Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(1121,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.1121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.l (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1121.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.1121 |
Dual form | 1155.2.l.b.1121.2 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −1.00000 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | 1.00000 | − | 1.41421i | 0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −1.41421 | + | 2.00000i | −0.577350 | + | 0.816497i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.82843 | 1.00000 | ||||||||
\(9\) | −1.00000 | − | 2.82843i | −0.333333 | − | 0.942809i | ||||
\(10\) | − | 1.41421i | − | 0.447214i | ||||||
\(11\) | −3.00000 | − | 1.41421i | −0.904534 | − | 0.426401i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.24264i | 1.73140i | 0.500566 | + | 0.865699i | \(0.333125\pi\) | ||||
−0.500566 | + | 0.865699i | \(0.666875\pi\) | |||||||
\(14\) | − | 1.41421i | − | 0.377964i | ||||||
\(15\) | 1.41421 | + | 1.00000i | 0.365148 | + | 0.258199i | ||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −0.171573 | −0.0416125 | −0.0208063 | − | 0.999784i | \(-0.506623\pi\) | ||||
−0.0208063 | + | 0.999784i | \(0.506623\pi\) | |||||||
\(18\) | 1.41421 | + | 4.00000i | 0.333333 | + | 0.942809i | ||||
\(19\) | − | 5.24264i | − | 1.20274i | −0.798969 | − | 0.601372i | \(-0.794621\pi\) | ||
0.798969 | − | 0.601372i | \(-0.205379\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.41421 | + | 1.00000i | 0.308607 | + | 0.218218i | ||||
\(22\) | 4.24264 | + | 2.00000i | 0.904534 | + | 0.426401i | ||||
\(23\) | − | 7.24264i | − | 1.51019i | −0.655613 | − | 0.755097i | \(-0.727590\pi\) | ||
0.655613 | − | 0.755097i | \(-0.272410\pi\) | |||||||
\(24\) | 2.82843 | − | 4.00000i | 0.577350 | − | 0.816497i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 8.82843i | − | 1.73140i | ||||||
\(27\) | −5.00000 | − | 1.41421i | −0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.171573 | 0.0318603 | 0.0159301 | − | 0.999873i | \(-0.494929\pi\) | ||||
0.0159301 | + | 0.999873i | \(0.494929\pi\) | |||||||
\(30\) | −2.00000 | − | 1.41421i | −0.365148 | − | 0.258199i | ||||
\(31\) | −0.242641 | −0.0435796 | −0.0217898 | − | 0.999763i | \(-0.506936\pi\) | ||||
−0.0217898 | + | 0.999763i | \(0.506936\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.00000 | + | 2.82843i | −0.870388 | + | 0.492366i | ||||
\(34\) | 0.242641 | 0.0416125 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.242641 | −0.0398899 | −0.0199449 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199449 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(38\) | 7.41421i | 1.20274i | ||||||||
\(39\) | 8.82843 | + | 6.24264i | 1.41368 | + | 0.999623i | ||||
\(40\) | 2.82843i | 0.447214i | ||||||||
\(41\) | −7.41421 | −1.15791 | −0.578953 | − | 0.815361i | \(-0.696538\pi\) | ||||
−0.578953 | + | 0.815361i | \(0.696538\pi\) | |||||||
\(42\) | −2.00000 | − | 1.41421i | −0.308607 | − | 0.218218i | ||||
\(43\) | − | 5.24264i | − | 0.799495i | −0.916625 | − | 0.399748i | \(-0.869098\pi\) | ||
0.916625 | − | 0.399748i | \(-0.130902\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | − | 1.00000i | 0.421637 | − | 0.149071i | ||||
\(46\) | 10.2426i | 1.51019i | ||||||||
\(47\) | − | 13.0711i | − | 1.90661i | −0.302007 | − | 0.953306i | \(-0.597657\pi\) | ||
0.302007 | − | 0.953306i | \(-0.402343\pi\) | |||||||
\(48\) | −4.00000 | + | 5.65685i | −0.577350 | + | 0.816497i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.41421 | 0.200000 | ||||||||
\(51\) | −0.171573 | + | 0.242641i | −0.0240250 | + | 0.0339765i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.58579i | 0.217825i | 0.994051 | + | 0.108912i | \(0.0347368\pi\) | ||||
−0.994051 | + | 0.108912i | \(0.965263\pi\) | |||||||
\(54\) | 7.07107 | + | 2.00000i | 0.962250 | + | 0.272166i | ||||
\(55\) | 1.41421 | − | 3.00000i | 0.190693 | − | 0.404520i | ||||
\(56\) | 2.82843i | 0.377964i | ||||||||
\(57\) | −7.41421 | − | 5.24264i | −0.982037 | − | 0.694405i | ||||
\(58\) | −0.242641 | −0.0318603 | ||||||||
\(59\) | − | 6.89949i | − | 0.898238i | −0.893472 | − | 0.449119i | \(-0.851738\pi\) | ||
0.893472 | − | 0.449119i | \(-0.148262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.757359i | − | 0.0969699i | −0.998824 | − | 0.0484850i | \(-0.984561\pi\) | ||
0.998824 | − | 0.0484850i | \(-0.0154393\pi\) | |||||||
\(62\) | 0.343146 | 0.0435796 | ||||||||
\(63\) | 2.82843 | − | 1.00000i | 0.356348 | − | 0.125988i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | −6.24264 | −0.774304 | ||||||||
\(66\) | 7.07107 | − | 4.00000i | 0.870388 | − | 0.492366i | ||||
\(67\) | 4.48528 | 0.547964 | 0.273982 | − | 0.961735i | \(-0.411659\pi\) | ||||
0.273982 | + | 0.961735i | \(0.411659\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −10.2426 | − | 7.24264i | −1.23307 | − | 0.871911i | ||||
\(70\) | 1.41421 | 0.169031 | ||||||||
\(71\) | 10.2426i | 1.21558i | 0.794099 | + | 0.607789i | \(0.207943\pi\) | ||||
−0.794099 | + | 0.607789i | \(0.792057\pi\) | |||||||
\(72\) | −2.82843 | − | 8.00000i | −0.333333 | − | 0.942809i | ||||
\(73\) | − | 10.4853i | − | 1.22721i | −0.789613 | − | 0.613605i | \(-0.789719\pi\) | ||
0.789613 | − | 0.613605i | \(-0.210281\pi\) | |||||||
\(74\) | 0.343146 | 0.0398899 | ||||||||
\(75\) | −1.00000 | + | 1.41421i | −0.115470 | + | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.41421 | − | 3.00000i | 0.161165 | − | 0.341882i | ||||
\(78\) | −12.4853 | − | 8.82843i | −1.41368 | − | 0.999623i | ||||
\(79\) | − | 2.24264i | − | 0.252317i | −0.992010 | − | 0.126158i | \(-0.959735\pi\) | ||
0.992010 | − | 0.126158i | \(-0.0402648\pi\) | |||||||
\(80\) | − | 4.00000i | − | 0.447214i | ||||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | 10.4853 | 1.15791 | ||||||||
\(83\) | −11.1421 | −1.22301 | −0.611504 | − | 0.791241i | \(-0.709435\pi\) | ||||
−0.611504 | + | 0.791241i | \(0.709435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.171573i | − | 0.0186097i | ||||||
\(86\) | 7.41421i | 0.799495i | ||||||||
\(87\) | 0.171573 | − | 0.242641i | 0.0183945 | − | 0.0260138i | ||||
\(88\) | −8.48528 | − | 4.00000i | −0.904534 | − | 0.426401i | ||||
\(89\) | 13.5858i | 1.44009i | 0.693927 | + | 0.720045i | \(0.255879\pi\) | ||||
−0.693927 | + | 0.720045i | \(0.744121\pi\) | |||||||
\(90\) | −4.00000 | + | 1.41421i | −0.421637 | + | 0.149071i | ||||
\(91\) | −6.24264 | −0.654407 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.242641 | + | 0.343146i | −0.0251607 | + | 0.0355826i | ||||
\(94\) | 18.4853i | 1.90661i | ||||||||
\(95\) | 5.24264 | 0.537884 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 1.41421 | 0.142857 | ||||||||
\(99\) | −1.00000 | + | 9.89949i | −0.100504 | + | 0.994937i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.4853 | −1.44134 | −0.720670 | − | 0.693279i | \(-0.756166\pi\) | ||||
−0.720670 | + | 0.693279i | \(0.756166\pi\) | |||||||
\(102\) | 0.242641 | − | 0.343146i | 0.0240250 | − | 0.0339765i | ||||
\(103\) | −17.4853 | −1.72288 | −0.861438 | − | 0.507863i | \(-0.830436\pi\) | ||||
−0.861438 | + | 0.507863i | \(0.830436\pi\) | |||||||
\(104\) | 17.6569i | 1.73140i | ||||||||
\(105\) | −1.00000 | + | 1.41421i | −0.0975900 | + | 0.138013i | ||||
\(106\) | − | 2.24264i | − | 0.217825i | ||||||
\(107\) | 4.58579 | 0.443325 | 0.221662 | − | 0.975123i | \(-0.428852\pi\) | ||||
0.221662 | + | 0.975123i | \(0.428852\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.2426i | − | 1.17263i | −0.810082 | − | 0.586316i | \(-0.800578\pi\) | ||
0.810082 | − | 0.586316i | \(-0.199422\pi\) | |||||||
\(110\) | −2.00000 | + | 4.24264i | −0.190693 | + | 0.404520i | ||||
\(111\) | −0.242641 | + | 0.343146i | −0.0230304 | + | 0.0325700i | ||||
\(112\) | − | 4.00000i | − | 0.377964i | ||||||
\(113\) | 0.899495i | 0.0846174i | 0.999105 | + | 0.0423087i | \(0.0134713\pi\) | ||||
−0.999105 | + | 0.0423087i | \(0.986529\pi\) | |||||||
\(114\) | 10.4853 | + | 7.41421i | 0.982037 | + | 0.694405i | ||||
\(115\) | 7.24264 | 0.675380 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.6569 | − | 6.24264i | 1.63238 | − | 0.577132i | ||||
