Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(844,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.844");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.d (of order \(2\), degree \(1\), not 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: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 844.5 | ||
Root | \(0.403032 + 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.844 |
Dual form | 845.2.d.b.844.6 |
$q$-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 \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.67513 | 1.89160 | 0.945802 | − | 0.324745i | \(-0.105279\pi\) | ||||
0.945802 | + | 0.324745i | \(0.105279\pi\) | |||||||
\(3\) | − | 0.481194i | − | 0.277818i | −0.990305 | − | 0.138909i | \(-0.955641\pi\) | ||
0.990305 | − | 0.138909i | \(-0.0443595\pi\) | |||||||
\(4\) | 5.15633 | 2.57816 | ||||||||
\(5\) | −1.48119 | + | 1.67513i | −0.662410 | + | 0.749141i | ||||
\(6\) | − | 1.28726i | − | 0.525521i | ||||||
\(7\) | −0.806063 | −0.304663 | −0.152332 | − | 0.988329i | \(-0.548678\pi\) | ||||
−0.152332 | + | 0.988329i | \(0.548678\pi\) | |||||||
\(8\) | 8.44358 | 2.98526 | ||||||||
\(9\) | 2.76845 | 0.922817 | ||||||||
\(10\) | −3.96239 | + | 4.48119i | −1.25302 | + | 1.41708i | ||||
\(11\) | 3.67513i | 1.10809i | 0.832486 | + | 0.554047i | \(0.186917\pi\) | ||||
−0.832486 | + | 0.554047i | \(0.813083\pi\) | |||||||
\(12\) | − | 2.48119i | − | 0.716259i | ||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.15633 | −0.576302 | ||||||||
\(15\) | 0.806063 | + | 0.712742i | 0.208125 | + | 0.184029i | ||||
\(16\) | 12.2750 | 3.06876 | ||||||||
\(17\) | − | 1.35026i | − | 0.327487i | −0.986503 | − | 0.163743i | \(-0.947643\pi\) | ||
0.986503 | − | 0.163743i | \(-0.0523569\pi\) | |||||||
\(18\) | 7.40597 | 1.74560 | ||||||||
\(19\) | 1.67513i | 0.384301i | 0.981365 | + | 0.192151i | \(0.0615462\pi\) | ||||
−0.981365 | + | 0.192151i | \(0.938454\pi\) | |||||||
\(20\) | −7.63752 | + | 8.63752i | −1.70780 | + | 1.93141i | ||||
\(21\) | 0.387873i | 0.0846409i | ||||||||
\(22\) | 9.83146i | 2.09607i | ||||||||
\(23\) | − | 6.48119i | − | 1.35142i | −0.737166 | − | 0.675711i | \(-0.763837\pi\) | ||
0.737166 | − | 0.675711i | \(-0.236163\pi\) | |||||||
\(24\) | − | 4.06300i | − | 0.829357i | ||||||
\(25\) | −0.612127 | − | 4.96239i | −0.122425 | − | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.77575i | − | 0.534193i | ||||||
\(28\) | −4.15633 | −0.785472 | ||||||||
\(29\) | −2.41819 | −0.449047 | −0.224523 | − | 0.974469i | \(-0.572083\pi\) | ||||
−0.224523 | + | 0.974469i | \(0.572083\pi\) | |||||||
\(30\) | 2.15633 | + | 1.90668i | 0.393689 | + | 0.348110i | ||||
\(31\) | − | 5.28726i | − | 0.949620i | −0.880088 | − | 0.474810i | \(-0.842517\pi\) | ||
0.880088 | − | 0.474810i | \(-0.157483\pi\) | |||||||
\(32\) | 15.9502 | 2.81962 | ||||||||
\(33\) | 1.76845 | 0.307848 | ||||||||
\(34\) | − | 3.61213i | − | 0.619475i | ||||||
\(35\) | 1.19394 | − | 1.35026i | 0.201812 | − | 0.228236i | ||||
\(36\) | 14.2750 | 2.37917 | ||||||||
\(37\) | −3.76845 | −0.619530 | −0.309765 | − | 0.950813i | \(-0.600250\pi\) | ||||
−0.309765 | + | 0.950813i | \(0.600250\pi\) | |||||||
\(38\) | 4.48119i | 0.726946i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.5066 | + | 14.1441i | −1.97747 | + | 2.23638i | ||||
\(41\) | − | 8.31265i | − | 1.29822i | −0.760695 | − | 0.649109i | \(-0.775142\pi\) | ||
0.760695 | − | 0.649109i | \(-0.224858\pi\) | |||||||
\(42\) | 1.03761i | 0.160107i | ||||||||
\(43\) | 6.79384i | 1.03605i | 0.855365 | + | 0.518026i | \(0.173333\pi\) | ||||
−0.855365 | + | 0.518026i | \(0.826667\pi\) | |||||||
\(44\) | 18.9502i | 2.85685i | ||||||||
\(45\) | −4.10062 | + | 4.63752i | −0.611284 | + | 0.691321i | ||||
\(46\) | − | 17.3380i | − | 2.55635i | ||||||
\(47\) | −3.19394 | −0.465884 | −0.232942 | − | 0.972491i | \(-0.574835\pi\) | ||||
−0.232942 | + | 0.972491i | \(0.574835\pi\) | |||||||
\(48\) | − | 5.90668i | − | 0.852556i | ||||||
\(49\) | −6.35026 | −0.907180 | ||||||||
\(50\) | −1.63752 | − | 13.2750i | −0.231580 | − | 1.87737i | ||||
\(51\) | −0.649738 | −0.0909816 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.73813i | 0.788193i | 0.919069 | + | 0.394097i | \(0.128943\pi\) | ||||
−0.919069 | + | 0.394097i | \(0.871057\pi\) | |||||||
\(54\) | − | 7.42548i | − | 1.01048i | ||||||
\(55\) | −6.15633 | − | 5.44358i | −0.830119 | − | 0.734013i | ||||
\(56\) | −6.80606 | −0.909498 | ||||||||
\(57\) | 0.806063 | 0.106766 | ||||||||
\(58\) | −6.46898 | −0.849418 | ||||||||
\(59\) | 5.98778i | 0.779543i | 0.920912 | + | 0.389771i | \(0.127446\pi\) | ||||
−0.920912 | + | 0.389771i | \(0.872554\pi\) | |||||||
\(60\) | 4.15633 | + | 3.67513i | 0.536579 | + | 0.474457i | ||||
\(61\) | −1.76845 | −0.226427 | −0.113214 | − | 0.993571i | \(-0.536114\pi\) | ||||
−0.113214 | + | 0.993571i | \(0.536114\pi\) | |||||||
\(62\) | − | 14.1441i | − | 1.79630i | ||||||
\(63\) | −2.23155 | −0.281149 | ||||||||
\(64\) | 18.1187 | 2.26484 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.73084 | 0.582326 | ||||||||
\(67\) | 9.89446 | 1.20880 | 0.604400 | − | 0.796681i | \(-0.293413\pi\) | ||||
0.604400 | + | 0.796681i | \(0.293413\pi\) | |||||||
\(68\) | − | 6.96239i | − | 0.844314i | ||||||
\(69\) | −3.11871 | −0.375449 | ||||||||
\(70\) | 3.19394 | − | 3.61213i | 0.381748 | − | 0.431732i | ||||
\(71\) | 8.56230i | 1.01616i | 0.861311 | + | 0.508079i | \(0.169644\pi\) | ||||
−0.861311 | + | 0.508079i | \(0.830356\pi\) | |||||||
\(72\) | 23.3757 | 2.75485 | ||||||||
\(73\) | −11.7685 | −1.37739 | −0.688697 | − | 0.725050i | \(-0.741817\pi\) | ||||
−0.688697 | + | 0.725050i | \(0.741817\pi\) | |||||||
\(74\) | −10.0811 | −1.17190 | ||||||||
\(75\) | −2.38787 | + | 0.294552i | −0.275728 | + | 0.0340119i | ||||
\(76\) | 8.63752i | 0.990791i | ||||||||
\(77\) | − | 2.96239i | − | 0.337596i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26187 | 0.254480 | 0.127240 | − | 0.991872i | \(-0.459388\pi\) | ||||
0.127240 | + | 0.991872i | \(0.459388\pi\) | |||||||
\(80\) | −18.1817 | + | 20.5623i | −2.03278 | + | 2.29893i | ||||
\(81\) | 6.96968 | 0.774409 | ||||||||
\(82\) | − | 22.2374i | − | 2.45571i | ||||||
\(83\) | −3.84367 | −0.421898 | −0.210949 | − | 0.977497i | \(-0.567655\pi\) | ||||
−0.210949 | + | 0.977497i | \(0.567655\pi\) | |||||||
\(84\) | 2.00000i | 0.218218i | ||||||||
\(85\) | 2.26187 | + | 2.00000i | 0.245334 | + | 0.216930i | ||||
\(86\) | 18.1744i | 1.95980i | ||||||||
\(87\) | 1.16362i | 0.124753i | ||||||||
\(88\) | 31.0313i | 3.30794i | ||||||||
\(89\) | 2.77575i | 0.294229i | 0.989120 | + | 0.147114i | \(0.0469985\pi\) | ||||
−0.989120 | + | 0.147114i | \(0.953001\pi\) | |||||||
\(90\) | −10.9697 | + | 12.4060i | −1.15631 | + | 1.30770i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 33.4191i | − | 3.48419i | ||||||
\(93\) | −2.54420 | −0.263821 | ||||||||
\(94\) | −8.54420 | −0.881267 | ||||||||
\(95\) | −2.80606 | − | 2.48119i | −0.287896 | − | 0.254565i | ||||
\(96\) | − | 7.67513i | − | 0.783340i | ||||||
\(97\) | −1.87399 | −0.190275 | −0.0951375 | − | 0.995464i | \(-0.530329\pi\) | ||||
−0.0951375 | + | 0.995464i | \(0.530329\pi\) | |||||||
\(98\) | −16.9878 | −1.71603 | ||||||||
\(99\) | 10.1744i | 1.02257i | ||||||||
\(100\) | −3.15633 | − | 25.5877i | −0.315633 | − | 2.55877i | ||||
\(101\) | −10.4993 | −1.04472 | −0.522359 | − | 0.852725i | \(-0.674948\pi\) | ||||
−0.522359 | + | 0.852725i | \(0.674948\pi\) | |||||||
\(102\) | −1.73813 | −0.172101 | ||||||||
\(103\) | − | 15.3684i | − | 1.51429i | −0.653247 | − | 0.757145i | \(-0.726594\pi\) | ||
0.653247 | − | 0.757145i | \(-0.273406\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.649738 | − | 0.574515i | −0.0634080 | − | 0.0560670i | ||||
\(106\) | 15.3503i | 1.49095i | ||||||||
\(107\) | − | 11.1309i | − | 1.07607i | −0.842923 | − | 0.538034i | \(-0.819167\pi\) | ||
