Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [714,2,Mod(205,714)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(714, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("714.205");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 714 = 2 \cdot 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 714.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: | \(5.70131870432\) |
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 | 613.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 714.613 |
Dual form | 714.2.i.i.205.1 |
$q$-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 \(\left(\mathbb{Z}/714\mathbb{Z}\right)^\times\).
\(n\) | \(239\) | \(409\) | \(547\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | 0.732294 | − | 0.680989i | \(-0.238450\pi\) |
−0.955901 | + | 0.293691i | \(0.905116\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −0.500000 | + | 0.866025i | −0.121268 | + | 0.210042i | ||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −2.00000 | − | 3.46410i | −0.458831 | − | 0.794719i | 0.540068 | − | 0.841621i | \(-0.318398\pi\) |
−0.998899 | + | 0.0469020i | \(0.985065\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.50000 | + | 0.866025i | −0.545545 | + | 0.188982i | ||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | −4.00000 | − | 6.92820i | −0.834058 | − | 1.44463i | −0.894795 | − | 0.446476i | \(-0.852679\pi\) |
0.0607377 | − | 0.998154i | \(-0.480655\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −0.500000 | − | 0.866025i | −0.0912871 | − | 0.158114i | ||||
\(31\) | 1.50000 | − | 2.59808i | 0.269408 | − | 0.466628i | −0.699301 | − | 0.714827i | \(-0.746505\pi\) |
0.968709 | + | 0.248199i | \(0.0798387\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | −1.00000 | −0.171499 | ||||||||
\(35\) | −0.500000 | + | 2.59808i | −0.0845154 | + | 0.439155i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 2.00000 | − | 3.46410i | 0.324443 | − | 0.561951i | ||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 1.00000 | 0.156174 | 0.0780869 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780869 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(42\) | −2.00000 | − | 1.73205i | −0.308607 | − | 0.267261i | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 1.00000 | + | 1.73205i | 0.150756 | + | 0.261116i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 4.00000 | − | 6.92820i | 0.589768 | − | 1.02151i | ||||
\(47\) | 4.50000 | + | 7.79423i | 0.656392 | + | 1.13691i | 0.981543 | + | 0.191243i | \(0.0612518\pi\) |
−0.325150 | + | 0.945662i | \(0.605415\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | 0.500000 | + | 0.866025i | 0.0700140 | + | 0.121268i | ||||
\(52\) | −0.500000 | + | 0.866025i | −0.0693375 | + | 0.120096i | ||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | −4.00000 | −0.529813 | ||||||||
\(58\) | 1.50000 | + | 2.59808i | 0.196960 | + | 0.341144i | ||||
\(59\) | −5.50000 | + | 9.52628i | −0.716039 | + | 1.24022i | 0.246518 | + | 0.969138i | \(0.420713\pi\) |
−0.962557 | + | 0.271078i | \(0.912620\pi\) | |||||||
\(60\) | 0.500000 | − | 0.866025i | 0.0645497 | − | 0.111803i | ||||
\(61\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(62\) | 3.00000 | 0.381000 | ||||||||
\(63\) | −0.500000 | + | 2.59808i | −0.0629941 | + | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | −0.500000 | − | 0.866025i | −0.0606339 | − | 0.105021i | ||||
\(69\) | −8.00000 | −0.963087 | ||||||||
\(70\) | −2.50000 | + | 0.866025i | −0.298807 | + | 0.103510i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −3.00000 | + | 5.19615i | −0.351123 | + | 0.608164i | −0.986447 | − | 0.164083i | \(-0.947534\pi\) |
0.635323 | + | 0.772246i | \(0.280867\pi\) | |||||||
\(74\) | 2.00000 | − | 3.46410i | 0.232495 | − | 0.402694i | ||||
\(75\) | −2.00000 | − | 3.46410i | −0.230940 | − | 0.400000i | ||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | −5.00000 | + | 1.73205i | −0.569803 | + | 0.197386i | ||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0.500000 | + | 0.866025i | 0.0552158 | + | 0.0956365i | ||||
\(83\) | 9.00000 | 0.987878 | 0.493939 | − | 0.869496i | \(-0.335557\pi\) | ||||
0.493939 | + | 0.869496i | \(0.335557\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 1.50000 | − | 2.59808i | 0.160817 | − | 0.278543i | ||||
\(88\) | −1.00000 | + | 1.73205i | −0.106600 | + | 0.184637i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | −2.00000 | − | 1.73205i | −0.209657 | − | 0.181568i | ||||
\(92\) | 8.00000 | 0.834058 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | −4.50000 | + | 7.79423i | −0.464140 | + | 0.803913i | ||||
\(95\) | −2.00000 | + | 3.46410i | −0.205196 | + | 0.355409i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | −7.00000 | + | 12.1244i | −0.696526 | + | 1.20642i | 0.273138 | + | 0.961975i | \(0.411939\pi\) |
−0.969664 | + | 0.244443i | \(0.921395\pi\) | |||||||
\(102\) | −0.500000 | + | 0.866025i | −0.0495074 | + | 0.0857493i | ||||
\(103\) | −7.00000 | − | 12.1244i | −0.689730 | − | 1.19465i | −0.971925 | − | 0.235291i | \(-0.924396\pi\) |
0.282194 | − | 0.959357i | \(-0.408938\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 2.00000 | + | 1.73205i | 0.195180 | + | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 8.00000 | − | 13.8564i | 0.766261 | − | 1.32720i | −0.173316 | − | 0.984866i | \(-0.555448\pi\) |
0.939577 | − | 0.342337i | \(-0.111218\pi\) | |||||||
\(110\) | −1.00000 | − | 1.73205i | −0.0953463 | − | 0.165145i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | −0.500000 | + | 2.59808i | −0.0472456 | + | 0.245495i | ||||
\(113\) | 15.0000 | 1.41108 | 0.705541 | − | 0.708669i | \(-0.250704\pi\) | ||||
0.705541 | + | 0.708669i | \(0.250704\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | −4.00000 | + | 6.92820i | −0.373002 | + | 0.646058i | ||||
\(116\) | −1.50000 | + | 2.59808i | −0.139272 | + | 0.241225i | ||||
\(117\) | −0.500000 | − | 0.866025i | −0.0462250 | − | 0.0800641i | ||||
\(118\) | −11.0000 | −1.01263 | ||||||||
\(119\) | 2.50000 | − | 0.866025i | 0.229175 | − | 0.0793884i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.500000 | − | 0.866025i | 0.0450835 | − | 0.0780869i | ||||
\(124\) | 1.50000 | + | 2.59808i | 0.134704 | + | 0.233314i | ||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | −2.50000 | + | 0.866025i | −0.222718 | + | 0.0771517i | ||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.00000 | + | 3.46410i | −0.176090 | + | 0.304997i | ||||
\(130\) | 0.500000 | − | 0.866025i | 0.0438529 | − | 0.0759555i | ||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 2.00000 | 0.174078 | ||||||||
\(133\) | −2.00000 | + | 10.3923i | −0.173422 | + | 0.901127i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 0.500000 | − | 0.866025i | 0.0428746 | − | 0.0742611i | ||||
\(137\) | −10.0000 | + | 17.3205i | −0.854358 | + | 1.47979i | 0.0228820 | + | 0.999738i | \(0.492716\pi\) |
−0.877240 | + | 0.480053i | \(0.840618\pi\) | |||||||
\(138\) | −4.00000 | − | 6.92820i | −0.340503 | − | 0.589768i | ||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | −2.00000 | − | 1.73205i | −0.169031 | − | 0.146385i | ||||
\(141\) | 9.00000 | 0.757937 | ||||||||
\(142\) | 2.00000 | + | 3.46410i | 0.167836 | + | 0.290701i | ||||
\(143\) | 1.00000 | − | 1.73205i | 0.0836242 | − | 0.144841i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −1.50000 | − | 2.59808i | −0.124568 | − | 0.215758i | ||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 6.50000 | + | 2.59808i | 0.536111 | + | 0.214286i | ||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | 1.00000 | + | 1.73205i | 0.0819232 | + | 0.141895i | 0.904076 | − | 0.427372i | \(-0.140560\pi\) |
−0.822153 | + | 0.569267i | \(0.807227\pi\) | |||||||
\(150\) | 2.00000 | − | 3.46410i | 0.163299 | − | 0.282843i | ||||
\(151\) | 2.00000 | − | 3.46410i | 0.162758 | − | 0.281905i | −0.773099 | − | 0.634285i | \(-0.781294\pi\) |
0.935857 | + | 0.352381i | \(0.114628\pi\) | |||||||
\(152\) | 2.00000 | + | 3.46410i | 0.162221 | + | 0.280976i | ||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −4.00000 | − | 3.46410i | −0.322329 | − | 0.279145i | ||||
\(155\) | −3.00000 | −0.240966 | ||||||||
\(156\) | 0.500000 | + | 0.866025i | 0.0400320 | + | 0.0693375i | ||||
\(157\) | −0.500000 | + | 0.866025i | −0.0399043 | + | 0.0691164i | −0.885288 | − | 0.465044i | \(-0.846039\pi\) |
