Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,2,Mod(99,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("490.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(3.91266969904\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 490.99 |
Dual form | 490.2.c.d.99.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | −1.00000 | + | 2.00000i | −0.316228 | + | 0.632456i | ||||
\(11\) | 3.00000 | 0.904534 | 0.452267 | − | 0.891883i | \(-0.350615\pi\) | ||||
0.452267 | + | 0.891883i | \(0.350615\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.00000i | − | 1.38675i | −0.720577 | − | 0.693375i | \(-0.756123\pi\) | ||
0.720577 | − | 0.693375i | \(-0.243877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 3.00000i | 0.707107i | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | 7.00000i | 1.45960i | 0.683660 | + | 0.729800i | \(0.260387\pi\) | ||||
−0.683660 | + | 0.729800i | \(0.739613\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 5.00000 | 0.980581 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.00000 | 0.742781 | 0.371391 | − | 0.928477i | \(-0.378881\pi\) | ||||
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 1.00000i | 0.164399i | 0.996616 | + | 0.0821995i | \(0.0261945\pi\) | ||||
−0.996616 | + | 0.0821995i | \(0.973806\pi\) | |||||||
\(38\) | − | 5.00000i | − | 0.811107i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | − | 2.00000i | 0.158114 | − | 0.316228i | ||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 6.00000 | + | 3.00000i | 0.894427 | + | 0.447214i | ||||
\(46\) | −7.00000 | −1.03209 | ||||||||
\(47\) | 7.00000i | 1.02105i | 0.859861 | + | 0.510527i | \(0.170550\pi\) | ||||
−0.859861 | + | 0.510527i | \(0.829450\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.00000i | 0.693375i | ||||||||
\(53\) | − | 9.00000i | − | 1.23625i | −0.786082 | − | 0.618123i | \(-0.787894\pi\) | ||
0.786082 | − | 0.618123i | \(-0.212106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 3.00000i | 0.809040 | + | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000i | 0.525226i | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 2.00000i | 0.254000i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.00000 | − | 10.0000i | 0.620174 | − | 1.24035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | − | 2.00000i | − | 0.242536i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | − | 3.00000i | − | 0.353553i | ||||||
\(73\) | − | 16.0000i | − | 1.87266i | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||
0.351123 | − | 0.936329i | \(-0.385800\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.00000 | 0.573539 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0000 | −1.57512 | −0.787562 | − | 0.616236i | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(80\) | 2.00000 | + | 1.00000i | 0.223607 | + | 0.111803i | ||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | − | 3.00000i | − | 0.331295i | ||||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | + | 4.00000i | −0.216930 | + | 0.433861i | ||||
\(86\) | 2.00000 | 0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3.00000i | − | 0.319801i | ||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | −3.00000 | + | 6.00000i | −0.316228 | + | 0.632456i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 7.00000i | − | 0.729800i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.00000 | −0.721995 | ||||||||
\(95\) | −10.0000 | − | 5.00000i | −1.02598 | − | 0.512989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000i | 1.21842i | 0.793011 | + | 0.609208i | \(0.208512\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.00000 | 0.904534 | ||||||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.00000i | − | 0.788263i | −0.919054 | − | 0.394132i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394132i | \(-0.128955\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.00000 | 0.874157 | ||||||||
\(107\) | − | 16.0000i | − | 1.54678i | −0.633932 | − | 0.773389i | \(-0.718560\pi\) | ||
0.633932 | − | 0.773389i | \(-0.281440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | −3.00000 | + | 6.00000i | −0.286039 | + | 0.572078i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.0000i | − | 1.31701i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||
0.752577 | − | 0.658505i | \(-0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.00000 | + | 14.0000i | −0.652753 | + | 1.30551i | ||||
\(116\) | −4.00000 | −0.371391 | ||||||||
\(117\) | − | 15.0000i | − | 1.38675i | ||||||
\(118\) | − | 4.00000i | − | 0.368230i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | − | 6.00000i | − | 0.543214i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.00000 | −0.179605 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.00000i | 0.621150i | 0.950549 | + | 0.310575i | \(0.100522\pi\) | ||||
−0.950549 | + | 0.310575i | \(0.899478\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.0000 | + | 5.00000i | 0.877058 | + | 0.438529i | ||||
\(131\) | 1.00000 | 0.0873704 | 0.0436852 | − | 0.999045i | \(-0.486090\pi\) | ||||
0.0436852 | + | 0.999045i | \(0.486090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | 0.171499 | ||||||||
\(137\) | − | 8.00000i | − | 0.683486i | −0.939793 | − | 0.341743i | \(-0.888983\pi\) | ||
0.939793 | − | 0.341743i | \(-0.111017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 6.00000i | − | 0.503509i | ||||||
\(143\) | − | 15.0000i | − | 1.25436i | ||||||
\(144\) | 3.00000 | 0.250000 | ||||||||
\(145\) | 8.00000 | + | 4.00000i | 0.664364 | + | 0.332182i | ||||
\(146\) | 16.0000 | 1.32417 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 1.00000i | − | 0.0821995i | ||||||
\(149\) | 18.0000 | 1.47462 | 0.737309 | − | 0.675556i | \(-0.236096\pi\) | ||||
0.737309 | + | 0.675556i | \(0.236096\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.00000 | −0.488273 | −0.244137 | − | 0.969741i | \(-0.578505\pi\) | ||||
−0.244137 | + | 0.969741i | \(0.578505\pi\) | |||||||
