Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,2,Mod(451,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1350.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.e (of order \(3\), 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: | \(10.7798042729\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 901.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1350.901 |
Dual form | 1350.2.e.i.451.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1350\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1027\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | 0.944911 | − | 0.327327i | \(-0.106148\pi\) |
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 5.19615i | 0.832050 | − | 1.44115i | −0.0643593 | − | 0.997927i | \(-0.520500\pi\) |
0.896410 | − | 0.443227i | \(-0.146166\pi\) | |||||||
\(14\) | −0.500000 | + | 0.866025i | −0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | − | 1.73205i | 0.213201 | − | 0.369274i | ||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | −0.809177 | − | 0.587565i | \(-0.800087\pi\) |
0.913434 | + | 0.406986i | \(0.133420\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | + | 1.73205i | 0.171499 | + | 0.297044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 3.00000 | + | 5.19615i | 0.486664 | + | 0.842927i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.50000 | + | 9.52628i | −0.858956 | + | 1.48775i | 0.0139704 | + | 0.999902i | \(0.495553\pi\) |
−0.872926 | + | 0.487852i | \(0.837780\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −3.50000 | − | 6.06218i | −0.510527 | − | 0.884260i | −0.999926 | − | 0.0121990i | \(-0.996117\pi\) |
0.489398 | − | 0.872060i | \(-0.337217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.00000 | + | 5.19615i | 0.416025 | + | 0.720577i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.500000 | − | 0.866025i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.50000 | + | 7.79423i | −0.590879 | + | 1.02343i | ||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.50000 | − | 9.52628i | 0.671932 | − | 1.16382i | −0.305424 | − | 0.952217i | \(-0.598798\pi\) |
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | −1.00000 | + | 1.73205i | −0.121268 | + | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.00000 | −0.468165 | −0.234082 | − | 0.972217i | \(-0.575209\pi\) | ||||
−0.234082 | + | 0.972217i | \(0.575209\pi\) | |||||||
\(74\) | 1.00000 | + | 1.73205i | 0.116248 | + | 0.201347i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.00000 | + | 5.19615i | −0.344124 | + | 0.596040i | ||||
\(77\) | 1.00000 | − | 1.73205i | 0.113961 | − | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | + | 10.3923i | 0.675053 | + | 1.16923i | 0.976453 | + | 0.215728i | \(0.0692125\pi\) |
−0.301401 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −11.0000 | −1.21475 | ||||||||
\(83\) | −5.50000 | − | 9.52628i | −0.603703 | − | 1.04565i | −0.992255 | − | 0.124218i | \(-0.960358\pi\) |
0.388552 | − | 0.921427i | \(-0.372976\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.00000 | + | 3.46410i | −0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | + | 1.73205i | 0.106600 | + | 0.184637i | ||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 0.500000 | + | 0.866025i | 0.0521286 | + | 0.0902894i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.50000 | − | 6.06218i | 0.360997 | − | 0.625266i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.00000 | + | 6.92820i | 0.406138 | + | 0.703452i | 0.994453 | − | 0.105180i | \(-0.0335417\pi\) |
−0.588315 | + | 0.808632i | \(0.700208\pi\) | |||||||
\(98\) | 6.00000 | 0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | − | 6.92820i | 0.394132 | − | 0.682656i | −0.598858 | − | 0.800855i | \(-0.704379\pi\) |
0.992990 | + | 0.118199i | \(0.0377120\pi\) | |||||||
\(104\) | −3.00000 | + | 5.19615i | −0.294174 | + | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.00000 | 0.670478 | 0.335239 | − | 0.942133i | \(-0.391183\pi\) | ||||
0.335239 | + | 0.942133i | \(0.391183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 0.866025i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 1.00000 | + | 1.73205i | 0.0916698 | + | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | −3.50000 | + | 6.06218i | −0.316875 | + | 0.548844i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | − | 10.3923i | 0.524222 | − | 0.907980i | −0.475380 | − | 0.879781i | \(-0.657689\pi\) |
