Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.a (trivial) |
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: | yes |
Analytic conductor: | \(27.5483886973\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 690) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.864641 | −0.260699 | −0.130350 | − | 0.991468i | \(-0.541610\pi\) | ||||
−0.130350 | + | 0.991468i | \(0.541610\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 5.52311 | 1.53184 | 0.765918 | − | 0.642938i | \(-0.222285\pi\) | ||||
0.765918 | + | 0.642938i | \(0.222285\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.52311 | −0.854481 | −0.427240 | − | 0.904138i | \(-0.640514\pi\) | ||||
−0.427240 | + | 0.904138i | \(0.640514\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 8.11704 | 1.86218 | 0.931088 | − | 0.364795i | \(-0.118861\pi\) | ||||
0.931088 | + | 0.364795i | \(0.118861\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0.864641 | 0.184342 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.52311 | −1.08317 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.25240 | −0.584148 | −0.292074 | − | 0.956396i | \(-0.594345\pi\) | ||||
−0.292074 | + | 0.956396i | \(0.594345\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.864641 | −0.150515 | ||||||||
\(34\) | 3.52311 | 0.604209 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 5.13536 | 0.844248 | 0.422124 | − | 0.906538i | \(-0.361285\pi\) | ||||
0.422124 | + | 0.906538i | \(0.361285\pi\) | |||||||
\(38\) | −8.11704 | −1.31676 | ||||||||
\(39\) | 5.52311 | 0.884406 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.52311 | 0.550218 | 0.275109 | − | 0.961413i | \(-0.411286\pi\) | ||||
0.275109 | + | 0.961413i | \(0.411286\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | 1.13536 | 0.173141 | 0.0865703 | − | 0.996246i | \(-0.472409\pi\) | ||||
0.0865703 | + | 0.996246i | \(0.472409\pi\) | |||||||
\(44\) | −0.864641 | −0.130350 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 5.52311 | 0.805629 | 0.402815 | − | 0.915282i | \(-0.368032\pi\) | ||||
0.402815 | + | 0.915282i | \(0.368032\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.52311 | −0.493335 | ||||||||
\(52\) | 5.52311 | 0.765918 | ||||||||
\(53\) | 1.34153 | 0.184273 | 0.0921364 | − | 0.995746i | \(-0.470630\pi\) | ||||
0.0921364 | + | 0.995746i | \(0.470630\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 8.11704 | 1.07513 | ||||||||
\(58\) | 2.00000 | 0.262613 | ||||||||
\(59\) | −10.9817 | −1.42969 | −0.714846 | − | 0.699282i | \(-0.753503\pi\) | ||||
−0.714846 | + | 0.699282i | \(0.753503\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.91087 | −0.756809 | −0.378405 | − | 0.925640i | \(-0.623527\pi\) | ||||
−0.378405 | + | 0.925640i | \(0.623527\pi\) | |||||||
\(62\) | 3.25240 | 0.413055 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.864641 | 0.106430 | ||||||||
\(67\) | −5.91087 | −0.722128 | −0.361064 | − | 0.932541i | \(-0.617586\pi\) | ||||
−0.361064 | + | 0.932541i | \(0.617586\pi\) | |||||||
\(68\) | −3.52311 | −0.427240 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.79383 | −0.687601 | −0.343801 | − | 0.939043i | \(-0.611714\pi\) | ||||
−0.343801 | + | 0.939043i | \(0.611714\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 15.2524 | 1.78516 | 0.892579 | − | 0.450891i | \(-0.148894\pi\) | ||||
0.892579 | + | 0.450891i | \(0.148894\pi\) | |||||||
\(74\) | −5.13536 | −0.596973 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.11704 | 0.931088 | ||||||||
\(77\) | −1.72928 | −0.197070 | ||||||||
\(78\) | −5.52311 | −0.625370 | ||||||||
\(79\) | −3.79383 | −0.426840 | −0.213420 | − | 0.976961i | \(-0.568460\pi\) | ||||
−0.213420 | + | 0.976961i | \(0.568460\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.52311 | −0.389063 | ||||||||
\(83\) | 8.32320 | 0.913590 | 0.456795 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456795 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.13536 | −0.122429 | ||||||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 0.864641 | 0.0921710 | ||||||||
\(89\) | 4.77551 | 0.506203 | 0.253102 | − | 0.967440i | \(-0.418549\pi\) | ||||
0.253102 | + | 0.967440i | \(0.418549\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.0462 | 1.15796 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −3.25240 | −0.337258 | ||||||||
\(94\) | −5.52311 | −0.569666 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −1.04623 | −0.106228 | −0.0531142 | − | 0.998588i | \(-0.516915\pi\) | ||||
−0.0531142 | + | 0.998588i | \(0.516915\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | −0.864641 | −0.0868997 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.04623 | 0.900133 | 0.450067 | − | 0.892995i | \(-0.351400\pi\) | ||||
0.450067 | + | 0.892995i | \(0.351400\pi\) | |||||||
\(102\) | 3.52311 | 0.348840 | ||||||||
\(103\) | 11.3169 | 1.11509 | 0.557546 | − | 0.830146i | \(-0.311743\pi\) | ||||
0.557546 | + | 0.830146i | \(0.311743\pi\) | |||||||
\(104\) | −5.52311 | −0.541586 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.34153 | −0.130301 | ||||||||
\(107\) | 5.64015 | 0.545254 | 0.272627 | − | 0.962120i | \(-0.412108\pi\) | ||||
0.272627 | + | 0.962120i | \(0.412108\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −12.1816 | −1.16678 | −0.583392 | − | 0.812191i | \(-0.698275\pi\) | ||||
−0.583392 | + | 0.812191i | \(0.698275\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.13536 | 0.487427 | ||||||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | 5.79383 | 0.545038 | 0.272519 | − | 0.962150i | \(-0.412143\pi\) | ||||
0.272519 | + | 0.962150i | \(0.412143\pi\) | |||||||
\(114\) | −8.11704 | −0.760230 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | 5.52311 | 0.510612 | ||||||||
\(118\) | 10.9817 | 1.01095 | ||||||||
\(119\) | −7.04623 | −0.645927 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2524 | −0.932036 | ||||||||
\(122\) | 5.91087 | 0.535145 | ||||||||
\(123\) | 3.52311 | 0.317669 | ||||||||
\(124\) | −3.25240 | −0.292074 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 0.747604 | 0.0663391 | 0.0331696 | − | 0.999450i | \(-0.489440\pi\) | ||||
0.0331696 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.13536 | 0.0999628 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7572 | 1.72619 | 0.863097 | − | 0.505039i | \(-0.168522\pi\) | ||||
0.863097 | + | 0.505039i | \(0.168522\pi\) | |||||||
\(132\) | −0.864641 | −0.0752573 | ||||||||
\(133\) | 16.2341 | 1.40767 | ||||||||
