Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(121,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.i (of order \(3\), degree \(2\), 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: | \(3.03431527681\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.121 |
Dual form | 380.2.i.a.201.1 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.00000 | − | 1.73205i | −0.577350 | − | 1.00000i | −0.995782 | − | 0.0917517i | \(-0.970753\pi\) |
0.418432 | − | 0.908248i | \(-0.362580\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.00000 | −1.51186 | −0.755929 | − | 0.654654i | \(-0.772814\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 5.19615i | −0.832050 | + | 1.44115i | 0.0643593 | + | 0.997927i | \(0.479500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | − | 1.73205i | 0.258199 | − | 0.447214i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.50000 | − | 2.59808i | 0.802955 | − | 0.596040i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00000 | + | 6.92820i | 0.872872 | + | 1.51186i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | + | 0.866025i | −0.0928477 | + | 0.160817i | −0.908708 | − | 0.417432i | \(-0.862930\pi\) |
0.815861 | + | 0.578249i | \(0.196264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.00000 | + | 5.19615i | 0.522233 | + | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 3.46410i | −0.338062 | − | 0.585540i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.0000 | 1.92154 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | − | 1.73205i | −0.156174 | − | 0.270501i | 0.777312 | − | 0.629115i | \(-0.216583\pi\) |
−0.933486 | + | 0.358614i | \(0.883249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00000 | + | 5.19615i | −0.437595 | + | 0.757937i | −0.997503 | − | 0.0706177i | \(-0.977503\pi\) |
0.559908 | + | 0.828554i | \(0.310836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000 | 1.28571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | − | 3.46410i | −1.05963 | − | 0.458831i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.500000 | + | 0.866025i | 0.0650945 | + | 0.112747i | 0.896736 | − | 0.442566i | \(-0.145932\pi\) |
−0.831641 | + | 0.555313i | \(0.812598\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | − | 6.06218i | 0.448129 | − | 0.776182i | −0.550135 | − | 0.835076i | \(-0.685424\pi\) |
0.998264 | + | 0.0588933i | \(0.0187572\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | − | 3.46410i | 0.251976 | − | 0.436436i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.00000 | −0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.00000 | − | 12.1244i | 0.855186 | − | 1.48123i | −0.0212861 | − | 0.999773i | \(-0.506776\pi\) |
0.876472 | − | 0.481452i | \(-0.159891\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | 0.963087 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.50000 | − | 12.9904i | −0.890086 | − | 1.54167i | −0.839771 | − | 0.542941i | \(-0.817311\pi\) |
−0.0503155 | − | 0.998733i | \(-0.516023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 10.3923i | −0.702247 | − | 1.21633i | −0.967676 | − | 0.252197i | \(-0.918847\pi\) |
0.265429 | − | 0.964130i | \(-0.414486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | 0.230940 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000 | 1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.50000 | + | 9.52628i | 0.611111 | + | 1.05848i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0000 | 1.75623 | 0.878114 | − | 0.478451i | \(-0.158802\pi\) | ||||
0.878114 | + | 0.478451i | \(0.158802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.50000 | + | 14.7224i | −0.900998 | + | 1.56057i | −0.0747975 | + | 0.997199i | \(0.523831\pi\) |
−0.826201 | + | 0.563376i | \(0.809502\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | − | 20.7846i | 1.25794 | − | 2.17882i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.00000 | + | 8.66025i | 0.518476 | + | 0.898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | + | 1.73205i | 0.410391 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | − | 10.3923i | −0.609208 | − | 1.05518i | −0.991371 | − | 0.131084i | \(-0.958154\pi\) |
0.382164 | − | 0.924095i | \(-0.375179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.50000 | − | 2.59808i | 0.150756 | − | 0.261116i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.50000 | + | 9.52628i | −0.547270 | + | 0.947900i | 0.451190 | + | 0.892428i | \(0.351000\pi\) |
−0.998460 | + | 0.0554722i | \(0.982334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.00000 | + | 6.92820i | −0.390360 | + | 0.676123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | + | 6.92820i | 0.379663 | + | 0.657596i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0000 | 1.31701 | 0.658505 | − | 0.752577i | \(-0.271189\pi\) | ||||
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | −0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.00000 | − | 5.19615i | −0.277350 | − | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | + | 6.92820i | 0.366679 | + | 0.635107i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | + | 3.46410i | −0.180334 | + | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | + | 15.5885i | −0.798621 | + | 1.38325i | 0.121894 | + | 0.992543i | \(0.461103\pi\) |
−0.920514 | + | 0.390709i | \(0.872230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0000 | + | 17.3205i | 0.873704 | + | 1.51330i | 0.858137 | + | 0.513421i | \(0.171622\pi\) |
0.0155672 | + | 0.999879i | \(0.495045\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.0000 | + | 10.3923i | −1.21395 | + | 0.901127i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.00000 | − | 3.46410i | −0.172133 | − | 0.298142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.0000 | 1.01058 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00000 | − | 15.5885i | 0.752618 | − | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.00000 | − | 15.5885i | −0.742307 | − | 1.28571i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.50000 | + | 14.7224i | 0.696347 | + | 1.20611i | 0.969724 | + | 0.244202i | \(0.0785259\pi\) |
