Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 811.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.811 |
Dual form | 930.2.i.h.211.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | 1.50000 | − | 2.59808i | 0.566947 | − | 0.981981i | −0.429919 | − | 0.902867i | \(-0.641458\pi\) |
0.996866 | − | 0.0791130i | \(-0.0252088\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −3.00000 | − | 5.19615i | −0.832050 | − | 1.44115i | −0.896410 | − | 0.443227i | \(-0.853834\pi\) |
0.0643593 | − | 0.997927i | \(-0.479500\pi\) | |||||||
\(14\) | 1.50000 | − | 2.59808i | 0.400892 | − | 0.694365i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.00000 | + | 6.92820i | −0.970143 | + | 1.68034i | −0.275029 | + | 0.961436i | \(0.588688\pi\) |
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | 2.00000 | − | 3.46410i | 0.458831 | − | 0.794719i | −0.540068 | − | 0.841621i | \(-0.681602\pi\) |
0.998899 | + | 0.0469020i | \(0.0149348\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −1.50000 | − | 2.59808i | −0.327327 | − | 0.566947i | ||||
\(22\) | −2.50000 | − | 4.33013i | −0.533002 | − | 0.923186i | ||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −3.00000 | − | 5.19615i | −0.588348 | − | 1.01905i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 3.50000 | + | 4.33013i | 0.628619 | + | 0.777714i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −5.00000 | −0.870388 | ||||||||
\(34\) | −4.00000 | + | 6.92820i | −0.685994 | + | 1.18818i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.00000 | − | 1.73205i | 0.164399 | − | 0.284747i | −0.772043 | − | 0.635571i | \(-0.780765\pi\) |
0.936442 | + | 0.350823i | \(0.114098\pi\) | |||||||
\(38\) | 2.00000 | − | 3.46410i | 0.324443 | − | 0.561951i | ||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | −1.50000 | − | 2.59808i | −0.231455 | − | 0.400892i | ||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | −2.50000 | − | 4.33013i | −0.376889 | − | 0.652791i | ||||
\(45\) | 0.500000 | − | 0.866025i | 0.0745356 | − | 0.129099i | ||||
\(46\) | 8.00000 | 1.17954 | ||||||||
\(47\) | 12.0000 | 1.75038 | 0.875190 | − | 0.483779i | \(-0.160736\pi\) | ||||
0.875190 | + | 0.483779i | \(0.160736\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −1.00000 | − | 1.73205i | −0.142857 | − | 0.247436i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 4.00000 | + | 6.92820i | 0.560112 | + | 0.970143i | ||||
\(52\) | −3.00000 | − | 5.19615i | −0.416025 | − | 0.720577i | ||||
\(53\) | −2.50000 | − | 4.33013i | −0.343401 | − | 0.594789i | 0.641661 | − | 0.766989i | \(-0.278246\pi\) |
−0.985062 | + | 0.172200i | \(0.944912\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 2.50000 | − | 4.33013i | 0.337100 | − | 0.583874i | ||||
\(56\) | 1.50000 | − | 2.59808i | 0.200446 | − | 0.347183i | ||||
\(57\) | −2.00000 | − | 3.46410i | −0.264906 | − | 0.458831i | ||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −5.50000 | + | 9.52628i | −0.716039 | + | 1.24022i | 0.246518 | + | 0.969138i | \(0.420713\pi\) |
−0.962557 | + | 0.271078i | \(0.912620\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | 12.0000 | 1.53644 | 0.768221 | − | 0.640184i | \(-0.221142\pi\) | ||||
0.768221 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(62\) | 3.50000 | + | 4.33013i | 0.444500 | + | 0.549927i | ||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | −5.00000 | −0.615457 | ||||||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | −4.00000 | + | 6.92820i | −0.485071 | + | 0.840168i | ||||
\(69\) | 4.00000 | − | 6.92820i | 0.481543 | − | 0.834058i | ||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −3.00000 | − | 5.19615i | −0.351123 | − | 0.608164i | 0.635323 | − | 0.772246i | \(-0.280867\pi\) |
−0.986447 | + | 0.164083i | \(0.947534\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | −15.0000 | −1.70941 | ||||||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | −1.50000 | − | 2.59808i | −0.164646 | − | 0.285176i | 0.771883 | − | 0.635764i | \(-0.219315\pi\) |
−0.936530 | + | 0.350588i | \(0.885982\pi\) | |||||||
\(84\) | −1.50000 | − | 2.59808i | −0.163663 | − | 0.283473i | ||||
\(85\) | −8.00000 | −0.867722 | ||||||||
\(86\) | −4.00000 | + | 6.92820i | −0.431331 | + | 0.747087i | ||||
\(87\) | −0.500000 | + | 0.866025i | −0.0536056 | + | 0.0928477i | ||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0.500000 | − | 0.866025i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | −18.0000 | −1.88691 | ||||||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | 5.50000 | − | 0.866025i | 0.570323 | − | 0.0898027i | ||||
\(94\) | 12.0000 | 1.23771 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 13.0000 | 1.31995 | 0.659975 | − | 0.751288i | \(-0.270567\pi\) | ||||
0.659975 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(98\) | −1.00000 | − | 1.73205i | −0.101015 | − | 0.174964i | ||||
\(99\) | −2.50000 | + | 4.33013i | −0.251259 | + | 0.435194i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.00000 | −0.0995037 | −0.0497519 | − | 0.998762i | \(-0.515843\pi\) | ||||
−0.0497519 | + | 0.998762i | \(0.515843\pi\) | |||||||
\(102\) | 4.00000 | + | 6.92820i | 0.396059 | + | 0.685994i | ||||
\(103\) | 3.50000 | + | 6.06218i | 0.344865 | + | 0.597324i | 0.985329 | − | 0.170664i | \(-0.0545913\pi\) |
−0.640464 | + | 0.767988i | \(0.721258\pi\) | |||||||
\(104\) | −3.00000 | − | 5.19615i | −0.294174 | − | 0.509525i | ||||
\(105\) | 1.50000 | − | 2.59808i | 0.146385 | − | 0.253546i | ||||
\(106\) | −2.50000 | − | 4.33013i | −0.242821 | − | 0.420579i | ||||
\(107\) | 2.50000 | − | 4.33013i | 0.241684 | − | 0.418609i | −0.719510 | − | 0.694482i | \(-0.755634\pi\) |
0.961194 | + | 0.275873i | \(0.0889669\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 2.50000 | − | 4.33013i | 0.238366 | − | 0.412861i | ||||
\(111\) | −1.00000 | − | 1.73205i | −0.0949158 | − | 0.164399i | ||||
\(112\) | 1.50000 | − | 2.59808i | 0.141737 | − | 0.245495i | ||||
\(113\) | 5.00000 | + | 8.66025i | 0.470360 | + | 0.814688i | 0.999425 | − | 0.0338931i | \(-0.0107906\pi\) |
−0.529065 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | 4.00000 | + | 6.92820i | 0.373002 | + | 0.646058i | ||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | −3.00000 | + | 5.19615i | −0.277350 | + | 0.480384i | ||||
\(118\) | −5.50000 | + | 9.52628i | −0.506316 | + | 0.876965i | ||||
\(119\) | 12.0000 | + | 20.7846i | 1.10004 | + | 1.90532i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 12.0000 | 1.08643 | ||||||||
\(123\) | 6.00000 | 0.541002 | ||||||||
\(124\) | 3.50000 | + | 4.33013i | 0.314309 | + | 0.388857i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −3.00000 | −0.267261 | ||||||||
\(127\) | −3.50000 | + | 6.06218i | −0.310575 | + | 0.537931i | −0.978487 | − | 0.206309i | \(-0.933855\pi\) |
0.667912 | + | 0.744240i | \(0.267188\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 4.00000 | + | 6.92820i | 0.352180 | + | 0.609994i | ||||
\(130\) | 3.00000 | − | 5.19615i | 0.263117 | − | 0.455733i | ||||
\(131\) | 8.00000 | − | 13.8564i | 0.698963 | − | 1.21064i | −0.269863 | − | 0.962899i | \(-0.586978\pi\) |
0.968826 | − | 0.247741i | \(-0.0796882\pi\) | |||||||
\(132\) | −5.00000 | −0.435194 | ||||||||
\(133\) | −6.00000 | − | 10.3923i | −0.520266 | − | 0.901127i | ||||
\(134\) | −5.00000 | − | 8.66025i | −0.431934 | − | 0.748132i | ||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | −4.00000 | + | 6.92820i | −0.342997 | + | 0.594089i | ||||
\(137\) | 3.00000 | + | 5.19615i | 0.256307 | + | 0.443937i | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 4.00000 | − | 6.92820i | 0.340503 | − | 0.589768i | ||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 3.00000 | 0.253546 | ||||||||
\(141\) | 6.00000 | − | 10.3923i | 0.505291 | − | 0.875190i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0000 | + | 25.9808i | −1.25436 | + | 2.17262i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −0.500000 | − | 0.866025i | −0.0415227 | − | 0.0719195i | ||||
\(146\) | −3.00000 | − | 5.19615i | −0.248282 | − | 0.430037i | ||||
\(147\) | −2.00000 | −0.164957 | ||||||||
\(148\) | 1.00000 | − | 1.73205i | 0.0821995 | − | 0.142374i | ||||
\(149\) | −6.50000 | + | 11.2583i | −0.532501 | + | 0.922318i | 0.466779 | + | 0.884374i | \(0.345414\pi\) |
