Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.366256 | −0.211458 | −0.105729 | − | 0.994395i | \(-0.533718\pi\) | ||||
−0.105729 | + | 0.994395i | \(0.533718\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.145528 | 0.0650819 | 0.0325409 | − | 0.999470i | \(-0.489640\pi\) | ||||
0.0325409 | + | 0.999470i | \(0.489640\pi\) | |||||||
\(6\) | −0.366256 | −0.149523 | ||||||||
\(7\) | 3.13381 | 1.18447 | 0.592234 | − | 0.805766i | \(-0.298246\pi\) | ||||
0.592234 | + | 0.805766i | \(0.298246\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.86586 | −0.955286 | ||||||||
\(10\) | 0.145528 | 0.0460198 | ||||||||
\(11\) | −2.53978 | −0.765771 | −0.382886 | − | 0.923796i | \(-0.625070\pi\) | ||||
−0.382886 | + | 0.923796i | \(0.625070\pi\) | |||||||
\(12\) | −0.366256 | −0.105729 | ||||||||
\(13\) | −2.06766 | −0.573467 | −0.286733 | − | 0.958010i | \(-0.592569\pi\) | ||||
−0.286733 | + | 0.958010i | \(0.592569\pi\) | |||||||
\(14\) | 3.13381 | 0.837546 | ||||||||
\(15\) | −0.0533003 | −0.0137621 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.60540 | 1.11697 | 0.558487 | − | 0.829514i | \(-0.311382\pi\) | ||||
0.558487 | + | 0.829514i | \(0.311382\pi\) | |||||||
\(18\) | −2.86586 | −0.675489 | ||||||||
\(19\) | −6.21209 | −1.42515 | −0.712575 | − | 0.701596i | \(-0.752471\pi\) | ||||
−0.712575 | + | 0.701596i | \(0.752471\pi\) | |||||||
\(20\) | 0.145528 | 0.0325409 | ||||||||
\(21\) | −1.14778 | −0.250465 | ||||||||
\(22\) | −2.53978 | −0.541482 | ||||||||
\(23\) | −6.81602 | −1.42124 | −0.710619 | − | 0.703577i | \(-0.751585\pi\) | ||||
−0.710619 | + | 0.703577i | \(0.751585\pi\) | |||||||
\(24\) | −0.366256 | −0.0747616 | ||||||||
\(25\) | −4.97882 | −0.995764 | ||||||||
\(26\) | −2.06766 | −0.405502 | ||||||||
\(27\) | 2.14840 | 0.413460 | ||||||||
\(28\) | 3.13381 | 0.592234 | ||||||||
\(29\) | −4.38115 | −0.813560 | −0.406780 | − | 0.913526i | \(-0.633348\pi\) | ||||
−0.406780 | + | 0.913526i | \(0.633348\pi\) | |||||||
\(30\) | −0.0533003 | −0.00973126 | ||||||||
\(31\) | 1.20348 | 0.216152 | 0.108076 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108076 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.930208 | 0.161928 | ||||||||
\(34\) | 4.60540 | 0.789819 | ||||||||
\(35\) | 0.456055 | 0.0770874 | ||||||||
\(36\) | −2.86586 | −0.477643 | ||||||||
\(37\) | −2.43469 | −0.400261 | −0.200131 | − | 0.979769i | \(-0.564137\pi\) | ||||
−0.200131 | + | 0.979769i | \(0.564137\pi\) | |||||||
\(38\) | −6.21209 | −1.00773 | ||||||||
\(39\) | 0.757294 | 0.121264 | ||||||||
\(40\) | 0.145528 | 0.0230099 | ||||||||
\(41\) | 3.27639 | 0.511686 | 0.255843 | − | 0.966718i | \(-0.417647\pi\) | ||||
0.255843 | + | 0.966718i | \(0.417647\pi\) | |||||||
\(42\) | −1.14778 | −0.177106 | ||||||||
\(43\) | −4.27587 | −0.652064 | −0.326032 | − | 0.945359i | \(-0.605712\pi\) | ||||
−0.326032 | + | 0.945359i | \(0.605712\pi\) | |||||||
\(44\) | −2.53978 | −0.382886 | ||||||||
\(45\) | −0.417061 | −0.0621718 | ||||||||
\(46\) | −6.81602 | −1.00497 | ||||||||
\(47\) | 9.97631 | 1.45519 | 0.727597 | − | 0.686004i | \(-0.240637\pi\) | ||||
0.727597 | + | 0.686004i | \(0.240637\pi\) | |||||||
\(48\) | −0.366256 | −0.0528645 | ||||||||
\(49\) | 2.82076 | 0.402965 | ||||||||
\(50\) | −4.97882 | −0.704112 | ||||||||
\(51\) | −1.68675 | −0.236193 | ||||||||
\(52\) | −2.06766 | −0.286733 | ||||||||
\(53\) | −12.2965 | −1.68905 | −0.844527 | − | 0.535513i | \(-0.820118\pi\) | ||||
−0.844527 | + | 0.535513i | \(0.820118\pi\) | |||||||
\(54\) | 2.14840 | 0.292361 | ||||||||
\(55\) | −0.369607 | −0.0498378 | ||||||||
\(56\) | 3.13381 | 0.418773 | ||||||||
\(57\) | 2.27521 | 0.301359 | ||||||||
\(58\) | −4.38115 | −0.575273 | ||||||||
\(59\) | −9.09481 | −1.18404 | −0.592022 | − | 0.805922i | \(-0.701670\pi\) | ||||
−0.592022 | + | 0.805922i | \(0.701670\pi\) | |||||||
\(60\) | −0.0533003 | −0.00688104 | ||||||||
\(61\) | −12.0357 | −1.54102 | −0.770510 | − | 0.637428i | \(-0.779998\pi\) | ||||
−0.770510 | + | 0.637428i | \(0.779998\pi\) | |||||||
\(62\) | 1.20348 | 0.152842 | ||||||||
\(63\) | −8.98105 | −1.13151 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.300902 | −0.0373223 | ||||||||
\(66\) | 0.930208 | 0.114501 | ||||||||
\(67\) | −2.84168 | −0.347167 | −0.173583 | − | 0.984819i | \(-0.555535\pi\) | ||||
−0.173583 | + | 0.984819i | \(0.555535\pi\) | |||||||
\(68\) | 4.60540 | 0.558487 | ||||||||
\(69\) | 2.49641 | 0.300532 | ||||||||
\(70\) | 0.456055 | 0.0545091 | ||||||||
\(71\) | 10.2637 | 1.21808 | 0.609040 | − | 0.793139i | \(-0.291555\pi\) | ||||
0.609040 | + | 0.793139i | \(0.291555\pi\) | |||||||
\(72\) | −2.86586 | −0.337744 | ||||||||
\(73\) | 6.04280 | 0.707257 | 0.353628 | − | 0.935386i | \(-0.384948\pi\) | ||||
0.353628 | + | 0.935386i | \(0.384948\pi\) | |||||||
\(74\) | −2.43469 | −0.283027 | ||||||||
\(75\) | 1.82352 | 0.210562 | ||||||||
\(76\) | −6.21209 | −0.712575 | ||||||||
\(77\) | −7.95917 | −0.907032 | ||||||||
\(78\) | 0.757294 | 0.0857466 | ||||||||
\(79\) | −2.04976 | −0.230616 | −0.115308 | − | 0.993330i | \(-0.536786\pi\) | ||||
−0.115308 | + | 0.993330i | \(0.536786\pi\) | |||||||
\(80\) | 0.145528 | 0.0162705 | ||||||||
\(81\) | 7.81071 | 0.867856 | ||||||||
\(82\) | 3.27639 | 0.361817 | ||||||||
\(83\) | −4.46848 | −0.490479 | −0.245240 | − | 0.969462i | \(-0.578867\pi\) | ||||
−0.245240 | + | 0.969462i | \(0.578867\pi\) | |||||||
\(84\) | −1.14778 | −0.125233 | ||||||||
\(85\) | 0.670212 | 0.0726947 | ||||||||
\(86\) | −4.27587 | −0.461079 | ||||||||
\(87\) | 1.60462 | 0.172034 | ||||||||
\(88\) | −2.53978 | −0.270741 | ||||||||
\(89\) | −2.54236 | −0.269489 | −0.134745 | − | 0.990880i | \(-0.543021\pi\) | ||||
−0.134745 | + | 0.990880i | \(0.543021\pi\) | |||||||
\(90\) | −0.417061 | −0.0439621 | ||||||||
\(91\) | −6.47966 | −0.679253 | ||||||||
\(92\) | −6.81602 | −0.710619 | ||||||||
\(93\) | −0.440782 | −0.0457070 | ||||||||
\(94\) | 9.97631 | 1.02898 | ||||||||
\(95\) | −0.904029 | −0.0927515 | ||||||||
\(96\) | −0.366256 | −0.0373808 | ||||||||
\(97\) | 16.3159 | 1.65663 | 0.828315 | − | 0.560262i | \(-0.189300\pi\) | ||||
0.828315 | + | 0.560262i | \(0.189300\pi\) | |||||||
\(98\) | 2.82076 | 0.284940 | ||||||||
\(99\) | 7.27863 | 0.731530 | ||||||||
\(100\) | −4.97882 | −0.497882 | ||||||||
\(101\) | −8.64376 | −0.860086 | −0.430043 | − | 0.902808i | \(-0.641502\pi\) | ||||
−0.430043 | + | 0.902808i | \(0.641502\pi\) | |||||||
\(102\) | −1.68675 | −0.167013 | ||||||||
\(103\) | 14.8501 | 1.46323 | 0.731613 | − | 0.681720i | \(-0.238768\pi\) | ||||
0.731613 | + | 0.681720i | \(0.238768\pi\) | |||||||
\(104\) | −2.06766 | −0.202751 | ||||||||
\(105\) | −0.167033 | −0.0163007 | ||||||||
\(106\) | −12.2965 | −1.19434 | ||||||||
\(107\) | −14.4849 | −1.40031 | −0.700154 | − | 0.713992i | \(-0.746885\pi\) | ||||
−0.700154 | + | 0.713992i | \(0.746885\pi\) | |||||||
\(108\) | 2.14840 | 0.206730 | ||||||||
\(109\) | 19.2878 | 1.84744 | 0.923720 | − | 0.383068i | \(-0.125132\pi\) | ||||
0.923720 | + | 0.383068i | \(0.125132\pi\) | |||||||
\(110\) | −0.369607 | −0.0352407 | ||||||||
\(111\) | 0.891721 | 0.0846384 | ||||||||
\(112\) | 3.13381 | 0.296117 | ||||||||
