Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(199,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.f (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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 12x^{12} + 25x^{10} + 53x^{8} + 100x^{6} + 192x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.12 | ||
Root | \(-0.422403 + 1.34966i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.199 |
Dual form | 300.3.f.b.199.11 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.696577 | + | 1.87477i | 0.348288 | + | 0.937387i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.02956 | + | 2.61185i | −0.757390 | + | 0.652962i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.20651 | − | 3.24721i | −0.201084 | − | 0.541201i | ||||
\(7\) | −5.46770 | −0.781100 | −0.390550 | − | 0.920582i | \(-0.627715\pi\) | ||||
−0.390550 | + | 0.920582i | \(0.627715\pi\) | |||||||
\(8\) | −7.00695 | − | 3.86039i | −0.875869 | − | 0.482549i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0403i | 1.00366i | 0.864965 | + | 0.501832i | \(0.167341\pi\) | ||||
−0.864965 | + | 0.501832i | \(0.832659\pi\) | |||||||
\(12\) | 5.24735 | − | 4.52386i | 0.437280 | − | 0.376988i | ||||
\(13\) | − | 10.1242i | − | 0.778784i | −0.921072 | − | 0.389392i | \(-0.872685\pi\) | ||
0.921072 | − | 0.389392i | \(-0.127315\pi\) | |||||||
\(14\) | −3.80867 | − | 10.2507i | −0.272048 | − | 0.732193i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.35649 | − | 15.8255i | 0.147280 | − | 0.989095i | ||||
\(17\) | − | 24.4146i | − | 1.43615i | −0.695964 | − | 0.718077i | \(-0.745023\pi\) | ||
0.695964 | − | 0.718077i | \(-0.254977\pi\) | |||||||
\(18\) | 2.08973 | + | 5.62432i | 0.116096 | + | 0.312462i | ||||
\(19\) | − | 23.7757i | − | 1.25135i | −0.780082 | − | 0.625677i | \(-0.784823\pi\) | ||
0.780082 | − | 0.625677i | \(-0.215177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.47033 | 0.450968 | ||||||||
\(22\) | −20.6981 | + | 7.69043i | −0.940823 | + | 0.349565i | ||||
\(23\) | −37.2526 | −1.61968 | −0.809838 | − | 0.586653i | \(-0.800445\pi\) | ||||
−0.809838 | + | 0.586653i | \(0.800445\pi\) | |||||||
\(24\) | 12.1364 | + | 6.68640i | 0.505683 | + | 0.278600i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 18.9806 | − | 7.05227i | 0.730022 | − | 0.271241i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 16.5647 | − | 14.2808i | 0.591598 | − | 0.510029i | ||||
\(29\) | 25.7726 | 0.888712 | 0.444356 | − | 0.895850i | \(-0.353433\pi\) | ||||
0.444356 | + | 0.895850i | \(0.353433\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.83647i | − | 0.156015i | −0.996953 | − | 0.0780076i | \(-0.975144\pi\) | ||
0.996953 | − | 0.0780076i | \(-0.0248558\pi\) | |||||||
\(32\) | 31.3108 | − | 6.60580i | 0.978461 | − | 0.206431i | ||||
\(33\) | − | 19.1224i | − | 0.579466i | ||||||
\(34\) | 45.7719 | − | 17.0066i | 1.34623 | − | 0.500196i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.08868 | + | 7.83555i | −0.252463 | + | 0.217654i | ||||
\(37\) | 35.6493i | 0.963495i | 0.876310 | + | 0.481747i | \(0.159998\pi\) | ||||
−0.876310 | + | 0.481747i | \(0.840002\pi\) | |||||||
\(38\) | 44.5741 | − | 16.5616i | 1.17300 | − | 0.435832i | ||||
\(39\) | 17.5356i | 0.449631i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.30410 | −0.226929 | −0.113465 | − | 0.993542i | \(-0.536195\pi\) | ||||
−0.113465 | + | 0.993542i | \(0.536195\pi\) | |||||||
\(42\) | 6.59682 | + | 17.7547i | 0.157067 | + | 0.422732i | ||||
\(43\) | −70.0287 | −1.62857 | −0.814287 | − | 0.580462i | \(-0.802872\pi\) | ||||
−0.814287 | + | 0.580462i | \(0.802872\pi\) | |||||||
\(44\) | −28.8356 | − | 33.4473i | −0.655355 | − | 0.760166i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −25.9493 | − | 69.8401i | −0.564114 | − | 1.51826i | ||||
\(47\) | 38.0223 | 0.808984 | 0.404492 | − | 0.914542i | \(-0.367448\pi\) | ||||
0.404492 | + | 0.914542i | \(0.367448\pi\) | |||||||
\(48\) | −4.08156 | + | 27.4106i | −0.0850324 | + | 0.571054i | ||||
\(49\) | −19.1043 | −0.389883 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42.2873i | 0.829164i | ||||||||
\(52\) | 26.4428 | + | 30.6718i | 0.508516 | + | 0.589843i | ||||
\(53\) | − | 55.7762i | − | 1.05238i | −0.850366 | − | 0.526191i | \(-0.823620\pi\) | ||
0.850366 | − | 0.526191i | \(-0.176380\pi\) | |||||||
\(54\) | −3.61952 | − | 9.74162i | −0.0670281 | − | 0.180400i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 38.3119 | + | 21.1075i | 0.684141 | + | 0.376919i | ||||
\(57\) | 41.1808i | 0.722470i | ||||||||
\(58\) | 17.9526 | + | 48.3179i | 0.309528 | + | 0.833067i | ||||
\(59\) | − | 55.5411i | − | 0.941374i | −0.882300 | − | 0.470687i | \(-0.844006\pi\) | ||
0.882300 | − | 0.470687i | \(-0.155994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −82.2412 | −1.34822 | −0.674108 | − | 0.738633i | \(-0.735472\pi\) | ||||
−0.674108 | + | 0.738633i | \(0.735472\pi\) | |||||||
\(62\) | 9.06729 | − | 3.36897i | 0.146247 | − | 0.0543383i | ||||
\(63\) | −16.4031 | −0.260367 | ||||||||
\(64\) | 34.1947 | + | 54.0992i | 0.534293 | + | 0.845299i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 35.8502 | − | 13.3202i | 0.543184 | − | 0.201821i | ||||
\(67\) | −104.493 | −1.55960 | −0.779802 | − | 0.626026i | \(-0.784680\pi\) | ||||
−0.779802 | + | 0.626026i | \(0.784680\pi\) | |||||||
\(68\) | 63.7673 | + | 73.9656i | 0.937754 | + | 1.08773i | ||||
\(69\) | 64.5233 | 0.935120 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 76.7471i | 1.08094i | 0.841362 | + | 0.540472i | \(0.181754\pi\) | ||||
−0.841362 | + | 0.540472i | \(0.818246\pi\) | |||||||
\(72\) | −21.0209 | − | 11.5812i | −0.291956 | − | 0.160850i | ||||
\(73\) | 93.5215i | 1.28112i | 0.767910 | + | 0.640558i | \(0.221297\pi\) | ||||
−0.767910 | + | 0.640558i | \(0.778703\pi\) | |||||||
\(74\) | −66.8344 | + | 24.8325i | −0.903168 | + | 0.335574i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 62.0986 | + | 72.0300i | 0.817087 | + | 0.947764i | ||||
\(77\) | − | 60.3651i | − | 0.783963i | ||||||
\(78\) | −32.8753 | + | 12.2149i | −0.421478 | + | 0.156601i | ||||
\(79\) | 49.3762i | 0.625016i | 0.949915 | + | 0.312508i | \(0.101169\pi\) | ||||
−0.949915 | + | 0.312508i | \(0.898831\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −6.48102 | − | 17.4431i | −0.0790368 | − | 0.212721i | ||||
\(83\) | 72.3768 | 0.872010 | 0.436005 | − | 0.899944i | \(-0.356393\pi\) | ||||
0.436005 | + | 0.899944i | \(0.356393\pi\) | |||||||
\(84\) | −28.6910 | + | 24.7351i | −0.341559 | + | 0.294465i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −48.7804 | − | 131.288i | −0.567214 | − | 1.52661i | ||||
\(87\) | −44.6395 | −0.513098 | ||||||||
\(88\) | 42.6199 | − | 77.3589i | 0.484318 | − | 0.879079i | ||||
\(89\) | −115.691 | −1.29990 | −0.649950 | − | 0.759977i | \(-0.725210\pi\) | ||||
−0.649950 | + | 0.759977i | \(0.725210\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 55.3560i | 0.608308i | ||||||||
\(92\) | 112.859 | − | 97.2980i | 1.22673 | − | 1.05759i | ||||
\(93\) | 8.37701i | 0.0900754i | ||||||||
\(94\) | 26.4854 | + | 71.2832i | 0.281760 | + | 0.758332i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −54.2318 | + | 11.4416i | −0.564915 | + | 0.119183i | ||||
\(97\) | − | 72.9589i | − | 0.752154i | −0.926588 | − | 0.376077i | \(-0.877273\pi\) | ||
0.926588 | − | 0.376077i | \(-0.122727\pi\) | |||||||
\(98\) | −13.3076 | − | 35.8162i | −0.135792 | − | 0.365471i | ||||
\(99\) | 33.1209i | 0.334555i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 29.4092 | 0.291180 | 0.145590 | − | 0.989345i | \(-0.453492\pi\) | ||||
0.145590 | + | 0.989345i | \(0.453492\pi\) | |||||||
\(102\) | −79.2792 | + | 29.4564i | −0.777247 | + | 0.288788i | ||||
\(103\) | −28.1884 | −0.273673 | −0.136837 | − | 0.990594i | \(-0.543694\pi\) | ||||
−0.136837 | + | 0.990594i | \(0.543694\pi\) | |||||||
\(104\) | −39.0833 | + | 70.9397i | −0.375801 | + | 0.682112i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 104.568 | − | 38.8524i | 0.986490 | − | 0.366532i | ||||
\(107\) | 4.50700 | 0.0421215 | 0.0210607 | − | 0.999778i | \(-0.493296\pi\) | ||||
0.0210607 | + | 0.999778i | \(0.493296\pi\) | |||||||
\(108\) | 15.7421 | − | 13.5716i | 0.145760 | − | 0.125663i | ||||
\(109\) | −193.315 | −1.77353 | −0.886767 | − | 0.462217i | \(-0.847054\pi\) | ||||
−0.886767 | + | 0.462217i | \(0.847054\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 61.7464i | − | 0.556274i | ||||||
\(112\) | −12.8846 | + | 86.5292i | −0.115041 | + | 0.772582i | ||||
\(113\) | − | 75.5727i | − | 0.668785i | −0.942434 | − | 0.334392i | \(-0.891469\pi\) | ||
0.942434 | − | 0.334392i | \(-0.108531\pi\) | |||||||
