Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.220036.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 5x^{3} + 11x^{2} - 2x - 1 \) |
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 | \(1.75849\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.75849 | 1.01527 | 0.507634 | − | 0.861573i | \(-0.330520\pi\) | ||||
0.507634 | + | 0.861573i | \(0.330520\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.75849 | 0.717902 | ||||||||
\(7\) | −2.87831 | −1.08790 | −0.543949 | − | 0.839118i | \(-0.683072\pi\) | ||||
−0.543949 | + | 0.839118i | \(0.683072\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.0923014 | 0.0307671 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.75849 | 0.507634 | ||||||||
\(13\) | −6.11317 | −1.69549 | −0.847744 | − | 0.530405i | \(-0.822040\pi\) | ||||
−0.847744 | + | 0.530405i | \(0.822040\pi\) | |||||||
\(14\) | −2.87831 | −0.769261 | ||||||||
\(15\) | −1.75849 | −0.454041 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.37367 | 1.78838 | 0.894189 | − | 0.447690i | \(-0.147753\pi\) | ||||
0.894189 | + | 0.447690i | \(0.147753\pi\) | |||||||
\(18\) | 0.0923014 | 0.0217556 | ||||||||
\(19\) | 1.00335 | 0.230184 | 0.115092 | − | 0.993355i | \(-0.463284\pi\) | ||||
0.115092 | + | 0.993355i | \(0.463284\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −5.06149 | −1.10451 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.92081 | −0.609030 | −0.304515 | − | 0.952508i | \(-0.598494\pi\) | ||||
−0.304515 | + | 0.952508i | \(0.598494\pi\) | |||||||
\(24\) | 1.75849 | 0.358951 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −6.11317 | −1.19889 | ||||||||
\(27\) | −5.11317 | −0.984030 | ||||||||
\(28\) | −2.87831 | −0.543949 | ||||||||
\(29\) | 0.302996 | 0.0562650 | 0.0281325 | − | 0.999604i | \(-0.491044\pi\) | ||||
0.0281325 | + | 0.999604i | \(0.491044\pi\) | |||||||
\(30\) | −1.75849 | −0.321056 | ||||||||
\(31\) | −0.117276 | −0.0210634 | −0.0105317 | − | 0.999945i | \(-0.503352\pi\) | ||||
−0.0105317 | + | 0.999945i | \(0.503352\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.75849 | 0.306115 | ||||||||
\(34\) | 7.37367 | 1.26457 | ||||||||
\(35\) | 2.87831 | 0.486523 | ||||||||
\(36\) | 0.0923014 | 0.0153836 | ||||||||
\(37\) | −9.01235 | −1.48162 | −0.740811 | − | 0.671714i | \(-0.765558\pi\) | ||||
−0.740811 | + | 0.671714i | \(0.765558\pi\) | |||||||
\(38\) | 1.00335 | 0.162765 | ||||||||
\(39\) | −10.7500 | −1.72137 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.87755 | −1.38644 | −0.693220 | − | 0.720726i | \(-0.743809\pi\) | ||||
−0.693220 | + | 0.720726i | \(0.743809\pi\) | |||||||
\(42\) | −5.06149 | −0.781005 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −0.0923014 | −0.0137595 | ||||||||
\(46\) | −2.92081 | −0.430649 | ||||||||
\(47\) | −8.82587 | −1.28739 | −0.643693 | − | 0.765284i | \(-0.722599\pi\) | ||||
−0.643693 | + | 0.765284i | \(0.722599\pi\) | |||||||
\(48\) | 1.75849 | 0.253817 | ||||||||
\(49\) | 1.28467 | 0.183524 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 12.9666 | 1.81568 | ||||||||
\(52\) | −6.11317 | −0.847744 | ||||||||
\(53\) | 6.30888 | 0.866592 | 0.433296 | − | 0.901252i | \(-0.357350\pi\) | ||||
0.433296 | + | 0.901252i | \(0.357350\pi\) | |||||||
\(54\) | −5.11317 | −0.695814 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −2.87831 | −0.384630 | ||||||||
\(57\) | 1.76438 | 0.233698 | ||||||||
\(58\) | 0.302996 | 0.0397854 | ||||||||
\(59\) | −6.09342 | −0.793296 | −0.396648 | − | 0.917971i | \(-0.629827\pi\) | ||||
−0.396648 | + | 0.917971i | \(0.629827\pi\) | |||||||
\(60\) | −1.75849 | −0.227021 | ||||||||
\(61\) | −7.87501 | −1.00829 | −0.504146 | − | 0.863618i | \(-0.668193\pi\) | ||||
−0.504146 | + | 0.863618i | \(0.668193\pi\) | |||||||
\(62\) | −0.117276 | −0.0148941 | ||||||||
\(63\) | −0.265672 | −0.0334715 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.11317 | 0.758246 | ||||||||
\(66\) | 1.75849 | 0.216456 | ||||||||
\(67\) | 7.04775 | 0.861019 | 0.430510 | − | 0.902586i | \(-0.358334\pi\) | ||||
0.430510 | + | 0.902586i | \(0.358334\pi\) | |||||||
\(68\) | 7.37367 | 0.894189 | ||||||||
\(69\) | −5.13622 | −0.618328 | ||||||||
\(70\) | 2.87831 | 0.344024 | ||||||||
\(71\) | −1.67725 | −0.199053 | −0.0995266 | − | 0.995035i | \(-0.531733\pi\) | ||||
−0.0995266 | + | 0.995035i | \(0.531733\pi\) | |||||||
\(72\) | 0.0923014 | 0.0108778 | ||||||||
\(73\) | 6.08124 | 0.711756 | 0.355878 | − | 0.934533i | \(-0.384182\pi\) | ||||
0.355878 | + | 0.934533i | \(0.384182\pi\) | |||||||
\(74\) | −9.01235 | −1.04766 | ||||||||
\(75\) | 1.75849 | 0.203053 | ||||||||
\(76\) | 1.00335 | 0.115092 | ||||||||
\(77\) | −2.87831 | −0.328014 | ||||||||
\(78\) | −10.7500 | −1.21719 | ||||||||
\(79\) | −0.246729 | −0.0277592 | −0.0138796 | − | 0.999904i | \(-0.504418\pi\) | ||||
−0.0138796 | + | 0.999904i | \(0.504418\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −9.26838 | −1.02982 | ||||||||
\(82\) | −8.87755 | −0.980362 | ||||||||
\(83\) | −11.0924 | −1.21754 | −0.608772 | − | 0.793345i | \(-0.708338\pi\) | ||||
−0.608772 | + | 0.793345i | \(0.708338\pi\) | |||||||
\(84\) | −5.06149 | −0.552254 | ||||||||
\(85\) | −7.37367 | −0.799787 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | 0.532817 | 0.0571240 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −5.85080 | −0.620183 | −0.310092 | − | 0.950707i | \(-0.600360\pi\) | ||||
−0.310092 | + | 0.950707i | \(0.600360\pi\) | |||||||
\(90\) | −0.0923014 | −0.00972942 | ||||||||
\(91\) | 17.5956 | 1.84452 | ||||||||
\(92\) | −2.92081 | −0.304515 | ||||||||
\(93\) | −0.206229 | −0.0213850 | ||||||||
\(94\) | −8.82587 | −0.910319 | ||||||||
\(95\) | −1.00335 | −0.102941 | ||||||||
\(96\) | 1.75849 | 0.179476 | ||||||||
\(97\) | 6.27629 | 0.637261 | 0.318630 | − | 0.947879i | \(-0.396777\pi\) | ||||
0.318630 | + | 0.947879i | \(0.396777\pi\) | |||||||
\(98\) | 1.28467 | 0.129771 | ||||||||
\(99\) | 0.0923014 | 0.00927664 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −5.22081 | −0.519490 | −0.259745 | − | 0.965677i | \(-0.583639\pi\) | ||||
−0.259745 | + | 0.965677i | \(0.583639\pi\) | |||||||
\(102\) | 12.9666 | 1.28388 | ||||||||
\(103\) | 10.8854 | 1.07257 | 0.536287 | − | 0.844036i | \(-0.319826\pi\) | ||||
0.536287 | + | 0.844036i | \(0.319826\pi\) | |||||||
\(104\) | −6.11317 | −0.599446 | ||||||||
\(105\) | 5.06149 | 0.493951 | ||||||||
\(106\) | 6.30888 | 0.612773 | ||||||||
\(107\) | −9.84487 | −0.951739 | −0.475870 | − | 0.879516i | \(-0.657867\pi\) | ||||
−0.475870 | + | 0.879516i | \(0.657867\pi\) | |||||||
\(108\) | −5.11317 | −0.492015 | ||||||||
\(109\) | −8.98172 | −0.860293 | −0.430146 | − | 0.902759i | \(-0.641538\pi\) | ||||
−0.430146 | + | 0.902759i | \(0.641538\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | −15.8482 | −1.50424 | ||||||||
\(112\) | −2.87831 | −0.271975 | ||||||||
\(113\) | −15.5047 | −1.45856 | −0.729281 | − | 0.684215i | \(-0.760145\pi\) | ||||
−0.729281 | + | 0.684215i | \(0.760145\pi\) | |||||||
\(114\) | 1.76438 | 0.165250 | ||||||||
\(115\) | 2.92081 | 0.272367 | ||||||||
\(116\) | 0.302996 | 0.0281325 | ||||||||