0.842923 | − | 0.538034i | \(-0.180833\pi\) | |||||||
\(108\) | − | 14.3127i | − | 1.37724i | ||||||
\(109\) | − | 9.58769i | − | 0.918334i | −0.888350 | − | 0.459167i | \(-0.848148\pi\) | ||
0.888350 | − | 0.459167i | \(-0.151852\pi\) | |||||||
\(110\) | −16.4690 | − | 14.5623i | −1.57026 | − | 1.38846i | ||||
\(111\) | 1.81336i | 0.172116i | ||||||||
\(112\) | −9.89446 | −0.934939 | ||||||||
\(113\) | 0.574515i | 0.0540459i | 0.999635 | + | 0.0270229i | \(0.00860271\pi\) | ||||
−0.999635 | + | 0.0270229i | \(0.991397\pi\) | |||||||
\(114\) | 2.15633 | 0.201958 | ||||||||
\(115\) | 10.8568 | + | 9.59991i | 1.01241 | + | 0.895196i | ||||
\(116\) | −12.4690 | −1.15772 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.0181i | 1.47459i | ||||||||
\(119\) | 1.08840i | 0.0997732i | ||||||||
\(120\) | 6.80606 | + | 6.01810i | 0.621306 | + | 0.549375i | ||||
\(121\) | −2.50659 | −0.227872 | ||||||||
\(122\) | −4.73084 | −0.428310 | ||||||||
\(123\) | −4.00000 | −0.360668 | ||||||||
\(124\) | − | 27.2628i | − | 2.44827i | ||||||
\(125\) | 9.21933 | + | 6.32487i | 0.824602 | + | 0.565713i | ||||
\(126\) | −5.96968 | −0.531822 | ||||||||
\(127\) | − | 4.29455i | − | 0.381080i | −0.981679 | − | 0.190540i | \(-0.938976\pi\) | ||
0.981679 | − | 0.190540i | \(-0.0610239\pi\) | |||||||
\(128\) | 16.5696 | 1.46456 | ||||||||
\(129\) | 3.26916 | 0.287833 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.836381 | −0.0730749 | −0.0365375 | − | 0.999332i | \(-0.511633\pi\) | ||||
−0.0365375 | + | 0.999332i | \(0.511633\pi\) | |||||||
\(132\) | 9.11871 | 0.793682 | ||||||||
\(133\) | − | 1.35026i | − | 0.117083i | ||||||
\(134\) | 26.4690 | 2.28657 | ||||||||
\(135\) | 4.64974 | + | 4.11142i | 0.400186 | + | 0.353855i | ||||
\(136\) | − | 11.4010i | − | 0.977632i | ||||||
\(137\) | 14.9380 | 1.27624 | 0.638118 | − | 0.769939i | \(-0.279713\pi\) | ||||
0.638118 | + | 0.769939i | \(0.279713\pi\) | |||||||
\(138\) | −8.34297 | −0.710201 | ||||||||
\(139\) | 8.43866 | 0.715758 | 0.357879 | − | 0.933768i | \(-0.383500\pi\) | ||||
0.357879 | + | 0.933768i | \(0.383500\pi\) | |||||||
\(140\) | 6.15633 | − | 6.96239i | 0.520304 | − | 0.588429i | ||||
\(141\) | 1.53690i | 0.129431i | ||||||||
\(142\) | 22.9053i | 1.92217i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 33.9829 | 2.83190 | ||||||||
\(145\) | 3.58181 | − | 4.05079i | 0.297453 | − | 0.336399i | ||||
\(146\) | −31.4821 | −2.60548 | ||||||||
\(147\) | 3.05571i | 0.252031i | ||||||||
\(148\) | −19.4314 | −1.59725 | ||||||||
\(149\) | 11.3503i | 0.929850i | 0.885350 | + | 0.464925i | \(0.153919\pi\) | ||||
−0.885350 | + | 0.464925i | \(0.846081\pi\) | |||||||
\(150\) | −6.38787 | + | 0.787965i | −0.521568 | + | 0.0643371i | ||||
\(151\) | − | 13.9878i | − | 1.13831i | −0.822230 | − | 0.569155i | \(-0.807271\pi\) | ||
0.822230 | − | 0.569155i | \(-0.192729\pi\) | |||||||
\(152\) | 14.1441i | 1.14724i | ||||||||
\(153\) | − | 3.73813i | − | 0.302210i | ||||||
\(154\) | − | 7.92478i | − | 0.638597i | ||||||
\(155\) | 8.85685 | + | 7.83146i | 0.711399 | + | 0.629038i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.77575i | − | 0.221529i | −0.993847 | − | 0.110764i | \(-0.964670\pi\) | ||
0.993847 | − | 0.110764i | \(-0.0353299\pi\) | |||||||
\(158\) | 6.05079 | 0.481375 | ||||||||
\(159\) | 2.76116 | 0.218974 | ||||||||
\(160\) | −23.6253 | + | 26.7186i | −1.86774 | + | 2.11229i | ||||
\(161\) | 5.22425i | 0.411729i | ||||||||
\(162\) | 18.6448 | 1.46487 | ||||||||
\(163\) | 2.23155 | 0.174788 | 0.0873942 | − | 0.996174i | \(-0.472146\pi\) | ||||
0.0873942 | + | 0.996174i | \(0.472146\pi\) | |||||||
\(164\) | − | 42.8627i | − | 3.34702i | ||||||
\(165\) | −2.61942 | + | 2.96239i | −0.203922 | + | 0.230622i | ||||
\(166\) | −10.2823 | −0.798064 | ||||||||
\(167\) | 15.6932 | 1.21438 | 0.607189 | − | 0.794557i | \(-0.292297\pi\) | ||||
0.607189 | + | 0.794557i | \(0.292297\pi\) | |||||||
\(168\) | 3.27504i | 0.252675i | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.05079 | + | 5.35026i | 0.464074 | + | 0.410346i | ||||
\(171\) | 4.63752i | 0.354640i | ||||||||
\(172\) | 35.0313i | 2.67111i | ||||||||
\(173\) | 25.5877i | 1.94540i | 0.232075 | + | 0.972698i | \(0.425449\pi\) | ||||
−0.232075 | + | 0.972698i | \(0.574551\pi\) | |||||||
\(174\) | 3.11283i | 0.235983i | ||||||||
\(175\) | 0.493413 | + | 4.00000i | 0.0372985 | + | 0.302372i | ||||
\(176\) | 45.1124i | 3.40047i | ||||||||
\(177\) | 2.88129 | 0.216571 | ||||||||
\(178\) | 7.42548i | 0.556564i | ||||||||
\(179\) | 12.1260 | 0.906340 | 0.453170 | − | 0.891424i | \(-0.350293\pi\) | ||||
0.453170 | + | 0.891424i | \(0.350293\pi\) | |||||||
\(180\) | −21.1441 | + | 23.9126i | −1.57599 | + | 1.78234i | ||||
\(181\) | 2.73084 | 0.202982 | 0.101491 | − | 0.994836i | \(-0.467639\pi\) | ||||
0.101491 | + | 0.994836i | \(0.467639\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.850969i | 0.0629054i | ||||||||
\(184\) | − | 54.7245i | − | 4.03434i | ||||||
\(185\) | 5.58181 | − | 6.31265i | 0.410383 | − | 0.464115i | ||||
\(186\) | −6.80606 | −0.499045 | ||||||||
\(187\) | 4.96239 | 0.362886 | ||||||||
\(188\) | −16.4690 | −1.20112 | ||||||||
\(189\) | 2.23743i | 0.162749i | ||||||||
\(190\) | −7.50659 | − | 6.63752i | −0.544585 | − | 0.481536i | ||||
\(191\) | 20.6253 | 1.49239 | 0.746197 | − | 0.665725i | \(-0.231878\pi\) | ||||
0.746197 | + | 0.665725i | \(0.231878\pi\) | |||||||
\(192\) | − | 8.71862i | − | 0.629212i | ||||||
\(193\) | −21.7889 | −1.56840 | −0.784200 | − | 0.620508i | \(-0.786927\pi\) | ||||
−0.784200 | + | 0.620508i | \(0.786927\pi\) | |||||||
\(194\) | −5.01317 | −0.359925 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −32.7440 | −2.33886 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 27.2179i | 1.93429i | ||||||||
\(199\) | −16.7513 | −1.18747 | −0.593734 | − | 0.804661i | \(-0.702347\pi\) | ||||
−0.593734 | + | 0.804661i | \(0.702347\pi\) | |||||||
\(200\) | −5.16854 | − | 41.9003i | −0.365471 | − | 2.96280i | ||||
\(201\) | − | 4.76116i | − | 0.335826i | ||||||
\(202\) | −28.0870 | −1.97619 | ||||||||
\(203\) | 1.94921 | 0.136808 | ||||||||
\(204\) | −3.35026 | −0.234565 | ||||||||
\(205\) | 13.9248 | + | 12.3127i | 0.972549 | + | 0.859953i | ||||
\(206\) | − | 41.1124i | − | 2.86443i | ||||||
\(207\) | − | 17.9429i | − | 1.24712i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.15633 | −0.425842 | ||||||||
\(210\) | −1.73813 | − | 1.53690i | −0.119943 | − | 0.106056i | ||||
\(211\) | −4.90175 | −0.337451 | −0.168725 | − | 0.985663i | \(-0.553965\pi\) | ||||
−0.168725 | + | 0.985663i | \(0.553965\pi\) | |||||||
\(212\) | 29.5877i | 2.03209i | ||||||||
\(213\) | 4.12013 | 0.282307 | ||||||||
\(214\) | − | 29.7767i | − | 2.03549i | ||||||
\(215\) | −11.3806 | − | 10.0630i | −0.776149 | − | 0.686291i | ||||
\(216\) | − | 23.4372i | − | 1.59470i | ||||||
\(217\) | 4.26187i | 0.289314i | ||||||||
\(218\) | − | 25.6483i | − | 1.73712i | ||||||
\(219\) | 5.66291i | 0.382664i | ||||||||
\(220\) | −31.7440 | − | 28.0689i | −2.14018 | − | 1.89240i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.85097i | 0.325576i | ||||||||
\(223\) | −24.9076 | −1.66794 | −0.833969 | − | 0.551811i | \(-0.813937\pi\) | ||||
−0.833969 | + | 0.551811i | \(0.813937\pi\) | |||||||
\(224\) | −12.8568 | −0.859034 | ||||||||
\(225\) | −1.69464 | − | 13.7381i | −0.112976 | − | 0.915876i | ||||
\(226\) | 1.53690i | 0.102233i | ||||||||
\(227\) | 9.95509 | 0.660743 | 0.330371 | − | 0.943851i | \(-0.392826\pi\) | ||||
0.330371 | + | 0.943851i | \(0.392826\pi\) | |||||||
\(228\) | 4.15633 | 0.275259 | ||||||||
\(229\) | 5.35026i | 0.353555i | 0.984251 | + | 0.176778i | \(0.0565673\pi\) | ||||
−0.984251 | + | 0.176778i | \(0.943433\pi\) | |||||||
\(230\) | 29.0435 | + | 25.6810i | 1.91507 | + | 1.69336i | ||||
\(231\) | −1.42548 | −0.0937900 | ||||||||
\(232\) | −20.4182 | −1.34052 | ||||||||