0.999602 | − | 0.0281993i | \(-0.00897729\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.00000 | + | 5.19615i | 0.260133 | + | 0.450564i | ||||
\(134\) | 11.0000 | 0.950255 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | + | 13.8564i | −0.678551 | + | 1.17529i | 0.296866 | + | 0.954919i | \(0.404058\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.00000 | + | 5.19615i | 0.251754 | + | 0.436051i | ||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | − | 3.46410i | −0.165521 | − | 0.286691i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | −0.500000 | + | 0.866025i | −0.0409616 | + | 0.0709476i | −0.885779 | − | 0.464107i | \(-0.846375\pi\) |
0.844818 | + | 0.535054i | \(0.179709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | −6.00000 | + | 10.3923i | −0.477334 | + | 0.826767i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.00000 | 0.313304 | 0.156652 | − | 0.987654i | \(-0.449930\pi\) | ||||
0.156652 | + | 0.987654i | \(0.449930\pi\) | |||||||
\(164\) | −5.50000 | − | 9.52628i | −0.429478 | − | 0.743877i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.50000 | − | 9.52628i | 0.426883 | − | 0.739383i | ||||
\(167\) | −1.50000 | + | 2.59808i | −0.116073 | + | 0.201045i | −0.918208 | − | 0.396098i | \(-0.870364\pi\) |
0.802135 | + | 0.597143i | \(0.203697\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | −2.00000 | − | 3.46410i | −0.152057 | − | 0.263371i | 0.779926 | − | 0.625871i | \(-0.215256\pi\) |
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | + | 1.73205i | −0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.500000 | − | 0.866025i | −0.0374766 | − | 0.0649113i | ||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0000 | −0.966282 | −0.483141 | − | 0.875542i | \(-0.660504\pi\) | ||||
−0.483141 | + | 0.875542i | \(0.660504\pi\) | |||||||
\(182\) | 3.00000 | + | 5.19615i | 0.222375 | + | 0.385164i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | − | 3.46410i | −0.146254 | − | 0.253320i | ||||
\(188\) | 7.00000 | 0.510527 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.00000 | − | 8.66025i | 0.359908 | − | 0.623379i | −0.628037 | − | 0.778183i | \(-0.716141\pi\) |
0.987945 | + | 0.154805i | \(0.0494748\pi\) | |||||||
\(194\) | −4.00000 | + | 6.92820i | −0.287183 | + | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 5.19615i | 0.214286 | + | 0.371154i | ||||
\(197\) | −8.00000 | −0.569976 | −0.284988 | − | 0.958531i | \(-0.591990\pi\) | ||||
−0.284988 | + | 0.958531i | \(0.591990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.0000 | −1.27599 | −0.637993 | − | 0.770042i | \(-0.720235\pi\) | ||||
−0.637993 | + | 0.770042i | \(0.720235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.00000 | + | 1.73205i | −0.0703598 | + | 0.121867i | ||||
\(203\) | −4.50000 | + | 7.79423i | −0.315838 | + | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.00000 | −0.416025 | ||||||||
\(209\) | −6.00000 | − | 10.3923i | −0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | + | 15.5885i | −0.619586 | + | 1.07315i | 0.369976 | + | 0.929041i | \(0.379366\pi\) |
−0.989561 | + | 0.144112i | \(0.953967\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.50000 | − | 2.59808i | −0.102538 | − | 0.177601i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 3.50000 | + | 6.06218i | 0.237050 | + | 0.410582i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | − | 10.3923i | 0.403604 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.5000 | − | 19.9186i | −0.770097 | − | 1.33385i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.167412 | − | 0.985887i | \(-0.446459\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | −4.00000 | − | 6.92820i | −0.265489 | − | 0.459841i | 0.702202 | − | 0.711977i | \(-0.252200\pi\) |
−0.967692 | + | 0.252136i | \(0.918867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.50000 | − | 6.06218i | 0.231287 | − | 0.400600i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
0.958187 | + | 0.286143i | \(0.0923732\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.50000 | − | 7.79423i | −0.295439 | − | 0.511716i | ||||
\(233\) | 10.0000 | 0.655122 | 0.327561 | − | 0.944830i | \(-0.393773\pi\) | ||||
0.327561 | + | 0.944830i | \(0.393773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.00000 | + | 1.73205i | −0.0648204 | + | 0.112272i | ||||