\(117\) | −0.564254 | −0.0521653 | ||||||||
\(118\) | −6.09342 | −0.560945 | ||||||||
\(119\) | −21.2237 | −1.94557 | ||||||||
\(120\) | −1.75849 | −0.160528 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −7.87501 | −0.712970 | ||||||||
\(123\) | −15.6111 | −1.40761 | ||||||||
\(124\) | −0.117276 | −0.0105317 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.265672 | −0.0236679 | ||||||||
\(127\) | −5.26491 | −0.467186 | −0.233593 | − | 0.972335i | \(-0.575048\pi\) | ||||
−0.233593 | + | 0.972335i | \(0.575048\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.75849 | −0.154827 | ||||||||
\(130\) | 6.11317 | 0.536161 | ||||||||
\(131\) | 16.0097 | 1.39877 | 0.699386 | − | 0.714745i | \(-0.253457\pi\) | ||||
0.699386 | + | 0.714745i | \(0.253457\pi\) | |||||||
\(132\) | 1.75849 | 0.153057 | ||||||||
\(133\) | −2.88795 | −0.250417 | ||||||||
\(134\) | 7.04775 | 0.608833 | ||||||||
\(135\) | 5.11317 | 0.440072 | ||||||||
\(136\) | 7.37367 | 0.632287 | ||||||||
\(137\) | 6.51704 | 0.556788 | 0.278394 | − | 0.960467i | \(-0.410198\pi\) | ||||
0.278394 | + | 0.960467i | \(0.410198\pi\) | |||||||
\(138\) | −5.13622 | −0.437224 | ||||||||
\(139\) | −0.750610 | −0.0636659 | −0.0318330 | − | 0.999493i | \(-0.510134\pi\) | ||||
−0.0318330 | + | 0.999493i | \(0.510134\pi\) | |||||||
\(140\) | 2.87831 | 0.243262 | ||||||||
\(141\) | −15.5202 | −1.30704 | ||||||||
\(142\) | −1.67725 | −0.140752 | ||||||||
\(143\) | −6.11317 | −0.511209 | ||||||||
\(144\) | 0.0923014 | 0.00769178 | ||||||||
\(145\) | −0.302996 | −0.0251625 | ||||||||
\(146\) | 6.08124 | 0.503287 | ||||||||
\(147\) | 2.25908 | 0.186326 | ||||||||
\(148\) | −9.01235 | −0.740811 | ||||||||
\(149\) | −17.8142 | −1.45940 | −0.729700 | − | 0.683768i | \(-0.760340\pi\) | ||||
−0.729700 | + | 0.683768i | \(0.760340\pi\) | |||||||
\(150\) | 1.75849 | 0.143580 | ||||||||
\(151\) | 5.09012 | 0.414228 | 0.207114 | − | 0.978317i | \(-0.433593\pi\) | ||||
0.207114 | + | 0.978317i | \(0.433593\pi\) | |||||||
\(152\) | 1.00335 | 0.0813823 | ||||||||
\(153\) | 0.680600 | 0.0550233 | ||||||||
\(154\) | −2.87831 | −0.231941 | ||||||||
\(155\) | 0.117276 | 0.00941984 | ||||||||
\(156\) | −10.7500 | −0.860687 | ||||||||
\(157\) | 13.3265 | 1.06357 | 0.531786 | − | 0.846879i | \(-0.321521\pi\) | ||||
0.531786 | + | 0.846879i | \(0.321521\pi\) | |||||||
\(158\) | −0.246729 | −0.0196287 | ||||||||
\(159\) | 11.0941 | 0.879822 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 8.40698 | 0.662563 | ||||||||
\(162\) | −9.26838 | −0.728193 | ||||||||
\(163\) | 2.04615 | 0.160267 | 0.0801335 | − | 0.996784i | \(-0.474465\pi\) | ||||
0.0801335 | + | 0.996784i | \(0.474465\pi\) | |||||||
\(164\) | −8.87755 | −0.693220 | ||||||||
\(165\) | −1.75849 | −0.136899 | ||||||||
\(166\) | −11.0924 | −0.860934 | ||||||||
\(167\) | −1.95019 | −0.150911 | −0.0754553 | − | 0.997149i | \(-0.524041\pi\) | ||||
−0.0754553 | + | 0.997149i | \(0.524041\pi\) | |||||||
\(168\) | −5.06149 | −0.390502 | ||||||||
\(169\) | 24.3709 | 1.87468 | ||||||||
\(170\) | −7.37367 | −0.565535 | ||||||||
\(171\) | 0.0926104 | 0.00708210 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 18.9095 | 1.43766 | 0.718831 | − | 0.695185i | \(-0.244678\pi\) | ||||
0.718831 | + | 0.695185i | \(0.244678\pi\) | |||||||
\(174\) | 0.532817 | 0.0403928 | ||||||||
\(175\) | −2.87831 | −0.217580 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −10.7152 | −0.805407 | ||||||||
\(178\) | −5.85080 | −0.438536 | ||||||||
\(179\) | −2.47257 | −0.184808 | −0.0924041 | − | 0.995722i | \(-0.529455\pi\) | ||||
−0.0924041 | + | 0.995722i | \(0.529455\pi\) | |||||||
\(180\) | −0.0923014 | −0.00687974 | ||||||||
\(181\) | −9.12851 | −0.678517 | −0.339258 | − | 0.940693i | \(-0.610176\pi\) | ||||
−0.339258 | + | 0.940693i | \(0.610176\pi\) | |||||||
\(182\) | 17.5956 | 1.30427 | ||||||||
\(183\) | −13.8482 | −1.02369 | ||||||||
\(184\) | −2.92081 | −0.215325 | ||||||||
\(185\) | 9.01235 | 0.662601 | ||||||||
\(186\) | −0.206229 | −0.0151215 | ||||||||
\(187\) | 7.37367 | 0.539216 | ||||||||
\(188\) | −8.82587 | −0.643693 | ||||||||
\(189\) | 14.7173 | 1.07053 | ||||||||
\(190\) | −1.00335 | −0.0727905 | ||||||||
\(191\) | −3.45134 | −0.249730 | −0.124865 | − | 0.992174i | \(-0.539850\pi\) | ||||
−0.124865 | + | 0.992174i | \(0.539850\pi\) | |||||||
\(192\) | 1.75849 | 0.126908 | ||||||||
\(193\) | −15.2283 | −1.09615 | −0.548077 | − | 0.836428i | \(-0.684640\pi\) | ||||
−0.548077 | + | 0.836428i | \(0.684640\pi\) | |||||||
\(194\) | 6.27629 | 0.450611 | ||||||||
\(195\) | 10.7500 | 0.769822 | ||||||||
\(196\) | 1.28467 | 0.0917619 | ||||||||
\(197\) | 14.0812 | 1.00325 | 0.501623 | − | 0.865086i | \(-0.332736\pi\) | ||||
0.501623 | + | 0.865086i | \(0.332736\pi\) | |||||||
\(198\) | 0.0923014 | 0.00655957 | ||||||||
\(199\) | −18.2532 | −1.29394 | −0.646968 | − | 0.762517i | \(-0.723963\pi\) | ||||
−0.646968 | + | 0.762517i | \(0.723963\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 12.3934 | 0.874165 | ||||||||
\(202\) | −5.22081 | −0.367335 | ||||||||
\(203\) | −0.872118 | −0.0612107 | ||||||||
\(204\) | 12.9666 | 0.907841 | ||||||||
\(205\) | 8.87755 | 0.620035 | ||||||||
\(206\) | 10.8854 | 0.758424 | ||||||||
\(207\) | −0.269594 | −0.0187381 | ||||||||
\(208\) | −6.11317 | −0.423872 | ||||||||
\(209\) | 1.00335 | 0.0694030 | ||||||||
\(210\) | 5.06149 | 0.349276 | ||||||||
\(211\) | −1.39128 | −0.0957800 | −0.0478900 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478900 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(212\) | 6.30888 | 0.433296 | ||||||||
\(213\) | −2.94944 | −0.202092 | ||||||||
\(214\) | −9.84487 | −0.672981 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | −5.11317 | −0.347907 | ||||||||
\(217\) | 0.337557 | 0.0229148 | ||||||||
\(218\) | −8.98172 | −0.608319 | ||||||||
\(219\) | 10.6938 | 0.722622 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −45.0765 | −3.03217 | ||||||||
\(222\) | −15.8482 | −1.06366 | ||||||||
\(223\) | 11.5694 | 0.774743 | 0.387372 | − | 0.921924i | \(-0.373383\pi\) | ||||
0.387372 | + | 0.921924i | \(0.373383\pi\) | |||||||
\(224\) | −2.87831 | −0.192315 | ||||||||
\(225\) | 0.0923014 | 0.00615343 | ||||||||
\(226\) | −15.5047 | −1.03136 | ||||||||
\(227\) | 24.8235 | 1.64759 | 0.823797 | − | 0.566885i | \(-0.191852\pi\) | ||||
0.823797 | + | 0.566885i | \(0.191852\pi\) | |||||||
\(228\) | 1.76438 | 0.116849 | ||||||||
\(229\) | 9.98296 | 0.659693 | 0.329846 | − | 0.944035i | \(-0.393003\pi\) | ||||
0.329846 | + | 0.944035i | \(0.393003\pi\) | |||||||
\(230\) | 2.92081 | 0.192592 | ||||||||
\(231\) | −5.06149 | −0.333022 | ||||||||
\(232\) | 0.302996 | 0.0198927 | ||||||||
\(233\) | 3.93004 | 0.257466 | 0.128733 | − | 0.991679i | \(-0.458909\pi\) | ||||
0.128733 | + | 0.991679i | \(0.458909\pi\) | |||||||
\(234\) | −0.564254 | −0.0368864 | ||||||||
\(235\) | 8.82587 | 0.575736 | ||||||||
\(236\) | −6.09342 | −0.396648 | ||||||||
\(237\) | −0.433871 | −0.0281830 | ||||||||
\(238\) | −21.2237 | −1.37573 | ||||||||
\(239\) | −8.03473 | −0.519724 | −0.259862 | − | 0.965646i | \(-0.583677\pi\) | ||||
