Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.46816 | −0.519072 | −0.259536 | − | 0.965733i | \(-0.583570\pi\) | ||||
−0.259536 | + | 0.965733i | \(0.583570\pi\) | |||||||
\(3\) | 0.999287 | 0.192313 | 0.0961564 | − | 0.995366i | \(-0.469345\pi\) | ||||
0.0961564 | + | 0.995366i | \(0.469345\pi\) | |||||||
\(4\) | −5.84451 | −0.730564 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −1.46711 | −0.0998242 | ||||||||
\(7\) | 27.4651 | 1.48298 | 0.741489 | − | 0.670965i | \(-0.234120\pi\) | ||||
0.741489 | + | 0.670965i | \(0.234120\pi\) | |||||||
\(8\) | 20.3259 | 0.898287 | ||||||||
\(9\) | −26.0014 | −0.963016 | ||||||||
\(10\) | −7.34079 | −0.232136 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −5.84034 | −0.140497 | ||||||||
\(13\) | 0.949891 | 0.0202656 | 0.0101328 | − | 0.999949i | \(-0.496775\pi\) | ||||
0.0101328 | + | 0.999949i | \(0.496775\pi\) | |||||||
\(14\) | −40.3232 | −0.769773 | ||||||||
\(15\) | 4.99643 | 0.0860049 | ||||||||
\(16\) | 16.9145 | 0.264288 | ||||||||
\(17\) | −5.50905 | −0.0785965 | −0.0392983 | − | 0.999228i | \(-0.512512\pi\) | ||||
−0.0392983 | + | 0.999228i | \(0.512512\pi\) | |||||||
\(18\) | 38.1742 | 0.499875 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | −29.2226 | −0.326718 | ||||||||
\(21\) | 27.4455 | 0.285196 | ||||||||
\(22\) | 16.1497 | 0.156506 | ||||||||
\(23\) | 129.850 | 1.17720 | 0.588598 | − | 0.808426i | \(-0.299680\pi\) | ||||
0.588598 | + | 0.808426i | \(0.299680\pi\) | |||||||
\(24\) | 20.3114 | 0.172752 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −1.39459 | −0.0105193 | ||||||||
\(27\) | −52.9636 | −0.377513 | ||||||||
\(28\) | −160.520 | −1.08341 | ||||||||
\(29\) | 74.3341 | 0.475983 | 0.237991 | − | 0.971267i | \(-0.423511\pi\) | ||||
0.237991 | + | 0.971267i | \(0.423511\pi\) | |||||||
\(30\) | −7.33555 | −0.0446427 | ||||||||
\(31\) | 38.6646 | 0.224012 | 0.112006 | − | 0.993708i | \(-0.464272\pi\) | ||||
0.112006 | + | 0.993708i | \(0.464272\pi\) | |||||||
\(32\) | −187.440 | −1.03547 | ||||||||
\(33\) | −10.9922 | −0.0579845 | ||||||||
\(34\) | 8.08815 | 0.0407973 | ||||||||
\(35\) | 137.326 | 0.663208 | ||||||||
\(36\) | 151.966 | 0.703545 | ||||||||
\(37\) | −155.865 | −0.692542 | −0.346271 | − | 0.938135i | \(-0.612552\pi\) | ||||
−0.346271 | + | 0.938135i | \(0.612552\pi\) | |||||||
\(38\) | −27.8950 | −0.119083 | ||||||||
\(39\) | 0.949214 | 0.00389733 | ||||||||
\(40\) | 101.630 | 0.401726 | ||||||||
\(41\) | 138.008 | 0.525690 | 0.262845 | − | 0.964838i | \(-0.415339\pi\) | ||||
0.262845 | + | 0.964838i | \(0.415339\pi\) | |||||||
\(42\) | −40.2944 | −0.148037 | ||||||||
\(43\) | 377.536 | 1.33892 | 0.669461 | − | 0.742847i | \(-0.266525\pi\) | ||||
0.669461 | + | 0.742847i | \(0.266525\pi\) | |||||||
\(44\) | 64.2897 | 0.220273 | ||||||||
\(45\) | −130.007 | −0.430674 | ||||||||
\(46\) | −190.640 | −0.611050 | ||||||||
\(47\) | 41.3581 | 0.128355 | 0.0641776 | − | 0.997938i | \(-0.479558\pi\) | ||||
0.0641776 | + | 0.997938i | \(0.479558\pi\) | |||||||
\(48\) | 16.9024 | 0.0508260 | ||||||||
\(49\) | 411.334 | 1.19922 | ||||||||
\(50\) | −36.7039 | −0.103814 | ||||||||
\(51\) | −5.50512 | −0.0151151 | ||||||||
\(52\) | −5.55165 | −0.0148053 | ||||||||
\(53\) | −269.904 | −0.699512 | −0.349756 | − | 0.936841i | \(-0.613736\pi\) | ||||
−0.349756 | + | 0.936841i | \(0.613736\pi\) | |||||||
\(54\) | 77.7589 | 0.195956 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 558.254 | 1.33214 | ||||||||
\(57\) | 18.9864 | 0.0441196 | ||||||||
\(58\) | −109.134 | −0.247069 | ||||||||
\(59\) | −492.457 | −1.08665 | −0.543326 | − | 0.839522i | \(-0.682835\pi\) | ||||
−0.543326 | + | 0.839522i | \(0.682835\pi\) | |||||||
\(60\) | −29.2017 | −0.0628321 | ||||||||
\(61\) | −210.420 | −0.441664 | −0.220832 | − | 0.975312i | \(-0.570877\pi\) | ||||
−0.220832 | + | 0.975312i | \(0.570877\pi\) | |||||||
\(62\) | −56.7657 | −0.116278 | ||||||||
\(63\) | −714.133 | −1.42813 | ||||||||
\(64\) | 139.877 | 0.273196 | ||||||||
\(65\) | 4.74946 | 0.00906304 | ||||||||
\(66\) | 16.1382 | 0.0300981 | ||||||||
\(67\) | −871.951 | −1.58994 | −0.794969 | − | 0.606650i | \(-0.792513\pi\) | ||||
−0.794969 | + | 0.606650i | \(0.792513\pi\) | |||||||
\(68\) | 32.1977 | 0.0574198 | ||||||||
\(69\) | 129.757 | 0.226390 | ||||||||
\(70\) | −201.616 | −0.344253 | ||||||||
\(71\) | −512.428 | −0.856535 | −0.428268 | − | 0.903652i | \(-0.640876\pi\) | ||||
−0.428268 | + | 0.903652i | \(0.640876\pi\) | |||||||
\(72\) | −528.503 | −0.865065 | ||||||||
\(73\) | 23.1747 | 0.0371560 | 0.0185780 | − | 0.999827i | \(-0.494086\pi\) | ||||
0.0185780 | + | 0.999827i | \(0.494086\pi\) | |||||||
\(74\) | 228.834 | 0.359479 | ||||||||
\(75\) | 24.9822 | 0.0384626 | ||||||||
\(76\) | −111.046 | −0.167603 | ||||||||
\(77\) | −302.117 | −0.447135 | ||||||||
\(78\) | −1.39360 | −0.00202299 | ||||||||
\(79\) | 872.732 | 1.24291 | 0.621456 | − | 0.783449i | \(-0.286542\pi\) | ||||
0.621456 | + | 0.783449i | \(0.286542\pi\) | |||||||
\(80\) | 84.5723 | 0.118193 | ||||||||
\(81\) | 649.113 | 0.890415 | ||||||||
\(82\) | −202.618 | −0.272871 | ||||||||
\(83\) | 36.2788 | 0.0479773 | 0.0239886 | − | 0.999712i | \(-0.492363\pi\) | ||||
0.0239886 | + | 0.999712i | \(0.492363\pi\) | |||||||
\(84\) | −160.406 | −0.208354 | ||||||||
\(85\) | −27.5453 | −0.0351494 | ||||||||
\(86\) | −554.282 | −0.694997 | ||||||||
\(87\) | 74.2811 | 0.0915376 | ||||||||
\(88\) | −223.585 | −0.270844 | ||||||||
\(89\) | 1272.99 | 1.51614 | 0.758071 | − | 0.652172i | \(-0.226142\pi\) | ||||
0.758071 | + | 0.652172i | \(0.226142\pi\) | |||||||
\(90\) | 190.871 | 0.223551 | ||||||||
\(91\) | 26.0889 | 0.0300534 | ||||||||
\(92\) | −758.908 | −0.860018 | ||||||||
\(93\) | 38.6370 | 0.0430803 | ||||||||
\(94\) | −60.7201 | −0.0666256 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | −187.307 | −0.199135 | ||||||||
\(97\) | −797.313 | −0.834586 | −0.417293 | − | 0.908772i | \(-0.637021\pi\) | ||||
−0.417293 | + | 0.908772i | \(0.637021\pi\) | |||||||
\(98\) | −603.903 | −0.622484 | ||||||||
\(99\) | 286.016 | 0.290360 | ||||||||
\(100\) | −146.113 | −0.146113 | ||||||||
\(101\) | 1779.44 | 1.75308 | 0.876541 | − | 0.481327i | \(-0.159845\pi\) | ||||
0.876541 | + | 0.481327i | \(0.159845\pi\) | |||||||
\(102\) | 8.08238 | 0.00784584 | ||||||||
\(103\) | 129.027 | 0.123431 | 0.0617157 | − | 0.998094i | \(-0.480343\pi\) | ||||
0.0617157 | + | 0.998094i | \(0.480343\pi\) | |||||||
\(104\) | 19.3074 | 0.0182043 | ||||||||
\(105\) | 137.228 | 0.127543 | ||||||||
\(106\) | 396.261 | 0.363097 | ||||||||
\(107\) | 1384.43 | 1.25082 | 0.625412 | − | 0.780295i | \(-0.284931\pi\) | ||||
0.625412 | + | 0.780295i | \(0.284931\pi\) | |||||||
\(108\) | 309.547 | 0.275798 | ||||||||
\(109\) | 1848.94 | 1.62474 | 0.812370 | − | 0.583142i | \(-0.198177\pi\) | ||||
0.812370 | + | 0.583142i | \(0.198177\pi\) | |||||||
\(110\) | 80.7487 | 0.0699917 | ||||||||
\(111\) | −155.754 | −0.133185 | ||||||||
\(112\) | 464.558 | 0.391934 | ||||||||
\(113\) | 344.635 | 0.286907 | 0.143453 | − | 0.989657i | \(-0.454179\pi\) | ||||
0.143453 | + | 0.989657i | \(0.454179\pi\) | |||||||
\(114\) | −27.8751 | −0.0229012 | ||||||||
