Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3700,2,Mod(149,3700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3700 = 2^{2} \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3700.d (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: | \(29.5446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{6} + 139x^{4} + 273x^{2} + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{37}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 740) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.1 | ||
Root | \(-2.24418i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3700.149 |
Dual form | 3700.2.d.i.149.8 |
$q$-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 \(\left(\mathbb{Z}/3700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) | \(1851\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 3.24418i | − 1.87303i | −0.350629 | − | 0.936515i | \(-0.614032\pi\) | ||||
0.350629 | − | 0.936515i | \(-0.385968\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.24418i | 0.470256i | 0.971964 | + | 0.235128i | \(0.0755510\pi\) | ||||
−0.971964 | + | 0.235128i | \(0.924449\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.52471 | −2.50824 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.19063 | −1.86654 | −0.933272 | − | 0.359169i | \(-0.883060\pi\) | ||||
−0.933272 | + | 0.359169i | \(0.883060\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.66592i | − 0.462042i | −0.972949 | − | 0.231021i | \(-0.925793\pi\) | ||||
0.972949 | − | 0.231021i | \(-0.0742066\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.66592i | 1.37419i | 0.726569 | + | 0.687093i | \(0.241114\pi\) | ||||
−0.726569 | + | 0.687093i | \(0.758886\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.94645 | 1.13479 | 0.567396 | − | 0.823445i | \(-0.307951\pi\) | ||||
0.567396 | + | 0.823445i | \(0.307951\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.03635 | 0.880804 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.48836i | 0.935888i | 0.883758 | + | 0.467944i | \(0.155005\pi\) | ||||
−0.883758 | + | 0.467944i | \(0.844995\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.6790i | 2.82497i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.48836 | 0.833468 | 0.416734 | − | 0.909028i | \(-0.363175\pi\) | ||||
0.416734 | + | 0.909028i | \(0.363175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.385383 | 0.0692169 | 0.0346084 | − | 0.999401i | \(-0.488982\pi\) | ||||
0.0346084 | + | 0.999401i | \(0.488982\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 20.0835i | 3.49609i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.00000i | 0.164399i | ||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.40453 | −0.865418 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.190629 | −0.0297712 | −0.0148856 | − | 0.999889i | \(-0.504738\pi\) | ||||
−0.0148856 | + | 0.999889i | \(0.504738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.56106i | − 0.695556i | −0.937577 | − | 0.347778i | \(-0.886936\pi\) | ||||
0.937577 | − | 0.347778i | \(-0.113064\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 6.08765i | − 0.887975i | −0.896033 | − | 0.443987i | \(-0.853563\pi\) | ||||
0.896033 | − | 0.443987i | \(-0.146437\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.45201 | 0.778859 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.3813 | 2.57389 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 1.70227i | − 0.233824i | −0.993142 | − | 0.116912i | \(-0.962700\pi\) | ||||
0.993142 | − | 0.116912i | \(-0.0372996\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 16.0472i | − 2.12550i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.10298 | 0.794540 | 0.397270 | − | 0.917702i | \(-0.369958\pi\) | ||||
0.397270 | + | 0.917702i | \(0.369958\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 9.36211i | − 1.17951i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.4348i | 1.64132i | 0.571414 | + | 0.820662i | \(0.306395\pi\) | ||||
−0.571414 | + | 0.820662i | \(0.693605\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.5611 | 1.75295 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.6790 | −1.97943 | −0.989716 | − | 0.143046i | \(-0.954310\pi\) | ||||
−0.989716 | + | 0.143046i | \(0.954310\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.786097i | 0.0920057i | 0.998941 | + | 0.0460028i | \(0.0146483\pi\) | ||||
−0.998941 | + | 0.0460028i | \(0.985352\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.70227i | − 0.877755i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.9464 | 1.23157 | 0.615786 | − | 0.787914i | \(-0.288839\pi\) | ||||
0.615786 | + | 0.787914i | \(0.288839\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 25.0472 | 2.78302 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 13.8052i | − 1.51532i | −0.652648 | − | 0.757661i | \(-0.726342\pi\) | ||||
0.652648 | − | 0.757661i | \(-0.273658\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 14.5611i | − 1.56111i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.33183 | −0.565173 | −0.282586 | − | 0.959242i | \(-0.591192\pi\) | ||||
−0.282586 | + | 0.959242i | \(0.591192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.07270 | 0.217278 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 1.25025i | − 0.129645i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 0.561064i | − 0.0569674i | −0.999594 | − | 0.0284837i | \(-0.990932\pi\) | ||||
0.999594 | − | 0.0284837i | \(-0.00906787\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 46.5827 | 4.68174 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.1696 | 1.01191 | 0.505957 | − | 0.862559i | \(-0.331139\pi\) | ||||