−0.273377 | + | 0.961907i | \(0.588141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.00000 | 0.244137 | 0.122068 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122068 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.50000 | − | 4.33013i | −0.200805 | − | 0.347804i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | − | 15.5885i | −0.718278 | − | 1.24409i | −0.961681 | − | 0.274169i | \(-0.911597\pi\) |
0.243403 | − | 0.969925i | \(-0.421736\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | − | 13.8564i | 0.630488 | − | 1.09204i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.0000 | 1.40987 | 0.704934 | − | 0.709273i | \(-0.250976\pi\) | ||||
0.704934 | + | 0.709273i | \(0.250976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.00000 | + | 5.19615i | −0.233550 | + | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.00000 | + | 6.92820i | −0.309529 | + | 0.536120i | −0.978259 | − | 0.207385i | \(-0.933505\pi\) |
0.668730 | + | 0.743505i | \(0.266838\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.500000 | + | 4.33013i | 0.0382360 | + | 0.331133i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.00000 | − | 3.46410i | 0.151186 | − | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.00000 | − | 1.73205i | 0.0751646 | − | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.0000 | −1.12115 | −0.560576 | − | 0.828103i | \(-0.689420\pi\) | ||||
−0.560576 | + | 0.828103i | \(0.689420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.00000 | + | 1.73205i | −0.0743294 | + | 0.128742i | −0.900794 | − | 0.434246i | \(-0.857015\pi\) |
0.826465 | + | 0.562988i | \(0.190348\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0000 | −1.03491 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.0000 | 1.16383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0000 | −0.940647 | −0.470323 | − | 0.882494i | \(-0.655863\pi\) | ||||
−0.470323 | + | 0.882494i | \(0.655863\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.00000 | − | 13.8564i | −0.575853 | − | 0.997406i | −0.995948 | − | 0.0899262i | \(-0.971337\pi\) |
0.420096 | − | 0.907480i | \(-0.361996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.00000 | + | 10.3923i | 0.429669 | + | 0.744208i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.5000 | + | 19.9186i | −0.815213 | + | 1.41199i | 0.0939612 | + | 0.995576i | \(0.470047\pi\) |
−0.909175 | + | 0.416415i | \(0.863286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −28.0000 | −1.97497 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.00000 | − | 3.46410i | 0.140372 | − | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | − | 1.73205i | 0.0698430 | − | 0.120972i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | − | 3.46410i | −0.139010 | − | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5000 | + | 7.79423i | −0.726300 | + | 0.539138i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.500000 | + | 0.866025i | 0.0344214 | + | 0.0596196i | 0.882723 | − | 0.469894i | \(-0.155708\pi\) |
−0.848301 | + | 0.529514i | \(0.822374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.0000 | + | 25.9808i | −1.02778 | + | 1.78017i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.0000 | 1.35769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0000 | + | 20.7846i | −0.810885 | + | 1.40449i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.0000 | 0.807207 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.500000 | − | 0.866025i | −0.0333333 | − | 0.0577350i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.0000 | 1.38772 | 0.693860 | − | 0.720110i | \(-0.255909\pi\) | ||||
0.693860 | + | 0.720110i | \(0.255909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | − | 20.7846i | −0.789542 | − | 1.36753i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.00000 | + | 8.66025i | 0.327561 | + | 0.567352i | 0.982027 | − | 0.188739i | \(-0.0604400\pi\) |
−0.654466 | + | 0.756091i | \(0.727107\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00000 | − | 1.73205i | 0.0649570 | − | 0.112509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0000 | 0.970269 | 0.485135 | − | 0.874439i | \(-0.338771\pi\) | ||||
0.485135 | + | 0.874439i | \(0.338771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.00000 | − | 8.66025i | 0.320750 | − | 0.555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.50000 | + | 7.79423i | 0.287494 | + | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | + | 25.9808i | 0.190885 | + | 1.65312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.0000 | − | 27.7128i | −1.01396 | − | 1.75623i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5000 | + | 26.8468i | −0.978351 | + | 1.69455i | −0.309951 | + | 0.950753i | \(0.600313\pi\) |
−0.668400 | + | 0.743802i | \(0.733021\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 10.3923i | 0.377217 | − | 0.653359i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.00000 | + | 15.5885i | −0.561405 | + | 0.972381i | 0.435970 | + | 0.899961i | \(0.356405\pi\) |
−0.997374 | + | 0.0724199i | \(0.976928\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | 0.994192 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.500000 | − | 0.866025i | −0.0309492 | − | 0.0536056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.00000 | − | 8.66025i | −0.308313 | − | 0.534014i | 0.669680 | − | 0.742650i | \(-0.266431\pi\) |
−0.977993 | + | 0.208635i | \(0.933098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.0000 | 2.08077 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.500000 | + | 0.866025i | 0.0304855 | + | 0.0528025i | 0.880866 | − | 0.473366i | \(-0.156961\pi\) |
−0.850380 | + | 0.526169i | \(0.823628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.50000 | − | 14.7224i | −0.516338 | − | 0.894324i | −0.999820 | − | 0.0189696i | \(-0.993961\pi\) |
0.483482 | − | 0.875354i | \(-0.339372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −48.0000 | −2.90509 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.50000 | − | 2.59808i | 0.0904534 | − | 0.156670i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.0000 | 0.961347 | 0.480673 | − | 0.876900i | \(-0.340392\pi\) | ||||