\(239\) | 14.0000 | − | 24.2487i | 0.905585 | − | 1.56852i | 0.0854543 | − | 0.996342i | \(-0.472766\pi\) |
0.820130 | − | 0.572177i | \(-0.193901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.0000 | − | 31.1769i | 1.14531 | − | 1.98374i | ||||
\(248\) | −1.00000 | + | 1.73205i | −0.0635001 | + | 0.109985i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | −9.50000 | − | 16.4545i | −0.596083 | − | 1.03245i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.00000 | − | 10.3923i | 0.374270 | − | 0.648254i | −0.615948 | − | 0.787787i | \(-0.711227\pi\) |
0.990217 | + | 0.139533i | \(0.0445601\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00000 | + | 1.73205i | 0.0621370 | + | 0.107624i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000 | 0.741362 | ||||||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.00000 | + | 5.19615i | −0.183942 | + | 0.318597i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.50000 | + | 9.52628i | 0.335966 | + | 0.581910i | ||||
\(269\) | −3.00000 | −0.182913 | −0.0914566 | − | 0.995809i | \(-0.529152\pi\) | ||||
−0.0914566 | + | 0.995809i | \(0.529152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.0000 | −0.850439 | −0.425220 | − | 0.905090i | \(-0.639803\pi\) | ||||
−0.425220 | + | 0.905090i | \(0.639803\pi\) | |||||||
\(272\) | −1.00000 | − | 1.73205i | −0.0606339 | − | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | + | 10.3923i | −0.362473 | + | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.0000 | + | 19.0526i | 0.660926 | + | 1.14476i | 0.980373 | + | 0.197153i | \(0.0631696\pi\) |
−0.319447 | + | 0.947604i | \(0.603497\pi\) | |||||||
\(278\) | −16.0000 | −0.959616 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.50000 | − | 2.59808i | −0.0894825 | − | 0.154988i | 0.817810 | − | 0.575488i | \(-0.195188\pi\) |
−0.907293 | + | 0.420500i | \(0.861855\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.500000 | + | 0.866025i | −0.0297219 | + | 0.0514799i | −0.880504 | − | 0.474039i | \(-0.842796\pi\) |
0.850782 | + | 0.525519i | \(0.176129\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | −11.0000 | −0.649309 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00000 | − | 3.46410i | 0.117041 | − | 0.202721i | ||||
\(293\) | −9.00000 | + | 15.5885i | −0.525786 | + | 0.910687i | 0.473763 | + | 0.880652i | \(0.342895\pi\) |
−0.999549 | + | 0.0300351i | \(0.990438\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −3.00000 | − | 5.19615i | −0.173494 | − | 0.300501i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | + | 3.46410i | −0.115278 | + | 0.199667i | ||||
\(302\) | 5.00000 | − | 8.66025i | 0.287718 | − | 0.498342i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.00000 | − | 5.19615i | −0.172062 | − | 0.298020i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.00000 | −0.513657 | −0.256829 | − | 0.966457i | \(-0.582678\pi\) | ||||
−0.256829 | + | 0.966457i | \(0.582678\pi\) | |||||||
\(308\) | 1.00000 | + | 1.73205i | 0.0569803 | + | 0.0986928i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.00000 | − | 5.19615i | 0.170114 | − | 0.294647i | −0.768345 | − | 0.640036i | \(-0.778920\pi\) |
0.938460 | + | 0.345389i | \(0.112253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0000 | + | 19.0526i | 0.621757 | + | 1.07691i | 0.989158 | + | 0.146852i | \(0.0469141\pi\) |
−0.367402 | + | 0.930062i | \(0.619753\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | −1.00000 | − | 1.73205i | −0.0561656 | − | 0.0972817i | 0.836576 | − | 0.547852i | \(-0.184554\pi\) |
−0.892741 | + | 0.450570i | \(0.851221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.500000 | + | 0.866025i | 0.0278639 | + | 0.0482617i | ||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | + | 3.46410i | 0.110770 | + | 0.191859i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.50000 | − | 9.52628i | 0.303687 | − | 0.526001i | ||||
\(329\) | 3.50000 | − | 6.06218i | 0.192961 | − | 0.334219i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00000 | + | 6.92820i | 0.219860 | + | 0.380808i | 0.954765 | − | 0.297361i | \(-0.0961066\pi\) |
−0.734905 | + | 0.678170i | \(0.762773\pi\) | |||||||
\(332\) | 11.0000 | 0.603703 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.00000 | −0.164153 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.00000 | + | 6.92820i | −0.217894 | + | 0.377403i | −0.954164 | − | 0.299285i | \(-0.903252\pi\) |
