Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(221,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, 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("770.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.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: | \(6.14848095564\) |
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 | 221.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.221 |
Dual form | 770.2.i.d.331.1 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | + | 2.59808i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | −1.50000 | − | 2.59808i | −0.433013 | − | 0.750000i | ||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 2.50000 | − | 0.866025i | 0.668153 | − | 0.231455i | ||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 3.00000 | − | 5.19615i | 0.707107 | − | 1.22474i | ||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 6.00000 | + | 5.19615i | 1.30931 | + | 1.13389i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 1.50000 | − | 2.59808i | 0.306186 | − | 0.530330i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −0.500000 | − | 0.866025i | −0.0980581 | − | 0.169842i | ||||
\(27\) | 9.00000 | 1.73205 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 1.50000 | + | 2.59808i | 0.273861 | + | 0.474342i | ||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.50000 | + | 2.59808i | 0.261116 | + | 0.452267i | ||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | −2.50000 | + | 0.866025i | −0.422577 | + | 0.146385i | ||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | 2.00000 | − | 3.46410i | 0.324443 | − | 0.561951i | ||||
\(39\) | 1.50000 | − | 2.59808i | 0.240192 | − | 0.416025i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | −12.0000 | −1.87409 | −0.937043 | − | 0.349215i | \(-0.886448\pi\) | ||||
−0.937043 | + | 0.349215i | \(0.886448\pi\) | |||||||
\(42\) | −1.50000 | + | 7.79423i | −0.231455 | + | 1.20268i | ||||
\(43\) | 12.0000 | 1.82998 | 0.914991 | − | 0.403473i | \(-0.132197\pi\) | ||||
0.914991 | + | 0.403473i | \(0.132197\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | −3.00000 | + | 5.19615i | −0.447214 | + | 0.774597i | ||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | 3.00000 | + | 5.19615i | 0.437595 | + | 0.757937i | 0.997503 | − | 0.0706177i | \(-0.0224970\pi\) |
−0.559908 | + | 0.828554i | \(0.689164\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 9.00000 | + | 15.5885i | 1.26025 | + | 2.18282i | ||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 4.50000 | + | 7.79423i | 0.612372 | + | 1.06066i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −0.500000 | + | 2.59808i | −0.0668153 | + | 0.347183i | ||||
\(57\) | 12.0000 | 1.58944 | ||||||||
\(58\) | 0.500000 | + | 0.866025i | 0.0656532 | + | 0.113715i | ||||
\(59\) | −7.50000 | + | 12.9904i | −0.976417 | + | 1.69120i | −0.301239 | + | 0.953549i | \(0.597400\pi\) |
−0.675178 | + | 0.737655i | \(0.735933\pi\) | |||||||
\(60\) | −1.50000 | + | 2.59808i | −0.193649 | + | 0.335410i | ||||
\(61\) | −1.50000 | − | 2.59808i | −0.192055 | − | 0.332650i | 0.753876 | − | 0.657017i | \(-0.228182\pi\) |
−0.945931 | + | 0.324367i | \(0.894849\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | −15.0000 | + | 5.19615i | −1.88982 | + | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.500000 | + | 0.866025i | 0.0620174 | + | 0.107417i | ||||
\(66\) | −1.50000 | + | 2.59808i | −0.184637 | + | 0.319801i | ||||
\(67\) | 3.50000 | − | 6.06218i | 0.427593 | − | 0.740613i | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 12.0000 | 1.44463 | ||||||||
\(70\) | −2.00000 | − | 1.73205i | −0.239046 | − | 0.207020i | ||||
\(71\) | 10.0000 | 1.18678 | 0.593391 | − | 0.804914i | \(-0.297789\pi\) | ||||
0.593391 | + | 0.804914i | \(0.297789\pi\) | |||||||
\(72\) | 3.00000 | + | 5.19615i | 0.353553 | + | 0.612372i | ||||
\(73\) | 2.00000 | − | 3.46410i | 0.234082 | − | 0.405442i | −0.724923 | − | 0.688830i | \(-0.758125\pi\) |
0.959006 | + | 0.283387i | \(0.0914581\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | −1.50000 | − | 2.59808i | −0.173205 | − | 0.300000i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | −2.00000 | − | 1.73205i | −0.227921 | − | 0.197386i | ||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | −7.50000 | − | 12.9904i | −0.843816 | − | 1.46153i | −0.886646 | − | 0.462450i | \(-0.846971\pi\) |
0.0428296 | − | 0.999082i | \(-0.486363\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −6.00000 | − | 10.3923i | −0.662589 | − | 1.14764i | ||||
\(83\) | 10.0000 | 1.09764 | 0.548821 | − | 0.835940i | \(-0.315077\pi\) | ||||
0.548821 | + | 0.835940i | \(0.315077\pi\) | |||||||
\(84\) | −7.50000 | + | 2.59808i | −0.818317 | + | 0.283473i | ||||
\(85\) | −6.00000 | −0.650791 | ||||||||
\(86\) | 6.00000 | + | 10.3923i | 0.646997 | + | 1.12063i | ||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | −6.00000 | −0.632456 | ||||||||
\(91\) | −0.500000 | + | 2.59808i | −0.0524142 | + | 0.272352i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | −12.0000 | − | 20.7846i | −1.24434 | − | 2.15526i | ||||
\(94\) | −3.00000 | + | 5.19615i | −0.309426 | + | 0.535942i | ||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | 1.50000 | + | 2.59808i | 0.153093 | + | 0.265165i | ||||
\(97\) | −5.00000 | −0.507673 | −0.253837 | − | 0.967247i | \(-0.581693\pi\) | ||||
−0.253837 | + | 0.967247i | \(0.581693\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 1.50000 | − | 2.59808i | 0.149256 | − | 0.258518i | −0.781697 | − | 0.623658i | \(-0.785646\pi\) |
0.930953 | + | 0.365140i | \(0.118979\pi\) | |||||||
\(102\) | −9.00000 | + | 15.5885i | −0.891133 | + | 1.54349i | ||||
\(103\) | −3.00000 | − | 5.19615i | −0.295599 | − | 0.511992i | 0.679525 | − | 0.733652i | \(-0.262186\pi\) |
−0.975124 | + | 0.221660i | \(0.928852\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 1.50000 | − | 7.79423i | 0.146385 | − | 0.760639i | ||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | 1.00000 | + | 1.73205i | 0.0966736 | + | 0.167444i | 0.910306 | − | 0.413936i | \(-0.135846\pi\) |
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(108\) | −4.50000 | + | 7.79423i | −0.433013 | + | 0.750000i | ||||
\(109\) | 3.00000 | − | 5.19615i | 0.287348 | − | 0.497701i | −0.685828 | − | 0.727764i | \(-0.740560\pi\) |
0.973176 | + | 0.230063i | \(0.0738931\pi\) | |||||||
\(110\) | −0.500000 | − | 0.866025i | −0.0476731 | − | 0.0825723i | ||||
\(111\) | 24.0000 | 2.27798 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | −15.0000 | −1.41108 | −0.705541 | − | 0.708669i | \(-0.749296\pi\) | ||||
−0.705541 | + | 0.708669i | \(0.749296\pi\) | |||||||
\(114\) | 6.00000 | + | 10.3923i | 0.561951 | + | 0.973329i | ||||
\(115\) | −2.00000 | + | 3.46410i | −0.186501 | + | 0.323029i | ||||
\(116\) | −0.500000 | + | 0.866025i | −0.0464238 | + | 0.0804084i | ||||
\(117\) | 3.00000 | + | 5.19615i | 0.277350 | + | 0.480384i | ||||
\(118\) | −15.0000 | −1.38086 | ||||||||
\(119\) | −12.0000 | − | 10.3923i | −1.10004 | − | 0.952661i | ||||
\(120\) | −3.00000 | −0.273861 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 1.50000 | − | 2.59808i | 0.135804 | − | 0.235219i | ||||
\(123\) | 18.0000 | − | 31.1769i | 1.62301 | − | 2.81113i | ||||
\(124\) | −4.00000 | − | 6.92820i | −0.359211 | − | 0.622171i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −12.0000 | − | 10.3923i | −1.06904 | − | 0.925820i | ||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −18.0000 | + | 31.1769i | −1.58481 | + | 2.74497i | ||||
\(130\) | −0.500000 | + | 0.866025i | −0.0438529 | + | 0.0759555i | ||||
\(131\) | −4.00000 | − | 6.92820i | −0.349482 | − | 0.605320i | 0.636676 | − | 0.771132i | \(-0.280309\pi\) |
−0.986157 | + | 0.165812i | \(0.946976\pi\) | |||||||
\(132\) | −3.00000 | −0.261116 | ||||||||
\(133\) | −10.0000 | + | 3.46410i | −0.867110 | + | 0.300376i | ||||
\(134\) | 7.00000 | 0.604708 | ||||||||
\(135\) | −4.50000 | − | 7.79423i | −0.387298 | − | 0.670820i | ||||
\(136\) | −3.00000 | + | 5.19615i | −0.257248 | + | 0.445566i | ||||
\(137\) | −3.50000 | + | 6.06218i | −0.299025 | + | 0.517927i | −0.975913 | − | 0.218159i | \(-0.929995\pi\) |
0.676888 | + | 0.736086i | \(0.263328\pi\) | |||||||
\(138\) | 6.00000 | + | 10.3923i | 0.510754 | + | 0.884652i | ||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0.500000 | − | 2.59808i | 0.0422577 | − | 0.219578i | ||||
\(141\) | −18.0000 | −1.51587 | ||||||||
\(142\) | 5.00000 | + | 8.66025i | 0.419591 | + | 0.726752i | ||||