\(233\) | 10.7612i | 0.704987i | 0.935814 | + | 0.352493i | \(0.114666\pi\) | ||||
−0.935814 | + | 0.352493i | \(0.885334\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.73084 | − | 5.35026i | 0.308606 | − | 0.349013i | ||||
\(236\) | 30.8749i | 2.00979i | ||||||||
\(237\) | − | 1.08840i | − | 0.0706990i | ||||||
\(238\) | 2.91160i | 0.188731i | ||||||||
\(239\) | 11.8618i | 0.767274i | 0.923484 | + | 0.383637i | \(0.125329\pi\) | ||||
−0.923484 | + | 0.383637i | \(0.874671\pi\) | |||||||
\(240\) | 9.89446 | + | 8.74894i | 0.638685 | + | 0.564742i | ||||
\(241\) | 28.6253i | 1.84392i | 0.387288 | + | 0.921959i | \(0.373412\pi\) | ||||
−0.387288 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(242\) | −6.70545 | −0.431043 | ||||||||
\(243\) | − | 11.6810i | − | 0.749337i | ||||||
\(244\) | −9.11871 | −0.583766 | ||||||||
\(245\) | 9.40597 | − | 10.6375i | 0.600925 | − | 0.679606i | ||||
\(246\) | −10.7005 | −0.682240 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 44.6434i | − | 2.83486i | ||||||
\(249\) | 1.84955i | 0.117211i | ||||||||
\(250\) | 24.6629 | + | 16.9199i | 1.55982 | + | 1.07011i | ||||
\(251\) | 19.3865 | 1.22366 | 0.611831 | − | 0.790988i | \(-0.290433\pi\) | ||||
0.611831 | + | 0.790988i | \(0.290433\pi\) | |||||||
\(252\) | −11.5066 | −0.724847 | ||||||||
\(253\) | 23.8192 | 1.49750 | ||||||||
\(254\) | − | 11.4885i | − | 0.720852i | ||||||
\(255\) | 0.962389 | − | 1.08840i | 0.0602671 | − | 0.0681580i | ||||
\(256\) | 8.08840 | 0.505525 | ||||||||
\(257\) | 22.8627i | 1.42614i | 0.701094 | + | 0.713069i | \(0.252695\pi\) | ||||
−0.701094 | + | 0.713069i | \(0.747305\pi\) | |||||||
\(258\) | 8.74543 | 0.544467 | ||||||||
\(259\) | 3.03761 | 0.188748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.69464 | −0.414388 | ||||||||
\(262\) | −2.23743 | −0.138229 | ||||||||
\(263\) | 21.8822i | 1.34932i | 0.738130 | + | 0.674658i | \(0.235709\pi\) | ||||
−0.738130 | + | 0.674658i | \(0.764291\pi\) | |||||||
\(264\) | 14.9321 | 0.919005 | ||||||||
\(265\) | −9.61213 | − | 8.49929i | −0.590468 | − | 0.522107i | ||||
\(266\) | − | 3.61213i | − | 0.221474i | ||||||
\(267\) | 1.33567 | 0.0817419 | ||||||||
\(268\) | 51.0191 | 3.11648 | ||||||||
\(269\) | −22.7513 | −1.38717 | −0.693586 | − | 0.720374i | \(-0.743970\pi\) | ||||
−0.693586 | + | 0.720374i | \(0.743970\pi\) | |||||||
\(270\) | 12.4387 | + | 10.9986i | 0.756993 | + | 0.669353i | ||||
\(271\) | − | 0.123638i | − | 0.00751049i | −0.999993 | − | 0.00375525i | \(-0.998805\pi\) | ||
0.999993 | − | 0.00375525i | \(-0.00119534\pi\) | |||||||
\(272\) | − | 16.5745i | − | 1.00498i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.9610 | 2.41413 | ||||||||
\(275\) | 18.2374 | − | 2.24965i | 1.09976 | − | 0.135659i | ||||
\(276\) | −16.0811 | −0.967969 | ||||||||
\(277\) | − | 15.3503i | − | 0.922308i | −0.887320 | − | 0.461154i | \(-0.847436\pi\) | ||
0.887320 | − | 0.461154i | \(-0.152564\pi\) | |||||||
\(278\) | 22.5745 | 1.35393 | ||||||||
\(279\) | − | 14.6375i | − | 0.876325i | ||||||
\(280\) | 10.0811 | − | 11.4010i | 0.602461 | − | 0.681343i | ||||
\(281\) | − | 13.9248i | − | 0.830683i | −0.909666 | − | 0.415341i | \(-0.863662\pi\) | ||
0.909666 | − | 0.415341i | \(-0.136338\pi\) | |||||||
\(282\) | 4.11142i | 0.244831i | ||||||||
\(283\) | − | 20.3815i | − | 1.21156i | −0.795634 | − | 0.605778i | \(-0.792862\pi\) | ||
0.795634 | − | 0.605778i | \(-0.207138\pi\) | |||||||
\(284\) | 44.1500i | 2.61982i | ||||||||
\(285\) | −1.19394 | + | 1.35026i | −0.0707227 | + | 0.0799826i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.70052i | 0.395519i | ||||||||
\(288\) | 44.1573 | 2.60199 | ||||||||
\(289\) | 15.1768 | 0.892753 | ||||||||
\(290\) | 9.58181 | − | 10.8364i | 0.562663 | − | 0.636334i | ||||
\(291\) | 0.901754i | 0.0528618i | ||||||||
\(292\) | −60.6820 | −3.55114 | ||||||||
\(293\) | 5.38058 | 0.314337 | 0.157168 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157168 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(294\) | 8.17442i | 0.476742i | ||||||||
\(295\) | −10.0303 | − | 8.86907i | −0.583988 | − | 0.516377i | ||||
\(296\) | −31.8192 | −1.84946 | ||||||||
\(297\) | 10.2012 | 0.591935 | ||||||||
\(298\) | 30.3634i | 1.75891i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.3127 | + | 1.51881i | −0.710871 | + | 0.0876883i | ||||
\(301\) | − | 5.47627i | − | 0.315647i | ||||||
\(302\) | − | 37.4191i | − | 2.15323i | ||||||
\(303\) | 5.05220i | 0.290241i | ||||||||
\(304\) | 20.5623i | 1.17933i | ||||||||
\(305\) | 2.61942 | − | 2.96239i | 0.149988 | − | 0.169626i | ||||
\(306\) | − | 10.0000i | − | 0.571662i | ||||||
\(307\) | 19.1695 | 1.09406 | 0.547031 | − | 0.837113i | \(-0.315758\pi\) | ||||
0.547031 | + | 0.837113i | \(0.315758\pi\) | |||||||
\(308\) | − | 15.2750i | − | 0.870376i | ||||||
\(309\) | −7.39517 | −0.420696 | ||||||||
\(310\) | 23.6932 | + | 20.9502i | 1.34568 | + | 1.18989i | ||||
\(311\) | 25.2506 | 1.43183 | 0.715915 | − | 0.698187i | \(-0.246010\pi\) | ||||
0.715915 | + | 0.698187i | \(0.246010\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.81194i | 0.158940i | 0.996837 | + | 0.0794702i | \(0.0253229\pi\) | ||||
−0.996837 | + | 0.0794702i | \(0.974677\pi\) | |||||||
\(314\) | − | 7.42548i | − | 0.419044i | ||||||
\(315\) | 3.30536 | − | 3.73813i | 0.186236 | − | 0.210620i | ||||
\(316\) | 11.6629 | 0.656090 | ||||||||
\(317\) | −23.7685 | −1.33497 | −0.667485 | − | 0.744624i | \(-0.732629\pi\) | ||||
−0.667485 | + | 0.744624i | \(0.732629\pi\) | |||||||
\(318\) | 7.38646 | 0.414212 | ||||||||
\(319\) | − | 8.88717i | − | 0.497586i | ||||||
\(320\) | −26.8373 | + | 30.3512i | −1.50025 | + | 1.69668i | ||||
\(321\) | −5.35614 | −0.298951 | ||||||||
\(322\) | 13.9756i | 0.778828i | ||||||||
\(323\) | 2.26187 | 0.125854 | ||||||||
\(324\) | 35.9380 | 1.99655 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.96968 | 0.330630 | ||||||||
\(327\) | −4.61354 | −0.255129 | ||||||||
\(328\) | − | 70.1886i | − | 3.87551i | ||||||
\(329\) | 2.57452 | 0.141938 | ||||||||
\(330\) | −7.00729 | + | 7.92478i | −0.385739 | + | 0.436245i | ||||
\(331\) | − | 11.8011i | − | 0.648649i | −0.945946 | − | 0.324325i | \(-0.894863\pi\) | ||
0.945946 | − | 0.324325i | \(-0.105137\pi\) | |||||||
\(332\) | −19.8192 | −1.08772 | ||||||||
\(333\) | −10.4328 | −0.571713 | ||||||||
\(334\) | 41.9814 | 2.29712 | ||||||||
\(335\) | −14.6556 | + | 16.5745i | −0.800722 | + | 0.905563i | ||||
\(336\) | 4.76116i | 0.259742i | ||||||||
\(337\) | 16.1114i | 0.877645i | 0.898574 | + | 0.438822i | \(0.144604\pi\) | ||||
−0.898574 | + | 0.438822i | \(0.855396\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.276454 | 0.0150149 | ||||||||
\(340\) | 11.6629 | + | 10.3127i | 0.632510 | + | 0.559282i | ||||
\(341\) | 19.4314 | 1.05227 | ||||||||
\(342\) | 12.4060i | 0.670838i | ||||||||
\(343\) | 10.7612 | 0.581048 | ||||||||
\(344\) | 57.3644i | 3.09288i | ||||||||
\(345\) | 4.61942 | − | 5.22425i | 0.248701 | − | 0.281264i | ||||
\(346\) | 68.4504i | 3.67992i | ||||||||
\(347\) | − | 27.4944i | − | 1.47598i | −0.674814 | − | 0.737988i | \(-0.735776\pi\) | ||
0.674814 | − | 0.737988i | \(-0.264224\pi\) | |||||||
\(348\) | 6.00000i | 0.321634i | ||||||||
\(349\) | − | 17.6023i | − | 0.942228i | −0.882072 | − | 0.471114i | \(-0.843852\pi\) | ||
0.882072 | − | 0.471114i | \(-0.156148\pi\) | |||||||
\(350\) | 1.31994 | + | 10.7005i | 0.0705540 | + | 0.571967i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 58.6190i | 3.12440i | ||||||||
\(353\) | −15.7685 | −0.839270 | −0.419635 | − | 0.907693i | \(-0.637842\pi\) | ||||
−0.419635 | + | 0.907693i | \(0.637842\pi\) | |||||||
\(354\) | 7.70782 | 0.409666 | ||||||||
\(355\) | −14.3430 | − | 12.6824i | −0.761246 | − | 0.673113i | ||||
\(356\) | 14.3127i | 0.758569i | ||||||||
\(357\) | 0.523730 | 0.0277187 | ||||||||
