Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(221,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(1\) |
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 | 331.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.331 |
Dual form | 770.2.i.e.221.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −0.500000 | − | 0.866025i | −0.150756 | − | 0.261116i | ||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | −1.00000 | − | 1.73205i | −0.235702 | − | 0.408248i | ||||
\(19\) | −3.00000 | + | 5.19615i | −0.688247 | + | 1.19208i | 0.284157 | + | 0.958778i | \(0.408286\pi\) |
−0.972404 | + | 0.233301i | \(0.925047\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 2.00000 | + | 1.73205i | 0.436436 | + | 0.377964i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.00000 | + | 1.73205i | −0.208514 | + | 0.361158i | −0.951247 | − | 0.308431i | \(-0.900196\pi\) |
0.742732 | + | 0.669588i | \(0.233529\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −1.50000 | + | 2.59808i | −0.294174 | + | 0.509525i | ||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | −7.00000 | −1.29987 | −0.649934 | − | 0.759991i | \(-0.725203\pi\) | ||||
−0.649934 | + | 0.759991i | \(0.725203\pi\) | |||||||
\(30\) | 0.500000 | − | 0.866025i | 0.0912871 | − | 0.158114i | ||||
\(31\) | 4.00000 | + | 6.92820i | 0.718421 | + | 1.24434i | 0.961625 | + | 0.274367i | \(0.0884683\pi\) |
−0.243204 | + | 0.969975i | \(0.578198\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | − | 2.59808i | 0.0845154 | − | 0.439155i | ||||
\(36\) | −2.00000 | −0.333333 | ||||||||
\(37\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(38\) | 3.00000 | + | 5.19615i | 0.486664 | + | 0.842927i | ||||
\(39\) | 1.50000 | + | 2.59808i | 0.240192 | + | 0.416025i | ||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 2.50000 | − | 0.866025i | 0.385758 | − | 0.133631i | ||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 1.00000 | + | 1.73205i | 0.149071 | + | 0.258199i | ||||
\(46\) | 1.00000 | + | 1.73205i | 0.147442 | + | 0.255377i | ||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.50000 | + | 2.59808i | 0.208013 | + | 0.360288i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | −2.50000 | + | 4.33013i | −0.340207 | + | 0.589256i | ||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | −3.50000 | + | 6.06218i | −0.459573 | + | 0.796003i | ||||
\(59\) | 0.500000 | + | 0.866025i | 0.0650945 | + | 0.112747i | 0.896736 | − | 0.442566i | \(-0.145932\pi\) |
−0.831641 | + | 0.555313i | \(0.812598\pi\) | |||||||
\(60\) | −0.500000 | − | 0.866025i | −0.0645497 | − | 0.111803i | ||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | 8.00000 | 1.01600 | ||||||||
\(63\) | −1.00000 | + | 5.19615i | −0.125988 | + | 0.654654i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.50000 | − | 2.59808i | 0.186052 | − | 0.322252i | ||||
\(66\) | 0.500000 | + | 0.866025i | 0.0615457 | + | 0.106600i | ||||
\(67\) | 2.50000 | + | 4.33013i | 0.305424 | + | 0.529009i | 0.977356 | − | 0.211604i | \(-0.0678686\pi\) |
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | −2.00000 | − | 1.73205i | −0.239046 | − | 0.207020i | ||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | −1.00000 | + | 1.73205i | −0.117851 | + | 0.204124i | ||||
\(73\) | −7.00000 | − | 12.1244i | −0.819288 | − | 1.41905i | −0.906208 | − | 0.422833i | \(-0.861036\pi\) |
0.0869195 | − | 0.996215i | \(-0.472298\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 6.00000 | 0.688247 | ||||||||
\(77\) | 2.00000 | + | 1.73205i | 0.227921 | + | 0.197386i | ||||
\(78\) | 3.00000 | 0.339683 | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.00000 | + | 3.46410i | −0.220863 | + | 0.382546i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.00000 | + | 5.19615i | −0.323498 | + | 0.560316i | ||||
\(87\) | 3.50000 | + | 6.06218i | 0.375239 | + | 0.649934i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 3.00000 | − | 5.19615i | 0.317999 | − | 0.550791i | −0.662071 | − | 0.749441i | \(-0.730322\pi\) |
0.980071 | + | 0.198650i | \(0.0636557\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | 7.50000 | − | 2.59808i | 0.786214 | − | 0.272352i | ||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 4.00000 | − | 6.92820i | 0.414781 | − | 0.718421i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 7.50000 | + | 12.9904i | 0.746278 | + | 1.29259i | 0.949595 | + | 0.313478i | \(0.101494\pi\) |
−0.203317 | + | 0.979113i | \(0.565172\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 3.00000 | 0.294174 | ||||||||
\(105\) | −2.50000 | + | 0.866025i | −0.243975 | + | 0.0845154i | ||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | 2.50000 | + | 4.33013i | 0.240563 | + | 0.416667i | ||||
\(109\) | −9.00000 | − | 15.5885i | −0.862044 | − | 1.49310i | −0.869953 | − | 0.493135i | \(-0.835851\pi\) |
0.00790932 | − | 0.999969i | \(-0.497482\pi\) | |||||||
\(110\) | 0.500000 | − | 0.866025i | 0.0476731 | − | 0.0825723i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | −13.0000 | −1.22294 | −0.611469 | − | 0.791269i | \(-0.709421\pi\) | ||||
−0.611469 | + | 0.791269i | \(0.709421\pi\) | |||||||
\(114\) | 3.00000 | − | 5.19615i | 0.280976 | − | 0.486664i | ||||
\(115\) | −1.00000 | − | 1.73205i | −0.0932505 | − | 0.161515i | ||||
\(116\) | 3.50000 | + | 6.06218i | 0.324967 | + | 0.562859i | ||||
\(117\) | −3.00000 | + | 5.19615i | −0.277350 | + | 0.480384i | ||||
\(118\) | 1.00000 | 0.0920575 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | −0.500000 | − | 0.866025i | −0.0452679 | − | 0.0784063i | ||||
\(123\) | 2.00000 | + | 3.46410i | 0.180334 | + | 0.312348i | ||||
\(124\) | 4.00000 | − | 6.92820i | 0.359211 | − | 0.622171i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.00000 | + | 3.46410i | 0.356348 | + | 0.308607i | ||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.00000 | + | 5.19615i | 0.264135 | + | 0.457496i | ||||
\(130\) | −1.50000 | − | 2.59808i | −0.131559 | − | 0.227866i | ||||
\(131\) | 7.00000 | − | 12.1244i | 0.611593 | − | 1.05931i | −0.379379 | − | 0.925241i | \(-0.623862\pi\) |
0.990972 | − | 0.134069i | \(-0.0428042\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 3.00000 | − | 15.5885i | 0.260133 | − | 1.35169i | ||||
\(134\) | 5.00000 | 0.431934 | ||||||||
\(135\) | 2.50000 | − | 4.33013i | 0.215166 | − | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.50000 | + | 2.59808i | 0.128154 | + | 0.221969i | 0.922961 | − | 0.384893i | \(-0.125762\pi\) |
−0.794808 | + | 0.606861i | \(0.792428\pi\) | |||||||
\(138\) | 1.00000 | − | 1.73205i | 0.0851257 | − | 0.147442i | ||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | −2.50000 | + | 0.866025i | −0.211289 | + | 0.0731925i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.00000 | − | 6.92820i | 0.335673 | − | 0.581402i | ||||
\(143\) | 1.50000 | + | 2.59808i | 0.125436 | + | 0.217262i | ||||
\(144\) | 1.00000 | + | 1.73205i | 0.0833333 | + | 0.144338i | ||||
\(145\) | 3.50000 | − | 6.06218i | 0.290659 | − | 0.503436i | ||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | −6.50000 | − | 2.59808i | −0.536111 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 0.500000 | + | 0.866025i | 0.0408248 | + | 0.0707107i | ||||
\(151\) | 8.50000 | + | 14.7224i | 0.691720 | + | 1.19809i | 0.971274 | + | 0.237964i | \(0.0764802\pi\) |
−0.279554 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(152\) | 3.00000 | − | 5.19615i | 0.243332 | − | 0.421464i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50000 | − | 0.866025i | 0.201456 | − | 0.0697863i | ||||
\(155\) | −8.00000 | −0.642575 | ||||||||
\(156\) | 1.50000 | − | 2.59808i | 0.120096 | − | 0.208013i | ||||
\(157\) | −3.00000 | − | 5.19615i | −0.239426 | − | 0.414698i | 0.721124 | − | 0.692806i | \(-0.243626\pi\) |
−0.960550 | + | 0.278108i | \(0.910293\pi\) | |||||||
\(158\) | −6.50000 | − | 11.2583i | −0.517112 | − | 0.895665i | ||||
\(159\) | −3.00000 | + | 5.19615i | −0.237915 | + | 0.412082i | ||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 1.00000 | − | 5.19615i | 0.0788110 | − | 0.409514i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 5.50000 | − | 9.52628i | 0.430793 | − | 0.746156i | −0.566149 | − | 0.824303i | \(-0.691567\pi\) |
