Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (of order \(4\), degree \(2\), 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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.737 |
Dual form | 2070.2.j.f.323.2 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.00000 | − | 1.00000i | 0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 2.00000i | 0.755929 | + | 0.755929i | 0.975579 | − | 0.219650i | \(-0.0704915\pi\) |
−0.219650 | + | 0.975579i | \(0.570491\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.707107 | − | 2.12132i | 0.223607 | − | 0.670820i | ||||
\(11\) | − | 4.82843i | − | 1.45583i | −0.685670 | − | 0.727913i | \(-0.740491\pi\) | ||
0.685670 | − | 0.727913i | \(-0.259509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.41421 | + | 1.41421i | −0.392232 | + | 0.392232i | −0.875482 | − | 0.483250i | \(-0.839456\pi\) |
0.483250 | + | 0.875482i | \(0.339456\pi\) | |||||||
\(14\) | 2.82843 | 0.755929 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.58579 | − | 2.58579i | 0.627145 | − | 0.627145i | −0.320203 | − | 0.947349i | \(-0.603751\pi\) |
0.947349 | + | 0.320203i | \(0.103751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.585786i | 0.134389i | 0.997740 | + | 0.0671943i | \(0.0214047\pi\) | ||||
−0.997740 | + | 0.0671943i | \(0.978595\pi\) | |||||||
\(20\) | −1.00000 | − | 2.00000i | −0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.41421 | − | 3.41421i | −0.727913 | − | 0.727913i | ||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 2.00000i | 0.392232i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | − | 2.00000i | 0.377964 | − | 0.377964i | ||||
\(29\) | −0.828427 | −0.153835 | −0.0769175 | − | 0.997037i | \(-0.524508\pi\) | ||||
−0.0769175 | + | 0.997037i | \(0.524508\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.828427 | 0.148790 | 0.0743950 | − | 0.997229i | \(-0.476297\pi\) | ||||
0.0743950 | + | 0.997229i | \(0.476297\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 3.65685i | − | 0.627145i | ||||||
\(35\) | 6.00000 | + | 2.00000i | 1.01419 | + | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.41421 | − | 1.41421i | −0.232495 | − | 0.232495i | 0.581238 | − | 0.813733i | \(-0.302568\pi\) |
−0.813733 | + | 0.581238i | \(0.802568\pi\) | |||||||
\(38\) | 0.414214 | + | 0.414214i | 0.0671943 | + | 0.0671943i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.12132 | − | 0.707107i | −0.335410 | − | 0.111803i | ||||
\(41\) | − | 5.41421i | − | 0.845558i | −0.906233 | − | 0.422779i | \(-0.861055\pi\) | ||
0.906233 | − | 0.422779i | \(-0.138945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.24264 | − | 2.24264i | 0.341999 | − | 0.341999i | −0.515119 | − | 0.857119i | \(-0.672252\pi\) |
0.857119 | + | 0.515119i | \(0.172252\pi\) | |||||||
\(44\) | −4.82843 | −0.727913 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −0.707107 | − | 4.94975i | −0.100000 | − | 0.700000i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.41421 | + | 1.41421i | 0.196116 | + | 0.196116i | ||||
\(53\) | 8.65685 | + | 8.65685i | 1.18911 | + | 1.18911i | 0.977314 | + | 0.211797i | \(0.0679314\pi\) |
0.211797 | + | 0.977314i | \(0.432069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.82843 | − | 9.65685i | −0.651065 | − | 1.30213i | ||||
\(56\) | − | 2.82843i | − | 0.377964i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.585786 | + | 0.585786i | −0.0769175 | + | 0.0769175i | ||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.41421 | 0.693219 | 0.346610 | − | 0.938010i | \(-0.387333\pi\) | ||||
0.346610 | + | 0.938010i | \(0.387333\pi\) | |||||||
\(62\) | 0.585786 | − | 0.585786i | 0.0743950 | − | 0.0743950i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −1.41421 | + | 4.24264i | −0.175412 | + | 0.526235i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.82843 | + | 6.82843i | 0.834225 | + | 0.834225i | 0.988092 | − | 0.153866i | \(-0.0491726\pi\) |
−0.153866 | + | 0.988092i | \(0.549173\pi\) | |||||||
\(68\) | −2.58579 | − | 2.58579i | −0.313573 | − | 0.313573i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.65685 | − | 2.82843i | 0.676123 | − | 0.338062i | ||||
\(71\) | − | 7.41421i | − | 0.879905i | −0.898021 | − | 0.439953i | \(-0.854995\pi\) | ||
0.898021 | − | 0.439953i | \(-0.145005\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.82843 | + | 9.82843i | −1.15033 | + | 1.15033i | −0.163844 | + | 0.986486i | \(0.552389\pi\) |
−0.986486 | + | 0.163844i | \(0.947611\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.585786 | 0.0671943 | ||||||||
\(77\) | 9.65685 | − | 9.65685i | 1.10050 | − | 1.10050i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.17157i | 0.131812i | 0.997826 | + | 0.0659061i | \(0.0209938\pi\) | ||||
−0.997826 | + | 0.0659061i | \(0.979006\pi\) | |||||||
\(80\) | −2.00000 | + | 1.00000i | −0.223607 | + | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.82843 | − | 3.82843i | −0.422779 | − | 0.422779i | ||||
\(83\) | −0.757359 | − | 0.757359i | −0.0831310 | − | 0.0831310i | 0.664319 | − | 0.747450i | \(-0.268722\pi\) |
−0.747450 | + | 0.664319i | \(0.768722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.58579 | − | 7.75736i | 0.280468 | − | 0.841404i | ||||
\(86\) | − | 3.17157i | − | 0.341999i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.41421 | + | 3.41421i | −0.363956 | + | 0.363956i | ||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.65685 | −0.592999 | ||||||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.585786 | + | 1.17157i | 0.0601004 | + | 0.120201i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.07107 | − | 9.07107i | −0.921027 | − | 0.921027i | 0.0760747 | − | 0.997102i | \(-0.475761\pi\) |
−0.997102 | + | 0.0760747i | \(0.975761\pi\) | |||||||
\(98\) | 0.707107 | + | 0.707107i | 0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.00000 | − | 3.00000i | −0.400000 | − | 0.300000i | ||||
\(101\) | 3.65685i | 0.363871i | 0.983311 | + | 0.181935i | \(0.0582361\pi\) | ||||
−0.983311 | + | 0.181935i | \(0.941764\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.17157 | + | 5.17157i | −0.509570 | + | 0.509570i | −0.914394 | − | 0.404824i | \(-0.867333\pi\) |
0.404824 | + | 0.914394i | \(0.367333\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.2426 | 1.18911 | ||||||||
\(107\) | −4.07107 | + | 4.07107i | −0.393565 | + | 0.393565i | −0.875956 | − | 0.482391i | \(-0.839768\pi\) |
0.482391 | + | 0.875956i | \(0.339768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 19.0711i | − | 1.82668i | −0.407201 | − | 0.913339i | \(-0.633495\pi\) | ||
0.407201 | − | 0.913339i | \(-0.366505\pi\) | |||||||
\(110\) | −10.2426 | − | 3.41421i | −0.976597 | − | 0.325532i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | − | 2.00000i | −0.188982 | − | 0.188982i | ||||
\(113\) | 12.2426 | + | 12.2426i | 1.15169 | + | 1.15169i | 0.986214 | + | 0.165477i | \(0.0529164\pi\) |
0.165477 | + | 0.986214i | \(0.447084\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.12132 | − | 0.707107i | −0.197814 | − | 0.0659380i | ||||
\(116\) | 0.828427i | 0.0769175i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.00000 | + | 2.00000i | −0.184115 | + | 0.184115i | ||||
\(119\) | 10.3431 | 0.948155 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.3137 | −1.11943 | ||||||||
\(122\) | 3.82843 | − | 3.82843i | 0.346610 | − | 0.346610i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 0.828427i | − | 0.0743950i | ||||||
\(125\) | 2.00000 | − | 11.0000i | 0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.58579 | − | 1.58579i | −0.140716 | − | 0.140716i | 0.633240 | − | 0.773956i | \(-0.281725\pi\) |
−0.773956 | + | 0.633240i | \(0.781725\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.00000 | + | 4.00000i | 0.175412 | + | 0.350823i | ||||
