Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1004,2,Mod(1,1004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1004, 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("1004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1004 = 2^{2} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1004.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: | \(8.01698036294\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 6x^{5} + 18x^{4} + 8x^{3} - 17x^{2} - 9x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.40474\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1004.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.40474 | −0.811027 | −0.405513 | − | 0.914089i | \(-0.632907\pi\) | ||||
−0.405513 | + | 0.914089i | \(0.632907\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.59588 | 1.16091 | 0.580456 | − | 0.814292i | \(-0.302874\pi\) | ||||
0.580456 | + | 0.814292i | \(0.302874\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.10443 | 0.417434 | 0.208717 | − | 0.977976i | \(-0.433071\pi\) | ||||
0.208717 | + | 0.977976i | \(0.433071\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.02671 | −0.342236 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.46000 | −1.64625 | −0.823125 | − | 0.567860i | \(-0.807772\pi\) | ||||
−0.823125 | + | 0.567860i | \(0.807772\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.10841 | −0.584768 | −0.292384 | − | 0.956301i | \(-0.594449\pi\) | ||||
−0.292384 | + | 0.956301i | \(0.594449\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.64653 | −0.941530 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.93466 | −0.469223 | −0.234612 | − | 0.972089i | \(-0.575382\pi\) | ||||
−0.234612 | + | 0.972089i | \(0.575382\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.08955 | −0.938207 | −0.469104 | − | 0.883143i | \(-0.655423\pi\) | ||||
−0.469104 | + | 0.883143i | \(0.655423\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.55143 | −0.338550 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.90552 | −0.605842 | −0.302921 | − | 0.953016i | \(-0.597962\pi\) | ||||
−0.302921 | + | 0.953016i | \(0.597962\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.73858 | 0.347717 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65647 | 1.08859 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.78201 | 1.07369 | 0.536846 | − | 0.843680i | \(-0.319616\pi\) | ||||
0.536846 | + | 0.843680i | \(0.319616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.15076 | −0.206682 | −0.103341 | − | 0.994646i | \(-0.532953\pi\) | ||||
−0.103341 | + | 0.994646i | \(0.532953\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.66987 | 1.33515 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.86696 | 0.484604 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.95339 | −0.321136 | −0.160568 | − | 0.987025i | \(-0.551333\pi\) | ||||
−0.160568 | + | 0.987025i | \(0.551333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.96177 | 0.474263 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.94481 | 0.459902 | 0.229951 | − | 0.973202i | \(-0.426143\pi\) | ||||
0.229951 | + | 0.973202i | \(0.426143\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.50361 | −0.991792 | −0.495896 | − | 0.868382i | \(-0.665160\pi\) | ||||
−0.495896 | + | 0.868382i | \(0.665160\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.66521 | −0.397306 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.0399 | −1.61033 | −0.805164 | − | 0.593052i | \(-0.797923\pi\) | ||||
−0.805164 | + | 0.593052i | \(0.797923\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.78024 | −0.825749 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.71769 | 0.380552 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0920517 | 0.0126443 | 0.00632214 | − | 0.999980i | \(-0.497988\pi\) | ||||
0.00632214 | + | 0.999980i | \(0.497988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.1735 | −1.91115 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.74475 | 0.760911 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.65539 | 0.215513 | 0.107757 | − | 0.994177i | \(-0.465633\pi\) | ||||
0.107757 | + | 0.994177i | \(0.465633\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.04551 | 0.646011 | 0.323006 | − | 0.946397i | \(-0.395307\pi\) | ||||
0.323006 | + | 0.946397i | \(0.395307\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.13392 | −0.142861 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.47318 | −0.678865 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.55699 | 1.04540 | 0.522701 | − | 0.852516i | \(-0.324924\pi\) | ||||
0.522701 | + | 0.852516i | \(0.324924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.08149 | 0.491354 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.42422 | −0.881093 | −0.440546 | − | 0.897730i | \(-0.645215\pi\) | ||||
−0.440546 | + | 0.897730i | \(0.645215\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9708 | −1.28403 | −0.642017 | − | 0.766690i | \(-0.721902\pi\) | ||||
−0.642017 | + | 0.766690i | \(0.721902\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.44226 | −0.282008 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.03016 | −0.687201 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.18613 | −0.808503 | −0.404251 | − | 0.914648i | \(-0.632468\pi\) | ||||
−0.404251 | + | 0.914648i | \(0.632468\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.86575 | −0.540639 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.37870 | −0.700153 | −0.350077 | − | 0.936721i | \(-0.613844\pi\) | ||||
−0.350077 | + | 0.936721i | \(0.613844\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.02213 | −0.544727 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.12221 | −0.870793 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.8905 | 1.47239 | 0.736197 | − | 0.676768i | \(-0.236620\pi\) | ||||
0.736197 | + | 0.676768i | \(0.236620\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.32859 | −0.244102 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.61651 | 0.167625 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.6160 | −1.08918 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.75331 | −0.279557 | −0.139778 | − | 0.990183i | \(-0.544639\pi\) | ||||
−0.139778 | + | 0.990183i | \(0.544639\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.60582 | 0.563406 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.06894 | −0.305370 | −0.152685 | − | 0.988275i | \(-0.548792\pi\) | ||||