0.845383 | + | 0.534160i | \(0.179372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −4.00000 | + | 20.7846i | −0.315244 | + | 1.63806i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −8.00000 | − | 13.8564i | −0.626608 | − | 1.08532i | −0.988227 | − | 0.152992i | \(-0.951109\pi\) |
0.361619 | − | 0.932326i | \(-0.382224\pi\) | |||||||
\(164\) | −0.500000 | + | 0.866025i | −0.0390434 | + | 0.0676252i | ||||
\(165\) | −1.00000 | + | 1.73205i | −0.0778499 | + | 0.134840i | ||||
\(166\) | 4.50000 | + | 7.79423i | 0.349268 | + | 0.604949i | ||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 2.50000 | − | 0.866025i | 0.192879 | − | 0.0668153i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0.500000 | + | 0.866025i | 0.0383482 | + | 0.0664211i | ||||
\(171\) | −2.00000 | + | 3.46410i | −0.152944 | + | 0.264906i | ||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −10.5000 | − | 18.1865i | −0.798300 | − | 1.38270i | −0.920722 | − | 0.390218i | \(-0.872399\pi\) |
0.122422 | − | 0.992478i | \(-0.460934\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | −2.00000 | −0.150756 | ||||||||
\(177\) | 5.50000 | + | 9.52628i | 0.413405 | + | 0.716039i | ||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | 10.5000 | − | 18.1865i | 0.784807 | − | 1.35933i | −0.144308 | − | 0.989533i | \(-0.546095\pi\) |
0.929114 | − | 0.369792i | \(-0.120571\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 16.0000 | 1.18927 | 0.594635 | − | 0.803996i | \(-0.297296\pi\) | ||||
0.594635 | + | 0.803996i | \(0.297296\pi\) | |||||||
\(182\) | 0.500000 | − | 2.59808i | 0.0370625 | − | 0.192582i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.00000 | + | 6.92820i | 0.294884 | + | 0.510754i | ||||
\(185\) | −2.00000 | + | 3.46410i | −0.147043 | + | 0.254686i | ||||
\(186\) | 1.50000 | − | 2.59808i | 0.109985 | − | 0.190500i | ||||
\(187\) | 1.00000 | + | 1.73205i | 0.0731272 | + | 0.126660i | ||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | 2.00000 | + | 1.73205i | 0.145479 | + | 0.125988i | ||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | −1.50000 | − | 2.59808i | −0.108536 | − | 0.187990i | 0.806641 | − | 0.591041i | \(-0.201283\pi\) |
−0.915177 | + | 0.403051i | \(0.867950\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | 4.00000 | + | 6.92820i | 0.287183 | + | 0.497416i | ||||
\(195\) | −1.00000 | −0.0716115 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 1.00000 | 0.0712470 | 0.0356235 | − | 0.999365i | \(-0.488658\pi\) | ||||
0.0356235 | + | 0.999365i | \(0.488658\pi\) | |||||||
\(198\) | −1.00000 | − | 1.73205i | −0.0710669 | − | 0.123091i | ||||
\(199\) | 2.50000 | − | 4.33013i | 0.177220 | − | 0.306955i | −0.763707 | − | 0.645563i | \(-0.776623\pi\) |
0.940927 | + | 0.338608i | \(0.109956\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | −6.00000 | − | 10.3923i | −0.423207 | − | 0.733017i | ||||
\(202\) | −14.0000 | −0.985037 | ||||||||
\(203\) | −6.00000 | − | 5.19615i | −0.421117 | − | 0.364698i | ||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | −0.500000 | − | 0.866025i | −0.0349215 | − | 0.0604858i | ||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | −4.00000 | + | 6.92820i | −0.278019 | + | 0.481543i | ||||
\(208\) | −0.500000 | − | 0.866025i | −0.0346688 | − | 0.0600481i | ||||
\(209\) | −8.00000 | −0.553372 | ||||||||
\(210\) | −0.500000 | + | 2.59808i | −0.0345033 | + | 0.179284i | ||||
\(211\) | 3.00000 | 0.206529 | 0.103264 | − | 0.994654i | \(-0.467071\pi\) | ||||
0.103264 | + | 0.994654i | \(0.467071\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.00000 | − | 3.46410i | 0.137038 | − | 0.237356i | ||||
\(214\) | −6.00000 | + | 10.3923i | −0.410152 | + | 0.710403i | ||||
\(215\) | 2.00000 | + | 3.46410i | 0.136399 | + | 0.236250i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −7.50000 | + | 2.59808i | −0.509133 | + | 0.176369i | ||||
\(218\) | 16.0000 | 1.08366 | ||||||||
\(219\) | 3.00000 | + | 5.19615i | 0.202721 | + | 0.351123i | ||||
\(220\) | 1.00000 | − | 1.73205i | 0.0674200 | − | 0.116775i | ||||
\(221\) | −0.500000 | + | 0.866025i | −0.0336336 | + | 0.0582552i | ||||
\(222\) | −2.00000 | − | 3.46410i | −0.134231 | − | 0.232495i | ||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | −2.50000 | + | 0.866025i | −0.167038 | + | 0.0578638i | ||||
\(225\) | −4.00000 | −0.266667 | ||||||||
\(226\) | 7.50000 | + | 12.9904i | 0.498893 | + | 0.864107i | ||||
\(227\) | −5.00000 | + | 8.66025i | −0.331862 | + | 0.574801i | −0.982877 | − | 0.184263i | \(-0.941010\pi\) |
0.651015 | + | 0.759065i | \(0.274343\pi\) | |||||||
\(228\) | 2.00000 | − | 3.46410i | 0.132453 | − | 0.229416i | ||||
\(229\) | 4.50000 | + | 7.79423i | 0.297368 | + | 0.515057i | 0.975533 | − | 0.219853i | \(-0.0705577\pi\) |
−0.678165 | + | 0.734910i | \(0.737224\pi\) | |||||||
\(230\) | −8.00000 | −0.527504 | ||||||||
\(231\) | −1.00000 | + | 5.19615i | −0.0657952 | + | 0.341882i | ||||
\(232\) | −3.00000 | −0.196960 | ||||||||
\(233\) | 5.50000 | + | 9.52628i | 0.360317 | + | 0.624087i | 0.988013 | − | 0.154371i | \(-0.0493352\pi\) |
−0.627696 | + | 0.778459i | \(0.716002\pi\) | |||||||
\(234\) | 0.500000 | − | 0.866025i | 0.0326860 | − | 0.0566139i | ||||
\(235\) | 4.50000 | − | 7.79423i | 0.293548 | − | 0.508439i | ||||
\(236\) | −5.50000 | − | 9.52628i | −0.358020 | − | 0.620108i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | + | 1.73205i | 0.129641 | + | 0.112272i | ||||
\(239\) | 13.0000 | 0.840900 | 0.420450 | − | 0.907316i | \(-0.361872\pi\) | ||||
0.420450 | + | 0.907316i | \(0.361872\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | −9.00000 | + | 15.5885i | −0.579741 | + | 1.00414i | 0.415768 | + | 0.909471i | \(0.363513\pi\) |
−0.995509 | + | 0.0946700i | \(0.969820\pi\) | |||||||
\(242\) | −3.50000 | + | 6.06218i | −0.224989 | + | 0.389692i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.50000 | − | 4.33013i | 0.351382 | − | 0.276642i | ||||
\(246\) | 1.00000 | 0.0637577 | ||||||||
\(247\) | −2.00000 | − | 3.46410i | −0.127257 | − | 0.220416i | ||||
\(248\) | −1.50000 | + | 2.59808i | −0.0952501 | + | 0.164978i | ||||
\(249\) | 4.50000 | − | 7.79423i | 0.285176 | − | 0.493939i | ||||
\(250\) | −4.50000 | − | 7.79423i | −0.284605 | − | 0.492950i | ||||
\(251\) | 23.0000 | 1.45175 | 0.725874 | − | 0.687828i | \(-0.241436\pi\) | ||||
0.725874 | + | 0.687828i | \(0.241436\pi\) | |||||||
\(252\) | −2.00000 | − | 1.73205i | −0.125988 | − | 0.109109i | ||||
\(253\) | −16.0000 | −1.00591 | ||||||||
\(254\) | −4.00000 | − | 6.92820i | −0.250982 | − | 0.434714i | ||||
\(255\) | 0.500000 | − | 0.866025i | 0.0313112 | − | 0.0542326i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −7.00000 | − | 12.1244i | −0.436648 | − | 0.756297i | 0.560781 | − | 0.827964i | \(-0.310501\pi\) |
−0.997429 | + | 0.0716680i | \(0.977168\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | −2.00000 | + | 10.3923i | −0.124274 | + | 0.645746i | ||||
\(260\) | 1.00000 | 0.0620174 | ||||||||
\(261\) | −1.50000 | − | 2.59808i | −0.0928477 | − | 0.160817i | ||||
\(262\) | −3.00000 | + | 5.19615i | −0.185341 | + | 0.321019i | ||||
\(263\) | 4.00000 | − | 6.92820i | 0.246651 | − | 0.427211i | −0.715944 | − | 0.698158i | \(-0.754003\pi\) |
0.962594 | + | 0.270947i | \(0.0873367\pi\) | |||||||
\(264\) | 1.00000 | + | 1.73205i | 0.0615457 | + | 0.106600i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.0000 | + | 3.46410i | −0.613139 | + | 0.212398i | ||||
\(267\) | 6.00000 | 0.367194 | ||||||||
\(268\) | 6.00000 | + | 10.3923i | 0.366508 | + | 0.634811i | ||||
\(269\) | 2.50000 | − | 4.33013i | 0.152428 | − | 0.264013i | −0.779692 | − | 0.626164i | \(-0.784624\pi\) |
0.932119 | + | 0.362151i | \(0.117958\pi\) | |||||||
\(270\) | −0.500000 | + | 0.866025i | −0.0304290 | + | 0.0527046i | ||||
\(271\) | −9.00000 | − | 15.5885i | −0.546711 | − | 0.946931i | −0.998497 | − | 0.0548050i | \(-0.982546\pi\) |
0.451786 | − | 0.892126i | \(-0.350787\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | −2.50000 | + | 0.866025i | −0.151307 | + | 0.0524142i | ||||
\(274\) | −20.0000 | −1.20824 | ||||||||
\(275\) | −4.00000 | − | 6.92820i | −0.241209 | − | 0.417786i | ||||
\(276\) | 4.00000 | − | 6.92820i | 0.240772 | − | 0.417029i | ||||
\(277\) | −14.0000 | + | 24.2487i | −0.841178 | + | 1.45696i | 0.0477206 | + | 0.998861i | \(0.484804\pi\) |