0.480673 | + | 0.876900i | \(0.340392\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.50000 | − | 4.33013i | 0.149671 | − | 0.259238i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.0000 | − | 22.5167i | 0.775515 | − | 1.34323i | −0.158990 | − | 0.987280i | \(-0.550824\pi\) |
0.934505 | − | 0.355951i | \(-0.115843\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0000 | + | 22.5167i | 0.772770 | + | 1.33848i | 0.936039 | + | 0.351895i | \(0.114463\pi\) |
−0.163270 | + | 0.986581i | \(0.552204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | − | 8.66025i | −0.0592349 | − | 0.512989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000 | + | 6.92820i | 0.236113 | + | 0.408959i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.0000 | + | 20.7846i | −0.703452 | + | 1.21842i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.0000 | 0.934730 | 0.467365 | − | 0.884064i | \(-0.345203\pi\) | ||||
0.467365 | + | 0.884064i | \(0.345203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.500000 | + | 0.866025i | −0.0291111 | + | 0.0504219i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.0000 | 0.696311 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | − | 20.7846i | −0.693978 | − | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.0000 | 1.26387 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.00000 | 0.400819 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | + | 12.1244i | 0.399511 | + | 0.691974i | 0.993666 | − | 0.112377i | \(-0.0358466\pi\) |
−0.594154 | + | 0.804351i | \(0.702513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0000 | + | 29.4449i | −0.960897 | + | 1.66432i | −0.240640 | + | 0.970614i | \(0.577357\pi\) |
−0.720257 | + | 0.693708i | \(0.755976\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.00000 | 0.225374 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.50000 | − | 2.59808i | 0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | + | 20.7846i | 0.669775 | + | 1.16008i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | − | 3.46410i | −0.445132 | − | 0.192748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.00000 | − | 5.19615i | −0.166410 | − | 0.288231i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.00000 | + | 12.1244i | −0.387101 | + | 0.670478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | − | 20.7846i | 0.661581 | − | 1.14589i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 14.0000 | 0.764902 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | − | 3.46410i | −0.108947 | − | 0.188702i | 0.806397 | − | 0.591375i | \(-0.201415\pi\) |
−0.915344 | + | 0.402673i | \(0.868081\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.0000 | − | 24.2487i | −0.760376 | − | 1.31701i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.0000 | 0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.00000 | + | 6.92820i | 0.215353 | + | 0.373002i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.0000 | − | 20.7846i | 0.640513 | − | 1.10940i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.0000 | −1.91609 | −0.958043 | − | 0.286623i | \(-0.907467\pi\) | ||||
−0.958043 | + | 0.286623i | \(0.907467\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.50000 | − | 12.9904i | 0.398059 | − | 0.689458i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.00000 | − | 13.8564i | 0.423405 | − | 0.733359i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.50000 | − | 18.1865i | 0.289474 | − | 0.957186i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | + | 3.46410i | 0.104973 | + | 0.181818i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | − | 10.3923i | 0.314054 | − | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | + | 20.7846i | −0.623009 | + | 1.07908i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0000 | −0.621336 | −0.310668 | − | 0.950518i | \(-0.600553\pi\) | ||||
−0.310668 | + | 0.950518i | \(0.600553\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | + | 1.73205i | 0.0516398 | + | 0.0894427i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.00000 | − | 5.19615i | −0.154508 | − | 0.267615i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.0000 | −0.975964 | −0.487982 | − | 0.872854i | \(-0.662267\pi\) | ||||
−0.487982 | + | 0.872854i | \(0.662267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.0000 | 1.84434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.00000 | + | 15.5885i | 0.459879 | + | 0.796533i | 0.998954 | − | 0.0457244i | \(-0.0145596\pi\) |
−0.539076 | + | 0.842257i | \(0.681226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | + | 10.3923i | 0.305788 | + | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.5000 | − | 18.1865i | 0.532371 | − | 0.922094i | −0.466915 | − | 0.884302i | \(-0.654634\pi\) |
0.999286 | − | 0.0377914i | \(-0.0120322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.0000 | − | 34.6410i | 1.00887 | − | 1.74741i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.500000 | + | 0.866025i | −0.0251577 | + | 0.0435745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | + | 6.92820i | 0.200754 | + | 0.347717i | 0.948772 | − | 0.315963i | \(-0.102327\pi\) |
−0.748017 | + | 0.663679i | \(0.768994\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 32.0000 | + | 13.8564i | 1.60200 | + | 0.693688i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0000 | − | 25.9808i | 0.747203 | − | 1.29419i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.50000 | + | 9.52628i | −0.273297 | + | 0.473365i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000 | 0.594818 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.500000 | − | 0.866025i | 0.0247234 | − | 0.0428222i | −0.853399 | − | 0.521258i | \(-0.825463\pi\) |
0.878122 | + | 0.478436i | \(0.158796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 24.0000 | 1.18383 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.00000 | − | 3.46410i | −0.0984136 | − | 0.170457i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.00000 | + | 13.8564i | 0.392705 | + | 0.680184i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.00000 | −0.244266 | −0.122133 | − | 0.992514i | \(-0.538973\pi\) | ||||
