Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(289,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.j (of order \(3\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.447703281.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.4 | ||
Root | \(1.19003 + 0.764088i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.529 |
Dual form | 546.2.j.d.289.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.05781 | + | 3.56422i | 0.920279 | + | 1.59397i | 0.798983 | + | 0.601353i | \(0.205372\pi\) |
0.121296 | + | 0.992616i | \(0.461295\pi\) | |||||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −2.61442 | + | 0.405935i | −0.988160 | + | 0.153429i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.05781 | + | 3.56422i | 0.650735 | + | 1.12711i | ||||
\(11\) | −2.02237 | − | 3.50284i | −0.609767 | − | 1.05615i | −0.991279 | − | 0.131783i | \(-0.957930\pi\) |
0.381512 | − | 0.924364i | \(-0.375404\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.81454 | + | 3.11568i | 0.503263 | + | 0.864133i | ||||
\(14\) | −2.61442 | + | 0.405935i | −0.698734 | + | 0.108491i | ||||
\(15\) | −2.05781 | + | 3.56422i | −0.531323 | + | 0.920279i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.715381 | 0.173505 | 0.0867527 | − | 0.996230i | \(-0.472351\pi\) | ||||
0.0867527 | + | 0.996230i | \(0.472351\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.92440 | − | 3.33315i | 0.441487 | − | 0.764677i | −0.556313 | − | 0.830973i | \(-0.687785\pi\) |
0.997800 | + | 0.0662953i | \(0.0211179\pi\) | |||||||
\(20\) | 2.05781 | + | 3.56422i | 0.460139 | + | 0.796985i | ||||
\(21\) | −1.65876 | − | 2.06119i | −0.361972 | − | 0.449789i | ||||
\(22\) | −2.02237 | − | 3.50284i | −0.431170 | − | 0.746809i | ||||
\(23\) | −4.09781 | −0.854453 | −0.427227 | − | 0.904145i | \(-0.640509\pi\) | ||||
−0.427227 | + | 0.904145i | \(0.640509\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −5.96913 | + | 10.3388i | −1.19383 | + | 2.06777i | ||||
\(26\) | 1.81454 | + | 3.11568i | 0.355861 | + | 0.611035i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.61442 | + | 0.405935i | −0.494080 | + | 0.0767145i | ||||
\(29\) | 4.50457 | − | 7.80214i | 0.836478 | − | 1.44882i | −0.0563442 | − | 0.998411i | \(-0.517944\pi\) |
0.892822 | − | 0.450410i | \(-0.148722\pi\) | |||||||
\(30\) | −2.05781 | + | 3.56422i | −0.375702 | + | 0.650735i | ||||
\(31\) | 1.82642 | − | 3.16346i | 0.328035 | − | 0.568174i | −0.654087 | − | 0.756420i | \(-0.726947\pi\) |
0.982122 | + | 0.188246i | \(0.0602802\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.02237 | − | 3.50284i | 0.352049 | − | 0.609767i | ||||
\(34\) | 0.715381 | 0.122687 | ||||||||
\(35\) | −6.82682 | − | 8.48306i | −1.15394 | − | 1.43390i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 7.19594 | 1.18301 | 0.591503 | − | 0.806303i | \(-0.298535\pi\) | ||||
0.591503 | + | 0.806303i | \(0.298535\pi\) | |||||||
\(38\) | 1.92440 | − | 3.33315i | 0.312178 | − | 0.540709i | ||||
\(39\) | −1.79099 | + | 3.12928i | −0.286787 | + | 0.501085i | ||||
\(40\) | 2.05781 | + | 3.56422i | 0.325368 | + | 0.563553i | ||||
\(41\) | −2.88423 | + | 4.99563i | −0.450441 | + | 0.780187i | −0.998413 | − | 0.0563098i | \(-0.982067\pi\) |
0.547972 | + | 0.836496i | \(0.315400\pi\) | |||||||
\(42\) | −1.65876 | − | 2.06119i | −0.255953 | − | 0.318049i | ||||
\(43\) | 1.28209 | + | 2.22064i | 0.195516 | + | 0.338644i | 0.947070 | − | 0.321028i | \(-0.104028\pi\) |
−0.751553 | + | 0.659672i | \(0.770695\pi\) | |||||||
\(44\) | −2.02237 | − | 3.50284i | −0.304883 | − | 0.528074i | ||||
\(45\) | −4.11561 | −0.613519 | ||||||||
\(46\) | −4.09781 | −0.604190 | ||||||||
\(47\) | 1.28800 | + | 2.23088i | 0.187874 | + | 0.325408i | 0.944541 | − | 0.328393i | \(-0.106507\pi\) |
−0.756667 | + | 0.653800i | \(0.773174\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 6.67043 | − | 2.12257i | 0.952919 | − | 0.303225i | ||||
\(50\) | −5.96913 | + | 10.3388i | −0.844163 | + | 1.46213i | ||||
\(51\) | 0.357690 | + | 0.619538i | 0.0500867 | + | 0.0867527i | ||||
\(52\) | 1.81454 | + | 3.11568i | 0.251631 | + | 0.432067i | ||||
\(53\) | −1.35888 | + | 2.35365i | −0.186656 | + | 0.323298i | −0.944133 | − | 0.329564i | \(-0.893098\pi\) |
0.757477 | + | 0.652862i | \(0.226432\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 8.32328 | − | 14.4163i | 1.12231 | − | 1.94390i | ||||
\(56\) | −2.61442 | + | 0.405935i | −0.349367 | + | 0.0542453i | ||||
\(57\) | 3.84879 | 0.509785 | ||||||||
\(58\) | 4.50457 | − | 7.80214i | 0.591479 | − | 1.02447i | ||||
\(59\) | 12.9027 | 1.67978 | 0.839892 | − | 0.542754i | \(-0.182618\pi\) | ||||
0.839892 | + | 0.542754i | \(0.182618\pi\) | |||||||
\(60\) | −2.05781 | + | 3.56422i | −0.265662 | + | 0.460139i | ||||
\(61\) | 4.71538 | − | 8.16728i | 0.603743 | − | 1.04571i | −0.388506 | − | 0.921446i | \(-0.627009\pi\) |
0.992249 | − | 0.124267i | \(-0.0396579\pi\) | |||||||
\(62\) | 1.82642 | − | 3.16346i | 0.231956 | − | 0.401760i | ||||
\(63\) | 0.955663 | − | 2.46713i | 0.120402 | − | 0.310829i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.37100 | + | 12.8789i | −0.914260 | + | 1.59743i | ||||
\(66\) | 2.02237 | − | 3.50284i | 0.248936 | − | 0.431170i | ||||
\(67\) | 0.583158 | + | 1.01006i | 0.0712441 | + | 0.123398i | 0.899447 | − | 0.437030i | \(-0.143970\pi\) |
−0.828203 | + | 0.560429i | \(0.810636\pi\) | |||||||
\(68\) | 0.715381 | 0.0867527 | ||||||||
\(69\) | −2.04891 | − | 3.54881i | −0.246659 | − | 0.427227i | ||||
\(70\) | −6.82682 | − | 8.48306i | −0.815961 | − | 1.01392i | ||||
\(71\) | 5.10254 | + | 8.83786i | 0.605560 | + | 1.04886i | 0.991963 | + | 0.126531i | \(0.0403843\pi\) |
−0.386402 | + | 0.922330i | \(0.626282\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | −1.25673 | + | 2.17673i | −0.147090 | + | 0.254767i | −0.930151 | − | 0.367178i | \(-0.880324\pi\) |
0.783061 | + | 0.621945i | \(0.213657\pi\) | |||||||
\(74\) | 7.19594 | 0.836512 | ||||||||
\(75\) | −11.9383 | −1.37851 | ||||||||
\(76\) | 1.92440 | − | 3.33315i | 0.220743 | − | 0.382339i | ||||
\(77\) | 6.70925 | + | 8.33697i | 0.764590 | + | 0.950086i | ||||
\(78\) | −1.79099 | + | 3.12928i | −0.202789 | + | 0.354321i | ||||
\(79\) | −6.70468 | − | 11.6129i | −0.754336 | − | 1.30655i | −0.945704 | − | 0.325030i | \(-0.894626\pi\) |
0.191368 | − | 0.981518i | \(-0.438708\pi\) | |||||||
\(80\) | 2.05781 | + | 3.56422i | 0.230070 | + | 0.398492i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.88423 | + | 4.99563i | −0.318510 | + | 0.551675i | ||||
\(83\) | −15.5024 | −1.70161 | −0.850807 | − | 0.525479i | \(-0.823886\pi\) | ||||
−0.850807 | + | 0.525479i | \(0.823886\pi\) | |||||||
\(84\) | −1.65876 | − | 2.06119i | −0.180986 | − | 0.224894i | ||||
\(85\) | 1.47212 | + | 2.54978i | 0.159673 | + | 0.276562i | ||||
\(86\) | 1.28209 | + | 2.22064i | 0.138251 | + | 0.239458i | ||||
\(87\) | 9.00914 | 0.965881 | ||||||||
\(88\) | −2.02237 | − | 3.50284i | −0.215585 | − | 0.373404i | ||||
\(89\) | −10.9137 | −1.15685 | −0.578425 | − | 0.815736i | \(-0.696332\pi\) | ||||
−0.578425 | + | 0.815736i | \(0.696332\pi\) | |||||||
\(90\) | −4.11561 | −0.433824 | ||||||||
\(91\) | −6.00874 | − | 7.40912i | −0.629887 | − | 0.776687i | ||||
\(92\) | −4.09781 | −0.427227 | ||||||||
\(93\) | 3.65285 | 0.378783 | ||||||||
\(94\) | 1.28800 | + | 2.23088i | 0.132847 | + | 0.230098i | ||||
\(95\) | 15.8401 | 1.62516 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −3.10135 | − | 5.37170i | −0.314895 | − | 0.545414i | 0.664520 | − | 0.747270i | \(-0.268636\pi\) |
−0.979415 | + | 0.201856i | \(0.935303\pi\) | |||||||
\(98\) | 6.67043 | − | 2.12257i | 0.673816 | − | 0.214412i | ||||
\(99\) | 4.04474 | 0.406511 | ||||||||
\(100\) | −5.96913 | + | 10.3388i | −0.596913 | + | 1.03388i | ||||
\(101\) | −8.15325 | − | 14.1218i | −0.811278 | − | 1.40518i | −0.911970 | − | 0.410257i | \(-0.865439\pi\) |
0.100692 | − | 0.994918i | \(-0.467894\pi\) | |||||||
\(102\) | 0.357690 | + | 0.619538i | 0.0354166 | + | 0.0613434i | ||||
\(103\) | 1.46023 | + | 2.52920i | 0.143881 | + | 0.249209i | 0.928955 | − | 0.370193i | \(-0.120708\pi\) |
−0.785074 | + | 0.619402i | \(0.787375\pi\) | |||||||
\(104\) | 1.81454 | + | 3.11568i | 0.177930 | + | 0.305517i | ||||
\(105\) | 3.93314 | − | 10.1537i | 0.383835 | − | 0.990903i | ||||
\(106\) | −1.35888 | + | 2.35365i | −0.131986 | + | 0.228606i | ||||
\(107\) | −4.03877 | −0.390442 | −0.195221 | − | 0.980759i | \(-0.562542\pi\) | ||||
−0.195221 | + | 0.980759i | \(0.562542\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 6.93314 | − | 12.0085i | 0.664074 | − | 1.15021i | −0.315461 | − | 0.948938i | \(-0.602159\pi\) |
0.979535 | − | 0.201272i | \(-0.0645074\pi\) | |||||||
\(110\) | 8.32328 | − | 14.4163i | 0.793594 | − | 1.37454i | ||||
\(111\) | 3.59797 | + | 6.23187i | 0.341504 | + | 0.591503i | ||||
\(112\) | −2.61442 | + | 0.405935i | −0.247040 | + | 0.0383572i | ||||
\(113\) | −7.30902 | − | 12.6596i | −0.687575 | − | 1.19091i | −0.972620 | − | 0.232401i | \(-0.925342\pi\) |
0.285045 | − | 0.958514i | \(-0.407991\pi\) | |||||||
\(114\) | 3.84879 | 0.360472 | ||||||||
\(115\) | −8.43251 | − | 14.6055i | −0.786335 | − | 1.36197i | ||||
\(116\) | 4.50457 | − | 7.80214i | 0.418239 | − | 0.724411i | ||||
\(117\) | −3.60553 | + | 0.0135995i | −0.333331 | + | 0.00125727i | ||||
\(118\) | 12.9027 | 1.18779 | ||||||||
\(119\) | −1.87031 | + | 0.290398i | −0.171451 | + | 0.0266207i | ||||
\(120\) | −2.05781 | + | 3.56422i | −0.187851 | + | 0.325368i | ||||
\(121\) | −2.67994 | + | 4.64180i | −0.243631 | + | 0.421982i | ||||
\(122\) | 4.71538 | − | 8.16728i | 0.426911 | − | 0.739431i | ||||