−0.999280 | + | 0.0379444i | \(0.987919\pi\) | |||||||
\(150\) | 0.500000 | + | 0.866025i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | 2.00000 | − | 3.46410i | 0.162221 | − | 0.280976i | ||||
\(153\) | 8.00000 | 0.646762 | ||||||||
\(154\) | −15.0000 | −1.20873 | ||||||||
\(155\) | −2.00000 | + | 5.19615i | −0.160644 | + | 0.417365i | ||||
\(156\) | −6.00000 | −0.480384 | ||||||||
\(157\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(158\) | −4.00000 | + | 6.92820i | −0.318223 | + | 0.551178i | ||||
\(159\) | −5.00000 | −0.396526 | ||||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | 12.0000 | − | 20.7846i | 0.945732 | − | 1.63806i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 3.00000 | + | 5.19615i | 0.234261 | + | 0.405751i | ||||
\(165\) | −2.50000 | − | 4.33013i | −0.194625 | − | 0.337100i | ||||
\(166\) | −1.50000 | − | 2.59808i | −0.116423 | − | 0.201650i | ||||
\(167\) | 9.00000 | − | 15.5885i | 0.696441 | − | 1.20627i | −0.273252 | − | 0.961943i | \(-0.588099\pi\) |
0.969693 | − | 0.244328i | \(-0.0785675\pi\) | |||||||
\(168\) | −1.50000 | − | 2.59808i | −0.115728 | − | 0.200446i | ||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | −8.00000 | −0.613572 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | −4.00000 | + | 6.92820i | −0.304997 | + | 0.528271i | ||||
\(173\) | 2.50000 | + | 4.33013i | 0.190071 | + | 0.329213i | 0.945274 | − | 0.326278i | \(-0.105795\pi\) |
−0.755202 | + | 0.655492i | \(0.772461\pi\) | |||||||
\(174\) | −0.500000 | + | 0.866025i | −0.0379049 | + | 0.0656532i | ||||
\(175\) | 1.50000 | + | 2.59808i | 0.113389 | + | 0.196396i | ||||
\(176\) | −2.50000 | − | 4.33013i | −0.188445 | − | 0.326396i | ||||
\(177\) | 5.50000 | + | 9.52628i | 0.413405 | + | 0.716039i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.50000 | + | 9.52628i | −0.411089 | + | 0.712028i | −0.995009 | − | 0.0997838i | \(-0.968185\pi\) |
0.583920 | + | 0.811811i | \(0.301518\pi\) | |||||||
\(180\) | 0.500000 | − | 0.866025i | 0.0372678 | − | 0.0645497i | ||||
\(181\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(182\) | −18.0000 | −1.33425 | ||||||||
\(183\) | 6.00000 | − | 10.3923i | 0.443533 | − | 0.768221i | ||||
\(184\) | 8.00000 | 0.589768 | ||||||||
\(185\) | 2.00000 | 0.147043 | ||||||||
\(186\) | 5.50000 | − | 0.866025i | 0.403280 | − | 0.0635001i | ||||
\(187\) | 40.0000 | 2.92509 | ||||||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | −1.50000 | + | 2.59808i | −0.109109 | + | 0.188982i | ||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 13.0000 | + | 22.5167i | 0.940647 | + | 1.62925i | 0.764241 | + | 0.644931i | \(0.223114\pi\) |
0.176406 | + | 0.984317i | \(0.443553\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 6.50000 | − | 11.2583i | 0.467880 | − | 0.810392i | −0.531446 | − | 0.847092i | \(-0.678351\pi\) |
0.999326 | + | 0.0366998i | \(0.0116845\pi\) | |||||||
\(194\) | 13.0000 | 0.933346 | ||||||||
\(195\) | −3.00000 | − | 5.19615i | −0.214834 | − | 0.372104i | ||||
\(196\) | −1.00000 | − | 1.73205i | −0.0714286 | − | 0.123718i | ||||
\(197\) | 5.00000 | + | 8.66025i | 0.356235 | + | 0.617018i | 0.987329 | − | 0.158689i | \(-0.0507268\pi\) |
−0.631093 | + | 0.775707i | \(0.717394\pi\) | |||||||
\(198\) | −2.50000 | + | 4.33013i | −0.177667 | + | 0.307729i | ||||
\(199\) | −9.50000 | − | 16.4545i | −0.673437 | − | 1.16643i | −0.976923 | − | 0.213591i | \(-0.931484\pi\) |
0.303486 | − | 0.952836i | \(-0.401849\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −10.0000 | −0.705346 | ||||||||
\(202\) | −1.00000 | −0.0703598 | ||||||||
\(203\) | −1.50000 | + | 2.59808i | −0.105279 | + | 0.182349i | ||||
\(204\) | 4.00000 | + | 6.92820i | 0.280056 | + | 0.485071i | ||||
\(205\) | −3.00000 | + | 5.19615i | −0.209529 | + | 0.362915i | ||||
\(206\) | 3.50000 | + | 6.06218i | 0.243857 | + | 0.422372i | ||||
\(207\) | −4.00000 | − | 6.92820i | −0.278019 | − | 0.481543i | ||||
\(208\) | −3.00000 | − | 5.19615i | −0.208013 | − | 0.360288i | ||||
\(209\) | −20.0000 | −1.38343 | ||||||||
\(210\) | 1.50000 | − | 2.59808i | 0.103510 | − | 0.179284i | ||||
\(211\) | 8.00000 | − | 13.8564i | 0.550743 | − | 0.953914i | −0.447478 | − | 0.894295i | \(-0.647678\pi\) |
0.998221 | − | 0.0596196i | \(-0.0189888\pi\) | |||||||
\(212\) | −2.50000 | − | 4.33013i | −0.171701 | − | 0.297394i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.50000 | − | 4.33013i | 0.170896 | − | 0.296001i | ||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 16.5000 | − | 2.59808i | 1.12009 | − | 0.176369i | ||||
\(218\) | −12.0000 | −0.812743 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 2.50000 | − | 4.33013i | 0.168550 | − | 0.291937i | ||||
\(221\) | 48.0000 | 3.22883 | ||||||||
\(222\) | −1.00000 | − | 1.73205i | −0.0671156 | − | 0.116248i | ||||
\(223\) | −0.500000 | + | 0.866025i | −0.0334825 | + | 0.0579934i | −0.882281 | − | 0.470723i | \(-0.843993\pi\) |
0.848799 | + | 0.528716i | \(0.177326\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 5.00000 | + | 8.66025i | 0.332595 | + | 0.576072i | ||||
\(227\) | 12.5000 | + | 21.6506i | 0.829654 | + | 1.43700i | 0.898310 | + | 0.439363i | \(0.144796\pi\) |
−0.0686556 | + | 0.997640i | \(0.521871\pi\) | |||||||
\(228\) | −2.00000 | − | 3.46410i | −0.132453 | − | 0.229416i | ||||
\(229\) | 1.00000 | − | 1.73205i | 0.0660819 | − | 0.114457i | −0.831092 | − | 0.556136i | \(-0.812283\pi\) |
0.897173 | + | 0.441679i | \(0.145617\pi\) | |||||||
\(230\) | 4.00000 | + | 6.92820i | 0.263752 | + | 0.456832i | ||||
\(231\) | −7.50000 | + | 12.9904i | −0.493464 | + | 0.854704i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | 6.00000 | + | 10.3923i | 0.391397 | + | 0.677919i | ||||
\(236\) | −5.50000 | + | 9.52628i | −0.358020 | + | 0.620108i | ||||
\(237\) | 4.00000 | + | 6.92820i | 0.259828 | + | 0.450035i | ||||
\(238\) | 12.0000 | + | 20.7846i | 0.777844 | + | 1.34727i | ||||
\(239\) | −3.00000 | − | 5.19615i | −0.194054 | − | 0.336111i | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 2.50000 | − | 4.33013i | 0.161039 | − | 0.278928i | −0.774202 | − | 0.632938i | \(-0.781849\pi\) |
0.935242 | + | 0.354010i | \(0.115182\pi\) | |||||||
\(242\) | −7.00000 | + | 12.1244i | −0.449977 | + | 0.779383i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 12.0000 | 0.768221 | ||||||||
\(245\) | 1.00000 | − | 1.73205i | 0.0638877 | − | 0.110657i | ||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | −24.0000 | −1.52708 | ||||||||
\(248\) | 3.50000 | + | 4.33013i | 0.222250 | + | 0.274963i | ||||
\(249\) | −3.00000 | −0.190117 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −10.0000 | + | 17.3205i | −0.631194 | + | 1.09326i | 0.356113 | + | 0.934443i | \(0.384102\pi\) |
−0.987308 | + | 0.158818i | \(0.949232\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | −20.0000 | − | 34.6410i | −1.25739 | − | 2.17786i | ||||
\(254\) | −3.50000 | + | 6.06218i | −0.219610 | + | 0.380375i | ||||
\(255\) | −4.00000 | + | 6.92820i | −0.250490 | + | 0.433861i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.00000 | − | 13.8564i | −0.499026 | − | 0.864339i | 0.500973 | − | 0.865463i | \(-0.332976\pi\) |
−0.999999 | + | 0.00112398i | \(0.999642\pi\) | |||||||
\(258\) | 4.00000 | + | 6.92820i | 0.249029 | + | 0.431331i | ||||
\(259\) | −3.00000 | − | 5.19615i | −0.186411 | − | 0.322873i | ||||
\(260\) | 3.00000 | − | 5.19615i | 0.186052 | − | 0.322252i | ||||
\(261\) | 0.500000 | + | 0.866025i | 0.0309492 | + | 0.0536056i | ||||
\(262\) | 8.00000 | − | 13.8564i | 0.494242 | − | 0.856052i | ||||
\(263\) | −6.00000 | −0.369976 | −0.184988 | − | 0.982741i | \(-0.559225\pi\) | ||||
−0.184988 | + | 0.982741i | \(0.559225\pi\) | |||||||
\(264\) | −5.00000 | −0.307729 | ||||||||
\(265\) | 2.50000 | − | 4.33013i | 0.153574 | − | 0.265998i | ||||
\(266\) | −6.00000 | − | 10.3923i | −0.367884 | − | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.00000 | − | 8.66025i | −0.305424 | − | 0.529009i | ||||
\(269\) | 9.00000 | + | 15.5885i | 0.548740 | + | 0.950445i | 0.998361 | + | 0.0572259i | \(0.0182255\pi\) |
−0.449622 | + | 0.893219i | \(0.648441\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −17.0000 | −1.03268 | −0.516338 | − | 0.856385i | \(-0.672705\pi\) | ||||
−0.516338 | + | 0.856385i | \(0.672705\pi\) | |||||||
