Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(31,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.c (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: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.85100625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + x^{5} + 3x^{4} + 2x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 31.8 | ||
Root | \(1.04064 + 0.957636i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.31 |
Dual form | 60.3.c.a.31.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.87477 | + | 0.696577i | 0.937387 | + | 0.348288i | ||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 3.02956 | + | 2.61185i | 0.757390 | + | 0.652962i | ||||
\(5\) | −2.23607 | −0.447214 | ||||||||
\(6\) | −1.20651 | + | 3.24721i | −0.201084 | + | 0.541201i | ||||
\(7\) | − | 5.46770i | − | 0.781100i | −0.920582 | − | 0.390550i | \(-0.872285\pi\) | ||
0.920582 | − | 0.390550i | \(-0.127715\pi\) | |||||||
\(8\) | 3.86039 | + | 7.00695i | 0.482549 | + | 0.875869i | ||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −4.19212 | − | 1.55759i | −0.419212 | − | 0.155759i | ||||
\(11\) | − | 11.0403i | − | 1.00366i | −0.864965 | − | 0.501832i | \(-0.832659\pi\) | ||
0.864965 | − | 0.501832i | \(-0.167341\pi\) | |||||||
\(12\) | −4.52386 | + | 5.24735i | −0.376988 | + | 0.437280i | ||||
\(13\) | 10.1242 | 0.778784 | 0.389392 | − | 0.921072i | \(-0.372685\pi\) | ||||
0.389392 | + | 0.921072i | \(0.372685\pi\) | |||||||
\(14\) | 3.80867 | − | 10.2507i | 0.272048 | − | 0.732193i | ||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 2.35649 | + | 15.8255i | 0.147280 | + | 0.989095i | ||||
\(17\) | −24.4146 | −1.43615 | −0.718077 | − | 0.695964i | \(-0.754977\pi\) | ||||
−0.718077 | + | 0.695964i | \(0.754977\pi\) | |||||||
\(18\) | −5.62432 | − | 2.08973i | −0.312462 | − | 0.116096i | ||||
\(19\) | − | 23.7757i | − | 1.25135i | −0.780082 | − | 0.625677i | \(-0.784823\pi\) | ||
0.780082 | − | 0.625677i | \(-0.215177\pi\) | |||||||
\(20\) | −6.77431 | − | 5.84027i | −0.338715 | − | 0.292014i | ||||
\(21\) | 9.47033 | 0.450968 | ||||||||
\(22\) | 7.69043 | − | 20.6981i | 0.349565 | − | 0.940823i | ||||
\(23\) | 37.2526i | 1.61968i | 0.586653 | + | 0.809838i | \(0.300445\pi\) | ||||
−0.586653 | + | 0.809838i | \(0.699555\pi\) | |||||||
\(24\) | −12.1364 | + | 6.68640i | −0.505683 | + | 0.278600i | ||||
\(25\) | 5.00000 | 0.200000 | ||||||||
\(26\) | 18.9806 | + | 7.05227i | 0.730022 | + | 0.271241i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 14.2808 | − | 16.5647i | 0.510029 | − | 0.591598i | ||||
\(29\) | −25.7726 | −0.888712 | −0.444356 | − | 0.895850i | \(-0.646567\pi\) | ||||
−0.444356 | + | 0.895850i | \(0.646567\pi\) | |||||||
\(30\) | 2.69783 | − | 7.26097i | 0.0899277 | − | 0.242032i | ||||
\(31\) | 4.83647i | 0.156015i | 0.996953 | + | 0.0780076i | \(0.0248558\pi\) | ||||
−0.996953 | + | 0.0780076i | \(0.975144\pi\) | |||||||
\(32\) | −6.60580 | + | 31.3108i | −0.206431 | + | 0.978461i | ||||
\(33\) | 19.1224 | 0.579466 | ||||||||
\(34\) | −45.7719 | − | 17.0066i | −1.34623 | − | 0.500196i | ||||
\(35\) | 12.2261i | 0.349319i | ||||||||
\(36\) | −9.08868 | − | 7.83555i | −0.252463 | − | 0.217654i | ||||
\(37\) | 35.6493 | 0.963495 | 0.481747 | − | 0.876310i | \(-0.340002\pi\) | ||||
0.481747 | + | 0.876310i | \(0.340002\pi\) | |||||||
\(38\) | 16.5616 | − | 44.5741i | 0.435832 | − | 1.17300i | ||||
\(39\) | 17.5356i | 0.449631i | ||||||||
\(40\) | −8.63210 | − | 15.6680i | −0.215803 | − | 0.391700i | ||||
\(41\) | −9.30410 | −0.226929 | −0.113465 | − | 0.993542i | \(-0.536195\pi\) | ||||
−0.113465 | + | 0.993542i | \(0.536195\pi\) | |||||||
\(42\) | 17.7547 | + | 6.59682i | 0.422732 | + | 0.157067i | ||||
\(43\) | 70.0287i | 1.62857i | 0.580462 | + | 0.814287i | \(0.302872\pi\) | ||||
−0.580462 | + | 0.814287i | \(0.697128\pi\) | |||||||
\(44\) | 28.8356 | − | 33.4473i | 0.655355 | − | 0.760166i | ||||
\(45\) | 6.70820 | 0.149071 | ||||||||
\(46\) | −25.9493 | + | 69.8401i | −0.564114 | + | 1.51826i | ||||
\(47\) | 38.0223i | 0.808984i | 0.914542 | + | 0.404492i | \(0.132552\pi\) | ||||
−0.914542 | + | 0.404492i | \(0.867448\pi\) | |||||||
\(48\) | −27.4106 | + | 4.08156i | −0.571054 | + | 0.0850324i | ||||
\(49\) | 19.1043 | 0.389883 | ||||||||
\(50\) | 9.37387 | + | 3.48288i | 0.187477 | + | 0.0696577i | ||||
\(51\) | − | 42.2873i | − | 0.829164i | ||||||
\(52\) | 30.6718 | + | 26.4428i | 0.589843 | + | 0.508516i | ||||
\(53\) | 55.7762 | 1.05238 | 0.526191 | − | 0.850366i | \(-0.323620\pi\) | ||||
0.526191 | + | 0.850366i | \(0.323620\pi\) | |||||||
\(54\) | 3.61952 | − | 9.74162i | 0.0670281 | − | 0.180400i | ||||
\(55\) | 24.6869i | 0.448853i | ||||||||
\(56\) | 38.3119 | − | 21.1075i | 0.684141 | − | 0.376919i | ||||
\(57\) | 41.1808 | 0.722470 | ||||||||
\(58\) | −48.3179 | − | 17.9526i | −0.833067 | − | 0.309528i | ||||
\(59\) | − | 55.5411i | − | 0.941374i | −0.882300 | − | 0.470687i | \(-0.844006\pi\) | ||
0.882300 | − | 0.470687i | \(-0.155994\pi\) | |||||||
\(60\) | 10.1156 | − | 11.7334i | 0.168594 | − | 0.195557i | ||||
\(61\) | −82.2412 | −1.34822 | −0.674108 | − | 0.738633i | \(-0.735472\pi\) | ||||
−0.674108 | + | 0.738633i | \(0.735472\pi\) | |||||||
\(62\) | −3.36897 | + | 9.06729i | −0.0543383 | + | 0.146247i | ||||
\(63\) | 16.4031i | 0.260367i | ||||||||
\(64\) | −34.1947 | + | 54.0992i | −0.534293 | + | 0.845299i | ||||
\(65\) | −22.6384 | −0.348283 | ||||||||
\(66\) | 35.8502 | + | 13.3202i | 0.543184 | + | 0.201821i | ||||
\(67\) | − | 104.493i | − | 1.55960i | −0.626026 | − | 0.779802i | \(-0.715320\pi\) | ||
0.626026 | − | 0.779802i | \(-0.284680\pi\) | |||||||
\(68\) | −73.9656 | − | 63.7673i | −1.08773 | − | 0.937754i | ||||
\(69\) | −64.5233 | −0.935120 | ||||||||
\(70\) | −8.51645 | + | 22.9213i | −0.121664 | + | 0.327447i | ||||
\(71\) | − | 76.7471i | − | 1.08094i | −0.841362 | − | 0.540472i | \(-0.818246\pi\) | ||
0.841362 | − | 0.540472i | \(-0.181754\pi\) | |||||||
\(72\) | −11.5812 | − | 21.0209i | −0.160850 | − | 0.291956i | ||||
\(73\) | −93.5215 | −1.28112 | −0.640558 | − | 0.767910i | \(-0.721297\pi\) | ||||
−0.640558 | + | 0.767910i | \(0.721297\pi\) | |||||||
\(74\) | 66.8344 | + | 24.8325i | 0.903168 | + | 0.335574i | ||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 62.0986 | − | 72.0300i | 0.817087 | − | 0.947764i | ||||
\(77\) | −60.3651 | −0.783963 | ||||||||
\(78\) | −12.2149 | + | 32.8753i | −0.156601 | + | 0.421478i | ||||
\(79\) | 49.3762i | 0.625016i | 0.949915 | + | 0.312508i | \(0.101169\pi\) | ||||
−0.949915 | + | 0.312508i | \(0.898831\pi\) | |||||||
\(80\) | −5.26927 | − | 35.3869i | −0.0658658 | − | 0.442337i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −17.4431 | − | 6.48102i | −0.212721 | − | 0.0790368i | ||||
\(83\) | − | 72.3768i | − | 0.872010i | −0.899944 | − | 0.436005i | \(-0.856393\pi\) | ||
0.899944 | − | 0.436005i | \(-0.143607\pi\) | |||||||
\(84\) | 28.6910 | + | 24.7351i | 0.341559 | + | 0.294465i | ||||
\(85\) | 54.5927 | 0.642267 | ||||||||
\(86\) | −48.7804 | + | 131.288i | −0.567214 | + | 1.52661i | ||||
\(87\) | − | 44.6395i | − | 0.513098i | ||||||
\(88\) | 77.3589 | − | 42.6199i | 0.879079 | − | 0.484318i | ||||
\(89\) | 115.691 | 1.29990 | 0.649950 | − | 0.759977i | \(-0.274790\pi\) | ||||
0.649950 | + | 0.759977i | \(0.274790\pi\) | |||||||
\(90\) | 12.5764 | + | 4.67278i | 0.139737 | + | 0.0519198i | ||||
\(91\) | − | 55.3560i | − | 0.608308i | ||||||
\(92\) | −97.2980 | + | 112.859i | −1.05759 | + | 1.22673i | ||||
\(93\) | −8.37701 | −0.0900754 | ||||||||
\(94\) | −26.4854 | + | 71.2832i | −0.281760 | + | 0.758332i | ||||
\(95\) | 53.1641i | 0.559623i | ||||||||
\(96\) | −54.2318 | − | 11.4416i | −0.564915 | − | 0.119183i | ||||
\(97\) | −72.9589 | −0.752154 | −0.376077 | − | 0.926588i | \(-0.622727\pi\) | ||||
−0.376077 | + | 0.926588i | \(0.622727\pi\) | |||||||
\(98\) | 35.8162 | + | 13.3076i | 0.365471 | + | 0.135792i | ||||
\(99\) | 33.1209i | 0.334555i | ||||||||
\(100\) | 15.1478 | + | 13.0592i | 0.151478 | + | 0.130592i | ||||
\(101\) | 29.4092 | 0.291180 | 0.145590 | − | 0.989345i | \(-0.453492\pi\) | ||||
0.145590 | + | 0.989345i | \(0.453492\pi\) | |||||||
\(102\) | 29.4564 | − | 79.2792i | 0.288788 | − | 0.777247i | ||||
\(103\) | 28.1884i | 0.273673i | 0.990594 | + | 0.136837i | \(0.0436935\pi\) | ||||
−0.990594 | + | 0.136837i | \(0.956306\pi\) | |||||||
\(104\) | 39.0833 | + | 70.9397i | 0.375801 | + | 0.682112i | ||||
\(105\) | −21.1763 | −0.201679 | ||||||||
\(106\) | 104.568 | + | 38.8524i | 0.986490 | + | 0.366532i | ||||
\(107\) | 4.50700i | 0.0421215i | 0.999778 | + | 0.0210607i | \(0.00670434\pi\) | ||||
−0.999778 | + | 0.0210607i | \(0.993296\pi\) | |||||||
\(108\) | 13.5716 | − | 15.7421i | 0.125663 | − | 0.145760i | ||||
\(109\) | 193.315 | 1.77353 | 0.886767 | − | 0.462217i | \(-0.152946\pi\) | ||||
0.886767 | + | 0.462217i | \(0.152946\pi\) | |||||||
\(110\) | −17.1963 | + | 46.2824i | −0.156330 | + | 0.420749i | ||||
\(111\) | 61.7464i | 0.556274i | ||||||||
\(112\) | 86.5292 | − | 12.8846i | 0.772582 | − | 0.115041i | ||||
\(113\) | 75.5727 | 0.668785 | 0.334392 | − | 0.942434i | \(-0.391469\pi\) | ||||
0.334392 | + | 0.942434i | \(0.391469\pi\) | |||||||
