Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, 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("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (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: | \(4.35983195036\) |
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 | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.g.295.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 0.500000 | − | 0.866025i | 0.188982 | − | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.00000 | + | 1.73205i | 0.316228 | + | 0.547723i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 2.50000 | + | 2.59808i | 0.693375 | + | 0.720577i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | + | 1.73205i | 0.258199 | + | 0.447214i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.500000 | − | 0.866025i | 0.121268 | − | 0.210042i | −0.799000 | − | 0.601331i | \(-0.794637\pi\) |
0.920268 | + | 0.391289i | \(0.127971\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | −1.00000 | + | 1.73205i | −0.223607 | + | 0.387298i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.500000 | + | 0.866025i | 0.0944911 | + | 0.163663i | ||||
\(29\) | −4.50000 | − | 7.79423i | −0.835629 | − | 1.44735i | −0.893517 | − | 0.449029i | \(-0.851770\pi\) |
0.0578882 | − | 0.998323i | \(-0.481563\pi\) | |||||||
\(30\) | −1.00000 | + | 1.73205i | −0.182574 | + | 0.316228i | ||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 1.00000 | − | 1.73205i | 0.169031 | − | 0.292770i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −1.00000 | + | 3.46410i | −0.160128 | + | 0.554700i | ||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | −2.50000 | − | 4.33013i | −0.390434 | − | 0.676252i | 0.602072 | − | 0.798441i | \(-0.294342\pi\) |
−0.992507 | + | 0.122189i | \(0.961009\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.0771517 | + | 0.133631i | ||||
\(43\) | 1.00000 | − | 1.73205i | 0.152499 | − | 0.264135i | −0.779647 | − | 0.626219i | \(-0.784601\pi\) |
0.932145 | + | 0.362084i | \(0.117935\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | −1.00000 | + | 1.73205i | −0.149071 | + | 0.258199i | ||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | −7.00000 | −1.02105 | −0.510527 | − | 0.859861i | \(-0.670550\pi\) | ||||
−0.510527 | + | 0.859861i | \(0.670550\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −3.50000 | + | 0.866025i | −0.485363 | + | 0.120096i | ||||
\(53\) | −1.00000 | −0.137361 | −0.0686803 | − | 0.997639i | \(-0.521879\pi\) | ||||
−0.0686803 | + | 0.997639i | \(0.521879\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 1.00000 | + | 1.73205i | 0.134840 | + | 0.233550i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | 4.50000 | − | 7.79423i | 0.590879 | − | 1.02343i | ||||
\(59\) | −5.00000 | + | 8.66025i | −0.650945 | + | 1.12747i | 0.331949 | + | 0.943297i | \(0.392294\pi\) |
−0.982894 | + | 0.184172i | \(0.941040\pi\) | |||||||
\(60\) | −2.00000 | −0.258199 | ||||||||
\(61\) | 5.50000 | − | 9.52628i | 0.704203 | − | 1.21972i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
0.966978 | − | 0.254858i | \(-0.0820288\pi\) | |||||||
\(62\) | 1.00000 | + | 1.73205i | 0.127000 | + | 0.219971i | ||||
\(63\) | 0.500000 | + | 0.866025i | 0.0629941 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.00000 | + | 5.19615i | 0.620174 | + | 0.644503i | ||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 0.500000 | + | 0.866025i | 0.0606339 | + | 0.105021i | ||||
\(69\) | −3.00000 | + | 5.19615i | −0.361158 | + | 0.625543i | ||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | 4.00000 | − | 6.92820i | 0.474713 | − | 0.822226i | −0.524868 | − | 0.851184i | \(-0.675885\pi\) |
0.999581 | + | 0.0289572i | \(0.00921865\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | −0.500000 | − | 0.866025i | −0.0573539 | − | 0.0993399i | ||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | −3.50000 | + | 0.866025i | −0.396297 | + | 0.0980581i | ||||
\(79\) | 11.0000 | 1.23760 | 0.618798 | − | 0.785550i | \(-0.287620\pi\) | ||||
0.618798 | + | 0.785550i | \(0.287620\pi\) | |||||||
\(80\) | −1.00000 | − | 1.73205i | −0.111803 | − | 0.193649i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.50000 | − | 4.33013i | 0.276079 | − | 0.478183i | ||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | −0.500000 | + | 0.866025i | −0.0545545 | + | 0.0944911i | ||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 4.50000 | − | 7.79423i | 0.482451 | − | 0.835629i | ||||
\(88\) | −0.500000 | − | 0.866025i | −0.0533002 | − | 0.0923186i | ||||
\(89\) | −5.50000 | − | 9.52628i | −0.582999 | − | 1.00978i | −0.995122 | − | 0.0986553i | \(-0.968546\pi\) |
0.412123 | − | 0.911128i | \(-0.364787\pi\) | |||||||
\(90\) | −2.00000 | −0.210819 | ||||||||
\(91\) | 3.50000 | − | 0.866025i | 0.366900 | − | 0.0907841i | ||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 1.00000 | + | 1.73205i | 0.103695 | + | 0.179605i | ||||
\(94\) | −3.50000 | − | 6.06218i | −0.360997 | − | 0.625266i | ||||
\(95\) | −1.00000 | + | 1.73205i | −0.102598 | + | 0.177705i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.00000 | − | 12.1244i | 0.710742 | − | 1.23104i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) |
0.964579 | − | 0.263795i | \(-0.0849741\pi\) | |||||||
\(98\) | 0.500000 | − | 0.866025i | 0.0505076 | − | 0.0874818i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0.500000 | + | 0.866025i | 0.0495074 | + | 0.0857493i | ||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | −0.500000 | − | 0.866025i | −0.0485643 | − | 0.0841158i | ||||
\(107\) | −1.50000 | − | 2.59808i | −0.145010 | − | 0.251166i | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 16.0000 | 1.53252 | 0.766261 | − | 0.642529i | \(-0.222115\pi\) | ||||
0.766261 | + | 0.642529i | \(0.222115\pi\) | |||||||
\(110\) | −1.00000 | + | 1.73205i | −0.0953463 | + | 0.165145i | ||||
\(111\) | −1.00000 | + | 1.73205i | −0.0949158 | + | 0.164399i | ||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | −0.500000 | − | 0.866025i | −0.0468293 | − | 0.0811107i | ||||
\(115\) | 6.00000 | + | 10.3923i | 0.559503 | + | 0.969087i | ||||
\(116\) | 9.00000 | 0.835629 | ||||||||
\(117\) | −3.50000 | + | 0.866025i | −0.323575 | + | 0.0800641i | ||||
\(118\) | −10.0000 | −0.920575 | ||||||||
\(119\) | −0.500000 | − | 0.866025i | −0.0458349 | − | 0.0793884i | ||||
\(120\) | −1.00000 | − | 1.73205i | −0.0912871 | − | 0.158114i | ||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 11.0000 | 0.995893 | ||||||||
\(123\) | 2.50000 | − | 4.33013i | 0.225417 | − | 0.390434i | ||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | −0.500000 | + | 0.866025i | −0.0445435 | + | 0.0771517i | ||||
\(127\) | 6.00000 | + | 10.3923i | 0.532414 | + | 0.922168i | 0.999284 | + | 0.0378419i | \(0.0120483\pi\) |
−0.466870 | + | 0.884326i | \(0.654618\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | −2.00000 | + | 6.92820i | −0.175412 | + | 0.607644i | ||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | −0.500000 | − | 0.866025i | −0.0435194 | − | 0.0753778i | ||||
\(133\) | 0.500000 | + | 0.866025i | 0.0433555 | + | 0.0750939i | ||||
\(134\) | 1.00000 | − | 1.73205i | 0.0863868 | − | 0.149626i | ||||
\(135\) | −2.00000 | −0.172133 | ||||||||
\(136\) | −0.500000 | + | 0.866025i | −0.0428746 | + | 0.0742611i | ||||
\(137\) | 5.00000 | − | 8.66025i | 0.427179 | − | 0.739895i | −0.569442 | − | 0.822031i | \(-0.692841\pi\) |
0.996621 | + | 0.0821359i | \(0.0261741\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 1.00000 | + | 1.73205i | 0.0845154 | + | 0.146385i | ||||
\(141\) | −3.50000 | − | 6.06218i | −0.294753 | − | 0.510527i | ||||
\(142\) | 8.00000 | 0.671345 | ||||||||
\(143\) | −1.00000 | + | 3.46410i | −0.0836242 | + | 0.289683i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −9.00000 | − | 15.5885i | −0.747409 | − | 1.29455i | ||||
\(146\) | 4.00000 | + | 6.92820i | 0.331042 | + | 0.573382i | ||||
\(147\) | 0.500000 | − | 0.866025i | 0.0412393 | − | 0.0714286i | ||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0.500000 | − | 0.866025i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | −3.00000 | −0.244137 | −0.122068 | − | 0.992522i | \(-0.538953\pi\) | ||||
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(152\) | 0.500000 | − | 0.866025i | 0.0405554 | − | 0.0702439i | ||||
\(153\) | 0.500000 | + | 0.866025i | 0.0404226 | + | 0.0700140i | ||||
\(154\) | 0.500000 | + | 0.866025i | 0.0402911 | + | 0.0697863i | ||||