\(134\) | 5.91087 | 0.510621 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.52311 | 0.302105 | ||||||||
\(137\) | 0.476886 | 0.0407431 | 0.0203715 | − | 0.999792i | \(-0.493515\pi\) | ||||
0.0203715 | + | 0.999792i | \(0.493515\pi\) | |||||||
\(138\) | −1.00000 | −0.0851257 | ||||||||
\(139\) | −3.45856 | −0.293352 | −0.146676 | − | 0.989185i | \(-0.546857\pi\) | ||||
−0.146676 | + | 0.989185i | \(0.546857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.52311 | 0.465130 | ||||||||
\(142\) | 5.79383 | 0.486208 | ||||||||
\(143\) | −4.77551 | −0.399348 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.2524 | −1.26230 | ||||||||
\(147\) | −3.00000 | −0.247436 | ||||||||
\(148\) | 5.13536 | 0.422124 | ||||||||
\(149\) | −8.86464 | −0.726220 | −0.363110 | − | 0.931746i | \(-0.618285\pi\) | ||||
−0.363110 | + | 0.931746i | \(0.618285\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.71096 | −0.546130 | −0.273065 | − | 0.961996i | \(-0.588037\pi\) | ||||
−0.273065 | + | 0.961996i | \(0.588037\pi\) | |||||||
\(152\) | −8.11704 | −0.658379 | ||||||||
\(153\) | −3.52311 | −0.284827 | ||||||||
\(154\) | 1.72928 | 0.139349 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.52311 | 0.442203 | ||||||||
\(157\) | −14.6864 | −1.17210 | −0.586050 | − | 0.810275i | \(-0.699318\pi\) | ||||
−0.586050 | + | 0.810275i | \(0.699318\pi\) | |||||||
\(158\) | 3.79383 | 0.301821 | ||||||||
\(159\) | 1.34153 | 0.106390 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −23.2803 | −1.82345 | −0.911727 | − | 0.410797i | \(-0.865251\pi\) | ||||
−0.911727 | + | 0.410797i | \(0.865251\pi\) | |||||||
\(164\) | 3.52311 | 0.275109 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.32320 | −0.646006 | ||||||||
\(167\) | −5.93545 | −0.459299 | −0.229649 | − | 0.973273i | \(-0.573758\pi\) | ||||
−0.229649 | + | 0.973273i | \(0.573758\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | 17.5048 | 1.34652 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.11704 | 0.620725 | ||||||||
\(172\) | 1.13536 | 0.0865703 | ||||||||
\(173\) | 25.8217 | 1.96319 | 0.981595 | − | 0.190973i | \(-0.0611644\pi\) | ||||
0.981595 | + | 0.190973i | \(0.0611644\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.864641 | −0.0651748 | ||||||||
\(177\) | −10.9817 | −0.825433 | ||||||||
\(178\) | −4.77551 | −0.357940 | ||||||||
\(179\) | −23.3449 | −1.74488 | −0.872438 | − | 0.488725i | \(-0.837462\pi\) | ||||
−0.872438 | + | 0.488725i | \(0.837462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3694 | 0.993742 | 0.496871 | − | 0.867824i | \(-0.334482\pi\) | ||||
0.496871 | + | 0.867824i | \(0.334482\pi\) | |||||||
\(182\) | −11.0462 | −0.818801 | ||||||||
\(183\) | −5.91087 | −0.436944 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.25240 | 0.238477 | ||||||||
\(187\) | 3.04623 | 0.222762 | ||||||||
\(188\) | 5.52311 | 0.402815 | ||||||||
\(189\) | 2.00000 | 0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.2341 | 0.885227 | 0.442613 | − | 0.896713i | \(-0.354051\pi\) | ||||
0.442613 | + | 0.896713i | \(0.354051\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 7.45856 | 0.536879 | 0.268440 | − | 0.963297i | \(-0.413492\pi\) | ||||
0.268440 | + | 0.963297i | \(0.413492\pi\) | |||||||
\(194\) | 1.04623 | 0.0751148 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0.864641 | 0.0614474 | ||||||||
\(199\) | 22.8401 | 1.61909 | 0.809545 | − | 0.587059i | \(-0.199714\pi\) | ||||
0.809545 | + | 0.587059i | \(0.199714\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.91087 | −0.416921 | ||||||||
\(202\) | −9.04623 | −0.636490 | ||||||||
\(203\) | −4.00000 | −0.280745 | ||||||||
\(204\) | −3.52311 | −0.246667 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −11.3169 | −0.788489 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 5.52311 | 0.382959 | ||||||||
\(209\) | −7.01832 | −0.485467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.2341 | 1.66834 | 0.834171 | − | 0.551506i | \(-0.185946\pi\) | ||||
0.834171 | + | 0.551506i | \(0.185946\pi\) | |||||||
\(212\) | 1.34153 | 0.0921364 | ||||||||
\(213\) | −5.79383 | −0.396987 | ||||||||
\(214\) | −5.64015 | −0.385553 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −6.50479 | −0.441574 | ||||||||
\(218\) | 12.1816 | 0.825041 | ||||||||
\(219\) | 15.2524 | 1.03066 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.4586 | −1.30892 | ||||||||
\(222\) | −5.13536 | −0.344663 | ||||||||
\(223\) | 13.9634 | 0.935055 | 0.467528 | − | 0.883978i | \(-0.345145\pi\) | ||||
0.467528 | + | 0.883978i | \(0.345145\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.79383 | −0.385400 | ||||||||
\(227\) | −4.45231 | −0.295510 | −0.147755 | − | 0.989024i | \(-0.547205\pi\) | ||||
−0.147755 | + | 0.989024i | \(0.547205\pi\) | |||||||
\(228\) | 8.11704 | 0.537564 | ||||||||
\(229\) | −4.05249 | −0.267796 | −0.133898 | − | 0.990995i | \(-0.542749\pi\) | ||||
−0.133898 | + | 0.990995i | \(0.542749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.72928 | −0.113778 | ||||||||
\(232\) | 2.00000 | 0.131306 | ||||||||
\(233\) | −24.5327 | −1.60719 | −0.803595 | − | 0.595176i | \(-0.797082\pi\) | ||||
−0.803595 | + | 0.595176i | \(0.797082\pi\) | |||||||
\(234\) | −5.52311 | −0.361057 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.9817 | −0.714846 | ||||||||
\(237\) | −3.79383 | −0.246436 | ||||||||
\(238\) | 7.04623 | 0.456739 | ||||||||
\(239\) | 10.7755 | 0.697010 | 0.348505 | − | 0.937307i | \(-0.386689\pi\) | ||||
0.348505 | + | 0.937307i | \(0.386689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7755 | −0.694112 | −0.347056 | − | 0.937844i | \(-0.612819\pi\) | ||||
−0.347056 | + | 0.937844i | \(0.612819\pi\) | |||||||
\(242\) | 10.2524 | 0.659049 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.91087 | −0.378405 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.52311 | −0.224626 | ||||||||
\(247\) | 44.8313 | 2.85255 | ||||||||
\(248\) | 3.25240 | 0.206527 | ||||||||
\(249\) | 8.32320 | 0.527462 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.91087 | −0.246852 | −0.123426 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123426 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | −0.864641 | −0.0543595 | ||||||||
\(254\) | −0.747604 | −0.0469088 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.0925 | 1.75236 | 0.876180 | − | 0.481985i | \(-0.160084\pi\) | ||||
0.876180 | + | 0.481985i | \(0.160084\pi\) | |||||||
\(258\) | −1.13536 | −0.0706844 | ||||||||