−0.888899 | + | 0.458103i | \(0.848529\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0.500000 | − | 2.59808i | 0.0298807 | − | 0.155265i | ||||
\(281\) | 20.0000 | 1.19310 | 0.596550 | − | 0.802576i | \(-0.296538\pi\) | ||||
0.596550 | + | 0.802576i | \(0.296538\pi\) | |||||||
\(282\) | 4.50000 | + | 7.79423i | 0.267971 | + | 0.464140i | ||||
\(283\) | 6.50000 | − | 11.2583i | 0.386385 | − | 0.669238i | −0.605575 | − | 0.795788i | \(-0.707057\pi\) |
0.991960 | + | 0.126550i | \(0.0403903\pi\) | |||||||
\(284\) | −2.00000 | + | 3.46410i | −0.118678 | + | 0.205557i | ||||
\(285\) | 2.00000 | + | 3.46410i | 0.118470 | + | 0.205196i | ||||
\(286\) | 2.00000 | 0.118262 | ||||||||
\(287\) | −2.00000 | − | 1.73205i | −0.118056 | − | 0.102240i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −0.500000 | − | 0.866025i | −0.0294118 | − | 0.0509427i | ||||
\(290\) | 1.50000 | − | 2.59808i | 0.0880830 | − | 0.152564i | ||||
\(291\) | 4.00000 | − | 6.92820i | 0.234484 | − | 0.406138i | ||||
\(292\) | −3.00000 | − | 5.19615i | −0.175562 | − | 0.304082i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 1.00000 | + | 6.92820i | 0.0583212 | + | 0.404061i | ||||
\(295\) | 11.0000 | 0.640445 | ||||||||
\(296\) | 2.00000 | + | 3.46410i | 0.116248 | + | 0.201347i | ||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | −1.00000 | + | 1.73205i | −0.0579284 | + | 0.100335i | ||||
\(299\) | −4.00000 | − | 6.92820i | −0.231326 | − | 0.400668i | ||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 8.00000 | + | 6.92820i | 0.461112 | + | 0.399335i | ||||
\(302\) | 4.00000 | 0.230174 | ||||||||
\(303\) | 7.00000 | + | 12.1244i | 0.402139 | + | 0.696526i | ||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.500000 | + | 0.866025i | 0.0285831 | + | 0.0495074i | ||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 1.00000 | − | 5.19615i | 0.0569803 | − | 0.296078i | ||||
\(309\) | −14.0000 | −0.796432 | ||||||||
\(310\) | −1.50000 | − | 2.59808i | −0.0851943 | − | 0.147561i | ||||
\(311\) | 9.00000 | − | 15.5885i | 0.510343 | − | 0.883940i | −0.489585 | − | 0.871956i | \(-0.662852\pi\) |
0.999928 | − | 0.0119847i | \(-0.00381495\pi\) | |||||||
\(312\) | −0.500000 | + | 0.866025i | −0.0283069 | + | 0.0490290i | ||||
\(313\) | −4.00000 | − | 6.92820i | −0.226093 | − | 0.391605i | 0.730554 | − | 0.682855i | \(-0.239262\pi\) |
−0.956647 | + | 0.291250i | \(0.905929\pi\) | |||||||
\(314\) | −1.00000 | −0.0564333 | ||||||||
\(315\) | 2.50000 | − | 0.866025i | 0.140859 | − | 0.0487950i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.50000 | + | 9.52628i | 0.308911 | + | 0.535049i | 0.978124 | − | 0.208021i | \(-0.0667022\pi\) |
−0.669214 | + | 0.743070i | \(0.733369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.00000 | − | 5.19615i | 0.167968 | − | 0.290929i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | −20.0000 | + | 6.92820i | −1.11456 | + | 0.386094i | ||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 2.00000 | − | 3.46410i | 0.110940 | − | 0.192154i | ||||
\(326\) | 8.00000 | − | 13.8564i | 0.443079 | − | 0.767435i | ||||
\(327\) | −8.00000 | − | 13.8564i | −0.442401 | − | 0.766261i | ||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 4.50000 | − | 23.3827i | 0.248093 | − | 1.28913i | ||||
\(330\) | −2.00000 | −0.110096 | ||||||||
\(331\) | 11.0000 | + | 19.0526i | 0.604615 | + | 1.04722i | 0.992112 | + | 0.125353i | \(0.0400062\pi\) |
−0.387498 | + | 0.921871i | \(0.626660\pi\) | |||||||
\(332\) | −4.50000 | + | 7.79423i | −0.246970 | + | 0.427764i | ||||
\(333\) | −2.00000 | + | 3.46410i | −0.109599 | + | 0.189832i | ||||
\(334\) | 1.00000 | + | 1.73205i | 0.0547176 | + | 0.0947736i | ||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 2.00000 | + | 1.73205i | 0.109109 | + | 0.0944911i | ||||
\(337\) | 34.0000 | 1.85210 | 0.926049 | − | 0.377403i | \(-0.123183\pi\) | ||||
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | 7.50000 | − | 12.9904i | 0.407344 | − | 0.705541i | ||||
\(340\) | −0.500000 | + | 0.866025i | −0.0271163 | + | 0.0469668i | ||||
\(341\) | −3.00000 | − | 5.19615i | −0.162459 | − | 0.281387i | ||||
\(342\) | −4.00000 | −0.216295 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 4.00000 | + | 6.92820i | 0.215353 | + | 0.373002i | ||||
\(346\) | 10.5000 | − | 18.1865i | 0.564483 | − | 0.977714i | ||||
\(347\) | 2.00000 | − | 3.46410i | 0.107366 | − | 0.185963i | −0.807337 | − | 0.590091i | \(-0.799092\pi\) |
0.914702 | + | 0.404128i | \(0.132425\pi\) | |||||||
\(348\) | 1.50000 | + | 2.59808i | 0.0804084 | + | 0.139272i | ||||
\(349\) | 27.0000 | 1.44528 | 0.722638 | − | 0.691226i | \(-0.242929\pi\) | ||||
0.722638 | + | 0.691226i | \(0.242929\pi\) | |||||||
\(350\) | −8.00000 | − | 6.92820i | −0.427618 | − | 0.370328i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −1.00000 | − | 1.73205i | −0.0533002 | − | 0.0923186i | ||||
\(353\) | −14.0000 | + | 24.2487i | −0.745145 | + | 1.29063i | 0.204982 | + | 0.978766i | \(0.434286\pi\) |
−0.950127 | + | 0.311863i | \(0.899047\pi\) | |||||||
\(354\) | −5.50000 | + | 9.52628i | −0.292322 | + | 0.506316i | ||||
\(355\) | −2.00000 | − | 3.46410i | −0.106149 | − | 0.183855i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0.500000 | − | 2.59808i | 0.0264628 | − | 0.137505i | ||||
\(358\) | 21.0000 | 1.10988 | ||||||||
\(359\) | −7.50000 | − | 12.9904i | −0.395835 | − | 0.685606i | 0.597372 | − | 0.801964i | \(-0.296211\pi\) |
−0.993207 | + | 0.116358i | \(0.962878\pi\) | |||||||
\(360\) | 0.500000 | − | 0.866025i | 0.0263523 | − | 0.0456435i | ||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 8.00000 | + | 13.8564i | 0.420471 | + | 0.728277i | ||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 2.50000 | − | 0.866025i | 0.131036 | − | 0.0453921i | ||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.0000 | − | 27.7128i | 0.835193 | − | 1.44660i | −0.0586798 | − | 0.998277i | \(-0.518689\pi\) |
0.893873 | − | 0.448320i | \(-0.147978\pi\) | |||||||
\(368\) | −4.00000 | + | 6.92820i | −0.208514 | + | 0.361158i | ||||
\(369\) | −0.500000 | − | 0.866025i | −0.0260290 | − | 0.0450835i | ||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.00000 | 0.155543 | ||||||||
\(373\) | −9.50000 | − | 16.4545i | −0.491891 | − | 0.851981i | 0.508065 | − | 0.861319i | \(-0.330361\pi\) |
−0.999956 | + | 0.00933789i | \(0.997028\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | −4.50000 | + | 7.79423i | −0.232379 | + | 0.402492i | ||||
\(376\) | −4.50000 | − | 7.79423i | −0.232070 | − | 0.401957i | ||||
\(377\) | 3.00000 | 0.154508 | ||||||||
\(378\) | −0.500000 | + | 2.59808i | −0.0257172 | + | 0.133631i | ||||
\(379\) | 8.00000 | 0.410932 | 0.205466 | − | 0.978664i | \(-0.434129\pi\) | ||||
0.205466 | + | 0.978664i | \(0.434129\pi\) | |||||||
\(380\) | −2.00000 | − | 3.46410i | −0.102598 | − | 0.177705i | ||||
\(381\) | −4.00000 | + | 6.92820i | −0.204926 | + | 0.354943i | ||||
\(382\) | 1.50000 | − | 2.59808i | 0.0767467 | − | 0.132929i | ||||
\(383\) | −12.0000 | − | 20.7846i | −0.613171 | − | 1.06204i | −0.990702 | − | 0.136047i | \(-0.956560\pi\) |
0.377531 | − | 0.925997i | \(-0.376773\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 4.00000 | + | 3.46410i | 0.203859 | + | 0.176547i | ||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 2.00000 | + | 3.46410i | 0.101666 | + | 0.176090i | ||||
\(388\) | −4.00000 | + | 6.92820i | −0.203069 | + | 0.351726i | ||||
\(389\) | 1.00000 | − | 1.73205i | 0.0507020 | − | 0.0878185i | −0.839561 | − | 0.543266i | \(-0.817187\pi\) |
0.890263 | + | 0.455448i | \(0.150521\pi\) | |||||||
\(390\) | −0.500000 | − | 0.866025i | −0.0253185 | − | 0.0438529i | ||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | −1.00000 | − | 6.92820i | −0.0505076 | − | 0.349927i | ||||
\(393\) | 6.00000 | 0.302660 | ||||||||
\(394\) | 0.500000 | + | 0.866025i | 0.0251896 | + | 0.0436297i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.00000 | − | 1.73205i | 0.0502519 | − | 0.0870388i | ||||
\(397\) | 4.00000 | + | 6.92820i | 0.200754 | + | 0.347717i | 0.948772 | − | 0.315963i | \(-0.102327\pi\) |
−0.748017 | + | 0.663679i | \(0.768994\pi\) | |||||||
\(398\) | 5.00000 | 0.250627 | ||||||||
