Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.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: | \(32.0200112105\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-1.06458\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | 0.696154 | 0.401925 | 0.200962 | − | 0.979599i | \(-0.435593\pi\) | ||||
0.200962 | + | 0.979599i | \(0.435593\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −0.696154 | −0.284204 | ||||||||
\(7\) | 2.65990 | 1.00535 | 0.502675 | − | 0.864476i | \(-0.332349\pi\) | ||||
0.502675 | + | 0.864476i | \(0.332349\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.51537 | −0.838456 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −2.85414 | −0.860556 | −0.430278 | − | 0.902697i | \(-0.641584\pi\) | ||||
−0.430278 | + | 0.902697i | \(0.641584\pi\) | |||||||
\(12\) | 0.696154 | 0.200962 | ||||||||
\(13\) | 0.0375050 | 0.0104020 | 0.00520101 | − | 0.999986i | \(-0.498344\pi\) | ||||
0.00520101 | + | 0.999986i | \(0.498344\pi\) | |||||||
\(14\) | −2.65990 | −0.710889 | ||||||||
\(15\) | 0.696154 | 0.179746 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.02960 | −0.249713 | −0.124857 | − | 0.992175i | \(-0.539847\pi\) | ||||
−0.124857 | + | 0.992175i | \(0.539847\pi\) | |||||||
\(18\) | 2.51537 | 0.592878 | ||||||||
\(19\) | −7.38755 | −1.69482 | −0.847410 | − | 0.530939i | \(-0.821839\pi\) | ||||
−0.847410 | + | 0.530939i | \(0.821839\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.85170 | 0.404075 | ||||||||
\(22\) | 2.85414 | 0.608505 | ||||||||
\(23\) | −1.48829 | −0.310331 | −0.155165 | − | 0.987889i | \(-0.549591\pi\) | ||||
−0.155165 | + | 0.987889i | \(0.549591\pi\) | |||||||
\(24\) | −0.696154 | −0.142102 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.0375050 | −0.00735534 | ||||||||
\(27\) | −3.83955 | −0.738921 | ||||||||
\(28\) | 2.65990 | 0.502675 | ||||||||
\(29\) | 9.65453 | 1.79280 | 0.896401 | − | 0.443245i | \(-0.146173\pi\) | ||||
0.896401 | + | 0.443245i | \(0.146173\pi\) | |||||||
\(30\) | −0.696154 | −0.127100 | ||||||||
\(31\) | 4.28085 | 0.768863 | 0.384431 | − | 0.923154i | \(-0.374398\pi\) | ||||
0.384431 | + | 0.923154i | \(0.374398\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.98692 | −0.345879 | ||||||||
\(34\) | 1.02960 | 0.176574 | ||||||||
\(35\) | 2.65990 | 0.449606 | ||||||||
\(36\) | −2.51537 | −0.419228 | ||||||||
\(37\) | −1.90641 | −0.313412 | −0.156706 | − | 0.987645i | \(-0.550087\pi\) | ||||
−0.156706 | + | 0.987645i | \(0.550087\pi\) | |||||||
\(38\) | 7.38755 | 1.19842 | ||||||||
\(39\) | 0.0261093 | 0.00418083 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 8.37519 | 1.30798 | 0.653992 | − | 0.756501i | \(-0.273093\pi\) | ||||
0.653992 | + | 0.756501i | \(0.273093\pi\) | |||||||
\(42\) | −1.85170 | −0.285724 | ||||||||
\(43\) | −6.07292 | −0.926111 | −0.463055 | − | 0.886329i | \(-0.653247\pi\) | ||||
−0.463055 | + | 0.886329i | \(0.653247\pi\) | |||||||
\(44\) | −2.85414 | −0.430278 | ||||||||
\(45\) | −2.51537 | −0.374969 | ||||||||
\(46\) | 1.48829 | 0.219437 | ||||||||
\(47\) | −3.89157 | −0.567644 | −0.283822 | − | 0.958877i | \(-0.591602\pi\) | ||||
−0.283822 | + | 0.958877i | \(0.591602\pi\) | |||||||
\(48\) | 0.696154 | 0.100481 | ||||||||
\(49\) | 0.0750867 | 0.0107267 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.716757 | −0.100366 | ||||||||
\(52\) | 0.0375050 | 0.00520101 | ||||||||
\(53\) | −9.19937 | −1.26363 | −0.631815 | − | 0.775119i | \(-0.717690\pi\) | ||||
−0.631815 | + | 0.775119i | \(0.717690\pi\) | |||||||
\(54\) | 3.83955 | 0.522496 | ||||||||
\(55\) | −2.85414 | −0.384852 | ||||||||
\(56\) | −2.65990 | −0.355445 | ||||||||
\(57\) | −5.14287 | −0.681190 | ||||||||
\(58\) | −9.65453 | −1.26770 | ||||||||
\(59\) | −10.3821 | −1.35164 | −0.675820 | − | 0.737067i | \(-0.736210\pi\) | ||||
−0.675820 | + | 0.737067i | \(0.736210\pi\) | |||||||
\(60\) | 0.696154 | 0.0898731 | ||||||||
\(61\) | −14.5560 | −1.86371 | −0.931854 | − | 0.362834i | \(-0.881809\pi\) | ||||
−0.931854 | + | 0.362834i | \(0.881809\pi\) | |||||||
\(62\) | −4.28085 | −0.543668 | ||||||||
\(63\) | −6.69064 | −0.842941 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0375050 | 0.00465193 | ||||||||
\(66\) | 1.98692 | 0.244573 | ||||||||
\(67\) | −3.35202 | −0.409515 | −0.204757 | − | 0.978813i | \(-0.565641\pi\) | ||||
−0.204757 | + | 0.978813i | \(0.565641\pi\) | |||||||
\(68\) | −1.02960 | −0.124857 | ||||||||
\(69\) | −1.03608 | −0.124730 | ||||||||
\(70\) | −2.65990 | −0.317919 | ||||||||
\(71\) | 12.4861 | 1.48182 | 0.740911 | − | 0.671603i | \(-0.234394\pi\) | ||||
0.740911 | + | 0.671603i | \(0.234394\pi\) | |||||||
\(72\) | 2.51537 | 0.296439 | ||||||||
\(73\) | 6.72519 | 0.787124 | 0.393562 | − | 0.919298i | \(-0.371243\pi\) | ||||
0.393562 | + | 0.919298i | \(0.371243\pi\) | |||||||
\(74\) | 1.90641 | 0.221616 | ||||||||
\(75\) | 0.696154 | 0.0803850 | ||||||||
\(76\) | −7.38755 | −0.847410 | ||||||||
\(77\) | −7.59174 | −0.865159 | ||||||||
\(78\) | −0.0261093 | −0.00295629 | ||||||||
\(79\) | −6.67283 | −0.750752 | −0.375376 | − | 0.926873i | \(-0.622486\pi\) | ||||
−0.375376 | + | 0.926873i | \(0.622486\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 4.87319 | 0.541466 | ||||||||
\(82\) | −8.37519 | −0.924885 | ||||||||
\(83\) | −7.88459 | −0.865447 | −0.432723 | − | 0.901527i | \(-0.642447\pi\) | ||||
−0.432723 | + | 0.901527i | \(0.642447\pi\) | |||||||
\(84\) | 1.85170 | 0.202037 | ||||||||
\(85\) | −1.02960 | −0.111675 | ||||||||
\(86\) | 6.07292 | 0.654859 | ||||||||
\(87\) | 6.72104 | 0.720571 | ||||||||
\(88\) | 2.85414 | 0.304252 | ||||||||
\(89\) | −5.63871 | −0.597702 | −0.298851 | − | 0.954300i | \(-0.596603\pi\) | ||||
−0.298851 | + | 0.954300i | \(0.596603\pi\) | |||||||
\(90\) | 2.51537 | 0.265143 | ||||||||
\(91\) | 0.0997598 | 0.0104577 | ||||||||
\(92\) | −1.48829 | −0.155165 | ||||||||
\(93\) | 2.98013 | 0.309025 | ||||||||
\(94\) | 3.89157 | 0.401385 | ||||||||
\(95\) | −7.38755 | −0.757947 | ||||||||
\(96\) | −0.696154 | −0.0710509 | ||||||||
\(97\) | 0.00211457 | 0.000214702 0 | 0.000107351 | − | 1.00000i | \(-0.499966\pi\) | ||||
0.000107351 | 1.00000i | \(0.499966\pi\) | ||||||||
\(98\) | −0.0750867 | −0.00758490 | ||||||||
\(99\) | 7.17922 | 0.721538 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −9.15058 | −0.910517 | −0.455258 | − | 0.890359i | \(-0.650453\pi\) | ||||
−0.455258 | + | 0.890359i | \(0.650453\pi\) | |||||||
\(102\) | 0.716757 | 0.0709695 | ||||||||
\(103\) | −3.39406 | −0.334427 | −0.167213 | − | 0.985921i | \(-0.553477\pi\) | ||||
−0.167213 | + | 0.985921i | \(0.553477\pi\) | |||||||
\(104\) | −0.0375050 | −0.00367767 | ||||||||
\(105\) | 1.85170 | 0.180708 | ||||||||
\(106\) | 9.19937 | 0.893522 | ||||||||
\(107\) | −17.1126 | −1.65434 | −0.827171 | − | 0.561950i | \(-0.810051\pi\) | ||||
−0.827171 | + | 0.561950i | \(0.810051\pi\) | |||||||
\(108\) | −3.83955 | −0.369461 | ||||||||
\(109\) | 6.07832 | 0.582198 | 0.291099 | − | 0.956693i | \(-0.405979\pi\) | ||||
0.291099 | + | 0.956693i | \(0.405979\pi\) | |||||||
\(110\) | 2.85414 | 0.272132 | ||||||||
\(111\) | −1.32716 | −0.125968 | ||||||||
\(112\) | 2.65990 | 0.251337 | ||||||||