\(131\) | 5.65685i | 0.494242i | 0.968985 | + | 0.247121i | \(0.0794845\pi\) | ||||
−0.968985 | + | 0.247121i | \(0.920516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.17157 | + | 1.17157i | −0.101588 | + | 0.101588i | ||||
\(134\) | 9.65685 | 0.834225 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.65685 | −0.313573 | ||||||||
\(137\) | 1.07107 | − | 1.07107i | 0.0915075 | − | 0.0915075i | −0.659871 | − | 0.751379i | \(-0.729389\pi\) |
0.751379 | + | 0.659871i | \(0.229389\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.82843i | 0.579180i | 0.957151 | + | 0.289590i | \(0.0935189\pi\) | ||||
−0.957151 | + | 0.289590i | \(0.906481\pi\) | |||||||
\(140\) | 2.00000 | − | 6.00000i | 0.169031 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.24264 | − | 5.24264i | −0.439953 | − | 0.439953i | ||||
\(143\) | 6.82843 | + | 6.82843i | 0.571022 | + | 0.571022i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.65685 | + | 0.828427i | −0.137594 | + | 0.0687971i | ||||
\(146\) | 13.8995i | 1.15033i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.41421 | + | 1.41421i | −0.116248 | + | 0.116248i | ||||
\(149\) | −11.6569 | −0.954967 | −0.477483 | − | 0.878641i | \(-0.658451\pi\) | ||||
−0.477483 | + | 0.878641i | \(0.658451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9706 | −1.38104 | −0.690522 | − | 0.723311i | \(-0.742619\pi\) | ||||
−0.690522 | + | 0.723311i | \(0.742619\pi\) | |||||||
\(152\) | 0.414214 | − | 0.414214i | 0.0335972 | − | 0.0335972i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 13.6569i | − | 1.10050i | ||||||
\(155\) | 1.65685 | − | 0.828427i | 0.133082 | − | 0.0665409i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.24264 | − | 4.24264i | −0.338600 | − | 0.338600i | 0.517241 | − | 0.855840i | \(-0.326959\pi\) |
−0.855840 | + | 0.517241i | \(0.826959\pi\) | |||||||
\(158\) | 0.828427 | + | 0.828427i | 0.0659061 | + | 0.0659061i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.707107 | + | 2.12132i | −0.0559017 | + | 0.167705i | ||||
\(161\) | − | 2.82843i | − | 0.222911i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.48528 | + | 6.48528i | −0.507966 | + | 0.507966i | −0.913902 | − | 0.405935i | \(-0.866946\pi\) |
0.405935 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(164\) | −5.41421 | −0.422779 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.07107 | −0.0831310 | ||||||||
\(167\) | 15.8995 | − | 15.8995i | 1.23034 | − | 1.23034i | 0.266507 | − | 0.963833i | \(-0.414131\pi\) |
0.963833 | − | 0.266507i | \(-0.0858695\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000i | 0.692308i | ||||||||
\(170\) | −3.65685 | − | 7.31371i | −0.280468 | − | 0.560936i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.24264 | − | 2.24264i | −0.171000 | − | 0.171000i | ||||
\(173\) | −9.89949 | − | 9.89949i | −0.752645 | − | 0.752645i | 0.222327 | − | 0.974972i | \(-0.428635\pi\) |
−0.974972 | + | 0.222327i | \(0.928635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0000 | − | 2.00000i | 1.05830 | − | 0.151186i | ||||
\(176\) | 4.82843i | 0.363956i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.89949 | − | 9.89949i | 0.741999 | − | 0.741999i | ||||
\(179\) | −23.3137 | −1.74255 | −0.871274 | − | 0.490797i | \(-0.836706\pi\) | ||||
−0.871274 | + | 0.490797i | \(0.836706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.4142 | 0.997071 | 0.498535 | − | 0.866869i | \(-0.333871\pi\) | ||||
0.498535 | + | 0.866869i | \(0.333871\pi\) | |||||||
\(182\) | −4.00000 | + | 4.00000i | −0.296500 | + | 0.296500i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.00000i | 0.0737210i | ||||||||
\(185\) | −4.24264 | − | 1.41421i | −0.311925 | − | 0.103975i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4853 | − | 12.4853i | −0.913014 | − | 0.913014i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.24264 | + | 0.414214i | 0.0901506 | + | 0.0300502i | ||||
\(191\) | 9.17157i | 0.663632i | 0.943344 | + | 0.331816i | \(0.107661\pi\) | ||||
−0.943344 | + | 0.331816i | \(0.892339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | + | 5.00000i | −0.359908 | + | 0.359908i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) |
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | −12.8284 | −0.921027 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 7.07107 | − | 7.07107i | 0.503793 | − | 0.503793i | −0.408822 | − | 0.912614i | \(-0.634060\pi\) |
0.912614 | + | 0.408822i | \(0.134060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.34315i | − | 0.449654i | −0.974399 | − | 0.224827i | \(-0.927818\pi\) | ||
0.974399 | − | 0.224827i | \(-0.0721816\pi\) | |||||||
\(200\) | −4.94975 | + | 0.707107i | −0.350000 | + | 0.0500000i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.58579 | + | 2.58579i | 0.181935 | + | 0.181935i | ||||
\(203\) | −1.65685 | − | 1.65685i | −0.116288 | − | 0.116288i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.41421 | − | 10.8284i | −0.378145 | − | 0.756290i | ||||
\(206\) | 7.31371i | 0.509570i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.41421 | − | 1.41421i | 0.0980581 | − | 0.0980581i | ||||
\(209\) | 2.82843 | 0.195646 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.8284 | −1.02083 | −0.510416 | − | 0.859928i | \(-0.670508\pi\) | ||||
−0.510416 | + | 0.859928i | \(0.670508\pi\) | |||||||
\(212\) | 8.65685 | − | 8.65685i | 0.594555 | − | 0.594555i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.75736i | 0.393565i | ||||||||
\(215\) | 2.24264 | − | 6.72792i | 0.152947 | − | 0.458840i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.65685 | + | 1.65685i | 0.112475 | + | 0.112475i | ||||
\(218\) | −13.4853 | − | 13.4853i | −0.913339 | − | 0.913339i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.65685 | + | 4.82843i | −0.651065 | + | 0.325532i | ||||
\(221\) | 7.31371i | 0.491973i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.24264 | + | 3.24264i | −0.217143 | + | 0.217143i | −0.807293 | − | 0.590150i | \(-0.799069\pi\) |
0.590150 | + | 0.807293i | \(0.299069\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.3137 | 1.15169 | ||||||||
\(227\) | 4.89949 | − | 4.89949i | 0.325191 | − | 0.325191i | −0.525563 | − | 0.850754i | \(-0.676145\pi\) |
0.850754 | + | 0.525563i | \(0.176145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.4142i | 0.886436i | 0.896414 | + | 0.443218i | \(0.146163\pi\) | ||||
−0.896414 | + | 0.443218i | \(0.853837\pi\) | |||||||
\(230\) | −2.00000 | + | 1.00000i | −0.131876 | + | 0.0659380i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.585786 | + | 0.585786i | 0.0384588 | + | 0.0384588i | ||||
\(233\) | 13.1716 | + | 13.1716i | 0.862898 | + | 0.862898i | 0.991674 | − | 0.128775i | \(-0.0411046\pi\) |
−0.128775 | + | 0.991674i | \(0.541105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.82843i | 0.184115i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.31371 | − | 7.31371i | 0.474077 | − | 0.474077i | ||||
\(239\) | −9.55635 | −0.618149 | −0.309074 | − | 0.951038i | \(-0.600019\pi\) | ||||
−0.309074 | + | 0.951038i | \(0.600019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7990 | 0.888871 | 0.444436 | − | 0.895811i | \(-0.353404\pi\) | ||||
0.444436 | + | 0.895811i | \(0.353404\pi\) | |||||||
\(242\) | −8.70711 | + | 8.70711i | −0.559714 | + | 0.559714i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.41421i | − | 0.346610i | ||||||
\(245\) | 1.00000 | + | 2.00000i | 0.0638877 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.828427 | − | 0.828427i | −0.0527116 | − | 0.0527116i | ||||
\(248\) | −0.585786 | − | 0.585786i | −0.0371975 | − | 0.0371975i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.36396 | − | 9.19239i | −0.402492 | − | 0.581378i | ||||
\(251\) | 28.8284i | 1.81963i | 0.415009 | + | 0.909817i | \(0.363778\pi\) | ||||
