Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4025,2,Mod(1,4025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4025, 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("4025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4025 = 5^{2} \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4025.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1397868136\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2777.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 805) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.50848\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50848 | −1.77376 | −0.886882 | − | 0.461996i | \(-0.847133\pi\) | ||||
−0.886882 | + | 0.461996i | \(0.847133\pi\) | |||||||
\(3\) | −0.817356 | −0.471901 | −0.235950 | − | 0.971765i | \(-0.575820\pi\) | ||||
−0.235950 | + | 0.971765i | \(0.575820\pi\) | |||||||
\(4\) | 4.29248 | 2.14624 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.05032 | 0.837040 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −5.75064 | −2.03316 | ||||||||
\(9\) | −2.33193 | −0.777310 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.50848 | 1.05785 | 0.528923 | − | 0.848670i | \(-0.322596\pi\) | ||||
0.528923 | + | 0.848670i | \(0.322596\pi\) | |||||||
\(12\) | −3.50848 | −1.01281 | ||||||||
\(13\) | 0.541840 | 0.150279 | 0.0751397 | − | 0.997173i | \(-0.476060\pi\) | ||||
0.0751397 | + | 0.997173i | \(0.476060\pi\) | |||||||
\(14\) | −2.50848 | −0.670420 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.84041 | 1.46010 | ||||||||
\(17\) | −0.856807 | −0.207806 | −0.103903 | − | 0.994587i | \(-0.533133\pi\) | ||||
−0.103903 | + | 0.994587i | \(0.533133\pi\) | |||||||
\(18\) | 5.84960 | 1.37876 | ||||||||
\(19\) | −3.98360 | −0.913901 | −0.456951 | − | 0.889492i | \(-0.651058\pi\) | ||||
−0.456951 | + | 0.889492i | \(0.651058\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.817356 | −0.178362 | ||||||||
\(22\) | −8.80096 | −1.87637 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 4.70032 | 0.959448 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.35920 | −0.266560 | ||||||||
\(27\) | 4.35808 | 0.838713 | ||||||||
\(28\) | 4.29248 | 0.811202 | ||||||||
\(29\) | 0.916320 | 0.170156 | 0.0850781 | − | 0.996374i | \(-0.472886\pi\) | ||||
0.0850781 | + | 0.996374i | \(0.472886\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.314967 | 0.0565698 | 0.0282849 | − | 0.999600i | \(-0.490995\pi\) | ||||
0.0282849 | + | 0.999600i | \(0.490995\pi\) | |||||||
\(32\) | −3.14929 | −0.556720 | ||||||||
\(33\) | −2.86768 | −0.499198 | ||||||||
\(34\) | 2.14929 | 0.368599 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.0098 | −1.66829 | ||||||||
\(37\) | 3.44176 | 0.565822 | 0.282911 | − | 0.959146i | \(-0.408700\pi\) | ||||
0.282911 | + | 0.959146i | \(0.408700\pi\) | |||||||
\(38\) | 9.99279 | 1.62105 | ||||||||
\(39\) | −0.442876 | −0.0709169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.60745 | −0.563388 | −0.281694 | − | 0.959504i | \(-0.590896\pi\) | ||||
−0.281694 | + | 0.959504i | \(0.590896\pi\) | |||||||
\(42\) | 2.05032 | 0.316371 | ||||||||
\(43\) | −12.6839 | −1.93428 | −0.967140 | − | 0.254245i | \(-0.918173\pi\) | ||||
−0.967140 | + | 0.254245i | \(0.918173\pi\) | |||||||
\(44\) | 15.0601 | 2.27039 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.50848 | −0.369855 | ||||||||
\(47\) | 9.91689 | 1.44653 | 0.723263 | − | 0.690572i | \(-0.242641\pi\) | ||||
0.723263 | + | 0.690572i | \(0.242641\pi\) | |||||||
\(48\) | −4.77369 | −0.689023 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.700316 | 0.0980639 | ||||||||
\(52\) | 2.32584 | 0.322536 | ||||||||
\(53\) | −3.29248 | −0.452257 | −0.226128 | − | 0.974098i | \(-0.572607\pi\) | ||||
−0.226128 | + | 0.974098i | \(0.572607\pi\) | |||||||
\(54\) | −10.9322 | −1.48768 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.75064 | −0.768461 | ||||||||
\(57\) | 3.25602 | 0.431271 | ||||||||
\(58\) | −2.29857 | −0.301817 | ||||||||
\(59\) | −6.76151 | −0.880273 | −0.440137 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440137 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.19184 | −0.408673 | −0.204336 | − | 0.978901i | \(-0.565504\pi\) | ||||
−0.204336 | + | 0.978901i | \(0.565504\pi\) | |||||||
\(62\) | −0.790090 | −0.100341 | ||||||||
\(63\) | −2.33193 | −0.293796 | ||||||||
\(64\) | −3.78090 | −0.472612 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.19351 | 0.885460 | ||||||||
\(67\) | −0.788104 | −0.0962823 | −0.0481411 | − | 0.998841i | \(-0.515330\pi\) | ||||
−0.0481411 | + | 0.998841i | \(0.515330\pi\) | |||||||
\(68\) | −3.67783 | −0.446002 | ||||||||
\(69\) | −0.817356 | −0.0983981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.25303 | −0.386063 | −0.193032 | − | 0.981193i | \(-0.561832\pi\) | ||||
−0.193032 | + | 0.981193i | \(0.561832\pi\) | |||||||
\(72\) | 13.4101 | 1.58039 | ||||||||
\(73\) | 5.04621 | 0.590615 | 0.295307 | − | 0.955402i | \(-0.404578\pi\) | ||||
0.295307 | + | 0.955402i | \(0.404578\pi\) | |||||||
\(74\) | −8.63360 | −1.00364 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −17.0995 | −1.96145 | ||||||||
\(77\) | 3.50848 | 0.399829 | ||||||||
\(78\) | 1.11095 | 0.125790 | ||||||||
\(79\) | 6.73424 | 0.757661 | 0.378831 | − | 0.925466i | \(-0.376326\pi\) | ||||
0.378831 | + | 0.925466i | \(0.376326\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.43369 | 0.381521 | ||||||||
\(82\) | 9.04921 | 0.999318 | ||||||||
\(83\) | 3.37306 | 0.370241 | 0.185121 | − | 0.982716i | \(-0.440732\pi\) | ||||
0.185121 | + | 0.982716i | \(0.440732\pi\) | |||||||
\(84\) | −3.50848 | −0.382807 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 31.8174 | 3.43096 | ||||||||
\(87\) | −0.748959 | −0.0802968 | ||||||||
\(88\) | −20.1760 | −2.15077 | ||||||||
\(89\) | −4.40642 | −0.467079 | −0.233540 | − | 0.972347i | \(-0.575031\pi\) | ||||
−0.233540 | + | 0.972347i | \(0.575031\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.541840 | 0.0568003 | ||||||||
\(92\) | 4.29248 | 0.447522 | ||||||||
\(93\) | −0.257440 | −0.0266953 | ||||||||
\(94\) | −24.8763 | −2.56580 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.57409 | 0.262717 | ||||||||
\(97\) | −15.3951 | −1.56314 | −0.781568 | − | 0.623820i | \(-0.785580\pi\) | ||||
−0.781568 | + | 0.623820i | \(0.785580\pi\) | |||||||
\(98\) | −2.50848 | −0.253395 | ||||||||
\(99\) | −8.18153 | −0.822275 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.01895 | 0.897419 | 0.448709 | − | 0.893678i | \(-0.351884\pi\) | ||||
0.448709 | + | 0.893678i | \(0.351884\pi\) | |||||||
\(102\) | −1.75673 | −0.173942 | ||||||||
\(103\) | −11.3428 | −1.11764 | −0.558820 | − | 0.829289i | \(-0.688746\pi\) | ||||
−0.558820 | + | 0.829289i | \(0.688746\pi\) | |||||||
\(104\) | −3.11593 | −0.305542 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.25912 | 0.802197 | ||||||||
\(107\) | 6.98970 | 0.675719 | 0.337860 | − | 0.941196i | \(-0.390297\pi\) | ||||
