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 | 949.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.949 |
Dual form | 1050.2.o.a.499.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 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 | 0.192201 | + | 0.981356i | \(0.438437\pi\) |
−0.945979 | + | 0.324227i | \(0.894896\pi\) | |||||||
\(12\) | −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 | 0.857321 | − | 0.514782i | \(-0.172127\pi\) |
−0.0171533 | + | 0.999853i | \(0.505460\pi\) | |||||||
\(18\) | 0.866025 | + | 0.500000i | 0.204124 | + | 0.117851i | ||||
\(19\) | 4.00000 | + | 6.92820i | 0.917663 | + | 1.58944i | 0.802955 | + | 0.596040i | \(0.203260\pi\) |
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 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 | −0.0932891 | − | 0.995639i | \(-0.529738\pi\) |
0.815604 | + | 0.578610i | \(0.196405\pi\) | |||||||
\(24\) | −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 | −0.968709 | − | 0.248199i | \(-0.920161\pi\) |
0.699301 | + | 0.714827i | \(0.253495\pi\) | |||||||
\(32\) | −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 | −0.756948 | − | 0.653476i | \(-0.773310\pi\) |
0.187453 | + | 0.982274i | \(0.439977\pi\) | |||||||
\(38\) | 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 | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 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 | −0.828554 | − | 0.559908i | \(-0.810836\pi\) |
0.0706177 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(48\) | 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 | −0.142269 | − | 0.989828i | \(-0.545440\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(54\) | −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 | 0.246518 | + | 0.969138i | \(0.420713\pi\) |
−0.962557 | + | 0.271078i | \(0.912620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | + | 5.19615i | 0.384111 | + | 0.665299i | 0.991645 | − | 0.128994i | \(-0.0411748\pi\) |
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(62\) | 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 | 0.602056 | − | 0.798454i | \(-0.294348\pi\) |
−0.390453 | + | 0.920623i | \(0.627682\pi\) | |||||||
\(68\) | 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 | 0.912245 | − | 0.409644i | \(-0.134347\pi\) |
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(74\) | −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 | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.00000i | 0.768350i | 0.923260 | + | 0.384175i | \(0.125514\pi\) | ||||
−0.923260 | + | 0.384175i | \(0.874486\pi\) | |||||||
\(84\) | 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 | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 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 | \(0.115646\pi\) | ||||
−0.934725 | + | 0.355371i | \(0.884354\pi\) | |||||||
\(98\) | 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 | −0.999996 | − | 0.00286291i | \(-0.999089\pi\) |
0.502477 | + | 0.864590i | \(0.332422\pi\) | |||||||
\(102\) | −3.46410 | − | 2.00000i | −0.342997 | − | 0.198030i | ||||
\(103\) | −6.92820 | + | 4.00000i | −0.682656 | + | 0.394132i | −0.800855 | − | 0.598858i | \(-0.795621\pi\) |
0.118199 | + | 0.992990i | \(0.462288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 2.59808 | − | 1.50000i | 0.251166 | − | 0.145010i | −0.369132 | − | 0.929377i | \(-0.620345\pi\) |
0.620298 | + | 0.784366i | \(0.287012\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −1.00000 | + | 1.73205i | −0.0957826 | + | 0.165900i | −0.909935 | − | 0.414751i | \(-0.863869\pi\) |
0.814152 | + | 0.580651i | \(0.197202\pi\) | |||||||
\(110\) | 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 | \(-0.728811\pi\) | ||
0.658505 | − | 0.752577i | \(-0.271189\pi\) | |||||||
\(114\) | −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 | \(0.130750\pi\) | ||||