\(113\) | 2.43644 | 0.229201 | 0.114600 | − | 0.993412i | \(-0.463441\pi\) | ||||
0.114600 | + | 0.993412i | \(0.463441\pi\) | |||||||
\(114\) | 2.27521 | 0.213093 | ||||||||
\(115\) | −0.991919 | −0.0924969 | ||||||||
\(116\) | −4.38115 | −0.406780 | ||||||||
\(117\) | 5.92563 | 0.547824 | ||||||||
\(118\) | −9.09481 | −0.837245 | ||||||||
\(119\) | 14.4324 | 1.32302 | ||||||||
\(120\) | −0.0533003 | −0.00486563 | ||||||||
\(121\) | −4.54954 | −0.413594 | ||||||||
\(122\) | −12.0357 | −1.08967 | ||||||||
\(123\) | −1.20000 | −0.108200 | ||||||||
\(124\) | 1.20348 | 0.108076 | ||||||||
\(125\) | −1.45219 | −0.129888 | ||||||||
\(126\) | −8.98105 | −0.800095 | ||||||||
\(127\) | 1.39622 | 0.123894 | 0.0619471 | − | 0.998079i | \(-0.480269\pi\) | ||||
0.0619471 | + | 0.998079i | \(0.480269\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.56606 | 0.137884 | ||||||||
\(130\) | −0.300902 | −0.0263908 | ||||||||
\(131\) | −8.88147 | −0.775978 | −0.387989 | − | 0.921664i | \(-0.626830\pi\) | ||||
−0.387989 | + | 0.921664i | \(0.626830\pi\) | |||||||
\(132\) | 0.930208 | 0.0809642 | ||||||||
\(133\) | −19.4675 | −1.68805 | ||||||||
\(134\) | −2.84168 | −0.245484 | ||||||||
\(135\) | 0.312652 | 0.0269088 | ||||||||
\(136\) | 4.60540 | 0.394910 | ||||||||
\(137\) | 0.731194 | 0.0624701 | 0.0312351 | − | 0.999512i | \(-0.490056\pi\) | ||||
0.0312351 | + | 0.999512i | \(0.490056\pi\) | |||||||
\(138\) | 2.49641 | 0.212508 | ||||||||
\(139\) | 9.69652 | 0.822448 | 0.411224 | − | 0.911534i | \(-0.365101\pi\) | ||||
0.411224 | + | 0.911534i | \(0.365101\pi\) | |||||||
\(140\) | 0.456055 | 0.0385437 | ||||||||
\(141\) | −3.65388 | −0.307712 | ||||||||
\(142\) | 10.2637 | 0.861313 | ||||||||
\(143\) | 5.25140 | 0.439144 | ||||||||
\(144\) | −2.86586 | −0.238821 | ||||||||
\(145\) | −0.637578 | −0.0529480 | ||||||||
\(146\) | 6.04280 | 0.500106 | ||||||||
\(147\) | −1.03312 | −0.0852102 | ||||||||
\(148\) | −2.43469 | −0.200131 | ||||||||
\(149\) | 10.3327 | 0.846486 | 0.423243 | − | 0.906016i | \(-0.360892\pi\) | ||||
0.423243 | + | 0.906016i | \(0.360892\pi\) | |||||||
\(150\) | 1.82352 | 0.148890 | ||||||||
\(151\) | −10.8539 | −0.883281 | −0.441640 | − | 0.897192i | \(-0.645603\pi\) | ||||
−0.441640 | + | 0.897192i | \(0.645603\pi\) | |||||||
\(152\) | −6.21209 | −0.503867 | ||||||||
\(153\) | −13.1984 | −1.06703 | ||||||||
\(154\) | −7.95917 | −0.641368 | ||||||||
\(155\) | 0.175140 | 0.0140676 | ||||||||
\(156\) | 0.757294 | 0.0606320 | ||||||||
\(157\) | −17.7596 | −1.41737 | −0.708685 | − | 0.705525i | \(-0.750711\pi\) | ||||
−0.708685 | + | 0.705525i | \(0.750711\pi\) | |||||||
\(158\) | −2.04976 | −0.163070 | ||||||||
\(159\) | 4.50366 | 0.357164 | ||||||||
\(160\) | 0.145528 | 0.0115050 | ||||||||
\(161\) | −21.3601 | −1.68341 | ||||||||
\(162\) | 7.81071 | 0.613667 | ||||||||
\(163\) | −24.9541 | −1.95456 | −0.977280 | − | 0.211954i | \(-0.932017\pi\) | ||||
−0.977280 | + | 0.211954i | \(0.932017\pi\) | |||||||
\(164\) | 3.27639 | 0.255843 | ||||||||
\(165\) | 0.135371 | 0.0105386 | ||||||||
\(166\) | −4.46848 | −0.346821 | ||||||||
\(167\) | 8.04828 | 0.622795 | 0.311397 | − | 0.950280i | \(-0.399203\pi\) | ||||
0.311397 | + | 0.950280i | \(0.399203\pi\) | |||||||
\(168\) | −1.14778 | −0.0885528 | ||||||||
\(169\) | −8.72477 | −0.671136 | ||||||||
\(170\) | 0.670212 | 0.0514029 | ||||||||
\(171\) | 17.8029 | 1.36143 | ||||||||
\(172\) | −4.27587 | −0.326032 | ||||||||
\(173\) | 24.5022 | 1.86287 | 0.931433 | − | 0.363914i | \(-0.118560\pi\) | ||||
0.931433 | + | 0.363914i | \(0.118560\pi\) | |||||||
\(174\) | 1.60462 | 0.121646 | ||||||||
\(175\) | −15.6027 | −1.17945 | ||||||||
\(176\) | −2.53978 | −0.191443 | ||||||||
\(177\) | 3.33103 | 0.250375 | ||||||||
\(178\) | −2.54236 | −0.190558 | ||||||||
\(179\) | 9.70775 | 0.725591 | 0.362795 | − | 0.931869i | \(-0.381822\pi\) | ||||
0.362795 | + | 0.931869i | \(0.381822\pi\) | |||||||
\(180\) | −0.417061 | −0.0310859 | ||||||||
\(181\) | −0.414124 | −0.0307816 | −0.0153908 | − | 0.999882i | \(-0.504899\pi\) | ||||
−0.0153908 | + | 0.999882i | \(0.504899\pi\) | |||||||
\(182\) | −6.47966 | −0.480304 | ||||||||
\(183\) | 4.40816 | 0.325861 | ||||||||
\(184\) | −6.81602 | −0.502484 | ||||||||
\(185\) | −0.354315 | −0.0260498 | ||||||||
\(186\) | −0.440782 | −0.0323197 | ||||||||
\(187\) | −11.6967 | −0.855346 | ||||||||
\(188\) | 9.97631 | 0.727597 | ||||||||
\(189\) | 6.73269 | 0.489731 | ||||||||
\(190\) | −0.904029 | −0.0655852 | ||||||||
\(191\) | −23.9950 | −1.73622 | −0.868110 | − | 0.496372i | \(-0.834665\pi\) | ||||
−0.868110 | + | 0.496372i | \(0.834665\pi\) | |||||||
\(192\) | −0.366256 | −0.0264322 | ||||||||
\(193\) | −10.9892 | −0.791021 | −0.395510 | − | 0.918461i | \(-0.629432\pi\) | ||||
−0.395510 | + | 0.918461i | \(0.629432\pi\) | |||||||
\(194\) | 16.3159 | 1.17141 | ||||||||
\(195\) | 0.110207 | 0.00789209 | ||||||||
\(196\) | 2.82076 | 0.201483 | ||||||||
\(197\) | −22.9589 | −1.63576 | −0.817878 | − | 0.575392i | \(-0.804850\pi\) | ||||
−0.817878 | + | 0.575392i | \(0.804850\pi\) | |||||||
\(198\) | 7.27863 | 0.517270 | ||||||||
\(199\) | 8.57194 | 0.607649 | 0.303824 | − | 0.952728i | \(-0.401736\pi\) | ||||
0.303824 | + | 0.952728i | \(0.401736\pi\) | |||||||
\(200\) | −4.97882 | −0.352056 | ||||||||
\(201\) | 1.04078 | 0.0734111 | ||||||||
\(202\) | −8.64376 | −0.608173 | ||||||||
\(203\) | −13.7297 | −0.963636 | ||||||||
\(204\) | −1.68675 | −0.118096 | ||||||||
\(205\) | 0.476805 | 0.0333015 | ||||||||
\(206\) | 14.8501 | 1.03466 | ||||||||
\(207\) | 19.5337 | 1.35769 | ||||||||
\(208\) | −2.06766 | −0.143367 | ||||||||
\(209\) | 15.7773 | 1.09134 | ||||||||
\(210\) | −0.167033 | −0.0115264 | ||||||||
\(211\) | 9.10006 | 0.626474 | 0.313237 | − | 0.949675i | \(-0.398587\pi\) | ||||
0.313237 | + | 0.949675i | \(0.398587\pi\) | |||||||
\(212\) | −12.2965 | −0.844527 | ||||||||
\(213\) | −3.75915 | −0.257573 | ||||||||
\(214\) | −14.4849 | −0.990167 | ||||||||
\(215\) | −0.622256 | −0.0424375 | ||||||||
\(216\) | 2.14840 | 0.146180 | ||||||||
\(217\) | 3.77148 | 0.256025 | ||||||||
\(218\) | 19.2878 | 1.30634 | ||||||||
\(219\) | −2.21321 | −0.149555 | ||||||||
\(220\) | −0.369607 | −0.0249189 | ||||||||
\(221\) | −9.52241 | −0.640547 | ||||||||
\(222\) | 0.891721 | 0.0598484 | ||||||||
\(223\) | 7.41982 | 0.496868 | 0.248434 | − | 0.968649i | \(-0.420084\pi\) | ||||
0.248434 | + | 0.968649i | \(0.420084\pi\) | |||||||
\(224\) | 3.13381 | 0.209386 | ||||||||
\(225\) | 14.2686 | 0.951239 | ||||||||
\(226\) | 2.43644 | 0.162069 | ||||||||
\(227\) | −1.27244 | −0.0844550 | −0.0422275 | − | 0.999108i | \(-0.513445\pi\) | ||||
−0.0422275 | + | 0.999108i | \(0.513445\pi\) | |||||||
\(228\) | 2.27521 | 0.150680 | ||||||||
\(229\) | −11.0765 | −0.731957 | −0.365978 | − | 0.930623i | \(-0.619266\pi\) | ||||
−0.365978 | + | 0.930623i | \(0.619266\pi\) | |||||||
\(230\) | −0.991919 | −0.0654052 | ||||||||
\(231\) | 2.91509 | 0.191799 | ||||||||
\(232\) | −4.38115 | −0.287637 | ||||||||
\(233\) | 4.85323 | 0.317946 | 0.158973 | − | 0.987283i | \(-0.449182\pi\) | ||||
0.158973 | + | 0.987283i | \(0.449182\pi\) | |||||||
\(234\) | 5.92563 | 0.387370 | ||||||||
\(235\) | 1.45183 | 0.0947068 | ||||||||
