Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(89\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −2.96590 | −1.71236 | −0.856182 | − | 0.516674i | \(-0.827170\pi\) | ||||
−0.856182 | + | 0.516674i | \(0.827170\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.55325 | −1.58906 | −0.794531 | − | 0.607223i | \(-0.792283\pi\) | ||||
−0.794531 | + | 0.607223i | \(0.792283\pi\) | |||||||
\(6\) | 2.96590 | 1.21082 | ||||||||
\(7\) | 2.76315 | 1.04437 | 0.522186 | − | 0.852832i | \(-0.325117\pi\) | ||||
0.522186 | + | 0.852832i | \(0.325117\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 5.79657 | 1.93219 | ||||||||
\(10\) | 3.55325 | 1.12364 | ||||||||
\(11\) | 0.525847 | 0.158549 | 0.0792744 | − | 0.996853i | \(-0.474740\pi\) | ||||
0.0792744 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(12\) | −2.96590 | −0.856182 | ||||||||
\(13\) | 1.74773 | 0.484732 | 0.242366 | − | 0.970185i | \(-0.422077\pi\) | ||||
0.242366 | + | 0.970185i | \(0.422077\pi\) | |||||||
\(14\) | −2.76315 | −0.738482 | ||||||||
\(15\) | 10.5386 | 2.72105 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.404331 | 0.0980647 | 0.0490323 | − | 0.998797i | \(-0.484386\pi\) | ||||
0.0490323 | + | 0.998797i | \(0.484386\pi\) | |||||||
\(18\) | −5.79657 | −1.36627 | ||||||||
\(19\) | 6.67379 | 1.53107 | 0.765537 | − | 0.643392i | \(-0.222474\pi\) | ||||
0.765537 | + | 0.643392i | \(0.222474\pi\) | |||||||
\(20\) | −3.55325 | −0.794531 | ||||||||
\(21\) | −8.19522 | −1.78834 | ||||||||
\(22\) | −0.525847 | −0.112111 | ||||||||
\(23\) | −9.22100 | −1.92271 | −0.961356 | − | 0.275309i | \(-0.911220\pi\) | ||||
−0.961356 | + | 0.275309i | \(0.911220\pi\) | |||||||
\(24\) | 2.96590 | 0.605412 | ||||||||
\(25\) | 7.62560 | 1.52512 | ||||||||
\(26\) | −1.74773 | −0.342757 | ||||||||
\(27\) | −8.29436 | −1.59625 | ||||||||
\(28\) | 2.76315 | 0.522186 | ||||||||
\(29\) | 8.91123 | 1.65477 | 0.827387 | − | 0.561632i | \(-0.189826\pi\) | ||||
0.827387 | + | 0.561632i | \(0.189826\pi\) | |||||||
\(30\) | −10.5386 | −1.92408 | ||||||||
\(31\) | 0.930175 | 0.167064 | 0.0835322 | − | 0.996505i | \(-0.473380\pi\) | ||||
0.0835322 | + | 0.996505i | \(0.473380\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.55961 | −0.271493 | ||||||||
\(34\) | −0.404331 | −0.0693422 | ||||||||
\(35\) | −9.81816 | −1.65957 | ||||||||
\(36\) | 5.79657 | 0.966095 | ||||||||
\(37\) | −9.29553 | −1.52818 | −0.764088 | − | 0.645112i | \(-0.776811\pi\) | ||||
−0.764088 | + | 0.645112i | \(0.776811\pi\) | |||||||
\(38\) | −6.67379 | −1.08263 | ||||||||
\(39\) | −5.18358 | −0.830037 | ||||||||
\(40\) | 3.55325 | 0.561818 | ||||||||
\(41\) | −1.05461 | −0.164703 | −0.0823513 | − | 0.996603i | \(-0.526243\pi\) | ||||
−0.0823513 | + | 0.996603i | \(0.526243\pi\) | |||||||
\(42\) | 8.19522 | 1.26455 | ||||||||
\(43\) | −0.266653 | −0.0406641 | −0.0203321 | − | 0.999793i | \(-0.506472\pi\) | ||||
−0.0203321 | + | 0.999793i | \(0.506472\pi\) | |||||||
\(44\) | 0.525847 | 0.0792744 | ||||||||
\(45\) | −20.5967 | −3.07037 | ||||||||
\(46\) | 9.22100 | 1.35956 | ||||||||
\(47\) | −11.6624 | −1.70114 | −0.850571 | − | 0.525861i | \(-0.823743\pi\) | ||||
−0.850571 | + | 0.525861i | \(0.823743\pi\) | |||||||
\(48\) | −2.96590 | −0.428091 | ||||||||
\(49\) | 0.634983 | 0.0907118 | ||||||||
\(50\) | −7.62560 | −1.07842 | ||||||||
\(51\) | −1.19921 | −0.167922 | ||||||||
\(52\) | 1.74773 | 0.242366 | ||||||||
\(53\) | −11.3924 | −1.56486 | −0.782430 | − | 0.622739i | \(-0.786020\pi\) | ||||
−0.782430 | + | 0.622739i | \(0.786020\pi\) | |||||||
\(54\) | 8.29436 | 1.12872 | ||||||||
\(55\) | −1.86847 | −0.251944 | ||||||||
\(56\) | −2.76315 | −0.369241 | ||||||||
\(57\) | −19.7938 | −2.62176 | ||||||||
\(58\) | −8.91123 | −1.17010 | ||||||||
\(59\) | 2.58507 | 0.336548 | 0.168274 | − | 0.985740i | \(-0.446181\pi\) | ||||
0.168274 | + | 0.985740i | \(0.446181\pi\) | |||||||
\(60\) | 10.5386 | 1.36053 | ||||||||
\(61\) | 2.18120 | 0.279274 | 0.139637 | − | 0.990203i | \(-0.455406\pi\) | ||||
0.139637 | + | 0.990203i | \(0.455406\pi\) | |||||||
\(62\) | −0.930175 | −0.118132 | ||||||||
\(63\) | 16.0168 | 2.01792 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.21011 | −0.770269 | ||||||||
\(66\) | 1.55961 | 0.191975 | ||||||||
\(67\) | 10.0583 | 1.22882 | 0.614411 | − | 0.788986i | \(-0.289394\pi\) | ||||
0.614411 | + | 0.788986i | \(0.289394\pi\) | |||||||
\(68\) | 0.404331 | 0.0490323 | ||||||||
\(69\) | 27.3486 | 3.29238 | ||||||||
\(70\) | 9.81816 | 1.17349 | ||||||||
\(71\) | 12.2881 | 1.45832 | 0.729162 | − | 0.684341i | \(-0.239910\pi\) | ||||
0.729162 | + | 0.684341i | \(0.239910\pi\) | |||||||
\(72\) | −5.79657 | −0.683133 | ||||||||
\(73\) | 11.1510 | 1.30513 | 0.652564 | − | 0.757734i | \(-0.273693\pi\) | ||||
0.652564 | + | 0.757734i | \(0.273693\pi\) | |||||||
\(74\) | 9.29553 | 1.08058 | ||||||||
\(75\) | −22.6168 | −2.61156 | ||||||||
\(76\) | 6.67379 | 0.765537 | ||||||||
\(77\) | 1.45299 | 0.165584 | ||||||||
\(78\) | 5.18358 | 0.586925 | ||||||||
\(79\) | −11.9811 | −1.34797 | −0.673987 | − | 0.738743i | \(-0.735420\pi\) | ||||
−0.673987 | + | 0.738743i | \(0.735420\pi\) | |||||||
\(80\) | −3.55325 | −0.397266 | ||||||||
\(81\) | 7.21053 | 0.801170 | ||||||||
\(82\) | 1.05461 | 0.116462 | ||||||||
\(83\) | −6.06295 | −0.665495 | −0.332748 | − | 0.943016i | \(-0.607976\pi\) | ||||
−0.332748 | + | 0.943016i | \(0.607976\pi\) | |||||||
\(84\) | −8.19522 | −0.894172 | ||||||||
\(85\) | −1.43669 | −0.155831 | ||||||||
\(86\) | 0.266653 | 0.0287539 | ||||||||
\(87\) | −26.4298 | −2.83358 | ||||||||
\(88\) | −0.525847 | −0.0560555 | ||||||||
\(89\) | −16.8855 | −1.78986 | −0.894931 | − | 0.446205i | \(-0.852775\pi\) | ||||
−0.894931 | + | 0.446205i | \(0.852775\pi\) | |||||||
\(90\) | 20.5967 | 2.17108 | ||||||||
\(91\) | 4.82922 | 0.506240 | ||||||||
\(92\) | −9.22100 | −0.961356 | ||||||||
\(93\) | −2.75881 | −0.286075 | ||||||||
\(94\) | 11.6624 | 1.20289 | ||||||||
\(95\) | −23.7137 | −2.43297 | ||||||||
\(96\) | 2.96590 | 0.302706 | ||||||||
\(97\) | −7.78289 | −0.790233 | −0.395117 | − | 0.918631i | \(-0.629296\pi\) | ||||
−0.395117 | + | 0.918631i | \(0.629296\pi\) | |||||||
\(98\) | −0.634983 | −0.0641430 | ||||||||
\(99\) | 3.04811 | 0.306347 | ||||||||
\(100\) | 7.62560 | 0.762560 | ||||||||
\(101\) | 16.5848 | 1.65025 | 0.825125 | − | 0.564950i | \(-0.191104\pi\) | ||||
0.825125 | + | 0.564950i | \(0.191104\pi\) | |||||||
\(102\) | 1.19921 | 0.118739 | ||||||||
\(103\) | 9.35729 | 0.922001 | 0.461001 | − | 0.887400i | \(-0.347491\pi\) | ||||
0.461001 | + | 0.887400i | \(0.347491\pi\) | |||||||
\(104\) | −1.74773 | −0.171379 | ||||||||
\(105\) | 29.1197 | 2.84179 | ||||||||
\(106\) | 11.3924 | 1.10652 | ||||||||
\(107\) | −12.2662 | −1.18582 | −0.592912 | − | 0.805268i | \(-0.702022\pi\) | ||||
−0.592912 | + | 0.805268i | \(0.702022\pi\) | |||||||
\(108\) | −8.29436 | −0.798125 | ||||||||
\(109\) | 10.5900 | 1.01433 | 0.507167 | − | 0.861848i | \(-0.330693\pi\) | ||||
0.507167 | + | 0.861848i | \(0.330693\pi\) | |||||||
\(110\) | 1.86847 | 0.178151 | ||||||||
\(111\) | 27.5696 | 2.61679 | ||||||||
\(112\) | 2.76315 | 0.261093 | ||||||||