\(143\) | −0.500000 | + | 0.866025i | −0.0418121 | + | 0.0724207i | ||||
\(144\) | −3.00000 | + | 5.19615i | −0.250000 | + | 0.433013i | ||||
\(145\) | −0.500000 | − | 0.866025i | −0.0415227 | − | 0.0719195i | ||||
\(146\) | 4.00000 | 0.331042 | ||||||||
\(147\) | 16.5000 | − | 12.9904i | 1.36090 | − | 1.07143i | ||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 1.50000 | − | 2.59808i | 0.122474 | − | 0.212132i | ||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | 2.00000 | + | 3.46410i | 0.162221 | + | 0.280976i | ||||
\(153\) | −36.0000 | −2.91043 | ||||||||
\(154\) | 0.500000 | − | 2.59808i | 0.0402911 | − | 0.209359i | ||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 1.50000 | + | 2.59808i | 0.120096 | + | 0.208013i | ||||
\(157\) | 6.00000 | − | 10.3923i | 0.478852 | − | 0.829396i | −0.520854 | − | 0.853646i | \(-0.674386\pi\) |
0.999706 | + | 0.0242497i | \(0.00771967\pi\) | |||||||
\(158\) | 7.50000 | − | 12.9904i | 0.596668 | − | 1.03346i | ||||
\(159\) | 9.00000 | + | 15.5885i | 0.713746 | + | 1.23625i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −10.0000 | + | 3.46410i | −0.788110 | + | 0.273009i | ||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −7.50000 | − | 12.9904i | −0.587445 | − | 1.01749i | −0.994566 | − | 0.104111i | \(-0.966800\pi\) |
0.407120 | − | 0.913375i | \(-0.366533\pi\) | |||||||
\(164\) | 6.00000 | − | 10.3923i | 0.468521 | − | 0.811503i | ||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 5.00000 | + | 8.66025i | 0.388075 | + | 0.672166i | ||||
\(167\) | −7.00000 | −0.541676 | −0.270838 | − | 0.962625i | \(-0.587301\pi\) | ||||
−0.270838 | + | 0.962625i | \(0.587301\pi\) | |||||||
\(168\) | −6.00000 | − | 5.19615i | −0.462910 | − | 0.400892i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −3.00000 | − | 5.19615i | −0.230089 | − | 0.398527i | ||||
\(171\) | −12.0000 | + | 20.7846i | −0.917663 | + | 1.58944i | ||||
\(172\) | −6.00000 | + | 10.3923i | −0.457496 | + | 0.792406i | ||||
\(173\) | 0.500000 | + | 0.866025i | 0.0380143 | + | 0.0658427i | 0.884407 | − | 0.466717i | \(-0.154563\pi\) |
−0.846392 | + | 0.532560i | \(0.821230\pi\) | |||||||
\(174\) | −3.00000 | −0.227429 | ||||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −22.5000 | − | 38.9711i | −1.69120 | − | 2.92925i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −3.50000 | + | 6.06218i | −0.261602 | + | 0.453108i | −0.966668 | − | 0.256034i | \(-0.917584\pi\) |
0.705066 | + | 0.709142i | \(0.250918\pi\) | |||||||
\(180\) | −3.00000 | − | 5.19615i | −0.223607 | − | 0.387298i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −2.50000 | + | 0.866025i | −0.185312 | + | 0.0641941i | ||||
\(183\) | 9.00000 | 0.665299 | ||||||||
\(184\) | 2.00000 | + | 3.46410i | 0.147442 | + | 0.255377i | ||||
\(185\) | −4.00000 | + | 6.92820i | −0.294086 | + | 0.509372i | ||||
\(186\) | 12.0000 | − | 20.7846i | 0.879883 | − | 1.52400i | ||||
\(187\) | −3.00000 | − | 5.19615i | −0.219382 | − | 0.379980i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 4.50000 | − | 23.3827i | 0.327327 | − | 1.70084i | ||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | −1.50000 | + | 2.59808i | −0.108253 | + | 0.187500i | ||||
\(193\) | −2.00000 | + | 3.46410i | −0.143963 | + | 0.249351i | −0.928986 | − | 0.370116i | \(-0.879318\pi\) |
0.785022 | + | 0.619467i | \(0.212651\pi\) | |||||||
\(194\) | −2.50000 | − | 4.33013i | −0.179490 | − | 0.310885i | ||||
\(195\) | −3.00000 | −0.214834 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | 25.0000 | 1.78118 | 0.890588 | − | 0.454811i | \(-0.150293\pi\) | ||||
0.890588 | + | 0.454811i | \(0.150293\pi\) | |||||||
\(198\) | −3.00000 | − | 5.19615i | −0.213201 | − | 0.369274i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 10.5000 | + | 18.1865i | 0.740613 | + | 1.28278i | ||||
\(202\) | 3.00000 | 0.211079 | ||||||||
\(203\) | 0.500000 | − | 2.59808i | 0.0350931 | − | 0.182349i | ||||
\(204\) | −18.0000 | −1.26025 | ||||||||
\(205\) | 6.00000 | + | 10.3923i | 0.419058 | + | 0.725830i | ||||
\(206\) | 3.00000 | − | 5.19615i | 0.209020 | − | 0.362033i | ||||
\(207\) | −12.0000 | + | 20.7846i | −0.834058 | + | 1.44463i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 7.50000 | − | 2.59808i | 0.517549 | − | 0.179284i | ||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | 3.00000 | + | 5.19615i | 0.206041 | + | 0.356873i | ||||
\(213\) | −15.0000 | + | 25.9808i | −1.02778 | + | 1.78017i | ||||
\(214\) | −1.00000 | + | 1.73205i | −0.0683586 | + | 0.118401i | ||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | 16.0000 | + | 13.8564i | 1.08615 | + | 0.940634i | ||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | 6.00000 | + | 10.3923i | 0.405442 | + | 0.702247i | ||||
\(220\) | 0.500000 | − | 0.866025i | 0.0337100 | − | 0.0583874i | ||||
\(221\) | −3.00000 | + | 5.19615i | −0.201802 | + | 0.349531i | ||||
\(222\) | 12.0000 | + | 20.7846i | 0.805387 | + | 1.39497i | ||||
\(223\) | −12.0000 | −0.803579 | −0.401790 | − | 0.915732i | \(-0.631612\pi\) | ||||
−0.401790 | + | 0.915732i | \(0.631612\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | 6.00000 | 0.400000 | ||||||||
\(226\) | −7.50000 | − | 12.9904i | −0.498893 | − | 0.864107i | ||||
\(227\) | −9.00000 | + | 15.5885i | −0.597351 | + | 1.03464i | 0.395860 | + | 0.918311i | \(0.370447\pi\) |
−0.993210 | + | 0.116331i | \(0.962887\pi\) | |||||||
\(228\) | −6.00000 | + | 10.3923i | −0.397360 | + | 0.688247i | ||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | −4.00000 | −0.263752 | ||||||||
\(231\) | 7.50000 | − | 2.59808i | 0.493464 | − | 0.170941i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | 8.00000 | + | 13.8564i | 0.524097 | + | 0.907763i | 0.999606 | + | 0.0280525i | \(0.00893057\pi\) |
−0.475509 | + | 0.879711i | \(0.657736\pi\) | |||||||
\(234\) | −3.00000 | + | 5.19615i | −0.196116 | + | 0.339683i | ||||
\(235\) | 3.00000 | − | 5.19615i | 0.195698 | − | 0.338960i | ||||
\(236\) | −7.50000 | − | 12.9904i | −0.488208 | − | 0.845602i | ||||
\(237\) | 45.0000 | 2.92306 | ||||||||
\(238\) | 3.00000 | − | 15.5885i | 0.194461 | − | 1.01045i | ||||
\(239\) | −11.0000 | −0.711531 | −0.355765 | − | 0.934575i | \(-0.615780\pi\) | ||||
−0.355765 | + | 0.934575i | \(0.615780\pi\) | |||||||
\(240\) | −1.50000 | − | 2.59808i | −0.0968246 | − | 0.167705i | ||||
\(241\) | 8.00000 | − | 13.8564i | 0.515325 | − | 0.892570i | −0.484516 | − | 0.874782i | \(-0.661004\pi\) |
0.999842 | − | 0.0177875i | \(-0.00566223\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.00000 | 0.192055 | ||||||||
\(245\) | 1.00000 | + | 6.92820i | 0.0638877 | + | 0.442627i | ||||
\(246\) | 36.0000 | 2.29528 | ||||||||
\(247\) | 2.00000 | + | 3.46410i | 0.127257 | + | 0.220416i | ||||
\(248\) | 4.00000 | − | 6.92820i | 0.254000 | − | 0.439941i | ||||
\(249\) | −15.0000 | + | 25.9808i | −0.950586 | + | 1.64646i | ||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 3.00000 | − | 15.5885i | 0.188982 | − | 0.981981i | ||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | −0.500000 | − | 0.866025i | −0.0313728 | − | 0.0543393i | ||||
\(255\) | 9.00000 | − | 15.5885i | 0.563602 | − | 0.976187i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.50000 | − | 12.9904i | −0.467837 | − | 0.810318i | 0.531487 | − | 0.847066i | \(-0.321633\pi\) |
−0.999325 | + | 0.0367485i | \(0.988300\pi\) | |||||||
\(258\) | −36.0000 | −2.24126 | ||||||||
\(259\) | −20.0000 | + | 6.92820i | −1.24274 | + | 0.430498i | ||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 4.00000 | − | 6.92820i | 0.247121 | − | 0.428026i | ||||
\(263\) | 7.50000 | − | 12.9904i | 0.462470 | − | 0.801021i | −0.536614 | − | 0.843828i | \(-0.680297\pi\) |
0.999083 | + | 0.0428069i | \(0.0136300\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −8.00000 | − | 6.92820i | −0.490511 | − | 0.424795i | ||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 3.50000 | + | 6.06218i | 0.213797 | + | 0.370306i | ||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 4.50000 | − | 7.79423i | 0.273861 | − | 0.474342i | ||||
\(271\) | 10.5000 | + | 18.1865i | 0.637830 | + | 1.10475i | 0.985908 | + | 0.167288i | \(0.0535009\pi\) |
−0.348079 | + | 0.937465i | \(0.613166\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | −6.00000 | − | 5.19615i | −0.363137 | − | 0.314485i | ||||
\(274\) | −7.00000 | −0.422885 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | −12.5000 | + | 21.6506i | −0.751052 | + | 1.30086i | 0.196261 | + | 0.980552i | \(0.437120\pi\) |