\(114\) | −77.2047 | + | 28.6856i | −0.677234 | + | 0.251628i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −78.0798 | + | 67.3142i | −0.673102 | + | 0.580295i | ||||
\(117\) | − | 30.3726i | − | 0.259595i | ||||||
\(118\) | 104.127 | − | 38.6886i | 0.882432 | − | 0.327870i | ||||
\(119\) | 133.492i | 1.12178i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.888544 | −0.00734334 | ||||||||
\(122\) | −57.2873 | − | 154.184i | −0.469568 | − | 1.26380i | ||||
\(123\) | 16.1152 | 0.131018 | ||||||||
\(124\) | 12.6321 | + | 14.6524i | 0.101872 | + | 0.118164i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.4260 | − | 30.7521i | −0.0906827 | − | 0.244064i | ||||
\(127\) | 131.306 | 1.03390 | 0.516951 | − | 0.856015i | \(-0.327067\pi\) | ||||
0.516951 | + | 0.856015i | \(0.327067\pi\) | |||||||
\(128\) | −77.6045 | + | 101.792i | −0.606285 | + | 0.795247i | ||||
\(129\) | 121.293 | 0.940258 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 75.7533i | − | 0.578270i | −0.957288 | − | 0.289135i | \(-0.906632\pi\) | ||
0.957288 | − | 0.289135i | \(-0.0933676\pi\) | |||||||
\(132\) | 49.9448 | + | 57.9324i | 0.378370 | + | 0.438882i | ||||
\(133\) | 129.999i | 0.977433i | ||||||||
\(134\) | −72.7877 | − | 195.902i | −0.543192 | − | 1.46195i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −94.2500 | + | 171.072i | −0.693014 | + | 1.25788i | ||||
\(137\) | 66.7927i | 0.487538i | 0.969833 | + | 0.243769i | \(0.0783839\pi\) | ||||
−0.969833 | + | 0.243769i | \(0.921616\pi\) | |||||||
\(138\) | 44.9454 | + | 120.967i | 0.325692 | + | 0.876570i | ||||
\(139\) | − | 38.1214i | − | 0.274255i | −0.990553 | − | 0.137127i | \(-0.956213\pi\) | ||
0.990553 | − | 0.137127i | \(-0.0437869\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −65.8565 | −0.467067 | ||||||||
\(142\) | −143.884 | + | 53.4602i | −1.01326 | + | 0.376481i | ||||
\(143\) | 111.774 | 0.781638 | ||||||||
\(144\) | 7.06946 | − | 47.4765i | 0.0490935 | − | 0.329698i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −175.332 | + | 65.1449i | −1.20090 | + | 0.446198i | ||||
\(147\) | 33.0895 | 0.225099 | ||||||||
\(148\) | −93.1106 | − | 108.002i | −0.629126 | − | 0.729742i | ||||
\(149\) | 126.717 | 0.850449 | 0.425225 | − | 0.905088i | \(-0.360195\pi\) | ||||
0.425225 | + | 0.905088i | \(0.360195\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 68.4403i | − | 0.453247i | −0.973982 | − | 0.226623i | \(-0.927231\pi\) | ||
0.973982 | − | 0.226623i | \(-0.0727687\pi\) | |||||||
\(152\) | −91.7836 | + | 166.595i | −0.603840 | + | 1.09602i | ||||
\(153\) | − | 73.2438i | − | 0.478718i | ||||||
\(154\) | 113.171 | − | 42.0489i | 0.734877 | − | 0.273045i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −45.8004 | − | 53.1252i | −0.293592 | − | 0.340546i | ||||
\(157\) | 25.5777i | 0.162915i | 0.996677 | + | 0.0814577i | \(0.0259575\pi\) | ||||
−0.996677 | + | 0.0814577i | \(0.974042\pi\) | |||||||
\(158\) | −92.5693 | + | 34.3943i | −0.585882 | + | 0.217686i | ||||
\(159\) | 96.6073i | 0.607593i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 203.686 | 1.26513 | ||||||||
\(162\) | 6.26919 | + | 16.8730i | 0.0386987 | + | 0.104154i | ||||
\(163\) | 63.4771 | 0.389430 | 0.194715 | − | 0.980860i | \(-0.437622\pi\) | ||||
0.194715 | + | 0.980860i | \(0.437622\pi\) | |||||||
\(164\) | 28.1873 | − | 24.3009i | 0.171874 | − | 0.148176i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 50.4160 | + | 135.690i | 0.303711 | + | 0.817411i | ||||
\(167\) | −12.3771 | −0.0741144 | −0.0370572 | − | 0.999313i | \(-0.511798\pi\) | ||||
−0.0370572 | + | 0.999313i | \(0.511798\pi\) | |||||||
\(168\) | −66.3582 | − | 36.5592i | −0.394989 | − | 0.217614i | ||||
\(169\) | 66.5008 | 0.393496 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 71.3272i | − | 0.417118i | ||||||
\(172\) | 212.156 | − | 182.904i | 1.23347 | − | 1.06340i | ||||
\(173\) | − | 59.3729i | − | 0.343196i | −0.985167 | − | 0.171598i | \(-0.945107\pi\) | ||
0.985167 | − | 0.171598i | \(-0.0548930\pi\) | |||||||
\(174\) | −31.0948 | − | 83.6890i | −0.178706 | − | 0.480971i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 174.719 | + | 26.0164i | 0.992720 | + | 0.147820i | ||||
\(177\) | 96.2000i | 0.543503i | ||||||||
\(178\) | −80.5877 | − | 216.895i | −0.452740 | − | 1.21851i | ||||
\(179\) | − | 252.782i | − | 1.41219i | −0.708118 | − | 0.706094i | \(-0.750455\pi\) | ||
0.708118 | − | 0.706094i | \(-0.249545\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 125.373 | 0.692670 | 0.346335 | − | 0.938111i | \(-0.387426\pi\) | ||||
0.346335 | + | 0.938111i | \(0.387426\pi\) | |||||||
\(182\) | −103.780 | + | 38.5597i | −0.570220 | + | 0.211867i | ||||
\(183\) | 142.446 | 0.778393 | ||||||||
\(184\) | 261.027 | + | 143.809i | 1.41862 | + | 0.781573i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.7050 | + | 5.83523i | −0.0844355 | + | 0.0313722i | ||||
\(187\) | 269.545 | 1.44142 | ||||||||
\(188\) | −115.191 | + | 99.3084i | −0.612717 | + | 0.528236i | ||||
\(189\) | 28.4110 | 0.150323 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 97.4640i | − | 0.510283i | −0.966904 | − | 0.255141i | \(-0.917878\pi\) | ||
0.966904 | − | 0.255141i | \(-0.0821220\pi\) | |||||||
\(192\) | −59.2270 | − | 93.7025i | −0.308474 | − | 0.488034i | ||||
\(193\) | 342.376i | 1.77397i | 0.461798 | + | 0.886985i | \(0.347204\pi\) | ||||
−0.461798 | + | 0.886985i | \(0.652796\pi\) | |||||||
\(194\) | 136.782 | − | 50.8215i | 0.705060 | − | 0.261966i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 57.8775 | − | 49.8974i | 0.295293 | − | 0.254579i | ||||
\(197\) | 74.4829i | 0.378086i | 0.981969 | + | 0.189043i | \(0.0605386\pi\) | ||||
−0.981969 | + | 0.189043i | \(0.939461\pi\) | |||||||
\(198\) | −62.0943 | + | 23.0713i | −0.313608 | + | 0.116522i | ||||
\(199\) | − | 178.027i | − | 0.894606i | −0.894382 | − | 0.447303i | \(-0.852385\pi\) | ||
0.894382 | − | 0.447303i | \(-0.147615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 180.988 | 0.900438 | ||||||||
\(202\) | 20.4858 | + | 55.1356i | 0.101415 | + | 0.272949i | ||||
\(203\) | −140.917 | −0.694173 | ||||||||
\(204\) | −110.448 | − | 128.112i | −0.541413 | − | 0.628000i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −19.6354 | − | 52.8468i | −0.0953172 | − | 0.256538i | ||||
\(207\) | −111.758 | −0.539892 | ||||||||
\(208\) | −160.220 | − | 23.8575i | −0.770291 | − | 0.114700i | ||||
\(209\) | 262.491 | 1.25594 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 185.893i | − | 0.881008i | −0.897751 | − | 0.440504i | \(-0.854800\pi\) | ||
0.897751 | − | 0.440504i | \(-0.145200\pi\) | |||||||
\(212\) | 145.679 | + | 168.978i | 0.687166 | + | 0.797064i | ||||
\(213\) | − | 132.930i | − | 0.624084i | ||||||
\(214\) | 3.13947 | + | 8.44961i | 0.0146704 | + | 0.0394842i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 36.4092 | + | 20.0592i | 0.168561 | + | 0.0928666i | ||||
\(217\) | 26.4444i | 0.121863i | ||||||||
\(218\) | −134.659 | − | 362.422i | −0.617701 | − | 1.66249i | ||||
\(219\) | − | 161.984i | − | 0.739653i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −247.178 | −1.11845 | ||||||||
\(222\) | 115.761 | − | 43.0111i | 0.521444 | − | 0.193744i | ||||
\(223\) | 202.724 | 0.909074 | 0.454537 | − | 0.890728i | \(-0.349805\pi\) | ||||
0.454537 | + | 0.890728i | \(0.349805\pi\) | |||||||
\(224\) | −171.198 | + | 36.1186i | −0.764276 | + | 0.161244i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 141.682 | − | 52.6422i | 0.626910 | − | 0.232930i | ||||
\(227\) | −51.2708 | −0.225863 | −0.112931 | − | 0.993603i | \(-0.536024\pi\) | ||||
−0.112931 | + | 0.993603i | \(0.536024\pi\) | |||||||
\(228\) | −107.558 | − | 124.760i | −0.471745 | − | 0.547192i | ||||
\(229\) | −337.056 | −1.47186 | −0.735930 | − | 0.677058i | \(-0.763255\pi\) | ||||
−0.735930 | + | 0.677058i | \(0.763255\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 104.555i | 0.452621i | ||||||||
\(232\) | −180.588 | − | 99.4925i | −0.778395 | − | 0.428847i | ||||
\(233\) | 80.2851i | 0.344571i | 0.985047 | + | 0.172286i | \(0.0551152\pi\) | ||||
−0.985047 | + | 0.172286i | \(0.944885\pi\) | |||||||
\(234\) | 56.9417 | − | 21.1568i | 0.243341 | − | 0.0904138i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 145.065 | + | 168.265i | 0.614682 | + | 0.712988i | ||||
\(237\) | − | 85.5221i | − | 0.360853i | ||||||
\(238\) | −250.267 | + | 92.9873i | −1.05154 | + | 0.390703i | ||||
\(239\) | 330.808i | 1.38413i | 0.721834 | + | 0.692066i | \(0.243299\pi\) | ||||
−0.721834 | + | 0.692066i | \(0.756701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −359.914 | −1.49342 | −0.746710 | − | 0.665150i | \(-0.768368\pi\) | ||||