\(113\) | 17.3588 | 1.63298 | 0.816488 | − | 0.577362i | \(-0.195918\pi\) | ||||
0.816488 | + | 0.577362i | \(0.195918\pi\) | |||||||
\(114\) | 19.7938 | 1.85386 | ||||||||
\(115\) | 32.7645 | 3.05531 | ||||||||
\(116\) | 8.91123 | 0.827387 | ||||||||
\(117\) | 10.1308 | 0.936594 | ||||||||
\(118\) | −2.58507 | −0.237975 | ||||||||
\(119\) | 1.11723 | 0.102416 | ||||||||
\(120\) | −10.5386 | −0.962038 | ||||||||
\(121\) | −10.7235 | −0.974862 | ||||||||
\(122\) | −2.18120 | −0.197477 | ||||||||
\(123\) | 3.12787 | 0.282031 | ||||||||
\(124\) | 0.930175 | 0.0835322 | ||||||||
\(125\) | −9.32942 | −0.834448 | ||||||||
\(126\) | −16.0168 | −1.42689 | ||||||||
\(127\) | −10.8304 | −0.961046 | −0.480523 | − | 0.876982i | \(-0.659553\pi\) | ||||
−0.480523 | + | 0.876982i | \(0.659553\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.790865 | 0.0696318 | ||||||||
\(130\) | 6.21011 | 0.544663 | ||||||||
\(131\) | −4.60183 | −0.402064 | −0.201032 | − | 0.979585i | \(-0.564429\pi\) | ||||
−0.201032 | + | 0.979585i | \(0.564429\pi\) | |||||||
\(132\) | −1.55961 | −0.135747 | ||||||||
\(133\) | 18.4407 | 1.59901 | ||||||||
\(134\) | −10.0583 | −0.868909 | ||||||||
\(135\) | 29.4719 | 2.53654 | ||||||||
\(136\) | −0.404331 | −0.0346711 | ||||||||
\(137\) | 6.63810 | 0.567131 | 0.283566 | − | 0.958953i | \(-0.408483\pi\) | ||||
0.283566 | + | 0.958953i | \(0.408483\pi\) | |||||||
\(138\) | −27.3486 | −2.32807 | ||||||||
\(139\) | −8.64286 | −0.733078 | −0.366539 | − | 0.930403i | \(-0.619457\pi\) | ||||
−0.366539 | + | 0.930403i | \(0.619457\pi\) | |||||||
\(140\) | −9.81816 | −0.829786 | ||||||||
\(141\) | 34.5896 | 2.91297 | ||||||||
\(142\) | −12.2881 | −1.03119 | ||||||||
\(143\) | 0.919036 | 0.0768537 | ||||||||
\(144\) | 5.79657 | 0.483048 | ||||||||
\(145\) | −31.6639 | −2.62954 | ||||||||
\(146\) | −11.1510 | −0.922865 | ||||||||
\(147\) | −1.88330 | −0.155332 | ||||||||
\(148\) | −9.29553 | −0.764088 | ||||||||
\(149\) | 8.43034 | 0.690640 | 0.345320 | − | 0.938485i | \(-0.387770\pi\) | ||||
0.345320 | + | 0.938485i | \(0.387770\pi\) | |||||||
\(150\) | 22.6168 | 1.84665 | ||||||||
\(151\) | 6.86075 | 0.558320 | 0.279160 | − | 0.960245i | \(-0.409944\pi\) | ||||
0.279160 | + | 0.960245i | \(0.409944\pi\) | |||||||
\(152\) | −6.67379 | −0.541316 | ||||||||
\(153\) | 2.34373 | 0.189480 | ||||||||
\(154\) | −1.45299 | −0.117086 | ||||||||
\(155\) | −3.30514 | −0.265476 | ||||||||
\(156\) | −5.18358 | −0.415019 | ||||||||
\(157\) | −3.40902 | −0.272070 | −0.136035 | − | 0.990704i | \(-0.543436\pi\) | ||||
−0.136035 | + | 0.990704i | \(0.543436\pi\) | |||||||
\(158\) | 11.9811 | 0.953162 | ||||||||
\(159\) | 33.7886 | 2.67961 | ||||||||
\(160\) | 3.55325 | 0.280909 | ||||||||
\(161\) | −25.4790 | −2.00802 | ||||||||
\(162\) | −7.21053 | −0.566513 | ||||||||
\(163\) | 8.29841 | 0.649982 | 0.324991 | − | 0.945717i | \(-0.394639\pi\) | ||||
0.324991 | + | 0.945717i | \(0.394639\pi\) | |||||||
\(164\) | −1.05461 | −0.0823513 | ||||||||
\(165\) | 5.54169 | 0.431420 | ||||||||
\(166\) | 6.06295 | 0.470576 | ||||||||
\(167\) | −8.46894 | −0.655346 | −0.327673 | − | 0.944791i | \(-0.606264\pi\) | ||||
−0.327673 | + | 0.944791i | \(0.606264\pi\) | |||||||
\(168\) | 8.19522 | 0.632275 | ||||||||
\(169\) | −9.94546 | −0.765035 | ||||||||
\(170\) | 1.43669 | 0.110189 | ||||||||
\(171\) | 38.6851 | 2.95833 | ||||||||
\(172\) | −0.266653 | −0.0203321 | ||||||||
\(173\) | −17.5748 | −1.33619 | −0.668094 | − | 0.744077i | \(-0.732889\pi\) | ||||
−0.668094 | + | 0.744077i | \(0.732889\pi\) | |||||||
\(174\) | 26.4298 | 2.00364 | ||||||||
\(175\) | 21.0707 | 1.59279 | ||||||||
\(176\) | 0.525847 | 0.0396372 | ||||||||
\(177\) | −7.66707 | −0.576293 | ||||||||
\(178\) | 16.8855 | 1.26562 | ||||||||
\(179\) | 16.6868 | 1.24723 | 0.623614 | − | 0.781732i | \(-0.285664\pi\) | ||||
0.623614 | + | 0.781732i | \(0.285664\pi\) | |||||||
\(180\) | −20.5967 | −1.53519 | ||||||||
\(181\) | −21.7269 | −1.61495 | −0.807473 | − | 0.589904i | \(-0.799166\pi\) | ||||
−0.807473 | + | 0.589904i | \(0.799166\pi\) | |||||||
\(182\) | −4.82922 | −0.357966 | ||||||||
\(183\) | −6.46923 | −0.478219 | ||||||||
\(184\) | 9.22100 | 0.679781 | ||||||||
\(185\) | 33.0294 | 2.42837 | ||||||||
\(186\) | 2.75881 | 0.202286 | ||||||||
\(187\) | 0.212616 | 0.0155480 | ||||||||
\(188\) | −11.6624 | −0.850571 | ||||||||
\(189\) | −22.9185 | −1.66708 | ||||||||
\(190\) | 23.7137 | 1.72037 | ||||||||
\(191\) | 13.3276 | 0.964350 | 0.482175 | − | 0.876075i | \(-0.339847\pi\) | ||||
0.482175 | + | 0.876075i | \(0.339847\pi\) | |||||||
\(192\) | −2.96590 | −0.214046 | ||||||||
\(193\) | −6.42123 | −0.462210 | −0.231105 | − | 0.972929i | \(-0.574234\pi\) | ||||
−0.231105 | + | 0.972929i | \(0.574234\pi\) | |||||||
\(194\) | 7.78289 | 0.558779 | ||||||||
\(195\) | 18.4186 | 1.31898 | ||||||||
\(196\) | 0.634983 | 0.0453559 | ||||||||
\(197\) | 12.8234 | 0.913630 | 0.456815 | − | 0.889562i | \(-0.348990\pi\) | ||||
0.456815 | + | 0.889562i | \(0.348990\pi\) | |||||||
\(198\) | −3.04811 | −0.216620 | ||||||||
\(199\) | 16.3445 | 1.15863 | 0.579315 | − | 0.815104i | \(-0.303320\pi\) | ||||
0.579315 | + | 0.815104i | \(0.303320\pi\) | |||||||
\(200\) | −7.62560 | −0.539211 | ||||||||
\(201\) | −29.8321 | −2.10419 | ||||||||
\(202\) | −16.5848 | −1.16690 | ||||||||
\(203\) | 24.6231 | 1.72820 | ||||||||
\(204\) | −1.19921 | −0.0839612 | ||||||||
\(205\) | 3.74730 | 0.261723 | ||||||||
\(206\) | −9.35729 | −0.651953 | ||||||||
\(207\) | −53.4502 | −3.71505 | ||||||||
\(208\) | 1.74773 | 0.121183 | ||||||||
\(209\) | 3.50940 | 0.242750 | ||||||||
\(210\) | −29.1197 | −2.00945 | ||||||||
\(211\) | 9.74762 | 0.671054 | 0.335527 | − | 0.942031i | \(-0.391086\pi\) | ||||
0.335527 | + | 0.942031i | \(0.391086\pi\) | |||||||
\(212\) | −11.3924 | −0.782430 | ||||||||
\(213\) | −36.4452 | −2.49718 | ||||||||
\(214\) | 12.2662 | 0.838504 | ||||||||
\(215\) | 0.947484 | 0.0646178 | ||||||||
\(216\) | 8.29436 | 0.564360 | ||||||||
\(217\) | 2.57021 | 0.174477 | ||||||||
\(218\) | −10.5900 | −0.717242 | ||||||||
\(219\) | −33.0728 | −2.23485 | ||||||||
\(220\) | −1.86847 | −0.125972 | ||||||||
\(221\) | 0.706660 | 0.0475351 | ||||||||
\(222\) | −27.5696 | −1.85035 | ||||||||
\(223\) | 23.4967 | 1.57345 | 0.786726 | − | 0.617302i | \(-0.211774\pi\) | ||||
0.786726 | + | 0.617302i | \(0.211774\pi\) | |||||||
\(224\) | −2.76315 | −0.184621 | ||||||||
\(225\) | 44.2023 | 2.94682 | ||||||||
\(226\) | −17.3588 | −1.15469 | ||||||||
\(227\) | −15.5615 | −1.03285 | −0.516427 | − | 0.856331i | \(-0.672738\pi\) | ||||
−0.516427 | + | 0.856331i | \(0.672738\pi\) | |||||||
\(228\) | −19.7938 | −1.31088 | ||||||||
\(229\) | 14.5342 | 0.960446 | 0.480223 | − | 0.877147i | \(-0.340556\pi\) | ||||
0.480223 | + | 0.877147i | \(0.340556\pi\) | |||||||
\(230\) | −32.7645 | −2.16043 | ||||||||
\(231\) | −4.30943 | −0.283540 | ||||||||
\(232\) | −8.91123 | −0.585051 | ||||||||
\(233\) | −9.69239 | −0.634970 | −0.317485 | − | 0.948263i | \(-0.602838\pi\) | ||||
−0.317485 | + | 0.948263i | \(0.602838\pi\) | |||||||
\(234\) | −10.1308 | −0.662272 | ||||||||
