Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, 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("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 3x^{8} - 16x^{7} + 44x^{6} + 87x^{5} - 209x^{4} - 160x^{3} + 348x^{2} + 12x - 100 \) |
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 | 1.9 | ||
Root | \(-2.50055\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | 2.50055 | 1.44369 | 0.721847 | − | 0.692053i | \(-0.243294\pi\) | ||||
0.721847 | + | 0.692053i | \(0.243294\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.67075 | 0.747184 | 0.373592 | − | 0.927593i | \(-0.378126\pi\) | ||||
0.373592 | + | 0.927593i | \(0.378126\pi\) | |||||||
\(6\) | −2.50055 | −1.02085 | ||||||||
\(7\) | −2.56147 | −0.968143 | −0.484071 | − | 0.875028i | \(-0.660843\pi\) | ||||
−0.484071 | + | 0.875028i | \(0.660843\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.25275 | 1.08425 | ||||||||
\(10\) | −1.67075 | −0.528339 | ||||||||
\(11\) | 0.797665 | 0.240505 | 0.120253 | − | 0.992743i | \(-0.461630\pi\) | ||||
0.120253 | + | 0.992743i | \(0.461630\pi\) | |||||||
\(12\) | 2.50055 | 0.721847 | ||||||||
\(13\) | 4.57607 | 1.26917 | 0.634586 | − | 0.772852i | \(-0.281170\pi\) | ||||
0.634586 | + | 0.772852i | \(0.281170\pi\) | |||||||
\(14\) | 2.56147 | 0.684580 | ||||||||
\(15\) | 4.17781 | 1.07871 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.52539 | 1.34010 | 0.670052 | − | 0.742314i | \(-0.266272\pi\) | ||||
0.670052 | + | 0.742314i | \(0.266272\pi\) | |||||||
\(18\) | −3.25275 | −0.766682 | ||||||||
\(19\) | −2.88478 | −0.661814 | −0.330907 | − | 0.943663i | \(-0.607355\pi\) | ||||
−0.330907 | + | 0.943663i | \(0.607355\pi\) | |||||||
\(20\) | 1.67075 | 0.373592 | ||||||||
\(21\) | −6.40507 | −1.39770 | ||||||||
\(22\) | −0.797665 | −0.170063 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −2.50055 | −0.510423 | ||||||||
\(25\) | −2.20858 | −0.441716 | ||||||||
\(26\) | −4.57607 | −0.897441 | ||||||||
\(27\) | 0.632025 | 0.121633 | ||||||||
\(28\) | −2.56147 | −0.484071 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −4.17781 | −0.762760 | ||||||||
\(31\) | 2.79767 | 0.502476 | 0.251238 | − | 0.967925i | \(-0.419162\pi\) | ||||
0.251238 | + | 0.967925i | \(0.419162\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.99460 | 0.347216 | ||||||||
\(34\) | −5.52539 | −0.947597 | ||||||||
\(35\) | −4.27958 | −0.723381 | ||||||||
\(36\) | 3.25275 | 0.542126 | ||||||||
\(37\) | 10.0324 | 1.64932 | 0.824662 | − | 0.565626i | \(-0.191366\pi\) | ||||
0.824662 | + | 0.565626i | \(0.191366\pi\) | |||||||
\(38\) | 2.88478 | 0.467973 | ||||||||
\(39\) | 11.4427 | 1.83230 | ||||||||
\(40\) | −1.67075 | −0.264170 | ||||||||
\(41\) | 8.03244 | 1.25446 | 0.627228 | − | 0.778835i | \(-0.284189\pi\) | ||||
0.627228 | + | 0.778835i | \(0.284189\pi\) | |||||||
\(42\) | 6.40507 | 0.988324 | ||||||||
\(43\) | 4.20344 | 0.641018 | 0.320509 | − | 0.947245i | \(-0.396146\pi\) | ||||
0.320509 | + | 0.947245i | \(0.396146\pi\) | |||||||
\(44\) | 0.797665 | 0.120253 | ||||||||
\(45\) | 5.43455 | 0.810136 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −3.01372 | −0.439596 | −0.219798 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219798 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(48\) | 2.50055 | 0.360923 | ||||||||
\(49\) | −0.438895 | −0.0626993 | ||||||||
\(50\) | 2.20858 | 0.312340 | ||||||||
\(51\) | 13.8165 | 1.93470 | ||||||||
\(52\) | 4.57607 | 0.634586 | ||||||||
\(53\) | 2.83475 | 0.389383 | 0.194692 | − | 0.980864i | \(-0.437629\pi\) | ||||
0.194692 | + | 0.980864i | \(0.437629\pi\) | |||||||
\(54\) | −0.632025 | −0.0860077 | ||||||||
\(55\) | 1.33270 | 0.179702 | ||||||||
\(56\) | 2.56147 | 0.342290 | ||||||||
\(57\) | −7.21354 | −0.955456 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −4.44699 | −0.578948 | −0.289474 | − | 0.957186i | \(-0.593480\pi\) | ||||
−0.289474 | + | 0.957186i | \(0.593480\pi\) | |||||||
\(60\) | 4.17781 | 0.539353 | ||||||||
\(61\) | 1.99094 | 0.254913 | 0.127457 | − | 0.991844i | \(-0.459319\pi\) | ||||
0.127457 | + | 0.991844i | \(0.459319\pi\) | |||||||
\(62\) | −2.79767 | −0.355304 | ||||||||
\(63\) | −8.33182 | −1.04971 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.64549 | 0.948306 | ||||||||
\(66\) | −1.99460 | −0.245519 | ||||||||
\(67\) | −8.31278 | −1.01557 | −0.507784 | − | 0.861484i | \(-0.669535\pi\) | ||||
−0.507784 | + | 0.861484i | \(0.669535\pi\) | |||||||
\(68\) | 5.52539 | 0.670052 | ||||||||
\(69\) | −2.50055 | −0.301031 | ||||||||
\(70\) | 4.27958 | 0.511508 | ||||||||
\(71\) | −5.77544 | −0.685419 | −0.342709 | − | 0.939441i | \(-0.611345\pi\) | ||||
−0.342709 | + | 0.939441i | \(0.611345\pi\) | |||||||
\(72\) | −3.25275 | −0.383341 | ||||||||
\(73\) | 2.16312 | 0.253174 | 0.126587 | − | 0.991956i | \(-0.459598\pi\) | ||||
0.126587 | + | 0.991956i | \(0.459598\pi\) | |||||||
\(74\) | −10.0324 | −1.16625 | ||||||||
\(75\) | −5.52266 | −0.637702 | ||||||||
\(76\) | −2.88478 | −0.330907 | ||||||||
\(77\) | −2.04319 | −0.232843 | ||||||||
\(78\) | −11.4427 | −1.29563 | ||||||||
\(79\) | −9.57229 | −1.07697 | −0.538484 | − | 0.842636i | \(-0.681003\pi\) | ||||
−0.538484 | + | 0.842636i | \(0.681003\pi\) | |||||||
\(80\) | 1.67075 | 0.186796 | ||||||||
\(81\) | −8.17785 | −0.908650 | ||||||||
\(82\) | −8.03244 | −0.887035 | ||||||||
\(83\) | 8.08767 | 0.887737 | 0.443869 | − | 0.896092i | \(-0.353606\pi\) | ||||
0.443869 | + | 0.896092i | \(0.353606\pi\) | |||||||
\(84\) | −6.40507 | −0.698851 | ||||||||
\(85\) | 9.23157 | 1.00130 | ||||||||
\(86\) | −4.20344 | −0.453268 | ||||||||
\(87\) | 2.50055 | 0.268087 | ||||||||
\(88\) | −0.797665 | −0.0850314 | ||||||||
\(89\) | 11.4861 | 1.21752 | 0.608761 | − | 0.793354i | \(-0.291667\pi\) | ||||
0.608761 | + | 0.793354i | \(0.291667\pi\) | |||||||
\(90\) | −5.43455 | −0.572852 | ||||||||
\(91\) | −11.7214 | −1.22874 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 6.99570 | 0.725421 | ||||||||
\(94\) | 3.01372 | 0.310841 | ||||||||
\(95\) | −4.81976 | −0.494497 | ||||||||
\(96\) | −2.50055 | −0.255211 | ||||||||
\(97\) | −2.22607 | −0.226023 | −0.113012 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113012 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(98\) | 0.438895 | 0.0443351 | ||||||||
\(99\) | 2.59461 | 0.260768 | ||||||||
\(100\) | −2.20858 | −0.220858 | ||||||||
\(101\) | −13.7286 | −1.36604 | −0.683022 | − | 0.730398i | \(-0.739335\pi\) | ||||
−0.683022 | + | 0.730398i | \(0.739335\pi\) | |||||||
\(102\) | −13.8165 | −1.36804 | ||||||||
\(103\) | −0.609882 | −0.0600935 | −0.0300467 | − | 0.999548i | \(-0.509566\pi\) | ||||
−0.0300467 | + | 0.999548i | \(0.509566\pi\) | |||||||
\(104\) | −4.57607 | −0.448720 | ||||||||
\(105\) | −10.7013 | −1.04434 | ||||||||
\(106\) | −2.83475 | −0.275336 | ||||||||
\(107\) | 4.12882 | 0.399149 | 0.199574 | − | 0.979883i | \(-0.436044\pi\) | ||||
0.199574 | + | 0.979883i | \(0.436044\pi\) | |||||||
\(108\) | 0.632025 | 0.0608166 | ||||||||
\(109\) | 16.5257 | 1.58288 | 0.791438 | − | 0.611250i | \(-0.209333\pi\) | ||||
0.791438 | + | 0.611250i | \(0.209333\pi\) | |||||||
\(110\) | −1.33270 | −0.127068 | ||||||||
