Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(324,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("931.324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.f (of order \(3\), degree \(2\), 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: | \(7.43407242818\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.2672476416.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} - 4x^{5} + 24x^{4} - 10x^{3} + 9x^{2} + 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 704.3 | ||
Root | \(0.375512 + 0.650406i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.704 |
Dual form | 931.2.f.o.324.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/931\mathbb{Z}\right)^\times\).
\(n\) | \(248\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.375512 | + | 0.650406i | 0.265527 | + | 0.459906i | 0.967702 | − | 0.252098i | \(-0.0811207\pi\) |
−0.702174 | + | 0.712005i | \(0.747787\pi\) | |||||||
\(3\) | 1.16576 | − | 2.01915i | 0.673050 | − | 1.16576i | −0.303984 | − | 0.952677i | \(-0.598317\pi\) |
0.977035 | − | 0.213080i | \(-0.0683497\pi\) | |||||||
\(4\) | 0.717981 | − | 1.24358i | 0.358991 | − | 0.621790i | ||||
\(5\) | 2.13271 | + | 3.69397i | 0.953779 | + | 1.65199i | 0.737138 | + | 0.675742i | \(0.236177\pi\) |
0.216641 | + | 0.976251i | \(0.430490\pi\) | |||||||
\(6\) | 1.75102 | 0.714853 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.58049 | 0.912341 | ||||||||
\(9\) | −1.21798 | − | 2.10961i | −0.405994 | − | 0.703202i | ||||
\(10\) | −1.60172 | + | 2.77426i | −0.506508 | + | 0.877298i | ||||
\(11\) | −2.04950 | + | 3.54983i | −0.617946 | + | 1.07031i | 0.371913 | + | 0.928267i | \(0.378702\pi\) |
−0.989860 | + | 0.142047i | \(0.954632\pi\) | |||||||
\(12\) | −1.67398 | − | 2.89943i | −0.483238 | − | 0.836992i | ||||
\(13\) | 2.18699 | 0.606561 | 0.303281 | − | 0.952901i | \(-0.401918\pi\) | ||||
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.94491 | 2.56777 | ||||||||
\(16\) | −0.466957 | − | 0.808794i | −0.116739 | − | 0.202198i | ||||
\(17\) | 0.295021 | − | 0.510992i | 0.0715531 | − | 0.123934i | −0.828029 | − | 0.560685i | \(-0.810538\pi\) |
0.899582 | + | 0.436752i | \(0.143871\pi\) | |||||||
\(18\) | 0.914733 | − | 1.58436i | 0.215605 | − | 0.373438i | ||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | ||||
\(20\) | 6.12500 | 1.36959 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.07844 | −0.656326 | ||||||||
\(23\) | 2.18494 | + | 3.78442i | 0.455591 | + | 0.789107i | 0.998722 | − | 0.0505410i | \(-0.0160946\pi\) |
−0.543131 | + | 0.839648i | \(0.682761\pi\) | |||||||
\(24\) | 3.00823 | − | 5.21040i | 0.614052 | − | 1.06357i | ||||
\(25\) | −6.59694 | + | 11.4262i | −1.31939 | + | 2.28525i | ||||
\(26\) | 0.821240 | + | 1.42243i | 0.161058 | + | 0.278961i | ||||
\(27\) | 1.31506 | 0.253084 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.36442 | −1.36754 | −0.683769 | − | 0.729698i | \(-0.739661\pi\) | ||||
−0.683769 | + | 0.729698i | \(0.739661\pi\) | |||||||
\(30\) | 3.73444 | + | 6.46823i | 0.681811 | + | 1.18093i | ||||
\(31\) | 2.25925 | − | 3.91314i | 0.405773 | − | 0.702820i | −0.588638 | − | 0.808397i | \(-0.700336\pi\) |
0.994411 | + | 0.105577i | \(0.0336689\pi\) | |||||||
\(32\) | 2.93119 | − | 5.07697i | 0.518166 | − | 0.897489i | ||||
\(33\) | 4.77843 | + | 8.27649i | 0.831818 | + | 1.44075i | ||||
\(34\) | 0.443136 | 0.0759972 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.49795 | −0.582992 | ||||||||
\(37\) | −4.47723 | − | 7.75479i | −0.736052 | − | 1.27488i | −0.954260 | − | 0.298978i | \(-0.903354\pi\) |
0.218208 | − | 0.975902i | \(-0.429979\pi\) | |||||||
\(38\) | 0.375512 | − | 0.650406i | 0.0609161 | − | 0.105510i | ||||
\(39\) | 2.54950 | − | 4.41586i | 0.408246 | − | 0.707103i | ||||
\(40\) | 5.50345 | + | 9.53226i | 0.870172 | + | 1.50718i | ||||
\(41\) | 2.17744 | 0.340058 | 0.170029 | − | 0.985439i | \(-0.445614\pi\) | ||||
0.170029 | + | 0.985439i | \(0.445614\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.69594 | −1.32612 | −0.663059 | − | 0.748567i | \(-0.730742\pi\) | ||||
−0.663059 | + | 0.748567i | \(0.730742\pi\) | |||||||
\(44\) | 2.94300 | + | 5.09743i | 0.443674 | + | 0.768466i | ||||
\(45\) | 5.19521 | − | 8.99837i | 0.774457 | − | 1.34140i | ||||
\(46\) | −1.64094 | + | 2.84219i | −0.241944 | + | 0.419059i | ||||
\(47\) | −5.91665 | − | 10.2479i | −0.863032 | − | 1.49481i | −0.868989 | − | 0.494832i | \(-0.835229\pi\) |
0.00595694 | − | 0.999982i | \(-0.498104\pi\) | |||||||
\(48\) | −2.17744 | −0.314286 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −9.90893 | −1.40133 | ||||||||
\(51\) | −0.687846 | − | 1.19138i | −0.0963177 | − | 0.166827i | ||||
\(52\) | 1.57022 | − | 2.71969i | 0.217750 | − | 0.377154i | ||||
\(53\) | −2.20498 | + | 3.81914i | −0.302877 | + | 0.524599i | −0.976786 | − | 0.214216i | \(-0.931281\pi\) |
0.673909 | + | 0.738814i | \(0.264614\pi\) | |||||||
\(54\) | 0.493821 | + | 0.855324i | 0.0672006 | + | 0.116395i | ||||
\(55\) | −17.4840 | −2.35754 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.33152 | −0.308817 | ||||||||
\(58\) | −2.76543 | − | 4.78986i | −0.363119 | − | 0.628940i | ||||
\(59\) | 5.35892 | − | 9.28193i | 0.697672 | − | 1.20840i | −0.271599 | − | 0.962410i | \(-0.587552\pi\) |
0.969271 | − | 0.245993i | \(-0.0791142\pi\) | |||||||
\(60\) | 7.14026 | − | 12.3673i | 0.921804 | − | 1.59661i | ||||
\(61\) | −1.21525 | − | 2.10488i | −0.155597 | − | 0.269502i | 0.777679 | − | 0.628662i | \(-0.216397\pi\) |
−0.933276 | + | 0.359159i | \(0.883064\pi\) | |||||||
\(62\) | 3.39350 | 0.430975 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.53496 | 0.316869 | ||||||||
\(65\) | 4.66422 | + | 8.07866i | 0.578525 | + | 1.00204i | ||||
\(66\) | −3.58872 | + | 6.21584i | −0.441741 | + | 0.765117i | ||||
\(67\) | 2.82674 | − | 4.89606i | 0.345341 | − | 0.598148i | −0.640075 | − | 0.768313i | \(-0.721097\pi\) |
0.985416 | + | 0.170164i | \(0.0544299\pi\) | |||||||
\(68\) | −0.423639 | − | 0.733765i | −0.0513738 | − | 0.0889821i | ||||
\(69\) | 10.1884 | 1.22654 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.32434 | 0.987918 | 0.493959 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493959 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(72\) | −3.14299 | − | 5.44382i | −0.370405 | − | 0.641560i | ||||
\(73\) | −5.33974 | + | 9.24870i | −0.624970 | + | 1.08248i | 0.363577 | + | 0.931564i | \(0.381555\pi\) |
−0.988547 | + | 0.150915i | \(0.951778\pi\) | |||||||
\(74\) | 3.36251 | − | 5.82404i | 0.390884 | − | 0.677031i | ||||
\(75\) | 15.3809 | + | 26.6405i | 1.77603 | + | 3.07618i | ||||
\(76\) | −1.43596 | −0.164716 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.82947 | 0.433602 | ||||||||
\(79\) | −4.28188 | − | 7.41644i | −0.481750 | − | 0.834415i | 0.518031 | − | 0.855362i | \(-0.326665\pi\) |
−0.999781 | + | 0.0209472i | \(0.993332\pi\) | |||||||
\(80\) | 1.99177 | − | 3.44985i | 0.222687 | − | 0.385705i | ||||
\(81\) | 5.18699 | − | 8.98412i | 0.576332 | − | 0.998236i | ||||
\(82\) | 0.817653 | + | 1.41622i | 0.0902947 | + | 0.156395i | ||||
\(83\) | 4.25826 | 0.467404 | 0.233702 | − | 0.972308i | \(-0.424916\pi\) | ||||
0.233702 | + | 0.972308i | \(0.424916\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.51678 | 0.272983 | ||||||||
\(86\) | −3.26543 | − | 5.65589i | −0.352120 | − | 0.609890i | ||||
\(87\) | −8.58513 | + | 14.8699i | −0.920423 | + | 1.59422i | ||||
\(88\) | −5.28871 | + | 9.16031i | −0.563778 | + | 0.976492i | ||||
\(89\) | 1.89555 | + | 3.28319i | 0.200928 | + | 0.348018i | 0.948828 | − | 0.315794i | \(-0.102271\pi\) |
−0.747900 | + | 0.663812i | \(0.768938\pi\) | |||||||
\(90\) | 7.80346 | 0.822557 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.27498 | 0.654212 | ||||||||
\(93\) | −5.26748 | − | 9.12354i | −0.546212 | − | 0.946067i | ||||
\(94\) | 4.44354 | − | 7.69644i | 0.458317 | − | 0.793828i | ||||
\(95\) | 2.13271 | − | 3.69397i | 0.218812 | − | 0.378993i | ||||
\(96\) | −6.83411 | − | 11.8370i | −0.697503 | − | 1.20811i | ||||
\(97\) | −2.11026 | −0.214265 | −0.107132 | − | 0.994245i | \(-0.534167\pi\) | ||||
−0.107132 | + | 0.994245i | \(0.534167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.98499 | 1.00353 | ||||||||
\(100\) | 9.47297 | + | 16.4077i | 0.947297 | + | 1.64077i | ||||
\(101\) | 7.53032 | − | 13.0429i | 0.749294 | − | 1.29782i | −0.198867 | − | 0.980027i | \(-0.563726\pi\) |
0.948161 | − | 0.317789i | \(-0.102941\pi\) | |||||||
\(102\) | 0.516589 | − | 0.894759i | 0.0511499 | − | 0.0885943i | ||||
\(103\) | 2.44692 | + | 4.23818i | 0.241102 | + | 0.417601i | 0.961028 | − | 0.276450i | \(-0.0891579\pi\) |
−0.719927 | + | 0.694050i | \(0.755825\pi\) | |||||||
\(104\) | 5.64350 | 0.553391 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.31198 | −0.321688 | ||||||||
\(107\) | −0.444325 | − | 0.769593i | −0.0429545 | − | 0.0743994i | 0.843749 | − | 0.536738i | \(-0.180344\pi\) |
−0.886703 | + | 0.462339i | \(0.847010\pi\) | |||||||
\(108\) | 0.944190 | − | 1.63538i | 0.0908547 | − | 0.157365i | ||||
