Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 49 x^{12} + 79 x^{11} + 956 x^{10} - 1179 x^{9} - 9396 x^{8} + 8315 x^{7} + 48570 x^{6} - 28124 x^{5} - 125592 x^{4} + 40576 x^{3} + 138096 x^{2} + \cdots - 43744 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.15319\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.15319 | −1.41015 | −0.705074 | − | 0.709134i | \(-0.749086\pi\) | ||||
−0.705074 | + | 0.709134i | \(0.749086\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −5.11963 | −1.93504 | −0.967520 | − | 0.252796i | \(-0.918650\pi\) | ||||
−0.967520 | + | 0.252796i | \(0.918650\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.15319 | −0.997125 | ||||||||
\(11\) | 2.30228 | 0.694164 | 0.347082 | − | 0.937835i | \(-0.387173\pi\) | ||||
0.347082 | + | 0.937835i | \(0.387173\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −0.811206 | −0.224988 | −0.112494 | − | 0.993652i | \(-0.535884\pi\) | ||||
−0.112494 | + | 0.993652i | \(0.535884\pi\) | |||||||
\(14\) | −5.11963 | −1.36828 | ||||||||
\(15\) | 3.15319 | 0.814149 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −5.24117 | −1.20241 | −0.601203 | − | 0.799096i | \(-0.705312\pi\) | ||||
−0.601203 | + | 0.799096i | \(0.705312\pi\) | |||||||
\(20\) | −3.15319 | −0.705074 | ||||||||
\(21\) | 5.11963 | 1.11720 | ||||||||
\(22\) | 2.30228 | 0.490848 | ||||||||
\(23\) | −3.26815 | −0.681457 | −0.340729 | − | 0.940162i | \(-0.610674\pi\) | ||||
−0.340729 | + | 0.940162i | \(0.610674\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.94258 | 0.988516 | ||||||||
\(26\) | −0.811206 | −0.159091 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.11963 | −0.967520 | ||||||||
\(29\) | −8.27378 | −1.53640 | −0.768201 | − | 0.640209i | \(-0.778848\pi\) | ||||
−0.768201 | + | 0.640209i | \(0.778848\pi\) | |||||||
\(30\) | 3.15319 | 0.575690 | ||||||||
\(31\) | −8.46791 | −1.52088 | −0.760441 | − | 0.649407i | \(-0.775017\pi\) | ||||
−0.760441 | + | 0.649407i | \(0.775017\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.30228 | −0.400776 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 16.1432 | 2.72869 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.64496 | −0.763627 | −0.381814 | − | 0.924239i | \(-0.624700\pi\) | ||||
−0.381814 | + | 0.924239i | \(0.624700\pi\) | |||||||
\(38\) | −5.24117 | −0.850230 | ||||||||
\(39\) | 0.811206 | 0.129897 | ||||||||
\(40\) | −3.15319 | −0.498562 | ||||||||
\(41\) | −4.54510 | −0.709825 | −0.354912 | − | 0.934900i | \(-0.615489\pi\) | ||||
−0.354912 | + | 0.934900i | \(0.615489\pi\) | |||||||
\(42\) | 5.11963 | 0.789977 | ||||||||
\(43\) | 0.284370 | 0.0433659 | 0.0216830 | − | 0.999765i | \(-0.493098\pi\) | ||||
0.0216830 | + | 0.999765i | \(0.493098\pi\) | |||||||
\(44\) | 2.30228 | 0.347082 | ||||||||
\(45\) | −3.15319 | −0.470049 | ||||||||
\(46\) | −3.26815 | −0.481863 | ||||||||
\(47\) | −6.61944 | −0.965544 | −0.482772 | − | 0.875746i | \(-0.660370\pi\) | ||||
−0.482772 | + | 0.875746i | \(0.660370\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 19.2106 | 2.74438 | ||||||||
\(50\) | 4.94258 | 0.698986 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −0.811206 | −0.112494 | ||||||||
\(53\) | 13.2381 | 1.81840 | 0.909199 | − | 0.416362i | \(-0.136695\pi\) | ||||
0.909199 | + | 0.416362i | \(0.136695\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −7.25952 | −0.978873 | ||||||||
\(56\) | −5.11963 | −0.684140 | ||||||||
\(57\) | 5.24117 | 0.694210 | ||||||||
\(58\) | −8.27378 | −1.08640 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 3.15319 | 0.407074 | ||||||||
\(61\) | −2.14012 | −0.274014 | −0.137007 | − | 0.990570i | \(-0.543748\pi\) | ||||
−0.137007 | + | 0.990570i | \(0.543748\pi\) | |||||||
\(62\) | −8.46791 | −1.07543 | ||||||||
\(63\) | −5.11963 | −0.645013 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.55788 | 0.317266 | ||||||||
\(66\) | −2.30228 | −0.283391 | ||||||||
\(67\) | −13.5658 | −1.65733 | −0.828666 | − | 0.559744i | \(-0.810900\pi\) | ||||
−0.828666 | + | 0.559744i | \(0.810900\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | 3.26815 | 0.393440 | ||||||||
\(70\) | 16.1432 | 1.92948 | ||||||||
\(71\) | −2.05889 | −0.244345 | −0.122172 | − | 0.992509i | \(-0.538986\pi\) | ||||
−0.122172 | + | 0.992509i | \(0.538986\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 12.6553 | 1.48119 | 0.740594 | − | 0.671953i | \(-0.234544\pi\) | ||||
0.740594 | + | 0.671953i | \(0.234544\pi\) | |||||||
\(74\) | −4.64496 | −0.539966 | ||||||||
\(75\) | −4.94258 | −0.570720 | ||||||||
\(76\) | −5.24117 | −0.601203 | ||||||||
\(77\) | −11.7868 | −1.34323 | ||||||||
\(78\) | 0.811206 | 0.0918510 | ||||||||
\(79\) | 4.35553 | 0.490035 | 0.245018 | − | 0.969519i | \(-0.421206\pi\) | ||||
0.245018 | + | 0.969519i | \(0.421206\pi\) | |||||||
\(80\) | −3.15319 | −0.352537 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −4.54510 | −0.501922 | ||||||||
\(83\) | 7.85392 | 0.862080 | 0.431040 | − | 0.902333i | \(-0.358147\pi\) | ||||
0.431040 | + | 0.902333i | \(0.358147\pi\) | |||||||
\(84\) | 5.11963 | 0.558598 | ||||||||
\(85\) | −3.15319 | −0.342011 | ||||||||
\(86\) | 0.284370 | 0.0306644 | ||||||||
\(87\) | 8.27378 | 0.887042 | ||||||||
\(88\) | 2.30228 | 0.245424 | ||||||||
\(89\) | 5.97840 | 0.633709 | 0.316854 | − | 0.948474i | \(-0.397373\pi\) | ||||
0.316854 | + | 0.948474i | \(0.397373\pi\) | |||||||
\(90\) | −3.15319 | −0.332375 | ||||||||
\(91\) | 4.15308 | 0.435361 | ||||||||
\(92\) | −3.26815 | −0.340729 | ||||||||
\(93\) | 8.46791 | 0.878081 | ||||||||
\(94\) | −6.61944 | −0.682743 | ||||||||
\(95\) | 16.5264 | 1.69557 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 5.62903 | 0.571542 | 0.285771 | − | 0.958298i | \(-0.407750\pi\) | ||||
0.285771 | + | 0.958298i | \(0.407750\pi\) | |||||||
\(98\) | 19.2106 | 1.94057 | ||||||||
\(99\) | 2.30228 | 0.231388 | ||||||||
\(100\) | 4.94258 | 0.494258 | ||||||||
\(101\) | −9.49591 | −0.944878 | −0.472439 | − | 0.881363i | \(-0.656626\pi\) | ||||
−0.472439 | + | 0.881363i | \(0.656626\pi\) | |||||||
\(102\) | −1.00000 | −0.0990148 | ||||||||
\(103\) | −13.8577 | −1.36544 | −0.682719 | − | 0.730681i | \(-0.739203\pi\) | ||||
−0.682719 | + | 0.730681i | \(0.739203\pi\) | |||||||
\(104\) | −0.811206 | −0.0795453 | ||||||||
\(105\) | −16.1432 | −1.57541 | ||||||||
\(106\) | 13.2381 | 1.28580 | ||||||||
\(107\) | 16.6567 | 1.61026 | 0.805130 | − | 0.593098i | \(-0.202095\pi\) | ||||
0.805130 | + | 0.593098i | \(0.202095\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −3.89060 | −0.372652 | −0.186326 | − | 0.982488i | \(-0.559658\pi\) | ||||
−0.186326 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(110\) | −7.25952 | −0.692168 | ||||||||
\(111\) | 4.64496 | 0.440880 | ||||||||
\(112\) | −5.11963 | −0.483760 | ||||||||
\(113\) | −8.95400 | −0.842322 | −0.421161 | − | 0.906986i | \(-0.638377\pi\) | ||||
−0.421161 | + | 0.906986i | \(0.638377\pi\) | |||||||
\(114\) | 5.24117 | 0.490880 | ||||||||
\(115\) | 10.3051 | 0.960955 | ||||||||
\(116\) | −8.27378 | −0.768201 | ||||||||
