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 | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.211 |
Dual form | 930.2.i.c.811.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0.996866 | + | 0.0791130i | \(0.0252088\pi\) |
−0.429919 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −2.00000 | + | 3.46410i | −0.554700 | + | 0.960769i | 0.443227 | + | 0.896410i | \(0.353834\pi\) |
−0.997927 | + | 0.0643593i | \(0.979500\pi\) | |||||||
\(14\) | −1.50000 | − | 2.59808i | −0.400892 | − | 0.694365i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | −1.50000 | + | 2.59808i | −0.327327 | + | 0.566947i | ||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 2.00000 | 0.417029 | 0.208514 | − | 0.978019i | \(-0.433137\pi\) | ||||
0.208514 | + | 0.978019i | \(0.433137\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.50000 | + | 2.59808i | 0.283473 | + | 0.490990i | ||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −3.50000 | + | 4.33013i | −0.628619 | + | 0.777714i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 3.00000 | 0.522233 | ||||||||
\(34\) | −2.00000 | − | 3.46410i | −0.342997 | − | 0.594089i | ||||
\(35\) | 3.00000 | 0.507093 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | 3.00000 | + | 5.19615i | 0.493197 | + | 0.854242i | 0.999969 | − | 0.00783774i | \(-0.00249486\pi\) |
−0.506772 | + | 0.862080i | \(0.669162\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 1.00000 | − | 1.73205i | 0.156174 | − | 0.270501i | −0.777312 | − | 0.629115i | \(-0.783417\pi\) |
0.933486 | + | 0.358614i | \(0.116751\pi\) | |||||||
\(42\) | 1.50000 | − | 2.59808i | 0.231455 | − | 0.400892i | ||||
\(43\) | −2.00000 | − | 3.46410i | −0.304997 | − | 0.528271i | 0.672264 | − | 0.740312i | \(-0.265322\pi\) |
−0.977261 | + | 0.212041i | \(0.931989\pi\) | |||||||
\(44\) | 1.50000 | − | 2.59808i | 0.226134 | − | 0.391675i | ||||
\(45\) | 0.500000 | + | 0.866025i | 0.0745356 | + | 0.129099i | ||||
\(46\) | −2.00000 | −0.294884 | ||||||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 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 | ||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | −2.00000 | + | 3.46410i | −0.277350 | + | 0.480384i | ||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −1.50000 | − | 2.59808i | −0.202260 | − | 0.350325i | ||||
\(56\) | −1.50000 | − | 2.59808i | −0.200446 | − | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 3.50000 | − | 4.33013i | 0.444500 | − | 0.549927i | ||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.00000 | + | 3.46410i | 0.248069 | + | 0.429669i | ||||
\(66\) | −3.00000 | −0.369274 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | 1.00000 | + | 1.73205i | 0.120386 | + | 0.208514i | ||||
\(70\) | −3.00000 | −0.358569 | ||||||||
\(71\) | −2.00000 | + | 3.46410i | −0.237356 | + | 0.411113i | −0.959955 | − | 0.280155i | \(-0.909614\pi\) |
0.722599 | + | 0.691268i | \(0.242948\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −1.00000 | + | 1.73205i | −0.117041 | + | 0.202721i | −0.918594 | − | 0.395203i | \(-0.870674\pi\) |
0.801553 | + | 0.597924i | \(0.204008\pi\) | |||||||
\(74\) | −3.00000 | − | 5.19615i | −0.348743 | − | 0.604040i | ||||
\(75\) | 0.500000 | − | 0.866025i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000 | 1.02565 | ||||||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 2.00000 | + | 3.46410i | 0.225018 | + | 0.389742i | 0.956325 | − | 0.292306i | \(-0.0944227\pi\) |
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0.500000 | − | 0.866025i | 0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | −4.50000 | + | 7.79423i | −0.493939 | + | 0.855528i | −0.999976 | − | 0.00698436i | \(-0.997777\pi\) |
0.506036 | + | 0.862512i | \(0.331110\pi\) | |||||||
\(84\) | −1.50000 | + | 2.59808i | −0.163663 | + | 0.283473i | ||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | 0.500000 | + | 0.866025i | 0.0536056 | + | 0.0928477i | ||||
\(88\) | −1.50000 | + | 2.59808i | −0.159901 | + | 0.276956i | ||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | −0.500000 | − | 0.866025i | −0.0527046 | − | 0.0912871i | ||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | −5.50000 | − | 0.866025i | −0.570323 | − | 0.0898027i | ||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 11.0000 | 1.11688 | 0.558440 | − | 0.829545i | \(-0.311400\pi\) | ||||
0.558440 | + | 0.829545i | \(0.311400\pi\) | |||||||
\(98\) | 1.00000 | − | 1.73205i | 0.101015 | − | 0.174964i | ||||
\(99\) | 1.50000 | + | 2.59808i | 0.150756 | + | 0.261116i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −19.0000 | −1.89057 | −0.945285 | − | 0.326245i | \(-0.894217\pi\) | ||||
−0.945285 | + | 0.326245i | \(0.894217\pi\) | |||||||
\(102\) | 2.00000 | − | 3.46410i | 0.198030 | − | 0.342997i | ||||
\(103\) | −6.50000 | + | 11.2583i | −0.640464 | + | 1.10932i | 0.344865 | + | 0.938652i | \(0.387925\pi\) |
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 1.50000 | + | 2.59808i | 0.146385 | + | 0.253546i | ||||
\(106\) | −1.50000 | + | 2.59808i | −0.145693 | + | 0.252347i | ||||
\(107\) | 1.50000 | + | 2.59808i | 0.145010 | + | 0.251166i | 0.929377 | − | 0.369132i | \(-0.120345\pi\) |
−0.784366 | + | 0.620298i | \(0.787012\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | 1.50000 | + | 2.59808i | 0.143019 | + | 0.247717i | ||||
\(111\) | −3.00000 | + | 5.19615i | −0.284747 | + | 0.493197i | ||||
\(112\) | 1.50000 | + | 2.59808i | 0.141737 | + | 0.245495i | ||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | − | 1.73205i | 0.0932505 | − | 0.161515i | ||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −2.00000 | − | 3.46410i | −0.184900 | − | 0.320256i | ||||
\(118\) | −4.50000 | − | 7.79423i | −0.414259 | − | 0.717517i | ||||
\(119\) | −6.00000 | + | 10.3923i | −0.550019 | + | 0.952661i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 2.00000 | 0.181071 | ||||||||
\(123\) | 2.00000 | 0.180334 | ||||||||
\(124\) | −3.50000 | + | 4.33013i | −0.314309 | + | 0.388857i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | 6.50000 | + | 11.2583i | 0.576782 | + | 0.999015i | 0.995846 | + | 0.0910585i | \(0.0290250\pi\) |
−0.419064 | + | 0.907957i | \(0.637642\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | −2.00000 | − | 3.46410i | −0.175412 | − | 0.303822i | ||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.00000 | − | 1.73205i | 0.0863868 | − | 0.149626i | ||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −2.00000 | − | 3.46410i | −0.171499 | − | 0.297044i | ||||
\(137\) | 8.00000 | − | 13.8564i | 0.683486 | − | 1.18383i | −0.290424 | − | 0.956898i | \(-0.593796\pi\) |
0.973910 | − | 0.226935i | \(-0.0728704\pi\) | |||||||
\(138\) | −1.00000 | − | 1.73205i | −0.0851257 | − | 0.147442i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 3.00000 | 0.253546 | ||||||||
\(141\) | 2.00000 | + | 3.46410i | 0.168430 | + | 0.291730i | ||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | 6.00000 | + | 10.3923i | 0.501745 | + | 0.869048i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0.500000 | − | 0.866025i | 0.0415227 | − | 0.0719195i | ||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | −2.00000 | −0.164957 | ||||||||
\(148\) | 3.00000 | + | 5.19615i | 0.246598 | + | 0.427121i | ||||
\(149\) | −9.50000 | − | 16.4545i | −0.778270 | − | 1.34800i | −0.932938 | − | 0.360037i | \(-0.882764\pi\) |
0.154668 | − | 0.987967i | \(-0.450569\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 9.00000 | 0.732410 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | −9.00000 | −0.725241 | ||||||||
\(155\) | 2.00000 | + | 5.19615i | 0.160644 | + | 0.417365i | ||||
\(156\) | −4.00000 | −0.320256 | ||||||||
\(157\) | 22.0000 | 1.75579 | 0.877896 | − | 0.478852i | \(-0.158947\pi\) | ||||
0.877896 | + | 0.478852i | \(0.158947\pi\) | |||||||
\(158\) | −2.00000 | − | 3.46410i | −0.159111 | − | 0.275589i | ||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | 3.00000 | + | 5.19615i | 0.236433 | + | 0.409514i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | 1.00000 | − | 1.73205i | 0.0780869 | − | 0.135250i | ||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 4.50000 | − | 7.79423i | 0.349268 | − | 0.604949i | ||||