\(115\) | 649.248 | 0.526458 | ||||||||
\(116\) | −434.447 | −0.347736 | ||||||||
\(117\) | −24.6985 | −0.0195161 | ||||||||
\(118\) | 723.004 | 0.564050 | ||||||||
\(119\) | −151.307 | −0.116557 | ||||||||
\(120\) | 101.557 | 0.0772571 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 308.929 | 0.229255 | ||||||||
\(123\) | 137.910 | 0.101097 | ||||||||
\(124\) | −225.976 | −0.163655 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 1048.46 | 0.741303 | ||||||||
\(127\) | −545.874 | −0.381406 | −0.190703 | − | 0.981648i | \(-0.561077\pi\) | ||||
−0.190703 | + | 0.981648i | \(0.561077\pi\) | |||||||
\(128\) | 1294.16 | 0.893664 | ||||||||
\(129\) | 377.266 | 0.257492 | ||||||||
\(130\) | −6.97295 | −0.00470437 | ||||||||
\(131\) | 425.277 | 0.283638 | 0.141819 | − | 0.989893i | \(-0.454705\pi\) | ||||
0.141819 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(132\) | 64.2438 | 0.0423614 | ||||||||
\(133\) | 521.838 | 0.340219 | ||||||||
\(134\) | 1280.16 | 0.825292 | ||||||||
\(135\) | −264.818 | −0.168829 | ||||||||
\(136\) | −111.977 | −0.0706023 | ||||||||
\(137\) | −868.742 | −0.541764 | −0.270882 | − | 0.962613i | \(-0.587315\pi\) | ||||
−0.270882 | + | 0.962613i | \(0.587315\pi\) | |||||||
\(138\) | −190.504 | −0.117513 | ||||||||
\(139\) | −1778.19 | −1.08507 | −0.542533 | − | 0.840034i | \(-0.682535\pi\) | ||||
−0.542533 | + | 0.840034i | \(0.682535\pi\) | |||||||
\(140\) | −802.602 | −0.484516 | ||||||||
\(141\) | 41.3285 | 0.0246843 | ||||||||
\(142\) | 752.325 | 0.444603 | ||||||||
\(143\) | −10.4488 | −0.00611030 | ||||||||
\(144\) | −439.800 | −0.254514 | ||||||||
\(145\) | 371.671 | 0.212866 | ||||||||
\(146\) | −34.0241 | −0.0192867 | ||||||||
\(147\) | 411.041 | 0.230626 | ||||||||
\(148\) | 910.955 | 0.505946 | ||||||||
\(149\) | 3375.04 | 1.85566 | 0.927832 | − | 0.372998i | \(-0.121670\pi\) | ||||
0.927832 | + | 0.372998i | \(0.121670\pi\) | |||||||
\(150\) | −36.6777 | −0.0199648 | ||||||||
\(151\) | 313.175 | 0.168780 | 0.0843902 | − | 0.996433i | \(-0.473106\pi\) | ||||
0.0843902 | + | 0.996433i | \(0.473106\pi\) | |||||||
\(152\) | 386.193 | 0.206081 | ||||||||
\(153\) | 143.243 | 0.0756897 | ||||||||
\(154\) | 443.555 | 0.232095 | ||||||||
\(155\) | 193.323 | 0.100181 | ||||||||
\(156\) | −5.54769 | −0.00284725 | ||||||||
\(157\) | 1837.22 | 0.933924 | 0.466962 | − | 0.884277i | \(-0.345348\pi\) | ||||
0.466962 | + | 0.884277i | \(0.345348\pi\) | |||||||
\(158\) | −1281.31 | −0.645161 | ||||||||
\(159\) | −269.711 | −0.134525 | ||||||||
\(160\) | −937.202 | −0.463077 | ||||||||
\(161\) | 3566.34 | 1.74576 | ||||||||
\(162\) | −953.000 | −0.462190 | ||||||||
\(163\) | 3901.40 | 1.87473 | 0.937365 | − | 0.348349i | \(-0.113258\pi\) | ||||
0.937365 | + | 0.348349i | \(0.113258\pi\) | |||||||
\(164\) | −806.592 | −0.384050 | ||||||||
\(165\) | −54.9608 | −0.0259315 | ||||||||
\(166\) | −53.2630 | −0.0249037 | ||||||||
\(167\) | 3170.82 | 1.46926 | 0.734628 | − | 0.678470i | \(-0.237357\pi\) | ||||
0.734628 | + | 0.678470i | \(0.237357\pi\) | |||||||
\(168\) | 557.856 | 0.256188 | ||||||||
\(169\) | −2196.10 | −0.999589 | ||||||||
\(170\) | 40.4408 | 0.0182451 | ||||||||
\(171\) | −494.027 | −0.220931 | ||||||||
\(172\) | −2206.51 | −0.978169 | ||||||||
\(173\) | −861.694 | −0.378690 | −0.189345 | − | 0.981911i | \(-0.560636\pi\) | ||||
−0.189345 | + | 0.981911i | \(0.560636\pi\) | |||||||
\(174\) | −109.056 | −0.0475146 | ||||||||
\(175\) | 686.629 | 0.296596 | ||||||||
\(176\) | −186.059 | −0.0796859 | ||||||||
\(177\) | −492.106 | −0.208977 | ||||||||
\(178\) | −1868.95 | −0.786987 | ||||||||
\(179\) | 2490.28 | 1.03984 | 0.519922 | − | 0.854214i | \(-0.325961\pi\) | ||||
0.519922 | + | 0.854214i | \(0.325961\pi\) | |||||||
\(180\) | 759.828 | 0.314635 | ||||||||
\(181\) | −335.209 | −0.137657 | −0.0688283 | − | 0.997629i | \(-0.521926\pi\) | ||||
−0.0688283 | + | 0.997629i | \(0.521926\pi\) | |||||||
\(182\) | −38.3026 | −0.0155999 | ||||||||
\(183\) | −210.270 | −0.0849375 | ||||||||
\(184\) | 2639.31 | 1.05746 | ||||||||
\(185\) | −779.325 | −0.309714 | ||||||||
\(186\) | −56.7252 | −0.0223618 | ||||||||
\(187\) | 60.5996 | 0.0236977 | ||||||||
\(188\) | −241.718 | −0.0937717 | ||||||||
\(189\) | −1454.65 | −0.559844 | ||||||||
\(190\) | −139.475 | −0.0532557 | ||||||||
\(191\) | −4150.26 | −1.57226 | −0.786131 | − | 0.618060i | \(-0.787919\pi\) | ||||
−0.786131 | + | 0.618060i | \(0.787919\pi\) | |||||||
\(192\) | 139.777 | 0.0525391 | ||||||||
\(193\) | 3316.91 | 1.23708 | 0.618539 | − | 0.785754i | \(-0.287725\pi\) | ||||
0.618539 | + | 0.785754i | \(0.287725\pi\) | |||||||
\(194\) | 1170.58 | 0.433210 | ||||||||
\(195\) | 4.74607 | 0.00174294 | ||||||||
\(196\) | −2404.05 | −0.876110 | ||||||||
\(197\) | 1351.31 | 0.488716 | 0.244358 | − | 0.969685i | \(-0.421423\pi\) | ||||
0.244358 | + | 0.969685i | \(0.421423\pi\) | |||||||
\(198\) | −419.916 | −0.150718 | ||||||||
\(199\) | 2323.05 | 0.827521 | 0.413761 | − | 0.910386i | \(-0.364215\pi\) | ||||
0.413761 | + | 0.910386i | \(0.364215\pi\) | |||||||
\(200\) | 508.148 | 0.179657 | ||||||||
\(201\) | −871.329 | −0.305765 | ||||||||
\(202\) | −2612.50 | −0.909976 | ||||||||
\(203\) | 2041.60 | 0.705872 | ||||||||
\(204\) | 32.1748 | 0.0110426 | ||||||||
\(205\) | 690.042 | 0.235096 | ||||||||
\(206\) | −189.432 | −0.0640698 | ||||||||
\(207\) | −3376.28 | −1.13366 | ||||||||
\(208\) | 16.0669 | 0.00535595 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −201.472 | −0.0662042 | ||||||||
\(211\) | 2366.42 | 0.772089 | 0.386045 | − | 0.922480i | \(-0.373841\pi\) | ||||
0.386045 | + | 0.922480i | \(0.373841\pi\) | |||||||
\(212\) | 1577.46 | 0.511039 | ||||||||
\(213\) | −512.062 | −0.164723 | ||||||||
\(214\) | −2032.56 | −0.649267 | ||||||||
\(215\) | 1887.68 | 0.598784 | ||||||||
\(216\) | −1076.53 | −0.339115 | ||||||||
\(217\) | 1061.93 | 0.332205 | ||||||||
\(218\) | −2714.54 | −0.843357 | ||||||||
\(219\) | 23.1581 | 0.00714558 | ||||||||
\(220\) | 321.448 | 0.0985093 | ||||||||
\(221\) | −5.23300 | −0.00159280 | ||||||||
\(222\) | 228.671 | 0.0691324 | ||||||||
\(223\) | −3157.89 | −0.948288 | −0.474144 | − | 0.880447i | \(-0.657242\pi\) | ||||
−0.474144 | + | 0.880447i | \(0.657242\pi\) | |||||||
\(224\) | −5148.08 | −1.53558 | ||||||||
\(225\) | −650.036 | −0.192603 | ||||||||
\(226\) | −505.978 | −0.148925 | ||||||||
\(227\) | −1657.86 | −0.484739 | −0.242370 | − | 0.970184i | \(-0.577925\pi\) | ||||
−0.242370 | + | 0.970184i | \(0.577925\pi\) | |||||||
\(228\) | −110.967 | −0.0322322 | ||||||||
\(229\) | 508.933 | 0.146861 | 0.0734306 | − | 0.997300i | \(-0.476605\pi\) | ||||
0.0734306 | + | 0.997300i | \(0.476605\pi\) | |||||||
\(230\) | −953.198 | −0.273270 | ||||||||
\(231\) | −301.901 | −0.0859897 | ||||||||
\(232\) | 1510.91 | 0.427569 | ||||||||
\(233\) | 2857.06 | 0.803314 | 0.401657 | − | 0.915790i | \(-0.368434\pi\) | ||||
0.401657 | + | 0.915790i | \(0.368434\pi\) | |||||||
\(234\) | 36.2613 | 0.0101302 | ||||||||
\(235\) | 206.790 | 0.0574022 | ||||||||
\(236\) | 2878.17 | 0.793869 | ||||||||
\(237\) | 872.109 | 0.239028 | ||||||||
\(238\) | 222.142 | 0.0605015 | ||||||||
