Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(229,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("380.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.c (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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.3 | ||
Root | \(0.874032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.229 |
Dual form | 380.2.c.a.229.2 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.874032i | 0.504623i | 0.967646 | + | 0.252311i | \(0.0811907\pi\) | ||||
−0.967646 | + | 0.252311i | \(0.918809\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 2.82843i | − 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | 0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.763932 | −0.230334 | −0.115167 | − | 0.993346i | \(-0.536740\pi\) | ||||
−0.115167 | + | 0.993346i | \(0.536740\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.45052i | − 1.51170i | −0.654743 | − | 0.755852i | \(-0.727223\pi\) | ||||
0.654743 | − | 0.755852i | \(-0.272777\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.95440i | 0.504623i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.40492i | 1.79596i | 0.440040 | + | 0.897978i | \(0.354964\pi\) | ||||
−0.440040 | + | 0.897978i | \(0.645036\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.47214 | 0.539464 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.08036i | − 0.225271i | −0.993636 | − | 0.112636i | \(-0.964071\pi\) | ||||
0.993636 | − | 0.112636i | \(-0.0359293\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57649i | 0.880746i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 0.667701i | − 0.116232i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 6.32456i | − 1.06904i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.62210i | 0.431070i | 0.976496 | + | 0.215535i | \(0.0691495\pi\) | ||||
−0.976496 | + | 0.215535i | \(0.930850\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.76393 | 0.762840 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528i | 1.29399i | 0.762493 | + | 0.646997i | \(0.223975\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.00000 | 0.745356 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 8.48528i | − 1.23771i | −0.785507 | − | 0.618853i | \(-0.787598\pi\) | ||||
0.785507 | − | 0.618853i | \(-0.212402\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.47214 | −0.906280 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.62210i | 0.360173i | 0.983651 | + | 0.180086i | \(0.0576377\pi\) | ||||
−0.983651 | + | 0.180086i | \(0.942362\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.70820 | −0.230334 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.874032i | 0.115768i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.52786 | 0.198911 | 0.0994555 | − | 0.995042i | \(-0.468290\pi\) | ||||
0.0994555 | + | 0.995042i | \(0.468290\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.7082 | −1.49908 | −0.749541 | − | 0.661958i | \(-0.769726\pi\) | ||||
−0.749541 | + | 0.661958i | \(0.769726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 6.32456i | − 0.796819i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 12.1877i | − 1.51170i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.1074i | − 1.35698i | −0.734609 | − | 0.678491i | \(-0.762634\pi\) | ||||
0.734609 | − | 0.678491i | \(-0.237366\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.944272 | 0.113677 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4721 | −1.24281 | −0.621407 | − | 0.783488i | \(-0.713439\pi\) | ||||
−0.621407 | + | 0.783488i | \(0.713439\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.24419i | 0.613786i | 0.951744 | + | 0.306893i | \(0.0992894\pi\) | ||||
−0.951744 | + | 0.306893i | \(0.900711\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.37016i | 0.504623i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.16073i | 0.246238i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4164 | −1.73448 | −0.867241 | − | 0.497889i | \(-0.834109\pi\) | ||||
−0.867241 | + | 0.497889i | \(0.834109\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70820 | 0.300912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.7295i | 1.50701i | 0.657445 | + | 0.753503i | \(0.271637\pi\) | ||||
−0.657445 | + | 0.753503i | \(0.728363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.5579i | 1.79596i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.90879i | 0.419066i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.94427 | −0.312092 | −0.156046 | − | 0.987750i | \(-0.549875\pi\) | ||||
−0.156046 | + | 0.987750i | \(0.549875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.4164 | −1.61608 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 3.49613i | − 0.362532i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.23607 | 0.229416 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 13.9358i | − 1.41497i | −0.706730 | − | 0.707483i | \(-0.749830\pi\) | ||||
0.706730 | − | 0.707483i | \(-0.250170\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.70820 | −0.171681 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.23607 | 0.521008 | 0.260504 | − | 0.965473i | \(-0.416111\pi\) | ||||
0.260504 | + | 0.965473i | \(0.416111\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.86319i | − 0.577717i | −0.957372 | − | 0.288858i | \(-0.906724\pi\) | ||||
0.957372 | − | 0.288858i | \(-0.0932757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.52786 | 0.539464 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2681i | 1.28268i | 0.767258 | + | 0.641338i | \(0.221620\pi\) | ||||
−0.767258 | + | 0.641338i | \(0.778380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.29180 | −0.217528 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 16.3516i | − 1.53823i | −0.639113 | − | 0.769113i | \(-0.720698\pi\) | ||||
0.639113 | − | 0.769113i | \(-0.279302\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 2.41577i | − 0.225271i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 12.1877i | − 1.12676i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 20.9443 | 1.91996 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.4164 | −0.946946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.24419i | − 0.472853i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.5927i | 1.73857i | 0.494314 | + | 0.869284i | \(0.335419\pi\) | ||||