0.736270 | + | 0.676688i | \(0.236585\pi\) | |||||||
\(338\) | 11.5000 | − | 19.9186i | 0.625518 | − | 1.08343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | −0.216612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.0000 | 0.701934 | ||||||||
\(344\) | −2.00000 | − | 3.46410i | −0.107833 | − | 0.186772i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | − | 3.46410i | 0.107521 | − | 0.186231i | ||||
\(347\) | −6.00000 | + | 10.3923i | −0.322097 | + | 0.557888i | −0.980921 | − | 0.194409i | \(-0.937721\pi\) |
0.658824 | + | 0.752297i | \(0.271054\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.50000 | + | 9.52628i | 0.294408 | + | 0.509930i | 0.974847 | − | 0.222875i | \(-0.0715441\pi\) |
−0.680439 | + | 0.732805i | \(0.738211\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.00000 | −0.106600 | ||||||||
\(353\) | −8.00000 | − | 13.8564i | −0.425797 | − | 0.737502i | 0.570697 | − | 0.821160i | \(-0.306673\pi\) |
−0.996495 | + | 0.0836583i | \(0.973340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.500000 | − | 0.866025i | 0.0264999 | − | 0.0458993i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.00000 | − | 1.73205i | −0.0528516 | − | 0.0915417i | ||||
\(359\) | −30.0000 | −1.58334 | −0.791670 | − | 0.610949i | \(-0.790788\pi\) | ||||
−0.791670 | + | 0.610949i | \(0.790788\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | −6.50000 | − | 11.2583i | −0.341632 | − | 0.591725i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | + | 5.19615i | −0.157243 | + | 0.272352i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | + | 13.8564i | 0.417597 | + | 0.723299i | 0.995697 | − | 0.0926670i | \(-0.0295392\pi\) |
−0.578101 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | + | 10.3923i | −0.310668 | + | 0.538093i | −0.978507 | − | 0.206213i | \(-0.933886\pi\) |
0.667839 | + | 0.744306i | \(0.267219\pi\) | |||||||
\(374\) | 2.00000 | − | 3.46410i | 0.103418 | − | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.50000 | + | 6.06218i | 0.180499 | + | 0.312633i | ||||
\(377\) | 54.0000 | 2.78114 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.00000 | + | 5.19615i | −0.153493 | + | 0.265858i | ||||
\(383\) | 16.0000 | − | 27.7128i | 0.817562 | − | 1.41606i | −0.0899119 | − | 0.995950i | \(-0.528659\pi\) |
0.907474 | − | 0.420109i | \(-0.138008\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.00000 | −0.406138 | ||||||||
\(389\) | 9.50000 | + | 16.4545i | 0.481669 | + | 0.834275i | 0.999779 | − | 0.0210389i | \(-0.00669738\pi\) |
−0.518110 | + | 0.855314i | \(0.673364\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | − | 1.73205i | 0.0505722 | − | 0.0875936i | ||||
\(392\) | −3.00000 | + | 5.19615i | −0.151523 | + | 0.262445i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00000 | − | 6.92820i | −0.201517 | − | 0.349038i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00000 | −0.200754 | −0.100377 | − | 0.994949i | \(-0.532005\pi\) | ||||
−0.100377 | + | 0.994949i | \(0.532005\pi\) | |||||||
\(398\) | −9.00000 | − | 15.5885i | −0.451129 | − | 0.781379i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.00000 | + | 8.66025i | −0.249688 | + | 0.432472i | −0.963439 | − | 0.267927i | \(-0.913661\pi\) |
0.713751 | + | 0.700399i | \(0.246995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.00000 | − | 10.3923i | −0.298881 | − | 0.517678i | ||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9.00000 | −0.446663 | ||||||||
\(407\) | −2.00000 | − | 3.46410i | −0.0991363 | − | 0.171709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0000 | + | 32.9090i | −0.939490 | + | 1.62724i | −0.173064 | + | 0.984911i | \(0.555367\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.00000 | + | 6.92820i | 0.197066 | + | 0.341328i | ||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.00000 | − | 5.19615i | −0.147087 | − | 0.254762i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.00000 | − | 10.3923i | 0.293470 | − | 0.508304i | ||||
\(419\) | 17.0000 | − | 29.4449i | 0.830504 | − | 1.43848i | −0.0671345 | − | 0.997744i | \(-0.521386\pi\) |
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0000 | − | 19.0526i | −0.536107 | − | 0.928565i | −0.999109 | − | 0.0422075i | \(-0.986561\pi\) |
0.463002 | − | 0.886357i | \(-0.346772\pi\) | |||||||
