Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (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: | \(8.38429221223\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.a.949.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.59808 | − | 0.500000i | −0.981981 | − | 0.188982i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.46410 | − | 2.00000i | 0.840168 | − | 0.485071i | −0.0171533 | − | 0.999853i | \(-0.505460\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 4.00000 | − | 6.92820i | 0.917663 | − | 1.58944i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.50000 | − | 0.866025i | 0.545545 | − | 0.188982i | ||||
\(22\) | − | 5.00000i | − | 1.06600i | ||||||
\(23\) | 3.46410 | + | 2.00000i | 0.722315 | + | 0.417029i | 0.815604 | − | 0.578610i | \(-0.196405\pi\) |
−0.0932891 | + | 0.995639i | \(0.529738\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −0.866025 | − | 2.50000i | −0.163663 | − | 0.472456i | ||||
\(29\) | 5.00000 | 0.928477 | 0.464238 | − | 0.885710i | \(-0.346328\pi\) | ||||
0.464238 | + | 0.885710i | \(0.346328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 4.33013 | + | 2.50000i | 0.753778 | + | 0.435194i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.46410 | − | 2.00000i | −0.569495 | − | 0.328798i | 0.187453 | − | 0.982274i | \(-0.439977\pi\) |
−0.756948 | + | 0.653476i | \(0.773310\pi\) | |||||||
\(38\) | 6.92820 | − | 4.00000i | 1.12390 | − | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 2.59808 | + | 0.500000i | 0.400892 | + | 0.0771517i | ||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 2.50000 | − | 4.33013i | 0.376889 | − | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | + | 3.46410i | 0.294884 | + | 0.510754i | ||||
\(47\) | −5.19615 | − | 3.00000i | −0.757937 | − | 0.437595i | 0.0706177 | − | 0.997503i | \(-0.477503\pi\) |
−0.828554 | + | 0.559908i | \(0.810836\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 6.50000 | + | 2.59808i | 0.928571 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.79423 | + | 4.50000i | −1.07062 | + | 0.618123i | −0.928351 | − | 0.371706i | \(-0.878773\pi\) |
−0.142269 | + | 0.989828i | \(0.545440\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | − | 2.59808i | 0.0668153 | − | 0.347183i | ||||
\(57\) | 8.00000i | 1.05963i | ||||||||
\(58\) | 4.33013 | + | 2.50000i | 0.568574 | + | 0.328266i | ||||
\(59\) | −5.50000 | − | 9.52628i | −0.716039 | − | 1.24022i | −0.962557 | − | 0.271078i | \(-0.912620\pi\) |
0.246518 | − | 0.969138i | \(-0.420713\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | − | 5.19615i | 0.384111 | − | 0.665299i | −0.607535 | − | 0.794293i | \(-0.707841\pi\) |
0.991645 | + | 0.128994i | \(0.0411748\pi\) | |||||||
\(62\) | − | 3.00000i | − | 0.381000i | ||||||
\(63\) | −1.73205 | + | 2.00000i | −0.218218 | + | 0.251976i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.50000 | + | 4.33013i | 0.307729 | + | 0.533002i | ||||
\(67\) | 1.73205 | − | 1.00000i | 0.211604 | − | 0.122169i | −0.390453 | − | 0.920623i | \(-0.627682\pi\) |
0.602056 | + | 0.798454i | \(0.294348\pi\) | |||||||
\(68\) | 3.46410 | + | 2.00000i | 0.420084 | + | 0.242536i | ||||
\(69\) | −4.00000 | −0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | 8.66025 | − | 5.00000i | 1.01361 | − | 0.585206i | 0.101361 | − | 0.994850i | \(-0.467680\pi\) |
0.912245 | + | 0.409644i | \(0.134347\pi\) | |||||||
\(74\) | −2.00000 | − | 3.46410i | −0.232495 | − | 0.402694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | 4.33013 | + | 12.5000i | 0.493464 | + | 1.42451i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | − | 2.59808i | 0.168763 | − | 0.292306i | −0.769222 | − | 0.638982i | \(-0.779356\pi\) |
0.937985 | + | 0.346675i | \(0.112689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.00000i | − | 0.768350i | −0.923260 | − | 0.384175i | \(-0.874486\pi\) | ||
0.923260 | − | 0.384175i | \(-0.125514\pi\) | |||||||
\(84\) | 2.00000 | + | 1.73205i | 0.218218 | + | 0.188982i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | −4.33013 | + | 2.50000i | −0.464238 | + | 0.268028i | ||||
\(88\) | 4.33013 | − | 2.50000i | 0.461593 | − | 0.266501i | ||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.00000i | 0.417029i | ||||||||
\(93\) | 2.59808 | + | 1.50000i | 0.269408 | + | 0.155543i | ||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 7.00000i | − | 0.710742i | −0.934725 | − | 0.355371i | \(-0.884354\pi\) | ||
0.934725 | − | 0.355371i | \(-0.115646\pi\) | |||||||
\(98\) | 4.33013 | + | 5.50000i | 0.437409 | + | 0.555584i | ||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00000 | − | 8.66025i | −0.497519 | − | 0.861727i | 0.502477 | − | 0.864590i | \(-0.332422\pi\) |
−0.999996 | + | 0.00286291i | \(0.999089\pi\) | |||||||
\(102\) | −3.46410 | + | 2.00000i | −0.342997 | + | 0.198030i | ||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 2.59808 | + | 1.50000i | 0.251166 | + | 0.145010i | 0.620298 | − | 0.784366i | \(-0.287012\pi\) |
−0.369132 | + | 0.929377i | \(0.620345\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 1.73205 | − | 2.00000i | 0.163663 | − | 0.188982i | ||||
\(113\) | 16.0000i | 1.50515i | 0.658505 | + | 0.752577i | \(0.271189\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | −4.00000 | + | 6.92820i | −0.374634 | + | 0.648886i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.50000 | + | 4.33013i | 0.232119 | + | 0.402042i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 11.0000i | − | 1.01263i | ||||||
\(119\) | −10.0000 | + | 3.46410i | −0.916698 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 5.19615 | − | 3.00000i | 0.470438 | − | 0.271607i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.50000 | − | 2.59808i | 0.134704 | − | 0.233314i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.50000 | + | 0.866025i | −0.222718 | + | 0.0771517i | ||||
\(127\) | − | 9.00000i | − | 0.798621i | −0.916816 | − | 0.399310i | \(-0.869250\pi\) | ||
0.916816 | − | 0.399310i | \(-0.130750\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −1.00000 | − | 1.73205i | −0.0880451 | − | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | + | 0.866025i | −0.0436852 | + | 0.0756650i | −0.887041 | − | 0.461690i | \(-0.847243\pi\) |
0.843356 | + | 0.537355i | \(0.180577\pi\) | |||||||
\(132\) | 5.00000i | 0.435194i | ||||||||
\(133\) | −13.8564 | + | 16.0000i | −1.20150 | + | 1.38738i | ||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 1.73205 | − | 1.00000i | 0.147979 | − | 0.0854358i | −0.424182 | − | 0.905577i | \(-0.639438\pi\) |
0.572161 | + | 0.820141i | \(0.306105\pi\) | |||||||
\(138\) | −3.46410 | − | 2.00000i | −0.294884 | − | 0.170251i | ||||
\(139\) | 14.0000 | 1.18746 | 0.593732 | − | 0.804663i | \(-0.297654\pi\) | ||||
0.593732 | + | 0.804663i | \(0.297654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 1.73205 | + | 1.00000i | 0.145350 | + | 0.0839181i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | −6.92820 | + | 1.00000i | −0.571429 | + | 0.0824786i | ||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −9.00000 | + | 15.5885i | −0.737309 | + | 1.27706i | 0.216394 | + | 0.976306i | \(0.430570\pi\) |