\(236\) | −9.09481 | −0.592022 | ||||||||
\(237\) | 0.750737 | 0.0487656 | ||||||||
\(238\) | 14.4324 | 0.935516 | ||||||||
\(239\) | 7.33698 | 0.474590 | 0.237295 | − | 0.971438i | \(-0.423739\pi\) | ||||
0.237295 | + | 0.971438i | \(0.423739\pi\) | |||||||
\(240\) | −0.0533003 | −0.00344052 | ||||||||
\(241\) | 8.26943 | 0.532681 | 0.266340 | − | 0.963879i | \(-0.414185\pi\) | ||||
0.266340 | + | 0.963879i | \(0.414185\pi\) | |||||||
\(242\) | −4.54954 | −0.292455 | ||||||||
\(243\) | −9.30593 | −0.596975 | ||||||||
\(244\) | −12.0357 | −0.770510 | ||||||||
\(245\) | 0.410498 | 0.0262258 | ||||||||
\(246\) | −1.20000 | −0.0765090 | ||||||||
\(247\) | 12.8445 | 0.817276 | ||||||||
\(248\) | 1.20348 | 0.0764212 | ||||||||
\(249\) | 1.63661 | 0.103716 | ||||||||
\(250\) | −1.45219 | −0.0918448 | ||||||||
\(251\) | 17.8436 | 1.12628 | 0.563138 | − | 0.826363i | \(-0.309594\pi\) | ||||
0.563138 | + | 0.826363i | \(0.309594\pi\) | |||||||
\(252\) | −8.98105 | −0.565753 | ||||||||
\(253\) | 17.3112 | 1.08834 | ||||||||
\(254\) | 1.39622 | 0.0876065 | ||||||||
\(255\) | −0.245469 | −0.0153719 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −1.53187 | −0.0955552 | −0.0477776 | − | 0.998858i | \(-0.515214\pi\) | ||||
−0.0477776 | + | 0.998858i | \(0.515214\pi\) | |||||||
\(258\) | 1.56606 | 0.0974987 | ||||||||
\(259\) | −7.62987 | −0.474097 | ||||||||
\(260\) | −0.300902 | −0.0186611 | ||||||||
\(261\) | 12.5558 | 0.777182 | ||||||||
\(262\) | −8.88147 | −0.548699 | ||||||||
\(263\) | −26.3877 | −1.62714 | −0.813568 | − | 0.581470i | \(-0.802478\pi\) | ||||
−0.813568 | + | 0.581470i | \(0.802478\pi\) | |||||||
\(264\) | 0.930208 | 0.0572503 | ||||||||
\(265\) | −1.78948 | −0.109927 | ||||||||
\(266\) | −19.4675 | −1.19363 | ||||||||
\(267\) | 0.931153 | 0.0569857 | ||||||||
\(268\) | −2.84168 | −0.173583 | ||||||||
\(269\) | −7.79866 | −0.475493 | −0.237746 | − | 0.971327i | \(-0.576409\pi\) | ||||
−0.237746 | + | 0.971327i | \(0.576409\pi\) | |||||||
\(270\) | 0.312652 | 0.0190274 | ||||||||
\(271\) | −3.63476 | −0.220796 | −0.110398 | − | 0.993887i | \(-0.535213\pi\) | ||||
−0.110398 | + | 0.993887i | \(0.535213\pi\) | |||||||
\(272\) | 4.60540 | 0.279243 | ||||||||
\(273\) | 2.37321 | 0.143633 | ||||||||
\(274\) | 0.731194 | 0.0441730 | ||||||||
\(275\) | 12.6451 | 0.762528 | ||||||||
\(276\) | 2.49641 | 0.150266 | ||||||||
\(277\) | 12.5130 | 0.751832 | 0.375916 | − | 0.926654i | \(-0.377328\pi\) | ||||
0.375916 | + | 0.926654i | \(0.377328\pi\) | |||||||
\(278\) | 9.69652 | 0.581559 | ||||||||
\(279\) | −3.44901 | −0.206487 | ||||||||
\(280\) | 0.456055 | 0.0272545 | ||||||||
\(281\) | −5.90991 | −0.352556 | −0.176278 | − | 0.984340i | \(-0.556406\pi\) | ||||
−0.176278 | + | 0.984340i | \(0.556406\pi\) | |||||||
\(282\) | −3.65388 | −0.217585 | ||||||||
\(283\) | −7.92713 | −0.471219 | −0.235610 | − | 0.971848i | \(-0.575709\pi\) | ||||
−0.235610 | + | 0.971848i | \(0.575709\pi\) | |||||||
\(284\) | 10.2637 | 0.609040 | ||||||||
\(285\) | 0.331106 | 0.0196130 | ||||||||
\(286\) | 5.25140 | 0.310522 | ||||||||
\(287\) | 10.2676 | 0.606076 | ||||||||
\(288\) | −2.86586 | −0.168872 | ||||||||
\(289\) | 4.20969 | 0.247629 | ||||||||
\(290\) | −0.637578 | −0.0374399 | ||||||||
\(291\) | −5.97580 | −0.350308 | ||||||||
\(292\) | 6.04280 | 0.353628 | ||||||||
\(293\) | 3.87756 | 0.226529 | 0.113265 | − | 0.993565i | \(-0.463869\pi\) | ||||
0.113265 | + | 0.993565i | \(0.463869\pi\) | |||||||
\(294\) | −1.03312 | −0.0602527 | ||||||||
\(295\) | −1.32354 | −0.0770598 | ||||||||
\(296\) | −2.43469 | −0.141514 | ||||||||
\(297\) | −5.45646 | −0.316616 | ||||||||
\(298\) | 10.3327 | 0.598556 | ||||||||
\(299\) | 14.0932 | 0.815033 | ||||||||
\(300\) | 1.82352 | 0.105281 | ||||||||
\(301\) | −13.3998 | −0.772349 | ||||||||
\(302\) | −10.8539 | −0.624574 | ||||||||
\(303\) | 3.16583 | 0.181872 | ||||||||
\(304\) | −6.21209 | −0.356288 | ||||||||
\(305\) | −1.75153 | −0.100292 | ||||||||
\(306\) | −13.1984 | −0.754503 | ||||||||
\(307\) | 0.0374509 | 0.00213744 | 0.00106872 | − | 0.999999i | \(-0.499660\pi\) | ||||
0.00106872 | + | 0.999999i | \(0.499660\pi\) | |||||||
\(308\) | −7.95917 | −0.453516 | ||||||||
\(309\) | −5.43894 | −0.309411 | ||||||||
\(310\) | 0.175140 | 0.00994727 | ||||||||
\(311\) | −6.10882 | −0.346399 | −0.173200 | − | 0.984887i | \(-0.555411\pi\) | ||||
−0.173200 | + | 0.984887i | \(0.555411\pi\) | |||||||
\(312\) | 0.757294 | 0.0428733 | ||||||||
\(313\) | −22.3535 | −1.26349 | −0.631747 | − | 0.775174i | \(-0.717662\pi\) | ||||
−0.631747 | + | 0.775174i | \(0.717662\pi\) | |||||||
\(314\) | −17.7596 | −1.00223 | ||||||||
\(315\) | −1.30699 | −0.0736405 | ||||||||
\(316\) | −2.04976 | −0.115308 | ||||||||
\(317\) | 18.5695 | 1.04297 | 0.521484 | − | 0.853261i | \(-0.325379\pi\) | ||||
0.521484 | + | 0.853261i | \(0.325379\pi\) | |||||||
\(318\) | 4.50366 | 0.252553 | ||||||||
\(319\) | 11.1271 | 0.623001 | ||||||||
\(320\) | 0.145528 | 0.00813524 | ||||||||
\(321\) | 5.30517 | 0.296106 | ||||||||
\(322\) | −21.3601 | −1.19035 | ||||||||
\(323\) | −28.6091 | −1.59185 | ||||||||
\(324\) | 7.81071 | 0.433928 | ||||||||
\(325\) | 10.2945 | 0.571038 | ||||||||
\(326\) | −24.9541 | −1.38208 | ||||||||
\(327\) | −7.06428 | −0.390656 | ||||||||
\(328\) | 3.27639 | 0.180908 | ||||||||
\(329\) | 31.2639 | 1.72363 | ||||||||
\(330\) | 0.135371 | 0.00745192 | ||||||||
\(331\) | 10.4416 | 0.573923 | 0.286961 | − | 0.957942i | \(-0.407355\pi\) | ||||
0.286961 | + | 0.957942i | \(0.407355\pi\) | |||||||
\(332\) | −4.46848 | −0.245240 | ||||||||
\(333\) | 6.97748 | 0.382364 | ||||||||
\(334\) | 8.04828 | 0.440382 | ||||||||
\(335\) | −0.413543 | −0.0225943 | ||||||||
\(336\) | −1.14778 | −0.0626163 | ||||||||
\(337\) | 0.466859 | 0.0254314 | 0.0127157 | − | 0.999919i | \(-0.495952\pi\) | ||||
0.0127157 | + | 0.999919i | \(0.495952\pi\) | |||||||
\(338\) | −8.72477 | −0.474565 | ||||||||
\(339\) | −0.892358 | −0.0484663 | ||||||||
\(340\) | 0.670212 | 0.0363474 | ||||||||
\(341\) | −3.05657 | −0.165523 | ||||||||
\(342\) | 17.8029 | 0.962673 | ||||||||
\(343\) | −13.0969 | −0.707169 | ||||||||
\(344\) | −4.27587 | −0.230539 | ||||||||
\(345\) | 0.363296 | 0.0195592 | ||||||||
\(346\) | 24.5022 | 1.31724 | ||||||||
\(347\) | 22.9790 | 1.23358 | 0.616790 | − | 0.787128i | \(-0.288433\pi\) | ||||
0.616790 | + | 0.787128i | \(0.288433\pi\) | |||||||
\(348\) | 1.60462 | 0.0860168 | ||||||||
\(349\) | 13.9854 | 0.748619 | 0.374310 | − | 0.927304i | \(-0.377880\pi\) | ||||
0.374310 | + | 0.927304i | \(0.377880\pi\) | |||||||
\(350\) | −15.6027 | −0.833998 | ||||||||
\(351\) | −4.44218 | −0.237106 | ||||||||
\(352\) | −2.53978 | −0.135371 | ||||||||
\(353\) | 7.83916 | 0.417237 | 0.208618 | − | 0.977997i | \(-0.433103\pi\) | ||||
0.208618 | + | 0.977997i | \(0.433103\pi\) | |||||||
\(354\) | 3.33103 | 0.177042 | ||||||||
\(355\) | 1.49365 | 0.0792750 | ||||||||
\(356\) | −2.54236 | −0.134745 | ||||||||
\(357\) | −5.28596 | −0.279763 | ||||||||
\(358\) | 9.70775 | 0.513070 | ||||||||
\(359\) | 0.0947581 | 0.00500114 | 0.00250057 | − | 0.999997i | \(-0.499204\pi\) | ||||
0.00250057 | + | 0.999997i | \(0.499204\pi\) | |||||||
\(360\) | −0.417061 | −0.0219810 | ||||||||