\(422\) | −18.0000 | −0.876226 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.50000 | + | 6.06218i | −0.169377 | + | 0.293369i | ||||
\(428\) | 1.50000 | − | 2.59808i | 0.0725052 | − | 0.125583i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 1.00000 | + | 1.73205i | 0.0480015 | + | 0.0831411i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.50000 | + | 6.06218i | −0.167620 | + | 0.290326i | ||||
\(437\) | 3.00000 | − | 5.19615i | 0.143509 | − | 0.248566i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.0000 | − | 20.7846i | −0.572729 | − | 0.991995i | −0.996284 | − | 0.0861252i | \(-0.972552\pi\) |
0.423556 | − | 0.905870i | \(-0.360782\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | −4.50000 | − | 7.79423i | −0.213801 | − | 0.370315i | 0.739100 | − | 0.673596i | \(-0.235251\pi\) |
−0.952901 | + | 0.303281i | \(0.901918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.5000 | − | 19.9186i | 0.544541 | − | 0.943172i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | + | 0.866025i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.0000 | 1.03594 | ||||||||
\(452\) | 6.00000 | + | 10.3923i | 0.282216 | + | 0.488813i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.00000 | − | 6.92820i | 0.187729 | − | 0.325157i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.00000 | + | 8.66025i | 0.233890 | + | 0.405110i | 0.958950 | − | 0.283577i | \(-0.0915211\pi\) |
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 7.00000 | 0.327089 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.5000 | − | 18.1865i | −0.489034 | − | 0.847031i | 0.510887 | − | 0.859648i | \(-0.329317\pi\) |
−0.999920 | + | 0.0126168i | \(0.995984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.0000 | + | 31.1769i | −0.836531 | + | 1.44891i | 0.0562469 | + | 0.998417i | \(0.482087\pi\) |
−0.892778 | + | 0.450497i | \(0.851247\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.00000 | + | 8.66025i | 0.231621 | + | 0.401179i | ||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.0000 | 0.507933 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | − | 3.46410i | 0.0920575 | − | 0.159448i | ||||
\(473\) | 4.00000 | − | 6.92820i | 0.183920 | − | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.00000 | −0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 28.0000 | 1.28069 | ||||||||
\(479\) | 14.0000 | + | 24.2487i | 0.639676 | + | 1.10795i | 0.985504 | + | 0.169654i | \(0.0542649\pi\) |
−0.345827 | + | 0.938298i | \(0.612402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | − | 10.3923i | 0.273576 | − | 0.473848i | ||||
\(482\) | 0.500000 | − | 0.866025i | 0.0227744 | − | 0.0394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | + | 6.06218i | 0.159091 | + | 0.275554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.0000 | −0.543772 | −0.271886 | − | 0.962329i | \(-0.587647\pi\) | ||||
−0.271886 | + | 0.962329i | \(0.587647\pi\) | |||||||
\(488\) | −3.50000 | − | 6.06218i | −0.158438 | − | 0.274422i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | + | 15.5885i | 0.405340 | + | 0.702069i | ||||
\(494\) | 36.0000 | 1.61972 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | 3.00000 | + | 5.19615i | 0.134568 | + | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0000 | − | 20.7846i | 0.537194 | − | 0.930447i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) |
0.999054 | − | 0.0434940i | \(-0.0138489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.00000 | − | 15.5885i | −0.401690 | − | 0.695747i | ||||
\(503\) | −27.0000 | −1.20387 | −0.601935 | − | 0.798545i | \(-0.705603\pi\) | ||||
−0.601935 | + | 0.798545i | \(0.705603\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.00000 | − | 1.73205i | −0.0444554 | − | 0.0769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.50000 | − | 16.4545i | 0.421494 | − | 0.730050i | ||||
\(509\) | −7.50000 | + | 12.9904i | −0.332432 | + | 0.575789i | −0.982988 | − | 0.183669i | \(-0.941202\pi\) |
0.650556 | + | 0.759458i | \(0.274536\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.00000 | − | 3.46410i | −0.0884748 | − | 0.153243i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0000 | 0.529297 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.00000 | + | 12.1244i | −0.307860 | + | 0.533229i | ||||
