Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(19,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.m (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Root | \(-0.455024 + 1.94755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.19 |
Dual form | 144.3.m.c.91.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.455024 | − | 1.94755i | −0.227512 | − | 0.973775i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.58591 | + | 1.77236i | −0.896477 | + | 0.443091i | ||||
\(5\) | 3.40572 | − | 3.40572i | 0.681145 | − | 0.681145i | −0.279113 | − | 0.960258i | \(-0.590040\pi\) |
0.960258 | + | 0.279113i | \(0.0900405\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.1303 | 1.73290 | 0.866452 | − | 0.499261i | \(-0.166395\pi\) | ||||
0.866452 | + | 0.499261i | \(0.166395\pi\) | |||||||
\(8\) | 5.08344 | + | 6.17727i | 0.635430 | + | 0.772158i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.18251 | − | 5.08314i | −0.818251 | − | 0.508314i | ||||
\(11\) | −9.81086 | − | 9.81086i | −0.891896 | − | 0.891896i | 0.102805 | − | 0.994702i | \(-0.467218\pi\) |
−0.994702 | + | 0.102805i | \(0.967218\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −7.76859 | − | 7.76859i | −0.597584 | − | 0.597584i | 0.342085 | − | 0.939669i | \(-0.388867\pi\) |
−0.939669 | + | 0.342085i | \(0.888867\pi\) | |||||||
\(14\) | −5.51959 | − | 23.6244i | −0.394256 | − | 1.68746i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.71745 | − | 12.7111i | 0.607341 | − | 0.794442i | ||||
\(17\) | −9.73087 | −0.572404 | −0.286202 | − | 0.958169i | \(-0.592393\pi\) | ||||
−0.286202 | + | 0.958169i | \(0.592393\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.2823 | − | 11.2823i | 0.593806 | − | 0.593806i | −0.344851 | − | 0.938657i | \(-0.612071\pi\) |
0.938657 | + | 0.344851i | \(0.112071\pi\) | |||||||
\(20\) | −6.17643 | + | 18.2488i | −0.308821 | + | 0.912440i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.6430 | + | 23.5713i | −0.665589 | + | 1.07142i | ||||
\(23\) | 20.2635 | 0.881020 | 0.440510 | − | 0.897748i | \(-0.354798\pi\) | ||||
0.440510 | + | 0.897748i | \(0.354798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.80207i | 0.0720830i | ||||||||
\(26\) | −11.5948 | + | 18.6646i | −0.445955 | + | 0.717870i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −43.4982 | + | 21.4994i | −1.55351 | + | 0.767834i | ||||
\(29\) | 16.4069 | + | 16.4069i | 0.565754 | + | 0.565754i | 0.930936 | − | 0.365182i | \(-0.118993\pi\) |
−0.365182 | + | 0.930936i | \(0.618993\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 26.3542i | − | 0.850134i | −0.905162 | − | 0.425067i | \(-0.860251\pi\) | ||
0.905162 | − | 0.425067i | \(-0.139749\pi\) | |||||||
\(32\) | −29.1771 | − | 13.1414i | −0.911785 | − | 0.410668i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.42778 | + | 18.9514i | 0.130229 | + | 0.557393i | ||||
\(35\) | 41.3125 | − | 41.3125i | 1.18036 | − | 1.18036i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −23.7263 | + | 23.7263i | −0.641250 | + | 0.641250i | −0.950863 | − | 0.309613i | \(-0.899801\pi\) |
0.309613 | + | 0.950863i | \(0.399801\pi\) | |||||||
\(38\) | −27.1066 | − | 16.8392i | −0.713332 | − | 0.443136i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 38.3509 | + | 3.72526i | 0.958772 | + | 0.0931315i | ||||
\(41\) | 24.7452i | 0.603542i | 0.953380 | + | 0.301771i | \(0.0975779\pi\) | ||||
−0.953380 | + | 0.301771i | \(0.902422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.8844 | + | 29.8844i | 0.694987 | + | 0.694987i | 0.963325 | − | 0.268338i | \(-0.0864744\pi\) |
−0.268338 | + | 0.963325i | \(0.586474\pi\) | |||||||
\(44\) | 52.5692 | + | 17.7924i | 1.19476 | + | 0.404373i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.22036 | − | 39.4641i | −0.200443 | − | 0.857915i | ||||
\(47\) | 31.3325i | 0.666648i | 0.942812 | + | 0.333324i | \(0.108170\pi\) | ||||
−0.942812 | + | 0.333324i | \(0.891830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 98.1448 | 2.00295 | ||||||||
\(50\) | 3.50963 | − | 0.819987i | 0.0701926 | − | 0.0163997i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 41.6262 | + | 14.0887i | 0.800504 | + | 0.270936i | ||||
\(53\) | −36.8742 | + | 36.8742i | −0.695739 | + | 0.695739i | −0.963489 | − | 0.267750i | \(-0.913720\pi\) |
0.267750 | + | 0.963489i | \(0.413720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −66.8262 | −1.21502 | ||||||||
\(56\) | 61.6638 | + | 74.9322i | 1.10114 | + | 1.33808i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.4877 | − | 39.4188i | 0.422202 | − | 0.679634i | ||||
\(59\) | 14.1325 | + | 14.1325i | 0.239534 | + | 0.239534i | 0.816657 | − | 0.577123i | \(-0.195825\pi\) |
−0.577123 | + | 0.816657i | \(0.695825\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42.5199 | − | 42.5199i | −0.697048 | − | 0.697048i | 0.266725 | − | 0.963773i | \(-0.414059\pi\) |
−0.963773 | + | 0.266725i | \(0.914059\pi\) | |||||||
\(62\) | −51.3260 | + | 11.9918i | −0.827839 | + | 0.193416i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.3172 | + | 62.8036i | −0.192457 | + | 0.981305i | ||||
\(65\) | −52.9153 | −0.814082 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48.7789 | − | 48.7789i | 0.728044 | − | 0.728044i | −0.242186 | − | 0.970230i | \(-0.577864\pi\) |
0.970230 | + | 0.242186i | \(0.0778644\pi\) | |||||||
\(68\) | 34.8940 | − | 17.2467i | 0.513147 | − | 0.253627i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −99.2565 | − | 61.6601i | −1.41795 | − | 0.880858i | ||||
\(71\) | −7.73935 | −0.109005 | −0.0545025 | − | 0.998514i | \(-0.517357\pi\) | ||||
−0.0545025 | + | 0.998514i | \(0.517357\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 85.4163i | 1.17009i | 0.811002 | + | 0.585043i | \(0.198923\pi\) | ||||
−0.811002 | + | 0.585043i | \(0.801077\pi\) | |||||||
\(74\) | 57.0041 | + | 35.4121i | 0.770326 | + | 0.478541i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20.4610 | + | 60.4537i | −0.269223 | + | 0.795443i | ||||
\(77\) | −119.009 | − | 119.009i | −1.54557 | − | 1.54557i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 105.294i | 1.33283i | 0.745581 | + | 0.666416i | \(0.232172\pi\) | ||||
−0.745581 | + | 0.666416i | \(0.767828\pi\) | |||||||
\(80\) | −10.1954 | − | 76.3854i | −0.127443 | − | 0.954817i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 48.1926 | − | 11.2597i | 0.587715 | − | 0.137313i | ||||
\(83\) | 62.1229 | − | 62.1229i | 0.748469 | − | 0.748469i | −0.225723 | − | 0.974192i | \(-0.572474\pi\) |
0.974192 | + | 0.225723i | \(0.0724743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −33.1407 | + | 33.1407i | −0.389890 | + | 0.389890i | ||||
\(86\) | 44.6033 | − | 71.7996i | 0.518643 | − | 0.834879i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.7313 | − | 110.477i | 0.121947 | − | 1.25542i | ||||
\(89\) | 127.172i | 1.42890i | 0.699685 | + | 0.714451i | \(0.253324\pi\) | ||||
−0.699685 | + | 0.714451i | \(0.746676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −94.2355 | − | 94.2355i | −1.03555 | − | 1.03555i | ||||
\(92\) | −72.6629 | + | 35.9142i | −0.789814 | + | 0.390372i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 61.0215 | − | 14.2570i | 0.649165 | − | 0.151670i | ||||
\(95\) | − | 76.8489i | − | 0.808936i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −147.348 | −1.51905 | −0.759525 | − | 0.650478i | \(-0.774569\pi\) | ||||
−0.759525 | + | 0.650478i | \(0.774569\pi\) | |||||||
\(98\) | −44.6582 | − | 191.142i | −0.455696 | − | 1.95043i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.19393 | − | 6.46207i | −0.0319393 | − | 0.0646207i | ||||
\(101\) | −12.7690 | + | 12.7690i | −0.126426 | + | 0.126426i | −0.767489 | − | 0.641063i | \(-0.778494\pi\) |
0.641063 | + | 0.767489i | \(0.278494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.7621 | −0.172448 | −0.0862240 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862240 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(104\) | 8.49746 | − | 87.4798i | 0.0817063 | − | 0.841152i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 88.5929 | + | 55.0357i | 0.835782 | + | 0.519204i | ||||
\(107\) | 15.8889 | + | 15.8889i | 0.148494 | + | 0.148494i | 0.777445 | − | 0.628951i | \(-0.216515\pi\) |
−0.628951 | + | 0.777445i | \(0.716515\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −79.3257 | − | 79.3257i | −0.727758 | − | 0.727758i | 0.242414 | − | 0.970173i | \(-0.422061\pi\) |
−0.970173 | + | 0.242414i | \(0.922061\pi\) | |||||||
\(110\) | 30.4075 | + | 130.147i | 0.276432 | + | 1.18316i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 117.876 | − | 154.189i | 1.05246 | − | 1.37669i | ||||
\(113\) | 167.538 | 1.48263 | 0.741317 | − | 0.671155i | \(-0.234201\pi\) | ||||