−0.259862 | + | 0.965646i | \(0.583677\pi\) | |||||||
\(240\) | −1.75849 | −0.113510 | ||||||||
\(241\) | 11.4440 | 0.737175 | 0.368588 | − | 0.929593i | \(-0.379841\pi\) | ||||
0.368588 | + | 0.929593i | \(0.379841\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −0.958887 | −0.0615126 | ||||||||
\(244\) | −7.87501 | −0.504146 | ||||||||
\(245\) | −1.28467 | −0.0820743 | ||||||||
\(246\) | −15.6111 | −0.995329 | ||||||||
\(247\) | −6.13364 | −0.390274 | ||||||||
\(248\) | −0.117276 | −0.00744703 | ||||||||
\(249\) | −19.5058 | −1.23613 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −21.3745 | −1.34915 | −0.674574 | − | 0.738208i | \(-0.735672\pi\) | ||||
−0.674574 | + | 0.738208i | \(0.735672\pi\) | |||||||
\(252\) | −0.265672 | −0.0167358 | ||||||||
\(253\) | −2.92081 | −0.183629 | ||||||||
\(254\) | −5.26491 | −0.330350 | ||||||||
\(255\) | −12.9666 | −0.811997 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.4183 | 1.77268 | 0.886342 | − | 0.463031i | \(-0.153238\pi\) | ||||
0.886342 | + | 0.463031i | \(0.153238\pi\) | |||||||
\(258\) | −1.75849 | −0.109479 | ||||||||
\(259\) | 25.9403 | 1.61185 | ||||||||
\(260\) | 6.11317 | 0.379123 | ||||||||
\(261\) | 0.0279670 | 0.00173111 | ||||||||
\(262\) | 16.0097 | 0.989081 | ||||||||
\(263\) | −12.0841 | −0.745140 | −0.372570 | − | 0.928004i | \(-0.621523\pi\) | ||||
−0.372570 | + | 0.928004i | \(0.621523\pi\) | |||||||
\(264\) | 1.75849 | 0.108228 | ||||||||
\(265\) | −6.30888 | −0.387552 | ||||||||
\(266\) | −2.88795 | −0.177071 | ||||||||
\(267\) | −10.2886 | −0.629651 | ||||||||
\(268\) | 7.04775 | 0.430510 | ||||||||
\(269\) | 2.31705 | 0.141273 | 0.0706365 | − | 0.997502i | \(-0.477497\pi\) | ||||
0.0706365 | + | 0.997502i | \(0.477497\pi\) | |||||||
\(270\) | 5.11317 | 0.311178 | ||||||||
\(271\) | 18.4363 | 1.11992 | 0.559962 | − | 0.828518i | \(-0.310816\pi\) | ||||
0.559962 | + | 0.828518i | \(0.310816\pi\) | |||||||
\(272\) | 7.37367 | 0.447095 | ||||||||
\(273\) | 30.9418 | 1.87268 | ||||||||
\(274\) | 6.51704 | 0.393709 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −5.13622 | −0.309164 | ||||||||
\(277\) | 10.4719 | 0.629193 | 0.314597 | − | 0.949225i | \(-0.398131\pi\) | ||||
0.314597 | + | 0.949225i | \(0.398131\pi\) | |||||||
\(278\) | −0.750610 | −0.0450186 | ||||||||
\(279\) | −0.0108247 | −0.000648060 0 | ||||||||
\(280\) | 2.87831 | 0.172012 | ||||||||
\(281\) | 1.41051 | 0.0841442 | 0.0420721 | − | 0.999115i | \(-0.486604\pi\) | ||||
0.0420721 | + | 0.999115i | \(0.486604\pi\) | |||||||
\(282\) | −15.5202 | −0.924217 | ||||||||
\(283\) | −7.93645 | −0.471773 | −0.235887 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235887 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(284\) | −1.67725 | −0.0995266 | ||||||||
\(285\) | −1.76438 | −0.104513 | ||||||||
\(286\) | −6.11317 | −0.361479 | ||||||||
\(287\) | 25.5523 | 1.50831 | ||||||||
\(288\) | 0.0923014 | 0.00543891 | ||||||||
\(289\) | 37.3710 | 2.19830 | ||||||||
\(290\) | −0.302996 | −0.0177926 | ||||||||
\(291\) | 11.0368 | 0.646990 | ||||||||
\(292\) | 6.08124 | 0.355878 | ||||||||
\(293\) | 19.2752 | 1.12607 | 0.563035 | − | 0.826433i | \(-0.309634\pi\) | ||||
0.563035 | + | 0.826433i | \(0.309634\pi\) | |||||||
\(294\) | 2.25908 | 0.131752 | ||||||||
\(295\) | 6.09342 | 0.354773 | ||||||||
\(296\) | −9.01235 | −0.523832 | ||||||||
\(297\) | −5.11317 | −0.296696 | ||||||||
\(298\) | −17.8142 | −1.03195 | ||||||||
\(299\) | 17.8554 | 1.03260 | ||||||||
\(300\) | 1.75849 | 0.101527 | ||||||||
\(301\) | 2.87831 | 0.165903 | ||||||||
\(302\) | 5.09012 | 0.292904 | ||||||||
\(303\) | −9.18076 | −0.527421 | ||||||||
\(304\) | 1.00335 | 0.0575460 | ||||||||
\(305\) | 7.87501 | 0.450922 | ||||||||
\(306\) | 0.680600 | 0.0389073 | ||||||||
\(307\) | 22.7434 | 1.29803 | 0.649016 | − | 0.760775i | \(-0.275181\pi\) | ||||
0.649016 | + | 0.760775i | \(0.275181\pi\) | |||||||
\(308\) | −2.87831 | −0.164007 | ||||||||
\(309\) | 19.1420 | 1.08895 | ||||||||
\(310\) | 0.117276 | 0.00666083 | ||||||||
\(311\) | −18.3887 | −1.04273 | −0.521363 | − | 0.853335i | \(-0.674576\pi\) | ||||
−0.521363 | + | 0.853335i | \(0.674576\pi\) | |||||||
\(312\) | −10.7500 | −0.608597 | ||||||||
\(313\) | −26.7205 | −1.51033 | −0.755165 | − | 0.655535i | \(-0.772443\pi\) | ||||
−0.755165 | + | 0.655535i | \(0.772443\pi\) | |||||||
\(314\) | 13.3265 | 0.752059 | ||||||||
\(315\) | 0.265672 | 0.0149689 | ||||||||
\(316\) | −0.246729 | −0.0138796 | ||||||||
\(317\) | 12.6603 | 0.711071 | 0.355536 | − | 0.934663i | \(-0.384298\pi\) | ||||
0.355536 | + | 0.934663i | \(0.384298\pi\) | |||||||
\(318\) | 11.0941 | 0.622128 | ||||||||
\(319\) | 0.302996 | 0.0169645 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −17.3121 | −0.966269 | ||||||||
\(322\) | 8.40698 | 0.468503 | ||||||||
\(323\) | 7.39836 | 0.411656 | ||||||||
\(324\) | −9.26838 | −0.514910 | ||||||||
\(325\) | −6.11317 | −0.339098 | ||||||||
\(326\) | 2.04615 | 0.113326 | ||||||||
\(327\) | −15.7943 | −0.873427 | ||||||||
\(328\) | −8.87755 | −0.490181 | ||||||||
\(329\) | 25.4036 | 1.40055 | ||||||||
\(330\) | −1.75849 | −0.0968019 | ||||||||
\(331\) | 3.34862 | 0.184057 | 0.0920285 | − | 0.995756i | \(-0.470665\pi\) | ||||
0.0920285 | + | 0.995756i | \(0.470665\pi\) | |||||||
\(332\) | −11.0924 | −0.608772 | ||||||||
\(333\) | −0.831852 | −0.0455852 | ||||||||
\(334\) | −1.95019 | −0.106710 | ||||||||
\(335\) | −7.04775 | −0.385060 | ||||||||
\(336\) | −5.06149 | −0.276127 | ||||||||
\(337\) | 14.9016 | 0.811741 | 0.405871 | − | 0.913931i | \(-0.366968\pi\) | ||||
0.405871 | + | 0.913931i | \(0.366968\pi\) | |||||||
\(338\) | 24.3709 | 1.32560 | ||||||||
\(339\) | −27.2650 | −1.48083 | ||||||||
\(340\) | −7.37367 | −0.399893 | ||||||||
\(341\) | −0.117276 | −0.00635085 | ||||||||
\(342\) | 0.0926104 | 0.00500780 | ||||||||
\(343\) | 16.4505 | 0.888243 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | 5.13622 | 0.276525 | ||||||||
\(346\) | 18.9095 | 1.01658 | ||||||||
\(347\) | 12.4727 | 0.669568 | 0.334784 | − | 0.942295i | \(-0.391337\pi\) | ||||
0.334784 | + | 0.942295i | \(0.391337\pi\) | |||||||
\(348\) | 0.532817 | 0.0285620 | ||||||||
\(349\) | −13.3681 | −0.715580 | −0.357790 | − | 0.933802i | \(-0.616470\pi\) | ||||
−0.357790 | + | 0.933802i | \(0.616470\pi\) | |||||||
\(350\) | −2.87831 | −0.153852 | ||||||||
\(351\) | 31.2577 | 1.66841 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −23.5669 | −1.25434 | −0.627170 | − | 0.778882i | \(-0.715787\pi\) | ||||
−0.627170 | + | 0.778882i | \(0.715787\pi\) | |||||||
\(354\) | −10.7152 | −0.569509 | ||||||||
\(355\) | 1.67725 | 0.0890193 | ||||||||
\(356\) | −5.85080 | −0.310092 | ||||||||
\(357\) | −37.3218 | −1.97528 | ||||||||
\(358\) | −2.47257 | −0.130679 | ||||||||
\(359\) | −32.4228 | −1.71121 | −0.855606 | − | 0.517628i | \(-0.826815\pi\) | ||||
−0.855606 | + | 0.517628i | \(0.826815\pi\) | |||||||
\(360\) | −0.0923014 | −0.00486471 | ||||||||
\(361\) | −17.9933 | −0.947015 | ||||||||
\(362\) | −9.12851 | −0.479784 | ||||||||
\(363\) | 1.75849 | 0.0922970 | ||||||||
\(364\) | 17.5956 | 0.922260 | ||||||||