\(117\) | −0.811206 | −0.0749960 | ||||||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | −5.11963 | −0.469316 | ||||||||
\(120\) | 3.15319 | 0.287845 | ||||||||
\(121\) | −5.69951 | −0.518137 | ||||||||
\(122\) | −2.14012 | −0.193757 | ||||||||
\(123\) | 4.54510 | 0.409818 | ||||||||
\(124\) | −8.46791 | −0.760441 | ||||||||
\(125\) | 0.181060 | 0.0161945 | ||||||||
\(126\) | −5.11963 | −0.456093 | ||||||||
\(127\) | 8.72754 | 0.774444 | 0.387222 | − | 0.921987i | \(-0.373435\pi\) | ||||
0.387222 | + | 0.921987i | \(0.373435\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.284370 | −0.0250373 | ||||||||
\(130\) | 2.55788 | 0.224341 | ||||||||
\(131\) | −12.3287 | −1.07716 | −0.538580 | − | 0.842574i | \(-0.681039\pi\) | ||||
−0.538580 | + | 0.842574i | \(0.681039\pi\) | |||||||
\(132\) | −2.30228 | −0.200388 | ||||||||
\(133\) | 26.8329 | 2.32670 | ||||||||
\(134\) | −13.5658 | −1.17191 | ||||||||
\(135\) | 3.15319 | 0.271383 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 4.23705 | 0.361995 | 0.180998 | − | 0.983484i | \(-0.442067\pi\) | ||||
0.180998 | + | 0.983484i | \(0.442067\pi\) | |||||||
\(138\) | 3.26815 | 0.278204 | ||||||||
\(139\) | −5.15360 | −0.437122 | −0.218561 | − | 0.975823i | \(-0.570136\pi\) | ||||
−0.218561 | + | 0.975823i | \(0.570136\pi\) | |||||||
\(140\) | 16.1432 | 1.36435 | ||||||||
\(141\) | 6.61944 | 0.557457 | ||||||||
\(142\) | −2.05889 | −0.172778 | ||||||||
\(143\) | −1.86762 | −0.156179 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 26.0887 | 2.16655 | ||||||||
\(146\) | 12.6553 | 1.04736 | ||||||||
\(147\) | −19.2106 | −1.58447 | ||||||||
\(148\) | −4.64496 | −0.381814 | ||||||||
\(149\) | 20.1215 | 1.64842 | 0.824208 | − | 0.566288i | \(-0.191621\pi\) | ||||
0.824208 | + | 0.566288i | \(0.191621\pi\) | |||||||
\(150\) | −4.94258 | −0.403560 | ||||||||
\(151\) | 5.88208 | 0.478677 | 0.239339 | − | 0.970936i | \(-0.423069\pi\) | ||||
0.239339 | + | 0.970936i | \(0.423069\pi\) | |||||||
\(152\) | −5.24117 | −0.425115 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −11.7868 | −0.949810 | ||||||||
\(155\) | 26.7009 | 2.14467 | ||||||||
\(156\) | 0.811206 | 0.0649485 | ||||||||
\(157\) | −4.50079 | −0.359202 | −0.179601 | − | 0.983740i | \(-0.557481\pi\) | ||||
−0.179601 | + | 0.983740i | \(0.557481\pi\) | |||||||
\(158\) | 4.35553 | 0.346507 | ||||||||
\(159\) | −13.2381 | −1.04985 | ||||||||
\(160\) | −3.15319 | −0.249281 | ||||||||
\(161\) | 16.7318 | 1.31865 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 12.6561 | 0.991300 | 0.495650 | − | 0.868522i | \(-0.334930\pi\) | ||||
0.495650 | + | 0.868522i | \(0.334930\pi\) | |||||||
\(164\) | −4.54510 | −0.354912 | ||||||||
\(165\) | 7.25952 | 0.565153 | ||||||||
\(166\) | 7.85392 | 0.609583 | ||||||||
\(167\) | 1.56094 | 0.120789 | 0.0603946 | − | 0.998175i | \(-0.480764\pi\) | ||||
0.0603946 | + | 0.998175i | \(0.480764\pi\) | |||||||
\(168\) | 5.11963 | 0.394988 | ||||||||
\(169\) | −12.3419 | −0.949380 | ||||||||
\(170\) | −3.15319 | −0.241838 | ||||||||
\(171\) | −5.24117 | −0.400802 | ||||||||
\(172\) | 0.284370 | 0.0216830 | ||||||||
\(173\) | −18.3308 | −1.39366 | −0.696831 | − | 0.717235i | \(-0.745407\pi\) | ||||
−0.696831 | + | 0.717235i | \(0.745407\pi\) | |||||||
\(174\) | 8.27378 | 0.627233 | ||||||||
\(175\) | −25.3042 | −1.91282 | ||||||||
\(176\) | 2.30228 | 0.173541 | ||||||||
\(177\) | −1.00000 | −0.0751646 | ||||||||
\(178\) | 5.97840 | 0.448100 | ||||||||
\(179\) | 4.45467 | 0.332958 | 0.166479 | − | 0.986045i | \(-0.446760\pi\) | ||||
0.166479 | + | 0.986045i | \(0.446760\pi\) | |||||||
\(180\) | −3.15319 | −0.235025 | ||||||||
\(181\) | 4.16845 | 0.309838 | 0.154919 | − | 0.987927i | \(-0.450488\pi\) | ||||
0.154919 | + | 0.987927i | \(0.450488\pi\) | |||||||
\(182\) | 4.15308 | 0.307847 | ||||||||
\(183\) | 2.14012 | 0.158202 | ||||||||
\(184\) | −3.26815 | −0.240932 | ||||||||
\(185\) | 14.6464 | 1.07683 | ||||||||
\(186\) | 8.46791 | 0.620897 | ||||||||
\(187\) | 2.30228 | 0.168359 | ||||||||
\(188\) | −6.61944 | −0.482772 | ||||||||
\(189\) | 5.11963 | 0.372399 | ||||||||
\(190\) | 16.5264 | 1.19895 | ||||||||
\(191\) | 19.3340 | 1.39896 | 0.699480 | − | 0.714652i | \(-0.253415\pi\) | ||||
0.699480 | + | 0.714652i | \(0.253415\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 2.51412 | 0.180970 | 0.0904852 | − | 0.995898i | \(-0.471158\pi\) | ||||
0.0904852 | + | 0.995898i | \(0.471158\pi\) | |||||||
\(194\) | 5.62903 | 0.404141 | ||||||||
\(195\) | −2.55788 | −0.183174 | ||||||||
\(196\) | 19.2106 | 1.37219 | ||||||||
\(197\) | 10.0295 | 0.714570 | 0.357285 | − | 0.933995i | \(-0.383703\pi\) | ||||
0.357285 | + | 0.933995i | \(0.383703\pi\) | |||||||
\(198\) | 2.30228 | 0.163616 | ||||||||
\(199\) | 19.8206 | 1.40504 | 0.702521 | − | 0.711663i | \(-0.252058\pi\) | ||||
0.702521 | + | 0.711663i | \(0.252058\pi\) | |||||||
\(200\) | 4.94258 | 0.349493 | ||||||||
\(201\) | 13.5658 | 0.956861 | ||||||||
\(202\) | −9.49591 | −0.668130 | ||||||||
\(203\) | 42.3587 | 2.97300 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 14.3315 | 1.00096 | ||||||||
\(206\) | −13.8577 | −0.965510 | ||||||||
\(207\) | −3.26815 | −0.227152 | ||||||||
\(208\) | −0.811206 | −0.0562470 | ||||||||
\(209\) | −12.0666 | −0.834667 | ||||||||
\(210\) | −16.1432 | −1.11398 | ||||||||
\(211\) | 12.0737 | 0.831188 | 0.415594 | − | 0.909550i | \(-0.363574\pi\) | ||||
0.415594 | + | 0.909550i | \(0.363574\pi\) | |||||||
\(212\) | 13.2381 | 0.909199 | ||||||||
\(213\) | 2.05889 | 0.141073 | ||||||||
\(214\) | 16.6567 | 1.13863 | ||||||||
\(215\) | −0.896670 | −0.0611524 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 43.3526 | 2.94297 | ||||||||
\(218\) | −3.89060 | −0.263505 | ||||||||
\(219\) | −12.6553 | −0.855164 | ||||||||
\(220\) | −7.25952 | −0.489436 | ||||||||
\(221\) | −0.811206 | −0.0545676 | ||||||||
\(222\) | 4.64496 | 0.311749 | ||||||||
\(223\) | −16.0016 | −1.07155 | −0.535775 | − | 0.844361i | \(-0.679980\pi\) | ||||
−0.535775 | + | 0.844361i | \(0.679980\pi\) | |||||||
\(224\) | −5.11963 | −0.342070 | ||||||||
\(225\) | 4.94258 | 0.329505 | ||||||||
\(226\) | −8.95400 | −0.595612 | ||||||||
\(227\) | 16.1709 | 1.07330 | 0.536650 | − | 0.843805i | \(-0.319690\pi\) | ||||
0.536650 | + | 0.843805i | \(0.319690\pi\) | |||||||
\(228\) | 5.24117 | 0.347105 | ||||||||
\(229\) | 9.83530 | 0.649935 | 0.324967 | − | 0.945725i | \(-0.394647\pi\) | ||||
0.324967 | + | 0.945725i | \(0.394647\pi\) | |||||||
\(230\) | 10.3051 | 0.679498 | ||||||||
\(231\) | 11.7868 | 0.775516 | ||||||||
\(232\) | −8.27378 | −0.543200 | ||||||||
\(233\) | −11.5963 | −0.759697 | −0.379848 | − | 0.925049i | \(-0.624024\pi\) | ||||
−0.379848 | + | 0.925049i | \(0.624024\pi\) | |||||||
\(234\) | −0.811206 | −0.0530302 | ||||||||
\(235\) | 20.8723 | 1.36156 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −4.35553 | −0.282922 | ||||||||
\(238\) | −5.11963 | −0.331857 | ||||||||
\(239\) | 8.56045 | 0.553730 | 0.276865 | − | 0.960909i | \(-0.410705\pi\) | ||||
0.276865 | + | 0.960909i | \(0.410705\pi\) | |||||||
