Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3850,2,Mod(1849,3850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3850.1849");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3850.c (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: | \(30.7424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 770) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1849.5 | ||
Root | \(-0.671462 - 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3850.1849 |
Dual form | 3850.2.c.ba.1849.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3850\mathbb{Z}\right)^\times\).
\(n\) | \(1751\) | \(2201\) | \(2927\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 1.14637i | − 0.661854i | −0.943656 | − | 0.330927i | \(-0.892639\pi\) | ||||
0.943656 | − | 0.330927i | \(-0.107361\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.14637 | 0.468002 | ||||||||
\(7\) | − 1.00000i | − 0.377964i | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.68585 | 0.561949 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.14637i | 0.330927i | ||||||||
\(13\) | − 4.68585i | − 1.29962i | −0.760097 | − | 0.649810i | \(-0.774848\pi\) | ||||
0.760097 | − | 0.649810i | \(-0.225152\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 0.292731i | − 0.0709977i | −0.999370 | − | 0.0354988i | \(-0.988698\pi\) | ||||
0.999370 | − | 0.0354988i | \(-0.0113020\pi\) | |||||||
\(18\) | 1.68585i | 0.397358i | ||||||||
\(19\) | −6.51806 | −1.49535 | −0.747673 | − | 0.664068i | \(-0.768829\pi\) | ||||
−0.747673 | + | 0.664068i | \(0.768829\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.14637 | −0.250157 | ||||||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | − 2.85363i | − 0.595024i | −0.954718 | − | 0.297512i | \(-0.903843\pi\) | ||||
0.954718 | − | 0.297512i | \(-0.0961568\pi\) | |||||||
\(24\) | −1.14637 | −0.234001 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.68585 | 0.918970 | ||||||||
\(27\) | − 5.37169i | − 1.03378i | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 1.43910 | 0.267234 | 0.133617 | − | 0.991033i | \(-0.457341\pi\) | ||||
0.133617 | + | 0.991033i | \(0.457341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.978577 | 0.175758 | 0.0878788 | − | 0.996131i | \(-0.471991\pi\) | ||||
0.0878788 | + | 0.996131i | \(0.471991\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 1.14637i | − 0.199557i | ||||||||
\(34\) | 0.292731 | 0.0502029 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.68585 | −0.280974 | ||||||||
\(37\) | 0.853635i | 0.140337i | 0.997535 | + | 0.0701683i | \(0.0223536\pi\) | ||||
−0.997535 | + | 0.0701683i | \(0.977646\pi\) | |||||||
\(38\) | − 6.51806i | − 1.05737i | ||||||||
\(39\) | −5.37169 | −0.860159 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.22533 | −0.972233 | −0.486116 | − | 0.873894i | \(-0.661587\pi\) | ||||
−0.486116 | + | 0.873894i | \(0.661587\pi\) | |||||||
\(42\) | − 1.14637i | − 0.176888i | ||||||||
\(43\) | 10.3503i | 1.57840i | 0.614135 | + | 0.789201i | \(0.289505\pi\) | ||||
−0.614135 | + | 0.789201i | \(0.710495\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.85363 | 0.420745 | ||||||||
\(47\) | − 9.95715i | − 1.45240i | −0.687483 | − | 0.726200i | \(-0.741285\pi\) | ||||
0.687483 | − | 0.726200i | \(-0.258715\pi\) | |||||||
\(48\) | − 1.14637i | − 0.165464i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.335577 | −0.0469901 | ||||||||
\(52\) | 4.68585i | 0.649810i | ||||||||
\(53\) | − 5.43910i | − 0.747117i | −0.927607 | − | 0.373559i | \(-0.878137\pi\) | ||||
0.927607 | − | 0.373559i | \(-0.121863\pi\) | |||||||
\(54\) | 5.37169 | 0.730995 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 7.47208i | 0.989701i | ||||||||
\(58\) | 1.43910i | 0.188963i | ||||||||
\(59\) | 9.37169 | 1.22009 | 0.610045 | − | 0.792367i | \(-0.291151\pi\) | ||||
0.610045 | + | 0.792367i | \(0.291151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.9572 | −1.53096 | −0.765478 | − | 0.643462i | \(-0.777498\pi\) | ||||
−0.765478 | + | 0.643462i | \(0.777498\pi\) | |||||||
\(62\) | 0.978577i | 0.124279i | ||||||||
\(63\) | − 1.68585i | − 0.212397i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.14637 | 0.141108 | ||||||||
\(67\) | − 0.585462i | − 0.0715256i | −0.999360 | − | 0.0357628i | \(-0.988614\pi\) | ||||
0.999360 | − | 0.0357628i | \(-0.0113861\pi\) | |||||||
\(68\) | 0.292731i | 0.0354988i | ||||||||
\(69\) | −3.27131 | −0.393819 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.335577 | −0.0398256 | −0.0199128 | − | 0.999802i | \(-0.506339\pi\) | ||||
−0.0199128 | + | 0.999802i | \(0.506339\pi\) | |||||||
\(72\) | − 1.68585i | − 0.198679i | ||||||||
\(73\) | 3.70727i | 0.433903i | 0.976182 | + | 0.216952i | \(0.0696114\pi\) | ||||
−0.976182 | + | 0.216952i | \(0.930389\pi\) | |||||||
\(74\) | −0.853635 | −0.0992330 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.51806 | 0.747673 | ||||||||
\(77\) | − 1.00000i | − 0.113961i | ||||||||
\(78\) | − 5.37169i | − 0.608224i | ||||||||
\(79\) | 2.51806 | 0.283304 | 0.141652 | − | 0.989917i | \(-0.454759\pi\) | ||||
0.141652 | + | 0.989917i | \(0.454759\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.10038 | −0.122265 | ||||||||
\(82\) | − 6.22533i | − 0.687472i | ||||||||
\(83\) | 1.70727i | 0.187397i | 0.995601 | + | 0.0936986i | \(0.0298690\pi\) | ||||
−0.995601 | + | 0.0936986i | \(0.970131\pi\) | |||||||
\(84\) | 1.14637 | 0.125079 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.3503 | −1.11610 | ||||||||
\(87\) | − 1.64973i | − 0.176870i | ||||||||
\(88\) | − 1.00000i | − 0.106600i | ||||||||
\(89\) | −13.0790 | −1.38637 | −0.693184 | − | 0.720761i | \(-0.743792\pi\) | ||||
−0.693184 | + | 0.720761i | \(0.743792\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.68585 | −0.491210 | ||||||||
\(92\) | 2.85363i | 0.297512i | ||||||||
\(93\) | − 1.12181i | − 0.116326i | ||||||||
\(94\) | 9.95715 | 1.02700 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.14637 | 0.117000 | ||||||||
\(97\) | 9.10352i | 0.924322i | 0.886796 | + | 0.462161i | \(0.152926\pi\) | ||||
−0.886796 | + | 0.462161i | \(0.847074\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | 1.68585 | 0.169434 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.7862 | −1.07327 | −0.536635 | − | 0.843814i | \(-0.680305\pi\) | ||||
−0.536635 | + | 0.843814i | \(0.680305\pi\) | |||||||
\(102\) | − 0.335577i | − 0.0332270i | ||||||||
\(103\) | − 7.66442i | − 0.755198i | −0.925969 | − | 0.377599i | \(-0.876750\pi\) | ||||
0.925969 | − | 0.377599i | \(-0.123250\pi\) | |||||||
\(104\) | −4.68585 | −0.459485 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.43910 | 0.528292 | ||||||||
