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: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 3 x^{16} - 24 x^{15} + 70 x^{14} + 228 x^{13} - 638 x^{12} - 1075 x^{11} + 2854 x^{10} + \cdots - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(2.15213\) 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 | ||||||||
\(3\) | 2.15213 | 1.24254 | 0.621268 | − | 0.783598i | \(-0.286618\pi\) | ||||
0.621268 | + | 0.783598i | \(0.286618\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −2.15213 | −0.878605 | ||||||||
\(7\) | −4.40972 | −1.66672 | −0.833359 | − | 0.552733i | \(-0.813585\pi\) | ||||
−0.833359 | + | 0.552733i | \(0.813585\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.63168 | 0.543894 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.46745 | 1.04547 | 0.522737 | − | 0.852494i | \(-0.324911\pi\) | ||||
0.522737 | + | 0.852494i | \(0.324911\pi\) | |||||||
\(12\) | 2.15213 | 0.621268 | ||||||||
\(13\) | −2.43182 | −0.674466 | −0.337233 | − | 0.941421i | \(-0.609491\pi\) | ||||
−0.337233 | + | 0.941421i | \(0.609491\pi\) | |||||||
\(14\) | 4.40972 | 1.17855 | ||||||||
\(15\) | −2.15213 | −0.555679 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.79853 | 1.16381 | 0.581907 | − | 0.813255i | \(-0.302307\pi\) | ||||
0.581907 | + | 0.813255i | \(0.302307\pi\) | |||||||
\(18\) | −1.63168 | −0.384591 | ||||||||
\(19\) | −6.67647 | −1.53169 | −0.765844 | − | 0.643026i | \(-0.777679\pi\) | ||||
−0.765844 | + | 0.643026i | \(0.777679\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | −9.49031 | −2.07096 | ||||||||
\(22\) | −3.46745 | −0.739262 | ||||||||
\(23\) | −0.931214 | −0.194172 | −0.0970858 | − | 0.995276i | \(-0.530952\pi\) | ||||
−0.0970858 | + | 0.995276i | \(0.530952\pi\) | |||||||
\(24\) | −2.15213 | −0.439303 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.43182 | 0.476920 | ||||||||
\(27\) | −2.94480 | −0.566727 | ||||||||
\(28\) | −4.40972 | −0.833359 | ||||||||
\(29\) | 6.55653 | 1.21752 | 0.608759 | − | 0.793355i | \(-0.291668\pi\) | ||||
0.608759 | + | 0.793355i | \(0.291668\pi\) | |||||||
\(30\) | 2.15213 | 0.392924 | ||||||||
\(31\) | −4.82923 | −0.867355 | −0.433677 | − | 0.901068i | \(-0.642784\pi\) | ||||
−0.433677 | + | 0.901068i | \(0.642784\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.46241 | 1.29904 | ||||||||
\(34\) | −4.79853 | −0.822941 | ||||||||
\(35\) | 4.40972 | 0.745379 | ||||||||
\(36\) | 1.63168 | 0.271947 | ||||||||
\(37\) | 8.15269 | 1.34029 | 0.670147 | − | 0.742229i | \(-0.266231\pi\) | ||||
0.670147 | + | 0.742229i | \(0.266231\pi\) | |||||||
\(38\) | 6.67647 | 1.08307 | ||||||||
\(39\) | −5.23361 | −0.838048 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −0.0826739 | −0.0129115 | −0.00645575 | − | 0.999979i | \(-0.502055\pi\) | ||||
−0.00645575 | + | 0.999979i | \(0.502055\pi\) | |||||||
\(42\) | 9.49031 | 1.46439 | ||||||||
\(43\) | 1.98104 | 0.302106 | 0.151053 | − | 0.988526i | \(-0.451734\pi\) | ||||
0.151053 | + | 0.988526i | \(0.451734\pi\) | |||||||
\(44\) | 3.46745 | 0.522737 | ||||||||
\(45\) | −1.63168 | −0.243237 | ||||||||
\(46\) | 0.931214 | 0.137300 | ||||||||
\(47\) | 11.6223 | 1.69529 | 0.847646 | − | 0.530562i | \(-0.178019\pi\) | ||||
0.847646 | + | 0.530562i | \(0.178019\pi\) | |||||||
\(48\) | 2.15213 | 0.310634 | ||||||||
\(49\) | 12.4456 | 1.77795 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 10.3271 | 1.44608 | ||||||||
\(52\) | −2.43182 | −0.337233 | ||||||||
\(53\) | −5.51735 | −0.757866 | −0.378933 | − | 0.925424i | \(-0.623709\pi\) | ||||
−0.378933 | + | 0.925424i | \(0.623709\pi\) | |||||||
\(54\) | 2.94480 | 0.400737 | ||||||||
\(55\) | −3.46745 | −0.467550 | ||||||||
\(56\) | 4.40972 | 0.589274 | ||||||||
\(57\) | −14.3687 | −1.90318 | ||||||||
\(58\) | −6.55653 | −0.860915 | ||||||||
\(59\) | 10.7443 | 1.39879 | 0.699393 | − | 0.714737i | \(-0.253454\pi\) | ||||
0.699393 | + | 0.714737i | \(0.253454\pi\) | |||||||
\(60\) | −2.15213 | −0.277839 | ||||||||
\(61\) | −13.5180 | −1.73080 | −0.865401 | − | 0.501080i | \(-0.832936\pi\) | ||||
−0.865401 | + | 0.501080i | \(0.832936\pi\) | |||||||
\(62\) | 4.82923 | 0.613312 | ||||||||
\(63\) | −7.19527 | −0.906518 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.43182 | 0.301630 | ||||||||
\(66\) | −7.46241 | −0.918559 | ||||||||
\(67\) | 11.5935 | 1.41638 | 0.708188 | − | 0.706024i | \(-0.249513\pi\) | ||||
0.708188 | + | 0.706024i | \(0.249513\pi\) | |||||||
\(68\) | 4.79853 | 0.581907 | ||||||||
\(69\) | −2.00410 | −0.241265 | ||||||||
\(70\) | −4.40972 | −0.527062 | ||||||||
\(71\) | 15.4391 | 1.83228 | 0.916142 | − | 0.400855i | \(-0.131287\pi\) | ||||
0.916142 | + | 0.400855i | \(0.131287\pi\) | |||||||
\(72\) | −1.63168 | −0.192296 | ||||||||
\(73\) | 5.98090 | 0.700011 | 0.350005 | − | 0.936748i | \(-0.386180\pi\) | ||||
0.350005 | + | 0.936748i | \(0.386180\pi\) | |||||||
\(74\) | −8.15269 | −0.947731 | ||||||||
\(75\) | 2.15213 | 0.248507 | ||||||||
\(76\) | −6.67647 | −0.765844 | ||||||||
\(77\) | −15.2905 | −1.74251 | ||||||||
\(78\) | 5.23361 | 0.592590 | ||||||||
\(79\) | −10.6192 | −1.19476 | −0.597379 | − | 0.801959i | \(-0.703791\pi\) | ||||
−0.597379 | + | 0.801959i | \(0.703791\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −11.2327 | −1.24807 | ||||||||
\(82\) | 0.0826739 | 0.00912981 | ||||||||
\(83\) | 9.12066 | 1.00112 | 0.500561 | − | 0.865701i | \(-0.333127\pi\) | ||||
0.500561 | + | 0.865701i | \(0.333127\pi\) | |||||||
\(84\) | −9.49031 | −1.03548 | ||||||||
\(85\) | −4.79853 | −0.520474 | ||||||||
\(86\) | −1.98104 | −0.213621 | ||||||||
\(87\) | 14.1105 | 1.51281 | ||||||||
\(88\) | −3.46745 | −0.369631 | ||||||||
\(89\) | −9.01860 | −0.955970 | −0.477985 | − | 0.878368i | \(-0.658633\pi\) | ||||
−0.477985 | + | 0.878368i | \(0.658633\pi\) | |||||||
\(90\) | 1.63168 | 0.171995 | ||||||||
\(91\) | 10.7237 | 1.12414 | ||||||||
\(92\) | −0.931214 | −0.0970858 | ||||||||
\(93\) | −10.3931 | −1.07772 | ||||||||
\(94\) | −11.6223 | −1.19875 | ||||||||
\(95\) | 6.67647 | 0.684992 | ||||||||
\(96\) | −2.15213 | −0.219651 | ||||||||
\(97\) | 7.88077 | 0.800171 | 0.400086 | − | 0.916478i | \(-0.368980\pi\) | ||||
0.400086 | + | 0.916478i | \(0.368980\pi\) | |||||||
\(98\) | −12.4456 | −1.25720 | ||||||||
\(99\) | 5.65777 | 0.568628 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −12.8713 | −1.28074 | −0.640369 | − | 0.768067i | \(-0.721219\pi\) | ||||
−0.640369 | + | 0.768067i | \(0.721219\pi\) | |||||||
\(102\) | −10.3271 | −1.02253 | ||||||||
\(103\) | −7.57098 | −0.745991 | −0.372996 | − | 0.927833i | \(-0.621669\pi\) | ||||
−0.372996 | + | 0.927833i | \(0.621669\pi\) | |||||||
\(104\) | 2.43182 | 0.238460 | ||||||||
\(105\) | 9.49031 | 0.926159 | ||||||||
\(106\) | 5.51735 | 0.535892 | ||||||||
\(107\) | 14.6280 | 1.41414 | 0.707071 | − | 0.707142i | \(-0.250016\pi\) | ||||
0.707071 | + | 0.707142i | \(0.250016\pi\) | |||||||
\(108\) | −2.94480 | −0.283364 | ||||||||
\(109\) | 3.10204 | 0.297122 | 0.148561 | − | 0.988903i | \(-0.452536\pi\) | ||||
0.148561 | + | 0.988903i | \(0.452536\pi\) | |||||||
\(110\) | 3.46745 | 0.330608 | ||||||||