−0.746710 | + | 0.665150i | \(0.768368\pi\) | |||||||
\(242\) | −0.618939 | − | 1.66582i | −0.00255760 | − | 0.00688355i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 249.155 | − | 214.802i | 1.02113 | − | 0.880334i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.2255 | + | 30.2123i | 0.0456319 | + | 0.122814i | ||||
\(247\) | −240.710 | −0.974534 | ||||||||
\(248\) | −18.6707 | + | 33.8889i | −0.0752850 | + | 0.136649i | ||||
\(249\) | −125.360 | −0.503455 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 312.213i | − | 1.24388i | −0.783067 | − | 0.621938i | \(-0.786346\pi\) | ||
0.783067 | − | 0.621938i | \(-0.213654\pi\) | |||||||
\(252\) | 49.6942 | − | 42.8424i | 0.197199 | − | 0.170010i | ||||
\(253\) | − | 411.280i | − | 1.62561i | ||||||
\(254\) | 91.4645 | + | 246.169i | 0.360096 | + | 0.969167i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −244.894 | − | 74.5853i | −0.956617 | − | 0.291349i | ||||
\(257\) | 80.2592i | 0.312293i | 0.987734 | + | 0.156146i | \(0.0499072\pi\) | ||||
−0.987734 | + | 0.156146i | \(0.950093\pi\) | |||||||
\(258\) | 84.4901 | + | 227.398i | 0.327481 | + | 0.881386i | ||||
\(259\) | − | 194.920i | − | 0.752586i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 77.3179 | 0.296237 | ||||||||
\(262\) | 142.020 | − | 52.7680i | 0.542063 | − | 0.201405i | ||||
\(263\) | 487.967 | 1.85539 | 0.927694 | − | 0.373342i | \(-0.121788\pi\) | ||||
0.927694 | + | 0.373342i | \(0.121788\pi\) | |||||||
\(264\) | −73.8199 | + | 133.990i | −0.279621 | + | 0.507536i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −243.718 | + | 90.5540i | −0.916233 | + | 0.340428i | ||||
\(267\) | 200.383 | 0.750498 | ||||||||
\(268\) | 316.569 | − | 272.921i | 1.18123 | − | 1.01836i | ||||
\(269\) | 309.553 | 1.15076 | 0.575378 | − | 0.817888i | \(-0.304855\pi\) | ||||
0.575378 | + | 0.817888i | \(0.304855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 48.9693i | − | 0.180698i | −0.995910 | − | 0.0903492i | \(-0.971202\pi\) | ||
0.995910 | − | 0.0903492i | \(-0.0287983\pi\) | |||||||
\(272\) | −386.374 | − | 57.5327i | −1.42049 | − | 0.211517i | ||||
\(273\) | − | 95.8794i | − | 0.351207i | ||||||
\(274\) | −125.221 | + | 46.5262i | −0.457012 | + | 0.169804i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −195.477 | + | 168.525i | −0.708251 | + | 0.610598i | ||||
\(277\) | − | 199.644i | − | 0.720736i | −0.932810 | − | 0.360368i | \(-0.882651\pi\) | ||
0.932810 | − | 0.360368i | \(-0.117349\pi\) | |||||||
\(278\) | 71.4690 | − | 26.5545i | 0.257083 | − | 0.0955197i | ||||
\(279\) | − | 14.5094i | − | 0.0520051i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 61.1598 | 0.217650 | 0.108825 | − | 0.994061i | \(-0.465291\pi\) | ||||
0.108825 | + | 0.994061i | \(0.465291\pi\) | |||||||
\(282\) | −45.8741 | − | 123.466i | −0.162674 | − | 0.437823i | ||||
\(283\) | −432.506 | −1.52829 | −0.764145 | − | 0.645044i | \(-0.776839\pi\) | ||||
−0.764145 | + | 0.645044i | \(0.776839\pi\) | |||||||
\(284\) | −200.452 | − | 232.510i | −0.705816 | − | 0.818697i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 77.8593 | + | 209.551i | 0.272235 | + | 0.732697i | ||||
\(287\) | 50.8720 | 0.177254 | ||||||||
\(288\) | 93.9323 | − | 19.8174i | 0.326154 | − | 0.0688105i | ||||
\(289\) | −307.073 | −1.06254 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 126.369i | 0.434256i | ||||||||
\(292\) | −244.264 | − | 283.329i | −0.836521 | − | 0.970305i | ||||
\(293\) | 283.234i | 0.966668i | 0.875436 | + | 0.483334i | \(0.160574\pi\) | ||||
−0.875436 | + | 0.483334i | \(0.839426\pi\) | |||||||
\(294\) | 23.0494 | + | 62.0354i | 0.0783993 | + | 0.211005i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 137.620 | − | 249.793i | 0.464933 | − | 0.843895i | ||||
\(297\) | − | 57.3672i | − | 0.193155i | ||||||
\(298\) | 88.2681 | + | 237.566i | 0.296202 | + | 0.797200i | ||||
\(299\) | 377.152i | 1.26138i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 382.896 | 1.27208 | ||||||||
\(302\) | 128.310 | − | 47.6739i | 0.424868 | − | 0.157861i | ||||
\(303\) | −50.9382 | −0.168113 | ||||||||
\(304\) | −376.263 | − | 56.0272i | −1.23771 | − | 0.184300i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 137.316 | − | 51.0199i | 0.448744 | − | 0.166732i | ||||
\(307\) | −100.077 | −0.325983 | −0.162992 | − | 0.986627i | \(-0.552114\pi\) | ||||
−0.162992 | + | 0.986627i | \(0.552114\pi\) | |||||||
\(308\) | 157.665 | + | 182.880i | 0.511898 | + | 0.593766i | ||||
\(309\) | 48.8237 | 0.158005 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 404.185i | 1.29963i | 0.760092 | + | 0.649815i | \(0.225154\pi\) | ||||
−0.760092 | + | 0.649815i | \(0.774846\pi\) | |||||||
\(312\) | 67.6943 | − | 122.871i | 0.216969 | − | 0.393818i | ||||
\(313\) | 128.579i | 0.410795i | 0.978679 | + | 0.205398i | \(0.0658487\pi\) | ||||
−0.978679 | + | 0.205398i | \(0.934151\pi\) | |||||||
\(314\) | −47.9525 | + | 17.8168i | −0.152715 | + | 0.0567415i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −128.963 | − | 149.588i | −0.408112 | − | 0.473381i | ||||
\(317\) | 85.9315i | 0.271077i | 0.990772 | + | 0.135539i | \(0.0432765\pi\) | ||||
−0.990772 | + | 0.135539i | \(0.956724\pi\) | |||||||
\(318\) | −181.117 | + | 67.2944i | −0.569550 | + | 0.211618i | ||||
\(319\) | 284.538i | 0.891969i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.80635 | −0.0243189 | ||||||||
\(322\) | 141.883 | + | 381.865i | 0.440630 | + | 1.18592i | ||||
\(323\) | −580.475 | −1.79714 | ||||||||
\(324\) | −27.2661 | + | 23.5066i | −0.0841545 | + | 0.0725514i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 44.2167 | + | 119.005i | 0.135634 | + | 0.365047i | ||||
\(327\) | 334.832 | 1.02395 | ||||||||
\(328\) | 65.1934 | + | 35.9175i | 0.198760 | + | 0.109505i | ||||
\(329\) | −207.894 | −0.631898 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 183.391i | − | 0.554052i | −0.960862 | − | 0.277026i | \(-0.910651\pi\) | ||
0.960862 | − | 0.277026i | \(-0.0893488\pi\) | |||||||
\(332\) | −219.270 | + | 189.037i | −0.660452 | + | 0.569390i | ||||
\(333\) | 106.948i | 0.321165i | ||||||||
\(334\) | −8.62160 | − | 23.2043i | −0.0258132 | − | 0.0694739i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 22.3167 | − | 149.873i | 0.0664188 | − | 0.446050i | ||||
\(337\) | 168.130i | 0.498901i | 0.968388 | + | 0.249451i | \(0.0802500\pi\) | ||||
−0.968388 | + | 0.249451i | \(0.919750\pi\) | |||||||
\(338\) | 46.3229 | + | 124.674i | 0.137050 | + | 0.368858i | ||||
\(339\) | 130.896i | 0.386123i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.3962 | 0.156587 | ||||||||
\(342\) | 133.722 | − | 49.6849i | 0.391001 | − | 0.145277i | ||||
\(343\) | 372.374 | 1.08564 | ||||||||
\(344\) | 490.688 | + | 270.338i | 1.42642 | + | 0.785867i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 111.311 | − | 41.3578i | 0.321708 | − | 0.119531i | ||||
\(347\) | −137.414 | −0.396006 | −0.198003 | − | 0.980201i | \(-0.563446\pi\) | ||||
−0.198003 | + | 0.980201i | \(0.563446\pi\) | |||||||
\(348\) | 135.238 | − | 116.592i | 0.388615 | − | 0.335034i | ||||
\(349\) | 13.4893 | 0.0386513 | 0.0193256 | − | 0.999813i | \(-0.493848\pi\) | ||||
0.0193256 | + | 0.999813i | \(0.493848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 52.6068i | 0.149877i | ||||||||
\(352\) | 72.9301 | + | 345.681i | 0.207188 | + | 0.982047i | ||||
\(353\) | − | 243.547i | − | 0.689935i | −0.938615 | − | 0.344968i | \(-0.887890\pi\) | ||
0.938615 | − | 0.344968i | \(-0.112110\pi\) | |||||||
\(354\) | −180.353 | + | 67.0107i | −0.509473 | + | 0.189296i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 350.493 | − | 302.168i | 0.984532 | − | 0.848786i | ||||
\(357\) | − | 231.215i | − | 0.647660i | ||||||
\(358\) | 473.909 | − | 176.082i | 1.32377 | − | 0.491849i | ||||
\(359\) | 17.9166i | 0.0499068i | 0.999689 | + | 0.0249534i | \(0.00794374\pi\) | ||||
−0.999689 | + | 0.0249534i | \(0.992056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −204.285 | −0.565887 | ||||||||
\(362\) | 87.3321 | + | 235.047i | 0.241249 | + | 0.649300i | ||||
\(363\) | 1.53900 | 0.00423968 | ||||||||
\(364\) | −144.582 | − | 167.704i | −0.397202 | − | 0.460727i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 99.2245 | + | 267.054i | 0.271105 | + | 0.729656i | ||||
\(367\) | −238.417 | −0.649637 | −0.324818 | − | 0.945776i | \(-0.605303\pi\) | ||||
−0.324818 | + | 0.945776i | \(0.605303\pi\) | |||||||
\(368\) | −87.7852 | + | 589.541i | −0.238547 | + | 1.60201i | ||||
\(369\) | −27.9123 | −0.0756431 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 304.968i | 0.822016i | ||||||||
