Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [161,2,Mod(1,161)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(161, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("161.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 161 = 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 161.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: | \(1.28559147254\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.2147108.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.11948\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 161.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11948 | 1.49870 | 0.749350 | − | 0.662174i | \(-0.230366\pi\) | ||||
0.749350 | + | 0.662174i | \(0.230366\pi\) | |||||||
\(3\) | −1.84074 | −1.06275 | −0.531375 | − | 0.847137i | \(-0.678324\pi\) | ||||
−0.531375 | + | 0.847137i | \(0.678324\pi\) | |||||||
\(4\) | 2.49221 | 1.24610 | ||||||||
\(5\) | 2.40920 | 1.07743 | 0.538714 | − | 0.842489i | \(-0.318910\pi\) | ||||
0.538714 | + | 0.842489i | \(0.318910\pi\) | |||||||
\(6\) | −3.90141 | −1.59274 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.04322 | 0.368835 | ||||||||
\(9\) | 0.388311 | 0.129437 | ||||||||
\(10\) | 5.10626 | 1.61474 | ||||||||
\(11\) | 5.87722 | 1.77205 | 0.886024 | − | 0.463640i | \(-0.153457\pi\) | ||||
0.886024 | + | 0.463640i | \(0.153457\pi\) | |||||||
\(12\) | −4.58750 | −1.32430 | ||||||||
\(13\) | −6.24994 | −1.73342 | −0.866711 | − | 0.498811i | \(-0.833770\pi\) | ||||
−0.866711 | + | 0.498811i | \(0.833770\pi\) | |||||||
\(14\) | 2.11948 | 0.566456 | ||||||||
\(15\) | −4.43471 | −1.14504 | ||||||||
\(16\) | −2.77332 | −0.693330 | ||||||||
\(17\) | −5.42479 | −1.31570 | −0.657852 | − | 0.753147i | \(-0.728535\pi\) | ||||
−0.657852 | + | 0.753147i | \(0.728535\pi\) | |||||||
\(18\) | 0.823019 | 0.193987 | ||||||||
\(19\) | −2.23897 | −0.513654 | −0.256827 | − | 0.966457i | \(-0.582677\pi\) | ||||
−0.256827 | + | 0.966457i | \(0.582677\pi\) | |||||||
\(20\) | 6.00423 | 1.34259 | ||||||||
\(21\) | −1.84074 | −0.401682 | ||||||||
\(22\) | 12.4567 | 2.65577 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.92030 | −0.391979 | ||||||||
\(25\) | 0.804258 | 0.160852 | ||||||||
\(26\) | −13.2466 | −2.59788 | ||||||||
\(27\) | 4.80743 | 0.925191 | ||||||||
\(28\) | 2.49221 | 0.470983 | ||||||||
\(29\) | 0.642864 | 0.119377 | 0.0596884 | − | 0.998217i | \(-0.480989\pi\) | ||||
0.0596884 | + | 0.998217i | \(0.480989\pi\) | |||||||
\(30\) | −9.39929 | −1.71607 | ||||||||
\(31\) | 7.84074 | 1.40824 | 0.704119 | − | 0.710082i | \(-0.251342\pi\) | ||||
0.704119 | + | 0.710082i | \(0.251342\pi\) | |||||||
\(32\) | −7.96445 | −1.40793 | ||||||||
\(33\) | −10.8184 | −1.88324 | ||||||||
\(34\) | −11.4977 | −1.97185 | ||||||||
\(35\) | 2.40920 | 0.407230 | ||||||||
\(36\) | 0.967751 | 0.161292 | ||||||||
\(37\) | 0.557492 | 0.0916511 | 0.0458256 | − | 0.998949i | \(-0.485408\pi\) | ||||
0.0458256 | + | 0.998949i | \(0.485408\pi\) | |||||||
\(38\) | −4.74545 | −0.769813 | ||||||||
\(39\) | 11.5045 | 1.84219 | ||||||||
\(40\) | 2.51334 | 0.397393 | ||||||||
\(41\) | 2.56847 | 0.401127 | 0.200564 | − | 0.979681i | \(-0.435723\pi\) | ||||
0.200564 | + | 0.979681i | \(0.435723\pi\) | |||||||
\(42\) | −3.90141 | −0.602000 | ||||||||
\(43\) | −8.81841 | −1.34479 | −0.672397 | − | 0.740191i | \(-0.734735\pi\) | ||||
−0.672397 | + | 0.740191i | \(0.734735\pi\) | |||||||
\(44\) | 14.6472 | 2.20815 | ||||||||
\(45\) | 0.935520 | 0.139459 | ||||||||
\(46\) | −2.11948 | −0.312501 | ||||||||
\(47\) | 4.26766 | 0.622502 | 0.311251 | − | 0.950328i | \(-0.399252\pi\) | ||||
0.311251 | + | 0.950328i | \(0.399252\pi\) | |||||||
\(48\) | 5.10495 | 0.736836 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.70461 | 0.241068 | ||||||||
\(51\) | 9.98561 | 1.39826 | ||||||||
\(52\) | −15.5761 | −2.16002 | ||||||||
\(53\) | 3.01559 | 0.414223 | 0.207111 | − | 0.978317i | \(-0.433594\pi\) | ||||
0.207111 | + | 0.978317i | \(0.433594\pi\) | |||||||
\(54\) | 10.1893 | 1.38658 | ||||||||
\(55\) | 14.1594 | 1.90925 | ||||||||
\(56\) | 1.04322 | 0.139407 | ||||||||
\(57\) | 4.12134 | 0.545885 | ||||||||
\(58\) | 1.36254 | 0.178910 | ||||||||
\(59\) | 4.17024 | 0.542919 | 0.271459 | − | 0.962450i | \(-0.412494\pi\) | ||||
0.271459 | + | 0.962450i | \(0.412494\pi\) | |||||||
\(60\) | −11.0522 | −1.42683 | ||||||||
\(61\) | −0.148289 | −0.0189865 | −0.00949325 | − | 0.999955i | \(-0.503022\pi\) | ||||
−0.00949325 | + | 0.999955i | \(0.503022\pi\) | |||||||
\(62\) | 16.6183 | 2.11053 | ||||||||
\(63\) | 0.388311 | 0.0489226 | ||||||||
\(64\) | −11.3339 | −1.41673 | ||||||||
\(65\) | −15.0574 | −1.86764 | ||||||||
\(66\) | −22.9294 | −2.82242 | ||||||||
\(67\) | 13.3396 | 1.62969 | 0.814843 | − | 0.579681i | \(-0.196823\pi\) | ||||
0.814843 | + | 0.579681i | \(0.196823\pi\) | |||||||
\(68\) | −13.5197 | −1.63950 | ||||||||
\(69\) | 1.84074 | 0.221599 | ||||||||
\(70\) | 5.10626 | 0.610315 | ||||||||
\(71\) | −7.93141 | −0.941285 | −0.470643 | − | 0.882324i | \(-0.655978\pi\) | ||||
−0.470643 | + | 0.882324i | \(0.655978\pi\) | |||||||
\(72\) | 0.405095 | 0.0477409 | ||||||||
\(73\) | 4.28111 | 0.501066 | 0.250533 | − | 0.968108i | \(-0.419394\pi\) | ||||
0.250533 | + | 0.968108i | \(0.419394\pi\) | |||||||
\(74\) | 1.18159 | 0.137358 | ||||||||
\(75\) | −1.48043 | −0.170945 | ||||||||
\(76\) | −5.57996 | −0.640066 | ||||||||
\(77\) | 5.87722 | 0.669771 | ||||||||
\(78\) | 24.3836 | 2.76090 | ||||||||
\(79\) | −0.861628 | −0.0969407 | −0.0484704 | − | 0.998825i | \(-0.515435\pi\) | ||||
−0.0484704 | + | 0.998825i | \(0.515435\pi\) | |||||||
\(80\) | −6.68149 | −0.747013 | ||||||||
\(81\) | −10.0141 | −1.11268 | ||||||||
\(82\) | 5.44382 | 0.601169 | ||||||||
\(83\) | −4.81841 | −0.528889 | −0.264444 | − | 0.964401i | \(-0.585189\pi\) | ||||
−0.264444 | + | 0.964401i | \(0.585189\pi\) | |||||||
\(84\) | −4.58750 | −0.500537 | ||||||||
\(85\) | −13.0694 | −1.41758 | ||||||||
\(86\) | −18.6905 | −2.01544 | ||||||||
\(87\) | −1.18334 | −0.126868 | ||||||||
\(88\) | 6.13125 | 0.653593 | ||||||||
\(89\) | 6.32964 | 0.670941 | 0.335470 | − | 0.942051i | \(-0.391105\pi\) | ||||
0.335470 | + | 0.942051i | \(0.391105\pi\) | |||||||
\(90\) | 1.98282 | 0.209007 | ||||||||
\(91\) | −6.24994 | −0.655172 | ||||||||
\(92\) | −2.49221 | −0.259830 | ||||||||
\(93\) | −14.4327 | −1.49660 | ||||||||
\(94\) | 9.04523 | 0.932944 | ||||||||
\(95\) | −5.39412 | −0.553425 | ||||||||
\(96\) | 14.6605 | 1.49628 | ||||||||
\(97\) | 10.4822 | 1.06430 | 0.532151 | − | 0.846649i | \(-0.321384\pi\) | ||||
0.532151 | + | 0.846649i | \(0.321384\pi\) | |||||||
\(98\) | 2.11948 | 0.214100 | ||||||||
\(99\) | 2.28219 | 0.229369 | ||||||||
\(100\) | 2.00438 | 0.200438 | ||||||||
\(101\) | −1.57308 | −0.156527 | −0.0782636 | − | 0.996933i | \(-0.524938\pi\) | ||||
−0.0782636 | + | 0.996933i | \(0.524938\pi\) | |||||||
\(102\) | 21.1643 | 2.09558 | ||||||||
\(103\) | 5.01559 | 0.494201 | 0.247100 | − | 0.968990i | \(-0.420522\pi\) | ||||
0.247100 | + | 0.968990i | \(0.420522\pi\) | |||||||
\(104\) | −6.52008 | −0.639346 | ||||||||
\(105\) | −4.43471 | −0.432783 | ||||||||
\(106\) | 6.39148 | 0.620796 | ||||||||
\(107\) | −5.81204 | −0.561872 | −0.280936 | − | 0.959727i | \(-0.590645\pi\) | ||||