\(114\) | 77.2047 | + | 28.6856i | 0.677234 | + | 0.251628i | ||||
\(115\) | − | 83.2992i | − | 0.724341i | ||||||
\(116\) | −78.0798 | − | 67.3142i | −0.673102 | − | 0.580295i | ||||
\(117\) | −30.3726 | −0.259595 | ||||||||
\(118\) | 38.6886 | − | 104.127i | 0.327870 | − | 0.882432i | ||||
\(119\) | 133.492i | 1.12178i | ||||||||
\(120\) | 27.1378 | − | 14.9512i | 0.226148 | − | 0.124594i | ||||
\(121\) | −0.888544 | −0.00734334 | ||||||||
\(122\) | −154.184 | − | 57.2873i | −1.26380 | − | 0.469568i | ||||
\(123\) | − | 16.1152i | − | 0.131018i | ||||||
\(124\) | −12.6321 | + | 14.6524i | −0.101872 | + | 0.118164i | ||||
\(125\) | −11.1803 | −0.0894427 | ||||||||
\(126\) | −11.4260 | + | 30.7521i | −0.0906827 | + | 0.244064i | ||||
\(127\) | 131.306i | 1.03390i | 0.856015 | + | 0.516951i | \(0.172933\pi\) | ||||
−0.856015 | + | 0.516951i | \(0.827067\pi\) | |||||||
\(128\) | −101.792 | + | 77.6045i | −0.795247 | + | 0.606285i | ||||
\(129\) | −121.293 | −0.940258 | ||||||||
\(130\) | −42.4418 | − | 15.7694i | −0.326476 | − | 0.121303i | ||||
\(131\) | 75.7533i | 0.578270i | 0.957288 | + | 0.289135i | \(0.0933676\pi\) | ||||
−0.957288 | + | 0.289135i | \(0.906632\pi\) | |||||||
\(132\) | 57.9324 | + | 49.9448i | 0.438882 | + | 0.378370i | ||||
\(133\) | −129.999 | −0.977433 | ||||||||
\(134\) | 72.7877 | − | 195.902i | 0.543192 | − | 1.46195i | ||||
\(135\) | 11.6190i | 0.0860663i | ||||||||
\(136\) | −94.2500 | − | 171.072i | −0.693014 | − | 1.25788i | ||||
\(137\) | 66.7927 | 0.487538 | 0.243769 | − | 0.969833i | \(-0.421616\pi\) | ||||
0.243769 | + | 0.969833i | \(0.421616\pi\) | |||||||
\(138\) | −120.967 | − | 44.9454i | −0.876570 | − | 0.325692i | ||||
\(139\) | − | 38.1214i | − | 0.274255i | −0.990553 | − | 0.137127i | \(-0.956213\pi\) | ||
0.990553 | − | 0.137127i | \(-0.0437869\pi\) | |||||||
\(140\) | −31.9329 | + | 37.0399i | −0.228092 | + | 0.264571i | ||||
\(141\) | −65.8565 | −0.467067 | ||||||||
\(142\) | 53.4602 | − | 143.884i | 0.376481 | − | 1.01326i | ||||
\(143\) | − | 111.774i | − | 0.781638i | ||||||
\(144\) | −7.06946 | − | 47.4765i | −0.0490935 | − | 0.329698i | ||||
\(145\) | 57.6294 | 0.397444 | ||||||||
\(146\) | −175.332 | − | 65.1449i | −1.20090 | − | 0.446198i | ||||
\(147\) | 33.0895i | 0.225099i | ||||||||
\(148\) | 108.002 | + | 93.1106i | 0.729742 | + | 0.629126i | ||||
\(149\) | −126.717 | −0.850449 | −0.425225 | − | 0.905088i | \(-0.639805\pi\) | ||||
−0.425225 | + | 0.905088i | \(0.639805\pi\) | |||||||
\(150\) | −6.03253 | + | 16.2360i | −0.0402169 | + | 0.108240i | ||||
\(151\) | 68.4403i | 0.453247i | 0.973982 | + | 0.226623i | \(0.0727687\pi\) | ||||
−0.973982 | + | 0.226623i | \(0.927231\pi\) | |||||||
\(152\) | 166.595 | − | 91.7836i | 1.09602 | − | 0.603840i | ||||
\(153\) | 73.2438 | 0.478718 | ||||||||
\(154\) | −113.171 | − | 42.0489i | −0.734877 | − | 0.273045i | ||||
\(155\) | − | 10.8147i | − | 0.0697721i | ||||||
\(156\) | −45.8004 | + | 53.1252i | −0.293592 | + | 0.340546i | ||||
\(157\) | 25.5777 | 0.162915 | 0.0814577 | − | 0.996677i | \(-0.474042\pi\) | ||||
0.0814577 | + | 0.996677i | \(0.474042\pi\) | |||||||
\(158\) | −34.3943 | + | 92.5693i | −0.217686 | + | 0.585882i | ||||
\(159\) | 96.6073i | 0.607593i | ||||||||
\(160\) | 14.7710 | − | 70.0130i | 0.0923189 | − | 0.437581i | ||||
\(161\) | 203.686 | 1.26513 | ||||||||
\(162\) | 16.8730 | + | 6.26919i | 0.104154 | + | 0.0386987i | ||||
\(163\) | − | 63.4771i | − | 0.389430i | −0.980860 | − | 0.194715i | \(-0.937622\pi\) | ||
0.980860 | − | 0.194715i | \(-0.0623782\pi\) | |||||||
\(164\) | −28.1873 | − | 24.3009i | −0.171874 | − | 0.148176i | ||||
\(165\) | −42.7590 | −0.259145 | ||||||||
\(166\) | 50.4160 | − | 135.690i | 0.303711 | − | 0.817411i | ||||
\(167\) | − | 12.3771i | − | 0.0741144i | −0.999313 | − | 0.0370572i | \(-0.988202\pi\) | ||
0.999313 | − | 0.0370572i | \(-0.0117984\pi\) | |||||||
\(168\) | 36.5592 | + | 66.3582i | 0.217614 | + | 0.394989i | ||||
\(169\) | −66.5008 | −0.393496 | ||||||||
\(170\) | 102.349 | + | 38.0280i | 0.602053 | + | 0.223694i | ||||
\(171\) | 71.3272i | 0.417118i | ||||||||
\(172\) | −182.904 | + | 212.156i | −1.06340 | + | 1.23347i | ||||
\(173\) | 59.3729 | 0.343196 | 0.171598 | − | 0.985167i | \(-0.445107\pi\) | ||||
0.171598 | + | 0.985167i | \(0.445107\pi\) | |||||||
\(174\) | 31.0948 | − | 83.6890i | 0.178706 | − | 0.480971i | ||||
\(175\) | − | 27.3385i | − | 0.156220i | ||||||
\(176\) | 174.719 | − | 26.0164i | 0.992720 | − | 0.147820i | ||||
\(177\) | 96.2000 | 0.543503 | ||||||||
\(178\) | 216.895 | + | 80.5877i | 1.21851 | + | 0.452740i | ||||
\(179\) | − | 252.782i | − | 1.41219i | −0.708118 | − | 0.706094i | \(-0.750455\pi\) | ||
0.708118 | − | 0.706094i | \(-0.249545\pi\) | |||||||
\(180\) | 20.3229 | + | 17.5208i | 0.112905 | + | 0.0973379i | ||||
\(181\) | 125.373 | 0.692670 | 0.346335 | − | 0.938111i | \(-0.387426\pi\) | ||||
0.346335 | + | 0.938111i | \(0.387426\pi\) | |||||||
\(182\) | 38.5597 | − | 103.780i | 0.211867 | − | 0.570220i | ||||
\(183\) | − | 142.446i | − | 0.778393i | ||||||
\(184\) | −261.027 | + | 143.809i | −1.41862 | + | 0.781573i | ||||
\(185\) | −79.7143 | −0.430888 | ||||||||
\(186\) | −15.7050 | − | 5.83523i | −0.0844355 | − | 0.0313722i | ||||
\(187\) | 269.545i | 1.44142i | ||||||||
\(188\) | −99.3084 | + | 115.191i | −0.528236 | + | 0.612717i | ||||
\(189\) | −28.4110 | −0.150323 | ||||||||
\(190\) | −37.0329 | + | 99.6708i | −0.194910 | + | 0.524583i | ||||
\(191\) | 97.4640i | 0.510283i | 0.966904 | + | 0.255141i | \(0.0821220\pi\) | ||||
−0.966904 | + | 0.255141i | \(0.917878\pi\) | |||||||
\(192\) | −93.7025 | − | 59.2270i | −0.488034 | − | 0.308474i | ||||
\(193\) | −342.376 | −1.77397 | −0.886985 | − | 0.461798i | \(-0.847204\pi\) | ||||
−0.886985 | + | 0.461798i | \(0.847204\pi\) | |||||||
\(194\) | −136.782 | − | 50.8215i | −0.705060 | − | 0.261966i | ||||
\(195\) | − | 39.2108i | − | 0.201081i | ||||||
\(196\) | 57.8775 | + | 49.8974i | 0.295293 | + | 0.254579i | ||||
\(197\) | 74.4829 | 0.378086 | 0.189043 | − | 0.981969i | \(-0.439461\pi\) | ||||
0.189043 | + | 0.981969i | \(0.439461\pi\) | |||||||
\(198\) | −23.0713 | + | 62.0943i | −0.116522 | + | 0.313608i | ||||
\(199\) | − | 178.027i | − | 0.894606i | −0.894382 | − | 0.447303i | \(-0.852385\pi\) | ||
0.894382 | − | 0.447303i | \(-0.147615\pi\) | |||||||
\(200\) | 19.3020 | + | 35.0348i | 0.0965098 | + | 0.175174i | ||||
\(201\) | 180.988 | 0.900438 | ||||||||
\(202\) | 55.1356 | + | 20.4858i | 0.272949 | + | 0.101415i | ||||
\(203\) | 140.917i | 0.694173i | ||||||||
\(204\) | 110.448 | − | 128.112i | 0.541413 | − | 0.628000i | ||||
\(205\) | 20.8046 | 0.101486 | ||||||||
\(206\) | −19.6354 | + | 52.8468i | −0.0953172 | + | 0.256538i | ||||
\(207\) | − | 111.758i | − | 0.539892i | ||||||
\(208\) | 23.8575 | + | 160.220i | 0.114700 | + | 0.770291i | ||||
\(209\) | −262.491 | −1.25594 | ||||||||
\(210\) | −39.7008 | − | 14.7509i | −0.189052 | − | 0.0702425i | ||||
\(211\) | 185.893i | 0.881008i | 0.897751 | + | 0.440504i | \(0.145200\pi\) | ||||
−0.897751 | + | 0.440504i | \(0.854800\pi\) | |||||||
\(212\) | 168.978 | + | 145.679i | 0.797064 | + | 0.687166i | ||||
\(213\) | 132.930 | 0.624084 | ||||||||
\(214\) | −3.13947 | + | 8.44961i | −0.0146704 | + | 0.0394842i | ||||
\(215\) | − | 156.589i | − | 0.728321i | ||||||
\(216\) | 36.4092 | − | 20.0592i | 0.168561 | − | 0.0928666i | ||||
\(217\) | 26.4444 | 0.121863 | ||||||||
\(218\) | 362.422 | + | 134.659i | 1.66249 | + | 0.617701i | ||||
\(219\) | − | 161.984i | − | 0.739653i | ||||||
\(220\) | −64.4784 | + | 74.7905i | −0.293084 | + | 0.339957i | ||||
\(221\) | −247.178 | −1.11845 | ||||||||
\(222\) | −43.0111 | + | 115.761i | −0.193744 | + | 0.521444i | ||||
\(223\) | − | 202.724i | − | 0.909074i | −0.890728 | − | 0.454537i | \(-0.849805\pi\) | ||
0.890728 | − | 0.454537i | \(-0.150195\pi\) | |||||||
\(224\) | 171.198 | + | 36.1186i | 0.764276 | + | 0.161244i | ||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 141.682 | + | 52.6422i | 0.626910 | + | 0.232930i | ||||
\(227\) | − | 51.2708i | − | 0.225863i | −0.993603 | − | 0.112931i | \(-0.963976\pi\) | ||
0.993603 | − | 0.112931i | \(-0.0360240\pi\) | |||||||
\(228\) | 124.760 | + | 107.558i | 0.547192 | + | 0.471745i | ||||
\(229\) | 337.056 | 1.47186 | 0.735930 | − | 0.677058i | \(-0.236745\pi\) | ||||
0.735930 | + | 0.677058i | \(0.236745\pi\) | |||||||
\(230\) | 58.0243 | − | 156.167i | 0.252280 | − | 0.678988i | ||||
\(231\) | − | 104.555i | − | 0.452621i | ||||||
\(232\) | −99.4925 | − | 180.588i | −0.428847 | − | 0.778395i | ||||
\(233\) | −80.2851 | −0.344571 | −0.172286 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172286 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(234\) | −56.9417 | − | 21.1568i | −0.243341 | − | 0.0904138i | ||||
\(235\) | − | 85.0203i | − | 0.361789i | ||||||
\(236\) | 145.065 | − | 168.265i | 0.614682 | − | 0.712988i | ||||
\(237\) | −85.5221 | −0.360853 | ||||||||
\(238\) | −92.9873 | + | 250.267i | −0.390703 | + | 1.05154i | ||||
\(239\) | 330.808i | 1.38413i | 0.721834 | + | 0.692066i | \(0.243299\pi\) | ||||
−0.721834 | + | 0.692066i | \(0.756701\pi\) | |||||||
\(240\) | 61.2920 | − | 9.12664i | 0.255383 | − | 0.0380277i | ||||
