Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(724,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.724");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.bb (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 724.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.724 |
Dual form | 975.2.bb.f.874.2 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | + | 1.00000i | 1.22474 | + | 0.707107i | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) |
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(3\) | −0.866025 | − | 0.500000i | −0.500000 | − | 0.288675i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | − | 1.73205i | −0.408248 | − | 0.707107i | ||||
\(7\) | −4.33013 | + | 2.50000i | −1.63663 | + | 0.944911i | −0.654654 | + | 0.755929i | \(0.727186\pi\) |
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.500000 | + | 0.866025i | 0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.73205i | −0.301511 | + | 0.522233i | −0.976478 | − | 0.215615i | \(-0.930824\pi\) |
0.674967 | + | 0.737848i | \(0.264158\pi\) | |||||||
\(12\) | − | 2.00000i | − | 0.577350i | ||||||
\(13\) | −2.59808 | − | 2.50000i | −0.720577 | − | 0.693375i | ||||
\(14\) | −10.0000 | −2.67261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −1.73205 | + | 1.00000i | −0.420084 | + | 0.242536i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) |
0.275029 | + | 0.961436i | \(0.411312\pi\) | |||||||
\(18\) | 2.00000i | 0.471405i | ||||||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.00000 | 1.09109 | ||||||||
\(22\) | −3.46410 | + | 2.00000i | −0.738549 | + | 0.426401i | ||||
\(23\) | −5.19615 | − | 3.00000i | −1.08347 | − | 0.625543i | −0.151642 | − | 0.988436i | \(-0.548456\pi\) |
−0.931831 | + | 0.362892i | \(0.881789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.00000 | − | 6.92820i | −0.392232 | − | 1.35873i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −8.66025 | − | 5.00000i | −1.63663 | − | 0.944911i | ||||
\(29\) | −2.00000 | + | 3.46410i | −0.371391 | + | 0.643268i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.618389 | + | 0.785872i | \(0.287786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.00000 | −1.25724 | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 6.92820 | − | 4.00000i | 1.22474 | − | 0.707107i | ||||
\(33\) | 1.73205 | − | 1.00000i | 0.301511 | − | 0.174078i | ||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | −1.73205 | − | 1.00000i | −0.284747 | − | 0.164399i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
−0.635571 | + | 0.772043i | \(0.719235\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 3.46410i | 0.160128 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 8.66025 | + | 5.00000i | 1.33631 | + | 0.771517i | ||||
\(43\) | 0.866025 | − | 0.500000i | 0.132068 | − | 0.0762493i | −0.432511 | − | 0.901629i | \(-0.642372\pi\) |
0.564578 | + | 0.825380i | \(0.309039\pi\) | |||||||
\(44\) | −4.00000 | −0.603023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | − | 10.3923i | −0.884652 | − | 1.53226i | ||||
\(47\) | 8.00000i | 1.16692i | 0.812142 | + | 0.583460i | \(0.198301\pi\) | ||||
−0.812142 | + | 0.583460i | \(0.801699\pi\) | |||||||
\(48\) | −3.46410 | + | 2.00000i | −0.500000 | + | 0.288675i | ||||
\(49\) | 9.00000 | − | 15.5885i | 1.28571 | − | 2.22692i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | 0.280056 | ||||||||
\(52\) | 1.73205 | − | 7.00000i | 0.240192 | − | 0.970725i | ||||
\(53\) | − | 4.00000i | − | 0.549442i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||
0.961524 | − | 0.274721i | \(-0.0885855\pi\) | |||||||
\(54\) | 1.00000 | − | 1.73205i | 0.136083 | − | 0.235702i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.92820 | + | 4.00000i | −0.909718 | + | 0.525226i | ||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | −12.1244 | − | 7.00000i | −1.53979 | − | 0.889001i | ||||
\(63\) | −4.33013 | − | 2.50000i | −0.545545 | − | 0.314970i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | −6.06218 | − | 3.50000i | −0.740613 | − | 0.427593i | 0.0816792 | − | 0.996659i | \(-0.473972\pi\) |
−0.822292 | + | 0.569066i | \(0.807305\pi\) | |||||||
\(68\) | −3.46410 | − | 2.00000i | −0.420084 | − | 0.242536i | ||||
\(69\) | 3.00000 | + | 5.19615i | 0.361158 | + | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | − | 10.3923i | −0.712069 | − | 1.23334i | −0.964079 | − | 0.265615i | \(-0.914425\pi\) |
0.252010 | − | 0.967725i | \(-0.418908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.0000i | 1.75562i | 0.479012 | + | 0.877809i | \(0.340995\pi\) | ||||
−0.479012 | + | 0.877809i | \(0.659005\pi\) | |||||||
\(74\) | −2.00000 | − | 3.46410i | −0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 10.0000i | − | 1.13961i | ||||||
\(78\) | −1.73205 | + | 7.00000i | −0.196116 | + | 0.792594i | ||||
\(79\) | −3.00000 | −0.337526 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −10.3923 | + | 6.00000i | −1.14764 | + | 0.662589i | ||||
\(83\) | 8.00000i | 0.878114i | 0.898459 | + | 0.439057i | \(0.144687\pi\) | ||||
−0.898459 | + | 0.439057i | \(0.855313\pi\) | |||||||
\(84\) | 5.00000 | + | 8.66025i | 0.545545 | + | 0.944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 3.46410 | − | 2.00000i | 0.371391 | − | 0.214423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.00000 | − | 12.1244i | 0.741999 | − | 1.28518i | −0.209585 | − | 0.977790i | \(-0.567211\pi\) |
0.951584 | − | 0.307389i | \(-0.0994552\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.5000 | + | 4.33013i | 1.83450 | + | 0.453921i | ||||
\(92\) | − | 12.0000i | − | 1.25109i | ||||||
\(93\) | 6.06218 | + | 3.50000i | 0.628619 | + | 0.362933i | ||||
\(94\) | −8.00000 | + | 13.8564i | −0.825137 | + | 1.42918i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −8.00000 | −0.816497 | ||||||||
\(97\) | 4.33013 | − | 2.50000i | 0.439658 | − | 0.253837i | −0.263795 | − | 0.964579i | \(-0.584974\pi\) |
0.703452 | + | 0.710742i | \(0.251641\pi\) | |||||||
\(98\) | 31.1769 | − | 18.0000i | 3.14934 | − | 1.81827i | ||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | 3.46410 | + | 2.00000i | 0.342997 | + | 0.198030i | ||||
\(103\) | − | 7.00000i | − | 0.689730i | −0.938652 | − | 0.344865i | \(-0.887925\pi\) | ||
0.938652 | − | 0.344865i | \(-0.112075\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | − | 6.92820i | 0.388514 | − | 0.672927i | ||||
\(107\) | 3.46410 | + | 2.00000i | 0.334887 | + | 0.193347i | 0.658009 | − | 0.753010i | \(-0.271399\pi\) |
−0.323122 | + | 0.946357i | \(0.604732\pi\) | |||||||
\(108\) | 1.73205 | − | 1.00000i | 0.166667 | − | 0.0962250i | ||||
\(109\) | 11.0000 | 1.05361 | 0.526804 | − | 0.849987i | \(-0.323390\pi\) | ||||
0.526804 | + | 0.849987i | \(0.323390\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.00000 | + | 1.73205i | 0.0949158 | + | 0.164399i | ||||
\(112\) | 20.0000i | 1.88982i | ||||||||
\(113\) | −1.73205 | + | 1.00000i | −0.162938 | + | 0.0940721i | −0.579252 | − | 0.815149i | \(-0.696655\pi\) |
0.416314 | + | 0.909221i | \(0.363322\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.00000 | −0.742781 | ||||||||
\(117\) | 0.866025 | − | 3.50000i | 0.0800641 | − | 0.323575i | ||||
\(118\) | 24.0000i | 2.20938i | ||||||||
\(119\) | 5.00000 | − | 8.66025i | 0.458349 | − | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 26.0000i | 2.35393i | ||||||||
\(123\) | 5.19615 | − | 3.00000i | 0.468521 | − | 0.270501i | ||||
\(124\) | −7.00000 | − | 12.1244i | −0.628619 | − | 1.08880i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.00000 | − | 8.66025i | −0.445435 | − | 0.771517i | ||||
\(127\) | −9.52628 | − | 5.50000i | −0.845321 | − | 0.488046i | 0.0137486 | − | 0.999905i | \(-0.495624\pi\) |