\(361\) | 19.5900 | 1.03105 | ||||||||
\(362\) | −0.414124 | −0.0217659 | ||||||||
\(363\) | 1.66629 | 0.0874578 | ||||||||
\(364\) | −6.47966 | −0.339627 | ||||||||
\(365\) | 0.879394 | 0.0460296 | ||||||||
\(366\) | 4.40816 | 0.230418 | ||||||||
\(367\) | −17.6038 | −0.918911 | −0.459456 | − | 0.888201i | \(-0.651955\pi\) | ||||
−0.459456 | + | 0.888201i | \(0.651955\pi\) | |||||||
\(368\) | −6.81602 | −0.355310 | ||||||||
\(369\) | −9.38966 | −0.488806 | ||||||||
\(370\) | −0.354315 | −0.0184200 | ||||||||
\(371\) | −38.5349 | −2.00063 | ||||||||
\(372\) | −0.440782 | −0.0228535 | ||||||||
\(373\) | −20.5251 | −1.06275 | −0.531376 | − | 0.847136i | \(-0.678325\pi\) | ||||
−0.531376 | + | 0.847136i | \(0.678325\pi\) | |||||||
\(374\) | −11.6967 | −0.604821 | ||||||||
\(375\) | 0.531874 | 0.0274659 | ||||||||
\(376\) | 9.97631 | 0.514489 | ||||||||
\(377\) | 9.05875 | 0.466549 | ||||||||
\(378\) | 6.73269 | 0.346292 | ||||||||
\(379\) | −0.641769 | −0.0329655 | −0.0164827 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164827 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(380\) | −0.904029 | −0.0463757 | ||||||||
\(381\) | −0.511373 | −0.0261984 | ||||||||
\(382\) | −23.9950 | −1.22769 | ||||||||
\(383\) | −35.4842 | −1.81316 | −0.906580 | − | 0.422034i | \(-0.861316\pi\) | ||||
−0.906580 | + | 0.422034i | \(0.861316\pi\) | |||||||
\(384\) | −0.366256 | −0.0186904 | ||||||||
\(385\) | −1.15828 | −0.0590314 | ||||||||
\(386\) | −10.9892 | −0.559336 | ||||||||
\(387\) | 12.2540 | 0.622907 | ||||||||
\(388\) | 16.3159 | 0.828315 | ||||||||
\(389\) | −28.2847 | −1.43409 | −0.717046 | − | 0.697025i | \(-0.754506\pi\) | ||||
−0.717046 | + | 0.697025i | \(0.754506\pi\) | |||||||
\(390\) | 0.110207 | 0.00558055 | ||||||||
\(391\) | −31.3905 | −1.58749 | ||||||||
\(392\) | 2.82076 | 0.142470 | ||||||||
\(393\) | 3.25289 | 0.164087 | ||||||||
\(394\) | −22.9589 | −1.15665 | ||||||||
\(395\) | −0.298297 | −0.0150089 | ||||||||
\(396\) | 7.27863 | 0.365765 | ||||||||
\(397\) | −14.8003 | −0.742808 | −0.371404 | − | 0.928471i | \(-0.621124\pi\) | ||||
−0.371404 | + | 0.928471i | \(0.621124\pi\) | |||||||
\(398\) | 8.57194 | 0.429673 | ||||||||
\(399\) | 7.13008 | 0.356950 | ||||||||
\(400\) | −4.97882 | −0.248941 | ||||||||
\(401\) | 3.97515 | 0.198509 | 0.0992547 | − | 0.995062i | \(-0.468354\pi\) | ||||
0.0992547 | + | 0.995062i | \(0.468354\pi\) | |||||||
\(402\) | 1.04078 | 0.0519095 | ||||||||
\(403\) | −2.48839 | −0.123956 | ||||||||
\(404\) | −8.64376 | −0.430043 | ||||||||
\(405\) | 1.13667 | 0.0564817 | ||||||||
\(406\) | −13.7297 | −0.681393 | ||||||||
\(407\) | 6.18358 | 0.306509 | ||||||||
\(408\) | −1.68675 | −0.0835067 | ||||||||
\(409\) | −13.7296 | −0.678883 | −0.339442 | − | 0.940627i | \(-0.610238\pi\) | ||||
−0.339442 | + | 0.940627i | \(0.610238\pi\) | |||||||
\(410\) | 0.476805 | 0.0235477 | ||||||||
\(411\) | −0.267804 | −0.0132098 | ||||||||
\(412\) | 14.8501 | 0.731613 | ||||||||
\(413\) | −28.5014 | −1.40246 | ||||||||
\(414\) | 19.5337 | 0.960031 | ||||||||
\(415\) | −0.650287 | −0.0319213 | ||||||||
\(416\) | −2.06766 | −0.101376 | ||||||||
\(417\) | −3.55141 | −0.173913 | ||||||||
\(418\) | 15.7773 | 0.771693 | ||||||||
\(419\) | 30.7099 | 1.50028 | 0.750138 | − | 0.661281i | \(-0.229987\pi\) | ||||
0.750138 | + | 0.661281i | \(0.229987\pi\) | |||||||
\(420\) | −0.167033 | −0.00815037 | ||||||||
\(421\) | −7.56377 | −0.368635 | −0.184318 | − | 0.982867i | \(-0.559008\pi\) | ||||
−0.184318 | + | 0.982867i | \(0.559008\pi\) | |||||||
\(422\) | 9.10006 | 0.442984 | ||||||||
\(423\) | −28.5907 | −1.39013 | ||||||||
\(424\) | −12.2965 | −0.597171 | ||||||||
\(425\) | −22.9295 | −1.11224 | ||||||||
\(426\) | −3.75915 | −0.182131 | ||||||||
\(427\) | −37.7177 | −1.82529 | ||||||||
\(428\) | −14.4849 | −0.700154 | ||||||||
\(429\) | −1.92336 | −0.0928605 | ||||||||
\(430\) | −0.622256 | −0.0300079 | ||||||||
\(431\) | 17.9161 | 0.862989 | 0.431495 | − | 0.902115i | \(-0.357986\pi\) | ||||
0.431495 | + | 0.902115i | \(0.357986\pi\) | |||||||
\(432\) | 2.14840 | 0.103365 | ||||||||
\(433\) | −10.3180 | −0.495853 | −0.247927 | − | 0.968779i | \(-0.579749\pi\) | ||||
−0.247927 | + | 0.968779i | \(0.579749\pi\) | |||||||
\(434\) | 3.77148 | 0.181037 | ||||||||
\(435\) | 0.233517 | 0.0111963 | ||||||||
\(436\) | 19.2878 | 0.923720 | ||||||||
\(437\) | 42.3417 | 2.02548 | ||||||||
\(438\) | −2.21321 | −0.105751 | ||||||||
\(439\) | 21.4870 | 1.02552 | 0.512760 | − | 0.858532i | \(-0.328623\pi\) | ||||
0.512760 | + | 0.858532i | \(0.328623\pi\) | |||||||
\(440\) | −0.369607 | −0.0176203 | ||||||||
\(441\) | −8.08389 | −0.384947 | ||||||||
\(442\) | −9.52241 | −0.452935 | ||||||||
\(443\) | 19.8834 | 0.944691 | 0.472345 | − | 0.881414i | \(-0.343407\pi\) | ||||
0.472345 | + | 0.881414i | \(0.343407\pi\) | |||||||
\(444\) | 0.891721 | 0.0423192 | ||||||||
\(445\) | −0.369983 | −0.0175389 | ||||||||
\(446\) | 7.41982 | 0.351339 | ||||||||
\(447\) | −3.78440 | −0.178996 | ||||||||
\(448\) | 3.13381 | 0.148059 | ||||||||
\(449\) | 8.72808 | 0.411903 | 0.205952 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205952 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(450\) | 14.2686 | 0.672628 | ||||||||
\(451\) | −8.32130 | −0.391835 | ||||||||
\(452\) | 2.43644 | 0.114600 | ||||||||
\(453\) | 3.97532 | 0.186777 | ||||||||
\(454\) | −1.27244 | −0.0597187 | ||||||||
\(455\) | −0.942969 | −0.0442071 | ||||||||
\(456\) | 2.27521 | 0.106547 | ||||||||
\(457\) | −34.1222 | −1.59617 | −0.798084 | − | 0.602547i | \(-0.794153\pi\) | ||||
−0.798084 | + | 0.602547i | \(0.794153\pi\) | |||||||
\(458\) | −11.0765 | −0.517572 | ||||||||
\(459\) | 9.89425 | 0.461824 | ||||||||
\(460\) | −0.991919 | −0.0462485 | ||||||||
\(461\) | 31.1089 | 1.44888 | 0.724442 | − | 0.689335i | \(-0.242097\pi\) | ||||
0.724442 | + | 0.689335i | \(0.242097\pi\) | |||||||
\(462\) | 2.91509 | 0.135622 | ||||||||
\(463\) | −21.6416 | −1.00577 | −0.502885 | − | 0.864353i | \(-0.667728\pi\) | ||||
−0.502885 | + | 0.864353i | \(0.667728\pi\) | |||||||
\(464\) | −4.38115 | −0.203390 | ||||||||
\(465\) | −0.0641459 | −0.00297470 | ||||||||
\(466\) | 4.85323 | 0.224821 | ||||||||
\(467\) | 36.4205 | 1.68534 | 0.842671 | − | 0.538429i | \(-0.180982\pi\) | ||||
0.842671 | + | 0.538429i | \(0.180982\pi\) | |||||||
\(468\) | 5.92563 | 0.273912 | ||||||||
\(469\) | −8.90529 | −0.411208 | ||||||||
\(470\) | 1.45183 | 0.0669678 | ||||||||
\(471\) | 6.50455 | 0.299714 | ||||||||
\(472\) | −9.09481 | −0.418622 | ||||||||
\(473\) | 10.8597 | 0.499332 | ||||||||
\(474\) | 0.750737 | 0.0344825 | ||||||||
\(475\) | 30.9289 | 1.41911 | ||||||||
\(476\) | 14.4324 | 0.661510 | ||||||||
\(477\) | 35.2400 | 1.61353 | ||||||||
\(478\) | 7.33698 | 0.335586 | ||||||||
\(479\) | −15.4475 | −0.705814 | −0.352907 | − | 0.935658i | \(-0.614807\pi\) | ||||
−0.352907 | + | 0.935658i | \(0.614807\pi\) | |||||||
\(480\) | −0.0533003 | −0.00243281 | ||||||||
\(481\) | 5.03413 | 0.229536 | ||||||||
\(482\) | 8.26943 | 0.376662 | ||||||||
\(483\) | 7.82326 | 0.355971 | ||||||||
\(484\) | −4.54954 | −0.206797 | ||||||||
\(485\) | 2.37441 | 0.107817 | ||||||||
\(486\) | −9.30593 | −0.422125 | ||||||||