−0.152685 | + | 0.988275i | \(0.548792\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.79994 | −0.275886 | −0.137943 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137943 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.02733 | −0.393027 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.66878 | 0.451348 | 0.225674 | − | 0.974203i | \(-0.427542\pi\) | ||||
0.225674 | + | 0.974203i | \(0.427542\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.48753 | −0.334045 | −0.167022 | − | 0.985953i | \(-0.553415\pi\) | ||||
−0.167022 | + | 0.985953i | \(0.553415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.74401 | 0.260450 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.92000 | 0.556907 | 0.278453 | − | 0.960450i | \(-0.410178\pi\) | ||||
0.278453 | + | 0.960450i | \(0.410178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.54237 | −0.703329 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.16472 | 0.200129 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.13668 | −0.195870 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.8116 | 1.71014 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.13669 | −0.372993 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.46624 | −0.757243 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.21223 | 0.551246 | 0.275623 | − | 0.961266i | \(-0.411116\pi\) | ||||
0.275623 | + | 0.961266i | \(0.411116\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.13588 | 0.804370 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.0021 | −1.83497 | −0.917483 | − | 0.397775i | \(-0.869782\pi\) | ||||
−0.917483 | + | 0.397775i | \(0.869782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.51661 | −0.391639 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.6835 | 1.26376 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.1926 | 1.12712 | 0.563561 | − | 0.826074i | \(-0.309431\pi\) | ||||
0.563561 | + | 0.826074i | \(0.309431\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.3023 | 1.55238 | 0.776189 | − | 0.630500i | \(-0.217150\pi\) | ||||
0.776189 | + | 0.630500i | \(0.217150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.5081 | 1.30602 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5119 | 0.962675 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.0094 | 1.24646 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.11973 | 0.669704 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.18031 | −0.752080 | −0.376040 | − | 0.926603i | \(-0.622715\pi\) | ||||
−0.376040 | + | 0.926603i | \(0.622715\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.48773 | −0.690721 | −0.345361 | − | 0.938470i | \(-0.612243\pi\) | ||||
−0.345361 | + | 0.938470i | \(0.612243\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.98633 | 0.160585 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.98723 | −0.239940 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.28279 | −0.261995 | −0.130997 | − | 0.991383i | \(-0.541818\pi\) | ||||
−0.130997 | + | 0.991383i | \(0.541818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.129309 | −0.0102548 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.20893 | −0.252899 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.22646 | 0.722672 | 0.361336 | − | 0.932436i | \(-0.382321\pi\) | ||||
0.361336 | + | 0.932436i | \(0.382321\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.9101 | 1.55000 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.73551 | 0.366445 | 0.183222 | − | 0.983071i | \(-0.441347\pi\) | ||||
0.183222 | + | 0.983071i | \(0.441347\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.55460 | −0.658046 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.19877 | 0.321088 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.0022 | 1.52074 | 0.760370 | − | 0.649490i | \(-0.225018\pi\) | ||||
0.760370 | + | 0.649490i | \(0.225018\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.92014 | 0.145149 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.32539 | −0.174787 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0679 | 1.27571 | 0.637857 | − | 0.770154i | \(-0.279821\pi\) | ||||
0.637857 | + | 0.770154i | \(0.279821\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.50078 | −0.185881 | −0.0929406 | − | 0.995672i | \(-0.529627\pi\) | ||||
−0.0929406 | + | 0.995672i | \(0.529627\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.08762 | −0.523932 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.07077 | −0.372810 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.5632 | 0.772459 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.24716 | 0.454414 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.68883 | −0.556344 | −0.278172 | − | 0.960531i | \(-0.589728\pi\) | ||||
−0.278172 | + | 0.960531i | \(0.589728\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.5929 | −1.12240 | −0.561200 | − | 0.827680i | \(-0.689660\pi\) | ||||
−0.561200 | + | 0.827680i | \(0.689660\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.68839 | 0.550577 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.8677 | 0.845540 | 0.422770 | − | 0.906237i | \(-0.361058\pi\) | ||||
0.422770 | + | 0.906237i | \(0.361058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.6493 | −1.25113 | −0.625564 | − | 0.780173i | \(-0.715131\pi\) | ||||
−0.625564 | + | 0.780173i | \(0.715131\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.0203 | −0.847849 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.38580 | 0.448195 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.64437 | 0.533906 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.98312 | 0.207341 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.3289 | 1.54452 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.98934 | 0.687695 | 0.343847 | − | 0.939026i | \(-0.388270\pi\) | ||||
0.343847 | + | 0.939026i | \(0.388270\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.4291 | 0.714590 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.8826 | −1.15138 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.27093 | −0.0862761 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.4111 | 1.04139 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.07905 | 0.274387 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.67597 | 0.580986 | 0.290493 | − | 0.956877i | \(-0.406181\pi\) | ||||
0.290493 | + | 0.956877i | \(0.406181\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.78502 | −0.119001 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.23123 | −0.479954 | −0.239977 | − | 0.970779i | \(-0.577140\pi\) | ||||