−0.947313 | + | 0.320309i | \(0.896213\pi\) | |||||||
\(278\) | 8.00000 | + | 13.8564i | 0.479808 | + | 0.831052i | ||||
\(279\) | 48.0000 | 2.87368 | ||||||||
\(280\) | 2.50000 | − | 0.866025i | 0.149404 | − | 0.0517549i | ||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | −9.00000 | − | 15.5885i | −0.535942 | − | 0.928279i | ||||
\(283\) | 8.00000 | − | 13.8564i | 0.475551 | − | 0.823678i | −0.524057 | − | 0.851683i | \(-0.675582\pi\) |
0.999608 | + | 0.0280052i | \(0.00891551\pi\) | |||||||
\(284\) | −5.00000 | + | 8.66025i | −0.296695 | + | 0.513892i | ||||
\(285\) | −6.00000 | − | 10.3923i | −0.355409 | − | 0.615587i | ||||
\(286\) | −1.00000 | −0.0591312 | ||||||||
\(287\) | −6.00000 | + | 31.1769i | −0.354169 | + | 1.84032i | ||||
\(288\) | −6.00000 | −0.353553 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 0.500000 | − | 0.866025i | 0.0293610 | − | 0.0508548i | ||||
\(291\) | 7.50000 | − | 12.9904i | 0.439658 | − | 0.761510i | ||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | 26.0000 | 1.51894 | 0.759468 | − | 0.650545i | \(-0.225459\pi\) | ||||
0.759468 | + | 0.650545i | \(0.225459\pi\) | |||||||
\(294\) | 19.5000 | + | 7.79423i | 1.13726 | + | 0.454569i | ||||
\(295\) | 15.0000 | 0.873334 | ||||||||
\(296\) | 4.00000 | + | 6.92820i | 0.232495 | + | 0.402694i | ||||
\(297\) | 4.50000 | − | 7.79423i | 0.261116 | − | 0.452267i | ||||
\(298\) | −3.00000 | + | 5.19615i | −0.173785 | + | 0.301005i | ||||
\(299\) | 2.00000 | + | 3.46410i | 0.115663 | + | 0.200334i | ||||
\(300\) | 3.00000 | 0.173205 | ||||||||
\(301\) | 6.00000 | − | 31.1769i | 0.345834 | − | 1.79701i | ||||
\(302\) | 5.00000 | 0.287718 | ||||||||
\(303\) | 4.50000 | + | 7.79423i | 0.258518 | + | 0.447767i | ||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | −1.50000 | + | 2.59808i | −0.0858898 | + | 0.148765i | ||||
\(306\) | −18.0000 | − | 31.1769i | −1.02899 | − | 1.78227i | ||||
\(307\) | −26.0000 | −1.48390 | −0.741949 | − | 0.670456i | \(-0.766098\pi\) | ||||
−0.741949 | + | 0.670456i | \(0.766098\pi\) | |||||||
\(308\) | 2.50000 | − | 0.866025i | 0.142451 | − | 0.0493464i | ||||
\(309\) | 18.0000 | 1.02398 | ||||||||
\(310\) | 4.00000 | + | 6.92820i | 0.227185 | + | 0.393496i | ||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | −1.50000 | + | 2.59808i | −0.0849208 | + | 0.147087i | ||||
\(313\) | 1.50000 | + | 2.59808i | 0.0847850 | + | 0.146852i | 0.905300 | − | 0.424774i | \(-0.139646\pi\) |
−0.820515 | + | 0.571626i | \(0.806313\pi\) | |||||||
\(314\) | 12.0000 | 0.677199 | ||||||||
\(315\) | 12.0000 | + | 10.3923i | 0.676123 | + | 0.585540i | ||||
\(316\) | 15.0000 | 0.843816 | ||||||||
\(317\) | 12.0000 | + | 20.7846i | 0.673987 | + | 1.16738i | 0.976764 | + | 0.214318i | \(0.0687530\pi\) |
−0.302777 | + | 0.953062i | \(0.597914\pi\) | |||||||
\(318\) | −9.00000 | + | 15.5885i | −0.504695 | + | 0.874157i | ||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | −8.00000 | − | 6.92820i | −0.445823 | − | 0.386094i | ||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 0.500000 | − | 0.866025i | 0.0277350 | − | 0.0480384i | ||||
\(326\) | 7.50000 | − | 12.9904i | 0.415387 | − | 0.719471i | ||||
\(327\) | 9.00000 | + | 15.5885i | 0.497701 | + | 0.862044i | ||||
\(328\) | 12.0000 | 0.662589 | ||||||||
\(329\) | 15.0000 | − | 5.19615i | 0.826977 | − | 0.286473i | ||||
\(330\) | 3.00000 | 0.165145 | ||||||||
\(331\) | 3.50000 | + | 6.06218i | 0.192377 | + | 0.333207i | 0.946038 | − | 0.324057i | \(-0.105047\pi\) |
−0.753660 | + | 0.657264i | \(0.771714\pi\) | |||||||
\(332\) | −5.00000 | + | 8.66025i | −0.274411 | + | 0.475293i | ||||
\(333\) | −24.0000 | + | 41.5692i | −1.31519 | + | 2.27798i | ||||
\(334\) | −3.50000 | − | 6.06218i | −0.191511 | − | 0.331708i | ||||
\(335\) | −7.00000 | −0.382451 | ||||||||
\(336\) | 1.50000 | − | 7.79423i | 0.0818317 | − | 0.425210i | ||||
\(337\) | −32.0000 | −1.74315 | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||||
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 22.5000 | − | 38.9711i | 1.22203 | − | 2.11662i | ||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | 4.00000 | + | 6.92820i | 0.216612 | + | 0.375183i | ||||
\(342\) | −24.0000 | −1.29777 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −12.0000 | −0.646997 | ||||||||
\(345\) | −6.00000 | − | 10.3923i | −0.323029 | − | 0.559503i | ||||
\(346\) | −0.500000 | + | 0.866025i | −0.0268802 | + | 0.0465578i | ||||
\(347\) | −15.0000 | + | 25.9808i | −0.805242 | + | 1.39472i | 0.110885 | + | 0.993833i | \(0.464631\pi\) |
−0.916127 | + | 0.400887i | \(0.868702\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | −34.0000 | −1.81998 | −0.909989 | − | 0.414632i | \(-0.863910\pi\) | ||||
−0.909989 | + | 0.414632i | \(0.863910\pi\) | |||||||
\(350\) | −0.500000 | + | 2.59808i | −0.0267261 | + | 0.138873i | ||||
\(351\) | −9.00000 | −0.480384 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 9.00000 | − | 15.5885i | 0.479022 | − | 0.829690i | −0.520689 | − | 0.853746i | \(-0.674325\pi\) |
0.999711 | + | 0.0240566i | \(0.00765819\pi\) | |||||||
\(354\) | 22.5000 | − | 38.9711i | 1.19586 | − | 2.07129i | ||||
\(355\) | −5.00000 | − | 8.66025i | −0.265372 | − | 0.459639i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 45.0000 | − | 15.5885i | 2.38165 | − | 0.825029i | ||||
\(358\) | −7.00000 | −0.369961 | ||||||||
\(359\) | −1.50000 | − | 2.59808i | −0.0791670 | − | 0.137121i | 0.823724 | − | 0.566991i | \(-0.191893\pi\) |
−0.902891 | + | 0.429870i | \(0.858559\pi\) | |||||||
\(360\) | 3.00000 | − | 5.19615i | 0.158114 | − | 0.273861i | ||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 1.00000 | + | 1.73205i | 0.0525588 | + | 0.0910346i | ||||
\(363\) | 3.00000 | 0.157459 | ||||||||
\(364\) | −2.00000 | − | 1.73205i | −0.104828 | − | 0.0907841i | ||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 4.50000 | + | 7.79423i | 0.235219 | + | 0.407411i | ||||
\(367\) | 12.0000 | − | 20.7846i | 0.626395 | − | 1.08495i | −0.361874 | − | 0.932227i | \(-0.617863\pi\) |
0.988269 | − | 0.152721i | \(-0.0488036\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 36.0000 | + | 62.3538i | 1.87409 | + | 3.24601i | ||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | −12.0000 | − | 10.3923i | −0.623009 | − | 0.539542i | ||||
\(372\) | 24.0000 | 1.24434 | ||||||||
\(373\) | 1.50000 | + | 2.59808i | 0.0776671 | + | 0.134523i | 0.902243 | − | 0.431228i | \(-0.141920\pi\) |
−0.824576 | + | 0.565751i | \(0.808586\pi\) | |||||||
\(374\) | 3.00000 | − | 5.19615i | 0.155126 | − | 0.268687i | ||||
\(375\) | −1.50000 | + | 2.59808i | −0.0774597 | + | 0.134164i | ||||
\(376\) | −3.00000 | − | 5.19615i | −0.154713 | − | 0.267971i | ||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 22.5000 | − | 7.79423i | 1.15728 | − | 0.400892i | ||||
\(379\) | 13.0000 | 0.667765 | 0.333883 | − | 0.942615i | \(-0.391641\pi\) | ||||
0.333883 | + | 0.942615i | \(0.391641\pi\) | |||||||
\(380\) | −2.00000 | − | 3.46410i | −0.102598 | − | 0.177705i | ||||
\(381\) | 1.50000 | − | 2.59808i | 0.0768473 | − | 0.133103i | ||||
\(382\) | −9.00000 | + | 15.5885i | −0.460480 | + | 0.797575i | ||||
\(383\) | 7.00000 | + | 12.1244i | 0.357683 | + | 0.619526i | 0.987573 | − | 0.157159i | \(-0.0502334\pi\) |
−0.629890 | + | 0.776684i | \(0.716900\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | −0.500000 | + | 2.59808i | −0.0254824 | + | 0.132410i | ||||
\(386\) | −4.00000 | −0.203595 | ||||||||
\(387\) | −36.0000 | − | 62.3538i | −1.82998 | − | 3.16962i | ||||
\(388\) | 2.50000 | − | 4.33013i | 0.126918 | − | 0.219829i | ||||
\(389\) | 11.0000 | − | 19.0526i | 0.557722 | − | 0.966003i | −0.439964 | − | 0.898015i | \(-0.645009\pi\) |
0.997686 | − | 0.0679877i | \(-0.0216579\pi\) | |||||||
\(390\) | −1.50000 | − | 2.59808i | −0.0759555 | − | 0.131559i | ||||
\(391\) | −24.0000 | −1.21373 | ||||||||
\(392\) | 6.50000 | + | 2.59808i | 0.328300 | + | 0.131223i | ||||
\(393\) | 24.0000 | 1.21064 | ||||||||
\(394\) | 12.5000 | + | 21.6506i | 0.629741 | + | 1.09074i | ||||
\(395\) | −7.50000 | + | 12.9904i | −0.377366 | + | 0.653617i | ||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | 6.00000 | − | 31.1769i | 0.300376 | − | 1.56080i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −11.5000 | − | 19.9186i | −0.574283 | − | 0.994687i | −0.996119 | − | 0.0880147i | \(-0.971948\pi\) |
0.421837 | − | 0.906672i | \(-0.361386\pi\) | |||||||