\(107\) | 9.56404i | 0.924591i | 0.886726 | + | 0.462295i | \(0.152974\pi\) | ||||
−0.886726 | + | 0.462295i | \(0.847026\pi\) | |||||||
\(108\) | 5.37169i | 0.516891i | ||||||||
\(109\) | −3.14637 | −0.301367 | −0.150684 | − | 0.988582i | \(-0.548147\pi\) | ||||
−0.150684 | + | 0.988582i | \(0.548147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.978577 | 0.0928824 | ||||||||
\(112\) | − 1.00000i | − 0.0944911i | ||||||||
\(113\) | 2.58546i | 0.243220i | 0.992578 | + | 0.121610i | \(0.0388057\pi\) | ||||
−0.992578 | + | 0.121610i | \(0.961194\pi\) | |||||||
\(114\) | −7.47208 | −0.699824 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.43910 | −0.133617 | ||||||||
\(117\) | − 7.89962i | − 0.730320i | ||||||||
\(118\) | 9.37169i | 0.862734i | ||||||||
\(119\) | −0.292731 | −0.0268346 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − 11.9572i | − 1.08255i | ||||||||
\(123\) | 7.13650i | 0.643477i | ||||||||
\(124\) | −0.978577 | −0.0878788 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.68585 | 0.150187 | ||||||||
\(127\) | − 13.3717i | − 1.18655i | −0.805001 | − | 0.593273i | \(-0.797836\pi\) | ||||
0.805001 | − | 0.593273i | \(-0.202164\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 11.8652 | 1.04467 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.4391 | −0.999438 | −0.499719 | − | 0.866187i | \(-0.666563\pi\) | ||||
−0.499719 | + | 0.866187i | \(0.666563\pi\) | |||||||
\(132\) | 1.14637i | 0.0997783i | ||||||||
\(133\) | 6.51806i | 0.565187i | ||||||||
\(134\) | 0.585462 | 0.0505762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.292731 | −0.0251015 | ||||||||
\(137\) | 10.0000i | 0.854358i | 0.904167 | + | 0.427179i | \(0.140493\pi\) | ||||
−0.904167 | + | 0.427179i | \(0.859507\pi\) | |||||||
\(138\) | − 3.27131i | − 0.278472i | ||||||||
\(139\) | 14.1825 | 1.20294 | 0.601471 | − | 0.798895i | \(-0.294581\pi\) | ||||
0.601471 | + | 0.798895i | \(0.294581\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.4145 | −0.961278 | ||||||||
\(142\) | − 0.335577i | − 0.0281610i | ||||||||
\(143\) | − 4.68585i | − 0.391850i | ||||||||
\(144\) | 1.68585 | 0.140487 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.70727 | −0.306816 | ||||||||
\(147\) | 1.14637i | 0.0945506i | ||||||||
\(148\) | − 0.853635i | − 0.0701683i | ||||||||
\(149\) | −11.5970 | −0.950065 | −0.475032 | − | 0.879968i | \(-0.657564\pi\) | ||||
−0.475032 | + | 0.879968i | \(0.657564\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.73183 | 0.140934 | 0.0704671 | − | 0.997514i | \(-0.477551\pi\) | ||||
0.0704671 | + | 0.997514i | \(0.477551\pi\) | |||||||
\(152\) | 6.51806i | 0.528684i | ||||||||
\(153\) | − 0.493499i | − 0.0398971i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.37169 | 0.430080 | ||||||||
\(157\) | − 12.2927i | − 0.981067i | −0.871422 | − | 0.490533i | \(-0.836802\pi\) | ||||
0.871422 | − | 0.490533i | \(-0.163198\pi\) | |||||||
\(158\) | 2.51806i | 0.200326i | ||||||||
\(159\) | −6.23519 | −0.494483 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.85363 | −0.224898 | ||||||||
\(162\) | − 1.10038i | − 0.0864543i | ||||||||
\(163\) | − 23.9143i | − 1.87311i | −0.350516 | − | 0.936557i | \(-0.613994\pi\) | ||||
0.350516 | − | 0.936557i | \(-0.386006\pi\) | |||||||
\(164\) | 6.22533 | 0.486116 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.70727 | −0.132510 | ||||||||
\(167\) | − 8.00000i | − 0.619059i | −0.950890 | − | 0.309529i | \(-0.899829\pi\) | ||||
0.950890 | − | 0.309529i | \(-0.100171\pi\) | |||||||
\(168\) | 1.14637i | 0.0884440i | ||||||||
\(169\) | −8.95715 | −0.689012 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.9884 | −0.840307 | ||||||||
\(172\) | − 10.3503i | − 0.789201i | ||||||||
\(173\) | 7.37169i | 0.560459i | 0.959933 | + | 0.280230i | \(0.0904106\pi\) | ||||
−0.959933 | + | 0.280230i | \(0.909589\pi\) | |||||||
\(174\) | 1.64973 | 0.125066 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | − 10.7434i | − 0.807522i | ||||||||
\(178\) | − 13.0790i | − 0.980310i | ||||||||
\(179\) | −1.56404 | −0.116902 | −0.0584509 | − | 0.998290i | \(-0.518616\pi\) | ||||
−0.0584509 | + | 0.998290i | \(0.518616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7862 | 1.09905 | 0.549526 | − | 0.835477i | \(-0.314808\pi\) | ||||
0.549526 | + | 0.835477i | \(0.314808\pi\) | |||||||
\(182\) | − 4.68585i | − 0.347338i | ||||||||
\(183\) | 13.7073i | 1.01327i | ||||||||
\(184\) | −2.85363 | −0.210373 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.12181 | 0.0822549 | ||||||||
\(187\) | − 0.292731i | − 0.0214066i | ||||||||
\(188\) | 9.95715i | 0.726200i | ||||||||
\(189\) | −5.37169 | −0.390733 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.9572 | −1.29933 | −0.649667 | − | 0.760219i | \(-0.725092\pi\) | ||||
−0.649667 | + | 0.760219i | \(0.725092\pi\) | |||||||
\(192\) | 1.14637i | 0.0827318i | ||||||||
\(193\) | − 18.6430i | − 1.34195i | −0.741479 | − | 0.670976i | \(-0.765875\pi\) | ||||
0.741479 | − | 0.670976i | \(-0.234125\pi\) | |||||||
\(194\) | −9.10352 | −0.653595 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − 15.0361i | − 1.07128i | −0.844447 | − | 0.535639i | \(-0.820071\pi\) | ||||
0.844447 | − | 0.535639i | \(-0.179929\pi\) | |||||||
\(198\) | 1.68585i | 0.119808i | ||||||||
\(199\) | −15.3288 | −1.08663 | −0.543317 | − | 0.839528i | \(-0.682832\pi\) | ||||
−0.543317 | + | 0.839528i | \(0.682832\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.671153 | −0.0473395 | ||||||||
\(202\) | − 10.7862i | − 0.758917i | ||||||||
\(203\) | − 1.43910i | − 0.101005i | ||||||||
\(204\) | 0.335577 | 0.0234951 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.66442 | 0.534006 | ||||||||
\(207\) | − 4.81079i | − 0.334373i | ||||||||
\(208\) | − 4.68585i | − 0.324905i | ||||||||
\(209\) | −6.51806 | −0.450863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.04285 | 0.140635 | 0.0703176 | − | 0.997525i | \(-0.477599\pi\) | ||||
0.0703176 | + | 0.997525i | \(0.477599\pi\) | |||||||
\(212\) | 5.43910i | 0.373559i | ||||||||
\(213\) | 0.384694i | 0.0263588i | ||||||||
\(214\) | −9.56404 | −0.653784 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.37169 | −0.365497 | ||||||||
\(217\) | − 0.978577i | − 0.0664301i | ||||||||
\(218\) | − 3.14637i | − 0.213099i | ||||||||
\(219\) | 4.24989 | 0.287181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.37169 | −0.0922700 | ||||||||
\(222\) | 0.978577i | 0.0656778i | ||||||||
\(223\) | − 11.0790i | − 0.741902i | −0.928652 | − | 0.370951i | \(-0.879032\pi\) | ||||
0.928652 | − | 0.370951i | \(-0.120968\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.58546 | −0.171982 | ||||||||
