | \(0.615889\pi\) | |||||||
\(62\) | −1.55104 | − | 1.55104i | −0.196982 | − | 0.196982i | ||||
\(63\) | −1.84299 | − | 1.84299i | −0.232194 | − | 0.232194i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.97723 | − | 2.77675i | −0.369279 | − | 0.344413i | ||||
\(66\) | 2.12868 | + | 2.12868i | 0.262023 | + | 0.262023i | ||||
\(67\) | −3.93891 | − | 3.93891i | −0.481215 | − | 0.481215i | 0.424305 | − | 0.905519i | \(-0.360519\pi\) |
−0.905519 | + | 0.424305i | \(0.860519\pi\) | |||||||
\(68\) | 5.42248i | 0.657573i | ||||||||
\(69\) | 0.0153162 | − | 0.0153162i | 0.00184386 | − | 0.00184386i | ||||
\(70\) | −5.82450 | + | 0.202937i | −0.696161 | + | 0.0242556i | ||||
\(71\) | 9.00950 | 1.06923 | 0.534615 | − | 0.845095i | \(-0.320456\pi\) | ||||
0.534615 | + | 0.845095i | \(0.320456\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −8.50501 | + | 8.50501i | −0.995437 | + | 0.995437i | −0.999990 | − | 0.00455309i | \(-0.998551\pi\) |
0.00455309 | + | 0.999990i | \(0.498551\pi\) | |||||||
\(74\) | −2.27285 | + | 5.64218i | −0.264214 | + | 0.655890i | ||||
\(75\) | −3.77303 | − | 3.28089i | −0.435672 | − | 0.378845i | ||||
\(76\) | 0.509592 | + | 0.509592i | 0.0584543 | + | 0.0584543i | ||||
\(77\) | 5.54815 | + | 5.54815i | 0.632271 | + | 0.632271i | ||||
\(78\) | −1.28741 | + | 1.28741i | −0.145770 | + | 0.145770i | ||||
\(79\) | 2.16377 | + | 2.16377i | 0.243444 | + | 0.243444i | 0.818273 | − | 0.574830i | \(-0.194932\pi\) |
−0.574830 | + | 0.818273i | \(0.694932\pi\) | |||||||
\(80\) | 1.63524 | + | 1.52512i | 0.182825 | + | 0.170514i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | − | 6.35587i | − | 0.701888i | ||||||
\(83\) | 0.925954 | + | 0.925954i | 0.101637 | + | 0.101637i | 0.756097 | − | 0.654460i | \(-0.227104\pi\) |
−0.654460 | + | 0.756097i | \(0.727104\pi\) | |||||||
\(84\) | 2.60638i | 0.284379i | ||||||||
\(85\) | −8.26996 | + | 8.86704i | −0.897003 | + | 0.961766i | ||||
\(86\) | 7.86706 | 0.848327 | ||||||||
\(87\) | 6.61614i | 0.709325i | ||||||||
\(88\) | − | 3.01042i | − | 0.320911i | ||||||
\(89\) | −1.03976 | + | 1.03976i | −0.110214 | + | 0.110214i | −0.760063 | − | 0.649849i | \(-0.774832\pi\) |
0.649849 | + | 0.760063i | \(0.274832\pi\) | |||||||
\(90\) | −1.52512 | + | 1.63524i | −0.160762 | + | 0.172369i | ||||
\(91\) | −3.35547 | + | 3.35547i | −0.351749 | + | 0.351749i | ||||
\(92\) | −0.0216604 | −0.00225825 | ||||||||
\(93\) | −2.19350 | −0.227455 | ||||||||
\(94\) | 0.176174 | − | 0.176174i | 0.0181710 | − | 0.0181710i | ||||
\(95\) | 0.0561127 | + | 1.61050i | 0.00575704 | + | 0.165233i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | 7.65590i | 0.777339i | 0.921377 | + | 0.388670i | \(0.127065\pi\) | ||||
−0.921377 | + | 0.388670i | \(0.872935\pi\) | |||||||
\(98\) | − | 0.206804i | − | 0.0208904i | ||||||
\(99\) | 3.01042 | 0.302558 | ||||||||
\(100\) | 0.347996 | + | 4.98788i | 0.0347996 | + | 0.498788i | ||||
\(101\) | 16.6519i | 1.65693i | 0.560040 | + | 0.828465i | \(0.310786\pi\) | ||||
−0.560040 | + | 0.828465i | \(0.689214\pi\) | |||||||
\(102\) | 3.83427 | + | 3.83427i | 0.379650 | + | 0.379650i | ||||
\(103\) | − | 15.2064i | − | 1.49833i | −0.662383 | − | 0.749165i | \(-0.730455\pi\) | ||
0.662383 | − | 0.749165i | \(-0.269545\pi\) | |||||||
\(104\) | 1.82067 | 0.178531 | ||||||||
\(105\) | −3.97505 | + | 4.26204i | −0.387925 | + | 0.415933i | ||||
\(106\) | −2.05089 | − | 2.05089i | −0.199200 | − | 0.199200i | ||||
\(107\) | −7.85181 | + | 7.85181i | −0.759063 | + | 0.759063i | −0.976152 | − | 0.217089i | \(-0.930344\pi\) |
0.217089 | + | 0.976152i | \(0.430344\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 5.15891 | + | 5.15891i | 0.494134 | + | 0.494134i | 0.909606 | − | 0.415472i | \(-0.136384\pi\) |
−0.415472 | + | 0.909606i | \(0.636384\pi\) | |||||||
\(110\) | 4.59126 | − | 4.92274i | 0.437759 | − | 0.469365i | ||||
\(111\) | 2.38247 | + | 5.59677i | 0.226134 | + | 0.531222i | ||||
\(112\) | 1.84299 | − | 1.84299i | 0.174146 | − | 0.174146i | ||||
\(113\) | − | 3.80319i | − | 0.357774i | −0.983870 | − | 0.178887i | \(-0.942750\pi\) | ||
0.983870 | − | 0.178887i | \(-0.0572497\pi\) | |||||||
\(114\) | 0.720673 | 0.0674972 | ||||||||
\(115\) | −0.0354199 | − | 0.0330348i | −0.00330292 | − | 0.00308051i | ||||
\(116\) | 4.67832 | − | 4.67832i | 0.434371 | − | 0.434371i | ||||
\(117\) | 1.82067i | 0.168321i | ||||||||
\(118\) | −2.84934 | − | 2.84934i | −0.262303 | − | 0.262303i | ||||
\(119\) | 9.99356 | + | 9.99356i | 0.916108 | + | 0.916108i | ||||
\(120\) | 2.23471 | − | 0.0778616i | 0.204000 | − | 0.00710776i | ||||
\(121\) | 1.93740 | 0.176127 | ||||||||
\(122\) | −4.51718 | − | 4.51718i | −0.408966 | − | 0.408966i | ||||
\(123\) | −4.49428 | − | 4.49428i | −0.405235 | − | 0.405235i | ||||
\(124\) | 1.55104 | + | 1.55104i | 0.139287 | + | 0.139287i | ||||
\(125\) | −7.03807 | + | 8.68709i | −0.629504 | + | 0.776997i | ||||
\(126\) | 1.84299 | + | 1.84299i | 0.164186 | + | 0.164186i | ||||
\(127\) | 9.77118 | − | 9.77118i | 0.867052 | − | 0.867052i | −0.125093 | − | 0.992145i | \(-0.539923\pi\) |
0.992145 | + | 0.125093i | \(0.0399229\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.56285 | − | 5.56285i | 0.489782 | − | 0.489782i | ||||
\(130\) | 2.97723 | + | 2.77675i | 0.261120 | + | 0.243537i | ||||
\(131\) | 2.21257 | + | 2.21257i | 0.193313 | + | 0.193313i | 0.797126 | − | 0.603813i | \(-0.206353\pi\) |
−0.603813 | + | 0.797126i | \(0.706353\pi\) | |||||||
\(132\) | −2.12868 | − | 2.12868i | −0.185278 | − | 0.185278i | ||||
\(133\) | 1.87834 | 0.162873 | ||||||||
\(134\) | 3.93891 | + | 3.93891i | 0.340270 | + | 0.340270i | ||||
\(135\) | 0.0778616 | + | 2.23471i | 0.00670126 | + | 0.192333i | ||||
\(136\) | − | 5.42248i | − | 0.464974i | ||||||
\(137\) | −5.72235 | + | 5.72235i | −0.488894 | + | 0.488894i | −0.907957 | − | 0.419063i | \(-0.862359\pi\) |
0.419063 | + | 0.907957i | \(0.362359\pi\) | |||||||
\(138\) | −0.0153162 | + | 0.0153162i | −0.00130380 | + | 0.00130380i | ||||
\(139\) | −4.18150 | −0.354670 | −0.177335 | − | 0.984151i | \(-0.556748\pi\) | ||||
−0.177335 | + | 0.984151i | \(0.556748\pi\) | |||||||
\(140\) | 5.82450 | − | 0.202937i | 0.492260 | − | 0.0171513i | ||||
\(141\) | − | 0.249148i | − | 0.0209820i | ||||||
\(142\) | −9.00950 | −0.756060 | ||||||||
\(143\) | − | 5.48097i | − | 0.458342i | ||||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 14.7852 | − | 0.515143i | 1.22784 | − | 0.0427803i | ||||
\(146\) | 8.50501 | − | 8.50501i | 0.703880 | − | 0.703880i | ||||
\(147\) | −0.146233 | − | 0.146233i | −0.0120611 | − | 0.0120611i | ||||
\(148\) | 2.27285 | − | 5.64218i | 0.186827 | − | 0.463784i | ||||
\(149\) | − | 2.65031i | − | 0.217122i | −0.994090 | − | 0.108561i | \(-0.965376\pi\) | ||
0.994090 | − | 0.108561i | \(-0.0346243\pi\) | |||||||
\(150\) | 3.77303 | + | 3.28089i | 0.308067 | + | 0.267884i | ||||
\(151\) | − | 3.91246i | − | 0.318391i | −0.987247 | − | 0.159196i | \(-0.949110\pi\) | ||
0.987247 | − | 0.159196i | \(-0.0508901\pi\) | |||||||
\(152\) | −0.509592 | − | 0.509592i | −0.0413334 | − | 0.0413334i | ||||
\(153\) | 5.42248 | 0.438382 | ||||||||
\(154\) | −5.54815 | − | 5.54815i | −0.447083 | − | 0.447083i | ||||
\(155\) | 0.170789 | + | 4.90183i | 0.0137181 | + | 0.393725i | ||||
\(156\) | 1.28741 | − | 1.28741i | 0.103075 | − | 0.103075i | ||||
\(157\) | −12.9226 | + | 12.9226i | −1.03134 | + | 1.03134i | −0.0318468 | + | 0.999493i | \(0.510139\pi\) |
−0.999493 | + | 0.0318468i | \(0.989861\pi\) | |||||||
\(158\) | −2.16377 | − | 2.16377i | −0.172141 | − | 0.172141i | ||||
\(159\) | −2.90039 | −0.230016 | ||||||||
\(160\) | −1.63524 | − | 1.52512i | −0.129277 | − | 0.120572i | ||||
\(161\) | −0.0399199 | + | 0.0399199i | −0.00314613 | + | 0.00314613i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | − | 8.59786i | − | 0.673437i | −0.941605 | − | 0.336718i | \(-0.890683\pi\) | ||
0.941605 | − | 0.336718i | \(-0.109317\pi\) | |||||||
\(164\) | 6.35587i | 0.496310i | ||||||||
\(165\) | −0.234396 | − | 6.72741i | −0.0182477 | − | 0.523728i | ||||
\(166\) | −0.925954 | − | 0.925954i | −0.0718680 | − | 0.0718680i | ||||
\(167\) | − | 4.59086i | − | 0.355252i | −0.984098 | − | 0.177626i | \(-0.943158\pi\) | ||
0.984098 | − | 0.177626i | \(-0.0568417\pi\) | |||||||
\(168\) | − | 2.60638i | − | 0.201086i | ||||||
\(169\) | −9.68516 | −0.745012 | ||||||||
\(170\) | 8.26996 | − | 8.86704i | 0.634277 | − | 0.680071i | ||||
\(171\) | 0.509592 | − | 0.509592i | 0.0389695 | − | 0.0389695i | ||||
\(172\) | −7.86706 | −0.599858 | ||||||||
\(173\) | 6.49792 | − | 6.49792i | 0.494028 | − | 0.494028i | −0.415545 | − | 0.909573i | \(-0.636409\pi\) |
0.909573 | + | 0.415545i | \(0.136409\pi\) | |||||||
\(174\) | − | 6.61614i | − | 0.501568i | ||||||