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50000 | − | 16.4545i | −0.773099 | − | 1.33905i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) |
0.162758 | − | 0.986666i | \(-0.447961\pi\) | |||||||
\(152\) | 6.92820 | + | 4.00000i | 0.561951 | + | 0.324443i | ||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | −2.50000 | + | 12.9904i | −0.201456 | + | 1.04679i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.46410 | − | 2.00000i | 0.276465 | − | 0.159617i | −0.355357 | − | 0.934731i | \(-0.615641\pi\) |
0.631822 | + | 0.775113i | \(0.282307\pi\) | |||||||
\(158\) | 2.59808 | − | 1.50000i | 0.206692 | − | 0.119334i | ||||
\(159\) | 4.50000 | − | 7.79423i | 0.356873 | − | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | − | 6.92820i | −0.630488 | − | 0.546019i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 3.46410 | + | 2.00000i | 0.271329 | + | 0.156652i | 0.629492 | − | 0.777007i | \(-0.283263\pi\) |
−0.358162 | + | 0.933659i | \(0.616597\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50000 | − | 6.06218i | 0.271653 | − | 0.470516i | ||||
\(167\) | 14.0000i | 1.08335i | 0.840587 | + | 0.541676i | \(0.182210\pi\) | ||||
−0.840587 | + | 0.541676i | \(0.817790\pi\) | |||||||
\(168\) | 0.866025 | + | 2.50000i | 0.0668153 | + | 0.192879i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | − | 6.92820i | −0.305888 | − | 0.529813i | ||||
\(172\) | −1.73205 | + | 1.00000i | −0.132068 | + | 0.0762493i | ||||
\(173\) | −19.0526 | − | 11.0000i | −1.44854 | − | 0.836315i | −0.450145 | − | 0.892956i | \(-0.648628\pi\) |
−0.998395 | + | 0.0566411i | \(0.981961\pi\) | |||||||
\(174\) | −5.00000 | −0.379049 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.00000 | 0.376889 | ||||||||
\(177\) | 9.52628 | + | 5.50000i | 0.716039 | + | 0.413405i | ||||
\(178\) | −5.19615 | + | 3.00000i | −0.389468 | + | 0.224860i | ||||
\(179\) | 6.00000 | + | 10.3923i | 0.448461 | + | 0.776757i | 0.998286 | − | 0.0585225i | \(-0.0186389\pi\) |
−0.549825 | + | 0.835280i | \(0.685306\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | −2.00000 | + | 3.46410i | −0.147442 | + | 0.255377i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.50000 | + | 2.59808i | 0.109985 | + | 0.190500i | ||||
\(187\) | −17.3205 | − | 10.0000i | −1.26660 | − | 0.731272i | ||||
\(188\) | − | 6.00000i | − | 0.437595i | ||||||
\(189\) | 0.500000 | − | 2.59808i | 0.0363696 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | + | 20.7846i | −0.868290 | + | 1.50392i | −0.00454614 | + | 0.999990i | \(0.501447\pi\) |
−0.863743 | + | 0.503932i | \(0.831886\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 4.33013 | − | 2.50000i | 0.311689 | − | 0.179954i | −0.335993 | − | 0.941865i | \(-0.609072\pi\) |
0.647682 | + | 0.761911i | \(0.275738\pi\) | |||||||
\(194\) | 3.50000 | − | 6.06218i | 0.251285 | − | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | − | 2.00000i | − | 0.142494i | −0.997459 | − | 0.0712470i | \(-0.977302\pi\) | ||
0.997459 | − | 0.0712470i | \(-0.0226979\pi\) | |||||||
\(198\) | −4.33013 | − | 2.50000i | −0.307729 | − | 0.177667i | ||||
\(199\) | −2.00000 | − | 3.46410i | −0.141776 | − | 0.245564i | 0.786389 | − | 0.617731i | \(-0.211948\pi\) |
−0.928166 | + | 0.372168i | \(0.878615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | + | 1.73205i | −0.0705346 | + | 0.122169i | ||||
\(202\) | − | 10.0000i | − | 0.703598i | ||||||
\(203\) | −12.9904 | − | 2.50000i | −0.911746 | − | 0.175466i | ||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.00000 | − | 6.92820i | −0.278693 | − | 0.482711i | ||||
\(207\) | 3.46410 | − | 2.00000i | 0.240772 | − | 0.139010i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −40.0000 | −2.76686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | −7.79423 | − | 4.50000i | −0.535310 | − | 0.309061i | ||||
\(213\) | −1.73205 | + | 1.00000i | −0.118678 | + | 0.0685189i | ||||
\(214\) | 1.50000 | + | 2.59808i | 0.102538 | + | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.59808 | + | 7.50000i | 0.176369 | + | 0.509133i | ||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | −5.00000 | + | 8.66025i | −0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.46410 | + | 2.00000i | 0.232495 | + | 0.134231i | ||||
\(223\) | − | 7.00000i | − | 0.468755i | −0.972146 | − | 0.234377i | \(-0.924695\pi\) | ||
0.972146 | − | 0.234377i | \(-0.0753051\pi\) | |||||||
\(224\) | 2.50000 | − | 0.866025i | 0.167038 | − | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.00000 | + | 13.8564i | −0.532152 | + | 0.921714i | ||||
\(227\) | −2.59808 | + | 1.50000i | −0.172440 | + | 0.0995585i | −0.583736 | − | 0.811943i | \(-0.698410\pi\) |
0.411296 | + | 0.911502i | \(0.365076\pi\) | |||||||
\(228\) | −6.92820 | + | 4.00000i | −0.458831 | + | 0.264906i | ||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.0000 | − | 8.66025i | −0.657952 | − | 0.569803i | ||||
\(232\) | 5.00000i | 0.328266i | ||||||||
\(233\) | 3.46410 | + | 2.00000i | 0.226941 | + | 0.131024i | 0.609160 | − | 0.793047i | \(-0.291507\pi\) |
−0.382219 | + | 0.924072i | \(0.624840\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.50000 | − | 9.52628i | 0.358020 | − | 0.620108i | ||||
\(237\) | 3.00000i | 0.194871i | ||||||||
\(238\) | −10.3923 | − | 2.00000i | −0.673633 | − | 0.129641i | ||||
\(239\) | 12.0000 | 0.776215 | 0.388108 | − | 0.921614i | \(-0.373129\pi\) | ||||
0.388108 | + | 0.921614i | \(0.373129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5000 | + | 21.6506i | 0.805196 | + | 1.39464i | 0.916159 | + | 0.400815i | \(0.131273\pi\) |
−0.110963 | + | 0.993825i | \(0.535394\pi\) | |||||||
\(242\) | −12.1244 | + | 7.00000i | −0.779383 | + | 0.449977i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.59808 | − | 1.50000i | 0.164978 | − | 0.0952501i | ||||
\(249\) | 3.50000 | + | 6.06218i | 0.221803 | + | 0.384175i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | −2.59808 | − | 0.500000i | −0.163663 | − | 0.0314970i | ||||
\(253\) | − | 20.0000i | − | 1.25739i | ||||||
\(254\) | 4.50000 | − | 7.79423i | 0.282355 | − | 0.489053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.19615 | − | 3.00000i | −0.324127 | − | 0.187135i | 0.329104 | − | 0.944294i | \(-0.393253\pi\) |
−0.653231 | + | 0.757159i | \(0.726587\pi\) | |||||||
\(258\) | − | 2.00000i | − | 0.124515i | ||||||
\(259\) | 8.00000 | + | 6.92820i | 0.497096 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.50000 | − | 4.33013i | 0.154746 | − | 0.268028i | ||||
\(262\) | −0.866025 | + | 0.500000i | −0.0535032 | + | 0.0308901i | ||||
\(263\) | −25.9808 | + | 15.0000i | −1.60204 | + | 0.924940i | −0.610964 | + | 0.791658i | \(0.709218\pi\) |
−0.991078 | + | 0.133281i | \(0.957449\pi\) | |||||||
\(264\) | −2.50000 | + | 4.33013i | −0.153864 | + | 0.266501i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −20.0000 | + | 6.92820i | −1.22628 | + | 0.424795i | ||||
\(267\) | − | 6.00000i | − | 0.367194i | ||||||
\(268\) | 1.73205 | + | 1.00000i | 0.105802 | + | 0.0610847i | ||||
\(269\) | 15.5000 | + | 26.8468i | 0.945052 | + | 1.63688i | 0.755648 | + | 0.654978i | \(0.227322\pi\) |
0.189404 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.50000 | + | 12.9904i | −0.455593 | + | 0.789109i | −0.998722 | − | 0.0505395i | \(-0.983906\pi\) |