\(358\) | 32.4387 | 1.71444 | ||||||||
\(359\) | − | 14.8242i | − | 0.782389i | −0.920308 | − | 0.391195i | \(-0.872062\pi\) | ||
0.920308 | − | 0.391195i | \(-0.127938\pi\) | |||||||
\(360\) | −34.6239 | + | 39.1573i | −1.82484 | + | 2.06377i | ||||
\(361\) | 16.1939 | 0.852312 | ||||||||
\(362\) | 7.30536 | 0.383961 | ||||||||
\(363\) | 1.20616i | 0.0633067i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17.4314 | − | 19.7137i | 0.912399 | − | 1.03186i | ||||
\(366\) | 2.27645i | 0.118992i | ||||||||
\(367\) | 27.0313i | 1.41102i | 0.708700 | + | 0.705510i | \(0.249282\pi\) | ||||
−0.708700 | + | 0.705510i | \(0.750718\pi\) | |||||||
\(368\) | − | 79.5569i | − | 4.14719i | ||||||
\(369\) | − | 23.0132i | − | 1.19802i | ||||||
\(370\) | 14.9321 | − | 16.8872i | 0.776281 | − | 0.877922i | ||||
\(371\) | − | 4.62530i | − | 0.240134i | ||||||
\(372\) | −13.1187 | −0.680174 | ||||||||
\(373\) | 12.9525i | 0.670657i | 0.942101 | + | 0.335329i | \(0.108847\pi\) | ||||
−0.942101 | + | 0.335329i | \(0.891153\pi\) | |||||||
\(374\) | 13.2750 | 0.686436 | ||||||||
\(375\) | 3.04349 | − | 4.43629i | 0.157165 | − | 0.229089i | ||||
\(376\) | −26.9683 | −1.39078 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 5.98541i | 0.307856i | ||||||||
\(379\) | 30.2858i | 1.55568i | 0.628463 | + | 0.777840i | \(0.283684\pi\) | ||||
−0.628463 | + | 0.777840i | \(0.716316\pi\) | |||||||
\(380\) | −14.4690 | − | 12.7938i | −0.742243 | − | 0.656310i | ||||
\(381\) | −2.06651 | −0.105871 | ||||||||
\(382\) | 55.1754 | 2.82302 | ||||||||
\(383\) | 21.0943 | 1.07787 | 0.538934 | − | 0.842348i | \(-0.318827\pi\) | ||||
0.538934 | + | 0.842348i | \(0.318827\pi\) | |||||||
\(384\) | − | 7.97319i | − | 0.406880i | ||||||
\(385\) | 4.96239 | + | 4.38787i | 0.252907 | + | 0.223627i | ||||
\(386\) | −58.2882 | −2.96679 | ||||||||
\(387\) | 18.8084i | 0.956086i | ||||||||
\(388\) | −9.66291 | −0.490560 | ||||||||
\(389\) | −6.77575 | −0.343544 | −0.171772 | − | 0.985137i | \(-0.554949\pi\) | ||||
−0.171772 | + | 0.985137i | \(0.554949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.75131 | −0.442573 | ||||||||
\(392\) | −53.6190 | −2.70817 | ||||||||
\(393\) | 0.402462i | 0.0203015i | ||||||||
\(394\) | 5.35026 | 0.269542 | ||||||||
\(395\) | −3.35026 | + | 3.78892i | −0.168570 | + | 0.190641i | ||||
\(396\) | 52.4626i | 2.63635i | ||||||||
\(397\) | −10.4690 | −0.525423 | −0.262711 | − | 0.964874i | \(-0.584617\pi\) | ||||
−0.262711 | + | 0.964874i | \(0.584617\pi\) | |||||||
\(398\) | −44.8119 | −2.24622 | ||||||||
\(399\) | −0.649738 | −0.0325276 | ||||||||
\(400\) | −7.51388 | − | 60.9135i | −0.375694 | − | 3.04568i | ||||
\(401\) | − | 5.01317i | − | 0.250346i | −0.992135 | − | 0.125173i | \(-0.960051\pi\) | ||
0.992135 | − | 0.125173i | \(-0.0399486\pi\) | |||||||
\(402\) | − | 12.7367i | − | 0.635250i | ||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −54.1378 | −2.69345 | ||||||||
\(405\) | −10.3235 | + | 11.6751i | −0.512977 | + | 0.580142i | ||||
\(406\) | 5.21440 | 0.258787 | ||||||||
\(407\) | − | 13.8496i | − | 0.686497i | ||||||
\(408\) | −5.48612 | −0.271603 | ||||||||
\(409\) | 14.3879i | 0.711435i | 0.934594 | + | 0.355717i | \(0.115763\pi\) | ||||
−0.934594 | + | 0.355717i | \(0.884237\pi\) | |||||||
\(410\) | 37.2506 | + | 32.9380i | 1.83968 | + | 1.62669i | ||||
\(411\) | − | 7.18806i | − | 0.354561i | ||||||
\(412\) | − | 79.2443i | − | 3.90408i | ||||||
\(413\) | − | 4.82653i | − | 0.237498i | ||||||
\(414\) | − | 47.9995i | − | 2.35905i | ||||||
\(415\) | 5.69323 | − | 6.43866i | 0.279470 | − | 0.316061i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 4.06063i | − | 0.198850i | ||||||
\(418\) | −16.4690 | −0.805524 | ||||||||
\(419\) | −17.4617 | −0.853059 | −0.426529 | − | 0.904474i | \(-0.640264\pi\) | ||||
−0.426529 | + | 0.904474i | \(0.640264\pi\) | |||||||
\(420\) | −3.35026 | − | 2.96239i | −0.163476 | − | 0.144550i | ||||
\(421\) | 2.88717i | 0.140712i | 0.997522 | + | 0.0703559i | \(0.0224135\pi\) | ||||
−0.997522 | + | 0.0703559i | \(0.977586\pi\) | |||||||
\(422\) | −13.1128 | −0.638323 | ||||||||
\(423\) | −8.84226 | −0.429925 | ||||||||
\(424\) | 48.4504i | 2.35296i | ||||||||
\(425\) | −6.70052 | + | 0.826531i | −0.325023 | + | 0.0400927i | ||||
\(426\) | 11.0219 | 0.534012 | ||||||||
\(427\) | 1.42548 | 0.0689840 | ||||||||
\(428\) | − | 57.3947i | − | 2.77428i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −30.4445 | − | 26.9199i | −1.46817 | − | 1.29819i | ||||
\(431\) | 0.889535i | 0.0428474i | 0.999770 | + | 0.0214237i | \(0.00681990\pi\) | ||||
−0.999770 | + | 0.0214237i | \(0.993180\pi\) | |||||||
\(432\) | − | 34.0724i | − | 1.63931i | ||||||
\(433\) | 25.2506i | 1.21347i | 0.794906 | + | 0.606733i | \(0.207520\pi\) | ||||
−0.794906 | + | 0.606733i | \(0.792480\pi\) | |||||||
\(434\) | 11.4010i | 0.547268i | ||||||||
\(435\) | −1.94921 | − | 1.72355i | −0.0934577 | − | 0.0826377i | ||||
\(436\) | − | 49.4372i | − | 2.36761i | ||||||
\(437\) | 10.8568 | 0.519354 | ||||||||
\(438\) | 15.1490i | 0.723849i | ||||||||
\(439\) | 28.8119 | 1.37512 | 0.687560 | − | 0.726128i | \(-0.258682\pi\) | ||||
0.687560 | + | 0.726128i | \(0.258682\pi\) | |||||||
\(440\) | −51.9814 | − | 45.9633i | −2.47812 | − | 2.19122i | ||||
\(441\) | −17.5804 | −0.837162 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.9805i | 1.75700i | 0.477746 | + | 0.878498i | \(0.341454\pi\) | ||||
−0.477746 | + | 0.878498i | \(0.658546\pi\) | |||||||
\(444\) | 9.35026i | 0.443744i | ||||||||
\(445\) | −4.64974 | − | 4.11142i | −0.220419 | − | 0.194900i | ||||
\(446\) | −66.6312 | −3.15508 | ||||||||
\(447\) | 5.46168 | 0.258329 | ||||||||
\(448\) | −14.6048 | −0.690013 | ||||||||
\(449\) | − | 12.6859i | − | 0.598686i | −0.954146 | − | 0.299343i | \(-0.903232\pi\) | ||
0.954146 | − | 0.299343i | \(-0.0967675\pi\) | |||||||
\(450\) | −4.53339 | − | 36.7513i | −0.213706 | − | 1.73247i | ||||
\(451\) | 30.5501 | 1.43855 | ||||||||
\(452\) | 2.96239i | 0.139339i | ||||||||
\(453\) | −6.73084 | −0.316242 | ||||||||
\(454\) | 26.6312 | 1.24986 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.80606 | 0.318723 | ||||||||
\(457\) | −25.0494 | −1.17176 | −0.585880 | − | 0.810398i | \(-0.699251\pi\) | ||||
−0.585880 | + | 0.810398i | \(0.699251\pi\) | |||||||
\(458\) | 14.3127i | 0.668786i | ||||||||
\(459\) | −3.74798 | −0.174941 | ||||||||
\(460\) | 55.9814 | + | 49.5002i | 2.61015 | + | 2.30796i | ||||
\(461\) | − | 36.8872i | − | 1.71801i | −0.511970 | − | 0.859003i | \(-0.671084\pi\) | ||
0.511970 | − | 0.859003i | \(-0.328916\pi\) | |||||||
\(462\) | −3.81336 | −0.177413 | ||||||||
\(463\) | −39.0191 | −1.81337 | −0.906685 | − | 0.421809i | \(-0.861395\pi\) | ||||
−0.906685 | + | 0.421809i | \(0.861395\pi\) | |||||||
\(464\) | −29.6834 | −1.37802 | ||||||||
\(465\) | 3.76845 | − | 4.26187i | 0.174758 | − | 0.197639i | ||||
\(466\) | 28.7875i | 1.33356i | ||||||||
\(467\) | 32.7694i | 1.51639i | 0.652029 | + | 0.758194i | \(0.273918\pi\) | ||||
−0.652029 | + | 0.758194i | \(0.726082\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.97556 | −0.368277 | ||||||||
\(470\) | 12.6556 | − | 14.3127i | 0.583760 | − | 0.660193i | ||||
\(471\) | −1.33567 | −0.0615446 | ||||||||
\(472\) | 50.5583i | 2.32714i | ||||||||
\(473\) | −24.9683 | −1.14804 | ||||||||
\(474\) | − | 2.91160i | − | 0.133734i | ||||||
\(475\) | 8.31265 | − | 1.02539i | 0.381411 | − | 0.0470482i | ||||
\(476\) | 5.61213i | 0.257231i | ||||||||
\(477\) | 15.8858i | 0.727359i | ||||||||
\(478\) | 31.7318i | 1.45138i | ||||||||
\(479\) | 16.8749i | 0.771036i | 0.922700 | + | 0.385518i | \(0.125977\pi\) | ||||
−0.922700 | + | 0.385518i | \(0.874023\pi\) | |||||||
\(480\) | 12.8568 | + | 11.3684i | 0.586832 | + | 0.518892i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 76.5764i | 3.48796i | ||||||||
\(483\) | 2.51388 | 0.114386 | ||||||||