\(227\) | − 18.5426i | − 1.23072i | −0.788248 | − | 0.615358i | \(-0.789011\pi\) | ||||
0.788248 | − | 0.615358i | \(-0.210989\pi\) | |||||||
\(228\) | − 7.47208i | − 0.494850i | ||||||||
\(229\) | 8.01469 | 0.529626 | 0.264813 | − | 0.964300i | \(-0.414690\pi\) | ||||
0.264813 | + | 0.964300i | \(0.414690\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.14637 | −0.0754253 | ||||||||
\(232\) | − 1.43910i | − 0.0944813i | ||||||||
\(233\) | − 27.9572i | − 1.83153i | −0.401710 | − | 0.915767i | \(-0.631584\pi\) | ||||
0.401710 | − | 0.915767i | \(-0.368416\pi\) | |||||||
\(234\) | 7.89962 | 0.516414 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.37169 | −0.610045 | ||||||||
\(237\) | − 2.88661i | − 0.187506i | ||||||||
\(238\) | − 0.292731i | − 0.0189749i | ||||||||
\(239\) | 28.8108 | 1.86362 | 0.931808 | − | 0.362953i | \(-0.118231\pi\) | ||||
0.931808 | + | 0.362953i | \(0.118231\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.51806 | −0.548696 | −0.274348 | − | 0.961630i | \(-0.588462\pi\) | ||||
−0.274348 | + | 0.961630i | \(0.588462\pi\) | |||||||
\(242\) | 1.00000i | 0.0642824i | ||||||||
\(243\) | − 14.8536i | − 0.952861i | ||||||||
\(244\) | 11.9572 | 0.765478 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.13650 | −0.455007 | ||||||||
\(247\) | 30.5426i | 1.94338i | ||||||||
\(248\) | − 0.978577i | − 0.0621397i | ||||||||
\(249\) | 1.95715 | 0.124030 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.1281 | −1.45983 | −0.729916 | − | 0.683537i | \(-0.760441\pi\) | ||||
−0.729916 | + | 0.683537i | \(0.760441\pi\) | |||||||
\(252\) | 1.68585i | 0.106198i | ||||||||
\(253\) | − 2.85363i | − 0.179406i | ||||||||
\(254\) | 13.3717 | 0.839015 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.8108i | 0.923872i | 0.886913 | + | 0.461936i | \(0.152845\pi\) | ||||
−0.886913 | + | 0.461936i | \(0.847155\pi\) | |||||||
\(258\) | 11.8652i | 0.738695i | ||||||||
\(259\) | 0.853635 | 0.0530423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.42610 | 0.150172 | ||||||||
\(262\) | − 11.4391i | − 0.706710i | ||||||||
\(263\) | − 18.7434i | − 1.15577i | −0.816119 | − | 0.577883i | \(-0.803879\pi\) | ||||
0.816119 | − | 0.577883i | \(-0.196121\pi\) | |||||||
\(264\) | −1.14637 | −0.0705539 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −6.51806 | −0.399648 | ||||||||
\(267\) | 14.9933i | 0.917573i | ||||||||
\(268\) | 0.585462i | 0.0357628i | ||||||||
\(269\) | −12.6858 | −0.773470 | −0.386735 | − | 0.922191i | \(-0.626397\pi\) | ||||
−0.386735 | + | 0.922191i | \(0.626397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.12181 | 0.0681449 | 0.0340725 | − | 0.999419i | \(-0.489152\pi\) | ||||
0.0340725 | + | 0.999419i | \(0.489152\pi\) | |||||||
\(272\) | − 0.292731i | − 0.0177494i | ||||||||
\(273\) | 5.37169i | 0.325110i | ||||||||
\(274\) | −10.0000 | −0.604122 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.27131 | 0.196910 | ||||||||
\(277\) | 30.1151i | 1.80944i | 0.426007 | + | 0.904720i | \(0.359920\pi\) | ||||
−0.426007 | + | 0.904720i | \(0.640080\pi\) | |||||||
\(278\) | 14.1825i | 0.850609i | ||||||||
\(279\) | 1.64973 | 0.0987668 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.3356 | −0.855189 | −0.427594 | − | 0.903971i | \(-0.640639\pi\) | ||||
−0.427594 | + | 0.903971i | \(0.640639\pi\) | |||||||
\(282\) | − 11.4145i | − 0.679726i | ||||||||
\(283\) | − 3.21377i | − 0.191039i | −0.995428 | − | 0.0955194i | \(-0.969549\pi\) | ||||
0.995428 | − | 0.0955194i | \(-0.0304512\pi\) | |||||||
\(284\) | 0.335577 | 0.0199128 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.68585 | 0.277080 | ||||||||
\(287\) | 6.22533i | 0.367469i | ||||||||
\(288\) | 1.68585i | 0.0993394i | ||||||||
\(289\) | 16.9143 | 0.994959 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4360 | 0.611767 | ||||||||
\(292\) | − 3.70727i | − 0.216952i | ||||||||
\(293\) | 16.6858i | 0.974798i | 0.873179 | + | 0.487399i | \(0.162054\pi\) | ||||
−0.873179 | + | 0.487399i | \(0.837946\pi\) | |||||||
\(294\) | −1.14637 | −0.0668574 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.853635 | 0.0496165 | ||||||||
\(297\) | − 5.37169i | − 0.311697i | ||||||||
\(298\) | − 11.5970i | − 0.671797i | ||||||||
\(299\) | −13.3717 | −0.773305 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3503 | 0.596580 | ||||||||
\(302\) | 1.73183i | 0.0996555i | ||||||||
\(303\) | 12.3650i | 0.710349i | ||||||||
\(304\) | −6.51806 | −0.373836 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.493499 | 0.0282115 | ||||||||
\(307\) | − 6.29273i | − 0.359145i | −0.983745 | − | 0.179573i | \(-0.942529\pi\) | ||||
0.983745 | − | 0.179573i | \(-0.0574715\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | −8.78623 | −0.499831 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.3931 | −1.15639 | −0.578194 | − | 0.815900i | \(-0.696242\pi\) | ||||
−0.578194 | + | 0.815900i | \(0.696242\pi\) | |||||||
\(312\) | 5.37169i | 0.304112i | ||||||||
\(313\) | − 12.0674i | − 0.682090i | −0.940047 | − | 0.341045i | \(-0.889219\pi\) | ||||
0.940047 | − | 0.341045i | \(-0.110781\pi\) | |||||||
\(314\) | 12.2927 | 0.693719 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.51806 | −0.141652 | ||||||||
\(317\) | 28.7679i | 1.61577i | 0.589341 | + | 0.807884i | \(0.299387\pi\) | ||||
−0.589341 | + | 0.807884i | \(0.700613\pi\) | |||||||
\(318\) | − 6.23519i | − 0.349652i | ||||||||
\(319\) | 1.43910 | 0.0805739 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.9639 | 0.611944 | ||||||||
\(322\) | − 2.85363i | − 0.159027i | ||||||||
\(323\) | 1.90804i | 0.106166i | ||||||||
\(324\) | 1.10038 | 0.0611325 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 23.9143 | 1.32449 | ||||||||
\(327\) | 3.60688i | 0.199461i | ||||||||
\(328\) | 6.22533i | 0.343736i | ||||||||
\(329\) | −9.95715 | −0.548956 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.80765 | −0.209288 | −0.104644 | − | 0.994510i | \(-0.533370\pi\) | ||||
−0.104644 | + | 0.994510i | \(0.533370\pi\) | |||||||
\(332\) | − 1.70727i | − 0.0936986i | ||||||||
\(333\) | 1.43910i | 0.0788620i | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.14637 | −0.0625394 | ||||||||
\(337\) | 15.3717i | 0.837349i | 0.908136 | + | 0.418675i | \(0.137505\pi\) | ||||
−0.908136 | + | 0.418675i | \(0.862495\pi\) | |||||||
\(338\) | − 8.95715i | − 0.487205i | ||||||||
\(339\) | 2.96388 | 0.160976 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.978577 | 0.0529929 | ||||||||
\(342\) | − 10.9884i | − 0.594187i | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 10.3503 | 0.558049 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.37169 | −0.396305 | ||||||||