\(113\) | 8.57048 | 0.806243 | 0.403122 | − | 0.915146i | \(-0.367925\pi\) | ||||
0.403122 | + | 0.915146i | \(0.367925\pi\) | |||||||
\(114\) | 5.14287 | 0.481674 | ||||||||
\(115\) | −1.48829 | −0.138784 | ||||||||
\(116\) | 9.65453 | 0.896401 | ||||||||
\(117\) | −0.0943390 | −0.00872165 | ||||||||
\(118\) | 10.3821 | 0.955753 | ||||||||
\(119\) | −2.73862 | −0.251049 | ||||||||
\(120\) | −0.696154 | −0.0635499 | ||||||||
\(121\) | −2.85389 | −0.259444 | ||||||||
\(122\) | 14.5560 | 1.31784 | ||||||||
\(123\) | 5.83042 | 0.525711 | ||||||||
\(124\) | 4.28085 | 0.384431 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 6.69064 | 0.596050 | ||||||||
\(127\) | −4.07183 | −0.361317 | −0.180658 | − | 0.983546i | \(-0.557823\pi\) | ||||
−0.180658 | + | 0.983546i | \(0.557823\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.22769 | −0.372227 | ||||||||
\(130\) | −0.0375050 | −0.00328941 | ||||||||
\(131\) | 1.30068 | 0.113641 | 0.0568206 | − | 0.998384i | \(-0.481904\pi\) | ||||
0.0568206 | + | 0.998384i | \(0.481904\pi\) | |||||||
\(132\) | −1.98692 | −0.172939 | ||||||||
\(133\) | −19.6502 | −1.70389 | ||||||||
\(134\) | 3.35202 | 0.289571 | ||||||||
\(135\) | −3.83955 | −0.330456 | ||||||||
\(136\) | 1.02960 | 0.0882871 | ||||||||
\(137\) | 17.9925 | 1.53720 | 0.768601 | − | 0.639728i | \(-0.220953\pi\) | ||||
0.768601 | + | 0.639728i | \(0.220953\pi\) | |||||||
\(138\) | 1.03608 | 0.0881971 | ||||||||
\(139\) | 4.30048 | 0.364762 | 0.182381 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182381 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(140\) | 2.65990 | 0.224803 | ||||||||
\(141\) | −2.70913 | −0.228150 | ||||||||
\(142\) | −12.4861 | −1.04781 | ||||||||
\(143\) | −0.107045 | −0.00895152 | ||||||||
\(144\) | −2.51537 | −0.209614 | ||||||||
\(145\) | 9.65453 | 0.801765 | ||||||||
\(146\) | −6.72519 | −0.556581 | ||||||||
\(147\) | 0.0522719 | 0.00431131 | ||||||||
\(148\) | −1.90641 | −0.156706 | ||||||||
\(149\) | −11.2429 | −0.921058 | −0.460529 | − | 0.887645i | \(-0.652340\pi\) | ||||
−0.460529 | + | 0.887645i | \(0.652340\pi\) | |||||||
\(150\) | −0.696154 | −0.0568407 | ||||||||
\(151\) | −18.0929 | −1.47238 | −0.736189 | − | 0.676776i | \(-0.763377\pi\) | ||||
−0.736189 | + | 0.676776i | \(0.763377\pi\) | |||||||
\(152\) | 7.38755 | 0.599209 | ||||||||
\(153\) | 2.58981 | 0.209374 | ||||||||
\(154\) | 7.59174 | 0.611760 | ||||||||
\(155\) | 4.28085 | 0.343846 | ||||||||
\(156\) | 0.0261093 | 0.00209042 | ||||||||
\(157\) | −22.1158 | −1.76503 | −0.882517 | − | 0.470281i | \(-0.844153\pi\) | ||||
−0.882517 | + | 0.470281i | \(0.844153\pi\) | |||||||
\(158\) | 6.67283 | 0.530862 | ||||||||
\(159\) | −6.40418 | −0.507884 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −3.95872 | −0.311991 | ||||||||
\(162\) | −4.87319 | −0.382874 | ||||||||
\(163\) | −18.2881 | −1.43243 | −0.716216 | − | 0.697879i | \(-0.754127\pi\) | ||||
−0.716216 | + | 0.697879i | \(0.754127\pi\) | |||||||
\(164\) | 8.37519 | 0.653992 | ||||||||
\(165\) | −1.98692 | −0.154682 | ||||||||
\(166\) | 7.88459 | 0.611963 | ||||||||
\(167\) | 17.8347 | 1.38009 | 0.690044 | − | 0.723768i | \(-0.257591\pi\) | ||||
0.690044 | + | 0.723768i | \(0.257591\pi\) | |||||||
\(168\) | −1.85170 | −0.142862 | ||||||||
\(169\) | −12.9986 | −0.999892 | ||||||||
\(170\) | 1.02960 | 0.0789663 | ||||||||
\(171\) | 18.5824 | 1.42103 | ||||||||
\(172\) | −6.07292 | −0.463055 | ||||||||
\(173\) | 13.3119 | 1.01208 | 0.506042 | − | 0.862509i | \(-0.331108\pi\) | ||||
0.506042 | + | 0.862509i | \(0.331108\pi\) | |||||||
\(174\) | −6.72104 | −0.509521 | ||||||||
\(175\) | 2.65990 | 0.201070 | ||||||||
\(176\) | −2.85414 | −0.215139 | ||||||||
\(177\) | −7.22757 | −0.543257 | ||||||||
\(178\) | 5.63871 | 0.422639 | ||||||||
\(179\) | 11.0871 | 0.828688 | 0.414344 | − | 0.910120i | \(-0.364011\pi\) | ||||
0.414344 | + | 0.910120i | \(0.364011\pi\) | |||||||
\(180\) | −2.51537 | −0.187485 | ||||||||
\(181\) | −8.93318 | −0.663998 | −0.331999 | − | 0.943280i | \(-0.607723\pi\) | ||||
−0.331999 | + | 0.943280i | \(0.607723\pi\) | |||||||
\(182\) | −0.0997598 | −0.00739469 | ||||||||
\(183\) | −10.1332 | −0.749070 | ||||||||
\(184\) | 1.48829 | 0.109718 | ||||||||
\(185\) | −1.90641 | −0.140162 | ||||||||
\(186\) | −2.98013 | −0.218514 | ||||||||
\(187\) | 2.93861 | 0.214892 | ||||||||
\(188\) | −3.89157 | −0.283822 | ||||||||
\(189\) | −10.2128 | −0.742874 | ||||||||
\(190\) | 7.38755 | 0.535949 | ||||||||
\(191\) | 6.21680 | 0.449832 | 0.224916 | − | 0.974378i | \(-0.427789\pi\) | ||||
0.224916 | + | 0.974378i | \(0.427789\pi\) | |||||||
\(192\) | 0.696154 | 0.0502406 | ||||||||
\(193\) | 20.8831 | 1.50320 | 0.751598 | − | 0.659621i | \(-0.229283\pi\) | ||||
0.751598 | + | 0.659621i | \(0.229283\pi\) | |||||||
\(194\) | −0.00211457 | −0.000151817 0 | ||||||||
\(195\) | 0.0261093 | 0.00186972 | ||||||||
\(196\) | 0.0750867 | 0.00536333 | ||||||||
\(197\) | 6.64050 | 0.473116 | 0.236558 | − | 0.971617i | \(-0.423981\pi\) | ||||
0.236558 | + | 0.971617i | \(0.423981\pi\) | |||||||
\(198\) | −7.17922 | −0.510205 | ||||||||
\(199\) | −13.3555 | −0.946748 | −0.473374 | − | 0.880861i | \(-0.656964\pi\) | ||||
−0.473374 | + | 0.880861i | \(0.656964\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −2.33352 | −0.164594 | ||||||||
\(202\) | 9.15058 | 0.643833 | ||||||||
\(203\) | 25.6801 | 1.80239 | ||||||||
\(204\) | −0.716757 | −0.0501830 | ||||||||
\(205\) | 8.37519 | 0.584948 | ||||||||
\(206\) | 3.39406 | 0.236475 | ||||||||
\(207\) | 3.74361 | 0.260199 | ||||||||
\(208\) | 0.0375050 | 0.00260051 | ||||||||
\(209\) | 21.0851 | 1.45849 | ||||||||
\(210\) | −1.85170 | −0.127780 | ||||||||
\(211\) | −25.4796 | −1.75409 | −0.877045 | − | 0.480408i | \(-0.840489\pi\) | ||||
−0.877045 | + | 0.480408i | \(0.840489\pi\) | |||||||
\(212\) | −9.19937 | −0.631815 | ||||||||
\(213\) | 8.69222 | 0.595581 | ||||||||
\(214\) | 17.1126 | 1.16980 | ||||||||
\(215\) | −6.07292 | −0.414169 | ||||||||
\(216\) | 3.83955 | 0.261248 | ||||||||
\(217\) | 11.3866 | 0.772976 | ||||||||
\(218\) | −6.07832 | −0.411676 | ||||||||
\(219\) | 4.68177 | 0.316365 | ||||||||
\(220\) | −2.85414 | −0.192426 | ||||||||
\(221\) | −0.0386150 | −0.00259753 | ||||||||
\(222\) | 1.32716 | 0.0890728 | ||||||||
\(223\) | 17.6475 | 1.18177 | 0.590883 | − | 0.806757i | \(-0.298780\pi\) | ||||
0.590883 | + | 0.806757i | \(0.298780\pi\) | |||||||
\(224\) | −2.65990 | −0.177722 | ||||||||
\(225\) | −2.51537 | −0.167691 | ||||||||
\(226\) | −8.57048 | −0.570100 | ||||||||
\(227\) | 17.6554 | 1.17183 | 0.585916 | − | 0.810372i | \(-0.300735\pi\) | ||||
0.585916 | + | 0.810372i | \(0.300735\pi\) | |||||||
\(228\) | −5.14287 | −0.340595 | ||||||||
\(229\) | −17.2580 | −1.14044 | −0.570219 | − | 0.821493i | \(-0.693142\pi\) | ||||
−0.570219 | + | 0.821493i | \(0.693142\pi\) | |||||||
\(230\) | 1.48829 | 0.0981352 | ||||||||
\(231\) | −5.28502 | −0.347729 | ||||||||
\(232\) | −9.65453 | −0.633851 | ||||||||
\(233\) | −17.3621 | −1.13743 | −0.568715 | − | 0.822535i | \(-0.692559\pi\) | ||||
−0.568715 | + | 0.822535i | \(0.692559\pi\) | |||||||
\(234\) | 0.0943390 | 0.00616713 | ||||||||