\(241\) | −359.914 | −1.49342 | −0.746710 | − | 0.665150i | \(-0.768368\pi\) | ||||
−0.746710 | + | 0.665150i | \(0.768368\pi\) | |||||||
\(242\) | −1.66582 | − | 0.618939i | −0.00688355 | − | 0.00255760i | ||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | −249.155 | − | 214.802i | −1.02113 | − | 0.880334i | ||||
\(245\) | −42.7184 | −0.174361 | ||||||||
\(246\) | 11.2255 | − | 30.2123i | 0.0456319 | − | 0.122814i | ||||
\(247\) | − | 240.710i | − | 0.974534i | ||||||
\(248\) | −33.8889 | + | 18.6707i | −0.136649 | + | 0.0752850i | ||||
\(249\) | 125.360 | 0.503455 | ||||||||
\(250\) | −20.9606 | − | 7.78796i | −0.0838425 | − | 0.0311519i | ||||
\(251\) | 312.213i | 1.24388i | 0.783067 | + | 0.621938i | \(0.213654\pi\) | ||||
−0.783067 | + | 0.621938i | \(0.786346\pi\) | |||||||
\(252\) | −42.8424 | + | 49.6942i | −0.170010 | + | 0.197199i | ||||
\(253\) | 411.280 | 1.62561 | ||||||||
\(254\) | −91.4645 | + | 246.169i | −0.360096 | + | 0.969167i | ||||
\(255\) | 94.5574i | 0.370813i | ||||||||
\(256\) | −244.894 | + | 74.5853i | −0.956617 | + | 0.291349i | ||||
\(257\) | 80.2592 | 0.312293 | 0.156146 | − | 0.987734i | \(-0.450093\pi\) | ||||
0.156146 | + | 0.987734i | \(0.450093\pi\) | |||||||
\(258\) | −227.398 | − | 84.4901i | −0.881386 | − | 0.327481i | ||||
\(259\) | − | 194.920i | − | 0.752586i | ||||||
\(260\) | −68.5843 | − | 59.1280i | −0.263786 | − | 0.227415i | ||||
\(261\) | 77.3179 | 0.296237 | ||||||||
\(262\) | −52.7680 | + | 142.020i | −0.201405 | + | 0.542063i | ||||
\(263\) | − | 487.967i | − | 1.85539i | −0.373342 | − | 0.927694i | \(-0.621788\pi\) | ||
0.373342 | − | 0.927694i | \(-0.378212\pi\) | |||||||
\(264\) | 73.8199 | + | 133.990i | 0.279621 | + | 0.507536i | ||||
\(265\) | −124.719 | −0.470639 | ||||||||
\(266\) | −243.718 | − | 90.5540i | −0.916233 | − | 0.340428i | ||||
\(267\) | 200.383i | 0.750498i | ||||||||
\(268\) | 272.921 | − | 316.569i | 1.01836 | − | 1.18123i | ||||
\(269\) | −309.553 | −1.15076 | −0.575378 | − | 0.817888i | \(-0.695145\pi\) | ||||
−0.575378 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(270\) | −8.09349 | + | 21.7829i | −0.0299759 | + | 0.0806775i | ||||
\(271\) | 48.9693i | 0.180698i | 0.995910 | + | 0.0903492i | \(0.0287983\pi\) | ||||
−0.995910 | + | 0.0903492i | \(0.971202\pi\) | |||||||
\(272\) | −57.5327 | − | 386.374i | −0.211517 | − | 1.42049i | ||||
\(273\) | 95.8794 | 0.351207 | ||||||||
\(274\) | 125.221 | + | 46.5262i | 0.457012 | + | 0.169804i | ||||
\(275\) | − | 55.2016i | − | 0.200733i | ||||||
\(276\) | −195.477 | − | 168.525i | −0.708251 | − | 0.610598i | ||||
\(277\) | −199.644 | −0.720736 | −0.360368 | − | 0.932810i | \(-0.617349\pi\) | ||||
−0.360368 | + | 0.932810i | \(0.617349\pi\) | |||||||
\(278\) | 26.5545 | − | 71.4690i | 0.0955197 | − | 0.257083i | ||||
\(279\) | − | 14.5094i | − | 0.0520051i | ||||||
\(280\) | −85.6680 | + | 47.1977i | −0.305957 | + | 0.168563i | ||||
\(281\) | 61.1598 | 0.217650 | 0.108825 | − | 0.994061i | \(-0.465291\pi\) | ||||
0.108825 | + | 0.994061i | \(0.465291\pi\) | |||||||
\(282\) | −123.466 | − | 45.8741i | −0.437823 | − | 0.162674i | ||||
\(283\) | 432.506i | 1.52829i | 0.645044 | + | 0.764145i | \(0.276839\pi\) | ||||
−0.645044 | + | 0.764145i | \(0.723161\pi\) | |||||||
\(284\) | 200.452 | − | 232.510i | 0.705816 | − | 0.818697i | ||||
\(285\) | −92.0830 | −0.323098 | ||||||||
\(286\) | 77.8593 | − | 209.551i | 0.272235 | − | 0.732697i | ||||
\(287\) | 50.8720i | 0.177254i | ||||||||
\(288\) | 19.8174 | − | 93.9323i | 0.0688105 | − | 0.326154i | ||||
\(289\) | 307.073 | 1.06254 | ||||||||
\(290\) | 108.042 | + | 40.1433i | 0.372559 | + | 0.138425i | ||||
\(291\) | − | 126.369i | − | 0.434256i | ||||||
\(292\) | −283.329 | − | 244.264i | −0.970305 | − | 0.836521i | ||||
\(293\) | −283.234 | −0.966668 | −0.483334 | − | 0.875436i | \(-0.660574\pi\) | ||||
−0.483334 | + | 0.875436i | \(0.660574\pi\) | |||||||
\(294\) | −23.0494 | + | 62.0354i | −0.0783993 | + | 0.211005i | ||||
\(295\) | 124.194i | 0.420995i | ||||||||
\(296\) | 137.620 | + | 249.793i | 0.464933 | + | 0.843895i | ||||
\(297\) | −57.3672 | −0.193155 | ||||||||
\(298\) | −237.566 | − | 88.2681i | −0.797200 | − | 0.296202i | ||||
\(299\) | 377.152i | 1.26138i | ||||||||
\(300\) | −22.6193 | + | 26.2368i | −0.0753976 | + | 0.0874559i | ||||
\(301\) | 382.896 | 1.27208 | ||||||||
\(302\) | −47.6739 | + | 128.310i | −0.157861 | + | 0.424868i | ||||
\(303\) | 50.9382i | 0.168113i | ||||||||
\(304\) | 376.263 | − | 56.0272i | 1.23771 | − | 0.184300i | ||||
\(305\) | 183.897 | 0.602940 | ||||||||
\(306\) | 137.316 | + | 51.0199i | 0.448744 | + | 0.166732i | ||||
\(307\) | − | 100.077i | − | 0.325983i | −0.986627 | − | 0.162992i | \(-0.947886\pi\) | ||
0.986627 | − | 0.162992i | \(-0.0521144\pi\) | |||||||
\(308\) | −182.880 | − | 157.665i | −0.593766 | − | 0.511898i | ||||
\(309\) | −48.8237 | −0.158005 | ||||||||
\(310\) | 7.53325 | − | 20.2751i | 0.0243008 | − | 0.0654035i | ||||
\(311\) | − | 404.185i | − | 1.29963i | −0.760092 | − | 0.649815i | \(-0.774846\pi\) | ||
0.760092 | − | 0.649815i | \(-0.225154\pi\) | |||||||
\(312\) | −122.871 | + | 67.6943i | −0.393818 | + | 0.216969i | ||||
\(313\) | −128.579 | −0.410795 | −0.205398 | − | 0.978679i | \(-0.565849\pi\) | ||||
−0.205398 | + | 0.978679i | \(0.565849\pi\) | |||||||
\(314\) | 47.9525 | + | 17.8168i | 0.152715 | + | 0.0567415i | ||||
\(315\) | − | 36.6784i | − | 0.116440i | ||||||
\(316\) | −128.963 | + | 149.588i | −0.408112 | + | 0.473381i | ||||
\(317\) | 85.9315 | 0.271077 | 0.135539 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135539 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(318\) | −67.2944 | + | 181.117i | −0.211618 | + | 0.569550i | ||||
\(319\) | 284.538i | 0.891969i | ||||||||
\(320\) | 76.4618 | − | 120.969i | 0.238943 | − | 0.378029i | ||||
\(321\) | −7.80635 | −0.0243189 | ||||||||
\(322\) | 381.865 | + | 141.883i | 1.18592 | + | 0.440630i | ||||
\(323\) | 580.475i | 1.79714i | ||||||||
\(324\) | 27.2661 | + | 23.5066i | 0.0841545 | + | 0.0725514i | ||||
\(325\) | 50.6209 | 0.155757 | ||||||||
\(326\) | 44.2167 | − | 119.005i | 0.135634 | − | 0.365047i | ||||
\(327\) | 334.832i | 1.02395i | ||||||||
\(328\) | −35.9175 | − | 65.1934i | −0.109505 | − | 0.198760i | ||||
\(329\) | 207.894 | 0.631898 | ||||||||
\(330\) | −80.1634 | − | 29.7849i | −0.242919 | − | 0.0902573i | ||||
\(331\) | 183.391i | 0.554052i | 0.960862 | + | 0.277026i | \(0.0893488\pi\) | ||||
−0.960862 | + | 0.277026i | \(0.910651\pi\) | |||||||
\(332\) | 189.037 | − | 219.270i | 0.569390 | − | 0.660452i | ||||
\(333\) | −106.948 | −0.321165 | ||||||||
\(334\) | 8.62160 | − | 23.2043i | 0.0258132 | − | 0.0694739i | ||||
\(335\) | 233.654i | 0.697476i | ||||||||
\(336\) | 22.3167 | + | 149.873i | 0.0664188 | + | 0.446050i | ||||
\(337\) | 168.130 | 0.498901 | 0.249451 | − | 0.968388i | \(-0.419750\pi\) | ||||
0.249451 | + | 0.968388i | \(0.419750\pi\) | |||||||
\(338\) | −124.674 | − | 46.3229i | −0.368858 | − | 0.137050i | ||||
\(339\) | 130.896i | 0.386123i | ||||||||
\(340\) | 165.392 | + | 142.588i | 0.486447 | + | 0.419376i | ||||
\(341\) | 53.3962 | 0.156587 | ||||||||
\(342\) | −49.6849 | + | 133.722i | −0.145277 | + | 0.391001i | ||||
\(343\) | − | 372.374i | − | 1.08564i | ||||||
\(344\) | −490.688 | + | 270.338i | −1.42642 | + | 0.785867i | ||||
\(345\) | 144.279 | 0.418199 | ||||||||
\(346\) | 111.311 | + | 41.3578i | 0.321708 | + | 0.119531i | ||||
\(347\) | − | 137.414i | − | 0.396006i | −0.980201 | − | 0.198003i | \(-0.936554\pi\) | ||
0.980201 | − | 0.198003i | \(-0.0634455\pi\) | |||||||
\(348\) | 116.592 | − | 135.238i | 0.335034 | − | 0.388615i | ||||
\(349\) | −13.4893 | −0.0386513 | −0.0193256 | − | 0.999813i | \(-0.506152\pi\) | ||||
−0.0193256 | + | 0.999813i | \(0.506152\pi\) | |||||||
\(350\) | 19.0434 | − | 51.2535i | 0.0544096 | − | 0.146439i | ||||
\(351\) | − | 52.6068i | − | 0.149877i | ||||||
\(352\) | 345.681 | + | 72.9301i | 0.982047 | + | 0.207188i | ||||
\(353\) | 243.547 | 0.689935 | 0.344968 | − | 0.938615i | \(-0.387890\pi\) | ||||
0.344968 | + | 0.938615i | \(0.387890\pi\) | |||||||
\(354\) | 180.353 | + | 67.0107i | 0.509473 | + | 0.189296i | ||||
\(355\) | 171.612i | 0.483413i | ||||||||
\(356\) | 350.493 | + | 302.168i | 0.984532 | + | 0.848786i | ||||
\(357\) | −231.215 | −0.647660 | ||||||||
\(358\) | 176.082 | − | 473.909i | 0.491849 | − | 1.32377i | ||||
\(359\) | 17.9166i | 0.0499068i | 0.999689 | + | 0.0249534i | \(0.00794374\pi\) | ||||
−0.999689 | + | 0.0249534i | \(0.992056\pi\) | |||||||
\(360\) | 25.8963 | + | 47.0041i | 0.0719342 | + | 0.130567i | ||||
\(361\) | −204.285 | −0.565887 | ||||||||
\(362\) | 235.047 | + | 87.3321i | 0.649300 | + | 0.241249i | ||||
\(363\) | − | 1.53900i | − | 0.00423968i | ||||||
\(364\) | 144.582 | − | 167.704i | 0.397202 | − | 0.460727i | ||||
\(365\) | 209.120 | 0.572933 | ||||||||
\(366\) | 99.2245 | − | 267.054i | 0.271105 | − | 0.729656i | ||||
\(367\) | − | 238.417i | − | 0.649637i | −0.945776 | − | 0.324818i | \(-0.894697\pi\) | ||
0.945776 | − | 0.324818i | \(-0.105303\pi\) | |||||||
\(368\) | −589.541 | + | 87.7852i | −1.60201 | + | 0.238547i | ||||
\(369\) | 27.9123 | 0.0756431 | ||||||||