\(123\) | −5.76846 | −0.520124 | ||||||||
\(124\) | 1.82642 | − | 3.16346i | 0.164018 | − | 0.284087i | ||||
\(125\) | −28.5552 | −2.55405 | ||||||||
\(126\) | 0.955663 | − | 2.46713i | 0.0851372 | − | 0.219789i | ||||
\(127\) | −1.26603 | + | 2.19283i | −0.112342 | + | 0.194582i | −0.916714 | − | 0.399544i | \(-0.869169\pi\) |
0.804372 | + | 0.594126i | \(0.202502\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −1.28209 | + | 2.22064i | −0.112881 | + | 0.195516i | ||||
\(130\) | −7.37100 | + | 12.8789i | −0.646480 | + | 1.12955i | ||||
\(131\) | 6.21657 | + | 10.7674i | 0.543144 | + | 0.940753i | 0.998721 | + | 0.0505568i | \(0.0160996\pi\) |
−0.455577 | + | 0.890196i | \(0.650567\pi\) | |||||||
\(132\) | 2.02237 | − | 3.50284i | 0.176025 | − | 0.304883i | ||||
\(133\) | −3.67815 | + | 9.49545i | −0.318936 | + | 0.823360i | ||||
\(134\) | 0.583158 | + | 1.01006i | 0.0503772 | + | 0.0872558i | ||||
\(135\) | −2.05781 | − | 3.56422i | −0.177108 | − | 0.306760i | ||||
\(136\) | 0.715381 | 0.0613434 | ||||||||
\(137\) | −10.3848 | −0.887234 | −0.443617 | − | 0.896216i | \(-0.646305\pi\) | ||||
−0.443617 | + | 0.896216i | \(0.646305\pi\) | |||||||
\(138\) | −2.04891 | − | 3.54881i | −0.174415 | − | 0.302095i | ||||
\(139\) | −0.636394 | − | 1.10227i | −0.0539783 | − | 0.0934931i | 0.837774 | − | 0.546018i | \(-0.183857\pi\) |
−0.891752 | + | 0.452525i | \(0.850524\pi\) | |||||||
\(140\) | −6.82682 | − | 8.48306i | −0.576972 | − | 0.716950i | ||||
\(141\) | −1.28800 | + | 2.23088i | −0.108469 | + | 0.187874i | ||||
\(142\) | 5.10254 | + | 8.83786i | 0.428196 | + | 0.741657i | ||||
\(143\) | 7.24406 | − | 12.6571i | 0.605779 | − | 1.05844i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 37.0781 | 3.07917 | ||||||||
\(146\) | −1.25673 | + | 2.17673i | −0.104008 | + | 0.180147i | ||||
\(147\) | 5.17342 | + | 4.71548i | 0.426696 | + | 0.388926i | ||||
\(148\) | 7.19594 | 0.591503 | ||||||||
\(149\) | −11.6810 | + | 20.2320i | −0.956942 | + | 1.65747i | −0.227083 | + | 0.973875i | \(0.572919\pi\) |
−0.729859 | + | 0.683598i | \(0.760414\pi\) | |||||||
\(150\) | −11.9383 | −0.974755 | ||||||||
\(151\) | 1.19832 | − | 2.07555i | 0.0975178 | − | 0.168906i | −0.813139 | − | 0.582070i | \(-0.802243\pi\) |
0.910657 | + | 0.413164i | \(0.135576\pi\) | |||||||
\(152\) | 1.92440 | − | 3.33315i | 0.156089 | − | 0.270354i | ||||
\(153\) | −0.357690 | + | 0.619538i | −0.0289176 | + | 0.0500867i | ||||
\(154\) | 6.70925 | + | 8.33697i | 0.540647 | + | 0.671812i | ||||
\(155\) | 15.0337 | 1.20754 | ||||||||
\(156\) | −1.79099 | + | 3.12928i | −0.143394 | + | 0.250543i | ||||
\(157\) | 5.79083 | − | 10.0300i | 0.462158 | − | 0.800482i | −0.536910 | − | 0.843640i | \(-0.680409\pi\) |
0.999068 | + | 0.0431579i | \(0.0137419\pi\) | |||||||
\(158\) | −6.70468 | − | 11.6129i | −0.533396 | − | 0.923869i | ||||
\(159\) | −2.71776 | −0.215532 | ||||||||
\(160\) | 2.05781 | + | 3.56422i | 0.162684 | + | 0.281777i | ||||
\(161\) | 10.7134 | − | 1.66344i | 0.844336 | − | 0.131098i | ||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | −8.95432 | + | 15.5093i | −0.701356 | + | 1.21478i | 0.266634 | + | 0.963798i | \(0.414088\pi\) |
−0.967990 | + | 0.250987i | \(0.919245\pi\) | |||||||
\(164\) | −2.88423 | + | 4.99563i | −0.225220 | + | 0.390093i | ||||
\(165\) | 16.6466 | 1.29593 | ||||||||
\(166\) | −15.5024 | −1.20322 | ||||||||
\(167\) | 3.15398 | − | 5.46286i | 0.244062 | − | 0.422728i | −0.717805 | − | 0.696244i | \(-0.754853\pi\) |
0.961868 | + | 0.273516i | \(0.0881865\pi\) | |||||||
\(168\) | −1.65876 | − | 2.06119i | −0.127976 | − | 0.159024i | ||||
\(169\) | −6.41489 | + | 11.3070i | −0.493453 | + | 0.869773i | ||||
\(170\) | 1.47212 | + | 2.54978i | 0.112906 | + | 0.195559i | ||||
\(171\) | 1.92440 | + | 3.33315i | 0.147162 | + | 0.254892i | ||||
\(172\) | 1.28209 | + | 2.22064i | 0.0977582 | + | 0.169322i | ||||
\(173\) | 1.82563 | − | 3.16209i | 0.138800 | − | 0.240409i | −0.788242 | − | 0.615365i | \(-0.789009\pi\) |
0.927043 | + | 0.374956i | \(0.122342\pi\) | |||||||
\(174\) | 9.00914 | 0.682981 | ||||||||
\(175\) | 11.4090 | − | 29.4532i | 0.862436 | − | 2.22645i | ||||
\(176\) | −2.02237 | − | 3.50284i | −0.152442 | − | 0.264037i | ||||
\(177\) | 6.45133 | + | 11.1740i | 0.484912 | + | 0.839892i | ||||
\(178\) | −10.9137 | −0.818016 | ||||||||
\(179\) | −6.25956 | − | 10.8419i | −0.467861 | − | 0.810360i | 0.531464 | − | 0.847081i | \(-0.321642\pi\) |
−0.999326 | + | 0.0367210i | \(0.988309\pi\) | |||||||
\(180\) | −4.11561 | −0.306760 | ||||||||
\(181\) | −18.1728 | −1.35077 | −0.675385 | − | 0.737465i | \(-0.736023\pi\) | ||||
−0.675385 | + | 0.737465i | \(0.736023\pi\) | |||||||
\(182\) | −6.00874 | − | 7.40912i | −0.445397 | − | 0.549200i | ||||
\(183\) | 9.43076 | 0.697142 | ||||||||
\(184\) | −4.09781 | −0.302095 | ||||||||
\(185\) | 14.8079 | + | 25.6480i | 1.08870 | + | 1.88568i | ||||
\(186\) | 3.65285 | 0.267840 | ||||||||
\(187\) | −1.44676 | − | 2.50587i | −0.105798 | − | 0.183247i | ||||
\(188\) | 1.28800 | + | 2.23088i | 0.0939371 | + | 0.162704i | ||||
\(189\) | 2.61442 | − | 0.405935i | 0.190171 | − | 0.0295274i | ||||
\(190\) | 15.8401 | 1.14916 | ||||||||
\(191\) | −2.23004 | + | 3.86254i | −0.161360 | + | 0.279483i | −0.935357 | − | 0.353706i | \(-0.884921\pi\) |
0.773997 | + | 0.633190i | \(0.218255\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 4.34243 | + | 7.52130i | 0.312575 | + | 0.541395i | 0.978919 | − | 0.204249i | \(-0.0654752\pi\) |
−0.666344 | + | 0.745644i | \(0.732142\pi\) | |||||||
\(194\) | −3.10135 | − | 5.37170i | −0.222664 | − | 0.385666i | ||||
\(195\) | −14.8389 | + | 0.0559702i | −1.06264 | + | 0.00400811i | ||||
\(196\) | 6.67043 | − | 2.12257i | 0.476460 | − | 0.151612i | ||||
\(197\) | −1.23397 | + | 2.13730i | −0.0879166 | + | 0.152276i | −0.906630 | − | 0.421926i | \(-0.861354\pi\) |
0.818714 | + | 0.574202i | \(0.194688\pi\) | |||||||
\(198\) | 4.04474 | 0.287447 | ||||||||
\(199\) | 20.5681 | 1.45804 | 0.729018 | − | 0.684494i | \(-0.239977\pi\) | ||||
0.729018 | + | 0.684494i | \(0.239977\pi\) | |||||||
\(200\) | −5.96913 | + | 10.3388i | −0.422081 | + | 0.731066i | ||||
\(201\) | −0.583158 | + | 1.01006i | −0.0411328 | + | 0.0712441i | ||||
\(202\) | −8.15325 | − | 14.1218i | −0.573660 | − | 0.993609i | ||||
\(203\) | −8.60970 | + | 22.2267i | −0.604282 | + | 1.56001i | ||||
\(204\) | 0.357690 | + | 0.619538i | 0.0250433 | + | 0.0433763i | ||||
\(205\) | −23.7407 | −1.65813 | ||||||||
\(206\) | 1.46023 | + | 2.52920i | 0.101739 | + | 0.176217i | ||||
\(207\) | 2.04891 | − | 3.54881i | 0.142409 | − | 0.246659i | ||||
\(208\) | 1.81454 | + | 3.11568i | 0.125816 | + | 0.216033i | ||||
\(209\) | −15.5673 | −1.07682 | ||||||||
\(210\) | 3.93314 | − | 10.1537i | 0.271412 | − | 0.700674i | ||||
\(211\) | 2.22726 | − | 3.85773i | 0.153331 | − | 0.265577i | −0.779119 | − | 0.626876i | \(-0.784333\pi\) |
0.932450 | + | 0.361299i | \(0.117667\pi\) | |||||||
\(212\) | −1.35888 | + | 2.35365i | −0.0933281 | + | 0.161649i | ||||
\(213\) | −5.10254 | + | 8.83786i | −0.349620 | + | 0.605560i | ||||
\(214\) | −4.03877 | −0.276084 | ||||||||
\(215\) | −5.27657 | + | 9.13929i | −0.359859 | + | 0.623294i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.49089 | + | 9.01203i | −0.236977 | + | 0.611777i | ||||
\(218\) | 6.93314 | − | 12.0085i | 0.469571 | − | 0.813321i | ||||
\(219\) | −2.51347 | −0.169844 | ||||||||
\(220\) | 8.32328 | − | 14.4163i | 0.561155 | − | 0.971950i | ||||
\(221\) | 1.29809 | + | 2.22890i | 0.0873188 | + | 0.149932i | ||||
\(222\) | 3.59797 | + | 6.23187i | 0.241480 | + | 0.418256i | ||||
\(223\) | −2.49662 | + | 4.32427i | −0.167186 | + | 0.289574i | −0.937429 | − | 0.348175i | \(-0.886801\pi\) |
0.770243 | + | 0.637750i | \(0.220135\pi\) | |||||||
\(224\) | −2.61442 | + | 0.405935i | −0.174684 | + | 0.0271227i | ||||
\(225\) | −5.96913 | − | 10.3388i | −0.397942 | − | 0.689256i | ||||
\(226\) | −7.30902 | − | 12.6596i | −0.486189 | − | 0.842104i | ||||
\(227\) | −1.57273 | −0.104385 | −0.0521927 | − | 0.998637i | \(-0.516621\pi\) | ||||
−0.0521927 | + | 0.998637i | \(0.516621\pi\) | |||||||
\(228\) | 3.84879 | 0.254892 | ||||||||
\(229\) | 0.828619 | + | 1.43521i | 0.0547567 | + | 0.0948413i | 0.892104 | − | 0.451829i | \(-0.149228\pi\) |
−0.837348 | + | 0.546671i | \(0.815895\pi\) | |||||||
\(230\) | −8.43251 | − | 14.6055i | −0.556023 | − | 0.963060i | ||||
\(231\) | −3.86540 | + | 9.97887i | −0.254325 | + | 0.656561i | ||||
\(232\) | 4.50457 | − | 7.80214i | 0.295739 | − | 0.512236i | ||||
\(233\) | −3.86181 | − | 6.68885i | −0.252996 | − | 0.438201i | 0.711354 | − | 0.702834i | \(-0.248082\pi\) |
−0.964349 | + | 0.264633i | \(0.914749\pi\) | |||||||
\(234\) | −3.60553 | + | 0.0135995i | −0.235701 | + | 0.000889026i | ||||
\(235\) | −5.30091 | + | 9.18145i | −0.345793 | + | 0.598932i | ||||
\(236\) | 12.9027 | 0.839892 | ||||||||
\(237\) | 6.70468 | − | 11.6129i | 0.435516 | − | 0.754336i | ||||
\(238\) | −1.87031 | + | 0.290398i | −0.121234 | + | 0.0188237i | ||||
\(239\) | −28.7630 | −1.86052 | −0.930261 | − | 0.366899i | \(-0.880420\pi\) | ||||
−0.930261 | + | 0.366899i | \(0.880420\pi\) | |||||||
\(240\) | −2.05781 | + | 3.56422i | −0.132831 | + | 0.230070i | ||||
\(241\) | 25.6204 | 1.65036 | 0.825178 | − | 0.564872i | \(-0.191075\pi\) | ||||
0.825178 | + | 0.564872i | \(0.191075\pi\) | |||||||
\(242\) | −2.67994 | + | 4.64180i | −0.172273 | + | 0.298386i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 4.71538 | − | 8.16728i | 0.301871 | − | 0.522856i | ||||
\(245\) | 21.2918 | + | 19.4071i | 1.36028 | + | 1.23987i | ||||
\(246\) | −5.76846 | −0.367784 | ||||||||