0.543130 | + | 0.839649i | \(0.317239\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | 13.8564 | − | 8.00000i | 0.832551 | − | 0.480673i | −0.0221745 | − | 0.999754i | \(-0.507059\pi\) |
0.854725 | + | 0.519081i | \(0.173726\pi\) | |||||||
\(278\) | 12.1244 | + | 7.00000i | 0.727171 | + | 0.419832i | ||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 5.19615 | + | 3.00000i | 0.309426 | + | 0.178647i | ||||
\(283\) | 8.66025 | − | 5.00000i | 0.514799 | − | 0.297219i | −0.220005 | − | 0.975499i | \(-0.570607\pi\) |
0.734804 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(284\) | 1.00000 | + | 1.73205i | 0.0593391 | + | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.50000 | + | 6.06218i | 0.205174 | + | 0.355371i | ||||
\(292\) | 8.66025 | + | 5.00000i | 0.506803 | + | 0.292603i | ||||
\(293\) | − | 21.0000i | − | 1.22683i | −0.789760 | − | 0.613417i | \(-0.789795\pi\) | ||
0.789760 | − | 0.613417i | \(-0.210205\pi\) | |||||||
\(294\) | −6.50000 | − | 2.59808i | −0.379088 | − | 0.151523i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.00000 | − | 3.46410i | 0.116248 | − | 0.201347i | ||||
\(297\) | 4.33013 | − | 2.50000i | 0.251259 | − | 0.145065i | ||||
\(298\) | −15.5885 | + | 9.00000i | −0.903015 | + | 0.521356i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | − | 5.19615i | 0.0576390 | − | 0.299501i | ||||
\(302\) | − | 19.0000i | − | 1.09333i | ||||||
\(303\) | 8.66025 | + | 5.00000i | 0.497519 | + | 0.287242i | ||||
\(304\) | 4.00000 | + | 6.92820i | 0.229416 | + | 0.397360i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | − | 3.46410i | 0.114332 | − | 0.198030i | ||||
\(307\) | − | 28.0000i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(308\) | −8.66025 | + | 10.0000i | −0.493464 | + | 0.569803i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.0000 | + | 27.7128i | 0.907277 | + | 1.57145i | 0.817832 | + | 0.575458i | \(0.195176\pi\) |
0.0894452 | + | 0.995992i | \(0.471491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.866025 | − | 0.500000i | −0.0489506 | − | 0.0282617i | 0.475325 | − | 0.879810i | \(-0.342331\pi\) |
−0.524276 | + | 0.851549i | \(0.675664\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.00000 | 0.168763 | ||||||||
\(317\) | 2.59808 | + | 1.50000i | 0.145922 | + | 0.0842484i | 0.571184 | − | 0.820822i | \(-0.306484\pi\) |
−0.425261 | + | 0.905071i | \(0.639818\pi\) | |||||||
\(318\) | 7.79423 | − | 4.50000i | 0.437079 | − | 0.252347i | ||||
\(319\) | −12.5000 | − | 21.6506i | −0.699866 | − | 1.21220i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00000 | −0.167444 | ||||||||
\(322\) | −3.46410 | − | 10.0000i | −0.193047 | − | 0.557278i | ||||
\(323\) | − | 32.0000i | − | 1.78053i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | 1.73205 | + | 1.00000i | 0.0957826 | + | 0.0553001i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000 | + | 10.3923i | 0.661581 | + | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | − | 3.46410i | 0.109930 | − | 0.190404i | −0.805812 | − | 0.592172i | \(-0.798271\pi\) |
0.915742 | + | 0.401768i | \(0.131604\pi\) | |||||||
\(332\) | 6.06218 | − | 3.50000i | 0.332705 | − | 0.192087i | ||||
\(333\) | −3.46410 | + | 2.00000i | −0.189832 | + | 0.109599i | ||||
\(334\) | −7.00000 | + | 12.1244i | −0.383023 | + | 0.663415i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | + | 2.59808i | −0.0272772 | + | 0.141737i | ||||
\(337\) | − | 9.00000i | − | 0.490261i | −0.969490 | − | 0.245131i | \(-0.921169\pi\) | ||
0.969490 | − | 0.245131i | \(-0.0788309\pi\) | |||||||
\(338\) | 11.2583 | + | 6.50000i | 0.612372 | + | 0.353553i | ||||
\(339\) | −8.00000 | − | 13.8564i | −0.434500 | − | 0.752577i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.50000 | + | 12.9904i | −0.406148 | + | 0.703469i | ||||
\(342\) | − | 8.00000i | − | 0.432590i | ||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0000 | − | 19.0526i | −0.591364 | − | 1.02427i | ||||
\(347\) | −10.3923 | + | 6.00000i | −0.557888 | + | 0.322097i | −0.752297 | − | 0.658824i | \(-0.771054\pi\) |
0.194409 | + | 0.980921i | \(0.437721\pi\) | |||||||
\(348\) | −4.33013 | − | 2.50000i | −0.232119 | − | 0.134014i | ||||
\(349\) | 14.0000 | 0.749403 | 0.374701 | − | 0.927146i | \(-0.377745\pi\) | ||||
0.374701 | + | 0.927146i | \(0.377745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.33013 | + | 2.50000i | 0.230797 | + | 0.133250i | ||||
\(353\) | 20.7846 | − | 12.0000i | 1.10625 | − | 0.638696i | 0.168397 | − | 0.985719i | \(-0.446141\pi\) |
0.937856 | + | 0.347024i | \(0.112808\pi\) | |||||||
\(354\) | 5.50000 | + | 9.52628i | 0.292322 | + | 0.506316i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 6.92820 | − | 8.00000i | 0.366679 | − | 0.423405i | ||||
\(358\) | 12.0000i | 0.634220i | ||||||||
\(359\) | 5.00000 | − | 8.66025i | 0.263890 | − | 0.457071i | −0.703382 | − | 0.710812i | \(-0.748328\pi\) |
0.967272 | + | 0.253741i | \(0.0816611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 14.0000i | − | 0.734809i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | −14.7224 | + | 8.50000i | −0.768505 | + | 0.443696i | −0.832341 | − | 0.554264i | \(-0.813000\pi\) |
0.0638362 | + | 0.997960i | \(0.479666\pi\) | |||||||
\(368\) | −3.46410 | + | 2.00000i | −0.180579 | + | 0.104257i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.5000 | − | 7.79423i | 1.16814 | − | 0.404656i | ||||
\(372\) | 3.00000i | 0.155543i | ||||||||
\(373\) | 27.7128 | + | 16.0000i | 1.43492 | + | 0.828449i | 0.997490 | − | 0.0708063i | \(-0.0225572\pi\) |
0.437425 | + | 0.899255i | \(0.355891\pi\) | |||||||
\(374\) | −10.0000 | − | 17.3205i | −0.517088 | − | 0.895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | − | 5.19615i | 0.154713 | − | 0.267971i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.73205 | − | 2.00000i | 0.0890871 | − | 0.102869i | ||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.50000 | + | 7.79423i | 0.230542 | + | 0.399310i | ||||
\(382\) | −20.7846 | + | 12.0000i | −1.06343 | + | 0.613973i | ||||
\(383\) | 29.4449 | + | 17.0000i | 1.50456 | + | 0.868659i | 0.999986 | + | 0.00529229i | \(0.00168460\pi\) |
0.504576 | + | 0.863367i | \(0.331649\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.00000 | 0.254493 | ||||||||
\(387\) | 1.73205 | + | 1.00000i | 0.0880451 | + | 0.0508329i | ||||
\(388\) | 6.06218 | − | 3.50000i | 0.307760 | − | 0.177686i | ||||
\(389\) | −1.00000 | − | 1.73205i | −0.0507020 | − | 0.0878185i | 0.839561 | − | 0.543266i | \(-0.182813\pi\) |
−0.890263 | + | 0.455448i | \(0.849479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | −2.59808 | + | 6.50000i | −0.131223 | + | 0.328300i | ||||
\(393\) | − | 1.00000i | − | 0.0504433i | ||||||
\(394\) | 1.00000 | − | 1.73205i | 0.0503793 | − | 0.0872595i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.50000 | − | 4.33013i | −0.125630 | − | 0.217597i | ||||
\(397\) | 31.1769 | + | 18.0000i | 1.56472 | + | 0.903394i | 0.996768 | + | 0.0803356i | \(0.0255992\pi\) |
0.567957 | + | 0.823058i | \(0.307734\pi\) | |||||||
\(398\) | − | 4.00000i | − | 0.200502i | ||||||