\(402\) | −10.5000 | + | 18.1865i | −0.523692 | + | 0.907062i | ||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | 1.50000 | + | 2.59808i | 0.0746278 | + | 0.129259i | ||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | 2.50000 | − | 0.866025i | 0.124073 | − | 0.0429801i | ||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | −9.00000 | − | 15.5885i | −0.445566 | − | 0.771744i | ||||
\(409\) | 7.00000 | − | 12.1244i | 0.346128 | − | 0.599511i | −0.639430 | − | 0.768849i | \(-0.720830\pi\) |
0.985558 | + | 0.169338i | \(0.0541630\pi\) | |||||||
\(410\) | −6.00000 | + | 10.3923i | −0.296319 | + | 0.513239i | ||||
\(411\) | −10.5000 | − | 18.1865i | −0.517927 | − | 0.897076i | ||||
\(412\) | 6.00000 | 0.295599 | ||||||||
\(413\) | 30.0000 | + | 25.9808i | 1.47620 | + | 1.27843i | ||||
\(414\) | −24.0000 | −1.17954 | ||||||||
\(415\) | −5.00000 | − | 8.66025i | −0.245440 | − | 0.425115i | ||||
\(416\) | −0.500000 | + | 0.866025i | −0.0245145 | + | 0.0424604i | ||||
\(417\) | −24.0000 | + | 41.5692i | −1.17529 | + | 2.03565i | ||||
\(418\) | −2.00000 | − | 3.46410i | −0.0978232 | − | 0.169435i | ||||
\(419\) | −24.0000 | −1.17248 | −0.586238 | − | 0.810139i | \(-0.699392\pi\) | ||||
−0.586238 | + | 0.810139i | \(0.699392\pi\) | |||||||
\(420\) | 6.00000 | + | 5.19615i | 0.292770 | + | 0.253546i | ||||
\(421\) | 32.0000 | 1.55958 | 0.779792 | − | 0.626038i | \(-0.215325\pi\) | ||||
0.779792 | + | 0.626038i | \(0.215325\pi\) | |||||||
\(422\) | 4.00000 | + | 6.92820i | 0.194717 | + | 0.337260i | ||||
\(423\) | 18.0000 | − | 31.1769i | 0.875190 | − | 1.51587i | ||||
\(424\) | −3.00000 | + | 5.19615i | −0.145693 | + | 0.252347i | ||||
\(425\) | 3.00000 | + | 5.19615i | 0.145521 | + | 0.252050i | ||||
\(426\) | −30.0000 | −1.45350 | ||||||||
\(427\) | −7.50000 | + | 2.59808i | −0.362950 | + | 0.125730i | ||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | −1.50000 | − | 2.59808i | −0.0724207 | − | 0.125436i | ||||
\(430\) | 6.00000 | − | 10.3923i | 0.289346 | − | 0.501161i | ||||
\(431\) | −3.50000 | + | 6.06218i | −0.168589 | + | 0.292005i | −0.937924 | − | 0.346841i | \(-0.887254\pi\) |
0.769335 | + | 0.638846i | \(0.220588\pi\) | |||||||
\(432\) | −4.50000 | − | 7.79423i | −0.216506 | − | 0.375000i | ||||
\(433\) | −10.0000 | −0.480569 | −0.240285 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240285 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(434\) | −4.00000 | + | 20.7846i | −0.192006 | + | 0.997693i | ||||
\(435\) | 3.00000 | 0.143839 | ||||||||
\(436\) | 3.00000 | + | 5.19615i | 0.143674 | + | 0.248851i | ||||
\(437\) | −8.00000 | + | 13.8564i | −0.382692 | + | 0.662842i | ||||
\(438\) | −6.00000 | + | 10.3923i | −0.286691 | + | 0.496564i | ||||
\(439\) | 9.50000 | + | 16.4545i | 0.453410 | + | 0.785330i | 0.998595 | − | 0.0529862i | \(-0.0168739\pi\) |
−0.545185 | + | 0.838316i | \(0.683541\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 6.00000 | + | 41.5692i | 0.285714 | + | 1.97949i | ||||
\(442\) | −6.00000 | −0.285391 | ||||||||
\(443\) | 14.0000 | + | 24.2487i | 0.665160 | + | 1.15209i | 0.979242 | + | 0.202695i | \(0.0649700\pi\) |
−0.314082 | + | 0.949396i | \(0.601697\pi\) | |||||||
\(444\) | −12.0000 | + | 20.7846i | −0.569495 | + | 0.986394i | ||||
\(445\) | −3.00000 | + | 5.19615i | −0.142214 | + | 0.246321i | ||||
\(446\) | −6.00000 | − | 10.3923i | −0.284108 | − | 0.492090i | ||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | 0.500000 | − | 2.59808i | 0.0236228 | − | 0.122748i | ||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | 3.00000 | + | 5.19615i | 0.141421 | + | 0.244949i | ||||
\(451\) | −6.00000 | + | 10.3923i | −0.282529 | + | 0.489355i | ||||
\(452\) | 7.50000 | − | 12.9904i | 0.352770 | − | 0.611016i | ||||
\(453\) | 7.50000 | + | 12.9904i | 0.352381 | + | 0.610341i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | 2.50000 | − | 0.866025i | 0.117202 | − | 0.0405999i | ||||
\(456\) | −12.0000 | −0.561951 | ||||||||
\(457\) | −17.0000 | − | 29.4449i | −0.795226 | − | 1.37737i | −0.922695 | − | 0.385530i | \(-0.874019\pi\) |
0.127469 | − | 0.991843i | \(-0.459315\pi\) | |||||||
\(458\) | −2.00000 | + | 3.46410i | −0.0934539 | + | 0.161867i | ||||
\(459\) | 27.0000 | − | 46.7654i | 1.26025 | − | 2.18282i | ||||
\(460\) | −2.00000 | − | 3.46410i | −0.0932505 | − | 0.161515i | ||||
\(461\) | −15.0000 | −0.698620 | −0.349310 | − | 0.937007i | \(-0.613584\pi\) | ||||
−0.349310 | + | 0.937007i | \(0.613584\pi\) | |||||||
\(462\) | 6.00000 | + | 5.19615i | 0.279145 | + | 0.241747i | ||||
\(463\) | 34.0000 | 1.58011 | 0.790057 | − | 0.613033i | \(-0.210051\pi\) | ||||
0.790057 | + | 0.613033i | \(0.210051\pi\) | |||||||
\(464\) | −0.500000 | − | 0.866025i | −0.0232119 | − | 0.0402042i | ||||
\(465\) | −12.0000 | + | 20.7846i | −0.556487 | + | 0.963863i | ||||
\(466\) | −8.00000 | + | 13.8564i | −0.370593 | + | 0.641886i | ||||
\(467\) | 18.0000 | + | 31.1769i | 0.832941 | + | 1.44270i | 0.895696 | + | 0.444667i | \(0.146678\pi\) |
−0.0627555 | + | 0.998029i | \(0.519989\pi\) | |||||||
\(468\) | −6.00000 | −0.277350 | ||||||||
\(469\) | −14.0000 | − | 12.1244i | −0.646460 | − | 0.559851i | ||||
\(470\) | 6.00000 | 0.276759 | ||||||||
\(471\) | 18.0000 | + | 31.1769i | 0.829396 | + | 1.43656i | ||||
\(472\) | 7.50000 | − | 12.9904i | 0.345215 | − | 0.597931i | ||||
\(473\) | 6.00000 | − | 10.3923i | 0.275880 | − | 0.477839i | ||||
\(474\) | 22.5000 | + | 38.9711i | 1.03346 | + | 1.79000i | ||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 15.0000 | − | 5.19615i | 0.687524 | − | 0.238165i | ||||
\(477\) | −36.0000 | −1.64833 | ||||||||
\(478\) | −5.50000 | − | 9.52628i | −0.251564 | − | 0.435722i | ||||
\(479\) | 7.50000 | − | 12.9904i | 0.342684 | − | 0.593546i | −0.642246 | − | 0.766498i | \(-0.721997\pi\) |
0.984930 | + | 0.172953i | \(0.0553307\pi\) | |||||||
\(480\) | 1.50000 | − | 2.59808i | 0.0684653 | − | 0.118585i | ||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 16.0000 | 0.728780 | ||||||||
\(483\) | 6.00000 | − | 31.1769i | 0.273009 | − | 1.41860i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 2.50000 | + | 4.33013i | 0.113519 | + | 0.196621i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000 | − | 31.1769i | 0.815658 | − | 1.41276i | −0.0931967 | − | 0.995648i | \(-0.529709\pi\) |
0.908855 | − | 0.417113i | \(-0.136958\pi\) | |||||||
\(488\) | 1.50000 | + | 2.59808i | 0.0679018 | + | 0.117609i | ||||
\(489\) | 45.0000 | 2.03497 | ||||||||
\(490\) | −5.50000 | + | 4.33013i | −0.248465 | + | 0.195615i | ||||
\(491\) | −14.0000 | −0.631811 | −0.315906 | − | 0.948791i | \(-0.602308\pi\) | ||||
−0.315906 | + | 0.948791i | \(0.602308\pi\) | |||||||
\(492\) | 18.0000 | + | 31.1769i | 0.811503 | + | 1.40556i | ||||
\(493\) | 3.00000 | − | 5.19615i | 0.135113 | − | 0.234023i | ||||
\(494\) | −2.00000 | + | 3.46410i | −0.0899843 | + | 0.155857i | ||||
\(495\) | 3.00000 | + | 5.19615i | 0.134840 | + | 0.233550i | ||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 5.00000 | − | 25.9808i | 0.224281 | − | 1.16540i | ||||
\(498\) | −30.0000 | −1.34433 | ||||||||
\(499\) | −18.0000 | − | 31.1769i | −0.805791 | − | 1.39567i | −0.915756 | − | 0.401735i | \(-0.868407\pi\) |
0.109965 | − | 0.993935i | \(-0.464926\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 10.5000 | − | 18.1865i | 0.469105 | − | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.00000 | 0.401290 | 0.200645 | − | 0.979664i | \(-0.435696\pi\) | ||||
0.200645 | + | 0.979664i | \(0.435696\pi\) | |||||||
\(504\) | 15.0000 | − | 5.19615i | 0.668153 | − | 0.231455i | ||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | −2.00000 | − | 3.46410i | −0.0889108 | − | 0.153998i | ||||
\(507\) | 18.0000 | − | 31.1769i | 0.799408 | − | 1.38462i | ||||
\(508\) | 0.500000 | − | 0.866025i | 0.0221839 | − | 0.0384237i | ||||
\(509\) | 21.0000 | + | 36.3731i | 0.930809 | + | 1.61221i | 0.781943 | + | 0.623350i | \(0.214229\pi\) |
0.148866 | + | 0.988857i | \(0.452438\pi\) | |||||||
\(510\) | 18.0000 | 0.797053 | ||||||||
\(511\) | −8.00000 | − | 6.92820i | −0.353899 | − | 0.306486i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −18.0000 | − | 31.1769i | −0.794719 | − | 1.37649i | ||||
\(514\) | 7.50000 | − | 12.9904i | 0.330811 | − | 0.572981i | ||||
\(515\) | −3.00000 | + | 5.19615i | −0.132196 | + | 0.228970i | ||||
\(516\) | −18.0000 | − | 31.1769i | −0.792406 | − | 1.37249i | ||||
\(517\) | 6.00000 | 0.263880 | ||||||||
\(518\) | −16.0000 | − | 13.8564i | −0.703000 | − | 0.608816i | ||||
\(519\) | −3.00000 | −0.131685 | ||||||||
\(520\) | −0.500000 | − | 0.866025i | −0.0219265 | − | 0.0379777i | ||||