−0.122133 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.5000 | − | 21.6506i | −0.609213 | − | 1.05519i | −0.991370 | − | 0.131090i | \(-0.958152\pi\) |
0.382158 | − | 0.924097i | \(-0.375181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 5.19615i | −0.145865 | − | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.0000 | + | 24.2487i | −0.677507 | + | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −36.0000 | −1.73810 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.5000 | + | 23.3827i | −0.650272 | + | 1.12630i | 0.332785 | + | 0.943003i | \(0.392012\pi\) |
−0.983057 | + | 0.183301i | \(0.941322\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.00000 | + | 1.73205i | 0.0479463 | + | 0.0830455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000 | + | 17.3205i | 0.0956730 | + | 0.828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.500000 | − | 0.866025i | −0.0238637 | − | 0.0413331i | 0.853847 | − | 0.520524i | \(-0.174263\pi\) |
−0.877711 | + | 0.479191i | \(0.840930\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.50000 | + | 7.79423i | −0.214286 | + | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.00000 | − | 10.3923i | 0.285069 | − | 0.493753i | −0.687557 | − | 0.726130i | \(-0.741317\pi\) |
0.972626 | + | 0.232377i | \(0.0746503\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.0000 | −0.805877 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.0000 | − | 29.4449i | 0.804072 | − | 1.39269i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.00000 | −0.0471929 | −0.0235965 | − | 0.999722i | \(-0.507512\pi\) | ||||
−0.0235965 | + | 0.999722i | \(0.507512\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.00000 | + | 5.19615i | 0.141264 | + | 0.244677i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.00000 | − | 5.19615i | −0.140952 | − | 0.244137i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0000 | 1.12514 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.00000 | −0.0935561 | −0.0467780 | − | 0.998905i | \(-0.514895\pi\) | ||||
−0.0467780 | + | 0.998905i | \(0.514895\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.00000 | + | 6.92820i | 0.186704 | + | 0.323381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.5000 | − | 30.3109i | −0.815056 | − | 1.41172i | −0.909288 | − | 0.416169i | \(-0.863373\pi\) |
0.0942312 | − | 0.995550i | \(-0.469961\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.00000 | + | 8.66025i | −0.231869 | + | 0.401610i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.0000 | −0.925490 | −0.462745 | − | 0.886492i | \(-0.653135\pi\) | ||||
−0.462745 | + | 0.886492i | \(0.653135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −28.0000 | + | 48.4974i | −1.29292 | + | 2.23940i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.0000 | + | 31.1769i | −0.829396 | + | 1.43656i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.500000 | + | 4.33013i | 0.0229416 | + | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.00000 | + | 5.19615i | 0.137361 | + | 0.237915i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.50000 | − | 2.59808i | 0.0685367 | − | 0.118709i | −0.829721 | − | 0.558179i | \(-0.811500\pi\) |
0.898257 | + | 0.439470i | \(0.144834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | − | 20.7846i | 0.547153 | − | 0.947697i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −32.0000 | −1.45605 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000 | − | 10.3923i | 0.272446 | − | 0.471890i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 34.0000 | 1.54069 | 0.770344 | − | 0.637629i | \(-0.220085\pi\) | ||||
0.770344 | + | 0.637629i | \(0.220085\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.0000 | − | 31.1769i | −0.813988 | − | 1.40987i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5000 | + | 21.6506i | 0.564117 | + | 0.977079i | 0.997131 | + | 0.0756923i | \(0.0241167\pi\) |
−0.433014 | + | 0.901387i | \(0.642550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.00000 | 0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 30.0000 | + | 51.9615i | 1.34568 | + | 2.33079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.0000 | − | 31.1769i | −0.805791 | − | 1.39567i | −0.915756 | − | 0.401735i | \(-0.868407\pi\) |
0.109965 | − | 0.993935i | \(-0.464926\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 16.0000 | 0.714827 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.0000 | + | 19.0526i | −0.490466 | + | 0.849512i | −0.999940 | − | 0.0109744i | \(-0.996507\pi\) |
0.509474 | + | 0.860486i | \(0.329840\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.0000 | −0.489494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.0000 | + | 39.8372i | −1.02147 | + | 1.76923i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.0000 | + | 41.5692i | 1.06170 | + | 1.83891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.0000 | + | 10.3923i | −0.618115 | + | 0.458831i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.00000 | − | 15.5885i | 0.395820 | − | 0.685580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −45.0000 | −1.97149 | −0.985743 | − | 0.168259i | \(-0.946186\pi\) | ||||
−0.985743 | + | 0.168259i | \(0.946186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.00000 | − | 8.66025i | 0.218635 | − | 0.378686i | −0.735756 | − | 0.677247i | \(-0.763173\pi\) |
0.954391 | + | 0.298560i | \(0.0965063\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.00000 | −0.349149 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.00000 | + | 8.66025i | 0.217803 | + | 0.377247i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.00000 | −0.0433963 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 10.3923i | −0.259403 | − | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0000 | + | 25.9808i | 0.647298 | + | 1.12115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −27.0000 | −1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | 0.171656 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.50000 | − | 6.06218i | 0.149924 | − | 0.259675i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | − | 6.92820i | 0.171028 | − | 0.296229i | −0.767752 | − | 0.640747i | \(-0.778625\pi\) |