0.505957 | + | 0.862559i | \(0.331139\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 2.00000i | − 0.197066i | −0.995134 | − | 0.0985329i | \(-0.968585\pi\) | ||||
0.995134 | − | 0.0985329i | \(-0.0314150\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.50751i | 0.339084i | 0.985523 | + | 0.169542i | \(0.0542288\pi\) | ||||
−0.985523 | + | 0.169542i | \(0.945771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4540 | 1.38444 | 0.692219 | − | 0.721687i | \(-0.256633\pi\) | ||||
0.692219 | + | 0.721687i | \(0.256633\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.24418 | 0.307924 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.7153i | 1.76059i | 0.474425 | + | 0.880296i | \(0.342656\pi\) | ||||
−0.474425 | + | 0.880296i | \(0.657344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.5355i | 1.15891i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.04943 | −0.646220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.3239 | 2.48399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.618435i | 0.0557624i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.80525i | 0.870075i | 0.900412 | + | 0.435037i | \(0.143265\pi\) | ||||
−0.900412 | + | 0.435037i | \(0.856735\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.7969 | −1.30280 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7899 | 1.20483 | 0.602415 | − | 0.798183i | \(-0.294205\pi\) | ||||
0.602415 | + | 0.798183i | \(0.294205\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.15428i | 0.533644i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.53779i | 0.473125i | 0.971616 | + | 0.236563i | \(0.0760209\pi\) | ||||
−0.971616 | + | 0.236563i | \(0.923979\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.4307 | −1.81773 | −0.908863 | − | 0.417094i | \(-0.863049\pi\) | ||||
−0.908863 | + | 0.417094i | \(0.863049\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.7494 | −1.66320 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.3131i | 0.862422i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 17.6873i | − 1.45883i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9787 | −1.39095 | −0.695474 | − | 0.718552i | \(-0.744805\pi\) | ||||
−0.695474 | + | 0.718552i | \(0.744805\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.56106 | −0.533932 | −0.266966 | − | 0.963706i | \(-0.586021\pi\) | ||||
−0.266966 | + | 0.963706i | \(0.586021\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 42.6344i | − 3.44679i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.19063i | 0.653683i | 0.945079 | + | 0.326842i | \(0.105984\pi\) | ||||
−0.945079 | + | 0.326842i | \(0.894016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.52246 | −0.437960 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.58434 | −0.440108 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.7131i | 1.70070i | 0.526217 | + | 0.850350i | \(0.323610\pi\) | ||||
−0.526217 | + | 0.850350i | \(0.676390\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 17.3318i | − 1.34118i | −0.741829 | − | 0.670589i | \(-0.766042\pi\) | ||||
0.741829 | − | 0.670589i | \(-0.233958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2247 | 0.786517 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −37.2206 | −2.84633 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.8355i | 1.66012i | 0.557671 | + | 0.830062i | \(0.311695\pi\) | ||||
−0.557671 | + | 0.830062i | \(0.688305\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 19.7992i | − 1.48820i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.03028 | 0.600211 | 0.300106 | − | 0.953906i | \(-0.402978\pi\) | ||||
0.300106 | + | 0.953906i | \(0.402978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.16961 | −0.161266 | −0.0806329 | − | 0.996744i | \(-0.525694\pi\) | ||||
−0.0806329 | + | 0.996744i | \(0.525694\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 6.48836i | − 0.479634i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 35.0756i | − 2.56498i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.2633 | −1.32846 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.4115 | −1.91107 | −0.955536 | − | 0.294875i | \(-0.904722\pi\) | ||||
−0.955536 | + | 0.294875i | \(0.904722\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.40453i | 0.101100i | 0.998722 | + | 0.0505502i | \(0.0160975\pi\) | ||||
−0.998722 | + | 0.0505502i | \(0.983903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.4992i | 1.46051i | 0.683177 | + | 0.730253i | \(0.260598\pi\) | ||||
−0.683177 | + | 0.730253i | \(0.739402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.89702 | 0.276252 | 0.138126 | − | 0.990415i | \(-0.455892\pi\) | ||||
0.138126 | + | 0.990415i | \(0.455892\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 43.5850 | 3.07425 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.58434i | 0.391944i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 33.7736i | − 2.34743i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −30.6216 | −2.11814 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.05737 | 0.417007 | 0.208503 | − | 0.978022i | \(-0.433141\pi\) | ||||
0.208503 | + | 0.978022i | \(0.433141\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 54.1097i | 3.70753i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.479487i | 0.0325497i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.55024 | 0.172329 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.43894 | 0.634932 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 8.29361i | − 0.555381i | −0.960671 | − | 0.277691i | \(-0.910431\pi\) | ||||
0.960671 | − | 0.277691i | \(-0.0895690\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 18.3813i | − 1.22001i | −0.792399 | − | 0.610003i | \(-0.791168\pi\) | ||||