\(521\) | −5.00000 | + | 8.66025i | −0.219054 | + | 0.379413i | −0.954519 | − | 0.298150i | \(-0.903630\pi\) |
0.735465 | + | 0.677563i | \(0.236964\pi\) | |||||||
\(522\) | 3.00000 | − | 5.19615i | 0.131306 | − | 0.227429i | ||||
\(523\) | −11.0000 | − | 19.0526i | −0.480996 | − | 0.833110i | 0.518766 | − | 0.854916i | \(-0.326392\pi\) |
−0.999762 | + | 0.0218062i | \(0.993058\pi\) | |||||||
\(524\) | 8.00000 | 0.349482 | ||||||||
\(525\) | −7.50000 | + | 2.59808i | −0.327327 | + | 0.113389i | ||||
\(526\) | 15.0000 | 0.654031 | ||||||||
\(527\) | 24.0000 | + | 41.5692i | 1.04546 | + | 1.81078i | ||||
\(528\) | 1.50000 | − | 2.59808i | 0.0652791 | − | 0.113067i | ||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | −3.00000 | − | 5.19615i | −0.130312 | − | 0.225706i | ||||
\(531\) | 90.0000 | 3.90567 | ||||||||
\(532\) | 2.00000 | − | 10.3923i | 0.0867110 | − | 0.450564i | ||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | 9.00000 | + | 15.5885i | 0.389468 | + | 0.674579i | ||||
\(535\) | 1.00000 | − | 1.73205i | 0.0432338 | − | 0.0748831i | ||||
\(536\) | −3.50000 | + | 6.06218i | −0.151177 | + | 0.261846i | ||||
\(537\) | −10.5000 | − | 18.1865i | −0.453108 | − | 0.784807i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.50000 | + | 4.33013i | −0.236902 | + | 0.186512i | ||||
\(540\) | 9.00000 | 0.387298 | ||||||||
\(541\) | 8.50000 | + | 14.7224i | 0.365444 | + | 0.632967i | 0.988847 | − | 0.148933i | \(-0.0475840\pi\) |
−0.623404 | + | 0.781900i | \(0.714251\pi\) | |||||||
\(542\) | −10.5000 | + | 18.1865i | −0.451014 | + | 0.781179i | ||||
\(543\) | −3.00000 | + | 5.19615i | −0.128742 | + | 0.222988i | ||||
\(544\) | −3.00000 | − | 5.19615i | −0.128624 | − | 0.222783i | ||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 1.50000 | − | 7.79423i | 0.0641941 | − | 0.333562i | ||||
\(547\) | 18.0000 | 0.769624 | 0.384812 | − | 0.922995i | \(-0.374266\pi\) | ||||
0.384812 | + | 0.922995i | \(0.374266\pi\) | |||||||
\(548\) | −3.50000 | − | 6.06218i | −0.149513 | − | 0.258963i | ||||
\(549\) | −9.00000 | + | 15.5885i | −0.384111 | + | 0.665299i | ||||
\(550\) | −0.500000 | + | 0.866025i | −0.0213201 | + | 0.0369274i | ||||
\(551\) | −2.00000 | − | 3.46410i | −0.0852029 | − | 0.147576i | ||||
\(552\) | −12.0000 | −0.510754 | ||||||||
\(553\) | −37.5000 | + | 12.9904i | −1.59466 | + | 0.552407i | ||||
\(554\) | −25.0000 | −1.06215 | ||||||||
\(555\) | −12.0000 | − | 20.7846i | −0.509372 | − | 0.882258i | ||||
\(556\) | −8.00000 | + | 13.8564i | −0.339276 | + | 0.587643i | ||||
\(557\) | −3.00000 | + | 5.19615i | −0.127114 | + | 0.220168i | −0.922557 | − | 0.385860i | \(-0.873905\pi\) |
0.795443 | + | 0.606028i | \(0.207238\pi\) | |||||||
\(558\) | 24.0000 | + | 41.5692i | 1.01600 | + | 1.75977i | ||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 2.00000 | + | 1.73205i | 0.0845154 | + | 0.0731925i | ||||
\(561\) | 18.0000 | 0.759961 | ||||||||
\(562\) | −6.00000 | − | 10.3923i | −0.253095 | − | 0.438373i | ||||
\(563\) | 14.0000 | − | 24.2487i | 0.590030 | − | 1.02196i | −0.404198 | − | 0.914671i | \(-0.632449\pi\) |
0.994228 | − | 0.107290i | \(-0.0342173\pi\) | |||||||
\(564\) | 9.00000 | − | 15.5885i | 0.378968 | − | 0.656392i | ||||
\(565\) | 7.50000 | + | 12.9904i | 0.315527 | + | 0.546509i | ||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 18.0000 | + | 15.5885i | 0.755929 | + | 0.654654i | ||||
\(568\) | −10.0000 | −0.419591 | ||||||||
\(569\) | 2.00000 | + | 3.46410i | 0.0838444 | + | 0.145223i | 0.904898 | − | 0.425628i | \(-0.139947\pi\) |
−0.821054 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(570\) | 6.00000 | − | 10.3923i | 0.251312 | − | 0.435286i | ||||
\(571\) | −15.0000 | + | 25.9808i | −0.627730 | + | 1.08726i | 0.360276 | + | 0.932846i | \(0.382683\pi\) |
−0.988006 | + | 0.154415i | \(0.950651\pi\) | |||||||
\(572\) | −0.500000 | − | 0.866025i | −0.0209061 | − | 0.0362103i | ||||
\(573\) | −54.0000 | −2.25588 | ||||||||
\(574\) | −30.0000 | + | 10.3923i | −1.25218 | + | 0.433766i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −3.00000 | − | 5.19615i | −0.125000 | − | 0.216506i | ||||
\(577\) | 15.5000 | − | 26.8468i | 0.645273 | − | 1.11765i | −0.338965 | − | 0.940799i | \(-0.610077\pi\) |
0.984238 | − | 0.176847i | \(-0.0565899\pi\) | |||||||
\(578\) | 9.50000 | − | 16.4545i | 0.395148 | − | 0.684416i | ||||
\(579\) | −6.00000 | − | 10.3923i | −0.249351 | − | 0.431889i | ||||
\(580\) | 1.00000 | 0.0415227 | ||||||||
\(581\) | 5.00000 | − | 25.9808i | 0.207435 | − | 1.07786i | ||||
\(582\) | 15.0000 | 0.621770 | ||||||||
\(583\) | −3.00000 | − | 5.19615i | −0.124247 | − | 0.215203i | ||||
\(584\) | −2.00000 | + | 3.46410i | −0.0827606 | + | 0.143346i | ||||
\(585\) | 3.00000 | − | 5.19615i | 0.124035 | − | 0.214834i | ||||
\(586\) | 13.0000 | + | 22.5167i | 0.537025 | + | 0.930155i | ||||
\(587\) | 11.0000 | 0.454019 | 0.227009 | − | 0.973893i | \(-0.427105\pi\) | ||||
0.227009 | + | 0.973893i | \(0.427105\pi\) | |||||||
\(588\) | 3.00000 | + | 20.7846i | 0.123718 | + | 0.857143i | ||||
\(589\) | 32.0000 | 1.31854 | ||||||||
\(590\) | 7.50000 | + | 12.9904i | 0.308770 | + | 0.534806i | ||||
\(591\) | −37.5000 | + | 64.9519i | −1.54254 | + | 2.67176i | ||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 9.00000 | 0.369274 | ||||||||
\(595\) | −3.00000 | + | 15.5885i | −0.122988 | + | 0.639064i | ||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −6.00000 | − | 10.3923i | −0.245564 | − | 0.425329i | ||||
\(598\) | −2.00000 | + | 3.46410i | −0.0817861 | + | 0.141658i | ||||
\(599\) | 6.00000 | − | 10.3923i | 0.245153 | − | 0.424618i | −0.717021 | − | 0.697051i | \(-0.754495\pi\) |
0.962175 | + | 0.272433i | \(0.0878284\pi\) | |||||||
\(600\) | 1.50000 | + | 2.59808i | 0.0612372 | + | 0.106066i | ||||
\(601\) | 26.0000 | 1.06056 | 0.530281 | − | 0.847822i | \(-0.322086\pi\) | ||||
0.530281 | + | 0.847822i | \(0.322086\pi\) | |||||||
\(602\) | 30.0000 | − | 10.3923i | 1.22271 | − | 0.423559i | ||||
\(603\) | −42.0000 | −1.71037 | ||||||||
\(604\) | 2.50000 | + | 4.33013i | 0.101724 | + | 0.176190i | ||||
\(605\) | −0.500000 | + | 0.866025i | −0.0203279 | + | 0.0352089i | ||||
\(606\) | −4.50000 | + | 7.79423i | −0.182800 | + | 0.316619i | ||||
\(607\) | 8.00000 | + | 13.8564i | 0.324710 | + | 0.562414i | 0.981454 | − | 0.191700i | \(-0.0614000\pi\) |
−0.656744 | + | 0.754114i | \(0.728067\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | 6.00000 | + | 5.19615i | 0.243132 | + | 0.210559i | ||||
\(610\) | −3.00000 | −0.121466 | ||||||||
\(611\) | −3.00000 | − | 5.19615i | −0.121367 | − | 0.210214i | ||||
\(612\) | 18.0000 | − | 31.1769i | 0.727607 | − | 1.26025i | ||||
\(613\) | 13.0000 | − | 22.5167i | 0.525065 | − | 0.909439i | −0.474509 | − | 0.880251i | \(-0.657374\pi\) |
0.999574 | − | 0.0291886i | \(-0.00929235\pi\) | |||||||
\(614\) | −13.0000 | − | 22.5167i | −0.524637 | − | 0.908698i | ||||
\(615\) | −36.0000 | −1.45166 | ||||||||
\(616\) | 2.00000 | + | 1.73205i | 0.0805823 | + | 0.0697863i | ||||
\(617\) | −3.00000 | −0.120775 | −0.0603877 | − | 0.998175i | \(-0.519234\pi\) | ||||
−0.0603877 | + | 0.998175i | \(0.519234\pi\) | |||||||
\(618\) | 9.00000 | + | 15.5885i | 0.362033 | + | 0.627060i | ||||
\(619\) | −14.0000 | + | 24.2487i | −0.562708 | + | 0.974638i | 0.434551 | + | 0.900647i | \(0.356907\pi\) |
−0.997259 | + | 0.0739910i | \(0.976426\pi\) | |||||||
\(620\) | −4.00000 | + | 6.92820i | −0.160644 | + | 0.278243i | ||||
\(621\) | −18.0000 | − | 31.1769i | −0.722315 | − | 1.25109i | ||||
\(622\) | −6.00000 | −0.240578 | ||||||||
\(623\) | −15.0000 | + | 5.19615i | −0.600962 | + | 0.208179i | ||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −1.50000 | + | 2.59808i | −0.0599521 | + | 0.103840i | ||||
\(627\) | 6.00000 | − | 10.3923i | 0.239617 | − | 0.415029i | ||||
\(628\) | 6.00000 | + | 10.3923i | 0.239426 | + | 0.414698i | ||||
\(629\) | −48.0000 | −1.91389 | ||||||||
\(630\) | −3.00000 | + | 15.5885i | −0.119523 | + | 0.621059i | ||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | 7.50000 | + | 12.9904i | 0.298334 | + | 0.516730i | ||||
\(633\) | −12.0000 | + | 20.7846i | −0.476957 | + | 0.826114i | ||||
\(634\) | −12.0000 | + | 20.7846i | −0.476581 | + | 0.825462i | ||||
\(635\) | 0.500000 | + | 0.866025i | 0.0198419 | + | 0.0343672i | ||||
\(636\) | −18.0000 | −0.713746 | ||||||||
\(637\) | 6.50000 | + | 2.59808i | 0.257539 | + | 0.102940i | ||||
\(638\) | 1.00000 | 0.0395904 | ||||||||