\(111\) | 17.5457 | 1.66536 | ||||||||
\(112\) | −4.40972 | −0.416679 | ||||||||
\(113\) | 18.2558 | 1.71736 | 0.858681 | − | 0.512511i | \(-0.171285\pi\) | ||||
0.858681 | + | 0.512511i | \(0.171285\pi\) | |||||||
\(114\) | 14.3687 | 1.34575 | ||||||||
\(115\) | 0.931214 | 0.0868361 | ||||||||
\(116\) | 6.55653 | 0.608759 | ||||||||
\(117\) | −3.96796 | −0.366838 | ||||||||
\(118\) | −10.7443 | −0.989092 | ||||||||
\(119\) | −21.1602 | −1.93975 | ||||||||
\(120\) | 2.15213 | 0.196462 | ||||||||
\(121\) | 1.02318 | 0.0930160 | ||||||||
\(122\) | 13.5180 | 1.22386 | ||||||||
\(123\) | −0.177925 | −0.0160430 | ||||||||
\(124\) | −4.82923 | −0.433677 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 7.19527 | 0.641005 | ||||||||
\(127\) | 14.0072 | 1.24294 | 0.621471 | − | 0.783437i | \(-0.286535\pi\) | ||||
0.621471 | + | 0.783437i | \(0.286535\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.26347 | 0.375378 | ||||||||
\(130\) | −2.43182 | −0.213285 | ||||||||
\(131\) | −20.3081 | −1.77433 | −0.887165 | − | 0.461451i | \(-0.847329\pi\) | ||||
−0.887165 | + | 0.461451i | \(0.847329\pi\) | |||||||
\(132\) | 7.46241 | 0.649519 | ||||||||
\(133\) | 29.4414 | 2.55289 | ||||||||
\(134\) | −11.5935 | −1.00153 | ||||||||
\(135\) | 2.94480 | 0.253448 | ||||||||
\(136\) | −4.79853 | −0.411471 | ||||||||
\(137\) | 2.07544 | 0.177317 | 0.0886584 | − | 0.996062i | \(-0.471742\pi\) | ||||
0.0886584 | + | 0.996062i | \(0.471742\pi\) | |||||||
\(138\) | 2.00410 | 0.170600 | ||||||||
\(139\) | 6.92751 | 0.587584 | 0.293792 | − | 0.955869i | \(-0.405083\pi\) | ||||
0.293792 | + | 0.955869i | \(0.405083\pi\) | |||||||
\(140\) | 4.40972 | 0.372689 | ||||||||
\(141\) | 25.0128 | 2.10646 | ||||||||
\(142\) | −15.4391 | −1.29562 | ||||||||
\(143\) | −8.43221 | −0.705137 | ||||||||
\(144\) | 1.63168 | 0.135974 | ||||||||
\(145\) | −6.55653 | −0.544490 | ||||||||
\(146\) | −5.98090 | −0.494982 | ||||||||
\(147\) | 26.7847 | 2.20916 | ||||||||
\(148\) | 8.15269 | 0.670147 | ||||||||
\(149\) | 18.5148 | 1.51679 | 0.758396 | − | 0.651794i | \(-0.225983\pi\) | ||||
0.758396 | + | 0.651794i | \(0.225983\pi\) | |||||||
\(150\) | −2.15213 | −0.175721 | ||||||||
\(151\) | 10.2224 | 0.831883 | 0.415942 | − | 0.909391i | \(-0.363452\pi\) | ||||
0.415942 | + | 0.909391i | \(0.363452\pi\) | |||||||
\(152\) | 6.67647 | 0.541534 | ||||||||
\(153\) | 7.82968 | 0.632992 | ||||||||
\(154\) | 15.2905 | 1.23214 | ||||||||
\(155\) | 4.82923 | 0.387893 | ||||||||
\(156\) | −5.23361 | −0.419024 | ||||||||
\(157\) | 2.44008 | 0.194740 | 0.0973698 | − | 0.995248i | \(-0.468957\pi\) | ||||
0.0973698 | + | 0.995248i | \(0.468957\pi\) | |||||||
\(158\) | 10.6192 | 0.844821 | ||||||||
\(159\) | −11.8741 | −0.941675 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 4.10639 | 0.323629 | ||||||||
\(162\) | 11.2327 | 0.882521 | ||||||||
\(163\) | 10.5301 | 0.824784 | 0.412392 | − | 0.911006i | \(-0.364693\pi\) | ||||
0.412392 | + | 0.911006i | \(0.364693\pi\) | |||||||
\(164\) | −0.0826739 | −0.00645575 | ||||||||
\(165\) | −7.46241 | −0.580948 | ||||||||
\(166\) | −9.12066 | −0.707900 | ||||||||
\(167\) | 22.0520 | 1.70644 | 0.853219 | − | 0.521554i | \(-0.174647\pi\) | ||||
0.853219 | + | 0.521554i | \(0.174647\pi\) | |||||||
\(168\) | 9.49031 | 0.732193 | ||||||||
\(169\) | −7.08624 | −0.545095 | ||||||||
\(170\) | 4.79853 | 0.368030 | ||||||||
\(171\) | −10.8939 | −0.833077 | ||||||||
\(172\) | 1.98104 | 0.151053 | ||||||||
\(173\) | −6.99836 | −0.532076 | −0.266038 | − | 0.963963i | \(-0.585715\pi\) | ||||
−0.266038 | + | 0.963963i | \(0.585715\pi\) | |||||||
\(174\) | −14.1105 | −1.06972 | ||||||||
\(175\) | −4.40972 | −0.333343 | ||||||||
\(176\) | 3.46745 | 0.261369 | ||||||||
\(177\) | 23.1232 | 1.73804 | ||||||||
\(178\) | 9.01860 | 0.675973 | ||||||||
\(179\) | 24.9744 | 1.86668 | 0.933338 | − | 0.358999i | \(-0.116882\pi\) | ||||
0.933338 | + | 0.358999i | \(0.116882\pi\) | |||||||
\(180\) | −1.63168 | −0.121619 | ||||||||
\(181\) | −5.63024 | −0.418492 | −0.209246 | − | 0.977863i | \(-0.567101\pi\) | ||||
−0.209246 | + | 0.977863i | \(0.567101\pi\) | |||||||
\(182\) | −10.7237 | −0.794890 | ||||||||
\(183\) | −29.0925 | −2.15058 | ||||||||
\(184\) | 0.931214 | 0.0686500 | ||||||||
\(185\) | −8.15269 | −0.599397 | ||||||||
\(186\) | 10.3931 | 0.762062 | ||||||||
\(187\) | 16.6386 | 1.21674 | ||||||||
\(188\) | 11.6223 | 0.847646 | ||||||||
\(189\) | 12.9857 | 0.944574 | ||||||||
\(190\) | −6.67647 | −0.484362 | ||||||||
\(191\) | −8.02334 | −0.580549 | −0.290274 | − | 0.956943i | \(-0.593747\pi\) | ||||
−0.290274 | + | 0.956943i | \(0.593747\pi\) | |||||||
\(192\) | 2.15213 | 0.155317 | ||||||||
\(193\) | −9.60240 | −0.691196 | −0.345598 | − | 0.938383i | \(-0.612324\pi\) | ||||
−0.345598 | + | 0.938383i | \(0.612324\pi\) | |||||||
\(194\) | −7.88077 | −0.565807 | ||||||||
\(195\) | 5.23361 | 0.374787 | ||||||||
\(196\) | 12.4456 | 0.888973 | ||||||||
\(197\) | 4.73915 | 0.337650 | 0.168825 | − | 0.985646i | \(-0.446003\pi\) | ||||
0.168825 | + | 0.985646i | \(0.446003\pi\) | |||||||
\(198\) | −5.65777 | −0.402080 | ||||||||
\(199\) | 6.77589 | 0.480330 | 0.240165 | − | 0.970732i | \(-0.422798\pi\) | ||||
0.240165 | + | 0.970732i | \(0.422798\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 24.9508 | 1.75990 | ||||||||
\(202\) | 12.8713 | 0.905619 | ||||||||
\(203\) | −28.9125 | −2.02926 | ||||||||
\(204\) | 10.3271 | 0.723040 | ||||||||
\(205\) | 0.0826739 | 0.00577420 | ||||||||
\(206\) | 7.57098 | 0.527495 | ||||||||
\(207\) | −1.51945 | −0.105609 | ||||||||
\(208\) | −2.43182 | −0.168617 | ||||||||
\(209\) | −23.1503 | −1.60134 | ||||||||
\(210\) | −9.49031 | −0.654894 | ||||||||
\(211\) | −4.97267 | −0.342333 | −0.171166 | − | 0.985242i | \(-0.554754\pi\) | ||||
−0.171166 | + | 0.985242i | \(0.554754\pi\) | |||||||
\(212\) | −5.51735 | −0.378933 | ||||||||
\(213\) | 33.2270 | 2.27668 | ||||||||
\(214\) | −14.6280 | −0.999950 | ||||||||
\(215\) | −1.98104 | −0.135106 | ||||||||
\(216\) | 2.94480 | 0.200368 | ||||||||
\(217\) | 21.2955 | 1.44563 | ||||||||
\(218\) | −3.10204 | −0.210097 | ||||||||
\(219\) | 12.8717 | 0.869788 | ||||||||
\(220\) | −3.46745 | −0.233775 | ||||||||
\(221\) | −11.6692 | −0.784954 | ||||||||
\(222\) | −17.5457 | −1.17759 | ||||||||
\(223\) | −16.9371 | −1.13419 | −0.567096 | − | 0.823652i | \(-0.691933\pi\) | ||||
−0.567096 | + | 0.823652i | \(0.691933\pi\) | |||||||
\(224\) | 4.40972 | 0.294637 | ||||||||
\(225\) | 1.63168 | 0.108779 | ||||||||
\(226\) | −18.2558 | −1.21436 | ||||||||
\(227\) | −2.04807 | −0.135935 | −0.0679675 | − | 0.997688i | \(-0.521651\pi\) | ||||
−0.0679675 | + | 0.997688i | \(0.521651\pi\) | |||||||
\(228\) | −14.3687 | −0.951588 | ||||||||
\(229\) | 2.04352 | 0.135040 | 0.0675198 | − | 0.997718i | \(-0.478491\pi\) | ||||
0.0675198 | + | 0.997718i | \(0.478491\pi\) | |||||||
\(230\) | −0.931214 | −0.0614024 | ||||||||
\(231\) | −32.9071 | −2.16513 | ||||||||
\(232\) | −6.55653 | −0.430457 | ||||||||
\(233\) | −18.1255 | −1.18744 | −0.593722 | − | 0.804671i | \(-0.702342\pi\) | ||||
−0.593722 | + | 0.804671i | \(0.702342\pi\) | |||||||