−0.494314 | + | 0.869284i | \(0.664581\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.41641 | −0.652978 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.82843i | − 0.245256i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.2333i | 0.880746i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.40492i | 0.632645i | 0.948652 | + | 0.316322i | \(0.102448\pi\) | ||||
−0.948652 | + | 0.316322i | \(0.897552\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.29180 | −0.194388 | −0.0971938 | − | 0.995265i | \(-0.530987\pi\) | ||||
−0.0971938 | + | 0.995265i | \(0.530987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.41641 | 0.624574 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.16383i | 0.348197i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 0.874032i | − 0.0720889i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.6525 | 1.03653 | 0.518266 | − | 0.855220i | \(-0.326578\pi\) | ||||
0.518266 | + | 0.855220i | \(0.326578\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 16.5579i | 1.33863i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.94427 | −0.718421 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.412662i | 0.0329340i | 0.999864 | + | 0.0164670i | \(0.00524185\pi\) | ||||
−0.999864 | + | 0.0164670i | \(0.994758\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.29180 | −0.181751 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.05573 | −0.240825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.48528i | − 0.664619i | −0.943170 | − | 0.332309i | \(-0.892172\pi\) | ||||
0.943170 | − | 0.332309i | \(-0.107828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.49302i | − 0.116232i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 17.4319i | − 1.34892i | −0.738310 | − | 0.674462i | \(-0.764376\pi\) | ||||
0.738310 | − | 0.674462i | \(-0.235624\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.7082 | −1.28525 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.23607 | 0.170996 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.94665i | 0.680201i | 0.940389 | + | 0.340101i | \(0.110461\pi\) | ||||
−0.940389 | + | 0.340101i | \(0.889539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 14.1421i | − 1.06904i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.33540i | 0.100375i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.4721 | 1.67965 | 0.839823 | − | 0.542860i | \(-0.182659\pi\) | ||||
0.839823 | + | 0.542860i | \(0.182659\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.00000 | 0.445976 | 0.222988 | − | 0.974821i | \(-0.428419\pi\) | ||||
0.222988 | + | 0.974821i | \(0.428419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 10.2333i | − 0.756471i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.86319i | 0.431070i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 5.65685i | − 0.413670i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.9443 | 0.941557 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.05573 | −0.221105 | −0.110552 | − | 0.993870i | \(-0.535262\pi\) | ||||
−0.110552 | + | 0.993870i | \(0.535262\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.9358i | 1.00312i | 0.865123 | + | 0.501561i | \(0.167241\pi\) | ||||
−0.865123 | + | 0.501561i | \(0.832759\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.6525 | 0.762840 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.6491i | − 0.901212i | −0.892723 | − | 0.450606i | \(-0.851208\pi\) | ||||
0.892723 | − | 0.450606i | \(-0.148792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.70820 | 0.684764 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 12.6491i | − 0.887794i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.4164 | −0.937043 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.41577i | − 0.167907i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.763932 | −0.0528423 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.4164 | 1.06131 | 0.530655 | − | 0.847588i | \(-0.321946\pi\) | ||||
0.530655 | + | 0.847588i | \(0.321946\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 9.15298i | − 0.627152i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.9737i | 1.29399i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137i | 0.768025i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.58359 | −0.309730 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 40.3607 | 2.71495 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7673i | 1.25675i | 0.777909 | + | 0.628377i | \(0.216280\pi\) | ||||
−0.777909 | + | 0.628377i | \(0.783720\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.1803 | 0.745356 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 5.86319i | − 0.389153i | −0.980887 | − | 0.194577i | \(-0.937667\pi\) | ||||
0.980887 | − | 0.194577i | \(-0.0623333\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.70820 | −0.509372 | −0.254686 | − | 0.967024i | \(-0.581972\pi\) | ||||
−0.254686 | + | 0.967024i | \(0.581972\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.88854 | −0.124257 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 12.6491i | − 0.828671i | −0.910124 | − | 0.414335i | \(-0.864014\pi\) | ||||
0.910124 | − | 0.414335i | \(-0.135986\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 18.9737i | − 1.23771i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 13.4744i | − 0.875259i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.8885 | 1.93333 | 0.966665 | − | 0.256046i | \(-0.0824199\pi\) | ||||
0.966665 | + | 0.256046i | \(0.0824199\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.8328 | −1.85728 | −0.928642 | − | 0.370976i | \(-0.879023\pi\) | ||||
−0.928642 | + | 0.370976i | \(0.879023\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0965i | 1.03259i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.23607 | −0.142857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 5.45052i | − 0.346808i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.88854 | −0.371682 | −0.185841 | − | 0.982580i | \(-0.559501\pi\) | ||||
