Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(881,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.b (of order \(2\), degree \(1\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16x^{13} + 2x^{12} + 96x^{10} - 80x^{9} + 2x^{8} - 240x^{7} + 864x^{6} + 162x^{4} - 3888x^{3} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.11 | ||
Root | \(-1.11192 + 1.32802i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.881 |
Dual form | 1470.2.b.c.881.3 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −1.53549 | + | 0.801418i | −0.886516 | + | 0.462699i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.801418 | − | 1.53549i | −0.327177 | − | 0.626861i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.71546 | − | 2.46114i | 0.571820 | − | 0.820379i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | 5.48447i | 1.65363i | 0.562475 | + | 0.826815i | \(0.309849\pi\) | ||||
−0.562475 | + | 0.826815i | \(0.690151\pi\) | |||||||
\(12\) | 1.53549 | − | 0.801418i | 0.443258 | − | 0.231349i | ||||
\(13\) | − | 4.37587i | − | 1.21365i | −0.794837 | − | 0.606824i | \(-0.792443\pi\) | ||
0.794837 | − | 0.606824i | \(-0.207557\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.53549 | − | 0.801418i | 0.396462 | − | 0.206925i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.99274 | 1.69599 | 0.847994 | − | 0.530005i | \(-0.177810\pi\) | ||||
0.847994 | + | 0.530005i | \(0.177810\pi\) | |||||||
\(18\) | 2.46114 | + | 1.71546i | 0.580096 | + | 0.404338i | ||||
\(19\) | − | 4.64816i | − | 1.06636i | −0.846001 | − | 0.533181i | \(-0.820996\pi\) | ||
0.846001 | − | 0.533181i | \(-0.179004\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.48447 | −1.16929 | ||||||||
\(23\) | 7.99511i | 1.66710i | 0.552447 | + | 0.833548i | \(0.313694\pi\) | ||||
−0.552447 | + | 0.833548i | \(0.686306\pi\) | |||||||
\(24\) | 0.801418 | + | 1.53549i | 0.163589 | + | 0.313431i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.37587 | 0.858178 | ||||||||
\(27\) | −0.661673 | + | 5.15385i | −0.127339 | + | 0.991859i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.40414i | − | 0.632134i | −0.948737 | − | 0.316067i | \(-0.897638\pi\) | ||
0.948737 | − | 0.316067i | \(-0.102362\pi\) | |||||||
\(30\) | 0.801418 | + | 1.53549i | 0.146318 | + | 0.280341i | ||||
\(31\) | 3.85766i | 0.692856i | 0.938077 | + | 0.346428i | \(0.112605\pi\) | ||||
−0.938077 | + | 0.346428i | \(0.887395\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −4.39535 | − | 8.42134i | −0.765132 | − | 1.46597i | ||||
\(34\) | 6.99274i | 1.19925i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.71546 | + | 2.46114i | −0.285910 | + | 0.410190i | ||||
\(37\) | 9.25252 | 1.52111 | 0.760553 | − | 0.649276i | \(-0.224928\pi\) | ||||
0.760553 | + | 0.649276i | \(0.224928\pi\) | |||||||
\(38\) | 4.64816 | 0.754032 | ||||||||
\(39\) | 3.50690 | + | 6.71910i | 0.561553 | + | 1.07592i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −4.36516 | −0.681724 | −0.340862 | − | 0.940113i | \(-0.610719\pi\) | ||||
−0.340862 | + | 0.940113i | \(0.610719\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.48092 | 0.225838 | 0.112919 | − | 0.993604i | \(-0.463980\pi\) | ||||
0.112919 | + | 0.993604i | \(0.463980\pi\) | |||||||
\(44\) | − | 5.48447i | − | 0.826815i | ||||||
\(45\) | −1.71546 | + | 2.46114i | −0.255726 | + | 0.366885i | ||||
\(46\) | −7.99511 | −1.17882 | ||||||||
\(47\) | −7.51483 | −1.09615 | −0.548075 | − | 0.836429i | \(-0.684639\pi\) | ||||
−0.548075 | + | 0.836429i | \(0.684639\pi\) | |||||||
\(48\) | −1.53549 | + | 0.801418i | −0.221629 | + | 0.115675i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −10.7373 | + | 5.60410i | −1.50352 | + | 0.784732i | ||||
\(52\) | 4.37587i | 0.606824i | ||||||||
\(53\) | 4.68750i | 0.643877i | 0.946761 | + | 0.321939i | \(0.104334\pi\) | ||||
−0.946761 | + | 0.321939i | \(0.895666\pi\) | |||||||
\(54\) | −5.15385 | − | 0.661673i | −0.701350 | − | 0.0900422i | ||||
\(55\) | − | 5.48447i | − | 0.739525i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.72512 | + | 7.13721i | 0.493404 | + | 0.945346i | ||||
\(58\) | 3.40414 | 0.446986 | ||||||||
\(59\) | −6.00852 | −0.782243 | −0.391122 | − | 0.920339i | \(-0.627913\pi\) | ||||
−0.391122 | + | 0.920339i | \(0.627913\pi\) | |||||||
\(60\) | −1.53549 | + | 0.801418i | −0.198231 | + | 0.103463i | ||||
\(61\) | 6.75039i | 0.864298i | 0.901802 | + | 0.432149i | \(0.142245\pi\) | ||||
−0.901802 | + | 0.432149i | \(0.857755\pi\) | |||||||
\(62\) | −3.85766 | −0.489923 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 4.37587i | 0.542759i | ||||||||
\(66\) | 8.42134 | − | 4.39535i | 1.03660 | − | 0.541030i | ||||
\(67\) | −5.98178 | −0.730791 | −0.365396 | − | 0.930852i | \(-0.619066\pi\) | ||||
−0.365396 | + | 0.930852i | \(0.619066\pi\) | |||||||
\(68\) | −6.99274 | −0.847994 | ||||||||
\(69\) | −6.40743 | − | 12.2764i | −0.771363 | − | 1.47791i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.42464i | 0.525108i | 0.964917 | + | 0.262554i | \(0.0845647\pi\) | ||||
−0.964917 | + | 0.262554i | \(0.915435\pi\) | |||||||
\(72\) | −2.46114 | − | 1.71546i | −0.290048 | − | 0.202169i | ||||
\(73\) | 10.7067i | 1.25313i | 0.779370 | + | 0.626564i | \(0.215539\pi\) | ||||
−0.779370 | + | 0.626564i | \(0.784461\pi\) | |||||||
\(74\) | 9.25252i | 1.07558i | ||||||||
\(75\) | −1.53549 | + | 0.801418i | −0.177303 | + | 0.0925397i | ||||
\(76\) | 4.64816i | 0.533181i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.71910 | + | 3.50690i | −0.760788 | + | 0.397078i | ||||
\(79\) | 4.87263 | 0.548214 | 0.274107 | − | 0.961699i | \(-0.411618\pi\) | ||||
0.274107 | + | 0.961699i | \(0.411618\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −3.11440 | − | 8.44396i | −0.346044 | − | 0.938218i | ||||
\(82\) | − | 4.36516i | − | 0.482052i | ||||||
\(83\) | 9.22718 | 1.01281 | 0.506407 | − | 0.862294i | \(-0.330973\pi\) | ||||
0.506407 | + | 0.862294i | \(0.330973\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.99274 | −0.758469 | ||||||||
\(86\) | 1.48092i | 0.159692i | ||||||||
\(87\) | 2.72814 | + | 5.22703i | 0.292487 | + | 0.560396i | ||||
\(88\) | 5.48447 | 0.584646 | ||||||||
\(89\) | −0.525443 | −0.0556969 | −0.0278484 | − | 0.999612i | \(-0.508866\pi\) | ||||
−0.0278484 | + | 0.999612i | \(0.508866\pi\) | |||||||
\(90\) | −2.46114 | − | 1.71546i | −0.259427 | − | 0.180825i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 7.99511i | − | 0.833548i | ||||||
\(93\) | −3.09160 | − | 5.92340i | −0.320583 | − | 0.614228i | ||||
\(94\) | − | 7.51483i | − | 0.775096i | ||||||
\(95\) | 4.64816i | 0.476892i | ||||||||
\(96\) | −0.801418 | − | 1.53549i | −0.0817943 | − | 0.156715i | ||||
\(97\) | 2.60272i | 0.264267i | 0.991232 | + | 0.132133i | \(0.0421827\pi\) | ||||
−0.991232 | + | 0.132133i | \(0.957817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.4980 | + | 9.40838i | 1.35660 | + | 0.945578i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 1.59753 | 0.158960 | 0.0794799 | − | 0.996836i | \(-0.474674\pi\) | ||||
0.0794799 | + | 0.996836i | \(0.474674\pi\) | |||||||
\(102\) | −5.60410 | − | 10.7373i | −0.554889 | − | 1.06315i | ||||
\(103\) | 9.40273i | 0.926479i | 0.886233 | + | 0.463239i | \(0.153313\pi\) | ||||
−0.886233 | + | 0.463239i | \(0.846687\pi\) | |||||||
\(104\) | −4.37587 | −0.429089 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.68750 | −0.455290 | ||||||||
\(107\) | − | 5.31279i | − | 0.513607i | −0.966464 | − | 0.256804i | \(-0.917331\pi\) | ||
0.966464 | − | 0.256804i | \(-0.0826693\pi\) | |||||||
\(108\) | 0.661673 | − | 5.15385i | 0.0636695 | − | 0.495930i | ||||
\(109\) | −14.5402 | −1.39269 | −0.696347 | − | 0.717705i | \(-0.745192\pi\) | ||||
−0.696347 | + | 0.717705i | \(0.745192\pi\) | |||||||
\(110\) | 5.48447 | 0.522923 | ||||||||
\(111\) | −14.2072 | + | 7.41513i | −1.34848 | + | 0.703813i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.2482i | 1.34036i | 0.742198 | + | 0.670180i | \(0.233783\pi\) | ||||
−0.742198 | + | 0.670180i | \(0.766217\pi\) | |||||||