\(111\) | 25.0866 | 2.38112 | ||||||||
\(112\) | −2.56147 | −0.242036 | ||||||||
\(113\) | −7.88907 | −0.742141 | −0.371071 | − | 0.928605i | \(-0.621009\pi\) | ||||
−0.371071 | + | 0.928605i | \(0.621009\pi\) | |||||||
\(114\) | 7.21354 | 0.675610 | ||||||||
\(115\) | −1.67075 | −0.155799 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 14.8848 | 1.37610 | ||||||||
\(118\) | 4.44699 | 0.409378 | ||||||||
\(119\) | −14.1531 | −1.29741 | ||||||||
\(120\) | −4.17781 | −0.381380 | ||||||||
\(121\) | −10.3637 | −0.942157 | ||||||||
\(122\) | −1.99094 | −0.180251 | ||||||||
\(123\) | 20.0855 | 1.81105 | ||||||||
\(124\) | 2.79767 | 0.251238 | ||||||||
\(125\) | −12.0438 | −1.07723 | ||||||||
\(126\) | 8.33182 | 0.742257 | ||||||||
\(127\) | 5.24015 | 0.464989 | 0.232494 | − | 0.972598i | \(-0.425311\pi\) | ||||
0.232494 | + | 0.972598i | \(0.425311\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.5109 | 0.925434 | ||||||||
\(130\) | −7.64549 | −0.670554 | ||||||||
\(131\) | −13.2715 | −1.15953 | −0.579767 | − | 0.814782i | \(-0.696856\pi\) | ||||
−0.579767 | + | 0.814782i | \(0.696856\pi\) | |||||||
\(132\) | 1.99460 | 0.173608 | ||||||||
\(133\) | 7.38926 | 0.640730 | ||||||||
\(134\) | 8.31278 | 0.718115 | ||||||||
\(135\) | 1.05596 | 0.0908824 | ||||||||
\(136\) | −5.52539 | −0.473798 | ||||||||
\(137\) | −14.2454 | −1.21707 | −0.608534 | − | 0.793528i | \(-0.708242\pi\) | ||||
−0.608534 | + | 0.793528i | \(0.708242\pi\) | |||||||
\(138\) | 2.50055 | 0.212861 | ||||||||
\(139\) | 7.66694 | 0.650301 | 0.325151 | − | 0.945662i | \(-0.394585\pi\) | ||||
0.325151 | + | 0.945662i | \(0.394585\pi\) | |||||||
\(140\) | −4.27958 | −0.361691 | ||||||||
\(141\) | −7.53596 | −0.634642 | ||||||||
\(142\) | 5.77544 | 0.484664 | ||||||||
\(143\) | 3.65017 | 0.305243 | ||||||||
\(144\) | 3.25275 | 0.271063 | ||||||||
\(145\) | 1.67075 | 0.138749 | ||||||||
\(146\) | −2.16312 | −0.179021 | ||||||||
\(147\) | −1.09748 | −0.0905186 | ||||||||
\(148\) | 10.0324 | 0.824662 | ||||||||
\(149\) | 7.10247 | 0.581857 | 0.290929 | − | 0.956745i | \(-0.406036\pi\) | ||||
0.290929 | + | 0.956745i | \(0.406036\pi\) | |||||||
\(150\) | 5.52266 | 0.450923 | ||||||||
\(151\) | 10.5988 | 0.862516 | 0.431258 | − | 0.902229i | \(-0.358070\pi\) | ||||
0.431258 | + | 0.902229i | \(0.358070\pi\) | |||||||
\(152\) | 2.88478 | 0.233986 | ||||||||
\(153\) | 17.9727 | 1.45301 | ||||||||
\(154\) | 2.04319 | 0.164645 | ||||||||
\(155\) | 4.67421 | 0.375442 | ||||||||
\(156\) | 11.4427 | 0.916148 | ||||||||
\(157\) | −2.81055 | −0.224307 | −0.112153 | − | 0.993691i | \(-0.535775\pi\) | ||||
−0.112153 | + | 0.993691i | \(0.535775\pi\) | |||||||
\(158\) | 9.57229 | 0.761531 | ||||||||
\(159\) | 7.08845 | 0.562150 | ||||||||
\(160\) | −1.67075 | −0.132085 | ||||||||
\(161\) | 2.56147 | 0.201872 | ||||||||
\(162\) | 8.17785 | 0.642513 | ||||||||
\(163\) | 3.78302 | 0.296309 | 0.148154 | − | 0.988964i | \(-0.452667\pi\) | ||||
0.148154 | + | 0.988964i | \(0.452667\pi\) | |||||||
\(164\) | 8.03244 | 0.627228 | ||||||||
\(165\) | 3.33249 | 0.259434 | ||||||||
\(166\) | −8.08767 | −0.627725 | ||||||||
\(167\) | −3.69622 | −0.286022 | −0.143011 | − | 0.989721i | \(-0.545678\pi\) | ||||
−0.143011 | + | 0.989721i | \(0.545678\pi\) | |||||||
\(168\) | 6.40507 | 0.494162 | ||||||||
\(169\) | 7.94040 | 0.610800 | ||||||||
\(170\) | −9.23157 | −0.708029 | ||||||||
\(171\) | −9.38348 | −0.717572 | ||||||||
\(172\) | 4.20344 | 0.320509 | ||||||||
\(173\) | −19.2973 | −1.46715 | −0.733575 | − | 0.679609i | \(-0.762150\pi\) | ||||
−0.733575 | + | 0.679609i | \(0.762150\pi\) | |||||||
\(174\) | −2.50055 | −0.189566 | ||||||||
\(175\) | 5.65720 | 0.427644 | ||||||||
\(176\) | 0.797665 | 0.0601263 | ||||||||
\(177\) | −11.1199 | −0.835824 | ||||||||
\(178\) | −11.4861 | −0.860918 | ||||||||
\(179\) | −15.3120 | −1.14447 | −0.572234 | − | 0.820090i | \(-0.693923\pi\) | ||||
−0.572234 | + | 0.820090i | \(0.693923\pi\) | |||||||
\(180\) | 5.43455 | 0.405068 | ||||||||
\(181\) | 9.51985 | 0.707605 | 0.353802 | − | 0.935320i | \(-0.384889\pi\) | ||||
0.353802 | + | 0.935320i | \(0.384889\pi\) | |||||||
\(182\) | 11.7214 | 0.868851 | ||||||||
\(183\) | 4.97844 | 0.368017 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 16.7618 | 1.23235 | ||||||||
\(186\) | −6.99570 | −0.512950 | ||||||||
\(187\) | 4.40741 | 0.322302 | ||||||||
\(188\) | −3.01372 | −0.219798 | ||||||||
\(189\) | −1.61891 | −0.117758 | ||||||||
\(190\) | 4.81976 | 0.349662 | ||||||||
\(191\) | −22.7186 | −1.64386 | −0.821931 | − | 0.569588i | \(-0.807103\pi\) | ||||
−0.821931 | + | 0.569588i | \(0.807103\pi\) | |||||||
\(192\) | 2.50055 | 0.180462 | ||||||||
\(193\) | −10.7819 | −0.776098 | −0.388049 | − | 0.921639i | \(-0.626851\pi\) | ||||
−0.388049 | + | 0.921639i | \(0.626851\pi\) | |||||||
\(194\) | 2.22607 | 0.159822 | ||||||||
\(195\) | 19.1179 | 1.36906 | ||||||||
\(196\) | −0.438895 | −0.0313497 | ||||||||
\(197\) | −10.7522 | −0.766063 | −0.383031 | − | 0.923735i | \(-0.625120\pi\) | ||||
−0.383031 | + | 0.923735i | \(0.625120\pi\) | |||||||
\(198\) | −2.59461 | −0.184391 | ||||||||
\(199\) | 13.6905 | 0.970493 | 0.485247 | − | 0.874377i | \(-0.338730\pi\) | ||||
0.485247 | + | 0.874377i | \(0.338730\pi\) | |||||||
\(200\) | 2.20858 | 0.156170 | ||||||||
\(201\) | −20.7865 | −1.46617 | ||||||||
\(202\) | 13.7286 | 0.965939 | ||||||||
\(203\) | −2.56147 | −0.179780 | ||||||||
\(204\) | 13.8165 | 0.967350 | ||||||||
\(205\) | 13.4202 | 0.937310 | ||||||||
\(206\) | 0.609882 | 0.0424925 | ||||||||
\(207\) | −3.25275 | −0.226082 | ||||||||
\(208\) | 4.57607 | 0.317293 | ||||||||
\(209\) | −2.30109 | −0.159170 | ||||||||
\(210\) | 10.7013 | 0.738460 | ||||||||
\(211\) | −19.9301 | −1.37204 | −0.686022 | − | 0.727581i | \(-0.740645\pi\) | ||||
−0.686022 | + | 0.727581i | \(0.740645\pi\) | |||||||
\(212\) | 2.83475 | 0.194692 | ||||||||
\(213\) | −14.4418 | −0.989535 | ||||||||
\(214\) | −4.12882 | −0.282241 | ||||||||
\(215\) | 7.02291 | 0.478959 | ||||||||
\(216\) | −0.632025 | −0.0430038 | ||||||||
\(217\) | −7.16612 | −0.486468 | ||||||||
\(218\) | −16.5257 | −1.11926 | ||||||||
\(219\) | 5.40898 | 0.365505 | ||||||||
\(220\) | 1.33270 | 0.0898508 | ||||||||
\(221\) | 25.2846 | 1.70082 | ||||||||
\(222\) | −25.0866 | −1.68370 | ||||||||
\(223\) | 0.826796 | 0.0553664 | 0.0276832 | − | 0.999617i | \(-0.491187\pi\) | ||||
0.0276832 | + | 0.999617i | \(0.491187\pi\) | |||||||
\(224\) | 2.56147 | 0.171145 | ||||||||
\(225\) | −7.18396 | −0.478931 | ||||||||
\(226\) | 7.88907 | 0.524773 | ||||||||
\(227\) | −8.39006 | −0.556868 | −0.278434 | − | 0.960455i | \(-0.589815\pi\) | ||||
−0.278434 | + | 0.960455i | \(0.589815\pi\) | |||||||
\(228\) | −7.21354 | −0.477728 | ||||||||
\(229\) | 23.8313 | 1.57482 | 0.787409 | − | 0.616431i | \(-0.211422\pi\) | ||||
0.787409 | + | 0.616431i | \(0.211422\pi\) | |||||||
\(230\) | 1.67075 | 0.110166 | ||||||||
\(231\) | −5.10911 | −0.336155 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 12.4854 | 0.817945 | 0.408973 | − | 0.912547i | \(-0.365887\pi\) | ||||
0.408973 | + | 0.912547i | \(0.365887\pi\) | |||||||