0.996942 | + | 0.0781474i | \(0.0249005\pi\) | |||||||
\(164\) | 2.00000 | + | 3.46410i | 0.156174 | + | 0.270501i | ||||
\(165\) | −0.500000 | − | 0.866025i | −0.0389249 | − | 0.0674200i | ||||
\(166\) | −3.00000 | + | 5.19615i | −0.232845 | + | 0.403300i | ||||
\(167\) | 19.0000 | 1.47026 | 0.735132 | − | 0.677924i | \(-0.237120\pi\) | ||||
0.735132 | + | 0.677924i | \(0.237120\pi\) | |||||||
\(168\) | −2.00000 | − | 1.73205i | −0.154303 | − | 0.133631i | ||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.00000 | + | 10.3923i | 0.458831 | + | 0.794719i | ||||
\(172\) | 3.00000 | + | 5.19615i | 0.228748 | + | 0.396203i | ||||
\(173\) | −4.50000 | + | 7.79423i | −0.342129 | + | 0.592584i | −0.984828 | − | 0.173534i | \(-0.944481\pi\) |
0.642699 | + | 0.766119i | \(0.277815\pi\) | |||||||
\(174\) | 7.00000 | 0.530669 | ||||||||
\(175\) | 2.00000 | + | 1.73205i | 0.151186 | + | 0.130931i | ||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0.500000 | − | 0.866025i | 0.0375823 | − | 0.0650945i | ||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −7.50000 | − | 12.9904i | −0.560576 | − | 0.970947i | −0.997446 | − | 0.0714220i | \(-0.977246\pi\) |
0.436870 | − | 0.899525i | \(-0.356087\pi\) | |||||||
\(180\) | 1.00000 | − | 1.73205i | 0.0745356 | − | 0.129099i | ||||
\(181\) | 12.0000 | 0.891953 | 0.445976 | − | 0.895045i | \(-0.352856\pi\) | ||||
0.445976 | + | 0.895045i | \(0.352856\pi\) | |||||||
\(182\) | 1.50000 | − | 7.79423i | 0.111187 | − | 0.577747i | ||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 1.00000 | − | 1.73205i | 0.0737210 | − | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.00000 | − | 6.92820i | −0.293294 | − | 0.508001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.5000 | − | 4.33013i | 0.909241 | − | 0.314970i | ||||
\(190\) | −6.00000 | −0.435286 | ||||||||
\(191\) | −2.00000 | + | 3.46410i | −0.144715 | + | 0.250654i | −0.929267 | − | 0.369410i | \(-0.879560\pi\) |
0.784552 | + | 0.620063i | \(0.212893\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −4.00000 | − | 6.92820i | −0.287926 | − | 0.498703i | 0.685388 | − | 0.728178i | \(-0.259632\pi\) |
−0.973315 | + | 0.229475i | \(0.926299\pi\) | |||||||
\(194\) | −3.50000 | + | 6.06218i | −0.251285 | + | 0.435239i | ||||
\(195\) | −3.00000 | −0.214834 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 11.0000 | 0.783718 | 0.391859 | − | 0.920025i | \(-0.371832\pi\) | ||||
0.391859 | + | 0.920025i | \(0.371832\pi\) | |||||||
\(198\) | −1.00000 | + | 1.73205i | −0.0710669 | + | 0.123091i | ||||
\(199\) | 3.00000 | + | 5.19615i | 0.212664 | + | 0.368345i | 0.952548 | − | 0.304390i | \(-0.0984526\pi\) |
−0.739883 | + | 0.672735i | \(0.765119\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 2.50000 | − | 4.33013i | 0.176336 | − | 0.305424i | ||||
\(202\) | 15.0000 | 1.05540 | ||||||||
\(203\) | 17.5000 | − | 6.06218i | 1.22826 | − | 0.425481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.00000 | − | 3.46410i | 0.139686 | − | 0.241943i | ||||
\(206\) | 2.00000 | + | 3.46410i | 0.139347 | + | 0.241355i | ||||
\(207\) | 2.00000 | + | 3.46410i | 0.139010 | + | 0.240772i | ||||
\(208\) | 1.50000 | − | 2.59808i | 0.104006 | − | 0.180144i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | −0.500000 | + | 2.59808i | −0.0345033 | + | 0.179284i | ||||
\(211\) | −12.0000 | −0.826114 | −0.413057 | − | 0.910705i | \(-0.635539\pi\) | ||||
−0.413057 | + | 0.910705i | \(0.635539\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | −4.00000 | − | 6.92820i | −0.274075 | − | 0.474713i | ||||
\(214\) | 3.00000 | + | 5.19615i | 0.205076 | + | 0.355202i | ||||
\(215\) | 3.00000 | − | 5.19615i | 0.204598 | − | 0.354375i | ||||
\(216\) | 5.00000 | 0.340207 | ||||||||
\(217\) | −16.0000 | − | 13.8564i | −1.08615 | − | 0.940634i | ||||
\(218\) | −18.0000 | −1.21911 | ||||||||
\(219\) | −7.00000 | + | 12.1244i | −0.473016 | + | 0.819288i | ||||
\(220\) | −0.500000 | − | 0.866025i | −0.0337100 | − | 0.0583874i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.0000 | −0.803579 | −0.401790 | − | 0.915732i | \(-0.631612\pi\) | ||||
−0.401790 | + | 0.915732i | \(0.631612\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | −6.50000 | + | 11.2583i | −0.432374 | + | 0.748893i | ||||
\(227\) | 4.00000 | + | 6.92820i | 0.265489 | + | 0.459841i | 0.967692 | − | 0.252136i | \(-0.0811332\pi\) |
−0.702202 | + | 0.711977i | \(0.747800\pi\) | |||||||
\(228\) | −3.00000 | − | 5.19615i | −0.198680 | − | 0.344124i | ||||
\(229\) | −13.0000 | + | 22.5167i | −0.859064 | + | 1.48794i | 0.0137585 | + | 0.999905i | \(0.495620\pi\) |
−0.872823 | + | 0.488037i | \(0.837713\pi\) | |||||||
\(230\) | −2.00000 | −0.131876 | ||||||||
\(231\) | 0.500000 | − | 2.59808i | 0.0328976 | − | 0.170941i | ||||
\(232\) | 7.00000 | 0.459573 | ||||||||
\(233\) | 6.00000 | − | 10.3923i | 0.393073 | − | 0.680823i | −0.599780 | − | 0.800165i | \(-0.704745\pi\) |
0.992853 | + | 0.119342i | \(0.0380786\pi\) | |||||||
\(234\) | 3.00000 | + | 5.19615i | 0.196116 | + | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.500000 | − | 0.866025i | 0.0325472 | − | 0.0563735i | ||||
\(237\) | −13.0000 | −0.844441 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.00000 | 0.582162 | 0.291081 | − | 0.956698i | \(-0.405985\pi\) | ||||
0.291081 | + | 0.956698i | \(0.405985\pi\) | |||||||
\(240\) | −0.500000 | + | 0.866025i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 0.500000 | + | 0.866025i | 0.0321412 | + | 0.0556702i | ||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 1.00000 | + | 6.92820i | 0.0638877 | + | 0.442627i | ||||
\(246\) | 4.00000 | 0.255031 | ||||||||
\(247\) | 9.00000 | − | 15.5885i | 0.572656 | − | 0.991870i | ||||
\(248\) | −4.00000 | − | 6.92820i | −0.254000 | − | 0.439941i | ||||
\(249\) | 3.00000 | + | 5.19615i | 0.190117 | + | 0.329293i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | 4.00000 | 0.252478 | 0.126239 | − | 0.992000i | \(-0.459709\pi\) | ||||
0.126239 | + | 0.992000i | \(0.459709\pi\) | |||||||
\(252\) | 5.00000 | − | 1.73205i | 0.314970 | − | 0.109109i | ||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | −9.50000 | + | 16.4545i | −0.596083 | + | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.50000 | + | 11.2583i | −0.405459 | + | 0.702275i | −0.994375 | − | 0.105919i | \(-0.966222\pi\) |
0.588916 | + | 0.808194i | \(0.299555\pi\) | |||||||
\(258\) | 6.00000 | 0.373544 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3.00000 | −0.186052 | ||||||||
\(261\) | −7.00000 | + | 12.1244i | −0.433289 | + | 0.750479i | ||||
\(262\) | −7.00000 | − | 12.1244i | −0.432461 | − | 0.749045i | ||||
\(263\) | 4.50000 | + | 7.79423i | 0.277482 | + | 0.480613i | 0.970758 | − | 0.240059i | \(-0.0771668\pi\) |
−0.693276 | + | 0.720672i | \(0.743833\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −12.0000 | − | 10.3923i | −0.735767 | − | 0.637193i | ||||
\(267\) | −6.00000 | −0.367194 | ||||||||
\(268\) | 2.50000 | − | 4.33013i | 0.152712 | − | 0.264505i | ||||
\(269\) | 7.00000 | + | 12.1244i | 0.426798 | + | 0.739235i | 0.996586 | − | 0.0825561i | \(-0.0263084\pi\) |
−0.569789 | + | 0.821791i | \(0.692975\pi\) | |||||||
\(270\) | −2.50000 | − | 4.33013i | −0.152145 | − | 0.263523i | ||||
\(271\) | 0.500000 | − | 0.866025i | 0.0303728 | − | 0.0526073i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | − | 5.19615i | −0.363137 | − | 0.314485i | ||||
\(274\) | 3.00000 | 0.181237 | ||||||||
\(275\) | −0.500000 | + | 0.866025i | −0.0301511 | + | 0.0522233i | ||||
\(276\) | −1.00000 | − | 1.73205i | −0.0601929 | − | 0.104257i | ||||
\(277\) | 8.50000 | + | 14.7224i | 0.510716 | + | 0.884585i | 0.999923 | + | 0.0124177i | \(0.00395278\pi\) |
−0.489207 | + | 0.872167i | \(0.662714\pi\) | |||||||
\(278\) | −8.00000 | + | 13.8564i | −0.479808 | + | 0.831052i | ||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | −0.500000 | + | 2.59808i | −0.0298807 | + | 0.155265i | ||||
\(281\) | −8.00000 | −0.477240 | −0.238620 | − | 0.971113i | \(-0.576695\pi\) | ||||