\(235\) | −3.89157 | −0.253858 | ||||||||
\(236\) | −10.3821 | −0.675820 | ||||||||
\(237\) | −4.64532 | −0.301746 | ||||||||
\(238\) | 2.73862 | 0.177519 | ||||||||
\(239\) | 12.6335 | 0.817193 | 0.408596 | − | 0.912715i | \(-0.366018\pi\) | ||||
0.408596 | + | 0.912715i | \(0.366018\pi\) | |||||||
\(240\) | 0.696154 | 0.0449366 | ||||||||
\(241\) | −5.73290 | −0.369288 | −0.184644 | − | 0.982805i | \(-0.559113\pi\) | ||||
−0.184644 | + | 0.982805i | \(0.559113\pi\) | |||||||
\(242\) | 2.85389 | 0.183455 | ||||||||
\(243\) | 14.9111 | 0.956550 | ||||||||
\(244\) | −14.5560 | −0.931854 | ||||||||
\(245\) | 0.0750867 | 0.00479711 | ||||||||
\(246\) | −5.83042 | −0.371734 | ||||||||
\(247\) | −0.277070 | −0.0176296 | ||||||||
\(248\) | −4.28085 | −0.271834 | ||||||||
\(249\) | −5.48889 | −0.347844 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 21.4087 | 1.35130 | 0.675652 | − | 0.737220i | \(-0.263862\pi\) | ||||
0.675652 | + | 0.737220i | \(0.263862\pi\) | |||||||
\(252\) | −6.69064 | −0.421471 | ||||||||
\(253\) | 4.24780 | 0.267057 | ||||||||
\(254\) | 4.07183 | 0.255490 | ||||||||
\(255\) | −0.716757 | −0.0448851 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.1176 | 1.25490 | 0.627449 | − | 0.778658i | \(-0.284099\pi\) | ||||
0.627449 | + | 0.778658i | \(0.284099\pi\) | |||||||
\(258\) | 4.22769 | 0.263204 | ||||||||
\(259\) | −5.07087 | −0.315088 | ||||||||
\(260\) | 0.0375050 | 0.00232596 | ||||||||
\(261\) | −24.2847 | −1.50319 | ||||||||
\(262\) | −1.30068 | −0.0803564 | ||||||||
\(263\) | −27.0762 | −1.66959 | −0.834795 | − | 0.550561i | \(-0.814414\pi\) | ||||
−0.834795 | + | 0.550561i | \(0.814414\pi\) | |||||||
\(264\) | 1.98692 | 0.122287 | ||||||||
\(265\) | −9.19937 | −0.565113 | ||||||||
\(266\) | 19.6502 | 1.20483 | ||||||||
\(267\) | −3.92541 | −0.240231 | ||||||||
\(268\) | −3.35202 | −0.204757 | ||||||||
\(269\) | −3.84789 | −0.234610 | −0.117305 | − | 0.993096i | \(-0.537425\pi\) | ||||
−0.117305 | + | 0.993096i | \(0.537425\pi\) | |||||||
\(270\) | 3.83955 | 0.233667 | ||||||||
\(271\) | 0.630614 | 0.0383071 | 0.0191535 | − | 0.999817i | \(-0.493903\pi\) | ||||
0.0191535 | + | 0.999817i | \(0.493903\pi\) | |||||||
\(272\) | −1.02960 | −0.0624284 | ||||||||
\(273\) | 0.0694482 | 0.00420319 | ||||||||
\(274\) | −17.9925 | −1.08697 | ||||||||
\(275\) | −2.85414 | −0.172111 | ||||||||
\(276\) | −1.03608 | −0.0623648 | ||||||||
\(277\) | 18.0685 | 1.08563 | 0.542816 | − | 0.839852i | \(-0.317358\pi\) | ||||
0.542816 | + | 0.839852i | \(0.317358\pi\) | |||||||
\(278\) | −4.30048 | −0.257926 | ||||||||
\(279\) | −10.7679 | −0.644658 | ||||||||
\(280\) | −2.65990 | −0.158960 | ||||||||
\(281\) | −16.3568 | −0.975766 | −0.487883 | − | 0.872909i | \(-0.662231\pi\) | ||||
−0.487883 | + | 0.872909i | \(0.662231\pi\) | |||||||
\(282\) | 2.70913 | 0.161326 | ||||||||
\(283\) | −1.20167 | −0.0714321 | −0.0357160 | − | 0.999362i | \(-0.511371\pi\) | ||||
−0.0357160 | + | 0.999362i | \(0.511371\pi\) | |||||||
\(284\) | 12.4861 | 0.740911 | ||||||||
\(285\) | −5.14287 | −0.304638 | ||||||||
\(286\) | 0.107045 | 0.00632968 | ||||||||
\(287\) | 22.2772 | 1.31498 | ||||||||
\(288\) | 2.51537 | 0.148220 | ||||||||
\(289\) | −15.9399 | −0.937643 | ||||||||
\(290\) | −9.65453 | −0.566934 | ||||||||
\(291\) | 0.00147207 | 8.62941e−5 0 | ||||||||
\(292\) | 6.72519 | 0.393562 | ||||||||
\(293\) | −17.6326 | −1.03011 | −0.515054 | − | 0.857158i | \(-0.672228\pi\) | ||||
−0.515054 | + | 0.857158i | \(0.672228\pi\) | |||||||
\(294\) | −0.0522719 | −0.00304856 | ||||||||
\(295\) | −10.3821 | −0.604471 | ||||||||
\(296\) | 1.90641 | 0.110808 | ||||||||
\(297\) | 10.9586 | 0.635883 | ||||||||
\(298\) | 11.2429 | 0.651286 | ||||||||
\(299\) | −0.0558185 | −0.00322807 | ||||||||
\(300\) | 0.696154 | 0.0401925 | ||||||||
\(301\) | −16.1534 | −0.931065 | ||||||||
\(302\) | 18.0929 | 1.04113 | ||||||||
\(303\) | −6.37021 | −0.365959 | ||||||||
\(304\) | −7.38755 | −0.423705 | ||||||||
\(305\) | −14.5560 | −0.833475 | ||||||||
\(306\) | −2.58981 | −0.148050 | ||||||||
\(307\) | 29.5550 | 1.68679 | 0.843397 | − | 0.537291i | \(-0.180552\pi\) | ||||
0.843397 | + | 0.537291i | \(0.180552\pi\) | |||||||
\(308\) | −7.59174 | −0.432579 | ||||||||
\(309\) | −2.36279 | −0.134414 | ||||||||
\(310\) | −4.28085 | −0.243136 | ||||||||
\(311\) | 13.4662 | 0.763597 | 0.381799 | − | 0.924246i | \(-0.375305\pi\) | ||||
0.381799 | + | 0.924246i | \(0.375305\pi\) | |||||||
\(312\) | −0.0261093 | −0.00147815 | ||||||||
\(313\) | 18.4655 | 1.04373 | 0.521865 | − | 0.853028i | \(-0.325236\pi\) | ||||
0.521865 | + | 0.853028i | \(0.325236\pi\) | |||||||
\(314\) | 22.1158 | 1.24807 | ||||||||
\(315\) | −6.69064 | −0.376975 | ||||||||
\(316\) | −6.67283 | −0.375376 | ||||||||
\(317\) | 0.377432 | 0.0211987 | 0.0105993 | − | 0.999944i | \(-0.496626\pi\) | ||||
0.0105993 | + | 0.999944i | \(0.496626\pi\) | |||||||
\(318\) | 6.40418 | 0.359129 | ||||||||
\(319\) | −27.5554 | −1.54281 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −11.9130 | −0.664921 | ||||||||
\(322\) | 3.95872 | 0.220611 | ||||||||
\(323\) | 7.60619 | 0.423220 | ||||||||
\(324\) | 4.87319 | 0.270733 | ||||||||
\(325\) | 0.0375050 | 0.00208041 | ||||||||
\(326\) | 18.2881 | 1.01288 | ||||||||
\(327\) | 4.23145 | 0.234000 | ||||||||
\(328\) | −8.37519 | −0.462442 | ||||||||
\(329\) | −10.3512 | −0.570680 | ||||||||
\(330\) | 1.98692 | 0.109376 | ||||||||
\(331\) | 9.69431 | 0.532848 | 0.266424 | − | 0.963856i | \(-0.414158\pi\) | ||||
0.266424 | + | 0.963856i | \(0.414158\pi\) | |||||||
\(332\) | −7.88459 | −0.432723 | ||||||||
\(333\) | 4.79533 | 0.262782 | ||||||||
\(334\) | −17.8347 | −0.975869 | ||||||||
\(335\) | −3.35202 | −0.183141 | ||||||||
\(336\) | 1.85170 | 0.101019 | ||||||||
\(337\) | 9.62228 | 0.524159 | 0.262079 | − | 0.965046i | \(-0.415592\pi\) | ||||
0.262079 | + | 0.965046i | \(0.415592\pi\) | |||||||
\(338\) | 12.9986 | 0.707030 | ||||||||
\(339\) | 5.96638 | 0.324049 | ||||||||
\(340\) | −1.02960 | −0.0558376 | ||||||||
\(341\) | −12.2181 | −0.661649 | ||||||||
\(342\) | −18.5824 | −1.00482 | ||||||||
\(343\) | −18.4196 | −0.994565 | ||||||||
\(344\) | 6.07292 | 0.327430 | ||||||||
\(345\) | −1.03608 | −0.0557808 | ||||||||
\(346\) | −13.3119 | −0.715651 | ||||||||
\(347\) | −34.3809 | −1.84566 | −0.922831 | − | 0.385204i | \(-0.874131\pi\) | ||||
−0.922831 | + | 0.385204i | \(0.874131\pi\) | |||||||
\(348\) | 6.72104 | 0.360286 | ||||||||
\(349\) | −26.4606 | −1.41641 | −0.708203 | − | 0.706009i | \(-0.750494\pi\) | ||||
−0.708203 | + | 0.706009i | \(0.750494\pi\) | |||||||
\(350\) | −2.65990 | −0.142178 | ||||||||
\(351\) | −0.144002 | −0.00768628 | ||||||||
\(352\) | 2.85414 | 0.152126 | ||||||||
\(353\) | −22.8742 | −1.21747 | −0.608734 | − | 0.793374i | \(-0.708323\pi\) | ||||
−0.608734 | + | 0.793374i | \(0.708323\pi\) | |||||||
\(354\) | 7.22757 | 0.384141 | ||||||||
\(355\) | 12.4861 | 0.662691 | ||||||||
\(356\) | −5.63871 | −0.298851 | ||||||||
\(357\) | −1.90650 | −0.100903 | ||||||||
\(358\) | −11.0871 | −0.585971 | ||||||||
\(359\) | −12.7326 | −0.672000 | −0.336000 | − | 0.941862i | \(-0.609074\pi\) | ||||
−0.336000 | + | 0.941862i | \(0.609074\pi\) | |||||||