−0.280936 | + | 0.959727i | \(0.590645\pi\) | |||||||
\(108\) | 11.9811 | 1.15288 | ||||||||
\(109\) | 7.65030 | 0.732766 | 0.366383 | − | 0.930464i | \(-0.380596\pi\) | ||||
0.366383 | + | 0.930464i | \(0.380596\pi\) | |||||||
\(110\) | 30.0106 | 2.86140 | ||||||||
\(111\) | −1.02620 | −0.0974022 | ||||||||
\(112\) | −2.77332 | −0.262054 | ||||||||
\(113\) | 10.4999 | 0.987745 | 0.493873 | − | 0.869534i | \(-0.335581\pi\) | ||||
0.493873 | + | 0.869534i | \(0.335581\pi\) | |||||||
\(114\) | 8.73512 | 0.818119 | ||||||||
\(115\) | −2.40920 | −0.224659 | ||||||||
\(116\) | 1.60215 | 0.148756 | ||||||||
\(117\) | −2.42692 | −0.224369 | ||||||||
\(118\) | 8.83875 | 0.813673 | ||||||||
\(119\) | −5.42479 | −0.497290 | ||||||||
\(120\) | −4.62639 | −0.422329 | ||||||||
\(121\) | 23.5417 | 2.14015 | ||||||||
\(122\) | −0.314297 | −0.0284551 | ||||||||
\(123\) | −4.72787 | −0.426298 | ||||||||
\(124\) | 19.5407 | 1.75481 | ||||||||
\(125\) | −10.1084 | −0.904122 | ||||||||
\(126\) | 0.823019 | 0.0733203 | ||||||||
\(127\) | −17.9732 | −1.59486 | −0.797432 | − | 0.603409i | \(-0.793809\pi\) | ||||
−0.797432 | + | 0.603409i | \(0.793809\pi\) | |||||||
\(128\) | −8.09304 | −0.715331 | ||||||||
\(129\) | 16.2324 | 1.42918 | ||||||||
\(130\) | −31.9138 | −2.79903 | ||||||||
\(131\) | −13.0641 | −1.14142 | −0.570708 | − | 0.821153i | \(-0.693331\pi\) | ||||
−0.570708 | + | 0.821153i | \(0.693331\pi\) | |||||||
\(132\) | −26.9617 | −2.34671 | ||||||||
\(133\) | −2.23897 | −0.194143 | ||||||||
\(134\) | 28.2730 | 2.44241 | ||||||||
\(135\) | 11.5821 | 0.996826 | ||||||||
\(136\) | −5.65926 | −0.485278 | ||||||||
\(137\) | −15.0262 | −1.28377 | −0.641887 | − | 0.766799i | \(-0.721848\pi\) | ||||
−0.641887 | + | 0.766799i | \(0.721848\pi\) | |||||||
\(138\) | 3.90141 | 0.332110 | ||||||||
\(139\) | −12.7987 | −1.08557 | −0.542786 | − | 0.839871i | \(-0.682631\pi\) | ||||
−0.542786 | + | 0.839871i | \(0.682631\pi\) | |||||||
\(140\) | 6.00423 | 0.507450 | ||||||||
\(141\) | −7.85563 | −0.661564 | ||||||||
\(142\) | −16.8105 | −1.41071 | ||||||||
\(143\) | −36.7322 | −3.07170 | ||||||||
\(144\) | −1.07691 | −0.0897426 | ||||||||
\(145\) | 1.54879 | 0.128620 | ||||||||
\(146\) | 9.07375 | 0.750949 | ||||||||
\(147\) | −1.84074 | −0.151821 | ||||||||
\(148\) | 1.38939 | 0.114207 | ||||||||
\(149\) | −21.1303 | −1.73106 | −0.865532 | − | 0.500854i | \(-0.833019\pi\) | ||||
−0.865532 | + | 0.500854i | \(0.833019\pi\) | |||||||
\(150\) | −3.13774 | −0.256195 | ||||||||
\(151\) | 19.5264 | 1.58904 | 0.794520 | − | 0.607239i | \(-0.207723\pi\) | ||||
0.794520 | + | 0.607239i | \(0.207723\pi\) | |||||||
\(152\) | −2.33574 | −0.189453 | ||||||||
\(153\) | −2.10651 | −0.170301 | ||||||||
\(154\) | 12.4567 | 1.00379 | ||||||||
\(155\) | 18.8899 | 1.51728 | ||||||||
\(156\) | 28.6716 | 2.29556 | ||||||||
\(157\) | −4.60638 | −0.367630 | −0.183815 | − | 0.982961i | \(-0.558845\pi\) | ||||
−0.183815 | + | 0.982961i | \(0.558845\pi\) | |||||||
\(158\) | −1.82621 | −0.145285 | ||||||||
\(159\) | −5.55090 | −0.440215 | ||||||||
\(160\) | −19.1880 | −1.51694 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | −21.2248 | −1.66758 | ||||||||
\(163\) | 16.3229 | 1.27851 | 0.639254 | − | 0.768996i | \(-0.279243\pi\) | ||||
0.639254 | + | 0.768996i | \(0.279243\pi\) | |||||||
\(164\) | 6.40115 | 0.499846 | ||||||||
\(165\) | −26.0637 | −2.02906 | ||||||||
\(166\) | −10.2125 | −0.792646 | ||||||||
\(167\) | 16.7254 | 1.29425 | 0.647125 | − | 0.762384i | \(-0.275971\pi\) | ||||
0.647125 | + | 0.762384i | \(0.275971\pi\) | |||||||
\(168\) | −1.92030 | −0.148154 | ||||||||
\(169\) | 26.0617 | 2.00475 | ||||||||
\(170\) | −27.7004 | −2.12452 | ||||||||
\(171\) | −0.869415 | −0.0664858 | ||||||||
\(172\) | −21.9773 | −1.67575 | ||||||||
\(173\) | 9.27650 | 0.705279 | 0.352640 | − | 0.935759i | \(-0.385284\pi\) | ||||
0.352640 | + | 0.935759i | \(0.385284\pi\) | |||||||
\(174\) | −2.50807 | −0.190137 | ||||||||
\(175\) | 0.804258 | 0.0607962 | ||||||||
\(176\) | −16.2994 | −1.22861 | ||||||||
\(177\) | −7.67631 | −0.576987 | ||||||||
\(178\) | 13.4156 | 1.00554 | ||||||||
\(179\) | −7.48254 | −0.559272 | −0.279636 | − | 0.960106i | \(-0.590214\pi\) | ||||
−0.279636 | + | 0.960106i | \(0.590214\pi\) | |||||||
\(180\) | 2.33151 | 0.173780 | ||||||||
\(181\) | −10.6482 | −0.791472 | −0.395736 | − | 0.918364i | \(-0.629510\pi\) | ||||
−0.395736 | + | 0.918364i | \(0.629510\pi\) | |||||||
\(182\) | −13.2466 | −0.981906 | ||||||||
\(183\) | 0.272962 | 0.0201779 | ||||||||
\(184\) | −1.04322 | −0.0769074 | ||||||||
\(185\) | 1.34311 | 0.0987475 | ||||||||
\(186\) | −30.5899 | −2.24296 | ||||||||
\(187\) | −31.8827 | −2.33149 | ||||||||
\(188\) | 10.6359 | 0.775701 | ||||||||
\(189\) | 4.80743 | 0.349689 | ||||||||
\(190\) | −11.4327 | −0.829419 | ||||||||
\(191\) | 3.30294 | 0.238992 | 0.119496 | − | 0.992835i | \(-0.461872\pi\) | ||||
0.119496 | + | 0.992835i | \(0.461872\pi\) | |||||||
\(192\) | 20.8627 | 1.50563 | ||||||||
\(193\) | 9.38315 | 0.675414 | 0.337707 | − | 0.941251i | \(-0.390349\pi\) | ||||
0.337707 | + | 0.941251i | \(0.390349\pi\) | |||||||
\(194\) | 22.2168 | 1.59507 | ||||||||
\(195\) | 27.7167 | 1.98483 | ||||||||
\(196\) | 2.49221 | 0.178015 | ||||||||
\(197\) | −23.0929 | −1.64530 | −0.822651 | − | 0.568547i | \(-0.807506\pi\) | ||||
−0.822651 | + | 0.568547i | \(0.807506\pi\) | |||||||
\(198\) | 4.83706 | 0.343755 | ||||||||
\(199\) | 21.6149 | 1.53224 | 0.766118 | − | 0.642699i | \(-0.222186\pi\) | ||||
0.766118 | + | 0.642699i | \(0.222186\pi\) | |||||||
\(200\) | 0.839020 | 0.0593277 | ||||||||
\(201\) | −24.5546 | −1.73195 | ||||||||
\(202\) | −3.33411 | −0.234587 | ||||||||
\(203\) | 0.642864 | 0.0451202 | ||||||||
\(204\) | 24.8862 | 1.74238 | ||||||||
\(205\) | 6.18796 | 0.432186 | ||||||||
\(206\) | 10.6304 | 0.740659 | ||||||||
\(207\) | −0.388311 | −0.0269895 | ||||||||
\(208\) | 17.3331 | 1.20183 | ||||||||
\(209\) | −13.1589 | −0.910219 | ||||||||
\(210\) | −9.39929 | −0.648612 | ||||||||
\(211\) | 15.4579 | 1.06416 | 0.532081 | − | 0.846693i | \(-0.321410\pi\) | ||||
0.532081 | + | 0.846693i | \(0.321410\pi\) | |||||||
\(212\) | 7.51547 | 0.516164 | ||||||||
\(213\) | 14.5996 | 1.00035 | ||||||||
\(214\) | −12.3185 | −0.842077 | ||||||||
\(215\) | −21.2453 | −1.44892 | ||||||||
\(216\) | 5.01522 | 0.341243 | ||||||||
\(217\) | 7.84074 | 0.532264 | ||||||||
\(218\) | 16.2147 | 1.09820 | ||||||||
\(219\) | −7.88040 | −0.532508 | ||||||||
\(220\) | 35.2882 | 2.37913 | ||||||||
\(221\) | 33.9046 | 2.28067 | ||||||||
\(222\) | −2.17500 | −0.145977 | ||||||||
\(223\) | −11.0708 | −0.741357 | −0.370679 | − | 0.928761i | \(-0.620875\pi\) | ||||
−0.370679 | + | 0.928761i | \(0.620875\pi\) | |||||||
\(224\) | −7.96445 | −0.532147 | ||||||||
\(225\) | 0.312302 | 0.0208201 | ||||||||
\(226\) | 22.2543 | 1.48033 | ||||||||
\(227\) | −2.44676 | −0.162397 | −0.0811984 | − | 0.996698i | \(-0.525875\pi\) | ||||
−0.0811984 | + | 0.996698i | \(0.525875\pi\) | |||||||
\(228\) | 10.2712 | 0.680230 | ||||||||
\(229\) | −5.74097 | −0.379374 | −0.189687 | − | 0.981845i | \(-0.560747\pi\) | ||||
−0.189687 | + | 0.981845i | \(0.560747\pi\) | |||||||
\(230\) | −5.10626 | −0.336697 | ||||||||
\(231\) | −10.8184 | −0.711799 | ||||||||
