Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.c.415.1 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.50000 | − | 0.866025i | −0.545545 | − | 0.188982i | ||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | −1.00000 | − | 1.73205i | −0.196116 | − | 0.339683i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.50000 | + | 0.866025i | 0.472456 | + | 0.163663i | ||||
\(29\) | −7.00000 | −1.29987 | −0.649934 | − | 0.759991i | \(-0.725203\pi\) | ||||
−0.649934 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | −3.50000 | + | 6.06218i | −0.628619 | + | 1.08880i | 0.359211 | + | 0.933257i | \(0.383046\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −2.00000 | + | 1.73205i | −0.338062 | + | 0.292770i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | 1.00000 | − | 1.73205i | 0.160128 | − | 0.277350i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0.500000 | + | 2.59808i | 0.0771517 | + | 0.400892i | ||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | −3.00000 | − | 5.19615i | −0.437595 | − | 0.757937i | 0.559908 | − | 0.828554i | \(-0.310836\pi\) |
−0.997503 | + | 0.0706177i | \(0.977503\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −1.00000 | − | 1.73205i | −0.140028 | − | 0.242536i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | −0.500000 | − | 2.59808i | −0.0668153 | − | 0.347183i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 3.50000 | + | 6.06218i | 0.459573 | + | 0.796003i | ||||
\(59\) | 4.50000 | − | 7.79423i | 0.585850 | − | 1.01472i | −0.408919 | − | 0.912571i | \(-0.634094\pi\) |
0.994769 | − | 0.102151i | \(-0.0325726\pi\) | |||||||
\(60\) | 0.500000 | − | 0.866025i | 0.0645497 | − | 0.111803i | ||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | 7.00000 | 0.889001 | ||||||||
\(63\) | −2.00000 | + | 1.73205i | −0.251976 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | −1.50000 | + | 2.59808i | −0.184637 | + | 0.319801i | ||||
\(67\) | −5.00000 | + | 8.66025i | −0.610847 | + | 1.05802i | 0.380251 | + | 0.924883i | \(0.375838\pi\) |
−0.991098 | + | 0.133135i | \(0.957496\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 2.50000 | + | 0.866025i | 0.298807 | + | 0.103510i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 5.00000 | − | 8.66025i | 0.585206 | − | 1.01361i | −0.409644 | − | 0.912245i | \(-0.634347\pi\) |
0.994850 | − | 0.101361i | \(-0.0323196\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | −2.00000 | − | 3.46410i | −0.230940 | − | 0.400000i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | −7.50000 | − | 2.59808i | −0.854704 | − | 0.296078i | ||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 7.50000 | + | 12.9904i | 0.843816 | + | 1.46153i | 0.886646 | + | 0.462450i | \(0.153029\pi\) |
−0.0428296 | + | 0.999082i | \(0.513637\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.00000 | + | 1.73205i | 0.110432 | + | 0.191273i | ||||
\(83\) | 1.00000 | 0.109764 | 0.0548821 | − | 0.998493i | \(-0.482522\pi\) | ||||
0.0548821 | + | 0.998493i | \(0.482522\pi\) | |||||||
\(84\) | 2.00000 | − | 1.73205i | 0.218218 | − | 0.188982i | ||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 3.00000 | + | 5.19615i | 0.323498 | + | 0.560316i | ||||
\(87\) | −3.50000 | + | 6.06218i | −0.375239 | + | 0.649934i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | −1.00000 | − | 5.19615i | −0.104828 | − | 0.544705i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 3.50000 | + | 6.06218i | 0.362933 | + | 0.628619i | ||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | 5.50000 | + | 4.33013i | 0.555584 | + | 0.437409i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | 5.00000 | − | 8.66025i | 0.497519 | − | 0.861727i | −0.502477 | − | 0.864590i | \(-0.667578\pi\) |
0.999996 | + | 0.00286291i | \(0.000911295\pi\) | |||||||
\(102\) | −1.00000 | + | 1.73205i | −0.0990148 | + | 0.171499i | ||||
\(103\) | 4.00000 | + | 6.92820i | 0.394132 | + | 0.682656i | 0.992990 | − | 0.118199i | \(-0.0377120\pi\) |
−0.598858 | + | 0.800855i | \(0.704379\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0.500000 | + | 2.59808i | 0.0487950 | + | 0.253546i | ||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | −1.50000 | − | 2.59808i | −0.145010 | − | 0.251166i | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −5.00000 | + | 8.66025i | −0.478913 | + | 0.829502i | −0.999708 | − | 0.0241802i | \(-0.992302\pi\) |
0.520794 | + | 0.853682i | \(0.325636\pi\) | |||||||
\(110\) | 1.50000 | + | 2.59808i | 0.143019 | + | 0.247717i | ||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | −2.00000 | + | 1.73205i | −0.188982 | + | 0.163663i | ||||
\(113\) | 10.0000 | 0.940721 | 0.470360 | − | 0.882474i | \(-0.344124\pi\) | ||||
0.470360 | + | 0.882474i | \(0.344124\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | −0.500000 | + | 0.866025i | −0.0466252 | + | 0.0807573i | ||||
\(116\) | 3.50000 | − | 6.06218i | 0.324967 | − | 0.562859i | ||||
\(117\) | −1.00000 | − | 1.73205i | −0.0924500 | − | 0.160128i | ||||
\(118\) | −9.00000 | −0.828517 | ||||||||
\(119\) | −5.00000 | − | 1.73205i | −0.458349 | − | 0.158777i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −3.00000 | + | 5.19615i | −0.271607 | + | 0.470438i | ||||
\(123\) | −1.00000 | + | 1.73205i | −0.0901670 | + | 0.156174i | ||||
\(124\) | −3.50000 | − | 6.06218i | −0.314309 | − | 0.544400i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 2.50000 | + | 0.866025i | 0.222718 | + | 0.0771517i | ||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −3.00000 | + | 5.19615i | −0.264135 | + | 0.457496i | ||||
\(130\) | −1.00000 | + | 1.73205i | −0.0877058 | + | 0.151911i | ||||
\(131\) | −3.50000 | − | 6.06218i | −0.305796 | − | 0.529655i | 0.671642 | − | 0.740876i | \(-0.265589\pi\) |
−0.977438 | + | 0.211221i | \(0.932256\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 4.00000 | − | 3.46410i | 0.346844 | − | 0.300376i | ||||
\(134\) | 10.0000 | 0.863868 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 1.00000 | − | 1.73205i | 0.0857493 | − | 0.148522i | ||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | 0.500000 | + | 0.866025i | 0.0425628 | + | 0.0737210i | ||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | −0.500000 | − | 2.59808i | −0.0422577 | − | 0.219578i | ||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 4.00000 | + | 6.92820i | 0.335673 | + | 0.581402i | ||||
\(143\) | 3.00000 | − | 5.19615i | 0.250873 | − | 0.434524i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 3.50000 | + | 6.06218i | 0.290659 | + | 0.503436i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | −1.00000 | + | 6.92820i | −0.0824786 | + | 0.571429i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 11.0000 | + | 19.0526i | 0.901155 | + | 1.56085i | 0.825997 | + | 0.563675i | \(0.190613\pi\) |
0.0751583 | + | 0.997172i | \(0.476054\pi\) | |||||||
\(150\) | −2.00000 | + | 3.46410i | −0.163299 | + | 0.282843i | ||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | −2.00000 | −0.161690 | ||||||||
\(154\) | 1.50000 | + | 7.79423i | 0.120873 | + | 0.628077i | ||||
\(155\) | 7.00000 | 0.562254 | ||||||||
\(156\) | 1.00000 | + | 1.73205i | 0.0800641 | + | 0.138675i | ||||
\(157\) | −3.00000 | + | 5.19615i | −0.239426 | + | 0.414698i | −0.960550 | − | 0.278108i | \(-0.910293\pi\) |
0.721124 | + | 0.692806i | \(0.243626\pi\) | |||||||
\(158\) | 7.50000 | − | 12.9904i | 0.596668 | − | 1.03346i | ||||
\(159\) | −4.50000 | − | 7.79423i | −0.356873 | − | 0.618123i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −2.00000 | + | 1.73205i | −0.157622 | + | 0.136505i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −1.00000 | − | 1.73205i | −0.0783260 | − | 0.135665i | 0.824202 | − | 0.566296i | \(-0.191624\pi\) |
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(164\) | 1.00000 | − | 1.73205i | 0.0780869 | − | 0.135250i | ||||
\(165\) | −1.50000 | + | 2.59808i | −0.116775 | + | 0.202260i | ||||
\(166\) | −0.500000 | − | 0.866025i | −0.0388075 | − | 0.0672166i | ||||
\(167\) | 6.00000 | 0.464294 | 0.232147 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232147 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(168\) | −2.50000 | − | 0.866025i | −0.192879 | − | 0.0668153i | ||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 1.00000 | + | 1.73205i | 0.0766965 | + | 0.132842i | ||||