\(639\) | −30.0000 | − | 51.9615i | −1.18678 | − | 2.05557i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −18.5000 | + | 32.0429i | −0.730706 | + | 1.26562i | 0.225876 | + | 0.974156i | \(0.427476\pi\) |
−0.956582 | + | 0.291464i | \(0.905858\pi\) | |||||||
\(642\) | −3.00000 | − | 5.19615i | −0.118401 | − | 0.205076i | ||||
\(643\) | 47.0000 | 1.85350 | 0.926750 | − | 0.375680i | \(-0.122591\pi\) | ||||
0.926750 | + | 0.375680i | \(0.122591\pi\) | |||||||
\(644\) | 2.00000 | − | 10.3923i | 0.0788110 | − | 0.409514i | ||||
\(645\) | 36.0000 | 1.41750 | ||||||||
\(646\) | −12.0000 | − | 20.7846i | −0.472134 | − | 0.817760i | ||||
\(647\) | 11.0000 | − | 19.0526i | 0.432455 | − | 0.749033i | −0.564629 | − | 0.825345i | \(-0.690981\pi\) |
0.997084 | + | 0.0763112i | \(0.0243142\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 7.50000 | + | 12.9904i | 0.294401 | + | 0.509917i | ||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | −60.0000 | + | 20.7846i | −2.35159 | + | 0.814613i | ||||
\(652\) | 15.0000 | 0.587445 | ||||||||
\(653\) | 12.0000 | + | 20.7846i | 0.469596 | + | 0.813365i | 0.999396 | − | 0.0347583i | \(-0.0110661\pi\) |
−0.529799 | + | 0.848123i | \(0.677733\pi\) | |||||||
\(654\) | −9.00000 | + | 15.5885i | −0.351928 | + | 0.609557i | ||||
\(655\) | −4.00000 | + | 6.92820i | −0.156293 | + | 0.270707i | ||||
\(656\) | 6.00000 | + | 10.3923i | 0.234261 | + | 0.405751i | ||||
\(657\) | −24.0000 | −0.936329 | ||||||||
\(658\) | 12.0000 | + | 10.3923i | 0.467809 | + | 0.405134i | ||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 1.50000 | + | 2.59808i | 0.0583874 | + | 0.101130i | ||||
\(661\) | −1.00000 | + | 1.73205i | −0.0388955 | + | 0.0673690i | −0.884818 | − | 0.465937i | \(-0.845717\pi\) |
0.845922 | + | 0.533306i | \(0.179051\pi\) | |||||||
\(662\) | −3.50000 | + | 6.06218i | −0.136031 | + | 0.235613i | ||||
\(663\) | −9.00000 | − | 15.5885i | −0.349531 | − | 0.605406i | ||||
\(664\) | −10.0000 | −0.388075 | ||||||||
\(665\) | 8.00000 | + | 6.92820i | 0.310227 | + | 0.268664i | ||||
\(666\) | −48.0000 | −1.85996 | ||||||||
\(667\) | −2.00000 | − | 3.46410i | −0.0774403 | − | 0.134131i | ||||
\(668\) | 3.50000 | − | 6.06218i | 0.135419 | − | 0.234553i | ||||
\(669\) | 18.0000 | − | 31.1769i | 0.695920 | − | 1.20537i | ||||
\(670\) | −3.50000 | − | 6.06218i | −0.135217 | − | 0.234202i | ||||
\(671\) | −3.00000 | −0.115814 | ||||||||
\(672\) | 7.50000 | − | 2.59808i | 0.289319 | − | 0.100223i | ||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | −16.0000 | − | 27.7128i | −0.616297 | − | 1.06746i | ||||
\(675\) | −4.50000 | + | 7.79423i | −0.173205 | + | 0.300000i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | −13.0000 | − | 22.5167i | −0.499631 | − | 0.865386i | 0.500369 | − | 0.865812i | \(-0.333198\pi\) |
−1.00000 | 0.000426509i | \(0.999864\pi\) | ||||||||
\(678\) | 45.0000 | 1.72821 | ||||||||
\(679\) | −2.50000 | + | 12.9904i | −0.0959412 | + | 0.498525i | ||||
\(680\) | 6.00000 | 0.230089 | ||||||||
\(681\) | −27.0000 | − | 46.7654i | −1.03464 | − | 1.79205i | ||||
\(682\) | −4.00000 | + | 6.92820i | −0.153168 | + | 0.265295i | ||||
\(683\) | 1.50000 | − | 2.59808i | 0.0573959 | − | 0.0994126i | −0.835900 | − | 0.548882i | \(-0.815054\pi\) |
0.893296 | + | 0.449469i | \(0.148387\pi\) | |||||||
\(684\) | −12.0000 | − | 20.7846i | −0.458831 | − | 0.794719i | ||||
\(685\) | 7.00000 | 0.267456 | ||||||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | −12.0000 | −0.457829 | ||||||||
\(688\) | −6.00000 | − | 10.3923i | −0.228748 | − | 0.396203i | ||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 6.00000 | − | 10.3923i | 0.228416 | − | 0.395628i | ||||
\(691\) | −18.5000 | − | 32.0429i | −0.703773 | − | 1.21897i | −0.967132 | − | 0.254273i | \(-0.918164\pi\) |
0.263359 | − | 0.964698i | \(-0.415170\pi\) | |||||||
\(692\) | −1.00000 | −0.0380143 | ||||||||
\(693\) | −3.00000 | + | 15.5885i | −0.113961 | + | 0.592157i | ||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | −8.00000 | − | 13.8564i | −0.303457 | − | 0.525603i | ||||
\(696\) | 1.50000 | − | 2.59808i | 0.0568574 | − | 0.0984798i | ||||
\(697\) | −36.0000 | + | 62.3538i | −1.36360 | + | 2.36182i | ||||
\(698\) | −17.0000 | − | 29.4449i | −0.643459 | − | 1.11450i | ||||
\(699\) | −48.0000 | −1.81553 | ||||||||
\(700\) | −2.50000 | + | 0.866025i | −0.0944911 | + | 0.0327327i | ||||
\(701\) | 15.0000 | 0.566542 | 0.283271 | − | 0.959040i | \(-0.408580\pi\) | ||||
0.283271 | + | 0.959040i | \(0.408580\pi\) | |||||||
\(702\) | −4.50000 | − | 7.79423i | −0.169842 | − | 0.294174i | ||||
\(703\) | −16.0000 | + | 27.7128i | −0.603451 | + | 1.04521i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 9.00000 | + | 15.5885i | 0.338960 | + | 0.587095i | ||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | −6.00000 | − | 5.19615i | −0.225653 | − | 0.195421i | ||||
\(708\) | 45.0000 | 1.69120 | ||||||||
\(709\) | −22.0000 | − | 38.1051i | −0.826227 | − | 1.43107i | −0.900978 | − | 0.433865i | \(-0.857149\pi\) |
0.0747503 | − | 0.997202i | \(-0.476184\pi\) | |||||||
\(710\) | 5.00000 | − | 8.66025i | 0.187647 | − | 0.325014i | ||||
\(711\) | −45.0000 | + | 77.9423i | −1.68763 | + | 2.92306i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 32.0000 | 1.19841 | ||||||||
\(714\) | 36.0000 | + | 31.1769i | 1.34727 | + | 1.16677i | ||||
\(715\) | 1.00000 | 0.0373979 | ||||||||
\(716\) | −3.50000 | − | 6.06218i | −0.130801 | − | 0.226554i | ||||
\(717\) | 16.5000 | − | 28.5788i | 0.616204 | − | 1.06730i | ||||
\(718\) | 1.50000 | − | 2.59808i | 0.0559795 | − | 0.0969593i | ||||
\(719\) | −25.0000 | − | 43.3013i | −0.932343 | − | 1.61486i | −0.779305 | − | 0.626644i | \(-0.784428\pi\) |
−0.153037 | − | 0.988220i | \(-0.548906\pi\) | |||||||
\(720\) | 6.00000 | 0.223607 | ||||||||
\(721\) | −15.0000 | + | 5.19615i | −0.558629 | + | 0.193515i | ||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 24.0000 | + | 41.5692i | 0.892570 | + | 1.54598i | ||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | −0.500000 | + | 0.866025i | −0.0185695 | + | 0.0321634i | ||||
\(726\) | 1.50000 | + | 2.59808i | 0.0556702 | + | 0.0964237i | ||||
\(727\) | −26.0000 | −0.964287 | −0.482143 | − | 0.876092i | \(-0.660142\pi\) | ||||
−0.482143 | + | 0.876092i | \(0.660142\pi\) | |||||||
\(728\) | 0.500000 | − | 2.59808i | 0.0185312 | − | 0.0962911i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −2.00000 | − | 3.46410i | −0.0740233 | − | 0.128212i | ||||
\(731\) | 36.0000 | − | 62.3538i | 1.33151 | − | 2.30624i | ||||
\(732\) | −4.50000 | + | 7.79423i | −0.166325 | + | 0.288083i | ||||
\(733\) | 6.50000 | + | 11.2583i | 0.240083 | + | 0.415836i | 0.960738 | − | 0.277458i | \(-0.0894920\pi\) |
−0.720655 | + | 0.693294i | \(0.756159\pi\) | |||||||
\(734\) | 24.0000 | 0.885856 | ||||||||
\(735\) | −19.5000 | − | 7.79423i | −0.719268 | − | 0.287494i | ||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −3.50000 | − | 6.06218i | −0.128924 | − | 0.223303i | ||||
\(738\) | −36.0000 | + | 62.3538i | −1.32518 | + | 2.29528i | ||||
\(739\) | −15.0000 | + | 25.9808i | −0.551784 | + | 0.955718i | 0.446362 | + | 0.894852i | \(0.352719\pi\) |
−0.998146 | + | 0.0608653i | \(0.980614\pi\) | |||||||
\(740\) | −4.00000 | − | 6.92820i | −0.147043 | − | 0.254686i | ||||
\(741\) | −12.0000 | −0.440831 | ||||||||
\(742\) | 3.00000 | − | 15.5885i | 0.110133 | − | 0.572270i | ||||
\(743\) | −20.0000 | −0.733729 | −0.366864 | − | 0.930274i | \(-0.619569\pi\) | ||||
−0.366864 | + | 0.930274i | \(0.619569\pi\) | |||||||
\(744\) | 12.0000 | + | 20.7846i | 0.439941 | + | 0.762001i | ||||
\(745\) | 3.00000 | − | 5.19615i | 0.109911 | − | 0.190372i | ||||
\(746\) | −1.50000 | + | 2.59808i | −0.0549189 | + | 0.0951223i | ||||
\(747\) | −30.0000 | − | 51.9615i | −1.09764 | − | 1.90117i | ||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | 5.00000 | − | 1.73205i | 0.182696 | − | 0.0632878i | ||||
\(750\) | −3.00000 | −0.109545 | ||||||||
\(751\) | 10.0000 | + | 17.3205i | 0.364905 | + | 0.632034i | 0.988761 | − | 0.149505i | \(-0.0477681\pi\) |
−0.623856 | + | 0.781540i | \(0.714435\pi\) | |||||||
\(752\) | 3.00000 | − | 5.19615i | 0.109399 | − | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.500000 | − | 0.866025i | −0.0182089 | − | 0.0315388i | ||||
\(755\) | −5.00000 | −0.181969 | ||||||||
\(756\) | 18.0000 | + | 15.5885i | 0.654654 | + | 0.566947i | ||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | 6.50000 | + | 11.2583i | 0.236091 | + | 0.408921i | ||||