\(259\) | 10.2707 | 0.638191 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | −19.7572 | −1.22060 | ||||||||
\(263\) | 29.5510 | 1.82219 | 0.911097 | − | 0.412192i | \(-0.135237\pi\) | ||||
0.911097 | + | 0.412192i | \(0.135237\pi\) | |||||||
\(264\) | 0.864641 | 0.0532150 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −16.2341 | −0.995375 | ||||||||
\(267\) | 4.77551 | 0.292256 | ||||||||
\(268\) | −5.91087 | −0.361064 | ||||||||
\(269\) | −17.2803 | −1.05360 | −0.526799 | − | 0.849990i | \(-0.676608\pi\) | ||||
−0.526799 | + | 0.849990i | \(0.676608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.96336 | 0.605231 | 0.302615 | − | 0.953113i | \(-0.402140\pi\) | ||||
0.302615 | + | 0.953113i | \(0.402140\pi\) | |||||||
\(272\) | −3.52311 | −0.213620 | ||||||||
\(273\) | 11.0462 | 0.668548 | ||||||||
\(274\) | −0.476886 | −0.0288097 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | 27.0741 | 1.62673 | 0.813364 | − | 0.581756i | \(-0.197634\pi\) | ||||
0.813364 | + | 0.581756i | \(0.197634\pi\) | |||||||
\(278\) | 3.45856 | 0.207431 | ||||||||
\(279\) | −3.25240 | −0.194716 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.2803 | −1.62741 | −0.813703 | − | 0.581281i | \(-0.802552\pi\) | ||||
−0.813703 | + | 0.581281i | \(0.802552\pi\) | |||||||
\(282\) | −5.52311 | −0.328897 | ||||||||
\(283\) | −30.9205 | −1.83803 | −0.919015 | − | 0.394222i | \(-0.871014\pi\) | ||||
−0.919015 | + | 0.394222i | \(0.871014\pi\) | |||||||
\(284\) | −5.79383 | −0.343801 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.77551 | 0.282382 | ||||||||
\(287\) | 7.04623 | 0.415926 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −4.58767 | −0.269863 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.04623 | −0.0613310 | ||||||||
\(292\) | 15.2524 | 0.892579 | ||||||||
\(293\) | 11.0708 | 0.646764 | 0.323382 | − | 0.946269i | \(-0.395180\pi\) | ||||
0.323382 | + | 0.946269i | \(0.395180\pi\) | |||||||
\(294\) | 3.00000 | 0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.13536 | −0.298487 | ||||||||
\(297\) | −0.864641 | −0.0501716 | ||||||||
\(298\) | 8.86464 | 0.513515 | ||||||||
\(299\) | 5.52311 | 0.319410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.27072 | 0.130882 | ||||||||
\(302\) | 6.71096 | 0.386172 | ||||||||
\(303\) | 9.04623 | 0.519692 | ||||||||
\(304\) | 8.11704 | 0.465544 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.52311 | 0.201403 | ||||||||
\(307\) | 4.23407 | 0.241651 | 0.120826 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120826 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(308\) | −1.72928 | −0.0985350 | ||||||||
\(309\) | 11.3169 | 0.643799 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.2803 | −0.753057 | −0.376528 | − | 0.926405i | \(-0.622882\pi\) | ||||
−0.376528 | + | 0.926405i | \(0.622882\pi\) | |||||||
\(312\) | −5.52311 | −0.312685 | ||||||||
\(313\) | −31.9634 | −1.80668 | −0.903338 | − | 0.428930i | \(-0.858891\pi\) | ||||
−0.903338 | + | 0.428930i | \(0.858891\pi\) | |||||||
\(314\) | 14.6864 | 0.828800 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.79383 | −0.213420 | ||||||||
\(317\) | −13.2803 | −0.745896 | −0.372948 | − | 0.927852i | \(-0.621653\pi\) | ||||
−0.372948 | + | 0.927852i | \(0.621653\pi\) | |||||||
\(318\) | −1.34153 | −0.0752291 | ||||||||
\(319\) | 1.72928 | 0.0968212 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.64015 | 0.314803 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | −28.5972 | −1.59119 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.2803 | 1.28938 | ||||||||
\(327\) | −12.1816 | −0.673643 | ||||||||
\(328\) | −3.52311 | −0.194531 | ||||||||
\(329\) | 11.0462 | 0.608998 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.8217 | −0.649782 | −0.324891 | − | 0.945752i | \(-0.605328\pi\) | ||||
−0.324891 | + | 0.945752i | \(0.605328\pi\) | |||||||
\(332\) | 8.32320 | 0.456795 | ||||||||
\(333\) | 5.13536 | 0.281416 | ||||||||
\(334\) | 5.93545 | 0.324773 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | 13.2803 | 0.723424 | 0.361712 | − | 0.932290i | \(-0.382192\pi\) | ||||
0.361712 | + | 0.932290i | \(0.382192\pi\) | |||||||
\(338\) | −17.5048 | −0.952135 | ||||||||
\(339\) | 5.79383 | 0.314678 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.81215 | 0.152287 | ||||||||
\(342\) | −8.11704 | −0.438919 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | −1.13536 | −0.0612145 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.8217 | −1.38819 | ||||||||
\(347\) | −24.3632 | −1.30788 | −0.653942 | − | 0.756545i | \(-0.726886\pi\) | ||||
−0.653942 | + | 0.756545i | \(0.726886\pi\) | |||||||
\(348\) | −2.00000 | −0.107211 | ||||||||
\(349\) | 3.49521 | 0.187094 | 0.0935471 | − | 0.995615i | \(-0.470179\pi\) | ||||
0.0935471 | + | 0.995615i | \(0.470179\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.52311 | 0.294802 | ||||||||
\(352\) | 0.864641 | 0.0460855 | ||||||||
\(353\) | 31.5789 | 1.68078 | 0.840388 | − | 0.541985i | \(-0.182327\pi\) | ||||
0.840388 | + | 0.541985i | \(0.182327\pi\) | |||||||
\(354\) | 10.9817 | 0.583670 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.77551 | 0.253102 | ||||||||
\(357\) | −7.04623 | −0.372926 | ||||||||
\(358\) | 23.3449 | 1.23381 | ||||||||
\(359\) | −21.1878 | −1.11825 | −0.559126 | − | 0.829083i | \(-0.688863\pi\) | ||||
−0.559126 | + | 0.829083i | \(0.688863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.8863 | 2.46770 | ||||||||
\(362\) | −13.3694 | −0.702682 | ||||||||
\(363\) | −10.2524 | −0.538111 | ||||||||
\(364\) | 11.0462 | 0.578980 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 5.91087 | 0.308966 | ||||||||
\(367\) | 13.0462 | 0.681008 | 0.340504 | − | 0.940243i | \(-0.389402\pi\) | ||||
0.340504 | + | 0.940243i | \(0.389402\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 3.52311 | 0.183406 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.68305 | 0.139297 | ||||||||
\(372\) | −3.25240 | −0.168629 | ||||||||
\(373\) | 18.8646 | 0.976774 | 0.488387 | − | 0.872627i | \(-0.337585\pi\) | ||||
0.488387 | + | 0.872627i | \(0.337585\pi\) | |||||||
\(374\) | −3.04623 | −0.157517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.52311 | −0.284833 | ||||||||
\(377\) | −11.0462 | −0.568910 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 26.7509 | 1.37410 | 0.687052 | − | 0.726609i | \(-0.258905\pi\) | ||||
0.687052 | + | 0.726609i | \(0.258905\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.747604 | 0.0383009 | ||||||||