\(234\) | 3.96796 | 0.259394 | ||||||||
\(235\) | −11.6223 | −0.758158 | ||||||||
\(236\) | 10.7443 | 0.699393 | ||||||||
\(237\) | −22.8540 | −1.48453 | ||||||||
\(238\) | 21.1602 | 1.37161 | ||||||||
\(239\) | −18.3347 | −1.18598 | −0.592988 | − | 0.805212i | \(-0.702052\pi\) | ||||
−0.592988 | + | 0.805212i | \(0.702052\pi\) | |||||||
\(240\) | −2.15213 | −0.138920 | ||||||||
\(241\) | 28.9759 | 1.86650 | 0.933252 | − | 0.359222i | \(-0.116958\pi\) | ||||
0.933252 | + | 0.359222i | \(0.116958\pi\) | |||||||
\(242\) | −1.02318 | −0.0657722 | ||||||||
\(243\) | −15.3398 | −0.984048 | ||||||||
\(244\) | −13.5180 | −0.865401 | ||||||||
\(245\) | −12.4456 | −0.795122 | ||||||||
\(246\) | 0.177925 | 0.0113441 | ||||||||
\(247\) | 16.2360 | 1.03307 | ||||||||
\(248\) | 4.82923 | 0.306656 | ||||||||
\(249\) | 19.6289 | 1.24393 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 22.6586 | 1.43020 | 0.715101 | − | 0.699022i | \(-0.246381\pi\) | ||||
0.715101 | + | 0.699022i | \(0.246381\pi\) | |||||||
\(252\) | −7.19527 | −0.453259 | ||||||||
\(253\) | −3.22893 | −0.203001 | ||||||||
\(254\) | −14.0072 | −0.878892 | ||||||||
\(255\) | −10.3271 | −0.646707 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 26.1168 | 1.62912 | 0.814561 | − | 0.580078i | \(-0.196978\pi\) | ||||
0.814561 | + | 0.580078i | \(0.196978\pi\) | |||||||
\(258\) | −4.26347 | −0.265432 | ||||||||
\(259\) | −35.9511 | −2.23389 | ||||||||
\(260\) | 2.43182 | 0.150815 | ||||||||
\(261\) | 10.6982 | 0.662201 | ||||||||
\(262\) | 20.3081 | 1.25464 | ||||||||
\(263\) | 1.18678 | 0.0731799 | 0.0365900 | − | 0.999330i | \(-0.488350\pi\) | ||||
0.0365900 | + | 0.999330i | \(0.488350\pi\) | |||||||
\(264\) | −7.46241 | −0.459280 | ||||||||
\(265\) | 5.51735 | 0.338928 | ||||||||
\(266\) | −29.4414 | −1.80517 | ||||||||
\(267\) | −19.4092 | −1.18783 | ||||||||
\(268\) | 11.5935 | 0.708188 | ||||||||
\(269\) | −2.59446 | −0.158187 | −0.0790935 | − | 0.996867i | \(-0.525203\pi\) | ||||
−0.0790935 | + | 0.996867i | \(0.525203\pi\) | |||||||
\(270\) | −2.94480 | −0.179215 | ||||||||
\(271\) | −19.7248 | −1.19820 | −0.599099 | − | 0.800675i | \(-0.704475\pi\) | ||||
−0.599099 | + | 0.800675i | \(0.704475\pi\) | |||||||
\(272\) | 4.79853 | 0.290954 | ||||||||
\(273\) | 23.0787 | 1.39679 | ||||||||
\(274\) | −2.07544 | −0.125382 | ||||||||
\(275\) | 3.46745 | 0.209095 | ||||||||
\(276\) | −2.00410 | −0.120632 | ||||||||
\(277\) | 24.9859 | 1.50126 | 0.750629 | − | 0.660724i | \(-0.229750\pi\) | ||||
0.750629 | + | 0.660724i | \(0.229750\pi\) | |||||||
\(278\) | −6.92751 | −0.415484 | ||||||||
\(279\) | −7.87977 | −0.471749 | ||||||||
\(280\) | −4.40972 | −0.263531 | ||||||||
\(281\) | 9.29610 | 0.554559 | 0.277279 | − | 0.960789i | \(-0.410567\pi\) | ||||
0.277279 | + | 0.960789i | \(0.410567\pi\) | |||||||
\(282\) | −25.0128 | −1.48949 | ||||||||
\(283\) | 10.8220 | 0.643302 | 0.321651 | − | 0.946858i | \(-0.395762\pi\) | ||||
0.321651 | + | 0.946858i | \(0.395762\pi\) | |||||||
\(284\) | 15.4391 | 0.916142 | ||||||||
\(285\) | 14.3687 | 0.851127 | ||||||||
\(286\) | 8.43221 | 0.498607 | ||||||||
\(287\) | 0.364569 | 0.0215198 | ||||||||
\(288\) | −1.63168 | −0.0961479 | ||||||||
\(289\) | 6.02590 | 0.354464 | ||||||||
\(290\) | 6.55653 | 0.385013 | ||||||||
\(291\) | 16.9605 | 0.994241 | ||||||||
\(292\) | 5.98090 | 0.350005 | ||||||||
\(293\) | −23.2472 | −1.35812 | −0.679058 | − | 0.734085i | \(-0.737612\pi\) | ||||
−0.679058 | + | 0.734085i | \(0.737612\pi\) | |||||||
\(294\) | −26.7847 | −1.56211 | ||||||||
\(295\) | −10.7443 | −0.625557 | ||||||||
\(296\) | −8.15269 | −0.473865 | ||||||||
\(297\) | −10.2109 | −0.592499 | ||||||||
\(298\) | −18.5148 | −1.07253 | ||||||||
\(299\) | 2.26455 | 0.130962 | ||||||||
\(300\) | 2.15213 | 0.124254 | ||||||||
\(301\) | −8.73584 | −0.503526 | ||||||||
\(302\) | −10.2224 | −0.588230 | ||||||||
\(303\) | −27.7007 | −1.59136 | ||||||||
\(304\) | −6.67647 | −0.382922 | ||||||||
\(305\) | 13.5180 | 0.774038 | ||||||||
\(306\) | −7.82968 | −0.447593 | ||||||||
\(307\) | −9.50961 | −0.542742 | −0.271371 | − | 0.962475i | \(-0.587477\pi\) | ||||
−0.271371 | + | 0.962475i | \(0.587477\pi\) | |||||||
\(308\) | −15.2905 | −0.871255 | ||||||||
\(309\) | −16.2938 | −0.926920 | ||||||||
\(310\) | −4.82923 | −0.274282 | ||||||||
\(311\) | 0.632277 | 0.0358531 | 0.0179266 | − | 0.999839i | \(-0.494293\pi\) | ||||
0.0179266 | + | 0.999839i | \(0.494293\pi\) | |||||||
\(312\) | 5.23361 | 0.296295 | ||||||||
\(313\) | −20.3452 | −1.14998 | −0.574990 | − | 0.818160i | \(-0.694994\pi\) | ||||
−0.574990 | + | 0.818160i | \(0.694994\pi\) | |||||||
\(314\) | −2.44008 | −0.137702 | ||||||||
\(315\) | 7.19527 | 0.405407 | ||||||||
\(316\) | −10.6192 | −0.597379 | ||||||||
\(317\) | −35.2623 | −1.98053 | −0.990265 | − | 0.139192i | \(-0.955549\pi\) | ||||
−0.990265 | + | 0.139192i | \(0.955549\pi\) | |||||||
\(318\) | 11.8741 | 0.665865 | ||||||||
\(319\) | 22.7344 | 1.27288 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 31.4814 | 1.75712 | ||||||||
\(322\) | −4.10639 | −0.228840 | ||||||||
\(323\) | −32.0373 | −1.78260 | ||||||||
\(324\) | −11.2327 | −0.624037 | ||||||||
\(325\) | −2.43182 | −0.134893 | ||||||||
\(326\) | −10.5301 | −0.583211 | ||||||||
\(327\) | 6.67601 | 0.369184 | ||||||||
\(328\) | 0.0826739 | 0.00456490 | ||||||||
\(329\) | −51.2513 | −2.82557 | ||||||||
\(330\) | 7.46241 | 0.410792 | ||||||||
\(331\) | 10.6941 | 0.587799 | 0.293899 | − | 0.955836i | \(-0.405047\pi\) | ||||
0.293899 | + | 0.955836i | \(0.405047\pi\) | |||||||
\(332\) | 9.12066 | 0.500561 | ||||||||
\(333\) | 13.3026 | 0.728978 | ||||||||
\(334\) | −22.0520 | −1.20663 | ||||||||
\(335\) | −11.5935 | −0.633422 | ||||||||
\(336\) | −9.49031 | −0.517739 | ||||||||
\(337\) | −24.6450 | −1.34250 | −0.671249 | − | 0.741232i | \(-0.734242\pi\) | ||||
−0.671249 | + | 0.741232i | \(0.734242\pi\) | |||||||
\(338\) | 7.08624 | 0.385441 | ||||||||
\(339\) | 39.2889 | 2.13388 | ||||||||
\(340\) | −4.79853 | −0.260237 | ||||||||
\(341\) | −16.7451 | −0.906797 | ||||||||
\(342\) | 10.8939 | 0.589074 | ||||||||
\(343\) | −24.0137 | −1.29662 | ||||||||
\(344\) | −1.98104 | −0.106811 | ||||||||
\(345\) | 2.00410 | 0.107897 | ||||||||
\(346\) | 6.99836 | 0.376234 | ||||||||
\(347\) | 9.99727 | 0.536682 | 0.268341 | − | 0.963324i | \(-0.413525\pi\) | ||||
0.268341 | + | 0.963324i | \(0.413525\pi\) | |||||||
\(348\) | 14.1105 | 0.756404 | ||||||||
\(349\) | 12.2481 | 0.655627 | 0.327814 | − | 0.944742i | \(-0.393688\pi\) | ||||
0.327814 | + | 0.944742i | \(0.393688\pi\) | |||||||
\(350\) | 4.40972 | 0.235709 | ||||||||
\(351\) | 7.16123 | 0.382238 | ||||||||
\(352\) | −3.46745 | −0.184815 | ||||||||
\(353\) | −4.98404 | −0.265274 | −0.132637 | − | 0.991165i | \(-0.542344\pi\) | ||||
−0.132637 | + | 0.991165i | \(0.542344\pi\) | |||||||
\(354\) | −23.1232 | −1.22898 | ||||||||
\(355\) | −15.4391 | −0.819422 | ||||||||
\(356\) | −9.01860 | −0.477985 | ||||||||
\(357\) | −45.5395 | −2.41021 | ||||||||
\(358\) | −24.9744 | −1.31994 | ||||||||
\(359\) | 32.0394 | 1.69098 | 0.845488 | − | 0.533995i | \(-0.179310\pi\) | ||||