\(272\) | −4.00000 | + | 6.92820i | −0.242536 | + | 0.420084i | ||||
\(273\) | −9.00000 | + | 15.5885i | −0.544705 | + | 0.943456i | ||||
\(274\) | 3.00000 | + | 5.19615i | 0.181237 | + | 0.313911i | ||||
\(275\) | 5.00000 | 0.301511 | ||||||||
\(276\) | 4.00000 | − | 6.92820i | 0.240772 | − | 0.417029i | ||||
\(277\) | −24.0000 | −1.44202 | −0.721010 | − | 0.692925i | \(-0.756322\pi\) | ||||
−0.721010 | + | 0.692925i | \(0.756322\pi\) | |||||||
\(278\) | −10.0000 | −0.599760 | ||||||||
\(279\) | 2.00000 | − | 5.19615i | 0.119737 | − | 0.311086i | ||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −8.00000 | −0.477240 | −0.238620 | − | 0.971113i | \(-0.576695\pi\) | ||||
−0.238620 | + | 0.971113i | \(0.576695\pi\) | |||||||
\(282\) | 6.00000 | − | 10.3923i | 0.357295 | − | 0.618853i | ||||
\(283\) | −6.00000 | −0.356663 | −0.178331 | − | 0.983970i | \(-0.557070\pi\) | ||||
−0.178331 | + | 0.983970i | \(0.557070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.00000 | − | 3.46410i | 0.118470 | − | 0.205196i | ||||
\(286\) | −15.0000 | + | 25.9808i | −0.886969 | + | 1.53627i | ||||
\(287\) | 18.0000 | 1.06251 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | −23.5000 | − | 40.7032i | −1.38235 | − | 2.39431i | ||||
\(290\) | −0.500000 | − | 0.866025i | −0.0293610 | − | 0.0508548i | ||||
\(291\) | 6.50000 | − | 11.2583i | 0.381037 | − | 0.659975i | ||||
\(292\) | −3.00000 | − | 5.19615i | −0.175562 | − | 0.304082i | ||||
\(293\) | −4.50000 | + | 7.79423i | −0.262893 | + | 0.455344i | −0.967009 | − | 0.254741i | \(-0.918010\pi\) |
0.704117 | + | 0.710084i | \(0.251343\pi\) | |||||||
\(294\) | −2.00000 | −0.116642 | ||||||||
\(295\) | −11.0000 | −0.640445 | ||||||||
\(296\) | 1.00000 | − | 1.73205i | 0.0581238 | − | 0.100673i | ||||
\(297\) | 2.50000 | + | 4.33013i | 0.145065 | + | 0.251259i | ||||
\(298\) | −6.50000 | + | 11.2583i | −0.376535 | + | 0.652178i | ||||
\(299\) | −24.0000 | − | 41.5692i | −1.38796 | − | 2.40401i | ||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | 12.0000 | + | 20.7846i | 0.691669 | + | 1.19800i | ||||
\(302\) | −5.00000 | −0.287718 | ||||||||
\(303\) | −0.500000 | + | 0.866025i | −0.0287242 | + | 0.0497519i | ||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 6.00000 | + | 10.3923i | 0.343559 | + | 0.595062i | ||||
\(306\) | 8.00000 | 0.457330 | ||||||||
\(307\) | −1.00000 | + | 1.73205i | −0.0570730 | + | 0.0988534i | −0.893150 | − | 0.449758i | \(-0.851510\pi\) |
0.836077 | + | 0.548612i | \(0.184843\pi\) | |||||||
\(308\) | −15.0000 | −0.854704 | ||||||||
\(309\) | 7.00000 | 0.398216 | ||||||||
\(310\) | −2.00000 | + | 5.19615i | −0.113592 | + | 0.295122i | ||||
\(311\) | −22.0000 | −1.24751 | −0.623753 | − | 0.781622i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781622i | \(0.714393\pi\) | |||||||
\(312\) | −6.00000 | −0.339683 | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.50000 | − | 2.59808i | −0.0845154 | − | 0.146385i | ||||
\(316\) | −4.00000 | + | 6.92820i | −0.225018 | + | 0.389742i | ||||
\(317\) | 15.5000 | − | 26.8468i | 0.870567 | − | 1.50787i | 0.00915525 | − | 0.999958i | \(-0.497086\pi\) |
0.861411 | − | 0.507908i | \(-0.169581\pi\) | |||||||
\(318\) | −5.00000 | −0.280386 | ||||||||
\(319\) | 2.50000 | + | 4.33013i | 0.139973 | + | 0.242441i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | −2.50000 | − | 4.33013i | −0.139536 | − | 0.241684i | ||||
\(322\) | 12.0000 | − | 20.7846i | 0.668734 | − | 1.15828i | ||||
\(323\) | 16.0000 | + | 27.7128i | 0.890264 | + | 1.54198i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 6.00000 | 0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.00000 | + | 10.3923i | −0.331801 | + | 0.574696i | ||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | 18.0000 | − | 31.1769i | 0.992372 | − | 1.71884i | ||||
\(330\) | −2.50000 | − | 4.33013i | −0.137620 | − | 0.238366i | ||||
\(331\) | 6.00000 | + | 10.3923i | 0.329790 | + | 0.571213i | 0.982470 | − | 0.186421i | \(-0.0596888\pi\) |
−0.652680 | + | 0.757634i | \(0.726355\pi\) | |||||||
\(332\) | −1.50000 | − | 2.59808i | −0.0823232 | − | 0.142588i | ||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 9.00000 | − | 15.5885i | 0.492458 | − | 0.852962i | ||||
\(335\) | 5.00000 | − | 8.66025i | 0.273179 | − | 0.473160i | ||||
\(336\) | −1.50000 | − | 2.59808i | −0.0818317 | − | 0.141737i | ||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | −11.5000 | + | 19.9186i | −0.625518 | + | 1.08343i | ||||
\(339\) | 10.0000 | 0.543125 | ||||||||
\(340\) | −8.00000 | −0.433861 | ||||||||
\(341\) | 10.0000 | − | 25.9808i | 0.541530 | − | 1.40694i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −4.00000 | + | 6.92820i | −0.215666 | + | 0.373544i | ||||
\(345\) | 8.00000 | 0.430706 | ||||||||
\(346\) | 2.50000 | + | 4.33013i | 0.134401 | + | 0.232789i | ||||
\(347\) | −2.50000 | + | 4.33013i | −0.134207 | + | 0.232453i | −0.925294 | − | 0.379250i | \(-0.876182\pi\) |
0.791087 | + | 0.611703i | \(0.209515\pi\) | |||||||
\(348\) | −0.500000 | + | 0.866025i | −0.0268028 | + | 0.0464238i | ||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 1.50000 | + | 2.59808i | 0.0801784 | + | 0.138873i | ||||
\(351\) | 3.00000 | + | 5.19615i | 0.160128 | + | 0.277350i | ||||
\(352\) | −2.50000 | − | 4.33013i | −0.133250 | − | 0.230797i | ||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 5.50000 | + | 9.52628i | 0.292322 | + | 0.506316i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.0000 | 1.27021 | ||||||||
\(358\) | −5.50000 | + | 9.52628i | −0.290684 | + | 0.503480i | ||||
\(359\) | −2.00000 | − | 3.46410i | −0.105556 | − | 0.182828i | 0.808409 | − | 0.588621i | \(-0.200329\pi\) |
−0.913965 | + | 0.405793i | \(0.866996\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.00000 | + | 12.1244i | 0.367405 | + | 0.636364i | ||||
\(364\) | −18.0000 | −0.943456 | ||||||||
\(365\) | 3.00000 | − | 5.19615i | 0.157027 | − | 0.271979i | ||||
\(366\) | 6.00000 | − | 10.3923i | 0.313625 | − | 0.543214i | ||||
\(367\) | −2.00000 | − | 3.46410i | −0.104399 | − | 0.180825i | 0.809093 | − | 0.587680i | \(-0.199959\pi\) |
−0.913493 | + | 0.406855i | \(0.866625\pi\) | |||||||
\(368\) | 8.00000 | 0.417029 | ||||||||
\(369\) | 3.00000 | − | 5.19615i | 0.156174 | − | 0.270501i | ||||
\(370\) | 2.00000 | 0.103975 | ||||||||
\(371\) | −15.0000 | −0.778761 | ||||||||
\(372\) | 5.50000 | − | 0.866025i | 0.285162 | − | 0.0449013i | ||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 40.0000 | 2.06835 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 12.0000 | 0.618853 | ||||||||
\(377\) | 3.00000 | + | 5.19615i | 0.154508 | + | 0.267615i | ||||
\(378\) | −1.50000 | + | 2.59808i | −0.0771517 | + | 0.133631i | ||||
\(379\) | −14.0000 | + | 24.2487i | −0.719132 | + | 1.24557i | 0.242213 | + | 0.970223i | \(0.422127\pi\) |
−0.961344 | + | 0.275349i | \(0.911206\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | 3.50000 | + | 6.06218i | 0.179310 | + | 0.310575i | ||||
\(382\) | 13.0000 | + | 22.5167i | 0.665138 | + | 1.15205i | ||||
\(383\) | −11.0000 | − | 19.0526i | −0.562074 | − | 0.973540i | −0.997315 | − | 0.0732266i | \(-0.976670\pi\) |
0.435242 | − | 0.900314i | \(-0.356663\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −7.50000 | − | 12.9904i | −0.382235 | − | 0.662051i | ||||
\(386\) | 6.50000 | − | 11.2583i | 0.330841 | − | 0.573034i | ||||
\(387\) | 8.00000 | 0.406663 | ||||||||
\(388\) | 13.0000 | 0.659975 | ||||||||
\(389\) | −15.0000 | + | 25.9808i | −0.760530 | + | 1.31728i | 0.182047 | + | 0.983290i | \(0.441728\pi\) |
−0.942578 | + | 0.333987i | \(0.891606\pi\) | |||||||
\(390\) | −3.00000 | − | 5.19615i | −0.151911 | − | 0.263117i | ||||
\(391\) | −32.0000 | + | 55.4256i | −1.61831 | + | 2.80299i | ||||
\(392\) | −1.00000 | − | 1.73205i | −0.0505076 | − | 0.0874818i | ||||
\(393\) | −8.00000 | − | 13.8564i | −0.403547 | − | 0.698963i | ||||
\(394\) | 5.00000 | + | 8.66025i | 0.251896 | + | 0.436297i | ||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | −2.50000 | + | 4.33013i | −0.125630 | + | 0.217597i | ||||
\(397\) | 10.0000 | − | 17.3205i | 0.501886 | − | 0.869291i | −0.498112 | − | 0.867113i | \(-0.665973\pi\) |
0.999998 | − | 0.00217869i | \(-0.000693499\pi\) | |||||||
\(398\) | −9.50000 | − | 16.4545i | −0.476192 | − | 0.824789i | ||||