\(155\) | 4.00000 | 0.321288 | ||||||||
\(156\) | −2.50000 | − | 2.59808i | −0.200160 | − | 0.208013i | ||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | 5.50000 | + | 9.52628i | 0.437557 | + | 0.757870i | ||||
\(159\) | −0.500000 | − | 0.866025i | −0.0396526 | − | 0.0686803i | ||||
\(160\) | 1.00000 | − | 1.73205i | 0.0790569 | − | 0.136931i | ||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −1.00000 | + | 1.73205i | −0.0783260 | + | 0.135665i | −0.902528 | − | 0.430632i | \(-0.858291\pi\) |
0.824202 | + | 0.566296i | \(0.191624\pi\) | |||||||
\(164\) | 5.00000 | 0.390434 | ||||||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | −6.00000 | − | 10.3923i | −0.465690 | − | 0.806599i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 2.00000 | 0.153393 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 1.00000 | + | 1.73205i | 0.0762493 | + | 0.132068i | ||||
\(173\) | −4.00000 | + | 6.92820i | −0.304114 | + | 0.526742i | −0.977064 | − | 0.212947i | \(-0.931694\pi\) |
0.672949 | + | 0.739689i | \(0.265027\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 0.500000 | − | 0.866025i | 0.0376889 | − | 0.0652791i | ||||
\(177\) | −10.0000 | −0.751646 | ||||||||
\(178\) | 5.50000 | − | 9.52628i | 0.412242 | − | 0.714025i | ||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | −1.00000 | − | 1.73205i | −0.0745356 | − | 0.129099i | ||||
\(181\) | −19.0000 | −1.41226 | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 2.50000 | + | 2.59808i | 0.185312 | + | 0.192582i | ||||
\(183\) | 11.0000 | 0.813143 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 2.00000 | + | 3.46410i | 0.147043 | + | 0.254686i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 3.50000 | − | 6.06218i | 0.255264 | − | 0.442130i | ||||
\(189\) | −0.500000 | + | 0.866025i | −0.0363696 | + | 0.0629941i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 5.50000 | + | 9.52628i | 0.395899 | + | 0.685717i | 0.993215 | − | 0.116289i | \(-0.0370998\pi\) |
−0.597317 | + | 0.802005i | \(0.703766\pi\) | |||||||
\(194\) | 14.0000 | 1.00514 | ||||||||
\(195\) | −2.00000 | + | 6.92820i | −0.143223 | + | 0.496139i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −13.5000 | − | 23.3827i | −0.961835 | − | 1.66595i | −0.717888 | − | 0.696159i | \(-0.754891\pi\) |
−0.243947 | − | 0.969788i | \(-0.578442\pi\) | |||||||
\(198\) | −0.500000 | − | 0.866025i | −0.0355335 | − | 0.0615457i | ||||
\(199\) | −5.00000 | + | 8.66025i | −0.354441 | + | 0.613909i | −0.987022 | − | 0.160585i | \(-0.948662\pi\) |
0.632581 | + | 0.774494i | \(0.281995\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 1.00000 | − | 1.73205i | 0.0705346 | − | 0.122169i | ||||
\(202\) | −1.00000 | + | 1.73205i | −0.0703598 | + | 0.121867i | ||||
\(203\) | −9.00000 | −0.631676 | ||||||||
\(204\) | −0.500000 | + | 0.866025i | −0.0350070 | + | 0.0606339i | ||||
\(205\) | −5.00000 | − | 8.66025i | −0.349215 | − | 0.604858i | ||||
\(206\) | −7.00000 | − | 12.1244i | −0.487713 | − | 0.844744i | ||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 1.00000 | − | 3.46410i | 0.0693375 | − | 0.240192i | ||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | 1.00000 | + | 1.73205i | 0.0690066 | + | 0.119523i | ||||
\(211\) | 3.00000 | + | 5.19615i | 0.206529 | + | 0.357718i | 0.950619 | − | 0.310361i | \(-0.100450\pi\) |
−0.744090 | + | 0.668079i | \(0.767117\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.0343401 | − | 0.0594789i | ||||
\(213\) | 8.00000 | 0.548151 | ||||||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | 2.00000 | − | 3.46410i | 0.136399 | − | 0.236250i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.00000 | − | 1.73205i | 0.0678844 | − | 0.117579i | ||||
\(218\) | 8.00000 | + | 13.8564i | 0.541828 | + | 0.938474i | ||||
\(219\) | 4.00000 | + | 6.92820i | 0.270295 | + | 0.468165i | ||||
\(220\) | −2.00000 | −0.134840 | ||||||||
\(221\) | 3.50000 | − | 0.866025i | 0.235435 | − | 0.0582552i | ||||
\(222\) | −2.00000 | −0.134231 | ||||||||
\(223\) | −10.0000 | − | 17.3205i | −0.669650 | − | 1.15987i | −0.978002 | − | 0.208595i | \(-0.933111\pi\) |
0.308353 | − | 0.951272i | \(-0.400222\pi\) | |||||||
\(224\) | −0.500000 | − | 0.866025i | −0.0334077 | − | 0.0578638i | ||||
\(225\) | 0.500000 | − | 0.866025i | 0.0333333 | − | 0.0577350i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | −1.00000 | + | 1.73205i | −0.0663723 | + | 0.114960i | −0.897302 | − | 0.441417i | \(-0.854476\pi\) |
0.830930 | + | 0.556378i | \(0.187809\pi\) | |||||||
\(228\) | 0.500000 | − | 0.866025i | 0.0331133 | − | 0.0573539i | ||||
\(229\) | −23.0000 | −1.51988 | −0.759941 | − | 0.649992i | \(-0.774772\pi\) | ||||
−0.759941 | + | 0.649992i | \(0.774772\pi\) | |||||||
\(230\) | −6.00000 | + | 10.3923i | −0.395628 | + | 0.685248i | ||||
\(231\) | 0.500000 | + | 0.866025i | 0.0328976 | + | 0.0569803i | ||||
\(232\) | 4.50000 | + | 7.79423i | 0.295439 | + | 0.511716i | ||||
\(233\) | 18.0000 | 1.17922 | 0.589610 | − | 0.807688i | \(-0.299282\pi\) | ||||
0.589610 | + | 0.807688i | \(0.299282\pi\) | |||||||
\(234\) | −2.50000 | − | 2.59808i | −0.163430 | − | 0.169842i | ||||
\(235\) | −14.0000 | −0.913259 | ||||||||
\(236\) | −5.00000 | − | 8.66025i | −0.325472 | − | 0.563735i | ||||
\(237\) | 5.50000 | + | 9.52628i | 0.357263 | + | 0.618798i | ||||
\(238\) | 0.500000 | − | 0.866025i | 0.0324102 | − | 0.0561361i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 1.00000 | − | 1.73205i | 0.0645497 | − | 0.111803i | ||||
\(241\) | −8.00000 | + | 13.8564i | −0.515325 | + | 0.892570i | 0.484516 | + | 0.874782i | \(0.338996\pi\) |
−0.999842 | + | 0.0177875i | \(0.994338\pi\) | |||||||
\(242\) | 10.0000 | 0.642824 | ||||||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 5.50000 | + | 9.52628i | 0.352101 | + | 0.609858i | ||||
\(245\) | −1.00000 | − | 1.73205i | −0.0638877 | − | 0.110657i | ||||
\(246\) | 5.00000 | 0.318788 | ||||||||
\(247\) | −3.50000 | + | 0.866025i | −0.222700 | + | 0.0551039i | ||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | 4.00000 | − | 6.92820i | 0.252478 | − | 0.437304i | −0.711730 | − | 0.702454i | \(-0.752088\pi\) |
0.964207 | + | 0.265149i | \(0.0854212\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | −3.00000 | + | 5.19615i | −0.188608 | + | 0.326679i | ||||
\(254\) | −6.00000 | + | 10.3923i | −0.376473 | + | 0.652071i | ||||
\(255\) | 2.00000 | 0.125245 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.50000 | + | 7.79423i | 0.280702 | + | 0.486191i | 0.971558 | − | 0.236802i | \(-0.0760993\pi\) |
−0.690856 | + | 0.722993i | \(0.742766\pi\) | |||||||
\(258\) | 1.00000 | + | 1.73205i | 0.0622573 | + | 0.107833i | ||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | −7.00000 | + | 1.73205i | −0.434122 | + | 0.107417i | ||||
\(261\) | 9.00000 | 0.557086 | ||||||||
\(262\) | −4.00000 | − | 6.92820i | −0.247121 | − | 0.428026i | ||||
\(263\) | 14.0000 | + | 24.2487i | 0.863277 | + | 1.49524i | 0.868748 | + | 0.495255i | \(0.164925\pi\) |
−0.00547092 | + | 0.999985i | \(0.501741\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | −2.00000 | −0.122859 | ||||||||
\(266\) | −0.500000 | + | 0.866025i | −0.0306570 | + | 0.0530994i | ||||
\(267\) | 5.50000 | − | 9.52628i | 0.336595 | − | 0.582999i | ||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | −8.00000 | + | 13.8564i | −0.487769 | + | 0.844840i | −0.999901 | − | 0.0140665i | \(-0.995522\pi\) |
0.512132 | + | 0.858906i | \(0.328856\pi\) | |||||||
\(270\) | −1.00000 | − | 1.73205i | −0.0608581 | − | 0.105409i | ||||
\(271\) | −1.00000 | − | 1.73205i | −0.0607457 | − | 0.105215i | 0.834053 | − | 0.551684i | \(-0.186015\pi\) |
−0.894799 | + | 0.446469i | \(0.852681\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | 2.50000 | + | 2.59808i | 0.151307 | + | 0.157243i | ||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | −3.00000 | − | 5.19615i | −0.180579 | − | 0.312772i | ||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 9.00000 | 0.539784 | ||||||||
\(279\) | −1.00000 | + | 1.73205i | −0.0598684 | + | 0.103695i | ||||
\(280\) | −1.00000 | + | 1.73205i | −0.0597614 | + | 0.103510i | ||||
\(281\) | −20.0000 | −1.19310 | −0.596550 | − | 0.802576i | \(-0.703462\pi\) | ||||
−0.596550 | + | 0.802576i | \(0.703462\pi\) | |||||||
\(282\) | 3.50000 | − | 6.06218i | 0.208422 | − | 0.360997i | ||||
\(283\) | 14.0000 | + | 24.2487i | 0.832214 | + | 1.44144i | 0.896279 | + | 0.443491i | \(0.146260\pi\) |
−0.0640654 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(284\) | 4.00000 | + | 6.92820i | 0.237356 | + | 0.411113i | ||||