\(372\) | −21.8795 | − | 25.3787i | −0.0588158 | − | 0.0682222i | ||||
\(373\) | 181.271i | 0.485981i | 0.970029 | + | 0.242990i | \(0.0781283\pi\) | ||||
−0.970029 | + | 0.242990i | \(0.921872\pi\) | |||||||
\(374\) | 187.759 | + | 505.336i | 0.502029 | + | 1.35117i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −266.420 | − | 146.781i | −0.708564 | − | 0.390375i | ||||
\(377\) | − | 260.927i | − | 0.692114i | ||||||
\(378\) | 19.7904 | + | 53.2642i | 0.0523557 | + | 0.140911i | ||||
\(379\) | − | 306.206i | − | 0.807931i | −0.914774 | − | 0.403965i | \(-0.867632\pi\) | ||
0.914774 | − | 0.403965i | \(-0.132368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −227.428 | −0.596924 | ||||||||
\(382\) | 182.723 | − | 67.8912i | 0.478333 | − | 0.177726i | ||||
\(383\) | −144.027 | −0.376050 | −0.188025 | − | 0.982164i | \(-0.560209\pi\) | ||||
−0.188025 | + | 0.982164i | \(0.560209\pi\) | |||||||
\(384\) | 134.415 | − | 176.308i | 0.350039 | − | 0.459136i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −641.878 | + | 238.491i | −1.66290 | + | 0.617853i | ||||
\(387\) | −210.086 | −0.542858 | ||||||||
\(388\) | 190.558 | + | 221.034i | 0.491128 | + | 0.569674i | ||||
\(389\) | −14.0099 | −0.0360152 | −0.0180076 | − | 0.999838i | \(-0.505732\pi\) | ||||
−0.0180076 | + | 0.999838i | \(0.505732\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 909.506i | 2.32610i | ||||||||
\(392\) | 133.863 | + | 73.7499i | 0.341486 | + | 0.188138i | ||||
\(393\) | 131.209i | 0.333864i | ||||||||
\(394\) | −139.639 | + | 51.8831i | −0.354413 | + | 0.131683i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −86.5069 | − | 100.342i | −0.218452 | − | 0.253389i | ||||
\(397\) | 39.1084i | 0.0985098i | 0.998786 | + | 0.0492549i | \(0.0156847\pi\) | ||||
−0.998786 | + | 0.0492549i | \(0.984315\pi\) | |||||||
\(398\) | 333.760 | − | 124.009i | 0.838592 | − | 0.311581i | ||||
\(399\) | − | 225.164i | − | 0.564321i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −121.067 | −0.301913 | −0.150957 | − | 0.988540i | \(-0.548235\pi\) | ||||
−0.150957 | + | 0.988540i | \(0.548235\pi\) | |||||||
\(402\) | 126.072 | + | 339.312i | 0.313612 | + | 0.844059i | ||||
\(403\) | −48.9653 | −0.121502 | ||||||||
\(404\) | −89.0970 | + | 76.8124i | −0.220537 | + | 0.190130i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −98.1595 | − | 264.188i | −0.241772 | − | 0.650709i | ||||
\(407\) | −393.579 | −0.967026 | ||||||||
\(408\) | 163.246 | − | 296.305i | 0.400112 | − | 0.726239i | ||||
\(409\) | 541.795 | 1.32468 | 0.662342 | − | 0.749202i | \(-0.269563\pi\) | ||||
0.662342 | + | 0.749202i | \(0.269563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 115.688i | − | 0.281480i | ||||||
\(412\) | 85.3983 | − | 73.6237i | 0.207278 | − | 0.178698i | ||||
\(413\) | 303.682i | 0.735307i | ||||||||
\(414\) | −77.8478 | − | 209.520i | −0.188038 | − | 0.506088i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −66.8784 | − | 316.996i | −0.160765 | − | 0.762009i | ||||
\(417\) | 66.0282i | 0.158341i | ||||||||
\(418\) | 182.845 | + | 492.112i | 0.437429 | + | 1.17730i | ||||
\(419\) | − | 687.825i | − | 1.64159i | −0.571224 | − | 0.820794i | \(-0.693531\pi\) | ||
0.571224 | − | 0.820794i | \(-0.306469\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −454.396 | −1.07932 | −0.539662 | − | 0.841882i | \(-0.681448\pi\) | ||||
−0.539662 | + | 0.841882i | \(0.681448\pi\) | |||||||
\(422\) | 348.507 | − | 129.489i | 0.825846 | − | 0.306845i | ||||
\(423\) | 114.067 | 0.269661 | ||||||||
\(424\) | −215.318 | + | 390.821i | −0.507826 | + | 0.921749i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 249.214 | − | 92.5959i | 0.585008 | − | 0.217361i | ||||
\(427\) | 449.670 | 1.05309 | ||||||||
\(428\) | −13.6542 | + | 11.7716i | −0.0319024 | + | 0.0275037i | ||||
\(429\) | −193.599 | −0.451279 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 466.145i | 1.08154i | 0.841169 | + | 0.540772i | \(0.181868\pi\) | ||||
−0.841169 | + | 0.540772i | \(0.818132\pi\) | |||||||
\(432\) | −12.2447 | + | 82.2318i | −0.0283441 | + | 0.190351i | ||||
\(433\) | − | 457.094i | − | 1.05565i | −0.849355 | − | 0.527823i | \(-0.823009\pi\) | ||
0.849355 | − | 0.527823i | \(-0.176991\pi\) | |||||||
\(434\) | −49.5772 | + | 18.4205i | −0.114233 | + | 0.0424436i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 585.660 | − | 504.910i | 1.34326 | − | 1.15805i | ||||
\(437\) | 885.706i | 2.02679i | ||||||||
\(438\) | 303.684 | − | 112.834i | 0.693341 | − | 0.257613i | ||||
\(439\) | 777.467i | 1.77100i | 0.464644 | + | 0.885498i | \(0.346182\pi\) | ||||
−0.464644 | + | 0.885498i | \(0.653818\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −57.3128 | −0.129961 | ||||||||
\(442\) | −172.178 | − | 463.403i | −0.389544 | − | 1.04842i | ||||
\(443\) | −247.484 | −0.558654 | −0.279327 | − | 0.960196i | \(-0.590111\pi\) | ||||
−0.279327 | + | 0.960196i | \(0.590111\pi\) | |||||||
\(444\) | 161.272 | + | 187.065i | 0.363226 | + | 0.421316i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 141.213 | + | 380.061i | 0.316620 | + | 0.852155i | ||||
\(447\) | −219.480 | −0.491007 | ||||||||
\(448\) | −186.967 | − | 295.798i | −0.417336 | − | 0.660263i | ||||
\(449\) | −412.508 | −0.918726 | −0.459363 | − | 0.888249i | \(-0.651922\pi\) | ||||
−0.459363 | + | 0.888249i | \(0.651922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 102.720i | − | 0.227761i | ||||||
\(452\) | 197.384 | + | 228.952i | 0.436691 | + | 0.506531i | ||||
\(453\) | 118.542i | 0.261682i | ||||||||
\(454\) | −35.7141 | − | 96.1213i | −0.0786654 | − | 0.211721i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 158.974 | − | 288.552i | 0.348627 | − | 0.632789i | ||||
\(457\) | − | 745.400i | − | 1.63107i | −0.578706 | − | 0.815537i | \(-0.696442\pi\) | ||
0.578706 | − | 0.815537i | \(-0.303558\pi\) | |||||||
\(458\) | −234.785 | − | 631.904i | −0.512631 | − | 1.37970i | ||||
\(459\) | 126.862i | 0.276388i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 81.6151 | 0.177039 | 0.0885196 | − | 0.996074i | \(-0.471786\pi\) | ||||
0.0885196 | + | 0.996074i | \(0.471786\pi\) | |||||||
\(462\) | −196.018 | + | 72.8309i | −0.424281 | + | 0.157643i | ||||
\(463\) | −292.248 | −0.631205 | −0.315603 | − | 0.948891i | \(-0.602207\pi\) | ||||
−0.315603 | + | 0.948891i | \(0.602207\pi\) | |||||||
\(464\) | 60.7329 | − | 407.865i | 0.130890 | − | 0.879020i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −150.517 | + | 55.9248i | −0.322997 | + | 0.120010i | ||||
\(467\) | −51.4163 | −0.110099 | −0.0550495 | − | 0.998484i | \(-0.517532\pi\) | ||||
−0.0550495 | + | 0.998484i | \(0.517532\pi\) | |||||||
\(468\) | 79.3285 | + | 92.0155i | 0.169505 | + | 0.196614i | ||||
\(469\) | 571.339 | 1.21821 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 44.3019i | − | 0.0940592i | ||||||
\(472\) | −214.410 | + | 389.174i | −0.454259 | + | 0.824520i | ||||
\(473\) | − | 773.139i | − | 1.63454i | ||||||
\(474\) | 160.335 | − | 59.5727i | 0.338259 | − | 0.125681i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −348.660 | − | 404.422i | −0.732480 | − | 0.849625i | ||||
\(477\) | − | 167.329i | − | 0.350794i | ||||||
\(478\) | −620.190 | + | 230.433i | −1.29747 | + | 0.482077i | ||||
\(479\) | 122.593i | 0.255935i | 0.991778 | + | 0.127967i | \(0.0408453\pi\) | ||||
−0.991778 | + | 0.127967i | \(0.959155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 360.920 | 0.750354 | ||||||||
\(482\) | −250.708 | − | 674.758i | −0.520141 | − | 1.39991i | ||||
\(483\) | −352.794 | −0.730423 | ||||||||
\(484\) | 2.69190 | − | 2.32074i | 0.00556177 | − | 0.00479492i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.8586 | − | 29.2248i | −0.0223427 | − | 0.0601334i | ||||
\(487\) | 65.9859 | 0.135495 | 0.0677474 | − | 0.997703i | \(-0.478419\pi\) | ||||
0.0677474 | + | 0.997703i | \(0.478419\pi\) | |||||||
\(488\) | 576.260 | + | 317.483i | 1.18086 | + | 0.650580i | ||||
\(489\) | −109.946 | −0.224837 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 361.163i | − | 0.735567i | −0.929911 | − | 0.367783i | \(-0.880117\pi\) | ||
0.929911 | − | 0.367783i | \(-0.119883\pi\) | |||||||
\(492\) | −48.8219 | + | 42.0904i | −0.0992315 | + | 0.0855496i | ||||
\(493\) | − | 629.229i | − | 1.27633i | ||||||
\(494\) | −167.673 | − | 451.277i | −0.339419 | − | 0.913516i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −76.5396 | − | 11.3971i | −0.154314 | − | 0.0229780i | ||||
\(497\) | − | 419.630i | − | 0.844326i | ||||||
\(498\) | −87.3231 | − | 235.022i | −0.175348 | − | 0.471933i | ||||