−0.916816 | + | 0.399310i | \(0.869250\pi\) | |||||||
\(128\) | −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 | 0.843356 | − | 0.537355i | \(-0.180577\pi\) |
−0.887041 | + | 0.461690i | \(0.847243\pi\) | |||||||
\(132\) | − | 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 | 0.572161 | − | 0.820141i | \(-0.306105\pi\) |
−0.424182 | + | 0.905577i | \(0.639438\pi\) | |||||||
\(138\) | −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 | −0.953703 | − | 0.300750i | \(-0.902763\pi\) |
0.216394 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.50000 | + | 16.4545i | −0.773099 | + | 1.33905i | 0.162758 | + | 0.986666i | \(0.447961\pi\) |
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | 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 | 0.631822 | − | 0.775113i | \(-0.282307\pi\) |
−0.355357 | + | 0.934731i | \(0.615641\pi\) | |||||||
\(158\) | 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 | −0.358162 | − | 0.933659i | \(-0.616597\pi\) |
0.629492 | + | 0.777007i | \(0.283263\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50000 | + | 6.06218i | 0.271653 | + | 0.470516i | ||||
\(167\) | − | 14.0000i | − | 1.08335i | −0.840587 | − | 0.541676i | \(-0.817790\pi\) | ||
0.840587 | − | 0.541676i | \(-0.182210\pi\) | |||||||
\(168\) | 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 | −0.998395 | − | 0.0566411i | \(-0.981961\pi\) |
−0.450145 | + | 0.892956i | \(0.648628\pi\) | |||||||
\(174\) | −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 | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 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 | −0.863743 | − | 0.503932i | \(-0.831886\pi\) |
−0.00454614 | − | 0.999990i | \(-0.501447\pi\) | |||||||
\(192\) | 0.866025 | + | 0.500000i | 0.0625000 | + | 0.0360844i | ||||
\(193\) | 4.33013 | + | 2.50000i | 0.311689 | + | 0.179954i | 0.647682 | − | 0.761911i | \(-0.275738\pi\) |
−0.335993 | + | 0.941865i | \(0.609072\pi\) | |||||||
\(194\) | 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 | \(0.0226979\pi\) | ||||
−0.997459 | + | 0.0712470i | \(0.977302\pi\) | |||||||
\(198\) | −4.33013 | + | 2.50000i | −0.307729 | + | 0.177667i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | 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 | \(0.0753051\pi\) | ||||
−0.972146 | + | 0.234377i | \(0.924695\pi\) | |||||||
\(224\) | 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 | 0.411296 | − | 0.911502i | \(-0.365076\pi\) |
−0.583736 | + | 0.811943i | \(0.698410\pi\) | |||||||
\(228\) | −6.92820 | − | 4.00000i | −0.458831 | − | 0.264906i | ||||
\(229\) | −10.0000 | − | 17.3205i | −0.660819 | − | 1.14457i | −0.980401 | − | 0.197013i | \(-0.936876\pi\) |
0.319582 | − | 0.947559i | \(-0.396457\pi\) | |||||||
\(230\) | 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 | −0.382219 | − | 0.924072i | \(-0.624840\pi\) |
0.609160 | + | 0.793047i | \(0.291507\pi\) | |||||||
\(234\) | 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 | −0.110963 | − | 0.993825i | \(-0.535394\pi\) |
0.916159 | − | 0.400815i | \(-0.131273\pi\) | |||||||
\(242\) | −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 | −0.653231 | − | 0.757159i | \(-0.726587\pi\) |
0.329104 | + | 0.944294i | \(0.393253\pi\) | |||||||
\(258\) | 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 | −0.991078 | − | 0.133281i | \(-0.957449\pi\) |
−0.610964 | − | 0.791658i | \(-0.709218\pi\) | |||||||
\(264\) | −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 | 0.189404 | − | 0.981899i | \(-0.439344\pi\) |
0.755648 | − | 0.654978i | \(-0.227322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.50000 | − | 12.9904i | −0.455593 | − | 0.789109i | 0.543130 | − | 0.839649i | \(-0.317239\pi\) |
−0.998722 | + | 0.0505395i | \(0.983906\pi\) | |||||||