\(175\) | 9.83394 | + | 8.55123i | 0.743376 | + | 0.646412i | ||||
\(176\) | 3.01042i | 0.226919i | ||||||||
\(177\) | −4.02957 | −0.302881 | ||||||||
\(178\) | 1.03976 | − | 1.03976i | 0.0779333 | − | 0.0779333i | ||||
\(179\) | −11.1786 | + | 11.1786i | −0.835528 | + | 0.835528i | −0.988267 | − | 0.152738i | \(-0.951191\pi\) |
0.152738 | + | 0.988267i | \(0.451191\pi\) | |||||||
\(180\) | 1.52512 | − | 1.63524i | 0.113676 | − | 0.121883i | ||||
\(181\) | −12.7902 | −0.950689 | −0.475345 | − | 0.879800i | \(-0.657677\pi\) | ||||
−0.475345 | + | 0.879800i | \(0.657677\pi\) | |||||||
\(182\) | 3.35547 | − | 3.35547i | 0.248724 | − | 0.248724i | ||||
\(183\) | −6.38826 | −0.472234 | ||||||||
\(184\) | 0.0216604 | 0.00159683 | ||||||||
\(185\) | 12.3217 | − | 5.75991i | 0.905907 | − | 0.423477i | ||||
\(186\) | 2.19350 | 0.160835 | ||||||||
\(187\) | −16.3239 | −1.19372 | ||||||||
\(188\) | −0.176174 | + | 0.176174i | −0.0128488 | + | 0.0128488i | ||||
\(189\) | 2.60638 | 0.189586 | ||||||||
\(190\) | −0.0561127 | − | 1.61050i | −0.00407084 | − | 0.116838i | ||||
\(191\) | 15.7097 | − | 15.7097i | 1.13672 | − | 1.13672i | 0.147683 | − | 0.989035i | \(-0.452819\pi\) |
0.989035 | − | 0.147683i | \(-0.0471814\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 21.0634 | 1.51618 | 0.758088 | − | 0.652152i | \(-0.226134\pi\) | ||||
0.758088 | + | 0.652152i | \(0.226134\pi\) | |||||||
\(194\) | − | 7.65590i | − | 0.549662i | ||||||
\(195\) | 4.06867 | − | 0.141760i | 0.291364 | − | 0.0101517i | ||||
\(196\) | 0.206804i | 0.0147717i | ||||||||
\(197\) | −5.52601 | + | 5.52601i | −0.393712 | + | 0.393712i | −0.876008 | − | 0.482296i | \(-0.839803\pi\) |
0.482296 | + | 0.876008i | \(0.339803\pi\) | |||||||
\(198\) | −3.01042 | −0.213941 | ||||||||
\(199\) | 5.69096 | − | 5.69096i | 0.403421 | − | 0.403421i | −0.476015 | − | 0.879437i | \(-0.657919\pi\) |
0.879437 | + | 0.476015i | \(0.157919\pi\) | |||||||
\(200\) | −0.347996 | − | 4.98788i | −0.0246071 | − | 0.352696i | ||||
\(201\) | 5.57046 | 0.392910 | ||||||||
\(202\) | − | 16.6519i | − | 1.17163i | ||||||
\(203\) | − | 17.2442i | − | 1.21030i | ||||||
\(204\) | −3.83427 | − | 3.83427i | −0.268453 | − | 0.268453i | ||||
\(205\) | −9.69348 | + | 10.3933i | −0.677022 | + | 0.725903i | ||||
\(206\) | 15.2064i | 1.05948i | ||||||||
\(207\) | 0.0216604i | 0.00150550i | ||||||||
\(208\) | −1.82067 | −0.126241 | ||||||||
\(209\) | −1.53408 | + | 1.53408i | −0.106115 | + | 0.106115i | ||||
\(210\) | 3.97505 | − | 4.26204i | 0.274304 | − | 0.294109i | ||||
\(211\) | 2.18341 | 0.150312 | 0.0751561 | − | 0.997172i | \(-0.476054\pi\) | ||||
0.0751561 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(212\) | 2.05089 | + | 2.05089i | 0.140855 | + | 0.140855i | ||||
\(213\) | −6.37068 | + | 6.37068i | −0.436512 | + | 0.436512i | ||||
\(214\) | 7.85181 | − | 7.85181i | 0.536739 | − | 0.536739i | ||||
\(215\) | −12.8645 | − | 11.9982i | −0.877352 | − | 0.818273i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 5.71708 | 0.388101 | ||||||||
\(218\) | −5.15891 | − | 5.15891i | −0.349405 | − | 0.349405i | ||||
\(219\) | − | 12.0279i | − | 0.812771i | ||||||
\(220\) | −4.59126 | + | 4.92274i | −0.309542 | + | 0.331891i | ||||
\(221\) | − | 9.87255i | − | 0.664100i | ||||||
\(222\) | −2.38247 | − | 5.59677i | −0.159901 | − | 0.375631i | ||||
\(223\) | −15.3328 | − | 15.3328i | −1.02676 | − | 1.02676i | −0.999632 | − | 0.0271298i | \(-0.991363\pi\) |
−0.0271298 | − | 0.999632i | \(-0.508637\pi\) | |||||||
\(224\) | −1.84299 | + | 1.84299i | −0.123140 | + | 0.123140i | ||||
\(225\) | 4.98788 | − | 0.347996i | 0.332525 | − | 0.0231998i | ||||
\(226\) | 3.80319i | 0.252985i | ||||||||
\(227\) | 3.20189i | 0.212517i | 0.994339 | + | 0.106258i | \(0.0338870\pi\) | ||||
−0.994339 | + | 0.106258i | \(0.966113\pi\) | |||||||
\(228\) | −0.720673 | −0.0477277 | ||||||||
\(229\) | − | 21.2446i | − | 1.40389i | −0.712233 | − | 0.701943i | \(-0.752316\pi\) | ||
0.712233 | − | 0.701943i | \(-0.247684\pi\) | |||||||
\(230\) | 0.0354199 | + | 0.0330348i | 0.00233552 | + | 0.00217825i | ||||
\(231\) | −7.84627 | −0.516247 | ||||||||
\(232\) | −4.67832 | + | 4.67832i | −0.307147 | + | 0.307147i | ||||
\(233\) | −12.0202 | + | 12.0202i | −0.787472 | + | 0.787472i | −0.981079 | − | 0.193607i | \(-0.937981\pi\) |
0.193607 | + | 0.981079i | \(0.437981\pi\) | |||||||
\(234\) | − | 1.82067i | − | 0.119021i | ||||||
\(235\) | −0.556773 | + | 0.0193990i | −0.0363199 | + | 0.00126545i | ||||
\(236\) | 2.84934 | + | 2.84934i | 0.185476 | + | 0.185476i | ||||
\(237\) | −3.06004 | −0.198771 | ||||||||
\(238\) | −9.99356 | − | 9.99356i | −0.647786 | − | 0.647786i | ||||
\(239\) | −10.1337 | − | 10.1337i | −0.655496 | − | 0.655496i | 0.298815 | − | 0.954311i | \(-0.403409\pi\) |
−0.954311 | + | 0.298815i | \(0.903409\pi\) | |||||||
\(240\) | −2.23471 | + | 0.0778616i | −0.144250 | + | 0.00502594i | ||||
\(241\) | 10.2389 | − | 10.2389i | 0.659546 | − | 0.659546i | −0.295727 | − | 0.955273i | \(-0.595562\pi\) |
0.955273 | + | 0.295727i | \(0.0955618\pi\) | |||||||
\(242\) | −1.93740 | −0.124541 | ||||||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 4.51718 | + | 4.51718i | 0.289183 | + | 0.289183i | ||||
\(245\) | −0.315402 | + | 0.338174i | −0.0201503 | + | 0.0216052i | ||||
\(246\) | 4.49428 | + | 4.49428i | 0.286545 | + | 0.286545i | ||||
\(247\) | −0.927800 | − | 0.927800i | −0.0590345 | − | 0.0590345i | ||||
\(248\) | −1.55104 | − | 1.55104i | −0.0984909 | − | 0.0984909i | ||||
\(249\) | −1.30950 | −0.0829860 | ||||||||
\(250\) | 7.03807 | − | 8.68709i | 0.445127 | − | 0.549420i | ||||
\(251\) | 3.84833 | + | 3.84833i | 0.242905 | + | 0.242905i | 0.818051 | − | 0.575146i | \(-0.195055\pi\) |
−0.575146 | + | 0.818051i | \(0.695055\pi\) | |||||||
\(252\) | −1.84299 | − | 1.84299i | −0.116097 | − | 0.116097i | ||||
\(253\) | − | 0.0652069i | − | 0.00409952i | ||||||
\(254\) | −9.77118 | + | 9.77118i | −0.613099 | + | 0.613099i | ||||
\(255\) | −0.422203 | − | 12.1177i | −0.0264394 | − | 0.758839i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.13559i | 0.195593i | 0.995206 | + | 0.0977963i | \(0.0311794\pi\) | ||||
−0.995206 | + | 0.0977963i | \(0.968821\pi\) | |||||||
\(258\) | −5.56285 | + | 5.56285i | −0.346328 | + | 0.346328i | ||||
\(259\) | −6.20962 | − | 14.5873i | −0.385847 | − | 0.906410i | ||||
\(260\) | −2.97723 | − | 2.77675i | −0.184640 | − | 0.172207i | ||||
\(261\) | −4.67832 | − | 4.67832i | −0.289581 | − | 0.289581i | ||||
\(262\) | −2.21257 | − | 2.21257i | −0.136693 | − | 0.136693i | ||||
\(263\) | 20.7027 | − | 20.7027i | 1.27658 | − | 1.27658i | 0.334018 | − | 0.942567i | \(-0.391595\pi\) |
0.942567 | − | 0.334018i | \(-0.108405\pi\) | |||||||
\(264\) | 2.12868 | + | 2.12868i | 0.131012 | + | 0.131012i | ||||
\(265\) | 0.225829 | + | 6.48154i | 0.0138726 | + | 0.398158i | ||||
\(266\) | −1.87834 | −0.115169 | ||||||||
\(267\) | − | 1.47044i | − | 0.0899896i | ||||||
\(268\) | −3.93891 | − | 3.93891i | −0.240607 | − | 0.240607i | ||||
\(269\) | 15.5877i | 0.950397i | 0.879879 | + | 0.475199i | \(0.157624\pi\) | ||||
−0.879879 | + | 0.475199i | \(0.842376\pi\) | |||||||
\(270\) | −0.0778616 | − | 2.23471i | −0.00473851 | − | 0.136000i | ||||
\(271\) | 30.3127 | 1.84136 | 0.920682 | − | 0.390314i | \(-0.127633\pi\) | ||||
0.920682 | + | 0.390314i | \(0.127633\pi\) | |||||||
\(272\) | 5.42248i | 0.328786i | ||||||||
\(273\) | − | 4.74535i | − | 0.287202i | ||||||
\(274\) | 5.72235 | − | 5.72235i | 0.345700 | − | 0.345700i | ||||
\(275\) | −15.0156 | + | 1.04761i | −0.905473 | + | 0.0631735i | ||||
\(276\) | 0.0153162 | − | 0.0153162i | 0.000921929 | − | 0.000921929i | ||||
\(277\) | 14.8230 | 0.890629 | 0.445315 | − | 0.895374i | \(-0.353092\pi\) | ||||
0.445315 | + | 0.895374i | \(0.353092\pi\) | |||||||
\(278\) | 4.18150 | 0.250789 | ||||||||
\(279\) | 1.55104 | − | 1.55104i | 0.0928581 | − | 0.0928581i | ||||
\(280\) | −5.82450 | + | 0.202937i | −0.348080 | + | 0.0121278i | ||||
\(281\) | 22.8948 | − | 22.8948i | 1.36579 | − | 1.36579i | 0.499436 | − | 0.866351i | \(-0.333541\pi\) |
0.866351 | − | 0.499436i | \(-0.166459\pi\) | |||||||
\(282\) | 0.249148i | 0.0148365i | ||||||||
\(283\) | − | 23.6708i | − | 1.40708i | −0.710655 | − | 0.703541i | \(-0.751601\pi\) | ||
0.710655 | − | 0.703541i | \(-0.248399\pi\) | |||||||
\(284\) | 9.00950 | 0.534615 | ||||||||
\(285\) | −1.17847 | − | 1.09911i | −0.0698065 | − | 0.0651059i | ||||
\(286\) | 5.48097i | 0.324097i | ||||||||
\(287\) | 11.7138 | + | 11.7138i | 0.691442 | + | 0.691442i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −12.4033 | −0.729607 | ||||||||
\(290\) | −14.7852 | + | 0.515143i | −0.868215 | + | 0.0302503i | ||||
\(291\) | −5.41354 | − | 5.41354i | −0.317347 | − | 0.317347i | ||||
