Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −2.87355 | −1.65905 | −0.829524 | − | 0.558472i | \(-0.811388\pi\) | ||||
−0.829524 | + | 0.558472i | \(0.811388\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.00628 | 0.897234 | 0.448617 | − | 0.893724i | \(-0.351917\pi\) | ||||
0.448617 | + | 0.893724i | \(0.351917\pi\) | |||||||
\(6\) | −2.87355 | −1.17312 | ||||||||
\(7\) | 0.474155 | 0.179214 | 0.0896068 | − | 0.995977i | \(-0.471439\pi\) | ||||
0.0896068 | + | 0.995977i | \(0.471439\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 5.25731 | 1.75244 | ||||||||
\(10\) | 2.00628 | 0.634440 | ||||||||
\(11\) | 3.13649 | 0.945688 | 0.472844 | − | 0.881146i | \(-0.343227\pi\) | ||||
0.472844 | + | 0.881146i | \(0.343227\pi\) | |||||||
\(12\) | −2.87355 | −0.829524 | ||||||||
\(13\) | 5.27734 | 1.46367 | 0.731836 | − | 0.681481i | \(-0.238664\pi\) | ||||
0.731836 | + | 0.681481i | \(0.238664\pi\) | |||||||
\(14\) | 0.474155 | 0.126723 | ||||||||
\(15\) | −5.76514 | −1.48855 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.17091 | −1.01159 | −0.505797 | − | 0.862653i | \(-0.668801\pi\) | ||||
−0.505797 | + | 0.862653i | \(0.668801\pi\) | |||||||
\(18\) | 5.25731 | 1.23916 | ||||||||
\(19\) | −7.51640 | −1.72438 | −0.862190 | − | 0.506585i | \(-0.830907\pi\) | ||||
−0.862190 | + | 0.506585i | \(0.830907\pi\) | |||||||
\(20\) | 2.00628 | 0.448617 | ||||||||
\(21\) | −1.36251 | −0.297324 | ||||||||
\(22\) | 3.13649 | 0.668702 | ||||||||
\(23\) | 5.06333 | 1.05578 | 0.527888 | − | 0.849314i | \(-0.322984\pi\) | ||||
0.527888 | + | 0.849314i | \(0.322984\pi\) | |||||||
\(24\) | −2.87355 | −0.586562 | ||||||||
\(25\) | −0.974857 | −0.194971 | ||||||||
\(26\) | 5.27734 | 1.03497 | ||||||||
\(27\) | −6.48651 | −1.24833 | ||||||||
\(28\) | 0.474155 | 0.0896068 | ||||||||
\(29\) | −7.99676 | −1.48496 | −0.742481 | − | 0.669867i | \(-0.766351\pi\) | ||||
−0.742481 | + | 0.669867i | \(0.766351\pi\) | |||||||
\(30\) | −5.76514 | −1.05257 | ||||||||
\(31\) | −2.39818 | −0.430726 | −0.215363 | − | 0.976534i | \(-0.569093\pi\) | ||||
−0.215363 | + | 0.976534i | \(0.569093\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −9.01288 | −1.56894 | ||||||||
\(34\) | −4.17091 | −0.715304 | ||||||||
\(35\) | 0.951285 | 0.160797 | ||||||||
\(36\) | 5.25731 | 0.876219 | ||||||||
\(37\) | −0.569544 | −0.0936325 | −0.0468163 | − | 0.998904i | \(-0.514908\pi\) | ||||
−0.0468163 | + | 0.998904i | \(0.514908\pi\) | |||||||
\(38\) | −7.51640 | −1.21932 | ||||||||
\(39\) | −15.1647 | −2.42830 | ||||||||
\(40\) | 2.00628 | 0.317220 | ||||||||
\(41\) | −11.4748 | −1.79206 | −0.896030 | − | 0.443994i | \(-0.853561\pi\) | ||||
−0.896030 | + | 0.443994i | \(0.853561\pi\) | |||||||
\(42\) | −1.36251 | −0.210240 | ||||||||
\(43\) | 0.986101 | 0.150379 | 0.0751895 | − | 0.997169i | \(-0.476044\pi\) | ||||
0.0751895 | + | 0.997169i | \(0.476044\pi\) | |||||||
\(44\) | 3.13649 | 0.472844 | ||||||||
\(45\) | 10.5476 | 1.57235 | ||||||||
\(46\) | 5.06333 | 0.746547 | ||||||||
\(47\) | −12.5668 | −1.83305 | −0.916525 | − | 0.399978i | \(-0.869018\pi\) | ||||
−0.916525 | + | 0.399978i | \(0.869018\pi\) | |||||||
\(48\) | −2.87355 | −0.414762 | ||||||||
\(49\) | −6.77518 | −0.967882 | ||||||||
\(50\) | −0.974857 | −0.137866 | ||||||||
\(51\) | 11.9853 | 1.67828 | ||||||||
\(52\) | 5.27734 | 0.731836 | ||||||||
\(53\) | −3.91121 | −0.537246 | −0.268623 | − | 0.963245i | \(-0.586569\pi\) | ||||
−0.268623 | + | 0.963245i | \(0.586569\pi\) | |||||||
\(54\) | −6.48651 | −0.882703 | ||||||||
\(55\) | 6.29267 | 0.848503 | ||||||||
\(56\) | 0.474155 | 0.0633616 | ||||||||
\(57\) | 21.5988 | 2.86083 | ||||||||
\(58\) | −7.99676 | −1.05003 | ||||||||
\(59\) | −14.7429 | −1.91936 | −0.959679 | − | 0.281098i | \(-0.909301\pi\) | ||||
−0.959679 | + | 0.281098i | \(0.909301\pi\) | |||||||
\(60\) | −5.76514 | −0.744277 | ||||||||
\(61\) | −2.93433 | −0.375702 | −0.187851 | − | 0.982197i | \(-0.560152\pi\) | ||||
−0.187851 | + | 0.982197i | \(0.560152\pi\) | |||||||
\(62\) | −2.39818 | −0.304569 | ||||||||
\(63\) | 2.49278 | 0.314061 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.5878 | 1.31326 | ||||||||
\(66\) | −9.01288 | −1.10941 | ||||||||
\(67\) | 15.4928 | 1.89275 | 0.946373 | − | 0.323077i | \(-0.104717\pi\) | ||||
0.946373 | + | 0.323077i | \(0.104717\pi\) | |||||||
\(68\) | −4.17091 | −0.505797 | ||||||||
\(69\) | −14.5497 | −1.75158 | ||||||||
\(70\) | 0.951285 | 0.113700 | ||||||||
\(71\) | −3.47675 | −0.412614 | −0.206307 | − | 0.978487i | \(-0.566145\pi\) | ||||
−0.206307 | + | 0.978487i | \(0.566145\pi\) | |||||||
\(72\) | 5.25731 | 0.619580 | ||||||||
\(73\) | −15.9455 | −1.86628 | −0.933140 | − | 0.359513i | \(-0.882943\pi\) | ||||
−0.933140 | + | 0.359513i | \(0.882943\pi\) | |||||||
\(74\) | −0.569544 | −0.0662082 | ||||||||
\(75\) | 2.80130 | 0.323467 | ||||||||
\(76\) | −7.51640 | −0.862190 | ||||||||
\(77\) | 1.48718 | 0.169480 | ||||||||
\(78\) | −15.1647 | −1.71707 | ||||||||
\(79\) | 12.4960 | 1.40590 | 0.702952 | − | 0.711237i | \(-0.251865\pi\) | ||||
0.702952 | + | 0.711237i | \(0.251865\pi\) | |||||||
\(80\) | 2.00628 | 0.224308 | ||||||||
\(81\) | 2.86741 | 0.318601 | ||||||||
\(82\) | −11.4748 | −1.26718 | ||||||||
\(83\) | 4.50846 | 0.494868 | 0.247434 | − | 0.968905i | \(-0.420413\pi\) | ||||
0.247434 | + | 0.968905i | \(0.420413\pi\) | |||||||
\(84\) | −1.36251 | −0.148662 | ||||||||
\(85\) | −8.36799 | −0.907636 | ||||||||
\(86\) | 0.986101 | 0.106334 | ||||||||
\(87\) | 22.9791 | 2.46362 | ||||||||
\(88\) | 3.13649 | 0.334351 | ||||||||
\(89\) | −11.7024 | −1.24045 | −0.620227 | − | 0.784422i | \(-0.712960\pi\) | ||||
−0.620227 | + | 0.784422i | \(0.712960\pi\) | |||||||
\(90\) | 10.5476 | 1.11182 | ||||||||
\(91\) | 2.50228 | 0.262310 | ||||||||
\(92\) | 5.06333 | 0.527888 | ||||||||
\(93\) | 6.89130 | 0.714594 | ||||||||
\(94\) | −12.5668 | −1.29616 | ||||||||
\(95\) | −15.0800 | −1.54717 | ||||||||
\(96\) | −2.87355 | −0.293281 | ||||||||
\(97\) | 8.57923 | 0.871089 | 0.435544 | − | 0.900167i | \(-0.356556\pi\) | ||||
0.435544 | + | 0.900167i | \(0.356556\pi\) | |||||||
\(98\) | −6.77518 | −0.684396 | ||||||||
\(99\) | 16.4895 | 1.65726 | ||||||||
\(100\) | −0.974857 | −0.0974857 | ||||||||
\(101\) | 0.137329 | 0.0136647 | 0.00683236 | − | 0.999977i | \(-0.497825\pi\) | ||||
0.00683236 | + | 0.999977i | \(0.497825\pi\) | |||||||
\(102\) | 11.9853 | 1.18672 | ||||||||
\(103\) | −3.54690 | −0.349486 | −0.174743 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174743 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(104\) | 5.27734 | 0.517486 | ||||||||
\(105\) | −2.73357 | −0.266769 | ||||||||
\(106\) | −3.91121 | −0.379890 | ||||||||
\(107\) | 8.85259 | 0.855812 | 0.427906 | − | 0.903823i | \(-0.359251\pi\) | ||||
0.427906 | + | 0.903823i | \(0.359251\pi\) | |||||||
\(108\) | −6.48651 | −0.624165 | ||||||||
\(109\) | −18.9773 | −1.81770 | −0.908848 | − | 0.417127i | \(-0.863037\pi\) | ||||
−0.908848 | + | 0.417127i | \(0.863037\pi\) | |||||||
\(110\) | 6.29267 | 0.599982 | ||||||||
\(111\) | 1.63662 | 0.155341 | ||||||||
\(112\) | 0.474155 | 0.0448034 | ||||||||