\(152\) | 5.00000i | 0.405554i | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | + | 2.00000i | 0.321288 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.00000i | 0.718278i | 0.933284 | + | 0.359139i | \(0.116930\pi\) | ||||
−0.933284 | + | 0.359139i | \(0.883070\pi\) | |||||||
\(158\) | − | 14.0000i | − | 1.11378i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | + | 2.00000i | −0.0790569 | + | 0.158114i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | 12.0000i | 0.939913i | 0.882690 | + | 0.469956i | \(0.155730\pi\) | ||||
−0.882690 | + | 0.469956i | \(0.844270\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | − | 15.0000i | − | 1.16073i | −0.814355 | − | 0.580367i | \(-0.802909\pi\) | ||
0.814355 | − | 0.580367i | \(-0.197091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | −4.00000 | − | 2.00000i | −0.306786 | − | 0.153393i | ||||
\(171\) | −15.0000 | −1.14708 | ||||||||
\(172\) | 2.00000i | 0.152499i | ||||||||
\(173\) | 9.00000i | 0.684257i | 0.939653 | + | 0.342129i | \(0.111148\pi\) | ||||
−0.939653 | + | 0.342129i | \(0.888852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000 | 0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.00000i | 0.149906i | ||||||||
\(179\) | −13.0000 | −0.971666 | −0.485833 | − | 0.874052i | \(-0.661484\pi\) | ||||
−0.485833 | + | 0.874052i | \(0.661484\pi\) | |||||||
\(180\) | −6.00000 | − | 3.00000i | −0.447214 | − | 0.223607i | ||||
\(181\) | −26.0000 | −1.93256 | −0.966282 | − | 0.257485i | \(-0.917106\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.00000 | 0.516047 | ||||||||
\(185\) | −1.00000 | + | 2.00000i | −0.0735215 | + | 0.147043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.00000i | 0.438763i | ||||||||
\(188\) | − | 7.00000i | − | 0.510527i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.00000 | − | 10.0000i | 0.362738 | − | 0.725476i | ||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | −12.0000 | −0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.00000i | − | 0.356235i | −0.984009 | − | 0.178118i | \(-0.942999\pi\) | ||
0.984009 | − | 0.178118i | \(-0.0570008\pi\) | |||||||
\(198\) | 9.00000i | 0.639602i | ||||||||
\(199\) | 18.0000 | 1.27599 | 0.637993 | − | 0.770042i | \(-0.279765\pi\) | ||||
0.637993 | + | 0.770042i | \(0.279765\pi\) | |||||||
\(200\) | 4.00000 | − | 3.00000i | 0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | − | 3.00000i | −0.419058 | − | 0.209529i | ||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 21.0000i | 1.45960i | ||||||||
\(208\) | − | 5.00000i | − | 0.346688i | ||||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | −0.619586 | −0.309793 | − | 0.950804i | \(-0.600260\pi\) | ||||
−0.309793 | + | 0.950804i | \(0.600260\pi\) | |||||||
\(212\) | 9.00000i | 0.618123i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.0000 | 1.09374 | ||||||||
\(215\) | 2.00000 | − | 4.00000i | 0.136399 | − | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.00000 | − | 3.00000i | −0.404520 | − | 0.202260i | ||||
\(221\) | 10.0000 | 0.672673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.00000 | + | 12.0000i | 0.600000 | + | 0.800000i | ||||
\(226\) | 14.0000 | 0.931266 | ||||||||
\(227\) | 6.00000i | 0.398234i | 0.979976 | + | 0.199117i | \(0.0638074\pi\) | ||||
−0.979976 | + | 0.199117i | \(0.936193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0000 | 1.05731 | 0.528655 | − | 0.848837i | \(-0.322697\pi\) | ||||
0.528655 | + | 0.848837i | \(0.322697\pi\) | |||||||
\(230\) | −14.0000 | − | 7.00000i | −0.923133 | − | 0.461566i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 4.00000i | − | 0.262613i | ||||||
\(233\) | 8.00000i | 0.524097i | 0.965055 | + | 0.262049i | \(0.0843981\pi\) | ||||
−0.965055 | + | 0.262049i | \(0.915602\pi\) | |||||||
\(234\) | 15.0000 | 0.980581 | ||||||||
\(235\) | −7.00000 | + | 14.0000i | −0.456630 | + | 0.913259i | ||||
\(236\) | 4.00000 | 0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.00000 | 0.579741 | 0.289870 | − | 0.957066i | \(-0.406388\pi\) | ||||
0.289870 | + | 0.957066i | \(0.406388\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.0000i | 1.59071i | ||||||||
\(248\) | − | 2.00000i | − | 0.127000i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0000 | + | 2.00000i | −0.695701 | + | 0.126491i | ||||
\(251\) | −5.00000 | −0.315597 | −0.157799 | − | 0.987471i | \(-0.550440\pi\) | ||||
−0.157799 | + | 0.987471i | \(0.550440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.0000i | 1.32026i | ||||||||
\(254\) | −7.00000 | −0.439219 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5.00000 | + | 10.0000i | −0.310087 | + | 0.620174i | ||||
\(261\) | 12.0000 | 0.742781 | ||||||||
\(262\) | 1.00000i | 0.0617802i | ||||||||
\(263\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | − | 18.0000i | 0.552866 | − | 1.10573i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.00000i | − | 0.122169i | ||||||
\(269\) | −10.0000 | −0.609711 | −0.304855 | − | 0.952399i | \(-0.598608\pi\) | ||||
−0.304855 | + | 0.952399i | \(0.598608\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | −1.45790 | −0.728948 | − | 0.684569i | \(-0.759990\pi\) | ||||
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(272\) | 2.00000i | 0.121268i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | 0.483298 | ||||||||
\(275\) | 9.00000 | + | 12.0000i | 0.542720 | + | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.00000i | − | 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | 16.0000i | 0.959616i | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0000i | 0.832214i | 0.909316 | + | 0.416107i | \(0.136606\pi\) | ||||
−0.909316 | + | 0.416107i | \(0.863394\pi\) | |||||||
\(284\) | 6.00000 | 0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0000 | 0.886969 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −4.00000 | + | 8.00000i | −0.234888 | + | 0.469776i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.0000i | 0.936329i | ||||||||
