Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4600,2,Mod(4049,4600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4600.4049");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4600.e (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: | \(36.7311849298\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 184) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4049.1 | ||
Root | \(-2.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.o.4049.4 |
$q$-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 \(\left(\mathbb{Z}/4600\mathbb{Z}\right)^\times\).
\(n\) | \(1151\) | \(1201\) | \(2301\) | \(2577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.56155i | − 1.47891i | −0.673204 | − | 0.739457i | \(-0.735083\pi\) | ||||
0.673204 | − | 0.739457i | \(-0.264917\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.56155 | −1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.12311 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.56155i | 1.26515i | 0.774500 | + | 0.632574i | \(0.218001\pi\) | ||||
−0.774500 | + | 0.632574i | \(0.781999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.12311i | 0.757464i | 0.925506 | + | 0.378732i | \(0.123640\pi\) | ||||
−0.925506 | + | 0.378732i | \(0.876360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.12311 | −1.17532 | −0.587661 | − | 0.809108i | \(-0.699951\pi\) | ||||
−0.587661 | + | 0.809108i | \(0.699951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845i | 0.276829i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.561553 | 0.104278 | 0.0521389 | − | 0.998640i | \(-0.483396\pi\) | ||||
0.0521389 | + | 0.998640i | \(0.483396\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.56155 | −1.17849 | −0.589245 | − | 0.807955i | \(-0.700575\pi\) | ||||
−0.589245 | + | 0.807955i | \(0.700575\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 13.1231i | − 2.28444i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.24621i | 1.35567i | 0.735215 | + | 0.677834i | \(0.237081\pi\) | ||||
−0.735215 | + | 0.677834i | \(0.762919\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.6847 | 1.87104 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.8078 | 1.68789 | 0.843945 | − | 0.536430i | \(-0.180228\pi\) | ||||
0.843945 | + | 0.536430i | \(0.180228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 8.00000i | − 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 11.6847i | − 1.70438i | −0.523230 | − | 0.852191i | \(-0.675273\pi\) | ||||
0.523230 | − | 0.852191i | \(-0.324727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.00000 | 1.12022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.1231i | 1.73820i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.24621 | 0.813187 | 0.406594 | − | 0.913609i | \(-0.366716\pi\) | ||||
0.406594 | + | 0.913609i | \(0.366716\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2462 | 1.56797 | 0.783983 | − | 0.620782i | \(-0.213185\pi\) | ||||
0.783983 | + | 0.620782i | \(0.213185\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.12311i | 0.625887i | 0.949772 | + | 0.312943i | \(0.101315\pi\) | ||||
−0.949772 | + | 0.312943i | \(0.898685\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.56155 | −0.308375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.43845 | 1.12014 | 0.560069 | − | 0.828446i | \(-0.310775\pi\) | ||||
0.560069 | + | 0.828446i | \(0.310775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 2.31534i | − 0.270990i | −0.990778 | − | 0.135495i | \(-0.956737\pi\) | ||||
0.990778 | − | 0.135495i | \(-0.0432625\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.12311 | 0.576394 | 0.288197 | − | 0.957571i | \(-0.406944\pi\) | ||||
0.288197 | + | 0.957571i | \(0.406944\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 2.24621i | − 0.246554i | −0.992372 | − | 0.123277i | \(-0.960660\pi\) | ||||
0.992372 | − | 0.123277i | \(-0.0393403\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.43845i | − 0.154218i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.3693 | 1.41714 | 0.708572 | − | 0.705638i | \(-0.249340\pi\) | ||||
0.708572 | + | 0.705638i | \(0.249340\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.8078i | 1.74288i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3693i | 1.35745i | 0.734393 | + | 0.678724i | \(0.237467\pi\) | ||||
−0.734393 | + | 0.678724i | \(0.762533\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.2462 | −1.83381 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24621 | −0.422514 | −0.211257 | − | 0.977431i | \(-0.567756\pi\) | ||||
−0.211257 | + | 0.977431i | \(0.567756\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.24621i | 0.221326i | 0.993858 | + | 0.110663i | \(0.0352974\pi\) | ||||
−0.993858 | + | 0.110663i | \(0.964703\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 2.87689i | − 0.278120i | −0.990284 | − | 0.139060i | \(-0.955592\pi\) | ||||
0.990284 | − | 0.139060i | \(-0.0444081\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.87689 | −0.467122 | −0.233561 | − | 0.972342i | \(-0.575038\pi\) | ||||
