Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.j (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: | \(5.03057532734\) |
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 | 421.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.421 |
Dual form | 630.2.j.b.211.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | −1.50000 | − | 0.866025i | −0.866025 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −1.50000 | + | 0.866025i | −0.612372 | + | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 1.73205i | 0.500000i | ||||||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.00000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | −7.00000 | −1.60591 | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||||
−0.802955 | + | 0.596040i | \(0.796740\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 1.50000 | − | 0.866025i | 0.327327 | − | 0.188982i | ||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 3.00000 | − | 5.19615i | 0.557086 | − | 0.964901i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.997738 | − | 0.0672232i | \(-0.0214140\pi\) | |||||||
\(30\) | −1.50000 | − | 0.866025i | −0.273861 | − | 0.158114i | ||||
\(31\) | 5.00000 | + | 8.66025i | 0.898027 | + | 1.55543i | 0.830014 | + | 0.557743i | \(0.188333\pi\) |
0.0680129 | + | 0.997684i | \(0.478334\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 4.50000 | − | 2.59808i | 0.783349 | − | 0.452267i | ||||
\(34\) | 1.50000 | − | 2.59808i | 0.257248 | − | 0.445566i | ||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 1.50000 | − | 2.59808i | 0.250000 | − | 0.433013i | ||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | −3.50000 | + | 6.06218i | −0.567775 | + | 0.983415i | ||||
\(39\) | − | 6.92820i | − | 1.10940i | ||||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −4.50000 | − | 7.79423i | −0.702782 | − | 1.21725i | −0.967486 | − | 0.252924i | \(-0.918608\pi\) |
0.264704 | − | 0.964330i | \(-0.414726\pi\) | |||||||
\(42\) | − | 1.73205i | − | 0.267261i | ||||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −6.00000 | + | 10.3923i | −0.875190 | + | 1.51587i | −0.0186297 | + | 0.999826i | \(0.505930\pi\) |
−0.856560 | + | 0.516047i | \(0.827403\pi\) | |||||||
\(48\) | 1.50000 | − | 0.866025i | 0.216506 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | −4.50000 | − | 2.59808i | −0.630126 | − | 0.363803i | ||||
\(52\) | 2.00000 | − | 3.46410i | 0.277350 | − | 0.480384i | ||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | −3.00000 | −0.404520 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 10.5000 | + | 6.06218i | 1.39076 | + | 0.802955i | ||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | −4.50000 | − | 7.79423i | −0.585850 | − | 1.01472i | −0.994769 | − | 0.102151i | \(-0.967427\pi\) |
0.408919 | − | 0.912571i | \(-0.365906\pi\) | |||||||
\(60\) | −1.50000 | + | 0.866025i | −0.193649 | + | 0.111803i | ||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 10.0000 | 1.27000 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.00000 | + | 3.46410i | −0.248069 | + | 0.429669i | ||||
\(66\) | − | 5.19615i | − | 0.639602i | ||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | −1.50000 | − | 2.59808i | −0.181902 | − | 0.315063i | ||||
\(69\) | − | 10.3923i | − | 1.25109i | ||||||
\(70\) | −0.500000 | + | 0.866025i | −0.0597614 | + | 0.103510i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | −1.50000 | − | 2.59808i | −0.176777 | − | 0.306186i | ||||
\(73\) | −7.00000 | −0.819288 | −0.409644 | − | 0.912245i | \(-0.634347\pi\) | ||||
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | 1.50000 | − | 0.866025i | 0.173205 | − | 0.100000i | ||||
\(76\) | 3.50000 | + | 6.06218i | 0.401478 | + | 0.695379i | ||||
\(77\) | −1.50000 | − | 2.59808i | −0.170941 | − | 0.296078i | ||||
\(78\) | −6.00000 | − | 3.46410i | −0.679366 | − | 0.392232i | ||||
\(79\) | −1.00000 | + | 1.73205i | −0.112509 | + | 0.194871i | −0.916781 | − | 0.399390i | \(-0.869222\pi\) |
0.804272 | + | 0.594261i | \(0.202555\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −9.00000 | −0.993884 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | −1.50000 | − | 0.866025i | −0.163663 | − | 0.0944911i | ||||
\(85\) | 1.50000 | + | 2.59808i | 0.162698 | + | 0.281801i | ||||
\(86\) | −0.500000 | − | 0.866025i | −0.0539164 | − | 0.0933859i | ||||
\(87\) | −9.00000 | + | 5.19615i | −0.964901 | + | 0.557086i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 1.50000 | + | 2.59808i | 0.158114 | + | 0.273861i | ||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 3.00000 | − | 5.19615i | 0.312772 | − | 0.541736i | ||||
\(93\) | − | 17.3205i | − | 1.79605i | ||||||
\(94\) | 6.00000 | + | 10.3923i | 0.618853 | + | 1.07188i | ||||
\(95\) | −3.50000 | − | 6.06218i | −0.359092 | − | 0.621966i | ||||
\(96\) | − | 1.73205i | − | 0.176777i | ||||||
\(97\) | −5.50000 | + | 9.52628i | −0.558440 | + | 0.967247i | 0.439187 | + | 0.898396i | \(0.355267\pi\) |
−0.997627 | + | 0.0688512i | \(0.978067\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −9.00000 | −0.904534 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | −4.50000 | + | 2.59808i | −0.445566 | + | 0.257248i | ||||
\(103\) | 2.00000 | + | 3.46410i | 0.197066 | + | 0.341328i | 0.947576 | − | 0.319531i | \(-0.103525\pi\) |
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(104\) | −2.00000 | − | 3.46410i | −0.196116 | − | 0.339683i | ||||
\(105\) | 1.50000 | + | 0.866025i | 0.146385 | + | 0.0845154i | ||||
\(106\) | 3.00000 | − | 5.19615i | 0.291386 | − | 0.504695i | ||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | −16.0000 | −1.53252 | −0.766261 | − | 0.642529i | \(-0.777885\pi\) | ||||
−0.766261 | + | 0.642529i | \(0.777885\pi\) | |||||||
\(110\) | −1.50000 | + | 2.59808i | −0.143019 | + | 0.247717i | ||||
\(111\) | −12.0000 | − | 6.92820i | −1.13899 | − | 0.657596i | ||||
\(112\) | −0.500000 | − | 0.866025i | −0.0472456 | − | 0.0818317i | ||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | 10.5000 | − | 6.06218i | 0.983415 | − | 0.567775i | ||||
\(115\) | −3.00000 | + | 5.19615i | −0.279751 | + | 0.484544i | ||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | −6.00000 | + | 10.3923i | −0.554700 | + | 0.960769i | ||||
\(118\) | −9.00000 | −0.828517 | ||||||||
\(119\) | −1.50000 | + | 2.59808i | −0.137505 | + | 0.238165i | ||||
\(120\) | 1.73205i | 0.158114i | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 7.00000 | + | 12.1244i | 0.633750 | + | 1.09769i | ||||
\(123\) | 15.5885i | 1.40556i | ||||||||
\(124\) | 5.00000 | − | 8.66025i | 0.449013 | − | 0.777714i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −1.50000 | + | 2.59808i | −0.133631 | + | 0.231455i | ||||
\(127\) | −10.0000 | −0.887357 | −0.443678 | − | 0.896186i | \(-0.646327\pi\) | ||||
−0.443678 | + | 0.896186i | \(0.646327\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −1.50000 | + | 0.866025i | −0.132068 | + | 0.0762493i | ||||
\(130\) | 2.00000 | + | 3.46410i | 0.175412 | + | 0.303822i | ||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | −4.50000 | − | 2.59808i | −0.391675 | − | 0.226134i | ||||
\(133\) | 3.50000 | − | 6.06218i | 0.303488 | − | 0.525657i | ||||
\(134\) | 7.00000 | 0.604708 | ||||||||
\(135\) | 4.50000 | − | 2.59808i | 0.387298 | − | 0.223607i | ||||
\(136\) | −3.00000 | −0.257248 | ||||||||
\(137\) | 10.5000 | − | 18.1865i | 0.897076 | − | 1.55378i | 0.0658609 | − | 0.997829i | \(-0.479021\pi\) |
0.831215 | − | 0.555952i | \(-0.187646\pi\) | |||||||
\(138\) | −9.00000 | − | 5.19615i | −0.766131 | − | 0.442326i | ||||
\(139\) | −5.50000 | − | 9.52628i | −0.466504 | − | 0.808008i | 0.532764 | − | 0.846264i | \(-0.321153\pi\) |
−0.999268 | + | 0.0382553i | \(0.987820\pi\) | |||||||
\(140\) | 0.500000 | + | 0.866025i | 0.0422577 | + | 0.0731925i | ||||
\(141\) | 18.0000 | − | 10.3923i | 1.51587 | − | 0.875190i | ||||
\(142\) | 3.00000 | − | 5.19615i | 0.251754 | − | 0.436051i | ||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | −3.50000 | + | 6.06218i | −0.289662 | + | 0.501709i | ||||
\(147\) | 1.73205i | 0.142857i | ||||||||