0.845488 | + | 0.533995i | \(0.179310\pi\) | |||||||
\(360\) | 1.63168 | 0.0859973 | ||||||||
\(361\) | 25.5753 | 1.34607 | ||||||||
\(362\) | 5.63024 | 0.295919 | ||||||||
\(363\) | 2.20201 | 0.115576 | ||||||||
\(364\) | 10.7237 | 0.562072 | ||||||||
\(365\) | −5.98090 | −0.313054 | ||||||||
\(366\) | 29.0925 | 1.52069 | ||||||||
\(367\) | 26.6423 | 1.39072 | 0.695359 | − | 0.718662i | \(-0.255245\pi\) | ||||
0.695359 | + | 0.718662i | \(0.255245\pi\) | |||||||
\(368\) | −0.931214 | −0.0485429 | ||||||||
\(369\) | −0.134898 | −0.00702249 | ||||||||
\(370\) | 8.15269 | 0.423838 | ||||||||
\(371\) | 24.3300 | 1.26315 | ||||||||
\(372\) | −10.3931 | −0.538859 | ||||||||
\(373\) | −2.41595 | −0.125093 | −0.0625466 | − | 0.998042i | \(-0.519922\pi\) | ||||
−0.0625466 | + | 0.998042i | \(0.519922\pi\) | |||||||
\(374\) | −16.6386 | −0.860364 | ||||||||
\(375\) | −2.15213 | −0.111136 | ||||||||
\(376\) | −11.6223 | −0.599377 | ||||||||
\(377\) | −15.9443 | −0.821174 | ||||||||
\(378\) | −12.9857 | −0.667915 | ||||||||
\(379\) | −15.0140 | −0.771219 | −0.385610 | − | 0.922662i | \(-0.626009\pi\) | ||||
−0.385610 | + | 0.922662i | \(0.626009\pi\) | |||||||
\(380\) | 6.67647 | 0.342496 | ||||||||
\(381\) | 30.1455 | 1.54440 | ||||||||
\(382\) | 8.02334 | 0.410510 | ||||||||
\(383\) | −3.77917 | −0.193107 | −0.0965533 | − | 0.995328i | \(-0.530782\pi\) | ||||
−0.0965533 | + | 0.995328i | \(0.530782\pi\) | |||||||
\(384\) | −2.15213 | −0.109826 | ||||||||
\(385\) | 15.2905 | 0.779274 | ||||||||
\(386\) | 9.60240 | 0.488749 | ||||||||
\(387\) | 3.23243 | 0.164314 | ||||||||
\(388\) | 7.88077 | 0.400086 | ||||||||
\(389\) | 16.0079 | 0.811632 | 0.405816 | − | 0.913955i | \(-0.366987\pi\) | ||||
0.405816 | + | 0.913955i | \(0.366987\pi\) | |||||||
\(390\) | −5.23361 | −0.265014 | ||||||||
\(391\) | −4.46846 | −0.225980 | ||||||||
\(392\) | −12.4456 | −0.628599 | ||||||||
\(393\) | −43.7059 | −2.20467 | ||||||||
\(394\) | −4.73915 | −0.238755 | ||||||||
\(395\) | 10.6192 | 0.534312 | ||||||||
\(396\) | 5.65777 | 0.284314 | ||||||||
\(397\) | 22.9613 | 1.15240 | 0.576198 | − | 0.817310i | \(-0.304536\pi\) | ||||
0.576198 | + | 0.817310i | \(0.304536\pi\) | |||||||
\(398\) | −6.77589 | −0.339644 | ||||||||
\(399\) | 63.3618 | 3.17206 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | −24.9508 | −1.24443 | ||||||||
\(403\) | 11.7438 | 0.585001 | ||||||||
\(404\) | −12.8713 | −0.640369 | ||||||||
\(405\) | 11.2327 | 0.558155 | ||||||||
\(406\) | 28.9125 | 1.43490 | ||||||||
\(407\) | 28.2690 | 1.40124 | ||||||||
\(408\) | −10.3271 | −0.511267 | ||||||||
\(409\) | −2.56055 | −0.126611 | −0.0633054 | − | 0.997994i | \(-0.520164\pi\) | ||||
−0.0633054 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(410\) | −0.0826739 | −0.00408298 | ||||||||
\(411\) | 4.46663 | 0.220322 | ||||||||
\(412\) | −7.57098 | −0.372996 | ||||||||
\(413\) | −47.3793 | −2.33138 | ||||||||
\(414\) | 1.51945 | 0.0746767 | ||||||||
\(415\) | −9.12066 | −0.447715 | ||||||||
\(416\) | 2.43182 | 0.119230 | ||||||||
\(417\) | 14.9089 | 0.730094 | ||||||||
\(418\) | 23.1503 | 1.13232 | ||||||||
\(419\) | −30.6276 | −1.49626 | −0.748129 | − | 0.663553i | \(-0.769048\pi\) | ||||
−0.748129 | + | 0.663553i | \(0.769048\pi\) | |||||||
\(420\) | 9.49031 | 0.463080 | ||||||||
\(421\) | 37.2917 | 1.81749 | 0.908743 | − | 0.417356i | \(-0.137043\pi\) | ||||
0.908743 | + | 0.417356i | \(0.137043\pi\) | |||||||
\(422\) | 4.97267 | 0.242066 | ||||||||
\(423\) | 18.9640 | 0.922060 | ||||||||
\(424\) | 5.51735 | 0.267946 | ||||||||
\(425\) | 4.79853 | 0.232763 | ||||||||
\(426\) | −33.2270 | −1.60985 | ||||||||
\(427\) | 59.6106 | 2.88476 | ||||||||
\(428\) | 14.6280 | 0.707071 | ||||||||
\(429\) | −18.1473 | −0.876158 | ||||||||
\(430\) | 1.98104 | 0.0955344 | ||||||||
\(431\) | −21.7748 | −1.04885 | −0.524427 | − | 0.851456i | \(-0.675720\pi\) | ||||
−0.524427 | + | 0.851456i | \(0.675720\pi\) | |||||||
\(432\) | −2.94480 | −0.141682 | ||||||||
\(433\) | −27.6818 | −1.33030 | −0.665151 | − | 0.746709i | \(-0.731633\pi\) | ||||
−0.665151 | + | 0.746709i | \(0.731633\pi\) | |||||||
\(434\) | −21.2955 | −1.02222 | ||||||||
\(435\) | −14.1105 | −0.676549 | ||||||||
\(436\) | 3.10204 | 0.148561 | ||||||||
\(437\) | 6.21722 | 0.297410 | ||||||||
\(438\) | −12.8717 | −0.615033 | ||||||||
\(439\) | −4.06381 | −0.193955 | −0.0969776 | − | 0.995287i | \(-0.530918\pi\) | ||||
−0.0969776 | + | 0.995287i | \(0.530918\pi\) | |||||||
\(440\) | 3.46745 | 0.165304 | ||||||||
\(441\) | 20.3073 | 0.967015 | ||||||||
\(442\) | 11.6692 | 0.555046 | ||||||||
\(443\) | −5.79090 | −0.275134 | −0.137567 | − | 0.990492i | \(-0.543928\pi\) | ||||
−0.137567 | + | 0.990492i | \(0.543928\pi\) | |||||||
\(444\) | 17.5457 | 0.832681 | ||||||||
\(445\) | 9.01860 | 0.427523 | ||||||||
\(446\) | 16.9371 | 0.801995 | ||||||||
\(447\) | 39.8463 | 1.88467 | ||||||||
\(448\) | −4.40972 | −0.208340 | ||||||||
\(449\) | 11.5422 | 0.544708 | 0.272354 | − | 0.962197i | \(-0.412198\pi\) | ||||
0.272354 | + | 0.962197i | \(0.412198\pi\) | |||||||
\(450\) | −1.63168 | −0.0769183 | ||||||||
\(451\) | −0.286667 | −0.0134986 | ||||||||
\(452\) | 18.2558 | 0.858681 | ||||||||
\(453\) | 21.9999 | 1.03364 | ||||||||
\(454\) | 2.04807 | 0.0961205 | ||||||||
\(455\) | −10.7237 | −0.502733 | ||||||||
\(456\) | 14.3687 | 0.672875 | ||||||||
\(457\) | 29.2402 | 1.36780 | 0.683900 | − | 0.729576i | \(-0.260283\pi\) | ||||
0.683900 | + | 0.729576i | \(0.260283\pi\) | |||||||
\(458\) | −2.04352 | −0.0954873 | ||||||||
\(459\) | −14.1307 | −0.659566 | ||||||||
\(460\) | 0.931214 | 0.0434181 | ||||||||
\(461\) | −30.8494 | −1.43680 | −0.718400 | − | 0.695631i | \(-0.755125\pi\) | ||||
−0.718400 | + | 0.695631i | \(0.755125\pi\) | |||||||
\(462\) | 32.9071 | 1.53098 | ||||||||
\(463\) | 28.7096 | 1.33425 | 0.667125 | − | 0.744946i | \(-0.267525\pi\) | ||||
0.667125 | + | 0.744946i | \(0.267525\pi\) | |||||||
\(464\) | 6.55653 | 0.304379 | ||||||||
\(465\) | 10.3931 | 0.481971 | ||||||||
\(466\) | 18.1255 | 0.839649 | ||||||||
\(467\) | −3.13314 | −0.144985 | −0.0724923 | − | 0.997369i | \(-0.523095\pi\) | ||||
−0.0724923 | + | 0.997369i | \(0.523095\pi\) | |||||||
\(468\) | −3.96796 | −0.183419 | ||||||||
\(469\) | −51.1242 | −2.36070 | ||||||||
\(470\) | 11.6223 | 0.536099 | ||||||||
\(471\) | 5.25138 | 0.241971 | ||||||||
\(472\) | −10.7443 | −0.494546 | ||||||||
\(473\) | 6.86916 | 0.315844 | ||||||||
\(474\) | 22.8540 | 1.04972 | ||||||||
\(475\) | −6.67647 | −0.306338 | ||||||||
\(476\) | −21.1602 | −0.969875 | ||||||||
\(477\) | −9.00257 | −0.412199 | ||||||||
\(478\) | 18.3347 | 0.838611 | ||||||||
\(479\) | 28.5029 | 1.30233 | 0.651165 | − | 0.758936i | \(-0.274280\pi\) | ||||
0.651165 | + | 0.758936i | \(0.274280\pi\) | |||||||
\(480\) | 2.15213 | 0.0982311 | ||||||||
\(481\) | −19.8259 | −0.903983 | ||||||||
\(482\) | −28.9759 | −1.31982 | ||||||||
\(483\) | 8.83751 | 0.402121 | ||||||||
\(484\) | 1.02318 | 0.0465080 | ||||||||
\(485\) | −7.88077 | −0.357848 | ||||||||
\(486\) | 15.3398 | 0.695827 | ||||||||
\(487\) | −33.4999 | −1.51803 | −0.759013 | − | 0.651075i | \(-0.774318\pi\) | ||||