−0.239977 | + | 0.970779i | \(0.577140\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.43014 | 0.0945064 | 0.0472532 | − | 0.998883i | \(-0.484953\pi\) | ||||
0.0472532 | + | 0.998883i | \(0.484953\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.47081 | 0.557338 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.2713 | 0.869434 | 0.434717 | − | 0.900567i | \(-0.356848\pi\) | ||||
0.434717 | + | 0.900567i | \(0.356848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −28.6581 | −1.86945 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0946 | 0.655717 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.5612 | 1.58873 | 0.794367 | − | 0.607438i | \(-0.207803\pi\) | ||||
0.794367 | + | 0.607438i | \(0.207803\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.2498 | −0.917909 | −0.458954 | − | 0.888460i | \(-0.651776\pi\) | ||||
−0.458954 | + | 0.888460i | \(0.651776\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.1343 | −0.650117 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.0048 | −0.958622 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.62246 | 0.548634 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.96041 | 0.567843 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8641 | 0.997368 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.05478 | 0.441788 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.65887 | 0.103478 | 0.0517388 | − | 0.998661i | \(-0.483524\pi\) | ||||
0.0517388 | + | 0.998661i | \(0.483524\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.15738 | −0.134053 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.93643 | −0.367456 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.5458 | 0.711947 | 0.355973 | − | 0.934496i | \(-0.384149\pi\) | ||||
0.355973 | + | 0.934496i | \(0.384149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.238955 | 0.0146789 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.5126 | −1.19415 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.3225 | −1.90977 | −0.954883 | − | 0.296981i | \(-0.904020\pi\) | ||||
−0.954883 | + | 0.296981i | \(0.904020\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.81449 | 0.231714 | 0.115857 | − | 0.993266i | \(-0.463039\pi\) | ||||
0.115857 | + | 0.993266i | \(0.463039\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.27106 | 0.197973 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −9.49266 | −0.572429 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.9064 | −1.43640 | −0.718198 | − | 0.695839i | \(-0.755033\pi\) | ||||
−0.718198 | + | 0.695839i | \(0.755033\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.18149 | 0.0707341 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.78573 | 0.106528 | 0.0532638 | − | 0.998580i | \(-0.483038\pi\) | ||||
0.0532638 | + | 0.998580i | \(0.483038\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.2483 | 1.44141 | 0.720707 | − | 0.693240i | \(-0.243817\pi\) | ||||
0.720707 | + | 0.693240i | \(0.243817\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.9127 | 0.883351 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.25233 | 0.191979 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2571 | −0.779830 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.86769 | 0.226728 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.10405 | 0.415023 | 0.207511 | − | 0.978233i | \(-0.433464\pi\) | ||||
0.207511 | + | 0.978233i | \(0.433464\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.29719 | 0.250192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −30.8843 | −1.79209 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.12603 | 0.354277 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.18276 | −0.414008 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.31105 | 0.247664 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.0975 | 0.749962 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0293 | 1.25728 | 0.628638 | − | 0.777698i | \(-0.283613\pi\) | ||||
0.628638 | + | 0.777698i | \(0.283613\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.93319 | 0.223751 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −28.7818 | −1.63207 | −0.816033 | − | 0.578005i | \(-0.803832\pi\) | ||||
−0.816033 | + | 0.578005i | \(0.803832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.68002 | −0.377577 | −0.188788 | − | 0.982018i | \(-0.560456\pi\) | ||||
−0.188788 | + | 0.982018i | \(0.560456\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.94353 | −0.165849 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9722 | 1.23408 | 0.617042 | − | 0.786930i | \(-0.288331\pi\) | ||||
0.617042 | + | 0.786930i | \(0.288331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.5697 | −1.76757 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.55842 | −0.366055 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.91187 | 0.440228 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.66565 | −0.203334 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.89907 | 0.270919 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.1927 | −0.672205 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.3052 | −1.55580 | −0.777898 | − | 0.628391i | \(-0.783714\pi\) | ||||
−0.777898 | + | 0.628391i | \(0.783714\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.00556 | 0.109904 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.2129 | 1.21362 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.4431 | −0.950188 | −0.475094 | − | 0.879935i | \(-0.657586\pi\) | ||||
−0.475094 | + | 0.879935i | \(0.657586\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.31606 | −0.451666 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.28313 | 0.340251 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.1148 | −0.762129 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.5951 | 0.570419 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.2757 | 1.08846 | 0.544228 | − | 0.838938i | \(-0.316823\pi\) | ||||
0.544228 | + | 0.838938i | \(0.316823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.1505 | 1.45333 | 0.726667 | − | 0.686989i | \(-0.241068\pi\) | ||||
0.726667 | + | 0.686989i | \(0.241068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.9262 | −0.636572 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.2047 | 0.915712 | 0.457856 | − | 0.889026i | \(-0.348618\pi\) | ||||
