Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,5,Mod(191,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.191");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.0783881868\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.246034965625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 7x^{6} - 21x^{5} + 49x^{4} - 84x^{3} + 112x^{2} - 192x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{28}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 20) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.7 | ||
Root | \(1.95003 + 0.444269i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.191 |
Dual form | 320.5.b.d.191.2 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 12.9912i | 1.44347i | 0.692171 | + | 0.721733i | \(0.256654\pi\) | ||||
−0.692171 | + | 0.721733i | \(0.743346\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 11.1803 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 78.0345i | 1.59254i | 0.604940 | + | 0.796271i | \(0.293197\pi\) | ||||
−0.604940 | + | 0.796271i | \(0.706803\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −87.7712 | −1.08360 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 95.6447i | 0.790452i | 0.918584 | + | 0.395226i | \(0.129334\pi\) | ||||
−0.918584 | + | 0.395226i | \(0.870666\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 159.654 | 0.944698 | 0.472349 | − | 0.881412i | \(-0.343406\pi\) | ||||
0.472349 | + | 0.881412i | \(0.343406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 145.246i | 0.645538i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 22.5103 | 0.0778903 | 0.0389451 | − | 0.999241i | \(-0.487600\pi\) | ||||
0.0389451 | + | 0.999241i | \(0.487600\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 324.934i | 0.900094i | 0.893005 | + | 0.450047i | \(0.148593\pi\) | ||||
−0.893005 | + | 0.450047i | \(0.851407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1013.76 | −2.29878 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 204.951i | 0.387431i | 0.981058 | + | 0.193715i | \(0.0620538\pi\) | ||||
−0.981058 | + | 0.193715i | \(0.937946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 125.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 87.9664i | − 0.120667i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −295.747 | −0.351662 | −0.175831 | − | 0.984420i | \(-0.556261\pi\) | ||||
−0.175831 | + | 0.984420i | \(0.556261\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 407.262i | − 0.423789i | −0.977293 | − | 0.211895i | \(-0.932037\pi\) | ||||
0.977293 | − | 0.211895i | \(-0.0679634\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1242.54 | −1.14099 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 872.453i | 0.712206i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2156.28 | 1.57508 | 0.787540 | − | 0.616263i | \(-0.211354\pi\) | ||||
0.787540 | + | 0.616263i | \(0.211354\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2074.10i | 1.36364i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1368.98 | 0.814383 | 0.407191 | − | 0.913343i | \(-0.366508\pi\) | ||||
0.407191 | + | 0.913343i | \(0.366508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1234.22i | − 0.667507i | −0.942660 | − | 0.333754i | \(-0.891685\pi\) | ||||
0.942660 | − | 0.333754i | \(-0.108315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −981.312 | −0.484599 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1983.43i | − 0.897887i | −0.893560 | − | 0.448943i | \(-0.851800\pi\) | ||||
0.893560 | − | 0.448943i | \(-0.148200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3688.39 | −1.53619 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 292.436i | 0.112432i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4595.72 | −1.63607 | −0.818035 | − | 0.575168i | \(-0.804937\pi\) | ||||
−0.818035 | + | 0.575168i | \(0.804937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1069.34i | 0.353501i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4221.28 | −1.29926 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1389.15i | 0.399068i | 0.979891 | + | 0.199534i | \(0.0639428\pi\) | ||||
−0.979891 | + | 0.199534i | \(0.936057\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2651.94 | −0.712694 | −0.356347 | − | 0.934354i | \(-0.615978\pi\) | ||||
−0.356347 | + | 0.934354i | \(0.615978\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 6849.19i | − 1.72567i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1784.99 | 0.422482 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8936.51i | − 1.99076i | −0.0960241 | − | 0.995379i | \(-0.530613\pi\) | ||||
0.0960241 | − | 0.995379i | \(-0.469387\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2662.56 | −0.559243 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3375.13i | 0.669535i | 0.942301 | + | 0.334767i | \(0.108658\pi\) | ||||
−0.942301 | + | 0.334767i | \(0.891342\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1467.63 | −0.275404 | −0.137702 | − | 0.990474i | \(-0.543972\pi\) | ||||
−0.137702 | + | 0.990474i | \(0.543972\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1623.90i | 0.288693i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7463.59 | −1.25883 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 6306.01i | − 1.01042i | −0.862997 | − | 0.505208i | \(-0.831416\pi\) | ||||
0.862997 | − | 0.505208i | \(-0.168584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5966.68 | −0.909416 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6104.16i | − 0.886073i | −0.896504 | − | 0.443037i | \(-0.853901\pi\) | ||||
0.896504 | − | 0.443037i | \(-0.146099\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 251.673 | 0.0348336 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 3842.11i | − 0.507612i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1708.55 | 0.215698 | 0.107849 | − | 0.994167i | \(-0.465604\pi\) | ||||
0.107849 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12458.5i | 1.50447i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5290.82 | 0.611726 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3632.87i | 0.402534i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1988.16 | −0.211304 | −0.105652 | − | 0.994403i | \(-0.533693\pi\) | ||||
−0.105652 | + | 0.994403i | \(0.533693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 8394.85i | − 0.856530i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6012.56 | 0.589408 | 0.294704 | − | 0.955589i | \(-0.404779\pi\) | ||||
0.294704 | + | 0.955589i | \(0.404779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10161.1i | 0.957780i | 0.877875 | + | 0.478890i | \(0.158961\pi\) | ||||