\(114\) | −7.13721 | + | 3.72512i | −0.668461 | + | 0.348889i | ||||
\(115\) | − | 7.99511i | − | 0.745548i | ||||||
\(116\) | 3.40414i | 0.316067i | ||||||||
\(117\) | −10.7696 | − | 7.50662i | −0.995651 | − | 0.693988i | ||||
\(118\) | − | 6.00852i | − | 0.553129i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.801418 | − | 1.53549i | −0.0731591 | − | 0.140170i | ||||
\(121\) | −19.0794 | −1.73449 | ||||||||
\(122\) | −6.75039 | −0.611151 | ||||||||
\(123\) | 6.70267 | − | 3.49832i | 0.604359 | − | 0.315433i | ||||
\(124\) | − | 3.85766i | − | 0.346428i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.88266 | 0.433266 | 0.216633 | − | 0.976253i | \(-0.430492\pi\) | ||||
0.216633 | + | 0.976253i | \(0.430492\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −2.27394 | + | 1.18684i | −0.200209 | + | 0.104495i | ||||
\(130\) | −4.37587 | −0.383789 | ||||||||
\(131\) | −14.3521 | −1.25395 | −0.626974 | − | 0.779040i | \(-0.715707\pi\) | ||||
−0.626974 | + | 0.779040i | \(0.715707\pi\) | |||||||
\(132\) | 4.39535 | + | 8.42134i | 0.382566 | + | 0.732984i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 5.98178i | − | 0.516747i | ||||||
\(135\) | 0.661673 | − | 5.15385i | 0.0569477 | − | 0.443573i | ||||
\(136\) | − | 6.99274i | − | 0.599623i | ||||||
\(137\) | 5.65795i | 0.483392i | 0.970352 | + | 0.241696i | \(0.0777036\pi\) | ||||
−0.970352 | + | 0.241696i | \(0.922296\pi\) | |||||||
\(138\) | 12.2764 | − | 6.40743i | 1.04504 | − | 0.545436i | ||||
\(139\) | 8.20450i | 0.695897i | 0.937514 | + | 0.347949i | \(0.113122\pi\) | ||||
−0.937514 | + | 0.347949i | \(0.886878\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.5389 | − | 6.02252i | 0.971755 | − | 0.507187i | ||||
\(142\) | −4.42464 | −0.371307 | ||||||||
\(143\) | 23.9993 | 2.00692 | ||||||||
\(144\) | 1.71546 | − | 2.46114i | 0.142955 | − | 0.205095i | ||||
\(145\) | 3.40414i | 0.282699i | ||||||||
\(146\) | −10.7067 | −0.886095 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.25252 | −0.760553 | ||||||||
\(149\) | − | 10.5894i | − | 0.867516i | −0.901029 | − | 0.433758i | \(-0.857187\pi\) | ||
0.901029 | − | 0.433758i | \(-0.142813\pi\) | |||||||
\(150\) | −0.801418 | − | 1.53549i | −0.0654355 | − | 0.125372i | ||||
\(151\) | −16.4546 | −1.33906 | −0.669528 | − | 0.742787i | \(-0.733504\pi\) | ||||
−0.669528 | + | 0.742787i | \(0.733504\pi\) | |||||||
\(152\) | −4.64816 | −0.377016 | ||||||||
\(153\) | 11.9958 | − | 17.2101i | 0.969800 | − | 1.39135i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.85766i | − | 0.309855i | ||||||
\(156\) | −3.50690 | − | 6.71910i | −0.280776 | − | 0.537959i | ||||
\(157\) | 8.65512i | 0.690754i | 0.938464 | + | 0.345377i | \(0.112249\pi\) | ||||
−0.938464 | + | 0.345377i | \(0.887751\pi\) | |||||||
\(158\) | 4.87263i | 0.387646i | ||||||||
\(159\) | −3.75664 | − | 7.19761i | −0.297921 | − | 0.570807i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.44396 | − | 3.11440i | 0.663421 | − | 0.244690i | ||||
\(163\) | 19.1573 | 1.50051 | 0.750256 | − | 0.661148i | \(-0.229930\pi\) | ||||
0.750256 | + | 0.661148i | \(0.229930\pi\) | |||||||
\(164\) | 4.36516 | 0.340862 | ||||||||
\(165\) | 4.39535 | + | 8.42134i | 0.342177 | + | 0.655601i | ||||
\(166\) | 9.22718i | 0.716168i | ||||||||
\(167\) | 3.99462 | 0.309113 | 0.154556 | − | 0.987984i | \(-0.450605\pi\) | ||||
0.154556 | + | 0.987984i | \(0.450605\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.14821 | −0.472939 | ||||||||
\(170\) | − | 6.99274i | − | 0.536319i | ||||||
\(171\) | −11.4398 | − | 7.97374i | −0.874821 | − | 0.609767i | ||||
\(172\) | −1.48092 | −0.112919 | ||||||||
\(173\) | 18.7253 | 1.42366 | 0.711830 | − | 0.702352i | \(-0.247867\pi\) | ||||
0.711830 | + | 0.702352i | \(0.247867\pi\) | |||||||
\(174\) | −5.22703 | + | 2.72814i | −0.396260 | + | 0.206820i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.48447i | 0.413407i | ||||||||
\(177\) | 9.22603 | − | 4.81534i | 0.693471 | − | 0.361943i | ||||
\(178\) | − | 0.525443i | − | 0.0393836i | ||||||
\(179\) | − | 10.9143i | − | 0.815776i | −0.913032 | − | 0.407888i | \(-0.866265\pi\) | ||
0.913032 | − | 0.407888i | \(-0.133735\pi\) | |||||||
\(180\) | 1.71546 | − | 2.46114i | 0.127863 | − | 0.183442i | ||||
\(181\) | − | 11.1025i | − | 0.825244i | −0.910902 | − | 0.412622i | \(-0.864613\pi\) | ||
0.910902 | − | 0.412622i | \(-0.135387\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.40988 | − | 10.3651i | −0.399910 | − | 0.766214i | ||||
\(184\) | 7.99511 | 0.589408 | ||||||||
\(185\) | −9.25252 | −0.680259 | ||||||||
\(186\) | 5.92340 | − | 3.09160i | 0.434324 | − | 0.226687i | ||||
\(187\) | 38.3515i | 2.80454i | ||||||||
\(188\) | 7.51483 | 0.548075 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.64816 | −0.337213 | ||||||||
\(191\) | 18.3911i | 1.33073i | 0.746517 | + | 0.665366i | \(0.231725\pi\) | ||||
−0.746517 | + | 0.665366i | \(0.768275\pi\) | |||||||
\(192\) | 1.53549 | − | 0.801418i | 0.110814 | − | 0.0578373i | ||||
\(193\) | 23.3665 | 1.68196 | 0.840978 | − | 0.541070i | \(-0.181980\pi\) | ||||
0.840978 | + | 0.541070i | \(0.181980\pi\) | |||||||
\(194\) | −2.60272 | −0.186865 | ||||||||
\(195\) | −3.50690 | − | 6.71910i | −0.251134 | − | 0.481165i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.30178i | 0.448983i | 0.974476 | + | 0.224492i | \(0.0720722\pi\) | ||||
−0.974476 | + | 0.224492i | \(0.927928\pi\) | |||||||
\(198\) | −9.40838 | + | 13.4980i | −0.668625 | + | 0.959263i | ||||
\(199\) | 11.0277i | 0.781734i | 0.920447 | + | 0.390867i | \(0.127825\pi\) | ||||
−0.920447 | + | 0.390867i | \(0.872175\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 9.18497 | − | 4.79391i | 0.647858 | − | 0.338136i | ||||
\(202\) | 1.59753i | 0.112402i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 10.7373 | − | 5.60410i | 0.751760 | − | 0.392366i | ||||
\(205\) | 4.36516 | 0.304876 | ||||||||
\(206\) | −9.40273 | −0.655119 | ||||||||
\(207\) | 19.6771 | + | 13.7153i | 1.36765 | + | 0.953279i | ||||
\(208\) | − | 4.37587i | − | 0.303412i | ||||||
\(209\) | 25.4927 | 1.76337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4672 | 1.13365 | 0.566823 | − | 0.823840i | \(-0.308172\pi\) | ||||
0.566823 | + | 0.823840i | \(0.308172\pi\) | |||||||
\(212\) | − | 4.68750i | − | 0.321939i | ||||||
\(213\) | −3.54598 | − | 6.79398i | −0.242967 | − | 0.465516i | ||||
\(214\) | 5.31279 | 0.363175 | ||||||||
\(215\) | −1.48092 | −0.100998 | ||||||||
\(216\) | 5.15385 | + | 0.661673i | 0.350675 | + | 0.0450211i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 14.5402i | − | 0.984783i | ||||||
\(219\) | −8.58056 | − | 16.4401i | −0.579821 | − | 1.11092i | ||||
\(220\) | 5.48447i | 0.369763i | ||||||||
\(221\) | − | 30.5993i | − | 2.05833i | ||||||
\(222\) | −7.41513 | − | 14.2072i | −0.497671 | − | 0.953522i | ||||
\(223\) | − | 13.5203i | − | 0.905387i | −0.891666 | − | 0.452693i | \(-0.850463\pi\) | ||
0.891666 | − | 0.452693i | \(-0.149537\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.71546 | − | 2.46114i | 0.114364 | − | 0.164076i | ||||
\(226\) | −14.2482 | −0.947778 | ||||||||
\(227\) | 5.57785 | 0.370215 | 0.185108 | − | 0.982718i | \(-0.440737\pi\) | ||||
0.185108 | + | 0.982718i | \(0.440737\pi\) | |||||||
\(228\) | −3.72512 | − | 7.13721i | −0.246702 | − | 0.472673i | ||||
\(229\) | 11.6640i | 0.770776i | 0.922755 | + | 0.385388i | \(0.125932\pi\) | ||||
−0.922755 | + | 0.385388i | \(0.874068\pi\) | |||||||
\(230\) | 7.99511 | 0.527182 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.40414 | −0.223493 | ||||||||
\(233\) | 22.7275i | 1.48893i | 0.667663 | + | 0.744464i | \(0.267295\pi\) | ||||
−0.667663 | + | 0.744464i | \(0.732705\pi\) | |||||||
\(234\) | 7.50662 | − | 10.7696i | 0.490723 | − | 0.704031i | ||||
\(235\) | 7.51483 | 0.490213 | ||||||||
\(236\) | 6.00852 | 0.391122 | ||||||||
\(237\) | −7.48188 | + | 3.90501i | −0.486000 | + | 0.253658i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5.34353i | − | 0.345644i | −0.984953 | − | 0.172822i | \(-0.944711\pi\) | ||
0.984953 | − | 0.172822i | \(-0.0552886\pi\) | |||||||