\(109\) | 0.555675 | − | 0.962457i | 0.0532240 | − | 0.0921867i | −0.838186 | − | 0.545385i | \(-0.816384\pi\) |
0.891410 | + | 0.453198i | \(0.149717\pi\) | |||||||
\(110\) | −6.56544 | − | 11.3717i | −0.625990 | − | 1.08425i | ||||
\(111\) | −20.8775 | −1.98160 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9161 | −1.21504 | −0.607522 | − | 0.794303i | \(-0.707836\pi\) | ||||
−0.607522 | + | 0.794303i | \(0.707836\pi\) | |||||||
\(114\) | −0.875512 | − | 1.51643i | −0.0819992 | − | 0.142027i | ||||
\(115\) | −9.31970 | + | 16.1422i | −0.869067 | + | 1.50527i | ||||
\(116\) | −5.28752 | + | 9.15825i | −0.490934 | + | 0.850322i | ||||
\(117\) | −2.66371 | − | 4.61368i | −0.246260 | − | 0.426535i | ||||
\(118\) | 8.04936 | 0.741004 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 25.6628 | 2.34268 | ||||||||
\(121\) | −2.90087 | − | 5.02446i | −0.263716 | − | 0.456769i | ||||
\(122\) | 0.912685 | − | 1.58082i | 0.0826306 | − | 0.143120i | ||||
\(123\) | 2.53836 | − | 4.39657i | 0.228876 | − | 0.396426i | ||||
\(124\) | −3.24420 | − | 5.61912i | −0.291338 | − | 0.504612i | ||||
\(125\) | −34.9505 | −3.12606 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.11373 | −0.276299 | −0.138149 | − | 0.990411i | \(-0.544115\pi\) | ||||
−0.138149 | + | 0.990411i | \(0.544115\pi\) | |||||||
\(128\) | −4.91047 | − | 8.50518i | −0.434028 | − | 0.751759i | ||||
\(129\) | −10.1374 | + | 17.5584i | −0.892544 | + | 1.54593i | ||||
\(130\) | −3.50294 | + | 6.06727i | −0.307228 | + | 0.532135i | ||||
\(131\) | 1.85360 | + | 3.21054i | 0.161950 | + | 0.280506i | 0.935568 | − | 0.353147i | \(-0.114888\pi\) |
−0.773618 | + | 0.633652i | \(0.781555\pi\) | |||||||
\(132\) | 13.7233 | 1.19446 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.24590 | 0.366790 | ||||||||
\(135\) | 2.80465 | + | 4.85780i | 0.241386 | + | 0.418093i | ||||
\(136\) | 0.761299 | − | 1.31861i | 0.0652809 | − | 0.113070i | ||||
\(137\) | −0.580491 | + | 1.00544i | −0.0495947 | + | 0.0859005i | −0.889757 | − | 0.456434i | \(-0.849126\pi\) |
0.840162 | + | 0.542335i | \(0.182460\pi\) | |||||||
\(138\) | 3.82588 | + | 6.62662i | 0.325681 | + | 0.564095i | ||||
\(139\) | 4.24633 | 0.360169 | 0.180084 | − | 0.983651i | \(-0.442363\pi\) | ||||
0.180084 | + | 0.983651i | \(0.442363\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.5895 | −2.32346 | ||||||||
\(142\) | 3.12589 | + | 5.41420i | 0.262319 | + | 0.454350i | ||||
\(143\) | −4.48222 | + | 7.76344i | −0.374822 | + | 0.649211i | ||||
\(144\) | −1.13749 | + | 1.97019i | −0.0947909 | + | 0.164183i | ||||
\(145\) | −15.7062 | − | 27.2040i | −1.30433 | − | 2.25917i | ||||
\(146\) | −8.02055 | −0.663785 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.8583 | −1.05694 | ||||||||
\(149\) | 11.9966 | + | 20.7787i | 0.982799 | + | 1.70226i | 0.651335 | + | 0.758791i | \(0.274209\pi\) |
0.331465 | + | 0.943468i | \(0.392457\pi\) | |||||||
\(150\) | −11.5514 | + | 20.0076i | −0.943169 | + | 1.63362i | ||||
\(151\) | −4.25035 | + | 7.36181i | −0.345888 | + | 0.599096i | −0.985515 | − | 0.169590i | \(-0.945756\pi\) |
0.639627 | + | 0.768686i | \(0.279089\pi\) | |||||||
\(152\) | −1.29025 | − | 2.23477i | −0.104653 | − | 0.181264i | ||||
\(153\) | −1.43732 | −0.116201 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.2734 | 1.54807 | ||||||||
\(156\) | −3.66098 | − | 6.34101i | −0.293113 | − | 0.507687i | ||||
\(157\) | 2.21938 | − | 3.84409i | 0.177126 | − | 0.306791i | −0.763769 | − | 0.645490i | \(-0.776653\pi\) |
0.940895 | + | 0.338698i | \(0.109987\pi\) | |||||||
\(158\) | 3.21580 | − | 5.56993i | 0.255835 | − | 0.443119i | ||||
\(159\) | 5.14094 | + | 8.90437i | 0.407703 | + | 0.706163i | ||||
\(160\) | 25.0055 | 1.97686 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 7.79110 | 0.612127 | ||||||||
\(163\) | 0.0734531 | + | 0.127225i | 0.00575329 | + | 0.00996500i | 0.868888 | − | 0.495009i | \(-0.164835\pi\) |
−0.863134 | + | 0.504974i | \(0.831502\pi\) | |||||||
\(164\) | 1.56336 | − | 2.70782i | 0.122078 | − | 0.211445i | ||||
\(165\) | −20.3821 | + | 35.3028i | −1.58674 | + | 2.74832i | ||||
\(166\) | 1.59903 | + | 2.76960i | 0.124109 | + | 0.214962i | ||||
\(167\) | −0.885641 | −0.0685329 | −0.0342665 | − | 0.999413i | \(-0.510909\pi\) | ||||
−0.0342665 | + | 0.999413i | \(0.510909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.21709 | −0.632084 | ||||||||
\(170\) | 0.945083 | + | 1.63693i | 0.0724845 | + | 0.125547i | ||||
\(171\) | −1.21798 | + | 2.10961i | −0.0931414 | + | 0.161326i | ||||
\(172\) | −6.24352 | + | 10.8141i | −0.476064 | + | 0.824567i | ||||
\(173\) | 12.1319 | + | 21.0131i | 0.922371 | + | 1.59759i | 0.795735 | + | 0.605645i | \(0.207085\pi\) |
0.126636 | + | 0.991949i | \(0.459582\pi\) | |||||||
\(174\) | −12.8953 | −0.977589 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.82811 | 0.288555 | ||||||||
\(177\) | −12.4944 | − | 21.6410i | −0.939137 | − | 1.62663i | ||||
\(178\) | −1.42361 | + | 2.46576i | −0.106704 | + | 0.184816i | ||||
\(179\) | 6.47332 | − | 11.2121i | 0.483838 | − | 0.838033i | −0.515989 | − | 0.856595i | \(-0.672576\pi\) |
0.999828 | + | 0.0185624i | \(0.00590893\pi\) | |||||||
\(180\) | −7.46013 | − | 12.9213i | −0.556046 | − | 0.963099i | ||||
\(181\) | −18.6034 | −1.38278 | −0.691391 | − | 0.722481i | \(-0.743002\pi\) | ||||
−0.691391 | + | 0.722481i | \(0.743002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.66677 | −0.418899 | ||||||||
\(184\) | 5.63821 | + | 9.76567i | 0.415655 | + | 0.719935i | ||||
\(185\) | 19.0973 | − | 33.0775i | 1.40406 | − | 2.43191i | ||||
\(186\) | 3.95600 | − | 6.85200i | 0.290068 | − | 0.502413i | ||||
\(187\) | 1.20929 | + | 2.09455i | 0.0884320 | + | 0.153169i | ||||
\(188\) | −16.9922 | −1.23928 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.20344 | 0.232402 | ||||||||
\(191\) | 11.6444 | + | 20.1687i | 0.842559 | + | 1.45935i | 0.887725 | + | 0.460375i | \(0.152285\pi\) |
−0.0451659 | + | 0.998980i | \(0.514382\pi\) | |||||||
\(192\) | 2.95514 | − | 5.11846i | 0.213269 | − | 0.369393i | ||||
\(193\) | −1.59422 | + | 2.76127i | −0.114754 | + | 0.198760i | −0.917681 | − | 0.397317i | \(-0.869941\pi\) |
0.802927 | + | 0.596077i | \(0.203275\pi\) | |||||||
\(194\) | −0.792429 | − | 1.37253i | −0.0568931 | − | 0.0985417i | ||||
\(195\) | 21.7494 | 1.55751 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.25178 | −0.587915 | −0.293958 | − | 0.955818i | \(-0.594972\pi\) | ||||
−0.293958 | + | 0.955818i | \(0.594972\pi\) | |||||||
\(198\) | 3.74949 | + | 6.49430i | 0.266464 | + | 0.461530i | ||||
\(199\) | −9.80120 | + | 16.9762i | −0.694789 | + | 1.20341i | 0.275463 | + | 0.961312i | \(0.411169\pi\) |
−0.970252 | + | 0.242098i | \(0.922165\pi\) | |||||||
\(200\) | −17.0234 | + | 29.4853i | −1.20373 | + | 2.08493i | ||||
\(201\) | −6.59059 | − | 11.4152i | −0.464864 | − | 0.805168i | ||||
\(202\) | 11.3109 | 0.795832 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.97544 | −0.138309 | ||||||||
\(205\) | 4.64385 | + | 8.04338i | 0.324340 | + | 0.561774i | ||||
\(206\) | −1.83769 | + | 3.18298i | −0.128038 | + | 0.221769i | ||||
\(207\) | 5.32243 | − | 9.21872i | 0.369934 | − | 0.640745i | ||||
\(208\) | −1.02123 | − | 1.76882i | −0.0708095 | − | 0.122646i | ||||
\(209\) | 4.09899 | 0.283533 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.49078 | 0.653372 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(212\) | 3.16627 | + | 5.48414i | 0.217460 | + | 0.376652i | ||||
\(213\) | 9.70416 | − | 16.8081i | 0.664918 | − | 1.15167i | ||||
\(214\) | 0.333699 | − | 0.577983i | 0.0228112 | − | 0.0395101i | ||||
\(215\) | −18.5460 | − | 32.1225i | −1.26482 | − | 2.19074i | ||||
\(216\) | 3.39350 | 0.230899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.834651 | 0.0565297 | ||||||||
\(219\) | 12.4497 | + | 21.5635i | 0.841272 | + | 1.45713i | ||||
\(220\) | −12.5532 | + | 21.7427i | −0.846334 | + | 1.46589i | ||||
\(221\) | 0.645207 | − | 1.11753i | 0.0434013 | − | 0.0751733i | ||||
\(222\) | −7.83974 | − | 13.5788i | −0.526169 | − | 0.911351i | ||||
\(223\) | 18.8829 | 1.26449 | 0.632247 | − | 0.774767i | \(-0.282133\pi\) | ||||
0.632247 | + | 0.774767i | \(0.282133\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 32.1398 | 2.14265 | ||||||||
\(226\) | −4.85015 | − | 8.40071i | −0.322627 | − | 0.558807i | ||||
\(227\) | −10.2703 | + | 17.7886i | −0.681660 | + | 1.18067i | 0.292813 | + | 0.956170i | \(0.405409\pi\) |
−0.974474 | + | 0.224501i | \(0.927925\pi\) | |||||||
\(228\) | −1.67398 | + | 2.89943i | −0.110862 | + | 0.192019i | ||||
\(229\) | −3.49250 | − | 6.04918i | −0.230791 | − | 0.399741i | 0.727250 | − | 0.686372i | \(-0.240798\pi\) |
−0.958041 | + | 0.286631i | \(0.907465\pi\) | |||||||
\(230\) | −13.9986 | −0.923043 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.0038 | −1.24766 | ||||||||
\(233\) | −9.76325 | − | 16.9104i | −0.639612 | − | 1.10784i | −0.985518 | − | 0.169571i | \(-0.945762\pi\) |
0.345907 | − | 0.938269i | \(-0.387571\pi\) | |||||||