−0.185841 | + | 0.982580i | \(0.559501\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.825324i | 0.0518877i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.4721 | −0.906280 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.4319i | 1.08737i | 0.839288 | + | 0.543687i | \(0.182972\pi\) | ||||
−0.839288 | + | 0.543687i | \(0.817028\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.41641 | 0.460833 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.0000 | 0.618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.8902i | 0.979832i | 0.871770 | + | 0.489916i | \(0.162973\pi\) | ||||
−0.871770 | + | 0.489916i | \(0.837027\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.86319i | 0.360173i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 2.57339i | − 0.157489i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.9443 | −0.911168 | −0.455584 | − | 0.890193i | \(-0.650570\pi\) | ||||
−0.455584 | + | 0.890193i | \(0.650570\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.1246 | 1.28323 | 0.641614 | − | 0.767027i | \(-0.278265\pi\) | ||||
0.641614 | + | 0.767027i | \(0.278265\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 13.4744i | − 0.815510i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.81966 | −0.230334 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 22.2148i | 1.33476i | 0.744719 | + | 0.667378i | \(0.232583\pi\) | ||||
−0.744719 | + | 0.667378i | \(0.767417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.94427 | −0.535480 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.4164 | −1.51622 | −0.758108 | − | 0.652129i | \(-0.773876\pi\) | ||||
−0.758108 | + | 0.652129i | \(0.773876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.41577i | − 0.143602i | −0.997419 | − | 0.0718012i | \(-0.977125\pi\) | ||||
0.997419 | − | 0.0718012i | \(-0.0228747\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.95440i | 0.115768i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.9706i | 1.00174i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.8328 | −2.22546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1803 | 0.714024 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.62210i | 0.153184i | 0.997062 | + | 0.0765922i | \(0.0244040\pi\) | ||||
−0.997062 | + | 0.0765922i | \(0.975596\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.41641 | 0.198911 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 3.49613i | − 0.202866i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.88854 | −0.340543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.0000 | 1.38334 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.57649i | 0.262913i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −26.1803 | −1.49908 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.45052i | 0.311078i | 0.987830 | + | 0.155539i | \(0.0497114\pi\) | ||||
−0.987830 | + | 0.155539i | \(0.950289\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.12461 | 0.291529 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.70820 | −0.550502 | −0.275251 | − | 0.961372i | \(-0.588761\pi\) | ||||
−0.275251 | + | 0.961372i | \(0.588761\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 10.4884i | − 0.592839i | −0.955058 | − | 0.296419i | \(-0.904207\pi\) | ||||
0.955058 | − | 0.296419i | \(-0.0957926\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 14.1421i | − 0.796819i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.94665i | 0.502494i | 0.967923 | + | 0.251247i | \(0.0808406\pi\) | ||||
−0.967923 | + | 0.251247i | \(0.919159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.41641 | −0.191282 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.5967 | −0.647267 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.40492i | 0.412021i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 27.2526i | − 1.51170i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.74806i | − 0.0966682i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.0000 | −1.32316 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.41641 | 0.407643 | 0.203821 | − | 0.979008i | \(-0.434664\pi\) | ||||
0.203821 | + | 0.979008i | \(0.434664\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.86319i | 0.321301i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 24.8369i | − 1.35698i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 16.7642i | − 0.913206i | −0.889671 | − | 0.456603i | \(-0.849066\pi\) | ||||
0.889671 | − | 0.456603i | \(-0.150934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.2918 | 0.776224 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.05573 | 0.165477 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 16.9706i | − 0.916324i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.11146 | 0.113677 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.40802i | 0.505049i | 0.967590 | + | 0.252525i | \(0.0812608\pi\) | ||||
−0.967590 | + | 0.252525i | \(0.918739\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4164 | −1.36051 | −0.680255 | − | 0.732976i | \(-0.738131\pi\) | ||||
−0.680255 | + | 0.732976i | \(0.738131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.9443 | 1.33143 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.56564i | 0.509128i | 0.967056 | + | 0.254564i | \(0.0819319\pi\) | ||||
−0.967056 | + | 0.254564i | \(0.918068\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.4164 | −1.24281 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.3060i | 0.968854i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.1246 | −1.53714 | −0.768569 | − | 0.639767i | \(-0.779031\pi\) | ||||
−0.768569 | + | 0.639767i | \(0.779031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 9.10427i | − 0.477850i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7264i | 0.613786i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8.48528i | − 0.442928i | −0.975169 | − | 0.221464i | \(-0.928916\pi\) | ||||
0.975169 | − | 0.221464i | \(-0.0710835\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.4164 | −0.698430 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.41641 | 0.385041 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1105i | 0.678835i | 0.940636 | + | 0.339417i | \(0.110230\pi\) | ||||