−0.415009 | + | 0.909817i | \(0.636222\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.41421 | + | 3.41421i | −0.214650 | + | 0.214650i | ||||
\(254\) | −2.24264 | −0.140716 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.8284 | − | 10.8284i | 0.675459 | − | 0.675459i | −0.283510 | − | 0.958969i | \(-0.591499\pi\) |
0.958969 | + | 0.283510i | \(0.0914991\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 5.65685i | − | 0.351500i | ||||||
\(260\) | 4.24264 | + | 1.41421i | 0.263117 | + | 0.0877058i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000 | + | 4.00000i | 0.247121 | + | 0.247121i | ||||
\(263\) | 12.1421 | + | 12.1421i | 0.748716 | + | 0.748716i | 0.974238 | − | 0.225522i | \(-0.0724087\pi\) |
−0.225522 | + | 0.974238i | \(0.572409\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.9706 | + | 8.65685i | 1.59536 | + | 0.531786i | ||||
\(266\) | 1.65685i | 0.101588i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.82843 | − | 6.82843i | 0.417113 | − | 0.417113i | ||||
\(269\) | 2.00000 | 0.121942 | 0.0609711 | − | 0.998140i | \(-0.480580\pi\) | ||||
0.0609711 | + | 0.998140i | \(0.480580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.97056 | 0.544923 | 0.272461 | − | 0.962167i | \(-0.412162\pi\) | ||||
0.272461 | + | 0.962167i | \(0.412162\pi\) | |||||||
\(272\) | −2.58579 | + | 2.58579i | −0.156786 | + | 0.156786i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.51472i | − | 0.0915075i | ||||||
\(275\) | −19.3137 | − | 14.4853i | −1.16466 | − | 0.873495i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.7279 | + | 22.7279i | 1.36559 | + | 1.36559i | 0.866620 | + | 0.498968i | \(0.166288\pi\) |
0.498968 | + | 0.866620i | \(0.333712\pi\) | |||||||
\(278\) | 4.82843 | + | 4.82843i | 0.289590 | + | 0.289590i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.82843 | − | 5.65685i | −0.169031 | − | 0.338062i | ||||
\(281\) | 30.9706i | 1.84755i | 0.382937 | + | 0.923774i | \(0.374913\pi\) | ||||
−0.382937 | + | 0.923774i | \(0.625087\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.82843 | + | 2.82843i | −0.168133 | + | 0.168133i | −0.786158 | − | 0.618026i | \(-0.787933\pi\) |
0.618026 | + | 0.786158i | \(0.287933\pi\) | |||||||
\(284\) | −7.41421 | −0.439953 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.65685 | 0.571022 | ||||||||
\(287\) | 10.8284 | − | 10.8284i | 0.639182 | − | 0.639182i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.62742i | 0.213377i | ||||||||
\(290\) | −0.585786 | + | 1.75736i | −0.0343986 | + | 0.103196i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.82843 | + | 9.82843i | 0.575165 | + | 0.575165i | ||||
\(293\) | −7.34315 | − | 7.34315i | −0.428991 | − | 0.428991i | 0.459293 | − | 0.888285i | \(-0.348103\pi\) |
−0.888285 | + | 0.459293i | \(0.848103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.65685 | + | 2.82843i | −0.329355 | + | 0.164677i | ||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.24264 | + | 8.24264i | −0.477483 | + | 0.477483i | ||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.97056 | 0.517055 | ||||||||
\(302\) | −12.0000 | + | 12.0000i | −0.690522 | + | 0.690522i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.585786i | − | 0.0335972i | ||||||
\(305\) | 10.8284 | − | 5.41421i | 0.620034 | − | 0.310017i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.8284 | + | 10.8284i | 0.618011 | + | 0.618011i | 0.945021 | − | 0.327010i | \(-0.106041\pi\) |
−0.327010 | + | 0.945021i | \(0.606041\pi\) | |||||||
\(308\) | −9.65685 | − | 9.65685i | −0.550250 | − | 0.550250i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.585786 | − | 1.75736i | 0.0332704 | − | 0.0998113i | ||||
\(311\) | 31.2132i | 1.76994i | 0.465650 | + | 0.884969i | \(0.345821\pi\) | ||||
−0.465650 | + | 0.884969i | \(0.654179\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.928932 | − | 0.928932i | 0.0525064 | − | 0.0525064i | −0.680366 | − | 0.732872i | \(-0.738179\pi\) |
0.732872 | + | 0.680366i | \(0.238179\pi\) | |||||||
\(314\) | −6.00000 | −0.338600 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.17157 | 0.0659061 | ||||||||
\(317\) | 10.7279 | − | 10.7279i | 0.602540 | − | 0.602540i | −0.338446 | − | 0.940986i | \(-0.609901\pi\) |
0.940986 | + | 0.338446i | \(0.109901\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000i | 0.223957i | ||||||||
\(320\) | 1.00000 | + | 2.00000i | 0.0559017 | + | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00000 | − | 2.00000i | −0.111456 | − | 0.111456i | ||||
\(323\) | 1.51472 | + | 1.51472i | 0.0842812 | + | 0.0842812i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.41421 | + | 9.89949i | 0.0784465 | + | 0.549125i | ||||
\(326\) | 9.17157i | 0.507966i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.82843 | + | 3.82843i | −0.211390 | + | 0.211390i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.7990 | −1.74783 | −0.873915 | − | 0.486078i | \(-0.838427\pi\) | ||||
−0.873915 | + | 0.486078i | \(0.838427\pi\) | |||||||
\(332\) | −0.757359 | + | 0.757359i | −0.0415655 | + | 0.0415655i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 22.4853i | − | 1.23034i | ||||||
\(335\) | 20.4853 | + | 6.82843i | 1.11923 | + | 0.373077i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.24264 | + | 2.24264i | 0.122164 | + | 0.122164i | 0.765546 | − | 0.643381i | \(-0.222469\pi\) |
−0.643381 | + | 0.765546i | \(0.722469\pi\) | |||||||
\(338\) | 6.36396 | + | 6.36396i | 0.346154 | + | 0.346154i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.75736 | − | 2.58579i | −0.420702 | − | 0.140234i | ||||
\(341\) | − | 4.00000i | − | 0.216612i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0000 | − | 12.0000i | 0.647939 | − | 0.647939i | ||||
\(344\) | −3.17157 | −0.171000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.0000 | −0.752645 | ||||||||
\(347\) | −10.0000 | + | 10.0000i | −0.536828 | + | 0.536828i | −0.922596 | − | 0.385768i | \(-0.873937\pi\) |
0.385768 | + | 0.922596i | \(0.373937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6569i | 1.26632i | 0.774020 | + | 0.633161i | \(0.218243\pi\) | ||||
−0.774020 | + | 0.633161i | \(0.781757\pi\) | |||||||
\(350\) | 8.48528 | − | 11.3137i | 0.453557 | − | 0.604743i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.41421 | + | 3.41421i | 0.181978 | + | 0.181978i | ||||
\(353\) | 5.89949 | + | 5.89949i | 0.313998 | + | 0.313998i | 0.846456 | − | 0.532458i | \(-0.178732\pi\) |
−0.532458 | + | 0.846456i | \(0.678732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.41421 | − | 14.8284i | −0.393506 | − | 0.787011i | ||||
\(356\) | − | 14.0000i | − | 0.741999i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.4853 | + | 16.4853i | −0.871274 | + | 0.871274i | ||||
\(359\) | 6.82843 | 0.360391 | 0.180195 | − | 0.983631i | \(-0.442327\pi\) | ||||
0.180195 | + | 0.983631i | \(0.442327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6569 | 0.981940 | ||||||||
\(362\) | 9.48528 | − | 9.48528i | 0.498535 | − | 0.498535i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.65685i | 0.296500i | ||||||||
\(365\) | −9.82843 | + | 29.4853i | −0.514443 | + | 1.54333i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.00000 | + | 6.00000i | 0.313197 | + | 0.313197i | 0.846147 | − | 0.532950i | \(-0.178916\pi\) |
−0.532950 | + | 0.846147i | \(0.678916\pi\) | |||||||
\(368\) | 0.707107 | + | 0.707107i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | + | 2.00000i | −0.207950 | + | 0.103975i | ||||
\(371\) | 34.6274i | 1.79777i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.24264 | − | 4.24264i | 0.219676 | − | 0.219676i | −0.588686 | − | 0.808362i | \(-0.700355\pi\) |
0.808362 | + | 0.588686i | \(0.200355\pi\) | |||||||
\(374\) | −17.6569 | −0.913014 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.17157 | − | 1.17157i | 0.0603391 | − | 0.0603391i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0416i | 1.54313i | 0.636148 | + | 0.771567i | \(0.280527\pi\) | ||||