−0.238620 | + | 0.971113i | \(0.576695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.00000 | − | 8.66025i | −0.297219 | − | 0.514799i | 0.678280 | − | 0.734804i | \(-0.262726\pi\) |
−0.975499 | + | 0.220005i | \(0.929393\pi\) | |||||||
\(284\) | −4.00000 | − | 6.92820i | −0.237356 | − | 0.411113i | ||||
\(285\) | −3.00000 | + | 5.19615i | −0.177705 | + | 0.307794i | ||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 10.0000 | − | 3.46410i | 0.590281 | − | 0.204479i | ||||
\(288\) | 2.00000 | 0.117851 | ||||||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | −3.50000 | − | 6.06218i | −0.205527 | − | 0.355983i | ||||
\(291\) | 3.50000 | + | 6.06218i | 0.205174 | + | 0.355371i | ||||
\(292\) | −7.00000 | + | 12.1244i | −0.409644 | + | 0.709524i | ||||
\(293\) | 26.0000 | 1.51894 | 0.759468 | − | 0.650545i | \(-0.225459\pi\) | ||||
0.759468 | + | 0.650545i | \(0.225459\pi\) | |||||||
\(294\) | −5.50000 | + | 4.33013i | −0.320767 | + | 0.252538i | ||||
\(295\) | −1.00000 | −0.0582223 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.50000 | + | 4.33013i | 0.145065 | + | 0.251259i | ||||
\(298\) | −9.00000 | − | 15.5885i | −0.521356 | − | 0.903015i | ||||
\(299\) | 3.00000 | − | 5.19615i | 0.173494 | − | 0.300501i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 15.0000 | − | 5.19615i | 0.864586 | − | 0.299501i | ||||
\(302\) | 17.0000 | 0.978240 | ||||||||
\(303\) | 7.50000 | − | 12.9904i | 0.430864 | − | 0.746278i | ||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 0.500000 | + | 0.866025i | 0.0286299 | + | 0.0495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.0000 | −1.48390 | −0.741949 | − | 0.670456i | \(-0.766098\pi\) | ||||
−0.741949 | + | 0.670456i | \(0.766098\pi\) | |||||||
\(308\) | 0.500000 | − | 2.59808i | 0.0284901 | − | 0.148039i | ||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | −4.00000 | + | 6.92820i | −0.227185 | + | 0.393496i | ||||
\(311\) | −6.00000 | − | 10.3923i | −0.340229 | − | 0.589294i | 0.644246 | − | 0.764818i | \(-0.277171\pi\) |
−0.984475 | + | 0.175525i | \(0.943838\pi\) | |||||||
\(312\) | −1.50000 | − | 2.59808i | −0.0849208 | − | 0.147087i | ||||
\(313\) | 6.50000 | − | 11.2583i | 0.367402 | − | 0.636358i | −0.621757 | − | 0.783210i | \(-0.713581\pi\) |
0.989158 | + | 0.146852i | \(0.0469141\pi\) | |||||||
\(314\) | −6.00000 | −0.338600 | ||||||||
\(315\) | −4.00000 | − | 3.46410i | −0.225374 | − | 0.195180i | ||||
\(316\) | −13.0000 | −0.731307 | ||||||||
\(317\) | 10.0000 | − | 17.3205i | 0.561656 | − | 0.972817i | −0.435696 | − | 0.900094i | \(-0.643498\pi\) |
0.997352 | − | 0.0727229i | \(-0.0231689\pi\) | |||||||
\(318\) | 3.00000 | + | 5.19615i | 0.168232 | + | 0.291386i | ||||
\(319\) | 3.50000 | + | 6.06218i | 0.195962 | + | 0.339417i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 6.00000 | 0.334887 | ||||||||
\(322\) | −4.00000 | − | 3.46410i | −0.222911 | − | 0.193047i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 1.50000 | + | 2.59808i | 0.0832050 | + | 0.144115i | ||||
\(326\) | −5.50000 | − | 9.52628i | −0.304617 | − | 0.527612i | ||||
\(327\) | −9.00000 | + | 15.5885i | −0.497701 | + | 0.862044i | ||||
\(328\) | 4.00000 | 0.220863 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.00000 | −0.0550482 | ||||||||
\(331\) | −6.50000 | + | 11.2583i | −0.357272 | + | 0.618814i | −0.987504 | − | 0.157593i | \(-0.949627\pi\) |
0.630232 | + | 0.776407i | \(0.282960\pi\) | |||||||
\(332\) | 3.00000 | + | 5.19615i | 0.164646 | + | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.50000 | − | 16.4545i | 0.519817 | − | 0.900349i | ||||
\(335\) | −5.00000 | −0.273179 | ||||||||
\(336\) | −2.50000 | + | 0.866025i | −0.136386 | + | 0.0472456i | ||||
\(337\) | −4.00000 | −0.217894 | −0.108947 | − | 0.994048i | \(-0.534748\pi\) | ||||
−0.108947 | + | 0.994048i | \(0.534748\pi\) | |||||||
\(338\) | −2.00000 | + | 3.46410i | −0.108786 | + | 0.188422i | ||||
\(339\) | 6.50000 | + | 11.2583i | 0.353032 | + | 0.611469i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.00000 | − | 6.92820i | 0.216612 | − | 0.375183i | ||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 6.00000 | 0.323498 | ||||||||
\(345\) | −1.00000 | + | 1.73205i | −0.0538382 | + | 0.0932505i | ||||
\(346\) | 4.50000 | + | 7.79423i | 0.241921 | + | 0.419020i | ||||
\(347\) | 13.0000 | + | 22.5167i | 0.697877 | + | 1.20876i | 0.969201 | + | 0.246270i | \(0.0792049\pi\) |
−0.271325 | + | 0.962488i | \(0.587462\pi\) | |||||||
\(348\) | 3.50000 | − | 6.06218i | 0.187620 | − | 0.324967i | ||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 2.50000 | − | 0.866025i | 0.133631 | − | 0.0462910i | ||||
\(351\) | 15.0000 | 0.800641 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 3.00000 | + | 5.19615i | 0.159674 | + | 0.276563i | 0.934751 | − | 0.355303i | \(-0.115622\pi\) |
−0.775077 | + | 0.631867i | \(0.782289\pi\) | |||||||
\(354\) | −0.500000 | − | 0.866025i | −0.0265747 | − | 0.0460287i | ||||
\(355\) | −4.00000 | + | 6.92820i | −0.212298 | + | 0.367711i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.0000 | −0.792775 | ||||||||
\(359\) | −15.5000 | + | 26.8468i | −0.818059 | + | 1.41692i | 0.0890519 | + | 0.996027i | \(0.471616\pi\) |
−0.907111 | + | 0.420892i | \(0.861717\pi\) | |||||||
\(360\) | −1.00000 | − | 1.73205i | −0.0527046 | − | 0.0912871i | ||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | 6.00000 | − | 10.3923i | 0.315353 | − | 0.546207i | ||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | −6.00000 | − | 5.19615i | −0.314485 | − | 0.272352i | ||||
\(365\) | 14.0000 | 0.732793 | ||||||||
\(366\) | −0.500000 | + | 0.866025i | −0.0261354 | + | 0.0452679i | ||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | −1.00000 | − | 1.73205i | −0.0521286 | − | 0.0902894i | ||||
\(369\) | −4.00000 | + | 6.92820i | −0.208232 | + | 0.360668i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 10.3923i | 0.623009 | + | 0.539542i | ||||
\(372\) | −8.00000 | −0.414781 | ||||||||
\(373\) | 0.500000 | − | 0.866025i | 0.0258890 | − | 0.0448411i | −0.852791 | − | 0.522253i | \(-0.825092\pi\) |
0.878680 | + | 0.477412i | \(0.158425\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.0000 | 1.08156 | ||||||||
\(378\) | 2.50000 | − | 12.9904i | 0.128586 | − | 0.668153i | ||||
\(379\) | −7.00000 | −0.359566 | −0.179783 | − | 0.983706i | \(-0.557540\pi\) | ||||
−0.179783 | + | 0.983706i | \(0.557540\pi\) | |||||||
\(380\) | −3.00000 | + | 5.19615i | −0.153897 | + | 0.266557i | ||||
\(381\) | 9.50000 | + | 16.4545i | 0.486700 | + | 0.842989i | ||||
\(382\) | 2.00000 | + | 3.46410i | 0.102329 | + | 0.177239i | ||||
\(383\) | −8.00000 | + | 13.8564i | −0.408781 | + | 0.708029i | −0.994753 | − | 0.102302i | \(-0.967379\pi\) |
0.585973 | + | 0.810331i | \(0.300713\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −2.50000 | + | 0.866025i | −0.127412 | + | 0.0441367i | ||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | −6.00000 | + | 10.3923i | −0.304997 | + | 0.528271i | ||||
\(388\) | 3.50000 | + | 6.06218i | 0.177686 | + | 0.307760i | ||||
\(389\) | 16.0000 | + | 27.7128i | 0.811232 | + | 1.40510i | 0.912002 | + | 0.410186i | \(0.134536\pi\) |
−0.100770 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(390\) | −1.50000 | + | 2.59808i | −0.0759555 | + | 0.131559i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | −14.0000 | −0.706207 | ||||||||
\(394\) | 5.50000 | − | 9.52628i | 0.277086 | − | 0.479927i | ||||
\(395\) | 6.50000 | + | 11.2583i | 0.327050 | + | 0.566468i | ||||
\(396\) | 1.00000 | + | 1.73205i | 0.0502519 | + | 0.0870388i | ||||
\(397\) | −13.0000 | + | 22.5167i | −0.652451 | + | 1.13008i | 0.330075 | + | 0.943955i | \(0.392926\pi\) |
−0.982526 | + | 0.186124i | \(0.940407\pi\) | |||||||
\(398\) | 6.00000 | 0.300753 | ||||||||
\(399\) | −15.0000 | + | 5.19615i | −0.750939 | + | 0.260133i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 16.5000 | − | 28.5788i | 0.823971 | − | 1.42716i | −0.0787327 | − | 0.996896i | \(-0.525087\pi\) |
0.902703 | − | 0.430263i | \(-0.141579\pi\) | |||||||
\(402\) | −2.50000 | − | 4.33013i | −0.124689 | − | 0.215967i | ||||