\(240\) | 1.53549 | − | 0.801418i | 0.0991155 | − | 0.0517313i | ||||
\(241\) | 14.8146i | 0.954292i | 0.878824 | + | 0.477146i | \(0.158329\pi\) | ||||
−0.878824 | + | 0.477146i | \(0.841671\pi\) | |||||||
\(242\) | − | 19.0794i | − | 1.22647i | ||||||
\(243\) | 11.5493 | + | 10.4697i | 0.740886 | + | 0.671631i | ||||
\(244\) | − | 6.75039i | − | 0.432149i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.49832 | + | 6.70267i | 0.223045 | + | 0.427346i | ||||
\(247\) | −20.3397 | −1.29419 | ||||||||
\(248\) | 3.85766 | 0.244962 | ||||||||
\(249\) | −14.1682 | + | 7.39483i | −0.897876 | + | 0.468628i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | 11.9052 | 0.751446 | 0.375723 | − | 0.926732i | \(-0.377394\pi\) | ||||
0.375723 | + | 0.926732i | \(0.377394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −43.8489 | −2.75676 | ||||||||
\(254\) | 4.88266i | 0.306366i | ||||||||
\(255\) | 10.7373 | − | 5.60410i | 0.672395 | − | 0.350943i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.1928 | 1.44673 | 0.723364 | − | 0.690467i | \(-0.242595\pi\) | ||||
0.723364 | + | 0.690467i | \(0.242595\pi\) | |||||||
\(258\) | −1.18684 | − | 2.27394i | −0.0738892 | − | 0.141569i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4.37587i | − | 0.271380i | ||||||
\(261\) | −8.37807 | − | 5.83967i | −0.518589 | − | 0.361467i | ||||
\(262\) | − | 14.3521i | − | 0.886675i | ||||||
\(263\) | 9.86287i | 0.608171i | 0.952645 | + | 0.304085i | \(0.0983508\pi\) | ||||
−0.952645 | + | 0.304085i | \(0.901649\pi\) | |||||||
\(264\) | −8.42134 | + | 4.39535i | −0.518298 | + | 0.270515i | ||||
\(265\) | − | 4.68750i | − | 0.287951i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.806813 | − | 0.421099i | 0.0493762 | − | 0.0257709i | ||||
\(268\) | 5.98178 | 0.365396 | ||||||||
\(269\) | −20.3827 | −1.24275 | −0.621376 | − | 0.783512i | \(-0.713426\pi\) | ||||
−0.621376 | + | 0.783512i | \(0.713426\pi\) | |||||||
\(270\) | 5.15385 | + | 0.661673i | 0.313653 | + | 0.0402681i | ||||
\(271\) | 20.2646i | 1.23099i | 0.788142 | + | 0.615493i | \(0.211043\pi\) | ||||
−0.788142 | + | 0.615493i | \(0.788957\pi\) | |||||||
\(272\) | 6.99274 | 0.423997 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.65795 | −0.341810 | ||||||||
\(275\) | 5.48447i | 0.330726i | ||||||||
\(276\) | 6.40743 | + | 12.2764i | 0.385682 | + | 0.738954i | ||||
\(277\) | −19.8717 | −1.19398 | −0.596988 | − | 0.802250i | \(-0.703636\pi\) | ||||
−0.596988 | + | 0.802250i | \(0.703636\pi\) | |||||||
\(278\) | −8.20450 | −0.492073 | ||||||||
\(279\) | 9.49423 | + | 6.61766i | 0.568405 | + | 0.396189i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.8001i | 1.24083i | 0.784273 | + | 0.620416i | \(0.213036\pi\) | ||||
−0.784273 | + | 0.620416i | \(0.786964\pi\) | |||||||
\(282\) | 6.02252 | + | 11.5389i | 0.358636 | + | 0.687134i | ||||
\(283\) | − | 8.58090i | − | 0.510082i | −0.966930 | − | 0.255041i | \(-0.917911\pi\) | ||
0.966930 | − | 0.255041i | \(-0.0820889\pi\) | |||||||
\(284\) | − | 4.42464i | − | 0.262554i | ||||||
\(285\) | −3.72512 | − | 7.13721i | −0.220657 | − | 0.422772i | ||||
\(286\) | 23.9993i | 1.41911i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.46114 | + | 1.71546i | 0.145024 | + | 0.101084i | ||||
\(289\) | 31.8984 | 1.87638 | ||||||||
\(290\) | −3.40414 | −0.199898 | ||||||||
\(291\) | −2.08587 | − | 3.99646i | −0.122276 | − | 0.234276i | ||||
\(292\) | − | 10.7067i | − | 0.626564i | ||||||
\(293\) | −2.72492 | −0.159192 | −0.0795958 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795958 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00852 | 0.349830 | ||||||||
\(296\) | − | 9.25252i | − | 0.537792i | ||||||
\(297\) | −28.2661 | − | 3.62892i | −1.64017 | − | 0.210571i | ||||
\(298\) | 10.5894 | 0.613426 | ||||||||
\(299\) | 34.9856 | 2.02327 | ||||||||
\(300\) | 1.53549 | − | 0.801418i | 0.0886516 | − | 0.0462699i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 16.4546i | − | 0.946856i | ||||||
\(303\) | −2.45298 | + | 1.28029i | −0.140920 | + | 0.0735505i | ||||
\(304\) | − | 4.64816i | − | 0.266590i | ||||||
\(305\) | − | 6.75039i | − | 0.386526i | ||||||
\(306\) | 17.2101 | + | 11.9958i | 0.983836 | + | 0.685752i | ||||
\(307\) | 25.3383i | 1.44613i | 0.690778 | + | 0.723067i | \(0.257268\pi\) | ||||
−0.690778 | + | 0.723067i | \(0.742732\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.53552 | − | 14.4378i | −0.428680 | − | 0.821338i | ||||
\(310\) | 3.85766 | 0.219100 | ||||||||
\(311\) | −3.05993 | −0.173513 | −0.0867563 | − | 0.996230i | \(-0.527650\pi\) | ||||
−0.0867563 | + | 0.996230i | \(0.527650\pi\) | |||||||
\(312\) | 6.71910 | − | 3.50690i | 0.380394 | − | 0.198539i | ||||
\(313\) | − | 32.4069i | − | 1.83174i | −0.401470 | − | 0.915872i | \(-0.631501\pi\) | ||
0.401470 | − | 0.915872i | \(-0.368499\pi\) | |||||||
\(314\) | −8.65512 | −0.488437 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.87263 | −0.274107 | ||||||||
\(317\) | − | 12.8954i | − | 0.724280i | −0.932124 | − | 0.362140i | \(-0.882046\pi\) | ||
0.932124 | − | 0.362140i | \(-0.117954\pi\) | |||||||
\(318\) | 7.19761 | − | 3.75664i | 0.403622 | − | 0.210662i | ||||
\(319\) | 18.6699 | 1.04531 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 4.25777 | + | 8.15774i | 0.237645 | + | 0.455321i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 32.5034i | − | 1.80854i | ||||||
\(324\) | 3.11440 | + | 8.44396i | 0.173022 | + | 0.469109i | ||||
\(325\) | − | 4.37587i | − | 0.242729i | ||||||
\(326\) | 19.1573i | 1.06102i | ||||||||
\(327\) | 22.3263 | − | 11.6527i | 1.23464 | − | 0.644398i | ||||
\(328\) | 4.36516i | 0.241026i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −8.42134 | + | 4.39535i | −0.463580 | + | 0.241956i | ||||
\(331\) | 34.4890 | 1.89568 | 0.947842 | − | 0.318740i | \(-0.103260\pi\) | ||||
0.947842 | + | 0.318740i | \(0.103260\pi\) | |||||||
\(332\) | −9.22718 | −0.506407 | ||||||||
\(333\) | 15.8723 | − | 22.7717i | 0.869798 | − | 1.24788i | ||||
\(334\) | 3.99462i | 0.218576i | ||||||||
\(335\) | 5.98178 | 0.326820 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.05685 | 0.0575704 | 0.0287852 | − | 0.999586i | \(-0.490836\pi\) | ||||
0.0287852 | + | 0.999586i | \(0.490836\pi\) | |||||||
\(338\) | − | 6.14821i | − | 0.334419i | ||||||
\(339\) | −11.4188 | − | 21.8780i | −0.620183 | − | 1.18825i | ||||
\(340\) | 6.99274 | 0.379235 | ||||||||
\(341\) | −21.1572 | −1.14573 | ||||||||
\(342\) | 7.97374 | − | 11.4398i | 0.431170 | − | 0.618592i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 1.48092i | − | 0.0798459i | ||||||
\(345\) | 6.40743 | + | 12.2764i | 0.344964 | + | 0.660940i | ||||
\(346\) | 18.7253i | 1.00668i | ||||||||
\(347\) | − | 2.51957i | − | 0.135258i | −0.997711 | − | 0.0676288i | \(-0.978457\pi\) | ||
0.997711 | − | 0.0676288i | \(-0.0215433\pi\) | |||||||
\(348\) | −2.72814 | − | 5.22703i | −0.146244 | − | 0.280198i | ||||
\(349\) | 4.67230i | 0.250102i | 0.992150 | + | 0.125051i | \(0.0399095\pi\) | ||||
−0.992150 | + | 0.125051i | \(0.960090\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.5526 | + | 2.89539i | 1.20377 | + | 0.154545i | ||||
\(352\) | −5.48447 | −0.292323 | ||||||||
\(353\) | −17.3565 | −0.923791 | −0.461895 | − | 0.886934i | \(-0.652830\pi\) | ||||
−0.461895 | + | 0.886934i | \(0.652830\pi\) | |||||||
\(354\) | 4.81534 | + | 9.22603i | 0.255932 | + | 0.490358i | ||||
\(355\) | − | 4.42464i | − | 0.234835i | ||||||
\(356\) | 0.525443 | 0.0278484 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.9143 | 0.576841 | ||||||||
\(359\) | − | 7.07262i | − | 0.373279i | −0.982429 | − | 0.186639i | \(-0.940240\pi\) | ||
0.982429 | − | 0.186639i | \(-0.0597596\pi\) | |||||||
\(360\) | 2.46114 | + | 1.71546i | 0.129713 | + | 0.0904127i | ||||
\(361\) | −2.60543 | −0.137128 | ||||||||
\(362\) | 11.1025 | 0.583536 | ||||||||
\(363\) | 29.2962 | − | 15.2905i | 1.53765 | − | 0.802546i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.7067i | − | 0.560416i | ||||||
\(366\) | 10.3651 | − | 5.40988i | 0.541795 | − | 0.282779i | ||||