0.741317 | + | 0.671155i | \(0.234201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 69.0118 | − | 69.0118i | 0.600102 | − | 0.600102i | ||||
\(116\) | −87.9125 | − | 29.7546i | −0.757866 | − | 0.256505i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 21.0932 | − | 33.9545i | 0.178756 | − | 0.287750i | ||||
\(119\) | −118.039 | −0.991921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 71.5059i | 0.590958i | ||||||||
\(122\) | −63.4621 | + | 102.157i | −0.520181 | + | 0.837355i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 46.7092 | + | 94.5035i | 0.376687 | + | 0.762125i | ||||
\(125\) | 91.2805 | + | 91.2805i | 0.730244 | + | 0.730244i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 198.247i | 1.56100i | 0.625156 | + | 0.780500i | \(0.285035\pi\) | ||||
−0.625156 | + | 0.780500i | \(0.714965\pi\) | |||||||
\(128\) | 127.918 | − | 4.58871i | 0.999357 | − | 0.0358493i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 24.0778 | + | 103.055i | 0.185213 | + | 0.792733i | ||||
\(131\) | −134.339 | + | 134.339i | −1.02549 | + | 1.02549i | −0.0258197 | + | 0.999667i | \(0.508220\pi\) |
−0.999667 | + | 0.0258197i | \(0.991780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 136.858 | − | 136.858i | 1.02901 | − | 1.02901i | ||||
\(134\) | −117.195 | − | 72.8039i | −0.874590 | − | 0.543313i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −49.4663 | − | 60.1102i | −0.363723 | − | 0.441987i | ||||
\(137\) | − | 255.937i | − | 1.86816i | −0.357069 | − | 0.934078i | \(-0.616224\pi\) | ||
0.357069 | − | 0.934078i | \(-0.383776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.7231 | − | 21.7231i | −0.156281 | − | 0.156281i | 0.624635 | − | 0.780917i | \(-0.285248\pi\) |
−0.780917 | + | 0.624635i | \(0.785248\pi\) | |||||||
\(140\) | −74.9220 | + | 221.364i | −0.535157 | + | 1.58117i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.52159 | + | 15.0728i | 0.0247999 | + | 0.106146i | ||||
\(143\) | 152.433i | 1.06597i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 111.755 | 0.770722 | ||||||||
\(146\) | 166.353 | − | 38.8665i | 1.13940 | − | 0.266209i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 43.0286 | − | 127.132i | 0.290734 | − | 0.858998i | ||||
\(149\) | 34.2444 | − | 34.2444i | 0.229828 | − | 0.229828i | −0.582793 | − | 0.812621i | \(-0.698040\pi\) |
0.812621 | + | 0.582793i | \(0.198040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4645 | −0.0957913 | −0.0478956 | − | 0.998852i | \(-0.515251\pi\) | ||||
−0.0478956 | + | 0.998852i | \(0.515251\pi\) | |||||||
\(152\) | 127.047 | + | 12.3409i | 0.835835 | + | 0.0811898i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −177.624 | + | 285.928i | −1.15340 | + | 1.85667i | ||||
\(155\) | −89.7550 | − | 89.7550i | −0.579064 | − | 0.579064i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 31.4652 | + | 31.4652i | 0.200415 | + | 0.200415i | 0.800178 | − | 0.599763i | \(-0.204738\pi\) |
−0.599763 | + | 0.800178i | \(0.704738\pi\) | |||||||
\(158\) | 205.065 | − | 47.9111i | 1.29788 | − | 0.303235i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −144.125 | + | 54.6133i | −0.900782 | + | 0.341333i | ||||
\(161\) | 245.802 | 1.52672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31.4002 | − | 31.4002i | 0.192640 | − | 0.192640i | −0.604196 | − | 0.796836i | \(-0.706506\pi\) |
0.796836 | + | 0.604196i | \(0.206506\pi\) | |||||||
\(164\) | −43.8576 | − | 88.7341i | −0.267424 | − | 0.541062i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −149.255 | − | 92.7201i | −0.899126 | − | 0.558555i | ||||
\(167\) | −36.4796 | −0.218441 | −0.109220 | − | 0.994018i | \(-0.534835\pi\) | ||||
−0.109220 | + | 0.994018i | \(0.534835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 48.2981i | − | 0.285788i | ||||||
\(170\) | 79.6229 | + | 49.4633i | 0.468370 | + | 0.290961i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −160.129 | − | 54.1967i | −0.930982 | − | 0.315097i | ||||
\(173\) | −97.6419 | − | 97.6419i | −0.564404 | − | 0.564404i | 0.366151 | − | 0.930555i | \(-0.380675\pi\) |
−0.930555 | + | 0.366151i | \(0.880675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.8598i | 0.124913i | ||||||||
\(176\) | −220.043 | + | 29.3700i | −1.25024 | + | 0.166875i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 247.674 | − | 57.8664i | 1.39143 | − | 0.325092i | ||||
\(179\) | −89.7427 | + | 89.7427i | −0.501356 | + | 0.501356i | −0.911859 | − | 0.410503i | \(-0.865353\pi\) |
0.410503 | + | 0.911859i | \(0.365353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −115.497 | + | 115.497i | −0.638108 | + | 0.638108i | −0.950088 | − | 0.311981i | \(-0.899008\pi\) |
0.311981 | + | 0.950088i | \(0.399008\pi\) | |||||||
\(182\) | −140.649 | + | 226.408i | −0.772796 | + | 1.24400i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 103.008 | + | 125.173i | 0.559827 | + | 0.680287i | ||||
\(185\) | 161.610i | 0.873569i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 95.4682 | + | 95.4682i | 0.510525 | + | 0.510525i | ||||
\(188\) | −55.5325 | − | 112.355i | −0.295386 | − | 0.597634i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −149.667 | + | 34.9681i | −0.787722 | + | 0.184043i | ||||
\(191\) | − | 62.6278i | − | 0.327894i | −0.986469 | − | 0.163947i | \(-0.947577\pi\) | ||
0.986469 | − | 0.163947i | \(-0.0524227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 223.342 | 1.15721 | 0.578607 | − | 0.815607i | \(-0.303597\pi\) | ||||
0.578607 | + | 0.815607i | \(0.303597\pi\) | |||||||
\(194\) | 67.0468 | + | 286.967i | 0.345602 | + | 1.47921i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −351.938 | + | 173.948i | −1.79560 | + | 0.887491i | ||||
\(197\) | −29.0959 | + | 29.0959i | −0.147695 | + | 0.147695i | −0.777087 | − | 0.629393i | \(-0.783304\pi\) |
0.629393 | + | 0.777087i | \(0.283304\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6967 | 0.0587776 | 0.0293888 | − | 0.999568i | \(-0.490644\pi\) | ||||
0.0293888 | + | 0.999568i | \(0.490644\pi\) | |||||||
\(200\) | −11.1319 | + | 9.16074i | −0.0556595 | + | 0.0458037i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.6786 | + | 19.0581i | 0.151874 | + | 0.0943472i | ||||
\(203\) | 199.021 | + | 199.021i | 0.980398 | + | 0.980398i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 84.2755 | + | 84.2755i | 0.411100 | + | 0.411100i | ||||
\(206\) | 8.08220 | + | 34.5927i | 0.0392340 | + | 0.167926i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −174.238 | + | 23.2562i | −0.837682 | + | 0.111809i | ||||
\(209\) | −221.378 | −1.05923 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.215765 | + | 0.215765i | −0.00102258 | + | 0.00102258i | −0.707618 | − | 0.706595i | \(-0.750230\pi\) |
0.706595 | + | 0.707618i | \(0.250230\pi\) | |||||||
\(212\) | 66.8728 | − | 197.582i | 0.315438 | − | 0.931989i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.7146 | − | 38.1742i | 0.110816 | − | 0.178384i | ||||
\(215\) | 203.556 | 0.946773 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 319.684i | − | 1.47320i | ||||||
\(218\) | −118.396 | + | 190.586i | −0.543099 | + | 0.874247i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 239.632 | − | 118.440i | 1.08924 | − | 0.538365i | ||||
\(221\) | 75.5951 | + | 75.5951i | 0.342059 | + | 0.342059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 371.347i | − | 1.66523i | −0.553850 | − | 0.832617i | \(-0.686842\pi\) | ||
0.553850 | − | 0.832617i | \(-0.313158\pi\) | |||||||
\(224\) | −353.928 | − | 159.409i | −1.58004 | − | 0.711648i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −76.2337 | − | 326.288i | −0.337317 | − | 1.44375i | ||||
\(227\) | 209.823 | − | 209.823i | 0.924330 | − | 0.924330i | −0.0730018 | − | 0.997332i | \(-0.523258\pi\) |
0.997332 | + | 0.0730018i | \(0.0232579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 152.751 | − | 152.751i | 0.667037 | − | 0.667037i | −0.289992 | − | 0.957029i | \(-0.593653\pi\) |
0.957029 | + | 0.289992i | \(0.0936527\pi\) | |||||||
\(230\) | −165.806 | − | 103.002i | −0.720895 | − | 0.447834i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17.9462 | + | 184.753i | −0.0773544 | + | 0.796350i | ||||
\(233\) | − | 272.899i | − | 1.17124i | −0.810586 | − | 0.585619i | \(-0.800851\pi\) | ||
0.810586 | − | 0.585619i | \(-0.199149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 106.710 | + | 106.710i | 0.454084 | + | 0.454084i | ||||
\(236\) | −75.7259 | − | 25.6299i | −0.320873 | − | 0.108601i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 53.7104 | + | 229.886i | 0.225674 | + | 0.965908i | ||||
\(239\) | 104.650i | 0.437866i | 0.975740 | + | 0.218933i | \(0.0702576\pi\) | ||||