\(167\) | −1.00000 | − | 1.73205i | −0.0773823 | − | 0.134030i | 0.824737 | − | 0.565516i | \(-0.191323\pi\) |
−0.902120 | + | 0.431486i | \(0.857990\pi\) | |||||||
\(168\) | 1.50000 | − | 2.59808i | 0.115728 | − | 0.200446i | ||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | −4.00000 | −0.306786 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.00000 | − | 3.46410i | −0.152499 | − | 0.264135i | ||||
\(173\) | 0.500000 | − | 0.866025i | 0.0380143 | − | 0.0658427i | −0.846392 | − | 0.532560i | \(-0.821230\pi\) |
0.884407 | + | 0.466717i | \(0.154563\pi\) | |||||||
\(174\) | −0.500000 | − | 0.866025i | −0.0379049 | − | 0.0656532i | ||||
\(175\) | 1.50000 | − | 2.59808i | 0.113389 | − | 0.196396i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | −4.50000 | + | 7.79423i | −0.338241 | + | 0.585850i | ||||
\(178\) | −10.0000 | −0.749532 | ||||||||
\(179\) | −9.50000 | − | 16.4545i | −0.710063 | − | 1.22987i | −0.964833 | − | 0.262864i | \(-0.915333\pi\) |
0.254770 | − | 0.967002i | \(-0.418000\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | −1.00000 | + | 1.73205i | −0.0743294 | + | 0.128742i | −0.900794 | − | 0.434246i | \(-0.857015\pi\) |
0.826465 | + | 0.562988i | \(0.190348\pi\) | |||||||
\(182\) | 12.0000 | 0.889499 | ||||||||
\(183\) | −1.00000 | − | 1.73205i | −0.0739221 | − | 0.128037i | ||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | 6.00000 | 0.441129 | ||||||||
\(186\) | 5.50000 | + | 0.866025i | 0.403280 | + | 0.0635001i | ||||
\(187\) | 12.0000 | 0.877527 | ||||||||
\(188\) | 4.00000 | 0.291730 | ||||||||
\(189\) | −1.50000 | − | 2.59808i | −0.109109 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.00000 | − | 12.1244i | 0.506502 | − | 0.877288i | −0.493469 | − | 0.869763i | \(-0.664272\pi\) |
0.999972 | − | 0.00752447i | \(-0.00239513\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | −10.5000 | − | 18.1865i | −0.755807 | − | 1.30910i | −0.944972 | − | 0.327150i | \(-0.893912\pi\) |
0.189166 | − | 0.981945i | \(-0.439422\pi\) | |||||||
\(194\) | −11.0000 | −0.789754 | ||||||||
\(195\) | −2.00000 | + | 3.46410i | −0.143223 | + | 0.248069i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | 9.00000 | − | 15.5885i | 0.641223 | − | 1.11063i | −0.343937 | − | 0.938993i | \(-0.611761\pi\) |
0.985160 | − | 0.171639i | \(-0.0549062\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | 5.50000 | − | 9.52628i | 0.389885 | − | 0.675300i | −0.602549 | − | 0.798082i | \(-0.705848\pi\) |
0.992434 | + | 0.122782i | \(0.0391815\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | 19.0000 | 1.33684 | ||||||||
\(203\) | 1.50000 | + | 2.59808i | 0.105279 | + | 0.182349i | ||||
\(204\) | −2.00000 | + | 3.46410i | −0.140028 | + | 0.242536i | ||||
\(205\) | −1.00000 | − | 1.73205i | −0.0698430 | − | 0.120972i | ||||
\(206\) | 6.50000 | − | 11.2583i | 0.452876 | − | 0.784405i | ||||
\(207\) | −1.00000 | + | 1.73205i | −0.0695048 | + | 0.120386i | ||||
\(208\) | −2.00000 | + | 3.46410i | −0.138675 | + | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.50000 | − | 2.59808i | −0.103510 | − | 0.179284i | ||||
\(211\) | −4.00000 | − | 6.92820i | −0.275371 | − | 0.476957i | 0.694857 | − | 0.719148i | \(-0.255467\pi\) |
−0.970229 | + | 0.242190i | \(0.922134\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | −1.50000 | − | 2.59808i | −0.102538 | − | 0.177601i | ||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −16.5000 | − | 2.59808i | −1.12009 | − | 0.176369i | ||||
\(218\) | 4.00000 | 0.270914 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | −1.50000 | − | 2.59808i | −0.101130 | − | 0.175162i | ||||
\(221\) | −16.0000 | −1.07628 | ||||||||
\(222\) | 3.00000 | − | 5.19615i | 0.201347 | − | 0.348743i | ||||
\(223\) | −4.50000 | − | 7.79423i | −0.301342 | − | 0.521940i | 0.675098 | − | 0.737728i | \(-0.264101\pi\) |
−0.976440 | + | 0.215788i | \(0.930768\pi\) | |||||||
\(224\) | −1.50000 | − | 2.59808i | −0.100223 | − | 0.173591i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −6.00000 | + | 10.3923i | −0.399114 | + | 0.691286i | ||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0000 | − | 19.0526i | −0.726900 | − | 1.25903i | −0.958187 | − | 0.286143i | \(-0.907627\pi\) |
0.231287 | − | 0.972886i | \(-0.425707\pi\) | |||||||
\(230\) | −1.00000 | + | 1.73205i | −0.0659380 | + | 0.114208i | ||||
\(231\) | 4.50000 | + | 7.79423i | 0.296078 | + | 0.512823i | ||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 2.00000 | + | 3.46410i | 0.130744 | + | 0.226455i | ||||
\(235\) | 2.00000 | − | 3.46410i | 0.130466 | − | 0.225973i | ||||
\(236\) | 4.50000 | + | 7.79423i | 0.292925 | + | 0.507361i | ||||
\(237\) | −2.00000 | + | 3.46410i | −0.129914 | + | 0.225018i | ||||
\(238\) | 6.00000 | − | 10.3923i | 0.388922 | − | 0.673633i | ||||
\(239\) | 12.0000 | − | 20.7846i | 0.776215 | − | 1.34444i | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −7.50000 | − | 12.9904i | −0.483117 | − | 0.836784i | 0.516695 | − | 0.856170i | \(-0.327162\pi\) |
−0.999812 | + | 0.0193858i | \(0.993829\pi\) | |||||||
\(242\) | −1.00000 | − | 1.73205i | −0.0642824 | − | 0.111340i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 1.00000 | + | 1.73205i | 0.0638877 | + | 0.110657i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.50000 | − | 4.33013i | 0.222250 | − | 0.274963i | ||||
\(249\) | −9.00000 | −0.570352 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | 3.00000 | − | 5.19615i | 0.188608 | − | 0.326679i | ||||
\(254\) | −6.50000 | − | 11.2583i | −0.407846 | − | 0.706410i | ||||
\(255\) | 2.00000 | + | 3.46410i | 0.125245 | + | 0.216930i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.00000 | + | 8.66025i | −0.311891 | + | 0.540212i | −0.978772 | − | 0.204953i | \(-0.934296\pi\) |
0.666880 | + | 0.745165i | \(0.267629\pi\) | |||||||
\(258\) | −2.00000 | + | 3.46410i | −0.124515 | + | 0.215666i | ||||
\(259\) | −9.00000 | + | 15.5885i | −0.559233 | + | 0.968620i | ||||
\(260\) | 2.00000 | + | 3.46410i | 0.124035 | + | 0.214834i | ||||
\(261\) | −0.500000 | + | 0.866025i | −0.0309492 | + | 0.0536056i | ||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | −6.00000 | −0.369976 | −0.184988 | − | 0.982741i | \(-0.559225\pi\) | ||||
−0.184988 | + | 0.982741i | \(0.559225\pi\) | |||||||
\(264\) | −3.00000 | −0.184637 | ||||||||
\(265\) | −1.50000 | − | 2.59808i | −0.0921443 | − | 0.159599i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.00000 | + | 8.66025i | 0.305995 | + | 0.529999i | ||||
\(268\) | −1.00000 | + | 1.73205i | −0.0610847 | + | 0.105802i | ||||
\(269\) | −7.00000 | + | 12.1244i | −0.426798 | + | 0.739235i | −0.996586 | − | 0.0825561i | \(-0.973692\pi\) |
0.569789 | + | 0.821791i | \(0.307025\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 1.00000 | 0.0607457 | 0.0303728 | − | 0.999539i | \(-0.490331\pi\) | ||||
0.0303728 | + | 0.999539i | \(0.490331\pi\) | |||||||
\(272\) | 2.00000 | + | 3.46410i | 0.121268 | + | 0.210042i | ||||
\(273\) | −6.00000 | − | 10.3923i | −0.363137 | − | 0.628971i | ||||
\(274\) | −8.00000 | + | 13.8564i | −0.483298 | + | 0.837096i | ||||
\(275\) | −3.00000 | −0.180907 | ||||||||
\(276\) | 1.00000 | + | 1.73205i | 0.0601929 | + | 0.104257i | ||||
\(277\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | −2.00000 | − | 5.19615i | −0.119737 | − | 0.311086i | ||||
\(280\) | −3.00000 | −0.179284 | ||||||||
\(281\) | −26.0000 | −1.55103 | −0.775515 | − | 0.631329i | \(-0.782510\pi\) | ||||
−0.775515 | + | 0.631329i | \(0.782510\pi\) | |||||||
\(282\) | −2.00000 | − | 3.46410i | −0.119098 | − | 0.206284i | ||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −2.00000 | + | 3.46410i | −0.118678 | + | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −0.500000 | + | 0.866025i | −0.0293610 | + | 0.0508548i | ||||
\(291\) | 5.50000 | + | 9.52628i | 0.322416 | + | 0.558440i | ||||
\(292\) | −1.00000 | + | 1.73205i | −0.0585206 | + | 0.101361i | ||||