\(293\) | − | 9.00000i | − | 0.525786i | −0.964825 | − | 0.262893i | \(-0.915323\pi\) | ||
0.964825 | − | 0.262893i | \(-0.0846766\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | − | 4.00000i | −0.465778 | − | 0.232889i | ||||
\(296\) | 1.00000 | 0.0581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.0000i | 1.04271i | ||||||||
\(299\) | 35.0000 | 2.02410 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 6.00000i | − | 0.345261i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.00000 | −0.286770 | ||||||||
\(305\) | −12.0000 | − | 6.00000i | −0.687118 | − | 0.343559i | ||||
\(306\) | −6.00000 | −0.342997 | ||||||||
\(307\) | 22.0000i | 1.25561i | 0.778372 | + | 0.627803i | \(0.216046\pi\) | ||||
−0.778372 | + | 0.627803i | \(0.783954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.00000 | + | 4.00000i | −0.113592 | + | 0.227185i | ||||
\(311\) | −6.00000 | −0.340229 | −0.170114 | − | 0.985424i | \(-0.554414\pi\) | ||||
−0.170114 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 22.0000i | − | 1.24351i | −0.783210 | − | 0.621757i | \(-0.786419\pi\) | ||
0.783210 | − | 0.621757i | \(-0.213581\pi\) | |||||||
\(314\) | −9.00000 | −0.507899 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | − | 2.00000i | − | 0.112331i | −0.998421 | − | 0.0561656i | \(-0.982113\pi\) | ||
0.998421 | − | 0.0561656i | \(-0.0178875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | −2.00000 | − | 1.00000i | −0.111803 | − | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.0000i | − | 0.556415i | ||||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | 20.0000 | − | 15.0000i | 1.10940 | − | 0.832050i | ||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000i | 0.165647i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | 0.274825 | 0.137412 | − | 0.990514i | \(-0.456121\pi\) | ||||
0.137412 | + | 0.990514i | \(0.456121\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | 3.00000i | 0.164399i | ||||||||
\(334\) | 15.0000 | 0.820763 | ||||||||
\(335\) | −2.00000 | + | 4.00000i | −0.109272 | + | 0.218543i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.0000i | 0.544735i | 0.962193 | + | 0.272367i | \(0.0878066\pi\) | ||||
−0.962193 | + | 0.272367i | \(0.912193\pi\) | |||||||
\(338\) | − | 12.0000i | − | 0.652714i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.00000 | − | 4.00000i | 0.108465 | − | 0.216930i | ||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | − | 15.0000i | − | 0.811107i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.00000 | −0.483843 | ||||||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0000 | −0.642345 | −0.321173 | − | 0.947021i | \(-0.604077\pi\) | ||||
−0.321173 | + | 0.947021i | \(0.604077\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.00000i | 0.159901i | ||||||||
\(353\) | 24.0000i | 1.27739i | 0.769460 | + | 0.638696i | \(0.220526\pi\) | ||||
−0.769460 | + | 0.638696i | \(0.779474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | − | 6.00000i | −0.636894 | − | 0.318447i | ||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 13.0000i | − | 0.687071i | ||||||
\(359\) | −16.0000 | −0.844448 | −0.422224 | − | 0.906492i | \(-0.638750\pi\) | ||||
−0.422224 | + | 0.906492i | \(0.638750\pi\) | |||||||
\(360\) | 3.00000 | − | 6.00000i | 0.158114 | − | 0.316228i | ||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | − | 26.0000i | − | 1.36653i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.0000 | − | 32.0000i | 0.837478 | − | 1.67496i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.0000i | − | 0.678594i | −0.940679 | − | 0.339297i | \(-0.889811\pi\) | ||
0.940679 | − | 0.339297i | \(-0.110189\pi\) | |||||||
\(368\) | 7.00000i | 0.364900i | ||||||||
\(369\) | −9.00000 | −0.468521 | ||||||||
\(370\) | −2.00000 | − | 1.00000i | −0.103975 | − | 0.0519875i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.0000i | − | 1.34623i | −0.739538 | − | 0.673114i | \(-0.764956\pi\) | ||
0.739538 | − | 0.673114i | \(-0.235044\pi\) | |||||||
\(374\) | −6.00000 | −0.310253 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.00000 | 0.360997 | ||||||||
\(377\) | − | 20.0000i | − | 1.03005i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | 10.0000 | + | 5.00000i | 0.512989 | + | 0.256495i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 20.0000i | − | 1.02329i | ||||||
\(383\) | 21.0000i | 1.07305i | 0.843884 | + | 0.536525i | \(0.180263\pi\) | ||||
−0.843884 | + | 0.536525i | \(0.819737\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | − | 6.00000i | − | 0.304997i | ||||||
\(388\) | − | 12.0000i | − | 0.609208i | ||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.0000 | −0.708010 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.00000 | 0.251896 | ||||||||
\(395\) | −28.0000 | − | 14.0000i | −1.40883 | − | 0.704416i | ||||
\(396\) | −9.00000 | −0.452267 | ||||||||
\(397\) | 14.0000i | 0.702640i | 0.936255 | + | 0.351320i | \(0.114267\pi\) | ||||
−0.936255 | + | 0.351320i | \(0.885733\pi\) | |||||||
\(398\) | 18.0000i | 0.902258i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | −15.0000 | −0.749064 | −0.374532 | − | 0.927214i | \(-0.622197\pi\) | ||||
−0.374532 | + | 0.927214i | \(0.622197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 10.0000i | − | 0.498135i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | + | 9.00000i | 0.894427 | + | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.0000 | −0.692255 | −0.346128 | − | 0.938187i | \(-0.612504\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 3.00000 | − | 6.00000i | 0.148159 | − | 0.296319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.00000i | 0.394132i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −21.0000 | −1.03209 | ||||||||
\(415\) | 6.00000 | − | 12.0000i | 0.294528 | − | 0.589057i | ||||
\(416\) | 5.00000 | 0.245145 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 15.0000i | − | 0.733674i | ||||||
\(419\) | 35.0000 | 1.70986 | 0.854931 | − | 0.518742i | \(-0.173599\pi\) | ||||