\(292\) | −8.50501 | + | 8.50501i | −0.497718 | + | 0.497718i | ||||
\(293\) | 5.16020 | + | 5.16020i | 0.301462 | + | 0.301462i | 0.841586 | − | 0.540124i | \(-0.181623\pi\) |
−0.540124 | + | 0.841586i | \(0.681623\pi\) | |||||||
\(294\) | 0.146233 | + | 0.146233i | 0.00852847 | + | 0.00852847i | ||||
\(295\) | 0.313749 | + | 9.00493i | 0.0182672 | + | 0.524287i | ||||
\(296\) | −2.27285 | + | 5.64218i | −0.132107 | + | 0.327945i | ||||
\(297\) | −2.12868 | + | 2.12868i | −0.123519 | + | 0.123519i | ||||
\(298\) | 2.65031i | 0.153529i | ||||||||
\(299\) | 0.0394365 | 0.00228067 | ||||||||
\(300\) | −3.77303 | − | 3.28089i | −0.217836 | − | 0.189422i | ||||
\(301\) | −14.4989 | + | 14.4989i | −0.835701 | + | 0.835701i | ||||
\(302\) | 3.91246i | 0.225137i | ||||||||
\(303\) | −11.7747 | − | 11.7747i | −0.676439 | − | 0.676439i | ||||
\(304\) | 0.509592 | + | 0.509592i | 0.0292271 | + | 0.0292271i | ||||
\(305\) | 0.497400 | + | 14.2759i | 0.0284810 | + | 0.817437i | ||||
\(306\) | −5.42248 | −0.309983 | ||||||||
\(307\) | 16.3280 | + | 16.3280i | 0.931889 | + | 0.931889i | 0.997824 | − | 0.0659354i | \(-0.0210031\pi\) |
−0.0659354 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(308\) | 5.54815 | + | 5.54815i | 0.316135 | + | 0.316135i | ||||
\(309\) | 10.7525 | + | 10.7525i | 0.611691 | + | 0.611691i | ||||
\(310\) | −0.170789 | − | 4.90183i | −0.00970017 | − | 0.278405i | ||||
\(311\) | −20.2566 | − | 20.2566i | −1.14865 | − | 1.14865i | −0.986819 | − | 0.161827i | \(-0.948261\pi\) |
−0.161827 | − | 0.986819i | \(-0.551739\pi\) | |||||||
\(312\) | −1.28741 | + | 1.28741i | −0.0728851 | + | 0.0728851i | ||||
\(313\) | 18.3942 | 1.03970 | 0.519852 | − | 0.854256i | \(-0.325987\pi\) | ||||
0.519852 | + | 0.854256i | \(0.325987\pi\) | |||||||
\(314\) | 12.9226 | − | 12.9226i | 0.729267 | − | 0.729267i | ||||
\(315\) | −0.202937 | − | 5.82450i | −0.0114342 | − | 0.328173i | ||||
\(316\) | 2.16377 | + | 2.16377i | 0.121722 | + | 0.121722i | ||||
\(317\) | −3.40194 | − | 3.40194i | −0.191072 | − | 0.191072i | 0.605087 | − | 0.796159i | \(-0.293138\pi\) |
−0.796159 | + | 0.605087i | \(0.793138\pi\) | |||||||
\(318\) | 2.90039 | 0.162646 | ||||||||
\(319\) | 14.0837 | + | 14.0837i | 0.788535 | + | 0.788535i | ||||
\(320\) | 1.63524 | + | 1.52512i | 0.0914125 | + | 0.0852570i | ||||
\(321\) | − | 11.1041i | − | 0.619773i | ||||||
\(322\) | 0.0399199 | − | 0.0399199i | 0.00222465 | − | 0.00222465i | ||||
\(323\) | −2.76326 | + | 2.76326i | −0.153752 | + | 0.153752i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −0.633587 | − | 9.08127i | −0.0351451 | − | 0.503738i | ||||
\(326\) | 8.59786i | 0.476192i | ||||||||
\(327\) | −7.29580 | −0.403459 | ||||||||
\(328\) | − | 6.35587i | − | 0.350944i | ||||||
\(329\) | 0.649372i | 0.0358010i | ||||||||
\(330\) | 0.234396 | + | 6.72741i | 0.0129031 | + | 0.370332i | ||||
\(331\) | 2.61136 | − | 2.61136i | 0.143533 | − | 0.143533i | −0.631689 | − | 0.775222i | \(-0.717638\pi\) |
0.775222 | + | 0.631689i | \(0.217638\pi\) | |||||||
\(332\) | 0.925954 | + | 0.925954i | 0.0508183 | + | 0.0508183i | ||||
\(333\) | −5.64218 | − | 2.27285i | −0.309189 | − | 0.124552i | ||||
\(334\) | 4.59086i | 0.251201i | ||||||||
\(335\) | −0.433725 | − | 12.4484i | −0.0236969 | − | 0.680128i | ||||
\(336\) | 2.60638i | 0.142189i | ||||||||
\(337\) | −3.23500 | − | 3.23500i | −0.176222 | − | 0.176222i | 0.613485 | − | 0.789707i | \(-0.289767\pi\) |
−0.789707 | + | 0.613485i | \(0.789767\pi\) | |||||||
\(338\) | 9.68516 | 0.526803 | ||||||||
\(339\) | 2.68926 | + | 2.68926i | 0.146061 | + | 0.146061i | ||||
\(340\) | −8.26996 | + | 8.86704i | −0.448501 | + | 0.480883i | ||||
\(341\) | −4.66926 | + | 4.66926i | −0.252855 | + | 0.252855i | ||||
\(342\) | −0.509592 | + | 0.509592i | −0.0275556 | + | 0.0275556i | ||||
\(343\) | 13.2820 | + | 13.2820i | 0.717163 | + | 0.717163i | ||||
\(344\) | 7.86706 | 0.424163 | ||||||||
\(345\) | 0.0484048 | − | 0.00168651i | 0.00260603 | − | 9.07989e-5i | ||||
\(346\) | −6.49792 | + | 6.49792i | −0.349330 | + | 0.349330i | ||||
\(347\) | 17.9326 | 0.962675 | 0.481337 | − | 0.876535i | \(-0.340151\pi\) | ||||
0.481337 | + | 0.876535i | \(0.340151\pi\) | |||||||
\(348\) | 6.61614i | 0.354662i | ||||||||
\(349\) | − | 34.1023i | − | 1.82545i | −0.408571 | − | 0.912727i | \(-0.633973\pi\) | ||
0.408571 | − | 0.912727i | \(-0.366027\pi\) | |||||||
\(350\) | −9.83394 | − | 8.55123i | −0.525646 | − | 0.457083i | ||||
\(351\) | −1.28741 | − | 1.28741i | −0.0687168 | − | 0.0687168i | ||||
\(352\) | − | 3.01042i | − | 0.160456i | ||||||
\(353\) | − | 7.23850i | − | 0.385266i | −0.981271 | − | 0.192633i | \(-0.938297\pi\) | ||
0.981271 | − | 0.192633i | \(-0.0617027\pi\) | |||||||
\(354\) | 4.02957 | 0.214169 | ||||||||
\(355\) | 14.7327 | + | 13.7406i | 0.781929 | + | 0.729275i | ||||
\(356\) | −1.03976 | + | 1.03976i | −0.0551071 | + | 0.0551071i | ||||
\(357\) | −14.1330 | −0.747999 | ||||||||
\(358\) | 11.1786 | − | 11.1786i | 0.590808 | − | 0.590808i | ||||
\(359\) | − | 29.3398i | − | 1.54849i | −0.632884 | − | 0.774247i | \(-0.718129\pi\) | ||
0.632884 | − | 0.774247i | \(-0.281871\pi\) | |||||||
\(360\) | −1.52512 | + | 1.63524i | −0.0803811 | + | 0.0861845i | ||||
\(361\) | − | 18.4806i | − | 0.972665i | ||||||
\(362\) | 12.7902 | 0.672239 | ||||||||
\(363\) | −1.36995 | + | 1.36995i | −0.0719037 | + | 0.0719037i | ||||
\(364\) | −3.35547 | + | 3.35547i | −0.175874 | + | 0.175874i | ||||
\(365\) | −26.8789 | + | 0.936512i | −1.40691 | + | 0.0490193i | ||||
\(366\) | 6.38826 | 0.333920 | ||||||||
\(367\) | 7.30169 | − | 7.30169i | 0.381145 | − | 0.381145i | −0.490370 | − | 0.871515i | \(-0.663138\pi\) |
0.871515 | + | 0.490370i | \(0.163138\pi\) | |||||||
\(368\) | −0.0216604 | −0.00112913 | ||||||||
\(369\) | 6.35587 | 0.330873 | ||||||||
\(370\) | −12.3217 | + | 5.75991i | −0.640573 | + | 0.299443i | ||||
\(371\) | 7.55951 | 0.392470 | ||||||||
\(372\) | −2.19350 | −0.113728 | ||||||||
\(373\) | −0.813457 | + | 0.813457i | −0.0421192 | + | 0.0421192i | −0.727853 | − | 0.685733i | \(-0.759482\pi\) |
0.685733 | + | 0.727853i | \(0.259482\pi\) | |||||||
\(374\) | 16.3239 | 0.844090 | ||||||||
\(375\) | −1.16604 | − | 11.1194i | −0.0602138 | − | 0.574202i | ||||
\(376\) | 0.176174 | − | 0.176174i | 0.00908548 | − | 0.00908548i | ||||
\(377\) | −8.51767 | + | 8.51767i | −0.438682 | + | 0.438682i | ||||
\(378\) | −2.60638 | −0.134058 | ||||||||
\(379\) | 14.5201i | 0.745847i | 0.927862 | + | 0.372924i | \(0.121645\pi\) | ||||
−0.927862 | + | 0.372924i | \(0.878355\pi\) | |||||||
\(380\) | 0.0561127 | + | 1.61050i | 0.00287852 | + | 0.0826167i | ||||
\(381\) | 13.8185i | 0.707945i | ||||||||
\(382\) | −15.7097 | + | 15.7097i | −0.803781 | + | 0.803781i | ||||
\(383\) | −14.8639 | −0.759507 | −0.379754 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 0.610923 | + | 17.5342i | 0.0311355 | + | 0.893624i | ||||
\(386\) | −21.0634 | −1.07210 | ||||||||
\(387\) | 7.86706i | 0.399905i | ||||||||
\(388\) | 7.65590i | 0.388670i | ||||||||
\(389\) | −25.0493 | − | 25.0493i | −1.27005 | − | 1.27005i | −0.946062 | − | 0.323986i | \(-0.894977\pi\) |
−0.323986 | − | 0.946062i | \(-0.605023\pi\) | |||||||
\(390\) | −4.06867 | + | 0.141760i | −0.206025 | + | 0.00717831i | ||||
\(391\) | − | 0.117453i | − | 0.00593987i | ||||||
\(392\) | − | 0.206804i | − | 0.0104452i | ||||||
\(393\) | −3.12905 | −0.157840 | ||||||||
\(394\) | 5.52601 | − | 5.52601i | 0.278396 | − | 0.278396i | ||||
\(395\) | 0.238260 | + | 6.83831i | 0.0119881 | + | 0.344073i | ||||
\(396\) | 3.01042 | 0.151279 | ||||||||
\(397\) | −5.32491 | − | 5.32491i | −0.267250 | − | 0.267250i | 0.560741 | − | 0.827991i | \(-0.310516\pi\) |
−0.827991 | + | 0.560741i | \(0.810516\pi\) | |||||||
\(398\) | −5.69096 | + | 5.69096i | −0.285262 | + | 0.285262i | ||||
\(399\) | −1.32819 | + | 1.32819i | −0.0664926 | + | 0.0664926i | ||||
\(400\) | 0.347996 | + | 4.98788i | 0.0173998 | + | 0.249394i | ||||
\(401\) | −5.09805 | − | 5.09805i | −0.254584 | − | 0.254584i | 0.568263 | − | 0.822847i | \(-0.307616\pi\) |
−0.822847 | + | 0.568263i | \(0.807616\pi\) | |||||||
\(402\) | −5.57046 | −0.277829 | ||||||||
\(403\) | −2.82393 | − | 2.82393i | −0.140670 | − | 0.140670i | ||||
\(404\) | 16.6519i | 0.828465i | ||||||||
\(405\) | −1.63524 | − | 1.52512i | −0.0812556 | − | 0.0757840i | ||||
\(406\) | 17.2442i | 0.855813i | ||||||||
\(407\) | 16.9853 | + | 6.84223i | 0.841930 | + | 0.339157i | ||||
\(408\) | 3.83427 | + | 3.83427i | 0.189825 | + | 0.189825i | ||||
\(409\) | −15.3174 | + | 15.3174i | −0.757396 | + | 0.757396i | −0.975848 | − | 0.218451i | \(-0.929899\pi\) |
0.218451 | + | 0.975848i | \(0.429899\pi\) | |||||||
\(410\) | 9.69348 | − | 10.3933i | 0.478727 | − | 0.513291i | ||||