\(234\) | −14.8848 | −0.973051 | ||||||||
\(235\) | −5.03519 | −0.328459 | ||||||||
\(236\) | −4.44699 | −0.289474 | ||||||||
\(237\) | −23.9360 | −1.55481 | ||||||||
\(238\) | 14.1531 | 0.917409 | ||||||||
\(239\) | 17.6596 | 1.14230 | 0.571152 | − | 0.820844i | \(-0.306497\pi\) | ||||
0.571152 | + | 0.820844i | \(0.306497\pi\) | |||||||
\(240\) | 4.17781 | 0.269676 | ||||||||
\(241\) | −13.0049 | −0.837719 | −0.418859 | − | 0.908051i | \(-0.637570\pi\) | ||||
−0.418859 | + | 0.908051i | \(0.637570\pi\) | |||||||
\(242\) | 10.3637 | 0.666206 | ||||||||
\(243\) | −22.3452 | −1.43345 | ||||||||
\(244\) | 1.99094 | 0.127457 | ||||||||
\(245\) | −0.733286 | −0.0468480 | ||||||||
\(246\) | −20.0855 | −1.28061 | ||||||||
\(247\) | −13.2009 | −0.839956 | ||||||||
\(248\) | −2.79767 | −0.177652 | ||||||||
\(249\) | 20.2236 | 1.28162 | ||||||||
\(250\) | 12.0438 | 0.761715 | ||||||||
\(251\) | 6.59864 | 0.416502 | 0.208251 | − | 0.978075i | \(-0.433223\pi\) | ||||
0.208251 | + | 0.978075i | \(0.433223\pi\) | |||||||
\(252\) | −8.33182 | −0.524855 | ||||||||
\(253\) | −0.797665 | −0.0501488 | ||||||||
\(254\) | −5.24015 | −0.328797 | ||||||||
\(255\) | 23.0840 | 1.44558 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.405645 | −0.0253035 | −0.0126517 | − | 0.999920i | \(-0.504027\pi\) | ||||
−0.0126517 | + | 0.999920i | \(0.504027\pi\) | |||||||
\(258\) | −10.5109 | −0.654380 | ||||||||
\(259\) | −25.6978 | −1.59678 | ||||||||
\(260\) | 7.64549 | 0.474153 | ||||||||
\(261\) | 3.25275 | 0.201340 | ||||||||
\(262\) | 13.2715 | 0.819915 | ||||||||
\(263\) | 24.4097 | 1.50516 | 0.752582 | − | 0.658499i | \(-0.228808\pi\) | ||||
0.752582 | + | 0.658499i | \(0.228808\pi\) | |||||||
\(264\) | −1.99460 | −0.122759 | ||||||||
\(265\) | 4.73618 | 0.290941 | ||||||||
\(266\) | −7.38926 | −0.453065 | ||||||||
\(267\) | 28.7215 | 1.75773 | ||||||||
\(268\) | −8.31278 | −0.507784 | ||||||||
\(269\) | −19.3943 | −1.18249 | −0.591245 | − | 0.806492i | \(-0.701363\pi\) | ||||
−0.591245 | + | 0.806492i | \(0.701363\pi\) | |||||||
\(270\) | −1.05596 | −0.0642636 | ||||||||
\(271\) | 32.8754 | 1.99704 | 0.998520 | − | 0.0543852i | \(-0.0173199\pi\) | ||||
0.998520 | + | 0.0543852i | \(0.0173199\pi\) | |||||||
\(272\) | 5.52539 | 0.335026 | ||||||||
\(273\) | −29.3101 | −1.77393 | ||||||||
\(274\) | 14.2454 | 0.860596 | ||||||||
\(275\) | −1.76171 | −0.106235 | ||||||||
\(276\) | −2.50055 | −0.150515 | ||||||||
\(277\) | −4.27774 | −0.257024 | −0.128512 | − | 0.991708i | \(-0.541020\pi\) | ||||
−0.128512 | + | 0.991708i | \(0.541020\pi\) | |||||||
\(278\) | −7.66694 | −0.459833 | ||||||||
\(279\) | 9.10012 | 0.544810 | ||||||||
\(280\) | 4.27958 | 0.255754 | ||||||||
\(281\) | −25.1758 | −1.50186 | −0.750930 | − | 0.660381i | \(-0.770395\pi\) | ||||
−0.750930 | + | 0.660381i | \(0.770395\pi\) | |||||||
\(282\) | 7.53596 | 0.448760 | ||||||||
\(283\) | −1.12929 | −0.0671295 | −0.0335648 | − | 0.999437i | \(-0.510686\pi\) | ||||
−0.0335648 | + | 0.999437i | \(0.510686\pi\) | |||||||
\(284\) | −5.77544 | −0.342709 | ||||||||
\(285\) | −12.0520 | −0.713902 | ||||||||
\(286\) | −3.65017 | −0.215839 | ||||||||
\(287\) | −20.5748 | −1.21449 | ||||||||
\(288\) | −3.25275 | −0.191670 | ||||||||
\(289\) | 13.5299 | 0.795879 | ||||||||
\(290\) | −1.67075 | −0.0981101 | ||||||||
\(291\) | −5.56640 | −0.326308 | ||||||||
\(292\) | 2.16312 | 0.126587 | ||||||||
\(293\) | −32.9587 | −1.92547 | −0.962735 | − | 0.270446i | \(-0.912829\pi\) | ||||
−0.962735 | + | 0.270446i | \(0.912829\pi\) | |||||||
\(294\) | 1.09748 | 0.0640063 | ||||||||
\(295\) | −7.42982 | −0.432581 | ||||||||
\(296\) | −10.0324 | −0.583124 | ||||||||
\(297\) | 0.504144 | 0.0292534 | ||||||||
\(298\) | −7.10247 | −0.411435 | ||||||||
\(299\) | −4.57607 | −0.264641 | ||||||||
\(300\) | −5.52266 | −0.318851 | ||||||||
\(301\) | −10.7670 | −0.620597 | ||||||||
\(302\) | −10.5988 | −0.609891 | ||||||||
\(303\) | −34.3290 | −1.97215 | ||||||||
\(304\) | −2.88478 | −0.165453 | ||||||||
\(305\) | 3.32637 | 0.190467 | ||||||||
\(306\) | −17.9727 | −1.02743 | ||||||||
\(307\) | 9.51666 | 0.543145 | 0.271572 | − | 0.962418i | \(-0.412456\pi\) | ||||
0.271572 | + | 0.962418i | \(0.412456\pi\) | |||||||
\(308\) | −2.04319 | −0.116422 | ||||||||
\(309\) | −1.52504 | −0.0867566 | ||||||||
\(310\) | −4.67421 | −0.265477 | ||||||||
\(311\) | −12.9151 | −0.732347 | −0.366174 | − | 0.930547i | \(-0.619332\pi\) | ||||
−0.366174 | + | 0.930547i | \(0.619332\pi\) | |||||||
\(312\) | −11.4427 | −0.647815 | ||||||||
\(313\) | −12.8731 | −0.727629 | −0.363814 | − | 0.931471i | \(-0.618526\pi\) | ||||
−0.363814 | + | 0.931471i | \(0.618526\pi\) | |||||||
\(314\) | 2.81055 | 0.158609 | ||||||||
\(315\) | −13.9204 | −0.784327 | ||||||||
\(316\) | −9.57229 | −0.538484 | ||||||||
\(317\) | 0.422244 | 0.0237156 | 0.0118578 | − | 0.999930i | \(-0.496225\pi\) | ||||
0.0118578 | + | 0.999930i | \(0.496225\pi\) | |||||||
\(318\) | −7.08845 | −0.397500 | ||||||||
\(319\) | 0.797665 | 0.0446607 | ||||||||
\(320\) | 1.67075 | 0.0933980 | ||||||||
\(321\) | 10.3243 | 0.576248 | ||||||||
\(322\) | −2.56147 | −0.142745 | ||||||||
\(323\) | −15.9395 | −0.886899 | ||||||||
\(324\) | −8.17785 | −0.454325 | ||||||||
\(325\) | −10.1066 | −0.560614 | ||||||||
\(326\) | −3.78302 | −0.209522 | ||||||||
\(327\) | 41.3234 | 2.28519 | ||||||||
\(328\) | −8.03244 | −0.443517 | ||||||||
\(329\) | 7.71954 | 0.425592 | ||||||||
\(330\) | −3.33249 | −0.183448 | ||||||||
\(331\) | −3.74901 | −0.206064 | −0.103032 | − | 0.994678i | \(-0.532854\pi\) | ||||
−0.103032 | + | 0.994678i | \(0.532854\pi\) | |||||||
\(332\) | 8.08767 | 0.443869 | ||||||||
\(333\) | 32.6331 | 1.78828 | ||||||||
\(334\) | 3.69622 | 0.202248 | ||||||||
\(335\) | −13.8886 | −0.758817 | ||||||||
\(336\) | −6.40507 | −0.349425 | ||||||||
\(337\) | −7.09496 | −0.386487 | −0.193243 | − | 0.981151i | \(-0.561901\pi\) | ||||
−0.193243 | + | 0.981151i | \(0.561901\pi\) | |||||||
\(338\) | −7.94040 | −0.431901 | ||||||||
\(339\) | −19.7270 | −1.07142 | ||||||||
\(340\) | 9.23157 | 0.500652 | ||||||||
\(341\) | 2.23160 | 0.120848 | ||||||||
\(342\) | 9.38348 | 0.507400 | ||||||||
\(343\) | 19.0545 | 1.02884 | ||||||||
\(344\) | −4.20344 | −0.226634 | ||||||||
\(345\) | −4.17781 | −0.224926 | ||||||||
\(346\) | 19.2973 | 1.03743 | ||||||||
\(347\) | −13.3641 | −0.717421 | −0.358711 | − | 0.933449i | \(-0.616784\pi\) | ||||
−0.358711 | + | 0.933449i | \(0.616784\pi\) | |||||||
\(348\) | 2.50055 | 0.134044 | ||||||||
\(349\) | 2.15690 | 0.115456 | 0.0577280 | − | 0.998332i | \(-0.481614\pi\) | ||||
0.0577280 | + | 0.998332i | \(0.481614\pi\) | |||||||
\(350\) | −5.65720 | −0.302390 | ||||||||
\(351\) | 2.89219 | 0.154374 | ||||||||
\(352\) | −0.797665 | −0.0425157 | ||||||||
\(353\) | −30.3090 | −1.61318 | −0.806592 | − | 0.591109i | \(-0.798690\pi\) | ||||
−0.806592 | + | 0.591109i | \(0.798690\pi\) | |||||||
\(354\) | 11.1199 | 0.591017 | ||||||||
\(355\) | −9.64935 | −0.512134 | ||||||||
\(356\) | 11.4861 | 0.608761 | ||||||||
\(357\) | −35.3905 | −1.87307 | ||||||||
\(358\) | 15.3120 | 0.809262 | ||||||||
\(359\) | 36.0830 | 1.90439 | 0.952193 | − | 0.305496i | \(-0.0988224\pi\) | ||||