\(399\) | −12.0000 | −0.600751 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | −10.0000 | −0.498755 | ||||||||
\(403\) | 12.0000 | − | 31.1769i | 0.597763 | − | 1.55303i | ||||
\(404\) | −1.00000 | −0.0497519 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −1.50000 | + | 2.59808i | −0.0744438 | + | 0.128940i | ||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 4.00000 | + | 6.92820i | 0.198030 | + | 0.342997i | ||||
\(409\) | 4.50000 | − | 7.79423i | 0.222511 | − | 0.385400i | −0.733059 | − | 0.680165i | \(-0.761908\pi\) |
0.955570 | + | 0.294765i | \(0.0952414\pi\) | |||||||
\(410\) | −3.00000 | + | 5.19615i | −0.148159 | + | 0.256620i | ||||
\(411\) | 6.00000 | 0.295958 | ||||||||
\(412\) | 3.50000 | + | 6.06218i | 0.172433 | + | 0.298662i | ||||
\(413\) | 16.5000 | + | 28.5788i | 0.811912 | + | 1.40627i | ||||
\(414\) | −4.00000 | − | 6.92820i | −0.196589 | − | 0.340503i | ||||
\(415\) | 1.50000 | − | 2.59808i | 0.0736321 | − | 0.127535i | ||||
\(416\) | −3.00000 | − | 5.19615i | −0.147087 | − | 0.254762i | ||||
\(417\) | −5.00000 | + | 8.66025i | −0.244851 | + | 0.424094i | ||||
\(418\) | −20.0000 | −0.978232 | ||||||||
\(419\) | −27.0000 | −1.31904 | −0.659518 | − | 0.751689i | \(-0.729240\pi\) | ||||
−0.659518 | + | 0.751689i | \(0.729240\pi\) | |||||||
\(420\) | 1.50000 | − | 2.59808i | 0.0731925 | − | 0.126773i | ||||
\(421\) | −16.0000 | − | 27.7128i | −0.779792 | − | 1.35064i | −0.932061 | − | 0.362301i | \(-0.881991\pi\) |
0.152269 | − | 0.988339i | \(-0.451342\pi\) | |||||||
\(422\) | 8.00000 | − | 13.8564i | 0.389434 | − | 0.674519i | ||||
\(423\) | −6.00000 | − | 10.3923i | −0.291730 | − | 0.505291i | ||||
\(424\) | −2.50000 | − | 4.33013i | −0.121411 | − | 0.210290i | ||||
\(425\) | −4.00000 | − | 6.92820i | −0.194029 | − | 0.336067i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | − | 31.1769i | 0.871081 | − | 1.50876i | ||||
\(428\) | 2.50000 | − | 4.33013i | 0.120842 | − | 0.209305i | ||||
\(429\) | 15.0000 | + | 25.9808i | 0.724207 | + | 1.25436i | ||||
\(430\) | −8.00000 | −0.385794 | ||||||||
\(431\) | 15.0000 | − | 25.9808i | 0.722525 | − | 1.25145i | −0.237460 | − | 0.971397i | \(-0.576315\pi\) |
0.959985 | − | 0.280052i | \(-0.0903517\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 16.5000 | − | 2.59808i | 0.792025 | − | 0.124712i | ||||
\(435\) | −1.00000 | −0.0479463 | ||||||||
\(436\) | −12.0000 | −0.574696 | ||||||||
\(437\) | 16.0000 | − | 27.7128i | 0.765384 | − | 1.32568i | ||||
\(438\) | −6.00000 | −0.286691 | ||||||||
\(439\) | 2.50000 | + | 4.33013i | 0.119318 | + | 0.206666i | 0.919498 | − | 0.393095i | \(-0.128596\pi\) |
−0.800179 | + | 0.599761i | \(0.795262\pi\) | |||||||
\(440\) | 2.50000 | − | 4.33013i | 0.119183 | − | 0.206431i | ||||
\(441\) | −1.00000 | + | 1.73205i | −0.0476190 | + | 0.0824786i | ||||
\(442\) | 48.0000 | 2.28313 | ||||||||
\(443\) | 8.00000 | + | 13.8564i | 0.380091 | + | 0.658338i | 0.991075 | − | 0.133306i | \(-0.0425592\pi\) |
−0.610984 | + | 0.791643i | \(0.709226\pi\) | |||||||
\(444\) | −1.00000 | − | 1.73205i | −0.0474579 | − | 0.0821995i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.500000 | + | 0.866025i | −0.0236757 | + | 0.0410075i | ||||
\(447\) | 6.50000 | + | 11.2583i | 0.307439 | + | 0.532501i | ||||
\(448\) | 1.50000 | − | 2.59808i | 0.0708683 | − | 0.122748i | ||||
\(449\) | −24.0000 | −1.13263 | −0.566315 | − | 0.824189i | \(-0.691631\pi\) | ||||
−0.566315 | + | 0.824189i | \(0.691631\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 15.0000 | − | 25.9808i | 0.706322 | − | 1.22339i | ||||
\(452\) | 5.00000 | + | 8.66025i | 0.235180 | + | 0.407344i | ||||
\(453\) | −2.50000 | + | 4.33013i | −0.117460 | + | 0.203447i | ||||
\(454\) | 12.5000 | + | 21.6506i | 0.586654 | + | 1.01611i | ||||
\(455\) | −9.00000 | − | 15.5885i | −0.421927 | − | 0.730798i | ||||
\(456\) | −2.00000 | − | 3.46410i | −0.0936586 | − | 0.162221i | ||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | 1.00000 | − | 1.73205i | 0.0467269 | − | 0.0809334i | ||||
\(459\) | 4.00000 | − | 6.92820i | 0.186704 | − | 0.323381i | ||||
\(460\) | 4.00000 | + | 6.92820i | 0.186501 | + | 0.323029i | ||||
\(461\) | 1.00000 | 0.0465746 | 0.0232873 | − | 0.999729i | \(-0.492587\pi\) | ||||
0.0232873 | + | 0.999729i | \(0.492587\pi\) | |||||||
\(462\) | −7.50000 | + | 12.9904i | −0.348932 | + | 0.604367i | ||||
\(463\) | 27.0000 | 1.25480 | 0.627398 | − | 0.778699i | \(-0.284120\pi\) | ||||
0.627398 | + | 0.778699i | \(0.284120\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 3.50000 | + | 4.33013i | 0.162309 | + | 0.200805i | ||||
\(466\) | −14.0000 | −0.648537 | ||||||||
\(467\) | 23.0000 | 1.06431 | 0.532157 | − | 0.846646i | \(-0.321382\pi\) | ||||
0.532157 | + | 0.846646i | \(0.321382\pi\) | |||||||
\(468\) | −3.00000 | + | 5.19615i | −0.138675 | + | 0.240192i | ||||
\(469\) | −30.0000 | −1.38527 | ||||||||
\(470\) | 6.00000 | + | 10.3923i | 0.276759 | + | 0.479361i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.50000 | + | 9.52628i | −0.253158 | + | 0.438483i | ||||
\(473\) | 40.0000 | 1.83920 | ||||||||
\(474\) | 4.00000 | + | 6.92820i | 0.183726 | + | 0.318223i | ||||
\(475\) | 2.00000 | + | 3.46410i | 0.0917663 | + | 0.158944i | ||||
\(476\) | 12.0000 | + | 20.7846i | 0.550019 | + | 0.952661i | ||||
\(477\) | −2.50000 | + | 4.33013i | −0.114467 | + | 0.198263i | ||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | −6.00000 | + | 10.3923i | −0.274147 | + | 0.474837i | −0.969920 | − | 0.243426i | \(-0.921729\pi\) |
0.695773 | + | 0.718262i | \(0.255062\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 2.50000 | − | 4.33013i | 0.113872 | − | 0.197232i | ||||
\(483\) | −12.0000 | − | 20.7846i | −0.546019 | − | 0.945732i | ||||
\(484\) | −7.00000 | + | 12.1244i | −0.318182 | + | 0.551107i | ||||
\(485\) | 6.50000 | + | 11.2583i | 0.295150 | + | 0.511214i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −8.50000 | − | 14.7224i | −0.385172 | − | 0.667137i | 0.606621 | − | 0.794991i | \(-0.292524\pi\) |
−0.991793 | + | 0.127854i | \(0.959191\pi\) | |||||||
\(488\) | 12.0000 | 0.543214 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | 3.50000 | + | 6.06218i | 0.157953 | + | 0.273582i | 0.934130 | − | 0.356932i | \(-0.116177\pi\) |
−0.776178 | + | 0.630514i | \(0.782844\pi\) | |||||||
\(492\) | 6.00000 | 0.270501 | ||||||||
\(493\) | 4.00000 | − | 6.92820i | 0.180151 | − | 0.312031i | ||||
\(494\) | −24.0000 | −1.07981 | ||||||||
\(495\) | −5.00000 | −0.224733 | ||||||||
\(496\) | 3.50000 | + | 4.33013i | 0.157155 | + | 0.194428i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.00000 | −0.134433 | ||||||||
\(499\) | 19.0000 | − | 32.9090i | 0.850557 | − | 1.47321i | −0.0301498 | − | 0.999545i | \(-0.509598\pi\) |
0.880707 | − | 0.473662i | \(-0.157068\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −9.00000 | − | 15.5885i | −0.402090 | − | 0.696441i | ||||
\(502\) | −10.0000 | + | 17.3205i | −0.446322 | + | 0.773052i | ||||
\(503\) | −7.00000 | + | 12.1244i | −0.312115 | + | 0.540598i | −0.978820 | − | 0.204723i | \(-0.934371\pi\) |
0.666705 | + | 0.745321i | \(0.267704\pi\) | |||||||
\(504\) | −3.00000 | −0.133631 | ||||||||
\(505\) | −0.500000 | − | 0.866025i | −0.0222497 | − | 0.0385376i | ||||
\(506\) | −20.0000 | − | 34.6410i | −0.889108 | − | 1.53998i | ||||
\(507\) | 11.5000 | + | 19.9186i | 0.510733 | + | 0.884615i | ||||
\(508\) | −3.50000 | + | 6.06218i | −0.155287 | + | 0.268966i | ||||
\(509\) | 10.5000 | + | 18.1865i | 0.465404 | + | 0.806104i | 0.999220 | − | 0.0394971i | \(-0.0125756\pi\) |
−0.533815 | + | 0.845601i | \(0.679242\pi\) | |||||||
\(510\) | −4.00000 | + | 6.92820i | −0.177123 | + | 0.306786i | ||||
\(511\) | −18.0000 | −0.796273 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | −8.00000 | − | 13.8564i | −0.352865 | − | 0.611180i | ||||
\(515\) | −3.50000 | + | 6.06218i | −0.154228 | + | 0.267131i | ||||
\(516\) | 4.00000 | + | 6.92820i | 0.176090 | + | 0.304997i | ||||
\(517\) | −30.0000 | − | 51.9615i | −1.31940 | − | 2.28527i | ||||
\(518\) | −3.00000 | − | 5.19615i | −0.131812 | − | 0.228306i | ||||
\(519\) | 5.00000 | 0.219476 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | 1.00000 | − | 1.73205i | 0.0438108 | − | 0.0758825i | −0.843288 | − | 0.537461i | \(-0.819383\pi\) |
0.887099 | + | 0.461579i | \(0.152717\pi\) | |||||||