\(118\) | 9.75736i | 0.898238i | ||||||||
\(119\) | − | 0.171573i | − | 0.0157281i | ||||||
\(120\) | 4.00000 | + | 2.82843i | 0.365148 | + | 0.258199i | ||||
\(121\) | 7.00000 | + | 8.48528i | 0.636364 | + | 0.771389i | ||||
\(122\) | 1.07107i | 0.0969699i | ||||||||
\(123\) | −7.41421 | + | 10.4853i | −0.668517 | + | 0.945426i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −4.00000 | + | 1.41421i | −0.356348 | + | 0.125988i | ||||
\(127\) | − | 4.75736i | − | 0.422147i | −0.977470 | − | 0.211074i | \(-0.932304\pi\) | ||
0.977470 | − | 0.211074i | \(-0.0676960\pi\) | |||||||
\(128\) | −11.3137 | −1.00000 | ||||||||
\(129\) | −7.41421 | − | 5.24264i | −0.652785 | − | 0.461589i | ||||
\(130\) | 8.82843 | 0.774304 | ||||||||
\(131\) | −16.5858 | −1.44911 | −0.724553 | − | 0.689219i | \(-0.757954\pi\) | ||||
−0.724553 | + | 0.689219i | \(0.757954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.24264 | 0.454595 | ||||||||
\(134\) | −6.34315 | −0.547964 | ||||||||
\(135\) | 1.41421 | − | 5.00000i | 0.121716 | − | 0.430331i | ||||
\(136\) | −0.485281 | −0.0416125 | ||||||||
\(137\) | − | 2.48528i | − | 0.212332i | −0.994348 | − | 0.106166i | \(-0.966143\pi\) | ||
0.994348 | − | 0.106166i | \(-0.0338575\pi\) | |||||||
\(138\) | 14.4853 | + | 10.2426i | 1.23307 | + | 0.871911i | ||||
\(139\) | − | 4.48528i | − | 0.380437i | −0.981742 | − | 0.190218i | \(-0.939080\pi\) | ||
0.981742 | − | 0.190218i | \(-0.0609196\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.4853 | − | 13.0711i | −1.55674 | − | 1.10078i | ||||
\(142\) | − | 14.4853i | − | 1.21558i | ||||||
\(143\) | 8.82843 | − | 18.7279i | 0.738270 | − | 1.56611i | ||||
\(144\) | 4.00000 | + | 11.3137i | 0.333333 | + | 0.942809i | ||||
\(145\) | 0.171573i | 0.0142484i | ||||||||
\(146\) | 14.8284i | 1.22721i | ||||||||
\(147\) | −1.00000 | + | 1.41421i | −0.0824786 | + | 0.116642i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 1.41421 | − | 2.00000i | 0.115470 | − | 0.163299i | ||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | − | 14.8284i | − | 1.20274i | ||||||
\(153\) | 0.171573 | + | 0.485281i | 0.0138708 | + | 0.0392327i | ||||
\(154\) | −2.00000 | + | 4.24264i | −0.161165 | + | 0.341882i | ||||
\(155\) | − | 0.242641i | − | 0.0194894i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0000 | 0.877896 | 0.438948 | − | 0.898513i | \(-0.355351\pi\) | ||||
0.438948 | + | 0.898513i | \(0.355351\pi\) | |||||||
\(158\) | 3.17157i | 0.252317i | ||||||||
\(159\) | 2.24264 | + | 1.58579i | 0.177853 | + | 0.125761i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.24264 | 0.570800 | ||||||||
\(162\) | 9.89949 | − | 8.00000i | 0.777778 | − | 0.628539i | ||||
\(163\) | −6.24264 | −0.488961 | −0.244481 | − | 0.969654i | \(-0.578617\pi\) | ||||
−0.244481 | + | 0.969654i | \(0.578617\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.82843 | − | 5.00000i | −0.220193 | − | 0.389249i | ||||
\(166\) | 15.7574 | 1.22301 | ||||||||
\(167\) | −8.14214 | −0.630057 | −0.315029 | − | 0.949082i | \(-0.602014\pi\) | ||||
−0.315029 | + | 0.949082i | \(0.602014\pi\) | |||||||
\(168\) | 4.00000 | + | 2.82843i | 0.308607 | + | 0.218218i | ||||
\(169\) | −25.9706 | −1.99774 | ||||||||
\(170\) | 0.242641i | 0.0186097i | ||||||||
\(171\) | −14.8284 | + | 5.24264i | −1.13396 | + | 0.400915i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.82843 | 0.215041 | 0.107521 | − | 0.994203i | \(-0.465709\pi\) | ||||
0.107521 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(174\) | −0.242641 | + | 0.343146i | −0.0183945 | + | 0.0260138i | ||||
\(175\) | − | 1.00000i | − | 0.0755929i | ||||||
\(176\) | 12.0000 | + | 5.65685i | 0.904534 | + | 0.426401i | ||||
\(177\) | −9.75736 | − | 6.89949i | −0.733408 | − | 0.518598i | ||||
\(178\) | − | 19.2132i | − | 1.44009i | ||||||
\(179\) | − | 10.5858i | − | 0.791219i | −0.918419 | − | 0.395609i | \(-0.870533\pi\) | ||
0.918419 | − | 0.395609i | \(-0.129467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.9706 | 1.70739 | 0.853694 | − | 0.520775i | \(-0.174357\pi\) | ||||
0.853694 | + | 0.520775i | \(0.174357\pi\) | |||||||
\(182\) | 8.82843 | 0.654407 | ||||||||
\(183\) | −1.07107 | − | 0.757359i | −0.0791756 | − | 0.0559856i | ||||
\(184\) | − | 20.4853i | − | 1.51019i | ||||||
\(185\) | − | 0.242641i | − | 0.0178393i | ||||||
\(186\) | 0.343146 | − | 0.485281i | 0.0251607 | − | 0.0355826i | ||||
\(187\) | 0.514719 | + | 0.242641i | 0.0376400 | + | 0.0177436i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.41421 | − | 5.00000i | 0.102869 | − | 0.363696i | ||||
\(190\) | −7.41421 | −0.537884 | ||||||||
\(191\) | 14.8284i | 1.07295i | 0.843917 | + | 0.536474i | \(0.180244\pi\) | ||||
−0.843917 | + | 0.536474i | \(0.819756\pi\) | |||||||
\(192\) | 8.00000 | − | 11.3137i | 0.577350 | − | 0.816497i | ||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | 9.89949 | 0.710742 | ||||||||
\(195\) | −6.24264 | + | 8.82843i | −0.447045 | + | 0.632217i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00000 | 0.427482 | 0.213741 | − | 0.976890i | \(-0.431435\pi\) | ||||
0.213741 | + | 0.976890i | \(0.431435\pi\) | |||||||
\(198\) | 1.41421 | − | 14.0000i | 0.100504 | − | 0.994937i | ||||
\(199\) | 24.4853 | 1.73572 | 0.867858 | − | 0.496813i | \(-0.165496\pi\) | ||||
0.867858 | + | 0.496813i | \(0.165496\pi\) | |||||||
\(200\) | −2.82843 | −0.200000 | ||||||||
\(201\) | 4.48528 | − | 6.34315i | 0.316367 | − | 0.447411i | ||||
\(202\) | 20.4853 | 1.44134 | ||||||||
\(203\) | 0.171573i | 0.0120421i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 7.41421i | − | 0.517831i | ||||||
\(206\) | 24.7279 | 1.72288 | ||||||||
\(207\) | −20.4853 | + | 7.24264i | −1.42383 | + | 0.503398i | ||||
\(208\) | − | 24.9706i | − | 1.73140i | ||||||
\(209\) | −7.41421 | + | 15.7279i | −0.512852 | + | 1.08792i | ||||
\(210\) | 1.41421 | − | 2.00000i | 0.0975900 | − | 0.138013i | ||||
\(211\) | − | 8.00000i | − | 0.550743i | −0.961338 | − | 0.275371i | \(-0.911199\pi\) | ||
0.961338 | − | 0.275371i | \(-0.0888008\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.4853 | + | 10.2426i | 0.992515 | + | 0.701814i | ||||
\(214\) | −6.48528 | −0.443325 | ||||||||
\(215\) | 5.24264 | 0.357545 | ||||||||
\(216\) | −14.1421 | − | 4.00000i | −0.962250 | − | 0.272166i | ||||
\(217\) | − | 0.242641i | − | 0.0164715i | ||||||
\(218\) | 17.3137i | 1.17263i | ||||||||
\(219\) | −14.8284 | − | 10.4853i | −1.00201 | − | 0.708530i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.07107i | − | 0.0720478i | ||||||
\(222\) | 0.343146 | − | 0.485281i | 0.0230304 | − | 0.0325700i | ||||
\(223\) | 17.0000 | 1.13840 | 0.569202 | − | 0.822198i | \(-0.307252\pi\) | ||||
0.569202 | + | 0.822198i | \(0.307252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | + | 2.82843i | 0.0666667 | + | 0.188562i | ||||
\(226\) | − | 1.27208i | − | 0.0846174i | ||||||
\(227\) | −11.8284 | −0.785080 | −0.392540 | − | 0.919735i | \(-0.628404\pi\) | ||||
−0.392540 | + | 0.919735i | \(0.628404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.72792 | −0.444594 | −0.222297 | − | 0.974979i | \(-0.571355\pi\) | ||||
−0.222297 | + | 0.974979i | \(0.571355\pi\) | |||||||
\(230\) | −10.2426 | −0.675380 | ||||||||
\(231\) | −2.82843 | − | 5.00000i | −0.186097 | − | 0.328976i | ||||
\(232\) | 0.485281 | 0.0318603 | ||||||||
\(233\) | 21.5563 | 1.41220 | 0.706102 | − | 0.708110i | \(-0.250452\pi\) | ||||
0.706102 | + | 0.708110i | \(0.250452\pi\) | |||||||
\(234\) | −24.9706 | + | 8.82843i | −1.63238 | + | 0.577132i | ||||
\(235\) | 13.0711 | 0.852662 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.17157 | − | 2.24264i | −0.206016 | − | 0.145675i | ||||
\(238\) | 0.242641i | 0.0157281i | ||||||||
\(239\) | 2.65685 | 0.171858 | 0.0859288 | − | 0.996301i | \(-0.472614\pi\) | ||||
0.0859288 | + | 0.996301i | \(0.472614\pi\) | |||||||
\(240\) | −5.65685 | − | 4.00000i | −0.365148 | − | 0.258199i | ||||
\(241\) | 26.4853i | 1.70607i | 0.521856 | + | 0.853033i | \(0.325240\pi\) | ||||
−0.521856 | + | 0.853033i | \(0.674760\pi\) | |||||||
\(242\) | −9.89949 | − | 12.0000i | −0.636364 | − | 0.771389i | ||||