\(247\) | 13.8769 | − | 0.0523416i | 0.882967 | − | 0.00333042i | ||||
\(248\) | 1.82642 | − | 3.16346i | 0.115978 | − | 0.200880i | ||||
\(249\) | −7.75122 | − | 13.4255i | −0.491213 | − | 0.850807i | ||||
\(250\) | −28.5552 | −1.80599 | ||||||||
\(251\) | 0.339652 | + | 0.588295i | 0.0214387 | + | 0.0371329i | 0.876546 | − | 0.481319i | \(-0.159842\pi\) |
−0.855107 | + | 0.518452i | \(0.826509\pi\) | |||||||
\(252\) | 0.955663 | − | 2.46713i | 0.0602011 | − | 0.155414i | ||||
\(253\) | 8.28729 | + | 14.3540i | 0.521017 | + | 0.902428i | ||||
\(254\) | −1.26603 | + | 2.19283i | −0.0794379 | + | 0.137590i | ||||
\(255\) | −1.47212 | + | 2.54978i | −0.0921874 | + | 0.159673i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.44587 | −0.152569 | −0.0762846 | − | 0.997086i | \(-0.524306\pi\) | ||||
−0.0762846 | + | 0.997086i | \(0.524306\pi\) | |||||||
\(258\) | −1.28209 | + | 2.22064i | −0.0798192 | + | 0.138251i | ||||
\(259\) | −18.8133 | + | 2.92108i | −1.16900 | + | 0.181507i | ||||
\(260\) | −7.37100 | + | 12.8789i | −0.457130 | + | 0.798715i | ||||
\(261\) | 4.50457 | + | 7.80214i | 0.278826 | + | 0.482941i | ||||
\(262\) | 6.21657 | + | 10.7674i | 0.384061 | + | 0.665213i | ||||
\(263\) | −12.6596 | − | 21.9271i | −0.780625 | − | 1.35208i | −0.931578 | − | 0.363541i | \(-0.881568\pi\) |
0.150953 | − | 0.988541i | \(-0.451766\pi\) | |||||||
\(264\) | 2.02237 | − | 3.50284i | 0.124468 | − | 0.215585i | ||||
\(265\) | −11.1852 | −0.687103 | ||||||||
\(266\) | −3.67815 | + | 9.49545i | −0.225522 | + | 0.582204i | ||||
\(267\) | −5.45685 | − | 9.45154i | −0.333954 | − | 0.578425i | ||||
\(268\) | 0.583158 | + | 1.01006i | 0.0356220 | + | 0.0616992i | ||||
\(269\) | −13.5665 | −0.827167 | −0.413583 | − | 0.910466i | \(-0.635723\pi\) | ||||
−0.413583 | + | 0.910466i | \(0.635723\pi\) | |||||||
\(270\) | −2.05781 | − | 3.56422i | −0.125234 | − | 0.216912i | ||||
\(271\) | −4.85940 | −0.295188 | −0.147594 | − | 0.989048i | \(-0.547153\pi\) | ||||
−0.147594 | + | 0.989048i | \(0.547153\pi\) | |||||||
\(272\) | 0.715381 | 0.0433763 | ||||||||
\(273\) | 3.41211 | − | 8.90828i | 0.206511 | − | 0.539154i | ||||
\(274\) | −10.3848 | −0.627369 | ||||||||
\(275\) | 48.2871 | 2.91182 | ||||||||
\(276\) | −2.04891 | − | 3.54881i | −0.123330 | − | 0.213613i | ||||
\(277\) | 12.0625 | 0.724767 | 0.362384 | − | 0.932029i | \(-0.381963\pi\) | ||||
0.362384 | + | 0.932029i | \(0.381963\pi\) | |||||||
\(278\) | −0.636394 | − | 1.10227i | −0.0381684 | − | 0.0661096i | ||||
\(279\) | 1.82642 | + | 3.16346i | 0.109345 | + | 0.189391i | ||||
\(280\) | −6.82682 | − | 8.48306i | −0.407981 | − | 0.506960i | ||||
\(281\) | 18.3963 | 1.09743 | 0.548716 | − | 0.836009i | \(-0.315117\pi\) | ||||
0.548716 | + | 0.836009i | \(0.315117\pi\) | |||||||
\(282\) | −1.28800 | + | 2.23088i | −0.0766994 | + | 0.132847i | ||||
\(283\) | 0.347153 | + | 0.601286i | 0.0206361 | + | 0.0357428i | 0.876159 | − | 0.482022i | \(-0.160098\pi\) |
−0.855523 | + | 0.517765i | \(0.826764\pi\) | |||||||
\(284\) | 5.10254 | + | 8.83786i | 0.302780 | + | 0.524431i | ||||
\(285\) | 7.92007 | + | 13.7180i | 0.469144 | + | 0.812582i | ||||
\(286\) | 7.24406 | − | 12.6571i | 0.428350 | − | 0.748430i | ||||
\(287\) | 5.51270 | − | 14.2315i | 0.325404 | − | 0.840060i | ||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −16.4882 | −0.969896 | ||||||||
\(290\) | 37.0781 | 2.17730 | ||||||||
\(291\) | 3.10135 | − | 5.37170i | 0.181805 | − | 0.314895i | ||||
\(292\) | −1.25673 | + | 2.17673i | −0.0735448 | + | 0.127383i | ||||
\(293\) | 5.44518 | + | 9.43133i | 0.318111 | + | 0.550984i | 0.980094 | − | 0.198535i | \(-0.0636183\pi\) |
−0.661983 | + | 0.749519i | \(0.730285\pi\) | |||||||
\(294\) | 5.17342 | + | 4.71548i | 0.301720 | + | 0.275012i | ||||
\(295\) | 26.5512 | + | 45.9880i | 1.54587 | + | 2.67752i | ||||
\(296\) | 7.19594 | 0.418256 | ||||||||
\(297\) | 2.02237 | + | 3.50284i | 0.117350 | + | 0.203256i | ||||
\(298\) | −11.6810 | + | 20.2320i | −0.676661 | + | 1.17201i | ||||
\(299\) | −7.43565 | − | 12.7675i | −0.430015 | − | 0.738362i | ||||
\(300\) | −11.9383 | −0.689256 | ||||||||
\(301\) | −4.25335 | − | 5.28525i | −0.245159 | − | 0.304637i | ||||
\(302\) | 1.19832 | − | 2.07555i | 0.0689555 | − | 0.119434i | ||||
\(303\) | 8.15325 | − | 14.1218i | 0.468392 | − | 0.811278i | ||||
\(304\) | 1.92440 | − | 3.33315i | 0.110372 | − | 0.191169i | ||||
\(305\) | 38.8134 | 2.22245 | ||||||||
\(306\) | −0.357690 | + | 0.619538i | −0.0204478 | + | 0.0354166i | ||||
\(307\) | 23.7724 | 1.35676 | 0.678382 | − | 0.734709i | \(-0.262681\pi\) | ||||
0.678382 | + | 0.734709i | \(0.262681\pi\) | |||||||
\(308\) | 6.70925 | + | 8.33697i | 0.382295 | + | 0.475043i | ||||
\(309\) | −1.46023 | + | 2.52920i | −0.0830697 | + | 0.143881i | ||||
\(310\) | 15.0337 | 0.853857 | ||||||||
\(311\) | −10.9242 | + | 18.9212i | −0.619454 | + | 1.07293i | 0.370132 | + | 0.928979i | \(0.379312\pi\) |
−0.989586 | + | 0.143946i | \(0.954021\pi\) | |||||||
\(312\) | −1.79099 | + | 3.12928i | −0.101395 | + | 0.177160i | ||||
\(313\) | 16.0323 | + | 27.7688i | 0.906199 | + | 1.56958i | 0.819300 | + | 0.573365i | \(0.194362\pi\) |
0.0868992 | + | 0.996217i | \(0.472304\pi\) | |||||||
\(314\) | 5.79083 | − | 10.0300i | 0.326795 | − | 0.566026i | ||||
\(315\) | 10.7600 | − | 1.67067i | 0.606255 | − | 0.0941316i | ||||
\(316\) | −6.70468 | − | 11.6129i | −0.377168 | − | 0.653274i | ||||
\(317\) | 10.3068 | + | 17.8520i | 0.578889 | + | 1.00267i | 0.995607 | + | 0.0936296i | \(0.0298469\pi\) |
−0.416718 | + | 0.909036i | \(0.636820\pi\) | |||||||
\(318\) | −2.71776 | −0.152404 | ||||||||
\(319\) | −36.4396 | −2.04023 | ||||||||
\(320\) | 2.05781 | + | 3.56422i | 0.115035 | + | 0.199246i | ||||
\(321\) | −2.01938 | − | 3.49768i | −0.112711 | − | 0.195221i | ||||
\(322\) | 10.7134 | − | 1.66344i | 0.597036 | − | 0.0927002i | ||||
\(323\) | 1.37668 | − | 2.38447i | 0.0766003 | − | 0.132676i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −43.0437 | + | 0.162354i | −2.38764 | + | 0.00900579i | ||||
\(326\) | −8.95432 | + | 15.5093i | −0.495934 | + | 0.858982i | ||||
\(327\) | 13.8663 | 0.766807 | ||||||||
\(328\) | −2.88423 | + | 4.99563i | −0.159255 | + | 0.275838i | ||||
\(329\) | −4.27298 | − | 5.30963i | −0.235577 | − | 0.292730i | ||||
\(330\) | 16.6466 | 0.916363 | ||||||||
\(331\) | −5.99781 | + | 10.3885i | −0.329669 | + | 0.571004i | −0.982446 | − | 0.186546i | \(-0.940271\pi\) |
0.652777 | + | 0.757550i | \(0.273604\pi\) | |||||||
\(332\) | −15.5024 | −0.850807 | ||||||||
\(333\) | −3.59797 | + | 6.23187i | −0.197168 | + | 0.341504i | ||||
\(334\) | 3.15398 | − | 5.46286i | 0.172578 | − | 0.298914i | ||||
\(335\) | −2.40005 | + | 4.15701i | −0.131129 | + | 0.227122i | ||||
\(336\) | −1.65876 | − | 2.06119i | −0.0904929 | − | 0.112447i | ||||
\(337\) | −17.6146 | −0.959526 | −0.479763 | − | 0.877398i | \(-0.659277\pi\) | ||||
−0.479763 | + | 0.877398i | \(0.659277\pi\) | |||||||
\(338\) | −6.41489 | + | 11.3070i | −0.348924 | + | 0.615022i | ||||
\(339\) | 7.30902 | − | 12.6596i | 0.396972 | − | 0.687575i | ||||
\(340\) | 1.47212 | + | 2.54978i | 0.0798367 | + | 0.138281i | ||||
\(341\) | −14.7748 | −0.800100 | ||||||||
\(342\) | 1.92440 | + | 3.33315i | 0.104059 | + | 0.180236i | ||||
\(343\) | −16.5777 | + | 8.25707i | −0.895113 | + | 0.445840i | ||||
\(344\) | 1.28209 | + | 2.22064i | 0.0691255 | + | 0.119729i | ||||
\(345\) | 8.43251 | − | 14.6055i | 0.453991 | − | 0.786335i | ||||
\(346\) | 1.82563 | − | 3.16209i | 0.0981467 | − | 0.169995i | ||||
\(347\) | −15.8504 | −0.850893 | −0.425447 | − | 0.904984i | \(-0.639883\pi\) | ||||
−0.425447 | + | 0.904984i | \(0.639883\pi\) | |||||||
\(348\) | 9.00914 | 0.482941 | ||||||||
\(349\) | 5.15206 | − | 8.92363i | 0.275783 | − | 0.477671i | −0.694549 | − | 0.719445i | \(-0.744396\pi\) |
0.970332 | + | 0.241775i | \(0.0777294\pi\) | |||||||
\(350\) | 11.4090 | − | 29.4532i | 0.609834 | − | 1.57434i | ||||
\(351\) | −1.81454 | − | 3.11568i | −0.0968530 | − | 0.166303i | ||||
\(352\) | −2.02237 | − | 3.50284i | −0.107793 | − | 0.186702i | ||||
\(353\) | 8.00975 | + | 13.8733i | 0.426316 | + | 0.738401i | 0.996542 | − | 0.0830868i | \(-0.0264779\pi\) |
−0.570226 | + | 0.821488i | \(0.693145\pi\) | |||||||
\(354\) | 6.45133 | + | 11.1740i | 0.342884 | + | 0.593893i | ||||
\(355\) | −21.0001 | + | 36.3732i | −1.11457 | + | 1.93049i | ||||
\(356\) | −10.9137 | −0.578425 | ||||||||
\(357\) | −1.18665 | − | 1.47454i | −0.0628040 | − | 0.0780408i | ||||
\(358\) | −6.25956 | − | 10.8419i | −0.330828 | − | 0.573011i | ||||
\(359\) | 4.55623 | + | 7.89162i | 0.240469 | + | 0.416504i | 0.960848 | − | 0.277077i | \(-0.0893656\pi\) |
−0.720379 | + | 0.693580i | \(0.756032\pi\) | |||||||
\(360\) | −4.11561 | −0.216912 | ||||||||
\(361\) | 2.09340 | + | 3.62588i | 0.110179 | + | 0.190836i | ||||
\(362\) | −18.1728 | −0.955139 | ||||||||
\(363\) | −5.35989 | −0.281321 | ||||||||
\(364\) | −6.00874 | − | 7.40912i | −0.314944 | − | 0.388343i | ||||
\(365\) | −10.3445 | −0.541454 | ||||||||
\(366\) | 9.43076 | 0.492954 | ||||||||
\(367\) | −5.11189 | − | 8.85406i | −0.266839 | − | 0.462178i | 0.701205 | − | 0.712960i | \(-0.252646\pi\) |
−0.968044 | + | 0.250782i | \(0.919312\pi\) | |||||||
\(368\) | −4.09781 | −0.213613 | ||||||||
\(369\) | −2.88423 | − | 4.99563i | −0.150147 | − | 0.260062i | ||||
\(370\) | 14.8079 | + | 25.6480i | 0.769824 | + | 1.33337i | ||||
\(371\) | 2.59726 | − | 6.70504i | 0.134843 | − | 0.348109i | ||||
\(372\) | 3.65285 | 0.189391 | ||||||||
\(373\) | 14.0796 | − | 24.3866i | 0.729015 | − | 1.26269i | −0.228284 | − | 0.973594i | \(-0.573312\pi\) |