\(232\) | 0.670650 | 0.0440303 | ||||||||
\(233\) | 8.66481 | 0.567651 | 0.283825 | − | 0.958876i | \(-0.408396\pi\) | ||||
0.283825 | + | 0.958876i | \(0.408396\pi\) | |||||||
\(234\) | −5.14382 | −0.336262 | ||||||||
\(235\) | 10.2817 | 0.670701 | ||||||||
\(236\) | 10.3931 | 0.676533 | ||||||||
\(237\) | 1.58603 | 0.103024 | ||||||||
\(238\) | −11.4977 | −0.745288 | ||||||||
\(239\) | −0.995387 | −0.0643862 | −0.0321931 | − | 0.999482i | \(-0.510249\pi\) | ||||
−0.0321931 | + | 0.999482i | \(0.510249\pi\) | |||||||
\(240\) | 12.2989 | 0.793888 | ||||||||
\(241\) | −13.9247 | −0.896967 | −0.448483 | − | 0.893791i | \(-0.648036\pi\) | ||||
−0.448483 | + | 0.893791i | \(0.648036\pi\) | |||||||
\(242\) | 49.8961 | 3.20745 | ||||||||
\(243\) | 4.01111 | 0.257313 | ||||||||
\(244\) | −0.369568 | −0.0236591 | ||||||||
\(245\) | 2.40920 | 0.153918 | ||||||||
\(246\) | −10.0206 | −0.638892 | ||||||||
\(247\) | 13.9934 | 0.890378 | ||||||||
\(248\) | 8.17963 | 0.519407 | ||||||||
\(249\) | 8.86941 | 0.562076 | ||||||||
\(250\) | −21.4246 | −1.35501 | ||||||||
\(251\) | −0.229739 | −0.0145010 | −0.00725049 | − | 0.999974i | \(-0.502308\pi\) | ||||
−0.00725049 | + | 0.999974i | \(0.502308\pi\) | |||||||
\(252\) | 0.967751 | 0.0609626 | ||||||||
\(253\) | −5.87722 | −0.369497 | ||||||||
\(254\) | −38.0939 | −2.39022 | ||||||||
\(255\) | 24.0574 | 1.50653 | ||||||||
\(256\) | 5.51468 | 0.344667 | ||||||||
\(257\) | −4.24568 | −0.264838 | −0.132419 | − | 0.991194i | \(-0.542274\pi\) | ||||
−0.132419 | + | 0.991194i | \(0.542274\pi\) | |||||||
\(258\) | 34.4042 | 2.14191 | ||||||||
\(259\) | 0.557492 | 0.0346409 | ||||||||
\(260\) | −37.5261 | −2.32727 | ||||||||
\(261\) | 0.249631 | 0.0154518 | ||||||||
\(262\) | −27.6892 | −1.71064 | ||||||||
\(263\) | 2.99220 | 0.184507 | 0.0922535 | − | 0.995736i | \(-0.470593\pi\) | ||||
0.0922535 | + | 0.995736i | \(0.470593\pi\) | |||||||
\(264\) | −11.2860 | −0.694606 | ||||||||
\(265\) | 7.26516 | 0.446295 | ||||||||
\(266\) | −4.74545 | −0.290962 | ||||||||
\(267\) | −11.6512 | −0.713042 | ||||||||
\(268\) | 33.2449 | 2.03076 | ||||||||
\(269\) | −8.92878 | −0.544397 | −0.272199 | − | 0.962241i | \(-0.587751\pi\) | ||||
−0.272199 | + | 0.962241i | \(0.587751\pi\) | |||||||
\(270\) | 24.5480 | 1.49394 | ||||||||
\(271\) | 20.9773 | 1.27428 | 0.637140 | − | 0.770748i | \(-0.280117\pi\) | ||||
0.637140 | + | 0.770748i | \(0.280117\pi\) | |||||||
\(272\) | 15.0447 | 0.912218 | ||||||||
\(273\) | 11.5045 | 0.696284 | ||||||||
\(274\) | −31.8478 | −1.92399 | ||||||||
\(275\) | 4.72680 | 0.285036 | ||||||||
\(276\) | 4.58750 | 0.276135 | ||||||||
\(277\) | 5.82584 | 0.350041 | 0.175020 | − | 0.984565i | \(-0.444001\pi\) | ||||
0.175020 | + | 0.984565i | \(0.444001\pi\) | |||||||
\(278\) | −27.1266 | −1.62695 | ||||||||
\(279\) | 3.04464 | 0.182278 | ||||||||
\(280\) | 2.51334 | 0.150201 | ||||||||
\(281\) | −21.1877 | −1.26395 | −0.631976 | − | 0.774988i | \(-0.717756\pi\) | ||||
−0.631976 | + | 0.774988i | \(0.717756\pi\) | |||||||
\(282\) | −16.6499 | −0.991486 | ||||||||
\(283\) | −12.8049 | −0.761173 | −0.380587 | − | 0.924745i | \(-0.624278\pi\) | ||||
−0.380587 | + | 0.924745i | \(0.624278\pi\) | |||||||
\(284\) | −19.7667 | −1.17294 | ||||||||
\(285\) | 9.92916 | 0.588152 | ||||||||
\(286\) | −77.8533 | −4.60356 | ||||||||
\(287\) | 2.56847 | 0.151612 | ||||||||
\(288\) | −3.09268 | −0.182238 | ||||||||
\(289\) | 12.4283 | 0.731079 | ||||||||
\(290\) | 3.28263 | 0.192763 | ||||||||
\(291\) | −19.2949 | −1.13109 | ||||||||
\(292\) | 10.6694 | 0.624381 | ||||||||
\(293\) | −3.11921 | −0.182226 | −0.0911132 | − | 0.995841i | \(-0.529043\pi\) | ||||
−0.0911132 | + | 0.995841i | \(0.529043\pi\) | |||||||
\(294\) | −3.90141 | −0.227535 | ||||||||
\(295\) | 10.0469 | 0.584956 | ||||||||
\(296\) | 0.581588 | 0.0338041 | ||||||||
\(297\) | 28.2543 | 1.63948 | ||||||||
\(298\) | −44.7854 | −2.59435 | ||||||||
\(299\) | 6.24994 | 0.361443 | ||||||||
\(300\) | −3.68953 | −0.213015 | ||||||||
\(301\) | −8.81841 | −0.508284 | ||||||||
\(302\) | 41.3859 | 2.38149 | ||||||||
\(303\) | 2.89562 | 0.166349 | ||||||||
\(304\) | 6.20937 | 0.356132 | ||||||||
\(305\) | −0.357259 | −0.0204566 | ||||||||
\(306\) | −4.46470 | −0.255230 | ||||||||
\(307\) | −16.1152 | −0.919746 | −0.459873 | − | 0.887985i | \(-0.652105\pi\) | ||||
−0.459873 | + | 0.887985i | \(0.652105\pi\) | |||||||
\(308\) | 14.6472 | 0.834604 | ||||||||
\(309\) | −9.23237 | −0.525211 | ||||||||
\(310\) | 40.0369 | 2.27394 | ||||||||
\(311\) | 30.2428 | 1.71491 | 0.857457 | − | 0.514556i | \(-0.172043\pi\) | ||||
0.857457 | + | 0.514556i | \(0.172043\pi\) | |||||||
\(312\) | 12.0017 | 0.679465 | ||||||||
\(313\) | −20.4956 | −1.15848 | −0.579241 | − | 0.815156i | \(-0.696651\pi\) | ||||
−0.579241 | + | 0.815156i | \(0.696651\pi\) | |||||||
\(314\) | −9.76315 | −0.550967 | ||||||||
\(315\) | 0.935520 | 0.0527106 | ||||||||
\(316\) | −2.14736 | −0.120798 | ||||||||
\(317\) | 2.95042 | 0.165712 | 0.0828559 | − | 0.996562i | \(-0.473596\pi\) | ||||
0.0828559 | + | 0.996562i | \(0.473596\pi\) | |||||||
\(318\) | −11.7650 | −0.659751 | ||||||||
\(319\) | 3.77825 | 0.211541 | ||||||||
\(320\) | −27.3056 | −1.52643 | ||||||||
\(321\) | 10.6984 | 0.597129 | ||||||||
\(322\) | −2.11948 | −0.118114 | ||||||||
\(323\) | 12.1459 | 0.675817 | ||||||||
\(324\) | −24.9573 | −1.38652 | ||||||||
\(325\) | −5.02656 | −0.278823 | ||||||||
\(326\) | 34.5961 | 1.91610 | ||||||||
\(327\) | −14.0822 | −0.778747 | ||||||||
\(328\) | 2.67948 | 0.147950 | ||||||||
\(329\) | 4.26766 | 0.235284 | ||||||||
\(330\) | −55.2416 | −3.04095 | ||||||||
\(331\) | −21.2497 | −1.16799 | −0.583994 | − | 0.811758i | \(-0.698511\pi\) | ||||
−0.583994 | + | 0.811758i | \(0.698511\pi\) | |||||||
\(332\) | −12.0085 | −0.659050 | ||||||||
\(333\) | 0.216480 | 0.0118630 | ||||||||
\(334\) | 35.4492 | 1.93969 | ||||||||
\(335\) | 32.1377 | 1.75587 | ||||||||
\(336\) | 5.10495 | 0.278498 | ||||||||
\(337\) | −24.8118 | −1.35158 | −0.675792 | − | 0.737092i | \(-0.736198\pi\) | ||||
−0.675792 | + | 0.737092i | \(0.736198\pi\) | |||||||
\(338\) | 55.2374 | 3.00452 | ||||||||
\(339\) | −19.3275 | −1.04973 | ||||||||
\(340\) | −32.5717 | −1.76645 | ||||||||
\(341\) | 46.0817 | 2.49546 | ||||||||
\(342\) | −1.84271 | −0.0996423 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −9.19956 | −0.496007 | ||||||||
\(345\) | 4.43471 | 0.238757 | ||||||||
\(346\) | 19.6614 | 1.05700 | ||||||||
\(347\) | 11.8158 | 0.634304 | 0.317152 | − | 0.948375i | \(-0.397274\pi\) | ||||
0.317152 | + | 0.948375i | \(0.397274\pi\) | |||||||
\(348\) | −2.94913 | −0.158090 | ||||||||
\(349\) | −12.1614 | −0.650984 | −0.325492 | − | 0.945545i | \(-0.605530\pi\) | ||||
−0.325492 | + | 0.945545i | \(0.605530\pi\) | |||||||
\(350\) | 1.70461 | 0.0911152 | ||||||||
\(351\) | −30.0462 | −1.60375 | ||||||||
\(352\) | −46.8088 | −2.49492 | ||||||||
\(353\) | 17.5264 | 0.932838 | 0.466419 | − | 0.884564i | \(-0.345544\pi\) | ||||
0.466419 | + | 0.884564i | \(0.345544\pi\) | |||||||
\(354\) | −16.2698 | −0.864730 | ||||||||
\(355\) | −19.1084 | −1.01417 | ||||||||
\(356\) | 15.7748 | 0.836061 | ||||||||
\(357\) | 9.98561 | 0.528494 | ||||||||
\(358\) | −15.8591 | −0.838181 | ||||||||