\(367\) | − | 8.54263i | − | 0.445922i | −0.974827 | − | 0.222961i | \(-0.928428\pi\) | ||
0.974827 | − | 0.222961i | \(-0.0715722\pi\) | |||||||
\(368\) | 7.99511i | 0.416774i | ||||||||
\(369\) | −7.48826 | + | 10.7433i | −0.389823 | + | 0.559272i | ||||
\(370\) | − | 9.25252i | − | 0.481016i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.09160 | + | 5.92340i | 0.160292 | + | 0.307114i | ||||
\(373\) | 19.8185 | 1.02616 | 0.513081 | − | 0.858340i | \(-0.328504\pi\) | ||||
0.513081 | + | 0.858340i | \(0.328504\pi\) | |||||||
\(374\) | −38.3515 | −1.98311 | ||||||||
\(375\) | 1.53549 | − | 0.801418i | 0.0792924 | − | 0.0413850i | ||||
\(376\) | 7.51483i | 0.387548i | ||||||||
\(377\) | −14.8961 | −0.767187 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4542 | 0.639728 | 0.319864 | − | 0.947463i | \(-0.396363\pi\) | ||||
0.319864 | + | 0.947463i | \(0.396363\pi\) | |||||||
\(380\) | − | 4.64816i | − | 0.238446i | ||||||
\(381\) | −7.49728 | + | 3.91305i | −0.384097 | + | 0.200472i | ||||
\(382\) | −18.3911 | −0.940970 | ||||||||
\(383\) | −27.5102 | −1.40571 | −0.702853 | − | 0.711335i | \(-0.748091\pi\) | ||||
−0.702853 | + | 0.711335i | \(0.748091\pi\) | |||||||
\(384\) | 0.801418 | + | 1.53549i | 0.0408972 | + | 0.0783577i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.3665i | 1.18932i | ||||||||
\(387\) | 2.54046 | − | 3.64475i | 0.129139 | − | 0.185273i | ||||
\(388\) | − | 2.60272i | − | 0.132133i | ||||||
\(389\) | − | 30.6518i | − | 1.55411i | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||
0.629435 | − | 0.777053i | \(-0.283286\pi\) | |||||||
\(390\) | 6.71910 | − | 3.50690i | 0.340235 | − | 0.177579i | ||||
\(391\) | 55.9078i | 2.82738i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 22.0375 | − | 11.5020i | 1.11164 | − | 0.580200i | ||||
\(394\) | −6.30178 | −0.317479 | ||||||||
\(395\) | −4.87263 | −0.245169 | ||||||||
\(396\) | −13.4980 | − | 9.40838i | −0.678301 | − | 0.472789i | ||||
\(397\) | 5.68732i | 0.285439i | 0.989763 | + | 0.142719i | \(0.0455846\pi\) | ||||
−0.989763 | + | 0.142719i | \(0.954415\pi\) | |||||||
\(398\) | −11.0277 | −0.552769 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − | 12.7853i | − | 0.638467i | −0.947676 | − | 0.319234i | \(-0.896575\pi\) | ||
0.947676 | − | 0.319234i | \(-0.103425\pi\) | |||||||
\(402\) | 4.79391 | + | 9.18497i | 0.239098 | + | 0.458105i | ||||
\(403\) | 16.8806 | 0.840883 | ||||||||
\(404\) | −1.59753 | −0.0794799 | ||||||||
\(405\) | 3.11440 | + | 8.44396i | 0.154756 | + | 0.419584i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 50.7451i | 2.51534i | ||||||||
\(408\) | 5.60410 | + | 10.7373i | 0.277445 | + | 0.531575i | ||||
\(409\) | 14.6466i | 0.724228i | 0.932134 | + | 0.362114i | \(0.117945\pi\) | ||||
−0.932134 | + | 0.362114i | \(0.882055\pi\) | |||||||
\(410\) | 4.36516i | 0.215580i | ||||||||
\(411\) | −4.53438 | − | 8.68773i | −0.223665 | − | 0.428534i | ||||
\(412\) | − | 9.40273i | − | 0.463239i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −13.7153 | + | 19.6771i | −0.674070 | + | 0.967076i | ||||
\(415\) | −9.22718 | −0.452945 | ||||||||
\(416\) | 4.37587 | 0.214545 | ||||||||
\(417\) | −6.57523 | − | 12.5979i | −0.321991 | − | 0.616924i | ||||
\(418\) | 25.4927i | 1.24689i | ||||||||
\(419\) | −38.2058 | −1.86647 | −0.933237 | − | 0.359261i | \(-0.883029\pi\) | ||||
−0.933237 | + | 0.359261i | \(0.883029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.5971 | 0.662681 | 0.331341 | − | 0.943511i | \(-0.392499\pi\) | ||||
0.331341 | + | 0.943511i | \(0.392499\pi\) | |||||||
\(422\) | 16.4672i | 0.801609i | ||||||||
\(423\) | −12.8914 | + | 18.4950i | −0.626801 | + | 0.899259i | ||||
\(424\) | 4.68750 | 0.227645 | ||||||||
\(425\) | 6.99274 | 0.339198 | ||||||||
\(426\) | 6.79398 | − | 3.54598i | 0.329170 | − | 0.171803i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.31279i | 0.256804i | ||||||||
\(429\) | −36.8507 | + | 19.2335i | −1.77917 | + | 0.928600i | ||||
\(430\) | − | 1.48092i | − | 0.0714163i | ||||||
\(431\) | − | 24.8072i | − | 1.19492i | −0.801899 | − | 0.597460i | \(-0.796177\pi\) | ||
0.801899 | − | 0.597460i | \(-0.203823\pi\) | |||||||
\(432\) | −0.661673 | + | 5.15385i | −0.0318347 | + | 0.247965i | ||||
\(433\) | − | 10.5514i | − | 0.507069i | −0.967326 | − | 0.253535i | \(-0.918407\pi\) | ||
0.967326 | − | 0.253535i | \(-0.0815932\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.72814 | − | 5.22703i | −0.130804 | − | 0.250617i | ||||
\(436\) | 14.5402 | 0.696347 | ||||||||
\(437\) | 37.1626 | 1.77773 | ||||||||
\(438\) | 16.4401 | − | 8.58056i | 0.785537 | − | 0.409995i | ||||
\(439\) | 11.2224i | 0.535615i | 0.963472 | + | 0.267807i | \(0.0862991\pi\) | ||||
−0.963472 | + | 0.267807i | \(0.913701\pi\) | |||||||
\(440\) | −5.48447 | −0.261462 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.5993 | 1.45546 | ||||||||
\(443\) | − | 14.1488i | − | 0.672230i | −0.941821 | − | 0.336115i | \(-0.890887\pi\) | ||
0.941821 | − | 0.336115i | \(-0.109113\pi\) | |||||||
\(444\) | 14.2072 | − | 7.41513i | 0.674242 | − | 0.351907i | ||||
\(445\) | 0.525443 | 0.0249084 | ||||||||
\(446\) | 13.5203 | 0.640205 | ||||||||
\(447\) | 8.48652 | + | 16.2599i | 0.401398 | + | 0.769066i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 1.16231i | − | 0.0548527i | −0.999624 | − | 0.0274264i | \(-0.991269\pi\) | ||
0.999624 | − | 0.0274264i | \(-0.00873118\pi\) | |||||||
\(450\) | 2.46114 | + | 1.71546i | 0.116019 | + | 0.0808675i | ||||
\(451\) | − | 23.9406i | − | 1.12732i | ||||||
\(452\) | − | 14.2482i | − | 0.670180i | ||||||
\(453\) | 25.2659 | − | 13.1870i | 1.18709 | − | 0.619580i | ||||
\(454\) | 5.57785i | 0.261782i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.13721 | − | 3.72512i | 0.334230 | − | 0.174445i | ||||
\(457\) | −27.8911 | −1.30469 | −0.652345 | − | 0.757922i | \(-0.726215\pi\) | ||||
−0.652345 | + | 0.757922i | \(0.726215\pi\) | |||||||
\(458\) | −11.6640 | −0.545021 | ||||||||
\(459\) | −4.62690 | + | 36.0395i | −0.215965 | + | 1.68218i | ||||
\(460\) | 7.99511i | 0.372774i | ||||||||
\(461\) | −17.1662 | −0.799511 | −0.399755 | − | 0.916622i | \(-0.630905\pi\) | ||||
−0.399755 | + | 0.916622i | \(0.630905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1372 | −1.81886 | −0.909430 | − | 0.415856i | \(-0.863482\pi\) | ||||
−0.909430 | + | 0.415856i | \(0.863482\pi\) | |||||||
\(464\) | − | 3.40414i | − | 0.158033i | ||||||
\(465\) | 3.09160 | + | 5.92340i | 0.143369 | + | 0.274691i | ||||
\(466\) | −22.7275 | −1.05283 | ||||||||
\(467\) | −5.33074 | −0.246677 | −0.123339 | − | 0.992365i | \(-0.539360\pi\) | ||||
−0.123339 | + | 0.992365i | \(0.539360\pi\) | |||||||
\(468\) | 10.7696 | + | 7.50662i | 0.497825 | + | 0.346994i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7.51483i | 0.346633i | ||||||||
\(471\) | −6.93636 | − | 13.2898i | −0.319611 | − | 0.612364i | ||||
\(472\) | 6.00852i | 0.276565i | ||||||||
\(473\) | 8.12206i | 0.373453i | ||||||||
\(474\) | −3.90501 | − | 7.48188i | −0.179363 | − | 0.343654i | ||||
\(475\) | − | 4.64816i | − | 0.213272i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5366 | + | 8.04121i | 0.528224 | + | 0.368182i | ||||
\(478\) | 5.34353 | 0.244407 | ||||||||
\(479\) | 6.57119 | 0.300245 | 0.150123 | − | 0.988667i | \(-0.452033\pi\) | ||||
0.150123 | + | 0.988667i | \(0.452033\pi\) | |||||||
\(480\) | 0.801418 | + | 1.53549i | 0.0365795 | + | 0.0700852i | ||||
\(481\) | − | 40.4878i | − | 1.84608i | ||||||
\(482\) | −14.8146 | −0.674786 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.0794 | 0.867244 | ||||||||
\(485\) | − | 2.60272i | − | 0.118184i | ||||||
\(486\) | −10.4697 | + | 11.5493i | −0.474915 | + | 0.523885i | ||||
\(487\) | 26.0143 | 1.17882 | 0.589410 | − | 0.807834i | \(-0.299360\pi\) | ||||
0.589410 | + | 0.807834i | \(0.299360\pi\) | |||||||
\(488\) | 6.75039 | 0.305576 | ||||||||
\(489\) | −29.4158 | + | 15.3530i | −1.33023 | + | 0.694285i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 30.2128i | − | 1.36349i | −0.731591 | − | 0.681743i | \(-0.761222\pi\) | ||