\(148\) | −4.00000 | − | 6.92820i | −0.328798 | − | 0.569495i | ||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | − | 1.73205i | − | 0.141421i | ||||||
\(151\) | −7.00000 | + | 12.1244i | −0.569652 | + | 0.986666i | 0.426948 | + | 0.904276i | \(0.359589\pi\) |
−0.996600 | + | 0.0823900i | \(0.973745\pi\) | |||||||
\(152\) | 7.00000 | 0.567775 | ||||||||
\(153\) | 4.50000 | + | 7.79423i | 0.363803 | + | 0.630126i | ||||
\(154\) | −3.00000 | −0.241747 | ||||||||
\(155\) | −5.00000 | + | 8.66025i | −0.401610 | + | 0.695608i | ||||
\(156\) | −6.00000 | + | 3.46410i | −0.480384 | + | 0.277350i | ||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | 1.00000 | + | 1.73205i | 0.0795557 | + | 0.137795i | ||||
\(159\) | −9.00000 | − | 5.19615i | −0.713746 | − | 0.412082i | ||||
\(160\) | −0.500000 | + | 0.866025i | −0.0395285 | + | 0.0684653i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 4.50000 | + | 7.79423i | 0.353553 | + | 0.612372i | ||||
\(163\) | 8.00000 | 0.626608 | 0.313304 | − | 0.949653i | \(-0.398564\pi\) | ||||
0.313304 | + | 0.949653i | \(0.398564\pi\) | |||||||
\(164\) | −4.50000 | + | 7.79423i | −0.351391 | + | 0.608627i | ||||
\(165\) | 4.50000 | + | 2.59808i | 0.350325 | + | 0.202260i | ||||
\(166\) | −6.00000 | − | 10.3923i | −0.465690 | − | 0.806599i | ||||
\(167\) | −3.00000 | − | 5.19615i | −0.232147 | − | 0.402090i | 0.726293 | − | 0.687386i | \(-0.241242\pi\) |
−0.958440 | + | 0.285295i | \(0.907908\pi\) | |||||||
\(168\) | −1.50000 | + | 0.866025i | −0.115728 | + | 0.0668153i | ||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 3.00000 | 0.230089 | ||||||||
\(171\) | −10.5000 | − | 18.1865i | −0.802955 | − | 1.39076i | ||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | −3.00000 | + | 5.19615i | −0.228086 | + | 0.395056i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) |
0.729155 | + | 0.684349i | \(0.239913\pi\) | |||||||
\(174\) | 10.3923i | 0.787839i | ||||||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 15.5885i | 1.17170i | ||||||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 3.00000 | 0.223607 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | −2.00000 | + | 3.46410i | −0.148250 | + | 0.256776i | ||||
\(183\) | 21.0000 | − | 12.1244i | 1.55236 | − | 0.896258i | ||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 4.00000 | + | 6.92820i | 0.294086 | + | 0.509372i | ||||
\(186\) | −15.0000 | − | 8.66025i | −1.09985 | − | 0.635001i | ||||
\(187\) | −4.50000 | + | 7.79423i | −0.329073 | + | 0.569970i | ||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | −7.00000 | −0.507833 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | −1.50000 | − | 0.866025i | −0.108253 | − | 0.0625000i | ||||
\(193\) | 0.500000 | + | 0.866025i | 0.0359908 | + | 0.0623379i | 0.883460 | − | 0.468507i | \(-0.155208\pi\) |
−0.847469 | + | 0.530845i | \(0.821875\pi\) | |||||||
\(194\) | 5.50000 | + | 9.52628i | 0.394877 | + | 0.683947i | ||||
\(195\) | 6.00000 | − | 3.46410i | 0.429669 | − | 0.248069i | ||||
\(196\) | −0.500000 | + | 0.866025i | −0.0357143 | + | 0.0618590i | ||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | −4.50000 | + | 7.79423i | −0.319801 | + | 0.553912i | ||||
\(199\) | 20.0000 | 1.41776 | 0.708881 | − | 0.705328i | \(-0.249200\pi\) | ||||
0.708881 | + | 0.705328i | \(0.249200\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | − | 12.1244i | − | 0.855186i | ||||||
\(202\) | 6.00000 | + | 10.3923i | 0.422159 | + | 0.731200i | ||||
\(203\) | 3.00000 | + | 5.19615i | 0.210559 | + | 0.364698i | ||||
\(204\) | 5.19615i | 0.363803i | ||||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 4.00000 | 0.278693 | ||||||||
\(207\) | −9.00000 | + | 15.5885i | −0.625543 | + | 1.08347i | ||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 10.5000 | − | 18.1865i | 0.726300 | − | 1.25799i | ||||
\(210\) | 1.50000 | − | 0.866025i | 0.103510 | − | 0.0597614i | ||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | −9.00000 | − | 5.19615i | −0.616670 | − | 0.356034i | ||||
\(214\) | 1.50000 | − | 2.59808i | 0.102538 | − | 0.177601i | ||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −10.0000 | −0.678844 | ||||||||
\(218\) | −8.00000 | + | 13.8564i | −0.541828 | + | 0.938474i | ||||
\(219\) | 10.5000 | + | 6.06218i | 0.709524 | + | 0.409644i | ||||
\(220\) | 1.50000 | + | 2.59808i | 0.101130 | + | 0.175162i | ||||
\(221\) | 6.00000 | + | 10.3923i | 0.403604 | + | 0.699062i | ||||
\(222\) | −12.0000 | + | 6.92820i | −0.805387 | + | 0.464991i | ||||
\(223\) | 5.00000 | − | 8.66025i | 0.334825 | − | 0.579934i | −0.648626 | − | 0.761107i | \(-0.724656\pi\) |
0.983451 | + | 0.181173i | \(0.0579895\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | − | 12.1244i | − | 0.802955i | ||||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 3.00000 | + | 5.19615i | 0.197814 | + | 0.342624i | ||||
\(231\) | 5.19615i | 0.341882i | ||||||||
\(232\) | −3.00000 | + | 5.19615i | −0.196960 | + | 0.341144i | ||||
\(233\) | 9.00000 | 0.589610 | 0.294805 | − | 0.955557i | \(-0.404745\pi\) | ||||
0.294805 | + | 0.955557i | \(0.404745\pi\) | |||||||
\(234\) | 6.00000 | + | 10.3923i | 0.392232 | + | 0.679366i | ||||
\(235\) | −12.0000 | −0.782794 | ||||||||
\(236\) | −4.50000 | + | 7.79423i | −0.292925 | + | 0.507361i | ||||
\(237\) | 3.00000 | − | 1.73205i | 0.194871 | − | 0.112509i | ||||
\(238\) | 1.50000 | + | 2.59808i | 0.0972306 | + | 0.168408i | ||||
\(239\) | −3.00000 | − | 5.19615i | −0.194054 | − | 0.336111i | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | 1.50000 | + | 0.866025i | 0.0968246 | + | 0.0559017i | ||||
\(241\) | −2.50000 | + | 4.33013i | −0.161039 | + | 0.278928i | −0.935242 | − | 0.354010i | \(-0.884818\pi\) |
0.774202 | + | 0.632938i | \(0.218151\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | 13.5000 | − | 7.79423i | 0.866025 | − | 0.500000i | ||||
\(244\) | 14.0000 | 0.896258 | ||||||||
\(245\) | 0.500000 | − | 0.866025i | 0.0319438 | − | 0.0553283i | ||||
\(246\) | 13.5000 | + | 7.79423i | 0.860729 | + | 0.496942i | ||||
\(247\) | −14.0000 | − | 24.2487i | −0.890799 | − | 1.54291i | ||||
\(248\) | −5.00000 | − | 8.66025i | −0.317500 | − | 0.549927i | ||||
\(249\) | −18.0000 | + | 10.3923i | −1.14070 | + | 0.658586i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −9.00000 | −0.568075 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(252\) | 1.50000 | + | 2.59808i | 0.0944911 | + | 0.163663i | ||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | −5.00000 | + | 8.66025i | −0.313728 | + | 0.543393i | ||||
\(255\) | − | 5.19615i | − | 0.325396i | ||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.50000 | + | 12.9904i | 0.467837 | + | 0.810318i | 0.999325 | − | 0.0367485i | \(-0.0117000\pi\) |
−0.531487 | + | 0.847066i | \(0.678367\pi\) | |||||||
\(258\) | 1.73205i | 0.107833i | ||||||||
\(259\) | −4.00000 | + | 6.92820i | −0.248548 | + | 0.430498i | ||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 18.0000 | 1.11417 | ||||||||
\(262\) | −12.0000 | −0.741362 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −4.50000 | + | 2.59808i | −0.276956 | + | 0.159901i | ||||
\(265\) | 3.00000 | + | 5.19615i | 0.184289 | + | 0.319197i | ||||
\(266\) | −3.50000 | − | 6.06218i | −0.214599 | − | 0.371696i | ||||
\(267\) | −9.00000 | − | 5.19615i | −0.550791 | − | 0.317999i | ||||
\(268\) | 3.50000 | − | 6.06218i | 0.213797 | − | 0.370306i | ||||
\(269\) | 30.0000 | 1.82913 | 0.914566 | − | 0.404436i | \(-0.132532\pi\) | ||||
0.914566 | + | 0.404436i | \(0.132532\pi\) | |||||||
\(270\) | − | 5.19615i | − | 0.316228i | ||||||
\(271\) | 20.0000 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | −1.50000 | + | 2.59808i | −0.0909509 | + | 0.157532i | ||||
\(273\) | 6.00000 | + | 3.46410i | 0.363137 | + | 0.209657i | ||||
\(274\) | −10.5000 | − | 18.1865i | −0.634328 | − | 1.09869i | ||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | −9.00000 | + | 5.19615i | −0.541736 | + | 0.312772i | ||||
\(277\) | 11.0000 | − | 19.0526i | 0.660926 | − | 1.14476i | −0.319447 | − | 0.947604i | \(-0.603497\pi\) |
0.980373 | − | 0.197153i | \(-0.0631696\pi\) | |||||||
\(278\) | −11.0000 | −0.659736 | ||||||||