−0.759013 | + | 0.651075i | \(0.774318\pi\) | |||||||
\(488\) | 13.5180 | 0.611931 | ||||||||
\(489\) | 22.6623 | 1.02482 | ||||||||
\(490\) | 12.4456 | 0.562236 | ||||||||
\(491\) | −29.8201 | −1.34576 | −0.672881 | − | 0.739751i | \(-0.734943\pi\) | ||||
−0.672881 | + | 0.739751i | \(0.734943\pi\) | |||||||
\(492\) | −0.177925 | −0.00802150 | ||||||||
\(493\) | 31.4617 | 1.41696 | ||||||||
\(494\) | −16.2360 | −0.730492 | ||||||||
\(495\) | −5.65777 | −0.254298 | ||||||||
\(496\) | −4.82923 | −0.216839 | ||||||||
\(497\) | −68.0821 | −3.05390 | ||||||||
\(498\) | −19.6289 | −0.879591 | ||||||||
\(499\) | 31.0553 | 1.39023 | 0.695114 | − | 0.718899i | \(-0.255354\pi\) | ||||
0.695114 | + | 0.718899i | \(0.255354\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 47.4589 | 2.12031 | ||||||||
\(502\) | −22.6586 | −1.01130 | ||||||||
\(503\) | 6.72531 | 0.299867 | 0.149933 | − | 0.988696i | \(-0.452094\pi\) | ||||
0.149933 | + | 0.988696i | \(0.452094\pi\) | |||||||
\(504\) | 7.19527 | 0.320503 | ||||||||
\(505\) | 12.8713 | 0.572764 | ||||||||
\(506\) | 3.22893 | 0.143544 | ||||||||
\(507\) | −15.2505 | −0.677300 | ||||||||
\(508\) | 14.0072 | 0.621471 | ||||||||
\(509\) | −4.87672 | −0.216157 | −0.108078 | − | 0.994142i | \(-0.534470\pi\) | ||||
−0.108078 | + | 0.994142i | \(0.534470\pi\) | |||||||
\(510\) | 10.3271 | 0.457291 | ||||||||
\(511\) | −26.3741 | −1.16672 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 19.6609 | 0.868050 | ||||||||
\(514\) | −26.1168 | −1.15196 | ||||||||
\(515\) | 7.57098 | 0.333617 | ||||||||
\(516\) | 4.26347 | 0.187689 | ||||||||
\(517\) | 40.2998 | 1.77238 | ||||||||
\(518\) | 35.9511 | 1.57960 | ||||||||
\(519\) | −15.0614 | −0.661123 | ||||||||
\(520\) | −2.43182 | −0.106642 | ||||||||
\(521\) | −26.0269 | −1.14026 | −0.570129 | − | 0.821555i | \(-0.693107\pi\) | ||||
−0.570129 | + | 0.821555i | \(0.693107\pi\) | |||||||
\(522\) | −10.6982 | −0.468247 | ||||||||
\(523\) | −3.22399 | −0.140975 | −0.0704877 | − | 0.997513i | \(-0.522456\pi\) | ||||
−0.0704877 | + | 0.997513i | \(0.522456\pi\) | |||||||
\(524\) | −20.3081 | −0.887165 | ||||||||
\(525\) | −9.49031 | −0.414191 | ||||||||
\(526\) | −1.18678 | −0.0517460 | ||||||||
\(527\) | −23.1732 | −1.00944 | ||||||||
\(528\) | 7.46241 | 0.324760 | ||||||||
\(529\) | −22.1328 | −0.962297 | ||||||||
\(530\) | −5.51735 | −0.239658 | ||||||||
\(531\) | 17.5313 | 0.760793 | ||||||||
\(532\) | 29.4414 | 1.27645 | ||||||||
\(533\) | 0.201048 | 0.00870837 | ||||||||
\(534\) | 19.4092 | 0.839920 | ||||||||
\(535\) | −14.6280 | −0.632424 | ||||||||
\(536\) | −11.5935 | −0.500764 | ||||||||
\(537\) | 53.7483 | 2.31941 | ||||||||
\(538\) | 2.59446 | 0.111855 | ||||||||
\(539\) | 43.1545 | 1.85880 | ||||||||
\(540\) | 2.94480 | 0.126724 | ||||||||
\(541\) | −33.9837 | −1.46107 | −0.730537 | − | 0.682873i | \(-0.760730\pi\) | ||||
−0.730537 | + | 0.682873i | \(0.760730\pi\) | |||||||
\(542\) | 19.7248 | 0.847255 | ||||||||
\(543\) | −12.1170 | −0.519992 | ||||||||
\(544\) | −4.79853 | −0.205735 | ||||||||
\(545\) | −3.10204 | −0.132877 | ||||||||
\(546\) | −23.0787 | −0.987679 | ||||||||
\(547\) | −9.62648 | −0.411598 | −0.205799 | − | 0.978594i | \(-0.565979\pi\) | ||||
−0.205799 | + | 0.978594i | \(0.565979\pi\) | |||||||
\(548\) | 2.07544 | 0.0886584 | ||||||||
\(549\) | −22.0571 | −0.941373 | ||||||||
\(550\) | −3.46745 | −0.147852 | ||||||||
\(551\) | −43.7745 | −1.86486 | ||||||||
\(552\) | 2.00410 | 0.0853001 | ||||||||
\(553\) | 46.8279 | 1.99132 | ||||||||
\(554\) | −24.9859 | −1.06155 | ||||||||
\(555\) | −17.5457 | −0.744773 | ||||||||
\(556\) | 6.92751 | 0.293792 | ||||||||
\(557\) | 9.92615 | 0.420585 | 0.210292 | − | 0.977639i | \(-0.432558\pi\) | ||||
0.210292 | + | 0.977639i | \(0.432558\pi\) | |||||||
\(558\) | 7.87977 | 0.333577 | ||||||||
\(559\) | −4.81754 | −0.203760 | ||||||||
\(560\) | 4.40972 | 0.186345 | ||||||||
\(561\) | 35.8086 | 1.51184 | ||||||||
\(562\) | −9.29610 | −0.392132 | ||||||||
\(563\) | 16.8071 | 0.708335 | 0.354168 | − | 0.935182i | \(-0.384764\pi\) | ||||
0.354168 | + | 0.935182i | \(0.384764\pi\) | |||||||
\(564\) | 25.0128 | 1.05323 | ||||||||
\(565\) | −18.2558 | −0.768027 | ||||||||
\(566\) | −10.8220 | −0.454883 | ||||||||
\(567\) | 49.5329 | 2.08019 | ||||||||
\(568\) | −15.4391 | −0.647810 | ||||||||
\(569\) | −19.5970 | −0.821549 | −0.410775 | − | 0.911737i | \(-0.634742\pi\) | ||||
−0.410775 | + | 0.911737i | \(0.634742\pi\) | |||||||
\(570\) | −14.3687 | −0.601837 | ||||||||
\(571\) | 24.4096 | 1.02151 | 0.510755 | − | 0.859726i | \(-0.329366\pi\) | ||||
0.510755 | + | 0.859726i | \(0.329366\pi\) | |||||||
\(572\) | −8.43221 | −0.352568 | ||||||||
\(573\) | −17.2673 | −0.721352 | ||||||||
\(574\) | −0.364569 | −0.0152168 | ||||||||
\(575\) | −0.931214 | −0.0388343 | ||||||||
\(576\) | 1.63168 | 0.0679868 | ||||||||
\(577\) | −5.57481 | −0.232082 | −0.116041 | − | 0.993244i | \(-0.537020\pi\) | ||||
−0.116041 | + | 0.993244i | \(0.537020\pi\) | |||||||
\(578\) | −6.02590 | −0.250644 | ||||||||
\(579\) | −20.6657 | −0.858835 | ||||||||
\(580\) | −6.55653 | −0.272245 | ||||||||
\(581\) | −40.2195 | −1.66859 | ||||||||
\(582\) | −16.9605 | −0.703035 | ||||||||
\(583\) | −19.1311 | −0.792329 | ||||||||
\(584\) | −5.98090 | −0.247491 | ||||||||
\(585\) | 3.96796 | 0.164055 | ||||||||
\(586\) | 23.2472 | 0.960333 | ||||||||
\(587\) | 8.03347 | 0.331577 | 0.165788 | − | 0.986161i | \(-0.446983\pi\) | ||||
0.165788 | + | 0.986161i | \(0.446983\pi\) | |||||||
\(588\) | 26.7847 | 1.10458 | ||||||||
\(589\) | 32.2422 | 1.32852 | ||||||||
\(590\) | 10.7443 | 0.442335 | ||||||||
\(591\) | 10.1993 | 0.419543 | ||||||||
\(592\) | 8.15269 | 0.335073 | ||||||||
\(593\) | 30.0881 | 1.23557 | 0.617785 | − | 0.786347i | \(-0.288030\pi\) | ||||
0.617785 | + | 0.786347i | \(0.288030\pi\) | |||||||
\(594\) | 10.2109 | 0.418960 | ||||||||
\(595\) | 21.1602 | 0.867483 | ||||||||
\(596\) | 18.5148 | 0.758396 | ||||||||
\(597\) | 14.5826 | 0.596827 | ||||||||
\(598\) | −2.26455 | −0.0926042 | ||||||||
\(599\) | 13.6904 | 0.559376 | 0.279688 | − | 0.960091i | \(-0.409769\pi\) | ||||
0.279688 | + | 0.960091i | \(0.409769\pi\) | |||||||
\(600\) | −2.15213 | −0.0878605 | ||||||||
\(601\) | 4.51699 | 0.184252 | 0.0921260 | − | 0.995747i | \(-0.470634\pi\) | ||||
0.0921260 | + | 0.995747i | \(0.470634\pi\) | |||||||
\(602\) | 8.73584 | 0.356046 | ||||||||
\(603\) | 18.9170 | 0.770359 | ||||||||
\(604\) | 10.2224 | 0.415942 | ||||||||
\(605\) | −1.02318 | −0.0415980 | ||||||||
\(606\) | 27.7007 | 1.12526 | ||||||||
\(607\) | −27.0474 | −1.09782 | −0.548911 | − | 0.835881i | \(-0.684957\pi\) | ||||
−0.548911 | + | 0.835881i | \(0.684957\pi\) | |||||||
\(608\) | 6.67647 | 0.270767 | ||||||||
\(609\) | −62.2235 | −2.52142 | ||||||||
\(610\) | −13.5180 | −0.547327 | ||||||||
\(611\) | −28.2635 | −1.14342 | ||||||||
\(612\) | 7.82968 | 0.316496 | ||||||||
\(613\) | 23.4893 | 0.948724 | 0.474362 | − | 0.880330i | \(-0.342679\pi\) | ||||
0.474362 | + | 0.880330i | \(0.342679\pi\) | |||||||
\(614\) | 9.50961 | 0.383777 | ||||||||
\(615\) | 0.177925 | 0.00717465 | ||||||||