\(487\) | −2.56916 | −0.116420 | −0.0582098 | − | 0.998304i | \(-0.518539\pi\) | ||||
−0.0582098 | + | 0.998304i | \(0.518539\pi\) | |||||||
\(488\) | −12.0357 | −0.544833 | ||||||||
\(489\) | 9.13960 | 0.413307 | ||||||||
\(490\) | 0.410498 | 0.0185444 | ||||||||
\(491\) | 29.1338 | 1.31479 | 0.657394 | − | 0.753547i | \(-0.271659\pi\) | ||||
0.657394 | + | 0.753547i | \(0.271659\pi\) | |||||||
\(492\) | −1.20000 | −0.0541000 | ||||||||
\(493\) | −20.1769 | −0.908724 | ||||||||
\(494\) | 12.8445 | 0.577901 | ||||||||
\(495\) | 1.05924 | 0.0476094 | ||||||||
\(496\) | 1.20348 | 0.0540379 | ||||||||
\(497\) | 32.1646 | 1.44278 | ||||||||
\(498\) | 1.63661 | 0.0733381 | ||||||||
\(499\) | 3.87695 | 0.173556 | 0.0867781 | − | 0.996228i | \(-0.472343\pi\) | ||||
0.0867781 | + | 0.996228i | \(0.472343\pi\) | |||||||
\(500\) | −1.45219 | −0.0649441 | ||||||||
\(501\) | −2.94773 | −0.131695 | ||||||||
\(502\) | 17.8436 | 0.796397 | ||||||||
\(503\) | 26.0304 | 1.16064 | 0.580318 | − | 0.814390i | \(-0.302928\pi\) | ||||
0.580318 | + | 0.814390i | \(0.302928\pi\) | |||||||
\(504\) | −8.98105 | −0.400048 | ||||||||
\(505\) | −1.25790 | −0.0559760 | ||||||||
\(506\) | 17.3112 | 0.769575 | ||||||||
\(507\) | 3.19550 | 0.141917 | ||||||||
\(508\) | 1.39622 | 0.0619471 | ||||||||
\(509\) | 6.19562 | 0.274616 | 0.137308 | − | 0.990528i | \(-0.456155\pi\) | ||||
0.137308 | + | 0.990528i | \(0.456155\pi\) | |||||||
\(510\) | −0.245469 | −0.0108696 | ||||||||
\(511\) | 18.9370 | 0.837723 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −13.3461 | −0.589243 | ||||||||
\(514\) | −1.53187 | −0.0675677 | ||||||||
\(515\) | 2.16110 | 0.0952295 | ||||||||
\(516\) | 1.56606 | 0.0689420 | ||||||||
\(517\) | −25.3376 | −1.11435 | ||||||||
\(518\) | −7.62987 | −0.335237 | ||||||||
\(519\) | −8.97406 | −0.393917 | ||||||||
\(520\) | −0.300902 | −0.0131954 | ||||||||
\(521\) | 43.1143 | 1.88887 | 0.944435 | − | 0.328698i | \(-0.106610\pi\) | ||||
0.944435 | + | 0.328698i | \(0.106610\pi\) | |||||||
\(522\) | 12.5558 | 0.549550 | ||||||||
\(523\) | 9.19146 | 0.401914 | 0.200957 | − | 0.979600i | \(-0.435595\pi\) | ||||
0.200957 | + | 0.979600i | \(0.435595\pi\) | |||||||
\(524\) | −8.88147 | −0.387989 | ||||||||
\(525\) | 5.71457 | 0.249404 | ||||||||
\(526\) | −26.3877 | −1.15056 | ||||||||
\(527\) | 5.54251 | 0.241436 | ||||||||
\(528\) | 0.930208 | 0.0404821 | ||||||||
\(529\) | 23.4582 | 1.01992 | ||||||||
\(530\) | −1.78948 | −0.0777300 | ||||||||
\(531\) | 26.0644 | 1.13110 | ||||||||
\(532\) | −19.4675 | −0.844023 | ||||||||
\(533\) | −6.77447 | −0.293435 | ||||||||
\(534\) | 0.931153 | 0.0402950 | ||||||||
\(535\) | −2.10795 | −0.0911346 | ||||||||
\(536\) | −2.84168 | −0.122742 | ||||||||
\(537\) | −3.55552 | −0.153432 | ||||||||
\(538\) | −7.79866 | −0.336224 | ||||||||
\(539\) | −7.16410 | −0.308579 | ||||||||
\(540\) | 0.312652 | 0.0134544 | ||||||||
\(541\) | 1.26912 | 0.0545639 | 0.0272819 | − | 0.999628i | \(-0.491315\pi\) | ||||
0.0272819 | + | 0.999628i | \(0.491315\pi\) | |||||||
\(542\) | −3.63476 | −0.156126 | ||||||||
\(543\) | 0.151675 | 0.00650901 | ||||||||
\(544\) | 4.60540 | 0.197455 | ||||||||
\(545\) | 2.80691 | 0.120235 | ||||||||
\(546\) | 2.37321 | 0.101564 | ||||||||
\(547\) | 3.13477 | 0.134033 | 0.0670166 | − | 0.997752i | \(-0.478652\pi\) | ||||
0.0670166 | + | 0.997752i | \(0.478652\pi\) | |||||||
\(548\) | 0.731194 | 0.0312351 | ||||||||
\(549\) | 34.4927 | 1.47211 | ||||||||
\(550\) | 12.6451 | 0.539189 | ||||||||
\(551\) | 27.2161 | 1.15944 | ||||||||
\(552\) | 2.49641 | 0.106254 | ||||||||
\(553\) | −6.42356 | −0.273158 | ||||||||
\(554\) | 12.5130 | 0.531625 | ||||||||
\(555\) | 0.129770 | 0.00550843 | ||||||||
\(556\) | 9.69652 | 0.411224 | ||||||||
\(557\) | 6.03607 | 0.255756 | 0.127878 | − | 0.991790i | \(-0.459183\pi\) | ||||
0.127878 | + | 0.991790i | \(0.459183\pi\) | |||||||
\(558\) | −3.44901 | −0.146008 | ||||||||
\(559\) | 8.84106 | 0.373937 | ||||||||
\(560\) | 0.456055 | 0.0192719 | ||||||||
\(561\) | 4.28398 | 0.180870 | ||||||||
\(562\) | −5.90991 | −0.249295 | ||||||||
\(563\) | 25.1785 | 1.06115 | 0.530575 | − | 0.847638i | \(-0.321976\pi\) | ||||
0.530575 | + | 0.847638i | \(0.321976\pi\) | |||||||
\(564\) | −3.65388 | −0.153856 | ||||||||
\(565\) | 0.354568 | 0.0149168 | ||||||||
\(566\) | −7.92713 | −0.333202 | ||||||||
\(567\) | 24.4773 | 1.02795 | ||||||||
\(568\) | 10.2637 | 0.430656 | ||||||||
\(569\) | 31.3964 | 1.31620 | 0.658102 | − | 0.752929i | \(-0.271360\pi\) | ||||
0.658102 | + | 0.752929i | \(0.271360\pi\) | |||||||
\(570\) | 0.331106 | 0.0138685 | ||||||||
\(571\) | −23.3479 | −0.977081 | −0.488540 | − | 0.872541i | \(-0.662471\pi\) | ||||
−0.488540 | + | 0.872541i | \(0.662471\pi\) | |||||||
\(572\) | 5.25140 | 0.219572 | ||||||||
\(573\) | 8.78832 | 0.367137 | ||||||||
\(574\) | 10.2676 | 0.428561 | ||||||||
\(575\) | 33.9358 | 1.41522 | ||||||||
\(576\) | −2.86586 | −0.119411 | ||||||||
\(577\) | −16.1065 | −0.670523 | −0.335262 | − | 0.942125i | \(-0.608825\pi\) | ||||
−0.335262 | + | 0.942125i | \(0.608825\pi\) | |||||||
\(578\) | 4.20969 | 0.175100 | ||||||||
\(579\) | 4.02486 | 0.167268 | ||||||||
\(580\) | −0.637578 | −0.0264740 | ||||||||
\(581\) | −14.0034 | −0.580957 | ||||||||
\(582\) | −5.97580 | −0.247705 | ||||||||
\(583\) | 31.2303 | 1.29343 | ||||||||
\(584\) | 6.04280 | 0.250053 | ||||||||
\(585\) | 0.862342 | 0.0356534 | ||||||||
\(586\) | 3.87756 | 0.160180 | ||||||||
\(587\) | −4.63216 | −0.191190 | −0.0955948 | − | 0.995420i | \(-0.530475\pi\) | ||||
−0.0955948 | + | 0.995420i | \(0.530475\pi\) | |||||||
\(588\) | −1.03312 | −0.0426051 | ||||||||
\(589\) | −7.47613 | −0.308049 | ||||||||
\(590\) | −1.32354 | −0.0544895 | ||||||||
\(591\) | 8.40884 | 0.345893 | ||||||||
\(592\) | −2.43469 | −0.100065 | ||||||||
\(593\) | −5.43873 | −0.223342 | −0.111671 | − | 0.993745i | \(-0.535620\pi\) | ||||
−0.111671 | + | 0.993745i | \(0.535620\pi\) | |||||||
\(594\) | −5.45646 | −0.223881 | ||||||||
\(595\) | 2.10032 | 0.0861046 | ||||||||
\(596\) | 10.3327 | 0.423243 | ||||||||
\(597\) | −3.13952 | −0.128492 | ||||||||
\(598\) | 14.0932 | 0.576315 | ||||||||
\(599\) | −24.6352 | −1.00657 | −0.503284 | − | 0.864121i | \(-0.667875\pi\) | ||||
−0.503284 | + | 0.864121i | \(0.667875\pi\) | |||||||
\(600\) | 1.82352 | 0.0744450 | ||||||||
\(601\) | 25.1987 | 1.02788 | 0.513939 | − | 0.857827i | \(-0.328186\pi\) | ||||
0.513939 | + | 0.857827i | \(0.328186\pi\) | |||||||
\(602\) | −13.3998 | −0.546133 | ||||||||
\(603\) | 8.14385 | 0.331643 | ||||||||
\(604\) | −10.8539 | −0.441640 | ||||||||
\(605\) | −0.662083 | −0.0269175 | ||||||||
\(606\) | 3.16583 | 0.128603 | ||||||||
\(607\) | 12.1295 | 0.492321 | 0.246161 | − | 0.969229i | \(-0.420831\pi\) | ||||
0.246161 | + | 0.969229i | \(0.420831\pi\) | |||||||
\(608\) | −6.21209 | −0.251933 | ||||||||
\(609\) | 5.02858 | 0.203768 | ||||||||
\(610\) | −1.75153 | −0.0709175 | ||||||||
\(611\) | −20.6277 | −0.834506 | ||||||||
\(612\) | −13.1984 | −0.533514 | ||||||||
\(613\) | −13.9487 | −0.563382 | −0.281691 | − | 0.959505i | \(-0.590895\pi\) | ||||
−0.281691 | + | 0.959505i | \(0.590895\pi\) | |||||||
\(614\) | 0.0374509 | 0.00151140 | ||||||||