0.952193 | + | 0.305496i | \(0.0988224\pi\) | |||||||
\(360\) | −5.43455 | −0.286426 | ||||||||
\(361\) | −10.6781 | −0.562003 | ||||||||
\(362\) | −9.51985 | −0.500352 | ||||||||
\(363\) | −25.9150 | −1.36019 | ||||||||
\(364\) | −11.7214 | −0.614370 | ||||||||
\(365\) | 3.61404 | 0.189167 | ||||||||
\(366\) | −4.97844 | −0.260227 | ||||||||
\(367\) | −31.3302 | −1.63542 | −0.817712 | − | 0.575628i | \(-0.804758\pi\) | ||||
−0.817712 | + | 0.575628i | \(0.804758\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 26.1276 | 1.36015 | ||||||||
\(370\) | −16.7618 | −0.871402 | ||||||||
\(371\) | −7.26112 | −0.376979 | ||||||||
\(372\) | 6.99570 | 0.362710 | ||||||||
\(373\) | 15.6582 | 0.810752 | 0.405376 | − | 0.914150i | \(-0.367141\pi\) | ||||
0.405376 | + | 0.914150i | \(0.367141\pi\) | |||||||
\(374\) | −4.40741 | −0.227902 | ||||||||
\(375\) | −30.1161 | −1.55519 | ||||||||
\(376\) | 3.01372 | 0.155421 | ||||||||
\(377\) | 4.57607 | 0.235679 | ||||||||
\(378\) | 1.61891 | 0.0832677 | ||||||||
\(379\) | −16.3594 | −0.840328 | −0.420164 | − | 0.907448i | \(-0.638027\pi\) | ||||
−0.420164 | + | 0.907448i | \(0.638027\pi\) | |||||||
\(380\) | −4.81976 | −0.247248 | ||||||||
\(381\) | 13.1033 | 0.671301 | ||||||||
\(382\) | 22.7186 | 1.16239 | ||||||||
\(383\) | −5.88216 | −0.300564 | −0.150282 | − | 0.988643i | \(-0.548018\pi\) | ||||
−0.150282 | + | 0.988643i | \(0.548018\pi\) | |||||||
\(384\) | −2.50055 | −0.127606 | ||||||||
\(385\) | −3.41367 | −0.173977 | ||||||||
\(386\) | 10.7819 | 0.548784 | ||||||||
\(387\) | 13.6727 | 0.695025 | ||||||||
\(388\) | −2.22607 | −0.113012 | ||||||||
\(389\) | 23.6381 | 1.19850 | 0.599249 | − | 0.800563i | \(-0.295466\pi\) | ||||
0.599249 | + | 0.800563i | \(0.295466\pi\) | |||||||
\(390\) | −19.1179 | −0.968074 | ||||||||
\(391\) | −5.52539 | −0.279431 | ||||||||
\(392\) | 0.438895 | 0.0221676 | ||||||||
\(393\) | −33.1860 | −1.67401 | ||||||||
\(394\) | 10.7522 | 0.541688 | ||||||||
\(395\) | −15.9930 | −0.804693 | ||||||||
\(396\) | 2.59461 | 0.130384 | ||||||||
\(397\) | −11.5658 | −0.580470 | −0.290235 | − | 0.956955i | \(-0.593734\pi\) | ||||
−0.290235 | + | 0.956955i | \(0.593734\pi\) | |||||||
\(398\) | −13.6905 | −0.686242 | ||||||||
\(399\) | 18.4772 | 0.925018 | ||||||||
\(400\) | −2.20858 | −0.110429 | ||||||||
\(401\) | 19.1684 | 0.957222 | 0.478611 | − | 0.878027i | \(-0.341140\pi\) | ||||
0.478611 | + | 0.878027i | \(0.341140\pi\) | |||||||
\(402\) | 20.7865 | 1.03674 | ||||||||
\(403\) | 12.8023 | 0.637728 | ||||||||
\(404\) | −13.7286 | −0.683022 | ||||||||
\(405\) | −13.6632 | −0.678929 | ||||||||
\(406\) | 2.56147 | 0.127123 | ||||||||
\(407\) | 8.00253 | 0.396671 | ||||||||
\(408\) | −13.8165 | −0.684020 | ||||||||
\(409\) | −21.3116 | −1.05379 | −0.526896 | − | 0.849930i | \(-0.676644\pi\) | ||||
−0.526896 | + | 0.849930i | \(0.676644\pi\) | |||||||
\(410\) | −13.4202 | −0.662779 | ||||||||
\(411\) | −35.6214 | −1.75707 | ||||||||
\(412\) | −0.609882 | −0.0300467 | ||||||||
\(413\) | 11.3908 | 0.560505 | ||||||||
\(414\) | 3.25275 | 0.159864 | ||||||||
\(415\) | 13.5125 | 0.663303 | ||||||||
\(416\) | −4.57607 | −0.224360 | ||||||||
\(417\) | 19.1716 | 0.938836 | ||||||||
\(418\) | 2.30109 | 0.112550 | ||||||||
\(419\) | −14.3124 | −0.699208 | −0.349604 | − | 0.936898i | \(-0.613684\pi\) | ||||
−0.349604 | + | 0.936898i | \(0.613684\pi\) | |||||||
\(420\) | −10.7013 | −0.522170 | ||||||||
\(421\) | −9.65385 | −0.470500 | −0.235250 | − | 0.971935i | \(-0.575591\pi\) | ||||
−0.235250 | + | 0.971935i | \(0.575591\pi\) | |||||||
\(422\) | 19.9301 | 0.970182 | ||||||||
\(423\) | −9.80289 | −0.476633 | ||||||||
\(424\) | −2.83475 | −0.137668 | ||||||||
\(425\) | −12.2033 | −0.591945 | ||||||||
\(426\) | 14.4418 | 0.699707 | ||||||||
\(427\) | −5.09971 | −0.246792 | ||||||||
\(428\) | 4.12882 | 0.199574 | ||||||||
\(429\) | 9.12744 | 0.440677 | ||||||||
\(430\) | −7.02291 | −0.338675 | ||||||||
\(431\) | 5.59657 | 0.269577 | 0.134789 | − | 0.990874i | \(-0.456964\pi\) | ||||
0.134789 | + | 0.990874i | \(0.456964\pi\) | |||||||
\(432\) | 0.632025 | 0.0304083 | ||||||||
\(433\) | 1.30326 | 0.0626305 | 0.0313152 | − | 0.999510i | \(-0.490030\pi\) | ||||
0.0313152 | + | 0.999510i | \(0.490030\pi\) | |||||||
\(434\) | 7.16612 | 0.343985 | ||||||||
\(435\) | 4.17781 | 0.200311 | ||||||||
\(436\) | 16.5257 | 0.791438 | ||||||||
\(437\) | 2.88478 | 0.137998 | ||||||||
\(438\) | −5.40898 | −0.258451 | ||||||||
\(439\) | 40.7442 | 1.94462 | 0.972308 | − | 0.233702i | \(-0.0750841\pi\) | ||||
0.972308 | + | 0.233702i | \(0.0750841\pi\) | |||||||
\(440\) | −1.33270 | −0.0635341 | ||||||||
\(441\) | −1.42762 | −0.0679818 | ||||||||
\(442\) | −25.2846 | −1.20266 | ||||||||
\(443\) | −34.5364 | −1.64087 | −0.820436 | − | 0.571739i | \(-0.806269\pi\) | ||||
−0.820436 | + | 0.571739i | \(0.806269\pi\) | |||||||
\(444\) | 25.0866 | 1.19056 | ||||||||
\(445\) | 19.1904 | 0.909713 | ||||||||
\(446\) | −0.826796 | −0.0391499 | ||||||||
\(447\) | 17.7601 | 0.840024 | ||||||||
\(448\) | −2.56147 | −0.121018 | ||||||||
\(449\) | 29.2908 | 1.38232 | 0.691159 | − | 0.722703i | \(-0.257101\pi\) | ||||
0.691159 | + | 0.722703i | \(0.257101\pi\) | |||||||
\(450\) | 7.18396 | 0.338655 | ||||||||
\(451\) | 6.40720 | 0.301703 | ||||||||
\(452\) | −7.88907 | −0.371071 | ||||||||
\(453\) | 26.5028 | 1.24521 | ||||||||
\(454\) | 8.39006 | 0.393765 | ||||||||
\(455\) | −19.5837 | −0.918096 | ||||||||
\(456\) | 7.21354 | 0.337805 | ||||||||
\(457\) | 14.8536 | 0.694822 | 0.347411 | − | 0.937713i | \(-0.387061\pi\) | ||||
0.347411 | + | 0.937713i | \(0.387061\pi\) | |||||||
\(458\) | −23.8313 | −1.11356 | ||||||||
\(459\) | 3.49218 | 0.163001 | ||||||||
\(460\) | −1.67075 | −0.0778993 | ||||||||
\(461\) | −4.31663 | −0.201046 | −0.100523 | − | 0.994935i | \(-0.532052\pi\) | ||||
−0.100523 | + | 0.994935i | \(0.532052\pi\) | |||||||
\(462\) | 5.10911 | 0.237697 | ||||||||
\(463\) | 29.3881 | 1.36578 | 0.682891 | − | 0.730520i | \(-0.260722\pi\) | ||||
0.682891 | + | 0.730520i | \(0.260722\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 11.6881 | 0.542023 | ||||||||
\(466\) | −12.4854 | −0.578375 | ||||||||
\(467\) | −18.9264 | −0.875810 | −0.437905 | − | 0.899021i | \(-0.644279\pi\) | ||||
−0.437905 | + | 0.899021i | \(0.644279\pi\) | |||||||
\(468\) | 14.8848 | 0.688051 | ||||||||
\(469\) | 21.2929 | 0.983215 | ||||||||
\(470\) | 5.03519 | 0.232256 | ||||||||
\(471\) | −7.02793 | −0.323830 | ||||||||
\(472\) | 4.44699 | 0.204689 | ||||||||
\(473\) | 3.35294 | 0.154168 | ||||||||
\(474\) | 23.9360 | 1.09942 | ||||||||
\(475\) | 6.37126 | 0.292333 | ||||||||
\(476\) | −14.1531 | −0.648706 | ||||||||
\(477\) | 9.22076 | 0.422189 | ||||||||
\(478\) | −17.6596 | −0.807731 | ||||||||
\(479\) | −16.1906 | −0.739768 | −0.369884 | − | 0.929078i | \(-0.620603\pi\) | ||||
−0.369884 | + | 0.929078i | \(0.620603\pi\) | |||||||
\(480\) | −4.17781 | −0.190690 | ||||||||
\(481\) | 45.9091 | 2.09328 | ||||||||
\(482\) | 13.0049 | 0.592357 | ||||||||
\(483\) | 6.40507 | 0.291441 | ||||||||
\(484\) | −10.3637 | −0.471079 | ||||||||
\(485\) | −3.71922 | −0.168881 | ||||||||