−0.233561 | + | 0.972342i | \(0.575038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1231 | 2.00492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 11.1231i | − 1.04637i | −0.852218 | − | 0.523187i | \(-0.824743\pi\) | ||||
0.852218 | − | 0.523187i | \(-0.175257\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 16.2462i | − 1.50196i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 27.6847i | − 2.49624i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6847i | 1.03685i | 0.855124 | + | 0.518423i | \(0.173481\pi\) | ||||
−0.855124 | + | 0.518423i | \(0.826519\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −20.4924 | −1.80426 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.6847 | 1.37037 | 0.685187 | − | 0.728367i | \(-0.259720\pi\) | ||||
0.685187 | + | 0.728367i | \(0.259720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 15.1231i | − 1.29205i | −0.763315 | − | 0.646027i | \(-0.776429\pi\) | ||||
0.763315 | − | 0.646027i | \(-0.223571\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6847 | 1.33036 | 0.665178 | − | 0.746685i | \(-0.268356\pi\) | ||||
0.665178 | + | 0.746685i | \(0.268356\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.9309 | −2.52063 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 23.3693i | 1.95424i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 17.9309i | − 1.47891i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.75379 | 0.307522 | 0.153761 | − | 0.988108i | \(-0.450861\pi\) | ||||
0.153761 | + | 0.988108i | \(0.450861\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5616 | −1.18500 | −0.592501 | − | 0.805570i | \(-0.701859\pi\) | ||||
−0.592501 | + | 0.805570i | \(0.701859\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 11.1231i | − 0.899250i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 12.8769i | − 1.02769i | −0.857884 | − | 0.513844i | \(-0.828221\pi\) | ||||
0.857884 | − | 0.513844i | \(-0.171779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.12311 | 0.406289 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.93087i | − 0.777846i | −0.921270 | − | 0.388923i | \(-0.872847\pi\) | ||||
0.921270 | − | 0.388923i | \(-0.127153\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.0000i | 1.23812i | 0.785345 | + | 0.619059i | \(0.212486\pi\) | ||||
−0.785345 | + | 0.619059i | \(0.787514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.80776 | −0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.2462 | 1.39532 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 10.0000i | − 0.760286i | −0.924928 | − | 0.380143i | \(-0.875875\pi\) | ||||
0.924928 | − | 0.380143i | \(-0.124125\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 16.0000i | − 1.20263i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.6847 | 1.17233 | 0.586163 | − | 0.810193i | \(-0.300638\pi\) | ||||
0.586163 | + | 0.810193i | \(0.300638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2462 | 1.50489 | 0.752445 | − | 0.658656i | \(-0.228875\pi\) | ||||
0.752445 | + | 0.658656i | \(0.228875\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 31.3693i | − 2.31889i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.0000i | 1.17004i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.630683 | 0.0456346 | 0.0228173 | − | 0.999740i | \(-0.492736\pi\) | ||||
0.0228173 | + | 0.999740i | \(0.492736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 4.56155i | − 0.328348i | −0.986431 | − | 0.164174i | \(-0.947504\pi\) | ||||
0.986431 | − | 0.164174i | \(-0.0524958\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 11.9309i | − 0.850039i | −0.905184 | − | 0.425020i | \(-0.860267\pi\) | ||||
0.905184 | − | 0.425020i | \(-0.139733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.87689 | −0.203938 | −0.101969 | − | 0.994788i | \(-0.532514\pi\) | ||||
−0.101969 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.1231 | 0.925633 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.56155i | 0.247545i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −26.2462 | −1.81549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 24.1771i | − 1.65659i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.93087 | −0.400771 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2462 | −0.958304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.49242i | 0.300835i | 0.988623 | + | 0.150417i | \(0.0480618\pi\) | ||||
−0.988623 | + | 0.150417i | \(0.951938\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 10.2462i | − 0.680065i | −0.940414 | − | 0.340032i | \(-0.889562\pi\) | ||||
0.940414 | − | 0.340032i | \(-0.110438\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.1231 | −1.52802 | −0.764009 | − | 0.645206i | \(-0.776772\pi\) | ||||
−0.764009 | + | 0.645206i | \(0.776772\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.0540i | 1.37929i | 0.724147 | + | 0.689646i | \(0.242234\pi\) | ||||
−0.724147 | + | 0.689646i | \(0.757766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 13.1231i | − 0.852437i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0540 | 0.715022 | 0.357511 | − | 0.933909i | \(-0.383625\pi\) | ||||