\(243\) | 1.00000 | + | 15.5563i | 0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.00000i | − | 0.0638877i | ||||||
\(246\) | 10.4853 | − | 14.8284i | 0.668517 | − | 0.945426i | ||||
\(247\) | 32.7279 | 2.08243 | ||||||||
\(248\) | −0.686292 | −0.0435796 | ||||||||
\(249\) | −11.1421 | + | 15.7574i | −0.706104 | + | 0.998582i | ||||
\(250\) | 1.41421i | 0.0894427i | ||||||||
\(251\) | 4.97056i | 0.313739i | 0.987619 | + | 0.156870i | \(0.0501402\pi\) | ||||
−0.987619 | + | 0.156870i | \(0.949860\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.2426 | + | 21.7279i | −0.643949 | + | 1.36602i | ||||
\(254\) | 6.72792i | 0.422147i | ||||||||
\(255\) | −0.242641 | − | 0.171573i | −0.0151947 | − | 0.0107443i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 13.7574i | − | 0.858160i | −0.903266 | − | 0.429080i | \(-0.858838\pi\) | ||
0.903266 | − | 0.429080i | \(-0.141162\pi\) | |||||||
\(258\) | 10.4853 | + | 7.41421i | 0.652785 | + | 0.461589i | ||||
\(259\) | − | 0.242641i | − | 0.0150770i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.171573 | − | 0.485281i | −0.0106201 | − | 0.0300382i | ||||
\(262\) | 23.4558 | 1.44911 | ||||||||
\(263\) | −15.1716 | −0.935519 | −0.467760 | − | 0.883856i | \(-0.654939\pi\) | ||||
−0.467760 | + | 0.883856i | \(0.654939\pi\) | |||||||
\(264\) | −14.1421 | + | 8.00000i | −0.870388 | + | 0.492366i | ||||
\(265\) | −1.58579 | −0.0974141 | ||||||||
\(266\) | −7.41421 | −0.454595 | ||||||||
\(267\) | 19.2132 | + | 13.5858i | 1.17583 | + | 0.831437i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 30.5563i | − | 1.86305i | −0.363673 | − | 0.931527i | \(-0.618477\pi\) | ||
0.363673 | − | 0.931527i | \(-0.381523\pi\) | |||||||
\(270\) | −2.00000 | + | 7.07107i | −0.121716 | + | 0.430331i | ||||
\(271\) | 23.2426i | 1.41189i | 0.708267 | + | 0.705945i | \(0.249477\pi\) | ||||
−0.708267 | + | 0.705945i | \(0.750523\pi\) | |||||||
\(272\) | 0.686292 | 0.0416125 | ||||||||
\(273\) | −6.24264 | + | 8.82843i | −0.377822 | + | 0.534321i | ||||
\(274\) | 3.51472i | 0.212332i | ||||||||
\(275\) | 3.00000 | + | 1.41421i | 0.180907 | + | 0.0852803i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.48528i | 0.509831i | 0.966963 | + | 0.254916i | \(0.0820477\pi\) | ||||
−0.966963 | + | 0.254916i | \(0.917952\pi\) | |||||||
\(278\) | 6.34315i | 0.380437i | ||||||||
\(279\) | 0.242641 | + | 0.686292i | 0.0145265 | + | 0.0410872i | ||||
\(280\) | −2.82843 | −0.169031 | ||||||||
\(281\) | 17.3137 | 1.03285 | 0.516425 | − | 0.856333i | \(-0.327263\pi\) | ||||
0.516425 | + | 0.856333i | \(0.327263\pi\) | |||||||
\(282\) | 26.1421 | + | 18.4853i | 1.55674 | + | 1.10078i | ||||
\(283\) | − | 13.2132i | − | 0.785443i | −0.919657 | − | 0.392722i | \(-0.871534\pi\) | ||
0.919657 | − | 0.392722i | \(-0.128466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.24264 | − | 7.41421i | 0.310547 | − | 0.439180i | ||||
\(286\) | −12.4853 | + | 26.4853i | −0.738270 | + | 1.56611i | ||||
\(287\) | − | 7.41421i | − | 0.437647i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9706 | −0.998268 | ||||||||
\(290\) | − | 0.242641i | − | 0.0142484i | ||||||
\(291\) | −7.00000 | + | 9.89949i | −0.410347 | + | 0.580319i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6569 | 0.856263 | 0.428131 | − | 0.903717i | \(-0.359172\pi\) | ||||
0.428131 | + | 0.903717i | \(0.359172\pi\) | |||||||
\(294\) | 1.41421 | − | 2.00000i | 0.0824786 | − | 0.116642i | ||||
\(295\) | 6.89949 | 0.401704 | ||||||||
\(296\) | −0.686292 | −0.0398899 | ||||||||
\(297\) | 13.0000 | + | 11.3137i | 0.754337 | + | 0.656488i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 45.2132 | 2.61475 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.24264 | 0.302181 | ||||||||
\(302\) | 14.1421i | 0.813788i | ||||||||
\(303\) | −14.4853 | + | 20.4853i | −0.832158 | + | 1.17685i | ||||
\(304\) | 20.9706i | 1.20274i | ||||||||
\(305\) | 0.757359 | 0.0433663 | ||||||||
\(306\) | −0.242641 | − | 0.686292i | −0.0138708 | − | 0.0392327i | ||||
\(307\) | 3.51472i | 0.200596i | 0.994957 | + | 0.100298i | \(0.0319796\pi\) | ||||
−0.994957 | + | 0.100298i | \(0.968020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4853 | + | 24.7279i | −0.994703 | + | 1.40672i | ||||
\(310\) | 0.343146i | 0.0194894i | ||||||||
\(311\) | 9.17157i | 0.520072i | 0.965599 | + | 0.260036i | \(0.0837345\pi\) | ||||
−0.965599 | + | 0.260036i | \(0.916266\pi\) | |||||||
\(312\) | 24.9706 | + | 17.6569i | 1.41368 | + | 0.999623i | ||||
\(313\) | 24.4558 | 1.38233 | 0.691163 | − | 0.722699i | \(-0.257099\pi\) | ||||
0.691163 | + | 0.722699i | \(0.257099\pi\) | |||||||
\(314\) | −15.5563 | −0.877896 | ||||||||
\(315\) | 1.00000 | + | 2.82843i | 0.0563436 | + | 0.159364i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 27.1716i | − | 1.52611i | −0.646335 | − | 0.763054i | \(-0.723699\pi\) | ||
0.646335 | − | 0.763054i | \(-0.276301\pi\) | |||||||
\(318\) | −3.17157 | − | 2.24264i | −0.177853 | − | 0.125761i | ||||
\(319\) | −0.514719 | − | 0.242641i | −0.0288187 | − | 0.0135853i | ||||
\(320\) | 8.00000i | 0.447214i | ||||||||
\(321\) | 4.58579 | − | 6.48528i | 0.255954 | − | 0.361973i | ||||
\(322\) | −10.2426 | −0.570800 | ||||||||
\(323\) | 0.899495i | 0.0500492i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.24264i | − | 0.346279i | ||||||
\(326\) | 8.82843 | 0.488961 | ||||||||
\(327\) | −17.3137 | − | 12.2426i | −0.957450 | − | 0.677020i | ||||
\(328\) | −20.9706 | −1.15791 | ||||||||
\(329\) | 13.0711 | 0.720631 | ||||||||
\(330\) | 4.00000 | + | 7.07107i | 0.220193 | + | 0.389249i | ||||
\(331\) | 19.4853 | 1.07101 | 0.535504 | − | 0.844533i | \(-0.320122\pi\) | ||||
0.535504 | + | 0.844533i | \(0.320122\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.242641 | + | 0.686292i | 0.0132966 | + | 0.0376085i | ||||
\(334\) | 11.5147 | 0.630057 | ||||||||
\(335\) | 4.48528i | 0.245057i | ||||||||
\(336\) | −5.65685 | − | 4.00000i | −0.308607 | − | 0.218218i | ||||
\(337\) | − | 18.7574i | − | 1.02178i | −0.859647 | − | 0.510889i | \(-0.829316\pi\) | ||
0.859647 | − | 0.510889i | \(-0.170684\pi\) | |||||||
\(338\) | 36.7279 | 1.99774 | ||||||||
\(339\) | 1.27208 | + | 0.899495i | 0.0690898 | + | 0.0488539i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.727922 | + | 0.343146i | 0.0394192 | + | 0.0185824i | ||||
\(342\) | 20.9706 | − | 7.41421i | 1.13396 | − | 0.400915i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | − | 14.8284i | − | 0.799495i | ||||||
\(345\) | 7.24264 | − | 10.2426i | 0.389931 | − | 0.551445i | ||||
\(346\) | −4.00000 | −0.215041 | ||||||||
\(347\) | 21.1716 | 1.13655 | 0.568275 | − | 0.822839i | \(-0.307611\pi\) | ||||
0.568275 | + | 0.822839i | \(0.307611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2426i | 1.13709i | 0.822651 | + | 0.568546i | \(0.192494\pi\) | ||||
−0.822651 | + | 0.568546i | \(0.807506\pi\) | |||||||
\(350\) | 1.41421i | 0.0755929i | ||||||||
\(351\) | 8.82843 | − | 31.2132i | 0.471227 | − | 1.66604i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000i | 0.958043i | 0.877803 | + | 0.479022i | \(0.159008\pi\) | ||||
−0.877803 | + | 0.479022i | \(0.840992\pi\) | |||||||
\(354\) | 13.7990 | + | 9.75736i | 0.733408 | + | 0.518598i | ||||
\(355\) | −10.2426 | −0.543623 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.242641 | − | 0.171573i | −0.0128419 | − | 0.00908060i | ||||
\(358\) | 14.9706i | 0.791219i | ||||||||
\(359\) | 31.6274 | 1.66923 | 0.834616 | − | 0.550833i | \(-0.185690\pi\) | ||||
0.834616 | + | 0.550833i | \(0.185690\pi\) | |||||||
\(360\) | 8.00000 | − | 2.82843i | 0.421637 | − | 0.149071i | ||||
\(361\) | −8.48528 | −0.446594 | ||||||||
\(362\) | −32.4853 | −1.70739 | ||||||||
\(363\) | 19.0000 | − | 1.41421i | 0.997241 | − | 0.0742270i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.4853 | 0.548825 | ||||||||
\(366\) | 1.51472 | + | 1.07107i | 0.0791756 | + | 0.0559856i | ||||
\(367\) | 3.00000 | 0.156599 | 0.0782994 | − | 0.996930i | \(-0.475051\pi\) | ||||
0.0782994 | + | 0.996930i | \(0.475051\pi\) | |||||||
\(368\) | 28.9706i | 1.51019i | ||||||||
\(369\) | 7.41421 | + | 20.9706i | 0.385969 | + | 1.09168i | ||||