\(365\) | −6.08124 | −0.318307 | ||||||||
\(366\) | −13.8482 | −0.723855 | ||||||||
\(367\) | 28.5536 | 1.49048 | 0.745242 | − | 0.666794i | \(-0.232334\pi\) | ||||
0.745242 | + | 0.666794i | \(0.232334\pi\) | |||||||
\(368\) | −2.92081 | −0.152258 | ||||||||
\(369\) | −0.819410 | −0.0426568 | ||||||||
\(370\) | 9.01235 | 0.468530 | ||||||||
\(371\) | −18.1589 | −0.942764 | ||||||||
\(372\) | −0.206229 | −0.0106925 | ||||||||
\(373\) | −6.42137 | −0.332486 | −0.166243 | − | 0.986085i | \(-0.553164\pi\) | ||||
−0.166243 | + | 0.986085i | \(0.553164\pi\) | |||||||
\(374\) | 7.37367 | 0.381283 | ||||||||
\(375\) | −1.75849 | −0.0908082 | ||||||||
\(376\) | −8.82587 | −0.455160 | ||||||||
\(377\) | −1.85227 | −0.0953967 | ||||||||
\(378\) | 14.7173 | 0.756976 | ||||||||
\(379\) | −0.677659 | −0.0348090 | −0.0174045 | − | 0.999849i | \(-0.505540\pi\) | ||||
−0.0174045 | + | 0.999849i | \(0.505540\pi\) | |||||||
\(380\) | −1.00335 | −0.0514707 | ||||||||
\(381\) | −9.25832 | −0.474318 | ||||||||
\(382\) | −3.45134 | −0.176586 | ||||||||
\(383\) | −19.4006 | −0.991322 | −0.495661 | − | 0.868516i | \(-0.665074\pi\) | ||||
−0.495661 | + | 0.868516i | \(0.665074\pi\) | |||||||
\(384\) | 1.75849 | 0.0897378 | ||||||||
\(385\) | 2.87831 | 0.146692 | ||||||||
\(386\) | −15.2283 | −0.775098 | ||||||||
\(387\) | −0.0923014 | −0.00469194 | ||||||||
\(388\) | 6.27629 | 0.318630 | ||||||||
\(389\) | −22.7919 | −1.15560 | −0.577799 | − | 0.816179i | \(-0.696088\pi\) | ||||
−0.577799 | + | 0.816179i | \(0.696088\pi\) | |||||||
\(390\) | 10.7500 | 0.544346 | ||||||||
\(391\) | −21.5371 | −1.08918 | ||||||||
\(392\) | 1.28467 | 0.0648855 | ||||||||
\(393\) | 28.1529 | 1.42013 | ||||||||
\(394\) | 14.0812 | 0.709403 | ||||||||
\(395\) | 0.246729 | 0.0124143 | ||||||||
\(396\) | 0.0923014 | 0.00463832 | ||||||||
\(397\) | −9.26539 | −0.465017 | −0.232508 | − | 0.972594i | \(-0.574693\pi\) | ||||
−0.232508 | + | 0.972594i | \(0.574693\pi\) | |||||||
\(398\) | −18.2532 | −0.914951 | ||||||||
\(399\) | −5.07844 | −0.254240 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −5.89124 | −0.294195 | −0.147097 | − | 0.989122i | \(-0.546993\pi\) | ||||
−0.147097 | + | 0.989122i | \(0.546993\pi\) | |||||||
\(402\) | 12.3934 | 0.618128 | ||||||||
\(403\) | 0.716928 | 0.0357127 | ||||||||
\(404\) | −5.22081 | −0.259745 | ||||||||
\(405\) | 9.26838 | 0.460550 | ||||||||
\(406\) | −0.872118 | −0.0432825 | ||||||||
\(407\) | −9.01235 | −0.446726 | ||||||||
\(408\) | 12.9666 | 0.641940 | ||||||||
\(409\) | 20.6012 | 1.01866 | 0.509332 | − | 0.860570i | \(-0.329892\pi\) | ||||
0.509332 | + | 0.860570i | \(0.329892\pi\) | |||||||
\(410\) | 8.87755 | 0.438431 | ||||||||
\(411\) | 11.4602 | 0.565289 | ||||||||
\(412\) | 10.8854 | 0.536287 | ||||||||
\(413\) | 17.5387 | 0.863025 | ||||||||
\(414\) | −0.269594 | −0.0132498 | ||||||||
\(415\) | 11.0924 | 0.544502 | ||||||||
\(416\) | −6.11317 | −0.299723 | ||||||||
\(417\) | −1.31994 | −0.0646379 | ||||||||
\(418\) | 1.00335 | 0.0490754 | ||||||||
\(419\) | 27.8925 | 1.36264 | 0.681319 | − | 0.731987i | \(-0.261407\pi\) | ||||
0.681319 | + | 0.731987i | \(0.261407\pi\) | |||||||
\(420\) | 5.06149 | 0.246975 | ||||||||
\(421\) | 2.66284 | 0.129779 | 0.0648895 | − | 0.997892i | \(-0.479330\pi\) | ||||
0.0648895 | + | 0.997892i | \(0.479330\pi\) | |||||||
\(422\) | −1.39128 | −0.0677267 | ||||||||
\(423\) | −0.814640 | −0.0396092 | ||||||||
\(424\) | 6.30888 | 0.306387 | ||||||||
\(425\) | 7.37367 | 0.357676 | ||||||||
\(426\) | −2.94944 | −0.142901 | ||||||||
\(427\) | 22.6667 | 1.09692 | ||||||||
\(428\) | −9.84487 | −0.475870 | ||||||||
\(429\) | −10.7500 | −0.519014 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 19.8330 | 0.955322 | 0.477661 | − | 0.878544i | \(-0.341485\pi\) | ||||
0.477661 | + | 0.878544i | \(0.341485\pi\) | |||||||
\(432\) | −5.11317 | −0.246008 | ||||||||
\(433\) | −13.7880 | −0.662610 | −0.331305 | − | 0.943524i | \(-0.607489\pi\) | ||||
−0.331305 | + | 0.943524i | \(0.607489\pi\) | |||||||
\(434\) | 0.337557 | 0.0162032 | ||||||||
\(435\) | −0.532817 | −0.0255466 | ||||||||
\(436\) | −8.98172 | −0.430146 | ||||||||
\(437\) | −2.93058 | −0.140189 | ||||||||
\(438\) | 10.6938 | 0.510971 | ||||||||
\(439\) | 40.2252 | 1.91984 | 0.959922 | − | 0.280266i | \(-0.0904227\pi\) | ||||
0.959922 | + | 0.280266i | \(0.0904227\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 0.118577 | 0.00564650 | ||||||||
\(442\) | −45.0765 | −2.14407 | ||||||||
\(443\) | 6.67693 | 0.317230 | 0.158615 | − | 0.987340i | \(-0.449297\pi\) | ||||
0.158615 | + | 0.987340i | \(0.449297\pi\) | |||||||
\(444\) | −15.8482 | −0.752121 | ||||||||
\(445\) | 5.85080 | 0.277354 | ||||||||
\(446\) | 11.5694 | 0.547826 | ||||||||
\(447\) | −31.3262 | −1.48168 | ||||||||
\(448\) | −2.87831 | −0.135987 | ||||||||
\(449\) | 15.0258 | 0.709110 | 0.354555 | − | 0.935035i | \(-0.384632\pi\) | ||||
0.354555 | + | 0.935035i | \(0.384632\pi\) | |||||||
\(450\) | 0.0923014 | 0.00435113 | ||||||||
\(451\) | −8.87755 | −0.418028 | ||||||||
\(452\) | −15.5047 | −0.729281 | ||||||||
\(453\) | 8.95095 | 0.420552 | ||||||||
\(454\) | 24.8235 | 1.16502 | ||||||||
\(455\) | −17.5956 | −0.824894 | ||||||||
\(456\) | 1.76438 | 0.0826248 | ||||||||
\(457\) | −14.1718 | −0.662928 | −0.331464 | − | 0.943468i | \(-0.607542\pi\) | ||||
−0.331464 | + | 0.943468i | \(0.607542\pi\) | |||||||
\(458\) | 9.98296 | 0.466473 | ||||||||
\(459\) | −37.7028 | −1.75982 | ||||||||
\(460\) | 2.92081 | 0.136183 | ||||||||
\(461\) | 9.92192 | 0.462110 | 0.231055 | − | 0.972941i | \(-0.425782\pi\) | ||||
0.231055 | + | 0.972941i | \(0.425782\pi\) | |||||||
\(462\) | −5.06149 | −0.235482 | ||||||||
\(463\) | −22.3009 | −1.03641 | −0.518205 | − | 0.855256i | \(-0.673400\pi\) | ||||
−0.518205 | + | 0.855256i | \(0.673400\pi\) | |||||||
\(464\) | 0.302996 | 0.0140663 | ||||||||
\(465\) | 0.206229 | 0.00956365 | ||||||||
\(466\) | 3.93004 | 0.182056 | ||||||||
\(467\) | 24.4941 | 1.13345 | 0.566726 | − | 0.823906i | \(-0.308210\pi\) | ||||
0.566726 | + | 0.823906i | \(0.308210\pi\) | |||||||
\(468\) | −0.564254 | −0.0260827 | ||||||||
\(469\) | −20.2856 | −0.936702 | ||||||||
\(470\) | 8.82587 | 0.407107 | ||||||||
\(471\) | 23.4346 | 1.07981 | ||||||||
\(472\) | −6.09342 | −0.280472 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −0.433871 | −0.0199284 | ||||||||
\(475\) | 1.00335 | 0.0460368 | ||||||||
\(476\) | −21.2237 | −0.972787 | ||||||||
\(477\) | 0.582319 | 0.0266625 | ||||||||
\(478\) | −8.03473 | −0.367500 | ||||||||
\(479\) | −17.0102 | −0.777218 | −0.388609 | − | 0.921403i | \(-0.627044\pi\) | ||||
−0.388609 | + | 0.921403i | \(0.627044\pi\) | |||||||
\(480\) | −1.75849 | −0.0802639 | ||||||||
\(481\) | 55.0940 | 2.51207 | ||||||||
\(482\) | 11.4440 | 0.521262 | ||||||||
\(483\) | 14.7836 | 0.672678 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.27629 | −0.284992 | ||||||||
\(486\) | −0.958887 | −0.0434960 | ||||||||
\(487\) | −36.1457 | −1.63792 | −0.818958 | − | 0.573853i | \(-0.805448\pi\) | ||||
−0.818958 | + | 0.573853i | \(0.805448\pi\) | |||||||
\(488\) | −7.87501 | −0.356485 | ||||||||