−0.636148 | + | 0.771567i | \(0.719473\pi\) | |||||||
\(380\) | 1.17157 | − | 0.585786i | 0.0601004 | − | 0.0300502i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.48528 | + | 6.48528i | 0.331816 | + | 0.331816i | ||||
\(383\) | −16.8284 | − | 16.8284i | −0.859892 | − | 0.859892i | 0.131433 | − | 0.991325i | \(-0.458042\pi\) |
−0.991325 | + | 0.131433i | \(0.958042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.65685 | − | 28.9706i | 0.492159 | − | 1.47648i | ||||
\(386\) | 7.07107i | 0.359908i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.07107 | + | 9.07107i | −0.460514 | + | 0.460514i | ||||
\(389\) | −20.2843 | −1.02845 | −0.514227 | − | 0.857654i | \(-0.671921\pi\) | ||||
−0.514227 | + | 0.857654i | \(0.671921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.65685 | −0.184935 | ||||||||
\(392\) | 0.707107 | − | 0.707107i | 0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 10.0000i | − | 0.503793i | ||||||
\(395\) | 1.17157 | + | 2.34315i | 0.0589482 | + | 0.117896i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.41421 | + | 5.41421i | 0.271732 | + | 0.271732i | 0.829797 | − | 0.558065i | \(-0.188456\pi\) |
−0.558065 | + | 0.829797i | \(0.688456\pi\) | |||||||
\(398\) | −4.48528 | − | 4.48528i | −0.224827 | − | 0.224827i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | − | 34.0000i | − | 1.69788i | −0.528490 | − | 0.848939i | \(-0.677242\pi\) | ||
0.528490 | − | 0.848939i | \(-0.322758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.17157 | + | 1.17157i | −0.0583602 | + | 0.0583602i | ||||
\(404\) | 3.65685 | 0.181935 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.34315 | −0.116288 | ||||||||
\(407\) | −6.82843 | + | 6.82843i | −0.338473 | + | 0.338473i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.31371i | − | 0.262746i | −0.991333 | − | 0.131373i | \(-0.958061\pi\) | ||
0.991333 | − | 0.131373i | \(-0.0419386\pi\) | |||||||
\(410\) | −11.4853 | − | 3.82843i | −0.567218 | − | 0.189073i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.17157 | + | 5.17157i | 0.254785 | + | 0.254785i | ||||
\(413\) | −5.65685 | − | 5.65685i | −0.278356 | − | 0.278356i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.27208 | − | 0.757359i | −0.111532 | − | 0.0371773i | ||||
\(416\) | − | 2.00000i | − | 0.0980581i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.00000 | − | 2.00000i | 0.0978232 | − | 0.0978232i | ||||
\(419\) | −33.6569 | −1.64424 | −0.822122 | − | 0.569311i | \(-0.807210\pi\) | ||||
−0.822122 | + | 0.569311i | \(0.807210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.27208 | −0.159471 | −0.0797357 | − | 0.996816i | \(-0.525408\pi\) | ||||
−0.0797357 | + | 0.996816i | \(0.525408\pi\) | |||||||
\(422\) | −10.4853 | + | 10.4853i | −0.510416 | + | 0.510416i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.2426i | − | 0.594555i | ||||||
\(425\) | −2.58579 | − | 18.1005i | −0.125429 | − | 0.878003i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8284 | + | 10.8284i | 0.524024 | + | 0.524024i | ||||
\(428\) | 4.07107 | + | 4.07107i | 0.196782 | + | 0.196782i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.17157 | − | 6.34315i | −0.152947 | − | 0.305894i | ||||
\(431\) | 10.8284i | 0.521587i | 0.965395 | + | 0.260793i | \(0.0839842\pi\) | ||||
−0.965395 | + | 0.260793i | \(0.916016\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.5858 | + | 20.5858i | −0.989290 | + | 0.989290i | −0.999943 | − | 0.0106535i | \(-0.996609\pi\) |
0.0106535 | + | 0.999943i | \(0.496609\pi\) | |||||||
\(434\) | 2.34315 | 0.112475 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −19.0711 | −0.913339 | ||||||||
\(437\) | 0.414214 | − | 0.414214i | 0.0198145 | − | 0.0198145i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.14214i | − | 0.197693i | −0.995103 | − | 0.0988467i | \(-0.968485\pi\) | ||
0.995103 | − | 0.0988467i | \(-0.0315153\pi\) | |||||||
\(440\) | −3.41421 | + | 10.2426i | −0.162766 | + | 0.488299i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.17157 | + | 5.17157i | 0.245987 | + | 0.245987i | ||||
\(443\) | 4.82843 | + | 4.82843i | 0.229405 | + | 0.229405i | 0.812444 | − | 0.583039i | \(-0.198136\pi\) |
−0.583039 | + | 0.812444i | \(0.698136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.0000 | − | 14.0000i | 1.32733 | − | 0.663664i | ||||
\(446\) | 4.58579i | 0.217143i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.00000 | + | 2.00000i | −0.0944911 | + | 0.0944911i | ||||
\(449\) | −4.92893 | −0.232611 | −0.116305 | − | 0.993214i | \(-0.537105\pi\) | ||||
−0.116305 | + | 0.993214i | \(0.537105\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −26.1421 | −1.23099 | ||||||||
\(452\) | 12.2426 | − | 12.2426i | 0.575845 | − | 0.575845i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 6.92893i | − | 0.325191i | ||||||
\(455\) | −11.3137 | + | 5.65685i | −0.530395 | + | 0.265197i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.27208 | − | 1.27208i | −0.0595053 | − | 0.0595053i | 0.676728 | − | 0.736233i | \(-0.263397\pi\) |
−0.736233 | + | 0.676728i | \(0.763397\pi\) | |||||||
\(458\) | 9.48528 | + | 9.48528i | 0.443218 | + | 0.443218i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.707107 | + | 2.12132i | −0.0329690 | + | 0.0989071i | ||||
\(461\) | − | 13.5147i | − | 0.629443i | −0.949184 | − | 0.314722i | \(-0.898089\pi\) | ||
0.949184 | − | 0.314722i | \(-0.101911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.8701 | + | 25.8701i | −1.20228 | + | 1.20228i | −0.228813 | + | 0.973470i | \(0.573484\pi\) |
−0.973470 | + | 0.228813i | \(0.926516\pi\) | |||||||
\(464\) | 0.828427 | 0.0384588 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.6274 | 0.862898 | ||||||||
\(467\) | −7.92893 | + | 7.92893i | −0.366907 | + | 0.366907i | −0.866348 | − | 0.499441i | \(-0.833539\pi\) |
0.499441 | + | 0.866348i | \(0.333539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.3137i | 1.26123i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.00000 | + | 2.00000i | 0.0920575 | + | 0.0920575i | ||||
\(473\) | −10.8284 | − | 10.8284i | −0.497892 | − | 0.497892i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.34315 | + | 1.75736i | 0.107511 | + | 0.0806332i | ||||
\(476\) | − | 10.3431i | − | 0.474077i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.75736 | + | 6.75736i | −0.309074 | + | 0.309074i | ||||
\(479\) | −18.6274 | −0.851108 | −0.425554 | − | 0.904933i | \(-0.639921\pi\) | ||||
−0.425554 | + | 0.904933i | \(0.639921\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 9.75736 | − | 9.75736i | 0.444436 | − | 0.444436i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.3137i | 0.559714i | ||||||||
\(485\) | −27.2132 | − | 9.07107i | −1.23569 | − | 0.411896i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.2132 | + | 28.2132i | 1.27846 | + | 1.27846i | 0.941528 | + | 0.336934i | \(0.109390\pi\) |
0.336934 | + | 0.941528i | \(0.390610\pi\) | |||||||
\(488\) | −3.82843 | − | 3.82843i | −0.173305 | − | 0.173305i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.12132 | + | 0.707107i | 0.0958315 | + | 0.0319438i | ||||
\(491\) | − | 9.17157i | − | 0.413907i | −0.978351 | − | 0.206954i | \(-0.933645\pi\) | ||
0.978351 | − | 0.206954i | \(-0.0663549\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.14214 | + | 2.14214i | −0.0964769 | + | 0.0964769i | ||||
\(494\) | −1.17157 | −0.0527116 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.828427 | −0.0371975 | ||||||||
\(497\) | 14.8284 | − | 14.8284i | 0.665146 | − | 0.665146i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9706i | 0.580642i | 0.956929 | + | 0.290321i | \(0.0937621\pi\) | ||||
−0.956929 | + | 0.290321i | \(0.906238\pi\) | |||||||