\(615\) | −0.174633 | −0.00704186 | ||||||||
\(616\) | −7.95917 | −0.320684 | ||||||||
\(617\) | −14.1094 | −0.568022 | −0.284011 | − | 0.958821i | \(-0.591665\pi\) | ||||
−0.284011 | + | 0.958821i | \(0.591665\pi\) | |||||||
\(618\) | −5.43894 | −0.218786 | ||||||||
\(619\) | 5.42921 | 0.218218 | 0.109109 | − | 0.994030i | \(-0.465200\pi\) | ||||
0.109109 | + | 0.994030i | \(0.465200\pi\) | |||||||
\(620\) | 0.175140 | 0.00703378 | ||||||||
\(621\) | −14.6436 | −0.587626 | ||||||||
\(622\) | −6.10882 | −0.244941 | ||||||||
\(623\) | −7.96727 | −0.319202 | ||||||||
\(624\) | 0.757294 | 0.0303160 | ||||||||
\(625\) | 24.6828 | 0.987311 | ||||||||
\(626\) | −22.3535 | −0.893426 | ||||||||
\(627\) | −5.77853 | −0.230772 | ||||||||
\(628\) | −17.7596 | −0.708685 | ||||||||
\(629\) | −11.2127 | −0.447081 | ||||||||
\(630\) | −1.30699 | −0.0520717 | ||||||||
\(631\) | −35.2104 | −1.40171 | −0.700853 | − | 0.713306i | \(-0.747197\pi\) | ||||
−0.700853 | + | 0.713306i | \(0.747197\pi\) | |||||||
\(632\) | −2.04976 | −0.0815351 | ||||||||
\(633\) | −3.33295 | −0.132473 | ||||||||
\(634\) | 18.5695 | 0.737490 | ||||||||
\(635\) | 0.203188 | 0.00806327 | ||||||||
\(636\) | 4.50366 | 0.178582 | ||||||||
\(637\) | −5.83238 | −0.231087 | ||||||||
\(638\) | 11.1271 | 0.440528 | ||||||||
\(639\) | −29.4144 | −1.16361 | ||||||||
\(640\) | 0.145528 | 0.00575248 | ||||||||
\(641\) | −0.729928 | −0.0288304 | −0.0144152 | − | 0.999896i | \(-0.504589\pi\) | ||||
−0.0144152 | + | 0.999896i | \(0.504589\pi\) | |||||||
\(642\) | 5.30517 | 0.209379 | ||||||||
\(643\) | 43.7932 | 1.72703 | 0.863517 | − | 0.504320i | \(-0.168257\pi\) | ||||
0.863517 | + | 0.504320i | \(0.168257\pi\) | |||||||
\(644\) | −21.3601 | −0.841706 | ||||||||
\(645\) | 0.227905 | 0.00897375 | ||||||||
\(646\) | −28.6091 | −1.12561 | ||||||||
\(647\) | −7.02332 | −0.276115 | −0.138058 | − | 0.990424i | \(-0.544086\pi\) | ||||
−0.138058 | + | 0.990424i | \(0.544086\pi\) | |||||||
\(648\) | 7.81071 | 0.306833 | ||||||||
\(649\) | 23.0988 | 0.906706 | ||||||||
\(650\) | 10.2945 | 0.403785 | ||||||||
\(651\) | −1.38133 | −0.0541385 | ||||||||
\(652\) | −24.9541 | −0.977280 | ||||||||
\(653\) | 46.5540 | 1.82180 | 0.910898 | − | 0.412631i | \(-0.135390\pi\) | ||||
0.910898 | + | 0.412631i | \(0.135390\pi\) | |||||||
\(654\) | −7.06428 | −0.276235 | ||||||||
\(655\) | −1.29250 | −0.0505021 | ||||||||
\(656\) | 3.27639 | 0.127922 | ||||||||
\(657\) | −17.3178 | −0.675632 | ||||||||
\(658\) | 31.2639 | 1.21879 | ||||||||
\(659\) | 35.1288 | 1.36842 | 0.684212 | − | 0.729283i | \(-0.260146\pi\) | ||||
0.684212 | + | 0.729283i | \(0.260146\pi\) | |||||||
\(660\) | 0.135371 | 0.00526930 | ||||||||
\(661\) | −41.8079 | −1.62614 | −0.813070 | − | 0.582166i | \(-0.802205\pi\) | ||||
−0.813070 | + | 0.582166i | \(0.802205\pi\) | |||||||
\(662\) | 10.4416 | 0.405825 | ||||||||
\(663\) | 3.48764 | 0.135449 | ||||||||
\(664\) | −4.46848 | −0.173411 | ||||||||
\(665\) | −2.83306 | −0.109861 | ||||||||
\(666\) | 6.97748 | 0.270372 | ||||||||
\(667\) | 29.8620 | 1.15626 | ||||||||
\(668\) | 8.04828 | 0.311397 | ||||||||
\(669\) | −2.71755 | −0.105067 | ||||||||
\(670\) | −0.413543 | −0.0159766 | ||||||||
\(671\) | 30.5681 | 1.18007 | ||||||||
\(672\) | −1.14778 | −0.0442764 | ||||||||
\(673\) | −29.6673 | −1.14359 | −0.571794 | − | 0.820397i | \(-0.693752\pi\) | ||||
−0.571794 | + | 0.820397i | \(0.693752\pi\) | |||||||
\(674\) | 0.466859 | 0.0179827 | ||||||||
\(675\) | −10.6965 | −0.411709 | ||||||||
\(676\) | −8.72477 | −0.335568 | ||||||||
\(677\) | −46.9476 | −1.80434 | −0.902171 | − | 0.431378i | \(-0.858027\pi\) | ||||
−0.902171 | + | 0.431378i | \(0.858027\pi\) | |||||||
\(678\) | −0.892358 | −0.0342708 | ||||||||
\(679\) | 51.1310 | 1.96223 | ||||||||
\(680\) | 0.670212 | 0.0257015 | ||||||||
\(681\) | 0.466039 | 0.0178587 | ||||||||
\(682\) | −3.05657 | −0.117042 | ||||||||
\(683\) | −15.2140 | −0.582149 | −0.291074 | − | 0.956700i | \(-0.594013\pi\) | ||||
−0.291074 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(684\) | 17.8029 | 0.680713 | ||||||||
\(685\) | 0.106409 | 0.00406567 | ||||||||
\(686\) | −13.0969 | −0.500044 | ||||||||
\(687\) | 4.05684 | 0.154778 | ||||||||
\(688\) | −4.27587 | −0.163016 | ||||||||
\(689\) | 25.4250 | 0.968616 | ||||||||
\(690\) | 0.363296 | 0.0138304 | ||||||||
\(691\) | 21.7467 | 0.827283 | 0.413642 | − | 0.910440i | \(-0.364257\pi\) | ||||
0.413642 | + | 0.910440i | \(0.364257\pi\) | |||||||
\(692\) | 24.5022 | 0.931433 | ||||||||
\(693\) | 22.8099 | 0.866475 | ||||||||
\(694\) | 22.9790 | 0.872272 | ||||||||
\(695\) | 1.41111 | 0.0535265 | ||||||||
\(696\) | 1.60462 | 0.0608230 | ||||||||
\(697\) | 15.0891 | 0.571540 | ||||||||
\(698\) | 13.9854 | 0.529354 | ||||||||
\(699\) | −1.77752 | −0.0672321 | ||||||||
\(700\) | −15.6027 | −0.589726 | ||||||||
\(701\) | 29.1399 | 1.10060 | 0.550299 | − | 0.834968i | \(-0.314514\pi\) | ||||
0.550299 | + | 0.834968i | \(0.314514\pi\) | |||||||
\(702\) | −4.44218 | −0.167659 | ||||||||
\(703\) | 15.1245 | 0.570432 | ||||||||
\(704\) | −2.53978 | −0.0957214 | ||||||||
\(705\) | −0.531740 | −0.0200265 | ||||||||
\(706\) | 7.83916 | 0.295031 | ||||||||
\(707\) | −27.0879 | −1.01874 | ||||||||
\(708\) | 3.33103 | 0.125188 | ||||||||
\(709\) | −38.6116 | −1.45009 | −0.725044 | − | 0.688702i | \(-0.758181\pi\) | ||||
−0.725044 | + | 0.688702i | \(0.758181\pi\) | |||||||
\(710\) | 1.49365 | 0.0560559 | ||||||||
\(711\) | 5.87432 | 0.220304 | ||||||||
\(712\) | −2.54236 | −0.0952789 | ||||||||
\(713\) | −8.20296 | −0.307203 | ||||||||
\(714\) | −5.28596 | −0.197822 | ||||||||
\(715\) | 0.764223 | 0.0285803 | ||||||||
\(716\) | 9.70775 | 0.362795 | ||||||||
\(717\) | −2.68721 | −0.100356 | ||||||||
\(718\) | 0.0947581 | 0.00353634 | ||||||||
\(719\) | 10.6266 | 0.396305 | 0.198152 | − | 0.980171i | \(-0.436506\pi\) | ||||
0.198152 | + | 0.980171i | \(0.436506\pi\) | |||||||
\(720\) | −0.417061 | −0.0155429 | ||||||||
\(721\) | 46.5375 | 1.73315 | ||||||||
\(722\) | 19.5900 | 0.729065 | ||||||||
\(723\) | −3.02873 | −0.112640 | ||||||||
\(724\) | −0.414124 | −0.0153908 | ||||||||
\(725\) | 21.8130 | 0.810114 | ||||||||
\(726\) | 1.66629 | 0.0618420 | ||||||||
\(727\) | −31.1513 | −1.15534 | −0.577669 | − | 0.816271i | \(-0.696037\pi\) | ||||
−0.577669 | + | 0.816271i | \(0.696037\pi\) | |||||||
\(728\) | −6.47966 | −0.240152 | ||||||||
\(729\) | −20.0238 | −0.741621 | ||||||||
\(730\) | 0.879394 | 0.0325478 | ||||||||
\(731\) | −19.6921 | −0.728338 | ||||||||
\(732\) | 4.40816 | 0.162930 | ||||||||
\(733\) | −16.0978 | −0.594588 | −0.297294 | − | 0.954786i | \(-0.596084\pi\) | ||||
−0.297294 | + | 0.954786i | \(0.596084\pi\) | |||||||
\(734\) | −17.6038 | −0.649768 | ||||||||
\(735\) | −0.150347 | −0.00554564 | ||||||||
\(736\) | −6.81602 | −0.251242 | ||||||||
\(737\) | 7.21723 | 0.265850 | ||||||||
\(738\) | −9.38966 | −0.345638 | ||||||||
\(739\) | 10.8504 | 0.399138 | 0.199569 | − | 0.979884i | \(-0.436046\pi\) | ||||
0.199569 | + | 0.979884i | \(0.436046\pi\) | |||||||
\(740\) | −0.354315 | −0.0130249 | ||||||||
\(741\) | −4.70437 | −0.172819 | ||||||||
\(742\) | −38.5349 | −1.41466 | ||||||||