0.337860 | + | 0.941196i | \(0.390297\pi\) | |||||||
\(108\) | 18.7070 | 1.80008 | ||||||||
\(109\) | −1.25855 | −0.120548 | −0.0602738 | − | 0.998182i | \(-0.519197\pi\) | ||||
−0.0602738 | + | 0.998182i | \(0.519197\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81314 | −0.267012 | ||||||||
\(112\) | 5.84041 | 0.551867 | ||||||||
\(113\) | −4.70752 | −0.442846 | −0.221423 | − | 0.975178i | \(-0.571070\pi\) | ||||
−0.221423 | + | 0.975178i | \(0.571070\pi\) | |||||||
\(114\) | −8.16767 | −0.764972 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.93328 | 0.365196 | ||||||||
\(117\) | −1.26353 | −0.116814 | ||||||||
\(118\) | 16.9611 | 1.56140 | ||||||||
\(119\) | −0.856807 | −0.0785434 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.30944 | 0.119040 | ||||||||
\(122\) | 8.00666 | 0.724889 | ||||||||
\(123\) | 2.94857 | 0.265863 | ||||||||
\(124\) | 1.35199 | 0.121412 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.84960 | 0.521124 | ||||||||
\(127\) | −13.1863 | −1.17010 | −0.585048 | − | 0.810999i | \(-0.698924\pi\) | ||||
−0.585048 | + | 0.810999i | \(0.698924\pi\) | |||||||
\(128\) | 15.7829 | 1.39502 | ||||||||
\(129\) | 10.3673 | 0.912788 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0509 | 1.48974 | 0.744871 | − | 0.667208i | \(-0.232511\pi\) | ||||
0.744871 | + | 0.667208i | \(0.232511\pi\) | |||||||
\(132\) | −12.3094 | −1.07140 | ||||||||
\(133\) | −3.98360 | −0.345422 | ||||||||
\(134\) | 1.97694 | 0.170782 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.92719 | 0.422503 | ||||||||
\(137\) | −18.7251 | −1.59979 | −0.799895 | − | 0.600141i | \(-0.795111\pi\) | ||||
−0.799895 | + | 0.600141i | \(0.795111\pi\) | |||||||
\(138\) | 2.05032 | 0.174535 | ||||||||
\(139\) | −11.1067 | −0.942061 | −0.471031 | − | 0.882117i | \(-0.656118\pi\) | ||||
−0.471031 | + | 0.882117i | \(0.656118\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.10562 | −0.682617 | ||||||||
\(142\) | 8.16015 | 0.684785 | ||||||||
\(143\) | 1.90104 | 0.158973 | ||||||||
\(144\) | −13.6194 | −1.13495 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.6583 | −1.04761 | ||||||||
\(147\) | −0.817356 | −0.0674144 | ||||||||
\(148\) | 14.7737 | 1.21439 | ||||||||
\(149\) | −13.1738 | −1.07924 | −0.539618 | − | 0.841910i | \(-0.681431\pi\) | ||||
−0.539618 | + | 0.841910i | \(0.681431\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.80395 | 0.390940 | 0.195470 | − | 0.980710i | \(-0.437377\pi\) | ||||
0.195470 | + | 0.980710i | \(0.437377\pi\) | |||||||
\(152\) | 22.9083 | 1.85811 | ||||||||
\(153\) | 1.99801 | 0.161530 | ||||||||
\(154\) | −8.80096 | −0.709201 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.90104 | −0.152205 | ||||||||
\(157\) | 18.7865 | 1.49933 | 0.749665 | − | 0.661818i | \(-0.230215\pi\) | ||||
0.749665 | + | 0.661818i | \(0.230215\pi\) | |||||||
\(158\) | −16.8927 | −1.34391 | ||||||||
\(159\) | 2.69113 | 0.213420 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | −8.61333 | −0.676727 | ||||||||
\(163\) | −8.84960 | −0.693154 | −0.346577 | − | 0.938021i | \(-0.612656\pi\) | ||||
−0.346577 | + | 0.938021i | \(0.612656\pi\) | |||||||
\(164\) | −15.4849 | −1.20917 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.46126 | −0.656721 | ||||||||
\(167\) | 16.7251 | 1.29422 | 0.647112 | − | 0.762395i | \(-0.275977\pi\) | ||||
0.647112 | + | 0.762395i | \(0.275977\pi\) | |||||||
\(168\) | 4.70032 | 0.362637 | ||||||||
\(169\) | −12.7064 | −0.977416 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.28948 | 0.710385 | ||||||||
\(172\) | −54.4454 | −4.15143 | ||||||||
\(173\) | −10.3253 | −0.785017 | −0.392509 | − | 0.919748i | \(-0.628393\pi\) | ||||
−0.392509 | + | 0.919748i | \(0.628393\pi\) | |||||||
\(174\) | 1.87875 | 0.142428 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 20.4910 | 1.54457 | ||||||||
\(177\) | 5.52656 | 0.415401 | ||||||||
\(178\) | 11.0534 | 0.828489 | ||||||||
\(179\) | 24.9770 | 1.86687 | 0.933433 | − | 0.358752i | \(-0.116798\pi\) | ||||
0.933433 | + | 0.358752i | \(0.116798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.81493 | 0.134902 | 0.0674512 | − | 0.997723i | \(-0.478513\pi\) | ||||
0.0674512 | + | 0.997723i | \(0.478513\pi\) | |||||||
\(182\) | −1.35920 | −0.100750 | ||||||||
\(183\) | 2.60886 | 0.192853 | ||||||||
\(184\) | −5.75064 | −0.423943 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.645784 | 0.0473512 | ||||||||
\(187\) | −3.00609 | −0.219827 | ||||||||
\(188\) | 42.5680 | 3.10459 | ||||||||
\(189\) | 4.35808 | 0.317004 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.1084 | 0.948492 | 0.474246 | − | 0.880392i | \(-0.342721\pi\) | ||||
0.474246 | + | 0.880392i | \(0.342721\pi\) | |||||||
\(192\) | 3.09034 | 0.223026 | ||||||||
\(193\) | 10.4607 | 0.752978 | 0.376489 | − | 0.926421i | \(-0.377131\pi\) | ||||
0.376489 | + | 0.926421i | \(0.377131\pi\) | |||||||
\(194\) | 38.6183 | 2.77263 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.29248 | 0.306606 | ||||||||
\(197\) | 14.3223 | 1.02042 | 0.510211 | − | 0.860049i | \(-0.329567\pi\) | ||||
0.510211 | + | 0.860049i | \(0.329567\pi\) | |||||||
\(198\) | 20.5232 | 1.45852 | ||||||||
\(199\) | −14.7918 | −1.04856 | −0.524280 | − | 0.851546i | \(-0.675666\pi\) | ||||
−0.524280 | + | 0.851546i | \(0.675666\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.644162 | 0.0454356 | ||||||||
\(202\) | −22.6239 | −1.59181 | ||||||||
\(203\) | 0.916320 | 0.0643130 | ||||||||
\(204\) | 3.00609 | 0.210469 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 28.4532 | 1.98243 | ||||||||
\(207\) | −2.33193 | −0.162080 | ||||||||
\(208\) | 3.16457 | 0.219423 | ||||||||
\(209\) | −13.9764 | −0.966768 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.61731 | −0.662083 | −0.331041 | − | 0.943616i | \(-0.607400\pi\) | ||||
−0.331041 | + | 0.943616i | \(0.607400\pi\) | |||||||
\(212\) | −14.1329 | −0.970651 | ||||||||
\(213\) | 2.65888 | 0.182183 | ||||||||
\(214\) | −17.5335 | −1.19857 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −25.0618 | −1.70524 | ||||||||
\(217\) | 0.314967 | 0.0213814 | ||||||||
\(218\) | 3.15706 | 0.213823 | ||||||||
\(219\) | −4.12455 | −0.278711 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.464253 | −0.0312290 | ||||||||
\(222\) | 7.05672 | 0.473616 | ||||||||
\(223\) | 23.3606 | 1.56434 | 0.782172 | − | 0.623063i | \(-0.214112\pi\) | ||||
0.782172 | + | 0.623063i | \(0.214112\pi\) | |||||||
\(224\) | −3.14929 | −0.210420 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8087 | 0.785505 | ||||||||
\(227\) | 2.21499 | 0.147014 | 0.0735072 | − | 0.997295i | \(-0.476581\pi\) | ||||
0.0735072 | + | 0.997295i | \(0.476581\pi\) | |||||||
\(228\) | 13.9764 | 0.925610 | ||||||||
\(229\) | 4.57708 | 0.302462 | 0.151231 | − | 0.988498i | \(-0.451676\pi\) | ||||
0.151231 | + | 0.988498i | \(0.451676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.86768 | −0.188679 | ||||||||
