Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,4,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(9.73531515095\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.56155 | −0.905646 | −0.452823 | − | 0.891601i | \(-0.649583\pi\) | ||||
−0.452823 | + | 0.891601i | \(0.649583\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −1.43845 | −0.179806 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −7.68466 | −0.522875 | ||||||||
\(7\) | 6.24621 | 0.337264 | 0.168632 | − | 0.985679i | \(-0.446065\pi\) | ||||
0.168632 | + | 0.985679i | \(0.446065\pi\) | |||||||
\(8\) | 24.1771 | 1.06849 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 12.8078 | 0.405017 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −4.31534 | −0.103811 | ||||||||
\(13\) | −49.1231 | −1.04802 | −0.524011 | − | 0.851711i | \(-0.675565\pi\) | ||||
−0.524011 | + | 0.851711i | \(0.675565\pi\) | |||||||
\(14\) | −16.0000 | −0.305441 | ||||||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | −50.4233 | −0.787864 | ||||||||
\(17\) | 82.7083 | 1.17998 | 0.589992 | − | 0.807409i | \(-0.299131\pi\) | ||||
0.589992 | + | 0.807409i | \(0.299131\pi\) | |||||||
\(18\) | −23.0540 | −0.301882 | ||||||||
\(19\) | −130.354 | −1.57396 | −0.786981 | − | 0.616977i | \(-0.788357\pi\) | ||||
−0.786981 | + | 0.616977i | \(0.788357\pi\) | |||||||
\(20\) | 7.19224 | 0.0804116 | ||||||||
\(21\) | 18.7386 | 0.194719 | ||||||||
\(22\) | 28.1771 | 0.273062 | ||||||||
\(23\) | −185.693 | −1.68347 | −0.841733 | − | 0.539895i | \(-0.818464\pi\) | ||||
−0.841733 | + | 0.539895i | \(0.818464\pi\) | |||||||
\(24\) | 72.5312 | 0.616891 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 125.831 | 0.949137 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −8.98485 | −0.0606420 | ||||||||
\(29\) | −8.90720 | −0.0570354 | −0.0285177 | − | 0.999593i | \(-0.509079\pi\) | ||||
−0.0285177 | + | 0.999593i | \(0.509079\pi\) | |||||||
\(30\) | 38.4233 | 0.233837 | ||||||||
\(31\) | 5.26137 | 0.0304829 | 0.0152414 | − | 0.999884i | \(-0.495148\pi\) | ||||
0.0152414 | + | 0.999884i | \(0.495148\pi\) | |||||||
\(32\) | −64.2547 | −0.354961 | ||||||||
\(33\) | −33.0000 | −0.174078 | ||||||||
\(34\) | −211.862 | −1.06865 | ||||||||
\(35\) | −31.2311 | −0.150829 | ||||||||
\(36\) | −12.9460 | −0.0599353 | ||||||||
\(37\) | −416.894 | −1.85235 | −0.926175 | − | 0.377094i | \(-0.876923\pi\) | ||||
−0.926175 | + | 0.377094i | \(0.876923\pi\) | |||||||
\(38\) | 333.909 | 1.42545 | ||||||||
\(39\) | −147.369 | −0.605076 | ||||||||
\(40\) | −120.885 | −0.477842 | ||||||||
\(41\) | −298.479 | −1.13694 | −0.568471 | − | 0.822703i | \(-0.692465\pi\) | ||||
−0.568471 | + | 0.822703i | \(0.692465\pi\) | |||||||
\(42\) | −48.0000 | −0.176347 | ||||||||
\(43\) | −513.633 | −1.82159 | −0.910793 | − | 0.412863i | \(-0.864529\pi\) | ||||
−0.910793 | + | 0.412863i | \(0.864529\pi\) | |||||||
\(44\) | 15.8229 | 0.0542135 | ||||||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | 475.663 | 1.52462 | ||||||||
\(47\) | 557.295 | 1.72957 | 0.864786 | − | 0.502140i | \(-0.167454\pi\) | ||||
0.864786 | + | 0.502140i | \(0.167454\pi\) | |||||||
\(48\) | −151.270 | −0.454873 | ||||||||
\(49\) | −303.985 | −0.886253 | ||||||||
\(50\) | −64.0388 | −0.181129 | ||||||||
\(51\) | 248.125 | 0.681264 | ||||||||
\(52\) | 70.6610 | 0.188441 | ||||||||
\(53\) | −168.064 | −0.435574 | −0.217787 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217787 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(54\) | −69.1619 | −0.174292 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | 151.015 | 0.360362 | ||||||||
\(57\) | −391.062 | −0.908728 | ||||||||
\(58\) | 22.8163 | 0.0516539 | ||||||||
\(59\) | 618.773 | 1.36538 | 0.682689 | − | 0.730709i | \(-0.260810\pi\) | ||||
0.682689 | + | 0.730709i | \(0.260810\pi\) | |||||||
\(60\) | 21.5767 | 0.0464257 | ||||||||
\(61\) | 786.405 | 1.65064 | 0.825319 | − | 0.564667i | \(-0.190996\pi\) | ||||
0.825319 | + | 0.564667i | \(0.190996\pi\) | |||||||
\(62\) | −13.4773 | −0.0276067 | ||||||||
\(63\) | 56.2159 | 0.112421 | ||||||||
\(64\) | 567.978 | 1.10933 | ||||||||
\(65\) | 245.616 | 0.468690 | ||||||||
\(66\) | 84.5312 | 0.157653 | ||||||||
\(67\) | −339.015 | −0.618169 | −0.309084 | − | 0.951035i | \(-0.600023\pi\) | ||||
−0.309084 | + | 0.951035i | \(0.600023\pi\) | |||||||
\(68\) | −118.972 | −0.212168 | ||||||||
\(69\) | −557.080 | −0.971949 | ||||||||
\(70\) | 80.0000 | 0.136598 | ||||||||
\(71\) | 1120.71 | 1.87329 | 0.936645 | − | 0.350280i | \(-0.113913\pi\) | ||||
0.936645 | + | 0.350280i | \(0.113913\pi\) | |||||||
\(72\) | 217.594 | 0.356162 | ||||||||
\(73\) | −123.430 | −0.197896 | −0.0989478 | − | 0.995093i | \(-0.531548\pi\) | ||||
−0.0989478 | + | 0.995093i | \(0.531548\pi\) | |||||||
\(74\) | 1067.90 | 1.67757 | ||||||||
\(75\) | 75.0000 | 0.115470 | ||||||||
\(76\) | 187.508 | 0.283008 | ||||||||
\(77\) | −68.7083 | −0.101689 | ||||||||
\(78\) | 377.494 | 0.547985 | ||||||||
\(79\) | −309.835 | −0.441255 | −0.220628 | − | 0.975358i | \(-0.570811\pi\) | ||||
−0.220628 | + | 0.975358i | \(0.570811\pi\) | |||||||
\(80\) | 252.116 | 0.352343 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 764.570 | 1.02967 | ||||||||
\(83\) | −1021.22 | −1.35053 | −0.675263 | − | 0.737577i | \(-0.735970\pi\) | ||||
−0.675263 | + | 0.737577i | \(0.735970\pi\) | |||||||
\(84\) | −26.9545 | −0.0350117 | ||||||||
\(85\) | −413.542 | −0.527705 | ||||||||
\(86\) | 1315.70 | 1.64971 | ||||||||
\(87\) | −26.7216 | −0.0329294 | ||||||||
\(88\) | −265.948 | −0.322161 | ||||||||
\(89\) | −141.879 | −0.168979 | −0.0844894 | − | 0.996424i | \(-0.526926\pi\) | ||||
−0.0844894 | + | 0.996424i | \(0.526926\pi\) | |||||||
\(90\) | 115.270 | 0.135006 | ||||||||
\(91\) | −306.833 | −0.353460 | ||||||||
\(92\) | 267.110 | 0.302697 | ||||||||
\(93\) | 15.7841 | 0.0175993 | ||||||||
\(94\) | −1427.54 | −1.56638 | ||||||||
\(95\) | 651.771 | 0.703898 | ||||||||
\(96\) | −192.764 | −0.204937 | ||||||||
\(97\) | 798.345 | 0.835666 | 0.417833 | − | 0.908524i | \(-0.362790\pi\) | ||||
0.417833 | + | 0.908524i | \(0.362790\pi\) | |||||||
\(98\) | 778.673 | 0.802631 | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | −35.9612 | −0.0359612 | ||||||||
\(101\) | 241.400 | 0.237823 | 0.118912 | − | 0.992905i | \(-0.462059\pi\) | ||||
0.118912 | + | 0.992905i | \(0.462059\pi\) | |||||||
\(102\) | −635.585 | −0.616983 | ||||||||
\(103\) | 1168.38 | 1.11771 | 0.558853 | − | 0.829267i | \(-0.311242\pi\) | ||||
0.558853 | + | 0.829267i | \(0.311242\pi\) | |||||||
\(104\) | −1187.65 | −1.11980 | ||||||||
\(105\) | −93.6932 | −0.0870811 | ||||||||
\(106\) | 430.506 | 0.394476 | ||||||||
\(107\) | −2106.82 | −1.90350 | −0.951748 | − | 0.306882i | \(-0.900714\pi\) | ||||
−0.951748 | + | 0.306882i | \(0.900714\pi\) | |||||||
\(108\) | −38.8381 | −0.0346037 | ||||||||
\(109\) | 493.792 | 0.433914 | 0.216957 | − | 0.976181i | \(-0.430387\pi\) | ||||
0.216957 | + | 0.976181i | \(0.430387\pi\) | |||||||
\(110\) | −140.885 | −0.122117 | ||||||||
\(111\) | −1250.68 | −1.06945 | ||||||||
\(112\) | −314.955 | −0.265718 | ||||||||
\(113\) | 170.000 | 0.141524 | 0.0707622 | − | 0.997493i | \(-0.477457\pi\) | ||||