−0.859069 | + | 0.511859i | \(0.828957\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.00000 | −0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 3.46410 | + | 2.00000i | 0.301511 | + | 0.174078i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7.00000 | − | 12.1244i | −0.604708 | − | 1.04738i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.73205 | − | 1.00000i | 0.147979 | − | 0.0854358i | −0.424182 | − | 0.905577i | \(-0.639438\pi\) |
0.572161 | + | 0.820141i | \(0.306105\pi\) | |||||||
\(138\) | 12.0000i | 1.02151i | ||||||||
\(139\) | −1.50000 | − | 2.59808i | −0.127228 | − | 0.220366i | 0.795373 | − | 0.606120i | \(-0.207275\pi\) |
−0.922602 | + | 0.385754i | \(0.873941\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.00000 | − | 6.92820i | 0.336861 | − | 0.583460i | ||||
\(142\) | − | 24.0000i | − | 2.01404i | ||||||
\(143\) | 6.92820 | − | 2.00000i | 0.579365 | − | 0.167248i | ||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.0000 | + | 25.9808i | −1.24141 | + | 2.15018i | ||||
\(147\) | −15.5885 | + | 9.00000i | −1.28571 | + | 0.742307i | ||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.73205 | − | 1.00000i | −0.140028 | − | 0.0808452i | ||||
\(154\) | 10.0000 | − | 17.3205i | 0.805823 | − | 1.39573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.00000 | + | 5.19615i | −0.400320 | + | 0.416025i | ||||
\(157\) | 15.0000i | 1.19713i | 0.801074 | + | 0.598565i | \(0.204262\pi\) | ||||
−0.801074 | + | 0.598565i | \(0.795738\pi\) | |||||||
\(158\) | −5.19615 | − | 3.00000i | −0.413384 | − | 0.238667i | ||||
\(159\) | −2.00000 | + | 3.46410i | −0.158610 | + | 0.274721i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 30.0000 | 2.36433 | ||||||||
\(162\) | −1.73205 | + | 1.00000i | −0.136083 | + | 0.0785674i | ||||
\(163\) | −12.9904 | + | 7.50000i | −1.01749 | + | 0.587445i | −0.913375 | − | 0.407120i | \(-0.866533\pi\) |
−0.104111 | + | 0.994566i | \(0.533200\pi\) | |||||||
\(164\) | −12.0000 | −0.937043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.00000 | + | 13.8564i | −0.620920 | + | 1.07547i | ||||
\(167\) | 10.3923 | + | 6.00000i | 0.804181 | + | 0.464294i | 0.844931 | − | 0.534875i | \(-0.179641\pi\) |
−0.0407502 | + | 0.999169i | \(0.512975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | + | 12.9904i | 0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.73205 | + | 1.00000i | 0.132068 | + | 0.0762493i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 8.00000 | 0.606478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.00000 | + | 6.92820i | 0.301511 | + | 0.522233i | ||||
\(177\) | − | 12.0000i | − | 0.901975i | ||||||
\(178\) | 24.2487 | − | 14.0000i | 1.81752 | − | 1.04934i | ||||
\(179\) | −3.00000 | + | 5.19615i | −0.224231 | + | 0.388379i | −0.956088 | − | 0.293079i | \(-0.905320\pi\) |
0.731858 | + | 0.681457i | \(0.238654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 25.9808 | + | 25.0000i | 1.92582 | + | 1.85312i | ||||
\(183\) | − | 13.0000i | − | 0.960988i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.00000 | + | 12.1244i | 0.513265 | + | 0.889001i | ||||
\(187\) | − | 4.00000i | − | 0.292509i | ||||||
\(188\) | −13.8564 | + | 8.00000i | −1.01058 | + | 0.583460i | ||||
\(189\) | 2.50000 | + | 4.33013i | 0.181848 | + | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | −6.92820 | − | 4.00000i | −0.500000 | − | 0.288675i | ||||
\(193\) | 9.52628 | + | 5.50000i | 0.685717 | + | 0.395899i | 0.802005 | − | 0.597317i | \(-0.203766\pi\) |
−0.116289 | + | 0.993215i | \(0.537100\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 36.0000 | 2.57143 | ||||||||
\(197\) | −10.3923 | − | 6.00000i | −0.740421 | − | 0.427482i | 0.0818013 | − | 0.996649i | \(-0.473933\pi\) |
−0.822222 | + | 0.569166i | \(0.807266\pi\) | |||||||
\(198\) | −3.46410 | − | 2.00000i | −0.246183 | − | 0.142134i | ||||
\(199\) | 8.50000 | + | 14.7224i | 0.602549 | + | 1.04365i | 0.992434 | + | 0.122782i | \(0.0391815\pi\) |
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.50000 | + | 6.06218i | 0.246871 | + | 0.427593i | ||||
\(202\) | 31.1769 | − | 18.0000i | 2.19360 | − | 1.26648i | ||||
\(203\) | − | 20.0000i | − | 1.40372i | ||||||
\(204\) | 2.00000 | + | 3.46410i | 0.140028 | + | 0.242536i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.00000 | − | 12.1244i | 0.487713 | − | 0.844744i | ||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | −13.8564 | + | 4.00000i | −0.960769 | + | 0.277350i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.50000 | + | 12.9904i | −0.516321 | + | 0.894295i | 0.483499 | + | 0.875345i | \(0.339366\pi\) |
−0.999820 | + | 0.0189499i | \(0.993968\pi\) | |||||||
\(212\) | 6.92820 | − | 4.00000i | 0.475831 | − | 0.274721i | ||||
\(213\) | 12.0000i | 0.822226i | ||||||||
\(214\) | 4.00000 | + | 6.92820i | 0.273434 | + | 0.473602i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.3109 | − | 17.5000i | 2.05764 | − | 1.18798i | ||||
\(218\) | 19.0526 | + | 11.0000i | 1.29040 | + | 0.745014i | ||||
\(219\) | 7.50000 | − | 12.9904i | 0.506803 | − | 0.877809i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.00000 | + | 1.73205i | 0.470871 | + | 0.116510i | ||||
\(222\) | 4.00000i | 0.268462i | ||||||||
\(223\) | 6.92820 | + | 4.00000i | 0.463947 | + | 0.267860i | 0.713702 | − | 0.700449i | \(-0.247017\pi\) |
−0.249756 | + | 0.968309i | \(0.580350\pi\) | |||||||
\(224\) | −20.0000 | + | 34.6410i | −1.33631 | + | 2.31455i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.00000 | −0.266076 | ||||||||
\(227\) | −8.66025 | + | 5.00000i | −0.574801 | + | 0.331862i | −0.759065 | − | 0.651015i | \(-0.774343\pi\) |
0.184263 | + | 0.982877i | \(0.441010\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | −0.925146 | −0.462573 | − | 0.886581i | \(-0.653074\pi\) | ||||
−0.462573 | + | 0.886581i | \(0.653074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | + | 8.66025i | −0.328976 | + | 0.569803i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 14.0000i | − | 0.917170i | −0.888650 | − | 0.458585i | \(-0.848356\pi\) | ||
0.888650 | − | 0.458585i | \(-0.151644\pi\) | |||||||
\(234\) | 5.00000 | − | 5.19615i | 0.326860 | − | 0.339683i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −12.0000 | + | 20.7846i | −0.781133 | + | 1.35296i | ||||
\(237\) | 2.59808 | + | 1.50000i | 0.168763 | + | 0.0974355i | ||||
\(238\) | 17.3205 | − | 10.0000i | 1.12272 | − | 0.648204i | ||||
\(239\) | −12.0000 | −0.776215 | −0.388108 | − | 0.921614i | \(-0.626871\pi\) | ||||
−0.388108 | + | 0.921614i | \(0.626871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.00000 | − | 8.66025i | −0.322078 | − | 0.557856i | 0.658838 | − | 0.752285i | \(-0.271048\pi\) |
−0.980917 | + | 0.194429i | \(0.937715\pi\) | |||||||
\(242\) | 14.0000i | 0.899954i | ||||||||
\(243\) | 0.866025 | − | 0.500000i | 0.0555556 | − | 0.0320750i | ||||
\(244\) | −13.0000 | + | 22.5167i | −0.832240 | + | 1.44148i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | − | 6.92820i | 0.253490 | − | 0.439057i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | − | 10.0000i | − | 0.629941i | ||||||
\(253\) | 10.3923 | − | 6.00000i | 0.653359 | − | 0.377217i | ||||
\(254\) | −11.0000 | − | 19.0526i | −0.690201 | − | 1.19546i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −19.0526 | − | 11.0000i | −1.18847 | − | 0.686161i | −0.230508 | − | 0.973070i | \(-0.574039\pi\) |
−0.957958 | + | 0.286909i | \(0.907372\pi\) | |||||||
\(258\) | −1.73205 | − | 1.00000i | −0.107833 | − | 0.0622573i | ||||
\(259\) | 10.0000 | 0.621370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.00000 | −0.247594 | ||||||||
\(262\) | −6.92820 | − | 4.00000i | −0.428026 | − | 0.247121i | ||||