\(403\) | −12.0000 | − | 20.7846i | −0.597763 | − | 1.03536i | ||||
\(404\) | 7.50000 | − | 12.9904i | 0.373139 | − | 0.646296i | ||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 3.50000 | − | 18.1865i | 0.173702 | − | 0.902583i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.00000 | + | 6.92820i | 0.197787 | + | 0.342578i | 0.947811 | − | 0.318834i | \(-0.103291\pi\) |
−0.750023 | + | 0.661411i | \(0.769958\pi\) | |||||||
\(410\) | −2.00000 | − | 3.46410i | −0.0987730 | − | 0.171080i | ||||
\(411\) | 1.50000 | − | 2.59808i | 0.0739895 | − | 0.128154i | ||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | −2.00000 | − | 1.73205i | −0.0984136 | − | 0.0852286i | ||||
\(414\) | 4.00000 | 0.196589 | ||||||||
\(415\) | 3.00000 | − | 5.19615i | 0.147264 | − | 0.255069i | ||||
\(416\) | −1.50000 | − | 2.59808i | −0.0735436 | − | 0.127381i | ||||
\(417\) | 8.00000 | + | 13.8564i | 0.391762 | + | 0.678551i | ||||
\(418\) | 3.00000 | − | 5.19615i | 0.146735 | − | 0.254152i | ||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 2.00000 | + | 1.73205i | 0.0975900 | + | 0.0845154i | ||||
\(421\) | −12.0000 | −0.584844 | −0.292422 | − | 0.956289i | \(-0.594461\pi\) | ||||
−0.292422 | + | 0.956289i | \(0.594461\pi\) | |||||||
\(422\) | −6.00000 | + | 10.3923i | −0.292075 | + | 0.505889i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | + | 5.19615i | 0.145693 | + | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | −0.500000 | + | 2.59808i | −0.0241967 | + | 0.125730i | ||||
\(428\) | 6.00000 | 0.290021 | ||||||||
\(429\) | 1.50000 | − | 2.59808i | 0.0724207 | − | 0.125436i | ||||
\(430\) | −3.00000 | − | 5.19615i | −0.144673 | − | 0.250581i | ||||
\(431\) | 18.5000 | + | 32.0429i | 0.891114 | + | 1.54345i | 0.838542 | + | 0.544837i | \(0.183408\pi\) |
0.0525716 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(432\) | 2.50000 | − | 4.33013i | 0.120281 | − | 0.208333i | ||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | −20.0000 | + | 6.92820i | −0.960031 | + | 0.332564i | ||||
\(435\) | −7.00000 | −0.335624 | ||||||||
\(436\) | −9.00000 | + | 15.5885i | −0.431022 | + | 0.746552i | ||||
\(437\) | −6.00000 | − | 10.3923i | −0.287019 | − | 0.497131i | ||||
\(438\) | 7.00000 | + | 12.1244i | 0.334473 | + | 0.579324i | ||||
\(439\) | −12.5000 | + | 21.6506i | −0.596592 | + | 1.03333i | 0.396728 | + | 0.917936i | \(0.370146\pi\) |
−0.993320 | + | 0.115392i | \(0.963188\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −2.00000 | − | 13.8564i | −0.0952381 | − | 0.659829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.0000 | + | 34.6410i | −0.950229 | + | 1.64584i | −0.205301 | + | 0.978699i | \(0.565817\pi\) |
−0.744927 | + | 0.667146i | \(0.767516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.00000 | + | 5.19615i | 0.142214 | + | 0.246321i | ||||
\(446\) | −6.00000 | + | 10.3923i | −0.284108 | + | 0.492090i | ||||
\(447\) | −18.0000 | −0.851371 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | 26.0000 | 1.22702 | 0.613508 | − | 0.789689i | \(-0.289758\pi\) | ||||
0.613508 | + | 0.789689i | \(0.289758\pi\) | |||||||
\(450\) | −1.00000 | + | 1.73205i | −0.0471405 | + | 0.0816497i | ||||
\(451\) | 2.00000 | + | 3.46410i | 0.0941763 | + | 0.163118i | ||||
\(452\) | 6.50000 | + | 11.2583i | 0.305734 | + | 0.529547i | ||||
\(453\) | 8.50000 | − | 14.7224i | 0.399365 | − | 0.691720i | ||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | −1.50000 | + | 7.79423i | −0.0703211 | + | 0.365399i | ||||
\(456\) | −6.00000 | −0.280976 | ||||||||
\(457\) | 20.0000 | − | 34.6410i | 0.935561 | − | 1.62044i | 0.161929 | − | 0.986802i | \(-0.448228\pi\) |
0.773631 | − | 0.633636i | \(-0.218438\pi\) | |||||||
\(458\) | 13.0000 | + | 22.5167i | 0.607450 | + | 1.05213i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00000 | + | 1.73205i | −0.0466252 | + | 0.0807573i | ||||
\(461\) | −23.0000 | −1.07122 | −0.535608 | − | 0.844466i | \(-0.679918\pi\) | ||||
−0.535608 | + | 0.844466i | \(0.679918\pi\) | |||||||
\(462\) | −2.00000 | − | 1.73205i | −0.0930484 | − | 0.0805823i | ||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 3.50000 | − | 6.06218i | 0.162483 | − | 0.281430i | ||||
\(465\) | 4.00000 | + | 6.92820i | 0.185496 | + | 0.321288i | ||||
\(466\) | −6.00000 | − | 10.3923i | −0.277945 | − | 0.481414i | ||||
\(467\) | 18.0000 | − | 31.1769i | 0.832941 | − | 1.44270i | −0.0627555 | − | 0.998029i | \(-0.519989\pi\) |
0.895696 | − | 0.444667i | \(-0.146678\pi\) | |||||||
\(468\) | 6.00000 | 0.277350 | ||||||||
\(469\) | −10.0000 | − | 8.66025i | −0.461757 | − | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | + | 5.19615i | −0.138233 | + | 0.239426i | ||||
\(472\) | −0.500000 | − | 0.866025i | −0.0230144 | − | 0.0398621i | ||||
\(473\) | 3.00000 | + | 5.19615i | 0.137940 | + | 0.238919i | ||||
\(474\) | −6.50000 | + | 11.2583i | −0.298555 | + | 0.517112i | ||||
\(475\) | 6.00000 | 0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | 4.50000 | − | 7.79423i | 0.205825 | − | 0.356500i | ||||
\(479\) | −20.5000 | − | 35.5070i | −0.936669 | − | 1.62236i | −0.771631 | − | 0.636071i | \(-0.780559\pi\) |
−0.165038 | − | 0.986287i | \(-0.552775\pi\) | |||||||
\(480\) | 0.500000 | + | 0.866025i | 0.0228218 | + | 0.0395285i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | −5.00000 | + | 1.73205i | −0.227508 | + | 0.0788110i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 3.50000 | − | 6.06218i | 0.158927 | − | 0.275269i | ||||
\(486\) | 8.00000 | + | 13.8564i | 0.362887 | + | 0.628539i | ||||
\(487\) | −1.00000 | − | 1.73205i | −0.0453143 | − | 0.0784867i | 0.842479 | − | 0.538730i | \(-0.181096\pi\) |
−0.887793 | + | 0.460243i | \(0.847762\pi\) | |||||||
\(488\) | −0.500000 | + | 0.866025i | −0.0226339 | + | 0.0392031i | ||||
\(489\) | −11.0000 | −0.497437 | ||||||||
\(490\) | 6.50000 | + | 2.59808i | 0.293640 | + | 0.117369i | ||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 2.00000 | − | 3.46410i | 0.0901670 | − | 0.156174i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −9.00000 | − | 15.5885i | −0.404929 | − | 0.701358i | ||||
\(495\) | 1.00000 | − | 1.73205i | 0.0449467 | − | 0.0778499i | ||||
\(496\) | −8.00000 | −0.359211 | ||||||||
\(497\) | −20.0000 | + | 6.92820i | −0.897123 | + | 0.310772i | ||||
\(498\) | 6.00000 | 0.268866 | ||||||||
\(499\) | 2.00000 | − | 3.46410i | 0.0895323 | − | 0.155074i | −0.817781 | − | 0.575529i | \(-0.804796\pi\) |
0.907314 | + | 0.420455i | \(0.138129\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | −9.50000 | − | 16.4545i | −0.424429 | − | 0.735132i | ||||
\(502\) | 2.00000 | − | 3.46410i | 0.0892644 | − | 0.154610i | ||||
\(503\) | 3.00000 | 0.133763 | 0.0668817 | − | 0.997761i | \(-0.478695\pi\) | ||||
0.0668817 | + | 0.997761i | \(0.478695\pi\) | |||||||
\(504\) | 1.00000 | − | 5.19615i | 0.0445435 | − | 0.231455i | ||||
\(505\) | −15.0000 | −0.667491 | ||||||||
\(506\) | 1.00000 | − | 1.73205i | 0.0444554 | − | 0.0769991i | ||||
\(507\) | 2.00000 | + | 3.46410i | 0.0888231 | + | 0.153846i | ||||
\(508\) | 9.50000 | + | 16.4545i | 0.421494 | + | 0.730050i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0000 | + | 24.2487i | 1.23865 | + | 1.07270i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 15.0000 | − | 25.9808i | 0.662266 | − | 1.14708i | ||||
\(514\) | 6.50000 | + | 11.2583i | 0.286703 | + | 0.496584i | ||||
\(515\) | −2.00000 | − | 3.46410i | −0.0881305 | − | 0.152647i | ||||
\(516\) | 3.00000 | − | 5.19615i | 0.132068 | − | 0.228748i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000 | 0.395056 | ||||||||
\(520\) | −1.50000 | + | 2.59808i | −0.0657794 | + | 0.113933i | ||||
\(521\) | 5.00000 | + | 8.66025i | 0.219054 | + | 0.379413i | 0.954519 | − | 0.298150i | \(-0.0963696\pi\) |
−0.735465 | + | 0.677563i | \(0.763036\pi\) | |||||||
\(522\) | 7.00000 | + | 12.1244i | 0.306382 | + | 0.530669i | ||||
\(523\) | −17.0000 | + | 29.4449i | −0.743358 | + | 1.28753i | 0.207600 | + | 0.978214i | \(0.433435\pi\) |
−0.950958 | + | 0.309320i | \(0.899899\pi\) | |||||||
\(524\) | −14.0000 | −0.611593 | ||||||||