−0.975740 | + | 0.218933i | \(0.929742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 148.875 | 0.617737 | 0.308869 | − | 0.951105i | \(-0.400050\pi\) | ||||
0.308869 | + | 0.951105i | \(0.400050\pi\) | |||||||
\(242\) | 139.261 | − | 32.5369i | 0.575460 | − | 0.134450i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 227.833 | + | 77.1117i | 0.933743 | + | 0.316031i | ||||
\(245\) | 334.254 | − | 334.254i | 1.36430 | − | 1.36430i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −175.295 | −0.709698 | ||||||||
\(248\) | 162.797 | − | 133.970i | 0.656438 | − | 0.540201i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 136.239 | − | 219.308i | 0.544954 | − | 0.877233i | ||||
\(251\) | −143.712 | − | 143.712i | −0.572558 | − | 0.572558i | 0.360284 | − | 0.932843i | \(-0.382680\pi\) |
−0.932843 | + | 0.360284i | \(0.882680\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −198.802 | − | 198.802i | −0.785778 | − | 0.785778i | ||||
\(254\) | 386.096 | − | 90.2071i | 1.52006 | − | 0.355146i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −67.1424 | − | 247.038i | −0.262275 | − | 0.964993i | ||||
\(257\) | −134.023 | −0.521489 | −0.260745 | − | 0.965408i | \(-0.583968\pi\) | ||||
−0.260745 | + | 0.965408i | \(0.583968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −287.807 | + | 287.807i | −1.11122 | + | 1.11122i | ||||
\(260\) | 189.749 | − | 93.7853i | 0.729806 | − | 0.360713i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 322.759 | + | 200.504i | 1.23190 | + | 0.765283i | ||||
\(263\) | −290.386 | −1.10413 | −0.552066 | − | 0.833801i | \(-0.686160\pi\) | ||||
−0.552066 | + | 0.833801i | \(0.686160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 251.166i | 0.947798i | ||||||||
\(266\) | −328.812 | − | 204.264i | −1.23613 | − | 0.767911i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −88.4627 | + | 261.371i | −0.330085 | + | 0.975264i | ||||
\(269\) | 74.2628 | + | 74.2628i | 0.276070 | + | 0.276070i | 0.831538 | − | 0.555468i | \(-0.187461\pi\) |
−0.555468 | + | 0.831538i | \(0.687461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 70.8329i | 0.261376i | 0.991424 | + | 0.130688i | \(0.0417186\pi\) | ||||
−0.991424 | + | 0.130688i | \(0.958281\pi\) | |||||||
\(272\) | −94.5593 | + | 123.690i | −0.347644 | + | 0.454742i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −498.451 | + | 116.458i | −1.81916 | + | 0.425028i | ||||
\(275\) | 17.6799 | − | 17.6799i | 0.0642906 | − | 0.0642906i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −96.6953 | + | 96.6953i | −0.349081 | + | 0.349081i | −0.859767 | − | 0.510686i | \(-0.829391\pi\) |
0.510686 | + | 0.859767i | \(0.329391\pi\) | |||||||
\(278\) | −32.4223 | + | 52.1914i | −0.116627 | + | 0.187739i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 465.209 | + | 45.1886i | 1.66146 | + | 0.161388i | ||||
\(281\) | 138.151i | 0.491640i | 0.969316 | + | 0.245820i | \(0.0790572\pi\) | ||||
−0.969316 | + | 0.245820i | \(0.920943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −295.011 | − | 295.011i | −1.04244 | − | 1.04244i | −0.999059 | − | 0.0433821i | \(-0.986187\pi\) |
−0.0433821 | − | 0.999059i | \(-0.513813\pi\) | |||||||
\(284\) | 27.7526 | − | 13.7170i | 0.0977204 | − | 0.0482991i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 296.871 | − | 69.3607i | 1.03801 | − | 0.242520i | ||||
\(287\) | 300.168i | 1.04588i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −194.310 | −0.672353 | ||||||||
\(290\) | −50.8510 | − | 217.648i | −0.175348 | − | 0.750510i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −151.389 | − | 306.295i | −0.518455 | − | 1.04896i | ||||
\(293\) | 33.4759 | − | 33.4759i | 0.114252 | − | 0.114252i | −0.647669 | − | 0.761922i | \(-0.724256\pi\) |
0.761922 | + | 0.647669i | \(0.224256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 96.2630 | 0.326315 | ||||||||
\(296\) | −267.174 | − | 25.9523i | −0.902616 | − | 0.0876768i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −82.2748 | − | 51.1107i | −0.276090 | − | 0.171513i | ||||
\(299\) | −157.418 | − | 157.418i | −0.526483 | − | 0.526483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 362.508 | + | 362.508i | 1.20434 | + | 1.20434i | ||||
\(302\) | 6.58169 | + | 28.1703i | 0.0217937 | + | 0.0932792i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −33.7749 | − | 253.046i | −0.111102 | − | 0.832387i | ||||
\(305\) | −289.622 | −0.949582 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −92.6638 | + | 92.6638i | −0.301836 | + | 0.301836i | −0.841732 | − | 0.539896i | \(-0.818464\pi\) |
0.539896 | + | 0.841732i | \(0.318464\pi\) | |||||||
\(308\) | 637.682 | + | 215.828i | 2.07040 | + | 0.700739i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −133.962 | + | 215.643i | −0.432135 | + | 0.695623i | ||||
\(311\) | 18.5610 | 0.0596817 | 0.0298408 | − | 0.999555i | \(-0.490500\pi\) | ||||
0.0298408 | + | 0.999555i | \(0.490500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 55.1534i | − | 0.176209i | −0.996111 | − | 0.0881045i | \(-0.971919\pi\) | ||
0.996111 | − | 0.0881045i | \(-0.0280809\pi\) | |||||||
\(314\) | 46.9626 | − | 75.5975i | 0.149563 | − | 0.240756i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −186.619 | − | 377.573i | −0.590566 | − | 1.19485i | ||||
\(317\) | −62.2977 | − | 62.2977i | −0.196523 | − | 0.196523i | 0.601985 | − | 0.798507i | \(-0.294377\pi\) |
−0.798507 | + | 0.601985i | \(0.794377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 321.931i | − | 1.00919i | ||||||
\(320\) | 171.943 | + | 255.841i | 0.537320 | + | 0.799502i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −111.846 | − | 478.712i | −0.347348 | − | 1.48668i | ||||
\(323\) | −109.787 | + | 109.787i | −0.339897 | + | 0.339897i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.9996 | − | 13.9996i | 0.0430756 | − | 0.0430756i | ||||
\(326\) | −75.4414 | − | 46.8657i | −0.231415 | − | 0.143760i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −152.858 | + | 125.791i | −0.466030 | + | 0.383509i | ||||
\(329\) | 380.073i | 1.15524i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 373.767 | + | 373.767i | 1.12921 | + | 1.12921i | 0.990307 | + | 0.138899i | \(0.0443564\pi\) |
0.138899 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(332\) | −112.663 | + | 332.871i | −0.339345 | + | 1.00262i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.5991 | + | 71.0459i | 0.0496979 | + | 0.212712i | ||||
\(335\) | − | 332.255i | − | 0.991807i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −519.936 | −1.54284 | −0.771419 | − | 0.636328i | \(-0.780453\pi\) | ||||
−0.771419 | + | 0.636328i | \(0.780453\pi\) | |||||||
\(338\) | −94.0630 | + | 21.9768i | −0.278293 | + | 0.0650201i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 60.1020 | − | 177.577i | 0.176771 | − | 0.522284i | ||||
\(341\) | −258.557 | + | 258.557i | −0.758231 | + | 0.758231i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 596.142 | 1.73802 | ||||||||
\(344\) | −32.6883 | + | 336.520i | −0.0950240 | + | 0.978255i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −145.733 | + | 234.592i | −0.421194 | + | 0.678011i | ||||
\(347\) | −122.160 | − | 122.160i | −0.352045 | − | 0.352045i | 0.508825 | − | 0.860870i | \(-0.330080\pi\) |
−0.860870 | + | 0.508825i | \(0.830080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −279.483 | − | 279.483i | −0.800810 | − | 0.800810i | 0.182412 | − | 0.983222i | \(-0.441609\pi\) |
−0.983222 | + | 0.182412i | \(0.941609\pi\) | |||||||
\(350\) | 42.5730 | − | 9.94671i | 0.121637 | − | 0.0284192i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 157.324 | + | 415.181i | 0.446944 | + | 1.17949i | ||||
\(353\) | 212.266 | 0.601320 | 0.300660 | − | 0.953731i | \(-0.402793\pi\) | ||||
0.300660 | + | 0.953731i | \(0.402793\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.3581 | + | 26.3581i | −0.0742482 | + | 0.0742482i | ||||
\(356\) | −225.396 | − | 456.028i | −0.633134 | − | 1.28098i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 215.614 | + | 133.943i | 0.602272 | + | 0.374144i | ||||
\(359\) | 435.033 | 1.21179 | 0.605895 | − | 0.795545i | \(-0.292815\pi\) | ||||
0.605895 | + | 0.795545i | \(0.292815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 106.419i | 0.294789i | ||||||||
\(362\) | 277.491 | + | 172.383i | 0.766551 | + | 0.476196i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 504.939 | + | 170.900i | 1.38720 | + | 0.469505i | ||||
\(365\) | 290.905 | + | 290.905i | 0.796999 | + | 0.796999i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 125.535i | 0.342058i | 0.985266 | + | 0.171029i | \(0.0547091\pi\) | ||||
−0.985266 | + | 0.171029i | \(0.945291\pi\) | |||||||