\(232\) | −5.26942 | −0.345955 | ||||||||
\(233\) | 9.60558 | 0.629283 | 0.314641 | − | 0.949211i | \(-0.398116\pi\) | ||||
0.314641 | + | 0.949211i | \(0.398116\pi\) | |||||||
\(234\) | 3.16955 | 0.207200 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.0236 | −1.88928 | ||||||||
\(237\) | −5.50427 | −0.357541 | ||||||||
\(238\) | 2.14929 | 0.139317 | ||||||||
\(239\) | 24.1497 | 1.56212 | 0.781059 | − | 0.624458i | \(-0.214680\pi\) | ||||
0.781059 | + | 0.624458i | \(0.214680\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.0321 | 1.41921 | 0.709605 | − | 0.704600i | \(-0.248873\pi\) | ||||
0.709605 | + | 0.704600i | \(0.248873\pi\) | |||||||
\(242\) | −3.28471 | −0.211149 | ||||||||
\(243\) | −15.8808 | −1.01875 | ||||||||
\(244\) | −13.7009 | −0.877109 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.39642 | −0.471579 | ||||||||
\(247\) | −2.15848 | −0.137341 | ||||||||
\(248\) | −1.81126 | −0.115015 | ||||||||
\(249\) | −2.75699 | −0.174717 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.87519 | 0.433958 | 0.216979 | − | 0.976176i | \(-0.430380\pi\) | ||||
0.216979 | + | 0.976176i | \(0.430380\pi\) | |||||||
\(252\) | −10.0098 | −0.630555 | ||||||||
\(253\) | 3.50848 | 0.220576 | ||||||||
\(254\) | 33.0776 | 2.07547 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0293 | −2.00183 | ||||||||
\(257\) | −6.39921 | −0.399172 | −0.199586 | − | 0.979880i | \(-0.563960\pi\) | ||||
−0.199586 | + | 0.979880i | \(0.563960\pi\) | |||||||
\(258\) | −26.0061 | −1.61907 | ||||||||
\(259\) | 3.44176 | 0.213861 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.13679 | −0.132264 | ||||||||
\(262\) | −42.7718 | −2.64245 | ||||||||
\(263\) | −27.8958 | −1.72013 | −0.860065 | − | 0.510185i | \(-0.829577\pi\) | ||||
−0.860065 | + | 0.510185i | \(0.829577\pi\) | |||||||
\(264\) | 16.4910 | 1.01495 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.99279 | 0.612698 | ||||||||
\(267\) | 3.60161 | 0.220415 | ||||||||
\(268\) | −3.38292 | −0.206645 | ||||||||
\(269\) | −1.70442 | −0.103921 | −0.0519603 | − | 0.998649i | \(-0.516547\pi\) | ||||
−0.0519603 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.0575 | 0.914681 | 0.457340 | − | 0.889292i | \(-0.348802\pi\) | ||||
0.457340 | + | 0.889292i | \(0.348802\pi\) | |||||||
\(272\) | −5.00411 | −0.303419 | ||||||||
\(273\) | −0.442876 | −0.0268041 | ||||||||
\(274\) | 46.9714 | 2.83765 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.50848 | −0.211186 | ||||||||
\(277\) | −14.8658 | −0.893200 | −0.446600 | − | 0.894734i | \(-0.647365\pi\) | ||||
−0.446600 | + | 0.894734i | \(0.647365\pi\) | |||||||
\(278\) | 27.8610 | 1.67099 | ||||||||
\(279\) | −0.734482 | −0.0439723 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.5471 | −1.52401 | −0.762005 | − | 0.647571i | \(-0.775785\pi\) | ||||
−0.762005 | + | 0.647571i | \(0.775785\pi\) | |||||||
\(282\) | 20.3328 | 1.21080 | ||||||||
\(283\) | −5.94968 | −0.353672 | −0.176836 | − | 0.984240i | \(-0.556586\pi\) | ||||
−0.176836 | + | 0.984240i | \(0.556586\pi\) | |||||||
\(284\) | −13.9635 | −0.828584 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.76871 | −0.281980 | ||||||||
\(287\) | −3.60745 | −0.212941 | ||||||||
\(288\) | 7.34391 | 0.432744 | ||||||||
\(289\) | −16.2659 | −0.956817 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.5833 | 0.737645 | ||||||||
\(292\) | 21.6608 | 1.26760 | ||||||||
\(293\) | −14.4206 | −0.842460 | −0.421230 | − | 0.906954i | \(-0.638401\pi\) | ||||
−0.421230 | + | 0.906954i | \(0.638401\pi\) | |||||||
\(294\) | 2.05032 | 0.119577 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −19.7923 | −1.15041 | ||||||||
\(297\) | 15.2903 | 0.887230 | ||||||||
\(298\) | 33.0461 | 1.91431 | ||||||||
\(299\) | 0.541840 | 0.0313354 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.6839 | −0.731089 | ||||||||
\(302\) | −12.0506 | −0.693436 | ||||||||
\(303\) | −7.37169 | −0.423492 | ||||||||
\(304\) | −23.2659 | −1.33439 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.01198 | −0.286516 | ||||||||
\(307\) | −27.3695 | −1.56206 | −0.781030 | − | 0.624493i | \(-0.785306\pi\) | ||||
−0.781030 | + | 0.624493i | \(0.785306\pi\) | |||||||
\(308\) | 15.0601 | 0.858128 | ||||||||
\(309\) | 9.27110 | 0.527415 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.3542 | 1.26759 | 0.633796 | − | 0.773500i | \(-0.281496\pi\) | ||||
0.633796 | + | 0.773500i | \(0.281496\pi\) | |||||||
\(312\) | 2.54682 | 0.144185 | ||||||||
\(313\) | −17.4227 | −0.984788 | −0.492394 | − | 0.870372i | \(-0.663878\pi\) | ||||
−0.492394 | + | 0.870372i | \(0.663878\pi\) | |||||||
\(314\) | −47.1257 | −2.65946 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.9066 | 1.62612 | ||||||||
\(317\) | 8.00864 | 0.449810 | 0.224905 | − | 0.974381i | \(-0.427793\pi\) | ||||
0.224905 | + | 0.974381i | \(0.427793\pi\) | |||||||
\(318\) | −6.75064 | −0.378557 | ||||||||
\(319\) | 3.21489 | 0.179999 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.71307 | −0.318872 | ||||||||
\(322\) | −2.50848 | −0.139792 | ||||||||
\(323\) | 3.41318 | 0.189914 | ||||||||
\(324\) | 14.7390 | 0.818834 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 22.1991 | 1.22949 | ||||||||
\(327\) | 1.02869 | 0.0568864 | ||||||||
\(328\) | 20.7451 | 1.14546 | ||||||||
\(329\) | 9.91689 | 0.546736 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.0528 | −1.43199 | −0.715995 | − | 0.698106i | \(-0.754027\pi\) | ||||
−0.715995 | + | 0.698106i | \(0.754027\pi\) | |||||||
\(332\) | 14.4788 | 0.794627 | ||||||||
\(333\) | −8.02595 | −0.439819 | ||||||||
\(334\) | −41.9545 | −2.29565 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.77369 | −0.260426 | ||||||||
\(337\) | −29.8174 | −1.62426 | −0.812128 | − | 0.583479i | \(-0.801691\pi\) | ||||
−0.812128 | + | 0.583479i | \(0.801691\pi\) | |||||||
\(338\) | 31.8738 | 1.73371 | ||||||||
\(339\) | 3.84772 | 0.208979 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.10506 | 0.0598422 | ||||||||
\(342\) | −23.3025 | −1.26005 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 72.9406 | 3.93270 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.9008 | 1.39244 | ||||||||
\(347\) | −31.1746 | −1.67354 | −0.836770 | − | 0.547555i | \(-0.815559\pi\) | ||||
−0.836770 | + | 0.547555i | \(0.815559\pi\) | |||||||
\(348\) | −3.21489 | −0.172336 | ||||||||
\(349\) | −1.97075 | −0.105492 | −0.0527459 | − | 0.998608i | \(-0.516797\pi\) | ||||
−0.0527459 | + | 0.998608i | \(0.516797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.36138 | 0.126041 | ||||||||
\(352\) | −11.0492 | −0.588925 | ||||||||
\(353\) | 8.17722 | 0.435230 | 0.217615 | − | 0.976035i | \(-0.430172\pi\) | ||||
0.217615 | + | 0.976035i | \(0.430172\pi\) | |||||||
\(354\) | −13.8633 | −0.736824 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −18.9145 | −1.00246 | ||||||||
\(357\) | 0.700316 | 0.0370647 | ||||||||
\(358\) | −62.6542 | −3.31138 | ||||||||