\(525\) | 0.500000 | − | 2.59808i | 0.0218218 | − | 0.113389i | ||||
\(526\) | 9.00000 | 0.392419 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −0.500000 | − | 0.866025i | −0.0217597 | − | 0.0376889i | ||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 3.00000 | − | 5.19615i | 0.130312 | − | 0.225706i | ||||
\(531\) | 2.00000 | 0.0867926 | ||||||||
\(532\) | −15.0000 | + | 5.19615i | −0.650332 | + | 0.225282i | ||||
\(533\) | 12.0000 | 0.519778 | ||||||||
\(534\) | −3.00000 | + | 5.19615i | −0.129823 | + | 0.224860i | ||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | −2.50000 | − | 4.33013i | −0.107984 | − | 0.187033i | ||||
\(537\) | −7.50000 | + | 12.9904i | −0.323649 | + | 0.560576i | ||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | −6.50000 | − | 2.59808i | −0.279975 | − | 0.111907i | ||||
\(540\) | −5.00000 | −0.215166 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | −0.500000 | − | 0.866025i | −0.0214768 | − | 0.0371990i | ||||
\(543\) | −6.00000 | − | 10.3923i | −0.257485 | − | 0.445976i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.0000 | 0.771035 | ||||||||
\(546\) | −7.50000 | + | 2.59808i | −0.320970 | + | 0.111187i | ||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 1.50000 | − | 2.59808i | 0.0640768 | − | 0.110984i | ||||
\(549\) | −1.00000 | − | 1.73205i | −0.0426790 | − | 0.0739221i | ||||
\(550\) | 0.500000 | + | 0.866025i | 0.0213201 | + | 0.0369274i | ||||
\(551\) | 21.0000 | − | 36.3731i | 0.894630 | − | 1.54954i | ||||
\(552\) | −2.00000 | −0.0851257 | ||||||||
\(553\) | −6.50000 | + | 33.7750i | −0.276408 | + | 1.43626i | ||||
\(554\) | 17.0000 | 0.722261 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.00000 | + | 13.8564i | 0.339276 | + | 0.587643i | ||||
\(557\) | 9.00000 | + | 15.5885i | 0.381342 | + | 0.660504i | 0.991254 | − | 0.131965i | \(-0.0421286\pi\) |
−0.609912 | + | 0.792469i | \(0.708795\pi\) | |||||||
\(558\) | 8.00000 | − | 13.8564i | 0.338667 | − | 0.586588i | ||||
\(559\) | 18.0000 | 0.761319 | ||||||||
\(560\) | 2.00000 | + | 1.73205i | 0.0845154 | + | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.00000 | + | 6.92820i | −0.168730 | + | 0.292249i | ||||
\(563\) | −19.0000 | − | 32.9090i | −0.800755 | − | 1.38695i | −0.919120 | − | 0.393977i | \(-0.871099\pi\) |
0.118366 | − | 0.992970i | \(-0.462235\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.50000 | − | 11.2583i | 0.273457 | − | 0.473642i | ||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | −8.00000 | −0.335673 | ||||||||
\(569\) | −9.00000 | + | 15.5885i | −0.377300 | + | 0.653502i | −0.990668 | − | 0.136295i | \(-0.956481\pi\) |
0.613369 | + | 0.789797i | \(0.289814\pi\) | |||||||
\(570\) | 3.00000 | + | 5.19615i | 0.125656 | + | 0.217643i | ||||
\(571\) | 14.0000 | + | 24.2487i | 0.585882 | + | 1.01478i | 0.994765 | + | 0.102190i | \(0.0325850\pi\) |
−0.408883 | + | 0.912587i | \(0.634082\pi\) | |||||||
\(572\) | 1.50000 | − | 2.59808i | 0.0627182 | − | 0.108631i | ||||
\(573\) | 4.00000 | 0.167102 | ||||||||
\(574\) | 2.00000 | − | 10.3923i | 0.0834784 | − | 0.433766i | ||||
\(575\) | 2.00000 | 0.0834058 | ||||||||
\(576\) | 1.00000 | − | 1.73205i | 0.0416667 | − | 0.0721688i | ||||
\(577\) | −15.5000 | − | 26.8468i | −0.645273 | − | 1.11765i | −0.984238 | − | 0.176847i | \(-0.943410\pi\) |
0.338965 | − | 0.940799i | \(-0.389923\pi\) | |||||||
\(578\) | −8.50000 | − | 14.7224i | −0.353553 | − | 0.612372i | ||||
\(579\) | −4.00000 | + | 6.92820i | −0.166234 | + | 0.287926i | ||||
\(580\) | −7.00000 | −0.290659 | ||||||||
\(581\) | 15.0000 | − | 5.19615i | 0.622305 | − | 0.215573i | ||||
\(582\) | 7.00000 | 0.290159 | ||||||||
\(583\) | −3.00000 | + | 5.19615i | −0.124247 | + | 0.215203i | ||||
\(584\) | 7.00000 | + | 12.1244i | 0.289662 | + | 0.501709i | ||||
\(585\) | −3.00000 | − | 5.19615i | −0.124035 | − | 0.214834i | ||||
\(586\) | 13.0000 | − | 22.5167i | 0.537025 | − | 0.930155i | ||||
\(587\) | 17.0000 | 0.701665 | 0.350833 | − | 0.936438i | \(-0.385899\pi\) | ||||
0.350833 | + | 0.936438i | \(0.385899\pi\) | |||||||
\(588\) | 1.00000 | + | 6.92820i | 0.0412393 | + | 0.285714i | ||||
\(589\) | −48.0000 | −1.97781 | ||||||||
\(590\) | −0.500000 | + | 0.866025i | −0.0205847 | + | 0.0356537i | ||||
\(591\) | −5.50000 | − | 9.52628i | −0.226240 | − | 0.391859i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15.0000 | + | 25.9808i | −0.615976 | + | 1.06690i | 0.374236 | + | 0.927333i | \(0.377905\pi\) |
−0.990212 | + | 0.139569i | \(0.955428\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 3.00000 | − | 5.19615i | 0.122782 | − | 0.212664i | ||||
\(598\) | −3.00000 | − | 5.19615i | −0.122679 | − | 0.212486i | ||||
\(599\) | −16.0000 | − | 27.7128i | −0.653742 | − | 1.13231i | −0.982208 | − | 0.187799i | \(-0.939865\pi\) |
0.328465 | − | 0.944516i | \(-0.393469\pi\) | |||||||
\(600\) | 0.500000 | − | 0.866025i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | 4.00000 | 0.163163 | 0.0815817 | − | 0.996667i | \(-0.474003\pi\) | ||||
0.0815817 | + | 0.996667i | \(0.474003\pi\) | |||||||
\(602\) | 3.00000 | − | 15.5885i | 0.122271 | − | 0.635338i | ||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | 8.50000 | − | 14.7224i | 0.345860 | − | 0.599047i | ||||
\(605\) | −0.500000 | − | 0.866025i | −0.0203279 | − | 0.0352089i | ||||
\(606\) | −7.50000 | − | 12.9904i | −0.304667 | − | 0.527698i | ||||
\(607\) | 12.0000 | − | 20.7846i | 0.487065 | − | 0.843621i | −0.512824 | − | 0.858494i | \(-0.671401\pi\) |
0.999889 | + | 0.0148722i | \(0.00473415\pi\) | |||||||
\(608\) | −6.00000 | −0.243332 | ||||||||
\(609\) | −14.0000 | − | 12.1244i | −0.567309 | − | 0.491304i | ||||
\(610\) | 1.00000 | 0.0404888 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.00000 | − | 5.19615i | −0.121169 | − | 0.209871i | 0.799060 | − | 0.601251i | \(-0.205331\pi\) |
−0.920229 | + | 0.391381i | \(0.871998\pi\) | |||||||
\(614\) | −13.0000 | + | 22.5167i | −0.524637 | + | 0.908698i | ||||
\(615\) | −4.00000 | −0.161296 | ||||||||
\(616\) | −2.00000 | − | 1.73205i | −0.0805823 | − | 0.0697863i | ||||
\(617\) | 27.0000 | 1.08698 | 0.543490 | − | 0.839416i | \(-0.317103\pi\) | ||||
0.543490 | + | 0.839416i | \(0.317103\pi\) | |||||||
\(618\) | 2.00000 | − | 3.46410i | 0.0804518 | − | 0.139347i | ||||
\(619\) | −16.0000 | − | 27.7128i | −0.643094 | − | 1.11387i | −0.984738 | − | 0.174042i | \(-0.944317\pi\) |
0.341644 | − | 0.939829i | \(-0.389016\pi\) | |||||||
\(620\) | 4.00000 | + | 6.92820i | 0.160644 | + | 0.278243i | ||||
\(621\) | 5.00000 | − | 8.66025i | 0.200643 | − | 0.347524i | ||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | −3.00000 | + | 15.5885i | −0.120192 | + | 0.624538i | ||||
\(624\) | −3.00000 | −0.120096 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −6.50000 | − | 11.2583i | −0.259792 | − | 0.449973i | ||||
\(627\) | −3.00000 | − | 5.19615i | −0.119808 | − | 0.207514i | ||||
\(628\) | −3.00000 | + | 5.19615i | −0.119713 | + | 0.207349i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −5.00000 | + | 1.73205i | −0.199205 | + | 0.0690066i | ||||
\(631\) | −14.0000 | −0.557331 | −0.278666 | − | 0.960388i | \(-0.589892\pi\) | ||||
−0.278666 | + | 0.960388i | \(0.589892\pi\) | |||||||
\(632\) | −6.50000 | + | 11.2583i | −0.258556 | + | 0.447832i | ||||
\(633\) | 6.00000 | + | 10.3923i | 0.238479 | + | 0.413057i | ||||
\(634\) | −10.0000 | − | 17.3205i | −0.397151 | − | 0.687885i | ||||
\(635\) | 9.50000 | − | 16.4545i | 0.376996 | − | 0.652976i | ||||
\(636\) | 6.00000 | 0.237915 | ||||||||
\(637\) | −16.5000 | + | 12.9904i | −0.653754 | + | 0.514698i | ||||
\(638\) | 7.00000 | 0.277133 | ||||||||
\(639\) | 8.00000 | − | 13.8564i | 0.316475 | − | 0.548151i | ||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −0.500000 | − | 0.866025i | −0.0197488 | − | 0.0342059i | 0.855982 | − | 0.517005i | \(-0.172953\pi\) |
−0.875731 | + | 0.482800i | \(0.839620\pi\) | |||||||
\(642\) | 3.00000 | − | 5.19615i | 0.118401 | − | 0.205076i | ||||
\(643\) | 37.0000 | 1.45914 | 0.729569 | − | 0.683907i | \(-0.239721\pi\) | ||||
0.729569 | + | 0.683907i | \(0.239721\pi\) | |||||||