\(368\) | 196.909 | − | 257.570i | 0.535079 | − | 0.699919i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 314.744 | − | 73.5365i | 0.850660 | − | 0.198747i | ||||
\(371\) | −447.295 | + | 447.295i | −1.20565 | + | 1.20565i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −302.389 | + | 302.389i | −0.810694 | + | 0.810694i | −0.984738 | − | 0.174044i | \(-0.944317\pi\) |
0.174044 | + | 0.984738i | \(0.444317\pi\) | |||||||
\(374\) | 142.489 | − | 229.370i | 0.380986 | − | 0.613287i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −193.549 | + | 159.277i | −0.514758 | + | 0.423608i | ||||
\(377\) | − | 254.917i | − | 0.676171i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 189.784 | + | 189.784i | 0.500751 | + | 0.500751i | 0.911671 | − | 0.410921i | \(-0.134793\pi\) |
−0.410921 | + | 0.911671i | \(0.634793\pi\) | |||||||
\(380\) | 136.204 | + | 275.573i | 0.358432 | + | 0.725192i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −121.971 | + | 28.4972i | −0.319296 | + | 0.0745999i | ||||
\(383\) | − | 639.916i | − | 1.67080i | −0.549644 | − | 0.835399i | \(-0.685237\pi\) | ||
0.549644 | − | 0.835399i | \(-0.314763\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −810.623 | −2.10551 | ||||||||
\(386\) | −101.626 | − | 434.970i | −0.263280 | − | 1.12687i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 528.376 | − | 261.154i | 1.36179 | − | 0.673078i | ||||
\(389\) | −499.333 | + | 499.333i | −1.28363 | + | 1.28363i | −0.345046 | + | 0.938586i | \(0.612137\pi\) |
−0.938586 | + | 0.345046i | \(0.887863\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −197.181 | −0.504300 | ||||||||
\(392\) | 498.913 | + | 606.266i | 1.27274 | + | 1.54660i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 69.9050 | + | 43.4264i | 0.177424 | + | 0.110219i | ||||
\(395\) | 358.601 | + | 358.601i | 0.907851 | + | 0.907851i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 492.518 | + | 492.518i | 1.24060 | + | 1.24060i | 0.959753 | + | 0.280846i | \(0.0906151\pi\) |
0.280846 | + | 0.959753i | \(0.409385\pi\) | |||||||
\(398\) | −5.32230 | − | 22.7800i | −0.0133726 | − | 0.0572361i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.9063 | + | 17.5116i | 0.0572657 | + | 0.0437789i | ||||
\(401\) | −705.045 | −1.75822 | −0.879109 | − | 0.476621i | \(-0.841862\pi\) | ||||
−0.879109 | + | 0.476621i | \(0.841862\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −204.735 | + | 204.735i | −0.508026 | + | 0.508026i | ||||
\(404\) | 23.1572 | − | 68.4200i | 0.0573198 | − | 0.169356i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 297.044 | − | 478.162i | 0.731635 | − | 1.17774i | ||||
\(407\) | 465.550 | 1.14386 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 279.815i | − | 0.684144i | −0.939674 | − | 0.342072i | \(-0.888871\pi\) | ||
0.939674 | − | 0.342072i | \(-0.111129\pi\) | |||||||
\(410\) | 125.783 | − | 202.478i | 0.306789 | − | 0.493849i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 63.6934 | − | 31.4810i | 0.154596 | − | 0.0764102i | ||||
\(413\) | 171.432 | + | 171.432i | 0.415090 | + | 0.415090i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 423.147i | − | 1.01963i | ||||||
\(416\) | 124.575 | + | 328.755i | 0.299459 | + | 0.790276i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 100.732 | + | 431.146i | 0.240987 | + | 1.03145i | ||||
\(419\) | 573.583 | − | 573.583i | 1.36893 | − | 1.36893i | 0.506968 | − | 0.861965i | \(-0.330766\pi\) |
0.861965 | − | 0.506968i | \(-0.169234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −213.341 | + | 213.341i | −0.506749 | + | 0.506749i | −0.913527 | − | 0.406778i | \(-0.866652\pi\) |
0.406778 | + | 0.913527i | \(0.366652\pi\) | |||||||
\(422\) | 0.518392 | + | 0.322035i | 0.00122842 | + | 0.000763117i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −415.229 | − | 40.3338i | −0.979314 | − | 0.0951269i | ||||
\(425\) | − | 17.5358i | − | 0.0412606i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −515.781 | − | 515.781i | −1.20792 | − | 1.20792i | ||||
\(428\) | −85.1369 | − | 28.8152i | −0.198918 | − | 0.0673251i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −92.6230 | − | 396.436i | −0.215402 | − | 0.921944i | ||||
\(431\) | 166.900i | 0.387239i | 0.981077 | + | 0.193619i | \(0.0620227\pi\) | ||||
−0.981077 | + | 0.193619i | \(0.937977\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 233.153 | 0.538459 | 0.269230 | − | 0.963076i | \(-0.413231\pi\) | ||||
0.269230 | + | 0.963076i | \(0.413231\pi\) | |||||||
\(434\) | −622.602 | + | 145.464i | −1.43457 | + | 0.335171i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 425.048 | + | 143.860i | 0.974882 | + | 0.329955i | ||||
\(437\) | 228.619 | − | 228.619i | 0.523155 | − | 0.523155i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 440.480 | 1.00337 | 0.501686 | − | 0.865050i | \(-0.332713\pi\) | ||||
0.501686 | + | 0.865050i | \(0.332713\pi\) | |||||||
\(440\) | −339.707 | − | 412.803i | −0.772061 | − | 0.938189i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 112.828 | − | 181.623i | 0.255266 | − | 0.410912i | ||||
\(443\) | 312.524 | + | 312.524i | 0.705473 | + | 0.705473i | 0.965580 | − | 0.260107i | \(-0.0837579\pi\) |
−0.260107 | + | 0.965580i | \(0.583758\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 433.114 | + | 433.114i | 0.973290 | + | 0.973290i | ||||
\(446\) | −723.217 | + | 168.972i | −1.62156 | + | 0.378861i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −149.412 | + | 761.827i | −0.333509 | + | 1.70051i | ||||
\(449\) | 734.338 | 1.63550 | 0.817748 | − | 0.575576i | \(-0.195222\pi\) | ||||
0.817748 | + | 0.575576i | \(0.195222\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 242.772 | − | 242.772i | 0.538297 | − | 0.538297i | ||||
\(452\) | −600.774 | + | 296.938i | −1.32915 | + | 0.656942i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −504.115 | − | 313.166i | −1.11039 | − | 0.689794i | ||||
\(455\) | −641.880 | −1.41073 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 692.749i | − | 1.51586i | −0.652335 | − | 0.757931i | \(-0.726211\pi\) | ||
0.652335 | − | 0.757931i | \(-0.273789\pi\) | |||||||
\(458\) | −366.997 | − | 227.986i | −0.801303 | − | 0.497785i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −125.156 | + | 369.784i | −0.272078 | + | 0.803878i | ||||
\(461\) | −298.447 | − | 298.447i | −0.647391 | − | 0.647391i | 0.304971 | − | 0.952362i | \(-0.401353\pi\) |
−0.952362 | + | 0.304971i | \(0.901353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 281.830i | − | 0.608705i | −0.952560 | − | 0.304352i | \(-0.901560\pi\) | ||
0.952560 | − | 0.304352i | \(-0.0984400\pi\) | |||||||
\(464\) | 367.982 | − | 49.1159i | 0.793065 | − | 0.105853i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −531.484 | + | 124.175i | −1.14052 | + | 0.266471i | ||||
\(467\) | −198.116 | + | 198.116i | −0.424232 | + | 0.424232i | −0.886658 | − | 0.462426i | \(-0.846979\pi\) |
0.462426 | + | 0.886658i | \(0.346979\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 591.704 | − | 591.704i | 1.26163 | − | 1.26163i | ||||
\(470\) | 159.267 | − | 256.378i | 0.338866 | − | 0.545485i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.4585 | + | 159.142i | −0.0327510 | + | 0.337166i | ||||
\(473\) | − | 586.384i | − | 1.23971i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.3316 | + | 20.3316i | 0.0428033 | + | 0.0428033i | ||||
\(476\) | 423.276 | − | 209.207i | 0.889234 | − | 0.439512i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 203.811 | − | 47.6182i | 0.426383 | − | 0.0996197i | ||||
\(479\) | − | 917.713i | − | 1.91589i | −0.286945 | − | 0.957947i | \(-0.592640\pi\) | ||
0.286945 | − | 0.957947i | \(-0.407360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 368.639 | 0.766401 | ||||||||
\(482\) | −67.7416 | − | 289.941i | −0.140543 | − | 0.601537i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −126.735 | − | 256.413i | −0.261848 | − | 0.529780i | ||||
\(485\) | −501.826 | + | 501.826i | −1.03469 | + | 1.03469i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −426.183 | −0.875119 | −0.437559 | − | 0.899190i | \(-0.644157\pi\) | ||||
−0.437559 | + | 0.899190i | \(0.644157\pi\) | |||||||
\(488\) | 46.5093 | − | 478.805i | 0.0953059 | − | 0.981157i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −803.070 | − | 498.883i | −1.63892 | − | 1.01813i | ||||
\(491\) | 266.299 | + | 266.299i | 0.542361 | + | 0.542361i | 0.924220 | − | 0.381859i | \(-0.124716\pi\) |
−0.381859 | + | 0.924220i | \(0.624716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −159.653 | − | 159.653i | −0.323840 | − | 0.323840i | ||||
\(494\) | 79.7636 | + | 341.396i | 0.161465 | + | 0.691086i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −334.989 | − | 256.095i | −0.675382 | − | 0.516321i | ||||