\(522\) | 0.500000 | + | 0.866025i | 0.0218844 | + | 0.0379049i | ||||
\(523\) | 20.0000 | 0.874539 | 0.437269 | − | 0.899331i | \(-0.355946\pi\) | ||||
0.437269 | + | 0.899331i | \(0.355946\pi\) | |||||||
\(524\) | 8.00000 | − | 13.8564i | 0.349482 | − | 0.605320i | ||||
\(525\) | 3.00000 | 0.130931 | ||||||||
\(526\) | −6.00000 | −0.261612 | ||||||||
\(527\) | −44.0000 | + | 6.92820i | −1.91667 | + | 0.301797i | ||||
\(528\) | −5.00000 | −0.217597 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 2.50000 | − | 4.33013i | 0.108593 | − | 0.188089i | ||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | −6.00000 | − | 10.3923i | −0.260133 | − | 0.450564i | ||||
\(533\) | 18.0000 | − | 31.1769i | 0.779667 | − | 1.35042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.00000 | 0.216169 | ||||||||
\(536\) | −5.00000 | − | 8.66025i | −0.215967 | − | 0.374066i | ||||
\(537\) | 5.50000 | + | 9.52628i | 0.237343 | + | 0.411089i | ||||
\(538\) | 9.00000 | + | 15.5885i | 0.388018 | + | 0.672066i | ||||
\(539\) | −5.00000 | + | 8.66025i | −0.215365 | + | 0.373024i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | −4.00000 | + | 6.92820i | −0.171973 | + | 0.297867i | −0.939110 | − | 0.343617i | \(-0.888348\pi\) |
0.767136 | + | 0.641484i | \(0.221681\pi\) | |||||||
\(542\) | −17.0000 | −0.730213 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | + | 6.92820i | −0.171499 | + | 0.297044i | ||||
\(545\) | −6.00000 | − | 10.3923i | −0.257012 | − | 0.445157i | ||||
\(546\) | −9.00000 | + | 15.5885i | −0.385164 | + | 0.667124i | ||||
\(547\) | 16.0000 | + | 27.7128i | 0.684111 | + | 1.18491i | 0.973715 | + | 0.227768i | \(0.0731428\pi\) |
−0.289605 | + | 0.957146i | \(0.593524\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | −6.00000 | − | 10.3923i | −0.256074 | − | 0.443533i | ||||
\(550\) | 5.00000 | 0.213201 | ||||||||
\(551\) | −2.00000 | + | 3.46410i | −0.0852029 | + | 0.147576i | ||||
\(552\) | 4.00000 | − | 6.92820i | 0.170251 | − | 0.294884i | ||||
\(553\) | 12.0000 | + | 20.7846i | 0.510292 | + | 0.883852i | ||||
\(554\) | −24.0000 | −1.01966 | ||||||||
\(555\) | 1.00000 | − | 1.73205i | 0.0424476 | − | 0.0735215i | ||||
\(556\) | −10.0000 | −0.424094 | ||||||||
\(557\) | −21.0000 | −0.889799 | −0.444899 | − | 0.895581i | \(-0.646761\pi\) | ||||
−0.444899 | + | 0.895581i | \(0.646761\pi\) | |||||||
\(558\) | 2.00000 | − | 5.19615i | 0.0846668 | − | 0.219971i | ||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 20.0000 | − | 34.6410i | 0.844401 | − | 1.46254i | ||||
\(562\) | −8.00000 | −0.337460 | ||||||||
\(563\) | −22.5000 | − | 38.9711i | −0.948262 | − | 1.64244i | −0.749085 | − | 0.662474i | \(-0.769506\pi\) |
−0.199177 | − | 0.979963i | \(-0.563827\pi\) | |||||||
\(564\) | 6.00000 | − | 10.3923i | 0.252646 | − | 0.437595i | ||||
\(565\) | −5.00000 | + | 8.66025i | −0.210352 | + | 0.364340i | ||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | 1.50000 | + | 2.59808i | 0.0629941 | + | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.0000 | − | 36.3731i | −0.880366 | − | 1.52484i | −0.850935 | − | 0.525271i | \(-0.823964\pi\) |
−0.0294311 | − | 0.999567i | \(-0.509370\pi\) | |||||||
\(570\) | 2.00000 | − | 3.46410i | 0.0837708 | − | 0.145095i | ||||
\(571\) | 22.0000 | + | 38.1051i | 0.920671 | + | 1.59465i | 0.798379 | + | 0.602155i | \(0.205691\pi\) |
0.122292 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(572\) | −15.0000 | + | 25.9808i | −0.627182 | + | 1.08631i | ||||
\(573\) | 26.0000 | 1.08617 | ||||||||
\(574\) | 18.0000 | 0.751305 | ||||||||
\(575\) | −4.00000 | + | 6.92820i | −0.166812 | + | 0.288926i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 15.0000 | − | 25.9808i | 0.624458 | − | 1.08159i | −0.364187 | − | 0.931326i | \(-0.618653\pi\) |
0.988645 | − | 0.150268i | \(-0.0480135\pi\) | |||||||
\(578\) | −23.5000 | − | 40.7032i | −0.977471 | − | 1.69303i | ||||
\(579\) | −6.50000 | − | 11.2583i | −0.270131 | − | 0.467880i | ||||
\(580\) | −0.500000 | − | 0.866025i | −0.0207614 | − | 0.0359597i | ||||
\(581\) | −9.00000 | −0.373383 | ||||||||
\(582\) | 6.50000 | − | 11.2583i | 0.269434 | − | 0.466673i | ||||
\(583\) | −12.5000 | + | 21.6506i | −0.517697 | + | 0.896678i | ||||
\(584\) | −3.00000 | − | 5.19615i | −0.124141 | − | 0.215018i | ||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | 37.0000 | 1.52715 | 0.763577 | − | 0.645717i | \(-0.223441\pi\) | ||||
0.763577 | + | 0.645717i | \(0.223441\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | 22.0000 | − | 3.46410i | 0.906494 | − | 0.142736i | ||||
\(590\) | −11.0000 | −0.452863 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 2.50000 | + | 4.33013i | 0.102576 | + | 0.177667i | ||||
\(595\) | −12.0000 | + | 20.7846i | −0.491952 | + | 0.852086i | ||||
\(596\) | −6.50000 | + | 11.2583i | −0.266250 | + | 0.461159i | ||||
\(597\) | −19.0000 | −0.777618 | ||||||||
\(598\) | −24.0000 | − | 41.5692i | −0.981433 | − | 1.69989i | ||||
\(599\) | 8.00000 | + | 13.8564i | 0.326871 | + | 0.566157i | 0.981889 | − | 0.189456i | \(-0.0606724\pi\) |
−0.655018 | + | 0.755613i | \(0.727339\pi\) | |||||||
\(600\) | 0.500000 | + | 0.866025i | 0.0204124 | + | 0.0353553i | ||||
\(601\) | −11.0000 | + | 19.0526i | −0.448699 | + | 0.777170i | −0.998302 | − | 0.0582563i | \(-0.981446\pi\) |
0.549602 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(602\) | 12.0000 | + | 20.7846i | 0.489083 | + | 0.847117i | ||||
\(603\) | −5.00000 | + | 8.66025i | −0.203616 | + | 0.352673i | ||||
\(604\) | −5.00000 | −0.203447 | ||||||||
\(605\) | −14.0000 | −0.569181 | ||||||||
\(606\) | −0.500000 | + | 0.866025i | −0.0203111 | + | 0.0351799i | ||||
\(607\) | 12.0000 | + | 20.7846i | 0.487065 | + | 0.843621i | 0.999889 | − | 0.0148722i | \(-0.00473415\pi\) |
−0.512824 | + | 0.858494i | \(0.671401\pi\) | |||||||
\(608\) | 2.00000 | − | 3.46410i | 0.0811107 | − | 0.140488i | ||||
\(609\) | 1.50000 | + | 2.59808i | 0.0607831 | + | 0.105279i | ||||
\(610\) | 6.00000 | + | 10.3923i | 0.242933 | + | 0.420772i | ||||
\(611\) | −36.0000 | − | 62.3538i | −1.45640 | − | 2.52257i | ||||
\(612\) | 8.00000 | 0.323381 | ||||||||
\(613\) | −8.00000 | + | 13.8564i | −0.323117 | + | 0.559655i | −0.981129 | − | 0.193352i | \(-0.938064\pi\) |
0.658012 | + | 0.753007i | \(0.271397\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 3.00000 | + | 5.19615i | 0.120972 | + | 0.209529i | ||||
\(616\) | −15.0000 | −0.604367 | ||||||||
\(617\) | 16.0000 | − | 27.7128i | 0.644136 | − | 1.11568i | −0.340365 | − | 0.940294i | \(-0.610551\pi\) |
0.984500 | − | 0.175382i | \(-0.0561162\pi\) | |||||||
\(618\) | 7.00000 | 0.281581 | ||||||||
\(619\) | −4.00000 | −0.160774 | −0.0803868 | − | 0.996764i | \(-0.525616\pi\) | ||||
−0.0803868 | + | 0.996764i | \(0.525616\pi\) | |||||||
\(620\) | −2.00000 | + | 5.19615i | −0.0803219 | + | 0.208683i | ||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | −22.0000 | −0.882120 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0.500000 | − | 0.866025i | 0.0199840 | − | 0.0346133i | ||||
\(627\) | −10.0000 | + | 17.3205i | −0.399362 | + | 0.691714i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.00000 | + | 13.8564i | 0.318981 | + | 0.552491i | ||||
\(630\) | −1.50000 | − | 2.59808i | −0.0597614 | − | 0.103510i | ||||
\(631\) | 18.5000 | + | 32.0429i | 0.736473 | + | 1.27561i | 0.954074 | + | 0.299571i | \(0.0968437\pi\) |
−0.217601 | + | 0.976038i | \(0.569823\pi\) | |||||||
\(632\) | −4.00000 | + | 6.92820i | −0.159111 | + | 0.275589i | ||||
\(633\) | −8.00000 | − | 13.8564i | −0.317971 | − | 0.550743i | ||||
\(634\) | 15.5000 | − | 26.8468i | 0.615584 | − | 1.06622i | ||||
\(635\) | −7.00000 | −0.277787 | ||||||||
\(636\) | −5.00000 | −0.198263 | ||||||||
\(637\) | −6.00000 | + | 10.3923i | −0.237729 | + | 0.411758i | ||||
\(638\) | 2.50000 | + | 4.33013i | 0.0989759 | + | 0.171431i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 6.00000 | + | 10.3923i | 0.236986 | + | 0.410471i | 0.959848 | − | 0.280521i | \(-0.0905072\pi\) |
−0.722862 | + | 0.690992i | \(0.757174\pi\) | |||||||
\(642\) | −2.50000 | − | 4.33013i | −0.0986671 | − | 0.170896i | ||||
\(643\) | 40.0000 | 1.57745 | 0.788723 | − | 0.614749i | \(-0.210743\pi\) | ||||
0.788723 | + | 0.614749i | \(0.210743\pi\) | |||||||