\(272\) | − | 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 | 0.854725 | − | 0.519081i | \(-0.173726\pi\) |
−0.0221745 | + | 0.999754i | \(0.507059\pi\) | |||||||
\(278\) | 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 | 0.734804 | − | 0.678280i | \(-0.237274\pi\) |
−0.220005 | + | 0.975499i | \(0.570607\pi\) | |||||||
\(284\) | 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 | \(0.210205\pi\) | ||||
−0.789760 | + | 0.613417i | \(0.789795\pi\) | |||||||
\(294\) | −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 | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | −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 | 0.0894452 | − | 0.995992i | \(-0.471491\pi\) |
0.817832 | − | 0.575458i | \(-0.195176\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.866025 | + | 0.500000i | −0.0489506 | + | 0.0282617i | −0.524276 | − | 0.851549i | \(-0.675664\pi\) |
0.475325 | + | 0.879810i | \(0.342331\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.00000 | 0.168763 | ||||||||
\(317\) | 2.59808 | − | 1.50000i | 0.145922 | − | 0.0842484i | −0.425261 | − | 0.905071i | \(-0.639818\pi\) |
0.571184 | + | 0.820822i | \(0.306484\pi\) | |||||||
\(318\) | 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 | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 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 | \(0.0788309\pi\) | ||||
−0.969490 | + | 0.245131i | \(0.921169\pi\) | |||||||
\(338\) | 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 | 0.194409 | − | 0.980921i | \(-0.437721\pi\) |
−0.752297 | + | 0.658824i | \(0.771054\pi\) | |||||||
\(348\) | −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 | 0.937856 | − | 0.347024i | \(-0.112808\pi\) |
0.168397 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(354\) | 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 | 0.967272 | − | 0.253741i | \(-0.0816611\pi\) |
−0.703382 | + | 0.710812i | \(0.748328\pi\) | |||||||
\(360\) | 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 | 0.0638362 | − | 0.997960i | \(-0.479666\pi\) |
−0.832341 | + | 0.554264i | \(0.813000\pi\) | |||||||
\(368\) | −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 | 0.437425 | − | 0.899255i | \(-0.355891\pi\) |
0.997490 | + | 0.0708063i | \(0.0225572\pi\) | |||||||
\(374\) | −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 | 0.504576 | − | 0.863367i | \(-0.331649\pi\) |
0.999986 | − | 0.00529229i | \(-0.00168460\pi\) | |||||||
\(384\) | 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 | −0.890263 | − | 0.455448i | \(-0.849479\pi\) |
0.839561 | + | 0.543266i | \(0.182813\pi\) | |||||||
\(390\) | 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 | 0.567957 | − | 0.823058i | \(-0.307734\pi\) |
0.996768 | − | 0.0803356i | \(-0.0255992\pi\) | |||||||
\(398\) | 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 | −0.992932 | − | 0.118686i | \(-0.962132\pi\) |
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(402\) | −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 | 0.371750 | + | 0.928333i | \(0.378758\pi\) |
−0.989835 | + | 0.142222i | \(0.954575\pi\) | |||||||
\(410\) | 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 | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | −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 | 0.987619 | − | 0.156871i | \(-0.0501406\pi\) |
−0.629664 | + | 0.776868i | \(0.716807\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.50000 | + | 4.33013i | 0.261905 | + | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7224 | + | 8.50000i | −0.699484 | + | 0.403847i | −0.807155 | − | 0.590339i | \(-0.798994\pi\) |
0.107671 | + | 0.994187i | \(0.465661\pi\) | |||||||
\(444\) | 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 | 0.283577 | − | 0.958950i | \(-0.408479\pi\) |
0.972263 | + | 0.233890i | \(0.0751456\pi\) | |||||||