\(382\) | −12.2341 | −0.625950 | ||||||||
\(383\) | −22.5048 | −1.14994 | −0.574971 | − | 0.818174i | \(-0.694987\pi\) | ||||
−0.574971 | + | 0.818174i | \(0.694987\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.45856 | −0.379631 | ||||||||
\(387\) | 1.13536 | 0.0577135 | ||||||||
\(388\) | −1.04623 | −0.0531142 | ||||||||
\(389\) | −7.67680 | −0.389229 | −0.194614 | − | 0.980880i | \(-0.562346\pi\) | ||||
−0.194614 | + | 0.980880i | \(0.562346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.52311 | −0.178172 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 19.7572 | 0.996618 | ||||||||
\(394\) | −2.00000 | −0.100759 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.864641 | −0.0434498 | ||||||||
\(397\) | −31.7938 | −1.59569 | −0.797843 | − | 0.602865i | \(-0.794026\pi\) | ||||
−0.797843 | + | 0.602865i | \(0.794026\pi\) | |||||||
\(398\) | −22.8401 | −1.14487 | ||||||||
\(399\) | 16.2341 | 0.812720 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0925 | −0.903494 | −0.451747 | − | 0.892146i | \(-0.649199\pi\) | ||||
−0.451747 | + | 0.892146i | \(0.649199\pi\) | |||||||
\(402\) | 5.91087 | 0.294807 | ||||||||
\(403\) | −17.9634 | −0.894818 | ||||||||
\(404\) | 9.04623 | 0.450067 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | 0.198517 | ||||||||
\(407\) | −4.44024 | −0.220095 | ||||||||
\(408\) | 3.52311 | 0.174420 | ||||||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.476886 | 0.0235230 | ||||||||
\(412\) | 11.3169 | 0.557546 | ||||||||
\(413\) | −21.9634 | −1.08075 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.52311 | −0.270793 | ||||||||
\(417\) | −3.45856 | −0.169367 | ||||||||
\(418\) | 7.01832 | 0.343277 | ||||||||
\(419\) | 20.4523 | 0.999161 | 0.499580 | − | 0.866268i | \(-0.333488\pi\) | ||||
0.499580 | + | 0.866268i | \(0.333488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.9571 | −0.631490 | −0.315745 | − | 0.948844i | \(-0.602254\pi\) | ||||
−0.315745 | + | 0.948844i | \(0.602254\pi\) | |||||||
\(422\) | −24.2341 | −1.17970 | ||||||||
\(423\) | 5.52311 | 0.268543 | ||||||||
\(424\) | −1.34153 | −0.0651503 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.79383 | 0.280712 | ||||||||
\(427\) | −11.8217 | −0.572094 | ||||||||
\(428\) | 5.64015 | 0.272627 | ||||||||
\(429\) | −4.77551 | −0.230564 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.3728 | 1.60751 | 0.803755 | − | 0.594961i | \(-0.202832\pi\) | ||||
0.803755 | + | 0.594961i | \(0.202832\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 19.0096 | 0.913542 | 0.456771 | − | 0.889584i | \(-0.349006\pi\) | ||||
0.456771 | + | 0.889584i | \(0.349006\pi\) | |||||||
\(434\) | 6.50479 | 0.312240 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1816 | −0.583392 | ||||||||
\(437\) | 8.11704 | 0.388291 | ||||||||
\(438\) | −15.2524 | −0.728788 | ||||||||
\(439\) | 32.5972 | 1.55578 | 0.777891 | − | 0.628399i | \(-0.216290\pi\) | ||||
0.777891 | + | 0.628399i | \(0.216290\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 19.4586 | 0.925549 | ||||||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | 5.13536 | 0.243713 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.9634 | −0.661184 | ||||||||
\(447\) | −8.86464 | −0.419283 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | 39.5789 | 1.86785 | 0.933923 | − | 0.357475i | \(-0.116362\pi\) | ||||
0.933923 | + | 0.357475i | \(0.116362\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.04623 | −0.143441 | ||||||||
\(452\) | 5.79383 | 0.272519 | ||||||||
\(453\) | −6.71096 | −0.315308 | ||||||||
\(454\) | 4.45231 | 0.208957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.11704 | −0.380115 | ||||||||
\(457\) | 24.5048 | 1.14629 | 0.573143 | − | 0.819455i | \(-0.305724\pi\) | ||||
0.573143 | + | 0.819455i | \(0.305724\pi\) | |||||||
\(458\) | 4.05249 | 0.189360 | ||||||||
\(459\) | −3.52311 | −0.164445 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2341 | 0.849245 | 0.424623 | − | 0.905370i | \(-0.360407\pi\) | ||||
0.424623 | + | 0.905370i | \(0.360407\pi\) | |||||||
\(462\) | 1.72928 | 0.0804535 | ||||||||
\(463\) | −4.20617 | −0.195477 | −0.0977386 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977386 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 24.5327 | 1.13646 | ||||||||
\(467\) | 19.1912 | 0.888062 | 0.444031 | − | 0.896012i | \(-0.353548\pi\) | ||||
0.444031 | + | 0.896012i | \(0.353548\pi\) | |||||||
\(468\) | 5.52311 | 0.255306 | ||||||||
\(469\) | −11.8217 | −0.545877 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.6864 | −0.676713 | ||||||||
\(472\) | 10.9817 | 0.505473 | ||||||||
\(473\) | −0.981678 | −0.0451376 | ||||||||
\(474\) | 3.79383 | 0.174257 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.04623 | −0.322963 | ||||||||
\(477\) | 1.34153 | 0.0614243 | ||||||||
\(478\) | −10.7755 | −0.492860 | ||||||||
\(479\) | −25.6801 | −1.17335 | −0.586677 | − | 0.809821i | \(-0.699564\pi\) | ||||
−0.586677 | + | 0.809821i | \(0.699564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.3632 | 1.29325 | ||||||||
\(482\) | 10.7755 | 0.490811 | ||||||||
\(483\) | 2.00000 | 0.0910032 | ||||||||
\(484\) | −10.2524 | −0.466018 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 8.74760 | 0.396392 | 0.198196 | − | 0.980162i | \(-0.436492\pi\) | ||||
0.198196 | + | 0.980162i | \(0.436492\pi\) | |||||||
\(488\) | 5.91087 | 0.267572 | ||||||||
\(489\) | −23.2803 | −1.05277 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.8863 | 1.07797 | 0.538987 | − | 0.842314i | \(-0.318807\pi\) | ||||
0.538987 | + | 0.842314i | \(0.318807\pi\) | |||||||
\(492\) | 3.52311 | 0.158834 | ||||||||
\(493\) | 7.04623 | 0.317346 | ||||||||
\(494\) | −44.8313 | −2.01706 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.25240 | −0.146037 | ||||||||
\(497\) | −11.5877 | −0.519778 | ||||||||
\(498\) | −8.32320 | −0.372972 | ||||||||
\(499\) | 29.7293 | 1.33087 | 0.665433 | − | 0.746458i | \(-0.268247\pi\) | ||||
0.665433 | + | 0.746458i | \(0.268247\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.93545 | −0.265176 | ||||||||
\(502\) | 3.91087 | 0.174551 | ||||||||
\(503\) | 0.775511 | 0.0345783 | 0.0172892 | − | 0.999851i | \(-0.494496\pi\) | ||||
0.0172892 | + | 0.999851i | \(0.494496\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.864641 | 0.0384380 | ||||||||
\(507\) | 17.5048 | 0.777415 | ||||||||
\(508\) | 0.747604 | 0.0331696 | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.5048 | 1.34945 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 8.11704 | 0.358376 | ||||||||