\(234\) | 2.00051 | − | 3.46498i | 0.130777 | − | 0.226513i | ||||
\(235\) | 25.2370 | − | 43.7118i | 1.64628 | − | 2.85145i | ||||
\(236\) | −7.69521 | − | 13.3285i | −0.500916 | − | 0.867612i | ||||
\(237\) | −19.9666 | −1.29697 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8056 | −1.15175 | −0.575873 | − | 0.817539i | \(-0.695338\pi\) | ||||
−0.575873 | + | 0.817539i | \(0.695338\pi\) | |||||||
\(240\) | −4.64385 | − | 8.04338i | −0.299759 | − | 0.519198i | ||||
\(241\) | −7.61340 | + | 13.1868i | −0.490422 | + | 0.849436i | −0.999939 | − | 0.0110245i | \(-0.996491\pi\) |
0.509517 | + | 0.860461i | \(0.329824\pi\) | |||||||
\(242\) | 2.17862 | − | 3.77349i | 0.140047 | − | 0.242569i | ||||
\(243\) | −10.1209 | − | 17.5300i | −0.649259 | − | 1.12455i | ||||
\(244\) | −3.49012 | −0.223432 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.81274 | 0.243092 | ||||||||
\(247\) | −1.09349 | − | 1.89399i | −0.0695773 | − | 0.120511i | ||||
\(248\) | 5.82998 | − | 10.0978i | 0.370204 | − | 0.641212i | ||||
\(249\) | 4.96409 | − | 8.59806i | 0.314587 | − | 0.544880i | ||||
\(250\) | −13.1243 | − | 22.7320i | −0.830055 | − | 1.43770i | ||||
\(251\) | 6.70311 | 0.423097 | 0.211548 | − | 0.977368i | \(-0.432149\pi\) | ||||
0.211548 | + | 0.977368i | \(0.432149\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.9121 | −1.12612 | ||||||||
\(254\) | −1.16924 | − | 2.02519i | −0.0733648 | − | 0.127072i | ||||
\(255\) | 2.93396 | − | 5.08177i | 0.183732 | − | 0.318233i | ||||
\(256\) | 6.22284 | − | 10.7783i | 0.388927 | − | 0.673642i | ||||
\(257\) | −4.12568 | − | 7.14588i | −0.257353 | − | 0.445748i | 0.708179 | − | 0.706033i | \(-0.249517\pi\) |
−0.965532 | + | 0.260285i | \(0.916184\pi\) | |||||||
\(258\) | −15.2268 | −0.947979 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 13.3953 | 0.830741 | ||||||||
\(261\) | 8.96973 | + | 15.5360i | 0.555212 | + | 0.961656i | ||||
\(262\) | −1.39210 | + | 2.41119i | −0.0860043 | + | 0.148964i | ||||
\(263\) | 0.350152 | − | 0.606482i | 0.0215913 | − | 0.0373973i | −0.855028 | − | 0.518582i | \(-0.826460\pi\) |
0.876619 | + | 0.481185i | \(0.159793\pi\) | |||||||
\(264\) | 12.3307 | + | 21.3574i | 0.758902 | + | 1.31446i | ||||
\(265\) | −18.8104 | −1.15551 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.83902 | 0.540939 | ||||||||
\(268\) | −4.05909 | − | 7.03055i | −0.247949 | − | 0.429459i | ||||
\(269\) | −6.98260 | + | 12.0942i | −0.425736 | + | 0.737397i | −0.996489 | − | 0.0837251i | \(-0.973318\pi\) |
0.570752 | + | 0.821122i | \(0.306652\pi\) | |||||||
\(270\) | −2.10636 | + | 3.64832i | −0.128189 | + | 0.222030i | ||||
\(271\) | 4.16285 | + | 7.21027i | 0.252875 | + | 0.437993i | 0.964316 | − | 0.264753i | \(-0.0852905\pi\) |
−0.711441 | + | 0.702746i | \(0.751957\pi\) | |||||||
\(272\) | −0.551049 | −0.0334122 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.871925 | −0.0526749 | ||||||||
\(275\) | −27.0408 | − | 46.8361i | −1.63062 | − | 2.82432i | ||||
\(276\) | 7.31511 | − | 12.6701i | 0.440318 | − | 0.762653i | ||||
\(277\) | 7.57504 | − | 13.1203i | 0.455140 | − | 0.788325i | −0.543556 | − | 0.839373i | \(-0.682923\pi\) |
0.998696 | + | 0.0510473i | \(0.0162559\pi\) | |||||||
\(278\) | 1.59455 | + | 2.76184i | 0.0956346 | + | 0.165644i | ||||
\(279\) | −11.0069 | −0.658966 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2038 | −0.608708 | −0.304354 | − | 0.952559i | \(-0.598441\pi\) | ||||
−0.304354 | + | 0.952559i | \(0.598441\pi\) | |||||||
\(282\) | −10.3602 | − | 17.9444i | −0.616940 | − | 1.06857i | ||||
\(283\) | 3.14558 | − | 5.44831i | 0.186985 | − | 0.323868i | −0.757258 | − | 0.653115i | \(-0.773462\pi\) |
0.944244 | + | 0.329247i | \(0.106795\pi\) | |||||||
\(284\) | 5.97672 | − | 10.3520i | 0.354653 | − | 0.614277i | ||||
\(285\) | −4.97246 | − | 8.61255i | −0.294543 | − | 0.510163i | ||||
\(286\) | −6.73251 | −0.398102 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −14.2805 | −0.841488 | ||||||||
\(289\) | 8.32593 | + | 14.4209i | 0.489760 | + | 0.848290i | ||||
\(290\) | 11.7957 | − | 20.4308i | 0.692670 | − | 1.19974i | ||||
\(291\) | −2.46005 | + | 4.26094i | −0.144211 | + | 0.249781i | ||||
\(292\) | 7.66767 | + | 13.2808i | 0.448716 | + | 0.777200i | ||||
\(293\) | −1.48286 | −0.0866294 | −0.0433147 | − | 0.999061i | \(-0.513792\pi\) | ||||
−0.0433147 | + | 0.999061i | \(0.513792\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 45.7162 | 2.66170 | ||||||||
\(296\) | −11.5535 | − | 20.0112i | −0.671531 | − | 1.16313i | ||||
\(297\) | −2.69521 | + | 4.66825i | −0.156392 | + | 0.270879i | ||||
\(298\) | −9.00973 | + | 15.6053i | −0.521920 | + | 0.903991i | ||||
\(299\) | 4.77843 | + | 8.27649i | 0.276344 | + | 0.478642i | ||||
\(300\) | 44.1727 | 2.55031 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.38422 | −0.367371 | ||||||||
\(303\) | −17.5570 | − | 30.4097i | −1.00863 | − | 1.74699i | ||||
\(304\) | −0.466957 | + | 0.808794i | −0.0267818 | + | 0.0463875i | ||||
\(305\) | 5.18358 | − | 8.97822i | 0.296811 | − | 0.514092i | ||||
\(306\) | −0.539731 | − | 0.934842i | −0.0308544 | − | 0.0534414i | ||||
\(307\) | 29.9624 | 1.71004 | 0.855022 | − | 0.518592i | \(-0.173544\pi\) | ||||
0.855022 | + | 0.518592i | \(0.173544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.4100 | 0.649095 | ||||||||
\(310\) | 7.23738 | + | 12.5355i | 0.411055 | + | 0.711969i | ||||
\(311\) | 2.19057 | − | 3.79418i | 0.124216 | − | 0.215148i | −0.797210 | − | 0.603702i | \(-0.793692\pi\) |
0.921426 | + | 0.388553i | \(0.127025\pi\) | |||||||
\(312\) | 6.57895 | − | 11.3951i | 0.372460 | − | 0.645119i | ||||
\(313\) | 10.2268 | + | 17.7133i | 0.578053 | + | 1.00122i | 0.995703 | + | 0.0926086i | \(0.0295205\pi\) |
−0.417650 | + | 0.908608i | \(0.637146\pi\) | |||||||
\(314\) | 3.33362 | 0.188127 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.2972 | −0.691774 | ||||||||
\(317\) | 4.40824 | + | 7.63529i | 0.247591 | + | 0.428841i | 0.962857 | − | 0.270012i | \(-0.0870276\pi\) |
−0.715266 | + | 0.698853i | \(0.753694\pi\) | |||||||
\(318\) | −3.86097 | + | 6.68740i | −0.216513 | + | 0.375011i | ||||
\(319\) | 15.0934 | − | 26.1425i | 0.845066 | − | 1.46370i | ||||
\(320\) | 5.40634 | + | 9.36405i | 0.302223 | + | 0.523466i | ||||
\(321\) | −2.07190 | −0.115642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.590042 | −0.0328308 | ||||||||
\(324\) | −7.44832 | − | 12.9009i | −0.413796 | − | 0.716715i | ||||
\(325\) | −14.4274 | + | 24.9890i | −0.800290 | + | 1.38614i | ||||
\(326\) | −0.0551651 | + | 0.0955487i | −0.00305531 | + | 0.00529195i | ||||
\(327\) | −1.29556 | − | 2.24398i | −0.0716449 | − | 0.124093i | ||||
\(328\) | 5.61885 | 0.310249 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −30.6148 | −1.68529 | ||||||||
\(331\) | −6.02899 | − | 10.4425i | −0.331383 | − | 0.573973i | 0.651400 | − | 0.758734i | \(-0.274182\pi\) |
−0.982783 | + | 0.184762i | \(0.940849\pi\) | |||||||
\(332\) | 3.05735 | − | 5.29548i | 0.167794 | − | 0.290627i | ||||
\(333\) | −10.9064 | + | 18.8904i | −0.597665 | + | 1.03519i | ||||
\(334\) | −0.332569 | − | 0.576026i | −0.0181974 | − | 0.0315187i | ||||
\(335\) | 24.1145 | 1.31752 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.5871 | 1.50277 | 0.751383 | − | 0.659866i | \(-0.229387\pi\) | ||||
0.751383 | + | 0.659866i | \(0.229387\pi\) | |||||||
\(338\) | −3.08562 | − | 5.34444i | −0.167835 | − | 0.290699i | ||||
\(339\) | −15.0570 | + | 26.0796i | −0.817786 | + | 1.41645i | ||||
\(340\) | 1.80700 | − | 3.12982i | 0.0979985 | − | 0.169738i | ||||
\(341\) | 9.26065 | + | 16.0399i | 0.501493 | + | 0.868611i | ||||
\(342\) | −1.82947 | −0.0989262 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −22.4398 | −1.20987 | ||||||||
\(345\) | 21.7290 | + | 37.6358i | 1.16985 | + | 2.02624i | ||||
\(346\) | −9.11135 | + | 15.7813i | −0.489829 | + | 0.848409i | ||||
\(347\) | −0.495768 | + | 0.858695i | −0.0266142 | + | 0.0460972i | −0.879026 | − | 0.476774i | \(-0.841806\pi\) |
0.852412 | + | 0.522871i | \(0.175139\pi\) | |||||||
\(348\) | 12.3279 | + | 21.3526i | 0.660846 | + | 1.14462i | ||||
\(349\) | −31.6583 | −1.69463 | −0.847316 | − | 0.531090i | \(-0.821783\pi\) | ||||
−0.847316 | + | 0.531090i | \(0.821783\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.87602 | 0.153511 | ||||||||
\(352\) | 12.0149 | + | 20.8104i | 0.640397 | + | 1.10920i | ||||
\(353\) | 4.45191 | − | 7.71093i | 0.236951 | − | 0.410411i | −0.722887 | − | 0.690966i | \(-0.757185\pi\) |
0.959838 | + | 0.280555i | \(0.0905186\pi\) | |||||||
\(354\) | 9.38360 | − | 16.2529i | 0.498733 | − | 0.863831i | ||||
\(355\) | 17.7534 | + | 30.7499i | 0.942255 | + | 1.63203i | ||||
\(356\) | 5.44389 | 0.288525 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.72323 | 0.513889 | ||||||||
\(359\) | 10.8499 | + | 18.7925i | 0.572635 | + | 0.991833i | 0.996294 | + | 0.0860111i | \(0.0274120\pi\) |
−0.423659 | + | 0.905822i | \(0.639255\pi\) | |||||||
\(360\) | 13.4062 | − | 23.2202i | 0.706569 | − | 1.22381i | ||||
\(361\) | −0.500000 | + | 0.866025i | −0.0263158 | + | 0.0455803i | ||||