\(497\) | −93.8809 | −0.188895 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −264.104 | + | 264.104i | −0.529266 | + | 0.529266i | −0.920353 | − | 0.391088i | \(-0.872099\pi\) |
0.391088 | + | 0.920353i | \(0.372099\pi\) | |||||||
\(500\) | −489.106 | − | 165.541i | −0.978211 | − | 0.331082i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −214.494 | + | 345.279i | −0.427279 | + | 0.687807i | ||||
\(503\) | 574.766 | 1.14268 | 0.571338 | − | 0.820715i | \(-0.306425\pi\) | ||||
0.571338 | + | 0.820715i | \(0.306425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 86.9756i | 0.172229i | ||||||||
\(506\) | −296.717 | + | 477.636i | −0.586398 | + | 0.943946i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −351.366 | − | 710.895i | −0.691665 | − | 1.39940i | ||||
\(509\) | −170.592 | − | 170.592i | −0.335152 | − | 0.335152i | 0.519387 | − | 0.854539i | \(-0.326160\pi\) |
−0.854539 | + | 0.519387i | \(0.826160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1036.13i | 2.02765i | ||||||||
\(512\) | −450.568 | + | 243.172i | −0.880016 | + | 0.474944i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 60.9835 | + | 261.016i | 0.118645 | + | 0.507813i | ||||
\(515\) | −60.4930 | + | 60.4930i | −0.117462 | + | 0.117462i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 307.398 | − | 307.398i | 0.594581 | − | 0.594581i | ||||
\(518\) | 691.478 | + | 429.560i | 1.33490 | + | 0.829266i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −268.992 | − | 326.872i | −0.517293 | − | 0.628600i | ||||
\(521\) | 37.1210i | 0.0712496i | 0.999365 | + | 0.0356248i | \(0.0113421\pi\) | ||||
−0.999365 | + | 0.0356248i | \(0.988658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −199.555 | − | 199.555i | −0.381558 | − | 0.381558i | 0.490105 | − | 0.871663i | \(-0.336958\pi\) |
−0.871663 | + | 0.490105i | \(0.836958\pi\) | |||||||
\(524\) | 243.629 | − | 719.823i | 0.464941 | − | 1.37371i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 132.133 | + | 565.542i | 0.251203 | + | 1.07518i | ||||
\(527\) | 256.449i | 0.486620i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −118.392 | −0.223804 | ||||||||
\(530\) | 489.159 | − | 114.287i | 0.922942 | − | 0.215635i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −248.198 | + | 733.323i | −0.466538 | + | 1.37843i | ||||
\(533\) | 192.236 | − | 192.236i | 0.360667 | − | 0.360667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 108.226 | 0.202292 | ||||||||
\(536\) | 549.286 | + | 53.3555i | 1.02479 | + | 0.0995439i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 110.839 | − | 178.422i | 0.206021 | − | 0.331639i | ||||
\(539\) | −962.884 | − | 962.884i | −1.78643 | − | 1.78643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 278.121 | + | 278.121i | 0.514086 | + | 0.514086i | 0.915776 | − | 0.401690i | \(-0.131577\pi\) |
−0.401690 | + | 0.915776i | \(0.631577\pi\) | |||||||
\(542\) | 137.951 | − | 32.2307i | 0.254521 | − | 0.0594661i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 283.919 | + | 127.877i | 0.521910 | + | 0.235068i | ||||
\(545\) | −540.323 | −0.991418 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 724.938 | − | 724.938i | 1.32530 | − | 1.32530i | 0.415876 | − | 0.909421i | \(-0.363475\pi\) |
0.909421 | − | 0.415876i | \(-0.136525\pi\) | |||||||
\(548\) | 453.614 | + | 917.767i | 0.827763 | + | 1.67476i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −42.4773 | − | 26.3877i | −0.0772314 | − | 0.0479777i | ||||
\(551\) | 370.215 | 0.671897 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1277.25i | 2.30967i | ||||||||
\(554\) | 232.318 | + | 144.320i | 0.419346 | + | 0.260506i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 116.398 | + | 39.3958i | 0.209350 | + | 0.0708558i | ||||
\(557\) | −268.298 | − | 268.298i | −0.481685 | − | 0.481685i | 0.423985 | − | 0.905669i | \(-0.360631\pi\) |
−0.905669 | + | 0.423985i | \(0.860631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 464.320i | − | 0.830625i | ||||||
\(560\) | −123.674 | − | 926.579i | −0.220846 | − | 1.65461i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 269.056 | − | 62.8619i | 0.478747 | − | 0.111854i | ||||
\(563\) | 78.4662 | − | 78.4662i | 0.139372 | − | 0.139372i | −0.633979 | − | 0.773350i | \(-0.718579\pi\) |
0.773350 | + | 0.633979i | \(0.218579\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 570.587 | − | 570.587i | 1.00989 | − | 1.00989i | ||||
\(566\) | −440.311 | + | 708.785i | −0.777935 | + | 1.25227i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −39.3426 | − | 47.8080i | −0.0692651 | − | 0.0841691i | ||||
\(569\) | 801.999i | 1.40949i | 0.709461 | + | 0.704744i | \(0.248938\pi\) | ||||
−0.709461 | + | 0.704744i | \(0.751062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 79.9964 | + | 79.9964i | 0.140099 | + | 0.140099i | 0.773678 | − | 0.633579i | \(-0.218415\pi\) |
−0.633579 | + | 0.773678i | \(0.718415\pi\) | |||||||
\(572\) | −270.167 | − | 546.611i | −0.472320 | − | 0.955613i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 584.592 | − | 136.583i | 1.01845 | − | 0.237950i | ||||
\(575\) | 36.5163i | 0.0635066i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −237.186 | −0.411068 | −0.205534 | − | 0.978650i | \(-0.565893\pi\) | ||||
−0.205534 | + | 0.978650i | \(0.565893\pi\) | |||||||
\(578\) | 88.4158 | + | 378.429i | 0.152968 | + | 0.654721i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −400.742 | + | 198.070i | −0.690934 | + | 0.341500i | ||||
\(581\) | 753.571 | − | 753.571i | 1.29702 | − | 1.29702i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 723.534 | 1.24105 | ||||||||
\(584\) | −527.639 | + | 434.209i | −0.903492 | + | 0.743509i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −80.4283 | − | 49.9637i | −0.137250 | − | 0.0852622i | ||||
\(587\) | 267.958 | + | 267.958i | 0.456487 | + | 0.456487i | 0.897500 | − | 0.441014i | \(-0.145381\pi\) |
−0.441014 | + | 0.897500i | \(0.645381\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −297.336 | − | 297.336i | −0.504815 | − | 0.504815i | ||||
\(590\) | −43.8020 | − | 187.477i | −0.0742407 | − | 0.317758i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 71.0273 | + | 532.145i | 0.119979 | + | 0.898893i | ||||
\(593\) | 607.086 | 1.02375 | 0.511877 | − | 0.859059i | \(-0.328950\pi\) | ||||
0.511877 | + | 0.859059i | \(0.328950\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −402.007 | + | 402.007i | −0.675642 | + | 0.675642i | ||||
\(596\) | −62.1037 | + | 183.491i | −0.104201 | + | 0.307871i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −234.951 | + | 378.210i | −0.392895 | + | 0.632457i | ||||
\(599\) | −575.392 | −0.960587 | −0.480294 | − | 0.877108i | \(-0.659470\pi\) | ||||
−0.480294 | + | 0.877108i | \(0.659470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 310.094i | − | 0.515963i | −0.966150 | − | 0.257981i | \(-0.916943\pi\) | ||
0.966150 | − | 0.257981i | \(-0.0830573\pi\) | |||||||
\(602\) | 541.052 | − | 870.952i | 0.898758 | − | 1.44676i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 51.8683 | − | 25.6363i | 0.0858746 | − | 0.0424443i | ||||
\(605\) | 243.529 | + | 243.529i | 0.402528 | + | 0.402528i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 556.510i | − | 0.916820i | −0.888741 | − | 0.458410i | \(-0.848419\pi\) | ||
0.888741 | − | 0.458410i | \(-0.151581\pi\) | |||||||
\(608\) | −477.451 | + | 180.920i | −0.785281 | + | 0.297566i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 131.785 | + | 564.054i | 0.216041 | + | 0.924679i | ||||
\(611\) | 243.409 | − | 243.409i | 0.398378 | − | 0.398378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −326.241 | + | 326.241i | −0.532204 | + | 0.532204i | −0.921228 | − | 0.389024i | \(-0.872812\pi\) |
0.389024 | + | 0.921228i | \(0.372812\pi\) | |||||||
\(614\) | 222.632 | + | 138.303i | 0.362592 | + | 0.225249i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 130.175 | − | 1340.12i | 0.211323 | − | 2.17553i | ||||
\(617\) | 502.068i | 0.813725i | 0.913490 | + | 0.406862i | \(0.133377\pi\) | ||||
−0.913490 | + | 0.406862i | \(0.866623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 304.429 | + | 304.429i | 0.491808 | + | 0.491808i | 0.908876 | − | 0.417067i | \(-0.136942\pi\) |
−0.417067 | + | 0.908876i | \(0.636942\pi\) | |||||||
\(620\) | 480.932 | + | 162.774i | 0.775696 | + | 0.262539i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.44570 | − | 36.1485i | −0.0135783 | − | 0.0581166i | ||||
\(623\) | 1542.64i | 2.47615i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 576.701 | 0.922721 | ||||||||
\(626\) | −107.414 | + | 25.0961i | −0.171588 | + | 0.0400896i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −168.599 | − | 57.0635i | −0.268470 | − | 0.0908654i | ||||