\(486\) | 22.3452 | 1.01360 | ||||||||
\(487\) | −31.6066 | −1.43223 | −0.716116 | − | 0.697981i | \(-0.754082\pi\) | ||||
−0.716116 | + | 0.697981i | \(0.754082\pi\) | |||||||
\(488\) | −1.99094 | −0.0901255 | ||||||||
\(489\) | 9.45963 | 0.427779 | ||||||||
\(490\) | 0.733286 | 0.0331265 | ||||||||
\(491\) | −24.1949 | −1.09190 | −0.545950 | − | 0.837818i | \(-0.683831\pi\) | ||||
−0.545950 | + | 0.837818i | \(0.683831\pi\) | |||||||
\(492\) | 20.0855 | 0.905526 | ||||||||
\(493\) | 5.52539 | 0.248851 | ||||||||
\(494\) | 13.2009 | 0.593939 | ||||||||
\(495\) | 4.33496 | 0.194842 | ||||||||
\(496\) | 2.79767 | 0.125619 | ||||||||
\(497\) | 14.7936 | 0.663583 | ||||||||
\(498\) | −20.2236 | −0.906242 | ||||||||
\(499\) | 4.23893 | 0.189761 | 0.0948803 | − | 0.995489i | \(-0.469753\pi\) | ||||
0.0948803 | + | 0.995489i | \(0.469753\pi\) | |||||||
\(500\) | −12.0438 | −0.538614 | ||||||||
\(501\) | −9.24258 | −0.412928 | ||||||||
\(502\) | −6.59864 | −0.294512 | ||||||||
\(503\) | −9.94415 | −0.443388 | −0.221694 | − | 0.975116i | \(-0.571159\pi\) | ||||
−0.221694 | + | 0.975116i | \(0.571159\pi\) | |||||||
\(504\) | 8.33182 | 0.371129 | ||||||||
\(505\) | −22.9371 | −1.02069 | ||||||||
\(506\) | 0.797665 | 0.0354606 | ||||||||
\(507\) | 19.8554 | 0.881808 | ||||||||
\(508\) | 5.24015 | 0.232494 | ||||||||
\(509\) | −20.8154 | −0.922627 | −0.461314 | − | 0.887237i | \(-0.652622\pi\) | ||||
−0.461314 | + | 0.887237i | \(0.652622\pi\) | |||||||
\(510\) | −23.0840 | −1.02218 | ||||||||
\(511\) | −5.54075 | −0.245108 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.82325 | −0.0804985 | ||||||||
\(514\) | 0.405645 | 0.0178922 | ||||||||
\(515\) | −1.01896 | −0.0449009 | ||||||||
\(516\) | 10.5109 | 0.462717 | ||||||||
\(517\) | −2.40394 | −0.105725 | ||||||||
\(518\) | 25.6978 | 1.12909 | ||||||||
\(519\) | −48.2540 | −2.11811 | ||||||||
\(520\) | −7.64549 | −0.335277 | ||||||||
\(521\) | 11.9399 | 0.523097 | 0.261549 | − | 0.965190i | \(-0.415767\pi\) | ||||
0.261549 | + | 0.965190i | \(0.415767\pi\) | |||||||
\(522\) | −3.25275 | −0.142369 | ||||||||
\(523\) | 31.7743 | 1.38939 | 0.694696 | − | 0.719303i | \(-0.255539\pi\) | ||||
0.694696 | + | 0.719303i | \(0.255539\pi\) | |||||||
\(524\) | −13.2715 | −0.579767 | ||||||||
\(525\) | 14.1461 | 0.617387 | ||||||||
\(526\) | −24.4097 | −1.06431 | ||||||||
\(527\) | 15.4582 | 0.673369 | ||||||||
\(528\) | 1.99460 | 0.0868040 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −4.73618 | −0.205726 | ||||||||
\(531\) | −14.4649 | −0.627725 | ||||||||
\(532\) | 7.38926 | 0.320365 | ||||||||
\(533\) | 36.7570 | 1.59212 | ||||||||
\(534\) | −28.7215 | −1.24290 | ||||||||
\(535\) | 6.89825 | 0.298238 | ||||||||
\(536\) | 8.31278 | 0.359058 | ||||||||
\(537\) | −38.2883 | −1.65226 | ||||||||
\(538\) | 19.3943 | 0.836147 | ||||||||
\(539\) | −0.350092 | −0.0150795 | ||||||||
\(540\) | 1.05596 | 0.0454412 | ||||||||
\(541\) | −32.9076 | −1.41481 | −0.707403 | − | 0.706810i | \(-0.750134\pi\) | ||||
−0.707403 | + | 0.706810i | \(0.750134\pi\) | |||||||
\(542\) | −32.8754 | −1.41212 | ||||||||
\(543\) | 23.8049 | 1.02156 | ||||||||
\(544\) | −5.52539 | −0.236899 | ||||||||
\(545\) | 27.6104 | 1.18270 | ||||||||
\(546\) | 29.3101 | 1.25435 | ||||||||
\(547\) | 12.7196 | 0.543850 | 0.271925 | − | 0.962319i | \(-0.412340\pi\) | ||||
0.271925 | + | 0.962319i | \(0.412340\pi\) | |||||||
\(548\) | −14.2454 | −0.608534 | ||||||||
\(549\) | 6.47603 | 0.276390 | ||||||||
\(550\) | 1.76171 | 0.0751194 | ||||||||
\(551\) | −2.88478 | −0.122896 | ||||||||
\(552\) | 2.50055 | 0.106431 | ||||||||
\(553\) | 24.5191 | 1.04266 | ||||||||
\(554\) | 4.27774 | 0.181744 | ||||||||
\(555\) | 41.9136 | 1.77913 | ||||||||
\(556\) | 7.66694 | 0.325151 | ||||||||
\(557\) | −37.1466 | −1.57395 | −0.786975 | − | 0.616985i | \(-0.788354\pi\) | ||||
−0.786975 | + | 0.616985i | \(0.788354\pi\) | |||||||
\(558\) | −9.10012 | −0.385239 | ||||||||
\(559\) | 19.2352 | 0.813563 | ||||||||
\(560\) | −4.27958 | −0.180845 | ||||||||
\(561\) | 11.0210 | 0.465305 | ||||||||
\(562\) | 25.1758 | 1.06198 | ||||||||
\(563\) | −16.8374 | −0.709613 | −0.354807 | − | 0.934940i | \(-0.615453\pi\) | ||||
−0.354807 | + | 0.934940i | \(0.615453\pi\) | |||||||
\(564\) | −7.53596 | −0.317321 | ||||||||
\(565\) | −13.1807 | −0.554516 | ||||||||
\(566\) | 1.12929 | 0.0474678 | ||||||||
\(567\) | 20.9473 | 0.879703 | ||||||||
\(568\) | 5.77544 | 0.242332 | ||||||||
\(569\) | 11.7904 | 0.494279 | 0.247139 | − | 0.968980i | \(-0.420509\pi\) | ||||
0.247139 | + | 0.968980i | \(0.420509\pi\) | |||||||
\(570\) | 12.0520 | 0.504805 | ||||||||
\(571\) | −20.8665 | −0.873235 | −0.436618 | − | 0.899647i | \(-0.643824\pi\) | ||||
−0.436618 | + | 0.899647i | \(0.643824\pi\) | |||||||
\(572\) | 3.65017 | 0.152621 | ||||||||
\(573\) | −56.8090 | −2.37323 | ||||||||
\(574\) | 20.5748 | 0.858777 | ||||||||
\(575\) | 2.20858 | 0.0921041 | ||||||||
\(576\) | 3.25275 | 0.135531 | ||||||||
\(577\) | −5.34570 | −0.222544 | −0.111272 | − | 0.993790i | \(-0.535493\pi\) | ||||
−0.111272 | + | 0.993790i | \(0.535493\pi\) | |||||||
\(578\) | −13.5299 | −0.562771 | ||||||||
\(579\) | −26.9607 | −1.12045 | ||||||||
\(580\) | 1.67075 | 0.0693743 | ||||||||
\(581\) | −20.7163 | −0.859456 | ||||||||
\(582\) | 5.56640 | 0.230735 | ||||||||
\(583\) | 2.26118 | 0.0936487 | ||||||||
\(584\) | −2.16312 | −0.0895104 | ||||||||
\(585\) | 24.8689 | 1.02820 | ||||||||
\(586\) | 32.9587 | 1.36151 | ||||||||
\(587\) | −18.7393 | −0.773452 | −0.386726 | − | 0.922195i | \(-0.626394\pi\) | ||||
−0.386726 | + | 0.922195i | \(0.626394\pi\) | |||||||
\(588\) | −1.09748 | −0.0452593 | ||||||||
\(589\) | −8.07065 | −0.332545 | ||||||||
\(590\) | 7.42982 | 0.305881 | ||||||||
\(591\) | −26.8864 | −1.10596 | ||||||||
\(592\) | 10.0324 | 0.412331 | ||||||||
\(593\) | 27.5959 | 1.13323 | 0.566614 | − | 0.823983i | \(-0.308253\pi\) | ||||
0.566614 | + | 0.823983i | \(0.308253\pi\) | |||||||
\(594\) | −0.504144 | −0.0206853 | ||||||||
\(595\) | −23.6464 | −0.969406 | ||||||||
\(596\) | 7.10247 | 0.290929 | ||||||||
\(597\) | 34.2338 | 1.40109 | ||||||||
\(598\) | 4.57607 | 0.187129 | ||||||||
\(599\) | −11.2382 | −0.459181 | −0.229590 | − | 0.973287i | \(-0.573739\pi\) | ||||
−0.229590 | + | 0.973287i | \(0.573739\pi\) | |||||||
\(600\) | 5.52266 | 0.225462 | ||||||||
\(601\) | 11.2614 | 0.459361 | 0.229680 | − | 0.973266i | \(-0.426232\pi\) | ||||
0.229680 | + | 0.973266i | \(0.426232\pi\) | |||||||
\(602\) | 10.7670 | 0.438828 | ||||||||
\(603\) | −27.0394 | −1.10113 | ||||||||
\(604\) | 10.5988 | 0.431258 | ||||||||
\(605\) | −17.3153 | −0.703965 | ||||||||
\(606\) | 34.3290 | 1.39452 | ||||||||
\(607\) | 0.676999 | 0.0274785 | 0.0137393 | − | 0.999906i | \(-0.495627\pi\) | ||||
0.0137393 | + | 0.999906i | \(0.495627\pi\) | |||||||
\(608\) | 2.88478 | 0.116993 | ||||||||
\(609\) | −6.40507 | −0.259547 | ||||||||
\(610\) | −3.32637 | −0.134681 | ||||||||
\(611\) | −13.7910 | −0.557924 | ||||||||
\(612\) | 17.9727 | 0.726505 | ||||||||
\(613\) | 24.4238 | 0.986468 | 0.493234 | − | 0.869897i | \(-0.335815\pi\) | ||||
0.493234 | + | 0.869897i | \(0.335815\pi\) | |||||||