\(370\) | −149.446 | − | 55.5271i | −0.403909 | − | 0.150073i | ||||
\(371\) | − | 304.968i | − | 0.822016i | ||||||
\(372\) | −25.3787 | − | 21.8795i | −0.0682222 | − | 0.0588158i | ||||
\(373\) | −181.271 | −0.485981 | −0.242990 | − | 0.970029i | \(-0.578128\pi\) | ||||
−0.242990 | + | 0.970029i | \(0.578128\pi\) | |||||||
\(374\) | −187.759 | + | 505.336i | −0.502029 | + | 1.35117i | ||||
\(375\) | − | 19.3649i | − | 0.0516398i | ||||||
\(376\) | −266.420 | + | 146.781i | −0.708564 | + | 0.390375i | ||||
\(377\) | −260.927 | −0.692114 | ||||||||
\(378\) | −53.2642 | − | 19.7904i | −0.140911 | − | 0.0523557i | ||||
\(379\) | − | 306.206i | − | 0.807931i | −0.914774 | − | 0.403965i | \(-0.867632\pi\) | ||
0.914774 | − | 0.403965i | \(-0.132368\pi\) | |||||||
\(380\) | −138.857 | + | 161.064i | −0.365412 | + | 0.423853i | ||||
\(381\) | −227.428 | −0.596924 | ||||||||
\(382\) | −67.8912 | + | 182.723i | −0.177726 | + | 0.478333i | ||||
\(383\) | 144.027i | 0.376050i | 0.982164 | + | 0.188025i | \(0.0602086\pi\) | ||||
−0.982164 | + | 0.188025i | \(0.939791\pi\) | |||||||
\(384\) | −134.415 | − | 176.308i | −0.350039 | − | 0.459136i | ||||
\(385\) | 134.981 | 0.350599 | ||||||||
\(386\) | −641.878 | − | 238.491i | −1.66290 | − | 0.617853i | ||||
\(387\) | − | 210.086i | − | 0.542858i | ||||||
\(388\) | −221.034 | − | 190.558i | −0.569674 | − | 0.491128i | ||||
\(389\) | 14.0099 | 0.0360152 | 0.0180076 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180076 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(390\) | 27.3133 | − | 73.5114i | 0.0700342 | − | 0.188491i | ||||
\(391\) | − | 909.506i | − | 2.32610i | ||||||
\(392\) | 73.7499 | + | 133.863i | 0.188138 | + | 0.341486i | ||||
\(393\) | −131.209 | −0.333864 | ||||||||
\(394\) | 139.639 | + | 51.8831i | 0.354413 | + | 0.131683i | ||||
\(395\) | − | 110.409i | − | 0.279515i | ||||||
\(396\) | −86.5069 | + | 100.342i | −0.218452 | + | 0.253389i | ||||
\(397\) | 39.1084 | 0.0985098 | 0.0492549 | − | 0.998786i | \(-0.484315\pi\) | ||||
0.0492549 | + | 0.998786i | \(0.484315\pi\) | |||||||
\(398\) | 124.009 | − | 333.760i | 0.311581 | − | 0.838592i | ||||
\(399\) | − | 225.164i | − | 0.564321i | ||||||
\(400\) | 11.7824 | + | 79.1276i | 0.0294561 | + | 0.197819i | ||||
\(401\) | −121.067 | −0.301913 | −0.150957 | − | 0.988540i | \(-0.548235\pi\) | ||||
−0.150957 | + | 0.988540i | \(0.548235\pi\) | |||||||
\(402\) | 339.312 | + | 126.072i | 0.844059 | + | 0.313612i | ||||
\(403\) | 48.9653i | 0.121502i | ||||||||
\(404\) | 89.0970 | + | 76.8124i | 0.220537 | + | 0.190130i | ||||
\(405\) | −20.1246 | −0.0496904 | ||||||||
\(406\) | −98.1595 | + | 264.188i | −0.241772 | + | 0.650709i | ||||
\(407\) | − | 393.579i | − | 0.967026i | ||||||
\(408\) | 296.305 | − | 163.246i | 0.726239 | − | 0.400112i | ||||
\(409\) | −541.795 | −1.32468 | −0.662342 | − | 0.749202i | \(-0.730437\pi\) | ||||
−0.662342 | + | 0.749202i | \(0.730437\pi\) | |||||||
\(410\) | 39.0039 | + | 14.4920i | 0.0951316 | + | 0.0353463i | ||||
\(411\) | 115.688i | 0.281480i | ||||||||
\(412\) | −73.6237 | + | 85.3983i | −0.178698 | + | 0.207278i | ||||
\(413\) | −303.682 | −0.735307 | ||||||||
\(414\) | 77.8478 | − | 209.520i | 0.188038 | − | 0.506088i | ||||
\(415\) | 161.839i | 0.389975i | ||||||||
\(416\) | −66.8784 | + | 316.996i | −0.160765 | + | 0.762009i | ||||
\(417\) | 66.0282 | 0.158341 | ||||||||
\(418\) | −492.112 | − | 182.845i | −1.17730 | − | 0.437429i | ||||
\(419\) | − | 687.825i | − | 1.64159i | −0.571224 | − | 0.820794i | \(-0.693531\pi\) | ||
0.571224 | − | 0.820794i | \(-0.306469\pi\) | |||||||
\(420\) | −64.1549 | − | 55.3093i | −0.152750 | − | 0.131689i | ||||
\(421\) | −454.396 | −1.07932 | −0.539662 | − | 0.841882i | \(-0.681448\pi\) | ||||
−0.539662 | + | 0.841882i | \(0.681448\pi\) | |||||||
\(422\) | −129.489 | + | 348.507i | −0.306845 | + | 0.825846i | ||||
\(423\) | − | 114.067i | − | 0.269661i | ||||||
\(424\) | 215.318 | + | 390.821i | 0.507826 | + | 0.921749i | ||||
\(425\) | −122.073 | −0.287231 | ||||||||
\(426\) | 249.214 | + | 92.5959i | 0.585008 | + | 0.217361i | ||||
\(427\) | 449.670i | 1.05309i | ||||||||
\(428\) | −11.7716 | + | 13.6542i | −0.0275037 | + | 0.0319024i | ||||
\(429\) | 193.599 | 0.451279 | ||||||||
\(430\) | 109.076 | − | 293.569i | 0.253666 | − | 0.682719i | ||||
\(431\) | − | 466.145i | − | 1.08154i | −0.841169 | − | 0.540772i | \(-0.818132\pi\) | ||
0.841169 | − | 0.540772i | \(-0.181868\pi\) | |||||||
\(432\) | 82.2318 | − | 12.2447i | 0.190351 | − | 0.0283441i | ||||
\(433\) | 457.094 | 1.05565 | 0.527823 | − | 0.849355i | \(-0.323009\pi\) | ||||
0.527823 | + | 0.849355i | \(0.323009\pi\) | |||||||
\(434\) | 49.5772 | + | 18.4205i | 0.114233 | + | 0.0424436i | ||||
\(435\) | 99.8170i | 0.229464i | ||||||||
\(436\) | 585.660 | + | 504.910i | 1.34326 | + | 1.15805i | ||||
\(437\) | 885.706 | 2.02679 | ||||||||
\(438\) | 112.834 | − | 303.684i | 0.257613 | − | 0.693341i | ||||
\(439\) | 777.467i | 1.77100i | 0.464644 | + | 0.885498i | \(0.346182\pi\) | ||||
−0.464644 | + | 0.885498i | \(0.653818\pi\) | |||||||
\(440\) | −172.980 | + | 95.3011i | −0.393136 | + | 0.216593i | ||||
\(441\) | −57.3128 | −0.129961 | ||||||||
\(442\) | −463.403 | − | 172.178i | −1.04842 | − | 0.389544i | ||||
\(443\) | 247.484i | 0.558654i | 0.960196 | + | 0.279327i | \(0.0901114\pi\) | ||||
−0.960196 | + | 0.279327i | \(0.909889\pi\) | |||||||
\(444\) | −161.272 | + | 187.065i | −0.363226 | + | 0.421316i | ||||
\(445\) | −258.693 | −0.581333 | ||||||||
\(446\) | 141.213 | − | 380.061i | 0.316620 | − | 0.852155i | ||||
\(447\) | − | 219.480i | − | 0.491007i | ||||||
\(448\) | 295.798 | + | 186.967i | 0.660263 | + | 0.417336i | ||||
\(449\) | 412.508 | 0.918726 | 0.459363 | − | 0.888249i | \(-0.348078\pi\) | ||||
0.459363 | + | 0.888249i | \(0.348078\pi\) | |||||||
\(450\) | −28.1216 | − | 10.4487i | −0.0624925 | − | 0.0232192i | ||||
\(451\) | 102.720i | 0.227761i | ||||||||
\(452\) | 228.952 | + | 197.384i | 0.506531 | + | 0.436691i | ||||
\(453\) | −118.542 | −0.261682 | ||||||||
\(454\) | 35.7141 | − | 96.1213i | 0.0786654 | − | 0.211721i | ||||
\(455\) | 123.780i | 0.272044i | ||||||||
\(456\) | 158.974 | + | 288.552i | 0.348627 | + | 0.632789i | ||||
\(457\) | −745.400 | −1.63107 | −0.815537 | − | 0.578706i | \(-0.803558\pi\) | ||||
−0.815537 | + | 0.578706i | \(0.803558\pi\) | |||||||
\(458\) | 631.904 | + | 234.785i | 1.37970 | + | 0.512631i | ||||
\(459\) | 126.862i | 0.276388i | ||||||||
\(460\) | 217.565 | − | 252.360i | 0.472967 | − | 0.548609i | ||||
\(461\) | 81.6151 | 0.177039 | 0.0885196 | − | 0.996074i | \(-0.471786\pi\) | ||||
0.0885196 | + | 0.996074i | \(0.471786\pi\) | |||||||
\(462\) | 72.8309 | − | 196.018i | 0.157643 | − | 0.424281i | ||||
\(463\) | 292.248i | 0.631205i | 0.948891 | + | 0.315603i | \(0.102207\pi\) | ||||
−0.948891 | + | 0.315603i | \(0.897793\pi\) | |||||||
\(464\) | −60.7329 | − | 407.865i | −0.130890 | − | 0.879020i | ||||
\(465\) | 18.7316 | 0.0402829 | ||||||||
\(466\) | −150.517 | − | 55.9248i | −0.322997 | − | 0.120010i | ||||
\(467\) | − | 51.4163i | − | 0.110099i | −0.998484 | − | 0.0550495i | \(-0.982468\pi\) | ||
0.998484 | − | 0.0550495i | \(-0.0175317\pi\) | |||||||
\(468\) | −92.0155 | − | 79.3285i | −0.196614 | − | 0.169505i | ||||
\(469\) | −571.339 | −1.21821 | ||||||||
\(470\) | 59.2232 | − | 159.394i | 0.126007 | − | 0.339136i | ||||
\(471\) | 44.3019i | 0.0940592i | ||||||||
\(472\) | 389.174 | − | 214.410i | 0.824520 | − | 0.454259i | ||||
\(473\) | 773.139 | 1.63454 | ||||||||
\(474\) | −160.335 | − | 59.5727i | −0.338259 | − | 0.125681i | ||||
\(475\) | − | 118.879i | − | 0.250271i | ||||||
\(476\) | −348.660 | + | 404.422i | −0.732480 | + | 0.849625i | ||||
\(477\) | −167.329 | −0.350794 | ||||||||
\(478\) | −230.433 | + | 620.190i | −0.482077 | + | 1.29747i | ||||
\(479\) | 122.593i | 0.255935i | 0.991778 | + | 0.127967i | \(0.0408453\pi\) | ||||
−0.991778 | + | 0.127967i | \(0.959155\pi\) | |||||||
\(480\) | 121.266 | + | 25.5842i | 0.252638 | + | 0.0533003i | ||||
\(481\) | 360.920 | 0.750354 | ||||||||
\(482\) | −674.758 | − | 250.708i | −1.39991 | − | 0.520141i | ||||
\(483\) | 352.794i | 0.730423i | ||||||||
\(484\) | −2.69190 | − | 2.32074i | −0.00556177 | − | 0.00479492i | ||||
\(485\) | 163.141 | 0.336373 | ||||||||
\(486\) | −10.8586 | + | 29.2248i | −0.0223427 | + | 0.0601334i | ||||
\(487\) | 65.9859i | 0.135495i | 0.997703 | + | 0.0677474i | \(0.0215812\pi\) | ||||
−0.997703 | + | 0.0677474i | \(0.978419\pi\) | |||||||
\(488\) | −317.483 | − | 576.260i | −0.650580 | − | 1.18086i | ||||
\(489\) | 109.946 | 0.224837 | ||||||||
\(490\) | −80.0874 | − | 29.7566i | −0.163444 | − | 0.0607279i | ||||
\(491\) | 361.163i | 0.735567i | 0.929911 | + | 0.367783i | \(0.119883\pi\) | ||||
−0.929911 | + | 0.367783i | \(0.880117\pi\) | |||||||
\(492\) | 42.0904 | − | 48.8219i | 0.0855496 | − | 0.0992315i | ||||
\(493\) | 629.229 | 1.27633 | ||||||||
\(494\) | 167.673 | − | 451.277i | 0.339419 | − | 0.913516i | ||||
\(495\) | − | 74.0607i | − | 0.149618i | ||||||
\(496\) | −76.5396 | + | 11.3971i | −0.154314 | + | 0.0229780i | ||||
\(497\) | −419.630 | −0.844326 | ||||||||
\(498\) | 235.022 | + | 87.3231i | 0.471933 | + | 0.175348i | ||||