\(359\) | 7.70275 | 0.406535 | 0.203268 | − | 0.979123i | \(-0.434844\pi\) | ||||
0.203268 | + | 0.979123i | \(0.434844\pi\) | |||||||
\(360\) | 0.975956 | 0.0514374 | ||||||||
\(361\) | −13.9870 | −0.736160 | ||||||||
\(362\) | −22.5686 | −1.18618 | ||||||||
\(363\) | −43.3340 | −2.27445 | ||||||||
\(364\) | −15.5761 | −0.816411 | ||||||||
\(365\) | 10.3141 | 0.539863 | ||||||||
\(366\) | 0.578537 | 0.0302406 | ||||||||
\(367\) | 15.0819 | 0.787271 | 0.393635 | − | 0.919267i | \(-0.371217\pi\) | ||||
0.393635 | + | 0.919267i | \(0.371217\pi\) | |||||||
\(368\) | 2.77332 | 0.144569 | ||||||||
\(369\) | 0.997364 | 0.0519207 | ||||||||
\(370\) | 2.84670 | 0.147993 | ||||||||
\(371\) | 3.01559 | 0.156561 | ||||||||
\(372\) | −35.9693 | −1.86492 | ||||||||
\(373\) | −21.5089 | −1.11369 | −0.556843 | − | 0.830618i | \(-0.687988\pi\) | ||||
−0.556843 | + | 0.830618i | \(0.687988\pi\) | |||||||
\(374\) | −67.5747 | −3.49421 | ||||||||
\(375\) | 18.6069 | 0.960856 | ||||||||
\(376\) | 4.45212 | 0.229600 | ||||||||
\(377\) | −4.01786 | −0.206930 | ||||||||
\(378\) | 10.1893 | 0.524079 | ||||||||
\(379\) | 34.7117 | 1.78302 | 0.891511 | − | 0.452999i | \(-0.149646\pi\) | ||||
0.891511 | + | 0.452999i | \(0.149646\pi\) | |||||||
\(380\) | −13.4433 | −0.689625 | ||||||||
\(381\) | 33.0839 | 1.69494 | ||||||||
\(382\) | 7.00052 | 0.358178 | ||||||||
\(383\) | −10.2963 | −0.526119 | −0.263059 | − | 0.964780i | \(-0.584732\pi\) | ||||
−0.263059 | + | 0.964780i | \(0.584732\pi\) | |||||||
\(384\) | 14.8972 | 0.760218 | ||||||||
\(385\) | 14.1594 | 0.721630 | ||||||||
\(386\) | 19.8874 | 1.01224 | ||||||||
\(387\) | −3.42428 | −0.174066 | ||||||||
\(388\) | 26.1237 | 1.32623 | ||||||||
\(389\) | −26.1594 | −1.32633 | −0.663167 | − | 0.748471i | \(-0.730788\pi\) | ||||
−0.663167 | + | 0.748471i | \(0.730788\pi\) | |||||||
\(390\) | 58.7450 | 2.97467 | ||||||||
\(391\) | 5.42479 | 0.274343 | ||||||||
\(392\) | 1.04322 | 0.0526907 | ||||||||
\(393\) | 24.0476 | 1.21304 | ||||||||
\(394\) | −48.9450 | −2.46582 | ||||||||
\(395\) | −2.07584 | −0.104447 | ||||||||
\(396\) | 5.68768 | 0.285817 | ||||||||
\(397\) | −4.52380 | −0.227043 | −0.113522 | − | 0.993536i | \(-0.536213\pi\) | ||||
−0.113522 | + | 0.993536i | \(0.536213\pi\) | |||||||
\(398\) | 45.8123 | 2.29636 | ||||||||
\(399\) | 4.12134 | 0.206325 | ||||||||
\(400\) | −2.23046 | −0.111523 | ||||||||
\(401\) | −18.0222 | −0.899987 | −0.449994 | − | 0.893032i | \(-0.648574\pi\) | ||||
−0.449994 | + | 0.893032i | \(0.648574\pi\) | |||||||
\(402\) | −52.0431 | −2.59567 | ||||||||
\(403\) | −49.0041 | −2.44107 | ||||||||
\(404\) | −3.92044 | −0.195049 | ||||||||
\(405\) | −24.1261 | −1.19884 | ||||||||
\(406\) | 1.36254 | 0.0676216 | ||||||||
\(407\) | 3.27650 | 0.162410 | ||||||||
\(408\) | 10.4172 | 0.515729 | ||||||||
\(409\) | 4.67260 | 0.231045 | 0.115523 | − | 0.993305i | \(-0.463146\pi\) | ||||
0.115523 | + | 0.993305i | \(0.463146\pi\) | |||||||
\(410\) | 13.1153 | 0.647717 | ||||||||
\(411\) | 27.6593 | 1.36433 | ||||||||
\(412\) | 12.4999 | 0.615825 | ||||||||
\(413\) | 4.17024 | 0.205204 | ||||||||
\(414\) | −0.823019 | −0.0404492 | ||||||||
\(415\) | −11.6085 | −0.569840 | ||||||||
\(416\) | 49.7773 | 2.44053 | ||||||||
\(417\) | 23.5591 | 1.15369 | ||||||||
\(418\) | −27.8900 | −1.36415 | ||||||||
\(419\) | −12.7674 | −0.623728 | −0.311864 | − | 0.950127i | \(-0.600953\pi\) | ||||
−0.311864 | + | 0.950127i | \(0.600953\pi\) | |||||||
\(420\) | −11.0522 | −0.539292 | ||||||||
\(421\) | 28.1367 | 1.37130 | 0.685649 | − | 0.727932i | \(-0.259518\pi\) | ||||
0.685649 | + | 0.727932i | \(0.259518\pi\) | |||||||
\(422\) | 32.7626 | 1.59486 | ||||||||
\(423\) | 1.65718 | 0.0805748 | ||||||||
\(424\) | 3.14593 | 0.152780 | ||||||||
\(425\) | −4.36293 | −0.211633 | ||||||||
\(426\) | 30.9437 | 1.49923 | ||||||||
\(427\) | −0.148289 | −0.00717622 | ||||||||
\(428\) | −14.4848 | −0.700150 | ||||||||
\(429\) | 67.6144 | 3.26445 | ||||||||
\(430\) | −45.0291 | −2.17150 | ||||||||
\(431\) | −5.49352 | −0.264613 | −0.132307 | − | 0.991209i | \(-0.542238\pi\) | ||||
−0.132307 | + | 0.991209i | \(0.542238\pi\) | |||||||
\(432\) | −13.3325 | −0.641462 | ||||||||
\(433\) | −21.0177 | −1.01005 | −0.505023 | − | 0.863106i | \(-0.668516\pi\) | ||||
−0.505023 | + | 0.863106i | \(0.668516\pi\) | |||||||
\(434\) | 16.6183 | 0.797704 | ||||||||
\(435\) | −2.85091 | −0.136691 | ||||||||
\(436\) | 19.0661 | 0.913102 | ||||||||
\(437\) | 2.23897 | 0.107104 | ||||||||
\(438\) | −16.7024 | −0.798070 | ||||||||
\(439\) | 39.2674 | 1.87413 | 0.937066 | − | 0.349153i | \(-0.113531\pi\) | ||||
0.937066 | + | 0.349153i | \(0.113531\pi\) | |||||||
\(440\) | 14.7714 | 0.704199 | ||||||||
\(441\) | 0.388311 | 0.0184910 | ||||||||
\(442\) | 71.8602 | 3.41804 | ||||||||
\(443\) | 14.5489 | 0.691240 | 0.345620 | − | 0.938375i | \(-0.387669\pi\) | ||||
0.345620 | + | 0.938375i | \(0.387669\pi\) | |||||||
\(444\) | −2.55749 | −0.121373 | ||||||||
\(445\) | 15.2494 | 0.722890 | ||||||||
\(446\) | −23.4644 | −1.11107 | ||||||||
\(447\) | 38.8954 | 1.83969 | ||||||||
\(448\) | −11.3339 | −0.535475 | ||||||||
\(449\) | 11.3660 | 0.536395 | 0.268197 | − | 0.963364i | \(-0.413572\pi\) | ||||
0.268197 | + | 0.963364i | \(0.413572\pi\) | |||||||
\(450\) | 0.661919 | 0.0312032 | ||||||||
\(451\) | 15.0954 | 0.710816 | ||||||||
\(452\) | 26.1679 | 1.23083 | ||||||||
\(453\) | −35.9430 | −1.68875 | ||||||||
\(454\) | −5.18586 | −0.243384 | ||||||||
\(455\) | −15.0574 | −0.705900 | ||||||||
\(456\) | 4.29948 | 0.201342 | ||||||||
\(457\) | −9.42744 | −0.440997 | −0.220499 | − | 0.975387i | \(-0.570768\pi\) | ||||
−0.220499 | + | 0.975387i | \(0.570768\pi\) | |||||||
\(458\) | −12.1679 | −0.568568 | ||||||||
\(459\) | −26.0793 | −1.21728 | ||||||||
\(460\) | −6.00423 | −0.279949 | ||||||||
\(461\) | −28.7697 | −1.33994 | −0.669968 | − | 0.742390i | \(-0.733692\pi\) | ||||
−0.669968 | + | 0.742390i | \(0.733692\pi\) | |||||||
\(462\) | −22.9294 | −1.06677 | ||||||||
\(463\) | −4.65928 | −0.216535 | −0.108268 | − | 0.994122i | \(-0.534530\pi\) | ||||
−0.108268 | + | 0.994122i | \(0.534530\pi\) | |||||||
\(464\) | −1.78287 | −0.0827675 | ||||||||
\(465\) | −34.7714 | −1.61248 | ||||||||
\(466\) | 18.3649 | 0.850738 | ||||||||
\(467\) | 7.82926 | 0.362295 | 0.181147 | − | 0.983456i | \(-0.442019\pi\) | ||||
0.181147 | + | 0.983456i | \(0.442019\pi\) | |||||||
\(468\) | −6.04839 | −0.279587 | ||||||||
\(469\) | 13.3396 | 0.615964 | ||||||||
\(470\) | 21.7918 | 1.00518 | ||||||||
\(471\) | 8.47914 | 0.390698 | ||||||||
\(472\) | 4.35049 | 0.200247 | ||||||||
\(473\) | −51.8277 | −2.38304 | ||||||||
\(474\) | 3.36156 | 0.154402 | ||||||||
\(475\) | −1.80070 | −0.0826220 | ||||||||
\(476\) | −13.5197 | −0.619674 | ||||||||
\(477\) | 1.17099 | 0.0536158 | ||||||||
\(478\) | −2.10971 | −0.0964957 | ||||||||
\(479\) | −33.9427 | −1.55088 | −0.775440 | − | 0.631421i | \(-0.782472\pi\) | ||||
−0.775440 | + | 0.631421i | \(0.782472\pi\) | |||||||
\(480\) | 35.3200 | 1.61213 | ||||||||
\(481\) | −3.48429 | −0.158870 | ||||||||
\(482\) | −29.5131 | −1.34428 | ||||||||
\(483\) | 1.84074 | 0.0837564 | ||||||||
\(484\) | 58.6707 | 2.66685 | ||||||||
\(485\) | 25.2536 | 1.14671 | ||||||||
\(486\) | 8.50149 | 0.385635 | ||||||||