\(399\) | 8.00000 | + | 6.92820i | 0.400501 | + | 0.346844i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −15.0000 | − | 25.9808i | −0.749064 | − | 1.29742i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
0.199207 | − | 0.979957i | \(-0.436163\pi\) | |||||||
\(402\) | 6.00000 | − | 10.3923i | 0.299253 | − | 0.518321i | ||||
\(403\) | 1.50000 | − | 2.59808i | 0.0747203 | − | 0.129419i | ||||
\(404\) | −7.00000 | − | 12.1244i | −0.348263 | − | 0.603209i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 1.50000 | − | 7.79423i | 0.0744438 | − | 0.386821i | ||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | −0.500000 | − | 0.866025i | −0.0247537 | − | 0.0428746i | ||||
\(409\) | −13.0000 | + | 22.5167i | −0.642809 | + | 1.11338i | 0.341994 | + | 0.939702i | \(0.388898\pi\) |
−0.984803 | + | 0.173675i | \(0.944436\pi\) | |||||||
\(410\) | 0.500000 | − | 0.866025i | 0.0246932 | − | 0.0427699i | ||||
\(411\) | 10.0000 | + | 17.3205i | 0.493264 | + | 0.854358i | ||||
\(412\) | 14.0000 | 0.689730 | ||||||||
\(413\) | 27.5000 | − | 9.52628i | 1.35319 | − | 0.468758i | ||||
\(414\) | −8.00000 | −0.393179 | ||||||||
\(415\) | −4.50000 | − | 7.79423i | −0.220896 | − | 0.382604i | ||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.00000 | − | 6.92820i | −0.195646 | − | 0.338869i | ||||
\(419\) | 4.00000 | 0.195413 | 0.0977064 | − | 0.995215i | \(-0.468849\pi\) | ||||
0.0977064 | + | 0.995215i | \(0.468849\pi\) | |||||||
\(420\) | −2.50000 | + | 0.866025i | −0.121988 | + | 0.0422577i | ||||
\(421\) | 17.0000 | 0.828529 | 0.414265 | − | 0.910156i | \(-0.364039\pi\) | ||||
0.414265 | + | 0.910156i | \(0.364039\pi\) | |||||||
\(422\) | 1.50000 | + | 2.59808i | 0.0730189 | + | 0.126472i | ||||
\(423\) | 4.50000 | − | 7.79423i | 0.218797 | − | 0.378968i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.00000 | + | 3.46410i | 0.0970143 | + | 0.168034i | ||||
\(426\) | 4.00000 | 0.193801 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | −1.00000 | − | 1.73205i | −0.0482805 | − | 0.0836242i | ||||
\(430\) | −2.00000 | + | 3.46410i | −0.0964486 | + | 0.167054i | ||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 19.0000 | 0.913082 | 0.456541 | − | 0.889702i | \(-0.349088\pi\) | ||||
0.456541 | + | 0.889702i | \(0.349088\pi\) | |||||||
\(434\) | −6.00000 | − | 5.19615i | −0.288009 | − | 0.249423i | ||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | −16.0000 | + | 27.7128i | −0.765384 | + | 1.32568i | ||||
\(438\) | −3.00000 | + | 5.19615i | −0.143346 | + | 0.248282i | ||||
\(439\) | 0.500000 | + | 0.866025i | 0.0238637 | + | 0.0413331i | 0.877711 | − | 0.479191i | \(-0.159070\pi\) |
−0.853847 | + | 0.520524i | \(0.825737\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | −1.00000 | −0.0475651 | ||||||||
\(443\) | −16.5000 | − | 28.5788i | −0.783939 | − | 1.35782i | −0.929631 | − | 0.368492i | \(-0.879874\pi\) |
0.145692 | − | 0.989330i | \(-0.453459\pi\) | |||||||
\(444\) | 2.00000 | − | 3.46410i | 0.0949158 | − | 0.164399i | ||||
\(445\) | 3.00000 | − | 5.19615i | 0.142214 | − | 0.246321i | ||||
\(446\) | −8.00000 | − | 13.8564i | −0.378811 | − | 0.656120i | ||||
\(447\) | 2.00000 | 0.0945968 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | −2.00000 | − | 3.46410i | −0.0942809 | − | 0.163299i | ||||
\(451\) | 1.00000 | − | 1.73205i | 0.0470882 | − | 0.0815591i | ||||
\(452\) | −7.50000 | + | 12.9904i | −0.352770 | + | 0.611016i | ||||
\(453\) | −2.00000 | − | 3.46410i | −0.0939682 | − | 0.162758i | ||||
\(454\) | −10.0000 | −0.469323 | ||||||||
\(455\) | −0.500000 | + | 2.59808i | −0.0234404 | + | 0.121800i | ||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | −0.500000 | − | 0.866025i | −0.0233890 | − | 0.0405110i | 0.854094 | − | 0.520119i | \(-0.174112\pi\) |
−0.877483 | + | 0.479608i | \(0.840779\pi\) | |||||||
\(458\) | −4.50000 | + | 7.79423i | −0.210271 | + | 0.364200i | ||||
\(459\) | 0.500000 | − | 0.866025i | 0.0233380 | − | 0.0404226i | ||||
\(460\) | −4.00000 | − | 6.92820i | −0.186501 | − | 0.323029i | ||||
\(461\) | −20.0000 | −0.931493 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(462\) | −5.00000 | + | 1.73205i | −0.232621 | + | 0.0805823i | ||||
\(463\) | −18.0000 | −0.836531 | −0.418265 | − | 0.908325i | \(-0.637362\pi\) | ||||
−0.418265 | + | 0.908325i | \(0.637362\pi\) | |||||||
\(464\) | −1.50000 | − | 2.59808i | −0.0696358 | − | 0.120613i | ||||
\(465\) | −1.50000 | + | 2.59808i | −0.0695608 | + | 0.120483i | ||||
\(466\) | −5.50000 | + | 9.52628i | −0.254783 | + | 0.441296i | ||||
\(467\) | 1.50000 | + | 2.59808i | 0.0694117 | + | 0.120225i | 0.898642 | − | 0.438682i | \(-0.144554\pi\) |
−0.829231 | + | 0.558906i | \(0.811221\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −30.0000 | + | 10.3923i | −1.38527 | + | 0.479872i | ||||
\(470\) | 9.00000 | 0.415139 | ||||||||
\(471\) | 0.500000 | + | 0.866025i | 0.0230388 | + | 0.0399043i | ||||
\(472\) | 5.50000 | − | 9.52628i | 0.253158 | − | 0.438483i | ||||
\(473\) | −4.00000 | + | 6.92820i | −0.183920 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | −0.734130 | ||||||||
\(476\) | −0.500000 | + | 2.59808i | −0.0229175 | + | 0.119083i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.50000 | + | 11.2583i | 0.297303 | + | 0.514944i | ||||
\(479\) | −13.0000 | + | 22.5167i | −0.593985 | + | 1.02881i | 0.399704 | + | 0.916644i | \(0.369113\pi\) |
−0.993689 | + | 0.112168i | \(0.964220\pi\) | |||||||
\(480\) | −0.500000 | + | 0.866025i | −0.0228218 | + | 0.0395285i | ||||
\(481\) | −2.00000 | − | 3.46410i | −0.0911922 | − | 0.157949i | ||||
\(482\) | −18.0000 | −0.819878 | ||||||||
\(483\) | 16.0000 | + | 13.8564i | 0.728025 | + | 0.630488i | ||||
\(484\) | −7.00000 | −0.318182 | ||||||||
\(485\) | −4.00000 | − | 6.92820i | −0.181631 | − | 0.314594i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 13.5000 | − | 23.3827i | 0.611743 | − | 1.05957i | −0.379203 | − | 0.925313i | \(-0.623802\pi\) |
0.990947 | − | 0.134257i | \(-0.0428648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 6.50000 | + | 2.59808i | 0.293640 | + | 0.117369i | ||||
\(491\) | 28.0000 | 1.26362 | 0.631811 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631811 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(492\) | 0.500000 | + | 0.866025i | 0.0225417 | + | 0.0390434i | ||||
\(493\) | −1.50000 | + | 2.59808i | −0.0675566 | + | 0.117011i | ||||
\(494\) | 2.00000 | − | 3.46410i | 0.0899843 | − | 0.155857i | ||||
\(495\) | 1.00000 | + | 1.73205i | 0.0449467 | + | 0.0778499i | ||||
\(496\) | −3.00000 | −0.134704 | ||||||||
\(497\) | −8.00000 | − | 6.92820i | −0.358849 | − | 0.310772i | ||||
\(498\) | 9.00000 | 0.403300 | ||||||||
\(499\) | −6.50000 | − | 11.2583i | −0.290980 | − | 0.503992i | 0.683062 | − | 0.730361i | \(-0.260648\pi\) |
−0.974042 | + | 0.226369i | \(0.927315\pi\) | |||||||
\(500\) | 4.50000 | − | 7.79423i | 0.201246 | − | 0.348569i | ||||
\(501\) | 1.00000 | − | 1.73205i | 0.0446767 | − | 0.0773823i | ||||
\(502\) | 11.5000 | + | 19.9186i | 0.513270 | + | 0.889010i | ||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | ||||
\(505\) | 14.0000 | 0.622992 | ||||||||
\(506\) | −8.00000 | − | 13.8564i | −0.355643 | − | 0.615992i | ||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 4.00000 | − | 6.92820i | 0.177471 | − | 0.307389i | ||||
\(509\) | −14.0000 | − | 24.2487i | −0.620539 | − | 1.07481i | −0.989385 | − | 0.145315i | \(-0.953580\pi\) |
0.368846 | − | 0.929490i | \(-0.379753\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | 15.0000 | − | 5.19615i | 0.663561 | − | 0.229864i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.00000 | + | 3.46410i | 0.0883022 | + | 0.152944i | ||||
\(514\) | 7.00000 | − | 12.1244i | 0.308757 | − | 0.534782i | ||||
\(515\) | −7.00000 | + | 12.1244i | −0.308457 | + | 0.534263i | ||||
\(516\) | −2.00000 | − | 3.46410i | −0.0880451 | − | 0.152499i | ||||
\(517\) | 18.0000 | 0.791639 | ||||||||
\(518\) | −10.0000 | + | 3.46410i | −0.439375 | + | 0.152204i | ||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | 0.500000 | + | 0.866025i | 0.0219265 | + | 0.0379777i | ||||
\(521\) | −5.00000 | + | 8.66025i | −0.219054 | + | 0.379413i | −0.954519 | − | 0.298150i | \(-0.903630\pi\) |
0.735465 | + | 0.677563i | \(0.236964\pi\) | |||||||
\(522\) | 1.50000 | − | 2.59808i | 0.0656532 | − | 0.113715i | ||||
\(523\) | 20.0000 | + | 34.6410i | 0.874539 | + | 1.51475i | 0.857253 | + | 0.514895i | \(0.172169\pi\) |