0.957300 | − | 0.289097i | \(-0.0933550\pi\) | |||||||
\(374\) | −1.44676 | − | 2.50587i | −0.0748104 | − | 0.129575i | ||||
\(375\) | −14.2776 | − | 24.7295i | −0.737292 | − | 1.27703i | ||||
\(376\) | 1.28800 | + | 2.23088i | 0.0664236 | + | 0.115049i | ||||
\(377\) | 32.4827 | − | 0.122520i | 1.67294 | − | 0.00631008i | ||||
\(378\) | 2.61442 | − | 0.405935i | 0.134472 | − | 0.0208790i | ||||
\(379\) | −3.08112 | + | 5.33666i | −0.158267 | + | 0.274126i | −0.934244 | − | 0.356635i | \(-0.883924\pi\) |
0.775977 | + | 0.630761i | \(0.217257\pi\) | |||||||
\(380\) | 15.8401 | 0.812582 | ||||||||
\(381\) | −2.53206 | −0.129722 | ||||||||
\(382\) | −2.23004 | + | 3.86254i | −0.114099 | + | 0.197625i | ||||
\(383\) | 9.48159 | − | 16.4226i | 0.484487 | − | 0.839156i | −0.515354 | − | 0.856977i | \(-0.672340\pi\) |
0.999841 | + | 0.0178215i | \(0.00567306\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | −15.9085 | + | 41.0692i | −0.810772 | + | 2.09308i | ||||
\(386\) | 4.34243 | + | 7.52130i | 0.221024 | + | 0.382824i | ||||
\(387\) | −2.56417 | −0.130344 | ||||||||
\(388\) | −3.10135 | − | 5.37170i | −0.157447 | − | 0.272707i | ||||
\(389\) | 1.08192 | − | 1.87394i | 0.0548554 | − | 0.0950123i | −0.837294 | − | 0.546753i | \(-0.815864\pi\) |
0.892149 | + | 0.451741i | \(0.149197\pi\) | |||||||
\(390\) | −14.8389 | + | 0.0559702i | −0.751399 | + | 0.00283416i | ||||
\(391\) | −2.93150 | −0.148252 | ||||||||
\(392\) | 6.67043 | − | 2.12257i | 0.336908 | − | 0.107206i | ||||
\(393\) | −6.21657 | + | 10.7674i | −0.313584 | + | 0.543144i | ||||
\(394\) | −1.23397 | + | 2.13730i | −0.0621664 | + | 0.107675i | ||||
\(395\) | 27.5939 | − | 47.7940i | 1.38840 | − | 2.40478i | ||||
\(396\) | 4.04474 | 0.203256 | ||||||||
\(397\) | −10.3858 | + | 17.9888i | −0.521249 | + | 0.902830i | 0.478445 | + | 0.878117i | \(0.341200\pi\) |
−0.999695 | + | 0.0247127i | \(0.992133\pi\) | |||||||
\(398\) | 20.5681 | 1.03099 | ||||||||
\(399\) | −10.0624 | + | 1.56236i | −0.503749 | + | 0.0782157i | ||||
\(400\) | −5.96913 | + | 10.3388i | −0.298457 | + | 0.516942i | ||||
\(401\) | 2.30807 | 0.115259 | 0.0576297 | − | 0.998338i | \(-0.481646\pi\) | ||||
0.0576297 | + | 0.998338i | \(0.481646\pi\) | |||||||
\(402\) | −0.583158 | + | 1.01006i | −0.0290853 | + | 0.0503772i | ||||
\(403\) | 13.1704 | − | 0.0496768i | 0.656066 | − | 0.00247458i | ||||
\(404\) | −8.15325 | − | 14.1218i | −0.405639 | − | 0.702588i | ||||
\(405\) | 2.05781 | − | 3.56422i | 0.102253 | − | 0.177108i | ||||
\(406\) | −8.60970 | + | 22.2267i | −0.427292 | + | 1.10309i | ||||
\(407\) | −14.5528 | − | 25.2063i | −0.721358 | − | 1.24943i | ||||
\(408\) | 0.357690 | + | 0.619538i | 0.0177083 | + | 0.0306717i | ||||
\(409\) | 16.0313 | 0.792698 | 0.396349 | − | 0.918100i | \(-0.370277\pi\) | ||||
0.396349 | + | 0.918100i | \(0.370277\pi\) | |||||||
\(410\) | −23.7407 | −1.17247 | ||||||||
\(411\) | −5.19240 | − | 8.99351i | −0.256122 | − | 0.443617i | ||||
\(412\) | 1.46023 | + | 2.52920i | 0.0719405 | + | 0.124605i | ||||
\(413\) | −33.7330 | + | 5.23764i | −1.65989 | + | 0.257727i | ||||
\(414\) | 2.04891 | − | 3.54881i | 0.100698 | − | 0.174415i | ||||
\(415\) | −31.9010 | − | 55.2542i | −1.56596 | − | 2.71232i | ||||
\(416\) | 1.81454 | + | 3.11568i | 0.0889652 | + | 0.152759i | ||||
\(417\) | 0.636394 | − | 1.10227i | 0.0311644 | − | 0.0539783i | ||||
\(418\) | −15.5673 | −0.761424 | ||||||||
\(419\) | 1.48519 | − | 2.57242i | 0.0725561 | − | 0.125671i | −0.827465 | − | 0.561518i | \(-0.810218\pi\) |
0.900021 | + | 0.435847i | \(0.143551\pi\) | |||||||
\(420\) | 3.93314 | − | 10.1537i | 0.191917 | − | 0.495451i | ||||
\(421\) | 34.3026 | 1.67181 | 0.835903 | − | 0.548878i | \(-0.184945\pi\) | ||||
0.835903 | + | 0.548878i | \(0.184945\pi\) | |||||||
\(422\) | 2.22726 | − | 3.85773i | 0.108422 | − | 0.187792i | ||||
\(423\) | −2.57600 | −0.125250 | ||||||||
\(424\) | −1.35888 | + | 2.35365i | −0.0659929 | + | 0.114303i | ||||
\(425\) | −4.27020 | + | 7.39621i | −0.207135 | + | 0.358769i | ||||
\(426\) | −5.10254 | + | 8.83786i | −0.247219 | + | 0.428196i | ||||
\(427\) | −9.01263 | + | 23.2669i | −0.436152 | + | 1.12596i | ||||
\(428\) | −4.03877 | −0.195221 | ||||||||
\(429\) | 14.5834 | − | 0.0550063i | 0.704093 | − | 0.00265573i | ||||
\(430\) | −5.27657 | + | 9.13929i | −0.254459 | + | 0.440736i | ||||
\(431\) | 11.7248 | + | 20.3079i | 0.564762 | + | 0.978196i | 0.997072 | + | 0.0764711i | \(0.0243653\pi\) |
−0.432310 | + | 0.901725i | \(0.642301\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 0.402426 | + | 0.697022i | 0.0193394 | + | 0.0334968i | 0.875533 | − | 0.483158i | \(-0.160510\pi\) |
−0.856194 | + | 0.516655i | \(0.827177\pi\) | |||||||
\(434\) | −3.49089 | + | 9.01203i | −0.167568 | + | 0.432591i | ||||
\(435\) | 18.5391 | + | 32.1106i | 0.888880 | + | 1.53959i | ||||
\(436\) | 6.93314 | − | 12.0085i | 0.332037 | − | 0.575105i | ||||
\(437\) | −7.88581 | + | 13.6586i | −0.377230 | + | 0.653381i | ||||
\(438\) | −2.51347 | −0.120098 | ||||||||
\(439\) | −1.59775 | −0.0762566 | −0.0381283 | − | 0.999273i | \(-0.512140\pi\) | ||||
−0.0381283 | + | 0.999273i | \(0.512140\pi\) | |||||||
\(440\) | 8.32328 | − | 14.4163i | 0.396797 | − | 0.687272i | ||||
\(441\) | −1.49702 | + | 6.83805i | −0.0712865 | + | 0.325621i | ||||
\(442\) | 1.29809 | + | 2.22890i | 0.0617437 | + | 0.106018i | ||||
\(443\) | −3.27335 | − | 5.66960i | −0.155521 | − | 0.269371i | 0.777727 | − | 0.628602i | \(-0.216372\pi\) |
−0.933249 | + | 0.359231i | \(0.883039\pi\) | |||||||
\(444\) | 3.59797 | + | 6.23187i | 0.170752 | + | 0.295751i | ||||
\(445\) | −22.4583 | − | 38.8989i | −1.06462 | − | 1.84398i | ||||
\(446\) | −2.49662 | + | 4.32427i | −0.118218 | + | 0.204760i | ||||
\(447\) | −23.3619 | −1.10498 | ||||||||
\(448\) | −2.61442 | + | 0.405935i | −0.123520 | + | 0.0191786i | ||||
\(449\) | −6.34113 | − | 10.9832i | −0.299257 | − | 0.518328i | 0.676710 | − | 0.736250i | \(-0.263405\pi\) |
−0.975966 | + | 0.217923i | \(0.930072\pi\) | |||||||
\(450\) | −5.96913 | − | 10.3388i | −0.281388 | − | 0.487378i | ||||
\(451\) | 23.3319 | 1.09866 | ||||||||
\(452\) | −7.30902 | − | 12.6596i | −0.343788 | − | 0.595457i | ||||
\(453\) | 2.39664 | 0.112604 | ||||||||
\(454\) | −1.57273 | −0.0738117 | ||||||||
\(455\) | 14.0429 | − | 36.6630i | 0.658343 | − | 1.71879i | ||||
\(456\) | 3.84879 | 0.180236 | ||||||||
\(457\) | −10.7551 | −0.503100 | −0.251550 | − | 0.967844i | \(-0.580940\pi\) | ||||
−0.251550 | + | 0.967844i | \(0.580940\pi\) | |||||||
\(458\) | 0.828619 | + | 1.43521i | 0.0387188 | + | 0.0670629i | ||||
\(459\) | −0.715381 | −0.0333911 | ||||||||
\(460\) | −8.43251 | − | 14.6055i | −0.393168 | − | 0.680986i | ||||
\(461\) | 9.19640 | + | 15.9286i | 0.428319 | + | 0.741870i | 0.996724 | − | 0.0808788i | \(-0.0257727\pi\) |
−0.568405 | + | 0.822749i | \(0.692439\pi\) | |||||||
\(462\) | −3.86540 | + | 9.97887i | −0.179835 | + | 0.464259i | ||||
\(463\) | −34.6818 | −1.61180 | −0.805901 | − | 0.592050i | \(-0.798319\pi\) | ||||
−0.805901 | + | 0.592050i | \(0.798319\pi\) | |||||||
\(464\) | 4.50457 | − | 7.80214i | 0.209119 | − | 0.362205i | ||||
\(465\) | 7.51685 | + | 13.0196i | 0.348586 | + | 0.603768i | ||||
\(466\) | −3.86181 | − | 6.68885i | −0.178895 | − | 0.309855i | ||||
\(467\) | 14.1236 | + | 24.4627i | 0.653561 | + | 1.13200i | 0.982253 | + | 0.187563i | \(0.0600589\pi\) |
−0.328692 | + | 0.944437i | \(0.606608\pi\) | |||||||
\(468\) | −3.60553 | + | 0.0135995i | −0.166665 | + | 0.000628636i | ||||
\(469\) | −1.93464 | − | 2.40400i | −0.0893334 | − | 0.111006i | ||||
\(470\) | −5.30091 | + | 9.18145i | −0.244513 | + | 0.423509i | ||||
\(471\) | 11.5817 | 0.533654 | ||||||||
\(472\) | 12.9027 | 0.593893 | ||||||||
\(473\) | 5.18570 | − | 8.98189i | 0.238439 | − | 0.412988i | ||||
\(474\) | 6.70468 | − | 11.6129i | 0.307956 | − | 0.533396i | ||||
\(475\) | 22.9739 | + | 39.7920i | 1.05412 | + | 1.82578i | ||||
\(476\) | −1.87031 | + | 0.290398i | −0.0857255 | + | 0.0133104i | ||||
\(477\) | −1.35888 | − | 2.35365i | −0.0622187 | − | 0.107766i | ||||
\(478\) | −28.7630 | −1.31559 | ||||||||
\(479\) | 6.22925 | + | 10.7894i | 0.284622 | + | 0.492979i | 0.972517 | − | 0.232830i | \(-0.0747987\pi\) |
−0.687896 | + | 0.725810i | \(0.741465\pi\) | |||||||
\(480\) | −2.05781 | + | 3.56422i | −0.0939256 | + | 0.162684i | ||||
\(481\) | 13.0573 | + | 22.4202i | 0.595363 | + | 1.02227i | ||||
\(482\) | 25.6204 | 1.16698 | ||||||||
\(483\) | 6.79730 | + | 8.44638i | 0.309288 | + | 0.384323i | ||||
\(484\) | −2.67994 | + | 4.64180i | −0.121816 | + | 0.210991i | ||||
\(485\) | 12.7640 | − | 22.1078i | 0.579582 | − | 1.00387i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 8.34097 | 0.377966 | 0.188983 | − | 0.981980i | \(-0.439481\pi\) | ||||
0.188983 | + | 0.981980i | \(0.439481\pi\) | |||||||
\(488\) | 4.71538 | − | 8.16728i | 0.213455 | − | 0.369715i | ||||
\(489\) | −17.9086 | −0.809856 | ||||||||
\(490\) | 21.2918 | + | 19.4071i | 0.961865 | + | 0.876723i | ||||
\(491\) | 8.82502 | − | 15.2854i | 0.398268 | − | 0.689820i | −0.595245 | − | 0.803545i | \(-0.702945\pi\) |
0.993512 | + | 0.113725i | \(0.0362781\pi\) | |||||||
\(492\) | −5.76846 | −0.260062 | ||||||||
\(493\) | 3.22248 | − | 5.58150i | 0.145133 | − | 0.251378i | ||||
\(494\) | 13.8769 | − | 0.0523416i | 0.624352 | − | 0.00235496i | ||||
\(495\) | 8.32328 | + | 14.4163i | 0.374104 | + | 0.647967i | ||||
\(496\) | 1.82642 | − | 3.16346i | 0.0820088 | − | 0.142043i | ||||
\(497\) | −16.9278 | − | 21.0346i | −0.759316 | − | 0.943532i | ||||
\(498\) | −7.75122 | − | 13.4255i | −0.347340 | − | 0.601611i | ||||