\(293\) | −10.5000 | − | 18.1865i | −0.613417 | − | 1.06247i | −0.990660 | − | 0.136355i | \(-0.956461\pi\) |
0.377244 | − | 0.926114i | \(-0.376872\pi\) | |||||||
\(294\) | 2.00000 | 0.116642 | ||||||||
\(295\) | 9.00000 | 0.524000 | ||||||||
\(296\) | −3.00000 | − | 5.19615i | −0.174371 | − | 0.302020i | ||||
\(297\) | −1.50000 | + | 2.59808i | −0.0870388 | + | 0.150756i | ||||
\(298\) | 9.50000 | + | 16.4545i | 0.550320 | + | 0.953183i | ||||
\(299\) | −4.00000 | + | 6.92820i | −0.231326 | + | 0.400668i | ||||
\(300\) | 0.500000 | − | 0.866025i | 0.0288675 | − | 0.0500000i | ||||
\(301\) | 6.00000 | − | 10.3923i | 0.345834 | − | 0.599002i | ||||
\(302\) | −9.00000 | −0.517892 | ||||||||
\(303\) | −9.50000 | − | 16.4545i | −0.545761 | − | 0.945285i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00000 | + | 1.73205i | −0.0572598 | + | 0.0991769i | ||||
\(306\) | 4.00000 | 0.228665 | ||||||||
\(307\) | 4.00000 | + | 6.92820i | 0.228292 | + | 0.395413i | 0.957302 | − | 0.289090i | \(-0.0933526\pi\) |
−0.729010 | + | 0.684503i | \(0.760019\pi\) | |||||||
\(308\) | 9.00000 | 0.512823 | ||||||||
\(309\) | −13.0000 | −0.739544 | ||||||||
\(310\) | −2.00000 | − | 5.19615i | −0.113592 | − | 0.295122i | ||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 4.00000 | 0.226455 | ||||||||
\(313\) | −10.5000 | − | 18.1865i | −0.593495 | − | 1.02796i | −0.993757 | − | 0.111563i | \(-0.964414\pi\) |
0.400262 | − | 0.916401i | \(-0.368919\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | −1.50000 | + | 2.59808i | −0.0845154 | + | 0.146385i | ||||
\(316\) | 2.00000 | + | 3.46410i | 0.112509 | + | 0.194871i | ||||
\(317\) | −6.50000 | − | 11.2583i | −0.365076 | − | 0.632331i | 0.623712 | − | 0.781654i | \(-0.285624\pi\) |
−0.988788 | + | 0.149323i | \(0.952290\pi\) | |||||||
\(318\) | −3.00000 | −0.168232 | ||||||||
\(319\) | 1.50000 | − | 2.59808i | 0.0839839 | − | 0.145464i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | −1.50000 | + | 2.59808i | −0.0837218 | + | 0.145010i | ||||
\(322\) | −3.00000 | − | 5.19615i | −0.167183 | − | 0.289570i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 4.00000 | 0.221880 | ||||||||
\(326\) | 10.0000 | 0.553849 | ||||||||
\(327\) | −2.00000 | − | 3.46410i | −0.110600 | − | 0.191565i | ||||
\(328\) | −1.00000 | + | 1.73205i | −0.0552158 | + | 0.0956365i | ||||
\(329\) | 6.00000 | + | 10.3923i | 0.330791 | + | 0.572946i | ||||
\(330\) | −1.50000 | + | 2.59808i | −0.0825723 | + | 0.143019i | ||||
\(331\) | 15.0000 | − | 25.9808i | 0.824475 | − | 1.42803i | −0.0778456 | − | 0.996965i | \(-0.524804\pi\) |
0.902320 | − | 0.431066i | \(-0.141863\pi\) | |||||||
\(332\) | −4.50000 | + | 7.79423i | −0.246970 | + | 0.427764i | ||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | 1.00000 | + | 1.73205i | 0.0547176 | + | 0.0947736i | ||||
\(335\) | 1.00000 | + | 1.73205i | 0.0546358 | + | 0.0946320i | ||||
\(336\) | −1.50000 | + | 2.59808i | −0.0818317 | + | 0.141737i | ||||
\(337\) | 25.0000 | 1.36184 | 0.680918 | − | 0.732359i | \(-0.261581\pi\) | ||||
0.680918 | + | 0.732359i | \(0.261581\pi\) | |||||||
\(338\) | 1.50000 | + | 2.59808i | 0.0815892 | + | 0.141317i | ||||
\(339\) | 12.0000 | 0.651751 | ||||||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 6.00000 | + | 15.5885i | 0.324918 | + | 0.844162i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | 2.00000 | + | 3.46410i | 0.107833 | + | 0.186772i | ||||
\(345\) | 2.00000 | 0.107676 | ||||||||
\(346\) | −0.500000 | + | 0.866025i | −0.0268802 | + | 0.0465578i | ||||
\(347\) | −9.50000 | − | 16.4545i | −0.509987 | − | 0.883323i | −0.999933 | − | 0.0115703i | \(-0.996317\pi\) |
0.489946 | − | 0.871753i | \(-0.337016\pi\) | |||||||
\(348\) | 0.500000 | + | 0.866025i | 0.0268028 | + | 0.0464238i | ||||
\(349\) | 12.0000 | 0.642345 | 0.321173 | − | 0.947021i | \(-0.395923\pi\) | ||||
0.321173 | + | 0.947021i | \(0.395923\pi\) | |||||||
\(350\) | −1.50000 | + | 2.59808i | −0.0801784 | + | 0.138873i | ||||
\(351\) | 2.00000 | − | 3.46410i | 0.106752 | − | 0.184900i | ||||
\(352\) | −1.50000 | + | 2.59808i | −0.0799503 | + | 0.138478i | ||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 4.50000 | − | 7.79423i | 0.239172 | − | 0.414259i | ||||
\(355\) | 2.00000 | + | 3.46410i | 0.106149 | + | 0.183855i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | −12.0000 | −0.635107 | ||||||||
\(358\) | 9.50000 | + | 16.4545i | 0.502091 | + | 0.869646i | ||||
\(359\) | −15.0000 | + | 25.9808i | −0.791670 | + | 1.37121i | 0.133263 | + | 0.991081i | \(0.457455\pi\) |
−0.924932 | + | 0.380131i | \(0.875879\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | 1.00000 | − | 1.73205i | 0.0525588 | − | 0.0910346i | ||||
\(363\) | −1.00000 | + | 1.73205i | −0.0524864 | + | 0.0909091i | ||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | 1.00000 | + | 1.73205i | 0.0523424 | + | 0.0906597i | ||||
\(366\) | 1.00000 | + | 1.73205i | 0.0522708 | + | 0.0905357i | ||||
\(367\) | −16.0000 | + | 27.7128i | −0.835193 | + | 1.44660i | 0.0586798 | + | 0.998277i | \(0.481311\pi\) |
−0.893873 | + | 0.448320i | \(0.852022\pi\) | |||||||
\(368\) | 2.00000 | 0.104257 | ||||||||
\(369\) | 1.00000 | + | 1.73205i | 0.0520579 | + | 0.0901670i | ||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 9.00000 | 0.467257 | ||||||||
\(372\) | −5.50000 | − | 0.866025i | −0.285162 | − | 0.0449013i | ||||
\(373\) | 24.0000 | 1.24267 | 0.621336 | − | 0.783544i | \(-0.286590\pi\) | ||||
0.621336 | + | 0.783544i | \(0.286590\pi\) | |||||||
\(374\) | −12.0000 | −0.620505 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | −4.00000 | −0.206284 | ||||||||
\(377\) | −2.00000 | + | 3.46410i | −0.103005 | + | 0.178410i | ||||
\(378\) | 1.50000 | + | 2.59808i | 0.0771517 | + | 0.133631i | ||||
\(379\) | 9.00000 | + | 15.5885i | 0.462299 | + | 0.800725i | 0.999075 | − | 0.0429994i | \(-0.0136914\pi\) |
−0.536776 | + | 0.843725i | \(0.680358\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.50000 | + | 11.2583i | −0.333005 | + | 0.576782i | ||||
\(382\) | −7.00000 | + | 12.1244i | −0.358151 | + | 0.620336i | ||||
\(383\) | −3.00000 | + | 5.19615i | −0.153293 | + | 0.265511i | −0.932436 | − | 0.361335i | \(-0.882321\pi\) |
0.779143 | + | 0.626846i | \(0.215654\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 4.50000 | − | 7.79423i | 0.229341 | − | 0.397231i | ||||
\(386\) | 10.5000 | + | 18.1865i | 0.534436 | + | 0.925670i | ||||
\(387\) | 4.00000 | 0.203331 | ||||||||
\(388\) | 11.0000 | 0.558440 | ||||||||
\(389\) | 13.0000 | + | 22.5167i | 0.659126 | + | 1.14164i | 0.980842 | + | 0.194804i | \(0.0624070\pi\) |
−0.321716 | + | 0.946836i | \(0.604260\pi\) | |||||||
\(390\) | 2.00000 | − | 3.46410i | 0.101274 | − | 0.175412i | ||||
\(391\) | 4.00000 | + | 6.92820i | 0.202289 | + | 0.350374i | ||||
\(392\) | 1.00000 | − | 1.73205i | 0.0505076 | − | 0.0874818i | ||||
\(393\) | 6.00000 | − | 10.3923i | 0.302660 | − | 0.524222i | ||||
\(394\) | −9.00000 | + | 15.5885i | −0.453413 | + | 0.785335i | ||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 1.50000 | + | 2.59808i | 0.0753778 | + | 0.130558i | ||||
\(397\) | 5.00000 | + | 8.66025i | 0.250943 | + | 0.434646i | 0.963786 | − | 0.266678i | \(-0.0859261\pi\) |
−0.712843 | + | 0.701324i | \(0.752593\pi\) | |||||||
\(398\) | −5.50000 | + | 9.52628i | −0.275690 | + | 0.477509i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −8.00000 | −0.399501 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(402\) | 2.00000 | 0.0997509 | ||||||||
\(403\) | −8.00000 | − | 20.7846i | −0.398508 | − | 1.03536i | ||||
\(404\) | −19.0000 | −0.945285 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −1.50000 | − | 2.59808i | −0.0744438 | − | 0.128940i | ||||
\(407\) | 18.0000 | 0.892227 | ||||||||
\(408\) | 2.00000 | − | 3.46410i | 0.0990148 | − | 0.171499i | ||||
\(409\) | 6.50000 | + | 11.2583i | 0.321404 | + | 0.556689i | 0.980778 | − | 0.195127i | \(-0.0625118\pi\) |
−0.659374 | + | 0.751815i | \(0.729178\pi\) | |||||||
\(410\) | 1.00000 | + | 1.73205i | 0.0493865 | + | 0.0855399i | ||||