0.792399 | − | 0.610003i | \(-0.208832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.1674 | 0.870123 | 0.435062 | − | 0.900401i | \(-0.356727\pi\) | ||||
0.435062 | + | 0.900401i | \(0.356727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.9875 | −1.64406 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.2480i | 0.671369i | 0.941975 | + | 0.335684i | \(0.108968\pi\) | ||||
−0.941975 | + | 0.335684i | \(0.891032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 35.5123i | − 2.30677i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.7666 | 0.696436 | 0.348218 | − | 0.937414i | \(-0.386787\pi\) | ||||
0.348218 | + | 0.937414i | \(0.386787\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8435 | 0.956152 | 0.478076 | − | 0.878319i | \(-0.341334\pi\) | ||||
0.478076 | + | 0.878319i | \(0.341334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 37.2206i | − 2.38770i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 8.24036i | − 0.524322i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −44.7867 | −2.83824 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.4842 | 1.54543 | 0.772716 | − | 0.634752i | \(-0.218898\pi\) | ||||
0.772716 | + | 0.634752i | \(0.218898\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 27.7858i | − 1.74688i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.07045i | 0.565799i | 0.959150 | + | 0.282899i | \(0.0912963\pi\) | ||||
−0.959150 | + | 0.282899i | \(0.908704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.24418 | −0.0773097 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −33.7736 | −2.09054 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.3430i | 1.56272i | 0.624081 | + | 0.781359i | \(0.285473\pi\) | ||||
−0.624081 | + | 0.781359i | \(0.714527\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.2974i | 1.05859i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1310 | 0.800611 | 0.400306 | − | 0.916382i | \(-0.368904\pi\) | ||||
0.400306 | + | 0.916382i | \(0.368904\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.3966 | 1.60348 | 0.801739 | − | 0.597674i | \(-0.203908\pi\) | ||||
0.801739 | + | 0.597674i | \(0.203908\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 6.72422i | − 0.406968i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.3602i | 1.46366i | 0.681485 | + | 0.731832i | \(0.261335\pi\) | ||||
−0.681485 | + | 0.731832i | \(0.738665\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.89990 | −0.173612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.43894 | −0.205150 | −0.102575 | − | 0.994725i | \(-0.532708\pi\) | ||||
−0.102575 | + | 0.994725i | \(0.532708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 26.3813i | − 1.56820i | −0.620633 | − | 0.784102i | \(-0.713124\pi\) | ||||
0.620633 | − | 0.784102i | \(-0.286876\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 0.237177i | − 0.0140001i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.1026 | −0.888388 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.82019 | −0.106702 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.6404i | 1.49793i | 0.662611 | + | 0.748964i | \(0.269448\pi\) | ||||
−0.662611 | + | 0.748964i | \(0.730552\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 90.8722i | − 5.27294i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.47723 | 0.432420 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.67479 | 0.327090 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 32.9921i | − 1.89534i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 3.20978i | − 0.183192i | −0.995796 | − | 0.0915958i | \(-0.970803\pi\) | ||||
0.995796 | − | 0.0915958i | \(-0.0291968\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.48836 | −0.369110 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 31.5337 | 1.78811 | 0.894055 | − | 0.447957i | \(-0.147848\pi\) | ||||
0.894055 | + | 0.447957i | \(0.147848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.12587i | − 0.0636380i | −0.999494 | − | 0.0318190i | \(-0.989870\pi\) | ||||
0.999494 | − | 0.0318190i | \(-0.0101300\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.415662i | 0.0233459i | 0.999932 | + | 0.0116729i | \(0.00371570\pi\) | ||||
−0.999932 | + | 0.0116729i | \(0.996284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.7858 | −1.55571 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.3790 | 0.635114 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.0262i | 1.55942i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 46.8913i | − 2.59309i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.57414 | 0.417576 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.5913 | 1.68145 | 0.840726 | − | 0.541461i | \(-0.182128\pi\) | ||||
0.840726 | + | 0.541461i | \(0.182128\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 7.52471i | − 0.412352i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.52697i | 0.518967i | 0.965748 | + | 0.259483i | \(0.0835523\pi\) | ||||
−0.965748 | + | 0.259483i | \(0.916448\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 60.7160 | 3.29764 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.38577 | −0.129196 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.4926i | 0.836520i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 1.46509i | − 0.0786501i | −0.999226 | − | 0.0393250i | \(-0.987479\pi\) | ||||
0.999226 | − | 0.0393250i | \(-0.0125208\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.8224 | −1.32872 | −0.664358 | − | 0.747415i | \(-0.731295\pi\) | ||||
−0.664358 | + | 0.747415i | \(0.731295\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.4540 | 1.30526 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11.1221i | − 0.591971i | −0.955192 | − | 0.295986i | \(-0.904352\pi\) | ||||