\(399\) | 4.00000 | − | 20.7846i | 0.200250 | − | 1.04053i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.0000 | + | 20.7846i | −0.599251 | + | 1.03793i | 0.393680 | + | 0.919247i | \(0.371202\pi\) |
−0.992932 | + | 0.118686i | \(0.962132\pi\) | |||||||
\(402\) | −1.73205 | + | 1.00000i | −0.0863868 | + | 0.0498755i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 5.00000 | − | 8.66025i | 0.248759 | − | 0.430864i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.0000 | − | 8.66025i | −0.496292 | − | 0.429801i | ||||
\(407\) | 20.0000i | 0.991363i | ||||||||
\(408\) | −3.46410 | − | 2.00000i | −0.171499 | − | 0.0990148i | ||||
\(409\) | −12.5000 | − | 21.6506i | −0.618085 | − | 1.07056i | −0.989835 | − | 0.142222i | \(-0.954575\pi\) |
0.371750 | − | 0.928333i | \(-0.378758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.00000 | + | 1.73205i | −0.0493264 | + | 0.0854358i | ||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | 9.52628 | + | 27.5000i | 0.468758 | + | 1.35319i | ||||
\(414\) | 4.00000 | 0.196589 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.1244 | + | 7.00000i | −0.593732 | + | 0.342791i | ||||
\(418\) | −34.6410 | − | 20.0000i | −1.69435 | − | 0.978232i | ||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.0000 | 1.46211 | 0.731055 | − | 0.682318i | \(-0.239028\pi\) | ||||
0.731055 | + | 0.682318i | \(0.239028\pi\) | |||||||
\(422\) | 1.73205 | + | 1.00000i | 0.0843149 | + | 0.0486792i | ||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | −4.50000 | − | 7.79423i | −0.218539 | − | 0.378521i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.00000 | −0.0969003 | ||||||||
\(427\) | −10.3923 | + | 12.0000i | −0.502919 | + | 0.580721i | ||||
\(428\) | 3.00000i | 0.145010i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 14.0000i | 0.672797i | 0.941720 | + | 0.336399i | \(0.109209\pi\) | ||||
−0.941720 | + | 0.336399i | \(0.890791\pi\) | |||||||
\(434\) | −1.50000 | + | 7.79423i | −0.0720023 | + | 0.374135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | 27.7128 | − | 16.0000i | 1.32568 | − | 0.765384i | ||||
\(438\) | −8.66025 | + | 5.00000i | −0.413803 | + | 0.238909i | ||||
\(439\) | 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 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7224 | − | 8.50000i | −0.699484 | − | 0.403847i | 0.107671 | − | 0.994187i | \(-0.465661\pi\) |
−0.807155 | + | 0.590339i | \(0.798994\pi\) | |||||||
\(444\) | 2.00000 | + | 3.46410i | 0.0949158 | + | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.50000 | − | 6.06218i | 0.165730 | − | 0.287052i | ||||
\(447\) | − | 18.0000i | − | 0.851371i | ||||||
\(448\) | 2.59808 | + | 0.500000i | 0.122748 | + | 0.0236228i | ||||
\(449\) | −16.0000 | −0.755087 | −0.377543 | − | 0.925992i | \(-0.623231\pi\) | ||||
−0.377543 | + | 0.925992i | \(0.623231\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −13.8564 | + | 8.00000i | −0.651751 | + | 0.376288i | ||||
\(453\) | 16.4545 | + | 9.50000i | 0.773099 | + | 0.446349i | ||||
\(454\) | −3.00000 | −0.140797 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.00000 | −0.374634 | ||||||||
\(457\) | 26.8468 | + | 15.5000i | 1.25584 | + | 0.725059i | 0.972263 | − | 0.233890i | \(-0.0751456\pi\) |
0.283577 | + | 0.958950i | \(0.408479\pi\) | |||||||
\(458\) | −17.3205 | + | 10.0000i | −0.809334 | + | 0.467269i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.0000 | −0.652045 | −0.326023 | − | 0.945362i | \(-0.605709\pi\) | ||||
−0.326023 | + | 0.945362i | \(0.605709\pi\) | |||||||
\(462\) | −4.33013 | − | 12.5000i | −0.201456 | − | 0.581553i | ||||
\(463\) | 16.0000i | 0.743583i | 0.928316 | + | 0.371792i | \(0.121256\pi\) | ||||
−0.928316 | + | 0.371792i | \(0.878744\pi\) | |||||||
\(464\) | −2.50000 | + | 4.33013i | −0.116060 | + | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.00000 | + | 3.46410i | 0.0926482 | + | 0.160471i | ||||
\(467\) | −17.3205 | − | 10.0000i | −0.801498 | − | 0.462745i | 0.0424970 | − | 0.999097i | \(-0.486469\pi\) |
−0.843995 | + | 0.536352i | \(0.819802\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00000 | + | 1.73205i | −0.230879 | + | 0.0799787i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.00000 | + | 3.46410i | −0.0921551 | + | 0.159617i | ||||
\(472\) | 9.52628 | − | 5.50000i | 0.438483 | − | 0.253158i | ||||
\(473\) | 8.66025 | − | 5.00000i | 0.398199 | − | 0.229900i | ||||
\(474\) | −1.50000 | + | 2.59808i | −0.0688973 | + | 0.119334i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.00000 | − | 6.92820i | −0.366679 | − | 0.317554i | ||||
\(477\) | 9.00000i | 0.412082i | ||||||||
\(478\) | 10.3923 | + | 6.00000i | 0.475333 | + | 0.274434i | ||||
\(479\) | 19.0000 | + | 32.9090i | 0.868132 | + | 1.50365i | 0.863903 | + | 0.503658i | \(0.168013\pi\) |
0.00422900 | + | 0.999991i | \(0.498654\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 25.0000i | 1.13872i | ||||||||
\(483\) | 10.3923 | + | 2.00000i | 0.472866 | + | 0.0910032i | ||||
\(484\) | −14.0000 | −0.636364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | −4.33013 | + | 2.50000i | −0.196217 | + | 0.113286i | −0.594890 | − | 0.803807i | \(-0.702804\pi\) |
0.398673 | + | 0.917093i | \(0.369471\pi\) | |||||||
\(488\) | 5.19615 | + | 3.00000i | 0.235219 | + | 0.135804i | ||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | 0.406164 | 0.203082 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203082 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.3205 | − | 10.0000i | 0.780076 | − | 0.450377i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | −5.19615 | − | 1.00000i | −0.233079 | − | 0.0448561i | ||||
\(498\) | 7.00000i | 0.313678i | ||||||||
\(499\) | 5.00000 | − | 8.66025i | 0.223831 | − | 0.387686i | −0.732137 | − | 0.681157i | \(-0.761477\pi\) |
0.955968 | + | 0.293471i | \(0.0948104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.00000 | − | 12.1244i | −0.312737 | − | 0.541676i | ||||
\(502\) | 18.1865 | + | 10.5000i | 0.811705 | + | 0.468638i | ||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | −2.00000 | − | 1.73205i | −0.0890871 | − | 0.0771517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 10.0000 | − | 17.3205i | 0.444554 | − | 0.769991i | ||||
\(507\) | −11.2583 | + | 6.50000i | −0.500000 | + | 0.288675i | ||||
\(508\) | 7.79423 | − | 4.50000i | 0.345813 | − | 0.199655i | ||||
\(509\) | 7.50000 | − | 12.9904i | 0.332432 | − | 0.575789i | −0.650556 | − | 0.759458i | \(-0.725464\pi\) |
0.982988 | + | 0.183669i | \(0.0587976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.0000 | + | 8.66025i | −1.10593 | + | 0.383107i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 6.92820 | + | 4.00000i | 0.305888 | + | 0.176604i | ||||
\(514\) | −3.00000 | − | 5.19615i | −0.132324 | − | 0.229192i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.00000 | − | 1.73205i | 0.0440225 | − | 0.0762493i | ||||
\(517\) | 30.0000i | 1.31940i | ||||||||
\(518\) | 3.46410 | + | 10.0000i | 0.152204 | + | 0.439375i | ||||
\(519\) | 22.0000 | 0.965693 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.00000 | + | 15.5885i | 0.394297 | + | 0.682943i | 0.993011 | − | 0.118020i | \(-0.0376547\pi\) |
−0.598714 | + | 0.800963i | \(0.704321\pi\) | |||||||