\(235\) | 41.4396 | 2.70322 | ||||||||
\(236\) | 2.58507 | 0.168274 | ||||||||
\(237\) | 35.5347 | 2.30822 | ||||||||
\(238\) | −1.11723 | −0.0724190 | ||||||||
\(239\) | −20.6560 | −1.33613 | −0.668064 | − | 0.744104i | \(-0.732877\pi\) | ||||
−0.668064 | + | 0.744104i | \(0.732877\pi\) | |||||||
\(240\) | 10.5386 | 0.680263 | ||||||||
\(241\) | −19.0386 | −1.22638 | −0.613192 | − | 0.789934i | \(-0.710115\pi\) | ||||
−0.613192 | + | 0.789934i | \(0.710115\pi\) | |||||||
\(242\) | 10.7235 | 0.689332 | ||||||||
\(243\) | 3.49734 | 0.224355 | ||||||||
\(244\) | 2.18120 | 0.139637 | ||||||||
\(245\) | −2.25625 | −0.144147 | ||||||||
\(246\) | −3.12787 | −0.199426 | ||||||||
\(247\) | 11.6640 | 0.742160 | ||||||||
\(248\) | −0.930175 | −0.0590662 | ||||||||
\(249\) | 17.9821 | 1.13957 | ||||||||
\(250\) | 9.32942 | 0.590044 | ||||||||
\(251\) | 20.4574 | 1.29126 | 0.645629 | − | 0.763651i | \(-0.276595\pi\) | ||||
0.645629 | + | 0.763651i | \(0.276595\pi\) | |||||||
\(252\) | 16.0168 | 1.00896 | ||||||||
\(253\) | −4.84884 | −0.304844 | ||||||||
\(254\) | 10.8304 | 0.679562 | ||||||||
\(255\) | 4.26108 | 0.266839 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 30.5506 | 1.90570 | 0.952848 | − | 0.303447i | \(-0.0981377\pi\) | ||||
0.952848 | + | 0.303447i | \(0.0981377\pi\) | |||||||
\(258\) | −0.790865 | −0.0492371 | ||||||||
\(259\) | −25.6849 | −1.59598 | ||||||||
\(260\) | −6.21011 | −0.385135 | ||||||||
\(261\) | 51.6546 | 3.19734 | ||||||||
\(262\) | 4.60183 | 0.284302 | ||||||||
\(263\) | 13.1452 | 0.810571 | 0.405285 | − | 0.914190i | \(-0.367172\pi\) | ||||
0.405285 | + | 0.914190i | \(0.367172\pi\) | |||||||
\(264\) | 1.55961 | 0.0959874 | ||||||||
\(265\) | 40.4799 | 2.48666 | ||||||||
\(266\) | −18.4407 | −1.13067 | ||||||||
\(267\) | 50.0808 | 3.06489 | ||||||||
\(268\) | 10.0583 | 0.614411 | ||||||||
\(269\) | 2.18874 | 0.133450 | 0.0667248 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667248 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(270\) | −29.4719 | −1.79361 | ||||||||
\(271\) | 3.13707 | 0.190563 | 0.0952817 | − | 0.995450i | \(-0.469625\pi\) | ||||
0.0952817 | + | 0.995450i | \(0.469625\pi\) | |||||||
\(272\) | 0.404331 | 0.0245162 | ||||||||
\(273\) | −14.3230 | −0.866867 | ||||||||
\(274\) | −6.63810 | −0.401022 | ||||||||
\(275\) | 4.00990 | 0.241806 | ||||||||
\(276\) | 27.3486 | 1.64619 | ||||||||
\(277\) | 21.6799 | 1.30262 | 0.651309 | − | 0.758812i | \(-0.274220\pi\) | ||||
0.651309 | + | 0.758812i | \(0.274220\pi\) | |||||||
\(278\) | 8.64286 | 0.518364 | ||||||||
\(279\) | 5.39182 | 0.322800 | ||||||||
\(280\) | 9.81816 | 0.586747 | ||||||||
\(281\) | 4.47708 | 0.267080 | 0.133540 | − | 0.991043i | \(-0.457365\pi\) | ||||
0.133540 | + | 0.991043i | \(0.457365\pi\) | |||||||
\(282\) | −34.5896 | −2.05978 | ||||||||
\(283\) | −30.2162 | −1.79616 | −0.898082 | − | 0.439827i | \(-0.855040\pi\) | ||||
−0.898082 | + | 0.439827i | \(0.855040\pi\) | |||||||
\(284\) | 12.2881 | 0.729162 | ||||||||
\(285\) | 70.3324 | 4.16613 | ||||||||
\(286\) | −0.919036 | −0.0543438 | ||||||||
\(287\) | −2.91404 | −0.172011 | ||||||||
\(288\) | −5.79657 | −0.341566 | ||||||||
\(289\) | −16.8365 | −0.990383 | ||||||||
\(290\) | 31.6639 | 1.85937 | ||||||||
\(291\) | 23.0833 | 1.35317 | ||||||||
\(292\) | 11.1510 | 0.652564 | ||||||||
\(293\) | −23.6619 | −1.38234 | −0.691171 | − | 0.722691i | \(-0.742905\pi\) | ||||
−0.691171 | + | 0.722691i | \(0.742905\pi\) | |||||||
\(294\) | 1.88330 | 0.109836 | ||||||||
\(295\) | −9.18542 | −0.534796 | ||||||||
\(296\) | 9.29553 | 0.540292 | ||||||||
\(297\) | −4.36156 | −0.253084 | ||||||||
\(298\) | −8.43034 | −0.488356 | ||||||||
\(299\) | −16.1158 | −0.931999 | ||||||||
\(300\) | −22.6168 | −1.30578 | ||||||||
\(301\) | −0.736800 | −0.0424685 | ||||||||
\(302\) | −6.86075 | −0.394792 | ||||||||
\(303\) | −49.1889 | −2.82583 | ||||||||
\(304\) | 6.67379 | 0.382768 | ||||||||
\(305\) | −7.75036 | −0.443784 | ||||||||
\(306\) | −2.34373 | −0.133982 | ||||||||
\(307\) | 21.4101 | 1.22194 | 0.610968 | − | 0.791655i | \(-0.290780\pi\) | ||||
0.610968 | + | 0.791655i | \(0.290780\pi\) | |||||||
\(308\) | 1.45299 | 0.0827920 | ||||||||
\(309\) | −27.7528 | −1.57880 | ||||||||
\(310\) | 3.30514 | 0.187720 | ||||||||
\(311\) | −28.4872 | −1.61536 | −0.807680 | − | 0.589622i | \(-0.799277\pi\) | ||||
−0.807680 | + | 0.589622i | \(0.799277\pi\) | |||||||
\(312\) | 5.18358 | 0.293462 | ||||||||
\(313\) | −15.6149 | −0.882605 | −0.441303 | − | 0.897358i | \(-0.645483\pi\) | ||||
−0.441303 | + | 0.897358i | \(0.645483\pi\) | |||||||
\(314\) | 3.40902 | 0.192382 | ||||||||
\(315\) | −56.9117 | −3.20661 | ||||||||
\(316\) | −11.9811 | −0.673987 | ||||||||
\(317\) | 19.5055 | 1.09554 | 0.547769 | − | 0.836629i | \(-0.315477\pi\) | ||||
0.547769 | + | 0.836629i | \(0.315477\pi\) | |||||||
\(318\) | −33.7886 | −1.89477 | ||||||||
\(319\) | 4.68595 | 0.262363 | ||||||||
\(320\) | −3.55325 | −0.198633 | ||||||||
\(321\) | 36.3805 | 2.03056 | ||||||||
\(322\) | 25.4790 | 1.41989 | ||||||||
\(323\) | 2.69842 | 0.150144 | ||||||||
\(324\) | 7.21053 | 0.400585 | ||||||||
\(325\) | 13.3275 | 0.739274 | ||||||||
\(326\) | −8.29841 | −0.459607 | ||||||||
\(327\) | −31.4087 | −1.73691 | ||||||||
\(328\) | 1.05461 | 0.0582311 | ||||||||
\(329\) | −32.2250 | −1.77662 | ||||||||
\(330\) | −5.54169 | −0.305060 | ||||||||
\(331\) | 23.6814 | 1.30165 | 0.650823 | − | 0.759229i | \(-0.274424\pi\) | ||||
0.650823 | + | 0.759229i | \(0.274424\pi\) | |||||||
\(332\) | −6.06295 | −0.332748 | ||||||||
\(333\) | −53.8822 | −2.95273 | ||||||||
\(334\) | 8.46894 | 0.463400 | ||||||||
\(335\) | −35.7398 | −1.95268 | ||||||||
\(336\) | −8.19522 | −0.447086 | ||||||||
\(337\) | 11.9124 | 0.648910 | 0.324455 | − | 0.945901i | \(-0.394819\pi\) | ||||
0.324455 | + | 0.945901i | \(0.394819\pi\) | |||||||
\(338\) | 9.94546 | 0.540962 | ||||||||
\(339\) | −51.4844 | −2.79625 | ||||||||
\(340\) | −1.43669 | −0.0779155 | ||||||||
\(341\) | 0.489130 | 0.0264879 | ||||||||
\(342\) | −38.6851 | −2.09185 | ||||||||
\(343\) | −17.5875 | −0.949635 | ||||||||
\(344\) | 0.266653 | 0.0143769 | ||||||||
\(345\) | −97.1764 | −5.23180 | ||||||||
\(346\) | 17.5748 | 0.944827 | ||||||||
\(347\) | 11.1351 | 0.597762 | 0.298881 | − | 0.954290i | \(-0.403387\pi\) | ||||
0.298881 | + | 0.954290i | \(0.403387\pi\) | |||||||
\(348\) | −26.4298 | −1.41679 | ||||||||
\(349\) | −29.6691 | −1.58815 | −0.794075 | − | 0.607819i | \(-0.792044\pi\) | ||||
−0.794075 | + | 0.607819i | \(0.792044\pi\) | |||||||
\(350\) | −21.0707 | −1.12627 | ||||||||
\(351\) | −14.4963 | −0.773753 | ||||||||
\(352\) | −0.525847 | −0.0280277 | ||||||||
\(353\) | 33.4239 | 1.77897 | 0.889487 | − | 0.456961i | \(-0.151062\pi\) | ||||
0.889487 | + | 0.456961i | \(0.151062\pi\) | |||||||
\(354\) | 7.66707 | 0.407500 | ||||||||
\(355\) | −43.6625 | −2.31737 | ||||||||
\(356\) | −16.8855 | −0.894931 | ||||||||
\(357\) | −3.31358 | −0.175373 | ||||||||
\(358\) | −16.6868 | −0.881924 | ||||||||
\(359\) | −12.3282 | −0.650659 | −0.325329 | − | 0.945601i | \(-0.605475\pi\) | ||||
−0.325329 | + | 0.945601i | \(0.605475\pi\) | |||||||