0.955192 | − | 0.295986i | \(-0.0956480\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.8696i | 1.21039i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.50369 | −0.237696 | −0.118848 | − | 0.992912i | \(-0.537920\pi\) | ||||
−0.118848 | + | 0.992912i | \(0.537920\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.46734 | 0.287755 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 88.6436i | − 4.65258i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.8888i | 0.933786i | 0.884314 | + | 0.466893i | \(0.154627\pi\) | ||||
−0.884314 | + | 0.466893i | \(0.845373\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.43443 | 0.0746734 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.11793 | 0.109957 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 30.8850i | − 1.59916i | −0.600558 | − | 0.799581i | \(-0.705055\pi\) | ||||
0.600558 | − | 0.799581i | \(-0.294945\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 7.47723i | − 0.385097i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.7816 | −1.06748 | −0.533739 | − | 0.845649i | \(-0.679214\pi\) | ||||
−0.533739 | + | 0.845649i | \(0.679214\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 31.8100 | 1.62968 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 34.6599i | − 1.77104i | −0.464602 | − | 0.885520i | \(-0.653803\pi\) | ||||
0.464602 | − | 0.885520i | \(-0.346197\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.3207i | 1.74462i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.73636 | 0.442951 | 0.221476 | − | 0.975166i | \(-0.428913\pi\) | ||||
0.221476 | + | 0.975166i | \(0.428913\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.4307 | −1.28609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 44.7370i | − 2.25668i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.29773i | 0.316074i | 0.987433 | + | 0.158037i | \(0.0505166\pi\) | ||||
−0.987433 | + | 0.158037i | \(0.949483\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.9656 | 0.999530 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.7625 | −1.53621 | −0.768103 | − | 0.640326i | \(-0.778799\pi\) | ||||
−0.768103 | + | 0.640326i | \(0.778799\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 0.642016i | − 0.0319811i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 6.19063i | − 0.306858i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.4884 | −0.617510 | −0.308755 | − | 0.951142i | \(-0.599912\pi\) | ||||
−0.308755 | + | 0.951142i | \(0.599912\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 17.9656 | 0.886178 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.59321i | 0.373638i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 69.5250i | 3.40466i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.49631 | −0.366219 | −0.183109 | − | 0.983093i | \(-0.558616\pi\) | ||||
−0.183109 | + | 0.983093i | \(0.558616\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.36249 | 0.0664038 | 0.0332019 | − | 0.999449i | \(-0.489430\pi\) | ||||
0.0332019 | + | 0.999449i | \(0.489430\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.8078i | 2.22725i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.48836i | 0.120420i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 33.4575 | 1.61534 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.1180 | −1.20989 | −0.604946 | − | 0.796267i | \(-0.706805\pi\) | ||||
−0.604946 | + | 0.796267i | \(0.706805\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 18.2168i | − 0.875443i | −0.899111 | − | 0.437721i | \(-0.855786\pi\) | ||||
0.899111 | − | 0.437721i | \(-0.144214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.2015i | 1.06204i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.9232 | 0.664517 | 0.332258 | − | 0.943188i | \(-0.392189\pi\) | ||||
0.332258 | + | 0.943188i | \(0.392189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.0248 | −1.95356 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.721415i | 0.0342754i | 0.999853 | + | 0.0171377i | \(0.00545537\pi\) | ||||
−0.999853 | + | 0.0171377i | \(0.994545\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 55.0819i | 2.60528i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.8696 | 0.796127 | 0.398063 | − | 0.917358i | \(-0.369682\pi\) | ||||
0.398063 | + | 0.917358i | \(0.369682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.18011 | 0.0555694 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 21.2853i | 1.00007i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.46221i | 0.115177i | 0.998340 | + | 0.0575887i | \(0.0183412\pi\) | ||||
−0.998340 | + | 0.0575887i | \(0.981659\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −83.1699 | −3.88204 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5145 | 0.676008 | 0.338004 | − | 0.941145i | \(-0.390248\pi\) | ||||
0.338004 | + | 0.941145i | \(0.390248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.5378i | 1.55863i | 0.626630 | + | 0.779317i | \(0.284434\pi\) | ||||
−0.626630 | + | 0.779317i | \(0.715566\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000i | 0.277647i | 0.990317 | + | 0.138823i | \(0.0443321\pi\) | ||||
−0.990317 | + | 0.138823i | \(0.955668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.7153 | −0.771843 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 26.5719 | 1.22437 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.2359i | 1.29829i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.8091i | 0.586487i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2550 | −0.971166 | −0.485583 | − | 0.874191i | \(-0.661393\pi\) | ||||