\(347\) | 3.02142i | 0.162198i | 0.996706 | + | 0.0810992i | \(0.0258431\pi\) | ||||
−0.996706 | + | 0.0810992i | \(0.974157\pi\) | |||||||
\(348\) | 1.64973i | 0.0884348i | ||||||||
\(349\) | −11.0361 | −0.590750 | −0.295375 | − | 0.955381i | \(-0.595445\pi\) | ||||
−0.295375 | + | 0.955381i | \(0.595445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.1709 | −1.34352 | ||||||||
\(352\) | 1.00000i | 0.0533002i | ||||||||
\(353\) | − 23.9817i | − 1.27642i | −0.769863 | − | 0.638209i | \(-0.779676\pi\) | ||||
0.769863 | − | 0.638209i | \(-0.220324\pi\) | |||||||
\(354\) | 10.7434 | 0.571004 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 13.0790 | 0.693184 | ||||||||
\(357\) | 0.335577i | 0.0177606i | ||||||||
\(358\) | − 1.56404i | − 0.0826620i | ||||||||
\(359\) | 10.5181 | 0.555122 | 0.277561 | − | 0.960708i | \(-0.410474\pi\) | ||||
0.277561 | + | 0.960708i | \(0.410474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.4851 | 1.23606 | ||||||||
\(362\) | 14.7862i | 0.777147i | ||||||||
\(363\) | − 1.14637i | − 0.0601686i | ||||||||
\(364\) | 4.68585 | 0.245605 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −13.7073 | −0.716490 | ||||||||
\(367\) | − 35.5787i | − 1.85719i | −0.371089 | − | 0.928597i | \(-0.621015\pi\) | ||||
0.371089 | − | 0.928597i | \(-0.378985\pi\) | |||||||
\(368\) | − 2.85363i | − 0.148756i | ||||||||
\(369\) | −10.4949 | −0.546345 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.43910 | −0.282384 | ||||||||
\(372\) | 1.12181i | 0.0581630i | ||||||||
\(373\) | − 7.50650i | − 0.388672i | −0.980935 | − | 0.194336i | \(-0.937745\pi\) | ||||
0.980935 | − | 0.194336i | \(-0.0622552\pi\) | |||||||
\(374\) | 0.292731 | 0.0151368 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.95715 | −0.513501 | ||||||||
\(377\) | − 6.74338i | − 0.347302i | ||||||||
\(378\) | − 5.37169i | − 0.276290i | ||||||||
\(379\) | −33.4868 | −1.72010 | −0.860050 | − | 0.510210i | \(-0.829568\pi\) | ||||
−0.860050 | + | 0.510210i | \(0.829568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15.3288 | −0.785321 | ||||||||
\(382\) | − 17.9572i | − 0.918768i | ||||||||
\(383\) | − 15.6644i | − 0.800415i | −0.916425 | − | 0.400207i | \(-0.868938\pi\) | ||||
0.916425 | − | 0.400207i | \(-0.131062\pi\) | |||||||
\(384\) | −1.14637 | −0.0585002 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.6430 | 0.948904 | ||||||||
\(387\) | 17.4490i | 0.886981i | ||||||||
\(388\) | − 9.10352i | − 0.462161i | ||||||||
\(389\) | 19.6216 | 0.994853 | 0.497427 | − | 0.867506i | \(-0.334278\pi\) | ||||
0.497427 | + | 0.867506i | \(0.334278\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.835347 | −0.0422453 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 13.1134i | 0.661483i | ||||||||
\(394\) | 15.0361 | 0.757509 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.68585 | −0.0847170 | ||||||||
\(397\) | 10.2499i | 0.514427i | 0.966355 | + | 0.257213i | \(0.0828044\pi\) | ||||
−0.966355 | + | 0.257213i | \(0.917196\pi\) | |||||||
\(398\) | − 15.3288i | − 0.768366i | ||||||||
\(399\) | 7.47208 | 0.374072 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.8866 | −0.843277 | −0.421639 | − | 0.906764i | \(-0.638545\pi\) | ||||
−0.421639 | + | 0.906764i | \(0.638545\pi\) | |||||||
\(402\) | − 0.671153i | − 0.0334741i | ||||||||
\(403\) | − 4.58546i | − 0.228418i | ||||||||
\(404\) | 10.7862 | 0.536635 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.43910 | 0.0714212 | ||||||||
\(407\) | 0.853635i | 0.0423131i | ||||||||
\(408\) | 0.335577i | 0.0166135i | ||||||||
\(409\) | −18.2744 | −0.903613 | −0.451807 | − | 0.892116i | \(-0.649220\pi\) | ||||
−0.451807 | + | 0.892116i | \(0.649220\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.4637 | 0.565460 | ||||||||
\(412\) | 7.66442i | 0.377599i | ||||||||
\(413\) | − 9.37169i | − 0.461151i | ||||||||
\(414\) | 4.81079 | 0.236437 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.68585 | 0.229743 | ||||||||
\(417\) | − 16.2583i | − 0.796173i | ||||||||
\(418\) | − 6.51806i | − 0.318809i | ||||||||
\(419\) | 37.2860 | 1.82154 | 0.910770 | − | 0.412914i | \(-0.135489\pi\) | ||||
0.910770 | + | 0.412914i | \(0.135489\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.78623 | −0.135793 | −0.0678963 | − | 0.997692i | \(-0.521629\pi\) | ||||
−0.0678963 | + | 0.997692i | \(0.521629\pi\) | |||||||
\(422\) | 2.04285i | 0.0994442i | ||||||||
\(423\) | − 16.7862i | − 0.816174i | ||||||||
\(424\) | −5.43910 | −0.264146 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.384694 | −0.0186385 | ||||||||
\(427\) | 11.9572i | 0.578647i | ||||||||
\(428\) | − 9.56404i | − 0.462295i | ||||||||
\(429\) | −5.37169 | −0.259348 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.0477 | 1.83269 | 0.916346 | − | 0.400387i | \(-0.131124\pi\) | ||||
0.916346 | + | 0.400387i | \(0.131124\pi\) | |||||||
\(432\) | − 5.37169i | − 0.258446i | ||||||||
\(433\) | 10.8108i | 0.519533i | 0.965671 | + | 0.259767i | \(0.0836457\pi\) | ||||
−0.965671 | + | 0.259767i | \(0.916354\pi\) | |||||||
\(434\) | 0.978577 | 0.0469732 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.14637 | 0.150684 | ||||||||
\(437\) | 18.6002i | 0.889766i | ||||||||
\(438\) | 4.24989i | 0.203067i | ||||||||
\(439\) | −30.9933 | −1.47923 | −0.739614 | − | 0.673031i | \(-0.764992\pi\) | ||||
−0.739614 | + | 0.673031i | \(0.764992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68585 | −0.0802784 | ||||||||
\(442\) | − 1.37169i | − 0.0652448i | ||||||||
\(443\) | − 25.3717i | − 1.20545i | −0.797951 | − | 0.602723i | \(-0.794083\pi\) | ||||
0.797951 | − | 0.602723i | \(-0.205917\pi\) | |||||||
\(444\) | −0.978577 | −0.0464412 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 11.0790 | 0.524604 | ||||||||
\(447\) | 13.2944i | 0.628805i | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | 0.886615 | 0.0418419 | 0.0209210 | − | 0.999781i | \(-0.493340\pi\) | ||||
0.0209210 | + | 0.999781i | \(0.493340\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.22533 | −0.293139 | ||||||||
\(452\) | − 2.58546i | − 0.121610i | ||||||||
\(453\) | − 1.98531i | − 0.0932779i | ||||||||
\(454\) | 18.5426 | 0.870248 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 7.47208 | 0.349912 | ||||||||
\(457\) | 29.9143i | 1.39933i | 0.714470 | + | 0.699666i | \(0.246668\pi\) | ||||
−0.714470 | + | 0.699666i | \(0.753332\pi\) | |||||||
\(458\) | 8.01469i | 0.374502i | ||||||||
\(459\) | −1.57246 | −0.0733962 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.33558 | −0.108779 | −0.0543893 | − | 0.998520i | \(-0.517321\pi\) | ||||