\(285\) | −2.00000 | −0.118470 | ||||||||
\(286\) | −3.50000 | + | 0.866025i | −0.206959 | + | 0.0512092i | ||||
\(287\) | −5.00000 | −0.295141 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 8.00000 | + | 13.8564i | 0.470588 | + | 0.815083i | ||||
\(290\) | 9.00000 | − | 15.5885i | 0.528498 | − | 0.915386i | ||||
\(291\) | 14.0000 | 0.820695 | ||||||||
\(292\) | −4.00000 | + | 6.92820i | −0.234082 | + | 0.405442i | ||||
\(293\) | −10.0000 | + | 17.3205i | −0.584206 | + | 1.01187i | 0.410768 | + | 0.911740i | \(0.365261\pi\) |
−0.994974 | + | 0.100135i | \(0.968073\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | −10.0000 | + | 17.3205i | −0.582223 | + | 1.00844i | ||||
\(296\) | −1.00000 | − | 1.73205i | −0.0581238 | − | 0.100673i | ||||
\(297\) | −0.500000 | − | 0.866025i | −0.0290129 | − | 0.0502519i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −6.00000 | + | 20.7846i | −0.346989 | + | 1.20201i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −1.00000 | − | 1.73205i | −0.0576390 | − | 0.0998337i | ||||
\(302\) | −1.50000 | − | 2.59808i | −0.0863153 | − | 0.149502i | ||||
\(303\) | −1.00000 | + | 1.73205i | −0.0574485 | + | 0.0995037i | ||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 11.0000 | − | 19.0526i | 0.629858 | − | 1.09095i | ||||
\(306\) | −0.500000 | + | 0.866025i | −0.0285831 | + | 0.0495074i | ||||
\(307\) | 19.0000 | 1.08439 | 0.542194 | − | 0.840254i | \(-0.317594\pi\) | ||||
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | −0.500000 | + | 0.866025i | −0.0284901 | + | 0.0493464i | ||||
\(309\) | −7.00000 | − | 12.1244i | −0.398216 | − | 0.689730i | ||||
\(310\) | 2.00000 | + | 3.46410i | 0.113592 | + | 0.196748i | ||||
\(311\) | −15.0000 | −0.850572 | −0.425286 | − | 0.905059i | \(-0.639826\pi\) | ||||
−0.425286 | + | 0.905059i | \(0.639826\pi\) | |||||||
\(312\) | 1.00000 | − | 3.46410i | 0.0566139 | − | 0.196116i | ||||
\(313\) | −12.0000 | −0.678280 | −0.339140 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339140 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(314\) | 1.00000 | + | 1.73205i | 0.0564333 | + | 0.0977453i | ||||
\(315\) | 1.00000 | + | 1.73205i | 0.0563436 | + | 0.0975900i | ||||
\(316\) | −5.50000 | + | 9.52628i | −0.309399 | + | 0.535895i | ||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | 0.500000 | − | 0.866025i | 0.0280386 | − | 0.0485643i | ||||
\(319\) | 4.50000 | − | 7.79423i | 0.251952 | − | 0.436393i | ||||
\(320\) | 2.00000 | 0.111803 | ||||||||
\(321\) | 1.50000 | − | 2.59808i | 0.0837218 | − | 0.145010i | ||||
\(322\) | 3.00000 | + | 5.19615i | 0.167183 | + | 0.289570i | ||||
\(323\) | 0.500000 | + | 0.866025i | 0.0278207 | + | 0.0481869i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −2.50000 | − | 2.59808i | −0.138675 | − | 0.144115i | ||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 8.00000 | + | 13.8564i | 0.442401 | + | 0.766261i | ||||
\(328\) | 2.50000 | + | 4.33013i | 0.138039 | + | 0.239091i | ||||
\(329\) | −3.50000 | + | 6.06218i | −0.192961 | + | 0.334219i | ||||
\(330\) | −2.00000 | −0.110096 | ||||||||
\(331\) | −13.0000 | + | 22.5167i | −0.714545 | + | 1.23763i | 0.248590 | + | 0.968609i | \(0.420033\pi\) |
−0.963135 | + | 0.269019i | \(0.913301\pi\) | |||||||
\(332\) | 6.00000 | − | 10.3923i | 0.329293 | − | 0.570352i | ||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | − | 3.46410i | −0.109272 | − | 0.189264i | ||||
\(336\) | −0.500000 | − | 0.866025i | −0.0272772 | − | 0.0472456i | ||||
\(337\) | −33.0000 | −1.79762 | −0.898812 | − | 0.438334i | \(-0.855569\pi\) | ||||
−0.898812 | + | 0.438334i | \(0.855569\pi\) | |||||||
\(338\) | −11.5000 | + | 6.06218i | −0.625518 | + | 0.329739i | ||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 1.00000 | + | 1.73205i | 0.0542326 | + | 0.0939336i | ||||
\(341\) | 1.00000 | + | 1.73205i | 0.0541530 | + | 0.0937958i | ||||
\(342\) | 0.500000 | − | 0.866025i | 0.0270369 | − | 0.0468293i | ||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.00000 | + | 1.73205i | −0.0539164 | + | 0.0933859i | ||||
\(345\) | −6.00000 | + | 10.3923i | −0.323029 | + | 0.559503i | ||||
\(346\) | −8.00000 | −0.430083 | ||||||||
\(347\) | 1.50000 | − | 2.59808i | 0.0805242 | − | 0.139472i | −0.822951 | − | 0.568112i | \(-0.807674\pi\) |
0.903475 | + | 0.428640i | \(0.141007\pi\) | |||||||
\(348\) | 4.50000 | + | 7.79423i | 0.241225 | + | 0.417815i | ||||
\(349\) | 3.00000 | + | 5.19615i | 0.160586 | + | 0.278144i | 0.935079 | − | 0.354439i | \(-0.115328\pi\) |
−0.774493 | + | 0.632583i | \(0.781995\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −2.50000 | − | 2.59808i | −0.133440 | − | 0.138675i | ||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −13.0000 | − | 22.5167i | −0.691920 | − | 1.19844i | −0.971208 | − | 0.238233i | \(-0.923432\pi\) |
0.279288 | − | 0.960207i | \(-0.409902\pi\) | |||||||
\(354\) | −5.00000 | − | 8.66025i | −0.265747 | − | 0.460287i | ||||
\(355\) | 8.00000 | − | 13.8564i | 0.424596 | − | 0.735422i | ||||
\(356\) | 11.0000 | 0.582999 | ||||||||
\(357\) | 0.500000 | − | 0.866025i | 0.0264628 | − | 0.0458349i | ||||
\(358\) | −6.00000 | + | 10.3923i | −0.317110 | + | 0.549250i | ||||
\(359\) | −30.0000 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | 1.00000 | − | 1.73205i | 0.0527046 | − | 0.0912871i | ||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −9.50000 | − | 16.4545i | −0.499309 | − | 0.864828i | ||||
\(363\) | 10.0000 | 0.524864 | ||||||||
\(364\) | −1.00000 | + | 3.46410i | −0.0524142 | + | 0.181568i | ||||
\(365\) | 16.0000 | 0.837478 | ||||||||
\(366\) | 5.50000 | + | 9.52628i | 0.287490 | + | 0.497947i | ||||
\(367\) | 7.00000 | + | 12.1244i | 0.365397 | + | 0.632886i | 0.988840 | − | 0.148983i | \(-0.0475999\pi\) |
−0.623443 | + | 0.781869i | \(0.714267\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 5.00000 | 0.260290 | ||||||||
\(370\) | −2.00000 | + | 3.46410i | −0.103975 | + | 0.180090i | ||||
\(371\) | −0.500000 | + | 0.866025i | −0.0259587 | + | 0.0449618i | ||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(374\) | 0.500000 | + | 0.866025i | 0.0258544 | + | 0.0447811i | ||||
\(375\) | −6.00000 | − | 10.3923i | −0.309839 | − | 0.536656i | ||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | 9.00000 | − | 31.1769i | 0.463524 | − | 1.60569i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(380\) | −1.00000 | − | 1.73205i | −0.0512989 | − | 0.0888523i | ||||
\(381\) | −6.00000 | + | 10.3923i | −0.307389 | + | 0.532414i | ||||
\(382\) | −4.00000 | −0.204658 | ||||||||
\(383\) | −4.50000 | + | 7.79423i | −0.229939 | + | 0.398266i | −0.957790 | − | 0.287469i | \(-0.907186\pi\) |
0.727851 | + | 0.685736i | \(0.240519\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 2.00000 | 0.101929 | ||||||||
\(386\) | −5.50000 | + | 9.52628i | −0.279943 | + | 0.484875i | ||||
\(387\) | 1.00000 | + | 1.73205i | 0.0508329 | + | 0.0880451i | ||||
\(388\) | 7.00000 | + | 12.1244i | 0.355371 | + | 0.615521i | ||||
\(389\) | 22.0000 | 1.11544 | 0.557722 | − | 0.830028i | \(-0.311675\pi\) | ||||
0.557722 | + | 0.830028i | \(0.311675\pi\) | |||||||
\(390\) | −7.00000 | + | 1.73205i | −0.354459 | + | 0.0877058i | ||||
\(391\) | 6.00000 | 0.303433 | ||||||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | −4.00000 | − | 6.92820i | −0.201773 | − | 0.349482i | ||||
\(394\) | 13.5000 | − | 23.3827i | 0.680120 | − | 1.17800i | ||||
\(395\) | 22.0000 | 1.10694 | ||||||||
\(396\) | 0.500000 | − | 0.866025i | 0.0251259 | − | 0.0435194i | ||||
\(397\) | 10.5000 | − | 18.1865i | 0.526980 | − | 0.912756i | −0.472526 | − | 0.881317i | \(-0.656658\pi\) |
0.999506 | − | 0.0314391i | \(-0.0100090\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | −0.500000 | + | 0.866025i | −0.0250313 | + | 0.0433555i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −3.00000 | − | 5.19615i | −0.149813 | − | 0.259483i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.931158 | + | 0.364615i | \(0.881200\pi\) | |||||||
\(402\) | 2.00000 | 0.0997509 | ||||||||
\(403\) | 5.00000 | + | 5.19615i | 0.249068 | + | 0.258839i | ||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | −1.00000 | − | 1.73205i | −0.0496904 | − | 0.0860663i | ||||
\(406\) | −4.50000 | − | 7.79423i | −0.223331 | − | 0.386821i | ||||
\(407\) | −1.00000 | + | 1.73205i | −0.0495682 | + | 0.0858546i | ||||
\(408\) | −1.00000 | −0.0495074 | ||||||||