\(360\) | 2.51537 | 0.132572 | ||||||||
\(361\) | 35.5759 | 1.87242 | ||||||||
\(362\) | 8.93318 | 0.469518 | ||||||||
\(363\) | −1.98674 | −0.104277 | ||||||||
\(364\) | 0.0997598 | 0.00522883 | ||||||||
\(365\) | 6.72519 | 0.352013 | ||||||||
\(366\) | 10.1332 | 0.529673 | ||||||||
\(367\) | 6.86945 | 0.358582 | 0.179291 | − | 0.983796i | \(-0.442620\pi\) | ||||
0.179291 | + | 0.983796i | \(0.442620\pi\) | |||||||
\(368\) | −1.48829 | −0.0775827 | ||||||||
\(369\) | −21.0667 | −1.09669 | ||||||||
\(370\) | 1.90641 | 0.0991095 | ||||||||
\(371\) | −24.4694 | −1.27039 | ||||||||
\(372\) | 2.98013 | 0.154513 | ||||||||
\(373\) | 29.5706 | 1.53111 | 0.765554 | − | 0.643372i | \(-0.222465\pi\) | ||||
0.765554 | + | 0.643372i | \(0.222465\pi\) | |||||||
\(374\) | −2.93861 | −0.151952 | ||||||||
\(375\) | 0.696154 | 0.0359492 | ||||||||
\(376\) | 3.89157 | 0.200692 | ||||||||
\(377\) | 0.362094 | 0.0186488 | ||||||||
\(378\) | 10.2128 | 0.525291 | ||||||||
\(379\) | 26.8611 | 1.37976 | 0.689881 | − | 0.723922i | \(-0.257663\pi\) | ||||
0.689881 | + | 0.723922i | \(0.257663\pi\) | |||||||
\(380\) | −7.38755 | −0.378973 | ||||||||
\(381\) | −2.83462 | −0.145222 | ||||||||
\(382\) | −6.21680 | −0.318079 | ||||||||
\(383\) | −15.9093 | −0.812925 | −0.406463 | − | 0.913667i | \(-0.633238\pi\) | ||||
−0.406463 | + | 0.913667i | \(0.633238\pi\) | |||||||
\(384\) | −0.696154 | −0.0355255 | ||||||||
\(385\) | −7.59174 | −0.386911 | ||||||||
\(386\) | −20.8831 | −1.06292 | ||||||||
\(387\) | 15.2756 | 0.776504 | ||||||||
\(388\) | 0.00211457 | 0.000107351 0 | ||||||||
\(389\) | −21.0610 | −1.06783 | −0.533916 | − | 0.845537i | \(-0.679280\pi\) | ||||
−0.533916 | + | 0.845537i | \(0.679280\pi\) | |||||||
\(390\) | −0.0261093 | −0.00132210 | ||||||||
\(391\) | 1.53234 | 0.0774938 | ||||||||
\(392\) | −0.0750867 | −0.00379245 | ||||||||
\(393\) | 0.905475 | 0.0456752 | ||||||||
\(394\) | −6.64050 | −0.334543 | ||||||||
\(395\) | −6.67283 | −0.335746 | ||||||||
\(396\) | 7.17922 | 0.360769 | ||||||||
\(397\) | 22.2540 | 1.11690 | 0.558448 | − | 0.829540i | \(-0.311397\pi\) | ||||
0.558448 | + | 0.829540i | \(0.311397\pi\) | |||||||
\(398\) | 13.3555 | 0.669452 | ||||||||
\(399\) | −13.6795 | −0.684834 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 2.33352 | 0.116386 | ||||||||
\(403\) | 0.160553 | 0.00799773 | ||||||||
\(404\) | −9.15058 | −0.455258 | ||||||||
\(405\) | 4.87319 | 0.242151 | ||||||||
\(406\) | −25.6801 | −1.27448 | ||||||||
\(407\) | 5.44116 | 0.269708 | ||||||||
\(408\) | 0.716757 | 0.0354848 | ||||||||
\(409\) | −23.7118 | −1.17247 | −0.586235 | − | 0.810141i | \(-0.699391\pi\) | ||||
−0.586235 | + | 0.810141i | \(0.699391\pi\) | |||||||
\(410\) | −8.37519 | −0.413621 | ||||||||
\(411\) | 12.5256 | 0.617840 | ||||||||
\(412\) | −3.39406 | −0.167213 | ||||||||
\(413\) | −27.6155 | −1.35887 | ||||||||
\(414\) | −3.74361 | −0.183988 | ||||||||
\(415\) | −7.88459 | −0.387040 | ||||||||
\(416\) | −0.0375050 | −0.00183884 | ||||||||
\(417\) | 2.99380 | 0.146607 | ||||||||
\(418\) | −21.0851 | −1.03131 | ||||||||
\(419\) | −33.8273 | −1.65257 | −0.826287 | − | 0.563250i | \(-0.809551\pi\) | ||||
−0.826287 | + | 0.563250i | \(0.809551\pi\) | |||||||
\(420\) | 1.85170 | 0.0903538 | ||||||||
\(421\) | −9.07170 | −0.442127 | −0.221064 | − | 0.975259i | \(-0.570953\pi\) | ||||
−0.221064 | + | 0.975259i | \(0.570953\pi\) | |||||||
\(422\) | 25.4796 | 1.24033 | ||||||||
\(423\) | 9.78873 | 0.475944 | ||||||||
\(424\) | 9.19937 | 0.446761 | ||||||||
\(425\) | −1.02960 | −0.0499427 | ||||||||
\(426\) | −8.69222 | −0.421140 | ||||||||
\(427\) | −38.7176 | −1.87368 | ||||||||
\(428\) | −17.1126 | −0.827171 | ||||||||
\(429\) | −0.0745196 | −0.00359784 | ||||||||
\(430\) | 6.07292 | 0.292862 | ||||||||
\(431\) | 13.1477 | 0.633302 | 0.316651 | − | 0.948542i | \(-0.397442\pi\) | ||||
0.316651 | + | 0.948542i | \(0.397442\pi\) | |||||||
\(432\) | −3.83955 | −0.184730 | ||||||||
\(433\) | 12.6569 | 0.608250 | 0.304125 | − | 0.952632i | \(-0.401636\pi\) | ||||
0.304125 | + | 0.952632i | \(0.401636\pi\) | |||||||
\(434\) | −11.3866 | −0.546576 | ||||||||
\(435\) | 6.72104 | 0.322249 | ||||||||
\(436\) | 6.07832 | 0.291099 | ||||||||
\(437\) | 10.9948 | 0.525955 | ||||||||
\(438\) | −4.68177 | −0.223704 | ||||||||
\(439\) | −22.3147 | −1.06502 | −0.532510 | − | 0.846424i | \(-0.678751\pi\) | ||||
−0.532510 | + | 0.846424i | \(0.678751\pi\) | |||||||
\(440\) | 2.85414 | 0.136066 | ||||||||
\(441\) | −0.188871 | −0.00899384 | ||||||||
\(442\) | 0.0386150 | 0.00183673 | ||||||||
\(443\) | −0.221149 | −0.0105071 | −0.00525356 | − | 0.999986i | \(-0.501672\pi\) | ||||
−0.00525356 | + | 0.999986i | \(0.501672\pi\) | |||||||
\(444\) | −1.32716 | −0.0629840 | ||||||||
\(445\) | −5.63871 | −0.267301 | ||||||||
\(446\) | −17.6475 | −0.835634 | ||||||||
\(447\) | −7.82682 | −0.370196 | ||||||||
\(448\) | 2.65990 | 0.125669 | ||||||||
\(449\) | 41.8242 | 1.97381 | 0.986904 | − | 0.161311i | \(-0.0515721\pi\) | ||||
0.986904 | + | 0.161311i | \(0.0515721\pi\) | |||||||
\(450\) | 2.51537 | 0.118576 | ||||||||
\(451\) | −23.9040 | −1.12559 | ||||||||
\(452\) | 8.57048 | 0.403122 | ||||||||
\(453\) | −12.5954 | −0.591785 | ||||||||
\(454\) | −17.6554 | −0.828611 | ||||||||
\(455\) | 0.0997598 | 0.00467681 | ||||||||
\(456\) | 5.14287 | 0.240837 | ||||||||
\(457\) | −23.0398 | −1.07776 | −0.538879 | − | 0.842383i | \(-0.681152\pi\) | ||||
−0.538879 | + | 0.842383i | \(0.681152\pi\) | |||||||
\(458\) | 17.2580 | 0.806411 | ||||||||
\(459\) | 3.95318 | 0.184519 | ||||||||
\(460\) | −1.48829 | −0.0693921 | ||||||||
\(461\) | 10.3050 | 0.479950 | 0.239975 | − | 0.970779i | \(-0.422861\pi\) | ||||
0.239975 | + | 0.970779i | \(0.422861\pi\) | |||||||
\(462\) | 5.28502 | 0.245881 | ||||||||
\(463\) | −7.58923 | −0.352701 | −0.176351 | − | 0.984327i | \(-0.556429\pi\) | ||||
−0.176351 | + | 0.984327i | \(0.556429\pi\) | |||||||
\(464\) | 9.65453 | 0.448200 | ||||||||
\(465\) | 2.98013 | 0.138200 | ||||||||
\(466\) | 17.3621 | 0.804284 | ||||||||
\(467\) | −14.0631 | −0.650764 | −0.325382 | − | 0.945583i | \(-0.605493\pi\) | ||||
−0.325382 | + | 0.945583i | \(0.605493\pi\) | |||||||
\(468\) | −0.0943390 | −0.00436082 | ||||||||
\(469\) | −8.91606 | −0.411705 | ||||||||
\(470\) | 3.89157 | 0.179505 | ||||||||
\(471\) | −15.3960 | −0.709411 | ||||||||
\(472\) | 10.3821 | 0.477877 | ||||||||
\(473\) | 17.3330 | 0.796970 | ||||||||
\(474\) | 4.64532 | 0.213367 | ||||||||
\(475\) | −7.38755 | −0.338964 | ||||||||
\(476\) | −2.73862 | −0.125525 | ||||||||
\(477\) | 23.1398 | 1.05950 | ||||||||
\(478\) | −12.6335 | −0.577843 | ||||||||
\(479\) | 40.4539 | 1.84839 | 0.924193 | − | 0.381925i | \(-0.124739\pi\) | ||||
0.924193 | + | 0.381925i | \(0.124739\pi\) | |||||||
\(480\) | −0.696154 | −0.0317749 | ||||||||
\(481\) | −0.0715000 | −0.00326012 | ||||||||
\(482\) | 5.73290 | 0.261126 | ||||||||
\(483\) | −2.75588 | −0.125397 | ||||||||
\(484\) | −2.85389 | −0.129722 | ||||||||
\(485\) | 0.00211457 | 9.60177e−5 0 | ||||||||
\(486\) | −14.9111 | −0.676383 | ||||||||
\(487\) | −23.5057 | −1.06514 | −0.532571 | − | 0.846385i | \(-0.678774\pi\) | ||||