\(113\) | −7.64564 | −0.719242 | −0.359621 | − | 0.933099i | \(-0.617094\pi\) | ||||
−0.359621 | + | 0.933099i | \(0.617094\pi\) | |||||||
\(114\) | 21.5988 | 2.02291 | ||||||||
\(115\) | 10.1584 | 0.947279 | ||||||||
\(116\) | −7.99676 | −0.742481 | ||||||||
\(117\) | 27.7447 | 2.56499 | ||||||||
\(118\) | −14.7429 | −1.35719 | ||||||||
\(119\) | −1.97766 | −0.181291 | ||||||||
\(120\) | −5.76514 | −0.526283 | ||||||||
\(121\) | −1.16241 | −0.105674 | ||||||||
\(122\) | −2.93433 | −0.265662 | ||||||||
\(123\) | 32.9734 | 2.97311 | ||||||||
\(124\) | −2.39818 | −0.215363 | ||||||||
\(125\) | −11.9872 | −1.07217 | ||||||||
\(126\) | 2.49278 | 0.222075 | ||||||||
\(127\) | 8.05309 | 0.714596 | 0.357298 | − | 0.933990i | \(-0.383698\pi\) | ||||
0.357298 | + | 0.933990i | \(0.383698\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.83362 | −0.249486 | ||||||||
\(130\) | 10.5878 | 0.928612 | ||||||||
\(131\) | 0.752333 | 0.0657316 | 0.0328658 | − | 0.999460i | \(-0.489537\pi\) | ||||
0.0328658 | + | 0.999460i | \(0.489537\pi\) | |||||||
\(132\) | −9.01288 | −0.784471 | ||||||||
\(133\) | −3.56394 | −0.309032 | ||||||||
\(134\) | 15.4928 | 1.33837 | ||||||||
\(135\) | −13.0137 | −1.12004 | ||||||||
\(136\) | −4.17091 | −0.357652 | ||||||||
\(137\) | −10.8307 | −0.925332 | −0.462666 | − | 0.886533i | \(-0.653107\pi\) | ||||
−0.462666 | + | 0.886533i | \(0.653107\pi\) | |||||||
\(138\) | −14.5497 | −1.23856 | ||||||||
\(139\) | 8.73015 | 0.740482 | 0.370241 | − | 0.928936i | \(-0.379275\pi\) | ||||
0.370241 | + | 0.928936i | \(0.379275\pi\) | |||||||
\(140\) | 0.951285 | 0.0803983 | ||||||||
\(141\) | 36.1113 | 3.04112 | ||||||||
\(142\) | −3.47675 | −0.291762 | ||||||||
\(143\) | 16.5524 | 1.38418 | ||||||||
\(144\) | 5.25731 | 0.438109 | ||||||||
\(145\) | −16.0437 | −1.33236 | ||||||||
\(146\) | −15.9455 | −1.31966 | ||||||||
\(147\) | 19.4688 | 1.60576 | ||||||||
\(148\) | −0.569544 | −0.0468163 | ||||||||
\(149\) | 9.85012 | 0.806953 | 0.403477 | − | 0.914990i | \(-0.367802\pi\) | ||||
0.403477 | + | 0.914990i | \(0.367802\pi\) | |||||||
\(150\) | 2.80130 | 0.228726 | ||||||||
\(151\) | 6.45762 | 0.525514 | 0.262757 | − | 0.964862i | \(-0.415368\pi\) | ||||
0.262757 | + | 0.964862i | \(0.415368\pi\) | |||||||
\(152\) | −7.51640 | −0.609660 | ||||||||
\(153\) | −21.9278 | −1.77275 | ||||||||
\(154\) | 1.48718 | 0.119841 | ||||||||
\(155\) | −4.81141 | −0.386462 | ||||||||
\(156\) | −15.1647 | −1.21415 | ||||||||
\(157\) | 14.5023 | 1.15741 | 0.578704 | − | 0.815538i | \(-0.303559\pi\) | ||||
0.578704 | + | 0.815538i | \(0.303559\pi\) | |||||||
\(158\) | 12.4960 | 0.994125 | ||||||||
\(159\) | 11.2391 | 0.891316 | ||||||||
\(160\) | 2.00628 | 0.158610 | ||||||||
\(161\) | 2.40080 | 0.189210 | ||||||||
\(162\) | 2.86741 | 0.225285 | ||||||||
\(163\) | 5.38961 | 0.422147 | 0.211073 | − | 0.977470i | \(-0.432304\pi\) | ||||
0.211073 | + | 0.977470i | \(0.432304\pi\) | |||||||
\(164\) | −11.4748 | −0.896030 | ||||||||
\(165\) | −18.0823 | −1.40771 | ||||||||
\(166\) | 4.50846 | 0.349924 | ||||||||
\(167\) | 6.36959 | 0.492894 | 0.246447 | − | 0.969156i | \(-0.420737\pi\) | ||||
0.246447 | + | 0.969156i | \(0.420737\pi\) | |||||||
\(168\) | −1.36251 | −0.105120 | ||||||||
\(169\) | 14.8504 | 1.14234 | ||||||||
\(170\) | −8.36799 | −0.641795 | ||||||||
\(171\) | −39.5161 | −3.02187 | ||||||||
\(172\) | 0.986101 | 0.0751895 | ||||||||
\(173\) | 7.81112 | 0.593868 | 0.296934 | − | 0.954898i | \(-0.404036\pi\) | ||||
0.296934 | + | 0.954898i | \(0.404036\pi\) | |||||||
\(174\) | 22.9791 | 1.74204 | ||||||||
\(175\) | −0.462233 | −0.0349415 | ||||||||
\(176\) | 3.13649 | 0.236422 | ||||||||
\(177\) | 42.3644 | 3.18431 | ||||||||
\(178\) | −11.7024 | −0.877134 | ||||||||
\(179\) | 15.4458 | 1.15447 | 0.577237 | − | 0.816576i | \(-0.304131\pi\) | ||||
0.577237 | + | 0.816576i | \(0.304131\pi\) | |||||||
\(180\) | 10.5476 | 0.786173 | ||||||||
\(181\) | −11.0557 | −0.821766 | −0.410883 | − | 0.911688i | \(-0.634780\pi\) | ||||
−0.410883 | + | 0.911688i | \(0.634780\pi\) | |||||||
\(182\) | 2.50228 | 0.185481 | ||||||||
\(183\) | 8.43196 | 0.623308 | ||||||||
\(184\) | 5.06333 | 0.373273 | ||||||||
\(185\) | −1.14266 | −0.0840102 | ||||||||
\(186\) | 6.89130 | 0.505294 | ||||||||
\(187\) | −13.0820 | −0.956652 | ||||||||
\(188\) | −12.5668 | −0.916525 | ||||||||
\(189\) | −3.07561 | −0.223718 | ||||||||
\(190\) | −15.0800 | −1.09402 | ||||||||
\(191\) | 0.561071 | 0.0405977 | 0.0202988 | − | 0.999794i | \(-0.493538\pi\) | ||||
0.0202988 | + | 0.999794i | \(0.493538\pi\) | |||||||
\(192\) | −2.87355 | −0.207381 | ||||||||
\(193\) | −12.0776 | −0.869368 | −0.434684 | − | 0.900583i | \(-0.643140\pi\) | ||||
−0.434684 | + | 0.900583i | \(0.643140\pi\) | |||||||
\(194\) | 8.57923 | 0.615953 | ||||||||
\(195\) | −30.4246 | −2.17875 | ||||||||
\(196\) | −6.77518 | −0.483941 | ||||||||
\(197\) | 3.06465 | 0.218347 | 0.109173 | − | 0.994023i | \(-0.465180\pi\) | ||||
0.109173 | + | 0.994023i | \(0.465180\pi\) | |||||||
\(198\) | 16.4895 | 1.17186 | ||||||||
\(199\) | 22.3326 | 1.58312 | 0.791560 | − | 0.611092i | \(-0.209269\pi\) | ||||
0.791560 | + | 0.611092i | \(0.209269\pi\) | |||||||
\(200\) | −0.974857 | −0.0689328 | ||||||||
\(201\) | −44.5194 | −3.14015 | ||||||||
\(202\) | 0.137329 | 0.00966241 | ||||||||
\(203\) | −3.79170 | −0.266125 | ||||||||
\(204\) | 11.9853 | 0.839141 | ||||||||
\(205\) | −23.0216 | −1.60790 | ||||||||
\(206\) | −3.54690 | −0.247124 | ||||||||
\(207\) | 26.6195 | 1.85018 | ||||||||
\(208\) | 5.27734 | 0.365918 | ||||||||
\(209\) | −23.5751 | −1.63073 | ||||||||
\(210\) | −2.73357 | −0.188634 | ||||||||
\(211\) | −12.4694 | −0.858426 | −0.429213 | − | 0.903203i | \(-0.641209\pi\) | ||||
−0.429213 | + | 0.903203i | \(0.641209\pi\) | |||||||
\(212\) | −3.91121 | −0.268623 | ||||||||
\(213\) | 9.99063 | 0.684547 | ||||||||
\(214\) | 8.85259 | 0.605151 | ||||||||
\(215\) | 1.97839 | 0.134925 | ||||||||
\(216\) | −6.48651 | −0.441351 | ||||||||
\(217\) | −1.13711 | −0.0771919 | ||||||||
\(218\) | −18.9773 | −1.28531 | ||||||||
\(219\) | 45.8203 | 3.09625 | ||||||||
\(220\) | 6.29267 | 0.424252 | ||||||||
\(221\) | −22.0113 | −1.48064 | ||||||||
\(222\) | 1.63662 | 0.109842 | ||||||||
\(223\) | 0.373646 | 0.0250212 | 0.0125106 | − | 0.999922i | \(-0.496018\pi\) | ||||
0.0125106 | + | 0.999922i | \(0.496018\pi\) | |||||||
\(224\) | 0.474155 | 0.0316808 | ||||||||
\(225\) | −5.12513 | −0.341675 | ||||||||
\(226\) | −7.64564 | −0.508581 | ||||||||
\(227\) | −24.1798 | −1.60487 | −0.802434 | − | 0.596741i | \(-0.796462\pi\) | ||||
−0.802434 | + | 0.596741i | \(0.796462\pi\) | |||||||
\(228\) | 21.5988 | 1.43041 | ||||||||
\(229\) | −6.68006 | −0.441431 | −0.220715 | − | 0.975338i | \(-0.570839\pi\) | ||||
−0.220715 | + | 0.975338i | \(0.570839\pi\) | |||||||
\(230\) | 10.1584 | 0.669827 | ||||||||
\(231\) | −4.27350 | −0.281176 | ||||||||
\(232\) | −7.99676 | −0.525013 | ||||||||
\(233\) | −11.6049 | −0.760259 | −0.380130 | − | 0.924933i | \(-0.624121\pi\) | ||||
−0.380130 | + | 0.924933i | \(0.624121\pi\) | |||||||
\(234\) | 27.7447 | 1.81372 | ||||||||
\(235\) | −25.2124 | −1.64467 | ||||||||