\(500\) | −11.0000 | − | 2.00000i | −0.491935 | − | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 20.3848 | + | 20.3848i | 0.909817 | + | 0.909817i | ||||
\(503\) | 25.7990 | + | 25.7990i | 1.15032 | + | 1.15032i | 0.986488 | + | 0.163832i | \(0.0523854\pi\) |
0.163832 | + | 0.986488i | \(0.447615\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.65685 | + | 7.31371i | 0.162728 | + | 0.325456i | ||||
\(506\) | 4.82843i | 0.214650i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.58579 | + | 1.58579i | −0.0703579 | + | 0.0703579i | ||||
\(509\) | 11.4558 | 0.507771 | 0.253886 | − | 0.967234i | \(-0.418291\pi\) | ||||
0.253886 | + | 0.967234i | \(0.418291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.3137 | −1.73914 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 15.3137i | − | 0.675459i | ||||||
\(515\) | −5.17157 | + | 15.5147i | −0.227887 | + | 0.683660i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.00000 | − | 4.00000i | −0.175750 | − | 0.175750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | − | 2.00000i | 0.175412 | − | 0.0877058i | ||||
\(521\) | − | 12.1421i | − | 0.531957i | −0.963979 | − | 0.265978i | \(-0.914305\pi\) | ||
0.963979 | − | 0.265978i | \(-0.0856950\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2132 | − | 15.2132i | 0.665227 | − | 0.665227i | −0.291380 | − | 0.956607i | \(-0.594115\pi\) |
0.956607 | + | 0.291380i | \(0.0941145\pi\) | |||||||
\(524\) | 5.65685 | 0.247121 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.1716 | 0.748716 | ||||||||
\(527\) | 2.14214 | − | 2.14214i | 0.0933129 | − | 0.0933129i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | 24.4853 | − | 12.2426i | 1.06357 | − | 0.531786i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.17157 | + | 1.17157i | 0.0507941 | + | 0.0507941i | ||||
\(533\) | 7.65685 | + | 7.65685i | 0.331655 | + | 0.331655i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.07107 | + | 12.2132i | −0.176008 | + | 0.528023i | ||||
\(536\) | − | 9.65685i | − | 0.417113i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.41421 | − | 1.41421i | 0.0609711 | − | 0.0609711i | ||||
\(539\) | 4.82843 | 0.207975 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.3137 | 0.916348 | 0.458174 | − | 0.888863i | \(-0.348504\pi\) | ||||
0.458174 | + | 0.888863i | \(0.348504\pi\) | |||||||
\(542\) | 6.34315 | − | 6.34315i | 0.272461 | − | 0.272461i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.65685i | 0.156786i | ||||||||
\(545\) | −19.0711 | − | 38.1421i | −0.816915 | − | 1.63383i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.142136 | − | 0.142136i | −0.00607728 | − | 0.00607728i | 0.704062 | − | 0.710139i | \(-0.251368\pi\) |
−0.710139 | + | 0.704062i | \(0.751368\pi\) | |||||||
\(548\) | −1.07107 | − | 1.07107i | −0.0457537 | − | 0.0457537i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.8995 | + | 3.41421i | −1.01908 | + | 0.145583i | ||||
\(551\) | − | 0.485281i | − | 0.0206737i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.34315 | + | 2.34315i | −0.0996407 | + | 0.0996407i | ||||
\(554\) | 32.1421 | 1.36559 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.82843 | 0.289590 | ||||||||
\(557\) | −14.1716 | + | 14.1716i | −0.600469 | + | 0.600469i | −0.940437 | − | 0.339968i | \(-0.889584\pi\) |
0.339968 | + | 0.940437i | \(0.389584\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.34315i | 0.268286i | ||||||||
\(560\) | −6.00000 | − | 2.00000i | −0.253546 | − | 0.0845154i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 21.8995 | + | 21.8995i | 0.923774 | + | 0.923774i | ||||
\(563\) | −28.0711 | − | 28.0711i | −1.18305 | − | 1.18305i | −0.978949 | − | 0.204106i | \(-0.934571\pi\) |
−0.204106 | − | 0.978949i | \(-0.565429\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.7279 | + | 12.2426i | 1.54516 | + | 0.515052i | ||||
\(566\) | 4.00000i | 0.168133i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.24264 | + | 5.24264i | −0.219976 | + | 0.219976i | ||||
\(569\) | −5.31371 | −0.222762 | −0.111381 | − | 0.993778i | \(-0.535527\pi\) | ||||
−0.111381 | + | 0.993778i | \(0.535527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.7574 | −0.743122 | −0.371561 | − | 0.928408i | \(-0.621177\pi\) | ||||
−0.371561 | + | 0.928408i | \(0.621177\pi\) | |||||||
\(572\) | 6.82843 | − | 6.82843i | 0.285511 | − | 0.285511i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 15.3137i | − | 0.639182i | ||||||
\(575\) | −4.94975 | + | 0.707107i | −0.206419 | + | 0.0294884i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.14214 | + | 1.14214i | 0.0475477 | + | 0.0475477i | 0.730481 | − | 0.682933i | \(-0.239296\pi\) |
−0.682933 | + | 0.730481i | \(0.739296\pi\) | |||||||
\(578\) | 2.56497 | + | 2.56497i | 0.106689 | + | 0.106689i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.828427 | + | 1.65685i | 0.0343986 | + | 0.0687971i | ||||
\(581\) | − | 3.02944i | − | 0.125682i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.7990 | − | 41.7990i | 1.73114 | − | 1.73114i | ||||
\(584\) | 13.8995 | 0.575165 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.3848 | −0.428991 | ||||||||
\(587\) | 18.6274 | − | 18.6274i | 0.768836 | − | 0.768836i | −0.209066 | − | 0.977902i | \(-0.567042\pi\) |
0.977902 | + | 0.209066i | \(0.0670423\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.485281i | 0.0199957i | ||||||||
\(590\) | −2.00000 | + | 6.00000i | −0.0823387 | + | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.41421 | + | 1.41421i | 0.0581238 | + | 0.0581238i | ||||
\(593\) | −16.4853 | − | 16.4853i | −0.676969 | − | 0.676969i | 0.282344 | − | 0.959313i | \(-0.408888\pi\) |
−0.959313 | + | 0.282344i | \(0.908888\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.6863 | − | 10.3431i | 0.848055 | − | 0.424028i | ||||
\(596\) | 11.6569i | 0.477483i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.41421 | − | 1.41421i | 0.0578315 | − | 0.0578315i | ||||
\(599\) | −17.5563 | −0.717333 | −0.358666 | − | 0.933466i | \(-0.616768\pi\) | ||||
−0.358666 | + | 0.933466i | \(0.616768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.3431 | 0.585069 | 0.292535 | − | 0.956255i | \(-0.405501\pi\) | ||||
0.292535 | + | 0.956255i | \(0.405501\pi\) | |||||||
\(602\) | 6.34315 | − | 6.34315i | 0.258527 | − | 0.258527i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.9706i | 0.690522i | ||||||||
\(605\) | −24.6274 | + | 12.3137i | −1.00125 | + | 0.500623i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0710678 | + | 0.0710678i | 0.00288455 | + | 0.00288455i | 0.708548 | − | 0.705663i | \(-0.249351\pi\) |
−0.705663 | + | 0.708548i | \(0.749351\pi\) | |||||||
\(608\) | −0.414214 | − | 0.414214i | −0.0167986 | − | 0.0167986i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.82843 | − | 11.4853i | 0.155008 | − | 0.465025i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.4558 | − | 17.4558i | 0.705035 | − | 0.705035i | −0.260452 | − | 0.965487i | \(-0.583872\pi\) |
0.965487 | + | 0.260452i | \(0.0838715\pi\) | |||||||
\(614\) | 15.3137 | 0.618011 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.6569 | −0.550250 | ||||||||
\(617\) | 23.2132 | − | 23.2132i | 0.934528 | − | 0.934528i | −0.0634562 | − | 0.997985i | \(-0.520212\pi\) |
0.997985 | + | 0.0634562i | \(0.0202123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.41421i | 0.298002i | 0.988837 | + | 0.149001i | \(0.0476058\pi\) | ||||
−0.988837 | + | 0.149001i | \(0.952394\pi\) | |||||||
\(620\) | −0.828427 | − | 1.65685i | −0.0332704 | − | 0.0665409i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.0711 | + | 22.0711i | 0.884969 | + | 0.884969i | ||||
\(623\) | 28.0000 | + | 28.0000i | 1.12180 | + | 1.12180i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | − | 1.31371i | − | 0.0525064i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.24264 | + | 4.24264i | −0.169300 | + | 0.169300i | ||||