\(240\) | 3.15319 | 0.203537 | ||||||||
\(241\) | 0.644767 | 0.0415331 | 0.0207666 | − | 0.999784i | \(-0.493389\pi\) | ||||
0.0207666 | + | 0.999784i | \(0.493389\pi\) | |||||||
\(242\) | −5.69951 | −0.366378 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.14012 | −0.137007 | ||||||||
\(245\) | −60.5747 | −3.86998 | ||||||||
\(246\) | 4.54510 | 0.289785 | ||||||||
\(247\) | 4.25167 | 0.270527 | ||||||||
\(248\) | −8.46791 | −0.537713 | ||||||||
\(249\) | −7.85392 | −0.497722 | ||||||||
\(250\) | 0.181060 | 0.0114512 | ||||||||
\(251\) | −17.2624 | −1.08959 | −0.544796 | − | 0.838569i | \(-0.683393\pi\) | ||||
−0.544796 | + | 0.838569i | \(0.683393\pi\) | |||||||
\(252\) | −5.11963 | −0.322507 | ||||||||
\(253\) | −7.52421 | −0.473043 | ||||||||
\(254\) | 8.72754 | 0.547615 | ||||||||
\(255\) | 3.15319 | 0.197460 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.2591 | 1.45086 | 0.725431 | − | 0.688295i | \(-0.241641\pi\) | ||||
0.725431 | + | 0.688295i | \(0.241641\pi\) | |||||||
\(258\) | −0.284370 | −0.0177041 | ||||||||
\(259\) | 23.7805 | 1.47765 | ||||||||
\(260\) | 2.55788 | 0.158633 | ||||||||
\(261\) | −8.27378 | −0.512134 | ||||||||
\(262\) | −12.3287 | −0.761667 | ||||||||
\(263\) | −17.8743 | −1.10218 | −0.551089 | − | 0.834447i | \(-0.685787\pi\) | ||||
−0.551089 | + | 0.834447i | \(0.685787\pi\) | |||||||
\(264\) | −2.30228 | −0.141696 | ||||||||
\(265\) | −41.7423 | −2.56421 | ||||||||
\(266\) | 26.8329 | 1.64523 | ||||||||
\(267\) | −5.97840 | −0.365872 | ||||||||
\(268\) | −13.5658 | −0.828666 | ||||||||
\(269\) | 8.34596 | 0.508862 | 0.254431 | − | 0.967091i | \(-0.418112\pi\) | ||||
0.254431 | + | 0.967091i | \(0.418112\pi\) | |||||||
\(270\) | 3.15319 | 0.191897 | ||||||||
\(271\) | −27.4856 | −1.66963 | −0.834815 | − | 0.550531i | \(-0.814425\pi\) | ||||
−0.834815 | + | 0.550531i | \(0.814425\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −4.15308 | −0.251356 | ||||||||
\(274\) | 4.23705 | 0.255969 | ||||||||
\(275\) | 11.3792 | 0.686192 | ||||||||
\(276\) | 3.26815 | 0.196720 | ||||||||
\(277\) | 21.1091 | 1.26832 | 0.634161 | − | 0.773201i | \(-0.281346\pi\) | ||||
0.634161 | + | 0.773201i | \(0.281346\pi\) | |||||||
\(278\) | −5.15360 | −0.309092 | ||||||||
\(279\) | −8.46791 | −0.506961 | ||||||||
\(280\) | 16.1432 | 0.964738 | ||||||||
\(281\) | −6.47421 | −0.386219 | −0.193109 | − | 0.981177i | \(-0.561857\pi\) | ||||
−0.193109 | + | 0.981177i | \(0.561857\pi\) | |||||||
\(282\) | 6.61944 | 0.394182 | ||||||||
\(283\) | 7.80340 | 0.463864 | 0.231932 | − | 0.972732i | \(-0.425495\pi\) | ||||
0.231932 | + | 0.972732i | \(0.425495\pi\) | |||||||
\(284\) | −2.05889 | −0.122172 | ||||||||
\(285\) | −16.5264 | −0.978938 | ||||||||
\(286\) | −1.86762 | −0.110435 | ||||||||
\(287\) | 23.2692 | 1.37354 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 26.0887 | 1.53198 | ||||||||
\(291\) | −5.62903 | −0.329980 | ||||||||
\(292\) | 12.6553 | 0.740594 | ||||||||
\(293\) | 2.54573 | 0.148723 | 0.0743615 | − | 0.997231i | \(-0.476308\pi\) | ||||
0.0743615 | + | 0.997231i | \(0.476308\pi\) | |||||||
\(294\) | −19.2106 | −1.12039 | ||||||||
\(295\) | −3.15319 | −0.183586 | ||||||||
\(296\) | −4.64496 | −0.269983 | ||||||||
\(297\) | −2.30228 | −0.133592 | ||||||||
\(298\) | 20.1215 | 1.16561 | ||||||||
\(299\) | 2.65115 | 0.153320 | ||||||||
\(300\) | −4.94258 | −0.285360 | ||||||||
\(301\) | −1.45587 | −0.0839148 | ||||||||
\(302\) | 5.88208 | 0.338476 | ||||||||
\(303\) | 9.49591 | 0.545526 | ||||||||
\(304\) | −5.24117 | −0.300602 | ||||||||
\(305\) | 6.74819 | 0.386400 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 4.59402 | 0.262195 | 0.131097 | − | 0.991369i | \(-0.458150\pi\) | ||||
0.131097 | + | 0.991369i | \(0.458150\pi\) | |||||||
\(308\) | −11.7868 | −0.671617 | ||||||||
\(309\) | 13.8577 | 0.788336 | ||||||||
\(310\) | 26.7009 | 1.51651 | ||||||||
\(311\) | −6.04953 | −0.343038 | −0.171519 | − | 0.985181i | \(-0.554867\pi\) | ||||
−0.171519 | + | 0.985181i | \(0.554867\pi\) | |||||||
\(312\) | 0.811206 | 0.0459255 | ||||||||
\(313\) | 3.18784 | 0.180187 | 0.0900936 | − | 0.995933i | \(-0.471283\pi\) | ||||
0.0900936 | + | 0.995933i | \(0.471283\pi\) | |||||||
\(314\) | −4.50079 | −0.253994 | ||||||||
\(315\) | 16.1432 | 0.909564 | ||||||||
\(316\) | 4.35553 | 0.245018 | ||||||||
\(317\) | −8.16915 | −0.458825 | −0.229413 | − | 0.973329i | \(-0.573680\pi\) | ||||
−0.229413 | + | 0.973329i | \(0.573680\pi\) | |||||||
\(318\) | −13.2381 | −0.742358 | ||||||||
\(319\) | −19.0485 | −1.06651 | ||||||||
\(320\) | −3.15319 | −0.176268 | ||||||||
\(321\) | −16.6567 | −0.929684 | ||||||||
\(322\) | 16.7318 | 0.932424 | ||||||||
\(323\) | −5.24117 | −0.291626 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −4.00945 | −0.222404 | ||||||||
\(326\) | 12.6561 | 0.700955 | ||||||||
\(327\) | 3.89060 | 0.215151 | ||||||||
\(328\) | −4.54510 | −0.250961 | ||||||||
\(329\) | 33.8891 | 1.86837 | ||||||||
\(330\) | 7.25952 | 0.399623 | ||||||||
\(331\) | 20.3364 | 1.11779 | 0.558896 | − | 0.829238i | \(-0.311225\pi\) | ||||
0.558896 | + | 0.829238i | \(0.311225\pi\) | |||||||
\(332\) | 7.85392 | 0.431040 | ||||||||
\(333\) | −4.64496 | −0.254542 | ||||||||
\(334\) | 1.56094 | 0.0854109 | ||||||||
\(335\) | 42.7756 | 2.33708 | ||||||||
\(336\) | 5.11963 | 0.279299 | ||||||||
\(337\) | 19.9935 | 1.08912 | 0.544558 | − | 0.838723i | \(-0.316698\pi\) | ||||
0.544558 | + | 0.838723i | \(0.316698\pi\) | |||||||
\(338\) | −12.3419 | −0.671313 | ||||||||
\(339\) | 8.95400 | 0.486315 | ||||||||
\(340\) | −3.15319 | −0.171005 | ||||||||
\(341\) | −19.4955 | −1.05574 | ||||||||
\(342\) | −5.24117 | −0.283410 | ||||||||
\(343\) | −62.5140 | −3.37544 | ||||||||
\(344\) | 0.284370 | 0.0153322 | ||||||||
\(345\) | −10.3051 | −0.554808 | ||||||||
\(346\) | −18.3308 | −0.985468 | ||||||||
\(347\) | 5.46345 | 0.293294 | 0.146647 | − | 0.989189i | \(-0.453152\pi\) | ||||
0.146647 | + | 0.989189i | \(0.453152\pi\) | |||||||
\(348\) | 8.27378 | 0.443521 | ||||||||
\(349\) | 18.1267 | 0.970301 | 0.485150 | − | 0.874431i | \(-0.338765\pi\) | ||||
0.485150 | + | 0.874431i | \(0.338765\pi\) | |||||||
\(350\) | −25.3042 | −1.35257 | ||||||||
\(351\) | 0.811206 | 0.0432990 | ||||||||
\(352\) | 2.30228 | 0.122712 | ||||||||
\(353\) | 22.8832 | 1.21795 | 0.608975 | − | 0.793189i | \(-0.291581\pi\) | ||||
0.608975 | + | 0.793189i | \(0.291581\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 6.49205 | 0.344562 | ||||||||
\(356\) | 5.97840 | 0.316854 | ||||||||
\(357\) | 5.11963 | 0.270960 | ||||||||
\(358\) | 4.45467 | 0.235437 | ||||||||
\(359\) | −36.1346 | −1.90711 | −0.953554 | − | 0.301221i | \(-0.902606\pi\) | ||||
−0.953554 | + | 0.301221i | \(0.902606\pi\) | |||||||
\(360\) | −3.15319 | −0.166187 | ||||||||
\(361\) | 8.46984 | 0.445781 | ||||||||
\(362\) | 4.16845 | 0.219089 | ||||||||
\(363\) | 5.69951 | 0.299146 | ||||||||
\(364\) | 4.15308 | 0.217680 | ||||||||
\(365\) | −39.9044 | −2.08869 | ||||||||
\(366\) | 2.14012 | 0.111866 | ||||||||