\(484\) | −12.9248 | −0.587490 | ||||||||
\(485\) | 2.77575 | − | 3.13918i | 0.126040 | − | 0.142543i | ||||
\(486\) | − | 31.2482i | − | 1.41745i | ||||||
\(487\) | −9.24472 | −0.418918 | −0.209459 | − | 0.977817i | \(-0.567170\pi\) | ||||
−0.209459 | + | 0.977817i | \(0.567170\pi\) | |||||||
\(488\) | −14.9321 | −0.675943 | ||||||||
\(489\) | − | 1.07381i | − | 0.0485593i | ||||||
\(490\) | 25.1622 | − | 28.4568i | 1.13671 | − | 1.28555i | ||||
\(491\) | 25.7499 | 1.16208 | 0.581038 | − | 0.813876i | \(-0.302647\pi\) | ||||
0.581038 | + | 0.813876i | \(0.302647\pi\) | |||||||
\(492\) | −20.6253 | −0.929860 | ||||||||
\(493\) | 3.26519i | 0.147057i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −17.0435 | − | 15.0703i | −0.766048 | − | 0.677360i | ||||
\(496\) | − | 64.9013i | − | 2.91415i | ||||||
\(497\) | − | 6.90175i | − | 0.309586i | ||||||
\(498\) | 4.94780i | 0.221716i | ||||||||
\(499\) | 27.7015i | 1.24009i | 0.784567 | + | 0.620044i | \(0.212885\pi\) | ||||
−0.784567 | + | 0.620044i | \(0.787115\pi\) | |||||||
\(500\) | 47.5379 | + | 32.6131i | 2.12596 | + | 1.45850i | ||||
\(501\) | − | 7.55149i | − | 0.337376i | ||||||
\(502\) | 51.8613 | 2.31468 | ||||||||
\(503\) | 2.35519i | 0.105013i | 0.998621 | + | 0.0525063i | \(0.0167210\pi\) | ||||
−0.998621 | + | 0.0525063i | \(0.983279\pi\) | |||||||
\(504\) | −18.8423 | −0.839301 | ||||||||
\(505\) | 15.5515 | − | 17.5877i | 0.692032 | − | 0.782642i | ||||
\(506\) | 63.7196 | 2.83268 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 22.1441i | − | 0.982486i | ||||||
\(509\) | − | 21.5125i | − | 0.953523i | −0.879033 | − | 0.476762i | \(-0.841810\pi\) | ||
0.879033 | − | 0.476762i | \(-0.158190\pi\) | |||||||
\(510\) | 2.57452 | − | 2.91160i | 0.114001 | − | 0.128928i | ||||
\(511\) | 9.48612 | 0.419641 | ||||||||
\(512\) | −11.5017 | −0.508306 | ||||||||
\(513\) | 4.64974 | 0.205291 | ||||||||
\(514\) | 61.1608i | 2.69769i | ||||||||
\(515\) | 25.7440 | + | 22.7635i | 1.13442 | + | 1.00308i | ||||
\(516\) | 16.8568 | 0.742081 | ||||||||
\(517\) | − | 11.7381i | − | 0.516243i | ||||||
\(518\) | 8.12601 | 0.357036 | ||||||||
\(519\) | 12.3127 | 0.540465 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.7440 | 1.65360 | 0.826798 | − | 0.562499i | \(-0.190160\pi\) | ||||
0.826798 | + | 0.562499i | \(0.190160\pi\) | |||||||
\(522\) | −17.9090 | −0.783858 | ||||||||
\(523\) | 23.7416i | 1.03815i | 0.854729 | + | 0.519075i | \(0.173723\pi\) | ||||
−0.854729 | + | 0.519075i | \(0.826277\pi\) | |||||||
\(524\) | −4.31265 | −0.188399 | ||||||||
\(525\) | 1.92478 | − | 0.237428i | 0.0840042 | − | 0.0103622i | ||||
\(526\) | 58.5379i | 2.55237i | ||||||||
\(527\) | −7.13918 | −0.310988 | ||||||||
\(528\) | 21.7078 | 0.944712 | ||||||||
\(529\) | −19.0059 | −0.826343 | ||||||||
\(530\) | −25.7137 | − | 22.7367i | −1.11693 | − | 0.987620i | ||||
\(531\) | 16.5769i | 0.719376i | ||||||||
\(532\) | − | 6.96239i | − | 0.301858i | ||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.57310 | 0.154623 | ||||||||
\(535\) | 18.6458 | + | 16.4871i | 0.806127 | + | 0.712798i | ||||
\(536\) | 83.5447 | 3.60858 | ||||||||
\(537\) | − | 5.83497i | − | 0.251797i | ||||||
\(538\) | −60.8627 | −2.62398 | ||||||||
\(539\) | − | 23.3380i | − | 1.00524i | ||||||
\(540\) | 23.9756 | + | 21.1998i | 1.03174 | + | 0.912295i | ||||
\(541\) | − | 13.0376i | − | 0.560531i | −0.959923 | − | 0.280265i | \(-0.909578\pi\) | ||
0.959923 | − | 0.280265i | \(-0.0904225\pi\) | |||||||
\(542\) | − | 0.330749i | − | 0.0142069i | ||||||
\(543\) | − | 1.31406i | − | 0.0563919i | ||||||
\(544\) | − | 21.5369i | − | 0.923387i | ||||||
\(545\) | 16.0606 | + | 14.2012i | 0.687962 | + | 0.608314i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.43041i | − | 0.360458i | −0.983625 | − | 0.180229i | \(-0.942316\pi\) | ||
0.983625 | − | 0.180229i | \(-0.0576839\pi\) | |||||||
\(548\) | 77.0249 | 3.29034 | ||||||||
\(549\) | −4.89587 | −0.208951 | ||||||||
\(550\) | 48.7875 | − | 6.01810i | 2.08031 | − | 0.256613i | ||||
\(551\) | − | 4.05079i | − | 0.172569i | ||||||
\(552\) | −26.3331 | −1.12081 | ||||||||
\(553\) | −1.82321 | −0.0775306 | ||||||||
\(554\) | − | 41.0640i | − | 1.74464i | ||||||
\(555\) | −3.03761 | − | 2.68594i | −0.128939 | − | 0.114012i | ||||
\(556\) | 43.5125 | 1.84534 | ||||||||
\(557\) | −13.6932 | −0.580201 | −0.290100 | − | 0.956996i | \(-0.593689\pi\) | ||||
−0.290100 | + | 0.956996i | \(0.593689\pi\) | |||||||
\(558\) | − | 39.1573i | − | 1.65766i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 14.6556 | − | 16.5745i | 0.619313 | − | 0.700401i | ||||
\(561\) | − | 2.38787i | − | 0.100816i | ||||||
\(562\) | − | 37.2506i | − | 1.57132i | ||||||
\(563\) | 8.86907i | 0.373787i | 0.982380 | + | 0.186893i | \(0.0598419\pi\) | ||||
−0.982380 | + | 0.186893i | \(0.940158\pi\) | |||||||
\(564\) | 7.92478i | 0.333693i | ||||||||
\(565\) | −0.962389 | − | 0.850969i | −0.0404880 | − | 0.0358005i | ||||
\(566\) | − | 54.5233i | − | 2.29178i | ||||||
\(567\) | −5.61801 | −0.235934 | ||||||||
\(568\) | 72.2965i | 3.03349i | ||||||||
\(569\) | −32.7816 | −1.37428 | −0.687139 | − | 0.726526i | \(-0.741134\pi\) | ||||
−0.687139 | + | 0.726526i | \(0.741134\pi\) | |||||||
\(570\) | −3.19394 | + | 3.61213i | −0.133779 | + | 0.151295i | ||||
\(571\) | −40.2882 | −1.68601 | −0.843005 | − | 0.537906i | \(-0.819215\pi\) | ||||
−0.843005 | + | 0.537906i | \(0.819215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.92478i | − | 0.414614i | ||||||
\(574\) | 17.9248i | 0.748166i | ||||||||
\(575\) | −32.1622 | + | 3.96731i | −1.34126 | + | 0.165448i | ||||
\(576\) | 50.1608 | 2.09003 | ||||||||
\(577\) | 28.8568 | 1.20133 | 0.600663 | − | 0.799502i | \(-0.294903\pi\) | ||||
0.600663 | + | 0.799502i | \(0.294903\pi\) | |||||||
\(578\) | 40.5999 | 1.68873 | ||||||||
\(579\) | 10.4847i | 0.435729i | ||||||||
\(580\) | 18.4690 | − | 20.8872i | 0.766882 | − | 0.867292i | ||||
\(581\) | 3.09825 | 0.128537 | ||||||||
\(582\) | 2.41231i | 0.0999935i | ||||||||
\(583\) | −21.0884 | −0.873392 | ||||||||
\(584\) | −99.3679 | −4.11187 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.3938 | 0.594600 | ||||||||
\(587\) | 41.6786 | 1.72026 | 0.860131 | − | 0.510074i | \(-0.170382\pi\) | ||||
0.860131 | + | 0.510074i | \(0.170382\pi\) | |||||||
\(588\) | 15.7562i | 0.649776i | ||||||||
\(589\) | 8.85685 | 0.364940 | ||||||||
\(590\) | −26.8324 | − | 23.7259i | −1.10467 | − | 0.976781i | ||||
\(591\) | − | 0.962389i | − | 0.0395874i | ||||||
\(592\) | −46.2579 | −1.90119 | ||||||||
\(593\) | 22.4993 | 0.923935 | 0.461968 | − | 0.886897i | \(-0.347144\pi\) | ||||
0.461968 | + | 0.886897i | \(0.347144\pi\) | |||||||
\(594\) | 27.2896 | 1.11971 | ||||||||
\(595\) | −1.82321 | − | 1.61213i | −0.0747442 | − | 0.0660908i | ||||
\(596\) | 58.5256i | 2.39730i | ||||||||
\(597\) | 8.06063i | 0.329900i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.15045 | −0.169583 | −0.0847913 | − | 0.996399i | \(-0.527022\pi\) | ||||
−0.0847913 | + | 0.996399i | \(0.527022\pi\) | |||||||
\(600\) | −20.1622 | + | 2.48707i | −0.823119 | + | 0.101534i | ||||
\(601\) | 27.9248 | 1.13908 | 0.569538 | − | 0.821965i | \(-0.307122\pi\) | ||||
0.569538 | + | 0.821965i | \(0.307122\pi\) | |||||||
\(602\) | − | 14.6497i | − | 0.597079i | ||||||
\(603\) | 27.3923 | 1.11550 | ||||||||
\(604\) | − | 72.1255i | − | 2.93475i | ||||||
\(605\) | 3.71274 | − | 4.19886i | 0.150944 | − | 0.170708i | ||||
\(606\) | 13.5153i | 0.549021i | ||||||||
\(607\) | − | 8.19489i | − | 0.332620i | −0.986073 | − | 0.166310i | \(-0.946815\pi\) | ||
0.986073 | − | 0.166310i | \(-0.0531853\pi\) | |||||||
\(608\) | 26.7186i | 1.08358i | ||||||||
\(609\) | − | 0.937951i | − | 0.0380077i | ||||||
\(610\) | 7.00729 | − | 7.92478i | 0.283717 | − | 0.320865i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | − | 19.2750i | − | 0.779147i | ||||||