−0.0543893 | + | 0.998520i | \(0.517321\pi\) | |||||||
\(462\) | − 1.14637i | − 0.0533337i | ||||||||
\(463\) | − 0.110250i | − 0.00512374i | −0.999997 | − | 0.00256187i | \(-0.999185\pi\) | ||||
0.999997 | − | 0.00256187i | \(-0.000815470\pi\) | |||||||
\(464\) | 1.43910 | 0.0668084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.9572 | 1.29509 | ||||||||
\(467\) | 36.6760i | 1.69716i | 0.529066 | + | 0.848581i | \(0.322543\pi\) | ||||
−0.529066 | + | 0.848581i | \(0.677457\pi\) | |||||||
\(468\) | 7.89962i | 0.365160i | ||||||||
\(469\) | −0.585462 | −0.0270341 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.0920 | −0.649323 | ||||||||
\(472\) | − 9.37169i | − 0.431367i | ||||||||
\(473\) | 10.3503i | 0.475906i | ||||||||
\(474\) | 2.88661 | 0.132587 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.292731 | 0.0134173 | ||||||||
\(477\) | − 9.16948i | − 0.419842i | ||||||||
\(478\) | 28.8108i | 1.31777i | ||||||||
\(479\) | 42.7434 | 1.95300 | 0.976498 | − | 0.215529i | \(-0.0691474\pi\) | ||||
0.976498 | + | 0.215529i | \(0.0691474\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | − 8.51806i | − 0.387987i | ||||||||
\(483\) | 3.27131i | 0.148850i | ||||||||
\(484\) | −1.00000 | −0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.8536 | 0.673775 | ||||||||
\(487\) | − 36.1396i | − 1.63764i | −0.574048 | − | 0.818822i | \(-0.694628\pi\) | ||||
0.574048 | − | 0.818822i | \(-0.305372\pi\) | |||||||
\(488\) | 11.9572i | 0.541275i | ||||||||
\(489\) | −27.4145 | −1.23973 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.54262 | 0.114747 | 0.0573733 | − | 0.998353i | \(-0.481727\pi\) | ||||
0.0573733 | + | 0.998353i | \(0.481727\pi\) | |||||||
\(492\) | − 7.13650i | − 0.321738i | ||||||||
\(493\) | − 0.421268i | − 0.0189730i | ||||||||
\(494\) | −30.5426 | −1.37418 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.978577 | 0.0439394 | ||||||||
\(497\) | 0.335577i | 0.0150527i | ||||||||
\(498\) | 1.95715i | 0.0877022i | ||||||||
\(499\) | −3.13650 | −0.140409 | −0.0702045 | − | 0.997533i | \(-0.522365\pi\) | ||||
−0.0702045 | + | 0.997533i | \(0.522365\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.17092 | −0.409727 | ||||||||
\(502\) | − 23.1281i | − 1.03226i | ||||||||
\(503\) | 28.5855i | 1.27456i | 0.770631 | + | 0.637281i | \(0.219941\pi\) | ||||
−0.770631 | + | 0.637281i | \(0.780059\pi\) | |||||||
\(504\) | −1.68585 | −0.0750936 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.85363 | 0.126860 | ||||||||
\(507\) | 10.2682i | 0.456026i | ||||||||
\(508\) | 13.3717i | 0.593273i | ||||||||
\(509\) | −2.20077 | −0.0975473 | −0.0487737 | − | 0.998810i | \(-0.515531\pi\) | ||||
−0.0487737 | + | 0.998810i | \(0.515531\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.70727 | 0.164000 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 35.0130i | 1.54586i | ||||||||
\(514\) | −14.8108 | −0.653276 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −11.8652 | −0.522336 | ||||||||
\(517\) | − 9.95715i | − 0.437915i | ||||||||
\(518\) | 0.853635i | 0.0375065i | ||||||||
\(519\) | 8.45065 | 0.370943 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.1940 | 1.62950 | 0.814750 | − | 0.579812i | \(-0.196874\pi\) | ||||
0.814750 | + | 0.579812i | \(0.196874\pi\) | |||||||
\(522\) | 2.42610i | 0.106187i | ||||||||
\(523\) | − 30.4078i | − 1.32964i | −0.747003 | − | 0.664820i | \(-0.768508\pi\) | ||||
0.747003 | − | 0.664820i | \(-0.231492\pi\) | |||||||
\(524\) | 11.4391 | 0.499719 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7434 | 0.817250 | ||||||||
\(527\) | − 0.286460i | − 0.0124784i | ||||||||
\(528\) | − 1.14637i | − 0.0498892i | ||||||||
\(529\) | 14.8568 | 0.645947 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.7992 | 0.685628 | ||||||||
\(532\) | − 6.51806i | − 0.282594i | ||||||||
\(533\) | 29.1709i | 1.26353i | ||||||||
\(534\) | −14.9933 | −0.648822 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.585462 | −0.0252881 | ||||||||
\(537\) | 1.79296i | 0.0773720i | ||||||||
\(538\) | − 12.6858i | − 0.546926i | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.0607 | 1.67935 | 0.839675 | − | 0.543090i | \(-0.182746\pi\) | ||||
0.839675 | + | 0.543090i | \(0.182746\pi\) | |||||||
\(542\) | 1.12181i | 0.0481857i | ||||||||
\(543\) | − 16.9504i | − 0.727412i | ||||||||
\(544\) | 0.292731 | 0.0125507 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.37169 | −0.229887 | ||||||||
\(547\) | − 0.585462i | − 0.0250325i | −0.999922 | − | 0.0125163i | \(-0.996016\pi\) | ||||
0.999922 | − | 0.0125163i | \(-0.00398416\pi\) | |||||||
\(548\) | − 10.0000i | − 0.427179i | ||||||||
\(549\) | −20.1579 | −0.860319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.38011 | −0.399606 | ||||||||
\(552\) | 3.27131i | 0.139236i | ||||||||
\(553\) | − 2.51806i | − 0.107079i | ||||||||
\(554\) | −30.1151 | −1.27947 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.1825 | −0.601471 | ||||||||
\(557\) | 17.4637i | 0.739959i | 0.929040 | + | 0.369979i | \(0.120635\pi\) | ||||
−0.929040 | + | 0.369979i | \(0.879365\pi\) | |||||||
\(558\) | 1.64973i | 0.0698387i | ||||||||
\(559\) | 48.4998 | 2.05132 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.335577 | −0.0141681 | ||||||||
\(562\) | − 14.3356i | − 0.604710i | ||||||||
\(563\) | 18.1579i | 0.765265i | 0.923901 | + | 0.382633i | \(0.124982\pi\) | ||||
−0.923901 | + | 0.382633i | \(0.875018\pi\) | |||||||
\(564\) | 11.4145 | 0.480639 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.21377 | 0.135085 | ||||||||
\(567\) | 1.10038i | 0.0462118i | ||||||||
\(568\) | 0.335577i | 0.0140805i | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.03612 | −0.378150 | −0.189075 | − | 0.981963i | \(-0.560549\pi\) | ||||
−0.189075 | + | 0.981963i | \(0.560549\pi\) | |||||||
\(572\) | 4.68585i | 0.195925i | ||||||||
\(573\) | 20.5855i | 0.859970i | ||||||||
\(574\) | −6.22533 | −0.259840 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.68585 | −0.0702436 | ||||||||
\(577\) | 19.3963i | 0.807476i | 0.914875 | + | 0.403738i | \(0.132289\pi\) | ||||
−0.914875 | + | 0.403738i | \(0.867711\pi\) | |||||||
\(578\) | 16.9143i | 0.703542i | ||||||||
\(579\) | −21.3717 | −0.888177 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.70727 | 0.0708295 | ||||||||
\(582\) | 10.4360i | 0.432584i | ||||||||
\(583\) | − 5.43910i | − 0.225264i | ||||||||
\(584\) | 3.70727 | 0.153408 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.6858 | −0.689286 | ||||||||
\(587\) | 17.2614i | 0.712456i | 0.934399 | + | 0.356228i | \(0.115937\pi\) | ||||
−0.934399 | + | 0.356228i | \(0.884063\pi\) | |||||||