\(489\) | 3.59815 | 0.162714 | ||||||||
\(490\) | −1.28467 | −0.0580353 | ||||||||
\(491\) | 28.3175 | 1.27795 | 0.638975 | − | 0.769227i | \(-0.279359\pi\) | ||||
0.638975 | + | 0.769227i | \(0.279359\pi\) | |||||||
\(492\) | −15.6111 | −0.703804 | ||||||||
\(493\) | 2.23420 | 0.100623 | ||||||||
\(494\) | −6.13364 | −0.275965 | ||||||||
\(495\) | −0.0923014 | −0.00414864 | ||||||||
\(496\) | −0.117276 | −0.00526585 | ||||||||
\(497\) | 4.82765 | 0.216550 | ||||||||
\(498\) | −19.5058 | −0.874077 | ||||||||
\(499\) | −24.3532 | −1.09020 | −0.545099 | − | 0.838372i | \(-0.683508\pi\) | ||||
−0.545099 | + | 0.838372i | \(0.683508\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −3.42941 | −0.153215 | ||||||||
\(502\) | −21.3745 | −0.953991 | ||||||||
\(503\) | −11.6274 | −0.518438 | −0.259219 | − | 0.965819i | \(-0.583465\pi\) | ||||
−0.259219 | + | 0.965819i | \(0.583465\pi\) | |||||||
\(504\) | −0.265672 | −0.0118340 | ||||||||
\(505\) | 5.22081 | 0.232323 | ||||||||
\(506\) | −2.92081 | −0.129846 | ||||||||
\(507\) | 42.8560 | 1.90330 | ||||||||
\(508\) | −5.26491 | −0.233593 | ||||||||
\(509\) | −15.5004 | −0.687044 | −0.343522 | − | 0.939145i | \(-0.611620\pi\) | ||||
−0.343522 | + | 0.939145i | \(0.611620\pi\) | |||||||
\(510\) | −12.9666 | −0.574169 | ||||||||
\(511\) | −17.5037 | −0.774318 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.13029 | −0.226508 | ||||||||
\(514\) | 28.4183 | 1.25348 | ||||||||
\(515\) | −10.8854 | −0.479670 | ||||||||
\(516\) | −1.75849 | −0.0774134 | ||||||||
\(517\) | −8.82587 | −0.388161 | ||||||||
\(518\) | 25.9403 | 1.13975 | ||||||||
\(519\) | 33.2522 | 1.45961 | ||||||||
\(520\) | 6.11317 | 0.268080 | ||||||||
\(521\) | −15.7083 | −0.688193 | −0.344096 | − | 0.938934i | \(-0.611815\pi\) | ||||
−0.344096 | + | 0.938934i | \(0.611815\pi\) | |||||||
\(522\) | 0.0279670 | 0.00122408 | ||||||||
\(523\) | −41.8613 | −1.83047 | −0.915233 | − | 0.402926i | \(-0.867993\pi\) | ||||
−0.915233 | + | 0.402926i | \(0.867993\pi\) | |||||||
\(524\) | 16.0097 | 0.699386 | ||||||||
\(525\) | −5.06149 | −0.220902 | ||||||||
\(526\) | −12.0841 | −0.526894 | ||||||||
\(527\) | −0.864755 | −0.0376693 | ||||||||
\(528\) | 1.75849 | 0.0765286 | ||||||||
\(529\) | −14.4689 | −0.629082 | ||||||||
\(530\) | −6.30888 | −0.274040 | ||||||||
\(531\) | −0.562431 | −0.0244074 | ||||||||
\(532\) | −2.88795 | −0.125208 | ||||||||
\(533\) | 54.2700 | 2.35069 | ||||||||
\(534\) | −10.2886 | −0.445231 | ||||||||
\(535\) | 9.84487 | 0.425631 | ||||||||
\(536\) | 7.04775 | 0.304416 | ||||||||
\(537\) | −4.34799 | −0.187630 | ||||||||
\(538\) | 2.31705 | 0.0998950 | ||||||||
\(539\) | 1.28467 | 0.0553345 | ||||||||
\(540\) | 5.11317 | 0.220036 | ||||||||
\(541\) | 39.5168 | 1.69896 | 0.849480 | − | 0.527620i | \(-0.176916\pi\) | ||||
0.849480 | + | 0.527620i | \(0.176916\pi\) | |||||||
\(542\) | 18.4363 | 0.791906 | ||||||||
\(543\) | −16.0524 | −0.688876 | ||||||||
\(544\) | 7.37367 | 0.316144 | ||||||||
\(545\) | 8.98172 | 0.384735 | ||||||||
\(546\) | 30.9418 | 1.32418 | ||||||||
\(547\) | 19.2902 | 0.824791 | 0.412395 | − | 0.911005i | \(-0.364692\pi\) | ||||
0.412395 | + | 0.911005i | \(0.364692\pi\) | |||||||
\(548\) | 6.51704 | 0.278394 | ||||||||
\(549\) | −0.726875 | −0.0310223 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 0.304011 | 0.0129513 | ||||||||
\(552\) | −5.13622 | −0.218612 | ||||||||
\(553\) | 0.710162 | 0.0301992 | ||||||||
\(554\) | 10.4719 | 0.444907 | ||||||||
\(555\) | 15.8482 | 0.672717 | ||||||||
\(556\) | −0.750610 | −0.0318330 | ||||||||
\(557\) | 38.9409 | 1.64998 | 0.824989 | − | 0.565149i | \(-0.191181\pi\) | ||||
0.824989 | + | 0.565149i | \(0.191181\pi\) | |||||||
\(558\) | −0.0108247 | −0.000458248 0 | ||||||||
\(559\) | 6.11317 | 0.258560 | ||||||||
\(560\) | 2.87831 | 0.121631 | ||||||||
\(561\) | 12.9666 | 0.547448 | ||||||||
\(562\) | 1.41051 | 0.0594989 | ||||||||
\(563\) | 40.9127 | 1.72426 | 0.862132 | − | 0.506683i | \(-0.169129\pi\) | ||||
0.862132 | + | 0.506683i | \(0.169129\pi\) | |||||||
\(564\) | −15.5202 | −0.653520 | ||||||||
\(565\) | 15.5047 | 0.652288 | ||||||||
\(566\) | −7.93645 | −0.333594 | ||||||||
\(567\) | 26.6773 | 1.12034 | ||||||||
\(568\) | −1.67725 | −0.0703759 | ||||||||
\(569\) | 19.7648 | 0.828584 | 0.414292 | − | 0.910144i | \(-0.364029\pi\) | ||||
0.414292 | + | 0.910144i | \(0.364029\pi\) | |||||||
\(570\) | −1.76438 | −0.0739018 | ||||||||
\(571\) | 35.8529 | 1.50040 | 0.750199 | − | 0.661212i | \(-0.229958\pi\) | ||||
0.750199 | + | 0.661212i | \(0.229958\pi\) | |||||||
\(572\) | −6.11317 | −0.255605 | ||||||||
\(573\) | −6.06916 | −0.253543 | ||||||||
\(574\) | 25.5523 | 1.06653 | ||||||||
\(575\) | −2.92081 | −0.121806 | ||||||||
\(576\) | 0.0923014 | 0.00384589 | ||||||||
\(577\) | −39.7095 | −1.65313 | −0.826564 | − | 0.562843i | \(-0.809708\pi\) | ||||
−0.826564 | + | 0.562843i | \(0.809708\pi\) | |||||||
\(578\) | 37.3710 | 1.55443 | ||||||||
\(579\) | −26.7788 | −1.11289 | ||||||||
\(580\) | −0.302996 | −0.0125812 | ||||||||
\(581\) | 31.9272 | 1.32456 | ||||||||
\(582\) | 11.0368 | 0.457491 | ||||||||
\(583\) | 6.30888 | 0.261287 | ||||||||
\(584\) | 6.08124 | 0.251644 | ||||||||
\(585\) | 0.564254 | 0.0233290 | ||||||||
\(586\) | 19.2752 | 0.796251 | ||||||||
\(587\) | 11.4755 | 0.473644 | 0.236822 | − | 0.971553i | \(-0.423894\pi\) | ||||
0.236822 | + | 0.971553i | \(0.423894\pi\) | |||||||
\(588\) | 2.25908 | 0.0931628 | ||||||||
\(589\) | −0.117669 | −0.00484845 | ||||||||
\(590\) | 6.09342 | 0.250862 | ||||||||
\(591\) | 24.7618 | 1.01856 | ||||||||
\(592\) | −9.01235 | −0.370405 | ||||||||
\(593\) | 16.8427 | 0.691646 | 0.345823 | − | 0.938300i | \(-0.387600\pi\) | ||||
0.345823 | + | 0.938300i | \(0.387600\pi\) | |||||||
\(594\) | −5.11317 | −0.209796 | ||||||||
\(595\) | 21.2237 | 0.870087 | ||||||||
\(596\) | −17.8142 | −0.729700 | ||||||||
\(597\) | −32.0982 | −1.31369 | ||||||||
\(598\) | 17.8554 | 0.730161 | ||||||||
\(599\) | −15.3188 | −0.625910 | −0.312955 | − | 0.949768i | \(-0.601319\pi\) | ||||
−0.312955 | + | 0.949768i | \(0.601319\pi\) | |||||||
\(600\) | 1.75849 | 0.0717902 | ||||||||
\(601\) | 3.31412 | 0.135186 | 0.0675928 | − | 0.997713i | \(-0.478468\pi\) | ||||
0.0675928 | + | 0.997713i | \(0.478468\pi\) | |||||||
\(602\) | 2.87831 | 0.117311 | ||||||||
\(603\) | 0.650517 | 0.0264911 | ||||||||
\(604\) | 5.09012 | 0.207114 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −9.18076 | −0.372943 | ||||||||
\(607\) | −3.93348 | −0.159655 | −0.0798276 | − | 0.996809i | \(-0.525437\pi\) | ||||
−0.0798276 | + | 0.996809i | \(0.525437\pi\) | |||||||
\(608\) | 1.00335 | 0.0406911 | ||||||||
\(609\) | −1.53361 | −0.0621452 | ||||||||
\(610\) | 7.87501 | 0.318850 | ||||||||
\(611\) | 53.9541 | 2.18275 | ||||||||
\(612\) | 0.680600 | 0.0275116 | ||||||||
\(613\) | −14.6246 | −0.590683 | −0.295342 | − | 0.955392i | \(-0.595433\pi\) | ||||
−0.295342 | + | 0.955392i | \(0.595433\pi\) | |||||||
\(614\) | 22.7434 | 0.917847 | ||||||||
\(615\) | 15.6111 | 0.629501 | ||||||||
\(616\) | −2.87831 | −0.115970 | ||||||||
\(617\) | −4.54410 | −0.182939 | −0.0914693 | − | 0.995808i | \(-0.529156\pi\) | ||||