\(644\) | −5.00000 | + | 1.73205i | −0.197028 | + | 0.0682524i | ||||
\(645\) | −6.00000 | −0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.00000 | + | 5.19615i | 0.117942 | + | 0.204282i | 0.918952 | − | 0.394369i | \(-0.129037\pi\) |
−0.801010 | + | 0.598651i | \(0.795704\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 0.500000 | − | 0.866025i | 0.0196267 | − | 0.0339945i | ||||
\(650\) | 3.00000 | 0.117670 | ||||||||
\(651\) | −4.00000 | + | 20.7846i | −0.156772 | + | 0.814613i | ||||
\(652\) | −11.0000 | −0.430793 | ||||||||
\(653\) | −11.0000 | + | 19.0526i | −0.430463 | + | 0.745584i | −0.996913 | − | 0.0785119i | \(-0.974983\pi\) |
0.566450 | + | 0.824096i | \(0.308316\pi\) | |||||||
\(654\) | 9.00000 | + | 15.5885i | 0.351928 | + | 0.609557i | ||||
\(655\) | 7.00000 | + | 12.1244i | 0.273513 | + | 0.473738i | ||||
\(656\) | 2.00000 | − | 3.46410i | 0.0780869 | − | 0.135250i | ||||
\(657\) | −28.0000 | −1.09238 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.0000 | −0.545363 | −0.272681 | − | 0.962104i | \(-0.587910\pi\) | ||||
−0.272681 | + | 0.962104i | \(0.587910\pi\) | |||||||
\(660\) | −0.500000 | + | 0.866025i | −0.0194625 | + | 0.0337100i | ||||
\(661\) | −17.0000 | − | 29.4449i | −0.661223 | − | 1.14527i | −0.980294 | − | 0.197542i | \(-0.936704\pi\) |
0.319071 | − | 0.947731i | \(-0.396629\pi\) | |||||||
\(662\) | 6.50000 | + | 11.2583i | 0.252630 | + | 0.437567i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 12.0000 | + | 10.3923i | 0.465340 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.00000 | − | 12.1244i | 0.271041 | − | 0.469457i | ||||
\(668\) | −9.50000 | − | 16.4545i | −0.367566 | − | 0.636643i | ||||
\(669\) | 6.00000 | + | 10.3923i | 0.231973 | + | 0.401790i | ||||
\(670\) | −2.50000 | + | 4.33013i | −0.0965834 | + | 0.167287i | ||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | −0.500000 | + | 2.59808i | −0.0192879 | + | 0.100223i | ||||
\(673\) | −34.0000 | −1.31060 | −0.655302 | − | 0.755367i | \(-0.727459\pi\) | ||||
−0.655302 | + | 0.755367i | \(0.727459\pi\) | |||||||
\(674\) | −2.00000 | + | 3.46410i | −0.0770371 | + | 0.133432i | ||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 2.00000 | + | 3.46410i | 0.0769231 | + | 0.133235i | ||||
\(677\) | 3.00000 | − | 5.19615i | 0.115299 | − | 0.199704i | −0.802600 | − | 0.596518i | \(-0.796551\pi\) |
0.917899 | + | 0.396813i | \(0.129884\pi\) | |||||||
\(678\) | 13.0000 | 0.499262 | ||||||||
\(679\) | 17.5000 | − | 6.06218i | 0.671588 | − | 0.232645i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.00000 | − | 6.92820i | 0.153280 | − | 0.265489i | ||||
\(682\) | −4.00000 | − | 6.92820i | −0.153168 | − | 0.265295i | ||||
\(683\) | 0.500000 | + | 0.866025i | 0.0191320 | + | 0.0331375i | 0.875433 | − | 0.483340i | \(-0.160576\pi\) |
−0.856301 | + | 0.516477i | \(0.827243\pi\) | |||||||
\(684\) | 6.00000 | − | 10.3923i | 0.229416 | − | 0.397360i | ||||
\(685\) | −3.00000 | −0.114624 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | 26.0000 | 0.991962 | ||||||||
\(688\) | 3.00000 | − | 5.19615i | 0.114374 | − | 0.198101i | ||||
\(689\) | 9.00000 | + | 15.5885i | 0.342873 | + | 0.593873i | ||||
\(690\) | 1.00000 | + | 1.73205i | 0.0380693 | + | 0.0659380i | ||||
\(691\) | 13.5000 | − | 23.3827i | 0.513564 | − | 0.889519i | −0.486312 | − | 0.873785i | \(-0.661658\pi\) |
0.999876 | − | 0.0157341i | \(-0.00500851\pi\) | |||||||
\(692\) | 9.00000 | 0.342129 | ||||||||
\(693\) | 5.00000 | − | 1.73205i | 0.189934 | − | 0.0657952i | ||||
\(694\) | 26.0000 | 0.986947 | ||||||||
\(695\) | 8.00000 | − | 13.8564i | 0.303457 | − | 0.525603i | ||||
\(696\) | −3.50000 | − | 6.06218i | −0.132667 | − | 0.229786i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13.0000 | + | 22.5167i | −0.492057 | + | 0.852268i | ||||
\(699\) | −12.0000 | −0.453882 | ||||||||
\(700\) | 0.500000 | − | 2.59808i | 0.0188982 | − | 0.0981981i | ||||
\(701\) | −5.00000 | −0.188847 | −0.0944237 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944237 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(702\) | 7.50000 | − | 12.9904i | 0.283069 | − | 0.490290i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | 0.225813 | ||||||||
\(707\) | −30.0000 | − | 25.9808i | −1.12827 | − | 0.977107i | ||||
\(708\) | −1.00000 | −0.0375823 | ||||||||
\(709\) | 9.00000 | − | 15.5885i | 0.338002 | − | 0.585437i | −0.646055 | − | 0.763291i | \(-0.723582\pi\) |
0.984057 | + | 0.177854i | \(0.0569156\pi\) | |||||||
\(710\) | 4.00000 | + | 6.92820i | 0.150117 | + | 0.260011i | ||||
\(711\) | −13.0000 | − | 22.5167i | −0.487538 | − | 0.844441i | ||||
\(712\) | −3.00000 | + | 5.19615i | −0.112430 | + | 0.194734i | ||||
\(713\) | −16.0000 | −0.599205 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | −0.112194 | ||||||||
\(716\) | −7.50000 | + | 12.9904i | −0.280288 | + | 0.485473i | ||||
\(717\) | −4.50000 | − | 7.79423i | −0.168056 | − | 0.291081i | ||||
\(718\) | 15.5000 | + | 26.8468i | 0.578455 | + | 1.00191i | ||||
\(719\) | 2.00000 | − | 3.46410i | 0.0745874 | − | 0.129189i | −0.826319 | − | 0.563202i | \(-0.809569\pi\) |
0.900907 | + | 0.434013i | \(0.142903\pi\) | |||||||
\(720\) | −2.00000 | −0.0745356 | ||||||||
\(721\) | 2.00000 | − | 10.3923i | 0.0744839 | − | 0.387030i | ||||
\(722\) | −17.0000 | −0.632674 | ||||||||
\(723\) | 5.00000 | − | 8.66025i | 0.185952 | − | 0.322078i | ||||
\(724\) | −6.00000 | − | 10.3923i | −0.222988 | − | 0.386227i | ||||
\(725\) | 3.50000 | + | 6.06218i | 0.129987 | + | 0.225144i | ||||
\(726\) | 0.500000 | − | 0.866025i | 0.0185567 | − | 0.0321412i | ||||
\(727\) | −22.0000 | −0.815935 | −0.407967 | − | 0.912996i | \(-0.633762\pi\) | ||||
−0.407967 | + | 0.912996i | \(0.633762\pi\) | |||||||
\(728\) | −7.50000 | + | 2.59808i | −0.277968 | + | 0.0962911i | ||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 7.00000 | − | 12.1244i | 0.259082 | − | 0.448743i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.500000 | + | 0.866025i | 0.0184805 | + | 0.0320092i | ||||
\(733\) | 23.5000 | − | 40.7032i | 0.867992 | − | 1.50341i | 0.00394730 | − | 0.999992i | \(-0.498744\pi\) |
0.864045 | − | 0.503415i | \(-0.167923\pi\) | |||||||
\(734\) | −8.00000 | −0.295285 | ||||||||
\(735\) | 5.50000 | − | 4.33013i | 0.202871 | − | 0.159719i | ||||
\(736\) | −2.00000 | −0.0737210 | ||||||||
\(737\) | 2.50000 | − | 4.33013i | 0.0920887 | − | 0.159502i | ||||
\(738\) | 4.00000 | + | 6.92820i | 0.147242 | + | 0.255031i | ||||
\(739\) | 6.00000 | + | 10.3923i | 0.220714 | + | 0.382287i | 0.955025 | − | 0.296526i | \(-0.0958281\pi\) |
−0.734311 | + | 0.678813i | \(0.762495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.0000 | −0.661247 | ||||||||
\(742\) | 15.0000 | − | 5.19615i | 0.550667 | − | 0.190757i | ||||
\(743\) | 40.0000 | 1.46746 | 0.733729 | − | 0.679442i | \(-0.237778\pi\) | ||||
0.733729 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(744\) | −4.00000 | + | 6.92820i | −0.146647 | + | 0.254000i | ||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | −0.500000 | − | 0.866025i | −0.0183063 | − | 0.0317074i | ||||
\(747\) | −6.00000 | + | 10.3923i | −0.219529 | + | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.00000 | − | 15.5885i | 0.109618 | − | 0.569590i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 25.0000 | − | 43.3013i | 0.912263 | − | 1.58009i | 0.101403 | − | 0.994845i | \(-0.467667\pi\) |
0.810860 | − | 0.585240i | \(-0.199000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.00000 | − | 3.46410i | −0.0728841 | − | 0.126239i | ||||
\(754\) | 10.5000 | − | 18.1865i | 0.382387 | − | 0.662314i | ||||
\(755\) | −17.0000 | −0.618693 | ||||||||
\(756\) | −10.0000 | − | 8.66025i | −0.363696 | − | 0.314970i | ||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | −3.50000 | + | 6.06218i | −0.127126 | + | 0.220188i | ||||
\(759\) | −1.00000 | − | 1.73205i | −0.0362977 | − | 0.0628695i | ||||
\(760\) | 3.00000 | + | 5.19615i | 0.108821 | + | 0.188484i | ||||
\(761\) | 15.0000 | − | 25.9808i | 0.543750 | − | 0.941802i | −0.454935 | − | 0.890525i | \(-0.650337\pi\) |
0.998684 | − | 0.0512772i | \(-0.0163292\pi\) | |||||||