\(644\) | 12.0000 | − | 20.7846i | 0.472866 | − | 0.819028i | ||||
\(645\) | −4.00000 | + | 6.92820i | −0.157500 | + | 0.272798i | ||||
\(646\) | 16.0000 | + | 27.7128i | 0.629512 | + | 1.09035i | ||||
\(647\) | −12.0000 | −0.471769 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 55.0000 | 2.15894 | ||||||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 6.00000 | − | 15.5885i | 0.235159 | − | 0.610960i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.00000 | −0.352197 | −0.176099 | − | 0.984373i | \(-0.556348\pi\) | ||||
−0.176099 | + | 0.984373i | \(0.556348\pi\) | |||||||
\(654\) | −6.00000 | + | 10.3923i | −0.234619 | + | 0.406371i | ||||
\(655\) | 16.0000 | 0.625172 | ||||||||
\(656\) | 3.00000 | + | 5.19615i | 0.117130 | + | 0.202876i | ||||
\(657\) | −3.00000 | + | 5.19615i | −0.117041 | + | 0.202721i | ||||
\(658\) | 18.0000 | − | 31.1769i | 0.701713 | − | 1.21540i | ||||
\(659\) | 15.0000 | 0.584317 | 0.292159 | − | 0.956370i | \(-0.405627\pi\) | ||||
0.292159 | + | 0.956370i | \(0.405627\pi\) | |||||||
\(660\) | −2.50000 | − | 4.33013i | −0.0973124 | − | 0.168550i | ||||
\(661\) | −4.00000 | − | 6.92820i | −0.155582 | − | 0.269476i | 0.777689 | − | 0.628649i | \(-0.216392\pi\) |
−0.933271 | + | 0.359174i | \(0.883059\pi\) | |||||||
\(662\) | 6.00000 | + | 10.3923i | 0.233197 | + | 0.403908i | ||||
\(663\) | 24.0000 | − | 41.5692i | 0.932083 | − | 1.61441i | ||||
\(664\) | −1.50000 | − | 2.59808i | −0.0582113 | − | 0.100825i | ||||
\(665\) | 6.00000 | − | 10.3923i | 0.232670 | − | 0.402996i | ||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | −8.00000 | −0.309761 | ||||||||
\(668\) | 9.00000 | − | 15.5885i | 0.348220 | − | 0.603136i | ||||
\(669\) | 0.500000 | + | 0.866025i | 0.0193311 | + | 0.0334825i | ||||
\(670\) | 5.00000 | − | 8.66025i | 0.193167 | − | 0.334575i | ||||
\(671\) | −30.0000 | − | 51.9615i | −1.15814 | − | 2.00595i | ||||
\(672\) | −1.50000 | − | 2.59808i | −0.0578638 | − | 0.100223i | ||||
\(673\) | 2.50000 | + | 4.33013i | 0.0963679 | + | 0.166914i | 0.910179 | − | 0.414216i | \(-0.135944\pi\) |
−0.813811 | + | 0.581130i | \(0.802611\pi\) | |||||||
\(674\) | 23.0000 | 0.885927 | ||||||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | −19.5000 | − | 33.7750i | −0.749446 | − | 1.29808i | −0.948089 | − | 0.318006i | \(-0.896987\pi\) |
0.198643 | − | 0.980072i | \(-0.436347\pi\) | |||||||
\(678\) | 10.0000 | 0.384048 | ||||||||
\(679\) | 19.5000 | − | 33.7750i | 0.748341 | − | 1.29617i | ||||
\(680\) | −8.00000 | −0.306786 | ||||||||
\(681\) | 25.0000 | 0.958002 | ||||||||
\(682\) | 10.0000 | − | 25.9808i | 0.382920 | − | 0.994855i | ||||
\(683\) | 9.00000 | 0.344375 | 0.172188 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172188 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(684\) | −4.00000 | −0.152944 | ||||||||
\(685\) | −3.00000 | + | 5.19615i | −0.114624 | + | 0.198535i | ||||
\(686\) | 15.0000 | 0.572703 | ||||||||
\(687\) | −1.00000 | − | 1.73205i | −0.0381524 | − | 0.0660819i | ||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | −15.0000 | + | 25.9808i | −0.571454 | + | 0.989788i | ||||
\(690\) | 8.00000 | 0.304555 | ||||||||
\(691\) | −5.00000 | − | 8.66025i | −0.190209 | − | 0.329452i | 0.755110 | − | 0.655598i | \(-0.227583\pi\) |
−0.945319 | + | 0.326146i | \(0.894250\pi\) | |||||||
\(692\) | 2.50000 | + | 4.33013i | 0.0950357 | + | 0.164607i | ||||
\(693\) | 7.50000 | + | 12.9904i | 0.284901 | + | 0.493464i | ||||
\(694\) | −2.50000 | + | 4.33013i | −0.0948987 | + | 0.164369i | ||||
\(695\) | −5.00000 | − | 8.66025i | −0.189661 | − | 0.328502i | ||||
\(696\) | −0.500000 | + | 0.866025i | −0.0189525 | + | 0.0328266i | ||||
\(697\) | −48.0000 | −1.81813 | ||||||||
\(698\) | −20.0000 | −0.757011 | ||||||||
\(699\) | −7.00000 | + | 12.1244i | −0.264764 | + | 0.458585i | ||||
\(700\) | 1.50000 | + | 2.59808i | 0.0566947 | + | 0.0981981i | ||||
\(701\) | −15.5000 | + | 26.8468i | −0.585427 | + | 1.01399i | 0.409395 | + | 0.912357i | \(0.365740\pi\) |
−0.994822 | + | 0.101632i | \(0.967594\pi\) | |||||||
\(702\) | 3.00000 | + | 5.19615i | 0.113228 | + | 0.196116i | ||||
\(703\) | −4.00000 | − | 6.92820i | −0.150863 | − | 0.261302i | ||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | 12.0000 | 0.451946 | ||||||||
\(706\) | 9.00000 | − | 15.5885i | 0.338719 | − | 0.586679i | ||||
\(707\) | −1.50000 | + | 2.59808i | −0.0564133 | + | 0.0977107i | ||||
\(708\) | 5.50000 | + | 9.52628i | 0.206703 | + | 0.358020i | ||||
\(709\) | −22.0000 | −0.826227 | −0.413114 | − | 0.910679i | \(-0.635559\pi\) | ||||
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.0000 | + | 34.6410i | 1.04861 | + | 1.29732i | ||||
\(714\) | 24.0000 | 0.898177 | ||||||||
\(715\) | −30.0000 | −1.12194 | ||||||||
\(716\) | −5.50000 | + | 9.52628i | −0.205545 | + | 0.356014i | ||||
\(717\) | −6.00000 | −0.224074 | ||||||||
\(718\) | −2.00000 | − | 3.46410i | −0.0746393 | − | 0.129279i | ||||
\(719\) | 3.00000 | − | 5.19615i | 0.111881 | − | 0.193784i | −0.804648 | − | 0.593753i | \(-0.797646\pi\) |
0.916529 | + | 0.399969i | \(0.130979\pi\) | |||||||
\(720\) | 0.500000 | − | 0.866025i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | 21.0000 | 0.782081 | ||||||||
\(722\) | 1.50000 | + | 2.59808i | 0.0558242 | + | 0.0966904i | ||||
\(723\) | −2.50000 | − | 4.33013i | −0.0929760 | − | 0.161039i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.500000 | − | 0.866025i | 0.0185695 | − | 0.0321634i | ||||
\(726\) | 7.00000 | + | 12.1244i | 0.259794 | + | 0.449977i | ||||
\(727\) | −9.50000 | + | 16.4545i | −0.352335 | + | 0.610263i | −0.986658 | − | 0.162805i | \(-0.947946\pi\) |
0.634323 | + | 0.773068i | \(0.281279\pi\) | |||||||
\(728\) | −18.0000 | −0.667124 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.00000 | − | 5.19615i | 0.111035 | − | 0.192318i | ||||
\(731\) | −32.0000 | − | 55.4256i | −1.18356 | − | 2.04999i | ||||
\(732\) | 6.00000 | − | 10.3923i | 0.221766 | − | 0.384111i | ||||
\(733\) | 23.0000 | + | 39.8372i | 0.849524 | + | 1.47142i | 0.881633 | + | 0.471935i | \(0.156444\pi\) |
−0.0321090 | + | 0.999484i | \(0.510222\pi\) | |||||||
\(734\) | −2.00000 | − | 3.46410i | −0.0738213 | − | 0.127862i | ||||
\(735\) | −1.00000 | − | 1.73205i | −0.0368856 | − | 0.0638877i | ||||
\(736\) | 8.00000 | 0.294884 | ||||||||
\(737\) | −25.0000 | + | 43.3013i | −0.920887 | + | 1.59502i | ||||
\(738\) | 3.00000 | − | 5.19615i | 0.110432 | − | 0.191273i | ||||
\(739\) | 5.00000 | + | 8.66025i | 0.183928 | + | 0.318573i | 0.943215 | − | 0.332184i | \(-0.107785\pi\) |
−0.759287 | + | 0.650756i | \(0.774452\pi\) | |||||||
\(740\) | 2.00000 | 0.0735215 | ||||||||
\(741\) | −12.0000 | + | 20.7846i | −0.440831 | + | 0.763542i | ||||
\(742\) | −15.0000 | −0.550667 | ||||||||
\(743\) | −24.0000 | −0.880475 | −0.440237 | − | 0.897881i | \(-0.645106\pi\) | ||||
−0.440237 | + | 0.897881i | \(0.645106\pi\) | |||||||
\(744\) | 5.50000 | − | 0.866025i | 0.201640 | − | 0.0317500i | ||||
\(745\) | −13.0000 | −0.476283 | ||||||||
\(746\) | 4.00000 | 0.146450 | ||||||||
\(747\) | −1.50000 | + | 2.59808i | −0.0548821 | + | 0.0950586i | ||||
\(748\) | 40.0000 | 1.46254 | ||||||||
\(749\) | −7.50000 | − | 12.9904i | −0.274044 | − | 0.474658i | ||||
\(750\) | −0.500000 | + | 0.866025i | −0.0182574 | + | 0.0316228i | ||||
\(751\) | −7.50000 | + | 12.9904i | −0.273679 | + | 0.474026i | −0.969801 | − | 0.243898i | \(-0.921574\pi\) |
0.696122 | + | 0.717923i | \(0.254907\pi\) | |||||||
\(752\) | 12.0000 | 0.437595 | ||||||||
\(753\) | 10.0000 | + | 17.3205i | 0.364420 | + | 0.631194i | ||||
\(754\) | 3.00000 | + | 5.19615i | 0.109254 | + | 0.189233i | ||||
\(755\) | −2.50000 | − | 4.33013i | −0.0909843 | − | 0.157589i | ||||
\(756\) | −1.50000 | + | 2.59808i | −0.0545545 | + | 0.0944911i | ||||
\(757\) | −18.0000 | − | 31.1769i | −0.654221 | − | 1.13314i | −0.982088 | − | 0.188420i | \(-0.939663\pi\) |
0.327867 | − | 0.944724i | \(-0.393670\pi\) | |||||||
\(758\) | −14.0000 | + | 24.2487i | −0.508503 | + | 0.880753i | ||||
\(759\) | −40.0000 | −1.45191 | ||||||||
\(760\) | 4.00000 | 0.145095 | ||||||||
\(761\) | 7.00000 | − | 12.1244i | 0.253750 | − | 0.439508i | −0.710805 | − | 0.703389i | \(-0.751669\pi\) |
0.964555 | + | 0.263881i | \(0.0850027\pi\) | |||||||
\(762\) | 3.50000 | + | 6.06218i | 0.126792 | + | 0.219610i | ||||