\(499\) | − | 711.138i | − | 1.42513i | −0.701608 | − | 0.712564i | \(-0.747534\pi\) | ||
0.701608 | − | 0.712564i | \(-0.252466\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.4378 | 0.0427900 | ||||||||
\(502\) | 585.328 | − | 217.480i | 1.16599 | − | 0.433227i | ||||
\(503\) | −353.756 | −0.703292 | −0.351646 | − | 0.936133i | \(-0.614378\pi\) | ||||
−0.351646 | + | 0.936133i | \(0.614378\pi\) | |||||||
\(504\) | 114.936 | + | 63.3224i | 0.228047 | + | 0.125640i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 771.057 | − | 286.488i | 1.52383 | − | 0.566182i | ||||
\(507\) | −115.183 | −0.227185 | ||||||||
\(508\) | −397.799 | + | 342.951i | −0.783068 | + | 0.675100i | ||||
\(509\) | −478.049 | −0.939192 | −0.469596 | − | 0.882881i | \(-0.655600\pi\) | ||||
−0.469596 | + | 0.882881i | \(0.655600\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 511.348i | − | 1.00068i | ||||||
\(512\) | −30.7568 | − | 511.075i | −0.0600720 | − | 0.998194i | ||||
\(513\) | 123.542i | 0.240823i | ||||||||
\(514\) | −150.468 | + | 55.9067i | −0.292739 | + | 0.108768i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −367.466 | + | 316.800i | −0.712142 | + | 0.613953i | ||||
\(517\) | 419.778i | 0.811949i | ||||||||
\(518\) | 365.431 | − | 135.777i | 0.705464 | − | 0.262117i | ||||
\(519\) | 102.837i | 0.198144i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.7365 | −0.0685921 | −0.0342960 | − | 0.999412i | \(-0.510919\pi\) | ||||
−0.0342960 | + | 0.999412i | \(0.510919\pi\) | |||||||
\(522\) | 53.8579 | + | 144.954i | 0.103176 | + | 0.277689i | ||||
\(523\) | −733.562 | −1.40260 | −0.701302 | − | 0.712864i | \(-0.747398\pi\) | ||||
−0.701302 | + | 0.712864i | \(0.747398\pi\) | |||||||
\(524\) | 197.856 | + | 229.499i | 0.377588 | + | 0.437976i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 339.906 | + | 914.828i | 0.646210 | + | 1.73922i | ||||
\(527\) | −118.081 | −0.224062 | ||||||||
\(528\) | −302.622 | − | 45.0617i | −0.573147 | − | 0.0853441i | ||||
\(529\) | 858.753 | 1.62335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 166.623i | − | 0.313791i | ||||||
\(532\) | −339.537 | − | 393.839i | −0.638227 | − | 0.740298i | ||||
\(533\) | 94.1965i | 0.176729i | ||||||||
\(534\) | 139.582 | + | 375.673i | 0.261390 | + | 0.703507i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 732.181 | + | 403.386i | 1.36601 | + | 0.752585i | ||||
\(537\) | 437.831i | 0.815327i | ||||||||
\(538\) | 215.628 | + | 580.342i | 0.400795 | + | 1.07870i | ||||
\(539\) | − | 210.917i | − | 0.391312i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 608.939 | 1.12558 | 0.562790 | − | 0.826600i | \(-0.309728\pi\) | ||||
0.562790 | + | 0.826600i | \(0.309728\pi\) | |||||||
\(542\) | 91.8064 | − | 34.1109i | 0.169384 | − | 0.0629352i | ||||
\(543\) | −217.153 | −0.399913 | ||||||||
\(544\) | −161.278 | − | 764.440i | −0.296467 | − | 1.40522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 179.752 | − | 66.7874i | 0.329217 | − | 0.122321i | ||||
\(547\) | −78.5868 | −0.143669 | −0.0718344 | − | 0.997417i | \(-0.522885\pi\) | ||||
−0.0718344 | + | 0.997417i | \(0.522885\pi\) | |||||||
\(548\) | −174.452 | − | 202.353i | −0.318344 | − | 0.369257i | ||||
\(549\) | −246.724 | −0.449405 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 612.763i | − | 1.11209i | ||||||
\(552\) | −452.112 | − | 249.085i | −0.819043 | − | 0.451242i | ||||
\(553\) | − | 269.974i | − | 0.488200i | ||||||
\(554\) | 374.287 | − | 139.067i | 0.675609 | − | 0.251024i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 99.5673 | + | 115.491i | 0.179078 | + | 0.207718i | ||||
\(557\) | − | 928.488i | − | 1.66694i | −0.552561 | − | 0.833472i | \(-0.686349\pi\) | ||
0.552561 | − | 0.833472i | \(-0.313651\pi\) | |||||||
\(558\) | 27.2019 | − | 10.1069i | 0.0487489 | − | 0.0181128i | ||||
\(559\) | 708.984i | 1.26831i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −466.866 | −0.832202 | ||||||||
\(562\) | 42.6025 | + | 114.661i | 0.0758051 | + | 0.204023i | ||||
\(563\) | 447.978 | 0.795697 | 0.397849 | − | 0.917451i | \(-0.369757\pi\) | ||||
0.397849 | + | 0.917451i | \(0.369757\pi\) | |||||||
\(564\) | 199.516 | − | 172.007i | 0.353752 | − | 0.304977i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −301.274 | − | 810.852i | −0.532286 | − | 1.43260i | ||||
\(567\) | −49.2093 | −0.0867889 | ||||||||
\(568\) | 296.274 | − | 537.763i | 0.521609 | − | 0.946766i | ||||
\(569\) | −571.441 | −1.00429 | −0.502145 | − | 0.864783i | \(-0.667456\pi\) | ||||
−0.502145 | + | 0.864783i | \(0.667456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 990.801i | 1.73520i | 0.497260 | + | 0.867602i | \(0.334340\pi\) | ||||
−0.497260 | + | 0.867602i | \(0.665660\pi\) | |||||||
\(572\) | −338.627 | + | 291.937i | −0.592005 | + | 0.510380i | ||||
\(573\) | 168.813i | 0.294612i | ||||||||
\(574\) | 35.4363 | + | 95.3736i | 0.0617357 | + | 0.166156i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 102.584 | + | 162.298i | 0.178098 | + | 0.281766i | ||||
\(577\) | 826.638i | 1.43265i | 0.697768 | + | 0.716324i | \(0.254177\pi\) | ||||
−0.697768 | + | 0.716324i | \(0.745823\pi\) | |||||||
\(578\) | −213.900 | − | 575.693i | −0.370069 | − | 0.996008i | ||||
\(579\) | − | 593.013i | − | 1.02420i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −395.735 | −0.681127 | ||||||||
\(582\) | −236.913 | + | 88.0254i | −0.407066 | + | 0.151246i | ||||
\(583\) | 615.787 | 1.05624 | ||||||||
\(584\) | 361.030 | − | 655.301i | 0.618202 | − | 1.12209i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −530.999 | + | 197.294i | −0.906142 | + | 0.336679i | ||||
\(587\) | 900.009 | 1.53323 | 0.766617 | − | 0.642104i | \(-0.221938\pi\) | ||||
0.766617 | + | 0.642104i | \(0.221938\pi\) | |||||||
\(588\) | −100.247 | + | 86.4249i | −0.170488 | + | 0.146981i | ||||
\(589\) | −114.991 | −0.195230 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 129.008i | − | 0.218288i | ||||||
\(592\) | 564.169 | + | 84.0071i | 0.952987 | + | 0.141904i | ||||
\(593\) | 704.088i | 1.18733i | 0.804711 | + | 0.593666i | \(0.202320\pi\) | ||||
−0.804711 | + | 0.593666i | \(0.797680\pi\) | |||||||
\(594\) | 107.551 | − | 39.9606i | 0.181061 | − | 0.0672738i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −383.897 | + | 330.965i | −0.644122 | + | 0.555311i | ||||
\(597\) | 308.351i | 0.516501i | ||||||||
\(598\) | −707.075 | + | 262.715i | −1.18240 | + | 0.439323i | ||||
\(599\) | − | 376.098i | − | 0.627876i | −0.949444 | − | 0.313938i | \(-0.898352\pi\) | ||
0.949444 | − | 0.313938i | \(-0.101648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 430.191 | 0.715791 | 0.357896 | − | 0.933762i | \(-0.383494\pi\) | ||||
0.357896 | + | 0.933762i | \(0.383494\pi\) | |||||||
\(602\) | 266.716 | + | 717.844i | 0.443051 | + | 1.19243i | ||||
\(603\) | −313.480 | −0.519868 | ||||||||
\(604\) | 178.756 | + | 207.344i | 0.295953 | + | 0.343285i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −35.4824 | − | 95.4977i | −0.0585518 | − | 0.157587i | ||||
\(607\) | −93.4019 | −0.153875 | −0.0769373 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769373 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(608\) | −157.058 | − | 744.436i | −0.258319 | − | 1.22440i | ||||
\(609\) | 244.075 | 0.400781 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 384.944i | − | 0.630024i | ||||||
\(612\) | 191.302 | + | 221.897i | 0.312585 | + | 0.362576i | ||||
\(613\) | 156.506i | 0.255312i | 0.991818 | + | 0.127656i | \(0.0407454\pi\) | ||||
−0.991818 | + | 0.127656i | \(0.959255\pi\) | |||||||
\(614\) | −69.7113 | − | 187.622i | −0.113536 | − | 0.305573i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −233.033 | + | 422.976i | −0.378301 | + | 0.686649i | ||||
\(617\) | − | 553.493i | − | 0.897072i | −0.893765 | − | 0.448536i | \(-0.851946\pi\) | ||
0.893765 | − | 0.448536i | \(-0.148054\pi\) | |||||||
\(618\) | 34.0094 | + | 91.5334i | 0.0550314 | + | 0.148112i | ||||
\(619\) | − | 14.4398i | − | 0.0233276i | −0.999932 | − | 0.0116638i | \(-0.996287\pi\) | ||
0.999932 | − | 0.0116638i | \(-0.00371278\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 193.570 | 0.311707 | ||||||||
\(622\) | −757.756 | + | 281.546i | −1.21826 | + | 0.452646i | ||||
\(623\) | 632.564 | 1.01535 | ||||||||
\(624\) | 277.510 | + | 41.3224i | 0.444728 | + | 0.0662219i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −241.056 | + | 89.5651i | −0.385074 | + | 0.143075i | ||||
\(627\) | −454.649 | −0.725117 | ||||||||
\(628\) | −66.8051 | − | 77.4893i | −0.106378 | − | 0.123391i | ||||
\(629\) | 870.364 | 1.38373 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 352.389i | 0.558460i | 0.960224 | + | 0.279230i | \(0.0900793\pi\) | ||||