−0.940636 | + | 0.339417i | \(0.889770\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.77198i | 0.504623i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 24.3755i | − 1.25540i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1246 | −0.877320 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 36.4056i | − 1.86024i | −0.367257 | − | 0.930120i | \(-0.619703\pi\) | ||||
0.367257 | − | 0.930120i | \(-0.380297\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.83153i | 0.246238i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.9737i | 0.964486i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 14.9443 | 0.757705 | 0.378852 | − | 0.925457i | \(-0.376319\pi\) | ||||
0.378852 | + | 0.925457i | \(0.376319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −34.4721 | −1.73448 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.7264i | − 0.588530i | −0.955724 | − | 0.294265i | \(-0.904925\pi\) | ||||
0.955724 | − | 0.294265i | \(-0.0950748\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.47214 | 0.123762 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.47214 | −0.223328 | −0.111664 | − | 0.993746i | \(-0.535618\pi\) | ||||
−0.111664 | + | 0.993746i | \(0.535618\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.8021i | 1.08604i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.05573 | 0.300912 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 2.00310i | − 0.0992901i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4164 | −0.861186 | −0.430593 | − | 0.902546i | \(-0.641696\pi\) | ||||
−0.430593 | + | 0.902546i | \(0.641696\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.47214 | −0.319247 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4.32145i | − 0.212645i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.7000i | 1.50701i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 2.00310i | − 0.0980924i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9443 | 1.02319 | 0.511597 | − | 0.859225i | \(-0.329054\pi\) | ||||
0.511597 | + | 0.859225i | \(0.329054\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0000 | 0.682318 | 0.341159 | − | 0.940006i | \(-0.389181\pi\) | ||||
0.341159 | + | 0.940006i | \(0.389181\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 18.9737i | − 0.922531i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 37.0246i | 1.79596i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.1158i | 1.60259i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.63932 | −0.175708 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.52786 | 0.0735946 | 0.0367973 | − | 0.999323i | \(-0.488284\pi\) | ||||
0.0367973 | + | 0.999323i | \(0.488284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 28.4906i | − 1.36917i | −0.728933 | − | 0.684585i | \(-0.759983\pi\) | ||||
0.728933 | − | 0.684585i | \(-0.240017\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.74032i | 0.419066i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1.08036i | − 0.0516808i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.8328 | 0.898841 | 0.449421 | − | 0.893320i | \(-0.351630\pi\) | ||||
0.449421 | + | 0.893320i | \(0.351630\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.23607 | −0.106479 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 13.7295i | − 0.652307i | −0.945317 | − | 0.326153i | \(-0.894247\pi\) | ||||
0.945317 | − | 0.326153i | \(-0.105753\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.58359 | −0.312092 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.0587i | 0.523057i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.4721 | 0.777368 | 0.388684 | − | 0.921371i | \(-0.372930\pi\) | ||||
0.388684 | + | 0.921371i | \(0.372930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.58359 | 0.215833 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 6.99226i | − 0.328525i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −34.4721 | −1.61608 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 37.9473i | − 1.77510i | −0.460710 | − | 0.887551i | \(-0.652405\pi\) | ||||
0.460710 | − | 0.887551i | \(-0.347595\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.8885 | −1.58178 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.8885 | 1.11260 | 0.556300 | − | 0.830981i | \(-0.312220\pi\) | ||||
0.556300 | + | 0.830981i | \(0.312220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5548i | 0.676419i | 0.941071 | + | 0.338209i | \(0.109821\pi\) | ||||
−0.941071 | + | 0.338209i | \(0.890179\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 7.81758i | − 0.362532i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 30.7000i | − 1.42063i | −0.703885 | − | 0.710314i | \(-0.748553\pi\) | ||||
0.703885 | − | 0.710314i | \(-0.251447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −31.4164 | −1.45067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.360680 | −0.0166192 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6.48218i | − 0.298051i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | 0.229416 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.86319i | 0.268457i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.2361 | −0.513389 | −0.256695 | − | 0.966493i | \(-0.582633\pi\) | ||||
−0.256695 | + | 0.966493i | \(0.582633\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2918 | 0.651650 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 2.67080i | − 0.121526i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 31.1614i | − 1.41497i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.6947i | 0.484624i | 0.970198 | + | 0.242312i | \(0.0779057\pi\) | ||||
−0.970198 | + | 0.242312i | \(0.922094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.41641 | 0.335382 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.88854 | 0.265746 | 0.132873 | − | 0.991133i | \(-0.457580\pi\) | ||||
0.132873 | + | 0.991133i | \(0.457580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.1158i | 1.49146i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.81966 | −0.171681 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.6197i | 1.32862i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.1246 | 0.766603 | 0.383301 | − | 0.923623i | \(-0.374787\pi\) | ||||