\(263\) | 8.66025 | + | 5.00000i | 0.534014 | + | 0.308313i | 0.742650 | − | 0.669680i | \(-0.233569\pi\) |
−0.208635 | + | 0.977993i | \(0.566902\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1244 | + | 7.00000i | −0.741999 | + | 0.428393i | ||||
\(268\) | − | 14.0000i | − | 0.855186i | ||||||
\(269\) | −3.00000 | − | 5.19615i | −0.182913 | − | 0.316815i | 0.759958 | − | 0.649972i | \(-0.225219\pi\) |
−0.942871 | + | 0.333157i | \(0.891886\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.5000 | + | 25.1147i | −0.880812 | + | 1.52561i | −0.0303728 | + | 0.999539i | \(0.509669\pi\) |
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 8.00000i | 0.485071i | ||||||||
\(273\) | −12.9904 | − | 12.5000i | −0.786214 | − | 0.756534i | ||||
\(274\) | 4.00000 | 0.241649 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.00000 | + | 10.3923i | −0.361158 | + | 0.625543i | ||||
\(277\) | −8.66025 | + | 5.00000i | −0.520344 | + | 0.300421i | −0.737075 | − | 0.675810i | \(-0.763794\pi\) |
0.216731 | + | 0.976231i | \(0.430460\pi\) | |||||||
\(278\) | − | 6.00000i | − | 0.359856i | ||||||
\(279\) | −3.50000 | − | 6.06218i | −0.209540 | − | 0.362933i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 13.8564 | − | 8.00000i | 0.825137 | − | 0.476393i | ||||
\(283\) | −4.33013 | − | 2.50000i | −0.257399 | − | 0.148610i | 0.365748 | − | 0.930714i | \(-0.380813\pi\) |
−0.623148 | + | 0.782104i | \(0.714146\pi\) | |||||||
\(284\) | 12.0000 | − | 20.7846i | 0.712069 | − | 1.23334i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.0000 | + | 3.46410i | 0.827837 | + | 0.204837i | ||||
\(287\) | − | 30.0000i | − | 1.77084i | ||||||
\(288\) | 6.92820 | + | 4.00000i | 0.408248 | + | 0.235702i | ||||
\(289\) | −6.50000 | + | 11.2583i | −0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.00000 | −0.293105 | ||||||||
\(292\) | −25.9808 | + | 15.0000i | −1.52041 | + | 0.877809i | ||||
\(293\) | 13.8564 | − | 8.00000i | 0.809500 | − | 0.467365i | −0.0372823 | − | 0.999305i | \(-0.511870\pi\) |
0.846782 | + | 0.531940i | \(0.178537\pi\) | |||||||
\(294\) | −36.0000 | −2.09956 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73205 | + | 1.00000i | 0.100504 | + | 0.0580259i | ||||
\(298\) | − | 24.0000i | − | 1.39028i | ||||||
\(299\) | 6.00000 | + | 20.7846i | 0.346989 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.50000 | + | 4.33013i | −0.144098 | + | 0.249584i | ||||
\(302\) | −13.8564 | − | 8.00000i | −0.797347 | − | 0.460348i | ||||
\(303\) | −15.5885 | + | 9.00000i | −0.895533 | + | 0.517036i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.00000 | − | 3.46410i | −0.114332 | − | 0.198030i | ||||
\(307\) | 31.0000i | 1.76926i | 0.466290 | + | 0.884632i | \(0.345590\pi\) | ||||
−0.466290 | + | 0.884632i | \(0.654410\pi\) | |||||||
\(308\) | 17.3205 | − | 10.0000i | 0.986928 | − | 0.569803i | ||||
\(309\) | −3.50000 | + | 6.06218i | −0.199108 | + | 0.344865i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.0000 | −1.24751 | −0.623753 | − | 0.781622i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781622i | \(0.714393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 31.0000i | − | 1.75222i | −0.482108 | − | 0.876112i | \(-0.660129\pi\) | ||
0.482108 | − | 0.876112i | \(-0.339871\pi\) | |||||||
\(314\) | −15.0000 | + | 25.9808i | −0.846499 | + | 1.46618i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | − | 5.19615i | −0.168763 | − | 0.292306i | ||||
\(317\) | − | 12.0000i | − | 0.673987i | −0.941507 | − | 0.336994i | \(-0.890590\pi\) | ||
0.941507 | − | 0.336994i | \(-0.109410\pi\) | |||||||
\(318\) | −6.92820 | + | 4.00000i | −0.388514 | + | 0.224309i | ||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | − | 3.46410i | −0.111629 | − | 0.193347i | ||||
\(322\) | 51.9615 | + | 30.0000i | 2.89570 | + | 1.67183i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −2.00000 | −0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −30.0000 | −1.66155 | ||||||||
\(327\) | −9.52628 | − | 5.50000i | −0.526804 | − | 0.304151i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −20.0000 | − | 34.6410i | −1.10264 | − | 1.90982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.50000 | − | 7.79423i | −0.247342 | − | 0.428410i | 0.715445 | − | 0.698669i | \(-0.246224\pi\) |
−0.962788 | + | 0.270259i | \(0.912891\pi\) | |||||||
\(332\) | −13.8564 | + | 8.00000i | −0.760469 | + | 0.439057i | ||||
\(333\) | − | 2.00000i | − | 0.109599i | ||||||
\(334\) | 12.0000 | + | 20.7846i | 0.656611 | + | 1.13728i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 10.0000 | − | 17.3205i | 0.545545 | − | 0.944911i | ||||
\(337\) | 1.00000i | 0.0544735i | 0.999629 | + | 0.0272367i | \(0.00867079\pi\) | ||||
−0.999629 | + | 0.0272367i | \(0.991329\pi\) | |||||||
\(338\) | −12.1244 | + | 23.0000i | −0.659478 | + | 1.25104i | ||||
\(339\) | 2.00000 | 0.108625 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.00000 | − | 12.1244i | 0.379071 | − | 0.656571i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 55.0000i | 2.96972i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.8564 | − | 8.00000i | 0.743851 | − | 0.429463i | −0.0796169 | − | 0.996826i | \(-0.525370\pi\) |
0.823468 | + | 0.567363i | \(0.192036\pi\) | |||||||
\(348\) | 6.92820 | + | 4.00000i | 0.371391 | + | 0.214423i | ||||
\(349\) | 1.50000 | − | 2.59808i | 0.0802932 | − | 0.139072i | −0.823083 | − | 0.567922i | \(-0.807748\pi\) |
0.903376 | + | 0.428850i | \(0.141081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.50000 | + | 2.59808i | −0.133440 | + | 0.138675i | ||||
\(352\) | 16.0000i | 0.852803i | ||||||||
\(353\) | −5.19615 | − | 3.00000i | −0.276563 | − | 0.159674i | 0.355303 | − | 0.934751i | \(-0.384378\pi\) |
−0.631867 | + | 0.775077i | \(0.717711\pi\) | |||||||
\(354\) | 12.0000 | − | 20.7846i | 0.637793 | − | 1.10469i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 28.0000 | 1.48400 | ||||||||
\(357\) | −8.66025 | + | 5.00000i | −0.458349 | + | 0.264628i | ||||
\(358\) | −10.3923 | + | 6.00000i | −0.549250 | + | 0.317110i | ||||
\(359\) | −2.00000 | −0.105556 | −0.0527780 | − | 0.998606i | \(-0.516808\pi\) | ||||
−0.0527780 | + | 0.998606i | \(0.516808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | −38.1051 | − | 22.0000i | −2.00276 | − | 1.15629i | ||||
\(363\) | − | 7.00000i | − | 0.367405i | ||||||
\(364\) | 10.0000 | + | 34.6410i | 0.524142 | + | 1.81568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 13.0000 | − | 22.5167i | 0.679521 | − | 1.17696i | ||||
\(367\) | 6.06218 | + | 3.50000i | 0.316443 | + | 0.182699i | 0.649806 | − | 0.760100i | \(-0.274850\pi\) |
−0.333363 | + | 0.942799i | \(0.608183\pi\) | |||||||
\(368\) | −20.7846 | + | 12.0000i | −1.08347 | + | 0.625543i | ||||
\(369\) | −6.00000 | −0.312348 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0000 | + | 17.3205i | 0.519174 | + | 0.899236i | ||||
\(372\) | 14.0000i | 0.725866i | ||||||||
\(373\) | 11.2583 | − | 6.50000i | 0.582934 | − | 0.336557i | −0.179364 | − | 0.983783i | \(-0.557404\pi\) |
0.762299 | + | 0.647225i | \(0.224071\pi\) | |||||||
\(374\) | 4.00000 | − | 6.92820i | 0.206835 | − | 0.358249i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.8564 | − | 4.00000i | 0.713641 | − | 0.206010i | ||||
\(378\) | 10.0000i | 0.514344i | ||||||||
\(379\) | −2.50000 | + | 4.33013i | −0.128416 | + | 0.222424i | −0.923063 | − | 0.384648i | \(-0.874323\pi\) |
0.794647 | + | 0.607072i | \(0.207656\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.50000 | + | 9.52628i | 0.281774 | + | 0.488046i | ||||
\(382\) | − | 24.0000i | − | 1.22795i | ||||||
\(383\) | −15.5885 | + | 9.00000i | −0.796533 | + | 0.459879i | −0.842257 | − | 0.539076i | \(-0.818774\pi\) |