\(360\) | 20.5967 | 1.08554 | ||||||||
\(361\) | 25.5395 | 1.34419 | ||||||||
\(362\) | 21.7269 | 1.14194 | ||||||||
\(363\) | 31.8048 | 1.66932 | ||||||||
\(364\) | 4.82922 | 0.253120 | ||||||||
\(365\) | −39.6224 | −2.07393 | ||||||||
\(366\) | 6.46923 | 0.338152 | ||||||||
\(367\) | −12.9043 | −0.673598 | −0.336799 | − | 0.941577i | \(-0.609344\pi\) | ||||
−0.336799 | + | 0.941577i | \(0.609344\pi\) | |||||||
\(368\) | −9.22100 | −0.480678 | ||||||||
\(369\) | −6.11313 | −0.318237 | ||||||||
\(370\) | −33.0294 | −1.71712 | ||||||||
\(371\) | −31.4787 | −1.63430 | ||||||||
\(372\) | −2.75881 | −0.143037 | ||||||||
\(373\) | 21.1322 | 1.09418 | 0.547092 | − | 0.837072i | \(-0.315735\pi\) | ||||
0.547092 | + | 0.837072i | \(0.315735\pi\) | |||||||
\(374\) | −0.212616 | −0.0109941 | ||||||||
\(375\) | 27.6701 | 1.42888 | ||||||||
\(376\) | 11.6624 | 0.601444 | ||||||||
\(377\) | 15.5744 | 0.802122 | ||||||||
\(378\) | 22.9185 | 1.17880 | ||||||||
\(379\) | −23.5472 | −1.20954 | −0.604770 | − | 0.796400i | \(-0.706735\pi\) | ||||
−0.604770 | + | 0.796400i | \(0.706735\pi\) | |||||||
\(380\) | −23.7137 | −1.21649 | ||||||||
\(381\) | 32.1220 | 1.64566 | ||||||||
\(382\) | −13.3276 | −0.681898 | ||||||||
\(383\) | −31.1585 | −1.59212 | −0.796062 | − | 0.605215i | \(-0.793087\pi\) | ||||
−0.796062 | + | 0.605215i | \(0.793087\pi\) | |||||||
\(384\) | 2.96590 | 0.151353 | ||||||||
\(385\) | −5.16285 | −0.263123 | ||||||||
\(386\) | 6.42123 | 0.326832 | ||||||||
\(387\) | −1.54567 | −0.0785708 | ||||||||
\(388\) | −7.78289 | −0.395117 | ||||||||
\(389\) | −15.5165 | −0.786720 | −0.393360 | − | 0.919385i | \(-0.628687\pi\) | ||||
−0.393360 | + | 0.919385i | \(0.628687\pi\) | |||||||
\(390\) | −18.4186 | −0.932661 | ||||||||
\(391\) | −3.72834 | −0.188550 | ||||||||
\(392\) | −0.634983 | −0.0320715 | ||||||||
\(393\) | 13.6486 | 0.688480 | ||||||||
\(394\) | −12.8234 | −0.646034 | ||||||||
\(395\) | 42.5717 | 2.14202 | ||||||||
\(396\) | 3.04811 | 0.153173 | ||||||||
\(397\) | 8.60718 | 0.431982 | 0.215991 | − | 0.976395i | \(-0.430702\pi\) | ||||
0.215991 | + | 0.976395i | \(0.430702\pi\) | |||||||
\(398\) | −16.3445 | −0.819275 | ||||||||
\(399\) | −54.6932 | −2.73809 | ||||||||
\(400\) | 7.62560 | 0.381280 | ||||||||
\(401\) | −6.41977 | −0.320588 | −0.160294 | − | 0.987069i | \(-0.551244\pi\) | ||||
−0.160294 | + | 0.987069i | \(0.551244\pi\) | |||||||
\(402\) | 29.8321 | 1.48789 | ||||||||
\(403\) | 1.62569 | 0.0809814 | ||||||||
\(404\) | 16.5848 | 0.825125 | ||||||||
\(405\) | −25.6208 | −1.27311 | ||||||||
\(406\) | −24.6231 | −1.22202 | ||||||||
\(407\) | −4.88803 | −0.242291 | ||||||||
\(408\) | 1.19921 | 0.0593696 | ||||||||
\(409\) | −26.7924 | −1.32480 | −0.662399 | − | 0.749151i | \(-0.730462\pi\) | ||||
−0.662399 | + | 0.749151i | \(0.730462\pi\) | |||||||
\(410\) | −3.74730 | −0.185066 | ||||||||
\(411\) | −19.6879 | −0.971135 | ||||||||
\(412\) | 9.35729 | 0.461001 | ||||||||
\(413\) | 7.14294 | 0.351481 | ||||||||
\(414\) | 53.4502 | 2.62693 | ||||||||
\(415\) | 21.5432 | 1.05751 | ||||||||
\(416\) | −1.74773 | −0.0856893 | ||||||||
\(417\) | 25.6339 | 1.25530 | ||||||||
\(418\) | −3.50940 | −0.171650 | ||||||||
\(419\) | 2.70657 | 0.132225 | 0.0661123 | − | 0.997812i | \(-0.478940\pi\) | ||||
0.0661123 | + | 0.997812i | \(0.478940\pi\) | |||||||
\(420\) | 29.1197 | 1.42090 | ||||||||
\(421\) | −33.3581 | −1.62577 | −0.812886 | − | 0.582423i | \(-0.802105\pi\) | ||||
−0.812886 | + | 0.582423i | \(0.802105\pi\) | |||||||
\(422\) | −9.74762 | −0.474507 | ||||||||
\(423\) | −67.6022 | −3.28693 | ||||||||
\(424\) | 11.3924 | 0.553262 | ||||||||
\(425\) | 3.08327 | 0.149560 | ||||||||
\(426\) | 36.4452 | 1.76577 | ||||||||
\(427\) | 6.02698 | 0.291666 | ||||||||
\(428\) | −12.2662 | −0.592912 | ||||||||
\(429\) | −2.72577 | −0.131601 | ||||||||
\(430\) | −0.947484 | −0.0456917 | ||||||||
\(431\) | 4.33168 | 0.208650 | 0.104325 | − | 0.994543i | \(-0.466732\pi\) | ||||
0.104325 | + | 0.994543i | \(0.466732\pi\) | |||||||
\(432\) | −8.29436 | −0.399062 | ||||||||
\(433\) | 15.5145 | 0.745578 | 0.372789 | − | 0.927916i | \(-0.378402\pi\) | ||||
0.372789 | + | 0.927916i | \(0.378402\pi\) | |||||||
\(434\) | −2.57021 | −0.123374 | ||||||||
\(435\) | 93.9119 | 4.50273 | ||||||||
\(436\) | 10.5900 | 0.507167 | ||||||||
\(437\) | −61.5391 | −2.94381 | ||||||||
\(438\) | 33.0728 | 1.58028 | ||||||||
\(439\) | −11.2187 | −0.535440 | −0.267720 | − | 0.963497i | \(-0.586270\pi\) | ||||
−0.267720 | + | 0.963497i | \(0.586270\pi\) | |||||||
\(440\) | 1.86847 | 0.0890757 | ||||||||
\(441\) | 3.68072 | 0.175273 | ||||||||
\(442\) | −0.706660 | −0.0336124 | ||||||||
\(443\) | 8.86735 | 0.421300 | 0.210650 | − | 0.977562i | \(-0.432442\pi\) | ||||
0.210650 | + | 0.977562i | \(0.432442\pi\) | |||||||
\(444\) | 27.5696 | 1.30840 | ||||||||
\(445\) | 59.9985 | 2.84420 | ||||||||
\(446\) | −23.4967 | −1.11260 | ||||||||
\(447\) | −25.0035 | −1.18263 | ||||||||
\(448\) | 2.76315 | 0.130546 | ||||||||
\(449\) | −14.5144 | −0.684976 | −0.342488 | − | 0.939522i | \(-0.611270\pi\) | ||||
−0.342488 | + | 0.939522i | \(0.611270\pi\) | |||||||
\(450\) | −44.2023 | −2.08372 | ||||||||
\(451\) | −0.554564 | −0.0261134 | ||||||||
\(452\) | 17.3588 | 0.816488 | ||||||||
\(453\) | −20.3483 | −0.956047 | ||||||||
\(454\) | 15.5615 | 0.730338 | ||||||||
\(455\) | −17.1594 | −0.804447 | ||||||||
\(456\) | 19.7938 | 0.926930 | ||||||||
\(457\) | 25.0221 | 1.17048 | 0.585242 | − | 0.810859i | \(-0.301000\pi\) | ||||
0.585242 | + | 0.810859i | \(0.301000\pi\) | |||||||
\(458\) | −14.5342 | −0.679138 | ||||||||
\(459\) | −3.35367 | −0.156536 | ||||||||
\(460\) | 32.7645 | 1.52765 | ||||||||
\(461\) | 19.7791 | 0.921203 | 0.460602 | − | 0.887607i | \(-0.347634\pi\) | ||||
0.460602 | + | 0.887607i | \(0.347634\pi\) | |||||||
\(462\) | 4.30943 | 0.200493 | ||||||||
\(463\) | −29.3979 | −1.36623 | −0.683117 | − | 0.730309i | \(-0.739376\pi\) | ||||
−0.683117 | + | 0.730309i | \(0.739376\pi\) | |||||||
\(464\) | 8.91123 | 0.413694 | ||||||||
\(465\) | 9.80273 | 0.454591 | ||||||||
\(466\) | 9.69239 | 0.448991 | ||||||||
\(467\) | −7.21932 | −0.334070 | −0.167035 | − | 0.985951i | \(-0.553419\pi\) | ||||
−0.167035 | + | 0.985951i | \(0.553419\pi\) | |||||||
\(468\) | 10.1308 | 0.468297 | ||||||||
\(469\) | 27.7927 | 1.28335 | ||||||||
\(470\) | −41.4396 | −1.91147 | ||||||||
\(471\) | 10.1108 | 0.465883 | ||||||||
\(472\) | −2.58507 | −0.118988 | ||||||||
\(473\) | −0.140218 | −0.00644725 | ||||||||
\(474\) | −35.5347 | −1.63216 | ||||||||
\(475\) | 50.8917 | 2.33507 | ||||||||
\(476\) | 1.11723 | 0.0512080 | ||||||||
\(477\) | −66.0366 | −3.02361 | ||||||||
\(478\) | 20.6560 | 0.944785 | ||||||||
\(479\) | −40.0520 | −1.83002 | −0.915011 | − | 0.403428i | \(-0.867819\pi\) | ||||
−0.915011 | + | 0.403428i | \(0.867819\pi\) | |||||||
\(480\) | −10.5386 | −0.481019 | ||||||||
\(481\) | −16.2460 | −0.740756 | ||||||||
\(482\) | 19.0386 | 0.867185 | ||||||||
\(483\) | 75.5681 | 3.43847 | ||||||||
\(484\) | −10.7235 | −0.487431 | ||||||||
\(485\) | 27.6546 | 1.25573 | ||||||||
\(486\) | −3.49734 | −0.158643 | ||||||||