\(518\) | −1.00000 | + | 1.73205i | −0.0439375 | + | 0.0761019i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.0000 | 1.62100 | 0.810500 | − | 0.585739i | \(-0.199196\pi\) | ||||
0.810500 | + | 0.585739i | \(0.199196\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.0000 | −1.26808 | −0.634041 | − | 0.773300i | \(-0.718605\pi\) | ||||
−0.634041 | + | 0.773300i | \(0.718605\pi\) | |||||||
\(524\) | 6.00000 | + | 10.3923i | 0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.00000 | + | 13.8564i | −0.348817 | + | 0.604168i | ||||
\(527\) | 2.00000 | − | 3.46410i | 0.0871214 | − | 0.150899i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.00000 | −0.260133 | ||||||||
\(533\) | 33.0000 | + | 57.1577i | 1.42939 | + | 2.47577i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.50000 | + | 9.52628i | −0.237564 | + | 0.411473i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.50000 | − | 2.59808i | −0.0646696 | − | 0.112011i | ||||
\(539\) | −12.0000 | −0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.0000 | −0.730887 | −0.365444 | − | 0.930834i | \(-0.619083\pi\) | ||||
−0.365444 | + | 0.930834i | \(0.619083\pi\) | |||||||
\(542\) | −7.00000 | − | 12.1244i | −0.300676 | − | 0.520786i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.00000 | − | 1.73205i | 0.0428746 | − | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.5000 | − | 30.3109i | −0.748246 | − | 1.29600i | −0.948663 | − | 0.316289i | \(-0.897563\pi\) |
0.200417 | − | 0.979711i | \(-0.435770\pi\) | |||||||
\(548\) | −12.0000 | −0.512615 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.0000 | + | 46.7654i | 1.15024 | + | 1.99227i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | + | 10.3923i | −0.255146 | + | 0.441926i | ||||
\(554\) | −11.0000 | + | 19.0526i | −0.467345 | + | 0.809466i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | − | 13.8564i | −0.339276 | − | 0.587643i | ||||
\(557\) | 24.0000 | 1.01691 | 0.508456 | − | 0.861088i | \(-0.330216\pi\) | ||||
0.508456 | + | 0.861088i | \(0.330216\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.0000 | 1.01509 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.50000 | − | 2.59808i | 0.0632737 | − | 0.109593i | ||||
\(563\) | −18.5000 | + | 32.0429i | −0.779682 | + | 1.35045i | 0.152443 | + | 0.988312i | \(0.451286\pi\) |
−0.932125 | + | 0.362137i | \(0.882047\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.00000 | −0.0420331 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −1.00000 | − | 1.73205i | −0.0419222 | − | 0.0726113i | 0.844303 | − | 0.535866i | \(-0.180015\pi\) |
−0.886225 | + | 0.463255i | \(0.846681\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | − | 17.3205i | 0.418487 | − | 0.724841i | −0.577301 | − | 0.816532i | \(-0.695894\pi\) |
0.995788 | + | 0.0916910i | \(0.0292272\pi\) | |||||||
\(572\) | 6.00000 | − | 10.3923i | 0.250873 | − | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.50000 | − | 9.52628i | −0.229566 | − | 0.397619i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0000 | 1.33218 | 0.666089 | − | 0.745873i | \(-0.267967\pi\) | ||||
0.666089 | + | 0.745873i | \(0.267967\pi\) | |||||||
\(578\) | −6.50000 | − | 11.2583i | −0.270364 | − | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.50000 | − | 9.52628i | 0.228178 | − | 0.395217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.00000 | 0.165521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 1.50000 | + | 2.59808i | 0.0619116 | + | 0.107234i | 0.895320 | − | 0.445424i | \(-0.146947\pi\) |
−0.833408 | + | 0.552658i | \(0.813614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | − | 10.3923i | 0.247226 | − | 0.428207i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00000 | − | 1.73205i | −0.0410997 | − | 0.0711868i | ||||
\(593\) | 30.0000 | 1.23195 | 0.615976 | − | 0.787765i | \(-0.288762\pi\) | ||||
0.615976 | + | 0.787765i | \(0.288762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.500000 | − | 0.866025i | −0.0204808 | − | 0.0354738i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.00000 | − | 5.19615i | 0.122679 | − | 0.212486i | ||||
\(599\) | −6.00000 | + | 10.3923i | −0.245153 | + | 0.424618i | −0.962175 | − | 0.272433i | \(-0.912172\pi\) |
0.717021 | + | 0.697051i | \(0.245505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.0000 | + | 19.0526i | 0.448699 | + | 0.777170i | 0.998302 | − | 0.0582563i | \(-0.0185541\pi\) |
−0.549602 | + | 0.835426i | \(0.685221\pi\) | |||||||