\(411\) | − | 8.09263i | − | 0.399180i | ||||||
\(412\) | − | 15.2064i | − | 0.749165i | ||||||
\(413\) | 10.5026 | 0.516798 | ||||||||
\(414\) | − | 0.0216604i | − | 0.00106455i | ||||||
\(415\) | 0.101960 | + | 2.92635i | 0.00500500 | + | 0.143649i | ||||
\(416\) | 1.82067 | 0.0892657 | ||||||||
\(417\) | 2.95676 | − | 2.95676i | 0.144793 | − | 0.144793i | ||||
\(418\) | 1.53408 | − | 1.53408i | 0.0750345 | − | 0.0750345i | ||||
\(419\) | − | 15.6256i | − | 0.763360i | −0.924294 | − | 0.381680i | \(-0.875346\pi\) | ||
0.924294 | − | 0.381680i | \(-0.124654\pi\) | |||||||
\(420\) | −3.97505 | + | 4.26204i | −0.193962 | + | 0.207966i | ||||
\(421\) | 15.7260 | + | 15.7260i | 0.766440 | + | 0.766440i | 0.977478 | − | 0.211038i | \(-0.0676844\pi\) |
−0.211038 | + | 0.977478i | \(0.567684\pi\) | |||||||
\(422\) | −2.18341 | −0.106287 | ||||||||
\(423\) | 0.176174 | + | 0.176174i | 0.00856587 | + | 0.00856587i | ||||
\(424\) | −2.05089 | − | 2.05089i | −0.0995998 | − | 0.0995998i | ||||
\(425\) | −27.0467 | + | 1.88700i | −1.31196 | + | 0.0915332i | ||||
\(426\) | 6.37068 | − | 6.37068i | 0.308660 | − | 0.308660i | ||||
\(427\) | 16.6502 | 0.805760 | ||||||||
\(428\) | −7.85181 | + | 7.85181i | −0.379532 | + | 0.379532i | ||||
\(429\) | 3.87563 | + | 3.87563i | 0.187117 | + | 0.187117i | ||||
\(430\) | 12.8645 | + | 11.9982i | 0.620381 | + | 0.578606i | ||||
\(431\) | 7.16507 | + | 7.16507i | 0.345129 | + | 0.345129i | 0.858292 | − | 0.513162i | \(-0.171526\pi\) |
−0.513162 | + | 0.858292i | \(0.671526\pi\) | |||||||
\(432\) | 0.707107 | + | 0.707107i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 12.9982 | + | 12.9982i | 0.624652 | + | 0.624652i | 0.946717 | − | 0.322065i | \(-0.104377\pi\) |
−0.322065 | + | 0.946717i | \(0.604377\pi\) | |||||||
\(434\) | −5.71708 | −0.274429 | ||||||||
\(435\) | −10.0904 | + | 10.8190i | −0.483799 | + | 0.518729i | ||||
\(436\) | 5.15891 | + | 5.15891i | 0.247067 | + | 0.247067i | ||||
\(437\) | −0.0110380 | − | 0.0110380i | −0.000528019 | − | 0.000528019i | ||||
\(438\) | 12.0279i | 0.574716i | ||||||||
\(439\) | 10.5684 | − | 10.5684i | 0.504400 | − | 0.504400i | −0.408402 | − | 0.912802i | \(-0.633914\pi\) |
0.912802 | + | 0.408402i | \(0.133914\pi\) | |||||||
\(440\) | 4.59126 | − | 4.92274i | 0.218879 | − | 0.234682i | ||||
\(441\) | 0.206804 | 0.00984783 | ||||||||
\(442\) | 9.87255i | 0.469589i | ||||||||
\(443\) | −17.5773 | + | 17.5773i | −0.835121 | + | 0.835121i | −0.988212 | − | 0.153091i | \(-0.951077\pi\) |
0.153091 | + | 0.988212i | \(0.451077\pi\) | |||||||
\(444\) | 2.38247 | + | 5.59677i | 0.113067 | + | 0.265611i | ||||
\(445\) | −3.28601 | + | 0.114491i | −0.155772 | + | 0.00542739i | ||||
\(446\) | 15.3328 | + | 15.3328i | 0.726030 | + | 0.726030i | ||||
\(447\) | 1.87406 | + | 1.87406i | 0.0886398 | + | 0.0886398i | ||||
\(448\) | 1.84299 | − | 1.84299i | 0.0870729 | − | 0.0870729i | ||||
\(449\) | −9.93203 | − | 9.93203i | −0.468722 | − | 0.468722i | 0.432779 | − | 0.901500i | \(-0.357533\pi\) |
−0.901500 | + | 0.432779i | \(0.857533\pi\) | |||||||
\(450\) | −4.98788 | + | 0.347996i | −0.235131 | + | 0.0164047i | ||||
\(451\) | −19.1338 | −0.900975 | ||||||||
\(452\) | − | 3.80319i | − | 0.178887i | ||||||
\(453\) | 2.76653 | + | 2.76653i | 0.129983 | + | 0.129983i | ||||
\(454\) | − | 3.20189i | − | 0.150272i | ||||||
\(455\) | −10.6045 | + | 0.369480i | −0.497146 | + | 0.0173215i | ||||
\(456\) | 0.720673 | 0.0337486 | ||||||||
\(457\) | − | 8.27570i | − | 0.387121i | −0.981088 | − | 0.193560i | \(-0.937996\pi\) | ||
0.981088 | − | 0.193560i | \(-0.0620036\pi\) | |||||||
\(458\) | 21.2446i | 0.992697i | ||||||||
\(459\) | −3.83427 | + | 3.83427i | −0.178969 | + | 0.178969i | ||||
\(460\) | −0.0354199 | − | 0.0330348i | −0.00165146 | − | 0.00154026i | ||||
\(461\) | −3.89734 | + | 3.89734i | −0.181517 | + | 0.181517i | −0.792017 | − | 0.610499i | \(-0.790969\pi\) |
0.610499 | + | 0.792017i | \(0.290969\pi\) | |||||||
\(462\) | 7.84627 | 0.365042 | ||||||||
\(463\) | 37.2821 | 1.73265 | 0.866323 | − | 0.499484i | \(-0.166477\pi\) | ||||
0.866323 | + | 0.499484i | \(0.166477\pi\) | |||||||
\(464\) | 4.67832 | − | 4.67832i | 0.217185 | − | 0.217185i | ||||
\(465\) | −3.58689 | − | 3.34535i | −0.166338 | − | 0.155137i | ||||
\(466\) | 12.0202 | − | 12.0202i | 0.556827 | − | 0.556827i | ||||
\(467\) | − | 11.9336i | − | 0.552219i | −0.961126 | − | 0.276109i | \(-0.910955\pi\) | ||
0.961126 | − | 0.276109i | \(-0.0890452\pi\) | |||||||
\(468\) | 1.82067i | 0.0841605i | ||||||||
\(469\) | −14.5187 | −0.670412 | ||||||||
\(470\) | 0.556773 | − | 0.0193990i | 0.0256820 | − | 0.000894810i | ||||
\(471\) | − | 18.2754i | − | 0.842085i | ||||||
\(472\) | −2.84934 | − | 2.84934i | −0.131151 | − | 0.131151i | ||||
\(473\) | − | 23.6831i | − | 1.08895i | ||||||
\(474\) | 3.06004 | 0.140552 | ||||||||
\(475\) | −2.36445 | + | 2.71912i | −0.108488 | + | 0.124762i | ||||
\(476\) | 9.99356 | + | 9.99356i | 0.458054 | + | 0.458054i | ||||
\(477\) | 2.05089 | − | 2.05089i | 0.0939036 | − | 0.0939036i | ||||
\(478\) | 10.1337 | + | 10.1337i | 0.463506 | + | 0.463506i | ||||
\(479\) | 0.903277 | + | 0.903277i | 0.0412718 | + | 0.0412718i | 0.727441 | − | 0.686170i | \(-0.240709\pi\) |
−0.686170 | + | 0.727441i | \(0.740709\pi\) | |||||||
\(480\) | 2.23471 | − | 0.0778616i | 0.102000 | − | 0.00355388i | ||||
\(481\) | −4.13811 | + | 10.2725i | −0.188682 | + | 0.468387i | ||||
\(482\) | −10.2389 | + | 10.2389i | −0.466369 | + | 0.466369i | ||||
\(483\) | − | 0.0564552i | − | 0.00256880i | ||||||
\(484\) | 1.93740 | 0.0880637 | ||||||||
\(485\) | −11.6762 | + | 12.5192i | −0.530189 | + | 0.568468i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | − | 1.67383i | − | 0.0758483i | −0.999281 | − | 0.0379241i | \(-0.987925\pi\) | ||
0.999281 | − | 0.0379241i | \(-0.0120745\pi\) | |||||||
\(488\) | −4.51718 | − | 4.51718i | −0.204483 | − | 0.204483i | ||||
\(489\) | 6.07961 | + | 6.07961i | 0.274929 | + | 0.274929i | ||||
\(490\) | 0.315402 | − | 0.338174i | 0.0142484 | − | 0.0152772i | ||||
\(491\) | 9.36601 | 0.422682 | 0.211341 | − | 0.977412i | \(-0.432217\pi\) | ||||
0.211341 | + | 0.977412i | \(0.432217\pi\) | |||||||
\(492\) | −4.49428 | − | 4.49428i | −0.202618 | − | 0.202618i | ||||
\(493\) | 25.3681 | + | 25.3681i | 1.14252 | + | 1.14252i | ||||
\(494\) | 0.927800 | + | 0.927800i | 0.0417437 | + | 0.0417437i | ||||
\(495\) | 4.92274 | + | 4.59126i | 0.221261 | + | 0.206362i | ||||
\(496\) | 1.55104 | + | 1.55104i | 0.0696436 | + | 0.0696436i | ||||
\(497\) | 16.6044 | − | 16.6044i | 0.744808 | − | 0.744808i | ||||
\(498\) | 1.30950 | 0.0586800 | ||||||||
\(499\) | −11.8837 | + | 11.8837i | −0.531986 | + | 0.531986i | −0.921163 | − | 0.389177i | \(-0.872760\pi\) |
0.389177 | + | 0.921163i | \(0.372760\pi\) | |||||||
\(500\) | −7.03807 | + | 8.68709i | −0.314752 | + | 0.388499i | ||||
\(501\) | 3.24623 | + | 3.24623i | 0.145031 | + | 0.145031i | ||||
\(502\) | −3.84833 | − | 3.84833i | −0.171759 | − | 0.171759i | ||||
\(503\) | −25.4862 | −1.13637 | −0.568187 | − | 0.822900i | \(-0.692355\pi\) | ||||
−0.568187 | + | 0.822900i | \(0.692355\pi\) | |||||||
\(504\) | 1.84299 | + | 1.84299i | 0.0820931 | + | 0.0820931i | ||||
\(505\) | −25.3963 | + | 27.2299i | −1.13012 | + | 1.21171i | ||||
\(506\) | 0.0652069i | 0.00289880i | ||||||||
\(507\) | 6.84844 | − | 6.84844i | 0.304150 | − | 0.304150i | ||||
\(508\) | 9.77118 | − | 9.77118i | 0.433526 | − | 0.433526i | ||||
\(509\) | −21.0744 | −0.934105 | −0.467053 | − | 0.884230i | \(-0.654684\pi\) | ||||
−0.467053 | + | 0.884230i | \(0.654684\pi\) | |||||||
\(510\) | 0.422203 | + | 12.1177i | 0.0186955 | + | 0.536580i | ||||
\(511\) | 31.3492i | 1.38681i | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.720673i | 0.0318185i | ||||||||
\(514\) | − | 3.13559i | − | 0.138305i | ||||||
\(515\) | 23.1916 | − | 24.8660i | 1.02195 | − | 1.09573i | ||||
\(516\) | 5.56285 | − | 5.56285i | 0.244891 | − | 0.244891i | ||||
\(517\) | −0.530357 | − | 0.530357i | −0.0233251 | − | 0.0233251i | ||||
\(518\) | 6.20962 | + | 14.5873i | 0.272835 | + | 0.640929i | ||||
\(519\) | 9.18945i | 0.403372i | ||||||||
\(520\) | 2.97723 | + | 2.77675i | 0.130560 | + | 0.121768i | ||||
\(521\) | 26.1425i | 1.14532i | 0.819792 | + | 0.572661i | \(0.194089\pi\) | ||||
−0.819792 | + | 0.572661i | \(0.805911\pi\) | |||||||
\(522\) | 4.67832 | + | 4.67832i | 0.204764 | + | 0.204764i | ||||
\(523\) | 18.6818 | 0.816898 | 0.408449 | − | 0.912781i | \(-0.366070\pi\) | ||||
0.408449 | + | 0.912781i | \(0.366070\pi\) | |||||||
\(524\) | 2.21257 | + | 2.21257i | 0.0966567 | + | 0.0966567i | ||||
\(525\) | −13.0003 | + | 0.907010i | −0.567379 | + | 0.0395851i | ||||