\(370\) | 0.343146i | 0.0178393i | ||||||||
\(371\) | −1.58579 | −0.0823299 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 36.2132i | − | 1.87505i | −0.347920 | − | 0.937524i | \(-0.613112\pi\) | ||
0.347920 | − | 0.937524i | \(-0.386888\pi\) | |||||||
\(374\) | −0.727922 | − | 0.343146i | −0.0376400 | − | 0.0177436i | ||||
\(375\) | −1.41421 | − | 1.00000i | −0.0730297 | − | 0.0516398i | ||||
\(376\) | − | 36.9706i | − | 1.90661i | ||||||
\(377\) | 1.07107i | 0.0551628i | ||||||||
\(378\) | −2.00000 | + | 7.07107i | −0.102869 | + | 0.363696i | ||||
\(379\) | −32.4558 | −1.66714 | −0.833572 | − | 0.552410i | \(-0.813708\pi\) | ||||
−0.833572 | + | 0.552410i | \(0.813708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.72792 | − | 4.75736i | −0.344682 | − | 0.243727i | ||||
\(382\) | − | 20.9706i | − | 1.07295i | ||||||
\(383\) | − | 34.5858i | − | 1.76725i | −0.468194 | − | 0.883626i | \(-0.655095\pi\) | ||
0.468194 | − | 0.883626i | \(-0.344905\pi\) | |||||||
\(384\) | −11.3137 | + | 16.0000i | −0.577350 | + | 0.816497i | ||||
\(385\) | 3.00000 | + | 1.41421i | 0.152894 | + | 0.0720750i | ||||
\(386\) | − | 14.1421i | − | 0.719816i | ||||||
\(387\) | −14.8284 | + | 5.24264i | −0.753771 | + | 0.266498i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.2426i | 0.519322i | 0.965700 | + | 0.259661i | \(0.0836109\pi\) | ||||
−0.965700 | + | 0.259661i | \(0.916389\pi\) | |||||||
\(390\) | 8.82843 | − | 12.4853i | 0.447045 | − | 0.632217i | ||||
\(391\) | 1.24264i | 0.0628430i | ||||||||
\(392\) | −2.82843 | −0.142857 | ||||||||
\(393\) | −16.5858 | + | 23.4558i | −0.836642 | + | 1.18319i | ||||
\(394\) | −8.48528 | −0.427482 | ||||||||
\(395\) | 2.24264 | 0.112839 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −34.0000 | −1.70641 | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −34.6274 | −1.73572 | ||||||||
\(399\) | 5.24264 | − | 7.41421i | 0.262460 | − | 0.371175i | ||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 30.7279i | 1.53448i | 0.641361 | + | 0.767240i | \(0.278370\pi\) | ||||
−0.641361 | + | 0.767240i | \(0.721630\pi\) | |||||||
\(402\) | −6.34315 | + | 8.97056i | −0.316367 | + | 0.447411i | ||||
\(403\) | − | 1.51472i | − | 0.0754535i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.65685 | − | 7.00000i | −0.281091 | − | 0.347833i | ||||
\(406\) | − | 0.242641i | − | 0.0120421i | ||||||
\(407\) | 0.727922 | + | 0.343146i | 0.0360818 | + | 0.0170091i | ||||
\(408\) | −0.485281 | + | 0.686292i | −0.0240250 | + | 0.0339765i | ||||
\(409\) | 1.51472i | 0.0748980i | 0.999299 | + | 0.0374490i | \(0.0119232\pi\) | ||||
−0.999299 | + | 0.0374490i | \(0.988077\pi\) | |||||||
\(410\) | 10.4853i | 0.517831i | ||||||||
\(411\) | −3.51472 | − | 2.48528i | −0.173368 | − | 0.122590i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.89949 | 0.339502 | ||||||||
\(414\) | 28.9706 | − | 10.2426i | 1.42383 | − | 0.503398i | ||||
\(415\) | − | 11.1421i | − | 0.546946i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.34315 | − | 4.48528i | −0.310625 | − | 0.219645i | ||||
\(418\) | 10.4853 | − | 22.2426i | 0.512852 | − | 1.08792i | ||||
\(419\) | 28.4142i | 1.38813i | 0.719915 | + | 0.694063i | \(0.244181\pi\) | ||||
−0.719915 | + | 0.694063i | \(0.755819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.51472 | −0.220034 | −0.110017 | − | 0.993930i | \(-0.535091\pi\) | ||||
−0.110017 | + | 0.993930i | \(0.535091\pi\) | |||||||
\(422\) | 11.3137i | 0.550743i | ||||||||
\(423\) | −36.9706 | + | 13.0711i | −1.79757 | + | 0.635537i | ||||
\(424\) | 4.48528i | 0.217825i | ||||||||
\(425\) | 0.171573 | 0.00832251 | ||||||||
\(426\) | −20.4853 | − | 14.4853i | −0.992515 | − | 0.701814i | ||||
\(427\) | 0.757359 | 0.0366512 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6569 | − | 31.2132i | −0.852481 | − | 1.50699i | ||||
\(430\) | −7.41421 | −0.357545 | ||||||||
\(431\) | −12.3431 | −0.594548 | −0.297274 | − | 0.954792i | \(-0.596078\pi\) | ||||
−0.297274 | + | 0.954792i | \(0.596078\pi\) | |||||||
\(432\) | 20.0000 | + | 5.65685i | 0.962250 | + | 0.272166i | ||||
\(433\) | −12.0000 | −0.576683 | −0.288342 | − | 0.957528i | \(-0.593104\pi\) | ||||
−0.288342 | + | 0.957528i | \(0.593104\pi\) | |||||||
\(434\) | 0.343146i | 0.0164715i | ||||||||
\(435\) | 0.242641 | + | 0.171573i | 0.0116337 | + | 0.00822629i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.9706 | −1.81638 | ||||||||
\(438\) | 20.9706 | + | 14.8284i | 1.00201 | + | 0.708530i | ||||
\(439\) | 3.24264i | 0.154763i | 0.997002 | + | 0.0773814i | \(0.0246559\pi\) | ||||
−0.997002 | + | 0.0773814i | \(0.975344\pi\) | |||||||
\(440\) | 4.00000 | − | 8.48528i | 0.190693 | − | 0.404520i | ||||
\(441\) | 1.00000 | + | 2.82843i | 0.0476190 | + | 0.134687i | ||||
\(442\) | 1.51472i | 0.0720478i | ||||||||
\(443\) | 11.3137i | 0.537531i | 0.963206 | + | 0.268765i | \(0.0866156\pi\) | ||||
−0.963206 | + | 0.268765i | \(0.913384\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5858 | −0.644028 | ||||||||
\(446\) | −24.0416 | −1.13840 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.00000i | 0.377964i | ||||||||
\(449\) | − | 36.7279i | − | 1.73330i | −0.498919 | − | 0.866649i | \(-0.666269\pi\) | ||
0.498919 | − | 0.866649i | \(-0.333731\pi\) | |||||||
\(450\) | −1.41421 | − | 4.00000i | −0.0666667 | − | 0.188562i | ||||
\(451\) | 22.2426 | + | 10.4853i | 1.04737 | + | 0.493733i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.1421 | − | 10.0000i | −0.664455 | − | 0.469841i | ||||
\(454\) | 16.7279 | 0.785080 | ||||||||
\(455\) | − | 6.24264i | − | 0.292660i | ||||||
\(456\) | −20.9706 | − | 14.8284i | −0.982037 | − | 0.694405i | ||||
\(457\) | 10.2132i | 0.477754i | 0.971050 | + | 0.238877i | \(0.0767792\pi\) | ||||
−0.971050 | + | 0.238877i | \(0.923221\pi\) | |||||||
\(458\) | 9.51472 | 0.444594 | ||||||||
\(459\) | 0.857864 | + | 0.242641i | 0.0400417 | + | 0.0113255i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6569 | 1.38126 | 0.690629 | − | 0.723210i | \(-0.257334\pi\) | ||||
0.690629 | + | 0.723210i | \(0.257334\pi\) | |||||||
\(462\) | 4.00000 | + | 7.07107i | 0.186097 | + | 0.328976i | ||||
\(463\) | 26.0000 | 1.20832 | 0.604161 | − | 0.796862i | \(-0.293508\pi\) | ||||
0.604161 | + | 0.796862i | \(0.293508\pi\) | |||||||
\(464\) | −0.686292 | −0.0318603 | ||||||||
\(465\) | −0.343146 | − | 0.242641i | −0.0159130 | − | 0.0112522i | ||||
\(466\) | −30.4853 | −1.41220 | ||||||||
\(467\) | − | 0.343146i | − | 0.0158789i | −0.999968 | − | 0.00793945i | \(-0.997473\pi\) | ||
0.999968 | − | 0.00793945i | \(-0.00252723\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.48528i | 0.207111i | ||||||||
\(470\) | −18.4853 | −0.852662 | ||||||||
\(471\) | 11.0000 | − | 15.5563i | 0.506853 | − | 0.716799i | ||||
\(472\) | − | 19.5147i | − | 0.898238i | ||||||
\(473\) | −7.41421 | + | 15.7279i | −0.340906 | + | 0.723171i | ||||
\(474\) | 4.48528 | + | 3.17157i | 0.206016 | + | 0.145675i | ||||
\(475\) | 5.24264i | 0.240549i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.48528 | − | 1.58579i | 0.205367 | − | 0.0726082i | ||||
\(478\) | −3.75736 | −0.171858 | ||||||||
\(479\) | −27.2132 | −1.24340 | −0.621702 | − | 0.783254i | \(-0.713558\pi\) | ||||
−0.621702 | + | 0.783254i | \(0.713558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.51472i | − | 0.0690652i | ||||||
\(482\) | − | 37.4558i | − | 1.70607i | ||||||
\(483\) | 7.24264 | − | 10.2426i | 0.329552 | − | 0.466056i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7.00000i | − | 0.317854i | ||||||
\(486\) | −1.41421 | − | 22.0000i | −0.0641500 | − | 0.997940i | ||||
\(487\) | 3.02944 | 0.137277 | 0.0686385 | − | 0.997642i | \(-0.478135\pi\) | ||||
0.0686385 | + | 0.997642i | \(0.478135\pi\) | |||||||
\(488\) | − | 2.14214i | − | 0.0969699i | ||||||
\(489\) | −6.24264 | + | 8.82843i | −0.282302 | + | 0.399235i | ||||
\(490\) | 1.41421i | 0.0638877i | ||||||||
\(491\) | 15.3431 | 0.692426 | 0.346213 | − | 0.938156i | \(-0.387467\pi\) | ||||
0.346213 | + | 0.938156i | \(0.387467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0294373 | −0.00132579 | ||||||||
\(494\) | −46.2843 | −2.08243 | ||||||||