\(171\) | 1.00000 | − | 1.73205i | 0.0764719 | − | 0.132453i | ||||
\(172\) | 3.00000 | − | 5.19615i | 0.228748 | − | 0.396203i | ||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 7.00000 | 0.530669 | ||||||||
\(175\) | −10.0000 | − | 3.46410i | −0.755929 | − | 0.261861i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | −4.50000 | − | 7.79423i | −0.338241 | − | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | −4.00000 | + | 3.46410i | −0.296500 | + | 0.256776i | ||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | 1.00000 | − | 1.73205i | 0.0735215 | − | 0.127343i | ||||
\(186\) | 3.50000 | − | 6.06218i | 0.256632 | − | 0.444500i | ||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | 6.00000 | 0.437595 | ||||||||
\(189\) | 0.500000 | + | 2.59808i | 0.0363696 | + | 0.188982i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | −5.00000 | − | 8.66025i | −0.361787 | − | 0.626634i | 0.626468 | − | 0.779447i | \(-0.284500\pi\) |
−0.988255 | + | 0.152813i | \(0.951167\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 11.5000 | − | 19.9186i | 0.827788 | − | 1.43377i | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) |
0.899770 | − | 0.436365i | \(-0.143734\pi\) | |||||||
\(194\) | −2.50000 | − | 4.33013i | −0.179490 | − | 0.310885i | ||||
\(195\) | −2.00000 | −0.143223 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | 14.0000 | 0.997459 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(198\) | 1.50000 | + | 2.59808i | 0.106600 | + | 0.184637i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 2.00000 | − | 3.46410i | 0.141421 | − | 0.244949i | ||||
\(201\) | 5.00000 | + | 8.66025i | 0.352673 | + | 0.610847i | ||||
\(202\) | −10.0000 | −0.703598 | ||||||||
\(203\) | 3.50000 | + | 18.1865i | 0.245652 | + | 1.27644i | ||||
\(204\) | 2.00000 | 0.140028 | ||||||||
\(205\) | 1.00000 | + | 1.73205i | 0.0698430 | + | 0.120972i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | −1.00000 | − | 1.73205i | −0.0693375 | − | 0.120096i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 2.00000 | − | 1.73205i | 0.138013 | − | 0.119523i | ||||
\(211\) | 6.00000 | 0.413057 | 0.206529 | − | 0.978441i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978441i | \(0.433783\pi\) | |||||||
\(212\) | 4.50000 | + | 7.79423i | 0.309061 | + | 0.535310i | ||||
\(213\) | −4.00000 | + | 6.92820i | −0.274075 | + | 0.474713i | ||||
\(214\) | −1.50000 | + | 2.59808i | −0.102538 | + | 0.177601i | ||||
\(215\) | 3.00000 | + | 5.19615i | 0.204598 | + | 0.354375i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 17.5000 | + | 6.06218i | 1.18798 | + | 0.411527i | ||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | −5.00000 | − | 8.66025i | −0.337869 | − | 0.585206i | ||||
\(220\) | 1.50000 | − | 2.59808i | 0.101130 | − | 0.175162i | ||||
\(221\) | 2.00000 | − | 3.46410i | 0.134535 | − | 0.233021i | ||||
\(222\) | −1.00000 | − | 1.73205i | −0.0671156 | − | 0.116248i | ||||
\(223\) | 13.0000 | 0.870544 | 0.435272 | − | 0.900299i | \(-0.356652\pi\) | ||||
0.435272 | + | 0.900299i | \(0.356652\pi\) | |||||||
\(224\) | 2.50000 | + | 0.866025i | 0.167038 | + | 0.0578638i | ||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | −5.00000 | − | 8.66025i | −0.332595 | − | 0.576072i | ||||
\(227\) | 4.50000 | − | 7.79423i | 0.298675 | − | 0.517321i | −0.677158 | − | 0.735838i | \(-0.736789\pi\) |
0.975833 | + | 0.218517i | \(0.0701218\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | −11.0000 | − | 19.0526i | −0.726900 | − | 1.25903i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.231287 | − | 0.972886i | \(-0.425707\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −6.00000 | + | 5.19615i | −0.394771 | + | 0.341882i | ||||
\(232\) | −7.00000 | −0.459573 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | −1.00000 | + | 1.73205i | −0.0653720 | + | 0.113228i | ||||
\(235\) | −3.00000 | + | 5.19615i | −0.195698 | + | 0.338960i | ||||
\(236\) | 4.50000 | + | 7.79423i | 0.292925 | + | 0.507361i | ||||
\(237\) | 15.0000 | 0.974355 | ||||||||
\(238\) | 1.00000 | + | 5.19615i | 0.0648204 | + | 0.336817i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | 13.5000 | − | 23.3827i | 0.869611 | − | 1.50621i | 0.00721719 | − | 0.999974i | \(-0.497703\pi\) |
0.862394 | − | 0.506237i | \(-0.168964\pi\) | |||||||
\(242\) | 1.00000 | − | 1.73205i | 0.0642824 | − | 0.111340i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 5.50000 | + | 4.33013i | 0.351382 | + | 0.276642i | ||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 2.00000 | + | 3.46410i | 0.127257 | + | 0.220416i | ||||
\(248\) | −3.50000 | + | 6.06218i | −0.222250 | + | 0.384949i | ||||
\(249\) | 0.500000 | − | 0.866025i | 0.0316862 | − | 0.0548821i | ||||
\(250\) | 4.50000 | + | 7.79423i | 0.284605 | + | 0.492950i | ||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | −0.500000 | − | 2.59808i | −0.0314970 | − | 0.163663i | ||||
\(253\) | −3.00000 | −0.188608 | ||||||||
\(254\) | 3.50000 | + | 6.06218i | 0.219610 | + | 0.380375i | ||||
\(255\) | −1.00000 | + | 1.73205i | −0.0626224 | + | 0.108465i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.00000 | + | 3.46410i | 0.124757 | + | 0.216085i | 0.921638 | − | 0.388051i | \(-0.126852\pi\) |
−0.796881 | + | 0.604136i | \(0.793518\pi\) | |||||||
\(258\) | 6.00000 | 0.373544 | ||||||||
\(259\) | 4.00000 | − | 3.46410i | 0.248548 | − | 0.215249i | ||||
\(260\) | 2.00000 | 0.124035 | ||||||||
\(261\) | 3.50000 | + | 6.06218i | 0.216645 | + | 0.375239i | ||||
\(262\) | −3.50000 | + | 6.06218i | −0.216231 | + | 0.374523i | ||||
\(263\) | 1.00000 | − | 1.73205i | 0.0616626 | − | 0.106803i | −0.833546 | − | 0.552450i | \(-0.813693\pi\) |
0.895209 | + | 0.445647i | \(0.147026\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | −5.00000 | − | 1.73205i | −0.306570 | − | 0.106199i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.00000 | − | 8.66025i | −0.305424 | − | 0.529009i | ||||
\(269\) | 13.5000 | − | 23.3827i | 0.823110 | − | 1.42567i | −0.0802460 | − | 0.996775i | \(-0.525571\pi\) |
0.903356 | − | 0.428892i | \(-0.141096\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 4.50000 | + | 7.79423i | 0.273356 | + | 0.473466i | 0.969719 | − | 0.244224i | \(-0.0785331\pi\) |
−0.696363 | + | 0.717689i | \(0.745200\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | −5.00000 | − | 1.73205i | −0.302614 | − | 0.104828i | ||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −6.00000 | − | 10.3923i | −0.361814 | − | 0.626680i | ||||
\(276\) | 0.500000 | − | 0.866025i | 0.0300965 | − | 0.0521286i | ||||
\(277\) | 4.00000 | − | 6.92820i | 0.240337 | − | 0.416275i | −0.720473 | − | 0.693482i | \(-0.756075\pi\) |
0.960810 | + | 0.277207i | \(0.0894088\pi\) | |||||||
\(278\) | −7.00000 | − | 12.1244i | −0.419832 | − | 0.727171i | ||||
\(279\) | 7.00000 | 0.419079 | ||||||||
\(280\) | −2.00000 | + | 1.73205i | −0.119523 | + | 0.103510i | ||||
\(281\) | −4.00000 | −0.238620 | −0.119310 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(282\) | 3.00000 | + | 5.19615i | 0.178647 | + | 0.309426i | ||||
\(283\) | −3.00000 | + | 5.19615i | −0.178331 | + | 0.308879i | −0.941309 | − | 0.337546i | \(-0.890403\pi\) |
0.762978 | + | 0.646425i | \(0.223737\pi\) | |||||||
\(284\) | 4.00000 | − | 6.92820i | 0.237356 | − | 0.411113i | ||||
\(285\) | −1.00000 | − | 1.73205i | −0.0592349 | − | 0.102598i | ||||
\(286\) | −6.00000 | −0.354787 | ||||||||
\(287\) | 1.00000 | + | 5.19615i | 0.0590281 | + | 0.306719i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 3.50000 | − | 6.06218i | 0.205527 | − | 0.355983i | ||||
\(291\) | 2.50000 | − | 4.33013i | 0.146553 | − | 0.253837i | ||||
\(292\) | 5.00000 | + | 8.66025i | 0.292603 | + | 0.506803i | ||||
\(293\) | 19.0000 | 1.10999 | 0.554996 | − | 0.831853i | \(-0.312720\pi\) | ||||
0.554996 | + | 0.831853i | \(0.312720\pi\) | |||||||
\(294\) | 6.50000 | − | 2.59808i | 0.379088 | − | 0.151523i | ||||
\(295\) | −9.00000 | −0.524000 | ||||||||
\(296\) | 1.00000 | + | 1.73205i | 0.0581238 | + | 0.100673i | ||||
\(297\) | −1.50000 | + | 2.59808i | −0.0870388 | + | 0.150756i | ||||
\(298\) | 11.0000 | − | 19.0526i | 0.637213 | − | 1.10369i | ||||