−0.877875 | + | 0.478890i | \(0.841039\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11334.2 | −1.02805 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12961.6i | 1.13212i | 0.824364 | + | 0.566060i | \(0.191533\pi\) | ||||
−0.824364 | + | 0.566060i | \(0.808467\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1002.18 | −0.0843517 | −0.0421758 | − | 0.999110i | \(-0.513429\pi\) | ||||
−0.0421758 | + | 0.999110i | \(0.513429\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28012.7i | 2.27358i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9956.56 | −0.779745 | −0.389872 | − | 0.920869i | \(-0.627481\pi\) | ||||
−0.389872 | + | 0.920869i | \(0.627481\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2291.42i | 0.173264i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14013.0 | −1.02367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1756.58i | 0.124044i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5493.10 | 0.375186 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17784.7i | 1.17553i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1397.54 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 21746.1i | − 1.34826i | −0.738613 | − | 0.674130i | \(-0.764519\pi\) | ||||
0.738613 | − | 0.674130i | \(-0.235481\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16034.0 | 0.963524 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 26640.6i | 1.55239i | 0.630491 | + | 0.776197i | \(0.282854\pi\) | ||||
−0.630491 | + | 0.776197i | \(0.717146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25356.1 | −1.43344 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 983.494i | − 0.0539640i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 34924.8 | 1.86077 | 0.930385 | − | 0.366584i | \(-0.119473\pi\) | ||||
0.930385 | + | 0.366584i | \(0.119473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 16591.6i | − 0.858736i | −0.903130 | − | 0.429368i | \(-0.858736\pi\) | ||||
0.903130 | − | 0.429368i | \(-0.141264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25767.2 | 1.29607 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15270.1i | 0.746738i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3306.56 | −0.157268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 47916.6i | − 2.21744i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10061.9 | 0.453217 | 0.226609 | − | 0.973986i | \(-0.427236\pi\) | ||||
0.226609 | + | 0.973986i | \(0.427236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2823.63i | 0.123838i | 0.998081 | + | 0.0619190i | \(0.0197221\pi\) | ||||
−0.998081 | + | 0.0619190i | \(0.980278\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1975.76 | −0.0844016 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4553.32i | − 0.189524i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 39136.1 | 1.58774 | 0.793869 | − | 0.608089i | \(-0.208064\pi\) | ||||
0.793869 | + | 0.608089i | \(0.208064\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 59703.9i | − 2.36161i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15993.2 | −0.616999 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9169.48i | 0.345119i | 0.984999 | + | 0.172560i | \(0.0552038\pi\) | ||||
−0.984999 | + | 0.172560i | \(0.944796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −13892.0 | −0.510267 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5446.76i | 0.195301i | 0.995221 | + | 0.0976507i | \(0.0311328\pi\) | ||||
−0.995221 | + | 0.0976507i | \(0.968867\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3071.61 | −0.107546 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 28519.9i | − 0.975338i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16187.9 | 0.540876 | 0.270438 | − | 0.962737i | \(-0.412832\pi\) | ||||
0.270438 | + | 0.962737i | \(0.412832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9754.32i | 0.318508i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18046.8 | −0.576041 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3484.14i | − 0.108740i | −0.998521 | − | 0.0543700i | \(-0.982685\pi\) | ||||
0.998521 | − | 0.0543700i | \(-0.0173151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12654.0 | 0.386251 | 0.193125 | − | 0.981174i | \(-0.438138\pi\) | ||||
0.193125 | + | 0.981174i | \(0.438138\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 34451.8i | − 1.02875i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24108.0 | 0.704397 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2152.99i | 0.0615685i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6864.42 | 0.192168 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12436.5i | 0.340903i | 0.985366 | + | 0.170452i | \(0.0545227\pi\) | ||||
−0.985366 | + | 0.170452i | \(0.945477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21537.6 | 0.578206 | 0.289103 | − | 0.957298i | \(-0.406643\pi\) | ||||
0.289103 | + | 0.957298i | \(0.406643\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23189.1i | 0.609838i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 30840.7 | 0.794679 | 0.397339 | − | 0.917672i | \(-0.369934\pi\) | ||||
0.397339 | + | 0.917672i | \(0.369934\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 57562.7i | 1.45357i | 0.686866 | + | 0.726784i | \(0.258986\pi\) | ||||
−0.686866 | + | 0.726784i | \(0.741014\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 116096. | 2.87359 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 23078.5i | − 0.560036i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15305.6 | 0.364203 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 17988.8i | − 0.419818i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −31078.2 | −0.711481 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 42485.0i | 0.954270i | 0.878830 | + | 0.477135i | \(0.158325\pi\) | ||||
−0.878830 | + | 0.477135i | \(0.841675\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −43846.9 | −0.966451 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 13799.0i | − 0.298518i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31780.5 | 0.674902 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 19066.2i | − 0.397536i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3593.86 | 0.0735828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14687.7i | 0.295354i | 0.989036 | + | 0.147677i | \(0.0471796\pi\) | ||||
−0.989036 | + | 0.147677i | \(0.952820\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10971.4 | −0.216719 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 54734.7i | 1.06221i | 0.847305 | + | 0.531106i | \(0.178223\pi\) | ||||
−0.847305 | + | 0.531106i | \(0.821777\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14583.3 | 0.278090 | 0.139045 | − | 0.990286i | \(-0.455597\pi\) | ||||