\(236\) | −14.7429 | −0.959679 | ||||||||
\(237\) | −35.9078 | −2.33246 | ||||||||
\(238\) | −1.97766 | −0.128192 | ||||||||
\(239\) | 8.85678 | 0.572897 | 0.286449 | − | 0.958096i | \(-0.407525\pi\) | ||||
0.286449 | + | 0.958096i | \(0.407525\pi\) | |||||||
\(240\) | −5.76514 | −0.372138 | ||||||||
\(241\) | 9.26722 | 0.596954 | 0.298477 | − | 0.954417i | \(-0.403521\pi\) | ||||
0.298477 | + | 0.954417i | \(0.403521\pi\) | |||||||
\(242\) | −1.16241 | −0.0747228 | ||||||||
\(243\) | 11.2199 | 0.719756 | ||||||||
\(244\) | −2.93433 | −0.187851 | ||||||||
\(245\) | −13.5929 | −0.868417 | ||||||||
\(246\) | 32.9734 | 2.10231 | ||||||||
\(247\) | −39.6666 | −2.52393 | ||||||||
\(248\) | −2.39818 | −0.152285 | ||||||||
\(249\) | −12.9553 | −0.821009 | ||||||||
\(250\) | −11.9872 | −0.758138 | ||||||||
\(251\) | 6.32352 | 0.399137 | 0.199569 | − | 0.979884i | \(-0.436046\pi\) | ||||
0.199569 | + | 0.979884i | \(0.436046\pi\) | |||||||
\(252\) | 2.49278 | 0.157030 | ||||||||
\(253\) | 15.8811 | 0.998435 | ||||||||
\(254\) | 8.05309 | 0.505296 | ||||||||
\(255\) | 24.0459 | 1.50581 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.3014 | 1.45350 | 0.726750 | − | 0.686902i | \(-0.241030\pi\) | ||||
0.726750 | + | 0.686902i | \(0.241030\pi\) | |||||||
\(258\) | −2.83362 | −0.176413 | ||||||||
\(259\) | −0.270052 | −0.0167802 | ||||||||
\(260\) | 10.5878 | 0.656628 | ||||||||
\(261\) | −42.0415 | −2.60230 | ||||||||
\(262\) | 0.752333 | 0.0464793 | ||||||||
\(263\) | −32.2528 | −1.98879 | −0.994397 | − | 0.105709i | \(-0.966289\pi\) | ||||
−0.994397 | + | 0.105709i | \(0.966289\pi\) | |||||||
\(264\) | −9.01288 | −0.554705 | ||||||||
\(265\) | −7.84696 | −0.482035 | ||||||||
\(266\) | −3.56394 | −0.218519 | ||||||||
\(267\) | 33.6276 | 2.05797 | ||||||||
\(268\) | 15.4928 | 0.946373 | ||||||||
\(269\) | −9.79631 | −0.597292 | −0.298646 | − | 0.954364i | \(-0.596535\pi\) | ||||
−0.298646 | + | 0.954364i | \(0.596535\pi\) | |||||||
\(270\) | −13.0137 | −0.791991 | ||||||||
\(271\) | 10.6748 | 0.648451 | 0.324225 | − | 0.945980i | \(-0.394896\pi\) | ||||
0.324225 | + | 0.945980i | \(0.394896\pi\) | |||||||
\(272\) | −4.17091 | −0.252898 | ||||||||
\(273\) | −7.19043 | −0.435185 | ||||||||
\(274\) | −10.8307 | −0.654308 | ||||||||
\(275\) | −3.05763 | −0.184382 | ||||||||
\(276\) | −14.5497 | −0.875792 | ||||||||
\(277\) | 18.6153 | 1.11849 | 0.559243 | − | 0.829004i | \(-0.311092\pi\) | ||||
0.559243 | + | 0.829004i | \(0.311092\pi\) | |||||||
\(278\) | 8.73015 | 0.523600 | ||||||||
\(279\) | −12.6080 | −0.754820 | ||||||||
\(280\) | 0.951285 | 0.0568502 | ||||||||
\(281\) | 26.5735 | 1.58524 | 0.792622 | − | 0.609714i | \(-0.208716\pi\) | ||||
0.792622 | + | 0.609714i | \(0.208716\pi\) | |||||||
\(282\) | 36.1113 | 2.15039 | ||||||||
\(283\) | −23.3476 | −1.38787 | −0.693935 | − | 0.720037i | \(-0.744125\pi\) | ||||
−0.693935 | + | 0.720037i | \(0.744125\pi\) | |||||||
\(284\) | −3.47675 | −0.206307 | ||||||||
\(285\) | 43.3331 | 2.56683 | ||||||||
\(286\) | 16.5524 | 0.978761 | ||||||||
\(287\) | −5.44082 | −0.321162 | ||||||||
\(288\) | 5.25731 | 0.309790 | ||||||||
\(289\) | 0.396457 | 0.0233210 | ||||||||
\(290\) | −16.0437 | −0.942119 | ||||||||
\(291\) | −24.6529 | −1.44518 | ||||||||
\(292\) | −15.9455 | −0.933140 | ||||||||
\(293\) | 10.9773 | 0.641301 | 0.320651 | − | 0.947198i | \(-0.396098\pi\) | ||||
0.320651 | + | 0.947198i | \(0.396098\pi\) | |||||||
\(294\) | 19.4688 | 1.13545 | ||||||||
\(295\) | −29.5783 | −1.72211 | ||||||||
\(296\) | −0.569544 | −0.0331041 | ||||||||
\(297\) | −20.3449 | −1.18053 | ||||||||
\(298\) | 9.85012 | 0.570602 | ||||||||
\(299\) | 26.7209 | 1.54531 | ||||||||
\(300\) | 2.80130 | 0.161733 | ||||||||
\(301\) | 0.467565 | 0.0269500 | ||||||||
\(302\) | 6.45762 | 0.371594 | ||||||||
\(303\) | −0.394621 | −0.0226704 | ||||||||
\(304\) | −7.51640 | −0.431095 | ||||||||
\(305\) | −5.88708 | −0.337093 | ||||||||
\(306\) | −21.9278 | −1.25353 | ||||||||
\(307\) | −25.7684 | −1.47068 | −0.735340 | − | 0.677699i | \(-0.762977\pi\) | ||||
−0.735340 | + | 0.677699i | \(0.762977\pi\) | |||||||
\(308\) | 1.48718 | 0.0847401 | ||||||||
\(309\) | 10.1922 | 0.579814 | ||||||||
\(310\) | −4.81141 | −0.273270 | ||||||||
\(311\) | 7.77395 | 0.440820 | 0.220410 | − | 0.975407i | \(-0.429260\pi\) | ||||
0.220410 | + | 0.975407i | \(0.429260\pi\) | |||||||
\(312\) | −15.1647 | −0.858534 | ||||||||
\(313\) | −14.1309 | −0.798727 | −0.399363 | − | 0.916793i | \(-0.630769\pi\) | ||||
−0.399363 | + | 0.916793i | \(0.630769\pi\) | |||||||
\(314\) | 14.5023 | 0.818411 | ||||||||
\(315\) | 5.00121 | 0.281786 | ||||||||
\(316\) | 12.4960 | 0.702952 | ||||||||
\(317\) | 12.4982 | 0.701969 | 0.350984 | − | 0.936381i | \(-0.385847\pi\) | ||||
0.350984 | + | 0.936381i | \(0.385847\pi\) | |||||||
\(318\) | 11.2391 | 0.630256 | ||||||||
\(319\) | −25.0818 | −1.40431 | ||||||||
\(320\) | 2.00628 | 0.112154 | ||||||||
\(321\) | −25.4384 | −1.41983 | ||||||||
\(322\) | 2.40080 | 0.133791 | ||||||||
\(323\) | 31.3502 | 1.74437 | ||||||||
\(324\) | 2.86741 | 0.159300 | ||||||||
\(325\) | −5.14466 | −0.285374 | ||||||||
\(326\) | 5.38961 | 0.298503 | ||||||||
\(327\) | 54.5323 | 3.01564 | ||||||||
\(328\) | −11.4748 | −0.633589 | ||||||||
\(329\) | −5.95859 | −0.328508 | ||||||||
\(330\) | −18.0823 | −0.995399 | ||||||||
\(331\) | −22.5909 | −1.24171 | −0.620854 | − | 0.783926i | \(-0.713214\pi\) | ||||
−0.620854 | + | 0.783926i | \(0.713214\pi\) | |||||||
\(332\) | 4.50846 | 0.247434 | ||||||||
\(333\) | −2.99427 | −0.164085 | ||||||||
\(334\) | 6.36959 | 0.348529 | ||||||||
\(335\) | 31.0828 | 1.69823 | ||||||||
\(336\) | −1.36251 | −0.0743310 | ||||||||
\(337\) | 22.9344 | 1.24932 | 0.624658 | − | 0.780899i | \(-0.285239\pi\) | ||||
0.624658 | + | 0.780899i | \(0.285239\pi\) | |||||||
\(338\) | 14.8504 | 0.807754 | ||||||||
\(339\) | 21.9702 | 1.19326 | ||||||||
\(340\) | −8.36799 | −0.453818 | ||||||||
\(341\) | −7.52187 | −0.407332 | ||||||||
\(342\) | −39.5161 | −2.13678 | ||||||||
\(343\) | −6.53157 | −0.352671 | ||||||||
\(344\) | 0.986101 | 0.0531670 | ||||||||
\(345\) | −29.1908 | −1.57158 | ||||||||
\(346\) | 7.81112 | 0.419928 | ||||||||
\(347\) | −20.7794 | −1.11550 | −0.557749 | − | 0.830010i | \(-0.688335\pi\) | ||||
−0.557749 | + | 0.830010i | \(0.688335\pi\) | |||||||
\(348\) | 22.9791 | 1.23181 | ||||||||
\(349\) | 20.9301 | 1.12036 | 0.560181 | − | 0.828370i | \(-0.310732\pi\) | ||||
0.560181 | + | 0.828370i | \(0.310732\pi\) | |||||||
\(350\) | −0.462233 | −0.0247074 | ||||||||
\(351\) | −34.2316 | −1.82715 | ||||||||
\(352\) | 3.13649 | 0.167176 | ||||||||
\(353\) | −25.8437 | −1.37552 | −0.687761 | − | 0.725937i | \(-0.741406\pi\) | ||||
−0.687761 | + | 0.725937i | \(0.741406\pi\) | |||||||
\(354\) | 42.3644 | 2.25164 | ||||||||
\(355\) | −6.97532 | −0.370211 | ||||||||
\(356\) | −11.7024 | −0.620227 | ||||||||
\(357\) | 5.68290 | 0.300771 | ||||||||
\(358\) | 15.4458 | 0.816337 | ||||||||
\(359\) | −16.6639 | −0.879488 | −0.439744 | − | 0.898123i | \(-0.644931\pi\) | ||||
−0.439744 | + | 0.898123i | \(0.644931\pi\) | |||||||
\(360\) | 10.5476 | 0.555908 | ||||||||