\(763\) | −18.0000 | + | 31.1769i | −0.651644 | + | 1.12868i | ||||
\(764\) | 13.0000 | + | 22.5167i | 0.470323 | + | 0.814624i | ||||
\(765\) | 4.00000 | + | 6.92820i | 0.144620 | + | 0.250490i | ||||
\(766\) | −11.0000 | − | 19.0526i | −0.397446 | − | 0.688397i | ||||
\(767\) | 66.0000 | 2.38312 | ||||||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 11.5000 | − | 19.9186i | 0.414701 | − | 0.718283i | −0.580696 | − | 0.814120i | \(-0.697220\pi\) |
0.995397 | + | 0.0958377i | \(0.0305530\pi\) | |||||||
\(770\) | −7.50000 | − | 12.9904i | −0.270281 | − | 0.468141i | ||||
\(771\) | −16.0000 | −0.576226 | ||||||||
\(772\) | 6.50000 | − | 11.2583i | 0.233940 | − | 0.405196i | ||||
\(773\) | 14.0000 | 0.503545 | 0.251773 | − | 0.967786i | \(-0.418987\pi\) | ||||
0.251773 | + | 0.967786i | \(0.418987\pi\) | |||||||
\(774\) | 8.00000 | 0.287554 | ||||||||
\(775\) | −5.50000 | + | 0.866025i | −0.197566 | + | 0.0311086i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | −6.00000 | −0.215249 | ||||||||
\(778\) | −15.0000 | + | 25.9808i | −0.537776 | + | 0.931455i | ||||
\(779\) | 24.0000 | 0.859889 | ||||||||
\(780\) | −3.00000 | − | 5.19615i | −0.107417 | − | 0.186052i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −32.0000 | + | 55.4256i | −1.14432 | + | 1.98202i | ||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.00000 | − | 13.8564i | −0.285351 | − | 0.494242i | ||||
\(787\) | −2.00000 | + | 3.46410i | −0.0712923 | + | 0.123482i | −0.899468 | − | 0.436987i | \(-0.856046\pi\) |
0.828176 | + | 0.560469i | \(0.189379\pi\) | |||||||
\(788\) | 5.00000 | + | 8.66025i | 0.178118 | + | 0.308509i | ||||
\(789\) | −3.00000 | + | 5.19615i | −0.106803 | + | 0.184988i | ||||
\(790\) | −8.00000 | −0.284627 | ||||||||
\(791\) | 30.0000 | 1.06668 | ||||||||
\(792\) | −2.50000 | + | 4.33013i | −0.0888336 | + | 0.153864i | ||||
\(793\) | −36.0000 | − | 62.3538i | −1.27840 | − | 2.21425i | ||||
\(794\) | 10.0000 | − | 17.3205i | 0.354887 | − | 0.614682i | ||||
\(795\) | −2.50000 | − | 4.33013i | −0.0886659 | − | 0.153574i | ||||
\(796\) | −9.50000 | − | 16.4545i | −0.336719 | − | 0.583214i | ||||
\(797\) | 4.50000 | + | 7.79423i | 0.159398 | + | 0.276086i | 0.934652 | − | 0.355564i | \(-0.115711\pi\) |
−0.775254 | + | 0.631650i | \(0.782378\pi\) | |||||||
\(798\) | −12.0000 | −0.424795 | ||||||||
\(799\) | −48.0000 | + | 83.1384i | −1.69812 | + | 2.94123i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.00000 | 0.0706225 | ||||||||
\(803\) | −15.0000 | + | 25.9808i | −0.529339 | + | 0.916841i | ||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | 24.0000 | 0.845889 | ||||||||
\(806\) | 12.0000 | − | 31.1769i | 0.422682 | − | 1.09816i | ||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −1.00000 | −0.0351799 | ||||||||
\(809\) | −22.0000 | + | 38.1051i | −0.773479 | + | 1.33970i | 0.162167 | + | 0.986763i | \(0.448152\pi\) |
−0.935645 | + | 0.352941i | \(0.885182\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 3.00000 | + | 5.19615i | 0.105344 | + | 0.182462i | 0.913879 | − | 0.405987i | \(-0.133072\pi\) |
−0.808535 | + | 0.588449i | \(0.799739\pi\) | |||||||
\(812\) | −1.50000 | + | 2.59808i | −0.0526397 | + | 0.0911746i | ||||
\(813\) | −8.50000 | + | 14.7224i | −0.298108 | + | 0.516338i | ||||
\(814\) | −10.0000 | −0.350500 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.00000 | + | 6.92820i | 0.140028 | + | 0.242536i | ||||
\(817\) | 16.0000 | + | 27.7128i | 0.559769 | + | 0.969549i | ||||
\(818\) | 4.50000 | − | 7.79423i | 0.157339 | − | 0.272519i | ||||
\(819\) | 9.00000 | + | 15.5885i | 0.314485 | + | 0.544705i | ||||
\(820\) | −3.00000 | + | 5.19615i | −0.104765 | + | 0.181458i | ||||
\(821\) | −25.0000 | −0.872506 | −0.436253 | − | 0.899824i | \(-0.643695\pi\) | ||||
−0.436253 | + | 0.899824i | \(0.643695\pi\) | |||||||
\(822\) | 6.00000 | 0.209274 | ||||||||
\(823\) | −15.5000 | + | 26.8468i | −0.540296 | + | 0.935820i | 0.458591 | + | 0.888648i | \(0.348354\pi\) |
−0.998887 | + | 0.0471726i | \(0.984979\pi\) | |||||||
\(824\) | 3.50000 | + | 6.06218i | 0.121928 | + | 0.211186i | ||||
\(825\) | 2.50000 | − | 4.33013i | 0.0870388 | − | 0.150756i | ||||
\(826\) | 16.5000 | + | 28.5788i | 0.574108 | + | 0.994385i | ||||
\(827\) | −14.0000 | − | 24.2487i | −0.486828 | − | 0.843210i | 0.513058 | − | 0.858354i | \(-0.328513\pi\) |
−0.999885 | + | 0.0151439i | \(0.995179\pi\) | |||||||
\(828\) | −4.00000 | − | 6.92820i | −0.139010 | − | 0.240772i | ||||
\(829\) | 32.0000 | 1.11141 | 0.555703 | − | 0.831381i | \(-0.312449\pi\) | ||||
0.555703 | + | 0.831381i | \(0.312449\pi\) | |||||||
\(830\) | 1.50000 | − | 2.59808i | 0.0520658 | − | 0.0901805i | ||||
\(831\) | −12.0000 | + | 20.7846i | −0.416275 | + | 0.721010i | ||||
\(832\) | −3.00000 | − | 5.19615i | −0.104006 | − | 0.180144i | ||||
\(833\) | 16.0000 | 0.554367 | ||||||||
\(834\) | −5.00000 | + | 8.66025i | −0.173136 | + | 0.299880i | ||||
\(835\) | 18.0000 | 0.622916 | ||||||||
\(836\) | −20.0000 | −0.691714 | ||||||||
\(837\) | −3.50000 | − | 4.33013i | −0.120978 | − | 0.149671i | ||||
\(838\) | −27.0000 | −0.932700 | ||||||||
\(839\) | 28.0000 | 0.966667 | 0.483334 | − | 0.875436i | \(-0.339426\pi\) | ||||
0.483334 | + | 0.875436i | \(0.339426\pi\) | |||||||
\(840\) | 1.50000 | − | 2.59808i | 0.0517549 | − | 0.0896421i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −16.0000 | − | 27.7128i | −0.551396 | − | 0.955047i | ||||
\(843\) | −4.00000 | + | 6.92820i | −0.137767 | + | 0.238620i | ||||
\(844\) | 8.00000 | − | 13.8564i | 0.275371 | − | 0.476957i | ||||
\(845\) | −23.0000 | −0.791224 | ||||||||
\(846\) | −6.00000 | − | 10.3923i | −0.206284 | − | 0.357295i | ||||
\(847\) | 21.0000 | + | 36.3731i | 0.721569 | + | 1.24979i | ||||
\(848\) | −2.50000 | − | 4.33013i | −0.0858504 | − | 0.148697i | ||||
\(849\) | −3.00000 | + | 5.19615i | −0.102960 | + | 0.178331i | ||||
\(850\) | −4.00000 | − | 6.92820i | −0.137199 | − | 0.237635i | ||||
\(851\) | 8.00000 | − | 13.8564i | 0.274236 | − | 0.474991i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.0000 | 1.36957 | 0.684787 | − | 0.728743i | \(-0.259895\pi\) | ||||
0.684787 | + | 0.728743i | \(0.259895\pi\) | |||||||
\(854\) | 18.0000 | − | 31.1769i | 0.615947 | − | 1.06685i | ||||
\(855\) | −2.00000 | − | 3.46410i | −0.0683986 | − | 0.118470i | ||||
\(856\) | 2.50000 | − | 4.33013i | 0.0854482 | − | 0.148001i | ||||
\(857\) | 12.0000 | + | 20.7846i | 0.409912 | + | 0.709989i | 0.994880 | − | 0.101068i | \(-0.0322260\pi\) |
−0.584967 | + | 0.811057i | \(0.698893\pi\) | |||||||
\(858\) | 15.0000 | + | 25.9808i | 0.512092 | + | 0.886969i | ||||
\(859\) | −21.0000 | − | 36.3731i | −0.716511 | − | 1.24103i | −0.962374 | − | 0.271728i | \(-0.912405\pi\) |
0.245863 | − | 0.969305i | \(-0.420929\pi\) | |||||||
\(860\) | −8.00000 | −0.272798 | ||||||||
\(861\) | 9.00000 | − | 15.5885i | 0.306719 | − | 0.531253i | ||||
\(862\) | 15.0000 | − | 25.9808i | 0.510902 | − | 0.884908i | ||||
\(863\) | −24.0000 | − | 41.5692i | −0.816970 | − | 1.41503i | −0.907905 | − | 0.419176i | \(-0.862319\pi\) |
0.0909355 | − | 0.995857i | \(-0.471014\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −2.50000 | + | 4.33013i | −0.0850026 | + | 0.147229i | ||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | −47.0000 | −1.59620 | ||||||||
\(868\) | 16.5000 | − | 2.59808i | 0.560046 | − | 0.0881845i | ||||
\(869\) | 40.0000 | 1.35691 | ||||||||
\(870\) | −1.00000 | −0.0339032 | ||||||||
\(871\) | −30.0000 | + | 51.9615i | −1.01651 | + | 1.76065i | ||||
\(872\) | −12.0000 | −0.406371 | ||||||||
\(873\) | −6.50000 | − | 11.2583i | −0.219992 | − | 0.381037i | ||||
\(874\) | 16.0000 | − | 27.7128i | 0.541208 | − | 0.937400i | ||||
\(875\) | −1.50000 | + | 2.59808i | −0.0507093 | + | 0.0878310i | ||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | 4.00000 | + | 6.92820i | 0.135070 | + | 0.233949i | 0.925624 | − | 0.378444i | \(-0.123541\pi\) |
−0.790554 | + | 0.612392i | \(0.790207\pi\) | |||||||
\(878\) | 2.50000 | + | 4.33013i | 0.0843709 | + | 0.146135i | ||||
\(879\) | 4.50000 | + | 7.79423i | 0.151781 | + | 0.262893i | ||||
\(880\) | 2.50000 | − | 4.33013i | 0.0842750 | − | 0.145969i | ||||
\(881\) | −9.00000 | − | 15.5885i | −0.303218 | − | 0.525188i | 0.673645 | − | 0.739055i | \(-0.264728\pi\) |