0.0172859 | + | 0.999851i | \(0.494497\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | −2.00000 | + | 10.3923i | −0.0872872 | + | 0.453557i | ||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | 1.50000 | + | 2.59808i | 0.0653410 | + | 0.113174i | ||||
\(528\) | −1.00000 | + | 1.73205i | −0.0435194 | + | 0.0753778i | ||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.0000 | 0.477359 | ||||||||
\(532\) | −8.00000 | − | 6.92820i | −0.346844 | − | 0.300376i | ||||
\(533\) | 1.00000 | 0.0433148 | ||||||||
\(534\) | 3.00000 | + | 5.19615i | 0.129823 | + | 0.224860i | ||||
\(535\) | 6.00000 | − | 10.3923i | 0.259403 | − | 0.449299i | ||||
\(536\) | −6.00000 | + | 10.3923i | −0.259161 | + | 0.448879i | ||||
\(537\) | −10.5000 | − | 18.1865i | −0.453108 | − | 0.784807i | ||||
\(538\) | 5.00000 | 0.215565 | ||||||||
\(539\) | 13.0000 | + | 5.19615i | 0.559950 | + | 0.223814i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | 16.0000 | + | 27.7128i | 0.687894 | + | 1.19147i | 0.972518 | + | 0.232828i | \(0.0747978\pi\) |
−0.284624 | + | 0.958639i | \(0.591869\pi\) | |||||||
\(542\) | 9.00000 | − | 15.5885i | 0.386583 | − | 0.669582i | ||||
\(543\) | 8.00000 | − | 13.8564i | 0.343313 | − | 0.594635i | ||||
\(544\) | 0.500000 | + | 0.866025i | 0.0214373 | + | 0.0371305i | ||||
\(545\) | −16.0000 | −0.685365 | ||||||||
\(546\) | −2.00000 | − | 1.73205i | −0.0855921 | − | 0.0741249i | ||||
\(547\) | −41.0000 | −1.75303 | −0.876517 | − | 0.481371i | \(-0.840139\pi\) | ||||
−0.876517 | + | 0.481371i | \(0.840139\pi\) | |||||||
\(548\) | −10.0000 | − | 17.3205i | −0.427179 | − | 0.739895i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.00000 | − | 6.92820i | 0.170561 | − | 0.295420i | ||||
\(551\) | −6.00000 | − | 10.3923i | −0.255609 | − | 0.442727i | ||||
\(552\) | 8.00000 | 0.340503 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −28.0000 | −1.18961 | ||||||||
\(555\) | 2.00000 | + | 3.46410i | 0.0848953 | + | 0.147043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.00000 | + | 13.8564i | −0.338971 | + | 0.587115i | −0.984239 | − | 0.176841i | \(-0.943412\pi\) |
0.645269 | + | 0.763956i | \(0.276745\pi\) | |||||||
\(558\) | −1.50000 | − | 2.59808i | −0.0635001 | − | 0.109985i | ||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 2.50000 | − | 0.866025i | 0.105644 | − | 0.0365963i | ||||
\(561\) | 2.00000 | 0.0844401 | ||||||||
\(562\) | 10.0000 | + | 17.3205i | 0.421825 | + | 0.730622i | ||||
\(563\) | −6.00000 | + | 10.3923i | −0.252870 | + | 0.437983i | −0.964315 | − | 0.264758i | \(-0.914708\pi\) |
0.711445 | + | 0.702742i | \(0.248041\pi\) | |||||||
\(564\) | −4.50000 | + | 7.79423i | −0.189484 | + | 0.328196i | ||||
\(565\) | −7.50000 | − | 12.9904i | −0.315527 | − | 0.546509i | ||||
\(566\) | 13.0000 | 0.546431 | ||||||||
\(567\) | 2.50000 | − | 0.866025i | 0.104990 | − | 0.0363696i | ||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | 1.00000 | + | 1.73205i | 0.0419222 | + | 0.0726113i | 0.886225 | − | 0.463255i | \(-0.153319\pi\) |
−0.844303 | + | 0.535866i | \(0.819985\pi\) | |||||||
\(570\) | −2.00000 | + | 3.46410i | −0.0837708 | + | 0.145095i | ||||
\(571\) | 6.00000 | − | 10.3923i | 0.251092 | − | 0.434904i | −0.712735 | − | 0.701434i | \(-0.752544\pi\) |
0.963827 | + | 0.266529i | \(0.0858769\pi\) | |||||||
\(572\) | 1.00000 | + | 1.73205i | 0.0418121 | + | 0.0724207i | ||||
\(573\) | −3.00000 | −0.125327 | ||||||||
\(574\) | 0.500000 | − | 2.59808i | 0.0208696 | − | 0.108442i | ||||
\(575\) | −32.0000 | −1.33449 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 7.50000 | − | 12.9904i | 0.312229 | − | 0.540797i | −0.666616 | − | 0.745402i | \(-0.732258\pi\) |
0.978845 | + | 0.204605i | \(0.0655910\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | −7.00000 | − | 12.1244i | −0.290910 | − | 0.503871i | ||||
\(580\) | 3.00000 | 0.124568 | ||||||||
\(581\) | −18.0000 | − | 15.5885i | −0.746766 | − | 0.646718i | ||||
\(582\) | 8.00000 | 0.331611 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.00000 | − | 5.19615i | 0.124141 | − | 0.215018i | ||||
\(585\) | −0.500000 | + | 0.866025i | −0.0206725 | + | 0.0358057i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | −5.50000 | + | 4.33013i | −0.226816 | + | 0.178571i | ||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 5.50000 | + | 9.52628i | 0.226431 | + | 0.392191i | ||||
\(591\) | 0.500000 | − | 0.866025i | 0.0205673 | − | 0.0356235i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | −11.0000 | − | 19.0526i | −0.451716 | − | 0.782395i | 0.546777 | − | 0.837278i | \(-0.315855\pi\) |
−0.998493 | + | 0.0548835i | \(0.982521\pi\) | |||||||
\(594\) | −2.00000 | −0.0820610 | ||||||||
\(595\) | −2.00000 | − | 1.73205i | −0.0819920 | − | 0.0710072i | ||||
\(596\) | −2.00000 | −0.0819232 | ||||||||
\(597\) | −2.50000 | − | 4.33013i | −0.102318 | − | 0.177220i | ||||
\(598\) | 4.00000 | − | 6.92820i | 0.163572 | − | 0.283315i | ||||
\(599\) | −5.50000 | + | 9.52628i | −0.224724 | + | 0.389233i | −0.956237 | − | 0.292595i | \(-0.905481\pi\) |
0.731513 | + | 0.681828i | \(0.238815\pi\) | |||||||
\(600\) | 2.00000 | + | 3.46410i | 0.0816497 | + | 0.141421i | ||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | −2.00000 | + | 10.3923i | −0.0815139 | + | 0.423559i | ||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | 2.00000 | + | 3.46410i | 0.0813788 | + | 0.140952i | ||||
\(605\) | 3.50000 | − | 6.06218i | 0.142295 | − | 0.246463i | ||||
\(606\) | −7.00000 | + | 12.1244i | −0.284356 | + | 0.492518i | ||||
\(607\) | −0.500000 | − | 0.866025i | −0.0202944 | − | 0.0351509i | 0.855700 | − | 0.517472i | \(-0.173127\pi\) |
−0.875994 | + | 0.482322i | \(0.839794\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | −7.50000 | + | 2.59808i | −0.303915 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.50000 | + | 7.79423i | 0.182051 | + | 0.315321i | ||||
\(612\) | −0.500000 | + | 0.866025i | −0.0202113 | + | 0.0350070i | ||||
\(613\) | 13.0000 | − | 22.5167i | 0.525065 | − | 0.909439i | −0.474509 | − | 0.880251i | \(-0.657374\pi\) |
0.999574 | − | 0.0291886i | \(-0.00929235\pi\) | |||||||
\(614\) | 10.0000 | + | 17.3205i | 0.403567 | + | 0.698999i | ||||
\(615\) | −1.00000 | −0.0403239 | ||||||||
\(616\) | 5.00000 | − | 1.73205i | 0.201456 | − | 0.0697863i | ||||
\(617\) | 17.0000 | 0.684394 | 0.342197 | − | 0.939628i | \(-0.388829\pi\) | ||||
0.342197 | + | 0.939628i | \(0.388829\pi\) | |||||||
\(618\) | −7.00000 | − | 12.1244i | −0.281581 | − | 0.487713i | ||||
\(619\) | −14.0000 | + | 24.2487i | −0.562708 | + | 0.974638i | 0.434551 | + | 0.900647i | \(0.356907\pi\) |
−0.997259 | + | 0.0739910i | \(0.976426\pi\) | |||||||
\(620\) | 1.50000 | − | 2.59808i | 0.0602414 | − | 0.104341i | ||||
\(621\) | 4.00000 | + | 6.92820i | 0.160514 | + | 0.278019i | ||||
\(622\) | 18.0000 | 0.721734 | ||||||||
\(623\) | 3.00000 | − | 15.5885i | 0.120192 | − | 0.624538i | ||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 4.00000 | − | 6.92820i | 0.159872 | − | 0.276907i | ||||
\(627\) | −4.00000 | + | 6.92820i | −0.159745 | + | 0.276686i | ||||
\(628\) | −0.500000 | − | 0.866025i | −0.0199522 | − | 0.0345582i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 2.00000 | + | 1.73205i | 0.0796819 | + | 0.0690066i | ||||
\(631\) | −38.0000 | −1.51276 | −0.756378 | − | 0.654135i | \(-0.773033\pi\) | ||||
−0.756378 | + | 0.654135i | \(0.773033\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.50000 | − | 2.59808i | 0.0596196 | − | 0.103264i | ||||
\(634\) | −5.50000 | + | 9.52628i | −0.218433 | + | 0.378337i | ||||
\(635\) | 4.00000 | + | 6.92820i | 0.158735 | + | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | + | 6.92820i | 0.0396214 | + | 0.274505i | ||||
\(638\) | 6.00000 | 0.237542 | ||||||||
\(639\) | −2.00000 | − | 3.46410i | −0.0791188 | − | 0.137038i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −15.0000 | + | 25.9808i | −0.592464 | + | 1.02618i | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | 6.00000 | + | 10.3923i | 0.236801 | + | 0.410152i | ||||
\(643\) | 45.0000 | 1.77463 | 0.887313 | − | 0.461167i | \(-0.152569\pi\) | ||||
0.887313 | + | 0.461167i | \(0.152569\pi\) | |||||||
\(644\) | −16.0000 | − | 13.8564i | −0.630488 | − | 0.546019i | ||||
\(645\) | 4.00000 | 0.157500 | ||||||||
\(646\) | 2.00000 | + | 3.46410i | 0.0786889 | + | 0.136293i | ||||