0.139045 | + | 0.990286i | \(0.455597\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − 96961.0i | − 1.81708i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −99275.8 | −1.82865 | −0.914327 | − | 0.404976i | \(-0.867280\pi\) | ||||
−0.914327 | + | 0.404976i | \(0.867280\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 22175.4i | − 0.401547i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 81922.6 | 1.45850 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 61775.6i | 1.08149i | 0.841188 | + | 0.540743i | \(0.181857\pi\) | ||||
−0.841188 | + | 0.540743i | \(0.818143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 97702.4 | 1.68218 | 0.841088 | − | 0.540899i | \(-0.181916\pi\) | ||||
0.841088 | + | 0.540899i | \(0.181916\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 84639.6i | − 1.43338i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −41237.5 | −0.687005 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 51877.0i | 0.850317i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 79300.3 | 1.27902 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 72156.2i | − 1.14532i | −0.819794 | − | 0.572659i | \(-0.805912\pi\) | ||||
0.819794 | − | 0.572659i | \(-0.194088\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19602.5 | −0.306245 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3269.53i | 0.0502811i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1740.16 | −0.0263465 | −0.0131732 | − | 0.999913i | \(-0.504193\pi\) | ||||
−0.0131732 | + | 0.999913i | \(0.504193\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 168265.i | 2.50838i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25958.1 | 0.381059 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 55537.8i | − 0.802929i | −0.915875 | − | 0.401464i | \(-0.868501\pi\) | ||||
0.915875 | − | 0.401464i | \(-0.131499\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −51381.7 | −0.731673 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22196.1i | 0.311353i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 60126.3 | 0.830922 | 0.415461 | − | 0.909611i | \(-0.363620\pi\) | ||||
0.415461 | + | 0.909611i | \(0.363620\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 65827.7i | 0.896334i | 0.893950 | + | 0.448167i | \(0.147923\pi\) | ||||
−0.893950 | + | 0.448167i | \(0.852077\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −161851. | −2.17165 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11955.6i | 0.158090i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −61361.9 | −0.799723 | −0.399861 | − | 0.916576i | \(-0.630942\pi\) | ||||
−0.399861 | + | 0.916576i | \(0.630942\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 35745.8i | 0.459216i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26231.4 | −0.332207 | −0.166104 | − | 0.986108i | \(-0.553119\pi\) | ||||
−0.166104 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 91765.5i | 1.14579i | 0.819627 | + | 0.572897i | \(0.194180\pi\) | ||||
−0.819627 | + | 0.572897i | \(0.805820\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −47195.4 | −0.581045 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 106828.i | 1.29694i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −83014.3 | −0.993933 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 25828.6i | − 0.305010i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −82014.2 | −0.955331 | −0.477665 | − | 0.878542i | \(-0.658517\pi\) | ||||
−0.477665 | + | 0.878542i | \(0.658517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15531.2i | 0.178469i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8413.52 | 0.0953816 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32721.2i | 0.366005i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 96311.9 | 1.06303 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 78110.3i | 0.850791i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −29649.5 | −0.318727 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 14373.1i | − 0.152501i | −0.997089 | − | 0.0762507i | \(-0.975705\pi\) | ||||
0.997089 | − | 0.0762507i | \(-0.0242949\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −132005. | −1.38252 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 178570.i | − 1.84623i | −0.384520 | − | 0.923117i | \(-0.625633\pi\) | ||||
0.384520 | − | 0.923117i | \(-0.374367\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 188132. | 1.92032 | 0.960162 | − | 0.279444i | \(-0.0901501\pi\) | ||||
0.960162 | + | 0.279444i | \(0.0901501\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 76576.3i | − 0.771744i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −104987. | −1.04477 | −0.522383 | − | 0.852711i | \(-0.674957\pi\) | ||||
−0.522383 | + | 0.852711i | \(0.674957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 28286.7i | − 0.277971i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −168387. | −1.63418 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7314.36i | 0.0701086i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 19956.7 | 0.188940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 13019.6i | − 0.121759i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 154776. | 1.42992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 107333.i | − 0.979660i | −0.871818 | − | 0.489830i | \(-0.837059\pi\) | ||||
0.871818 | − | 0.489830i | \(-0.162941\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −189260. | −1.70675 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 99913.2i | − 0.890294i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 48193.1 | 0.424351 | 0.212176 | − | 0.977232i | \(-0.431945\pi\) | ||||
0.212176 | + | 0.977232i | \(0.431945\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 129348.i | − 1.12554i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38952.4 | 0.334985 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 100461.i | − 0.853904i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29768.3 | −0.250101 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 158887.i | 1.31956i | 0.751460 | + | 0.659778i | \(0.229350\pi\) | ||||
−0.751460 | + | 0.659778i | \(0.770650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 155827. | 1.27935 | 0.639677 | − | 0.768643i | \(-0.279068\pi\) | ||||
0.639677 | + | 0.768643i | \(0.279068\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 14044.2i | − 0.113994i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −197430. | −1.58439 | −0.792197 | − | 0.610265i | \(-0.791063\pi\) | ||||
−0.792197 | + | 0.610265i | \(0.791063\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37735.0i | 0.299425i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22820.1 | −0.179053 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12434.1i | 0.0964774i | 0.998836 | + | 0.0482387i | \(0.0153608\pi\) | ||||