\(522\) | 4.33013 | − | 2.50000i | 0.189525 | − | 0.109422i | ||||
\(523\) | −6.92820 | − | 4.00000i | −0.302949 | − | 0.174908i | 0.340818 | − | 0.940129i | \(-0.389296\pi\) |
−0.643767 | + | 0.765222i | \(0.722629\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −30.0000 | −1.30806 | ||||||||
\(527\) | −10.3923 | − | 6.00000i | −0.452696 | − | 0.261364i | ||||
\(528\) | −4.33013 | + | 2.50000i | −0.188445 | + | 0.108799i | ||||
\(529\) | −3.50000 | − | 6.06218i | −0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0000 | −0.477359 | ||||||||
\(532\) | −20.7846 | − | 4.00000i | −0.901127 | − | 0.173422i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.00000 | − | 5.19615i | 0.129823 | − | 0.224860i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | −10.3923 | − | 6.00000i | −0.448461 | − | 0.258919i | ||||
\(538\) | 31.0000i | 1.33650i | ||||||||
\(539\) | −5.00000 | − | 34.6410i | −0.215365 | − | 1.49209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | − | 15.5885i | 0.386940 | − | 0.670200i | −0.605096 | − | 0.796152i | \(-0.706865\pi\) |
0.992036 | + | 0.125952i | \(0.0401986\pi\) | |||||||
\(542\) | −12.9904 | + | 7.50000i | −0.557985 | + | 0.322153i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.00000 | + | 3.46410i | −0.0857493 | + | 0.148522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.0000i | 0.513083i | 0.966533 | + | 0.256541i | \(0.0825830\pi\) | ||||
−0.966533 | + | 0.256541i | \(0.917417\pi\) | |||||||
\(548\) | 1.73205 | + | 1.00000i | 0.0739895 | + | 0.0427179i | ||||
\(549\) | −3.00000 | − | 5.19615i | −0.128037 | − | 0.221766i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0000 | − | 34.6410i | 0.852029 | − | 1.47576i | ||||
\(552\) | − | 4.00000i | − | 0.170251i | ||||||
\(553\) | −5.19615 | + | 6.00000i | −0.220963 | + | 0.255146i | ||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.00000 | + | 12.1244i | 0.296866 | + | 0.514187i | ||||
\(557\) | 19.9186 | − | 11.5000i | 0.843978 | − | 0.487271i | −0.0146368 | − | 0.999893i | \(-0.504659\pi\) |
0.858614 | + | 0.512622i | \(0.171326\pi\) | |||||||
\(558\) | −2.59808 | − | 1.50000i | −0.109985 | − | 0.0635001i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.0000 | 0.844401 | ||||||||
\(562\) | 1.73205 | + | 1.00000i | 0.0730622 | + | 0.0421825i | ||||
\(563\) | 14.7224 | − | 8.50000i | 0.620477 | − | 0.358232i | −0.156578 | − | 0.987666i | \(-0.550046\pi\) |
0.777055 | + | 0.629433i | \(0.216713\pi\) | |||||||
\(564\) | 3.00000 | + | 5.19615i | 0.126323 | + | 0.218797i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 10.0000 | 0.420331 | ||||||||
\(567\) | 0.866025 | + | 2.50000i | 0.0363696 | + | 0.104990i | ||||
\(568\) | 2.00000i | 0.0839181i | ||||||||
\(569\) | 12.0000 | − | 20.7846i | 0.503066 | − | 0.871336i | −0.496928 | − | 0.867792i | \(-0.665539\pi\) |
0.999994 | − | 0.00354413i | \(-0.00112814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0000 | + | 25.9808i | 0.627730 | + | 1.08726i | 0.988006 | + | 0.154415i | \(0.0493493\pi\) |
−0.360276 | + | 0.932846i | \(0.617317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 24.0000i | − | 1.00261i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −26.8468 | + | 15.5000i | −1.11765 | + | 0.645273i | −0.940799 | − | 0.338965i | \(-0.889923\pi\) |
−0.176847 | + | 0.984238i | \(0.556590\pi\) | |||||||
\(578\) | −0.866025 | + | 0.500000i | −0.0360219 | + | 0.0207973i | ||||
\(579\) | −2.50000 | + | 4.33013i | −0.103896 | + | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50000 | + | 18.1865i | −0.145204 | + | 0.754505i | ||||
\(582\) | 7.00000i | 0.290159i | ||||||||
\(583\) | 38.9711 | + | 22.5000i | 1.61402 | + | 0.931855i | ||||
\(584\) | 5.00000 | + | 8.66025i | 0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.5000 | − | 18.1865i | 0.433751 | − | 0.751279i | ||||
\(587\) | − | 35.0000i | − | 1.44460i | −0.691577 | − | 0.722302i | \(-0.743084\pi\) | ||
0.691577 | − | 0.722302i | \(-0.256916\pi\) | |||||||
\(588\) | −4.33013 | − | 5.50000i | −0.178571 | − | 0.226816i | ||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.00000 | + | 1.73205i | 0.0411345 | + | 0.0712470i | ||||
\(592\) | 3.46410 | − | 2.00000i | 0.142374 | − | 0.0821995i | ||||
\(593\) | −31.1769 | − | 18.0000i | −1.28028 | − | 0.739171i | −0.303383 | − | 0.952869i | \(-0.598116\pi\) |
−0.976900 | + | 0.213697i | \(0.931449\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 3.46410 | + | 2.00000i | 0.141776 | + | 0.0818546i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.0000 | − | 25.9808i | −0.612883 | − | 1.06155i | −0.990752 | − | 0.135686i | \(-0.956676\pi\) |
0.377869 | − | 0.925859i | \(-0.376657\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.0000 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | 3.46410 | − | 4.00000i | 0.141186 | − | 0.163028i | ||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | 9.50000 | − | 16.4545i | 0.386550 | − | 0.669523i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.00000 | + | 8.66025i | 0.203111 | + | 0.351799i | ||||
\(607\) | −23.3827 | − | 13.5000i | −0.949074 | − | 0.547948i | −0.0562808 | − | 0.998415i | \(-0.517924\pi\) |
−0.892793 | + | 0.450467i | \(0.851258\pi\) | |||||||
\(608\) | 8.00000i | 0.324443i | ||||||||
\(609\) | 12.5000 | − | 4.33013i | 0.506526 | − | 0.175466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 3.46410 | − | 2.00000i | 0.140028 | − | 0.0808452i | ||||
\(613\) | 10.3923 | − | 6.00000i | 0.419741 | − | 0.242338i | −0.275225 | − | 0.961380i | \(-0.588752\pi\) |
0.694967 | + | 0.719042i | \(0.255419\pi\) | |||||||
\(614\) | 14.0000 | − | 24.2487i | 0.564994 | − | 0.978598i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.5000 | + | 4.33013i | −0.503639 | + | 0.174466i | ||||
\(617\) | − | 2.00000i | − | 0.0805170i | −0.999189 | − | 0.0402585i | \(-0.987182\pi\) | ||
0.999189 | − | 0.0402585i | \(-0.0128181\pi\) | |||||||
\(618\) | 6.92820 | + | 4.00000i | 0.278693 | + | 0.160904i | ||||
\(619\) | 5.00000 | + | 8.66025i | 0.200967 | + | 0.348085i | 0.948840 | − | 0.315757i | \(-0.102258\pi\) |
−0.747873 | + | 0.663842i | \(0.768925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | 32.0000i | 1.28308i | ||||||||
\(623\) | 10.3923 | − | 12.0000i | 0.416359 | − | 0.480770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.500000 | − | 0.866025i | −0.0199840 | − | 0.0346133i | ||||
\(627\) | 34.6410 | − | 20.0000i | 1.38343 | − | 0.798723i | ||||
\(628\) | 3.46410 | + | 2.00000i | 0.138233 | + | 0.0798087i | ||||
\(629\) | −16.0000 | −0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0000 | −0.756378 | −0.378189 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378189 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(632\) | 2.59808 | + | 1.50000i | 0.103346 | + | 0.0596668i | ||||
\(633\) | −1.73205 | + | 1.00000i | −0.0688428 | + | 0.0397464i | ||||
\(634\) | 1.50000 | + | 2.59808i | 0.0595726 | + | 0.103183i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 25.0000i | − | 0.989759i | ||||||
\(639\) | 1.00000 | − | 1.73205i | 0.0395594 | − | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0000 | − | 22.5167i | −0.513469 | − | 0.889355i | −0.999878 | − | 0.0156233i | \(-0.995027\pi\) |