\(239\) | −5340.10 | −1.44528 | −0.722640 | − | 0.691224i | \(-0.757072\pi\) | ||||
−0.722640 | + | 0.691224i | \(0.757072\pi\) | |||||||
\(240\) | 84.5119 | 0.0227301 | ||||||||
\(241\) | 5574.54 | 1.48999 | 0.744995 | − | 0.667070i | \(-0.232452\pi\) | ||||
0.744995 | + | 0.667070i | \(0.232452\pi\) | |||||||
\(242\) | −177.647 | −0.0471884 | ||||||||
\(243\) | 2078.67 | 0.548751 | ||||||||
\(244\) | 1229.80 | 0.322664 | ||||||||
\(245\) | 2056.67 | 0.536309 | ||||||||
\(246\) | −202.473 | −0.0524766 | ||||||||
\(247\) | 18.0479 | 0.00464924 | ||||||||
\(248\) | 785.893 | 0.201227 | ||||||||
\(249\) | 36.2529 | 0.00922664 | ||||||||
\(250\) | −183.520 | −0.0464272 | ||||||||
\(251\) | 3401.23 | 0.855313 | 0.427656 | − | 0.903941i | \(-0.359339\pi\) | ||||
0.427656 | + | 0.903941i | \(0.359339\pi\) | |||||||
\(252\) | 4173.76 | 1.04334 | ||||||||
\(253\) | −1428.35 | −0.354938 | ||||||||
\(254\) | 801.429 | 0.197977 | ||||||||
\(255\) | −27.5256 | −0.00675969 | ||||||||
\(256\) | −3019.05 | −0.737072 | ||||||||
\(257\) | −6956.03 | −1.68835 | −0.844173 | − | 0.536070i | \(-0.819908\pi\) | ||||
−0.844173 | + | 0.536070i | \(0.819908\pi\) | |||||||
\(258\) | −553.886 | −0.133657 | ||||||||
\(259\) | −4280.85 | −1.02702 | ||||||||
\(260\) | −27.7583 | −0.00662113 | ||||||||
\(261\) | −1932.79 | −0.458379 | ||||||||
\(262\) | −624.373 | −0.147229 | ||||||||
\(263\) | −276.795 | −0.0648971 | −0.0324485 | − | 0.999473i | \(-0.510331\pi\) | ||||
−0.0324485 | + | 0.999473i | \(0.510331\pi\) | |||||||
\(264\) | −223.426 | −0.0520867 | ||||||||
\(265\) | −1349.52 | −0.312831 | ||||||||
\(266\) | −766.140 | −0.176598 | ||||||||
\(267\) | 1272.08 | 0.291573 | ||||||||
\(268\) | 5096.13 | 1.16155 | ||||||||
\(269\) | 2950.20 | 0.668687 | 0.334344 | − | 0.942451i | \(-0.391485\pi\) | ||||
0.334344 | + | 0.942451i | \(0.391485\pi\) | |||||||
\(270\) | 388.795 | 0.0876344 | ||||||||
\(271\) | 8394.98 | 1.88177 | 0.940883 | − | 0.338732i | \(-0.109998\pi\) | ||||
0.940883 | + | 0.338732i | \(0.109998\pi\) | |||||||
\(272\) | −93.1826 | −0.0207721 | ||||||||
\(273\) | 26.0703 | 0.00577965 | ||||||||
\(274\) | 1275.45 | 0.281215 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −758.366 | −0.165392 | ||||||||
\(277\) | −4775.19 | −1.03579 | −0.517894 | − | 0.855445i | \(-0.673284\pi\) | ||||
−0.517894 | + | 0.855445i | \(0.673284\pi\) | |||||||
\(278\) | 2610.67 | 0.563228 | ||||||||
\(279\) | −1005.33 | −0.215727 | ||||||||
\(280\) | 2791.27 | 0.595751 | ||||||||
\(281\) | −3968.84 | −0.842565 | −0.421283 | − | 0.906929i | \(-0.638420\pi\) | ||||
−0.421283 | + | 0.906929i | \(0.638420\pi\) | |||||||
\(282\) | −60.6768 | −0.0128129 | ||||||||
\(283\) | 5683.26 | 1.19376 | 0.596881 | − | 0.802329i | \(-0.296406\pi\) | ||||
0.596881 | + | 0.802329i | \(0.296406\pi\) | |||||||
\(284\) | 2994.89 | 0.625754 | ||||||||
\(285\) | 94.9322 | 0.0197309 | ||||||||
\(286\) | 15.3405 | 0.00317169 | ||||||||
\(287\) | 3790.42 | 0.779586 | ||||||||
\(288\) | 4873.72 | 0.997176 | ||||||||
\(289\) | −4882.65 | −0.993823 | ||||||||
\(290\) | −545.671 | −0.110493 | ||||||||
\(291\) | −796.744 | −0.160502 | ||||||||
\(292\) | −135.445 | −0.0271449 | ||||||||
\(293\) | 4247.87 | 0.846974 | 0.423487 | − | 0.905902i | \(-0.360806\pi\) | ||||
0.423487 | + | 0.905902i | \(0.360806\pi\) | |||||||
\(294\) | −603.472 | −0.119712 | ||||||||
\(295\) | −2462.28 | −0.485965 | ||||||||
\(296\) | −3168.10 | −0.622102 | ||||||||
\(297\) | 582.600 | 0.113824 | ||||||||
\(298\) | −4955.09 | −0.963223 | ||||||||
\(299\) | 123.343 | 0.0238566 | ||||||||
\(300\) | −146.009 | −0.0280994 | ||||||||
\(301\) | 10369.1 | 1.98559 | ||||||||
\(302\) | −459.790 | −0.0876091 | ||||||||
\(303\) | 1778.17 | 0.337140 | ||||||||
\(304\) | 321.375 | 0.0606319 | ||||||||
\(305\) | −1052.10 | −0.197518 | ||||||||
\(306\) | −210.304 | −0.0392884 | ||||||||
\(307\) | 5824.49 | 1.08280 | 0.541402 | − | 0.840764i | \(-0.317894\pi\) | ||||
0.541402 | + | 0.840764i | \(0.317894\pi\) | |||||||
\(308\) | 1765.72 | 0.326661 | ||||||||
\(309\) | 128.935 | 0.0237374 | ||||||||
\(310\) | −283.828 | −0.0520012 | ||||||||
\(311\) | −4674.13 | −0.852236 | −0.426118 | − | 0.904667i | \(-0.640119\pi\) | ||||
−0.426118 | + | 0.904667i | \(0.640119\pi\) | |||||||
\(312\) | 19.2936 | 0.00350092 | ||||||||
\(313\) | 9811.34 | 1.77179 | 0.885894 | − | 0.463888i | \(-0.153546\pi\) | ||||
0.885894 | + | 0.463888i | \(0.153546\pi\) | |||||||
\(314\) | −2697.33 | −0.484774 | ||||||||
\(315\) | −3570.66 | −0.638680 | ||||||||
\(316\) | −5100.69 | −0.908027 | ||||||||
\(317\) | 445.411 | 0.0789172 | 0.0394586 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394586 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(318\) | 395.979 | 0.0698282 | ||||||||
\(319\) | −817.676 | −0.143514 | ||||||||
\(320\) | 699.383 | 0.122177 | ||||||||
\(321\) | 1383.44 | 0.240549 | ||||||||
\(322\) | −5235.95 | −0.906173 | ||||||||
\(323\) | −104.672 | −0.0180313 | ||||||||
\(324\) | −3793.75 | −0.650506 | ||||||||
\(325\) | 23.7473 | 0.00405312 | ||||||||
\(326\) | −5727.86 | −0.973120 | ||||||||
\(327\) | 1847.62 | 0.312458 | ||||||||
\(328\) | 2805.15 | 0.472221 | ||||||||
\(329\) | 1135.90 | 0.190348 | ||||||||
\(330\) | 80.6910 | 0.0134603 | ||||||||
\(331\) | −3569.06 | −0.592668 | −0.296334 | − | 0.955084i | \(-0.595764\pi\) | ||||
−0.296334 | + | 0.955084i | \(0.595764\pi\) | |||||||
\(332\) | −212.032 | −0.0350505 | ||||||||
\(333\) | 4052.71 | 0.666929 | ||||||||
\(334\) | −4655.27 | −0.762650 | ||||||||
\(335\) | −4359.76 | −0.711042 | ||||||||
\(336\) | 464.226 | 0.0753739 | ||||||||
\(337\) | 9309.15 | 1.50475 | 0.752376 | − | 0.658734i | \(-0.228908\pi\) | ||||
0.752376 | + | 0.658734i | \(0.228908\pi\) | |||||||
\(338\) | 3224.22 | 0.518859 | ||||||||
\(339\) | 344.389 | 0.0551759 | ||||||||
\(340\) | 160.989 | 0.0256789 | ||||||||
\(341\) | −425.310 | −0.0675421 | ||||||||
\(342\) | 725.310 | 0.114679 | ||||||||
\(343\) | 1876.80 | 0.295446 | ||||||||
\(344\) | 7673.76 | 1.20274 | ||||||||
\(345\) | 648.785 | 0.101245 | ||||||||
\(346\) | 1265.10 | 0.196567 | ||||||||
\(347\) | −7243.49 | −1.12061 | −0.560304 | − | 0.828287i | \(-0.689316\pi\) | ||||
−0.560304 | + | 0.828287i | \(0.689316\pi\) | |||||||
\(348\) | −434.137 | −0.0668741 | ||||||||
\(349\) | −6364.57 | −0.976182 | −0.488091 | − | 0.872793i | \(-0.662307\pi\) | ||||
−0.488091 | + | 0.872793i | \(0.662307\pi\) | |||||||
\(350\) | −1008.08 | −0.153955 | ||||||||
\(351\) | −50.3097 | −0.00765052 | ||||||||
\(352\) | 2061.85 | 0.312207 | ||||||||
\(353\) | 10638.7 | 1.60408 | 0.802042 | − | 0.597268i | \(-0.203747\pi\) | ||||
0.802042 | + | 0.597268i | \(0.203747\pi\) | |||||||
\(354\) | 722.488 | 0.108474 | ||||||||
\(355\) | −2562.14 | −0.383054 | ||||||||
\(356\) | −7440.01 | −1.10764 | ||||||||
\(357\) | −151.199 | −0.0224154 | ||||||||
\(358\) | −3656.12 | −0.539754 | ||||||||
\(359\) | 1082.99 | 0.159215 | 0.0796074 | − | 0.996826i | \(-0.474633\pi\) | ||||
0.0796074 | + | 0.996826i | \(0.474633\pi\) | |||||||
\(360\) | −2642.52 | −0.386869 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 492.139 | 0.0714537 | ||||||||