−0.485583 | + | 0.874191i | \(0.661393\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.66592 | 0.0759592 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.1166i | 0.824334i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.7176i | − 1.07475i | −0.843344 | − | 0.537373i | \(-0.819417\pi\) | ||||
0.843344 | − | 0.537373i | \(-0.180583\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 70.4412 | 3.18546 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3318 | 0.511398 | 0.255699 | − | 0.966756i | \(-0.417694\pi\) | ||||
0.255699 | + | 0.966756i | \(0.417694\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.4307i | 1.14534i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 20.7517i | − 0.930841i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.65666 | 0.163694 | 0.0818472 | − | 0.996645i | \(-0.473918\pi\) | ||||
0.0818472 | + | 0.996645i | \(0.473918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −56.2276 | −2.51206 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 11.1100i | − 0.495370i | −0.968841 | − | 0.247685i | \(-0.920330\pi\) | ||||
0.968841 | − | 0.247685i | \(-0.0796698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 33.1709i | − 1.47317i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.62956 | −0.426823 | −0.213411 | − | 0.976962i | \(-0.568457\pi\) | ||||
−0.213411 | + | 0.976962i | \(0.568457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.978047 | −0.0432663 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 72.6089i | 3.20576i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.6864i | 1.65745i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 70.8384 | 3.10946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.6236 | 0.640670 | 0.320335 | − | 0.947304i | \(-0.396205\pi\) | ||||
0.320335 | + | 0.947304i | \(0.396205\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 23.4389i | − 1.02491i | −0.858713 | − | 0.512457i | \(-0.828736\pi\) | ||||
0.858713 | − | 0.512457i | \(-0.171264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.18355i | 0.0951169i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.85460 | 0.124113 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −45.9232 | −1.99290 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.317572i | 0.0137556i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 26.0517i | − 1.12421i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −33.7514 | −1.45378 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.0150 | 0.903506 | 0.451753 | − | 0.892143i | \(-0.350799\pi\) | ||||
0.451753 | + | 0.892143i | \(0.350799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.03860i | 0.302055i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 10.1753i | − 0.435064i | −0.976053 | − | 0.217532i | \(-0.930199\pi\) | ||||
0.976053 | − | 0.217532i | \(-0.0698007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.0494 | −0.642294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.2015 | 0.945814 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6194i | 0.579154i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.7415i | 1.21782i | 0.793241 | + | 0.608908i | \(0.208392\pi\) | ||||
−0.793241 | + | 0.608908i | \(0.791608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.59835 | −0.321376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −113.792 | −4.80428 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 36.7281i | − 1.54791i | −0.633243 | − | 0.773953i | \(-0.718277\pi\) | ||||
0.633243 | − | 0.773953i | \(-0.281723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 31.1632i | 1.30873i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.2480 | −0.429619 | −0.214809 | − | 0.976656i | \(-0.568913\pi\) | ||||
−0.214809 | + | 0.976656i | \(0.568913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.0602 | −0.881344 | −0.440672 | − | 0.897668i | \(-0.645260\pi\) | ||||
−0.440672 | + | 0.897668i | \(0.645260\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 85.6838i | 3.57949i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 5.14315i | − 0.214112i | −0.994253 | − | 0.107056i | \(-0.965858\pi\) | ||||
0.994253 | − | 0.107056i | \(-0.0341424\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.55656 | 0.189364 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.1762 | 0.712590 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5381i | 0.436443i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 4.86962i | − 0.200991i | −0.994938 | − | 0.100495i | \(-0.967957\pi\) | ||||
0.994938 | − | 0.100495i | \(-0.0320428\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.90628 | 0.0785468 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 66.5031 | 2.73557 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17.5569i | 0.720974i | 0.932764 | + | 0.360487i | \(0.117389\pi\) | ||||
−0.932764 | + | 0.360487i | \(0.882611\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 12.6426i | − 0.517429i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.9764 | −1.87855 | −0.939273 | − | 0.343171i | \(-0.888499\pi\) | ||||
−0.939273 | + | 0.343171i | \(0.888499\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.2764 | −1.52054 | −0.760268 | − | 0.649609i | \(-0.774932\pi\) | ||||
−0.760268 | + | 0.649609i | \(0.774932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 101.093i | − 4.11683i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 3.96560i | − 0.160959i | −0.996756 | − | 0.0804793i | \(-0.974355\pi\) | ||||
0.996756 | − | 0.0804793i | \(-0.0256451\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.1166 | 0.734122 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.1415 | −0.410282 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.3239i | 0.497757i | 0.968535 | + | 0.248879i | \(0.0800620\pi\) | ||||