\(487\) | −12.1659 | −0.551288 | −0.275644 | − | 0.961260i | \(-0.588891\pi\) | ||||
−0.275644 | + | 0.961260i | \(0.588891\pi\) | |||||||
\(488\) | −2.18120 | −0.0987384 | ||||||||
\(489\) | −24.6123 | −1.11301 | ||||||||
\(490\) | 2.25625 | 0.101927 | ||||||||
\(491\) | −8.63426 | −0.389659 | −0.194829 | − | 0.980837i | \(-0.562415\pi\) | ||||
−0.194829 | + | 0.980837i | \(0.562415\pi\) | |||||||
\(492\) | 3.12787 | 0.141015 | ||||||||
\(493\) | 3.60309 | 0.162275 | ||||||||
\(494\) | −11.6640 | −0.524786 | ||||||||
\(495\) | −10.8307 | −0.486804 | ||||||||
\(496\) | 0.930175 | 0.0417661 | ||||||||
\(497\) | 33.9537 | 1.52303 | ||||||||
\(498\) | −17.9821 | −0.805798 | ||||||||
\(499\) | 17.1640 | 0.768367 | 0.384184 | − | 0.923257i | \(-0.374483\pi\) | ||||
0.384184 | + | 0.923257i | \(0.374483\pi\) | |||||||
\(500\) | −9.32942 | −0.417224 | ||||||||
\(501\) | 25.1180 | 1.12219 | ||||||||
\(502\) | −20.4574 | −0.913057 | ||||||||
\(503\) | −8.05769 | −0.359274 | −0.179637 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179637 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(504\) | −16.0168 | −0.713444 | ||||||||
\(505\) | −58.9300 | −2.62235 | ||||||||
\(506\) | 4.84884 | 0.215557 | ||||||||
\(507\) | 29.4972 | 1.31002 | ||||||||
\(508\) | −10.8304 | −0.480523 | ||||||||
\(509\) | 41.6844 | 1.84763 | 0.923814 | − | 0.382841i | \(-0.125054\pi\) | ||||
0.923814 | + | 0.382841i | \(0.125054\pi\) | |||||||
\(510\) | −4.26108 | −0.188684 | ||||||||
\(511\) | 30.8119 | 1.36304 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −55.3548 | −2.44398 | ||||||||
\(514\) | −30.5506 | −1.34753 | ||||||||
\(515\) | −33.2488 | −1.46512 | ||||||||
\(516\) | 0.790865 | 0.0348159 | ||||||||
\(517\) | −6.13266 | −0.269714 | ||||||||
\(518\) | 25.6849 | 1.12853 | ||||||||
\(519\) | 52.1251 | 2.28804 | ||||||||
\(520\) | 6.21011 | 0.272331 | ||||||||
\(521\) | −10.7712 | −0.471894 | −0.235947 | − | 0.971766i | \(-0.575819\pi\) | ||||
−0.235947 | + | 0.971766i | \(0.575819\pi\) | |||||||
\(522\) | −51.6546 | −2.26086 | ||||||||
\(523\) | −37.5747 | −1.64303 | −0.821513 | − | 0.570189i | \(-0.806870\pi\) | ||||
−0.821513 | + | 0.570189i | \(0.806870\pi\) | |||||||
\(524\) | −4.60183 | −0.201032 | ||||||||
\(525\) | −62.4935 | −2.72744 | ||||||||
\(526\) | −13.1452 | −0.573160 | ||||||||
\(527\) | 0.376099 | 0.0163831 | ||||||||
\(528\) | −1.55961 | −0.0678734 | ||||||||
\(529\) | 62.0268 | 2.69682 | ||||||||
\(530\) | −40.4799 | −1.75833 | ||||||||
\(531\) | 14.9846 | 0.650275 | ||||||||
\(532\) | 18.4407 | 0.799505 | ||||||||
\(533\) | −1.84317 | −0.0798365 | ||||||||
\(534\) | −50.0808 | −2.16721 | ||||||||
\(535\) | 43.5851 | 1.88435 | ||||||||
\(536\) | −10.0583 | −0.434454 | ||||||||
\(537\) | −49.4914 | −2.13571 | ||||||||
\(538\) | −2.18874 | −0.0943631 | ||||||||
\(539\) | 0.333904 | 0.0143823 | ||||||||
\(540\) | 29.4719 | 1.26827 | ||||||||
\(541\) | −14.1269 | −0.607363 | −0.303681 | − | 0.952774i | \(-0.598216\pi\) | ||||
−0.303681 | + | 0.952774i | \(0.598216\pi\) | |||||||
\(542\) | −3.13707 | −0.134749 | ||||||||
\(543\) | 64.4398 | 2.76538 | ||||||||
\(544\) | −0.404331 | −0.0173356 | ||||||||
\(545\) | −37.6288 | −1.61184 | ||||||||
\(546\) | 14.3230 | 0.612968 | ||||||||
\(547\) | −32.6020 | −1.39396 | −0.696980 | − | 0.717091i | \(-0.745473\pi\) | ||||
−0.696980 | + | 0.717091i | \(0.745473\pi\) | |||||||
\(548\) | 6.63810 | 0.283566 | ||||||||
\(549\) | 12.6435 | 0.539611 | ||||||||
\(550\) | −4.00990 | −0.170983 | ||||||||
\(551\) | 59.4717 | 2.53358 | ||||||||
\(552\) | −27.3486 | −1.16403 | ||||||||
\(553\) | −33.1054 | −1.40779 | ||||||||
\(554\) | −21.6799 | −0.921090 | ||||||||
\(555\) | −97.9619 | −4.15825 | ||||||||
\(556\) | −8.64286 | −0.366539 | ||||||||
\(557\) | 12.9021 | 0.546681 | 0.273340 | − | 0.961917i | \(-0.411871\pi\) | ||||
0.273340 | + | 0.961917i | \(0.411871\pi\) | |||||||
\(558\) | −5.39182 | −0.228254 | ||||||||
\(559\) | −0.466035 | −0.0197112 | ||||||||
\(560\) | −9.81816 | −0.414893 | ||||||||
\(561\) | −0.630599 | −0.0266239 | ||||||||
\(562\) | −4.47708 | −0.188854 | ||||||||
\(563\) | 2.86995 | 0.120954 | 0.0604771 | − | 0.998170i | \(-0.480738\pi\) | ||||
0.0604771 | + | 0.998170i | \(0.480738\pi\) | |||||||
\(564\) | 34.5896 | 1.45649 | ||||||||
\(565\) | −61.6801 | −2.59490 | ||||||||
\(566\) | 30.2162 | 1.27008 | ||||||||
\(567\) | 19.9238 | 0.836719 | ||||||||
\(568\) | −12.2881 | −0.515595 | ||||||||
\(569\) | −14.0169 | −0.587620 | −0.293810 | − | 0.955864i | \(-0.594923\pi\) | ||||
−0.293810 | + | 0.955864i | \(0.594923\pi\) | |||||||
\(570\) | −70.3324 | −2.94590 | ||||||||
\(571\) | 6.16938 | 0.258181 | 0.129090 | − | 0.991633i | \(-0.458794\pi\) | ||||
0.129090 | + | 0.991633i | \(0.458794\pi\) | |||||||
\(572\) | 0.919036 | 0.0384268 | ||||||||
\(573\) | −39.5283 | −1.65132 | ||||||||
\(574\) | 2.91404 | 0.121630 | ||||||||
\(575\) | −70.3157 | −2.93237 | ||||||||
\(576\) | 5.79657 | 0.241524 | ||||||||
\(577\) | 3.97321 | 0.165407 | 0.0827034 | − | 0.996574i | \(-0.473645\pi\) | ||||
0.0827034 | + | 0.996574i | \(0.473645\pi\) | |||||||
\(578\) | 16.8365 | 0.700307 | ||||||||
\(579\) | 19.0447 | 0.791472 | ||||||||
\(580\) | −31.6639 | −1.31477 | ||||||||
\(581\) | −16.7528 | −0.695024 | ||||||||
\(582\) | −23.0833 | −0.956834 | ||||||||
\(583\) | −5.99064 | −0.248107 | ||||||||
\(584\) | −11.1510 | −0.461432 | ||||||||
\(585\) | −35.9973 | −1.48831 | ||||||||
\(586\) | 23.6619 | 0.977464 | ||||||||
\(587\) | 7.12695 | 0.294161 | 0.147080 | − | 0.989125i | \(-0.453012\pi\) | ||||
0.147080 | + | 0.989125i | \(0.453012\pi\) | |||||||
\(588\) | −1.88330 | −0.0776659 | ||||||||
\(589\) | 6.20779 | 0.255788 | ||||||||
\(590\) | 9.18542 | 0.378158 | ||||||||
\(591\) | −38.0330 | −1.56447 | ||||||||
\(592\) | −9.29553 | −0.382044 | ||||||||
\(593\) | −7.00548 | −0.287681 | −0.143840 | − | 0.989601i | \(-0.545945\pi\) | ||||
−0.143840 | + | 0.989601i | \(0.545945\pi\) | |||||||
\(594\) | 4.36156 | 0.178957 | ||||||||
\(595\) | −3.96979 | −0.162745 | ||||||||
\(596\) | 8.43034 | 0.345320 | ||||||||
\(597\) | −48.4761 | −1.98400 | ||||||||
\(598\) | 16.1158 | 0.659023 | ||||||||
\(599\) | −27.9284 | −1.14113 | −0.570563 | − | 0.821254i | \(-0.693275\pi\) | ||||
−0.570563 | + | 0.821254i | \(0.693275\pi\) | |||||||
\(600\) | 22.6168 | 0.923326 | ||||||||
\(601\) | −26.2857 | −1.07222 | −0.536108 | − | 0.844149i | \(-0.680106\pi\) | ||||
−0.536108 | + | 0.844149i | \(0.680106\pi\) | |||||||
\(602\) | 0.736800 | 0.0300297 | ||||||||
\(603\) | 58.3039 | 2.37432 | ||||||||
\(604\) | 6.86075 | 0.279160 | ||||||||
\(605\) | 38.1032 | 1.54912 | ||||||||
\(606\) | 49.1889 | 1.99816 | ||||||||
\(607\) | −25.9106 | −1.05168 | −0.525839 | − | 0.850584i | \(-0.676248\pi\) | ||||
−0.525839 | + | 0.850584i | \(0.676248\pi\) | |||||||
\(608\) | −6.67379 | −0.270658 | ||||||||
\(609\) | −73.0295 | −2.95931 | ||||||||
\(610\) | 7.75036 | 0.313803 | ||||||||
\(611\) | −20.3827 | −0.824597 | ||||||||
\(612\) | 2.34373 | 0.0947398 | ||||||||
\(613\) | −0.653109 | −0.0263788 | −0.0131894 | − | 0.999913i | \(-0.504198\pi\) | ||||
−0.0131894 | + | 0.999913i | \(0.504198\pi\) | |||||||