\(363\) | 120.914 | 0.0174830 | ||||||||
\(364\) | −152.477 | −0.0219559 | ||||||||
\(365\) | 115.873 | 0.0166167 | ||||||||
\(366\) | 308.709 | 0.0440887 | ||||||||
\(367\) | −3288.73 | −0.467767 | −0.233883 | − | 0.972265i | \(-0.575143\pi\) | ||||
−0.233883 | + | 0.972265i | \(0.575143\pi\) | |||||||
\(368\) | 2196.34 | 0.311119 | ||||||||
\(369\) | −3588.41 | −0.506248 | ||||||||
\(370\) | 1144.17 | 0.160764 | ||||||||
\(371\) | −7412.95 | −1.03736 | ||||||||
\(372\) | −225.814 | −0.0314729 | ||||||||
\(373\) | 3224.99 | 0.447678 | 0.223839 | − | 0.974626i | \(-0.428141\pi\) | ||||
0.223839 | + | 0.974626i | \(0.428141\pi\) | |||||||
\(374\) | −88.9697 | −0.0123008 | ||||||||
\(375\) | 124.911 | 0.0172010 | ||||||||
\(376\) | 840.641 | 0.115300 | ||||||||
\(377\) | 70.6094 | 0.00964607 | ||||||||
\(378\) | 2135.66 | 0.290599 | ||||||||
\(379\) | −3475.11 | −0.470988 | −0.235494 | − | 0.971876i | \(-0.575671\pi\) | ||||
−0.235494 | + | 0.971876i | \(0.575671\pi\) | |||||||
\(380\) | −555.229 | −0.0749543 | ||||||||
\(381\) | −545.485 | −0.0733492 | ||||||||
\(382\) | 6093.23 | 0.816117 | ||||||||
\(383\) | −4049.69 | −0.540286 | −0.270143 | − | 0.962820i | \(-0.587071\pi\) | ||||
−0.270143 | + | 0.962820i | \(0.587071\pi\) | |||||||
\(384\) | 1293.24 | 0.171863 | ||||||||
\(385\) | −1510.58 | −0.199965 | ||||||||
\(386\) | −4869.74 | −0.642133 | ||||||||
\(387\) | −9816.47 | −1.28940 | ||||||||
\(388\) | 4659.91 | 0.609719 | ||||||||
\(389\) | 4760.34 | 0.620460 | 0.310230 | − | 0.950661i | \(-0.399594\pi\) | ||||
0.310230 | + | 0.950661i | \(0.399594\pi\) | |||||||
\(390\) | −6.96798 | −0.000904711 0 | ||||||||
\(391\) | −715.348 | −0.0925236 | ||||||||
\(392\) | 8360.74 | 1.07725 | ||||||||
\(393\) | 424.973 | 0.0545472 | ||||||||
\(394\) | −1983.94 | −0.253679 | ||||||||
\(395\) | 4363.66 | 0.555847 | ||||||||
\(396\) | −1671.62 | −0.212127 | ||||||||
\(397\) | −2855.98 | −0.361052 | −0.180526 | − | 0.983570i | \(-0.557780\pi\) | ||||
−0.180526 | + | 0.983570i | \(0.557780\pi\) | |||||||
\(398\) | −3410.61 | −0.429543 | ||||||||
\(399\) | 521.465 | 0.0654284 | ||||||||
\(400\) | 422.861 | 0.0528577 | ||||||||
\(401\) | 11554.3 | 1.43889 | 0.719444 | − | 0.694550i | \(-0.244397\pi\) | ||||
0.719444 | + | 0.694550i | \(0.244397\pi\) | |||||||
\(402\) | 1279.25 | 0.158714 | ||||||||
\(403\) | 36.7272 | 0.00453973 | ||||||||
\(404\) | −10400.0 | −1.28074 | ||||||||
\(405\) | 3245.56 | 0.398206 | ||||||||
\(406\) | −2997.39 | −0.366399 | ||||||||
\(407\) | 1714.52 | 0.208809 | ||||||||
\(408\) | −111.897 | −0.0135777 | ||||||||
\(409\) | −12734.6 | −1.53957 | −0.769786 | − | 0.638302i | \(-0.779637\pi\) | ||||
−0.769786 | + | 0.638302i | \(0.779637\pi\) | |||||||
\(410\) | −1013.09 | −0.122032 | ||||||||
\(411\) | −868.122 | −0.104188 | ||||||||
\(412\) | −754.101 | −0.0901745 | ||||||||
\(413\) | −13525.4 | −1.61148 | ||||||||
\(414\) | 4956.90 | 0.588451 | ||||||||
\(415\) | 181.394 | 0.0214561 | ||||||||
\(416\) | −178.048 | −0.0209844 | ||||||||
\(417\) | −1776.92 | −0.208672 | ||||||||
\(418\) | 306.845 | 0.0359050 | ||||||||
\(419\) | −570.293 | −0.0664931 | −0.0332466 | − | 0.999447i | \(-0.510585\pi\) | ||||
−0.0332466 | + | 0.999447i | \(0.510585\pi\) | |||||||
\(420\) | −802.029 | −0.0931786 | ||||||||
\(421\) | 8162.00 | 0.944873 | 0.472437 | − | 0.881365i | \(-0.343375\pi\) | ||||
0.472437 | + | 0.881365i | \(0.343375\pi\) | |||||||
\(422\) | −3474.27 | −0.400770 | ||||||||
\(423\) | −1075.37 | −0.123608 | ||||||||
\(424\) | −5486.05 | −0.628363 | ||||||||
\(425\) | −137.726 | −0.0157193 | ||||||||
\(426\) | 751.788 | 0.0855029 | ||||||||
\(427\) | −5779.21 | −0.654977 | ||||||||
\(428\) | −8091.33 | −0.913807 | ||||||||
\(429\) | −10.4414 | −0.00117509 | ||||||||
\(430\) | −2771.41 | −0.310812 | ||||||||
\(431\) | −7827.12 | −0.874755 | −0.437377 | − | 0.899278i | \(-0.644093\pi\) | ||||
−0.437377 | + | 0.899278i | \(0.644093\pi\) | |||||||
\(432\) | −895.851 | −0.0997723 | ||||||||
\(433\) | −9972.80 | −1.10684 | −0.553420 | − | 0.832902i | \(-0.686678\pi\) | ||||
−0.553420 | + | 0.832902i | \(0.686678\pi\) | |||||||
\(434\) | −1559.08 | −0.172438 | ||||||||
\(435\) | 371.406 | 0.0409369 | ||||||||
\(436\) | −10806.2 | −1.18698 | ||||||||
\(437\) | 2467.14 | 0.270067 | ||||||||
\(438\) | −33.9998 | −0.00370907 | ||||||||
\(439\) | −13895.3 | −1.51067 | −0.755337 | − | 0.655336i | \(-0.772527\pi\) | ||||
−0.755337 | + | 0.655336i | \(0.772527\pi\) | |||||||
\(440\) | −1117.93 | −0.121125 | ||||||||
\(441\) | −10695.3 | −1.15487 | ||||||||
\(442\) | 7.68287 | 0.000826780 0 | ||||||||
\(443\) | 462.220 | 0.0495728 | 0.0247864 | − | 0.999693i | \(-0.492109\pi\) | ||||
0.0247864 | + | 0.999693i | \(0.492109\pi\) | |||||||
\(444\) | 910.305 | 0.0972999 | ||||||||
\(445\) | 6364.95 | 0.678039 | ||||||||
\(446\) | 4636.29 | 0.492230 | ||||||||
\(447\) | 3372.63 | 0.356868 | ||||||||
\(448\) | 3841.73 | 0.405144 | ||||||||
\(449\) | −9422.16 | −0.990333 | −0.495166 | − | 0.868798i | \(-0.664893\pi\) | ||||
−0.495166 | + | 0.868798i | \(0.664893\pi\) | |||||||
\(450\) | 954.355 | 0.0999749 | ||||||||
\(451\) | −1518.09 | −0.158501 | ||||||||
\(452\) | −2014.22 | −0.209604 | ||||||||
\(453\) | 312.952 | 0.0324586 | ||||||||
\(454\) | 2433.99 | 0.251615 | ||||||||
\(455\) | 130.445 | 0.0134403 | ||||||||
\(456\) | 385.917 | 0.0396321 | ||||||||
\(457\) | −16201.5 | −1.65837 | −0.829184 | − | 0.558975i | \(-0.811195\pi\) | ||||
−0.829184 | + | 0.558975i | \(0.811195\pi\) | |||||||
\(458\) | −747.194 | −0.0762316 | ||||||||
\(459\) | 291.779 | 0.0296712 | ||||||||
\(460\) | −3794.54 | −0.384612 | ||||||||
\(461\) | 12564.5 | 1.26938 | 0.634691 | − | 0.772766i | \(-0.281127\pi\) | ||||
0.634691 | + | 0.772766i | \(0.281127\pi\) | |||||||
\(462\) | 443.238 | 0.0446349 | ||||||||
\(463\) | 6140.02 | 0.616309 | 0.308154 | − | 0.951336i | \(-0.400289\pi\) | ||||
0.308154 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(464\) | 1257.32 | 0.125797 | ||||||||
\(465\) | 193.185 | 0.0192661 | ||||||||
\(466\) | −4194.61 | −0.416978 | ||||||||
\(467\) | −5064.23 | −0.501808 | −0.250904 | − | 0.968012i | \(-0.580728\pi\) | ||||
−0.250904 | + | 0.968012i | \(0.580728\pi\) | |||||||
\(468\) | 144.351 | 0.0142577 | ||||||||
\(469\) | −23948.3 | −2.35784 | ||||||||
\(470\) | −303.601 | −0.0297959 | ||||||||
\(471\) | 1835.91 | 0.179606 | ||||||||
\(472\) | −10009.6 | −0.976125 | ||||||||
\(473\) | −4152.89 | −0.403700 | ||||||||
\(474\) | −1280.39 | −0.124073 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 884.315 | 0.0851523 | ||||||||
\(477\) | 7017.89 | 0.673641 | ||||||||
\(478\) | 7840.10 | 0.750205 | ||||||||
\(479\) | 18459.1 | 1.76079 | 0.880393 | − | 0.474245i | \(-0.157279\pi\) | ||||
0.880393 | + | 0.474245i | \(0.157279\pi\) | |||||||
\(480\) | −936.534 | −0.0890557 | ||||||||
\(481\) | −148.055 | −0.0140348 | ||||||||
\(482\) | −8184.30 | −0.773412 | ||||||||
\(483\) | 3563.79 | 0.335731 | ||||||||
\(484\) | −707.186 | −0.0664149 | ||||||||
\(485\) | −3986.56 | −0.373238 | ||||||||
\(486\) | −3051.81 | −0.284841 | ||||||||
\(487\) | 5767.97 | 0.536697 | 0.268349 | − | 0.963322i | \(-0.413522\pi\) | ||||