0.457856 | + | 0.889026i | \(0.348618\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.2724 | −1.02287 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00148 | 0.158855 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.5600 | −1.24345 | −0.621725 | − | 0.783235i | \(-0.713568\pi\) | ||||
−0.621725 | + | 0.783235i | \(0.713568\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.27558 | −0.119767 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.4253 | −1.38697 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.4788 | −1.49065 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.66133 | 0.452118 | 0.226059 | − | 0.974114i | \(-0.427416\pi\) | ||||
0.226059 | + | 0.974114i | \(0.427416\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.02346 | −0.157395 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.101664 | 0.00527815 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.6387 | −0.913297 | −0.456649 | − | 0.889647i | \(-0.650950\pi\) | ||||
−0.456649 | + | 0.889647i | \(0.650950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.8929 | 0.614145 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.1909 | −0.627861 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.78961 | −0.246026 | −0.123013 | − | 0.992405i | \(-0.539256\pi\) | ||||
−0.123013 | + | 0.992405i | \(0.539256\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.72657 | −0.447075 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.4931 | 1.55813 | 0.779063 | − | 0.626946i | \(-0.215695\pi\) | ||||
0.779063 | + | 0.626946i | \(0.215695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.6536 | −0.797780 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.67731 | 0.339427 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.9287 | 1.01043 | 0.505214 | − | 0.862994i | \(-0.331414\pi\) | ||||
0.505214 | + | 0.862994i | \(0.331414\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.62117 | 0.284275 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.5025 | 1.48821 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −18.6543 | −0.938601 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.65870 | −0.233814 | −0.116907 | − | 0.993143i | \(-0.537298\pi\) | ||||
−0.116907 | + | 0.993143i | \(0.537298\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.34465 | 0.317630 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.41181 | 0.370128 | 0.185064 | − | 0.982726i | \(-0.440751\pi\) | ||||
0.185064 | + | 0.982726i | \(0.440751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.42627 | 0.120861 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.6309 | −0.627634 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6655 | 0.528670 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.64037 | −0.278899 | −0.139449 | − | 0.990229i | \(-0.544533\pi\) | ||||
−0.139449 | + | 0.990229i | \(0.544533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.5322 | −0.914126 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.82826 | 0.0899626 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.5583 | −0.812816 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.7099 | −1.25902 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.5560 | 0.662255 | 0.331128 | − | 0.943586i | \(-0.392571\pi\) | ||||
0.331128 | + | 0.943586i | \(0.392571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.7306 | 1.35151 | 0.675753 | − | 0.737129i | \(-0.263819\pi\) | ||||
0.675753 | + | 0.737129i | \(0.263819\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 11.3347 | 0.551112 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.36356 | −0.163157 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.57239 | 0.269667 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.1712 | −0.780755 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.2175 | 0.588496 | 0.294248 | − | 0.955729i | \(-0.404931\pi\) | ||||
0.294248 | + | 0.955729i | \(0.404931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3759 | −0.738920 | −0.369460 | − | 0.929247i | \(-0.620457\pi\) | ||||
−0.369460 | + | 0.929247i | \(0.620457\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.0843 | −1.01091 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.8823 | 0.568405 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.6780 | −1.17782 | −0.588908 | − | 0.808200i | \(-0.700442\pi\) | ||||
−0.588908 | + | 0.808200i | \(0.700442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.93462 | 0.282601 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.76904 | 0.274095 | 0.137048 | − | 0.990564i | \(-0.456239\pi\) | ||||
0.137048 | + | 0.990564i | \(0.456239\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.0581 | 1.70932 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.8959 | 0.609957 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.1886 | 1.09434 | 0.547169 | − | 0.837022i | \(-0.315705\pi\) | ||||
0.547169 | + | 0.837022i | \(0.315705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0787 | −0.757114 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.9230 | 0.560193 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.04472 | −0.283381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.5427 | −1.24162 | −0.620808 | − | 0.783963i | \(-0.713195\pi\) | ||||
−0.620808 | + | 0.783963i | \(0.713195\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −10.9433 | −0.510791 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.18616 | −0.381267 | −0.190634 | − | 0.981661i | \(-0.561054\pi\) | ||||
−0.190634 | + | 0.981661i | \(0.561054\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.28673 | 0.431591 | 0.215796 | − | 0.976439i | \(-0.430766\pi\) | ||||
0.215796 | + | 0.976439i | \(0.430766\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.19627 | 0.194598 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.6019 | 1.41609 | 0.708043 | − | 0.706170i | \(-0.249578\pi\) | ||||
0.708043 | + | 0.706170i | \(0.249578\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.45056 | 0.436386 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.61146 | 0.212485 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.5097 | 1.63274 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.11003 | −0.326230 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.0945102 | −0.00432733 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.7624 | −0.674509 | −0.337255 | − | 0.941413i | \(-0.609498\pi\) | ||||