0.731591 | − | 0.681743i | \(-0.238778\pi\) | |||||||
\(492\) | −6.70267 | + | 3.49832i | −0.302180 | + | 0.157716i | ||||
\(493\) | − | 23.8043i | − | 1.07209i | ||||||
\(494\) | − | 20.3397i | − | 0.915128i | ||||||
\(495\) | −13.4980 | − | 9.40838i | −0.606691 | − | 0.422875i | ||||
\(496\) | 3.85766i | 0.173214i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.39483 | − | 14.1682i | −0.331370 | − | 0.634894i | ||||
\(499\) | −9.86296 | −0.441527 | −0.220763 | − | 0.975327i | \(-0.570855\pi\) | ||||
−0.220763 | + | 0.975327i | \(0.570855\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −6.13370 | + | 3.20136i | −0.274033 | + | 0.143026i | ||||
\(502\) | 11.9052i | 0.531353i | ||||||||
\(503\) | 2.92257 | 0.130311 | 0.0651554 | − | 0.997875i | \(-0.479246\pi\) | ||||
0.0651554 | + | 0.997875i | \(0.479246\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59753 | −0.0710890 | ||||||||
\(506\) | − | 43.8489i | − | 1.94932i | ||||||
\(507\) | 9.44052 | − | 4.92728i | 0.419268 | − | 0.218828i | ||||
\(508\) | −4.88266 | −0.216633 | ||||||||
\(509\) | 34.1660 | 1.51438 | 0.757190 | − | 0.653194i | \(-0.226572\pi\) | ||||
0.757190 | + | 0.653194i | \(0.226572\pi\) | |||||||
\(510\) | 5.60410 | + | 10.7373i | 0.248154 | + | 0.475455i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 23.9559 | + | 3.07556i | 1.05768 | + | 0.135789i | ||||
\(514\) | 23.1928i | 1.02299i | ||||||||
\(515\) | − | 9.40273i | − | 0.414334i | ||||||
\(516\) | 2.27394 | − | 1.18684i | 0.100105 | − | 0.0522475i | ||||
\(517\) | − | 41.2148i | − | 1.81263i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.7525 | + | 15.0068i | −1.26210 | + | 0.658725i | ||||
\(520\) | 4.37587 | 0.191894 | ||||||||
\(521\) | 14.5920 | 0.639286 | 0.319643 | − | 0.947538i | \(-0.396437\pi\) | ||||
0.319643 | + | 0.947538i | \(0.396437\pi\) | |||||||
\(522\) | 5.83967 | − | 8.37807i | 0.255596 | − | 0.366698i | ||||
\(523\) | − | 5.13396i | − | 0.224492i | −0.993680 | − | 0.112246i | \(-0.964196\pi\) | ||
0.993680 | − | 0.112246i | \(-0.0358045\pi\) | |||||||
\(524\) | 14.3521 | 0.626974 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.86287 | −0.430042 | ||||||||
\(527\) | 26.9756i | 1.17508i | ||||||||
\(528\) | −4.39535 | − | 8.42134i | −0.191283 | − | 0.366492i | ||||
\(529\) | −40.9219 | −1.77921 | ||||||||
\(530\) | 4.68750 | 0.203612 | ||||||||
\(531\) | −10.3074 | + | 14.7878i | −0.447302 | + | 0.641736i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.1014i | 0.827372i | ||||||||
\(534\) | 0.421099 | + | 0.806813i | 0.0182228 | + | 0.0349142i | ||||
\(535\) | 5.31279i | 0.229692i | ||||||||
\(536\) | 5.98178i | 0.258374i | ||||||||
\(537\) | 8.74694 | + | 16.7589i | 0.377458 | + | 0.723198i | ||||
\(538\) | − | 20.3827i | − | 0.878759i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.661673 | + | 5.15385i | −0.0284739 | + | 0.221786i | ||||
\(541\) | −30.8179 | −1.32497 | −0.662483 | − | 0.749077i | \(-0.730497\pi\) | ||||
−0.662483 | + | 0.749077i | \(0.730497\pi\) | |||||||
\(542\) | −20.2646 | −0.870439 | ||||||||
\(543\) | 8.89776 | + | 17.0478i | 0.381839 | + | 0.731592i | ||||
\(544\) | 6.99274i | 0.299811i | ||||||||
\(545\) | 14.5402 | 0.622832 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.79462 | −0.418788 | −0.209394 | − | 0.977831i | \(-0.567149\pi\) | ||||
−0.209394 | + | 0.977831i | \(0.567149\pi\) | |||||||
\(548\) | − | 5.65795i | − | 0.241696i | ||||||
\(549\) | 16.6136 | + | 11.5800i | 0.709052 | + | 0.494223i | ||||
\(550\) | −5.48447 | −0.233858 | ||||||||
\(551\) | −15.8230 | −0.674083 | ||||||||
\(552\) | −12.2764 | + | 6.40743i | −0.522519 | + | 0.272718i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 19.8717i | − | 0.844268i | ||||||
\(555\) | 14.2072 | − | 7.41513i | 0.603060 | − | 0.314755i | ||||
\(556\) | − | 8.20450i | − | 0.347949i | ||||||
\(557\) | 2.19574i | 0.0930365i | 0.998917 | + | 0.0465183i | \(0.0148126\pi\) | ||||
−0.998917 | + | 0.0465183i | \(0.985187\pi\) | |||||||
\(558\) | −6.61766 | + | 9.49423i | −0.280148 | + | 0.401923i | ||||
\(559\) | − | 6.48031i | − | 0.274088i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −30.7355 | − | 58.8883i | −1.29765 | − | 2.48626i | ||||
\(562\) | −20.8001 | −0.877401 | ||||||||
\(563\) | 22.7822 | 0.960155 | 0.480078 | − | 0.877226i | \(-0.340608\pi\) | ||||
0.480078 | + | 0.877226i | \(0.340608\pi\) | |||||||
\(564\) | −11.5389 | + | 6.02252i | −0.485877 | + | 0.253594i | ||||
\(565\) | − | 14.2482i | − | 0.599427i | ||||||
\(566\) | 8.58090 | 0.360682 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.42464 | 0.185654 | ||||||||
\(569\) | 7.00282i | 0.293573i | 0.989168 | + | 0.146787i | \(0.0468931\pi\) | ||||
−0.989168 | + | 0.146787i | \(0.953107\pi\) | |||||||
\(570\) | 7.13721 | − | 3.72512i | 0.298945 | − | 0.156028i | ||||
\(571\) | 20.4402 | 0.855397 | 0.427698 | − | 0.903921i | \(-0.359325\pi\) | ||||
0.427698 | + | 0.903921i | \(0.359325\pi\) | |||||||
\(572\) | −23.9993 | −1.00346 | ||||||||
\(573\) | −14.7389 | − | 28.2393i | −0.615728 | − | 1.17972i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.99511i | 0.333419i | ||||||||
\(576\) | −1.71546 | + | 2.46114i | −0.0714775 | + | 0.102547i | ||||
\(577\) | − | 27.2878i | − | 1.13601i | −0.823027 | − | 0.568003i | \(-0.807716\pi\) | ||
0.823027 | − | 0.568003i | \(-0.192284\pi\) | |||||||
\(578\) | 31.8984i | 1.32680i | ||||||||
\(579\) | −35.8790 | + | 18.7263i | −1.49108 | + | 0.778239i | ||||
\(580\) | − | 3.40414i | − | 0.141349i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.99646 | − | 2.08587i | 0.165658 | − | 0.0864620i | ||||
\(583\) | −25.7084 | −1.06473 | ||||||||
\(584\) | 10.7067 | 0.443048 | ||||||||
\(585\) | 10.7696 | + | 7.50662i | 0.445269 | + | 0.310361i | ||||
\(586\) | − | 2.72492i | − | 0.112565i | ||||||
\(587\) | −40.1596 | −1.65757 | −0.828783 | − | 0.559570i | \(-0.810966\pi\) | ||||
−0.828783 | + | 0.559570i | \(0.810966\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.9310 | 0.738835 | ||||||||
\(590\) | 6.00852i | 0.247367i | ||||||||
\(591\) | −5.05036 | − | 9.67632i | −0.207744 | − | 0.398031i | ||||
\(592\) | 9.25252 | 0.380276 | ||||||||
\(593\) | 2.62320 | 0.107722 | 0.0538609 | − | 0.998548i | \(-0.482847\pi\) | ||||
0.0538609 | + | 0.998548i | \(0.482847\pi\) | |||||||
\(594\) | 3.62892 | − | 28.2661i | 0.148896 | − | 1.15977i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.5894i | 0.433758i | ||||||||
\(597\) | −8.83780 | − | 16.9329i | −0.361707 | − | 0.693019i | ||||
\(598\) | 34.9856i | 1.43067i | ||||||||
\(599\) | − | 41.8523i | − | 1.71004i | −0.518595 | − | 0.855020i | \(-0.673545\pi\) | ||
0.518595 | − | 0.855020i | \(-0.326455\pi\) | |||||||
\(600\) | 0.801418 | + | 1.53549i | 0.0327177 | + | 0.0626861i | ||||
\(601\) | 31.5777i | 1.28808i | 0.764992 | + | 0.644040i | \(0.222743\pi\) | ||||
−0.764992 | + | 0.644040i | \(0.777257\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.2615 | + | 14.7220i | −0.417881 | + | 0.599526i | ||||
\(604\) | 16.4546 | 0.669528 | ||||||||
\(605\) | 19.0794 | 0.775687 | ||||||||
\(606\) | −1.28029 | − | 2.45298i | −0.0520080 | − | 0.0996457i | ||||
\(607\) | 6.41971i | 0.260568i | 0.991477 | + | 0.130284i | \(0.0415889\pi\) | ||||
−0.991477 | + | 0.130284i | \(0.958411\pi\) | |||||||
\(608\) | 4.64816 | 0.188508 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.75039 | 0.273315 | ||||||||
\(611\) | 32.8839i | 1.33034i | ||||||||
\(612\) | −11.9958 | + | 17.2101i | −0.484900 | + | 0.695677i | ||||
\(613\) | −38.0165 | −1.53547 | −0.767736 | − | 0.640766i | \(-0.778617\pi\) | ||||
−0.767736 | + | 0.640766i | \(0.778617\pi\) | |||||||
\(614\) | −25.3383 | −1.02257 | ||||||||
\(615\) | −6.70267 | + | 3.49832i | −0.270278 | + | 0.141066i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 33.5160i | − | 1.34930i | −0.738136 | − | 0.674652i | \(-0.764294\pi\) | ||
0.738136 | − | 0.674652i | \(-0.235706\pi\) | |||||||
\(618\) | 14.4378 | − | 7.53552i | 0.580774 | − | 0.303123i | ||||
\(619\) | 0.791382i | 0.0318083i | 0.999874 | + | 0.0159042i | \(0.00506266\pi\) | ||||