\(514\) | −28.0925 | −1.23911 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.13536 | 0.0499814 | ||||||||
\(517\) | −4.77551 | −0.210027 | ||||||||
\(518\) | −10.2707 | −0.451269 | ||||||||
\(519\) | 25.8217 | 1.13345 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4219 | 0.588025 | 0.294012 | − | 0.955802i | \(-0.405009\pi\) | ||||
0.294012 | + | 0.955802i | \(0.405009\pi\) | |||||||
\(522\) | 2.00000 | 0.0875376 | ||||||||
\(523\) | −41.9667 | −1.83507 | −0.917537 | − | 0.397649i | \(-0.869826\pi\) | ||||
−0.917537 | + | 0.397649i | \(0.869826\pi\) | |||||||
\(524\) | 19.7572 | 0.863097 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29.5510 | −1.28849 | ||||||||
\(527\) | 11.4586 | 0.499143 | ||||||||
\(528\) | −0.864641 | −0.0376287 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.9817 | −0.476564 | ||||||||
\(532\) | 16.2341 | 0.703836 | ||||||||
\(533\) | 19.4586 | 0.842844 | ||||||||
\(534\) | −4.77551 | −0.206657 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.91087 | 0.255311 | ||||||||
\(537\) | −23.3449 | −1.00740 | ||||||||
\(538\) | 17.2803 | 0.745007 | ||||||||
\(539\) | 2.59392 | 0.111728 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.58767 | −0.0682591 | −0.0341295 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341295 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(542\) | −9.96336 | −0.427963 | ||||||||
\(543\) | 13.3694 | 0.573737 | ||||||||
\(544\) | 3.52311 | 0.151052 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −11.0462 | −0.472735 | ||||||||
\(547\) | −20.6464 | −0.882777 | −0.441388 | − | 0.897316i | \(-0.645514\pi\) | ||||
−0.441388 | + | 0.897316i | \(0.645514\pi\) | |||||||
\(548\) | 0.476886 | 0.0203715 | ||||||||
\(549\) | −5.91087 | −0.252270 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.2341 | −0.691595 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | −7.58767 | −0.322660 | ||||||||
\(554\) | −27.0741 | −1.15027 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.45856 | −0.146676 | ||||||||
\(557\) | 9.47063 | 0.401283 | 0.200642 | − | 0.979665i | \(-0.435697\pi\) | ||||
0.200642 | + | 0.979665i | \(0.435697\pi\) | |||||||
\(558\) | 3.25240 | 0.137685 | ||||||||
\(559\) | 6.27072 | 0.265223 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.04623 | 0.128612 | ||||||||
\(562\) | 27.2803 | 1.15075 | ||||||||
\(563\) | 1.51105 | 0.0636832 | 0.0318416 | − | 0.999493i | \(-0.489863\pi\) | ||||
0.0318416 | + | 0.999493i | \(0.489863\pi\) | |||||||
\(564\) | 5.52311 | 0.232565 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 30.9205 | 1.29968 | ||||||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | 5.79383 | 0.243104 | ||||||||
\(569\) | −20.0000 | −0.838444 | −0.419222 | − | 0.907884i | \(-0.637697\pi\) | ||||
−0.419222 | + | 0.907884i | \(0.637697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.1633 | −1.47154 | −0.735768 | − | 0.677233i | \(-0.763179\pi\) | ||||
−0.735768 | + | 0.677233i | \(0.763179\pi\) | |||||||
\(572\) | −4.77551 | −0.199674 | ||||||||
\(573\) | 12.2341 | 0.511086 | ||||||||
\(574\) | −7.04623 | −0.294104 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −22.7110 | −0.945470 | −0.472735 | − | 0.881205i | \(-0.656733\pi\) | ||||
−0.472735 | + | 0.881205i | \(0.656733\pi\) | |||||||
\(578\) | 4.58767 | 0.190822 | ||||||||
\(579\) | 7.45856 | 0.309967 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.6464 | 0.690609 | ||||||||
\(582\) | 1.04623 | 0.0433676 | ||||||||
\(583\) | −1.15994 | −0.0480398 | ||||||||
\(584\) | −15.2524 | −0.631149 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.0708 | −0.457331 | ||||||||
\(587\) | 3.76593 | 0.155436 | 0.0777182 | − | 0.996975i | \(-0.475237\pi\) | ||||
0.0777182 | + | 0.996975i | \(0.475237\pi\) | |||||||
\(588\) | −3.00000 | −0.123718 | ||||||||
\(589\) | −26.3998 | −1.08779 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.00000 | 0.0822690 | ||||||||
\(592\) | 5.13536 | 0.211062 | ||||||||
\(593\) | 1.04623 | 0.0429635 | 0.0214817 | − | 0.999769i | \(-0.493162\pi\) | ||||
0.0214817 | + | 0.999769i | \(0.493162\pi\) | |||||||
\(594\) | 0.864641 | 0.0354766 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.86464 | −0.363110 | ||||||||
\(597\) | 22.8401 | 0.934781 | ||||||||
\(598\) | −5.52311 | −0.225857 | ||||||||
\(599\) | −21.2803 | −0.869490 | −0.434745 | − | 0.900554i | \(-0.643161\pi\) | ||||
−0.434745 | + | 0.900554i | \(0.643161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.8034 | 1.25650 | 0.628249 | − | 0.778012i | \(-0.283772\pi\) | ||||
0.628249 | + | 0.778012i | \(0.283772\pi\) | |||||||
\(602\) | −2.27072 | −0.0925476 | ||||||||
\(603\) | −5.91087 | −0.240709 | ||||||||
\(604\) | −6.71096 | −0.273065 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.04623 | −0.367478 | ||||||||
\(607\) | −22.0925 | −0.896705 | −0.448353 | − | 0.893857i | \(-0.647989\pi\) | ||||
−0.448353 | + | 0.893857i | \(0.647989\pi\) | |||||||
\(608\) | −8.11704 | −0.329189 | ||||||||
\(609\) | −4.00000 | −0.162088 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 30.5048 | 1.23409 | ||||||||
\(612\) | −3.52311 | −0.142413 | ||||||||
\(613\) | −41.4985 | −1.67611 | −0.838055 | − | 0.545586i | \(-0.816307\pi\) | ||||
−0.838055 | + | 0.545586i | \(0.816307\pi\) | |||||||
\(614\) | −4.23407 | −0.170873 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.72928 | 0.0696747 | ||||||||
\(617\) | −30.9325 | −1.24530 | −0.622648 | − | 0.782502i | \(-0.713943\pi\) | ||||
−0.622648 | + | 0.782502i | \(0.713943\pi\) | |||||||
\(618\) | −11.3169 | −0.455234 | ||||||||
\(619\) | 14.5660 | 0.585458 | 0.292729 | − | 0.956196i | \(-0.405437\pi\) | ||||
0.292729 | + | 0.956196i | \(0.405437\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 13.2803 | 0.532492 | ||||||||
\(623\) | 9.55102 | 0.382654 | ||||||||
\(624\) | 5.52311 | 0.221102 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.9634 | 1.27751 | ||||||||
\(627\) | −7.01832 | −0.280285 | ||||||||
\(628\) | −14.6864 | −0.586050 | ||||||||
\(629\) | −18.0925 | −0.721394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.4036 | −1.52882 | −0.764412 | − | 0.644729i | \(-0.776970\pi\) | ||||
−0.764412 | + | 0.644729i | \(0.776970\pi\) | |||||||
\(632\) | 3.79383 | 0.150911 | ||||||||
\(633\) | 24.2341 | 0.963218 | ||||||||
\(634\) | 13.2803 | 0.527428 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.34153 | 0.0531950 | ||||||||