\(361\) | 37.4962 | 1.97348 | ||||||||
\(362\) | −11.0557 | −0.581077 | ||||||||
\(363\) | 3.34026 | 0.175318 | ||||||||
\(364\) | 2.50228 | 0.131155 | ||||||||
\(365\) | −31.9911 | −1.67449 | ||||||||
\(366\) | 8.43196 | 0.440745 | ||||||||
\(367\) | −0.0793847 | −0.00414385 | −0.00207192 | − | 0.999998i | \(-0.500660\pi\) | ||||
−0.00207192 | + | 0.999998i | \(0.500660\pi\) | |||||||
\(368\) | 5.06333 | 0.263944 | ||||||||
\(369\) | −60.3265 | −3.14047 | ||||||||
\(370\) | −1.14266 | −0.0594042 | ||||||||
\(371\) | −1.85452 | −0.0962818 | ||||||||
\(372\) | 6.89130 | 0.357297 | ||||||||
\(373\) | −14.5444 | −0.753078 | −0.376539 | − | 0.926401i | \(-0.622886\pi\) | ||||
−0.376539 | + | 0.926401i | \(0.622886\pi\) | |||||||
\(374\) | −13.0820 | −0.676455 | ||||||||
\(375\) | 34.4459 | 1.77878 | ||||||||
\(376\) | −12.5668 | −0.648081 | ||||||||
\(377\) | −42.2017 | −2.17350 | ||||||||
\(378\) | −3.07561 | −0.158192 | ||||||||
\(379\) | −5.02379 | −0.258055 | −0.129027 | − | 0.991641i | \(-0.541186\pi\) | ||||
−0.129027 | + | 0.991641i | \(0.541186\pi\) | |||||||
\(380\) | −15.0800 | −0.773586 | ||||||||
\(381\) | −23.1410 | −1.18555 | ||||||||
\(382\) | 0.561071 | 0.0287069 | ||||||||
\(383\) | 30.2657 | 1.54650 | 0.773252 | − | 0.634099i | \(-0.218629\pi\) | ||||
0.773252 | + | 0.634099i | \(0.218629\pi\) | |||||||
\(384\) | −2.87355 | −0.146640 | ||||||||
\(385\) | 2.98370 | 0.152063 | ||||||||
\(386\) | −12.0776 | −0.614736 | ||||||||
\(387\) | 5.18424 | 0.263530 | ||||||||
\(388\) | 8.57923 | 0.435544 | ||||||||
\(389\) | 33.7613 | 1.71177 | 0.855884 | − | 0.517168i | \(-0.173014\pi\) | ||||
0.855884 | + | 0.517168i | \(0.173014\pi\) | |||||||
\(390\) | −30.4246 | −1.54061 | ||||||||
\(391\) | −21.1187 | −1.06802 | ||||||||
\(392\) | −6.77518 | −0.342198 | ||||||||
\(393\) | −2.16187 | −0.109052 | ||||||||
\(394\) | 3.06465 | 0.154395 | ||||||||
\(395\) | 25.0703 | 1.26143 | ||||||||
\(396\) | 16.4895 | 0.828630 | ||||||||
\(397\) | −12.1085 | −0.607706 | −0.303853 | − | 0.952719i | \(-0.598273\pi\) | ||||
−0.303853 | + | 0.952719i | \(0.598273\pi\) | |||||||
\(398\) | 22.3326 | 1.11943 | ||||||||
\(399\) | 10.2412 | 0.512699 | ||||||||
\(400\) | −0.974857 | −0.0487429 | ||||||||
\(401\) | 39.6423 | 1.97964 | 0.989821 | − | 0.142318i | \(-0.0454554\pi\) | ||||
0.989821 | + | 0.142318i | \(0.0454554\pi\) | |||||||
\(402\) | −44.5194 | −2.22042 | ||||||||
\(403\) | −12.6560 | −0.630441 | ||||||||
\(404\) | 0.137329 | 0.00683236 | ||||||||
\(405\) | 5.75281 | 0.285859 | ||||||||
\(406\) | −3.79170 | −0.188179 | ||||||||
\(407\) | −1.78637 | −0.0885471 | ||||||||
\(408\) | 11.9853 | 0.593362 | ||||||||
\(409\) | 1.71914 | 0.0850059 | 0.0425029 | − | 0.999096i | \(-0.486467\pi\) | ||||
0.0425029 | + | 0.999096i | \(0.486467\pi\) | |||||||
\(410\) | −23.0216 | −1.13695 | ||||||||
\(411\) | 31.1227 | 1.53517 | ||||||||
\(412\) | −3.54690 | −0.174743 | ||||||||
\(413\) | −6.99040 | −0.343975 | ||||||||
\(414\) | 26.6195 | 1.30828 | ||||||||
\(415\) | 9.04521 | 0.444012 | ||||||||
\(416\) | 5.27734 | 0.258743 | ||||||||
\(417\) | −25.0866 | −1.22849 | ||||||||
\(418\) | −23.5751 | −1.15310 | ||||||||
\(419\) | −9.23743 | −0.451278 | −0.225639 | − | 0.974211i | \(-0.572447\pi\) | ||||
−0.225639 | + | 0.974211i | \(0.572447\pi\) | |||||||
\(420\) | −2.73357 | −0.133385 | ||||||||
\(421\) | 29.7368 | 1.44928 | 0.724641 | − | 0.689127i | \(-0.242006\pi\) | ||||
0.724641 | + | 0.689127i | \(0.242006\pi\) | |||||||
\(422\) | −12.4694 | −0.606999 | ||||||||
\(423\) | −66.0674 | −3.21231 | ||||||||
\(424\) | −3.91121 | −0.189945 | ||||||||
\(425\) | 4.06604 | 0.197232 | ||||||||
\(426\) | 9.99063 | 0.484047 | ||||||||
\(427\) | −1.39133 | −0.0673310 | ||||||||
\(428\) | 8.85259 | 0.427906 | ||||||||
\(429\) | −47.5641 | −2.29642 | ||||||||
\(430\) | 1.97839 | 0.0954065 | ||||||||
\(431\) | −34.9712 | −1.68450 | −0.842252 | − | 0.539083i | \(-0.818771\pi\) | ||||
−0.842252 | + | 0.539083i | \(0.818771\pi\) | |||||||
\(432\) | −6.48651 | −0.312083 | ||||||||
\(433\) | −2.66594 | −0.128117 | −0.0640584 | − | 0.997946i | \(-0.520404\pi\) | ||||
−0.0640584 | + | 0.997946i | \(0.520404\pi\) | |||||||
\(434\) | −1.13711 | −0.0545829 | ||||||||
\(435\) | 46.1025 | 2.21044 | ||||||||
\(436\) | −18.9773 | −0.908848 | ||||||||
\(437\) | −38.0580 | −1.82056 | ||||||||
\(438\) | 45.8203 | 2.18938 | ||||||||
\(439\) | −8.69016 | −0.414759 | −0.207379 | − | 0.978261i | \(-0.566493\pi\) | ||||
−0.207379 | + | 0.978261i | \(0.566493\pi\) | |||||||
\(440\) | 6.29267 | 0.299991 | ||||||||
\(441\) | −35.6192 | −1.69615 | ||||||||
\(442\) | −22.0113 | −1.04697 | ||||||||
\(443\) | −23.0163 | −1.09354 | −0.546768 | − | 0.837284i | \(-0.684142\pi\) | ||||
−0.546768 | + | 0.837284i | \(0.684142\pi\) | |||||||
\(444\) | 1.63662 | 0.0776704 | ||||||||
\(445\) | −23.4783 | −1.11298 | ||||||||
\(446\) | 0.373646 | 0.0176927 | ||||||||
\(447\) | −28.3049 | −1.33877 | ||||||||
\(448\) | 0.474155 | 0.0224017 | ||||||||
\(449\) | 18.6419 | 0.879764 | 0.439882 | − | 0.898056i | \(-0.355020\pi\) | ||||
0.439882 | + | 0.898056i | \(0.355020\pi\) | |||||||
\(450\) | −5.12513 | −0.241601 | ||||||||
\(451\) | −35.9906 | −1.69473 | ||||||||
\(452\) | −7.64564 | −0.359621 | ||||||||
\(453\) | −18.5563 | −0.871852 | ||||||||
\(454\) | −24.1798 | −1.13481 | ||||||||
\(455\) | 5.02026 | 0.235353 | ||||||||
\(456\) | 21.5988 | 1.01146 | ||||||||
\(457\) | −11.6584 | −0.545358 | −0.272679 | − | 0.962105i | \(-0.587910\pi\) | ||||
−0.272679 | + | 0.962105i | \(0.587910\pi\) | |||||||
\(458\) | −6.68006 | −0.312139 | ||||||||
\(459\) | 27.0546 | 1.26280 | ||||||||
\(460\) | 10.1584 | 0.473639 | ||||||||
\(461\) | 29.5786 | 1.37761 | 0.688806 | − | 0.724946i | \(-0.258135\pi\) | ||||
0.688806 | + | 0.724946i | \(0.258135\pi\) | |||||||
\(462\) | −4.27350 | −0.198821 | ||||||||
\(463\) | −34.6632 | −1.61094 | −0.805469 | − | 0.592639i | \(-0.798086\pi\) | ||||
−0.805469 | + | 0.592639i | \(0.798086\pi\) | |||||||
\(464\) | −7.99676 | −0.371240 | ||||||||
\(465\) | 13.8258 | 0.641158 | ||||||||
\(466\) | −11.6049 | −0.537585 | ||||||||
\(467\) | −5.43995 | −0.251731 | −0.125866 | − | 0.992047i | \(-0.540171\pi\) | ||||
−0.125866 | + | 0.992047i | \(0.540171\pi\) | |||||||
\(468\) | 27.7447 | 1.28250 | ||||||||
\(469\) | 7.34598 | 0.339206 | ||||||||
\(470\) | −25.2124 | −1.16296 | ||||||||
\(471\) | −41.6731 | −1.92019 | ||||||||
\(472\) | −14.7429 | −0.678595 | ||||||||
\(473\) | 3.09290 | 0.142212 | ||||||||
\(474\) | −35.9078 | −1.64930 | ||||||||
\(475\) | 7.32741 | 0.336205 | ||||||||
\(476\) | −1.97766 | −0.0906457 | ||||||||
\(477\) | −20.5625 | −0.941490 | ||||||||
\(478\) | 8.85678 | 0.405100 | ||||||||
\(479\) | 5.97601 | 0.273051 | 0.136525 | − | 0.990637i | \(-0.456406\pi\) | ||||
0.136525 | + | 0.990637i | \(0.456406\pi\) | |||||||
\(480\) | −5.76514 | −0.263142 | ||||||||
\(481\) | −3.00568 | −0.137047 | ||||||||
\(482\) | 9.26722 | 0.422110 | ||||||||
\(483\) | −6.89883 | −0.313908 | ||||||||
\(484\) | −1.16241 | −0.0528370 | ||||||||
\(485\) | 17.2123 | 0.781570 | ||||||||
\(486\) | 11.2199 | 0.508945 | ||||||||