\(614\) | −21.4101 | −0.864039 | ||||||||
\(615\) | −11.1141 | −0.448164 | ||||||||
\(616\) | −1.45299 | −0.0585428 | ||||||||
\(617\) | 11.2932 | 0.454649 | 0.227324 | − | 0.973819i | \(-0.427002\pi\) | ||||
0.227324 | + | 0.973819i | \(0.427002\pi\) | |||||||
\(618\) | 27.7528 | 1.11638 | ||||||||
\(619\) | 39.7936 | 1.59944 | 0.799720 | − | 0.600373i | \(-0.204981\pi\) | ||||
0.799720 | + | 0.600373i | \(0.204981\pi\) | |||||||
\(620\) | −3.30514 | −0.132738 | ||||||||
\(621\) | 76.4823 | 3.06913 | ||||||||
\(622\) | 28.4872 | 1.14223 | ||||||||
\(623\) | −46.6572 | −1.86928 | ||||||||
\(624\) | −5.18358 | −0.207509 | ||||||||
\(625\) | −4.97823 | −0.199129 | ||||||||
\(626\) | 15.6149 | 0.624096 | ||||||||
\(627\) | −10.4085 | −0.415676 | ||||||||
\(628\) | −3.40902 | −0.136035 | ||||||||
\(629\) | −3.75847 | −0.149860 | ||||||||
\(630\) | 56.9117 | 2.26741 | ||||||||
\(631\) | −7.64944 | −0.304520 | −0.152260 | − | 0.988341i | \(-0.548655\pi\) | ||||
−0.152260 | + | 0.988341i | \(0.548655\pi\) | |||||||
\(632\) | 11.9811 | 0.476581 | ||||||||
\(633\) | −28.9105 | −1.14909 | ||||||||
\(634\) | −19.5055 | −0.774663 | ||||||||
\(635\) | 38.4833 | 1.52716 | ||||||||
\(636\) | 33.7886 | 1.33981 | ||||||||
\(637\) | 1.10978 | 0.0439709 | ||||||||
\(638\) | −4.68595 | −0.185518 | ||||||||
\(639\) | 71.2286 | 2.81776 | ||||||||
\(640\) | 3.55325 | 0.140455 | ||||||||
\(641\) | 24.3399 | 0.961369 | 0.480684 | − | 0.876894i | \(-0.340388\pi\) | ||||
0.480684 | + | 0.876894i | \(0.340388\pi\) | |||||||
\(642\) | −36.3805 | −1.43582 | ||||||||
\(643\) | 5.13312 | 0.202431 | 0.101215 | − | 0.994865i | \(-0.467727\pi\) | ||||
0.101215 | + | 0.994865i | \(0.467727\pi\) | |||||||
\(644\) | −25.4790 | −1.00401 | ||||||||
\(645\) | −2.81014 | −0.110649 | ||||||||
\(646\) | −2.69842 | −0.106168 | ||||||||
\(647\) | −1.12682 | −0.0442997 | −0.0221499 | − | 0.999755i | \(-0.507051\pi\) | ||||
−0.0221499 | + | 0.999755i | \(0.507051\pi\) | |||||||
\(648\) | −7.21053 | −0.283256 | ||||||||
\(649\) | 1.35935 | 0.0533593 | ||||||||
\(650\) | −13.3275 | −0.522746 | ||||||||
\(651\) | −7.62299 | −0.298768 | ||||||||
\(652\) | 8.29841 | 0.324991 | ||||||||
\(653\) | 28.9590 | 1.13325 | 0.566626 | − | 0.823975i | \(-0.308248\pi\) | ||||
0.566626 | + | 0.823975i | \(0.308248\pi\) | |||||||
\(654\) | 31.4087 | 1.22818 | ||||||||
\(655\) | 16.3515 | 0.638904 | ||||||||
\(656\) | −1.05461 | −0.0411756 | ||||||||
\(657\) | 64.6377 | 2.52176 | ||||||||
\(658\) | 32.2250 | 1.25626 | ||||||||
\(659\) | 10.4674 | 0.407750 | 0.203875 | − | 0.978997i | \(-0.434646\pi\) | ||||
0.203875 | + | 0.978997i | \(0.434646\pi\) | |||||||
\(660\) | 5.54169 | 0.215710 | ||||||||
\(661\) | −12.4685 | −0.484967 | −0.242484 | − | 0.970156i | \(-0.577962\pi\) | ||||
−0.242484 | + | 0.970156i | \(0.577962\pi\) | |||||||
\(662\) | −23.6814 | −0.920403 | ||||||||
\(663\) | −2.09588 | −0.0813973 | ||||||||
\(664\) | 6.06295 | 0.235288 | ||||||||
\(665\) | −65.5244 | −2.54093 | ||||||||
\(666\) | 53.8822 | 2.08789 | ||||||||
\(667\) | −82.1705 | −3.18165 | ||||||||
\(668\) | −8.46894 | −0.327673 | ||||||||
\(669\) | −69.6888 | −2.69432 | ||||||||
\(670\) | 35.7398 | 1.38075 | ||||||||
\(671\) | 1.14698 | 0.0442786 | ||||||||
\(672\) | 8.19522 | 0.316138 | ||||||||
\(673\) | −2.34563 | −0.0904175 | −0.0452087 | − | 0.998978i | \(-0.514395\pi\) | ||||
−0.0452087 | + | 0.998978i | \(0.514395\pi\) | |||||||
\(674\) | −11.9124 | −0.458849 | ||||||||
\(675\) | −63.2495 | −2.43447 | ||||||||
\(676\) | −9.94546 | −0.382518 | ||||||||
\(677\) | 16.0140 | 0.615469 | 0.307735 | − | 0.951472i | \(-0.400429\pi\) | ||||
0.307735 | + | 0.951472i | \(0.400429\pi\) | |||||||
\(678\) | 51.4844 | 1.97725 | ||||||||
\(679\) | −21.5053 | −0.825297 | ||||||||
\(680\) | 1.43669 | 0.0550946 | ||||||||
\(681\) | 46.1539 | 1.76862 | ||||||||
\(682\) | −0.489130 | −0.0187297 | ||||||||
\(683\) | 0.738062 | 0.0282412 | 0.0141206 | − | 0.999900i | \(-0.495505\pi\) | ||||
0.0141206 | + | 0.999900i | \(0.495505\pi\) | |||||||
\(684\) | 38.6851 | 1.47916 | ||||||||
\(685\) | −23.5868 | −0.901207 | ||||||||
\(686\) | 17.5875 | 0.671493 | ||||||||
\(687\) | −43.1069 | −1.64463 | ||||||||
\(688\) | −0.266653 | −0.0101660 | ||||||||
\(689\) | −19.9107 | −0.758537 | ||||||||
\(690\) | 97.1764 | 3.69944 | ||||||||
\(691\) | 42.8442 | 1.62987 | 0.814935 | − | 0.579552i | \(-0.196773\pi\) | ||||
0.814935 | + | 0.579552i | \(0.196773\pi\) | |||||||
\(692\) | −17.5748 | −0.668094 | ||||||||
\(693\) | 8.42238 | 0.319940 | ||||||||
\(694\) | −11.1351 | −0.422681 | ||||||||
\(695\) | 30.7103 | 1.16491 | ||||||||
\(696\) | 26.4298 | 1.00182 | ||||||||
\(697\) | −0.426412 | −0.0161515 | ||||||||
\(698\) | 29.6691 | 1.12299 | ||||||||
\(699\) | 28.7467 | 1.08730 | ||||||||
\(700\) | 21.0707 | 0.796396 | ||||||||
\(701\) | −30.9266 | −1.16808 | −0.584041 | − | 0.811724i | \(-0.698529\pi\) | ||||
−0.584041 | + | 0.811724i | \(0.698529\pi\) | |||||||
\(702\) | 14.4963 | 0.547126 | ||||||||
\(703\) | −62.0365 | −2.33975 | ||||||||
\(704\) | 0.525847 | 0.0198186 | ||||||||
\(705\) | −122.906 | −4.62890 | ||||||||
\(706\) | −33.4239 | −1.25792 | ||||||||
\(707\) | 45.8263 | 1.72347 | ||||||||
\(708\) | −7.66707 | −0.288146 | ||||||||
\(709\) | 29.3904 | 1.10378 | 0.551889 | − | 0.833917i | \(-0.313907\pi\) | ||||
0.551889 | + | 0.833917i | \(0.313907\pi\) | |||||||
\(710\) | 43.6625 | 1.63863 | ||||||||
\(711\) | −69.4491 | −2.60454 | ||||||||
\(712\) | 16.8855 | 0.632812 | ||||||||
\(713\) | −8.57714 | −0.321216 | ||||||||
\(714\) | 3.31358 | 0.124008 | ||||||||
\(715\) | −3.26557 | −0.122125 | ||||||||
\(716\) | 16.6868 | 0.623614 | ||||||||
\(717\) | 61.2637 | 2.28794 | ||||||||
\(718\) | 12.3282 | 0.460085 | ||||||||
\(719\) | −46.8953 | −1.74890 | −0.874450 | − | 0.485115i | \(-0.838778\pi\) | ||||
−0.874450 | + | 0.485115i | \(0.838778\pi\) | |||||||
\(720\) | −20.5967 | −0.767593 | ||||||||
\(721\) | 25.8556 | 0.962912 | ||||||||
\(722\) | −25.5395 | −0.950483 | ||||||||
\(723\) | 56.4667 | 2.10002 | ||||||||
\(724\) | −21.7269 | −0.807473 | ||||||||
\(725\) | 67.9535 | 2.52373 | ||||||||
\(726\) | −31.8048 | −1.18039 | ||||||||
\(727\) | −39.6718 | −1.47134 | −0.735672 | − | 0.677338i | \(-0.763134\pi\) | ||||
−0.735672 | + | 0.677338i | \(0.763134\pi\) | |||||||
\(728\) | −4.82922 | −0.178983 | ||||||||
\(729\) | −32.0044 | −1.18535 | ||||||||
\(730\) | 39.6224 | 1.46649 | ||||||||
\(731\) | −0.107816 | −0.00398771 | ||||||||
\(732\) | −6.46923 | −0.239110 | ||||||||
\(733\) | 20.3814 | 0.752804 | 0.376402 | − | 0.926456i | \(-0.377161\pi\) | ||||
0.376402 | + | 0.926456i | \(0.377161\pi\) | |||||||
\(734\) | 12.9043 | 0.476306 | ||||||||
\(735\) | 6.69183 | 0.246832 | ||||||||
\(736\) | 9.22100 | 0.339891 | ||||||||
\(737\) | 5.28915 | 0.194828 | ||||||||
\(738\) | 6.11313 | 0.225027 | ||||||||
\(739\) | −17.1026 | −0.629130 | −0.314565 | − | 0.949236i | \(-0.601859\pi\) | ||||
−0.314565 | + | 0.949236i | \(0.601859\pi\) | |||||||
\(740\) | 33.0294 | 1.21418 | ||||||||
\(741\) | −34.5942 | −1.27085 | ||||||||
\(742\) | 31.4787 | 1.15562 | ||||||||