\(367\) | −8.33428 | −0.435046 | −0.217523 | − | 0.976055i | \(-0.569798\pi\) | ||||
−0.217523 | + | 0.976055i | \(0.569798\pi\) | |||||||
\(368\) | −3.26815 | −0.170364 | ||||||||
\(369\) | −4.54510 | −0.236608 | ||||||||
\(370\) | 14.6464 | 0.761432 | ||||||||
\(371\) | −67.7744 | −3.51867 | ||||||||
\(372\) | 8.46791 | 0.439041 | ||||||||
\(373\) | 31.3538 | 1.62344 | 0.811719 | − | 0.584048i | \(-0.198532\pi\) | ||||
0.811719 | + | 0.584048i | \(0.198532\pi\) | |||||||
\(374\) | 2.30228 | 0.119048 | ||||||||
\(375\) | −0.181060 | −0.00934990 | ||||||||
\(376\) | −6.61944 | −0.341371 | ||||||||
\(377\) | 6.71174 | 0.345672 | ||||||||
\(378\) | 5.11963 | 0.263326 | ||||||||
\(379\) | −19.0407 | −0.978055 | −0.489028 | − | 0.872268i | \(-0.662648\pi\) | ||||
−0.489028 | + | 0.872268i | \(0.662648\pi\) | |||||||
\(380\) | 16.5264 | 0.847785 | ||||||||
\(381\) | −8.72754 | −0.447125 | ||||||||
\(382\) | 19.3340 | 0.989214 | ||||||||
\(383\) | −33.1369 | −1.69321 | −0.846607 | − | 0.532218i | \(-0.821359\pi\) | ||||
−0.846607 | + | 0.532218i | \(0.821359\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 37.1661 | 1.89416 | ||||||||
\(386\) | 2.51412 | 0.127965 | ||||||||
\(387\) | 0.284370 | 0.0144553 | ||||||||
\(388\) | 5.62903 | 0.285771 | ||||||||
\(389\) | −19.1532 | −0.971104 | −0.485552 | − | 0.874208i | \(-0.661381\pi\) | ||||
−0.485552 | + | 0.874208i | \(0.661381\pi\) | |||||||
\(390\) | −2.55788 | −0.129523 | ||||||||
\(391\) | −3.26815 | −0.165278 | ||||||||
\(392\) | 19.2106 | 0.970284 | ||||||||
\(393\) | 12.3287 | 0.621898 | ||||||||
\(394\) | 10.0295 | 0.505277 | ||||||||
\(395\) | −13.7338 | −0.691022 | ||||||||
\(396\) | 2.30228 | 0.115694 | ||||||||
\(397\) | −13.1806 | −0.661514 | −0.330757 | − | 0.943716i | \(-0.607304\pi\) | ||||
−0.330757 | + | 0.943716i | \(0.607304\pi\) | |||||||
\(398\) | 19.8206 | 0.993515 | ||||||||
\(399\) | −26.8329 | −1.34332 | ||||||||
\(400\) | 4.94258 | 0.247129 | ||||||||
\(401\) | −25.2188 | −1.25937 | −0.629684 | − | 0.776851i | \(-0.716816\pi\) | ||||
−0.629684 | + | 0.776851i | \(0.716816\pi\) | |||||||
\(402\) | 13.5658 | 0.676603 | ||||||||
\(403\) | 6.86922 | 0.342180 | ||||||||
\(404\) | −9.49591 | −0.472439 | ||||||||
\(405\) | −3.15319 | −0.156683 | ||||||||
\(406\) | 42.3587 | 2.10223 | ||||||||
\(407\) | −10.6940 | −0.530082 | ||||||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | 22.9408 | 1.13435 | 0.567175 | − | 0.823597i | \(-0.308036\pi\) | ||||
0.567175 | + | 0.823597i | \(0.308036\pi\) | |||||||
\(410\) | 14.3315 | 0.707784 | ||||||||
\(411\) | −4.23705 | −0.208998 | ||||||||
\(412\) | −13.8577 | −0.682719 | ||||||||
\(413\) | −5.11963 | −0.251921 | ||||||||
\(414\) | −3.26815 | −0.160621 | ||||||||
\(415\) | −24.7649 | −1.21566 | ||||||||
\(416\) | −0.811206 | −0.0397726 | ||||||||
\(417\) | 5.15360 | 0.252373 | ||||||||
\(418\) | −12.0666 | −0.590198 | ||||||||
\(419\) | −32.8647 | −1.60554 | −0.802772 | − | 0.596285i | \(-0.796643\pi\) | ||||
−0.802772 | + | 0.596285i | \(0.796643\pi\) | |||||||
\(420\) | −16.1432 | −0.787705 | ||||||||
\(421\) | 12.3415 | 0.601488 | 0.300744 | − | 0.953705i | \(-0.402765\pi\) | ||||
0.300744 | + | 0.953705i | \(0.402765\pi\) | |||||||
\(422\) | 12.0737 | 0.587739 | ||||||||
\(423\) | −6.61944 | −0.321848 | ||||||||
\(424\) | 13.2381 | 0.642901 | ||||||||
\(425\) | 4.94258 | 0.239750 | ||||||||
\(426\) | 2.05889 | 0.0997534 | ||||||||
\(427\) | 10.9566 | 0.530228 | ||||||||
\(428\) | 16.6567 | 0.805130 | ||||||||
\(429\) | 1.86762 | 0.0901697 | ||||||||
\(430\) | −0.896670 | −0.0432413 | ||||||||
\(431\) | 0.409194 | 0.0197102 | 0.00985508 | − | 0.999951i | \(-0.496863\pi\) | ||||
0.00985508 | + | 0.999951i | \(0.496863\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 30.9599 | 1.48784 | 0.743918 | − | 0.668270i | \(-0.232965\pi\) | ||||
0.743918 | + | 0.668270i | \(0.232965\pi\) | |||||||
\(434\) | 43.3526 | 2.08099 | ||||||||
\(435\) | −26.0887 | −1.25086 | ||||||||
\(436\) | −3.89060 | −0.186326 | ||||||||
\(437\) | 17.1289 | 0.819389 | ||||||||
\(438\) | −12.6553 | −0.604692 | ||||||||
\(439\) | 36.5792 | 1.74583 | 0.872915 | − | 0.487872i | \(-0.162227\pi\) | ||||
0.872915 | + | 0.487872i | \(0.162227\pi\) | |||||||
\(440\) | −7.25952 | −0.346084 | ||||||||
\(441\) | 19.2106 | 0.914793 | ||||||||
\(442\) | −0.811206 | −0.0385851 | ||||||||
\(443\) | −21.9137 | −1.04115 | −0.520576 | − | 0.853815i | \(-0.674283\pi\) | ||||
−0.520576 | + | 0.853815i | \(0.674283\pi\) | |||||||
\(444\) | 4.64496 | 0.220440 | ||||||||
\(445\) | −18.8510 | −0.893623 | ||||||||
\(446\) | −16.0016 | −0.757700 | ||||||||
\(447\) | −20.1215 | −0.951713 | ||||||||
\(448\) | −5.11963 | −0.241880 | ||||||||
\(449\) | −34.0550 | −1.60716 | −0.803578 | − | 0.595199i | \(-0.797073\pi\) | ||||
−0.803578 | + | 0.595199i | \(0.797073\pi\) | |||||||
\(450\) | 4.94258 | 0.232995 | ||||||||
\(451\) | −10.4641 | −0.492735 | ||||||||
\(452\) | −8.95400 | −0.421161 | ||||||||
\(453\) | −5.88208 | −0.276364 | ||||||||
\(454\) | 16.1709 | 0.758938 | ||||||||
\(455\) | −13.0954 | −0.613923 | ||||||||
\(456\) | 5.24117 | 0.245440 | ||||||||
\(457\) | −33.0570 | −1.54634 | −0.773171 | − | 0.634198i | \(-0.781330\pi\) | ||||
−0.773171 | + | 0.634198i | \(0.781330\pi\) | |||||||
\(458\) | 9.83530 | 0.459573 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 10.3051 | 0.480478 | ||||||||
\(461\) | −29.0470 | −1.35285 | −0.676427 | − | 0.736509i | \(-0.736473\pi\) | ||||
−0.676427 | + | 0.736509i | \(0.736473\pi\) | |||||||
\(462\) | 11.7868 | 0.548373 | ||||||||
\(463\) | 33.9259 | 1.57667 | 0.788336 | − | 0.615245i | \(-0.210943\pi\) | ||||
0.788336 | + | 0.615245i | \(0.210943\pi\) | |||||||
\(464\) | −8.27378 | −0.384100 | ||||||||
\(465\) | −26.7009 | −1.23822 | ||||||||
\(466\) | −11.5963 | −0.537187 | ||||||||
\(467\) | 6.51149 | 0.301316 | 0.150658 | − | 0.988586i | \(-0.451861\pi\) | ||||
0.150658 | + | 0.988586i | \(0.451861\pi\) | |||||||
\(468\) | −0.811206 | −0.0374980 | ||||||||
\(469\) | 69.4521 | 3.20700 | ||||||||
\(470\) | 20.8723 | 0.962768 | ||||||||
\(471\) | 4.50079 | 0.207385 | ||||||||
\(472\) | 1.00000 | 0.0460287 | ||||||||
\(473\) | 0.654698 | 0.0301031 | ||||||||
\(474\) | −4.35553 | −0.200056 | ||||||||
\(475\) | −25.9049 | −1.18860 | ||||||||
\(476\) | −5.11963 | −0.234658 | ||||||||
\(477\) | 13.2381 | 0.606133 | ||||||||
\(478\) | 8.56045 | 0.391546 | ||||||||
\(479\) | 18.6065 | 0.850153 | 0.425077 | − | 0.905157i | \(-0.360247\pi\) | ||||
0.425077 | + | 0.905157i | \(0.360247\pi\) | |||||||
\(480\) | 3.15319 | 0.143923 | ||||||||
\(481\) | 3.76802 | 0.171807 | ||||||||
\(482\) | 0.644767 | 0.0293683 | ||||||||
\(483\) | −16.7318 | −0.761321 | ||||||||
\(484\) | −5.69951 | −0.259068 | ||||||||
\(485\) | −17.7494 | −0.805958 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 16.9762 | 0.769267 | 0.384633 | − | 0.923069i | \(-0.374328\pi\) | ||||
0.384633 | + | 0.923069i | \(0.374328\pi\) | |||||||
\(488\) | −2.14012 | −0.0968786 | ||||||||
\(489\) | −12.6561 | −0.572327 | ||||||||