−0.532571 | + | 0.846385i | \(0.678774\pi\) | |||||||
\(488\) | 14.5560 | 0.658920 | ||||||||
\(489\) | −12.7313 | −0.575730 | ||||||||
\(490\) | −0.0750867 | −0.00339207 | ||||||||
\(491\) | 29.0932 | 1.31296 | 0.656478 | − | 0.754345i | \(-0.272045\pi\) | ||||
0.656478 | + | 0.754345i | \(0.272045\pi\) | |||||||
\(492\) | 5.83042 | 0.262856 | ||||||||
\(493\) | −9.94026 | −0.447687 | ||||||||
\(494\) | 0.277070 | 0.0124660 | ||||||||
\(495\) | 7.17922 | 0.322682 | ||||||||
\(496\) | 4.28085 | 0.192216 | ||||||||
\(497\) | 33.2117 | 1.48975 | ||||||||
\(498\) | 5.48889 | 0.245963 | ||||||||
\(499\) | 1.02863 | 0.0460480 | 0.0230240 | − | 0.999735i | \(-0.492671\pi\) | ||||
0.0230240 | + | 0.999735i | \(0.492671\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 12.4157 | 0.554691 | ||||||||
\(502\) | −21.4087 | −0.955517 | ||||||||
\(503\) | −17.3276 | −0.772600 | −0.386300 | − | 0.922373i | \(-0.626247\pi\) | ||||
−0.386300 | + | 0.922373i | \(0.626247\pi\) | |||||||
\(504\) | 6.69064 | 0.298025 | ||||||||
\(505\) | −9.15058 | −0.407195 | ||||||||
\(506\) | −4.24780 | −0.188838 | ||||||||
\(507\) | −9.04902 | −0.401881 | ||||||||
\(508\) | −4.07183 | −0.180658 | ||||||||
\(509\) | −36.9550 | −1.63800 | −0.819000 | − | 0.573793i | \(-0.805471\pi\) | ||||
−0.819000 | + | 0.573793i | \(0.805471\pi\) | |||||||
\(510\) | 0.716757 | 0.0317385 | ||||||||
\(511\) | 17.8884 | 0.791335 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 28.3648 | 1.25234 | ||||||||
\(514\) | −20.1176 | −0.887347 | ||||||||
\(515\) | −3.39406 | −0.149560 | ||||||||
\(516\) | −4.22769 | −0.186113 | ||||||||
\(517\) | 11.1071 | 0.488489 | ||||||||
\(518\) | 5.07087 | 0.222801 | ||||||||
\(519\) | 9.26712 | 0.406782 | ||||||||
\(520\) | −0.0375050 | −0.00164470 | ||||||||
\(521\) | 22.6421 | 0.991966 | 0.495983 | − | 0.868332i | \(-0.334808\pi\) | ||||
0.495983 | + | 0.868332i | \(0.334808\pi\) | |||||||
\(522\) | 24.2847 | 1.06291 | ||||||||
\(523\) | 24.0765 | 1.05279 | 0.526397 | − | 0.850239i | \(-0.323543\pi\) | ||||
0.526397 | + | 0.850239i | \(0.323543\pi\) | |||||||
\(524\) | 1.30068 | 0.0568206 | ||||||||
\(525\) | 1.85170 | 0.0808149 | ||||||||
\(526\) | 27.0762 | 1.18058 | ||||||||
\(527\) | −4.40754 | −0.191995 | ||||||||
\(528\) | −1.98692 | −0.0864697 | ||||||||
\(529\) | −20.7850 | −0.903695 | ||||||||
\(530\) | 9.19937 | 0.399595 | ||||||||
\(531\) | 26.1149 | 1.13329 | ||||||||
\(532\) | −19.6502 | −0.851943 | ||||||||
\(533\) | 0.314112 | 0.0136057 | ||||||||
\(534\) | 3.92541 | 0.169869 | ||||||||
\(535\) | −17.1126 | −0.739844 | ||||||||
\(536\) | 3.35202 | 0.144785 | ||||||||
\(537\) | 7.71832 | 0.333070 | ||||||||
\(538\) | 3.84789 | 0.165894 | ||||||||
\(539\) | −0.214308 | −0.00923089 | ||||||||
\(540\) | −3.83955 | −0.165228 | ||||||||
\(541\) | 13.0610 | 0.561537 | 0.280768 | − | 0.959776i | \(-0.409411\pi\) | ||||
0.280768 | + | 0.959776i | \(0.409411\pi\) | |||||||
\(542\) | −0.630614 | −0.0270872 | ||||||||
\(543\) | −6.21887 | −0.266877 | ||||||||
\(544\) | 1.02960 | 0.0441435 | ||||||||
\(545\) | 6.07832 | 0.260367 | ||||||||
\(546\) | −0.0694482 | −0.00297211 | ||||||||
\(547\) | −14.7095 | −0.628933 | −0.314466 | − | 0.949269i | \(-0.601826\pi\) | ||||
−0.314466 | + | 0.949269i | \(0.601826\pi\) | |||||||
\(548\) | 17.9925 | 0.768601 | ||||||||
\(549\) | 36.6138 | 1.56264 | ||||||||
\(550\) | 2.85414 | 0.121701 | ||||||||
\(551\) | −71.3233 | −3.03848 | ||||||||
\(552\) | 1.03608 | 0.0440986 | ||||||||
\(553\) | −17.7491 | −0.754768 | ||||||||
\(554\) | −18.0685 | −0.767658 | ||||||||
\(555\) | −1.32716 | −0.0563346 | ||||||||
\(556\) | 4.30048 | 0.182381 | ||||||||
\(557\) | −0.463082 | −0.0196214 | −0.00981071 | − | 0.999952i | \(-0.503123\pi\) | ||||
−0.00981071 | + | 0.999952i | \(0.503123\pi\) | |||||||
\(558\) | 10.7679 | 0.455842 | ||||||||
\(559\) | −0.227765 | −0.00963343 | ||||||||
\(560\) | 2.65990 | 0.112401 | ||||||||
\(561\) | 2.04572 | 0.0863706 | ||||||||
\(562\) | 16.3568 | 0.689971 | ||||||||
\(563\) | 23.6664 | 0.997422 | 0.498711 | − | 0.866768i | \(-0.333807\pi\) | ||||
0.498711 | + | 0.866768i | \(0.333807\pi\) | |||||||
\(564\) | −2.70913 | −0.114075 | ||||||||
\(565\) | 8.57048 | 0.360563 | ||||||||
\(566\) | 1.20167 | 0.0505101 | ||||||||
\(567\) | 12.9622 | 0.544362 | ||||||||
\(568\) | −12.4861 | −0.523903 | ||||||||
\(569\) | −15.1693 | −0.635931 | −0.317966 | − | 0.948102i | \(-0.603000\pi\) | ||||
−0.317966 | + | 0.948102i | \(0.603000\pi\) | |||||||
\(570\) | 5.14287 | 0.215411 | ||||||||
\(571\) | 27.6020 | 1.15511 | 0.577553 | − | 0.816353i | \(-0.304008\pi\) | ||||
0.577553 | + | 0.816353i | \(0.304008\pi\) | |||||||
\(572\) | −0.107045 | −0.00447576 | ||||||||
\(573\) | 4.32785 | 0.180799 | ||||||||
\(574\) | −22.2772 | −0.929832 | ||||||||
\(575\) | −1.48829 | −0.0620661 | ||||||||
\(576\) | −2.51537 | −0.104807 | ||||||||
\(577\) | 1.39037 | 0.0578820 | 0.0289410 | − | 0.999581i | \(-0.490787\pi\) | ||||
0.0289410 | + | 0.999581i | \(0.490787\pi\) | |||||||
\(578\) | 15.9399 | 0.663014 | ||||||||
\(579\) | 14.5378 | 0.604172 | ||||||||
\(580\) | 9.65453 | 0.400883 | ||||||||
\(581\) | −20.9723 | −0.870076 | ||||||||
\(582\) | −0.00147207 | −6.10191e−5 0 | ||||||||
\(583\) | 26.2563 | 1.08742 | ||||||||
\(584\) | −6.72519 | −0.278291 | ||||||||
\(585\) | −0.0943390 | −0.00390044 | ||||||||
\(586\) | 17.6326 | 0.728396 | ||||||||
\(587\) | −28.6625 | −1.18303 | −0.591514 | − | 0.806294i | \(-0.701470\pi\) | ||||
−0.591514 | + | 0.806294i | \(0.701470\pi\) | |||||||
\(588\) | 0.0522719 | 0.00215566 | ||||||||
\(589\) | −31.6250 | −1.30308 | ||||||||
\(590\) | 10.3821 | 0.427426 | ||||||||
\(591\) | 4.62281 | 0.190157 | ||||||||
\(592\) | −1.90641 | −0.0783530 | ||||||||
\(593\) | −29.1603 | −1.19747 | −0.598735 | − | 0.800947i | \(-0.704330\pi\) | ||||
−0.598735 | + | 0.800947i | \(0.704330\pi\) | |||||||
\(594\) | −10.9586 | −0.449637 | ||||||||
\(595\) | −2.73862 | −0.112273 | ||||||||
\(596\) | −11.2429 | −0.460529 | ||||||||
\(597\) | −9.29751 | −0.380522 | ||||||||
\(598\) | 0.0558185 | 0.00228259 | ||||||||
\(599\) | −31.1199 | −1.27152 | −0.635762 | − | 0.771885i | \(-0.719314\pi\) | ||||
−0.635762 | + | 0.771885i | \(0.719314\pi\) | |||||||
\(600\) | −0.696154 | −0.0284204 | ||||||||
\(601\) | 29.9444 | 1.22146 | 0.610729 | − | 0.791840i | \(-0.290876\pi\) | ||||
0.610729 | + | 0.791840i | \(0.290876\pi\) | |||||||
\(602\) | 16.1534 | 0.658362 | ||||||||
\(603\) | 8.43157 | 0.343360 | ||||||||
\(604\) | −18.0929 | −0.736189 | ||||||||
\(605\) | −2.85389 | −0.116027 | ||||||||
\(606\) | 6.37021 | 0.258772 | ||||||||
\(607\) | 1.87477 | 0.0760944 | 0.0380472 | − | 0.999276i | \(-0.487886\pi\) | ||||
0.0380472 | + | 0.999276i | \(0.487886\pi\) | |||||||
\(608\) | 7.38755 | 0.299605 | ||||||||
\(609\) | 17.8773 | 0.724426 | ||||||||
\(610\) | 14.5560 | 0.589356 | ||||||||
\(611\) | −0.145953 | −0.00590464 | ||||||||
\(612\) | 2.58981 | 0.104687 | ||||||||
\(613\) | −25.8197 | −1.04285 | −0.521425 | − | 0.853297i | \(-0.674599\pi\) | ||||
−0.521425 | + | 0.853297i | \(0.674599\pi\) | |||||||
\(614\) | −29.5550 | −1.19274 | ||||||||
\(615\) | 5.83042 | 0.235105 | ||||||||