\(602\) | −4.00000 | −0.163028 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.500000 | + | 0.866025i | −0.0202944 | + | 0.0351509i | −0.875994 | − | 0.482322i | \(-0.839794\pi\) |
0.855700 | + | 0.517472i | \(0.173127\pi\) | |||||||
\(608\) | 3.00000 | − | 5.19615i | 0.121666 | − | 0.210732i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −42.0000 | −1.69914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.0000 | −1.37325 | −0.686624 | − | 0.727013i | \(-0.740908\pi\) | ||||
−0.686624 | + | 0.727013i | \(0.740908\pi\) | |||||||
\(614\) | −4.50000 | − | 7.79423i | −0.181605 | − | 0.314549i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | + | 1.73205i | −0.0402911 | + | 0.0697863i | ||||
\(617\) | −16.0000 | + | 27.7128i | −0.644136 | + | 1.11568i | 0.340365 | + | 0.940294i | \(0.389449\pi\) |
−0.984500 | + | 0.175382i | \(0.943884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 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 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.00000 | 0.240578 | ||||||||
\(623\) | −0.500000 | − | 0.866025i | −0.0200321 | − | 0.0346966i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.0000 | + | 19.0526i | −0.439648 | + | 0.761493i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | −6.00000 | − | 10.3923i | −0.238667 | − | 0.413384i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.00000 | − | 1.73205i | 0.0397151 | − | 0.0687885i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.0000 | − | 31.1769i | −0.713186 | − | 1.23527i | ||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.50000 | + | 11.2583i | 0.256735 | + | 0.444677i | 0.965365 | − | 0.260902i | \(-0.0840201\pi\) |
−0.708631 | + | 0.705580i | \(0.750687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.5000 | − | 28.5788i | 0.650696 | − | 1.12704i | −0.332258 | − | 0.943189i | \(-0.607810\pi\) |
0.982954 | − | 0.183851i | \(-0.0588563\pi\) | |||||||
\(644\) | −0.500000 | + | 0.866025i | −0.0197028 | + | 0.0341262i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | −33.0000 | −1.29736 | −0.648682 | − | 0.761060i | \(-0.724679\pi\) | ||||
−0.648682 | + | 0.761060i | \(0.724679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | + | 3.46410i | −0.0783260 | + | 0.135665i | ||||
\(653\) | −13.0000 | + | 22.5167i | −0.508729 | + | 0.881145i | 0.491220 | + | 0.871036i | \(0.336551\pi\) |
−0.999949 | + | 0.0101092i | \(0.996782\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 11.0000 | 0.429478 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.00000 | 0.272888 | ||||||||
\(659\) | 10.0000 | + | 17.3205i | 0.389545 | + | 0.674711i | 0.992388 | − | 0.123148i | \(-0.0392990\pi\) |
−0.602844 | + | 0.797859i | \(0.705966\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | −4.00000 | + | 6.92820i | −0.155464 | + | 0.269272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.50000 | + | 9.52628i | 0.213441 | + | 0.369691i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | 0.348481 | ||||||||
\(668\) | −1.50000 | − | 2.59808i | −0.0580367 | − | 0.100523i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.00000 | − | 12.1244i | 0.270232 | − | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.00000 | − | 5.19615i | −0.115642 | − | 0.200297i | 0.802395 | − | 0.596794i | \(-0.203559\pi\) |
−0.918036 | + | 0.396497i | \(0.870226\pi\) | |||||||
\(674\) | −8.00000 | −0.308148 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.0000 | 0.884615 | ||||||||
\(677\) | 11.0000 | + | 19.0526i | 0.422764 | + | 0.732249i | 0.996209 | − | 0.0869952i | \(-0.0277265\pi\) |
−0.573444 | + | 0.819244i | \(0.694393\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.00000 | + | 6.92820i | −0.153506 | + | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.00000 | − | 3.46410i | −0.0765840 | − | 0.132647i | ||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.50000 | + | 11.2583i | 0.248171 | + | 0.429845i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0000 | + | 38.1051i | 0.836919 | + | 1.44959i | 0.892458 | + | 0.451130i | \(0.148979\pi\) |
−0.0555386 | + | 0.998457i | \(0.517688\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.0000 | + | 19.0526i | −0.416655 | + | 0.721667i | ||||
\(698\) | −5.50000 | + | 9.52628i | −0.208178 | + | 0.360575i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | 0.452589 | ||||||||