\(490\) | −60.5747 | −2.73649 | ||||||||
\(491\) | −34.6125 | −1.56204 | −0.781020 | − | 0.624507i | \(-0.785300\pi\) | ||||
−0.781020 | + | 0.624507i | \(0.785300\pi\) | |||||||
\(492\) | 4.54510 | 0.204909 | ||||||||
\(493\) | −8.27378 | −0.372632 | ||||||||
\(494\) | 4.25167 | 0.191292 | ||||||||
\(495\) | −7.25952 | −0.326291 | ||||||||
\(496\) | −8.46791 | −0.380220 | ||||||||
\(497\) | 10.5407 | 0.472817 | ||||||||
\(498\) | −7.85392 | −0.351943 | ||||||||
\(499\) | 30.0368 | 1.34463 | 0.672317 | − | 0.740264i | \(-0.265299\pi\) | ||||
0.672317 | + | 0.740264i | \(0.265299\pi\) | |||||||
\(500\) | 0.181060 | 0.00809725 | ||||||||
\(501\) | −1.56094 | −0.0697377 | ||||||||
\(502\) | −17.2624 | −0.770458 | ||||||||
\(503\) | −36.5156 | −1.62815 | −0.814074 | − | 0.580761i | \(-0.802755\pi\) | ||||
−0.814074 | + | 0.580761i | \(0.802755\pi\) | |||||||
\(504\) | −5.11963 | −0.228047 | ||||||||
\(505\) | 29.9424 | 1.33242 | ||||||||
\(506\) | −7.52421 | −0.334492 | ||||||||
\(507\) | 12.3419 | 0.548125 | ||||||||
\(508\) | 8.72754 | 0.387222 | ||||||||
\(509\) | −13.9137 | −0.616712 | −0.308356 | − | 0.951271i | \(-0.599779\pi\) | ||||
−0.308356 | + | 0.951271i | \(0.599779\pi\) | |||||||
\(510\) | 3.15319 | 0.139625 | ||||||||
\(511\) | −64.7904 | −2.86616 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 5.24117 | 0.231403 | ||||||||
\(514\) | 23.2591 | 1.02591 | ||||||||
\(515\) | 43.6958 | 1.92547 | ||||||||
\(516\) | −0.284370 | −0.0125187 | ||||||||
\(517\) | −15.2398 | −0.670246 | ||||||||
\(518\) | 23.7805 | 1.04486 | ||||||||
\(519\) | 18.3308 | 0.804631 | ||||||||
\(520\) | 2.55788 | 0.112171 | ||||||||
\(521\) | 19.4571 | 0.852432 | 0.426216 | − | 0.904621i | \(-0.359846\pi\) | ||||
0.426216 | + | 0.904621i | \(0.359846\pi\) | |||||||
\(522\) | −8.27378 | −0.362133 | ||||||||
\(523\) | 10.7728 | 0.471061 | 0.235531 | − | 0.971867i | \(-0.424317\pi\) | ||||
0.235531 | + | 0.971867i | \(0.424317\pi\) | |||||||
\(524\) | −12.3287 | −0.538580 | ||||||||
\(525\) | 25.3042 | 1.10437 | ||||||||
\(526\) | −17.8743 | −0.779357 | ||||||||
\(527\) | −8.46791 | −0.368868 | ||||||||
\(528\) | −2.30228 | −0.100194 | ||||||||
\(529\) | −12.3192 | −0.535616 | ||||||||
\(530\) | −41.7423 | −1.81317 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 26.8329 | 1.16335 | ||||||||
\(533\) | 3.68701 | 0.159702 | ||||||||
\(534\) | −5.97840 | −0.258711 | ||||||||
\(535\) | −52.5216 | −2.27070 | ||||||||
\(536\) | −13.5658 | −0.585955 | ||||||||
\(537\) | −4.45467 | −0.192233 | ||||||||
\(538\) | 8.34596 | 0.359820 | ||||||||
\(539\) | 44.2283 | 1.90505 | ||||||||
\(540\) | 3.15319 | 0.135691 | ||||||||
\(541\) | −21.3313 | −0.917104 | −0.458552 | − | 0.888668i | \(-0.651632\pi\) | ||||
−0.458552 | + | 0.888668i | \(0.651632\pi\) | |||||||
\(542\) | −27.4856 | −1.18061 | ||||||||
\(543\) | −4.16845 | −0.178885 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 12.2678 | 0.525494 | ||||||||
\(546\) | −4.15308 | −0.177735 | ||||||||
\(547\) | −27.0982 | −1.15863 | −0.579317 | − | 0.815102i | \(-0.696681\pi\) | ||||
−0.579317 | + | 0.815102i | \(0.696681\pi\) | |||||||
\(548\) | 4.23705 | 0.180998 | ||||||||
\(549\) | −2.14012 | −0.0913380 | ||||||||
\(550\) | 11.3792 | 0.485211 | ||||||||
\(551\) | 43.3642 | 1.84738 | ||||||||
\(552\) | 3.26815 | 0.139102 | ||||||||
\(553\) | −22.2987 | −0.948237 | ||||||||
\(554\) | 21.1091 | 0.896839 | ||||||||
\(555\) | −14.6464 | −0.621706 | ||||||||
\(556\) | −5.15360 | −0.218561 | ||||||||
\(557\) | −19.2460 | −0.815479 | −0.407739 | − | 0.913098i | \(-0.633683\pi\) | ||||
−0.407739 | + | 0.913098i | \(0.633683\pi\) | |||||||
\(558\) | −8.46791 | −0.358475 | ||||||||
\(559\) | −0.230682 | −0.00975682 | ||||||||
\(560\) | 16.1432 | 0.682173 | ||||||||
\(561\) | −2.30228 | −0.0972023 | ||||||||
\(562\) | −6.47421 | −0.273098 | ||||||||
\(563\) | −29.5931 | −1.24720 | −0.623600 | − | 0.781743i | \(-0.714331\pi\) | ||||
−0.623600 | + | 0.781743i | \(0.714331\pi\) | |||||||
\(564\) | 6.61944 | 0.278729 | ||||||||
\(565\) | 28.2336 | 1.18780 | ||||||||
\(566\) | 7.80340 | 0.328001 | ||||||||
\(567\) | −5.11963 | −0.215004 | ||||||||
\(568\) | −2.05889 | −0.0863890 | ||||||||
\(569\) | 15.8532 | 0.664602 | 0.332301 | − | 0.943173i | \(-0.392175\pi\) | ||||
0.332301 | + | 0.943173i | \(0.392175\pi\) | |||||||
\(570\) | −16.5264 | −0.692214 | ||||||||
\(571\) | 17.3922 | 0.727840 | 0.363920 | − | 0.931430i | \(-0.381438\pi\) | ||||
0.363920 | + | 0.931430i | \(0.381438\pi\) | |||||||
\(572\) | −1.86762 | −0.0780893 | ||||||||
\(573\) | −19.3340 | −0.807690 | ||||||||
\(574\) | 23.2692 | 0.971239 | ||||||||
\(575\) | −16.1531 | −0.673631 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −1.99984 | −0.0832545 | −0.0416273 | − | 0.999133i | \(-0.513254\pi\) | ||||
−0.0416273 | + | 0.999133i | \(0.513254\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −2.51412 | −0.104483 | ||||||||
\(580\) | 26.0887 | 1.08328 | ||||||||
\(581\) | −40.2092 | −1.66816 | ||||||||
\(582\) | −5.62903 | −0.233331 | ||||||||
\(583\) | 30.4779 | 1.26227 | ||||||||
\(584\) | 12.6553 | 0.523679 | ||||||||
\(585\) | 2.55788 | 0.105755 | ||||||||
\(586\) | 2.54573 | 0.105163 | ||||||||
\(587\) | −15.0836 | −0.622567 | −0.311283 | − | 0.950317i | \(-0.600759\pi\) | ||||
−0.311283 | + | 0.950317i | \(0.600759\pi\) | |||||||
\(588\) | −19.2106 | −0.792234 | ||||||||
\(589\) | 44.3817 | 1.82872 | ||||||||
\(590\) | −3.15319 | −0.129815 | ||||||||
\(591\) | −10.0295 | −0.412557 | ||||||||
\(592\) | −4.64496 | −0.190907 | ||||||||
\(593\) | −15.5987 | −0.640564 | −0.320282 | − | 0.947322i | \(-0.603778\pi\) | ||||
−0.320282 | + | 0.947322i | \(0.603778\pi\) | |||||||
\(594\) | −2.30228 | −0.0944637 | ||||||||
\(595\) | 16.1432 | 0.661805 | ||||||||
\(596\) | 20.1215 | 0.824208 | ||||||||
\(597\) | −19.8206 | −0.811201 | ||||||||
\(598\) | 2.65115 | 0.108413 | ||||||||
\(599\) | 19.3460 | 0.790455 | 0.395228 | − | 0.918583i | \(-0.370666\pi\) | ||||
0.395228 | + | 0.918583i | \(0.370666\pi\) | |||||||
\(600\) | −4.94258 | −0.201780 | ||||||||
\(601\) | −38.9533 | −1.58894 | −0.794470 | − | 0.607304i | \(-0.792251\pi\) | ||||
−0.794470 | + | 0.607304i | \(0.792251\pi\) | |||||||
\(602\) | −1.45587 | −0.0593367 | ||||||||
\(603\) | −13.5658 | −0.552444 | ||||||||
\(604\) | 5.88208 | 0.239339 | ||||||||
\(605\) | 17.9716 | 0.730649 | ||||||||
\(606\) | 9.49591 | 0.385745 | ||||||||
\(607\) | 12.5488 | 0.509341 | 0.254671 | − | 0.967028i | \(-0.418033\pi\) | ||||
0.254671 | + | 0.967028i | \(0.418033\pi\) | |||||||
\(608\) | −5.24117 | −0.212557 | ||||||||
\(609\) | −42.3587 | −1.71646 | ||||||||
\(610\) | 6.74819 | 0.273226 | ||||||||
\(611\) | 5.36973 | 0.217236 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −45.0873 | −1.82106 | −0.910530 | − | 0.413443i | \(-0.864326\pi\) | ||||
−0.910530 | + | 0.413443i | \(0.864326\pi\) | |||||||
\(614\) | 4.59402 | 0.185400 | ||||||||
\(615\) | −14.3315 | −0.577903 | ||||||||
\(616\) | −11.7868 | −0.474905 | ||||||||
\(617\) | 44.3400 | 1.78506 | 0.892530 | − | 0.450988i | \(-0.148928\pi\) | ||||