\(299\) | −1.00000 | − | 1.73205i | −0.0578315 | − | 0.100167i | ||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 3.00000 | + | 15.5885i | 0.172917 | + | 0.898504i | ||||
\(302\) | −5.00000 | −0.287718 | ||||||||
\(303\) | −5.00000 | − | 8.66025i | −0.287242 | − | 0.497519i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | −3.00000 | + | 5.19615i | −0.171780 | + | 0.297531i | ||||
\(306\) | 1.00000 | + | 1.73205i | 0.0571662 | + | 0.0990148i | ||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 6.00000 | − | 5.19615i | 0.341882 | − | 0.296078i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | −3.50000 | − | 6.06218i | −0.198787 | − | 0.344309i | ||||
\(311\) | 1.00000 | − | 1.73205i | 0.0567048 | − | 0.0982156i | −0.836280 | − | 0.548303i | \(-0.815274\pi\) |
0.892984 | + | 0.450088i | \(0.148607\pi\) | |||||||
\(312\) | 1.00000 | − | 1.73205i | 0.0566139 | − | 0.0980581i | ||||
\(313\) | 12.5000 | + | 21.6506i | 0.706542 | + | 1.22377i | 0.966132 | + | 0.258047i | \(0.0830791\pi\) |
−0.259590 | + | 0.965719i | \(0.583588\pi\) | |||||||
\(314\) | 6.00000 | 0.338600 | ||||||||
\(315\) | 2.50000 | + | 0.866025i | 0.140859 | + | 0.0487950i | ||||
\(316\) | −15.0000 | −0.843816 | ||||||||
\(317\) | 15.5000 | + | 26.8468i | 0.870567 | + | 1.50787i | 0.861411 | + | 0.507908i | \(0.169581\pi\) |
0.00915525 | + | 0.999958i | \(0.497086\pi\) | |||||||
\(318\) | −4.50000 | + | 7.79423i | −0.252347 | + | 0.437079i | ||||
\(319\) | −10.5000 | + | 18.1865i | −0.587887 | + | 1.01825i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | 2.50000 | + | 0.866025i | 0.139320 | + | 0.0482617i | ||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 4.00000 | − | 6.92820i | 0.221880 | − | 0.384308i | ||||
\(326\) | −1.00000 | + | 1.73205i | −0.0553849 | + | 0.0959294i | ||||
\(327\) | 5.00000 | + | 8.66025i | 0.276501 | + | 0.478913i | ||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | −12.0000 | + | 10.3923i | −0.661581 | + | 0.572946i | ||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | −5.00000 | − | 8.66025i | −0.274825 | − | 0.476011i | 0.695266 | − | 0.718752i | \(-0.255287\pi\) |
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(332\) | −0.500000 | + | 0.866025i | −0.0274411 | + | 0.0475293i | ||||
\(333\) | 1.00000 | − | 1.73205i | 0.0547997 | − | 0.0949158i | ||||
\(334\) | −3.00000 | − | 5.19615i | −0.164153 | − | 0.284321i | ||||
\(335\) | 10.0000 | 0.546358 | ||||||||
\(336\) | 0.500000 | + | 2.59808i | 0.0272772 | + | 0.141737i | ||||
\(337\) | −9.00000 | −0.490261 | −0.245131 | − | 0.969490i | \(-0.578831\pi\) | ||||
−0.245131 | + | 0.969490i | \(0.578831\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 5.00000 | − | 8.66025i | 0.271563 | − | 0.470360i | ||||
\(340\) | 1.00000 | − | 1.73205i | 0.0542326 | − | 0.0939336i | ||||
\(341\) | 10.5000 | + | 18.1865i | 0.568607 | + | 0.984856i | ||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | 0.500000 | + | 0.866025i | 0.0269191 | + | 0.0466252i | ||||
\(346\) | 3.00000 | − | 5.19615i | 0.161281 | − | 0.279347i | ||||
\(347\) | −18.0000 | + | 31.1769i | −0.966291 | + | 1.67366i | −0.260184 | + | 0.965559i | \(0.583783\pi\) |
−0.706107 | + | 0.708105i | \(0.749550\pi\) | |||||||
\(348\) | −3.50000 | − | 6.06218i | −0.187620 | − | 0.324967i | ||||
\(349\) | 16.0000 | 0.856460 | 0.428230 | − | 0.903670i | \(-0.359137\pi\) | ||||
0.428230 | + | 0.903670i | \(0.359137\pi\) | |||||||
\(350\) | 2.00000 | + | 10.3923i | 0.106904 | + | 0.555492i | ||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 1.50000 | + | 2.59808i | 0.0799503 | + | 0.138478i | ||||
\(353\) | 13.0000 | − | 22.5167i | 0.691920 | − | 1.19844i | −0.279288 | − | 0.960207i | \(-0.590098\pi\) |
0.971208 | − | 0.238233i | \(-0.0765683\pi\) | |||||||
\(354\) | −4.50000 | + | 7.79423i | −0.239172 | + | 0.414259i | ||||
\(355\) | 4.00000 | + | 6.92820i | 0.212298 | + | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | + | 3.46410i | −0.211702 | + | 0.183340i | ||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −15.0000 | − | 25.9808i | −0.791670 | − | 1.37121i | −0.924932 | − | 0.380131i | \(-0.875879\pi\) |
0.133263 | − | 0.991081i | \(-0.457455\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | −8.00000 | − | 13.8564i | −0.420471 | − | 0.728277i | ||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 5.00000 | + | 1.73205i | 0.262071 | + | 0.0907841i | ||||
\(365\) | −10.0000 | −0.523424 | ||||||||
\(366\) | 3.00000 | + | 5.19615i | 0.156813 | + | 0.271607i | ||||
\(367\) | −3.50000 | + | 6.06218i | −0.182699 | + | 0.316443i | −0.942799 | − | 0.333363i | \(-0.891817\pi\) |
0.760100 | + | 0.649806i | \(0.225150\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | 1.00000 | + | 1.73205i | 0.0520579 | + | 0.0901670i | ||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | −22.5000 | − | 7.79423i | −1.16814 | − | 0.404656i | ||||
\(372\) | −7.00000 | −0.362933 | ||||||||
\(373\) | −16.0000 | − | 27.7128i | −0.828449 | − | 1.43492i | −0.899255 | − | 0.437425i | \(-0.855891\pi\) |
0.0708063 | − | 0.997490i | \(-0.477443\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | −4.50000 | + | 7.79423i | −0.232379 | + | 0.402492i | ||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | −14.0000 | −0.721037 | ||||||||
\(378\) | 2.00000 | − | 1.73205i | 0.102869 | − | 0.0890871i | ||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 1.00000 | + | 1.73205i | 0.0512989 | + | 0.0888523i | ||||
\(381\) | −3.50000 | + | 6.06218i | −0.179310 | + | 0.310575i | ||||
\(382\) | −5.00000 | + | 8.66025i | −0.255822 | + | 0.443097i | ||||
\(383\) | −4.00000 | − | 6.92820i | −0.204390 | − | 0.354015i | 0.745548 | − | 0.666452i | \(-0.232188\pi\) |
−0.949938 | + | 0.312437i | \(0.898855\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 1.50000 | + | 7.79423i | 0.0764471 | + | 0.397231i | ||||
\(386\) | −23.0000 | −1.17067 | ||||||||
\(387\) | 3.00000 | + | 5.19615i | 0.152499 | + | 0.264135i | ||||
\(388\) | −2.50000 | + | 4.33013i | −0.126918 | + | 0.219829i | ||||
\(389\) | −19.0000 | + | 32.9090i | −0.963338 | + | 1.66855i | −0.249323 | + | 0.968420i | \(0.580208\pi\) |
−0.714015 | + | 0.700130i | \(0.753125\pi\) | |||||||
\(390\) | 1.00000 | + | 1.73205i | 0.0506370 | + | 0.0877058i | ||||
\(391\) | −2.00000 | −0.101144 | ||||||||
\(392\) | −6.50000 | + | 2.59808i | −0.328300 | + | 0.131223i | ||||
\(393\) | −7.00000 | −0.353103 | ||||||||
\(394\) | −7.00000 | − | 12.1244i | −0.352655 | − | 0.610816i | ||||
\(395\) | 7.50000 | − | 12.9904i | 0.377366 | − | 0.653617i | ||||
\(396\) | 1.50000 | − | 2.59808i | 0.0753778 | − | 0.130558i | ||||
\(397\) | 19.0000 | + | 32.9090i | 0.953583 | + | 1.65165i | 0.737579 | + | 0.675261i | \(0.235969\pi\) |
0.216004 | + | 0.976392i | \(0.430698\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | −1.00000 | − | 5.19615i | −0.0500626 | − | 0.260133i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −2.00000 | − | 3.46410i | −0.0998752 | − | 0.172989i | 0.811758 | − | 0.583994i | \(-0.198511\pi\) |
−0.911633 | + | 0.411005i | \(0.865178\pi\) | |||||||
\(402\) | 5.00000 | − | 8.66025i | 0.249377 | − | 0.431934i | ||||
\(403\) | −7.00000 | + | 12.1244i | −0.348695 | + | 0.603957i | ||||
\(404\) | 5.00000 | + | 8.66025i | 0.248759 | + | 0.430864i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 14.0000 | − | 12.1244i | 0.694808 | − | 0.601722i | ||||
\(407\) | 6.00000 | 0.297409 | ||||||||
\(408\) | −1.00000 | − | 1.73205i | −0.0495074 | − | 0.0857493i | ||||
\(409\) | 14.5000 | − | 25.1147i | 0.716979 | − | 1.24184i | −0.245212 | − | 0.969469i | \(-0.578858\pi\) |
0.962191 | − | 0.272374i | \(-0.0878089\pi\) | |||||||
\(410\) | 1.00000 | − | 1.73205i | 0.0493865 | − | 0.0855399i | ||||
\(411\) | −3.00000 | − | 5.19615i | −0.147979 | − | 0.256307i | ||||
\(412\) | −8.00000 | −0.394132 | ||||||||
\(413\) | −22.5000 | − | 7.79423i | −1.10715 | − | 0.383529i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −0.500000 | − | 0.866025i | −0.0245440 | − | 0.0425115i | ||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 7.00000 | − | 12.1244i | 0.342791 | − | 0.593732i | ||||
\(418\) | −3.00000 | − | 5.19615i | −0.146735 | − | 0.254152i | ||||
\(419\) | −36.0000 | −1.75872 | −0.879358 | − | 0.476162i | \(-0.842028\pi\) | ||||