\(458\) | −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 | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | −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 | −0.843995 | − | 0.536352i | \(-0.819802\pi\) |
0.0424970 | + | 0.999097i | \(0.486469\pi\) | |||||||
\(468\) | 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 | 0.00422900 | − | 0.999991i | \(-0.498654\pi\) |
0.863903 | − | 0.503658i | \(-0.168013\pi\) | |||||||
\(480\) | 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 | 0.398673 | − | 0.917093i | \(-0.369471\pi\) |
−0.594890 | + | 0.803807i | \(0.702804\pi\) | |||||||
\(488\) | 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 | 0.955968 | − | 0.293471i | \(-0.0948104\pi\) |
−0.732137 | + | 0.681157i | \(0.761477\pi\) | |||||||
\(500\) | 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 | 0.982988 | − | 0.183669i | \(-0.0587976\pi\) |
−0.650556 | + | 0.759458i | \(0.725464\pi\) | |||||||
\(510\) | 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 | −0.598714 | − | 0.800963i | \(-0.704321\pi\) |
0.993011 | + | 0.118020i | \(0.0376547\pi\) | |||||||
\(522\) | 4.33013 | + | 2.50000i | 0.189525 | + | 0.109422i | ||||
\(523\) | −6.92820 | + | 4.00000i | −0.302949 | + | 0.174908i | −0.643767 | − | 0.765222i | \(-0.722629\pi\) |
0.340818 | + | 0.940129i | \(0.389296\pi\) | |||||||
\(524\) | −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 | 0.992036 | − | 0.125952i | \(-0.0401986\pi\) |
−0.605096 | + | 0.796152i | \(0.706865\pi\) | |||||||
\(542\) | −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 | \(-0.917417\pi\) | ||
0.966533 | − | 0.256541i | \(-0.0825830\pi\) | |||||||
\(548\) | 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 | 0.858614 | − | 0.512622i | \(-0.171326\pi\) |
−0.0146368 | + | 0.999893i | \(0.504659\pi\) | |||||||
\(558\) | −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 | 0.777055 | − | 0.629433i | \(-0.216713\pi\) |
−0.156578 | + | 0.987666i | \(0.550046\pi\) | |||||||
\(564\) | 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 | 0.999994 | + | 0.00354413i | \(0.00112814\pi\) |
−0.496928 | + | 0.867792i | \(0.665539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.0000 | − | 25.9808i | 0.627730 | − | 1.08726i | −0.360276 | − | 0.932846i | \(-0.617317\pi\) |
0.988006 | − | 0.154415i | \(-0.0493493\pi\) | |||||||
\(572\) | 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 | −0.176847 | − | 0.984238i | \(-0.556590\pi\) |
−0.940799 | + | 0.338965i | \(0.889923\pi\) | |||||||
\(578\) | −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 | \(0.256916\pi\) | ||||
−0.691577 | + | 0.722302i | \(0.743084\pi\) | |||||||
\(588\) | −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 | −0.976900 | − | 0.213697i | \(-0.931449\pi\) |
−0.303383 | + | 0.952869i | \(0.598116\pi\) | |||||||
\(594\) | 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 | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(600\) | 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 | −0.892793 | − | 0.450467i | \(-0.851258\pi\) |
−0.0562808 | + | 0.998415i | \(0.517924\pi\) | |||||||
\(608\) | − | 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 | 0.694967 | − | 0.719042i | \(-0.255419\pi\) |
−0.275225 | + | 0.961380i | \(0.588752\pi\) | |||||||
\(614\) | 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 | \(0.0128181\pi\) | ||||
−0.999189 | + | 0.0402585i | \(0.987182\pi\) | |||||||
\(618\) | 6.92820 | − | 4.00000i | 0.278693 | − | 0.160904i | ||||
\(619\) | 5.00000 | − | 8.66025i | 0.200967 | − | 0.348085i | −0.747873 | − | 0.663842i | \(-0.768925\pi\) |
0.948840 | + | 0.315757i | \(0.102258\pi\) | |||||||
\(620\) | 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 | 0.486409 | + | 0.873731i | \(0.338307\pi\) |
−0.999878 | + | 0.0156233i | \(0.995027\pi\) | |||||||