\(362\) | −6.98581 | − | 12.0998i | −0.367166 | − | 0.635950i | ||||
\(363\) | −13.5269 | −0.709976 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.5526 | −2.38433 | ||||||||
\(366\) | −2.12794 | − | 3.68570i | −0.111229 | − | 0.192655i | ||||
\(367\) | 6.38859 | − | 11.0654i | 0.333482 | − | 0.577608i | −0.649710 | − | 0.760182i | \(-0.725110\pi\) |
0.983192 | + | 0.182575i | \(0.0584431\pi\) | |||||||
\(368\) | 2.04055 | − | 3.53433i | 0.106371 | − | 0.184240i | ||||
\(369\) | −2.65208 | − | 4.59353i | −0.138062 | − | 0.239130i | ||||
\(370\) | 28.6851 | 1.49127 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −15.1278 | −0.784340 | ||||||||
\(373\) | 6.60912 | + | 11.4473i | 0.342207 | + | 0.592721i | 0.984842 | − | 0.173452i | \(-0.0554921\pi\) |
−0.642635 | + | 0.766172i | \(0.722159\pi\) | |||||||
\(374\) | −0.908206 | + | 1.57306i | −0.0469622 | + | 0.0813409i | ||||
\(375\) | −40.7438 | + | 70.5703i | −2.10400 | + | 3.64423i | ||||
\(376\) | −15.2679 | − | 26.4447i | −0.787379 | − | 1.36378i | ||||
\(377\) | −16.1059 | −0.829496 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.72767 | −0.0887443 | −0.0443722 | − | 0.999015i | \(-0.514129\pi\) | ||||
−0.0443722 | + | 0.999015i | \(0.514129\pi\) | |||||||
\(380\) | −3.06250 | − | 5.30440i | −0.157103 | − | 0.272110i | ||||
\(381\) | −3.62985 | + | 6.28709i | −0.185963 | + | 0.322097i | ||||
\(382\) | −8.74522 | + | 15.1472i | −0.447444 | + | 0.774996i | ||||
\(383\) | −2.42781 | − | 4.20510i | −0.124056 | − | 0.214870i | 0.797308 | − | 0.603573i | \(-0.206257\pi\) |
−0.921363 | + | 0.388702i | \(0.872923\pi\) | |||||||
\(384\) | −22.8977 | −1.16849 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.39459 | −0.121881 | ||||||||
\(387\) | 10.5915 | + | 18.3450i | 0.538396 | + | 0.932529i | ||||
\(388\) | −1.51513 | + | 2.62428i | −0.0769190 | + | 0.133228i | ||||
\(389\) | −5.31493 | + | 9.20572i | −0.269477 | + | 0.466749i | −0.968727 | − | 0.248129i | \(-0.920184\pi\) |
0.699250 | + | 0.714878i | \(0.253518\pi\) | |||||||
\(390\) | 8.16716 | + | 14.1459i | 0.413560 | + | 0.716307i | ||||
\(391\) | 2.57841 | 0.130396 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.64341 | 0.436002 | ||||||||
\(394\) | −3.09864 | − | 5.36701i | −0.156107 | − | 0.270386i | ||||
\(395\) | 18.2641 | − | 31.6343i | 0.918965 | − | 1.59169i | ||||
\(396\) | 7.16904 | − | 12.4171i | 0.360258 | − | 0.623985i | ||||
\(397\) | 6.37569 | + | 11.0430i | 0.319987 | + | 0.554233i | 0.980485 | − | 0.196594i | \(-0.0629882\pi\) |
−0.660498 | + | 0.750828i | \(0.729655\pi\) | |||||||
\(398\) | −14.7219 | −0.737941 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.3220 | 0.616098 | ||||||||
\(401\) | −9.62568 | − | 16.6722i | −0.480683 | − | 0.832568i | 0.519071 | − | 0.854731i | \(-0.326278\pi\) |
−0.999754 | + | 0.0221631i | \(0.992945\pi\) | |||||||
\(402\) | 4.94969 | − | 8.57311i | 0.246868 | − | 0.427588i | ||||
\(403\) | 4.94095 | − | 8.55798i | 0.246126 | − | 0.426303i | ||||
\(404\) | −10.8133 | − | 18.7291i | −0.537979 | − | 0.931808i | ||||
\(405\) | 44.2495 | 2.19877 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.7043 | 1.81936 | ||||||||
\(408\) | −1.77498 | − | 3.07436i | −0.0878746 | − | 0.152203i | ||||
\(409\) | 1.56990 | − | 2.71915i | 0.0776266 | − | 0.134453i | −0.824599 | − | 0.565718i | \(-0.808599\pi\) |
0.902225 | + | 0.431265i | \(0.141932\pi\) | |||||||
\(410\) | −3.48764 | + | 6.04077i | −0.172242 | + | 0.298333i | ||||
\(411\) | 1.35342 | + | 2.34420i | 0.0667595 | + | 0.115631i | ||||
\(412\) | 7.02736 | 0.346213 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 7.99455 | 0.392910 | ||||||||
\(415\) | 9.08165 | + | 15.7299i | 0.445800 | + | 0.772149i | ||||
\(416\) | 6.41047 | − | 11.1033i | 0.314299 | − | 0.544382i | ||||
\(417\) | 4.95019 | − | 8.57398i | 0.242412 | − | 0.419869i | ||||
\(418\) | 1.53922 | + | 2.66601i | 0.0752858 | + | 0.130399i | ||||
\(419\) | −12.4881 | −0.610085 | −0.305043 | − | 0.952339i | \(-0.598671\pi\) | ||||
−0.305043 | + | 0.952339i | \(0.598671\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.5141 | −0.707376 | −0.353688 | − | 0.935364i | \(-0.615072\pi\) | ||||
−0.353688 | + | 0.935364i | \(0.615072\pi\) | |||||||
\(422\) | 3.56390 | + | 6.17286i | 0.173488 | + | 0.300490i | ||||
\(423\) | −14.4127 | + | 24.9636i | −0.700771 | + | 1.21377i | ||||
\(424\) | −5.68993 | + | 9.85524i | −0.276327 | + | 0.478613i | ||||
\(425\) | 3.89248 | + | 6.74197i | 0.188813 | + | 0.327033i | ||||
\(426\) | 14.5761 | 0.706215 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.27607 | −0.0616811 | ||||||||
\(429\) | 10.4504 | + | 18.1006i | 0.504549 | + | 0.873904i | ||||
\(430\) | 13.9285 | − | 24.1248i | 0.671690 | − | 1.16340i | ||||
\(431\) | −11.8336 | + | 20.4963i | −0.570003 | + | 0.987274i | 0.426562 | + | 0.904458i | \(0.359725\pi\) |
−0.996565 | + | 0.0828154i | \(0.973609\pi\) | |||||||
\(432\) | −0.614077 | − | 1.06361i | −0.0295448 | − | 0.0511731i | ||||
\(433\) | −4.61912 | −0.221981 | −0.110990 | − | 0.993821i | \(-0.535402\pi\) | ||||
−0.110990 | + | 0.993821i | \(0.535402\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −73.2385 | −3.51152 | ||||||||
\(436\) | −0.797929 | − | 1.38205i | −0.0382139 | − | 0.0661883i | ||||
\(437\) | 2.18494 | − | 3.78442i | 0.104520 | − | 0.181034i | ||||
\(438\) | −9.35002 | + | 16.1947i | −0.446761 | + | 0.773813i | ||||
\(439\) | 9.48014 | + | 16.4201i | 0.452462 | + | 0.783688i | 0.998538 | − | 0.0540478i | \(-0.0172123\pi\) |
−0.546076 | + | 0.837736i | \(0.683879\pi\) | |||||||
\(440\) | −45.1172 | −2.15088 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.969132 | 0.0460969 | ||||||||
\(443\) | 11.2344 | + | 19.4586i | 0.533764 | + | 0.924507i | 0.999222 | + | 0.0394366i | \(0.0125563\pi\) |
−0.465458 | + | 0.885070i | \(0.654110\pi\) | |||||||
\(444\) | −14.9896 | + | 25.9628i | −0.711377 | + | 1.23214i | ||||
\(445\) | −8.08535 | + | 14.0042i | −0.383282 | + | 0.663864i | ||||
\(446\) | 7.09077 | + | 12.2816i | 0.335758 | + | 0.581549i | ||||
\(447\) | 55.9405 | 2.64589 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.7360 | 0.742629 | 0.371314 | − | 0.928507i | \(-0.378907\pi\) | ||||
0.371314 | + | 0.928507i | \(0.378907\pi\) | |||||||
\(450\) | 12.0689 | + | 20.9039i | 0.568933 | + | 0.985421i | ||||
\(451\) | −4.46265 | + | 7.72953i | −0.210138 | + | 0.363969i | ||||
\(452\) | −9.27352 | + | 16.0622i | −0.436190 | + | 0.755503i | ||||
\(453\) | 9.90974 | + | 17.1642i | 0.465600 | + | 0.806444i | ||||
\(454\) | −15.4264 | −0.723997 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.01645 | −0.281746 | ||||||||
\(457\) | −11.4283 | − | 19.7944i | −0.534594 | − | 0.925945i | −0.999183 | − | 0.0404180i | \(-0.987131\pi\) |
0.464588 | − | 0.885527i | \(-0.346202\pi\) | |||||||
\(458\) | 2.62295 | − | 4.54308i | 0.122562 | − | 0.212284i | ||||
\(459\) | 0.387971 | − | 0.671985i | 0.0181089 | − | 0.0313656i | ||||
\(460\) | 13.3827 | + | 23.1796i | 0.623974 | + | 1.08075i | ||||
\(461\) | −26.0021 | −1.21104 | −0.605519 | − | 0.795831i | \(-0.707035\pi\) | ||||
−0.605519 | + | 0.795831i | \(0.707035\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.3481 | 0.945654 | 0.472827 | − | 0.881155i | \(-0.343233\pi\) | ||||
0.472827 | + | 0.881155i | \(0.343233\pi\) | |||||||
\(464\) | 3.43887 | + | 5.95630i | 0.159646 | + | 0.276514i | ||||
\(465\) | 22.4681 | − | 38.9158i | 1.04193 | − | 1.80468i | ||||
\(466\) | 7.33243 | − | 12.7001i | 0.339668 | − | 0.588323i | ||||
\(467\) | 7.56509 | + | 13.1031i | 0.350071 | + | 0.606340i | 0.986262 | − | 0.165192i | \(-0.0528242\pi\) |
−0.636191 | + | 0.771532i | \(0.719491\pi\) | |||||||
\(468\) | −7.64997 | −0.353620 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 37.9073 | 1.74853 | ||||||||
\(471\) | −5.17453 | − | 8.96255i | −0.238430 | − | 0.412972i | ||||
\(472\) | 13.8287 | − | 23.9519i | 0.636515 | − | 1.10248i | ||||
\(473\) | 17.8223 | − | 30.8691i | 0.819470 | − | 1.41936i | ||||
\(474\) | −7.49768 | − | 12.9864i | −0.344380 | − | 0.596483i | ||||
\(475\) | 13.1939 | 0.605377 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.7425 | 0.491865 | ||||||||
\(478\) | −6.68621 | − | 11.5808i | −0.305820 | − | 0.529696i | ||||
\(479\) | 13.9632 | − | 24.1850i | 0.637997 | − | 1.10504i | −0.347875 | − | 0.937541i | \(-0.613097\pi\) |
0.985872 | − | 0.167502i | \(-0.0535699\pi\) | |||||||
\(480\) | 29.1504 | − | 50.4900i | 1.33053 | − | 2.30454i | ||||
\(481\) | −9.79165 | − | 16.9596i | −0.446461 | − | 0.773293i | ||||
\(482\) | −11.4357 | −0.520881 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.33109 | −0.378686 | ||||||||
\(485\) | −4.50059 | − | 7.79525i | −0.204361 | − | 0.353964i | ||||
\(486\) | 7.60107 | − | 13.1654i | 0.344792 | − | 0.597197i | ||||
\(487\) | −0.330326 | + | 0.572142i | −0.0149685 | + | 0.0259262i | −0.873413 | − | 0.486981i | \(-0.838098\pi\) |
0.858444 | + | 0.512907i | \(0.171431\pi\) | |||||||
\(488\) | −3.13595 | − | 5.43163i | −0.141958 | − | 0.245878i | ||||