\(629\) | −7.31371 | −0.291617 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6569 | 1.18062 | 0.590310 | − | 0.807176i | \(-0.299005\pi\) | ||||
0.590310 | + | 0.807176i | \(0.299005\pi\) | |||||||
\(632\) | 0.828427 | − | 0.828427i | 0.0329531 | − | 0.0329531i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 15.1716i | − | 0.602540i | ||||||
\(635\) | −4.75736 | − | 1.58579i | −0.188790 | − | 0.0629300i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.41421 | − | 1.41421i | −0.0560332 | − | 0.0560332i | ||||
\(638\) | 2.82843 | + | 2.82843i | 0.111979 | + | 0.111979i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | + | 0.707107i | 0.0838525 | + | 0.0279508i | ||||
\(641\) | 22.4853i | 0.888115i | 0.895998 | + | 0.444058i | \(0.146461\pi\) | ||||
−0.895998 | + | 0.444058i | \(0.853539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.79899 | + | 7.79899i | −0.307562 | + | 0.307562i | −0.843963 | − | 0.536401i | \(-0.819783\pi\) |
0.536401 | + | 0.843963i | \(0.319783\pi\) | |||||||
\(644\) | −2.82843 | −0.111456 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.14214 | 0.0842812 | ||||||||
\(647\) | 2.72792 | − | 2.72792i | 0.107246 | − | 0.107246i | −0.651448 | − | 0.758693i | \(-0.725838\pi\) |
0.758693 | + | 0.651448i | \(0.225838\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6569i | 0.536078i | ||||||||
\(650\) | 8.00000 | + | 6.00000i | 0.313786 | + | 0.235339i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.48528 | + | 6.48528i | 0.253983 | + | 0.253983i | ||||
\(653\) | −28.2426 | − | 28.2426i | −1.10522 | − | 1.10522i | −0.993770 | − | 0.111450i | \(-0.964451\pi\) |
−0.111450 | − | 0.993770i | \(-0.535549\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.65685 | + | 11.3137i | 0.221032 | + | 0.442063i | ||||
\(656\) | 5.41421i | 0.211390i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.9411 | 1.47798 | 0.738988 | − | 0.673718i | \(-0.235304\pi\) | ||||
0.738988 | + | 0.673718i | \(0.235304\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.5269 | 1.73190 | 0.865948 | − | 0.500134i | \(-0.166716\pi\) | ||||
0.865948 | + | 0.500134i | \(0.166716\pi\) | |||||||
\(662\) | −22.4853 | + | 22.4853i | −0.873915 | + | 0.873915i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.07107i | 0.0415655i | ||||||||
\(665\) | −1.17157 | + | 3.51472i | −0.0454316 | + | 0.136295i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.585786 | + | 0.585786i | 0.0226817 | + | 0.0226817i | ||||
\(668\) | −15.8995 | − | 15.8995i | −0.615170 | − | 0.615170i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.3137 | − | 9.65685i | 0.746154 | − | 0.373077i | ||||
\(671\) | − | 26.1421i | − | 1.00921i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.48528 | − | 1.48528i | 0.0572534 | − | 0.0572534i | −0.677900 | − | 0.735154i | \(-0.737110\pi\) |
0.735154 | + | 0.677900i | \(0.237110\pi\) | |||||||
\(674\) | 3.17157 | 0.122164 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.00000 | 0.346154 | ||||||||
\(677\) | −11.3431 | + | 11.3431i | −0.435953 | + | 0.435953i | −0.890647 | − | 0.454695i | \(-0.849748\pi\) |
0.454695 | + | 0.890647i | \(0.349748\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 36.2843i | − | 1.39246i | ||||||
\(680\) | −7.31371 | + | 3.65685i | −0.280468 | + | 0.140234i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.82843 | − | 2.82843i | −0.108306 | − | 0.108306i | ||||
\(683\) | 28.2843 | + | 28.2843i | 1.08227 | + | 1.08227i | 0.996298 | + | 0.0859698i | \(0.0273989\pi\) |
0.0859698 | + | 0.996298i | \(0.472601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.07107 | − | 3.21320i | 0.0409234 | − | 0.122770i | ||||
\(686\) | − | 16.9706i | − | 0.647939i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.24264 | + | 2.24264i | −0.0854999 | + | 0.0854999i | ||||
\(689\) | −24.4853 | −0.932815 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6863 | −0.482609 | −0.241305 | − | 0.970449i | \(-0.577575\pi\) | ||||
−0.241305 | + | 0.970449i | \(0.577575\pi\) | |||||||
\(692\) | −9.89949 | + | 9.89949i | −0.376322 | + | 0.376322i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.1421i | 0.536828i | ||||||||
\(695\) | 6.82843 | + | 13.6569i | 0.259017 | + | 0.518034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | − | 14.0000i | −0.530288 | − | 0.530288i | ||||
\(698\) | 16.7279 | + | 16.7279i | 0.633161 | + | 0.633161i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 14.0000i | −0.0755929 | − | 0.529150i | ||||
\(701\) | 19.9411i | 0.753166i | 0.926383 | + | 0.376583i | \(0.122901\pi\) | ||||
−0.926383 | + | 0.376583i | \(0.877099\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.828427 | − | 0.828427i | 0.0312447 | − | 0.0312447i | ||||
\(704\) | 4.82843 | 0.181978 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.34315 | 0.313998 | ||||||||
\(707\) | −7.31371 | + | 7.31371i | −0.275060 | + | 0.275060i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.10051i | 0.229109i | 0.993417 | + | 0.114555i | \(0.0365441\pi\) | ||||
−0.993417 | + | 0.114555i | \(0.963456\pi\) | |||||||
\(710\) | −15.7279 | − | 5.24264i | −0.590258 | − | 0.196753i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.89949 | − | 9.89949i | −0.370999 | − | 0.370999i | ||||
\(713\) | −0.585786 | − | 0.585786i | −0.0219379 | − | 0.0219379i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20.4853 | + | 6.82843i | 0.766106 | + | 0.255369i | ||||
\(716\) | 23.3137i | 0.871274i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.82843 | − | 4.82843i | 0.180195 | − | 0.180195i | ||||
\(719\) | −34.5269 | −1.28764 | −0.643818 | − | 0.765178i | \(-0.722651\pi\) | ||||
−0.643818 | + | 0.765178i | \(0.722651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.6863 | −0.770398 | ||||||||
\(722\) | 13.1924 | − | 13.1924i | 0.490970 | − | 0.490970i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 13.4142i | − | 0.498535i | ||||||
\(725\) | −2.48528 | + | 3.31371i | −0.0923010 | + | 0.123068i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.6569 | − | 13.6569i | −0.506505 | − | 0.506505i | 0.406947 | − | 0.913452i | \(-0.366593\pi\) |
−0.913452 | + | 0.406947i | \(0.866593\pi\) | |||||||
\(728\) | 4.00000 | + | 4.00000i | 0.148250 | + | 0.148250i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.8995 | + | 27.7990i | 0.514443 | + | 1.02889i | ||||
\(731\) | − | 11.5980i | − | 0.428967i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.0000 | + | 32.0000i | −1.18195 | + | 1.18195i | −0.202708 | + | 0.979239i | \(0.564974\pi\) |
−0.979239 | + | 0.202708i | \(0.935026\pi\) | |||||||
\(734\) | 8.48528 | 0.313197 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 32.9706 | − | 32.9706i | 1.21449 | − | 1.21449i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18.1421i | − | 0.667369i | −0.942685 | − | 0.333685i | \(-0.891708\pi\) | ||
0.942685 | − | 0.333685i | \(-0.108292\pi\) | |||||||
\(740\) | −1.41421 | + | 4.24264i | −0.0519875 | + | 0.155963i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24.4853 | + | 24.4853i | 0.898883 | + | 0.898883i | ||||
\(743\) | −13.5147 | − | 13.5147i | −0.495807 | − | 0.495807i | 0.414323 | − | 0.910130i | \(-0.364018\pi\) |
−0.910130 | + | 0.414323i | \(0.864018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.3137 | + | 11.6569i | −0.854148 | + | 0.427074i | ||||
\(746\) | − | 6.00000i | − | 0.219676i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.4853 | + | 12.4853i | −0.456507 | + | 0.456507i | ||||
\(749\) | −16.2843 | −0.595014 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.1421 | −0.370092 | −0.185046 | − | 0.982730i | \(-0.559243\pi\) | ||||
−0.185046 | + | 0.982730i | \(0.559243\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 1.65685i | − | 0.0603391i | ||||||