\(409\) | −10.0000 | + | 17.3205i | −0.494468 | + | 0.856444i | −0.999980 | − | 0.00637586i | \(-0.997970\pi\) |
0.505511 | + | 0.862820i | \(0.331304\pi\) | |||||||
\(410\) | 5.00000 | − | 8.66025i | 0.246932 | − | 0.427699i | ||||
\(411\) | 10.0000 | 0.493264 | ||||||||
\(412\) | 7.00000 | − | 12.1244i | 0.344865 | − | 0.597324i | ||||
\(413\) | 5.00000 | + | 8.66025i | 0.246034 | + | 0.426143i | ||||
\(414\) | −3.00000 | − | 5.19615i | −0.147442 | − | 0.255377i | ||||
\(415\) | −24.0000 | −1.17811 | ||||||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | 9.00000 | 0.440732 | ||||||||
\(418\) | −0.500000 | − | 0.866025i | −0.0244558 | − | 0.0423587i | ||||
\(419\) | 10.0000 | + | 17.3205i | 0.488532 | + | 0.846162i | 0.999913 | − | 0.0131919i | \(-0.00419923\pi\) |
−0.511381 | + | 0.859354i | \(0.670866\pi\) | |||||||
\(420\) | −1.00000 | + | 1.73205i | −0.0487950 | + | 0.0845154i | ||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | −3.00000 | + | 5.19615i | −0.146038 | + | 0.252945i | ||||
\(423\) | 3.50000 | − | 6.06218i | 0.170176 | − | 0.294753i | ||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | −0.500000 | + | 0.866025i | −0.0242536 | + | 0.0420084i | ||||
\(426\) | 4.00000 | + | 6.92820i | 0.193801 | + | 0.335673i | ||||
\(427\) | −5.50000 | − | 9.52628i | −0.266164 | − | 0.461009i | ||||
\(428\) | 3.00000 | 0.145010 | ||||||||
\(429\) | −3.50000 | + | 0.866025i | −0.168982 | + | 0.0418121i | ||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −14.0000 | − | 24.2487i | −0.674356 | − | 1.16802i | −0.976657 | − | 0.214807i | \(-0.931088\pi\) |
0.302300 | − | 0.953213i | \(-0.402245\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 9.00000 | − | 15.5885i | 0.432512 | − | 0.749133i | −0.564577 | − | 0.825381i | \(-0.690961\pi\) |
0.997089 | + | 0.0762473i | \(0.0242938\pi\) | |||||||
\(434\) | 2.00000 | 0.0960031 | ||||||||
\(435\) | 9.00000 | − | 15.5885i | 0.431517 | − | 0.747409i | ||||
\(436\) | −8.00000 | + | 13.8564i | −0.383131 | + | 0.663602i | ||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | −4.00000 | + | 6.92820i | −0.191127 | + | 0.331042i | ||||
\(439\) | 10.0000 | + | 17.3205i | 0.477274 | + | 0.826663i | 0.999661 | − | 0.0260459i | \(-0.00829161\pi\) |
−0.522387 | + | 0.852709i | \(0.674958\pi\) | |||||||
\(440\) | −1.00000 | − | 1.73205i | −0.0476731 | − | 0.0825723i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 2.50000 | + | 2.59808i | 0.118913 | + | 0.123578i | ||||
\(443\) | 35.0000 | 1.66290 | 0.831450 | − | 0.555599i | \(-0.187511\pi\) | ||||
0.831450 | + | 0.555599i | \(0.187511\pi\) | |||||||
\(444\) | −1.00000 | − | 1.73205i | −0.0474579 | − | 0.0821995i | ||||
\(445\) | −11.0000 | − | 19.0526i | −0.521450 | − | 0.903178i | ||||
\(446\) | 10.0000 | − | 17.3205i | 0.473514 | − | 0.820150i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.0236228 | − | 0.0409159i | ||||
\(449\) | 15.0000 | − | 25.9808i | 0.707894 | − | 1.22611i | −0.257743 | − | 0.966213i | \(-0.582979\pi\) |
0.965637 | − | 0.259895i | \(-0.0836878\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 2.50000 | − | 4.33013i | 0.117720 | − | 0.203898i | ||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | −1.50000 | − | 2.59808i | −0.0704761 | − | 0.122068i | ||||
\(454\) | −2.00000 | −0.0938647 | ||||||||
\(455\) | 7.00000 | − | 1.73205i | 0.328165 | − | 0.0811998i | ||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 3.00000 | + | 5.19615i | 0.140334 | + | 0.243066i | 0.927622 | − | 0.373519i | \(-0.121849\pi\) |
−0.787288 | + | 0.616585i | \(0.788516\pi\) | |||||||
\(458\) | −11.5000 | − | 19.9186i | −0.537360 | − | 0.930734i | ||||
\(459\) | −0.500000 | + | 0.866025i | −0.0233380 | + | 0.0404226i | ||||
\(460\) | −12.0000 | −0.559503 | ||||||||
\(461\) | 12.0000 | − | 20.7846i | 0.558896 | − | 0.968036i | −0.438693 | − | 0.898637i | \(-0.644559\pi\) |
0.997589 | − | 0.0693989i | \(-0.0221081\pi\) | |||||||
\(462\) | −0.500000 | + | 0.866025i | −0.0232621 | + | 0.0402911i | ||||
\(463\) | 1.00000 | 0.0464739 | 0.0232370 | − | 0.999730i | \(-0.492603\pi\) | ||||
0.0232370 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(464\) | −4.50000 | + | 7.79423i | −0.208907 | + | 0.361838i | ||||
\(465\) | 2.00000 | + | 3.46410i | 0.0927478 | + | 0.160644i | ||||
\(466\) | 9.00000 | + | 15.5885i | 0.416917 | + | 0.722121i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 1.00000 | − | 3.46410i | 0.0462250 | − | 0.160128i | ||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | −7.00000 | − | 12.1244i | −0.322886 | − | 0.559255i | ||||
\(471\) | 1.00000 | + | 1.73205i | 0.0460776 | + | 0.0798087i | ||||
\(472\) | 5.00000 | − | 8.66025i | 0.230144 | − | 0.398621i | ||||
\(473\) | 2.00000 | 0.0919601 | ||||||||
\(474\) | −5.50000 | + | 9.52628i | −0.252623 | + | 0.437557i | ||||
\(475\) | 0.500000 | − | 0.866025i | 0.0229416 | − | 0.0397360i | ||||
\(476\) | 1.00000 | 0.0458349 | ||||||||
\(477\) | 0.500000 | − | 0.866025i | 0.0228934 | − | 0.0396526i | ||||
\(478\) | −6.00000 | − | 10.3923i | −0.274434 | − | 0.475333i | ||||
\(479\) | −5.50000 | − | 9.52628i | −0.251301 | − | 0.435267i | 0.712583 | − | 0.701588i | \(-0.247525\pi\) |
−0.963884 | + | 0.266321i | \(0.914192\pi\) | |||||||
\(480\) | 2.00000 | 0.0912871 | ||||||||
\(481\) | −2.00000 | + | 6.92820i | −0.0911922 | + | 0.315899i | ||||
\(482\) | −16.0000 | −0.728780 | ||||||||
\(483\) | 3.00000 | + | 5.19615i | 0.136505 | + | 0.236433i | ||||
\(484\) | 5.00000 | + | 8.66025i | 0.227273 | + | 0.393648i | ||||
\(485\) | 14.0000 | − | 24.2487i | 0.635707 | − | 1.10108i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 14.5000 | − | 25.1147i | 0.657058 | − | 1.13806i | −0.324316 | − | 0.945949i | \(-0.605134\pi\) |
0.981374 | − | 0.192109i | \(-0.0615326\pi\) | |||||||
\(488\) | −5.50000 | + | 9.52628i | −0.248973 | + | 0.431234i | ||||
\(489\) | −2.00000 | −0.0904431 | ||||||||
\(490\) | 1.00000 | − | 1.73205i | 0.0451754 | − | 0.0782461i | ||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 2.50000 | + | 4.33013i | 0.112709 | + | 0.195217i | ||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | −2.50000 | − | 2.59808i | −0.112480 | − | 0.116893i | ||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | −1.00000 | − | 1.73205i | −0.0449013 | − | 0.0777714i | ||||
\(497\) | −4.00000 | − | 6.92820i | −0.179425 | − | 0.310772i | ||||
\(498\) | 6.00000 | − | 10.3923i | 0.268866 | − | 0.465690i | ||||
\(499\) | −30.0000 | −1.34298 | −0.671492 | − | 0.741012i | \(-0.734346\pi\) | ||||
−0.671492 | + | 0.741012i | \(0.734346\pi\) | |||||||
\(500\) | 6.00000 | − | 10.3923i | 0.268328 | − | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.00000 | 0.357057 | ||||||||
\(503\) | 4.00000 | − | 6.92820i | 0.178351 | − | 0.308913i | −0.762965 | − | 0.646440i | \(-0.776257\pi\) |
0.941316 | + | 0.337527i | \(0.109590\pi\) | |||||||
\(504\) | −0.500000 | − | 0.866025i | −0.0222718 | − | 0.0385758i | ||||
\(505\) | 2.00000 | + | 3.46410i | 0.0889988 | + | 0.154150i | ||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | −11.5000 | + | 6.06218i | −0.510733 | + | 0.269231i | ||||
\(508\) | −12.0000 | −0.532414 | ||||||||
\(509\) | 6.00000 | + | 10.3923i | 0.265945 | + | 0.460631i | 0.967811 | − | 0.251679i | \(-0.0809826\pi\) |
−0.701866 | + | 0.712309i | \(0.747649\pi\) | |||||||
\(510\) | 1.00000 | + | 1.73205i | 0.0442807 | + | 0.0766965i | ||||
\(511\) | 4.00000 | − | 6.92820i | 0.176950 | − | 0.306486i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0.500000 | − | 0.866025i | 0.0220755 | − | 0.0382360i | ||||
\(514\) | −4.50000 | + | 7.79423i | −0.198486 | + | 0.343789i | ||||
\(515\) | −28.0000 | −1.23383 | ||||||||
\(516\) | −1.00000 | + | 1.73205i | −0.0440225 | + | 0.0762493i | ||||
\(517\) | −3.50000 | − | 6.06218i | −0.153930 | − | 0.266614i | ||||
\(518\) | 1.00000 | + | 1.73205i | 0.0439375 | + | 0.0761019i | ||||
\(519\) | −8.00000 | −0.351161 | ||||||||
\(520\) | −5.00000 | − | 5.19615i | −0.219265 | − | 0.227866i | ||||
\(521\) | 19.0000 | 0.832405 | 0.416203 | − | 0.909272i | \(-0.363361\pi\) | ||||
0.416203 | + | 0.909272i | \(0.363361\pi\) | |||||||
\(522\) | 4.50000 | + | 7.79423i | 0.196960 | + | 0.341144i | ||||
\(523\) | 5.50000 | + | 9.52628i | 0.240498 | + | 0.416555i | 0.960856 | − | 0.277047i | \(-0.0893559\pi\) |
−0.720358 | + | 0.693602i | \(0.756023\pi\) | |||||||
\(524\) | 4.00000 | − | 6.92820i | 0.174741 | − | 0.302660i | ||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | −14.0000 | + | 24.2487i | −0.610429 | + | 1.05729i | ||||