−0.998836 | + | 0.0482387i | \(0.984639\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 24738.9 | 0.189830 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 71361.9i | 0.541568i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16408.6 | −0.123164 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 112753.i | − 0.837136i | −0.908185 | − | 0.418568i | \(-0.862532\pi\) | ||||
0.908185 | − | 0.418568i | \(-0.137468\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −120157. | −0.882461 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 358625.i | − 2.60551i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −129467. | −0.930552 | −0.465276 | − | 0.885166i | \(-0.654045\pi\) | ||||
−0.465276 | + | 0.885166i | \(0.654045\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18155.8i | 0.129108i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −47217.2 | −0.332214 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 259093.i | − 1.80376i | −0.431990 | − | 0.901878i | \(-0.642188\pi\) | ||||
0.431990 | − | 0.901878i | \(-0.357812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 282508. | 1.94617 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 191511.i | 1.30556i | 0.757548 | + | 0.652780i | \(0.226397\pi\) | ||||
−0.757548 | + | 0.652780i | \(0.773603\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −83445.5 | −0.562965 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 108329.i | 0.723308i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −255416. | −1.68791 | −0.843954 | − | 0.536415i | \(-0.819778\pi\) | ||||
−0.843954 | + | 0.536415i | \(0.819778\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4613.50i | 0.0301771i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −346094. | −2.24083 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 70503.3i | − 0.451872i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 142760. | 0.905789 | 0.452894 | − | 0.891564i | \(-0.350391\pi\) | ||||
0.452894 | + | 0.891564i | \(0.350391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 329406.i | − 2.06912i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 194681. | 1.21070 | 0.605348 | − | 0.795961i | \(-0.293034\pi\) | ||||
0.605348 | + | 0.795961i | \(0.293034\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 65020.9i | − 0.400353i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −66709.5 | −0.406703 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 206237.i | 1.24503i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −89149.0 | −0.532930 | −0.266465 | − | 0.963845i | \(-0.585856\pi\) | ||||
−0.266465 | + | 0.963845i | \(0.585856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 453715.i | 2.68596i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −108402. | −0.635532 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 68246.6i | − 0.396264i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 215545. | 1.23956 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 316683.i | 1.80384i | 0.431906 | + | 0.901918i | \(0.357841\pi\) | ||||
−0.431906 | + | 0.901918i | \(0.642159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −107801. | −0.608217 | −0.304109 | − | 0.952637i | \(-0.598359\pi\) | ||||
−0.304109 | + | 0.952637i | \(0.598359\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 174088.i | 0.972946i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2813.79 | 0.0155781 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 206943.i | − 1.13500i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −198376. | −1.07789 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 122818.i | − 0.661160i | −0.943778 | − | 0.330580i | \(-0.892756\pi\) | ||||
0.943778 | − | 0.330580i | \(-0.107244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −182503. | −0.973406 | −0.486703 | − | 0.873567i | \(-0.661801\pi\) | ||||
−0.486703 | + | 0.873567i | \(0.661801\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 42956.1i | − 0.227011i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −66595.5 | −0.348724 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 284219.i | 1.47477i | 0.675473 | + | 0.737385i | \(0.263940\pi\) | ||||
−0.675473 | + | 0.737385i | \(0.736060\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 323735. | 1.66461 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 290002.i | 1.47772i | 0.673858 | + | 0.738861i | \(0.264636\pi\) | ||||
−0.673858 | + | 0.738861i | \(0.735364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19102.1 | 0.0964632 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 130716.i | 0.654204i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 53644.3 | 0.266091 | 0.133046 | − | 0.991110i | \(-0.457524\pi\) | ||||
0.133046 | + | 0.991110i | \(0.457524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 130935.i | 0.643730i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −36682.4 | −0.178756 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 139291.i | 0.672820i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 51320.3 | 0.245729 | 0.122865 | − | 0.992423i | \(-0.460792\pi\) | ||||
0.122865 | + | 0.992423i | \(0.460792\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 1980.15i | − 0.00939881i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −71282.3 | −0.335413 | −0.167706 | − | 0.985837i | \(-0.553636\pi\) | ||||
−0.167706 | + | 0.985837i | \(0.553636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 107296.i | − 0.500519i | −0.968179 | − | 0.250260i | \(-0.919484\pi\) | ||||
0.968179 | − | 0.250260i | \(-0.0805160\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 59153.1 | 0.273572 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 32462.5i | − 0.148850i | −0.997227 | − | 0.0744248i | \(-0.976288\pi\) | ||||
0.997227 | − | 0.0744248i | \(-0.0237121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 697357. | 3.17037 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 508425.i | 2.29185i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 118047. | 0.527632 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 40616.8i | 0.180019i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 403372. | 1.77284 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 33919.3i | − 0.147835i | −0.997264 | − | 0.0739173i | \(-0.976450\pi\) | ||||
0.997264 | − | 0.0739173i | \(-0.0235501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 344259. | 1.48798 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 207771.i | − 0.890618i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22228.3 | −0.0944980 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 324548.i | − 1.36843i | −0.729282 | − | 0.684213i | \(-0.760146\pi\) | ||||