\(637\) | −16.5693 | −0.656501 | ||||||||
\(638\) | −1.72928 | −0.0684629 | ||||||||
\(639\) | −5.79383 | −0.229200 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.9267 | −1.26103 | −0.630515 | − | 0.776177i | \(-0.717156\pi\) | ||||
−0.630515 | + | 0.776177i | \(0.717156\pi\) | |||||||
\(642\) | −5.64015 | −0.222599 | ||||||||
\(643\) | −4.72302 | −0.186258 | −0.0931289 | − | 0.995654i | \(-0.529687\pi\) | ||||
−0.0931289 | + | 0.995654i | \(0.529687\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28.5972 | 1.12514 | ||||||||
\(647\) | −43.4586 | −1.70853 | −0.854266 | − | 0.519836i | \(-0.825993\pi\) | ||||
−0.854266 | + | 0.519836i | \(0.825993\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 9.49521 | 0.372720 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.50479 | −0.254943 | ||||||||
\(652\) | −23.2803 | −0.911727 | ||||||||
\(653\) | 2.36318 | 0.0924782 | 0.0462391 | − | 0.998930i | \(-0.485276\pi\) | ||||
0.0462391 | + | 0.998930i | \(0.485276\pi\) | |||||||
\(654\) | 12.1816 | 0.476338 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.52311 | 0.137555 | ||||||||
\(657\) | 15.2524 | 0.595053 | ||||||||
\(658\) | −11.0462 | −0.430627 | ||||||||
\(659\) | −22.4157 | −0.873190 | −0.436595 | − | 0.899658i | \(-0.643816\pi\) | ||||
−0.436595 | + | 0.899658i | \(0.643816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9937 | −0.583189 | −0.291594 | − | 0.956542i | \(-0.594186\pi\) | ||||
−0.291594 | + | 0.956542i | \(0.594186\pi\) | |||||||
\(662\) | 11.8217 | 0.459465 | ||||||||
\(663\) | −19.4586 | −0.755708 | ||||||||
\(664\) | −8.32320 | −0.323003 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.13536 | −0.198991 | ||||||||
\(667\) | −2.00000 | −0.0774403 | ||||||||
\(668\) | −5.93545 | −0.229649 | ||||||||
\(669\) | 13.9634 | 0.539855 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.11078 | 0.197299 | ||||||||
\(672\) | −2.00000 | −0.0771517 | ||||||||
\(673\) | −49.2158 | −1.89713 | −0.948564 | − | 0.316586i | \(-0.897464\pi\) | ||||
−0.948564 | + | 0.316586i | \(0.897464\pi\) | |||||||
\(674\) | −13.2803 | −0.511538 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 17.5048 | 0.673261 | ||||||||
\(677\) | −5.34153 | −0.205292 | −0.102646 | − | 0.994718i | \(-0.532731\pi\) | ||||
−0.102646 | + | 0.994718i | \(0.532731\pi\) | |||||||
\(678\) | −5.79383 | −0.222511 | ||||||||
\(679\) | −2.09246 | −0.0803011 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.45231 | −0.170613 | ||||||||
\(682\) | −2.81215 | −0.107683 | ||||||||
\(683\) | 27.1512 | 1.03891 | 0.519456 | − | 0.854497i | \(-0.326135\pi\) | ||||
0.519456 | + | 0.854497i | \(0.326135\pi\) | |||||||
\(684\) | 8.11704 | 0.310363 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | −4.05249 | −0.154612 | ||||||||
\(688\) | 1.13536 | 0.0432852 | ||||||||
\(689\) | 7.40940 | 0.282276 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1050 | 0.460495 | 0.230247 | − | 0.973132i | \(-0.426046\pi\) | ||||
0.230247 | + | 0.973132i | \(0.426046\pi\) | |||||||
\(692\) | 25.8217 | 0.981595 | ||||||||
\(693\) | −1.72928 | −0.0656900 | ||||||||
\(694\) | 24.3632 | 0.924814 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.00000 | 0.0758098 | ||||||||
\(697\) | −12.4123 | −0.470151 | ||||||||
\(698\) | −3.49521 | −0.132296 | ||||||||
\(699\) | −24.5327 | −0.927912 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.59392 | 0.0979711 | 0.0489856 | − | 0.998799i | \(-0.484401\pi\) | ||||
0.0489856 | + | 0.998799i | \(0.484401\pi\) | |||||||
\(702\) | −5.52311 | −0.208457 | ||||||||
\(703\) | 41.6839 | 1.57214 | ||||||||
\(704\) | −0.864641 | −0.0325874 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.5789 | −1.18849 | ||||||||
\(707\) | 18.0925 | 0.680437 | ||||||||
\(708\) | −10.9817 | −0.412717 | ||||||||
\(709\) | 4.00333 | 0.150348 | 0.0751741 | − | 0.997170i | \(-0.476049\pi\) | ||||
0.0751741 | + | 0.997170i | \(0.476049\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.79383 | −0.142280 | ||||||||
\(712\) | −4.77551 | −0.178970 | ||||||||
\(713\) | −3.25240 | −0.121803 | ||||||||
\(714\) | 7.04623 | 0.263698 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.3449 | −0.872438 | ||||||||
\(717\) | 10.7755 | 0.402419 | ||||||||
\(718\) | 21.1878 | 0.790723 | ||||||||
\(719\) | 20.2707 | 0.755970 | 0.377985 | − | 0.925812i | \(-0.376617\pi\) | ||||
0.377985 | + | 0.925812i | \(0.376617\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.6339 | 0.842930 | ||||||||
\(722\) | −46.8863 | −1.74493 | ||||||||
\(723\) | −10.7755 | −0.400746 | ||||||||
\(724\) | 13.3694 | 0.496871 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 10.2524 | 0.380502 | ||||||||
\(727\) | −32.6339 | −1.21032 | −0.605162 | − | 0.796102i | \(-0.706892\pi\) | ||||
−0.605162 | + | 0.796102i | \(0.706892\pi\) | |||||||
\(728\) | −11.0462 | −0.409400 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.00000 | −0.147945 | ||||||||
\(732\) | −5.91087 | −0.218472 | ||||||||
\(733\) | −1.13536 | −0.0419354 | −0.0209677 | − | 0.999780i | \(-0.506675\pi\) | ||||
−0.0209677 | + | 0.999780i | \(0.506675\pi\) | |||||||
\(734\) | −13.0462 | −0.481545 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 5.11078 | 0.188258 | ||||||||
\(738\) | −3.52311 | −0.129688 | ||||||||
\(739\) | −29.4219 | −1.08230 | −0.541151 | − | 0.840925i | \(-0.682011\pi\) | ||||
−0.541151 | + | 0.840925i | \(0.682011\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44.8313 | 1.64692 | ||||||||
\(742\) | −2.68305 | −0.0984980 | ||||||||
\(743\) | −27.4586 | −1.00736 | −0.503678 | − | 0.863891i | \(-0.668020\pi\) | ||||
−0.503678 | + | 0.863891i | \(0.668020\pi\) | |||||||
\(744\) | 3.25240 | 0.119239 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18.8646 | −0.690684 | ||||||||
\(747\) | 8.32320 | 0.304530 | ||||||||
\(748\) | 3.04623 | 0.111381 | ||||||||
\(749\) | 11.2803 | 0.412173 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.02791 | 0.146980 | 0.0734902 | − | 0.997296i | \(-0.476586\pi\) | ||||
0.0734902 | + | 0.997296i | \(0.476586\pi\) | |||||||
\(752\) | 5.52311 | 0.201407 | ||||||||
\(753\) | −3.91087 | −0.142520 | ||||||||
\(754\) | 11.0462 | 0.402280 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | −31.5110 | −1.14529 | −0.572644 | − | 0.819804i | \(-0.694082\pi\) | ||||
−0.572644 | + | 0.819804i | \(0.694082\pi\) | |||||||
\(758\) | −26.7509 | −0.971638 | ||||||||
\(759\) | −0.864641 | −0.0313845 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.9634 | −0.723671 | −0.361836 | − | 0.932242i | \(-0.617850\pi\) | ||||