\(411\) | 16.0000 | 0.789222 | ||||||||
\(412\) | −6.50000 | + | 11.2583i | −0.320232 | + | 0.554658i | ||||
\(413\) | −13.5000 | + | 23.3827i | −0.664292 | + | 1.15059i | ||||
\(414\) | 1.00000 | − | 1.73205i | 0.0491473 | − | 0.0851257i | ||||
\(415\) | 4.50000 | + | 7.79423i | 0.220896 | + | 0.382604i | ||||
\(416\) | 2.00000 | − | 3.46410i | 0.0980581 | − | 0.169842i | ||||
\(417\) | 2.00000 | + | 3.46410i | 0.0979404 | + | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.00000 | 0.439679 | 0.219839 | − | 0.975536i | \(-0.429447\pi\) | ||||
0.219839 | + | 0.975536i | \(0.429447\pi\) | |||||||
\(420\) | 1.50000 | + | 2.59808i | 0.0731925 | + | 0.126773i | ||||
\(421\) | 17.0000 | − | 29.4449i | 0.828529 | − | 1.43505i | −0.0706626 | − | 0.997500i | \(-0.522511\pi\) |
0.899192 | − | 0.437555i | \(-0.144155\pi\) | |||||||
\(422\) | 4.00000 | + | 6.92820i | 0.194717 | + | 0.337260i | ||||
\(423\) | −2.00000 | + | 3.46410i | −0.0972433 | + | 0.168430i | ||||
\(424\) | −1.50000 | + | 2.59808i | −0.0728464 | + | 0.126174i | ||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | 4.00000 | 0.193801 | ||||||||
\(427\) | −3.00000 | − | 5.19615i | −0.145180 | − | 0.251459i | ||||
\(428\) | 1.50000 | + | 2.59808i | 0.0725052 | + | 0.125583i | ||||
\(429\) | −6.00000 | + | 10.3923i | −0.289683 | + | 0.501745i | ||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | 16.0000 | + | 27.7128i | 0.770693 | + | 1.33488i | 0.937184 | + | 0.348836i | \(0.113423\pi\) |
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 16.5000 | + | 2.59808i | 0.792025 | + | 0.124712i | ||||
\(435\) | 1.00000 | 0.0479463 | ||||||||
\(436\) | −4.00000 | −0.191565 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 1.50000 | − | 2.59808i | 0.0715911 | − | 0.123999i | −0.828008 | − | 0.560717i | \(-0.810526\pi\) |
0.899599 | + | 0.436717i | \(0.143859\pi\) | |||||||
\(440\) | 1.50000 | + | 2.59808i | 0.0715097 | + | 0.123858i | ||||
\(441\) | −1.00000 | − | 1.73205i | −0.0476190 | − | 0.0824786i | ||||
\(442\) | 16.0000 | 0.761042 | ||||||||
\(443\) | −18.0000 | + | 31.1769i | −0.855206 | + | 1.48126i | 0.0212481 | + | 0.999774i | \(0.493236\pi\) |
−0.876454 | + | 0.481486i | \(0.840097\pi\) | |||||||
\(444\) | −3.00000 | + | 5.19615i | −0.142374 | + | 0.246598i | ||||
\(445\) | 5.00000 | − | 8.66025i | 0.237023 | − | 0.410535i | ||||
\(446\) | 4.50000 | + | 7.79423i | 0.213081 | + | 0.369067i | ||||
\(447\) | 9.50000 | − | 16.4545i | 0.449335 | − | 0.778270i | ||||
\(448\) | 1.50000 | + | 2.59808i | 0.0708683 | + | 0.122748i | ||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −3.00000 | − | 5.19615i | −0.141264 | − | 0.244677i | ||||
\(452\) | 6.00000 | − | 10.3923i | 0.282216 | − | 0.488813i | ||||
\(453\) | 4.50000 | + | 7.79423i | 0.211428 | + | 0.366205i | ||||
\(454\) | −1.50000 | + | 2.59808i | −0.0703985 | + | 0.121934i | ||||
\(455\) | −6.00000 | + | 10.3923i | −0.281284 | + | 0.487199i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0000 | −1.21623 | −0.608114 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | 11.0000 | + | 19.0526i | 0.513996 | + | 0.890268i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | 1.00000 | − | 1.73205i | 0.0466252 | − | 0.0807573i | ||||
\(461\) | −9.00000 | −0.419172 | −0.209586 | − | 0.977790i | \(-0.567212\pi\) | ||||
−0.209586 | + | 0.977790i | \(0.567212\pi\) | |||||||
\(462\) | −4.50000 | − | 7.79423i | −0.209359 | − | 0.362620i | ||||
\(463\) | −5.00000 | −0.232370 | −0.116185 | − | 0.993228i | \(-0.537067\pi\) | ||||
−0.116185 | + | 0.993228i | \(0.537067\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −3.50000 | + | 4.33013i | −0.162309 | + | 0.200805i | ||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | −27.0000 | −1.24941 | −0.624705 | − | 0.780860i | \(-0.714781\pi\) | ||||
−0.624705 | + | 0.780860i | \(0.714781\pi\) | |||||||
\(468\) | −2.00000 | − | 3.46410i | −0.0924500 | − | 0.160128i | ||||
\(469\) | −6.00000 | −0.277054 | ||||||||
\(470\) | −2.00000 | + | 3.46410i | −0.0922531 | + | 0.159787i | ||||
\(471\) | 11.0000 | + | 19.0526i | 0.506853 | + | 0.877896i | ||||
\(472\) | −4.50000 | − | 7.79423i | −0.207129 | − | 0.358758i | ||||
\(473\) | −12.0000 | −0.551761 | ||||||||
\(474\) | 2.00000 | − | 3.46410i | 0.0918630 | − | 0.159111i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.00000 | + | 10.3923i | −0.275010 | + | 0.476331i | ||||
\(477\) | 1.50000 | + | 2.59808i | 0.0686803 | + | 0.118958i | ||||
\(478\) | −12.0000 | + | 20.7846i | −0.548867 | + | 0.950666i | ||||
\(479\) | −6.00000 | − | 10.3923i | −0.274147 | − | 0.474837i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
−0.969920 | + | 0.243426i | \(0.921729\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 7.50000 | + | 12.9904i | 0.341616 | + | 0.591696i | ||||
\(483\) | −3.00000 | + | 5.19615i | −0.136505 | + | 0.236433i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 5.50000 | − | 9.52628i | 0.249742 | − | 0.432566i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −14.5000 | + | 25.1147i | −0.657058 | + | 1.13806i | 0.324316 | + | 0.945949i | \(0.394866\pi\) |
−0.981374 | + | 0.192109i | \(0.938467\pi\) | |||||||
\(488\) | 2.00000 | 0.0905357 | ||||||||
\(489\) | −5.00000 | − | 8.66025i | −0.226108 | − | 0.391630i | ||||
\(490\) | −1.00000 | − | 1.73205i | −0.0451754 | − | 0.0782461i | ||||
\(491\) | 9.50000 | − | 16.4545i | 0.428729 | − | 0.742580i | −0.568032 | − | 0.823007i | \(-0.692295\pi\) |
0.996761 | + | 0.0804264i | \(0.0256282\pi\) | |||||||
\(492\) | 2.00000 | 0.0901670 | ||||||||
\(493\) | 2.00000 | + | 3.46410i | 0.0900755 | + | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.00000 | 0.134840 | ||||||||
\(496\) | −3.50000 | + | 4.33013i | −0.157155 | + | 0.194428i | ||||
\(497\) | −12.0000 | −0.538274 | ||||||||
\(498\) | 9.00000 | 0.403300 | ||||||||
\(499\) | −11.0000 | − | 19.0526i | −0.492428 | − | 0.852910i | 0.507534 | − | 0.861632i | \(-0.330557\pi\) |
−0.999962 | + | 0.00872186i | \(0.997224\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 1.00000 | − | 1.73205i | 0.0446767 | − | 0.0773823i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.00000 | − | 12.1244i | −0.312115 | − | 0.540598i | 0.666705 | − | 0.745321i | \(-0.267704\pi\) |
−0.978820 | + | 0.204723i | \(0.934371\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | −9.50000 | + | 16.4545i | −0.422744 | + | 0.732215i | ||||
\(506\) | −3.00000 | + | 5.19615i | −0.133366 | + | 0.230997i | ||||
\(507\) | 1.50000 | − | 2.59808i | 0.0666173 | − | 0.115385i | ||||
\(508\) | 6.50000 | + | 11.2583i | 0.288391 | + | 0.499508i | ||||
\(509\) | 7.50000 | − | 12.9904i | 0.332432 | − | 0.575789i | −0.650556 | − | 0.759458i | \(-0.725464\pi\) |
0.982988 | + | 0.183669i | \(0.0587976\pi\) | |||||||
\(510\) | −2.00000 | − | 3.46410i | −0.0885615 | − | 0.153393i | ||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.00000 | − | 8.66025i | 0.220541 | − | 0.381987i | ||||
\(515\) | 6.50000 | + | 11.2583i | 0.286424 | + | 0.496101i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 6.00000 | − | 10.3923i | 0.263880 | − | 0.457053i | ||||
\(518\) | 9.00000 | − | 15.5885i | 0.395437 | − | 0.684917i | ||||
\(519\) | 1.00000 | 0.0438951 | ||||||||
\(520\) | −2.00000 | − | 3.46410i | −0.0877058 | − | 0.151911i | ||||
\(521\) | 12.0000 | + | 20.7846i | 0.525730 | + | 0.910590i | 0.999551 | + | 0.0299693i | \(0.00954094\pi\) |
−0.473821 | + | 0.880621i | \(0.657126\pi\) | |||||||
\(522\) | 0.500000 | − | 0.866025i | 0.0218844 | − | 0.0379049i | ||||
\(523\) | 8.00000 | 0.349816 | 0.174908 | − | 0.984585i | \(-0.444037\pi\) | ||||
0.174908 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(524\) | −6.00000 | − | 10.3923i | −0.262111 | − | 0.453990i | ||||
\(525\) | 3.00000 | 0.130931 | ||||||||
\(526\) | 6.00000 | 0.261612 | ||||||||
\(527\) | −22.0000 | − | 3.46410i | −0.958335 | − | 0.150899i | ||||
\(528\) | 3.00000 | 0.130558 | ||||||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 1.50000 | + | 2.59808i | 0.0651558 | + | 0.112853i | ||||