\(499\) | − | 711.138i | − | 1.42513i | −0.701608 | − | 0.712564i | \(-0.747534\pi\) | ||
0.701608 | − | 0.712564i | \(-0.252466\pi\) | |||||||
\(500\) | −33.8715 | − | 29.2014i | −0.0677431 | − | 0.0584027i | ||||
\(501\) | 21.4378 | 0.0427900 | ||||||||
\(502\) | −217.480 | + | 585.328i | −0.433227 | + | 1.16599i | ||||
\(503\) | 353.756i | 0.703292i | 0.936133 | + | 0.351646i | \(0.114378\pi\) | ||||
−0.936133 | + | 0.351646i | \(0.885622\pi\) | |||||||
\(504\) | −114.936 | + | 63.3224i | −0.228047 | + | 0.125640i | ||||
\(505\) | −65.7610 | −0.130220 | ||||||||
\(506\) | 771.057 | + | 286.488i | 1.52383 | + | 0.566182i | ||||
\(507\) | − | 115.183i | − | 0.227185i | ||||||
\(508\) | −342.951 | + | 397.799i | −0.675100 | + | 0.783068i | ||||
\(509\) | 478.049 | 0.939192 | 0.469596 | − | 0.882881i | \(-0.344400\pi\) | ||||
0.469596 | + | 0.882881i | \(0.344400\pi\) | |||||||
\(510\) | −65.8665 | + | 177.274i | −0.129150 | + | 0.347596i | ||||
\(511\) | 511.348i | 1.00068i | ||||||||
\(512\) | −511.075 | − | 30.7568i | −0.998194 | − | 0.0600720i | ||||
\(513\) | −123.542 | −0.240823 | ||||||||
\(514\) | 150.468 | + | 55.9067i | 0.292739 | + | 0.108768i | ||||
\(515\) | − | 63.0311i | − | 0.122390i | ||||||
\(516\) | −367.466 | − | 316.800i | −0.712142 | − | 0.613953i | ||||
\(517\) | 419.778 | 0.811949 | ||||||||
\(518\) | 135.777 | − | 365.431i | 0.262117 | − | 0.705464i | ||||
\(519\) | 102.837i | 0.198144i | ||||||||
\(520\) | −87.3930 | − | 158.626i | −0.168063 | − | 0.305050i | ||||
\(521\) | −35.7365 | −0.0685921 | −0.0342960 | − | 0.999412i | \(-0.510919\pi\) | ||||
−0.0342960 | + | 0.999412i | \(0.510919\pi\) | |||||||
\(522\) | 144.954 | + | 53.8579i | 0.277689 | + | 0.103176i | ||||
\(523\) | 733.562i | 1.40260i | 0.712864 | + | 0.701302i | \(0.247398\pi\) | ||||
−0.712864 | + | 0.701302i | \(0.752602\pi\) | |||||||
\(524\) | −197.856 | + | 229.499i | −0.377588 | + | 0.437976i | ||||
\(525\) | 47.3517 | 0.0901937 | ||||||||
\(526\) | 339.906 | − | 914.828i | 0.646210 | − | 1.73922i | ||||
\(527\) | − | 118.081i | − | 0.224062i | ||||||
\(528\) | 45.0617 | + | 302.622i | 0.0853441 | + | 0.573147i | ||||
\(529\) | −858.753 | −1.62335 | ||||||||
\(530\) | −233.821 | − | 86.8767i | −0.441172 | − | 0.163918i | ||||
\(531\) | 166.623i | 0.313791i | ||||||||
\(532\) | −393.839 | − | 339.537i | −0.740298 | − | 0.638227i | ||||
\(533\) | −94.1965 | −0.176729 | ||||||||
\(534\) | −139.582 | + | 375.673i | −0.261390 | + | 0.703507i | ||||
\(535\) | − | 10.0780i | − | 0.0188373i | ||||||
\(536\) | 732.181 | − | 403.386i | 1.36601 | − | 0.752585i | ||||
\(537\) | 437.831 | 0.815327 | ||||||||
\(538\) | −580.342 | − | 215.628i | −1.07870 | − | 0.400795i | ||||
\(539\) | − | 210.917i | − | 0.391312i | ||||||
\(540\) | −30.3469 | + | 35.2003i | −0.0561980 | + | 0.0651858i | ||||
\(541\) | 608.939 | 1.12558 | 0.562790 | − | 0.826600i | \(-0.309728\pi\) | ||||
0.562790 | + | 0.826600i | \(0.309728\pi\) | |||||||
\(542\) | −34.1109 | + | 91.8064i | −0.0629352 | + | 0.169384i | ||||
\(543\) | 217.153i | 0.399913i | ||||||||
\(544\) | 161.278 | − | 764.440i | 0.296467 | − | 1.40522i | ||||
\(545\) | −432.266 | −0.793148 | ||||||||
\(546\) | 179.752 | + | 66.7874i | 0.329217 | + | 0.122321i | ||||
\(547\) | − | 78.5868i | − | 0.143669i | −0.997417 | − | 0.0718344i | \(-0.977115\pi\) | ||
0.997417 | − | 0.0718344i | \(-0.0228853\pi\) | |||||||
\(548\) | 202.353 | + | 174.452i | 0.369257 | + | 0.318344i | ||||
\(549\) | 246.724 | 0.449405 | ||||||||
\(550\) | 38.4521 | − | 103.491i | 0.0699130 | − | 0.188165i | ||||
\(551\) | 612.763i | 1.11209i | ||||||||
\(552\) | −249.085 | − | 452.112i | −0.451242 | − | 0.819043i | ||||
\(553\) | 269.974 | 0.488200 | ||||||||
\(554\) | −374.287 | − | 139.067i | −0.675609 | − | 0.251024i | ||||
\(555\) | − | 138.069i | − | 0.248773i | ||||||
\(556\) | 99.5673 | − | 115.491i | 0.179078 | − | 0.207718i | ||||
\(557\) | −928.488 | −1.66694 | −0.833472 | − | 0.552561i | \(-0.813651\pi\) | ||||
−0.833472 | + | 0.552561i | \(0.813651\pi\) | |||||||
\(558\) | 10.1069 | − | 27.2019i | 0.0181128 | − | 0.0487489i | ||||
\(559\) | 708.984i | 1.26831i | ||||||||
\(560\) | −193.485 | + | 28.8108i | −0.345509 | + | 0.0514478i | ||||
\(561\) | −466.866 | −0.832202 | ||||||||
\(562\) | 114.661 | + | 42.6025i | 0.204023 | + | 0.0758051i | ||||
\(563\) | − | 447.978i | − | 0.795697i | −0.917451 | − | 0.397849i | \(-0.869757\pi\) | ||
0.917451 | − | 0.397849i | \(-0.130243\pi\) | |||||||
\(564\) | −199.516 | − | 172.007i | −0.353752 | − | 0.304977i | ||||
\(565\) | −168.986 | −0.299090 | ||||||||
\(566\) | −301.274 | + | 810.852i | −0.532286 | + | 1.43260i | ||||
\(567\) | − | 49.2093i | − | 0.0867889i | ||||||
\(568\) | 537.763 | − | 296.274i | 0.946766 | − | 0.521609i | ||||
\(569\) | 571.441 | 1.00429 | 0.502145 | − | 0.864783i | \(-0.332544\pi\) | ||||
0.502145 | + | 0.864783i | \(0.332544\pi\) | |||||||
\(570\) | −172.635 | − | 64.1429i | −0.302868 | − | 0.112531i | ||||
\(571\) | − | 990.801i | − | 1.73520i | −0.497260 | − | 0.867602i | \(-0.665660\pi\) | ||
0.497260 | − | 0.867602i | \(-0.334340\pi\) | |||||||
\(572\) | 291.937 | − | 338.627i | 0.510380 | − | 0.592005i | ||||
\(573\) | −168.813 | −0.294612 | ||||||||
\(574\) | −35.4363 | + | 95.3736i | −0.0617357 | + | 0.166156i | ||||
\(575\) | 186.263i | 0.323935i | ||||||||
\(576\) | 102.584 | − | 162.298i | 0.178098 | − | 0.281766i | ||||
\(577\) | 826.638 | 1.43265 | 0.716324 | − | 0.697768i | \(-0.245823\pi\) | ||||
0.716324 | + | 0.697768i | \(0.245823\pi\) | |||||||
\(578\) | 575.693 | + | 213.900i | 0.996008 | + | 0.370069i | ||||
\(579\) | − | 593.013i | − | 1.02420i | ||||||
\(580\) | 174.592 | + | 150.519i | 0.301020 | + | 0.259516i | ||||
\(581\) | −395.735 | −0.681127 | ||||||||
\(582\) | 88.0254 | − | 236.913i | 0.151246 | − | 0.407066i | ||||
\(583\) | − | 615.787i | − | 1.05624i | ||||||
\(584\) | −361.030 | − | 655.301i | −0.618202 | − | 1.12209i | ||||
\(585\) | 67.9151 | 0.116094 | ||||||||
\(586\) | −530.999 | − | 197.294i | −0.906142 | − | 0.336679i | ||||
\(587\) | 900.009i | 1.53323i | 0.642104 | + | 0.766617i | \(0.278062\pi\) | ||||
−0.642104 | + | 0.766617i | \(0.721938\pi\) | |||||||
\(588\) | −86.4249 | + | 100.247i | −0.146981 | + | 0.170488i | ||||
\(589\) | 114.991 | 0.195230 | ||||||||
\(590\) | −86.5104 | + | 232.835i | −0.146628 | + | 0.394636i | ||||
\(591\) | 129.008i | 0.218288i | ||||||||
\(592\) | 84.0071 | + | 564.169i | 0.141904 | + | 0.952987i | ||||
\(593\) | −704.088 | −1.18733 | −0.593666 | − | 0.804711i | \(-0.702320\pi\) | ||||
−0.593666 | + | 0.804711i | \(0.702320\pi\) | |||||||
\(594\) | −107.551 | − | 39.9606i | −0.181061 | − | 0.0672738i | ||||
\(595\) | − | 298.497i | − | 0.501675i | ||||||
\(596\) | −383.897 | − | 330.965i | −0.644122 | − | 0.555311i | ||||
\(597\) | 308.351 | 0.516501 | ||||||||
\(598\) | −262.715 | + | 707.075i | −0.439323 | + | 1.18240i | ||||
\(599\) | − | 376.098i | − | 0.627876i | −0.949444 | − | 0.313938i | \(-0.898352\pi\) | ||
0.949444 | − | 0.313938i | \(-0.101648\pi\) | |||||||
\(600\) | −60.6820 | + | 33.4320i | −0.101137 | + | 0.0557200i | ||||
\(601\) | 430.191 | 0.715791 | 0.357896 | − | 0.933762i | \(-0.383494\pi\) | ||||
0.357896 | + | 0.933762i | \(0.383494\pi\) | |||||||
\(602\) | 717.844 | + | 266.716i | 1.19243 | + | 0.443051i | ||||
\(603\) | 313.480i | 0.519868i | ||||||||
\(604\) | −178.756 | + | 207.344i | −0.295953 | + | 0.343285i | ||||
\(605\) | 1.98684 | 0.00328404 | ||||||||
\(606\) | −35.4824 | + | 95.4977i | −0.0585518 | + | 0.157587i | ||||
\(607\) | − | 93.4019i | − | 0.153875i | −0.997036 | − | 0.0769373i | \(-0.975486\pi\) | ||
0.997036 | − | 0.0769373i | \(-0.0245141\pi\) | |||||||
\(608\) | 744.436 | + | 157.058i | 1.22440 | + | 0.258319i | ||||
\(609\) | −244.075 | −0.400781 | ||||||||
\(610\) | 344.765 | + | 128.098i | 0.565189 | + | 0.209997i | ||||
\(611\) | 384.944i | 0.630024i | ||||||||
\(612\) | 221.897 | + | 191.302i | 0.362576 | + | 0.312585i | ||||
\(613\) | −156.506 | −0.255312 | −0.127656 | − | 0.991818i | \(-0.540745\pi\) | ||||
−0.127656 | + | 0.991818i | \(0.540745\pi\) | |||||||
\(614\) | 69.7113 | − | 187.622i | 0.113536 | − | 0.305573i | ||||
\(615\) | 36.0346i | 0.0585929i | ||||||||
\(616\) | −233.033 | − | 422.976i | −0.378301 | − | 0.686649i | ||||
\(617\) | −553.493 | −0.897072 | −0.448536 | − | 0.893765i | \(-0.648054\pi\) | ||||
−0.448536 | + | 0.893765i | \(0.648054\pi\) | |||||||
\(618\) | −91.5334 | − | 34.0094i | −0.148112 | − | 0.0550314i | ||||
\(619\) | − | 14.4398i | − | 0.0233276i | −0.999932 | − | 0.0116638i | \(-0.996287\pi\) | ||
0.999932 | − | 0.0116638i | \(-0.00371278\pi\) | |||||||
\(620\) | 28.2463 | − | 32.7637i | 0.0455586 | − | 0.0528447i | ||||
\(621\) | 193.570 | 0.311707 | ||||||||
\(622\) | 281.546 | − | 757.756i | 0.452646 | − | 1.21826i | ||||
\(623\) | − | 632.564i | − | 1.01535i | ||||||
\(624\) | −277.510 | + | 41.3224i | −0.444728 | + | 0.0662219i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | −241.056 | − | 89.5651i | −0.385074 | − | 0.143075i | ||||
\(627\) | − | 454.649i | − | 0.725117i | ||||||
\(628\) | 77.4893 | + | 66.8051i | 0.123391 | + | 0.106378i | ||||
\(629\) | −870.364 | −1.38373 | ||||||||