\(526\) | −20.7027 | + | 20.7027i | −0.902682 | + | 0.902682i | ||||
\(527\) | −8.41047 | + | 8.41047i | −0.366366 | + | 0.366366i | ||||
\(528\) | −2.12868 | − | 2.12868i | −0.0926391 | − | 0.0926391i | ||||
\(529\) | −22.9995 | −0.999980 | ||||||||
\(530\) | −0.225829 | − | 6.48154i | −0.00980939 | − | 0.281540i | ||||
\(531\) | 2.84934 | − | 2.84934i | 0.123651 | − | 0.123651i | ||||
\(532\) | 1.87834 | 0.0814365 | ||||||||
\(533\) | − | 11.5719i | − | 0.501236i | ||||||
\(534\) | 1.47044i | 0.0636322i | ||||||||
\(535\) | −24.8146 | + | 0.864586i | −1.07283 | + | 0.0373793i | ||||
\(536\) | 3.93891 | + | 3.93891i | 0.170135 | + | 0.170135i | ||||
\(537\) | − | 15.8089i | − | 0.682206i | ||||||
\(538\) | − | 15.5877i | − | 0.672032i | ||||||
\(539\) | −0.622567 | −0.0268159 | ||||||||
\(540\) | 0.0778616 | + | 2.23471i | 0.00335063 | + | 0.0961667i | ||||
\(541\) | −12.5483 | + | 12.5483i | −0.539494 | + | 0.539494i | −0.923380 | − | 0.383887i | \(-0.874585\pi\) |
0.383887 | + | 0.923380i | \(0.374585\pi\) | |||||||
\(542\) | −30.3127 | −1.30204 | ||||||||
\(543\) | 9.04405 | − | 9.04405i | 0.388117 | − | 0.388117i | ||||
\(544\) | − | 5.42248i | − | 0.232487i | ||||||
\(545\) | 0.568062 | + | 16.3040i | 0.0243331 | + | 0.698387i | ||||
\(546\) | 4.74535i | 0.203082i | ||||||||
\(547\) | 13.3305 | 0.569972 | 0.284986 | − | 0.958532i | \(-0.408011\pi\) | ||||
0.284986 | + | 0.958532i | \(0.408011\pi\) | |||||||
\(548\) | −5.72235 | + | 5.72235i | −0.244447 | + | 0.244447i | ||||
\(549\) | 4.51718 | − | 4.51718i | 0.192789 | − | 0.192789i | ||||
\(550\) | 15.0156 | − | 1.04761i | 0.640266 | − | 0.0446704i | ||||
\(551\) | 4.76807 | 0.203127 | ||||||||
\(552\) | −0.0153162 | + | 0.0153162i | −0.000651902 | + | 0.000651902i | ||||
\(553\) | 7.97561 | 0.339158 | ||||||||
\(554\) | −14.8230 | −0.629770 | ||||||||
\(555\) | −4.63986 | + | 12.7856i | −0.196951 | + | 0.542719i | ||||
\(556\) | −4.18150 | −0.177335 | ||||||||
\(557\) | 31.5142 | 1.33530 | 0.667650 | − | 0.744475i | \(-0.267300\pi\) | ||||
0.667650 | + | 0.744475i | \(0.267300\pi\) | |||||||
\(558\) | −1.55104 | + | 1.55104i | −0.0656606 | + | 0.0656606i | ||||
\(559\) | 14.3233 | 0.605812 | ||||||||
\(560\) | 5.82450 | − | 0.202937i | 0.246130 | − | 0.00857563i | ||||
\(561\) | 11.5428 | − | 11.5428i | 0.487336 | − | 0.487336i | ||||
\(562\) | −22.8948 | + | 22.8948i | −0.965757 | + | 0.965757i | ||||
\(563\) | −23.8203 | −1.00391 | −0.501953 | − | 0.864895i | \(-0.667385\pi\) | ||||
−0.501953 | + | 0.864895i | \(0.667385\pi\) | |||||||
\(564\) | − | 0.249148i | − | 0.0104910i | ||||||
\(565\) | 5.80034 | − | 6.21912i | 0.244022 | − | 0.261640i | ||||
\(566\) | 23.6708i | 0.994957i | ||||||||
\(567\) | −1.84299 | + | 1.84299i | −0.0773981 | + | 0.0773981i | ||||
\(568\) | −9.00950 | −0.378030 | ||||||||
\(569\) | 2.20968 | − | 2.20968i | 0.0926346 | − | 0.0926346i | −0.659271 | − | 0.751905i | \(-0.729135\pi\) |
0.751905 | + | 0.659271i | \(0.229135\pi\) | |||||||
\(570\) | 1.17847 | + | 1.09911i | 0.0493607 | + | 0.0460368i | ||||
\(571\) | −18.6714 | −0.781372 | −0.390686 | − | 0.920524i | \(-0.627762\pi\) | ||||
−0.390686 | + | 0.920524i | \(0.627762\pi\) | |||||||
\(572\) | − | 5.48097i | − | 0.229171i | ||||||
\(573\) | 22.2169i | 0.928126i | ||||||||
\(574\) | −11.7138 | − | 11.7138i | −0.488923 | − | 0.488923i | ||||
\(575\) | −0.00753775 | − | 0.108039i | −0.000314346 | − | 0.00450556i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 42.7062i | − | 1.77788i | −0.458023 | − | 0.888941i | \(-0.651442\pi\) | ||
0.458023 | − | 0.888941i | \(-0.348558\pi\) | |||||||
\(578\) | 12.4033 | 0.515910 | ||||||||
\(579\) | −14.8941 | + | 14.8941i | −0.618976 | + | 0.618976i | ||||
\(580\) | 14.7852 | − | 0.515143i | 0.613921 | − | 0.0213902i | ||||
\(581\) | 3.41304 | 0.141597 | ||||||||
\(582\) | 5.41354 | + | 5.41354i | 0.224398 | + | 0.224398i | ||||
\(583\) | −6.17402 | + | 6.17402i | −0.255702 | + | 0.255702i | ||||
\(584\) | 8.50501 | − | 8.50501i | 0.351940 | − | 0.351940i | ||||
\(585\) | −2.77675 | + | 2.97723i | −0.114804 | + | 0.123093i | ||||
\(586\) | −5.16020 | − | 5.16020i | −0.213166 | − | 0.213166i | ||||
\(587\) | −14.4564 | −0.596681 | −0.298341 | − | 0.954459i | \(-0.596433\pi\) | ||||
−0.298341 | + | 0.954459i | \(0.596433\pi\) | |||||||
\(588\) | −0.146233 | − | 0.146233i | −0.00603054 | − | 0.00603054i | ||||
\(589\) | 1.58079i | 0.0651354i | ||||||||
\(590\) | −0.313749 | − | 9.00493i | −0.0129168 | − | 0.370727i | ||||
\(591\) | − | 7.81496i | − | 0.321465i | ||||||
\(592\) | 2.27285 | − | 5.64218i | 0.0934137 | − | 0.231892i | ||||
\(593\) | 14.3909 | + | 14.3909i | 0.590963 | + | 0.590963i | 0.937892 | − | 0.346928i | \(-0.112775\pi\) |
−0.346928 | + | 0.937892i | \(0.612775\pi\) | |||||||
\(594\) | 2.12868 | − | 2.12868i | 0.0873410 | − | 0.0873410i | ||||
\(595\) | 1.10042 | + | 31.5832i | 0.0451128 | + | 1.29479i | ||||
\(596\) | − | 2.65031i | − | 0.108561i | ||||||
\(597\) | 8.04823i | 0.329392i | ||||||||
\(598\) | −0.0394365 | −0.00161268 | ||||||||
\(599\) | − | 32.8474i | − | 1.34211i | −0.741407 | − | 0.671055i | \(-0.765841\pi\) | ||
0.741407 | − | 0.671055i | \(-0.234159\pi\) | |||||||
\(600\) | 3.77303 | + | 3.28089i | 0.154033 | + | 0.133942i | ||||
\(601\) | 42.6376 | 1.73922 | 0.869611 | − | 0.493737i | \(-0.164369\pi\) | ||||
0.869611 | + | 0.493737i | \(0.164369\pi\) | |||||||
\(602\) | 14.4989 | − | 14.4989i | 0.590930 | − | 0.590930i | ||||
\(603\) | −3.93891 | + | 3.93891i | −0.160405 | + | 0.160405i | ||||
\(604\) | − | 3.91246i | − | 0.159196i | ||||||
\(605\) | 3.16811 | + | 2.95477i | 0.128802 | + | 0.120129i | ||||
\(606\) | 11.7747 | + | 11.7747i | 0.478315 | + | 0.478315i | ||||
\(607\) | −1.05109 | −0.0426623 | −0.0213312 | − | 0.999772i | \(-0.506790\pi\) | ||||
−0.0213312 | + | 0.999772i | \(0.506790\pi\) | |||||||
\(608\) | −0.509592 | − | 0.509592i | −0.0206667 | − | 0.0206667i | ||||
\(609\) | 12.1935 | + | 12.1935i | 0.494104 | + | 0.494104i | ||||
\(610\) | −0.497400 | − | 14.2759i | −0.0201391 | − | 0.578015i | ||||
\(611\) | 0.320755 | − | 0.320755i | 0.0129763 | − | 0.0129763i | ||||
\(612\) | 5.42248 | 0.219191 | ||||||||
\(613\) | 20.8463 | − | 20.8463i | 0.841976 | − | 0.841976i | −0.147140 | − | 0.989116i | \(-0.547007\pi\) |
0.989116 | + | 0.147140i | \(0.0470067\pi\) | |||||||
\(614\) | −16.3280 | − | 16.3280i | −0.658945 | − | 0.658945i | ||||
\(615\) | −0.494878 | − | 14.2035i | −0.0199554 | − | 0.572742i | ||||
\(616\) | −5.54815 | − | 5.54815i | −0.223541 | − | 0.223541i | ||||
\(617\) | 11.8344 | + | 11.8344i | 0.476435 | + | 0.476435i | 0.903990 | − | 0.427555i | \(-0.140625\pi\) |
−0.427555 | + | 0.903990i | \(0.640625\pi\) | |||||||
\(618\) | −10.7525 | − | 10.7525i | −0.432531 | − | 0.432531i | ||||
\(619\) | −2.66335 | −0.107049 | −0.0535246 | − | 0.998567i | \(-0.517046\pi\) | ||||
−0.0535246 | + | 0.998567i | \(0.517046\pi\) | |||||||
\(620\) | 0.170789 | + | 4.90183i | 0.00685906 | + | 0.196862i | ||||
\(621\) | −0.0153162 | − | 0.0153162i | −0.000614619 | − | 0.000614619i | ||||
\(622\) | 20.2566 | + | 20.2566i | 0.812216 | + | 0.812216i | ||||
\(623\) | 3.83252i | 0.153547i | ||||||||
\(624\) | 1.28741 | − | 1.28741i | 0.0515376 | − | 0.0515376i | ||||
\(625\) | −24.7578 | + | 3.47153i | −0.990312 | + | 0.138861i | ||||
\(626\) | −18.3942 | −0.735182 | ||||||||
\(627\) | − | 2.16952i | − | 0.0866424i | ||||||
\(628\) | −12.9226 | + | 12.9226i | −0.515670 | + | 0.515670i | ||||
\(629\) | 30.5946 | + | 12.3245i | 1.21989 | + | 0.491410i | ||||
\(630\) | 0.202937 | + | 5.82450i | 0.00808519 | + | 0.232054i | ||||
\(631\) | −20.5443 | − | 20.5443i | −0.817854 | − | 0.817854i | 0.167943 | − | 0.985797i | \(-0.446288\pi\) |
−0.985797 | + | 0.167943i | \(0.946288\pi\) | |||||||
\(632\) | −2.16377 | − | 2.16377i | −0.0860703 | − | 0.0860703i | ||||
\(633\) | −1.54391 | + | 1.54391i | −0.0613647 | + | 0.0613647i | ||||
\(634\) | 3.40194 | + | 3.40194i | 0.135108 | + | 0.135108i | ||||
\(635\) | 30.8805 | − | 1.07593i | 1.22545 | − | 0.0426971i | ||||
\(636\) | −2.90039 | −0.115008 | ||||||||
\(637\) | − | 0.376523i | − | 0.0149184i | ||||||
\(638\) | −14.0837 | − | 14.0837i | −0.557578 | − | 0.557578i | ||||
\(639\) | − | 9.00950i | − | 0.356410i | ||||||
\(640\) | −1.63524 | − | 1.52512i | −0.0646384 | − | 0.0602858i | ||||
\(641\) | 38.4309 | 1.51793 | 0.758964 | − | 0.651132i | \(-0.225706\pi\) | ||||
0.758964 | + | 0.651132i | \(0.225706\pi\) | |||||||
\(642\) | 11.1041i | 0.438245i | ||||||||
\(643\) | 33.4086i | 1.31751i | 0.752358 | + | 0.658754i | \(0.228916\pi\) | ||||
−0.752358 | + | 0.658754i | \(0.771084\pi\) | |||||||
\(644\) | −0.0399199 | + | 0.0399199i | −0.00157306 | + | 0.00157306i | ||||
\(645\) | 17.5806 | − | 0.612542i | 0.692236 | − | 0.0241188i | ||||