\(629\) | 230.877 | − | 230.877i | 0.367054 | − | 0.367054i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.60592 | 0.0136385 | 0.00681927 | − | 0.999977i | \(-0.497829\pi\) | ||||
0.00681927 | + | 0.999977i | \(0.497829\pi\) | |||||||
\(632\) | −650.427 | + | 535.254i | −1.02916 | + | 0.846921i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −92.9809 | + | 149.675i | −0.146658 | + | 0.236080i | ||||
\(635\) | 675.174 | + | 675.174i | 1.06327 | + | 1.06327i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −762.446 | − | 762.446i | −1.19693 | − | 1.19693i | ||||
\(638\) | −626.977 | + | 146.486i | −0.982723 | + | 0.229603i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 420.025 | − | 451.280i | 0.656289 | − | 0.705126i | ||||
\(641\) | 445.780 | 0.695445 | 0.347722 | − | 0.937598i | \(-0.386955\pi\) | ||||
0.347722 | + | 0.937598i | \(0.386955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −118.001 | + | 118.001i | −0.183517 | + | 0.183517i | −0.792886 | − | 0.609369i | \(-0.791423\pi\) |
0.609369 | + | 0.792886i | \(0.291423\pi\) | |||||||
\(644\) | −881.424 | + | 435.651i | −1.36867 | + | 0.676477i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 263.771 | + | 163.860i | 0.408314 | + | 0.253653i | ||||
\(647\) | −1081.35 | −1.67132 | −0.835662 | − | 0.549243i | \(-0.814916\pi\) | ||||
−0.835662 | + | 0.549243i | \(0.814916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 277.305i | − | 0.427280i | ||||||
\(650\) | −33.6350 | − | 20.8947i | −0.0517462 | − | 0.0321458i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −56.9457 | + | 168.251i | −0.0873400 | + | 0.258054i | ||||
\(653\) | 586.227 | + | 586.227i | 0.897744 | + | 0.897744i | 0.995236 | − | 0.0974927i | \(-0.0310823\pi\) |
−0.0974927 | + | 0.995236i | \(0.531082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 915.041i | 1.39701i | ||||||||
\(656\) | 314.538 | + | 240.461i | 0.479479 | + | 0.366556i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 740.211 | − | 172.942i | 1.12494 | − | 0.262830i | ||||
\(659\) | −469.999 | + | 469.999i | −0.713201 | + | 0.713201i | −0.967204 | − | 0.254003i | \(-0.918253\pi\) |
0.254003 | + | 0.967204i | \(0.418253\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −884.745 | + | 884.745i | −1.33849 | + | 1.33849i | −0.440976 | + | 0.897519i | \(0.645368\pi\) |
−0.897519 | + | 0.440976i | \(0.854632\pi\) | |||||||
\(662\) | 557.857 | − | 898.003i | 0.842685 | − | 1.35650i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 699.548 | + | 67.9515i | 1.05354 | + | 0.102337i | ||||
\(665\) | − | 932.202i | − | 1.40181i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 332.460 | + | 332.460i | 0.498441 | + | 0.498441i | ||||
\(668\) | 130.813 | − | 64.6552i | 0.195827 | − | 0.0967892i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −647.084 | + | 151.184i | −0.965797 | + | 0.225648i | ||||
\(671\) | 834.314i | 1.24339i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 684.329 | 1.01683 | 0.508417 | − | 0.861111i | \(-0.330231\pi\) | ||||
0.508417 | + | 0.861111i | \(0.330231\pi\) | |||||||
\(674\) | 236.584 | + | 1012.60i | 0.351014 | + | 1.50238i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 85.6018 | + | 173.192i | 0.126630 | + | 0.256202i | ||||
\(677\) | 383.762 | − | 383.762i | 0.566857 | − | 0.566857i | −0.364390 | − | 0.931246i | \(-0.618722\pi\) |
0.931246 | + | 0.364390i | \(0.118722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1787.38 | −2.63237 | ||||||||
\(680\) | −373.188 | − | 36.2500i | −0.548805 | − | 0.0533089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 621.202 | + | 385.903i | 0.910854 | + | 0.565840i | ||||
\(683\) | −903.626 | − | 903.626i | −1.32302 | − | 1.32302i | −0.911315 | − | 0.411709i | \(-0.864932\pi\) |
−0.411709 | − | 0.911315i | \(-0.635068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −871.652 | − | 871.652i | −1.27248 | − | 1.27248i | ||||
\(686\) | −271.259 | − | 1161.02i | −0.395421 | − | 1.69244i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 670.263 | − | 89.4625i | 0.974220 | − | 0.130033i | ||||
\(689\) | 572.920 | 0.831524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −63.6870 | + | 63.6870i | −0.0921665 | + | 0.0921665i | −0.751687 | − | 0.659520i | \(-0.770759\pi\) |
0.659520 | + | 0.751687i | \(0.270759\pi\) | |||||||
\(692\) | 523.192 | + | 177.078i | 0.756057 | + | 0.255893i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −182.326 | + | 293.497i | −0.262718 | + | 0.422907i | ||||
\(695\) | −147.966 | −0.212901 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 240.793i | − | 0.345470i | ||||||
\(698\) | −417.135 | + | 671.478i | −0.597615 | + | 0.962003i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −38.7434 | − | 78.3870i | −0.0553478 | − | 0.111981i | ||||
\(701\) | −218.312 | − | 218.312i | −0.311430 | − | 0.311430i | 0.534033 | − | 0.845463i | \(-0.320676\pi\) |
−0.845463 | + | 0.534033i | \(0.820676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 535.374i | 0.761557i | ||||||||
\(704\) | 736.999 | − | 495.314i | 1.04687 | − | 0.703571i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −96.5861 | − | 413.399i | −0.136808 | − | 0.585551i | ||||
\(707\) | −154.893 | + | 154.893i | −0.219084 | + | 0.219084i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −822.199 | + | 822.199i | −1.15966 | + | 1.15966i | −0.175112 | + | 0.984548i | \(0.556029\pi\) |
−0.984548 | + | 0.175112i | \(0.943971\pi\) | |||||||
\(710\) | 63.3273 | + | 39.3402i | 0.0891934 | + | 0.0554087i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −785.577 | + | 646.473i | −1.10334 | + | 0.907968i | ||||
\(713\) | − | 534.026i | − | 0.748985i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 519.145 | + | 519.145i | 0.726077 | + | 0.726077i | ||||
\(716\) | 162.752 | − | 480.866i | 0.227307 | − | 0.671600i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −197.950 | − | 847.248i | −0.275697 | − | 1.18001i | ||||
\(719\) | − | 340.913i | − | 0.474149i | −0.971491 | − | 0.237074i | \(-0.923811\pi\) | ||
0.971491 | − | 0.237074i | \(-0.0761885\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −215.461 | −0.298836 | ||||||||
\(722\) | 207.256 | − | 48.4231i | 0.287058 | − | 0.0670680i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 209.460 | − | 618.867i | 0.289309 | − | 0.854788i | ||||
\(725\) | −29.5664 | + | 29.5664i | −0.0407813 | + | 0.0407813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −803.090 | −1.10466 | −0.552331 | − | 0.833625i | \(-0.686262\pi\) | ||||
−0.552331 | + | 0.833625i | \(0.686262\pi\) | |||||||
\(728\) | 103.077 | − | 1061.16i | 0.141589 | − | 1.45763i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 434.183 | − | 698.920i | 0.594771 | − | 0.957424i | ||||
\(731\) | −290.802 | − | 290.802i | −0.397813 | − | 0.397813i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 481.592 | + | 481.592i | 0.657015 | + | 0.657015i | 0.954673 | − | 0.297658i | \(-0.0962054\pi\) |
−0.297658 | + | 0.954673i | \(0.596205\pi\) | |||||||
\(734\) | 244.486 | − | 57.1215i | 0.333087 | − | 0.0778222i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −591.229 | − | 266.290i | −0.803301 | − | 0.361807i | ||||
\(737\) | −957.127 | −1.29868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 173.622 | − | 173.622i | 0.234941 | − | 0.234941i | −0.579810 | − | 0.814752i | \(-0.696873\pi\) |
0.814752 | + | 0.579810i | \(0.196873\pi\) | |||||||
\(740\) | −286.432 | − | 579.519i | −0.387071 | − | 0.783134i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1074.66 | + | 667.600i | 1.44833 | + | 0.899731i | ||||
\(743\) | −1316.22 | −1.77149 | −0.885744 | − | 0.464173i | \(-0.846351\pi\) | ||||
−0.885744 | + | 0.464173i | \(0.846351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 233.254i | − | 0.313093i | ||||||
\(746\) | 726.512 | + | 451.323i | 0.973876 | + | 0.604991i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −511.545 | − | 173.136i | −0.683883 | − | 0.231465i | ||||
\(749\) | 192.737 | + | 192.737i | 0.257326 | + | 0.257326i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 322.977i | − | 0.430062i | −0.976607 | − | 0.215031i | \(-0.931015\pi\) | ||
0.976607 | − | 0.215031i | \(-0.0689853\pi\) | |||||||
\(752\) | 398.269 | + | 304.472i | 0.529613 | + | 0.404882i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −496.463 | + | 115.993i | −0.658439 | + | 0.153837i | ||||
\(755\) | −49.2621 | + | 49.2621i | −0.0652478 | + | 0.0652478i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −80.2744 | + | 80.2744i | −0.106043 | + | 0.106043i | −0.758138 | − | 0.652095i | \(-0.773890\pi\) |