−0.879358 | + | 0.476162i | \(0.842028\pi\) | |||||||
\(420\) | −2.50000 | − | 0.866025i | −0.121988 | − | 0.0422577i | ||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | −3.00000 | − | 5.19615i | −0.146038 | − | 0.252945i | ||||
\(423\) | −3.00000 | + | 5.19615i | −0.145865 | + | 0.252646i | ||||
\(424\) | 4.50000 | − | 7.79423i | 0.218539 | − | 0.378521i | ||||
\(425\) | −4.00000 | − | 6.92820i | −0.194029 | − | 0.336067i | ||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | −12.0000 | + | 10.3923i | −0.580721 | + | 0.502919i | ||||
\(428\) | 3.00000 | 0.145010 | ||||||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | 3.00000 | − | 5.19615i | 0.144673 | − | 0.250581i | ||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 38.0000 | 1.82616 | 0.913082 | − | 0.407777i | \(-0.133696\pi\) | ||||
0.913082 | + | 0.407777i | \(0.133696\pi\) | |||||||
\(434\) | −3.50000 | − | 18.1865i | −0.168005 | − | 0.872982i | ||||
\(435\) | 7.00000 | 0.335624 | ||||||||
\(436\) | −5.00000 | − | 8.66025i | −0.239457 | − | 0.414751i | ||||
\(437\) | 1.00000 | − | 1.73205i | 0.0478365 | − | 0.0828552i | ||||
\(438\) | −5.00000 | + | 8.66025i | −0.238909 | + | 0.413803i | ||||
\(439\) | −17.5000 | − | 30.3109i | −0.835229 | − | 1.44666i | −0.893843 | − | 0.448379i | \(-0.852001\pi\) |
0.0586141 | − | 0.998281i | \(-0.481332\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | −4.00000 | −0.190261 | ||||||||
\(443\) | 14.5000 | + | 25.1147i | 0.688916 | + | 1.19324i | 0.972189 | + | 0.234198i | \(0.0752464\pi\) |
−0.283273 | + | 0.959039i | \(0.591420\pi\) | |||||||
\(444\) | −1.00000 | + | 1.73205i | −0.0474579 | + | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.50000 | − | 11.2583i | −0.307784 | − | 0.533097i | ||||
\(447\) | 22.0000 | 1.04056 | ||||||||
\(448\) | −0.500000 | − | 2.59808i | −0.0236228 | − | 0.122748i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 2.00000 | + | 3.46410i | 0.0942809 | + | 0.163299i | ||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | −5.00000 | + | 8.66025i | −0.235180 | + | 0.407344i | ||||
\(453\) | −2.50000 | − | 4.33013i | −0.117460 | − | 0.203447i | ||||
\(454\) | −9.00000 | −0.422391 | ||||||||
\(455\) | −4.00000 | + | 3.46410i | −0.187523 | + | 0.162400i | ||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | −0.500000 | − | 0.866025i | −0.0233890 | − | 0.0405110i | 0.854094 | − | 0.520119i | \(-0.174112\pi\) |
−0.877483 | + | 0.479608i | \(0.840779\pi\) | |||||||
\(458\) | −11.0000 | + | 19.0526i | −0.513996 | + | 0.890268i | ||||
\(459\) | −1.00000 | + | 1.73205i | −0.0466760 | + | 0.0808452i | ||||
\(460\) | −0.500000 | − | 0.866025i | −0.0233126 | − | 0.0403786i | ||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 7.50000 | + | 2.59808i | 0.348932 | + | 0.120873i | ||||
\(463\) | −8.00000 | −0.371792 | −0.185896 | − | 0.982569i | \(-0.559519\pi\) | ||||
−0.185896 | + | 0.982569i | \(0.559519\pi\) | |||||||
\(464\) | 3.50000 | + | 6.06218i | 0.162483 | + | 0.281430i | ||||
\(465\) | 3.50000 | − | 6.06218i | 0.162309 | − | 0.281127i | ||||
\(466\) | 3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | ||||
\(467\) | −2.00000 | − | 3.46410i | −0.0925490 | − | 0.160300i | 0.816034 | − | 0.578004i | \(-0.196168\pi\) |
−0.908583 | + | 0.417704i | \(0.862835\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | 25.0000 | + | 8.66025i | 1.15439 | + | 0.399893i | ||||
\(470\) | 6.00000 | 0.276759 | ||||||||
\(471\) | 3.00000 | + | 5.19615i | 0.138233 | + | 0.239426i | ||||
\(472\) | 4.50000 | − | 7.79423i | 0.207129 | − | 0.358758i | ||||
\(473\) | −9.00000 | + | 15.5885i | −0.413820 | + | 0.716758i | ||||
\(474\) | −7.50000 | − | 12.9904i | −0.344486 | − | 0.596668i | ||||
\(475\) | 8.00000 | 0.367065 | ||||||||
\(476\) | 4.00000 | − | 3.46410i | 0.183340 | − | 0.158777i | ||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 6.00000 | + | 10.3923i | 0.274434 | + | 0.475333i | ||||
\(479\) | −14.0000 | + | 24.2487i | −0.639676 | + | 1.10795i | 0.345827 | + | 0.938298i | \(0.387598\pi\) |
−0.985504 | + | 0.169654i | \(0.945735\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 2.00000 | + | 3.46410i | 0.0911922 | + | 0.157949i | ||||
\(482\) | −27.0000 | −1.22982 | ||||||||
\(483\) | 0.500000 | + | 2.59808i | 0.0227508 | + | 0.118217i | ||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | −2.50000 | − | 4.33013i | −0.113519 | − | 0.196621i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 7.50000 | − | 12.9904i | 0.339857 | − | 0.588650i | −0.644548 | − | 0.764564i | \(-0.722955\pi\) |
0.984406 | + | 0.175913i | \(0.0562878\pi\) | |||||||
\(488\) | −3.00000 | − | 5.19615i | −0.135804 | − | 0.235219i | ||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 1.00000 | − | 6.92820i | 0.0451754 | − | 0.312984i | ||||
\(491\) | 19.0000 | 0.857458 | 0.428729 | − | 0.903433i | \(-0.358962\pi\) | ||||
0.428729 | + | 0.903433i | \(0.358962\pi\) | |||||||
\(492\) | −1.00000 | − | 1.73205i | −0.0450835 | − | 0.0780869i | ||||
\(493\) | −7.00000 | + | 12.1244i | −0.315264 | + | 0.546054i | ||||
\(494\) | 2.00000 | − | 3.46410i | 0.0899843 | − | 0.155857i | ||||
\(495\) | 1.50000 | + | 2.59808i | 0.0674200 | + | 0.116775i | ||||
\(496\) | 7.00000 | 0.314309 | ||||||||
\(497\) | 4.00000 | + | 20.7846i | 0.179425 | + | 0.932317i | ||||
\(498\) | −1.00000 | −0.0448111 | ||||||||
\(499\) | −3.00000 | − | 5.19615i | −0.134298 | − | 0.232612i | 0.791031 | − | 0.611776i | \(-0.209545\pi\) |
−0.925329 | + | 0.379165i | \(0.876211\pi\) | |||||||
\(500\) | 4.50000 | − | 7.79423i | 0.201246 | − | 0.348569i | ||||
\(501\) | 3.00000 | − | 5.19615i | 0.134030 | − | 0.232147i | ||||
\(502\) | 1.50000 | + | 2.59808i | 0.0669483 | + | 0.115958i | ||||
\(503\) | −28.0000 | −1.24846 | −0.624229 | − | 0.781241i | \(-0.714587\pi\) | ||||
−0.624229 | + | 0.781241i | \(0.714587\pi\) | |||||||
\(504\) | −2.00000 | + | 1.73205i | −0.0890871 | + | 0.0771517i | ||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 1.50000 | + | 2.59808i | 0.0666831 | + | 0.115499i | ||||
\(507\) | −4.50000 | + | 7.79423i | −0.199852 | + | 0.346154i | ||||
\(508\) | 3.50000 | − | 6.06218i | 0.155287 | − | 0.268966i | ||||
\(509\) | −8.50000 | − | 14.7224i | −0.376756 | − | 0.652560i | 0.613832 | − | 0.789436i | \(-0.289627\pi\) |
−0.990588 | + | 0.136876i | \(0.956294\pi\) | |||||||
\(510\) | 2.00000 | 0.0885615 | ||||||||
\(511\) | −25.0000 | − | 8.66025i | −1.10593 | − | 0.383107i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | − | 1.73205i | −0.0441511 | − | 0.0764719i | ||||
\(514\) | 2.00000 | − | 3.46410i | 0.0882162 | − | 0.152795i | ||||
\(515\) | 4.00000 | − | 6.92820i | 0.176261 | − | 0.305293i | ||||
\(516\) | −3.00000 | − | 5.19615i | −0.132068 | − | 0.228748i | ||||
\(517\) | −18.0000 | −0.791639 | ||||||||
\(518\) | −5.00000 | − | 1.73205i | −0.219687 | − | 0.0761019i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | −1.00000 | − | 1.73205i | −0.0438529 | − | 0.0759555i | ||||
\(521\) | 9.00000 | − | 15.5885i | 0.394297 | − | 0.682943i | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 3.50000 | − | 6.06218i | 0.153191 | − | 0.265334i | ||||
\(523\) | 6.00000 | + | 10.3923i | 0.262362 | + | 0.454424i | 0.966869 | − | 0.255273i | \(-0.0821653\pi\) |
−0.704507 | + | 0.709697i | \(0.748832\pi\) | |||||||
\(524\) | 7.00000 | 0.305796 | ||||||||
\(525\) | −8.00000 | + | 6.92820i | −0.349149 | + | 0.302372i | ||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | 7.00000 | + | 12.1244i | 0.304925 | + | 0.528145i | ||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | −9.00000 | −0.390567 | ||||||||
\(532\) | 1.00000 | + | 5.19615i | 0.0433555 | + | 0.225282i | ||||
\(533\) | −4.00000 | −0.173259 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.50000 | + | 2.59808i | −0.0648507 | + | 0.112325i | ||||
\(536\) | −5.00000 | + | 8.66025i | −0.215967 | + | 0.374066i | ||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | −27.0000 | −1.16405 | ||||||||
\(539\) | −3.00000 | + | 20.7846i | −0.129219 | + | 0.895257i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 4.00000 | + | 6.92820i | 0.171973 | + | 0.297867i | 0.939110 | − | 0.343617i | \(-0.111652\pi\) |
−0.767136 | + | 0.641484i | \(0.778319\pi\) | |||||||