0.0707622 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(114\) | 1001.73 | 0.822986 | ||||||||
\(115\) | 928.466 | 0.752869 | ||||||||
\(116\) | 12.8125 | 0.0102553 | ||||||||
\(117\) | −442.108 | −0.349341 | ||||||||
\(118\) | −1585.02 | −1.23655 | ||||||||
\(119\) | 516.614 | 0.397966 | ||||||||
\(120\) | −362.656 | −0.275882 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −2014.42 | −1.49489 | ||||||||
\(123\) | −895.437 | −0.656414 | ||||||||
\(124\) | −7.56820 | −0.00548100 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −144.000 | −0.101814 | ||||||||
\(127\) | −948.182 | −0.662500 | −0.331250 | − | 0.943543i | \(-0.607470\pi\) | ||||
−0.331250 | + | 0.943543i | \(0.607470\pi\) | |||||||
\(128\) | −940.868 | −0.649702 | ||||||||
\(129\) | −1540.90 | −1.05169 | ||||||||
\(130\) | −629.157 | −0.424467 | ||||||||
\(131\) | −1484.84 | −0.990312 | −0.495156 | − | 0.868804i | \(-0.664889\pi\) | ||||
−0.495156 | + | 0.868804i | \(0.664889\pi\) | |||||||
\(132\) | 47.4688 | 0.0313002 | ||||||||
\(133\) | −814.220 | −0.530841 | ||||||||
\(134\) | 868.405 | 0.559842 | ||||||||
\(135\) | −135.000 | −0.0860663 | ||||||||
\(136\) | 1999.65 | 1.26080 | ||||||||
\(137\) | 684.928 | 0.427134 | 0.213567 | − | 0.976928i | \(-0.431492\pi\) | ||||
0.213567 | + | 0.976928i | \(0.431492\pi\) | |||||||
\(138\) | 1426.99 | 0.880242 | ||||||||
\(139\) | 830.483 | 0.506767 | 0.253384 | − | 0.967366i | \(-0.418457\pi\) | ||||
0.253384 | + | 0.967366i | \(0.418457\pi\) | |||||||
\(140\) | 44.9242 | 0.0271199 | ||||||||
\(141\) | 1671.89 | 0.998569 | ||||||||
\(142\) | −2870.75 | −1.69654 | ||||||||
\(143\) | 540.354 | 0.315991 | ||||||||
\(144\) | −453.810 | −0.262621 | ||||||||
\(145\) | 44.5360 | 0.0255070 | ||||||||
\(146\) | 316.172 | 0.179223 | ||||||||
\(147\) | −911.955 | −0.511679 | ||||||||
\(148\) | 599.680 | 0.333063 | ||||||||
\(149\) | −1213.64 | −0.667285 | −0.333642 | − | 0.942700i | \(-0.608278\pi\) | ||||
−0.333642 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(150\) | −192.116 | −0.104575 | ||||||||
\(151\) | 30.8466 | 0.0166242 | 0.00831212 | − | 0.999965i | \(-0.497354\pi\) | ||||
0.00831212 | + | 0.999965i | \(0.497354\pi\) | |||||||
\(152\) | −3151.58 | −1.68176 | ||||||||
\(153\) | 744.375 | 0.393328 | ||||||||
\(154\) | 176.000 | 0.0920941 | ||||||||
\(155\) | −26.3068 | −0.0136324 | ||||||||
\(156\) | 211.983 | 0.108796 | ||||||||
\(157\) | 345.239 | 0.175497 | 0.0877485 | − | 0.996143i | \(-0.472033\pi\) | ||||
0.0877485 | + | 0.996143i | \(0.472033\pi\) | |||||||
\(158\) | 793.659 | 0.399621 | ||||||||
\(159\) | −504.193 | −0.251479 | ||||||||
\(160\) | 321.274 | 0.158743 | ||||||||
\(161\) | −1159.88 | −0.567772 | ||||||||
\(162\) | −207.486 | −0.100627 | ||||||||
\(163\) | 1921.49 | 0.923331 | 0.461665 | − | 0.887054i | \(-0.347252\pi\) | ||||
0.461665 | + | 0.887054i | \(0.347252\pi\) | |||||||
\(164\) | 429.346 | 0.204429 | ||||||||
\(165\) | 165.000 | 0.0778499 | ||||||||
\(166\) | 2615.91 | 1.22310 | ||||||||
\(167\) | 172.297 | 0.0798369 | 0.0399185 | − | 0.999203i | \(-0.487290\pi\) | ||||
0.0399185 | + | 0.999203i | \(0.487290\pi\) | |||||||
\(168\) | 453.045 | 0.208055 | ||||||||
\(169\) | 216.080 | 0.0983521 | ||||||||
\(170\) | 1059.31 | 0.477913 | ||||||||
\(171\) | −1173.19 | −0.524654 | ||||||||
\(172\) | 738.833 | 0.327532 | ||||||||
\(173\) | −1025.29 | −0.450587 | −0.225293 | − | 0.974291i | \(-0.572334\pi\) | ||||
−0.225293 | + | 0.974291i | \(0.572334\pi\) | |||||||
\(174\) | 68.4488 | 0.0298224 | ||||||||
\(175\) | 156.155 | 0.0674527 | ||||||||
\(176\) | 554.656 | 0.237550 | ||||||||
\(177\) | 1856.32 | 0.788302 | ||||||||
\(178\) | 363.430 | 0.153035 | ||||||||
\(179\) | 1658.29 | 0.692437 | 0.346219 | − | 0.938154i | \(-0.387466\pi\) | ||||
0.346219 | + | 0.938154i | \(0.387466\pi\) | |||||||
\(180\) | 64.7301 | 0.0268039 | ||||||||
\(181\) | −2021.81 | −0.830275 | −0.415137 | − | 0.909759i | \(-0.636266\pi\) | ||||
−0.415137 | + | 0.909759i | \(0.636266\pi\) | |||||||
\(182\) | 785.970 | 0.320110 | ||||||||
\(183\) | 2359.22 | 0.952996 | ||||||||
\(184\) | −4489.52 | −1.79876 | ||||||||
\(185\) | 2084.47 | 0.828396 | ||||||||
\(186\) | −40.4318 | −0.0159387 | ||||||||
\(187\) | −909.792 | −0.355778 | ||||||||
\(188\) | −801.640 | −0.310987 | ||||||||
\(189\) | 168.648 | 0.0649064 | ||||||||
\(190\) | −1669.55 | −0.637482 | ||||||||
\(191\) | 1440.22 | 0.545607 | 0.272803 | − | 0.962070i | \(-0.412049\pi\) | ||||
0.272803 | + | 0.962070i | \(0.412049\pi\) | |||||||
\(192\) | 1703.93 | 0.640473 | ||||||||
\(193\) | −2798.05 | −1.04356 | −0.521782 | − | 0.853079i | \(-0.674733\pi\) | ||||
−0.521782 | + | 0.853079i | \(0.674733\pi\) | |||||||
\(194\) | −2045.00 | −0.756817 | ||||||||
\(195\) | 736.847 | 0.270598 | ||||||||
\(196\) | 437.266 | 0.159354 | ||||||||
\(197\) | 458.943 | 0.165982 | 0.0829908 | − | 0.996550i | \(-0.473553\pi\) | ||||
0.0829908 | + | 0.996550i | \(0.473553\pi\) | |||||||
\(198\) | 253.594 | 0.0910208 | ||||||||
\(199\) | −2371.04 | −0.844615 | −0.422308 | − | 0.906453i | \(-0.638780\pi\) | ||||
−0.422308 | + | 0.906453i | \(0.638780\pi\) | |||||||
\(200\) | 604.427 | 0.213697 | ||||||||
\(201\) | −1017.05 | −0.356900 | ||||||||
\(202\) | −618.358 | −0.215384 | ||||||||
\(203\) | −55.6363 | −0.0192360 | ||||||||
\(204\) | −356.915 | −0.122495 | ||||||||
\(205\) | 1492.40 | 0.508456 | ||||||||
\(206\) | −2992.86 | −1.01225 | ||||||||
\(207\) | −1671.24 | −0.561155 | ||||||||
\(208\) | 2476.95 | 0.825699 | ||||||||
\(209\) | 1433.90 | 0.474568 | ||||||||
\(210\) | 240.000 | 0.0788646 | ||||||||
\(211\) | 4319.87 | 1.40944 | 0.704721 | − | 0.709484i | \(-0.251072\pi\) | ||||
0.704721 | + | 0.709484i | \(0.251072\pi\) | |||||||
\(212\) | 241.752 | 0.0783187 | ||||||||
\(213\) | 3362.12 | 1.08154 | ||||||||
\(214\) | 5396.73 | 1.72389 | ||||||||
\(215\) | 2568.16 | 0.814638 | ||||||||
\(216\) | 652.781 | 0.205630 | ||||||||
\(217\) | 32.8636 | 0.0102808 | ||||||||
\(218\) | −1264.87 | −0.392973 | ||||||||
\(219\) | −370.290 | −0.114255 | ||||||||
\(220\) | −79.1146 | −0.0242450 | ||||||||
\(221\) | −4062.89 | −1.23665 | ||||||||
\(222\) | 3203.69 | 0.968547 | ||||||||
\(223\) | −3837.73 | −1.15244 | −0.576219 | − | 0.817295i | \(-0.695473\pi\) | ||||
−0.576219 | + | 0.817295i | \(0.695473\pi\) | |||||||
\(224\) | −401.349 | −0.119715 | ||||||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −435.464 | −0.128171 | ||||||||
\(227\) | −5003.71 | −1.46303 | −0.731515 | − | 0.681825i | \(-0.761187\pi\) | ||||
−0.731515 | + | 0.681825i | \(0.761187\pi\) | |||||||
\(228\) | 562.523 | 0.163395 | ||||||||
\(229\) | −277.375 | −0.0800412 | −0.0400206 | − | 0.999199i | \(-0.512742\pi\) | ||||
−0.0400206 | + | 0.999199i | \(0.512742\pi\) | |||||||
\(230\) | −2378.31 | −0.681832 | ||||||||
\(231\) | −206.125 | −0.0587101 | ||||||||
\(232\) | −215.350 | −0.0609415 | ||||||||
\(233\) | 2269.91 | 0.638225 | 0.319113 | − | 0.947717i | \(-0.396615\pi\) | ||||
0.319113 | + | 0.947717i | \(0.396615\pi\) | |||||||
\(234\) | 1132.48 | 0.316379 | ||||||||
\(235\) | −2786.48 | −0.773488 | ||||||||
\(236\) | −890.072 | −0.245503 | ||||||||
\(237\) | −929.505 | −0.254759 | ||||||||
\(238\) | −1323.33 | −0.360416 | ||||||||