0.729282 | − | 0.684213i | \(-0.239854\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −119122. | −0.498168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 119081.i | 0.493946i | 0.969022 | + | 0.246973i | \(0.0794358\pi\) | ||||
−0.969022 | + | 0.246973i | \(0.920564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6657.36 | −0.0273910 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 93857.3i | − 0.383052i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −263376. | −1.06626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8360.30i | 0.0335754i | 0.999859 | + | 0.0167877i | \(0.00534394\pi\) | ||||
−0.999859 | + | 0.0167877i | \(0.994656\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −70759.9 | −0.281911 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 400265.i | − 1.58202i | −0.611805 | − | 0.791009i | \(-0.709556\pi\) | ||||
0.611805 | − | 0.791009i | \(-0.290444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 67222.4 | 0.263591 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 39903.9i | − 0.155238i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −271797. | −1.04908 | −0.524541 | − | 0.851385i | \(-0.675763\pi\) | ||||
−0.524541 | + | 0.851385i | \(0.675763\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 114526.i | − 0.438592i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28583.3 | 0.108612 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 113604.i | 0.428332i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 189705. | 0.709736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 210300.i | 0.780736i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −347896. | −1.28166 | −0.640832 | − | 0.767681i | \(-0.721410\pi\) | ||||
−0.640832 | + | 0.767681i | \(0.721410\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 275580.i | − 1.00750i | −0.863850 | − | 0.503750i | \(-0.831953\pi\) | ||||
0.863850 | − | 0.503750i | \(-0.168047\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −126720. | −0.459756 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 9167.58i | − 0.0330091i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 237836. | 0.849898 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 121928.i | − 0.432428i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 218563. | 0.769346 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 144916.i | 0.506299i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45263.2 | 0.156963 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 352775.i | − 1.21428i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 96023.1 | 0.328081 | 0.164041 | − | 0.986454i | \(-0.447547\pi\) | ||||
0.164041 | + | 0.986454i | \(0.447547\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 164390.i | 0.557540i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11204.7 | −0.0377232 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 102032.i | − 0.341007i | −0.985357 | − | 0.170503i | \(-0.945461\pi\) | ||||
0.985357 | − | 0.170503i | \(-0.0545394\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 232764. | 0.772272 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 96098.4i | − 0.316529i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 492087. | 1.60913 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 313192.i | 1.01677i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 423559. | 1.36522 | 0.682612 | − | 0.730781i | \(-0.260844\pi\) | ||||
0.682612 | + | 0.730781i | \(0.260844\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 197048.i | − 0.630593i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27969.9 | −0.0888721 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 498724.i | − 1.57342i | −0.617325 | − | 0.786708i | \(-0.711784\pi\) | ||||
0.617325 | − | 0.786708i | \(-0.288216\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −111318. | −0.348712 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 465607.i | − 1.44828i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 237219. | 0.732697 | 0.366349 | − | 0.930478i | \(-0.380608\pi\) | ||||
0.366349 | + | 0.930478i | \(0.380608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 281100.i | 0.862161i | 0.902314 | + | 0.431080i | \(0.141867\pi\) | ||||
−0.902314 | + | 0.431080i | \(0.858133\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −161565. | −0.492083 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 25618.8i | 0.0774861i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 404501. | 1.21498 | 0.607489 | − | 0.794328i | \(-0.292177\pi\) | ||||
0.607489 | + | 0.794328i | \(0.292177\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 279799.i | 0.834622i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 476335. | 1.41111 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 439556.i | − 1.29323i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −156670. | −0.457799 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 335843.i | − 0.974675i | −0.873214 | − | 0.487337i | \(-0.837968\pi\) | ||||
0.873214 | − | 0.487337i | \(-0.162032\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 132333. | 0.381450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 400658.i | 1.14709i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −139571. | −0.396905 | −0.198452 | − | 0.980111i | \(-0.563592\pi\) | ||||
−0.198452 | + | 0.980111i | \(0.563592\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19639.2i | 0.0554740i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −747809. | −2.09818 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 71633.1i | 0.199646i | 0.995005 | + | 0.0998228i | \(0.0318276\pi\) | ||||
−0.995005 | + | 0.0998228i | \(0.968172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 524251. | 1.45141 | 0.725706 | − | 0.688005i | \(-0.241514\pi\) | ||||
0.725706 | + | 0.688005i | \(0.241514\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 784369.i | 2.15718i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 61414.7 | 0.167788 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 89856.9i | 0.243879i | 0.992538 | + | 0.121939i | \(0.0389114\pi\) | ||||
−0.992538 | + | 0.121939i | \(0.961089\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 299817. | 0.808393 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 316663.i | − 0.848232i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −58041.7 | −0.154461 | −0.0772305 | − | 0.997013i | \(-0.524608\pi\) | ||||
−0.0772305 | + | 0.997013i | \(0.524608\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 198839.i | 0.525715i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −251038. | −0.659431 | −0.329716 | − | 0.944080i | \(-0.606953\pi\) | ||||
−0.329716 | + | 0.944080i | \(0.606953\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 37372.0i | − 0.0975360i | −0.998810 | − | 0.0487680i | \(-0.984470\pi\) | ||||