0.652095 | + | 0.758138i | \(0.273890\pi\) | |||||||
\(758\) | 283.258 | − | 455.971i | 0.373692 | − | 0.601545i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 474.716 | − | 390.657i | 0.624627 | − | 0.514023i | ||||
\(761\) | 596.664i | 0.784053i | 0.919954 | + | 0.392027i | \(0.128226\pi\) | ||||
−0.919954 | + | 0.392027i | \(0.871774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −962.246 | − | 962.246i | −1.26113 | − | 1.26113i | ||||
\(764\) | 110.999 | + | 224.578i | 0.145287 | + | 0.293950i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1246.27 | + | 291.177i | −1.62698 | + | 0.380127i | ||||
\(767\) | − | 219.580i | − | 0.286284i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1515.31 | 1.97050 | 0.985249 | − | 0.171129i | \(-0.0547416\pi\) | ||||
0.985249 | + | 0.171129i | \(0.0547416\pi\) | |||||||
\(770\) | 368.853 | + | 1578.73i | 0.479030 | + | 2.05030i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −800.884 | + | 395.844i | −1.03741 | + | 0.512751i | ||||
\(773\) | −607.901 | + | 607.901i | −0.786418 | + | 0.786418i | −0.980905 | − | 0.194487i | \(-0.937696\pi\) |
0.194487 | + | 0.980905i | \(0.437696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 47.4922 | 0.0612802 | ||||||||
\(776\) | −749.034 | − | 910.207i | −0.965250 | − | 1.17295i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1199.68 | + | 745.267i | 1.54201 | + | 0.957927i | ||||
\(779\) | 279.184 | + | 279.184i | 0.358387 | + | 0.358387i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 75.9297 | + | 75.9297i | 0.0972211 | + | 0.0972211i | ||||
\(782\) | 89.7221 | + | 384.020i | 0.114734 | + | 0.491074i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 953.717 | − | 1247.52i | 1.21648 | − | 1.59123i | ||||
\(785\) | 214.324 | 0.273024 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 356.009 | − | 356.009i | 0.452362 | − | 0.452362i | −0.443776 | − | 0.896138i | \(-0.646361\pi\) |
0.896138 | + | 0.443776i | \(0.146361\pi\) | |||||||
\(788\) | 52.7666 | − | 155.904i | 0.0669627 | − | 0.197847i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 535.222 | − | 861.566i | 0.677496 | − | 1.09059i | ||||
\(791\) | 2032.29 | 2.56926 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 660.640i | 0.833089i | ||||||||
\(794\) | 735.096 | − | 1183.31i | 0.925814 | − | 1.49032i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −41.9434 | + | 20.7309i | −0.0526927 | + | 0.0260438i | ||||
\(797\) | −971.380 | − | 971.380i | −1.21880 | − | 1.21880i | −0.968054 | − | 0.250742i | \(-0.919326\pi\) |
−0.250742 | − | 0.968054i | \(-0.580674\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 304.892i | − | 0.381592i | ||||||
\(800\) | 23.6818 | − | 52.5793i | 0.0296022 | − | 0.0657242i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 320.813 | + | 1373.11i | 0.400016 | + | 1.71211i | ||||
\(803\) | 838.008 | − | 838.008i | 1.04360 | − | 1.04360i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 837.135 | − | 837.135i | 1.03992 | − | 1.03992i | ||||
\(806\) | 491.890 | + | 305.572i | 0.610285 | + | 0.379121i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −143.788 | − | 13.9671i | −0.177956 | − | 0.0172860i | ||||
\(809\) | − | 678.276i | − | 0.838412i | −0.907891 | − | 0.419206i | \(-0.862308\pi\) | ||
0.907891 | − | 0.419206i | \(-0.137692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 204.625 | + | 204.625i | 0.252312 | + | 0.252312i | 0.821918 | − | 0.569606i | \(-0.192904\pi\) |
−0.569606 | + | 0.821918i | \(0.692904\pi\) | |||||||
\(812\) | −1066.41 | − | 360.933i | −1.31331 | − | 0.444498i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −211.836 | − | 906.682i | −0.260241 | − | 1.11386i | ||||
\(815\) | − | 213.881i | − | 0.262431i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 674.331 | 0.825375 | ||||||||
\(818\) | −544.954 | + | 127.323i | −0.666203 | + | 0.155651i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −451.571 | − | 152.837i | −0.550696 | − | 0.186387i | ||||
\(821\) | −326.524 | + | 326.524i | −0.397715 | + | 0.397715i | −0.877426 | − | 0.479711i | \(-0.840741\pi\) |
0.479711 | + | 0.877426i | \(0.340741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 804.270 | 0.977241 | 0.488621 | − | 0.872496i | \(-0.337500\pi\) | ||||
0.488621 | + | 0.872496i | \(0.337500\pi\) | |||||||
\(824\) | −90.2929 | − | 109.722i | −0.109579 | − | 0.133157i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 255.867 | − | 411.879i | 0.309767 | − | 0.498642i | ||||
\(827\) | −848.530 | − | 848.530i | −1.02603 | − | 1.02603i | −0.999652 | − | 0.0263821i | \(-0.991601\pi\) |
−0.0263821 | − | 0.999652i | \(-0.508399\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.5139 | + | 49.5139i | 0.0597273 | + | 0.0597273i | 0.736340 | − | 0.676612i | \(-0.236553\pi\) |
−0.676612 | + | 0.736340i | \(0.736553\pi\) | |||||||
\(830\) | −824.101 | + | 192.542i | −0.992892 | + | 0.231978i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 583.582 | − | 392.207i | 0.701421 | − | 0.471403i | ||||
\(833\) | −955.034 | −1.14650 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −124.240 | + | 124.240i | −0.148790 | + | 0.148790i | ||||
\(836\) | 793.842 | − | 392.363i | 0.949572 | − | 0.469334i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1378.08 | − | 856.088i | −1.64448 | − | 1.02158i | ||||
\(839\) | −866.213 | −1.03244 | −0.516218 | − | 0.856457i | \(-0.672660\pi\) | ||||
−0.516218 | + | 0.856457i | \(0.672660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 302.629i | − | 0.359844i | ||||||
\(842\) | 512.568 | + | 318.417i | 0.608751 | + | 0.378168i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0.391299 | − | 1.15613i | 0.000463625 | − | 0.00136982i | ||||
\(845\) | −164.490 | − | 164.490i | −0.194663 | − | 0.194663i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 867.390i | 1.02407i | ||||||||
\(848\) | 110.387 | + | 827.033i | 0.130173 | + | 0.975274i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −34.1518 | + | 7.97919i | −0.0401786 | + | 0.00938728i | ||||
\(851\) | −480.776 | + | 480.776i | −0.564954 | + | 0.564954i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 313.947 | − | 313.947i | 0.368050 | − | 0.368050i | −0.498715 | − | 0.866766i | \(-0.666195\pi\) |
0.866766 | + | 0.498715i | \(0.166195\pi\) | |||||||
\(854\) | −769.816 | + | 1239.20i | −0.901424 | + | 1.45106i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.3796 | + | 178.920i | −0.0203033 | + | 0.209019i | ||||
\(857\) | 473.297i | 0.552272i | 0.961119 | + | 0.276136i | \(0.0890540\pi\) | ||||
−0.961119 | + | 0.276136i | \(0.910946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −595.383 | − | 595.383i | −0.693112 | − | 0.693112i | 0.269803 | − | 0.962915i | \(-0.413041\pi\) |
−0.962915 | + | 0.269803i | \(0.913041\pi\) | |||||||
\(860\) | −729.934 | + | 360.776i | −0.848760 | + | 0.419507i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 325.046 | − | 75.9435i | 0.377084 | − | 0.0881015i | ||||
\(863\) | 742.134i | 0.859947i | 0.902842 | + | 0.429973i | \(0.141477\pi\) | ||||
−0.902842 | + | 0.429973i | \(0.858523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −665.083 | −0.768882 | ||||||||
\(866\) | −106.090 | − | 454.077i | −0.122506 | − | 0.524338i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 566.597 | + | 1146.36i | 0.652762 | + | 1.32069i | ||||
\(869\) | 1033.02 | − | 1033.02i | 1.18875 | − | 1.18875i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −757.887 | −0.870134 | ||||||||
\(872\) | 86.7682 | − | 893.263i | 0.0995048 | − | 1.02438i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −549.274 | − | 341.220i | −0.628459 | − | 0.390411i | ||||
\(875\) | 1107.26 | + | 1107.26i | 1.26544 | + | 1.26544i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −791.224 | − | 791.224i | −0.902194 | − | 0.902194i | 0.0934320 | − | 0.995626i | \(-0.470216\pi\) |
−0.995626 | + | 0.0934320i | \(0.970216\pi\) | |||||||
\(878\) | −200.429 | − | 857.858i | −0.228279 | − | 0.977059i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −649.380 | + | 849.432i | −0.737932 | + | 0.965264i | ||||
\(881\) | 1524.92 | 1.73090 | 0.865450 | − | 0.500995i | \(-0.167033\pi\) | ||||
0.865450 | + | 0.500995i | \(0.167033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −314.328 | + | 314.328i | −0.355978 | + | 0.355978i | −0.862328 | − | 0.506350i | \(-0.830994\pi\) |
0.506350 | + | 0.862328i | \(0.330994\pi\) | |||||||
\(884\) | −405.059 | − | 137.095i | −0.458212 | − | 0.155085i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 466.451 | − | 750.863i | 0.526468 | − | 0.847475i | ||||
\(887\) | 1520.80 | 1.71454 | 0.857271 | − | 0.514866i | \(-0.172158\pi\) | ||||