\(646\) | 2.76326 | − | 2.76326i | 0.108719 | − | 0.108719i | ||||
\(647\) | −48.3301 | −1.90005 | −0.950026 | − | 0.312170i | \(-0.898944\pi\) | ||||
−0.950026 | + | 0.312170i | \(0.898944\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −8.57769 | + | 8.57769i | −0.336704 | + | 0.336704i | ||||
\(650\) | 0.633587 | + | 9.08127i | 0.0248513 | + | 0.356197i | ||||
\(651\) | −4.04258 | + | 4.04258i | −0.158441 | + | 0.158441i | ||||
\(652\) | − | 8.59786i | − | 0.336718i | ||||||
\(653\) | − | 20.8734i | − | 0.816839i | −0.912794 | − | 0.408420i | \(-0.866080\pi\) | ||
0.912794 | − | 0.408420i | \(-0.133920\pi\) | |||||||
\(654\) | 7.29580 | 0.285288 | ||||||||
\(655\) | 0.243633 | + | 6.99253i | 0.00951952 | + | 0.273221i | ||||
\(656\) | 6.35587i | 0.248155i | ||||||||
\(657\) | 8.50501 | + | 8.50501i | 0.331812 | + | 0.331812i | ||||
\(658\) | − | 0.649372i | − | 0.0253152i | ||||||
\(659\) | 26.2240 | 1.02154 | 0.510771 | − | 0.859717i | \(-0.329360\pi\) | ||||
0.510771 | + | 0.859717i | \(0.329360\pi\) | |||||||
\(660\) | −0.234396 | − | 6.72741i | −0.00912384 | − | 0.261864i | ||||
\(661\) | 15.8166 | + | 15.8166i | 0.615196 | + | 0.615196i | 0.944295 | − | 0.329100i | \(-0.106745\pi\) |
−0.329100 | + | 0.944295i | \(0.606745\pi\) | |||||||
\(662\) | −2.61136 | + | 2.61136i | −0.101493 | + | 0.101493i | ||||
\(663\) | 6.98095 | + | 6.98095i | 0.271118 | + | 0.271118i | ||||
\(664\) | −0.925954 | − | 0.925954i | −0.0359340 | − | 0.0359340i | ||||
\(665\) | 3.07154 | + | 2.86471i | 0.119109 | + | 0.111089i | ||||
\(666\) | 5.64218 | + | 2.27285i | 0.218630 | + | 0.0880712i | ||||
\(667\) | −0.101334 | + | 0.101334i | −0.00392368 | + | 0.00392368i | ||||
\(668\) | − | 4.59086i | − | 0.177626i | ||||||
\(669\) | 21.6839 | 0.838347 | ||||||||
\(670\) | 0.433725 | + | 12.4484i | 0.0167563 | + | 0.480923i | ||||
\(671\) | −13.5986 | + | 13.5986i | −0.524968 | + | 0.524968i | ||||
\(672\) | − | 2.60638i | − | 0.100543i | ||||||
\(673\) | 19.5631 | + | 19.5631i | 0.754102 | + | 0.754102i | 0.975242 | − | 0.221140i | \(-0.0709779\pi\) |
−0.221140 | + | 0.975242i | \(0.570978\pi\) | |||||||
\(674\) | 3.23500 | + | 3.23500i | 0.124608 | + | 0.124608i | ||||
\(675\) | −3.28089 | + | 3.77303i | −0.126282 | + | 0.145224i | ||||
\(676\) | −9.68516 | −0.372506 | ||||||||
\(677\) | 4.35406 | + | 4.35406i | 0.167340 | + | 0.167340i | 0.785809 | − | 0.618469i | \(-0.212247\pi\) |
−0.618469 | + | 0.785809i | \(0.712247\pi\) | |||||||
\(678\) | −2.68926 | − | 2.68926i | −0.103281 | − | 0.103281i | ||||
\(679\) | 14.1097 | + | 14.1097i | 0.541481 | + | 0.541481i | ||||
\(680\) | 8.26996 | − | 8.86704i | 0.317138 | − | 0.340036i | ||||
\(681\) | −2.26408 | − | 2.26408i | −0.0867596 | − | 0.0867596i | ||||
\(682\) | 4.66926 | − | 4.66926i | 0.178795 | − | 0.178795i | ||||
\(683\) | −28.7474 | −1.09999 | −0.549995 | − | 0.835168i | \(-0.685370\pi\) | ||||
−0.549995 | + | 0.835168i | \(0.685370\pi\) | |||||||
\(684\) | 0.509592 | − | 0.509592i | 0.0194848 | − | 0.0194848i | ||||
\(685\) | −18.0847 | + | 0.630105i | −0.690981 | + | 0.0240751i | ||||
\(686\) | −13.2820 | − | 13.2820i | −0.507111 | − | 0.507111i | ||||
\(687\) | 15.0222 | + | 15.0222i | 0.573134 | + | 0.573134i | ||||
\(688\) | −7.86706 | −0.299929 | ||||||||
\(689\) | −3.73399 | − | 3.73399i | −0.142254 | − | 0.142254i | ||||
\(690\) | −0.0484048 | + | 0.00168651i | −0.00184274 | + | 6.42045e-5i | ||||
\(691\) | − | 43.9902i | − | 1.67347i | −0.547610 | − | 0.836733i | \(-0.684462\pi\) | ||
0.547610 | − | 0.836733i | \(-0.315538\pi\) | |||||||
\(692\) | 6.49792 | − | 6.49792i | 0.247014 | − | 0.247014i | ||||
\(693\) | 5.54815 | − | 5.54815i | 0.210757 | − | 0.210757i | ||||
\(694\) | −17.9326 | −0.680714 | ||||||||
\(695\) | −6.83773 | − | 6.37730i | −0.259370 | − | 0.241905i | ||||
\(696\) | − | 6.61614i | − | 0.250784i | ||||||
\(697\) | −34.4646 | −1.30544 | ||||||||
\(698\) | 34.1023i | 1.29079i | ||||||||
\(699\) | − | 16.9992i | − | 0.642968i | ||||||
\(700\) | 9.83394 | + | 8.55123i | 0.371688 | + | 0.323206i | ||||
\(701\) | −9.73870 | + | 9.73870i | −0.367826 | + | 0.367826i | −0.866684 | − | 0.498858i | \(-0.833753\pi\) |
0.498858 | + | 0.866684i | \(0.333753\pi\) | |||||||
\(702\) | 1.28741 | + | 1.28741i | 0.0485901 | + | 0.0485901i | ||||
\(703\) | 4.03344 | − | 1.71698i | 0.152124 | − | 0.0647572i | ||||
\(704\) | 3.01042i | 0.113459i | ||||||||
\(705\) | 0.379981 | − | 0.407415i | 0.0143109 | − | 0.0153441i | ||||
\(706\) | 7.23850i | 0.272424i | ||||||||
\(707\) | 30.6893 | + | 30.6893i | 1.15419 | + | 1.15419i | ||||
\(708\) | −4.02957 | −0.151441 | ||||||||
\(709\) | −10.8762 | − | 10.8762i | −0.408466 | − | 0.408466i | 0.472738 | − | 0.881203i | \(-0.343266\pi\) |
−0.881203 | + | 0.472738i | \(0.843266\pi\) | |||||||
\(710\) | −14.7327 | − | 13.7406i | −0.552907 | − | 0.515676i | ||||
\(711\) | 2.16377 | − | 2.16377i | 0.0811479 | − | 0.0811479i | ||||
\(712\) | 1.03976 | − | 1.03976i | 0.0389666 | − | 0.0389666i | ||||
\(713\) | −0.0335961 | − | 0.0335961i | −0.00125818 | − | 0.00125818i | ||||
\(714\) | 14.1330 | 0.528915 | ||||||||
\(715\) | 8.35916 | − | 8.96269i | 0.312615 | − | 0.335185i | ||||
\(716\) | −11.1786 | + | 11.1786i | −0.417764 | + | 0.417764i | ||||
\(717\) | 14.3313 | 0.535210 | ||||||||
\(718\) | 29.3398i | 1.09495i | ||||||||
\(719\) | 28.4189i | 1.05985i | 0.848045 | + | 0.529924i | \(0.177779\pi\) | ||||
−0.848045 | + | 0.529924i | \(0.822221\pi\) | |||||||
\(720\) | 1.52512 | − | 1.63524i | 0.0568380 | − | 0.0609417i | ||||
\(721\) | −28.0252 | − | 28.0252i | −1.04371 | − | 1.04371i | ||||
\(722\) | 18.4806i | 0.687778i | ||||||||
\(723\) | 14.4800i | 0.538517i | ||||||||
\(724\) | −12.7902 | −0.475345 | ||||||||
\(725\) | 24.9629 | + | 21.7068i | 0.927099 | + | 0.806171i | ||||
\(726\) | 1.36995 | − | 1.36995i | 0.0508436 | − | 0.0508436i | ||||
\(727\) | 2.22360 | 0.0824686 | 0.0412343 | − | 0.999150i | \(-0.486871\pi\) | ||||
0.0412343 | + | 0.999150i | \(0.486871\pi\) | |||||||
\(728\) | 3.35547 | − | 3.35547i | 0.124362 | − | 0.124362i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 26.8789 | − | 0.936512i | 0.994833 | − | 0.0346619i | ||||
\(731\) | − | 42.6590i | − | 1.57780i | ||||||
\(732\) | −6.38826 | −0.236117 | ||||||||
\(733\) | 11.8204 | − | 11.8204i | 0.436598 | − | 0.436598i | −0.454268 | − | 0.890865i | \(-0.650099\pi\) |
0.890865 | + | 0.454268i | \(0.150099\pi\) | |||||||
\(734\) | −7.30169 | + | 7.30169i | −0.269510 | + | 0.269510i | ||||
\(735\) | −0.0161021 | − | 0.462148i | −0.000593936 | − | 0.0170466i | ||||
\(736\) | 0.0216604 | 0.000798414 | ||||||||
\(737\) | 11.8578 | − | 11.8578i | 0.436786 | − | 0.436786i | ||||
\(738\) | −6.35587 | −0.233963 | ||||||||
\(739\) | −41.0418 | −1.50975 | −0.754874 | − | 0.655870i | \(-0.772302\pi\) | ||||
−0.754874 | + | 0.655870i | \(0.772302\pi\) | |||||||
\(740\) | 12.3217 | − | 5.75991i | 0.452953 | − | 0.211739i | ||||
\(741\) | 1.31211 | 0.0482014 | ||||||||
\(742\) | −7.55951 | −0.277518 | ||||||||
\(743\) | −21.4316 | + | 21.4316i | −0.786249 | + | 0.786249i | −0.980877 | − | 0.194628i | \(-0.937650\pi\) |
0.194628 | + | 0.980877i | \(0.437650\pi\) | |||||||
\(744\) | 2.19350 | 0.0804175 | ||||||||
\(745\) | 4.04206 | − | 4.33389i | 0.148090 | − | 0.158781i | ||||
\(746\) | 0.813457 | − | 0.813457i | 0.0297828 | − | 0.0297828i | ||||
\(747\) | 0.925954 | − | 0.925954i | 0.0338789 | − | 0.0338789i | ||||
\(748\) | −16.3239 | −0.596862 | ||||||||
\(749\) | 28.9416i | 1.05750i | ||||||||
\(750\) | 1.16604 | + | 11.1194i | 0.0425776 | + | 0.406022i | ||||
\(751\) | 38.7551i | 1.41419i | 0.707117 | + | 0.707097i | \(0.249995\pi\) | ||||
−0.707117 | + | 0.707097i | \(0.750005\pi\) | |||||||
\(752\) | −0.176174 | + | 0.176174i | −0.00642440 | + | 0.00642440i | ||||
\(753\) | −5.44236 | −0.198331 | ||||||||
\(754\) | 8.51767 | − | 8.51767i | 0.310195 | − | 0.310195i | ||||
\(755\) | 5.96698 | − | 6.39779i | 0.217161 | − | 0.232840i | ||||
\(756\) | 2.60638 | 0.0947930 | ||||||||
\(757\) | − | 47.4098i | − | 1.72314i | −0.507640 | − | 0.861569i | \(-0.669482\pi\) | ||
0.507640 | − | 0.861569i | \(-0.330518\pi\) | |||||||
\(758\) | − | 14.5201i | − | 0.527394i | ||||||
\(759\) | 0.0461082 | + | 0.0461082i | 0.00167362 | + | 0.00167362i | ||||
\(760\) | −0.0561127 | − | 1.61050i | −0.00203542 | − | 0.0584188i | ||||
\(761\) | − | 31.8594i | − | 1.15490i | −0.816425 | − | 0.577452i | \(-0.804047\pi\) | ||
0.816425 | − | 0.577452i | \(-0.195953\pi\) | |||||||
\(762\) | − | 13.8185i | − | 0.500593i | ||||||
\(763\) | 19.0156 | 0.688411 | ||||||||
\(764\) | 15.7097 | − | 15.7097i | 0.568359 | − | 0.568359i | ||||
\(765\) | 8.86704 | + | 8.26996i | 0.320589 | + | 0.299001i | ||||