0.892530 | + | 0.450988i | \(0.148928\pi\) | |||||||
\(618\) | 13.8577 | 0.557438 | ||||||||
\(619\) | −31.9344 | −1.28355 | −0.641775 | − | 0.766893i | \(-0.721802\pi\) | ||||
−0.641775 | + | 0.766893i | \(0.721802\pi\) | |||||||
\(620\) | 26.7009 | 1.07233 | ||||||||
\(621\) | 3.26815 | 0.131147 | ||||||||
\(622\) | −6.04953 | −0.242564 | ||||||||
\(623\) | −30.6072 | −1.22625 | ||||||||
\(624\) | 0.811206 | 0.0324742 | ||||||||
\(625\) | −25.2838 | −1.01135 | ||||||||
\(626\) | 3.18784 | 0.127412 | ||||||||
\(627\) | 12.0666 | 0.481895 | ||||||||
\(628\) | −4.50079 | −0.179601 | ||||||||
\(629\) | −4.64496 | −0.185207 | ||||||||
\(630\) | 16.1432 | 0.643159 | ||||||||
\(631\) | 26.8686 | 1.06962 | 0.534812 | − | 0.844971i | \(-0.320382\pi\) | ||||
0.534812 | + | 0.844971i | \(0.320382\pi\) | |||||||
\(632\) | 4.35553 | 0.173254 | ||||||||
\(633\) | −12.0737 | −0.479887 | ||||||||
\(634\) | −8.16915 | −0.324438 | ||||||||
\(635\) | −27.5196 | −1.09208 | ||||||||
\(636\) | −13.2381 | −0.524926 | ||||||||
\(637\) | −15.5838 | −0.617452 | ||||||||
\(638\) | −19.0485 | −0.754139 | ||||||||
\(639\) | −2.05889 | −0.0814483 | ||||||||
\(640\) | −3.15319 | −0.124641 | ||||||||
\(641\) | −31.0172 | −1.22511 | −0.612553 | − | 0.790429i | \(-0.709858\pi\) | ||||
−0.612553 | + | 0.790429i | \(0.709858\pi\) | |||||||
\(642\) | −16.6567 | −0.657386 | ||||||||
\(643\) | −17.8412 | −0.703588 | −0.351794 | − | 0.936077i | \(-0.614428\pi\) | ||||
−0.351794 | + | 0.936077i | \(0.614428\pi\) | |||||||
\(644\) | 16.7318 | 0.659323 | ||||||||
\(645\) | 0.896670 | 0.0353063 | ||||||||
\(646\) | −5.24117 | −0.206211 | ||||||||
\(647\) | 35.0191 | 1.37674 | 0.688372 | − | 0.725358i | \(-0.258326\pi\) | ||||
0.688372 | + | 0.725358i | \(0.258326\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 2.30228 | 0.0903724 | ||||||||
\(650\) | −4.00945 | −0.157264 | ||||||||
\(651\) | −43.3526 | −1.69912 | ||||||||
\(652\) | 12.6561 | 0.495650 | ||||||||
\(653\) | −8.73770 | −0.341933 | −0.170966 | − | 0.985277i | \(-0.554689\pi\) | ||||
−0.170966 | + | 0.985277i | \(0.554689\pi\) | |||||||
\(654\) | 3.89060 | 0.152134 | ||||||||
\(655\) | 38.8745 | 1.51895 | ||||||||
\(656\) | −4.54510 | −0.177456 | ||||||||
\(657\) | 12.6553 | 0.493729 | ||||||||
\(658\) | 33.8891 | 1.32113 | ||||||||
\(659\) | −15.0202 | −0.585103 | −0.292552 | − | 0.956250i | \(-0.594504\pi\) | ||||
−0.292552 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(660\) | 7.25952 | 0.282576 | ||||||||
\(661\) | −6.26283 | −0.243596 | −0.121798 | − | 0.992555i | \(-0.538866\pi\) | ||||
−0.121798 | + | 0.992555i | \(0.538866\pi\) | |||||||
\(662\) | 20.3364 | 0.790398 | ||||||||
\(663\) | 0.811206 | 0.0315046 | ||||||||
\(664\) | 7.85392 | 0.304791 | ||||||||
\(665\) | −84.6090 | −3.28100 | ||||||||
\(666\) | −4.64496 | −0.179989 | ||||||||
\(667\) | 27.0400 | 1.04699 | ||||||||
\(668\) | 1.56094 | 0.0603946 | ||||||||
\(669\) | 16.0016 | 0.618659 | ||||||||
\(670\) | 42.7756 | 1.65257 | ||||||||
\(671\) | −4.92715 | −0.190211 | ||||||||
\(672\) | 5.11963 | 0.197494 | ||||||||
\(673\) | 27.5408 | 1.06162 | 0.530811 | − | 0.847490i | \(-0.321888\pi\) | ||||
0.530811 | + | 0.847490i | \(0.321888\pi\) | |||||||
\(674\) | 19.9935 | 0.770121 | ||||||||
\(675\) | −4.94258 | −0.190240 | ||||||||
\(676\) | −12.3419 | −0.474690 | ||||||||
\(677\) | −9.22129 | −0.354403 | −0.177201 | − | 0.984175i | \(-0.556704\pi\) | ||||
−0.177201 | + | 0.984175i | \(0.556704\pi\) | |||||||
\(678\) | 8.95400 | 0.343876 | ||||||||
\(679\) | −28.8186 | −1.10596 | ||||||||
\(680\) | −3.15319 | −0.120919 | ||||||||
\(681\) | −16.1709 | −0.619670 | ||||||||
\(682\) | −19.4955 | −0.746521 | ||||||||
\(683\) | 5.55368 | 0.212506 | 0.106253 | − | 0.994339i | \(-0.466115\pi\) | ||||
0.106253 | + | 0.994339i | \(0.466115\pi\) | |||||||
\(684\) | −5.24117 | −0.200401 | ||||||||
\(685\) | −13.3602 | −0.510467 | ||||||||
\(686\) | −62.5140 | −2.38680 | ||||||||
\(687\) | −9.83530 | −0.375240 | ||||||||
\(688\) | 0.284370 | 0.0108415 | ||||||||
\(689\) | −10.7389 | −0.409118 | ||||||||
\(690\) | −10.3051 | −0.392308 | ||||||||
\(691\) | 7.82478 | 0.297668 | 0.148834 | − | 0.988862i | \(-0.452448\pi\) | ||||
0.148834 | + | 0.988862i | \(0.452448\pi\) | |||||||
\(692\) | −18.3308 | −0.696831 | ||||||||
\(693\) | −11.7868 | −0.447745 | ||||||||
\(694\) | 5.46345 | 0.207390 | ||||||||
\(695\) | 16.2502 | 0.616407 | ||||||||
\(696\) | 8.27378 | 0.313617 | ||||||||
\(697\) | −4.54510 | −0.172158 | ||||||||
\(698\) | 18.1267 | 0.686106 | ||||||||
\(699\) | 11.5963 | 0.438611 | ||||||||
\(700\) | −25.3042 | −0.956408 | ||||||||
\(701\) | 29.1820 | 1.10219 | 0.551095 | − | 0.834442i | \(-0.314210\pi\) | ||||
0.551095 | + | 0.834442i | \(0.314210\pi\) | |||||||
\(702\) | 0.811206 | 0.0306170 | ||||||||
\(703\) | 24.3450 | 0.918190 | ||||||||
\(704\) | 2.30228 | 0.0867704 | ||||||||
\(705\) | −20.8723 | −0.786097 | ||||||||
\(706\) | 22.8832 | 0.861221 | ||||||||
\(707\) | 48.6156 | 1.82838 | ||||||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 17.7849 | 0.667926 | 0.333963 | − | 0.942586i | \(-0.391614\pi\) | ||||
0.333963 | + | 0.942586i | \(0.391614\pi\) | |||||||
\(710\) | 6.49205 | 0.243642 | ||||||||
\(711\) | 4.35553 | 0.163345 | ||||||||
\(712\) | 5.97840 | 0.224050 | ||||||||
\(713\) | 27.6744 | 1.03642 | ||||||||
\(714\) | 5.11963 | 0.191597 | ||||||||
\(715\) | 5.88896 | 0.220235 | ||||||||
\(716\) | 4.45467 | 0.166479 | ||||||||
\(717\) | −8.56045 | −0.319696 | ||||||||
\(718\) | −36.1346 | −1.34853 | ||||||||
\(719\) | −19.3139 | −0.720287 | −0.360143 | − | 0.932897i | \(-0.617272\pi\) | ||||
−0.360143 | + | 0.932897i | \(0.617272\pi\) | |||||||
\(720\) | −3.15319 | −0.117512 | ||||||||
\(721\) | 70.9462 | 2.64218 | ||||||||
\(722\) | 8.46984 | 0.315215 | ||||||||
\(723\) | −0.644767 | −0.0239791 | ||||||||
\(724\) | 4.16845 | 0.154919 | ||||||||
\(725\) | −40.8938 | −1.51876 | ||||||||
\(726\) | 5.69951 | 0.211529 | ||||||||
\(727\) | −41.9027 | −1.55409 | −0.777043 | − | 0.629448i | \(-0.783281\pi\) | ||||
−0.777043 | + | 0.629448i | \(0.783281\pi\) | |||||||
\(728\) | 4.15308 | 0.153923 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −39.9044 | −1.47693 | ||||||||
\(731\) | 0.284370 | 0.0105178 | ||||||||
\(732\) | 2.14012 | 0.0791010 | ||||||||
\(733\) | −36.7993 | −1.35921 | −0.679607 | − | 0.733577i | \(-0.737850\pi\) | ||||
−0.679607 | + | 0.733577i | \(0.737850\pi\) | |||||||
\(734\) | −8.33428 | −0.307624 | ||||||||
\(735\) | 60.5747 | 2.23433 | ||||||||
\(736\) | −3.26815 | −0.120466 | ||||||||
\(737\) | −31.2324 | −1.15046 | ||||||||
\(738\) | −4.54510 | −0.167307 | ||||||||
\(739\) | 26.7651 | 0.984569 | 0.492285 | − | 0.870434i | \(-0.336162\pi\) | ||||
0.492285 | + | 0.870434i | \(0.336162\pi\) | |||||||
\(740\) | 14.6464 | 0.538413 | ||||||||
\(741\) | −4.25167 | −0.156189 | ||||||||
\(742\) | −67.7744 | −2.48808 | ||||||||
\(743\) | −11.0891 | −0.406820 | −0.203410 | − | 0.979094i | \(-0.565202\pi\) | ||||
−0.203410 | + | 0.979094i | \(0.565202\pi\) | |||||||