0.383301 | + | 0.923623i | \(0.374787\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 15.2361 | 0.680697 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 20.2117i | 0.901193i | 0.892728 | + | 0.450597i | \(0.148789\pi\) | ||||
−0.892728 | + | 0.450597i | \(0.851211\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.7082 | 0.521008 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 14.6035i | − 0.648564i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5836 | 0.469109 | 0.234555 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234555 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8328 | 0.656165 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.57649i | 0.202057i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 13.1105i | − 0.577717i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.48218i | 0.285086i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.81966 | −0.343245 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.111456 | 0.00488298 | 0.00244149 | − | 0.999997i | \(-0.499223\pi\) | ||||
0.00244149 | + | 0.999997i | \(0.499223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 24.8369i | − 1.08604i | −0.839720 | − | 0.543020i | \(-0.817281\pi\) | ||||
0.839720 | − | 0.543020i | \(-0.182719\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12.3607 | 0.539464 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 29.6197i | − 1.29025i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.8328 | 0.949253 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.41641 | 0.148259 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.7031i | 1.41653i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.6684i | 1.28268i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.6414i | 0.847588i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.763932 | 0.0329049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7082 | 0.503375 | 0.251688 | − | 0.967809i | \(-0.419014\pi\) | ||||
0.251688 | + | 0.967809i | \(0.419014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.24419i | 0.225050i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.47214 | −0.191565 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.27895i | 0.353982i | 0.984212 | + | 0.176991i | \(0.0566364\pi\) | ||||
−0.984212 | + | 0.176991i | \(0.943364\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26.1803 | −1.11735 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.47214 | 0.190519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.6042i | 1.85424i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.12461 | −0.217528 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 20.0540i | − 0.849716i | −0.905260 | − | 0.424858i | \(-0.860324\pi\) | ||||
0.905260 | − | 0.424858i | \(-0.139676\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.2492 | 1.95613 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.94427 | 0.208747 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.0810i | 1.26776i | 0.773429 | + | 0.633882i | \(0.218540\pi\) | ||||
−0.773429 | + | 0.633882i | \(0.781460\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 36.5632i | − 1.53823i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 7.65996i | − 0.321688i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 38.9443 | 1.63263 | 0.816314 | − | 0.577608i | \(-0.196014\pi\) | ||||
0.816314 | + | 0.577608i | \(0.196014\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.1246 | 1.05143 | 0.525716 | − | 0.850660i | \(-0.323797\pi\) | ||||
0.525716 | + | 0.850660i | \(0.323797\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 2.67080i | − 0.111574i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 5.40182i | − 0.225271i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.65685i | 0.235498i | 0.993043 | + | 0.117749i | \(0.0375678\pi\) | ||||
−0.993043 | + | 0.117749i | \(0.962432\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.1803 | −0.506198 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.8328 | 1.61106 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.00310i | − 0.0829601i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − 27.2526i | − 1.12676i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 5.40182i | − 0.222957i | −0.993767 | − | 0.111478i | \(-0.964441\pi\) | ||||
0.993767 | − | 0.111478i | \(-0.0355586\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0557 | 0.454772 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 2.16073i | − 0.0887304i | −0.999015 | − | 0.0443652i | \(-0.985873\pi\) | ||||
0.999015 | − | 0.0443652i | \(-0.0141265\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 46.8328 | 1.91996 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.9845i | 0.572348i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0000 | 1.47092 | 0.735460 | − | 0.677568i | \(-0.236966\pi\) | ||||
0.735460 | + | 0.677568i | \(0.236966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.8328 | 0.686625 | 0.343312 | − | 0.939221i | \(-0.388451\pi\) | ||||
0.343312 | + | 0.939221i | \(0.388451\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 24.8369i | − 1.01143i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.2918 | −0.946946 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 22.4211i | − 0.910044i | −0.890480 | − | 0.455022i | \(-0.849631\pi\) | ||||
0.890480 | − | 0.455022i | \(-0.150369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.0557 | 0.448001 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.2492 | −1.87104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 39.1853i | − 1.58268i | −0.611376 | − | 0.791340i | \(-0.709384\pi\) | ||||
0.611376 | − | 0.791340i | \(-0.290616\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 11.7264i | − 0.472853i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 3.08347i | − 0.124136i | −0.998072 | − | 0.0620678i | \(-0.980230\pi\) | ||||
0.998072 | − | 0.0620678i | \(-0.0197695\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.1246 | −1.65294 | −0.826469 | − | 0.562982i | \(-0.809654\pi\) | ||||