\(766\) | 14.8639 | 0.537053 | ||||||||
\(767\) | −5.18770 | − | 5.18770i | −0.187317 | − | 0.187317i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 14.3460 | − | 14.3460i | 0.517329 | − | 0.517329i | −0.399433 | − | 0.916762i | \(-0.630793\pi\) |
0.916762 | + | 0.399433i | \(0.130793\pi\) | |||||||
\(770\) | −0.610923 | − | 17.5342i | −0.0220161 | − | 0.631887i | ||||
\(771\) | −2.21719 | − | 2.21719i | −0.0798503 | − | 0.0798503i | ||||
\(772\) | 21.0634 | 0.758088 | ||||||||
\(773\) | −14.7324 | − | 14.7324i | −0.529887 | − | 0.529887i | 0.390652 | − | 0.920539i | \(-0.372250\pi\) |
−0.920539 | + | 0.390652i | \(0.872250\pi\) | |||||||
\(774\) | − | 7.86706i | − | 0.282776i | ||||||
\(775\) | −7.19662 | + | 8.27613i | −0.258510 | + | 0.297287i | ||||
\(776\) | − | 7.65590i | − | 0.274831i | ||||||
\(777\) | 14.7056 | + | 5.92391i | 0.527562 | + | 0.212519i | ||||
\(778\) | 25.0493 | + | 25.0493i | 0.898060 | + | 0.898060i | ||||
\(779\) | −3.23890 | + | 3.23890i | −0.116046 | + | 0.116046i | ||||
\(780\) | 4.06867 | − | 0.141760i | 0.145682 | − | 0.00507583i | ||||
\(781\) | 27.1223i | 0.970513i | ||||||||
\(782\) | 0.117453i | 0.00420012i | ||||||||
\(783\) | 6.61614 | 0.236442 | ||||||||
\(784\) | 0.206804i | 0.00738587i | ||||||||
\(785\) | −40.8402 | + | 1.42295i | −1.45765 | + | 0.0507873i | ||||
\(786\) | 3.12905 | 0.111610 | ||||||||
\(787\) | −20.6588 | + | 20.6588i | −0.736408 | + | 0.736408i | −0.971881 | − | 0.235473i | \(-0.924336\pi\) |
0.235473 | + | 0.971881i | \(0.424336\pi\) | |||||||
\(788\) | −5.52601 | + | 5.52601i | −0.196856 | + | 0.196856i | ||||
\(789\) | 29.2781i | 1.04233i | ||||||||
\(790\) | −0.238260 | − | 6.83831i | −0.00847689 | − | 0.243296i | ||||
\(791\) | −7.00924 | − | 7.00924i | −0.249220 | − | 0.249220i | ||||
\(792\) | −3.01042 | −0.106970 | ||||||||
\(793\) | −8.22430 | − | 8.22430i | −0.292053 | − | 0.292053i | ||||
\(794\) | 5.32491 | + | 5.32491i | 0.188974 | + | 0.188974i | ||||
\(795\) | −4.74282 | − | 4.42345i | −0.168211 | − | 0.156884i | ||||
\(796\) | 5.69096 | − | 5.69096i | 0.201711 | − | 0.201711i | ||||
\(797\) | 39.3879 | 1.39519 | 0.697595 | − | 0.716492i | \(-0.254253\pi\) | ||||
0.697595 | + | 0.716492i | \(0.254253\pi\) | |||||||
\(798\) | 1.32819 | − | 1.32819i | 0.0470174 | − | 0.0470174i | ||||
\(799\) | −0.955300 | − | 0.955300i | −0.0337961 | − | 0.0337961i | ||||
\(800\) | −0.347996 | − | 4.98788i | −0.0123035 | − | 0.176348i | ||||
\(801\) | 1.03976 | + | 1.03976i | 0.0367381 | + | 0.0367381i | ||||
\(802\) | 5.09805 | + | 5.09805i | 0.180018 | + | 0.180018i | ||||
\(803\) | −25.6036 | − | 25.6036i | −0.903532 | − | 0.903532i | ||||
\(804\) | 5.57046 | 0.196455 | ||||||||
\(805\) | −0.126161 | + | 0.00439569i | −0.00444659 | + | 0.000154928i | ||||
\(806\) | 2.82393 | + | 2.82393i | 0.0994685 | + | 0.0994685i | ||||
\(807\) | −11.0221 | − | 11.0221i | −0.387998 | − | 0.387998i | ||||
\(808\) | − | 16.6519i | − | 0.585813i | ||||||
\(809\) | −24.3142 | + | 24.3142i | −0.854841 | + | 0.854841i | −0.990725 | − | 0.135884i | \(-0.956613\pi\) |
0.135884 | + | 0.990725i | \(0.456613\pi\) | |||||||
\(810\) | 1.63524 | + | 1.52512i | 0.0574564 | + | 0.0535874i | ||||
\(811\) | −24.8998 | −0.874351 | −0.437176 | − | 0.899376i | \(-0.644021\pi\) | ||||
−0.437176 | + | 0.899376i | \(0.644021\pi\) | |||||||
\(812\) | − | 17.2442i | − | 0.605151i | ||||||
\(813\) | −21.4343 | + | 21.4343i | −0.751734 | + | 0.751734i | ||||
\(814\) | −16.9853 | − | 6.84223i | −0.595334 | − | 0.239820i | ||||
\(815\) | 13.1128 | − | 14.0595i | 0.459321 | − | 0.492484i | ||||
\(816\) | −3.83427 | − | 3.83427i | −0.134226 | − | 0.134226i | ||||
\(817\) | −4.00899 | − | 4.00899i | −0.140257 | − | 0.140257i | ||||
\(818\) | 15.3174 | − | 15.3174i | 0.535560 | − | 0.535560i | ||||
\(819\) | 3.35547 | + | 3.35547i | 0.117250 | + | 0.117250i | ||||
\(820\) | −9.69348 | + | 10.3933i | −0.338511 | + | 0.362951i | ||||
\(821\) | −52.1619 | −1.82046 | −0.910231 | − | 0.414101i | \(-0.864096\pi\) | ||||
−0.910231 | + | 0.414101i | \(0.864096\pi\) | |||||||
\(822\) | 8.09263i | 0.282263i | ||||||||
\(823\) | 0.798711 | + | 0.798711i | 0.0278413 | + | 0.0278413i | 0.720890 | − | 0.693049i | \(-0.243733\pi\) |
−0.693049 | + | 0.720890i | \(0.743733\pi\) | |||||||
\(824\) | 15.2064i | 0.529740i | ||||||||
\(825\) | 9.87684 | − | 11.3584i | 0.343867 | − | 0.395448i | ||||
\(826\) | −10.5026 | −0.365431 | ||||||||
\(827\) | − | 30.7971i | − | 1.07092i | −0.844561 | − | 0.535460i | \(-0.820138\pi\) | ||
0.844561 | − | 0.535460i | \(-0.179862\pi\) | |||||||
\(828\) | 0.0216604i | 0.000752752i | ||||||||
\(829\) | −4.01468 | + | 4.01468i | −0.139435 | + | 0.139435i | −0.773379 | − | 0.633944i | \(-0.781435\pi\) |
0.633944 | + | 0.773379i | \(0.281435\pi\) | |||||||
\(830\) | −0.101960 | − | 2.92635i | −0.00353907 | − | 0.101575i | ||||
\(831\) | −10.4815 | + | 10.4815i | −0.363598 | + | 0.363598i | ||||
\(832\) | −1.82067 | −0.0631204 | ||||||||
\(833\) | −1.12139 | −0.0388540 | ||||||||
\(834\) | −2.95676 | + | 2.95676i | −0.102384 | + | 0.102384i | ||||
\(835\) | 7.00164 | − | 7.50715i | 0.242302 | − | 0.259796i | ||||
\(836\) | −1.53408 | + | 1.53408i | −0.0530574 | + | 0.0530574i | ||||
\(837\) | 2.19350i | 0.0758184i | ||||||||
\(838\) | 15.6256i | 0.539777i | ||||||||
\(839\) | −26.0337 | −0.898784 | −0.449392 | − | 0.893335i | \(-0.648359\pi\) | ||||
−0.449392 | + | 0.893335i | \(0.648359\pi\) | |||||||
\(840\) | 3.97505 | − | 4.26204i | 0.137152 | − | 0.147054i | ||||
\(841\) | − | 14.7733i | − | 0.509425i | ||||||
\(842\) | −15.7260 | − | 15.7260i | −0.541955 | − | 0.541955i | ||||
\(843\) | 32.3781i | 1.11516i | ||||||||
\(844\) | 2.18341 | 0.0751561 | ||||||||
\(845\) | −15.8375 | − | 14.7711i | −0.544828 | − | 0.508140i | ||||
\(846\) | −0.176174 | − | 0.176174i | −0.00605698 | − | 0.00605698i | ||||
\(847\) | 3.57060 | − | 3.57060i | 0.122687 | − | 0.122687i | ||||
\(848\) | 2.05089 | + | 2.05089i | 0.0704277 | + | 0.0704277i | ||||
\(849\) | 16.7378 | + | 16.7378i | 0.574439 | + | 0.574439i | ||||
\(850\) | 27.0467 | − | 1.88700i | 0.927693 | − | 0.0647237i | ||||
\(851\) | −0.0492309 | + | 0.122212i | −0.00168761 | + | 0.00418937i | ||||
\(852\) | −6.37068 | + | 6.37068i | −0.218256 | + | 0.218256i | ||||
\(853\) | − | 24.2328i | − | 0.829714i | −0.909887 | − | 0.414857i | \(-0.863832\pi\) | ||
0.909887 | − | 0.414857i | \(-0.136168\pi\) | |||||||
\(854\) | −16.6502 | −0.569758 | ||||||||
\(855\) | 1.61050 | − | 0.0561127i | 0.0550778 | − | 0.00191901i | ||||
\(856\) | 7.85181 | − | 7.85181i | 0.268369 | − | 0.268369i | ||||
\(857\) | 38.1314i | 1.30254i | 0.758845 | + | 0.651272i | \(0.225764\pi\) | ||||
−0.758845 | + | 0.651272i | \(0.774236\pi\) | |||||||
\(858\) | −3.87563 | − | 3.87563i | −0.132312 | − | 0.132312i | ||||
\(859\) | 17.3872 | + | 17.3872i | 0.593243 | + | 0.593243i | 0.938506 | − | 0.345263i | \(-0.112210\pi\) |
−0.345263 | + | 0.938506i | \(0.612210\pi\) | |||||||
\(860\) | −12.8645 | − | 11.9982i | −0.438676 | − | 0.409136i | ||||
\(861\) | −16.5658 | −0.564560 | ||||||||
\(862\) | −7.16507 | − | 7.16507i | −0.244043 | − | 0.244043i | ||||
\(863\) | −36.1097 | − | 36.1097i | −1.22919 | − | 1.22919i | −0.964270 | − | 0.264920i | \(-0.914655\pi\) |
−0.264920 | − | 0.964270i | \(-0.585345\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 20.5358 | − | 0.715505i | 0.698237 | − | 0.0243279i | ||||
\(866\) | −12.9982 | − | 12.9982i | −0.441696 | − | 0.441696i | ||||
\(867\) | 8.77047 | − | 8.77047i | 0.297861 | − | 0.297861i | ||||
\(868\) | 5.71708 | 0.194050 | ||||||||
\(869\) | −6.51386 | + | 6.51386i | −0.220968 | + | 0.220968i | ||||
\(870\) | 10.0904 | − | 10.8190i | 0.342098 | − | 0.366797i | ||||
\(871\) | 7.17146 | + | 7.17146i | 0.242996 | + | 0.242996i | ||||
\(872\) | −5.15891 | − | 5.15891i | −0.174703 | − | 0.174703i | ||||
\(873\) | 7.65590 | 0.259113 | ||||||||
\(874\) | 0.0110380 | + | 0.0110380i | 0.000373365 | + | 0.000373365i | ||||
\(875\) | 3.03913 | + | 28.9813i | 0.102741 | + | 0.979745i | ||||
\(876\) | − | 12.0279i | − | 0.406385i | ||||||
\(877\) | −35.8135 | + | 35.8135i | −1.20934 | + | 1.20934i | −0.238096 | + | 0.971242i | \(0.576523\pi\) |
−0.971242 | + | 0.238096i | \(0.923477\pi\) | |||||||
\(878\) | −10.5684 | + | 10.5684i | −0.356665 | + | 0.356665i | ||||
\(879\) | −7.29762 | −0.246143 | ||||||||
\(880\) | −4.59126 | + | 4.92274i | −0.154771 | + | 0.165946i | ||||
\(881\) | 6.61073i | 0.222721i | 0.993780 | + | 0.111361i | \(0.0355209\pi\) | ||||
−0.993780 | + | 0.111361i | \(0.964479\pi\) | |||||||
\(882\) | −0.206804 | −0.00696347 | ||||||||
\(883\) | − | 49.4983i | − | 1.66575i | −0.553460 | − | 0.832876i | \(-0.686693\pi\) | ||
0.553460 | − | 0.832876i | \(-0.313307\pi\) | |||||||