0.268349 | + | 0.963322i | \(0.413522\pi\) | |||||||
\(488\) | −4276.97 | −0.396741 | ||||||||
\(489\) | 3898.61 | 0.360535 | ||||||||
\(490\) | −3019.52 | −0.278383 | ||||||||
\(491\) | −5789.31 | −0.532114 | −0.266057 | − | 0.963957i | \(-0.585721\pi\) | ||||
−0.266057 | + | 0.963957i | \(0.585721\pi\) | |||||||
\(492\) | −806.016 | −0.0738577 | ||||||||
\(493\) | −409.511 | −0.0374106 | ||||||||
\(494\) | −26.4972 | −0.00241329 | ||||||||
\(495\) | 1430.08 | 0.129853 | ||||||||
\(496\) | 653.990 | 0.0592037 | ||||||||
\(497\) | −14073.9 | −1.27022 | ||||||||
\(498\) | −53.2250 | −0.00478929 | ||||||||
\(499\) | −14813.4 | −1.32894 | −0.664470 | − | 0.747315i | \(-0.731343\pi\) | ||||
−0.664470 | + | 0.747315i | \(0.731343\pi\) | |||||||
\(500\) | −730.564 | −0.0653437 | ||||||||
\(501\) | 3168.56 | 0.282557 | ||||||||
\(502\) | −4993.53 | −0.443969 | ||||||||
\(503\) | 21117.0 | 1.87189 | 0.935946 | − | 0.352144i | \(-0.114547\pi\) | ||||
0.935946 | + | 0.352144i | \(0.114547\pi\) | |||||||
\(504\) | −14515.4 | −1.28287 | ||||||||
\(505\) | 8897.22 | 0.784002 | ||||||||
\(506\) | 2097.04 | 0.184238 | ||||||||
\(507\) | −2194.53 | −0.192234 | ||||||||
\(508\) | 3190.37 | 0.278641 | ||||||||
\(509\) | 14008.3 | 1.21986 | 0.609928 | − | 0.792457i | \(-0.291198\pi\) | ||||
0.609928 | + | 0.792457i | \(0.291198\pi\) | |||||||
\(510\) | 40.4119 | 0.00350876 | ||||||||
\(511\) | 636.496 | 0.0551016 | ||||||||
\(512\) | −5920.87 | −0.511070 | ||||||||
\(513\) | −1006.31 | −0.0866074 | ||||||||
\(514\) | 10212.5 | 0.876373 | ||||||||
\(515\) | 645.136 | 0.0552002 | ||||||||
\(516\) | −2204.94 | −0.188114 | ||||||||
\(517\) | −454.939 | −0.0387005 | ||||||||
\(518\) | 6284.97 | 0.533100 | ||||||||
\(519\) | −861.079 | −0.0728269 | ||||||||
\(520\) | 96.5371 | 0.00814122 | ||||||||
\(521\) | 2736.24 | 0.230090 | 0.115045 | − | 0.993360i | \(-0.463299\pi\) | ||||
0.115045 | + | 0.993360i | \(0.463299\pi\) | |||||||
\(522\) | 2837.65 | 0.237932 | ||||||||
\(523\) | −17940.9 | −1.50000 | −0.750002 | − | 0.661436i | \(-0.769947\pi\) | ||||
−0.750002 | + | 0.661436i | \(0.769947\pi\) | |||||||
\(524\) | −2485.53 | −0.207216 | ||||||||
\(525\) | 686.139 | 0.0570391 | ||||||||
\(526\) | 406.379 | 0.0336863 | ||||||||
\(527\) | −213.005 | −0.0176065 | ||||||||
\(528\) | −185.926 | −0.0153246 | ||||||||
\(529\) | 4693.92 | 0.385791 | ||||||||
\(530\) | 1981.31 | 0.162382 | ||||||||
\(531\) | 12804.6 | 1.04646 | ||||||||
\(532\) | −3049.89 | −0.248551 | ||||||||
\(533\) | 131.093 | 0.0106534 | ||||||||
\(534\) | −1867.62 | −0.151348 | ||||||||
\(535\) | 6922.16 | 0.559385 | ||||||||
\(536\) | −17723.2 | −1.42822 | ||||||||
\(537\) | 2488.50 | 0.199975 | ||||||||
\(538\) | −4331.36 | −0.347097 | ||||||||
\(539\) | −4524.67 | −0.361580 | ||||||||
\(540\) | 1547.73 | 0.123340 | ||||||||
\(541\) | −14189.7 | −1.12766 | −0.563830 | − | 0.825891i | \(-0.690673\pi\) | ||||
−0.563830 | + | 0.825891i | \(0.690673\pi\) | |||||||
\(542\) | −12325.1 | −0.976772 | ||||||||
\(543\) | −334.969 | −0.0264731 | ||||||||
\(544\) | 1032.62 | 0.0813845 | ||||||||
\(545\) | 9244.72 | 0.726606 | ||||||||
\(546\) | −38.2753 | −0.00300006 | ||||||||
\(547\) | −12478.2 | −0.975374 | −0.487687 | − | 0.873019i | \(-0.662159\pi\) | ||||
−0.487687 | + | 0.873019i | \(0.662159\pi\) | |||||||
\(548\) | 5077.38 | 0.395793 | ||||||||
\(549\) | 5471.21 | 0.425329 | ||||||||
\(550\) | 403.743 | 0.0313012 | ||||||||
\(551\) | 1412.35 | 0.109198 | ||||||||
\(552\) | 2637.43 | 0.203363 | ||||||||
\(553\) | 23969.7 | 1.84321 | ||||||||
\(554\) | 7010.73 | 0.537649 | ||||||||
\(555\) | −778.769 | −0.0595620 | ||||||||
\(556\) | 10392.7 | 0.792711 | ||||||||
\(557\) | 7471.85 | 0.568389 | 0.284194 | − | 0.958767i | \(-0.408274\pi\) | ||||
0.284194 | + | 0.958767i | \(0.408274\pi\) | |||||||
\(558\) | 1475.99 | 0.111978 | ||||||||
\(559\) | 358.618 | 0.0271340 | ||||||||
\(560\) | 2322.79 | 0.175278 | ||||||||
\(561\) | 60.5563 | 0.00455738 | ||||||||
\(562\) | 5826.88 | 0.437352 | ||||||||
\(563\) | −9496.59 | −0.710895 | −0.355447 | − | 0.934696i | \(-0.615671\pi\) | ||||
−0.355447 | + | 0.934696i | \(0.615671\pi\) | |||||||
\(564\) | −241.545 | −0.0180335 | ||||||||
\(565\) | 1723.17 | 0.128309 | ||||||||
\(566\) | −8343.92 | −0.619649 | ||||||||
\(567\) | 17828.0 | 1.32047 | ||||||||
\(568\) | −10415.6 | −0.769415 | ||||||||
\(569\) | 7966.13 | 0.586920 | 0.293460 | − | 0.955971i | \(-0.405193\pi\) | ||||
0.293460 | + | 0.955971i | \(0.405193\pi\) | |||||||
\(570\) | −139.375 | −0.0102417 | ||||||||
\(571\) | 609.893 | 0.0446992 | 0.0223496 | − | 0.999750i | \(-0.492885\pi\) | ||||
0.0223496 | + | 0.999750i | \(0.492885\pi\) | |||||||
\(572\) | 61.0682 | 0.00446397 | ||||||||
\(573\) | −4147.30 | −0.302366 | ||||||||
\(574\) | −5564.93 | −0.404662 | ||||||||
\(575\) | 3246.24 | 0.235439 | ||||||||
\(576\) | −3636.99 | −0.263092 | ||||||||
\(577\) | −8934.58 | −0.644630 | −0.322315 | − | 0.946633i | \(-0.604461\pi\) | ||||
−0.322315 | + | 0.946633i | \(0.604461\pi\) | |||||||
\(578\) | 7168.50 | 0.515866 | ||||||||
\(579\) | 3314.54 | 0.237906 | ||||||||
\(580\) | −2172.23 | −0.155512 | ||||||||
\(581\) | 996.402 | 0.0711493 | ||||||||
\(582\) | 1169.75 | 0.0833119 | ||||||||
\(583\) | 2968.94 | 0.210911 | ||||||||
\(584\) | 471.047 | 0.0333768 | ||||||||
\(585\) | −123.493 | −0.00872785 | ||||||||
\(586\) | −6236.54 | −0.439640 | ||||||||
\(587\) | 7111.59 | 0.500045 | 0.250023 | − | 0.968240i | \(-0.419562\pi\) | ||||
0.250023 | + | 0.968240i | \(0.419562\pi\) | |||||||
\(588\) | −2402.33 | −0.168487 | ||||||||
\(589\) | 734.627 | 0.0513918 | ||||||||
\(590\) | 3615.02 | 0.252251 | ||||||||
\(591\) | 1350.35 | 0.0939863 | ||||||||
\(592\) | −2636.37 | −0.183031 | ||||||||
\(593\) | −13508.6 | −0.935465 | −0.467733 | − | 0.883870i | \(-0.654929\pi\) | ||||
−0.467733 | + | 0.883870i | \(0.654929\pi\) | |||||||
\(594\) | −855.348 | −0.0590831 | ||||||||
\(595\) | −756.534 | −0.0521259 | ||||||||
\(596\) | −19725.5 | −1.35568 | ||||||||
\(597\) | 2321.39 | 0.159143 | ||||||||
\(598\) | −181.087 | −0.0123833 | ||||||||
\(599\) | −9603.94 | −0.655102 | −0.327551 | − | 0.944833i | \(-0.606223\pi\) | ||||
−0.327551 | + | 0.944833i | \(0.606223\pi\) | |||||||
\(600\) | 507.786 | 0.0345504 | ||||||||
\(601\) | −22522.2 | −1.52862 | −0.764308 | − | 0.644851i | \(-0.776919\pi\) | ||||
−0.764308 | + | 0.644851i | \(0.776919\pi\) | |||||||
\(602\) | −15223.4 | −1.03067 | ||||||||
\(603\) | 22672.0 | 1.53114 | ||||||||
\(604\) | −1830.36 | −0.123305 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | −2610.64 | −0.175000 | ||||||||
\(607\) | 4.23892 | 0.000283447 0 | 0.000141724 | − | 1.00000i | \(-0.499955\pi\) | ||||
0.000141724 | 1.00000i | \(0.499955\pi\) | ||||||||
\(608\) | −3561.37 | −0.237554 | ||||||||
\(609\) | 2040.14 | 0.135748 | ||||||||
\(610\) | 1544.65 | 0.102526 | ||||||||
\(611\) | 39.2857 | 0.00260119 | ||||||||
\(612\) | −837.187 | −0.0552962 | ||||||||
\(613\) | −2668.81 | −0.175844 | −0.0879220 | − | 0.996127i | \(-0.528023\pi\) | ||||
−0.0879220 | + | 0.996127i | \(0.528023\pi\) | |||||||
\(614\) | −8551.26 | −0.562054 | ||||||||