\(279\) | −15.0000 | + | 25.9808i | −0.898027 | + | 1.55543i | ||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 3.00000 | − | 5.19615i | 0.178965 | − | 0.309976i | −0.762561 | − | 0.646916i | \(-0.776058\pi\) |
0.941526 | + | 0.336939i | \(0.109392\pi\) | |||||||
\(282\) | − | 20.7846i | − | 1.23771i | ||||||
\(283\) | −10.0000 | − | 17.3205i | −0.594438 | − | 1.02960i | −0.993626 | − | 0.112728i | \(-0.964041\pi\) |
0.399188 | − | 0.916869i | \(-0.369292\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 12.1244i | 0.718185i | ||||||||
\(286\) | −6.00000 | + | 10.3923i | −0.354787 | + | 0.614510i | ||||
\(287\) | 9.00000 | 0.531253 | ||||||||
\(288\) | −1.50000 | + | 2.59808i | −0.0883883 | + | 0.153093i | ||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 3.00000 | − | 5.19615i | 0.176166 | − | 0.305129i | ||||
\(291\) | 16.5000 | − | 9.52628i | 0.967247 | − | 0.558440i | ||||
\(292\) | 3.50000 | + | 6.06218i | 0.204822 | + | 0.354762i | ||||
\(293\) | −9.00000 | − | 15.5885i | −0.525786 | − | 0.910687i | −0.999549 | − | 0.0300351i | \(-0.990438\pi\) |
0.473763 | − | 0.880652i | \(-0.342895\pi\) | |||||||
\(294\) | 1.50000 | + | 0.866025i | 0.0874818 | + | 0.0505076i | ||||
\(295\) | 4.50000 | − | 7.79423i | 0.262000 | − | 0.453798i | ||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | −12.0000 | −0.695141 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | −1.50000 | − | 0.866025i | −0.0866025 | − | 0.0500000i | ||||
\(301\) | 0.500000 | + | 0.866025i | 0.0288195 | + | 0.0499169i | ||||
\(302\) | 7.00000 | + | 12.1244i | 0.402805 | + | 0.697678i | ||||
\(303\) | 18.0000 | − | 10.3923i | 1.03407 | − | 0.597022i | ||||
\(304\) | 3.50000 | − | 6.06218i | 0.200739 | − | 0.347690i | ||||
\(305\) | −14.0000 | −0.801638 | ||||||||
\(306\) | 9.00000 | 0.514496 | ||||||||
\(307\) | 17.0000 | 0.970241 | 0.485121 | − | 0.874447i | \(-0.338776\pi\) | ||||
0.485121 | + | 0.874447i | \(0.338776\pi\) | |||||||
\(308\) | −1.50000 | + | 2.59808i | −0.0854704 | + | 0.148039i | ||||
\(309\) | − | 6.92820i | − | 0.394132i | ||||||
\(310\) | 5.00000 | + | 8.66025i | 0.283981 | + | 0.491869i | ||||
\(311\) | −9.00000 | − | 15.5885i | −0.510343 | − | 0.883940i | −0.999928 | − | 0.0119847i | \(-0.996185\pi\) |
0.489585 | − | 0.871956i | \(-0.337148\pi\) | |||||||
\(312\) | 6.92820i | 0.392232i | ||||||||
\(313\) | 0.500000 | − | 0.866025i | 0.0282617 | − | 0.0489506i | −0.851549 | − | 0.524276i | \(-0.824336\pi\) |
0.879810 | + | 0.475325i | \(0.157669\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | −1.50000 | − | 2.59808i | −0.0845154 | − | 0.146385i | ||||
\(316\) | 2.00000 | 0.112509 | ||||||||
\(317\) | −12.0000 | + | 20.7846i | −0.673987 | + | 1.16738i | 0.302777 | + | 0.953062i | \(0.402086\pi\) |
−0.976764 | + | 0.214318i | \(0.931247\pi\) | |||||||
\(318\) | −9.00000 | + | 5.19615i | −0.504695 | + | 0.291386i | ||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | −4.50000 | − | 2.59808i | −0.251166 | − | 0.145010i | ||||
\(322\) | −3.00000 | + | 5.19615i | −0.167183 | + | 0.289570i | ||||
\(323\) | −21.0000 | −1.16847 | ||||||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 4.00000 | − | 6.92820i | 0.221540 | − | 0.383718i | ||||
\(327\) | 24.0000 | + | 13.8564i | 1.32720 | + | 0.766261i | ||||
\(328\) | 4.50000 | + | 7.79423i | 0.248471 | + | 0.430364i | ||||
\(329\) | −6.00000 | − | 10.3923i | −0.330791 | − | 0.572946i | ||||
\(330\) | 4.50000 | − | 2.59808i | 0.247717 | − | 0.143019i | ||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | 12.0000 | + | 20.7846i | 0.657596 | + | 1.13899i | ||||
\(334\) | −6.00000 | −0.328305 | ||||||||
\(335\) | −3.50000 | + | 6.06218i | −0.191225 | + | 0.331212i | ||||
\(336\) | 1.73205i | 0.0944911i | ||||||||
\(337\) | −2.50000 | − | 4.33013i | −0.136184 | − | 0.235877i | 0.789865 | − | 0.613280i | \(-0.210150\pi\) |
−0.926049 | + | 0.377403i | \(0.876817\pi\) | |||||||
\(338\) | 1.50000 | + | 2.59808i | 0.0815892 | + | 0.141317i | ||||
\(339\) | − | 10.3923i | − | 0.564433i | ||||||
\(340\) | 1.50000 | − | 2.59808i | 0.0813489 | − | 0.140900i | ||||
\(341\) | −30.0000 | −1.62459 | ||||||||
\(342\) | −21.0000 | −1.13555 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −0.500000 | + | 0.866025i | −0.0269582 | + | 0.0466930i | ||||
\(345\) | 9.00000 | − | 5.19615i | 0.484544 | − | 0.279751i | ||||
\(346\) | 3.00000 | + | 5.19615i | 0.161281 | + | 0.279347i | ||||
\(347\) | −4.50000 | − | 7.79423i | −0.241573 | − | 0.418416i | 0.719590 | − | 0.694399i | \(-0.244330\pi\) |
−0.961162 | + | 0.275983i | \(0.910997\pi\) | |||||||
\(348\) | 9.00000 | + | 5.19615i | 0.482451 | + | 0.278543i | ||||
\(349\) | −10.0000 | + | 17.3205i | −0.535288 | + | 0.927146i | 0.463862 | + | 0.885908i | \(0.346463\pi\) |
−0.999149 | + | 0.0412379i | \(0.986870\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 18.0000 | − | 10.3923i | 0.960769 | − | 0.554700i | ||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −4.50000 | + | 7.79423i | −0.239511 | + | 0.414845i | −0.960574 | − | 0.278024i | \(-0.910320\pi\) |
0.721063 | + | 0.692869i | \(0.243654\pi\) | |||||||
\(354\) | 13.5000 | + | 7.79423i | 0.717517 | + | 0.414259i | ||||
\(355\) | 3.00000 | + | 5.19615i | 0.159223 | + | 0.275783i | ||||
\(356\) | −3.00000 | − | 5.19615i | −0.159000 | − | 0.275396i | ||||
\(357\) | 4.50000 | − | 2.59808i | 0.238165 | − | 0.137505i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 1.50000 | − | 2.59808i | 0.0790569 | − | 0.136931i | ||||
\(361\) | 30.0000 | 1.57895 | ||||||||
\(362\) | 10.0000 | − | 17.3205i | 0.525588 | − | 0.910346i | ||||
\(363\) | − | 3.46410i | − | 0.181818i | ||||||
\(364\) | 2.00000 | + | 3.46410i | 0.104828 | + | 0.181568i | ||||
\(365\) | −3.50000 | − | 6.06218i | −0.183198 | − | 0.317309i | ||||
\(366\) | − | 24.2487i | − | 1.26750i | ||||||
\(367\) | 14.0000 | − | 24.2487i | 0.730794 | − | 1.26577i | −0.225750 | − | 0.974185i | \(-0.572483\pi\) |
0.956544 | − | 0.291587i | \(-0.0941834\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 13.5000 | − | 23.3827i | 0.702782 | − | 1.21725i | ||||
\(370\) | 8.00000 | 0.415900 | ||||||||
\(371\) | −3.00000 | + | 5.19615i | −0.155752 | + | 0.269771i | ||||
\(372\) | −15.0000 | + | 8.66025i | −0.777714 | + | 0.449013i | ||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 4.50000 | + | 7.79423i | 0.232689 | + | 0.403030i | ||||
\(375\) | 1.50000 | + | 0.866025i | 0.0774597 | + | 0.0447214i | ||||
\(376\) | 6.00000 | − | 10.3923i | 0.309426 | − | 0.535942i | ||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | 4.50000 | − | 2.59808i | 0.231455 | − | 0.133631i | ||||
\(379\) | 5.00000 | 0.256833 | 0.128416 | − | 0.991720i | \(-0.459011\pi\) | ||||
0.128416 | + | 0.991720i | \(0.459011\pi\) | |||||||
\(380\) | −3.50000 | + | 6.06218i | −0.179546 | + | 0.310983i | ||||
\(381\) | 15.0000 | + | 8.66025i | 0.768473 | + | 0.443678i | ||||
\(382\) | −6.00000 | − | 10.3923i | −0.306987 | − | 0.531717i | ||||
\(383\) | 6.00000 | + | 10.3923i | 0.306586 | + | 0.531022i | 0.977613 | − | 0.210411i | \(-0.0674801\pi\) |
−0.671027 | + | 0.741433i | \(0.734147\pi\) | |||||||
\(384\) | −1.50000 | + | 0.866025i | −0.0765466 | + | 0.0441942i | ||||
\(385\) | 1.50000 | − | 2.59808i | 0.0764471 | − | 0.132410i | ||||
\(386\) | 1.00000 | 0.0508987 | ||||||||
\(387\) | 3.00000 | 0.152499 | ||||||||
\(388\) | 11.0000 | 0.558440 | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | − | 6.92820i | − | 0.350823i | ||||||
\(391\) | 9.00000 | + | 15.5885i | 0.455150 | + | 0.788342i | ||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | 20.7846i | 1.04844i | ||||||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | −2.00000 | −0.100631 | ||||||||
\(396\) | 4.50000 | + | 7.79423i | 0.226134 | + | 0.391675i | ||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | 10.0000 | − | 17.3205i | 0.501255 | − | 0.868199i | ||||
\(399\) | −10.5000 | + | 6.06218i | −0.525657 | + | 0.303488i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | −10.5000 | − | 6.06218i | −0.523692 | − | 0.302354i | ||||
\(403\) | −20.0000 | + | 34.6410i | −0.996271 | + | 1.72559i | ||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 6.00000 | 0.297775 | ||||||||