\(527\) | 1.00000 | − | 1.73205i | 0.0435607 | − | 0.0754493i | ||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −1.00000 | − | 1.73205i | −0.0434372 | − | 0.0752355i | ||||
\(531\) | −5.00000 | − | 8.66025i | −0.216982 | − | 0.375823i | ||||
\(532\) | −1.00000 | −0.0433555 | ||||||||
\(533\) | 5.00000 | − | 17.3205i | 0.216574 | − | 0.750234i | ||||
\(534\) | 11.0000 | 0.476017 | ||||||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | −16.0000 | −0.689809 | ||||||||
\(539\) | 0.500000 | − | 0.866025i | 0.0215365 | − | 0.0373024i | ||||
\(540\) | 1.00000 | − | 1.73205i | 0.0430331 | − | 0.0745356i | ||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | 1.00000 | − | 1.73205i | 0.0429537 | − | 0.0743980i | ||||
\(543\) | −9.50000 | − | 16.4545i | −0.407684 | − | 0.706129i | ||||
\(544\) | −0.500000 | − | 0.866025i | −0.0214373 | − | 0.0371305i | ||||
\(545\) | 32.0000 | 1.37073 | ||||||||
\(546\) | −1.00000 | + | 3.46410i | −0.0427960 | + | 0.148250i | ||||
\(547\) | 32.0000 | 1.36822 | 0.684111 | − | 0.729378i | \(-0.260191\pi\) | ||||
0.684111 | + | 0.729378i | \(0.260191\pi\) | |||||||
\(548\) | 5.00000 | + | 8.66025i | 0.213589 | + | 0.369948i | ||||
\(549\) | 5.50000 | + | 9.52628i | 0.234734 | + | 0.406572i | ||||
\(550\) | 0.500000 | − | 0.866025i | 0.0213201 | − | 0.0369274i | ||||
\(551\) | 9.00000 | 0.383413 | ||||||||
\(552\) | 3.00000 | − | 5.19615i | 0.127688 | − | 0.221163i | ||||
\(553\) | 5.50000 | − | 9.52628i | 0.233884 | − | 0.405099i | ||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | −2.00000 | + | 3.46410i | −0.0848953 | + | 0.147043i | ||||
\(556\) | 4.50000 | + | 7.79423i | 0.190843 | + | 0.330549i | ||||
\(557\) | 1.50000 | + | 2.59808i | 0.0635570 | + | 0.110084i | 0.896053 | − | 0.443947i | \(-0.146422\pi\) |
−0.832496 | + | 0.554031i | \(0.813089\pi\) | |||||||
\(558\) | −2.00000 | −0.0846668 | ||||||||
\(559\) | 7.00000 | − | 1.73205i | 0.296068 | − | 0.0732579i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0.500000 | + | 0.866025i | 0.0211100 | + | 0.0365636i | ||||
\(562\) | −10.0000 | − | 17.3205i | −0.421825 | − | 0.730622i | ||||
\(563\) | −17.0000 | + | 29.4449i | −0.716465 | + | 1.24095i | 0.245927 | + | 0.969288i | \(0.420908\pi\) |
−0.962392 | + | 0.271665i | \(0.912426\pi\) | |||||||
\(564\) | 7.00000 | 0.294753 | ||||||||
\(565\) | 6.00000 | − | 10.3923i | 0.252422 | − | 0.437208i | ||||
\(566\) | −14.0000 | + | 24.2487i | −0.588464 | + | 1.01925i | ||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −4.00000 | + | 6.92820i | −0.167836 | + | 0.290701i | ||||
\(569\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(570\) | −1.00000 | − | 1.73205i | −0.0418854 | − | 0.0725476i | ||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | −2.50000 | − | 2.59808i | −0.104530 | − | 0.108631i | ||||
\(573\) | −4.00000 | −0.167102 | ||||||||
\(574\) | −2.50000 | − | 4.33013i | −0.104348 | − | 0.180736i | ||||
\(575\) | −3.00000 | − | 5.19615i | −0.125109 | − | 0.216695i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 12.0000 | 0.499567 | 0.249783 | − | 0.968302i | \(-0.419641\pi\) | ||||
0.249783 | + | 0.968302i | \(0.419641\pi\) | |||||||
\(578\) | −8.00000 | + | 13.8564i | −0.332756 | + | 0.576351i | ||||
\(579\) | −5.50000 | + | 9.52628i | −0.228572 | + | 0.395899i | ||||
\(580\) | 18.0000 | 0.747409 | ||||||||
\(581\) | −6.00000 | + | 10.3923i | −0.248922 | + | 0.431145i | ||||
\(582\) | 7.00000 | + | 12.1244i | 0.290159 | + | 0.502571i | ||||
\(583\) | −0.500000 | − | 0.866025i | −0.0207079 | − | 0.0358671i | ||||
\(584\) | −8.00000 | −0.331042 | ||||||||
\(585\) | −7.00000 | + | 1.73205i | −0.289414 | + | 0.0716115i | ||||
\(586\) | −20.0000 | −0.826192 | ||||||||
\(587\) | 13.0000 | + | 22.5167i | 0.536567 | + | 0.929362i | 0.999086 | + | 0.0427523i | \(0.0136126\pi\) |
−0.462518 | + | 0.886610i | \(0.653054\pi\) | |||||||
\(588\) | 0.500000 | + | 0.866025i | 0.0206197 | + | 0.0357143i | ||||
\(589\) | −1.00000 | + | 1.73205i | −0.0412043 | + | 0.0713679i | ||||
\(590\) | −20.0000 | −0.823387 | ||||||||
\(591\) | 13.5000 | − | 23.3827i | 0.555316 | − | 0.961835i | ||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | −3.00000 | −0.123195 | −0.0615976 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615976 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(594\) | 0.500000 | − | 0.866025i | 0.0205152 | − | 0.0355335i | ||||
\(595\) | −1.00000 | − | 1.73205i | −0.0409960 | − | 0.0710072i | ||||
\(596\) | −3.00000 | − | 5.19615i | −0.122885 | − | 0.212843i | ||||
\(597\) | −10.0000 | −0.409273 | ||||||||
\(598\) | −21.0000 | + | 5.19615i | −0.858754 | + | 0.212486i | ||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0.500000 | + | 0.866025i | 0.0204124 | + | 0.0353553i | ||||
\(601\) | −1.00000 | − | 1.73205i | −0.0407909 | − | 0.0706518i | 0.844909 | − | 0.534910i | \(-0.179654\pi\) |
−0.885700 | + | 0.464258i | \(0.846321\pi\) | |||||||
\(602\) | 1.00000 | − | 1.73205i | 0.0407570 | − | 0.0705931i | ||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 1.50000 | − | 2.59808i | 0.0610341 | − | 0.105714i | ||||
\(605\) | 10.0000 | − | 17.3205i | 0.406558 | − | 0.704179i | ||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | 23.0000 | − | 39.8372i | 0.933541 | − | 1.61694i | 0.156326 | − | 0.987705i | \(-0.450035\pi\) |
0.777215 | − | 0.629235i | \(-0.216632\pi\) | |||||||
\(608\) | 0.500000 | + | 0.866025i | 0.0202777 | + | 0.0351220i | ||||
\(609\) | −4.50000 | − | 7.79423i | −0.182349 | − | 0.315838i | ||||
\(610\) | 22.0000 | 0.890754 | ||||||||
\(611\) | −17.5000 | − | 18.1865i | −0.707974 | − | 0.735748i | ||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −14.0000 | − | 24.2487i | −0.565455 | − | 0.979396i | −0.997007 | − | 0.0773084i | \(-0.975367\pi\) |
0.431553 | − | 0.902088i | \(-0.357966\pi\) | |||||||
\(614\) | 9.50000 | + | 16.4545i | 0.383389 | + | 0.664049i | ||||
\(615\) | 5.00000 | − | 8.66025i | 0.201619 | − | 0.349215i | ||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | 6.00000 | − | 10.3923i | 0.241551 | − | 0.418378i | −0.719605 | − | 0.694383i | \(-0.755677\pi\) |
0.961156 | + | 0.276005i | \(0.0890106\pi\) | |||||||
\(618\) | 7.00000 | − | 12.1244i | 0.281581 | − | 0.487713i | ||||
\(619\) | 11.0000 | 0.442127 | 0.221064 | − | 0.975259i | \(-0.429047\pi\) | ||||
0.221064 | + | 0.975259i | \(0.429047\pi\) | |||||||
\(620\) | −2.00000 | + | 3.46410i | −0.0803219 | + | 0.139122i | ||||
\(621\) | −3.00000 | − | 5.19615i | −0.120386 | − | 0.208514i | ||||
\(622\) | −7.50000 | − | 12.9904i | −0.300723 | − | 0.520867i | ||||
\(623\) | −11.0000 | −0.440706 | ||||||||
\(624\) | 3.50000 | − | 0.866025i | 0.140112 | − | 0.0346688i | ||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −6.00000 | − | 10.3923i | −0.239808 | − | 0.415360i | ||||
\(627\) | −0.500000 | − | 0.866025i | −0.0199681 | − | 0.0345857i | ||||
\(628\) | −1.00000 | + | 1.73205i | −0.0399043 | + | 0.0691164i | ||||
\(629\) | 2.00000 | 0.0797452 | ||||||||
\(630\) | −1.00000 | + | 1.73205i | −0.0398410 | + | 0.0690066i | ||||
\(631\) | 16.5000 | − | 28.5788i | 0.656855 | − | 1.13771i | −0.324571 | − | 0.945861i | \(-0.605220\pi\) |
0.981425 | − | 0.191844i | \(-0.0614468\pi\) | |||||||
\(632\) | −11.0000 | −0.437557 | ||||||||
\(633\) | −3.00000 | + | 5.19615i | −0.119239 | + | 0.206529i | ||||
\(634\) | 15.0000 | + | 25.9808i | 0.595726 | + | 1.03183i | ||||
\(635\) | 12.0000 | + | 20.7846i | 0.476205 | + | 0.824812i | ||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | 1.00000 | − | 3.46410i | 0.0396214 | − | 0.137253i | ||||
\(638\) | 9.00000 | 0.356313 | ||||||||
\(639\) | 4.00000 | + | 6.92820i | 0.158238 | + | 0.274075i | ||||
\(640\) | 1.00000 | + | 1.73205i | 0.0395285 | + | 0.0684653i | ||||
\(641\) | −1.00000 | + | 1.73205i | −0.0394976 | + | 0.0684119i | −0.885098 | − | 0.465404i | \(-0.845909\pi\) |
0.845601 | + | 0.533816i | \(0.179242\pi\) | |||||||
\(642\) | 3.00000 | 0.118401 | ||||||||
\(643\) | 21.5000 | − | 37.2391i | 0.847877 | − | 1.46857i | −0.0352216 | − | 0.999380i | \(-0.511214\pi\) |
0.883099 | − | 0.469187i | \(-0.155453\pi\) | |||||||
\(644\) | −3.00000 | + | 5.19615i | −0.118217 | + | 0.204757i | ||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | −0.500000 | + | 0.866025i | −0.0196722 | + | 0.0340733i | ||||
\(647\) | −19.5000 | − | 33.7750i | −0.766624 | − | 1.32783i | −0.939384 | − | 0.342868i | \(-0.888602\pi\) |
0.172760 | − | 0.984964i | \(-0.444732\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −10.0000 | −0.392534 | ||||||||