0.0457244 | + | 0.998954i | \(0.485440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.0000 | + | 19.0526i | 0.559885 | + | 0.969750i | ||||
\(387\) | 0.866025 | + | 0.500000i | 0.0440225 | + | 0.0254164i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | −8.00000 | −0.405616 | −0.202808 | − | 0.979219i | \(-0.565007\pi\) | ||||
−0.202808 | + | 0.979219i | \(0.565007\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.46410 | + | 2.00000i | 0.174741 | + | 0.100887i | ||||
\(394\) | −12.0000 | − | 20.7846i | −0.604551 | − | 1.04711i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.00000 | − | 3.46410i | −0.100504 | − | 0.174078i | ||||
\(397\) | 12.9904 | − | 7.50000i | 0.651969 | − | 0.376414i | −0.137241 | − | 0.990538i | \(-0.543824\pi\) |
0.789210 | + | 0.614123i | \(0.210490\pi\) | |||||||
\(398\) | 34.0000i | 1.70427i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.00000 | + | 13.8564i | −0.399501 | + | 0.691956i | −0.993664 | − | 0.112388i | \(-0.964150\pi\) |
0.594163 | + | 0.804344i | \(0.297483\pi\) | |||||||
\(402\) | 14.0000i | 0.698257i | ||||||||
\(403\) | 18.1865 | + | 17.5000i | 0.905936 | + | 0.871737i | ||||
\(404\) | 36.0000 | 1.79107 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.0000 | − | 34.6410i | 0.992583 | − | 1.71920i | ||||
\(407\) | 3.46410 | − | 2.00000i | 0.171709 | − | 0.0991363i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.50000 | − | 12.9904i | −0.370851 | − | 0.642333i | 0.618846 | − | 0.785513i | \(-0.287601\pi\) |
−0.989697 | + | 0.143180i | \(0.954267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | 12.1244 | − | 7.00000i | 0.597324 | − | 0.344865i | ||||
\(413\) | −51.9615 | − | 30.0000i | −2.55686 | − | 1.47620i | ||||
\(414\) | 6.00000 | − | 10.3923i | 0.294884 | − | 0.510754i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −28.0000 | − | 6.92820i | −1.37281 | − | 0.339683i | ||||
\(417\) | 3.00000i | 0.146911i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.0000 | − | 32.9090i | 0.928211 | − | 1.60771i | 0.141896 | − | 0.989882i | \(-0.454680\pi\) |
0.786314 | − | 0.617827i | \(-0.211987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | −25.9808 | + | 15.0000i | −1.26472 | + | 0.730189i | ||||
\(423\) | −6.92820 | + | 4.00000i | −0.336861 | + | 0.194487i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.0000 | + | 20.7846i | −0.581402 | + | 1.00702i | ||||
\(427\) | −56.2917 | − | 32.5000i | −2.72414 | − | 1.57279i | ||||
\(428\) | 8.00000i | 0.386695i | ||||||||
\(429\) | −7.00000 | − | 1.73205i | −0.337963 | − | 0.0836242i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0000 | − | 24.2487i | 0.674356 | − | 1.16802i | −0.302300 | − | 0.953213i | \(-0.597755\pi\) |
0.976657 | − | 0.214807i | \(-0.0689121\pi\) | |||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | 0.866025 | − | 0.500000i | 0.0416185 | − | 0.0240285i | −0.479046 | − | 0.877790i | \(-0.659017\pi\) |
0.520665 | + | 0.853761i | \(0.325684\pi\) | |||||||
\(434\) | 70.0000 | 3.36011 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 11.0000 | + | 19.0526i | 0.526804 | + | 0.912452i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 25.9808 | − | 15.0000i | 1.24141 | − | 0.716728i | ||||
\(439\) | 7.50000 | − | 12.9904i | 0.357955 | − | 0.619997i | −0.629664 | − | 0.776868i | \(-0.716807\pi\) |
0.987619 | + | 0.156871i | \(0.0501406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 18.0000 | 0.857143 | ||||||||
\(442\) | 10.3923 | + | 10.0000i | 0.494312 | + | 0.475651i | ||||
\(443\) | 26.0000i | 1.23530i | 0.786454 | + | 0.617649i | \(0.211915\pi\) | ||||
−0.786454 | + | 0.617649i | \(0.788085\pi\) | |||||||
\(444\) | −2.00000 | + | 3.46410i | −0.0949158 | + | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.00000 | + | 13.8564i | 0.378811 | + | 0.656120i | ||||
\(447\) | 12.0000i | 0.567581i | ||||||||
\(448\) | −34.6410 | + | 20.0000i | −1.63663 | + | 0.944911i | ||||
\(449\) | 9.00000 | + | 15.5885i | 0.424736 | + | 0.735665i | 0.996396 | − | 0.0848262i | \(-0.0270335\pi\) |
−0.571660 | + | 0.820491i | \(0.693700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.00000 | − | 10.3923i | −0.282529 | − | 0.489355i | ||||
\(452\) | −3.46410 | − | 2.00000i | −0.162938 | − | 0.0940721i | ||||
\(453\) | 6.92820 | + | 4.00000i | 0.325515 | + | 0.187936i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.3109 | + | 17.5000i | 1.41788 | + | 0.818615i | 0.996113 | − | 0.0880870i | \(-0.0280754\pi\) |
0.421771 | + | 0.906702i | \(0.361409\pi\) | |||||||
\(458\) | −24.2487 | − | 14.0000i | −1.13307 | − | 0.654177i | ||||
\(459\) | 1.00000 | + | 1.73205i | 0.0466760 | + | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.00000 | + | 1.73205i | 0.0465746 | + | 0.0806696i | 0.888373 | − | 0.459123i | \(-0.151836\pi\) |
−0.841798 | + | 0.539792i | \(0.818503\pi\) | |||||||
\(462\) | −17.3205 | + | 10.0000i | −0.805823 | + | 0.465242i | ||||
\(463\) | 3.00000i | 0.139422i | 0.997567 | + | 0.0697109i | \(0.0222077\pi\) | ||||
−0.997567 | + | 0.0697109i | \(0.977792\pi\) | |||||||
\(464\) | 8.00000 | + | 13.8564i | 0.371391 | + | 0.643268i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0000 | − | 24.2487i | 0.648537 | − | 1.12330i | ||||
\(467\) | 4.00000i | 0.185098i | 0.995708 | + | 0.0925490i | \(0.0295015\pi\) | ||||
−0.995708 | + | 0.0925490i | \(0.970499\pi\) | |||||||
\(468\) | 6.92820 | − | 2.00000i | 0.320256 | − | 0.0924500i | ||||
\(469\) | 35.0000 | 1.61615 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.50000 | − | 12.9904i | 0.345582 | − | 0.598565i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.00000i | 0.0919601i | ||||||||
\(474\) | 3.00000 | + | 5.19615i | 0.137795 | + | 0.238667i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 20.0000 | 0.916698 | ||||||||
\(477\) | 3.46410 | − | 2.00000i | 0.158610 | − | 0.0915737i | ||||
\(478\) | −20.7846 | − | 12.0000i | −0.950666 | − | 0.548867i | ||||
\(479\) | 21.0000 | − | 36.3731i | 0.959514 | − | 1.66193i | 0.235833 | − | 0.971794i | \(-0.424218\pi\) |
0.723681 | − | 0.690134i | \(-0.242449\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | + | 6.92820i | 0.0911922 | + | 0.315899i | ||||
\(482\) | − | 20.0000i | − | 0.910975i | ||||||
\(483\) | −25.9808 | − | 15.0000i | −1.18217 | − | 0.682524i | ||||
\(484\) | −7.00000 | + | 12.1244i | −0.318182 | + | 0.551107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.00000 | 0.0907218 | ||||||||
\(487\) | 24.2487 | − | 14.0000i | 1.09881 | − | 0.634401i | 0.162905 | − | 0.986642i | \(-0.447914\pi\) |
0.935909 | + | 0.352241i | \(0.114580\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.0000 | 0.678323 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | − | 20.7846i | 0.541552 | − | 0.937996i | −0.457263 | − | 0.889332i | \(-0.651170\pi\) |
0.998815 | − | 0.0486647i | \(-0.0154966\pi\) | |||||||
\(492\) | 10.3923 | + | 6.00000i | 0.468521 | + | 0.270501i | ||||
\(493\) | − | 8.00000i | − | 0.360302i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.0000 | + | 24.2487i | −0.628619 | + | 1.08880i | ||||
\(497\) | 51.9615 | + | 30.0000i | 2.33079 | + | 1.34568i | ||||
\(498\) | 13.8564 | − | 8.00000i | 0.620920 | − | 0.358489i | ||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | − | 10.3923i | −0.268060 | − | 0.464294i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.19615 | + | 3.00000i | −0.231685 | + | 0.133763i | −0.611349 | − | 0.791361i | \(-0.709373\pi\) |
0.379664 | + | 0.925124i | \(0.376040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.0000 | 1.06693 | ||||||||
\(507\) | 6.06218 | − | 11.5000i | 0.269231 | − | 0.510733i | ||||
\(508\) | − | 22.0000i | − | 0.976092i | ||||||
\(509\) | −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 | ||||||||