\(407\) | −12.0000 | + | 20.7846i | −0.594818 | + | 1.03025i | ||||
\(408\) | 4.50000 | + | 2.59808i | 0.222783 | + | 0.128624i | ||||
\(409\) | 9.50000 | + | 16.4545i | 0.469745 | + | 0.813622i | 0.999402 | − | 0.0345902i | \(-0.0110126\pi\) |
−0.529657 | + | 0.848212i | \(0.677679\pi\) | |||||||
\(410\) | −4.50000 | − | 7.79423i | −0.222239 | − | 0.384930i | ||||
\(411\) | −31.5000 | + | 18.1865i | −1.55378 | + | 0.897076i | ||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | 9.00000 | 0.442861 | ||||||||
\(414\) | 9.00000 | + | 15.5885i | 0.442326 | + | 0.766131i | ||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | −2.00000 | + | 3.46410i | −0.0980581 | + | 0.169842i | ||||
\(417\) | 19.0526i | 0.933008i | ||||||||
\(418\) | −10.5000 | − | 18.1865i | −0.513572 | − | 0.889532i | ||||
\(419\) | −12.0000 | − | 20.7846i | −0.586238 | − | 1.01539i | −0.994720 | − | 0.102628i | \(-0.967275\pi\) |
0.408481 | − | 0.912767i | \(-0.366058\pi\) | |||||||
\(420\) | − | 1.73205i | − | 0.0845154i | ||||||
\(421\) | −13.0000 | + | 22.5167i | −0.633581 | + | 1.09739i | 0.353233 | + | 0.935536i | \(0.385082\pi\) |
−0.986814 | + | 0.161859i | \(0.948251\pi\) | |||||||
\(422\) | 4.00000 | 0.194717 | ||||||||
\(423\) | −36.0000 | −1.75038 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −1.50000 | + | 2.59808i | −0.0727607 | + | 0.126025i | ||||
\(426\) | −9.00000 | + | 5.19615i | −0.436051 | + | 0.251754i | ||||
\(427\) | −7.00000 | − | 12.1244i | −0.338754 | − | 0.586739i | ||||
\(428\) | −1.50000 | − | 2.59808i | −0.0725052 | − | 0.125583i | ||||
\(429\) | 18.0000 | + | 10.3923i | 0.869048 | + | 0.501745i | ||||
\(430\) | 0.500000 | − | 0.866025i | 0.0241121 | − | 0.0417635i | ||||
\(431\) | 12.0000 | 0.578020 | 0.289010 | − | 0.957326i | \(-0.406674\pi\) | ||||
0.289010 | + | 0.957326i | \(0.406674\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | 11.0000 | 0.528626 | 0.264313 | − | 0.964437i | \(-0.414855\pi\) | ||||
0.264313 | + | 0.964437i | \(0.414855\pi\) | |||||||
\(434\) | −5.00000 | + | 8.66025i | −0.240008 | + | 0.415705i | ||||
\(435\) | −9.00000 | − | 5.19615i | −0.431517 | − | 0.249136i | ||||
\(436\) | 8.00000 | + | 13.8564i | 0.383131 | + | 0.663602i | ||||
\(437\) | −21.0000 | − | 36.3731i | −1.00457 | − | 1.73996i | ||||
\(438\) | 10.5000 | − | 6.06218i | 0.501709 | − | 0.289662i | ||||
\(439\) | 5.00000 | − | 8.66025i | 0.238637 | − | 0.413331i | −0.721686 | − | 0.692220i | \(-0.756633\pi\) |
0.960323 | + | 0.278889i | \(0.0899661\pi\) | |||||||
\(440\) | 3.00000 | 0.143019 | ||||||||
\(441\) | 1.50000 | − | 2.59808i | 0.0714286 | − | 0.123718i | ||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | −7.50000 | + | 12.9904i | −0.356336 | + | 0.617192i | −0.987346 | − | 0.158583i | \(-0.949307\pi\) |
0.631010 | + | 0.775775i | \(0.282641\pi\) | |||||||
\(444\) | 13.8564i | 0.657596i | ||||||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | −5.00000 | − | 8.66025i | −0.236757 | − | 0.410075i | ||||
\(447\) | 20.7846i | 0.983078i | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | −39.0000 | −1.84052 | −0.920262 | − | 0.391303i | \(-0.872024\pi\) | ||||
−0.920262 | + | 0.391303i | \(0.872024\pi\) | |||||||
\(450\) | −1.50000 | + | 2.59808i | −0.0707107 | + | 0.122474i | ||||
\(451\) | 27.0000 | 1.27138 | ||||||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | 21.0000 | − | 12.1244i | 0.986666 | − | 0.569652i | ||||
\(454\) | −1.50000 | − | 2.59808i | −0.0703985 | − | 0.121934i | ||||
\(455\) | −2.00000 | − | 3.46410i | −0.0937614 | − | 0.162400i | ||||
\(456\) | −10.5000 | − | 6.06218i | −0.491708 | − | 0.283887i | ||||
\(457\) | −5.50000 | + | 9.52628i | −0.257279 | + | 0.445621i | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | −20.0000 | −0.934539 | ||||||||
\(459\) | − | 15.5885i | − | 0.727607i | ||||||
\(460\) | 6.00000 | 0.279751 | ||||||||
\(461\) | 12.0000 | − | 20.7846i | 0.558896 | − | 0.968036i | −0.438693 | − | 0.898637i | \(-0.644559\pi\) |
0.997589 | − | 0.0693989i | \(-0.0221081\pi\) | |||||||
\(462\) | 4.50000 | + | 2.59808i | 0.209359 | + | 0.120873i | ||||
\(463\) | 2.00000 | + | 3.46410i | 0.0929479 | + | 0.160990i | 0.908750 | − | 0.417340i | \(-0.137038\pi\) |
−0.815802 | + | 0.578331i | \(0.803704\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 15.0000 | − | 8.66025i | 0.695608 | − | 0.401610i | ||||
\(466\) | 4.50000 | − | 7.79423i | 0.208458 | − | 0.361061i | ||||
\(467\) | −27.0000 | −1.24941 | −0.624705 | − | 0.780860i | \(-0.714781\pi\) | ||||
−0.624705 | + | 0.780860i | \(0.714781\pi\) | |||||||
\(468\) | 12.0000 | 0.554700 | ||||||||
\(469\) | −7.00000 | −0.323230 | ||||||||
\(470\) | −6.00000 | + | 10.3923i | −0.276759 | + | 0.479361i | ||||
\(471\) | − | 6.92820i | − | 0.319235i | ||||||
\(472\) | 4.50000 | + | 7.79423i | 0.207129 | + | 0.358758i | ||||
\(473\) | 1.50000 | + | 2.59808i | 0.0689701 | + | 0.119460i | ||||
\(474\) | − | 3.46410i | − | 0.159111i | ||||||
\(475\) | 3.50000 | − | 6.06218i | 0.160591 | − | 0.278152i | ||||
\(476\) | 3.00000 | 0.137505 | ||||||||
\(477\) | 9.00000 | + | 15.5885i | 0.412082 | + | 0.713746i | ||||
\(478\) | −6.00000 | −0.274434 | ||||||||
\(479\) | −15.0000 | + | 25.9808i | −0.685367 | + | 1.18709i | 0.287954 | + | 0.957644i | \(0.407025\pi\) |
−0.973321 | + | 0.229447i | \(0.926308\pi\) | |||||||
\(480\) | 1.50000 | − | 0.866025i | 0.0684653 | − | 0.0395285i | ||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 2.50000 | + | 4.33013i | 0.113872 | + | 0.197232i | ||||
\(483\) | 9.00000 | + | 5.19615i | 0.409514 | + | 0.236433i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | −11.0000 | −0.499484 | ||||||||
\(486\) | − | 15.5885i | − | 0.707107i | ||||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | 7.00000 | − | 12.1244i | 0.316875 | − | 0.548844i | ||||
\(489\) | −12.0000 | − | 6.92820i | −0.542659 | − | 0.313304i | ||||
\(490\) | −0.500000 | − | 0.866025i | −0.0225877 | − | 0.0391230i | ||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 13.5000 | − | 7.79423i | 0.608627 | − | 0.351391i | ||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | −28.0000 | −1.25978 | ||||||||
\(495\) | −4.50000 | − | 7.79423i | −0.202260 | − | 0.350325i | ||||
\(496\) | −10.0000 | −0.449013 | ||||||||
\(497\) | −3.00000 | + | 5.19615i | −0.134568 | + | 0.233079i | ||||
\(498\) | 20.7846i | 0.931381i | ||||||||
\(499\) | −8.50000 | − | 14.7224i | −0.380512 | − | 0.659067i | 0.610623 | − | 0.791921i | \(-0.290919\pi\) |
−0.991136 | + | 0.132855i | \(0.957586\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 10.3923i | 0.464294i | ||||||||
\(502\) | −4.50000 | + | 7.79423i | −0.200845 | + | 0.347873i | ||||
\(503\) | 42.0000 | 1.87269 | 0.936344 | − | 0.351085i | \(-0.114187\pi\) | ||||
0.936344 | + | 0.351085i | \(0.114187\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | −9.00000 | + | 15.5885i | −0.400099 | + | 0.692991i | ||||
\(507\) | 4.50000 | − | 2.59808i | 0.199852 | − | 0.115385i | ||||
\(508\) | 5.00000 | + | 8.66025i | 0.221839 | + | 0.384237i | ||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | −4.50000 | − | 2.59808i | −0.199263 | − | 0.115045i | ||||
\(511\) | 3.50000 | − | 6.06218i | 0.154831 | − | 0.268175i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 36.3731i | 1.60591i | ||||||||
\(514\) | 15.0000 | 0.661622 | ||||||||
\(515\) | −2.00000 | + | 3.46410i | −0.0881305 | + | 0.152647i | ||||
\(516\) | 1.50000 | + | 0.866025i | 0.0660338 | + | 0.0381246i | ||||
\(517\) | −18.0000 | − | 31.1769i | −0.791639 | − | 1.37116i | ||||
\(518\) | 4.00000 | + | 6.92820i | 0.175750 | + | 0.304408i | ||||
\(519\) | 9.00000 | − | 5.19615i | 0.395056 | − | 0.228086i | ||||
\(520\) | 2.00000 | − | 3.46410i | 0.0877058 | − | 0.151911i | ||||
\(521\) | −15.0000 | −0.657162 | −0.328581 | − | 0.944476i | \(-0.606570\pi\) | ||||
−0.328581 | + | 0.944476i | \(0.606570\pi\) | |||||||
\(522\) | 9.00000 | − | 15.5885i | 0.393919 | − | 0.682288i | ||||
\(523\) | −4.00000 | −0.174908 | −0.0874539 | − | 0.996169i | \(-0.527873\pi\) | ||||
−0.0874539 | + | 0.996169i | \(0.527873\pi\) | |||||||