\(359\) | −12.3064 | −0.649509 | −0.324755 | − | 0.945798i | \(-0.605282\pi\) | ||||
−0.324755 | + | 0.945798i | \(0.605282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.13090 | −0.164784 | ||||||||
\(362\) | −4.55271 | −0.239285 | ||||||||
\(363\) | −1.07028 | −0.0561751 | ||||||||
\(364\) | 2.32584 | 0.121907 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.54429 | −0.342075 | ||||||||
\(367\) | −36.8034 | −1.92112 | −0.960561 | − | 0.278069i | \(-0.910306\pi\) | ||||
−0.960561 | + | 0.278069i | \(0.910306\pi\) | |||||||
\(368\) | 5.84041 | 0.304452 | ||||||||
\(369\) | 8.41231 | 0.437927 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.29248 | −0.170937 | ||||||||
\(372\) | −1.10506 | −0.0572945 | ||||||||
\(373\) | 18.6234 | 0.964283 | 0.482142 | − | 0.876093i | \(-0.339859\pi\) | ||||
0.482142 | + | 0.876093i | \(0.339859\pi\) | |||||||
\(374\) | 7.54073 | 0.389922 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −57.0284 | −2.94102 | ||||||||
\(377\) | 0.496499 | 0.0255710 | ||||||||
\(378\) | −10.9322 | −0.562290 | ||||||||
\(379\) | −17.5845 | −0.903256 | −0.451628 | − | 0.892206i | \(-0.649157\pi\) | ||||
−0.451628 | + | 0.892206i | \(0.649157\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.7779 | 0.552169 | ||||||||
\(382\) | −32.8822 | −1.68240 | ||||||||
\(383\) | −16.1214 | −0.823764 | −0.411882 | − | 0.911237i | \(-0.635128\pi\) | ||||
−0.411882 | + | 0.911237i | \(0.635128\pi\) | |||||||
\(384\) | −12.9002 | −0.658312 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.2405 | −1.33561 | ||||||||
\(387\) | 29.5780 | 1.50353 | ||||||||
\(388\) | −66.0832 | −3.35486 | ||||||||
\(389\) | −22.3119 | −1.13126 | −0.565629 | − | 0.824660i | \(-0.691366\pi\) | ||||
−0.565629 | + | 0.824660i | \(0.691366\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.856807 | −0.0433306 | ||||||||
\(392\) | −5.75064 | −0.290451 | ||||||||
\(393\) | −13.9366 | −0.703010 | ||||||||
\(394\) | −35.9272 | −1.80999 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −35.1190 | −1.76480 | ||||||||
\(397\) | 30.1165 | 1.51150 | 0.755752 | − | 0.654858i | \(-0.227272\pi\) | ||||
0.755752 | + | 0.654858i | \(0.227272\pi\) | |||||||
\(398\) | 37.1049 | 1.85990 | ||||||||
\(399\) | 3.25602 | 0.163005 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.2492 | −0.561757 | −0.280879 | − | 0.959743i | \(-0.590626\pi\) | ||||
−0.280879 | + | 0.959743i | \(0.590626\pi\) | |||||||
\(402\) | −1.61587 | −0.0805921 | ||||||||
\(403\) | 0.170662 | 0.00850128 | ||||||||
\(404\) | 38.7136 | 1.92608 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.29857 | −0.114076 | ||||||||
\(407\) | 12.0754 | 0.598553 | ||||||||
\(408\) | −4.02727 | −0.199379 | ||||||||
\(409\) | −12.6669 | −0.626336 | −0.313168 | − | 0.949698i | \(-0.601390\pi\) | ||||
−0.313168 | + | 0.949698i | \(0.601390\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.3050 | 0.754941 | ||||||||
\(412\) | −48.6887 | −2.39872 | ||||||||
\(413\) | −6.76151 | −0.332712 | ||||||||
\(414\) | 5.84960 | 0.287492 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.70641 | −0.0836636 | ||||||||
\(417\) | 9.07815 | 0.444559 | ||||||||
\(418\) | 35.0595 | 1.71482 | ||||||||
\(419\) | −18.6714 | −0.912156 | −0.456078 | − | 0.889940i | \(-0.650746\pi\) | ||||
−0.456078 | + | 0.889940i | \(0.650746\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.1723 | −0.788192 | −0.394096 | − | 0.919069i | \(-0.628942\pi\) | ||||
−0.394096 | + | 0.919069i | \(0.628942\pi\) | |||||||
\(422\) | 24.1248 | 1.17438 | ||||||||
\(423\) | −23.1255 | −1.12440 | ||||||||
\(424\) | 18.9338 | 0.919509 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.66975 | −0.323150 | ||||||||
\(427\) | −3.19184 | −0.154464 | ||||||||
\(428\) | 30.0031 | 1.45026 | ||||||||
\(429\) | −1.55382 | −0.0750193 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.79673 | 0.182882 | 0.0914410 | − | 0.995810i | \(-0.470853\pi\) | ||||
0.0914410 | + | 0.995810i | \(0.470853\pi\) | |||||||
\(432\) | 25.4530 | 1.22461 | ||||||||
\(433\) | −32.6028 | −1.56679 | −0.783395 | − | 0.621524i | \(-0.786514\pi\) | ||||
−0.783395 | + | 0.621524i | \(0.786514\pi\) | |||||||
\(434\) | −0.790090 | −0.0379255 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.40231 | −0.258724 | ||||||||
\(437\) | −3.98360 | −0.190562 | ||||||||
\(438\) | 10.3464 | 0.494368 | ||||||||
\(439\) | −28.5319 | −1.36175 | −0.680877 | − | 0.732398i | \(-0.738401\pi\) | ||||
−0.680877 | + | 0.732398i | \(0.738401\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.33193 | −0.111044 | ||||||||
\(442\) | 1.16457 | 0.0553929 | ||||||||
\(443\) | 13.0072 | 0.617992 | 0.308996 | − | 0.951063i | \(-0.400007\pi\) | ||||
0.308996 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(444\) | −12.0754 | −0.573071 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −58.5997 | −2.77478 | ||||||||
\(447\) | 10.7676 | 0.509292 | ||||||||
\(448\) | −3.78090 | −0.178631 | ||||||||
\(449\) | 9.41571 | 0.444355 | 0.222177 | − | 0.975006i | \(-0.428684\pi\) | ||||
0.222177 | + | 0.975006i | \(0.428684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.6567 | −0.595979 | ||||||||
\(452\) | −20.2069 | −0.950454 | ||||||||
\(453\) | −3.92654 | −0.184485 | ||||||||
\(454\) | −5.55627 | −0.260769 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −18.7242 | −0.876841 | ||||||||
\(457\) | −4.21246 | −0.197051 | −0.0985253 | − | 0.995135i | \(-0.531413\pi\) | ||||
−0.0985253 | + | 0.995135i | \(0.531413\pi\) | |||||||
\(458\) | −11.4815 | −0.536496 | ||||||||
\(459\) | −3.73404 | −0.174290 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.4911 | −0.628342 | −0.314171 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314171 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(462\) | 7.19351 | 0.334673 | ||||||||
\(463\) | −14.4738 | −0.672655 | −0.336327 | − | 0.941745i | \(-0.609185\pi\) | ||||
−0.336327 | + | 0.941745i | \(0.609185\pi\) | |||||||
\(464\) | 5.35168 | 0.248446 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0954 | −1.11620 | ||||||||
\(467\) | −36.1865 | −1.67451 | −0.837256 | − | 0.546811i | \(-0.815842\pi\) | ||||
−0.837256 | + | 0.546811i | \(0.815842\pi\) | |||||||
\(468\) | −5.42369 | −0.250710 | ||||||||
\(469\) | −0.788104 | −0.0363913 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.3553 | −0.707534 | ||||||||
\(472\) | 38.8830 | 1.78973 | ||||||||
\(473\) | −44.5013 | −2.04617 | ||||||||
\(474\) | 13.8074 | 0.634193 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.67783 | −0.168573 | ||||||||
\(477\) | 7.67783 | 0.351544 | ||||||||
\(478\) | −60.5792 | −2.77083 | ||||||||
\(479\) | −29.4649 | −1.34629 | −0.673144 | − | 0.739512i | \(-0.735056\pi\) | ||||
−0.673144 | + | 0.739512i | \(0.735056\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.86489 | 0.0850315 | ||||||||
\(482\) | −55.2670 | −2.51734 | ||||||||
\(483\) | −0.817356 | −0.0371910 | ||||||||