\(759\) | 6.00000 | − | 10.3923i | 0.217786 | − | 0.377217i | ||||
\(760\) | 2.00000 | − | 3.46410i | 0.0725476 | − | 0.125656i | ||||
\(761\) | 11.0000 | + | 19.0526i | 0.398750 | + | 0.690655i | 0.993572 | − | 0.113203i | \(-0.0361109\pi\) |
−0.594822 | + | 0.803857i | \(0.702778\pi\) | |||||||
\(762\) | 3.00000 | 0.108679 | ||||||||
\(763\) | −12.0000 | − | 10.3923i | −0.434429 | − | 0.376227i | ||||
\(764\) | −18.0000 | −0.651217 | ||||||||
\(765\) | 18.0000 | + | 31.1769i | 0.650791 | + | 1.12720i | ||||
\(766\) | −7.00000 | + | 12.1244i | −0.252920 | + | 0.438071i | ||||
\(767\) | 7.50000 | − | 12.9904i | 0.270809 | − | 0.469055i | ||||
\(768\) | −1.50000 | − | 2.59808i | −0.0541266 | − | 0.0937500i | ||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | −2.50000 | + | 0.866025i | −0.0900937 | + | 0.0312094i | ||||
\(771\) | 45.0000 | 1.62064 | ||||||||
\(772\) | −2.00000 | − | 3.46410i | −0.0719816 | − | 0.124676i | ||||
\(773\) | 18.0000 | − | 31.1769i | 0.647415 | − | 1.12136i | −0.336323 | − | 0.941747i | \(-0.609183\pi\) |
0.983738 | − | 0.179609i | \(-0.0574833\pi\) | |||||||
\(774\) | 36.0000 | − | 62.3538i | 1.29399 | − | 2.24126i | ||||
\(775\) | −4.00000 | − | 6.92820i | −0.143684 | − | 0.248868i | ||||
\(776\) | 5.00000 | 0.179490 | ||||||||
\(777\) | 12.0000 | − | 62.3538i | 0.430498 | − | 2.23693i | ||||
\(778\) | 22.0000 | 0.788738 | ||||||||
\(779\) | 24.0000 | + | 41.5692i | 0.859889 | + | 1.48937i | ||||
\(780\) | 1.50000 | − | 2.59808i | 0.0537086 | − | 0.0930261i | ||||
\(781\) | 5.00000 | − | 8.66025i | 0.178914 | − | 0.309888i | ||||
\(782\) | −12.0000 | − | 20.7846i | −0.429119 | − | 0.743256i | ||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 12.0000 | + | 20.7846i | 0.428026 | + | 0.741362i | ||||
\(787\) | −14.0000 | + | 24.2487i | −0.499046 | + | 0.864373i | −0.999999 | − | 0.00110111i | \(-0.999650\pi\) |
0.500953 | + | 0.865474i | \(0.332983\pi\) | |||||||
\(788\) | −12.5000 | + | 21.6506i | −0.445294 | + | 0.771272i | ||||
\(789\) | 22.5000 | + | 38.9711i | 0.801021 | + | 1.38741i | ||||
\(790\) | −15.0000 | −0.533676 | ||||||||
\(791\) | −7.50000 | + | 38.9711i | −0.266669 | + | 1.38565i | ||||
\(792\) | 6.00000 | 0.213201 | ||||||||
\(793\) | 1.50000 | + | 2.59808i | 0.0532666 | + | 0.0922604i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | 9.00000 | − | 15.5885i | 0.319197 | − | 0.552866i | ||||
\(796\) | −2.00000 | − | 3.46410i | −0.0708881 | − | 0.122782i | ||||
\(797\) | −34.0000 | −1.20434 | −0.602171 | − | 0.798367i | \(-0.705697\pi\) | ||||
−0.602171 | + | 0.798367i | \(0.705697\pi\) | |||||||
\(798\) | 30.0000 | − | 10.3923i | 1.06199 | − | 0.367884i | ||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −18.0000 | + | 31.1769i | −0.635999 | + | 1.10158i | ||||
\(802\) | 11.5000 | − | 19.9186i | 0.406079 | − | 0.703350i | ||||
\(803\) | −2.00000 | − | 3.46410i | −0.0705785 | − | 0.122245i | ||||
\(804\) | −21.0000 | −0.740613 | ||||||||
\(805\) | 8.00000 | + | 6.92820i | 0.281963 | + | 0.244187i | ||||
\(806\) | 8.00000 | 0.281788 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.50000 | + | 2.59808i | −0.0527698 | + | 0.0914000i | ||||
\(809\) | 12.0000 | − | 20.7846i | 0.421898 | − | 0.730748i | −0.574228 | − | 0.818696i | \(-0.694698\pi\) |
0.996125 | + | 0.0879478i | \(0.0280309\pi\) | |||||||
\(810\) | 4.50000 | + | 7.79423i | 0.158114 | + | 0.273861i | ||||
\(811\) | −20.0000 | −0.702295 | −0.351147 | − | 0.936320i | \(-0.614208\pi\) | ||||
−0.351147 | + | 0.936320i | \(0.614208\pi\) | |||||||
\(812\) | 2.00000 | + | 1.73205i | 0.0701862 | + | 0.0607831i | ||||
\(813\) | −63.0000 | −2.20951 | ||||||||
\(814\) | −4.00000 | − | 6.92820i | −0.140200 | − | 0.242833i | ||||
\(815\) | −7.50000 | + | 12.9904i | −0.262714 | + | 0.455033i | ||||
\(816\) | 9.00000 | − | 15.5885i | 0.315063 | − | 0.545705i | ||||
\(817\) | −24.0000 | − | 41.5692i | −0.839654 | − | 1.45432i | ||||
\(818\) | 14.0000 | 0.489499 | ||||||||
\(819\) | 15.0000 | − | 5.19615i | 0.524142 | − | 0.181568i | ||||
\(820\) | −12.0000 | −0.419058 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 10.5000 | − | 18.1865i | 0.366230 | − | 0.634328i | ||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | 3.00000 | + | 5.19615i | 0.104510 | + | 0.181017i | ||||
\(825\) | −3.00000 | −0.104447 | ||||||||
\(826\) | −7.50000 | + | 38.9711i | −0.260958 | + | 1.35598i | ||||
\(827\) | −4.00000 | −0.139094 | −0.0695468 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695468 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(828\) | −12.0000 | − | 20.7846i | −0.417029 | − | 0.722315i | ||||
\(829\) | 3.00000 | − | 5.19615i | 0.104194 | − | 0.180470i | −0.809214 | − | 0.587513i | \(-0.800107\pi\) |
0.913409 | + | 0.407044i | \(0.133440\pi\) | |||||||
\(830\) | 5.00000 | − | 8.66025i | 0.173553 | − | 0.300602i | ||||
\(831\) | −37.5000 | − | 64.9519i | −1.30086 | − | 2.25316i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −33.0000 | + | 25.9808i | −1.14338 | + | 0.900180i | ||||
\(834\) | −48.0000 | −1.66210 | ||||||||
\(835\) | 3.50000 | + | 6.06218i | 0.121122 | + | 0.209790i | ||||
\(836\) | 2.00000 | − | 3.46410i | 0.0691714 | − | 0.119808i | ||||
\(837\) | −36.0000 | + | 62.3538i | −1.24434 | + | 2.15526i | ||||
\(838\) | −12.0000 | − | 20.7846i | −0.414533 | − | 0.717992i | ||||
\(839\) | 30.0000 | 1.03572 | 0.517858 | − | 0.855467i | \(-0.326730\pi\) | ||||
0.517858 | + | 0.855467i | \(0.326730\pi\) | |||||||
\(840\) | −1.50000 | + | 7.79423i | −0.0517549 | + | 0.268926i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 16.0000 | + | 27.7128i | 0.551396 | + | 0.955047i | ||||
\(843\) | 18.0000 | − | 31.1769i | 0.619953 | − | 1.07379i | ||||
\(844\) | −4.00000 | + | 6.92820i | −0.137686 | + | 0.238479i | ||||
\(845\) | 6.00000 | + | 10.3923i | 0.206406 | + | 0.357506i | ||||
\(846\) | 36.0000 | 1.23771 | ||||||||
\(847\) | −2.50000 | + | 0.866025i | −0.0859010 | + | 0.0297570i | ||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 24.0000 | + | 41.5692i | 0.823678 | + | 1.42665i | ||||
\(850\) | −3.00000 | + | 5.19615i | −0.102899 | + | 0.178227i | ||||
\(851\) | −16.0000 | + | 27.7128i | −0.548473 | + | 0.949983i | ||||
\(852\) | −15.0000 | − | 25.9808i | −0.513892 | − | 0.890086i | ||||
\(853\) | 26.0000 | 0.890223 | 0.445112 | − | 0.895475i | \(-0.353164\pi\) | ||||
0.445112 | + | 0.895475i | \(0.353164\pi\) | |||||||
\(854\) | −6.00000 | − | 5.19615i | −0.205316 | − | 0.177809i | ||||
\(855\) | 24.0000 | 0.820783 | ||||||||
\(856\) | −1.00000 | − | 1.73205i | −0.0341793 | − | 0.0592003i | ||||
\(857\) | −6.00000 | + | 10.3923i | −0.204956 | + | 0.354994i | −0.950119 | − | 0.311888i | \(-0.899038\pi\) |
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(858\) | 1.50000 | − | 2.59808i | 0.0512092 | − | 0.0886969i | ||||
\(859\) | −8.50000 | − | 14.7224i | −0.290016 | − | 0.502323i | 0.683797 | − | 0.729672i | \(-0.260327\pi\) |
−0.973813 | + | 0.227349i | \(0.926994\pi\) | |||||||
\(860\) | 12.0000 | 0.409197 | ||||||||
\(861\) | −72.0000 | − | 62.3538i | −2.45375 | − | 2.12501i | ||||
\(862\) | −7.00000 | −0.238421 | ||||||||
\(863\) | 24.0000 | + | 41.5692i | 0.816970 | + | 1.41503i | 0.907905 | + | 0.419176i | \(0.137681\pi\) |
−0.0909355 | + | 0.995857i | \(0.528986\pi\) | |||||||
\(864\) | 4.50000 | − | 7.79423i | 0.153093 | − | 0.265165i | ||||
\(865\) | 0.500000 | − | 0.866025i | 0.0170005 | − | 0.0294457i | ||||
\(866\) | −5.00000 | − | 8.66025i | −0.169907 | − | 0.294287i | ||||
\(867\) | 57.0000 | 1.93582 | ||||||||
\(868\) | −20.0000 | + | 6.92820i | −0.678844 | + | 0.235159i | ||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | 1.50000 | + | 2.59808i | 0.0508548 | + | 0.0880830i | ||||
\(871\) | −3.50000 | + | 6.06218i | −0.118593 | + | 0.205409i | ||||
\(872\) | −3.00000 | + | 5.19615i | −0.101593 | + | 0.175964i | ||||
\(873\) | 15.0000 | + | 25.9808i | 0.507673 | + | 0.879316i | ||||
\(874\) | −16.0000 | −0.541208 | ||||||||
\(875\) | 0.500000 | − | 2.59808i | 0.0169031 | − | 0.0878310i | ||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | 1.50000 | + | 2.59808i | 0.0506514 | + | 0.0877308i | 0.890239 | − | 0.455493i | \(-0.150537\pi\) |
−0.839588 | + | 0.543224i | \(0.817204\pi\) | |||||||
\(878\) | −9.50000 | + | 16.4545i | −0.320609 | + | 0.555312i | ||||
\(879\) | −39.0000 | + | 67.5500i | −1.31544 | + | 2.27840i | ||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | 53.0000 | 1.78562 | 0.892808 | − | 0.450438i | \(-0.148732\pi\) | ||||