\(630\) | 25.5494 | − | 68.7638i | 0.0405545 | − | 0.109149i | ||||
\(631\) | − | 352.389i | − | 0.558460i | −0.960224 | − | 0.279230i | \(-0.909921\pi\) | ||
0.960224 | − | 0.279230i | \(-0.0900793\pi\) | |||||||
\(632\) | −345.977 | + | 190.612i | −0.547432 | + | 0.301601i | ||||
\(633\) | −321.976 | −0.508650 | ||||||||
\(634\) | 161.102 | + | 59.8579i | 0.254104 | + | 0.0944130i | ||||
\(635\) | − | 293.608i | − | 0.462375i | ||||||
\(636\) | −252.324 | + | 292.678i | −0.396735 | + | 0.460185i | ||||
\(637\) | 193.415 | 0.303634 | ||||||||
\(638\) | −198.203 | + | 533.445i | −0.310662 | + | 0.836120i | ||||
\(639\) | 230.241i | 0.360315i | ||||||||
\(640\) | 227.613 | − | 173.529i | 0.355645 | − | 0.271139i | ||||
\(641\) | −545.742 | −0.851391 | −0.425696 | − | 0.904866i | \(-0.639971\pi\) | ||||
−0.425696 | + | 0.904866i | \(0.639971\pi\) | |||||||
\(642\) | −14.6352 | − | 5.43772i | −0.0227962 | − | 0.00846997i | ||||
\(643\) | − | 757.447i | − | 1.17799i | −0.808137 | − | 0.588995i | \(-0.799524\pi\) | ||
0.808137 | − | 0.588995i | \(-0.200476\pi\) | |||||||
\(644\) | 617.079 | + | 531.997i | 0.958197 | + | 0.826082i | ||||
\(645\) | 271.220 | 0.420496 | ||||||||
\(646\) | −404.345 | + | 1088.26i | −0.625922 | + | 1.68461i | ||||
\(647\) | 1161.36i | 1.79500i | 0.441016 | + | 0.897499i | \(0.354618\pi\) | ||||
−0.441016 | + | 0.897499i | \(0.645382\pi\) | |||||||
\(648\) | 34.7435 | + | 63.0626i | 0.0536166 | + | 0.0973188i | ||||
\(649\) | −613.191 | −0.944824 | ||||||||
\(650\) | 94.9029 | + | 35.2614i | 0.146004 | + | 0.0542483i | ||||
\(651\) | 45.8030i | 0.0703579i | ||||||||
\(652\) | 165.793 | − | 192.308i | 0.254283 | − | 0.294950i | ||||
\(653\) | −621.231 | −0.951348 | −0.475674 | − | 0.879622i | \(-0.657796\pi\) | ||||
−0.475674 | + | 0.879622i | \(0.657796\pi\) | |||||||
\(654\) | −233.236 | + | 627.734i | −0.356630 | + | 0.959838i | ||||
\(655\) | − | 169.390i | − | 0.258610i | ||||||
\(656\) | −21.9250 | − | 147.242i | −0.0334223 | − | 0.224455i | ||||
\(657\) | 280.565 | 0.427039 | ||||||||
\(658\) | 389.755 | + | 144.814i | 0.592333 | + | 0.220083i | ||||
\(659\) | − | 736.047i | − | 1.11692i | −0.829533 | − | 0.558458i | \(-0.811393\pi\) | ||
0.829533 | − | 0.558458i | \(-0.188607\pi\) | |||||||
\(660\) | −129.541 | − | 111.680i | −0.196274 | − | 0.169212i | ||||
\(661\) | 383.845 | 0.580704 | 0.290352 | − | 0.956920i | \(-0.406228\pi\) | ||||
0.290352 | + | 0.956920i | \(0.406228\pi\) | |||||||
\(662\) | −127.746 | + | 343.817i | −0.192970 | + | 0.519362i | ||||
\(663\) | − | 428.125i | − | 0.645739i | ||||||
\(664\) | 507.141 | − | 279.403i | 0.763766 | − | 0.420788i | ||||
\(665\) | 290.686 | 0.437121 | ||||||||
\(666\) | −200.503 | − | 74.4974i | −0.301056 | − | 0.111858i | ||||
\(667\) | − | 960.096i | − | 1.43942i | ||||||
\(668\) | 32.3271 | − | 37.4972i | 0.0483939 | − | 0.0561335i | ||||
\(669\) | 351.128 | 0.524854 | ||||||||
\(670\) | −162.758 | + | 438.050i | −0.242923 | + | 0.653805i | ||||
\(671\) | 907.968i | 1.35316i | ||||||||
\(672\) | −62.5592 | + | 296.523i | −0.0930940 | + | 0.441255i | ||||
\(673\) | 984.464 | 1.46280 | 0.731400 | − | 0.681949i | \(-0.238867\pi\) | ||||
0.731400 | + | 0.681949i | \(0.238867\pi\) | |||||||
\(674\) | 315.205 | + | 117.115i | 0.467664 | + | 0.173761i | ||||
\(675\) | − | 25.9808i | − | 0.0384900i | ||||||
\(676\) | −201.468 | − | 173.690i | −0.298030 | − | 0.256938i | ||||
\(677\) | 673.154 | 0.994319 | 0.497160 | − | 0.867659i | \(-0.334376\pi\) | ||||
0.497160 | + | 0.867659i | \(0.334376\pi\) | |||||||
\(678\) | −91.1789 | + | 245.400i | −0.134482 | + | 0.361947i | ||||
\(679\) | 398.918i | 0.587507i | ||||||||
\(680\) | 210.749 | + | 382.529i | 0.309925 | + | 0.562542i | ||||
\(681\) | 88.8037 | 0.130402 | ||||||||
\(682\) | 100.106 | + | 37.1945i | 0.146783 | + | 0.0545374i | ||||
\(683\) | − | 291.192i | − | 0.426343i | −0.977015 | − | 0.213171i | \(-0.931621\pi\) | ||
0.977015 | − | 0.213171i | \(-0.0683793\pi\) | |||||||
\(684\) | −186.296 | + | 216.090i | −0.272362 | + | 0.315921i | ||||
\(685\) | −149.353 | −0.218034 | ||||||||
\(686\) | 259.387 | − | 698.117i | 0.378115 | − | 1.01766i | ||||
\(687\) | 583.798i | 0.849778i | ||||||||
\(688\) | −1108.24 | + | 165.022i | −1.61081 | + | 0.239857i | ||||
\(689\) | 564.689 | 0.819578 | ||||||||
\(690\) | 270.490 | + | 100.501i | 0.392014 | + | 0.145654i | ||||
\(691\) | 943.693i | 1.36569i | 0.730563 | + | 0.682846i | \(0.239258\pi\) | ||||
−0.730563 | + | 0.682846i | \(0.760742\pi\) | |||||||
\(692\) | 179.874 | + | 155.073i | 0.259933 | + | 0.224094i | ||||
\(693\) | 181.095 | 0.261321 | ||||||||
\(694\) | 95.7193 | − | 257.620i | 0.137924 | − | 0.371211i | ||||
\(695\) | 85.2420i | 0.122650i | ||||||||
\(696\) | 312.787 | − | 172.326i | 0.449406 | − | 0.247595i | ||||
\(697\) | 227.156 | 0.325905 | ||||||||
\(698\) | −25.2894 | − | 9.39633i | −0.0362312 | − | 0.0134618i | ||||
\(699\) | − | 139.058i | − | 0.198938i | ||||||
\(700\) | 71.4040 | − | 82.8237i | 0.102006 | − | 0.118320i | ||||
\(701\) | 885.681 | 1.26345 | 0.631727 | − | 0.775191i | \(-0.282346\pi\) | ||||
0.631727 | + | 0.775191i | \(0.282346\pi\) | |||||||
\(702\) | 36.6447 | − | 98.6259i | 0.0522004 | − | 0.140493i | ||||
\(703\) | − | 847.588i | − | 1.20567i | ||||||
\(704\) | 597.272 | + | 377.521i | 0.848397 | + | 0.536251i | ||||
\(705\) | 147.260 | 0.208879 | ||||||||
\(706\) | 456.596 | + | 169.649i | 0.646737 | + | 0.240296i | ||||
\(707\) | − | 160.801i | − | 0.227441i | ||||||
\(708\) | 291.444 | + | 251.260i | 0.411644 | + | 0.354887i | ||||
\(709\) | −286.183 | −0.403644 | −0.201822 | − | 0.979422i | \(-0.564686\pi\) | ||||
−0.201822 | + | 0.979422i | \(0.564686\pi\) | |||||||
\(710\) | −119.541 | + | 321.733i | −0.168367 | + | 0.453146i | ||||
\(711\) | − | 148.129i | − | 0.208339i | ||||||
\(712\) | 446.613 | + | 810.642i | 0.627266 | + | 1.13854i | ||||
\(713\) | −180.171 | −0.252694 | ||||||||
\(714\) | −433.475 | − | 161.059i | −0.607108 | − | 0.225572i | ||||
\(715\) | 249.935i | 0.349559i | ||||||||
\(716\) | 660.228 | − | 765.818i | 0.922106 | − | 1.06958i | ||||
\(717\) | −572.976 | −0.799129 | ||||||||
\(718\) | −12.4803 | + | 33.5895i | −0.0173820 | + | 0.0467820i | ||||
\(719\) | 666.163i | 0.926513i | 0.886224 | + | 0.463257i | \(0.153319\pi\) | ||||
−0.886224 | + | 0.463257i | \(0.846681\pi\) | |||||||
\(720\) | 15.8078 | + | 106.161i | 0.0219553 | + | 0.147446i | ||||
\(721\) | 154.125 | 0.213766 | ||||||||
\(722\) | −382.989 | − | 142.300i | −0.530455 | − | 0.197092i | ||||
\(723\) | − | 623.389i | − | 0.862226i | ||||||
\(724\) | 379.826 | + | 327.456i | 0.524622 | + | 0.452287i | ||||
\(725\) | −128.863 | −0.177742 | ||||||||
\(726\) | 1.07203 | − | 2.88528i | 0.00147663 | − | 0.00397422i | ||||
\(727\) | 856.270i | 1.17781i | 0.808201 | + | 0.588907i | \(0.200441\pi\) | ||||
−0.808201 | + | 0.588907i | \(0.799559\pi\) | |||||||
\(728\) | 387.877 | − | 213.696i | 0.532798 | − | 0.293538i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 392.054 | + | 145.668i | 0.537060 | + | 0.199546i | ||||
\(731\) | − | 1709.72i | − | 2.33888i | ||||||
\(732\) | 372.047 | − | 431.549i | 0.508261 | − | 0.589547i | ||||
\(733\) | −769.487 | −1.04978 | −0.524889 | − | 0.851171i | \(-0.675893\pi\) | ||||
−0.524889 | + | 0.851171i | \(0.675893\pi\) | |||||||
\(734\) | 166.076 | − | 446.978i | 0.226261 | − | 0.608961i | ||||
\(735\) | − | 73.9905i | − | 0.100667i | ||||||
\(736\) | −1166.41 | − | 246.083i | −1.58479 | − | 0.334352i | ||||
\(737\) | −1153.64 | −1.56532 | ||||||||
\(738\) | 52.3293 | + | 19.4431i | 0.0709069 | + | 0.0263456i | ||||
\(739\) | 1156.70i | 1.56522i | 0.622511 | + | 0.782611i | \(0.286113\pi\) | ||||
−0.622511 | + | 0.782611i | \(0.713887\pi\) | |||||||
\(740\) | −241.499 | − | 208.202i | −0.326350 | − | 0.281354i | ||||
\(741\) | 416.922 | 0.562647 | ||||||||
\(742\) | 212.433 | − | 571.746i | 0.286298 | − | 0.770547i | ||||
\(743\) | − | 426.794i | − | 0.574421i | −0.957868 | − | 0.287210i | \(-0.907272\pi\) | ||
0.957868 | − | 0.287210i | \(-0.0927278\pi\) | |||||||
\(744\) | −32.3386 | − | 58.6973i | −0.0434658 | − | 0.0788942i | ||||
\(745\) | 283.348 | 0.380332 | ||||||||
\(746\) | −339.842 | − | 126.269i | −0.455552 | − | 0.169261i | ||||
\(747\) | 217.130i | 0.290670i | ||||||||
\(748\) | −704.011 | + | 816.603i | −0.941191 | + | 1.09172i | ||||
\(749\) | 24.6429 | 0.0329011 | ||||||||
\(750\) | 13.4892 | − | 36.3049i | 0.0179855 | − | 0.0484065i | ||||
\(751\) | 1222.03i | 1.62721i | 0.581420 | + | 0.813604i | \(0.302497\pi\) | ||||
−0.581420 | + | 0.813604i | \(0.697503\pi\) | |||||||
\(752\) | −601.722 | + | 89.5990i | −0.800162 | + | 0.119148i | ||||
\(753\) | −540.768 | −0.718152 | ||||||||
\(754\) | −489.179 | − | 181.756i | −0.648779 | − | 0.241055i | ||||
\(755\) | − | 153.037i | − | 0.202698i | ||||||
\(756\) | −86.0729 | − | 74.2053i | −0.113853 | − | 0.0981551i | ||||
\(757\) | −1312.95 | −1.73442 | −0.867209 | − | 0.497945i | \(-0.834088\pi\) | ||||
−0.867209 | + | 0.497945i | \(0.834088\pi\) | |||||||
\(758\) | 213.296 | − | 574.067i | 0.281393 | − | 0.757344i | ||||
\(759\) | 712.358i | 0.938548i | ||||||||
\(760\) | −372.519 | + | 205.234i | −0.490156 | + | 0.270045i | ||||