\(588\) | − 1.14637i | − 0.0472753i | ||||||||
\(589\) | −6.37842 | −0.262818 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.2369 | −0.709031 | ||||||||
\(592\) | 0.853635i | 0.0350842i | ||||||||
\(593\) | 11.0361i | 0.453199i | 0.973988 | + | 0.226599i | \(0.0727608\pi\) | ||||
−0.973988 | + | 0.226599i | \(0.927239\pi\) | |||||||
\(594\) | 5.37169 | 0.220403 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.5970 | 0.475032 | ||||||||
\(597\) | 17.5725i | 0.719193i | ||||||||
\(598\) | − 13.3717i | − 0.546809i | ||||||||
\(599\) | 41.7367 | 1.70531 | 0.852657 | − | 0.522472i | \(-0.174990\pi\) | ||||
0.852657 | + | 0.522472i | \(0.174990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3106 | 1.60351 | 0.801756 | − | 0.597652i | \(-0.203900\pi\) | ||||
0.801756 | + | 0.597652i | \(0.203900\pi\) | |||||||
\(602\) | 10.3503i | 0.421845i | ||||||||
\(603\) | − 0.986999i | − 0.0401937i | ||||||||
\(604\) | −1.73183 | −0.0704671 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12.3650 | −0.502292 | ||||||||
\(607\) | − 6.35027i | − 0.257749i | −0.991661 | − | 0.128875i | \(-0.958863\pi\) | ||||
0.991661 | − | 0.128875i | \(-0.0411365\pi\) | |||||||
\(608\) | − 6.51806i | − 0.264342i | ||||||||
\(609\) | −1.64973 | −0.0668505 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −46.6577 | −1.88757 | ||||||||
\(612\) | 0.493499i | 0.0199485i | ||||||||
\(613\) | 42.4507i | 1.71457i | 0.514846 | + | 0.857283i | \(0.327849\pi\) | ||||
−0.514846 | + | 0.857283i | \(0.672151\pi\) | |||||||
\(614\) | 6.29273 | 0.253954 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.00000 | −0.0402911 | ||||||||
\(617\) | − 0.677425i | − 0.0272721i | −0.999907 | − | 0.0136360i | \(-0.995659\pi\) | ||||
0.999907 | − | 0.0136360i | \(-0.00434062\pi\) | |||||||
\(618\) | − 8.78623i | − 0.353434i | ||||||||
\(619\) | 18.5426 | 0.745291 | 0.372645 | − | 0.927974i | \(-0.378451\pi\) | ||||
0.372645 | + | 0.927974i | \(0.378451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −15.3288 | −0.615125 | ||||||||
\(622\) | − 20.3931i | − 0.817689i | ||||||||
\(623\) | 13.0790i | 0.523998i | ||||||||
\(624\) | −5.37169 | −0.215040 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.0674 | 0.482310 | ||||||||
\(627\) | 7.47208i | 0.298406i | ||||||||
\(628\) | 12.2927i | 0.490533i | ||||||||
\(629\) | 0.249885 | 0.00996358 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3717 | 0.850794 | 0.425397 | − | 0.905007i | \(-0.360135\pi\) | ||||
0.425397 | + | 0.905007i | \(0.360135\pi\) | |||||||
\(632\) | − 2.51806i | − 0.100163i | ||||||||
\(633\) | − 2.34185i | − 0.0930801i | ||||||||
\(634\) | −28.7679 | −1.14252 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 6.23519 | 0.247241 | ||||||||
\(637\) | 4.68585i | 0.185660i | ||||||||
\(638\) | 1.43910i | 0.0569744i | ||||||||
\(639\) | −0.565731 | −0.0223800 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.8715 | 0.942866 | 0.471433 | − | 0.881902i | \(-0.343737\pi\) | ||||
0.471433 | + | 0.881902i | \(0.343737\pi\) | |||||||
\(642\) | 10.9639i | 0.432710i | ||||||||
\(643\) | − 0.311018i | − 0.0122654i | −0.999981 | − | 0.00613268i | \(-0.998048\pi\) | ||||
0.999981 | − | 0.00613268i | \(-0.00195211\pi\) | |||||||
\(644\) | 2.85363 | 0.112449 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.90804 | −0.0750707 | ||||||||
\(647\) | − 9.62158i | − 0.378263i | −0.981952 | − | 0.189132i | \(-0.939433\pi\) | ||||
0.981952 | − | 0.189132i | \(-0.0605673\pi\) | |||||||
\(648\) | 1.10038i | 0.0432272i | ||||||||
\(649\) | 9.37169 | 0.367871 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.12181 | −0.0439671 | ||||||||
\(652\) | 23.9143i | 0.936557i | ||||||||
\(653\) | 27.0607i | 1.05897i | 0.848321 | + | 0.529483i | \(0.177614\pi\) | ||||
−0.848321 | + | 0.529483i | \(0.822386\pi\) | |||||||
\(654\) | −3.60688 | −0.141040 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.22533 | −0.243058 | ||||||||
\(657\) | 6.24989i | 0.243831i | ||||||||
\(658\) | − 9.95715i | − 0.388170i | ||||||||
\(659\) | 26.4935 | 1.03204 | 0.516020 | − | 0.856576i | \(-0.327413\pi\) | ||||
0.516020 | + | 0.856576i | \(0.327413\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.0852 | 1.36466 | 0.682329 | − | 0.731046i | \(-0.260967\pi\) | ||||
0.682329 | + | 0.731046i | \(0.260967\pi\) | |||||||
\(662\) | − 3.80765i | − 0.147989i | ||||||||
\(663\) | 1.57246i | 0.0610693i | ||||||||
\(664\) | 1.70727 | 0.0662549 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.43910 | −0.0557639 | ||||||||
\(667\) | − 4.10666i | − 0.159010i | ||||||||
\(668\) | 8.00000i | 0.309529i | ||||||||
\(669\) | −12.7005 | −0.491031 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.9572 | −0.461601 | ||||||||
\(672\) | − 1.14637i | − 0.0442220i | ||||||||
\(673\) | − 32.6577i | − 1.25886i | −0.777057 | − | 0.629431i | \(-0.783288\pi\) | ||||
0.777057 | − | 0.629431i | \(-0.216712\pi\) | |||||||
\(674\) | −15.3717 | −0.592095 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.95715 | 0.344506 | ||||||||
\(677\) | 9.12808i | 0.350821i | 0.984495 | + | 0.175410i | \(0.0561252\pi\) | ||||
−0.984495 | + | 0.175410i | \(0.943875\pi\) | |||||||
\(678\) | 2.96388i | 0.113827i | ||||||||
\(679\) | 9.10352 | 0.349361 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.2566 | −0.814555 | ||||||||
\(682\) | 0.978577i | 0.0374717i | ||||||||
\(683\) | − 10.4935i | − 0.401523i | −0.979640 | − | 0.200761i | \(-0.935658\pi\) | ||||
0.979640 | − | 0.200761i | \(-0.0643416\pi\) | |||||||
\(684\) | 10.9884 | 0.420154 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | − 9.18777i | − 0.350535i | ||||||||
\(688\) | 10.3503i | 0.394600i | ||||||||
\(689\) | −25.4868 | −0.970969 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.70727 | 0.0649476 | 0.0324738 | − | 0.999473i | \(-0.489661\pi\) | ||||
0.0324738 | + | 0.999473i | \(0.489661\pi\) | |||||||
\(692\) | − 7.37169i | − 0.280230i | ||||||||
\(693\) | − 1.68585i | − 0.0640400i | ||||||||
\(694\) | −3.02142 | −0.114692 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.64973 | −0.0625329 | ||||||||
\(697\) | 1.82235i | 0.0690263i | ||||||||
\(698\) | − 11.0361i | − 0.417723i | ||||||||
\(699\) | −32.0491 | −1.21221 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3534 | −1.41082 | −0.705409 | − | 0.708800i | \(-0.749237\pi\) | ||||
−0.705409 | + | 0.708800i | \(0.749237\pi\) | |||||||
\(702\) | − 25.1709i | − 0.950015i | ||||||||
\(703\) | − 5.56404i | − 0.209852i | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.9817 | 0.902564 | ||||||||
\(707\) | 10.7862i | 0.405658i | ||||||||
\(708\) | 10.7434i | 0.403761i | ||||||||