\(487\) | −11.6880 | −0.529633 | −0.264817 | − | 0.964299i | \(-0.585311\pi\) | ||||
−0.264817 | + | 0.964299i | \(0.585311\pi\) | |||||||
\(488\) | −0.154699 | −0.00700289 | ||||||||
\(489\) | −30.0462 | −1.35873 | ||||||||
\(490\) | 5.10626 | 0.230677 | ||||||||
\(491\) | −19.6742 | −0.887885 | −0.443943 | − | 0.896055i | \(-0.646421\pi\) | ||||
−0.443943 | + | 0.896055i | \(0.646421\pi\) | |||||||
\(492\) | −11.7828 | −0.531211 | ||||||||
\(493\) | −3.48740 | −0.157065 | ||||||||
\(494\) | 29.6588 | 1.33441 | ||||||||
\(495\) | 5.49825 | 0.247128 | ||||||||
\(496\) | −21.7449 | −0.976374 | ||||||||
\(497\) | −7.93141 | −0.355772 | ||||||||
\(498\) | 18.7986 | 0.842384 | ||||||||
\(499\) | −30.1698 | −1.35059 | −0.675294 | − | 0.737549i | \(-0.735983\pi\) | ||||
−0.675294 | + | 0.737549i | \(0.735983\pi\) | |||||||
\(500\) | −25.1922 | −1.12663 | ||||||||
\(501\) | −30.7870 | −1.37546 | ||||||||
\(502\) | −0.486927 | −0.0217326 | ||||||||
\(503\) | 24.1110 | 1.07506 | 0.537529 | − | 0.843246i | \(-0.319358\pi\) | ||||
0.537529 | + | 0.843246i | \(0.319358\pi\) | |||||||
\(504\) | 0.405095 | 0.0180444 | ||||||||
\(505\) | −3.78987 | −0.168647 | ||||||||
\(506\) | −12.4567 | −0.553766 | ||||||||
\(507\) | −47.9728 | −2.13055 | ||||||||
\(508\) | −44.7929 | −1.98736 | ||||||||
\(509\) | 21.5774 | 0.956404 | 0.478202 | − | 0.878250i | \(-0.341289\pi\) | ||||
0.478202 | + | 0.878250i | \(0.341289\pi\) | |||||||
\(510\) | 50.9891 | 2.25784 | ||||||||
\(511\) | 4.28111 | 0.189385 | ||||||||
\(512\) | 27.8744 | 1.23188 | ||||||||
\(513\) | −10.7637 | −0.475228 | ||||||||
\(514\) | −8.99864 | −0.396913 | ||||||||
\(515\) | 12.0836 | 0.532466 | ||||||||
\(516\) | 40.4544 | 1.78091 | ||||||||
\(517\) | 25.0819 | 1.10310 | ||||||||
\(518\) | 1.18159 | 0.0519163 | ||||||||
\(519\) | −17.0756 | −0.749535 | ||||||||
\(520\) | −15.7082 | −0.688850 | ||||||||
\(521\) | −22.0862 | −0.967613 | −0.483807 | − | 0.875175i | \(-0.660746\pi\) | ||||
−0.483807 | + | 0.875175i | \(0.660746\pi\) | |||||||
\(522\) | 0.529089 | 0.0231576 | ||||||||
\(523\) | 5.79856 | 0.253553 | 0.126777 | − | 0.991931i | \(-0.459537\pi\) | ||||
0.126777 | + | 0.991931i | \(0.459537\pi\) | |||||||
\(524\) | −32.5585 | −1.42232 | ||||||||
\(525\) | −1.48043 | −0.0646111 | ||||||||
\(526\) | 6.34191 | 0.276521 | ||||||||
\(527\) | −42.5343 | −1.85283 | ||||||||
\(528\) | 30.0029 | 1.30571 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 15.3984 | 0.668863 | ||||||||
\(531\) | 1.61935 | 0.0702738 | ||||||||
\(532\) | −5.57996 | −0.241922 | ||||||||
\(533\) | −16.0528 | −0.695322 | ||||||||
\(534\) | −24.6945 | −1.06864 | ||||||||
\(535\) | −14.0024 | −0.605376 | ||||||||
\(536\) | 13.9161 | 0.601085 | ||||||||
\(537\) | 13.7734 | 0.594366 | ||||||||
\(538\) | −18.9244 | −0.815888 | ||||||||
\(539\) | 5.87722 | 0.253150 | ||||||||
\(540\) | 28.8649 | 1.24215 | ||||||||
\(541\) | 29.6582 | 1.27511 | 0.637553 | − | 0.770407i | \(-0.279947\pi\) | ||||
0.637553 | + | 0.770407i | \(0.279947\pi\) | |||||||
\(542\) | 44.4610 | 1.90976 | ||||||||
\(543\) | 19.6005 | 0.841137 | ||||||||
\(544\) | 43.2055 | 1.85242 | ||||||||
\(545\) | 18.4311 | 0.789502 | ||||||||
\(546\) | 24.3836 | 1.04352 | ||||||||
\(547\) | −7.24730 | −0.309872 | −0.154936 | − | 0.987924i | \(-0.549517\pi\) | ||||
−0.154936 | + | 0.987924i | \(0.549517\pi\) | |||||||
\(548\) | −37.4484 | −1.59972 | ||||||||
\(549\) | −0.0575824 | −0.00245756 | ||||||||
\(550\) | 10.0184 | 0.427184 | ||||||||
\(551\) | −1.43935 | −0.0613183 | ||||||||
\(552\) | 1.92030 | 0.0817333 | ||||||||
\(553\) | −0.861628 | −0.0366402 | ||||||||
\(554\) | 12.3478 | 0.524606 | ||||||||
\(555\) | −2.47231 | −0.104944 | ||||||||
\(556\) | −31.8970 | −1.35274 | ||||||||
\(557\) | 21.7634 | 0.922146 | 0.461073 | − | 0.887362i | \(-0.347465\pi\) | ||||
0.461073 | + | 0.887362i | \(0.347465\pi\) | |||||||
\(558\) | 6.45307 | 0.273180 | ||||||||
\(559\) | 55.1145 | 2.33109 | ||||||||
\(560\) | −6.68149 | −0.282345 | ||||||||
\(561\) | 58.6876 | 2.47779 | ||||||||
\(562\) | −44.9070 | −1.89429 | ||||||||
\(563\) | −26.9844 | −1.13726 | −0.568629 | − | 0.822594i | \(-0.692526\pi\) | ||||
−0.568629 | + | 0.822594i | \(0.692526\pi\) | |||||||
\(564\) | −19.5779 | −0.824377 | ||||||||
\(565\) | 25.2963 | 1.06422 | ||||||||
\(566\) | −27.1398 | −1.14077 | ||||||||
\(567\) | −10.0141 | −0.420555 | ||||||||
\(568\) | −8.27423 | −0.347179 | ||||||||
\(569\) | 37.4420 | 1.56965 | 0.784826 | − | 0.619717i | \(-0.212752\pi\) | ||||
0.784826 | + | 0.619717i | \(0.212752\pi\) | |||||||
\(570\) | 21.0447 | 0.881464 | ||||||||
\(571\) | −3.32489 | −0.139142 | −0.0695711 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695711 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(572\) | −91.5443 | −3.82766 | ||||||||
\(573\) | −6.07984 | −0.253989 | ||||||||
\(574\) | 5.44382 | 0.227221 | ||||||||
\(575\) | −0.804258 | −0.0335399 | ||||||||
\(576\) | −4.40107 | −0.183378 | ||||||||
\(577\) | −41.0573 | −1.70924 | −0.854618 | − | 0.519257i | \(-0.826209\pi\) | ||||
−0.854618 | + | 0.519257i | \(0.826209\pi\) | |||||||
\(578\) | 26.3417 | 1.09567 | ||||||||
\(579\) | −17.2719 | −0.717796 | ||||||||
\(580\) | 3.85990 | 0.160274 | ||||||||
\(581\) | −4.81841 | −0.199901 | ||||||||
\(582\) | −40.8952 | −1.69516 | ||||||||
\(583\) | 17.7233 | 0.734022 | ||||||||
\(584\) | 4.46616 | 0.184811 | ||||||||
\(585\) | −5.84694 | −0.241741 | ||||||||
\(586\) | −6.61112 | −0.273103 | ||||||||
\(587\) | −31.9182 | −1.31741 | −0.658703 | − | 0.752403i | \(-0.728895\pi\) | ||||
−0.658703 | + | 0.752403i | \(0.728895\pi\) | |||||||
\(588\) | −4.58750 | −0.189185 | ||||||||
\(589\) | −17.5551 | −0.723347 | ||||||||
\(590\) | 21.2943 | 0.876674 | ||||||||
\(591\) | 42.5080 | 1.74854 | ||||||||
\(592\) | −1.54610 | −0.0635445 | ||||||||
\(593\) | 36.5062 | 1.49913 | 0.749566 | − | 0.661930i | \(-0.230262\pi\) | ||||
0.749566 | + | 0.661930i | \(0.230262\pi\) | |||||||
\(594\) | 59.8845 | 2.45709 | ||||||||
\(595\) | −13.0694 | −0.535794 | ||||||||
\(596\) | −52.6611 | −2.15708 | ||||||||
\(597\) | −39.7873 | −1.62838 | ||||||||
\(598\) | 13.2466 | 0.541695 | ||||||||
\(599\) | −7.51073 | −0.306880 | −0.153440 | − | 0.988158i | \(-0.549035\pi\) | ||||
−0.153440 | + | 0.988158i | \(0.549035\pi\) | |||||||
\(600\) | −1.54441 | −0.0630505 | ||||||||
\(601\) | −6.05329 | −0.246919 | −0.123460 | − | 0.992350i | \(-0.539399\pi\) | ||||
−0.123460 | + | 0.992350i | \(0.539399\pi\) | |||||||
\(602\) | −18.6905 | −0.761766 | ||||||||
\(603\) | 5.17990 | 0.210942 | ||||||||
\(604\) | 48.6639 | 1.98011 | ||||||||
\(605\) | 56.7166 | 2.30586 | ||||||||
\(606\) | 6.13723 | 0.249308 | ||||||||
\(607\) | 24.4047 | 0.990557 | 0.495278 | − | 0.868734i | \(-0.335066\pi\) | ||||
0.495278 | + | 0.868734i | \(0.335066\pi\) | |||||||
\(608\) | 17.8321 | 0.723188 | ||||||||
\(609\) | −1.18334 | −0.0479515 | ||||||||
\(610\) | −0.757204 | −0.0306583 | ||||||||
\(611\) | −26.6726 | −1.07906 | ||||||||
\(612\) | −5.24985 | −0.212213 | ||||||||
\(613\) | 4.81180 | 0.194347 | 0.0971734 | − | 0.995267i | \(-0.469020\pi\) | ||||
0.0971734 | + | 0.995267i | \(0.469020\pi\) | |||||||
\(614\) | −34.1560 | −1.37842 | ||||||||
\(615\) | −11.3904 | −0.459305 | ||||||||
\(616\) | 6.13125 | 0.247035 | ||||||||