\(762\) | 19.0000 | 0.688297 | ||||||||
\(763\) | 36.0000 | + | 31.1769i | 1.30329 | + | 1.12868i | ||||
\(764\) | 4.00000 | 0.144715 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.00000 | + | 13.8564i | 0.289052 | + | 0.500652i | ||||
\(767\) | −1.50000 | − | 2.59808i | −0.0541619 | − | 0.0938111i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | −0.500000 | + | 2.59808i | −0.0180187 | + | 0.0936282i | ||||
\(771\) | 13.0000 | 0.468184 | ||||||||
\(772\) | −4.00000 | + | 6.92820i | −0.143963 | + | 0.249351i | ||||
\(773\) | −9.00000 | − | 15.5885i | −0.323708 | − | 0.560678i | 0.657542 | − | 0.753418i | \(-0.271596\pi\) |
−0.981250 | + | 0.192740i | \(0.938263\pi\) | |||||||
\(774\) | 6.00000 | + | 10.3923i | 0.215666 | + | 0.373544i | ||||
\(775\) | 4.00000 | − | 6.92820i | 0.143684 | − | 0.248868i | ||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.0000 | 1.14726 | ||||||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 1.50000 | + | 2.59808i | 0.0537086 | + | 0.0930261i | ||||
\(781\) | −4.00000 | − | 6.92820i | −0.143131 | − | 0.247911i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 35.0000 | 1.25080 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 6.00000 | 0.214149 | ||||||||
\(786\) | −7.00000 | + | 12.1244i | −0.249682 | + | 0.432461i | ||||
\(787\) | −9.00000 | − | 15.5885i | −0.320815 | − | 0.555668i | 0.659841 | − | 0.751405i | \(-0.270624\pi\) |
−0.980656 | + | 0.195737i | \(0.937290\pi\) | |||||||
\(788\) | −5.50000 | − | 9.52628i | −0.195929 | − | 0.339360i | ||||
\(789\) | 4.50000 | − | 7.79423i | 0.160204 | − | 0.277482i | ||||
\(790\) | 13.0000 | 0.462519 | ||||||||
\(791\) | 32.5000 | − | 11.2583i | 1.15557 | − | 0.400300i | ||||
\(792\) | 2.00000 | 0.0710669 | ||||||||
\(793\) | −1.50000 | + | 2.59808i | −0.0532666 | + | 0.0922604i | ||||
\(794\) | 13.0000 | + | 22.5167i | 0.461353 | + | 0.799086i | ||||
\(795\) | −3.00000 | − | 5.19615i | −0.106399 | − | 0.184289i | ||||
\(796\) | 3.00000 | − | 5.19615i | 0.106332 | − | 0.184173i | ||||
\(797\) | −24.0000 | −0.850124 | −0.425062 | − | 0.905164i | \(-0.639748\pi\) | ||||
−0.425062 | + | 0.905164i | \(0.639748\pi\) | |||||||
\(798\) | −3.00000 | + | 15.5885i | −0.106199 | + | 0.551825i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −6.00000 | − | 10.3923i | −0.212000 | − | 0.367194i | ||||
\(802\) | −16.5000 | − | 28.5788i | −0.582635 | − | 1.00915i | ||||
\(803\) | −7.00000 | + | 12.1244i | −0.247025 | + | 0.427859i | ||||
\(804\) | −5.00000 | −0.176336 | ||||||||
\(805\) | 4.00000 | + | 3.46410i | 0.140981 | + | 0.122094i | ||||
\(806\) | −24.0000 | −0.845364 | ||||||||
\(807\) | 7.00000 | − | 12.1244i | 0.246412 | − | 0.426798i | ||||
\(808\) | −7.50000 | − | 12.9904i | −0.263849 | − | 0.457000i | ||||
\(809\) | 24.0000 | + | 41.5692i | 0.843795 | + | 1.46150i | 0.886664 | + | 0.462415i | \(0.153017\pi\) |
−0.0428684 | + | 0.999081i | \(0.513650\pi\) | |||||||
\(810\) | 0.500000 | − | 0.866025i | 0.0175682 | − | 0.0304290i | ||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | −14.0000 | − | 12.1244i | −0.491304 | − | 0.425481i | ||||
\(813\) | −1.00000 | −0.0350715 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.50000 | + | 9.52628i | 0.192657 | + | 0.333691i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0000 | − | 31.1769i | 0.629740 | − | 1.09074i | ||||
\(818\) | 8.00000 | 0.279713 | ||||||||
\(819\) | 3.00000 | − | 15.5885i | 0.104828 | − | 0.544705i | ||||
\(820\) | −4.00000 | −0.139686 | ||||||||
\(821\) | −26.5000 | + | 45.8993i | −0.924856 | + | 1.60190i | −0.133064 | + | 0.991107i | \(0.542482\pi\) |
−0.791792 | + | 0.610791i | \(0.790852\pi\) | |||||||
\(822\) | −1.50000 | − | 2.59808i | −0.0523185 | − | 0.0906183i | ||||
\(823\) | 2.00000 | + | 3.46410i | 0.0697156 | + | 0.120751i | 0.898776 | − | 0.438408i | \(-0.144457\pi\) |
−0.829060 | + | 0.559159i | \(0.811124\pi\) | |||||||
\(824\) | 2.00000 | − | 3.46410i | 0.0696733 | − | 0.120678i | ||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | −2.50000 | + | 0.866025i | −0.0869861 | + | 0.0301329i | ||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 2.00000 | − | 3.46410i | 0.0695048 | − | 0.120386i | ||||
\(829\) | 2.00000 | + | 3.46410i | 0.0694629 | + | 0.120313i | 0.898665 | − | 0.438636i | \(-0.144538\pi\) |
−0.829202 | + | 0.558949i | \(0.811205\pi\) | |||||||
\(830\) | −3.00000 | − | 5.19615i | −0.104132 | − | 0.180361i | ||||
\(831\) | 8.50000 | − | 14.7224i | 0.294862 | − | 0.510716i | ||||
\(832\) | −3.00000 | −0.104006 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 16.0000 | 0.554035 | ||||||||
\(835\) | −9.50000 | + | 16.4545i | −0.328761 | + | 0.569431i | ||||
\(836\) | −3.00000 | − | 5.19615i | −0.103757 | − | 0.179713i | ||||
\(837\) | −20.0000 | − | 34.6410i | −0.691301 | − | 1.19737i | ||||
\(838\) | −4.00000 | + | 6.92820i | −0.138178 | + | 0.239331i | ||||
\(839\) | 2.00000 | 0.0690477 | 0.0345238 | − | 0.999404i | \(-0.489009\pi\) | ||||
0.0345238 | + | 0.999404i | \(0.489009\pi\) | |||||||
\(840\) | 2.50000 | − | 0.866025i | 0.0862582 | − | 0.0298807i | ||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −6.00000 | + | 10.3923i | −0.206774 | + | 0.358142i | ||||
\(843\) | 4.00000 | + | 6.92820i | 0.137767 | + | 0.238620i | ||||
\(844\) | 6.00000 | + | 10.3923i | 0.206529 | + | 0.357718i | ||||
\(845\) | 2.00000 | − | 3.46410i | 0.0688021 | − | 0.119169i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.500000 | − | 2.59808i | 0.0171802 | − | 0.0892710i | ||||
\(848\) | 6.00000 | 0.206041 | ||||||||
\(849\) | −5.00000 | + | 8.66025i | −0.171600 | + | 0.297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −4.00000 | + | 6.92820i | −0.137038 | + | 0.237356i | ||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | 2.00000 | + | 1.73205i | 0.0684386 | + | 0.0592696i | ||||
\(855\) | −12.0000 | −0.410391 | ||||||||
\(856\) | 3.00000 | − | 5.19615i | 0.102538 | − | 0.177601i | ||||
\(857\) | −15.0000 | − | 25.9808i | −0.512390 | − | 0.887486i | −0.999897 | − | 0.0143666i | \(-0.995427\pi\) |
0.487507 | − | 0.873119i | \(-0.337907\pi\) | |||||||
\(858\) | −1.50000 | − | 2.59808i | −0.0512092 | − | 0.0886969i | ||||
\(859\) | 15.5000 | − | 26.8468i | 0.528853 | − | 0.916001i | −0.470581 | − | 0.882357i | \(-0.655956\pi\) |
0.999434 | − | 0.0336436i | \(-0.0107111\pi\) | |||||||
\(860\) | −6.00000 | −0.204598 | ||||||||
\(861\) | −8.00000 | − | 6.92820i | −0.272639 | − | 0.236113i | ||||
\(862\) | 37.0000 | 1.26023 | ||||||||
\(863\) | −8.00000 | + | 13.8564i | −0.272323 | + | 0.471678i | −0.969456 | − | 0.245264i | \(-0.921125\pi\) |
0.697133 | + | 0.716942i | \(0.254459\pi\) | |||||||
\(864\) | −2.50000 | − | 4.33013i | −0.0850517 | − | 0.147314i | ||||
\(865\) | −4.50000 | − | 7.79423i | −0.153005 | − | 0.265012i | ||||
\(866\) | 13.0000 | − | 22.5167i | 0.441758 | − | 0.765147i | ||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | −4.00000 | + | 20.7846i | −0.135769 | + | 0.705476i | ||||
\(869\) | −13.0000 | −0.440995 | ||||||||
\(870\) | −3.50000 | + | 6.06218i | −0.118661 | + | 0.205527i | ||||
\(871\) | −7.50000 | − | 12.9904i | −0.254128 | − | 0.440162i | ||||
\(872\) | 9.00000 | + | 15.5885i | 0.304778 | + | 0.527892i | ||||
\(873\) | −7.00000 | + | 12.1244i | −0.236914 | + | 0.410347i | ||||
\(874\) | −12.0000 | −0.405906 | ||||||||
\(875\) | −2.50000 | + | 0.866025i | −0.0845154 | + | 0.0292770i | ||||
\(876\) | 14.0000 | 0.473016 | ||||||||
\(877\) | 14.5000 | − | 25.1147i | 0.489630 | − | 0.848064i | −0.510299 | − | 0.859997i | \(-0.670465\pi\) |
0.999929 | + | 0.0119329i | \(0.00379845\pi\) | |||||||
\(878\) | 12.5000 | + | 21.6506i | 0.421855 | + | 0.730674i | ||||
\(879\) | −13.0000 | − | 22.5167i | −0.438479 | − | 0.759468i | ||||
\(880\) | −0.500000 | + | 0.866025i | −0.0168550 | + | 0.0291937i | ||||
\(881\) | −35.0000 | −1.17918 | −0.589590 | − | 0.807703i | \(-0.700711\pi\) | ||||
−0.589590 | + | 0.807703i | \(0.700711\pi\) | |||||||
\(882\) | −13.0000 | − | 5.19615i | −0.437733 | − | 0.174964i | ||||
\(883\) | 37.0000 | 1.24515 | 0.622575 | − | 0.782560i | \(-0.286087\pi\) | ||||