0.938779 | + | 0.344519i | \(0.111958\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.50000 | + | 6.06218i | 0.149376 | + | 0.258727i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.500000 | + | 4.33013i | 0.0213007 | + | 0.184470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | − | 3.46410i | −0.0850487 | − | 0.147309i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.00000 | + | 6.92820i | −0.169791 | + | 0.294086i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.0000 | − | 34.6410i | 0.847427 | − | 1.46779i | −0.0360693 | − | 0.999349i | \(-0.511484\pi\) |
0.883497 | − | 0.468438i | \(-0.155183\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.00000 | − | 10.3923i | 0.253320 | − | 0.438763i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.0000 | 0.421450 | 0.210725 | − | 0.977545i | \(-0.432418\pi\) | ||||
0.210725 | + | 0.977545i | \(0.432418\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0000 | − | 38.1051i | −0.923913 | − | 1.60026i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.0000 | −0.712677 | −0.356339 | − | 0.934357i | \(-0.615975\pi\) | ||||
−0.356339 | + | 0.934357i | \(0.615975\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.0000 | −0.711428 | −0.355714 | − | 0.934595i | \(-0.615762\pi\) | ||||
−0.355714 | + | 0.934595i | \(0.615762\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.0000 | + | 22.5167i | 0.543083 | + | 0.940647i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.00000 | − | 3.46410i | −0.0834058 | − | 0.144463i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.0000 | −0.832611 | −0.416305 | − | 0.909225i | \(-0.636675\pi\) | ||||
−0.416305 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.0000 | + | 27.7128i | −0.664937 | + | 1.15171i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.0000 | −2.65517 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.00000 | + | 15.5885i | −0.372742 | + | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | − | 5.19615i | 0.124035 | − | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.00000 | + | 10.3923i | 0.247647 | + | 0.428936i | 0.962872 | − | 0.269957i | \(-0.0870095\pi\) |
−0.715226 | + | 0.698893i | \(0.753676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.5000 | + | 12.9904i | −0.721075 | + | 0.535259i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.00000 | − | 3.46410i | −0.0822690 | − | 0.142494i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | − | 3.46410i | 0.0821302 | − | 0.142254i | −0.822035 | − | 0.569438i | \(-0.807161\pi\) |
0.904165 | + | 0.427184i | \(0.140494\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.00000 | + | 6.92820i | −0.163984 | + | 0.284029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 46.0000 | 1.88265 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.0000 | 0.693444 | 0.346722 | − | 0.937968i | \(-0.387295\pi\) | ||||
0.346722 | + | 0.937968i | \(0.387295\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.00000 | + | 12.1244i | 0.285062 | + | 0.493742i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | − | 1.73205i | −0.0406558 | − | 0.0704179i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.0000 | −0.568242 | −0.284121 | − | 0.958788i | \(-0.591702\pi\) | ||||
−0.284121 | + | 0.958788i | \(0.591702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | −0.324176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.0000 | − | 31.1769i | −0.728202 | − | 1.26128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.0000 | + | 19.0526i | 0.444286 | + | 0.769526i | 0.998002 | − | 0.0631797i | \(-0.0201241\pi\) |
−0.553716 | + | 0.832705i | \(0.686791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.00000 | −0.161296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.00000 | − | 6.92820i | 0.161034 | − | 0.278919i | −0.774206 | − | 0.632934i | \(-0.781850\pi\) |
0.935240 | + | 0.354015i | \(0.115184\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.00000 | − | 13.8564i | 0.321029 | − | 0.556038i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 34.0000 | − | 58.8897i | 1.36218 | − | 2.35937i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 24.0000 | + | 10.3923i | 0.958468 | + | 0.415029i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.00000 | + | 6.92820i | 0.159490 | + | 0.276246i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.5000 | − | 28.5788i | 0.656855 | − | 1.13771i | −0.324571 | − | 0.945861i | \(-0.605220\pi\) |
0.981425 | − | 0.191844i | \(-0.0614468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00000 | − | 1.73205i | 0.0397464 | − | 0.0688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.0000 | −0.714308 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −27.0000 | + | 46.7654i | −1.06978 | + | 1.85291i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.0000 | 0.593391 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.50000 | − | 7.79423i | −0.177739 | − | 0.307854i | 0.763367 | − | 0.645966i | \(-0.223545\pi\) |
−0.941106 | + | 0.338112i | \(0.890212\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00000 | + | 1.73205i | 0.0394362 | + | 0.0683054i | 0.885070 | − | 0.465458i | \(-0.154110\pi\) |
−0.845634 | + | 0.533764i | \(0.820777\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0000 | −1.17942 | −0.589711 | − | 0.807614i | \(-0.700758\pi\) | ||||
−0.589711 | + | 0.807614i | \(0.700758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.50000 | − | 2.59808i | −0.0588802 | − | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0000 | − | 34.6410i | −0.783862 | − | 1.35769i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0000 | 0.469596 | 0.234798 | − | 0.972044i | \(-0.424557\pi\) | ||||