\(531\) | −9.00000 | −0.390567 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | + | 6.92820i | 0.173259 | + | 0.300094i | ||||
\(534\) | −5.00000 | − | 8.66025i | −0.216371 | − | 0.374766i | ||||
\(535\) | 3.00000 | 0.129701 | ||||||||
\(536\) | 1.00000 | − | 1.73205i | 0.0431934 | − | 0.0748132i | ||||
\(537\) | 9.50000 | − | 16.4545i | 0.409955 | − | 0.710063i | ||||
\(538\) | 7.00000 | − | 12.1244i | 0.301791 | − | 0.522718i | ||||
\(539\) | 3.00000 | + | 5.19615i | 0.129219 | + | 0.223814i | ||||
\(540\) | −0.500000 | + | 0.866025i | −0.0215166 | + | 0.0372678i | ||||
\(541\) | −5.00000 | − | 8.66025i | −0.214967 | − | 0.372333i | 0.738296 | − | 0.674477i | \(-0.235631\pi\) |
−0.953262 | + | 0.302144i | \(0.902298\pi\) | |||||||
\(542\) | −1.00000 | −0.0429537 | ||||||||
\(543\) | −2.00000 | −0.0858282 | ||||||||
\(544\) | −2.00000 | − | 3.46410i | −0.0857493 | − | 0.148522i | ||||
\(545\) | −2.00000 | + | 3.46410i | −0.0856706 | + | 0.148386i | ||||
\(546\) | 6.00000 | + | 10.3923i | 0.256776 | + | 0.444750i | ||||
\(547\) | −5.00000 | + | 8.66025i | −0.213785 | + | 0.370286i | −0.952896 | − | 0.303298i | \(-0.901912\pi\) |
0.739111 | + | 0.673583i | \(0.235246\pi\) | |||||||
\(548\) | 8.00000 | − | 13.8564i | 0.341743 | − | 0.591916i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 3.00000 | 0.127920 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.00000 | − | 1.73205i | −0.0425628 | − | 0.0737210i | ||||
\(553\) | −6.00000 | + | 10.3923i | −0.255146 | + | 0.441926i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.00000 | + | 5.19615i | 0.127343 | + | 0.220564i | ||||
\(556\) | 4.00000 | 0.169638 | ||||||||
\(557\) | 11.0000 | 0.466085 | 0.233042 | − | 0.972467i | \(-0.425132\pi\) | ||||
0.233042 | + | 0.972467i | \(0.425132\pi\) | |||||||
\(558\) | 2.00000 | + | 5.19615i | 0.0846668 | + | 0.219971i | ||||
\(559\) | 16.0000 | 0.676728 | ||||||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 6.00000 | + | 10.3923i | 0.253320 | + | 0.438763i | ||||
\(562\) | 26.0000 | 1.09674 | ||||||||
\(563\) | −11.5000 | + | 19.9186i | −0.484667 | + | 0.839468i | −0.999845 | − | 0.0176152i | \(-0.994393\pi\) |
0.515178 | + | 0.857083i | \(0.327726\pi\) | |||||||
\(564\) | 2.00000 | + | 3.46410i | 0.0842152 | + | 0.145865i | ||||
\(565\) | −6.00000 | − | 10.3923i | −0.252422 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.50000 | − | 2.59808i | 0.0629941 | − | 0.109109i | ||||
\(568\) | 2.00000 | − | 3.46410i | 0.0839181 | − | 0.145350i | ||||
\(569\) | −2.00000 | + | 3.46410i | −0.0838444 | + | 0.145223i | −0.904898 | − | 0.425628i | \(-0.860053\pi\) |
0.821054 | + | 0.570851i | \(0.193387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0000 | + | 19.0526i | −0.460336 | + | 0.797325i | −0.998978 | − | 0.0452101i | \(-0.985604\pi\) |
0.538642 | + | 0.842535i | \(0.318938\pi\) | |||||||
\(572\) | 6.00000 | + | 10.3923i | 0.250873 | + | 0.434524i | ||||
\(573\) | 14.0000 | 0.584858 | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | −1.00000 | − | 1.73205i | −0.0417029 | − | 0.0722315i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 13.0000 | + | 22.5167i | 0.541197 | + | 0.937381i | 0.998836 | + | 0.0482425i | \(0.0153620\pi\) |
−0.457639 | + | 0.889138i | \(0.651305\pi\) | |||||||
\(578\) | −0.500000 | + | 0.866025i | −0.0207973 | + | 0.0360219i | ||||
\(579\) | 10.5000 | − | 18.1865i | 0.436365 | − | 0.755807i | ||||
\(580\) | 0.500000 | − | 0.866025i | 0.0207614 | − | 0.0359597i | ||||
\(581\) | −27.0000 | −1.12015 | ||||||||
\(582\) | −5.50000 | − | 9.52628i | −0.227982 | − | 0.394877i | ||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | 1.00000 | − | 1.73205i | 0.0413803 | − | 0.0716728i | ||||
\(585\) | −4.00000 | −0.165380 | ||||||||
\(586\) | 10.5000 | + | 18.1865i | 0.433751 | + | 0.751279i | ||||
\(587\) | 11.0000 | 0.454019 | 0.227009 | − | 0.973893i | \(-0.427105\pi\) | ||||
0.227009 | + | 0.973893i | \(0.427105\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −9.00000 | −0.370524 | ||||||||
\(591\) | 18.0000 | 0.740421 | ||||||||
\(592\) | 3.00000 | + | 5.19615i | 0.123299 | + | 0.213561i | ||||
\(593\) | −20.0000 | −0.821302 | −0.410651 | − | 0.911793i | \(-0.634698\pi\) | ||||
−0.410651 | + | 0.911793i | \(0.634698\pi\) | |||||||
\(594\) | 1.50000 | − | 2.59808i | 0.0615457 | − | 0.106600i | ||||
\(595\) | 6.00000 | + | 10.3923i | 0.245976 | + | 0.426043i | ||||
\(596\) | −9.50000 | − | 16.4545i | −0.389135 | − | 0.674002i | ||||
\(597\) | 11.0000 | 0.450200 | ||||||||
\(598\) | 4.00000 | − | 6.92820i | 0.163572 | − | 0.283315i | ||||
\(599\) | 12.0000 | − | 20.7846i | 0.490307 | − | 0.849236i | −0.509631 | − | 0.860393i | \(-0.670218\pi\) |
0.999938 | + | 0.0111569i | \(0.00355143\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | −21.0000 | − | 36.3731i | −0.856608 | − | 1.48369i | −0.875145 | − | 0.483860i | \(-0.839234\pi\) |
0.0185374 | − | 0.999828i | \(-0.494099\pi\) | |||||||
\(602\) | −6.00000 | + | 10.3923i | −0.244542 | + | 0.423559i | ||||
\(603\) | −1.00000 | − | 1.73205i | −0.0407231 | − | 0.0705346i | ||||
\(604\) | 9.00000 | 0.366205 | ||||||||
\(605\) | 2.00000 | 0.0813116 | ||||||||
\(606\) | 9.50000 | + | 16.4545i | 0.385911 | + | 0.668418i | ||||
\(607\) | −16.0000 | + | 27.7128i | −0.649420 | + | 1.12483i | 0.333842 | + | 0.942629i | \(0.391655\pi\) |
−0.983262 | + | 0.182199i | \(0.941678\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.50000 | + | 2.59808i | −0.0607831 | + | 0.105279i | ||||
\(610\) | 1.00000 | − | 1.73205i | 0.0404888 | − | 0.0701287i | ||||
\(611\) | −8.00000 | + | 13.8564i | −0.323645 | + | 0.560570i | ||||
\(612\) | −4.00000 | −0.161690 | ||||||||
\(613\) | 8.00000 | + | 13.8564i | 0.323117 | + | 0.559655i | 0.981129 | − | 0.193352i | \(-0.0619359\pi\) |
−0.658012 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(614\) | −4.00000 | − | 6.92820i | −0.161427 | − | 0.279600i | ||||
\(615\) | 1.00000 | − | 1.73205i | 0.0403239 | − | 0.0698430i | ||||
\(616\) | −9.00000 | −0.362620 | ||||||||
\(617\) | −21.0000 | − | 36.3731i | −0.845428 | − | 1.46432i | −0.885249 | − | 0.465118i | \(-0.846012\pi\) |
0.0398207 | − | 0.999207i | \(-0.487321\pi\) | |||||||
\(618\) | 13.0000 | 0.522937 | ||||||||
\(619\) | 22.0000 | 0.884255 | 0.442127 | − | 0.896952i | \(-0.354224\pi\) | ||||
0.442127 | + | 0.896952i | \(0.354224\pi\) | |||||||
\(620\) | 2.00000 | + | 5.19615i | 0.0803219 | + | 0.208683i | ||||
\(621\) | −2.00000 | −0.0802572 | ||||||||
\(622\) | −24.0000 | −0.962312 | ||||||||
\(623\) | 15.0000 | + | 25.9808i | 0.600962 | + | 1.04090i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 10.5000 | + | 18.1865i | 0.419664 | + | 0.726880i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.0000 | 0.877896 | ||||||||
\(629\) | −12.0000 | + | 20.7846i | −0.478471 | + | 0.828737i | ||||
\(630\) | 1.50000 | − | 2.59808i | 0.0597614 | − | 0.103510i | ||||
\(631\) | −20.5000 | + | 35.5070i | −0.816092 | + | 1.41351i | 0.0924489 | + | 0.995717i | \(0.470531\pi\) |
−0.908541 | + | 0.417796i | \(0.862803\pi\) | |||||||
\(632\) | −2.00000 | − | 3.46410i | −0.0795557 | − | 0.137795i | ||||
\(633\) | 4.00000 | − | 6.92820i | 0.158986 | − | 0.275371i | ||||
\(634\) | 6.50000 | + | 11.2583i | 0.258148 | + | 0.447125i | ||||
\(635\) | 13.0000 | 0.515889 | ||||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | −4.00000 | − | 6.92820i | −0.158486 | − | 0.274505i | ||||
\(638\) | −1.50000 | + | 2.59808i | −0.0593856 | + | 0.102859i | ||||
\(639\) | −2.00000 | − | 3.46410i | −0.0791188 | − | 0.137038i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 5.00000 | − | 8.66025i | 0.197488 | − | 0.342059i | −0.750225 | − | 0.661182i | \(-0.770055\pi\) |
0.947713 | + | 0.319123i | \(0.103388\pi\) | |||||||
\(642\) | 1.50000 | − | 2.59808i | 0.0592003 | − | 0.102538i | ||||
\(643\) | −38.0000 | −1.49857 | −0.749287 | − | 0.662246i | \(-0.769604\pi\) | ||||
−0.749287 | + | 0.662246i | \(0.769604\pi\) | |||||||
\(644\) | 3.00000 | + | 5.19615i | 0.118217 | + | 0.204757i | ||||