\(884\) | − | 9.87255i | − | 0.332050i | ||||||
\(885\) | −6.58930 | − | 6.14559i | −0.221497 | − | 0.206582i | ||||
\(886\) | 17.5773 | − | 17.5773i | 0.590520 | − | 0.590520i | ||||
\(887\) | −17.0910 | − | 17.0910i | −0.573859 | − | 0.573859i | 0.359346 | − | 0.933204i | \(-0.383000\pi\) |
−0.933204 | + | 0.359346i | \(0.883000\pi\) | |||||||
\(888\) | −2.38247 | − | 5.59677i | −0.0799505 | − | 0.187815i | ||||
\(889\) | − | 36.0163i | − | 1.20795i | ||||||
\(890\) | 3.28601 | − | 0.114491i | 0.110147 | − | 0.00383774i | ||||
\(891\) | − | 3.01042i | − | 0.100853i | ||||||
\(892\) | −15.3328 | − | 15.3328i | −0.513381 | − | 0.513381i | ||||
\(893\) | −0.179554 | −0.00600854 | ||||||||
\(894\) | −1.87406 | − | 1.87406i | −0.0626778 | − | 0.0626778i | ||||
\(895\) | −35.3284 | + | 1.23091i | −1.18090 | + | 0.0411447i | ||||
\(896\) | −1.84299 | + | 1.84299i | −0.0615698 | + | 0.0615698i | ||||
\(897\) | −0.0278858 | + | 0.0278858i | −0.000931080 | + | 0.000931080i | ||||
\(898\) | 9.93203 | + | 9.93203i | 0.331436 | + | 0.331436i | ||||
\(899\) | 14.5125 | 0.484018 | ||||||||
\(900\) | 4.98788 | − | 0.347996i | 0.166263 | − | 0.0115999i | ||||
\(901\) | −11.1209 | + | 11.1209i | −0.370491 | + | 0.370491i | ||||
\(902\) | 19.1338 | 0.637086 | ||||||||
\(903\) | − | 20.5045i | − | 0.682347i | ||||||
\(904\) | 3.80319i | 0.126492i | ||||||||
\(905\) | −20.9150 | − | 19.5067i | −0.695239 | − | 0.648423i | ||||
\(906\) | −2.76653 | − | 2.76653i | −0.0919117 | − | 0.0919117i | ||||
\(907\) | − | 6.83317i | − | 0.226892i | −0.993544 | − | 0.113446i | \(-0.963811\pi\) | ||
0.993544 | − | 0.113446i | \(-0.0361888\pi\) | |||||||
\(908\) | 3.20189i | 0.106258i | ||||||||
\(909\) | 16.6519 | 0.552310 | ||||||||
\(910\) | 10.6045 | − | 0.369480i | 0.351535 | − | 0.0122482i | ||||
\(911\) | 35.7866 | − | 35.7866i | 1.18566 | − | 1.18566i | 0.207410 | − | 0.978254i | \(-0.433497\pi\) |
0.978254 | − | 0.207410i | \(-0.0665033\pi\) | |||||||
\(912\) | −0.720673 | −0.0238639 | ||||||||
\(913\) | −2.78751 | + | 2.78751i | −0.0922530 | + | 0.0922530i | ||||
\(914\) | 8.27570i | 0.273736i | ||||||||
\(915\) | −10.4463 | − | 9.74288i | −0.345344 | − | 0.322090i | ||||
\(916\) | − | 21.2446i | − | 0.701943i | ||||||
\(917\) | 8.15548 | 0.269318 | ||||||||
\(918\) | 3.83427 | − | 3.83427i | 0.126550 | − | 0.126550i | ||||
\(919\) | −19.0445 | + | 19.0445i | −0.628220 | + | 0.628220i | −0.947620 | − | 0.319400i | \(-0.896519\pi\) |
0.319400 | + | 0.947620i | \(0.396519\pi\) | |||||||
\(920\) | 0.0354199 | + | 0.0330348i | 0.00116776 | + | 0.00108913i | ||||
\(921\) | −23.0913 | −0.760884 | ||||||||
\(922\) | 3.89734 | − | 3.89734i | 0.128352 | − | 0.128352i | ||||
\(923\) | −16.4033 | −0.539922 | ||||||||
\(924\) | −7.84627 | −0.258123 | ||||||||
\(925\) | 28.9334 | + | 9.37325i | 0.951325 | + | 0.308190i | ||||
\(926\) | −37.2821 | −1.22517 | ||||||||
\(927\) | −15.2064 | −0.499443 | ||||||||
\(928\) | −4.67832 | + | 4.67832i | −0.153573 | + | 0.153573i | ||||
\(929\) | 9.46135 | 0.310417 | 0.155208 | − | 0.987882i | \(-0.450395\pi\) | ||||
0.155208 | + | 0.987882i | \(0.450395\pi\) | |||||||
\(930\) | 3.58689 | + | 3.34535i | 0.117619 | + | 0.109698i | ||||
\(931\) | −0.105386 | + | 0.105386i | −0.00345389 | + | 0.00345389i | ||||
\(932\) | −12.0202 | + | 12.0202i | −0.393736 | + | 0.393736i | ||||
\(933\) | 28.6472 | 0.937866 | ||||||||
\(934\) | 11.9336i | 0.390478i | ||||||||
\(935\) | −26.6935 | − | 24.8960i | −0.872970 | − | 0.814186i | ||||
\(936\) | − | 1.82067i | − | 0.0595105i | ||||||
\(937\) | 38.9228 | − | 38.9228i | 1.27155 | − | 1.27155i | 0.326279 | − | 0.945274i | \(-0.394205\pi\) |
0.945274 | − | 0.326279i | \(-0.105795\pi\) | |||||||
\(938\) | 14.5187 | 0.474053 | ||||||||
\(939\) | −13.0067 | + | 13.0067i | −0.424457 | + | 0.424457i | ||||
\(940\) | −0.556773 | + | 0.0193990i | −0.0181599 | + | 0.000632726i | ||||
\(941\) | 36.7551 | 1.19818 | 0.599090 | − | 0.800682i | \(-0.295529\pi\) | ||||
0.599090 | + | 0.800682i | \(0.295529\pi\) | |||||||
\(942\) | 18.2754i | 0.595444i | ||||||||
\(943\) | − | 0.137671i | − | 0.00448318i | ||||||
\(944\) | 2.84934 | + | 2.84934i | 0.0927380 | + | 0.0927380i | ||||
\(945\) | 4.26204 | + | 3.97505i | 0.138644 | + | 0.129308i | ||||
\(946\) | 23.6831i | 0.770004i | ||||||||
\(947\) | − | 18.0935i | − | 0.587961i | −0.955811 | − | 0.293980i | \(-0.905020\pi\) | ||
0.955811 | − | 0.293980i | \(-0.0949800\pi\) | |||||||
\(948\) | −3.06004 | −0.0993855 | ||||||||
\(949\) | 15.4848 | − | 15.4848i | 0.502659 | − | 0.502659i | ||||
\(950\) | 2.36445 | − | 2.71912i | 0.0767128 | − | 0.0882199i | ||||
\(951\) | 4.81106 | 0.156009 | ||||||||
\(952\) | −9.99356 | − | 9.99356i | −0.323893 | − | 0.323893i | ||||
\(953\) | 16.1464 | − | 16.1464i | 0.523032 | − | 0.523032i | −0.395454 | − | 0.918486i | \(-0.629413\pi\) |
0.918486 | + | 0.395454i | \(0.129413\pi\) | |||||||
\(954\) | −2.05089 | + | 2.05089i | −0.0663999 | + | 0.0663999i | ||||
\(955\) | 49.6485 | − | 1.72985i | 1.60659 | − | 0.0559765i | ||||
\(956\) | −10.1337 | − | 10.1337i | −0.327748 | − | 0.327748i | ||||
\(957\) | −19.9173 | −0.643836 | ||||||||
\(958\) | −0.903277 | − | 0.903277i | −0.0291836 | − | 0.0291836i | ||||
\(959\) | 21.0924i | 0.681110i | ||||||||
\(960\) | −2.23471 | + | 0.0778616i | −0.0721250 | + | 0.00251297i | ||||
\(961\) | − | 26.1886i | − | 0.844793i | ||||||
\(962\) | 4.13811 | − | 10.2725i | 0.133418 | − | 0.331200i | ||||
\(963\) | 7.85181 | + | 7.85181i | 0.253021 | + | 0.253021i | ||||
\(964\) | 10.2389 | − | 10.2389i | 0.329773 | − | 0.329773i | ||||
\(965\) | 34.4436 | + | 32.1243i | 1.10878 | + | 1.03412i | ||||
\(966\) | 0.0564552i | 0.00181642i | ||||||||
\(967\) | 15.5615i | 0.500424i | 0.968191 | + | 0.250212i | \(0.0805003\pi\) | ||||
−0.968191 | + | 0.250212i | \(0.919500\pi\) | |||||||
\(968\) | −1.93740 | −0.0622704 | ||||||||
\(969\) | − | 3.90783i | − | 0.125538i | ||||||
\(970\) | 11.6762 | − | 12.5192i | 0.374900 | − | 0.401968i | ||||
\(971\) | −20.1860 | −0.647799 | −0.323900 | − | 0.946091i | \(-0.604994\pi\) | ||||
−0.323900 | + | 0.946091i | \(0.604994\pi\) | |||||||
\(972\) | 0.707107 | − | 0.707107i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −7.70644 | + | 7.70644i | −0.247057 | + | 0.247057i | ||||
\(974\) | 1.67383i | 0.0536328i | ||||||||
\(975\) | 6.86944 | + | 5.97342i | 0.219998 | + | 0.191302i | ||||
\(976\) | 4.51718 | + | 4.51718i | 0.144591 | + | 0.144591i | ||||
\(977\) | 39.5332 | 1.26478 | 0.632389 | − | 0.774651i | \(-0.282074\pi\) | ||||
0.632389 | + | 0.774651i | \(0.282074\pi\) | |||||||
\(978\) | −6.07961 | − | 6.07961i | −0.194404 | − | 0.194404i | ||||
\(979\) | −3.13011 | − | 3.13011i | −0.100039 | − | 0.100039i | ||||
\(980\) | −0.315402 | + | 0.338174i | −0.0100752 | + | 0.0108026i | ||||
\(981\) | 5.15891 | − | 5.15891i | 0.164711 | − | 0.164711i | ||||
\(982\) | −9.36601 | −0.298881 | ||||||||
\(983\) | 14.9967 | − | 14.9967i | 0.478321 | − | 0.478321i | −0.426274 | − | 0.904594i | \(-0.640174\pi\) |
0.904594 | + | 0.426274i | \(0.140174\pi\) | |||||||
\(984\) | 4.49428 | + | 4.49428i | 0.143272 | + | 0.143272i | ||||
\(985\) | −17.4642 | + | 0.608485i | −0.556455 | + | 0.0193880i | ||||
\(986\) | −25.3681 | − | 25.3681i | −0.807885 | − | 0.807885i | ||||
\(987\) | −0.459175 | − | 0.459175i | −0.0146157 | − | 0.0146157i | ||||
\(988\) | −0.927800 | − | 0.927800i | −0.0295172 | − | 0.0295172i | ||||
\(989\) | 0.170404 | 0.00541853 | ||||||||
\(990\) | −4.92274 | − | 4.59126i | −0.156455 | − | 0.145920i | ||||
\(991\) | 14.9222 | + | 14.9222i | 0.474018 | + | 0.474018i | 0.903212 | − | 0.429194i | \(-0.141202\pi\) |
−0.429194 | + | 0.903212i | \(0.641202\pi\) | |||||||
\(992\) | −1.55104 | − | 1.55104i | −0.0492455 | − | 0.0492455i | ||||
\(993\) | 3.69302i | 0.117194i | ||||||||
\(994\) | −16.6044 | + | 16.6044i | −0.526659 | + | 0.526659i | ||||
\(995\) | 17.9855 | − | 0.626648i | 0.570178 | − | 0.0198661i | ||||
\(996\) | −1.30950 | −0.0414930 | ||||||||
\(997\) | − | 51.9341i | − | 1.64477i | −0.568932 | − | 0.822385i | \(-0.692643\pi\) | ||
0.568932 | − | 0.822385i | \(-0.307357\pi\) | |||||||
\(998\) | 11.8837 | − | 11.8837i | 0.376171 | − | 0.376171i | ||||
\(999\) | 5.59677 | − | 2.38247i | 0.177074 | − | 0.0753781i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1110.2.o.a.253.5 | yes | 36 | |
5.2 | odd | 4 | 1110.2.l.a.697.14 | yes | 36 | ||
37.6 | odd | 4 | 1110.2.l.a.43.14 | ✓ | 36 | ||
185.117 | even | 4 | inner | 1110.2.o.a.487.5 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.a.43.14 | ✓ | 36 | 37.6 | odd | 4 | ||
1110.2.l.a.697.14 | yes | 36 | 5.2 | odd | 4 | ||
1110.2.o.a.253.5 | yes | 36 | 1.1 | even | 1 | trivial | |
1110.2.o.a.487.5 | yes | 36 | 185.117 | even | 4 | inner |