0.622575 | + | 0.782560i | \(0.286087\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.500000 | + | 0.866025i | 0.0168073 | + | 0.0291111i | ||||
\(886\) | 20.0000 | + | 34.6410i | 0.671913 | + | 1.16379i | ||||
\(887\) | −23.5000 | + | 40.7032i | −0.789053 | + | 1.36668i | 0.137495 | + | 0.990502i | \(0.456095\pi\) |
−0.926548 | + | 0.376177i | \(0.877238\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 47.5000 | − | 16.4545i | 1.59310 | − | 0.551866i | ||||
\(890\) | 6.00000 | 0.201120 | ||||||||
\(891\) | −0.500000 | + | 0.866025i | −0.0167506 | + | 0.0290129i | ||||
\(892\) | 6.00000 | + | 10.3923i | 0.200895 | + | 0.347960i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −9.00000 | + | 15.5885i | −0.301005 | + | 0.521356i | ||||
\(895\) | 15.0000 | 0.501395 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 13.0000 | − | 22.5167i | 0.433816 | − | 0.751391i | ||||
\(899\) | −28.0000 | − | 48.4974i | −0.933852 | − | 1.61748i | ||||
\(900\) | 1.00000 | + | 1.73205i | 0.0333333 | + | 0.0577350i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 4.00000 | 0.133185 | ||||||||
\(903\) | −12.0000 | − | 10.3923i | −0.399335 | − | 0.345834i | ||||
\(904\) | 13.0000 | 0.432374 | ||||||||
\(905\) | −6.00000 | + | 10.3923i | −0.199447 | + | 0.345452i | ||||
\(906\) | −8.50000 | − | 14.7224i | −0.282394 | − | 0.489120i | ||||
\(907\) | −6.00000 | − | 10.3923i | −0.199227 | − | 0.345071i | 0.749051 | − | 0.662512i | \(-0.230510\pi\) |
−0.948278 | + | 0.317441i | \(0.897176\pi\) | |||||||
\(908\) | 4.00000 | − | 6.92820i | 0.132745 | − | 0.229920i | ||||
\(909\) | 30.0000 | 0.995037 | ||||||||
\(910\) | 6.00000 | + | 5.19615i | 0.198898 | + | 0.172251i | ||||
\(911\) | 4.00000 | 0.132526 | 0.0662630 | − | 0.997802i | \(-0.478892\pi\) | ||||
0.0662630 | + | 0.997802i | \(0.478892\pi\) | |||||||
\(912\) | −3.00000 | + | 5.19615i | −0.0993399 | + | 0.172062i | ||||
\(913\) | 3.00000 | + | 5.19615i | 0.0992855 | + | 0.171968i | ||||
\(914\) | −20.0000 | − | 34.6410i | −0.661541 | − | 1.14582i | ||||
\(915\) | 0.500000 | − | 0.866025i | 0.0165295 | − | 0.0286299i | ||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | −7.00000 | + | 36.3731i | −0.231160 | + | 1.20114i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | 1.00000 | + | 1.73205i | 0.0329690 | + | 0.0571040i | ||||
\(921\) | 13.0000 | + | 22.5167i | 0.428365 | + | 0.741949i | ||||
\(922\) | −11.5000 | + | 19.9186i | −0.378732 | + | 0.655984i | ||||
\(923\) | −24.0000 | −0.789970 | ||||||||
\(924\) | −2.50000 | + | 0.866025i | −0.0822440 | + | 0.0284901i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.00000 | − | 3.46410i | 0.0657241 | − | 0.113837i | ||||
\(927\) | 4.00000 | + | 6.92820i | 0.131377 | + | 0.227552i | ||||
\(928\) | −3.50000 | − | 6.06218i | −0.114893 | − | 0.199001i | ||||
\(929\) | 10.5000 | − | 18.1865i | 0.344494 | − | 0.596681i | −0.640768 | − | 0.767735i | \(-0.721384\pi\) |
0.985262 | + | 0.171054i | \(0.0547172\pi\) | |||||||
\(930\) | 8.00000 | 0.262330 | ||||||||
\(931\) | 6.00000 | + | 41.5692i | 0.196642 | + | 1.36238i | ||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | −6.00000 | + | 10.3923i | −0.196431 | + | 0.340229i | ||||
\(934\) | −18.0000 | − | 31.1769i | −0.588978 | − | 1.02014i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.00000 | − | 5.19615i | 0.0980581 | − | 0.169842i | ||||
\(937\) | −36.0000 | −1.17607 | −0.588034 | − | 0.808836i | \(-0.700098\pi\) | ||||
−0.588034 | + | 0.808836i | \(0.700098\pi\) | |||||||
\(938\) | −12.5000 | + | 4.33013i | −0.408139 | + | 0.141384i | ||||
\(939\) | −13.0000 | −0.424239 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.50000 | − | 2.59808i | −0.0488986 | − | 0.0846949i | 0.840540 | − | 0.541749i | \(-0.182238\pi\) |
−0.889439 | + | 0.457054i | \(0.848904\pi\) | |||||||
\(942\) | 3.00000 | + | 5.19615i | 0.0977453 | + | 0.169300i | ||||
\(943\) | 4.00000 | − | 6.92820i | 0.130258 | − | 0.225613i | ||||
\(944\) | −1.00000 | −0.0325472 | ||||||||
\(945\) | −2.50000 | + | 12.9904i | −0.0813250 | + | 0.422577i | ||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | −24.0000 | + | 41.5692i | −0.779895 | + | 1.35082i | 0.152106 | + | 0.988364i | \(0.451394\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(948\) | 6.50000 | + | 11.2583i | 0.211110 | + | 0.365654i | ||||
\(949\) | 21.0000 | + | 36.3731i | 0.681689 | + | 1.18072i | ||||
\(950\) | 3.00000 | − | 5.19615i | 0.0973329 | − | 0.168585i | ||||
\(951\) | −20.0000 | −0.648544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0000 | 0.971795 | 0.485898 | − | 0.874016i | \(-0.338493\pi\) | ||||
0.485898 | + | 0.874016i | \(0.338493\pi\) | |||||||
\(954\) | −6.00000 | + | 10.3923i | −0.194257 | + | 0.336463i | ||||
\(955\) | −2.00000 | − | 3.46410i | −0.0647185 | − | 0.112096i | ||||
\(956\) | −4.50000 | − | 7.79423i | −0.145540 | − | 0.252083i | ||||
\(957\) | 3.50000 | − | 6.06218i | 0.113139 | − | 0.195962i | ||||
\(958\) | −41.0000 | −1.32465 | ||||||||
\(959\) | −6.00000 | − | 5.19615i | −0.193750 | − | 0.167793i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | + | 10.3923i | 0.193347 | + | 0.334887i | ||||
\(964\) | 5.00000 | − | 8.66025i | 0.161039 | − | 0.278928i | ||||
\(965\) | 8.00000 | 0.257529 | ||||||||
\(966\) | −1.00000 | + | 5.19615i | −0.0321745 | + | 0.167183i | ||||
\(967\) | 24.0000 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(968\) | 0.500000 | − | 0.866025i | 0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.50000 | − | 6.06218i | −0.112378 | − | 0.194645i | ||||
\(971\) | 21.5000 | − | 37.2391i | 0.689968 | − | 1.19506i | −0.281880 | − | 0.959450i | \(-0.590958\pi\) |
0.971848 | − | 0.235610i | \(-0.0757087\pi\) | |||||||
\(972\) | 16.0000 | 0.513200 | ||||||||
\(973\) | 40.0000 | − | 13.8564i | 1.28234 | − | 0.444216i | ||||
\(974\) | −2.00000 | −0.0640841 | ||||||||
\(975\) | 1.50000 | − | 2.59808i | 0.0480384 | − | 0.0832050i | ||||
\(976\) | 0.500000 | + | 0.866025i | 0.0160046 | + | 0.0277208i | ||||
\(977\) | −15.0000 | − | 25.9808i | −0.479893 | − | 0.831198i | 0.519841 | − | 0.854263i | \(-0.325991\pi\) |
−0.999734 | + | 0.0230645i | \(0.992658\pi\) | |||||||
\(978\) | −5.50000 | + | 9.52628i | −0.175871 | + | 0.304617i | ||||
\(979\) | −6.00000 | −0.191761 | ||||||||
\(980\) | 5.50000 | − | 4.33013i | 0.175691 | − | 0.138321i | ||||
\(981\) | −36.0000 | −1.14939 | ||||||||
\(982\) | −18.0000 | + | 31.1769i | −0.574403 | + | 0.994895i | ||||
\(983\) | −7.00000 | − | 12.1244i | −0.223265 | − | 0.386707i | 0.732532 | − | 0.680732i | \(-0.238338\pi\) |
−0.955798 | + | 0.294025i | \(0.905005\pi\) | |||||||
\(984\) | −2.00000 | − | 3.46410i | −0.0637577 | − | 0.110432i | ||||
\(985\) | −5.50000 | + | 9.52628i | −0.175245 | + | 0.303533i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.0000 | −0.572656 | ||||||||
\(989\) | 6.00000 | − | 10.3923i | 0.190789 | − | 0.330456i | ||||
\(990\) | −1.00000 | − | 1.73205i | −0.0317821 | − | 0.0550482i | ||||
\(991\) | −28.0000 | − | 48.4974i | −0.889449 | − | 1.54057i | −0.840528 | − | 0.541769i | \(-0.817755\pi\) |
−0.0489218 | − | 0.998803i | \(-0.515578\pi\) | |||||||
\(992\) | −4.00000 | + | 6.92820i | −0.127000 | + | 0.219971i | ||||
\(993\) | 13.0000 | 0.412543 | ||||||||
\(994\) | −4.00000 | + | 20.7846i | −0.126872 | + | 0.659248i | ||||
\(995\) | −6.00000 | −0.190213 | ||||||||
\(996\) | 3.00000 | − | 5.19615i | 0.0950586 | − | 0.164646i | ||||
\(997\) | 3.00000 | + | 5.19615i | 0.0950110 | + | 0.164564i | 0.909613 | − | 0.415456i | \(-0.136378\pi\) |
−0.814602 | + | 0.580020i | \(0.803045\pi\) | |||||||
\(998\) | −2.00000 | − | 3.46410i | −0.0633089 | − | 0.109654i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 770.2.i.e.331.1 | yes | 2 | |
7.2 | even | 3 | 5390.2.a.o.1.1 | 1 | |||
7.4 | even | 3 | inner | 770.2.i.e.221.1 | ✓ | 2 | |
7.5 | odd | 6 | 5390.2.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.i.e.221.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
770.2.i.e.331.1 | yes | 2 | 1.1 | even | 1 | trivial | |
5390.2.a.f.1.1 | 1 | 7.5 | odd | 6 | |||
5390.2.a.o.1.1 | 1 | 7.2 | even | 3 |