−0.968535 | + | 0.248879i | \(0.919938\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.2551i | 1.29854i | 0.760558 | + | 0.649270i | \(0.224926\pi\) | ||||
−0.760558 | + | 0.649270i | \(0.775074\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.98755 | −0.361240 | −0.180620 | − | 0.983553i | \(-0.557810\pi\) | ||||
−0.180620 | + | 0.983553i | \(0.557810\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −65.8846 | −2.64386 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 6.63377i | − 0.265776i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 99.3421i | 3.96734i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.66592 | −0.225915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7246 | −0.426940 | −0.213470 | − | 0.976950i | \(-0.568476\pi\) | ||||
−0.213470 | + | 0.976950i | \(0.568476\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 19.6512i | − 0.781065i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 9.08259i | − 0.359865i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 125.505 | 4.96489 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.9321 | 1.37974 | 0.689868 | − | 0.723935i | \(-0.257669\pi\) | ||||
0.689868 | + | 0.723935i | \(0.257669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.1483i | 0.991751i | 0.868394 | + | 0.495876i | \(0.165153\pi\) | ||||
−0.868394 | + | 0.495876i | \(0.834847\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.9452i | 1.57041i | 0.619237 | + | 0.785204i | \(0.287442\pi\) | ||||
−0.619237 | + | 0.785204i | \(0.712558\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.7813 | −1.48305 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.55554 | 0.0609665 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.7392i | 1.55512i | 0.628811 | + | 0.777558i | \(0.283542\pi\) | ||||
−0.628811 | + | 0.777558i | \(0.716458\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 5.91515i | − 0.230772i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.4415 | 1.61433 | 0.807166 | − | 0.590325i | \(-0.201000\pi\) | ||||
0.807166 | + | 0.590325i | \(0.201000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.2210 | 0.825401 | 0.412700 | − | 0.910867i | \(-0.364586\pi\) | ||||
0.412700 | + | 0.910867i | \(0.364586\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 30.6216i | − 1.18925i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.1454i | 0.780033i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.9060 | −1.04024 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.3813 | −0.477973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 6.96590i | − 0.268516i | −0.990946 | − | 0.134258i | \(-0.957135\pi\) | ||||
0.990946 | − | 0.134258i | \(-0.0428651\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.9315i | 0.650730i | 0.945588 | + | 0.325365i | \(0.105487\pi\) | ||||
−0.945588 | + | 0.325365i | \(0.894513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.698066 | 0.0267893 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −59.6321 | −2.28511 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 49.3963i | 1.89010i | 0.326931 | + | 0.945048i | \(0.393985\pi\) | ||||
−0.326931 | + | 0.945048i | \(0.606015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 42.7173i | − 1.62977i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.83583 | −0.108037 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.1026 | −0.916906 | −0.458453 | − | 0.888719i | \(-0.651596\pi\) | ||||
−0.458453 | + | 0.888719i | \(0.651596\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 57.9573i | 2.20162i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.08009i | − 0.0409112i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 33.2464 | 1.25749 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −40.3768 | −1.52501 | −0.762504 | − | 0.646983i | \(-0.776030\pi\) | ||||
−0.762504 | + | 0.646983i | \(0.776030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.94645i | 0.186559i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.6528i | 0.475859i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.8435 | 1.30857 | 0.654287 | − | 0.756246i | \(-0.272969\pi\) | ||||
0.654287 | + | 0.756246i | \(0.272969\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −82.3689 | −3.08907 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.72974i | 0.0647793i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 34.9289i | − 1.30445i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.35541 | −0.0505483 | −0.0252742 | − | 0.999681i | \(-0.508046\pi\) | ||||
−0.0252742 | + | 0.999681i | \(0.508046\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48836 | 0.0926715 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 48.1549i | − 1.79090i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.5566i | 0.539873i | 0.962878 | + | 0.269936i | \(0.0870027\pi\) | ||||
−0.962878 | + | 0.269936i | \(0.912997\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −45.6089 | −1.68922 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.8426 | 0.955823 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 18.0415i | − 0.666377i | −0.942860 | − | 0.333189i | \(-0.891875\pi\) | ||||
0.942860 | − | 0.333189i | \(-0.108125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 83.1699i | − 3.06360i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.74431 | −0.284879 | −0.142439 | − | 0.989804i | \(-0.545495\pi\) | ||||
−0.142439 | + | 0.989804i | \(0.545495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.7332 | −0.982070 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.4689i | 1.11780i | 0.829236 | + | 0.558898i | \(0.188776\pi\) | ||||