0.234798 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.0000 | + | 17.3205i | −0.390732 | + | 0.676768i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.0000 | 0.468165 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | − | 31.1769i | 0.701180 | − | 1.21448i | −0.266872 | − | 0.963732i | \(-0.585990\pi\) |
0.968052 | − | 0.250748i | \(-0.0806766\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.5000 | + | 35.5070i | −0.797358 | + | 1.38106i | 0.123974 | + | 0.992286i | \(0.460436\pi\) |
−0.921331 | + | 0.388778i | \(0.872897\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.0000 | − | 20.7846i | −0.466041 | − | 0.807207i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.0000 | − | 6.92820i | −0.620453 | − | 0.268664i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | − | 3.46410i | −0.0774403 | − | 0.134131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.5000 | + | 18.1865i | −0.405348 | + | 0.702083i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.00000 | − | 3.46410i | 0.0769800 | − | 0.133333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −32.0000 | −1.22986 | −0.614930 | − | 0.788582i | \(-0.710816\pi\) | ||||
−0.614930 | + | 0.788582i | \(0.710816\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | + | 41.5692i | 0.921035 | + | 1.59528i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | + | 6.92820i | 0.153280 | + | 0.265489i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.00000 | 0.229584 | 0.114792 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114792 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.0000 | − | 36.3731i | −0.801200 | − | 1.38772i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.0000 | + | 31.1769i | 0.685745 | + | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.0000 | 1.40755 | 0.703773 | − | 0.710425i | \(-0.251497\pi\) | ||||
0.703773 | + | 0.710425i | \(0.251497\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.00000 | + | 10.3923i | −0.227921 | + | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.00000 | + | 3.46410i | −0.0757554 | + | 0.131212i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.0000 | − | 17.3205i | 0.378235 | − | 0.655122i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0000 | + | 36.3731i | 0.793159 | + | 1.37379i | 0.924002 | + | 0.382389i | \(0.124898\pi\) |
−0.130843 | + | 0.991403i | \(0.541768\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | + | 10.3923i | −0.528020 | + | 0.391953i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00000 | + | 10.3923i | 0.225973 | + | 0.391397i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.0000 | − | 38.1051i | 0.827395 | − | 1.43309i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50000 | + | 4.33013i | −0.0938895 | + | 0.162621i | −0.909145 | − | 0.416481i | \(-0.863263\pi\) |
0.815255 | + | 0.579102i | \(0.196597\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00000 | −0.0375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.0000 | − | 17.3205i | 0.374503 | − | 0.648658i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | 0.673162 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.0000 | − | 25.9808i | −0.560185 | − | 0.970269i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.5000 | − | 25.1147i | −0.540759 | − | 0.936622i | −0.998861 | − | 0.0477220i | \(-0.984804\pi\) |
0.458102 | − | 0.888900i | \(-0.348529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.0000 | 0.371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.500000 | − | 0.866025i | −0.0185695 | − | 0.0321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.0000 | − | 22.5167i | −0.482143 | − | 0.835097i | 0.517647 | − | 0.855595i | \(-0.326808\pi\) |
−0.999790 | + | 0.0204978i | \(0.993475\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.0000 | −0.443230 | −0.221615 | − | 0.975134i | \(-0.571133\pi\) | ||||
−0.221615 | + | 0.975134i | \(0.571133\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.00000 | − | 15.5885i | 0.331970 | − | 0.574989i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.0000 | + | 36.3731i | −0.773545 | + | 1.33982i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.50000 | + | 16.4545i | 0.349463 | + | 0.605288i | 0.986154 | − | 0.165831i | \(-0.0530307\pi\) |
−0.636691 | + | 0.771119i | \(0.719697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.0000 | − | 31.1769i | 1.54291 | − | 1.14531i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.0000 | − | 45.0333i | −0.953847 | − | 1.65211i | −0.736984 | − | 0.675910i | \(-0.763751\pi\) |
−0.216864 | − | 0.976202i | \(-0.569583\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.50000 | + | 14.7224i | −0.311416 | + | 0.539388i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.00000 | + | 13.8564i | −0.292705 | + | 0.506979i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.0000 | 1.75388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.50000 | + | 16.4545i | −0.346660 | + | 0.600433i | −0.985654 | − | 0.168779i | \(-0.946018\pi\) |
0.638994 | + | 0.769212i | \(0.279351\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 62.0000 | 2.25941 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.50000 | + | 2.59808i | 0.0545906 | + | 0.0945537i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.00000 | + | 12.1244i | 0.254419 | + | 0.440667i | 0.964738 | − | 0.263213i | \(-0.0847823\pi\) |
−0.710318 | + | 0.703881i | \(0.751449\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.0000 | −0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.0000 | 1.95750 | 0.978749 | − | 0.205061i | \(-0.0657392\pi\) | ||||
0.978749 | + | 0.205061i | \(0.0657392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | + | 24.2487i | 0.506834 | + | 0.877862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.00000 | + | 1.73205i | 0.0361551 | + | 0.0626224i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.50000 | + | 11.2583i | −0.234396 | + | 0.405986i | −0.959097 | − | 0.283078i | \(-0.908645\pi\) |
0.724701 | + | 0.689063i | \(0.241978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 36.0000 | 1.29651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.0000 | − | 46.7654i | 0.971123 | − | 1.68203i | 0.278944 | − | 0.960307i | \(-0.410016\pi\) |