\(487\) | 23.8893 | 1.08253 | 0.541264 | − | 0.840853i | \(-0.317946\pi\) | ||||
0.541264 | + | 0.840853i | \(0.317946\pi\) | |||||||
\(488\) | −2.93433 | −0.132831 | ||||||||
\(489\) | −15.4873 | −0.700362 | ||||||||
\(490\) | −13.5929 | −0.614063 | ||||||||
\(491\) | 17.3083 | 0.781111 | 0.390556 | − | 0.920579i | \(-0.372283\pi\) | ||||
0.390556 | + | 0.920579i | \(0.372283\pi\) | |||||||
\(492\) | 32.9734 | 1.48656 | ||||||||
\(493\) | 33.3537 | 1.50218 | ||||||||
\(494\) | −39.6666 | −1.78469 | ||||||||
\(495\) | 33.0825 | 1.48695 | ||||||||
\(496\) | −2.39818 | −0.107681 | ||||||||
\(497\) | −1.64852 | −0.0739461 | ||||||||
\(498\) | −12.9553 | −0.580541 | ||||||||
\(499\) | −22.6110 | −1.01221 | −0.506104 | − | 0.862472i | \(-0.668915\pi\) | ||||
−0.506104 | + | 0.862472i | \(0.668915\pi\) | |||||||
\(500\) | −11.9872 | −0.536084 | ||||||||
\(501\) | −18.3034 | −0.817734 | ||||||||
\(502\) | 6.32352 | 0.282233 | ||||||||
\(503\) | −5.34781 | −0.238447 | −0.119223 | − | 0.992867i | \(-0.538040\pi\) | ||||
−0.119223 | + | 0.992867i | \(0.538040\pi\) | |||||||
\(504\) | 2.49278 | 0.111037 | ||||||||
\(505\) | 0.275519 | 0.0122604 | ||||||||
\(506\) | 15.8811 | 0.706000 | ||||||||
\(507\) | −42.6733 | −1.89519 | ||||||||
\(508\) | 8.05309 | 0.357298 | ||||||||
\(509\) | −31.4902 | −1.39578 | −0.697889 | − | 0.716206i | \(-0.745877\pi\) | ||||
−0.697889 | + | 0.716206i | \(0.745877\pi\) | |||||||
\(510\) | 24.0459 | 1.06477 | ||||||||
\(511\) | −7.56064 | −0.334463 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 48.7552 | 2.15259 | ||||||||
\(514\) | 23.3014 | 1.02778 | ||||||||
\(515\) | −7.11605 | −0.313571 | ||||||||
\(516\) | −2.83362 | −0.124743 | ||||||||
\(517\) | −39.4155 | −1.73349 | ||||||||
\(518\) | −0.270052 | −0.0118654 | ||||||||
\(519\) | −22.4457 | −0.985255 | ||||||||
\(520\) | 10.5878 | 0.464306 | ||||||||
\(521\) | 22.5914 | 0.989749 | 0.494874 | − | 0.868965i | \(-0.335214\pi\) | ||||
0.494874 | + | 0.868965i | \(0.335214\pi\) | |||||||
\(522\) | −42.0415 | −1.84011 | ||||||||
\(523\) | 32.8113 | 1.43474 | 0.717369 | − | 0.696694i | \(-0.245346\pi\) | ||||
0.717369 | + | 0.696694i | \(0.245346\pi\) | |||||||
\(524\) | 0.752333 | 0.0328658 | ||||||||
\(525\) | 1.32825 | 0.0579697 | ||||||||
\(526\) | −32.2528 | −1.40629 | ||||||||
\(527\) | 10.0026 | 0.435719 | ||||||||
\(528\) | −9.01288 | −0.392235 | ||||||||
\(529\) | 2.63728 | 0.114664 | ||||||||
\(530\) | −7.84696 | −0.340850 | ||||||||
\(531\) | −77.5079 | −3.36356 | ||||||||
\(532\) | −3.56394 | −0.154516 | ||||||||
\(533\) | −60.5564 | −2.62299 | ||||||||
\(534\) | 33.6276 | 1.45521 | ||||||||
\(535\) | 17.7607 | 0.767864 | ||||||||
\(536\) | 15.4928 | 0.669186 | ||||||||
\(537\) | −44.3844 | −1.91533 | ||||||||
\(538\) | −9.79631 | −0.422349 | ||||||||
\(539\) | −21.2503 | −0.915315 | ||||||||
\(540\) | −13.0137 | −0.560022 | ||||||||
\(541\) | −12.0832 | −0.519497 | −0.259748 | − | 0.965676i | \(-0.583640\pi\) | ||||
−0.259748 | + | 0.965676i | \(0.583640\pi\) | |||||||
\(542\) | 10.6748 | 0.458524 | ||||||||
\(543\) | 31.7693 | 1.36335 | ||||||||
\(544\) | −4.17091 | −0.178826 | ||||||||
\(545\) | −38.0737 | −1.63090 | ||||||||
\(546\) | −7.19043 | −0.307722 | ||||||||
\(547\) | 13.1188 | 0.560919 | 0.280459 | − | 0.959866i | \(-0.409513\pi\) | ||||
0.280459 | + | 0.959866i | \(0.409513\pi\) | |||||||
\(548\) | −10.8307 | −0.462666 | ||||||||
\(549\) | −15.4267 | −0.658395 | ||||||||
\(550\) | −3.05763 | −0.130378 | ||||||||
\(551\) | 60.1068 | 2.56064 | ||||||||
\(552\) | −14.5497 | −0.619278 | ||||||||
\(553\) | 5.92502 | 0.251957 | ||||||||
\(554\) | 18.6153 | 0.790889 | ||||||||
\(555\) | 3.28350 | 0.139377 | ||||||||
\(556\) | 8.73015 | 0.370241 | ||||||||
\(557\) | −18.2352 | −0.772649 | −0.386324 | − | 0.922363i | \(-0.626255\pi\) | ||||
−0.386324 | + | 0.922363i | \(0.626255\pi\) | |||||||
\(558\) | −12.6080 | −0.533738 | ||||||||
\(559\) | 5.20400 | 0.220106 | ||||||||
\(560\) | 0.951285 | 0.0401991 | ||||||||
\(561\) | 37.5919 | 1.58713 | ||||||||
\(562\) | 26.5735 | 1.12094 | ||||||||
\(563\) | 10.1351 | 0.427145 | 0.213573 | − | 0.976927i | \(-0.431490\pi\) | ||||
0.213573 | + | 0.976927i | \(0.431490\pi\) | |||||||
\(564\) | 36.1113 | 1.52056 | ||||||||
\(565\) | −15.3393 | −0.645328 | ||||||||
\(566\) | −23.3476 | −0.981373 | ||||||||
\(567\) | 1.35959 | 0.0570976 | ||||||||
\(568\) | −3.47675 | −0.145881 | ||||||||
\(569\) | 9.95090 | 0.417163 | 0.208582 | − | 0.978005i | \(-0.433115\pi\) | ||||
0.208582 | + | 0.978005i | \(0.433115\pi\) | |||||||
\(570\) | 43.3331 | 1.81502 | ||||||||
\(571\) | 41.1917 | 1.72382 | 0.861909 | − | 0.507063i | \(-0.169269\pi\) | ||||
0.861909 | + | 0.507063i | \(0.169269\pi\) | |||||||
\(572\) | 16.5524 | 0.692089 | ||||||||
\(573\) | −1.61227 | −0.0673535 | ||||||||
\(574\) | −5.44082 | −0.227096 | ||||||||
\(575\) | −4.93602 | −0.205846 | ||||||||
\(576\) | 5.25731 | 0.219055 | ||||||||
\(577\) | 3.91645 | 0.163044 | 0.0815219 | − | 0.996672i | \(-0.474022\pi\) | ||||
0.0815219 | + | 0.996672i | \(0.474022\pi\) | |||||||
\(578\) | 0.396457 | 0.0164904 | ||||||||
\(579\) | 34.7058 | 1.44232 | ||||||||
\(580\) | −16.0437 | −0.666179 | ||||||||
\(581\) | 2.13771 | 0.0886871 | ||||||||
\(582\) | −24.6529 | −1.02189 | ||||||||
\(583\) | −12.2675 | −0.508067 | ||||||||
\(584\) | −15.9455 | −0.659830 | ||||||||
\(585\) | 55.6634 | 2.30140 | ||||||||
\(586\) | 10.9773 | 0.453468 | ||||||||
\(587\) | 14.6065 | 0.602873 | 0.301437 | − | 0.953486i | \(-0.402534\pi\) | ||||
0.301437 | + | 0.953486i | \(0.402534\pi\) | |||||||
\(588\) | 19.4688 | 0.802881 | ||||||||
\(589\) | 18.0257 | 0.742734 | ||||||||
\(590\) | −29.5783 | −1.21772 | ||||||||
\(591\) | −8.80642 | −0.362248 | ||||||||
\(592\) | −0.569544 | −0.0234081 | ||||||||
\(593\) | 4.28773 | 0.176076 | 0.0880380 | − | 0.996117i | \(-0.471940\pi\) | ||||
0.0880380 | + | 0.996117i | \(0.471940\pi\) | |||||||
\(594\) | −20.3449 | −0.834761 | ||||||||
\(595\) | −3.96772 | −0.162661 | ||||||||
\(596\) | 9.85012 | 0.403477 | ||||||||
\(597\) | −64.1741 | −2.62647 | ||||||||
\(598\) | 26.7209 | 1.09270 | ||||||||
\(599\) | −30.4161 | −1.24277 | −0.621385 | − | 0.783505i | \(-0.713430\pi\) | ||||
−0.621385 | + | 0.783505i | \(0.713430\pi\) | |||||||
\(600\) | 2.80130 | 0.114363 | ||||||||
\(601\) | 19.7703 | 0.806449 | 0.403224 | − | 0.915101i | \(-0.367889\pi\) | ||||
0.403224 | + | 0.915101i | \(0.367889\pi\) | |||||||
\(602\) | 0.467565 | 0.0190565 | ||||||||
\(603\) | 81.4504 | 3.31692 | ||||||||
\(604\) | 6.45762 | 0.262757 | ||||||||
\(605\) | −2.33212 | −0.0948143 | ||||||||
\(606\) | −0.394621 | −0.0160304 | ||||||||
\(607\) | −3.52900 | −0.143238 | −0.0716188 | − | 0.997432i | \(-0.522817\pi\) | ||||
−0.0716188 | + | 0.997432i | \(0.522817\pi\) | |||||||
\(608\) | −7.51640 | −0.304830 | ||||||||
\(609\) | 10.8957 | 0.441515 | ||||||||
\(610\) | −5.88708 | −0.238361 | ||||||||
\(611\) | −66.3191 | −2.68298 | ||||||||
\(612\) | −21.9278 | −0.886377 | ||||||||
\(613\) | −45.4906 | −1.83735 | −0.918673 | − | 0.395018i | \(-0.870738\pi\) | ||||
−0.918673 | + | 0.395018i | \(0.870738\pi\) | |||||||