0.486409 | − | 0.873731i | \(-0.338307\pi\) | |||||||
\(642\) | −2.59808 | − | 1.50000i | −0.102538 | − | 0.0592003i | ||||
\(643\) | 14.0000i | 0.552106i | 0.961142 | + | 0.276053i | \(0.0890266\pi\) | ||||
−0.961142 | + | 0.276053i | \(0.910973\pi\) | |||||||
\(644\) | 2.00000 | − | 10.3923i | 0.0788110 | − | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.0000 | − | 27.7128i | 0.629512 | − | 1.09035i | ||||
\(647\) | 15.5885 | − | 9.00000i | 0.612845 | − | 0.353827i | −0.161233 | − | 0.986916i | \(-0.551547\pi\) |
0.774078 | + | 0.633090i | \(0.218214\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −27.5000 | + | 47.6314i | −1.07947 | + | 1.86970i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | − | 5.19615i | −0.235159 | − | 0.203653i | ||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | 33.7750 | + | 19.5000i | 1.32172 | + | 0.763094i | 0.984003 | − | 0.178154i | \(-0.0570127\pi\) |
0.337715 | + | 0.941248i | \(0.390346\pi\) | |||||||
\(654\) | 1.00000 | + | 1.73205i | 0.0391031 | + | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 5.19615 | + | 15.0000i | 0.202567 | + | 0.584761i | ||||
\(659\) | 40.0000 | 1.55818 | 0.779089 | − | 0.626913i | \(-0.215682\pi\) | ||||
0.779089 | + | 0.626913i | \(0.215682\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | − | 8.66025i | −0.194477 | − | 0.336845i | 0.752252 | − | 0.658876i | \(-0.228968\pi\) |
−0.946729 | + | 0.322031i | \(0.895634\pi\) | |||||||
\(662\) | 3.46410 | − | 2.00000i | 0.134636 | − | 0.0777322i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.00000 | 0.271653 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | −0.154997 | ||||||||
\(667\) | 17.3205 | + | 10.0000i | 0.670653 | + | 0.387202i | ||||
\(668\) | −12.1244 | + | 7.00000i | −0.469105 | + | 0.270838i | ||||
\(669\) | 3.50000 | + | 6.06218i | 0.135318 | + | 0.234377i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.0000 | −1.15814 | ||||||||
\(672\) | −1.73205 | + | 2.00000i | −0.0668153 | + | 0.0771517i | ||||
\(673\) | − | 19.0000i | − | 0.732396i | −0.930537 | − | 0.366198i | \(-0.880659\pi\) | ||
0.930537 | − | 0.366198i | \(-0.119341\pi\) | |||||||
\(674\) | 4.50000 | − | 7.79423i | 0.173334 | − | 0.300222i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.50000 | + | 11.2583i | 0.250000 | + | 0.433013i | ||||
\(677\) | −23.3827 | − | 13.5000i | −0.898670 | − | 0.518847i | −0.0219013 | − | 0.999760i | \(-0.506972\pi\) |
−0.876768 | + | 0.480913i | \(0.840305\pi\) | |||||||
\(678\) | − | 16.0000i | − | 0.614476i | ||||||
\(679\) | −3.50000 | + | 18.1865i | −0.134318 | + | 0.697935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50000 | − | 2.59808i | 0.0574801 | − | 0.0995585i | ||||
\(682\) | −12.9904 | + | 7.50000i | −0.497427 | + | 0.287190i | ||||
\(683\) | −7.79423 | + | 4.50000i | −0.298238 | + | 0.172188i | −0.641651 | − | 0.766997i | \(-0.721750\pi\) |
0.343413 | + | 0.939184i | \(0.388417\pi\) | |||||||
\(684\) | 4.00000 | − | 6.92820i | 0.152944 | − | 0.264906i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | − | 20.0000i | − | 0.763048i | ||||||
\(688\) | −1.73205 | − | 1.00000i | −0.0660338 | − | 0.0381246i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | − | 22.0000i | − | 0.836315i | ||||||
\(693\) | 12.9904 | + | 2.50000i | 0.493464 | + | 0.0949671i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.50000 | − | 4.33013i | −0.0947623 | − | 0.164133i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 12.1244 | + | 7.00000i | 0.458914 | + | 0.264954i | ||||
\(699\) | −4.00000 | −0.151294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.00000 | −0.188847 | −0.0944237 | − | 0.995532i | \(-0.530101\pi\) | ||||
−0.0944237 | + | 0.995532i | \(0.530101\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.7128 | + | 16.0000i | −1.04521 | + | 0.603451i | ||||
\(704\) | 2.50000 | + | 4.33013i | 0.0942223 | + | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 8.66025 | + | 25.0000i | 0.325702 | + | 0.940222i | ||||
\(708\) | 11.0000i | 0.413405i | ||||||||
\(709\) | 19.0000 | − | 32.9090i | 0.713560 | − | 1.23592i | −0.249952 | − | 0.968258i | \(-0.580415\pi\) |
0.963512 | − | 0.267664i | \(-0.0862517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.50000 | − | 2.59808i | −0.0562544 | − | 0.0974355i | ||||
\(712\) | −5.19615 | − | 3.00000i | −0.194734 | − | 0.112430i | ||||
\(713\) | − | 12.0000i | − | 0.449404i | ||||||
\(714\) | 10.0000 | − | 3.46410i | 0.374241 | − | 0.129641i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.00000 | + | 10.3923i | −0.224231 | + | 0.388379i | ||||
\(717\) | −10.3923 | + | 6.00000i | −0.388108 | + | 0.224074i | ||||
\(718\) | 8.66025 | − | 5.00000i | 0.323198 | − | 0.186598i | ||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.0000 | + | 13.8564i | 0.595871 | + | 0.516040i | ||||
\(722\) | − | 45.0000i | − | 1.67473i | ||||||
\(723\) | −21.6506 | − | 12.5000i | −0.805196 | − | 0.464880i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | − | 7.00000i | − | 0.259616i | −0.991539 | − | 0.129808i | \(-0.958564\pi\) | ||
0.991539 | − | 0.129808i | \(-0.0414360\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | −5.19615 | + | 3.00000i | −0.192055 | + | 0.110883i | ||||
\(733\) | 5.19615 | + | 3.00000i | 0.191924 | + | 0.110808i | 0.592883 | − | 0.805289i | \(-0.297990\pi\) |
−0.400959 | + | 0.916096i | \(0.631323\pi\) | |||||||
\(734\) | −17.0000 | −0.627481 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −8.66025 | − | 5.00000i | −0.319005 | − | 0.184177i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0000 | − | 25.9808i | −0.551784 | − | 0.955718i | −0.998146 | − | 0.0608653i | \(-0.980614\pi\) |
0.446362 | − | 0.894852i | \(-0.352719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23.3827 | + | 4.50000i | 0.858405 | + | 0.165200i | ||||
\(743\) | 30.0000i | 1.10059i | 0.834969 | + | 0.550297i | \(0.185485\pi\) | ||||
−0.834969 | + | 0.550297i | \(0.814515\pi\) | |||||||
\(744\) | −1.50000 | + | 2.59808i | −0.0549927 | + | 0.0952501i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.0000 | + | 27.7128i | 0.585802 | + | 1.01464i | ||||
\(747\) | −6.06218 | − | 3.50000i | −0.221803 | − | 0.128058i | ||||
\(748\) | − | 20.0000i | − | 0.731272i | ||||||
\(749\) | −6.00000 | − | 5.19615i | −0.219235 | − | 0.189863i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5000 | + | 38.9711i | −0.821037 | + | 1.42208i | 0.0838743 | + | 0.996476i | \(0.473271\pi\) |
−0.904911 | + | 0.425601i | \(0.860063\pi\) | |||||||
\(752\) | 5.19615 | − | 3.00000i | 0.189484 | − | 0.109399i | ||||
\(753\) | −18.1865 | + | 10.5000i | −0.662754 | + | 0.382641i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.50000 | − | 0.866025i | 0.0909241 | − | 0.0314970i | ||||
\(757\) | 54.0000i | 1.96266i | 0.192323 | + | 0.981332i | \(0.438398\pi\) | ||||
−0.192323 | + | 0.981332i | \(0.561602\pi\) | |||||||
\(758\) | −13.8564 | − | 8.00000i | −0.503287 | − | 0.290573i | ||||
\(759\) | 10.0000 | + | 17.3205i | 0.362977 | + | 0.628695i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.00000 | + | 6.92820i | −0.145000 | + | 0.251147i | −0.929373 | − | 0.369142i | \(-0.879652\pi\) |
0.784373 | + | 0.620289i | \(0.212985\pi\) | |||||||