0.857271 | + | 0.514866i | \(0.172158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2404.80i | 2.70506i | ||||||||
\(890\) | 646.434 | − | 1040.59i | 0.726330 | − | 1.16920i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 658.162 | + | 1331.62i | 0.737850 | + | 1.49284i | ||||
\(893\) | 353.503 | + | 353.503i | 0.395860 | + | 0.395860i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 611.278i | 0.682992i | ||||||||
\(896\) | 1551.68 | − | 55.6625i | 1.73179 | − | 0.0621234i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −334.141 | − | 1430.16i | −0.372095 | − | 1.59261i | ||||
\(899\) | 432.389 | − | 432.389i | 0.480967 | − | 0.480967i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 358.818 | − | 358.818i | 0.398244 | − | 0.398244i | ||||
\(902\) | −583.278 | − | 362.344i | −0.646649 | − | 0.401711i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 851.668 | + | 1034.92i | 0.942111 | + | 1.14483i | ||||
\(905\) | 786.705i | 0.869288i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −216.886 | − | 216.886i | −0.239125 | − | 0.239125i | 0.577363 | − | 0.816488i | \(-0.304082\pi\) |
−0.816488 | + | 0.577363i | \(0.804082\pi\) | |||||||
\(908\) | −380.523 | + | 1124.29i | −0.419078 | + | 1.23820i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 292.071 | + | 1250.09i | 0.320957 | + | 1.37373i | ||||
\(911\) | 799.632i | 0.877752i | 0.898548 | + | 0.438876i | \(0.144623\pi\) | ||||
−0.898548 | + | 0.438876i | \(0.855377\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1218.96 | −1.33511 | ||||||||
\(914\) | −1349.16 | + | 315.217i | −1.47611 | + | 0.344877i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −277.021 | + | 818.483i | −0.302425 | + | 0.893541i | ||||
\(917\) | −1629.57 | + | 1629.57i | −1.77707 | + | 1.77707i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −640.590 | −0.697051 | −0.348525 | − | 0.937299i | \(-0.613317\pi\) | ||||
−0.348525 | + | 0.937299i | \(0.613317\pi\) | |||||||
\(920\) | 777.121 | + | 75.4867i | 0.844697 | + | 0.0820507i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −445.440 | + | 717.042i | −0.483124 | + | 0.777702i | ||||
\(923\) | 60.1238 | + | 60.1238i | 0.0651396 | + | 0.0651396i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −42.7565 | − | 42.7565i | −0.0462232 | − | 0.0462232i | ||||
\(926\) | −548.879 | + | 128.240i | −0.592742 | + | 0.138488i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −263.096 | − | 694.315i | −0.283509 | − | 0.748184i | ||||
\(929\) | −118.633 | −0.127699 | −0.0638496 | − | 0.997960i | \(-0.520338\pi\) | ||||
−0.0638496 | + | 0.997960i | \(0.520338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1107.30 | − | 1107.30i | 1.18937 | − | 1.18937i | ||||
\(932\) | 483.676 | + | 978.589i | 0.518966 | + | 1.04999i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 475.989 | + | 295.694i | 0.509624 | + | 0.316589i | ||||
\(935\) | 650.277 | 0.695483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 731.334i | − | 0.780506i | −0.920708 | − | 0.390253i | \(-0.872388\pi\) | ||
0.920708 | − | 0.390253i | \(-0.127612\pi\) | |||||||
\(938\) | −1421.61 | − | 883.135i | −1.51558 | − | 0.941508i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −571.780 | − | 193.523i | −0.608276 | − | 0.205875i | ||||
\(941\) | −980.281 | − | 980.281i | −1.04174 | − | 1.04174i | −0.999090 | − | 0.0426536i | \(-0.986419\pi\) |
−0.0426536 | − | 0.999090i | \(-0.513581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 501.424i | 0.531733i | ||||||||
\(944\) | 316.972 | − | 42.3074i | 0.335775 | − | 0.0448172i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1142.01 | + | 266.819i | −1.20720 | + | 0.282049i | ||||
\(947\) | 240.008 | − | 240.008i | 0.253441 | − | 0.253441i | −0.568939 | − | 0.822380i | \(-0.692646\pi\) |
0.822380 | + | 0.568939i | \(0.192646\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 663.564 | − | 663.564i | 0.699225 | − | 0.699225i | ||||
\(950\) | 30.3454 | − | 48.8481i | 0.0319425 | − | 0.0514191i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −600.043 | − | 729.156i | −0.630297 | − | 0.765920i | ||||
\(953\) | − | 780.049i | − | 0.818519i | −0.912418 | − | 0.409259i | \(-0.865787\pi\) | ||
0.912418 | − | 0.409259i | \(-0.134213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −213.293 | − | 213.293i | −0.223344 | − | 0.223344i | ||||
\(956\) | −185.478 | − | 375.265i | −0.194014 | − | 0.392536i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1787.29 | + | 417.582i | −1.86565 | + | 0.435889i | ||||
\(959\) | − | 3104.60i | − | 3.23733i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 266.459 | 0.277272 | ||||||||
\(962\) | −167.740 | − | 717.943i | −0.174365 | − | 0.746303i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −533.851 | + | 263.860i | −0.553787 | + | 0.273714i | ||||
\(965\) | 760.642 | − | 760.642i | 0.788230 | − | 0.788230i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1783.10 | 1.84395 | 0.921975 | − | 0.387249i | \(-0.126575\pi\) | ||||
0.921975 | + | 0.387249i | \(0.126575\pi\) | |||||||
\(968\) | −441.711 | + | 363.496i | −0.456313 | + | 0.375513i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1205.67 | + | 748.989i | 1.24296 | + | 0.772154i | ||||
\(971\) | 159.340 | + | 159.340i | 0.164099 | + | 0.164099i | 0.784380 | − | 0.620281i | \(-0.212981\pi\) |
−0.620281 | + | 0.784380i | \(0.712981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −263.509 | − | 263.509i | −0.270821 | − | 0.270821i | ||||
\(974\) | 193.923 | + | 830.013i | 0.199100 | + | 0.852169i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −953.659 | + | 127.288i | −0.977110 | + | 0.130418i | ||||
\(977\) | 970.922 | 0.993779 | 0.496889 | − | 0.867814i | \(-0.334475\pi\) | ||||
0.496889 | + | 0.867814i | \(0.334475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1247.67 | − | 1247.67i | 1.27443 | − | 1.27443i | ||||
\(980\) | −606.184 | + | 1791.02i | −0.618555 | + | 1.82758i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 397.459 | − | 639.804i | 0.404744 | − | 0.651531i | ||||
\(983\) | −1266.90 | −1.28881 | −0.644406 | − | 0.764684i | \(-0.722895\pi\) | ||||
−0.644406 | + | 0.764684i | \(0.722895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 198.185i | 0.201203i | ||||||||
\(986\) | −238.287 | + | 383.579i | −0.241670 | + | 0.389025i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 628.593 | − | 310.687i | 0.636227 | − | 0.314461i | ||||
\(989\) | 605.562 | + | 605.562i | 0.612297 | + | 0.612297i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 222.422i | 0.224442i | 0.993683 | + | 0.112221i | \(0.0357964\pi\) | ||||
−0.993683 | + | 0.112221i | \(0.964204\pi\) | |||||||
\(992\) | −346.330 | + | 768.938i | −0.349123 | + | 0.775139i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42.7180 | + | 182.838i | 0.0429759 | + | 0.183941i | ||||
\(995\) | 39.8359 | − | 39.8359i | 0.0400360 | − | 0.0400360i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −441.746 | + | 441.746i | −0.443075 | + | 0.443075i | −0.893044 | − | 0.449969i | \(-0.851435\pi\) |
0.449969 | + | 0.893044i | \(0.351435\pi\) | |||||||
\(998\) | 634.528 | + | 394.181i | 0.635800 | + | 0.394971i | ||||
\(999\) | 0 | 0 |
(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 | 144.3.m.c.19.4 | 16 | ||
3.2 | odd | 2 | 48.3.l.a.19.5 | ✓ | 16 | ||
4.3 | odd | 2 | 576.3.m.c.559.6 | 16 | |||
8.3 | odd | 2 | 1152.3.m.c.991.3 | 16 | |||
8.5 | even | 2 | 1152.3.m.f.991.3 | 16 | |||
12.11 | even | 2 | 192.3.l.a.175.6 | 16 | |||
16.3 | odd | 4 | 1152.3.m.f.415.3 | 16 | |||
16.5 | even | 4 | 576.3.m.c.271.6 | 16 | |||
16.11 | odd | 4 | inner | 144.3.m.c.91.4 | 16 | ||
16.13 | even | 4 | 1152.3.m.c.415.3 | 16 | |||
24.5 | odd | 2 | 384.3.l.a.223.7 | 16 | |||
24.11 | even | 2 | 384.3.l.b.223.3 | 16 | |||
48.5 | odd | 4 | 192.3.l.a.79.6 | 16 | |||
48.11 | even | 4 | 48.3.l.a.43.5 | yes | 16 | ||
48.29 | odd | 4 | 384.3.l.b.31.3 | 16 | |||
48.35 | even | 4 | 384.3.l.a.31.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.5 | ✓ | 16 | 3.2 | odd | 2 | ||
48.3.l.a.43.5 | yes | 16 | 48.11 | even | 4 | ||
144.3.m.c.19.4 | 16 | 1.1 | even | 1 | trivial | ||
144.3.m.c.91.4 | 16 | 16.11 | odd | 4 | inner | ||
192.3.l.a.79.6 | 16 | 48.5 | odd | 4 | |||
192.3.l.a.175.6 | 16 | 12.11 | even | 2 | |||
384.3.l.a.31.7 | 16 | 48.35 | even | 4 | |||
384.3.l.a.223.7 | 16 | 24.5 | odd | 2 | |||
384.3.l.b.31.3 | 16 | 48.29 | odd | 4 | |||
384.3.l.b.223.3 | 16 | 24.11 | even | 2 | |||
576.3.m.c.271.6 | 16 | 16.5 | even | 4 | |||
576.3.m.c.559.6 | 16 | 4.3 | odd | 2 | |||
1152.3.m.c.415.3 | 16 | 16.13 | even | 4 | |||
1152.3.m.c.991.3 | 16 | 8.3 | odd | 2 | |||
1152.3.m.f.415.3 | 16 | 16.3 | odd | 4 | |||
1152.3.m.f.991.3 | 16 | 8.5 | even | 2 |