0.998810 | − | 0.0487680i | \(-0.0155295\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18028.8 | 0.0467502 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 133326.i | 0.343509i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 403743.i | − 1.02700i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48538.6 | 0.122683 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 81639.6i | 0.205042i | 0.994731 | + | 0.102521i | \(0.0326908\pi\) | ||||
−0.994731 | + | 0.102521i | \(0.967309\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −551932. | −1.37746 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 243129.i | − 0.602960i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −588866. | −1.45124 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 296239.i | − 0.725505i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −72207.4 | −0.175738 | −0.0878690 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878690 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 221605.i | − 0.535990i | −0.963420 | − | 0.267995i | \(-0.913639\pi\) | ||||
0.963420 | − | 0.267995i | \(-0.0863611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 179266. | 0.430901 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 388806.i | − 0.928805i | −0.885624 | − | 0.464403i | \(-0.846269\pi\) | ||||
0.885624 | − | 0.464403i | \(-0.153731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −132865. | −0.315444 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 412866.i | 0.974199i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32328.2 | −0.0758150 | −0.0379075 | − | 0.999281i | \(-0.512069\pi\) | ||||
−0.0379075 | + | 0.999281i | \(0.512069\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 297851.i | 0.694252i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 128816. | 0.298427 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 593355.i | 1.36629i | 0.730282 | + | 0.683146i | \(0.239389\pi\) | ||||
−0.730282 | + | 0.683146i | \(0.760611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 574565. | 1.31503 | 0.657516 | − | 0.753440i | \(-0.271607\pi\) | ||||
0.657516 | + | 0.753440i | \(0.271607\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46688.5i | 0.106214i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −283490. | −0.641053 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 60613.6i | − 0.136244i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −190810. | −0.426334 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 253644.i | − 0.563351i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 296688. | 0.655043 | 0.327522 | − | 0.944844i | \(-0.393787\pi\) | ||||
0.327522 | + | 0.944844i | \(0.393787\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 10995.8i | − 0.0241334i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 348459. | 0.760282 | 0.380141 | − | 0.924929i | \(-0.375875\pi\) | ||||
0.380141 | + | 0.924929i | \(0.375875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 155145.i | − 0.336510i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −711070. | −1.53327 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 555433.i | − 1.19067i | −0.803479 | − | 0.595333i | \(-0.797020\pi\) | ||||
0.803479 | − | 0.595333i | \(-0.202980\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 390471. | 0.832162 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 189455.i | 0.401414i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −733725. | −1.54559 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 417213.i | 0.873780i | 0.899515 | + | 0.436890i | \(0.143920\pi\) | ||||
−0.899515 | + | 0.436890i | \(0.856080\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 655088. | 1.36406 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 185500.i | − 0.384039i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 30816.1 | 0.0634325 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.28971e6i | − 2.63960i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −752354. | −1.53104 | −0.765519 | − | 0.643413i | \(-0.777518\pi\) | ||||
−0.765519 | + | 0.643413i | \(0.777518\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 700650.i | 1.41772i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 288086. | 0.579620 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 469187.i | 0.938658i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −480953. | −0.956775 | −0.478388 | − | 0.878149i | \(-0.658779\pi\) | ||||
−0.478388 | + | 0.878149i | \(0.658779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 553486.i | 1.09488i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 83468.6 | 0.164189 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 170724.i | 0.333952i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −802539. | −1.56109 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 298189.i | 0.576811i | 0.957508 | + | 0.288406i | \(0.0931251\pi\) | ||||
−0.957508 | + | 0.288406i | \(0.906875\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −792916. | −1.52531 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.26927e6i | 2.42816i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −36968.4 | −0.0703323 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 104436.i | − 0.197597i | −0.995107 | − | 0.0987984i | \(-0.968500\pi\) | ||||
0.995107 | − | 0.0987984i | \(-0.0314999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 616269. | 1.15962 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 27782.7i | − 0.0519923i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 442720. | 0.823988 | 0.411994 | − | 0.911187i | \(-0.364833\pi\) | ||||
0.411994 | + | 0.911187i | \(0.364833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − 535724.i | − 0.991668i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 854730. | 1.57360 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 316611.i | 0.579744i | 0.957065 | + | 0.289872i | \(0.0936128\pi\) | ||||
−0.957065 | + | 0.289872i | \(0.906387\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −673945. | −1.22740 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 249871.i | 0.452626i | 0.974055 | + | 0.226313i | \(0.0726671\pi\) | ||||
−0.974055 | + | 0.226313i | \(0.927333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 112495. | 0.202685 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 535769.i | 0.960145i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.01146e6 | −1.80295 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 745034.i | 1.32098i | 0.750835 | + | 0.660490i | \(0.229651\pi\) | ||||
−0.750835 | + | 0.660490i | \(0.770349\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 937395. | 1.65323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31569.2i | 0.0553821i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 602045. | 1.05060 | 0.525300 | − | 0.850917i | \(-0.323953\pi\) | ||||
0.525300 | + | 0.850917i | \(0.323953\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 254659.i | − 0.442055i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −46391.1 | −0.0801061 | −0.0400530 | − | 0.999198i | \(-0.512753\pi\) | ||||
−0.0400530 | + | 0.999198i | \(0.512753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 78204.9i | − 0.134334i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22089.6 | −0.0377455 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 221784.i | 0.376999i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −169035. | −0.285841 | −0.142920 | − | 0.989734i | \(-0.545649\pi\) | ||||
−0.142920 | + | 0.989734i | \(0.545649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 22606.7i | − 0.0380302i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −581948. | −0.973924 | −0.486962 | − | 0.873423i | \(-0.661895\pi\) | ||||
−0.486962 | + | 0.873423i | \(0.661895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 50907.7i | − 0.0847579i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.18596e6 | −3.62076 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 444827.i | 0.733021i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −322813. | −0.529235 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26015.8i | 0.0424340i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 437555. | 0.710058 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 739795.i | 1.19443i | 0.802080 | + | 0.597217i | \(0.203727\pi\) | ||||
−0.802080 | + | 0.597217i | \(0.796273\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 721502. | 1.15900 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 776956.i | − 1.24178i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −423392. | −0.673281 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 667510.i | − 1.05615i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 59513.8 | 0.0936917 | 0.0468459 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468459 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 44647.6i | − 0.0699367i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −149961. | −0.233730 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 140371.i | − 0.217694i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −178810. | −0.275931 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 781113.i | 1.19941i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.07133e6 | −1.63691 | −0.818457 | − | 0.574568i | \(-0.805170\pi\) | ||||
−0.818457 | + | 0.574568i | \(0.805170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 1.12103e6i | − 1.70442i | −0.523199 | − | 0.852211i | \(-0.675262\pi\) | ||||
0.523199 | − | 0.852211i | \(-0.324738\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −855181. | −1.29383 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 102518.i | 0.154342i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 401040. | 0.600820 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 1.09350e6i | − 1.63024i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −210197. | −0.311846 | −0.155923 | − | 0.987769i | \(-0.549835\pi\) | ||||
−0.155923 | + | 0.987769i | \(0.549835\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 501270.i | − 0.740068i | −0.929018 | − | 0.370034i | \(-0.879346\pi\) | ||||
0.929018 | − | 0.370034i | \(-0.120654\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −155317. | −0.228198 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 599224.i | − 0.876149i | −0.898939 | − | 0.438075i | \(-0.855661\pi\) | ||||
0.898939 | − | 0.438075i | \(-0.144339\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 92189.6 | 0.134145 | 0.0670723 | − | 0.997748i | \(-0.478634\pi\) | ||||
0.0670723 | + | 0.997748i | \(0.478634\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 797165.i | − 1.15437i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −83026.8 | −0.119654 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 60896.6i | 0.0873414i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −35825.3 | −0.0511375 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 16114.0i | − 0.0228918i | −0.999934 | − | 0.0114459i | \(-0.996357\pi\) | ||||
0.999934 | − | 0.0114459i | \(-0.00364342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −619815. | −0.876334 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 340777.i | − 0.479530i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −34341.6 | −0.0480958 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 428651.i | 0.597499i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.19214e6 | −1.65391 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 441932.i | 0.610234i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 596015. | 0.819142 | 0.409571 | − | 0.912278i | \(-0.365678\pi\) | ||||
0.409571 | + | 0.912278i | \(0.365678\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 318862.i | − 0.436184i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14006.7 | −0.0190710 | −0.00953550 | − | 0.999955i | \(-0.503035\pi\) | ||||
−0.00953550 | + | 0.999955i | \(0.503035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 221377.i | 0.300017i | 0.988685 | + | 0.150008i | \(0.0479301\pi\) | ||||
−0.988685 | + | 0.150008i | \(0.952070\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.38782e6 | −1.87209 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1.44444e6i | − 1.93945i | −0.244208 | − | 0.969723i | \(-0.578528\pi\) | ||||
0.244208 | − | 0.969723i | \(-0.421472\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 180986. | 0.241887 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.07846e6i | − 1.43471i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 603136. | 0.798686 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 1.42675e6i | − 1.88067i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 174503. | 0.228968 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 109057.i | 0.142441i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.25884e6 | 1.63671 | 0.818353 | − | 0.574715i | \(-0.194887\pi\) | ||||
0.818353 | + | 0.574715i | \(0.194887\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1.06546e6i | − 1.37899i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 491927. | 0.633795 | 0.316897 | − | 0.948460i | \(-0.397359\pi\) | ||||
0.316897 | + | 0.948460i | \(0.397359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 97635.7i | − 0.125224i | −0.998038 | − | 0.0626120i | \(-0.980057\pi\) | ||||
0.998038 | − | 0.0626120i | \(-0.0199431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −201769. | −0.257613 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 668572.i | 0.849769i | 0.905248 | + | 0.424884i | \(0.139685\pi\) | ||||
−0.905248 | + | 0.424884i | \(0.860315\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.69695e6 | 2.14716 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 570681.i | − 0.718850i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 644485. | 0.808183 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 38953.9i | − 0.0486300i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −425088. | −0.528316 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 120447.i | 0.149030i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −103451. | −0.127434 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.25121e6i | 1.53445i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 141476. | 0.172737 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 659118.i | 0.801214i | 0.916250 | + | 0.400607i | \(0.131201\pi\) | ||||
−0.916250 | + | 0.400607i | \(0.868799\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −527729. | −0.638680 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 852700.i | 1.02745i | 0.857956 | + | 0.513724i | \(0.171734\pi\) | ||||
−0.857956 | + | 0.513724i | \(0.828266\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 583830. | 0.700398 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 385183.i | − 0.460071i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.07889e6 | −2.47225 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.11737e6i | 1.32302i | 0.749936 | + | 0.661511i | \(0.230084\pi\) | ||||
−0.749936 | + | 0.661511i | \(0.769916\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 186724. | 0.220131 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 538852.i | 0.632508i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 269536. | 0.315016 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 891852.i | − 1.03785i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −59813.4 | −0.0693054 | −0.0346527 | − | 0.999399i | \(-0.511033\pi\) | ||||
−0.0346527 | + | 0.999399i | \(0.511033\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 1.19848e6i | − 1.38272i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.31983e6 | 2.66498 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24071.2i | 0.0275343i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −981955. | −1.11844 | −0.559220 | − | 0.829019i | \(-0.688899\pi\) | ||||
−0.559220 | + | 0.829019i | \(0.688899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.44406e6i | 2.77192i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.07255e6 | −1.21126 | −0.605629 | − | 0.795747i | \(-0.707079\pi\) | ||||
−0.605629 | + | 0.795747i | \(0.707079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 280573.i | 0.315517i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 76746.5 | 0.0859400 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 877745.i | 0.978742i | 0.872076 | + | 0.489371i | \(0.162774\pi\) | ||||
−0.872076 | + | 0.489371i | \(0.837226\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −234313. | −0.260174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1.36391e6i | − 1.50808i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.25729e6 | 1.38436 | 0.692181 | − | 0.721724i | \(-0.256650\pi\) | ||||
0.692181 | + | 0.721724i | \(0.256650\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 139044.i | 0.152457i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 367478. | 0.401243 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.72534e6i | 2.96335i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 757659. | 0.820403 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 1.13766e6i | − 1.22676i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 240798. | 0.258582 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 506655.i | 0.541825i | 0.962604 | + | 0.270913i | \(0.0873254\pi\) | ||||
−0.962604 | + | 0.270913i | \(0.912675\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −95022.3 | −0.101199 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 424048.i | − 0.449755i | −0.974387 | − | 0.224878i | \(-0.927802\pi\) | ||||
0.974387 | − | 0.224878i | \(-0.0721982\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.29472e6 | 1.36757 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 259262.i | 0.272728i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −269406. | −0.282240 | −0.141120 | − | 0.989993i | \(-0.545070\pi\) | ||||
−0.141120 | + | 0.989993i | \(0.545070\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 163413.i | 0.170499i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 87962.8 | 0.0914031 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 758850.i | 0.785325i | 0.919683 | + | 0.392662i | \(0.128446\pi\) | ||||
−0.919683 | + | 0.392662i | \(0.871554\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 344809. | 0.355391 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.01073e6i | 2.06404i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 252955. | 0.258613 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1.22397e6i | − 1.24630i | −0.782102 | − | 0.623150i | \(-0.785853\pi\) | ||||
0.782102 | − | 0.623150i | \(-0.214147\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.39438e6 | 1.41411 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 643571.i | 0.650055i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.31108e6 | −1.31898 | −0.659489 | − | 0.751714i | \(-0.729227\pi\) | ||||
−0.659489 | + | 0.751714i | \(0.729227\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 189681.i | − 0.190061i |
(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 | 320.5.b.d.191.7 | 8 | ||
4.3 | odd | 2 | inner | 320.5.b.d.191.2 | 8 | ||
8.3 | odd | 2 | 20.5.b.a.11.7 | ✓ | 8 | ||
8.5 | even | 2 | 20.5.b.a.11.8 | yes | 8 | ||
24.5 | odd | 2 | 180.5.c.a.91.1 | 8 | |||
24.11 | even | 2 | 180.5.c.a.91.2 | 8 | |||
40.3 | even | 4 | 100.5.d.c.99.7 | 16 | |||
40.13 | odd | 4 | 100.5.d.c.99.9 | 16 | |||
40.19 | odd | 2 | 100.5.b.c.51.2 | 8 | |||
40.27 | even | 4 | 100.5.d.c.99.10 | 16 | |||
40.29 | even | 2 | 100.5.b.c.51.1 | 8 | |||
40.37 | odd | 4 | 100.5.d.c.99.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.5.b.a.11.7 | ✓ | 8 | 8.3 | odd | 2 | ||
20.5.b.a.11.8 | yes | 8 | 8.5 | even | 2 | ||
100.5.b.c.51.1 | 8 | 40.29 | even | 2 | |||
100.5.b.c.51.2 | 8 | 40.19 | odd | 2 | |||
100.5.d.c.99.7 | 16 | 40.3 | even | 4 | |||
100.5.d.c.99.8 | 16 | 40.37 | odd | 4 | |||
100.5.d.c.99.9 | 16 | 40.13 | odd | 4 | |||
100.5.d.c.99.10 | 16 | 40.27 | even | 4 | |||
180.5.c.a.91.1 | 8 | 24.5 | odd | 2 | |||
180.5.c.a.91.2 | 8 | 24.11 | even | 2 | |||
320.5.b.d.191.2 | 8 | 4.3 | odd | 2 | inner | ||
320.5.b.d.191.7 | 8 | 1.1 | even | 1 | trivial |