\(616\) | 7.59174 | 0.305880 | ||||||||
\(617\) | 35.2336 | 1.41845 | 0.709226 | − | 0.704982i | \(-0.249045\pi\) | ||||
0.709226 | + | 0.704982i | \(0.249045\pi\) | |||||||
\(618\) | 2.36279 | 0.0950453 | ||||||||
\(619\) | −16.0444 | −0.644880 | −0.322440 | − | 0.946590i | \(-0.604503\pi\) | ||||
−0.322440 | + | 0.946590i | \(0.604503\pi\) | |||||||
\(620\) | 4.28085 | 0.171923 | ||||||||
\(621\) | 5.71437 | 0.229310 | ||||||||
\(622\) | −13.4662 | −0.539945 | ||||||||
\(623\) | −14.9984 | −0.600899 | ||||||||
\(624\) | 0.0261093 | 0.00104521 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.4655 | −0.738029 | ||||||||
\(627\) | 14.6785 | 0.586202 | ||||||||
\(628\) | −22.1158 | −0.882517 | ||||||||
\(629\) | 1.96283 | 0.0782632 | ||||||||
\(630\) | 6.69064 | 0.266561 | ||||||||
\(631\) | −4.67025 | −0.185920 | −0.0929599 | − | 0.995670i | \(-0.529633\pi\) | ||||
−0.0929599 | + | 0.995670i | \(0.529633\pi\) | |||||||
\(632\) | 6.67283 | 0.265431 | ||||||||
\(633\) | −17.7378 | −0.705012 | ||||||||
\(634\) | −0.377432 | −0.0149897 | ||||||||
\(635\) | −4.07183 | −0.161586 | ||||||||
\(636\) | −6.40418 | −0.253942 | ||||||||
\(637\) | 0.00281613 | 0.000111579 0 | ||||||||
\(638\) | 27.5554 | 1.09093 | ||||||||
\(639\) | −31.4071 | −1.24244 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −13.1204 | −0.518226 | −0.259113 | − | 0.965847i | \(-0.583430\pi\) | ||||
−0.259113 | + | 0.965847i | \(0.583430\pi\) | |||||||
\(642\) | 11.9130 | 0.470170 | ||||||||
\(643\) | −4.64694 | −0.183257 | −0.0916286 | − | 0.995793i | \(-0.529207\pi\) | ||||
−0.0916286 | + | 0.995793i | \(0.529207\pi\) | |||||||
\(644\) | −3.95872 | −0.155995 | ||||||||
\(645\) | −4.22769 | −0.166465 | ||||||||
\(646\) | −7.60619 | −0.299261 | ||||||||
\(647\) | 42.6147 | 1.67536 | 0.837679 | − | 0.546163i | \(-0.183912\pi\) | ||||
0.837679 | + | 0.546163i | \(0.183912\pi\) | |||||||
\(648\) | −4.87319 | −0.191437 | ||||||||
\(649\) | 29.6321 | 1.16316 | ||||||||
\(650\) | −0.0375050 | −0.00147107 | ||||||||
\(651\) | 7.92686 | 0.310678 | ||||||||
\(652\) | −18.2881 | −0.716216 | ||||||||
\(653\) | 0.246098 | 0.00963054 | 0.00481527 | − | 0.999988i | \(-0.498467\pi\) | ||||
0.00481527 | + | 0.999988i | \(0.498467\pi\) | |||||||
\(654\) | −4.23145 | −0.165463 | ||||||||
\(655\) | 1.30068 | 0.0508219 | ||||||||
\(656\) | 8.37519 | 0.326996 | ||||||||
\(657\) | −16.9163 | −0.659970 | ||||||||
\(658\) | 10.3512 | 0.403532 | ||||||||
\(659\) | 16.4663 | 0.641438 | 0.320719 | − | 0.947174i | \(-0.396076\pi\) | ||||
0.320719 | + | 0.947174i | \(0.396076\pi\) | |||||||
\(660\) | −1.98692 | −0.0773408 | ||||||||
\(661\) | 46.2706 | 1.79972 | 0.899859 | − | 0.436182i | \(-0.143670\pi\) | ||||
0.899859 | + | 0.436182i | \(0.143670\pi\) | |||||||
\(662\) | −9.69431 | −0.376780 | ||||||||
\(663\) | −0.0268820 | −0.00104401 | ||||||||
\(664\) | 7.88459 | 0.305982 | ||||||||
\(665\) | −19.6502 | −0.762001 | ||||||||
\(666\) | −4.79533 | −0.185815 | ||||||||
\(667\) | −14.3688 | −0.556361 | ||||||||
\(668\) | 17.8347 | 0.690044 | ||||||||
\(669\) | 12.2854 | 0.474981 | ||||||||
\(670\) | 3.35202 | 0.129500 | ||||||||
\(671\) | 41.5449 | 1.60382 | ||||||||
\(672\) | −1.85170 | −0.0714310 | ||||||||
\(673\) | 28.1747 | 1.08606 | 0.543028 | − | 0.839715i | \(-0.317278\pi\) | ||||
0.543028 | + | 0.839715i | \(0.317278\pi\) | |||||||
\(674\) | −9.62228 | −0.370636 | ||||||||
\(675\) | −3.83955 | −0.147784 | ||||||||
\(676\) | −12.9986 | −0.499946 | ||||||||
\(677\) | 29.6039 | 1.13777 | 0.568885 | − | 0.822417i | \(-0.307375\pi\) | ||||
0.568885 | + | 0.822417i | \(0.307375\pi\) | |||||||
\(678\) | −5.96638 | −0.229137 | ||||||||
\(679\) | 0.00562455 | 0.000215851 0 | ||||||||
\(680\) | 1.02960 | 0.0394832 | ||||||||
\(681\) | 12.2909 | 0.470988 | ||||||||
\(682\) | 12.2181 | 0.467857 | ||||||||
\(683\) | 10.3329 | 0.395378 | 0.197689 | − | 0.980265i | \(-0.436656\pi\) | ||||
0.197689 | + | 0.980265i | \(0.436656\pi\) | |||||||
\(684\) | 18.5824 | 0.710517 | ||||||||
\(685\) | 17.9925 | 0.687458 | ||||||||
\(686\) | 18.4196 | 0.703264 | ||||||||
\(687\) | −12.0142 | −0.458370 | ||||||||
\(688\) | −6.07292 | −0.231528 | ||||||||
\(689\) | −0.345023 | −0.0131443 | ||||||||
\(690\) | 1.03608 | 0.0394430 | ||||||||
\(691\) | −5.72697 | −0.217864 | −0.108932 | − | 0.994049i | \(-0.534743\pi\) | ||||
−0.108932 | + | 0.994049i | \(0.534743\pi\) | |||||||
\(692\) | 13.3119 | 0.506042 | ||||||||
\(693\) | 19.0960 | 0.725398 | ||||||||
\(694\) | 34.3809 | 1.30508 | ||||||||
\(695\) | 4.30048 | 0.163127 | ||||||||
\(696\) | −6.72104 | −0.254760 | ||||||||
\(697\) | −8.62305 | −0.326621 | ||||||||
\(698\) | 26.4606 | 1.00155 | ||||||||
\(699\) | −12.0867 | −0.457161 | ||||||||
\(700\) | 2.65990 | 0.100535 | ||||||||
\(701\) | 44.3202 | 1.67395 | 0.836976 | − | 0.547239i | \(-0.184321\pi\) | ||||
0.836976 | + | 0.547239i | \(0.184321\pi\) | |||||||
\(702\) | 0.144002 | 0.00543502 | ||||||||
\(703\) | 14.0837 | 0.531177 | ||||||||
\(704\) | −2.85414 | −0.107569 | ||||||||
\(705\) | −2.70913 | −0.102032 | ||||||||
\(706\) | 22.8742 | 0.860881 | ||||||||
\(707\) | −24.3397 | −0.915387 | ||||||||
\(708\) | −7.22757 | −0.271629 | ||||||||
\(709\) | 10.1220 | 0.380139 | 0.190069 | − | 0.981771i | \(-0.439129\pi\) | ||||
0.190069 | + | 0.981771i | \(0.439129\pi\) | |||||||
\(710\) | −12.4861 | −0.468593 | ||||||||
\(711\) | 16.7846 | 0.629473 | ||||||||
\(712\) | 5.63871 | 0.211320 | ||||||||
\(713\) | −6.37116 | −0.238602 | ||||||||
\(714\) | 1.90650 | 0.0713491 | ||||||||
\(715\) | −0.107045 | −0.00400324 | ||||||||
\(716\) | 11.0871 | 0.414344 | ||||||||
\(717\) | 8.79486 | 0.328450 | ||||||||
\(718\) | 12.7326 | 0.475176 | ||||||||
\(719\) | 24.9058 | 0.928828 | 0.464414 | − | 0.885618i | \(-0.346265\pi\) | ||||
0.464414 | + | 0.885618i | \(0.346265\pi\) | |||||||
\(720\) | −2.51537 | −0.0937423 | ||||||||
\(721\) | −9.02788 | −0.336216 | ||||||||
\(722\) | −35.5759 | −1.32400 | ||||||||
\(723\) | −3.99098 | −0.148426 | ||||||||
\(724\) | −8.93318 | −0.331999 | ||||||||
\(725\) | 9.65453 | 0.358560 | ||||||||
\(726\) | 1.98674 | 0.0737350 | ||||||||
\(727\) | −35.9493 | −1.33329 | −0.666643 | − | 0.745377i | \(-0.732270\pi\) | ||||
−0.666643 | + | 0.745377i | \(0.732270\pi\) | |||||||
\(728\) | −0.0997598 | −0.00369734 | ||||||||
\(729\) | −4.23913 | −0.157005 | ||||||||
\(730\) | −6.72519 | −0.248911 | ||||||||
\(731\) | 6.25264 | 0.231262 | ||||||||
\(732\) | −10.1332 | −0.374535 | ||||||||
\(733\) | −6.50206 | −0.240159 | −0.120080 | − | 0.992764i | \(-0.538315\pi\) | ||||
−0.120080 | + | 0.992764i | \(0.538315\pi\) | |||||||
\(734\) | −6.86945 | −0.253556 | ||||||||
\(735\) | 0.0522719 | 0.00192808 | ||||||||
\(736\) | 1.48829 | 0.0548592 | ||||||||
\(737\) | 9.56714 | 0.352410 | ||||||||
\(738\) | 21.0667 | 0.775476 | ||||||||
\(739\) | −3.62083 | −0.133194 | −0.0665971 | − | 0.997780i | \(-0.521214\pi\) | ||||
−0.0665971 | + | 0.997780i | \(0.521214\pi\) | |||||||
\(740\) | −1.90641 | −0.0700810 | ||||||||
\(741\) | −0.192884 | −0.00708576 | ||||||||
\(742\) | 24.4694 | 0.898301 | ||||||||
\(743\) | −50.0811 | −1.83730 | −0.918649 | − | 0.395076i | \(-0.870718\pi\) | ||||