\(755\) | −33.9411 | + | 16.9706i | −1.23524 | + | 0.617622i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.1127 | − | 27.1127i | −0.985428 | − | 0.985428i | 0.0144676 | − | 0.999895i | \(-0.495395\pi\) |
−0.999895 | + | 0.0144676i | \(0.995395\pi\) | |||||||
\(758\) | 21.2426 | + | 21.2426i | 0.771567 | + | 0.771567i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.414214 | − | 1.24264i | 0.0150251 | − | 0.0450753i | ||||
\(761\) | − | 7.55635i | − | 0.273917i | −0.990577 | − | 0.136959i | \(-0.956267\pi\) | ||
0.990577 | − | 0.136959i | \(-0.0437328\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 38.1421 | − | 38.1421i | 1.38084 | − | 1.38084i | ||||
\(764\) | 9.17157 | 0.331816 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.7990 | −0.859892 | ||||||||
\(767\) | 4.00000 | − | 4.00000i | 0.144432 | − | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.3137i | 0.624348i | 0.950025 | + | 0.312174i | \(0.101057\pi\) | ||||
−0.950025 | + | 0.312174i | \(0.898943\pi\) | |||||||
\(770\) | −13.6569 | − | 27.3137i | −0.492159 | − | 0.984318i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.00000 | + | 5.00000i | 0.179954 | + | 0.179954i | ||||
\(773\) | −20.1716 | − | 20.1716i | −0.725521 | − | 0.725521i | 0.244203 | − | 0.969724i | \(-0.421474\pi\) |
−0.969724 | + | 0.244203i | \(0.921474\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.48528 | − | 3.31371i | 0.0892739 | − | 0.119032i | ||||
\(776\) | 12.8284i | 0.460514i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.3431 | + | 14.3431i | −0.514227 | + | 0.514227i | ||||
\(779\) | 3.17157 | 0.113633 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.7990 | −1.28099 | ||||||||
\(782\) | −2.58579 | + | 2.58579i | −0.0924675 | + | 0.0924675i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −12.7279 | − | 4.24264i | −0.454279 | − | 0.151426i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.82843 | − | 2.82843i | −0.100823 | − | 0.100823i | 0.654896 | − | 0.755719i | \(-0.272712\pi\) |
−0.755719 | + | 0.654896i | \(0.772712\pi\) | |||||||
\(788\) | −7.07107 | − | 7.07107i | −0.251896 | − | 0.251896i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.48528 | + | 0.828427i | 0.0884223 | + | 0.0294741i | ||||
\(791\) | 48.9706i | 1.74119i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.65685 | + | 7.65685i | −0.271903 | + | 0.271903i | ||||
\(794\) | 7.65685 | 0.271732 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.34315 | −0.224827 | ||||||||
\(797\) | 29.4853 | − | 29.4853i | 1.04442 | − | 1.04442i | 0.0454559 | − | 0.998966i | \(-0.485526\pi\) |
0.998966 | − | 0.0454559i | \(-0.0144741\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.707107 | + | 4.94975i | 0.0250000 | + | 0.175000i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.0416 | − | 24.0416i | −0.848939 | − | 0.848939i | ||||
\(803\) | 47.4558 | + | 47.4558i | 1.67468 | + | 1.67468i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.82843 | − | 5.65685i | −0.0996890 | − | 0.199378i | ||||
\(806\) | 1.65685i | 0.0583602i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.58579 | − | 2.58579i | 0.0909676 | − | 0.0909676i | ||||
\(809\) | 20.2426 | 0.711693 | 0.355847 | − | 0.934544i | \(-0.384193\pi\) | ||||
0.355847 | + | 0.934544i | \(0.384193\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9706 | −0.595917 | −0.297959 | − | 0.954579i | \(-0.596306\pi\) | ||||
−0.297959 | + | 0.954579i | \(0.596306\pi\) | |||||||
\(812\) | −1.65685 | + | 1.65685i | −0.0581442 | + | 0.0581442i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.65685i | 0.338473i | ||||||||
\(815\) | −6.48528 | + | 19.4558i | −0.227169 | + | 0.681508i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31371 | + | 1.31371i | 0.0459608 | + | 0.0459608i | ||||
\(818\) | −3.75736 | − | 3.75736i | −0.131373 | − | 0.131373i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.8284 | + | 5.41421i | −0.378145 | + | 0.189073i | ||||
\(821\) | − | 50.4853i | − | 1.76195i | −0.473164 | − | 0.880974i | \(-0.656888\pi\) | ||
0.473164 | − | 0.880974i | \(-0.343112\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.5858 | − | 25.5858i | 0.891864 | − | 0.891864i | −0.102834 | − | 0.994699i | \(-0.532791\pi\) |
0.994699 | + | 0.102834i | \(0.0327911\pi\) | |||||||
\(824\) | 7.31371 | 0.254785 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | −39.2426 | + | 39.2426i | −1.36460 | + | 1.36460i | −0.496649 | + | 0.867952i | \(0.665436\pi\) |
−0.867952 | + | 0.496649i | \(0.834564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.2843i | − | 0.357188i | −0.983923 | − | 0.178594i | \(-0.942845\pi\) | ||
0.983923 | − | 0.178594i | \(-0.0571548\pi\) | |||||||
\(830\) | −2.14214 | + | 1.07107i | −0.0743546 | + | 0.0371773i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.41421 | − | 1.41421i | −0.0490290 | − | 0.0490290i | ||||
\(833\) | 2.58579 | + | 2.58579i | 0.0895922 | + | 0.0895922i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.8995 | − | 47.6985i | 0.550225 | − | 1.65067i | ||||
\(836\) | − | 2.82843i | − | 0.0978232i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.7990 | + | 23.7990i | −0.822122 | + | 0.822122i | ||||
\(839\) | −11.5147 | −0.397532 | −0.198766 | − | 0.980047i | \(-0.563693\pi\) | ||||
−0.198766 | + | 0.980047i | \(0.563693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3137 | −0.976335 | ||||||||
\(842\) | −2.31371 | + | 2.31371i | −0.0797357 | + | 0.0797357i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.8284i | 0.510416i | ||||||||
\(845\) | 9.00000 | + | 18.0000i | 0.309609 | + | 0.619219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.6274 | − | 24.6274i | −0.846208 | − | 0.846208i | ||||
\(848\) | −8.65685 | − | 8.65685i | −0.297278 | − | 0.297278i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −14.6274 | − | 10.9706i | −0.501716 | − | 0.376287i | ||||
\(851\) | 2.00000i | 0.0685591i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.2132 | − | 37.2132i | 1.27416 | − | 1.27416i | 0.330269 | − | 0.943887i | \(-0.392861\pi\) |
0.943887 | − | 0.330269i | \(-0.107139\pi\) | |||||||
\(854\) | 15.3137 | 0.524024 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.75736 | 0.196782 | ||||||||
\(857\) | 20.2426 | − | 20.2426i | 0.691475 | − | 0.691475i | −0.271081 | − | 0.962557i | \(-0.587381\pi\) |
0.962557 | + | 0.271081i | \(0.0873812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.17157i | − | 0.0399736i | −0.999800 | − | 0.0199868i | \(-0.993638\pi\) | ||
0.999800 | − | 0.0199868i | \(-0.00636241\pi\) | |||||||
\(860\) | −6.72792 | − | 2.24264i | −0.229420 | − | 0.0764734i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.65685 | + | 7.65685i | 0.260793 | + | 0.260793i | ||||
\(863\) | 29.7574 | + | 29.7574i | 1.01295 | + | 1.01295i | 0.999915 | + | 0.0130373i | \(0.00415001\pi\) |
0.0130373 | + | 0.999915i | \(0.495850\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.6985 | − | 9.89949i | −1.00978 | − | 0.336593i | ||||
\(866\) | 29.1127i | 0.989290i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.65685 | − | 1.65685i | 0.0562373 | − | 0.0562373i | ||||
\(869\) | 5.65685 | 0.191896 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.3137 | −0.654420 | ||||||||
\(872\) | −13.4853 | + | 13.4853i | −0.456669 | + | 0.456669i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 0.585786i | − | 0.0198145i | ||||||
\(875\) | 26.0000 | − | 18.0000i | 0.878960 | − | 0.608511i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.0416 | − | 30.0416i | −1.01443 | − | 1.01443i | −0.999894 | − | 0.0145395i | \(-0.995372\pi\) |
−0.0145395 | − | 0.999894i | \(-0.504628\pi\) | |||||||
\(878\) | −2.92893 | − | 2.92893i | −0.0988467 | − | 0.0988467i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.82843 | + | 9.65685i | 0.162766 | + | 0.325532i | ||||