\(489\) | 0.342514 | 0.0154890 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.09463 | −0.229917 | −0.114959 | − | 0.993370i | \(-0.536674\pi\) | ||||
−0.114959 | + | 0.993370i | \(0.536674\pi\) | |||||||
\(492\) | −3.64499 | − | 6.31331i | −0.164329 | − | 0.284626i | ||||
\(493\) | −2.17266 | + | 3.76316i | −0.0978517 | + | 0.169484i | ||||
\(494\) | 0.821240 | − | 1.42243i | 0.0369493 | − | 0.0639981i | ||||
\(495\) | 21.2951 | + | 36.8843i | 0.957146 | + | 1.65782i | ||||
\(496\) | −4.21989 | −0.189479 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 7.45631 | 0.334125 | ||||||||
\(499\) | 6.39951 | + | 11.0843i | 0.286482 | + | 0.496201i | 0.972967 | − | 0.230943i | \(-0.0741809\pi\) |
−0.686486 | + | 0.727143i | \(0.740848\pi\) | |||||||
\(500\) | −25.0938 | + | 43.4637i | −1.12223 | + | 1.94376i | ||||
\(501\) | −1.03244 | + | 1.78824i | −0.0461261 | + | 0.0798928i | ||||
\(502\) | 2.51710 | + | 4.35974i | 0.112344 | + | 0.194585i | ||||
\(503\) | −32.1398 | −1.43304 | −0.716522 | − | 0.697565i | \(-0.754267\pi\) | ||||
−0.716522 | + | 0.697565i | \(0.754267\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.2401 | 2.85865 | ||||||||
\(506\) | −6.72621 | − | 11.6501i | −0.299016 | − | 0.517912i | ||||
\(507\) | −9.57913 | + | 16.5915i | −0.425424 | + | 0.736856i | ||||
\(508\) | −2.23560 | + | 3.87217i | −0.0991887 | + | 0.171800i | ||||
\(509\) | 18.2323 | + | 31.5792i | 0.808130 | + | 1.39972i | 0.914157 | + | 0.405360i | \(0.132854\pi\) |
−0.106027 | + | 0.994363i | \(0.533813\pi\) | |||||||
\(510\) | 4.40695 | 0.195143 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.2949 | −0.454973 | ||||||||
\(513\) | −0.657531 | − | 1.13888i | −0.0290307 | − | 0.0502826i | ||||
\(514\) | 3.09848 | − | 5.36673i | 0.136668 | − | 0.236716i | ||||
\(515\) | −10.4372 | + | 18.0777i | −0.459916 | + | 0.796598i | ||||
\(516\) | 14.5569 | + | 25.2132i | 0.640830 | + | 1.10995i | ||||
\(517\) | 48.5046 | 2.13323 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 56.5714 | 2.48321 | ||||||||
\(520\) | 12.0360 | + | 20.8469i | 0.527812 | + | 0.914198i | ||||
\(521\) | 17.7606 | − | 30.7623i | 0.778107 | − | 1.34772i | −0.154925 | − | 0.987926i | \(-0.549513\pi\) |
0.933032 | − | 0.359794i | \(-0.117153\pi\) | |||||||
\(522\) | −6.73648 | + | 11.6679i | −0.294848 | + | 0.510691i | ||||
\(523\) | 7.08114 | + | 12.2649i | 0.309636 | + | 0.536306i | 0.978283 | − | 0.207274i | \(-0.0664593\pi\) |
−0.668646 | + | 0.743581i | \(0.733126\pi\) | |||||||
\(524\) | 5.32341 | 0.232554 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.525946 | 0.0229323 | ||||||||
\(527\) | −1.33305 | − | 2.30892i | −0.0580687 | − | 0.100578i | ||||
\(528\) | 4.46265 | − | 7.72953i | 0.194212 | − | 0.336385i | ||||
\(529\) | 1.95209 | − | 3.38111i | 0.0848733 | − | 0.147005i | ||||
\(530\) | −7.06352 | − | 12.2344i | −0.306820 | − | 0.531427i | ||||
\(531\) | −26.1083 | −1.13300 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.76202 | 0.206266 | ||||||||
\(534\) | 3.31916 | + | 5.74895i | 0.143634 | + | 0.248781i | ||||
\(535\) | 1.89524 | − | 3.28265i | 0.0819382 | − | 0.141921i | ||||
\(536\) | 7.29438 | − | 12.6342i | 0.315069 | − | 0.545716i | ||||
\(537\) | −15.0926 | − | 26.1412i | −0.651295 | − | 1.12808i | ||||
\(538\) | −10.4882 | −0.452178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 8.05475 | 0.346621 | ||||||||
\(541\) | 8.37268 | + | 14.5019i | 0.359970 | + | 0.623486i | 0.987955 | − | 0.154739i | \(-0.0494537\pi\) |
−0.627986 | + | 0.778225i | \(0.716120\pi\) | |||||||
\(542\) | −3.12640 | + | 5.41509i | −0.134290 | + | 0.232598i | ||||
\(543\) | −21.6871 | + | 37.5631i | −0.930682 | + | 1.61199i | ||||
\(544\) | −1.72952 | − | 2.99562i | −0.0741527 | − | 0.128436i | ||||
\(545\) | 4.74039 | 0.203056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.3888 | −1.76966 | −0.884829 | − | 0.465917i | \(-0.845725\pi\) | ||||
−0.884829 | + | 0.465917i | \(0.845725\pi\) | |||||||
\(548\) | 0.833563 | + | 1.44377i | 0.0356081 | + | 0.0616750i | ||||
\(549\) | −2.96031 | + | 5.12741i | −0.126343 | + | 0.218833i | ||||
\(550\) | 20.3083 | − | 35.1750i | 0.865950 | − | 1.49987i | ||||
\(551\) | 3.68221 | + | 6.37778i | 0.156867 | + | 0.271702i | ||||
\(552\) | 26.2912 | 1.11903 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 11.3781 | 0.483408 | ||||||||
\(555\) | −44.5257 | − | 77.1208i | −1.89001 | − | 3.27359i | ||||
\(556\) | 3.04878 | − | 5.28065i | 0.129297 | − | 0.223949i | ||||
\(557\) | −18.8375 | + | 32.6275i | −0.798172 | + | 1.38247i | 0.122634 | + | 0.992452i | \(0.460866\pi\) |
−0.920806 | + | 0.390022i | \(0.872468\pi\) | |||||||
\(558\) | −4.13322 | − | 7.15896i | −0.174973 | − | 0.303063i | ||||
\(559\) | −19.0179 | −0.804372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.63895 | 0.238077 | ||||||||
\(562\) | −3.83165 | − | 6.63661i | −0.161628 | − | 0.279949i | ||||
\(563\) | −1.72907 | + | 2.99484i | −0.0728717 | + | 0.126217i | −0.900159 | − | 0.435562i | \(-0.856550\pi\) |
0.827287 | + | 0.561779i | \(0.189883\pi\) | |||||||
\(564\) | −19.8087 | + | 34.3098i | −0.834099 | + | 1.44470i | ||||
\(565\) | −27.5464 | − | 47.7117i | −1.15888 | − | 2.00725i | ||||
\(566\) | 4.72482 | 0.198599 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.4809 | 0.901318 | ||||||||
\(569\) | −3.84602 | − | 6.66151i | −0.161234 | − | 0.279265i | 0.774078 | − | 0.633091i | \(-0.218214\pi\) |
−0.935311 | + | 0.353826i | \(0.884881\pi\) | |||||||
\(570\) | 3.73444 | − | 6.46823i | 0.156418 | − | 0.270924i | ||||
\(571\) | 0.208566 | − | 0.361246i | 0.00872819 | − | 0.0151177i | −0.861628 | − | 0.507540i | \(-0.830555\pi\) |
0.870357 | + | 0.492422i | \(0.163888\pi\) | |||||||
\(572\) | 6.43630 | + | 11.1480i | 0.269115 | + | 0.466122i | ||||
\(573\) | 54.2982 | 2.26834 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −57.6557 | −2.40441 | ||||||||
\(576\) | −3.08753 | − | 5.34776i | −0.128647 | − | 0.222823i | ||||
\(577\) | 11.6453 | − | 20.1702i | 0.484798 | − | 0.839695i | −0.515049 | − | 0.857161i | \(-0.672226\pi\) |
0.999847 | + | 0.0174655i | \(0.00555972\pi\) | |||||||
\(578\) | −6.25297 | + | 10.8305i | −0.260089 | + | 0.450488i | ||||
\(579\) | 3.71694 | + | 6.43793i | 0.154471 | + | 0.267551i | ||||
\(580\) | −45.1071 | −1.87297 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.69512 | −0.153168 | ||||||||
\(583\) | −9.03819 | − | 15.6546i | −0.374324 | − | 0.648348i | ||||
\(584\) | −13.7792 | + | 23.8662i | −0.570186 | + | 0.987590i | ||||
\(585\) | 11.3619 | − | 19.6793i | 0.469755 | − | 0.813640i | ||||
\(586\) | −0.556830 | − | 0.964458i | −0.0230025 | − | 0.0398414i | ||||
\(587\) | 30.5061 | 1.25912 | 0.629562 | − | 0.776951i | \(-0.283234\pi\) | ||||
0.629562 | + | 0.776951i | \(0.283234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.51850 | −0.186182 | ||||||||
\(590\) | 17.1670 | + | 29.7341i | 0.706754 | + | 1.22413i | ||||
\(591\) | −9.61958 | + | 16.6616i | −0.395697 | + | 0.685366i | ||||
\(592\) | −4.18135 | + | 7.24231i | −0.171853 | + | 0.297657i | ||||
\(593\) | −16.3431 | − | 28.3070i | −0.671129 | − | 1.16243i | −0.977584 | − | 0.210544i | \(-0.932476\pi\) |
0.306455 | − | 0.951885i | \(-0.400857\pi\) | |||||||
\(594\) | −4.04834 | −0.166105 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 34.4533 | 1.41126 | ||||||||
\(597\) | 22.8516 | + | 39.5802i | 0.935256 | + | 1.61991i | ||||
\(598\) | −3.58872 | + | 6.21584i | −0.146754 | + | 0.254185i | ||||
\(599\) | 10.1869 | − | 17.6442i | 0.416225 | − | 0.720923i | −0.579331 | − | 0.815092i | \(-0.696686\pi\) |
0.995556 | + | 0.0941691i | \(0.0300194\pi\) | |||||||
\(600\) | 39.6902 | + | 68.7455i | 1.62035 | + | 2.80652i | ||||
\(601\) | −12.3891 | −0.505363 | −0.252682 | − | 0.967549i | \(-0.581313\pi\) | ||||
−0.252682 | + | 0.967549i | \(0.581313\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.7717 | −0.560826 | ||||||||
\(604\) | 6.10334 | + | 10.5713i | 0.248341 | + | 0.430140i | ||||
\(605\) | 12.3735 | − | 21.4315i | 0.503053 | − | 0.871313i | ||||
\(606\) | 13.1858 | − | 22.8384i | 0.535635 | − | 0.927747i | ||||
\(607\) | −16.6740 | − | 28.8802i | −0.676776 | − | 1.17221i | −0.975946 | − | 0.218011i | \(-0.930043\pi\) |
0.299170 | − | 0.954200i | \(-0.403290\pi\) | |||||||
\(608\) | −5.86237 | −0.237751 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.78599 | 0.315245 | ||||||||
\(611\) | −12.9396 | − | 22.4121i | −0.523481 | − | 0.906696i | ||||
\(612\) | −1.03197 | + | 1.78742i | −0.0417149 | + | 0.0722523i | ||||
\(613\) | 19.3992 | − | 33.6005i | 0.783528 | − | 1.35711i | −0.146346 | − | 0.989233i | \(-0.546751\pi\) |
0.929874 | − | 0.367877i | \(-0.119915\pi\) | |||||||
\(614\) | 11.2512 | + | 19.4877i | 0.454063 | + | 0.786460i | ||||
\(615\) | 21.6544 | 0.873190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.98936 | 0.0800887 | 0.0400443 | − | 0.999198i | \(-0.487250\pi\) | ||||
0.0400443 | + | 0.999198i | \(0.487250\pi\) | |||||||
\(618\) | 4.28461 | + | 7.42116i | 0.172352 | + | 0.298523i | ||||