−0.999874 | + | 0.0159042i | \(0.994937\pi\) | |||||||
\(620\) | 3.85766i | 0.154927i | ||||||||
\(621\) | −41.2056 | − | 5.29015i | −1.65353 | − | 0.212286i | ||||
\(622\) | − | 3.05993i | − | 0.122692i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.50690 | + | 6.71910i | 0.140388 | + | 0.268979i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 32.4069 | 1.29524 | ||||||||
\(627\) | −39.1438 | + | 20.4303i | −1.56325 | + | 0.815908i | ||||
\(628\) | − | 8.65512i | − | 0.345377i | ||||||
\(629\) | 64.7005 | 2.57978 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.5697 | 1.25677 | 0.628386 | − | 0.777902i | \(-0.283716\pi\) | ||||
0.628386 | + | 0.777902i | \(0.283716\pi\) | |||||||
\(632\) | − | 4.87263i | − | 0.193823i | ||||||
\(633\) | −25.2852 | + | 13.1971i | −1.00499 | + | 0.524537i | ||||
\(634\) | 12.8954 | 0.512143 | ||||||||
\(635\) | −4.88266 | −0.193763 | ||||||||
\(636\) | 3.75664 | + | 7.19761i | 0.148961 | + | 0.285404i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 18.6699i | 0.739149i | ||||||||
\(639\) | 10.8896 | + | 7.59028i | 0.430787 | + | 0.300267i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | − | 3.80187i | − | 0.150165i | −0.997177 | − | 0.0750824i | \(-0.976078\pi\) | ||
0.997177 | − | 0.0750824i | \(-0.0239220\pi\) | |||||||
\(642\) | −8.15774 | + | 4.25777i | −0.321960 | + | 0.168041i | ||||
\(643\) | 4.78358i | 0.188646i | 0.995542 | + | 0.0943230i | \(0.0300686\pi\) | ||||
−0.995542 | + | 0.0943230i | \(0.969931\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.27394 | − | 1.18684i | 0.0895362 | − | 0.0467316i | ||||
\(646\) | 32.5034 | 1.27883 | ||||||||
\(647\) | −16.5620 | −0.651121 | −0.325560 | − | 0.945521i | \(-0.605553\pi\) | ||||
−0.325560 | + | 0.945521i | \(0.605553\pi\) | |||||||
\(648\) | −8.44396 | + | 3.11440i | −0.331710 | + | 0.122345i | ||||
\(649\) | − | 32.9535i | − | 1.29354i | ||||||
\(650\) | 4.37587 | 0.171636 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.1573 | −0.750256 | ||||||||
\(653\) | 8.09175i | 0.316655i | 0.987387 | + | 0.158327i | \(0.0506101\pi\) | ||||
−0.987387 | + | 0.158327i | \(0.949390\pi\) | |||||||
\(654\) | 11.6527 | + | 22.3263i | 0.455658 | + | 0.873026i | ||||
\(655\) | 14.3521 | 0.560783 | ||||||||
\(656\) | −4.36516 | −0.170431 | ||||||||
\(657\) | 26.3507 | + | 18.3670i | 1.02804 | + | 0.716564i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.3747i | 1.30009i | 0.759894 | + | 0.650047i | \(0.225251\pi\) | ||||
−0.759894 | + | 0.650047i | \(0.774749\pi\) | |||||||
\(660\) | −4.39535 | − | 8.42134i | −0.171089 | − | 0.327800i | ||||
\(661\) | 26.5081i | 1.03105i | 0.856876 | + | 0.515523i | \(0.172402\pi\) | ||||
−0.856876 | + | 0.515523i | \(0.827598\pi\) | |||||||
\(662\) | 34.4890i | 1.34045i | ||||||||
\(663\) | 24.5228 | + | 46.9849i | 0.952387 | + | 1.82474i | ||||
\(664\) | − | 9.22718i | − | 0.358084i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 22.7717 | + | 15.8723i | 0.882387 | + | 0.615040i | ||||
\(667\) | 27.2165 | 1.05383 | ||||||||
\(668\) | −3.99462 | −0.154556 | ||||||||
\(669\) | 10.8354 | + | 20.7603i | 0.418921 | + | 0.802640i | ||||
\(670\) | 5.98178i | 0.231096i | ||||||||
\(671\) | −37.0223 | −1.42923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.9621 | 0.615295 | 0.307648 | − | 0.951500i | \(-0.400458\pi\) | ||||
0.307648 | + | 0.951500i | \(0.400458\pi\) | |||||||
\(674\) | 1.05685i | 0.0407085i | ||||||||
\(675\) | −0.661673 | + | 5.15385i | −0.0254678 | + | 0.198372i | ||||
\(676\) | 6.14821 | 0.236470 | ||||||||
\(677\) | 11.3672 | 0.436877 | 0.218438 | − | 0.975851i | \(-0.429904\pi\) | ||||
0.218438 | + | 0.975851i | \(0.429904\pi\) | |||||||
\(678\) | 21.8780 | − | 11.4188i | 0.840220 | − | 0.438536i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.99274i | 0.268159i | ||||||||
\(681\) | −8.56474 | + | 4.47019i | −0.328201 | + | 0.171298i | ||||
\(682\) | − | 21.1572i | − | 0.810151i | ||||||
\(683\) | 45.1270i | 1.72674i | 0.504574 | + | 0.863369i | \(0.331650\pi\) | ||||
−0.504574 | + | 0.863369i | \(0.668350\pi\) | |||||||
\(684\) | 11.4398 | + | 7.97374i | 0.437411 | + | 0.304883i | ||||
\(685\) | − | 5.65795i | − | 0.216179i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.34770 | − | 17.9099i | −0.356637 | − | 0.683305i | ||||
\(688\) | 1.48092 | 0.0564596 | ||||||||
\(689\) | 20.5119 | 0.781440 | ||||||||
\(690\) | −12.2764 | + | 6.40743i | −0.467355 | + | 0.243927i | ||||
\(691\) | − | 32.0881i | − | 1.22069i | −0.792135 | − | 0.610345i | \(-0.791031\pi\) | ||
0.792135 | − | 0.610345i | \(-0.208969\pi\) | |||||||
\(692\) | −18.7253 | −0.711830 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.51957 | 0.0956415 | ||||||||
\(695\) | − | 8.20450i | − | 0.311215i | ||||||
\(696\) | 5.22703 | − | 2.72814i | 0.198130 | − | 0.103410i | ||||
\(697\) | −30.5245 | −1.15620 | ||||||||
\(698\) | −4.67230 | −0.176849 | ||||||||
\(699\) | −18.2142 | − | 34.8978i | −0.688925 | − | 1.31996i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.71262i | − | 0.329071i | −0.986371 | − | 0.164536i | \(-0.947387\pi\) | ||
0.986371 | − | 0.164536i | \(-0.0526125\pi\) | |||||||
\(702\) | −2.89539 | + | 22.5526i | −0.109279 | + | 0.851192i | ||||
\(703\) | − | 43.0072i | − | 1.62205i | ||||||
\(704\) | − | 5.48447i | − | 0.206704i | ||||||
\(705\) | −11.5389 | + | 6.02252i | −0.434582 | + | 0.226821i | ||||
\(706\) | − | 17.3565i | − | 0.653219i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −9.22603 | + | 4.81534i | −0.346735 | + | 0.180971i | ||||
\(709\) | −22.5339 | −0.846279 | −0.423140 | − | 0.906064i | \(-0.639072\pi\) | ||||
−0.423140 | + | 0.906064i | \(0.639072\pi\) | |||||||
\(710\) | 4.42464 | 0.166054 | ||||||||
\(711\) | 8.35881 | − | 11.9922i | 0.313480 | − | 0.449744i | ||||
\(712\) | 0.525443i | 0.0196918i | ||||||||
\(713\) | −30.8424 | −1.15506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23.9993 | −0.897523 | ||||||||
\(716\) | 10.9143i | 0.407888i | ||||||||
\(717\) | 4.28240 | + | 8.20494i | 0.159929 | + | 0.306419i | ||||
\(718\) | 7.07262 | 0.263948 | ||||||||
\(719\) | −5.46856 | −0.203943 | −0.101971 | − | 0.994787i | \(-0.532515\pi\) | ||||
−0.101971 | + | 0.994787i | \(0.532515\pi\) | |||||||
\(720\) | −1.71546 | + | 2.46114i | −0.0639314 | + | 0.0917212i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 2.60543i | − | 0.0969639i | ||||||
\(723\) | −11.8727 | − | 22.7477i | −0.441550 | − | 0.845995i | ||||
\(724\) | 11.1025i | 0.412622i | ||||||||
\(725\) | − | 3.40414i | − | 0.126427i | ||||||
\(726\) | 15.2905 | + | 29.2962i | 0.567485 | + | 1.08728i | ||||
\(727\) | − | 37.3430i | − | 1.38498i | −0.721429 | − | 0.692488i | \(-0.756514\pi\) | ||
0.721429 | − | 0.692488i | \(-0.243486\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.1244 | − | 6.82032i | −0.967570 | − | 0.252605i | ||||
\(730\) | 10.7067 | 0.396274 | ||||||||
\(731\) | 10.3557 | 0.383019 | ||||||||
\(732\) | 5.40988 | + | 10.3651i | 0.199955 | + | 0.383107i | ||||
\(733\) | − | 5.62093i | − | 0.207614i | −0.994597 | − | 0.103807i | \(-0.966898\pi\) | ||
0.994597 | − | 0.103807i | \(-0.0331024\pi\) | |||||||
\(734\) | 8.54263 | 0.315314 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.99511 | −0.294704 | ||||||||
\(737\) | − | 32.8069i | − | 1.20846i | ||||||
\(738\) | −10.7433 | − | 7.48826i | −0.395465 | − | 0.275647i | ||||
\(739\) | 24.3382 | 0.895296 | 0.447648 | − | 0.894210i | \(-0.352262\pi\) | ||||
0.447648 | + | 0.894210i | \(0.352262\pi\) | |||||||
\(740\) | 9.25252 | 0.340129 | ||||||||
\(741\) | 31.2315 | − | 16.3006i | 1.14732 | − | 0.598819i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.46882i | 0.310691i | 0.987860 | + | 0.155345i | \(0.0496491\pi\) | ||||
−0.987860 | + | 0.155345i | \(0.950351\pi\) | |||||||
\(744\) | −5.92340 | + | 3.09160i | −0.217162 | + | 0.113343i | ||||
\(745\) | 10.5894i | 0.387965i | ||||||||
\(746\) | 19.8185i | 0.725605i | ||||||||
\(747\) | 15.8289 | − | 22.7094i | 0.579148 | − | 0.830892i | ||||