−0.976863 | + | 0.213866i | \(0.931394\pi\) | |||||||
\(882\) | −1.00000 | + | 1.73205i | −0.0336718 | + | 0.0583212i | ||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 48.0000 | 1.61441 | ||||||||
\(885\) | −5.50000 | + | 9.52628i | −0.184880 | + | 0.320222i | ||||
\(886\) | 8.00000 | + | 13.8564i | 0.268765 | + | 0.465515i | ||||
\(887\) | −18.0000 | + | 31.1769i | −0.604381 | + | 1.04682i | 0.387768 | + | 0.921757i | \(0.373246\pi\) |
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | −1.00000 | − | 1.73205i | −0.0335578 | − | 0.0581238i | ||||
\(889\) | 10.5000 | + | 18.1865i | 0.352159 | + | 0.609957i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | −0.500000 | + | 0.866025i | −0.0167412 | + | 0.0289967i | ||||
\(893\) | 24.0000 | − | 41.5692i | 0.803129 | − | 1.39106i | ||||
\(894\) | 6.50000 | + | 11.2583i | 0.217393 | + | 0.376535i | ||||
\(895\) | −11.0000 | −0.367689 | ||||||||
\(896\) | 1.50000 | − | 2.59808i | 0.0501115 | − | 0.0867956i | ||||
\(897\) | −48.0000 | −1.60267 | ||||||||
\(898\) | −24.0000 | −0.800890 | ||||||||
\(899\) | −3.50000 | − | 4.33013i | −0.116732 | − | 0.144418i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 40.0000 | 1.33259 | ||||||||
\(902\) | 15.0000 | − | 25.9808i | 0.499445 | − | 0.865065i | ||||
\(903\) | 24.0000 | 0.798670 | ||||||||
\(904\) | 5.00000 | + | 8.66025i | 0.166298 | + | 0.288036i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.50000 | + | 4.33013i | −0.0830569 | + | 0.143859i | ||||
\(907\) | −26.0000 | −0.863316 | −0.431658 | − | 0.902037i | \(-0.642071\pi\) | ||||
−0.431658 | + | 0.902037i | \(0.642071\pi\) | |||||||
\(908\) | 12.5000 | + | 21.6506i | 0.414827 | + | 0.718502i | ||||
\(909\) | 0.500000 | + | 0.866025i | 0.0165840 | + | 0.0287242i | ||||
\(910\) | −9.00000 | − | 15.5885i | −0.298347 | − | 0.516752i | ||||
\(911\) | −15.0000 | + | 25.9808i | −0.496972 | + | 0.860781i | −0.999994 | − | 0.00349271i | \(-0.998888\pi\) |
0.503022 | + | 0.864274i | \(0.332222\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | −7.50000 | + | 12.9904i | −0.248214 | + | 0.429919i | ||||
\(914\) | −22.0000 | −0.727695 | ||||||||
\(915\) | 12.0000 | 0.396708 | ||||||||
\(916\) | 1.00000 | − | 1.73205i | 0.0330409 | − | 0.0572286i | ||||
\(917\) | −24.0000 | − | 41.5692i | −0.792550 | − | 1.37274i | ||||
\(918\) | 4.00000 | − | 6.92820i | 0.132020 | − | 0.228665i | ||||
\(919\) | 11.5000 | + | 19.9186i | 0.379350 | + | 0.657053i | 0.990968 | − | 0.134100i | \(-0.0428143\pi\) |
−0.611618 | + | 0.791153i | \(0.709481\pi\) | |||||||
\(920\) | 4.00000 | + | 6.92820i | 0.131876 | + | 0.228416i | ||||
\(921\) | 1.00000 | + | 1.73205i | 0.0329511 | + | 0.0570730i | ||||
\(922\) | 1.00000 | 0.0329332 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −7.50000 | + | 12.9904i | −0.246732 | + | 0.427352i | ||||
\(925\) | 1.00000 | + | 1.73205i | 0.0328798 | + | 0.0569495i | ||||
\(926\) | 27.0000 | 0.887275 | ||||||||
\(927\) | 3.50000 | − | 6.06218i | 0.114955 | − | 0.199108i | ||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 12.0000 | 0.393707 | 0.196854 | − | 0.980433i | \(-0.436928\pi\) | ||||
0.196854 | + | 0.980433i | \(0.436928\pi\) | |||||||
\(930\) | 3.50000 | + | 4.33013i | 0.114770 | + | 0.141990i | ||||
\(931\) | −8.00000 | −0.262189 | ||||||||
\(932\) | −14.0000 | −0.458585 | ||||||||
\(933\) | −11.0000 | + | 19.0526i | −0.360124 | + | 0.623753i | ||||
\(934\) | 23.0000 | 0.752583 | ||||||||
\(935\) | 20.0000 | + | 34.6410i | 0.654070 | + | 1.13288i | ||||
\(936\) | −3.00000 | + | 5.19615i | −0.0980581 | + | 0.169842i | ||||
\(937\) | 19.0000 | − | 32.9090i | 0.620703 | − | 1.07509i | −0.368652 | − | 0.929567i | \(-0.620181\pi\) |
0.989355 | − | 0.145522i | \(-0.0464860\pi\) | |||||||
\(938\) | −30.0000 | −0.979535 | ||||||||
\(939\) | −0.500000 | − | 0.866025i | −0.0163169 | − | 0.0282617i | ||||
\(940\) | 6.00000 | + | 10.3923i | 0.195698 | + | 0.338960i | ||||
\(941\) | 7.50000 | + | 12.9904i | 0.244493 | + | 0.423474i | 0.961989 | − | 0.273088i | \(-0.0880451\pi\) |
−0.717496 | + | 0.696563i | \(0.754712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | + | 41.5692i | 0.781548 | + | 1.35368i | ||||
\(944\) | −5.50000 | + | 9.52628i | −0.179010 | + | 0.310054i | ||||
\(945\) | −3.00000 | −0.0975900 | ||||||||
\(946\) | 40.0000 | 1.30051 | ||||||||
\(947\) | −26.0000 | + | 45.0333i | −0.844886 | + | 1.46339i | 0.0408333 | + | 0.999166i | \(0.486999\pi\) |
−0.885720 | + | 0.464220i | \(0.846335\pi\) | |||||||
\(948\) | 4.00000 | + | 6.92820i | 0.129914 | + | 0.225018i | ||||
\(949\) | −18.0000 | + | 31.1769i | −0.584305 | + | 1.01205i | ||||
\(950\) | 2.00000 | + | 3.46410i | 0.0648886 | + | 0.112390i | ||||
\(951\) | −15.5000 | − | 26.8468i | −0.502622 | − | 0.870567i | ||||
\(952\) | 12.0000 | + | 20.7846i | 0.388922 | + | 0.673633i | ||||
\(953\) | −24.0000 | −0.777436 | −0.388718 | − | 0.921357i | \(-0.627082\pi\) | ||||
−0.388718 | + | 0.921357i | \(0.627082\pi\) | |||||||
\(954\) | −2.50000 | + | 4.33013i | −0.0809405 | + | 0.140193i | ||||
\(955\) | −13.0000 | + | 22.5167i | −0.420670 | + | 0.728622i | ||||
\(956\) | −3.00000 | − | 5.19615i | −0.0970269 | − | 0.168056i | ||||
\(957\) | 5.00000 | 0.161627 | ||||||||
\(958\) | −6.00000 | + | 10.3923i | −0.193851 | + | 0.335760i | ||||
\(959\) | 18.0000 | 0.581250 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −6.50000 | + | 30.3109i | −0.209677 | + | 0.977771i | ||||
\(962\) | −12.0000 | −0.386896 | ||||||||
\(963\) | −5.00000 | −0.161123 | ||||||||
\(964\) | 2.50000 | − | 4.33013i | 0.0805196 | − | 0.139464i | ||||
\(965\) | 13.0000 | 0.418485 | ||||||||
\(966\) | −12.0000 | − | 20.7846i | −0.386094 | − | 0.668734i | ||||
\(967\) | −8.00000 | + | 13.8564i | −0.257263 | + | 0.445592i | −0.965508 | − | 0.260375i | \(-0.916154\pi\) |
0.708245 | + | 0.705967i | \(0.249487\pi\) | |||||||
\(968\) | −7.00000 | + | 12.1244i | −0.224989 | + | 0.389692i | ||||
\(969\) | 32.0000 | 1.02799 | ||||||||
\(970\) | 6.50000 | + | 11.2583i | 0.208702 | + | 0.361483i | ||||
\(971\) | 16.5000 | + | 28.5788i | 0.529510 | + | 0.917139i | 0.999408 | + | 0.0344175i | \(0.0109576\pi\) |
−0.469897 | + | 0.882721i | \(0.655709\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −15.0000 | + | 25.9808i | −0.480878 | + | 0.832905i | ||||
\(974\) | −8.50000 | − | 14.7224i | −0.272358 | − | 0.471737i | ||||
\(975\) | 3.00000 | − | 5.19615i | 0.0960769 | − | 0.166410i | ||||
\(976\) | 12.0000 | 0.384111 | ||||||||
\(977\) | −56.0000 | −1.79160 | −0.895799 | − | 0.444459i | \(-0.853396\pi\) | ||||
−0.895799 | + | 0.444459i | \(0.853396\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | − | 1.73205i | 0.0319438 | − | 0.0553283i | ||||
\(981\) | 6.00000 | + | 10.3923i | 0.191565 | + | 0.331801i | ||||
\(982\) | 3.50000 | + | 6.06218i | 0.111689 | + | 0.193452i | ||||
\(983\) | 14.0000 | + | 24.2487i | 0.446531 | + | 0.773414i | 0.998157 | − | 0.0606773i | \(-0.0193260\pi\) |
−0.551627 | + | 0.834091i | \(0.685993\pi\) | |||||||
\(984\) | 6.00000 | 0.191273 | ||||||||
\(985\) | −5.00000 | + | 8.66025i | −0.159313 | + | 0.275939i | ||||
\(986\) | 4.00000 | − | 6.92820i | 0.127386 | − | 0.220639i | ||||
\(987\) | −18.0000 | − | 31.1769i | −0.572946 | − | 0.992372i | ||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | −32.0000 | + | 55.4256i | −1.01754 | + | 1.76243i | ||||
\(990\) | −5.00000 | −0.158910 | ||||||||
\(991\) | 8.00000 | 0.254128 | 0.127064 | − | 0.991894i | \(-0.459445\pi\) | ||||
0.127064 | + | 0.991894i | \(0.459445\pi\) | |||||||
\(992\) | 3.50000 | + | 4.33013i | 0.111125 | + | 0.137482i | ||||
\(993\) | 12.0000 | 0.380808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.50000 | − | 16.4545i | 0.301170 | − | 0.521642i | ||||
\(996\) | −3.00000 | −0.0950586 | ||||||||
\(997\) | 5.00000 | + | 8.66025i | 0.158352 | + | 0.274273i | 0.934274 | − | 0.356555i | \(-0.116049\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 19.0000 | − | 32.9090i | 0.601434 | − | 1.04172i | ||||
\(999\) | −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 | 930.2.i.h.811.1 | yes | 2 | |
31.25 | even | 3 | inner | 930.2.i.h.211.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.h.211.1 | ✓ | 2 | 31.25 | even | 3 | inner | |
930.2.i.h.811.1 | yes | 2 | 1.1 | even | 1 | trivial |