\(645\) | −2.00000 | − | 3.46410i | −0.0787499 | − | 0.136399i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.0000 | −0.943537 | −0.471769 | − | 0.881722i | \(-0.656384\pi\) | ||||
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 27.0000 | 1.05984 | ||||||||
\(650\) | −4.00000 | −0.156893 | ||||||||
\(651\) | −6.00000 | − | 15.5885i | −0.235159 | − | 0.610960i | ||||
\(652\) | −10.0000 | −0.391630 | ||||||||
\(653\) | −29.0000 | −1.13486 | −0.567429 | − | 0.823422i | \(-0.692062\pi\) | ||||
−0.567429 | + | 0.823422i | \(0.692062\pi\) | |||||||
\(654\) | 2.00000 | + | 3.46410i | 0.0782062 | + | 0.135457i | ||||
\(655\) | −12.0000 | −0.468879 | ||||||||
\(656\) | 1.00000 | − | 1.73205i | 0.0390434 | − | 0.0676252i | ||||
\(657\) | −1.00000 | − | 1.73205i | −0.0390137 | − | 0.0675737i | ||||
\(658\) | −6.00000 | − | 10.3923i | −0.233904 | − | 0.405134i | ||||
\(659\) | −37.0000 | −1.44132 | −0.720658 | − | 0.693291i | \(-0.756160\pi\) | ||||
−0.720658 | + | 0.693291i | \(0.756160\pi\) | |||||||
\(660\) | 1.50000 | − | 2.59808i | 0.0583874 | − | 0.101130i | ||||
\(661\) | 25.0000 | − | 43.3013i | 0.972387 | − | 1.68422i | 0.284087 | − | 0.958799i | \(-0.408310\pi\) |
0.688301 | − | 0.725426i | \(-0.258357\pi\) | |||||||
\(662\) | −15.0000 | + | 25.9808i | −0.582992 | + | 1.00977i | ||||
\(663\) | −8.00000 | − | 13.8564i | −0.310694 | − | 0.538138i | ||||
\(664\) | 4.50000 | − | 7.79423i | 0.174634 | − | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.00000 | 0.232495 | ||||||||
\(667\) | 2.00000 | 0.0774403 | ||||||||
\(668\) | −1.00000 | − | 1.73205i | −0.0386912 | − | 0.0670151i | ||||
\(669\) | 4.50000 | − | 7.79423i | 0.173980 | − | 0.301342i | ||||
\(670\) | −1.00000 | − | 1.73205i | −0.0386334 | − | 0.0669150i | ||||
\(671\) | −3.00000 | + | 5.19615i | −0.115814 | + | 0.200595i | ||||
\(672\) | 1.50000 | − | 2.59808i | 0.0578638 | − | 0.100223i | ||||
\(673\) | 9.50000 | − | 16.4545i | 0.366198 | − | 0.634274i | −0.622770 | − | 0.782405i | \(-0.713993\pi\) |
0.988968 | + | 0.148132i | \(0.0473259\pi\) | |||||||
\(674\) | −25.0000 | −0.962964 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | 16.5000 | − | 28.5788i | 0.634147 | − | 1.09837i | −0.352549 | − | 0.935793i | \(-0.614685\pi\) |
0.986695 | − | 0.162581i | \(-0.0519817\pi\) | |||||||
\(678\) | −12.0000 | −0.460857 | ||||||||
\(679\) | 16.5000 | + | 28.5788i | 0.633212 | + | 1.09676i | ||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 3.00000 | 0.114960 | ||||||||
\(682\) | −6.00000 | − | 15.5885i | −0.229752 | − | 0.596913i | ||||
\(683\) | 23.0000 | 0.880071 | 0.440035 | − | 0.897980i | \(-0.354966\pi\) | ||||
0.440035 | + | 0.897980i | \(0.354966\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00000 | − | 13.8564i | −0.305664 | − | 0.529426i | ||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | 11.0000 | − | 19.0526i | 0.419676 | − | 0.726900i | ||||
\(688\) | −2.00000 | − | 3.46410i | −0.0762493 | − | 0.132068i | ||||
\(689\) | 6.00000 | + | 10.3923i | 0.228582 | + | 0.395915i | ||||
\(690\) | −2.00000 | −0.0761387 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 0.500000 | − | 0.866025i | 0.0190071 | − | 0.0329213i | ||||
\(693\) | −4.50000 | + | 7.79423i | −0.170941 | + | 0.296078i | ||||
\(694\) | 9.50000 | + | 16.4545i | 0.360615 | + | 0.624604i | ||||
\(695\) | 2.00000 | − | 3.46410i | 0.0758643 | − | 0.131401i | ||||
\(696\) | −0.500000 | − | 0.866025i | −0.0189525 | − | 0.0328266i | ||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | −12.0000 | −0.454207 | ||||||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 1.50000 | − | 2.59808i | 0.0566947 | − | 0.0981981i | ||||
\(701\) | 7.50000 | + | 12.9904i | 0.283271 | + | 0.490640i | 0.972188 | − | 0.234200i | \(-0.0752470\pi\) |
−0.688917 | + | 0.724840i | \(0.741914\pi\) | |||||||
\(702\) | −2.00000 | + | 3.46410i | −0.0754851 | + | 0.130744i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 4.00000 | 0.150649 | ||||||||
\(706\) | 3.00000 | + | 5.19615i | 0.112906 | + | 0.195560i | ||||
\(707\) | −28.5000 | − | 49.3634i | −1.07185 | − | 1.85650i | ||||
\(708\) | −4.50000 | + | 7.79423i | −0.169120 | + | 0.292925i | ||||
\(709\) | 50.0000 | 1.87779 | 0.938895 | − | 0.344204i | \(-0.111851\pi\) | ||||
0.938895 | + | 0.344204i | \(0.111851\pi\) | |||||||
\(710\) | −2.00000 | − | 3.46410i | −0.0750587 | − | 0.130005i | ||||
\(711\) | −4.00000 | −0.150012 | ||||||||
\(712\) | −10.0000 | −0.374766 | ||||||||
\(713\) | −7.00000 | + | 8.66025i | −0.262152 | + | 0.324329i | ||||
\(714\) | 12.0000 | 0.449089 | ||||||||
\(715\) | 12.0000 | 0.448775 | ||||||||
\(716\) | −9.50000 | − | 16.4545i | −0.355032 | − | 0.614933i | ||||
\(717\) | 24.0000 | 0.896296 | ||||||||
\(718\) | 15.0000 | − | 25.9808i | 0.559795 | − | 0.969593i | ||||
\(719\) | 2.00000 | + | 3.46410i | 0.0745874 | + | 0.129189i | 0.900907 | − | 0.434013i | \(-0.142903\pi\) |
−0.826319 | + | 0.563202i | \(0.809569\pi\) | |||||||
\(720\) | 0.500000 | + | 0.866025i | 0.0186339 | + | 0.0322749i | ||||
\(721\) | −39.0000 | −1.45244 | ||||||||
\(722\) | −9.50000 | + | 16.4545i | −0.353553 | + | 0.612372i | ||||
\(723\) | 7.50000 | − | 12.9904i | 0.278928 | − | 0.483117i | ||||
\(724\) | −1.00000 | + | 1.73205i | −0.0371647 | + | 0.0643712i | ||||
\(725\) | −0.500000 | − | 0.866025i | −0.0185695 | − | 0.0321634i | ||||
\(726\) | 1.00000 | − | 1.73205i | 0.0371135 | − | 0.0642824i | ||||
\(727\) | −1.50000 | − | 2.59808i | −0.0556319 | − | 0.0963573i | 0.836868 | − | 0.547404i | \(-0.184384\pi\) |
−0.892500 | + | 0.451047i | \(0.851051\pi\) | |||||||
\(728\) | 12.0000 | 0.444750 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | − | 1.73205i | −0.0370117 | − | 0.0641061i | ||||
\(731\) | 8.00000 | − | 13.8564i | 0.295891 | − | 0.512498i | ||||
\(732\) | −1.00000 | − | 1.73205i | −0.0369611 | − | 0.0640184i | ||||
\(733\) | −9.00000 | + | 15.5885i | −0.332423 | + | 0.575773i | −0.982986 | − | 0.183679i | \(-0.941199\pi\) |
0.650564 | + | 0.759452i | \(0.274533\pi\) | |||||||
\(734\) | 16.0000 | − | 27.7128i | 0.590571 | − | 1.02290i | ||||
\(735\) | −1.00000 | + | 1.73205i | −0.0368856 | + | 0.0638877i | ||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 3.00000 | + | 5.19615i | 0.110506 | + | 0.191403i | ||||
\(738\) | −1.00000 | − | 1.73205i | −0.0368105 | − | 0.0637577i | ||||
\(739\) | −8.00000 | + | 13.8564i | −0.294285 | + | 0.509716i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 6.00000 | 0.220564 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.00000 | −0.330400 | ||||||||
\(743\) | 50.0000 | 1.83432 | 0.917161 | − | 0.398517i | \(-0.130475\pi\) | ||||
0.917161 | + | 0.398517i | \(0.130475\pi\) | |||||||
\(744\) | 5.50000 | + | 0.866025i | 0.201640 | + | 0.0317500i | ||||
\(745\) | −19.0000 | −0.696106 | ||||||||
\(746\) | −24.0000 | −0.878702 | ||||||||
\(747\) | −4.50000 | − | 7.79423i | −0.164646 | − | 0.285176i | ||||
\(748\) | 12.0000 | 0.438763 | ||||||||
\(749\) | −4.50000 | + | 7.79423i | −0.164426 | + | 0.284795i | ||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | 5.50000 | + | 9.52628i | 0.200698 | + | 0.347619i | 0.948753 | − | 0.316017i | \(-0.102346\pi\) |
−0.748056 | + | 0.663636i | \(0.769012\pi\) | |||||||
\(752\) | 4.00000 | 0.145865 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.00000 | − | 3.46410i | 0.0728357 | − | 0.126155i | ||||
\(755\) | 4.50000 | − | 7.79423i | 0.163772 | − | 0.283661i | ||||
\(756\) | −1.50000 | − | 2.59808i | −0.0545545 | − | 0.0944911i | ||||
\(757\) | 26.0000 | − | 45.0333i | 0.944986 | − | 1.63676i | 0.189207 | − | 0.981937i | \(-0.439408\pi\) |
0.755779 | − | 0.654827i | \(-0.227258\pi\) | |||||||
\(758\) | −9.00000 | − | 15.5885i | −0.326895 | − | 0.566198i | ||||
\(759\) | 6.00000 | 0.217786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(762\) | 6.50000 | − | 11.2583i | 0.235470 | − | 0.407846i | ||||
\(763\) | −6.00000 | − | 10.3923i | −0.217215 | − | 0.376227i | ||||
\(764\) | 7.00000 | − | 12.1244i | 0.253251 | − | 0.438644i | ||||
\(765\) | −2.00000 | + | 3.46410i | −0.0723102 | + | 0.125245i | ||||