\(613\) | −33.1392 | −1.33848 | −0.669239 | − | 0.743047i | \(-0.733380\pi\) | ||||
−0.669239 | + | 0.743047i | \(0.733380\pi\) | |||||||
\(614\) | 51.2809 | 2.06953 | ||||||||
\(615\) | 5.92478 | − | 6.70052i | 0.238910 | − | 0.270191i | ||||
\(616\) | − | 25.0132i | − | 1.00781i | ||||||
\(617\) | −29.0132 | −1.16803 | −0.584013 | − | 0.811744i | \(-0.698518\pi\) | ||||
−0.584013 | + | 0.811744i | \(0.698518\pi\) | |||||||
\(618\) | −19.7830 | −0.795791 | ||||||||
\(619\) | 12.2134i | 0.490900i | 0.969409 | + | 0.245450i | \(0.0789357\pi\) | ||||
−0.969409 | + | 0.245450i | \(0.921064\pi\) | |||||||
\(620\) | 45.6688 | + | 40.3815i | 1.83410 | + | 1.62176i | ||||
\(621\) | −17.9902 | −0.721920 | ||||||||
\(622\) | 67.5487 | 2.70845 | ||||||||
\(623\) | − | 2.23743i | − | 0.0896406i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | 7.52232i | 0.300652i | ||||||||
\(627\) | 2.96239i | 0.118306i | ||||||||
\(628\) | − | 14.3127i | − | 0.571137i | ||||||
\(629\) | 5.08840i | 0.202888i | ||||||||
\(630\) | 8.84226 | − | 10.0000i | 0.352284 | − | 0.398410i | ||||
\(631\) | 1.22188i | 0.0486424i | 0.999704 | + | 0.0243212i | \(0.00774245\pi\) | ||||
−0.999704 | + | 0.0243212i | \(0.992258\pi\) | |||||||
\(632\) | 19.0982 | 0.759687 | ||||||||
\(633\) | 2.35870i | 0.0937498i | ||||||||
\(634\) | −63.5837 | −2.52523 | ||||||||
\(635\) | 7.19394 | + | 6.36107i | 0.285483 | + | 0.252431i | ||||
\(636\) | 14.2374 | 0.564551 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 23.7743i | − | 0.941235i | ||||||
\(639\) | 23.7043i | 0.937728i | ||||||||
\(640\) | −24.5428 | + | 27.7562i | −0.970139 | + | 1.09716i | ||||
\(641\) | 22.1016 | 0.872960 | 0.436480 | − | 0.899714i | \(-0.356225\pi\) | ||||
0.436480 | + | 0.899714i | \(0.356225\pi\) | |||||||
\(642\) | −14.3284 | −0.565496 | ||||||||
\(643\) | −11.6688 | −0.460172 | −0.230086 | − | 0.973170i | \(-0.573901\pi\) | ||||
−0.230086 | + | 0.973170i | \(0.573901\pi\) | |||||||
\(644\) | 26.9380i | 1.06150i | ||||||||
\(645\) | −4.84226 | + | 5.47627i | −0.190664 | + | 0.215628i | ||||
\(646\) | 6.05079 | 0.238065 | ||||||||
\(647\) | 11.9575i | 0.470096i | 0.971984 | + | 0.235048i | \(0.0755248\pi\) | ||||
−0.971984 | + | 0.235048i | \(0.924475\pi\) | |||||||
\(648\) | 58.8491 | 2.31181 | ||||||||
\(649\) | −22.0059 | −0.863806 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.05079 | 0.0803766 | ||||||||
\(652\) | 11.5066 | 0.450633 | ||||||||
\(653\) | − | 10.9986i | − | 0.430408i | −0.976569 | − | 0.215204i | \(-0.930958\pi\) | ||
0.976569 | − | 0.215204i | \(-0.0690416\pi\) | |||||||
\(654\) | −12.3418 | −0.482604 | ||||||||
\(655\) | 1.23884 | − | 1.40105i | 0.0484056 | − | 0.0547434i | ||||
\(656\) | − | 102.038i | − | 3.98392i | ||||||
\(657\) | −32.5804 | −1.27108 | ||||||||
\(658\) | 6.88717 | 0.268490 | ||||||||
\(659\) | 2.63989 | 0.102835 | 0.0514177 | − | 0.998677i | \(-0.483626\pi\) | ||||
0.0514177 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(660\) | −13.5066 | + | 15.2750i | −0.525743 | + | 0.594580i | ||||
\(661\) | − | 18.3028i | − | 0.711896i | −0.934506 | − | 0.355948i | \(-0.884158\pi\) | ||
0.934506 | − | 0.355948i | \(-0.115842\pi\) | |||||||
\(662\) | − | 31.5696i | − | 1.22699i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.4544 | −1.25947 | ||||||||
\(665\) | 2.26187 | + | 2.00000i | 0.0877114 | + | 0.0775567i | ||||
\(666\) | −27.9090 | −1.08145 | ||||||||
\(667\) | 15.6728i | 0.606852i | ||||||||
\(668\) | 80.9194 | 3.13087 | ||||||||
\(669\) | 11.9854i | 0.463383i | ||||||||
\(670\) | −39.2057 | + | 44.3390i | −1.51465 | + | 1.71296i | ||||
\(671\) | − | 6.49929i | − | 0.250902i | ||||||
\(672\) | 6.18664i | 0.238655i | ||||||||
\(673\) | − | 6.71037i | − | 0.258666i | −0.991601 | − | 0.129333i | \(-0.958716\pi\) | ||
0.991601 | − | 0.129333i | \(-0.0412836\pi\) | |||||||
\(674\) | 43.1002i | 1.66016i | ||||||||
\(675\) | −13.7743 | + | 1.69911i | −0.530174 | + | 0.0653987i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.57593i | 0.0605679i | 0.999541 | + | 0.0302840i | \(0.00964116\pi\) | ||||
−0.999541 | + | 0.0302840i | \(0.990359\pi\) | |||||||
\(678\) | 0.739549 | 0.0284022 | ||||||||
\(679\) | 1.51056 | 0.0579698 | ||||||||
\(680\) | 19.0982 | + | 16.8872i | 0.732384 | + | 0.647593i | ||||
\(681\) | − | 4.79033i | − | 0.183566i | ||||||
\(682\) | 51.9814 | 1.99047 | ||||||||
\(683\) | 15.1939 | 0.581380 | 0.290690 | − | 0.956817i | \(-0.406115\pi\) | ||||
0.290690 | + | 0.956817i | \(0.406115\pi\) | |||||||
\(684\) | 23.9126i | 0.914320i | ||||||||
\(685\) | −22.1260 | + | 25.0230i | −0.845391 | + | 0.956081i | ||||
\(686\) | 28.7875 | 1.09911 | ||||||||
\(687\) | 2.57452 | 0.0982239 | ||||||||
\(688\) | 83.3947i | 3.17939i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 12.3576 | − | 13.9756i | 0.470444 | − | 0.532041i | ||||
\(691\) | − | 18.7127i | − | 0.711866i | −0.934511 | − | 0.355933i | \(-0.884163\pi\) | ||
0.934511 | − | 0.355933i | \(-0.115837\pi\) | |||||||
\(692\) | 131.938i | 5.01555i | ||||||||
\(693\) | − | 8.20123i | − | 0.311539i | ||||||
\(694\) | − | 73.5510i | − | 2.79196i | ||||||
\(695\) | −12.4993 | + | 14.1359i | −0.474125 | + | 0.536204i | ||||
\(696\) | 9.82512i | 0.372420i | ||||||||
\(697\) | −11.2243 | −0.425149 | ||||||||
\(698\) | − | 47.0884i | − | 1.78232i | ||||||
\(699\) | 5.17821 | 0.195858 | ||||||||
\(700\) | 2.54420 | + | 20.6253i | 0.0961617 | + | 0.779563i | ||||
\(701\) | −24.3028 | −0.917904 | −0.458952 | − | 0.888461i | \(-0.651775\pi\) | ||||
−0.458952 | + | 0.888461i | \(0.651775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.31265i | − | 0.238086i | ||||||
\(704\) | 66.5886i | 2.50965i | ||||||||
\(705\) | −2.57452 | − | 2.27645i | −0.0969619 | − | 0.0857362i | ||||
\(706\) | −42.1827 | −1.58757 | ||||||||
\(707\) | 8.46310 | 0.318287 | ||||||||
\(708\) | 14.8568 | 0.558355 | ||||||||
\(709\) | − | 9.66291i | − | 0.362898i | −0.983400 | − | 0.181449i | \(-0.941921\pi\) | ||
0.983400 | − | 0.181449i | \(-0.0580788\pi\) | |||||||
\(710\) | −38.3693 | − | 33.9271i | −1.43997 | − | 1.27326i | ||||
\(711\) | 6.26187 | 0.234838 | ||||||||
\(712\) | 23.4372i | 0.878348i | ||||||||
\(713\) | −34.2677 | −1.28334 | ||||||||
\(714\) | 1.40105 | 0.0524329 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 62.5256 | 2.33669 | ||||||||
\(717\) | 5.70782 | 0.213162 | ||||||||
\(718\) | − | 39.6566i | − | 1.47997i | ||||||
\(719\) | 28.4142 | 1.05967 | 0.529836 | − | 0.848100i | \(-0.322254\pi\) | ||||
0.529836 | + | 0.848100i | \(0.322254\pi\) | |||||||
\(720\) | −50.3352 | + | 56.9257i | −1.87588 | + | 2.12150i | ||||
\(721\) | 12.3879i | 0.461349i | ||||||||
\(722\) | 43.3209 | 1.61224 | ||||||||
\(723\) | 13.7743 | 0.512273 | ||||||||
\(724\) | 14.0811 | 0.523320 | ||||||||
\(725\) | 1.48024 | + | 12.0000i | 0.0549747 | + | 0.445669i | ||||
\(726\) | 3.22662i | 0.119751i | ||||||||
\(727\) | − | 34.8545i | − | 1.29268i | −0.763049 | − | 0.646341i | \(-0.776299\pi\) | ||
0.763049 | − | 0.646341i | \(-0.223701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.2882 | 0.566230 | ||||||||
\(730\) | 46.6312 | − | 52.7367i | 1.72590 | − | 1.95187i | ||||
\(731\) | 9.17347 | 0.339293 | ||||||||
\(732\) | 4.38787i | 0.162180i | ||||||||
\(733\) | −6.25202 | −0.230923 | −0.115462 | − | 0.993312i | \(-0.536835\pi\) | ||||
−0.115462 | + | 0.993312i | \(0.536835\pi\) | |||||||
\(734\) | 72.3122i | 2.66909i | ||||||||
\(735\) | −5.11871 | − | 4.52610i | −0.188807 | − | 0.166948i | ||||
\(736\) | − | 103.376i | − | 3.81050i | ||||||
\(737\) | 36.3634i | 1.33946i | ||||||||
\(738\) | − | 61.5633i | − | 2.26617i | ||||||
\(739\) | − | 32.0846i | − | 1.18025i | −0.807311 | − | 0.590126i | \(-0.799078\pi\) | ||
0.807311 | − | 0.590126i | \(-0.200922\pi\) | |||||||
\(740\) | 28.7816 | − | 32.5501i | 1.05803 | − | 1.19656i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 12.3733i | − | 0.454238i | ||||||