−0.826469 | + | 0.562982i | \(0.809654\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.94427 | 0.198407 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.32766i | 0.333641i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 0.667701i | − 0.0266654i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.4164 | −0.774183 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.70820 | −0.0680025 | −0.0340013 | − | 0.999422i | \(-0.510825\pi\) | ||||
−0.0340013 | + | 0.999422i | \(0.510825\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.4744i | 0.535561i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 43.8105i | 1.73857i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.45052i | 0.215958i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.4164 | −0.926339 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.1115 | −0.478374 | −0.239187 | − | 0.970974i | \(-0.576881\pi\) | ||||
−0.239187 | + | 0.970974i | \(0.576881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 30.7000i | − 1.21069i | −0.795963 | − | 0.605346i | \(-0.793035\pi\) | ||||
0.795963 | − | 0.605346i | \(-0.206965\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.5836 | −0.652978 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.40802i | 0.369867i | 0.982751 | + | 0.184934i | \(0.0592071\pi\) | ||||
−0.982751 | + | 0.184934i | \(0.940793\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.16718 | −0.0458160 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.88854 | −0.387563 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 22.2148i | − 0.869331i | −0.900592 | − | 0.434665i | \(-0.856867\pi\) | ||||
0.900592 | − | 0.434665i | \(-0.143133\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.7264i | 0.457489i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.9443 | 1.75078 | 0.875390 | − | 0.483417i | \(-0.160605\pi\) | ||||
0.875390 | + | 0.483417i | \(0.160605\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0000 | −1.01128 | −0.505641 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.2765i | 1.37003i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 6.32456i | − 0.245256i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 4.83153i | − 0.187078i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.4033 | −0.634186 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.94427 | 0.345290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 4.62520i | − 0.178288i | −0.996019 | − | 0.0891442i | \(-0.971587\pi\) | ||||
0.996019 | − | 0.0891442i | \(-0.0284132\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 22.8825i | 0.880746i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 42.7302i | − 1.64225i | −0.570746 | − | 0.821127i | \(-0.693346\pi\) | ||||
0.570746 | − | 0.821127i | \(-0.306654\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.4164 | −1.51266 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.12461 | 0.196376 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.5927i | 0.749692i | 0.927087 | + | 0.374846i | \(0.122304\pi\) | ||||
−0.927087 | + | 0.374846i | \(0.877696\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.5579i | 0.632645i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 6.73722i | − 0.257041i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.2918 | 0.544474 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.1246 | 0.955785 | 0.477893 | − | 0.878418i | \(-0.341401\pi\) | ||||
0.477893 | + | 0.878418i | \(0.341401\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.83153i | 0.183535i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.12461 | −0.194388 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 44.4295i | − 1.68289i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 11.0557 | 0.418166 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.875388 | 0.0330630 | 0.0165315 | − | 0.999863i | \(-0.494738\pi\) | ||||
0.0165315 | + | 0.999863i | \(0.494738\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.62210i | 0.0988942i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.5836 | 0.624574 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 14.8098i | − 0.556981i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.4164 | −1.25498 | −0.627490 | − | 0.778625i | \(-0.715918\pi\) | ||||
−0.627490 | + | 0.778625i | \(0.715918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −34.4721 | −1.29281 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.32145i | 0.161840i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.31061i | 0.348197i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.1235i | 0.975602i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5967 | −1.02919 | −0.514593 | − | 0.857435i | \(-0.672057\pi\) | ||||
−0.514593 | + | 0.857435i | \(0.672057\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.5836 | −0.617605 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 25.2008i | − 0.937228i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.3607 | 0.830455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.48528i | − 0.314702i | −0.987543 | − | 0.157351i | \(-0.949705\pi\) | ||||
0.987543 | − | 0.157351i | \(-0.0502953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5.94427 | −0.220158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −62.8328 | −2.32396 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 33.9411i | − 1.25364i | −0.779162 | − | 0.626822i | \(-0.784355\pi\) | ||||
0.779162 | − | 0.626822i | \(-0.215645\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 1.95440i | − 0.0720889i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.48528i | 0.312559i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.8328 | 0.692776 | 0.346388 | − | 0.938091i | \(-0.387408\pi\) | ||||
0.346388 | + | 0.938091i | \(0.387408\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.76393 | 0.175007 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 2.62210i | − 0.0961954i | −0.998843 | − | 0.0480977i | \(-0.984684\pi\) | ||||
0.998843 | − | 0.0480977i | \(-0.0153159\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.2918 | 1.03653 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 30.7000i | 1.12326i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 37.5279 | 1.37124 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.5836 | 0.751106 | 0.375553 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375553 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 5.14678i | − 0.187559i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.8885 | −0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.7727i | 1.40922i | 0.709597 | + | 0.704608i | \(0.248877\pi\) | ||||