\(647\) | −16.5000 | + | 28.5788i | −0.648682 | + | 1.12355i | 0.334756 | + | 0.942305i | \(0.391346\pi\) |
−0.983438 | + | 0.181245i | \(0.941987\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 11.0000 | + | 19.0526i | 0.431788 | + | 0.747878i | ||||
\(650\) | 4.00000 | 0.156893 | ||||||||
\(651\) | −1.50000 | + | 7.79423i | −0.0587896 | + | 0.305480i | ||||
\(652\) | 16.0000 | 0.626608 | ||||||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | 8.00000 | − | 13.8564i | 0.312825 | − | 0.541828i | ||||
\(655\) | 3.00000 | − | 5.19615i | 0.117220 | − | 0.203030i | ||||
\(656\) | −0.500000 | − | 0.866025i | −0.0195217 | − | 0.0338126i | ||||
\(657\) | 6.00000 | 0.234082 | ||||||||
\(658\) | 22.5000 | − | 7.79423i | 0.877141 | − | 0.303851i | ||||
\(659\) | 39.0000 | 1.51922 | 0.759612 | − | 0.650376i | \(-0.225389\pi\) | ||||
0.759612 | + | 0.650376i | \(0.225389\pi\) | |||||||
\(660\) | −1.00000 | − | 1.73205i | −0.0389249 | − | 0.0674200i | ||||
\(661\) | −23.5000 | + | 40.7032i | −0.914044 | + | 1.58317i | −0.105749 | + | 0.994393i | \(0.533724\pi\) |
−0.808295 | + | 0.588778i | \(0.799609\pi\) | |||||||
\(662\) | −11.0000 | + | 19.0526i | −0.427527 | + | 0.740499i | ||||
\(663\) | 0.500000 | + | 0.866025i | 0.0194184 | + | 0.0336336i | ||||
\(664\) | −9.00000 | −0.349268 | ||||||||
\(665\) | 10.0000 | − | 3.46410i | 0.387783 | − | 0.134332i | ||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | −12.0000 | − | 20.7846i | −0.464642 | − | 0.804783i | ||||
\(668\) | −1.00000 | + | 1.73205i | −0.0386912 | + | 0.0670151i | ||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | −6.00000 | − | 10.3923i | −0.231800 | − | 0.401490i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.500000 | + | 2.59808i | −0.0192879 | + | 0.100223i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | 17.0000 | + | 29.4449i | 0.654816 | + | 1.13417i | ||||
\(675\) | −2.00000 | + | 3.46410i | −0.0769800 | + | 0.133333i | ||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | −3.00000 | − | 5.19615i | −0.115299 | − | 0.199704i | 0.802600 | − | 0.596518i | \(-0.203449\pi\) |
−0.917899 | + | 0.396813i | \(0.870116\pi\) | |||||||
\(678\) | 15.0000 | 0.576072 | ||||||||
\(679\) | −16.0000 | − | 13.8564i | −0.614024 | − | 0.531760i | ||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | 5.00000 | + | 8.66025i | 0.191600 | + | 0.331862i | ||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | 2.00000 | − | 3.46410i | 0.0765279 | − | 0.132550i | −0.825222 | − | 0.564809i | \(-0.808950\pi\) |
0.901750 | + | 0.432259i | \(0.142283\pi\) | |||||||
\(684\) | −2.00000 | − | 3.46410i | −0.0764719 | − | 0.132453i | ||||
\(685\) | 20.0000 | 0.764161 | ||||||||
\(686\) | 18.5000 | + | 0.866025i | 0.706333 | + | 0.0330650i | ||||
\(687\) | 9.00000 | 0.343371 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −4.00000 | + | 6.92820i | −0.152277 | + | 0.263752i | ||||
\(691\) | 23.5000 | + | 40.7032i | 0.893982 | + | 1.54842i | 0.835059 | + | 0.550160i | \(0.185433\pi\) |
0.0589228 | + | 0.998263i | \(0.481233\pi\) | |||||||
\(692\) | 21.0000 | 0.798300 | ||||||||
\(693\) | 4.00000 | + | 3.46410i | 0.151947 | + | 0.131590i | ||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.50000 | + | 2.59808i | −0.0568574 | + | 0.0984798i | ||||
\(697\) | −0.500000 | + | 0.866025i | −0.0189389 | + | 0.0328031i | ||||
\(698\) | 13.5000 | + | 23.3827i | 0.510983 | + | 0.885048i | ||||
\(699\) | 11.0000 | 0.416058 | ||||||||
\(700\) | 2.00000 | − | 10.3923i | 0.0755929 | − | 0.392792i | ||||
\(701\) | 20.0000 | 0.755390 | 0.377695 | − | 0.925930i | \(-0.376717\pi\) | ||||
0.377695 | + | 0.925930i | \(0.376717\pi\) | |||||||
\(702\) | −0.500000 | − | 0.866025i | −0.0188713 | − | 0.0326860i | ||||
\(703\) | −8.00000 | + | 13.8564i | −0.301726 | + | 0.522604i | ||||
\(704\) | 1.00000 | − | 1.73205i | 0.0376889 | − | 0.0652791i | ||||
\(705\) | −4.50000 | − | 7.79423i | −0.169480 | − | 0.293548i | ||||
\(706\) | −28.0000 | −1.05379 | ||||||||
\(707\) | 35.0000 | − | 12.1244i | 1.31631 | − | 0.455983i | ||||
\(708\) | −11.0000 | −0.413405 | ||||||||
\(709\) | 21.0000 | + | 36.3731i | 0.788672 | + | 1.36602i | 0.926781 | + | 0.375602i | \(0.122564\pi\) |
−0.138109 | + | 0.990417i | \(0.544103\pi\) | |||||||
\(710\) | 2.00000 | − | 3.46410i | 0.0750587 | − | 0.130005i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | − | 5.19615i | −0.112430 | − | 0.194734i | ||||
\(713\) | −24.0000 | −0.898807 | ||||||||
\(714\) | 2.50000 | − | 0.866025i | 0.0935601 | − | 0.0324102i | ||||
\(715\) | −2.00000 | −0.0747958 | ||||||||
\(716\) | 10.5000 | + | 18.1865i | 0.392403 | + | 0.679663i | ||||
\(717\) | 6.50000 | − | 11.2583i | 0.242747 | − | 0.420450i | ||||
\(718\) | 7.50000 | − | 12.9904i | 0.279898 | − | 0.484797i | ||||
\(719\) | 25.0000 | + | 43.3013i | 0.932343 | + | 1.61486i | 0.779305 | + | 0.626644i | \(0.215572\pi\) |
0.153037 | + | 0.988220i | \(0.451094\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −7.00000 | + | 36.3731i | −0.260694 | + | 1.35460i | ||||
\(722\) | 3.00000 | 0.111648 | ||||||||
\(723\) | 9.00000 | + | 15.5885i | 0.334714 | + | 0.579741i | ||||
\(724\) | −8.00000 | + | 13.8564i | −0.297318 | + | 0.514969i | ||||
\(725\) | 6.00000 | − | 10.3923i | 0.222834 | − | 0.385961i | ||||
\(726\) | 3.50000 | + | 6.06218i | 0.129897 | + | 0.224989i | ||||
\(727\) | 26.0000 | 0.964287 | 0.482143 | − | 0.876092i | \(-0.339858\pi\) | ||||
0.482143 | + | 0.876092i | \(0.339858\pi\) | |||||||
\(728\) | 2.00000 | + | 1.73205i | 0.0741249 | + | 0.0641941i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 3.00000 | + | 5.19615i | 0.111035 | + | 0.192318i | ||||
\(731\) | 2.00000 | − | 3.46410i | 0.0739727 | − | 0.128124i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11.0000 | − | 19.0526i | −0.406294 | − | 0.703722i | 0.588177 | − | 0.808732i | \(-0.299846\pi\) |
−0.994471 | + | 0.105010i | \(0.966513\pi\) | |||||||
\(734\) | 32.0000 | 1.18114 | ||||||||
\(735\) | −1.00000 | − | 6.92820i | −0.0368856 | − | 0.255551i | ||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | −12.0000 | − | 20.7846i | −0.442026 | − | 0.765611i | ||||
\(738\) | 0.500000 | − | 0.866025i | 0.0184053 | − | 0.0318788i | ||||
\(739\) | −21.0000 | + | 36.3731i | −0.772497 | + | 1.33800i | 0.163693 | + | 0.986511i | \(0.447659\pi\) |
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(740\) | −2.00000 | − | 3.46410i | −0.0735215 | − | 0.127343i | ||||
\(741\) | −4.00000 | −0.146944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.0000 | −0.586983 | −0.293492 | − | 0.955962i | \(-0.594817\pi\) | ||||
−0.293492 | + | 0.955962i | \(0.594817\pi\) | |||||||
\(744\) | 1.50000 | + | 2.59808i | 0.0549927 | + | 0.0952501i | ||||
\(745\) | 1.00000 | − | 1.73205i | 0.0366372 | − | 0.0634574i | ||||
\(746\) | 9.50000 | − | 16.4545i | 0.347820 | − | 0.602441i | ||||
\(747\) | −4.50000 | − | 7.79423i | −0.164646 | − | 0.285176i | ||||
\(748\) | −2.00000 | −0.0731272 | ||||||||
\(749\) | 6.00000 | − | 31.1769i | 0.219235 | − | 1.13918i | ||||
\(750\) | −9.00000 | −0.328634 | ||||||||
\(751\) | 13.5000 | + | 23.3827i | 0.492622 | + | 0.853246i | 0.999964 | − | 0.00849853i | \(-0.00270520\pi\) |
−0.507342 | + | 0.861745i | \(0.669372\pi\) | |||||||
\(752\) | 4.50000 | − | 7.79423i | 0.164098 | − | 0.284226i | ||||
\(753\) | 11.5000 | − | 19.9186i | 0.419083 | − | 0.725874i | ||||
\(754\) | 1.50000 | + | 2.59808i | 0.0546268 | + | 0.0946164i | ||||
\(755\) | −4.00000 | −0.145575 | ||||||||
\(756\) | −2.50000 | + | 0.866025i | −0.0909241 | + | 0.0314970i | ||||
\(757\) | 27.0000 | 0.981332 | 0.490666 | − | 0.871348i | \(-0.336754\pi\) | ||||
0.490666 | + | 0.871348i | \(0.336754\pi\) | |||||||
\(758\) | 4.00000 | + | 6.92820i | 0.145287 | + | 0.251644i | ||||
\(759\) | −8.00000 | + | 13.8564i | −0.290382 | + | 0.502956i | ||||
\(760\) | 2.00000 | − | 3.46410i | 0.0725476 | − | 0.125656i | ||||
\(761\) | 18.0000 | + | 31.1769i | 0.652499 | + | 1.13016i | 0.982514 | + | 0.186187i | \(0.0596129\pi\) |
−0.330015 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(762\) | −8.00000 | −0.289809 | ||||||||
\(763\) | −40.0000 | + | 13.8564i | −1.44810 | + | 0.501636i | ||||
\(764\) | 3.00000 | 0.108536 | ||||||||
\(765\) | −0.500000 | − | 0.866025i | −0.0180775 | − | 0.0313112i | ||||