\(239\) | −1617.11 | −0.437665 | −0.218832 | − | 0.975762i | \(-0.570225\pi\) | ||||
−0.218832 | + | 0.975762i | \(0.570225\pi\) | |||||||
\(240\) | 756.349 | 0.203426 | ||||||||
\(241\) | 5646.63 | 1.50926 | 0.754629 | − | 0.656151i | \(-0.227817\pi\) | ||||
0.754629 | + | 0.656151i | \(0.227817\pi\) | |||||||
\(242\) | −309.948 | −0.0823314 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −1131.20 | −0.296794 | ||||||||
\(245\) | 1519.92 | 0.396344 | ||||||||
\(246\) | 2293.71 | 0.594478 | ||||||||
\(247\) | 6403.40 | 1.64955 | ||||||||
\(248\) | 127.204 | 0.0325705 | ||||||||
\(249\) | −3063.66 | −0.779726 | ||||||||
\(250\) | 320.194 | 0.0810034 | ||||||||
\(251\) | −6217.61 | −1.56355 | −0.781777 | − | 0.623558i | \(-0.785687\pi\) | ||||
−0.781777 | + | 0.623558i | \(0.785687\pi\) | |||||||
\(252\) | −80.8636 | −0.0202140 | ||||||||
\(253\) | 2042.62 | 0.507584 | ||||||||
\(254\) | 2428.82 | 0.599991 | ||||||||
\(255\) | −1240.62 | −0.304670 | ||||||||
\(256\) | −2133.74 | −0.520933 | ||||||||
\(257\) | 7712.75 | 1.87202 | 0.936008 | − | 0.351980i | \(-0.114491\pi\) | ||||
0.936008 | + | 0.351980i | \(0.114491\pi\) | |||||||
\(258\) | 3947.09 | 0.952462 | ||||||||
\(259\) | −2604.01 | −0.624730 | ||||||||
\(260\) | −353.305 | −0.0842732 | ||||||||
\(261\) | −80.1648 | −0.0190118 | ||||||||
\(262\) | 3803.49 | 0.896871 | ||||||||
\(263\) | 206.347 | 0.0483798 | 0.0241899 | − | 0.999707i | \(-0.492299\pi\) | ||||
0.0241899 | + | 0.999707i | \(0.492299\pi\) | |||||||
\(264\) | −797.844 | −0.186000 | ||||||||
\(265\) | 840.322 | 0.194795 | ||||||||
\(266\) | 2085.67 | 0.480753 | ||||||||
\(267\) | −425.636 | −0.0975600 | ||||||||
\(268\) | 487.655 | 0.111150 | ||||||||
\(269\) | 1712.47 | 0.388146 | 0.194073 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194073 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(270\) | 345.810 | 0.0779456 | ||||||||
\(271\) | −477.081 | −0.106940 | −0.0534698 | − | 0.998569i | \(-0.517028\pi\) | ||||
−0.0534698 | + | 0.998569i | \(0.517028\pi\) | |||||||
\(272\) | −4170.43 | −0.929666 | ||||||||
\(273\) | −920.500 | −0.204070 | ||||||||
\(274\) | −1754.48 | −0.386832 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | 801.329 | 0.174762 | ||||||||
\(277\) | 4283.48 | 0.929130 | 0.464565 | − | 0.885539i | \(-0.346211\pi\) | ||||
0.464565 | + | 0.885539i | \(0.346211\pi\) | |||||||
\(278\) | −2127.33 | −0.458952 | ||||||||
\(279\) | 47.3523 | 0.0101610 | ||||||||
\(280\) | −755.076 | −0.161159 | ||||||||
\(281\) | 3477.79 | 0.738319 | 0.369160 | − | 0.929366i | \(-0.379646\pi\) | ||||
0.369160 | + | 0.929366i | \(0.379646\pi\) | |||||||
\(282\) | −4282.62 | −0.904350 | ||||||||
\(283\) | −6568.27 | −1.37966 | −0.689829 | − | 0.723973i | \(-0.742314\pi\) | ||||
−0.689829 | + | 0.723973i | \(0.742314\pi\) | |||||||
\(284\) | −1612.08 | −0.336829 | ||||||||
\(285\) | 1955.31 | 0.406395 | ||||||||
\(286\) | −1384.15 | −0.286176 | ||||||||
\(287\) | −1864.36 | −0.383449 | ||||||||
\(288\) | −578.292 | −0.118320 | ||||||||
\(289\) | 1927.67 | 0.392360 | ||||||||
\(290\) | −114.081 | −0.0231003 | ||||||||
\(291\) | 2395.03 | 0.482472 | ||||||||
\(292\) | 177.547 | 0.0355828 | ||||||||
\(293\) | 8352.29 | 1.66534 | 0.832672 | − | 0.553766i | \(-0.186810\pi\) | ||||
0.832672 | + | 0.553766i | \(0.186810\pi\) | |||||||
\(294\) | 2336.02 | 0.463399 | ||||||||
\(295\) | −3093.86 | −0.610616 | ||||||||
\(296\) | −10079.3 | −1.97921 | ||||||||
\(297\) | −297.000 | −0.0580259 | ||||||||
\(298\) | 3108.81 | 0.604324 | ||||||||
\(299\) | 9121.83 | 1.76431 | ||||||||
\(300\) | −107.884 | −0.0207622 | ||||||||
\(301\) | −3208.26 | −0.614355 | ||||||||
\(302\) | −79.0152 | −0.0150557 | ||||||||
\(303\) | 724.199 | 0.137307 | ||||||||
\(304\) | 6572.89 | 1.24007 | ||||||||
\(305\) | −3932.03 | −0.738187 | ||||||||
\(306\) | −1906.76 | −0.356216 | ||||||||
\(307\) | 5383.89 | 1.00090 | 0.500448 | − | 0.865767i | \(-0.333169\pi\) | ||||
0.500448 | + | 0.865767i | \(0.333169\pi\) | |||||||
\(308\) | 98.8333 | 0.0182843 | ||||||||
\(309\) | 3505.14 | 0.645308 | ||||||||
\(310\) | 67.3863 | 0.0123461 | ||||||||
\(311\) | −1790.41 | −0.326447 | −0.163223 | − | 0.986589i | \(-0.552189\pi\) | ||||
−0.163223 | + | 0.986589i | \(0.552189\pi\) | |||||||
\(312\) | −3562.96 | −0.646516 | ||||||||
\(313\) | −809.076 | −0.146108 | −0.0730538 | − | 0.997328i | \(-0.523274\pi\) | ||||
−0.0730538 | + | 0.997328i | \(0.523274\pi\) | |||||||
\(314\) | −884.347 | −0.158938 | ||||||||
\(315\) | −281.080 | −0.0502763 | ||||||||
\(316\) | 445.682 | 0.0793403 | ||||||||
\(317\) | 10744.5 | 1.90370 | 0.951849 | − | 0.306567i | \(-0.0991804\pi\) | ||||
0.951849 | + | 0.306567i | \(0.0991804\pi\) | |||||||
\(318\) | 1291.52 | 0.227751 | ||||||||
\(319\) | 97.9792 | 0.0171968 | ||||||||
\(320\) | −2839.89 | −0.496109 | ||||||||
\(321\) | −6320.46 | −1.09898 | ||||||||
\(322\) | 2971.09 | 0.514200 | ||||||||
\(323\) | −10781.4 | −1.85725 | ||||||||
\(324\) | −116.514 | −0.0199784 | ||||||||
\(325\) | −1228.08 | −0.209605 | ||||||||
\(326\) | −4922.00 | −0.836210 | ||||||||
\(327\) | 1481.37 | 0.250521 | ||||||||
\(328\) | −7216.35 | −1.21481 | ||||||||
\(329\) | 3480.98 | 0.583322 | ||||||||
\(330\) | −422.656 | −0.0705044 | ||||||||
\(331\) | 3399.12 | 0.564449 | 0.282224 | − | 0.959348i | \(-0.408928\pi\) | ||||
0.282224 | + | 0.959348i | \(0.408928\pi\) | |||||||
\(332\) | 1468.97 | 0.242832 | ||||||||
\(333\) | −3752.05 | −0.617450 | ||||||||
\(334\) | −441.349 | −0.0723039 | ||||||||
\(335\) | 1695.08 | 0.276453 | ||||||||
\(336\) | −944.864 | −0.153412 | ||||||||
\(337\) | −11840.0 | −1.91384 | −0.956919 | − | 0.290356i | \(-0.906226\pi\) | ||||
−0.956919 | + | 0.290356i | \(0.906226\pi\) | |||||||
\(338\) | −553.499 | −0.0890721 | ||||||||
\(339\) | 510.000 | 0.0817091 | ||||||||
\(340\) | 594.858 | 0.0948844 | ||||||||
\(341\) | −57.8750 | −0.00919093 | ||||||||
\(342\) | 3005.18 | 0.475151 | ||||||||
\(343\) | −4041.20 | −0.636165 | ||||||||
\(344\) | −12418.1 | −1.94634 | ||||||||
\(345\) | 2785.40 | 0.434669 | ||||||||
\(346\) | 2626.34 | 0.408072 | ||||||||
\(347\) | −2076.67 | −0.321272 | −0.160636 | − | 0.987014i | \(-0.551355\pi\) | ||||
−0.160636 | + | 0.987014i | \(0.551355\pi\) | |||||||
\(348\) | 38.4376 | 0.00592090 | ||||||||
\(349\) | 5837.37 | 0.895322 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(350\) | −400.000 | −0.0610883 | ||||||||
\(351\) | −1326.32 | −0.201692 | ||||||||
\(352\) | 706.802 | 0.107025 | ||||||||
\(353\) | −2423.64 | −0.365431 | −0.182715 | − | 0.983166i | \(-0.558489\pi\) | ||||
−0.182715 | + | 0.983166i | \(0.558489\pi\) | |||||||
\(354\) | −4755.06 | −0.713922 | ||||||||
\(355\) | −5603.54 | −0.837761 | ||||||||
\(356\) | 204.085 | 0.0303834 | ||||||||
\(357\) | 1549.84 | 0.229765 | ||||||||
\(358\) | −4247.79 | −0.627103 | ||||||||
\(359\) | −3882.22 | −0.570740 | −0.285370 | − | 0.958417i | \(-0.592116\pi\) | ||||
−0.285370 | + | 0.958417i | \(0.592116\pi\) | |||||||
\(360\) | −1087.97 | −0.159281 | ||||||||
\(361\) | 10133.2 | 1.47736 | ||||||||
\(362\) | 5178.96 | 0.751935 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 441.363 | 0.0635542 | ||||||||
\(365\) | 617.150 | 0.0885016 | ||||||||