0.854931 | + | 0.518742i | \(0.173599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | − | 9.00000i | − | 0.438113i | ||||||
\(423\) | 21.0000i | 1.02105i | ||||||||
\(424\) | −9.00000 | −0.437079 | ||||||||
\(425\) | −8.00000 | + | 6.00000i | −0.388057 | + | 0.291043i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 16.0000i | 0.773389i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.00000 | + | 2.00000i | 0.192897 | + | 0.0964486i | ||||
\(431\) | 2.00000 | 0.0963366 | 0.0481683 | − | 0.998839i | \(-0.484662\pi\) | ||||
0.0481683 | + | 0.998839i | \(0.484662\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.0000i | 1.34559i | 0.739827 | + | 0.672797i | \(0.234907\pi\) | ||||
−0.739827 | + | 0.672797i | \(0.765093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − | 35.0000i | − | 1.67428i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.0000 | −1.33637 | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||||
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(440\) | 3.00000 | − | 6.00000i | 0.143019 | − | 0.286039i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10.0000i | 0.475651i | ||||||||
\(443\) | − | 30.0000i | − | 1.42534i | −0.701498 | − | 0.712672i | \(-0.747485\pi\) | ||
0.701498 | − | 0.712672i | \(-0.252515\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00000 | + | 2.00000i | 0.189618 | + | 0.0948091i | ||||
\(446\) | 8.00000 | 0.378811 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.00000 | −0.235965 | −0.117982 | − | 0.993016i | \(-0.537643\pi\) | ||||
−0.117982 | + | 0.993016i | \(0.537643\pi\) | |||||||
\(450\) | −12.0000 | + | 9.00000i | −0.565685 | + | 0.424264i | ||||
\(451\) | −9.00000 | −0.423793 | ||||||||
\(452\) | 14.0000i | 0.658505i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.00000 | −0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.0000i | − | 0.467780i | −0.972263 | − | 0.233890i | \(-0.924854\pi\) | ||
0.972263 | − | 0.233890i | \(-0.0751456\pi\) | |||||||
\(458\) | 16.0000i | 0.747631i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.00000 | − | 14.0000i | 0.326377 | − | 0.652753i | ||||
\(461\) | 32.0000 | 1.49039 | 0.745194 | − | 0.666847i | \(-0.232357\pi\) | ||||
0.745194 | + | 0.666847i | \(0.232357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000i | 0.790057i | 0.918669 | + | 0.395029i | \(0.129265\pi\) | ||||
−0.918669 | + | 0.395029i | \(0.870735\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.00000 | −0.370593 | ||||||||
\(467\) | − | 34.0000i | − | 1.57333i | −0.617379 | − | 0.786666i | \(-0.711805\pi\) | ||
0.617379 | − | 0.786666i | \(-0.288195\pi\) | |||||||
\(468\) | 15.0000i | 0.693375i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −14.0000 | − | 7.00000i | −0.645772 | − | 0.322886i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.00000i | 0.184115i | ||||||||
\(473\) | − | 6.00000i | − | 0.275880i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | − | 20.0000i | −0.688247 | − | 0.917663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 27.0000i | − | 1.23625i | ||||||
\(478\) | − | 20.0000i | − | 0.914779i | ||||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | 0.227980 | ||||||||
\(482\) | 9.00000i | 0.409939i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | −12.0000 | + | 24.0000i | −0.544892 | + | 1.08978i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 32.0000i | − | 1.45006i | −0.688718 | − | 0.725029i | \(-0.741826\pi\) | ||
0.688718 | − | 0.725029i | \(-0.258174\pi\) | |||||||
\(488\) | 6.00000i | 0.271607i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0000 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.00000i | 0.360302i | ||||||||
\(494\) | −25.0000 | −1.12480 | ||||||||
\(495\) | 18.0000 | + | 9.00000i | 0.809040 | + | 0.404520i | ||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 5.00000i | − | 0.223161i | ||||||
\(503\) | 40.0000i | 1.78351i | 0.452517 | + | 0.891756i | \(0.350526\pi\) | ||||
−0.452517 | + | 0.891756i | \(0.649474\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −21.0000 | −0.933564 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 7.00000i | − | 0.310575i | ||||||
\(509\) | −34.0000 | −1.50702 | −0.753512 | − | 0.657434i | \(-0.771642\pi\) | ||||
−0.753512 | + | 0.657434i | \(0.771642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | 8.00000 | − | 16.0000i | 0.352522 | − | 0.705044i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 21.0000i | 0.923579i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.0000 | − | 5.00000i | −0.438529 | − | 0.219265i | ||||
\(521\) | 27.0000 | 1.18289 | 0.591446 | − | 0.806345i | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | 12.0000i | 0.525226i | ||||||||
\(523\) | 16.0000i | 0.699631i | 0.936819 | + | 0.349816i | \(0.113756\pi\) | ||||
−0.936819 | + | 0.349816i | \(0.886244\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.00000i | 0.174243i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −26.0000 | −1.13043 | ||||||||
\(530\) | 18.0000 | + | 9.00000i | 0.781870 | + | 0.390935i | ||||
\(531\) | −12.0000 | −0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0000i | 0.649722i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.0000 | − | 32.0000i | 0.691740 | − | 1.38348i | ||||
\(536\) | 2.00000 | 0.0863868 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 10.0000i | − | 0.431131i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0000 | −0.687894 | −0.343947 | − | 0.938989i | \(-0.611764\pi\) | ||||
−0.343947 | + | 0.938989i | \(0.611764\pi\) | |||||||
\(542\) | − | 24.0000i | − | 1.03089i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.00000 | −0.0857493 | ||||||||
\(545\) | −4.00000 | − | 2.00000i | −0.171341 | − | 0.0856706i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.0000i | − | 1.11168i | −0.831289 | − | 0.555840i | \(-0.812397\pi\) | ||
0.831289 | − | 0.555840i | \(-0.187603\pi\) | |||||||
\(548\) | 8.00000i | 0.341743i | ||||||||
\(549\) | −18.0000 | −0.768221 | ||||||||
\(550\) | −12.0000 | + | 9.00000i | −0.511682 | + | 0.383761i | ||||
\(551\) | −20.0000 | −0.852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.0000 | −0.678551 | ||||||||
\(557\) | 23.0000i | 0.974541i | 0.873251 | + | 0.487271i | \(0.162007\pi\) | ||||
−0.873251 | + | 0.487271i | \(0.837993\pi\) | |||||||
\(558\) | 6.00000i | 0.254000i | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000i | 0.379642i | ||||||||
\(563\) | 2.00000i | 0.0842900i | 0.999112 | + | 0.0421450i | \(0.0134191\pi\) | ||||
−0.999112 | + | 0.0421450i | \(0.986581\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0000 | − | 28.0000i | 0.588984 | − | 1.17797i | ||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | 15.0000 | 0.628833 | 0.314416 | − | 0.949285i | \(-0.398191\pi\) | ||||
0.314416 | + | 0.949285i | \(0.398191\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 15.0000i | 0.627182i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.0000 | + | 21.0000i | −1.16768 | + | 0.875761i | ||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 4.00000i | 0.166522i | 0.996528 | + | 0.0832611i | \(0.0265335\pi\) | ||||
−0.996528 | + | 0.0832611i | \(0.973466\pi\) | |||||||
\(578\) | 13.0000i | 0.540729i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −8.00000 | − | 4.00000i | −0.332182 | − | 0.166091i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.0000i | − | 1.11823i | ||||||
\(584\) | −16.0000 | −0.662085 | ||||||||
\(585\) | 15.0000 | − | 30.0000i | 0.620174 | − | 1.24035i | ||||
\(586\) | 9.00000 | 0.371787 | ||||||||
\(587\) | − | 34.0000i | − | 1.40333i | −0.712507 | − | 0.701665i | \(-0.752440\pi\) | ||
0.712507 | − | 0.701665i | \(-0.247560\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0000 | −0.412043 | ||||||||
\(590\) | 4.00000 | − | 8.00000i | 0.164677 | − | 0.329355i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000i | 0.0410997i | ||||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 35.0000i | 1.43126i | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | 6.00000 | 0.244137 | ||||||||
\(605\) | −4.00000 | − | 2.00000i | −0.162623 | − | 0.0813116i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.0000i | 0.527654i | 0.964570 | + | 0.263827i | \(0.0849848\pi\) | ||||
−0.964570 | + | 0.263827i | \(0.915015\pi\) | |||||||
\(608\) | − | 5.00000i | − | 0.202777i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6.00000 | − | 12.0000i | 0.242933 | − | 0.485866i | ||||
\(611\) | 35.0000 | 1.41595 | ||||||||
\(612\) | − | 6.00000i | − | 0.242536i | ||||||
\(613\) | 15.0000i | 0.605844i | 0.953015 | + | 0.302922i | \(0.0979622\pi\) | ||||
−0.953015 | + | 0.302922i | \(0.902038\pi\) | |||||||
\(614\) | −22.0000 | −0.887848 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.0000i | 0.563619i | 0.959470 | + | 0.281809i | \(0.0909346\pi\) | ||||
−0.959470 | + | 0.281809i | \(0.909065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0000 | 0.763674 | 0.381837 | − | 0.924230i | \(-0.375291\pi\) | ||||
0.381837 | + | 0.924230i | \(0.375291\pi\) | |||||||
\(620\) | −4.00000 | − | 2.00000i | −0.160644 | − | 0.0803219i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 6.00000i | − | 0.240578i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 22.0000 | 0.879297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 9.00000i | − | 0.359139i | ||||||
\(629\) | −2.00000 | −0.0797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | 14.0000i | 0.556890i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | −7.00000 | + | 14.0000i | −0.277787 | + | 0.555573i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | −18.0000 | −0.712069 | ||||||||
\(640\) | 1.00000 | − | 2.00000i | 0.0395285 | − | 0.0790569i | ||||
\(641\) | −5.00000 | −0.197488 | −0.0987441 | − | 0.995113i | \(-0.531483\pi\) | ||||
−0.0987441 | + | 0.995113i | \(0.531483\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.0000i | − | 0.552106i | −0.961142 | − | 0.276053i | \(-0.910973\pi\) | ||
0.961142 | − | 0.276053i | \(-0.0890266\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.0000 | 0.393445 | ||||||||
\(647\) | 27.0000i | 1.06148i | 0.847535 | + | 0.530740i | \(0.178086\pi\) | ||||
−0.847535 | + | 0.530740i | \(0.821914\pi\) | |||||||
\(648\) | − | 9.00000i | − | 0.353553i | ||||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | 15.0000 | + | 20.0000i | 0.588348 | + | 0.784465i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 12.0000i | − | 0.469956i | ||||||
\(653\) | − | 3.00000i | − | 0.117399i | −0.998276 | − | 0.0586995i | \(-0.981305\pi\) | ||
0.998276 | − | 0.0586995i | \(-0.0186954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00000 | + | 1.00000i | 0.0781465 | + | 0.0390732i | ||||
\(656\) | −3.00000 | −0.117130 | ||||||||
\(657\) | − | 48.0000i | − | 1.87266i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.0000 | 1.40236 | 0.701180 | − | 0.712984i | \(-0.252657\pi\) | ||||
0.701180 | + | 0.712984i | \(0.252657\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | −0.622328 | −0.311164 | − | 0.950356i | \(-0.600719\pi\) | ||||
−0.311164 | + | 0.950356i | \(0.600719\pi\) | |||||||
\(662\) | 5.00000i | 0.194331i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.00000 | −0.116248 | ||||||||
\(667\) | 28.0000i | 1.08416i | ||||||||
\(668\) | 15.0000i | 0.580367i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.00000 | − | 2.00000i | −0.154533 | − | 0.0772667i | ||||
\(671\) | −18.0000 | −0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 32.0000i | − | 1.23351i | −0.787155 | − | 0.616755i | \(-0.788447\pi\) | ||
0.787155 | − | 0.616755i | \(-0.211553\pi\) | |||||||
\(674\) | −10.0000 | −0.385186 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.0000 | 0.461538 | ||||||||
\(677\) | 17.0000i | 0.653363i | 0.945134 | + | 0.326682i | \(0.105930\pi\) | ||||
−0.945134 | + | 0.326682i | \(0.894070\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | + | 2.00000i | 0.153393 | + | 0.0766965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000i | 0.229752i | ||||||||
\(683\) | 44.0000i | 1.68361i | 0.539779 | + | 0.841807i | \(0.318508\pi\) | ||||
−0.539779 | + | 0.841807i | \(0.681492\pi\) | |||||||
\(684\) | 15.0000 | 0.573539 | ||||||||
\(685\) | 8.00000 | − | 16.0000i | 0.305664 | − | 0.611329i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 2.00000i | − | 0.0762493i | ||||||
\(689\) | −45.0000 | −1.71436 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | − | 9.00000i | − | 0.342129i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 32.0000 | + | 16.0000i | 1.21383 | + | 0.606915i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 6.00000i | − | 0.227266i | ||||||
\(698\) | − | 12.0000i | − | 0.454207i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.00000i | − | 0.188579i | ||||||
\(704\) | −3.00000 | −0.113067 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.0000 | −0.450669 | −0.225335 | − | 0.974281i | \(-0.572348\pi\) | ||||
−0.225335 | + | 0.974281i | \(0.572348\pi\) | |||||||
\(710\) | 6.00000 | − | 12.0000i | 0.225176 | − | 0.450352i | ||||
\(711\) | −42.0000 | −1.57512 | ||||||||
\(712\) | − | 2.00000i | − | 0.0749532i | ||||||
\(713\) | 14.0000i | 0.524304i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.0000 | − | 30.0000i | 0.560968 | − | 1.12194i | ||||
\(716\) | 13.0000 | 0.485833 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 16.0000i | − | 0.597115i | ||||||
\(719\) | 26.0000 | 0.969636 | 0.484818 | − | 0.874615i | \(-0.338886\pi\) | ||||
0.484818 | + | 0.874615i | \(0.338886\pi\) | |||||||
\(720\) | 6.00000 | + | 3.00000i | 0.223607 | + | 0.111803i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 6.00000i | 0.223297i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.0000 | 0.966282 | ||||||||
\(725\) | 12.0000 | + | 16.0000i | 0.445669 | + | 0.594225i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.0000i | 1.07555i | 0.843088 | + | 0.537775i | \(0.180735\pi\) | ||||
−0.843088 | + | 0.537775i | \(0.819265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 32.0000 | + | 16.0000i | 1.18437 | + | 0.592187i | ||||
\(731\) | 4.00000 | 0.147945 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.0000i | 1.51437i | 0.653201 | + | 0.757185i | \(0.273426\pi\) | ||||
−0.653201 | + | 0.757185i | \(0.726574\pi\) | |||||||
\(734\) | 13.0000 | 0.479839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.00000 | −0.258023 | ||||||||
\(737\) | 6.00000i | 0.221013i | ||||||||
\(738\) | − | 9.00000i | − | 0.331295i | ||||||
\(739\) | 29.0000 | 1.06678 | 0.533391 | − | 0.845869i | \(-0.320917\pi\) | ||||
0.533391 | + | 0.845869i | \(0.320917\pi\) | |||||||
\(740\) | 1.00000 | − | 2.00000i | 0.0367607 | − | 0.0735215i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.0000i | 0.770415i | 0.922830 | + | 0.385208i | \(0.125870\pi\) | ||||
−0.922830 | + | 0.385208i | \(0.874130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.0000 | + | 18.0000i | 1.31894 | + | 0.659469i | ||||
\(746\) | 26.0000 | 0.951928 | ||||||||
\(747\) | − | 18.0000i | − | 0.658586i | ||||||
\(748\) | − | 6.00000i | − | 0.219382i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.0000 | 1.02173 | 0.510867 | − | 0.859660i | \(-0.329324\pi\) | ||||
0.510867 | + | 0.859660i | \(0.329324\pi\) | |||||||
\(752\) | 7.00000i | 0.255264i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.0000 | 0.728357 | ||||||||
\(755\) | −12.0000 | − | 6.00000i | −0.436725 | − | 0.218362i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000i | 1.52652i | 0.646094 | + | 0.763258i | \(0.276401\pi\) | ||||
−0.646094 | + | 0.763258i | \(0.723599\pi\) | |||||||
\(758\) | 29.0000i | 1.05333i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.00000 | + | 10.0000i | −0.181369 | + | 0.362738i | ||||
\(761\) | −1.00000 | −0.0362500 | −0.0181250 | − | 0.999836i | \(-0.505770\pi\) | ||||
−0.0181250 | + | 0.999836i | \(0.505770\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 20.0000 | 0.723575 | ||||||||
\(765\) | −6.00000 | + | 12.0000i | −0.216930 | + | 0.433861i | ||||
\(766\) | −21.0000 | −0.758761 | ||||||||
\(767\) | 20.0000i | 0.722158i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.0000 | −1.04577 | −0.522883 | − | 0.852404i | \(-0.675144\pi\) | ||||
−0.522883 | + | 0.852404i | \(0.675144\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 10.0000i | − | 0.359908i | ||||||
\(773\) | 45.0000i | 1.61854i | 0.587439 | + | 0.809269i | \(0.300136\pi\) | ||||
−0.587439 | + | 0.809269i | \(0.699864\pi\) | |||||||
\(774\) | 6.00000 | 0.215666 | ||||||||
\(775\) | 6.00000 | + | 8.00000i | 0.215526 | + | 0.287368i | ||||
\(776\) | 12.0000 | 0.430775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000i | 0.215110i | ||||||||
\(779\) | 15.0000 | 0.537431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | − | 14.0000i | − | 0.500639i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.00000 | + | 18.0000i | −0.321224 | + | 0.642448i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 18.0000i | − | 0.641631i | −0.947142 | − | 0.320815i | \(-0.896043\pi\) | ||
0.947142 | − | 0.320815i | \(-0.103957\pi\) | |||||||
\(788\) | 5.00000i | 0.178118i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.0000 | − | 28.0000i | 0.498098 | − | 0.996195i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 9.00000i | − | 0.319801i | ||||||
\(793\) | 30.0000i | 1.06533i | ||||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0000 | −0.637993 | ||||||||
\(797\) | 2.00000i | 0.0708436i | 0.999372 | + | 0.0354218i | \(0.0112775\pi\) | ||||
−0.999372 | + | 0.0354218i | \(0.988723\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.0000 | −0.495284 | ||||||||
\(800\) | −4.00000 | + | 3.00000i | −0.141421 | + | 0.106066i | ||||
\(801\) | 6.00000 | 0.212000 | ||||||||
\(802\) | − | 15.0000i | − | 0.529668i | ||||||
\(803\) | − | 48.0000i | − | 1.69388i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 10.0000 | 0.352235 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.00000 | 0.175791 | 0.0878953 | − | 0.996130i | \(-0.471986\pi\) | ||||
0.0878953 | + | 0.996130i | \(0.471986\pi\) | |||||||
\(810\) | −9.00000 | + | 18.0000i | −0.316228 | + | 0.632456i | ||||
\(811\) | 33.0000 | 1.15879 | 0.579393 | − | 0.815048i | \(-0.303290\pi\) | ||||
0.579393 | + | 0.815048i | \(0.303290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00000 | −0.105150 | ||||||||
\(815\) | −12.0000 | + | 24.0000i | −0.420342 | + | 0.840683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0000i | 0.349856i | ||||||||
\(818\) | − | 14.0000i | − | 0.489499i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | + | 3.00000i | 0.209529 | + | 0.104765i | ||||
\(821\) | −18.0000 | −0.628204 | −0.314102 | − | 0.949389i | \(-0.601703\pi\) | ||||
−0.314102 | + | 0.949389i | \(0.601703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000i | 0.836587i | 0.908312 | + | 0.418294i | \(0.137372\pi\) | ||||
−0.908312 | + | 0.418294i | \(0.862628\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.0000i | − | 0.765015i | −0.923952 | − | 0.382507i | \(-0.875061\pi\) | ||
0.923952 | − | 0.382507i | \(-0.124939\pi\) | |||||||
\(828\) | − | 21.0000i | − | 0.729800i | ||||||
\(829\) | −26.0000 | −0.903017 | −0.451509 | − | 0.892267i | \(-0.649114\pi\) | ||||
−0.451509 | + | 0.892267i | \(0.649114\pi\) | |||||||
\(830\) | 12.0000 | + | 6.00000i | 0.416526 | + | 0.208263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.00000i | 0.173344i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.0000 | − | 30.0000i | 0.519096 | − | 1.03819i | ||||
\(836\) | 15.0000 | 0.518786 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35.0000i | 1.20905i | ||||||||
\(839\) | −34.0000 | −1.17381 | −0.586905 | − | 0.809656i | \(-0.699654\pi\) | ||||
−0.586905 | + | 0.809656i | \(0.699654\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | − | 20.0000i | − | 0.689246i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.00000 | 0.309793 | ||||||||
\(845\) | −24.0000 | − | 12.0000i | −0.825625 | − | 0.412813i | ||||
\(846\) | −21.0000 | −0.721995 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 9.00000i | − | 0.309061i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.00000 | − | 8.00000i | −0.205798 | − | 0.274398i | ||||
\(851\) | −7.00000 | −0.239957 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 43.0000i | − | 1.47229i | −0.676823 | − | 0.736146i | \(-0.736644\pi\) | ||
0.676823 | − | 0.736146i | \(-0.263356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30.0000 | − | 15.0000i | −1.02598 | − | 0.512989i | ||||
\(856\) | −16.0000 | −0.546869 | ||||||||
\(857\) | − | 8.00000i | − | 0.273275i | −0.990621 | − | 0.136637i | \(-0.956370\pi\) | ||
0.990621 | − | 0.136637i | \(-0.0436295\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | −2.00000 | + | 4.00000i | −0.0681994 | + | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.00000i | 0.0681203i | ||||||||
\(863\) | 11.0000i | 0.374444i | 0.982318 | + | 0.187222i | \(0.0599484\pi\) | ||||
−0.982318 | + | 0.187222i | \(0.940052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.00000 | + | 18.0000i | −0.306009 | + | 0.612018i | ||||
\(866\) | −28.0000 | −0.951479 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −42.0000 | −1.42475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0000 | 0.338837 | ||||||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | 36.0000i | 1.21842i | ||||||||
\(874\) | 35.0000 | 1.18389 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.0000i | 1.04680i | 0.852088 | + | 0.523398i | \(0.175336\pi\) | ||||
−0.852088 | + | 0.523398i | \(0.824664\pi\) | |||||||
\(878\) | − | 28.0000i | − | 0.944954i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.00000 | + | 3.00000i | 0.202260 | + | 0.101130i | ||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.0000i | − | 0.538443i | −0.963078 | − | 0.269221i | \(-0.913234\pi\) | ||
0.963078 | − | 0.269221i | \(-0.0867663\pi\) | |||||||
\(884\) | −10.0000 | −0.336336 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.0000 | 1.00787 | ||||||||
\(887\) | − | 36.0000i | − | 1.20876i | −0.796696 | − | 0.604381i | \(-0.793421\pi\) | ||
0.796696 | − | 0.604381i | \(-0.206579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.00000 | + | 4.00000i | −0.0670402 | + | 0.134080i | ||||
\(891\) | 27.0000 | 0.904534 | ||||||||
\(892\) | 8.00000i | 0.267860i | ||||||||
\(893\) | − | 35.0000i | − | 1.17123i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.0000 | − | 13.0000i | −0.869084 | − | 0.434542i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 5.00000i | − | 0.166852i | ||||||
\(899\) | 8.00000 | 0.266815 | ||||||||
\(900\) | −9.00000 | − | 12.0000i | −0.300000 | − | 0.400000i | ||||
\(901\) | 18.0000 | 0.599667 | ||||||||
\(902\) | − | 9.00000i | − | 0.299667i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | −52.0000 | − | 26.0000i | −1.72854 | − | 0.864269i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 40.0000i | − | 1.32818i | −0.747653 | − | 0.664089i | \(-0.768820\pi\) | ||
0.747653 | − | 0.664089i | \(-0.231180\pi\) | |||||||
\(908\) | − | 6.00000i | − | 0.199117i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.00000 | 0.0662630 | 0.0331315 | − | 0.999451i | \(-0.489452\pi\) | ||||
0.0331315 | + | 0.999451i | \(0.489452\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.0000i | − | 0.595713i | ||||||
\(914\) | 10.0000 | 0.330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.0000 | −0.528655 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0000 | −0.659739 | −0.329870 | − | 0.944027i | \(-0.607005\pi\) | ||||
−0.329870 | + | 0.944027i | \(0.607005\pi\) | |||||||
\(920\) | 14.0000 | + | 7.00000i | 0.461566 | + | 0.230783i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.0000i | 1.05386i | ||||||||
\(923\) | 30.0000i | 0.987462i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | + | 3.00000i | −0.131519 | + | 0.0986394i | ||||
\(926\) | −17.0000 | −0.558655 | ||||||||
\(927\) | − | 24.0000i | − | 0.788263i | ||||||
\(928\) | 4.00000i | 0.131306i | ||||||||
\(929\) | 21.0000 | 0.688988 | 0.344494 | − | 0.938789i | \(-0.388051\pi\) | ||||
0.344494 | + | 0.938789i | \(0.388051\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 8.00000i | − | 0.262049i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.0000 | 1.11251 | ||||||||
\(935\) | −6.00000 | + | 12.0000i | −0.196221 | + | 0.392442i | ||||
\(936\) | −15.0000 | −0.490290 | ||||||||
\(937\) | 26.0000i | 0.849383i | 0.905338 | + | 0.424691i | \(0.139617\pi\) | ||||
−0.905338 | + | 0.424691i | \(0.860383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.00000 | − | 14.0000i | 0.228315 | − | 0.456630i | ||||
\(941\) | 28.0000 | 0.912774 | 0.456387 | − | 0.889781i | \(-0.349143\pi\) | ||||
0.456387 | + | 0.889781i | \(0.349143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 21.0000i | − | 0.683854i | ||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80.0000 | −2.59691 | ||||||||
\(950\) | 20.0000 | − | 15.0000i | 0.648886 | − | 0.486664i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 27.0000 | 0.874157 | ||||||||
\(955\) | −40.0000 | − | 20.0000i | −1.29437 | − | 0.647185i | ||||
\(956\) | 20.0000 | 0.646846 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 36.0000i | 1.16311i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 5.00000i | 0.161206i | ||||||||
\(963\) | − | 48.0000i | − | 1.54678i | ||||||
\(964\) | −9.00000 | −0.289870 | ||||||||
\(965\) | −10.0000 | + | 20.0000i | −0.321911 | + | 0.643823i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.0000i | 1.02905i | 0.857475 | + | 0.514525i | \(0.172032\pi\) | ||||
−0.857475 | + | 0.514525i | \(0.827968\pi\) | |||||||
\(968\) | 2.00000i | 0.0642824i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.0000 | − | 12.0000i | −0.770594 | − | 0.385297i | ||||
\(971\) | 33.0000 | 1.05902 | 0.529510 | − | 0.848304i | \(-0.322376\pi\) | ||||
0.529510 | + | 0.848304i | \(0.322376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 32.0000 | 1.02535 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | 54.0000i | 1.72761i | 0.503824 | + | 0.863807i | \(0.331926\pi\) | ||||
−0.503824 | + | 0.863807i | \(0.668074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.00000 | −0.191565 | ||||||||
\(982\) | 24.0000i | 0.765871i | ||||||||
\(983\) | − | 29.0000i | − | 0.924956i | −0.886631 | − | 0.462478i | \(-0.846960\pi\) | ||
0.886631 | − | 0.462478i | \(-0.153040\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.00000 | − | 10.0000i | 0.159313 | − | 0.318626i | ||||
\(986\) | −8.00000 | −0.254772 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 25.0000i | − | 0.795356i | ||||||
\(989\) | 14.0000 | 0.445174 | ||||||||
\(990\) | −9.00000 | + | 18.0000i | −0.286039 | + | 0.572078i | ||||
\(991\) | −8.00000 | −0.254128 | −0.127064 | − | 0.991894i | \(-0.540555\pi\) | ||||
−0.127064 | + | 0.991894i | \(0.540555\pi\) | |||||||
\(992\) | 2.00000i | 0.0635001i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | + | 18.0000i | 1.14128 | + | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0000i | 1.20347i | 0.798695 | + | 0.601736i | \(0.205524\pi\) | ||||
−0.798695 | + | 0.601736i | \(0.794476\pi\) | |||||||
\(998\) | − | 4.00000i | − | 0.126618i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 490.2.c.d.99.2 | 2 | ||
5.2 | odd | 4 | 2450.2.a.j.1.1 | 1 | |||
5.3 | odd | 4 | 2450.2.a.bb.1.1 | 1 | |||
5.4 | even | 2 | inner | 490.2.c.d.99.1 | 2 | ||
7.2 | even | 3 | 490.2.i.a.459.2 | 4 | |||
7.3 | odd | 6 | 70.2.i.b.9.1 | ✓ | 4 | ||
7.4 | even | 3 | 490.2.i.a.79.1 | 4 | |||
7.5 | odd | 6 | 70.2.i.b.39.2 | yes | 4 | ||
7.6 | odd | 2 | 490.2.c.a.99.2 | 2 | |||
21.5 | even | 6 | 630.2.u.a.109.1 | 4 | |||
21.17 | even | 6 | 630.2.u.a.289.2 | 4 | |||
28.3 | even | 6 | 560.2.bw.d.289.2 | 4 | |||
28.19 | even | 6 | 560.2.bw.d.529.1 | 4 | |||
35.3 | even | 12 | 350.2.e.c.51.1 | 2 | |||
35.4 | even | 6 | 490.2.i.a.79.2 | 4 | |||
35.9 | even | 6 | 490.2.i.a.459.1 | 4 | |||
35.12 | even | 12 | 350.2.e.j.151.1 | 2 | |||
35.13 | even | 4 | 2450.2.a.ba.1.1 | 1 | |||
35.17 | even | 12 | 350.2.e.j.51.1 | 2 | |||
35.19 | odd | 6 | 70.2.i.b.39.1 | yes | 4 | ||
35.24 | odd | 6 | 70.2.i.b.9.2 | yes | 4 | ||
35.27 | even | 4 | 2450.2.a.k.1.1 | 1 | |||
35.33 | even | 12 | 350.2.e.c.151.1 | 2 | |||
35.34 | odd | 2 | 490.2.c.a.99.1 | 2 | |||
105.59 | even | 6 | 630.2.u.a.289.1 | 4 | |||
105.89 | even | 6 | 630.2.u.a.109.2 | 4 | |||
140.19 | even | 6 | 560.2.bw.d.529.2 | 4 | |||
140.59 | even | 6 | 560.2.bw.d.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.i.b.9.1 | ✓ | 4 | 7.3 | odd | 6 | ||
70.2.i.b.9.2 | yes | 4 | 35.24 | odd | 6 | ||
70.2.i.b.39.1 | yes | 4 | 35.19 | odd | 6 | ||
70.2.i.b.39.2 | yes | 4 | 7.5 | odd | 6 | ||
350.2.e.c.51.1 | 2 | 35.3 | even | 12 | |||
350.2.e.c.151.1 | 2 | 35.33 | even | 12 | |||
350.2.e.j.51.1 | 2 | 35.17 | even | 12 | |||
350.2.e.j.151.1 | 2 | 35.12 | even | 12 | |||
490.2.c.a.99.1 | 2 | 35.34 | odd | 2 | |||
490.2.c.a.99.2 | 2 | 7.6 | odd | 2 | |||
490.2.c.d.99.1 | 2 | 5.4 | even | 2 | inner | ||
490.2.c.d.99.2 | 2 | 1.1 | even | 1 | trivial | ||
490.2.i.a.79.1 | 4 | 7.4 | even | 3 | |||
490.2.i.a.79.2 | 4 | 35.4 | even | 6 | |||
490.2.i.a.459.1 | 4 | 35.9 | even | 6 | |||
490.2.i.a.459.2 | 4 | 7.2 | even | 3 | |||
560.2.bw.d.289.1 | 4 | 140.59 | even | 6 | |||
560.2.bw.d.289.2 | 4 | 28.3 | even | 6 | |||
560.2.bw.d.529.1 | 4 | 28.19 | even | 6 | |||
560.2.bw.d.529.2 | 4 | 140.19 | even | 6 | |||
630.2.u.a.109.1 | 4 | 21.5 | even | 6 | |||
630.2.u.a.109.2 | 4 | 105.89 | even | 6 | |||
630.2.u.a.289.1 | 4 | 105.59 | even | 6 | |||
630.2.u.a.289.2 | 4 | 21.17 | even | 6 | |||
2450.2.a.j.1.1 | 1 | 5.2 | odd | 4 | |||
2450.2.a.k.1.1 | 1 | 35.27 | even | 4 | |||
2450.2.a.ba.1.1 | 1 | 35.13 | even | 4 | |||
2450.2.a.bb.1.1 | 1 | 5.3 | odd | 4 |