−0.361836 | + | 0.932242i | \(0.617850\pi\) | |||||||
\(762\) | −0.747604 | −0.0270828 | ||||||||
\(763\) | −24.3632 | −0.882006 | ||||||||
\(764\) | 12.2341 | 0.442613 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.5048 | 0.813131 | ||||||||
\(767\) | −60.6531 | −2.19006 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −46.4190 | −1.67391 | −0.836956 | − | 0.547271i | \(-0.815667\pi\) | ||||
−0.836956 | + | 0.547271i | \(0.815667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.0925 | 1.01173 | ||||||||
\(772\) | 7.45856 | 0.268440 | ||||||||
\(773\) | −29.0342 | −1.04429 | −0.522143 | − | 0.852858i | \(-0.674867\pi\) | ||||
−0.522143 | + | 0.852858i | \(0.674867\pi\) | |||||||
\(774\) | −1.13536 | −0.0408096 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.04623 | 0.0375574 | ||||||||
\(777\) | 10.2707 | 0.368460 | ||||||||
\(778\) | 7.67680 | 0.275226 | ||||||||
\(779\) | 28.5972 | 1.02460 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.00958 | 0.179257 | ||||||||
\(782\) | 3.52311 | 0.125986 | ||||||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −19.7572 | −0.704716 | ||||||||
\(787\) | 35.7693 | 1.27504 | 0.637518 | − | 0.770435i | \(-0.279961\pi\) | ||||
0.637518 | + | 0.770435i | \(0.279961\pi\) | |||||||
\(788\) | 2.00000 | 0.0712470 | ||||||||
\(789\) | 29.5510 | 1.05204 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.5877 | 0.412010 | ||||||||
\(792\) | 0.864641 | 0.0307237 | ||||||||
\(793\) | −32.6464 | −1.15931 | ||||||||
\(794\) | 31.7938 | 1.12832 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 22.8401 | 0.809545 | ||||||||
\(797\) | −22.8367 | −0.808919 | −0.404459 | − | 0.914556i | \(-0.632540\pi\) | ||||
−0.404459 | + | 0.914556i | \(0.632540\pi\) | |||||||
\(798\) | −16.2341 | −0.574680 | ||||||||
\(799\) | −19.4586 | −0.688394 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.77551 | 0.168734 | ||||||||
\(802\) | 18.0925 | 0.638867 | ||||||||
\(803\) | −13.1878 | −0.465389 | ||||||||
\(804\) | −5.91087 | −0.208460 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 17.9634 | 0.632732 | ||||||||
\(807\) | −17.2803 | −0.608295 | ||||||||
\(808\) | −9.04623 | −0.318245 | ||||||||
\(809\) | −36.9171 | −1.29794 | −0.648969 | − | 0.760815i | \(-0.724799\pi\) | ||||
−0.648969 | + | 0.760815i | \(0.724799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 51.8217 | 1.81971 | 0.909854 | − | 0.414929i | \(-0.136194\pi\) | ||||
0.909854 | + | 0.414929i | \(0.136194\pi\) | |||||||
\(812\) | −4.00000 | −0.140372 | ||||||||
\(813\) | 9.96336 | 0.349430 | ||||||||
\(814\) | 4.44024 | 0.155630 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.52311 | −0.123334 | ||||||||
\(817\) | 9.21575 | 0.322418 | ||||||||
\(818\) | −2.00000 | −0.0699284 | ||||||||
\(819\) | 11.0462 | 0.385986 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8709 | −0.623699 | −0.311849 | − | 0.950132i | \(-0.600948\pi\) | ||||
−0.311849 | + | 0.950132i | \(0.600948\pi\) | |||||||
\(822\) | −0.476886 | −0.0166333 | ||||||||
\(823\) | 9.00958 | 0.314054 | 0.157027 | − | 0.987594i | \(-0.449809\pi\) | ||||
0.157027 | + | 0.987594i | \(0.449809\pi\) | |||||||
\(824\) | −11.3169 | −0.394245 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21.9634 | 0.764203 | ||||||||
\(827\) | 42.1083 | 1.46425 | 0.732125 | − | 0.681171i | \(-0.238529\pi\) | ||||
0.732125 | + | 0.681171i | \(0.238529\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −35.5510 | −1.23474 | −0.617369 | − | 0.786674i | \(-0.711801\pi\) | ||||
−0.617369 | + | 0.786674i | \(0.711801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.0741 | 0.939191 | ||||||||
\(832\) | 5.52311 | 0.191480 | ||||||||
\(833\) | 10.5693 | 0.366206 | ||||||||
\(834\) | 3.45856 | 0.119760 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.01832 | −0.242734 | ||||||||
\(837\) | −3.25240 | −0.112419 | ||||||||
\(838\) | −20.4523 | −0.706513 | ||||||||
\(839\) | −25.6801 | −0.886576 | −0.443288 | − | 0.896379i | \(-0.646188\pi\) | ||||
−0.443288 | + | 0.896379i | \(0.646188\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 12.9571 | 0.446531 | ||||||||
\(843\) | −27.2803 | −0.939584 | ||||||||
\(844\) | 24.2341 | 0.834171 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.52311 | −0.189889 | ||||||||
\(847\) | −20.5048 | −0.704553 | ||||||||
\(848\) | 1.34153 | 0.0460682 | ||||||||
\(849\) | −30.9205 | −1.06119 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.13536 | 0.176038 | ||||||||
\(852\) | −5.79383 | −0.198493 | ||||||||
\(853\) | −11.6647 | −0.399393 | −0.199696 | − | 0.979858i | \(-0.563996\pi\) | ||||
−0.199696 | + | 0.979858i | \(0.563996\pi\) | |||||||
\(854\) | 11.8217 | 0.404532 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.64015 | −0.192776 | ||||||||
\(857\) | 41.5423 | 1.41906 | 0.709529 | − | 0.704677i | \(-0.248908\pi\) | ||||
0.709529 | + | 0.704677i | \(0.248908\pi\) | |||||||
\(858\) | 4.77551 | 0.163033 | ||||||||
\(859\) | 21.5510 | 0.735311 | 0.367656 | − | 0.929962i | \(-0.380161\pi\) | ||||
0.367656 | + | 0.929962i | \(0.380161\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.04623 | 0.240135 | ||||||||
\(862\) | −33.3728 | −1.13668 | ||||||||
\(863\) | −6.91713 | −0.235462 | −0.117731 | − | 0.993046i | \(-0.537562\pi\) | ||||
−0.117731 | + | 0.993046i | \(0.537562\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.0096 | −0.645972 | ||||||||
\(867\) | −4.58767 | −0.155805 | ||||||||
\(868\) | −6.50479 | −0.220787 | ||||||||
\(869\) | 3.28030 | 0.111277 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −32.6464 | −1.10618 | ||||||||
\(872\) | 12.1816 | 0.412521 | ||||||||
\(873\) | −1.04623 | −0.0354095 | ||||||||
\(874\) | −8.11704 | −0.274563 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.2524 | 0.515331 | ||||||||
\(877\) | 2.53270 | 0.0855232 | 0.0427616 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427616 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(878\) | −32.5972 | −1.10010 | ||||||||
\(879\) | 11.0708 | 0.373409 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.8680 | −0.366151 | −0.183076 | − | 0.983099i | \(-0.558605\pi\) | ||||
−0.183076 | + | 0.983099i | \(0.558605\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | 40.4190 | 1.36021 | 0.680104 | − | 0.733116i | \(-0.261935\pi\) | ||||
0.680104 | + | 0.733116i | \(0.261935\pi\) | |||||||
\(884\) | −19.4586 | −0.654462 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.00000 | −0.134383 | ||||||||