0.692179 | − | 0.721726i | \(-0.256651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.50000 | − | 4.33013i | 0.0898027 | − | 0.155543i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.0000 | − | 27.7128i | −0.573997 | − | 0.994192i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.00000 | − | 3.46410i | −0.286630 | − | 0.124114i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.5000 | + | 38.9711i | 0.805113 | + | 1.39450i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | − | 3.46410i | 0.0714742 | − | 0.123797i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.00000 | − | 15.5885i | 0.321224 | − | 0.556376i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.0000 | 1.35455 | 0.677277 | − | 0.735728i | \(-0.263160\pi\) | ||||
0.677277 | + | 0.735728i | \(0.263160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0000 | + | 17.3205i | −0.356009 | + | 0.616626i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −56.0000 | −1.99113 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.0000 | + | 36.3731i | 0.745732 | + | 1.29165i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.00000 | − | 10.3923i | −0.212798 | − | 0.368577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −22.0000 | −0.779280 | −0.389640 | − | 0.920967i | \(-0.627401\pi\) | ||||
−0.389640 | + | 0.920967i | \(0.627401\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.50000 | − | 14.7224i | −0.300333 | − | 0.520192i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.0000 | + | 31.1769i | 0.635206 | + | 1.10021i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | 0.563926 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.00000 | − | 1.73205i | 0.0352017 | − | 0.0609711i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 45.0000 | 1.58212 | 0.791058 | − | 0.611741i | \(-0.209531\pi\) | ||||
0.791058 | + | 0.611741i | \(0.209531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.50000 | − | 11.2583i | 0.228246 | − | 0.395333i | −0.729042 | − | 0.684468i | \(-0.760034\pi\) |
0.957288 | + | 0.289135i | \(0.0933677\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.0000 | + | 29.4449i | −0.596216 | + | 1.03268i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.00000 | + | 15.5885i | 0.315256 | + | 0.546040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000 | + | 20.7846i | 0.419314 | + | 0.726273i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5000 | + | 21.6506i | −0.436253 | + | 0.755612i | −0.997397 | − | 0.0721058i | \(-0.977028\pi\) |
0.561144 | + | 0.827718i | \(0.310361\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.00000 | −0.208893 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.00000 | − | 15.5885i | 0.312961 | − | 0.542064i | −0.666041 | − | 0.745915i | \(-0.732013\pi\) |
0.979002 | + | 0.203851i | \(0.0653459\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.0000 | −1.04194 | −0.520972 | − | 0.853574i | \(-0.674430\pi\) | ||||
−0.520972 | + | 0.853574i | \(0.674430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.0000 | − | 27.7128i | −0.555034 | − | 0.961347i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.00000 | − | 15.5885i | −0.311832 | − | 0.540108i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0000 | 0.691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | + | 24.2487i | 0.482759 | + | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −52.0000 | −1.79098 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.5000 | − | 19.9186i | 0.395612 | − | 0.685220i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.00000 | 0.274883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.0000 | − | 45.0333i | 0.892318 | − | 1.54554i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | − | 13.8564i | 0.274236 | − | 0.474991i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | − | 32.9090i | −0.650548 | − | 1.12678i | −0.982990 | − | 0.183658i | \(-0.941206\pi\) |
0.332443 | − | 0.943123i | \(-0.392127\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.50000 | + | 2.59808i | −0.119697 | + | 0.0888523i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.500000 | − | 0.866025i | 0.0170598 | − | 0.0295484i | −0.857369 | − | 0.514701i | \(-0.827903\pi\) |
0.874429 | + | 0.485153i | \(0.161236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.00000 | − | 13.8564i | 0.272639 | − | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.0000 | −0.883006 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.50000 | − | 2.59808i | −0.0508840 | − | 0.0881337i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42.0000 | + | 72.7461i | 1.42312 | + | 2.46491i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.0000 | 0.406138 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.00000 | 0.135225 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0000 | − | 34.6410i | −0.675352 | − | 1.16974i | −0.976366 | − | 0.216124i | \(-0.930658\pi\) |
0.301014 | − | 0.953620i | \(-0.402675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.0000 | − | 27.7128i | −0.539667 | − | 0.934730i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.00000 | −0.235836 | −0.117918 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117918 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.00000 | + | 6.92820i | −0.134611 | + | 0.233153i | −0.925449 | − | 0.378873i | \(-0.876312\pi\) |
0.790838 | + | 0.612026i | \(0.209645\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.00000 | 0.0672293 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0000 | + | 24.2487i | −0.470074 | + | 0.814192i | −0.999414 | − | 0.0342175i | \(-0.989106\pi\) |