−0.337255 | + | 0.941413i | \(0.609498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.11855 | 0.187790 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.50771 | 0.205108 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.14727 | −0.324541 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.8582 | −0.899860 | −0.449930 | − | 0.893064i | \(-0.648551\pi\) | ||||
−0.449930 | + | 0.893064i | \(0.648551\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.9608 | −0.586106 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3227 | −0.601246 | −0.300623 | − | 0.953743i | \(-0.597195\pi\) | ||||
−0.300623 | + | 0.953743i | \(0.597195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1862 | −0.503801 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.5520 | 0.654065 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.19950 | −0.367798 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.1660 | 0.768455 | 0.384228 | − | 0.923238i | \(-0.374468\pi\) | ||||
0.384228 | + | 0.923238i | \(0.374468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.65216 | −0.297196 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.93373 | 0.130809 | 0.0654043 | − | 0.997859i | \(-0.479166\pi\) | ||||
0.0654043 | + | 0.997859i | \(0.479166\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.96658 | −0.354508 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.0170 | 0.533693 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.6050 | 1.22357 | 0.611785 | − | 0.791024i | \(-0.290452\pi\) | ||||
0.611785 | + | 0.791024i | \(0.290452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.1164 | −0.535999 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −23.1324 | −1.02132 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.26831 | −0.320280 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 60.2775 | 2.65100 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −28.0979 | −1.23336 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.19886 | −0.403009 | −0.201505 | − | 0.979488i | \(-0.564583\pi\) | ||||
−0.201505 | + | 0.979488i | \(0.564583\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.1408 | −1.36169 | −0.680847 | − | 0.732426i | \(-0.738388\pi\) | ||||
−0.680847 | + | 0.732426i | \(0.738388\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.69729 | −0.117719 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.22632 | 0.0969800 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.5580 | −0.632955 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.69960 | −0.0737564 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.20887 | −0.268936 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.1196 | 0.523976 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −23.9760 | −1.03464 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 31.5601 | 1.35939 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.1556 | −1.51146 | −0.755728 | − | 0.654885i | \(-0.772717\pi\) | ||||
−0.755728 | + | 0.654885i | \(0.772717\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.51294 | 0.150755 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.05321 | −0.387797 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.6986 | −1.56912 | −0.784560 | − | 0.620053i | \(-0.787111\pi\) | ||||
−0.784560 | + | 0.620053i | \(0.787111\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.18026 | −0.221088 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.6458 | −1.00735 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.93655 | −0.337496 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.12310 | 0.302359 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.25209 | −0.0954243 | −0.0477121 | − | 0.998861i | \(-0.515193\pi\) | ||||
−0.0477121 | + | 0.998861i | \(0.515193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.7123 | 0.579969 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.8386 | −0.626485 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.40947 | −0.185837 | −0.0929184 | − | 0.995674i | \(-0.529620\pi\) | ||||
−0.0929184 | + | 0.995674i | \(0.529620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3676 | 0.646520 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.37386 | −0.225681 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.7973 | 0.746102 | 0.373051 | − | 0.927811i | \(-0.378312\pi\) | ||||
0.373051 | + | 0.927811i | \(0.378312\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.8568 | −0.872828 | −0.436414 | − | 0.899746i | \(-0.643752\pi\) | ||||
−0.436414 | + | 0.899746i | \(0.643752\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10.8008 | 0.451210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.05148 | −0.210661 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.6443 | −1.52552 | −0.762761 | − | 0.646680i | \(-0.776157\pi\) | ||||
−0.762761 | + | 0.646680i | \(0.776157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.9039 | 0.910297 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.04480 | −0.292268 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.502602 | −0.0208157 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.61936 | 0.232332 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.48348 | 0.143779 | 0.0718893 | − | 0.997413i | \(-0.477097\pi\) | ||||
0.0718893 | + | 0.997413i | \(0.477097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.70608 | 0.193911 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.6711 | −0.685756 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.51454 | 0.390715 | 0.195358 | − | 0.980732i | \(-0.437413\pi\) | ||||
0.195358 | + | 0.980732i | \(0.437413\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.54657 | −0.227387 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.7927 | 1.01470 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −43.5907 | −1.78107 | −0.890534 | − | 0.454917i | \(-0.849669\pi\) | ||||
−0.890534 | + | 0.454917i | \(0.849669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6914 | −0.803227 | −0.401613 | − | 0.915809i | \(-0.631550\pi\) | ||||
−0.401613 | + | 0.915809i | \(0.631550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.78553 | −0.357774 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 48.8325 | 1.98532 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.3315 | 0.784641 | 0.392320 | − | 0.919829i | \(-0.371672\pi\) | ||||
0.392320 | + | 0.919829i | \(0.371672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.97039 | −0.363498 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.2766 | 0.941669 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.0543 | 0.486868 | 0.243434 | − | 0.969917i | \(-0.421726\pi\) | ||||