\(887\) | −7.48647 | −0.251371 | −0.125686 | − | 0.992070i | \(-0.540113\pi\) | ||||
−0.125686 | + | 0.992070i | \(0.540113\pi\) | |||||||
\(888\) | −5.13536 | −0.172331 | ||||||||
\(889\) | 1.49521 | 0.0501477 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.864641 | −0.0289666 | ||||||||
\(892\) | 13.9634 | 0.467528 | ||||||||
\(893\) | 44.8313 | 1.50022 | ||||||||
\(894\) | 8.86464 | 0.296478 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 5.52311 | 0.184411 | ||||||||
\(898\) | −39.5789 | −1.32077 | ||||||||
\(899\) | 6.50479 | 0.216947 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.72635 | −0.157458 | ||||||||
\(902\) | 3.04623 | 0.101428 | ||||||||
\(903\) | 2.27072 | 0.0755648 | ||||||||
\(904\) | −5.79383 | −0.192700 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.71096 | 0.222957 | ||||||||
\(907\) | −22.6864 | −0.753289 | −0.376644 | − | 0.926358i | \(-0.622922\pi\) | ||||
−0.376644 | + | 0.926358i | \(0.622922\pi\) | |||||||
\(908\) | −4.45231 | −0.147755 | ||||||||
\(909\) | 9.04623 | 0.300044 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −35.8217 | −1.18683 | −0.593414 | − | 0.804898i | \(-0.702220\pi\) | ||||
−0.593414 | + | 0.804898i | \(0.702220\pi\) | |||||||
\(912\) | 8.11704 | 0.268782 | ||||||||
\(913\) | −7.19658 | −0.238172 | ||||||||
\(914\) | −24.5048 | −0.810546 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.05249 | −0.133898 | ||||||||
\(917\) | 39.5144 | 1.30488 | ||||||||
\(918\) | 3.52311 | 0.116280 | ||||||||
\(919\) | −13.2890 | −0.438365 | −0.219182 | − | 0.975684i | \(-0.570339\pi\) | ||||
−0.219182 | + | 0.975684i | \(0.570339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.23407 | 0.139517 | ||||||||
\(922\) | −18.2341 | −0.600507 | ||||||||
\(923\) | −32.0000 | −1.05329 | ||||||||
\(924\) | −1.72928 | −0.0568892 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.20617 | 0.138223 | ||||||||
\(927\) | 11.3169 | 0.371697 | ||||||||
\(928\) | 2.00000 | 0.0656532 | ||||||||
\(929\) | 41.1299 | 1.34943 | 0.674715 | − | 0.738078i | \(-0.264267\pi\) | ||||
0.674715 | + | 0.738078i | \(0.264267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.3511 | −0.798075 | ||||||||
\(932\) | −24.5327 | −0.803595 | ||||||||
\(933\) | −13.2803 | −0.434778 | ||||||||
\(934\) | −19.1912 | −0.627954 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.52311 | −0.180529 | ||||||||
\(937\) | 22.7755 | 0.744043 | 0.372022 | − | 0.928224i | \(-0.378665\pi\) | ||||
0.372022 | + | 0.928224i | \(0.378665\pi\) | |||||||
\(938\) | 11.8217 | 0.385993 | ||||||||
\(939\) | −31.9634 | −1.04308 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.7788 | −1.78574 | −0.892870 | − | 0.450315i | \(-0.851312\pi\) | ||||
−0.892870 | + | 0.450315i | \(0.851312\pi\) | |||||||
\(942\) | 14.6864 | 0.478508 | ||||||||
\(943\) | 3.52311 | 0.114728 | ||||||||
\(944\) | −10.9817 | −0.357423 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.981678 | 0.0319171 | ||||||||
\(947\) | −11.4094 | −0.370756 | −0.185378 | − | 0.982667i | \(-0.559351\pi\) | ||||
−0.185378 | + | 0.982667i | \(0.559351\pi\) | |||||||
\(948\) | −3.79383 | −0.123218 | ||||||||
\(949\) | 84.2407 | 2.73457 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.2803 | −0.430643 | ||||||||
\(952\) | 7.04623 | 0.228370 | ||||||||
\(953\) | −41.6714 | −1.34987 | −0.674934 | − | 0.737878i | \(-0.735828\pi\) | ||||
−0.674934 | + | 0.737878i | \(0.735828\pi\) | |||||||
\(954\) | −1.34153 | −0.0434335 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.7755 | 0.348505 | ||||||||
\(957\) | 1.72928 | 0.0558997 | ||||||||
\(958\) | 25.6801 | 0.829687 | ||||||||
\(959\) | 0.953771 | 0.0307989 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.4219 | −0.658772 | ||||||||
\(962\) | −28.3632 | −0.914465 | ||||||||
\(963\) | 5.64015 | 0.181751 | ||||||||
\(964\) | −10.7755 | −0.347056 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.00000 | −0.0643489 | ||||||||
\(967\) | −3.17533 | −0.102112 | −0.0510559 | − | 0.998696i | \(-0.516259\pi\) | ||||
−0.0510559 | + | 0.998696i | \(0.516259\pi\) | |||||||
\(968\) | 10.2524 | 0.329524 | ||||||||
\(969\) | −28.5972 | −0.918676 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −35.7326 | −1.14671 | −0.573357 | − | 0.819306i | \(-0.694359\pi\) | ||||
−0.573357 | + | 0.819306i | \(0.694359\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −6.91713 | −0.221753 | ||||||||
\(974\) | −8.74760 | −0.280291 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.91087 | −0.189202 | ||||||||
\(977\) | −2.02791 | −0.0648785 | −0.0324392 | − | 0.999474i | \(-0.510328\pi\) | ||||
−0.0324392 | + | 0.999474i | \(0.510328\pi\) | |||||||
\(978\) | 23.2803 | 0.744422 | ||||||||
\(979\) | −4.12910 | −0.131967 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1816 | −0.388928 | ||||||||
\(982\) | −23.8863 | −0.762242 | ||||||||
\(983\) | 1.67347 | 0.0533754 | 0.0266877 | − | 0.999644i | \(-0.491504\pi\) | ||||
0.0266877 | + | 0.999644i | \(0.491504\pi\) | |||||||
\(984\) | −3.52311 | −0.112313 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.04623 | −0.224398 | ||||||||
\(987\) | 11.0462 | 0.351605 | ||||||||
\(988\) | 44.8313 | 1.42627 | ||||||||
\(989\) | 1.13536 | 0.0361023 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.8496 | −1.77412 | −0.887061 | − | 0.461652i | \(-0.847257\pi\) | ||||
−0.887061 | + | 0.461652i | \(0.847257\pi\) | |||||||
\(992\) | 3.25240 | 0.103264 | ||||||||
\(993\) | −11.8217 | −0.375152 | ||||||||
\(994\) | 11.5877 | 0.367538 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.32320 | 0.263731 | ||||||||
\(997\) | −44.2062 | −1.40002 | −0.700012 | − | 0.714131i | \(-0.746822\pi\) | ||||
−0.700012 | + | 0.714131i | \(0.746822\pi\) | |||||||
\(998\) | −29.7293 | −0.941064 | ||||||||
\(999\) | 5.13536 | 0.162476 |
(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 | 3450.2.a.bq.1.2 | 3 | ||
5.2 | odd | 4 | 690.2.d.d.139.2 | ✓ | 6 | ||
5.3 | odd | 4 | 690.2.d.d.139.5 | yes | 6 | ||
5.4 | even | 2 | 3450.2.a.br.1.2 | 3 | |||
15.2 | even | 4 | 2070.2.d.d.829.5 | 6 | |||
15.8 | even | 4 | 2070.2.d.d.829.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.d.139.2 | ✓ | 6 | 5.2 | odd | 4 | ||
690.2.d.d.139.5 | yes | 6 | 5.3 | odd | 4 | ||
2070.2.d.d.829.2 | 6 | 15.8 | even | 4 | |||
2070.2.d.d.829.5 | 6 | 15.2 | even | 4 | |||
3450.2.a.bq.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3450.2.a.br.1.2 | 3 | 5.4 | even | 2 |