\(524\) | −6.00000 | + | 10.3923i | −0.262111 | + | 0.453990i | ||||
\(525\) | 1.73205i | 0.0755929i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 15.0000 | + | 25.9808i | 0.653410 | + | 1.13174i | ||||
\(528\) | 5.19615i | 0.226134i | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 6.00000 | 0.260623 | ||||||||
\(531\) | 13.5000 | − | 23.3827i | 0.585850 | − | 1.01472i | ||||
\(532\) | −7.00000 | −0.303488 | ||||||||
\(533\) | 18.0000 | − | 31.1769i | 0.779667 | − | 1.35042i | ||||
\(534\) | −9.00000 | + | 5.19615i | −0.389468 | + | 0.224860i | ||||
\(535\) | 1.50000 | + | 2.59808i | 0.0648507 | + | 0.112325i | ||||
\(536\) | −3.50000 | − | 6.06218i | −0.151177 | − | 0.261846i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.0000 | − | 25.9808i | 0.646696 | − | 1.12011i | ||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | −4.50000 | − | 2.59808i | −0.193649 | − | 0.111803i | ||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | 10.0000 | − | 17.3205i | 0.429537 | − | 0.743980i | ||||
\(543\) | −30.0000 | − | 17.3205i | −1.28742 | − | 0.743294i | ||||
\(544\) | 1.50000 | + | 2.59808i | 0.0643120 | + | 0.111392i | ||||
\(545\) | −8.00000 | − | 13.8564i | −0.342682 | − | 0.593543i | ||||
\(546\) | 6.00000 | − | 3.46410i | 0.256776 | − | 0.148250i | ||||
\(547\) | 18.5000 | − | 32.0429i | 0.791003 | − | 1.37006i | −0.134344 | − | 0.990935i | \(-0.542893\pi\) |
0.925347 | − | 0.379122i | \(-0.123774\pi\) | |||||||
\(548\) | −21.0000 | −0.897076 | ||||||||
\(549\) | −42.0000 | −1.79252 | ||||||||
\(550\) | −3.00000 | −0.127920 | ||||||||
\(551\) | −21.0000 | + | 36.3731i | −0.894630 | + | 1.54954i | ||||
\(552\) | 10.3923i | 0.442326i | ||||||||
\(553\) | −1.00000 | − | 1.73205i | −0.0425243 | − | 0.0736543i | ||||
\(554\) | −11.0000 | − | 19.0526i | −0.467345 | − | 0.809466i | ||||
\(555\) | − | 13.8564i | − | 0.588172i | ||||||
\(556\) | −5.50000 | + | 9.52628i | −0.233252 | + | 0.404004i | ||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 15.0000 | + | 25.9808i | 0.635001 | + | 1.09985i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0.500000 | − | 0.866025i | 0.0211289 | − | 0.0365963i | ||||
\(561\) | 13.5000 | − | 7.79423i | 0.569970 | − | 0.329073i | ||||
\(562\) | −3.00000 | − | 5.19615i | −0.126547 | − | 0.219186i | ||||
\(563\) | 13.5000 | + | 23.3827i | 0.568957 | + | 0.985463i | 0.996669 | + | 0.0815478i | \(0.0259863\pi\) |
−0.427712 | + | 0.903915i | \(0.640680\pi\) | |||||||
\(564\) | −18.0000 | − | 10.3923i | −0.757937 | − | 0.437595i | ||||
\(565\) | −3.00000 | + | 5.19615i | −0.126211 | + | 0.218604i | ||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | −4.50000 | − | 7.79423i | −0.188982 | − | 0.327327i | ||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −4.50000 | + | 7.79423i | −0.188650 | + | 0.326751i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | 10.5000 | + | 6.06218i | 0.439797 | + | 0.253917i | ||||
\(571\) | −2.50000 | − | 4.33013i | −0.104622 | − | 0.181210i | 0.808962 | − | 0.587861i | \(-0.200030\pi\) |
−0.913584 | + | 0.406651i | \(0.866697\pi\) | |||||||
\(572\) | 6.00000 | + | 10.3923i | 0.250873 | + | 0.434524i | ||||
\(573\) | −18.0000 | + | 10.3923i | −0.751961 | + | 0.434145i | ||||
\(574\) | 4.50000 | − | 7.79423i | 0.187826 | − | 0.325325i | ||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −31.0000 | −1.29055 | −0.645273 | − | 0.763952i | \(-0.723257\pi\) | ||||
−0.645273 | + | 0.763952i | \(0.723257\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | − | 1.73205i | − | 0.0719816i | ||||||
\(580\) | −3.00000 | − | 5.19615i | −0.124568 | − | 0.215758i | ||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | − | 19.0526i | − | 0.789754i | ||||||
\(583\) | −9.00000 | + | 15.5885i | −0.372742 | + | 0.645608i | ||||
\(584\) | 7.00000 | 0.289662 | ||||||||
\(585\) | −12.0000 | −0.496139 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 4.50000 | − | 7.79423i | 0.185735 | − | 0.321702i | −0.758089 | − | 0.652151i | \(-0.773867\pi\) |
0.943824 | + | 0.330449i | \(0.107200\pi\) | |||||||
\(588\) | 1.50000 | − | 0.866025i | 0.0618590 | − | 0.0357143i | ||||
\(589\) | −35.0000 | − | 60.6218i | −1.44215 | − | 2.49788i | ||||
\(590\) | −4.50000 | − | 7.79423i | −0.185262 | − | 0.320883i | ||||
\(591\) | −18.0000 | − | 10.3923i | −0.740421 | − | 0.427482i | ||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 13.5000 | − | 7.79423i | 0.553912 | − | 0.319801i | ||||
\(595\) | −3.00000 | −0.122988 | ||||||||
\(596\) | −6.00000 | + | 10.3923i | −0.245770 | + | 0.425685i | ||||
\(597\) | −30.0000 | − | 17.3205i | −1.22782 | − | 0.708881i | ||||
\(598\) | 12.0000 | + | 20.7846i | 0.490716 | + | 0.849946i | ||||
\(599\) | 12.0000 | + | 20.7846i | 0.490307 | + | 0.849236i | 0.999938 | − | 0.0111569i | \(-0.00355143\pi\) |
−0.509631 | + | 0.860393i | \(0.670218\pi\) | |||||||
\(600\) | −1.50000 | + | 0.866025i | −0.0612372 | + | 0.0353553i | ||||
\(601\) | −17.5000 | + | 30.3109i | −0.713840 | + | 1.23641i | 0.249565 | + | 0.968358i | \(0.419712\pi\) |
−0.963405 | + | 0.268049i | \(0.913621\pi\) | |||||||
\(602\) | 1.00000 | 0.0407570 | ||||||||
\(603\) | −10.5000 | + | 18.1865i | −0.427593 | + | 0.740613i | ||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | −1.00000 | + | 1.73205i | −0.0406558 | + | 0.0704179i | ||||
\(606\) | − | 20.7846i | − | 0.844317i | ||||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | −3.50000 | − | 6.06218i | −0.141944 | − | 0.245854i | ||||
\(609\) | − | 10.3923i | − | 0.421117i | ||||||
\(610\) | −7.00000 | + | 12.1244i | −0.283422 | + | 0.490901i | ||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 4.50000 | − | 7.79423i | 0.181902 | − | 0.315063i | ||||
\(613\) | 38.0000 | 1.53481 | 0.767403 | − | 0.641165i | \(-0.221549\pi\) | ||||
0.767403 | + | 0.641165i | \(0.221549\pi\) | |||||||
\(614\) | 8.50000 | − | 14.7224i | 0.343032 | − | 0.594149i | ||||
\(615\) | −13.5000 | + | 7.79423i | −0.544373 | + | 0.314294i | ||||
\(616\) | 1.50000 | + | 2.59808i | 0.0604367 | + | 0.104679i | ||||
\(617\) | −10.5000 | − | 18.1865i | −0.422714 | − | 0.732162i | 0.573490 | − | 0.819213i | \(-0.305589\pi\) |
−0.996204 | + | 0.0870504i | \(0.972256\pi\) | |||||||
\(618\) | −6.00000 | − | 3.46410i | −0.241355 | − | 0.139347i | ||||
\(619\) | 3.50000 | − | 6.06218i | 0.140677 | − | 0.243659i | −0.787075 | − | 0.616858i | \(-0.788405\pi\) |
0.927752 | + | 0.373198i | \(0.121739\pi\) | |||||||
\(620\) | 10.0000 | 0.401610 | ||||||||
\(621\) | 27.0000 | − | 15.5885i | 1.08347 | − | 0.625543i | ||||
\(622\) | −18.0000 | −0.721734 | ||||||||
\(623\) | −3.00000 | + | 5.19615i | −0.120192 | + | 0.208179i | ||||
\(624\) | 6.00000 | + | 3.46410i | 0.240192 | + | 0.138675i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | −31.5000 | + | 18.1865i | −1.25799 | + | 0.726300i | ||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | −3.00000 | −0.119523 | ||||||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | 1.00000 | − | 1.73205i | 0.0397779 | − | 0.0688973i | ||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | 12.0000 | + | 20.7846i | 0.476581 | + | 0.825462i | ||||
\(635\) | −5.00000 | − | 8.66025i | −0.198419 | − | 0.343672i | ||||
\(636\) | 10.3923i | 0.412082i | ||||||||
\(637\) | 2.00000 | − | 3.46410i | 0.0792429 | − | 0.137253i | ||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | 9.00000 | + | 15.5885i | 0.356034 | + | 0.616670i | ||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 7.50000 | − | 12.9904i | 0.296232 | − | 0.513089i | −0.679039 | − | 0.734103i | \(-0.737603\pi\) |
0.975271 | + | 0.221013i | \(0.0709364\pi\) | |||||||
\(642\) | −4.50000 | + | 2.59808i | −0.177601 | + | 0.102538i | ||||
\(643\) | 24.5000 | + | 42.4352i | 0.966186 | + | 1.67348i | 0.706395 | + | 0.707818i | \(0.250320\pi\) |
0.259791 | + | 0.965665i | \(0.416346\pi\) | |||||||
\(644\) | 3.00000 | + | 5.19615i | 0.118217 | + | 0.204757i | ||||
\(645\) | −1.50000 | − | 0.866025i | −0.0590624 | − | 0.0340997i | ||||
\(646\) | −10.5000 | + | 18.1865i | −0.413117 | + | 0.715540i | ||||
\(647\) | 18.0000 | 0.707653 | 0.353827 | − | 0.935311i | \(-0.384880\pi\) | ||||
0.353827 | + | 0.935311i | \(0.384880\pi\) | |||||||