\(743\) | 2.64080 | 0.0968817 | 0.0484409 | − | 0.998826i | \(-0.484575\pi\) | ||||
0.0484409 | + | 0.998826i | \(0.484575\pi\) | |||||||
\(744\) | 2.75881 | 0.101143 | ||||||||
\(745\) | −29.9551 | −1.09747 | ||||||||
\(746\) | −21.1322 | −0.773706 | ||||||||
\(747\) | −35.1443 | −1.28586 | ||||||||
\(748\) | 0.212616 | 0.00777402 | ||||||||
\(749\) | −33.8935 | −1.23844 | ||||||||
\(750\) | −27.6701 | −1.01037 | ||||||||
\(751\) | −5.57353 | −0.203381 | −0.101690 | − | 0.994816i | \(-0.532425\pi\) | ||||
−0.101690 | + | 0.994816i | \(0.532425\pi\) | |||||||
\(752\) | −11.6624 | −0.425285 | ||||||||
\(753\) | −60.6745 | −2.21110 | ||||||||
\(754\) | −15.5744 | −0.567186 | ||||||||
\(755\) | −24.3780 | −0.887205 | ||||||||
\(756\) | −22.9185 | −0.833539 | ||||||||
\(757\) | −1.11091 | −0.0403768 | −0.0201884 | − | 0.999796i | \(-0.506427\pi\) | ||||
−0.0201884 | + | 0.999796i | \(0.506427\pi\) | |||||||
\(758\) | 23.5472 | 0.855274 | ||||||||
\(759\) | 14.3812 | 0.522003 | ||||||||
\(760\) | 23.7137 | 0.860185 | ||||||||
\(761\) | 40.3452 | 1.46251 | 0.731256 | − | 0.682103i | \(-0.238935\pi\) | ||||
0.731256 | + | 0.682103i | \(0.238935\pi\) | |||||||
\(762\) | −32.1220 | −1.16366 | ||||||||
\(763\) | 29.2616 | 1.05934 | ||||||||
\(764\) | 13.3276 | 0.482175 | ||||||||
\(765\) | −8.32788 | −0.301095 | ||||||||
\(766\) | 31.1585 | 1.12580 | ||||||||
\(767\) | 4.51800 | 0.163135 | ||||||||
\(768\) | −2.96590 | −0.107023 | ||||||||
\(769\) | 22.7954 | 0.822025 | 0.411012 | − | 0.911630i | \(-0.365175\pi\) | ||||
0.411012 | + | 0.911630i | \(0.365175\pi\) | |||||||
\(770\) | 5.16285 | 0.186056 | ||||||||
\(771\) | −90.6102 | −3.26325 | ||||||||
\(772\) | −6.42123 | −0.231105 | ||||||||
\(773\) | −8.20615 | −0.295155 | −0.147577 | − | 0.989051i | \(-0.547148\pi\) | ||||
−0.147577 | + | 0.989051i | \(0.547148\pi\) | |||||||
\(774\) | 1.54567 | 0.0555580 | ||||||||
\(775\) | 7.09314 | 0.254793 | ||||||||
\(776\) | 7.78289 | 0.279390 | ||||||||
\(777\) | 76.1790 | 2.73291 | ||||||||
\(778\) | 15.5165 | 0.556295 | ||||||||
\(779\) | −7.03826 | −0.252172 | ||||||||
\(780\) | 18.4186 | 0.659491 | ||||||||
\(781\) | 6.46164 | 0.231216 | ||||||||
\(782\) | 3.72834 | 0.133325 | ||||||||
\(783\) | −73.9130 | −2.64143 | ||||||||
\(784\) | 0.634983 | 0.0226780 | ||||||||
\(785\) | 12.1131 | 0.432336 | ||||||||
\(786\) | −13.6486 | −0.486829 | ||||||||
\(787\) | 10.6059 | 0.378058 | 0.189029 | − | 0.981971i | \(-0.439466\pi\) | ||||
0.189029 | + | 0.981971i | \(0.439466\pi\) | |||||||
\(788\) | 12.8234 | 0.456815 | ||||||||
\(789\) | −38.9875 | −1.38799 | ||||||||
\(790\) | −42.5717 | −1.51463 | ||||||||
\(791\) | 47.9649 | 1.70543 | ||||||||
\(792\) | −3.04811 | −0.108310 | ||||||||
\(793\) | 3.81214 | 0.135373 | ||||||||
\(794\) | −8.60718 | −0.305457 | ||||||||
\(795\) | −120.059 | −4.25807 | ||||||||
\(796\) | 16.3445 | 0.579315 | ||||||||
\(797\) | 13.4124 | 0.475092 | 0.237546 | − | 0.971376i | \(-0.423657\pi\) | ||||
0.237546 | + | 0.971376i | \(0.423657\pi\) | |||||||
\(798\) | 54.6932 | 1.93612 | ||||||||
\(799\) | −4.71549 | −0.166822 | ||||||||
\(800\) | −7.62560 | −0.269606 | ||||||||
\(801\) | −97.8781 | −3.45835 | ||||||||
\(802\) | 6.41977 | 0.226690 | ||||||||
\(803\) | 5.86373 | 0.206927 | ||||||||
\(804\) | −29.8321 | −1.05210 | ||||||||
\(805\) | 90.5332 | 3.19088 | ||||||||
\(806\) | −1.62569 | −0.0572625 | ||||||||
\(807\) | −6.49157 | −0.228514 | ||||||||
\(808\) | −16.5848 | −0.583452 | ||||||||
\(809\) | −22.0775 | −0.776203 | −0.388101 | − | 0.921617i | \(-0.626869\pi\) | ||||
−0.388101 | + | 0.921617i | \(0.626869\pi\) | |||||||
\(810\) | 25.6208 | 0.900225 | ||||||||
\(811\) | −13.7393 | −0.482453 | −0.241227 | − | 0.970469i | \(-0.577550\pi\) | ||||
−0.241227 | + | 0.970469i | \(0.577550\pi\) | |||||||
\(812\) | 24.6231 | 0.864100 | ||||||||
\(813\) | −9.30424 | −0.326314 | ||||||||
\(814\) | 4.88803 | 0.171325 | ||||||||
\(815\) | −29.4864 | −1.03286 | ||||||||
\(816\) | −1.19921 | −0.0419806 | ||||||||
\(817\) | −1.77958 | −0.0622598 | ||||||||
\(818\) | 26.7924 | 0.936774 | ||||||||
\(819\) | 27.9929 | 0.978152 | ||||||||
\(820\) | 3.74730 | 0.130861 | ||||||||
\(821\) | −39.2727 | −1.37063 | −0.685314 | − | 0.728248i | \(-0.740335\pi\) | ||||
−0.685314 | + | 0.728248i | \(0.740335\pi\) | |||||||
\(822\) | 19.6879 | 0.686696 | ||||||||
\(823\) | −2.25543 | −0.0786193 | −0.0393096 | − | 0.999227i | \(-0.512516\pi\) | ||||
−0.0393096 | + | 0.999227i | \(0.512516\pi\) | |||||||
\(824\) | −9.35729 | −0.325977 | ||||||||
\(825\) | −11.8930 | −0.414060 | ||||||||
\(826\) | −7.14294 | −0.248535 | ||||||||
\(827\) | −24.5139 | −0.852433 | −0.426216 | − | 0.904621i | \(-0.640154\pi\) | ||||
−0.426216 | + | 0.904621i | \(0.640154\pi\) | |||||||
\(828\) | −53.4502 | −1.85752 | ||||||||
\(829\) | −13.4813 | −0.468225 | −0.234112 | − | 0.972210i | \(-0.575218\pi\) | ||||
−0.234112 | + | 0.972210i | \(0.575218\pi\) | |||||||
\(830\) | −21.5432 | −0.747775 | ||||||||
\(831\) | −64.3004 | −2.23056 | ||||||||
\(832\) | 1.74773 | 0.0605915 | ||||||||
\(833\) | 0.256743 | 0.00889563 | ||||||||
\(834\) | −25.6339 | −0.887628 | ||||||||
\(835\) | 30.0923 | 1.04139 | ||||||||
\(836\) | 3.50940 | 0.121375 | ||||||||
\(837\) | −7.71520 | −0.266676 | ||||||||
\(838\) | −2.70657 | −0.0934969 | ||||||||
\(839\) | −10.7520 | −0.371200 | −0.185600 | − | 0.982625i | \(-0.559423\pi\) | ||||
−0.185600 | + | 0.982625i | \(0.559423\pi\) | |||||||
\(840\) | −29.1197 | −1.00472 | ||||||||
\(841\) | 50.4101 | 1.73828 | ||||||||
\(842\) | 33.3581 | 1.14959 | ||||||||
\(843\) | −13.2786 | −0.457339 | ||||||||
\(844\) | 9.74762 | 0.335527 | ||||||||
\(845\) | 35.3387 | 1.21569 | ||||||||
\(846\) | 67.6022 | 2.32421 | ||||||||
\(847\) | −29.6306 | −1.01812 | ||||||||
\(848\) | −11.3924 | −0.391215 | ||||||||
\(849\) | 89.6182 | 3.07569 | ||||||||
\(850\) | −3.08327 | −0.105755 | ||||||||
\(851\) | 85.7141 | 2.93824 | ||||||||
\(852\) | −36.4452 | −1.24859 | ||||||||
\(853\) | −37.8022 | −1.29432 | −0.647161 | − | 0.762354i | \(-0.724044\pi\) | ||||
−0.647161 | + | 0.762354i | \(0.724044\pi\) | |||||||
\(854\) | −6.02698 | −0.206239 | ||||||||
\(855\) | −137.458 | −4.70097 | ||||||||
\(856\) | 12.2662 | 0.419252 | ||||||||
\(857\) | 29.9124 | 1.02179 | 0.510895 | − | 0.859643i | \(-0.329314\pi\) | ||||
0.510895 | + | 0.859643i | \(0.329314\pi\) | |||||||
\(858\) | 2.72577 | 0.0930563 | ||||||||
\(859\) | 9.07654 | 0.309687 | 0.154844 | − | 0.987939i | \(-0.450513\pi\) | ||||
0.154844 | + | 0.987939i | \(0.450513\pi\) | |||||||
\(860\) | 0.947484 | 0.0323089 | ||||||||
\(861\) | 8.64277 | 0.294545 | ||||||||
\(862\) | −4.33168 | −0.147538 | ||||||||
\(863\) | −29.2026 | −0.994068 | −0.497034 | − | 0.867731i | \(-0.665578\pi\) | ||||
−0.497034 | + | 0.867731i | \(0.665578\pi\) | |||||||
\(864\) | 8.29436 | 0.282180 | ||||||||
\(865\) | 62.4477 | 2.12329 | ||||||||
\(866\) | −15.5145 | −0.527203 | ||||||||
\(867\) | 49.9355 | 1.69590 | ||||||||
\(868\) | 2.57021 | 0.0872386 | ||||||||
\(869\) | −6.30021 | −0.213720 | ||||||||
\(870\) | −93.9119 | −3.18391 | ||||||||
\(871\) | 17.5792 | 0.595649 | ||||||||