\(766\) | 3.00000 | − | 5.19615i | 0.108394 | − | 0.187745i | ||||
\(767\) | −36.0000 | −1.29988 | ||||||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −22.5000 | − | 38.9711i | −0.811371 | − | 1.40534i | −0.911905 | − | 0.410402i | \(-0.865388\pi\) |
0.100534 | − | 0.994934i | \(-0.467945\pi\) | |||||||
\(770\) | −4.50000 | + | 7.79423i | −0.162169 | + | 0.280885i | ||||
\(771\) | −10.0000 | −0.360141 | ||||||||
\(772\) | −10.5000 | − | 18.1865i | −0.377903 | − | 0.654548i | ||||
\(773\) | 14.0000 | 0.503545 | 0.251773 | − | 0.967786i | \(-0.418987\pi\) | ||||
0.251773 | + | 0.967786i | \(0.418987\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | 5.50000 | + | 0.866025i | 0.197566 | + | 0.0311086i | ||||
\(776\) | −11.0000 | −0.394877 | ||||||||
\(777\) | −18.0000 | −0.645746 | ||||||||
\(778\) | −13.0000 | − | 22.5167i | −0.466073 | − | 0.807261i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −2.00000 | + | 3.46410i | −0.0716115 | + | 0.124035i | ||||
\(781\) | 6.00000 | + | 10.3923i | 0.214697 | + | 0.371866i | ||||
\(782\) | −4.00000 | − | 6.92820i | −0.143040 | − | 0.247752i | ||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −1.00000 | + | 1.73205i | −0.0357143 | + | 0.0618590i | ||||
\(785\) | 11.0000 | − | 19.0526i | 0.392607 | − | 0.680015i | ||||
\(786\) | −6.00000 | + | 10.3923i | −0.214013 | + | 0.370681i | ||||
\(787\) | −5.00000 | − | 8.66025i | −0.178231 | − | 0.308705i | 0.763044 | − | 0.646347i | \(-0.223704\pi\) |
−0.941275 | + | 0.337642i | \(0.890371\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | −3.00000 | − | 5.19615i | −0.106803 | − | 0.184988i | ||||
\(790\) | −4.00000 | −0.142314 | ||||||||
\(791\) | 36.0000 | 1.28001 | ||||||||
\(792\) | −1.50000 | − | 2.59808i | −0.0533002 | − | 0.0923186i | ||||
\(793\) | 4.00000 | − | 6.92820i | 0.142044 | − | 0.246028i | ||||
\(794\) | −5.00000 | − | 8.66025i | −0.177443 | − | 0.307341i | ||||
\(795\) | 1.50000 | − | 2.59808i | 0.0531995 | − | 0.0921443i | ||||
\(796\) | 5.50000 | − | 9.52628i | 0.194942 | − | 0.337650i | ||||
\(797\) | −11.5000 | + | 19.9186i | −0.407351 | + | 0.705552i | −0.994592 | − | 0.103860i | \(-0.966881\pi\) |
0.587241 | + | 0.809412i | \(0.300214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000 | + | 13.8564i | 0.283020 | + | 0.490204i | ||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | −5.00000 | + | 8.66025i | −0.176666 | + | 0.305995i | ||||
\(802\) | 8.00000 | 0.282490 | ||||||||
\(803\) | 3.00000 | + | 5.19615i | 0.105868 | + | 0.183368i | ||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | 6.00000 | 0.211472 | ||||||||
\(806\) | 8.00000 | + | 20.7846i | 0.281788 | + | 0.732107i | ||||
\(807\) | −14.0000 | −0.492823 | ||||||||
\(808\) | 19.0000 | 0.668418 | ||||||||
\(809\) | 8.00000 | + | 13.8564i | 0.281265 | + | 0.487165i | 0.971697 | − | 0.236232i | \(-0.0759127\pi\) |
−0.690432 | + | 0.723398i | \(0.742579\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 15.0000 | − | 25.9808i | 0.526721 | − | 0.912308i | −0.472794 | − | 0.881173i | \(-0.656755\pi\) |
0.999515 | − | 0.0311349i | \(-0.00991216\pi\) | |||||||
\(812\) | 1.50000 | + | 2.59808i | 0.0526397 | + | 0.0911746i | ||||
\(813\) | 0.500000 | + | 0.866025i | 0.0175358 | + | 0.0303728i | ||||
\(814\) | −18.0000 | −0.630900 | ||||||||
\(815\) | −5.00000 | + | 8.66025i | −0.175142 | + | 0.303355i | ||||
\(816\) | −2.00000 | + | 3.46410i | −0.0700140 | + | 0.121268i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −6.50000 | − | 11.2583i | −0.227267 | − | 0.393638i | ||||
\(819\) | 6.00000 | − | 10.3923i | 0.209657 | − | 0.363137i | ||||
\(820\) | −1.00000 | − | 1.73205i | −0.0349215 | − | 0.0604858i | ||||
\(821\) | 1.00000 | 0.0349002 | 0.0174501 | − | 0.999848i | \(-0.494445\pi\) | ||||
0.0174501 | + | 0.999848i | \(0.494445\pi\) | |||||||
\(822\) | −16.0000 | −0.558064 | ||||||||
\(823\) | 10.5000 | + | 18.1865i | 0.366007 | + | 0.633943i | 0.988937 | − | 0.148335i | \(-0.0473913\pi\) |
−0.622930 | + | 0.782277i | \(0.714058\pi\) | |||||||
\(824\) | 6.50000 | − | 11.2583i | 0.226438 | − | 0.392203i | ||||
\(825\) | −1.50000 | − | 2.59808i | −0.0522233 | − | 0.0904534i | ||||
\(826\) | 13.5000 | − | 23.3827i | 0.469725 | − | 0.813588i | ||||
\(827\) | −4.00000 | + | 6.92820i | −0.139094 | + | 0.240917i | −0.927154 | − | 0.374681i | \(-0.877752\pi\) |
0.788060 | + | 0.615598i | \(0.211086\pi\) | |||||||
\(828\) | −1.00000 | + | 1.73205i | −0.0347524 | + | 0.0601929i | ||||
\(829\) | 16.0000 | 0.555703 | 0.277851 | − | 0.960624i | \(-0.410378\pi\) | ||||
0.277851 | + | 0.960624i | \(0.410378\pi\) | |||||||
\(830\) | −4.50000 | − | 7.79423i | −0.156197 | − | 0.270542i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.00000 | + | 3.46410i | −0.0693375 | + | 0.120096i | ||||
\(833\) | −8.00000 | −0.277184 | ||||||||
\(834\) | −2.00000 | − | 3.46410i | −0.0692543 | − | 0.119952i | ||||
\(835\) | −2.00000 | −0.0692129 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.50000 | − | 4.33013i | 0.120978 | − | 0.149671i | ||||
\(838\) | −9.00000 | −0.310900 | ||||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | −1.50000 | − | 2.59808i | −0.0517549 | − | 0.0896421i | ||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −17.0000 | + | 29.4449i | −0.585859 | + | 1.01474i | ||||
\(843\) | −13.0000 | − | 22.5167i | −0.447744 | − | 0.775515i | ||||
\(844\) | −4.00000 | − | 6.92820i | −0.137686 | − | 0.238479i | ||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | 2.00000 | − | 3.46410i | 0.0687614 | − | 0.119098i | ||||
\(847\) | −3.00000 | + | 5.19615i | −0.103081 | + | 0.178542i | ||||
\(848\) | 1.50000 | − | 2.59808i | 0.0515102 | − | 0.0892183i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.00000 | + | 3.46410i | −0.0685994 | + | 0.118818i | ||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | −4.00000 | −0.137038 | ||||||||
\(853\) | −44.0000 | −1.50653 | −0.753266 | − | 0.657716i | \(-0.771523\pi\) | ||||
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(854\) | 3.00000 | + | 5.19615i | 0.102658 | + | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | − | 2.59808i | −0.0512689 | − | 0.0888004i | ||||
\(857\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(858\) | 6.00000 | − | 10.3923i | 0.204837 | − | 0.354787i | ||||
\(859\) | 11.0000 | − | 19.0526i | 0.375315 | − | 0.650065i | −0.615059 | − | 0.788481i | \(-0.710868\pi\) |
0.990374 | + | 0.138416i | \(0.0442012\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | 3.00000 | + | 5.19615i | 0.102240 | + | 0.177084i | ||||
\(862\) | −16.0000 | − | 27.7128i | −0.544962 | − | 0.943902i | ||||
\(863\) | −8.00000 | + | 13.8564i | −0.272323 | + | 0.471678i | −0.969456 | − | 0.245264i | \(-0.921125\pi\) |
0.697133 | + | 0.716942i | \(0.254459\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −0.500000 | − | 0.866025i | −0.0170005 | − | 0.0294457i | ||||
\(866\) | −26.0000 | −0.883516 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −16.5000 | − | 2.59808i | −0.560046 | − | 0.0881845i | ||||
\(869\) | 12.0000 | 0.407072 | ||||||||
\(870\) | −1.00000 | −0.0339032 | ||||||||
\(871\) | −4.00000 | − | 6.92820i | −0.135535 | − | 0.234753i | ||||
\(872\) | 4.00000 | 0.135457 | ||||||||
\(873\) | −5.50000 | + | 9.52628i | −0.186147 | + | 0.322416i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | − | 2.59808i | −0.0507093 | − | 0.0878310i | ||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | −17.0000 | + | 29.4449i | −0.574049 | + | 0.994282i | 0.422095 | + | 0.906552i | \(0.361295\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | −1.50000 | + | 2.59808i | −0.0506225 | + | 0.0876808i | ||||
\(879\) | 10.5000 | − | 18.1865i | 0.354156 | − | 0.613417i | ||||
\(880\) | −1.50000 | − | 2.59808i | −0.0505650 | − | 0.0875811i | ||||
\(881\) | −7.00000 | + | 12.1244i | −0.235836 | + | 0.408480i | −0.959515 | − | 0.281656i | \(-0.909116\pi\) |
0.723679 | + | 0.690136i | \(0.242449\pi\) | |||||||
\(882\) | 1.00000 | + | 1.73205i | 0.0336718 | + | 0.0583212i | ||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | −16.0000 | −0.538138 | ||||||||