\(881\) | − | 14.9706i | − | 0.504371i | −0.967679 | − | 0.252186i | \(-0.918851\pi\) | ||
0.967679 | − | 0.252186i | \(-0.0811493\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.9706 | + | 20.9706i | −0.705716 | + | 0.705716i | −0.965631 | − | 0.259916i | \(-0.916305\pi\) |
0.259916 | + | 0.965631i | \(0.416305\pi\) | |||||||
\(884\) | 7.31371 | 0.245987 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.82843 | 0.229405 | ||||||||
\(887\) | 36.2843 | − | 36.2843i | 1.21831 | − | 1.21831i | 0.250082 | − | 0.968225i | \(-0.419542\pi\) |
0.968225 | − | 0.250082i | \(-0.0804576\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.34315i | − | 0.212742i | ||||||
\(890\) | 9.89949 | − | 29.6985i | 0.331832 | − | 0.995495i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.24264 | + | 3.24264i | 0.108572 | + | 0.108572i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.6274 | + | 23.3137i | −1.55858 | + | 0.779291i | ||||
\(896\) | 2.82843i | 0.0944911i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.48528 | + | 3.48528i | −0.116305 | + | 0.116305i | ||||
\(899\) | −0.686292 | −0.0228891 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 44.7696 | 1.49149 | ||||||||
\(902\) | −18.4853 | + | 18.4853i | −0.615493 | + | 0.615493i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 17.3137i | − | 0.575845i | ||||||
\(905\) | 26.8284 | − | 13.4142i | 0.891807 | − | 0.445904i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −33.3553 | − | 33.3553i | −1.10755 | − | 1.10755i | −0.993472 | − | 0.114074i | \(-0.963610\pi\) |
−0.114074 | − | 0.993472i | \(-0.536390\pi\) | |||||||
\(908\) | −4.89949 | − | 4.89949i | −0.162595 | − | 0.162595i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | + | 12.0000i | −0.132599 | + | 0.397796i | ||||
\(911\) | − | 48.2843i | − | 1.59973i | −0.600180 | − | 0.799865i | \(-0.704905\pi\) | ||
0.600180 | − | 0.799865i | \(-0.295095\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.65685 | + | 3.65685i | −0.121024 | + | 0.121024i | ||||
\(914\) | −1.79899 | −0.0595053 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.4142 | 0.443218 | ||||||||
\(917\) | −11.3137 | + | 11.3137i | −0.373612 | + | 0.373612i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.9706i | 0.955651i | 0.878455 | + | 0.477825i | \(0.158575\pi\) | ||||
−0.878455 | + | 0.477825i | \(0.841425\pi\) | |||||||
\(920\) | 1.00000 | + | 2.00000i | 0.0329690 | + | 0.0659380i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.55635 | − | 9.55635i | −0.314722 | − | 0.314722i | ||||
\(923\) | 10.4853 | + | 10.4853i | 0.345127 | + | 0.345127i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.89949 | + | 1.41421i | −0.325493 | + | 0.0464991i | ||||
\(926\) | 36.5858i | 1.20228i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.585786 | − | 0.585786i | 0.0192294 | − | 0.0192294i | ||||
\(929\) | 9.69848 | 0.318197 | 0.159098 | − | 0.987263i | \(-0.449141\pi\) | ||||
0.159098 | + | 0.987263i | \(0.449141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.585786 | −0.0191984 | ||||||||
\(932\) | 13.1716 | − | 13.1716i | 0.431449 | − | 0.431449i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.2132i | 0.366907i | ||||||||
\(935\) | −37.4558 | − | 12.4853i | −1.22494 | − | 0.408312i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.5269 | + | 36.5269i | 1.19328 | + | 1.19328i | 0.976140 | + | 0.217142i | \(0.0696735\pi\) |
0.217142 | + | 0.976140i | \(0.430326\pi\) | |||||||
\(938\) | 19.3137 | + | 19.3137i | 0.630615 | + | 0.630615i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 45.9411i | − | 1.49764i | −0.662775 | − | 0.748819i | \(-0.730621\pi\) | ||
0.662775 | − | 0.748819i | \(-0.269379\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.82843 | + | 3.82843i | −0.124671 | + | 0.124671i | ||||
\(944\) | 2.82843 | 0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.3137 | −0.497892 | ||||||||
\(947\) | −25.4558 | + | 25.4558i | −0.827204 | + | 0.827204i | −0.987129 | − | 0.159925i | \(-0.948875\pi\) |
0.159925 | + | 0.987129i | \(0.448875\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 27.7990i | − | 0.902393i | ||||||
\(950\) | 2.89949 | − | 0.414214i | 0.0940720 | − | 0.0134389i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.31371 | − | 7.31371i | −0.237039 | − | 0.237039i | ||||
\(953\) | 29.0711 | + | 29.0711i | 0.941704 | + | 0.941704i | 0.998392 | − | 0.0566877i | \(-0.0180539\pi\) |
−0.0566877 | + | 0.998392i | \(0.518054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.17157 | + | 18.3431i | 0.296785 | + | 0.593570i | ||||
\(956\) | 9.55635i | 0.309074i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.1716 | + | 13.1716i | −0.425554 | + | 0.425554i | ||||
\(959\) | 4.28427 | 0.138346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3137 | −0.977862 | ||||||||
\(962\) | 2.82843 | − | 2.82843i | 0.0911922 | − | 0.0911922i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 13.7990i | − | 0.444436i | ||||||
\(965\) | −5.00000 | + | 15.0000i | −0.160956 | + | 0.482867i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.41421 | − | 2.41421i | −0.0776359 | − | 0.0776359i | 0.667223 | − | 0.744858i | \(-0.267483\pi\) |
−0.744858 | + | 0.667223i | \(0.767483\pi\) | |||||||
\(968\) | 8.70711 | + | 8.70711i | 0.279857 | + | 0.279857i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −25.6569 | + | 12.8284i | −0.823792 | + | 0.411896i | ||||
\(971\) | 50.6274i | 1.62471i | 0.583162 | + | 0.812356i | \(0.301815\pi\) | ||||
−0.583162 | + | 0.812356i | \(0.698185\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6569 | + | 13.6569i | −0.437819 | + | 0.437819i | ||||
\(974\) | 39.8995 | 1.27846 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.41421 | −0.173305 | ||||||||
\(977\) | 35.5563 | − | 35.5563i | 1.13755 | − | 1.13755i | 0.148660 | − | 0.988888i | \(-0.452504\pi\) |
0.988888 | − | 0.148660i | \(-0.0474960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 67.5980i | − | 2.16044i | ||||||
\(980\) | 2.00000 | − | 1.00000i | 0.0638877 | − | 0.0319438i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.48528 | − | 6.48528i | −0.206954 | − | 0.206954i | ||||
\(983\) | 29.9411 | + | 29.9411i | 0.954974 | + | 0.954974i | 0.999029 | − | 0.0440555i | \(-0.0140278\pi\) |
−0.0440555 | + | 0.999029i | \(0.514028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.07107 | − | 21.2132i | 0.225303 | − | 0.675909i | ||||
\(986\) | 3.02944i | 0.0964769i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.828427 | + | 0.828427i | −0.0263558 | + | 0.0263558i | ||||
\(989\) | −3.17157 | −0.100850 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.9411 | 1.33230 | 0.666152 | − | 0.745816i | \(-0.267940\pi\) | ||||
0.666152 | + | 0.745816i | \(0.267940\pi\) | |||||||
\(992\) | −0.585786 | + | 0.585786i | −0.0185987 | + | 0.0185987i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 20.9706i | − | 0.665146i | ||||||
\(995\) | −6.34315 | − | 12.6863i | −0.201091 | − | 0.402182i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.07107 | + | 5.07107i | 0.160602 | + | 0.160602i | 0.782834 | − | 0.622231i | \(-0.213774\pi\) |
−0.622231 | + | 0.782834i | \(0.713774\pi\) | |||||||
\(998\) | 9.17157 | + | 9.17157i | 0.290321 | + | 0.290321i | ||||
\(999\) | 0 | 0 |
(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 | 2070.2.j.f.737.2 | yes | 4 | |
3.2 | odd | 2 | 2070.2.j.a.737.1 | yes | 4 | ||
5.3 | odd | 4 | 2070.2.j.a.323.1 | ✓ | 4 | ||
15.8 | even | 4 | inner | 2070.2.j.f.323.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.a.323.1 | ✓ | 4 | 5.3 | odd | 4 | ||
2070.2.j.a.737.1 | yes | 4 | 3.2 | odd | 2 | ||
2070.2.j.f.323.2 | yes | 4 | 15.8 | even | 4 | inner | |
2070.2.j.f.737.2 | yes | 4 | 1.1 | even | 1 | trivial |