\(484\) | 5.62074 | 0.255488 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 39.8367 | 1.80703 | ||||||||
\(487\) | 2.36727 | 0.107271 | 0.0536357 | − | 0.998561i | \(-0.482919\pi\) | ||||
0.0536357 | + | 0.998561i | \(0.482919\pi\) | |||||||
\(488\) | 18.3551 | 0.830896 | ||||||||
\(489\) | 7.23327 | 0.327100 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.2619 | −0.643632 | −0.321816 | − | 0.946802i | \(-0.604293\pi\) | ||||
−0.321816 | + | 0.946802i | \(0.604293\pi\) | |||||||
\(492\) | 12.6567 | 0.570606 | ||||||||
\(493\) | −0.785110 | −0.0353596 | ||||||||
\(494\) | 5.41450 | 0.243610 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.83954 | 0.0825977 | ||||||||
\(497\) | −3.25303 | −0.145918 | ||||||||
\(498\) | 6.91586 | 0.309907 | ||||||||
\(499\) | −6.13811 | −0.274780 | −0.137390 | − | 0.990517i | \(-0.543871\pi\) | ||||
−0.137390 | + | 0.990517i | \(0.543871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6703 | −0.610745 | ||||||||
\(502\) | −17.2463 | −0.769739 | ||||||||
\(503\) | −4.15463 | −0.185246 | −0.0926229 | − | 0.995701i | \(-0.529525\pi\) | ||||
−0.0926229 | + | 0.995701i | \(0.529525\pi\) | |||||||
\(504\) | 13.4101 | 0.597333 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.80096 | −0.391250 | ||||||||
\(507\) | 10.3857 | 0.461243 | ||||||||
\(508\) | −56.6019 | −2.51130 | ||||||||
\(509\) | −17.7266 | −0.785717 | −0.392859 | − | 0.919599i | \(-0.628514\pi\) | ||||
−0.392859 | + | 0.919599i | \(0.628514\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.04621 | 0.223231 | ||||||||
\(512\) | 48.7791 | 2.15575 | ||||||||
\(513\) | −17.3609 | −0.766501 | ||||||||
\(514\) | 16.0523 | 0.708037 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 44.5013 | 1.95906 | ||||||||
\(517\) | 34.7932 | 1.53020 | ||||||||
\(518\) | −8.63360 | −0.379339 | ||||||||
\(519\) | 8.43943 | 0.370450 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.64137 | −0.0719097 | −0.0359549 | − | 0.999353i | \(-0.511447\pi\) | ||||
−0.0359549 | + | 0.999353i | \(0.511447\pi\) | |||||||
\(522\) | 5.36011 | 0.234605 | ||||||||
\(523\) | 10.9325 | 0.478046 | 0.239023 | − | 0.971014i | \(-0.423173\pi\) | ||||
0.239023 | + | 0.971014i | \(0.423173\pi\) | |||||||
\(524\) | 73.1906 | 3.19734 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 69.9761 | 3.05110 | ||||||||
\(527\) | −0.269866 | −0.0117556 | ||||||||
\(528\) | −16.7484 | −0.728881 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.7674 | 0.684245 | ||||||||
\(532\) | −17.0995 | −0.741359 | ||||||||
\(533\) | −1.95466 | −0.0846657 | ||||||||
\(534\) | −9.03458 | −0.390964 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.53210 | 0.195757 | ||||||||
\(537\) | −20.4151 | −0.880975 | ||||||||
\(538\) | 4.27552 | 0.184331 | ||||||||
\(539\) | 3.50848 | 0.151121 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.1080 | 1.25145 | 0.625725 | − | 0.780044i | \(-0.284803\pi\) | ||||
0.625725 | + | 0.780044i | \(0.284803\pi\) | |||||||
\(542\) | −37.7716 | −1.62243 | ||||||||
\(543\) | −1.48344 | −0.0636605 | ||||||||
\(544\) | 2.69833 | 0.115690 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.11095 | 0.0475441 | ||||||||
\(547\) | 11.3355 | 0.484670 | 0.242335 | − | 0.970193i | \(-0.422087\pi\) | ||||
0.242335 | + | 0.970193i | \(0.422087\pi\) | |||||||
\(548\) | −80.3769 | −3.43353 | ||||||||
\(549\) | 7.44314 | 0.317665 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.65025 | −0.155506 | ||||||||
\(552\) | 4.70032 | 0.200059 | ||||||||
\(553\) | 6.73424 | 0.286369 | ||||||||
\(554\) | 37.2906 | 1.58433 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −47.6754 | −2.02189 | ||||||||
\(557\) | 36.5791 | 1.54990 | 0.774952 | − | 0.632020i | \(-0.217774\pi\) | ||||
0.774952 | + | 0.632020i | \(0.217774\pi\) | |||||||
\(558\) | 1.84243 | 0.0779964 | ||||||||
\(559\) | −6.87266 | −0.290682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.45705 | 0.103737 | ||||||||
\(562\) | 64.0844 | 2.70324 | ||||||||
\(563\) | −27.4270 | −1.15591 | −0.577956 | − | 0.816068i | \(-0.696150\pi\) | ||||
−0.577956 | + | 0.816068i | \(0.696150\pi\) | |||||||
\(564\) | −34.7932 | −1.46506 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 14.9247 | 0.627330 | ||||||||
\(567\) | 3.43369 | 0.144201 | ||||||||
\(568\) | 18.7070 | 0.784927 | ||||||||
\(569\) | 33.7226 | 1.41373 | 0.706863 | − | 0.707351i | \(-0.250110\pi\) | ||||
0.706863 | + | 0.707351i | \(0.250110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9542 | −1.00245 | −0.501225 | − | 0.865317i | \(-0.667117\pi\) | ||||
−0.501225 | + | 0.865317i | \(0.667117\pi\) | |||||||
\(572\) | 8.16015 | 0.341193 | ||||||||
\(573\) | −10.7142 | −0.447594 | ||||||||
\(574\) | 9.04921 | 0.377707 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.81679 | 0.367366 | ||||||||
\(577\) | −9.86403 | −0.410645 | −0.205323 | − | 0.978694i | \(-0.565824\pi\) | ||||
−0.205323 | + | 0.978694i | \(0.565824\pi\) | |||||||
\(578\) | 40.8027 | 1.69717 | ||||||||
\(579\) | −8.55012 | −0.355331 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.37306 | 0.139938 | ||||||||
\(582\) | −31.5649 | −1.30841 | ||||||||
\(583\) | −11.5516 | −0.478418 | ||||||||
\(584\) | −29.0189 | −1.20081 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 36.1738 | 1.49433 | ||||||||
\(587\) | −40.1041 | −1.65527 | −0.827636 | − | 0.561265i | \(-0.810315\pi\) | ||||
−0.827636 | + | 0.561265i | \(0.810315\pi\) | |||||||
\(588\) | −3.50848 | −0.144687 | ||||||||
\(589\) | −1.25470 | −0.0516992 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.7064 | −0.481537 | ||||||||
\(592\) | 20.1013 | 0.826159 | ||||||||
\(593\) | 12.6878 | 0.521024 | 0.260512 | − | 0.965471i | \(-0.416109\pi\) | ||||
0.260512 | + | 0.965471i | \(0.416109\pi\) | |||||||
\(594\) | −38.3553 | −1.57374 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −56.5481 | −2.31630 | ||||||||
\(597\) | 12.0901 | 0.494816 | ||||||||
\(598\) | −1.35920 | −0.0555817 | ||||||||
\(599\) | 21.7401 | 0.888278 | 0.444139 | − | 0.895958i | \(-0.353510\pi\) | ||||
0.444139 | + | 0.895958i | \(0.353510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.04779 | 0.165113 | 0.0825564 | − | 0.996586i | \(-0.473692\pi\) | ||||
0.0825564 | + | 0.996586i | \(0.473692\pi\) | |||||||
\(602\) | 31.8174 | 1.29678 | ||||||||
\(603\) | 1.83780 | 0.0748412 | ||||||||
\(604\) | 20.6209 | 0.839051 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.4917 | 0.751176 | ||||||||
\(607\) | 31.7697 | 1.28949 | 0.644747 | − | 0.764396i | \(-0.276963\pi\) | ||||
0.644747 | + | 0.764396i | \(0.276963\pi\) | |||||||
\(608\) | 12.5455 | 0.508787 | ||||||||
\(609\) | −0.748959 | −0.0303494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.37337 | 0.217383 | ||||||||
\(612\) | 8.57643 | 0.346682 | ||||||||
\(613\) | −10.2630 | −0.414517 | −0.207259 | − | 0.978286i | \(-0.566454\pi\) | ||||
−0.207259 | + | 0.978286i | \(0.566454\pi\) | |||||||