\(542\) | 4.50000 | − | 7.79423i | 0.193292 | − | 0.334791i | ||||
\(543\) | 8.00000 | − | 13.8564i | 0.343313 | − | 0.594635i | ||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | 10.0000 | 0.428353 | ||||||||
\(546\) | 1.00000 | + | 5.19615i | 0.0427960 | + | 0.222375i | ||||
\(547\) | −38.0000 | −1.62476 | −0.812381 | − | 0.583127i | \(-0.801829\pi\) | ||||
−0.812381 | + | 0.583127i | \(0.801829\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | −3.00000 | + | 5.19615i | −0.128037 | + | 0.221766i | ||||
\(550\) | −6.00000 | + | 10.3923i | −0.255841 | + | 0.443129i | ||||
\(551\) | −7.00000 | − | 12.1244i | −0.298210 | − | 0.516515i | ||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 30.0000 | − | 25.9808i | 1.27573 | − | 1.10481i | ||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | −1.00000 | − | 1.73205i | −0.0424476 | − | 0.0735215i | ||||
\(556\) | −7.00000 | + | 12.1244i | −0.296866 | + | 0.514187i | ||||
\(557\) | −16.5000 | + | 28.5788i | −0.699127 | + | 1.21092i | 0.269642 | + | 0.962961i | \(0.413095\pi\) |
−0.968769 | + | 0.247964i | \(0.920239\pi\) | |||||||
\(558\) | −3.50000 | − | 6.06218i | −0.148167 | − | 0.256632i | ||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 2.50000 | + | 0.866025i | 0.105644 | + | 0.0365963i | ||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 2.00000 | + | 3.46410i | 0.0843649 | + | 0.146124i | ||||
\(563\) | 1.50000 | − | 2.59808i | 0.0632175 | − | 0.109496i | −0.832684 | − | 0.553748i | \(-0.813197\pi\) |
0.895902 | + | 0.444252i | \(0.146530\pi\) | |||||||
\(564\) | 3.00000 | − | 5.19615i | 0.126323 | − | 0.218797i | ||||
\(565\) | −5.00000 | − | 8.66025i | −0.210352 | − | 0.364340i | ||||
\(566\) | 6.00000 | 0.252199 | ||||||||
\(567\) | 2.50000 | + | 0.866025i | 0.104990 | + | 0.0363696i | ||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | 18.0000 | + | 31.1769i | 0.754599 | + | 1.30700i | 0.945573 | + | 0.325409i | \(0.105502\pi\) |
−0.190974 | + | 0.981595i | \(0.561165\pi\) | |||||||
\(570\) | −1.00000 | + | 1.73205i | −0.0418854 | + | 0.0725476i | ||||
\(571\) | −10.0000 | + | 17.3205i | −0.418487 | + | 0.724841i | −0.995788 | − | 0.0916910i | \(-0.970773\pi\) |
0.577301 | + | 0.816532i | \(0.304106\pi\) | |||||||
\(572\) | 3.00000 | + | 5.19615i | 0.125436 | + | 0.217262i | ||||
\(573\) | −10.0000 | −0.417756 | ||||||||
\(574\) | 4.00000 | − | 3.46410i | 0.166957 | − | 0.144589i | ||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 16.5000 | − | 28.5788i | 0.686904 | − | 1.18975i | −0.285930 | − | 0.958250i | \(-0.592303\pi\) |
0.972834 | − | 0.231502i | \(-0.0743641\pi\) | |||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | −11.5000 | − | 19.9186i | −0.477924 | − | 0.827788i | ||||
\(580\) | −7.00000 | −0.290659 | ||||||||
\(581\) | −0.500000 | − | 2.59808i | −0.0207435 | − | 0.107786i | ||||
\(582\) | −5.00000 | −0.207257 | ||||||||
\(583\) | −13.5000 | − | 23.3827i | −0.559113 | − | 0.968412i | ||||
\(584\) | 5.00000 | − | 8.66025i | 0.206901 | − | 0.358364i | ||||
\(585\) | −1.00000 | + | 1.73205i | −0.0413449 | + | 0.0716115i | ||||
\(586\) | −9.50000 | − | 16.4545i | −0.392441 | − | 0.679728i | ||||
\(587\) | −3.00000 | −0.123823 | −0.0619116 | − | 0.998082i | \(-0.519720\pi\) | ||||
−0.0619116 | + | 0.998082i | \(0.519720\pi\) | |||||||
\(588\) | −5.50000 | − | 4.33013i | −0.226816 | − | 0.178571i | ||||
\(589\) | −14.0000 | −0.576860 | ||||||||
\(590\) | 4.50000 | + | 7.79423i | 0.185262 | + | 0.320883i | ||||
\(591\) | 7.00000 | − | 12.1244i | 0.287942 | − | 0.498729i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | 6.00000 | + | 10.3923i | 0.246390 | + | 0.426761i | 0.962522 | − | 0.271205i | \(-0.0874221\pi\) |
−0.716131 | + | 0.697966i | \(0.754089\pi\) | |||||||
\(594\) | 3.00000 | 0.123091 | ||||||||
\(595\) | 1.00000 | + | 5.19615i | 0.0409960 | + | 0.213021i | ||||
\(596\) | −22.0000 | −0.901155 | ||||||||
\(597\) | −2.00000 | − | 3.46410i | −0.0818546 | − | 0.141776i | ||||
\(598\) | −1.00000 | + | 1.73205i | −0.0408930 | + | 0.0708288i | ||||
\(599\) | −12.0000 | + | 20.7846i | −0.490307 | + | 0.849236i | −0.999938 | − | 0.0111569i | \(-0.996449\pi\) |
0.509631 | + | 0.860393i | \(0.329782\pi\) | |||||||
\(600\) | −2.00000 | − | 3.46410i | −0.0816497 | − | 0.141421i | ||||
\(601\) | 23.0000 | 0.938190 | 0.469095 | − | 0.883148i | \(-0.344580\pi\) | ||||
0.469095 | + | 0.883148i | \(0.344580\pi\) | |||||||
\(602\) | 12.0000 | − | 10.3923i | 0.489083 | − | 0.423559i | ||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | 2.50000 | + | 4.33013i | 0.101724 | + | 0.176190i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | −5.00000 | + | 8.66025i | −0.203111 | + | 0.351799i | ||||
\(607\) | −10.5000 | − | 18.1865i | −0.426182 | − | 0.738169i | 0.570348 | − | 0.821403i | \(-0.306808\pi\) |
−0.996530 | + | 0.0832344i | \(0.973475\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 17.5000 | + | 6.06218i | 0.709136 | + | 0.245652i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | −6.00000 | − | 10.3923i | −0.242734 | − | 0.420428i | ||||
\(612\) | 1.00000 | − | 1.73205i | 0.0404226 | − | 0.0700140i | ||||
\(613\) | −18.0000 | + | 31.1769i | −0.727013 | + | 1.25922i | 0.231127 | + | 0.972924i | \(0.425759\pi\) |
−0.958140 | + | 0.286300i | \(0.907575\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | −7.50000 | − | 2.59808i | −0.302184 | − | 0.104679i | ||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | −4.00000 | − | 6.92820i | −0.160904 | − | 0.278693i | ||||
\(619\) | 8.00000 | − | 13.8564i | 0.321547 | − | 0.556936i | −0.659260 | − | 0.751915i | \(-0.729130\pi\) |
0.980807 | + | 0.194979i | \(0.0624638\pi\) | |||||||
\(620\) | −3.50000 | + | 6.06218i | −0.140563 | + | 0.243463i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | −2.00000 | −0.0801927 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.00000 | −0.0800641 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 12.5000 | − | 21.6506i | 0.499600 | − | 0.865333i | ||||
\(627\) | 3.00000 | − | 5.19615i | 0.119808 | − | 0.207514i | ||||
\(628\) | −3.00000 | − | 5.19615i | −0.119713 | − | 0.207349i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | −0.500000 | − | 2.59808i | −0.0199205 | − | 0.103510i | ||||
\(631\) | 31.0000 | 1.23409 | 0.617045 | − | 0.786928i | \(-0.288330\pi\) | ||||
0.617045 | + | 0.786928i | \(0.288330\pi\) | |||||||
\(632\) | 7.50000 | + | 12.9904i | 0.298334 | + | 0.516730i | ||||
\(633\) | 3.00000 | − | 5.19615i | 0.119239 | − | 0.206529i | ||||
\(634\) | 15.5000 | − | 26.8468i | 0.615584 | − | 1.06622i | ||||
\(635\) | 3.50000 | + | 6.06218i | 0.138893 | + | 0.240570i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | −13.0000 | + | 5.19615i | −0.515079 | + | 0.205879i | ||||
\(638\) | 21.0000 | 0.831398 | ||||||||
\(639\) | 4.00000 | + | 6.92820i | 0.158238 | + | 0.274075i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 6.00000 | − | 10.3923i | 0.236986 | − | 0.410471i | −0.722862 | − | 0.690992i | \(-0.757174\pi\) |
0.959848 | + | 0.280521i | \(0.0905072\pi\) | |||||||
\(642\) | 1.50000 | + | 2.59808i | 0.0592003 | + | 0.102538i | ||||
\(643\) | 4.00000 | 0.157745 | 0.0788723 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788723 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(644\) | −0.500000 | − | 2.59808i | −0.0197028 | − | 0.102379i | ||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | −2.00000 | − | 3.46410i | −0.0786889 | − | 0.136293i | ||||
\(647\) | −19.0000 | + | 32.9090i | −0.746967 | + | 1.29378i | 0.202303 | + | 0.979323i | \(0.435157\pi\) |
−0.949270 | + | 0.314462i | \(0.898176\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −13.5000 | − | 23.3827i | −0.529921 | − | 0.917851i | ||||
\(650\) | −8.00000 | −0.313786 | ||||||||
\(651\) | 14.0000 | − | 12.1244i | 0.548703 | − | 0.475191i | ||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | −5.50000 | − | 9.52628i | −0.215232 | − | 0.372792i | 0.738113 | − | 0.674678i | \(-0.235717\pi\) |
−0.953344 | + | 0.301885i | \(0.902384\pi\) | |||||||
\(654\) | 5.00000 | − | 8.66025i | 0.195515 | − | 0.338643i | ||||
\(655\) | −3.50000 | + | 6.06218i | −0.136756 | + | 0.236869i | ||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | 15.0000 | + | 5.19615i | 0.584761 | + | 0.202567i | ||||