−0.709597 | + | 0.704608i | \(0.751123\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.721360 | −0.0261837 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.5410 | −1.54211 | −0.771055 | − | 0.636768i | \(-0.780271\pi\) | ||||
−0.771055 | + | 0.636768i | \(0.780271\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.65685i | 0.204792i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 37.0246i | 1.33863i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 8.32766i | − 0.300694i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.5410 | 1.38982 | 0.694912 | − | 0.719094i | \(-0.255443\pi\) | ||||
0.694912 | + | 0.719094i | \(0.255443\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.2361 | −0.548714 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.86319i | 0.210884i | 0.994425 | + | 0.105442i | \(0.0336258\pi\) | ||||
−0.994425 | + | 0.105442i | \(0.966374\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −20.0000 | −0.718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.48218i | 0.232547i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.4667i | 0.731420i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.922740i | 0.0329340i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 24.8369i | − 0.885338i | −0.896685 | − | 0.442669i | \(-0.854032\pi\) | ||||
0.896685 | − | 0.442669i | \(-0.145968\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.8885 | −0.494445 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −46.2492 | −1.64443 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 63.8158i | 2.26617i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.12461 | −0.181751 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 52.2958i | 1.85241i | 0.377018 | + | 0.926206i | \(0.376950\pi\) | ||||
−0.377018 | + | 0.926206i | \(0.623050\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 62.8328 | 2.22287 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.58359 | −0.232620 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.00621i | − 0.141376i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.83282 | −0.240825 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 13.0618i | − 0.459796i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.52786 | 0.264666 | 0.132333 | − | 0.991205i | \(-0.457753\pi\) | ||||
0.132333 | + | 0.991205i | \(0.457753\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.4636i | 0.647546i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 18.9737i | − 0.664619i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.48528i | 0.296862i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −34.4721 | −1.20455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.9443 | 1.35916 | 0.679582 | − | 0.733599i | \(-0.262161\pi\) | ||||
0.679582 | + | 0.733599i | \(0.262161\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 35.9442i | − 1.25294i | −0.779447 | − | 0.626469i | \(-0.784500\pi\) | ||||
0.779447 | − | 0.626469i | \(-0.215500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 3.33851i | − 0.116232i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.86629i | 0.273538i | 0.990603 | + | 0.136769i | \(0.0436717\pi\) | ||||
−0.990603 | + | 0.136769i | \(0.956328\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.4164 | −0.673548 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 7.40492i | − 0.256565i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 38.9790i | − 1.34892i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 18.3060i | − 0.632747i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.3050 | −1.70220 | −0.851098 | − | 0.525007i | \(-0.824063\pi\) | ||||
−0.851098 | + | 0.525007i | \(0.824063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 22.2148i | − 0.765117i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −37.3607 | −1.28525 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.4621i | 1.01233i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.11146 | 0.0724650 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.83282 | 0.0971077 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 27.4589i | − 0.940176i | −0.882619 | − | 0.470088i | \(-0.844222\pi\) | ||||
0.882619 | − | 0.470088i | \(-0.155778\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.00000 | 0.170996 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 31.3190i | − 1.06984i | −0.844903 | − | 0.534919i | \(-0.820342\pi\) | ||||
0.844903 | − | 0.534919i | \(-0.179658\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0000 | −1.36478 | −0.682391 | − | 0.730987i | \(-0.739060\pi\) | ||||
−0.682391 | + | 0.730987i | \(0.739060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −14.8328 | −0.505501 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.86629i | 0.267772i | 0.990997 | + | 0.133886i | \(0.0427455\pi\) | ||||
−0.990997 | + | 0.133886i | \(0.957254\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.0053i | 0.680201i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 33.0671i | − 1.12302i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.7771 | 0.399510 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.5410 | −2.05135 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 31.1614i | − 1.05465i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 31.6228i | − 1.06904i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 13.9358i | − 0.470579i | −0.971925 | − | 0.235289i | \(-0.924396\pi\) | ||||
0.971925 | − | 0.235289i | \(-0.0756038\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.29180 | −0.0773004 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.652476 | 0.0219825 | 0.0109912 | − | 0.999940i | \(-0.496501\pi\) | ||||
0.0109912 | + | 0.999940i | \(0.496501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 52.9148i | − 1.78072i | −0.455253 | − | 0.890362i | \(-0.650451\pi\) | ||||
0.455253 | − | 0.890362i | \(-0.349549\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.98605i | 0.100375i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 49.0547i | 1.64710i | 0.567247 | + | 0.823548i | \(0.308009\pi\) | ||||