\(495\) | −9.89949 | − | 1.00000i | −0.444949 | − | 0.0449467i | ||||
\(496\) | 0.970563 | 0.0435796 | ||||||||
\(497\) | −10.2426 | −0.459445 | ||||||||
\(498\) | 15.7574 | − | 22.2843i | 0.706104 | − | 0.998582i | ||||
\(499\) | −11.4853 | −0.514152 | −0.257076 | − | 0.966391i | \(-0.582759\pi\) | ||||
−0.257076 | + | 0.966391i | \(0.582759\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.14214 | + | 11.5147i | −0.363764 | + | 0.514440i | ||||
\(502\) | − | 7.02944i | − | 0.313739i | ||||||
\(503\) | 10.4558 | 0.466203 | 0.233102 | − | 0.972452i | \(-0.425113\pi\) | ||||
0.233102 | + | 0.972452i | \(0.425113\pi\) | |||||||
\(504\) | 8.00000 | − | 2.82843i | 0.356348 | − | 0.125988i | ||||
\(505\) | − | 14.4853i | − | 0.644587i | ||||||
\(506\) | 14.4853 | − | 30.7279i | 0.643949 | − | 1.36602i | ||||
\(507\) | −25.9706 | + | 36.7279i | −1.15339 | + | 1.63114i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 28.7574i | 1.27465i | 0.770596 | + | 0.637324i | \(0.219959\pi\) | ||||
−0.770596 | + | 0.637324i | \(0.780041\pi\) | |||||||
\(510\) | 0.343146 | + | 0.242641i | 0.0151947 | + | 0.0107443i | ||||
\(511\) | 10.4853 | 0.463842 | ||||||||
\(512\) | 22.6274 | 1.00000 | ||||||||
\(513\) | −7.41421 | + | 26.2132i | −0.327346 | + | 1.15734i | ||||
\(514\) | 19.4558i | 0.858160i | ||||||||
\(515\) | − | 17.4853i | − | 0.770494i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.4853 | + | 39.2132i | −0.812982 | + | 1.72459i | ||||
\(518\) | 0.343146i | 0.0150770i | ||||||||
\(519\) | 2.82843 | − | 4.00000i | 0.124154 | − | 0.175581i | ||||
\(520\) | −17.6569 | −0.774304 | ||||||||
\(521\) | 7.58579i | 0.332339i | 0.986097 | + | 0.166170i | \(0.0531399\pi\) | ||||
−0.986097 | + | 0.166170i | \(0.946860\pi\) | |||||||
\(522\) | 0.242641 | + | 0.686292i | 0.0106201 | + | 0.0300382i | ||||
\(523\) | − | 26.9706i | − | 1.17934i | −0.807644 | − | 0.589670i | \(-0.799258\pi\) | ||
0.807644 | − | 0.589670i | \(-0.200742\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.41421 | − | 1.00000i | −0.0617213 | − | 0.0436436i | ||||
\(526\) | 21.4558 | 0.935519 | ||||||||
\(527\) | 0.0416306 | 0.00181346 | ||||||||
\(528\) | 20.0000 | − | 11.3137i | 0.870388 | − | 0.492366i | ||||
\(529\) | −29.4558 | −1.28069 | ||||||||
\(530\) | 2.24264 | 0.0974141 | ||||||||
\(531\) | −19.5147 | + | 6.89949i | −0.846867 | + | 0.299413i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 46.2843i | − | 2.00479i | ||||||
\(534\) | −27.1716 | − | 19.2132i | −1.17583 | − | 0.831437i | ||||
\(535\) | 4.58579i | 0.198261i | ||||||||
\(536\) | 12.6863 | 0.547964 | ||||||||
\(537\) | −14.9706 | − | 10.5858i | −0.646027 | − | 0.456810i | ||||
\(538\) | 43.2132i | 1.86305i | ||||||||
\(539\) | 3.00000 | + | 1.41421i | 0.129219 | + | 0.0609145i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7279i | 0.633203i | 0.948559 | + | 0.316601i | \(0.102542\pi\) | ||||
−0.948559 | + | 0.316601i | \(0.897458\pi\) | |||||||
\(542\) | − | 32.8701i | − | 1.41189i | ||||||
\(543\) | 22.9706 | − | 32.4853i | 0.985761 | − | 1.39408i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.2426 | 0.524417 | ||||||||
\(546\) | 8.82843 | − | 12.4853i | 0.377822 | − | 0.534321i | ||||
\(547\) | 14.7574i | 0.630979i | 0.948929 | + | 0.315490i | \(0.102169\pi\) | ||||
−0.948929 | + | 0.315490i | \(0.897831\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.14214 | + | 0.757359i | −0.0914241 | + | 0.0323233i | ||||
\(550\) | −4.24264 | − | 2.00000i | −0.180907 | − | 0.0852803i | ||||
\(551\) | − | 0.899495i | − | 0.0383198i | ||||||
\(552\) | −28.9706 | − | 20.4853i | −1.23307 | − | 0.871911i | ||||
\(553\) | 2.24264 | 0.0953668 | ||||||||
\(554\) | − | 12.0000i | − | 0.509831i | ||||||
\(555\) | −0.343146 | − | 0.242641i | −0.0145657 | − | 0.0102995i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.8284 | −1.39099 | −0.695493 | − | 0.718533i | \(-0.744814\pi\) | ||||
−0.695493 | + | 0.718533i | \(0.744814\pi\) | |||||||
\(558\) | −0.343146 | − | 0.970563i | −0.0145265 | − | 0.0410872i | ||||
\(559\) | 32.7279 | 1.38424 | ||||||||
\(560\) | 4.00000 | 0.169031 | ||||||||
\(561\) | 0.857864 | − | 0.485281i | 0.0362191 | − | 0.0204886i | ||||
\(562\) | −24.4853 | −1.03285 | ||||||||
\(563\) | −37.1127 | −1.56411 | −0.782057 | − | 0.623207i | \(-0.785829\pi\) | ||||
−0.782057 | + | 0.623207i | \(0.785829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.899495 | −0.0378420 | ||||||||
\(566\) | 18.6863i | 0.785443i | ||||||||
\(567\) | −5.65685 | − | 7.00000i | −0.237566 | − | 0.293972i | ||||
\(568\) | 28.9706i | 1.21558i | ||||||||
\(569\) | −11.1421 | −0.467103 | −0.233551 | − | 0.972344i | \(-0.575035\pi\) | ||||
−0.233551 | + | 0.972344i | \(0.575035\pi\) | |||||||
\(570\) | −7.41421 | + | 10.4853i | −0.310547 | + | 0.439180i | ||||
\(571\) | − | 36.1838i | − | 1.51424i | −0.653274 | − | 0.757122i | \(-0.726605\pi\) | ||
0.653274 | − | 0.757122i | \(-0.273395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20.9706 | + | 14.8284i | 0.876058 | + | 0.619466i | ||||
\(574\) | 10.4853i | 0.437647i | ||||||||
\(575\) | 7.24264i | 0.302039i | ||||||||
\(576\) | −8.00000 | − | 22.6274i | −0.333333 | − | 0.942809i | ||||
\(577\) | 29.4558 | 1.22626 | 0.613131 | − | 0.789981i | \(-0.289910\pi\) | ||||
0.613131 | + | 0.789981i | \(0.289910\pi\) | |||||||
\(578\) | 24.0000 | 0.998268 | ||||||||
\(579\) | 14.1421 | + | 10.0000i | 0.587727 | + | 0.415586i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.1421i | − | 0.462254i | ||||||
\(582\) | 9.89949 | − | 14.0000i | 0.410347 | − | 0.580319i | ||||
\(583\) | 2.24264 | − | 4.75736i | 0.0928807 | − | 0.197030i | ||||
\(584\) | − | 29.6569i | − | 1.22721i | ||||||
\(585\) | 6.24264 | + | 17.6569i | 0.258101 | + | 0.730021i | ||||
\(586\) | −20.7279 | −0.856263 | ||||||||
\(587\) | 12.0416i | 0.497011i | 0.968630 | + | 0.248506i | \(0.0799395\pi\) | ||||
−0.968630 | + | 0.248506i | \(0.920061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.27208i | 0.0524151i | ||||||||
\(590\) | −9.75736 | −0.401704 | ||||||||
\(591\) | 6.00000 | − | 8.48528i | 0.246807 | − | 0.349038i | ||||
\(592\) | 0.970563 | 0.0398899 | ||||||||
\(593\) | −21.1716 | −0.869412 | −0.434706 | − | 0.900572i | \(-0.643148\pi\) | ||||
−0.434706 | + | 0.900572i | \(0.643148\pi\) | |||||||
\(594\) | −18.3848 | − | 16.0000i | −0.754337 | − | 0.656488i | ||||
\(595\) | 0.171573 | 0.00703380 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.4853 | − | 34.6274i | 1.00212 | − | 1.41721i | ||||
\(598\) | −63.9411 | −2.61475 | ||||||||
\(599\) | − | 37.1127i | − | 1.51638i | −0.652032 | − | 0.758192i | \(-0.726083\pi\) | ||
0.652032 | − | 0.758192i | \(-0.273917\pi\) | |||||||
\(600\) | −2.82843 | + | 4.00000i | −0.115470 | + | 0.163299i | ||||
\(601\) | 29.7279i | 1.21263i | 0.795226 | + | 0.606314i | \(0.207352\pi\) | ||||
−0.795226 | + | 0.606314i | \(0.792648\pi\) | |||||||
\(602\) | −7.41421 | −0.302181 | ||||||||
\(603\) | −4.48528 | − | 12.6863i | −0.182655 | − | 0.516626i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.48528 | + | 7.00000i | −0.344976 | + | 0.284590i | ||||
\(606\) | 20.4853 | − | 28.9706i | 0.832158 | − | 1.17685i | ||||
\(607\) | 9.51472i | 0.386191i | 0.981180 | + | 0.193095i | \(0.0618526\pi\) | ||||
−0.981180 | + | 0.193095i | \(0.938147\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.242641 | + | 0.171573i | 0.00983230 | + | 0.00695248i | ||||
\(610\) | −1.07107 | −0.0433663 | ||||||||
\(611\) | 81.5980 | 3.30110 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.51472i | − | 0.0611789i | −0.999532 | − | 0.0305895i | \(-0.990262\pi\) | ||
0.999532 | − | 0.0305895i | \(-0.00973844\pi\) | |||||||
\(614\) | − | 4.97056i | − | 0.200596i | ||||||
\(615\) | −10.4853 | − | 7.41421i | −0.422807 | − | 0.298970i | ||||
\(616\) | 4.00000 | − | 8.48528i | 0.161165 | − | 0.341882i | ||||
\(617\) | 17.3137i | 0.697024i | 0.937304 | + | 0.348512i | \(0.113313\pi\) | ||||
−0.937304 | + | 0.348512i | \(0.886687\pi\) | |||||||
\(618\) | 24.7279 | − | 34.9706i | 0.994703 | − | 1.40672i | ||||
\(619\) | −14.4853 | −0.582213 | −0.291106 | − | 0.956691i | \(-0.594023\pi\) | ||||