\(659\) | 28.0000 | 1.09073 | 0.545363 | − | 0.838200i | \(-0.316392\pi\) | ||||
0.545363 | + | 0.838200i | \(0.316392\pi\) | |||||||
\(660\) | −1.50000 | − | 2.59808i | −0.0583874 | − | 0.101130i | ||||
\(661\) | −19.0000 | + | 32.9090i | −0.739014 | + | 1.28001i | 0.213925 | + | 0.976850i | \(0.431375\pi\) |
−0.952940 | + | 0.303160i | \(0.901958\pi\) | |||||||
\(662\) | −5.00000 | + | 8.66025i | −0.194331 | + | 0.336590i | ||||
\(663\) | −2.00000 | − | 3.46410i | −0.0776736 | − | 0.134535i | ||||
\(664\) | 1.00000 | 0.0388075 | ||||||||
\(665\) | −5.00000 | − | 1.73205i | −0.193892 | − | 0.0671660i | ||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | 3.50000 | + | 6.06218i | 0.135521 | + | 0.234728i | ||||
\(668\) | −3.00000 | + | 5.19615i | −0.116073 | + | 0.201045i | ||||
\(669\) | 6.50000 | − | 11.2583i | 0.251305 | − | 0.435272i | ||||
\(670\) | −5.00000 | − | 8.66025i | −0.193167 | − | 0.334575i | ||||
\(671\) | −18.0000 | −0.694882 | ||||||||
\(672\) | 2.00000 | − | 1.73205i | 0.0771517 | − | 0.0668153i | ||||
\(673\) | 25.0000 | 0.963679 | 0.481840 | − | 0.876259i | \(-0.339969\pi\) | ||||
0.481840 | + | 0.876259i | \(0.339969\pi\) | |||||||
\(674\) | 4.50000 | + | 7.79423i | 0.173334 | + | 0.300222i | ||||
\(675\) | −2.00000 | + | 3.46410i | −0.0769800 | + | 0.133333i | ||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | 17.5000 | + | 30.3109i | 0.672580 | + | 1.16494i | 0.977170 | + | 0.212459i | \(0.0681471\pi\) |
−0.304590 | + | 0.952483i | \(0.598520\pi\) | |||||||
\(678\) | −10.0000 | −0.384048 | ||||||||
\(679\) | −2.50000 | − | 12.9904i | −0.0959412 | − | 0.498525i | ||||
\(680\) | −2.00000 | −0.0766965 | ||||||||
\(681\) | −4.50000 | − | 7.79423i | −0.172440 | − | 0.298675i | ||||
\(682\) | 10.5000 | − | 18.1865i | 0.402066 | − | 0.696398i | ||||
\(683\) | 11.5000 | − | 19.9186i | 0.440035 | − | 0.762163i | −0.557656 | − | 0.830072i | \(-0.688299\pi\) |
0.997692 | + | 0.0679085i | \(0.0216326\pi\) | |||||||
\(684\) | 1.00000 | + | 1.73205i | 0.0382360 | + | 0.0662266i | ||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | −22.0000 | −0.839352 | ||||||||
\(688\) | 3.00000 | + | 5.19615i | 0.114374 | + | 0.198101i | ||||
\(689\) | 9.00000 | − | 15.5885i | 0.342873 | − | 0.593873i | ||||
\(690\) | 0.500000 | − | 0.866025i | 0.0190347 | − | 0.0329690i | ||||
\(691\) | 11.0000 | + | 19.0526i | 0.418460 | + | 0.724793i | 0.995785 | − | 0.0917209i | \(-0.0292368\pi\) |
−0.577325 | + | 0.816514i | \(0.695903\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 1.50000 | + | 7.79423i | 0.0569803 | + | 0.296078i | ||||
\(694\) | 36.0000 | 1.36654 | ||||||||
\(695\) | −7.00000 | − | 12.1244i | −0.265525 | − | 0.459903i | ||||
\(696\) | −3.50000 | + | 6.06218i | −0.132667 | + | 0.229786i | ||||
\(697\) | −2.00000 | + | 3.46410i | −0.0757554 | + | 0.131212i | ||||
\(698\) | −8.00000 | − | 13.8564i | −0.302804 | − | 0.524473i | ||||
\(699\) | 6.00000 | 0.226941 | ||||||||
\(700\) | 8.00000 | − | 6.92820i | 0.302372 | − | 0.261861i | ||||
\(701\) | −1.00000 | −0.0377695 | −0.0188847 | − | 0.999822i | \(-0.506012\pi\) | ||||
−0.0188847 | + | 0.999822i | \(0.506012\pi\) | |||||||
\(702\) | 1.00000 | + | 1.73205i | 0.0377426 | + | 0.0653720i | ||||
\(703\) | −2.00000 | + | 3.46410i | −0.0754314 | + | 0.130651i | ||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 3.00000 | + | 5.19615i | 0.112987 | + | 0.195698i | ||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | −25.0000 | − | 8.66025i | −0.940222 | − | 0.325702i | ||||
\(708\) | 9.00000 | 0.338241 | ||||||||
\(709\) | 14.0000 | + | 24.2487i | 0.525781 | + | 0.910679i | 0.999549 | + | 0.0300298i | \(0.00956021\pi\) |
−0.473768 | + | 0.880650i | \(0.657106\pi\) | |||||||
\(710\) | 4.00000 | − | 6.92820i | 0.150117 | − | 0.260011i | ||||
\(711\) | 7.50000 | − | 12.9904i | 0.281272 | − | 0.487177i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.00000 | 0.262152 | ||||||||
\(714\) | 5.00000 | + | 1.73205i | 0.187120 | + | 0.0648204i | ||||
\(715\) | −6.00000 | −0.224387 | ||||||||
\(716\) | 6.00000 | + | 10.3923i | 0.224231 | + | 0.388379i | ||||
\(717\) | −6.00000 | + | 10.3923i | −0.224074 | + | 0.388108i | ||||
\(718\) | −15.0000 | + | 25.9808i | −0.559795 | + | 0.969593i | ||||
\(719\) | 15.0000 | + | 25.9808i | 0.559406 | + | 0.968919i | 0.997546 | + | 0.0700124i | \(0.0223039\pi\) |
−0.438141 | + | 0.898906i | \(0.644363\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | 16.0000 | − | 13.8564i | 0.595871 | − | 0.516040i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | −13.5000 | − | 23.3827i | −0.502070 | − | 0.869611i | ||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | −14.0000 | + | 24.2487i | −0.519947 | + | 0.900575i | ||||
\(726\) | −1.00000 | − | 1.73205i | −0.0371135 | − | 0.0642824i | ||||
\(727\) | 5.00000 | 0.185440 | 0.0927199 | − | 0.995692i | \(-0.470444\pi\) | ||||
0.0927199 | + | 0.995692i | \(0.470444\pi\) | |||||||
\(728\) | −1.00000 | − | 5.19615i | −0.0370625 | − | 0.192582i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 5.00000 | + | 8.66025i | 0.185058 | + | 0.320530i | ||||
\(731\) | −6.00000 | + | 10.3923i | −0.221918 | + | 0.384373i | ||||
\(732\) | 3.00000 | − | 5.19615i | 0.110883 | − | 0.192055i | ||||
\(733\) | 14.0000 | + | 24.2487i | 0.517102 | + | 0.895647i | 0.999803 | + | 0.0198613i | \(0.00632248\pi\) |
−0.482701 | + | 0.875785i | \(0.660344\pi\) | |||||||
\(734\) | 7.00000 | 0.258375 | ||||||||
\(735\) | 6.50000 | − | 2.59808i | 0.239756 | − | 0.0958315i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 15.0000 | + | 25.9808i | 0.552532 | + | 0.957014i | ||||
\(738\) | 1.00000 | − | 1.73205i | 0.0368105 | − | 0.0637577i | ||||
\(739\) | 7.00000 | − | 12.1244i | 0.257499 | − | 0.446002i | −0.708072 | − | 0.706140i | \(-0.750435\pi\) |
0.965571 | + | 0.260138i | \(0.0837682\pi\) | |||||||
\(740\) | 1.00000 | + | 1.73205i | 0.0367607 | + | 0.0636715i | ||||
\(741\) | 4.00000 | 0.146944 | ||||||||
\(742\) | 4.50000 | + | 23.3827i | 0.165200 | + | 0.858405i | ||||
\(743\) | 48.0000 | 1.76095 | 0.880475 | − | 0.474093i | \(-0.157224\pi\) | ||||
0.880475 | + | 0.474093i | \(0.157224\pi\) | |||||||
\(744\) | 3.50000 | + | 6.06218i | 0.128316 | + | 0.222250i | ||||
\(745\) | 11.0000 | − | 19.0526i | 0.403009 | − | 0.698032i | ||||
\(746\) | −16.0000 | + | 27.7128i | −0.585802 | + | 1.01464i | ||||
\(747\) | −0.500000 | − | 0.866025i | −0.0182940 | − | 0.0316862i | ||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | −6.00000 | + | 5.19615i | −0.219235 | + | 0.189863i | ||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | −5.50000 | − | 9.52628i | −0.200698 | − | 0.347619i | 0.748056 | − | 0.663636i | \(-0.230988\pi\) |
−0.948753 | + | 0.316017i | \(0.897654\pi\) | |||||||
\(752\) | −3.00000 | + | 5.19615i | −0.109399 | + | 0.189484i | ||||
\(753\) | −1.50000 | + | 2.59808i | −0.0546630 | + | 0.0946792i | ||||
\(754\) | 7.00000 | + | 12.1244i | 0.254925 | + | 0.441543i | ||||
\(755\) | −5.00000 | −0.181969 | ||||||||
\(756\) | −2.50000 | − | 0.866025i | −0.0909241 | − | 0.0314970i | ||||
\(757\) | 8.00000 | 0.290765 | 0.145382 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145382 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(758\) | 2.00000 | + | 3.46410i | 0.0726433 | + | 0.125822i | ||||
\(759\) | −1.50000 | + | 2.59808i | −0.0544466 | + | 0.0943042i | ||||
\(760\) | 1.00000 | − | 1.73205i | 0.0362738 | − | 0.0628281i | ||||
\(761\) | −9.00000 | − | 15.5885i | −0.326250 | − | 0.565081i | 0.655515 | − | 0.755182i | \(-0.272452\pi\) |
−0.981764 | + | 0.190101i | \(0.939118\pi\) | |||||||
\(762\) | 7.00000 | 0.253583 | ||||||||
\(763\) | 25.0000 | + | 8.66025i | 0.905061 | + | 0.313522i | ||||
\(764\) | 10.0000 | 0.361787 | ||||||||
\(765\) | 1.00000 | + | 1.73205i | 0.0361551 | + | 0.0626224i | ||||
\(766\) | −4.00000 | + | 6.92820i | −0.144526 | + | 0.250326i | ||||
\(767\) | 9.00000 | − | 15.5885i | 0.324971 | − | 0.562867i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 15.0000 | 0.540914 | 0.270457 | − | 0.962732i | \(-0.412825\pi\) | ||||
0.270457 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(770\) | 6.00000 | − | 5.19615i | 0.216225 | − | 0.187256i | ||||
\(771\) | 4.00000 | 0.144056 | ||||||||