\(650\) | 1.00000 | − | 3.46410i | 0.0392232 | − | 0.135873i | ||||
\(651\) | 2.00000 | 0.0783862 | ||||||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | 24.5000 | + | 42.4352i | 0.958759 | + | 1.66062i | 0.725521 | + | 0.688200i | \(0.241599\pi\) |
0.233238 | + | 0.972420i | \(0.425068\pi\) | |||||||
\(654\) | −8.00000 | + | 13.8564i | −0.312825 | + | 0.541828i | ||||
\(655\) | −16.0000 | −0.625172 | ||||||||
\(656\) | −2.50000 | + | 4.33013i | −0.0976086 | + | 0.169063i | ||||
\(657\) | −4.00000 | + | 6.92820i | −0.156055 | + | 0.270295i | ||||
\(658\) | −7.00000 | −0.272888 | ||||||||
\(659\) | −4.50000 | + | 7.79423i | −0.175295 | + | 0.303620i | −0.940263 | − | 0.340448i | \(-0.889421\pi\) |
0.764968 | + | 0.644068i | \(0.222755\pi\) | |||||||
\(660\) | −1.00000 | − | 1.73205i | −0.0389249 | − | 0.0674200i | ||||
\(661\) | 13.0000 | + | 22.5167i | 0.505641 | + | 0.875797i | 0.999979 | + | 0.00652642i | \(0.00207744\pi\) |
−0.494337 | + | 0.869270i | \(0.664589\pi\) | |||||||
\(662\) | −26.0000 | −1.01052 | ||||||||
\(663\) | 2.50000 | + | 2.59808i | 0.0970920 | + | 0.100901i | ||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 1.00000 | + | 1.73205i | 0.0387783 | + | 0.0671660i | ||||
\(666\) | −1.00000 | − | 1.73205i | −0.0387492 | − | 0.0671156i | ||||
\(667\) | 27.0000 | − | 46.7654i | 1.04544 | − | 1.81076i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.0000 | − | 17.3205i | 0.386622 | − | 0.669650i | ||||
\(670\) | 2.00000 | − | 3.46410i | 0.0772667 | − | 0.133830i | ||||
\(671\) | 11.0000 | 0.424650 | ||||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | 20.5000 | + | 35.5070i | 0.790217 | + | 1.36870i | 0.925832 | + | 0.377934i | \(0.123365\pi\) |
−0.135615 | + | 0.990762i | \(0.543301\pi\) | |||||||
\(674\) | −16.5000 | − | 28.5788i | −0.635556 | − | 1.10082i | ||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | −4.00000 | −0.153732 | −0.0768662 | − | 0.997041i | \(-0.524491\pi\) | ||||
−0.0768662 | + | 0.997041i | \(0.524491\pi\) | |||||||
\(678\) | 3.00000 | + | 5.19615i | 0.115214 | + | 0.199557i | ||||
\(679\) | −7.00000 | − | 12.1244i | −0.268635 | − | 0.465290i | ||||
\(680\) | −1.00000 | + | 1.73205i | −0.0383482 | + | 0.0664211i | ||||
\(681\) | −2.00000 | −0.0766402 | ||||||||
\(682\) | −1.00000 | + | 1.73205i | −0.0382920 | + | 0.0663237i | ||||
\(683\) | 2.00000 | − | 3.46410i | 0.0765279 | − | 0.132550i | −0.825222 | − | 0.564809i | \(-0.808950\pi\) |
0.901750 | + | 0.432259i | \(0.142283\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 10.0000 | − | 17.3205i | 0.382080 | − | 0.661783i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | −11.5000 | − | 19.9186i | −0.438752 | − | 0.759941i | ||||
\(688\) | −2.00000 | −0.0762493 | ||||||||
\(689\) | −2.50000 | − | 2.59808i | −0.0952424 | − | 0.0989788i | ||||
\(690\) | −12.0000 | −0.456832 | ||||||||
\(691\) | 16.0000 | + | 27.7128i | 0.608669 | + | 1.05425i | 0.991460 | + | 0.130410i | \(0.0416295\pi\) |
−0.382791 | + | 0.923835i | \(0.625037\pi\) | |||||||
\(692\) | −4.00000 | − | 6.92820i | −0.152057 | − | 0.263371i | ||||
\(693\) | −0.500000 | + | 0.866025i | −0.0189934 | + | 0.0328976i | ||||
\(694\) | 3.00000 | 0.113878 | ||||||||
\(695\) | 9.00000 | − | 15.5885i | 0.341389 | − | 0.591304i | ||||
\(696\) | −4.50000 | + | 7.79423i | −0.170572 | + | 0.295439i | ||||
\(697\) | −5.00000 | −0.189389 | ||||||||
\(698\) | −3.00000 | + | 5.19615i | −0.113552 | + | 0.196677i | ||||
\(699\) | 9.00000 | + | 15.5885i | 0.340411 | + | 0.589610i | ||||
\(700\) | −0.500000 | − | 0.866025i | −0.0188982 | − | 0.0327327i | ||||
\(701\) | 1.00000 | 0.0377695 | 0.0188847 | − | 0.999822i | \(-0.493988\pi\) | ||||
0.0188847 | + | 0.999822i | \(0.493988\pi\) | |||||||
\(702\) | 1.00000 | − | 3.46410i | 0.0377426 | − | 0.130744i | ||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | −7.00000 | − | 12.1244i | −0.263635 | − | 0.456630i | ||||
\(706\) | 13.0000 | − | 22.5167i | 0.489261 | − | 0.847426i | ||||
\(707\) | 2.00000 | 0.0752177 | ||||||||
\(708\) | 5.00000 | − | 8.66025i | 0.187912 | − | 0.325472i | ||||
\(709\) | −12.0000 | + | 20.7846i | −0.450669 | + | 0.780582i | −0.998428 | − | 0.0560542i | \(-0.982148\pi\) |
0.547758 | + | 0.836637i | \(0.315481\pi\) | |||||||
\(710\) | 16.0000 | 0.600469 | ||||||||
\(711\) | −5.50000 | + | 9.52628i | −0.206266 | + | 0.357263i | ||||
\(712\) | 5.50000 | + | 9.52628i | 0.206121 | + | 0.357012i | ||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | 1.00000 | 0.0374241 | ||||||||
\(715\) | −2.00000 | + | 6.92820i | −0.0747958 | + | 0.259100i | ||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −6.00000 | − | 10.3923i | −0.224074 | − | 0.388108i | ||||
\(718\) | −15.0000 | − | 25.9808i | −0.559795 | − | 0.969593i | ||||
\(719\) | −7.50000 | + | 12.9904i | −0.279703 | + | 0.484459i | −0.971311 | − | 0.237814i | \(-0.923569\pi\) |
0.691608 | + | 0.722273i | \(0.256903\pi\) | |||||||
\(720\) | 2.00000 | 0.0745356 | ||||||||
\(721\) | −7.00000 | + | 12.1244i | −0.260694 | + | 0.451535i | ||||
\(722\) | −9.00000 | + | 15.5885i | −0.334945 | + | 0.580142i | ||||
\(723\) | −16.0000 | −0.595046 | ||||||||
\(724\) | 9.50000 | − | 16.4545i | 0.353065 | − | 0.611526i | ||||
\(725\) | 4.50000 | + | 7.79423i | 0.167126 | + | 0.289470i | ||||
\(726\) | 5.00000 | + | 8.66025i | 0.185567 | + | 0.321412i | ||||
\(727\) | −52.0000 | −1.92857 | −0.964287 | − | 0.264861i | \(-0.914674\pi\) | ||||
−0.964287 | + | 0.264861i | \(0.914674\pi\) | |||||||
\(728\) | −3.50000 | + | 0.866025i | −0.129719 | + | 0.0320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.00000 | + | 13.8564i | 0.296093 | + | 0.512849i | ||||
\(731\) | −1.00000 | − | 1.73205i | −0.0369863 | − | 0.0640622i | ||||
\(732\) | −5.50000 | + | 9.52628i | −0.203286 | + | 0.352101i | ||||
\(733\) | 43.0000 | 1.58824 | 0.794121 | − | 0.607760i | \(-0.207932\pi\) | ||||
0.794121 | + | 0.607760i | \(0.207932\pi\) | |||||||
\(734\) | −7.00000 | + | 12.1244i | −0.258375 | + | 0.447518i | ||||
\(735\) | 1.00000 | − | 1.73205i | 0.0368856 | − | 0.0638877i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 1.00000 | − | 1.73205i | 0.0368355 | − | 0.0638009i | ||||
\(738\) | 2.50000 | + | 4.33013i | 0.0920263 | + | 0.159394i | ||||
\(739\) | 19.0000 | + | 32.9090i | 0.698926 | + | 1.21058i | 0.968839 | + | 0.247691i | \(0.0796718\pi\) |
−0.269913 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | −2.50000 | − | 2.59808i | −0.0918398 | − | 0.0954427i | ||||
\(742\) | −1.00000 | −0.0367112 | ||||||||
\(743\) | 21.0000 | + | 36.3731i | 0.770415 | + | 1.33440i | 0.937336 | + | 0.348428i | \(0.113284\pi\) |
−0.166920 | + | 0.985970i | \(0.553382\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | −6.00000 | + | 10.3923i | −0.219823 | + | 0.380745i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | −0.500000 | + | 0.866025i | −0.0182818 | + | 0.0316650i | ||||
\(749\) | −3.00000 | −0.109618 | ||||||||
\(750\) | 6.00000 | − | 10.3923i | 0.219089 | − | 0.379473i | ||||
\(751\) | −11.5000 | − | 19.9186i | −0.419641 | − | 0.726839i | 0.576262 | − | 0.817265i | \(-0.304511\pi\) |
−0.995903 | + | 0.0904254i | \(0.971177\pi\) | |||||||
\(752\) | 3.50000 | + | 6.06218i | 0.127632 | + | 0.221065i | ||||
\(753\) | 8.00000 | 0.291536 | ||||||||
\(754\) | 31.5000 | − | 7.79423i | 1.14716 | − | 0.283849i | ||||
\(755\) | −6.00000 | −0.218362 | ||||||||
\(756\) | −0.500000 | − | 0.866025i | −0.0181848 | − | 0.0314970i | ||||
\(757\) | 18.0000 | + | 31.1769i | 0.654221 | + | 1.13314i | 0.982088 | + | 0.188420i | \(0.0603368\pi\) |
−0.327867 | + | 0.944724i | \(0.606330\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.00000 | −0.217786 | ||||||||
\(760\) | 1.00000 | − | 1.73205i | 0.0362738 | − | 0.0628281i | ||||
\(761\) | −5.00000 | + | 8.66025i | −0.181250 | + | 0.313934i | −0.942306 | − | 0.334752i | \(-0.891348\pi\) |
0.761057 | + | 0.648686i | \(0.224681\pi\) | |||||||
\(762\) | −12.0000 | −0.434714 | ||||||||
\(763\) | 8.00000 | − | 13.8564i | 0.289619 | − | 0.501636i | ||||
\(764\) | −2.00000 | − | 3.46410i | −0.0723575 | − | 0.125327i | ||||
\(765\) | 1.00000 | + | 1.73205i | 0.0361551 | + | 0.0626224i | ||||
\(766\) | −9.00000 | −0.325183 | ||||||||
\(767\) | −35.0000 | + | 8.66025i | −1.26378 | + | 0.312704i | ||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 23.0000 | + | 39.8372i | 0.829401 | + | 1.43657i | 0.898509 | + | 0.438956i | \(0.144652\pi\) |