0.529340 | + | 0.848410i | \(0.322439\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.0000 | − | 62.3538i | 1.20740 | − | 2.09128i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.5000 | − | 28.5788i | −0.552771 | − | 0.957427i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.00000 | + | 25.9808i | 0.100391 | + | 0.869413i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.50000 | − | 12.9904i | −0.250697 | − | 0.434221i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.0000 | + | 41.5692i | −0.801337 | + | 1.38796i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.50000 | − | 4.33013i | 0.0833797 | − | 0.144418i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.00000 | −0.0664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.0000 | − | 27.7128i | −0.531271 | − | 0.920189i | −0.999334 | − | 0.0364935i | \(-0.988381\pi\) |
0.468063 | − | 0.883695i | \(-0.344952\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.50000 | − | 9.52628i | −0.182423 | − | 0.315967i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.00000 | 0.231920 | 0.115960 | − | 0.993254i | \(-0.463006\pi\) | ||||
0.115960 | + | 0.993254i | \(0.463006\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0000 | −1.58857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.00000 | − | 12.1244i | −0.231413 | − | 0.400819i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −40.0000 | − | 69.2820i | −1.32092 | − | 2.28789i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | − | 24.2487i | 0.461316 | − | 0.799022i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 90.0000 | 2.96239 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | − | 3.46410i | 0.0657596 | − | 0.113899i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.5000 | + | 18.1865i | 0.344494 | + | 0.596681i | 0.985262 | − | 0.171054i | \(-0.0547172\pi\) |
−0.640768 | + | 0.767735i | \(0.721384\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.5000 | − | 23.3827i | 1.03237 | − | 0.766337i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.00000 | + | 5.19615i | −0.0981105 | + | 0.169932i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.00000 | + | 1.73205i | −0.0326686 | + | 0.0565836i | −0.881897 | − | 0.471441i | \(-0.843734\pi\) |
0.849229 | + | 0.528025i | \(0.177067\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 68.0000 | 2.21910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.5000 | + | 30.3109i | −0.570484 | + | 0.988107i | 0.426033 | + | 0.904708i | \(0.359911\pi\) |
−0.996516 | + | 0.0833989i | \(0.973422\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.00000 | 0.260516 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | + | 13.8564i | 0.260240 | + | 0.450749i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.00000 | + | 8.66025i | 0.162478 | + | 0.281420i | 0.935757 | − | 0.352646i | \(-0.114718\pi\) |
−0.773279 | + | 0.634066i | \(0.781385\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 72.0000 | 2.33722 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0000 | + | 24.2487i | 0.453504 | + | 0.785493i | 0.998601 | − | 0.0528806i | \(-0.0168403\pi\) |
−0.545096 | + | 0.838373i | \(0.683507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.50000 | − | 11.2583i | −0.210335 | − | 0.364311i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.00000 | −0.193952 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.0000 | − | 41.5692i | 0.775000 | − | 1.34234i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | − | 13.8564i | 0.257529 | − | 0.446054i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.00000 | + | 10.3923i | 0.192947 | + | 0.334194i | 0.946226 | − | 0.323508i | \(-0.104862\pi\) |
−0.753279 | + | 0.657702i | \(0.771529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.00000 | + | 17.3205i | 0.0642493 | + | 0.556415i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.0000 | − | 51.9615i | −0.962746 | − | 1.66752i | −0.715553 | − | 0.698558i | \(-0.753825\pi\) |
−0.247193 | − | 0.968966i | \(-0.579508\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.00000 | + | 10.3923i | −0.192154 | + | 0.332820i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0000 | 0.383914 | 0.191957 | − | 0.981403i | \(-0.438517\pi\) | ||||
0.191957 | + | 0.981403i | \(0.438517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.5000 | − | 44.1673i | 0.814984 | − | 1.41159i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.00000 | 0.223493 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | + | 1.73205i | 0.0318626 | + | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −48.0000 | −1.52786 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | − | 27.7128i | −0.508257 | − | 0.880327i | −0.999954 | − | 0.00956046i | \(-0.996957\pi\) |
0.491698 | − | 0.870766i | \(-0.336377\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.0000 | + | 34.6410i | 0.634681 | + | 1.09930i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.0000 | −0.729149 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.00000 | − | 8.66025i | 0.158352 | − | 0.274273i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.0000 | 0.506218 |
(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 | 380.2.i.a.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 3420.2.t.b.1261.1 | 2 | |||
4.3 | odd | 2 | 1520.2.q.g.881.1 | 2 | |||
5.2 | odd | 4 | 1900.2.s.b.349.1 | 4 | |||
5.3 | odd | 4 | 1900.2.s.b.349.2 | 4 | |||
5.4 | even | 2 | 1900.2.i.b.501.1 | 2 | |||
19.7 | even | 3 | 7220.2.a.e.1.1 | 1 | |||
19.11 | even | 3 | inner | 380.2.i.a.201.1 | yes | 2 | |
19.12 | odd | 6 | 7220.2.a.a.1.1 | 1 | |||
57.11 | odd | 6 | 3420.2.t.b.3241.1 | 2 | |||
76.11 | odd | 6 | 1520.2.q.g.961.1 | 2 | |||
95.49 | even | 6 | 1900.2.i.b.201.1 | 2 | |||
95.68 | odd | 12 | 1900.2.s.b.49.1 | 4 | |||
95.87 | odd | 12 | 1900.2.s.b.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.a.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
380.2.i.a.201.1 | yes | 2 | 19.11 | even | 3 | inner | |
1520.2.q.g.881.1 | 2 | 4.3 | odd | 2 | |||
1520.2.q.g.961.1 | 2 | 76.11 | odd | 6 | |||
1900.2.i.b.201.1 | 2 | 95.49 | even | 6 | |||
1900.2.i.b.501.1 | 2 | 5.4 | even | 2 | |||
1900.2.s.b.49.1 | 4 | 95.68 | odd | 12 | |||
1900.2.s.b.49.2 | 4 | 95.87 | odd | 12 | |||
1900.2.s.b.349.1 | 4 | 5.2 | odd | 4 | |||
1900.2.s.b.349.2 | 4 | 5.3 | odd | 4 | |||
3420.2.t.b.1261.1 | 2 | 3.2 | odd | 2 | |||
3420.2.t.b.3241.1 | 2 | 57.11 | odd | 6 | |||
7220.2.a.a.1.1 | 1 | 19.12 | odd | 6 | |||
7220.2.a.e.1.1 | 1 | 19.7 | even | 3 |