−0.960224 | + | 0.279230i | \(0.909921\pi\) | |||||||
\(632\) | 190.612 | − | 345.977i | 0.301601 | − | 0.547432i | ||||
\(633\) | 321.976i | 0.508650i | ||||||||
\(634\) | −161.102 | + | 59.8579i | −0.254104 | + | 0.0944130i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −252.324 | − | 292.678i | −0.396735 | − | 0.460185i | ||||
\(637\) | 193.415i | 0.303634i | ||||||||
\(638\) | −533.445 | + | 198.203i | −0.836120 | + | 0.310662i | ||||
\(639\) | 230.241i | 0.360315i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −545.742 | −0.851391 | −0.425696 | − | 0.904866i | \(-0.639971\pi\) | ||||
−0.425696 | + | 0.904866i | \(0.639971\pi\) | |||||||
\(642\) | −5.43772 | − | 14.6352i | −0.00846997 | − | 0.0227962i | ||||
\(643\) | 757.447 | 1.17799 | 0.588995 | − | 0.808137i | \(-0.299524\pi\) | ||||
0.588995 | + | 0.808137i | \(0.299524\pi\) | |||||||
\(644\) | −617.079 | + | 531.997i | −0.958197 | + | 0.826082i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −404.345 | − | 1088.26i | −0.625922 | − | 1.68461i | ||||
\(647\) | 1161.36 | 1.79500 | 0.897499 | − | 0.441016i | \(-0.145382\pi\) | ||||
0.897499 | + | 0.441016i | \(0.145382\pi\) | |||||||
\(648\) | −63.0626 | − | 34.7435i | −0.0973188 | − | 0.0536166i | ||||
\(649\) | 613.191 | 0.944824 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 45.8030i | − | 0.0703579i | ||||||
\(652\) | −192.308 | + | 165.793i | −0.294950 | + | 0.254283i | ||||
\(653\) | 621.231i | 0.951348i | 0.879622 | + | 0.475674i | \(0.157796\pi\) | ||||
−0.879622 | + | 0.475674i | \(0.842204\pi\) | |||||||
\(654\) | 233.236 | + | 627.734i | 0.356630 | + | 0.959838i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.9250 | + | 147.242i | −0.0334223 | + | 0.224455i | ||||
\(657\) | 280.565i | 0.427039i | ||||||||
\(658\) | −144.814 | − | 389.755i | −0.220083 | − | 0.592333i | ||||
\(659\) | − | 736.047i | − | 1.11692i | −0.829533 | − | 0.558458i | \(-0.811393\pi\) | ||
0.829533 | − | 0.558458i | \(-0.188607\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 383.845 | 0.580704 | 0.290352 | − | 0.956920i | \(-0.406228\pi\) | ||||
0.290352 | + | 0.956920i | \(0.406228\pi\) | |||||||
\(662\) | 343.817 | − | 127.746i | 0.519362 | − | 0.192970i | ||||
\(663\) | 428.125 | 0.645739 | ||||||||
\(664\) | −507.141 | − | 279.403i | −0.763766 | − | 0.420788i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −200.503 | + | 74.4974i | −0.301056 | + | 0.111858i | ||||
\(667\) | −960.096 | −1.43942 | ||||||||
\(668\) | 37.4972 | − | 32.3271i | 0.0561335 | − | 0.0483939i | ||||
\(669\) | −351.128 | −0.524854 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 907.968i | − | 1.35316i | ||||||
\(672\) | 296.523 | − | 62.5592i | 0.441255 | − | 0.0930940i | ||||
\(673\) | − | 984.464i | − | 1.46280i | −0.681949 | − | 0.731400i | \(-0.738867\pi\) | ||
0.681949 | − | 0.731400i | \(-0.261133\pi\) | |||||||
\(674\) | −315.205 | + | 117.115i | −0.467664 | + | 0.173761i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −201.468 | + | 173.690i | −0.298030 | + | 0.256938i | ||||
\(677\) | 673.154i | 0.994319i | 0.867659 | + | 0.497160i | \(0.165624\pi\) | ||||
−0.867659 | + | 0.497160i | \(0.834376\pi\) | |||||||
\(678\) | −245.400 | + | 91.1789i | −0.361947 | + | 0.134482i | ||||
\(679\) | 398.918i | 0.587507i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 88.8037 | 0.130402 | ||||||||
\(682\) | 37.1945 | + | 100.106i | 0.0545374 | + | 0.146783i | ||||
\(683\) | 291.192 | 0.426343 | 0.213171 | − | 0.977015i | \(-0.431621\pi\) | ||||
0.213171 | + | 0.977015i | \(0.431621\pi\) | |||||||
\(684\) | 186.296 | + | 216.090i | 0.272362 | + | 0.315921i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 259.387 | + | 698.117i | 0.378115 | + | 1.01766i | ||||
\(687\) | 583.798 | 0.849778 | ||||||||
\(688\) | −165.022 | + | 1108.24i | −0.239857 | + | 1.61081i | ||||
\(689\) | −564.689 | −0.819578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 943.693i | − | 1.36569i | −0.730563 | − | 0.682846i | \(-0.760742\pi\) | ||
0.730563 | − | 0.682846i | \(-0.239258\pi\) | |||||||
\(692\) | 155.073 | + | 179.874i | 0.224094 | + | 0.259933i | ||||
\(693\) | − | 181.095i | − | 0.261321i | ||||||
\(694\) | −95.7193 | − | 257.620i | −0.137924 | − | 0.371211i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 312.787 | + | 172.326i | 0.449406 | + | 0.247595i | ||||
\(697\) | 227.156i | 0.325905i | ||||||||
\(698\) | 9.39633 | + | 25.2894i | 0.0134618 | + | 0.0362312i | ||||
\(699\) | − | 139.058i | − | 0.198938i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 885.681 | 1.26345 | 0.631727 | − | 0.775191i | \(-0.282346\pi\) | ||||
0.631727 | + | 0.775191i | \(0.282346\pi\) | |||||||
\(702\) | −98.6259 | + | 36.6447i | −0.140493 | + | 0.0522004i | ||||
\(703\) | 847.588 | 1.20567 | ||||||||
\(704\) | −597.272 | + | 377.521i | −0.848397 | + | 0.536251i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 456.596 | − | 169.649i | 0.646737 | − | 0.240296i | ||||
\(707\) | −160.801 | −0.227441 | ||||||||
\(708\) | −251.260 | − | 291.444i | −0.354887 | − | 0.411644i | ||||
\(709\) | 286.183 | 0.403644 | 0.201822 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201822 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 148.129i | 0.208339i | ||||||||
\(712\) | 810.642 | + | 446.613i | 1.13854 | + | 0.627266i | ||||
\(713\) | 180.171i | 0.252694i | ||||||||
\(714\) | 433.475 | − | 161.059i | 0.607108 | − | 0.225572i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 660.228 | + | 765.818i | 0.922106 | + | 1.06958i | ||||
\(717\) | − | 572.976i | − | 0.799129i | ||||||
\(718\) | −33.5895 | + | 12.4803i | −0.0467820 | + | 0.0173820i | ||||
\(719\) | 666.163i | 0.926513i | 0.886224 | + | 0.463257i | \(0.153319\pi\) | ||||
−0.886224 | + | 0.463257i | \(0.846681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 154.125 | 0.213766 | ||||||||
\(722\) | −142.300 | − | 382.989i | −0.197092 | − | 0.530455i | ||||
\(723\) | 623.389 | 0.862226 | ||||||||
\(724\) | −379.826 | + | 327.456i | −0.524622 | + | 0.452287i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.07203 | + | 2.88528i | 0.00147663 | + | 0.00397422i | ||||
\(727\) | 856.270 | 1.17781 | 0.588907 | − | 0.808201i | \(-0.299559\pi\) | ||||
0.588907 | + | 0.808201i | \(0.299559\pi\) | |||||||
\(728\) | 213.696 | − | 387.877i | 0.293538 | − | 0.532798i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1709.72i | 2.33888i | ||||||||
\(732\) | −431.549 | + | 372.047i | −0.589547 | + | 0.508261i | ||||
\(733\) | 769.487i | 1.04978i | 0.851171 | + | 0.524889i | \(0.175893\pi\) | ||||
−0.851171 | + | 0.524889i | \(0.824107\pi\) | |||||||
\(734\) | −166.076 | − | 446.978i | −0.226261 | − | 0.608961i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1166.41 | + | 246.083i | −1.58479 | + | 0.334352i | ||||
\(737\) | − | 1153.64i | − | 1.56532i | ||||||
\(738\) | −19.4431 | − | 52.3293i | −0.0263456 | − | 0.0709069i | ||||
\(739\) | 1156.70i | 1.56522i | 0.622511 | + | 0.782611i | \(0.286113\pi\) | ||||
−0.622511 | + | 0.782611i | \(0.713887\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 416.922 | 0.562647 | ||||||||
\(742\) | −571.746 | + | 212.433i | −0.770547 | + | 0.286298i | ||||
\(743\) | 426.794 | 0.574421 | 0.287210 | − | 0.957868i | \(-0.407272\pi\) | ||||
0.287210 | + | 0.957868i | \(0.407272\pi\) | |||||||
\(744\) | 32.3386 | − | 58.6973i | 0.0434658 | − | 0.0788942i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −339.842 | + | 126.269i | −0.455552 | + | 0.169261i | ||||
\(747\) | 217.130 | 0.290670 | ||||||||
\(748\) | −816.603 | + | 704.011i | −1.09172 | + | 0.941191i | ||||
\(749\) | −24.6429 | −0.0329011 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1222.03i | − | 1.62721i | −0.581420 | − | 0.813604i | \(-0.697503\pi\) | ||
0.581420 | − | 0.813604i | \(-0.302497\pi\) | |||||||
\(752\) | 89.5990 | − | 601.722i | 0.119148 | − | 0.800162i | ||||
\(753\) | 540.768i | 0.718152i | ||||||||
\(754\) | 489.179 | − | 181.756i | 0.648779 | − | 0.241055i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −86.0729 | + | 74.2053i | −0.113853 | + | 0.0981551i | ||||
\(757\) | − | 1312.95i | − | 1.73442i | −0.497945 | − | 0.867209i | \(-0.665912\pi\) | ||
0.497945 | − | 0.867209i | \(-0.334088\pi\) | |||||||
\(758\) | 574.067 | − | 213.296i | 0.757344 | − | 0.281393i | ||||
\(759\) | 712.358i | 0.938548i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −189.584 | −0.249124 | −0.124562 | − | 0.992212i | \(-0.539753\pi\) | ||||
−0.124562 | + | 0.992212i | \(0.539753\pi\) | |||||||