\(748\) | − | 38.3515i | − | 1.40227i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0.801418 | + | 1.53549i | 0.0292636 | + | 0.0560682i | ||||
\(751\) | −30.1044 | −1.09853 | −0.549263 | − | 0.835650i | \(-0.685091\pi\) | ||||
−0.549263 | + | 0.835650i | \(0.685091\pi\) | |||||||
\(752\) | −7.51483 | −0.274038 | ||||||||
\(753\) | −18.2802 | + | 9.54100i | −0.666169 | + | 0.347693i | ||||
\(754\) | − | 14.8961i | − | 0.542483i | ||||||
\(755\) | 16.4546 | 0.598844 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.3263 | −0.884154 | −0.442077 | − | 0.896977i | \(-0.645758\pi\) | ||||
−0.442077 | + | 0.896977i | \(0.645758\pi\) | |||||||
\(758\) | 12.4542i | 0.452356i | ||||||||
\(759\) | 67.3296 | − | 35.1413i | 2.44391 | − | 1.27555i | ||||
\(760\) | 4.64816 | 0.168607 | ||||||||
\(761\) | −49.5903 | −1.79765 | −0.898824 | − | 0.438311i | \(-0.855577\pi\) | ||||
−0.898824 | + | 0.438311i | \(0.855577\pi\) | |||||||
\(762\) | −3.91305 | − | 7.49728i | −0.141755 | − | 0.271598i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 18.3911i | − | 0.665366i | ||||||
\(765\) | −11.9958 | + | 17.2101i | −0.433708 | + | 0.622232i | ||||
\(766\) | − | 27.5102i | − | 0.993985i | ||||||
\(767\) | 26.2925i | 0.949367i | ||||||||
\(768\) | −1.53549 | + | 0.801418i | −0.0554072 | + | 0.0289187i | ||||
\(769\) | 24.0765i | 0.868221i | 0.900860 | + | 0.434110i | \(0.142937\pi\) | ||||
−0.900860 | + | 0.434110i | \(0.857063\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.6123 | + | 18.5871i | −1.28255 | + | 0.669399i | ||||
\(772\) | −23.3665 | −0.840978 | ||||||||
\(773\) | 33.3050 | 1.19790 | 0.598949 | − | 0.800787i | \(-0.295585\pi\) | ||||
0.598949 | + | 0.800787i | \(0.295585\pi\) | |||||||
\(774\) | 3.64475 | + | 2.54046i | 0.131008 | + | 0.0913149i | ||||
\(775\) | 3.85766i | 0.138571i | ||||||||
\(776\) | 2.60272 | 0.0934323 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.6518 | 1.09892 | ||||||||
\(779\) | 20.2900i | 0.726965i | ||||||||
\(780\) | 3.50690 | + | 6.71910i | 0.125567 | + | 0.240582i | ||||
\(781\) | −24.2668 | −0.868333 | ||||||||
\(782\) | −55.9078 | −1.99926 | ||||||||
\(783\) | 17.5445 | + | 2.25243i | 0.626988 | + | 0.0804952i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 8.65512i | − | 0.308914i | ||||||
\(786\) | 11.5020 | + | 22.0375i | 0.410263 | + | 0.786051i | ||||
\(787\) | − | 1.98548i | − | 0.0707748i | −0.999374 | − | 0.0353874i | \(-0.988733\pi\) | ||
0.999374 | − | 0.0353874i | \(-0.0112665\pi\) | |||||||
\(788\) | − | 6.30178i | − | 0.224492i | ||||||
\(789\) | −7.90428 | − | 15.1443i | −0.281400 | − | 0.539153i | ||||
\(790\) | − | 4.87263i | − | 0.173361i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.40838 | − | 13.4980i | 0.334312 | − | 0.479632i | ||||
\(793\) | 29.5388 | 1.04895 | ||||||||
\(794\) | −5.68732 | −0.201836 | ||||||||
\(795\) | 3.75664 | + | 7.19761i | 0.133234 | + | 0.255273i | ||||
\(796\) | − | 11.0277i | − | 0.390867i | ||||||
\(797\) | 39.2292 | 1.38957 | 0.694785 | − | 0.719218i | \(-0.255500\pi\) | ||||
0.694785 | + | 0.719218i | \(0.255500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −52.5493 | −1.85906 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | −0.901377 | + | 1.29319i | −0.0318486 | + | 0.0456926i | ||||
\(802\) | 12.7853 | 0.451465 | ||||||||
\(803\) | −58.7207 | −2.07221 | ||||||||
\(804\) | −9.18497 | + | 4.79391i | −0.323929 | + | 0.169068i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.8806i | 0.594594i | ||||||||
\(807\) | 31.2974 | − | 16.3350i | 1.10172 | − | 0.575020i | ||||
\(808\) | − | 1.59753i | − | 0.0562008i | ||||||
\(809\) | 43.0358i | 1.51306i | 0.653961 | + | 0.756529i | \(0.273106\pi\) | ||||
−0.653961 | + | 0.756529i | \(0.726894\pi\) | |||||||
\(810\) | −8.44396 | + | 3.11440i | −0.296691 | + | 0.109429i | ||||
\(811\) | − | 46.2399i | − | 1.62370i | −0.583865 | − | 0.811850i | \(-0.698460\pi\) | ||
0.583865 | − | 0.811850i | \(-0.301540\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.2404 | − | 31.1161i | −0.569576 | − | 1.09129i | ||||
\(814\) | −50.7451 | −1.77862 | ||||||||
\(815\) | −19.1573 | −0.671049 | ||||||||
\(816\) | −10.7373 | + | 5.60410i | −0.375880 | + | 0.196183i | ||||
\(817\) | − | 6.88356i | − | 0.240825i | ||||||
\(818\) | −14.6466 | −0.512107 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.36516 | −0.152438 | ||||||||
\(821\) | − | 40.9505i | − | 1.42918i | −0.699542 | − | 0.714591i | \(-0.746613\pi\) | ||
0.699542 | − | 0.714591i | \(-0.253387\pi\) | |||||||
\(822\) | 8.68773 | − | 4.53438i | 0.303019 | − | 0.158155i | ||||
\(823\) | 8.93572 | 0.311480 | 0.155740 | − | 0.987798i | \(-0.450224\pi\) | ||||
0.155740 | + | 0.987798i | \(0.450224\pi\) | |||||||
\(824\) | 9.40273 | 0.327560 | ||||||||
\(825\) | −4.39535 | − | 8.42134i | −0.153026 | − | 0.293194i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 4.48639i | − | 0.156007i | −0.996953 | − | 0.0780036i | \(-0.975145\pi\) | ||
0.996953 | − | 0.0780036i | \(-0.0248546\pi\) | |||||||
\(828\) | −19.6771 | − | 13.7153i | −0.683826 | − | 0.476640i | ||||
\(829\) | − | 38.5514i | − | 1.33895i | −0.742837 | − | 0.669473i | \(-0.766520\pi\) | ||
0.742837 | − | 0.669473i | \(-0.233480\pi\) | |||||||
\(830\) | − | 9.22718i | − | 0.320280i | ||||||
\(831\) | 30.5128 | − | 15.9255i | 1.05848 | − | 0.552451i | ||||
\(832\) | 4.37587i | 0.151706i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.5979 | − | 6.57523i | 0.436231 | − | 0.227682i | ||||
\(835\) | −3.99462 | −0.138239 | ||||||||
\(836\) | −25.4927 | −0.881683 | ||||||||
\(837\) | −19.8818 | − | 2.55251i | −0.687216 | − | 0.0882275i | ||||
\(838\) | − | 38.2058i | − | 1.31980i | ||||||
\(839\) | −21.0084 | −0.725290 | −0.362645 | − | 0.931927i | \(-0.618126\pi\) | ||||
−0.362645 | + | 0.931927i | \(0.618126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.4118 | 0.600407 | ||||||||
\(842\) | 13.5971i | 0.468586i | ||||||||
\(843\) | −16.6696 | − | 31.9384i | −0.574131 | − | 1.10002i | ||||
\(844\) | −16.4672 | −0.566823 | ||||||||
\(845\) | 6.14821 | 0.211505 | ||||||||
\(846\) | −18.4950 | − | 12.8914i | −0.635872 | − | 0.443215i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.68750i | 0.160969i | ||||||||
\(849\) | 6.87688 | + | 13.1759i | 0.236014 | + | 0.452195i | ||||
\(850\) | 6.99274i | 0.239849i | ||||||||
\(851\) | 73.9750i | 2.53583i | ||||||||
\(852\) | 3.54598 | + | 6.79398i | 0.121483 | + | 0.232758i | ||||
\(853\) | 36.7293i | 1.25759i | 0.777572 | + | 0.628794i | \(0.216451\pi\) | ||||
−0.777572 | + | 0.628794i | \(0.783549\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4398 | + | 7.97374i | 0.391232 | + | 0.272696i | ||||
\(856\) | −5.31279 | −0.181588 | ||||||||
\(857\) | −13.3707 | −0.456733 | −0.228367 | − | 0.973575i | \(-0.573339\pi\) | ||||
−0.228367 | + | 0.973575i | \(0.573339\pi\) | |||||||
\(858\) | −19.2335 | − | 36.8507i | −0.656619 | − | 1.25806i | ||||
\(859\) | − | 1.51210i | − | 0.0515923i | −0.999667 | − | 0.0257962i | \(-0.991788\pi\) | ||
0.999667 | − | 0.0257962i | \(-0.00821208\pi\) | |||||||
\(860\) | 1.48092 | 0.0504990 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.8072 | 0.844936 | ||||||||
\(863\) | 1.38300i | 0.0470777i | 0.999723 | + | 0.0235389i | \(0.00749334\pi\) | ||||
−0.999723 | + | 0.0235389i | \(0.992507\pi\) | |||||||
\(864\) | −5.15385 | − | 0.661673i | −0.175338 | − | 0.0225106i | ||||
\(865\) | −18.7253 | −0.636680 | ||||||||
\(866\) | 10.5514 | 0.358552 | ||||||||
\(867\) | −48.9797 | + | 25.5639i | −1.66344 | + | 0.868197i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.7238i | 0.906543i | ||||||||
\(870\) | 5.22703 | − | 2.72814i | 0.177213 | − | 0.0924927i | ||||
\(871\) | 26.1755i | 0.886922i | ||||||||
\(872\) | 14.5402i | 0.492392i | ||||||||
\(873\) | 6.40566 | + | 4.46487i | 0.216799 | + | 0.151113i | ||||
\(874\) | 37.1626i | 1.25704i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.58056 | + | 16.4401i | 0.289910 | + | 0.555459i | ||||
\(877\) | −55.9731 | −1.89008 | −0.945039 | − | 0.326957i | \(-0.893977\pi\) | ||||
−0.945039 | + | 0.326957i | \(0.893977\pi\) | |||||||