\(709\) | 8.20704 | 0.308222 | 0.154111 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154111 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.24506 | 0.159202 | ||||||||
\(712\) | 13.0790i | 0.490155i | ||||||||
\(713\) | − 2.79250i | − 0.104580i | ||||||||
\(714\) | −0.335577 | −0.0125586 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.56404 | 0.0584509 | ||||||||
\(717\) | − 33.0277i | − 1.23344i | ||||||||
\(718\) | 10.5181i | 0.392530i | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.66442 | −0.285438 | ||||||||
\(722\) | 23.4851i | 0.874024i | ||||||||
\(723\) | 9.76481i | 0.363157i | ||||||||
\(724\) | −14.7862 | −0.549526 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.14637 | 0.0425456 | ||||||||
\(727\) | − 46.9442i | − 1.74106i | −0.492113 | − | 0.870531i | \(-0.663775\pi\) | ||||
0.492113 | − | 0.870531i | \(-0.336225\pi\) | |||||||
\(728\) | 4.68585i | 0.173669i | ||||||||
\(729\) | −20.3288 | −0.752920 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.02984 | 0.112063 | ||||||||
\(732\) | − 13.7073i | − 0.506635i | ||||||||
\(733\) | 42.0000i | 1.55131i | 0.631160 | + | 0.775653i | \(0.282579\pi\) | ||||
−0.631160 | + | 0.775653i | \(0.717421\pi\) | |||||||
\(734\) | 35.5787 | 1.31323 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.85363 | 0.105186 | ||||||||
\(737\) | − 0.585462i | − 0.0215658i | ||||||||
\(738\) | − 10.4949i | − 0.386324i | ||||||||
\(739\) | 0.871922 | 0.0320742 | 0.0160371 | − | 0.999871i | \(-0.494895\pi\) | ||||
0.0160371 | + | 0.999871i | \(0.494895\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 35.0130 | 1.28623 | ||||||||
\(742\) | − 5.43910i | − 0.199676i | ||||||||
\(743\) | 24.6712i | 0.905097i | 0.891740 | + | 0.452548i | \(0.149485\pi\) | ||||
−0.891740 | + | 0.452548i | \(0.850515\pi\) | |||||||
\(744\) | −1.12181 | −0.0411274 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.50650 | 0.274833 | ||||||||
\(747\) | 2.87819i | 0.105308i | ||||||||
\(748\) | 0.292731i | 0.0107033i | ||||||||
\(749\) | 9.56404 | 0.349462 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.75011 | −0.136844 | −0.0684218 | − | 0.997656i | \(-0.521796\pi\) | ||||
−0.0684218 | + | 0.997656i | \(0.521796\pi\) | |||||||
\(752\) | − 9.95715i | − 0.363100i | ||||||||
\(753\) | 26.5132i | 0.966196i | ||||||||
\(754\) | 6.74338 | 0.245580 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.37169 | 0.195367 | ||||||||
\(757\) | 15.7318i | 0.571783i | 0.958262 | + | 0.285891i | \(0.0922897\pi\) | ||||
−0.958262 | + | 0.285891i | \(0.907710\pi\) | |||||||
\(758\) | − 33.4868i | − 1.21629i | ||||||||
\(759\) | −3.27131 | −0.118741 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.2614 | 0.553227 | 0.276613 | − | 0.960981i | \(-0.410788\pi\) | ||||
0.276613 | + | 0.960981i | \(0.410788\pi\) | |||||||
\(762\) | − 15.3288i | − 0.555306i | ||||||||
\(763\) | 3.14637i | 0.113906i | ||||||||
\(764\) | 17.9572 | 0.649667 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.6644 | 0.565979 | ||||||||
\(767\) | − 43.9143i | − 1.58565i | ||||||||
\(768\) | − 1.14637i | − 0.0413659i | ||||||||
\(769\) | 9.63986 | 0.347622 | 0.173811 | − | 0.984779i | \(-0.444392\pi\) | ||||
0.173811 | + | 0.984779i | \(0.444392\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9786 | 0.611469 | ||||||||
\(772\) | 18.6430i | 0.670976i | ||||||||
\(773\) | − 12.8291i | − 0.461430i | −0.973021 | − | 0.230715i | \(-0.925894\pi\) | ||||
0.973021 | − | 0.230715i | \(-0.0741065\pi\) | |||||||
\(774\) | −17.4490 | −0.627190 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.10352 | 0.326797 | ||||||||
\(777\) | − 0.978577i | − 0.0351063i | ||||||||
\(778\) | 19.6216i | 0.703468i | ||||||||
\(779\) | 40.5770 | 1.45382 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.335577 | −0.0120079 | ||||||||
\(782\) | − 0.835347i | − 0.0298720i | ||||||||
\(783\) | − 7.73038i | − 0.276261i | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −13.1134 | −0.467739 | ||||||||
\(787\) | 10.8291i | 0.386015i | 0.981197 | + | 0.193007i | \(0.0618242\pi\) | ||||
−0.981197 | + | 0.193007i | \(0.938176\pi\) | |||||||
\(788\) | 15.0361i | 0.535639i | ||||||||
\(789\) | −21.4868 | −0.764949 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.58546 | 0.0919284 | ||||||||
\(792\) | − 1.68585i | − 0.0599039i | ||||||||
\(793\) | 56.0294i | 1.98966i | ||||||||
\(794\) | −10.2499 | −0.363755 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 15.3288 | 0.543317 | ||||||||
\(797\) | − 21.0790i | − 0.746655i | −0.927700 | − | 0.373328i | \(-0.878217\pi\) | ||||
0.927700 | − | 0.373328i | \(-0.121783\pi\) | |||||||
\(798\) | 7.47208i | 0.264509i | ||||||||
\(799\) | −2.91477 | −0.103117 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.0491 | −0.779067 | ||||||||
\(802\) | − 16.8866i | − 0.596287i | ||||||||
\(803\) | 3.70727i | 0.130827i | ||||||||
\(804\) | 0.671153 | 0.0236698 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.58546 | 0.161516 | ||||||||
\(807\) | 14.5426i | 0.511924i | ||||||||
\(808\) | 10.7862i | 0.379458i | ||||||||
\(809\) | −3.62158 | −0.127328 | −0.0636639 | − | 0.997971i | \(-0.520279\pi\) | ||||
−0.0636639 | + | 0.997971i | \(0.520279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.7188 | 1.21914 | 0.609571 | − | 0.792731i | \(-0.291342\pi\) | ||||
0.609571 | + | 0.792731i | \(0.291342\pi\) | |||||||
\(812\) | 1.43910i | 0.0505024i | ||||||||
\(813\) | − 1.28600i | − 0.0451020i | ||||||||
\(814\) | −0.853635 | −0.0299199 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.335577 | −0.0117475 | ||||||||
\(817\) | − 67.4637i | − 2.36025i | ||||||||
\(818\) | − 18.2744i | − 0.638951i | ||||||||
\(819\) | −7.89962 | −0.276035 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.7549 | −1.31766 | −0.658828 | − | 0.752293i | \(-0.728948\pi\) | ||||
−0.658828 | + | 0.752293i | \(0.728948\pi\) | |||||||
\(822\) | 11.4637i | 0.399841i | ||||||||
\(823\) | − 11.1892i | − 0.390031i | −0.980800 | − | 0.195016i | \(-0.937524\pi\) | ||||
0.980800 | − | 0.195016i | \(-0.0624758\pi\) | |||||||
\(824\) | −7.66442 | −0.267003 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.37169 | 0.326083 | ||||||||
\(827\) | − 7.91431i | − 0.275207i | −0.990487 | − | 0.137604i | \(-0.956060\pi\) | ||||
0.990487 | − | 0.137604i | \(-0.0439400\pi\) | |||||||
\(828\) | 4.81079i | 0.167186i | ||||||||
\(829\) | 44.7152 | 1.55302 | 0.776512 | − | 0.630102i | \(-0.216987\pi\) | ||||
0.776512 | + | 0.630102i | \(0.216987\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 34.5229 | 1.19759 | ||||||||
\(832\) | 4.68585i | 0.162452i | ||||||||
\(833\) | 0.292731i | 0.0101425i | ||||||||