\(614\) | 68.6559 | 2.77073 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −20.1760 | −0.812914 | ||||||||
\(617\) | 26.1681 | 1.05349 | 0.526745 | − | 0.850024i | \(-0.323412\pi\) | ||||
0.526745 | + | 0.850024i | \(0.323412\pi\) | |||||||
\(618\) | −23.2564 | −0.935509 | ||||||||
\(619\) | 43.7567 | 1.75873 | 0.879364 | − | 0.476149i | \(-0.157968\pi\) | ||||
0.879364 | + | 0.476149i | \(0.157968\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.35808 | 0.174884 | ||||||||
\(622\) | −56.0752 | −2.24841 | ||||||||
\(623\) | −4.40642 | −0.176539 | ||||||||
\(624\) | −2.58658 | −0.103546 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 43.7045 | 1.74678 | ||||||||
\(627\) | 11.4237 | 0.456218 | ||||||||
\(628\) | 80.6408 | 3.21792 | ||||||||
\(629\) | −2.94893 | −0.117581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.40642 | −0.255036 | −0.127518 | − | 0.991836i | \(-0.540701\pi\) | ||||
−0.127518 | + | 0.991836i | \(0.540701\pi\) | |||||||
\(632\) | −38.7262 | −1.54044 | ||||||||
\(633\) | 7.86076 | 0.312437 | ||||||||
\(634\) | −20.0895 | −0.797857 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11.5516 | 0.458051 | ||||||||
\(637\) | 0.541840 | 0.0214685 | ||||||||
\(638\) | −8.06449 | −0.319276 | ||||||||
\(639\) | 7.58583 | 0.300091 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.3613 | −1.55468 | −0.777339 | − | 0.629082i | \(-0.783431\pi\) | ||||
−0.777339 | + | 0.629082i | \(0.783431\pi\) | |||||||
\(642\) | 14.3311 | 0.565604 | ||||||||
\(643\) | 41.6534 | 1.64265 | 0.821324 | − | 0.570462i | \(-0.193236\pi\) | ||||
0.821324 | + | 0.570462i | \(0.193236\pi\) | |||||||
\(644\) | 4.29248 | 0.169147 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.56190 | −0.336863 | ||||||||
\(647\) | 9.36686 | 0.368249 | 0.184125 | − | 0.982903i | \(-0.441055\pi\) | ||||
0.184125 | + | 0.982903i | \(0.441055\pi\) | |||||||
\(648\) | −19.7459 | −0.775691 | ||||||||
\(649\) | −23.7226 | −0.931194 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.257440 | −0.0100899 | ||||||||
\(652\) | −37.9867 | −1.48767 | ||||||||
\(653\) | 7.37174 | 0.288479 | 0.144239 | − | 0.989543i | \(-0.453926\pi\) | ||||
0.144239 | + | 0.989543i | \(0.453926\pi\) | |||||||
\(654\) | −2.58044 | −0.100903 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.0690 | −0.822605 | ||||||||
\(657\) | −11.7674 | −0.459091 | ||||||||
\(658\) | −24.8763 | −0.969780 | ||||||||
\(659\) | −24.4032 | −0.950613 | −0.475307 | − | 0.879820i | \(-0.657663\pi\) | ||||
−0.475307 | + | 0.879820i | \(0.657663\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.0839 | −1.09234 | −0.546169 | − | 0.837675i | \(-0.683914\pi\) | ||||
−0.546169 | + | 0.837675i | \(0.683914\pi\) | |||||||
\(662\) | 65.3529 | 2.54001 | ||||||||
\(663\) | 0.379460 | 0.0147370 | ||||||||
\(664\) | −19.3972 | −0.752759 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 20.1329 | 0.780136 | ||||||||
\(667\) | 0.916320 | 0.0354800 | ||||||||
\(668\) | 71.7919 | 2.77771 | ||||||||
\(669\) | −19.0939 | −0.738215 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.1985 | −0.432313 | ||||||||
\(672\) | 2.57409 | 0.0992975 | ||||||||
\(673\) | 12.6286 | 0.486797 | 0.243399 | − | 0.969926i | \(-0.421738\pi\) | ||||
0.243399 | + | 0.969926i | \(0.421738\pi\) | |||||||
\(674\) | 74.7963 | 2.88105 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −54.5420 | −2.09777 | ||||||||
\(677\) | −14.4125 | −0.553919 | −0.276959 | − | 0.960882i | \(-0.589327\pi\) | ||||
−0.276959 | + | 0.960882i | \(0.589327\pi\) | |||||||
\(678\) | −9.65193 | −0.370680 | ||||||||
\(679\) | −15.3951 | −0.590810 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.81044 | −0.0693761 | ||||||||
\(682\) | −2.77201 | −0.106146 | ||||||||
\(683\) | −50.6830 | −1.93933 | −0.969666 | − | 0.244433i | \(-0.921398\pi\) | ||||
−0.969666 | + | 0.244433i | \(0.921398\pi\) | |||||||
\(684\) | 39.8749 | 1.52465 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.50848 | −0.0957743 | ||||||||
\(687\) | −3.74110 | −0.142732 | ||||||||
\(688\) | −74.0793 | −2.82425 | ||||||||
\(689\) | −1.78400 | −0.0679649 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.0879 | 1.25872 | 0.629362 | − | 0.777112i | \(-0.283316\pi\) | ||||
0.629362 | + | 0.777112i | \(0.283316\pi\) | |||||||
\(692\) | −44.3211 | −1.68483 | ||||||||
\(693\) | −8.18153 | −0.310791 | ||||||||
\(694\) | 78.2009 | 2.96846 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.30699 | 0.163256 | ||||||||
\(697\) | 3.09089 | 0.117076 | ||||||||
\(698\) | 4.94359 | 0.187117 | ||||||||
\(699\) | −7.85118 | −0.296959 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −36.8895 | −1.39330 | −0.696649 | − | 0.717412i | \(-0.745326\pi\) | ||||
−0.696649 | + | 0.717412i | \(0.745326\pi\) | |||||||
\(702\) | −5.92349 | −0.223568 | ||||||||
\(703\) | −13.7106 | −0.517106 | ||||||||
\(704\) | −13.2652 | −0.499951 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −20.5124 | −0.771995 | ||||||||
\(707\) | 9.01895 | 0.339192 | ||||||||
\(708\) | 23.7226 | 0.891551 | ||||||||
\(709\) | −18.4348 | −0.692334 | −0.346167 | − | 0.938173i | \(-0.612517\pi\) | ||||
−0.346167 | + | 0.938173i | \(0.612517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.7038 | −0.588938 | ||||||||
\(712\) | 25.3397 | 0.949646 | ||||||||
\(713\) | 0.314967 | 0.0117956 | ||||||||
\(714\) | −1.75673 | −0.0657440 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 107.213 | 4.00674 | ||||||||
\(717\) | −19.7389 | −0.737164 | ||||||||
\(718\) | 30.8705 | 1.15208 | ||||||||
\(719\) | 21.6203 | 0.806301 | 0.403151 | − | 0.915134i | \(-0.367915\pi\) | ||||
0.403151 | + | 0.915134i | \(0.367915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.3428 | −0.422428 | ||||||||
\(722\) | 7.85381 | 0.292289 | ||||||||
\(723\) | −18.0080 | −0.669726 | ||||||||
\(724\) | 7.79053 | 0.289533 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.68477 | 0.0996413 | ||||||||
\(727\) | 14.4447 | 0.535723 | 0.267861 | − | 0.963457i | \(-0.413683\pi\) | ||||
0.267861 | + | 0.963457i | \(0.413683\pi\) | |||||||
\(728\) | −3.11593 | −0.115484 | ||||||||
\(729\) | 2.67920 | 0.0992296 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8677 | 0.401956 | ||||||||
\(732\) | 11.1985 | 0.413908 | ||||||||
\(733\) | 39.7963 | 1.46991 | 0.734955 | − | 0.678116i | \(-0.237203\pi\) | ||||
0.734955 | + | 0.678116i | \(0.237203\pi\) | |||||||
\(734\) | 92.3207 | 3.40762 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.14929 | −0.116084 | ||||||||
\(737\) | −2.76505 | −0.101852 | ||||||||
\(738\) | −21.1021 | −0.776780 | ||||||||
\(739\) | −51.1491 | −1.88155 | −0.940775 | − | 0.339030i | \(-0.889901\pi\) | ||||
−0.940775 | + | 0.339030i | \(0.889901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.76424 | 0.0648111 | ||||||||
\(742\) | 8.25912 | 0.303202 | ||||||||
\(743\) | 11.9870 | 0.439759 | 0.219879 | − | 0.975527i | \(-0.429434\pi\) | ||||
0.219879 | + | 0.975527i | \(0.429434\pi\) | |||||||