\(619\) | 6.50072 | − | 11.2596i | 0.261286 | − | 0.452561i | −0.705298 | − | 0.708911i | \(-0.749187\pi\) |
0.966584 | + | 0.256350i | \(0.0825200\pi\) | |||||||
\(620\) | 13.8379 | − | 23.9680i | 0.555744 | − | 0.962576i | ||||
\(621\) | 2.87333 | + | 4.97675i | 0.115303 | + | 0.199710i | ||||
\(622\) | 3.29035 | 0.131931 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.76202 | −0.190633 | ||||||||
\(625\) | −41.5546 | − | 71.9747i | −1.66219 | − | 2.87899i | ||||
\(626\) | −7.68057 | + | 13.3031i | −0.306977 | + | 0.531700i | ||||
\(627\) | 4.77843 | − | 8.27649i | 0.190832 | − | 0.330531i | ||||
\(628\) | −3.18695 | − | 5.51996i | −0.127173 | − | 0.220271i | ||||
\(629\) | −5.28351 | −0.210667 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.9918 | −0.596814 | −0.298407 | − | 0.954439i | \(-0.596455\pi\) | ||||
−0.298407 | + | 0.954439i | \(0.596455\pi\) | |||||||
\(632\) | −11.0494 | − | 19.1381i | −0.439520 | − | 0.761271i | ||||
\(633\) | 11.0639 | − | 19.1633i | 0.439752 | − | 0.761674i | ||||
\(634\) | −3.31069 | + | 5.73429i | −0.131484 | + | 0.227738i | ||||
\(635\) | −6.64069 | − | 11.5020i | −0.263528 | − | 0.456444i | ||||
\(636\) | 14.7644 | 0.585447 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.6710 | 0.897552 | ||||||||
\(639\) | −10.1389 | − | 17.5611i | −0.401088 | − | 0.694706i | ||||
\(640\) | 20.9453 | − | 36.2782i | 0.827934 | − | 1.43402i | ||||
\(641\) | −12.0274 | + | 20.8320i | −0.475053 | + | 0.822815i | −0.999592 | − | 0.0285709i | \(-0.990904\pi\) |
0.524539 | + | 0.851386i | \(0.324238\pi\) | |||||||
\(642\) | −0.778024 | − | 1.34758i | −0.0307061 | − | 0.0531846i | ||||
\(643\) | 24.3676 | 0.960964 | 0.480482 | − | 0.877005i | \(-0.340462\pi\) | ||||
0.480482 | + | 0.877005i | \(0.340462\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −86.4803 | −3.40516 | ||||||||
\(646\) | −0.221568 | − | 0.383767i | −0.00871748 | − | 0.0150991i | ||||
\(647\) | 19.1201 | − | 33.1170i | 0.751688 | − | 1.30196i | −0.195316 | − | 0.980740i | \(-0.562573\pi\) |
0.947004 | − | 0.321222i | \(-0.104093\pi\) | |||||||
\(648\) | 13.3850 | − | 23.1835i | 0.525811 | − | 0.910732i | ||||
\(649\) | 21.9662 | + | 38.0466i | 0.862248 | + | 1.49346i | ||||
\(650\) | −21.6707 | −0.849995 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.210952 | 0.00826151 | ||||||||
\(653\) | −10.5812 | − | 18.3271i | −0.414074 | − | 0.717197i | 0.581257 | − | 0.813720i | \(-0.302561\pi\) |
−0.995331 | + | 0.0965234i | \(0.969228\pi\) | |||||||
\(654\) | 0.973000 | − | 1.68529i | 0.0380473 | − | 0.0658999i | ||||
\(655\) | −7.90642 | + | 13.6943i | −0.308929 | + | 0.535081i | ||||
\(656\) | −1.01677 | − | 1.76110i | −0.0396982 | − | 0.0687593i | ||||
\(657\) | 26.0148 | 1.01493 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.6069 | 0.958548 | 0.479274 | − | 0.877665i | \(-0.340900\pi\) | ||||
0.479274 | + | 0.877665i | \(0.340900\pi\) | |||||||
\(660\) | 29.2679 | + | 50.6935i | 1.13925 | + | 1.97324i | ||||
\(661\) | 19.0976 | − | 33.0781i | 0.742812 | − | 1.28659i | −0.208398 | − | 0.978044i | \(-0.566825\pi\) |
0.951210 | − | 0.308544i | \(-0.0998417\pi\) | |||||||
\(662\) | 4.52792 | − | 7.84258i | 0.175983 | − | 0.304811i | ||||
\(663\) | −1.50431 | − | 2.60554i | −0.0584226 | − | 0.101191i | ||||
\(664\) | 10.9884 | 0.426432 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.3819 | −0.634786 | ||||||||
\(667\) | −16.0908 | − | 27.8701i | −0.623039 | − | 1.07913i | ||||
\(668\) | −0.635874 | + | 1.10137i | −0.0246027 | + | 0.0426131i | ||||
\(669\) | 22.0129 | − | 38.1275i | 0.851068 | − | 1.47409i | ||||
\(670\) | 9.05529 | + | 15.6842i | 0.349836 | + | 0.605935i | ||||
\(671\) | 9.96264 | 0.384603 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0333 | −1.08060 | −0.540302 | − | 0.841471i | \(-0.681690\pi\) | ||||
−0.540302 | + | 0.841471i | \(0.681690\pi\) | |||||||
\(674\) | 10.3593 | + | 17.9428i | 0.399025 | + | 0.691132i | ||||
\(675\) | −8.67539 | + | 15.0262i | −0.333916 | + | 0.578359i | ||||
\(676\) | −5.89972 | + | 10.2186i | −0.226912 | + | 0.393023i | ||||
\(677\) | 2.61817 | + | 4.53481i | 0.100625 | + | 0.174287i | 0.911942 | − | 0.410319i | \(-0.134583\pi\) |
−0.811318 | + | 0.584606i | \(0.801249\pi\) | |||||||
\(678\) | −22.6164 | −0.868578 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.49454 | 0.249054 | ||||||||
\(681\) | 23.9452 | + | 41.4744i | 0.917584 | + | 1.58930i | ||||
\(682\) | −6.95497 | + | 12.0464i | −0.266320 | + | 0.461279i | ||||
\(683\) | 0.625857 | − | 1.08402i | 0.0239478 | − | 0.0414787i | −0.853803 | − | 0.520596i | \(-0.825710\pi\) |
0.877751 | + | 0.479117i | \(0.159043\pi\) | |||||||
\(684\) | 1.74898 | + | 3.02932i | 0.0668738 | + | 0.115829i | ||||
\(685\) | −4.95209 | −0.189210 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.2856 | −0.621335 | ||||||||
\(688\) | 4.06063 | + | 7.03322i | 0.154810 | + | 0.268139i | ||||
\(689\) | −4.82226 | + | 8.35240i | −0.183713 | + | 0.318201i | ||||
\(690\) | −16.3190 | + | 28.2654i | −0.621255 | + | 1.07604i | ||||
\(691\) | −25.4025 | − | 43.9984i | −0.966357 | − | 1.67378i | −0.705924 | − | 0.708288i | \(-0.749468\pi\) |
−0.260434 | − | 0.965492i | \(-0.583865\pi\) | |||||||
\(692\) | 34.8419 | 1.32449 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.744668 | −0.0282672 | ||||||||
\(695\) | 9.05620 | + | 15.6858i | 0.343521 | + | 0.594997i | ||||
\(696\) | −22.1539 | + | 38.3716i | −0.839740 | + | 1.45447i | ||||
\(697\) | 0.642389 | − | 1.11265i | 0.0243322 | − | 0.0421447i | ||||
\(698\) | −11.8881 | − | 20.5908i | −0.449971 | − | 0.779372i | ||||
\(699\) | −45.5263 | −1.72196 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.998799 | 0.0377241 | 0.0188621 | − | 0.999822i | \(-0.493996\pi\) | ||||
0.0188621 | + | 0.999822i | \(0.493996\pi\) | |||||||
\(702\) | 1.07998 | + | 1.87058i | 0.0407613 | + | 0.0706006i | ||||
\(703\) | −4.47723 | + | 7.75479i | −0.168862 | + | 0.292478i | ||||
\(704\) | −5.19538 | + | 8.99867i | −0.195808 | + | 0.339150i | ||||
\(705\) | −58.8405 | − | 101.915i | −2.21606 | − | 3.83833i | ||||
\(706\) | 6.68698 | 0.251668 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −35.8830 | −1.34857 | ||||||||
\(709\) | 6.98123 | + | 12.0918i | 0.262185 | + | 0.454119i | 0.966822 | − | 0.255449i | \(-0.0822234\pi\) |
−0.704637 | + | 0.709568i | \(0.748890\pi\) | |||||||
\(710\) | −13.3333 | + | 23.0939i | −0.500389 | + | 0.866698i | ||||
\(711\) | −10.4305 | + | 18.0662i | −0.391175 | + | 0.677534i | ||||
\(712\) | 4.89146 | + | 8.47225i | 0.183315 | + | 0.317511i | ||||
\(713\) | 19.7453 | 0.739467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.2372 | −1.42999 | ||||||||
\(716\) | −9.29544 | − | 16.1002i | −0.347387 | − | 0.601692i | ||||
\(717\) | −20.7570 | + | 35.9521i | −0.775184 | + | 1.34266i | ||||
\(718\) | −8.14852 | + | 14.1137i | −0.304100 | + | 0.526717i | ||||
\(719\) | 9.28469 | + | 16.0816i | 0.346260 | + | 0.599741i | 0.985582 | − | 0.169199i | \(-0.0541180\pi\) |
−0.639321 | + | 0.768940i | \(0.720785\pi\) | |||||||
\(720\) | −9.70377 | −0.361638 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.751024 | −0.0279502 | ||||||||
\(723\) | 17.7508 | + | 30.7452i | 0.660158 | + | 1.14343i | ||||
\(724\) | −13.3569 | + | 23.1348i | −0.496406 | + | 0.859800i | ||||
\(725\) | 48.5827 | − | 84.1477i | 1.80432 | − | 3.12517i | ||||
\(726\) | −5.07950 | − | 8.79795i | −0.188518 | − | 0.326522i | ||||
\(727\) | 32.1991 | 1.19420 | 0.597099 | − | 0.802168i | \(-0.296320\pi\) | ||||
0.597099 | + | 0.802168i | \(0.296320\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.0724 | −0.595272 | ||||||||
\(730\) | −17.1055 | − | 29.6277i | −0.633105 | − | 1.09657i | ||||
\(731\) | −2.56549 | + | 4.44355i | −0.0948879 | + | 0.164351i | ||||
\(732\) | −4.06863 | + | 7.04708i | −0.150381 | + | 0.260468i | ||||
\(733\) | 4.77812 | + | 8.27594i | 0.176484 | + | 0.305679i | 0.940674 | − | 0.339312i | \(-0.110194\pi\) |
−0.764190 | + | 0.644991i | \(0.776861\pi\) | |||||||
\(734\) | 9.59598 | 0.354194 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 25.6179 | 0.944287 | ||||||||
\(737\) | 11.5868 | + | 20.0689i | 0.426805 | + | 0.739247i | ||||
\(738\) | 1.99177 | − | 3.44985i | 0.0733182 | − | 0.126991i | ||||
\(739\) | 10.1425 | − | 17.5673i | 0.373097 | − | 0.646223i | −0.616943 | − | 0.787008i | \(-0.711629\pi\) |
0.990040 | + | 0.140785i | \(0.0449625\pi\) | |||||||
\(740\) | −27.4230 | − | 47.4981i | −1.00809 | − | 1.74606i | ||||
\(741\) | −5.09899 | −0.187316 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.965374 | 0.0354161 | 0.0177081 | − | 0.999843i | \(-0.494363\pi\) | ||||
0.0177081 | + | 0.999843i | \(0.494363\pi\) | |||||||
\(744\) | −13.5927 | − | 23.5432i | −0.498332 | − | 0.863136i | ||||
\(745\) | −51.1706 | + | 88.6301i | −1.87475 | + | 3.24716i | ||||
\(746\) | −4.96361 | + | 8.59722i | −0.181731 | + | 0.314767i | ||||
\(747\) | −5.18648 | − | 8.98324i | −0.189763 | − | 0.328680i | ||||
\(748\) | 3.47299 | 0.126985 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −61.1991 | −2.23468 | ||||||||