0.357511 | + | 0.933909i | \(0.383625\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.4924 | −1.70653 | −0.853263 | − | 0.521480i | \(-0.825380\pi\) | ||||
−0.853263 | + | 0.521480i | \(0.825380\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2462i | 1.42710i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 23.3693i | − 1.48695i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.75379 | −0.364632 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.2462 | 0.646735 | 0.323368 | − | 0.946273i | \(-0.395185\pi\) | ||||
0.323368 | + | 0.946273i | \(0.395185\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.12311i | − 0.322087i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6847i | 1.10314i | 0.834129 | + | 0.551569i | \(0.185971\pi\) | ||||
−0.834129 | + | 0.551569i | \(0.814029\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 10.8769i | − 0.670698i | −0.942094 | − | 0.335349i | \(-0.891146\pi\) | ||||
0.942094 | − | 0.335349i | \(-0.108854\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 34.2462i | − 2.09583i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −25.6847 | −1.56602 | −0.783011 | − | 0.622008i | \(-0.786317\pi\) | ||||
−0.783011 | + | 0.622008i | \(0.786317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.0000 | 1.45790 | 0.728948 | − | 0.684569i | \(-0.240010\pi\) | ||||
0.728948 | + | 0.684569i | \(0.240010\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.80776i | 0.168702i | 0.996436 | + | 0.0843511i | \(0.0268817\pi\) | ||||
−0.996436 | + | 0.0843511i | \(0.973118\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 23.3693 | 1.39908 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.12311 | −0.186309 | −0.0931544 | − | 0.995652i | \(-0.529695\pi\) | ||||
−0.0931544 | + | 0.995652i | \(0.529695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5.12311i | − 0.304537i | −0.988339 | − | 0.152269i | \(-0.951342\pi\) | ||||
0.988339 | − | 0.152269i | \(-0.0486578\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.24621 | 0.426248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.2462 | 2.00755 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.36932i | 0.547361i | 0.961821 | + | 0.273681i | \(0.0882411\pi\) | ||||
−0.961821 | + | 0.273681i | \(0.911759\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.36932i | 0.427611i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.56155 | 0.263801 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.8769i | 0.624861i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.75379i | 0.100094i | 0.998747 | + | 0.0500470i | \(0.0159371\pi\) | ||||
−0.998747 | + | 0.0500470i | \(0.984063\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.75379 | 0.327322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.43845 | 0.0815669 | 0.0407834 | − | 0.999168i | \(-0.487015\pi\) | ||||
0.0407834 | + | 0.999168i | \(0.487015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.36932i | 0.529585i | 0.964305 | + | 0.264793i | \(0.0853035\pi\) | ||||
−0.964305 | + | 0.264793i | \(0.914697\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.2462i | 1.13714i | 0.822635 | + | 0.568570i | \(0.192503\pi\) | ||||
−0.822635 | + | 0.568570i | \(0.807497\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.87689 | 0.161075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.36932 | −0.411315 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 16.0000i | − 0.890264i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.4924i | 0.690833i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.4233 | −1.67222 | −0.836108 | − | 0.548565i | \(-0.815174\pi\) | ||||
−0.836108 | + | 0.548565i | \(0.815174\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 29.3693i | − 1.60943i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 19.6155i | − 1.06853i | −0.845318 | − | 0.534263i | \(-0.820589\pi\) | ||||
0.845318 | − | 0.534263i | \(-0.179411\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.4924 | −1.54750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −33.6155 | −1.82038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 16.4924i | − 0.885360i | −0.896680 | − | 0.442680i | \(-0.854028\pi\) | ||||
0.896680 | − | 0.442680i | \(-0.145972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.3153 | 1.19451 | 0.597256 | − | 0.802050i | \(-0.296257\pi\) | ||||
0.597256 | + | 0.802050i | \(0.296257\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.56155 | −0.350230 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.4384i | 0.608807i | 0.952543 | + | 0.304404i | \(0.0984571\pi\) | ||||
−0.952543 | + | 0.304404i | \(0.901543\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.6155 | −0.929712 | −0.464856 | − | 0.885386i | \(-0.653894\pi\) | ||||
−0.464856 | + | 0.885386i | \(0.653894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24621 | 0.381380 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 39.0540i | − 2.04980i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 2.24621i | − 0.117251i | −0.998280 | − | 0.0586256i | \(-0.981328\pi\) | ||||