\(772\) | 11.5000 | + | 19.9186i | 0.413894 | + | 0.716886i | ||||
\(773\) | 7.00000 | − | 12.1244i | 0.251773 | − | 0.436083i | −0.712241 | − | 0.701935i | \(-0.752320\pi\) |
0.964014 | + | 0.265852i | \(0.0856532\pi\) | |||||||
\(774\) | 3.00000 | − | 5.19615i | 0.107833 | − | 0.186772i | ||||
\(775\) | 14.0000 | + | 24.2487i | 0.502895 | + | 0.871039i | ||||
\(776\) | 5.00000 | 0.179490 | ||||||||
\(777\) | −1.00000 | − | 5.19615i | −0.0358748 | − | 0.186411i | ||||
\(778\) | 38.0000 | 1.36237 | ||||||||
\(779\) | −2.00000 | − | 3.46410i | −0.0716574 | − | 0.124114i | ||||
\(780\) | 1.00000 | − | 1.73205i | 0.0358057 | − | 0.0620174i | ||||
\(781\) | −12.0000 | + | 20.7846i | −0.429394 | + | 0.743732i | ||||
\(782\) | 1.00000 | + | 1.73205i | 0.0357599 | + | 0.0619380i | ||||
\(783\) | 7.00000 | 0.250160 | ||||||||
\(784\) | 5.50000 | + | 4.33013i | 0.196429 | + | 0.154647i | ||||
\(785\) | 6.00000 | 0.214149 | ||||||||
\(786\) | 3.50000 | + | 6.06218i | 0.124841 | + | 0.216231i | ||||
\(787\) | 7.00000 | − | 12.1244i | 0.249523 | − | 0.432187i | −0.713871 | − | 0.700278i | \(-0.753059\pi\) |
0.963394 | + | 0.268091i | \(0.0863928\pi\) | |||||||
\(788\) | −7.00000 | + | 12.1244i | −0.249365 | + | 0.431912i | ||||
\(789\) | −1.00000 | − | 1.73205i | −0.0356009 | − | 0.0616626i | ||||
\(790\) | −15.0000 | −0.533676 | ||||||||
\(791\) | −5.00000 | − | 25.9808i | −0.177780 | − | 0.923770i | ||||
\(792\) | −3.00000 | −0.106600 | ||||||||
\(793\) | −6.00000 | − | 10.3923i | −0.213066 | − | 0.369042i | ||||
\(794\) | 19.0000 | − | 32.9090i | 0.674285 | − | 1.16790i | ||||
\(795\) | −4.50000 | + | 7.79423i | −0.159599 | + | 0.276433i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −15.0000 | −0.531327 | −0.265664 | − | 0.964066i | \(-0.585591\pi\) | ||||
−0.265664 | + | 0.964066i | \(0.585591\pi\) | |||||||
\(798\) | −4.00000 | + | 3.46410i | −0.141598 | + | 0.122628i | ||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 2.00000 | + | 3.46410i | 0.0707107 | + | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.00000 | + | 3.46410i | −0.0706225 | + | 0.122322i | ||||
\(803\) | −15.0000 | − | 25.9808i | −0.529339 | − | 0.916841i | ||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | 2.50000 | + | 0.866025i | 0.0881134 | + | 0.0305234i | ||||
\(806\) | 14.0000 | 0.493129 | ||||||||
\(807\) | −13.5000 | − | 23.3827i | −0.475223 | − | 0.823110i | ||||
\(808\) | 5.00000 | − | 8.66025i | 0.175899 | − | 0.304667i | ||||
\(809\) | 17.0000 | − | 29.4449i | 0.597688 | − | 1.03523i | −0.395473 | − | 0.918477i | \(-0.629419\pi\) |
0.993161 | − | 0.116749i | \(-0.0372472\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 46.0000 | 1.61528 | 0.807639 | − | 0.589677i | \(-0.200745\pi\) | ||||
0.807639 | + | 0.589677i | \(0.200745\pi\) | |||||||
\(812\) | −17.5000 | − | 6.06218i | −0.614130 | − | 0.212741i | ||||
\(813\) | 9.00000 | 0.315644 | ||||||||
\(814\) | −3.00000 | − | 5.19615i | −0.105150 | − | 0.182125i | ||||
\(815\) | −1.00000 | + | 1.73205i | −0.0350285 | + | 0.0606711i | ||||
\(816\) | −1.00000 | + | 1.73205i | −0.0350070 | + | 0.0606339i | ||||
\(817\) | −6.00000 | − | 10.3923i | −0.209913 | − | 0.363581i | ||||
\(818\) | −29.0000 | −1.01396 | ||||||||
\(819\) | −4.00000 | + | 3.46410i | −0.139771 | + | 0.121046i | ||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | −8.50000 | − | 14.7224i | −0.296652 | − | 0.513816i | 0.678716 | − | 0.734401i | \(-0.262537\pi\) |
−0.975368 | + | 0.220585i | \(0.929203\pi\) | |||||||
\(822\) | −3.00000 | + | 5.19615i | −0.104637 | + | 0.181237i | ||||
\(823\) | −8.00000 | + | 13.8564i | −0.278862 | + | 0.483004i | −0.971102 | − | 0.238664i | \(-0.923291\pi\) |
0.692240 | + | 0.721668i | \(0.256624\pi\) | |||||||
\(824\) | 4.00000 | + | 6.92820i | 0.139347 | + | 0.241355i | ||||
\(825\) | −12.0000 | −0.417786 | ||||||||
\(826\) | 4.50000 | + | 23.3827i | 0.156575 | + | 0.813588i | ||||
\(827\) | 5.00000 | 0.173867 | 0.0869335 | − | 0.996214i | \(-0.472293\pi\) | ||||
0.0869335 | + | 0.996214i | \(0.472293\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | 10.0000 | − | 17.3205i | 0.347314 | − | 0.601566i | −0.638457 | − | 0.769657i | \(-0.720427\pi\) |
0.985771 | + | 0.168091i | \(0.0537604\pi\) | |||||||
\(830\) | −0.500000 | + | 0.866025i | −0.0173553 | + | 0.0300602i | ||||
\(831\) | −4.00000 | − | 6.92820i | −0.138758 | − | 0.240337i | ||||
\(832\) | 2.00000 | 0.0693375 | ||||||||
\(833\) | −2.00000 | + | 13.8564i | −0.0692959 | + | 0.480096i | ||||
\(834\) | −14.0000 | −0.484780 | ||||||||
\(835\) | −3.00000 | − | 5.19615i | −0.103819 | − | 0.179820i | ||||
\(836\) | −3.00000 | + | 5.19615i | −0.103757 | + | 0.179713i | ||||
\(837\) | 3.50000 | − | 6.06218i | 0.120978 | − | 0.209540i | ||||
\(838\) | 18.0000 | + | 31.1769i | 0.621800 | + | 1.07699i | ||||
\(839\) | −26.0000 | −0.897620 | −0.448810 | − | 0.893627i | \(-0.648152\pi\) | ||||
−0.448810 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(840\) | 0.500000 | + | 2.59808i | 0.0172516 | + | 0.0896421i | ||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | 9.00000 | + | 15.5885i | 0.310160 | + | 0.537214i | ||||
\(843\) | −2.00000 | + | 3.46410i | −0.0688837 | + | 0.119310i | ||||
\(844\) | −3.00000 | + | 5.19615i | −0.103264 | + | 0.178859i | ||||
\(845\) | 4.50000 | + | 7.79423i | 0.154805 | + | 0.268130i | ||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 4.00000 | − | 3.46410i | 0.137442 | − | 0.119028i | ||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | 3.00000 | + | 5.19615i | 0.102960 | + | 0.178331i | ||||
\(850\) | −4.00000 | + | 6.92820i | −0.137199 | + | 0.237635i | ||||
\(851\) | 1.00000 | − | 1.73205i | 0.0342796 | − | 0.0593739i | ||||
\(852\) | −4.00000 | − | 6.92820i | −0.137038 | − | 0.237356i | ||||
\(853\) | 54.0000 | 1.84892 | 0.924462 | − | 0.381273i | \(-0.124514\pi\) | ||||
0.924462 | + | 0.381273i | \(0.124514\pi\) | |||||||
\(854\) | 15.0000 | + | 5.19615i | 0.513289 | + | 0.177809i | ||||
\(855\) | −2.00000 | −0.0683986 | ||||||||
\(856\) | −1.50000 | − | 2.59808i | −0.0512689 | − | 0.0888004i | ||||
\(857\) | −8.00000 | + | 13.8564i | −0.273275 | + | 0.473326i | −0.969698 | − | 0.244305i | \(-0.921440\pi\) |
0.696424 | + | 0.717631i | \(0.254773\pi\) | |||||||
\(858\) | −3.00000 | + | 5.19615i | −0.102418 | + | 0.177394i | ||||
\(859\) | −20.0000 | − | 34.6410i | −0.682391 | − | 1.18194i | −0.974249 | − | 0.225475i | \(-0.927607\pi\) |
0.291858 | − | 0.956462i | \(-0.405727\pi\) | |||||||
\(860\) | −6.00000 | −0.204598 | ||||||||
\(861\) | 5.00000 | + | 1.73205i | 0.170400 | + | 0.0590281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 3.00000 | − | 5.19615i | 0.102003 | − | 0.176674i | ||||
\(866\) | −19.0000 | − | 32.9090i | −0.645646 | − | 1.11829i | ||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | −14.0000 | + | 12.1244i | −0.475191 | + | 0.411527i | ||||
\(869\) | 45.0000 | 1.52652 | ||||||||
\(870\) | −3.50000 | − | 6.06218i | −0.118661 | − | 0.205527i | ||||
\(871\) | −10.0000 | + | 17.3205i | −0.338837 | + | 0.586883i | ||||
\(872\) | −5.00000 | + | 8.66025i | −0.169321 | + | 0.293273i | ||||
\(873\) | −2.50000 | − | 4.33013i | −0.0846122 | − | 0.146553i | ||||
\(874\) | −2.00000 | −0.0676510 | ||||||||
\(875\) | 4.50000 | + | 23.3827i | 0.152128 | + | 0.790479i | ||||
\(876\) | 10.0000 | 0.337869 | ||||||||
\(877\) | −25.0000 | − | 43.3013i | −0.844190 | − | 1.46218i | −0.886323 | − | 0.463068i | \(-0.846749\pi\) |
0.0421327 | − | 0.999112i | \(-0.486585\pi\) | |||||||
\(878\) | −17.5000 | + | 30.3109i | −0.590596 | + | 1.02294i | ||||
\(879\) | 9.50000 | − | 16.4545i | 0.320427 | − | 0.554996i | ||||
\(880\) | 1.50000 | + | 2.59808i | 0.0505650 | + | 0.0875811i | ||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 1.00000 | − | 6.92820i | 0.0336718 | − | 0.233285i | ||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | 2.00000 | + | 3.46410i | 0.0672673 | + | 0.116510i | ||||
\(885\) | −4.50000 | + | 7.79423i | −0.151266 | + | 0.262000i | ||||
\(886\) | 14.5000 | − | 25.1147i | 0.487137 | − | 0.843746i | ||||
\(887\) | 18.0000 | + | 31.1769i | 0.604381 | + | 1.04682i | 0.992149 | + | 0.125061i | \(0.0399128\pi\) |