−0.567247 | + | 0.823548i | \(0.691991\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.4164 | 1.85861 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.06888 | −0.0693102 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.48528i | − 0.283949i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.2492 | 1.67965 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 5.14678i | − 0.171846i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.8885 | −0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.4164 | −0.646854 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.9768i | 0.698063i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13.4164 | 0.445976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.5663i | 1.28057i | 0.768136 | + | 0.640287i | \(0.221185\pi\) | ||||
−0.768136 | + | 0.640287i | \(0.778815\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.7082 | 0.388337 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.4721 | −1.53969 | −0.769845 | − | 0.638231i | \(-0.779667\pi\) | ||||
−0.769845 | + | 0.638231i | \(0.779667\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 10.4884i | − 0.347115i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 22.8825i | − 0.756471i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.8328 | −0.885133 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.76393 | −0.156977 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 57.0786i | 1.87877i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.1105i | 0.431070i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 13.1105i | − 0.430605i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.52786 | −0.246981 | −0.123491 | − | 0.992346i | \(-0.539409\pi\) | ||||
−0.123491 | + | 0.992346i | \(0.539409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 8.48528i | − 0.277796i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − 12.6491i | − 0.413670i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.1915i | 1.41101i | 0.708707 | + | 0.705503i | \(0.249279\pi\) | ||||
−0.708707 | + | 0.705503i | \(0.750721\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.16718 | 0.299160 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.9443 | −1.26955 | −0.634773 | − | 0.772698i | \(-0.718907\pi\) | ||||
−0.634773 | + | 0.772698i | \(0.718907\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.48218i | 0.211089i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 28.9443 | 0.941557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.6706i | 1.54909i | 0.632521 | + | 0.774543i | \(0.282020\pi\) | ||||
−0.632521 | + | 0.774543i | \(0.717980\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.5836 | 0.927863 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.81966 | −0.253570 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 36.5632i | − 1.18440i | −0.805791 | − | 0.592199i | \(-0.798260\pi\) | ||||
0.805791 | − | 0.592199i | \(-0.201740\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.83282 | −0.221105 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 2.98605i | − 0.0965253i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.9443 | 0.676326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.6684i | 0.956050i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 31.1614i | 1.00312i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.41577i | 0.0776858i | 0.999245 | + | 0.0388429i | \(0.0123672\pi\) | ||||
−0.999245 | + | 0.0388429i | \(0.987633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.47214 | −0.207915 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −40.3607 | −1.29524 | −0.647618 | − | 0.761965i | \(-0.724235\pi\) | ||||
−0.647618 | + | 0.761965i | \(0.724235\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.48218i | 0.207809i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 23.8197 | 0.762840 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 24.9945i | − 0.799644i | −0.916593 | − | 0.399822i | \(-0.869072\pi\) | ||||
0.916593 | − | 0.399822i | \(-0.130928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.24922 | 0.0718855 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.47214 | −0.142784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 30.2387i | − 0.964464i | −0.876044 | − | 0.482232i | \(-0.839826\pi\) | ||||
0.876044 | − | 0.482232i | \(-0.160174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 28.2843i | − 0.901212i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 20.9768i | − 0.667698i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.16718 | 0.291500 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.8328 | 1.23357 | 0.616783 | − | 0.787134i | \(-0.288436\pi\) | ||||
0.616783 | + | 0.787134i | \(0.288436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.48218i | 0.205706i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35.7771 | 1.13421 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.7264i | 0.371378i | 0.982609 | + | 0.185689i | \(0.0594517\pi\) | ||||
−0.982609 | + | 0.185689i | \(0.940548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.0000 | −0.379663 |
(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 | 380.2.c.a.229.3 | yes | 4 | |
3.2 | odd | 2 | 3420.2.f.a.1369.1 | 4 | |||
4.3 | odd | 2 | 1520.2.d.f.609.2 | 4 | |||
5.2 | odd | 4 | 1900.2.a.j.1.3 | 4 | |||
5.3 | odd | 4 | 1900.2.a.j.1.2 | 4 | |||
5.4 | even | 2 | inner | 380.2.c.a.229.2 | ✓ | 4 | |
15.14 | odd | 2 | 3420.2.f.a.1369.2 | 4 | |||
20.3 | even | 4 | 7600.2.a.ce.1.3 | 4 | |||
20.7 | even | 4 | 7600.2.a.ce.1.2 | 4 | |||
20.19 | odd | 2 | 1520.2.d.f.609.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.c.a.229.2 | ✓ | 4 | 5.4 | even | 2 | inner | |
380.2.c.a.229.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1520.2.d.f.609.2 | 4 | 4.3 | odd | 2 | |||
1520.2.d.f.609.3 | 4 | 20.19 | odd | 2 | |||
1900.2.a.j.1.2 | 4 | 5.3 | odd | 4 | |||
1900.2.a.j.1.3 | 4 | 5.2 | odd | 4 | |||
3420.2.f.a.1369.1 | 4 | 3.2 | odd | 2 | |||
3420.2.f.a.1369.2 | 4 | 15.14 | odd | 2 | |||
7600.2.a.ce.1.2 | 4 | 20.7 | even | 4 | |||
7600.2.a.ce.1.3 | 4 | 20.3 | even | 4 |