\(511\) | −37.5000 | − | 64.9519i | −1.65890 | − | 2.87330i | ||||
\(512\) | − | 32.0000i | − | 1.41421i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.0000 | − | 38.1051i | −0.970378 | − | 1.68074i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.00000 | − | 1.73205i | −0.0440225 | − | 0.0762493i | ||||
\(517\) | −13.8564 | − | 8.00000i | −0.609404 | − | 0.351840i | ||||
\(518\) | 17.3205 | + | 10.0000i | 0.761019 | + | 0.439375i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.0000 | −1.31432 | −0.657162 | − | 0.753749i | \(-0.728243\pi\) | ||||
−0.657162 | + | 0.753749i | \(0.728243\pi\) | |||||||
\(522\) | −6.92820 | − | 4.00000i | −0.303239 | − | 0.175075i | ||||
\(523\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(524\) | −4.00000 | − | 6.92820i | −0.174741 | − | 0.302660i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.0000 | + | 17.3205i | 0.436021 | + | 0.755210i | ||||
\(527\) | 12.1244 | − | 7.00000i | 0.528145 | − | 0.304925i | ||||
\(528\) | − | 8.00000i | − | 0.348155i | ||||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | + | 10.3923i | −0.260378 | + | 0.450988i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.7846 | − | 6.00000i | 0.900281 | − | 0.259889i | ||||
\(534\) | −28.0000 | −1.21168 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.19615 | − | 3.00000i | 0.224231 | − | 0.129460i | ||||
\(538\) | − | 12.0000i | − | 0.517357i | ||||||
\(539\) | 18.0000 | + | 31.1769i | 0.775315 | + | 1.34288i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | 1.24681 | 0.623404 | − | 0.781900i | \(-0.285749\pi\) | ||||
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | −50.2295 | + | 29.0000i | −2.15754 | + | 1.24566i | ||||
\(543\) | 19.0526 | + | 11.0000i | 0.817624 | + | 0.472055i | ||||
\(544\) | −8.00000 | + | 13.8564i | −0.342997 | + | 0.594089i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.0000 | − | 34.6410i | −0.427960 | − | 1.48250i | ||||
\(547\) | 9.00000i | 0.384812i | 0.981315 | + | 0.192406i | \(0.0616291\pi\) | ||||
−0.981315 | + | 0.192406i | \(0.938371\pi\) | |||||||
\(548\) | 3.46410 | + | 2.00000i | 0.147979 | + | 0.0854358i | ||||
\(549\) | −6.50000 | + | 11.2583i | −0.277413 | + | 0.480494i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9904 | − | 7.50000i | 0.552407 | − | 0.318932i | ||||
\(554\) | −20.0000 | −0.849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.00000 | − | 5.19615i | 0.127228 | − | 0.220366i | ||||
\(557\) | −17.3205 | − | 10.0000i | −0.733893 | − | 0.423714i | 0.0859514 | − | 0.996299i | \(-0.472607\pi\) |
−0.819845 | + | 0.572586i | \(0.805940\pi\) | |||||||
\(558\) | − | 14.0000i | − | 0.592667i | ||||||
\(559\) | −3.50000 | − | 0.866025i | −0.148034 | − | 0.0366290i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.00000 | + | 3.46410i | −0.0844401 | + | 0.146254i | ||||
\(562\) | −20.7846 | − | 12.0000i | −0.876746 | − | 0.506189i | ||||
\(563\) | 22.5167 | − | 13.0000i | 0.948964 | − | 0.547885i | 0.0562051 | − | 0.998419i | \(-0.482100\pi\) |
0.892759 | + | 0.450535i | \(0.148767\pi\) | |||||||
\(564\) | 16.0000 | 0.673722 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.00000 | − | 8.66025i | −0.210166 | − | 0.364018i | ||||
\(567\) | − | 5.00000i | − | 0.209980i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.0000 | + | 17.3205i | −0.419222 | + | 0.726113i | −0.995861 | − | 0.0908852i | \(-0.971030\pi\) |
0.576640 | + | 0.816999i | \(0.304364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 10.3923 | + | 10.0000i | 0.434524 | + | 0.418121i | ||||
\(573\) | 12.0000i | 0.501307i | ||||||||
\(574\) | 30.0000 | − | 51.9615i | 1.25218 | − | 2.16883i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.00000 | + | 6.92820i | 0.166667 | + | 0.288675i | ||||
\(577\) | − | 2.00000i | − | 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | −22.5167 | + | 13.0000i | −0.936570 | + | 0.540729i | ||||
\(579\) | −5.50000 | − | 9.52628i | −0.228572 | − | 0.395899i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.0000 | − | 34.6410i | −0.829740 | − | 1.43715i | ||||
\(582\) | −8.66025 | − | 5.00000i | −0.358979 | − | 0.207257i | ||||
\(583\) | 6.92820 | + | 4.00000i | 0.286937 | + | 0.165663i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.0000 | 1.32191 | ||||||||
\(587\) | 24.2487 | + | 14.0000i | 1.00085 | + | 0.577842i | 0.908500 | − | 0.417885i | \(-0.137228\pi\) |
0.0923513 | + | 0.995726i | \(0.470562\pi\) | |||||||
\(588\) | −31.1769 | − | 18.0000i | −1.28571 | − | 0.742307i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.00000 | + | 10.3923i | 0.246807 | + | 0.427482i | ||||
\(592\) | −6.92820 | + | 4.00000i | −0.284747 | + | 0.164399i | ||||
\(593\) | − | 10.0000i | − | 0.410651i | −0.978694 | − | 0.205325i | \(-0.934175\pi\) | ||
0.978694 | − | 0.205325i | \(-0.0658253\pi\) | |||||||
\(594\) | 2.00000 | + | 3.46410i | 0.0820610 | + | 0.142134i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | − | 20.7846i | 0.491539 | − | 0.851371i | ||||
\(597\) | − | 17.0000i | − | 0.695764i | ||||||
\(598\) | −10.3923 | + | 42.0000i | −0.424973 | + | 1.71751i | ||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0000 | + | 19.0526i | −0.448699 | + | 0.777170i | −0.998302 | − | 0.0582563i | \(-0.981446\pi\) |
0.549602 | + | 0.835426i | \(0.314779\pi\) | |||||||
\(602\) | −8.66025 | + | 5.00000i | −0.352966 | + | 0.203785i | ||||
\(603\) | − | 7.00000i | − | 0.285062i | ||||||
\(604\) | −8.00000 | − | 13.8564i | −0.325515 | − | 0.563809i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −36.0000 | −1.46240 | ||||||||
\(607\) | −13.8564 | + | 8.00000i | −0.562414 | + | 0.324710i | −0.754114 | − | 0.656744i | \(-0.771933\pi\) |
0.191700 | + | 0.981454i | \(0.438600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.0000 | + | 17.3205i | −0.405220 | + | 0.701862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.0000 | − | 20.7846i | 0.809113 | − | 0.840855i | ||||
\(612\) | − | 4.00000i | − | 0.161690i | ||||||
\(613\) | 12.9904 | + | 7.50000i | 0.524677 | + | 0.302922i | 0.738846 | − | 0.673874i | \(-0.235371\pi\) |
−0.214169 | + | 0.976797i | \(0.568704\pi\) | |||||||
\(614\) | −31.0000 | + | 53.6936i | −1.25106 | + | 2.16690i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.19615 | + | 3.00000i | −0.209189 | + | 0.120775i | −0.600935 | − | 0.799298i | \(-0.705205\pi\) |
0.391745 | + | 0.920074i | \(0.371871\pi\) | |||||||
\(618\) | −12.1244 | + | 7.00000i | −0.487713 | + | 0.281581i | ||||
\(619\) | −37.0000 | −1.48716 | −0.743578 | − | 0.668649i | \(-0.766873\pi\) | ||||
−0.743578 | + | 0.668649i | \(0.766873\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.00000 | + | 5.19615i | −0.120386 | + | 0.208514i | ||||
\(622\) | −38.1051 | − | 22.0000i | −1.52788 | − | 0.882120i | ||||
\(623\) | 70.0000i | 2.80449i | ||||||||
\(624\) | 14.0000 | + | 3.46410i | 0.560449 | + | 0.138675i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.0000 | − | 53.6936i | 1.23901 | − | 2.14603i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −25.9808 | + | 15.0000i | −1.03675 | + | 0.598565i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.50000 | − | 6.06218i | −0.139333 | − | 0.241331i | 0.787911 | − | 0.615789i | \(-0.211162\pi\) |
−0.927244 | + | 0.374457i | \(0.877829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.9904 | − | 7.50000i | 0.516321 | − | 0.298098i | ||||
\(634\) | 12.0000 | − | 20.7846i | 0.476581 | − | 0.825462i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.00000 | −0.317221 | ||||||||
\(637\) | −62.3538 | + | 18.0000i | −2.47055 | + | 0.713186i | ||||
\(638\) | − | 16.0000i | − | 0.633446i | ||||||