\(366\) | −6043.26 | −0.863077 | ||||||||
\(367\) | 5666.65 | 0.805986 | 0.402993 | − | 0.915203i | \(-0.367970\pi\) | ||||
0.402993 | + | 0.915203i | \(0.367970\pi\) | |||||||
\(368\) | 9363.26 | 1.32634 | ||||||||
\(369\) | −2686.31 | −0.378981 | ||||||||
\(370\) | −5339.48 | −0.750233 | ||||||||
\(371\) | −1049.77 | −0.146903 | ||||||||
\(372\) | −22.7046 | −0.00316446 | ||||||||
\(373\) | 174.771 | 0.0242608 | 0.0121304 | − | 0.999926i | \(-0.496139\pi\) | ||||
0.0121304 | + | 0.999926i | \(0.496139\pi\) | |||||||
\(374\) | 2330.48 | 0.322209 | ||||||||
\(375\) | −375.000 | −0.0516398 | ||||||||
\(376\) | 13473.8 | 1.84802 | ||||||||
\(377\) | 437.550 | 0.0597744 | ||||||||
\(378\) | −432.000 | −0.0587822 | ||||||||
\(379\) | 252.686 | 0.0342470 | 0.0171235 | − | 0.999853i | \(-0.494549\pi\) | ||||
0.0171235 | + | 0.999853i | \(0.494549\pi\) | |||||||
\(380\) | −937.538 | −0.126565 | ||||||||
\(381\) | −2844.55 | −0.382495 | ||||||||
\(382\) | −3689.21 | −0.494126 | ||||||||
\(383\) | −11014.5 | −1.46950 | −0.734748 | − | 0.678340i | \(-0.762700\pi\) | ||||
−0.734748 | + | 0.678340i | \(0.762700\pi\) | |||||||
\(384\) | −2822.61 | −0.375105 | ||||||||
\(385\) | 343.542 | 0.0454766 | ||||||||
\(386\) | 7167.35 | 0.945099 | ||||||||
\(387\) | −4622.69 | −0.607196 | ||||||||
\(388\) | −1148.38 | −0.150258 | ||||||||
\(389\) | 8099.40 | 1.05567 | 0.527835 | − | 0.849347i | \(-0.323004\pi\) | ||||
0.527835 | + | 0.849347i | \(0.323004\pi\) | |||||||
\(390\) | −1887.47 | −0.245066 | ||||||||
\(391\) | −15358.4 | −1.98646 | ||||||||
\(392\) | −7349.47 | −0.946949 | ||||||||
\(393\) | −4454.51 | −0.571757 | ||||||||
\(394\) | −1175.61 | −0.150320 | ||||||||
\(395\) | 1549.18 | 0.197335 | ||||||||
\(396\) | 142.406 | 0.0180712 | ||||||||
\(397\) | −424.353 | −0.0536465 | −0.0268232 | − | 0.999640i | \(-0.508539\pi\) | ||||
−0.0268232 | + | 0.999640i | \(0.508539\pi\) | |||||||
\(398\) | 6073.54 | 0.764922 | ||||||||
\(399\) | −2442.66 | −0.306481 | ||||||||
\(400\) | −1260.58 | −0.157573 | ||||||||
\(401\) | −5904.18 | −0.735263 | −0.367632 | − | 0.929972i | \(-0.619831\pi\) | ||||
−0.367632 | + | 0.929972i | \(0.619831\pi\) | |||||||
\(402\) | 2605.22 | 0.323225 | ||||||||
\(403\) | −258.455 | −0.0319468 | ||||||||
\(404\) | −347.241 | −0.0427620 | ||||||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | 142.515 | 0.0174210 | ||||||||
\(407\) | 4585.83 | 0.558504 | ||||||||
\(408\) | 5998.94 | 0.727921 | ||||||||
\(409\) | 1370.47 | 0.165686 | 0.0828430 | − | 0.996563i | \(-0.473600\pi\) | ||||
0.0828430 | + | 0.996563i | \(0.473600\pi\) | |||||||
\(410\) | −3822.85 | −0.460481 | ||||||||
\(411\) | 2054.78 | 0.246606 | ||||||||
\(412\) | −1680.65 | −0.200970 | ||||||||
\(413\) | 3864.98 | 0.460493 | ||||||||
\(414\) | 4280.97 | 0.508208 | ||||||||
\(415\) | 5106.11 | 0.603973 | ||||||||
\(416\) | 3156.39 | 0.372007 | ||||||||
\(417\) | 2491.45 | 0.292582 | ||||||||
\(418\) | −3673.00 | −0.429790 | ||||||||
\(419\) | 1268.73 | 0.147927 | 0.0739635 | − | 0.997261i | \(-0.476435\pi\) | ||||
0.0739635 | + | 0.997261i | \(0.476435\pi\) | |||||||
\(420\) | 134.773 | 0.0156577 | ||||||||
\(421\) | −12241.9 | −1.41719 | −0.708594 | − | 0.705617i | \(-0.750670\pi\) | ||||
−0.708594 | + | 0.705617i | \(0.750670\pi\) | |||||||
\(422\) | −11065.6 | −1.27646 | ||||||||
\(423\) | 5015.66 | 0.576524 | ||||||||
\(424\) | −4063.31 | −0.465405 | ||||||||
\(425\) | 2067.71 | 0.235997 | ||||||||
\(426\) | −8612.26 | −0.979496 | ||||||||
\(427\) | 4912.05 | 0.556700 | ||||||||
\(428\) | 3030.55 | 0.342260 | ||||||||
\(429\) | 1621.06 | 0.182437 | ||||||||
\(430\) | −6578.48 | −0.737774 | ||||||||
\(431\) | 8050.11 | 0.899675 | 0.449838 | − | 0.893110i | \(-0.351482\pi\) | ||||
0.449838 | + | 0.893110i | \(0.351482\pi\) | |||||||
\(432\) | −1361.43 | −0.151624 | ||||||||
\(433\) | −16565.7 | −1.83856 | −0.919282 | − | 0.393600i | \(-0.871230\pi\) | ||||
−0.919282 | + | 0.393600i | \(0.871230\pi\) | |||||||
\(434\) | −84.1819 | −0.00931073 | ||||||||
\(435\) | 133.608 | 0.0147265 | ||||||||
\(436\) | −710.293 | −0.0780203 | ||||||||
\(437\) | 24205.9 | 2.64971 | ||||||||
\(438\) | 948.517 | 0.103475 | ||||||||
\(439\) | 4705.80 | 0.511607 | 0.255804 | − | 0.966729i | \(-0.417660\pi\) | ||||
0.255804 | + | 0.966729i | \(0.417660\pi\) | |||||||
\(440\) | 1329.74 | 0.144075 | ||||||||
\(441\) | −2735.86 | −0.295418 | ||||||||
\(442\) | 10407.3 | 1.11997 | ||||||||
\(443\) | 15094.0 | 1.61882 | 0.809408 | − | 0.587246i | \(-0.199788\pi\) | ||||
0.809408 | + | 0.587246i | \(0.199788\pi\) | |||||||
\(444\) | 1799.04 | 0.192294 | ||||||||
\(445\) | 709.394 | 0.0755696 | ||||||||
\(446\) | 9830.56 | 1.04370 | ||||||||
\(447\) | −3640.93 | −0.385257 | ||||||||
\(448\) | 3547.71 | 0.374138 | ||||||||
\(449\) | 973.478 | 0.102319 | 0.0511595 | − | 0.998690i | \(-0.483708\pi\) | ||||
0.0511595 | + | 0.998690i | \(0.483708\pi\) | |||||||
\(450\) | −576.349 | −0.0603764 | ||||||||
\(451\) | 3283.27 | 0.342801 | ||||||||
\(452\) | −244.536 | −0.0254469 | ||||||||
\(453\) | 92.5398 | 0.00959801 | ||||||||
\(454\) | 12817.3 | 1.32499 | ||||||||
\(455\) | 1534.17 | 0.158072 | ||||||||
\(456\) | −9454.75 | −0.970963 | ||||||||
\(457\) | 62.6577 | 0.00641358 | 0.00320679 | − | 0.999995i | \(-0.498979\pi\) | ||||
0.00320679 | + | 0.999995i | \(0.498979\pi\) | |||||||
\(458\) | 710.510 | 0.0724890 | ||||||||
\(459\) | 2233.12 | 0.227088 | ||||||||
\(460\) | −1335.55 | −0.135370 | ||||||||
\(461\) | −11866.2 | −1.19884 | −0.599419 | − | 0.800436i | \(-0.704602\pi\) | ||||
−0.599419 | + | 0.800436i | \(0.704602\pi\) | |||||||
\(462\) | 528.000 | 0.0531705 | ||||||||
\(463\) | −13144.8 | −1.31942 | −0.659711 | − | 0.751519i | \(-0.729321\pi\) | ||||
−0.659711 | + | 0.751519i | \(0.729321\pi\) | |||||||
\(464\) | 449.131 | 0.0449361 | ||||||||
\(465\) | −78.9205 | −0.00787065 | ||||||||
\(466\) | −5814.48 | −0.578006 | ||||||||
\(467\) | −10176.8 | −1.00840 | −0.504201 | − | 0.863586i | \(-0.668213\pi\) | ||||
−0.504201 | + | 0.863586i | \(0.668213\pi\) | |||||||
\(468\) | 635.949 | 0.0628136 | ||||||||
\(469\) | −2117.56 | −0.208486 | ||||||||
\(470\) | 7137.71 | 0.700506 | ||||||||
\(471\) | 1035.72 | 0.101323 | ||||||||
\(472\) | 14960.1 | 1.45889 | ||||||||
\(473\) | 5649.96 | 0.549229 | ||||||||
\(474\) | 2380.98 | 0.230721 | ||||||||
\(475\) | −3258.85 | −0.314793 | ||||||||
\(476\) | −743.121 | −0.0715565 | ||||||||
\(477\) | −1512.58 | −0.145191 | ||||||||
\(478\) | 4142.30 | 0.396369 | ||||||||
\(479\) | 3431.25 | 0.327302 | 0.163651 | − | 0.986518i | \(-0.447673\pi\) | ||||
0.163651 | + | 0.986518i | \(0.447673\pi\) | |||||||
\(480\) | 963.821 | 0.0916504 | ||||||||
\(481\) | 20479.1 | 1.94130 | ||||||||
\(482\) | −14464.1 | −1.36685 | ||||||||
\(483\) | −3479.64 | −0.327803 | ||||||||
\(484\) | −174.052 | −0.0163460 | ||||||||
\(485\) | −3991.72 | −0.373721 | ||||||||
\(486\) | −622.457 | −0.0580972 | ||||||||
\(487\) | −2833.20 | −0.263624 | −0.131812 | − | 0.991275i | \(-0.542079\pi\) | ||||
−0.131812 | + | 0.991275i | \(0.542079\pi\) | |||||||
\(488\) | 19013.0 | 1.76368 | ||||||||
\(489\) | 5764.48 | 0.533085 | ||||||||
\(490\) | −3893.37 | −0.358948 | ||||||||
\(491\) | −2667.29 | −0.245159 | −0.122580 | − | 0.992459i | \(-0.539117\pi\) | ||||