−0.291106 | + | 0.956691i | \(0.594023\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.2426 | + | 36.2132i | −0.411023 | + | 1.45319i | ||||
\(622\) | − | 12.9706i | − | 0.520072i | ||||||
\(623\) | −13.5858 | −0.544303 | ||||||||
\(624\) | −35.3137 | − | 24.9706i | −1.41368 | − | 0.999623i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −34.5858 | −1.38233 | ||||||||
\(627\) | 14.8284 | + | 26.2132i | 0.592190 | + | 1.04685i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.0416306 | 0.00165992 | ||||||||
\(630\) | −1.41421 | − | 4.00000i | −0.0563436 | − | 0.159364i | ||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | − | 6.34315i | − | 0.252317i | ||||||
\(633\) | −11.3137 | − | 8.00000i | −0.449680 | − | 0.317971i | ||||
\(634\) | 38.4264i | 1.52611i | ||||||||
\(635\) | 4.75736 | 0.188790 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.24264i | − | 0.247342i | ||||||
\(638\) | 0.727922 | + | 0.343146i | 0.0288187 | + | 0.0135853i | ||||
\(639\) | 28.9706 | − | 10.2426i | 1.14606 | − | 0.405193i | ||||
\(640\) | − | 11.3137i | − | 0.447214i | ||||||
\(641\) | − | 19.4558i | − | 0.768460i | −0.923237 | − | 0.384230i | \(-0.874467\pi\) | ||
0.923237 | − | 0.384230i | \(-0.125533\pi\) | |||||||
\(642\) | −6.48528 | + | 9.17157i | −0.255954 | + | 0.361973i | ||||
\(643\) | 17.9706 | 0.708690 | 0.354345 | − | 0.935115i | \(-0.384704\pi\) | ||||
0.354345 | + | 0.935115i | \(0.384704\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.24264 | − | 7.41421i | 0.206429 | − | 0.291934i | ||||
\(646\) | − | 1.27208i | − | 0.0500492i | ||||||
\(647\) | 4.20101i | 0.165159i | 0.996584 | + | 0.0825794i | \(0.0263158\pi\) | ||||
−0.996584 | + | 0.0825794i | \(0.973684\pi\) | |||||||
\(648\) | −19.7990 | + | 16.0000i | −0.777778 | + | 0.628539i | ||||
\(649\) | −9.75736 | + | 20.6985i | −0.383010 | + | 0.812487i | ||||
\(650\) | 8.82843i | 0.346279i | ||||||||
\(651\) | −0.343146 | − | 0.242641i | −0.0134489 | − | 0.00950984i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 24.2132i | − | 0.947536i | −0.880650 | − | 0.473768i | \(-0.842894\pi\) | ||
0.880650 | − | 0.473768i | \(-0.157106\pi\) | |||||||
\(654\) | 24.4853 | + | 17.3137i | 0.957450 | + | 0.677020i | ||||
\(655\) | − | 16.5858i | − | 0.648060i | ||||||
\(656\) | 29.6569 | 1.15791 | ||||||||
\(657\) | −29.6569 | + | 10.4853i | −1.15702 | + | 0.409070i | ||||
\(658\) | −18.4853 | −0.720631 | ||||||||
\(659\) | −43.2843 | −1.68612 | −0.843058 | − | 0.537823i | \(-0.819247\pi\) | ||||
−0.843058 | + | 0.537823i | \(0.819247\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.2132 | −0.980680 | −0.490340 | − | 0.871531i | \(-0.663127\pi\) | ||||
−0.490340 | + | 0.871531i | \(0.663127\pi\) | |||||||
\(662\) | −27.5563 | −1.07101 | ||||||||
\(663\) | −1.51472 | − | 1.07107i | −0.0588268 | − | 0.0415968i | ||||
\(664\) | −31.5147 | −1.22301 | ||||||||
\(665\) | 5.24264i | 0.203301i | ||||||||
\(666\) | −0.343146 | − | 0.970563i | −0.0132966 | − | 0.0376085i | ||||
\(667\) | − | 1.24264i | − | 0.0481152i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.0000 | − | 24.0416i | 0.657258 | − | 0.929503i | ||||
\(670\) | − | 6.34315i | − | 0.245057i | ||||||
\(671\) | −1.07107 | + | 2.27208i | −0.0413481 | + | 0.0877126i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 35.7279i | − | 1.37721i | −0.725137 | − | 0.688605i | \(-0.758223\pi\) | ||
0.725137 | − | 0.688605i | \(-0.241777\pi\) | |||||||
\(674\) | 26.5269i | 1.02178i | ||||||||
\(675\) | 5.00000 | + | 1.41421i | 0.192450 | + | 0.0544331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.8284 | 0.454603 | 0.227302 | − | 0.973824i | \(-0.427010\pi\) | ||||
0.227302 | + | 0.973824i | \(0.427010\pi\) | |||||||
\(678\) | −1.79899 | − | 1.27208i | −0.0690898 | − | 0.0488539i | ||||
\(679\) | − | 7.00000i | − | 0.268635i | ||||||
\(680\) | − | 0.485281i | − | 0.0186097i | ||||||
\(681\) | −11.8284 | + | 16.7279i | −0.453266 | + | 0.641015i | ||||
\(682\) | −1.02944 | − | 0.485281i | −0.0394192 | − | 0.0185824i | ||||
\(683\) | − | 0.343146i | − | 0.0131301i | −0.999978 | − | 0.00656505i | \(-0.997910\pi\) | ||
0.999978 | − | 0.00656505i | \(-0.00208974\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.48528 | 0.0949577 | ||||||||
\(686\) | 1.41421i | 0.0539949i | ||||||||
\(687\) | −6.72792 | + | 9.51472i | −0.256686 | + | 0.363009i | ||||
\(688\) | 20.9706i | 0.799495i | ||||||||
\(689\) | −9.89949 | −0.377141 | ||||||||
\(690\) | −10.2426 | + | 14.4853i | −0.389931 | + | 0.551445i | ||||
\(691\) | −42.9706 | −1.63468 | −0.817339 | − | 0.576158i | \(-0.804551\pi\) | ||||
−0.817339 | + | 0.576158i | \(0.804551\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.89949 | − | 1.00000i | −0.376051 | − | 0.0379869i | ||||
\(694\) | −29.9411 | −1.13655 | ||||||||
\(695\) | 4.48528 | 0.170136 | ||||||||
\(696\) | 0.485281 | − | 0.686292i | 0.0183945 | − | 0.0260138i | ||||
\(697\) | 1.27208 | 0.0481834 | ||||||||
\(698\) | − | 30.0416i | − | 1.13709i | ||||||
\(699\) | 21.5563 | − | 30.4853i | 0.815336 | − | 1.15306i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.02944 | −0.152190 | −0.0760949 | − | 0.997101i | \(-0.524245\pi\) | ||||
−0.0760949 | + | 0.997101i | \(0.524245\pi\) | |||||||
\(702\) | −12.4853 | + | 44.1421i | −0.471227 | + | 1.66604i | ||||
\(703\) | 1.27208i | 0.0479773i | ||||||||
\(704\) | −24.0000 | − | 11.3137i | −0.904534 | − | 0.426401i | ||||
\(705\) | 13.0711 | − | 18.4853i | 0.492285 | − | 0.696196i | ||||
\(706\) | − | 25.4558i | − | 0.958043i | ||||||
\(707\) | − | 14.4853i | − | 0.544775i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9411 | 0.636237 | 0.318119 | − | 0.948051i | \(-0.396949\pi\) | ||||
0.318119 | + | 0.948051i | \(0.396949\pi\) | |||||||
\(710\) | 14.4853 | 0.543623 | ||||||||
\(711\) | −6.34315 | + | 2.24264i | −0.237887 | + | 0.0841056i | ||||
\(712\) | 38.4264i | 1.44009i | ||||||||
\(713\) | 1.75736i | 0.0658136i | ||||||||
\(714\) | 0.343146 | + | 0.242641i | 0.0128419 | + | 0.00908060i | ||||
\(715\) | 18.7279 | + | 8.82843i | 0.700385 | + | 0.330164i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.65685 | − | 3.75736i | 0.0992220 | − | 0.140321i | ||||
\(718\) | −44.7279 | −1.66923 | ||||||||
\(719\) | 17.5269i | 0.653644i | 0.945086 | + | 0.326822i | \(0.105978\pi\) | ||||
−0.945086 | + | 0.326822i | \(0.894022\pi\) | |||||||
\(720\) | −11.3137 | + | 4.00000i | −0.421637 | + | 0.149071i | ||||
\(721\) | − | 17.4853i | − | 0.651186i | ||||||
\(722\) | 12.0000 | 0.446594 | ||||||||
\(723\) | 37.4558 | + | 26.4853i | 1.39300 | + | 0.984998i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.171573 | −0.00637206 | ||||||||
\(726\) | −26.8701 | + | 2.00000i | −0.997241 | + | 0.0742270i | ||||
\(727\) | −30.4558 | −1.12954 | −0.564772 | − | 0.825247i | \(-0.691036\pi\) | ||||
−0.564772 | + | 0.825247i | \(0.691036\pi\) | |||||||
\(728\) | −17.6569 | −0.654407 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | −14.8284 | −0.548825 | ||||||||
\(731\) | 0.899495i | 0.0332690i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 29.4558i | − | 1.08798i | −0.839093 | − | 0.543988i | \(-0.816914\pi\) | ||
0.839093 | − | 0.543988i | \(-0.183086\pi\) | |||||||
\(734\) | −4.24264 | −0.156599 | ||||||||
\(735\) | −1.41421 | − | 1.00000i | −0.0521641 | − | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.4558 | − | 6.34315i | −0.495652 | − | 0.233653i | ||||
\(738\) | −10.4853 | − | 29.6569i | −0.385969 | − | 1.09168i | ||||
\(739\) | − | 13.5147i | − | 0.497147i | −0.968613 | − | 0.248573i | \(-0.920038\pi\) | ||
0.968613 | − | 0.248573i | \(-0.0799617\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.7279 | − | 46.2843i | 1.20229 | − | 1.70030i | ||||
\(742\) | 2.24264 | 0.0823299 | ||||||||
\(743\) | 1.37258 | 0.0503552 | 0.0251776 | − | 0.999683i | \(-0.491985\pi\) | ||||
0.0251776 | + | 0.999683i | \(0.491985\pi\) | |||||||
\(744\) | −0.686292 | + | 0.970563i | −0.0251607 | + | 0.0355826i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 51.2132i | 1.87505i | ||||||||
\(747\) | 11.1421 | + | 31.5147i | 0.407669 | + | 1.15306i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.58579i | 0.167561i | ||||||||