\(872\) | −10.5900 | −0.358621 | ||||||||
\(873\) | −45.1141 | −1.52688 | ||||||||
\(874\) | 61.5391 | 2.08159 | ||||||||
\(875\) | −25.7786 | −0.871474 | ||||||||
\(876\) | −33.0728 | −1.11743 | ||||||||
\(877\) | 23.3461 | 0.788342 | 0.394171 | − | 0.919037i | \(-0.371032\pi\) | ||||
0.394171 | + | 0.919037i | \(0.371032\pi\) | |||||||
\(878\) | 11.2187 | 0.378613 | ||||||||
\(879\) | 70.1788 | 2.36707 | ||||||||
\(880\) | −1.86847 | −0.0629860 | ||||||||
\(881\) | −48.0477 | −1.61877 | −0.809385 | − | 0.587279i | \(-0.800199\pi\) | ||||
−0.809385 | + | 0.587279i | \(0.800199\pi\) | |||||||
\(882\) | −3.68072 | −0.123936 | ||||||||
\(883\) | −14.7204 | −0.495382 | −0.247691 | − | 0.968839i | \(-0.579672\pi\) | ||||
−0.247691 | + | 0.968839i | \(0.579672\pi\) | |||||||
\(884\) | 0.706660 | 0.0237675 | ||||||||
\(885\) | 27.2430 | 0.915765 | ||||||||
\(886\) | −8.86735 | −0.297904 | ||||||||
\(887\) | 42.0926 | 1.41333 | 0.706665 | − | 0.707548i | \(-0.250199\pi\) | ||||
0.706665 | + | 0.707548i | \(0.250199\pi\) | |||||||
\(888\) | −27.5696 | −0.925176 | ||||||||
\(889\) | −29.9261 | −1.00369 | ||||||||
\(890\) | −59.9985 | −2.01115 | ||||||||
\(891\) | 3.79164 | 0.127025 | ||||||||
\(892\) | 23.4967 | 0.786726 | ||||||||
\(893\) | −77.8327 | −2.60457 | ||||||||
\(894\) | 25.0035 | 0.836244 | ||||||||
\(895\) | −59.2923 | −1.98192 | ||||||||
\(896\) | −2.76315 | −0.0923103 | ||||||||
\(897\) | 47.7978 | 1.59592 | ||||||||
\(898\) | 14.5144 | 0.484351 | ||||||||
\(899\) | 8.28900 | 0.276454 | ||||||||
\(900\) | 44.2023 | 1.47341 | ||||||||
\(901\) | −4.60628 | −0.153458 | ||||||||
\(902\) | 0.554564 | 0.0184650 | ||||||||
\(903\) | 2.18528 | 0.0727215 | ||||||||
\(904\) | −17.3588 | −0.577345 | ||||||||
\(905\) | 77.2011 | 2.56625 | ||||||||
\(906\) | 20.3483 | 0.676027 | ||||||||
\(907\) | 12.6681 | 0.420636 | 0.210318 | − | 0.977633i | \(-0.432550\pi\) | ||||
0.210318 | + | 0.977633i | \(0.432550\pi\) | |||||||
\(908\) | −15.5615 | −0.516427 | ||||||||
\(909\) | 96.1351 | 3.18860 | ||||||||
\(910\) | 17.1594 | 0.568830 | ||||||||
\(911\) | 18.8793 | 0.625498 | 0.312749 | − | 0.949836i | \(-0.398750\pi\) | ||||
0.312749 | + | 0.949836i | \(0.398750\pi\) | |||||||
\(912\) | −19.7938 | −0.655439 | ||||||||
\(913\) | −3.18819 | −0.105514 | ||||||||
\(914\) | −25.0221 | −0.827657 | ||||||||
\(915\) | 22.9868 | 0.759920 | ||||||||
\(916\) | 14.5342 | 0.480223 | ||||||||
\(917\) | −12.7155 | −0.419904 | ||||||||
\(918\) | 3.35367 | 0.110687 | ||||||||
\(919\) | 8.08733 | 0.266777 | 0.133388 | − | 0.991064i | \(-0.457414\pi\) | ||||
0.133388 | + | 0.991064i | \(0.457414\pi\) | |||||||
\(920\) | −32.7645 | −1.08021 | ||||||||
\(921\) | −63.5001 | −2.09240 | ||||||||
\(922\) | −19.7791 | −0.651389 | ||||||||
\(923\) | 21.4761 | 0.706896 | ||||||||
\(924\) | −4.30943 | −0.141770 | ||||||||
\(925\) | −70.8840 | −2.33065 | ||||||||
\(926\) | 29.3979 | 0.966074 | ||||||||
\(927\) | 54.2402 | 1.78148 | ||||||||
\(928\) | −8.91123 | −0.292526 | ||||||||
\(929\) | −26.8763 | −0.881784 | −0.440892 | − | 0.897560i | \(-0.645338\pi\) | ||||
−0.440892 | + | 0.897560i | \(0.645338\pi\) | |||||||
\(930\) | −9.80273 | −0.321444 | ||||||||
\(931\) | 4.23775 | 0.138887 | ||||||||
\(932\) | −9.69239 | −0.317485 | ||||||||
\(933\) | 84.4901 | 2.76608 | ||||||||
\(934\) | 7.21932 | 0.236223 | ||||||||
\(935\) | −0.755479 | −0.0247068 | ||||||||
\(936\) | −10.1308 | −0.331136 | ||||||||
\(937\) | −3.67287 | −0.119987 | −0.0599937 | − | 0.998199i | \(-0.519108\pi\) | ||||
−0.0599937 | + | 0.998199i | \(0.519108\pi\) | |||||||
\(938\) | −27.7927 | −0.907464 | ||||||||
\(939\) | 46.3122 | 1.51134 | ||||||||
\(940\) | 41.4396 | 1.35161 | ||||||||
\(941\) | 14.7441 | 0.480643 | 0.240321 | − | 0.970693i | \(-0.422747\pi\) | ||||
0.240321 | + | 0.970693i | \(0.422747\pi\) | |||||||
\(942\) | −10.1108 | −0.329429 | ||||||||
\(943\) | 9.72457 | 0.316675 | ||||||||
\(944\) | 2.58507 | 0.0841370 | ||||||||
\(945\) | 81.4353 | 2.64909 | ||||||||
\(946\) | 0.140218 | 0.00455890 | ||||||||
\(947\) | −29.9323 | −0.972670 | −0.486335 | − | 0.873772i | \(-0.661667\pi\) | ||||
−0.486335 | + | 0.873772i | \(0.661667\pi\) | |||||||
\(948\) | 35.5347 | 1.15411 | ||||||||
\(949\) | 19.4889 | 0.632637 | ||||||||
\(950\) | −50.8917 | −1.65114 | ||||||||
\(951\) | −57.8514 | −1.87596 | ||||||||
\(952\) | −1.11723 | −0.0362095 | ||||||||
\(953\) | 35.0333 | 1.13484 | 0.567420 | − | 0.823429i | \(-0.307942\pi\) | ||||
0.567420 | + | 0.823429i | \(0.307942\pi\) | |||||||
\(954\) | 66.0366 | 2.13801 | ||||||||
\(955\) | −47.3563 | −1.53241 | ||||||||
\(956\) | −20.6560 | −0.668064 | ||||||||
\(957\) | −13.8981 | −0.449260 | ||||||||
\(958\) | 40.0520 | 1.29402 | ||||||||
\(959\) | 18.3420 | 0.592296 | ||||||||
\(960\) | 10.5386 | 0.340132 | ||||||||
\(961\) | −30.1348 | −0.972090 | ||||||||
\(962\) | 16.2460 | 0.523793 | ||||||||
\(963\) | −71.1022 | −2.29124 | ||||||||
\(964\) | −19.0386 | −0.613192 | ||||||||
\(965\) | 22.8163 | 0.734481 | ||||||||
\(966\) | −75.5681 | −2.43137 | ||||||||
\(967\) | 22.8316 | 0.734214 | 0.367107 | − | 0.930179i | \(-0.380348\pi\) | ||||
0.367107 | + | 0.930179i | \(0.380348\pi\) | |||||||
\(968\) | 10.7235 | 0.344666 | ||||||||
\(969\) | −8.00326 | −0.257102 | ||||||||
\(970\) | −27.6546 | −0.887935 | ||||||||
\(971\) | −57.0807 | −1.83181 | −0.915904 | − | 0.401397i | \(-0.868525\pi\) | ||||
−0.915904 | + | 0.401397i | \(0.868525\pi\) | |||||||
\(972\) | 3.49734 | 0.112177 | ||||||||
\(973\) | −23.8815 | −0.765605 | ||||||||
\(974\) | 12.1659 | 0.389820 | ||||||||
\(975\) | −39.5279 | −1.26591 | ||||||||
\(976\) | 2.18120 | 0.0698186 | ||||||||
\(977\) | −3.91047 | −0.125107 | −0.0625535 | − | 0.998042i | \(-0.519924\pi\) | ||||
−0.0625535 | + | 0.998042i | \(0.519924\pi\) | |||||||
\(978\) | 24.6123 | 0.787014 | ||||||||
\(979\) | −8.87920 | −0.283781 | ||||||||
\(980\) | −2.25625 | −0.0720734 | ||||||||
\(981\) | 61.3854 | 1.95989 | ||||||||
\(982\) | 8.63426 | 0.275530 | ||||||||
\(983\) | −41.5646 | −1.32571 | −0.662853 | − | 0.748749i | \(-0.730655\pi\) | ||||
−0.662853 | + | 0.748749i | \(0.730655\pi\) | |||||||
\(984\) | −3.12787 | −0.0997129 | ||||||||
\(985\) | −45.5648 | −1.45182 | ||||||||
\(986\) | −3.60309 | −0.114746 | ||||||||
\(987\) | 95.5763 | 3.04223 | ||||||||
\(988\) | 11.6640 | 0.371080 | ||||||||
\(989\) | 2.45880 | 0.0781854 | ||||||||
\(990\) | 10.8307 | 0.344222 | ||||||||
\(991\) | 27.5585 | 0.875424 | 0.437712 | − | 0.899115i | \(-0.355789\pi\) | ||||
0.437712 | + | 0.899115i | \(0.355789\pi\) | |||||||
\(992\) | −0.930175 | −0.0295331 | ||||||||
\(993\) | −70.2366 | −2.22889 | ||||||||
\(994\) | −33.9537 | −1.07695 | ||||||||
\(995\) | −58.0761 | −1.84113 | ||||||||
\(996\) | 17.9821 | 0.569785 | ||||||||
\(997\) | −41.2516 | −1.30645 | −0.653226 | − | 0.757163i | \(-0.726585\pi\) | ||||
−0.653226 | + | 0.757163i | \(0.726585\pi\) | |||||||
\(998\) | −17.1640 | −0.543318 | ||||||||
\(999\) | 77.1005 | 2.43935 |
(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 | 8002.2.a.f.1.8 | ✓ | 89 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.f.1.8 | ✓ | 89 | 1.1 | even | 1 | trivial |