\(762\) | 9.00000i | 0.326036i | ||||||||
\(763\) | 1.73205 | + | 5.00000i | 0.0627044 | + | 0.181012i | ||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.0000 | + | 29.4449i | 0.614235 | + | 1.06389i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 35.0000 | 1.26213 | 0.631066 | − | 0.775729i | \(-0.282618\pi\) | ||||
0.631066 | + | 0.775729i | \(0.282618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | 4.33013 | + | 2.50000i | 0.155845 | + | 0.0899770i | ||||
\(773\) | 8.66025 | − | 5.00000i | 0.311488 | − | 0.179838i | −0.336104 | − | 0.941825i | \(-0.609109\pi\) |
0.647592 | + | 0.761987i | \(0.275776\pi\) | |||||||
\(774\) | 1.00000 | + | 1.73205i | 0.0359443 | + | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.00000 | 0.251285 | ||||||||
\(777\) | −10.3923 | − | 2.00000i | −0.372822 | − | 0.0717496i | ||||
\(778\) | − | 2.00000i | − | 0.0717035i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | − | 8.66025i | −0.178914 | − | 0.309888i | ||||
\(782\) | 13.8564 | + | 8.00000i | 0.495504 | + | 0.286079i | ||||
\(783\) | 5.00000i | 0.178685i | ||||||||
\(784\) | −5.50000 | + | 4.33013i | −0.196429 | + | 0.154647i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.500000 | − | 0.866025i | 0.0178344 | − | 0.0308901i | ||||
\(787\) | 15.5885 | − | 9.00000i | 0.555668 | − | 0.320815i | −0.195737 | − | 0.980656i | \(-0.562710\pi\) |
0.751405 | + | 0.659841i | \(0.229376\pi\) | |||||||
\(788\) | 1.73205 | − | 1.00000i | 0.0617018 | − | 0.0356235i | ||||
\(789\) | 15.0000 | − | 25.9808i | 0.534014 | − | 0.924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.00000 | − | 41.5692i | 0.284447 | − | 1.47803i | ||||
\(792\) | − | 5.00000i | − | 0.177667i | ||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.0000 | + | 31.1769i | 0.638796 | + | 1.10643i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | − | 3.46410i | 0.0708881 | − | 0.122782i | ||||
\(797\) | − | 21.0000i | − | 0.743858i | −0.928261 | − | 0.371929i | \(-0.878696\pi\) | ||
0.928261 | − | 0.371929i | \(-0.121304\pi\) | |||||||
\(798\) | 13.8564 | − | 16.0000i | 0.490511 | − | 0.566394i | ||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.00000 | + | 5.19615i | 0.106000 | + | 0.183597i | ||||
\(802\) | −20.7846 | + | 12.0000i | −0.733930 | + | 0.423735i | ||||
\(803\) | −43.3013 | − | 25.0000i | −1.52807 | − | 0.882231i | ||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.8468 | − | 15.5000i | −0.945052 | − | 0.545626i | ||||
\(808\) | 8.66025 | − | 5.00000i | 0.304667 | − | 0.175899i | ||||
\(809\) | 20.0000 | + | 34.6410i | 0.703163 | + | 1.21791i | 0.967351 | + | 0.253442i | \(0.0815627\pi\) |
−0.264188 | + | 0.964471i | \(0.585104\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.0000 | −0.491606 | −0.245803 | − | 0.969320i | \(-0.579052\pi\) | ||||
−0.245803 | + | 0.969320i | \(0.579052\pi\) | |||||||
\(812\) | −4.33013 | − | 12.5000i | −0.151958 | − | 0.438664i | ||||
\(813\) | − | 15.0000i | − | 0.526073i | ||||||
\(814\) | −10.0000 | + | 17.3205i | −0.350500 | + | 0.607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.00000 | − | 3.46410i | −0.0700140 | − | 0.121268i | ||||
\(817\) | 13.8564 | + | 8.00000i | 0.484774 | + | 0.279885i | ||||
\(818\) | − | 25.0000i | − | 0.874105i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5000 | − | 21.6506i | 0.436253 | − | 0.755612i | −0.561144 | − | 0.827718i | \(-0.689639\pi\) |
0.997397 | + | 0.0721058i | \(0.0229719\pi\) | |||||||
\(822\) | −1.73205 | + | 1.00000i | −0.0604122 | + | 0.0348790i | ||||
\(823\) | 34.6410 | − | 20.0000i | 1.20751 | − | 0.697156i | 0.245295 | − | 0.969448i | \(-0.421115\pi\) |
0.962215 | + | 0.272292i | \(0.0877817\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.50000 | + | 28.5788i | −0.191369 | + | 0.994385i | ||||
\(827\) | − | 9.00000i | − | 0.312961i | −0.987681 | − | 0.156480i | \(-0.949985\pi\) | ||
0.987681 | − | 0.156480i | \(-0.0500148\pi\) | |||||||
\(828\) | 3.46410 | + | 2.00000i | 0.120386 | + | 0.0695048i | ||||
\(829\) | −16.0000 | − | 27.7128i | −0.555703 | − | 0.962506i | −0.997848 | − | 0.0655624i | \(-0.979116\pi\) |
0.442145 | − | 0.896943i | \(-0.354217\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | + | 13.8564i | −0.277517 | + | 0.480673i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.7128 | − | 4.00000i | 0.960192 | − | 0.138592i | ||||
\(834\) | −14.0000 | −0.484780 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −20.0000 | − | 34.6410i | −0.691714 | − | 1.19808i | ||||
\(837\) | 2.59808 | − | 1.50000i | 0.0898027 | − | 0.0518476i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 28.0000 | 0.966667 | 0.483334 | − | 0.875436i | \(-0.339426\pi\) | ||||
0.483334 | + | 0.875436i | \(0.339426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 25.9808 | + | 15.0000i | 0.895356 | + | 0.516934i | ||||
\(843\) | −1.73205 | + | 1.00000i | −0.0596550 | + | 0.0344418i | ||||
\(844\) | 1.00000 | + | 1.73205i | 0.0344214 | + | 0.0596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 24.2487 | − | 28.0000i | 0.833196 | − | 0.962091i | ||||
\(848\) | − | 9.00000i | − | 0.309061i | ||||||
\(849\) | −5.00000 | + | 8.66025i | −0.171600 | + | 0.297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | − | 13.8564i | −0.274236 | − | 0.474991i | ||||
\(852\) | −1.73205 | − | 1.00000i | −0.0593391 | − | 0.0342594i | ||||
\(853\) | 14.0000i | 0.479351i | 0.970853 | + | 0.239675i | \(0.0770410\pi\) | ||||
−0.970853 | + | 0.239675i | \(0.922959\pi\) | |||||||
\(854\) | −15.0000 | + | 5.19615i | −0.513289 | + | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | + | 2.59808i | −0.0512689 | + | 0.0888004i | ||||
\(857\) | 15.5885 | − | 9.00000i | 0.532492 | − | 0.307434i | −0.209539 | − | 0.977800i | \(-0.567196\pi\) |
0.742030 | + | 0.670366i | \(0.233863\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0000 | + | 29.4449i | −0.580033 | + | 1.00465i | 0.415442 | + | 0.909620i | \(0.363627\pi\) |
−0.995475 | + | 0.0950262i | \(0.969707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 12.0000i | − | 0.408722i | ||||||
\(863\) | −8.66025 | − | 5.00000i | −0.294798 | − | 0.170202i | 0.345305 | − | 0.938490i | \(-0.387775\pi\) |
−0.640104 | + | 0.768288i | \(0.721109\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.00000 | + | 12.1244i | −0.237870 | + | 0.412002i | ||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | −5.19615 | + | 6.00000i | −0.176369 | + | 0.203653i | ||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 1.73205 | − | 1.00000i | 0.0586546 | − | 0.0338643i | ||||
\(873\) | −6.06218 | − | 3.50000i | −0.205174 | − | 0.118457i | ||||
\(874\) | 32.0000 | 1.08242 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | −27.7128 | − | 16.0000i | −0.935795 | − | 0.540282i | −0.0471555 | − | 0.998888i | \(-0.515016\pi\) |
−0.888640 | + | 0.458606i | \(0.848349\pi\) | |||||||
\(878\) | 12.9904 | − | 7.50000i | 0.438404 | − | 0.253113i | ||||
\(879\) | 10.5000 | + | 18.1865i | 0.354156 | + | 0.613417i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 6.92820 | − | 1.00000i | 0.233285 | − | 0.0336718i | ||||
\(883\) | − | 40.0000i | − | 1.34611i | −0.739594 | − | 0.673054i | \(-0.764982\pi\) | ||