−0.0691074 | + | 0.997609i | \(0.522015\pi\) | |||||||
\(770\) | 1.00000 | + | 1.73205i | 0.0360375 | + | 0.0624188i | ||||
\(771\) | −4.50000 | + | 7.79423i | −0.162064 | + | 0.280702i | ||||
\(772\) | −11.0000 | −0.395899 | ||||||||
\(773\) | −27.0000 | + | 46.7654i | −0.971123 | + | 1.68203i | −0.278944 | + | 0.960307i | \(0.589984\pi\) |
−0.692179 | + | 0.721726i | \(0.743349\pi\) | |||||||
\(774\) | −1.00000 | + | 1.73205i | −0.0359443 | + | 0.0622573i | ||||
\(775\) | −2.00000 | −0.0718421 | ||||||||
\(776\) | −7.00000 | + | 12.1244i | −0.251285 | + | 0.435239i | ||||
\(777\) | 1.00000 | + | 1.73205i | 0.0358748 | + | 0.0621370i | ||||
\(778\) | 11.0000 | + | 19.0526i | 0.394369 | + | 0.683067i | ||||
\(779\) | 5.00000 | 0.179144 | ||||||||
\(780\) | −5.00000 | − | 5.19615i | −0.179029 | − | 0.186052i | ||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 3.00000 | + | 5.19615i | 0.107280 | + | 0.185814i | ||||
\(783\) | 4.50000 | + | 7.79423i | 0.160817 | + | 0.278543i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | 4.00000 | 0.142766 | ||||||||
\(786\) | 4.00000 | − | 6.92820i | 0.142675 | − | 0.247121i | ||||
\(787\) | 14.5000 | − | 25.1147i | 0.516869 | − | 0.895244i | −0.482939 | − | 0.875654i | \(-0.660431\pi\) |
0.999808 | − | 0.0195896i | \(-0.00623598\pi\) | |||||||
\(788\) | 27.0000 | 0.961835 | ||||||||
\(789\) | −14.0000 | + | 24.2487i | −0.498413 | + | 0.863277i | ||||
\(790\) | 11.0000 | + | 19.0526i | 0.391362 | + | 0.677860i | ||||
\(791\) | −3.00000 | − | 5.19615i | −0.106668 | − | 0.184754i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | 38.5000 | − | 9.52628i | 1.36718 | − | 0.338288i | ||||
\(794\) | 21.0000 | 0.745262 | ||||||||
\(795\) | −1.00000 | − | 1.73205i | −0.0354663 | − | 0.0614295i | ||||
\(796\) | −5.00000 | − | 8.66025i | −0.177220 | − | 0.306955i | ||||
\(797\) | −26.0000 | + | 45.0333i | −0.920967 | + | 1.59516i | −0.123045 | + | 0.992401i | \(0.539266\pi\) |
−0.797922 | + | 0.602761i | \(0.794067\pi\) | |||||||
\(798\) | −1.00000 | −0.0353996 | ||||||||
\(799\) | −3.50000 | + | 6.06218i | −0.123821 | + | 0.214464i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 11.0000 | 0.388666 | ||||||||
\(802\) | 3.00000 | − | 5.19615i | 0.105934 | − | 0.183483i | ||||
\(803\) | 4.00000 | + | 6.92820i | 0.141157 | + | 0.244491i | ||||
\(804\) | 1.00000 | + | 1.73205i | 0.0352673 | + | 0.0610847i | ||||
\(805\) | 12.0000 | 0.422944 | ||||||||
\(806\) | −2.00000 | + | 6.92820i | −0.0704470 | + | 0.244036i | ||||
\(807\) | −16.0000 | −0.563227 | ||||||||
\(808\) | −1.00000 | − | 1.73205i | −0.0351799 | − | 0.0609333i | ||||
\(809\) | 14.0000 | + | 24.2487i | 0.492214 | + | 0.852539i | 0.999960 | − | 0.00896753i | \(-0.00285449\pi\) |
−0.507746 | + | 0.861507i | \(0.669521\pi\) | |||||||
\(810\) | 1.00000 | − | 1.73205i | 0.0351364 | − | 0.0608581i | ||||
\(811\) | −36.0000 | −1.26413 | −0.632065 | − | 0.774915i | \(-0.717793\pi\) | ||||
−0.632065 | + | 0.774915i | \(0.717793\pi\) | |||||||
\(812\) | 4.50000 | − | 7.79423i | 0.157919 | − | 0.273524i | ||||
\(813\) | 1.00000 | − | 1.73205i | 0.0350715 | − | 0.0607457i | ||||
\(814\) | −2.00000 | −0.0701000 | ||||||||
\(815\) | −2.00000 | + | 3.46410i | −0.0700569 | + | 0.121342i | ||||
\(816\) | −0.500000 | − | 0.866025i | −0.0175035 | − | 0.0303170i | ||||
\(817\) | 1.00000 | + | 1.73205i | 0.0349856 | + | 0.0605968i | ||||
\(818\) | −20.0000 | −0.699284 | ||||||||
\(819\) | −1.00000 | + | 3.46410i | −0.0349428 | + | 0.121046i | ||||
\(820\) | 10.0000 | 0.349215 | ||||||||
\(821\) | 22.5000 | + | 38.9711i | 0.785255 | + | 1.36010i | 0.928846 | + | 0.370465i | \(0.120802\pi\) |
−0.143591 | + | 0.989637i | \(0.545865\pi\) | |||||||
\(822\) | 5.00000 | + | 8.66025i | 0.174395 | + | 0.302061i | ||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 0.500000 | − | 0.866025i | 0.0174078 | − | 0.0301511i | ||||
\(826\) | −5.00000 | + | 8.66025i | −0.173972 | + | 0.301329i | ||||
\(827\) | 16.0000 | 0.556375 | 0.278187 | − | 0.960527i | \(-0.410266\pi\) | ||||
0.278187 | + | 0.960527i | \(0.410266\pi\) | |||||||
\(828\) | 3.00000 | − | 5.19615i | 0.104257 | − | 0.180579i | ||||
\(829\) | −9.50000 | − | 16.4545i | −0.329949 | − | 0.571488i | 0.652553 | − | 0.757743i | \(-0.273698\pi\) |
−0.982501 | + | 0.186256i | \(0.940365\pi\) | |||||||
\(830\) | −12.0000 | − | 20.7846i | −0.416526 | − | 0.721444i | ||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 2.50000 | + | 2.59808i | 0.0866719 | + | 0.0900721i | ||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 4.50000 | + | 7.79423i | 0.155822 | + | 0.269892i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.500000 | − | 0.866025i | 0.0172929 | − | 0.0299521i | ||||
\(837\) | −2.00000 | −0.0691301 | ||||||||
\(838\) | −10.0000 | + | 17.3205i | −0.345444 | + | 0.598327i | ||||
\(839\) | −4.00000 | + | 6.92820i | −0.138095 | + | 0.239188i | −0.926776 | − | 0.375615i | \(-0.877431\pi\) |
0.788680 | + | 0.614804i | \(0.210765\pi\) | |||||||
\(840\) | −2.00000 | −0.0690066 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | −13.0000 | − | 22.5167i | −0.448010 | − | 0.775975i | ||||
\(843\) | −10.0000 | − | 17.3205i | −0.344418 | − | 0.596550i | ||||
\(844\) | −6.00000 | −0.206529 | ||||||||
\(845\) | −1.00000 | + | 25.9808i | −0.0344010 | + | 0.893765i | ||||
\(846\) | 7.00000 | 0.240665 | ||||||||
\(847\) | −5.00000 | − | 8.66025i | −0.171802 | − | 0.297570i | ||||
\(848\) | 0.500000 | + | 0.866025i | 0.0171701 | + | 0.0297394i | ||||
\(849\) | −14.0000 | + | 24.2487i | −0.480479 | + | 0.832214i | ||||
\(850\) | −1.00000 | −0.0342997 | ||||||||
\(851\) | −6.00000 | + | 10.3923i | −0.205677 | + | 0.356244i | ||||
\(852\) | −4.00000 | + | 6.92820i | −0.137038 | + | 0.237356i | ||||
\(853\) | −53.0000 | −1.81469 | −0.907343 | − | 0.420392i | \(-0.861893\pi\) | ||||
−0.907343 | + | 0.420392i | \(0.861893\pi\) | |||||||
\(854\) | 5.50000 | − | 9.52628i | 0.188206 | − | 0.325983i | ||||
\(855\) | −1.00000 | − | 1.73205i | −0.0341993 | − | 0.0592349i | ||||
\(856\) | 1.50000 | + | 2.59808i | 0.0512689 | + | 0.0888004i | ||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | −2.50000 | − | 2.59808i | −0.0853486 | − | 0.0886969i | ||||
\(859\) | 49.0000 | 1.67186 | 0.835929 | − | 0.548837i | \(-0.184929\pi\) | ||||
0.835929 | + | 0.548837i | \(0.184929\pi\) | |||||||
\(860\) | 2.00000 | + | 3.46410i | 0.0681994 | + | 0.118125i | ||||
\(861\) | −2.50000 | − | 4.33013i | −0.0851998 | − | 0.147570i | ||||
\(862\) | 14.0000 | − | 24.2487i | 0.476842 | − | 0.825914i | ||||
\(863\) | −50.0000 | −1.70202 | −0.851010 | − | 0.525150i | \(-0.824009\pi\) | ||||
−0.851010 | + | 0.525150i | \(0.824009\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −8.00000 | + | 13.8564i | −0.272008 | + | 0.471132i | ||||
\(866\) | 18.0000 | 0.611665 | ||||||||
\(867\) | −8.00000 | + | 13.8564i | −0.271694 | + | 0.470588i | ||||
\(868\) | 1.00000 | + | 1.73205i | 0.0339422 | + | 0.0587896i | ||||
\(869\) | 5.50000 | + | 9.52628i | 0.186575 | + | 0.323157i | ||||
\(870\) | 18.0000 | 0.610257 | ||||||||
\(871\) | 2.00000 | − | 6.92820i | 0.0677674 | − | 0.234753i | ||||
\(872\) | −16.0000 | −0.541828 | ||||||||
\(873\) | 7.00000 | + | 12.1244i | 0.236914 | + | 0.410347i | ||||
\(874\) | −3.00000 | − | 5.19615i | −0.101477 | − | 0.175762i | ||||
\(875\) | −6.00000 | + | 10.3923i | −0.202837 | + | 0.351324i | ||||
\(876\) | −8.00000 | −0.270295 | ||||||||
\(877\) | 10.0000 | − | 17.3205i | 0.337676 | − | 0.584872i | −0.646319 | − | 0.763067i | \(-0.723693\pi\) |
0.983995 | + | 0.178195i | \(0.0570259\pi\) | |||||||
\(878\) | −10.0000 | + | 17.3205i | −0.337484 | + | 0.584539i | ||||
\(879\) | −20.0000 | −0.674583 | ||||||||
\(880\) | 1.00000 | − | 1.73205i | 0.0337100 | − | 0.0583874i | ||||
\(881\) | −1.00000 | − | 1.73205i | −0.0336909 | − | 0.0583543i | 0.848688 | − | 0.528893i | \(-0.177393\pi\) |
−0.882379 | + | 0.470539i | \(0.844059\pi\) | |||||||
\(882\) | 0.500000 | + | 0.866025i | 0.0168359 | + | 0.0291606i | ||||
\(883\) | 46.0000 | 1.54802 | 0.774012 | − | 0.633171i | \(-0.218247\pi\) | ||||
0.774012 | + | 0.633171i | \(0.218247\pi\) | |||||||
\(884\) | −1.00000 | + | 3.46410i | −0.0336336 | + | 0.116510i | ||||
\(885\) | −20.0000 | −0.672293 | ||||||||
\(886\) | 17.5000 | + | 30.3109i | 0.587924 | + | 1.01831i | ||||
\(887\) | 10.5000 | + | 18.1865i | 0.352555 | + | 0.610644i | 0.986696 | − | 0.162573i | \(-0.0519794\pi\) |
−0.634141 | + | 0.773217i | \(0.718646\pi\) | |||||||