0.243434 | + | 0.969917i | \(0.421726\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.7383 | −0.433012 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.4697 | −1.18641 | −0.593203 | − | 0.805053i | \(-0.702137\pi\) | ||||
−0.593203 | + | 0.805053i | \(0.702137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.3548 | 0.697547 | 0.348773 | − | 0.937207i | \(-0.386598\pi\) | ||||
0.348773 | + | 0.937207i | \(0.386598\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.4350 | −0.659513 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3411 | 0.614627 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6702 | −1.22681 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −31.3663 | −1.25265 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.77914 | 0.150684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.7649 | −0.707211 | −0.353605 | − | 0.935395i | \(-0.615044\pi\) | ||||
−0.353605 | + | 0.935395i | \(0.615044\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0324 | −0.557739 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 16.1262 | 0.639949 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.1871 | 0.482872 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.62250 | 0.301542 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1757 | −0.757395 | −0.378698 | − | 0.925520i | \(-0.623628\pi\) | ||||
−0.378698 | + | 0.925520i | \(0.623628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.7582 | 1.41016 | 0.705082 | − | 0.709126i | \(-0.250910\pi\) | ||||
0.705082 | + | 0.709126i | \(0.250910\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.7156 | 0.933802 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.09564 | −0.357587 | −0.178793 | − | 0.983887i | \(-0.557219\pi\) | ||||
−0.178793 | + | 0.983887i | \(0.557219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.03842 | −0.354789 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.78532 | 0.0699722 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.8660 | −0.464351 | −0.232176 | − | 0.972674i | \(-0.574584\pi\) | ||||
−0.232176 | + | 0.972674i | \(0.574584\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −54.5190 | −2.13023 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.2638 | 0.439443 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.8059 | −0.654666 | −0.327333 | − | 0.944909i | \(-0.606150\pi\) | ||||
−0.327333 | + | 0.944909i | \(0.606150\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0205 | −1.28435 | −0.642175 | − | 0.766558i | \(-0.721968\pi\) | ||||
−0.642175 | + | 0.766558i | \(0.721968\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.73000 | −0.222535 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.7246 | −0.454659 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.7997 | −0.650488 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.1875 | −0.471195 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −27.5485 | −1.06350 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.47289 | 0.210965 | 0.105482 | − | 0.994421i | \(-0.466361\pi\) | ||||
0.105482 | + | 0.994421i | \(0.466361\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.83425 | 0.378521 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.1231 | −1.69579 | −0.847895 | − | 0.530165i | \(-0.822130\pi\) | ||||
−0.847895 | + | 0.530165i | \(0.822130\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.04083 | −0.116696 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.1580 | 0.389255 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 43.5772 | 1.66744 | 0.833718 | − | 0.552190i | \(-0.186208\pi\) | ||||
0.833718 | + | 0.552190i | \(0.186208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 34.2464 | 1.30849 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.00898 | −0.0766472 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.194083 | −0.00739397 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.94258 | 0.111941 | 0.0559705 | − | 0.998432i | \(-0.482175\pi\) | ||||
0.0559705 | + | 0.998432i | \(0.482175\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.19121 | 0.235185 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 47.5105 | 1.80217 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.69719 | −0.215797 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.6428 | −0.705134 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.1032 | −0.608209 | −0.304104 | − | 0.952639i | \(-0.598357\pi\) | ||||
−0.304104 | + | 0.952639i | \(0.598357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.98849 | 0.301292 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.2572 | 1.51617 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.38941 | −0.127472 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.5366 | −1.10927 | −0.554635 | − | 0.832094i | \(-0.687142\pi\) | ||||
−0.554635 | + | 0.832094i | \(0.687142\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.37806 | 0.276699 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.34354 | 0.125217 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.8835 | 1.11758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −34.5021 | −1.28851 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 50.1400 | 1.86990 | 0.934952 | − | 0.354773i | \(-0.115442\pi\) | ||||
0.934952 | + | 0.354773i | \(0.115442\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.09233 | −0.115164 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.0172 | 0.744449 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.0525 | 0.373341 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.63762 | 0.320352 | 0.160176 | − | 0.987088i | \(-0.448794\pi\) | ||||
0.160176 | + | 0.987088i | \(0.448794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.8333 | 1.06790 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.5823 | 0.465372 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.9558 | 1.91903 | 0.959515 | − | 0.281656i | \(-0.0908838\pi\) | ||||
0.959515 | + | 0.281656i | \(0.0908838\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.0778 | 0.777468 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −46.7211 | −1.72099 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6956 | −0.503803 | −0.251901 | − | 0.967753i | \(-0.581056\pi\) | ||||
−0.251901 | + | 0.967753i | \(0.581056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −12.1123 | −0.444957 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.06676 | −0.185882 | −0.0929408 | − | 0.995672i | \(-0.529627\pi\) | ||||