\(616\) | 15.2905 | 0.616070 | ||||||||
\(617\) | −30.7710 | −1.23879 | −0.619396 | − | 0.785079i | \(-0.712623\pi\) | ||||
−0.619396 | + | 0.785079i | \(0.712623\pi\) | |||||||
\(618\) | 16.2938 | 0.655432 | ||||||||
\(619\) | 23.2436 | 0.934237 | 0.467119 | − | 0.884195i | \(-0.345292\pi\) | ||||
0.467119 | + | 0.884195i | \(0.345292\pi\) | |||||||
\(620\) | 4.82923 | 0.193946 | ||||||||
\(621\) | 2.74224 | 0.110042 | ||||||||
\(622\) | −0.632277 | −0.0253520 | ||||||||
\(623\) | 39.7695 | 1.59333 | ||||||||
\(624\) | −5.23361 | −0.209512 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 20.3452 | 0.813159 | ||||||||
\(627\) | −49.8226 | −1.98972 | ||||||||
\(628\) | 2.44008 | 0.0973698 | ||||||||
\(629\) | 39.1209 | 1.55985 | ||||||||
\(630\) | −7.19527 | −0.286666 | ||||||||
\(631\) | 46.2842 | 1.84254 | 0.921272 | − | 0.388918i | \(-0.127151\pi\) | ||||
0.921272 | + | 0.388918i | \(0.127151\pi\) | |||||||
\(632\) | 10.6192 | 0.422411 | ||||||||
\(633\) | −10.7019 | −0.425361 | ||||||||
\(634\) | 35.2623 | 1.40045 | ||||||||
\(635\) | −14.0072 | −0.555860 | ||||||||
\(636\) | −11.8741 | −0.470838 | ||||||||
\(637\) | −30.2656 | −1.19916 | ||||||||
\(638\) | −22.7344 | −0.900064 | ||||||||
\(639\) | 25.1917 | 0.996569 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 5.18150 | 0.204657 | 0.102328 | − | 0.994751i | \(-0.467371\pi\) | ||||
0.102328 | + | 0.994751i | \(0.467371\pi\) | |||||||
\(642\) | −31.4814 | −1.24247 | ||||||||
\(643\) | 27.5627 | 1.08697 | 0.543484 | − | 0.839420i | \(-0.317105\pi\) | ||||
0.543484 | + | 0.839420i | \(0.317105\pi\) | |||||||
\(644\) | 4.10639 | 0.161815 | ||||||||
\(645\) | −4.26347 | −0.167874 | ||||||||
\(646\) | 32.0373 | 1.26049 | ||||||||
\(647\) | −31.4338 | −1.23579 | −0.617895 | − | 0.786261i | \(-0.712014\pi\) | ||||
−0.617895 | + | 0.786261i | \(0.712014\pi\) | |||||||
\(648\) | 11.2327 | 0.441261 | ||||||||
\(649\) | 37.2552 | 1.46240 | ||||||||
\(650\) | 2.43182 | 0.0953839 | ||||||||
\(651\) | 45.8309 | 1.79625 | ||||||||
\(652\) | 10.5301 | 0.412392 | ||||||||
\(653\) | 38.3897 | 1.50230 | 0.751152 | − | 0.660129i | \(-0.229499\pi\) | ||||
0.751152 | + | 0.660129i | \(0.229499\pi\) | |||||||
\(654\) | −6.67601 | −0.261053 | ||||||||
\(655\) | 20.3081 | 0.793505 | ||||||||
\(656\) | −0.0826739 | −0.00322788 | ||||||||
\(657\) | 9.75893 | 0.380732 | ||||||||
\(658\) | 51.2513 | 1.99798 | ||||||||
\(659\) | −6.96887 | −0.271469 | −0.135734 | − | 0.990745i | \(-0.543339\pi\) | ||||
−0.135734 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(660\) | −7.46241 | −0.290474 | ||||||||
\(661\) | −28.9996 | −1.12796 | −0.563978 | − | 0.825790i | \(-0.690730\pi\) | ||||
−0.563978 | + | 0.825790i | \(0.690730\pi\) | |||||||
\(662\) | −10.6941 | −0.415637 | ||||||||
\(663\) | −25.1136 | −0.975333 | ||||||||
\(664\) | −9.12066 | −0.353950 | ||||||||
\(665\) | −29.4414 | −1.14169 | ||||||||
\(666\) | −13.3026 | −0.515465 | ||||||||
\(667\) | −6.10553 | −0.236407 | ||||||||
\(668\) | 22.0520 | 0.853219 | ||||||||
\(669\) | −36.4509 | −1.40927 | ||||||||
\(670\) | 11.5935 | 0.447897 | ||||||||
\(671\) | −46.8729 | −1.80951 | ||||||||
\(672\) | 9.49031 | 0.366097 | ||||||||
\(673\) | −8.14549 | −0.313986 | −0.156993 | − | 0.987600i | \(-0.550180\pi\) | ||||
−0.156993 | + | 0.987600i | \(0.550180\pi\) | |||||||
\(674\) | 24.6450 | 0.949290 | ||||||||
\(675\) | −2.94480 | −0.113345 | ||||||||
\(676\) | −7.08624 | −0.272548 | ||||||||
\(677\) | −0.905278 | −0.0347927 | −0.0173963 | − | 0.999849i | \(-0.505538\pi\) | ||||
−0.0173963 | + | 0.999849i | \(0.505538\pi\) | |||||||
\(678\) | −39.2889 | −1.50888 | ||||||||
\(679\) | −34.7520 | −1.33366 | ||||||||
\(680\) | 4.79853 | 0.184015 | ||||||||
\(681\) | −4.40772 | −0.168904 | ||||||||
\(682\) | 16.7451 | 0.641202 | ||||||||
\(683\) | 4.86594 | 0.186190 | 0.0930951 | − | 0.995657i | \(-0.470324\pi\) | ||||
0.0930951 | + | 0.995657i | \(0.470324\pi\) | |||||||
\(684\) | −10.8939 | −0.416538 | ||||||||
\(685\) | −2.07544 | −0.0792985 | ||||||||
\(686\) | 24.0137 | 0.916847 | ||||||||
\(687\) | 4.39793 | 0.167791 | ||||||||
\(688\) | 1.98104 | 0.0755265 | ||||||||
\(689\) | 13.4172 | 0.511155 | ||||||||
\(690\) | −2.00410 | −0.0762947 | ||||||||
\(691\) | −12.9474 | −0.492542 | −0.246271 | − | 0.969201i | \(-0.579205\pi\) | ||||
−0.246271 | + | 0.969201i | \(0.579205\pi\) | |||||||
\(692\) | −6.99836 | −0.266038 | ||||||||
\(693\) | −24.9492 | −0.947741 | ||||||||
\(694\) | −9.99727 | −0.379491 | ||||||||
\(695\) | −6.92751 | −0.262775 | ||||||||
\(696\) | −14.1105 | −0.534859 | ||||||||
\(697\) | −0.396713 | −0.0150266 | ||||||||
\(698\) | −12.2481 | −0.463598 | ||||||||
\(699\) | −39.0086 | −1.47544 | ||||||||
\(700\) | −4.40972 | −0.166672 | ||||||||
\(701\) | 9.73753 | 0.367782 | 0.183891 | − | 0.982947i | \(-0.441131\pi\) | ||||
0.183891 | + | 0.982947i | \(0.441131\pi\) | |||||||
\(702\) | −7.16123 | −0.270283 | ||||||||
\(703\) | −54.4312 | −2.05291 | ||||||||
\(704\) | 3.46745 | 0.130684 | ||||||||
\(705\) | −25.0128 | −0.942038 | ||||||||
\(706\) | 4.98404 | 0.187577 | ||||||||
\(707\) | 56.7587 | 2.13463 | ||||||||
\(708\) | 23.1232 | 0.869021 | ||||||||
\(709\) | −38.3392 | −1.43986 | −0.719930 | − | 0.694047i | \(-0.755826\pi\) | ||||
−0.719930 | + | 0.694047i | \(0.755826\pi\) | |||||||
\(710\) | 15.4391 | 0.579419 | ||||||||
\(711\) | −17.3272 | −0.649822 | ||||||||
\(712\) | 9.01860 | 0.337986 | ||||||||
\(713\) | 4.49704 | 0.168416 | ||||||||
\(714\) | 45.5395 | 1.70427 | ||||||||
\(715\) | 8.43221 | 0.315347 | ||||||||
\(716\) | 24.9744 | 0.933338 | ||||||||
\(717\) | −39.4588 | −1.47362 | ||||||||
\(718\) | −32.0394 | −1.19570 | ||||||||
\(719\) | −26.7985 | −0.999416 | −0.499708 | − | 0.866194i | \(-0.666559\pi\) | ||||
−0.499708 | + | 0.866194i | \(0.666559\pi\) | |||||||
\(720\) | −1.63168 | −0.0608093 | ||||||||
\(721\) | 33.3859 | 1.24336 | ||||||||
\(722\) | −25.5753 | −0.951814 | ||||||||
\(723\) | 62.3601 | 2.31920 | ||||||||
\(724\) | −5.63024 | −0.209246 | ||||||||
\(725\) | 6.55653 | 0.243504 | ||||||||
\(726\) | −2.20201 | −0.0817243 | ||||||||
\(727\) | −10.1345 | −0.375868 | −0.187934 | − | 0.982182i | \(-0.560179\pi\) | ||||
−0.187934 | + | 0.982182i | \(0.560179\pi\) | |||||||
\(728\) | −10.7237 | −0.397445 | ||||||||
\(729\) | 0.684683 | 0.0253586 | ||||||||
\(730\) | 5.98090 | 0.221363 | ||||||||
\(731\) | 9.50609 | 0.351596 | ||||||||
\(732\) | −29.0925 | −1.07529 | ||||||||
\(733\) | −27.3842 | −1.01146 | −0.505730 | − | 0.862692i | \(-0.668777\pi\) | ||||
−0.505730 | + | 0.862692i | \(0.668777\pi\) | |||||||
\(734\) | −26.6423 | −0.983387 | ||||||||
\(735\) | −26.7847 | −0.987967 | ||||||||
\(736\) | 0.931214 | 0.0343250 | ||||||||
\(737\) | 40.1999 | 1.48078 | ||||||||
\(738\) | 0.134898 | 0.00496565 | ||||||||
\(739\) | −31.5324 | −1.15994 | −0.579969 | − | 0.814638i | \(-0.696936\pi\) | ||||
−0.579969 | + | 0.814638i | \(0.696936\pi\) | |||||||
\(740\) | −8.15269 | −0.299699 | ||||||||
\(741\) | 34.9421 | 1.28363 | ||||||||
\(742\) | −24.3300 | −0.893181 | ||||||||
\(743\) | −3.96578 | −0.145490 | −0.0727452 | − | 0.997351i | \(-0.523176\pi\) | ||||