−0.829236 | + | 0.558898i | \(0.811224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 103.881i | 3.80079i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.36398 | −0.159456 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9270 | −0.471713 | −0.235856 | − | 0.971788i | \(-0.575789\pi\) | ||||
−0.235856 | + | 0.971788i | \(0.575789\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 79.4313i | − 2.89464i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.4501i | 0.525197i | 0.964905 | + | 0.262598i | \(0.0845794\pi\) | ||||
−0.964905 | + | 0.262598i | \(0.915421\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −90.1421 | −3.27195 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.33977 | 0.0848168 | 0.0424084 | − | 0.999100i | \(-0.486497\pi\) | ||||
0.0424084 | + | 0.999100i | \(0.486497\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9833i | 0.651041i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 10.1670i | − 0.367111i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0449 | −0.903143 | −0.451571 | − | 0.892235i | \(-0.649136\pi\) | ||||
−0.451571 | + | 0.892235i | \(0.649136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.4262 | 1.05976 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 12.7900i | − 0.460024i | −0.973188 | − | 0.230012i | \(-0.926123\pi\) | ||||
0.973188 | − | 0.230012i | \(-0.0738765\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.03635i | 0.144803i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.942936 | −0.0337842 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 103.253 | 3.69470 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 65.8846i | 2.35453i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.4224i | 1.15573i | 0.816132 | + | 0.577866i | \(0.196114\pi\) | ||||
−0.816132 | + | 0.577866i | \(0.803886\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 82.2174 | 2.92702 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.2853 | −0.827929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 3.33183i | − 0.118317i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.4972i | 0.655206i | 0.944816 | + | 0.327603i | \(0.106241\pi\) | ||||
−0.944816 | + | 0.327603i | \(0.893759\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.4921 | 1.22024 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.1205 | 1.41759 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4.86643i | − 0.171733i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 42.5994i | − 1.49957i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.38126 | 0.224353 | 0.112177 | − | 0.993688i | \(-0.464218\pi\) | ||||
0.112177 | + | 0.993688i | \(0.464218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.88869 | 0.241895 | 0.120947 | − | 0.992659i | \(-0.461407\pi\) | ||||
0.120947 | + | 0.992659i | \(0.461407\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 85.6353i | − 3.00336i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 22.5611i | − 0.789312i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.5965 | −0.544985 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3921 | 0.781489 | 0.390745 | − | 0.920499i | \(-0.372218\pi\) | ||||
0.390745 | + | 0.920499i | \(0.372218\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1.51202i | − 0.0527057i | −0.999653 | − | 0.0263528i | \(-0.991611\pi\) | ||||
0.999653 | − | 0.0263528i | \(-0.00838934\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.30568i | 0.254043i | 0.991900 | + | 0.127022i | \(0.0405418\pi\) | ||||
−0.991900 | + | 0.127022i | \(0.959458\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.1438 | 1.63737 | 0.818685 | − | 0.574242i | \(-0.194703\pi\) | ||||
0.818685 | + | 0.574242i | \(0.194703\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 79.0290 | 2.74149 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.8906i | 1.07030i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.65704i | 0.195536i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.8313 | 0.442986 | 0.221493 | − | 0.975162i | \(-0.428907\pi\) | ||||
0.221493 | + | 0.975162i | \(0.428907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.85460 | −0.305331 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.1565i | 0.384251i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.9959i | 1.16811i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −85.5856 | −2.93729 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.48836 | −0.153859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 15.6060i | − 0.534339i | −0.963650 | − | 0.267169i | \(-0.913912\pi\) | ||||
0.963650 | − | 0.267169i | \(-0.0860883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 24.4157i | − 0.834023i | −0.908901 | − | 0.417012i | \(-0.863077\pi\) | ||||
0.908901 | − | 0.417012i | \(-0.136923\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.1973 | 1.57623 | 0.788116 | − | 0.615526i | \(-0.211057\pi\) | ||||
0.788116 | + | 0.615526i | \(0.211057\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.769445 | −0.0262226 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 18.3089i | − 0.623244i | −0.950206 | − | 0.311622i | \(-0.899128\pi\) | ||||
0.950206 | − | 0.311622i | \(-0.100872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 48.9956i | 1.66398i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −67.7654 | −2.29878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.3813 | 0.758360 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.22185i | 0.142888i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 15.9963i | − 0.540155i | −0.962839 | − | 0.270078i | \(-0.912951\pi\) | ||||
0.962839 | − | 0.270078i | \(-0.0870494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 83.1821 | 2.80566 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.2719 | −1.45787 | −0.728934 | − | 0.684584i | \(-0.759984\pi\) | ||||