\(639\) | 6.00000 | − | 10.3923i | 0.237356 | − | 0.411113i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00000 | − | 1.73205i | −0.0394976 | − | 0.0684119i | 0.845601 | − | 0.533816i | \(-0.179242\pi\) |
−0.885098 | + | 0.465404i | \(0.845909\pi\) | |||||||
\(642\) | − | 8.00000i | − | 0.315735i | ||||||
\(643\) | −16.4545 | + | 9.50000i | −0.648901 | + | 0.374643i | −0.788035 | − | 0.615630i | \(-0.788902\pi\) |
0.139134 | + | 0.990274i | \(0.455568\pi\) | |||||||
\(644\) | 30.0000 | + | 51.9615i | 1.18217 | + | 2.04757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 32.9090 | + | 19.0000i | 1.29378 | + | 0.746967i | 0.979323 | − | 0.202303i | \(-0.0648426\pi\) |
0.314462 | + | 0.949270i | \(0.398176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.0000 | −0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.0000 | −1.37176 | ||||||||
\(652\) | −25.9808 | − | 15.0000i | −1.01749 | − | 0.587445i | ||||
\(653\) | −36.3731 | − | 21.0000i | −1.42339 | − | 0.821794i | −0.426801 | − | 0.904345i | \(-0.640360\pi\) |
−0.996587 | + | 0.0825519i | \(0.973693\pi\) | |||||||
\(654\) | −11.0000 | − | 19.0526i | −0.430134 | − | 0.745014i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.0000 | + | 20.7846i | 0.468521 | + | 0.811503i | ||||
\(657\) | −12.9904 | + | 7.50000i | −0.506803 | + | 0.292603i | ||||
\(658\) | − | 80.0000i | − | 3.11872i | ||||||
\(659\) | −12.0000 | − | 20.7846i | −0.467454 | − | 0.809653i | 0.531855 | − | 0.846836i | \(-0.321495\pi\) |
−0.999309 | + | 0.0371821i | \(0.988162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5000 | + | 30.3109i | −0.680671 | + | 1.17896i | 0.294105 | + | 0.955773i | \(0.404978\pi\) |
−0.974776 | + | 0.223184i | \(0.928355\pi\) | |||||||
\(662\) | − | 18.0000i | − | 0.699590i | ||||||
\(663\) | −5.19615 | − | 5.00000i | −0.201802 | − | 0.194184i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.00000 | − | 3.46410i | 0.0774984 | − | 0.134231i | ||||
\(667\) | 20.7846 | − | 12.0000i | 0.804783 | − | 0.464642i | ||||
\(668\) | 24.0000i | 0.928588i | ||||||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.0000 | −1.00372 | ||||||||
\(672\) | 34.6410 | − | 20.0000i | 1.33631 | − | 0.771517i | ||||
\(673\) | −28.5788 | − | 16.5000i | −1.10163 | − | 0.636028i | −0.164984 | − | 0.986296i | \(-0.552757\pi\) |
−0.936650 | + | 0.350268i | \(0.886091\pi\) | |||||||
\(674\) | −1.00000 | + | 1.73205i | −0.0385186 | + | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.0000 | + | 13.8564i | −0.846154 | + | 0.532939i | ||||
\(677\) | 12.0000i | 0.461197i | 0.973049 | + | 0.230599i | \(0.0740685\pi\) | ||||
−0.973049 | + | 0.230599i | \(0.925932\pi\) | |||||||
\(678\) | 3.46410 | + | 2.00000i | 0.133038 | + | 0.0768095i | ||||
\(679\) | −12.5000 | + | 21.6506i | −0.479706 | + | 0.830875i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | 0.383201 | ||||||||
\(682\) | 24.2487 | − | 14.0000i | 0.928531 | − | 0.536088i | ||||
\(683\) | −17.3205 | + | 10.0000i | −0.662751 | + | 0.382639i | −0.793324 | − | 0.608799i | \(-0.791651\pi\) |
0.130573 | + | 0.991439i | \(0.458318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −55.0000 | + | 95.2628i | −2.09991 | + | 3.63715i | ||||
\(687\) | 12.1244 | + | 7.00000i | 0.462573 | + | 0.267067i | ||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | −10.0000 | + | 10.3923i | −0.380970 | + | 0.395915i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.5000 | + | 32.0429i | −0.703773 | + | 1.21897i | 0.263359 | + | 0.964698i | \(0.415170\pi\) |
−0.967132 | + | 0.254273i | \(0.918164\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.66025 | − | 5.00000i | 0.328976 | − | 0.189934i | ||||
\(694\) | 32.0000 | 1.21470 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 12.0000i | − | 0.454532i | ||||||
\(698\) | 5.19615 | − | 3.00000i | 0.196677 | − | 0.113552i | ||||
\(699\) | −7.00000 | + | 12.1244i | −0.264764 | + | 0.458585i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.0000 | 1.51078 | 0.755390 | − | 0.655276i | \(-0.227448\pi\) | ||||
0.755390 | + | 0.655276i | \(0.227448\pi\) | |||||||
\(702\) | −6.92820 | + | 2.00000i | −0.261488 | + | 0.0754851i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −8.00000 | + | 13.8564i | −0.301511 | + | 0.522233i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.00000 | − | 10.3923i | −0.225813 | − | 0.391120i | ||||
\(707\) | 90.0000i | 3.38480i | ||||||||
\(708\) | 20.7846 | − | 12.0000i | 0.781133 | − | 0.450988i | ||||
\(709\) | −11.5000 | − | 19.9186i | −0.431892 | − | 0.748058i | 0.565145 | − | 0.824992i | \(-0.308820\pi\) |
−0.997036 | + | 0.0769337i | \(0.975487\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | − | 2.59808i | −0.0562544 | − | 0.0974355i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 36.3731 | + | 21.0000i | 1.36218 | + | 0.786456i | ||||
\(714\) | −20.0000 | −0.748481 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | 10.3923 | + | 6.00000i | 0.388108 | + | 0.224074i | ||||
\(718\) | −3.46410 | − | 2.00000i | −0.129279 | − | 0.0746393i | ||||
\(719\) | 20.0000 | + | 34.6410i | 0.745874 | + | 1.29189i | 0.949785 | + | 0.312903i | \(0.101301\pi\) |
−0.203911 | + | 0.978989i | \(0.565365\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.5000 | + | 30.3109i | 0.651734 | + | 1.12884i | ||||
\(722\) | 32.9090 | − | 19.0000i | 1.22474 | − | 0.707107i | ||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | −22.0000 | − | 38.1051i | −0.817624 | − | 1.41617i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | − | 9.00000i | − | 0.333792i | −0.985975 | − | 0.166896i | \(-0.946626\pi\) | ||
0.985975 | − | 0.166896i | \(-0.0533743\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.00000 | + | 1.73205i | −0.0369863 | + | 0.0640622i | ||||
\(732\) | 22.5167 | − | 13.0000i | 0.832240 | − | 0.480494i | ||||
\(733\) | 7.00000i | 0.258551i | 0.991609 | + | 0.129275i | \(0.0412651\pi\) | ||||
−0.991609 | + | 0.129275i | \(0.958735\pi\) | |||||||
\(734\) | 7.00000 | + | 12.1244i | 0.258375 | + | 0.447518i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −48.0000 | −1.76930 | ||||||||
\(737\) | 12.1244 | − | 7.00000i | 0.446606 | − | 0.257848i | ||||
\(738\) | −10.3923 | − | 6.00000i | −0.382546 | − | 0.220863i | ||||
\(739\) | −18.0000 | + | 31.1769i | −0.662141 | + | 1.14686i | 0.317911 | + | 0.948120i | \(0.397019\pi\) |
−0.980052 | + | 0.198741i | \(0.936315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 40.0000i | 1.46845i | ||||||||
\(743\) | −20.7846 | − | 12.0000i | −0.762513 | − | 0.440237i | 0.0676840 | − | 0.997707i | \(-0.478439\pi\) |
−0.830197 | + | 0.557470i | \(0.811772\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.0000 | 0.951928 | ||||||||
\(747\) | −6.92820 | + | 4.00000i | −0.253490 | + | 0.146352i | ||||
\(748\) | 6.92820 | − | 4.00000i | 0.253320 | − | 0.146254i | ||||
\(749\) | −20.0000 | −0.730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | − | 24.2487i | 0.510867 | − | 0.884848i | −0.489053 | − | 0.872254i | \(-0.662658\pi\) |
0.999921 | − | 0.0125942i | \(-0.00400897\pi\) | |||||||
\(752\) | 27.7128 | + | 16.0000i | 1.01058 | + | 0.583460i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 28.0000 | + | 6.92820i | 1.01970 | + | 0.252310i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.00000 | + | 8.66025i | −0.181848 | + | 0.314970i | ||||
\(757\) | 1.73205 | + | 1.00000i | 0.0629525 | + | 0.0363456i | 0.531146 | − | 0.847280i | \(-0.321762\pi\) |
−0.468193 | + | 0.883626i | \(0.655095\pi\) | |||||||
\(758\) | −8.66025 | + | 5.00000i | −0.314555 | + | 0.181608i | ||||
\(759\) | −12.0000 | −0.435572 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.0000 | + | 31.1769i | 0.652499 | + | 1.13016i | 0.982514 | + | 0.186187i | \(0.0596129\pi\) |