\(743\) | −37.8758 | −1.38953 | −0.694763 | − | 0.719238i | \(-0.744491\pi\) | ||||
−0.694763 | + | 0.719238i | \(0.744491\pi\) | |||||||
\(744\) | −0.440782 | −0.0161599 | ||||||||
\(745\) | 1.50369 | 0.0550909 | ||||||||
\(746\) | −20.5251 | −0.751479 | ||||||||
\(747\) | 12.8060 | 0.468548 | ||||||||
\(748\) | −11.6967 | −0.427673 | ||||||||
\(749\) | −45.3929 | −1.65862 | ||||||||
\(750\) | 0.531874 | 0.0194213 | ||||||||
\(751\) | 43.2804 | 1.57933 | 0.789663 | − | 0.613541i | \(-0.210255\pi\) | ||||
0.789663 | + | 0.613541i | \(0.210255\pi\) | |||||||
\(752\) | 9.97631 | 0.363799 | ||||||||
\(753\) | −6.53530 | −0.238160 | ||||||||
\(754\) | 9.05875 | 0.329900 | ||||||||
\(755\) | −1.57955 | −0.0574856 | ||||||||
\(756\) | 6.73269 | 0.244865 | ||||||||
\(757\) | −14.0400 | −0.510292 | −0.255146 | − | 0.966903i | \(-0.582124\pi\) | ||||
−0.255146 | + | 0.966903i | \(0.582124\pi\) | |||||||
\(758\) | −0.641769 | −0.0233101 | ||||||||
\(759\) | −6.34032 | −0.230139 | ||||||||
\(760\) | −0.904029 | −0.0327926 | ||||||||
\(761\) | 10.4976 | 0.380536 | 0.190268 | − | 0.981732i | \(-0.439064\pi\) | ||||
0.190268 | + | 0.981732i | \(0.439064\pi\) | |||||||
\(762\) | −0.511373 | −0.0185251 | ||||||||
\(763\) | 60.4444 | 2.18824 | ||||||||
\(764\) | −23.9950 | −0.868110 | ||||||||
\(765\) | −1.92073 | −0.0694442 | ||||||||
\(766\) | −35.4842 | −1.28210 | ||||||||
\(767\) | 18.8050 | 0.679009 | ||||||||
\(768\) | −0.366256 | −0.0132161 | ||||||||
\(769\) | −45.1401 | −1.62779 | −0.813897 | − | 0.581009i | \(-0.802658\pi\) | ||||
−0.813897 | + | 0.581009i | \(0.802658\pi\) | |||||||
\(770\) | −1.15828 | −0.0417415 | ||||||||
\(771\) | 0.561055 | 0.0202059 | ||||||||
\(772\) | −10.9892 | −0.395510 | ||||||||
\(773\) | −1.89270 | −0.0680756 | −0.0340378 | − | 0.999421i | \(-0.510837\pi\) | ||||
−0.0340378 | + | 0.999421i | \(0.510837\pi\) | |||||||
\(774\) | 12.2540 | 0.440462 | ||||||||
\(775\) | −5.99192 | −0.215236 | ||||||||
\(776\) | 16.3159 | 0.585707 | ||||||||
\(777\) | 2.79448 | 0.100251 | ||||||||
\(778\) | −28.2847 | −1.01406 | ||||||||
\(779\) | −20.3532 | −0.729230 | ||||||||
\(780\) | 0.110207 | 0.00394605 | ||||||||
\(781\) | −26.0676 | −0.932771 | ||||||||
\(782\) | −31.3905 | −1.12252 | ||||||||
\(783\) | −9.41248 | −0.336375 | ||||||||
\(784\) | 2.82076 | 0.100741 | ||||||||
\(785\) | −2.58451 | −0.0922451 | ||||||||
\(786\) | 3.25289 | 0.116027 | ||||||||
\(787\) | −8.00059 | −0.285190 | −0.142595 | − | 0.989781i | \(-0.545545\pi\) | ||||
−0.142595 | + | 0.989781i | \(0.545545\pi\) | |||||||
\(788\) | −22.9589 | −0.817878 | ||||||||
\(789\) | 9.66465 | 0.344071 | ||||||||
\(790\) | −0.298297 | −0.0106129 | ||||||||
\(791\) | 7.63532 | 0.271481 | ||||||||
\(792\) | 7.27863 | 0.258635 | ||||||||
\(793\) | 24.8859 | 0.883723 | ||||||||
\(794\) | −14.8003 | −0.525245 | ||||||||
\(795\) | 0.655407 | 0.0232449 | ||||||||
\(796\) | 8.57194 | 0.303824 | ||||||||
\(797\) | 18.1319 | 0.642265 | 0.321133 | − | 0.947034i | \(-0.395936\pi\) | ||||
0.321133 | + | 0.947034i | \(0.395936\pi\) | |||||||
\(798\) | 7.13008 | 0.252402 | ||||||||
\(799\) | 45.9449 | 1.62541 | ||||||||
\(800\) | −4.97882 | −0.176028 | ||||||||
\(801\) | 7.28604 | 0.257439 | ||||||||
\(802\) | 3.97515 | 0.140367 | ||||||||
\(803\) | −15.3474 | −0.541597 | ||||||||
\(804\) | 1.04078 | 0.0367055 | ||||||||
\(805\) | −3.10848 | −0.109560 | ||||||||
\(806\) | −2.48839 | −0.0876500 | ||||||||
\(807\) | 2.85630 | 0.100547 | ||||||||
\(808\) | −8.64376 | −0.304086 | ||||||||
\(809\) | −15.6101 | −0.548824 | −0.274412 | − | 0.961612i | \(-0.588483\pi\) | ||||
−0.274412 | + | 0.961612i | \(0.588483\pi\) | |||||||
\(810\) | 1.13667 | 0.0399386 | ||||||||
\(811\) | −21.2366 | −0.745716 | −0.372858 | − | 0.927888i | \(-0.621622\pi\) | ||||
−0.372858 | + | 0.927888i | \(0.621622\pi\) | |||||||
\(812\) | −13.7297 | −0.481818 | ||||||||
\(813\) | 1.33125 | 0.0466891 | ||||||||
\(814\) | 6.18358 | 0.216734 | ||||||||
\(815\) | −3.63151 | −0.127206 | ||||||||
\(816\) | −1.68675 | −0.0590482 | ||||||||
\(817\) | 26.5621 | 0.929289 | ||||||||
\(818\) | −13.7296 | −0.480043 | ||||||||
\(819\) | 18.5698 | 0.648881 | ||||||||
\(820\) | 0.476805 | 0.0166507 | ||||||||
\(821\) | 41.5422 | 1.44983 | 0.724916 | − | 0.688838i | \(-0.241879\pi\) | ||||
0.724916 | + | 0.688838i | \(0.241879\pi\) | |||||||
\(822\) | −0.267804 | −0.00934074 | ||||||||
\(823\) | 32.6045 | 1.13652 | 0.568261 | − | 0.822848i | \(-0.307616\pi\) | ||||
0.568261 | + | 0.822848i | \(0.307616\pi\) | |||||||
\(824\) | 14.8501 | 0.517329 | ||||||||
\(825\) | −4.63134 | −0.161242 | ||||||||
\(826\) | −28.5014 | −0.991690 | ||||||||
\(827\) | 1.48271 | 0.0515589 | 0.0257794 | − | 0.999668i | \(-0.491793\pi\) | ||||
0.0257794 | + | 0.999668i | \(0.491793\pi\) | |||||||
\(828\) | 19.5337 | 0.678844 | ||||||||
\(829\) | 0.0891552 | 0.00309649 | 0.00154824 | − | 0.999999i | \(-0.499507\pi\) | ||||
0.00154824 | + | 0.999999i | \(0.499507\pi\) | |||||||
\(830\) | −0.650287 | −0.0225718 | ||||||||
\(831\) | −4.58295 | −0.158981 | ||||||||
\(832\) | −2.06766 | −0.0716833 | ||||||||
\(833\) | 12.9907 | 0.450102 | ||||||||
\(834\) | −3.55141 | −0.122975 | ||||||||
\(835\) | 1.17125 | 0.0405327 | ||||||||
\(836\) | 15.7773 | 0.545670 | ||||||||
\(837\) | 2.58556 | 0.0893702 | ||||||||
\(838\) | 30.7099 | 1.06086 | ||||||||
\(839\) | 36.6986 | 1.26698 | 0.633488 | − | 0.773752i | \(-0.281622\pi\) | ||||
0.633488 | + | 0.773752i | \(0.281622\pi\) | |||||||
\(840\) | −0.167033 | −0.00576318 | ||||||||
\(841\) | −9.80551 | −0.338121 | ||||||||
\(842\) | −7.56377 | −0.260665 | ||||||||
\(843\) | 2.16454 | 0.0745507 | ||||||||
\(844\) | 9.10006 | 0.313237 | ||||||||
\(845\) | −1.26969 | −0.0436788 | ||||||||
\(846\) | −28.5907 | −0.982968 | ||||||||
\(847\) | −14.2574 | −0.489889 | ||||||||
\(848\) | −12.2965 | −0.422263 | ||||||||
\(849\) | 2.90336 | 0.0996430 | ||||||||
\(850\) | −22.9295 | −0.786474 | ||||||||
\(851\) | 16.5949 | 0.568867 | ||||||||
\(852\) | −3.75915 | −0.128786 | ||||||||
\(853\) | −48.1940 | −1.65013 | −0.825066 | − | 0.565037i | \(-0.808862\pi\) | ||||
−0.825066 | + | 0.565037i | \(0.808862\pi\) | |||||||
\(854\) | −37.7177 | −1.29067 | ||||||||
\(855\) | 2.59082 | 0.0886041 | ||||||||
\(856\) | −14.4849 | −0.495083 | ||||||||
\(857\) | 1.44391 | 0.0493231 | 0.0246616 | − | 0.999696i | \(-0.492149\pi\) | ||||
0.0246616 | + | 0.999696i | \(0.492149\pi\) | |||||||
\(858\) | −1.92336 | −0.0656623 | ||||||||
\(859\) | −15.0933 | −0.514977 | −0.257489 | − | 0.966281i | \(-0.582895\pi\) | ||||
−0.257489 | + | 0.966281i | \(0.582895\pi\) | |||||||
\(860\) | −0.622256 | −0.0212188 | ||||||||
\(861\) | −3.76056 | −0.128160 | ||||||||
\(862\) | 17.9161 | 0.610226 | ||||||||
\(863\) | 35.2529 | 1.20002 | 0.600011 | − | 0.799992i | \(-0.295163\pi\) | ||||
0.600011 | + | 0.799992i | \(0.295163\pi\) | |||||||
\(864\) | 2.14840 | 0.0730902 | ||||||||
\(865\) | 3.56574 | 0.121239 | ||||||||
\(866\) | −10.3180 | −0.350621 | ||||||||
\(867\) | −1.54182 | −0.0523631 | ||||||||
\(868\) | 3.77148 | 0.128012 | ||||||||
\(869\) | 5.20593 | 0.176599 | ||||||||
\(870\) | 0.233517 | 0.00791696 | ||||||||
\(871\) | 5.87564 | 0.199088 | ||||||||