−0.122580 | + | 0.992459i | \(0.539117\pi\) | |||||||
\(492\) | 1288.04 | 0.118027 | ||||||||
\(493\) | −736.700 | −0.0673008 | ||||||||
\(494\) | −16402.7 | −1.49391 | ||||||||
\(495\) | 495.000 | 0.0449467 | ||||||||
\(496\) | −265.295 | −0.0240164 | ||||||||
\(497\) | 7000.18 | 0.631793 | ||||||||
\(498\) | 7847.74 | 0.706156 | ||||||||
\(499\) | −11137.0 | −0.999120 | −0.499560 | − | 0.866279i | \(-0.666505\pi\) | ||||
−0.499560 | + | 0.866279i | \(0.666505\pi\) | |||||||
\(500\) | 179.806 | 0.0160823 | ||||||||
\(501\) | 516.892 | 0.0460939 | ||||||||
\(502\) | 15926.7 | 1.41603 | ||||||||
\(503\) | 8780.30 | 0.778319 | 0.389159 | − | 0.921170i | \(-0.372766\pi\) | ||||
0.389159 | + | 0.921170i | \(0.372766\pi\) | |||||||
\(504\) | 1359.14 | 0.120121 | ||||||||
\(505\) | −1207.00 | −0.106358 | ||||||||
\(506\) | −5232.29 | −0.459691 | ||||||||
\(507\) | 648.239 | 0.0567836 | ||||||||
\(508\) | 1363.91 | 0.119121 | ||||||||
\(509\) | 13597.4 | 1.18408 | 0.592039 | − | 0.805910i | \(-0.298323\pi\) | ||||
0.592039 | + | 0.805910i | \(0.298323\pi\) | |||||||
\(510\) | 3177.93 | 0.275923 | ||||||||
\(511\) | −770.969 | −0.0667430 | ||||||||
\(512\) | 12992.6 | 1.12148 | ||||||||
\(513\) | −3519.56 | −0.302909 | ||||||||
\(514\) | −19756.6 | −1.69538 | ||||||||
\(515\) | −5841.89 | −0.499854 | ||||||||
\(516\) | 2216.50 | 0.189101 | ||||||||
\(517\) | −6130.25 | −0.521486 | ||||||||
\(518\) | 6670.30 | 0.565784 | ||||||||
\(519\) | −3075.88 | −0.260146 | ||||||||
\(520\) | 5938.27 | 0.500789 | ||||||||
\(521\) | 14001.3 | 1.17736 | 0.588682 | − | 0.808364i | \(-0.299647\pi\) | ||||
0.588682 | + | 0.808364i | \(0.299647\pi\) | |||||||
\(522\) | 205.346 | 0.0172180 | ||||||||
\(523\) | −14749.8 | −1.23320 | −0.616602 | − | 0.787275i | \(-0.711491\pi\) | ||||
−0.616602 | + | 0.787275i | \(0.711491\pi\) | |||||||
\(524\) | 2135.86 | 0.178064 | ||||||||
\(525\) | 468.466 | 0.0389439 | ||||||||
\(526\) | −528.568 | −0.0438149 | ||||||||
\(527\) | 435.159 | 0.0359693 | ||||||||
\(528\) | 1663.97 | 0.137150 | ||||||||
\(529\) | 22315.0 | 1.83406 | ||||||||
\(530\) | −2152.53 | −0.176415 | ||||||||
\(531\) | 5568.95 | 0.455126 | ||||||||
\(532\) | 1171.21 | 0.0954483 | ||||||||
\(533\) | 14662.2 | 1.19154 | ||||||||
\(534\) | 1090.29 | 0.0883548 | ||||||||
\(535\) | 10534.1 | 0.851269 | ||||||||
\(536\) | −8196.40 | −0.660505 | ||||||||
\(537\) | 4974.86 | 0.399779 | ||||||||
\(538\) | −4386.59 | −0.351523 | ||||||||
\(539\) | 3343.83 | 0.267215 | ||||||||
\(540\) | 194.190 | 0.0154752 | ||||||||
\(541\) | 1484.06 | 0.117939 | 0.0589694 | − | 0.998260i | \(-0.481219\pi\) | ||||
0.0589694 | + | 0.998260i | \(0.481219\pi\) | |||||||
\(542\) | 1222.07 | 0.0968493 | ||||||||
\(543\) | −6065.42 | −0.479359 | ||||||||
\(544\) | −5314.40 | −0.418847 | ||||||||
\(545\) | −2468.96 | −0.194052 | ||||||||
\(546\) | 2357.91 | 0.184815 | ||||||||
\(547\) | −16562.2 | −1.29460 | −0.647302 | − | 0.762234i | \(-0.724103\pi\) | ||||
−0.647302 | + | 0.762234i | \(0.724103\pi\) | |||||||
\(548\) | −985.233 | −0.0768012 | ||||||||
\(549\) | 7077.65 | 0.550212 | ||||||||
\(550\) | 704.427 | 0.0546125 | ||||||||
\(551\) | 1161.09 | 0.0897716 | ||||||||
\(552\) | −13468.6 | −1.03851 | ||||||||
\(553\) | −1935.30 | −0.148819 | ||||||||
\(554\) | −10972.3 | −0.841463 | ||||||||
\(555\) | 6253.41 | 0.478275 | ||||||||
\(556\) | −1194.61 | −0.0911197 | ||||||||
\(557\) | −8821.52 | −0.671059 | −0.335529 | − | 0.942030i | \(-0.608915\pi\) | ||||
−0.335529 | + | 0.942030i | \(0.608915\pi\) | |||||||
\(558\) | −121.295 | −0.00920223 | ||||||||
\(559\) | 25231.2 | 1.90906 | ||||||||
\(560\) | 1574.77 | 0.118833 | ||||||||
\(561\) | −2729.37 | −0.205409 | ||||||||
\(562\) | −8908.55 | −0.668656 | ||||||||
\(563\) | −5985.53 | −0.448064 | −0.224032 | − | 0.974582i | \(-0.571922\pi\) | ||||
−0.224032 | + | 0.974582i | \(0.571922\pi\) | |||||||
\(564\) | −2404.92 | −0.179549 | ||||||||
\(565\) | −850.000 | −0.0632916 | ||||||||
\(566\) | 16825.0 | 1.24948 | ||||||||
\(567\) | 505.943 | 0.0374737 | ||||||||
\(568\) | 27095.5 | 2.00158 | ||||||||
\(569\) | −3453.08 | −0.254413 | −0.127206 | − | 0.991876i | \(-0.540601\pi\) | ||||
−0.127206 | + | 0.991876i | \(0.540601\pi\) | |||||||
\(570\) | −5008.64 | −0.368050 | ||||||||
\(571\) | −21484.5 | −1.57460 | −0.787302 | − | 0.616568i | \(-0.788523\pi\) | ||||
−0.787302 | + | 0.616568i | \(0.788523\pi\) | |||||||
\(572\) | −777.271 | −0.0568170 | ||||||||
\(573\) | 4320.67 | 0.315006 | ||||||||
\(574\) | 4775.67 | 0.347269 | ||||||||
\(575\) | −4642.33 | −0.336693 | ||||||||
\(576\) | 5111.80 | 0.369777 | ||||||||
\(577\) | −13294.4 | −0.959189 | −0.479594 | − | 0.877490i | \(-0.659216\pi\) | ||||
−0.479594 | + | 0.877490i | \(0.659216\pi\) | |||||||
\(578\) | −4937.82 | −0.355340 | ||||||||
\(579\) | −8394.14 | −0.602502 | ||||||||
\(580\) | −64.0627 | −0.00458631 | ||||||||
\(581\) | −6378.77 | −0.455483 | ||||||||
\(582\) | −6135.01 | −0.436949 | ||||||||
\(583\) | 1848.71 | 0.131330 | ||||||||
\(584\) | −2984.18 | −0.211449 | ||||||||
\(585\) | 2210.54 | 0.156230 | ||||||||
\(586\) | −21394.8 | −1.50821 | ||||||||
\(587\) | 6695.73 | 0.470805 | 0.235402 | − | 0.971898i | \(-0.424359\pi\) | ||||
0.235402 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(588\) | 1311.80 | 0.0920028 | ||||||||
\(589\) | −685.841 | −0.0479789 | ||||||||
\(590\) | 7925.09 | 0.553002 | ||||||||
\(591\) | 1376.83 | 0.0958295 | ||||||||
\(592\) | 21021.2 | 1.45940 | ||||||||
\(593\) | −10239.6 | −0.709088 | −0.354544 | − | 0.935039i | \(-0.615364\pi\) | ||||
−0.354544 | + | 0.935039i | \(0.615364\pi\) | |||||||
\(594\) | 760.781 | 0.0525509 | ||||||||
\(595\) | −2583.07 | −0.177976 | ||||||||
\(596\) | 1745.76 | 0.119982 | ||||||||
\(597\) | −7113.11 | −0.487639 | ||||||||
\(598\) | −23366.0 | −1.59784 | ||||||||
\(599\) | −23890.8 | −1.62963 | −0.814817 | − | 0.579719i | \(-0.803162\pi\) | ||||
−0.814817 | + | 0.579719i | \(0.803162\pi\) | |||||||
\(600\) | 1813.28 | 0.123378 | ||||||||
\(601\) | −11343.8 | −0.769920 | −0.384960 | − | 0.922933i | \(-0.625785\pi\) | ||||
−0.384960 | + | 0.922933i | \(0.625785\pi\) | |||||||
\(602\) | 8218.12 | 0.556388 | ||||||||
\(603\) | −3051.14 | −0.206056 | ||||||||
\(604\) | −44.3712 | −0.00298914 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | −1855.07 | −0.124352 | ||||||||
\(607\) | −26032.5 | −1.74074 | −0.870369 | − | 0.492399i | \(-0.836120\pi\) | ||||
−0.870369 | + | 0.492399i | \(0.836120\pi\) | |||||||
\(608\) | 8375.87 | 0.558695 | ||||||||
\(609\) | −166.909 | −0.0111059 | ||||||||
\(610\) | 10072.1 | 0.668536 | ||||||||
\(611\) | −27376.1 | −1.81263 | ||||||||
\(612\) | −1070.74 | −0.0707226 | ||||||||
\(613\) | −4568.13 | −0.300987 | −0.150493 | − | 0.988611i | \(-0.548086\pi\) | ||||
−0.150493 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(614\) | −13791.1 | −0.906457 | ||||||||
\(615\) | 4477.19 | 0.293557 | ||||||||
\(616\) | −1661.17 | −0.108653 | ||||||||
\(617\) | −12755.9 | −0.832308 | −0.416154 | − | 0.909294i | \(-0.636622\pi\) | ||||
−0.416154 | + | 0.909294i | \(0.636622\pi\) | |||||||
\(618\) | −8978.59 | −0.584421 | ||||||||