\(751\) | 0.328889 | + | 0.569653i | 0.0120013 | + | 0.0207869i | 0.871964 | − | 0.489571i | \(-0.162846\pi\) |
−0.859962 | + | 0.510357i | \(0.829513\pi\) | |||||||
\(752\) | −5.52564 | + | 9.57069i | −0.201499 | + | 0.349007i | ||||
\(753\) | 7.81420 | − | 13.5346i | 0.284765 | − | 0.493228i | ||||
\(754\) | −6.04796 | − | 10.4754i | −0.220254 | − | 0.381491i | ||||
\(755\) | −36.2591 | −1.31960 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.47679 | −0.0536749 | −0.0268375 | − | 0.999640i | \(-0.508544\pi\) | ||||
−0.0268375 | + | 0.999640i | \(0.508544\pi\) | |||||||
\(758\) | −0.648760 | − | 1.12369i | −0.0235640 | − | 0.0408141i | ||||
\(759\) | −20.8812 | + | 36.1672i | −0.757938 | + | 1.31279i | ||||
\(760\) | 5.50345 | − | 9.53226i | 0.199631 | − | 0.345771i | ||||
\(761\) | 9.24235 | + | 16.0082i | 0.335035 | + | 0.580297i | 0.983492 | − | 0.180954i | \(-0.0579186\pi\) |
−0.648457 | + | 0.761252i | \(0.724585\pi\) | |||||||
\(762\) | −5.45221 | −0.197513 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 33.4418 | 1.20988 | ||||||||
\(765\) | −3.06540 | − | 5.30942i | −0.110830 | − | 0.191963i | ||||
\(766\) | 1.82335 | − | 3.15813i | 0.0658802 | − | 0.114108i | ||||
\(767\) | 11.7199 | − | 20.2995i | 0.423181 | − | 0.732971i | ||||
\(768\) | −14.5086 | − | 25.1297i | −0.523535 | − | 0.906790i | ||||
\(769\) | 4.34052 | 0.156523 | 0.0782617 | − | 0.996933i | \(-0.475063\pi\) | ||||
0.0782617 | + | 0.996933i | \(0.475063\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.2382 | −0.692845 | ||||||||
\(772\) | 2.28924 | + | 3.96507i | 0.0823914 | + | 0.142706i | ||||
\(773\) | 16.7757 | − | 29.0563i | 0.603379 | − | 1.04508i | −0.388926 | − | 0.921269i | \(-0.627154\pi\) |
0.992305 | − | 0.123814i | \(-0.0395127\pi\) | |||||||
\(774\) | −7.95446 | + | 13.7775i | −0.285917 | + | 0.495223i | ||||
\(775\) | 29.8083 | + | 51.6295i | 1.07075 | + | 1.85459i | ||||
\(776\) | −5.44551 | −0.195483 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.98328 | −0.286214 | ||||||||
\(779\) | −1.08872 | − | 1.88571i | −0.0390074 | − | 0.0675627i | ||||
\(780\) | 15.6157 | − | 27.0471i | 0.559130 | − | 0.968442i | ||||
\(781\) | −17.0607 | + | 29.5500i | −0.610480 | + | 1.05738i | ||||
\(782\) | 0.968225 | + | 1.67701i | 0.0346236 | + | 0.0599699i | ||||
\(783\) | −9.68467 | −0.346102 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.9333 | 0.675757 | ||||||||
\(786\) | 3.24570 | + | 5.62173i | 0.115770 | + | 0.200520i | ||||
\(787\) | −21.0285 | + | 36.4225i | −0.749587 | + | 1.29832i | 0.198435 | + | 0.980114i | \(0.436414\pi\) |
−0.948021 | + | 0.318208i | \(0.896919\pi\) | |||||||
\(788\) | −5.92463 | + | 10.2618i | −0.211056 | + | 0.365560i | ||||
\(789\) | −0.816386 | − | 1.41402i | −0.0290641 | − | 0.0503405i | ||||
\(790\) | 27.4335 | 0.976041 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 25.7662 | 0.915562 | ||||||||
\(793\) | −2.65774 | − | 4.60335i | −0.0943793 | − | 0.163470i | ||||
\(794\) | −4.78830 | + | 8.29358i | −0.169930 | + | 0.294328i | ||||
\(795\) | −21.9283 | + | 37.9810i | −0.777718 | + | 1.34705i | ||||
\(796\) | 14.0742 | + | 24.3772i | 0.498845 | + | 0.864025i | ||||
\(797\) | −2.71101 | −0.0960289 | −0.0480145 | − | 0.998847i | \(-0.515289\pi\) | ||||
−0.0480145 | + | 0.998847i | \(0.515289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.98214 | −0.247010 | ||||||||
\(800\) | 38.6738 | + | 66.9849i | 1.36732 | + | 2.36827i | ||||
\(801\) | 4.61749 | − | 7.99774i | 0.163151 | − | 0.282586i | ||||
\(802\) | 7.22912 | − | 12.5212i | 0.255269 | − | 0.442139i | ||||
\(803\) | −21.8876 | − | 37.9104i | −0.772395 | − | 1.33783i | ||||
\(804\) | −18.9277 | −0.667528 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.42155 | 0.261413 | ||||||||
\(807\) | 16.2800 | + | 28.1978i | 0.573084 | + | 0.992611i | ||||
\(808\) | 19.4319 | − | 33.6571i | 0.683612 | − | 1.18405i | ||||
\(809\) | −6.65791 | + | 11.5318i | −0.234079 | + | 0.405438i | −0.959005 | − | 0.283390i | \(-0.908541\pi\) |
0.724925 | + | 0.688828i | \(0.241874\pi\) | |||||||
\(810\) | 16.6162 | + | 28.7801i | 0.583834 | + | 1.01123i | ||||
\(811\) | 15.1310 | 0.531320 | 0.265660 | − | 0.964067i | \(-0.414410\pi\) | ||||
0.265660 | + | 0.964067i | \(0.414410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.4115 | 0.680791 | ||||||||
\(814\) | 13.7829 | + | 23.8727i | 0.483091 | + | 0.836737i | ||||
\(815\) | −0.313309 | + | 0.542667i | −0.0109747 | + | 0.0190088i | ||||
\(816\) | −0.642389 | + | 1.11265i | −0.0224881 | + | 0.0389506i | ||||
\(817\) | 4.34797 | + | 7.53090i | 0.152116 | + | 0.263473i | ||||
\(818\) | 2.35807 | 0.0824478 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.3368 | 0.465741 | ||||||||
\(821\) | 12.1867 | + | 21.1080i | 0.425319 | + | 0.736675i | 0.996450 | − | 0.0841843i | \(-0.0268285\pi\) |
−0.571131 | + | 0.820859i | \(0.693495\pi\) | |||||||
\(822\) | −1.01645 | + | 1.76055i | −0.0354529 | + | 0.0614062i | ||||
\(823\) | −5.89383 | + | 10.2084i | −0.205446 | + | 0.355843i | −0.950275 | − | 0.311413i | \(-0.899198\pi\) |
0.744829 | + | 0.667256i | \(0.232531\pi\) | |||||||
\(824\) | 6.31425 | + | 10.9366i | 0.219967 | + | 0.380994i | ||||
\(825\) | −126.092 | −4.38997 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.5429 | 0.610028 | 0.305014 | − | 0.952348i | \(-0.401339\pi\) | ||||
0.305014 | + | 0.952348i | \(0.401339\pi\) | |||||||
\(828\) | −7.64281 | − | 13.2377i | −0.265606 | − | 0.460043i | ||||
\(829\) | 25.4864 | − | 44.1438i | 0.885180 | − | 1.53318i | 0.0396720 | − | 0.999213i | \(-0.487369\pi\) |
0.845508 | − | 0.533963i | \(-0.179298\pi\) | |||||||
\(830\) | −6.82054 | + | 11.8135i | −0.236744 | + | 0.410053i | ||||
\(831\) | −17.6613 | − | 30.5903i | −0.612664 | − | 1.06117i | ||||
\(832\) | 5.54391 | 0.192201 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.43542 | 0.257468 | ||||||||
\(835\) | −1.88882 | − | 3.27153i | −0.0653653 | − | 0.113216i | ||||
\(836\) | 2.94300 | − | 5.09743i | 0.101786 | − | 0.176298i | ||||
\(837\) | 2.97105 | − | 5.14602i | 0.102695 | − | 0.177872i | ||||
\(838\) | −4.68944 | − | 8.12235i | −0.161994 | − | 0.280582i | ||||
\(839\) | 5.84311 | 0.201727 | 0.100863 | − | 0.994900i | \(-0.467840\pi\) | ||||
0.100863 | + | 0.994900i | \(0.467840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2347 | 0.870163 | ||||||||
\(842\) | −5.45023 | − | 9.44008i | −0.187827 | − | 0.325327i | ||||
\(843\) | −11.8952 | + | 20.6030i | −0.409691 | + | 0.709606i | ||||
\(844\) | 6.81420 | − | 11.8025i | 0.234555 | − | 0.406260i | ||||
\(845\) | −17.5247 | − | 30.3537i | −0.602868 | − | 1.04420i | ||||
\(846\) | −21.6486 | −0.744295 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.11852 | 0.141431 | ||||||||
\(849\) | −7.33397 | − | 12.7028i | −0.251701 | − | 0.435959i | ||||
\(850\) | −2.92334 | + | 5.06338i | −0.100270 | + | 0.173672i | ||||
\(851\) | 19.5650 | − | 33.8875i | 0.670678 | − | 1.16165i | ||||
\(852\) | −13.9348 | − | 24.1358i | −0.477399 | − | 0.826879i | ||||
\(853\) | 37.0096 | 1.26719 | 0.633593 | − | 0.773667i | \(-0.281579\pi\) | ||||
0.633593 | + | 0.773667i | \(0.281579\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.3904 | −0.355345 | ||||||||
\(856\) | −1.14658 | − | 1.98593i | −0.0391892 | − | 0.0678776i | ||||
\(857\) | 20.0635 | − | 34.7509i | 0.685355 | − | 1.18707i | −0.287970 | − | 0.957639i | \(-0.592980\pi\) |
0.973325 | − | 0.229430i | \(-0.0736862\pi\) | |||||||
\(858\) | −7.84848 | + | 13.5940i | −0.267943 | + | 0.464090i | ||||
\(859\) | −7.21938 | − | 12.5043i | −0.246322 | − | 0.426643i | 0.716180 | − | 0.697915i | \(-0.245889\pi\) |
−0.962503 | + | 0.271273i | \(0.912555\pi\) | |||||||
\(860\) | −53.2626 | −1.81624 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −17.7746 | −0.605405 | ||||||||
\(863\) | −15.3092 | − | 26.5162i | −0.521130 | − | 0.902623i | −0.999698 | − | 0.0245728i | \(-0.992177\pi\) |
0.478568 | − | 0.878050i | \(-0.341156\pi\) | |||||||
\(864\) | 3.85469 | − | 6.67652i | 0.131139 | − | 0.227140i | ||||
\(865\) | −51.7478 | + | 89.6298i | −1.75948 | + | 3.04750i | ||||
\(866\) | −1.73454 | − | 3.00431i | −0.0589420 | − | 0.102090i | ||||
\(867\) | 38.8240 | 1.31853 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 35.1028 | 1.19078 | ||||||||
\(870\) | −27.5020 | − | 47.6348i | −0.932404 | − | 1.61497i | ||||
\(871\) | 6.18204 | − | 10.7076i | 0.209471 | − | 0.362814i | ||||
\(872\) | 1.43391 | − | 2.48361i | 0.0485585 | − | 0.0841057i | ||||
\(873\) | 2.57026 | + | 4.45182i | 0.0869901 | + | 0.150671i | ||||
\(874\) | 3.28188 | 0.111011 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 35.7546 | 1.20804 | ||||||||
\(877\) | 8.03427 | + | 13.9158i | 0.271298 | + | 0.469902i | 0.969194 | − | 0.246297i | \(-0.0792138\pi\) |
−0.697897 | + | 0.716199i | \(0.745880\pi\) | |||||||
\(878\) | −7.11981 | + | 12.3319i | −0.240282 | + | 0.416181i | ||||
\(879\) | −1.72865 | + | 2.99411i | −0.0583059 | + | 0.100989i | ||||