\(744\) | 8.46791 | 0.310449 | ||||||||
\(745\) | −63.4467 | −2.32451 | ||||||||
\(746\) | 31.3538 | 1.14794 | ||||||||
\(747\) | 7.85392 | 0.287360 | ||||||||
\(748\) | 2.30228 | 0.0841797 | ||||||||
\(749\) | −85.2760 | −3.11592 | ||||||||
\(750\) | −0.181060 | −0.00661138 | ||||||||
\(751\) | 6.55245 | 0.239102 | 0.119551 | − | 0.992828i | \(-0.461854\pi\) | ||||
0.119551 | + | 0.992828i | \(0.461854\pi\) | |||||||
\(752\) | −6.61944 | −0.241386 | ||||||||
\(753\) | 17.2624 | 0.629076 | ||||||||
\(754\) | 6.71174 | 0.244427 | ||||||||
\(755\) | −18.5473 | −0.675005 | ||||||||
\(756\) | 5.11963 | 0.186199 | ||||||||
\(757\) | 33.3712 | 1.21290 | 0.606449 | − | 0.795122i | \(-0.292593\pi\) | ||||
0.606449 | + | 0.795122i | \(0.292593\pi\) | |||||||
\(758\) | −19.0407 | −0.691590 | ||||||||
\(759\) | 7.52421 | 0.273111 | ||||||||
\(760\) | 16.5264 | 0.599475 | ||||||||
\(761\) | −23.3228 | −0.845450 | −0.422725 | − | 0.906258i | \(-0.638926\pi\) | ||||
−0.422725 | + | 0.906258i | \(0.638926\pi\) | |||||||
\(762\) | −8.72754 | −0.316165 | ||||||||
\(763\) | 19.9184 | 0.721096 | ||||||||
\(764\) | 19.3340 | 0.699480 | ||||||||
\(765\) | −3.15319 | −0.114004 | ||||||||
\(766\) | −33.1369 | −1.19728 | ||||||||
\(767\) | −0.811206 | −0.0292909 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −35.0349 | −1.26339 | −0.631696 | − | 0.775216i | \(-0.717641\pi\) | ||||
−0.631696 | + | 0.775216i | \(0.717641\pi\) | |||||||
\(770\) | 37.1661 | 1.33937 | ||||||||
\(771\) | −23.2591 | −0.837655 | ||||||||
\(772\) | 2.51412 | 0.0904852 | ||||||||
\(773\) | −34.7894 | −1.25129 | −0.625644 | − | 0.780109i | \(-0.715164\pi\) | ||||
−0.625644 | + | 0.780109i | \(0.715164\pi\) | |||||||
\(774\) | 0.284370 | 0.0102215 | ||||||||
\(775\) | −41.8533 | −1.50342 | ||||||||
\(776\) | 5.62903 | 0.202070 | ||||||||
\(777\) | −23.7805 | −0.853121 | ||||||||
\(778\) | −19.1532 | −0.686674 | ||||||||
\(779\) | 23.8216 | 0.853498 | ||||||||
\(780\) | −2.55788 | −0.0915869 | ||||||||
\(781\) | −4.74013 | −0.169615 | ||||||||
\(782\) | −3.26815 | −0.116869 | ||||||||
\(783\) | 8.27378 | 0.295681 | ||||||||
\(784\) | 19.2106 | 0.686094 | ||||||||
\(785\) | 14.1918 | 0.506528 | ||||||||
\(786\) | 12.3287 | 0.439749 | ||||||||
\(787\) | −1.13792 | −0.0405625 | −0.0202813 | − | 0.999794i | \(-0.506456\pi\) | ||||
−0.0202813 | + | 0.999794i | \(0.506456\pi\) | |||||||
\(788\) | 10.0295 | 0.357285 | ||||||||
\(789\) | 17.8743 | 0.636343 | ||||||||
\(790\) | −13.7338 | −0.488626 | ||||||||
\(791\) | 45.8412 | 1.62993 | ||||||||
\(792\) | 2.30228 | 0.0818080 | ||||||||
\(793\) | 1.73608 | 0.0616499 | ||||||||
\(794\) | −13.1806 | −0.467761 | ||||||||
\(795\) | 41.7423 | 1.48045 | ||||||||
\(796\) | 19.8206 | 0.702521 | ||||||||
\(797\) | 39.6660 | 1.40504 | 0.702521 | − | 0.711664i | \(-0.252058\pi\) | ||||
0.702521 | + | 0.711664i | \(0.252058\pi\) | |||||||
\(798\) | −26.8329 | −0.949873 | ||||||||
\(799\) | −6.61944 | −0.234179 | ||||||||
\(800\) | 4.94258 | 0.174747 | ||||||||
\(801\) | 5.97840 | 0.211236 | ||||||||
\(802\) | −25.2188 | −0.890508 | ||||||||
\(803\) | 29.1360 | 1.02819 | ||||||||
\(804\) | 13.5658 | 0.478430 | ||||||||
\(805\) | −52.7583 | −1.85949 | ||||||||
\(806\) | 6.86922 | 0.241958 | ||||||||
\(807\) | −8.34596 | −0.293792 | ||||||||
\(808\) | −9.49591 | −0.334065 | ||||||||
\(809\) | −6.23422 | −0.219184 | −0.109592 | − | 0.993977i | \(-0.534954\pi\) | ||||
−0.109592 | + | 0.993977i | \(0.534954\pi\) | |||||||
\(810\) | −3.15319 | −0.110792 | ||||||||
\(811\) | 31.5603 | 1.10823 | 0.554116 | − | 0.832439i | \(-0.313056\pi\) | ||||
0.554116 | + | 0.832439i | \(0.313056\pi\) | |||||||
\(812\) | 42.3587 | 1.48650 | ||||||||
\(813\) | 27.4856 | 0.963961 | ||||||||
\(814\) | −10.6940 | −0.374825 | ||||||||
\(815\) | −39.9069 | −1.39788 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −1.49043 | −0.0521435 | ||||||||
\(818\) | 22.9408 | 0.802107 | ||||||||
\(819\) | 4.15308 | 0.145120 | ||||||||
\(820\) | 14.3315 | 0.500479 | ||||||||
\(821\) | 14.8908 | 0.519692 | 0.259846 | − | 0.965650i | \(-0.416328\pi\) | ||||
0.259846 | + | 0.965650i | \(0.416328\pi\) | |||||||
\(822\) | −4.23705 | −0.147784 | ||||||||
\(823\) | 41.6072 | 1.45034 | 0.725168 | − | 0.688572i | \(-0.241762\pi\) | ||||
0.725168 | + | 0.688572i | \(0.241762\pi\) | |||||||
\(824\) | −13.8577 | −0.482755 | ||||||||
\(825\) | −11.3792 | −0.396173 | ||||||||
\(826\) | −5.11963 | −0.178135 | ||||||||
\(827\) | −34.6335 | −1.20432 | −0.602162 | − | 0.798374i | \(-0.705694\pi\) | ||||
−0.602162 | + | 0.798374i | \(0.705694\pi\) | |||||||
\(828\) | −3.26815 | −0.113576 | ||||||||
\(829\) | 37.4839 | 1.30187 | 0.650935 | − | 0.759134i | \(-0.274377\pi\) | ||||
0.650935 | + | 0.759134i | \(0.274377\pi\) | |||||||
\(830\) | −24.7649 | −0.859601 | ||||||||
\(831\) | −21.1091 | −0.732266 | ||||||||
\(832\) | −0.811206 | −0.0281235 | ||||||||
\(833\) | 19.2106 | 0.665609 | ||||||||
\(834\) | 5.15360 | 0.178454 | ||||||||
\(835\) | −4.92194 | −0.170331 | ||||||||
\(836\) | −12.0666 | −0.417333 | ||||||||
\(837\) | 8.46791 | 0.292694 | ||||||||
\(838\) | −32.8647 | −1.13529 | ||||||||
\(839\) | −29.7976 | −1.02873 | −0.514363 | − | 0.857572i | \(-0.671972\pi\) | ||||
−0.514363 | + | 0.857572i | \(0.671972\pi\) | |||||||
\(840\) | −16.1432 | −0.556992 | ||||||||
\(841\) | 39.4554 | 1.36053 | ||||||||
\(842\) | 12.3415 | 0.425316 | ||||||||
\(843\) | 6.47421 | 0.222984 | ||||||||
\(844\) | 12.0737 | 0.415594 | ||||||||
\(845\) | 38.9164 | 1.33877 | ||||||||
\(846\) | −6.61944 | −0.227581 | ||||||||
\(847\) | 29.1794 | 1.00262 | ||||||||
\(848\) | 13.2381 | 0.454599 | ||||||||
\(849\) | −7.80340 | −0.267812 | ||||||||
\(850\) | 4.94258 | 0.169529 | ||||||||
\(851\) | 15.1805 | 0.520379 | ||||||||
\(852\) | 2.05889 | 0.0705363 | ||||||||
\(853\) | 2.96095 | 0.101381 | 0.0506905 | − | 0.998714i | \(-0.483858\pi\) | ||||
0.0506905 | + | 0.998714i | \(0.483858\pi\) | |||||||
\(854\) | 10.9566 | 0.374928 | ||||||||
\(855\) | 16.5264 | 0.565190 | ||||||||
\(856\) | 16.6567 | 0.569313 | ||||||||
\(857\) | 27.8680 | 0.951954 | 0.475977 | − | 0.879458i | \(-0.342095\pi\) | ||||
0.475977 | + | 0.879458i | \(0.342095\pi\) | |||||||
\(858\) | 1.86762 | 0.0637596 | ||||||||
\(859\) | −23.7399 | −0.809995 | −0.404997 | − | 0.914318i | \(-0.632728\pi\) | ||||
−0.404997 | + | 0.914318i | \(0.632728\pi\) | |||||||
\(860\) | −0.896670 | −0.0305762 | ||||||||
\(861\) | −23.2692 | −0.793013 | ||||||||
\(862\) | 0.409194 | 0.0139372 | ||||||||
\(863\) | 24.3687 | 0.829520 | 0.414760 | − | 0.909931i | \(-0.363866\pi\) | ||||
0.414760 | + | 0.909931i | \(0.363866\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 57.8003 | 1.96527 | ||||||||
\(866\) | 30.9599 | 1.05206 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 43.3526 | 1.47148 | ||||||||
\(869\) | 10.0276 | 0.340165 | ||||||||
\(870\) | −26.0887 | −0.884491 | ||||||||
\(871\) | 11.0047 | 0.372880 | ||||||||
\(872\) | −3.89060 | −0.131752 | ||||||||
\(873\) | 5.62903 | 0.190514 | ||||||||