\(885\) | 4.50000 | + | 7.79423i | 0.151266 | + | 0.262000i | ||||
\(886\) | 18.0000 | − | 31.1769i | 0.604722 | − | 1.04741i | ||||
\(887\) | 17.0000 | + | 29.4449i | 0.570804 | + | 0.988662i | 0.996484 | + | 0.0837878i | \(0.0267018\pi\) |
−0.425679 | + | 0.904874i | \(0.639965\pi\) | |||||||
\(888\) | 3.00000 | − | 5.19615i | 0.100673 | − | 0.174371i | ||||
\(889\) | −19.5000 | + | 33.7750i | −0.654009 | + | 1.13278i | ||||
\(890\) | −5.00000 | + | 8.66025i | −0.167600 | + | 0.290292i | ||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | −4.50000 | − | 7.79423i | −0.150671 | − | 0.260970i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −9.50000 | + | 16.4545i | −0.317728 | + | 0.550320i | ||||
\(895\) | −19.0000 | −0.635100 | ||||||||
\(896\) | −1.50000 | − | 2.59808i | −0.0501115 | − | 0.0867956i | ||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | −26.0000 | −0.867631 | ||||||||
\(899\) | −3.50000 | + | 4.33013i | −0.116732 | + | 0.144418i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 3.00000 | + | 5.19615i | 0.0998891 | + | 0.173013i | ||||
\(903\) | 12.0000 | 0.399335 | ||||||||
\(904\) | −6.00000 | + | 10.3923i | −0.199557 | + | 0.345643i | ||||
\(905\) | 1.00000 | + | 1.73205i | 0.0332411 | + | 0.0575753i | ||||
\(906\) | −4.50000 | − | 7.79423i | −0.149502 | − | 0.258946i | ||||
\(907\) | −16.0000 | −0.531271 | −0.265636 | − | 0.964073i | \(-0.585582\pi\) | ||||
−0.265636 | + | 0.964073i | \(0.585582\pi\) | |||||||
\(908\) | 1.50000 | − | 2.59808i | 0.0497792 | − | 0.0862202i | ||||
\(909\) | 9.50000 | − | 16.4545i | 0.315095 | − | 0.545761i | ||||
\(910\) | 6.00000 | − | 10.3923i | 0.198898 | − | 0.344502i | ||||
\(911\) | 14.0000 | + | 24.2487i | 0.463841 | + | 0.803396i | 0.999148 | − | 0.0412615i | \(-0.0131377\pi\) |
−0.535308 | + | 0.844657i | \(0.679804\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.5000 | + | 23.3827i | 0.446785 | + | 0.773854i | ||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | −11.0000 | − | 19.0526i | −0.363450 | − | 0.629514i | ||||
\(917\) | 18.0000 | − | 31.1769i | 0.594412 | − | 1.02955i | ||||
\(918\) | 2.00000 | + | 3.46410i | 0.0660098 | + | 0.114332i | ||||
\(919\) | −21.5000 | + | 37.2391i | −0.709220 | + | 1.22840i | 0.255927 | + | 0.966696i | \(0.417619\pi\) |
−0.965147 | + | 0.261708i | \(0.915714\pi\) | |||||||
\(920\) | −1.00000 | + | 1.73205i | −0.0329690 | + | 0.0571040i | ||||
\(921\) | −4.00000 | + | 6.92820i | −0.131804 | + | 0.228292i | ||||
\(922\) | 9.00000 | 0.296399 | ||||||||
\(923\) | −8.00000 | − | 13.8564i | −0.263323 | − | 0.456089i | ||||
\(924\) | 4.50000 | + | 7.79423i | 0.148039 | + | 0.256411i | ||||
\(925\) | 3.00000 | − | 5.19615i | 0.0986394 | − | 0.170848i | ||||
\(926\) | 5.00000 | 0.164310 | ||||||||
\(927\) | −6.50000 | − | 11.2583i | −0.213488 | − | 0.369772i | ||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 16.0000 | 0.524943 | 0.262471 | − | 0.964940i | \(-0.415462\pi\) | ||||
0.262471 | + | 0.964940i | \(0.415462\pi\) | |||||||
\(930\) | 3.50000 | − | 4.33013i | 0.114770 | − | 0.141990i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 12.0000 | + | 20.7846i | 0.392862 | + | 0.680458i | ||||
\(934\) | 27.0000 | 0.883467 | ||||||||
\(935\) | 6.00000 | − | 10.3923i | 0.196221 | − | 0.339865i | ||||
\(936\) | 2.00000 | + | 3.46410i | 0.0653720 | + | 0.113228i | ||||
\(937\) | 29.0000 | + | 50.2295i | 0.947389 | + | 1.64093i | 0.750896 | + | 0.660420i | \(0.229622\pi\) |
0.196492 | + | 0.980505i | \(0.437045\pi\) | |||||||
\(938\) | 6.00000 | 0.195907 | ||||||||
\(939\) | 10.5000 | − | 18.1865i | 0.342655 | − | 0.593495i | ||||
\(940\) | 2.00000 | − | 3.46410i | 0.0652328 | − | 0.112987i | ||||
\(941\) | 8.50000 | − | 14.7224i | 0.277092 | − | 0.479938i | −0.693569 | − | 0.720390i | \(-0.743963\pi\) |
0.970661 | + | 0.240453i | \(0.0772960\pi\) | |||||||
\(942\) | −11.0000 | − | 19.0526i | −0.358399 | − | 0.620766i | ||||
\(943\) | 2.00000 | − | 3.46410i | 0.0651290 | − | 0.112807i | ||||
\(944\) | 4.50000 | + | 7.79423i | 0.146463 | + | 0.253681i | ||||
\(945\) | −3.00000 | −0.0975900 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −24.0000 | − | 41.5692i | −0.779895 | − | 1.35082i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.152106 | − | 0.988364i | \(-0.451394\pi\) | |||||||
\(948\) | −2.00000 | + | 3.46410i | −0.0649570 | + | 0.112509i | ||||
\(949\) | −4.00000 | − | 6.92820i | −0.129845 | − | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.50000 | − | 11.2583i | 0.210777 | − | 0.365076i | ||||
\(952\) | 6.00000 | − | 10.3923i | 0.194461 | − | 0.336817i | ||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | −1.50000 | − | 2.59808i | −0.0485643 | − | 0.0841158i | ||||
\(955\) | −7.00000 | − | 12.1244i | −0.226515 | − | 0.392335i | ||||
\(956\) | 12.0000 | − | 20.7846i | 0.388108 | − | 0.672222i | ||||
\(957\) | 3.00000 | 0.0969762 | ||||||||
\(958\) | 6.00000 | + | 10.3923i | 0.193851 | + | 0.335760i | ||||
\(959\) | 48.0000 | 1.55000 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −6.50000 | − | 30.3109i | −0.209677 | − | 0.977771i | ||||
\(962\) | 24.0000 | 0.773791 | ||||||||
\(963\) | −3.00000 | −0.0966736 | ||||||||
\(964\) | −7.50000 | − | 12.9904i | −0.241559 | − | 0.418392i | ||||
\(965\) | −21.0000 | −0.676014 | ||||||||
\(966\) | 3.00000 | − | 5.19615i | 0.0965234 | − | 0.167183i | ||||
\(967\) | 24.0000 | + | 41.5692i | 0.771788 | + | 1.33678i | 0.936582 | + | 0.350448i | \(0.113971\pi\) |
−0.164794 | + | 0.986328i | \(0.552696\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.50000 | + | 9.52628i | −0.176594 | + | 0.305870i | ||||
\(971\) | 22.5000 | − | 38.9711i | 0.722059 | − | 1.25064i | −0.238114 | − | 0.971237i | \(-0.576529\pi\) |
0.960173 | − | 0.279406i | \(-0.0901376\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 6.00000 | + | 10.3923i | 0.192351 | + | 0.333162i | ||||
\(974\) | 14.5000 | − | 25.1147i | 0.464610 | − | 0.804728i | ||||
\(975\) | 2.00000 | + | 3.46410i | 0.0640513 | + | 0.110940i | ||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −52.0000 | −1.66363 | −0.831814 | − | 0.555055i | \(-0.812697\pi\) | ||||
−0.831814 | + | 0.555055i | \(0.812697\pi\) | |||||||
\(978\) | 5.00000 | + | 8.66025i | 0.159882 | + | 0.276924i | ||||
\(979\) | 15.0000 | − | 25.9808i | 0.479402 | − | 0.830349i | ||||
\(980\) | 1.00000 | + | 1.73205i | 0.0319438 | + | 0.0553283i | ||||
\(981\) | 2.00000 | − | 3.46410i | 0.0638551 | − | 0.110600i | ||||
\(982\) | −9.50000 | + | 16.4545i | −0.303157 | + | 0.525084i | ||||
\(983\) | 7.00000 | − | 12.1244i | 0.223265 | − | 0.386707i | −0.732532 | − | 0.680732i | \(-0.761662\pi\) |
0.955798 | + | 0.294025i | \(0.0949950\pi\) | |||||||
\(984\) | −2.00000 | −0.0637577 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | −2.00000 | − | 3.46410i | −0.0636930 | − | 0.110319i | ||||
\(987\) | −6.00000 | + | 10.3923i | −0.190982 | + | 0.330791i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | − | 6.92820i | −0.127193 | − | 0.220304i | ||||
\(990\) | −3.00000 | −0.0953463 | ||||||||
\(991\) | 56.0000 | 1.77890 | 0.889449 | − | 0.457034i | \(-0.151088\pi\) | ||||
0.889449 | + | 0.457034i | \(0.151088\pi\) | |||||||
\(992\) | 3.50000 | − | 4.33013i | 0.111125 | − | 0.137482i | ||||
\(993\) | 30.0000 | 0.952021 | ||||||||
\(994\) | 12.0000 | 0.380617 | ||||||||
\(995\) | −5.50000 | − | 9.52628i | −0.174362 | − | 0.302003i | ||||
\(996\) | −9.00000 | −0.285176 | ||||||||
\(997\) | 21.0000 | − | 36.3731i | 0.665077 | − | 1.15195i | −0.314188 | − | 0.949361i | \(-0.601732\pi\) |
0.979265 | − | 0.202586i | \(-0.0649345\pi\) | |||||||
\(998\) | 11.0000 | + | 19.0526i | 0.348199 | + | 0.603098i | ||||
\(999\) | −3.00000 | − | 5.19615i | −0.0949158 | − | 0.164399i |
(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.c.211.1 | ✓ | 2 | |
31.5 | even | 3 | inner | 930.2.i.c.811.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.c.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
930.2.i.c.811.1 | yes | 2 | 31.5 | even | 3 | inner |