−0.0914693 | + | 0.995808i | \(0.529156\pi\) | |||||||
\(618\) | 19.1420 | 0.770003 | ||||||||
\(619\) | 22.2242 | 0.893265 | 0.446632 | − | 0.894718i | \(-0.352623\pi\) | ||||
0.446632 | + | 0.894718i | \(0.352623\pi\) | |||||||
\(620\) | 0.117276 | 0.00470992 | ||||||||
\(621\) | 14.9346 | 0.599304 | ||||||||
\(622\) | −18.3887 | −0.737319 | ||||||||
\(623\) | 16.8404 | 0.674696 | ||||||||
\(624\) | −10.7500 | −0.430343 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −26.7205 | −1.06796 | ||||||||
\(627\) | 1.76438 | 0.0704626 | ||||||||
\(628\) | 13.3265 | 0.531786 | ||||||||
\(629\) | −66.4541 | −2.64970 | ||||||||
\(630\) | 0.265672 | 0.0105846 | ||||||||
\(631\) | −20.4796 | −0.815281 | −0.407640 | − | 0.913143i | \(-0.633648\pi\) | ||||
−0.407640 | + | 0.913143i | \(0.633648\pi\) | |||||||
\(632\) | −0.246729 | −0.00981435 | ||||||||
\(633\) | −2.44657 | −0.0972423 | ||||||||
\(634\) | 12.6603 | 0.502803 | ||||||||
\(635\) | 5.26491 | 0.208932 | ||||||||
\(636\) | 11.0941 | 0.439911 | ||||||||
\(637\) | −7.85339 | −0.311163 | ||||||||
\(638\) | 0.302996 | 0.0119957 | ||||||||
\(639\) | −0.154813 | −0.00612429 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 11.1457 | 0.440229 | 0.220115 | − | 0.975474i | \(-0.429357\pi\) | ||||
0.220115 | + | 0.975474i | \(0.429357\pi\) | |||||||
\(642\) | −17.3121 | −0.683256 | ||||||||
\(643\) | −43.7713 | −1.72617 | −0.863086 | − | 0.505057i | \(-0.831472\pi\) | ||||
−0.863086 | + | 0.505057i | \(0.831472\pi\) | |||||||
\(644\) | 8.40698 | 0.331282 | ||||||||
\(645\) | 1.75849 | 0.0692406 | ||||||||
\(646\) | 7.39836 | 0.291085 | ||||||||
\(647\) | −6.99255 | −0.274906 | −0.137453 | − | 0.990508i | \(-0.543892\pi\) | ||||
−0.137453 | + | 0.990508i | \(0.543892\pi\) | |||||||
\(648\) | −9.26838 | −0.364097 | ||||||||
\(649\) | −6.09342 | −0.239188 | ||||||||
\(650\) | −6.11317 | −0.239778 | ||||||||
\(651\) | 0.593591 | 0.0232647 | ||||||||
\(652\) | 2.04615 | 0.0801335 | ||||||||
\(653\) | −9.56862 | −0.374449 | −0.187225 | − | 0.982317i | \(-0.559949\pi\) | ||||
−0.187225 | + | 0.982317i | \(0.559949\pi\) | |||||||
\(654\) | −15.7943 | −0.617606 | ||||||||
\(655\) | −16.0097 | −0.625549 | ||||||||
\(656\) | −8.87755 | −0.346610 | ||||||||
\(657\) | 0.561307 | 0.0218987 | ||||||||
\(658\) | 25.4036 | 0.990335 | ||||||||
\(659\) | −42.3110 | −1.64820 | −0.824101 | − | 0.566443i | \(-0.808319\pi\) | ||||
−0.824101 | + | 0.566443i | \(0.808319\pi\) | |||||||
\(660\) | −1.75849 | −0.0684493 | ||||||||
\(661\) | −40.2884 | −1.56704 | −0.783519 | − | 0.621368i | \(-0.786577\pi\) | ||||
−0.783519 | + | 0.621368i | \(0.786577\pi\) | |||||||
\(662\) | 3.34862 | 0.130148 | ||||||||
\(663\) | −79.2668 | −3.07847 | ||||||||
\(664\) | −11.0924 | −0.430467 | ||||||||
\(665\) | 2.88795 | 0.111990 | ||||||||
\(666\) | −0.831852 | −0.0322336 | ||||||||
\(667\) | −0.884994 | −0.0342671 | ||||||||
\(668\) | −1.95019 | −0.0754553 | ||||||||
\(669\) | 20.3447 | 0.786571 | ||||||||
\(670\) | −7.04775 | −0.272278 | ||||||||
\(671\) | −7.87501 | −0.304012 | ||||||||
\(672\) | −5.06149 | −0.195251 | ||||||||
\(673\) | −29.1904 | −1.12521 | −0.562603 | − | 0.826727i | \(-0.690200\pi\) | ||||
−0.562603 | + | 0.826727i | \(0.690200\pi\) | |||||||
\(674\) | 14.9016 | 0.573988 | ||||||||
\(675\) | −5.11317 | −0.196806 | ||||||||
\(676\) | 24.3709 | 0.937341 | ||||||||
\(677\) | −19.7904 | −0.760607 | −0.380304 | − | 0.924862i | \(-0.624181\pi\) | ||||
−0.380304 | + | 0.924862i | \(0.624181\pi\) | |||||||
\(678\) | −27.2650 | −1.04710 | ||||||||
\(679\) | −18.0651 | −0.693275 | ||||||||
\(680\) | −7.37367 | −0.282767 | ||||||||
\(681\) | 43.6520 | 1.67275 | ||||||||
\(682\) | −0.117276 | −0.00449073 | ||||||||
\(683\) | −47.1398 | −1.80375 | −0.901877 | − | 0.431994i | \(-0.857810\pi\) | ||||
−0.901877 | + | 0.431994i | \(0.857810\pi\) | |||||||
\(684\) | 0.0926104 | 0.00354105 | ||||||||
\(685\) | −6.51704 | −0.249003 | ||||||||
\(686\) | 16.4505 | 0.628083 | ||||||||
\(687\) | 17.5550 | 0.669764 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | −38.5673 | −1.46930 | ||||||||
\(690\) | 5.13622 | 0.195533 | ||||||||
\(691\) | −7.07816 | −0.269266 | −0.134633 | − | 0.990896i | \(-0.542986\pi\) | ||||
−0.134633 | + | 0.990896i | \(0.542986\pi\) | |||||||
\(692\) | 18.9095 | 0.718831 | ||||||||
\(693\) | −0.265672 | −0.0100920 | ||||||||
\(694\) | 12.4727 | 0.473456 | ||||||||
\(695\) | 0.750610 | 0.0284723 | ||||||||
\(696\) | 0.532817 | 0.0201964 | ||||||||
\(697\) | −65.4602 | −2.47948 | ||||||||
\(698\) | −13.3681 | −0.505992 | ||||||||
\(699\) | 6.91095 | 0.261396 | ||||||||
\(700\) | −2.87831 | −0.108790 | ||||||||
\(701\) | 25.7318 | 0.971878 | 0.485939 | − | 0.873993i | \(-0.338478\pi\) | ||||
0.485939 | + | 0.873993i | \(0.338478\pi\) | |||||||
\(702\) | 31.2577 | 1.17975 | ||||||||
\(703\) | −9.04253 | −0.341045 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 15.5202 | 0.584526 | ||||||||
\(706\) | −23.5669 | −0.886953 | ||||||||
\(707\) | 15.0271 | 0.565153 | ||||||||
\(708\) | −10.7152 | −0.402703 | ||||||||
\(709\) | 2.78881 | 0.104736 | 0.0523680 | − | 0.998628i | \(-0.483323\pi\) | ||||
0.0523680 | + | 0.998628i | \(0.483323\pi\) | |||||||
\(710\) | 1.67725 | 0.0629461 | ||||||||
\(711\) | −0.0227734 | −0.000854070 0 | ||||||||
\(712\) | −5.85080 | −0.219268 | ||||||||
\(713\) | 0.342540 | 0.0128282 | ||||||||
\(714\) | −37.3218 | −1.39673 | ||||||||
\(715\) | 6.11317 | 0.228620 | ||||||||
\(716\) | −2.47257 | −0.0924041 | ||||||||
\(717\) | −14.1290 | −0.527658 | ||||||||
\(718\) | −32.4228 | −1.21001 | ||||||||
\(719\) | −28.9802 | −1.08078 | −0.540389 | − | 0.841415i | \(-0.681723\pi\) | ||||
−0.540389 | + | 0.841415i | \(0.681723\pi\) | |||||||
\(720\) | −0.0923014 | −0.00343987 | ||||||||
\(721\) | −31.3317 | −1.16685 | ||||||||
\(722\) | −17.9933 | −0.669641 | ||||||||
\(723\) | 20.1243 | 0.748430 | ||||||||
\(724\) | −9.12851 | −0.339258 | ||||||||
\(725\) | 0.302996 | 0.0112530 | ||||||||
\(726\) | 1.75849 | 0.0652638 | ||||||||
\(727\) | 30.1464 | 1.11807 | 0.559033 | − | 0.829145i | \(-0.311172\pi\) | ||||
0.559033 | + | 0.829145i | \(0.311172\pi\) | |||||||
\(728\) | 17.5956 | 0.652136 | ||||||||
\(729\) | 26.1190 | 0.967369 | ||||||||
\(730\) | −6.08124 | −0.225077 | ||||||||
\(731\) | −7.37367 | −0.272725 | ||||||||
\(732\) | −13.8482 | −0.511843 | ||||||||
\(733\) | 18.8479 | 0.696162 | 0.348081 | − | 0.937464i | \(-0.386833\pi\) | ||||
0.348081 | + | 0.937464i | \(0.386833\pi\) | |||||||
\(734\) | 28.5536 | 1.05393 | ||||||||
\(735\) | −2.25908 | −0.0833274 | ||||||||
\(736\) | −2.92081 | −0.107662 | ||||||||
\(737\) | 7.04775 | 0.259607 | ||||||||
\(738\) | −0.819410 | −0.0301629 | ||||||||
\(739\) | −21.8536 | −0.803899 | −0.401949 | − | 0.915662i | \(-0.631667\pi\) | ||||
−0.401949 | + | 0.915662i | \(0.631667\pi\) | |||||||
\(740\) | 9.01235 | 0.331301 | ||||||||
\(741\) | −10.7860 | −0.396232 | ||||||||
\(742\) | −18.1589 | −0.666635 | ||||||||
\(743\) | −47.8603 | −1.75582 | −0.877912 | − | 0.478821i | \(-0.841064\pi\) | ||||
−0.877912 | + | 0.478821i | \(0.841064\pi\) | |||||||