−0.330015 | + | 0.943976i | \(0.607054\pi\) | |||||||
\(762\) | 22.0000i | 0.796976i | ||||||||
\(763\) | −47.6314 | + | 27.5000i | −1.72437 | + | 0.995567i | ||||
\(764\) | 12.0000 | − | 20.7846i | 0.434145 | − | 0.751961i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −36.0000 | −1.30073 | ||||||||
\(767\) | 10.3923 | − | 42.0000i | 0.375244 | − | 1.51653i | ||||
\(768\) | 16.0000i | 0.577350i | ||||||||
\(769\) | −17.0000 | + | 29.4449i | −0.613036 | + | 1.06181i | 0.377690 | + | 0.925932i | \(0.376718\pi\) |
−0.990726 | + | 0.135877i | \(0.956615\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0000 | + | 19.0526i | 0.396155 | + | 0.686161i | ||||
\(772\) | 22.0000i | 0.791797i | ||||||||
\(773\) | 39.8372 | − | 23.0000i | 1.43284 | − | 0.827253i | 0.435507 | − | 0.900186i | \(-0.356569\pi\) |
0.997337 | + | 0.0729331i | \(0.0232359\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.66025 | − | 5.00000i | −0.310685 | − | 0.179374i | ||||
\(778\) | −13.8564 | − | 8.00000i | −0.496776 | − | 0.286814i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 20.7846 | + | 12.0000i | 0.743256 | + | 0.429119i | ||||
\(783\) | 3.46410 | + | 2.00000i | 0.123797 | + | 0.0714742i | ||||
\(784\) | −36.0000 | − | 62.3538i | −1.28571 | − | 2.22692i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.00000 | + | 6.92820i | 0.142675 | + | 0.247121i | ||||
\(787\) | −14.7224 | + | 8.50000i | −0.524798 | + | 0.302992i | −0.738896 | − | 0.673820i | \(-0.764652\pi\) |
0.214097 | + | 0.976812i | \(0.431319\pi\) | |||||||
\(788\) | − | 24.0000i | − | 0.854965i | ||||||
\(789\) | −5.00000 | − | 8.66025i | −0.178005 | − | 0.308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.00000 | − | 8.66025i | 0.177780 | − | 0.307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.2583 | − | 45.5000i | 0.399795 | − | 1.61575i | ||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.0000 | + | 29.4449i | −0.602549 | + | 1.04365i | ||||
\(797\) | −25.9808 | + | 15.0000i | −0.920286 | + | 0.531327i | −0.883726 | − | 0.468004i | \(-0.844973\pi\) |
−0.0365596 | + | 0.999331i | \(0.511640\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | − | 13.8564i | −0.283020 | − | 0.490204i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.0000 | 0.494666 | ||||||||
\(802\) | −27.7128 | + | 16.0000i | −0.978573 | + | 0.564980i | ||||
\(803\) | −25.9808 | − | 15.0000i | −0.916841 | − | 0.529339i | ||||
\(804\) | −7.00000 | + | 12.1244i | −0.246871 | + | 0.427593i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.0000 | + | 48.4974i | 0.493129 | + | 1.70825i | ||||
\(807\) | 6.00000i | 0.211210i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.00000 | − | 3.46410i | 0.0703163 | − | 0.121791i | −0.828724 | − | 0.559658i | \(-0.810932\pi\) |
0.899040 | + | 0.437867i | \(0.144266\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.0000 | 1.58016 | 0.790082 | − | 0.613001i | \(-0.210038\pi\) | ||||
0.790082 | + | 0.613001i | \(0.210038\pi\) | |||||||
\(812\) | 34.6410 | − | 20.0000i | 1.21566 | − | 0.701862i | ||||
\(813\) | 25.1147 | − | 14.5000i | 0.880812 | − | 0.508537i | ||||
\(814\) | 8.00000 | 0.280400 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.00000 | − | 6.92820i | 0.140028 | − | 0.242536i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | − | 30.0000i | − | 1.04893i | ||||||
\(819\) | 5.00000 | + | 17.3205i | 0.174714 | + | 0.605228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.0000 | − | 19.0526i | 0.383903 | − | 0.664939i | −0.607714 | − | 0.794156i | \(-0.707913\pi\) |
0.991616 | + | 0.129217i | \(0.0412465\pi\) | |||||||
\(822\) | −3.46410 | − | 2.00000i | −0.120824 | − | 0.0697580i | ||||
\(823\) | 17.3205 | − | 10.0000i | 0.603755 | − | 0.348578i | −0.166762 | − | 0.985997i | \(-0.553331\pi\) |
0.770517 | + | 0.637419i | \(0.219998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −60.0000 | − | 103.923i | −2.08767 | − | 3.61595i | ||||
\(827\) | − | 46.0000i | − | 1.59958i | −0.600282 | − | 0.799788i | \(-0.704945\pi\) | ||
0.600282 | − | 0.799788i | \(-0.295055\pi\) | |||||||
\(828\) | 10.3923 | − | 6.00000i | 0.361158 | − | 0.208514i | ||||
\(829\) | −5.50000 | + | 9.52628i | −0.191023 | + | 0.330861i | −0.945589 | − | 0.325362i | \(-0.894514\pi\) |
0.754567 | + | 0.656223i | \(0.227847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | −20.7846 | − | 20.0000i | −0.720577 | − | 0.693375i | ||||
\(833\) | 36.0000i | 1.24733i | ||||||||
\(834\) | −3.00000 | + | 5.19615i | −0.103882 | + | 0.179928i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.00000i | 0.241955i | ||||||||
\(838\) | 65.8179 | − | 38.0000i | 2.27364 | − | 1.31269i | ||||
\(839\) | −17.0000 | − | 29.4449i | −0.586905 | − | 1.01655i | −0.994635 | − | 0.103447i | \(-0.967013\pi\) |
0.407730 | − | 0.913103i | \(-0.366321\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | −39.8372 | − | 23.0000i | −1.37288 | − | 0.792632i | ||||
\(843\) | 10.3923 | + | 6.00000i | 0.357930 | + | 0.206651i | ||||
\(844\) | −30.0000 | −1.03264 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −16.0000 | −0.550091 | ||||||||
\(847\) | −30.3109 | − | 17.5000i | −1.04149 | − | 0.601307i | ||||
\(848\) | −13.8564 | − | 8.00000i | −0.475831 | − | 0.274721i | ||||
\(849\) | 2.50000 | + | 4.33013i | 0.0857998 | + | 0.148610i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | −20.7846 | + | 12.0000i | −0.712069 | + | 0.411113i | ||||
\(853\) | 9.00000i | 0.308154i | 0.988059 | + | 0.154077i | \(0.0492404\pi\) | ||||
−0.988059 | + | 0.154077i | \(0.950760\pi\) | |||||||
\(854\) | −65.0000 | − | 112.583i | −2.22425 | − | 3.85252i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0000i | 0.409912i | 0.978771 | + | 0.204956i | \(0.0657052\pi\) | ||||
−0.978771 | + | 0.204956i | \(0.934295\pi\) | |||||||
\(858\) | −10.3923 | − | 10.0000i | −0.354787 | − | 0.341394i | ||||
\(859\) | −43.0000 | −1.46714 | −0.733571 | − | 0.679613i | \(-0.762148\pi\) | ||||
−0.733571 | + | 0.679613i | \(0.762148\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0000 | + | 25.9808i | −0.511199 | + | 0.885422i | ||||
\(862\) | 48.4974 | − | 28.0000i | 1.65183 | − | 0.953684i | ||||
\(863\) | 6.00000i | 0.204242i | 0.994772 | + | 0.102121i | \(0.0325630\pi\) | ||||
−0.994772 | + | 0.102121i | \(0.967437\pi\) | |||||||
\(864\) | −4.00000 | − | 6.92820i | −0.136083 | − | 0.235702i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.00000 | 0.0679628 | ||||||||
\(867\) | 11.2583 | − | 6.50000i | 0.382353 | − | 0.220752i | ||||
\(868\) | 60.6218 | + | 35.0000i | 2.05764 | + | 1.18798i | ||||
\(869\) | 3.00000 | − | 5.19615i | 0.101768 | − | 0.176267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.00000 | + | 24.2487i | 0.237186 | + | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.33013 | + | 2.50000i | 0.146553 | + | 0.0846122i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 30.0000 | 1.01361 | ||||||||
\(877\) | −5.19615 | + | 3.00000i | −0.175462 | + | 0.101303i | −0.585159 | − | 0.810919i | \(-0.698968\pi\) |
0.409697 | + | 0.912222i | \(0.365634\pi\) | |||||||
\(878\) | 25.9808 | − | 15.0000i | 0.876808 | − | 0.506225i | ||||
\(879\) | −16.0000 | −0.539667 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.0000 | + | 17.3205i | −0.336909 | + | 0.583543i | −0.983850 | − | 0.178997i | \(-0.942715\pi\) |
0.646941 | + | 0.762540i | \(0.276048\pi\) | |||||||
\(882\) | 31.1769 | + | 18.0000i | 1.04978 | + | 0.606092i | ||||
\(883\) | − | 25.0000i | − | 0.841317i | −0.907219 | − | 0.420658i | \(-0.861799\pi\) | ||
0.907219 | − | 0.420658i | \(-0.138201\pi\) | |||||||
\(884\) | 4.00000 | + | 13.8564i | 0.134535 | + | 0.466041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.0000 | + | 45.0333i | −0.873487 | + | 1.51292i | ||||