−0.0727452 | + | 0.997351i | \(0.523176\pi\) | |||||||
\(744\) | 10.3931 | 0.381031 | ||||||||
\(745\) | −18.5148 | −0.678330 | ||||||||
\(746\) | 2.41595 | 0.0884542 | ||||||||
\(747\) | 14.8820 | 0.544505 | ||||||||
\(748\) | 16.6386 | 0.608369 | ||||||||
\(749\) | −64.5054 | −2.35698 | ||||||||
\(750\) | 2.15213 | 0.0785848 | ||||||||
\(751\) | 43.2721 | 1.57902 | 0.789511 | − | 0.613737i | \(-0.210334\pi\) | ||||
0.789511 | + | 0.613737i | \(0.210334\pi\) | |||||||
\(752\) | 11.6223 | 0.423823 | ||||||||
\(753\) | 48.7645 | 1.77708 | ||||||||
\(754\) | 15.9443 | 0.580658 | ||||||||
\(755\) | −10.2224 | −0.372029 | ||||||||
\(756\) | 12.9857 | 0.472287 | ||||||||
\(757\) | 1.81395 | 0.0659291 | 0.0329646 | − | 0.999457i | \(-0.489505\pi\) | ||||
0.0329646 | + | 0.999457i | \(0.489505\pi\) | |||||||
\(758\) | 15.0140 | 0.545334 | ||||||||
\(759\) | −6.94910 | −0.252236 | ||||||||
\(760\) | −6.67647 | −0.242181 | ||||||||
\(761\) | −6.77729 | −0.245677 | −0.122838 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122838 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(762\) | −30.1455 | −1.09205 | ||||||||
\(763\) | −13.6791 | −0.495218 | ||||||||
\(764\) | −8.02334 | −0.290274 | ||||||||
\(765\) | −7.82968 | −0.283083 | ||||||||
\(766\) | 3.77917 | 0.136547 | ||||||||
\(767\) | −26.1282 | −0.943435 | ||||||||
\(768\) | 2.15213 | 0.0776585 | ||||||||
\(769\) | 17.3853 | 0.626929 | 0.313464 | − | 0.949600i | \(-0.398510\pi\) | ||||
0.313464 | + | 0.949600i | \(0.398510\pi\) | |||||||
\(770\) | −15.2905 | −0.551030 | ||||||||
\(771\) | 56.2069 | 2.02424 | ||||||||
\(772\) | −9.60240 | −0.345598 | ||||||||
\(773\) | 21.9761 | 0.790426 | 0.395213 | − | 0.918590i | \(-0.370671\pi\) | ||||
0.395213 | + | 0.918590i | \(0.370671\pi\) | |||||||
\(774\) | −3.23243 | −0.116187 | ||||||||
\(775\) | −4.82923 | −0.173471 | ||||||||
\(776\) | −7.88077 | −0.282903 | ||||||||
\(777\) | −77.3715 | −2.77569 | ||||||||
\(778\) | −16.0079 | −0.573910 | ||||||||
\(779\) | 0.551970 | 0.0197764 | ||||||||
\(780\) | 5.23361 | 0.187393 | ||||||||
\(781\) | 53.5342 | 1.91560 | ||||||||
\(782\) | 4.46846 | 0.159792 | ||||||||
\(783\) | −19.3077 | −0.690000 | ||||||||
\(784\) | 12.4456 | 0.444487 | ||||||||
\(785\) | −2.44008 | −0.0870902 | ||||||||
\(786\) | 43.7059 | 1.55894 | ||||||||
\(787\) | 25.9506 | 0.925040 | 0.462520 | − | 0.886609i | \(-0.346945\pi\) | ||||
0.462520 | + | 0.886609i | \(0.346945\pi\) | |||||||
\(788\) | 4.73915 | 0.168825 | ||||||||
\(789\) | 2.55411 | 0.0909286 | ||||||||
\(790\) | −10.6192 | −0.377816 | ||||||||
\(791\) | −80.5030 | −2.86236 | ||||||||
\(792\) | −5.65777 | −0.201040 | ||||||||
\(793\) | 32.8734 | 1.16737 | ||||||||
\(794\) | −22.9613 | −0.814867 | ||||||||
\(795\) | 11.8741 | 0.421130 | ||||||||
\(796\) | 6.77589 | 0.240165 | ||||||||
\(797\) | −45.3858 | −1.60765 | −0.803824 | − | 0.594867i | \(-0.797205\pi\) | ||||
−0.803824 | + | 0.594867i | \(0.797205\pi\) | |||||||
\(798\) | −63.3618 | −2.24298 | ||||||||
\(799\) | 55.7702 | 1.97301 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −14.7155 | −0.519947 | ||||||||
\(802\) | −1.00000 | −0.0353112 | ||||||||
\(803\) | 20.7384 | 0.731843 | ||||||||
\(804\) | 24.9508 | 0.879948 | ||||||||
\(805\) | −4.10639 | −0.144731 | ||||||||
\(806\) | −11.7438 | −0.413658 | ||||||||
\(807\) | −5.58363 | −0.196553 | ||||||||
\(808\) | 12.8713 | 0.452810 | ||||||||
\(809\) | 40.5574 | 1.42592 | 0.712960 | − | 0.701204i | \(-0.247354\pi\) | ||||
0.712960 | + | 0.701204i | \(0.247354\pi\) | |||||||
\(810\) | −11.2327 | −0.394675 | ||||||||
\(811\) | −27.1581 | −0.953652 | −0.476826 | − | 0.878998i | \(-0.658213\pi\) | ||||
−0.476826 | + | 0.878998i | \(0.658213\pi\) | |||||||
\(812\) | −28.9125 | −1.01463 | ||||||||
\(813\) | −42.4505 | −1.48880 | ||||||||
\(814\) | −28.2690 | −0.990828 | ||||||||
\(815\) | −10.5301 | −0.368855 | ||||||||
\(816\) | 10.3271 | 0.361520 | ||||||||
\(817\) | −13.2264 | −0.462732 | ||||||||
\(818\) | 2.56055 | 0.0895274 | ||||||||
\(819\) | 17.4976 | 0.611416 | ||||||||
\(820\) | 0.0826739 | 0.00288710 | ||||||||
\(821\) | 43.3239 | 1.51201 | 0.756007 | − | 0.654563i | \(-0.227148\pi\) | ||||
0.756007 | + | 0.654563i | \(0.227148\pi\) | |||||||
\(822\) | −4.46663 | −0.155792 | ||||||||
\(823\) | −6.06111 | −0.211277 | −0.105639 | − | 0.994405i | \(-0.533689\pi\) | ||||
−0.105639 | + | 0.994405i | \(0.533689\pi\) | |||||||
\(824\) | 7.57098 | 0.263748 | ||||||||
\(825\) | 7.46241 | 0.259808 | ||||||||
\(826\) | 47.3793 | 1.64854 | ||||||||
\(827\) | 45.8403 | 1.59402 | 0.797011 | − | 0.603965i | \(-0.206413\pi\) | ||||
0.797011 | + | 0.603965i | \(0.206413\pi\) | |||||||
\(828\) | −1.51945 | −0.0528044 | ||||||||
\(829\) | 31.0200 | 1.07737 | 0.538685 | − | 0.842507i | \(-0.318921\pi\) | ||||
0.538685 | + | 0.842507i | \(0.318921\pi\) | |||||||
\(830\) | 9.12066 | 0.316583 | ||||||||
\(831\) | 53.7731 | 1.86537 | ||||||||
\(832\) | −2.43182 | −0.0843083 | ||||||||
\(833\) | 59.7207 | 2.06920 | ||||||||
\(834\) | −14.9089 | −0.516254 | ||||||||
\(835\) | −22.0520 | −0.763142 | ||||||||
\(836\) | −23.1503 | −0.800670 | ||||||||
\(837\) | 14.2211 | 0.491554 | ||||||||
\(838\) | 30.6276 | 1.05801 | ||||||||
\(839\) | 15.7606 | 0.544116 | 0.272058 | − | 0.962281i | \(-0.412296\pi\) | ||||
0.272058 | + | 0.962281i | \(0.412296\pi\) | |||||||
\(840\) | −9.49031 | −0.327447 | ||||||||
\(841\) | 13.9881 | 0.482349 | ||||||||
\(842\) | −37.2917 | −1.28516 | ||||||||
\(843\) | 20.0065 | 0.689059 | ||||||||
\(844\) | −4.97267 | −0.171166 | ||||||||
\(845\) | 7.08624 | 0.243774 | ||||||||
\(846\) | −18.9640 | −0.651995 | ||||||||
\(847\) | −4.51192 | −0.155031 | ||||||||
\(848\) | −5.51735 | −0.189467 | ||||||||
\(849\) | 23.2904 | 0.799325 | ||||||||
\(850\) | −4.79853 | −0.164588 | ||||||||
\(851\) | −7.59189 | −0.260247 | ||||||||
\(852\) | 33.2270 | 1.13834 | ||||||||
\(853\) | −33.6925 | −1.15361 | −0.576805 | − | 0.816882i | \(-0.695701\pi\) | ||||
−0.576805 | + | 0.816882i | \(0.695701\pi\) | |||||||
\(854\) | −59.6106 | −2.03983 | ||||||||
\(855\) | 10.8939 | 0.372563 | ||||||||
\(856\) | −14.6280 | −0.499975 | ||||||||
\(857\) | −23.4255 | −0.800198 | −0.400099 | − | 0.916472i | \(-0.631024\pi\) | ||||
−0.400099 | + | 0.916472i | \(0.631024\pi\) | |||||||
\(858\) | 18.1473 | 0.619537 | ||||||||
\(859\) | −18.6509 | −0.636361 | −0.318181 | − | 0.948030i | \(-0.603072\pi\) | ||||
−0.318181 | + | 0.948030i | \(0.603072\pi\) | |||||||
\(860\) | −1.98104 | −0.0675530 | ||||||||
\(861\) | 0.784601 | 0.0267391 | ||||||||
\(862\) | 21.7748 | 0.741651 | ||||||||
\(863\) | −22.4982 | −0.765849 | −0.382924 | − | 0.923780i | \(-0.625083\pi\) | ||||
−0.382924 | + | 0.923780i | \(0.625083\pi\) | |||||||
\(864\) | 2.94480 | 0.100184 | ||||||||
\(865\) | 6.99836 | 0.237951 | ||||||||
\(866\) | 27.6818 | 0.940665 | ||||||||
\(867\) | 12.9685 | 0.440435 | ||||||||
\(868\) | 21.2955 | 0.722817 | ||||||||
\(869\) | −36.8216 | −1.24909 | ||||||||
\(870\) | 14.1105 | 0.478392 | ||||||||
\(871\) | −28.1934 | −0.955297 | ||||||||
\(872\) | −3.10204 | −0.105048 | ||||||||