0.892808 | + | 0.450438i | \(0.148732\pi\) | |||||||
\(882\) | −33.0000 | + | 25.9808i | −1.11117 | + | 0.874818i | ||||
\(883\) | 3.00000 | 0.100958 | 0.0504790 | − | 0.998725i | \(-0.483925\pi\) | ||||
0.0504790 | + | 0.998725i | \(0.483925\pi\) | |||||||
\(884\) | −3.00000 | − | 5.19615i | −0.100901 | − | 0.174766i | ||||
\(885\) | −22.5000 | + | 38.9711i | −0.756329 | + | 1.31000i | ||||
\(886\) | −14.0000 | + | 24.2487i | −0.470339 | + | 0.814651i | ||||
\(887\) | −18.5000 | − | 32.0429i | −0.621169 | − | 1.07590i | −0.989268 | − | 0.146110i | \(-0.953325\pi\) |
0.368099 | − | 0.929787i | \(-0.380009\pi\) | |||||||
\(888\) | −24.0000 | −0.805387 | ||||||||
\(889\) | −0.500000 | + | 2.59808i | −0.0167695 | + | 0.0871367i | ||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 6.00000 | − | 10.3923i | 0.200895 | − | 0.347960i | ||||
\(893\) | 12.0000 | − | 20.7846i | 0.401565 | − | 0.695530i | ||||
\(894\) | −9.00000 | − | 15.5885i | −0.301005 | − | 0.521356i | ||||
\(895\) | 7.00000 | 0.233984 | ||||||||
\(896\) | 2.50000 | − | 0.866025i | 0.0835191 | − | 0.0289319i | ||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 13.0000 | + | 22.5167i | 0.433816 | + | 0.751391i | ||||
\(899\) | −4.00000 | + | 6.92820i | −0.133407 | + | 0.231069i | ||||
\(900\) | −3.00000 | + | 5.19615i | −0.100000 | + | 0.173205i | ||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | −12.0000 | −0.399556 | ||||||||
\(903\) | 72.0000 | + | 62.3538i | 2.39601 | + | 2.07501i | ||||
\(904\) | 15.0000 | 0.498893 | ||||||||
\(905\) | −1.00000 | − | 1.73205i | −0.0332411 | − | 0.0575753i | ||||
\(906\) | −7.50000 | + | 12.9904i | −0.249171 | + | 0.431577i | ||||
\(907\) | 10.0000 | − | 17.3205i | 0.332045 | − | 0.575118i | −0.650868 | − | 0.759191i | \(-0.725595\pi\) |
0.982913 | + | 0.184073i | \(0.0589282\pi\) | |||||||
\(908\) | −9.00000 | − | 15.5885i | −0.298675 | − | 0.517321i | ||||
\(909\) | −18.0000 | −0.597022 | ||||||||
\(910\) | 2.00000 | + | 1.73205i | 0.0662994 | + | 0.0574169i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −6.00000 | − | 10.3923i | −0.198680 | − | 0.344124i | ||||
\(913\) | 5.00000 | − | 8.66025i | 0.165476 | − | 0.286613i | ||||
\(914\) | 17.0000 | − | 29.4449i | 0.562310 | − | 0.973950i | ||||
\(915\) | −4.50000 | − | 7.79423i | −0.148765 | − | 0.257669i | ||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | −20.0000 | + | 6.92820i | −0.660458 | + | 0.228789i | ||||
\(918\) | 54.0000 | 1.78227 | ||||||||
\(919\) | 26.0000 | + | 45.0333i | 0.857661 | + | 1.48551i | 0.874154 | + | 0.485648i | \(0.161416\pi\) |
−0.0164935 | + | 0.999864i | \(0.505250\pi\) | |||||||
\(920\) | 2.00000 | − | 3.46410i | 0.0659380 | − | 0.114208i | ||||
\(921\) | 39.0000 | − | 67.5500i | 1.28509 | − | 2.22585i | ||||
\(922\) | −7.50000 | − | 12.9904i | −0.246999 | − | 0.427815i | ||||
\(923\) | −10.0000 | −0.329154 | ||||||||
\(924\) | −1.50000 | + | 7.79423i | −0.0493464 | + | 0.256411i | ||||
\(925\) | 8.00000 | 0.263038 | ||||||||
\(926\) | 17.0000 | + | 29.4449i | 0.558655 | + | 0.967618i | ||||
\(927\) | −18.0000 | + | 31.1769i | −0.591198 | + | 1.02398i | ||||
\(928\) | 0.500000 | − | 0.866025i | 0.0164133 | − | 0.0284287i | ||||
\(929\) | 16.5000 | + | 28.5788i | 0.541347 | + | 0.937641i | 0.998827 | + | 0.0484211i | \(0.0154190\pi\) |
−0.457480 | + | 0.889220i | \(0.651248\pi\) | |||||||
\(930\) | −24.0000 | −0.786991 | ||||||||
\(931\) | 4.00000 | + | 27.7128i | 0.131095 | + | 0.908251i | ||||
\(932\) | −16.0000 | −0.524097 | ||||||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | −18.0000 | + | 31.1769i | −0.588978 | + | 1.02014i | ||||
\(935\) | −3.00000 | + | 5.19615i | −0.0981105 | + | 0.169932i | ||||
\(936\) | −3.00000 | − | 5.19615i | −0.0980581 | − | 0.169842i | ||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 3.50000 | − | 18.1865i | 0.114279 | − | 0.593811i | ||||
\(939\) | −9.00000 | −0.293704 | ||||||||
\(940\) | 3.00000 | + | 5.19615i | 0.0978492 | + | 0.169480i | ||||
\(941\) | 8.50000 | − | 14.7224i | 0.277092 | − | 0.479938i | −0.693569 | − | 0.720390i | \(-0.743963\pi\) |
0.970661 | + | 0.240453i | \(0.0772960\pi\) | |||||||
\(942\) | −18.0000 | + | 31.1769i | −0.586472 | + | 1.01580i | ||||
\(943\) | 24.0000 | + | 41.5692i | 0.781548 | + | 1.35368i | ||||
\(944\) | 15.0000 | 0.488208 | ||||||||
\(945\) | −22.5000 | + | 7.79423i | −0.731925 | + | 0.253546i | ||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −18.0000 | − | 31.1769i | −0.584921 | − | 1.01311i | −0.994885 | − | 0.101012i | \(-0.967792\pi\) |
0.409964 | − | 0.912102i | \(-0.365541\pi\) | |||||||
\(948\) | −22.5000 | + | 38.9711i | −0.730766 | + | 1.26572i | ||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | 2.00000 | + | 3.46410i | 0.0648886 | + | 0.112390i | ||||
\(951\) | −72.0000 | −2.33476 | ||||||||
\(952\) | 12.0000 | + | 10.3923i | 0.388922 | + | 0.336817i | ||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | −18.0000 | − | 31.1769i | −0.582772 | − | 1.00939i | ||||
\(955\) | 9.00000 | − | 15.5885i | 0.291233 | − | 0.504431i | ||||
\(956\) | 5.50000 | − | 9.52628i | 0.177883 | − | 0.308102i | ||||
\(957\) | 1.50000 | + | 2.59808i | 0.0484881 | + | 0.0839839i | ||||
\(958\) | 15.0000 | 0.484628 | ||||||||
\(959\) | 14.0000 | + | 12.1244i | 0.452084 | + | 0.391516i | ||||
\(960\) | 3.00000 | 0.0968246 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | −4.00000 | + | 6.92820i | −0.128965 | + | 0.223374i | ||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 8.00000 | + | 13.8564i | 0.257663 | + | 0.446285i | ||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 30.0000 | − | 10.3923i | 0.965234 | − | 0.334367i | ||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 36.0000 | − | 62.3538i | 1.15649 | − | 2.00309i | ||||
\(970\) | −2.50000 | + | 4.33013i | −0.0802702 | + | 0.139032i | ||||
\(971\) | −22.5000 | − | 38.9711i | −0.722059 | − | 1.25064i | −0.960173 | − | 0.279406i | \(-0.909862\pi\) |
0.238114 | − | 0.971237i | \(-0.423471\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.00000 | − | 41.5692i | 0.256468 | − | 1.33265i | ||||
\(974\) | 36.0000 | 1.15351 | ||||||||
\(975\) | 1.50000 | + | 2.59808i | 0.0480384 | + | 0.0832050i | ||||
\(976\) | −1.50000 | + | 2.59808i | −0.0480138 | + | 0.0831624i | ||||
\(977\) | −9.00000 | + | 15.5885i | −0.287936 | + | 0.498719i | −0.973317 | − | 0.229465i | \(-0.926302\pi\) |
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(978\) | 22.5000 | + | 38.9711i | 0.719471 | + | 1.24616i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | −6.50000 | − | 2.59808i | −0.207635 | − | 0.0829925i | ||||
\(981\) | −36.0000 | −1.14939 | ||||||||
\(982\) | −7.00000 | − | 12.1244i | −0.223379 | − | 0.386904i | ||||
\(983\) | 21.0000 | − | 36.3731i | 0.669796 | − | 1.16012i | −0.308165 | − | 0.951333i | \(-0.599715\pi\) |
0.977961 | − | 0.208788i | \(-0.0669518\pi\) | |||||||
\(984\) | −18.0000 | + | 31.1769i | −0.573819 | + | 0.993884i | ||||
\(985\) | −12.5000 | − | 21.6506i | −0.398283 | − | 0.689847i | ||||
\(986\) | 6.00000 | 0.191079 | ||||||||
\(987\) | −9.00000 | + | 46.7654i | −0.286473 | + | 1.48856i | ||||
\(988\) | −4.00000 | −0.127257 | ||||||||
\(989\) | −24.0000 | − | 41.5692i | −0.763156 | − | 1.32182i | ||||
\(990\) | −3.00000 | + | 5.19615i | −0.0953463 | + | 0.165145i | ||||
\(991\) | 3.00000 | − | 5.19615i | 0.0952981 | − | 0.165061i | −0.814435 | − | 0.580255i | \(-0.802953\pi\) |
0.909733 | + | 0.415194i | \(0.136286\pi\) | |||||||
\(992\) | 4.00000 | + | 6.92820i | 0.127000 | + | 0.219971i | ||||
\(993\) | −21.0000 | −0.666415 | ||||||||
\(994\) | 25.0000 | − | 8.66025i | 0.792952 | − | 0.274687i | ||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | −15.0000 | − | 25.9808i | −0.475293 | − | 0.823232i | ||||
\(997\) | 21.0000 | − | 36.3731i | 0.665077 | − | 1.15195i | −0.314188 | − | 0.949361i | \(-0.601732\pi\) |
0.979265 | − | 0.202586i | \(-0.0649345\pi\) | |||||||
\(998\) | 18.0000 | − | 31.1769i | 0.569780 | − | 0.986888i | ||||
\(999\) | −36.0000 | − | 62.3538i | −1.13899 | − | 1.97279i |
(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 | 770.2.i.d.221.1 | ✓ | 2 | |
7.2 | even | 3 | inner | 770.2.i.d.331.1 | yes | 2 | |
7.3 | odd | 6 | 5390.2.a.a.1.1 | 1 | |||
7.4 | even | 3 | 5390.2.a.t.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.i.d.221.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
770.2.i.d.331.1 | yes | 2 | 7.2 | even | 3 | inner | |
5390.2.a.a.1.1 | 1 | 7.3 | odd | 6 | |||
5390.2.a.t.1.1 | 1 | 7.4 | even | 3 |