\(761\) | −189.584 | −0.249124 | −0.124562 | − | 0.992212i | \(-0.539753\pi\) | ||||
−0.124562 | + | 0.992212i | \(0.539753\pi\) | |||||||
\(762\) | −426.376 | − | 158.421i | −0.559549 | − | 0.207902i | ||||
\(763\) | − | 1056.99i | − | 1.38531i | ||||||
\(764\) | −254.561 | + | 295.273i | −0.333195 | + | 0.386483i | ||||
\(765\) | −163.778 | −0.214089 | ||||||||
\(766\) | −100.326 | + | 270.019i | −0.130974 | + | 0.352505i | ||||
\(767\) | − | 562.308i | − | 0.733127i | ||||||
\(768\) | −129.185 | − | 424.169i | −0.168210 | − | 0.552303i | ||||
\(769\) | 254.995 | 0.331594 | 0.165797 | − | 0.986160i | \(-0.446980\pi\) | ||||
0.165797 | + | 0.986160i | \(0.446980\pi\) | |||||||
\(770\) | 253.058 | + | 94.0243i | 0.328647 | + | 0.122109i | ||||
\(771\) | 139.013i | 0.180302i | ||||||||
\(772\) | −1037.25 | − | 894.235i | −1.34359 | − | 1.15834i | ||||
\(773\) | 23.2536 | 0.0300823 | 0.0150411 | − | 0.999887i | \(-0.495212\pi\) | ||||
0.0150411 | + | 0.999887i | \(0.495212\pi\) | |||||||
\(774\) | 146.341 | − | 393.864i | 0.189071 | − | 0.508869i | ||||
\(775\) | 24.1824i | 0.0312030i | ||||||||
\(776\) | −281.650 | − | 511.220i | −0.362951 | − | 0.658788i | ||||
\(777\) | 337.611 | 0.434506 | ||||||||
\(778\) | 26.2654 | + | 9.75897i | 0.0337602 | + | 0.0125437i | ||||
\(779\) | 221.212i | 0.283969i | ||||||||
\(780\) | 102.413 | − | 118.792i | 0.131298 | − | 0.152297i | ||||
\(781\) | −847.312 | −1.08491 | ||||||||
\(782\) | 633.541 | − | 1705.12i | 0.810155 | − | 2.18046i | ||||
\(783\) | 133.919i | 0.171033i | ||||||||
\(784\) | 45.0189 | + | 302.335i | 0.0574221 | + | 0.385631i | ||||
\(785\) | −57.1935 | −0.0728580 | ||||||||
\(786\) | −245.987 | − | 91.3969i | −0.312960 | − | 0.116281i | ||||
\(787\) | − | 220.593i | − | 0.280296i | −0.990131 | − | 0.140148i | \(-0.955242\pi\) | ||
0.990131 | − | 0.140148i | \(-0.0447579\pi\) | |||||||
\(788\) | 225.651 | + | 194.538i | 0.286359 | + | 0.246876i | ||||
\(789\) | 845.183 | 1.07121 | ||||||||
\(790\) | 76.9081 | − | 206.991i | 0.0973520 | − | 0.262014i | ||||
\(791\) | − | 413.209i | − | 0.522388i | ||||||
\(792\) | −232.077 | + | 127.860i | −0.293026 | + | 0.161439i | ||||
\(793\) | −832.625 | −1.04997 | ||||||||
\(794\) | 73.3194 | + | 27.2420i | 0.0923418 | + | 0.0343098i | ||||
\(795\) | − | 216.020i | − | 0.271724i | ||||||
\(796\) | 464.979 | − | 539.343i | 0.584144 | − | 0.677566i | ||||
\(797\) | 1010.38 | 1.26773 | 0.633867 | − | 0.773442i | \(-0.281467\pi\) | ||||
0.633867 | + | 0.773442i | \(0.281467\pi\) | |||||||
\(798\) | 156.844 | − | 422.132i | 0.196546 | − | 0.528987i | ||||
\(799\) | − | 928.298i | − | 1.16183i | ||||||
\(800\) | −33.0290 | + | 156.554i | −0.0412863 | + | 0.195692i | ||||
\(801\) | −347.073 | −0.433300 | ||||||||
\(802\) | −226.974 | − | 84.3327i | −0.283010 | − | 0.105153i | ||||
\(803\) | 1032.51i | 1.28581i | ||||||||
\(804\) | 548.314 | + | 472.713i | 0.681983 | + | 0.587952i | ||||
\(805\) | −455.455 | −0.565783 | ||||||||
\(806\) | −34.1081 | + | 91.7990i | −0.0423178 | + | 0.113894i | ||||
\(807\) | − | 536.162i | − | 0.664389i | ||||||
\(808\) | 113.531 | + | 206.069i | 0.140509 | + | 0.255036i | ||||
\(809\) | 1410.37 | 1.74335 | 0.871674 | − | 0.490086i | \(-0.163035\pi\) | ||||
0.871674 | + | 0.490086i | \(0.163035\pi\) | |||||||
\(810\) | −37.7291 | − | 14.0183i | −0.0465792 | − | 0.0173066i | ||||
\(811\) | 950.157i | 1.17159i | 0.810460 | + | 0.585793i | \(0.199217\pi\) | ||||
−0.810460 | + | 0.585793i | \(0.800783\pi\) | |||||||
\(812\) | −368.054 | + | 426.917i | −0.453269 | + | 0.525760i | ||||
\(813\) | −84.8173 | −0.104326 | ||||||||
\(814\) | 274.158 | − | 737.873i | 0.336804 | − | 0.906478i | ||||
\(815\) | 141.939i | 0.174158i | ||||||||
\(816\) | 669.219 | − | 99.6496i | 0.820121 | − | 0.122120i | ||||
\(817\) | 1664.98 | 2.03792 | ||||||||
\(818\) | −1015.74 | − | 377.402i | −1.24174 | − | 0.461372i | ||||
\(819\) | 166.068i | 0.202769i | ||||||||
\(820\) | 63.0288 | + | 54.3385i | 0.0768644 | + | 0.0662664i | ||||
\(821\) | 77.3347 | 0.0941957 | 0.0470979 | − | 0.998890i | \(-0.485003\pi\) | ||||
0.0470979 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(822\) | −80.5858 | + | 216.890i | −0.0980363 | + | 0.263856i | ||||
\(823\) | 1260.16i | 1.53118i | 0.643328 | + | 0.765591i | \(0.277553\pi\) | ||||
−0.643328 | + | 0.765591i | \(0.722447\pi\) | |||||||
\(824\) | −197.514 | + | 108.818i | −0.239702 | + | 0.132061i | ||||
\(825\) | 95.6119 | 0.115893 | ||||||||
\(826\) | −569.335 | − | 211.538i | −0.689268 | − | 0.256099i | ||||
\(827\) | 438.047i | 0.529681i | 0.964292 | + | 0.264841i | \(0.0853194\pi\) | ||||
−0.964292 | + | 0.264841i | \(0.914681\pi\) | |||||||
\(828\) | 291.894 | − | 338.577i | 0.352529 | − | 0.408909i | ||||
\(829\) | 361.388 | 0.435933 | 0.217966 | − | 0.975956i | \(-0.430058\pi\) | ||||
0.217966 | + | 0.975956i | \(0.430058\pi\) | |||||||
\(830\) | −112.734 | + | 303.413i | −0.135824 | + | 0.365557i | ||||
\(831\) | − | 345.793i | − | 0.416117i | ||||||
\(832\) | −346.194 | + | 547.710i | −0.416098 | + | 0.658305i | ||||
\(833\) | −466.423 | −0.559931 | ||||||||
\(834\) | 123.788 | + | 45.9937i | 0.148427 | + | 0.0551483i | ||||
\(835\) | 27.6760i | 0.0331450i | ||||||||
\(836\) | −795.234 | − | 685.588i | −0.951237 | − | 0.820082i | ||||
\(837\) | 25.1310 | 0.0300251 | ||||||||
\(838\) | 479.123 | − | 1289.52i | 0.571746 | − | 1.53880i | ||||
\(839\) | 785.017i | 0.935658i | 0.883819 | + | 0.467829i | \(0.154964\pi\) | ||||
−0.883819 | + | 0.467829i | \(0.845036\pi\) | |||||||
\(840\) | −81.7489 | − | 148.381i | −0.0973201 | − | 0.176645i | ||||
\(841\) | −176.771 | −0.210192 | ||||||||
\(842\) | −851.890 | − | 316.521i | −1.01175 | − | 0.375916i | ||||
\(843\) | 105.932i | 0.125661i | ||||||||
\(844\) | −485.524 | + | 563.173i | −0.575265 | + | 0.667267i | ||||
\(845\) | 148.700 | 0.175977 | ||||||||
\(846\) | 79.4563 | − | 213.849i | 0.0939199 | − | 0.252777i | ||||
\(847\) | 4.85829i | 0.00573588i | ||||||||
\(848\) | 131.436 | + | 882.688i | 0.154995 | + | 1.04091i | ||||
\(849\) | −749.123 | −0.882359 | ||||||||
\(850\) | −228.859 | − | 85.0332i | −0.269246 | − | 0.100039i | ||||
\(851\) | 1328.03i | 1.56055i | ||||||||
\(852\) | 402.719 | + | 347.193i | 0.472675 | + | 0.407503i | ||||
\(853\) | 1113.79 | 1.30573 | 0.652865 | − | 0.757474i | \(-0.273567\pi\) | ||||
0.652865 | + | 0.757474i | \(0.273567\pi\) | |||||||
\(854\) | −313.230 | + | 843.030i | −0.366780 | + | 0.987155i | ||||
\(855\) | − | 159.492i | − | 0.186541i | ||||||
\(856\) | −31.5803 | + | 17.3988i | −0.0368929 | + | 0.0203257i | ||||
\(857\) | −306.591 | −0.357749 | −0.178875 | − | 0.983872i | \(-0.557246\pi\) | ||||
−0.178875 | + | 0.983872i | \(0.557246\pi\) | |||||||
\(858\) | 362.954 | + | 134.856i | 0.423023 | + | 0.157175i | ||||
\(859\) | 204.542i | 0.238116i | 0.992887 | + | 0.119058i | \(0.0379875\pi\) | ||||
−0.992887 | + | 0.119058i | \(0.962013\pi\) | |||||||
\(860\) | 408.987 | − | 474.396i | 0.475566 | − | 0.551623i | ||||
\(861\) | −88.1130 | −0.102338 | ||||||||
\(862\) | 324.706 | − | 873.918i | 0.376689 | − | 1.01383i | ||||
\(863\) | − | 654.384i | − | 0.758266i | −0.925342 | − | 0.379133i | \(-0.876222\pi\) | ||
0.925342 | − | 0.379133i | \(-0.123778\pi\) | |||||||
\(864\) | 162.695 | + | 34.3248i | 0.188305 | + | 0.0397277i | ||||
\(865\) | −132.762 | −0.153482 | ||||||||
\(866\) | 856.949 | + | 318.401i | 0.989549 | + | 0.367669i | ||||
\(867\) | 531.866i | 0.613456i | ||||||||
\(868\) | 80.1149 | + | 69.0687i | 0.0922982 | + | 0.0795722i | ||||
\(869\) | 545.129 | 0.627306 | ||||||||
\(870\) | −69.5302 | + | 187.134i | −0.0799198 | + | 0.215097i | ||||
\(871\) | − | 1057.91i | − | 1.21459i | ||||||
\(872\) | 746.272 | + | 1354.55i | 0.855817 | + | 1.55338i | ||||
\(873\) | 218.877 | 0.250718 | ||||||||
\(874\) | 1660.50 | + | 616.963i | 1.89989 | + | 0.705907i | ||||
\(875\) | 61.1307i | 0.0698637i | ||||||||
\(876\) | 423.078 | − | 490.741i | 0.482966 | − | 0.560206i | ||||
\(877\) | −604.453 | −0.689228 | −0.344614 | − | 0.938744i | \(-0.611990\pi\) | ||||
−0.344614 | + | 0.938744i | \(0.611990\pi\) | |||||||
\(878\) | −541.565 | + | 1457.58i | −0.616817 | + | 1.66011i | ||||
\(879\) | − | 490.575i | − | 0.558106i | ||||||
\(880\) | −390.683 | + | 58.1744i | −0.443958 | + | 0.0661072i | ||||
\(881\) | 1436.81 | 1.63089 | 0.815445 | − | 0.578834i | \(-0.196492\pi\) | ||||
0.815445 | + | 0.578834i | \(0.196492\pi\) | |||||||
\(882\) | −107.449 | − | 39.9227i | −0.121824 | − | 0.0452639i | ||||
\(883\) | 120.993i | 0.137025i | 0.997650 | + | 0.0685123i | \(0.0218252\pi\) | ||||
−0.997650 | + | 0.0685123i | \(0.978175\pi\) | |||||||
\(884\) | −748.841 | − | 645.592i | −0.847105 | − | 0.730307i | ||||
\(885\) | −215.110 | −0.243062 | ||||||||
\(886\) | −172.392 | + | 463.977i | −0.194573 | + | 0.523676i | ||||
\(887\) | − | 286.448i | − | 0.322941i | −0.986878 | − | 0.161470i | \(-0.948376\pi\) | ||
0.986878 | − | 0.161470i | \(-0.0516236\pi\) | |||||||
\(888\) | −432.654 | + | 238.365i | −0.487223 | + | 0.268429i | ||||
\(889\) | 717.940 | 0.807582 | ||||||||
\(890\) | −484.991 | − | 180.200i | −0.544934 | − | 0.202471i | ||||
\(891\) | − | 99.3628i | − | 0.111518i | ||||||