\(617\) | −38.1414 | −1.53552 | −0.767758 | − | 0.640740i | \(-0.778628\pi\) | ||||
−0.767758 | + | 0.640740i | \(0.778628\pi\) | |||||||
\(618\) | −19.5679 | −0.787135 | ||||||||
\(619\) | −17.8340 | −0.716809 | −0.358404 | − | 0.933566i | \(-0.616679\pi\) | ||||
−0.358404 | + | 0.933566i | \(0.616679\pi\) | |||||||
\(620\) | 47.0776 | 1.89068 | ||||||||
\(621\) | −4.80743 | −0.192916 | ||||||||
\(622\) | 64.0992 | 2.57014 | ||||||||
\(623\) | 6.32964 | 0.253592 | ||||||||
\(624\) | −31.9056 | −1.27725 | ||||||||
\(625\) | −28.3745 | −1.13498 | ||||||||
\(626\) | −43.4402 | −1.73622 | ||||||||
\(627\) | 24.2220 | 0.967335 | ||||||||
\(628\) | −11.4801 | −0.458104 | ||||||||
\(629\) | −3.02428 | −0.120586 | ||||||||
\(630\) | 1.98282 | 0.0789974 | ||||||||
\(631\) | 22.2906 | 0.887377 | 0.443688 | − | 0.896181i | \(-0.353670\pi\) | ||||
0.443688 | + | 0.896181i | \(0.353670\pi\) | |||||||
\(632\) | −0.898870 | −0.0357551 | ||||||||
\(633\) | −28.4538 | −1.13094 | ||||||||
\(634\) | 6.25336 | 0.248352 | ||||||||
\(635\) | −43.3011 | −1.71835 | ||||||||
\(636\) | −13.8340 | −0.548553 | ||||||||
\(637\) | −6.24994 | −0.247632 | ||||||||
\(638\) | 8.00793 | 0.317037 | ||||||||
\(639\) | −3.07986 | −0.121837 | ||||||||
\(640\) | −19.4978 | −0.770718 | ||||||||
\(641\) | 28.4927 | 1.12540 | 0.562698 | − | 0.826663i | \(-0.309763\pi\) | ||||
0.562698 | + | 0.826663i | \(0.309763\pi\) | |||||||
\(642\) | 22.6752 | 0.894917 | ||||||||
\(643\) | 0.975186 | 0.0384576 | 0.0192288 | − | 0.999815i | \(-0.493879\pi\) | ||||
0.0192288 | + | 0.999815i | \(0.493879\pi\) | |||||||
\(644\) | −2.49221 | −0.0982067 | ||||||||
\(645\) | 39.1070 | 1.53984 | ||||||||
\(646\) | 25.7431 | 1.01285 | ||||||||
\(647\) | −27.5193 | −1.08190 | −0.540948 | − | 0.841056i | \(-0.681935\pi\) | ||||
−0.540948 | + | 0.841056i | \(0.681935\pi\) | |||||||
\(648\) | −10.4470 | −0.410396 | ||||||||
\(649\) | 24.5094 | 0.962078 | ||||||||
\(650\) | −10.6537 | −0.417873 | ||||||||
\(651\) | −14.4327 | −0.565663 | ||||||||
\(652\) | 40.6800 | 1.59315 | ||||||||
\(653\) | −26.1590 | −1.02368 | −0.511840 | − | 0.859081i | \(-0.671036\pi\) | ||||
−0.511840 | + | 0.859081i | \(0.671036\pi\) | |||||||
\(654\) | −29.8469 | −1.16711 | ||||||||
\(655\) | −31.4741 | −1.22979 | ||||||||
\(656\) | −7.12318 | −0.278113 | ||||||||
\(657\) | 1.66240 | 0.0648566 | ||||||||
\(658\) | 9.04523 | 0.352620 | ||||||||
\(659\) | −2.67085 | −0.104042 | −0.0520208 | − | 0.998646i | \(-0.516566\pi\) | ||||
−0.0520208 | + | 0.998646i | \(0.516566\pi\) | |||||||
\(660\) | −64.9562 | −2.52842 | ||||||||
\(661\) | −18.4928 | −0.719285 | −0.359643 | − | 0.933090i | \(-0.617101\pi\) | ||||
−0.359643 | + | 0.933090i | \(0.617101\pi\) | |||||||
\(662\) | −45.0384 | −1.75047 | ||||||||
\(663\) | −62.4095 | −2.42378 | ||||||||
\(664\) | −5.02667 | −0.195073 | ||||||||
\(665\) | −5.39412 | −0.209175 | ||||||||
\(666\) | 0.458826 | 0.0177792 | ||||||||
\(667\) | −0.642864 | −0.0248918 | ||||||||
\(668\) | 41.6831 | 1.61277 | ||||||||
\(669\) | 20.3785 | 0.787877 | ||||||||
\(670\) | 68.1153 | 2.63152 | ||||||||
\(671\) | −0.871528 | −0.0336450 | ||||||||
\(672\) | 14.6605 | 0.565539 | ||||||||
\(673\) | 47.5002 | 1.83100 | 0.915499 | − | 0.402321i | \(-0.131797\pi\) | ||||
0.915499 | + | 0.402321i | \(0.131797\pi\) | |||||||
\(674\) | −52.5882 | −2.02562 | ||||||||
\(675\) | 3.86641 | 0.148818 | ||||||||
\(676\) | 64.9512 | 2.49812 | ||||||||
\(677\) | 33.4288 | 1.28477 | 0.642386 | − | 0.766381i | \(-0.277944\pi\) | ||||
0.642386 | + | 0.766381i | \(0.277944\pi\) | |||||||
\(678\) | −40.9643 | −1.57323 | ||||||||
\(679\) | 10.4822 | 0.402268 | ||||||||
\(680\) | −13.6343 | −0.522852 | ||||||||
\(681\) | 4.50383 | 0.172587 | ||||||||
\(682\) | 97.6694 | 3.73995 | ||||||||
\(683\) | 46.7168 | 1.78757 | 0.893784 | − | 0.448498i | \(-0.148041\pi\) | ||||
0.893784 | + | 0.448498i | \(0.148041\pi\) | |||||||
\(684\) | −2.16676 | −0.0828482 | ||||||||
\(685\) | −36.2012 | −1.38317 | ||||||||
\(686\) | 2.11948 | 0.0809222 | ||||||||
\(687\) | 10.5676 | 0.403180 | ||||||||
\(688\) | 24.4563 | 0.932386 | ||||||||
\(689\) | −18.8472 | −0.718023 | ||||||||
\(690\) | 9.39929 | 0.357825 | ||||||||
\(691\) | −22.8670 | −0.869903 | −0.434952 | − | 0.900454i | \(-0.643235\pi\) | ||||
−0.434952 | + | 0.900454i | \(0.643235\pi\) | |||||||
\(692\) | 23.1190 | 0.878851 | ||||||||
\(693\) | 2.28219 | 0.0866931 | ||||||||
\(694\) | 25.0433 | 0.950631 | ||||||||
\(695\) | −30.8347 | −1.16963 | ||||||||
\(696\) | −1.23449 | −0.0467932 | ||||||||
\(697\) | −13.9334 | −0.527765 | ||||||||
\(698\) | −25.7758 | −0.975630 | ||||||||
\(699\) | −15.9496 | −0.603271 | ||||||||
\(700\) | 2.00438 | 0.0757583 | ||||||||
\(701\) | 39.0885 | 1.47635 | 0.738177 | − | 0.674607i | \(-0.235687\pi\) | ||||
0.738177 | + | 0.674607i | \(0.235687\pi\) | |||||||
\(702\) | −63.6823 | −2.40353 | ||||||||
\(703\) | −1.24821 | −0.0470769 | ||||||||
\(704\) | −66.6116 | −2.51052 | ||||||||
\(705\) | −18.9258 | −0.712787 | ||||||||
\(706\) | 37.1470 | 1.39805 | ||||||||
\(707\) | −1.57308 | −0.0591617 | ||||||||
\(708\) | −19.1309 | −0.718985 | ||||||||
\(709\) | 18.3762 | 0.690132 | 0.345066 | − | 0.938578i | \(-0.387856\pi\) | ||||
0.345066 | + | 0.938578i | \(0.387856\pi\) | |||||||
\(710\) | −40.4999 | −1.51993 | ||||||||
\(711\) | −0.334580 | −0.0125477 | ||||||||
\(712\) | 6.60323 | 0.247466 | ||||||||
\(713\) | −7.84074 | −0.293638 | ||||||||
\(714\) | 21.1643 | 0.792055 | ||||||||
\(715\) | −88.4954 | −3.30954 | ||||||||
\(716\) | −18.6480 | −0.696910 | ||||||||
\(717\) | 1.83224 | 0.0684264 | ||||||||
\(718\) | 16.3258 | 0.609275 | ||||||||
\(719\) | −11.2232 | −0.418553 | −0.209276 | − | 0.977857i | \(-0.567111\pi\) | ||||
−0.209276 | + | 0.977857i | \(0.567111\pi\) | |||||||
\(720\) | −2.59450 | −0.0966912 | ||||||||
\(721\) | 5.01559 | 0.186790 | ||||||||
\(722\) | −29.6453 | −1.10328 | ||||||||
\(723\) | 25.6316 | 0.953251 | ||||||||
\(724\) | −26.5374 | −0.986256 | ||||||||
\(725\) | 0.517028 | 0.0192019 | ||||||||
\(726\) | −91.8457 | −3.40871 | ||||||||
\(727\) | 7.71953 | 0.286302 | 0.143151 | − | 0.989701i | \(-0.454277\pi\) | ||||
0.143151 | + | 0.989701i | \(0.454277\pi\) | |||||||
\(728\) | −6.52008 | −0.241650 | ||||||||
\(729\) | 22.6590 | 0.839224 | ||||||||
\(730\) | 21.8605 | 0.809093 | ||||||||
\(731\) | 47.8380 | 1.76935 | ||||||||
\(732\) | 0.680277 | 0.0251437 | ||||||||
\(733\) | −23.2083 | −0.857217 | −0.428609 | − | 0.903490i | \(-0.640996\pi\) | ||||
−0.428609 | + | 0.903490i | \(0.640996\pi\) | |||||||
\(734\) | 31.9659 | 1.17988 | ||||||||
\(735\) | −4.43471 | −0.163577 | ||||||||
\(736\) | 7.96445 | 0.293573 | ||||||||
\(737\) | 78.3995 | 2.88788 | ||||||||
\(738\) | 2.11390 | 0.0778136 | ||||||||
\(739\) | 8.36545 | 0.307728 | 0.153864 | − | 0.988092i | \(-0.450828\pi\) | ||||
0.153864 | + | 0.988092i | \(0.450828\pi\) | |||||||
\(740\) | 3.34731 | 0.123050 | ||||||||
\(741\) | −25.7582 | −0.946249 | ||||||||
\(742\) | 6.39148 | 0.234639 | ||||||||
\(743\) | 9.54735 | 0.350258 | 0.175129 | − | 0.984545i | \(-0.443966\pi\) | ||||
0.175129 | + | 0.984545i | \(0.443966\pi\) | |||||||
\(744\) | −15.0566 | −0.552000 | ||||||||
\(745\) | −50.9072 | −1.86510 | ||||||||