−0.728934 | + | 0.684584i | \(0.759984\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.1438i | 1.58651i | 0.608887 | + | 0.793257i | \(0.291616\pi\) | ||||
−0.608887 | + | 0.793257i | \(0.708384\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 21.0988i | − 0.708428i | −0.935164 | − | 0.354214i | \(-0.884749\pi\) | ||||
0.935164 | − | 0.354214i | \(-0.115251\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.1995 | −0.409158 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −155.058 | −5.19463 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 30.1122i | − 1.00767i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 24.2575i | − 0.809934i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.72974 | 0.0576901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.64490 | 0.321318 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 18.4101i | − 0.612648i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.0756i | 1.23107i | 0.788108 | + | 0.615537i | \(0.211061\pi\) | ||||
−0.788108 | + | 0.615537i | \(0.788939\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −76.5234 | −2.53812 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.9187 | 0.858724 | 0.429362 | − | 0.903133i | \(-0.358739\pi\) | ||||
0.429362 | + | 0.903133i | \(0.358739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 85.4632i | 2.82842i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.1572i | 0.566579i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 49.0332 | 1.61745 | 0.808727 | − | 0.588184i | \(-0.200157\pi\) | ||||
0.808727 | + | 0.588184i | \(0.200157\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.4131 | −0.343123 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.7858i | 0.914580i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.0494i | 0.494288i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.2770 | 1.28864 | 0.644319 | − | 0.764757i | \(-0.277141\pi\) | ||||
0.644319 | + | 0.764757i | \(0.277141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.9681 | 0.883844 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 102.301i | − 3.34918i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.3855i | 0.567958i | 0.958830 | + | 0.283979i | \(0.0916546\pi\) | ||||
−0.958830 | + | 0.283979i | \(0.908345\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.65253 | −0.119196 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.4628 | −0.406277 | −0.203138 | − | 0.979150i | \(-0.565114\pi\) | ||||
−0.203138 | + | 0.979150i | \(0.565114\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.855612i | − 0.0278626i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 34.6478i | − 1.12590i | −0.826490 | − | 0.562951i | \(-0.809666\pi\) | ||||
0.826490 | − | 0.562951i | \(-0.190334\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.30957 | 0.0425105 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.34848 | 0.0437275 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0880i | 0.909861i | 0.890527 | + | 0.454930i | \(0.150336\pi\) | ||||
−0.890527 | + | 0.454930i | \(0.849664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 90.1421i | 2.91388i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.89002 | −0.222490 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8515 | −0.995209 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 26.3930i | − 0.850503i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 24.9302i | − 0.801700i | −0.916144 | − | 0.400850i | \(-0.868715\pi\) | ||||
0.916144 | − | 0.400850i | \(-0.131285\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 90.9219 | 2.92083 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.7858 | −0.506590 | −0.253295 | − | 0.967389i | \(-0.581514\pi\) | ||||
−0.253295 | + | 0.967389i | \(0.581514\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 26.6637i | − 0.854798i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.6525i | 1.20461i | 0.798266 | + | 0.602306i | \(0.205751\pi\) | ||||
−0.798266 | + | 0.602306i | \(0.794249\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.0074 | 1.05492 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −108.762 | −3.47250 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.9618i | 0.413417i | 0.978403 | + | 0.206708i | \(0.0662751\pi\) | ||||
−0.978403 | + | 0.206708i | \(0.933725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 24.5719i | − 0.782132i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 20.4717 | 0.650963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.7666 | −1.23146 | −0.615731 | − | 0.787956i | \(-0.711139\pi\) | ||||
−0.615731 | + | 0.787956i | \(0.711139\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 99.2439i | − 3.14941i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 14.6478i | − 0.463900i | −0.972728 | − | 0.231950i | \(-0.925489\pi\) | ||||
0.972728 | − | 0.231950i | \(-0.0745105\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.6790 | −0.464423 |
(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 | 3700.2.d.i.149.1 | 8 | ||
5.2 | odd | 4 | 3700.2.a.j.1.1 | 4 | |||
5.3 | odd | 4 | 740.2.a.f.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 3700.2.d.i.149.8 | 8 | ||
15.8 | even | 4 | 6660.2.a.r.1.4 | 4 | |||
20.3 | even | 4 | 2960.2.a.v.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
740.2.a.f.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
2960.2.a.v.1.1 | 4 | 20.3 | even | 4 | |||
3700.2.a.j.1.1 | 4 | 5.2 | odd | 4 | |||
3700.2.d.i.149.1 | 8 | 1.1 | even | 1 | trivial | ||
3700.2.d.i.149.8 | 8 | 5.4 | even | 2 | inner | ||
6660.2.a.r.1.4 | 4 | 15.8 | even | 4 |