\(744\) | 1.48045 | 0.0542758 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −46.7164 | −1.71041 | ||||||||
\(747\) | −7.86574 | −0.287792 | ||||||||
\(748\) | −12.9036 | −0.471802 | ||||||||
\(749\) | 6.98970 | 0.255398 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.3499 | −1.21696 | −0.608478 | − | 0.793571i | \(-0.708220\pi\) | ||||
−0.608478 | + | 0.793571i | \(0.708220\pi\) | |||||||
\(752\) | 57.9187 | 2.11208 | ||||||||
\(753\) | −5.61947 | −0.204785 | ||||||||
\(754\) | −1.24546 | −0.0453569 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 18.7070 | 0.680366 | ||||||||
\(757\) | 17.9791 | 0.653461 | 0.326730 | − | 0.945118i | \(-0.394053\pi\) | ||||
0.326730 | + | 0.945118i | \(0.394053\pi\) | |||||||
\(758\) | 44.1104 | 1.60216 | ||||||||
\(759\) | −2.86768 | −0.104090 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8968 | −1.08376 | −0.541880 | − | 0.840456i | \(-0.682287\pi\) | ||||
−0.541880 | + | 0.840456i | \(0.682287\pi\) | |||||||
\(762\) | −27.0362 | −0.979417 | ||||||||
\(763\) | −1.25855 | −0.0455627 | ||||||||
\(764\) | 56.2676 | 2.03569 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.4402 | 1.46116 | ||||||||
\(767\) | −3.66366 | −0.132287 | ||||||||
\(768\) | 26.1793 | 0.944664 | ||||||||
\(769\) | 6.44703 | 0.232486 | 0.116243 | − | 0.993221i | \(-0.462915\pi\) | ||||
0.116243 | + | 0.993221i | \(0.462915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.23043 | 0.188369 | ||||||||
\(772\) | 44.9024 | 1.61607 | ||||||||
\(773\) | 31.1639 | 1.12089 | 0.560444 | − | 0.828192i | \(-0.310630\pi\) | ||||
0.560444 | + | 0.828192i | \(0.310630\pi\) | |||||||
\(774\) | −74.1959 | −2.66692 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 88.5317 | 3.17810 | ||||||||
\(777\) | −2.81314 | −0.100921 | ||||||||
\(778\) | 55.9690 | 2.00658 | ||||||||
\(779\) | 14.3706 | 0.514881 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4132 | −0.408396 | ||||||||
\(782\) | 2.14929 | 0.0768583 | ||||||||
\(783\) | 3.99340 | 0.142712 | ||||||||
\(784\) | 5.84041 | 0.208586 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 34.9598 | 1.24697 | ||||||||
\(787\) | −14.3398 | −0.511160 | −0.255580 | − | 0.966788i | \(-0.582266\pi\) | ||||
−0.255580 | + | 0.966788i | \(0.582266\pi\) | |||||||
\(788\) | 61.4781 | 2.19007 | ||||||||
\(789\) | 22.8008 | 0.811730 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.70752 | −0.167380 | ||||||||
\(792\) | 47.0490 | 1.67181 | ||||||||
\(793\) | −1.72946 | −0.0614151 | ||||||||
\(794\) | −75.5467 | −2.68105 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −63.4933 | −2.25046 | ||||||||
\(797\) | 12.8167 | 0.453990 | 0.226995 | − | 0.973896i | \(-0.427110\pi\) | ||||
0.226995 | + | 0.973896i | \(0.427110\pi\) | |||||||
\(798\) | −8.16767 | −0.289132 | ||||||||
\(799\) | −8.49686 | −0.300597 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2755 | 0.363066 | ||||||||
\(802\) | 28.2184 | 0.996425 | ||||||||
\(803\) | 17.7045 | 0.624780 | ||||||||
\(804\) | 2.76505 | 0.0975158 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.428102 | −0.0150793 | ||||||||
\(807\) | 1.39312 | 0.0490402 | ||||||||
\(808\) | −51.8647 | −1.82459 | ||||||||
\(809\) | 45.2722 | 1.59169 | 0.795843 | − | 0.605503i | \(-0.207028\pi\) | ||||
0.795843 | + | 0.605503i | \(0.207028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.5019 | −1.80848 | −0.904239 | − | 0.427027i | \(-0.859561\pi\) | ||||
−0.904239 | + | 0.427027i | \(0.859561\pi\) | |||||||
\(812\) | 3.93328 | 0.138031 | ||||||||
\(813\) | −12.3074 | −0.431638 | ||||||||
\(814\) | −30.2908 | −1.06169 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.09014 | 0.143183 | ||||||||
\(817\) | 50.5277 | 1.76774 | ||||||||
\(818\) | 31.7746 | 1.11097 | ||||||||
\(819\) | −1.26353 | −0.0441514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.3886 | −1.09547 | −0.547734 | − | 0.836652i | \(-0.684510\pi\) | ||||
−0.547734 | + | 0.836652i | \(0.684510\pi\) | |||||||
\(822\) | −38.3924 | −1.33909 | ||||||||
\(823\) | 34.2009 | 1.19217 | 0.596084 | − | 0.802922i | \(-0.296723\pi\) | ||||
0.596084 | + | 0.802922i | \(0.296723\pi\) | |||||||
\(824\) | 65.2283 | 2.27234 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.9611 | 0.590153 | ||||||||
\(827\) | −12.4751 | −0.433803 | −0.216901 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216901 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(828\) | −10.0098 | −0.347863 | ||||||||
\(829\) | −11.0668 | −0.384367 | −0.192183 | − | 0.981359i | \(-0.561557\pi\) | ||||
−0.192183 | + | 0.981359i | \(0.561557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.1507 | 0.421502 | ||||||||
\(832\) | −2.04864 | −0.0710239 | ||||||||
\(833\) | −0.856807 | −0.0296866 | ||||||||
\(834\) | −22.7724 | −0.788543 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −59.9934 | −2.07491 | ||||||||
\(837\) | 1.37265 | 0.0474459 | ||||||||
\(838\) | 46.8368 | 1.61795 | ||||||||
\(839\) | −17.4038 | −0.600846 | −0.300423 | − | 0.953806i | \(-0.597128\pi\) | ||||
−0.300423 | + | 0.953806i | \(0.597128\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1604 | −0.971047 | ||||||||
\(842\) | 40.5680 | 1.39807 | ||||||||
\(843\) | 20.8811 | 0.719182 | ||||||||
\(844\) | −41.2821 | −1.42099 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 58.0098 | 1.99442 | ||||||||
\(847\) | 1.30944 | 0.0449929 | ||||||||
\(848\) | −19.2294 | −0.660341 | ||||||||
\(849\) | 4.86300 | 0.166898 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.44176 | 0.117982 | ||||||||
\(852\) | 11.4132 | 0.391009 | ||||||||
\(853\) | 24.9701 | 0.854961 | 0.427480 | − | 0.904025i | \(-0.359401\pi\) | ||||
0.427480 | + | 0.904025i | \(0.359401\pi\) | |||||||
\(854\) | 8.00666 | 0.273982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −40.1952 | −1.37384 | ||||||||
\(857\) | 12.2388 | 0.418068 | 0.209034 | − | 0.977908i | \(-0.432968\pi\) | ||||
0.209034 | + | 0.977908i | \(0.432968\pi\) | |||||||
\(858\) | 3.89773 | 0.133066 | ||||||||
\(859\) | −31.1201 | −1.06180 | −0.530901 | − | 0.847434i | \(-0.678146\pi\) | ||||
−0.530901 | + | 0.847434i | \(0.678146\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.94857 | 0.100487 | ||||||||
\(862\) | −9.52402 | −0.324390 | ||||||||
\(863\) | −28.3634 | −0.965502 | −0.482751 | − | 0.875758i | \(-0.660362\pi\) | ||||
−0.482751 | + | 0.875758i | \(0.660362\pi\) | |||||||
\(864\) | −13.7248 | −0.466929 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 81.7835 | 2.77912 | ||||||||
\(867\) | 13.2950 | 0.451522 | ||||||||
\(868\) | 1.35199 | 0.0458895 | ||||||||
\(869\) | 23.6270 | 0.801490 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.427027 | −0.0144692 | ||||||||
\(872\) | 7.23748 | 0.245092 | ||||||||
\(873\) | 35.9003 | 1.21504 | ||||||||
\(874\) | 9.99279 | 0.338011 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.7045 | −0.598181 | ||||||||