\(766\) | 12.0000 | − | 20.7846i | 0.433578 | − | 0.750978i | ||||
\(767\) | −5.50000 | + | 9.52628i | −0.198593 | + | 0.343974i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −46.0000 | −1.65880 | −0.829401 | − | 0.558653i | \(-0.811318\pi\) | ||||
−0.829401 | + | 0.558653i | \(0.811318\pi\) | |||||||
\(770\) | −1.00000 | + | 5.19615i | −0.0360375 | + | 0.187256i | ||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 7.00000 | + | 12.1244i | 0.251936 | + | 0.436365i | ||||
\(773\) | −23.0000 | + | 39.8372i | −0.827253 | + | 1.43284i | 0.0729331 | + | 0.997337i | \(0.476764\pi\) |
−0.900186 | + | 0.435507i | \(0.856569\pi\) | |||||||
\(774\) | −2.00000 | + | 3.46410i | −0.0718885 | + | 0.124515i | ||||
\(775\) | −6.00000 | − | 10.3923i | −0.215526 | − | 0.373303i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 8.00000 | + | 6.92820i | 0.286998 | + | 0.248548i | ||||
\(778\) | 2.00000 | 0.0717035 | ||||||||
\(779\) | −2.00000 | − | 3.46410i | −0.0716574 | − | 0.124114i | ||||
\(780\) | 0.500000 | − | 0.866025i | 0.0179029 | − | 0.0310087i | ||||
\(781\) | 4.00000 | − | 6.92820i | 0.143131 | − | 0.247911i | ||||
\(782\) | 4.00000 | + | 6.92820i | 0.143040 | + | 0.247752i | ||||
\(783\) | −3.00000 | −0.107211 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 1.00000 | 0.0356915 | ||||||||
\(786\) | 3.00000 | + | 5.19615i | 0.107006 | + | 0.185341i | ||||
\(787\) | −9.50000 | + | 16.4545i | −0.338638 | + | 0.586539i | −0.984177 | − | 0.177189i | \(-0.943300\pi\) |
0.645538 | + | 0.763728i | \(0.276633\pi\) | |||||||
\(788\) | −0.500000 | + | 0.866025i | −0.0178118 | + | 0.0308509i | ||||
\(789\) | −4.00000 | − | 6.92820i | −0.142404 | − | 0.246651i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.0000 | − | 25.9808i | −1.06668 | − | 0.923770i | ||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.00000 | + | 6.92820i | −0.141955 | + | 0.245873i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.50000 | + | 4.33013i | 0.0886102 | + | 0.153477i | ||||
\(797\) | 40.0000 | 1.41687 | 0.708436 | − | 0.705775i | \(-0.249401\pi\) | ||||
0.708436 | + | 0.705775i | \(0.249401\pi\) | |||||||
\(798\) | −2.00000 | + | 10.3923i | −0.0707992 | + | 0.367884i | ||||
\(799\) | −9.00000 | −0.318397 | ||||||||
\(800\) | −2.00000 | − | 3.46410i | −0.0707107 | − | 0.122474i | ||||
\(801\) | 3.00000 | − | 5.19615i | 0.106000 | − | 0.183597i | ||||
\(802\) | 15.0000 | − | 25.9808i | 0.529668 | − | 0.917413i | ||||
\(803\) | 6.00000 | + | 10.3923i | 0.211735 | + | 0.366736i | ||||
\(804\) | 12.0000 | 0.423207 | ||||||||
\(805\) | 20.0000 | − | 6.92820i | 0.704907 | − | 0.244187i | ||||
\(806\) | 3.00000 | 0.105670 | ||||||||
\(807\) | −2.50000 | − | 4.33013i | −0.0880042 | − | 0.152428i | ||||
\(808\) | 7.00000 | − | 12.1244i | 0.246259 | − | 0.426533i | ||||
\(809\) | 19.0000 | − | 32.9090i | 0.668004 | − | 1.15702i | −0.310457 | − | 0.950587i | \(-0.600482\pi\) |
0.978461 | − | 0.206430i | \(-0.0661846\pi\) | |||||||
\(810\) | 0.500000 | + | 0.866025i | 0.0175682 | + | 0.0304290i | ||||
\(811\) | 11.0000 | 0.386262 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(812\) | 7.50000 | − | 2.59808i | 0.263198 | − | 0.0911746i | ||||
\(813\) | −18.0000 | −0.631288 | ||||||||
\(814\) | −4.00000 | − | 6.92820i | −0.140200 | − | 0.242833i | ||||
\(815\) | −8.00000 | + | 13.8564i | −0.280228 | + | 0.485369i | ||||
\(816\) | 0.500000 | − | 0.866025i | 0.0175035 | − | 0.0303170i | ||||
\(817\) | 8.00000 | + | 13.8564i | 0.279885 | + | 0.484774i | ||||
\(818\) | −26.0000 | −0.909069 | ||||||||
\(819\) | −0.500000 | + | 2.59808i | −0.0174714 | + | 0.0907841i | ||||
\(820\) | 1.00000 | 0.0349215 | ||||||||
\(821\) | 1.00000 | + | 1.73205i | 0.0349002 | + | 0.0604490i | 0.882948 | − | 0.469471i | \(-0.155555\pi\) |
−0.848048 | + | 0.529920i | \(0.822222\pi\) | |||||||
\(822\) | −10.0000 | + | 17.3205i | −0.348790 | + | 0.604122i | ||||
\(823\) | −17.5000 | + | 30.3109i | −0.610012 | + | 1.05657i | 0.381226 | + | 0.924482i | \(0.375502\pi\) |
−0.991238 | + | 0.132089i | \(0.957831\pi\) | |||||||
\(824\) | 7.00000 | + | 12.1244i | 0.243857 | + | 0.422372i | ||||
\(825\) | −8.00000 | −0.278524 | ||||||||
\(826\) | 22.0000 | + | 19.0526i | 0.765478 | + | 0.662923i | ||||
\(827\) | −46.0000 | −1.59958 | −0.799788 | − | 0.600282i | \(-0.795055\pi\) | ||||
−0.799788 | + | 0.600282i | \(0.795055\pi\) | |||||||
\(828\) | −4.00000 | − | 6.92820i | −0.139010 | − | 0.240772i | ||||
\(829\) | 27.0000 | − | 46.7654i | 0.937749 | − | 1.62423i | 0.168091 | − | 0.985771i | \(-0.446240\pi\) |
0.769657 | − | 0.638457i | \(-0.220427\pi\) | |||||||
\(830\) | 4.50000 | − | 7.79423i | 0.156197 | − | 0.270542i | ||||
\(831\) | 14.0000 | + | 24.2487i | 0.485655 | + | 0.841178i | ||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | −6.50000 | − | 2.59808i | −0.225212 | − | 0.0900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.00000 | − | 1.73205i | −0.0346064 | − | 0.0599401i | ||||
\(836\) | 4.00000 | − | 6.92820i | 0.138343 | − | 0.239617i | ||||
\(837\) | −1.50000 | + | 2.59808i | −0.0518476 | + | 0.0898027i | ||||
\(838\) | 2.00000 | + | 3.46410i | 0.0690889 | + | 0.119665i | ||||
\(839\) | −26.0000 | −0.897620 | −0.448810 | − | 0.893627i | \(-0.648152\pi\) | ||||
−0.448810 | + | 0.893627i | \(0.648152\pi\) | |||||||
\(840\) | −2.00000 | − | 1.73205i | −0.0690066 | − | 0.0597614i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 8.50000 | + | 14.7224i | 0.292929 | + | 0.507369i | ||||
\(843\) | 10.0000 | − | 17.3205i | 0.344418 | − | 0.596550i | ||||
\(844\) | −1.50000 | + | 2.59808i | −0.0516321 | + | 0.0894295i | ||||
\(845\) | 6.00000 | + | 10.3923i | 0.206406 | + | 0.357506i | ||||
\(846\) | 9.00000 | 0.309426 | ||||||||
\(847\) | 3.50000 | − | 18.1865i | 0.120261 | − | 0.624897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.50000 | − | 11.2583i | −0.223079 | − | 0.386385i | ||||
\(850\) | −2.00000 | + | 3.46410i | −0.0685994 | + | 0.118818i | ||||
\(851\) | −16.0000 | + | 27.7128i | −0.548473 | + | 0.949983i | ||||
\(852\) | 2.00000 | + | 3.46410i | 0.0685189 | + | 0.118678i | ||||
\(853\) | 16.0000 | 0.547830 | 0.273915 | − | 0.961754i | \(-0.411681\pi\) | ||||
0.273915 | + | 0.961754i | \(0.411681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | 10.5000 | − | 18.1865i | 0.358673 | − | 0.621240i | −0.629066 | − | 0.777352i | \(-0.716563\pi\) |
0.987739 | + | 0.156112i | \(0.0498959\pi\) | |||||||
\(858\) | 1.00000 | − | 1.73205i | 0.0341394 | − | 0.0591312i | ||||
\(859\) | 4.00000 | + | 6.92820i | 0.136478 | + | 0.236387i | 0.926161 | − | 0.377128i | \(-0.123088\pi\) |
−0.789683 | + | 0.613515i | \(0.789755\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | −2.50000 | + | 0.866025i | −0.0851998 | + | 0.0295141i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.00000 | − | 10.3923i | −0.204242 | − | 0.353758i | 0.745649 | − | 0.666339i | \(-0.232140\pi\) |
−0.949891 | + | 0.312581i | \(0.898806\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −10.5000 | + | 18.1865i | −0.357011 | + | 0.618361i | ||||
\(866\) | 9.50000 | + | 16.4545i | 0.322823 | + | 0.559146i | ||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 1.50000 | − | 7.79423i | 0.0509133 | − | 0.264553i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.50000 | − | 2.59808i | −0.0508548 | − | 0.0880830i | ||||
\(871\) | 6.00000 | − | 10.3923i | 0.203302 | − | 0.352130i | ||||
\(872\) | −8.00000 | + | 13.8564i | −0.270914 | + | 0.469237i | ||||
\(873\) | −4.00000 | − | 6.92820i | −0.135379 | − | 0.234484i | ||||
\(874\) | −32.0000 | −1.08242 | ||||||||
\(875\) | 18.0000 | + | 15.5885i | 0.608511 | + | 0.526986i | ||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −15.0000 | − | 25.9808i | −0.506514 | − | 0.877308i | −0.999972 | − | 0.00753813i | \(-0.997601\pi\) |
0.493458 | − | 0.869770i | \(-0.335733\pi\) | |||||||
\(878\) | −0.500000 | + | 0.866025i | −0.0168742 | + | 0.0292269i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.00000 | + | 1.73205i | 0.0337100 | + | 0.0583874i | ||||
\(881\) | −35.0000 | −1.17918 | −0.589590 | − | 0.807703i | \(-0.700711\pi\) | ||||
−0.589590 | + | 0.807703i | \(0.700711\pi\) | |||||||
\(882\) | 6.50000 | + | 2.59808i | 0.218866 | + | 0.0874818i | ||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | −0.500000 | − | 0.866025i | −0.0168168 | − | 0.0291276i | ||||