\(874\) | 17.1289 | 0.579395 | ||||||||
\(875\) | −0.926961 | −0.0313370 | ||||||||
\(876\) | −12.6553 | −0.427582 | ||||||||
\(877\) | 15.0748 | 0.509041 | 0.254520 | − | 0.967067i | \(-0.418082\pi\) | ||||
0.254520 | + | 0.967067i | \(0.418082\pi\) | |||||||
\(878\) | 36.5792 | 1.23449 | ||||||||
\(879\) | −2.54573 | −0.0858652 | ||||||||
\(880\) | −7.25952 | −0.244718 | ||||||||
\(881\) | −3.14534 | −0.105969 | −0.0529846 | − | 0.998595i | \(-0.516873\pi\) | ||||
−0.0529846 | + | 0.998595i | \(0.516873\pi\) | |||||||
\(882\) | 19.2106 | 0.646856 | ||||||||
\(883\) | −4.13667 | −0.139210 | −0.0696051 | − | 0.997575i | \(-0.522174\pi\) | ||||
−0.0696051 | + | 0.997575i | \(0.522174\pi\) | |||||||
\(884\) | −0.811206 | −0.0272838 | ||||||||
\(885\) | 3.15319 | 0.105993 | ||||||||
\(886\) | −21.9137 | −0.736206 | ||||||||
\(887\) | 35.4633 | 1.19074 | 0.595370 | − | 0.803452i | \(-0.297005\pi\) | ||||
0.595370 | + | 0.803452i | \(0.297005\pi\) | |||||||
\(888\) | 4.64496 | 0.155875 | ||||||||
\(889\) | −44.6818 | −1.49858 | ||||||||
\(890\) | −18.8510 | −0.631887 | ||||||||
\(891\) | 2.30228 | 0.0771293 | ||||||||
\(892\) | −16.0016 | −0.535775 | ||||||||
\(893\) | 34.6936 | 1.16098 | ||||||||
\(894\) | −20.1215 | −0.672963 | ||||||||
\(895\) | −14.0464 | −0.469520 | ||||||||
\(896\) | −5.11963 | −0.171035 | ||||||||
\(897\) | −2.65115 | −0.0885192 | ||||||||
\(898\) | −34.0550 | −1.13643 | ||||||||
\(899\) | 70.0616 | 2.33668 | ||||||||
\(900\) | 4.94258 | 0.164753 | ||||||||
\(901\) | 13.2381 | 0.441026 | ||||||||
\(902\) | −10.4641 | −0.348416 | ||||||||
\(903\) | 1.45587 | 0.0484482 | ||||||||
\(904\) | −8.95400 | −0.297806 | ||||||||
\(905\) | −13.1439 | −0.436918 | ||||||||
\(906\) | −5.88208 | −0.195419 | ||||||||
\(907\) | −16.8760 | −0.560359 | −0.280179 | − | 0.959948i | \(-0.590394\pi\) | ||||
−0.280179 | + | 0.959948i | \(0.590394\pi\) | |||||||
\(908\) | 16.1709 | 0.536650 | ||||||||
\(909\) | −9.49591 | −0.314959 | ||||||||
\(910\) | −13.0954 | −0.434109 | ||||||||
\(911\) | 12.6083 | 0.417732 | 0.208866 | − | 0.977944i | \(-0.433023\pi\) | ||||
0.208866 | + | 0.977944i | \(0.433023\pi\) | |||||||
\(912\) | 5.24117 | 0.173552 | ||||||||
\(913\) | 18.0819 | 0.598425 | ||||||||
\(914\) | −33.0570 | −1.09343 | ||||||||
\(915\) | −6.74819 | −0.223088 | ||||||||
\(916\) | 9.83530 | 0.324967 | ||||||||
\(917\) | 63.1182 | 2.08435 | ||||||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −35.9069 | −1.18446 | −0.592230 | − | 0.805769i | \(-0.701752\pi\) | ||||
−0.592230 | + | 0.805769i | \(0.701752\pi\) | |||||||
\(920\) | 10.3051 | 0.339749 | ||||||||
\(921\) | −4.59402 | −0.151378 | ||||||||
\(922\) | −29.0470 | −0.956613 | ||||||||
\(923\) | 1.67018 | 0.0549747 | ||||||||
\(924\) | 11.7868 | 0.387758 | ||||||||
\(925\) | −22.9581 | −0.754857 | ||||||||
\(926\) | 33.9259 | 1.11488 | ||||||||
\(927\) | −13.8577 | −0.455146 | ||||||||
\(928\) | −8.27378 | −0.271600 | ||||||||
\(929\) | 11.0955 | 0.364031 | 0.182015 | − | 0.983296i | \(-0.441738\pi\) | ||||
0.182015 | + | 0.983296i | \(0.441738\pi\) | |||||||
\(930\) | −26.7009 | −0.875557 | ||||||||
\(931\) | −100.686 | −3.29986 | ||||||||
\(932\) | −11.5963 | −0.379848 | ||||||||
\(933\) | 6.04953 | 0.198053 | ||||||||
\(934\) | 6.51149 | 0.213063 | ||||||||
\(935\) | −7.25952 | −0.237412 | ||||||||
\(936\) | −0.811206 | −0.0265151 | ||||||||
\(937\) | −1.43815 | −0.0469823 | −0.0234912 | − | 0.999724i | \(-0.507478\pi\) | ||||
−0.0234912 | + | 0.999724i | \(0.507478\pi\) | |||||||
\(938\) | 69.4521 | 2.26769 | ||||||||
\(939\) | −3.18784 | −0.104031 | ||||||||
\(940\) | 20.8723 | 0.680780 | ||||||||
\(941\) | −8.61313 | −0.280780 | −0.140390 | − | 0.990096i | \(-0.544836\pi\) | ||||
−0.140390 | + | 0.990096i | \(0.544836\pi\) | |||||||
\(942\) | 4.50079 | 0.146644 | ||||||||
\(943\) | 14.8541 | 0.483715 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −16.1432 | −0.525137 | ||||||||
\(946\) | 0.654698 | 0.0212861 | ||||||||
\(947\) | 51.1785 | 1.66308 | 0.831539 | − | 0.555466i | \(-0.187460\pi\) | ||||
0.831539 | + | 0.555466i | \(0.187460\pi\) | |||||||
\(948\) | −4.35553 | −0.141461 | ||||||||
\(949\) | −10.2660 | −0.333250 | ||||||||
\(950\) | −25.9049 | −0.840465 | ||||||||
\(951\) | 8.16915 | 0.264903 | ||||||||
\(952\) | −5.11963 | −0.165928 | ||||||||
\(953\) | −4.65755 | −0.150873 | −0.0754364 | − | 0.997151i | \(-0.524035\pi\) | ||||
−0.0754364 | + | 0.997151i | \(0.524035\pi\) | |||||||
\(954\) | 13.2381 | 0.428600 | ||||||||
\(955\) | −60.9637 | −1.97274 | ||||||||
\(956\) | 8.56045 | 0.276865 | ||||||||
\(957\) | 19.0485 | 0.615752 | ||||||||
\(958\) | 18.6065 | 0.601149 | ||||||||
\(959\) | −21.6921 | −0.700475 | ||||||||
\(960\) | 3.15319 | 0.101769 | ||||||||
\(961\) | 40.7055 | 1.31308 | ||||||||
\(962\) | 3.76802 | 0.121486 | ||||||||
\(963\) | 16.6567 | 0.536754 | ||||||||
\(964\) | 0.644767 | 0.0207666 | ||||||||
\(965\) | −7.92749 | −0.255195 | ||||||||
\(966\) | −16.7318 | −0.538335 | ||||||||
\(967\) | 32.4044 | 1.04205 | 0.521027 | − | 0.853540i | \(-0.325549\pi\) | ||||
0.521027 | + | 0.853540i | \(0.325549\pi\) | |||||||
\(968\) | −5.69951 | −0.183189 | ||||||||
\(969\) | 5.24117 | 0.168371 | ||||||||
\(970\) | −17.7494 | −0.569898 | ||||||||
\(971\) | 15.8345 | 0.508152 | 0.254076 | − | 0.967184i | \(-0.418229\pi\) | ||||
0.254076 | + | 0.967184i | \(0.418229\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 26.3845 | 0.845849 | ||||||||
\(974\) | 16.9762 | 0.543954 | ||||||||
\(975\) | 4.00945 | 0.128405 | ||||||||
\(976\) | −2.14012 | −0.0685035 | ||||||||
\(977\) | 51.5831 | 1.65029 | 0.825145 | − | 0.564922i | \(-0.191094\pi\) | ||||
0.825145 | + | 0.564922i | \(0.191094\pi\) | |||||||
\(978\) | −12.6561 | −0.404696 | ||||||||
\(979\) | 13.7639 | 0.439898 | ||||||||
\(980\) | −60.5747 | −1.93499 | ||||||||
\(981\) | −3.89060 | −0.124217 | ||||||||
\(982\) | −34.6125 | −1.10453 | ||||||||
\(983\) | 27.4354 | 0.875054 | 0.437527 | − | 0.899205i | \(-0.355854\pi\) | ||||
0.437527 | + | 0.899205i | \(0.355854\pi\) | |||||||
\(984\) | 4.54510 | 0.144892 | ||||||||
\(985\) | −31.6248 | −1.00765 | ||||||||
\(986\) | −8.27378 | −0.263491 | ||||||||
\(987\) | −33.8891 | −1.07870 | ||||||||
\(988\) | 4.25167 | 0.135264 | ||||||||
\(989\) | −0.929364 | −0.0295520 | ||||||||
\(990\) | −7.25952 | −0.230723 | ||||||||
\(991\) | −18.6656 | −0.592932 | −0.296466 | − | 0.955043i | \(-0.595808\pi\) | ||||
−0.296466 | + | 0.955043i | \(0.595808\pi\) | |||||||
\(992\) | −8.46791 | −0.268856 | ||||||||
\(993\) | −20.3364 | −0.645357 | ||||||||
\(994\) | 10.5407 | 0.334332 | ||||||||
\(995\) | −62.4979 | −1.98132 | ||||||||
\(996\) | −7.85392 | −0.248861 | ||||||||
\(997\) | 39.8729 | 1.26279 | 0.631394 | − | 0.775462i | \(-0.282483\pi\) | ||||
0.631394 | + | 0.775462i | \(0.282483\pi\) | |||||||
\(998\) | 30.0368 | 0.950799 | ||||||||
\(999\) | 4.64496 | 0.146960 |
(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 | 6018.2.a.bc.1.2 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.bc.1.2 | ✓ | 14 | 1.1 | even | 1 | trivial |