\(892\) | 529.483 | − | 614.164i | 0.593591 | − | 0.688524i | ||||
\(893\) | 904.007 | 1.01233 | ||||||||
\(894\) | 152.885 | − | 411.476i | 0.171012 | − | 0.460264i | ||||
\(895\) | 565.237i | 0.631550i | ||||||||
\(896\) | 424.318 | + | 556.566i | 0.473569 | + | 0.621168i | ||||
\(897\) | −653.246 | −0.728256 | ||||||||
\(898\) | 773.360 | + | 287.344i | 0.861203 | + | 0.319982i | ||||
\(899\) | − | 124.649i | − | 0.138652i | ||||||
\(900\) | −45.4434 | − | 39.1777i | −0.0504927 | − | 0.0435308i | ||||
\(901\) | −1361.75 | −1.51138 | ||||||||
\(902\) | −71.5525 | + | 192.577i | −0.0793265 | + | 0.213500i | ||||
\(903\) | 663.195i | 0.734436i | ||||||||
\(904\) | 291.740 | + | 529.534i | 0.322721 | + | 0.585768i | ||||
\(905\) | −280.343 | −0.309771 | ||||||||
\(906\) | −222.240 | − | 82.5736i | −0.245298 | − | 0.0911409i | ||||
\(907\) | 234.706i | 0.258772i | 0.991594 | + | 0.129386i | \(0.0413006\pi\) | ||||
−0.991594 | + | 0.129386i | \(0.958699\pi\) | |||||||
\(908\) | 133.912 | − | 155.328i | 0.147480 | − | 0.171066i | ||||
\(909\) | −88.2276 | −0.0970601 | ||||||||
\(910\) | −86.2221 | + | 232.059i | −0.0947496 | + | 0.255010i | ||||
\(911\) | 491.244i | 0.539236i | 0.962967 | + | 0.269618i | \(0.0868974\pi\) | ||||
−0.962967 | + | 0.269618i | \(0.913103\pi\) | |||||||
\(912\) | 97.0420 | + | 651.707i | 0.106406 | + | 0.714591i | ||||
\(913\) | −799.063 | −0.875206 | ||||||||
\(914\) | −1397.46 | − | 519.229i | −1.52895 | − | 0.568084i | ||||
\(915\) | 318.519i | 0.348108i | ||||||||
\(916\) | 1021.13 | + | 880.339i | 1.11477 | + | 0.961069i | ||||
\(917\) | 414.197 | 0.451687 | ||||||||
\(918\) | −88.3691 | + | 237.838i | −0.0962627 | + | 0.259082i | ||||
\(919\) | − | 356.091i | − | 0.387477i | −0.981053 | − | 0.193738i | \(-0.937939\pi\) | ||
0.981053 | − | 0.193738i | \(-0.0620613\pi\) | |||||||
\(920\) | 583.674 | − | 321.568i | 0.634428 | − | 0.349530i | ||||
\(921\) | 173.338 | 0.188207 | ||||||||
\(922\) | 153.010 | + | 56.8511i | 0.165954 | + | 0.0616607i | ||||
\(923\) | − | 777.002i | − | 0.841822i | ||||||
\(924\) | 273.083 | − | 316.757i | 0.295545 | − | 0.342811i | ||||
\(925\) | 178.246 | 0.192699 | ||||||||
\(926\) | −203.573 | + | 547.899i | −0.219841 | + | 0.591684i | ||||
\(927\) | − | 84.5651i | − | 0.0912244i | ||||||
\(928\) | 170.249 | − | 806.961i | 0.183458 | − | 0.869570i | ||||
\(929\) | −916.019 | −0.986027 | −0.493014 | − | 0.870022i | \(-0.664105\pi\) | ||||
−0.493014 | + | 0.870022i | \(0.664105\pi\) | |||||||
\(930\) | 35.1175 | + | 13.0480i | 0.0377607 | + | 0.0140301i | ||||
\(931\) | − | 454.217i | − | 0.487881i | ||||||
\(932\) | −243.229 | − | 209.693i | −0.260975 | − | 0.224992i | ||||
\(933\) | 700.069 | 0.750342 | ||||||||
\(934\) | 35.8154 | − | 96.3939i | 0.0383462 | − | 0.103205i | ||||
\(935\) | − | 602.721i | − | 0.644621i | ||||||
\(936\) | −117.250 | − | 212.819i | −0.125267 | − | 0.227371i | ||||
\(937\) | 143.818 | 0.153488 | 0.0767440 | − | 0.997051i | \(-0.475548\pi\) | ||||
0.0767440 | + | 0.997051i | \(0.475548\pi\) | |||||||
\(938\) | −1071.13 | − | 397.981i | −1.14193 | − | 0.424287i | ||||
\(939\) | − | 222.705i | − | 0.237173i | ||||||
\(940\) | 222.060 | − | 257.574i | 0.236234 | − | 0.274015i | ||||
\(941\) | −1488.04 | −1.58133 | −0.790667 | − | 0.612246i | \(-0.790266\pi\) | ||||
−0.790667 | + | 0.612246i | \(0.790266\pi\) | |||||||
\(942\) | −30.8597 | + | 83.0561i | −0.0327597 | + | 0.0881699i | ||||
\(943\) | − | 346.602i | − | 0.367552i | ||||||
\(944\) | 878.966 | − | 130.882i | 0.931108 | − | 0.138646i | ||||
\(945\) | 63.5289 | 0.0672264 | ||||||||
\(946\) | 1449.46 | + | 538.551i | 1.53220 | + | 0.569292i | ||||
\(947\) | − | 1095.51i | − | 1.15682i | −0.815745 | − | 0.578411i | \(-0.803673\pi\) | ||
0.815745 | − | 0.578411i | \(-0.196327\pi\) | |||||||
\(948\) | −259.095 | − | 223.371i | −0.273307 | − | 0.235623i | ||||
\(949\) | −946.829 | −0.997713 | ||||||||
\(950\) | 82.8081 | − | 222.871i | 0.0871664 | − | 0.234601i | ||||
\(951\) | 148.838i | 0.156506i | ||||||||
\(952\) | −935.370 | + | 515.331i | −0.982532 | + | 0.541314i | ||||
\(953\) | 1277.86 | 1.34089 | 0.670443 | − | 0.741961i | \(-0.266104\pi\) | ||||
0.670443 | + | 0.741961i | \(0.266104\pi\) | |||||||
\(954\) | −313.704 | − | 116.557i | −0.328830 | − | 0.122177i | ||||
\(955\) | − | 217.936i | − | 0.228205i | ||||||
\(956\) | −864.020 | + | 1002.20i | −0.903786 | + | 1.04833i | ||||
\(957\) | −492.834 | −0.514978 | ||||||||
\(958\) | −85.3953 | + | 229.834i | −0.0891392 | + | 0.239910i | ||||
\(959\) | − | 365.202i | − | 0.380816i | ||||||
\(960\) | 209.525 | + | 132.436i | 0.218255 | + | 0.137954i | ||||
\(961\) | 937.609 | 0.975659 | ||||||||
\(962\) | 676.644 | + | 251.409i | 0.703372 | + | 0.261339i | ||||
\(963\) | − | 13.5210i | − | 0.0140405i | ||||||
\(964\) | −1090.38 | − | 940.041i | −1.13110 | − | 0.975146i | ||||
\(965\) | 765.576 | 0.793343 | ||||||||
\(966\) | −245.748 | + | 661.410i | −0.254398 | + | 0.684689i | ||||
\(967\) | − | 237.958i | − | 0.246079i | −0.992402 | − | 0.123039i | \(-0.960736\pi\) | ||
0.992402 | − | 0.123039i | \(-0.0392641\pi\) | |||||||
\(968\) | −3.43013 | − | 6.22598i | −0.00354352 | − | 0.00643180i | ||||
\(969\) | −1005.41 | −1.03758 | ||||||||
\(970\) | 305.853 | + | 113.640i | 0.315312 | + | 0.117155i | ||||
\(971\) | − | 1602.10i | − | 1.64995i | −0.565169 | − | 0.824975i | \(-0.691189\pi\) | ||
0.565169 | − | 0.824975i | \(-0.308811\pi\) | |||||||
\(972\) | −40.7147 | + | 47.2262i | −0.0418876 | + | 0.0485866i | ||||
\(973\) | −208.436 | −0.214220 | ||||||||
\(974\) | −45.9643 | + | 123.709i | −0.0471912 | + | 0.127011i | ||||
\(975\) | 87.6780i | 0.0899262i | ||||||||
\(976\) | −193.800 | − | 1301.51i | −0.198566 | − | 1.33351i | ||||
\(977\) | 918.977 | 0.940611 | 0.470305 | − | 0.882504i | \(-0.344144\pi\) | ||||
0.470305 | + | 0.882504i | \(0.344144\pi\) | |||||||
\(978\) | 206.123 | + | 76.5855i | 0.210760 | + | 0.0783083i | ||||
\(979\) | − | 1277.27i | − | 1.30466i | ||||||
\(980\) | −129.418 | − | 111.574i | −0.132059 | − | 0.113851i | ||||
\(981\) | −579.945 | −0.591178 | ||||||||
\(982\) | −251.578 | + | 677.100i | −0.256189 | + | 0.689511i | ||||
\(983\) | 1162.30i | 1.18240i | 0.806525 | + | 0.591200i | \(0.201346\pi\) | ||||
−0.806525 | + | 0.591200i | \(0.798654\pi\) | |||||||
\(984\) | 112.918 | − | 62.2109i | 0.114754 | − | 0.0632225i | ||||
\(985\) | −166.549 | −0.169085 | ||||||||
\(986\) | 1179.66 | + | 438.306i | 1.19641 | + | 0.444530i | ||||
\(987\) | 360.083i | 0.364826i | ||||||||
\(988\) | 628.698 | − | 729.245i | 0.636334 | − | 0.738103i | ||||
\(989\) | −2608.75 | −2.63776 | ||||||||
\(990\) | 51.5889 | − | 138.847i | 0.0521100 | − | 0.140250i | ||||
\(991\) | − | 491.614i | − | 0.496079i | −0.968750 | − | 0.248040i | \(-0.920214\pi\) | ||
0.968750 | − | 0.248040i | \(-0.0797863\pi\) | |||||||
\(992\) | −151.434 | − | 31.9488i | −0.152655 | − | 0.0322064i | ||||
\(993\) | −317.643 | −0.319882 | ||||||||
\(994\) | −786.712 | − | 292.305i | −0.791461 | − | 0.294069i | ||||
\(995\) | 398.080i | 0.400080i | ||||||||
\(996\) | 379.787 | + | 327.422i | 0.381312 | + | 0.328737i | ||||
\(997\) | −1262.51 | −1.26630 | −0.633152 | − | 0.774027i | \(-0.718239\pi\) | ||||
−0.633152 | + | 0.774027i | \(0.718239\pi\) | |||||||
\(998\) | 495.363 | − | 1333.22i | 0.496355 | − | 1.33590i | ||||
\(999\) | − | 185.239i | − | 0.185425i |
(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 | 60.3.c.a.31.8 | yes | 8 | |
3.2 | odd | 2 | 180.3.c.b.91.1 | 8 | |||
4.3 | odd | 2 | inner | 60.3.c.a.31.7 | ✓ | 8 | |
5.2 | odd | 4 | 300.3.f.b.199.6 | 16 | |||
5.3 | odd | 4 | 300.3.f.b.199.11 | 16 | |||
5.4 | even | 2 | 300.3.c.d.151.1 | 8 | |||
8.3 | odd | 2 | 960.3.e.c.511.8 | 8 | |||
8.5 | even | 2 | 960.3.e.c.511.3 | 8 | |||
12.11 | even | 2 | 180.3.c.b.91.2 | 8 | |||
15.2 | even | 4 | 900.3.f.f.199.11 | 16 | |||
15.8 | even | 4 | 900.3.f.f.199.6 | 16 | |||
15.14 | odd | 2 | 900.3.c.u.451.8 | 8 | |||
20.3 | even | 4 | 300.3.f.b.199.5 | 16 | |||
20.7 | even | 4 | 300.3.f.b.199.12 | 16 | |||
20.19 | odd | 2 | 300.3.c.d.151.2 | 8 | |||
24.5 | odd | 2 | 2880.3.e.j.2431.2 | 8 | |||
24.11 | even | 2 | 2880.3.e.j.2431.3 | 8 | |||
60.23 | odd | 4 | 900.3.f.f.199.12 | 16 | |||
60.47 | odd | 4 | 900.3.f.f.199.5 | 16 | |||
60.59 | even | 2 | 900.3.c.u.451.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.7 | ✓ | 8 | 4.3 | odd | 2 | inner | |
60.3.c.a.31.8 | yes | 8 | 1.1 | even | 1 | trivial | |
180.3.c.b.91.1 | 8 | 3.2 | odd | 2 | |||
180.3.c.b.91.2 | 8 | 12.11 | even | 2 | |||
300.3.c.d.151.1 | 8 | 5.4 | even | 2 | |||
300.3.c.d.151.2 | 8 | 20.19 | odd | 2 | |||
300.3.f.b.199.5 | 16 | 20.3 | even | 4 | |||
300.3.f.b.199.6 | 16 | 5.2 | odd | 4 | |||
300.3.f.b.199.11 | 16 | 5.3 | odd | 4 | |||
300.3.f.b.199.12 | 16 | 20.7 | even | 4 | |||
900.3.c.u.451.7 | 8 | 60.59 | even | 2 | |||
900.3.c.u.451.8 | 8 | 15.14 | odd | 2 | |||
900.3.f.f.199.5 | 16 | 60.47 | odd | 4 | |||
900.3.f.f.199.6 | 16 | 15.8 | even | 4 | |||
900.3.f.f.199.11 | 16 | 15.2 | even | 4 | |||
900.3.f.f.199.12 | 16 | 60.23 | odd | 4 | |||
960.3.e.c.511.3 | 8 | 8.5 | even | 2 | |||
960.3.e.c.511.8 | 8 | 8.3 | odd | 2 | |||
2880.3.e.j.2431.2 | 8 | 24.5 | odd | 2 | |||
2880.3.e.j.2431.3 | 8 | 24.11 | even | 2 |