\(619\) | −1138.94 | −0.0739545 | −0.0369772 | − | 0.999316i | \(-0.511773\pi\) | ||||
−0.0369772 | + | 0.999316i | \(0.511773\pi\) | |||||||
\(620\) | 37.8410 | 0.00245118 | ||||||||
\(621\) | −5013.72 | −0.323983 | ||||||||
\(622\) | 4586.24 | 0.295645 | ||||||||
\(623\) | −886.205 | −0.0569904 | ||||||||
\(624\) | 7430.85 | 0.476718 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 2072.49 | 0.132322 | ||||||||
\(627\) | 4301.69 | 0.273992 | ||||||||
\(628\) | −496.607 | −0.0315554 | ||||||||
\(629\) | −34480.6 | −2.18574 | ||||||||
\(630\) | 720.000 | 0.0455325 | ||||||||
\(631\) | 7997.36 | 0.504548 | 0.252274 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252274 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(632\) | −7490.91 | −0.471475 | ||||||||
\(633\) | 12959.6 | 0.813742 | ||||||||
\(634\) | −27522.7 | −1.72408 | ||||||||
\(635\) | 4740.91 | 0.296279 | ||||||||
\(636\) | 725.255 | 0.0452173 | ||||||||
\(637\) | 14932.7 | 0.928814 | ||||||||
\(638\) | −250.979 | −0.0155742 | ||||||||
\(639\) | 10086.4 | 0.624430 | ||||||||
\(640\) | 4704.34 | 0.290555 | ||||||||
\(641\) | −573.115 | −0.0353146 | −0.0176573 | − | 0.999844i | \(-0.505621\pi\) | ||||
−0.0176573 | + | 0.999844i | \(0.505621\pi\) | |||||||
\(642\) | 16190.2 | 0.995290 | ||||||||
\(643\) | −16027.8 | −0.983009 | −0.491504 | − | 0.870875i | \(-0.663553\pi\) | ||||
−0.491504 | + | 0.870875i | \(0.663553\pi\) | |||||||
\(644\) | 1668.42 | 0.102089 | ||||||||
\(645\) | 7704.49 | 0.470332 | ||||||||
\(646\) | 27617.1 | 1.68201 | ||||||||
\(647\) | −2622.74 | −0.159367 | −0.0796837 | − | 0.996820i | \(-0.525391\pi\) | ||||
−0.0796837 | + | 0.996820i | \(0.525391\pi\) | |||||||
\(648\) | 1958.34 | 0.118721 | ||||||||
\(649\) | −6806.50 | −0.411677 | ||||||||
\(650\) | 3145.79 | 0.189827 | ||||||||
\(651\) | 98.5908 | 0.00593560 | ||||||||
\(652\) | −2763.97 | −0.166020 | ||||||||
\(653\) | 3102.00 | 0.185897 | 0.0929484 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929484 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(654\) | −3794.62 | −0.226883 | ||||||||
\(655\) | 7424.19 | 0.442881 | ||||||||
\(656\) | 15050.3 | 0.895755 | ||||||||
\(657\) | −1110.87 | −0.0659652 | ||||||||
\(658\) | −8916.73 | −0.528283 | ||||||||
\(659\) | −20840.2 | −1.23190 | −0.615948 | − | 0.787787i | \(-0.711227\pi\) | ||||
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(660\) | −237.344 | −0.0139979 | ||||||||
\(661\) | 18242.9 | 1.07348 | 0.536738 | − | 0.843749i | \(-0.319657\pi\) | ||||
0.536738 | + | 0.843749i | \(0.319657\pi\) | |||||||
\(662\) | −8707.03 | −0.511191 | ||||||||
\(663\) | −12188.7 | −0.713980 | ||||||||
\(664\) | −24690.2 | −1.44302 | ||||||||
\(665\) | 4071.10 | 0.237399 | ||||||||
\(666\) | 9611.06 | 0.559191 | ||||||||
\(667\) | 1654.01 | 0.0960171 | ||||||||
\(668\) | −247.841 | −0.0143551 | ||||||||
\(669\) | −11513.2 | −0.665361 | ||||||||
\(670\) | −4342.03 | −0.250369 | ||||||||
\(671\) | −8650.46 | −0.497686 | ||||||||
\(672\) | −1204.05 | −0.0691177 | ||||||||
\(673\) | −12746.6 | −0.730084 | −0.365042 | − | 0.930991i | \(-0.618945\pi\) | ||||
−0.365042 | + | 0.930991i | \(0.618945\pi\) | |||||||
\(674\) | 30328.7 | 1.73326 | ||||||||
\(675\) | 675.000 | 0.0384900 | ||||||||
\(676\) | −310.819 | −0.0176843 | ||||||||
\(677\) | −7683.11 | −0.436168 | −0.218084 | − | 0.975930i | \(-0.569981\pi\) | ||||
−0.218084 | + | 0.975930i | \(0.569981\pi\) | |||||||
\(678\) | −1306.39 | −0.0739995 | ||||||||
\(679\) | 4986.63 | 0.281840 | ||||||||
\(680\) | −9998.23 | −0.563845 | ||||||||
\(681\) | −15011.1 | −0.844681 | ||||||||
\(682\) | 148.250 | 0.00832373 | ||||||||
\(683\) | −21397.1 | −1.19874 | −0.599368 | − | 0.800473i | \(-0.704582\pi\) | ||||
−0.599368 | + | 0.800473i | \(0.704582\pi\) | |||||||
\(684\) | 1687.57 | 0.0943359 | ||||||||
\(685\) | −3424.64 | −0.191020 | ||||||||
\(686\) | 10351.8 | 0.576140 | ||||||||
\(687\) | −832.124 | −0.0462118 | ||||||||
\(688\) | 25899.0 | 1.43516 | ||||||||
\(689\) | 8255.84 | 0.456491 | ||||||||
\(690\) | −7134.94 | −0.393656 | ||||||||
\(691\) | 26137.5 | 1.43895 | 0.719477 | − | 0.694516i | \(-0.244381\pi\) | ||||
0.719477 | + | 0.694516i | \(0.244381\pi\) | |||||||
\(692\) | 1474.83 | 0.0810181 | ||||||||
\(693\) | −618.375 | −0.0338963 | ||||||||
\(694\) | 5319.50 | 0.290959 | ||||||||
\(695\) | −4152.41 | −0.226633 | ||||||||
\(696\) | −646.051 | −0.0351846 | ||||||||
\(697\) | −24686.7 | −1.34157 | ||||||||
\(698\) | −14952.7 | −0.810845 | ||||||||
\(699\) | 6809.72 | 0.368479 | ||||||||
\(700\) | −224.621 | −0.0121284 | ||||||||
\(701\) | 13382.4 | 0.721036 | 0.360518 | − | 0.932752i | \(-0.382600\pi\) | ||||
0.360518 | + | 0.932752i | \(0.382600\pi\) | |||||||
\(702\) | 3397.45 | 0.182662 | ||||||||
\(703\) | 54343.9 | 2.91553 | ||||||||
\(704\) | −6247.76 | −0.334476 | ||||||||
\(705\) | −8359.43 | −0.446574 | ||||||||
\(706\) | 6208.27 | 0.330951 | ||||||||
\(707\) | 1507.83 | 0.0802092 | ||||||||
\(708\) | −2670.22 | −0.141741 | ||||||||
\(709\) | 18164.6 | 0.962179 | 0.481090 | − | 0.876671i | \(-0.340241\pi\) | ||||
0.481090 | + | 0.876671i | \(0.340241\pi\) | |||||||
\(710\) | 14353.8 | 0.758715 | ||||||||
\(711\) | −2788.52 | −0.147085 | ||||||||
\(712\) | −3430.21 | −0.180552 | ||||||||
\(713\) | −977.000 | −0.0513169 | ||||||||
\(714\) | −3970.00 | −0.208086 | ||||||||
\(715\) | −2701.77 | −0.141315 | ||||||||
\(716\) | −2385.36 | −0.124504 | ||||||||
\(717\) | −4851.32 | −0.252686 | ||||||||
\(718\) | 9944.50 | 0.516888 | ||||||||
\(719\) | 9665.62 | 0.501344 | 0.250672 | − | 0.968072i | \(-0.419348\pi\) | ||||
0.250672 | + | 0.968072i | \(0.419348\pi\) | |||||||
\(720\) | 2269.05 | 0.117448 | ||||||||
\(721\) | 7297.94 | 0.376962 | ||||||||
\(722\) | −25956.7 | −1.33796 | ||||||||
\(723\) | 16939.9 | 0.871371 | ||||||||
\(724\) | 2908.26 | 0.149288 | ||||||||
\(725\) | −222.680 | −0.0114071 | ||||||||
\(726\) | −929.844 | −0.0475341 | ||||||||
\(727\) | −29779.6 | −1.51921 | −0.759605 | − | 0.650385i | \(-0.774608\pi\) | ||||
−0.759605 | + | 0.650385i | \(0.774608\pi\) | |||||||
\(728\) | −7418.33 | −0.377667 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −1580.86 | −0.0801511 | ||||||||
\(731\) | −42481.7 | −2.14944 | ||||||||
\(732\) | −3393.61 | −0.171354 | ||||||||
\(733\) | 35029.5 | 1.76513 | 0.882567 | − | 0.470187i | \(-0.155814\pi\) | ||||
0.882567 | + | 0.470187i | \(0.155814\pi\) | |||||||
\(734\) | −14515.4 | −0.729937 | ||||||||
\(735\) | 4559.77 | 0.228830 | ||||||||
\(736\) | 11931.7 | 0.597564 | ||||||||
\(737\) | 3729.17 | 0.186385 | ||||||||
\(738\) | 6881.13 | 0.343222 | ||||||||
\(739\) | 23297.3 | 1.15968 | 0.579842 | − | 0.814729i | \(-0.303114\pi\) | ||||
0.579842 | + | 0.814729i | \(0.303114\pi\) | |||||||
\(740\) | −2998.40 | −0.148950 | ||||||||
\(741\) | 19210.2 | 0.952368 | ||||||||
\(742\) | 2689.03 | 0.133042 | ||||||||
\(743\) | 21570.4 | 1.06506 | 0.532530 | − | 0.846411i | \(-0.321241\pi\) | ||||
0.532530 | + | 0.846411i | \(0.321241\pi\) | |||||||
\(744\) | 381.613 | 0.0188046 | ||||||||
\(745\) | 6068.21 | 0.298419 | ||||||||
\(746\) | −447.684 | −0.0219717 | ||||||||
\(747\) | −9190.99 | −0.450175 | ||||||||
\(748\) | 1308.69 | 0.0639710 | ||||||||
\(749\) | −13159.6 | −0.641980 | ||||||||