\(704\) | −1.00000 | − | 1.73205i | −0.0376889 | − | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.00000 | − | 13.8564i | 0.301084 | − | 0.521493i | ||||
\(707\) | −1.00000 | + | 1.73205i | −0.0376089 | + | 0.0651405i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5000 | + | 23.3827i | 0.507003 | + | 0.878155i | 0.999967 | + | 0.00810550i | \(0.00258009\pi\) |
−0.492964 | + | 0.870050i | \(0.664087\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000 | 0.0374766 | ||||||||
\(713\) | −1.00000 | − | 1.73205i | −0.0374503 | − | 0.0648658i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.00000 | − | 1.73205i | 0.0373718 | − | 0.0647298i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.0000 | − | 25.9808i | −0.559795 | − | 0.969593i | ||||
\(719\) | 44.0000 | 1.64092 | 0.820462 | − | 0.571702i | \(-0.193717\pi\) | ||||
0.820462 | + | 0.571702i | \(0.193717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 8.50000 | + | 14.7224i | 0.316337 | + | 0.547912i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.50000 | − | 11.2583i | 0.241571 | − | 0.418413i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.5000 | − | 18.1865i | −0.389423 | − | 0.674501i | 0.602949 | − | 0.797780i | \(-0.293992\pi\) |
−0.992372 | + | 0.123279i | \(0.960659\pi\) | |||||||
\(728\) | −6.00000 | −0.222375 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.00000 | + | 6.92820i | 0.147945 | + | 0.256249i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.00000 | + | 3.46410i | −0.0738717 | + | 0.127950i | −0.900595 | − | 0.434659i | \(-0.856869\pi\) |
0.826723 | + | 0.562609i | \(0.190202\pi\) | |||||||
\(734\) | −8.00000 | + | 13.8564i | −0.295285 | + | 0.511449i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.500000 | − | 0.866025i | −0.0184302 | − | 0.0319221i | ||||
\(737\) | −22.0000 | −0.810380 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.0000 | 1.47142 | 0.735712 | − | 0.677295i | \(-0.236848\pi\) | ||||
0.735712 | + | 0.677295i | \(0.236848\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.50000 | + | 12.9904i | −0.275148 | + | 0.476571i | −0.970173 | − | 0.242415i | \(-0.922060\pi\) |
0.695024 | + | 0.718986i | \(0.255394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −12.0000 | −0.439351 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | −1.50000 | − | 2.59808i | −0.0548088 | − | 0.0949316i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0000 | + | 22.5167i | −0.474377 | + | 0.821645i | −0.999570 | − | 0.0293387i | \(-0.990660\pi\) |
0.525193 | + | 0.850983i | \(0.323993\pi\) | |||||||
\(752\) | −3.50000 | + | 6.06218i | −0.127632 | + | 0.221065i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 27.0000 | + | 46.7654i | 0.983282 | + | 1.70309i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | −8.00000 | − | 13.8564i | −0.290573 | − | 0.503287i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.50000 | + | 7.79423i | −0.163125 | + | 0.282541i | −0.935988 | − | 0.352032i | \(-0.885491\pi\) |
0.772863 | + | 0.634573i | \(0.218824\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.50000 | + | 6.06218i | 0.126709 | + | 0.219466i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 32.0000 | 1.15621 | ||||||||
\(767\) | 12.0000 | + | 20.7846i | 0.433295 | + | 0.750489i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.50000 | − | 12.9904i | 0.270457 | − | 0.468445i | −0.698522 | − | 0.715589i | \(-0.746159\pi\) |
0.968979 | + | 0.247143i | \(0.0794919\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.00000 | + | 8.66025i | 0.179954 | + | 0.311689i | ||||
\(773\) | −12.0000 | −0.431610 | −0.215805 | − | 0.976436i | \(-0.569238\pi\) | ||||
−0.215805 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.00000 | − | 6.92820i | −0.143592 | − | 0.248708i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.50000 | + | 16.4545i | −0.340592 | + | 0.589922i | ||||
\(779\) | −33.0000 | + | 57.1577i | −1.18235 | + | 2.04789i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.00000 | − | 10.3923i | −0.214697 | − | 0.371866i | ||||
\(782\) | 2.00000 | 0.0715199 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.0000 | + | 38.1051i | −0.784215 | + | 1.35830i | 0.145251 | + | 0.989395i | \(0.453601\pi\) |
−0.929467 | + | 0.368906i | \(0.879732\pi\) | |||||||
\(788\) | 4.00000 | − | 6.92820i | 0.142494 | − | 0.246807i | ||||
\(789\) | 0 | 0 |