\(877\) | −0.437656 | −0.0147786 | −0.00738929 | − | 0.999973i | \(-0.502352\pi\) | ||||
−0.00738929 | + | 0.999973i | \(0.502352\pi\) | |||||||
\(878\) | 71.5718 | 2.41543 | ||||||||
\(879\) | 11.7868 | 0.397557 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.4661 | 1.02643 | 0.513214 | − | 0.858261i | \(-0.328455\pi\) | ||||
0.513214 | + | 0.858261i | \(0.328455\pi\) | |||||||
\(882\) | 5.84960 | 0.196966 | ||||||||
\(883\) | −21.2473 | −0.715028 | −0.357514 | − | 0.933908i | \(-0.616376\pi\) | ||||
−0.357514 | + | 0.933908i | \(0.616376\pi\) | |||||||
\(884\) | −1.99279 | −0.0670249 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32.6284 | −1.09617 | ||||||||
\(887\) | −35.4964 | −1.19185 | −0.595927 | − | 0.803039i | \(-0.703215\pi\) | ||||
−0.595927 | + | 0.803039i | \(0.703215\pi\) | |||||||
\(888\) | 16.1774 | 0.542877 | ||||||||
\(889\) | −13.1863 | −0.442255 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.0470 | 0.403590 | ||||||||
\(892\) | 100.275 | 3.35746 | ||||||||
\(893\) | −39.5049 | −1.32198 | ||||||||
\(894\) | −27.0104 | −0.903364 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.7829 | 0.527269 | ||||||||
\(897\) | −0.442876 | −0.0147872 | ||||||||
\(898\) | −23.6191 | −0.788181 | ||||||||
\(899\) | 0.288611 | 0.00962571 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.82102 | 0.0939818 | ||||||||
\(902\) | 31.7490 | 1.05713 | ||||||||
\(903\) | 10.3673 | 0.345001 | ||||||||
\(904\) | 27.0713 | 0.900377 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.84965 | 0.327233 | ||||||||
\(907\) | −4.00055 | −0.132836 | −0.0664180 | − | 0.997792i | \(-0.521157\pi\) | ||||
−0.0664180 | + | 0.997792i | \(0.521157\pi\) | |||||||
\(908\) | 9.50781 | 0.315528 | ||||||||
\(909\) | −21.0316 | −0.697573 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.20704 | 0.0399910 | 0.0199955 | − | 0.999800i | \(-0.493635\pi\) | ||||
0.0199955 | + | 0.999800i | \(0.493635\pi\) | |||||||
\(912\) | 19.0165 | 0.629699 | ||||||||
\(913\) | 11.8343 | 0.391659 | ||||||||
\(914\) | 10.5669 | 0.349521 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.6470 | 0.649156 | ||||||||
\(917\) | 17.0509 | 0.563070 | ||||||||
\(918\) | 9.36676 | 0.309149 | ||||||||
\(919\) | −52.0360 | −1.71651 | −0.858255 | − | 0.513223i | \(-0.828451\pi\) | ||||
−0.858255 | + | 0.513223i | \(0.828451\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.3706 | 0.737137 | ||||||||
\(922\) | 33.8421 | 1.11453 | ||||||||
\(923\) | −1.76262 | −0.0580173 | ||||||||
\(924\) | −12.3094 | −0.404951 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 36.3073 | 1.19313 | ||||||||
\(927\) | 26.4506 | 0.868752 | ||||||||
\(928\) | −2.88575 | −0.0947295 | ||||||||
\(929\) | 55.5209 | 1.82158 | 0.910792 | − | 0.412866i | \(-0.135472\pi\) | ||||
0.910792 | + | 0.412866i | \(0.135472\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.98360 | −0.130557 | ||||||||
\(932\) | 41.2317 | 1.35059 | ||||||||
\(933\) | −18.2714 | −0.598177 | ||||||||
\(934\) | 90.7732 | 2.97019 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.26612 | 0.237501 | ||||||||
\(937\) | 58.3946 | 1.90767 | 0.953834 | − | 0.300335i | \(-0.0970984\pi\) | ||||
0.953834 | + | 0.300335i | \(0.0970984\pi\) | |||||||
\(938\) | 1.97694 | 0.0645495 | ||||||||
\(939\) | 14.2405 | 0.464722 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.4587 | −0.373543 | −0.186772 | − | 0.982403i | \(-0.559802\pi\) | ||||
−0.186772 | + | 0.982403i | \(0.559802\pi\) | |||||||
\(942\) | 38.5185 | 1.25500 | ||||||||
\(943\) | −3.60745 | −0.117475 | ||||||||
\(944\) | −39.4900 | −1.28529 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 111.631 | 3.62943 | ||||||||
\(947\) | −56.4647 | −1.83486 | −0.917428 | − | 0.397902i | \(-0.869738\pi\) | ||||
−0.917428 | + | 0.397902i | \(0.869738\pi\) | |||||||
\(948\) | −23.6270 | −0.767368 | ||||||||
\(949\) | 2.73424 | 0.0887572 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.54591 | −0.212266 | ||||||||
\(952\) | 4.92719 | 0.159691 | ||||||||
\(953\) | 19.7983 | 0.641331 | 0.320665 | − | 0.947193i | \(-0.396094\pi\) | ||||
0.320665 | + | 0.947193i | \(0.396094\pi\) | |||||||
\(954\) | −19.2597 | −0.623555 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 103.662 | 3.35268 | ||||||||
\(957\) | −2.62771 | −0.0849418 | ||||||||
\(958\) | 73.9122 | 2.38800 | ||||||||
\(959\) | −18.7251 | −0.604663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9008 | −0.996800 | ||||||||
\(962\) | −4.67803 | −0.150826 | ||||||||
\(963\) | −16.2995 | −0.525243 | ||||||||
\(964\) | 94.5721 | 3.04596 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.05032 | 0.0659680 | ||||||||
\(967\) | −1.83834 | −0.0591172 | −0.0295586 | − | 0.999563i | \(-0.509410\pi\) | ||||
−0.0295586 | + | 0.999563i | \(0.509410\pi\) | |||||||
\(968\) | −7.53012 | −0.242027 | ||||||||
\(969\) | −2.78978 | −0.0896207 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.673597 | 0.0216168 | 0.0108084 | − | 0.999942i | \(-0.496560\pi\) | ||||
0.0108084 | + | 0.999942i | \(0.496560\pi\) | |||||||
\(972\) | −68.1679 | −2.18649 | ||||||||
\(973\) | −11.1067 | −0.356066 | ||||||||
\(974\) | −5.93826 | −0.190274 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −18.6416 | −0.596704 | ||||||||
\(977\) | −29.2316 | −0.935201 | −0.467600 | − | 0.883940i | \(-0.654881\pi\) | ||||
−0.467600 | + | 0.883940i | \(0.654881\pi\) | |||||||
\(978\) | −18.1445 | −0.580198 | ||||||||
\(979\) | −15.4598 | −0.494099 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.93486 | 0.0937028 | ||||||||
\(982\) | 35.7758 | 1.14165 | ||||||||
\(983\) | 30.2475 | 0.964746 | 0.482373 | − | 0.875966i | \(-0.339775\pi\) | ||||
0.482373 | + | 0.875966i | \(0.339775\pi\) | |||||||
\(984\) | −16.9561 | −0.540542 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.96943 | 0.0627195 | ||||||||
\(987\) | −8.10562 | −0.258005 | ||||||||
\(988\) | −9.26521 | −0.294766 | ||||||||
\(989\) | −12.6839 | −0.403325 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.06295 | −0.287894 | −0.143947 | − | 0.989585i | \(-0.545980\pi\) | ||||
−0.143947 | + | 0.989585i | \(0.545980\pi\) | |||||||
\(992\) | −0.991922 | −0.0314936 | ||||||||
\(993\) | 21.2944 | 0.675757 | ||||||||
\(994\) | 8.16015 | 0.258824 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −11.8343 | −0.374985 | ||||||||
\(997\) | 5.02466 | 0.159133 | 0.0795663 | − | 0.996830i | \(-0.474646\pi\) | ||||
0.0795663 | + | 0.996830i | \(0.474646\pi\) | |||||||
\(998\) | 15.3973 | 0.487394 | ||||||||
\(999\) | 14.9995 | 0.474563 |
(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 | 4025.2.a.l.1.1 | 4 | ||
5.4 | even | 2 | 805.2.a.j.1.4 | ✓ | 4 | ||
15.14 | odd | 2 | 7245.2.a.bc.1.1 | 4 | |||
35.34 | odd | 2 | 5635.2.a.w.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
805.2.a.j.1.4 | ✓ | 4 | 5.4 | even | 2 | ||
4025.2.a.l.1.1 | 4 | 1.1 | even | 1 | trivial | ||
5635.2.a.w.1.4 | 4 | 35.34 | odd | 2 | |||
7245.2.a.bc.1.1 | 4 | 15.14 | odd | 2 |