−0.0929408 | + | 0.995672i | \(0.529627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.8310 | −0.873099 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.54906 | 0.239618 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.15633 | 0.188408 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.63750 | 0.205715 | 0.102858 | − | 0.994696i | \(-0.467201\pi\) | ||||
0.102858 | + | 0.994696i | \(0.467201\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.40474 | −0.0511915 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.0331 | −0.801867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.6494 | 1.84088 | 0.920442 | − | 0.390880i | \(-0.127829\pi\) | ||||
0.920442 | + | 0.390880i | \(0.127829\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.2849 | −0.808892 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.9970 | −0.978640 | −0.489320 | − | 0.872104i | \(-0.662755\pi\) | ||||
−0.489320 | + | 0.872104i | \(0.662755\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.85172 | −0.139442 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.15626 | 0.186425 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.49025 | −0.126025 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.1399 | −0.870509 | −0.435254 | − | 0.900308i | \(-0.643342\pi\) | ||||
−0.435254 | + | 0.900308i | \(0.643342\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.33028 | −0.0839230 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.2454 | −1.33963 | −0.669813 | − | 0.742530i | \(-0.733626\pi\) | ||||
−0.669813 | + | 0.742530i | \(0.733626\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00069 | −0.0718668 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.03055 | 0.108720 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.0429 | −0.431483 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.5362 | 1.45050 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32.7058 | 1.16881 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.52171 | −0.304153 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.6348 | −0.735550 | −0.367775 | − | 0.929915i | \(-0.619880\pi\) | ||||
−0.367775 | + | 0.929915i | \(0.619880\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −16.2189 | −0.577408 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.53820 | 0.232472 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.6380 | −0.377767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.335670 | −0.0119050 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.94230 | −0.139644 | −0.0698218 | − | 0.997559i | \(-0.522243\pi\) | ||||
−0.0698218 | + | 0.997559i | \(0.522243\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.3583 | 0.755603 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.2615 | −0.503906 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.9005 | 2.11384 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.32999 | −0.293593 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 43.9999 | 1.54887 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −41.2905 | −1.45170 | −0.725849 | − | 0.687854i | \(-0.758553\pi\) | ||||
−0.725849 | + | 0.687854i | \(0.758553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.94964 | −0.349379 | −0.174690 | − | 0.984624i | \(-0.555892\pi\) | ||||
−0.174690 | + | 0.984624i | \(0.555892\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.35837 | −0.187926 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 23.9508 | 0.838958 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.5969 | 0.930506 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.39078 | 0.0835405 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.35629 | −0.152036 | −0.0760178 | − | 0.997106i | \(-0.524221\pi\) | ||||
−0.0760178 | + | 0.997106i | \(0.524221\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 46.7715 | 1.63035 | 0.815175 | − | 0.579214i | \(-0.196641\pi\) | ||||
0.815175 | + | 0.579214i | \(0.196641\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.3347 | 0.464255 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.6169 | −1.06465 | −0.532327 | − | 0.846539i | \(-0.678682\pi\) | ||||
−0.532327 | + | 0.846539i | \(0.678682\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.8309 | −0.688756 | −0.344378 | − | 0.938831i | \(-0.611910\pi\) | ||||
−0.344378 | + | 0.938831i | \(0.611910\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.5822 | 1.16495 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 11.1828 | 0.387460 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.2928 | 0.425410 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.50923 | −0.224992 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.4176 | −0.394180 | −0.197090 | − | 0.980385i | \(-0.563149\pi\) | ||||
−0.197090 | + | 0.980385i | \(0.563149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.43163 | 0.152815 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.50848 | −0.0863968 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.2067 | −0.763934 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.7760 | 0.713871 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −34.0626 | −1.16903 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.67561 | 0.194557 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.4581 | 0.837428 | 0.418714 | − | 0.908118i | \(-0.362481\pi\) | ||||
0.418714 | + | 0.908118i | \(0.362481\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.8995 | 0.372755 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −56.4437 | −1.92808 | −0.964041 | − | 0.265754i | \(-0.914379\pi\) | ||||
−0.964041 | + | 0.265754i | \(0.914379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.2843 | 0.999167 | 0.499583 | − | 0.866266i | \(-0.333486\pi\) | ||||
0.499583 | + | 0.866266i | \(0.333486\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.56867 | −0.155700 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −56.3958 | −1.91973 | −0.959867 | − | 0.280454i | \(-0.909515\pi\) | ||||
−0.959867 | + | 0.280454i | \(0.909515\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.9233 | 1.76544 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.6228 | 0.632463 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.2362 | 1.33100 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.0417 | −0.611318 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.82685 | 0.0956743 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.35034 | −0.316099 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.55796 | 0.0863762 | 0.0431881 | − | 0.999067i | \(-0.486249\pi\) | ||||