\(872\) | 19.2878 | 0.653169 | ||||||||
\(873\) | −46.7591 | −1.58256 | ||||||||
\(874\) | 42.3417 | 1.43223 | ||||||||
\(875\) | −4.55090 | −0.153848 | ||||||||
\(876\) | −2.21321 | −0.0747775 | ||||||||
\(877\) | 7.74855 | 0.261650 | 0.130825 | − | 0.991405i | \(-0.458237\pi\) | ||||
0.130825 | + | 0.991405i | \(0.458237\pi\) | |||||||
\(878\) | 21.4870 | 0.725152 | ||||||||
\(879\) | −1.42018 | −0.0479014 | ||||||||
\(880\) | −0.369607 | −0.0124595 | ||||||||
\(881\) | −3.14237 | −0.105869 | −0.0529346 | − | 0.998598i | \(-0.516857\pi\) | ||||
−0.0529346 | + | 0.998598i | \(0.516857\pi\) | |||||||
\(882\) | −8.08389 | −0.272199 | ||||||||
\(883\) | 41.1843 | 1.38596 | 0.692981 | − | 0.720956i | \(-0.256297\pi\) | ||||
0.692981 | + | 0.720956i | \(0.256297\pi\) | |||||||
\(884\) | −9.52241 | −0.320273 | ||||||||
\(885\) | 0.484756 | 0.0162949 | ||||||||
\(886\) | 19.8834 | 0.667997 | ||||||||
\(887\) | 59.2748 | 1.99025 | 0.995126 | − | 0.0986119i | \(-0.0314402\pi\) | ||||
0.995126 | + | 0.0986119i | \(0.0314402\pi\) | |||||||
\(888\) | 0.891721 | 0.0299242 | ||||||||
\(889\) | 4.37548 | 0.146749 | ||||||||
\(890\) | −0.369983 | −0.0124019 | ||||||||
\(891\) | −19.8374 | −0.664579 | ||||||||
\(892\) | 7.41982 | 0.248434 | ||||||||
\(893\) | −61.9737 | −2.07387 | ||||||||
\(894\) | −3.78440 | −0.126569 | ||||||||
\(895\) | 1.41274 | 0.0472228 | ||||||||
\(896\) | 3.13381 | 0.104693 | ||||||||
\(897\) | −5.16173 | −0.172345 | ||||||||
\(898\) | 8.72808 | 0.291260 | ||||||||
\(899\) | −5.27264 | −0.175852 | ||||||||
\(900\) | 14.2686 | 0.475620 | ||||||||
\(901\) | −56.6303 | −1.88663 | ||||||||
\(902\) | −8.32130 | −0.277069 | ||||||||
\(903\) | 4.90774 | 0.163319 | ||||||||
\(904\) | 2.43644 | 0.0810346 | ||||||||
\(905\) | −0.0602665 | −0.00200333 | ||||||||
\(906\) | 3.97532 | 0.132071 | ||||||||
\(907\) | 30.9638 | 1.02814 | 0.514069 | − | 0.857749i | \(-0.328138\pi\) | ||||
0.514069 | + | 0.857749i | \(0.328138\pi\) | |||||||
\(908\) | −1.27244 | −0.0422275 | ||||||||
\(909\) | 24.7718 | 0.821628 | ||||||||
\(910\) | −0.942969 | −0.0312591 | ||||||||
\(911\) | 15.4184 | 0.510836 | 0.255418 | − | 0.966831i | \(-0.417787\pi\) | ||||
0.255418 | + | 0.966831i | \(0.417787\pi\) | |||||||
\(912\) | 2.27521 | 0.0753398 | ||||||||
\(913\) | 11.3489 | 0.375595 | ||||||||
\(914\) | −34.1222 | −1.12866 | ||||||||
\(915\) | 0.641509 | 0.0212076 | ||||||||
\(916\) | −11.0765 | −0.365978 | ||||||||
\(917\) | −27.8328 | −0.919121 | ||||||||
\(918\) | 9.89425 | 0.326559 | ||||||||
\(919\) | 22.9206 | 0.756080 | 0.378040 | − | 0.925789i | \(-0.376598\pi\) | ||||
0.378040 | + | 0.925789i | \(0.376598\pi\) | |||||||
\(920\) | −0.991919 | −0.0327026 | ||||||||
\(921\) | −0.0137166 | −0.000451978 0 | ||||||||
\(922\) | 31.1089 | 1.02452 | ||||||||
\(923\) | −21.2219 | −0.698528 | ||||||||
\(924\) | 2.91509 | 0.0958995 | ||||||||
\(925\) | 12.1219 | 0.398566 | ||||||||
\(926\) | −21.6416 | −0.711186 | ||||||||
\(927\) | −42.5583 | −1.39780 | ||||||||
\(928\) | −4.38115 | −0.143818 | ||||||||
\(929\) | −42.9821 | −1.41020 | −0.705098 | − | 0.709110i | \(-0.749097\pi\) | ||||
−0.705098 | + | 0.709110i | \(0.749097\pi\) | |||||||
\(930\) | −0.0641459 | −0.00210343 | ||||||||
\(931\) | −17.5228 | −0.574286 | ||||||||
\(932\) | 4.85323 | 0.158973 | ||||||||
\(933\) | 2.23739 | 0.0732488 | ||||||||
\(934\) | 36.4205 | 1.19172 | ||||||||
\(935\) | −1.70219 | −0.0556675 | ||||||||
\(936\) | 5.92563 | 0.193685 | ||||||||
\(937\) | −30.2550 | −0.988387 | −0.494194 | − | 0.869352i | \(-0.664537\pi\) | ||||
−0.494194 | + | 0.869352i | \(0.664537\pi\) | |||||||
\(938\) | −8.90529 | −0.290768 | ||||||||
\(939\) | 8.18710 | 0.267176 | ||||||||
\(940\) | 1.45183 | 0.0473534 | ||||||||
\(941\) | −23.9151 | −0.779611 | −0.389806 | − | 0.920897i | \(-0.627458\pi\) | ||||
−0.389806 | + | 0.920897i | \(0.627458\pi\) | |||||||
\(942\) | 6.50455 | 0.211930 | ||||||||
\(943\) | −22.3319 | −0.727228 | ||||||||
\(944\) | −9.09481 | −0.296011 | ||||||||
\(945\) | 0.979791 | 0.0318726 | ||||||||
\(946\) | 10.8597 | 0.353081 | ||||||||
\(947\) | 35.2690 | 1.14609 | 0.573044 | − | 0.819525i | \(-0.305763\pi\) | ||||
0.573044 | + | 0.819525i | \(0.305763\pi\) | |||||||
\(948\) | 0.750737 | 0.0243828 | ||||||||
\(949\) | −12.4945 | −0.405588 | ||||||||
\(950\) | 30.9289 | 1.00346 | ||||||||
\(951\) | −6.80119 | −0.220544 | ||||||||
\(952\) | 14.4324 | 0.467758 | ||||||||
\(953\) | −23.2328 | −0.752584 | −0.376292 | − | 0.926501i | \(-0.622801\pi\) | ||||
−0.376292 | + | 0.926501i | \(0.622801\pi\) | |||||||
\(954\) | 35.2400 | 1.14094 | ||||||||
\(955\) | −3.49194 | −0.112996 | ||||||||
\(956\) | 7.33698 | 0.237295 | ||||||||
\(957\) | −4.07538 | −0.131738 | ||||||||
\(958\) | −15.4475 | −0.499086 | ||||||||
\(959\) | 2.29142 | 0.0739939 | ||||||||
\(960\) | −0.0533003 | −0.00172026 | ||||||||
\(961\) | −29.5516 | −0.953278 | ||||||||
\(962\) | 5.03413 | 0.162307 | ||||||||
\(963\) | 41.5116 | 1.33769 | ||||||||
\(964\) | 8.26943 | 0.266340 | ||||||||
\(965\) | −1.59923 | −0.0514811 | ||||||||
\(966\) | 7.82326 | 0.251709 | ||||||||
\(967\) | 13.5908 | 0.437049 | 0.218525 | − | 0.975831i | \(-0.429876\pi\) | ||||
0.218525 | + | 0.975831i | \(0.429876\pi\) | |||||||
\(968\) | −4.54954 | −0.146228 | ||||||||
\(969\) | 10.4783 | 0.336610 | ||||||||
\(970\) | 2.37441 | 0.0762379 | ||||||||
\(971\) | 12.3132 | 0.395150 | 0.197575 | − | 0.980288i | \(-0.436693\pi\) | ||||
0.197575 | + | 0.980288i | \(0.436693\pi\) | |||||||
\(972\) | −9.30593 | −0.298488 | ||||||||
\(973\) | 30.3870 | 0.974164 | ||||||||
\(974\) | −2.56916 | −0.0823211 | ||||||||
\(975\) | −3.77043 | −0.120750 | ||||||||
\(976\) | −12.0357 | −0.385255 | ||||||||
\(977\) | −20.0142 | −0.640311 | −0.320155 | − | 0.947365i | \(-0.603735\pi\) | ||||
−0.320155 | + | 0.947365i | \(0.603735\pi\) | |||||||
\(978\) | 9.13960 | 0.292252 | ||||||||
\(979\) | 6.45702 | 0.206367 | ||||||||
\(980\) | 0.410498 | 0.0131129 | ||||||||
\(981\) | −55.2762 | −1.76483 | ||||||||
\(982\) | 29.1338 | 0.929696 | ||||||||
\(983\) | −18.8419 | −0.600964 | −0.300482 | − | 0.953787i | \(-0.597148\pi\) | ||||
−0.300482 | + | 0.953787i | \(0.597148\pi\) | |||||||
\(984\) | −1.20000 | −0.0382545 | ||||||||
\(985\) | −3.34116 | −0.106458 | ||||||||
\(986\) | −20.1769 | −0.642565 | ||||||||
\(987\) | −11.4506 | −0.364476 | ||||||||
\(988\) | 12.8445 | 0.408638 | ||||||||
\(989\) | 29.1444 | 0.926738 | ||||||||
\(990\) | 1.05924 | 0.0336649 | ||||||||
\(991\) | 12.7142 | 0.403880 | 0.201940 | − | 0.979398i | \(-0.435275\pi\) | ||||
0.201940 | + | 0.979398i | \(0.435275\pi\) | |||||||
\(992\) | 1.20348 | 0.0382106 | ||||||||
\(993\) | −3.82430 | −0.121360 | ||||||||
\(994\) | 32.1646 | 1.02020 | ||||||||
\(995\) | 1.24745 | 0.0395469 | ||||||||
\(996\) | 1.63661 | 0.0518578 | ||||||||
\(997\) | −28.6612 | −0.907711 | −0.453855 | − | 0.891075i | \(-0.649952\pi\) | ||||
−0.453855 | + | 0.891075i | \(0.649952\pi\) | |||||||
\(998\) | 3.87695 | 0.122723 | ||||||||
\(999\) | −5.23071 | −0.165492 |
(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 | 4034.2.a.a.1.17 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.a.1.17 | ✓ | 33 | 1.1 | even | 1 | trivial |