\(614\) | −25.7684 | −1.03993 | ||||||||
\(615\) | 66.1537 | 2.66758 | ||||||||
\(616\) | 1.48718 | 0.0599203 | ||||||||
\(617\) | −7.29572 | −0.293715 | −0.146857 | − | 0.989158i | \(-0.546916\pi\) | ||||
−0.146857 | + | 0.989158i | \(0.546916\pi\) | |||||||
\(618\) | 10.1922 | 0.409990 | ||||||||
\(619\) | 19.3059 | 0.775970 | 0.387985 | − | 0.921666i | \(-0.373171\pi\) | ||||
0.387985 | + | 0.921666i | \(0.373171\pi\) | |||||||
\(620\) | −4.81141 | −0.193231 | ||||||||
\(621\) | −32.8433 | −1.31796 | ||||||||
\(622\) | 7.77395 | 0.311707 | ||||||||
\(623\) | −5.54876 | −0.222306 | ||||||||
\(624\) | −15.1647 | −0.607075 | ||||||||
\(625\) | −19.1754 | −0.767015 | ||||||||
\(626\) | −14.1309 | −0.564785 | ||||||||
\(627\) | 67.7444 | 2.70545 | ||||||||
\(628\) | 14.5023 | 0.578704 | ||||||||
\(629\) | 2.37552 | 0.0947180 | ||||||||
\(630\) | 5.00121 | 0.199253 | ||||||||
\(631\) | 11.8848 | 0.473126 | 0.236563 | − | 0.971616i | \(-0.423979\pi\) | ||||
0.236563 | + | 0.971616i | \(0.423979\pi\) | |||||||
\(632\) | 12.4960 | 0.497062 | ||||||||
\(633\) | 35.8314 | 1.42417 | ||||||||
\(634\) | 12.4982 | 0.496367 | ||||||||
\(635\) | 16.1567 | 0.641160 | ||||||||
\(636\) | 11.2391 | 0.445658 | ||||||||
\(637\) | −35.7549 | −1.41666 | ||||||||
\(638\) | −25.0818 | −0.992997 | ||||||||
\(639\) | −18.2784 | −0.723081 | ||||||||
\(640\) | 2.00628 | 0.0793050 | ||||||||
\(641\) | −28.6778 | −1.13271 | −0.566353 | − | 0.824163i | \(-0.691646\pi\) | ||||
−0.566353 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(642\) | −25.4384 | −1.00397 | ||||||||
\(643\) | 2.10027 | 0.0828265 | 0.0414133 | − | 0.999142i | \(-0.486814\pi\) | ||||
0.0414133 | + | 0.999142i | \(0.486814\pi\) | |||||||
\(644\) | 2.40080 | 0.0946048 | ||||||||
\(645\) | −5.68501 | −0.223847 | ||||||||
\(646\) | 31.3502 | 1.23346 | ||||||||
\(647\) | −3.63405 | −0.142869 | −0.0714345 | − | 0.997445i | \(-0.522758\pi\) | ||||
−0.0714345 | + | 0.997445i | \(0.522758\pi\) | |||||||
\(648\) | 2.86741 | 0.112642 | ||||||||
\(649\) | −46.2409 | −1.81511 | ||||||||
\(650\) | −5.14466 | −0.201790 | ||||||||
\(651\) | 3.26754 | 0.128065 | ||||||||
\(652\) | 5.38961 | 0.211073 | ||||||||
\(653\) | 23.0756 | 0.903019 | 0.451510 | − | 0.892266i | \(-0.350886\pi\) | ||||
0.451510 | + | 0.892266i | \(0.350886\pi\) | |||||||
\(654\) | 54.5323 | 2.13238 | ||||||||
\(655\) | 1.50939 | 0.0589766 | ||||||||
\(656\) | −11.4748 | −0.448015 | ||||||||
\(657\) | −83.8305 | −3.27054 | ||||||||
\(658\) | −5.95859 | −0.232290 | ||||||||
\(659\) | −32.7884 | −1.27726 | −0.638628 | − | 0.769516i | \(-0.720498\pi\) | ||||
−0.638628 | + | 0.769516i | \(0.720498\pi\) | |||||||
\(660\) | −18.0823 | −0.703854 | ||||||||
\(661\) | −8.78604 | −0.341737 | −0.170869 | − | 0.985294i | \(-0.554657\pi\) | ||||
−0.170869 | + | 0.985294i | \(0.554657\pi\) | |||||||
\(662\) | −22.5909 | −0.878021 | ||||||||
\(663\) | 63.2507 | 2.45645 | ||||||||
\(664\) | 4.50846 | 0.174962 | ||||||||
\(665\) | −7.15024 | −0.277274 | ||||||||
\(666\) | −2.99427 | −0.116026 | ||||||||
\(667\) | −40.4902 | −1.56779 | ||||||||
\(668\) | 6.36959 | 0.246447 | ||||||||
\(669\) | −1.07369 | −0.0415113 | ||||||||
\(670\) | 31.0828 | 1.20083 | ||||||||
\(671\) | −9.20350 | −0.355297 | ||||||||
\(672\) | −1.36251 | −0.0525600 | ||||||||
\(673\) | −21.7062 | −0.836712 | −0.418356 | − | 0.908283i | \(-0.637394\pi\) | ||||
−0.418356 | + | 0.908283i | \(0.637394\pi\) | |||||||
\(674\) | 22.9344 | 0.883399 | ||||||||
\(675\) | 6.32342 | 0.243389 | ||||||||
\(676\) | 14.8504 | 0.571168 | ||||||||
\(677\) | 7.79013 | 0.299399 | 0.149700 | − | 0.988732i | \(-0.452169\pi\) | ||||
0.149700 | + | 0.988732i | \(0.452169\pi\) | |||||||
\(678\) | 21.9702 | 0.843759 | ||||||||
\(679\) | 4.06788 | 0.156111 | ||||||||
\(680\) | −8.36799 | −0.320898 | ||||||||
\(681\) | 69.4819 | 2.66255 | ||||||||
\(682\) | −7.52187 | −0.288027 | ||||||||
\(683\) | −9.95393 | −0.380877 | −0.190438 | − | 0.981699i | \(-0.560991\pi\) | ||||
−0.190438 | + | 0.981699i | \(0.560991\pi\) | |||||||
\(684\) | −39.5161 | −1.51093 | ||||||||
\(685\) | −21.7294 | −0.830239 | ||||||||
\(686\) | −6.53157 | −0.249376 | ||||||||
\(687\) | 19.1955 | 0.732354 | ||||||||
\(688\) | 0.986101 | 0.0375948 | ||||||||
\(689\) | −20.6408 | −0.786352 | ||||||||
\(690\) | −29.1908 | −1.11127 | ||||||||
\(691\) | 19.8504 | 0.755145 | 0.377572 | − | 0.925980i | \(-0.376759\pi\) | ||||
0.377572 | + | 0.925980i | \(0.376759\pi\) | |||||||
\(692\) | 7.81112 | 0.296934 | ||||||||
\(693\) | 7.81859 | 0.297004 | ||||||||
\(694\) | −20.7794 | −0.788776 | ||||||||
\(695\) | 17.5151 | 0.664385 | ||||||||
\(696\) | 22.9791 | 0.871022 | ||||||||
\(697\) | 47.8602 | 1.81284 | ||||||||
\(698\) | 20.9301 | 0.792216 | ||||||||
\(699\) | 33.3472 | 1.26131 | ||||||||
\(700\) | −0.462233 | −0.0174708 | ||||||||
\(701\) | 10.8325 | 0.409138 | 0.204569 | − | 0.978852i | \(-0.434421\pi\) | ||||
0.204569 | + | 0.978852i | \(0.434421\pi\) | |||||||
\(702\) | −34.2316 | −1.29199 | ||||||||
\(703\) | 4.28092 | 0.161458 | ||||||||
\(704\) | 3.13649 | 0.118211 | ||||||||
\(705\) | 72.4491 | 2.72859 | ||||||||
\(706\) | −25.8437 | −0.972641 | ||||||||
\(707\) | 0.0651151 | 0.00244890 | ||||||||
\(708\) | 42.3644 | 1.59215 | ||||||||
\(709\) | 7.46164 | 0.280228 | 0.140114 | − | 0.990135i | \(-0.455253\pi\) | ||||
0.140114 | + | 0.990135i | \(0.455253\pi\) | |||||||
\(710\) | −6.97532 | −0.261779 | ||||||||
\(711\) | 65.6951 | 2.46376 | ||||||||
\(712\) | −11.7024 | −0.438567 | ||||||||
\(713\) | −12.1428 | −0.454750 | ||||||||
\(714\) | 5.68290 | 0.212677 | ||||||||
\(715\) | 33.2086 | 1.24193 | ||||||||
\(716\) | 15.4458 | 0.577237 | ||||||||
\(717\) | −25.4504 | −0.950464 | ||||||||
\(718\) | −16.6639 | −0.621892 | ||||||||
\(719\) | 32.8904 | 1.22660 | 0.613302 | − | 0.789848i | \(-0.289841\pi\) | ||||
0.613302 | + | 0.789848i | \(0.289841\pi\) | |||||||
\(720\) | 10.5476 | 0.393087 | ||||||||
\(721\) | −1.68178 | −0.0626327 | ||||||||
\(722\) | 37.4962 | 1.39546 | ||||||||
\(723\) | −26.6298 | −0.990375 | ||||||||
\(724\) | −11.0557 | −0.410883 | ||||||||
\(725\) | 7.79570 | 0.289525 | ||||||||
\(726\) | 3.34026 | 0.123969 | ||||||||
\(727\) | 8.15963 | 0.302624 | 0.151312 | − | 0.988486i | \(-0.451650\pi\) | ||||
0.151312 | + | 0.988486i | \(0.451650\pi\) | |||||||
\(728\) | 2.50228 | 0.0927406 | ||||||||
\(729\) | −40.8432 | −1.51271 | ||||||||
\(730\) | −31.9911 | −1.18404 | ||||||||
\(731\) | −4.11294 | −0.152122 | ||||||||
\(732\) | 8.43196 | 0.311654 | ||||||||
\(733\) | −47.1494 | −1.74150 | −0.870752 | − | 0.491723i | \(-0.836367\pi\) | ||||
−0.870752 | + | 0.491723i | \(0.836367\pi\) | |||||||
\(734\) | −0.0793847 | −0.00293014 | ||||||||
\(735\) | 39.0599 | 1.44074 | ||||||||
\(736\) | 5.06333 | 0.186637 | ||||||||
\(737\) | 48.5930 | 1.78995 | ||||||||
\(738\) | −60.3265 | −2.22065 | ||||||||
\(739\) | 7.20872 | 0.265177 | 0.132589 | − | 0.991171i | \(-0.457671\pi\) | ||||
0.132589 | + | 0.991171i | \(0.457671\pi\) | |||||||
\(740\) | −1.14266 | −0.0420051 | ||||||||
\(741\) | 113.984 | 4.18731 | ||||||||
\(742\) | −1.85452 | −0.0680815 | ||||||||