\(648\) | 4.50000 | − | 7.79423i | 0.176777 | − | 0.306186i | ||||
\(649\) | 27.0000 | 1.05984 | ||||||||
\(650\) | −2.00000 | + | 3.46410i | −0.0784465 | + | 0.135873i | ||||
\(651\) | 15.0000 | + | 8.66025i | 0.587896 | + | 0.339422i | ||||
\(652\) | −4.00000 | − | 6.92820i | −0.156652 | − | 0.271329i | ||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | 24.0000 | − | 13.8564i | 0.938474 | − | 0.541828i | ||||
\(655\) | 6.00000 | − | 10.3923i | 0.234439 | − | 0.406061i | ||||
\(656\) | 9.00000 | 0.351391 | ||||||||
\(657\) | −10.5000 | − | 18.1865i | −0.409644 | − | 0.709524i | ||||
\(658\) | −12.0000 | −0.467809 | ||||||||
\(659\) | −6.00000 | + | 10.3923i | −0.233727 | + | 0.404827i | −0.958902 | − | 0.283738i | \(-0.908425\pi\) |
0.725175 | + | 0.688565i | \(0.241759\pi\) | |||||||
\(660\) | − | 5.19615i | − | 0.202260i | ||||||
\(661\) | −16.0000 | − | 27.7128i | −0.622328 | − | 1.07790i | −0.989051 | − | 0.147573i | \(-0.952854\pi\) |
0.366723 | − | 0.930330i | \(-0.380480\pi\) | |||||||
\(662\) | −14.0000 | − | 24.2487i | −0.544125 | − | 0.942453i | ||||
\(663\) | − | 20.7846i | − | 0.807207i | ||||||
\(664\) | −6.00000 | + | 10.3923i | −0.232845 | + | 0.403300i | ||||
\(665\) | 7.00000 | 0.271448 | ||||||||
\(666\) | 24.0000 | 0.929981 | ||||||||
\(667\) | 36.0000 | 1.39393 | ||||||||
\(668\) | −3.00000 | + | 5.19615i | −0.116073 | + | 0.201045i | ||||
\(669\) | −15.0000 | + | 8.66025i | −0.579934 | + | 0.334825i | ||||
\(670\) | 3.50000 | + | 6.06218i | 0.135217 | + | 0.234202i | ||||
\(671\) | −21.0000 | − | 36.3731i | −0.810696 | − | 1.40417i | ||||
\(672\) | 1.50000 | + | 0.866025i | 0.0578638 | + | 0.0334077i | ||||
\(673\) | 5.00000 | − | 8.66025i | 0.192736 | − | 0.333828i | −0.753420 | − | 0.657539i | \(-0.771597\pi\) |
0.946156 | + | 0.323711i | \(0.104931\pi\) | |||||||
\(674\) | −5.00000 | −0.192593 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 12.0000 | − | 20.7846i | 0.461197 | − | 0.798817i | −0.537823 | − | 0.843057i | \(-0.680753\pi\) |
0.999021 | + | 0.0442400i | \(0.0140866\pi\) | |||||||
\(678\) | −9.00000 | − | 5.19615i | −0.345643 | − | 0.199557i | ||||
\(679\) | −5.50000 | − | 9.52628i | −0.211071 | − | 0.365585i | ||||
\(680\) | −1.50000 | − | 2.59808i | −0.0575224 | − | 0.0996317i | ||||
\(681\) | −4.50000 | + | 2.59808i | −0.172440 | + | 0.0995585i | ||||
\(682\) | −15.0000 | + | 25.9808i | −0.574380 | + | 0.994855i | ||||
\(683\) | −9.00000 | −0.344375 | −0.172188 | − | 0.985064i | \(-0.555084\pi\) | ||||
−0.172188 | + | 0.985064i | \(0.555084\pi\) | |||||||
\(684\) | −10.5000 | + | 18.1865i | −0.401478 | + | 0.695379i | ||||
\(685\) | 21.0000 | 0.802369 | ||||||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 34.6410i | 1.32164i | ||||||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | − | 10.3923i | − | 0.395628i | ||||||
\(691\) | 8.00000 | − | 13.8564i | 0.304334 | − | 0.527123i | −0.672779 | − | 0.739844i | \(-0.734899\pi\) |
0.977113 | + | 0.212721i | \(0.0682327\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 4.50000 | − | 7.79423i | 0.170941 | − | 0.296078i | ||||
\(694\) | −9.00000 | −0.341635 | ||||||||
\(695\) | 5.50000 | − | 9.52628i | 0.208627 | − | 0.361352i | ||||
\(696\) | 9.00000 | − | 5.19615i | 0.341144 | − | 0.196960i | ||||
\(697\) | −13.5000 | − | 23.3827i | −0.511349 | − | 0.885682i | ||||
\(698\) | 10.0000 | + | 17.3205i | 0.378506 | + | 0.655591i | ||||
\(699\) | −13.5000 | − | 7.79423i | −0.510617 | − | 0.294805i | ||||
\(700\) | −0.500000 | + | 0.866025i | −0.0188982 | + | 0.0327327i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | − | 20.7846i | − | 0.784465i | ||||||
\(703\) | −56.0000 | −2.11208 | ||||||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | 18.0000 | + | 10.3923i | 0.677919 | + | 0.391397i | ||||
\(706\) | 4.50000 | + | 7.79423i | 0.169360 | + | 0.293340i | ||||
\(707\) | −6.00000 | − | 10.3923i | −0.225653 | − | 0.390843i | ||||
\(708\) | 13.5000 | − | 7.79423i | 0.507361 | − | 0.292925i | ||||
\(709\) | −19.0000 | + | 32.9090i | −0.713560 | + | 1.23592i | 0.249952 | + | 0.968258i | \(0.419585\pi\) |
−0.963512 | + | 0.267664i | \(0.913748\pi\) | |||||||
\(710\) | 6.00000 | 0.225176 | ||||||||
\(711\) | −6.00000 | −0.225018 | ||||||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | −30.0000 | + | 51.9615i | −1.12351 | + | 1.94597i | ||||
\(714\) | − | 5.19615i | − | 0.194461i | ||||||
\(715\) | −6.00000 | − | 10.3923i | −0.224387 | − | 0.388650i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.3923i | 0.388108i | ||||||||
\(718\) | 12.0000 | − | 20.7846i | 0.447836 | − | 0.775675i | ||||
\(719\) | 12.0000 | 0.447524 | 0.223762 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | −1.50000 | − | 2.59808i | −0.0559017 | − | 0.0968246i | ||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | 15.0000 | − | 25.9808i | 0.558242 | − | 0.966904i | ||||
\(723\) | 7.50000 | − | 4.33013i | 0.278928 | − | 0.161039i | ||||
\(724\) | −10.0000 | − | 17.3205i | −0.371647 | − | 0.643712i | ||||
\(725\) | 3.00000 | + | 5.19615i | 0.111417 | + | 0.192980i | ||||
\(726\) | −3.00000 | − | 1.73205i | −0.111340 | − | 0.0642824i | ||||
\(727\) | −10.0000 | + | 17.3205i | −0.370879 | + | 0.642382i | −0.989701 | − | 0.143149i | \(-0.954277\pi\) |
0.618822 | + | 0.785532i | \(0.287610\pi\) | |||||||
\(728\) | 4.00000 | 0.148250 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −7.00000 | −0.259082 | ||||||||
\(731\) | 1.50000 | − | 2.59808i | 0.0554795 | − | 0.0960933i | ||||
\(732\) | −21.0000 | − | 12.1244i | −0.776182 | − | 0.448129i | ||||
\(733\) | 8.00000 | + | 13.8564i | 0.295487 | + | 0.511798i | 0.975098 | − | 0.221774i | \(-0.0711849\pi\) |
−0.679611 | + | 0.733572i | \(0.737852\pi\) | |||||||
\(734\) | −14.0000 | − | 24.2487i | −0.516749 | − | 0.895036i | ||||
\(735\) | −1.50000 | + | 0.866025i | −0.0553283 | + | 0.0319438i | ||||
\(736\) | −3.00000 | + | 5.19615i | −0.110581 | + | 0.191533i | ||||
\(737\) | −21.0000 | −0.773545 | ||||||||
\(738\) | −13.5000 | − | 23.3827i | −0.496942 | − | 0.860729i | ||||
\(739\) | −19.0000 | −0.698926 | −0.349463 | − | 0.936950i | \(-0.613636\pi\) | ||||
−0.349463 | + | 0.936950i | \(0.613636\pi\) | |||||||
\(740\) | 4.00000 | − | 6.92820i | 0.147043 | − | 0.254686i | ||||
\(741\) | 48.4974i | 1.78160i | ||||||||
\(742\) | 3.00000 | + | 5.19615i | 0.110133 | + | 0.190757i | ||||
\(743\) | 3.00000 | + | 5.19615i | 0.110059 | + | 0.190628i | 0.915794 | − | 0.401648i | \(-0.131563\pi\) |
−0.805735 | + | 0.592277i | \(0.798229\pi\) | |||||||
\(744\) | 17.3205i | 0.635001i | ||||||||
\(745\) | 6.00000 | − | 10.3923i | 0.219823 | − | 0.380745i | ||||
\(746\) | −14.0000 | −0.512576 | ||||||||
\(747\) | 36.0000 | 1.31717 | ||||||||
\(748\) | 9.00000 | 0.329073 | ||||||||
\(749\) | −1.50000 | + | 2.59808i | −0.0548088 | + | 0.0949316i | ||||
\(750\) | 1.50000 | − | 0.866025i | 0.0547723 | − | 0.0316228i | ||||
\(751\) | −16.0000 | − | 27.7128i | −0.583848 | − | 1.01125i | −0.995018 | − | 0.0996961i | \(-0.968213\pi\) |
0.411170 | − | 0.911559i | \(-0.365120\pi\) | |||||||
\(752\) | −6.00000 | − | 10.3923i | −0.218797 | − | 0.378968i | ||||
\(753\) | 13.5000 | + | 7.79423i | 0.491967 | + | 0.284037i | ||||
\(754\) | 12.0000 | − | 20.7846i | 0.437014 | − | 0.756931i | ||||
\(755\) | −14.0000 | −0.509512 | ||||||||
\(756\) | − | 5.19615i | − | 0.188982i | ||||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 2.50000 | − | 4.33013i | 0.0908041 | − | 0.157277i | ||||
\(759\) | 27.0000 | + | 15.5885i | 0.980038 | + | 0.565825i | ||||
\(760\) | 3.50000 | + | 6.06218i | 0.126958 | + | 0.219898i | ||||
\(761\) | 3.00000 | + | 5.19615i | 0.108750 | + | 0.188360i | 0.915264 | − | 0.402854i | \(-0.131982\pi\) |
−0.806514 | + | 0.591215i | \(0.798649\pi\) | |||||||
\(762\) | 15.0000 | − | 8.66025i | 0.543393 | − | 0.313728i | ||||
\(763\) | 8.00000 | − | 13.8564i | 0.289619 | − | 0.501636i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | −4.50000 | + | 7.79423i | −0.162698 | + | 0.281801i | ||||
\(766\) | 12.0000 | 0.433578 | ||||||||
\(767\) | 18.0000 | − | 31.1769i | 0.649942 | − | 1.12573i | ||||