\(615\) | 689.549 | 0.0452119 | ||||||||
\(616\) | −6140.80 | −0.401656 | ||||||||
\(617\) | −21377.4 | −1.39485 | −0.697423 | − | 0.716660i | \(-0.745670\pi\) | ||||
−0.697423 | + | 0.716660i | \(0.745670\pi\) | |||||||
\(618\) | −189.297 | −0.0123214 | ||||||||
\(619\) | −15210.8 | −0.987680 | −0.493840 | − | 0.869553i | \(-0.664407\pi\) | ||||
−0.493840 | + | 0.869553i | \(0.664407\pi\) | |||||||
\(620\) | −1129.88 | −0.0731887 | ||||||||
\(621\) | −6877.30 | −0.444407 | ||||||||
\(622\) | 6862.36 | 0.442372 | ||||||||
\(623\) | 34962.8 | 2.24841 | ||||||||
\(624\) | 16.0554 | 0.00103002 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −14404.6 | −0.919685 | ||||||||
\(627\) | −208.851 | −0.0133026 | ||||||||
\(628\) | −10737.7 | −0.682292 | ||||||||
\(629\) | 858.668 | 0.0544314 | ||||||||
\(630\) | 5242.30 | 0.331521 | ||||||||
\(631\) | 10927.8 | 0.689427 | 0.344714 | − | 0.938708i | \(-0.387976\pi\) | ||||
0.344714 | + | 0.938708i | \(0.387976\pi\) | |||||||
\(632\) | 17739.1 | 1.11649 | ||||||||
\(633\) | 2364.73 | 0.148483 | ||||||||
\(634\) | −653.933 | −0.0409637 | ||||||||
\(635\) | −2729.37 | −0.170570 | ||||||||
\(636\) | 1576.33 | 0.0982793 | ||||||||
\(637\) | 390.723 | 0.0243030 | ||||||||
\(638\) | 1200.48 | 0.0744942 | ||||||||
\(639\) | 13323.9 | 0.824857 | ||||||||
\(640\) | 6470.82 | 0.399659 | ||||||||
\(641\) | 10053.4 | 0.619481 | 0.309740 | − | 0.950821i | \(-0.399758\pi\) | ||||
0.309740 | + | 0.950821i | \(0.399758\pi\) | |||||||
\(642\) | −2031.11 | −0.124862 | ||||||||
\(643\) | −4999.32 | −0.306616 | −0.153308 | − | 0.988178i | \(-0.548993\pi\) | ||||
−0.153308 | + | 0.988178i | \(0.548993\pi\) | |||||||
\(644\) | −20843.5 | −1.27539 | ||||||||
\(645\) | 1886.33 | 0.115154 | ||||||||
\(646\) | 153.675 | 0.00935953 | ||||||||
\(647\) | 800.105 | 0.0486173 | 0.0243086 | − | 0.999705i | \(-0.492262\pi\) | ||||
0.0243086 | + | 0.999705i | \(0.492262\pi\) | |||||||
\(648\) | 13193.8 | 0.799849 | ||||||||
\(649\) | 5417.03 | 0.327638 | ||||||||
\(650\) | −34.8648 | −0.00210386 | ||||||||
\(651\) | 1061.17 | 0.0638872 | ||||||||
\(652\) | −22801.8 | −1.36961 | ||||||||
\(653\) | −1865.37 | −0.111788 | −0.0558939 | − | 0.998437i | \(-0.517801\pi\) | ||||
−0.0558939 | + | 0.998437i | \(0.517801\pi\) | |||||||
\(654\) | −2712.60 | −0.162188 | ||||||||
\(655\) | 2126.38 | 0.126847 | ||||||||
\(656\) | 2334.34 | 0.138934 | ||||||||
\(657\) | −602.574 | −0.0357818 | ||||||||
\(658\) | −1667.69 | −0.0988043 | ||||||||
\(659\) | 3945.42 | 0.233220 | 0.116610 | − | 0.993178i | \(-0.462797\pi\) | ||||
0.116610 | + | 0.993178i | \(0.462797\pi\) | |||||||
\(660\) | 321.219 | 0.0189446 | ||||||||
\(661\) | −10405.0 | −0.612265 | −0.306133 | − | 0.951989i | \(-0.599035\pi\) | ||||
−0.306133 | + | 0.951989i | \(0.599035\pi\) | |||||||
\(662\) | 5239.94 | 0.307637 | ||||||||
\(663\) | −5.22927 | −0.000306317 0 | ||||||||
\(664\) | 737.400 | 0.0430974 | ||||||||
\(665\) | 2609.19 | 0.152150 | ||||||||
\(666\) | −5950.02 | −0.346184 | ||||||||
\(667\) | 9652.26 | 0.560325 | ||||||||
\(668\) | −18531.9 | −1.07339 | ||||||||
\(669\) | −3155.64 | −0.182368 | ||||||||
\(670\) | 6400.81 | 0.369082 | ||||||||
\(671\) | 2314.62 | 0.133167 | ||||||||
\(672\) | −5144.41 | −0.295312 | ||||||||
\(673\) | −27651.3 | −1.58377 | −0.791886 | − | 0.610669i | \(-0.790901\pi\) | ||||
−0.791886 | + | 0.610669i | \(0.790901\pi\) | |||||||
\(674\) | −13667.3 | −0.781075 | ||||||||
\(675\) | −1324.09 | −0.0755026 | ||||||||
\(676\) | 12835.1 | 0.730264 | ||||||||
\(677\) | 9932.92 | 0.563890 | 0.281945 | − | 0.959431i | \(-0.409020\pi\) | ||||
0.281945 | + | 0.959431i | \(0.409020\pi\) | |||||||
\(678\) | −505.617 | −0.0286403 | ||||||||
\(679\) | −21898.3 | −1.23767 | ||||||||
\(680\) | −559.883 | −0.0315743 | ||||||||
\(681\) | −1656.67 | −0.0932215 | ||||||||
\(682\) | 624.423 | 0.0350592 | ||||||||
\(683\) | −14535.6 | −0.814335 | −0.407168 | − | 0.913353i | \(-0.633484\pi\) | ||||
−0.407168 | + | 0.913353i | \(0.633484\pi\) | |||||||
\(684\) | 2887.35 | 0.161404 | ||||||||
\(685\) | −4343.71 | −0.242284 | ||||||||
\(686\) | −2755.44 | −0.153358 | ||||||||
\(687\) | 508.570 | 0.0282433 | ||||||||
\(688\) | 6385.81 | 0.353862 | ||||||||
\(689\) | −256.379 | −0.0141760 | ||||||||
\(690\) | −952.518 | −0.0525533 | ||||||||
\(691\) | 62.2591 | 0.00342756 | 0.00171378 | − | 0.999999i | \(-0.499454\pi\) | ||||
0.00171378 | + | 0.999999i | \(0.499454\pi\) | |||||||
\(692\) | 5036.18 | 0.276657 | ||||||||
\(693\) | 7855.46 | 0.430598 | ||||||||
\(694\) | 10634.6 | 0.581677 | ||||||||
\(695\) | −8890.96 | −0.485257 | ||||||||
\(696\) | 1509.83 | 0.0822271 | ||||||||
\(697\) | −760.295 | −0.0413174 | ||||||||
\(698\) | 9344.18 | 0.506709 | ||||||||
\(699\) | 2855.02 | 0.154488 | ||||||||
\(700\) | −4013.01 | −0.216682 | ||||||||
\(701\) | 22424.4 | 1.20822 | 0.604108 | − | 0.796902i | \(-0.293530\pi\) | ||||
0.604108 | + | 0.796902i | \(0.293530\pi\) | |||||||
\(702\) | 73.8625 | 0.00397117 | ||||||||
\(703\) | −2961.44 | −0.158880 | ||||||||
\(704\) | −1538.64 | −0.0823718 | ||||||||
\(705\) | 206.643 | 0.0110392 | ||||||||
\(706\) | −15619.3 | −0.832635 | ||||||||
\(707\) | 48872.7 | 2.59978 | ||||||||
\(708\) | 2876.12 | 0.152671 | ||||||||
\(709\) | 22285.4 | 1.18046 | 0.590231 | − | 0.807235i | \(-0.299037\pi\) | ||||
0.590231 | + | 0.807235i | \(0.299037\pi\) | |||||||
\(710\) | 3761.62 | 0.198833 | ||||||||
\(711\) | −22692.3 | −1.19694 | ||||||||
\(712\) | 25874.7 | 1.36193 | ||||||||
\(713\) | 5020.58 | 0.263706 | ||||||||
\(714\) | 221.984 | 0.0116352 | ||||||||
\(715\) | −52.2440 | −0.00273261 | ||||||||
\(716\) | −14554.5 | −0.759673 | ||||||||
\(717\) | −5336.29 | −0.277946 | ||||||||
\(718\) | −1590.00 | −0.0826440 | ||||||||
\(719\) | 23676.7 | 1.22809 | 0.614043 | − | 0.789273i | \(-0.289542\pi\) | ||||
0.614043 | + | 0.789273i | \(0.289542\pi\) | |||||||
\(720\) | −2199.00 | −0.113822 | ||||||||
\(721\) | 3543.75 | 0.183046 | ||||||||
\(722\) | −530.005 | −0.0273196 | ||||||||
\(723\) | 5570.56 | 0.286544 | ||||||||
\(724\) | 1959.13 | 0.100567 | ||||||||
\(725\) | 1858.35 | 0.0951966 | ||||||||
\(726\) | −177.520 | −0.00907493 | ||||||||
\(727\) | −34021.9 | −1.73563 | −0.867814 | − | 0.496889i | \(-0.834475\pi\) | ||||
−0.867814 | + | 0.496889i | \(0.834475\pi\) | |||||||
\(728\) | 530.281 | 0.0269966 | ||||||||
\(729\) | −15448.9 | −0.784883 | ||||||||
\(730\) | −170.120 | −0.00862525 | ||||||||
\(731\) | −2079.86 | −0.105235 | ||||||||
\(732\) | 1228.92 | 0.0620523 | ||||||||
\(733\) | −15018.8 | −0.756799 | −0.378399 | − | 0.925642i | \(-0.623525\pi\) | ||||
−0.378399 | + | 0.925642i | \(0.623525\pi\) | |||||||
\(734\) | 4828.38 | 0.242805 | ||||||||
\(735\) | 2055.20 | 0.103139 | ||||||||
\(736\) | −24339.1 | −1.21895 | ||||||||
\(737\) | 9591.47 | 0.479384 | ||||||||
\(738\) | 5268.36 | 0.262779 | ||||||||
\(739\) | 14623.9 | 0.727941 | 0.363971 | − | 0.931410i | \(-0.381421\pi\) | ||||
0.363971 | + | 0.931410i | \(0.381421\pi\) | |||||||
\(740\) | 4554.78 | 0.226266 | ||||||||
\(741\) | 18.0351 | 0.000894109 0 | ||||||||
\(742\) | 10883.4 | 0.538465 | ||||||||
\(743\) | 6946.02 | 0.342967 | 0.171484 | − | 0.985187i | \(-0.445144\pi\) | ||||