\(888\) | 1.00000 | − | 1.73205i | 0.0335578 | − | 0.0581238i | ||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | 11.0000 | − | 19.0526i | 0.368721 | − | 0.638643i | ||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 20.0000 | 0.669650 | ||||||||
\(893\) | 3.50000 | − | 6.06218i | 0.117123 | − | 0.202863i | ||||
\(894\) | −3.00000 | − | 5.19615i | −0.100335 | − | 0.173785i | ||||
\(895\) | 12.0000 | + | 20.7846i | 0.401116 | + | 0.694753i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −21.0000 | + | 5.19615i | −0.701170 | + | 0.173494i | ||||
\(898\) | 30.0000 | 1.00111 | ||||||||
\(899\) | −9.00000 | − | 15.5885i | −0.300167 | − | 0.519904i | ||||
\(900\) | 0.500000 | + | 0.866025i | 0.0166667 | + | 0.0288675i | ||||
\(901\) | −0.500000 | + | 0.866025i | −0.0166574 | + | 0.0288515i | ||||
\(902\) | 5.00000 | 0.166482 | ||||||||
\(903\) | 1.00000 | − | 1.73205i | 0.0332779 | − | 0.0576390i | ||||
\(904\) | −3.00000 | + | 5.19615i | −0.0997785 | + | 0.172821i | ||||
\(905\) | −38.0000 | −1.26316 | ||||||||
\(906\) | 1.50000 | − | 2.59808i | 0.0498342 | − | 0.0863153i | ||||
\(907\) | −17.0000 | − | 29.4449i | −0.564476 | − | 0.977701i | −0.997098 | − | 0.0761255i | \(-0.975745\pi\) |
0.432623 | − | 0.901575i | \(-0.357588\pi\) | |||||||
\(908\) | −1.00000 | − | 1.73205i | −0.0331862 | − | 0.0574801i | ||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 5.00000 | + | 5.19615i | 0.165748 | + | 0.172251i | ||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 0.500000 | + | 0.866025i | 0.0165567 | + | 0.0286770i | ||||
\(913\) | −6.00000 | − | 10.3923i | −0.198571 | − | 0.343935i | ||||
\(914\) | −3.00000 | + | 5.19615i | −0.0992312 | + | 0.171873i | ||||
\(915\) | 22.0000 | 0.727298 | ||||||||
\(916\) | 11.5000 | − | 19.9186i | 0.379971 | − | 0.658129i | ||||
\(917\) | −4.00000 | + | 6.92820i | −0.132092 | + | 0.228789i | ||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | −14.5000 | + | 25.1147i | −0.478311 | + | 0.828459i | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) |
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | −6.00000 | − | 10.3923i | −0.197814 | − | 0.342624i | ||||
\(921\) | 9.50000 | + | 16.4545i | 0.313036 | + | 0.542194i | ||||
\(922\) | 24.0000 | 0.790398 | ||||||||
\(923\) | 28.0000 | − | 6.92820i | 0.921631 | − | 0.228045i | ||||
\(924\) | −1.00000 | −0.0328976 | ||||||||
\(925\) | −1.00000 | − | 1.73205i | −0.0328798 | − | 0.0569495i | ||||
\(926\) | 0.500000 | + | 0.866025i | 0.0164310 | + | 0.0284594i | ||||
\(927\) | 7.00000 | − | 12.1244i | 0.229910 | − | 0.398216i | ||||
\(928\) | −9.00000 | −0.295439 | ||||||||
\(929\) | −6.50000 | + | 11.2583i | −0.213258 | + | 0.369374i | −0.952732 | − | 0.303811i | \(-0.901741\pi\) |
0.739474 | + | 0.673185i | \(0.235074\pi\) | |||||||
\(930\) | −2.00000 | + | 3.46410i | −0.0655826 | + | 0.113592i | ||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | −9.00000 | + | 15.5885i | −0.294805 | + | 0.510617i | ||||
\(933\) | −7.50000 | − | 12.9904i | −0.245539 | − | 0.425286i | ||||
\(934\) | 4.00000 | + | 6.92820i | 0.130884 | + | 0.226698i | ||||
\(935\) | 2.00000 | 0.0654070 | ||||||||
\(936\) | 3.50000 | − | 0.866025i | 0.114401 | − | 0.0283069i | ||||
\(937\) | −4.00000 | −0.130674 | −0.0653372 | − | 0.997863i | \(-0.520812\pi\) | ||||
−0.0653372 | + | 0.997863i | \(0.520812\pi\) | |||||||
\(938\) | −1.00000 | − | 1.73205i | −0.0326512 | − | 0.0565535i | ||||
\(939\) | −6.00000 | − | 10.3923i | −0.195803 | − | 0.339140i | ||||
\(940\) | 7.00000 | − | 12.1244i | 0.228315 | − | 0.395453i | ||||
\(941\) | 32.0000 | 1.04317 | 0.521585 | − | 0.853199i | \(-0.325341\pi\) | ||||
0.521585 | + | 0.853199i | \(0.325341\pi\) | |||||||
\(942\) | −1.00000 | + | 1.73205i | −0.0325818 | + | 0.0564333i | ||||
\(943\) | 15.0000 | − | 25.9808i | 0.488467 | − | 0.846050i | ||||
\(944\) | 10.0000 | 0.325472 | ||||||||
\(945\) | −1.00000 | + | 1.73205i | −0.0325300 | + | 0.0563436i | ||||
\(946\) | 1.00000 | + | 1.73205i | 0.0325128 | + | 0.0563138i | ||||
\(947\) | 9.50000 | + | 16.4545i | 0.308709 | + | 0.534699i | 0.978080 | − | 0.208229i | \(-0.0667699\pi\) |
−0.669372 | + | 0.742928i | \(0.733437\pi\) | |||||||
\(948\) | −11.0000 | −0.357263 | ||||||||
\(949\) | 20.0000 | + | 20.7846i | 0.649227 | + | 0.674697i | ||||
\(950\) | 1.00000 | 0.0324443 | ||||||||
\(951\) | 15.0000 | + | 25.9808i | 0.486408 | + | 0.842484i | ||||
\(952\) | 0.500000 | + | 0.866025i | 0.0162051 | + | 0.0280680i | ||||
\(953\) | 15.0000 | − | 25.9808i | 0.485898 | − | 0.841599i | −0.513971 | − | 0.857808i | \(-0.671826\pi\) |
0.999869 | + | 0.0162081i | \(0.00515944\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | −4.00000 | + | 6.92820i | −0.129437 | + | 0.224191i | ||||
\(956\) | 6.00000 | − | 10.3923i | 0.194054 | − | 0.336111i | ||||
\(957\) | 9.00000 | 0.290929 | ||||||||
\(958\) | 5.50000 | − | 9.52628i | 0.177697 | − | 0.307780i | ||||
\(959\) | −5.00000 | − | 8.66025i | −0.161458 | − | 0.279654i | ||||
\(960\) | 1.00000 | + | 1.73205i | 0.0322749 | + | 0.0559017i | ||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | −7.00000 | + | 1.73205i | −0.225689 | + | 0.0558436i | ||||
\(963\) | 3.00000 | 0.0966736 | ||||||||
\(964\) | −8.00000 | − | 13.8564i | −0.257663 | − | 0.446285i | ||||
\(965\) | 11.0000 | + | 19.0526i | 0.354103 | + | 0.613324i | ||||
\(966\) | −3.00000 | + | 5.19615i | −0.0965234 | + | 0.167183i | ||||
\(967\) | −32.0000 | −1.02905 | −0.514525 | − | 0.857475i | \(-0.672032\pi\) | ||||
−0.514525 | + | 0.857475i | \(0.672032\pi\) | |||||||
\(968\) | −5.00000 | + | 8.66025i | −0.160706 | + | 0.278351i | ||||
\(969\) | −0.500000 | + | 0.866025i | −0.0160623 | + | 0.0278207i | ||||
\(970\) | 28.0000 | 0.899026 | ||||||||
\(971\) | 29.0000 | − | 50.2295i | 0.930654 | − | 1.61194i | 0.148449 | − | 0.988920i | \(-0.452572\pi\) |
0.782206 | − | 0.623020i | \(-0.214095\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −4.50000 | − | 7.79423i | −0.144263 | − | 0.249871i | ||||
\(974\) | 29.0000 | 0.929220 | ||||||||
\(975\) | 1.00000 | − | 3.46410i | 0.0320256 | − | 0.110940i | ||||
\(976\) | −11.0000 | −0.352101 | ||||||||
\(977\) | −18.0000 | − | 31.1769i | −0.575871 | − | 0.997438i | −0.995946 | − | 0.0899487i | \(-0.971330\pi\) |
0.420075 | − | 0.907489i | \(-0.362004\pi\) | |||||||
\(978\) | −1.00000 | − | 1.73205i | −0.0319765 | − | 0.0553849i | ||||
\(979\) | 5.50000 | − | 9.52628i | 0.175781 | − | 0.304461i | ||||
\(980\) | 2.00000 | 0.0638877 | ||||||||
\(981\) | −8.00000 | + | 13.8564i | −0.255420 | + | 0.442401i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −48.0000 | −1.53096 | −0.765481 | − | 0.643458i | \(-0.777499\pi\) | ||||
−0.765481 | + | 0.643458i | \(0.777499\pi\) | |||||||
\(984\) | −2.50000 | + | 4.33013i | −0.0796971 | + | 0.138039i | ||||
\(985\) | −27.0000 | − | 46.7654i | −0.860292 | − | 1.49007i | ||||
\(986\) | −4.50000 | − | 7.79423i | −0.143309 | − | 0.248219i | ||||
\(987\) | −7.00000 | −0.222812 | ||||||||
\(988\) | 1.00000 | − | 3.46410i | 0.0318142 | − | 0.110208i | ||||
\(989\) | 12.0000 | 0.381578 | ||||||||
\(990\) | −1.00000 | − | 1.73205i | −0.0317821 | − | 0.0550482i | ||||
\(991\) | −22.5000 | − | 38.9711i | −0.714736 | − | 1.23796i | −0.963061 | − | 0.269282i | \(-0.913213\pi\) |
0.248325 | − | 0.968677i | \(-0.420120\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | −26.0000 | −0.825085 | ||||||||
\(994\) | 4.00000 | − | 6.92820i | 0.126872 | − | 0.219749i | ||||
\(995\) | −10.0000 | + | 17.3205i | −0.317021 | + | 0.549097i | ||||
\(996\) | 12.0000 | 0.380235 | ||||||||
\(997\) | 17.5000 | − | 30.3109i | 0.554231 | − | 0.959955i | −0.443732 | − | 0.896159i | \(-0.646346\pi\) |
0.997963 | − | 0.0637961i | \(-0.0203207\pi\) | |||||||
\(998\) | −15.0000 | − | 25.9808i | −0.474817 | − | 0.822407i | ||||
\(999\) | −1.00000 | − | 1.73205i | −0.0316386 | − | 0.0547997i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.l.g.211.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.r.d.757.1 | 2 | |||
13.3 | even | 3 | 7098.2.a.e.1.1 | 1 | |||
13.9 | even | 3 | inner | 546.2.l.g.295.1 | yes | 2 | |
13.10 | even | 6 | 7098.2.a.r.1.1 | 1 | |||
39.35 | odd | 6 | 1638.2.r.d.1387.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.g.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
546.2.l.g.295.1 | yes | 2 | 13.9 | even | 3 | inner | |
1638.2.r.d.757.1 | 2 | 3.2 | odd | 2 | |||
1638.2.r.d.1387.1 | 2 | 39.35 | odd | 6 | |||
7098.2.a.e.1.1 | 1 | 13.3 | even | 3 | |||
7098.2.a.r.1.1 | 1 | 13.10 | even | 6 |