−0.918649 | + | 0.395076i | \(0.870718\pi\) | |||||||
\(744\) | −2.98013 | −0.109257 | ||||||||
\(745\) | −11.2429 | −0.411910 | ||||||||
\(746\) | −29.5706 | −1.08266 | ||||||||
\(747\) | 19.8327 | 0.725639 | ||||||||
\(748\) | 2.93861 | 0.107446 | ||||||||
\(749\) | −45.5180 | −1.66319 | ||||||||
\(750\) | −0.696154 | −0.0254200 | ||||||||
\(751\) | 1.63536 | 0.0596753 | 0.0298376 | − | 0.999555i | \(-0.490501\pi\) | ||||
0.0298376 | + | 0.999555i | \(0.490501\pi\) | |||||||
\(752\) | −3.89157 | −0.141911 | ||||||||
\(753\) | 14.9037 | 0.543123 | ||||||||
\(754\) | −0.362094 | −0.0131867 | ||||||||
\(755\) | −18.0929 | −0.658468 | ||||||||
\(756\) | −10.2128 | −0.371437 | ||||||||
\(757\) | 8.12371 | 0.295261 | 0.147631 | − | 0.989043i | \(-0.452835\pi\) | ||||
0.147631 | + | 0.989043i | \(0.452835\pi\) | |||||||
\(758\) | −26.8611 | −0.975640 | ||||||||
\(759\) | 2.95712 | 0.107337 | ||||||||
\(760\) | 7.38755 | 0.267975 | ||||||||
\(761\) | 44.7571 | 1.62244 | 0.811222 | − | 0.584739i | \(-0.198803\pi\) | ||||
0.811222 | + | 0.584739i | \(0.198803\pi\) | |||||||
\(762\) | 2.83462 | 0.102688 | ||||||||
\(763\) | 16.1678 | 0.585312 | ||||||||
\(764\) | 6.21680 | 0.224916 | ||||||||
\(765\) | 2.58981 | 0.0936349 | ||||||||
\(766\) | 15.9093 | 0.574825 | ||||||||
\(767\) | −0.389382 | −0.0140598 | ||||||||
\(768\) | 0.696154 | 0.0251203 | ||||||||
\(769\) | −12.7234 | −0.458816 | −0.229408 | − | 0.973330i | \(-0.573679\pi\) | ||||
−0.229408 | + | 0.973330i | \(0.573679\pi\) | |||||||
\(770\) | 7.59174 | 0.273587 | ||||||||
\(771\) | 14.0049 | 0.504375 | ||||||||
\(772\) | 20.8831 | 0.751598 | ||||||||
\(773\) | 14.5070 | 0.521781 | 0.260891 | − | 0.965368i | \(-0.415984\pi\) | ||||
0.260891 | + | 0.965368i | \(0.415984\pi\) | |||||||
\(774\) | −15.2756 | −0.549071 | ||||||||
\(775\) | 4.28085 | 0.153773 | ||||||||
\(776\) | −0.00211457 | −7.59087e−5 0 | ||||||||
\(777\) | −3.53010 | −0.126642 | ||||||||
\(778\) | 21.0610 | 0.755072 | ||||||||
\(779\) | −61.8721 | −2.21680 | ||||||||
\(780\) | 0.0261093 | 0.000934862 0 | ||||||||
\(781\) | −35.6370 | −1.27519 | ||||||||
\(782\) | −1.53234 | −0.0547964 | ||||||||
\(783\) | −37.0690 | −1.32474 | ||||||||
\(784\) | 0.0750867 | 0.00268167 | ||||||||
\(785\) | −22.1158 | −0.789347 | ||||||||
\(786\) | −0.905475 | −0.0322972 | ||||||||
\(787\) | −15.4745 | −0.551605 | −0.275803 | − | 0.961214i | \(-0.588944\pi\) | ||||
−0.275803 | + | 0.961214i | \(0.588944\pi\) | |||||||
\(788\) | 6.64050 | 0.236558 | ||||||||
\(789\) | −18.8492 | −0.671049 | ||||||||
\(790\) | 6.67283 | 0.237409 | ||||||||
\(791\) | 22.7967 | 0.810556 | ||||||||
\(792\) | −7.17922 | −0.255102 | ||||||||
\(793\) | −0.545924 | −0.0193863 | ||||||||
\(794\) | −22.2540 | −0.789764 | ||||||||
\(795\) | −6.40418 | −0.227133 | ||||||||
\(796\) | −13.3555 | −0.473374 | ||||||||
\(797\) | 15.8753 | 0.562331 | 0.281166 | − | 0.959659i | \(-0.409279\pi\) | ||||
0.281166 | + | 0.959659i | \(0.409279\pi\) | |||||||
\(798\) | 13.6795 | 0.484251 | ||||||||
\(799\) | 4.00674 | 0.141748 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 14.1834 | 0.501147 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | −19.1946 | −0.677364 | ||||||||
\(804\) | −2.33352 | −0.0822971 | ||||||||
\(805\) | −3.95872 | −0.139526 | ||||||||
\(806\) | −0.160553 | −0.00565525 | ||||||||
\(807\) | −2.67872 | −0.0942954 | ||||||||
\(808\) | 9.15058 | 0.321916 | ||||||||
\(809\) | 20.3904 | 0.716888 | 0.358444 | − | 0.933551i | \(-0.383307\pi\) | ||||
0.358444 | + | 0.933551i | \(0.383307\pi\) | |||||||
\(810\) | −4.87319 | −0.171227 | ||||||||
\(811\) | −41.4037 | −1.45388 | −0.726941 | − | 0.686700i | \(-0.759059\pi\) | ||||
−0.726941 | + | 0.686700i | \(0.759059\pi\) | |||||||
\(812\) | 25.6801 | 0.901196 | ||||||||
\(813\) | 0.439004 | 0.0153966 | ||||||||
\(814\) | −5.44116 | −0.190713 | ||||||||
\(815\) | −18.2881 | −0.640603 | ||||||||
\(816\) | −0.716757 | −0.0250915 | ||||||||
\(817\) | 44.8640 | 1.56959 | ||||||||
\(818\) | 23.7118 | 0.829062 | ||||||||
\(819\) | −0.250933 | −0.00876830 | ||||||||
\(820\) | 8.37519 | 0.292474 | ||||||||
\(821\) | −22.2301 | −0.775836 | −0.387918 | − | 0.921694i | \(-0.626806\pi\) | ||||
−0.387918 | + | 0.921694i | \(0.626806\pi\) | |||||||
\(822\) | −12.5256 | −0.436879 | ||||||||
\(823\) | −30.5016 | −1.06322 | −0.531610 | − | 0.846989i | \(-0.678413\pi\) | ||||
−0.531610 | + | 0.846989i | \(0.678413\pi\) | |||||||
\(824\) | 3.39406 | 0.118238 | ||||||||
\(825\) | −1.98692 | −0.0691757 | ||||||||
\(826\) | 27.6155 | 0.960866 | ||||||||
\(827\) | 16.2473 | 0.564973 | 0.282487 | − | 0.959271i | \(-0.408841\pi\) | ||||
0.282487 | + | 0.959271i | \(0.408841\pi\) | |||||||
\(828\) | 3.74361 | 0.130099 | ||||||||
\(829\) | −13.2892 | −0.461552 | −0.230776 | − | 0.973007i | \(-0.574127\pi\) | ||||
−0.230776 | + | 0.973007i | \(0.574127\pi\) | |||||||
\(830\) | 7.88459 | 0.273678 | ||||||||
\(831\) | 12.5785 | 0.436342 | ||||||||
\(832\) | 0.0375050 | 0.00130025 | ||||||||
\(833\) | −0.0773089 | −0.00267859 | ||||||||
\(834\) | −2.99380 | −0.103667 | ||||||||
\(835\) | 17.8347 | 0.617194 | ||||||||
\(836\) | 21.0851 | 0.729244 | ||||||||
\(837\) | −16.4365 | −0.568129 | ||||||||
\(838\) | 33.8273 | 1.16855 | ||||||||
\(839\) | −36.4776 | −1.25935 | −0.629673 | − | 0.776860i | \(-0.716811\pi\) | ||||
−0.629673 | + | 0.776860i | \(0.716811\pi\) | |||||||
\(840\) | −1.85170 | −0.0638898 | ||||||||
\(841\) | 64.2100 | 2.21414 | ||||||||
\(842\) | 9.07170 | 0.312631 | ||||||||
\(843\) | −11.3869 | −0.392185 | ||||||||
\(844\) | −25.4796 | −0.877045 | ||||||||
\(845\) | −12.9986 | −0.447165 | ||||||||
\(846\) | −9.78873 | −0.336544 | ||||||||
\(847\) | −7.59106 | −0.260832 | ||||||||
\(848\) | −9.19937 | −0.315908 | ||||||||
\(849\) | −0.836550 | −0.0287103 | ||||||||
\(850\) | 1.02960 | 0.0353148 | ||||||||
\(851\) | 2.83730 | 0.0972613 | ||||||||
\(852\) | 8.69222 | 0.297791 | ||||||||
\(853\) | −52.3016 | −1.79077 | −0.895386 | − | 0.445290i | \(-0.853101\pi\) | ||||
−0.895386 | + | 0.445290i | \(0.853101\pi\) | |||||||
\(854\) | 38.7176 | 1.32489 | ||||||||
\(855\) | 18.5824 | 0.635505 | ||||||||
\(856\) | 17.1126 | 0.584898 | ||||||||
\(857\) | −3.70388 | −0.126522 | −0.0632611 | − | 0.997997i | \(-0.520150\pi\) | ||||
−0.0632611 | + | 0.997997i | \(0.520150\pi\) | |||||||
\(858\) | 0.0745196 | 0.00254406 | ||||||||
\(859\) | −16.4440 | −0.561063 | −0.280532 | − | 0.959845i | \(-0.590511\pi\) | ||||
−0.280532 | + | 0.959845i | \(0.590511\pi\) | |||||||
\(860\) | −6.07292 | −0.207085 | ||||||||
\(861\) | 15.5084 | 0.528523 | ||||||||
\(862\) | −13.1477 | −0.447812 | ||||||||
\(863\) | 46.7402 | 1.59105 | 0.795527 | − | 0.605918i | \(-0.207194\pi\) | ||||
0.795527 | + | 0.605918i | \(0.207194\pi\) | |||||||
\(864\) | 3.83955 | 0.130624 | ||||||||
\(865\) | 13.3119 | 0.452618 | ||||||||
\(866\) | −12.6569 | −0.430098 | ||||||||
\(867\) | −11.0967 | −0.376862 | ||||||||
\(868\) | 11.3866 | 0.386488 | ||||||||
\(869\) | 19.0452 | 0.646064 | ||||||||
\(870\) | −6.72104 | −0.227865 | ||||||||
\(871\) | −0.125718 | −0.00425978 | ||||||||
\(872\) | −6.07832 | −0.205838 | ||||||||