\(750\) | 960.582 | 0.0467673 | ||||||||
\(751\) | 28554.8 | 1.38746 | 0.693729 | − | 0.720236i | \(-0.255966\pi\) | ||||
0.693729 | + | 0.720236i | \(0.255966\pi\) | |||||||
\(752\) | −28100.7 | −1.36267 | ||||||||
\(753\) | −18652.8 | −0.902719 | ||||||||
\(754\) | −1120.81 | −0.0541344 | ||||||||
\(755\) | −154.233 | −0.00743458 | ||||||||
\(756\) | −242.591 | −0.0116706 | ||||||||
\(757\) | 7812.81 | 0.375114 | 0.187557 | − | 0.982254i | \(-0.439943\pi\) | ||||
0.187557 | + | 0.982254i | \(0.439943\pi\) | |||||||
\(758\) | −647.268 | −0.0310156 | ||||||||
\(759\) | 6127.87 | 0.293054 | ||||||||
\(760\) | 15757.9 | 0.752105 | ||||||||
\(761\) | 2875.13 | 0.136956 | 0.0684778 | − | 0.997653i | \(-0.478186\pi\) | ||||
0.0684778 | + | 0.997653i | \(0.478186\pi\) | |||||||
\(762\) | 7286.45 | 0.346405 | ||||||||
\(763\) | 3084.33 | 0.146344 | ||||||||
\(764\) | −2071.69 | −0.0981033 | ||||||||
\(765\) | −3721.87 | −0.175902 | ||||||||
\(766\) | 28214.3 | 1.33084 | ||||||||
\(767\) | −30396.0 | −1.43095 | ||||||||
\(768\) | −6401.22 | −0.300761 | ||||||||
\(769\) | −27657.7 | −1.29696 | −0.648479 | − | 0.761233i | \(-0.724594\pi\) | ||||
−0.648479 | + | 0.761233i | \(0.724594\pi\) | |||||||
\(770\) | −880.000 | −0.0411857 | ||||||||
\(771\) | 23138.2 | 1.08081 | ||||||||
\(772\) | 4024.84 | 0.187639 | ||||||||
\(773\) | −3929.35 | −0.182832 | −0.0914160 | − | 0.995813i | \(-0.529139\pi\) | ||||
−0.0914160 | + | 0.995813i | \(0.529139\pi\) | |||||||
\(774\) | 11841.3 | 0.549904 | ||||||||
\(775\) | 131.534 | 0.00609658 | ||||||||
\(776\) | 19301.6 | 0.892898 | ||||||||
\(777\) | −7812.02 | −0.360688 | ||||||||
\(778\) | −20747.0 | −0.956064 | ||||||||
\(779\) | 38908.0 | 1.78950 | ||||||||
\(780\) | −1059.91 | −0.0486552 | ||||||||
\(781\) | −12327.8 | −0.564818 | ||||||||
\(782\) | 39341.3 | 1.79903 | ||||||||
\(783\) | −240.495 | −0.0109765 | ||||||||
\(784\) | 15327.9 | 0.698247 | ||||||||
\(785\) | −1726.19 | −0.0784847 | ||||||||
\(786\) | 11410.5 | 0.517809 | ||||||||
\(787\) | −21125.7 | −0.956860 | −0.478430 | − | 0.878126i | \(-0.658794\pi\) | ||||
−0.478430 | + | 0.878126i | \(0.658794\pi\) | |||||||
\(788\) | −660.166 | −0.0298445 | ||||||||
\(789\) | 619.040 | 0.0279321 | ||||||||
\(790\) | −3968.30 | −0.178716 | ||||||||
\(791\) | 1061.86 | 0.0477310 | ||||||||
\(792\) | −2393.53 | −0.107387 | ||||||||
\(793\) | −38630.7 | −1.72991 | ||||||||
\(794\) | 1087.00 | 0.0485847 | ||||||||
\(795\) | 2520.97 | 0.112465 | ||||||||
\(796\) | 3410.61 | 0.151867 | ||||||||
\(797\) | 11696.3 | 0.519828 | 0.259914 | − | 0.965632i | \(-0.416306\pi\) | ||||
0.259914 | + | 0.965632i | \(0.416306\pi\) | |||||||
\(798\) | 6257.00 | 0.277563 | ||||||||
\(799\) | 46093.0 | 2.04087 | ||||||||
\(800\) | −1606.37 | −0.0709921 | ||||||||
\(801\) | −1276.91 | −0.0563263 | ||||||||
\(802\) | 15123.9 | 0.665888 | ||||||||
\(803\) | 1357.73 | 0.0596678 | ||||||||
\(804\) | 1462.97 | 0.0641727 | ||||||||
\(805\) | 5799.39 | 0.253915 | ||||||||
\(806\) | 662.045 | 0.0289324 | ||||||||
\(807\) | 5137.42 | 0.224096 | ||||||||
\(808\) | 5836.34 | 0.254111 | ||||||||
\(809\) | 14310.2 | 0.621902 | 0.310951 | − | 0.950426i | \(-0.399352\pi\) | ||||
0.310951 | + | 0.950426i | \(0.399352\pi\) | |||||||
\(810\) | 1037.43 | 0.0450019 | ||||||||
\(811\) | 21697.9 | 0.939477 | 0.469739 | − | 0.882806i | \(-0.344348\pi\) | ||||
0.469739 | + | 0.882806i | \(0.344348\pi\) | |||||||
\(812\) | 80.0299 | 0.00345874 | ||||||||
\(813\) | −1431.24 | −0.0617416 | ||||||||
\(814\) | −11746.9 | −0.505807 | ||||||||
\(815\) | −9607.46 | −0.412926 | ||||||||
\(816\) | −12511.3 | −0.536743 | ||||||||
\(817\) | 66954.1 | 2.86711 | ||||||||
\(818\) | −3510.54 | −0.150053 | ||||||||
\(819\) | −2761.50 | −0.117820 | ||||||||
\(820\) | −2146.73 | −0.0914233 | ||||||||
\(821\) | 3613.00 | 0.153587 | 0.0767934 | − | 0.997047i | \(-0.475532\pi\) | ||||
0.0767934 | + | 0.997047i | \(0.475532\pi\) | |||||||
\(822\) | −5263.44 | −0.223338 | ||||||||
\(823\) | −4763.98 | −0.201776 | −0.100888 | − | 0.994898i | \(-0.532168\pi\) | ||||
−0.100888 | + | 0.994898i | \(0.532168\pi\) | |||||||
\(824\) | 28248.0 | 1.19425 | ||||||||
\(825\) | −825.000 | −0.0348155 | ||||||||
\(826\) | −9900.36 | −0.417043 | ||||||||
\(827\) | −33571.7 | −1.41161 | −0.705806 | − | 0.708405i | \(-0.749415\pi\) | ||||
−0.705806 | + | 0.708405i | \(0.749415\pi\) | |||||||
\(828\) | 2403.99 | 0.100899 | ||||||||
\(829\) | 17980.5 | 0.753303 | 0.376652 | − | 0.926355i | \(-0.377075\pi\) | ||||
0.376652 | + | 0.926355i | \(0.377075\pi\) | |||||||
\(830\) | −13079.6 | −0.546986 | ||||||||
\(831\) | 12850.4 | 0.536434 | ||||||||
\(832\) | −27900.9 | −1.16261 | ||||||||
\(833\) | −25142.1 | −1.04576 | ||||||||
\(834\) | −6381.98 | −0.264976 | ||||||||
\(835\) | −861.486 | −0.0357041 | ||||||||
\(836\) | −2062.58 | −0.0853301 | ||||||||
\(837\) | 142.057 | 0.00586643 | ||||||||
\(838\) | −3249.91 | −0.133969 | ||||||||
\(839\) | −40139.5 | −1.65169 | −0.825847 | − | 0.563895i | \(-0.809302\pi\) | ||||
−0.825847 | + | 0.563895i | \(0.809302\pi\) | |||||||
\(840\) | −2265.23 | −0.0930450 | ||||||||
\(841\) | −24309.7 | −0.996747 | ||||||||
\(842\) | 31358.4 | 1.28347 | ||||||||
\(843\) | 10433.4 | 0.426269 | ||||||||
\(844\) | −6213.91 | −0.253426 | ||||||||
\(845\) | −1080.40 | −0.0439844 | ||||||||
\(846\) | −12847.9 | −0.522127 | ||||||||
\(847\) | 755.792 | 0.0306603 | ||||||||
\(848\) | 8474.36 | 0.343173 | ||||||||
\(849\) | −19704.8 | −0.796546 | ||||||||
\(850\) | −5296.54 | −0.213729 | ||||||||
\(851\) | 77414.4 | 3.11837 | ||||||||
\(852\) | −4836.24 | −0.194468 | ||||||||
\(853\) | −15369.2 | −0.616919 | −0.308459 | − | 0.951237i | \(-0.599813\pi\) | ||||
−0.308459 | + | 0.951237i | \(0.599813\pi\) | |||||||
\(854\) | −12582.5 | −0.504173 | ||||||||
\(855\) | 5865.94 | 0.234633 | ||||||||
\(856\) | −50936.8 | −2.03386 | ||||||||
\(857\) | 10324.9 | 0.411541 | 0.205770 | − | 0.978600i | \(-0.434030\pi\) | ||||
0.205770 | + | 0.978600i | \(0.434030\pi\) | |||||||
\(858\) | −4152.44 | −0.165224 | ||||||||
\(859\) | −27112.5 | −1.07691 | −0.538455 | − | 0.842655i | \(-0.680992\pi\) | ||||
−0.538455 | + | 0.842655i | \(0.680992\pi\) | |||||||
\(860\) | −3694.17 | −0.146477 | ||||||||
\(861\) | −5593.09 | −0.221384 | ||||||||
\(862\) | −20620.8 | −0.814787 | ||||||||
\(863\) | 30463.6 | 1.20161 | 0.600807 | − | 0.799394i | \(-0.294846\pi\) | ||||
0.600807 | + | 0.799394i | \(0.294846\pi\) | |||||||
\(864\) | −1734.88 | −0.0683122 | ||||||||
\(865\) | 5126.46 | 0.201508 | ||||||||
\(866\) | 42434.0 | 1.66509 | ||||||||
\(867\) | 5783.00 | 0.226529 | ||||||||
\(868\) | −47.2726 | −0.00184854 | ||||||||
\(869\) | 3408.19 | 0.133044 | ||||||||
\(870\) | −342.244 | −0.0133370 | ||||||||
\(871\) | 16653.5 | 0.647855 | ||||||||
\(872\) | 11938.4 | 0.463631 | ||||||||
\(873\) | 7185.10 | 0.278555 | ||||||||
\(874\) | −62004.6 | −2.39970 | ||||||||
\(875\) | −780.776 | −0.0301658 | ||||||||
\(876\) | 532.642 | 0.0205437 | ||||||||
\(877\) | −5086.12 | −0.195833 | −0.0979167 | − | 0.995195i | \(-0.531218\pi\) | ||||
−0.0979167 | + | 0.995195i | \(0.531218\pi\) | |||||||
\(878\) | −12054.2 | −0.463335 | ||||||||
\(879\) | 25056.9 | 0.961487 | ||||||||