\(743\) | 30.5442 | 1.12056 | 0.560279 | − | 0.828304i | \(-0.310694\pi\) | ||||
0.560279 | + | 0.828304i | \(0.310694\pi\) | |||||||
\(744\) | −21.4821 | −0.787574 | ||||||||
\(745\) | −19.0132 | − | 16.8119i | −0.696589 | − | 0.615942i | ||||
\(746\) | 34.6497i | 1.26862i | ||||||||
\(747\) | −10.6410 | −0.389335 | ||||||||
\(748\) | 25.5877 | 0.935579 | ||||||||
\(749\) | 8.97224i | 0.327838i | ||||||||
\(750\) | 8.14174 | − | 11.8677i | 0.297294 | − | 0.433345i | ||||
\(751\) | −28.1622 | −1.02765 | −0.513827 | − | 0.857894i | \(-0.671773\pi\) | ||||
−0.513827 | + | 0.857894i | \(0.671773\pi\) | |||||||
\(752\) | −39.2057 | −1.42968 | ||||||||
\(753\) | − | 9.32865i | − | 0.339955i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.4314 | + | 20.7186i | 0.852755 | + | 0.754028i | ||||
\(756\) | 11.5369i | 0.419593i | ||||||||
\(757\) | − | 35.4109i | − | 1.28703i | −0.765433 | − | 0.643515i | \(-0.777475\pi\) | ||
0.765433 | − | 0.643515i | \(-0.222525\pi\) | |||||||
\(758\) | 81.0186i | 2.94273i | ||||||||
\(759\) | − | 11.4617i | − | 0.416033i | ||||||
\(760\) | −23.6932 | − | 20.9502i | −0.859444 | − | 0.759943i | ||||
\(761\) | 19.2388i | 0.697407i | 0.937233 | + | 0.348704i | \(0.113378\pi\) | ||||
−0.937233 | + | 0.348704i | \(0.886622\pi\) | |||||||
\(762\) | −5.52820 | −0.200265 | ||||||||
\(763\) | 7.72829i | 0.279783i | ||||||||
\(764\) | 106.351 | 3.84764 | ||||||||
\(765\) | 6.26187 | + | 5.53690i | 0.226398 | + | 0.200187i | ||||
\(766\) | 56.4299 | 2.03890 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 3.89209i | − | 0.140444i | ||||||
\(769\) | − | 48.9643i | − | 1.76570i | −0.469657 | − | 0.882849i | \(-0.655622\pi\) | ||
0.469657 | − | 0.882849i | \(-0.344378\pi\) | |||||||
\(770\) | 13.2750 | + | 11.7381i | 0.478399 | + | 0.423013i | ||||
\(771\) | 11.0014 | 0.396206 | ||||||||
\(772\) | −112.351 | −4.04359 | ||||||||
\(773\) | −46.1681 | −1.66055 | −0.830275 | − | 0.557354i | \(-0.811817\pi\) | ||||
−0.830275 | + | 0.557354i | \(0.811817\pi\) | |||||||
\(774\) | 50.3150i | 1.80854i | ||||||||
\(775\) | −26.2374 | + | 3.23647i | −0.942476 | + | 0.116258i | ||||
\(776\) | −15.8232 | −0.568020 | ||||||||
\(777\) | − | 1.46168i | − | 0.0524375i | ||||||
\(778\) | −18.1260 | −0.649849 | ||||||||
\(779\) | 13.9248 | 0.498907 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.4676 | −1.12600 | ||||||||
\(782\) | −23.4109 | −0.837172 | ||||||||
\(783\) | 6.71228i | 0.239877i | ||||||||
\(784\) | −77.9497 | −2.78392 | ||||||||
\(785\) | 4.64974 | + | 4.11142i | 0.165956 | + | 0.146743i | ||||
\(786\) | 1.07664i | 0.0384024i | ||||||||
\(787\) | 22.6458 | 0.807234 | 0.403617 | − | 0.914928i | \(-0.367753\pi\) | ||||
0.403617 | + | 0.914928i | \(0.367753\pi\) | |||||||
\(788\) | 10.3127 | 0.367373 | ||||||||
\(789\) | 10.5296 | 0.374864 | ||||||||
\(790\) | −8.96239 | + | 10.1359i | −0.318867 | + | 0.360618i | ||||
\(791\) | − | 0.463096i | − | 0.0164658i | ||||||
\(792\) | 85.9086i | 3.05263i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −28.0059 | −0.993891 | ||||||||
\(795\) | −4.08981 | + | 4.62530i | −0.145051 | + | 0.164043i | ||||
\(796\) | −86.3752 | −3.06149 | ||||||||
\(797\) | 8.23743i | 0.291785i | 0.989300 | + | 0.145892i | \(0.0466053\pi\) | ||||
−0.989300 | + | 0.145892i | \(0.953395\pi\) | |||||||
\(798\) | −1.73813 | −0.0615293 | ||||||||
\(799\) | 4.31265i | 0.152571i | ||||||||
\(800\) | −9.76353 | − | 79.1509i | −0.345193 | − | 2.79841i | ||||
\(801\) | 7.68452i | 0.271519i | ||||||||
\(802\) | − | 13.4109i | − | 0.473555i | ||||||
\(803\) | − | 43.2506i | − | 1.52628i | ||||||
\(804\) | − | 24.5501i | − | 0.865814i | ||||||
\(805\) | −8.75131 | − | 7.73813i | −0.308443 | − | 0.272733i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.9478i | 0.385381i | ||||||||
\(808\) | −88.6516 | −3.11875 | ||||||||
\(809\) | −44.1319 | −1.55159 | −0.775797 | − | 0.630982i | \(-0.782652\pi\) | ||||
−0.775797 | + | 0.630982i | \(0.782652\pi\) | |||||||
\(810\) | −27.6166 | + | 31.2325i | −0.970348 | + | 1.09740i | ||||
\(811\) | 22.6883i | 0.796694i | 0.917235 | + | 0.398347i | \(0.130416\pi\) | ||||
−0.917235 | + | 0.398347i | \(0.869584\pi\) | |||||||
\(812\) | 10.0508 | 0.352713 | ||||||||
\(813\) | −0.0594941 | −0.00208655 | ||||||||
\(814\) | − | 37.0494i | − | 1.29858i | ||||||
\(815\) | −3.30536 | + | 3.73813i | −0.115782 | + | 0.130941i | ||||
\(816\) | −7.97556 | −0.279201 | ||||||||
\(817\) | −11.3806 | −0.398156 | ||||||||
\(818\) | 38.4894i | 1.34575i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 71.8007 | + | 63.4880i | 2.50739 | + | 2.21710i | ||||
\(821\) | − | 50.2736i | − | 1.75456i | −0.479978 | − | 0.877281i | \(-0.659355\pi\) | ||
0.479978 | − | 0.877281i | \(-0.340645\pi\) | |||||||
\(822\) | − | 19.2290i | − | 0.670688i | ||||||
\(823\) | − | 5.13093i | − | 0.178853i | −0.995993 | − | 0.0894265i | \(-0.971497\pi\) | ||
0.995993 | − | 0.0894265i | \(-0.0285034\pi\) | |||||||
\(824\) | − | 129.764i | − | 4.52054i | ||||||
\(825\) | −1.08252 | − | 8.77575i | −0.0376884 | − | 0.305532i | ||||
\(826\) | − | 12.9116i | − | 0.449252i | ||||||
\(827\) | −18.6946 | −0.650076 | −0.325038 | − | 0.945701i | \(-0.605377\pi\) | ||||
−0.325038 | + | 0.945701i | \(0.605377\pi\) | |||||||
\(828\) | − | 92.5193i | − | 3.21527i | ||||||
\(829\) | −3.44121 | −0.119518 | −0.0597591 | − | 0.998213i | \(-0.519033\pi\) | ||||
−0.0597591 | + | 0.998213i | \(0.519033\pi\) | |||||||
\(830\) | 15.2301 | − | 17.2243i | 0.528646 | − | 0.597863i | ||||
\(831\) | −7.38646 | −0.256233 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.57452i | 0.297089i | ||||||||
\(834\) | − | 10.8627i | − | 0.376146i | ||||||
\(835\) | −23.2447 | + | 26.2882i | −0.804417 | + | 0.909741i | ||||
\(836\) | −31.7440 | −1.09789 | ||||||||
\(837\) | −14.6761 | −0.507280 | ||||||||
\(838\) | −46.7123 | −1.61365 | ||||||||
\(839\) | − | 52.6248i | − | 1.81681i | −0.418090 | − | 0.908406i | \(-0.637300\pi\) | ||
0.418090 | − | 0.908406i | \(-0.362700\pi\) | |||||||
\(840\) | −5.48612 | − | 4.85097i | −0.189289 | − | 0.167374i | ||||
\(841\) | −23.1524 | −0.798357 | ||||||||
\(842\) | 7.72355i | 0.266171i | ||||||||
\(843\) | −6.70052 | −0.230778 | ||||||||
\(844\) | −25.2750 | −0.870003 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −23.6542 | −0.813248 | ||||||||
\(847\) | 2.02047 | 0.0694241 | ||||||||
\(848\) | 70.4358i | 2.41878i | ||||||||
\(849\) | −9.80748 | −0.336592 | ||||||||
\(850\) | −17.9248 | + | 2.21108i | −0.614815 | + | 0.0758394i | ||||
\(851\) | 24.4241i | 0.837246i | ||||||||
\(852\) | 21.2447 | 0.727832 | ||||||||
\(853\) | −6.31853 | −0.216342 | −0.108171 | − | 0.994132i | \(-0.534499\pi\) | ||||
−0.108171 | + | 0.994132i | \(0.534499\pi\) | |||||||
\(854\) | 3.81336 | 0.130490 | ||||||||
\(855\) | −7.76845 | − | 6.86907i | −0.265675 | − | 0.234917i | ||||
\(856\) | − | 93.9850i | − | 3.21234i | ||||||
\(857\) | − | 0.775746i | − | 0.0264990i | −0.999912 | − | 0.0132495i | \(-0.995782\pi\) | ||
0.999912 | − | 0.0132495i | \(-0.00421757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.24869 | −0.110844 | −0.0554220 | − | 0.998463i | \(-0.517650\pi\) | ||||
−0.0554220 | + | 0.998463i | \(0.517650\pi\) | |||||||
\(860\) | −58.6820 | − | 51.8881i | −2.00104 | − | 1.76937i | ||||
\(861\) | 3.22425 | 0.109882 | ||||||||
\(862\) | 2.37962i | 0.0810503i | ||||||||
\(863\) | 19.9208 | 0.678112 | 0.339056 | − | 0.940766i | \(-0.389892\pi\) | ||||
0.339056 | + | 0.940766i | \(0.389892\pi\) | |||||||
\(864\) | − | 44.2736i | − | 1.50622i | ||||||
\(865\) | −42.8627 | − | 37.9003i | −1.45738 | − | 1.28865i | ||||
\(866\) | 67.5487i | 2.29540i | ||||||||
\(867\) | − | 7.30299i | − | 0.248022i | ||||||
\(868\) | 21.9756i | 0.745899i | ||||||||
\(869\) | 8.31265i | 0.281987i | ||||||||