\(768\) | 1.73205i | 0.0625000i | ||||||||
\(769\) | 11.0000 | + | 19.0526i | 0.396670 | + | 0.687053i | 0.993313 | − | 0.115454i | \(-0.0368323\pi\) |
−0.596643 | + | 0.802507i | \(0.703499\pi\) | |||||||
\(770\) | −1.50000 | − | 2.59808i | −0.0540562 | − | 0.0936282i | ||||
\(771\) | − | 25.9808i | − | 0.935674i | ||||||
\(772\) | 0.500000 | − | 0.866025i | 0.0179954 | − | 0.0311689i | ||||
\(773\) | 6.00000 | 0.215805 | 0.107903 | − | 0.994161i | \(-0.465587\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465587\pi\) | |||||||
\(774\) | 1.50000 | − | 2.59808i | 0.0539164 | − | 0.0933859i | ||||
\(775\) | −10.0000 | −0.359211 | ||||||||
\(776\) | 5.50000 | − | 9.52628i | 0.197438 | − | 0.341974i | ||||
\(777\) | 12.0000 | − | 6.92820i | 0.430498 | − | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 31.5000 | + | 54.5596i | 1.12860 | + | 1.95480i | ||||
\(780\) | −6.00000 | − | 3.46410i | −0.214834 | − | 0.124035i | ||||
\(781\) | −9.00000 | + | 15.5885i | −0.322045 | + | 0.557799i | ||||
\(782\) | 18.0000 | 0.643679 | ||||||||
\(783\) | −27.0000 | − | 15.5885i | −0.964901 | − | 0.557086i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −2.00000 | + | 3.46410i | −0.0713831 | + | 0.123639i | ||||
\(786\) | 18.0000 | + | 10.3923i | 0.642039 | + | 0.370681i | ||||
\(787\) | −10.0000 | − | 17.3205i | −0.356462 | − | 0.617409i | 0.630905 | − | 0.775860i | \(-0.282684\pi\) |
−0.987367 | + | 0.158450i | \(0.949350\pi\) | |||||||
\(788\) | −6.00000 | − | 10.3923i | −0.213741 | − | 0.370211i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.00000 | + | 1.73205i | −0.0355784 | + | 0.0616236i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 9.00000 | 0.319801 | ||||||||
\(793\) | −56.0000 | −1.98862 | ||||||||
\(794\) | −2.00000 | + | 3.46410i | −0.0709773 | + | 0.122936i | ||||
\(795\) | − | 10.3923i | − | 0.368577i | ||||||
\(796\) | −10.0000 | − | 17.3205i | −0.354441 | − | 0.613909i | ||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 12.1244i | 0.429198i | ||||||||
\(799\) | −18.0000 | + | 31.1769i | −0.636794 | + | 1.10296i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 9.00000 | + | 15.5885i | 0.317999 | + | 0.550791i | ||||
\(802\) | 15.0000 | 0.529668 | ||||||||
\(803\) | 10.5000 | − | 18.1865i | 0.370537 | − | 0.641789i | ||||
\(804\) | −10.5000 | + | 6.06218i | −0.370306 | + | 0.213797i | ||||
\(805\) | −3.00000 | − | 5.19615i | −0.105736 | − | 0.183140i | ||||
\(806\) | 20.0000 | + | 34.6410i | 0.704470 | + | 1.22018i | ||||
\(807\) | −45.0000 | − | 25.9808i | −1.58408 | − | 0.914566i | ||||
\(808\) | 6.00000 | − | 10.3923i | 0.211079 | − | 0.365600i | ||||
\(809\) | 33.0000 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(810\) | −4.50000 | + | 7.79423i | −0.158114 | + | 0.273861i | ||||
\(811\) | 47.0000 | 1.65039 | 0.825197 | − | 0.564846i | \(-0.191064\pi\) | ||||
0.825197 | + | 0.564846i | \(0.191064\pi\) | |||||||
\(812\) | 3.00000 | − | 5.19615i | 0.105279 | − | 0.182349i | ||||
\(813\) | −30.0000 | − | 17.3205i | −1.05215 | − | 0.607457i | ||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 4.00000 | + | 6.92820i | 0.140114 | + | 0.242684i | ||||
\(816\) | 4.50000 | − | 2.59808i | 0.157532 | − | 0.0909509i | ||||
\(817\) | −3.50000 | + | 6.06218i | −0.122449 | + | 0.212089i | ||||
\(818\) | 19.0000 | 0.664319 | ||||||||
\(819\) | −6.00000 | − | 10.3923i | −0.209657 | − | 0.363137i | ||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −12.0000 | + | 20.7846i | −0.418803 | + | 0.725388i | −0.995819 | − | 0.0913446i | \(-0.970884\pi\) |
0.577016 | + | 0.816733i | \(0.304217\pi\) | |||||||
\(822\) | 36.3731i | 1.26866i | ||||||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | −2.00000 | − | 3.46410i | −0.0696733 | − | 0.120678i | ||||
\(825\) | 5.19615i | 0.180907i | ||||||||
\(826\) | 4.50000 | − | 7.79423i | 0.156575 | − | 0.271196i | ||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 18.0000 | 0.625543 | ||||||||
\(829\) | 56.0000 | 1.94496 | 0.972480 | − | 0.232986i | \(-0.0748495\pi\) | ||||
0.972480 | + | 0.232986i | \(0.0748495\pi\) | |||||||
\(830\) | 6.00000 | − | 10.3923i | 0.208263 | − | 0.360722i | ||||
\(831\) | −33.0000 | + | 19.0526i | −1.14476 | + | 0.660926i | ||||
\(832\) | 2.00000 | + | 3.46410i | 0.0693375 | + | 0.120096i | ||||
\(833\) | −1.50000 | − | 2.59808i | −0.0519719 | − | 0.0900180i | ||||
\(834\) | 16.5000 | + | 9.52628i | 0.571348 | + | 0.329868i | ||||
\(835\) | 3.00000 | − | 5.19615i | 0.103819 | − | 0.179820i | ||||
\(836\) | −21.0000 | −0.726300 | ||||||||
\(837\) | 45.0000 | − | 25.9808i | 1.55543 | − | 0.898027i | ||||
\(838\) | −24.0000 | −0.829066 | ||||||||
\(839\) | 15.0000 | − | 25.9808i | 0.517858 | − | 0.896956i | −0.481927 | − | 0.876211i | \(-0.660063\pi\) |
0.999785 | − | 0.0207443i | \(-0.00660359\pi\) | |||||||
\(840\) | −1.50000 | − | 0.866025i | −0.0517549 | − | 0.0298807i | ||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 13.0000 | + | 22.5167i | 0.448010 | + | 0.775975i | ||||
\(843\) | −9.00000 | + | 5.19615i | −0.309976 | + | 0.178965i | ||||
\(844\) | 2.00000 | − | 3.46410i | 0.0688428 | − | 0.119239i | ||||
\(845\) | −3.00000 | −0.103203 | ||||||||
\(846\) | −18.0000 | + | 31.1769i | −0.618853 | + | 1.07188i | ||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | −3.00000 | + | 5.19615i | −0.103020 | + | 0.178437i | ||||
\(849\) | 34.6410i | 1.18888i | ||||||||
\(850\) | 1.50000 | + | 2.59808i | 0.0514496 | + | 0.0891133i | ||||
\(851\) | 24.0000 | + | 41.5692i | 0.822709 | + | 1.42497i | ||||
\(852\) | 10.3923i | 0.356034i | ||||||||
\(853\) | −4.00000 | + | 6.92820i | −0.136957 | + | 0.237217i | −0.926343 | − | 0.376680i | \(-0.877066\pi\) |
0.789386 | + | 0.613897i | \(0.210399\pi\) | |||||||
\(854\) | −14.0000 | −0.479070 | ||||||||
\(855\) | 10.5000 | − | 18.1865i | 0.359092 | − | 0.621966i | ||||
\(856\) | −3.00000 | −0.102538 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 18.0000 | − | 10.3923i | 0.614510 | − | 0.354787i | ||||
\(859\) | 27.5000 | + | 47.6314i | 0.938288 | + | 1.62516i | 0.768663 | + | 0.639654i | \(0.220922\pi\) |
0.169625 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(860\) | −0.500000 | − | 0.866025i | −0.0170499 | − | 0.0295312i | ||||
\(861\) | −13.5000 | − | 7.79423i | −0.460079 | − | 0.265627i | ||||
\(862\) | 6.00000 | − | 10.3923i | 0.204361 | − | 0.353963i | ||||
\(863\) | 30.0000 | 1.02121 | 0.510606 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510606 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(864\) | 4.50000 | − | 2.59808i | 0.153093 | − | 0.0883883i | ||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 5.50000 | − | 9.52628i | 0.186898 | − | 0.323716i | ||||
\(867\) | 12.0000 | + | 6.92820i | 0.407541 | + | 0.235294i | ||||
\(868\) | 5.00000 | + | 8.66025i | 0.169711 | + | 0.293948i | ||||
\(869\) | −3.00000 | − | 5.19615i | −0.101768 | − | 0.176267i | ||||
\(870\) | −9.00000 | + | 5.19615i | −0.305129 | + | 0.176166i | ||||
\(871\) | −14.0000 | + | 24.2487i | −0.474372 | + | 0.821636i | ||||
\(872\) | 16.0000 | 0.541828 | ||||||||
\(873\) | −33.0000 | −1.11688 | ||||||||
\(874\) | −42.0000 | −1.42067 | ||||||||
\(875\) | 0.500000 | − | 0.866025i | 0.0169031 | − | 0.0292770i | ||||
\(876\) | − | 12.1244i | − | 0.409644i | ||||||
\(877\) | −25.0000 | − | 43.3013i | −0.844190 | − | 1.46218i | −0.886323 | − | 0.463068i | \(-0.846749\pi\) |
0.0421327 | − | 0.999112i | \(-0.486585\pi\) | |||||||
\(878\) | −5.00000 | − | 8.66025i | −0.168742 | − | 0.292269i | ||||
\(879\) | 31.1769i | 1.05157i | ||||||||
\(880\) | 1.50000 | − | 2.59808i | 0.0505650 | − | 0.0875811i | ||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | −1.50000 | − | 2.59808i | −0.0505076 | − | 0.0874818i | ||||
\(883\) | 29.0000 | 0.975928 | 0.487964 | − | 0.872864i | \(-0.337740\pi\) | ||||
0.487964 | + | 0.872864i | \(0.337740\pi\) | |||||||
\(884\) | 6.00000 | − | 10.3923i | 0.201802 | − | 0.349531i | ||||
\(885\) | −13.5000 | + | 7.79423i | −0.453798 | + | 0.262000i | ||||
\(886\) | 7.50000 | + | 12.9904i | 0.251967 | + | 0.436420i | ||||
\(887\) | 15.0000 | + | 25.9808i | 0.503651 | + | 0.872349i | 0.999991 | + | 0.00422062i | \(0.00134347\pi\) |