\(762\) | −158.421 | − | 426.376i | −0.207902 | − | 0.559549i | ||||
\(763\) | 1056.99 | 1.38531 | ||||||||
\(764\) | 254.561 | + | 295.273i | 0.333195 | + | 0.386483i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −100.326 | − | 270.019i | −0.130974 | − | 0.352505i | ||||
\(767\) | −562.308 | −0.733127 | ||||||||
\(768\) | 424.169 | + | 129.185i | 0.552303 | + | 0.168210i | ||||
\(769\) | −254.995 | −0.331594 | −0.165797 | − | 0.986160i | \(-0.553020\pi\) | ||||
−0.165797 | + | 0.986160i | \(0.553020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 139.013i | − | 0.180302i | ||||||
\(772\) | −894.235 | − | 1037.25i | −1.15834 | − | 1.34359i | ||||
\(773\) | − | 23.2536i | − | 0.0300823i | −0.999887 | − | 0.0150411i | \(-0.995212\pi\) | ||
0.999887 | − | 0.0150411i | \(-0.00478793\pi\) | |||||||
\(774\) | −146.341 | − | 393.864i | −0.189071 | − | 0.508869i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −281.650 | + | 511.220i | −0.362951 | + | 0.658788i | ||||
\(777\) | 337.611i | 0.434506i | ||||||||
\(778\) | −9.75897 | − | 26.2654i | −0.0125437 | − | 0.0337602i | ||||
\(779\) | 221.212i | 0.283969i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −847.312 | −1.08491 | ||||||||
\(782\) | −1705.12 | + | 633.541i | −2.18046 | + | 0.810155i | ||||
\(783\) | −133.919 | −0.171033 | ||||||||
\(784\) | −45.0189 | + | 302.335i | −0.0574221 | + | 0.385631i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −245.987 | + | 91.3969i | −0.312960 | + | 0.116281i | ||||
\(787\) | −220.593 | −0.280296 | −0.140148 | − | 0.990131i | \(-0.544758\pi\) | ||||
−0.140148 | + | 0.990131i | \(0.544758\pi\) | |||||||
\(788\) | −194.538 | − | 225.651i | −0.246876 | − | 0.286359i | ||||
\(789\) | −845.183 | −1.07121 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 413.209i | 0.522388i | ||||||||
\(792\) | 127.860 | − | 232.077i | 0.161439 | − | 0.293026i | ||||
\(793\) | 832.625i | 1.04997i | ||||||||
\(794\) | −73.3194 | + | 27.2420i | −0.0923418 | + | 0.0343098i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 464.979 | + | 539.343i | 0.584144 | + | 0.677566i | ||||
\(797\) | 1010.38i | 1.26773i | 0.773442 | + | 0.633867i | \(0.218533\pi\) | ||||
−0.773442 | + | 0.633867i | \(0.781467\pi\) | |||||||
\(798\) | 422.132 | − | 156.844i | 0.528987 | − | 0.196546i | ||||
\(799\) | − | 928.298i | − | 1.16183i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −347.073 | −0.433300 | ||||||||
\(802\) | −84.3327 | − | 226.974i | −0.105153 | − | 0.283010i | ||||
\(803\) | −1032.51 | −1.28581 | ||||||||
\(804\) | −548.314 | + | 472.713i | −0.681983 | + | 0.587952i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −34.1081 | − | 91.7990i | −0.0423178 | − | 0.113894i | ||||
\(807\) | −536.162 | −0.664389 | ||||||||
\(808\) | −206.069 | − | 113.531i | −0.255036 | − | 0.140509i | ||||
\(809\) | −1410.37 | −1.74335 | −0.871674 | − | 0.490086i | \(-0.836965\pi\) | ||||
−0.871674 | + | 0.490086i | \(0.836965\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 950.157i | − | 1.17159i | −0.810460 | − | 0.585793i | \(-0.800783\pi\) | ||
0.810460 | − | 0.585793i | \(-0.199217\pi\) | |||||||
\(812\) | 426.917 | − | 368.054i | 0.525760 | − | 0.453269i | ||||
\(813\) | 84.8173i | 0.104326i | ||||||||
\(814\) | −274.158 | − | 737.873i | −0.336804 | − | 0.906478i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 669.219 | + | 99.6496i | 0.820121 | + | 0.122120i | ||||
\(817\) | 1664.98i | 2.03792i | ||||||||
\(818\) | 377.402 | + | 1015.74i | 0.461372 | + | 1.24174i | ||||
\(819\) | 166.068i | 0.202769i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 77.3347 | 0.0941957 | 0.0470979 | − | 0.998890i | \(-0.485003\pi\) | ||||
0.0470979 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(822\) | 216.890 | − | 80.5858i | 0.263856 | − | 0.0980363i | ||||
\(823\) | −1260.16 | −1.53118 | −0.765591 | − | 0.643328i | \(-0.777553\pi\) | ||||
−0.765591 | + | 0.643328i | \(0.777553\pi\) | |||||||
\(824\) | 197.514 | + | 108.818i | 0.239702 | + | 0.132061i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −569.335 | + | 211.538i | −0.689268 | + | 0.256099i | ||||
\(827\) | 438.047 | 0.529681 | 0.264841 | − | 0.964292i | \(-0.414681\pi\) | ||||
0.264841 | + | 0.964292i | \(0.414681\pi\) | |||||||
\(828\) | 338.577 | − | 291.894i | 0.408909 | − | 0.352529i | ||||
\(829\) | −361.388 | −0.435933 | −0.217966 | − | 0.975956i | \(-0.569942\pi\) | ||||
−0.217966 | + | 0.975956i | \(0.569942\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 345.793i | 0.416117i | ||||||||
\(832\) | 547.710 | − | 346.194i | 0.658305 | − | 0.416098i | ||||
\(833\) | 466.423i | 0.559931i | ||||||||
\(834\) | −123.788 | + | 45.9937i | −0.148427 | + | 0.0551483i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −795.234 | + | 685.588i | −0.951237 | + | 0.820082i | ||||
\(837\) | 25.1310i | 0.0300251i | ||||||||
\(838\) | 1289.52 | − | 479.123i | 1.53880 | − | 0.571746i | ||||
\(839\) | 785.017i | 0.935658i | 0.883819 | + | 0.467829i | \(0.154964\pi\) | ||||
−0.883819 | + | 0.467829i | \(0.845036\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −176.771 | −0.210192 | ||||||||
\(842\) | −316.521 | − | 851.890i | −0.375916 | − | 1.01175i | ||||
\(843\) | −105.932 | −0.125661 | ||||||||
\(844\) | 485.524 | + | 563.173i | 0.575265 | + | 0.667267i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 79.4563 | + | 213.849i | 0.0939199 | + | 0.252777i | ||||
\(847\) | 4.85829 | 0.00573588 | ||||||||
\(848\) | −882.688 | − | 131.436i | −1.04091 | − | 0.154995i | ||||
\(849\) | 749.123 | 0.882359 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1328.03i | − | 1.56055i | ||||||
\(852\) | 347.193 | + | 402.719i | 0.407503 | + | 0.472675i | ||||
\(853\) | − | 1113.79i | − | 1.30573i | −0.757474 | − | 0.652865i | \(-0.773567\pi\) | ||
0.757474 | − | 0.652865i | \(-0.226433\pi\) | |||||||
\(854\) | 313.230 | + | 843.030i | 0.366780 | + | 0.987155i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.5803 | − | 17.3988i | −0.0368929 | − | 0.0203257i | ||||
\(857\) | − | 306.591i | − | 0.357749i | −0.983872 | − | 0.178875i | \(-0.942754\pi\) | ||
0.983872 | − | 0.178875i | \(-0.0572456\pi\) | |||||||
\(858\) | −134.856 | − | 362.954i | −0.157175 | − | 0.423023i | ||||
\(859\) | 204.542i | 0.238116i | 0.992887 | + | 0.119058i | \(0.0379875\pi\) | ||||
−0.992887 | + | 0.119058i | \(0.962013\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −88.1130 | −0.102338 | ||||||||
\(862\) | −873.918 | + | 324.706i | −1.01383 | + | 0.376689i | ||||
\(863\) | 654.384 | 0.758266 | 0.379133 | − | 0.925342i | \(-0.376222\pi\) | ||||
0.379133 | + | 0.925342i | \(0.376222\pi\) | |||||||
\(864\) | −162.695 | + | 34.3248i | −0.188305 | + | 0.0397277i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 856.949 | − | 318.401i | 0.989549 | − | 0.367669i | ||||
\(867\) | 531.866 | 0.613456 | ||||||||
\(868\) | −69.0687 | − | 80.1149i | −0.0795722 | − | 0.0922982i | ||||
\(869\) | −545.129 | −0.627306 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1057.91i | 1.21459i | ||||||||
\(872\) | 1354.55 | + | 746.272i | 1.55338 | + | 0.855817i | ||||
\(873\) | − | 218.877i | − | 0.250718i | ||||||
\(874\) | −1660.50 | + | 616.963i | −1.89989 | + | 0.705907i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 423.078 | + | 490.741i | 0.482966 | + | 0.560206i | ||||
\(877\) | − | 604.453i | − | 0.689228i | −0.938744 | − | 0.344614i | \(-0.888010\pi\) | ||
0.938744 | − | 0.344614i | \(-0.111990\pi\) | |||||||
\(878\) | −1457.58 | + | 541.565i | −1.66011 | + | 0.616817i | ||||
\(879\) | − | 490.575i | − | 0.558106i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1436.81 | 1.63089 | 0.815445 | − | 0.578834i | \(-0.196492\pi\) | ||||
0.815445 | + | 0.578834i | \(0.196492\pi\) | |||||||
\(882\) | −39.9227 | − | 107.449i | −0.0452639 | − | 0.121824i | ||||
\(883\) | −120.993 | −0.137025 | −0.0685123 | − | 0.997650i | \(-0.521825\pi\) | ||||
−0.0685123 | + | 0.997650i | \(0.521825\pi\) | |||||||
\(884\) | 748.841 | − | 645.592i | 0.847105 | − | 0.730307i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −172.392 | − | 463.977i | −0.194573 | − | 0.523676i | ||||
\(887\) | −286.448 | −0.322941 | −0.161470 | − | 0.986878i | \(-0.551624\pi\) | ||||
−0.161470 | + | 0.986878i | \(0.551624\pi\) | |||||||
\(888\) | −238.365 | + | 432.654i | −0.268429 | + | 0.487223i | ||||
\(889\) | −717.940 | −0.807582 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 99.3628i | 0.111518i | ||||||||
\(892\) | −614.164 | + | 529.483i | −0.688524 | + | 0.593591i | ||||
\(893\) | − | 904.007i | − | 1.01233i | ||||||