\(870\) | −5.21440 | − | 4.61071i | −0.176785 | − | 0.156318i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 80.9544i | − | 2.74146i | ||||||
\(873\) | −5.18806 | −0.175589 | ||||||||
\(874\) | 29.0435 | 0.982411 | ||||||||
\(875\) | −7.43136 | − | 5.09825i | −0.251226 | − | 0.172352i | ||||
\(876\) | 29.1998i | 0.986570i | ||||||||
\(877\) | 22.1378 | 0.747539 | 0.373770 | − | 0.927522i | \(-0.378065\pi\) | ||||
0.373770 | + | 0.927522i | \(0.378065\pi\) | |||||||
\(878\) | 77.0757 | 2.60118 | ||||||||
\(879\) | − | 2.58910i | − | 0.0873283i | ||||||
\(880\) | −75.5691 | − | 66.8202i | −2.54743 | − | 2.25251i | ||||
\(881\) | −2.23155 | −0.0751828 | −0.0375914 | − | 0.999293i | \(-0.511969\pi\) | ||||
−0.0375914 | + | 0.999293i | \(0.511969\pi\) | |||||||
\(882\) | −47.0299 | −1.58358 | ||||||||
\(883\) | 4.30440i | 0.144855i | 0.997374 | + | 0.0724273i | \(0.0230745\pi\) | ||||
−0.997374 | + | 0.0724273i | \(0.976925\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.26774 | + | 4.82653i | −0.143459 | + | 0.162242i | ||||
\(886\) | 98.9276i | 3.32354i | ||||||||
\(887\) | − | 15.9330i | − | 0.534979i | −0.963561 | − | 0.267489i | \(-0.913806\pi\) | ||
0.963561 | − | 0.267489i | \(-0.0861940\pi\) | |||||||
\(888\) | 15.3112i | 0.513811i | ||||||||
\(889\) | 3.46168i | 0.116101i | ||||||||
\(890\) | −12.4387 | − | 10.9986i | −0.416945 | − | 0.368673i | ||||
\(891\) | 25.6145i | 0.858118i | ||||||||
\(892\) | −128.432 | −4.30022 | ||||||||
\(893\) | − | 5.35026i | − | 0.179040i | ||||||
\(894\) | 14.6107 | 0.488655 | ||||||||
\(895\) | −17.9610 | + | 20.3127i | −0.600369 | + | 0.678977i | ||||
\(896\) | −13.3561 | −0.446197 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 33.9365i | − | 1.13248i | ||||||
\(899\) | 12.7856i | 0.426423i | ||||||||
\(900\) | −8.73813 | − | 70.8383i | −0.291271 | − | 2.36128i | ||||
\(901\) | 7.74798 | 0.258123 | ||||||||
\(902\) | 81.7255 | 2.72116 | ||||||||
\(903\) | −2.63515 | −0.0876923 | ||||||||
\(904\) | 4.85097i | 0.161341i | ||||||||
\(905\) | −4.04491 | + | 4.57452i | −0.134457 | + | 0.152062i | ||||
\(906\) | −18.0059 | −0.598205 | ||||||||
\(907\) | − | 51.9086i | − | 1.72360i | −0.507251 | − | 0.861798i | \(-0.669338\pi\) | ||
0.507251 | − | 0.861798i | \(-0.330662\pi\) | |||||||
\(908\) | 51.3317 | 1.70350 | ||||||||
\(909\) | −29.0668 | −0.964085 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.67750 | −0.320630 | −0.160315 | − | 0.987066i | \(-0.551251\pi\) | ||||
−0.160315 | + | 0.987066i | \(0.551251\pi\) | |||||||
\(912\) | 9.89446 | 0.327638 | ||||||||
\(913\) | − | 14.1260i | − | 0.467503i | ||||||
\(914\) | −67.0103 | −2.21651 | ||||||||
\(915\) | −1.42548 | − | 1.26045i | −0.0471251 | − | 0.0416692i | ||||
\(916\) | 27.5877i | 0.911523i | ||||||||
\(917\) | 0.674176 | 0.0222632 | ||||||||
\(918\) | −10.0263 | −0.330919 | ||||||||
\(919\) | −13.5515 | −0.447022 | −0.223511 | − | 0.974701i | \(-0.571752\pi\) | ||||
−0.223511 | + | 0.974701i | \(0.571752\pi\) | |||||||
\(920\) | 91.6707 | + | 81.0576i | 3.02229 | + | 2.67239i | ||||
\(921\) | − | 9.22425i | − | 0.303949i | ||||||
\(922\) | − | 98.6780i | − | 3.24979i | ||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.35026 | −0.241806 | ||||||||
\(925\) | 2.30677 | + | 18.7005i | 0.0758462 | + | 0.614869i | ||||
\(926\) | −104.381 | −3.43017 | ||||||||
\(927\) | − | 42.5466i | − | 1.39741i | ||||||
\(928\) | −38.5705 | −1.26614 | ||||||||
\(929\) | 9.44992i | 0.310042i | 0.987911 | + | 0.155021i | \(0.0495445\pi\) | ||||
−0.987911 | + | 0.155021i | \(0.950455\pi\) | |||||||
\(930\) | 10.0811 | − | 11.4010i | 0.330572 | − | 0.373855i | ||||
\(931\) | − | 10.6375i | − | 0.348631i | ||||||
\(932\) | 55.4880i | 1.81757i | ||||||||
\(933\) | − | 12.1504i | − | 0.397788i | ||||||
\(934\) | 87.6625i | 2.86840i | ||||||||
\(935\) | −7.35026 | + | 8.31265i | −0.240379 | + | 0.271853i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.0409i | − | 0.524035i | −0.965063 | − | 0.262017i | \(-0.915612\pi\) | ||
0.965063 | − | 0.262017i | \(-0.0843877\pi\) | |||||||
\(938\) | −21.3357 | −0.696634 | ||||||||
\(939\) | 1.35309 | 0.0441565 | ||||||||
\(940\) | 24.3938 | − | 27.5877i | 0.795636 | − | 0.899811i | ||||
\(941\) | − | 21.6747i | − | 0.706574i | −0.935515 | − | 0.353287i | \(-0.885064\pi\) | ||
0.935515 | − | 0.353287i | \(-0.114936\pi\) | |||||||
\(942\) | −3.57310 | −0.116418 | ||||||||
\(943\) | −53.8759 | −1.75444 | ||||||||
\(944\) | 73.5002i | 2.39223i | ||||||||
\(945\) | −3.74798 | − | 3.31406i | −0.121922 | − | 0.107807i | ||||
\(946\) | −66.7934 | −2.17164 | ||||||||
\(947\) | 4.63118 | 0.150493 | 0.0752466 | − | 0.997165i | \(-0.476026\pi\) | ||||
0.0752466 | + | 0.997165i | \(0.476026\pi\) | |||||||
\(948\) | − | 5.61213i | − | 0.182273i | ||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 22.2374 | − | 2.74306i | 0.721477 | − | 0.0889966i | ||||
\(951\) | 11.4372i | 0.370878i | ||||||||
\(952\) | 9.18997i | 0.297849i | ||||||||
\(953\) | − | 26.2981i | − | 0.851878i | −0.904752 | − | 0.425939i | \(-0.859944\pi\) | ||
0.904752 | − | 0.425939i | \(-0.140056\pi\) | |||||||
\(954\) | 42.4965i | 1.37587i | ||||||||
\(955\) | −30.5501 | + | 34.5501i | −0.988577 | + | 1.11801i | ||||
\(956\) | 61.1632i | 1.97816i | ||||||||
\(957\) | −4.27645 | −0.138238 | ||||||||
\(958\) | 45.1427i | 1.45849i | ||||||||
\(959\) | −12.0409 | −0.388822 | ||||||||
\(960\) | 14.6048 | + | 12.9140i | 0.471369 | + | 0.416797i | ||||
\(961\) | 3.04491 | 0.0982228 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 30.8155i | − | 0.993014i | ||||||
\(964\) | 147.601i | 4.75392i | ||||||||
\(965\) | 32.2736 | − | 36.4993i | 1.03892 | − | 1.17495i | ||||
\(966\) | 6.72496 | 0.216372 | ||||||||
\(967\) | −11.9405 | −0.383981 | −0.191990 | − | 0.981397i | \(-0.561494\pi\) | ||||
−0.191990 | + | 0.981397i | \(0.561494\pi\) | |||||||
\(968\) | −21.1646 | −0.680255 | ||||||||
\(969\) | − | 1.08840i | − | 0.0349643i | ||||||
\(970\) | 7.42548 | − | 8.39772i | 0.238418 | − | 0.269635i | ||||
\(971\) | 30.1524 | 0.967635 | 0.483818 | − | 0.875169i | \(-0.339250\pi\) | ||||
0.483818 | + | 0.875169i | \(0.339250\pi\) | |||||||
\(972\) | − | 60.2311i | − | 1.93191i | ||||||
\(973\) | −6.80209 | −0.218065 | ||||||||
\(974\) | −24.7308 | −0.792427 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −21.7078 | −0.694850 | ||||||||
\(977\) | 26.9321 | 0.861633 | 0.430817 | − | 0.902439i | \(-0.358226\pi\) | ||||
0.430817 | + | 0.902439i | \(0.358226\pi\) | |||||||
\(978\) | − | 2.87258i | − | 0.0918549i | ||||||
\(979\) | −10.2012 | −0.326033 | ||||||||
\(980\) | 48.5002 | − | 54.8505i | 1.54928 | − | 1.75214i | ||||
\(981\) | − | 26.5431i | − | 0.847455i | ||||||
\(982\) | 68.8843 | 2.19819 | ||||||||
\(983\) | −20.5902 | −0.656727 | −0.328363 | − | 0.944551i | \(-0.606497\pi\) | ||||
−0.328363 | + | 0.944551i | \(0.606497\pi\) | |||||||
\(984\) | −33.7743 | −1.07669 | ||||||||
\(985\) | −2.96239 | + | 3.35026i | −0.0943895 | + | 0.106748i | ||||
\(986\) | 8.73481i | 0.278173i | ||||||||
\(987\) | − | 1.23884i | − | 0.0394328i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.0322 | 1.40014 | ||||||||
\(990\) | −45.5936 | − | 40.3150i | −1.44906 | − | 1.28130i | ||||
\(991\) | −48.1378 | −1.52915 | −0.764573 | − | 0.644537i | \(-0.777050\pi\) | ||||
−0.764573 | + | 0.644537i | \(0.777050\pi\) | |||||||
\(992\) | − | 84.3327i | − | 2.67756i | ||||||
\(993\) | −5.67864 | −0.180206 | ||||||||
\(994\) | − | 18.4631i | − | 0.585614i | ||||||
\(995\) | 24.8119 | − | 28.0606i | 0.786591 | − | 0.889582i | ||||
\(996\) | 9.53690i | 0.302188i | ||||||||
\(997\) | − | 33.4255i | − | 1.05860i | −0.848436 | − | 0.529298i | \(-0.822455\pi\) | ||
0.848436 | − | 0.529298i | \(-0.177545\pi\) | |||||||
\(998\) | 74.1051i | 2.34576i | ||||||||
\(999\) | 10.4603i | 0.330948i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))