\(880\) | −2773.28 | −0.106236 | ||||||||
\(881\) | −10625.5 | −0.406338 | −0.203169 | − | 0.979144i | \(-0.565124\pi\) | ||||
−0.203169 | + | 0.979144i | \(0.565124\pi\) | |||||||
\(882\) | 7008.06 | 0.267544 | ||||||||
\(883\) | 13112.2 | 0.499728 | 0.249864 | − | 0.968281i | \(-0.419614\pi\) | ||||
0.249864 | + | 0.968281i | \(0.419614\pi\) | |||||||
\(884\) | 5844.25 | 0.222357 | ||||||||
\(885\) | −9281.59 | −0.352539 | ||||||||
\(886\) | −38664.0 | −1.46607 | ||||||||
\(887\) | −14442.8 | −0.546719 | −0.273360 | − | 0.961912i | \(-0.588135\pi\) | ||||
−0.273360 | + | 0.961912i | \(0.588135\pi\) | |||||||
\(888\) | −30237.8 | −1.14270 | ||||||||
\(889\) | −5922.54 | −0.223437 | ||||||||
\(890\) | −1817.15 | −0.0684393 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | 5520.38 | 0.207215 | ||||||||
\(893\) | −72645.8 | −2.72228 | ||||||||
\(894\) | 9326.43 | 0.348906 | ||||||||
\(895\) | −8291.44 | −0.309667 | ||||||||
\(896\) | −5876.86 | −0.219121 | ||||||||
\(897\) | 27365.5 | 1.01863 | ||||||||
\(898\) | −2493.61 | −0.0926648 | ||||||||
\(899\) | −46.8641 | −0.00173860 | ||||||||
\(900\) | −323.651 | −0.0119871 | ||||||||
\(901\) | −13900.3 | −0.513970 | ||||||||
\(902\) | −8410.27 | −0.310456 | ||||||||
\(903\) | −9624.77 | −0.354698 | ||||||||
\(904\) | 4110.10 | 0.151217 | ||||||||
\(905\) | 10109.0 | 0.371310 | ||||||||
\(906\) | −237.045 | −0.00869239 | ||||||||
\(907\) | −44981.9 | −1.64675 | −0.823374 | − | 0.567499i | \(-0.807911\pi\) | ||||
−0.823374 | + | 0.567499i | \(0.807911\pi\) | |||||||
\(908\) | 7197.57 | 0.263062 | ||||||||
\(909\) | 2172.60 | 0.0792745 | ||||||||
\(910\) | −3929.85 | −0.143157 | ||||||||
\(911\) | 6841.96 | 0.248830 | 0.124415 | − | 0.992230i | \(-0.460295\pi\) | ||||
0.124415 | + | 0.992230i | \(0.460295\pi\) | |||||||
\(912\) | 19718.7 | 0.715954 | ||||||||
\(913\) | 11233.4 | 0.407199 | ||||||||
\(914\) | −160.501 | −0.00580843 | ||||||||
\(915\) | −11796.1 | −0.426193 | ||||||||
\(916\) | 398.989 | 0.0143919 | ||||||||
\(917\) | −9274.61 | −0.333996 | ||||||||
\(918\) | −5720.27 | −0.205661 | ||||||||
\(919\) | −4753.54 | −0.170625 | −0.0853127 | − | 0.996354i | \(-0.527189\pi\) | ||||
−0.0853127 | + | 0.996354i | \(0.527189\pi\) | |||||||
\(920\) | 22447.6 | 0.804430 | ||||||||
\(921\) | 16151.7 | 0.577868 | ||||||||
\(922\) | 30395.9 | 1.08572 | ||||||||
\(923\) | −55052.7 | −1.96325 | ||||||||
\(924\) | 296.500 | 0.0105564 | ||||||||
\(925\) | −10422.3 | −0.370470 | ||||||||
\(926\) | 33671.2 | 1.19493 | ||||||||
\(927\) | 10515.4 | 0.372569 | ||||||||
\(928\) | 572.330 | 0.0202453 | ||||||||
\(929\) | −7507.93 | −0.265153 | −0.132576 | − | 0.991173i | \(-0.542325\pi\) | ||||
−0.132576 | + | 0.991173i | \(0.542325\pi\) | |||||||
\(930\) | 202.159 | 0.00712802 | ||||||||
\(931\) | 39625.7 | 1.39493 | ||||||||
\(932\) | −3265.14 | −0.114757 | ||||||||
\(933\) | −5371.24 | −0.188474 | ||||||||
\(934\) | 26068.3 | 0.913256 | ||||||||
\(935\) | 4548.96 | 0.159109 | ||||||||
\(936\) | −10688.9 | −0.373266 | ||||||||
\(937\) | 8540.47 | 0.297764 | 0.148882 | − | 0.988855i | \(-0.452433\pi\) | ||||
0.148882 | + | 0.988855i | \(0.452433\pi\) | |||||||
\(938\) | 5424.24 | 0.188814 | ||||||||
\(939\) | −2427.23 | −0.0843552 | ||||||||
\(940\) | 4008.20 | 0.139078 | ||||||||
\(941\) | 9101.13 | 0.315290 | 0.157645 | − | 0.987496i | \(-0.449610\pi\) | ||||
0.157645 | + | 0.987496i | \(0.449610\pi\) | |||||||
\(942\) | −2653.04 | −0.0917630 | ||||||||
\(943\) | 55425.5 | 1.91400 | ||||||||
\(944\) | −31200.6 | −1.07573 | ||||||||
\(945\) | −843.239 | −0.0290270 | ||||||||
\(946\) | −14472.7 | −0.497407 | ||||||||
\(947\) | 47540.0 | 1.63130 | 0.815650 | − | 0.578546i | \(-0.196380\pi\) | ||||
0.815650 | + | 0.578546i | \(0.196380\pi\) | |||||||
\(948\) | 1337.04 | 0.0458072 | ||||||||
\(949\) | 6063.26 | 0.207399 | ||||||||
\(950\) | 8347.73 | 0.285091 | ||||||||
\(951\) | 32233.6 | 1.09910 | ||||||||
\(952\) | 12490.2 | 0.425221 | ||||||||
\(953\) | 47370.7 | 1.61016 | 0.805082 | − | 0.593164i | \(-0.202121\pi\) | ||||
0.805082 | + | 0.593164i | \(0.202121\pi\) | |||||||
\(954\) | 3874.55 | 0.131492 | ||||||||
\(955\) | −7201.12 | −0.244003 | ||||||||
\(956\) | 2326.12 | 0.0786947 | ||||||||
\(957\) | 293.938 | 0.00992859 | ||||||||
\(958\) | −8789.33 | −0.296420 | ||||||||
\(959\) | 4278.20 | 0.144057 | ||||||||
\(960\) | −8519.67 | −0.286428 | ||||||||
\(961\) | −29763.3 | −0.999071 | ||||||||
\(962\) | −52458.4 | −1.75813 | ||||||||
\(963\) | −18961.4 | −0.634498 | ||||||||
\(964\) | −8122.38 | −0.271374 | ||||||||
\(965\) | 13990.2 | 0.466696 | ||||||||
\(966\) | 8913.27 | 0.296874 | ||||||||
\(967\) | −36171.6 | −1.20290 | −0.601448 | − | 0.798912i | \(-0.705409\pi\) | ||||
−0.601448 | + | 0.798912i | \(0.705409\pi\) | |||||||
\(968\) | 2925.43 | 0.0971351 | ||||||||
\(969\) | −32344.1 | −1.07228 | ||||||||
\(970\) | 10225.0 | 0.338459 | ||||||||
\(971\) | −31713.2 | −1.04812 | −0.524060 | − | 0.851681i | \(-0.675583\pi\) | ||||
−0.524060 | + | 0.851681i | \(0.675583\pi\) | |||||||
\(972\) | −349.543 | −0.0115346 | ||||||||
\(973\) | 5187.37 | 0.170914 | ||||||||
\(974\) | 7257.40 | 0.238750 | ||||||||
\(975\) | −3684.23 | −0.121015 | ||||||||
\(976\) | −39653.1 | −1.30048 | ||||||||
\(977\) | 22800.5 | 0.746626 | 0.373313 | − | 0.927706i | \(-0.378222\pi\) | ||||
0.373313 | + | 0.927706i | \(0.378222\pi\) | |||||||
\(978\) | −14766.0 | −0.482786 | ||||||||
\(979\) | 1560.67 | 0.0509490 | ||||||||
\(980\) | −2186.33 | −0.0712651 | ||||||||
\(981\) | 4444.12 | 0.144638 | ||||||||
\(982\) | 6832.41 | 0.222027 | ||||||||
\(983\) | −44597.4 | −1.44704 | −0.723518 | − | 0.690305i | \(-0.757476\pi\) | ||||
−0.723518 | + | 0.690305i | \(0.757476\pi\) | |||||||
\(984\) | −21649.1 | −0.701369 | ||||||||
\(985\) | −2294.72 | −0.0742292 | ||||||||
\(986\) | 1887.10 | 0.0609507 | ||||||||
\(987\) | 10443.0 | 0.336781 | ||||||||
\(988\) | −9210.95 | −0.296599 | ||||||||
\(989\) | 95378.1 | 3.06658 | ||||||||
\(990\) | −1267.97 | −0.0407057 | ||||||||
\(991\) | −34788.1 | −1.11512 | −0.557558 | − | 0.830138i | \(-0.688261\pi\) | ||||
−0.557558 | + | 0.830138i | \(0.688261\pi\) | |||||||
\(992\) | −338.068 | −0.0108202 | ||||||||
\(993\) | 10197.4 | 0.325885 | ||||||||
\(994\) | −17931.3 | −0.572180 | ||||||||
\(995\) | 11855.2 | 0.377723 | ||||||||
\(996\) | 4406.92 | 0.140199 | ||||||||
\(997\) | −20360.5 | −0.646765 | −0.323383 | − | 0.946268i | \(-0.604820\pi\) | ||||
−0.323383 | + | 0.946268i | \(0.604820\pi\) | |||||||
\(998\) | 28528.0 | 0.904849 | ||||||||
\(999\) | −11256.1 | −0.356485 |
(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 | 165.4.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 495.4.a.d.1.2 | 2 | |||
5.2 | odd | 4 | 825.4.c.j.199.1 | 4 | |||
5.3 | odd | 4 | 825.4.c.j.199.4 | 4 | |||
5.4 | even | 2 | 825.4.a.m.1.2 | 2 | |||
11.10 | odd | 2 | 1815.4.a.n.1.2 | 2 | |||
15.14 | odd | 2 | 2475.4.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
495.4.a.d.1.2 | 2 | 3.2 | odd | 2 | |||
825.4.a.m.1.2 | 2 | 5.4 | even | 2 | |||
825.4.c.j.199.1 | 4 | 5.2 | odd | 4 | |||
825.4.c.j.199.4 | 4 | 5.3 | odd | 4 | |||
1815.4.a.n.1.2 | 2 | 11.10 | odd | 2 | |||
2475.4.a.n.1.1 | 2 | 15.14 | odd | 2 |