\(746\) | −45.5877 | −1.66908 | ||||||||
\(747\) | −1.87104 | −0.0684578 | ||||||||
\(748\) | −79.4582 | −2.90528 | ||||||||
\(749\) | −5.81204 | −0.212367 | ||||||||
\(750\) | 39.4370 | 1.44003 | ||||||||
\(751\) | 2.83381 | 0.103407 | 0.0517035 | − | 0.998662i | \(-0.483535\pi\) | ||||
0.0517035 | + | 0.998662i | \(0.483535\pi\) | |||||||
\(752\) | −11.8356 | −0.431599 | ||||||||
\(753\) | 0.422889 | 0.0154109 | ||||||||
\(754\) | −8.51578 | −0.310126 | ||||||||
\(755\) | 47.0432 | 1.71208 | ||||||||
\(756\) | 11.9811 | 0.435749 | ||||||||
\(757\) | 49.7767 | 1.80916 | 0.904582 | − | 0.426300i | \(-0.140183\pi\) | ||||
0.904582 | + | 0.426300i | \(0.140183\pi\) | |||||||
\(758\) | 73.5709 | 2.67222 | ||||||||
\(759\) | 10.8184 | 0.392683 | ||||||||
\(760\) | −5.62727 | −0.204123 | ||||||||
\(761\) | 48.7458 | 1.76704 | 0.883518 | − | 0.468398i | \(-0.155169\pi\) | ||||
0.883518 | + | 0.468398i | \(0.155169\pi\) | |||||||
\(762\) | 70.1208 | 2.54021 | ||||||||
\(763\) | 7.65030 | 0.276959 | ||||||||
\(764\) | 8.23161 | 0.297809 | ||||||||
\(765\) | −5.07500 | −0.183487 | ||||||||
\(766\) | −21.8229 | −0.788495 | ||||||||
\(767\) | −26.0637 | −0.941107 | ||||||||
\(768\) | −10.1511 | −0.366295 | ||||||||
\(769\) | −13.3190 | −0.480296 | −0.240148 | − | 0.970736i | \(-0.577196\pi\) | ||||
−0.240148 | + | 0.970736i | \(0.577196\pi\) | |||||||
\(770\) | 30.0106 | 1.08151 | ||||||||
\(771\) | 7.81517 | 0.281457 | ||||||||
\(772\) | 23.3847 | 0.841635 | ||||||||
\(773\) | −13.9252 | −0.500855 | −0.250427 | − | 0.968135i | \(-0.580571\pi\) | ||||
−0.250427 | + | 0.968135i | \(0.580571\pi\) | |||||||
\(774\) | −7.25771 | −0.260873 | ||||||||
\(775\) | 6.30597 | 0.226517 | ||||||||
\(776\) | 10.9352 | 0.392552 | ||||||||
\(777\) | −1.02620 | −0.0368146 | ||||||||
\(778\) | −55.4444 | −1.98778 | ||||||||
\(779\) | −5.75071 | −0.206040 | ||||||||
\(780\) | 69.0756 | 2.47330 | ||||||||
\(781\) | −46.6146 | −1.66800 | ||||||||
\(782\) | 11.4977 | 0.411159 | ||||||||
\(783\) | 3.09052 | 0.110446 | ||||||||
\(784\) | −2.77332 | −0.0990472 | ||||||||
\(785\) | −11.0977 | −0.396094 | ||||||||
\(786\) | 50.9685 | 1.81798 | ||||||||
\(787\) | 45.7185 | 1.62969 | 0.814844 | − | 0.579680i | \(-0.196822\pi\) | ||||
0.814844 | + | 0.579680i | \(0.196822\pi\) | |||||||
\(788\) | −57.5523 | −2.05022 | ||||||||
\(789\) | −5.50785 | −0.196085 | ||||||||
\(790\) | −4.39970 | −0.156534 | ||||||||
\(791\) | 10.4999 | 0.373333 | ||||||||
\(792\) | 2.38083 | 0.0845991 | ||||||||
\(793\) | 0.926799 | 0.0329116 | ||||||||
\(794\) | −9.58812 | −0.340270 | ||||||||
\(795\) | −13.3732 | −0.474300 | ||||||||
\(796\) | 53.8687 | 1.90933 | ||||||||
\(797\) | −11.4211 | −0.404555 | −0.202277 | − | 0.979328i | \(-0.564834\pi\) | ||||
−0.202277 | + | 0.979328i | \(0.564834\pi\) | |||||||
\(798\) | 8.73512 | 0.309220 | ||||||||
\(799\) | −23.1511 | −0.819029 | ||||||||
\(800\) | −6.40547 | −0.226468 | ||||||||
\(801\) | 2.45787 | 0.0868446 | ||||||||
\(802\) | −38.1978 | −1.34881 | ||||||||
\(803\) | 25.1610 | 0.887913 | ||||||||
\(804\) | −61.1952 | −2.15819 | ||||||||
\(805\) | −2.40920 | −0.0849132 | ||||||||
\(806\) | −103.863 | −3.65843 | ||||||||
\(807\) | 16.4355 | 0.578558 | ||||||||
\(808\) | −1.64107 | −0.0577327 | ||||||||
\(809\) | 17.6307 | 0.619864 | 0.309932 | − | 0.950759i | \(-0.399694\pi\) | ||||
0.309932 | + | 0.950759i | \(0.399694\pi\) | |||||||
\(810\) | −51.1349 | −1.79670 | ||||||||
\(811\) | 30.9666 | 1.08738 | 0.543692 | − | 0.839285i | \(-0.317026\pi\) | ||||
0.543692 | + | 0.839285i | \(0.317026\pi\) | |||||||
\(812\) | 1.60215 | 0.0562244 | ||||||||
\(813\) | −38.6137 | −1.35424 | ||||||||
\(814\) | 6.94449 | 0.243404 | ||||||||
\(815\) | 39.3252 | 1.37750 | ||||||||
\(816\) | −27.6933 | −0.969459 | ||||||||
\(817\) | 19.7441 | 0.690759 | ||||||||
\(818\) | 9.90349 | 0.346267 | ||||||||
\(819\) | −2.42692 | −0.0848035 | ||||||||
\(820\) | 15.4217 | 0.538548 | ||||||||
\(821\) | 25.3060 | 0.883187 | 0.441593 | − | 0.897215i | \(-0.354413\pi\) | ||||
0.441593 | + | 0.897215i | \(0.354413\pi\) | |||||||
\(822\) | 58.6233 | 2.04472 | ||||||||
\(823\) | 45.6057 | 1.58972 | 0.794858 | − | 0.606795i | \(-0.207545\pi\) | ||||
0.794858 | + | 0.606795i | \(0.207545\pi\) | |||||||
\(824\) | 5.23237 | 0.182278 | ||||||||
\(825\) | −8.70079 | −0.302922 | ||||||||
\(826\) | 8.83875 | 0.307539 | ||||||||
\(827\) | −25.4338 | −0.884420 | −0.442210 | − | 0.896912i | \(-0.645805\pi\) | ||||
−0.442210 | + | 0.896912i | \(0.645805\pi\) | |||||||
\(828\) | −0.967751 | −0.0336317 | ||||||||
\(829\) | −5.12771 | −0.178093 | −0.0890463 | − | 0.996027i | \(-0.528382\pi\) | ||||
−0.0890463 | + | 0.996027i | \(0.528382\pi\) | |||||||
\(830\) | −24.6040 | −0.854019 | ||||||||
\(831\) | −10.7238 | −0.372006 | ||||||||
\(832\) | 70.8360 | 2.45580 | ||||||||
\(833\) | −5.42479 | −0.187958 | ||||||||
\(834\) | 49.9330 | 1.72904 | ||||||||
\(835\) | 40.2948 | 1.39446 | ||||||||
\(836\) | −32.7946 | −1.13423 | ||||||||
\(837\) | 37.6938 | 1.30289 | ||||||||
\(838\) | −27.0603 | −0.934782 | ||||||||
\(839\) | −7.81839 | −0.269921 | −0.134960 | − | 0.990851i | \(-0.543091\pi\) | ||||
−0.134960 | + | 0.990851i | \(0.543091\pi\) | |||||||
\(840\) | −4.62639 | −0.159626 | ||||||||
\(841\) | −28.5867 | −0.985749 | ||||||||
\(842\) | 59.6352 | 2.05517 | ||||||||
\(843\) | 39.0010 | 1.34327 | ||||||||
\(844\) | 38.5242 | 1.32606 | ||||||||
\(845\) | 62.7880 | 2.15997 | ||||||||
\(846\) | 3.51236 | 0.120757 | ||||||||
\(847\) | 23.5417 | 0.808901 | ||||||||
\(848\) | −8.36319 | −0.287193 | ||||||||
\(849\) | 23.5705 | 0.808937 | ||||||||
\(850\) | −9.24715 | −0.317175 | ||||||||
\(851\) | −0.557492 | −0.0191106 | ||||||||
\(852\) | 36.3853 | 1.24654 | ||||||||
\(853\) | −36.6540 | −1.25501 | −0.627505 | − | 0.778613i | \(-0.715924\pi\) | ||||
−0.627505 | + | 0.778613i | \(0.715924\pi\) | |||||||
\(854\) | −0.314297 | −0.0107550 | ||||||||
\(855\) | −2.09460 | −0.0716337 | ||||||||
\(856\) | −6.06326 | −0.207238 | ||||||||
\(857\) | 44.0599 | 1.50506 | 0.752529 | − | 0.658559i | \(-0.228834\pi\) | ||||
0.752529 | + | 0.658559i | \(0.228834\pi\) | |||||||
\(858\) | 143.307 | 4.89244 | ||||||||
\(859\) | −6.04906 | −0.206391 | −0.103196 | − | 0.994661i | \(-0.532907\pi\) | ||||
−0.103196 | + | 0.994661i | \(0.532907\pi\) | |||||||
\(860\) | −52.9477 | −1.80550 | ||||||||
\(861\) | −4.72787 | −0.161125 | ||||||||
\(862\) | −11.6434 | −0.396576 | ||||||||
\(863\) | −25.7890 | −0.877867 | −0.438933 | − | 0.898520i | \(-0.644644\pi\) | ||||
−0.438933 | + | 0.898520i | \(0.644644\pi\) | |||||||
\(864\) | −38.2885 | −1.30260 | ||||||||
\(865\) | 22.3490 | 0.759888 | ||||||||
\(866\) | −44.5467 | −1.51376 | ||||||||
\(867\) | −22.8773 | −0.776954 | ||||||||
\(868\) | 19.5407 | 0.663256 | ||||||||
\(869\) | −5.06397 | −0.171784 | ||||||||
\(870\) | −6.04246 | −0.204858 | ||||||||
\(871\) | −83.3714 | −2.82493 | ||||||||
\(872\) | 7.98097 | 0.270270 | ||||||||
\(873\) | 4.07034 | 0.137760 | ||||||||
\(874\) | 4.74545 | 0.160517 | ||||||||
\(875\) | −10.1084 | −0.341726 | ||||||||
\(876\) | −19.6396 | −0.663560 | ||||||||
\(877\) | 9.59839 | 0.324114 | 0.162057 | − | 0.986781i | \(-0.448187\pi\) | ||||
0.162057 | + | 0.986781i | \(0.448187\pi\) | |||||||