0.739594 | − | 0.673054i | \(-0.235018\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.50000 | − | 14.7224i | −0.285563 | − | 0.494610i | ||||
\(887\) | 31.1769 | + | 18.0000i | 1.04682 | + | 0.604381i | 0.921757 | − | 0.387768i | \(-0.126754\pi\) |
0.125061 | + | 0.992149i | \(0.460087\pi\) | |||||||
\(888\) | 4.00000i | 0.134231i | ||||||||
\(889\) | −4.50000 | + | 23.3827i | −0.150925 | + | 0.784230i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.50000 | + | 4.33013i | −0.0837532 | + | 0.145065i | ||||
\(892\) | 6.06218 | − | 3.50000i | 0.202977 | − | 0.117189i | ||||
\(893\) | −41.5692 | + | 24.0000i | −1.39106 | + | 0.803129i | ||||
\(894\) | 9.00000 | − | 15.5885i | 0.301005 | − | 0.521356i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | + | 1.73205i | 0.0668153 | + | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.8564 | − | 8.00000i | −0.462394 | − | 0.266963i | ||||
\(899\) | −7.50000 | − | 12.9904i | −0.250139 | − | 0.433253i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.0000 | + | 31.1769i | −0.599667 | + | 1.03865i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.73205 | + | 5.00000i | 0.0576390 | + | 0.166390i | ||||
\(904\) | −16.0000 | −0.532152 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9.50000 | + | 16.4545i | 0.315616 | + | 0.546664i | ||||
\(907\) | −10.3923 | + | 6.00000i | −0.345071 | + | 0.199227i | −0.662512 | − | 0.749051i | \(-0.730510\pi\) |
0.317441 | + | 0.948278i | \(0.397176\pi\) | |||||||
\(908\) | −2.59808 | − | 1.50000i | −0.0862202 | − | 0.0497792i | ||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −6.92820 | − | 4.00000i | −0.229416 | − | 0.132453i | ||||
\(913\) | −30.3109 | + | 17.5000i | −1.00314 | + | 0.579165i | ||||
\(914\) | 15.5000 | + | 26.8468i | 0.512694 | + | 0.888013i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | 1.73205 | − | 2.00000i | 0.0571974 | − | 0.0660458i | ||||
\(918\) | 4.00000i | 0.132020i | ||||||||
\(919\) | −16.0000 | + | 27.7128i | −0.527791 | + | 0.914161i | 0.471684 | + | 0.881768i | \(0.343646\pi\) |
−0.999475 | + | 0.0323936i | \(0.989687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0000 | + | 24.2487i | 0.461316 | + | 0.799022i | ||||
\(922\) | −12.1244 | − | 7.00000i | −0.399294 | − | 0.230533i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.50000 | − | 12.9904i | 0.0822440 | − | 0.427352i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.00000 | + | 13.8564i | −0.262896 | + | 0.455350i | ||||
\(927\) | −6.92820 | + | 4.00000i | −0.227552 | + | 0.131377i | ||||
\(928\) | −4.33013 | + | 2.50000i | −0.142143 | + | 0.0820665i | ||||
\(929\) | −3.00000 | + | 5.19615i | −0.0984268 | + | 0.170480i | −0.911034 | − | 0.412332i | \(-0.864714\pi\) |
0.812607 | + | 0.582812i | \(0.198048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 44.0000 | − | 34.6410i | 1.44204 | − | 1.13531i | ||||
\(932\) | 4.00000i | 0.131024i | ||||||||
\(933\) | −27.7128 | − | 16.0000i | −0.907277 | − | 0.523816i | ||||
\(934\) | −10.0000 | − | 17.3205i | −0.327210 | − | 0.566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 35.0000i | − | 1.14340i | −0.820463 | − | 0.571700i | \(-0.806284\pi\) | ||
0.820463 | − | 0.571700i | \(-0.193716\pi\) | |||||||
\(938\) | −5.19615 | − | 1.00000i | −0.169660 | − | 0.0326512i | ||||
\(939\) | 1.00000 | 0.0326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.50000 | + | 9.52628i | 0.179295 | + | 0.310548i | 0.941639 | − | 0.336624i | \(-0.109285\pi\) |
−0.762344 | + | 0.647172i | \(0.775952\pi\) | |||||||
\(942\) | −3.46410 | + | 2.00000i | −0.112867 | + | 0.0651635i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 11.0000 | 0.358020 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000 | 0.325128 | ||||||||
\(947\) | −27.7128 | − | 16.0000i | −0.900545 | − | 0.519930i | −0.0231683 | − | 0.999732i | \(-0.507375\pi\) |
−0.877377 | + | 0.479801i | \(0.840709\pi\) | |||||||
\(948\) | −2.59808 | + | 1.50000i | −0.0843816 | + | 0.0487177i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.00000 | −0.0972817 | ||||||||
\(952\) | −3.46410 | − | 10.0000i | −0.112272 | − | 0.324102i | ||||
\(953\) | 2.00000i | 0.0647864i | 0.999475 | + | 0.0323932i | \(0.0103129\pi\) | ||||
−0.999475 | + | 0.0323932i | \(0.989687\pi\) | |||||||
\(954\) | −4.50000 | + | 7.79423i | −0.145693 | + | 0.252347i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.00000 | + | 10.3923i | 0.194054 | + | 0.336111i | ||||
\(957\) | 21.6506 | + | 12.5000i | 0.699866 | + | 0.404068i | ||||
\(958\) | 38.0000i | 1.22772i | ||||||||
\(959\) | −5.00000 | + | 1.73205i | −0.161458 | + | 0.0559308i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.59808 | − | 1.50000i | 0.0837218 | − | 0.0483368i | ||||
\(964\) | −12.5000 | + | 21.6506i | −0.402598 | + | 0.697320i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.00000 | + | 6.92820i | 0.257396 | + | 0.222911i | ||||
\(967\) | 61.0000i | 1.96163i | 0.194946 | + | 0.980814i | \(0.437547\pi\) | ||||
−0.194946 | + | 0.980814i | \(0.562453\pi\) | |||||||
\(968\) | −12.1244 | − | 7.00000i | −0.389692 | − | 0.224989i | ||||
\(969\) | 16.0000 | + | 27.7128i | 0.513994 | + | 0.890264i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.50000 | + | 12.9904i | −0.240686 | + | 0.416881i | −0.960910 | − | 0.276861i | \(-0.910706\pi\) |
0.720224 | + | 0.693742i | \(0.244039\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | −36.3731 | − | 7.00000i | −1.16607 | − | 0.224410i | ||||
\(974\) | −5.00000 | −0.160210 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.00000 | + | 5.19615i | 0.0960277 | + | 0.166325i | ||||
\(977\) | 25.9808 | − | 15.0000i | 0.831198 | − | 0.479893i | −0.0230645 | − | 0.999734i | \(-0.507342\pi\) |
0.854263 | + | 0.519841i | \(0.174009\pi\) | |||||||
\(978\) | −3.46410 | − | 2.00000i | −0.110770 | − | 0.0639529i | ||||
\(979\) | 30.0000 | 0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 7.79423 | + | 4.50000i | 0.248724 | + | 0.143601i | ||||
\(983\) | −51.9615 | + | 30.0000i | −1.65732 | + | 0.956851i | −0.683369 | + | 0.730073i | \(0.739486\pi\) |
−0.973946 | + | 0.226778i | \(0.927181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 20.0000 | 0.636930 | ||||||||
\(987\) | −15.5885 | − | 3.00000i | −0.496186 | − | 0.0954911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | + | 6.92820i | −0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.5000 | − | 40.7032i | −0.746502 | − | 1.29298i | −0.949490 | − | 0.313798i | \(-0.898398\pi\) |
0.202988 | − | 0.979181i | \(-0.434935\pi\) | |||||||
\(992\) | 2.59808 | + | 1.50000i | 0.0824890 | + | 0.0476250i | ||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | −4.00000 | − | 3.46410i | −0.126872 | − | 0.109875i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.50000 | + | 6.06218i | −0.110902 | + | 0.192087i | ||||
\(997\) | −32.9090 | + | 19.0000i | −1.04224 | + | 0.601736i | −0.920466 | − | 0.390822i | \(-0.872191\pi\) |
−0.121771 | + | 0.992558i | \(0.538857\pi\) | |||||||
\(998\) | 8.66025 | − | 5.00000i | 0.274136 | − | 0.158272i | ||||
\(999\) | 2.00000 | − | 3.46410i | 0.0632772 | − | 0.109599i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))