\(642\) | −2.59808 | + | 1.50000i | −0.102538 | + | 0.0592003i | ||||
\(643\) | − | 14.0000i | − | 0.552106i | −0.961142 | − | 0.276053i | \(-0.910973\pi\) | ||
0.961142 | − | 0.276053i | \(-0.0890266\pi\) | |||||||
\(644\) | 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 | 0.774078 | − | 0.633090i | \(-0.218214\pi\) |
−0.161233 | + | 0.986916i | \(0.551547\pi\) | |||||||
\(648\) | 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 | 0.337715 | − | 0.941248i | \(-0.390346\pi\) |
0.984003 | + | 0.178154i | \(0.0570127\pi\) | |||||||
\(654\) | 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 | −0.946729 | − | 0.322031i | \(-0.895634\pi\) |
0.752252 | + | 0.658876i | \(0.228968\pi\) | |||||||
\(662\) | 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 | \(0.119341\pi\) | ||||
−0.930537 | + | 0.366198i | \(0.880659\pi\) | |||||||
\(674\) | 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 | −0.876768 | − | 0.480913i | \(-0.840305\pi\) |
−0.0219013 | + | 0.999760i | \(0.506972\pi\) | |||||||
\(678\) | 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 | 0.343413 | − | 0.939184i | \(-0.388417\pi\) |
−0.641651 | + | 0.766997i | \(0.721750\pi\) | |||||||
\(684\) | 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 | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 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 | 0.963512 | + | 0.267664i | \(0.0862517\pi\) |
−0.249952 | + | 0.968258i | \(0.580415\pi\) | |||||||
\(710\) | 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 | 0.804648 | − | 0.593753i | \(-0.202354\pi\) |
−0.916529 | + | 0.399969i | \(0.869021\pi\) | |||||||
\(720\) | 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 | \(0.0414360\pi\) | ||||
−0.991539 | + | 0.129808i | \(0.958564\pi\) | |||||||
\(728\) | 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 | −0.400959 | − | 0.916096i | \(-0.631323\pi\) |
0.592883 | + | 0.805289i | \(0.297990\pi\) | |||||||
\(734\) | −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 | 0.446362 | + | 0.894852i | \(0.352719\pi\) |
−0.998146 | + | 0.0608653i | \(0.980614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 23.3827 | − | 4.50000i | 0.858405 | − | 0.165200i | ||||
\(743\) | − | 30.0000i | − | 1.10059i | −0.834969 | − | 0.550297i | \(-0.814515\pi\) | ||
0.834969 | − | 0.550297i | \(-0.185485\pi\) | |||||||
\(744\) | −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 | −0.904911 | − | 0.425601i | \(-0.860063\pi\) |
0.0838743 | − | 0.996476i | \(-0.473271\pi\) | |||||||
\(752\) | 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 | \(-0.561602\pi\) | ||
0.192323 | − | 0.981332i | \(-0.438398\pi\) | |||||||
\(758\) | −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 | 0.784373 | − | 0.620289i | \(-0.212985\pi\) |
−0.929373 | + | 0.369142i | \(0.879652\pi\) | |||||||
\(762\) | − | 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 | 0.647592 | − | 0.761987i | \(-0.275776\pi\) |
−0.336104 | + | 0.941825i | \(0.609109\pi\) | |||||||
\(774\) | 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 | 0.751405 | − | 0.659841i | \(-0.229376\pi\) |
−0.195737 | + | 0.980656i | \(0.562710\pi\) | |||||||
\(788\) | 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 | \(0.121304\pi\) | ||||
−0.928261 | + | 0.371929i | \(0.878696\pi\) | |||||||
\(798\) | 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 | −0.264188 | − | 0.964471i | \(-0.585104\pi\) |
0.967351 | − | 0.253442i | \(-0.0815627\pi\) | |||||||
\(810\) | 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 | 0.997397 | − | 0.0721058i | \(-0.0229719\pi\) |
−0.561144 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(822\) | −1.73205 | − | 1.00000i | −0.0604122 | − | 0.0348790i | ||||
\(823\) | 34.6410 | + | 20.0000i | 1.20751 | + | 0.697156i | 0.962215 | − | 0.272292i | \(-0.0877817\pi\) |
0.245295 | + | 0.969448i | \(0.421115\pi\) | |||||||