\(878\) | −11.2224 | −0.378737 | ||||||||
\(879\) | 4.18409 | − | 2.18380i | 0.141126 | − | 0.0736578i | ||||
\(880\) | − | 5.48447i | − | 0.184881i | ||||||
\(881\) | −10.5177 | −0.354350 | −0.177175 | − | 0.984179i | \(-0.556696\pi\) | ||||
−0.177175 | + | 0.984179i | \(0.556696\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.6637 | 1.67132 | 0.835658 | − | 0.549251i | \(-0.185087\pi\) | ||||
0.835658 | + | 0.549251i | \(0.185087\pi\) | |||||||
\(884\) | 30.5993i | 1.02917i | ||||||||
\(885\) | −9.22603 | + | 4.81534i | −0.310130 | + | 0.161866i | ||||
\(886\) | 14.1488 | 0.475339 | ||||||||
\(887\) | 19.1044 | 0.641463 | 0.320732 | − | 0.947170i | \(-0.396071\pi\) | ||||
0.320732 | + | 0.947170i | \(0.396071\pi\) | |||||||
\(888\) | 7.41513 | + | 14.2072i | 0.248836 | + | 0.476761i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.525443i | 0.0176129i | ||||||||
\(891\) | 46.3106 | − | 17.0808i | 1.55146 | − | 0.572228i | ||||
\(892\) | 13.5203i | 0.452693i | ||||||||
\(893\) | 34.9302i | 1.16889i | ||||||||
\(894\) | −16.2599 | + | 8.48652i | −0.543812 | + | 0.283832i | ||||
\(895\) | 10.9143i | 0.364826i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −53.7200 | + | 28.0380i | −1.79366 | + | 0.936163i | ||||
\(898\) | 1.16231 | 0.0387867 | ||||||||
\(899\) | 13.1320 | 0.437978 | ||||||||
\(900\) | −1.71546 | + | 2.46114i | −0.0571820 | + | 0.0820379i | ||||
\(901\) | 32.7784i | 1.09201i | ||||||||
\(902\) | 23.9406 | 0.797135 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.2482 | 0.473889 | ||||||||
\(905\) | 11.1025i | 0.369060i | ||||||||
\(906\) | 13.1870 | + | 25.2659i | 0.438109 | + | 0.839403i | ||||
\(907\) | −18.2459 | −0.605846 | −0.302923 | − | 0.953015i | \(-0.597962\pi\) | ||||
−0.302923 | + | 0.953015i | \(0.597962\pi\) | |||||||
\(908\) | −5.57785 | −0.185108 | ||||||||
\(909\) | 2.74049 | − | 3.93173i | 0.0908964 | − | 0.130407i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.6428i | − | 1.21403i | −0.794690 | − | 0.607015i | \(-0.792367\pi\) | ||
0.794690 | − | 0.607015i | \(-0.207633\pi\) | |||||||
\(912\) | 3.72512 | + | 7.13721i | 0.123351 | + | 0.236337i | ||||
\(913\) | 50.6062i | 1.67482i | ||||||||
\(914\) | − | 27.8911i | − | 0.922556i | ||||||
\(915\) | 5.40988 | + | 10.3651i | 0.178845 | + | 0.342661i | ||||
\(916\) | − | 11.6640i | − | 0.385388i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −36.0395 | − | 4.62690i | −1.18948 | − | 0.152711i | ||||
\(919\) | 7.12268 | 0.234955 | 0.117478 | − | 0.993076i | \(-0.462519\pi\) | ||||
0.117478 | + | 0.993076i | \(0.462519\pi\) | |||||||
\(920\) | −7.99511 | −0.263591 | ||||||||
\(921\) | −20.3066 | − | 38.9067i | −0.669124 | − | 1.28202i | ||||
\(922\) | − | 17.1662i | − | 0.565340i | ||||||
\(923\) | 19.3616 | 0.637295 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.25252 | 0.304221 | ||||||||
\(926\) | − | 39.1372i | − | 1.28613i | ||||||
\(927\) | 23.1414 | + | 16.1300i | 0.760064 | + | 0.529779i | ||||
\(928\) | 3.40414 | 0.111747 | ||||||||
\(929\) | 59.7337 | 1.95980 | 0.979899 | − | 0.199493i | \(-0.0639296\pi\) | ||||
0.979899 | + | 0.199493i | \(0.0639296\pi\) | |||||||
\(930\) | −5.92340 | + | 3.09160i | −0.194236 | + | 0.101377i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 22.7275i | − | 0.744464i | ||||||
\(933\) | 4.69849 | − | 2.45228i | 0.153822 | − | 0.0802840i | ||||
\(934\) | − | 5.33074i | − | 0.174427i | ||||||
\(935\) | − | 38.3515i | − | 1.25423i | ||||||
\(936\) | −7.50662 | + | 10.7696i | −0.245362 | + | 0.352016i | ||||
\(937\) | 1.86949i | 0.0610737i | 0.999534 | + | 0.0305369i | \(0.00972170\pi\) | ||||
−0.999534 | + | 0.0305369i | \(0.990278\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.9714 | + | 49.7604i | 0.847545 | + | 1.62387i | ||||
\(940\) | −7.51483 | −0.245107 | ||||||||
\(941\) | −29.6514 | −0.966608 | −0.483304 | − | 0.875453i | \(-0.660563\pi\) | ||||
−0.483304 | + | 0.875453i | \(0.660563\pi\) | |||||||
\(942\) | 13.2898 | − | 6.93636i | 0.433007 | − | 0.225999i | ||||
\(943\) | − | 34.9000i | − | 1.13650i | ||||||
\(944\) | −6.00852 | −0.195561 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.12206 | −0.264071 | ||||||||
\(947\) | − | 3.19911i | − | 0.103957i | −0.998648 | − | 0.0519785i | \(-0.983447\pi\) | ||
0.998648 | − | 0.0519785i | \(-0.0165527\pi\) | |||||||
\(948\) | 7.48188 | − | 3.90501i | 0.243000 | − | 0.126829i | ||||
\(949\) | 46.8512 | 1.52086 | ||||||||
\(950\) | 4.64816 | 0.150806 | ||||||||
\(951\) | 10.3346 | + | 19.8008i | 0.335123 | + | 0.642085i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.78715i | 0.252250i | 0.992014 | + | 0.126125i | \(0.0402541\pi\) | ||||
−0.992014 | + | 0.126125i | \(0.959746\pi\) | |||||||
\(954\) | −8.04121 | + | 11.5366i | −0.260344 | + | 0.373510i | ||||
\(955\) | − | 18.3911i | − | 0.595122i | ||||||
\(956\) | 5.34353i | 0.172822i | ||||||||
\(957\) | −28.6675 | + | 14.9624i | −0.926688 | + | 0.483666i | ||||
\(958\) | 6.57119i | 0.212305i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.53549 | + | 0.801418i | −0.0495577 | + | 0.0258656i | ||||
\(961\) | 16.1185 | 0.519951 | ||||||||
\(962\) | 40.4878 | 1.30538 | ||||||||
\(963\) | −13.0755 | − | 9.11388i | −0.421353 | − | 0.293691i | ||||
\(964\) | − | 14.8146i | − | 0.477146i | ||||||
\(965\) | −23.3665 | −0.752193 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.08407 | 0.131335 | 0.0656674 | − | 0.997842i | \(-0.479082\pi\) | ||||
0.0656674 | + | 0.997842i | \(0.479082\pi\) | |||||||
\(968\) | 19.0794i | 0.613234i | ||||||||
\(969\) | 26.0488 | + | 49.9086i | 0.836808 | + | 1.60330i | ||||
\(970\) | 2.60272 | 0.0835684 | ||||||||
\(971\) | −0.634482 | −0.0203615 | −0.0101808 | − | 0.999948i | \(-0.503241\pi\) | ||||
−0.0101808 | + | 0.999948i | \(0.503241\pi\) | |||||||
\(972\) | −11.5493 | − | 10.4697i | −0.370443 | − | 0.335816i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 26.0143i | 0.833552i | ||||||||
\(975\) | 3.50690 | + | 6.71910i | 0.112311 | + | 0.215183i | ||||
\(976\) | 6.75039i | 0.216075i | ||||||||
\(977\) | − | 13.8771i | − | 0.443967i | −0.975050 | − | 0.221983i | \(-0.928747\pi\) | ||
0.975050 | − | 0.221983i | \(-0.0712531\pi\) | |||||||
\(978\) | −15.3530 | − | 29.4158i | −0.490933 | − | 0.940613i | ||||
\(979\) | − | 2.88178i | − | 0.0921020i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.9430 | + | 35.7853i | −0.796370 | + | 1.14254i | ||||
\(982\) | 30.2128 | 0.964131 | ||||||||
\(983\) | 36.3583 | 1.15965 | 0.579825 | − | 0.814741i | \(-0.303121\pi\) | ||||
0.579825 | + | 0.814741i | \(0.303121\pi\) | |||||||
\(984\) | −3.49832 | − | 6.70267i | −0.111522 | − | 0.213673i | ||||
\(985\) | − | 6.30178i | − | 0.200791i | ||||||
\(986\) | 23.8043 | 0.758083 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.3397 | 0.647093 | ||||||||
\(989\) | 11.8401i | 0.376494i | ||||||||
\(990\) | 9.40838 | − | 13.4980i | 0.299018 | − | 0.428995i | ||||
\(991\) | 12.3858 | 0.393449 | 0.196725 | − | 0.980459i | \(-0.436969\pi\) | ||||
0.196725 | + | 0.980459i | \(0.436969\pi\) | |||||||
\(992\) | −3.85766 | −0.122481 | ||||||||
\(993\) | −52.9574 | + | 27.6401i | −1.68055 | + | 0.877131i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 11.0277i | − | 0.349602i | ||||||
\(996\) | 14.1682 | − | 7.39483i | 0.448938 | − | 0.234314i | ||||
\(997\) | 26.3408i | 0.834221i | 0.908856 | + | 0.417111i | \(0.136957\pi\) | ||||
−0.908856 | + | 0.417111i | \(0.863043\pi\) | |||||||
\(998\) | − | 9.86296i | − | 0.312207i | ||||||
\(999\) | −6.12214 | + | 47.6861i | −0.193696 | + | 1.50872i |
(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 | 1470.2.b.c.881.11 | yes | 16 | |
3.2 | odd | 2 | 1470.2.b.d.881.6 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.b.d.881.14 | yes | 16 | ||
21.20 | even | 2 | inner | 1470.2.b.c.881.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.b.c.881.3 | ✓ | 16 | 21.20 | even | 2 | inner | |
1470.2.b.c.881.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1470.2.b.d.881.6 | yes | 16 | 3.2 | odd | 2 | ||
1470.2.b.d.881.14 | yes | 16 | 7.6 | odd | 2 |