0.171484 | + | 0.985187i | \(0.445144\pi\) | |||||||
\(744\) | 785.333 | 0.0386985 | ||||||||
\(745\) | 16875.2 | 0.829878 | ||||||||
\(746\) | −4734.80 | −0.232377 | ||||||||
\(747\) | −943.300 | −0.0462029 | ||||||||
\(748\) | −354.175 | −0.0173127 | ||||||||
\(749\) | 38023.6 | 1.85494 | ||||||||
\(750\) | −183.389 | −0.00892855 | ||||||||
\(751\) | 22467.2 | 1.09167 | 0.545833 | − | 0.837894i | \(-0.316213\pi\) | ||||
0.545833 | + | 0.837894i | \(0.316213\pi\) | |||||||
\(752\) | 699.549 | 0.0339228 | ||||||||
\(753\) | 3398.80 | 0.164488 | ||||||||
\(754\) | −103.666 | −0.00500700 | ||||||||
\(755\) | 1565.88 | 0.0754808 | ||||||||
\(756\) | 8501.74 | 0.409002 | ||||||||
\(757\) | 9254.70 | 0.444343 | 0.222172 | − | 0.975008i | \(-0.428685\pi\) | ||||
0.222172 | + | 0.975008i | \(0.428685\pi\) | |||||||
\(758\) | 5102.01 | 0.244477 | ||||||||
\(759\) | −1427.33 | −0.0682591 | ||||||||
\(760\) | 1930.96 | 0.0921624 | ||||||||
\(761\) | 15482.0 | 0.737479 | 0.368739 | − | 0.929533i | \(-0.379790\pi\) | ||||
0.368739 | + | 0.929533i | \(0.379790\pi\) | |||||||
\(762\) | 800.857 | 0.0380735 | ||||||||
\(763\) | 50781.5 | 2.40945 | ||||||||
\(764\) | 24256.2 | 1.14864 | ||||||||
\(765\) | 716.216 | 0.0338495 | ||||||||
\(766\) | 5945.58 | 0.280447 | ||||||||
\(767\) | −467.781 | −0.0220216 | ||||||||
\(768\) | −3016.89 | −0.141748 | ||||||||
\(769\) | −14148.0 | −0.663448 | −0.331724 | − | 0.943377i | \(-0.607630\pi\) | ||||
−0.331724 | + | 0.943377i | \(0.607630\pi\) | |||||||
\(770\) | 2217.77 | 0.103796 | ||||||||
\(771\) | −6951.06 | −0.324691 | ||||||||
\(772\) | −19385.7 | −0.903765 | ||||||||
\(773\) | 14157.1 | 0.658725 | 0.329362 | − | 0.944204i | \(-0.393166\pi\) | ||||
0.329362 | + | 0.944204i | \(0.393166\pi\) | |||||||
\(774\) | 14412.1 | 0.669293 | ||||||||
\(775\) | 966.615 | 0.0448024 | ||||||||
\(776\) | −16206.1 | −0.749698 | ||||||||
\(777\) | −4277.80 | −0.197510 | ||||||||
\(778\) | −6988.94 | −0.322064 | ||||||||
\(779\) | 2622.16 | 0.120602 | ||||||||
\(780\) | −27.7385 | −0.00127333 | ||||||||
\(781\) | 5636.71 | 0.258255 | ||||||||
\(782\) | 1050.24 | 0.0480264 | ||||||||
\(783\) | −3937.00 | −0.179690 | ||||||||
\(784\) | 6957.49 | 0.316941 | ||||||||
\(785\) | 9186.10 | 0.417664 | ||||||||
\(786\) | −623.927 | −0.0283139 | ||||||||
\(787\) | −36498.1 | −1.65313 | −0.826567 | − | 0.562839i | \(-0.809709\pi\) | ||||
−0.826567 | + | 0.562839i | \(0.809709\pi\) | |||||||
\(788\) | −7897.76 | −0.357038 | ||||||||
\(789\) | −276.598 | −0.0124805 | ||||||||
\(790\) | −6406.54 | −0.288525 | ||||||||
\(791\) | 9465.44 | 0.425477 | ||||||||
\(792\) | 5813.53 | 0.260827 | ||||||||
\(793\) | −199.876 | −0.00895057 | ||||||||
\(794\) | 4193.03 | 0.187412 | ||||||||
\(795\) | −1348.56 | −0.0601615 | ||||||||
\(796\) | −13577.1 | −0.604558 | ||||||||
\(797\) | 20745.1 | 0.921993 | 0.460997 | − | 0.887402i | \(-0.347492\pi\) | ||||
0.460997 | + | 0.887402i | \(0.347492\pi\) | |||||||
\(798\) | −765.593 | −0.0339620 | ||||||||
\(799\) | −227.844 | −0.0100883 | ||||||||
\(800\) | −4686.01 | −0.207094 | ||||||||
\(801\) | −33099.5 | −1.46007 | ||||||||
\(802\) | −16963.5 | −0.746887 | ||||||||
\(803\) | −254.921 | −0.0112030 | ||||||||
\(804\) | 5092.50 | 0.223381 | ||||||||
\(805\) | 17831.7 | 0.780726 | ||||||||
\(806\) | −53.9212 | −0.00235645 | ||||||||
\(807\) | 2948.10 | 0.128597 | ||||||||
\(808\) | 36168.9 | 1.57477 | ||||||||
\(809\) | −16878.4 | −0.733513 | −0.366757 | − | 0.930317i | \(-0.619532\pi\) | ||||
−0.366757 | + | 0.930317i | \(0.619532\pi\) | |||||||
\(810\) | −4765.00 | −0.206697 | ||||||||
\(811\) | −6831.84 | −0.295806 | −0.147903 | − | 0.989002i | \(-0.547252\pi\) | ||||
−0.147903 | + | 0.989002i | \(0.547252\pi\) | |||||||
\(812\) | −11932.1 | −0.515685 | ||||||||
\(813\) | 8388.99 | 0.361888 | ||||||||
\(814\) | −2517.18 | −0.108387 | ||||||||
\(815\) | 19507.0 | 0.838405 | ||||||||
\(816\) | −93.1161 | −0.00399475 | ||||||||
\(817\) | 7173.18 | 0.307170 | ||||||||
\(818\) | 18696.4 | 0.799149 | ||||||||
\(819\) | −678.349 | −0.0289419 | ||||||||
\(820\) | −4032.96 | −0.171752 | ||||||||
\(821\) | −14559.4 | −0.618912 | −0.309456 | − | 0.950914i | \(-0.600147\pi\) | ||||
−0.309456 | + | 0.950914i | \(0.600147\pi\) | |||||||
\(822\) | 1274.54 | 0.0540811 | ||||||||
\(823\) | 23405.6 | 0.991333 | 0.495667 | − | 0.868513i | \(-0.334924\pi\) | ||||
0.495667 | + | 0.868513i | \(0.334924\pi\) | |||||||
\(824\) | 2622.60 | 0.110877 | ||||||||
\(825\) | −274.804 | −0.0115969 | ||||||||
\(826\) | 19857.4 | 0.836474 | ||||||||
\(827\) | 7001.52 | 0.294398 | 0.147199 | − | 0.989107i | \(-0.452974\pi\) | ||||
0.147199 | + | 0.989107i | \(0.452974\pi\) | |||||||
\(828\) | 19732.7 | 0.828210 | ||||||||
\(829\) | 19603.5 | 0.821298 | 0.410649 | − | 0.911793i | \(-0.365302\pi\) | ||||
0.410649 | + | 0.911793i | \(0.365302\pi\) | |||||||
\(830\) | −266.315 | −0.0111373 | ||||||||
\(831\) | −4771.79 | −0.199195 | ||||||||
\(832\) | 132.867 | 0.00553648 | ||||||||
\(833\) | −2266.06 | −0.0942549 | ||||||||
\(834\) | 2608.80 | 0.108316 | ||||||||
\(835\) | 15854.1 | 0.657071 | ||||||||
\(836\) | 1221.50 | 0.0505342 | ||||||||
\(837\) | −2047.82 | −0.0845674 | ||||||||
\(838\) | 837.279 | 0.0345147 | ||||||||
\(839\) | 13398.8 | 0.551346 | 0.275673 | − | 0.961251i | \(-0.411099\pi\) | ||||
0.275673 | + | 0.961251i | \(0.411099\pi\) | |||||||
\(840\) | 2789.28 | 0.114571 | ||||||||
\(841\) | −18863.4 | −0.773440 | ||||||||
\(842\) | −11983.1 | −0.490457 | ||||||||
\(843\) | −3966.00 | −0.162036 | ||||||||
\(844\) | −13830.6 | −0.564061 | ||||||||
\(845\) | −10980.5 | −0.447030 | ||||||||
\(846\) | 1578.81 | 0.0641615 | ||||||||
\(847\) | 3323.28 | 0.134816 | ||||||||
\(848\) | −4565.28 | −0.184873 | ||||||||
\(849\) | 5679.21 | 0.229576 | ||||||||
\(850\) | 202.204 | 0.00815945 | ||||||||
\(851\) | −20239.0 | −0.815258 | ||||||||
\(852\) | 2992.75 | 0.120340 | ||||||||
\(853\) | 11175.1 | 0.448569 | 0.224284 | − | 0.974524i | \(-0.427996\pi\) | ||||
0.224284 | + | 0.974524i | \(0.427996\pi\) | |||||||
\(854\) | 8484.78 | 0.339980 | ||||||||
\(855\) | −2470.14 | −0.0988033 | ||||||||
\(856\) | 28139.9 | 1.12360 | ||||||||
\(857\) | 30444.6 | 1.21350 | 0.606748 | − | 0.794894i | \(-0.292474\pi\) | ||||
0.606748 | + | 0.794894i | \(0.292474\pi\) | |||||||
\(858\) | 15.3295 | 0.000609956 0 | ||||||||
\(859\) | 18409.9 | 0.731244 | 0.365622 | − | 0.930763i | \(-0.380856\pi\) | ||||
0.365622 | + | 0.930763i | \(0.380856\pi\) | |||||||
\(860\) | −11032.6 | −0.437450 | ||||||||
\(861\) | 3787.71 | 0.149924 | ||||||||
\(862\) | 11491.4 | 0.454061 | ||||||||
\(863\) | 3982.68 | 0.157094 | 0.0785468 | − | 0.996910i | \(-0.474972\pi\) | ||||
0.0785468 | + | 0.996910i | \(0.474972\pi\) | |||||||
\(864\) | 9927.52 | 0.390904 | ||||||||
\(865\) | −4308.47 | −0.169355 | ||||||||
\(866\) | 14641.6 | 0.574530 | ||||||||
\(867\) | −4879.17 | −0.191125 | ||||||||
\(868\) | −6206.45 | −0.242697 | ||||||||
\(869\) | −9600.05 | −0.374752 | ||||||||
\(870\) | −545.282 | −0.0212492 | ||||||||
\(871\) | −828.259 | −0.0322210 | ||||||||
\(872\) | 37581.5 | 1.45948 | ||||||||