0.0431881 | + | 0.999067i | \(0.486249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.97933 | −0.336594 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.7786 | −0.935883 | −0.467942 | − | 0.883759i | \(-0.655004\pi\) | ||||
−0.467942 | + | 0.883759i | \(0.655004\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.4792 | −0.453611 | −0.226805 | − | 0.973940i | \(-0.572828\pi\) | ||||
−0.226805 | + | 0.973940i | \(0.572828\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.03643 | −0.202912 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.1525 | 1.85184 | 0.925920 | − | 0.377720i | \(-0.123292\pi\) | ||||
0.925920 | + | 0.377720i | \(0.123292\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.86095 | 0.230109 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.5670 | 0.890027 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.1480 | 1.51082 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.3062 | 1.48099 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.60547 | −0.287328 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.65369 | −0.221913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.178088 | −0.00593299 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.0899 | 0.335771 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.49171 | −0.215792 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.7611 | 1.12102 | 0.560509 | − | 0.828148i | \(-0.310605\pi\) | ||||
0.560509 | + | 0.828148i | \(0.310605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.15090 | 0.104509 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5552 | 0.813549 | 0.406775 | − | 0.913528i | \(-0.366653\pi\) | ||||
0.406775 | + | 0.913528i | \(0.366653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.8277 | 1.15263 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.3986 | −0.608239 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −23.1953 | −0.765977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.9060 | −1.58027 | −0.790136 | − | 0.612932i | \(-0.789990\pi\) | ||||
−0.790136 | + | 0.612932i | \(0.789990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.9454 | −1.01968 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.6533 | 0.515235 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.39613 | −0.111664 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.87472 | 0.0944182 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.8411 | 0.782203 | 0.391101 | − | 0.920348i | \(-0.372094\pi\) | ||||
0.391101 | + | 0.920348i | \(0.372094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.6386 | 0.774724 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 40.4309 | 1.32365 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.4208 | 0.896757 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.2056 | 0.921436 | 0.460718 | − | 0.887546i | \(-0.347592\pi\) | ||||
0.460718 | + | 0.887546i | \(0.347592\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.38368 | 0.306225 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 52.0125 | 1.69556 | 0.847780 | − | 0.530348i | \(-0.177939\pi\) | ||||
0.847780 | + | 0.530348i | \(0.177939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.55619 | −0.278628 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.2169 | 0.527535 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.7512 | 0.446854 | 0.223427 | − | 0.974721i | \(-0.428276\pi\) | ||||
0.223427 | + | 0.974721i | \(0.428276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.1310 | 0.750862 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −30.8653 | −1.00087 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.03493 | −0.0335247 | −0.0167623 | − | 0.999860i | \(-0.505336\pi\) | ||||
−0.0167623 | + | 0.999860i | \(0.505336\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.9593 | −0.645866 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 44.3473 | 1.43354 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.5703 | 0.470499 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6758 | −0.957282 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.79348 | −0.154468 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −40.4772 | −1.30301 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.8068 | −0.701259 | −0.350630 | − | 0.936514i | \(-0.614032\pi\) | ||||
−0.350630 | + | 0.936514i | \(0.614032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.1141 | −0.357037 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.6620 | 1.49745 | 0.748727 | − | 0.662878i | \(-0.230665\pi\) | ||||
0.748727 | + | 0.662878i | \(0.230665\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.2135 | 0.648015 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.14928 | 0.164909 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.84332 | −0.218937 | −0.109469 | − | 0.993990i | \(-0.534915\pi\) | ||||
−0.109469 | + | 0.993990i | \(0.534915\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −75.8422 | −2.42393 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.58068 | 0.114322 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.4251 | −0.810934 | −0.405467 | − | 0.914110i | \(-0.632891\pi\) | ||||
−0.405467 | + | 0.914110i | \(0.632891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.8072 | 0.981598 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 17.1276 | 0.545176 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.8964 | 0.600869 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.474448 | 0.0150713 | 0.00753567 | − | 0.999972i | \(-0.497601\pi\) | ||||
0.00753567 | + | 0.999972i | \(0.497601\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 39.7615 | 1.26179 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.8155 | −1.45245 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.9430 | −1.04331 | −0.521657 | − | 0.853155i | \(-0.674686\pi\) | ||||
−0.521657 | + | 0.853155i | \(0.674686\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.0493 | −0.349585 |
(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 | 1004.2.a.a.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 9036.2.a.i.1.1 | 7 | |||
4.3 | odd | 2 | 4016.2.a.g.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.a.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
4016.2.a.g.1.5 | 7 | 4.3 | odd | 2 | |||
9036.2.a.i.1.1 | 7 | 3.2 | odd | 2 |