−0.387768 | + | 0.921757i | \(0.626754\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | 3.50000 | + | 18.1865i | 0.117386 | + | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | + | 2.59808i | 0.0502519 | + | 0.0870388i | ||||
\(892\) | −6.50000 | + | 11.2583i | −0.217636 | + | 0.376957i | ||||
\(893\) | 6.00000 | − | 10.3923i | 0.200782 | − | 0.347765i | ||||
\(894\) | −11.0000 | − | 19.0526i | −0.367895 | − | 0.637213i | ||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | −2.00000 | + | 1.73205i | −0.0668153 | + | 0.0578638i | ||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 15.0000 | + | 25.9808i | 0.500556 | + | 0.866989i | ||||
\(899\) | 24.5000 | − | 42.4352i | 0.817121 | − | 1.41529i | ||||
\(900\) | 2.00000 | − | 3.46410i | 0.0666667 | − | 0.115470i | ||||
\(901\) | −9.00000 | − | 15.5885i | −0.299833 | − | 0.519327i | ||||
\(902\) | 6.00000 | 0.199778 | ||||||||
\(903\) | 15.0000 | + | 5.19615i | 0.499169 | + | 0.172917i | ||||
\(904\) | 10.0000 | 0.332595 | ||||||||
\(905\) | −8.00000 | − | 13.8564i | −0.265929 | − | 0.460603i | ||||
\(906\) | −2.50000 | + | 4.33013i | −0.0830569 | + | 0.143859i | ||||
\(907\) | −23.0000 | + | 39.8372i | −0.763702 | + | 1.32277i | 0.177227 | + | 0.984170i | \(0.443287\pi\) |
−0.940930 | + | 0.338602i | \(0.890046\pi\) | |||||||
\(908\) | 4.50000 | + | 7.79423i | 0.149338 | + | 0.258661i | ||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 5.00000 | + | 1.73205i | 0.165748 | + | 0.0574169i | ||||
\(911\) | 22.0000 | 0.728893 | 0.364446 | − | 0.931224i | \(-0.381258\pi\) | ||||
0.364446 | + | 0.931224i | \(0.381258\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | 1.50000 | − | 2.59808i | 0.0496428 | − | 0.0859838i | ||||
\(914\) | −0.500000 | + | 0.866025i | −0.0165385 | + | 0.0286456i | ||||
\(915\) | 3.00000 | + | 5.19615i | 0.0991769 | + | 0.171780i | ||||
\(916\) | 22.0000 | 0.726900 | ||||||||
\(917\) | −14.0000 | + | 12.1244i | −0.462321 | + | 0.400381i | ||||
\(918\) | 2.00000 | 0.0660098 | ||||||||
\(919\) | −16.0000 | − | 27.7128i | −0.527791 | − | 0.914161i | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | −0.500000 | + | 0.866025i | −0.0164845 | + | 0.0285520i | ||||
\(921\) | −1.00000 | + | 1.73205i | −0.0329511 | + | 0.0570730i | ||||
\(922\) | −1.00000 | − | 1.73205i | −0.0329332 | − | 0.0570421i | ||||
\(923\) | −16.0000 | −0.526646 | ||||||||
\(924\) | −1.50000 | − | 7.79423i | −0.0493464 | − | 0.256411i | ||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 4.00000 | + | 6.92820i | 0.131448 | + | 0.227675i | ||||
\(927\) | 4.00000 | − | 6.92820i | 0.131377 | − | 0.227552i | ||||
\(928\) | 3.50000 | − | 6.06218i | 0.114893 | − | 0.199001i | ||||
\(929\) | −16.0000 | − | 27.7128i | −0.524943 | − | 0.909228i | −0.999578 | − | 0.0290452i | \(-0.990753\pi\) |
0.474635 | − | 0.880183i | \(-0.342580\pi\) | |||||||
\(930\) | −7.00000 | −0.229539 | ||||||||
\(931\) | −11.0000 | − | 8.66025i | −0.360510 | − | 0.283828i | ||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | −1.00000 | − | 1.73205i | −0.0327385 | − | 0.0567048i | ||||
\(934\) | −2.00000 | + | 3.46410i | −0.0654420 | + | 0.113349i | ||||
\(935\) | −3.00000 | + | 5.19615i | −0.0981105 | + | 0.169932i | ||||
\(936\) | −1.00000 | − | 1.73205i | −0.0326860 | − | 0.0566139i | ||||
\(937\) | 29.0000 | 0.947389 | 0.473694 | − | 0.880689i | \(-0.342920\pi\) | ||||
0.473694 | + | 0.880689i | \(0.342920\pi\) | |||||||
\(938\) | −5.00000 | − | 25.9808i | −0.163256 | − | 0.848302i | ||||
\(939\) | 25.0000 | 0.815844 | ||||||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | 7.50000 | − | 12.9904i | 0.244493 | − | 0.423474i | −0.717496 | − | 0.696563i | \(-0.754712\pi\) |
0.961989 | + | 0.273088i | \(0.0880451\pi\) | |||||||
\(942\) | 3.00000 | − | 5.19615i | 0.0977453 | − | 0.169300i | ||||
\(943\) | 1.00000 | + | 1.73205i | 0.0325645 | + | 0.0564033i | ||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 2.00000 | − | 1.73205i | 0.0650600 | − | 0.0563436i | ||||
\(946\) | 18.0000 | 0.585230 | ||||||||
\(947\) | 12.0000 | + | 20.7846i | 0.389948 | + | 0.675409i | 0.992442 | − | 0.122714i | \(-0.0391598\pi\) |
−0.602494 | + | 0.798123i | \(0.705826\pi\) | |||||||
\(948\) | −7.50000 | + | 12.9904i | −0.243589 | + | 0.421908i | ||||
\(949\) | 10.0000 | − | 17.3205i | 0.324614 | − | 0.562247i | ||||
\(950\) | −4.00000 | − | 6.92820i | −0.129777 | − | 0.224781i | ||||
\(951\) | 31.0000 | 1.00524 | ||||||||
\(952\) | −5.00000 | − | 1.73205i | −0.162051 | − | 0.0561361i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 4.50000 | + | 7.79423i | 0.145693 | + | 0.252347i | ||||
\(955\) | −5.00000 | + | 8.66025i | −0.161796 | + | 0.280239i | ||||
\(956\) | 6.00000 | − | 10.3923i | 0.194054 | − | 0.336111i | ||||
\(957\) | 10.5000 | + | 18.1865i | 0.339417 | + | 0.587887i | ||||
\(958\) | 28.0000 | 0.904639 | ||||||||
\(959\) | −15.0000 | − | 5.19615i | −0.484375 | − | 0.167793i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | 2.00000 | − | 3.46410i | 0.0644826 | − | 0.111687i | ||||
\(963\) | −1.50000 | + | 2.59808i | −0.0483368 | + | 0.0837218i | ||||
\(964\) | 13.5000 | + | 23.3827i | 0.434806 | + | 0.753106i | ||||
\(965\) | −23.0000 | −0.740396 | ||||||||
\(966\) | 2.00000 | − | 1.73205i | 0.0643489 | − | 0.0557278i | ||||
\(967\) | −13.0000 | −0.418052 | −0.209026 | − | 0.977910i | \(-0.567029\pi\) | ||||
−0.209026 | + | 0.977910i | \(0.567029\pi\) | |||||||
\(968\) | 1.00000 | + | 1.73205i | 0.0321412 | + | 0.0556702i | ||||
\(969\) | 2.00000 | − | 3.46410i | 0.0642493 | − | 0.111283i | ||||
\(970\) | −2.50000 | + | 4.33013i | −0.0802702 | + | 0.139032i | ||||
\(971\) | 8.50000 | + | 14.7224i | 0.272778 | + | 0.472465i | 0.969572 | − | 0.244806i | \(-0.0787242\pi\) |
−0.696794 | + | 0.717271i | \(0.745391\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −7.00000 | − | 36.3731i | −0.224410 | − | 1.16607i | ||||
\(974\) | −15.0000 | −0.480631 | ||||||||
\(975\) | −4.00000 | − | 6.92820i | −0.128103 | − | 0.221880i | ||||
\(976\) | −3.00000 | + | 5.19615i | −0.0960277 | + | 0.166325i | ||||
\(977\) | −15.0000 | + | 25.9808i | −0.479893 | + | 0.831198i | −0.999734 | − | 0.0230645i | \(-0.992658\pi\) |
0.519841 | + | 0.854263i | \(0.325991\pi\) | |||||||
\(978\) | 1.00000 | + | 1.73205i | 0.0319765 | + | 0.0553849i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.50000 | + | 2.59808i | −0.207635 | + | 0.0829925i | ||||
\(981\) | 10.0000 | 0.319275 | ||||||||
\(982\) | −9.50000 | − | 16.4545i | −0.303157 | − | 0.525084i | ||||
\(983\) | 25.0000 | − | 43.3013i | 0.797376 | − | 1.38110i | −0.123943 | − | 0.992289i | \(-0.539554\pi\) |
0.921319 | − | 0.388807i | \(-0.127113\pi\) | |||||||
\(984\) | −1.00000 | + | 1.73205i | −0.0318788 | + | 0.0552158i | ||||
\(985\) | −7.00000 | − | 12.1244i | −0.223039 | − | 0.386314i | ||||
\(986\) | 14.0000 | 0.445851 | ||||||||
\(987\) | 3.00000 | + | 15.5885i | 0.0954911 | + | 0.496186i | ||||
\(988\) | −4.00000 | −0.127257 | ||||||||
\(989\) | 3.00000 | + | 5.19615i | 0.0953945 | + | 0.165228i | ||||
\(990\) | 1.50000 | − | 2.59808i | 0.0476731 | − | 0.0825723i | ||||
\(991\) | −1.50000 | + | 2.59808i | −0.0476491 | + | 0.0825306i | −0.888866 | − | 0.458167i | \(-0.848506\pi\) |
0.841217 | + | 0.540697i | \(0.181840\pi\) | |||||||
\(992\) | −3.50000 | − | 6.06218i | −0.111125 | − | 0.192474i | ||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | 16.0000 | − | 13.8564i | 0.507489 | − | 0.439499i | ||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | 0.500000 | + | 0.866025i | 0.0158431 | + | 0.0274411i | ||||
\(997\) | −18.0000 | + | 31.1769i | −0.570066 | + | 0.987383i | 0.426493 | + | 0.904491i | \(0.359749\pi\) |
−0.996559 | + | 0.0828918i | \(0.973584\pi\) | |||||||
\(998\) | −3.00000 | + | 5.19615i | −0.0949633 | + | 0.164481i | ||||
\(999\) | −1.00000 | − | 1.73205i | −0.0316386 | − | 0.0547997i |
(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 | 966.2.i.c.277.1 | ✓ | 2 | |
7.2 | even | 3 | inner | 966.2.i.c.415.1 | yes | 2 | |
7.3 | odd | 6 | 6762.2.a.bh.1.1 | 1 | |||
7.4 | even | 3 | 6762.2.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.c.277.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
966.2.i.c.415.1 | yes | 2 | 7.2 | even | 3 | inner | |
6762.2.a.bb.1.1 | 1 | 7.4 | even | 3 | |||
6762.2.a.bh.1.1 | 1 | 7.3 | odd | 6 |