\(824\) | 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 | \(0.0500148\pi\) | ||||
−0.987681 | + | 0.156480i | \(0.949985\pi\) | |||||||
\(828\) | 3.46410 | − | 2.00000i | 0.120386 | − | 0.0695048i | ||||
\(829\) | −16.0000 | + | 27.7128i | −0.555703 | + | 0.962506i | 0.442145 | + | 0.896943i | \(0.354217\pi\) |
−0.997848 | + | 0.0655624i | \(0.979116\pi\) | |||||||
\(830\) | 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 | \(-0.922959\pi\) | ||
0.970853 | − | 0.239675i | \(-0.0770410\pi\) | |||||||
\(854\) | −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 | 0.742030 | − | 0.670366i | \(-0.233863\pi\) |
−0.209539 | + | 0.977800i | \(0.567196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.0000 | − | 29.4449i | −0.580033 | − | 1.00465i | −0.995475 | − | 0.0950262i | \(-0.969707\pi\) |
0.415442 | − | 0.909620i | \(-0.363627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | −8.66025 | + | 5.00000i | −0.294798 | + | 0.170202i | −0.640104 | − | 0.768288i | \(-0.721109\pi\) |
0.345305 | + | 0.938490i | \(0.387775\pi\) | |||||||
\(864\) | −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 | −0.888640 | − | 0.458606i | \(-0.848349\pi\) |
−0.0471555 | + | 0.998888i | \(0.515016\pi\) | |||||||
\(878\) | 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 | \(0.235018\pi\) | ||||
−0.739594 | + | 0.673054i | \(0.764982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.50000 | + | 14.7224i | −0.285563 | + | 0.494610i | ||||
\(887\) | 31.1769 | − | 18.0000i | 1.04682 | − | 0.604381i | 0.125061 | − | 0.992149i | \(-0.460087\pi\) |
0.921757 | + | 0.387768i | \(0.126754\pi\) | |||||||
\(888\) | − | 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 | 0.317441 | − | 0.948278i | \(-0.397176\pi\) |
−0.662512 | + | 0.749051i | \(0.730510\pi\) | |||||||
\(908\) | −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 | −0.999475 | − | 0.0323936i | \(-0.989687\pi\) |
0.471684 | − | 0.881768i | \(-0.343646\pi\) | |||||||
\(920\) | 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 | 0.812607 | − | 0.582812i | \(-0.198048\pi\) |
−0.911034 | + | 0.412332i | \(0.864714\pi\) | |||||||
\(930\) | 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 | \(0.193716\pi\) | ||||
−0.820463 | + | 0.571700i | \(0.806284\pi\) | |||||||
\(938\) | −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 | −0.762344 | − | 0.647172i | \(-0.775952\pi\) |
0.941639 | + | 0.336624i | \(0.109285\pi\) | |||||||
\(942\) | −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 | −0.877377 | − | 0.479801i | \(-0.840709\pi\) |
−0.0231683 | + | 0.999732i | \(0.507375\pi\) | |||||||
\(948\) | −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 | \(-0.989687\pi\) | ||
0.999475 | − | 0.0323932i | \(-0.0103129\pi\) | |||||||
\(954\) | −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 | \(-0.562453\pi\) | ||
0.194946 | − | 0.980814i | \(-0.437547\pi\) | |||||||
\(968\) | −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 | 0.720224 | − | 0.693742i | \(-0.244039\pi\) |
−0.960910 | + | 0.276861i | \(0.910706\pi\) | |||||||
\(972\) | − | 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 | 0.854263 | − | 0.519841i | \(-0.174009\pi\) |
−0.0230645 | + | 0.999734i | \(0.507342\pi\) | |||||||
\(978\) | −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 | −0.973946 | − | 0.226778i | \(-0.927181\pi\) |
−0.683369 | − | 0.730073i | \(-0.739486\pi\) | |||||||
\(984\) | 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 | 0.202988 | + | 0.979181i | \(0.434935\pi\) |
−0.949490 | + | 0.313798i | \(0.898398\pi\) | |||||||
\(992\) | 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 | −0.121771 | − | 0.992558i | \(-0.538857\pi\) |
−0.920466 | + | 0.390822i | \(0.872191\pi\) | |||||||
\(998\) | 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 \(a_p\))