\(878\) | 83.2266 | 2.80876 | ||||||||
\(879\) | 5.74165 | 0.193661 | ||||||||
\(880\) | −39.2686 | −1.32374 | ||||||||
\(881\) | −9.38385 | −0.316150 | −0.158075 | − | 0.987427i | \(-0.550529\pi\) | ||||
−0.158075 | + | 0.987427i | \(0.550529\pi\) | |||||||
\(882\) | 0.823019 | 0.0277125 | ||||||||
\(883\) | −4.98842 | −0.167874 | −0.0839368 | − | 0.996471i | \(-0.526749\pi\) | ||||
−0.0839368 | + | 0.996471i | \(0.526749\pi\) | |||||||
\(884\) | 84.4973 | 2.84195 | ||||||||
\(885\) | −18.4938 | −0.621662 | ||||||||
\(886\) | 30.8362 | 1.03596 | ||||||||
\(887\) | 36.6169 | 1.22948 | 0.614738 | − | 0.788732i | \(-0.289262\pi\) | ||||
0.614738 | + | 0.788732i | \(0.289262\pi\) | |||||||
\(888\) | −1.07055 | −0.0359253 | ||||||||
\(889\) | −17.9732 | −0.602802 | ||||||||
\(890\) | 32.3208 | 1.08340 | ||||||||
\(891\) | −58.8553 | −1.97173 | ||||||||
\(892\) | −27.5908 | −0.923808 | ||||||||
\(893\) | −9.55514 | −0.319750 | ||||||||
\(894\) | 82.4381 | 2.75714 | ||||||||
\(895\) | −18.0270 | −0.602575 | ||||||||
\(896\) | −8.09304 | −0.270370 | ||||||||
\(897\) | −11.5045 | −0.384124 | ||||||||
\(898\) | 24.0900 | 0.803895 | ||||||||
\(899\) | 5.04052 | 0.168111 | ||||||||
\(900\) | 0.778321 | 0.0259440 | ||||||||
\(901\) | −16.3589 | −0.544995 | ||||||||
\(902\) | 31.9945 | 1.06530 | ||||||||
\(903\) | 16.2324 | 0.540179 | ||||||||
\(904\) | 10.9537 | 0.364315 | ||||||||
\(905\) | −25.6536 | −0.852754 | ||||||||
\(906\) | −76.1806 | −2.53093 | ||||||||
\(907\) | 34.2361 | 1.13679 | 0.568395 | − | 0.822756i | \(-0.307564\pi\) | ||||
0.568395 | + | 0.822756i | \(0.307564\pi\) | |||||||
\(908\) | −6.09782 | −0.202363 | ||||||||
\(909\) | −0.610844 | −0.0202604 | ||||||||
\(910\) | −31.9138 | −1.05793 | ||||||||
\(911\) | 2.10958 | 0.0698934 | 0.0349467 | − | 0.999389i | \(-0.488874\pi\) | ||||
0.0349467 | + | 0.999389i | \(0.488874\pi\) | |||||||
\(912\) | −11.4298 | −0.378479 | ||||||||
\(913\) | −28.3188 | −0.937216 | ||||||||
\(914\) | −19.9813 | −0.660923 | ||||||||
\(915\) | 0.657620 | 0.0217402 | ||||||||
\(916\) | −14.3077 | −0.472739 | ||||||||
\(917\) | −13.0641 | −0.431415 | ||||||||
\(918\) | −55.2746 | −1.82433 | ||||||||
\(919\) | 49.7639 | 1.64156 | 0.820779 | − | 0.571245i | \(-0.193539\pi\) | ||||
0.820779 | + | 0.571245i | \(0.193539\pi\) | |||||||
\(920\) | −2.51334 | −0.0828622 | ||||||||
\(921\) | 29.6639 | 0.977460 | ||||||||
\(922\) | −60.9768 | −2.00816 | ||||||||
\(923\) | 49.5708 | 1.63164 | ||||||||
\(924\) | −26.9617 | −0.886975 | ||||||||
\(925\) | 0.448367 | 0.0147422 | ||||||||
\(926\) | −9.87527 | −0.324521 | ||||||||
\(927\) | 1.94761 | 0.0639678 | ||||||||
\(928\) | −5.12005 | −0.168074 | ||||||||
\(929\) | −45.0863 | −1.47923 | −0.739617 | − | 0.673028i | \(-0.764993\pi\) | ||||
−0.739617 | + | 0.673028i | \(0.764993\pi\) | |||||||
\(930\) | −73.6973 | −2.41663 | ||||||||
\(931\) | −2.23897 | −0.0733791 | ||||||||
\(932\) | 21.5945 | 0.707351 | ||||||||
\(933\) | −55.6691 | −1.82252 | ||||||||
\(934\) | 16.5940 | 0.542971 | ||||||||
\(935\) | −76.8118 | −2.51201 | ||||||||
\(936\) | −2.53182 | −0.0827551 | ||||||||
\(937\) | 14.8779 | 0.486040 | 0.243020 | − | 0.970021i | \(-0.421862\pi\) | ||||
0.243020 | + | 0.970021i | \(0.421862\pi\) | |||||||
\(938\) | 28.2730 | 0.923145 | ||||||||
\(939\) | 37.7271 | 1.23118 | ||||||||
\(940\) | 25.6240 | 0.835763 | ||||||||
\(941\) | 30.3917 | 0.990742 | 0.495371 | − | 0.868681i | \(-0.335032\pi\) | ||||
0.495371 | + | 0.868681i | \(0.335032\pi\) | |||||||
\(942\) | 17.9714 | 0.585540 | ||||||||
\(943\) | −2.56847 | −0.0836408 | ||||||||
\(944\) | −11.5654 | −0.376422 | ||||||||
\(945\) | 11.5821 | 0.376765 | ||||||||
\(946\) | −109.848 | −3.57146 | ||||||||
\(947\) | −26.5595 | −0.863068 | −0.431534 | − | 0.902097i | \(-0.642028\pi\) | ||||
−0.431534 | + | 0.902097i | \(0.642028\pi\) | |||||||
\(948\) | 3.95272 | 0.128378 | ||||||||
\(949\) | −26.7567 | −0.868559 | ||||||||
\(950\) | −3.81656 | −0.123826 | ||||||||
\(951\) | −5.43094 | −0.176110 | ||||||||
\(952\) | −5.65926 | −0.183418 | ||||||||
\(953\) | 8.75467 | 0.283592 | 0.141796 | − | 0.989896i | \(-0.454712\pi\) | ||||
0.141796 | + | 0.989896i | \(0.454712\pi\) | |||||||
\(954\) | 2.48188 | 0.0803540 | ||||||||
\(955\) | 7.95745 | 0.257497 | ||||||||
\(956\) | −2.48071 | −0.0802319 | ||||||||
\(957\) | −6.95476 | −0.224815 | ||||||||
\(958\) | −71.9409 | −2.32430 | ||||||||
\(959\) | −15.0262 | −0.485221 | ||||||||
\(960\) | 50.2624 | 1.62221 | ||||||||
\(961\) | 30.4771 | 0.983134 | ||||||||
\(962\) | −7.38489 | −0.238099 | ||||||||
\(963\) | −2.25688 | −0.0727270 | ||||||||
\(964\) | −34.7031 | −1.11771 | ||||||||
\(965\) | 22.6059 | 0.727710 | ||||||||
\(966\) | 3.90141 | 0.125526 | ||||||||
\(967\) | −19.3848 | −0.623372 | −0.311686 | − | 0.950185i | \(-0.600894\pi\) | ||||
−0.311686 | + | 0.950185i | \(0.600894\pi\) | |||||||
\(968\) | 24.5592 | 0.789363 | ||||||||
\(969\) | −22.3574 | −0.718224 | ||||||||
\(970\) | 53.5247 | 1.71857 | ||||||||
\(971\) | −17.9424 | −0.575799 | −0.287899 | − | 0.957661i | \(-0.592957\pi\) | ||||
−0.287899 | + | 0.957661i | \(0.592957\pi\) | |||||||
\(972\) | 9.99652 | 0.320639 | ||||||||
\(973\) | −12.7987 | −0.410308 | ||||||||
\(974\) | −24.7725 | −0.793762 | ||||||||
\(975\) | 9.25258 | 0.296320 | ||||||||
\(976\) | 0.411254 | 0.0131639 | ||||||||
\(977\) | 5.12609 | 0.163998 | 0.0819991 | − | 0.996632i | \(-0.473870\pi\) | ||||
0.0819991 | + | 0.996632i | \(0.473870\pi\) | |||||||
\(978\) | −63.6823 | −2.03634 | ||||||||
\(979\) | 37.2007 | 1.18894 | ||||||||
\(980\) | 6.00423 | 0.191798 | ||||||||
\(981\) | 2.97070 | 0.0948470 | ||||||||
\(982\) | −41.6992 | −1.33067 | ||||||||
\(983\) | −48.1332 | −1.53521 | −0.767606 | − | 0.640922i | \(-0.778552\pi\) | ||||
−0.767606 | + | 0.640922i | \(0.778552\pi\) | |||||||
\(984\) | −4.93222 | −0.157233 | ||||||||
\(985\) | −55.6355 | −1.77269 | ||||||||
\(986\) | −7.39148 | −0.235393 | ||||||||
\(987\) | −7.85563 | −0.250048 | ||||||||
\(988\) | 34.8744 | 1.10950 | ||||||||
\(989\) | 8.81841 | 0.280409 | ||||||||
\(990\) | 11.6535 | 0.370371 | ||||||||
\(991\) | −6.50910 | −0.206769 | −0.103384 | − | 0.994641i | \(-0.532967\pi\) | ||||
−0.103384 | + | 0.994641i | \(0.532967\pi\) | |||||||
\(992\) | −62.4471 | −1.98270 | ||||||||
\(993\) | 39.1151 | 1.24128 | ||||||||
\(994\) | −16.8105 | −0.533196 | ||||||||
\(995\) | 52.0746 | 1.65088 | ||||||||
\(996\) | 22.1044 | 0.700405 | ||||||||
\(997\) | 43.2321 | 1.36917 | 0.684587 | − | 0.728931i | \(-0.259982\pi\) | ||||
0.684587 | + | 0.728931i | \(0.259982\pi\) | |||||||
\(998\) | −63.9445 | −2.02413 | ||||||||
\(999\) | 2.68010 | 0.0847948 |
(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 | 161.2.a.d.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 1449.2.a.r.1.2 | 5 | |||
4.3 | odd | 2 | 2576.2.a.bd.1.4 | 5 | |||
5.4 | even | 2 | 4025.2.a.p.1.2 | 5 | |||
7.6 | odd | 2 | 1127.2.a.h.1.4 | 5 | |||
23.22 | odd | 2 | 3703.2.a.j.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
161.2.a.d.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
1127.2.a.h.1.4 | 5 | 7.6 | odd | 2 | |||
1449.2.a.r.1.2 | 5 | 3.2 | odd | 2 | |||
2576.2.a.bd.1.4 | 5 | 4.3 | odd | 2 | |||
3703.2.a.j.1.4 | 5 | 23.22 | odd | 2 | |||
4025.2.a.p.1.2 | 5 | 5.4 | even | 2 |