\(744\) | −0.206229 | −0.00756073 | ||||||||
\(745\) | 17.8142 | 0.652663 | ||||||||
\(746\) | −6.42137 | −0.235103 | ||||||||
\(747\) | −1.02384 | −0.0374603 | ||||||||
\(748\) | 7.37367 | 0.269608 | ||||||||
\(749\) | 28.3366 | 1.03540 | ||||||||
\(750\) | −1.75849 | −0.0642111 | ||||||||
\(751\) | 7.38256 | 0.269393 | 0.134697 | − | 0.990887i | \(-0.456994\pi\) | ||||
0.134697 | + | 0.990887i | \(0.456994\pi\) | |||||||
\(752\) | −8.82587 | −0.321846 | ||||||||
\(753\) | −37.5869 | −1.36974 | ||||||||
\(754\) | −1.85227 | −0.0674557 | ||||||||
\(755\) | −5.09012 | −0.185249 | ||||||||
\(756\) | 14.7173 | 0.535263 | ||||||||
\(757\) | 11.7032 | 0.425360 | 0.212680 | − | 0.977122i | \(-0.431781\pi\) | ||||
0.212680 | + | 0.977122i | \(0.431781\pi\) | |||||||
\(758\) | −0.677659 | −0.0246137 | ||||||||
\(759\) | −5.13622 | −0.186433 | ||||||||
\(760\) | −1.00335 | −0.0363953 | ||||||||
\(761\) | −42.4017 | −1.53706 | −0.768531 | − | 0.639813i | \(-0.779012\pi\) | ||||
−0.768531 | + | 0.639813i | \(0.779012\pi\) | |||||||
\(762\) | −9.25832 | −0.335394 | ||||||||
\(763\) | 25.8522 | 0.935912 | ||||||||
\(764\) | −3.45134 | −0.124865 | ||||||||
\(765\) | −0.680600 | −0.0246071 | ||||||||
\(766\) | −19.4006 | −0.700970 | ||||||||
\(767\) | 37.2501 | 1.34502 | ||||||||
\(768\) | 1.75849 | 0.0634542 | ||||||||
\(769\) | −46.6165 | −1.68103 | −0.840517 | − | 0.541785i | \(-0.817749\pi\) | ||||
−0.840517 | + | 0.541785i | \(0.817749\pi\) | |||||||
\(770\) | 2.87831 | 0.103727 | ||||||||
\(771\) | 49.9734 | 1.79975 | ||||||||
\(772\) | −15.2283 | −0.548077 | ||||||||
\(773\) | −25.8827 | −0.930935 | −0.465468 | − | 0.885065i | \(-0.654114\pi\) | ||||
−0.465468 | + | 0.885065i | \(0.654114\pi\) | |||||||
\(774\) | −0.0923014 | −0.00331770 | ||||||||
\(775\) | −0.117276 | −0.00421268 | ||||||||
\(776\) | 6.27629 | 0.225306 | ||||||||
\(777\) | 45.6159 | 1.63646 | ||||||||
\(778\) | −22.7919 | −0.817131 | ||||||||
\(779\) | −8.90728 | −0.319136 | ||||||||
\(780\) | 10.7500 | 0.384911 | ||||||||
\(781\) | −1.67725 | −0.0600168 | ||||||||
\(782\) | −21.5371 | −0.770164 | ||||||||
\(783\) | −1.54927 | −0.0553665 | ||||||||
\(784\) | 1.28467 | 0.0458810 | ||||||||
\(785\) | −13.3265 | −0.475644 | ||||||||
\(786\) | 28.1529 | 1.00418 | ||||||||
\(787\) | −21.6513 | −0.771787 | −0.385893 | − | 0.922543i | \(-0.626107\pi\) | ||||
−0.385893 | + | 0.922543i | \(0.626107\pi\) | |||||||
\(788\) | 14.0812 | 0.501623 | ||||||||
\(789\) | −21.2499 | −0.756516 | ||||||||
\(790\) | 0.246729 | 0.00877822 | ||||||||
\(791\) | 44.6274 | 1.58677 | ||||||||
\(792\) | 0.0923014 | 0.00327979 | ||||||||
\(793\) | 48.1413 | 1.70955 | ||||||||
\(794\) | −9.26539 | −0.328816 | ||||||||
\(795\) | −11.0941 | −0.393468 | ||||||||
\(796\) | −18.2532 | −0.646968 | ||||||||
\(797\) | −41.1403 | −1.45727 | −0.728633 | − | 0.684904i | \(-0.759844\pi\) | ||||
−0.728633 | + | 0.684904i | \(0.759844\pi\) | |||||||
\(798\) | −5.07844 | −0.179775 | ||||||||
\(799\) | −65.0791 | −2.30233 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −0.540036 | −0.0190813 | ||||||||
\(802\) | −5.89124 | −0.208027 | ||||||||
\(803\) | 6.08124 | 0.214602 | ||||||||
\(804\) | 12.3934 | 0.437082 | ||||||||
\(805\) | −8.40698 | −0.296307 | ||||||||
\(806\) | 0.716928 | 0.0252527 | ||||||||
\(807\) | 4.07452 | 0.143430 | ||||||||
\(808\) | −5.22081 | −0.183667 | ||||||||
\(809\) | 29.9119 | 1.05165 | 0.525823 | − | 0.850594i | \(-0.323758\pi\) | ||||
0.525823 | + | 0.850594i | \(0.323758\pi\) | |||||||
\(810\) | 9.26838 | 0.325658 | ||||||||
\(811\) | −39.1283 | −1.37398 | −0.686991 | − | 0.726666i | \(-0.741069\pi\) | ||||
−0.686991 | + | 0.726666i | \(0.741069\pi\) | |||||||
\(812\) | −0.872118 | −0.0306053 | ||||||||
\(813\) | 32.4201 | 1.13702 | ||||||||
\(814\) | −9.01235 | −0.315883 | ||||||||
\(815\) | −2.04615 | −0.0716736 | ||||||||
\(816\) | 12.9666 | 0.453920 | ||||||||
\(817\) | −1.00335 | −0.0351027 | ||||||||
\(818\) | 20.6012 | 0.720305 | ||||||||
\(819\) | 1.62410 | 0.0567506 | ||||||||
\(820\) | 8.87755 | 0.310018 | ||||||||
\(821\) | 53.7388 | 1.87550 | 0.937748 | − | 0.347316i | \(-0.112907\pi\) | ||||
0.937748 | + | 0.347316i | \(0.112907\pi\) | |||||||
\(822\) | 11.4602 | 0.399720 | ||||||||
\(823\) | −16.3835 | −0.571092 | −0.285546 | − | 0.958365i | \(-0.592175\pi\) | ||||
−0.285546 | + | 0.958365i | \(0.592175\pi\) | |||||||
\(824\) | 10.8854 | 0.379212 | ||||||||
\(825\) | 1.75849 | 0.0612229 | ||||||||
\(826\) | 17.5387 | 0.610251 | ||||||||
\(827\) | 7.49362 | 0.260579 | 0.130289 | − | 0.991476i | \(-0.458409\pi\) | ||||
0.130289 | + | 0.991476i | \(0.458409\pi\) | |||||||
\(828\) | −0.269594 | −0.00936905 | ||||||||
\(829\) | −29.7066 | −1.03175 | −0.515876 | − | 0.856663i | \(-0.672533\pi\) | ||||
−0.515876 | + | 0.856663i | \(0.672533\pi\) | |||||||
\(830\) | 11.0924 | 0.385021 | ||||||||
\(831\) | 18.4147 | 0.638799 | ||||||||
\(832\) | −6.11317 | −0.211936 | ||||||||
\(833\) | 9.47271 | 0.328210 | ||||||||
\(834\) | −1.31994 | −0.0457059 | ||||||||
\(835\) | 1.95019 | 0.0674893 | ||||||||
\(836\) | 1.00335 | 0.0347015 | ||||||||
\(837\) | 0.599652 | 0.0207270 | ||||||||
\(838\) | 27.8925 | 0.963530 | ||||||||
\(839\) | 31.8715 | 1.10033 | 0.550163 | − | 0.835057i | \(-0.314566\pi\) | ||||
0.550163 | + | 0.835057i | \(0.314566\pi\) | |||||||
\(840\) | 5.06149 | 0.174638 | ||||||||
\(841\) | −28.9082 | −0.996834 | ||||||||
\(842\) | 2.66284 | 0.0917677 | ||||||||
\(843\) | 2.48038 | 0.0854288 | ||||||||
\(844\) | −1.39128 | −0.0478900 | ||||||||
\(845\) | −24.3709 | −0.838383 | ||||||||
\(846\) | −0.814640 | −0.0280079 | ||||||||
\(847\) | −2.87831 | −0.0988999 | ||||||||
\(848\) | 6.30888 | 0.216648 | ||||||||
\(849\) | −13.9562 | −0.478976 | ||||||||
\(850\) | 7.37367 | 0.252915 | ||||||||
\(851\) | 26.3233 | 0.902352 | ||||||||
\(852\) | −2.94944 | −0.101046 | ||||||||
\(853\) | 0.155013 | 0.00530753 | 0.00265377 | − | 0.999996i | \(-0.499155\pi\) | ||||
0.00265377 | + | 0.999996i | \(0.499155\pi\) | |||||||
\(854\) | 22.6667 | 0.775639 | ||||||||
\(855\) | −0.0926104 | −0.00316721 | ||||||||
\(856\) | −9.84487 | −0.336491 | ||||||||
\(857\) | 53.9075 | 1.84145 | 0.920723 | − | 0.390217i | \(-0.127600\pi\) | ||||
0.920723 | + | 0.390217i | \(0.127600\pi\) | |||||||
\(858\) | −10.7500 | −0.366998 | ||||||||
\(859\) | −16.9691 | −0.578977 | −0.289489 | − | 0.957181i | \(-0.593485\pi\) | ||||
−0.289489 | + | 0.957181i | \(0.593485\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | 44.9336 | 1.53133 | ||||||||
\(862\) | 19.8330 | 0.675515 | ||||||||
\(863\) | −33.8618 | −1.15267 | −0.576334 | − | 0.817214i | \(-0.695517\pi\) | ||||
−0.576334 | + | 0.817214i | \(0.695517\pi\) | |||||||
\(864\) | −5.11317 | −0.173954 | ||||||||
\(865\) | −18.9095 | −0.642942 | ||||||||
\(866\) | −13.7880 | −0.468536 | ||||||||
\(867\) | 65.7167 | 2.23186 | ||||||||
\(868\) | 0.337557 | 0.0114574 | ||||||||
\(869\) | −0.246729 | −0.00836970 | ||||||||
\(870\) | −0.532817 | −0.0180642 | ||||||||
\(871\) | −43.0841 | −1.45985 | ||||||||
\(872\) | −8.98172 | −0.304159 | ||||||||