\(743\) | −3.81638 | −0.140009 | −0.0700047 | − | 0.997547i | \(-0.522301\pi\) | ||||
−0.0700047 | + | 0.997547i | \(0.522301\pi\) | |||||||
\(744\) | 6.89130 | 0.252647 | ||||||||
\(745\) | 19.7621 | 0.724026 | ||||||||
\(746\) | −14.5444 | −0.532507 | ||||||||
\(747\) | 23.7024 | 0.867225 | ||||||||
\(748\) | −13.0820 | −0.478326 | ||||||||
\(749\) | 4.19750 | 0.153373 | ||||||||
\(750\) | 34.4459 | 1.25779 | ||||||||
\(751\) | 25.1095 | 0.916260 | 0.458130 | − | 0.888885i | \(-0.348519\pi\) | ||||
0.458130 | + | 0.888885i | \(0.348519\pi\) | |||||||
\(752\) | −12.5668 | −0.458262 | ||||||||
\(753\) | −18.1710 | −0.662187 | ||||||||
\(754\) | −42.2017 | −1.53689 | ||||||||
\(755\) | 12.9558 | 0.471509 | ||||||||
\(756\) | −3.07561 | −0.111859 | ||||||||
\(757\) | −27.7020 | −1.00685 | −0.503423 | − | 0.864040i | \(-0.667926\pi\) | ||||
−0.503423 | + | 0.864040i | \(0.667926\pi\) | |||||||
\(758\) | −5.02379 | −0.182472 | ||||||||
\(759\) | −45.6352 | −1.65645 | ||||||||
\(760\) | −15.0800 | −0.547008 | ||||||||
\(761\) | −15.8264 | −0.573708 | −0.286854 | − | 0.957974i | \(-0.592609\pi\) | ||||
−0.286854 | + | 0.957974i | \(0.592609\pi\) | |||||||
\(762\) | −23.1410 | −0.838309 | ||||||||
\(763\) | −8.99818 | −0.325756 | ||||||||
\(764\) | 0.561071 | 0.0202988 | ||||||||
\(765\) | −43.9931 | −1.59058 | ||||||||
\(766\) | 30.2657 | 1.09354 | ||||||||
\(767\) | −77.8032 | −2.80931 | ||||||||
\(768\) | −2.87355 | −0.103690 | ||||||||
\(769\) | 31.2360 | 1.12640 | 0.563200 | − | 0.826321i | \(-0.309570\pi\) | ||||
0.563200 | + | 0.826321i | \(0.309570\pi\) | |||||||
\(770\) | 2.98370 | 0.107525 | ||||||||
\(771\) | −66.9578 | −2.41143 | ||||||||
\(772\) | −12.0776 | −0.434684 | ||||||||
\(773\) | 28.4596 | 1.02362 | 0.511811 | − | 0.859098i | \(-0.328975\pi\) | ||||
0.511811 | + | 0.859098i | \(0.328975\pi\) | |||||||
\(774\) | 5.18424 | 0.186344 | ||||||||
\(775\) | 2.33788 | 0.0839792 | ||||||||
\(776\) | 8.57923 | 0.307976 | ||||||||
\(777\) | 0.776010 | 0.0278392 | ||||||||
\(778\) | 33.7613 | 1.21040 | ||||||||
\(779\) | 86.2490 | 3.09019 | ||||||||
\(780\) | −30.4246 | −1.08938 | ||||||||
\(781\) | −10.9048 | −0.390204 | ||||||||
\(782\) | −21.1187 | −0.755202 | ||||||||
\(783\) | 51.8711 | 1.85372 | ||||||||
\(784\) | −6.77518 | −0.241971 | ||||||||
\(785\) | 29.0956 | 1.03847 | ||||||||
\(786\) | −2.16187 | −0.0771113 | ||||||||
\(787\) | 20.1144 | 0.717001 | 0.358501 | − | 0.933530i | \(-0.383288\pi\) | ||||
0.358501 | + | 0.933530i | \(0.383288\pi\) | |||||||
\(788\) | 3.06465 | 0.109173 | ||||||||
\(789\) | 92.6802 | 3.29950 | ||||||||
\(790\) | 25.0703 | 0.891962 | ||||||||
\(791\) | −3.62522 | −0.128898 | ||||||||
\(792\) | 16.4895 | 0.585930 | ||||||||
\(793\) | −15.4855 | −0.549905 | ||||||||
\(794\) | −12.1085 | −0.429713 | ||||||||
\(795\) | 22.5487 | 0.799719 | ||||||||
\(796\) | 22.3326 | 0.791560 | ||||||||
\(797\) | −56.2427 | −1.99222 | −0.996110 | − | 0.0881204i | \(-0.971914\pi\) | ||||
−0.996110 | + | 0.0881204i | \(0.971914\pi\) | |||||||
\(798\) | 10.2412 | 0.362533 | ||||||||
\(799\) | 52.4148 | 1.85430 | ||||||||
\(800\) | −0.974857 | −0.0344664 | ||||||||
\(801\) | −61.5233 | −2.17382 | ||||||||
\(802\) | 39.6423 | 1.39982 | ||||||||
\(803\) | −50.0130 | −1.76492 | ||||||||
\(804\) | −44.5194 | −1.57008 | ||||||||
\(805\) | 4.81667 | 0.169765 | ||||||||
\(806\) | −12.6560 | −0.445789 | ||||||||
\(807\) | 28.1502 | 0.990935 | ||||||||
\(808\) | 0.137329 | 0.00483121 | ||||||||
\(809\) | 14.2122 | 0.499676 | 0.249838 | − | 0.968288i | \(-0.419623\pi\) | ||||
0.249838 | + | 0.968288i | \(0.419623\pi\) | |||||||
\(810\) | 5.75281 | 0.202133 | ||||||||
\(811\) | 44.7633 | 1.57185 | 0.785925 | − | 0.618321i | \(-0.212187\pi\) | ||||
0.785925 | + | 0.618321i | \(0.212187\pi\) | |||||||
\(812\) | −3.79170 | −0.133063 | ||||||||
\(813\) | −30.6748 | −1.07581 | ||||||||
\(814\) | −1.78637 | −0.0626123 | ||||||||
\(815\) | 10.8130 | 0.378765 | ||||||||
\(816\) | 11.9853 | 0.419570 | ||||||||
\(817\) | −7.41193 | −0.259311 | ||||||||
\(818\) | 1.71914 | 0.0601082 | ||||||||
\(819\) | 13.1553 | 0.459682 | ||||||||
\(820\) | −23.0216 | −0.803948 | ||||||||
\(821\) | 23.3131 | 0.813633 | 0.406816 | − | 0.913510i | \(-0.366639\pi\) | ||||
0.406816 | + | 0.913510i | \(0.366639\pi\) | |||||||
\(822\) | 31.1227 | 1.08553 | ||||||||
\(823\) | 16.8012 | 0.585651 | 0.292826 | − | 0.956166i | \(-0.405404\pi\) | ||||
0.292826 | + | 0.956166i | \(0.405404\pi\) | |||||||
\(824\) | −3.54690 | −0.123562 | ||||||||
\(825\) | 8.78627 | 0.305899 | ||||||||
\(826\) | −6.99040 | −0.243227 | ||||||||
\(827\) | −27.9958 | −0.973508 | −0.486754 | − | 0.873539i | \(-0.661819\pi\) | ||||
−0.486754 | + | 0.873539i | \(0.661819\pi\) | |||||||
\(828\) | 26.6195 | 0.925092 | ||||||||
\(829\) | −17.8763 | −0.620869 | −0.310434 | − | 0.950595i | \(-0.600474\pi\) | ||||
−0.310434 | + | 0.950595i | \(0.600474\pi\) | |||||||
\(830\) | 9.04521 | 0.313964 | ||||||||
\(831\) | −53.4921 | −1.85562 | ||||||||
\(832\) | 5.27734 | 0.182959 | ||||||||
\(833\) | 28.2586 | 0.979103 | ||||||||
\(834\) | −25.0866 | −0.868677 | ||||||||
\(835\) | 12.7792 | 0.442241 | ||||||||
\(836\) | −23.5751 | −0.815363 | ||||||||
\(837\) | 15.5558 | 0.537688 | ||||||||
\(838\) | −9.23743 | −0.319102 | ||||||||
\(839\) | 17.9502 | 0.619709 | 0.309855 | − | 0.950784i | \(-0.399720\pi\) | ||||
0.309855 | + | 0.950784i | \(0.399720\pi\) | |||||||
\(840\) | −2.73357 | −0.0943171 | ||||||||
\(841\) | 34.9482 | 1.20511 | ||||||||
\(842\) | 29.7368 | 1.02480 | ||||||||
\(843\) | −76.3604 | −2.62999 | ||||||||
\(844\) | −12.4694 | −0.429213 | ||||||||
\(845\) | 29.7939 | 1.02494 | ||||||||
\(846\) | −66.0674 | −2.27144 | ||||||||
\(847\) | −0.551164 | −0.0189382 | ||||||||
\(848\) | −3.91121 | −0.134311 | ||||||||
\(849\) | 67.0906 | 2.30254 | ||||||||
\(850\) | 4.06604 | 0.139464 | ||||||||
\(851\) | −2.88379 | −0.0988550 | ||||||||
\(852\) | 9.99063 | 0.342273 | ||||||||
\(853\) | −2.16305 | −0.0740614 | −0.0370307 | − | 0.999314i | \(-0.511790\pi\) | ||||
−0.0370307 | + | 0.999314i | \(0.511790\pi\) | |||||||
\(854\) | −1.39133 | −0.0476102 | ||||||||
\(855\) | −79.2801 | −2.71132 | ||||||||
\(856\) | 8.85259 | 0.302575 | ||||||||
\(857\) | 34.8072 | 1.18899 | 0.594496 | − | 0.804098i | \(-0.297352\pi\) | ||||
0.594496 | + | 0.804098i | \(0.297352\pi\) | |||||||
\(858\) | −47.5641 | −1.62381 | ||||||||
\(859\) | 18.7338 | 0.639190 | 0.319595 | − | 0.947554i | \(-0.396453\pi\) | ||||
0.319595 | + | 0.947554i | \(0.396453\pi\) | |||||||
\(860\) | 1.97839 | 0.0674626 | ||||||||
\(861\) | 15.6345 | 0.532822 | ||||||||
\(862\) | −34.9712 | −1.19112 | ||||||||
\(863\) | −40.8284 | −1.38981 | −0.694907 | − | 0.719099i | \(-0.744555\pi\) | ||||
−0.694907 | + | 0.719099i | \(0.744555\pi\) | |||||||
\(864\) | −6.48651 | −0.220676 | ||||||||
\(865\) | 15.6713 | 0.532839 | ||||||||
\(866\) | −2.66594 | −0.0905922 | ||||||||
\(867\) | −1.13924 | −0.0386906 | ||||||||
\(868\) | −1.13711 | −0.0385960 | ||||||||
\(869\) | 39.1935 | 1.32955 | ||||||||
\(870\) | 46.1025 | 1.56302 | ||||||||
\(871\) | 81.7608 | 2.77036 | ||||||||
\(872\) | −18.9773 | −0.642653 | ||||||||