0.998280 | − | 0.0586256i | \(-0.0186718\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −38.4924 | −2.00384 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.4924i | 1.16461i | 0.812969 | + | 0.582307i | \(0.197850\pi\) | ||||
−0.812969 | + | 0.582307i | \(0.802150\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.56155i | 0.131927i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.4924 | −1.05263 | −0.526313 | − | 0.850291i | \(-0.676426\pi\) | ||||
−0.526313 | + | 0.850291i | \(0.676426\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.9309 | 1.53340 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.2462i | 1.34112i | 0.741856 | + | 0.670559i | \(0.233946\pi\) | ||||
−0.741856 | + | 0.670559i | \(0.766054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 28.4924i | 1.44835i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.36932 | −0.0694271 | −0.0347136 | − | 0.999397i | \(-0.511052\pi\) | ||||
−0.0347136 | + | 0.999397i | \(0.511052\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.12311 | 0.157942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 40.1771i | − 2.02667i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 20.5616i | − 1.03195i | −0.856602 | − | 0.515977i | \(-0.827429\pi\) | ||||
0.856602 | − | 0.515977i | \(-0.172571\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.7538 | −0.586956 | −0.293478 | − | 0.955966i | \(-0.594813\pi\) | ||||
−0.293478 | + | 0.955966i | \(0.594813\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 29.9309i | − 1.49096i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.2462i | 2.09407i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.3002 | 1.34991 | 0.674954 | − | 0.737860i | \(-0.264164\pi\) | ||||
0.674954 | + | 0.737860i | \(0.264164\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.7386 | −1.91084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 40.1771i | − 1.96748i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.4924 | 0.610295 | 0.305147 | − | 0.952305i | \(-0.401294\pi\) | ||||
0.305147 | + | 0.952305i | \(0.401294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.1231 | −1.32190 | −0.660950 | − | 0.750430i | \(-0.729846\pi\) | ||||
−0.660950 | + | 0.750430i | \(0.729846\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 41.6155i | 2.02342i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 59.8617 | 2.89015 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.4924 | −1.37243 | −0.686216 | − | 0.727398i | \(-0.740729\pi\) | ||||
−0.686216 | + | 0.727398i | \(0.740729\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7386i | 1.18886i | 0.804146 | + | 0.594431i | \(0.202623\pi\) | ||||
−0.804146 | + | 0.594431i | \(0.797377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.12311i | 0.245071i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.0540 | −0.527577 | −0.263789 | − | 0.964580i | \(-0.584972\pi\) | ||||
−0.263789 | + | 0.964580i | \(0.584972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −24.9309 | −1.18718 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.06913i | − 0.288353i | −0.989552 | − | 0.144177i | \(-0.953947\pi\) | ||||
0.989552 | − | 0.144177i | \(-0.0460533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 9.61553i | − 0.454799i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.24621 | 0.389163 | 0.194581 | − | 0.980886i | \(-0.437665\pi\) | ||||
0.194581 | + | 0.980886i | \(0.437665\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 55.3693 | 2.60724 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 37.3002i | 1.75252i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.36932i | 0.251166i | 0.992083 | + | 0.125583i | \(0.0400801\pi\) | ||||
−0.992083 | + | 0.125583i | \(0.959920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.49242 | −0.209688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.8078 | −0.503368 | −0.251684 | − | 0.967809i | \(-0.580984\pi\) | ||||
−0.251684 | + | 0.967809i | \(0.580984\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.4924i | 0.580572i | 0.956940 | + | 0.290286i | \(0.0937505\pi\) | ||||
−0.956940 | + | 0.290286i | \(0.906250\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.3693i | 0.711207i | 0.934637 | + | 0.355604i | \(0.115725\pi\) | ||||
−0.934637 | + | 0.355604i | \(0.884275\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −32.9848 | −1.51986 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 40.9848i | − 1.88449i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 7.12311i | − 0.326145i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2462 | −0.468161 | −0.234081 | − | 0.972217i | \(-0.575208\pi\) | ||||
−0.234081 | + | 0.972217i | \(0.575208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.6155 | −1.71512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 12.3153i | − 0.558061i | −0.960282 | − | 0.279031i | \(-0.909987\pi\) | ||||
0.960282 | − | 0.279031i | \(-0.0900131\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −25.4384 | −1.15037 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8078 | 0.578006 | 0.289003 | − | 0.957328i | \(-0.406676\pi\) | ||||
0.289003 | + | 0.957328i | \(0.406676\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.75379i | 0.0789867i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0540 | 1.03204 | 0.516019 | − | 0.856577i | \(-0.327413\pi\) | ||||
0.516019 | + | 0.856577i | \(0.327413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 40.9848 | 1.83107 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.36932i | 0.328582i | 0.986412 | + | 0.164291i | \(0.0525335\pi\) | ||||
−0.986412 | + | 0.164291i | \(0.947466\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.0000i | 0.888231i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.3002 | 0.678169 | 0.339084 | − | 0.940756i | \(-0.389883\pi\) | ||||
0.339084 | + | 0.940756i | \(0.389883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 7.36932i | − 0.325363i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 59.8617i | − 2.63272i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.6155 | −1.12440 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.6155 | 0.859372 | 0.429686 | − | 0.902978i | \(-0.358624\pi\) | ||||
0.429686 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.75379i | 0.251596i | 0.992056 | + | 0.125798i | \(0.0401491\pi\) | ||||
−0.992056 | + | 0.125798i | \(0.959851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 20.4924i | − 0.892664i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.2462 | −0.965403 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.3002i | 2.13543i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 40.1771i | − 1.73377i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.8617 | 1.54467 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9309 | 1.54479 | 0.772394 | − | 0.635143i | \(-0.219059\pi\) | ||||
0.772394 | + | 0.635143i | \(0.219059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 51.8617i | − 2.22560i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 43.5464i | − 1.86191i | −0.365135 | − | 0.930955i | \(-0.618977\pi\) | ||||
0.365135 | − | 0.930955i | \(-0.381023\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −43.6155 | −1.86147 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.87689 | −0.122560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.876894i | 0.0371552i | 0.999827 | + | 0.0185776i | \(0.00591378\pi\) | ||||
−0.999827 | + | 0.0185776i | \(0.994086\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.4924 | 1.54347 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.9848 | 1.73038 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.75379i | 0.242493i | 0.992622 | + | 0.121247i | \(0.0386892\pi\) | ||||
−0.992622 | + | 0.121247i | \(0.961311\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.24621 | 0.345699 | 0.172850 | − | 0.984948i | \(-0.444703\pi\) | ||||
0.172850 | + | 0.984948i | \(0.444703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5076 | −0.481577 | −0.240789 | − | 0.970578i | \(-0.577406\pi\) | ||||
−0.240789 | + | 0.970578i | \(0.577406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 1.61553i | − 0.0674897i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 15.9309i | − 0.663211i | −0.943418 | − | 0.331605i | \(-0.892410\pi\) | ||||
0.943418 | − | 0.331605i | \(-0.107590\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.6847 | −0.485598 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2462i | 0.424355i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.0540i | 0.951539i | 0.879570 | + | 0.475770i | \(0.157830\pi\) | ||||
−0.879570 | + | 0.475770i | \(0.842170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.6155 | 1.38510 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.5616 | −1.25713 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 44.7386i | − 1.83720i | −0.395194 | − | 0.918598i | \(-0.629323\pi\) | ||||
0.395194 | − | 0.918598i | \(-0.370677\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.36932i | 0.301606i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −38.8078 | −1.58300 | −0.791501 | − | 0.611168i | \(-0.790700\pi\) | ||||
−0.791501 | + | 0.611168i | \(0.790700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 18.2462i | − 0.743043i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.7386i | 0.598223i | 0.954218 | + | 0.299111i | \(0.0966902\pi\) | ||||
−0.954218 | + | 0.299111i | \(0.903310\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.3002 | 2.15629 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 28.1080i | − 1.13527i | −0.823281 | − | 0.567635i | \(-0.807859\pi\) | ||||
0.823281 | − | 0.567635i | \(-0.192141\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 34.9848i | − 1.40844i | −0.709983 | − | 0.704218i | \(-0.751298\pi\) | ||||
0.709983 | − | 0.704218i | \(-0.248702\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.4924 | −1.14521 | −0.572604 | − | 0.819832i | \(-0.694067\pi\) | ||||
−0.572604 | + | 0.819832i | \(0.694067\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.43845 | 0.0577229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 67.2311i | 2.68495i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.7538 | −1.02687 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.73863 | −0.268261 | −0.134130 | − | 0.990964i | \(-0.542824\pi\) | ||||
−0.134130 | + | 0.990964i | \(0.542824\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.2462i | 0.407250i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.9309i | 1.26515i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −33.6155 | −1.32981 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.3693 | −0.528056 | −0.264028 | − | 0.964515i | \(-0.585051\pi\) | ||||
−0.264028 | + | 0.964515i | \(0.585051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 23.3693i | − 0.921596i | −0.887505 | − | 0.460798i | \(-0.847563\pi\) | ||||
0.887505 | − | 0.460798i | \(-0.152437\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 29.3002i | 1.15191i | 0.817482 | + | 0.575955i | \(0.195370\pi\) | ||||
−0.817482 | + | 0.575955i | \(0.804630\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0000 | 1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0540i | 0.980438i | 0.871599 | + | 0.490219i | \(0.163083\pi\) | ||||
−0.871599 | + | 0.490219i | \(0.836917\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.24621i | 0.321715i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.24621 | −0.0875000 | −0.0437500 | − | 0.999043i | \(-0.513930\pi\) | ||||
−0.0437500 | + | 0.999043i | \(0.513930\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.246211 | −0.00957651 | −0.00478825 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478825 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 36.4924i | 1.41725i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 0.561553i | − 0.0217434i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.5076 | 0.444909 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 62.7386 | 2.42200 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 2.94602i | − 0.113561i | −0.998387 | − | 0.0567805i | \(-0.981916\pi\) | ||||
0.998387 | − | 0.0567805i | \(-0.0180835\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.9848i | 1.49831i | 0.662395 | + | 0.749155i | \(0.269540\pi\) | ||||
−0.662395 | + | 0.749155i | \(0.730460\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.2462 | −1.00576 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.3153i | 0.624289i | 0.950035 | + | 0.312145i | \(0.101047\pi\) | ||||
−0.950035 | + | 0.312145i | \(0.898953\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 59.2311i | 2.25981i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.12311 | −0.347563 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.9848 | 0.798301 | 0.399151 | − | 0.916885i | \(-0.369305\pi\) | ||||
0.399151 | + | 0.916885i | \(0.369305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.7538i | 1.27852i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 53.9309 | 2.03985 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.8617 | 1.12786 | 0.563931 | − | 0.825822i | \(-0.309288\pi\) | ||||
0.563931 | + | 0.825822i | \(0.309288\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 42.2462i | − 1.59335i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.3693 | 1.40343 | 0.701717 | − | 0.712456i | \(-0.252417\pi\) | ||||
0.701717 | + | 0.712456i | \(0.252417\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18.2462 | −0.684286 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.56155i | 0.245732i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 28.3153i | − 1.05746i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.49242 | −0.167539 | −0.0837695 | − | 0.996485i | \(-0.526696\pi\) | ||||
−0.0837695 | + | 0.996485i | \(0.526696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 67.8617i | 2.52381i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.3693i | 1.46013i | 0.683379 | + | 0.730064i | \(0.260510\pi\) | ||||
−0.683379 | + | 0.730064i | \(0.739490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.9848 | 1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.9848 | 0.924098 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.3693i | 1.82350i | 0.410749 | + | 0.911749i | \(0.365267\pi\) | ||||
−0.410749 | + | 0.911749i | \(0.634733\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26.2462i | 0.966792i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.315342 | −0.0116000 | −0.00580001 | − | 0.999983i | \(-0.501846\pi\) | ||||
−0.00580001 | + | 0.999983i | \(0.501846\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −59.8617 | −2.19908 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.2462i | 1.25637i | 0.778063 | + | 0.628186i | \(0.216202\pi\) | ||||
−0.778063 | + | 0.628186i | \(0.783798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.00000i | 0.292705i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.9848 | 1.49556 | 0.747779 | − | 0.663948i | \(-0.231120\pi\) | ||||
0.747779 | + | 0.663948i | \(0.231120\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 26.2462i | − 0.956465i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50758i | 0.0547938i | 0.999625 | + | 0.0273969i | \(0.00872180\pi\) | ||||
−0.999625 | + | 0.0273969i | \(0.991278\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.1231 | −0.476339 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.3153 | −0.663931 | −0.331965 | − | 0.943292i | \(-0.607712\pi\) | ||||
−0.331965 | + | 0.943292i | \(0.607712\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28.4924i | 1.02880i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.00000 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.3002 | 1.63145 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.63068i | 0.0946191i | 0.998880 | + | 0.0473095i | \(0.0150647\pi\) | ||||
−0.998880 | + | 0.0473095i | \(0.984935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −55.3693 | −1.98381 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.3542 | 1.73025 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.807764i | 0.0288671i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.2462i | 0.935576i | 0.883841 | + | 0.467788i | \(0.154949\pi\) | ||||
−0.883841 | + | 0.467788i | \(0.845051\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.8617 | −0.991904 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.8617i | 1.98371i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 12.2462i | − 0.433783i | −0.976196 | − | 0.216892i | \(-0.930408\pi\) | ||||
0.976196 | − | 0.216892i | \(-0.0695918\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.4924 | 1.29101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.6155 | −1.68241 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11.8617i | − 0.418592i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.7926i | 2.31601i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.0000 | −0.914111 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.9309 | 1.19147 | 0.595737 | − | 0.803180i | \(-0.296860\pi\) | ||||
0.595737 | + | 0.803180i | \(0.296860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 61.4773i | − 2.15610i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.9848i | 1.43388i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.7386 | −0.863384 | −0.431692 | − | 0.902021i | \(-0.642083\pi\) | ||||
−0.431692 | + | 0.902021i | \(0.642083\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 49.4384i | 1.72332i | 0.507489 | + | 0.861658i | \(0.330574\pi\) | ||||
−0.507489 | + | 0.861658i | \(0.669426\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 4.49242i | − 0.156217i | −0.996945 | − | 0.0781084i | \(-0.975112\pi\) | ||||
0.996945 | − | 0.0781084i | \(-0.0248880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2462 | 0.703180 | 0.351590 | − | 0.936154i | \(-0.385641\pi\) | ||||
0.351590 | + | 0.936154i | \(0.385641\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.19224 | 0.249496 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.8617i | 0.757464i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 9.43845i | − 0.326240i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −50.2462 | −1.73469 | −0.867346 | − | 0.497706i | \(-0.834176\pi\) | ||||
−0.867346 | + | 0.497706i | \(0.834176\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6847 | −0.989126 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.00000i | 0.275535i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.1231 | −0.450384 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.24621 | 0.282676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 34.9848i | − 1.19786i | −0.800802 | − | 0.598929i | \(-0.795593\pi\) | ||||
0.800802 | − | 0.598929i | \(-0.204407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 16.5616i | − 0.565732i | −0.959159 | − | 0.282866i | \(-0.908715\pi\) | ||||
0.959159 | − | 0.282866i | \(-0.0912852\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.9460 | −0.578191 | −0.289095 | − | 0.957300i | \(-0.593354\pi\) | ||||
−0.289095 | + | 0.957300i | \(0.593354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 8.17708i | − 0.278351i | −0.990268 | − | 0.139176i | \(-0.955555\pi\) | ||||
0.990268 | − | 0.139176i | \(-0.0444452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 18.5616i | − 0.630383i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.2462 | 0.890342 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.3693 | −0.791839 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 47.6155i | − 1.61154i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 30.9848i | − 1.04628i | −0.852246 | − | 0.523142i | \(-0.824760\pi\) | ||||
0.852246 | − | 0.523142i | \(-0.175240\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.0000 | 0.809500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.87689 | 0.164307 | 0.0821534 | − | 0.996620i | \(-0.473820\pi\) | ||||
0.0821534 | + | 0.996620i | \(0.473820\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.9848i | 1.24464i | 0.782763 | + | 0.622320i | \(0.213810\pi\) | ||||
−0.782763 | + | 0.622320i | \(0.786190\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 19.6847i | − 0.660946i | −0.943815 | − | 0.330473i | \(-0.892792\pi\) | ||||
0.943815 | − | 0.330473i | \(-0.107208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −35.8617 | −1.20141 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 59.8617i | 2.00320i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 11.6847i | − 0.390139i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.68466 | −0.122890 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.24621 | −0.208091 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.8769i | − 1.42370i | −0.702330 | − | 0.711852i | \(-0.747857\pi\) | ||||
0.702330 | − | 0.711852i | \(-0.252143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1231 | 0.501602 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.1231 | −1.22994 | −0.614972 | − | 0.788549i | \(-0.710833\pi\) | ||||
−0.614972 | + | 0.788549i | \(0.710833\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 11.5076i | − 0.380845i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.7538 | −1.24538 | −0.622691 | − | 0.782468i | \(-0.713961\pi\) | ||||
−0.622691 | + | 0.782468i | \(0.713961\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.49242 | 0.148030 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 43.0540i | 1.41714i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 8.00000i | − 0.262754i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.8078 | −1.14201 | −0.571003 | − | 0.820948i | \(-0.693445\pi\) | ||||
−0.571003 | + | 0.820948i | \(0.693445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.8617 | −1.17532 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 3.68466i | − 0.120630i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 15.7538i | − 0.514654i | −0.966324 | − | 0.257327i | \(-0.917158\pi\) | ||||
0.966324 | − | 0.257327i | \(-0.0828417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 39.1231 | 1.27538 | 0.637688 | − | 0.770294i | \(-0.279891\pi\) | ||||
0.637688 | + | 0.770294i | \(0.279891\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 10.8078i | − 0.351949i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.56155i | 0.0832393i | 0.999134 | + | 0.0416196i | \(0.0132518\pi\) | ||||
−0.999134 | + | 0.0416196i | \(0.986748\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.5616 | 0.342843 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 51.8617 | 1.68173 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.2462i | 1.43328i | 0.697446 | + | 0.716638i | \(0.254320\pi\) | ||||
−0.697446 | + | 0.716638i | \(0.745680\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 7.36932i | − 0.238216i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0540 | 0.388838 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.2462i | 0.330180i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 35.0540i | − 1.12726i | −0.826027 | − | 0.563630i | \(-0.809404\pi\) | ||||
0.826027 | − | 0.563630i | \(-0.190596\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −40.9848 | −1.31662 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.3693 | 1.00669 | 0.503345 | − | 0.864086i | \(-0.332103\pi\) | ||||
0.503345 | + | 0.864086i | \(0.332103\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 57.2311i | 1.83098i | 0.402337 | + | 0.915492i | \(0.368198\pi\) | ||||
−0.402337 | + | 0.915492i | \(0.631802\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 68.4924 | 2.18903 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.3693 | 0.554560 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.1080i | 0.705134i | 0.935787 | + | 0.352567i | \(0.114691\pi\) | ||||
−0.935787 | + | 0.352567i | \(0.885309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.98485 | 0.285413 | 0.142707 | − | 0.989765i | \(-0.454419\pi\) | ||||
0.142707 | + | 0.989765i | \(0.454419\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 77.9309i | 2.47306i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 14.0000i | − 0.443384i | −0.975117 | − | 0.221692i | \(-0.928842\pi\) | ||||
0.975117 | − | 0.221692i | \(-0.0711580\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.8617 | −0.375289 |
(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 | 4600.2.e.o.4049.1 | 4 | ||
5.2 | odd | 4 | 184.2.a.e.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 4600.2.a.s.1.2 | 2 | |||
5.4 | even | 2 | inner | 4600.2.e.o.4049.4 | 4 | ||
15.2 | even | 4 | 1656.2.a.j.1.1 | 2 | |||
20.3 | even | 4 | 9200.2.a.br.1.1 | 2 | |||
20.7 | even | 4 | 368.2.a.i.1.2 | 2 | |||
35.27 | even | 4 | 9016.2.a.w.1.2 | 2 | |||
40.27 | even | 4 | 1472.2.a.p.1.1 | 2 | |||
40.37 | odd | 4 | 1472.2.a.u.1.2 | 2 | |||
60.47 | odd | 4 | 3312.2.a.t.1.2 | 2 | |||
115.22 | even | 4 | 4232.2.a.o.1.1 | 2 | |||
460.367 | odd | 4 | 8464.2.a.bd.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.a.e.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
368.2.a.i.1.2 | 2 | 20.7 | even | 4 | |||
1472.2.a.p.1.1 | 2 | 40.27 | even | 4 | |||
1472.2.a.u.1.2 | 2 | 40.37 | odd | 4 | |||
1656.2.a.j.1.1 | 2 | 15.2 | even | 4 | |||
3312.2.a.t.1.2 | 2 | 60.47 | odd | 4 | |||
4232.2.a.o.1.1 | 2 | 115.22 | even | 4 | |||
4600.2.a.s.1.2 | 2 | 5.3 | odd | 4 | |||
4600.2.e.o.4049.1 | 4 | 1.1 | even | 1 | trivial | ||
4600.2.e.o.4049.4 | 4 | 5.4 | even | 2 | inner | ||
8464.2.a.bd.1.2 | 2 | 460.367 | odd | 4 | |||
9016.2.a.w.1.2 | 2 | 35.27 | even | 4 | |||
9200.2.a.br.1.1 | 2 | 20.3 | even | 4 |