\(885\) | 5.50000 | − | 9.52628i | 0.184880 | − | 0.320222i | ||||
\(886\) | 16.5000 | − | 28.5788i | 0.554328 | − | 0.960125i | ||||
\(887\) | 13.0000 | + | 22.5167i | 0.436497 | + | 0.756035i | 0.997417 | − | 0.0718351i | \(-0.0228855\pi\) |
−0.560919 | + | 0.827871i | \(0.689552\pi\) | |||||||
\(888\) | 4.00000 | 0.134231 | ||||||||
\(889\) | 16.0000 | + | 13.8564i | 0.536623 | + | 0.464729i | ||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | 1.00000 | + | 1.73205i | 0.0335013 | + | 0.0580259i | ||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | 18.0000 | − | 31.1769i | 0.602347 | − | 1.04330i | ||||
\(894\) | 1.00000 | + | 1.73205i | 0.0334450 | + | 0.0579284i | ||||
\(895\) | −21.0000 | −0.701953 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | −8.00000 | −0.267112 | ||||||||
\(898\) | −3.00000 | − | 5.19615i | −0.100111 | − | 0.173398i | ||||
\(899\) | 4.50000 | − | 7.79423i | 0.150083 | − | 0.259952i | ||||
\(900\) | 2.00000 | − | 3.46410i | 0.0666667 | − | 0.115470i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 2.00000 | 0.0665927 | ||||||||
\(903\) | 10.0000 | − | 3.46410i | 0.332779 | − | 0.115278i | ||||
\(904\) | −15.0000 | −0.498893 | ||||||||
\(905\) | −8.00000 | − | 13.8564i | −0.265929 | − | 0.460603i | ||||
\(906\) | 2.00000 | − | 3.46410i | 0.0664455 | − | 0.115087i | ||||
\(907\) | −23.5000 | + | 40.7032i | −0.780305 | + | 1.35153i | 0.151460 | + | 0.988463i | \(0.451603\pi\) |
−0.931764 | + | 0.363064i | \(0.881731\pi\) | |||||||
\(908\) | −5.00000 | − | 8.66025i | −0.165931 | − | 0.287401i | ||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | −2.50000 | + | 0.866025i | −0.0828742 | + | 0.0287085i | ||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 2.00000 | + | 3.46410i | 0.0662266 | + | 0.114708i | ||||
\(913\) | 9.00000 | − | 15.5885i | 0.297857 | − | 0.515903i | ||||
\(914\) | 0.500000 | − | 0.866025i | 0.0165385 | − | 0.0286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.00000 | −0.297368 | ||||||||
\(917\) | 3.00000 | − | 15.5885i | 0.0990687 | − | 0.514776i | ||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −29.0000 | − | 50.2295i | −0.956622 | − | 1.65692i | −0.730613 | − | 0.682792i | \(-0.760765\pi\) |
−0.226009 | − | 0.974125i | \(-0.572568\pi\) | |||||||
\(920\) | 4.00000 | − | 6.92820i | 0.131876 | − | 0.228416i | ||||
\(921\) | 10.0000 | − | 17.3205i | 0.329511 | − | 0.570730i | ||||
\(922\) | −10.0000 | − | 17.3205i | −0.329332 | − | 0.570421i | ||||
\(923\) | 4.00000 | 0.131662 | ||||||||
\(924\) | −4.00000 | − | 3.46410i | −0.131590 | − | 0.113961i | ||||
\(925\) | −16.0000 | −0.526077 | ||||||||
\(926\) | −9.00000 | − | 15.5885i | −0.295758 | − | 0.512268i | ||||
\(927\) | −7.00000 | + | 12.1244i | −0.229910 | + | 0.398216i | ||||
\(928\) | 1.50000 | − | 2.59808i | 0.0492399 | − | 0.0852860i | ||||
\(929\) | 2.50000 | + | 4.33013i | 0.0820223 | + | 0.142067i | 0.904118 | − | 0.427282i | \(-0.140529\pi\) |
−0.822096 | + | 0.569349i | \(0.807195\pi\) | |||||||
\(930\) | −3.00000 | −0.0983739 | ||||||||
\(931\) | 22.0000 | − | 17.3205i | 0.721021 | − | 0.567657i | ||||
\(932\) | −11.0000 | −0.360317 | ||||||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | −1.50000 | + | 2.59808i | −0.0490815 | + | 0.0850117i | ||||
\(935\) | 1.00000 | − | 1.73205i | 0.0327035 | − | 0.0566441i | ||||
\(936\) | 0.500000 | + | 0.866025i | 0.0163430 | + | 0.0283069i | ||||
\(937\) | −14.0000 | −0.457360 | −0.228680 | − | 0.973502i | \(-0.573441\pi\) | ||||
−0.228680 | + | 0.973502i | \(0.573441\pi\) | |||||||
\(938\) | −24.0000 | − | 20.7846i | −0.783628 | − | 0.678642i | ||||
\(939\) | −8.00000 | −0.261070 | ||||||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | 1.00000 | − | 1.73205i | 0.0325991 | − | 0.0564632i | −0.849266 | − | 0.527966i | \(-0.822955\pi\) |
0.881865 | + | 0.471503i | \(0.156288\pi\) | |||||||
\(942\) | −0.500000 | + | 0.866025i | −0.0162909 | + | 0.0282166i | ||||
\(943\) | −4.00000 | − | 6.92820i | −0.130258 | − | 0.225613i | ||||
\(944\) | 11.0000 | 0.358020 | ||||||||
\(945\) | 0.500000 | − | 2.59808i | 0.0162650 | − | 0.0845154i | ||||
\(946\) | −8.00000 | −0.260102 | ||||||||
\(947\) | −7.00000 | − | 12.1244i | −0.227469 | − | 0.393989i | 0.729588 | − | 0.683887i | \(-0.239712\pi\) |
−0.957057 | + | 0.289898i | \(0.906379\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.00000 | + | 5.19615i | −0.0973841 | + | 0.168674i | ||||
\(950\) | −8.00000 | − | 13.8564i | −0.259554 | − | 0.449561i | ||||
\(951\) | 11.0000 | 0.356699 | ||||||||
\(952\) | −2.50000 | + | 0.866025i | −0.0810255 | + | 0.0280680i | ||||
\(953\) | 20.0000 | 0.647864 | 0.323932 | − | 0.946080i | \(-0.394995\pi\) | ||||
0.323932 | + | 0.946080i | \(0.394995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.50000 | + | 2.59808i | −0.0485389 | + | 0.0840718i | ||||
\(956\) | −6.50000 | + | 11.2583i | −0.210225 | + | 0.364120i | ||||
\(957\) | −3.00000 | − | 5.19615i | −0.0969762 | − | 0.167968i | ||||
\(958\) | −26.0000 | −0.840022 | ||||||||
\(959\) | 50.0000 | − | 17.3205i | 1.61458 | − | 0.559308i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 2.00000 | − | 3.46410i | 0.0644826 | − | 0.111687i | ||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | −9.00000 | − | 15.5885i | −0.289870 | − | 0.502070i | ||||
\(965\) | −14.0000 | −0.450676 | ||||||||
\(966\) | −4.00000 | + | 20.7846i | −0.128698 | + | 0.668734i | ||||
\(967\) | −52.0000 | −1.67221 | −0.836104 | − | 0.548572i | \(-0.815172\pi\) | ||||
−0.836104 | + | 0.548572i | \(0.815172\pi\) | |||||||
\(968\) | −3.50000 | − | 6.06218i | −0.112494 | − | 0.194846i | ||||
\(969\) | 2.00000 | − | 3.46410i | 0.0642493 | − | 0.111283i | ||||
\(970\) | 4.00000 | − | 6.92820i | 0.128432 | − | 0.222451i | ||||
\(971\) | 14.0000 | + | 24.2487i | 0.449281 | + | 0.778178i | 0.998339 | − | 0.0576061i | \(-0.0183467\pi\) |
−0.549058 | + | 0.835784i | \(0.685013\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 27.0000 | 0.865136 | ||||||||
\(975\) | −2.00000 | − | 3.46410i | −0.0640513 | − | 0.110940i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.0000 | − | 45.0333i | 0.831814 | − | 1.44074i | −0.0647848 | − | 0.997899i | \(-0.520636\pi\) |
0.896599 | − | 0.442844i | \(-0.146031\pi\) | |||||||
\(978\) | −8.00000 | − | 13.8564i | −0.255812 | − | 0.443079i | ||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 1.00000 | + | 6.92820i | 0.0319438 | + | 0.221313i | ||||
\(981\) | −16.0000 | −0.510841 | ||||||||
\(982\) | 14.0000 | + | 24.2487i | 0.446758 | + | 0.773807i | ||||
\(983\) | −6.00000 | + | 10.3923i | −0.191370 | + | 0.331463i | −0.945705 | − | 0.325027i | \(-0.894626\pi\) |
0.754334 | + | 0.656490i | \(0.227960\pi\) | |||||||
\(984\) | −0.500000 | + | 0.866025i | −0.0159394 | + | 0.0276079i | ||||
\(985\) | −0.500000 | − | 0.866025i | −0.0159313 | − | 0.0275939i | ||||
\(986\) | −3.00000 | −0.0955395 | ||||||||
\(987\) | −18.0000 | − | 15.5885i | −0.572946 | − | 0.496186i | ||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | 16.0000 | + | 27.7128i | 0.508770 | + | 0.881216i | ||||
\(990\) | −1.00000 | + | 1.73205i | −0.0317821 | + | 0.0550482i | ||||
\(991\) | −12.5000 | + | 21.6506i | −0.397076 | + | 0.687755i | −0.993364 | − | 0.115015i | \(-0.963308\pi\) |
0.596288 | + | 0.802771i | \(0.296642\pi\) | |||||||
\(992\) | −1.50000 | − | 2.59808i | −0.0476250 | − | 0.0824890i | ||||
\(993\) | 22.0000 | 0.698149 | ||||||||
\(994\) | 2.00000 | − | 10.3923i | 0.0634361 | − | 0.329624i | ||||
\(995\) | −5.00000 | −0.158511 | ||||||||
\(996\) | 4.50000 | + | 7.79423i | 0.142588 | + | 0.246970i | ||||
\(997\) | 6.00000 | − | 10.3923i | 0.190022 | − | 0.329128i | −0.755235 | − | 0.655454i | \(-0.772477\pi\) |
0.945257 | + | 0.326326i | \(0.105811\pi\) | |||||||
\(998\) | 6.50000 | − | 11.2583i | 0.205754 | − | 0.356376i | ||||
\(999\) | 2.00000 | + | 3.46410i | 0.0632772 | + | 0.109599i |
(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 | 714.2.i.i.613.1 | yes | 2 | |
7.2 | even | 3 | inner | 714.2.i.i.205.1 | ✓ | 2 | |
7.3 | odd | 6 | 4998.2.a.m.1.1 | 1 | |||
7.4 | even | 3 | 4998.2.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
714.2.i.i.205.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
714.2.i.i.613.1 | yes | 2 | 1.1 | even | 1 | trivial | |
4998.2.a.e.1.1 | 1 | 7.4 | even | 3 | |||
4998.2.a.m.1.1 | 1 | 7.3 | odd | 6 |