\(614\) | −9.51666 | −0.384061 | ||||||||
\(615\) | 33.5580 | 1.35319 | ||||||||
\(616\) | 2.04319 | 0.0823226 | ||||||||
\(617\) | 27.8613 | 1.12166 | 0.560828 | − | 0.827933i | \(-0.310483\pi\) | ||||
0.560828 | + | 0.827933i | \(0.310483\pi\) | |||||||
\(618\) | 1.52504 | 0.0613462 | ||||||||
\(619\) | 35.3185 | 1.41957 | 0.709785 | − | 0.704419i | \(-0.248792\pi\) | ||||
0.709785 | + | 0.704419i | \(0.248792\pi\) | |||||||
\(620\) | 4.67421 | 0.187721 | ||||||||
\(621\) | −0.632025 | −0.0253623 | ||||||||
\(622\) | 12.9151 | 0.517848 | ||||||||
\(623\) | −29.4212 | −1.17873 | ||||||||
\(624\) | 11.4427 | 0.458074 | ||||||||
\(625\) | −9.07929 | −0.363172 | ||||||||
\(626\) | 12.8731 | 0.514511 | ||||||||
\(627\) | −5.75399 | −0.229792 | ||||||||
\(628\) | −2.81055 | −0.112153 | ||||||||
\(629\) | 55.4332 | 2.21026 | ||||||||
\(630\) | 13.9204 | 0.554603 | ||||||||
\(631\) | 3.46959 | 0.138122 | 0.0690611 | − | 0.997612i | \(-0.478000\pi\) | ||||
0.0690611 | + | 0.997612i | \(0.478000\pi\) | |||||||
\(632\) | 9.57229 | 0.380765 | ||||||||
\(633\) | −49.8362 | −1.98081 | ||||||||
\(634\) | −0.422244 | −0.0167694 | ||||||||
\(635\) | 8.75501 | 0.347432 | ||||||||
\(636\) | 7.08845 | 0.281075 | ||||||||
\(637\) | −2.00841 | −0.0795763 | ||||||||
\(638\) | −0.797665 | −0.0315799 | ||||||||
\(639\) | −18.7861 | −0.743166 | ||||||||
\(640\) | −1.67075 | −0.0660424 | ||||||||
\(641\) | −22.8078 | −0.900855 | −0.450427 | − | 0.892813i | \(-0.648728\pi\) | ||||
−0.450427 | + | 0.892813i | \(0.648728\pi\) | |||||||
\(642\) | −10.3243 | −0.407469 | ||||||||
\(643\) | 3.36423 | 0.132672 | 0.0663362 | − | 0.997797i | \(-0.478869\pi\) | ||||
0.0663362 | + | 0.997797i | \(0.478869\pi\) | |||||||
\(644\) | 2.56147 | 0.100936 | ||||||||
\(645\) | 17.5611 | 0.691469 | ||||||||
\(646\) | 15.9395 | 0.627132 | ||||||||
\(647\) | −18.1759 | −0.714570 | −0.357285 | − | 0.933995i | \(-0.616298\pi\) | ||||
−0.357285 | + | 0.933995i | \(0.616298\pi\) | |||||||
\(648\) | 8.17785 | 0.321256 | ||||||||
\(649\) | −3.54721 | −0.139240 | ||||||||
\(650\) | 10.1066 | 0.396414 | ||||||||
\(651\) | −17.9193 | −0.702311 | ||||||||
\(652\) | 3.78302 | 0.148154 | ||||||||
\(653\) | 21.2301 | 0.830798 | 0.415399 | − | 0.909639i | \(-0.363642\pi\) | ||||
0.415399 | + | 0.909639i | \(0.363642\pi\) | |||||||
\(654\) | −41.3234 | −1.61587 | ||||||||
\(655\) | −22.1734 | −0.866386 | ||||||||
\(656\) | 8.03244 | 0.313614 | ||||||||
\(657\) | 7.03609 | 0.274504 | ||||||||
\(658\) | −7.71954 | −0.300939 | ||||||||
\(659\) | −32.6757 | −1.27287 | −0.636433 | − | 0.771332i | \(-0.719591\pi\) | ||||
−0.636433 | + | 0.771332i | \(0.719591\pi\) | |||||||
\(660\) | 3.33249 | 0.129717 | ||||||||
\(661\) | −34.5493 | −1.34381 | −0.671907 | − | 0.740636i | \(-0.734524\pi\) | ||||
−0.671907 | + | 0.740636i | \(0.734524\pi\) | |||||||
\(662\) | 3.74901 | 0.145709 | ||||||||
\(663\) | 63.2253 | 2.45547 | ||||||||
\(664\) | −8.08767 | −0.313862 | ||||||||
\(665\) | 12.3456 | 0.478744 | ||||||||
\(666\) | −32.6331 | −1.26451 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −3.69622 | −0.143011 | ||||||||
\(669\) | 2.06745 | 0.0799321 | ||||||||
\(670\) | 13.8886 | 0.536564 | ||||||||
\(671\) | 1.58810 | 0.0613080 | ||||||||
\(672\) | 6.40507 | 0.247081 | ||||||||
\(673\) | 18.5932 | 0.716716 | 0.358358 | − | 0.933584i | \(-0.383337\pi\) | ||||
0.358358 | + | 0.933584i | \(0.383337\pi\) | |||||||
\(674\) | 7.09496 | 0.273288 | ||||||||
\(675\) | −1.39588 | −0.0537273 | ||||||||
\(676\) | 7.94040 | 0.305400 | ||||||||
\(677\) | 10.3135 | 0.396381 | 0.198190 | − | 0.980164i | \(-0.436494\pi\) | ||||
0.198190 | + | 0.980164i | \(0.436494\pi\) | |||||||
\(678\) | 19.7270 | 0.757612 | ||||||||
\(679\) | 5.70200 | 0.218823 | ||||||||
\(680\) | −9.23157 | −0.354015 | ||||||||
\(681\) | −20.9798 | −0.803946 | ||||||||
\(682\) | −2.23160 | −0.0854524 | ||||||||
\(683\) | 4.79758 | 0.183574 | 0.0917872 | − | 0.995779i | \(-0.470742\pi\) | ||||
0.0917872 | + | 0.995779i | \(0.470742\pi\) | |||||||
\(684\) | −9.38348 | −0.358786 | ||||||||
\(685\) | −23.8006 | −0.909373 | ||||||||
\(686\) | −19.0545 | −0.727503 | ||||||||
\(687\) | 59.5914 | 2.27355 | ||||||||
\(688\) | 4.20344 | 0.160254 | ||||||||
\(689\) | 12.9720 | 0.494195 | ||||||||
\(690\) | 4.17781 | 0.159046 | ||||||||
\(691\) | −15.7460 | −0.599008 | −0.299504 | − | 0.954095i | \(-0.596821\pi\) | ||||
−0.299504 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(692\) | −19.2973 | −0.733575 | ||||||||
\(693\) | −6.64600 | −0.252461 | ||||||||
\(694\) | 13.3641 | 0.507293 | ||||||||
\(695\) | 12.8096 | 0.485895 | ||||||||
\(696\) | −2.50055 | −0.0947831 | ||||||||
\(697\) | 44.3824 | 1.68110 | ||||||||
\(698\) | −2.15690 | −0.0816398 | ||||||||
\(699\) | 31.2204 | 1.18086 | ||||||||
\(700\) | 5.65720 | 0.213822 | ||||||||
\(701\) | 1.37538 | 0.0519474 | 0.0259737 | − | 0.999663i | \(-0.491731\pi\) | ||||
0.0259737 | + | 0.999663i | \(0.491731\pi\) | |||||||
\(702\) | −2.89219 | −0.109159 | ||||||||
\(703\) | −28.9414 | −1.09154 | ||||||||
\(704\) | 0.797665 | 0.0300631 | ||||||||
\(705\) | −12.5907 | −0.474195 | ||||||||
\(706\) | 30.3090 | 1.14069 | ||||||||
\(707\) | 35.1653 | 1.32253 | ||||||||
\(708\) | −11.1199 | −0.417912 | ||||||||
\(709\) | 28.2420 | 1.06065 | 0.530325 | − | 0.847795i | \(-0.322070\pi\) | ||||
0.530325 | + | 0.847795i | \(0.322070\pi\) | |||||||
\(710\) | 9.64935 | 0.362133 | ||||||||
\(711\) | −31.1363 | −1.16770 | ||||||||
\(712\) | −11.4861 | −0.430459 | ||||||||
\(713\) | −2.79767 | −0.104773 | ||||||||
\(714\) | 35.3905 | 1.32446 | ||||||||
\(715\) | 6.09854 | 0.228072 | ||||||||
\(716\) | −15.3120 | −0.572234 | ||||||||
\(717\) | 44.1587 | 1.64914 | ||||||||
\(718\) | −36.0830 | −1.34660 | ||||||||
\(719\) | 41.5078 | 1.54798 | 0.773990 | − | 0.633198i | \(-0.218258\pi\) | ||||
0.773990 | + | 0.633198i | \(0.218258\pi\) | |||||||
\(720\) | 5.43455 | 0.202534 | ||||||||
\(721\) | 1.56219 | 0.0581791 | ||||||||
\(722\) | 10.6781 | 0.397396 | ||||||||
\(723\) | −32.5194 | −1.20941 | ||||||||
\(724\) | 9.51985 | 0.353802 | ||||||||
\(725\) | −2.20858 | −0.0820245 | ||||||||
\(726\) | 25.9150 | 0.961797 | ||||||||
\(727\) | −5.52586 | −0.204943 | −0.102471 | − | 0.994736i | \(-0.532675\pi\) | ||||
−0.102471 | + | 0.994736i | \(0.532675\pi\) | |||||||
\(728\) | 11.7214 | 0.434425 | ||||||||
\(729\) | −31.3418 | −1.16081 | ||||||||
\(730\) | −3.61404 | −0.133762 | ||||||||
\(731\) | 23.2256 | 0.859031 | ||||||||
\(732\) | 4.97844 | 0.184008 | ||||||||
\(733\) | 25.6062 | 0.945785 | 0.472892 | − | 0.881120i | \(-0.343210\pi\) | ||||
0.472892 | + | 0.881120i | \(0.343210\pi\) | |||||||
\(734\) | 31.3302 | 1.15642 | ||||||||
\(735\) | −1.83362 | −0.0676341 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −6.63082 | −0.244249 | ||||||||
\(738\) | −26.1276 | −0.961769 | ||||||||
\(739\) | 33.8805 | 1.24631 | 0.623157 | − | 0.782097i | \(-0.285850\pi\) | ||||
0.623157 | + | 0.782097i | \(0.285850\pi\) | |||||||
\(740\) | 16.7618 | 0.616174 | ||||||||
\(741\) | −33.0096 | −1.21264 | ||||||||
\(742\) | 7.26112 | 0.266564 | ||||||||