−0.496340 | + | 0.868128i | \(0.665323\pi\) | |||||||
\(888\) | 12.0000 | + | 6.92820i | 0.402694 | + | 0.232495i | ||||
\(889\) | 5.00000 | − | 8.66025i | 0.167695 | − | 0.290456i | ||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | −10.0000 | −0.334825 | ||||||||
\(893\) | 42.0000 | − | 72.7461i | 1.40548 | − | 2.43436i | ||||
\(894\) | 18.0000 | + | 10.3923i | 0.602010 | + | 0.347571i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | 36.0000 | − | 20.7846i | 1.20201 | − | 0.693978i | ||||
\(898\) | −19.5000 | + | 33.7750i | −0.650723 | + | 1.12709i | ||||
\(899\) | 60.0000 | 2.00111 | ||||||||
\(900\) | 1.50000 | + | 2.59808i | 0.0500000 | + | 0.0866025i | ||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | 13.5000 | − | 23.3827i | 0.449501 | − | 0.778558i | ||||
\(903\) | − | 1.73205i | − | 0.0576390i | ||||||
\(904\) | −3.00000 | − | 5.19615i | −0.0997785 | − | 0.172821i | ||||
\(905\) | 10.0000 | + | 17.3205i | 0.332411 | + | 0.575753i | ||||
\(906\) | − | 24.2487i | − | 0.805609i | ||||||
\(907\) | 3.50000 | − | 6.06218i | 0.116216 | − | 0.201291i | −0.802049 | − | 0.597258i | \(-0.796257\pi\) |
0.918265 | + | 0.395966i | \(0.129590\pi\) | |||||||
\(908\) | −3.00000 | −0.0995585 | ||||||||
\(909\) | −36.0000 | −1.19404 | ||||||||
\(910\) | −4.00000 | −0.132599 | ||||||||
\(911\) | −21.0000 | + | 36.3731i | −0.695761 | + | 1.20509i | 0.274162 | + | 0.961683i | \(0.411599\pi\) |
−0.969923 | + | 0.243410i | \(0.921734\pi\) | |||||||
\(912\) | −10.5000 | + | 6.06218i | −0.347690 | + | 0.200739i | ||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 5.50000 | + | 9.52628i | 0.181924 | + | 0.315101i | ||||
\(915\) | 21.0000 | + | 12.1244i | 0.694239 | + | 0.400819i | ||||
\(916\) | −10.0000 | + | 17.3205i | −0.330409 | + | 0.572286i | ||||
\(917\) | 12.0000 | 0.396275 | ||||||||
\(918\) | −13.5000 | − | 7.79423i | −0.445566 | − | 0.257248i | ||||
\(919\) | −46.0000 | −1.51740 | −0.758700 | − | 0.651440i | \(-0.774165\pi\) | ||||
−0.758700 | + | 0.651440i | \(0.774165\pi\) | |||||||
\(920\) | 3.00000 | − | 5.19615i | 0.0989071 | − | 0.171312i | ||||
\(921\) | −25.5000 | − | 14.7224i | −0.840254 | − | 0.485121i | ||||
\(922\) | −12.0000 | − | 20.7846i | −0.395199 | − | 0.684505i | ||||
\(923\) | 12.0000 | + | 20.7846i | 0.394985 | + | 0.684134i | ||||
\(924\) | 4.50000 | − | 2.59808i | 0.148039 | − | 0.0854704i | ||||
\(925\) | −4.00000 | + | 6.92820i | −0.131519 | + | 0.227798i | ||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | −6.00000 | + | 10.3923i | −0.197066 | + | 0.341328i | ||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | − | 17.3205i | − | 0.567962i | ||||||
\(931\) | 3.50000 | + | 6.06218i | 0.114708 | + | 0.198680i | ||||
\(932\) | −4.50000 | − | 7.79423i | −0.147402 | − | 0.255308i | ||||
\(933\) | 31.1769i | 1.02069i | ||||||||
\(934\) | −13.5000 | + | 23.3827i | −0.441733 | + | 0.765105i | ||||
\(935\) | −9.00000 | −0.294331 | ||||||||
\(936\) | 6.00000 | − | 10.3923i | 0.196116 | − | 0.339683i | ||||
\(937\) | 38.0000 | 1.24141 | 0.620703 | − | 0.784046i | \(-0.286847\pi\) | ||||
0.620703 | + | 0.784046i | \(0.286847\pi\) | |||||||
\(938\) | −3.50000 | + | 6.06218i | −0.114279 | + | 0.197937i | ||||
\(939\) | −1.50000 | + | 0.866025i | −0.0489506 | + | 0.0282617i | ||||
\(940\) | 6.00000 | + | 10.3923i | 0.195698 | + | 0.338960i | ||||
\(941\) | 12.0000 | + | 20.7846i | 0.391189 | + | 0.677559i | 0.992607 | − | 0.121376i | \(-0.0387306\pi\) |
−0.601418 | + | 0.798935i | \(0.705397\pi\) | |||||||
\(942\) | −6.00000 | − | 3.46410i | −0.195491 | − | 0.112867i | ||||
\(943\) | 27.0000 | − | 46.7654i | 0.879241 | − | 1.52289i | ||||
\(944\) | 9.00000 | 0.292925 | ||||||||
\(945\) | 5.19615i | 0.169031i | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | −19.5000 | + | 33.7750i | −0.633665 | + | 1.09754i | 0.353131 | + | 0.935574i | \(0.385117\pi\) |
−0.986796 | + | 0.161966i | \(0.948217\pi\) | |||||||
\(948\) | −3.00000 | − | 1.73205i | −0.0974355 | − | 0.0562544i | ||||
\(949\) | −14.0000 | − | 24.2487i | −0.454459 | − | 0.787146i | ||||
\(950\) | −3.50000 | − | 6.06218i | −0.113555 | − | 0.196683i | ||||
\(951\) | 36.0000 | − | 20.7846i | 1.16738 | − | 0.673987i | ||||
\(952\) | 1.50000 | − | 2.59808i | 0.0486153 | − | 0.0842041i | ||||
\(953\) | 39.0000 | 1.26333 | 0.631667 | − | 0.775240i | \(-0.282371\pi\) | ||||
0.631667 | + | 0.775240i | \(0.282371\pi\) | |||||||
\(954\) | 18.0000 | 0.582772 | ||||||||
\(955\) | 12.0000 | 0.388311 | ||||||||
\(956\) | −3.00000 | + | 5.19615i | −0.0970269 | + | 0.168056i | ||||
\(957\) | − | 31.1769i | − | 1.00781i | ||||||
\(958\) | 15.0000 | + | 25.9808i | 0.484628 | + | 0.839400i | ||||
\(959\) | 10.5000 | + | 18.1865i | 0.339063 | + | 0.587274i | ||||
\(960\) | − | 1.73205i | − | 0.0559017i | ||||||
\(961\) | −34.5000 | + | 59.7558i | −1.11290 | + | 1.92760i | ||||
\(962\) | 32.0000 | 1.03172 | ||||||||
\(963\) | 4.50000 | + | 7.79423i | 0.145010 | + | 0.251166i | ||||
\(964\) | 5.00000 | 0.161039 | ||||||||
\(965\) | −0.500000 | + | 0.866025i | −0.0160956 | + | 0.0278783i | ||||
\(966\) | 9.00000 | − | 5.19615i | 0.289570 | − | 0.167183i | ||||
\(967\) | 11.0000 | + | 19.0526i | 0.353736 | + | 0.612689i | 0.986901 | − | 0.161328i | \(-0.0515777\pi\) |
−0.633165 | + | 0.774017i | \(0.718244\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | 31.5000 | + | 18.1865i | 1.01193 | + | 0.584236i | ||||
\(970\) | −5.50000 | + | 9.52628i | −0.176594 | + | 0.305870i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | −13.5000 | − | 7.79423i | −0.433013 | − | 0.250000i | ||||
\(973\) | 11.0000 | 0.352644 | ||||||||
\(974\) | 1.00000 | − | 1.73205i | 0.0320421 | − | 0.0554985i | ||||
\(975\) | 6.00000 | + | 3.46410i | 0.192154 | + | 0.110940i | ||||
\(976\) | −7.00000 | − | 12.1244i | −0.224065 | − | 0.388091i | ||||
\(977\) | 10.5000 | + | 18.1865i | 0.335925 | + | 0.581839i | 0.983662 | − | 0.180025i | \(-0.0576179\pi\) |
−0.647737 | + | 0.761864i | \(0.724285\pi\) | |||||||
\(978\) | −12.0000 | + | 6.92820i | −0.383718 | + | 0.221540i | ||||
\(979\) | −9.00000 | + | 15.5885i | −0.287641 | + | 0.498209i | ||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −24.0000 | − | 41.5692i | −0.766261 | − | 1.32720i | ||||
\(982\) | 9.00000 | 0.287202 | ||||||||
\(983\) | 18.0000 | − | 31.1769i | 0.574111 | − | 0.994389i | −0.422027 | − | 0.906583i | \(-0.638681\pi\) |
0.996138 | − | 0.0878058i | \(-0.0279855\pi\) | |||||||
\(984\) | − | 15.5885i | − | 0.496942i | ||||||
\(985\) | 6.00000 | + | 10.3923i | 0.191176 | + | 0.331126i | ||||
\(986\) | −9.00000 | − | 15.5885i | −0.286618 | − | 0.496438i | ||||
\(987\) | 20.7846i | 0.661581i | ||||||||
\(988\) | −14.0000 | + | 24.2487i | −0.445399 | + | 0.771454i | ||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | −9.00000 | −0.286039 | ||||||||
\(991\) | −4.00000 | −0.127064 | −0.0635321 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635321 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(992\) | −5.00000 | + | 8.66025i | −0.158750 | + | 0.274963i | ||||
\(993\) | −42.0000 | + | 24.2487i | −1.33283 | + | 0.769510i | ||||
\(994\) | 3.00000 | + | 5.19615i | 0.0951542 | + | 0.164812i | ||||
\(995\) | 10.0000 | + | 17.3205i | 0.317021 | + | 0.549097i | ||||
\(996\) | 18.0000 | + | 10.3923i | 0.570352 | + | 0.329293i | ||||
\(997\) | 5.00000 | − | 8.66025i | 0.158352 | − | 0.274273i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | −17.0000 | −0.538126 | ||||||||
\(999\) | − | 41.5692i | − | 1.31519i |
(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 | 630.2.j.b.421.1 | yes | 2 | |
3.2 | odd | 2 | 1890.2.j.a.1261.1 | 2 | |||
9.2 | odd | 6 | 5670.2.a.q.1.1 | 1 | |||
9.4 | even | 3 | inner | 630.2.j.b.211.1 | ✓ | 2 | |
9.5 | odd | 6 | 1890.2.j.a.631.1 | 2 | |||
9.7 | even | 3 | 5670.2.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.b.211.1 | ✓ | 2 | 9.4 | even | 3 | inner | |
630.2.j.b.421.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1890.2.j.a.631.1 | 2 | 9.5 | odd | 6 | |||
1890.2.j.a.1261.1 | 2 | 3.2 | odd | 2 | |||
5670.2.a.e.1.1 | 1 | 9.7 | even | 3 | |||
5670.2.a.q.1.1 | 1 | 9.2 | odd | 6 |