\(873\) | 20731.3 | 0.803720 | ||||||||
\(874\) | −3622.15 | −0.140184 | ||||||||
\(875\) | 3433.14 | 0.132642 | ||||||||
\(876\) | −135.348 | −0.00522030 | ||||||||
\(877\) | 45406.3 | 1.74830 | 0.874151 | − | 0.485655i | \(-0.161419\pi\) | ||||
0.874151 | + | 0.485655i | \(0.161419\pi\) | |||||||
\(878\) | 20400.5 | 0.784149 | ||||||||
\(879\) | 4244.84 | 0.162884 | ||||||||
\(880\) | −930.295 | −0.0356366 | ||||||||
\(881\) | −10197.7 | −0.389977 | −0.194989 | − | 0.980805i | \(-0.562467\pi\) | ||||
−0.194989 | + | 0.980805i | \(0.562467\pi\) | |||||||
\(882\) | 15702.3 | 0.599462 | ||||||||
\(883\) | 7588.55 | 0.289213 | 0.144607 | − | 0.989489i | \(-0.453808\pi\) | ||||
0.144607 | + | 0.989489i | \(0.453808\pi\) | |||||||
\(884\) | 30.5843 | 0.00116365 | ||||||||
\(885\) | −2460.53 | −0.0934573 | ||||||||
\(886\) | −678.612 | −0.0257319 | ||||||||
\(887\) | −17626.5 | −0.667237 | −0.333618 | − | 0.942708i | \(-0.608270\pi\) | ||||
−0.333618 | + | 0.942708i | \(0.608270\pi\) | |||||||
\(888\) | −3165.84 | −0.119638 | ||||||||
\(889\) | −14992.5 | −0.565616 | ||||||||
\(890\) | −9344.75 | −0.351951 | ||||||||
\(891\) | −7140.24 | −0.268470 | ||||||||
\(892\) | 18456.4 | 0.692785 | ||||||||
\(893\) | 785.803 | 0.0294467 | ||||||||
\(894\) | −4951.55 | −0.185240 | ||||||||
\(895\) | 12451.4 | 0.465032 | ||||||||
\(896\) | 35544.4 | 1.32528 | ||||||||
\(897\) | 123.255 | 0.00458792 | ||||||||
\(898\) | 13833.2 | 0.514054 | ||||||||
\(899\) | 2874.10 | 0.106626 | ||||||||
\(900\) | 3799.14 | 0.140709 | ||||||||
\(901\) | 1486.91 | 0.0549792 | ||||||||
\(902\) | 2228.80 | 0.0822737 | ||||||||
\(903\) | 10361.7 | 0.381855 | ||||||||
\(904\) | 7005.02 | 0.257725 | ||||||||
\(905\) | −1676.04 | −0.0615619 | ||||||||
\(906\) | −459.462 | −0.0168484 | ||||||||
\(907\) | −35631.0 | −1.30442 | −0.652209 | − | 0.758040i | \(-0.726157\pi\) | ||||
−0.652209 | + | 0.758040i | \(0.726157\pi\) | |||||||
\(908\) | 9689.36 | 0.354133 | ||||||||
\(909\) | −46268.1 | −1.68825 | ||||||||
\(910\) | −191.513 | −0.00697648 | ||||||||
\(911\) | 23992.4 | 0.872561 | 0.436281 | − | 0.899811i | \(-0.356296\pi\) | ||||
0.436281 | + | 0.899811i | \(0.356296\pi\) | |||||||
\(912\) | 321.145 | 0.0116603 | ||||||||
\(913\) | −399.067 | −0.0144657 | ||||||||
\(914\) | 23786.4 | 0.860813 | ||||||||
\(915\) | −1051.35 | −0.0379852 | ||||||||
\(916\) | −2974.47 | −0.107292 | ||||||||
\(917\) | 11680.3 | 0.420629 | ||||||||
\(918\) | −428.378 | −0.0154015 | ||||||||
\(919\) | 41244.8 | 1.48046 | 0.740229 | − | 0.672355i | \(-0.234717\pi\) | ||||
0.740229 | + | 0.672355i | \(0.234717\pi\) | |||||||
\(920\) | 13196.6 | 0.472911 | ||||||||
\(921\) | 5820.33 | 0.208237 | ||||||||
\(922\) | −18446.6 | −0.658901 | ||||||||
\(923\) | −486.751 | −0.0173582 | ||||||||
\(924\) | 1764.46 | 0.0628210 | ||||||||
\(925\) | −3896.63 | −0.138508 | ||||||||
\(926\) | −9014.52 | −0.319909 | ||||||||
\(927\) | −3354.89 | −0.118866 | ||||||||
\(928\) | −13933.2 | −0.492867 | ||||||||
\(929\) | −45369.4 | −1.60229 | −0.801143 | − | 0.598473i | \(-0.795774\pi\) | ||||
−0.801143 | + | 0.598473i | \(0.795774\pi\) | |||||||
\(930\) | −283.626 | −0.0100005 | ||||||||
\(931\) | 7815.35 | 0.275121 | ||||||||
\(932\) | −16698.1 | −0.586873 | ||||||||
\(933\) | −4670.79 | −0.163896 | ||||||||
\(934\) | 7435.08 | 0.260475 | ||||||||
\(935\) | 302.998 | 0.0105980 | ||||||||
\(936\) | −502.021 | −0.0175310 | ||||||||
\(937\) | 5150.15 | 0.179560 | 0.0897802 | − | 0.995962i | \(-0.471384\pi\) | ||||
0.0897802 | + | 0.995962i | \(0.471384\pi\) | |||||||
\(938\) | 35159.8 | 1.22389 | ||||||||
\(939\) | 9804.34 | 0.340737 | ||||||||
\(940\) | −1208.59 | −0.0419360 | ||||||||
\(941\) | 9951.44 | 0.344748 | 0.172374 | − | 0.985032i | \(-0.444856\pi\) | ||||
0.172374 | + | 0.985032i | \(0.444856\pi\) | |||||||
\(942\) | −2695.40 | −0.0932282 | ||||||||
\(943\) | 17920.3 | 0.618840 | ||||||||
\(944\) | −8329.64 | −0.287189 | ||||||||
\(945\) | −7273.27 | −0.250370 | ||||||||
\(946\) | 6097.10 | 0.209550 | ||||||||
\(947\) | 32172.3 | 1.10397 | 0.551984 | − | 0.833854i | \(-0.313871\pi\) | ||||
0.551984 | + | 0.833854i | \(0.313871\pi\) | |||||||
\(948\) | −5097.05 | −0.174625 | ||||||||
\(949\) | 22.0134 | 0.000752988 0 | ||||||||
\(950\) | −697.375 | −0.0238167 | ||||||||
\(951\) | 445.093 | 0.0151768 | ||||||||
\(952\) | −3075.45 | −0.104702 | ||||||||
\(953\) | −39981.3 | −1.35899 | −0.679497 | − | 0.733678i | \(-0.737802\pi\) | ||||
−0.679497 | + | 0.733678i | \(0.737802\pi\) | |||||||
\(954\) | −10303.4 | −0.349668 | ||||||||
\(955\) | −20751.3 | −0.703137 | ||||||||
\(956\) | 31210.3 | 1.05587 | ||||||||
\(957\) | −817.092 | −0.0275996 | ||||||||
\(958\) | −27100.8 | −0.913974 | ||||||||
\(959\) | −23860.1 | −0.803424 | ||||||||
\(960\) | 698.884 | 0.0234962 | ||||||||
\(961\) | −28296.0 | −0.949819 | ||||||||
\(962\) | 217.368 | 0.00728505 | ||||||||
\(963\) | −35997.2 | −1.20456 | ||||||||
\(964\) | −32580.5 | −1.08853 | ||||||||
\(965\) | 16584.5 | 0.553238 | ||||||||
\(966\) | −5232.21 | −0.174269 | ||||||||
\(967\) | −26637.2 | −0.885828 | −0.442914 | − | 0.896564i | \(-0.646055\pi\) | ||||
−0.442914 | + | 0.896564i | \(0.646055\pi\) | |||||||
\(968\) | 2459.44 | 0.0816625 | ||||||||
\(969\) | −104.597 | −0.00346765 | ||||||||
\(970\) | 5852.90 | 0.193738 | ||||||||
\(971\) | −47474.8 | −1.56904 | −0.784520 | − | 0.620104i | \(-0.787090\pi\) | ||||
−0.784520 | + | 0.620104i | \(0.787090\pi\) | |||||||
\(972\) | −12148.8 | −0.400898 | ||||||||
\(973\) | −48838.3 | −1.60913 | ||||||||
\(974\) | −8468.28 | −0.278584 | ||||||||
\(975\) | 23.7303 | 0.000779466 0 | ||||||||
\(976\) | −3559.13 | −0.116727 | ||||||||
\(977\) | −1905.99 | −0.0624136 | −0.0312068 | − | 0.999513i | \(-0.509935\pi\) | ||||
−0.0312068 | + | 0.999513i | \(0.509935\pi\) | |||||||
\(978\) | −5723.78 | −0.187143 | ||||||||
\(979\) | −14002.9 | −0.457134 | ||||||||
\(980\) | −12020.2 | −0.391809 | ||||||||
\(981\) | −48075.2 | −1.56465 | ||||||||
\(982\) | 8499.63 | 0.276206 | ||||||||
\(983\) | 33336.4 | 1.08166 | 0.540828 | − | 0.841133i | \(-0.318111\pi\) | ||||
0.540828 | + | 0.841133i | \(0.318111\pi\) | |||||||
\(984\) | 2803.15 | 0.0908140 | ||||||||
\(985\) | 6756.56 | 0.218560 | ||||||||
\(986\) | 601.226 | 0.0194188 | ||||||||
\(987\) | 1135.09 | 0.0366063 | ||||||||
\(988\) | −105.481 | −0.00339657 | ||||||||
\(989\) | 49022.9 | 1.57617 | ||||||||
\(990\) | −2099.58 | −0.0674031 | ||||||||
\(991\) | −17080.5 | −0.547506 | −0.273753 | − | 0.961800i | \(-0.588265\pi\) | ||||
−0.273753 | + | 0.961800i | \(0.588265\pi\) | |||||||
\(992\) | −7247.31 | −0.231958 | ||||||||
\(993\) | −3566.51 | −0.113978 | ||||||||
\(994\) | 20662.7 | 0.659337 | ||||||||
\(995\) | 11615.3 | 0.370079 | ||||||||
\(996\) | −211.881 | −0.00674066 | ||||||||
\(997\) | 2113.88 | 0.0671486 | 0.0335743 | − | 0.999436i | \(-0.489311\pi\) | ||||
0.0335743 | + | 0.999436i | \(0.489311\pi\) | |||||||
\(998\) | 21748.5 | 0.689815 | ||||||||
\(999\) | 8255.17 | 0.261444 |
(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 | 1045.4.a.h.1.9 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.h.1.9 | ✓ | 24 | 1.1 | even | 1 | trivial |