\(743\) | −50.4493 | −1.85081 | −0.925404 | − | 0.378983i | \(-0.876274\pi\) | ||||
−0.925404 | + | 0.378983i | \(0.876274\pi\) | |||||||
\(744\) | −6.99570 | −0.256475 | ||||||||
\(745\) | 11.8665 | 0.434755 | ||||||||
\(746\) | −15.6582 | −0.573288 | ||||||||
\(747\) | 26.3072 | 0.962530 | ||||||||
\(748\) | 4.40741 | 0.161151 | ||||||||
\(749\) | −10.5758 | −0.386433 | ||||||||
\(750\) | 30.1161 | 1.09968 | ||||||||
\(751\) | 4.77959 | 0.174410 | 0.0872049 | − | 0.996190i | \(-0.472207\pi\) | ||||
0.0872049 | + | 0.996190i | \(0.472207\pi\) | |||||||
\(752\) | −3.01372 | −0.109899 | ||||||||
\(753\) | 16.5002 | 0.601302 | ||||||||
\(754\) | −4.57607 | −0.166651 | ||||||||
\(755\) | 17.7080 | 0.644459 | ||||||||
\(756\) | −1.61891 | −0.0588792 | ||||||||
\(757\) | 46.3627 | 1.68508 | 0.842541 | − | 0.538633i | \(-0.181059\pi\) | ||||
0.842541 | + | 0.538633i | \(0.181059\pi\) | |||||||
\(758\) | 16.3594 | 0.594202 | ||||||||
\(759\) | −1.99460 | −0.0723995 | ||||||||
\(760\) | 4.81976 | 0.174831 | ||||||||
\(761\) | 45.1079 | 1.63516 | 0.817580 | − | 0.575815i | \(-0.195315\pi\) | ||||
0.817580 | + | 0.575815i | \(0.195315\pi\) | |||||||
\(762\) | −13.1033 | −0.474681 | ||||||||
\(763\) | −42.3300 | −1.53245 | ||||||||
\(764\) | −22.7186 | −0.821931 | ||||||||
\(765\) | 30.0280 | 1.08567 | ||||||||
\(766\) | 5.88216 | 0.212531 | ||||||||
\(767\) | −20.3497 | −0.734785 | ||||||||
\(768\) | 2.50055 | 0.0902309 | ||||||||
\(769\) | 13.2403 | 0.477456 | 0.238728 | − | 0.971087i | \(-0.423270\pi\) | ||||
0.238728 | + | 0.971087i | \(0.423270\pi\) | |||||||
\(770\) | 3.41367 | 0.123020 | ||||||||
\(771\) | −1.01434 | −0.0365304 | ||||||||
\(772\) | −10.7819 | −0.388049 | ||||||||
\(773\) | 23.0111 | 0.827651 | 0.413826 | − | 0.910356i | \(-0.364192\pi\) | ||||
0.413826 | + | 0.910356i | \(0.364192\pi\) | |||||||
\(774\) | −13.6727 | −0.491457 | ||||||||
\(775\) | −6.17886 | −0.221951 | ||||||||
\(776\) | 2.22607 | 0.0799112 | ||||||||
\(777\) | −64.2585 | −2.30526 | ||||||||
\(778\) | −23.6381 | −0.847466 | ||||||||
\(779\) | −23.1718 | −0.830217 | ||||||||
\(780\) | 19.1179 | 0.684532 | ||||||||
\(781\) | −4.60687 | −0.164847 | ||||||||
\(782\) | 5.52539 | 0.197588 | ||||||||
\(783\) | 0.632025 | 0.0225867 | ||||||||
\(784\) | −0.438895 | −0.0156748 | ||||||||
\(785\) | −4.69574 | −0.167598 | ||||||||
\(786\) | 33.1860 | 1.18371 | ||||||||
\(787\) | −44.0639 | −1.57071 | −0.785354 | − | 0.619047i | \(-0.787519\pi\) | ||||
−0.785354 | + | 0.619047i | \(0.787519\pi\) | |||||||
\(788\) | −10.7522 | −0.383031 | ||||||||
\(789\) | 61.0376 | 2.17300 | ||||||||
\(790\) | 15.9930 | 0.569004 | ||||||||
\(791\) | 20.2076 | 0.718499 | ||||||||
\(792\) | −2.59461 | −0.0921954 | ||||||||
\(793\) | 9.11066 | 0.323529 | ||||||||
\(794\) | 11.5658 | 0.410454 | ||||||||
\(795\) | 11.8431 | 0.420030 | ||||||||
\(796\) | 13.6905 | 0.485247 | ||||||||
\(797\) | 22.9165 | 0.811746 | 0.405873 | − | 0.913930i | \(-0.366968\pi\) | ||||
0.405873 | + | 0.913930i | \(0.366968\pi\) | |||||||
\(798\) | −18.4772 | −0.654087 | ||||||||
\(799\) | −16.6520 | −0.589105 | ||||||||
\(800\) | 2.20858 | 0.0780850 | ||||||||
\(801\) | 37.3614 | 1.32010 | ||||||||
\(802\) | −19.1684 | −0.676858 | ||||||||
\(803\) | 1.72544 | 0.0608896 | ||||||||
\(804\) | −20.7865 | −0.733085 | ||||||||
\(805\) | 4.27958 | 0.150835 | ||||||||
\(806\) | −12.8023 | −0.450942 | ||||||||
\(807\) | −48.4964 | −1.70715 | ||||||||
\(808\) | 13.7286 | 0.482969 | ||||||||
\(809\) | −31.9211 | −1.12229 | −0.561144 | − | 0.827718i | \(-0.689639\pi\) | ||||
−0.561144 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(810\) | 13.6632 | 0.480075 | ||||||||
\(811\) | 32.2097 | 1.13103 | 0.565517 | − | 0.824737i | \(-0.308677\pi\) | ||||
0.565517 | + | 0.824737i | \(0.308677\pi\) | |||||||
\(812\) | −2.56147 | −0.0898898 | ||||||||
\(813\) | 82.2067 | 2.88311 | ||||||||
\(814\) | −8.00253 | −0.280489 | ||||||||
\(815\) | 6.32050 | 0.221397 | ||||||||
\(816\) | 13.8165 | 0.483675 | ||||||||
\(817\) | −12.1260 | −0.424234 | ||||||||
\(818\) | 21.3116 | 0.745144 | ||||||||
\(819\) | −38.1270 | −1.33226 | ||||||||
\(820\) | 13.4202 | 0.468655 | ||||||||
\(821\) | 31.5158 | 1.09991 | 0.549954 | − | 0.835195i | \(-0.314645\pi\) | ||||
0.549954 | + | 0.835195i | \(0.314645\pi\) | |||||||
\(822\) | 35.6214 | 1.24244 | ||||||||
\(823\) | 37.8969 | 1.32100 | 0.660501 | − | 0.750825i | \(-0.270344\pi\) | ||||
0.660501 | + | 0.750825i | \(0.270344\pi\) | |||||||
\(824\) | 0.609882 | 0.0212463 | ||||||||
\(825\) | −4.40524 | −0.153371 | ||||||||
\(826\) | −11.3908 | −0.396337 | ||||||||
\(827\) | 23.5001 | 0.817178 | 0.408589 | − | 0.912719i | \(-0.366021\pi\) | ||||
0.408589 | + | 0.912719i | \(0.366021\pi\) | |||||||
\(828\) | −3.25275 | −0.113041 | ||||||||
\(829\) | 12.1249 | 0.421114 | 0.210557 | − | 0.977582i | \(-0.432472\pi\) | ||||
0.210557 | + | 0.977582i | \(0.432472\pi\) | |||||||
\(830\) | −13.5125 | −0.469026 | ||||||||
\(831\) | −10.6967 | −0.371064 | ||||||||
\(832\) | 4.57607 | 0.158647 | ||||||||
\(833\) | −2.42507 | −0.0840236 | ||||||||
\(834\) | −19.1716 | −0.663857 | ||||||||
\(835\) | −6.17547 | −0.213711 | ||||||||
\(836\) | −2.30109 | −0.0795848 | ||||||||
\(837\) | 1.76819 | 0.0611177 | ||||||||
\(838\) | 14.3124 | 0.494414 | ||||||||
\(839\) | 26.4482 | 0.913094 | 0.456547 | − | 0.889699i | \(-0.349086\pi\) | ||||
0.456547 | + | 0.889699i | \(0.349086\pi\) | |||||||
\(840\) | 10.7013 | 0.369230 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 9.65385 | 0.332693 | ||||||||
\(843\) | −62.9533 | −2.16823 | ||||||||
\(844\) | −19.9301 | −0.686022 | ||||||||
\(845\) | 13.2665 | 0.456380 | ||||||||
\(846\) | 9.80289 | 0.337030 | ||||||||
\(847\) | 26.5463 | 0.912143 | ||||||||
\(848\) | 2.83475 | 0.0973458 | ||||||||
\(849\) | −2.82386 | −0.0969145 | ||||||||
\(850\) | 12.2033 | 0.418568 | ||||||||
\(851\) | −10.0324 | −0.343908 | ||||||||
\(852\) | −14.4418 | −0.494767 | ||||||||
\(853\) | 14.0206 | 0.480057 | 0.240028 | − | 0.970766i | \(-0.422843\pi\) | ||||
0.240028 | + | 0.970766i | \(0.422843\pi\) | |||||||
\(854\) | 5.09971 | 0.174509 | ||||||||
\(855\) | −15.6775 | −0.536159 | ||||||||
\(856\) | −4.12882 | −0.141120 | ||||||||
\(857\) | 11.0292 | 0.376751 | 0.188375 | − | 0.982097i | \(-0.439678\pi\) | ||||
0.188375 | + | 0.982097i | \(0.439678\pi\) | |||||||
\(858\) | −9.12744 | −0.311606 | ||||||||
\(859\) | −42.6614 | −1.45559 | −0.727793 | − | 0.685796i | \(-0.759454\pi\) | ||||
−0.727793 | + | 0.685796i | \(0.759454\pi\) | |||||||
\(860\) | 7.02291 | 0.239479 | ||||||||
\(861\) | −51.4484 | −1.75336 | ||||||||
\(862\) | −5.59657 | −0.190620 | ||||||||
\(863\) | −0.518121 | −0.0176370 | −0.00881851 | − | 0.999961i | \(-0.502807\pi\) | ||||
−0.00881851 | + | 0.999961i | \(0.502807\pi\) | |||||||
\(864\) | −0.632025 | −0.0215019 | ||||||||
\(865\) | −32.2411 | −1.09623 | ||||||||
\(866\) | −1.30326 | −0.0442864 | ||||||||
\(867\) | 33.8323 | 1.14900 | ||||||||
\(868\) | −7.16612 | −0.243234 | ||||||||
\(869\) | −7.63549 | −0.259016 | ||||||||
\(870\) | −4.17781 | −0.141641 | ||||||||
\(871\) | −38.0399 | −1.28893 | ||||||||
\(872\) | −16.5257 | −0.559631 | ||||||||