\(894\) | −152.885 | − | 411.476i | −0.171012 | − | 0.460264i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 424.318 | − | 556.566i | 0.473569 | − | 0.621168i | ||||
\(897\) | − | 653.246i | − | 0.728256i | ||||||
\(898\) | −287.344 | − | 773.360i | −0.319982 | − | 0.861203i | ||||
\(899\) | − | 124.649i | − | 0.138652i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1361.75 | −1.51138 | ||||||||
\(902\) | 192.577 | − | 71.5525i | 0.213500 | − | 0.0793265i | ||||
\(903\) | −663.195 | −0.734436 | ||||||||
\(904\) | −291.740 | + | 529.534i | −0.322721 | + | 0.585768i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −222.240 | + | 82.5736i | −0.245298 | + | 0.0911409i | ||||
\(907\) | 234.706 | 0.258772 | 0.129386 | − | 0.991594i | \(-0.458699\pi\) | ||||
0.129386 | + | 0.991594i | \(0.458699\pi\) | |||||||
\(908\) | 155.328 | − | 133.912i | 0.171066 | − | 0.147480i | ||||
\(909\) | 88.2276 | 0.0970601 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 491.244i | − | 0.539236i | −0.962967 | − | 0.269618i | \(-0.913103\pi\) | ||
0.962967 | − | 0.269618i | \(-0.0868974\pi\) | |||||||
\(912\) | 651.707 | + | 97.0420i | 0.714591 | + | 0.106406i | ||||
\(913\) | 799.063i | 0.875206i | ||||||||
\(914\) | 1397.46 | − | 519.229i | 1.52895 | − | 0.568084i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1021.13 | − | 880.339i | 1.11477 | − | 0.961069i | ||||
\(917\) | 414.197i | 0.451687i | ||||||||
\(918\) | −237.838 | + | 88.3691i | −0.259082 | + | 0.0962627i | ||||
\(919\) | − | 356.091i | − | 0.387477i | −0.981053 | − | 0.193738i | \(-0.937939\pi\) | ||
0.981053 | − | 0.193738i | \(-0.0620613\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 173.338 | 0.188207 | ||||||||
\(922\) | 56.8511 | + | 153.010i | 0.0616607 | + | 0.165954i | ||||
\(923\) | 777.002 | 0.841822 | ||||||||
\(924\) | −273.083 | − | 316.757i | −0.295545 | − | 0.342811i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −203.573 | − | 547.899i | −0.219841 | − | 0.591684i | ||||
\(927\) | −84.5651 | −0.0912244 | ||||||||
\(928\) | 806.961 | − | 170.249i | 0.869570 | − | 0.183458i | ||||
\(929\) | 916.019 | 0.986027 | 0.493014 | − | 0.870022i | \(-0.335895\pi\) | ||||
0.493014 | + | 0.870022i | \(0.335895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 454.217i | 0.487881i | ||||||||
\(932\) | −209.693 | − | 243.229i | −0.224992 | − | 0.260975i | ||||
\(933\) | − | 700.069i | − | 0.750342i | ||||||
\(934\) | −35.8154 | − | 96.3939i | −0.0383462 | − | 0.103205i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −117.250 | + | 212.819i | −0.125267 | + | 0.227371i | ||||
\(937\) | 143.818i | 0.153488i | 0.997051 | + | 0.0767440i | \(0.0244524\pi\) | ||||
−0.997051 | + | 0.0767440i | \(0.975548\pi\) | |||||||
\(938\) | 397.981 | + | 1071.13i | 0.424287 | + | 1.14193i | ||||
\(939\) | − | 222.705i | − | 0.237173i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1488.04 | −1.58133 | −0.790667 | − | 0.612246i | \(-0.790266\pi\) | ||||
−0.790667 | + | 0.612246i | \(0.790266\pi\) | |||||||
\(942\) | 83.0561 | − | 30.8597i | 0.0881699 | − | 0.0327597i | ||||
\(943\) | 346.602 | 0.367552 | ||||||||
\(944\) | −878.966 | − | 130.882i | −0.931108 | − | 0.138646i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1449.46 | − | 538.551i | 1.53220 | − | 0.569292i | ||||
\(947\) | −1095.51 | −1.15682 | −0.578411 | − | 0.815745i | \(-0.696327\pi\) | ||||
−0.578411 | + | 0.815745i | \(0.696327\pi\) | |||||||
\(948\) | 223.371 | + | 259.095i | 0.235623 | + | 0.273307i | ||||
\(949\) | 946.829 | 0.997713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 148.838i | − | 0.156506i | ||||||
\(952\) | 515.331 | − | 935.370i | 0.541314 | − | 0.982532i | ||||
\(953\) | − | 1277.86i | − | 1.34089i | −0.741961 | − | 0.670443i | \(-0.766104\pi\) | ||
0.741961 | − | 0.670443i | \(-0.233896\pi\) | |||||||
\(954\) | 313.704 | − | 116.557i | 0.328830 | − | 0.122177i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −864.020 | − | 1002.20i | −0.903786 | − | 1.04833i | ||||
\(957\) | − | 492.834i | − | 0.514978i | ||||||
\(958\) | −229.834 | + | 85.3953i | −0.239910 | + | 0.0891392i | ||||
\(959\) | − | 365.202i | − | 0.380816i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 937.609 | 0.975659 | ||||||||
\(962\) | 251.409 | + | 676.644i | 0.261339 | + | 0.703372i | ||||
\(963\) | 13.5210 | 0.0140405 | ||||||||
\(964\) | 1090.38 | − | 940.041i | 1.13110 | − | 0.975146i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −245.748 | − | 661.410i | −0.254398 | − | 0.684689i | ||||
\(967\) | −237.958 | −0.246079 | −0.123039 | − | 0.992402i | \(-0.539264\pi\) | ||||
−0.123039 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(968\) | 6.22598 | + | 3.43013i | 0.00643180 | + | 0.00354352i | ||||
\(969\) | 1005.41 | 1.03758 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1602.10i | 1.64995i | 0.565169 | + | 0.824975i | \(0.308811\pi\) | ||||
−0.565169 | + | 0.824975i | \(0.691189\pi\) | |||||||
\(972\) | 47.2262 | − | 40.7147i | 0.0485866 | − | 0.0418876i | ||||
\(973\) | 208.436i | 0.214220i | ||||||||
\(974\) | 45.9643 | + | 123.709i | 0.0471912 | + | 0.127011i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −193.800 | + | 1301.51i | −0.198566 | + | 1.33351i | ||||
\(977\) | 918.977i | 0.940611i | 0.882504 | + | 0.470305i | \(0.155856\pi\) | ||||
−0.882504 | + | 0.470305i | \(0.844144\pi\) | |||||||
\(978\) | −76.5855 | − | 206.123i | −0.0783083 | − | 0.210760i | ||||
\(979\) | − | 1277.27i | − | 1.30466i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −579.945 | −0.591178 | ||||||||
\(982\) | 677.100 | − | 251.578i | 0.689511 | − | 0.256189i | ||||
\(983\) | −1162.30 | −1.18240 | −0.591200 | − | 0.806525i | \(-0.701346\pi\) | ||||
−0.591200 | + | 0.806525i | \(0.701346\pi\) | |||||||
\(984\) | −112.918 | − | 62.2109i | −0.114754 | − | 0.0632225i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1179.66 | − | 438.306i | 1.19641 | − | 0.444530i | ||||
\(987\) | 360.083 | 0.364826 | ||||||||
\(988\) | 729.245 | − | 628.698i | 0.738103 | − | 0.636334i | ||||
\(989\) | 2608.75 | 2.63776 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 491.614i | 0.496079i | 0.968750 | + | 0.248040i | \(0.0797863\pi\) | ||||
−0.968750 | + | 0.248040i | \(0.920214\pi\) | |||||||
\(992\) | −31.9488 | − | 151.434i | −0.0322064 | − | 0.152655i | ||||
\(993\) | 317.643i | 0.319882i | ||||||||
\(994\) | 786.712 | − | 292.305i | 0.791461 | − | 0.294069i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 379.787 | − | 327.422i | 0.381312 | − | 0.328737i | ||||
\(997\) | − | 1262.51i | − | 1.26630i | −0.774027 | − | 0.633152i | \(-0.781761\pi\) | ||
0.774027 | − | 0.633152i | \(-0.218239\pi\) | |||||||
\(998\) | 1333.22 | − | 495.363i | 1.33590 | − | 0.496355i | ||||
\(999\) | − | 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 | 300.3.f.b.199.12 | 16 | ||
3.2 | odd | 2 | 900.3.f.f.199.5 | 16 | |||
4.3 | odd | 2 | inner | 300.3.f.b.199.6 | 16 | ||
5.2 | odd | 4 | 300.3.c.d.151.2 | 8 | |||
5.3 | odd | 4 | 60.3.c.a.31.7 | ✓ | 8 | ||
5.4 | even | 2 | inner | 300.3.f.b.199.5 | 16 | ||
12.11 | even | 2 | 900.3.f.f.199.11 | 16 | |||
15.2 | even | 4 | 900.3.c.u.451.7 | 8 | |||
15.8 | even | 4 | 180.3.c.b.91.2 | 8 | |||
15.14 | odd | 2 | 900.3.f.f.199.12 | 16 | |||
20.3 | even | 4 | 60.3.c.a.31.8 | yes | 8 | ||
20.7 | even | 4 | 300.3.c.d.151.1 | 8 | |||
20.19 | odd | 2 | inner | 300.3.f.b.199.11 | 16 | ||
40.3 | even | 4 | 960.3.e.c.511.3 | 8 | |||
40.13 | odd | 4 | 960.3.e.c.511.8 | 8 | |||
60.23 | odd | 4 | 180.3.c.b.91.1 | 8 | |||
60.47 | odd | 4 | 900.3.c.u.451.8 | 8 | |||
60.59 | even | 2 | 900.3.f.f.199.6 | 16 | |||
120.53 | even | 4 | 2880.3.e.j.2431.3 | 8 | |||
120.83 | odd | 4 | 2880.3.e.j.2431.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.c.a.31.7 | ✓ | 8 | 5.3 | odd | 4 | ||
60.3.c.a.31.8 | yes | 8 | 20.3 | even | 4 | ||
180.3.c.b.91.1 | 8 | 60.23 | odd | 4 | |||
180.3.c.b.91.2 | 8 | 15.8 | even | 4 | |||
300.3.c.d.151.1 | 8 | 20.7 | even | 4 | |||
300.3.c.d.151.2 | 8 | 5.2 | odd | 4 | |||
300.3.f.b.199.5 | 16 | 5.4 | even | 2 | inner | ||
300.3.f.b.199.6 | 16 | 4.3 | odd | 2 | inner | ||
300.3.f.b.199.11 | 16 | 20.19 | odd | 2 | inner | ||
300.3.f.b.199.12 | 16 | 1.1 | even | 1 | trivial | ||
900.3.c.u.451.7 | 8 | 15.2 | even | 4 | |||
900.3.c.u.451.8 | 8 | 60.47 | odd | 4 | |||
900.3.f.f.199.5 | 16 | 3.2 | odd | 2 | |||
900.3.f.f.199.6 | 16 | 60.59 | even | 2 | |||
900.3.f.f.199.11 | 16 | 12.11 | even | 2 | |||
900.3.f.f.199.12 | 16 | 15.14 | odd | 2 | |||
960.3.e.c.511.3 | 8 | 40.3 | even | 4 | |||
960.3.e.c.511.8 | 8 | 40.13 | odd | 4 | |||
2880.3.e.j.2431.2 | 8 | 120.83 | odd | 4 | |||
2880.3.e.j.2431.3 | 8 | 120.53 | even | 4 |