\(887\) | −38.1051 | − | 22.0000i | −1.27944 | − | 0.738688i | −0.302698 | − | 0.953086i | \(-0.597887\pi\) |
−0.976746 | + | 0.214399i | \(0.931221\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.0000 | 1.84464 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 16.0000i | 0.535720i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −12.0000 | + | 20.7846i | −0.401340 | + | 0.695141i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.19615 | − | 21.0000i | 0.173494 | − | 0.701170i | ||||
\(898\) | 36.0000i | 1.20134i | ||||||||
\(899\) | 14.0000 | − | 24.2487i | 0.466926 | − | 0.808740i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00000 | + | 6.92820i | 0.133259 | + | 0.230812i | ||||
\(902\) | − | 24.0000i | − | 0.799113i | ||||||
\(903\) | 4.33013 | − | 2.50000i | 0.144098 | − | 0.0831948i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.00000 | + | 13.8564i | 0.265782 | + | 0.460348i | ||||
\(907\) | 17.3205 | + | 10.0000i | 0.575118 | + | 0.332045i | 0.759191 | − | 0.650868i | \(-0.225595\pi\) |
−0.184073 | + | 0.982913i | \(0.558928\pi\) | |||||||
\(908\) | −17.3205 | − | 10.0000i | −0.574801 | − | 0.331862i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.8564 | − | 8.00000i | −0.458580 | − | 0.264761i | ||||
\(914\) | 35.0000 | + | 60.6218i | 1.15770 | + | 2.00519i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | − | 24.2487i | −0.462573 | − | 0.801200i | ||||
\(917\) | 17.3205 | − | 10.0000i | 0.571974 | − | 0.330229i | ||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | 4.00000 | + | 6.92820i | 0.131948 | + | 0.228540i | 0.924427 | − | 0.381358i | \(-0.124544\pi\) |
−0.792480 | + | 0.609898i | \(0.791210\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.5000 | − | 26.8468i | 0.510742 | − | 0.884632i | ||||
\(922\) | 4.00000i | 0.131733i | ||||||||
\(923\) | −10.3923 | + | 42.0000i | −0.342067 | + | 1.38245i | ||||
\(924\) | −20.0000 | −0.657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.00000 | + | 5.19615i | −0.0985861 | + | 0.170756i | ||||
\(927\) | 6.06218 | − | 3.50000i | 0.199108 | − | 0.114955i | ||||
\(928\) | 32.0000i | 1.05045i | ||||||||
\(929\) | 26.0000 | + | 45.0333i | 0.853032 | + | 1.47750i | 0.878459 | + | 0.477819i | \(0.158572\pi\) |
−0.0254262 | + | 0.999677i | \(0.508094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 24.2487 | − | 14.0000i | 0.794293 | − | 0.458585i | ||||
\(933\) | 19.0526 | + | 11.0000i | 0.623753 | + | 0.360124i | ||||
\(934\) | −4.00000 | + | 6.92820i | −0.130884 | + | 0.226698i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.0000i | 0.980057i | 0.871706 | + | 0.490029i | \(0.163014\pi\) | ||||
−0.871706 | + | 0.490029i | \(0.836986\pi\) | |||||||
\(938\) | 60.6218 | + | 35.0000i | 1.97937 | + | 1.14279i | ||||
\(939\) | −15.5000 | + | 26.8468i | −0.505823 | + | 0.876112i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 25.9808 | − | 15.0000i | 0.846499 | − | 0.488726i | ||||
\(943\) | 31.1769 | − | 18.0000i | 1.01526 | − | 0.586161i | ||||
\(944\) | 48.0000 | 1.56227 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.00000 | + | 3.46410i | −0.0650256 | + | 0.112628i | ||||
\(947\) | 15.5885 | + | 9.00000i | 0.506557 | + | 0.292461i | 0.731417 | − | 0.681930i | \(-0.238859\pi\) |
−0.224860 | + | 0.974391i | \(0.572193\pi\) | |||||||
\(948\) | 6.00000i | 0.194871i | ||||||||
\(949\) | 37.5000 | − | 38.9711i | 1.21730 | − | 1.26506i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.00000 | + | 10.3923i | −0.194563 | + | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.19615 | − | 3.00000i | 0.168320 | − | 0.0971795i | −0.413473 | − | 0.910516i | \(-0.635685\pi\) |
0.581793 | + | 0.813337i | \(0.302351\pi\) | |||||||
\(954\) | 8.00000 | 0.259010 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −12.0000 | − | 20.7846i | −0.388108 | − | 0.672222i | ||||
\(957\) | 8.00000i | 0.258603i | ||||||||
\(958\) | 72.7461 | − | 42.0000i | 2.35032 | − | 1.35696i | ||||
\(959\) | −5.00000 | + | 8.66025i | −0.161458 | + | 0.279654i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | −3.46410 | + | 14.0000i | −0.111687 | + | 0.451378i | ||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 10.0000 | − | 17.3205i | 0.322078 | − | 0.557856i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −30.0000 | − | 51.9615i | −0.965234 | − | 1.67183i | ||||
\(967\) | 56.0000i | 1.80084i | 0.435023 | + | 0.900419i | \(0.356740\pi\) | ||||
−0.435023 | + | 0.900419i | \(0.643260\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0000 | − | 17.3205i | −0.320915 | − | 0.555842i | 0.659762 | − | 0.751475i | \(-0.270657\pi\) |
−0.980677 | + | 0.195633i | \(0.937324\pi\) | |||||||
\(972\) | 1.73205 | + | 1.00000i | 0.0555556 | + | 0.0320750i | ||||
\(973\) | 12.9904 | + | 7.50000i | 0.416452 | + | 0.240439i | ||||
\(974\) | 56.0000 | 1.79436 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 52.0000 | 1.66448 | ||||||||
\(977\) | 51.9615 | + | 30.0000i | 1.66240 | + | 0.959785i | 0.971566 | + | 0.236768i | \(0.0760881\pi\) |
0.690830 | + | 0.723017i | \(0.257245\pi\) | |||||||
\(978\) | 25.9808 | + | 15.0000i | 0.830773 | + | 0.479647i | ||||
\(979\) | 14.0000 | + | 24.2487i | 0.447442 | + | 0.774992i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.50000 | + | 9.52628i | 0.175601 | + | 0.304151i | ||||
\(982\) | 41.5692 | − | 24.0000i | 1.32653 | − | 0.765871i | ||||
\(983\) | 38.0000i | 1.21201i | 0.795460 | + | 0.606006i | \(0.207229\pi\) | ||||
−0.795460 | + | 0.606006i | \(0.792771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.00000 | − | 13.8564i | 0.254772 | − | 0.441278i | ||||
\(987\) | 40.0000i | 1.27321i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | −0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(992\) | −48.4974 | + | 28.0000i | −1.53979 | + | 0.889001i | ||||
\(993\) | 9.00000i | 0.285606i | ||||||||
\(994\) | 60.0000 | + | 103.923i | 1.90308 | + | 3.29624i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 16.0000 | 0.506979 | ||||||||
\(997\) | −25.1147 | + | 14.5000i | −0.795392 | + | 0.459220i | −0.841857 | − | 0.539700i | \(-0.818538\pi\) |
0.0464655 | + | 0.998920i | \(0.485204\pi\) | |||||||
\(998\) | −6.92820 | − | 4.00000i | −0.219308 | − | 0.126618i | ||||
\(999\) | −1.00000 | + | 1.73205i | −0.0316386 | + | 0.0547997i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 975.2.bb.f.724.2 | 4 | ||
5.2 | odd | 4 | 195.2.i.a.61.1 | yes | 2 | ||
5.3 | odd | 4 | 975.2.i.i.451.1 | 2 | |||
5.4 | even | 2 | inner | 975.2.bb.f.724.1 | 4 | ||
13.3 | even | 3 | inner | 975.2.bb.f.874.1 | 4 | ||
15.2 | even | 4 | 585.2.j.b.451.1 | 2 | |||
65.3 | odd | 12 | 975.2.i.i.601.1 | 2 | |||
65.17 | odd | 12 | 2535.2.a.c.1.1 | 1 | |||
65.22 | odd | 12 | 2535.2.a.m.1.1 | 1 | |||
65.29 | even | 6 | inner | 975.2.bb.f.874.2 | 4 | ||
65.42 | odd | 12 | 195.2.i.a.16.1 | ✓ | 2 | ||
195.17 | even | 12 | 7605.2.a.s.1.1 | 1 | |||
195.107 | even | 12 | 585.2.j.b.406.1 | 2 | |||
195.152 | even | 12 | 7605.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.i.a.16.1 | ✓ | 2 | 65.42 | odd | 12 | ||
195.2.i.a.61.1 | yes | 2 | 5.2 | odd | 4 | ||
585.2.j.b.406.1 | 2 | 195.107 | even | 12 | |||
585.2.j.b.451.1 | 2 | 15.2 | even | 4 | |||
975.2.i.i.451.1 | 2 | 5.3 | odd | 4 | |||
975.2.i.i.601.1 | 2 | 65.3 | odd | 12 | |||
975.2.bb.f.724.1 | 4 | 5.4 | even | 2 | inner | ||
975.2.bb.f.724.2 | 4 | 1.1 | even | 1 | trivial | ||
975.2.bb.f.874.1 | 4 | 13.3 | even | 3 | inner | ||
975.2.bb.f.874.2 | 4 | 65.29 | even | 6 | inner | ||
2535.2.a.c.1.1 | 1 | 65.17 | odd | 12 | |||
2535.2.a.m.1.1 | 1 | 65.22 | odd | 12 | |||
7605.2.a.a.1.1 | 1 | 195.152 | even | 12 | |||
7605.2.a.s.1.1 | 1 | 195.17 | even | 12 |