\(750\) | 2.00000 | + | 1.41421i | 0.0730297 | + | 0.0516398i | ||||
\(751\) | −25.9706 | −0.947679 | −0.473840 | − | 0.880611i | \(-0.657132\pi\) | ||||
−0.473840 | + | 0.880611i | \(0.657132\pi\) | |||||||
\(752\) | 52.2843i | 1.90661i | ||||||||
\(753\) | 7.02944 | + | 4.97056i | 0.256167 | + | 0.181137i | ||||
\(754\) | − | 1.51472i | − | 0.0551628i | ||||||
\(755\) | 10.0000 | 0.363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.4558 | 1.50674 | 0.753369 | − | 0.657598i | \(-0.228427\pi\) | ||||
0.753369 | + | 0.657598i | \(0.228427\pi\) | |||||||
\(758\) | 45.8995 | 1.66714 | ||||||||
\(759\) | 20.4853 | + | 36.2132i | 0.743569 | + | 1.31446i | ||||
\(760\) | 14.8284 | 0.537884 | ||||||||
\(761\) | 40.9706 | 1.48518 | 0.742591 | − | 0.669745i | \(-0.233597\pi\) | ||||
0.742591 | + | 0.669745i | \(0.233597\pi\) | |||||||
\(762\) | 9.51472 | + | 6.72792i | 0.344682 | + | 0.243727i | ||||
\(763\) | 12.2426 | 0.443213 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.485281 | + | 0.171573i | −0.0175454 | + | 0.00620323i | ||||
\(766\) | 48.9117i | 1.76725i | ||||||||
\(767\) | 43.0711 | 1.55521 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 41.6690i | − | 1.50262i | −0.659947 | − | 0.751312i | \(-0.729421\pi\) | ||
0.659947 | − | 0.751312i | \(-0.270579\pi\) | |||||||
\(770\) | −4.24264 | − | 2.00000i | −0.152894 | − | 0.0720750i | ||||
\(771\) | −19.4558 | − | 13.7574i | −0.700685 | − | 0.495459i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 9.17157i | − | 0.329879i | −0.986304 | − | 0.164939i | \(-0.947257\pi\) | ||
0.986304 | − | 0.164939i | \(-0.0527428\pi\) | |||||||
\(774\) | 20.9706 | − | 7.41421i | 0.753771 | − | 0.266498i | ||||
\(775\) | 0.242641 | 0.00871591 | ||||||||
\(776\) | −19.7990 | −0.710742 | ||||||||
\(777\) | −0.343146 | − | 0.242641i | −0.0123103 | − | 0.00870469i | ||||
\(778\) | − | 14.4853i | − | 0.519322i | ||||||
\(779\) | 38.8701i | 1.39266i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4853 | − | 30.7279i | 0.518324 | − | 1.09953i | ||||
\(782\) | − | 1.75736i | − | 0.0628430i | ||||||
\(783\) | −0.857864 | − | 0.242641i | −0.0306576 | − | 0.00867127i | ||||
\(784\) | 4.00000 | 0.142857 | ||||||||
\(785\) | 11.0000i | 0.392607i | ||||||||
\(786\) | 23.4558 | − | 33.1716i | 0.836642 | − | 1.18319i | ||||
\(787\) | 35.4558i | 1.26386i | 0.775024 | + | 0.631932i | \(0.217738\pi\) | ||||
−0.775024 | + | 0.631932i | \(0.782262\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.1716 | + | 21.4558i | −0.540122 | + | 0.763848i | ||||
\(790\) | −3.17157 | −0.112839 | ||||||||
\(791\) | −0.899495 | −0.0319824 | ||||||||
\(792\) | −2.82843 | + | 28.0000i | −0.100504 | + | 0.994937i | ||||
\(793\) | 4.72792 | 0.167893 | ||||||||
\(794\) | 48.0833 | 1.70641 | ||||||||
\(795\) | −1.58579 | + | 2.24264i | −0.0562420 | + | 0.0795383i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 31.7990i | − | 1.12638i | −0.826328 | − | 0.563189i | \(-0.809574\pi\) | ||
0.826328 | − | 0.563189i | \(-0.190426\pi\) | |||||||
\(798\) | −7.41421 | + | 10.4853i | −0.262460 | + | 0.371175i | ||||
\(799\) | 2.24264i | 0.0793389i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 38.4264 | − | 13.5858i | 1.35773 | − | 0.480030i | ||||
\(802\) | − | 43.4558i | − | 1.53448i | ||||||
\(803\) | −14.8284 | + | 31.4558i | −0.523284 | + | 1.11005i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.24264i | 0.255270i | ||||||||
\(806\) | 2.14214i | 0.0754535i | ||||||||
\(807\) | −43.2132 | − | 30.5563i | −1.52118 | − | 1.07563i | ||||
\(808\) | −40.9706 | −1.44134 | ||||||||
\(809\) | 26.8284 | 0.943237 | 0.471619 | − | 0.881803i | \(-0.343670\pi\) | ||||
0.471619 | + | 0.881803i | \(0.343670\pi\) | |||||||
\(810\) | 8.00000 | + | 9.89949i | 0.281091 | + | 0.347833i | ||||
\(811\) | 2.00000i | 0.0702295i | 0.999383 | + | 0.0351147i | \(0.0111797\pi\) | ||||
−0.999383 | + | 0.0351147i | \(0.988820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.8701 | + | 23.2426i | 1.15280 | + | 0.815155i | ||||
\(814\) | −1.02944 | − | 0.485281i | −0.0360818 | − | 0.0170091i | ||||
\(815\) | − | 6.24264i | − | 0.218670i | ||||||
\(816\) | 0.686292 | − | 0.970563i | 0.0240250 | − | 0.0339765i | ||||
\(817\) | −27.4853 | −0.961588 | ||||||||
\(818\) | − | 2.14214i | − | 0.0748980i | ||||||
\(819\) | 6.24264 | + | 17.6569i | 0.218136 | + | 0.616980i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.1421 | −1.01707 | −0.508534 | − | 0.861042i | \(-0.669812\pi\) | ||||
−0.508534 | + | 0.861042i | \(0.669812\pi\) | |||||||
\(822\) | 4.97056 | + | 3.51472i | 0.173368 | + | 0.122590i | ||||
\(823\) | −1.21320 | −0.0422896 | −0.0211448 | − | 0.999776i | \(-0.506731\pi\) | ||||
−0.0211448 | + | 0.999776i | \(0.506731\pi\) | |||||||
\(824\) | −49.4558 | −1.72288 | ||||||||
\(825\) | 5.00000 | − | 2.82843i | 0.174078 | − | 0.0984732i | ||||
\(826\) | −9.75736 | −0.339502 | ||||||||
\(827\) | 6.00000 | 0.208640 | 0.104320 | − | 0.994544i | \(-0.466733\pi\) | ||||
0.104320 | + | 0.994544i | \(0.466733\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −36.9706 | −1.28404 | −0.642020 | − | 0.766688i | \(-0.721904\pi\) | ||||
−0.642020 | + | 0.766688i | \(0.721904\pi\) | |||||||
\(830\) | 15.7574i | 0.546946i | ||||||||
\(831\) | 12.0000 | + | 8.48528i | 0.416275 | + | 0.294351i | ||||
\(832\) | 49.9411i | 1.73140i | ||||||||
\(833\) | 0.171573 | 0.00594465 | ||||||||
\(834\) | 8.97056 | + | 6.34315i | 0.310625 | + | 0.219645i | ||||
\(835\) | − | 8.14214i | − | 0.281770i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.21320 | + | 0.343146i | 0.0419344 | + | 0.0118609i | ||||
\(838\) | − | 40.1838i | − | 1.38813i | ||||||
\(839\) | − | 1.58579i | − | 0.0547474i | −0.999625 | − | 0.0273737i | \(-0.991286\pi\) | ||
0.999625 | − | 0.0273737i | \(-0.00871441\pi\) | |||||||
\(840\) | −2.82843 | + | 4.00000i | −0.0975900 | + | 0.138013i | ||||
\(841\) | −28.9706 | −0.998985 | ||||||||
\(842\) | 6.38478 | 0.220034 | ||||||||
\(843\) | 17.3137 | − | 24.4853i | 0.596316 | − | 0.843318i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 25.9706i | − | 0.893415i | ||||||
\(846\) | 52.2843 | − | 18.4853i | 1.79757 | − | 0.635537i | ||||
\(847\) | −8.48528 | + | 7.00000i | −0.291558 | + | 0.240523i | ||||
\(848\) | − | 6.34315i | − | 0.217825i | ||||||
\(849\) | −18.6863 | − | 13.2132i | −0.641312 | − | 0.453476i | ||||
\(850\) | −0.242641 | −0.00832251 | ||||||||
\(851\) | 1.75736i | 0.0602415i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.2426i | 1.51484i | 0.652928 | + | 0.757420i | \(0.273540\pi\) | ||||
−0.652928 | + | 0.757420i | \(0.726460\pi\) | |||||||
\(854\) | −1.07107 | −0.0366512 | ||||||||
\(855\) | −5.24264 | − | 14.8284i | −0.179295 | − | 0.507122i | ||||
\(856\) | 12.9706 | 0.443325 | ||||||||
\(857\) | 34.9706 | 1.19457 | 0.597286 | − | 0.802028i | \(-0.296246\pi\) | ||||
0.597286 | + | 0.802028i | \(0.296246\pi\) | |||||||
\(858\) | 24.9706 | + | 44.1421i | 0.852481 | + | 1.50699i | ||||
\(859\) | 44.1838 | 1.50753 | 0.753765 | − | 0.657144i | \(-0.228236\pi\) | ||||
0.753765 | + | 0.657144i | \(0.228236\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.4853 | − | 7.41421i | −0.357337 | − | 0.252676i | ||||
\(862\) | 17.4558 | 0.594548 | ||||||||
\(863\) | 23.8701i | 0.812546i | 0.913752 | + | 0.406273i | \(0.133172\pi\) | ||||
−0.913752 | + | 0.406273i | \(0.866828\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.82843i | 0.0961694i | ||||||||
\(866\) | 16.9706 | 0.576683 | ||||||||
\(867\) | −16.9706 | + | 24.0000i | −0.576351 | + | 0.815083i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.17157 | + | 6.72792i | −0.107588 | + | 0.228229i | ||||
\(870\) | −0.343146 | − | 0.242641i | −0.0116337 | − | 0.00822629i | ||||
\(871\) | 28.0000i | 0.948744i | ||||||||
\(872\) | − | 34.6274i | − | 1.17263i | ||||||
\(873\) | 7.00000 | + | 19.7990i | 0.236914 | + | 0.670094i | ||||
\(874\) | 53.6985 | 1.81638 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.7279i | 0.733700i | 0.930280 | + | 0.366850i | \(0.119564\pi\) | ||||
−0.930280 | + | 0.366850i | \(0.880436\pi\) | |||||||
\(878\) | − | 4.58579i | − | 0.154763i | ||||||