\(880\) | 8.16426 | + | 14.1409i | 0.275217 | + | 0.476690i | ||||
\(881\) | 40.2468 | 1.35595 | 0.677975 | − | 0.735085i | \(-0.262858\pi\) | ||||
0.677975 | + | 0.735085i | \(0.262858\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.564426 | −0.0189944 | −0.00949722 | − | 0.999955i | \(-0.503023\pi\) | ||||
−0.00949722 | + | 0.999955i | \(0.503023\pi\) | |||||||
\(884\) | −0.926494 | − | 1.60473i | −0.0311614 | − | 0.0539730i | ||||
\(885\) | 53.2940 | − | 92.3080i | 1.79146 | − | 3.10290i | ||||
\(886\) | −8.43733 | + | 14.6139i | −0.283458 | + | 0.490963i | ||||
\(887\) | −17.7918 | − | 30.8163i | −0.597390 | − | 1.03471i | −0.993205 | − | 0.116380i | \(-0.962871\pi\) |
0.395814 | − | 0.918331i | \(-0.370462\pi\) | |||||||
\(888\) | −53.8741 | −1.80790 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12.1446 | −0.407087 | ||||||||
\(891\) | 21.2614 | + | 36.8259i | 0.712284 | + | 1.23371i | ||||
\(892\) | 13.5576 | − | 23.4824i | 0.453942 | − | 0.786250i | ||||
\(893\) | −5.91665 | + | 10.2479i | −0.197993 | + | 0.342934i | ||||
\(894\) | 21.0063 | + | 36.3840i | 0.702557 | + | 1.21686i | ||||
\(895\) | 55.2229 | 1.84590 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 22.2820 | 0.743973 | ||||||||
\(898\) | 5.90906 | + | 10.2348i | 0.197188 | + | 0.341540i | ||||
\(899\) | −16.6381 | + | 28.8180i | −0.554911 | + | 0.961134i | ||||
\(900\) | 23.0758 | − | 39.9684i | 0.769193 | − | 1.33228i | ||||
\(901\) | 1.30103 | + | 2.25345i | 0.0433436 | + | 0.0750733i | ||||
\(902\) | −6.70311 | −0.223189 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −33.3299 | −1.10854 | ||||||||
\(905\) | −39.6758 | − | 68.7205i | −1.31887 | − | 2.28435i | ||||
\(906\) | −7.44246 | + | 12.8907i | −0.247259 | + | 0.428265i | ||||
\(907\) | −15.1841 | + | 26.2996i | −0.504179 | + | 0.873264i | 0.495809 | + | 0.868431i | \(0.334872\pi\) |
−0.999988 | + | 0.00483233i | \(0.998462\pi\) | |||||||
\(908\) | 14.7477 | + | 25.5438i | 0.489419 | + | 0.847699i | ||||
\(909\) | −36.6871 | −1.21684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9947 | 0.596191 | 0.298096 | − | 0.954536i | \(-0.403649\pi\) | ||||
0.298096 | + | 0.954536i | \(0.403649\pi\) | |||||||
\(912\) | 1.08872 | + | 1.88571i | 0.0360510 | + | 0.0624422i | ||||
\(913\) | −8.72728 | + | 15.1161i | −0.288831 | + | 0.500270i | ||||
\(914\) | 8.58295 | − | 14.8661i | 0.283899 | − | 0.491727i | ||||
\(915\) | −12.0856 | − | 20.9329i | −0.399537 | − | 0.692019i | ||||
\(916\) | −10.0302 | −0.331407 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.582751 | 0.0192336 | ||||||||
\(919\) | −20.9784 | − | 36.3357i | −0.692014 | − | 1.19860i | −0.971177 | − | 0.238360i | \(-0.923390\pi\) |
0.279163 | − | 0.960244i | \(-0.409943\pi\) | |||||||
\(920\) | −24.0494 | + | 41.6548i | −0.792885 | + | 1.37332i | ||||
\(921\) | 34.9289 | − | 60.4986i | 1.15095 | − | 1.99350i | ||||
\(922\) | −9.76411 | − | 16.9119i | −0.321564 | − | 0.556965i | ||||
\(923\) | 18.2052 | 0.599232 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 118.144 | 3.88456 | ||||||||
\(926\) | 7.64094 | + | 13.2345i | 0.251097 | + | 0.434913i | ||||
\(927\) | 5.96060 | − | 10.3241i | 0.195772 | − | 0.339087i | ||||
\(928\) | −21.5865 | + | 37.3889i | −0.708612 | + | 1.22735i | ||||
\(929\) | −9.55726 | − | 16.5537i | −0.313563 | − | 0.543108i | 0.665568 | − | 0.746338i | \(-0.268190\pi\) |
−0.979131 | + | 0.203230i | \(0.934856\pi\) | |||||||
\(930\) | 33.7481 | 1.10664 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −28.0393 | −0.918458 | ||||||||
\(933\) | −5.10736 | − | 8.84620i | −0.167207 | − | 0.289612i | ||||
\(934\) | −5.68157 | + | 9.84076i | −0.185907 | + | 0.322000i | ||||
\(935\) | −5.15814 | + | 8.93416i | −0.168689 | + | 0.292178i | ||||
\(936\) | −6.87368 | − | 11.9056i | −0.224673 | − | 0.389145i | ||||
\(937\) | −44.3779 | −1.44976 | −0.724881 | − | 0.688874i | \(-0.758105\pi\) | ||||
−0.724881 | + | 0.688874i | \(0.758105\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 47.6879 | 1.55623 | ||||||||
\(940\) | −36.2394 | − | 62.7686i | −1.18200 | − | 2.04728i | ||||
\(941\) | −18.8086 | + | 32.5774i | −0.613142 | + | 1.06199i | 0.377565 | + | 0.925983i | \(0.376761\pi\) |
−0.990707 | + | 0.136010i | \(0.956572\pi\) | |||||||
\(942\) | 3.88620 | − | 6.73109i | 0.126619 | − | 0.219311i | ||||
\(943\) | 4.75756 | + | 8.24034i | 0.154928 | + | 0.268342i | ||||
\(944\) | −10.0096 | −0.325783 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 26.7699 | 0.870366 | ||||||||
\(947\) | −14.5848 | − | 25.2616i | −0.473942 | − | 0.820891i | 0.525613 | − | 0.850724i | \(-0.323836\pi\) |
−0.999555 | + | 0.0298325i | \(0.990503\pi\) | |||||||
\(948\) | −14.3356 | + | 24.8300i | −0.465599 | + | 0.806441i | ||||
\(949\) | −11.6779 | + | 20.2268i | −0.379082 | + | 0.656590i | ||||
\(950\) | 4.95446 | + | 8.58138i | 0.160744 | + | 0.278417i | ||||
\(951\) | 20.5558 | 0.666566 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 25.0234 | 0.810586 | 0.405293 | − | 0.914187i | \(-0.367170\pi\) | ||||
0.405293 | + | 0.914187i | \(0.367170\pi\) | |||||||
\(954\) | 4.03394 | + | 6.98698i | 0.130603 | + | 0.226212i | ||||
\(955\) | −49.6683 | + | 86.0281i | −1.60723 | + | 2.78380i | ||||
\(956\) | −12.7841 | + | 22.1427i | −0.413466 | + | 0.716145i | ||||
\(957\) | −35.1904 | − | 60.9515i | −1.13754 | − | 1.97028i | ||||
\(958\) | 20.9735 | 0.677622 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 25.2099 | 0.813647 | ||||||||
\(961\) | 5.29157 | + | 9.16527i | 0.170696 | + | 0.295654i | ||||
\(962\) | 7.35376 | − | 12.7371i | 0.237095 | − | 0.410660i | ||||
\(963\) | −1.08236 | + | 1.87470i | −0.0348785 | + | 0.0604114i | ||||
\(964\) | 10.9326 | + | 18.9357i | 0.352114 | + | 0.609879i | ||||
\(965\) | −13.6000 | −0.437801 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.8469 | −0.927655 | −0.463828 | − | 0.885926i | \(-0.653524\pi\) | ||||
−0.463828 | + | 0.885926i | \(0.653524\pi\) | |||||||
\(968\) | −7.48567 | − | 12.9656i | −0.240599 | − | 0.416729i | ||||
\(969\) | −0.687846 | + | 1.19138i | −0.0220968 | + | 0.0382728i | ||||
\(970\) | 3.38005 | − | 5.85442i | 0.108527 | − | 0.187974i | ||||
\(971\) | 1.59964 | + | 2.77065i | 0.0513348 | + | 0.0889145i | 0.890551 | − | 0.454883i | \(-0.150319\pi\) |
−0.839216 | + | 0.543798i | \(0.816986\pi\) | |||||||
\(972\) | −29.0666 | −0.932312 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −0.496166 | −0.0158982 | ||||||||
\(975\) | 33.6378 | + | 58.2623i | 1.07727 | + | 1.86589i | ||||
\(976\) | −1.13494 | + | 1.96578i | −0.0363286 | + | 0.0629231i | ||||
\(977\) | 27.2484 | − | 47.1957i | 0.871755 | − | 1.50992i | 0.0115745 | − | 0.999933i | \(-0.496316\pi\) |
0.860180 | − | 0.509990i | \(-0.170351\pi\) | |||||||
\(978\) | 0.128618 | + | 0.222773i | 0.00411276 | + | 0.00712350i | ||||
\(979\) | −15.5397 | −0.496651 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.70721 | −0.0864345 | ||||||||
\(982\) | −1.91309 | − | 3.31358i | −0.0610493 | − | 0.105740i | ||||
\(983\) | −2.72880 | + | 4.72642i | −0.0870352 | + | 0.150749i | −0.906257 | − | 0.422728i | \(-0.861073\pi\) |
0.819221 | + | 0.573477i | \(0.194406\pi\) | |||||||
\(984\) | 6.55022 | − | 11.3453i | 0.208813 | − | 0.361675i | ||||
\(985\) | −17.5987 | − | 30.4818i | −0.560741 | − | 0.971232i | ||||
\(986\) | −3.26344 | −0.103929 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.14043 | −0.0999104 | ||||||||
\(989\) | −19.0001 | − | 32.9091i | −0.604168 | − | 1.04645i | ||||
\(990\) | −15.9932 | + | 27.7010i | −0.508296 | + | 0.880395i | ||||
\(991\) | −17.1455 | + | 29.6970i | −0.544646 | + | 0.943355i | 0.453983 | + | 0.891010i | \(0.350003\pi\) |
−0.998629 | + | 0.0523446i | \(0.983331\pi\) | |||||||
\(992\) | −13.2446 | − | 22.9403i | −0.420516 | − | 0.728355i | ||||
\(993\) | −28.1134 | −0.892151 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −83.6127 | −2.65070 | ||||||||
\(996\) | −7.12825 | − | 12.3465i | −0.225867 | − | 0.391214i | ||||
\(997\) | 11.6069 | − | 20.1037i | 0.367594 | − | 0.636691i | −0.621595 | − | 0.783339i | \(-0.713515\pi\) |
0.989189 | + | 0.146648i | \(0.0468483\pi\) | |||||||
\(998\) | −4.80619 | + | 8.32456i | −0.152137 | + | 0.263509i | ||||
\(999\) | −5.88784 | − | 10.1980i | −0.186283 | − | 0.322651i |
(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 | 931.2.f.o.704.3 | 8 | ||
7.2 | even | 3 | inner | 931.2.f.o.324.3 | 8 | ||
7.3 | odd | 6 | 931.2.a.m.1.2 | yes | 4 | ||
7.4 | even | 3 | 931.2.a.l.1.2 | ✓ | 4 | ||
7.5 | odd | 6 | 931.2.f.n.324.3 | 8 | |||
7.6 | odd | 2 | 931.2.f.n.704.3 | 8 | |||
21.11 | odd | 6 | 8379.2.a.bv.1.3 | 4 | |||
21.17 | even | 6 | 8379.2.a.bu.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.a.l.1.2 | ✓ | 4 | 7.4 | even | 3 | ||
931.2.a.m.1.2 | yes | 4 | 7.3 | odd | 6 | ||
931.2.f.n.324.3 | 8 | 7.5 | odd | 6 | |||
931.2.f.n.704.3 | 8 | 7.6 | odd | 2 | |||
931.2.f.o.324.3 | 8 | 7.2 | even | 3 | inner | ||
931.2.f.o.704.3 | 8 | 1.1 | even | 1 | trivial | ||
8379.2.a.bu.1.3 | 4 | 21.17 | even | 6 | |||
8379.2.a.bv.1.3 | 4 | 21.11 | odd | 6 |