\(499\) | −18.9853 | − | 32.8834i | −0.849897 | − | 1.47207i | −0.881299 | − | 0.472558i | \(-0.843331\pi\) |
0.0314021 | − | 0.999507i | \(-0.490003\pi\) | |||||||
\(500\) | −28.5552 | −1.27703 | ||||||||
\(501\) | 6.30796 | 0.281819 | ||||||||
\(502\) | 0.339652 | + | 0.588295i | 0.0151594 | + | 0.0262569i | ||||
\(503\) | −10.4517 | − | 18.1029i | −0.466019 | − | 0.807169i | 0.533228 | − | 0.845972i | \(-0.320979\pi\) |
−0.999247 | + | 0.0388027i | \(0.987646\pi\) | |||||||
\(504\) | 0.955663 | − | 2.46713i | 0.0425686 | − | 0.109895i | ||||
\(505\) | 33.5556 | − | 58.1200i | 1.49320 | − | 2.58631i | ||||
\(506\) | 8.28729 | + | 14.3540i | 0.368415 | + | 0.638113i | ||||
\(507\) | −12.9996 | + | 0.0980666i | −0.577334 | + | 0.00435529i | ||||
\(508\) | −1.26603 | + | 2.19283i | −0.0561711 | + | 0.0972911i | ||||
\(509\) | −15.0211 | −0.665797 | −0.332899 | − | 0.942963i | \(-0.608027\pi\) | ||||
−0.332899 | + | 0.942963i | \(0.608027\pi\) | |||||||
\(510\) | −1.47212 | + | 2.54978i | −0.0651864 | + | 0.112906i | ||||
\(511\) | 2.40203 | − | 6.20104i | 0.106259 | − | 0.274318i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.92440 | + | 3.33315i | −0.0849641 | + | 0.147162i | ||||
\(514\) | −2.44587 | −0.107883 | ||||||||
\(515\) | −6.00975 | + | 10.4092i | −0.264821 | + | 0.458684i | ||||
\(516\) | −1.28209 | + | 2.22064i | −0.0564407 | + | 0.0977582i | ||||
\(517\) | 5.20962 | − | 9.02333i | 0.229119 | − | 0.396846i | ||||
\(518\) | −18.8133 | + | 2.92108i | −0.826607 | + | 0.128345i | ||||
\(519\) | 3.65127 | 0.160273 | ||||||||
\(520\) | −7.37100 | + | 12.8789i | −0.323240 | + | 0.564777i | ||||
\(521\) | 10.4549 | − | 18.1084i | 0.458037 | − | 0.793344i | −0.540820 | − | 0.841138i | \(-0.681886\pi\) |
0.998857 | + | 0.0477946i | \(0.0152193\pi\) | |||||||
\(522\) | 4.50457 | + | 7.80214i | 0.197160 | + | 0.341491i | ||||
\(523\) | −12.3678 | −0.540806 | −0.270403 | − | 0.962747i | \(-0.587157\pi\) | ||||
−0.270403 | + | 0.962747i | \(0.587157\pi\) | |||||||
\(524\) | 6.21657 | + | 10.7674i | 0.271572 | + | 0.470377i | ||||
\(525\) | 31.2117 | − | 4.84616i | 1.36219 | − | 0.211504i | ||||
\(526\) | −12.6596 | − | 21.9271i | −0.551985 | − | 0.956067i | ||||
\(527\) | 1.30659 | − | 2.26308i | 0.0569159 | − | 0.0985812i | ||||
\(528\) | 2.02237 | − | 3.50284i | 0.0880123 | − | 0.152442i | ||||
\(529\) | −6.20792 | −0.269910 | ||||||||
\(530\) | −11.1852 | −0.485855 | ||||||||
\(531\) | −6.45133 | + | 11.1740i | −0.279964 | + | 0.484912i | ||||
\(532\) | −3.67815 | + | 9.49545i | −0.159468 | + | 0.411680i | ||||
\(533\) | −20.7983 | + | 0.0784481i | −0.900876 | + | 0.00339796i | ||||
\(534\) | −5.45685 | − | 9.45154i | −0.236141 | − | 0.409008i | ||||
\(535\) | −8.31100 | − | 14.3951i | −0.359316 | − | 0.622353i | ||||
\(536\) | 0.583158 | + | 1.01006i | 0.0251886 | + | 0.0436279i | ||||
\(537\) | 6.25956 | − | 10.8419i | 0.270120 | − | 0.467861i | ||||
\(538\) | −13.5665 | −0.584895 | ||||||||
\(539\) | −20.9251 | − | 19.0729i | −0.901308 | − | 0.821527i | ||||
\(540\) | −2.05781 | − | 3.56422i | −0.0885539 | − | 0.153380i | ||||
\(541\) | 2.37409 | + | 4.11204i | 0.102070 | + | 0.176791i | 0.912537 | − | 0.408993i | \(-0.134120\pi\) |
−0.810467 | + | 0.585784i | \(0.800787\pi\) | |||||||
\(542\) | −4.85940 | −0.208729 | ||||||||
\(543\) | −9.08638 | − | 15.7381i | −0.389934 | − | 0.675385i | ||||
\(544\) | 0.715381 | 0.0306717 | ||||||||
\(545\) | 57.0682 | 2.44453 | ||||||||
\(546\) | 3.41211 | − | 8.90828i | 0.146025 | − | 0.381239i | ||||
\(547\) | 2.85148 | 0.121921 | 0.0609603 | − | 0.998140i | \(-0.480584\pi\) | ||||
0.0609603 | + | 0.998140i | \(0.480584\pi\) | |||||||
\(548\) | −10.3848 | −0.443617 | ||||||||
\(549\) | 4.71538 | + | 8.16728i | 0.201248 | + | 0.348571i | ||||
\(550\) | 48.2871 | 2.05897 | ||||||||
\(551\) | −17.3371 | − | 30.0288i | −0.738587 | − | 1.27927i | ||||
\(552\) | −2.04891 | − | 3.54881i | −0.0872073 | − | 0.151047i | ||||
\(553\) | 22.2430 | + | 27.6393i | 0.945867 | + | 1.17534i | ||||
\(554\) | 12.0625 | 0.512488 | ||||||||
\(555\) | −14.8079 | + | 25.6480i | −0.628559 | + | 1.08870i | ||||
\(556\) | −0.636394 | − | 1.10227i | −0.0269891 | − | 0.0467466i | ||||
\(557\) | −7.04985 | − | 12.2107i | −0.298712 | − | 0.517384i | 0.677130 | − | 0.735864i | \(-0.263224\pi\) |
−0.975842 | + | 0.218480i | \(0.929890\pi\) | |||||||
\(558\) | 1.82642 | + | 3.16346i | 0.0773187 | + | 0.133920i | ||||
\(559\) | −4.59239 | + | 8.02400i | −0.194238 | + | 0.339379i | ||||
\(560\) | −6.82682 | − | 8.48306i | −0.288486 | − | 0.358475i | ||||
\(561\) | 1.44676 | − | 2.50587i | 0.0610824 | − | 0.105798i | ||||
\(562\) | 18.3963 | 0.776002 | ||||||||
\(563\) | −0.914813 | −0.0385548 | −0.0192774 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192774 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(564\) | −1.28800 | + | 2.23088i | −0.0542346 | + | 0.0939371i | ||||
\(565\) | 30.0811 | − | 52.1020i | 1.26552 | − | 2.19195i | ||||
\(566\) | 0.347153 | + | 0.601286i | 0.0145919 | + | 0.0252740i | ||||
\(567\) | 1.65876 | + | 2.06119i | 0.0696615 | + | 0.0865619i | ||||
\(568\) | 5.10254 | + | 8.83786i | 0.214098 | + | 0.370828i | ||||
\(569\) | −22.0768 | −0.925509 | −0.462755 | − | 0.886486i | \(-0.653139\pi\) | ||||
−0.462755 | + | 0.886486i | \(0.653139\pi\) | |||||||
\(570\) | 7.92007 | + | 13.7180i | 0.331735 | + | 0.574582i | ||||
\(571\) | −1.38518 | + | 2.39921i | −0.0579682 | + | 0.100404i | −0.893553 | − | 0.448957i | \(-0.851796\pi\) |
0.835585 | + | 0.549361i | \(0.185129\pi\) | |||||||
\(572\) | 7.24406 | − | 12.6571i | 0.302889 | − | 0.529220i | ||||
\(573\) | −4.46007 | −0.186322 | ||||||||
\(574\) | 5.51270 | − | 14.2315i | 0.230096 | − | 0.594012i | ||||
\(575\) | 24.4604 | − | 42.3666i | 1.02007 | − | 1.76681i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −13.6418 | + | 23.6282i | −0.567914 | + | 0.983656i | 0.428858 | + | 0.903372i | \(0.358916\pi\) |
−0.996772 | + | 0.0802839i | \(0.974417\pi\) | |||||||
\(578\) | −16.4882 | −0.685820 | ||||||||
\(579\) | −4.34243 | + | 7.52130i | −0.180465 | + | 0.312575i | ||||
\(580\) | 37.0781 | 1.53959 | ||||||||
\(581\) | 40.5299 | − | 6.29298i | 1.68147 | − | 0.261077i | ||||
\(582\) | 3.10135 | − | 5.37170i | 0.128555 | − | 0.222664i | ||||
\(583\) | 10.9926 | 0.455267 | ||||||||
\(584\) | −1.25673 | + | 2.17673i | −0.0520040 | + | 0.0900736i | ||||
\(585\) | −7.46794 | − | 12.8229i | −0.308761 | − | 0.530162i | ||||
\(586\) | 5.44518 | + | 9.43133i | 0.224938 | + | 0.389604i | ||||
\(587\) | −15.1737 | + | 26.2816i | −0.626286 | + | 1.08476i | 0.362005 | + | 0.932176i | \(0.382092\pi\) |
−0.988291 | + | 0.152583i | \(0.951241\pi\) | |||||||
\(588\) | 5.17342 | + | 4.71548i | 0.213348 | + | 0.194463i | ||||
\(589\) | −7.02952 | − | 12.1755i | −0.289646 | − | 0.501682i | ||||
\(590\) | 26.5512 | + | 45.9880i | 1.09309 | + | 1.89330i | ||||
\(591\) | −2.46794 | −0.101517 | ||||||||
\(592\) | 7.19594 | 0.295751 | ||||||||
\(593\) | −21.2192 | − | 36.7527i | −0.871367 | − | 1.50925i | −0.860583 | − | 0.509311i | \(-0.829900\pi\) |
−0.0107847 | − | 0.999942i | \(-0.503433\pi\) | |||||||
\(594\) | 2.02237 | + | 3.50284i | 0.0829788 | + | 0.143723i | ||||
\(595\) | −4.88378 | − | 6.06862i | −0.200215 | − | 0.248789i | ||||
\(596\) | −11.6810 | + | 20.2320i | −0.478471 | + | 0.828736i | ||||
\(597\) | 10.2841 | + | 17.8125i | 0.420899 | + | 0.729018i | ||||
\(598\) | −7.43565 | − | 12.7675i | −0.304066 | − | 0.522100i | ||||
\(599\) | 15.1759 | − | 26.2854i | 0.620071 | − | 1.07399i | −0.369401 | − | 0.929270i | \(-0.620437\pi\) |
0.989472 | − | 0.144724i | \(-0.0462294\pi\) | |||||||
\(600\) | −11.9383 | −0.487378 | ||||||||
\(601\) | −2.44125 | + | 4.22836i | −0.0995805 | + | 0.172479i | −0.911511 | − | 0.411275i | \(-0.865083\pi\) |
0.811931 | + | 0.583754i | \(0.198417\pi\) | |||||||
\(602\) | −4.25335 | − | 5.28525i | −0.173354 | − | 0.215411i | ||||
\(603\) | −1.16632 | −0.0474960 | ||||||||
\(604\) | 1.19832 | − | 2.07555i | 0.0487589 | − | 0.0844529i | ||||
\(605\) | −22.0592 | −0.896834 | ||||||||
\(606\) | 8.15325 | − | 14.1218i | 0.331203 | − | 0.573660i | ||||
\(607\) | 6.39843 | − | 11.0824i | 0.259704 | − | 0.449821i | −0.706458 | − | 0.707755i | \(-0.749708\pi\) |
0.966163 | + | 0.257933i | \(0.0830415\pi\) | |||||||
\(608\) | 1.92440 | − | 3.33315i | 0.0780445 | − | 0.135177i | ||||
\(609\) | −23.5537 | + | 3.65712i | −0.954445 | + | 0.148194i | ||||
\(610\) | 38.8134 | 1.57151 | ||||||||
\(611\) | −4.61358 | + | 8.06102i | −0.186646 | + | 0.326114i | ||||
\(612\) | −0.357690 | + | 0.619538i | −0.0144588 | + | 0.0250433i | ||||
\(613\) | −2.02495 | − | 3.50732i | −0.0817871 | − | 0.141659i | 0.822231 | − | 0.569155i | \(-0.192729\pi\) |
−0.904018 | + | 0.427495i | \(0.859396\pi\) | |||||||
\(614\) | 23.7724 | 0.959377 | ||||||||
\(615\) | −11.8704 | − | 20.5601i | −0.478660 | − | 0.829063i | ||||
\(616\) | 6.70925 | + | 8.33697i | 0.270324 | + | 0.335906i | ||||
\(617\) | −7.16474 | − | 12.4097i | −0.288441 | − | 0.499595i | 0.684996 | − | 0.728546i | \(-0.259804\pi\) |
−0.973438 | + | 0.228951i | \(0.926470\pi\) | |||||||
\(618\) | −1.46023 | + | 2.52920i | −0.0587391 | + | 0.101739i | ||||
\(619\) | −18.3950 | + | 31.8611i | −0.739358 | + | 1.28061i | 0.213427 | + | 0.976959i | \(0.431537\pi\) |
−0.952785 | + | 0.303646i | \(0.901796\pi\) | |||||||
\(620\) | 15.0337 | 0.603768 | ||||||||
\(621\) | 4.09781 | 0.164440 | ||||||||
\(622\) | −10.9242 | + | 18.9212i | −0.438020 | + | 0.758673i | ||||
\(623\) | 28.5330 | − | 4.43025i | 1.14315 | − | 0.177494i | ||||
\(624\) | −1.79099 | + | 3.12928i | −0.0716968 | + | 0.125271i | ||||
\(625\) | −28.9154 | − | 50.0829i | −1.15662 | − | 2.00332i | ||||
\(626\) | 16.0323 | + | 27.7688i | 0.640779 | + | 1.10986i | ||||
\(627\) | −7.78367 | − | 13.4817i | −0.310850 | − | 0.538408i | ||||
\(628\) | 5.79083 | − | 10.0300i | 0.231079 | − | 0.400241i | ||||
\(629\) | 5.14784 | 0.205258 | ||||||||
\(630\) | 10.7600 | − | 1.67067i | 0.428687 | − | 0.0665611i | ||||
\(631\) | −18.8504 | − | 32.6498i | −0.750422 | − | 1.29977i | −0.947618 | − | 0.319405i | \(-0.896517\pi\) |
0.197197 | − | 0.980364i | \(-0.436816\pi\) | |||||||
\(632\) | −6.70468 | − | 11.6129i | −0.266698 | − | 0.461935i | ||||
\(633\) | 4.45453 | 0.177052 | ||||||||
\(634\) | 10.3068 | + | 17.8520i | 0.409336 | + | 0.708992i | ||||
\(635\) | −10.4210 | −0.413544 | ||||||||
\(636\) | −2.71776 | −0.107766 | ||||||||
\(637\) | 18.7170 | + | 16.9314i | 0.741595 | + | 0.670848i | ||||
\(638\) | −36.4396 | −1.44266 | ||||||||
\(639\) | −10.2051 | −0.403707 | ||||||||
\(640\) | 2.05781 | + | 3.56422i | 0.0813419 | + | 0.140888i | ||||
\(641\) | −1.18808 | −0.0469264 | −0.0234632 | − | 0.999725i | \(-0.507469\pi\) | ||||
−0.0234632 | + | 0.999725i | \(0.507469\pi\) | |||||||
\(642\) | −2.01938 | − | 3.49768i | −0.0796987 | − | 0.138042i | ||||
\(643\) | −14.9781 | − | 25.9429i | −0.590679 | − | 1.02309i | −0.994141 | − | 0.108090i | \(-0.965527\pi\) |
0.403462 | − | 0.914996i | \(-0.367807\pi\) | |||||||
\(644\) | 10.7134 | − | 1.66344i | 0.422168 | − | 0.0655489i | ||||
\(645\) | −10.5531 | −0.415529 | ||||||||
\(646\) | 1.37668 | − | 2.38447i | 0.0541646 | − | 0.0938158i | ||||
\(647\) | 15.2109 | + | 26.3460i | 0.598002 | + | 1.03577i | 0.993116 | + | 0.117138i | \(0.0373718\pi\) |
−0.395114 | + | 0.918632i | \(0.629295\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −26.0939 | − | 45.1960i | −1.02428 | − | 1.77410i | ||||
\(650\) | −43.0437 | + | 0.162354i | −1.68831 | + | 0.00636806i | ||||
\(651\) | −9.55009 | + | 1.48282i | −0.374298 | + | 0.0581162i | ||||
\(652\) | −8.95432 | + | 15.5093i | −0.350678 | + | 0.607392i | ||||
\(653\) | −12.2930 | −0.481061 | −0.240530 | − | 0.970642i | \(-0.577321\pi\) | ||||
−0.240530 | + | 0.970642i | \(0.577321\pi\) | |||||||
\(654\) | 13.8663 | 0.542214 | ||||||||
\(655\) | −25.5850 | + | 44.3145i | −0.999688 | + | 1.73151i | ||||
\(656\) | −2.88423 | + | 4.99563i | −0.112610 | + | 0.195047i | ||||
\(657\) | −1.25673 | − | 2.17673i | −0.0490299 | − | 0.0849222i | ||||
\(658\) | −4.27298 | − | 5.30963i | −0.166578 | − | 0.206991i | ||||
\(659\) | 17.0038 | + | 29.4514i | 0.662374 | + | 1.14727i | 0.979990 | + | 0.199046i | \(0.0637844\pi\) |
−0.317616 | + | 0.948219i | \(0.602882\pi\) | |||||||
\(660\) | 16.6466 | 0.647967 | ||||||||
\(661\) | −6.90834 | − | 11.9656i | −0.268703 | − | 0.465408i | 0.699824 | − | 0.714315i | \(-0.253262\pi\) |
−0.968527 | + | 0.248908i | \(0.919928\pi\) | |||||||
\(662\) | −5.99781 | + | 10.3885i | −0.233111 | + | 0.403761i | ||||
\(663\) | −1.28124 | + | 2.23862i | −0.0497591 | + | 0.0869410i | ||||
\(664\) | −15.5024 | −0.601611 | ||||||||
\(665\) | −41.4128 | + | 6.43006i | −1.60592 | + | 0.249347i | ||||
\(666\) | −3.59797 | + | 6.23187i | −0.139419 | + | 0.241480i | ||||
\(667\) | −18.4589 | + | 31.9717i | −0.714731 | + | 1.23795i | ||||
\(668\) | 3.15398 | − | 5.46286i | 0.122031 | − | 0.211364i | ||||
\(669\) | −4.99324 | −0.193050 | ||||||||
\(670\) | −2.40005 | + | 4.15701i | −0.0927221 | + | 0.160599i | ||||
\(671\) | −38.1449 | −1.47257 | ||||||||
\(672\) | −1.65876 | − | 2.06119i | −0.0639881 | − | 0.0795122i | ||||
\(673\) | 19.8004 | − | 34.2952i | 0.763248 | − | 1.32198i | −0.177920 | − | 0.984045i | \(-0.556937\pi\) |
0.941168 | − | 0.337939i | \(-0.109730\pi\) | |||||||
\(674\) | −17.6146 | −0.678487 | ||||||||
\(675\) | 5.96913 | − | 10.3388i | 0.229752 | − | 0.397942i | ||||
\(676\) | −6.41489 | + | 11.3070i | −0.246726 | + | 0.434886i | ||||
\(677\) | 16.8735 | + | 29.2258i | 0.648503 | + | 1.12324i | 0.983481 | + | 0.181013i | \(0.0579378\pi\) |
−0.334978 | + | 0.942226i | \(0.608729\pi\) | |||||||
\(678\) | 7.30902 | − | 12.6596i | 0.280701 | − | 0.486189i | ||||
\(679\) | 10.2888 | + | 12.7850i | 0.394849 | + | 0.490642i | ||||
\(680\) | 1.47212 | + | 2.54978i | 0.0564530 | + | 0.0977795i | ||||
\(681\) | −0.786363 | − | 1.36202i | −0.0301335 | − | 0.0521927i | ||||
\(682\) | −14.7748 | −0.565756 | ||||||||
\(683\) | 16.7899 | 0.642448 | 0.321224 | − | 0.947003i | \(-0.395906\pi\) | ||||
0.321224 | + | 0.947003i | \(0.395906\pi\) | |||||||
\(684\) | 1.92440 | + | 3.33315i | 0.0735811 | + | 0.127446i | ||||
\(685\) | −21.3699 | − | 37.0138i | −0.816503 | − | 1.41422i | ||||
\(686\) | −16.5777 | + | 8.25707i | −0.632940 | + | 0.315256i | ||||
\(687\) | −0.828619 | + | 1.43521i | −0.0316138 | + | 0.0547567i | ||||
\(688\) | 1.28209 | + | 2.22064i | 0.0488791 | + | 0.0846610i | ||||
\(689\) | −9.79894 | + | 0.0369601i | −0.373310 | + | 0.00140807i | ||||
\(690\) | 8.43251 | − | 14.6055i | 0.321020 | − | 0.556023i | ||||
\(691\) | −3.35925 | −0.127792 | −0.0638960 | − | 0.997957i | \(-0.520353\pi\) | ||||
−0.0638960 | + | 0.997957i | \(0.520353\pi\) | |||||||
\(692\) | 1.82563 | − | 3.16209i | 0.0694002 | − | 0.120205i | ||||
\(693\) | −10.5747 | + | 1.64190i | −0.401698 | + | 0.0623706i | ||||
\(694\) | −15.8504 | −0.601672 | ||||||||
\(695\) | 2.61915 | − | 4.53651i | 0.0993501 | − | 0.172079i | ||||
\(696\) | 9.00914 | 0.341491 | ||||||||
\(697\) | −2.06332 | + | 3.57378i | −0.0781539 | + | 0.135367i | ||||
\(698\) | 5.15206 | − | 8.92363i | 0.195008 | − | 0.337764i | ||||
\(699\) | 3.86181 | − | 6.68885i | 0.146067 | − | 0.252996i | ||||
\(700\) | 11.4090 | − | 29.4532i | 0.431218 | − | 1.11323i | ||||
\(701\) | −51.6652 | −1.95137 | −0.975683 | − | 0.219186i | \(-0.929660\pi\) | ||||
−0.975683 | + | 0.219186i | \(0.929660\pi\) | |||||||
\(702\) | −1.81454 | − | 3.11568i | −0.0684854 | − | 0.117594i | ||||
\(703\) | 13.8478 | − | 23.9852i | 0.522281 | − | 0.904618i | ||||
\(704\) | −2.02237 | − | 3.50284i | −0.0762209 | − | 0.132018i | ||||
\(705\) | −10.6018 | −0.399288 | ||||||||
\(706\) | 8.00975 | + | 13.8733i | 0.301451 | + | 0.522128i | ||||
\(707\) | 27.0486 | + | 33.6108i | 1.01727 | + | 1.26406i | ||||
\(708\) | 6.45133 | + | 11.1740i | 0.242456 | + | 0.419946i | ||||
\(709\) | 9.65303 | − | 16.7195i | 0.362527 | − | 0.627916i | −0.625849 | − | 0.779944i | \(-0.715247\pi\) |
0.988376 | + | 0.152029i | \(0.0485806\pi\) | |||||||
\(710\) | −21.0001 | + | 36.3732i | −0.788119 | + | 1.36506i | ||||
\(711\) | 13.4094 | 0.502891 | ||||||||
\(712\) | −10.9137 | −0.409008 | ||||||||
\(713\) | −7.48434 | + | 12.9633i | −0.280291 | + | 0.485478i | ||||
\(714\) | −1.18665 | − | 1.47454i | −0.0444091 | − | 0.0551832i | ||||
\(715\) | 60.0196 | − | 0.226385i | 2.24461 | − | 0.00846631i | ||||
\(716\) | −6.25956 | − | 10.8419i | −0.233931 | − | 0.405180i | ||||
\(717\) | −14.3815 | − | 24.9095i | −0.537086 | − | 0.930261i | ||||
\(718\) | 4.55623 | + | 7.89162i | 0.170037 | + | 0.294513i | ||||
\(719\) | 4.27657 | − | 7.40724i | 0.159489 | − | 0.276243i | −0.775195 | − | 0.631721i | \(-0.782349\pi\) |
0.934685 | + | 0.355478i | \(0.115682\pi\) | |||||||
\(720\) | −4.11561 | −0.153380 | ||||||||
\(721\) | −4.84436 | − | 6.01963i | −0.180413 | − | 0.224183i | ||||
\(722\) | 2.09340 | + | 3.62588i | 0.0779084 | + | 0.134941i | ||||
\(723\) | 12.8102 | + | 22.1879i | 0.476417 | + | 0.825178i | ||||
\(724\) | −18.1728 | −0.675385 | ||||||||
\(725\) | 53.7767 | + | 93.1440i | 1.99722 | + | 3.45928i | ||||
\(726\) | −5.35989 | −0.198924 | ||||||||
\(727\) | 37.0524 | 1.37420 | 0.687100 | − | 0.726563i | \(-0.258884\pi\) | ||||
0.687100 | + | 0.726563i | \(0.258884\pi\) | |||||||
\(728\) | −6.00874 | − | 7.40912i | −0.222699 | − | 0.274600i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −10.3445 | −0.382866 | ||||||||
\(731\) | 0.917180 | + | 1.58860i | 0.0339231 | + | 0.0587566i | ||||
\(732\) | 9.43076 | 0.348571 | ||||||||
\(733\) | 7.89197 | + | 13.6693i | 0.291497 | + | 0.504887i | 0.974164 | − | 0.225843i | \(-0.0725135\pi\) |
−0.682667 | + | 0.730729i | \(0.739180\pi\) | |||||||
\(734\) | −5.11189 | − | 8.85406i | −0.188683 | − | 0.326809i | ||||
\(735\) | −6.16114 | + | 28.1428i | −0.227257 | + | 1.03806i | ||||
\(736\) | −4.09781 | −0.151047 | ||||||||
\(737\) | 2.35872 | − | 4.08542i | 0.0868845 | − | 0.150488i | ||||
\(738\) | −2.88423 | − | 4.99563i | −0.106170 | − | 0.183892i | ||||
\(739\) | 18.1725 | + | 31.4757i | 0.668487 | + | 1.15785i | 0.978327 | + | 0.207065i | \(0.0663911\pi\) |
−0.309840 | + | 0.950789i | \(0.600276\pi\) | |||||||
\(740\) | 14.8079 | + | 25.6480i | 0.544348 | + | 0.942838i | ||||
\(741\) | 6.98379 | + | 11.9916i | 0.256556 | + | 0.440522i | ||||
\(742\) | 2.59726 | − | 6.70504i | 0.0953483 | − | 0.246150i | ||||
\(743\) | −15.1149 | + | 26.1797i | −0.554511 | + | 0.960441i | 0.443430 | + | 0.896309i | \(0.353761\pi\) |
−0.997941 | + | 0.0641324i | \(0.979572\pi\) | |||||||
\(744\) | 3.65285 | 0.133920 | ||||||||
\(745\) | −96.1487 | −3.52262 | ||||||||
\(746\) | 14.0796 | − | 24.3866i | 0.515492 | − | 0.892858i | ||||
\(747\) | 7.75122 | − | 13.4255i | 0.283602 | − | 0.491213i | ||||
\(748\) | −1.44676 | − | 2.50587i | −0.0528989 | − | 0.0916236i | ||||
\(749\) | 10.5591 | − | 1.63948i | 0.385819 | − | 0.0599052i | ||||
\(750\) | −14.2776 | − | 24.7295i | −0.521344 | − | 0.902995i | ||||
\(751\) | 30.7238 | 1.12113 | 0.560563 | − | 0.828112i | \(-0.310585\pi\) | ||||
0.560563 | + | 0.828112i | \(0.310585\pi\) | |||||||
\(752\) | 1.28800 | + | 2.23088i | 0.0469686 | + | 0.0813520i | ||||
\(753\) | −0.339652 | + | 0.588295i | −0.0123776 | + | 0.0214387i | ||||
\(754\) | 32.4827 | − | 0.122520i | 1.18295 | − | 0.00446190i | ||||
\(755\) | 9.86363 | 0.358974 | ||||||||
\(756\) | 2.61442 | − | 0.405935i | 0.0950857 | − | 0.0147637i | ||||
\(757\) | −7.78491 | + | 13.4839i | −0.282947 | + | 0.490079i | −0.972109 | − | 0.234528i | \(-0.924646\pi\) |
0.689162 | + | 0.724607i | \(0.257979\pi\) | |||||||
\(758\) | −3.08112 | + | 5.33666i | −0.111911 | + | 0.193836i | ||||
\(759\) | −8.28729 | + | 14.3540i | −0.300809 | + | 0.521017i | ||||
\(760\) | 15.8401 | 0.574582 | ||||||||
\(761\) | −11.9278 | + | 20.6596i | −0.432382 | + | 0.748908i | −0.997078 | − | 0.0763911i | \(-0.975660\pi\) |
0.564696 | + | 0.825299i | \(0.308994\pi\) | |||||||
\(762\) | −2.53206 | −0.0917270 | ||||||||
\(763\) | −13.2515 | + | 34.2098i | −0.479736 | + | 1.23848i | ||||
\(764\) | −2.23004 | + | 3.86254i | −0.0806799 | + | 0.139742i | ||||
\(765\) | −2.94423 | −0.106449 | ||||||||
\(766\) | 9.48159 | − | 16.4226i | 0.342584 | − | 0.593373i | ||||
\(767\) | 23.4124 | + | 40.2005i | 0.845373 | + | 1.45156i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −23.2870 | + | 40.3342i | −0.839750 | + | 1.45449i | 0.0503539 | + | 0.998731i | \(0.483965\pi\) |
−0.890104 | + | 0.455758i | \(0.849368\pi\) | |||||||
\(770\) | −15.9085 | + | 41.0692i | −0.573302 | + | 1.48003i | ||||
\(771\) | −1.22293 | − | 2.11818i | −0.0440429 | − | 0.0762846i | ||||
\(772\) | 4.34243 | + | 7.52130i | 0.156287 | + | 0.270698i | ||||
\(773\) | 7.50660 | 0.269994 | 0.134997 | − | 0.990846i | \(-0.456898\pi\) | ||||
0.134997 | + | 0.990846i | \(0.456898\pi\) | |||||||
\(774\) | −2.56417 | −0.0921673 | ||||||||
\(775\) | 21.8043 | + | 37.7662i | 0.783234 | + | 1.35660i | ||||
\(776\) | −3.10135 | − | 5.37170i | −0.111332 | − | 0.192833i | ||||
\(777\) | −11.9364 | − | 14.8322i | −0.428215 | − | 0.532103i | ||||
\(778\) | 1.08192 | − | 1.87394i | 0.0387886 | − | 0.0671839i | ||||
\(779\) | 11.1008 | + | 19.2271i | 0.397727 | + | 0.688884i | ||||
\(780\) | −14.8389 | + | 0.0559702i | −0.531319 | + | 0.00200405i | ||||
\(781\) | 20.6384 | − | 35.7468i | 0.738501 | − | 1.27912i | ||||
\(782\) | −2.93150 | −0.104830 | ||||||||
\(783\) | −4.50457 | + | 7.80214i | −0.160980 | + | 0.278826i | ||||
\(784\) | 6.67043 | − | 2.12257i | 0.238230 | − | 0.0758061i | ||||
\(785\) | 47.6656 | 1.70126 | ||||||||
\(786\) | −6.21657 | + | 10.7674i | −0.221738 | + | 0.384061i | ||||
\(787\) | 42.4895 | 1.51459 | 0.757293 | − | 0.653075i | \(-0.226521\pi\) | ||||
0.757293 | + | 0.653075i | \(0.226521\pi\) | |||||||
\(788\) | −1.23397 | + | 2.13730i | −0.0439583 | + | 0.0761380i | ||||
\(789\) | 12.6596 | − | 21.9271i | 0.450694 | − | 0.780625i | ||||
\(790\) | 27.5939 | − | 47.7940i | 0.981746 | − | 1.70043i | ||||
\(791\) | 24.2479 | + | 30.1306i | 0.862155 | + | 1.07132i | ||||
\(792\) | 4.04474 | 0.143723 | ||||||||
\(793\) | 34.0029 | − | 0.128254i | 1.20748 | − | 0.00455442i | ||||
\(794\) | −10.3858 | + | 17.9888i | −0.368579 | + | 0.638397i | ||||
\(795\) | −5.59261 | − | 9.68669i | −0.198350 | − | 0.343552i | ||||
\(796\) | 20.5681 | 0.729018 | ||||||||
\(797\) | −9.27713 | − | 16.0685i | −0.328613 | − | 0.569174i | 0.653624 | − | 0.756819i | \(-0.273248\pi\) |
−0.982237 | + | 0.187645i | \(0.939914\pi\) | |||||||
\(798\) | −10.0624 | + | 1.56236i | −0.356204 | + | 0.0553069i | ||||
\(799\) | 0.921412 | + | 1.59593i | 0.0325972 | + | 0.0564600i | ||||
\(800\) | −5.96913 | + | 10.3388i | −0.211041 | + | 0.365533i | ||||
\(801\) | 5.45685 | − | 9.45154i | 0.192808 | − | 0.333954i | ||||
\(802\) | 2.30807 | 0.0815007 | ||||||||
\(803\) | 10.1663 | 0.358761 | ||||||||
\(804\) | −0.583158 | + | 1.01006i | −0.0205664 | + | 0.0356220i | ||||
\(805\) | 27.9750 | + | 34.7620i | 0.985991 | + | 1.22520i | ||||
\(806\) | 13.1704 | − | 0.0496768i | 0.463909 | − | 0.00174979i | ||||
\(807\) | −6.78327 | − | 11.7490i | −0.238783 | − | 0.413583i | ||||
\(808\) | −8.15325 | − | 14.1218i | −0.286830 | − | 0.496804i | ||||
\(809\) | −18.6681 | − | 32.3340i | −0.656334 | − | 1.13680i | −0.981558 | − | 0.191167i | \(-0.938773\pi\) |
0.325224 | − | 0.945637i | \(-0.394560\pi\) | |||||||
\(810\) | 2.05781 | − | 3.56422i | 0.0723039 | − | 0.125234i | ||||
\(811\) | 19.9446 | 0.700350 | 0.350175 | − | 0.936684i | \(-0.386122\pi\) | ||||
0.350175 | + | 0.936684i | \(0.386122\pi\) | |||||||
\(812\) | −8.60970 | + | 22.2267i | −0.302141 | + | 0.780003i | ||||
\(813\) | −2.42970 | − | 4.20837i | −0.0852133 | − | 0.147594i | ||||
\(814\) | −14.5528 | − | 25.2063i | −0.510077 | − | 0.883479i | ||||
\(815\) | −73.7050 | −2.58177 | ||||||||
\(816\) | 0.357690 | + | 0.619538i | 0.0125217 | + | 0.0216882i | ||||
\(817\) | 9.86896 | 0.345271 | ||||||||
\(818\) | 16.0313 | 0.560522 | ||||||||
\(819\) | 9.42086 | − | 1.49916i | 0.329191 | − | 0.0523850i | ||||
\(820\) | −23.7407 | −0.829063 | ||||||||
\(821\) | 24.1262 | 0.842011 | 0.421005 | − | 0.907058i | \(-0.361677\pi\) | ||||
0.421005 | + | 0.907058i | \(0.361677\pi\) | |||||||
\(822\) | −5.19240 | − | 8.99351i | −0.181106 | − | 0.313685i | ||||
\(823\) | 3.27706 | 0.114231 | 0.0571155 | − | 0.998368i | \(-0.481810\pi\) | ||||
0.0571155 | + | 0.998368i | \(0.481810\pi\) | |||||||
\(824\) | 1.46023 | + | 2.52920i | 0.0508696 | + | 0.0881087i | ||||
\(825\) | 24.1436 | + | 41.8179i | 0.840571 | + | 1.45591i | ||||
\(826\) | −33.7330 | + | 5.23764i | −1.17372 | + | 0.182241i | ||||
\(827\) | 49.4538 | 1.71968 | 0.859838 | − | 0.510566i | \(-0.170564\pi\) | ||||
0.859838 | + | 0.510566i | \(0.170564\pi\) | |||||||
\(828\) | 2.04891 | − | 3.54881i | 0.0712044 | − | 0.123330i | ||||
\(829\) | −18.2954 | − | 31.6886i | −0.635426 | − | 1.10059i | −0.986425 | − | 0.164215i | \(-0.947491\pi\) |
0.350998 | − | 0.936376i | \(-0.385842\pi\) | |||||||
\(830\) | −31.9010 | − | 55.2542i | −1.10730 | − | 1.91790i | ||||
\(831\) | 6.03127 | + | 10.4465i | 0.209222 | + | 0.362384i | ||||
\(832\) | 1.81454 | + | 3.11568i | 0.0629079 | + | 0.108017i | ||||
\(833\) | 4.77190 | − | 1.51845i | 0.165337 | − | 0.0526111i | ||||
\(834\) | 0.636394 | − | 1.10227i | 0.0220365 | − | 0.0381684i | ||||
\(835\) | 25.9611 | 0.898422 | ||||||||
\(836\) | −15.5673 | −0.538408 | ||||||||
\(837\) | −1.82642 | + | 3.16346i | −0.0631304 | + | 0.109345i | ||||
\(838\) | 1.48519 | − | 2.57242i | 0.0513049 | − | 0.0888627i | ||||
\(839\) | −21.2148 | − | 36.7451i | −0.732416 | − | 1.26858i | −0.955848 | − | 0.293862i | \(-0.905059\pi\) |
0.223431 | − | 0.974720i | \(-0.428274\pi\) | |||||||
\(840\) | 3.93314 | − | 10.1537i | 0.135706 | − | 0.350337i | ||||
\(841\) | −26.0823 | − | 45.1759i | −0.899389 | − | 1.55779i | ||||
\(842\) | 34.3026 | 1.18214 | ||||||||
\(843\) | 9.19816 | + | 15.9317i | 0.316801 | + | 0.548716i | ||||
\(844\) | 2.22726 | − | 3.85773i | 0.0766656 | − | 0.132789i | ||||
\(845\) | −53.5014 | + | 0.403604i | −1.84051 | + | 0.0138844i | ||||
\(846\) | −2.57600 | −0.0885648 | ||||||||
\(847\) | 5.12224 | − | 13.2235i | 0.176002 | − | 0.454365i | ||||
\(848\) | −1.35888 | + | 2.35365i | −0.0466641 | + | 0.0808245i | ||||
\(849\) | −0.347153 | + | 0.601286i | −0.0119143 | + | 0.0206361i | ||||
\(850\) | −4.27020 | + | 7.39621i | −0.146467 | + | 0.253688i | ||||
\(851\) | −29.4876 | −1.01082 | ||||||||
\(852\) | −5.10254 | + | 8.83786i | −0.174810 | + | 0.302780i | ||||
\(853\) | 31.5639 | 1.08073 | 0.540363 | − | 0.841432i | \(-0.318287\pi\) | ||||
0.540363 | + | 0.841432i | \(0.318287\pi\) | |||||||
\(854\) | −9.01263 | + | 23.2669i | −0.308406 | + | 0.796176i | ||||
\(855\) | −7.92007 | + | 13.7180i | −0.270861 | + | 0.469144i | ||||
\(856\) | −4.03877 | −0.138042 | ||||||||
\(857\) | −13.0273 | + | 22.5639i | −0.445004 | + | 0.770769i | −0.998052 | − | 0.0623801i | \(-0.980131\pi\) |
0.553049 | + | 0.833149i | \(0.313464\pi\) | |||||||
\(858\) | 14.5834 | − | 0.0550063i | 0.497869 | − | 0.00187789i | ||||
\(859\) | 19.9113 | + | 34.4875i | 0.679366 | + | 1.17670i | 0.975172 | + | 0.221449i | \(0.0710786\pi\) |
−0.295806 | + | 0.955248i | \(0.595588\pi\) | |||||||
\(860\) | −5.27657 | + | 9.13929i | −0.179930 | + | 0.311647i | ||||
\(861\) | 15.0812 | − | 2.34162i | 0.513966 | − | 0.0798021i | ||||
\(862\) | 11.7248 | + | 20.3079i | 0.399347 | + | 0.691689i | ||||
\(863\) | 10.4795 | + | 18.1510i | 0.356725 | + | 0.617866i | 0.987412 | − | 0.158172i | \(-0.0505600\pi\) |
−0.630687 | + | 0.776038i | \(0.717227\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 15.0272 | 0.510940 | ||||||||
\(866\) | 0.402426 | + | 0.697022i | 0.0136750 | + | 0.0236858i | ||||
\(867\) | −8.24412 | − | 14.2792i | −0.279985 | − | 0.484948i | ||||
\(868\) | −3.49089 | + | 9.01203i | −0.118489 | + | 0.305888i | ||||
\(869\) | −27.1187 | + | 46.9709i | −0.919938 | + | 1.59338i | ||||
\(870\) | 18.5391 | + | 32.1106i | 0.628533 | + | 1.08865i | ||||
\(871\) | −2.08885 | + | 3.64972i | −0.0707781 | + | 0.123666i | ||||
\(872\) | 6.93314 | − | 12.0085i | 0.234786 | − | 0.406661i | ||||
\(873\) | 6.20271 | 0.209930 | ||||||||
\(874\) | −7.88581 | + | 13.6586i | −0.266742 | + | 0.462010i | ||||
\(875\) | 74.6554 | − | 11.5915i | 2.52381 | − | 0.391866i | ||||
\(876\) | −2.51347 | −0.0849222 | ||||||||
\(877\) | 7.24457 | − | 12.5480i | 0.244632 | − | 0.423714i | −0.717396 | − | 0.696665i | \(-0.754666\pi\) |
0.962028 | + | 0.272951i | \(0.0879996\pi\) | |||||||
\(878\) | −1.59775 | −0.0539216 | ||||||||
\(879\) | −5.44518 | + | 9.43133i | −0.183661 | + | 0.318111i | ||||
\(880\) | 8.32328 | − | 14.4163i | 0.280578 | − | 0.485975i | ||||
\(881\) | −22.1191 | + | 38.3114i | −0.745211 | + | 1.29074i | 0.204886 | + | 0.978786i | \(0.434318\pi\) |
−0.950096 | + | 0.311957i | \(0.899016\pi\) | |||||||
\(882\) | −1.49702 | + | 6.83805i | −0.0504071 | + | 0.230249i | ||||
\(883\) | −51.8997 | −1.74656 | −0.873282 | − | 0.487216i | \(-0.838012\pi\) | ||||
−0.873282 | + | 0.487216i | \(0.838012\pi\) | |||||||
\(884\) | 1.29809 | + | 2.22890i | 0.0436594 | + | 0.0749659i | ||||
\(885\) | −26.5512 | + | 45.9880i | −0.892508 | + | 1.54587i | ||||
\(886\) | −3.27335 | − | 5.66960i | −0.109970 | − | 0.190474i | ||||
\(887\) | 28.7902 | 0.966681 | 0.483340 | − | 0.875433i | \(-0.339423\pi\) | ||||
0.483340 | + | 0.875433i | \(0.339423\pi\) | |||||||
\(888\) | 3.59797 | + | 6.23187i | 0.120740 | + | 0.209128i | ||||
\(889\) | 2.41980 | − | 6.24692i | 0.0811574 | − | 0.209515i | ||||
\(890\) | −22.4583 | − | 38.8989i | −0.752803 | − | 1.30389i | ||||
\(891\) | −2.02237 | + | 3.50284i | −0.0677519 | + | 0.117350i | ||||
\(892\) | −2.49662 | + | 4.32427i | −0.0835929 | + | 0.144787i | ||||
\(893\) | 9.91450 | 0.331776 | ||||||||
\(894\) | −23.3619 | −0.781340 | ||||||||
\(895\) | 25.7619 | − | 44.6210i | 0.861126 | − | 1.49151i | ||||
\(896\) | −2.61442 | + | 0.405935i | −0.0873418 | + | 0.0135613i | ||||
\(897\) | 7.33912 | − | 12.8232i | 0.245046 | − | 0.428154i | ||||
\(898\) | −6.34113 | − | 10.9832i | −0.211606 | − | 0.366513i | ||||
\(899\) | −16.4545 | − | 28.5000i | −0.548788 | − | 0.950529i | ||||
\(900\) | −5.96913 | − | 10.3388i | −0.198971 | − | 0.344628i | ||||
\(901\) | −0.972115 | + | 1.68375i | −0.0323859 | + | 0.0560939i | ||||
\(902\) | 23.3319 | 0.776867 | ||||||||
\(903\) | 2.45048 | − | 6.32614i | 0.0815470 | − | 0.210521i | ||||
\(904\) | −7.30902 | − | 12.6596i | −0.243095 | − | 0.421052i | ||||
\(905\) | −37.3960 | − | 64.7718i | −1.24309 | − | 2.15309i | ||||
\(906\) | 2.39664 | 0.0796229 | ||||||||
\(907\) | 16.5608 | + | 28.6841i | 0.549892 | + | 0.952441i | 0.998281 | + | 0.0586026i | \(0.0186645\pi\) |
−0.448389 | + | 0.893838i | \(0.648002\pi\) | |||||||
\(908\) | −1.57273 | −0.0521927 | ||||||||
\(909\) | 16.3065 | 0.540852 | ||||||||
\(910\) | 14.0429 | − | 36.6630i | 0.465519 | − | 1.21537i | ||||
\(911\) | −20.6630 | −0.684597 | −0.342298 | − | 0.939591i | \(-0.611205\pi\) | ||||
−0.342298 | + | 0.939591i | \(0.611205\pi\) | |||||||
\(912\) | 3.84879 | 0.127446 | ||||||||
\(913\) | 31.3516 | + | 54.3026i | 1.03759 | + | 1.79715i | ||||
\(914\) | −10.7551 | −0.355745 | ||||||||
\(915\) | 19.4067 | + | 33.6134i | 0.641565 | + | 1.11122i | ||||
\(916\) | 0.828619 | + | 1.43521i | 0.0273783 | + | 0.0474207i | ||||
\(917\) | −20.6236 | − | 25.6271i | −0.681052 | − | 0.846280i | ||||
\(918\) | −0.715381 | −0.0236111 | ||||||||
\(919\) | −25.8087 | + | 44.7020i | −0.851350 | + | 1.47458i | 0.0286403 | + | 0.999590i | \(0.490882\pi\) |
−0.879990 | + | 0.474992i | \(0.842451\pi\) | |||||||
\(920\) | −8.43251 | − | 14.6055i | −0.278011 | − | 0.481530i | ||||
\(921\) | 11.8862 | + | 20.5875i | 0.391664 | + | 0.678382i | ||||
\(922\) | 9.19640 | + | 15.9286i | 0.302867 | + | 0.524581i | ||||
\(923\) | −18.2772 | + | 31.9345i | −0.601600 | + | 1.05114i | ||||
\(924\) | −3.86540 | + | 9.97887i | −0.127162 | + | 0.328281i | ||||
\(925\) | −42.9535 | + | 74.3977i | −1.41230 | + | 2.44618i | ||||
\(926\) | −34.6818 | −1.13972 | ||||||||
\(927\) | −2.92046 | −0.0959206 | ||||||||
\(928\) | 4.50457 | − | 7.80214i | 0.147870 | − | 0.256118i | ||||
\(929\) | 17.2590 | − | 29.8935i | 0.566250 | − | 0.980773i | −0.430682 | − | 0.902504i | \(-0.641727\pi\) |
0.996932 | − | 0.0782698i | \(-0.0249396\pi\) | |||||||
\(930\) | 7.51685 | + | 13.0196i | 0.246487 | + | 0.426928i | ||||
\(931\) | 5.76170 | − | 26.3182i | 0.188832 | − | 0.862545i | ||||
\(932\) | −3.86181 | − | 6.68885i | −0.126498 | − | 0.219101i | ||||
\(933\) | −21.8484 | −0.715283 | ||||||||
\(934\) | 14.1236 | + | 24.4627i | 0.462137 | + | 0.800445i | ||||
\(935\) | 5.95432 | − | 10.3132i | 0.194727 | − | 0.337277i | ||||
\(936\) | −3.60553 | + | 0.0135995i | −0.117850 | + | 0.000444513i | ||||
\(937\) | 14.3652 | 0.469291 | 0.234646 | − | 0.972081i | \(-0.424607\pi\) | ||||
0.234646 | + | 0.972081i | \(0.424607\pi\) | |||||||
\(938\) | −1.93464 | − | 2.40400i | −0.0631683 | − | 0.0784934i | ||||
\(939\) | −16.0323 | + | 27.7688i | −0.523194 | + | 0.906199i | ||||
\(940\) | −5.30091 | + | 9.18145i | −0.172897 | + | 0.299466i | ||||
\(941\) | 4.16447 | − | 7.21307i | 0.135758 | − | 0.235139i | −0.790129 | − | 0.612941i | \(-0.789986\pi\) |
0.925887 | + | 0.377801i | \(0.123320\pi\) | |||||||
\(942\) | 11.5817 | 0.377351 | ||||||||
\(943\) | 11.8190 | − | 20.4712i | 0.384881 | − | 0.666633i | ||||
\(944\) | 12.9027 | 0.419946 | ||||||||
\(945\) | 6.82682 | + | 8.48306i | 0.222077 | + | 0.275954i | ||||
\(946\) | 5.18570 | − | 8.98189i | 0.168602 | − | 0.292027i | ||||
\(947\) | −0.321435 | −0.0104452 | −0.00522262 | − | 0.999986i | \(-0.501662\pi\) | ||||
−0.00522262 | + | 0.999986i | \(0.501662\pi\) | |||||||
\(948\) | 6.70468 | − | 11.6129i | 0.217758 | − | 0.377168i | ||||
\(949\) | −9.06238 | + | 0.0341819i | −0.294177 | + | 0.00110959i | ||||
\(950\) | 22.9739 | + | 39.7920i | 0.745373 | + | 1.29102i | ||||
\(951\) | −10.3068 | + | 17.8520i | −0.334222 | + | 0.578889i | ||||
\(952\) | −1.87031 | + | 0.290398i | −0.0606171 | + | 0.00941185i | ||||
\(953\) | −9.79426 | − | 16.9642i | −0.317267 | − | 0.549523i | 0.662650 | − | 0.748930i | \(-0.269432\pi\) |
−0.979917 | + | 0.199407i | \(0.936099\pi\) | |||||||
\(954\) | −1.35888 | − | 2.35365i | −0.0439953 | − | 0.0762021i | ||||
\(955\) | −18.3559 | −0.593984 | ||||||||
\(956\) | −28.7630 | −0.930261 | ||||||||
\(957\) | −18.2198 | − | 31.5576i | −0.588962 | − | 1.02011i | ||||
\(958\) | 6.22925 | + | 10.7894i | 0.201258 | + | 0.348589i | ||||
\(959\) | 27.1503 | − | 4.21555i | 0.876729 | − | 0.136127i | ||||
\(960\) | −2.05781 | + | 3.56422i | −0.0664154 | + | 0.115035i | ||||
\(961\) | 8.82835 | + | 15.2912i | 0.284786 | + | 0.493263i | ||||
\(962\) | 13.0573 | + | 22.4202i | 0.420985 | + | 0.722857i | ||||
\(963\) | 2.01938 | − | 3.49768i | 0.0650737 | − | 0.112711i | ||||
\(964\) | 25.6204 | 0.825178 | ||||||||
\(965\) | −17.8717 | + | 30.9548i | −0.575312 | + | 0.996469i | ||||
\(966\) | 6.79730 | + | 8.44638i | 0.218699 | + | 0.271758i | ||||
\(967\) | −21.5461 | −0.692875 | −0.346437 | − | 0.938073i | \(-0.612609\pi\) | ||||
−0.346437 | + | 0.938073i | \(0.612609\pi\) | |||||||
\(968\) | −2.67994 | + | 4.64180i | −0.0861366 | + | 0.149193i | ||||
\(969\) | 2.75335 | 0.0884504 | ||||||||
\(970\) | 12.7640 | − | 22.1078i | 0.409826 | − | 0.709840i | ||||
\(971\) | 8.53781 | − | 14.7879i | 0.273991 | − | 0.474567i | −0.695889 | − | 0.718150i | \(-0.744989\pi\) |
0.969880 | + | 0.243583i | \(0.0783227\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 2.11125 | + | 2.62346i | 0.0676837 | + | 0.0841043i | ||||
\(974\) | 8.34097 | 0.267262 | ||||||||
\(975\) | −21.6625 | − | 37.1958i | −0.693754 | − | 1.19122i | ||||
\(976\) | 4.71538 | − | 8.16728i | 0.150936 | − | 0.261428i | ||||
\(977\) | −4.36043 | − | 7.55249i | −0.139503 | − | 0.241626i | 0.787806 | − | 0.615924i | \(-0.211217\pi\) |
−0.927308 | + | 0.374298i | \(0.877884\pi\) | |||||||
\(978\) | −17.9086 | −0.572655 | ||||||||
\(979\) | 22.0715 | + | 38.2290i | 0.705409 | + | 1.22180i | ||||
\(980\) | 21.2918 | + | 19.4071i | 0.680141 | + | 0.619937i | ||||
\(981\) | 6.93314 | + | 12.0085i | 0.221358 | + | 0.383403i | ||||
\(982\) | 8.82502 | − | 15.2854i | 0.281618 | − | 0.487776i | ||||
\(983\) | 11.0826 | − | 19.1956i | 0.353480 | − | 0.612245i | −0.633377 | − | 0.773844i | \(-0.718332\pi\) |
0.986857 | + | 0.161598i | \(0.0516649\pi\) | |||||||
\(984\) | −5.76846 | −0.183892 | ||||||||
\(985\) | −10.1571 | −0.323631 | ||||||||
\(986\) | 3.22248 | − | 5.58150i | 0.102625 | − | 0.177751i | ||||
\(987\) | 2.46179 | − | 6.35532i | 0.0783596 | − | 0.202292i | ||||
\(988\) | 13.8769 | − | 0.0523416i | 0.441484 | − | 0.00166521i | ||||
\(989\) | −5.25375 | − | 9.09976i | −0.167060 | − | 0.289356i | ||||
\(990\) | 8.32328 | + | 14.4163i | 0.264531 | + | 0.458182i | ||||
\(991\) | −8.97605 | − | 15.5470i | −0.285134 | − | 0.493866i | 0.687508 | − | 0.726177i | \(-0.258705\pi\) |
−0.972642 | + | 0.232311i | \(0.925371\pi\) | |||||||
\(992\) | 1.82642 | − | 3.16346i | 0.0579890 | − | 0.100440i | ||||
\(993\) | −11.9956 | −0.380669 | ||||||||
\(994\) | −16.9278 | − | 21.0346i | −0.536917 | − | 0.667178i | ||||
\(995\) | 42.3252 | + | 73.3095i | 1.34180 | + | 2.32407i | ||||
\(996\) | −7.75122 | − | 13.4255i | −0.245607 | − | 0.425403i | ||||
\(997\) | 58.9494 | 1.86694 | 0.933472 | − | 0.358649i | \(-0.116763\pi\) | ||||
0.933472 | + | 0.358649i | \(0.116763\pi\) | |||||||
\(998\) | −18.9853 | − | 32.8834i | −0.600968 | − | 1.04091i | ||||
\(999\) | −7.19594 | −0.227670 |
(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 | 546.2.j.d.529.4 | yes | 8 | |
3.2 | odd | 2 | 1638.2.m.g.1621.1 | 8 | |||
7.2 | even | 3 | 546.2.k.b.373.4 | yes | 8 | ||
13.3 | even | 3 | 546.2.k.b.445.4 | yes | 8 | ||
21.2 | odd | 6 | 1638.2.p.i.919.1 | 8 | |||
39.29 | odd | 6 | 1638.2.p.i.991.1 | 8 | |||
91.16 | even | 3 | inner | 546.2.j.d.289.4 | ✓ | 8 | |
273.107 | odd | 6 | 1638.2.m.g.289.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.d.289.4 | ✓ | 8 | 91.16 | even | 3 | inner | |
546.2.j.d.529.4 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.k.b.373.4 | yes | 8 | 7.2 | even | 3 | ||
546.2.k.b.445.4 | yes | 8 | 13.3 | even | 3 | ||
1638.2.m.g.289.1 | 8 | 273.107 | odd | 6 | |||
1638.2.m.g.1621.1 | 8 | 3.2 | odd | 2 | |||
1638.2.p.i.919.1 | 8 | 21.2 | odd | 6 | |||
1638.2.p.i.991.1 | 8 | 39.29 | odd | 6 |