\(873\) | −7.24085 | −0.245066 | ||||||||
\(874\) | −2.88478 | −0.0975791 | ||||||||
\(875\) | 30.8497 | 1.04291 | ||||||||
\(876\) | 5.40898 | 0.182753 | ||||||||
\(877\) | 19.3340 | 0.652862 | 0.326431 | − | 0.945221i | \(-0.394154\pi\) | ||||
0.326431 | + | 0.945221i | \(0.394154\pi\) | |||||||
\(878\) | −40.7442 | −1.37505 | ||||||||
\(879\) | −82.4150 | −2.77979 | ||||||||
\(880\) | 1.33270 | 0.0449254 | ||||||||
\(881\) | 17.5513 | 0.591319 | 0.295660 | − | 0.955293i | \(-0.404461\pi\) | ||||
0.295660 | + | 0.955293i | \(0.404461\pi\) | |||||||
\(882\) | 1.42762 | 0.0480704 | ||||||||
\(883\) | −1.01735 | −0.0342366 | −0.0171183 | − | 0.999853i | \(-0.505449\pi\) | ||||
−0.0171183 | + | 0.999853i | \(0.505449\pi\) | |||||||
\(884\) | 25.2846 | 0.850412 | ||||||||
\(885\) | −18.5786 | −0.624514 | ||||||||
\(886\) | 34.5364 | 1.16027 | ||||||||
\(887\) | 20.0120 | 0.671937 | 0.335969 | − | 0.941873i | \(-0.390936\pi\) | ||||
0.335969 | + | 0.941873i | \(0.390936\pi\) | |||||||
\(888\) | −25.0866 | −0.841852 | ||||||||
\(889\) | −13.4225 | −0.450175 | ||||||||
\(890\) | −19.1904 | −0.643264 | ||||||||
\(891\) | −6.52319 | −0.218535 | ||||||||
\(892\) | 0.826796 | 0.0276832 | ||||||||
\(893\) | 8.69392 | 0.290931 | ||||||||
\(894\) | −17.7601 | −0.593986 | ||||||||
\(895\) | −25.5825 | −0.855129 | ||||||||
\(896\) | 2.56147 | 0.0855726 | ||||||||
\(897\) | −11.4427 | −0.382060 | ||||||||
\(898\) | −29.2908 | −0.977446 | ||||||||
\(899\) | 2.79767 | 0.0933074 | ||||||||
\(900\) | −7.18396 | −0.239465 | ||||||||
\(901\) | 15.6631 | 0.521814 | ||||||||
\(902\) | −6.40720 | −0.213336 | ||||||||
\(903\) | −26.9233 | −0.895952 | ||||||||
\(904\) | 7.88907 | 0.262387 | ||||||||
\(905\) | 15.9053 | 0.528711 | ||||||||
\(906\) | −26.5028 | −0.880496 | ||||||||
\(907\) | −14.1315 | −0.469228 | −0.234614 | − | 0.972089i | \(-0.575383\pi\) | ||||
−0.234614 | + | 0.972089i | \(0.575383\pi\) | |||||||
\(908\) | −8.39006 | −0.278434 | ||||||||
\(909\) | −44.6557 | −1.48113 | ||||||||
\(910\) | 19.5837 | 0.649192 | ||||||||
\(911\) | 0.128010 | 0.00424118 | 0.00212059 | − | 0.999998i | \(-0.499325\pi\) | ||||
0.00212059 | + | 0.999998i | \(0.499325\pi\) | |||||||
\(912\) | −7.21354 | −0.238864 | ||||||||
\(913\) | 6.45125 | 0.213505 | ||||||||
\(914\) | −14.8536 | −0.491314 | ||||||||
\(915\) | 8.31775 | 0.274976 | ||||||||
\(916\) | 23.8313 | 0.787409 | ||||||||
\(917\) | 33.9944 | 1.12259 | ||||||||
\(918\) | −3.49218 | −0.115259 | ||||||||
\(919\) | 4.54799 | 0.150024 | 0.0750121 | − | 0.997183i | \(-0.476100\pi\) | ||||
0.0750121 | + | 0.997183i | \(0.476100\pi\) | |||||||
\(920\) | 1.67075 | 0.0550832 | ||||||||
\(921\) | 23.7969 | 0.784134 | ||||||||
\(922\) | 4.31663 | 0.142161 | ||||||||
\(923\) | −26.4288 | −0.869915 | ||||||||
\(924\) | −5.10911 | −0.168077 | ||||||||
\(925\) | −22.1574 | −0.728532 | ||||||||
\(926\) | −29.3881 | −0.965754 | ||||||||
\(927\) | −1.98380 | −0.0651564 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 43.6631 | 1.43254 | 0.716271 | − | 0.697823i | \(-0.245848\pi\) | ||||
0.716271 | + | 0.697823i | \(0.245848\pi\) | |||||||
\(930\) | −11.6881 | −0.383268 | ||||||||
\(931\) | 1.26612 | 0.0414953 | ||||||||
\(932\) | 12.4854 | 0.408973 | ||||||||
\(933\) | −32.2948 | −1.05729 | ||||||||
\(934\) | 18.9264 | 0.619291 | ||||||||
\(935\) | 7.36371 | 0.240819 | ||||||||
\(936\) | −14.8848 | −0.486526 | ||||||||
\(937\) | 2.64749 | 0.0864896 | 0.0432448 | − | 0.999065i | \(-0.486230\pi\) | ||||
0.0432448 | + | 0.999065i | \(0.486230\pi\) | |||||||
\(938\) | −21.2929 | −0.695238 | ||||||||
\(939\) | −32.1898 | −1.05047 | ||||||||
\(940\) | −5.03519 | −0.164230 | ||||||||
\(941\) | 1.71934 | 0.0560488 | 0.0280244 | − | 0.999607i | \(-0.491078\pi\) | ||||
0.0280244 | + | 0.999607i | \(0.491078\pi\) | |||||||
\(942\) | 7.02793 | 0.228982 | ||||||||
\(943\) | −8.03244 | −0.261572 | ||||||||
\(944\) | −4.44699 | −0.144737 | ||||||||
\(945\) | −2.70480 | −0.0879872 | ||||||||
\(946\) | −3.35294 | −0.109013 | ||||||||
\(947\) | 3.71518 | 0.120727 | 0.0603635 | − | 0.998176i | \(-0.480774\pi\) | ||||
0.0603635 | + | 0.998176i | \(0.480774\pi\) | |||||||
\(948\) | −23.9360 | −0.777405 | ||||||||
\(949\) | 9.89857 | 0.321321 | ||||||||
\(950\) | −6.37126 | −0.206711 | ||||||||
\(951\) | 1.05584 | 0.0342380 | ||||||||
\(952\) | 14.1531 | 0.458704 | ||||||||
\(953\) | −30.0759 | −0.974255 | −0.487127 | − | 0.873331i | \(-0.661955\pi\) | ||||
−0.487127 | + | 0.873331i | \(0.661955\pi\) | |||||||
\(954\) | −9.22076 | −0.298533 | ||||||||
\(955\) | −37.9572 | −1.22827 | ||||||||
\(956\) | 17.6596 | 0.571152 | ||||||||
\(957\) | 1.99460 | 0.0644764 | ||||||||
\(958\) | 16.1906 | 0.523095 | ||||||||
\(959\) | 36.4891 | 1.17829 | ||||||||
\(960\) | 4.17781 | 0.134838 | ||||||||
\(961\) | −23.1731 | −0.747518 | ||||||||
\(962\) | −45.9091 | −1.48017 | ||||||||
\(963\) | 13.4301 | 0.432777 | ||||||||
\(964\) | −13.0049 | −0.418859 | ||||||||
\(965\) | −18.0139 | −0.579888 | ||||||||
\(966\) | −6.40507 | −0.206080 | ||||||||
\(967\) | −55.4004 | −1.78156 | −0.890778 | − | 0.454439i | \(-0.849840\pi\) | ||||
−0.890778 | + | 0.454439i | \(0.849840\pi\) | |||||||
\(968\) | 10.3637 | 0.333103 | ||||||||
\(969\) | −39.8576 | −1.28041 | ||||||||
\(970\) | 3.71922 | 0.119417 | ||||||||
\(971\) | −36.5221 | −1.17205 | −0.586025 | − | 0.810293i | \(-0.699308\pi\) | ||||
−0.586025 | + | 0.810293i | \(0.699308\pi\) | |||||||
\(972\) | −22.3452 | −0.716723 | ||||||||
\(973\) | −19.6386 | −0.629585 | ||||||||
\(974\) | 31.6066 | 1.01274 | ||||||||
\(975\) | −25.2721 | −0.809354 | ||||||||
\(976\) | 1.99094 | 0.0637283 | ||||||||
\(977\) | 18.6925 | 0.598025 | 0.299013 | − | 0.954249i | \(-0.403343\pi\) | ||||
0.299013 | + | 0.954249i | \(0.403343\pi\) | |||||||
\(978\) | −9.45963 | −0.302486 | ||||||||
\(979\) | 9.16205 | 0.292820 | ||||||||
\(980\) | −0.733286 | −0.0234240 | ||||||||
\(981\) | 53.7541 | 1.71623 | ||||||||
\(982\) | 24.1949 | 0.772090 | ||||||||
\(983\) | −20.0322 | −0.638928 | −0.319464 | − | 0.947598i | \(-0.603503\pi\) | ||||
−0.319464 | + | 0.947598i | \(0.603503\pi\) | |||||||
\(984\) | −20.0855 | −0.640303 | ||||||||
\(985\) | −17.9643 | −0.572390 | ||||||||
\(986\) | −5.52539 | −0.175964 | ||||||||
\(987\) | 19.3031 | 0.614424 | ||||||||
\(988\) | −13.2009 | −0.419978 | ||||||||
\(989\) | −4.20344 | −0.133661 | ||||||||
\(990\) | −4.33496 | −0.137774 | ||||||||
\(991\) | 51.9608 | 1.65059 | 0.825295 | − | 0.564703i | \(-0.191009\pi\) | ||||
0.825295 | + | 0.564703i | \(0.191009\pi\) | |||||||
\(992\) | −2.79767 | −0.0888260 | ||||||||
\(993\) | −9.37459 | −0.297494 | ||||||||
\(994\) | −14.7936 | −0.469224 | ||||||||
\(995\) | 22.8735 | 0.725137 | ||||||||
\(996\) | 20.2236 | 0.640810 | ||||||||
\(997\) | −17.3787 | −0.550388 | −0.275194 | − | 0.961389i | \(-0.588742\pi\) | ||||
−0.275194 | + | 0.961389i | \(0.588742\pi\) | |||||||
\(998\) | −4.23893 | −0.134181 | ||||||||
\(999\) | 6.34075 | 0.200612 |
(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 | 1334.2.a.j.1.9 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.j.1.9 | ✓ | 9 | 1.1 | even | 1 | trivial |