\(873\) | 12.8589 | 0.435209 | ||||||||
\(874\) | −6.21722 | −0.210301 | ||||||||
\(875\) | 4.40972 | 0.149076 | ||||||||
\(876\) | 12.8717 | 0.434894 | ||||||||
\(877\) | −39.5636 | −1.33597 | −0.667983 | − | 0.744176i | \(-0.732842\pi\) | ||||
−0.667983 | + | 0.744176i | \(0.732842\pi\) | |||||||
\(878\) | 4.06381 | 0.137147 | ||||||||
\(879\) | −50.0311 | −1.68751 | ||||||||
\(880\) | −3.46745 | −0.116888 | ||||||||
\(881\) | −37.7811 | −1.27288 | −0.636438 | − | 0.771328i | \(-0.719593\pi\) | ||||
−0.636438 | + | 0.771328i | \(0.719593\pi\) | |||||||
\(882\) | −20.3073 | −0.683783 | ||||||||
\(883\) | −9.33027 | −0.313988 | −0.156994 | − | 0.987600i | \(-0.550180\pi\) | ||||
−0.156994 | + | 0.987600i | \(0.550180\pi\) | |||||||
\(884\) | −11.6692 | −0.392477 | ||||||||
\(885\) | −23.1232 | −0.777276 | ||||||||
\(886\) | 5.79090 | 0.194549 | ||||||||
\(887\) | 9.03773 | 0.303457 | 0.151729 | − | 0.988422i | \(-0.451516\pi\) | ||||
0.151729 | + | 0.988422i | \(0.451516\pi\) | |||||||
\(888\) | −17.5457 | −0.588794 | ||||||||
\(889\) | −61.7680 | −2.07163 | ||||||||
\(890\) | −9.01860 | −0.302304 | ||||||||
\(891\) | −38.9486 | −1.30483 | ||||||||
\(892\) | −16.9371 | −0.567096 | ||||||||
\(893\) | −77.5963 | −2.59666 | ||||||||
\(894\) | −39.8463 | −1.33266 | ||||||||
\(895\) | −24.9744 | −0.834803 | ||||||||
\(896\) | 4.40972 | 0.147318 | ||||||||
\(897\) | 4.87361 | 0.162725 | ||||||||
\(898\) | −11.5422 | −0.385167 | ||||||||
\(899\) | −31.6630 | −1.05602 | ||||||||
\(900\) | 1.63168 | 0.0543894 | ||||||||
\(901\) | −26.4752 | −0.882016 | ||||||||
\(902\) | 0.286667 | 0.00954498 | ||||||||
\(903\) | −18.8007 | −0.625648 | ||||||||
\(904\) | −18.2558 | −0.607179 | ||||||||
\(905\) | 5.63024 | 0.187155 | ||||||||
\(906\) | −21.9999 | −0.730897 | ||||||||
\(907\) | 4.85636 | 0.161253 | 0.0806264 | − | 0.996744i | \(-0.474308\pi\) | ||||
0.0806264 | + | 0.996744i | \(0.474308\pi\) | |||||||
\(908\) | −2.04807 | −0.0679675 | ||||||||
\(909\) | −21.0018 | −0.696587 | ||||||||
\(910\) | 10.7237 | 0.355486 | ||||||||
\(911\) | −40.8202 | −1.35243 | −0.676216 | − | 0.736703i | \(-0.736381\pi\) | ||||
−0.676216 | + | 0.736703i | \(0.736381\pi\) | |||||||
\(912\) | −14.3687 | −0.475794 | ||||||||
\(913\) | 31.6254 | 1.04665 | ||||||||
\(914\) | −29.2402 | −0.967180 | ||||||||
\(915\) | 29.0925 | 0.961770 | ||||||||
\(916\) | 2.04352 | 0.0675198 | ||||||||
\(917\) | 89.5532 | 2.95731 | ||||||||
\(918\) | 14.1307 | 0.466383 | ||||||||
\(919\) | 11.2809 | 0.372122 | 0.186061 | − | 0.982538i | \(-0.440428\pi\) | ||||
0.186061 | + | 0.982538i | \(0.440428\pi\) | |||||||
\(920\) | −0.931214 | −0.0307012 | ||||||||
\(921\) | −20.4660 | −0.674376 | ||||||||
\(922\) | 30.8494 | 1.01597 | ||||||||
\(923\) | −37.5451 | −1.23581 | ||||||||
\(924\) | −32.9071 | −1.08257 | ||||||||
\(925\) | 8.15269 | 0.268059 | ||||||||
\(926\) | −28.7096 | −0.943457 | ||||||||
\(927\) | −12.3534 | −0.405740 | ||||||||
\(928\) | −6.55653 | −0.215229 | ||||||||
\(929\) | 25.7575 | 0.845077 | 0.422538 | − | 0.906345i | \(-0.361139\pi\) | ||||
0.422538 | + | 0.906345i | \(0.361139\pi\) | |||||||
\(930\) | −10.3931 | −0.340805 | ||||||||
\(931\) | −83.0929 | −2.72326 | ||||||||
\(932\) | −18.1255 | −0.593722 | ||||||||
\(933\) | 1.36074 | 0.0445488 | ||||||||
\(934\) | 3.13314 | 0.102520 | ||||||||
\(935\) | −16.6386 | −0.544142 | ||||||||
\(936\) | 3.96796 | 0.129697 | ||||||||
\(937\) | −51.6744 | −1.68813 | −0.844064 | − | 0.536242i | \(-0.819843\pi\) | ||||
−0.844064 | + | 0.536242i | \(0.819843\pi\) | |||||||
\(938\) | 51.1242 | 1.66927 | ||||||||
\(939\) | −43.7857 | −1.42889 | ||||||||
\(940\) | −11.6223 | −0.379079 | ||||||||
\(941\) | −46.5175 | −1.51643 | −0.758214 | − | 0.652006i | \(-0.773928\pi\) | ||||
−0.758214 | + | 0.652006i | \(0.773928\pi\) | |||||||
\(942\) | −5.25138 | −0.171099 | ||||||||
\(943\) | 0.0769871 | 0.00250705 | ||||||||
\(944\) | 10.7443 | 0.349697 | ||||||||
\(945\) | −12.9857 | −0.422426 | ||||||||
\(946\) | −6.86916 | −0.223336 | ||||||||
\(947\) | −24.5315 | −0.797167 | −0.398583 | − | 0.917132i | \(-0.630498\pi\) | ||||
−0.398583 | + | 0.917132i | \(0.630498\pi\) | |||||||
\(948\) | −22.8540 | −0.742264 | ||||||||
\(949\) | −14.5445 | −0.472134 | ||||||||
\(950\) | 6.67647 | 0.216613 | ||||||||
\(951\) | −75.8893 | −2.46088 | ||||||||
\(952\) | 21.1602 | 0.685805 | ||||||||
\(953\) | 59.0228 | 1.91194 | 0.955968 | − | 0.293469i | \(-0.0948099\pi\) | ||||
0.955968 | + | 0.293469i | \(0.0948099\pi\) | |||||||
\(954\) | 9.00257 | 0.291469 | ||||||||
\(955\) | 8.02334 | 0.259629 | ||||||||
\(956\) | −18.3347 | −0.592988 | ||||||||
\(957\) | 48.9275 | 1.58160 | ||||||||
\(958\) | −28.5029 | −0.920887 | ||||||||
\(959\) | −9.15211 | −0.295537 | ||||||||
\(960\) | −2.15213 | −0.0694598 | ||||||||
\(961\) | −7.67858 | −0.247696 | ||||||||
\(962\) | 19.8259 | 0.639212 | ||||||||
\(963\) | 23.8683 | 0.769144 | ||||||||
\(964\) | 28.9759 | 0.933252 | ||||||||
\(965\) | 9.60240 | 0.309112 | ||||||||
\(966\) | −8.83751 | −0.284342 | ||||||||
\(967\) | 17.0618 | 0.548669 | 0.274335 | − | 0.961634i | \(-0.411542\pi\) | ||||
0.274335 | + | 0.961634i | \(0.411542\pi\) | |||||||
\(968\) | −1.02318 | −0.0328861 | ||||||||
\(969\) | −68.9485 | −2.21495 | ||||||||
\(970\) | 7.88077 | 0.253036 | ||||||||
\(971\) | 1.62035 | 0.0519995 | 0.0259997 | − | 0.999662i | \(-0.491723\pi\) | ||||
0.0259997 | + | 0.999662i | \(0.491723\pi\) | |||||||
\(972\) | −15.3398 | −0.492024 | ||||||||
\(973\) | −30.5484 | −0.979336 | ||||||||
\(974\) | 33.4999 | 1.07341 | ||||||||
\(975\) | −5.23361 | −0.167610 | ||||||||
\(976\) | −13.5180 | −0.432700 | ||||||||
\(977\) | 8.03328 | 0.257007 | 0.128504 | − | 0.991709i | \(-0.458983\pi\) | ||||
0.128504 | + | 0.991709i | \(0.458983\pi\) | |||||||
\(978\) | −22.6623 | −0.724660 | ||||||||
\(979\) | −31.2715 | −0.999441 | ||||||||
\(980\) | −12.4456 | −0.397561 | ||||||||
\(981\) | 5.06155 | 0.161603 | ||||||||
\(982\) | 29.8201 | 0.951597 | ||||||||
\(983\) | 26.3578 | 0.840684 | 0.420342 | − | 0.907366i | \(-0.361910\pi\) | ||||
0.420342 | + | 0.907366i | \(0.361910\pi\) | |||||||
\(984\) | 0.177925 | 0.00567206 | ||||||||
\(985\) | −4.73915 | −0.151002 | ||||||||
\(986\) | −31.4617 | −1.00195 | ||||||||
\(987\) | −110.300 | −3.51088 | ||||||||
\(988\) | 16.2360 | 0.516536 | ||||||||
\(989\) | −1.84477 | −0.0586604 | ||||||||
\(990\) | 5.65777 | 0.179816 | ||||||||
\(991\) | 15.3012 | 0.486059 | 0.243030 | − | 0.970019i | \(-0.421859\pi\) | ||||
0.243030 | + | 0.970019i | \(0.421859\pi\) | |||||||
\(992\) | 4.82923 | 0.153328 | ||||||||
\(993\) | 23.0151 | 0.730361 | ||||||||
\(994\) | 68.0821 | 2.15943 | ||||||||
\(995\) | −6.77589 | −0.214810 | ||||||||
\(996\) | 19.6289 | 0.621965 | ||||||||
\(997\) | 4.24414 | 0.134413 | 0.0672066 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672066 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(998\) | −31.0553 | −0.983040 | ||||||||
\(999\) | −24.0080 | −0.759581 |
(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.l.1.14 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.l.1.14 | ✓ | 17 | 1.1 | even | 1 | trivial |