\(873\) | 0.579310 | 0.0196067 | ||||||||
\(874\) | −2.93058 | −0.0991285 | ||||||||
\(875\) | 2.87831 | 0.0973046 | ||||||||
\(876\) | 10.6938 | 0.361311 | ||||||||
\(877\) | 21.6429 | 0.730829 | 0.365415 | − | 0.930845i | \(-0.380927\pi\) | ||||
0.365415 | + | 0.930845i | \(0.380927\pi\) | |||||||
\(878\) | 40.2252 | 1.35754 | ||||||||
\(879\) | 33.8953 | 1.14326 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | 46.6118 | 1.57039 | 0.785196 | − | 0.619248i | \(-0.212562\pi\) | ||||
0.785196 | + | 0.619248i | \(0.212562\pi\) | |||||||
\(882\) | 0.118577 | 0.00399268 | ||||||||
\(883\) | −1.69841 | −0.0571560 | −0.0285780 | − | 0.999592i | \(-0.509098\pi\) | ||||
−0.0285780 | + | 0.999592i | \(0.509098\pi\) | |||||||
\(884\) | −45.0765 | −1.51609 | ||||||||
\(885\) | 10.7152 | 0.360189 | ||||||||
\(886\) | 6.67693 | 0.224316 | ||||||||
\(887\) | 12.2999 | 0.412989 | 0.206495 | − | 0.978448i | \(-0.433794\pi\) | ||||
0.206495 | + | 0.978448i | \(0.433794\pi\) | |||||||
\(888\) | −15.8482 | −0.531830 | ||||||||
\(889\) | 15.1541 | 0.508251 | ||||||||
\(890\) | 5.85080 | 0.196119 | ||||||||
\(891\) | −9.26838 | −0.310503 | ||||||||
\(892\) | 11.5694 | 0.387372 | ||||||||
\(893\) | −8.85542 | −0.296335 | ||||||||
\(894\) | −31.3262 | −1.04771 | ||||||||
\(895\) | 2.47257 | 0.0826488 | ||||||||
\(896\) | −2.87831 | −0.0961576 | ||||||||
\(897\) | 31.3986 | 1.04837 | ||||||||
\(898\) | 15.0258 | 0.501416 | ||||||||
\(899\) | −0.0355342 | −0.00118513 | ||||||||
\(900\) | 0.0923014 | 0.00307671 | ||||||||
\(901\) | 46.5196 | 1.54979 | ||||||||
\(902\) | −8.87755 | −0.295590 | ||||||||
\(903\) | 5.06149 | 0.168436 | ||||||||
\(904\) | −15.5047 | −0.515679 | ||||||||
\(905\) | 9.12851 | 0.303442 | ||||||||
\(906\) | 8.95095 | 0.297375 | ||||||||
\(907\) | 16.3225 | 0.541979 | 0.270990 | − | 0.962582i | \(-0.412649\pi\) | ||||
0.270990 | + | 0.962582i | \(0.412649\pi\) | |||||||
\(908\) | 24.8235 | 0.823797 | ||||||||
\(909\) | −0.481888 | −0.0159832 | ||||||||
\(910\) | −17.5956 | −0.583288 | ||||||||
\(911\) | −11.4590 | −0.379653 | −0.189826 | − | 0.981818i | \(-0.560793\pi\) | ||||
−0.189826 | + | 0.981818i | \(0.560793\pi\) | |||||||
\(912\) | 1.76438 | 0.0584245 | ||||||||
\(913\) | −11.0924 | −0.367103 | ||||||||
\(914\) | −14.1718 | −0.468761 | ||||||||
\(915\) | 13.8482 | 0.457806 | ||||||||
\(916\) | 9.98296 | 0.329846 | ||||||||
\(917\) | −46.0808 | −1.52172 | ||||||||
\(918\) | −37.7028 | −1.24438 | ||||||||
\(919\) | 20.0942 | 0.662847 | 0.331424 | − | 0.943482i | \(-0.392471\pi\) | ||||
0.331424 | + | 0.943482i | \(0.392471\pi\) | |||||||
\(920\) | 2.92081 | 0.0962961 | ||||||||
\(921\) | 39.9941 | 1.31785 | ||||||||
\(922\) | 9.92192 | 0.326761 | ||||||||
\(923\) | 10.2533 | 0.337492 | ||||||||
\(924\) | −5.06149 | −0.166511 | ||||||||
\(925\) | −9.01235 | −0.296324 | ||||||||
\(926\) | −22.3009 | −0.732853 | ||||||||
\(927\) | 1.00474 | 0.0330000 | ||||||||
\(928\) | 0.302996 | 0.00994635 | ||||||||
\(929\) | −46.9139 | −1.53919 | −0.769597 | − | 0.638530i | \(-0.779543\pi\) | ||||
−0.769597 | + | 0.638530i | \(0.779543\pi\) | |||||||
\(930\) | 0.206229 | 0.00676252 | ||||||||
\(931\) | 1.28897 | 0.0422442 | ||||||||
\(932\) | 3.93004 | 0.128733 | ||||||||
\(933\) | −32.3364 | −1.05865 | ||||||||
\(934\) | 24.4941 | 0.801472 | ||||||||
\(935\) | −7.37367 | −0.241145 | ||||||||
\(936\) | −0.564254 | −0.0184432 | ||||||||
\(937\) | −20.1611 | −0.658635 | −0.329317 | − | 0.944219i | \(-0.606819\pi\) | ||||
−0.329317 | + | 0.944219i | \(0.606819\pi\) | |||||||
\(938\) | −20.2856 | −0.662348 | ||||||||
\(939\) | −46.9878 | −1.53339 | ||||||||
\(940\) | 8.82587 | 0.287868 | ||||||||
\(941\) | −57.6666 | −1.87988 | −0.939938 | − | 0.341345i | \(-0.889117\pi\) | ||||
−0.939938 | + | 0.341345i | \(0.889117\pi\) | |||||||
\(942\) | 23.4346 | 0.763541 | ||||||||
\(943\) | 25.9296 | 0.844384 | ||||||||
\(944\) | −6.09342 | −0.198324 | ||||||||
\(945\) | −14.7173 | −0.478753 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | 32.9236 | 1.06987 | 0.534937 | − | 0.844892i | \(-0.320335\pi\) | ||||
0.534937 | + | 0.844892i | \(0.320335\pi\) | |||||||
\(948\) | −0.433871 | −0.0140915 | ||||||||
\(949\) | −37.1757 | −1.20677 | ||||||||
\(950\) | 1.00335 | 0.0325529 | ||||||||
\(951\) | 22.2630 | 0.721927 | ||||||||
\(952\) | −21.2237 | −0.687864 | ||||||||
\(953\) | 16.4551 | 0.533032 | 0.266516 | − | 0.963831i | \(-0.414127\pi\) | ||||
0.266516 | + | 0.963831i | \(0.414127\pi\) | |||||||
\(954\) | 0.582319 | 0.0188533 | ||||||||
\(955\) | 3.45134 | 0.111683 | ||||||||
\(956\) | −8.03473 | −0.259862 | ||||||||
\(957\) | 0.532817 | 0.0172235 | ||||||||
\(958\) | −17.0102 | −0.549576 | ||||||||
\(959\) | −18.7581 | −0.605729 | ||||||||
\(960\) | −1.75849 | −0.0567552 | ||||||||
\(961\) | −30.9862 | −0.999556 | ||||||||
\(962\) | 55.0940 | 1.77630 | ||||||||
\(963\) | −0.908695 | −0.0292823 | ||||||||
\(964\) | 11.4440 | 0.368588 | ||||||||
\(965\) | 15.2283 | 0.490215 | ||||||||
\(966\) | 14.7836 | 0.475655 | ||||||||
\(967\) | −2.15962 | −0.0694488 | −0.0347244 | − | 0.999397i | \(-0.511055\pi\) | ||||
−0.0347244 | + | 0.999397i | \(0.511055\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 13.0100 | 0.417941 | ||||||||
\(970\) | −6.27629 | −0.201520 | ||||||||
\(971\) | 42.7771 | 1.37278 | 0.686391 | − | 0.727233i | \(-0.259194\pi\) | ||||
0.686391 | + | 0.727233i | \(0.259194\pi\) | |||||||
\(972\) | −0.958887 | −0.0307563 | ||||||||
\(973\) | 2.16049 | 0.0692621 | ||||||||
\(974\) | −36.1457 | −1.15818 | ||||||||
\(975\) | −10.7500 | −0.344275 | ||||||||
\(976\) | −7.87501 | −0.252073 | ||||||||
\(977\) | −50.1432 | −1.60422 | −0.802112 | − | 0.597174i | \(-0.796290\pi\) | ||||
−0.802112 | + | 0.597174i | \(0.796290\pi\) | |||||||
\(978\) | 3.59815 | 0.115056 | ||||||||
\(979\) | −5.85080 | −0.186992 | ||||||||
\(980\) | −1.28467 | −0.0410372 | ||||||||
\(981\) | −0.829025 | −0.0264687 | ||||||||
\(982\) | 28.3175 | 0.903647 | ||||||||
\(983\) | 18.0026 | 0.574192 | 0.287096 | − | 0.957902i | \(-0.407310\pi\) | ||||
0.287096 | + | 0.957902i | \(0.407310\pi\) | |||||||
\(984\) | −15.6111 | −0.497664 | ||||||||
\(985\) | −14.0812 | −0.448666 | ||||||||
\(986\) | 2.23420 | 0.0711513 | ||||||||
\(987\) | 44.6721 | 1.42193 | ||||||||
\(988\) | −6.13364 | −0.195137 | ||||||||
\(989\) | 2.92081 | 0.0928762 | ||||||||
\(990\) | −0.0923014 | −0.00293353 | ||||||||
\(991\) | 51.0369 | 1.62124 | 0.810620 | − | 0.585572i | \(-0.199130\pi\) | ||||
0.810620 | + | 0.585572i | \(0.199130\pi\) | |||||||
\(992\) | −0.117276 | −0.00372352 | ||||||||
\(993\) | 5.88853 | 0.186867 | ||||||||
\(994\) | 4.82765 | 0.153124 | ||||||||
\(995\) | 18.2532 | 0.578666 | ||||||||
\(996\) | −19.5058 | −0.618066 | ||||||||
\(997\) | −23.5442 | −0.745651 | −0.372825 | − | 0.927901i | \(-0.621611\pi\) | ||||
−0.372825 | + | 0.927901i | \(0.621611\pi\) | |||||||
\(998\) | −24.3532 | −0.770886 | ||||||||
\(999\) | 46.0817 | 1.45796 |
(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 | 4730.2.a.v.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.v.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial |