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 | 4049.2 | ||
Root | \(-1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4600.4049 |
Dual form | 4600.2.e.o.4049.3 |
$q$-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 | ||||||||
\(3\) | − 1.56155i | − 0.901563i | −0.892634 | − | 0.450781i | \(-0.851145\pi\) | ||||
0.892634 | − | 0.450781i | \(-0.148855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.561553 | 0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.12311 | −0.941652 | −0.470826 | − | 0.882226i | \(-0.656044\pi\) | ||||
−0.470826 | + | 0.882226i | \(0.656044\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.438447i | − 0.121603i | −0.998150 | − | 0.0608017i | \(-0.980634\pi\) | ||||
0.998150 | − | 0.0608017i | \(-0.0193657\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.12311i | 1.24254i | 0.783598 | + | 0.621268i | \(0.213382\pi\) | ||||
−0.783598 | + | 0.621268i | \(0.786618\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12311 | 0.716490 | 0.358245 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358245 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.56155i | − 1.07032i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.56155 | −0.661364 | −0.330682 | − | 0.943742i | \(-0.607279\pi\) | ||||
−0.330682 | + | 0.943742i | \(0.607279\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.43845 | −0.437958 | −0.218979 | − | 0.975730i | \(-0.570273\pi\) | ||||
−0.218979 | + | 0.975730i | \(0.570273\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.87689i | 0.848958i | ||||||||
\(34\) | 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 | ||||||||
\(39\) | −0.684658 | −0.109633 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.80776 | −1.53172 | −0.765858 | − | 0.643010i | \(-0.777685\pi\) | ||||
−0.765858 | + | 0.643010i | \(0.777685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.00000i | 1.21999i | 0.792406 | + | 0.609994i | \(0.208828\pi\) | ||||
−0.792406 | + | 0.609994i | \(0.791172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 0.684658i | − 0.0998677i | −0.998753 | − | 0.0499338i | \(-0.984099\pi\) | ||||
0.998753 | − | 0.0499338i | \(-0.0159011\pi\) | |||||||
\(48\) | 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 | \(-0.956138\pi\) | ||||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 4.87689i | − 0.645960i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.2462 | −1.33394 | −0.666972 | − | 0.745083i | \(-0.732410\pi\) | ||||
−0.666972 | + | 0.745083i | \(0.732410\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.24621 | −0.543672 | −0.271836 | − | 0.962344i | \(-0.587631\pi\) | ||||
−0.271836 | + | 0.962344i | \(0.587631\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.12311i | 0.381548i | 0.981634 | + | 0.190774i | \(0.0610998\pi\) | ||||
−0.981634 | + | 0.190774i | \(0.938900\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.56155 | 0.187989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.5616 | 1.60946 | 0.804730 | − | 0.593641i | \(-0.202310\pi\) | ||||
0.804730 | + | 0.593641i | \(0.202310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.6847i | 1.71871i | 0.511380 | + | 0.859355i | \(0.329134\pi\) | ||||
−0.511380 | + | 0.859355i | \(0.670866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.12311 | −0.351377 | −0.175688 | − | 0.984446i | \(-0.556215\pi\) | ||||
−0.175688 | + | 0.984446i | \(0.556215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 14.2462i | − 1.56372i | −0.623451 | − | 0.781862i | \(-0.714270\pi\) | ||||
0.623451 | − | 0.781862i | \(-0.285730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.56155i | 0.596261i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.3693 | −1.20515 | −0.602573 | − | 0.798064i | \(-0.705858\pi\) | ||||
−0.602573 | + | 0.798064i | \(0.705858\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.80776i | 0.394847i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3693i | 1.15438i | 0.816610 | + | 0.577190i | \(0.195851\pi\) | ||||
−0.816610 | + | 0.577190i | \(0.804149\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.75379 | −0.176262 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.2462 | 1.21854 | 0.609272 | − | 0.792961i | \(-0.291462\pi\) | ||||
0.609272 | + | 0.792961i | \(0.291462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462i | 1.40372i | 0.712314 | + | 0.701860i | \(0.247647\pi\) | ||||
−0.712314 | + | 0.701860i | \(0.752353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.1231i | 1.07531i | 0.843165 | + | 0.537656i | \(0.180690\pi\) | ||||
−0.843165 | + | 0.537656i | \(0.819310\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.1231 | −1.25697 | −0.628483 | − | 0.777824i | \(-0.716324\pi\) | ||||
−0.628483 | + | 0.777824i | \(0.716324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.8769 | 1.22222 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.87689i | 0.270635i | 0.990802 | + | 0.135318i | \(0.0432055\pi\) | ||||
−0.990802 | + | 0.135318i | \(0.956794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 0.246211i | − 0.0227622i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.24621 | −0.113292 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.3153i | 1.38094i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.684658i | 0.0607536i | 0.999539 | + | 0.0303768i | \(0.00967073\pi\) | ||||
−0.999539 | + | 0.0303768i | \(0.990329\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4924 | 1.09990 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.31534 | 0.289663 | 0.144831 | − | 0.989456i | \(-0.453736\pi\) | ||||
0.144831 | + | 0.989456i | \(0.453736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.87689i | 0.587533i | 0.955877 | + | 0.293766i | \(0.0949088\pi\) | ||||
−0.955877 | + | 0.293766i | \(0.905091\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31534 | 0.281204 | 0.140602 | − | 0.990066i | \(-0.455096\pi\) | ||||
0.140602 | + | 0.990066i | \(0.455096\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.06913 | −0.0900370 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.36932i | 0.114508i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 10.9309i | − 0.901563i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.2462 | 1.65863 | 0.829317 | − | 0.558778i | \(-0.188730\pi\) | ||||
0.829317 | + | 0.558778i | \(0.188730\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4384 | −0.849469 | −0.424734 | − | 0.905318i | \(-0.639633\pi\) | ||||
−0.424734 | + | 0.905318i | \(0.639633\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.87689i | 0.232583i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.1231i | 1.68581i | 0.538064 | + | 0.842904i | \(0.319156\pi\) | ||||
−0.538064 | + | 0.842904i | \(0.680844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.12311 | −0.247678 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18.9309i | − 1.48278i | −0.671074 | − | 0.741390i | \(-0.734167\pi\) | ||||
0.671074 | − | 0.741390i | \(-0.265833\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 16.0000i | − 1.23812i | −0.785345 | − | 0.619059i | \(-0.787514\pi\) | ||||
0.785345 | − | 0.619059i | \(-0.212486\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8078 | 0.985213 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.75379 | 0.134116 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0000i | 0.760286i | 0.924928 | + | 0.380143i | \(0.124125\pi\) | ||||
−0.924928 | + | 0.380143i | \(0.875875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.0000i | 1.20263i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.31534 | 0.247800 | 0.123900 | − | 0.992295i | \(-0.460460\pi\) | ||||
0.123900 | + | 0.992295i | \(0.460460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.75379 | 0.279017 | 0.139508 | − | 0.990221i | \(-0.455448\pi\) | ||||
0.139508 | + | 0.990221i | \(0.455448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.63068i | 0.490154i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 16.0000i | − 1.17004i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.3693 | 1.83566 | 0.917830 | − | 0.396974i | \(-0.129940\pi\) | ||||
0.917830 | + | 0.396974i | \(0.129940\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.438447i | 0.0315601i | 0.999875 | + | 0.0157801i | \(0.00502316\pi\) | ||||
−0.999875 | + | 0.0157801i | \(0.994977\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 16.9309i | − 1.20627i | −0.797637 | − | 0.603137i | \(-0.793917\pi\) | ||||
0.797637 | − | 0.603137i | \(-0.206083\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.1231 | −0.788496 | −0.394248 | − | 0.919004i | \(-0.628995\pi\) | ||||
−0.394248 | + | 0.919004i | \(0.628995\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.87689 | 0.343990 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.561553i | 0.0390306i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.75379 | −0.674684 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 21.1771i | − 1.45103i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 22.9309 | 1.54952 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.24621 | 0.151097 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.4924i | 1.90799i | 0.299817 | + | 0.953997i | \(0.403075\pi\) | ||||
−0.299817 | + | 0.953997i | \(0.596925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 6.24621i | − 0.414576i | −0.978280 | − | 0.207288i | \(-0.933536\pi\) | ||||
0.978280 | − | 0.207288i | \(-0.0664637\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.8769 | −0.983093 | −0.491546 | − | 0.870851i | \(-0.663568\pi\) | ||||
−0.491546 | + | 0.870851i | \(0.663568\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.0540i | 1.05173i | 0.850568 | + | 0.525865i | \(0.176258\pi\) | ||||
−0.850568 | + | 0.525865i | \(0.823742\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.87689i | 0.316788i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0540 | −1.68529 | −0.842646 | − | 0.538468i | \(-0.819003\pi\) | ||||
−0.842646 | + | 0.538468i | \(0.819003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.49242 | 0.418214 | 0.209107 | − | 0.977893i | \(-0.432944\pi\) | ||||
0.209107 | + | 0.977893i | \(0.432944\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 5.75379i | − 0.369106i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.36932i | − 0.0871275i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.2462 | −1.40980 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.24621 | −0.394257 | −0.197129 | − | 0.980378i | \(-0.563162\pi\) | ||||
−0.197129 | + | 0.980378i | \(0.563162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 3.12311i | − 0.196348i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5.31534i | − 0.331562i | −0.986163 | − | 0.165781i | \(-0.946986\pi\) | ||||
0.986163 | − | 0.165781i | \(-0.0530145\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.1231i | 1.17918i | 0.807702 | + | 0.589591i | \(0.200711\pi\) | ||||
−0.807702 | + | 0.589591i | \(0.799289\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.7538i | 1.08651i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.3153 | −0.811851 | −0.405925 | − | 0.913906i | \(-0.633051\pi\) | ||||
−0.405925 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(270\) | 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 | ||||||||
\(277\) | 17.8078i | 1.06996i | 0.844863 | + | 0.534982i | \(0.179682\pi\) | ||||
−0.844863 | + | 0.534982i | \(0.820318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.36932 | −0.0819789 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.12311 | 0.305619 | 0.152809 | − | 0.988256i | \(-0.451168\pi\) | ||||
0.152809 | + | 0.988256i | \(0.451168\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 3.12311i | − 0.185649i | −0.995682 | − | 0.0928247i | \(-0.970410\pi\) | ||||
0.995682 | − | 0.0928247i | \(-0.0295896\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.24621 | −0.543895 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.7538 | 1.04075 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.3693i | 0.897885i | 0.893561 | + | 0.448943i | \(0.148199\pi\) | ||||
−0.893561 | + | 0.448943i | \(0.851801\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.3693i | 1.00787i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.438447 | 0.0253561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 19.1231i | − 1.09859i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.2462i | − 1.04137i | −0.853750 | − | 0.520683i | \(-0.825677\pi\) | ||||
0.853750 | − | 0.520683i | \(-0.174323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.2462 | 1.26554 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.56155 | 0.315367 | 0.157683 | − | 0.987490i | \(-0.449597\pi\) | ||||
0.157683 | + | 0.987490i | \(0.449597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.3693i | 0.868725i | 0.900738 | + | 0.434363i | \(0.143026\pi\) | ||||
−0.900738 | + | 0.434363i | \(0.856974\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.75379i | − 0.210834i | −0.994428 | − | 0.105417i | \(-0.966382\pi\) | ||||
0.994428 | − | 0.105417i | \(-0.0336177\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.1231 | 0.622774 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.3693 | 0.969461 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0000i | 0.890264i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.4924i | 1.13323i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.4233 | 1.72718 | 0.863590 | − | 0.504194i | \(-0.168211\pi\) | ||||
0.863590 | + | 0.504194i | \(0.168211\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.63068i | 0.253760i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 21.6155i | − 1.17747i | −0.808325 | − | 0.588736i | \(-0.799626\pi\) | ||||
0.808325 | − | 0.588736i | \(-0.200374\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.49242 | 0.243995 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.61553 | 0.412404 | ||||||||
\(342\) | 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 | ||||||||
\(349\) | 34.6847 | 1.85663 | 0.928314 | − | 0.371798i | \(-0.121259\pi\) | ||||
0.928314 | + | 0.371798i | \(0.121259\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.43845 | −0.130155 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 15.5616i | − 0.828258i | −0.910218 | − | 0.414129i | \(-0.864086\pi\) | ||||
0.910218 | − | 0.414129i | \(-0.135914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.6155 | 1.24638 | 0.623190 | − | 0.782071i | \(-0.285836\pi\) | ||||
0.623190 | + | 0.782071i | \(0.285836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.94602i | 0.102140i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 14.2462i | − 0.743646i | −0.928304 | − | 0.371823i | \(-0.878733\pi\) | ||||
0.928304 | − | 0.371823i | \(-0.121267\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.50758 | −0.286713 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.4924i | 0.543277i | 0.962399 | + | 0.271639i | \(0.0875655\pi\) | ||||
−0.962399 | + | 0.271639i | \(0.912434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.56155i | 0.0804241i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.4924 | 0.641693 | 0.320846 | − | 0.947131i | \(-0.396033\pi\) | ||||
0.320846 | + | 0.947131i | \(0.396033\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.06913 | 0.0547732 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 9.75379i | − 0.498395i | −0.968453 | − | 0.249198i | \(-0.919833\pi\) | ||||
0.968453 | − | 0.249198i | \(-0.0801669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.49242i | 0.228363i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.3693 | 1.18487 | 0.592436 | − | 0.805618i | \(-0.298166\pi\) | ||||
0.592436 | + | 0.805618i | \(0.298166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.12311 | −0.259087 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 5.17708i | − 0.261149i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.4384i | 0.825022i | 0.910953 | + | 0.412511i | \(0.135348\pi\) | ||||
−0.910953 | + | 0.412511i | \(0.864652\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.2462 | −1.41055 | −0.705274 | − | 0.708935i | \(-0.749176\pi\) | ||||
−0.705274 | + | 0.708935i | \(0.749176\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.06913i | 0.0532572i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 25.7538i | − 1.27657i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −26.3002 | −1.30046 | −0.650230 | − | 0.759737i | \(-0.725328\pi\) | ||||
−0.650230 | + | 0.759737i | \(0.725328\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.7386 | 0.529698 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 5.17708i | − 0.253523i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.4924 | −1.00112 | −0.500560 | − | 0.865702i | \(-0.666873\pi\) | ||||
−0.500560 | + | 0.865702i | \(0.666873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.8769 | −0.920004 | −0.460002 | − | 0.887918i | \(-0.652151\pi\) | ||||
−0.460002 | + | 0.887918i | \(0.652151\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 0.384472i | − 0.0186937i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.13826 | 0.103236 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.49242 | 0.216392 | 0.108196 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108196 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | 3.12311i | 0.149398i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0540 | 1.24349 | 0.621744 | − | 0.783220i | \(-0.286424\pi\) | ||||
0.621744 | + | 0.783220i | \(0.286424\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.93087 | 0.187184 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.9309i | 1.65962i | 0.558049 | + | 0.829808i | \(0.311550\pi\) | ||||
−0.558049 | + | 0.829808i | \(0.688450\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 31.6155i | − 1.49536i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.24621 | −0.389163 | −0.194581 | − | 0.980886i | \(-0.562335\pi\) | ||||
−0.194581 | + | 0.980886i | \(0.562335\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.6307 | 1.44234 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.3002i | 0.765850i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.3693i | 0.906058i | 0.891496 | + | 0.453029i | \(0.149657\pi\) | ||||
−0.891496 | + | 0.453029i | \(0.850343\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.4924 | 1.32991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.80776 | 0.456793 | 0.228397 | − | 0.973568i | \(-0.426652\pi\) | ||||
0.228397 | + | 0.973568i | \(0.426652\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.4924i | 0.952364i | 0.879347 | + | 0.476182i | \(0.157980\pi\) | ||||
−0.879347 | + | 0.476182i | \(0.842020\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.36932i | 0.433560i | 0.976220 | + | 0.216780i | \(0.0695555\pi\) | ||||
−0.976220 | + | 0.216780i | \(0.930445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 32.9848 | 1.51986 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 24.9848i | − 1.14880i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1.12311i | − 0.0514235i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.24621 | 0.285397 | 0.142698 | − | 0.989766i | \(-0.454422\pi\) | ||||
0.142698 | + | 0.989766i | \(0.454422\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.61553 | 0.164854 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.6847i | 1.11857i | 0.828976 | + | 0.559284i | \(0.188924\pi\) | ||||
−0.828976 | + | 0.559284i | \(0.811076\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.5616 | −1.33682 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.80776 | −0.352359 | −0.176180 | − | 0.984358i | \(-0.556374\pi\) | ||||
−0.176180 | + | 0.984358i | \(0.556374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 18.2462i | − 0.821768i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0540 | −0.629142 | −0.314571 | − | 0.949234i | \(-0.601861\pi\) | ||||
−0.314571 | + | 0.949234i | \(0.601861\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.9848 | −1.11624 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.3693i | 0.774460i | 0.921983 | + | 0.387230i | \(0.126568\pi\) | ||||
−0.921983 | + | 0.387230i | \(0.873432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 20.0000i | − 0.888231i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −38.3002 | −1.69763 | −0.848813 | − | 0.528693i | \(-0.822682\pi\) | ||||
−0.848813 | + | 0.528693i | \(0.822682\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 17.3693i | − 0.766874i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.13826i | 0.0940406i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.6155 | 0.685446 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.6155 | −0.946993 | −0.473497 | − | 0.880796i | \(-0.657008\pi\) | ||||
−0.473497 | + | 0.880796i | \(0.657008\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22.2462i | − 0.972759i | −0.873748 | − | 0.486379i | \(-0.838317\pi\) | ||||
0.873748 | − | 0.486379i | \(-0.161683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 12.4924i | − 0.544178i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.75379 | −0.249693 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.30019i | 0.186262i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 5.17708i | − 0.223408i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.8617 | −0.941652 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.06913 | 0.303926 | 0.151963 | − | 0.988386i | \(-0.451441\pi\) | ||||
0.151963 | + | 0.988386i | \(0.451441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5.86174i | − 0.251551i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 26.5464i | − 1.13504i | −0.823359 | − | 0.567521i | \(-0.807903\pi\) | ||||
0.823359 | − | 0.567521i | \(-0.192097\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.38447 | −0.101767 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.1231 | −0.473860 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.12311i | − 0.386558i | −0.981144 | − | 0.193279i | \(-0.938088\pi\) | ||||
0.981144 | − | 0.193279i | \(-0.0619123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.50758 | 0.148355 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.9848 | −1.05486 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 22.2462i | − 0.937566i | −0.883313 | − | 0.468783i | \(-0.844693\pi\) | ||||
0.883313 | − | 0.468783i | \(-0.155307\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.24621 | −0.345699 | −0.172850 | − | 0.984948i | \(-0.555297\pi\) | ||||
−0.172850 | + | 0.984948i | \(0.555297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.4924 | −1.86195 | −0.930975 | − | 0.365083i | \(-0.881041\pi\) | ||||
−0.930975 | + | 0.365083i | \(0.881041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 39.6155i | − 1.65496i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 12.9309i | − 0.538319i | −0.963096 | − | 0.269160i | \(-0.913254\pi\) | ||||
0.963096 | − | 0.269160i | \(-0.0867459\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.684658 | 0.0284534 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.24621i | 0.258692i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.0540i | 0.580070i | 0.957016 | + | 0.290035i | \(0.0936669\pi\) | ||||
−0.957016 | + | 0.290035i | \(0.906333\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.61553 | −0.313792 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.4384 | −1.08753 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 4.73863i | − 0.194592i | −0.995255 | − | 0.0972962i | \(-0.968981\pi\) | ||||
0.995255 | − | 0.0972962i | \(-0.0310194\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.3693i | 0.710879i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | −0.326871 | −0.163436 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163436 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.1922 | −0.742077 | −0.371038 | − | 0.928618i | \(-0.620998\pi\) | ||||
−0.371038 | + | 0.928618i | \(0.620998\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.75379i | 0.0714198i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.7386i | 1.41000i | 0.709208 | + | 0.704999i | \(0.249052\pi\) | ||||
−0.709208 | + | 0.704999i | \(0.750948\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.300187 | −0.0121442 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 46.1080i | − 1.86228i | −0.364659 | − | 0.931141i | \(-0.618814\pi\) | ||||
0.364659 | − | 0.931141i | \(-0.381186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 30.9848i | − 1.24740i | −0.781663 | − | 0.623701i | \(-0.785628\pi\) | ||||
0.781663 | − | 0.623701i | \(-0.214372\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.49242 | 0.180566 | 0.0902829 | − | 0.995916i | \(-0.471223\pi\) | ||||
0.0902829 | + | 0.995916i | \(0.471223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.56155 | 0.223177 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.2311i | 0.608270i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −42.2462 | −1.68447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.7386 | 1.70140 | 0.850699 | − | 0.525653i | \(-0.176179\pi\) | ||||
0.850699 | + | 0.525653i | \(0.176179\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.24621i | 0.248265i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.06913i | − 0.121603i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.61553 | 0.301266 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3693 | 0.449061 | 0.224531 | − | 0.974467i | \(-0.427915\pi\) | ||||
0.224531 | + | 0.974467i | \(0.427915\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.36932i | − 0.0540006i | −0.999635 | − | 0.0270003i | \(-0.991404\pi\) | ||||
0.999635 | − | 0.0270003i | \(-0.00859550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.3002i | 0.955339i | 0.878540 | + | 0.477669i | \(0.158518\pi\) | ||||
−0.878540 | + | 0.477669i | \(0.841482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 32.0000 | 1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0540i | 0.471709i | 0.971788 | + | 0.235854i | \(0.0757888\pi\) | ||||
−0.971788 | + | 0.235854i | \(0.924211\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.24621i | 0.321715i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.2462 | 0.554954 | 0.277477 | − | 0.960732i | \(-0.410502\pi\) | ||||
0.277477 | + | 0.960732i | \(0.410502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2462 | 0.631904 | 0.315952 | − | 0.948775i | \(-0.397676\pi\) | ||||
0.315952 | + | 0.948775i | \(0.397676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.50758i | − 0.136223i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 3.56155i | − 0.137904i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 44.4924 | 1.72018 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2614 | 0.511949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0540i | 1.54397i | 0.635642 | + | 0.771984i | \(0.280735\pi\) | ||||
−0.635642 | + | 0.771984i | \(0.719265\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26.9848i | 1.03711i | 0.855044 | + | 0.518556i | \(0.173530\pi\) | ||||
−0.855044 | + | 0.518556i | \(0.826470\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.75379 | −0.373766 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 28.6847i | − 1.09759i | −0.835958 | − | 0.548794i | \(-0.815087\pi\) | ||||
0.835958 | − | 0.548794i | \(-0.184913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.2311i | 0.886320i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.876894 | −0.0334070 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −44.9848 | −1.71130 | −0.855652 | − | 0.517551i | \(-0.826844\pi\) | ||||
−0.855652 | + | 0.517551i | \(0.826844\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 50.2462i | − 1.90321i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.0691 | 0.948202 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.8617 | −1.05232 | −0.526162 | − | 0.850385i | \(-0.676369\pi\) | ||||
−0.526162 | + | 0.850385i | \(0.676369\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.7538i | 0.971323i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6307 | 0.474355 | 0.237178 | − | 0.971466i | \(-0.423778\pi\) | ||||
0.237178 | + | 0.971466i | \(0.423778\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.75379 | −0.0657722 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.43845i | − 0.0913206i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 40.6847i | 1.51940i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.4924 | 1.06259 | 0.531294 | − | 0.847187i | \(-0.321706\pi\) | ||||
0.531294 | + | 0.847187i | \(0.321706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 10.1383i | − 0.377046i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 14.6307i | − 0.542622i | −0.962492 | − | 0.271311i | \(-0.912543\pi\) | ||||
0.962492 | − | 0.271311i | \(-0.0874572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9848 | −1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −40.9848 | −1.51588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 24.6307i | − 0.909755i | −0.890554 | − | 0.454878i | \(-0.849683\pi\) | ||||
0.890554 | − | 0.454878i | \(-0.150317\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 9.75379i | − 0.359285i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.6847 | −0.466613 | −0.233306 | − | 0.972403i | \(-0.574954\pi\) | ||||
−0.233306 | + | 0.972403i | \(0.574954\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.13826 | −0.0785510 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 17.7538i | − 0.651323i | −0.945486 | − | 0.325662i | \(-0.894413\pi\) | ||||
0.945486 | − | 0.325662i | \(-0.105587\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 8.00000i | − 0.292705i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.9848 | −0.911710 | −0.455855 | − | 0.890054i | \(-0.650666\pi\) | ||||
−0.455855 | + | 0.890054i | \(0.650666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.75379i | 0.355448i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 34.4924i | − 1.25365i | −0.779161 | − | 0.626824i | \(-0.784354\pi\) | ||||
0.779161 | − | 0.626824i | \(-0.215646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.87689 | −0.177020 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.6847 | −1.11232 | −0.556159 | − | 0.831076i | \(-0.687725\pi\) | ||||
−0.556159 | + | 0.831076i | \(0.687725\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.49242i | 0.162212i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.00000 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.30019 | −0.298924 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 27.3693i | − 0.984406i | −0.870480 | − | 0.492203i | \(-0.836192\pi\) | ||||
0.870480 | − | 0.492203i | \(-0.163808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.6307 | −1.09746 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.3542 | −1.51555 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.8078i | 0.707872i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9.75379i | − 0.347685i | −0.984773 | − | 0.173843i | \(-0.944382\pi\) | ||||
0.984773 | − | 0.173843i | \(-0.0556184\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.8617 | 1.06311 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.86174i | 0.0661123i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 4.24621i | − 0.150409i | −0.997168 | − | 0.0752043i | \(-0.976039\pi\) | ||||
0.997168 | − | 0.0752043i | \(-0.0239609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.50758 | 0.124089 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.38447 | −0.225584 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 45.8617i | − 1.61843i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.7926i | 0.731935i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.0000 | −0.914111 | −0.457056 | − | 0.889438i | \(-0.651096\pi\) | ||||
−0.457056 | + | 0.889438i | \(0.651096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.06913 | 0.178001 | 0.0890006 | − | 0.996032i | \(-0.471633\pi\) | ||||
0.0890006 | + | 0.996032i | \(0.471633\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 37.4773i | − 1.31439i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.9848i | 0.874109i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.7386 | 0.863384 | 0.431692 | − | 0.902021i | \(-0.357917\pi\) | ||||
0.431692 | + | 0.902021i | \(0.357917\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 53.5616i | − 1.86704i | −0.358527 | − | 0.933519i | \(-0.616721\pi\) | ||||
0.358527 | − | 0.933519i | \(-0.383279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 28.4924i | − 0.990779i | −0.868671 | − | 0.495389i | \(-0.835025\pi\) | ||||
0.868671 | − | 0.495389i | \(-0.164975\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.75379 | 0.130374 | 0.0651872 | − | 0.997873i | \(-0.479236\pi\) | ||||
0.0651872 | + | 0.997873i | \(0.479236\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.8078 | 0.964641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.8617i | 1.24254i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 13.5616i | 0.468756i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −33.7538 | −1.16531 | −0.582655 | − | 0.812720i | \(-0.697986\pi\) | ||||
−0.582655 | + | 0.812720i | \(0.697986\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3153 | −0.562598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 8.00000i | − 0.275535i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.87689 | −0.167375 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.24621 | −0.282676 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 30.9848i | − 1.06090i | −0.847716 | − | 0.530450i | \(-0.822023\pi\) | ||||
0.847716 | − | 0.530450i | \(-0.177977\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.4384i | 0.424889i | 0.977173 | + | 0.212445i | \(0.0681425\pi\) | ||||
−0.977173 | + | 0.212445i | \(0.931857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.0540 | −1.84430 | −0.922149 | − | 0.386835i | \(-0.873568\pi\) | ||||
−0.922149 | + | 0.386835i | \(0.873568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 37.1771i | − 1.26552i | −0.774347 | − | 0.632761i | \(-0.781921\pi\) | ||||
0.774347 | − | 0.632761i | \(-0.218079\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.4384i | 0.490355i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.75379 | 0.330875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.36932 | 0.0463975 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.38447i | 0.216082i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 34.9848i | − 1.18135i | −0.806908 | − | 0.590677i | \(-0.798861\pi\) | ||||
0.806908 | − | 0.590677i | \(-0.201139\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.0000 | 0.809500 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.1231 | 0.442129 | 0.221064 | − | 0.975259i | \(-0.429047\pi\) | ||||
0.221064 | + | 0.975259i | \(0.429047\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.9848i | 0.975418i | 0.873006 | + | 0.487709i | \(0.162167\pi\) | ||||
−0.873006 | + | 0.487709i | \(0.837833\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.31534i | 0.245625i | 0.992430 | + | 0.122813i | \(0.0391914\pi\) | ||||
−0.992430 | + | 0.122813i | \(0.960809\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.8617 | 0.732396 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 2.13826i | − 0.0715542i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 0.684658i | − 0.0228601i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.68466 | 0.289650 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.2462 | 0.341351 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.1231i | 1.69751i | 0.528782 | + | 0.848757i | \(0.322649\pi\) | ||||
−0.528782 | + | 0.848757i | \(0.677351\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.87689 | 0.228092 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.8769 | −0.956734 | −0.478367 | − | 0.878160i | \(-0.658771\pi\) | ||||
−0.478367 | + | 0.878160i | \(0.658771\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 44.4924i | 1.47248i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −54.2462 | −1.78942 | −0.894709 | − | 0.446650i | \(-0.852617\pi\) | ||||
−0.894709 | + | 0.446650i | \(0.852617\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.4924 | −0.938857 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.94602i | − 0.195716i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.00000i | 0.262754i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.1922 | −0.465632 | −0.232816 | − | 0.972521i | \(-0.574794\pi\) | ||||
−0.232816 | + | 0.972521i | \(0.574794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.8617 | 0.716490 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 8.68466i | − 0.284323i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.2462i | 1.05344i | 0.850040 | + | 0.526719i | \(0.176578\pi\) | ||||
−0.850040 | + | 0.526719i | \(0.823422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8769 | 1.00656 | 0.503279 | − | 0.864124i | \(-0.332127\pi\) | ||||
0.503279 | + | 0.864124i | \(0.332127\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9.80776i | − 0.319385i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.56155i | 0.0507436i | 0.999678 | + | 0.0253718i | \(0.00807697\pi\) | ||||
−0.999678 | + | 0.0253718i | \(0.991923\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.43845 | 0.209001 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.86174 | −0.190080 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 27.7538i | − 0.899033i | −0.893272 | − | 0.449517i | \(-0.851596\pi\) | ||||
0.893272 | − | 0.449517i | \(-0.148404\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 17.3693i | − 0.561470i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.0540 | −0.808193 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.24621i | 0.201281i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 2.05398i | − 0.0660514i | −0.999455 | − | 0.0330257i | \(-0.989486\pi\) | ||||
0.999455 | − | 0.0330257i | \(-0.0105143\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.9848 | 0.802629 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.63068 | 0.212789 | 0.106394 | − | 0.994324i | \(-0.466069\pi\) | ||||
0.106394 | + | 0.994324i | \(0.466069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.2311i | 0.807213i | 0.914933 | + | 0.403607i | \(0.132244\pi\) | ||||
−0.914933 | + | 0.403607i | \(0.867756\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.5076 | 1.13483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.36932 | −0.235284 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 52.1080i | 1.66199i | 0.556283 | + | 0.830993i | \(0.312227\pi\) | ||||
−0.556283 | + | 0.830993i | \(0.687773\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.9848 | −1.81018 | −0.905092 | − | 0.425217i | \(-0.860198\pi\) | ||||
−0.905092 | + | 0.425217i | \(0.860198\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 49.0691i | − 1.55716i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.0000i | 0.443384i | 0.975117 | + | 0.221692i | \(0.0711580\pi\) | ||||
−0.975117 | + | 0.221692i | \(0.928842\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.8617 | 1.45100 |
(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.4049.2 | 4 | ||
5.2 | odd | 4 | 4600.2.a.s.1.1 | 2 | |||
5.3 | odd | 4 | 184.2.a.e.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 4600.2.e.o.4049.3 | 4 | ||
15.8 | even | 4 | 1656.2.a.j.1.2 | 2 | |||
20.3 | even | 4 | 368.2.a.i.1.1 | 2 | |||
20.7 | even | 4 | 9200.2.a.br.1.2 | 2 | |||
35.13 | even | 4 | 9016.2.a.w.1.1 | 2 | |||
40.3 | even | 4 | 1472.2.a.p.1.2 | 2 | |||
40.13 | odd | 4 | 1472.2.a.u.1.1 | 2 | |||
60.23 | odd | 4 | 3312.2.a.t.1.1 | 2 | |||
115.68 | even | 4 | 4232.2.a.o.1.2 | 2 | |||
460.183 | odd | 4 | 8464.2.a.bd.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.a.e.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
368.2.a.i.1.1 | 2 | 20.3 | even | 4 | |||
1472.2.a.p.1.2 | 2 | 40.3 | even | 4 | |||
1472.2.a.u.1.1 | 2 | 40.13 | odd | 4 | |||
1656.2.a.j.1.2 | 2 | 15.8 | even | 4 | |||
3312.2.a.t.1.1 | 2 | 60.23 | odd | 4 | |||
4232.2.a.o.1.2 | 2 | 115.68 | even | 4 | |||
4600.2.a.s.1.1 | 2 | 5.2 | odd | 4 | |||
4600.2.e.o.4049.2 | 4 | 1.1 | even | 1 | trivial | ||
4600.2.e.o.4049.3 | 4 | 5.4 | even | 2 | inner | ||
8464.2.a.bd.1.1 | 2 | 460.183 | odd | 4 | |||
9016.2.a.w.1.1 | 2 | 35.13 | even | 4 | |||
9200.2.a.br.1.2 | 2 | 20.7 | even | 4 |