\(879\) | 14.6569 | − | 20.7279i | 0.494363 | − | 0.699135i | ||||
\(880\) | −5.65685 | + | 12.0000i | −0.190693 | + | 0.404520i | ||||
\(881\) | − | 24.2132i | − | 0.815764i | −0.913035 | − | 0.407882i | \(-0.866268\pi\) | ||
0.913035 | − | 0.407882i | \(-0.133732\pi\) | |||||||
\(882\) | −1.41421 | − | 4.00000i | −0.0476190 | − | 0.134687i | ||||
\(883\) | 28.9706 | 0.974937 | 0.487469 | − | 0.873141i | \(-0.337920\pi\) | ||||
0.487469 | + | 0.873141i | \(0.337920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.89949 | − | 9.75736i | 0.231924 | − | 0.327990i | ||||
\(886\) | − | 16.0000i | − | 0.537531i | ||||||
\(887\) | −30.9411 | −1.03890 | −0.519451 | − | 0.854500i | \(-0.673863\pi\) | ||||
−0.519451 | + | 0.854500i | \(0.673863\pi\) | |||||||
\(888\) | −0.686292 | + | 0.970563i | −0.0230304 | + | 0.0325700i | ||||
\(889\) | 4.75736 | 0.159557 | ||||||||
\(890\) | 19.2132 | 0.644028 | ||||||||
\(891\) | 29.0000 | − | 7.07107i | 0.971537 | − | 0.236890i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −68.5269 | −2.29317 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.5858 | 0.353844 | ||||||||
\(896\) | − | 11.3137i | − | 0.377964i | ||||||
\(897\) | 45.2132 | − | 63.9411i | 1.50962 | − | 2.13493i | ||||
\(898\) | 51.9411i | 1.73330i | ||||||||
\(899\) | −0.0416306 | −0.00138846 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.272078i | − | 0.00906423i | ||||||
\(902\) | −31.4558 | − | 14.8284i | −1.04737 | − | 0.493733i | ||||
\(903\) | 5.24264 | − | 7.41421i | 0.174464 | − | 0.246730i | ||||
\(904\) | 2.54416i | 0.0846174i | ||||||||
\(905\) | 22.9706i | 0.763567i | ||||||||
\(906\) | 20.0000 | + | 14.1421i | 0.664455 | + | 0.469841i | ||||
\(907\) | 5.27208 | 0.175056 | 0.0875282 | − | 0.996162i | \(-0.472103\pi\) | ||||
0.0875282 | + | 0.996162i | \(0.472103\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.4853 | + | 40.9706i | 0.480446 | + | 1.35891i | ||||
\(910\) | 8.82843i | 0.292660i | ||||||||
\(911\) | 58.2843i | 1.93104i | 0.260321 | + | 0.965522i | \(0.416171\pi\) | ||||
−0.260321 | + | 0.965522i | \(0.583829\pi\) | |||||||
\(912\) | 29.6569 | + | 20.9706i | 0.982037 | + | 0.694405i | ||||
\(913\) | 33.4264 | + | 15.7574i | 1.10625 | + | 0.521492i | ||||
\(914\) | − | 14.4437i | − | 0.477754i | ||||||
\(915\) | 0.757359 | − | 1.07107i | 0.0250375 | − | 0.0354084i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 16.5858i | − | 0.547711i | ||||||
\(918\) | −1.21320 | − | 0.343146i | −0.0400417 | − | 0.0113255i | ||||
\(919\) | 15.0294i | 0.495775i | 0.968789 | + | 0.247888i | \(0.0797364\pi\) | ||||
−0.968789 | + | 0.247888i | \(0.920264\pi\) | |||||||
\(920\) | 20.4853 | 0.675380 | ||||||||
\(921\) | 4.97056 | + | 3.51472i | 0.163786 | + | 0.115814i | ||||
\(922\) | −41.9411 | −1.38126 | ||||||||
\(923\) | −63.9411 | −2.10465 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.242641 | 0.00797798 | ||||||||
\(926\) | −36.7696 | −1.20832 | ||||||||
\(927\) | 17.4853 | + | 49.4558i | 0.574292 | + | 1.62434i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 19.7990i | − | 0.649584i | −0.945786 | − | 0.324792i | \(-0.894706\pi\) | ||
0.945786 | − | 0.324792i | \(-0.105294\pi\) | |||||||
\(930\) | 0.485281 | + | 0.343146i | 0.0159130 | + | 0.0112522i | ||||
\(931\) | 5.24264i | 0.171821i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9706 | + | 9.17157i | 0.424637 | + | 0.300264i | ||||
\(934\) | 0.485281i | 0.0158789i | ||||||||
\(935\) | −0.242641 | + | 0.514719i | −0.00793520 | + | 0.0168331i | ||||
\(936\) | 49.9411 | − | 17.6569i | 1.63238 | − | 0.577132i | ||||
\(937\) | 11.2721i | 0.368243i | 0.982904 | + | 0.184121i | \(0.0589439\pi\) | ||||
−0.982904 | + | 0.184121i | \(0.941056\pi\) | |||||||
\(938\) | − | 6.34315i | − | 0.207111i | ||||||
\(939\) | 24.4558 | − | 34.5858i | 0.798086 | − | 1.12866i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3848 | −0.794921 | −0.397460 | − | 0.917619i | \(-0.630108\pi\) | ||||
−0.397460 | + | 0.917619i | \(0.630108\pi\) | |||||||
\(942\) | −15.5563 | + | 22.0000i | −0.506853 | + | 0.716799i | ||||
\(943\) | 53.6985i | 1.74866i | ||||||||
\(944\) | 27.5980i | 0.898238i | ||||||||
\(945\) | 5.00000 | + | 1.41421i | 0.162650 | + | 0.0460044i | ||||
\(946\) | 10.4853 | − | 22.2426i | 0.340906 | − | 0.723171i | ||||
\(947\) | 26.3553i | 0.856433i | 0.903676 | + | 0.428217i | \(0.140858\pi\) | ||||
−0.903676 | + | 0.428217i | \(0.859142\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 65.4558 | 2.12479 | ||||||||
\(950\) | − | 7.41421i | − | 0.240549i | ||||||
\(951\) | −38.4264 | − | 27.1716i | −1.24606 | − | 0.881099i | ||||
\(952\) | − | 0.485281i | − | 0.0157281i | ||||||
\(953\) | −18.0000 | −0.583077 | −0.291539 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291539 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(954\) | −6.34315 | + | 2.24264i | −0.205367 | + | 0.0726082i | ||||
\(955\) | −14.8284 | −0.479837 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.857864 | + | 0.485281i | −0.0277308 | + | 0.0156869i | ||||
\(958\) | 38.4853 | 1.24340 | ||||||||
\(959\) | 2.48528 | 0.0802539 | ||||||||
\(960\) | 11.3137 | + | 8.00000i | 0.365148 | + | 0.258199i | ||||
\(961\) | −30.9411 | −0.998101 | ||||||||
\(962\) | 2.14214i | 0.0690652i | ||||||||
\(963\) | −4.58579 | − | 12.9706i | −0.147775 | − | 0.417971i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.0000 | −0.321911 | ||||||||
\(966\) | −10.2426 | + | 14.4853i | −0.329552 | + | 0.466056i | ||||
\(967\) | 2.21320i | 0.0711718i | 0.999367 | + | 0.0355859i | \(0.0113297\pi\) | ||||
−0.999367 | + | 0.0355859i | \(0.988670\pi\) | |||||||
\(968\) | 19.7990 | + | 24.0000i | 0.636364 | + | 0.771389i | ||||
\(969\) | 1.27208 | + | 0.899495i | 0.0408650 | + | 0.0288959i | ||||
\(970\) | 9.89949i | 0.317854i | ||||||||
\(971\) | 53.8701i | 1.72877i | 0.502828 | + | 0.864386i | \(0.332293\pi\) | ||||
−0.502828 | + | 0.864386i | \(0.667707\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.48528 | 0.143792 | ||||||||
\(974\) | −4.28427 | −0.137277 | ||||||||
\(975\) | −8.82843 | − | 6.24264i | −0.282736 | − | 0.199925i | ||||
\(976\) | 3.02944i | 0.0969699i | ||||||||
\(977\) | 42.8995i | 1.37248i | 0.727377 | + | 0.686238i | \(0.240739\pi\) | ||||
−0.727377 | + | 0.686238i | \(0.759261\pi\) | |||||||
\(978\) | 8.82843 | − | 12.4853i | 0.282302 | − | 0.399235i | ||||
\(979\) | 19.2132 | − | 40.7574i | 0.614057 | − | 1.30261i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.6274 | + | 12.2426i | −1.10557 | + | 0.390877i | ||||
\(982\) | −21.6985 | −0.692426 | ||||||||
\(983\) | 22.6274i | 0.721703i | 0.932623 | + | 0.360851i | \(0.117514\pi\) | ||||
−0.932623 | + | 0.360851i | \(0.882486\pi\) | |||||||
\(984\) | −20.9706 | + | 29.6569i | −0.668517 | + | 0.945426i | ||||
\(985\) | 6.00000i | 0.191176i | ||||||||
\(986\) | 0.0416306 | 0.00132579 | ||||||||
\(987\) | 13.0711 | − | 18.4853i | 0.416057 | − | 0.588393i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.9706 | −1.20739 | ||||||||
\(990\) | 14.0000 | + | 1.41421i | 0.444949 | + | 0.0449467i | ||||
\(991\) | 61.4853 | 1.95314 | 0.976572 | − | 0.215190i | \(-0.0690371\pi\) | ||||
0.976572 | + | 0.215190i | \(0.0690371\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.4853 | − | 27.5563i | 0.618347 | − | 0.874474i | ||||
\(994\) | 14.4853 | 0.459445 | ||||||||
\(995\) | 24.4853i | 0.776236i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.9706i | 1.29755i | 0.760980 | + | 0.648775i | \(0.224719\pi\) | ||||
−0.760980 | + | 0.648775i | \(0.775281\pi\) | |||||||
\(998\) | 16.2426 | 0.514152 | ||||||||
\(999\) | 1.21320 | + | 0.343146i | 0.0383841 | + | 0.0108567i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1155.2.l.b.1121.1 | ✓ | 4 | |
3.2 | odd | 2 | 1155.2.l.c.1121.4 | yes | 4 | ||
11.10 | odd | 2 | 1155.2.l.c.1121.3 | yes | 4 | ||
33.32 | even | 2 | inner | 1155.2.l.b.1121.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.l.b.1121.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1155.2.l.b.1121.2 | yes | 4 | 33.32 | even | 2 | inner | |
1155.2.l.c.1121.3 | yes | 4 | 11.10 | odd | 2 | ||
1155.2.l.c.1121.4 | yes | 4 | 3.2 | odd | 2 |