\(873\) | 45.1037 | 1.52653 | ||||||||
\(874\) | −38.0580 | −1.28733 | ||||||||
\(875\) | −5.68379 | −0.192147 | ||||||||
\(876\) | 45.8203 | 1.54812 | ||||||||
\(877\) | 12.8278 | 0.433165 | 0.216583 | − | 0.976264i | \(-0.430509\pi\) | ||||
0.216583 | + | 0.976264i | \(0.430509\pi\) | |||||||
\(878\) | −8.69016 | −0.293279 | ||||||||
\(879\) | −31.5439 | −1.06395 | ||||||||
\(880\) | 6.29267 | 0.212126 | ||||||||
\(881\) | −12.4564 | −0.419666 | −0.209833 | − | 0.977737i | \(-0.567292\pi\) | ||||
−0.209833 | + | 0.977737i | \(0.567292\pi\) | |||||||
\(882\) | −35.6192 | −1.19936 | ||||||||
\(883\) | 46.4232 | 1.56226 | 0.781132 | − | 0.624366i | \(-0.214642\pi\) | ||||
0.781132 | + | 0.624366i | \(0.214642\pi\) | |||||||
\(884\) | −22.0113 | −0.740320 | ||||||||
\(885\) | 84.9947 | 2.85707 | ||||||||
\(886\) | −23.0163 | −0.773247 | ||||||||
\(887\) | −26.8689 | −0.902169 | −0.451085 | − | 0.892481i | \(-0.648963\pi\) | ||||
−0.451085 | + | 0.892481i | \(0.648963\pi\) | |||||||
\(888\) | 1.63662 | 0.0549212 | ||||||||
\(889\) | 3.81841 | 0.128065 | ||||||||
\(890\) | −23.4783 | −0.786994 | ||||||||
\(891\) | 8.99360 | 0.301297 | ||||||||
\(892\) | 0.373646 | 0.0125106 | ||||||||
\(893\) | 94.4567 | 3.16087 | ||||||||
\(894\) | −28.3049 | −0.946656 | ||||||||
\(895\) | 30.9886 | 1.03583 | ||||||||
\(896\) | 0.474155 | 0.0158404 | ||||||||
\(897\) | −76.7840 | −2.56374 | ||||||||
\(898\) | 18.6419 | 0.622087 | ||||||||
\(899\) | 19.1777 | 0.639611 | ||||||||
\(900\) | −5.12513 | −0.170838 | ||||||||
\(901\) | 16.3133 | 0.543474 | ||||||||
\(902\) | −35.9906 | −1.19835 | ||||||||
\(903\) | −1.34357 | −0.0447113 | ||||||||
\(904\) | −7.64564 | −0.254290 | ||||||||
\(905\) | −22.1809 | −0.737317 | ||||||||
\(906\) | −18.5563 | −0.616492 | ||||||||
\(907\) | −11.9869 | −0.398017 | −0.199009 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199009 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(908\) | −24.1798 | −0.802434 | ||||||||
\(909\) | 0.721980 | 0.0239466 | ||||||||
\(910\) | 5.02026 | 0.166420 | ||||||||
\(911\) | 6.41774 | 0.212629 | 0.106315 | − | 0.994333i | \(-0.466095\pi\) | ||||
0.106315 | + | 0.994333i | \(0.466095\pi\) | |||||||
\(912\) | 21.5988 | 0.715207 | ||||||||
\(913\) | 14.1407 | 0.467990 | ||||||||
\(914\) | −11.6584 | −0.385626 | ||||||||
\(915\) | 16.9168 | 0.559253 | ||||||||
\(916\) | −6.68006 | −0.220715 | ||||||||
\(917\) | 0.356722 | 0.0117800 | ||||||||
\(918\) | 27.0546 | 0.892936 | ||||||||
\(919\) | −13.8151 | −0.455717 | −0.227858 | − | 0.973694i | \(-0.573172\pi\) | ||||
−0.227858 | + | 0.973694i | \(0.573172\pi\) | |||||||
\(920\) | 10.1584 | 0.334914 | ||||||||
\(921\) | 74.0469 | 2.43993 | ||||||||
\(922\) | 29.5786 | 0.974118 | ||||||||
\(923\) | −18.3480 | −0.603932 | ||||||||
\(924\) | −4.27350 | −0.140588 | ||||||||
\(925\) | 0.555224 | 0.0182557 | ||||||||
\(926\) | −34.6632 | −1.13910 | ||||||||
\(927\) | −18.6471 | −0.612453 | ||||||||
\(928\) | −7.99676 | −0.262507 | ||||||||
\(929\) | −32.6475 | −1.07113 | −0.535565 | − | 0.844494i | \(-0.679901\pi\) | ||||
−0.535565 | + | 0.844494i | \(0.679901\pi\) | |||||||
\(930\) | 13.8258 | 0.453367 | ||||||||
\(931\) | 50.9249 | 1.66900 | ||||||||
\(932\) | −11.6049 | −0.380130 | ||||||||
\(933\) | −22.3389 | −0.731341 | ||||||||
\(934\) | −5.43995 | −0.178001 | ||||||||
\(935\) | −26.2461 | −0.858340 | ||||||||
\(936\) | 27.7447 | 0.906862 | ||||||||
\(937\) | 52.4364 | 1.71302 | 0.856511 | − | 0.516129i | \(-0.172628\pi\) | ||||
0.856511 | + | 0.516129i | \(0.172628\pi\) | |||||||
\(938\) | 7.34598 | 0.239855 | ||||||||
\(939\) | 40.6059 | 1.32513 | ||||||||
\(940\) | −25.2124 | −0.822337 | ||||||||
\(941\) | −36.5728 | −1.19224 | −0.596119 | − | 0.802896i | \(-0.703292\pi\) | ||||
−0.596119 | + | 0.802896i | \(0.703292\pi\) | |||||||
\(942\) | −41.6731 | −1.35778 | ||||||||
\(943\) | −58.1006 | −1.89201 | ||||||||
\(944\) | −14.7429 | −0.479839 | ||||||||
\(945\) | −6.17053 | −0.200727 | ||||||||
\(946\) | 3.09290 | 0.100559 | ||||||||
\(947\) | 40.2995 | 1.30956 | 0.654779 | − | 0.755820i | \(-0.272762\pi\) | ||||
0.654779 | + | 0.755820i | \(0.272762\pi\) | |||||||
\(948\) | −35.9078 | −1.16623 | ||||||||
\(949\) | −84.1499 | −2.73162 | ||||||||
\(950\) | 7.32741 | 0.237733 | ||||||||
\(951\) | −35.9143 | −1.16460 | ||||||||
\(952\) | −1.97766 | −0.0640962 | ||||||||
\(953\) | 34.4306 | 1.11532 | 0.557659 | − | 0.830070i | \(-0.311700\pi\) | ||||
0.557659 | + | 0.830070i | \(0.311700\pi\) | |||||||
\(954\) | −20.5625 | −0.665734 | ||||||||
\(955\) | 1.12566 | 0.0364256 | ||||||||
\(956\) | 8.85678 | 0.286449 | ||||||||
\(957\) | 72.0739 | 2.32982 | ||||||||
\(958\) | 5.97601 | 0.193076 | ||||||||
\(959\) | −5.13544 | −0.165832 | ||||||||
\(960\) | −5.76514 | −0.186069 | ||||||||
\(961\) | −25.2487 | −0.814475 | ||||||||
\(962\) | −3.00568 | −0.0969071 | ||||||||
\(963\) | 46.5409 | 1.49976 | ||||||||
\(964\) | 9.26722 | 0.298477 | ||||||||
\(965\) | −24.2311 | −0.780026 | ||||||||
\(966\) | −6.89883 | −0.221966 | ||||||||
\(967\) | 30.7935 | 0.990252 | 0.495126 | − | 0.868821i | \(-0.335122\pi\) | ||||
0.495126 | + | 0.868821i | \(0.335122\pi\) | |||||||
\(968\) | −1.16241 | −0.0373614 | ||||||||
\(969\) | −90.0864 | −2.89399 | ||||||||
\(970\) | 17.2123 | 0.552654 | ||||||||
\(971\) | −19.9214 | −0.639310 | −0.319655 | − | 0.947534i | \(-0.603567\pi\) | ||||
−0.319655 | + | 0.947534i | \(0.603567\pi\) | |||||||
\(972\) | 11.2199 | 0.359878 | ||||||||
\(973\) | 4.13944 | 0.132704 | ||||||||
\(974\) | 23.8893 | 0.765463 | ||||||||
\(975\) | 14.7835 | 0.473449 | ||||||||
\(976\) | −2.93433 | −0.0939256 | ||||||||
\(977\) | −53.1745 | −1.70120 | −0.850602 | − | 0.525811i | \(-0.823762\pi\) | ||||
−0.850602 | + | 0.525811i | \(0.823762\pi\) | |||||||
\(978\) | −15.4873 | −0.495231 | ||||||||
\(979\) | −36.7046 | −1.17308 | ||||||||
\(980\) | −13.5929 | −0.434208 | ||||||||
\(981\) | −99.7697 | −3.18540 | ||||||||
\(982\) | 17.3083 | 0.552329 | ||||||||
\(983\) | −9.79688 | −0.312472 | −0.156236 | − | 0.987720i | \(-0.549936\pi\) | ||||
−0.156236 | + | 0.987720i | \(0.549936\pi\) | |||||||
\(984\) | 32.9734 | 1.05115 | ||||||||
\(985\) | 6.14852 | 0.195908 | ||||||||
\(986\) | 33.3537 | 1.06220 | ||||||||
\(987\) | 17.1223 | 0.545010 | ||||||||
\(988\) | −39.6666 | −1.26196 | ||||||||
\(989\) | 4.99295 | 0.158767 | ||||||||
\(990\) | 33.0825 | 1.05143 | ||||||||
\(991\) | −5.64566 | −0.179340 | −0.0896702 | − | 0.995972i | \(-0.528581\pi\) | ||||
−0.0896702 | + | 0.995972i | \(0.528581\pi\) | |||||||
\(992\) | −2.39818 | −0.0761423 | ||||||||
\(993\) | 64.9162 | 2.06005 | ||||||||
\(994\) | −1.64852 | −0.0522878 | ||||||||
\(995\) | 44.8055 | 1.42043 | ||||||||
\(996\) | −12.9553 | −0.410504 | ||||||||
\(997\) | 10.2970 | 0.326109 | 0.163055 | − | 0.986617i | \(-0.447865\pi\) | ||||
0.163055 | + | 0.986617i | \(0.447865\pi\) | |||||||
\(998\) | −22.6110 | −0.715739 | ||||||||
\(999\) | 3.69436 | 0.116884 |
(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 | 8002.2.a.d.1.7 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.7 | ✓ | 69 | 1.1 | even | 1 | trivial |