\(873\) | −0.00531893 | −0.000180018 0 | ||||||||
\(874\) | −10.9948 | −0.371906 | ||||||||
\(875\) | 2.65990 | 0.0899212 | ||||||||
\(876\) | 4.68177 | 0.158182 | ||||||||
\(877\) | 46.8547 | 1.58217 | 0.791085 | − | 0.611706i | \(-0.209516\pi\) | ||||
0.791085 | + | 0.611706i | \(0.209516\pi\) | |||||||
\(878\) | 22.3147 | 0.753083 | ||||||||
\(879\) | −12.2750 | −0.414026 | ||||||||
\(880\) | −2.85414 | −0.0962130 | ||||||||
\(881\) | 11.3007 | 0.380731 | 0.190366 | − | 0.981713i | \(-0.439033\pi\) | ||||
0.190366 | + | 0.981713i | \(0.439033\pi\) | |||||||
\(882\) | 0.188871 | 0.00635961 | ||||||||
\(883\) | 37.3318 | 1.25632 | 0.628158 | − | 0.778086i | \(-0.283809\pi\) | ||||
0.628158 | + | 0.778086i | \(0.283809\pi\) | |||||||
\(884\) | −0.0386150 | −0.00129876 | ||||||||
\(885\) | −7.22757 | −0.242952 | ||||||||
\(886\) | 0.221149 | 0.00742966 | ||||||||
\(887\) | 37.1233 | 1.24648 | 0.623239 | − | 0.782031i | \(-0.285816\pi\) | ||||
0.623239 | + | 0.782031i | \(0.285816\pi\) | |||||||
\(888\) | 1.32716 | 0.0445364 | ||||||||
\(889\) | −10.8307 | −0.363250 | ||||||||
\(890\) | 5.63871 | 0.189010 | ||||||||
\(891\) | −13.9088 | −0.465961 | ||||||||
\(892\) | 17.6475 | 0.590883 | ||||||||
\(893\) | 28.7492 | 0.962054 | ||||||||
\(894\) | 7.82682 | 0.261768 | ||||||||
\(895\) | 11.0871 | 0.370601 | ||||||||
\(896\) | −2.65990 | −0.0888611 | ||||||||
\(897\) | −0.0388583 | −0.00129744 | ||||||||
\(898\) | −41.8242 | −1.39569 | ||||||||
\(899\) | 41.3296 | 1.37842 | ||||||||
\(900\) | −2.51537 | −0.0838456 | ||||||||
\(901\) | 9.47163 | 0.315546 | ||||||||
\(902\) | 23.9040 | 0.795915 | ||||||||
\(903\) | −11.2452 | −0.374218 | ||||||||
\(904\) | −8.57048 | −0.285050 | ||||||||
\(905\) | −8.93318 | −0.296949 | ||||||||
\(906\) | 12.5954 | 0.418455 | ||||||||
\(907\) | −37.0817 | −1.23128 | −0.615639 | − | 0.788029i | \(-0.711102\pi\) | ||||
−0.615639 | + | 0.788029i | \(0.711102\pi\) | |||||||
\(908\) | 17.6554 | 0.585916 | ||||||||
\(909\) | 23.0171 | 0.763429 | ||||||||
\(910\) | −0.0997598 | −0.00330700 | ||||||||
\(911\) | −28.3851 | −0.940440 | −0.470220 | − | 0.882549i | \(-0.655825\pi\) | ||||
−0.470220 | + | 0.882549i | \(0.655825\pi\) | |||||||
\(912\) | −5.14287 | −0.170298 | ||||||||
\(913\) | 22.5037 | 0.744765 | ||||||||
\(914\) | 23.0398 | 0.762090 | ||||||||
\(915\) | −10.1332 | −0.334994 | ||||||||
\(916\) | −17.2580 | −0.570219 | ||||||||
\(917\) | 3.45969 | 0.114249 | ||||||||
\(918\) | −3.95318 | −0.130474 | ||||||||
\(919\) | 1.81903 | 0.0600043 | 0.0300022 | − | 0.999550i | \(-0.490449\pi\) | ||||
0.0300022 | + | 0.999550i | \(0.490449\pi\) | |||||||
\(920\) | 1.48829 | 0.0490676 | ||||||||
\(921\) | 20.5748 | 0.677964 | ||||||||
\(922\) | −10.3050 | −0.339376 | ||||||||
\(923\) | 0.468290 | 0.0154140 | ||||||||
\(924\) | −5.28502 | −0.173864 | ||||||||
\(925\) | −1.90641 | −0.0626824 | ||||||||
\(926\) | 7.58923 | 0.249397 | ||||||||
\(927\) | 8.53732 | 0.280402 | ||||||||
\(928\) | −9.65453 | −0.316925 | ||||||||
\(929\) | 29.2371 | 0.959238 | 0.479619 | − | 0.877477i | \(-0.340775\pi\) | ||||
0.479619 | + | 0.877477i | \(0.340775\pi\) | |||||||
\(930\) | −2.98013 | −0.0977223 | ||||||||
\(931\) | −0.554707 | −0.0181798 | ||||||||
\(932\) | −17.3621 | −0.568715 | ||||||||
\(933\) | 9.37454 | 0.306909 | ||||||||
\(934\) | 14.0631 | 0.460159 | ||||||||
\(935\) | 2.93861 | 0.0961028 | ||||||||
\(936\) | 0.0943390 | 0.00308357 | ||||||||
\(937\) | 10.5322 | 0.344073 | 0.172036 | − | 0.985091i | \(-0.444965\pi\) | ||||
0.172036 | + | 0.985091i | \(0.444965\pi\) | |||||||
\(938\) | 8.91606 | 0.291120 | ||||||||
\(939\) | 12.8548 | 0.419501 | ||||||||
\(940\) | −3.89157 | −0.126929 | ||||||||
\(941\) | −31.2021 | −1.01716 | −0.508580 | − | 0.861015i | \(-0.669829\pi\) | ||||
−0.508580 | + | 0.861015i | \(0.669829\pi\) | |||||||
\(942\) | 15.3960 | 0.501629 | ||||||||
\(943\) | −12.4647 | −0.405908 | ||||||||
\(944\) | −10.3821 | −0.337910 | ||||||||
\(945\) | −10.2128 | −0.332223 | ||||||||
\(946\) | −17.3330 | −0.563543 | ||||||||
\(947\) | 24.7127 | 0.803053 | 0.401527 | − | 0.915847i | \(-0.368480\pi\) | ||||
0.401527 | + | 0.915847i | \(0.368480\pi\) | |||||||
\(948\) | −4.64532 | −0.150873 | ||||||||
\(949\) | 0.252229 | 0.00818769 | ||||||||
\(950\) | 7.38755 | 0.239684 | ||||||||
\(951\) | 0.262751 | 0.00852027 | ||||||||
\(952\) | 2.73862 | 0.0887593 | ||||||||
\(953\) | −41.9226 | −1.35801 | −0.679003 | − | 0.734136i | \(-0.737588\pi\) | ||||
−0.679003 | + | 0.734136i | \(0.737588\pi\) | |||||||
\(954\) | −23.1398 | −0.749179 | ||||||||
\(955\) | 6.21680 | 0.201171 | ||||||||
\(956\) | 12.6335 | 0.408596 | ||||||||
\(957\) | −19.1828 | −0.620092 | ||||||||
\(958\) | −40.4539 | −1.30701 | ||||||||
\(959\) | 47.8583 | 1.54543 | ||||||||
\(960\) | 0.696154 | 0.0224683 | ||||||||
\(961\) | −12.6743 | −0.408850 | ||||||||
\(962\) | 0.0715000 | 0.00230525 | ||||||||
\(963\) | 43.0446 | 1.38709 | ||||||||
\(964\) | −5.73290 | −0.184644 | ||||||||
\(965\) | 20.8831 | 0.672250 | ||||||||
\(966\) | 2.75588 | 0.0886689 | ||||||||
\(967\) | 5.93617 | 0.190894 | 0.0954472 | − | 0.995434i | \(-0.469572\pi\) | ||||
0.0954472 | + | 0.995434i | \(0.469572\pi\) | |||||||
\(968\) | 2.85389 | 0.0917273 | ||||||||
\(969\) | 5.29508 | 0.170102 | ||||||||
\(970\) | −0.00211457 | −6.78948e−5 0 | ||||||||
\(971\) | −41.4457 | −1.33006 | −0.665029 | − | 0.746818i | \(-0.731581\pi\) | ||||
−0.665029 | + | 0.746818i | \(0.731581\pi\) | |||||||
\(972\) | 14.9111 | 0.478275 | ||||||||
\(973\) | 11.4389 | 0.366713 | ||||||||
\(974\) | 23.5057 | 0.753170 | ||||||||
\(975\) | 0.0261093 | 0.000836166 0 | ||||||||
\(976\) | −14.5560 | −0.465927 | ||||||||
\(977\) | 49.8864 | 1.59601 | 0.798004 | − | 0.602652i | \(-0.205889\pi\) | ||||
0.798004 | + | 0.602652i | \(0.205889\pi\) | |||||||
\(978\) | 12.7313 | 0.407102 | ||||||||
\(979\) | 16.0937 | 0.514356 | ||||||||
\(980\) | 0.0750867 | 0.00239856 | ||||||||
\(981\) | −15.2892 | −0.488147 | ||||||||
\(982\) | −29.0932 | −0.928400 | ||||||||
\(983\) | −44.4265 | −1.41698 | −0.708492 | − | 0.705719i | \(-0.750624\pi\) | ||||
−0.708492 | + | 0.705719i | \(0.750624\pi\) | |||||||
\(984\) | −5.83042 | −0.185867 | ||||||||
\(985\) | 6.64050 | 0.211584 | ||||||||
\(986\) | 9.94026 | 0.316562 | ||||||||
\(987\) | −7.20603 | −0.229370 | ||||||||
\(988\) | −0.277070 | −0.00881478 | ||||||||
\(989\) | 9.03828 | 0.287401 | ||||||||
\(990\) | −7.17922 | −0.228170 | ||||||||
\(991\) | −58.1947 | −1.84862 | −0.924308 | − | 0.381647i | \(-0.875357\pi\) | ||||
−0.924308 | + | 0.381647i | \(0.875357\pi\) | |||||||
\(992\) | −4.28085 | −0.135917 | ||||||||
\(993\) | 6.74873 | 0.214165 | ||||||||
\(994\) | −33.2117 | −1.05341 | ||||||||
\(995\) | −13.3555 | −0.423399 | ||||||||
\(996\) | −5.48889 | −0.173922 | ||||||||
\(997\) | 30.3412 | 0.960914 | 0.480457 | − | 0.877018i | \(-0.340471\pi\) | ||||
0.480457 | + | 0.877018i | \(0.340471\pi\) | |||||||
\(998\) | −1.02863 | −0.0325608 | ||||||||
\(999\) | 7.31975 | 0.231587 |
(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 | 4010.2.a.i.1.8 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.i.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial |