Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(100,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.i (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 10.0.7965937851507.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 100.5 | ||
Root | \(-0.893322 - 1.54728i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.100 |
Dual form | 429.2.i.c.133.5 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.893322 | − | 1.54728i | 0.631674 | − | 1.09409i | −0.355535 | − | 0.934663i | \(-0.615701\pi\) |
0.987209 | − | 0.159429i | \(-0.0509653\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.596049 | − | 1.03239i | −0.298024 | − | 0.516194i | ||||
\(5\) | −0.535309 | −0.239397 | −0.119699 | − | 0.992810i | \(-0.538193\pi\) | ||||
−0.119699 | + | 0.992810i | \(0.538193\pi\) | |||||||
\(6\) | 0.893322 | + | 1.54728i | 0.364697 | + | 0.631674i | ||||
\(7\) | −2.30994 | − | 4.00094i | −0.873077 | − | 1.51221i | −0.858798 | − | 0.512315i | \(-0.828788\pi\) |
−0.0142792 | − | 0.999898i | \(-0.504545\pi\) | |||||||
\(8\) | 1.44343 | 0.510331 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.478203 | + | 0.828272i | −0.151221 | + | 0.261923i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 1.19210 | 0.344129 | ||||||||
\(13\) | 1.10471 | − | 3.43214i | 0.306392 | − | 0.951905i | ||||
\(14\) | −8.25410 | −2.20600 | ||||||||
\(15\) | 0.267654 | − | 0.463591i | 0.0691080 | − | 0.119699i | ||||
\(16\) | 2.48155 | − | 4.29817i | 0.620387 | − | 1.07454i | ||||
\(17\) | −2.01117 | − | 3.48345i | −0.487780 | − | 0.844860i | 0.512121 | − | 0.858913i | \(-0.328860\pi\) |
−0.999901 | + | 0.0140535i | \(0.995526\pi\) | |||||||
\(18\) | −1.78664 | −0.421116 | ||||||||
\(19\) | 3.75422 | + | 6.50250i | 0.861277 | + | 1.49178i | 0.870697 | + | 0.491820i | \(0.163668\pi\) |
−0.00942037 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(20\) | 0.319070 | + | 0.552646i | 0.0713463 | + | 0.123575i | ||||
\(21\) | 4.61989 | 1.00814 | ||||||||
\(22\) | −0.893322 | − | 1.54728i | −0.190457 | − | 0.329881i | ||||
\(23\) | 2.59408 | − | 4.49308i | 0.540904 | − | 0.936873i | −0.457949 | − | 0.888979i | \(-0.651416\pi\) |
0.998852 | − | 0.0478941i | \(-0.0152510\pi\) | |||||||
\(24\) | −0.721717 | + | 1.25005i | −0.147320 | + | 0.255165i | ||||
\(25\) | −4.71344 | −0.942689 | ||||||||
\(26\) | −4.32362 | − | 4.77531i | −0.847932 | − | 0.936515i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.75368 | + | 4.76951i | −0.520396 | + | 0.901353i | ||||
\(29\) | 2.41231 | − | 4.17825i | 0.447955 | − | 0.775881i | −0.550298 | − | 0.834969i | \(-0.685486\pi\) |
0.998253 | + | 0.0590875i | \(0.0188191\pi\) | |||||||
\(30\) | −0.478203 | − | 0.828272i | −0.0873075 | − | 0.151221i | ||||
\(31\) | −3.58893 | −0.644591 | −0.322296 | − | 0.946639i | \(-0.604455\pi\) | ||||
−0.322296 | + | 0.946639i | \(0.604455\pi\) | |||||||
\(32\) | −2.99021 | − | 5.17920i | −0.528600 | − | 0.915562i | ||||
\(33\) | 0.500000 | + | 0.866025i | 0.0870388 | + | 0.150756i | ||||
\(34\) | −7.18648 | −1.23247 | ||||||||
\(35\) | 1.23653 | + | 2.14174i | 0.209012 | + | 0.362020i | ||||
\(36\) | −0.596049 | + | 1.03239i | −0.0993415 | + | 0.172065i | ||||
\(37\) | −1.99803 | + | 3.46070i | −0.328475 | + | 0.568935i | −0.982209 | − | 0.187789i | \(-0.939868\pi\) |
0.653735 | + | 0.756724i | \(0.273201\pi\) | |||||||
\(38\) | 13.4149 | 2.17619 | ||||||||
\(39\) | 2.41997 | + | 2.67278i | 0.387505 | + | 0.427987i | ||||
\(40\) | −0.772682 | −0.122172 | ||||||||
\(41\) | −4.70959 | + | 8.15724i | −0.735514 | + | 1.27395i | 0.218984 | + | 0.975728i | \(0.429726\pi\) |
−0.954498 | + | 0.298219i | \(0.903608\pi\) | |||||||
\(42\) | 4.12705 | − | 7.14826i | 0.636817 | − | 1.10300i | ||||
\(43\) | 3.90683 | + | 6.76683i | 0.595787 | + | 1.03193i | 0.993435 | + | 0.114395i | \(0.0364929\pi\) |
−0.397649 | + | 0.917538i | \(0.630174\pi\) | |||||||
\(44\) | −1.19210 | −0.179716 | ||||||||
\(45\) | 0.267654 | + | 0.463591i | 0.0398995 | + | 0.0691080i | ||||
\(46\) | −4.63470 | − | 8.02754i | −0.683350 | − | 1.18360i | ||||
\(47\) | 9.31634 | 1.35893 | 0.679464 | − | 0.733709i | \(-0.262212\pi\) | ||||
0.679464 | + | 0.733709i | \(0.262212\pi\) | |||||||
\(48\) | 2.48155 | + | 4.29817i | 0.358181 | + | 0.620387i | ||||
\(49\) | −7.17168 | + | 12.4217i | −1.02453 | + | 1.77453i | ||||
\(50\) | −4.21062 | + | 7.29302i | −0.595472 | + | 1.03139i | ||||
\(51\) | 4.02234 | 0.563240 | ||||||||
\(52\) | −4.20176 | + | 0.905235i | −0.582680 | + | 0.125534i | ||||
\(53\) | 7.61596 | 1.04613 | 0.523066 | − | 0.852292i | \(-0.324788\pi\) | ||||
0.523066 | + | 0.852292i | \(0.324788\pi\) | |||||||
\(54\) | 0.893322 | − | 1.54728i | 0.121566 | − | 0.210558i | ||||
\(55\) | −0.267654 | + | 0.463591i | −0.0360905 | + | 0.0625106i | ||||
\(56\) | −3.33425 | − | 5.77509i | −0.445558 | − | 0.771729i | ||||
\(57\) | −7.50844 | −0.994517 | ||||||||
\(58\) | −4.30994 | − | 7.46504i | −0.565923 | − | 0.980208i | ||||
\(59\) | −2.07790 | − | 3.59903i | −0.270520 | − | 0.468554i | 0.698475 | − | 0.715634i | \(-0.253862\pi\) |
−0.968995 | + | 0.247080i | \(0.920529\pi\) | |||||||
\(60\) | −0.638140 | −0.0823836 | ||||||||
\(61\) | 4.87922 | + | 8.45107i | 0.624721 | + | 1.08205i | 0.988595 | + | 0.150600i | \(0.0481205\pi\) |
−0.363874 | + | 0.931448i | \(0.618546\pi\) | |||||||
\(62\) | −3.20607 | + | 5.55308i | −0.407172 | + | 0.705242i | ||||
\(63\) | −2.30994 | + | 4.00094i | −0.291026 | + | 0.504071i | ||||
\(64\) | −0.758694 | −0.0948368 | ||||||||
\(65\) | −0.591362 | + | 1.83726i | −0.0733494 | + | 0.227884i | ||||
\(66\) | 1.78664 | 0.219921 | ||||||||
\(67\) | −3.91130 | + | 6.77458i | −0.477842 | + | 0.827647i | −0.999677 | − | 0.0253997i | \(-0.991914\pi\) |
0.521835 | + | 0.853046i | \(0.325248\pi\) | |||||||
\(68\) | −2.39751 | + | 4.15261i | −0.290741 | + | 0.503578i | ||||
\(69\) | 2.59408 | + | 4.49308i | 0.312291 | + | 0.540904i | ||||
\(70\) | 4.41849 | 0.528110 | ||||||||
\(71\) | −5.18779 | − | 8.98551i | −0.615677 | − | 1.06638i | −0.990265 | − | 0.139193i | \(-0.955549\pi\) |
0.374588 | − | 0.927191i | \(-0.377784\pi\) | |||||||
\(72\) | −0.721717 | − | 1.25005i | −0.0850551 | − | 0.147320i | ||||
\(73\) | 1.96904 | 0.230459 | 0.115230 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115230 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(74\) | 3.56978 | + | 6.18303i | 0.414978 | + | 0.718763i | ||||
\(75\) | 2.35672 | − | 4.08196i | 0.272131 | − | 0.471344i | ||||
\(76\) | 4.47540 | − | 7.75161i | 0.513363 | − | 0.889171i | ||||
\(77\) | −4.61989 | −0.526485 | ||||||||
\(78\) | 6.29735 | − | 1.35671i | 0.713034 | − | 0.153617i | ||||
\(79\) | 8.39852 | 0.944907 | 0.472453 | − | 0.881356i | \(-0.343368\pi\) | ||||
0.472453 | + | 0.881356i | \(0.343368\pi\) | |||||||
\(80\) | −1.32839 | + | 2.30085i | −0.148519 | + | 0.257243i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 8.41435 | + | 14.5741i | 0.929210 | + | 1.60944i | ||||
\(83\) | 7.36522 | 0.808438 | 0.404219 | − | 0.914662i | \(-0.367543\pi\) | ||||
0.404219 | + | 0.914662i | \(0.367543\pi\) | |||||||
\(84\) | −2.75368 | − | 4.76951i | −0.300451 | − | 0.520396i | ||||
\(85\) | 1.07660 | + | 1.86472i | 0.116773 | + | 0.202257i | ||||
\(86\) | 13.9602 | 1.50537 | ||||||||
\(87\) | 2.41231 | + | 4.17825i | 0.258627 | + | 0.447955i | ||||
\(88\) | 0.721717 | − | 1.25005i | 0.0769353 | − | 0.133256i | ||||
\(89\) | −1.68762 | + | 2.92305i | −0.178888 | + | 0.309842i | −0.941500 | − | 0.337014i | \(-0.890583\pi\) |
0.762612 | + | 0.646856i | \(0.223917\pi\) | |||||||
\(90\) | 0.956406 | 0.100814 | ||||||||
\(91\) | −16.2836 | + | 3.50817i | −1.70699 | + | 0.367757i | ||||
\(92\) | −6.18480 | −0.644810 | ||||||||
\(93\) | 1.79447 | − | 3.10811i | 0.186077 | − | 0.322296i | ||||
\(94\) | 8.32249 | − | 14.4150i | 0.858400 | − | 1.48679i | ||||
\(95\) | −2.00967 | − | 3.48084i | −0.206187 | − | 0.357127i | ||||
\(96\) | 5.98042 | 0.610374 | ||||||||
\(97\) | −5.95675 | − | 10.3174i | −0.604816 | − | 1.04757i | −0.992081 | − | 0.125603i | \(-0.959913\pi\) |
0.387264 | − | 0.921969i | \(-0.373420\pi\) | |||||||
\(98\) | 12.8132 | + | 22.1932i | 1.29433 | + | 2.24185i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 2.80944 | + | 4.86610i | 0.280944 | + | 0.486610i | ||||
\(101\) | −5.61321 | + | 9.72236i | −0.558535 | + | 0.967411i | 0.439084 | + | 0.898446i | \(0.355303\pi\) |
−0.997619 | + | 0.0689652i | \(0.978030\pi\) | |||||||
\(102\) | 3.59324 | − | 6.22368i | 0.355784 | − | 0.616236i | ||||
\(103\) | 7.92989 | 0.781356 | 0.390678 | − | 0.920527i | \(-0.372241\pi\) | ||||
0.390678 | + | 0.920527i | \(0.372241\pi\) | |||||||
\(104\) | 1.59458 | − | 4.95407i | 0.156361 | − | 0.485787i | ||||
\(105\) | −2.47307 | −0.241346 | ||||||||
\(106\) | 6.80350 | − | 11.7840i | 0.660815 | − | 1.14456i | ||||
\(107\) | 6.35241 | − | 11.0027i | 0.614111 | − | 1.06367i | −0.376429 | − | 0.926446i | \(-0.622848\pi\) |
0.990540 | − | 0.137226i | \(-0.0438186\pi\) | |||||||
\(108\) | −0.596049 | − | 1.03239i | −0.0573548 | − | 0.0993415i | ||||
\(109\) | −3.62992 | −0.347683 | −0.173842 | − | 0.984774i | \(-0.555618\pi\) | ||||
−0.173842 | + | 0.984774i | \(0.555618\pi\) | |||||||
\(110\) | 0.478203 | + | 0.828272i | 0.0455949 | + | 0.0789726i | ||||
\(111\) | −1.99803 | − | 3.46070i | −0.189645 | − | 0.328475i | ||||
\(112\) | −22.9290 | −2.16658 | ||||||||
\(113\) | −6.87759 | − | 11.9123i | −0.646989 | − | 1.12062i | −0.983838 | − | 0.179059i | \(-0.942695\pi\) |
0.336849 | − | 0.941559i | \(-0.390639\pi\) | |||||||
\(114\) | −6.70745 | + | 11.6176i | −0.628211 | + | 1.08809i | ||||
\(115\) | −1.38863 | + | 2.40519i | −0.129491 | + | 0.224285i | ||||
\(116\) | −5.75142 | −0.534006 | ||||||||
\(117\) | −3.52468 | + | 0.759363i | −0.325857 | + | 0.0702032i | ||||
\(118\) | −7.42494 | −0.683521 | ||||||||
\(119\) | −9.29137 | + | 16.0931i | −0.851739 | + | 1.47525i | ||||
\(120\) | 0.386341 | − | 0.669163i | 0.0352680 | − | 0.0610859i | ||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 17.4349 | 1.57848 | ||||||||
\(123\) | −4.70959 | − | 8.15724i | −0.424649 | − | 0.735514i | ||||
\(124\) | 2.13918 | + | 3.70517i | 0.192104 | + | 0.332734i | ||||
\(125\) | 5.19969 | 0.465074 | ||||||||
\(126\) | 4.12705 | + | 7.14826i | 0.367667 | + | 0.636817i | ||||
\(127\) | 0.0993951 | − | 0.172157i | 0.00881989 | − | 0.0152765i | −0.861582 | − | 0.507619i | \(-0.830526\pi\) |
0.870402 | + | 0.492342i | \(0.163859\pi\) | |||||||
\(128\) | 5.30267 | − | 9.18449i | 0.468694 | − | 0.811802i | ||||
\(129\) | −7.81367 | −0.687955 | ||||||||
\(130\) | 2.31447 | + | 2.55626i | 0.202993 | + | 0.224199i | ||||
\(131\) | 21.7985 | 1.90454 | 0.952272 | − | 0.305251i | \(-0.0987405\pi\) | ||||
0.952272 | + | 0.305251i | \(0.0987405\pi\) | |||||||
\(132\) | 0.596049 | − | 1.03239i | 0.0518794 | − | 0.0898578i | ||||
\(133\) | 17.3441 | − | 30.0408i | 1.50392 | − | 2.60487i | ||||
\(134\) | 6.98811 | + | 12.1038i | 0.603681 | + | 1.04561i | ||||
\(135\) | −0.535309 | −0.0460720 | ||||||||
\(136\) | −2.90299 | − | 5.02812i | −0.248929 | − | 0.431158i | ||||
\(137\) | 7.24914 | + | 12.5559i | 0.619336 | + | 1.07272i | 0.989607 | + | 0.143798i | \(0.0459315\pi\) |
−0.370271 | + | 0.928924i | \(0.620735\pi\) | |||||||
\(138\) | 9.26941 | 0.789064 | ||||||||
\(139\) | 0.615714 | + | 1.06645i | 0.0522242 | + | 0.0904549i | 0.890956 | − | 0.454090i | \(-0.150036\pi\) |
−0.838732 | + | 0.544545i | \(0.816702\pi\) | |||||||
\(140\) | 1.47407 | − | 2.55316i | 0.124582 | − | 0.215781i | ||||
\(141\) | −4.65817 | + | 8.06819i | −0.392289 | + | 0.679464i | ||||
\(142\) | −18.5375 | −1.55563 | ||||||||
\(143\) | −2.41997 | − | 2.67278i | −0.202368 | − | 0.223509i | ||||
\(144\) | −4.96310 | −0.413592 | ||||||||
\(145\) | −1.29133 | + | 2.23665i | −0.107239 | + | 0.185744i | ||||
\(146\) | 1.75899 | − | 3.04666i | 0.145575 | − | 0.252144i | ||||
\(147\) | −7.17168 | − | 12.4217i | −0.591510 | − | 1.02453i | ||||
\(148\) | 4.76370 | 0.391574 | ||||||||
\(149\) | −2.96573 | − | 5.13679i | −0.242962 | − | 0.420822i | 0.718595 | − | 0.695429i | \(-0.244786\pi\) |
−0.961557 | + | 0.274607i | \(0.911452\pi\) | |||||||
\(150\) | −4.21062 | − | 7.29302i | −0.343796 | − | 0.595472i | ||||
\(151\) | 19.7316 | 1.60573 | 0.802867 | − | 0.596159i | \(-0.203307\pi\) | ||||
0.802867 | + | 0.596159i | \(0.203307\pi\) | |||||||
\(152\) | 5.41897 | + | 9.38592i | 0.439536 | + | 0.761299i | ||||
\(153\) | −2.01117 | + | 3.48345i | −0.162593 | + | 0.281620i | ||||
\(154\) | −4.12705 | + | 7.14826i | −0.332567 | + | 0.576023i | ||||
\(155\) | 1.92119 | 0.154313 | ||||||||
\(156\) | 1.31692 | − | 4.09145i | 0.105438 | − | 0.327578i | ||||
\(157\) | −21.5886 | −1.72296 | −0.861480 | − | 0.507791i | \(-0.830462\pi\) | ||||
−0.861480 | + | 0.507791i | \(0.830462\pi\) | |||||||
\(158\) | 7.50258 | − | 12.9949i | 0.596873 | − | 1.03381i | ||||
\(159\) | −3.80798 | + | 6.59561i | −0.301992 | + | 0.523066i | ||||
\(160\) | 1.60069 | + | 2.77247i | 0.126545 | + | 0.219183i | ||||
\(161\) | −23.9687 | −1.88900 | ||||||||
\(162\) | 0.893322 | + | 1.54728i | 0.0701860 | + | 0.121566i | ||||
\(163\) | 3.24389 | + | 5.61858i | 0.254081 | + | 0.440081i | 0.964645 | − | 0.263551i | \(-0.0848937\pi\) |
−0.710565 | + | 0.703632i | \(0.751560\pi\) | |||||||
\(164\) | 11.2286 | 0.876804 | ||||||||
\(165\) | −0.267654 | − | 0.463591i | −0.0208369 | − | 0.0360905i | ||||
\(166\) | 6.57952 | − | 11.3961i | 0.510670 | − | 0.884506i | ||||
\(167\) | −12.4782 | + | 21.6128i | −0.965589 | + | 1.67245i | −0.257564 | + | 0.966261i | \(0.582920\pi\) |
−0.708025 | + | 0.706187i | \(0.750414\pi\) | |||||||
\(168\) | 6.66850 | 0.514486 | ||||||||
\(169\) | −10.5592 | − | 7.58306i | −0.812248 | − | 0.583312i | ||||
\(170\) | 3.84699 | 0.295050 | ||||||||
\(171\) | 3.75422 | − | 6.50250i | 0.287092 | − | 0.497258i | ||||
\(172\) | 4.65733 | − | 8.06673i | 0.355118 | − | 0.615082i | ||||
\(173\) | −1.29597 | − | 2.24468i | −0.0985307 | − | 0.170660i | 0.812546 | − | 0.582897i | \(-0.198081\pi\) |
−0.911077 | + | 0.412237i | \(0.864748\pi\) | |||||||
\(174\) | 8.61989 | 0.653472 | ||||||||
\(175\) | 10.8878 | + | 18.8582i | 0.823040 | + | 1.42555i | ||||
\(176\) | −2.48155 | − | 4.29817i | −0.187054 | − | 0.323987i | ||||
\(177\) | 4.15580 | 0.312369 | ||||||||
\(178\) | 3.01518 | + | 5.22245i | 0.225997 | + | 0.391439i | ||||
\(179\) | 6.47062 | − | 11.2074i | 0.483637 | − | 0.837683i | −0.516187 | − | 0.856476i | \(-0.672649\pi\) |
0.999823 | + | 0.0187927i | \(0.00598226\pi\) | |||||||
\(180\) | 0.319070 | − | 0.552646i | 0.0237821 | − | 0.0411918i | ||||
\(181\) | 10.6703 | 0.793119 | 0.396560 | − | 0.918009i | \(-0.370204\pi\) | ||||
0.396560 | + | 0.918009i | \(0.370204\pi\) | |||||||
\(182\) | −9.11840 | + | 28.3292i | −0.675901 | + | 2.09990i | ||||
\(183\) | −9.75845 | −0.721365 | ||||||||
\(184\) | 3.74439 | − | 6.48547i | 0.276040 | − | 0.478115i | ||||
\(185\) | 1.06956 | − | 1.85254i | 0.0786360 | − | 0.136201i | ||||
\(186\) | −3.20607 | − | 5.55308i | −0.235081 | − | 0.407172i | ||||
\(187\) | −4.02234 | −0.294142 | ||||||||
\(188\) | −5.55299 | − | 9.61807i | −0.404994 | − | 0.701470i | ||||
\(189\) | −2.30994 | − | 4.00094i | −0.168024 | − | 0.291026i | ||||
\(190\) | −7.18111 | −0.520973 | ||||||||
\(191\) | −3.47247 | − | 6.01449i | −0.251259 | − | 0.435193i | 0.712614 | − | 0.701557i | \(-0.247511\pi\) |
−0.963873 | + | 0.266363i | \(0.914178\pi\) | |||||||
\(192\) | 0.379347 | − | 0.657049i | 0.0273770 | − | 0.0474184i | ||||
\(193\) | −2.01255 | + | 3.48584i | −0.144866 | + | 0.250916i | −0.929323 | − | 0.369268i | \(-0.879609\pi\) |
0.784457 | + | 0.620184i | \(0.212942\pi\) | |||||||
\(194\) | −21.2852 | −1.52819 | ||||||||
\(195\) | −1.29543 | − | 1.43076i | −0.0927676 | − | 0.102459i | ||||
\(196\) | 17.0987 | 1.22134 | ||||||||
\(197\) | 3.59923 | − | 6.23405i | 0.256434 | − | 0.444157i | −0.708850 | − | 0.705360i | \(-0.750786\pi\) |
0.965284 | + | 0.261202i | \(0.0841189\pi\) | |||||||
\(198\) | −0.893322 | + | 1.54728i | −0.0634856 | + | 0.109960i | ||||
\(199\) | 3.90499 | + | 6.76363i | 0.276817 | + | 0.479461i | 0.970592 | − | 0.240731i | \(-0.0773871\pi\) |
−0.693775 | + | 0.720192i | \(0.744054\pi\) | |||||||
\(200\) | −6.80354 | −0.481083 | ||||||||
\(201\) | −3.91130 | − | 6.77458i | −0.275882 | − | 0.477842i | ||||
\(202\) | 10.0288 | + | 17.3704i | 0.705624 | + | 1.22218i | ||||
\(203\) | −22.2892 | −1.56440 | ||||||||
\(204\) | −2.39751 | − | 4.15261i | −0.167859 | − | 0.290741i | ||||
\(205\) | 2.52108 | − | 4.36664i | 0.176080 | − | 0.304979i | ||||
\(206\) | 7.08395 | − | 12.2698i | 0.493562 | − | 0.854875i | ||||
\(207\) | −5.18817 | −0.360602 | ||||||||
\(208\) | −12.0105 | − | 13.2653i | −0.832781 | − | 0.919781i | ||||
\(209\) | 7.50844 | 0.519369 | ||||||||
\(210\) | −2.20924 | + | 3.82652i | −0.152452 | + | 0.264055i | ||||
\(211\) | −13.4909 | + | 23.3669i | −0.928750 | + | 1.60864i | −0.143333 | + | 0.989674i | \(0.545782\pi\) |
−0.785417 | + | 0.618967i | \(0.787551\pi\) | |||||||
\(212\) | −4.53948 | − | 7.86261i | −0.311773 | − | 0.540007i | ||||
\(213\) | 10.3756 | 0.710923 | ||||||||
\(214\) | −11.3495 | − | 19.6579i | −0.775836 | − | 1.34379i | ||||
\(215\) | −2.09136 | − | 3.62234i | −0.142630 | − | 0.247042i | ||||
\(216\) | 1.44343 | 0.0982132 | ||||||||
\(217\) | 8.29023 | + | 14.3591i | 0.562778 | + | 0.974759i | ||||
\(218\) | −3.24269 | + | 5.61650i | −0.219622 | + | 0.380397i | ||||
\(219\) | −0.984522 | + | 1.70524i | −0.0665279 | + | 0.115230i | ||||
\(220\) | 0.638140 | 0.0430234 | ||||||||
\(221\) | −14.1774 | + | 3.05441i | −0.953678 | + | 0.205462i | ||||
\(222\) | −7.13955 | −0.479175 | ||||||||
\(223\) | −11.5140 | + | 19.9428i | −0.771032 | + | 1.33547i | 0.165966 | + | 0.986131i | \(0.446926\pi\) |
−0.936998 | + | 0.349335i | \(0.886408\pi\) | |||||||
\(224\) | −13.8144 | + | 23.9273i | −0.923016 | + | 1.59871i | ||||
\(225\) | 2.35672 | + | 4.08196i | 0.157115 | + | 0.272131i | ||||
\(226\) | −24.5756 | −1.63475 | ||||||||
\(227\) | 1.56880 | + | 2.71724i | 0.104125 | + | 0.180350i | 0.913380 | − | 0.407107i | \(-0.133462\pi\) |
−0.809255 | + | 0.587457i | \(0.800129\pi\) | |||||||
\(228\) | 4.47540 | + | 7.75161i | 0.296390 | + | 0.513363i | ||||
\(229\) | −9.84336 | −0.650468 | −0.325234 | − | 0.945634i | \(-0.605443\pi\) | ||||
−0.325234 | + | 0.945634i | \(0.605443\pi\) | |||||||
\(230\) | 2.48100 | + | 4.29721i | 0.163592 | + | 0.283350i | ||||
\(231\) | 2.30994 | − | 4.00094i | 0.151983 | − | 0.263243i | ||||
\(232\) | 3.48201 | − | 6.03102i | 0.228605 | − | 0.395956i | ||||
\(233\) | −1.00285 | −0.0656991 | −0.0328496 | − | 0.999460i | \(-0.510458\pi\) | ||||
−0.0328496 | + | 0.999460i | \(0.510458\pi\) | |||||||
\(234\) | −1.97373 | + | 6.13202i | −0.129027 | + | 0.400863i | ||||
\(235\) | −4.98712 | −0.325324 | ||||||||
\(236\) | −2.47706 | + | 4.29039i | −0.161243 | + | 0.279281i | ||||
\(237\) | −4.19926 | + | 7.27333i | −0.272771 | + | 0.472453i | ||||
\(238\) | 16.6004 | + | 28.7527i | 1.07604 | + | 1.86376i | ||||
\(239\) | −4.57272 | −0.295785 | −0.147892 | − | 0.989003i | \(-0.547249\pi\) | ||||
−0.147892 | + | 0.989003i | \(0.547249\pi\) | |||||||
\(240\) | −1.32839 | − | 2.30085i | −0.0857475 | − | 0.148519i | ||||
\(241\) | −12.3916 | − | 21.4629i | −0.798214 | − | 1.38255i | −0.920778 | − | 0.390086i | \(-0.872445\pi\) |
0.122564 | − | 0.992461i | \(-0.460888\pi\) | |||||||
\(242\) | −1.78664 | −0.114850 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 5.81651 | − | 10.0745i | 0.372364 | − | 0.644954i | ||||
\(245\) | 3.83906 | − | 6.64945i | 0.245269 | − | 0.424818i | ||||
\(246\) | −16.8287 | −1.07296 | ||||||||
\(247\) | 26.4648 | − | 5.70163i | 1.68392 | − | 0.362786i | ||||
\(248\) | −5.18039 | −0.328955 | ||||||||
\(249\) | −3.68261 | + | 6.37847i | −0.233376 | + | 0.404219i | ||||
\(250\) | 4.64500 | − | 8.04537i | 0.293776 | − | 0.508834i | ||||
\(251\) | −0.255317 | − | 0.442223i | −0.0161155 | − | 0.0279128i | 0.857855 | − | 0.513891i | \(-0.171797\pi\) |
−0.873971 | + | 0.485979i | \(0.838463\pi\) | |||||||
\(252\) | 5.50736 | 0.346931 | ||||||||
\(253\) | −2.59408 | − | 4.49308i | −0.163089 | − | 0.282478i | ||||
\(254\) | −0.177584 | − | 0.307584i | −0.0111426 | − | 0.0192995i | ||||
\(255\) | −2.15319 | −0.134838 | ||||||||
\(256\) | −10.2327 | − | 17.7235i | −0.639542 | − | 1.10772i | ||||
\(257\) | 4.02806 | − | 6.97680i | 0.251263 | − | 0.435201i | −0.712611 | − | 0.701560i | \(-0.752487\pi\) |
0.963874 | + | 0.266359i | \(0.0858207\pi\) | |||||||
\(258\) | −6.98012 | + | 12.0899i | −0.434563 | + | 0.752686i | ||||
\(259\) | 18.4614 | 1.14713 | ||||||||
\(260\) | 2.24924 | − | 0.484580i | 0.139492 | − | 0.0300524i | ||||
\(261\) | −4.82462 | −0.298637 | ||||||||
\(262\) | 19.4731 | − | 33.7284i | 1.20305 | − | 2.08375i | ||||
\(263\) | −0.208161 | + | 0.360546i | −0.0128358 | + | 0.0222322i | −0.872372 | − | 0.488843i | \(-0.837419\pi\) |
0.859536 | + | 0.511075i | \(0.170753\pi\) | |||||||
\(264\) | 0.721717 | + | 1.25005i | 0.0444186 | + | 0.0769353i | ||||
\(265\) | −4.07689 | −0.250441 | ||||||||
\(266\) | −30.9877 | − | 53.6722i | −1.89998 | − | 3.29086i | ||||
\(267\) | −1.68762 | − | 2.92305i | −0.103281 | − | 0.178888i | ||||
\(268\) | 9.32532 | 0.569634 | ||||||||
\(269\) | 0.458296 | + | 0.793792i | 0.0279428 | + | 0.0483984i | 0.879659 | − | 0.475606i | \(-0.157771\pi\) |
−0.851716 | + | 0.524004i | \(0.824438\pi\) | |||||||
\(270\) | −0.478203 | + | 0.828272i | −0.0291025 | + | 0.0504070i | ||||
\(271\) | 4.04304 | − | 7.00275i | 0.245597 | − | 0.425387i | −0.716702 | − | 0.697379i | \(-0.754349\pi\) |
0.962299 | + | 0.271993i | \(0.0876826\pi\) | |||||||
\(272\) | −19.9633 | −1.21045 | ||||||||
\(273\) | 5.10364 | − | 15.8561i | 0.308887 | − | 0.959656i | ||||
\(274\) | 25.9033 | 1.56487 | ||||||||
\(275\) | −2.35672 | + | 4.08196i | −0.142116 | + | 0.246152i | ||||
\(276\) | 3.09240 | − | 5.35620i | 0.186141 | − | 0.322405i | ||||
\(277\) | −4.67288 | − | 8.09367i | −0.280766 | − | 0.486301i | 0.690807 | − | 0.723039i | \(-0.257255\pi\) |
−0.971574 | + | 0.236737i | \(0.923922\pi\) | |||||||
\(278\) | 2.20012 | 0.131955 | ||||||||
\(279\) | 1.79447 | + | 3.10811i | 0.107432 | + | 0.186077i | ||||
\(280\) | 1.78485 | + | 3.09146i | 0.106665 | + | 0.184750i | ||||
\(281\) | 9.89315 | 0.590176 | 0.295088 | − | 0.955470i | \(-0.404651\pi\) | ||||
0.295088 | + | 0.955470i | \(0.404651\pi\) | |||||||
\(282\) | 8.32249 | + | 14.4150i | 0.495597 | + | 0.858400i | ||||
\(283\) | −1.83539 | + | 3.17899i | −0.109103 | + | 0.188971i | −0.915407 | − | 0.402530i | \(-0.868131\pi\) |
0.806304 | + | 0.591501i | \(0.201464\pi\) | |||||||
\(284\) | −6.18435 | + | 10.7116i | −0.366974 | + | 0.635617i | ||||
\(285\) | 4.01933 | 0.238085 | ||||||||
\(286\) | −6.29735 | + | 1.35671i | −0.372370 | + | 0.0802241i | ||||
\(287\) | 43.5155 | 2.56864 | ||||||||
\(288\) | −2.99021 | + | 5.17920i | −0.176200 | + | 0.305187i | ||||
\(289\) | 0.410406 | − | 0.710844i | 0.0241415 | − | 0.0418143i | ||||
\(290\) | 2.30715 | + | 3.99610i | 0.135481 | + | 0.234659i | ||||
\(291\) | 11.9135 | 0.698381 | ||||||||
\(292\) | −1.17365 | − | 2.03282i | −0.0686825 | − | 0.118962i | ||||
\(293\) | 7.06601 | + | 12.2387i | 0.412800 | + | 0.714991i | 0.995195 | − | 0.0979150i | \(-0.0312173\pi\) |
−0.582394 | + | 0.812906i | \(0.697884\pi\) | |||||||
\(294\) | −25.6265 | −1.49457 | ||||||||
\(295\) | 1.11232 | + | 1.92659i | 0.0647616 | + | 0.112170i | ||||
\(296\) | −2.88403 | + | 4.99529i | −0.167631 | + | 0.290345i | ||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | −10.5974 | −0.613891 | ||||||||
\(299\) | −12.5552 | − | 13.8668i | −0.726086 | − | 0.801939i | ||||
\(300\) | −5.61889 | −0.324407 | ||||||||
\(301\) | 18.0491 | − | 31.2620i | 1.04033 | − | 1.80191i | ||||
\(302\) | 17.6267 | − | 30.5303i | 1.01430 | − | 1.75682i | ||||
\(303\) | −5.61321 | − | 9.72236i | −0.322470 | − | 0.558535i | ||||
\(304\) | 37.2651 | 2.13730 | ||||||||
\(305\) | −2.61189 | − | 4.52393i | −0.149556 | − | 0.259039i | ||||
\(306\) | 3.59324 | + | 6.22368i | 0.205412 | + | 0.355784i | ||||
\(307\) | 3.45187 | 0.197009 | 0.0985044 | − | 0.995137i | \(-0.468594\pi\) | ||||
0.0985044 | + | 0.995137i | \(0.468594\pi\) | |||||||
\(308\) | 2.75368 | + | 4.76951i | 0.156905 | + | 0.271768i | ||||
\(309\) | −3.96495 | + | 6.86749i | −0.225558 | + | 0.390678i | ||||
\(310\) | 1.71624 | − | 2.97261i | 0.0974758 | − | 0.168833i | ||||
\(311\) | 29.0347 | 1.64640 | 0.823202 | − | 0.567748i | \(-0.192185\pi\) | ||||
0.823202 | + | 0.567748i | \(0.192185\pi\) | |||||||
\(312\) | 3.49306 | + | 3.85798i | 0.197756 | + | 0.218415i | ||||
\(313\) | 13.2960 | 0.751537 | 0.375768 | − | 0.926714i | \(-0.377379\pi\) | ||||
0.375768 | + | 0.926714i | \(0.377379\pi\) | |||||||
\(314\) | −19.2856 | + | 33.4036i | −1.08835 | + | 1.88508i | ||||
\(315\) | 1.23653 | − | 2.14174i | 0.0696707 | − | 0.120673i | ||||
\(316\) | −5.00593 | − | 8.67052i | −0.281605 | − | 0.487755i | ||||
\(317\) | −10.4283 | −0.585710 | −0.292855 | − | 0.956157i | \(-0.594605\pi\) | ||||
−0.292855 | + | 0.956157i | \(0.594605\pi\) | |||||||
\(318\) | 6.80350 | + | 11.7840i | 0.381521 | + | 0.660815i | ||||
\(319\) | −2.41231 | − | 4.17825i | −0.135064 | − | 0.233937i | ||||
\(320\) | 0.406136 | 0.0227037 | ||||||||
\(321\) | 6.35241 | + | 11.0027i | 0.354557 | + | 0.614111i | ||||
\(322\) | −21.4118 | + | 37.0863i | −1.19323 | + | 2.06674i | ||||
\(323\) | 15.1007 | − | 26.1552i | 0.840227 | − | 1.45532i | ||||
\(324\) | 1.19210 | 0.0662277 | ||||||||
\(325\) | −5.20700 | + | 16.1772i | −0.288832 | + | 0.897351i | ||||
\(326\) | 11.5913 | 0.641985 | ||||||||
\(327\) | 1.81496 | − | 3.14360i | 0.100367 | − | 0.173842i | ||||
\(328\) | −6.79797 | + | 11.7744i | −0.375355 | + | 0.650134i | ||||
\(329\) | −21.5202 | − | 37.2741i | −1.18645 | − | 2.05499i | ||||
\(330\) | −0.956406 | −0.0526484 | ||||||||
\(331\) | 7.31168 | + | 12.6642i | 0.401886 | + | 0.696088i | 0.993954 | − | 0.109801i | \(-0.0350213\pi\) |
−0.592067 | + | 0.805889i | \(0.701688\pi\) | |||||||
\(332\) | −4.39003 | − | 7.60376i | −0.240934 | − | 0.417311i | ||||
\(333\) | 3.99607 | 0.218983 | ||||||||
\(334\) | 22.2940 | + | 38.6144i | 1.21987 | + | 2.11289i | ||||
\(335\) | 2.09376 | − | 3.62649i | 0.114394 | − | 0.198136i | ||||
\(336\) | 11.4645 | − | 19.8571i | 0.625439 | − | 1.08329i | ||||
\(337\) | 4.53149 | 0.246846 | 0.123423 | − | 0.992354i | \(-0.460613\pi\) | ||||
0.123423 | + | 0.992354i | \(0.460613\pi\) | |||||||
\(338\) | −21.1659 | + | 9.56395i | −1.15127 | + | 0.520210i | ||||
\(339\) | 13.7552 | 0.747079 | ||||||||
\(340\) | 1.28341 | − | 2.22293i | 0.0696025 | − | 0.120555i | ||||
\(341\) | −1.79447 | + | 3.10811i | −0.0971758 | + | 0.168313i | ||||
\(342\) | −6.70745 | − | 11.6176i | −0.362698 | − | 0.628211i | ||||
\(343\) | 33.9255 | 1.83181 | ||||||||
\(344\) | 5.63926 | + | 9.76748i | 0.304048 | + | 0.526627i | ||||
\(345\) | −1.38863 | − | 2.40519i | −0.0747616 | − | 0.129491i | ||||
\(346\) | −4.63087 | −0.248957 | ||||||||
\(347\) | −13.0510 | − | 22.6049i | −0.700612 | − | 1.21350i | −0.968252 | − | 0.249977i | \(-0.919577\pi\) |
0.267639 | − | 0.963519i | \(-0.413756\pi\) | |||||||
\(348\) | 2.87571 | − | 4.98088i | 0.154154 | − | 0.267003i | ||||
\(349\) | 2.45211 | − | 4.24718i | 0.131258 | − | 0.227346i | −0.792904 | − | 0.609347i | \(-0.791432\pi\) |
0.924162 | + | 0.382001i | \(0.124765\pi\) | |||||||
\(350\) | 38.9052 | 2.07957 | ||||||||
\(351\) | 1.10471 | − | 3.43214i | 0.0589652 | − | 0.183194i | ||||
\(352\) | −5.98042 | −0.318758 | ||||||||
\(353\) | −12.7908 | + | 22.1543i | −0.680784 | + | 1.17915i | 0.293958 | + | 0.955818i | \(0.405027\pi\) |
−0.974742 | + | 0.223334i | \(0.928306\pi\) | |||||||
\(354\) | 3.71247 | − | 6.43018i | 0.197315 | − | 0.341760i | ||||
\(355\) | 2.77707 | + | 4.81002i | 0.147391 | + | 0.255289i | ||||
\(356\) | 4.02362 | 0.213252 | ||||||||
\(357\) | −9.29137 | − | 16.0931i | −0.491751 | − | 0.851739i | ||||
\(358\) | −11.5607 | − | 20.0237i | −0.611002 | − | 1.05829i | ||||
\(359\) | −18.9318 | −0.999180 | −0.499590 | − | 0.866262i | \(-0.666516\pi\) | ||||
−0.499590 | + | 0.866262i | \(0.666516\pi\) | |||||||
\(360\) | 0.386341 | + | 0.669163i | 0.0203620 | + | 0.0352680i | ||||
\(361\) | −18.6883 | + | 32.3691i | −0.983595 | + | 1.70364i | ||||
\(362\) | 9.53204 | − | 16.5100i | 0.500993 | − | 0.867745i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 13.3276 | + | 14.7200i | 0.698558 | + | 0.771536i | ||||
\(365\) | −1.05405 | −0.0551713 | ||||||||
\(366\) | −8.71744 | + | 15.0990i | −0.455668 | + | 0.789240i | ||||
\(367\) | 18.3510 | − | 31.7848i | 0.957914 | − | 1.65916i | 0.230359 | − | 0.973106i | \(-0.426010\pi\) |
0.727555 | − | 0.686049i | \(-0.240657\pi\) | |||||||
\(368\) | −12.8747 | − | 22.2996i | −0.671140 | − | 1.16245i | ||||
\(369\) | 9.41917 | 0.490342 | ||||||||
\(370\) | −1.91093 | − | 3.30983i | −0.0993446 | − | 0.172070i | ||||
\(371\) | −17.5924 | − | 30.4710i | −0.913353 | − | 1.58197i | ||||
\(372\) | −4.27836 | −0.221823 | ||||||||
\(373\) | −0.346728 | − | 0.600550i | −0.0179529 | − | 0.0310953i | 0.856909 | − | 0.515467i | \(-0.172382\pi\) |
−0.874862 | + | 0.484372i | \(0.839048\pi\) | |||||||
\(374\) | −3.59324 | + | 6.22368i | −0.185802 | + | 0.321819i | ||||
\(375\) | −2.59985 | + | 4.50306i | −0.134255 | + | 0.232537i | ||||
\(376\) | 13.4475 | 0.693503 | ||||||||
\(377\) | −11.6754 | − | 12.8952i | −0.601316 | − | 0.664135i | ||||
\(378\) | −8.25410 | −0.424545 | ||||||||
\(379\) | −2.27022 | + | 3.93214i | −0.116613 | + | 0.201980i | −0.918424 | − | 0.395598i | \(-0.870537\pi\) |
0.801810 | + | 0.597579i | \(0.203871\pi\) | |||||||
\(380\) | −2.39572 | + | 4.14951i | −0.122898 | + | 0.212865i | ||||
\(381\) | 0.0993951 | + | 0.172157i | 0.00509217 | + | 0.00881989i | ||||
\(382\) | −12.4081 | −0.634855 | ||||||||
\(383\) | 10.0957 | + | 17.4863i | 0.515868 | + | 0.893509i | 0.999830 | + | 0.0184206i | \(0.00586378\pi\) |
−0.483962 | + | 0.875089i | \(0.660803\pi\) | |||||||
\(384\) | 5.30267 | + | 9.18449i | 0.270601 | + | 0.468694i | ||||
\(385\) | 2.47307 | 0.126039 | ||||||||
\(386\) | 3.59571 | + | 6.22795i | 0.183017 | + | 0.316994i | ||||
\(387\) | 3.90683 | − | 6.76683i | 0.198596 | − | 0.343978i | ||||
\(388\) | −7.10103 | + | 12.2993i | −0.360500 | + | 0.624404i | ||||
\(389\) | −20.8841 | −1.05887 | −0.529434 | − | 0.848351i | \(-0.677596\pi\) | ||||
−0.529434 | + | 0.848351i | \(0.677596\pi\) | |||||||
\(390\) | −3.37103 | + | 0.726260i | −0.170698 | + | 0.0367756i | ||||
\(391\) | −20.8685 | −1.05537 | ||||||||
\(392\) | −10.3518 | + | 17.9299i | −0.522847 | + | 0.905598i | ||||
\(393\) | −10.8992 | + | 18.8781i | −0.549794 | + | 0.952272i | ||||
\(394\) | −6.43054 | − | 11.1380i | −0.323966 | − | 0.561126i | ||||
\(395\) | −4.49580 | −0.226208 | ||||||||
\(396\) | 0.596049 | + | 1.03239i | 0.0299526 | + | 0.0518794i | ||||
\(397\) | 6.70535 | + | 11.6140i | 0.336532 | + | 0.582890i | 0.983778 | − | 0.179391i | \(-0.0574127\pi\) |
−0.647246 | + | 0.762281i | \(0.724079\pi\) | |||||||
\(398\) | 13.9536 | 0.699433 | ||||||||
\(399\) | 17.3441 | + | 30.0408i | 0.868289 | + | 1.50392i | ||||
\(400\) | −11.6966 | + | 20.2592i | −0.584832 | + | 1.01296i | ||||
\(401\) | 8.03094 | − | 13.9100i | 0.401046 | − | 0.694632i | −0.592806 | − | 0.805345i | \(-0.701980\pi\) |
0.993852 | + | 0.110713i | \(0.0353134\pi\) | |||||||
\(402\) | −13.9762 | −0.697071 | ||||||||
\(403\) | −3.96474 | + | 12.3177i | −0.197498 | + | 0.613590i | ||||
\(404\) | 13.3830 | 0.665829 | ||||||||
\(405\) | 0.267654 | − | 0.463591i | 0.0132998 | − | 0.0230360i | ||||
\(406\) | −19.9115 | + | 34.4877i | −0.988189 | + | 1.71159i | ||||
\(407\) | 1.99803 | + | 3.46070i | 0.0990389 | + | 0.171540i | ||||
\(408\) | 5.80598 | 0.287439 | ||||||||
\(409\) | 10.3126 | + | 17.8619i | 0.509924 | + | 0.883214i | 0.999934 | + | 0.0114971i | \(0.00365971\pi\) |
−0.490010 | + | 0.871717i | \(0.663007\pi\) | |||||||
\(410\) | −4.50428 | − | 7.80164i | −0.222450 | − | 0.385295i | ||||
\(411\) | −14.4983 | −0.715148 | ||||||||
\(412\) | −4.72660 | − | 8.18672i | −0.232863 | − | 0.403331i | ||||
\(413\) | −9.59966 | + | 16.6271i | −0.472369 | + | 0.818166i | ||||
\(414\) | −4.63470 | + | 8.02754i | −0.227783 | + | 0.394532i | ||||
\(415\) | −3.94267 | −0.193538 | ||||||||
\(416\) | −21.0791 | + | 4.54132i | −1.03349 | + | 0.222656i | ||||
\(417\) | −1.23143 | −0.0603033 | ||||||||
\(418\) | 6.70745 | − | 11.6176i | 0.328072 | − | 0.568238i | ||||
\(419\) | −2.47998 | + | 4.29544i | −0.121155 | + | 0.209846i | −0.920223 | − | 0.391394i | \(-0.871993\pi\) |
0.799069 | + | 0.601240i | \(0.205326\pi\) | |||||||
\(420\) | 1.47407 | + | 2.55316i | 0.0719272 | + | 0.124582i | ||||
\(421\) | −4.21892 | −0.205617 | −0.102809 | − | 0.994701i | \(-0.532783\pi\) | ||||
−0.102809 | + | 0.994701i | \(0.532783\pi\) | |||||||
\(422\) | 24.1034 | + | 41.7483i | 1.17333 | + | 2.03228i | ||||
\(423\) | −4.65817 | − | 8.06819i | −0.226488 | − | 0.392289i | ||||
\(424\) | 10.9931 | 0.533873 | ||||||||
\(425\) | 9.47953 | + | 16.4190i | 0.459825 | + | 0.796440i | ||||
\(426\) | 9.26873 | − | 16.0539i | 0.449072 | − | 0.777815i | ||||
\(427\) | 22.5415 | − | 39.0430i | 1.09086 | − | 1.88942i | ||||
\(428\) | −15.1454 | −0.732080 | ||||||||
\(429\) | 3.52468 | − | 0.759363i | 0.170173 | − | 0.0366624i | ||||
\(430\) | −7.47304 | −0.360382 | ||||||||
\(431\) | 1.88481 | − | 3.26459i | 0.0907882 | − | 0.157250i | −0.817055 | − | 0.576560i | \(-0.804395\pi\) |
0.907843 | + | 0.419310i | \(0.137728\pi\) | |||||||
\(432\) | 2.48155 | − | 4.29817i | 0.119394 | − | 0.206796i | ||||
\(433\) | 8.32647 | + | 14.4219i | 0.400145 | + | 0.693071i | 0.993743 | − | 0.111690i | \(-0.0356265\pi\) |
−0.593598 | + | 0.804761i | \(0.702293\pi\) | |||||||
\(434\) | 29.6234 | 1.42197 | ||||||||
\(435\) | −1.29133 | − | 2.23665i | −0.0619146 | − | 0.107239i | ||||
\(436\) | 2.16361 | + | 3.74748i | 0.103618 | + | 0.179472i | ||||
\(437\) | 38.9550 | 1.86347 | ||||||||
\(438\) | 1.75899 | + | 3.04666i | 0.0840479 | + | 0.145575i | ||||
\(439\) | −14.8257 | + | 25.6789i | −0.707592 | + | 1.22559i | 0.258156 | + | 0.966103i | \(0.416885\pi\) |
−0.965748 | + | 0.259482i | \(0.916448\pi\) | |||||||
\(440\) | −0.386341 | + | 0.669163i | −0.0184181 | + | 0.0319011i | ||||
\(441\) | 14.3434 | 0.683017 | ||||||||
\(442\) | −7.93899 | + | 24.6650i | −0.377619 | + | 1.17320i | ||||
\(443\) | 10.3758 | 0.492971 | 0.246486 | − | 0.969146i | \(-0.420724\pi\) | ||||
0.246486 | + | 0.969146i | \(0.420724\pi\) | |||||||
\(444\) | −2.38185 | + | 4.12549i | −0.113038 | + | 0.195787i | ||||
\(445\) | 0.903399 | − | 1.56473i | 0.0428252 | − | 0.0741754i | ||||
\(446\) | 20.5714 | + | 35.6306i | 0.974082 | + | 1.68716i | ||||
\(447\) | 5.93145 | 0.280548 | ||||||||
\(448\) | 1.75254 | + | 3.03549i | 0.0827998 | + | 0.143413i | ||||
\(449\) | 3.55561 | + | 6.15849i | 0.167800 | + | 0.290637i | 0.937646 | − | 0.347592i | \(-0.113001\pi\) |
−0.769846 | + | 0.638229i | \(0.779667\pi\) | |||||||
\(450\) | 8.42125 | 0.396981 | ||||||||
\(451\) | 4.70959 | + | 8.15724i | 0.221766 | + | 0.384109i | ||||
\(452\) | −8.19876 | + | 14.2007i | −0.385637 | + | 0.667943i | ||||
\(453\) | −9.86579 | + | 17.0880i | −0.463535 | + | 0.802867i | ||||
\(454\) | 5.60577 | 0.263092 | ||||||||
\(455\) | 8.71676 | − | 1.87796i | 0.408648 | − | 0.0880399i | ||||
\(456\) | −10.8379 | −0.507533 | ||||||||
\(457\) | 10.2724 | − | 17.7924i | 0.480525 | − | 0.832293i | −0.519226 | − | 0.854637i | \(-0.673780\pi\) |
0.999750 | + | 0.0223441i | \(0.00711293\pi\) | |||||||
\(458\) | −8.79329 | + | 15.2304i | −0.410884 | + | 0.711671i | ||||
\(459\) | −2.01117 | − | 3.48345i | −0.0938733 | − | 0.162593i | ||||
\(460\) | 3.31078 | 0.154366 | ||||||||
\(461\) | −0.938105 | − | 1.62485i | −0.0436919 | − | 0.0756766i | 0.843352 | − | 0.537361i | \(-0.180579\pi\) |
−0.887044 | + | 0.461684i | \(0.847245\pi\) | |||||||
\(462\) | −4.12705 | − | 7.14826i | −0.192008 | − | 0.332567i | ||||
\(463\) | −4.84844 | −0.225326 | −0.112663 | − | 0.993633i | \(-0.535938\pi\) | ||||
−0.112663 | + | 0.993633i | \(0.535938\pi\) | |||||||
\(464\) | −11.9725 | − | 20.7371i | −0.555811 | − | 0.962693i | ||||
\(465\) | −0.960593 | + | 1.66380i | −0.0445464 | + | 0.0771567i | ||||
\(466\) | −0.895871 | + | 1.55169i | −0.0415004 | + | 0.0718809i | ||||
\(467\) | −7.31136 | −0.338330 | −0.169165 | − | 0.985588i | \(-0.554107\pi\) | ||||
−0.169165 | + | 0.985588i | \(0.554107\pi\) | |||||||
\(468\) | 2.88484 | + | 3.18622i | 0.133352 | + | 0.147283i | ||||
\(469\) | 36.1396 | 1.66877 | ||||||||
\(470\) | −4.45510 | + | 7.71646i | −0.205499 | + | 0.355934i | ||||
\(471\) | 10.7943 | − | 18.6963i | 0.497376 | − | 0.861480i | ||||
\(472\) | −2.99931 | − | 5.19496i | −0.138054 | − | 0.239117i | ||||
\(473\) | 7.81367 | 0.359273 | ||||||||
\(474\) | 7.50258 | + | 12.9949i | 0.344605 | + | 0.596873i | ||||
\(475\) | −17.6953 | − | 30.6492i | −0.811916 | − | 1.40628i | ||||
\(476\) | 22.1524 | 1.01536 | ||||||||
\(477\) | −3.80798 | − | 6.59561i | −0.174355 | − | 0.301992i | ||||
\(478\) | −4.08491 | + | 7.07528i | −0.186840 | + | 0.323616i | ||||
\(479\) | −2.70089 | + | 4.67808i | −0.123407 | + | 0.213747i | −0.921109 | − | 0.389305i | \(-0.872715\pi\) |
0.797702 | + | 0.603052i | \(0.206049\pi\) | |||||||
\(480\) | −3.20137 | −0.146122 | ||||||||
\(481\) | 9.67036 | + | 10.6806i | 0.440930 | + | 0.486994i | ||||
\(482\) | −44.2788 | −2.01684 | ||||||||
\(483\) | 11.9844 | − | 20.7575i | 0.545308 | − | 0.944501i | ||||
\(484\) | −0.596049 | + | 1.03239i | −0.0270931 | + | 0.0469267i | ||||
\(485\) | 3.18870 | + | 5.52299i | 0.144791 | + | 0.250786i | ||||
\(486\) | −1.78664 | −0.0810438 | ||||||||
\(487\) | −4.80532 | − | 8.32306i | −0.217750 | − | 0.377154i | 0.736370 | − | 0.676579i | \(-0.236538\pi\) |
−0.954120 | + | 0.299425i | \(0.903205\pi\) | |||||||
\(488\) | 7.04284 | + | 12.1986i | 0.318814 | + | 0.552202i | ||||
\(489\) | −6.48777 | −0.293387 | ||||||||
\(490\) | −6.85904 | − | 11.8802i | −0.309860 | − | 0.536693i | ||||
\(491\) | 4.75881 | − | 8.24250i | 0.214762 | − | 0.371979i | −0.738437 | − | 0.674323i | \(-0.764436\pi\) |
0.953199 | + | 0.302344i | \(0.0977691\pi\) | |||||||
\(492\) | −5.61429 | + | 9.72423i | −0.253112 | + | 0.438402i | ||||
\(493\) | −19.4063 | −0.874014 | ||||||||
\(494\) | 14.8196 | − | 46.0419i | 0.666766 | − | 2.07152i | ||||
\(495\) | 0.535309 | 0.0240603 | ||||||||
\(496\) | −8.90611 | + | 15.4258i | −0.399896 | + | 0.692641i | ||||
\(497\) | −23.9670 | + | 41.5121i | −1.07507 | + | 1.86207i | ||||
\(498\) | 6.57952 | + | 11.3961i | 0.294835 | + | 0.510670i | ||||
\(499\) | −25.6619 | −1.14879 | −0.574393 | − | 0.818580i | \(-0.694762\pi\) | ||||
−0.574393 | + | 0.818580i | \(0.694762\pi\) | |||||||
\(500\) | −3.09927 | − | 5.36809i | −0.138604 | − | 0.240068i | ||||
\(501\) | −12.4782 | − | 21.6128i | −0.557483 | − | 0.965589i | ||||
\(502\) | −0.912323 | −0.0407190 | ||||||||
\(503\) | 10.0579 | + | 17.4208i | 0.448460 | + | 0.776756i | 0.998286 | − | 0.0585234i | \(-0.0186392\pi\) |
−0.549826 | + | 0.835279i | \(0.685306\pi\) | |||||||
\(504\) | −3.33425 | + | 5.77509i | −0.148519 | + | 0.257243i | ||||
\(505\) | 3.00480 | − | 5.20446i | 0.133712 | − | 0.231596i | ||||
\(506\) | −9.26941 | −0.412075 | ||||||||
\(507\) | 11.8467 | − | 5.35303i | 0.526132 | − | 0.237736i | ||||
\(508\) | −0.236977 | −0.0105142 | ||||||||
\(509\) | −9.89193 | + | 17.1333i | −0.438452 | + | 0.759421i | −0.997570 | − | 0.0696668i | \(-0.977806\pi\) |
0.559118 | + | 0.829088i | \(0.311140\pi\) | |||||||
\(510\) | −1.92349 | + | 3.33159i | −0.0851737 | + | 0.147525i | ||||
\(511\) | −4.54838 | − | 7.87803i | −0.201209 | − | 0.348504i | ||||
\(512\) | −15.3536 | −0.678541 | ||||||||
\(513\) | 3.75422 | + | 6.50250i | 0.165753 | + | 0.287092i | ||||
\(514\) | −7.19671 | − | 12.4651i | −0.317433 | − | 0.549810i | ||||
\(515\) | −4.24494 | −0.187054 | ||||||||
\(516\) | 4.65733 | + | 8.06673i | 0.205027 | + | 0.355118i | ||||
\(517\) | 4.65817 | − | 8.06819i | 0.204866 | − | 0.354838i | ||||
\(518\) | 16.4920 | − | 28.5649i | 0.724615 | − | 1.25507i | ||||
\(519\) | 2.59194 | 0.113773 | ||||||||
\(520\) | −0.853592 | + | 2.65196i | −0.0374325 | + | 0.116296i | ||||
\(521\) | −7.29955 | −0.319799 | −0.159900 | − | 0.987133i | \(-0.551117\pi\) | ||||
−0.159900 | + | 0.987133i | \(0.551117\pi\) | |||||||
\(522\) | −4.30994 | + | 7.46504i | −0.188641 | + | 0.326736i | ||||
\(523\) | 15.3646 | − | 26.6122i | 0.671846 | − | 1.16367i | −0.305534 | − | 0.952181i | \(-0.598835\pi\) |
0.977380 | − | 0.211491i | \(-0.0678318\pi\) | |||||||
\(524\) | −12.9930 | − | 22.5045i | −0.567601 | − | 0.983113i | ||||
\(525\) | −21.7756 | −0.950364 | ||||||||
\(526\) | 0.371910 | + | 0.644167i | 0.0162161 | + | 0.0280870i | ||||
\(527\) | 7.21795 | + | 12.5019i | 0.314419 | + | 0.544589i | ||||
\(528\) | 4.96310 | 0.215991 | ||||||||
\(529\) | −1.95853 | − | 3.39228i | −0.0851536 | − | 0.147490i | ||||
\(530\) | −3.64197 | + | 6.30808i | −0.158197 | + | 0.274006i | ||||
\(531\) | −2.07790 | + | 3.59903i | −0.0901732 | + | 0.156185i | ||||
\(532\) | −41.3517 | −1.79282 | ||||||||
\(533\) | 22.7941 | + | 25.1754i | 0.987322 | + | 1.09047i | ||||
\(534\) | −6.03036 | −0.260959 | ||||||||
\(535\) | −3.40050 | + | 5.88984i | −0.147016 | + | 0.254640i | ||||
\(536\) | −5.64571 | + | 9.77865i | −0.243857 | + | 0.422374i | ||||
\(537\) | 6.47062 | + | 11.2074i | 0.279228 | + | 0.483637i | ||||
\(538\) | 1.63762 | 0.0706030 | ||||||||
\(539\) | 7.17168 | + | 12.4217i | 0.308906 | + | 0.535041i | ||||
\(540\) | 0.319070 | + | 0.552646i | 0.0137306 | + | 0.0237821i | ||||
\(541\) | −1.87138 | −0.0804568 | −0.0402284 | − | 0.999191i | \(-0.512809\pi\) | ||||
−0.0402284 | + | 0.999191i | \(0.512809\pi\) | |||||||
\(542\) | −7.22347 | − | 12.5114i | −0.310275 | − | 0.537412i | ||||
\(543\) | −5.33516 | + | 9.24077i | −0.228954 | + | 0.396560i | ||||
\(544\) | −12.0276 | + | 20.8325i | −0.515681 | + | 0.893185i | ||||
\(545\) | 1.94313 | 0.0832344 | ||||||||
\(546\) | −19.9746 | − | 22.0614i | −0.854836 | − | 0.944140i | ||||
\(547\) | 24.7950 | 1.06016 | 0.530078 | − | 0.847949i | \(-0.322163\pi\) | ||||
0.530078 | + | 0.847949i | \(0.322163\pi\) | |||||||
\(548\) | 8.64169 | − | 14.9678i | 0.369155 | − | 0.639395i | ||||
\(549\) | 4.87922 | − | 8.45107i | 0.208240 | − | 0.360683i | ||||
\(550\) | 4.21062 | + | 7.29302i | 0.179542 | + | 0.310975i | ||||
\(551\) | 36.2254 | 1.54325 | ||||||||
\(552\) | 3.74439 | + | 6.48547i | 0.159372 | + | 0.276040i | ||||
\(553\) | −19.4001 | − | 33.6020i | −0.824976 | − | 1.42890i | ||||
\(554\) | −16.6976 | −0.709411 | ||||||||
\(555\) | 1.06956 | + | 1.85254i | 0.0454005 | + | 0.0786360i | ||||
\(556\) | 0.733991 | − | 1.27131i | 0.0311282 | − | 0.0539155i | ||||
\(557\) | 2.94986 | − | 5.10930i | 0.124989 | − | 0.216488i | −0.796739 | − | 0.604323i | \(-0.793444\pi\) |
0.921729 | + | 0.387835i | \(0.126777\pi\) | |||||||
\(558\) | 6.41215 | 0.271448 | ||||||||
\(559\) | 27.5407 | − | 5.93341i | 1.16485 | − | 0.250957i | ||||
\(560\) | 12.2741 | 0.518674 | ||||||||
\(561\) | 2.01117 | − | 3.48345i | 0.0849116 | − | 0.147071i | ||||
\(562\) | 8.83777 | − | 15.3075i | 0.372799 | − | 0.645706i | ||||
\(563\) | 11.2847 | + | 19.5457i | 0.475595 | + | 0.823754i | 0.999609 | − | 0.0279551i | \(-0.00889955\pi\) |
−0.524014 | + | 0.851709i | \(0.675566\pi\) | |||||||
\(564\) | 11.1060 | 0.467646 | ||||||||
\(565\) | 3.68163 | + | 6.37677i | 0.154887 | + | 0.268273i | ||||
\(566\) | 3.27919 | + | 5.67972i | 0.137835 | + | 0.238736i | ||||
\(567\) | 4.61989 | 0.194017 | ||||||||
\(568\) | −7.48823 | − | 12.9700i | −0.314199 | − | 0.544209i | ||||
\(569\) | 7.96900 | − | 13.8027i | 0.334078 | − | 0.578640i | −0.649229 | − | 0.760593i | \(-0.724908\pi\) |
0.983307 | + | 0.181953i | \(0.0582418\pi\) | |||||||
\(570\) | 3.59056 | − | 6.21903i | 0.150392 | − | 0.260486i | ||||
\(571\) | −40.2086 | −1.68268 | −0.841339 | − | 0.540508i | \(-0.818232\pi\) | ||||
−0.841339 | + | 0.540508i | \(0.818232\pi\) | |||||||
\(572\) | −1.31692 | + | 4.09145i | −0.0550634 | + | 0.171072i | ||||
\(573\) | 6.94493 | 0.290129 | ||||||||
\(574\) | 38.8734 | − | 67.3307i | 1.62254 | − | 2.81033i | ||||
\(575\) | −12.2271 | + | 21.1779i | −0.509904 | + | 0.883180i | ||||
\(576\) | 0.379347 | + | 0.657049i | 0.0158061 | + | 0.0273770i | ||||
\(577\) | −32.5372 | −1.35454 | −0.677271 | − | 0.735734i | \(-0.736838\pi\) | ||||
−0.677271 | + | 0.735734i | \(0.736838\pi\) | |||||||
\(578\) | −0.733249 | − | 1.27003i | −0.0304992 | − | 0.0528261i | ||||
\(579\) | −2.01255 | − | 3.48584i | −0.0836387 | − | 0.144866i | ||||
\(580\) | 3.07879 | 0.127840 | ||||||||
\(581\) | −17.0133 | − | 29.4678i | −0.705829 | − | 1.22253i | ||||
\(582\) | 10.6426 | − | 18.4335i | 0.441149 | − | 0.764093i | ||||
\(583\) | 3.80798 | − | 6.59561i | 0.157710 | − | 0.273162i | ||||
\(584\) | 2.84219 | 0.117610 | ||||||||
\(585\) | 1.88679 | − | 0.406494i | 0.0780092 | − | 0.0168064i | ||||
\(586\) | 25.2489 | 1.04302 | ||||||||
\(587\) | −11.7315 | + | 20.3195i | −0.484209 | + | 0.838675i | −0.999835 | − | 0.0181386i | \(-0.994226\pi\) |
0.515626 | + | 0.856814i | \(0.327559\pi\) | |||||||
\(588\) | −8.54935 | + | 14.8079i | −0.352569 | + | 0.610668i | ||||
\(589\) | −13.4736 | − | 23.3370i | −0.555172 | − | 0.961585i | ||||
\(590\) | 3.97463 | 0.163633 | ||||||||
\(591\) | 3.59923 | + | 6.23405i | 0.148052 | + | 0.256434i | ||||
\(592\) | 9.91644 | + | 17.1758i | 0.407563 | + | 0.705920i | ||||
\(593\) | −28.1332 | −1.15529 | −0.577646 | − | 0.816288i | \(-0.696028\pi\) | ||||
−0.577646 | + | 0.816288i | \(0.696028\pi\) | |||||||
\(594\) | −0.893322 | − | 1.54728i | −0.0366535 | − | 0.0634856i | ||||
\(595\) | 4.97375 | − | 8.61479i | 0.203904 | − | 0.353172i | ||||
\(596\) | −3.53544 | + | 6.12355i | −0.144817 | + | 0.250831i | ||||
\(597\) | −7.80997 | −0.319641 | ||||||||
\(598\) | −32.6717 | + | 7.03885i | −1.33604 | + | 0.287840i | ||||
\(599\) | −24.4419 | −0.998668 | −0.499334 | − | 0.866410i | \(-0.666422\pi\) | ||||
−0.499334 | + | 0.866410i | \(0.666422\pi\) | |||||||
\(600\) | 3.40177 | − | 5.89204i | 0.138877 | − | 0.240542i | ||||
\(601\) | −11.8039 | + | 20.4450i | −0.481492 | + | 0.833969i | −0.999774 | − | 0.0212408i | \(-0.993238\pi\) |
0.518282 | + | 0.855210i | \(0.326572\pi\) | |||||||
\(602\) | −32.2474 | − | 55.8541i | −1.31431 | − | 2.27644i | ||||
\(603\) | 7.82261 | 0.318561 | ||||||||
\(604\) | −11.7610 | − | 20.3706i | −0.478548 | − | 0.828869i | ||||
\(605\) | 0.267654 | + | 0.463591i | 0.0108817 | + | 0.0188476i | ||||
\(606\) | −20.0576 | −0.814785 | ||||||||
\(607\) | −15.9891 | − | 27.6940i | −0.648978 | − | 1.12406i | −0.983367 | − | 0.181628i | \(-0.941863\pi\) |
0.334389 | − | 0.942435i | \(-0.391470\pi\) | |||||||
\(608\) | 22.4518 | − | 38.8877i | 0.910542 | − | 1.57710i | ||||
\(609\) | 11.1446 | − | 19.3030i | 0.451602 | − | 0.782198i | ||||
\(610\) | −9.33304 | −0.377884 | ||||||||
\(611\) | 10.2919 | − | 31.9750i | 0.416365 | − | 1.29357i | ||||
\(612\) | 4.79502 | 0.193827 | ||||||||
\(613\) | 6.74245 | − | 11.6783i | 0.272325 | − | 0.471680i | −0.697132 | − | 0.716943i | \(-0.745541\pi\) |
0.969457 | + | 0.245262i | \(0.0788741\pi\) | |||||||
\(614\) | 3.08363 | − | 5.34101i | 0.124445 | − | 0.215546i | ||||
\(615\) | 2.52108 | + | 4.36664i | 0.101660 | + | 0.176080i | ||||
\(616\) | −6.66850 | −0.268682 | ||||||||
\(617\) | 10.6931 | + | 18.5209i | 0.430487 | + | 0.745625i | 0.996915 | − | 0.0784862i | \(-0.0250087\pi\) |
−0.566429 | + | 0.824111i | \(0.691675\pi\) | |||||||
\(618\) | 7.08395 | + | 12.2698i | 0.284958 | + | 0.493562i | ||||
\(619\) | 1.22293 | 0.0491539 | 0.0245769 | − | 0.999698i | \(-0.492176\pi\) | ||||
0.0245769 | + | 0.999698i | \(0.492176\pi\) | |||||||
\(620\) | −1.14512 | − | 1.98341i | −0.0459892 | − | 0.0796556i | ||||
\(621\) | 2.59408 | − | 4.49308i | 0.104097 | − | 0.180301i | ||||
\(622\) | 25.9373 | − | 44.9247i | 1.03999 | − | 1.80132i | ||||
\(623\) | 15.5932 | 0.624730 | ||||||||
\(624\) | 17.4933 | − | 3.76880i | 0.700294 | − | 0.150873i | ||||
\(625\) | 20.7838 | 0.831351 | ||||||||
\(626\) | 11.8777 | − | 20.5727i | 0.474726 | − | 0.822250i | ||||
\(627\) | −3.75422 | + | 6.50250i | −0.149929 | + | 0.259685i | ||||
\(628\) | 12.8679 | + | 22.2878i | 0.513484 | + | 0.889381i | ||||
\(629\) | 16.0735 | 0.640894 | ||||||||
\(630\) | −2.20924 | − | 3.82652i | −0.0880184 | − | 0.152452i | ||||
\(631\) | −9.16247 | − | 15.8699i | −0.364752 | − | 0.631770i | 0.623984 | − | 0.781437i | \(-0.285513\pi\) |
−0.988736 | + | 0.149667i | \(0.952180\pi\) | |||||||
\(632\) | 12.1227 | 0.482215 | ||||||||
\(633\) | −13.4909 | − | 23.3669i | −0.536214 | − | 0.928750i | ||||
\(634\) | −9.31580 | + | 16.1354i | −0.369978 | + | 0.640820i | ||||
\(635\) | −0.0532071 | + | 0.0921573i | −0.00211146 | + | 0.00365715i | ||||
\(636\) | 9.07897 | 0.360004 | ||||||||
\(637\) | 34.7105 | + | 38.3367i | 1.37528 | + | 1.51895i | ||||
\(638\) | −8.61989 | −0.341265 | ||||||||
\(639\) | −5.18779 | + | 8.98551i | −0.205226 | + | 0.355461i | ||||
\(640\) | −2.83856 | + | 4.91653i | −0.112204 | + | 0.194343i | ||||
\(641\) | 5.78650 | + | 10.0225i | 0.228553 | + | 0.395866i | 0.957380 | − | 0.288833i | \(-0.0932672\pi\) |
−0.728826 | + | 0.684699i | \(0.759934\pi\) | |||||||
\(642\) | 22.6990 | 0.895858 | ||||||||
\(643\) | 4.71459 | + | 8.16590i | 0.185925 | + | 0.322032i | 0.943888 | − | 0.330266i | \(-0.107138\pi\) |
−0.757963 | + | 0.652298i | \(0.773805\pi\) | |||||||
\(644\) | 14.2865 | + | 24.7450i | 0.562969 | + | 0.975090i | ||||
\(645\) | 4.18272 | 0.164695 | ||||||||
\(646\) | −26.9796 | − | 46.7301i | −1.06150 | − | 1.83857i | ||||
\(647\) | 5.17601 | − | 8.96512i | 0.203490 | − | 0.352455i | −0.746161 | − | 0.665766i | \(-0.768105\pi\) |
0.949651 | + | 0.313311i | \(0.101438\pi\) | |||||||
\(648\) | −0.721717 | + | 1.25005i | −0.0283517 | + | 0.0491066i | ||||
\(649\) | −4.15580 | −0.163129 | ||||||||
\(650\) | 20.3792 | + | 22.5082i | 0.799336 | + | 0.882842i | ||||
\(651\) | −16.5805 | −0.649840 | ||||||||
\(652\) | 3.86703 | − | 6.69789i | 0.151445 | − | 0.262310i | ||||
\(653\) | 1.03022 | − | 1.78439i | 0.0403155 | − | 0.0698286i | −0.845164 | − | 0.534508i | \(-0.820497\pi\) |
0.885479 | + | 0.464679i | \(0.153830\pi\) | |||||||
\(654\) | −3.24269 | − | 5.61650i | −0.126799 | − | 0.219622i | ||||
\(655\) | −11.6689 | −0.455943 | ||||||||
\(656\) | 23.3741 | + | 40.4852i | 0.912607 | + | 1.58068i | ||||
\(657\) | −0.984522 | − | 1.70524i | −0.0384099 | − | 0.0665279i | ||||
\(658\) | −76.8980 | −2.99779 | ||||||||
\(659\) | 9.78831 | + | 16.9539i | 0.381299 | + | 0.660428i | 0.991248 | − | 0.132012i | \(-0.0421437\pi\) |
−0.609950 | + | 0.792440i | \(0.708810\pi\) | |||||||
\(660\) | −0.319070 | + | 0.552646i | −0.0124198 | + | 0.0215117i | ||||
\(661\) | −13.8637 | + | 24.0126i | −0.539236 | + | 0.933983i | 0.459710 | + | 0.888069i | \(0.347953\pi\) |
−0.998945 | + | 0.0459141i | \(0.985380\pi\) | |||||||
\(662\) | 26.1268 | 1.01545 | ||||||||
\(663\) | 4.44352 | − | 13.8052i | 0.172572 | − | 0.536151i | ||||
\(664\) | 10.6312 | 0.412571 | ||||||||
\(665\) | −9.28443 | + | 16.0811i | −0.360035 | + | 0.623598i | ||||
\(666\) | 3.56978 | − | 6.18303i | 0.138326 | − | 0.239588i | ||||
\(667\) | −12.5155 | − | 21.6774i | −0.484601 | − | 0.839354i | ||||
\(668\) | 29.7504 | 1.15108 | ||||||||
\(669\) | −11.5140 | − | 19.9428i | −0.445155 | − | 0.771032i | ||||
\(670\) | −3.74080 | − | 6.47925i | −0.144520 | − | 0.250315i | ||||
\(671\) | 9.75845 | 0.376721 | ||||||||
\(672\) | −13.8144 | − | 23.9273i | −0.532904 | − | 0.923016i | ||||
\(673\) | −17.6580 | + | 30.5846i | −0.680667 | + | 1.17895i | 0.294110 | + | 0.955771i | \(0.404977\pi\) |
−0.974778 | + | 0.223179i | \(0.928357\pi\) | |||||||
\(674\) | 4.04808 | − | 7.01149i | 0.155926 | − | 0.270072i | ||||
\(675\) | −4.71344 | −0.181421 | ||||||||
\(676\) | −1.53484 | + | 15.4211i | −0.0590323 | + | 0.593119i | ||||
\(677\) | −10.2365 | −0.393421 | −0.196710 | − | 0.980462i | \(-0.563026\pi\) | ||||
−0.196710 | + | 0.980462i | \(0.563026\pi\) | |||||||
\(678\) | 12.2878 | − | 21.2831i | 0.471910 | − | 0.817373i | ||||
\(679\) | −27.5195 | + | 47.6652i | −1.05610 | + | 1.82922i | ||||
\(680\) | 1.55399 | + | 2.69160i | 0.0595930 | + | 0.103218i | ||||
\(681\) | −3.13760 | −0.120233 | ||||||||
\(682\) | 3.20607 | + | 5.55308i | 0.122767 | + | 0.212638i | ||||
\(683\) | −12.7476 | − | 22.0795i | −0.487774 | − | 0.844849i | 0.512127 | − | 0.858910i | \(-0.328858\pi\) |
−0.999901 | + | 0.0140606i | \(0.995524\pi\) | |||||||
\(684\) | −8.95079 | −0.342242 | ||||||||
\(685\) | −3.88053 | − | 6.72127i | −0.148267 | − | 0.256807i | ||||
\(686\) | 30.3064 | − | 52.4922i | 1.15710 | − | 2.00416i | ||||
\(687\) | 4.92168 | − | 8.52460i | 0.187774 | − | 0.325234i | ||||
\(688\) | 38.7800 | 1.47847 | ||||||||
\(689\) | 8.41344 | − | 26.1391i | 0.320526 | − | 0.995819i | ||||
\(690\) | −4.96199 | −0.188900 | ||||||||
\(691\) | −15.4711 | + | 26.7967i | −0.588547 | + | 1.01939i | 0.405876 | + | 0.913928i | \(0.366966\pi\) |
−0.994423 | + | 0.105465i | \(0.966367\pi\) | |||||||
\(692\) | −1.54492 | + | 2.67588i | −0.0587291 | + | 0.101722i | ||||
\(693\) | 2.30994 | + | 4.00094i | 0.0877475 | + | 0.151983i | ||||
\(694\) | −46.6349 | −1.77024 | ||||||||
\(695\) | −0.329597 | − | 0.570878i | −0.0125023 | − | 0.0216547i | ||||
\(696\) | 3.48201 | + | 6.03102i | 0.131985 | + | 0.228605i | ||||
\(697\) | 37.8871 | 1.43508 | ||||||||
\(698\) | −4.38105 | − | 7.58820i | −0.165825 | − | 0.287218i | ||||
\(699\) | 0.501427 | − | 0.868497i | 0.0189657 | − | 0.0328496i | ||||
\(700\) | 12.9793 | − | 22.4808i | 0.490572 | − | 0.849696i | ||||
\(701\) | 2.39678 | 0.0905252 | 0.0452626 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452626 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(702\) | −4.32362 | − | 4.77531i | −0.163185 | − | 0.180232i | ||||
\(703\) | −30.0042 | −1.13163 | ||||||||
\(704\) | −0.379347 | + | 0.657049i | −0.0142972 | + | 0.0247634i | ||||
\(705\) | 2.49356 | − | 4.31897i | 0.0939128 | − | 0.162662i | ||||
\(706\) | 22.8526 | + | 39.5818i | 0.860067 | + | 1.48968i | ||||
\(707\) | 51.8648 | 1.95058 | ||||||||
\(708\) | −2.47706 | − | 4.29039i | −0.0930936 | − | 0.161243i | ||||
\(709\) | −10.3136 | − | 17.8637i | −0.387336 | − | 0.670886i | 0.604754 | − | 0.796412i | \(-0.293271\pi\) |
−0.992090 | + | 0.125526i | \(0.959938\pi\) | |||||||
\(710\) | 9.92326 | 0.372413 | ||||||||
\(711\) | −4.19926 | − | 7.27333i | −0.157484 | − | 0.272771i | ||||
\(712\) | −2.43597 | + | 4.21922i | −0.0912919 | + | 0.158122i | ||||
\(713\) | −9.30999 | + | 16.1254i | −0.348662 | + | 0.603900i | ||||
\(714\) | −33.2007 | −1.24251 | ||||||||
\(715\) | 1.29543 | + | 1.43076i | 0.0484463 | + | 0.0535075i | ||||
\(716\) | −15.4272 | −0.576542 | ||||||||
\(717\) | 2.28636 | − | 3.96009i | 0.0853857 | − | 0.147892i | ||||
\(718\) | −16.9122 | + | 29.2927i | −0.631156 | + | 1.09319i | ||||
\(719\) | −6.73768 | − | 11.6700i | −0.251273 | − | 0.435217i | 0.712604 | − | 0.701567i | \(-0.247516\pi\) |
−0.963877 | + | 0.266349i | \(0.914182\pi\) | |||||||
\(720\) | 2.65679 | 0.0990127 | ||||||||
\(721\) | −18.3176 | − | 31.7270i | −0.682183 | − | 1.18158i | ||||
\(722\) | 33.3894 | + | 57.8321i | 1.24262 | + | 2.15229i | ||||
\(723\) | 24.7832 | 0.921698 | ||||||||
\(724\) | −6.36004 | − | 11.0159i | −0.236369 | − | 0.409403i | ||||
\(725\) | −11.3703 | + | 19.6939i | −0.422282 | + | 0.731414i | ||||
\(726\) | 0.893322 | − | 1.54728i | 0.0331543 | − | 0.0574249i | ||||
\(727\) | −44.9188 | −1.66594 | −0.832972 | − | 0.553315i | \(-0.813363\pi\) | ||||
−0.832972 | + | 0.553315i | \(0.813363\pi\) | |||||||
\(728\) | −23.5043 | + | 5.06382i | −0.871128 | + | 0.187677i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −0.941603 | + | 1.63090i | −0.0348503 | + | 0.0603625i | ||||
\(731\) | 15.7146 | − | 27.2185i | 0.581225 | − | 1.00671i | ||||
\(732\) | 5.81651 | + | 10.0745i | 0.214985 | + | 0.372364i | ||||
\(733\) | 7.31571 | 0.270212 | 0.135106 | − | 0.990831i | \(-0.456863\pi\) | ||||
0.135106 | + | 0.990831i | \(0.456863\pi\) | |||||||
\(734\) | −32.7867 | − | 56.7882i | −1.21018 | − | 2.09609i | ||||
\(735\) | 3.83906 | + | 6.64945i | 0.141606 | + | 0.245269i | ||||
\(736\) | −31.0274 | −1.14369 | ||||||||
\(737\) | 3.91130 | + | 6.77458i | 0.144075 | + | 0.249545i | ||||
\(738\) | 8.41435 | − | 14.5741i | 0.309737 | − | 0.536480i | ||||
\(739\) | −17.6096 | + | 30.5008i | −0.647781 | + | 1.12199i | 0.335871 | + | 0.941908i | \(0.390969\pi\) |
−0.983652 | + | 0.180081i | \(0.942364\pi\) | |||||||
\(740\) | −2.55005 | −0.0937418 | ||||||||
\(741\) | −8.29466 | + | 25.7700i | −0.304712 | + | 0.946686i | ||||
\(742\) | −62.8628 | −2.30777 | ||||||||
\(743\) | −3.98545 | + | 6.90300i | −0.146212 | + | 0.253247i | −0.929824 | − | 0.368003i | \(-0.880041\pi\) |
0.783613 | + | 0.621250i | \(0.213375\pi\) | |||||||
\(744\) | 2.59019 | − | 4.48635i | 0.0949611 | − | 0.164477i | ||||
\(745\) | 1.58758 | + | 2.74977i | 0.0581644 | + | 0.100744i | ||||
\(746\) | −1.23896 | −0.0453615 | ||||||||
\(747\) | −3.68261 | − | 6.37847i | −0.134740 | − | 0.233376i | ||||
\(748\) | 2.39751 | + | 4.15261i | 0.0876616 | + | 0.151834i | ||||
\(749\) | −58.6949 | −2.14466 | ||||||||
\(750\) | 4.64500 | + | 8.04537i | 0.169611 | + | 0.293776i | ||||
\(751\) | 17.1442 | − | 29.6946i | 0.625601 | − | 1.08357i | −0.362824 | − | 0.931858i | \(-0.618187\pi\) |
0.988424 | − | 0.151714i | \(-0.0484793\pi\) | |||||||
\(752\) | 23.1190 | − | 40.0432i | 0.843061 | − | 1.46023i | ||||
\(753\) | 0.510635 | 0.0186086 | ||||||||
\(754\) | −30.3823 | + | 6.54563i | −1.10646 | + | 0.238378i | ||||
\(755\) | −10.5625 | −0.384408 | ||||||||
\(756\) | −2.75368 | + | 4.76951i | −0.100150 | + | 0.173465i | ||||
\(757\) | 20.7720 | − | 35.9781i | 0.754970 | − | 1.30765i | −0.190419 | − | 0.981703i | \(-0.560985\pi\) |
0.945389 | − | 0.325944i | \(-0.105682\pi\) | |||||||
\(758\) | 4.05608 | + | 7.02534i | 0.147323 | + | 0.255172i | ||||
\(759\) | 5.18817 | 0.188318 | ||||||||
\(760\) | −2.90082 | − | 5.02437i | −0.105224 | − | 0.182253i | ||||
\(761\) | −16.3870 | − | 28.3832i | −0.594029 | − | 1.02889i | −0.993683 | − | 0.112223i | \(-0.964203\pi\) |
0.399654 | − | 0.916666i | \(-0.369130\pi\) | |||||||
\(762\) | 0.355167 | 0.0128664 | ||||||||
\(763\) | 8.38491 | + | 14.5231i | 0.303554 | + | 0.525771i | ||||
\(764\) | −4.13952 | + | 7.16986i | −0.149763 | + | 0.259396i | ||||
\(765\) | 1.07660 | − | 1.86472i | 0.0389244 | − | 0.0674190i | ||||
\(766\) | 36.0750 | 1.30344 | ||||||||
\(767\) | −14.6479 | + | 3.15576i | −0.528904 | + | 0.113948i | ||||
\(768\) | 20.4653 | 0.738479 | ||||||||
\(769\) | 19.3953 | − | 33.5936i | 0.699412 | − | 1.21142i | −0.269258 | − | 0.963068i | \(-0.586778\pi\) |
0.968670 | − | 0.248350i | \(-0.0798882\pi\) | |||||||
\(770\) | 2.20924 | − | 3.82652i | 0.0796156 | − | 0.137898i | ||||
\(771\) | 4.02806 | + | 6.97680i | 0.145067 | + | 0.251263i | ||||
\(772\) | 4.79831 | 0.172695 | ||||||||
\(773\) | −18.4521 | − | 31.9600i | −0.663676 | − | 1.14952i | −0.979642 | − | 0.200751i | \(-0.935662\pi\) |
0.315966 | − | 0.948770i | \(-0.397671\pi\) | |||||||
\(774\) | −6.98012 | − | 12.0899i | −0.250895 | − | 0.434563i | ||||
\(775\) | 16.9162 | 0.607649 | ||||||||
\(776\) | −8.59817 | − | 14.8925i | −0.308656 | − | 0.534608i | ||||
\(777\) | −9.23069 | + | 15.9880i | −0.331149 | + | 0.573567i | ||||
\(778\) | −18.6563 | + | 32.3136i | −0.668859 | + | 1.15850i | ||||
\(779\) | −70.7233 | −2.53392 | ||||||||
\(780\) | −0.704961 | + | 2.19019i | −0.0252417 | + | 0.0784214i | ||||
\(781\) | −10.3756 | −0.371267 | ||||||||
\(782\) | −18.6423 | + | 32.2895i | −0.666649 | + | 1.15467i | ||||
\(783\) | 2.41231 | − | 4.17825i | 0.0862090 | − | 0.149318i | ||||
\(784\) | 35.5938 | + | 61.6502i | 1.27121 | + | 2.20179i | ||||
\(785\) | 11.5566 | 0.412472 | ||||||||
\(786\) | 19.4731 | + | 33.7284i | 0.694582 | + | 1.20305i | ||||
\(787\) | 4.08771 | + | 7.08013i | 0.145711 | + | 0.252379i | 0.929638 | − | 0.368474i | \(-0.120120\pi\) |
−0.783927 | + | 0.620853i | \(0.786786\pi\) | |||||||
\(788\) | −8.58127 | −0.305695 | ||||||||
\(789\) | −0.208161 | − | 0.360546i | −0.00741074 | − | 0.0128358i | ||||
\(790\) | −4.01620 | + | 6.95626i | −0.142890 | + | 0.247492i | ||||
\(791\) | −31.7737 | + | 55.0336i | −1.12974 | + | 1.95677i | ||||
\(792\) | −1.44343 | −0.0512902 | ||||||||
\(793\) | 34.3954 | − | 7.41021i | 1.22142 | − | 0.263144i | ||||
\(794\) | 23.9602 | 0.850314 | ||||||||
\(795\) | 2.03844 | − | 3.53069i | 0.0722961 | − | 0.125221i | ||||
\(796\) | 4.65513 | − | 8.06291i | 0.164997 | − | 0.285782i | ||||
\(797\) | −6.50600 | − | 11.2687i | −0.230454 | − | 0.399159i | 0.727487 | − | 0.686121i | \(-0.240688\pi\) |
−0.957942 | + | 0.286962i | \(0.907355\pi\) | |||||||
\(798\) | 61.9754 | 2.19390 | ||||||||
\(799\) | −18.7367 | − | 32.4530i | −0.662858 | − | 1.14810i | ||||
\(800\) | 14.0942 | + | 24.4119i | 0.498305 | + | 0.863090i | ||||
\(801\) | 3.37524 | 0.119258 | ||||||||
\(802\) | −14.3484 | − | 24.8522i | −0.506661 | − | 0.877562i | ||||
\(803\) | 0.984522 | − | 1.70524i | 0.0347430 | − | 0.0601767i | ||||
\(804\) | −4.66266 | + | 8.07596i | −0.164439 | + | 0.284817i | ||||
\(805\) | 12.8307 | 0.452222 | ||||||||
\(806\) | 15.5172 | + | 17.1383i | 0.546570 | + | 0.603669i | ||||
\(807\) | −0.916592 | −0.0322656 | ||||||||
\(808\) | −8.10229 | + | 14.0336i | −0.285038 | + | 0.493700i | ||||
\(809\) | −20.9034 | + | 36.2057i | −0.734923 | + | 1.27292i | 0.219834 | + | 0.975537i | \(0.429448\pi\) |
−0.954757 | + | 0.297387i | \(0.903885\pi\) | |||||||
\(810\) | −0.478203 | − | 0.828272i | −0.0168023 | − | 0.0291025i | ||||
\(811\) | −32.7280 | −1.14924 | −0.574618 | − | 0.818422i | \(-0.694849\pi\) | ||||
−0.574618 | + | 0.818422i | \(0.694849\pi\) | |||||||
\(812\) | 13.2855 | + | 23.0111i | 0.466229 | + | 0.807532i | ||||
\(813\) | 4.04304 | + | 7.00275i | 0.141796 | + | 0.245597i | ||||
\(814\) | 7.13955 | 0.250241 | ||||||||
\(815\) | −1.73648 | − | 3.00767i | −0.0608263 | − | 0.105354i | ||||
\(816\) | 9.98163 | − | 17.2887i | 0.349427 | − | 0.605225i | ||||
\(817\) | −29.3342 | + | 50.8084i | −1.02627 | + | 1.77756i | ||||
\(818\) | 36.8498 | 1.28842 | ||||||||
\(819\) | 11.1800 | + | 12.3479i | 0.390660 | + | 0.431472i | ||||
\(820\) | −6.01075 | −0.209905 | ||||||||
\(821\) | −14.4593 | + | 25.0443i | −0.504634 | + | 0.874053i | 0.495351 | + | 0.868693i | \(0.335039\pi\) |
−0.999986 | + | 0.00535974i | \(0.998294\pi\) | |||||||
\(822\) | −12.9516 | + | 22.4329i | −0.451740 | + | 0.782437i | ||||
\(823\) | 17.6582 | + | 30.5849i | 0.615527 | + | 1.06612i | 0.990292 | + | 0.139004i | \(0.0443900\pi\) |
−0.374765 | + | 0.927120i | \(0.622277\pi\) | |||||||
\(824\) | 11.4463 | 0.398750 | ||||||||
\(825\) | −2.35672 | − | 4.08196i | −0.0820505 | − | 0.142116i | ||||
\(826\) | 17.1512 | + | 29.7067i | 0.596766 | + | 1.03363i | ||||
\(827\) | 50.2296 | 1.74665 | 0.873327 | − | 0.487135i | \(-0.161958\pi\) | ||||
0.873327 | + | 0.487135i | \(0.161958\pi\) | |||||||
\(828\) | 3.09240 | + | 5.35620i | 0.107468 | + | 0.186141i | ||||
\(829\) | 5.23523 | − | 9.06768i | 0.181827 | − | 0.314934i | −0.760676 | − | 0.649132i | \(-0.775132\pi\) |
0.942503 | + | 0.334198i | \(0.108466\pi\) | |||||||
\(830\) | −3.52207 | + | 6.10041i | −0.122253 | + | 0.211748i | ||||
\(831\) | 9.34576 | 0.324201 | ||||||||
\(832\) | −0.838139 | + | 2.60395i | −0.0290572 | + | 0.0902757i | ||||
\(833\) | 57.6938 | 1.99897 | ||||||||
\(834\) | −1.10006 | + | 1.90536i | −0.0380920 | + | 0.0659773i | ||||
\(835\) | 6.67966 | − | 11.5695i | 0.231159 | − | 0.400380i | ||||
\(836\) | −4.47540 | − | 7.75161i | −0.154785 | − | 0.268095i | ||||
\(837\) | −3.58893 | −0.124052 | ||||||||
\(838\) | 4.43083 | + | 7.67443i | 0.153061 | + | 0.265109i | ||||
\(839\) | −8.28161 | − | 14.3442i | −0.285913 | − | 0.495216i | 0.686917 | − | 0.726736i | \(-0.258964\pi\) |
−0.972830 | + | 0.231520i | \(0.925630\pi\) | |||||||
\(840\) | −3.56971 | −0.123167 | ||||||||
\(841\) | 2.86150 | + | 4.95626i | 0.0986724 | + | 0.170906i | ||||
\(842\) | −3.76885 | + | 6.52784i | −0.129883 | + | 0.224964i | ||||
\(843\) | −4.94657 | + | 8.56772i | −0.170369 | + | 0.295088i | ||||
\(844\) | 32.1649 | 1.10716 | ||||||||
\(845\) | 5.65244 | + | 4.05928i | 0.194450 | + | 0.139643i | ||||
\(846\) | −16.6450 | −0.572266 | ||||||||
\(847\) | −2.30994 | + | 4.00094i | −0.0793706 | + | 0.137474i | ||||
\(848\) | 18.8994 | − | 32.7347i | 0.649007 | − | 1.12411i | ||||
\(849\) | −1.83539 | − | 3.17899i | −0.0629904 | − | 0.109103i | ||||
\(850\) | 33.8731 | 1.16184 | ||||||||
\(851\) | 10.3661 | + | 17.9547i | 0.355346 | + | 0.615478i | ||||
\(852\) | −6.18435 | − | 10.7116i | −0.211872 | − | 0.366974i | ||||
\(853\) | 21.1084 | 0.722736 | 0.361368 | − | 0.932423i | \(-0.382310\pi\) | ||||
0.361368 | + | 0.932423i | \(0.382310\pi\) | |||||||
\(854\) | −40.2736 | − | 69.7559i | −1.37813 | − | 2.38700i | ||||
\(855\) | −2.00967 | + | 3.48084i | −0.0687291 | + | 0.119042i | ||||
\(856\) | 9.16929 | − | 15.8817i | 0.313400 | − | 0.542824i | ||||
\(857\) | 32.6369 | 1.11485 | 0.557427 | − | 0.830226i | \(-0.311789\pi\) | ||||
0.557427 | + | 0.830226i | \(0.311789\pi\) | |||||||
\(858\) | 1.97373 | − | 6.13202i | 0.0673819 | − | 0.209344i | ||||
\(859\) | 15.0101 | 0.512137 | 0.256068 | − | 0.966659i | \(-0.417573\pi\) | ||||
0.256068 | + | 0.966659i | \(0.417573\pi\) | |||||||
\(860\) | −2.49311 | + | 4.31819i | −0.0850143 | + | 0.147249i | ||||
\(861\) | −21.7578 | + | 37.6855i | −0.741502 | + | 1.28432i | ||||
\(862\) | −3.36749 | − | 5.83266i | −0.114697 | − | 0.198661i | ||||
\(863\) | −20.5468 | −0.699423 | −0.349711 | − | 0.936858i | \(-0.613720\pi\) | ||||
−0.349711 | + | 0.936858i | \(0.613720\pi\) | |||||||
\(864\) | −2.99021 | − | 5.17920i | −0.101729 | − | 0.176200i | ||||
\(865\) | 0.693743 | + | 1.20160i | 0.0235880 | + | 0.0408556i | ||||
\(866\) | 29.7529 | 1.01104 | ||||||||
\(867\) | 0.410406 | + | 0.710844i | 0.0139381 | + | 0.0241415i | ||||
\(868\) | 9.88277 | − | 17.1175i | 0.335443 | − | 0.581004i | ||||
\(869\) | 4.19926 | − | 7.27333i | 0.142450 | − | 0.246731i | ||||
\(870\) | −4.61430 | −0.156439 | ||||||||
\(871\) | 18.9305 | + | 20.9081i | 0.641434 | + | 0.708445i | ||||
\(872\) | −5.23955 | −0.177433 | ||||||||
\(873\) | −5.95675 | + | 10.3174i | −0.201605 | + | 0.349191i | ||||
\(874\) | 34.7994 | − | 60.2743i | 1.17711 | − | 2.03881i | ||||
\(875\) | −12.0110 | − | 20.8037i | −0.406046 | − | 0.703292i | ||||
\(876\) | 2.34729 | 0.0793077 | ||||||||
\(877\) | 18.3606 | + | 31.8015i | 0.619994 | + | 1.07386i | 0.989486 | + | 0.144627i | \(0.0461984\pi\) |
−0.369492 | + | 0.929234i | \(0.620468\pi\) | |||||||
\(878\) | 26.4883 | + | 45.8790i | 0.893935 | + | 1.54834i | ||||
\(879\) | −14.1320 | −0.476661 | ||||||||
\(880\) | 1.32839 | + | 2.30085i | 0.0447802 | + | 0.0775615i | ||||
\(881\) | −21.6593 | + | 37.5150i | −0.729721 | + | 1.26391i | 0.227281 | + | 0.973829i | \(0.427016\pi\) |
−0.957001 | + | 0.290084i | \(0.906317\pi\) | |||||||
\(882\) | 12.8132 | − | 22.1932i | 0.431444 | − | 0.747284i | ||||
\(883\) | −23.4531 | −0.789261 | −0.394630 | − | 0.918840i | \(-0.629127\pi\) | ||||
−0.394630 | + | 0.918840i | \(0.629127\pi\) | |||||||
\(884\) | 11.6038 | + | 12.8160i | 0.390278 | + | 0.431050i | ||||
\(885\) | −2.22464 | −0.0747803 | ||||||||
\(886\) | 9.26897 | − | 16.0543i | 0.311397 | − | 0.539356i | ||||
\(887\) | −12.3370 | + | 21.3683i | −0.414235 | + | 0.717477i | −0.995348 | − | 0.0963466i | \(-0.969284\pi\) |
0.581113 | + | 0.813823i | \(0.302618\pi\) | |||||||
\(888\) | −2.88403 | − | 4.99529i | −0.0967817 | − | 0.167631i | ||||
\(889\) | −0.918388 | −0.0308018 | ||||||||
\(890\) | −1.61405 | − | 2.79562i | −0.0541031 | − | 0.0937094i | ||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | 27.4515 | 0.919145 | ||||||||
\(893\) | 34.9756 | + | 60.5795i | 1.17041 | + | 2.02721i | ||||
\(894\) | 5.29870 | − | 9.17761i | 0.177215 | − | 0.306945i | ||||
\(895\) | −3.46378 | + | 5.99944i | −0.115781 | + | 0.200539i | ||||
\(896\) | −48.9954 | −1.63682 | ||||||||
\(897\) | 18.2866 | − | 3.93970i | 0.610573 | − | 0.131543i | ||||
\(898\) | 12.7052 | 0.423978 | ||||||||
\(899\) | −8.65763 | + | 14.9954i | −0.288748 | + | 0.500126i | ||||
\(900\) | 2.80944 | − | 4.86610i | 0.0936481 | − | 0.162203i | ||||
\(901\) | −15.3170 | − | 26.5298i | −0.510282 | − | 0.883835i | ||||
\(902\) | 16.8287 | 0.560335 | ||||||||
\(903\) | 18.0491 | + | 31.2620i | 0.600638 | + | 1.04033i | ||||
\(904\) | −9.92734 | − | 17.1947i | −0.330178 | − | 0.571886i | ||||
\(905\) | −5.71192 | −0.189871 | ||||||||
\(906\) | 17.6267 | + | 30.5303i | 0.585606 | + | 1.01430i | ||||
\(907\) | −4.82458 | + | 8.35642i | −0.160198 | + | 0.277470i | −0.934939 | − | 0.354807i | \(-0.884546\pi\) |
0.774742 | + | 0.632278i | \(0.217880\pi\) | |||||||
\(908\) | 1.87016 | − | 3.23922i | 0.0620635 | − | 0.107497i | ||||
\(909\) | 11.2264 | 0.372357 | ||||||||
\(910\) | 4.88116 | − | 15.1649i | 0.161809 | − | 0.502711i | ||||
\(911\) | −9.69851 | −0.321326 | −0.160663 | − | 0.987009i | \(-0.551363\pi\) | ||||
−0.160663 | + | 0.987009i | \(0.551363\pi\) | |||||||
\(912\) | −18.6326 | + | 32.2725i | −0.616986 | + | 1.06865i | ||||
\(913\) | 3.68261 | − | 6.37847i | 0.121877 | − | 0.211097i | ||||
\(914\) | −18.3532 | − | 31.7887i | −0.607070 | − | 1.05148i | ||||
\(915\) | 5.22378 | 0.172693 | ||||||||
\(916\) | 5.86713 | + | 10.1622i | 0.193855 | + | 0.335767i | ||||
\(917\) | −50.3533 | − | 87.2145i | −1.66281 | − | 2.88008i | ||||
\(918\) | −7.18648 | −0.237189 | ||||||||
\(919\) | 27.1078 | + | 46.9520i | 0.894202 | + | 1.54880i | 0.834789 | + | 0.550570i | \(0.185590\pi\) |
0.0594134 | + | 0.998233i | \(0.481077\pi\) | |||||||
\(920\) | −2.00440 | + | 3.47173i | −0.0660832 | + | 0.114459i | ||||
\(921\) | −1.72594 | + | 2.98941i | −0.0568715 | + | 0.0985044i | ||||
\(922\) | −3.35212 | −0.110396 | ||||||||
\(923\) | −36.5706 | + | 7.87883i | −1.20374 | + | 0.259335i | ||||
\(924\) | −5.50736 | −0.181179 | ||||||||
\(925\) | 9.41762 | − | 16.3118i | 0.309650 | − | 0.536329i | ||||
\(926\) | −4.33121 | + | 7.50188i | −0.142333 | + | 0.246527i | ||||
\(927\) | −3.96495 | − | 6.86749i | −0.130226 | − | 0.225558i | ||||
\(928\) | −28.8533 | −0.947156 | ||||||||
\(929\) | −0.617623 | − | 1.06975i | −0.0202635 | − | 0.0350975i | 0.855716 | − | 0.517446i | \(-0.173117\pi\) |
−0.875979 | + | 0.482349i | \(0.839784\pi\) | |||||||
\(930\) | 1.71624 | + | 2.97261i | 0.0562777 | + | 0.0974758i | ||||
\(931\) | −107.696 | −3.52960 | ||||||||
\(932\) | 0.597750 | + | 1.03533i | 0.0195799 | + | 0.0339135i | ||||
\(933\) | −14.5173 | + | 25.1448i | −0.475276 | + | 0.823202i | ||||
\(934\) | −6.53140 | + | 11.3127i | −0.213714 | + | 0.370164i | ||||
\(935\) | 2.15319 | 0.0704169 | ||||||||
\(936\) | −5.08764 | + | 1.09609i | −0.166295 | + | 0.0358268i | ||||
\(937\) | 39.1734 | 1.27974 | 0.639869 | − | 0.768484i | \(-0.278989\pi\) | ||||
0.639869 | + | 0.768484i | \(0.278989\pi\) | |||||||
\(938\) | 32.2843 | − | 55.9180i | 1.05412 | − | 1.82579i | ||||
\(939\) | −6.64802 | + | 11.5147i | −0.216950 | + | 0.375768i | ||||
\(940\) | 2.97257 | + | 5.14863i | 0.0969544 | + | 0.167930i | ||||
\(941\) | −1.34392 | −0.0438107 | −0.0219053 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219053 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(942\) | −19.2856 | − | 33.4036i | −0.628359 | − | 1.08835i | ||||
\(943\) | 24.4341 | + | 42.3211i | 0.795684 | + | 1.37817i | ||||
\(944\) | −20.6256 | −0.671308 | ||||||||
\(945\) | 1.23653 | + | 2.14174i | 0.0402244 | + | 0.0696707i | ||||
\(946\) | 6.98012 | − | 12.0899i | 0.226943 | − | 0.393077i | ||||
\(947\) | −9.31931 | + | 16.1415i | −0.302837 | + | 0.524529i | −0.976777 | − | 0.214257i | \(-0.931267\pi\) |
0.673940 | + | 0.738786i | \(0.264600\pi\) | |||||||
\(948\) | 10.0119 | 0.325170 | ||||||||
\(949\) | 2.17523 | − | 6.75805i | 0.0706109 | − | 0.219375i | ||||
\(950\) | −63.2304 | −2.05147 | ||||||||
\(951\) | 5.21413 | − | 9.03114i | 0.169080 | − | 0.292855i | ||||
\(952\) | −13.4115 | + | 23.2294i | −0.434668 | + | 0.752868i | ||||
\(953\) | 27.5812 | + | 47.7721i | 0.893443 | + | 1.54749i | 0.835720 | + | 0.549156i | \(0.185051\pi\) |
0.0577236 | + | 0.998333i | \(0.481616\pi\) | |||||||
\(954\) | −13.6070 | −0.440543 | ||||||||
\(955\) | 1.85884 | + | 3.21961i | 0.0601507 | + | 0.104184i | ||||
\(956\) | 2.72557 | + | 4.72082i | 0.0881511 | + | 0.152682i | ||||
\(957\) | 4.82462 | 0.155958 | ||||||||
\(958\) | 4.82553 | + | 8.35807i | 0.155906 | + | 0.270037i | ||||
\(959\) | 33.4902 | − | 58.0068i | 1.08146 | − | 1.87314i | ||||
\(960\) | −0.203068 | + | 0.351724i | −0.00655398 | + | 0.0113518i | ||||
\(961\) | −18.1196 | −0.584502 | ||||||||
\(962\) | 25.1646 | − | 5.42151i | 0.811340 | − | 0.174797i | ||||
\(963\) | −12.7048 | −0.409407 | ||||||||
\(964\) | −14.7720 | + | 25.5859i | −0.475775 | + | 0.824066i | ||||
\(965\) | 1.07733 | − | 1.86600i | 0.0346806 | − | 0.0600686i | ||||
\(966\) | −21.4118 | − | 37.0863i | −0.688914 | − | 1.19323i | ||||
\(967\) | −17.8380 | −0.573631 | −0.286816 | − | 0.957986i | \(-0.592597\pi\) | ||||
−0.286816 | + | 0.957986i | \(0.592597\pi\) | |||||||
\(968\) | −0.721717 | − | 1.25005i | −0.0231969 | − | 0.0401781i | ||||
\(969\) | 15.1007 | + | 26.1552i | 0.485105 | + | 0.840227i | ||||
\(970\) | 11.3941 | 0.365844 | ||||||||
\(971\) | −19.2134 | − | 33.2786i | −0.616587 | − | 1.06796i | −0.990104 | − | 0.140337i | \(-0.955182\pi\) |
0.373517 | − | 0.927623i | \(-0.378152\pi\) | |||||||
\(972\) | −0.596049 | + | 1.03239i | −0.0191183 | + | 0.0331138i | ||||
\(973\) | 2.84453 | − | 4.92687i | 0.0911914 | − | 0.157948i | ||||
\(974\) | −17.1708 | −0.550188 | ||||||||
\(975\) | −11.4064 | − | 12.5980i | −0.365297 | − | 0.403459i | ||||
\(976\) | 48.4321 | 1.55028 | ||||||||
\(977\) | 11.3263 | − | 19.6177i | 0.362360 | − | 0.627627i | −0.625988 | − | 0.779832i | \(-0.715304\pi\) |
0.988349 | + | 0.152206i | \(0.0486376\pi\) | |||||||
\(978\) | −5.79567 | + | 10.0384i | −0.185325 | + | 0.320993i | ||||
\(979\) | 1.68762 | + | 2.92305i | 0.0539366 | + | 0.0934210i | ||||
\(980\) | −9.15308 | −0.292384 | ||||||||
\(981\) | 1.81496 | + | 3.14360i | 0.0579472 | + | 0.100367i | ||||
\(982\) | −8.50230 | − | 14.7264i | −0.271319 | − | 0.469939i | ||||
\(983\) | 18.4666 | 0.588993 | 0.294496 | − | 0.955653i | \(-0.404848\pi\) | ||||
0.294496 | + | 0.955653i | \(0.404848\pi\) | |||||||
\(984\) | −6.79797 | − | 11.7744i | −0.216711 | − | 0.375355i | ||||
\(985\) | −1.92670 | + | 3.33714i | −0.0613897 | + | 0.106330i | ||||
\(986\) | −17.3360 | + | 30.0269i | −0.552092 | + | 0.956252i | ||||
\(987\) | 43.0404 | 1.36999 | ||||||||
\(988\) | −21.6606 | − | 23.9235i | −0.689116 | − | 0.761108i | ||||
\(989\) | 40.5386 | 1.28905 | ||||||||
\(990\) | 0.478203 | − | 0.828272i | 0.0151983 | − | 0.0263242i | ||||
\(991\) | 11.7661 | − | 20.3795i | 0.373763 | − | 0.647376i | −0.616378 | − | 0.787450i | \(-0.711401\pi\) |
0.990141 | + | 0.140074i | \(0.0447341\pi\) | |||||||
\(992\) | 10.7317 | + | 18.5878i | 0.340731 | + | 0.590163i | ||||
\(993\) | −14.6234 | −0.464059 | ||||||||
\(994\) | 42.8205 | + | 74.1673i | 1.35818 | + | 2.35244i | ||||
\(995\) | −2.09037 | − | 3.62063i | −0.0662693 | − | 0.114782i | ||||
\(996\) | 8.78007 | 0.278207 | ||||||||
\(997\) | −11.8933 | − | 20.5998i | −0.376664 | − | 0.652401i | 0.613910 | − | 0.789376i | \(-0.289596\pi\) |
−0.990575 | + | 0.136974i | \(0.956262\pi\) | |||||||
\(998\) | −22.9244 | + | 39.7061i | −0.725658 | + | 1.25688i | ||||
\(999\) | −1.99803 | + | 3.46070i | −0.0632150 | + | 0.109492i |
(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 | 429.2.i.c.100.5 | ✓ | 10 | |
13.3 | even | 3 | inner | 429.2.i.c.133.5 | yes | 10 | |
13.4 | even | 6 | 5577.2.a.p.1.5 | 5 | |||
13.9 | even | 3 | 5577.2.a.v.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.i.c.100.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
429.2.i.c.133.5 | yes | 10 | 13.3 | even | 3 | inner | |
5577.2.a.p.1.5 | 5 | 13.4 | even | 6 | |||
5577.2.a.v.1.1 | 5 | 13.9 | even | 3 |