\(834\) | 16.2583 | 0.562979 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.51806 | 0.225432 | ||||||||
\(837\) | − 5.25662i | − 0.181695i | ||||||||
\(838\) | 37.2860i | 1.28802i | ||||||||
\(839\) | −21.6791 | −0.748446 | −0.374223 | − | 0.927339i | \(-0.622091\pi\) | ||||
−0.374223 | + | 0.927339i | \(0.622091\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9290 | −0.928586 | ||||||||
\(842\) | − 2.78623i | − 0.0960198i | ||||||||
\(843\) | 16.4338i | 0.566010i | ||||||||
\(844\) | −2.04285 | −0.0703176 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.7862 | 0.577122 | ||||||||
\(847\) | − 1.00000i | − 0.0343604i | ||||||||
\(848\) | − 5.43910i | − 0.186779i | ||||||||
\(849\) | −3.68415 | −0.126440 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.43596 | 0.0835037 | ||||||||
\(852\) | − 0.384694i | − 0.0131794i | ||||||||
\(853\) | − 9.41454i | − 0.322348i | −0.986926 | − | 0.161174i | \(-0.948472\pi\) | ||||
0.986926 | − | 0.161174i | \(-0.0515280\pi\) | |||||||
\(854\) | −11.9572 | −0.409165 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.56404 | 0.326892 | ||||||||
\(857\) | − 25.8652i | − 0.883538i | −0.897129 | − | 0.441769i | \(-0.854351\pi\) | ||||
0.897129 | − | 0.441769i | \(-0.145649\pi\) | |||||||
\(858\) | − 5.37169i | − 0.183387i | ||||||||
\(859\) | 29.2860 | 0.999225 | 0.499613 | − | 0.866249i | \(-0.333476\pi\) | ||||
0.499613 | + | 0.866249i | \(0.333476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.13650 | 0.243211 | ||||||||
\(862\) | 38.0477i | 1.29591i | ||||||||
\(863\) | 20.3110i | 0.691395i | 0.938346 | + | 0.345698i | \(0.112358\pi\) | ||||
−0.938346 | + | 0.345698i | \(0.887642\pi\) | |||||||
\(864\) | 5.37169 | 0.182749 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −10.8108 | −0.367366 | ||||||||
\(867\) | − 19.3900i | − 0.658518i | ||||||||
\(868\) | 0.978577i | 0.0332151i | ||||||||
\(869\) | 2.51806 | 0.0854193 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.74338 | −0.0929560 | ||||||||
\(872\) | 3.14637i | 0.106549i | ||||||||
\(873\) | 15.3471i | 0.519422i | ||||||||
\(874\) | −18.6002 | −0.629160 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.24989 | −0.143590 | ||||||||
\(877\) | − 38.3650i | − 1.29549i | −0.761856 | − | 0.647746i | \(-0.775712\pi\) | ||||
0.761856 | − | 0.647746i | \(-0.224288\pi\) | |||||||
\(878\) | − 30.9933i | − 1.04597i | ||||||||
\(879\) | 19.1281 | 0.645174 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 40.5426 | 1.36592 | 0.682958 | − | 0.730458i | \(-0.260693\pi\) | ||||
0.682958 | + | 0.730458i | \(0.260693\pi\) | |||||||
\(882\) | − 1.68585i | − 0.0567654i | ||||||||
\(883\) | − 28.0491i | − 0.943928i | −0.881618 | − | 0.471964i | \(-0.843545\pi\) | ||||
0.881618 | − | 0.471964i | \(-0.156455\pi\) | |||||||
\(884\) | 1.37169 | 0.0461350 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.3717 | 0.852379 | ||||||||
\(887\) | − 6.65769i | − 0.223543i | −0.993734 | − | 0.111772i | \(-0.964347\pi\) | ||||
0.993734 | − | 0.111772i | \(-0.0356525\pi\) | |||||||
\(888\) | − 0.978577i | − 0.0328389i | ||||||||
\(889\) | −13.3717 | −0.448472 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.10038 | −0.0368643 | ||||||||
\(892\) | 11.0790i | 0.370951i | ||||||||
\(893\) | 64.9013i | 2.17184i | ||||||||
\(894\) | −13.2944 | −0.444632 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 15.3288i | 0.511815i | ||||||||
\(898\) | 0.886615i | 0.0295867i | ||||||||
\(899\) | 1.40827 | 0.0469683 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.59219 | −0.0530436 | ||||||||
\(902\) | − 6.22533i | − 0.207281i | ||||||||
\(903\) | − 11.8652i | − 0.394849i | ||||||||
\(904\) | 2.58546 | 0.0859912 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.98531 | 0.0659574 | ||||||||
\(907\) | 39.5787i | 1.31419i | 0.753808 | + | 0.657095i | \(0.228215\pi\) | ||||
−0.753808 | + | 0.657095i | \(0.771785\pi\) | |||||||
\(908\) | 18.5426i | 0.615358i | ||||||||
\(909\) | −18.1839 | −0.603123 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.3356 | −0.806274 | −0.403137 | − | 0.915140i | \(-0.632080\pi\) | ||||
−0.403137 | + | 0.915140i | \(0.632080\pi\) | |||||||
\(912\) | 7.47208i | 0.247425i | ||||||||
\(913\) | 1.70727i | 0.0565024i | ||||||||
\(914\) | −29.9143 | −0.989477 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.01469 | −0.264813 | ||||||||
\(917\) | 11.4391i | 0.377752i | ||||||||
\(918\) | − 1.57246i | − 0.0518989i | ||||||||
\(919\) | −50.6331 | −1.67023 | −0.835117 | − | 0.550073i | \(-0.814600\pi\) | ||||
−0.835117 | + | 0.550073i | \(0.814600\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.21377 | −0.237702 | ||||||||
\(922\) | − 2.33558i | − 0.0769181i | ||||||||
\(923\) | 1.57246i | 0.0517582i | ||||||||
\(924\) | 1.14637 | 0.0377127 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.110250 | 0.00362303 | ||||||||
\(927\) | − 12.9210i | − 0.424383i | ||||||||
\(928\) | 1.43910i | 0.0472407i | ||||||||
\(929\) | −47.1512 | −1.54698 | −0.773490 | − | 0.633808i | \(-0.781491\pi\) | ||||
−0.773490 | + | 0.633808i | \(0.781491\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.51806 | 0.213621 | ||||||||
\(932\) | 27.9572i | 0.915767i | ||||||||
\(933\) | 23.3780i | 0.765360i | ||||||||
\(934\) | −36.6760 | −1.20007 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.89962 | −0.258207 | ||||||||
\(937\) | − 42.0294i | − 1.37304i | −0.727111 | − | 0.686520i | \(-0.759137\pi\) | ||||
0.727111 | − | 0.686520i | \(-0.240863\pi\) | |||||||
\(938\) | − 0.585462i | − 0.0191160i | ||||||||
\(939\) | −13.8337 | −0.451444 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.7434 | −1.19780 | −0.598900 | − | 0.800824i | \(-0.704395\pi\) | ||||
−0.598900 | + | 0.800824i | \(0.704395\pi\) | |||||||
\(942\) | − 14.0920i | − 0.459141i | ||||||||
\(943\) | 17.7648i | 0.578502i | ||||||||
\(944\) | 9.37169 | 0.305023 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.3503 | −0.336516 | ||||||||
\(947\) | 18.8782i | 0.613459i | 0.951797 | + | 0.306729i | \(0.0992347\pi\) | ||||
−0.951797 | + | 0.306729i | \(0.900765\pi\) | |||||||
\(948\) | 2.88661i | 0.0937529i | ||||||||
\(949\) | 17.3717 | 0.563909 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.9786 | 1.06940 | ||||||||
\(952\) | 0.292731i | 0.00948747i | ||||||||
\(953\) | 43.2285i | 1.40031i | 0.713992 | + | 0.700154i | \(0.246885\pi\) | ||||
−0.713992 | + | 0.700154i | \(0.753115\pi\) | |||||||
\(954\) | 9.16948 | 0.296873 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.8108 | −0.931808 | ||||||||
\(957\) | − 1.64973i | − 0.0533282i | ||||||||
\(958\) | 42.7434i | 1.38098i | ||||||||
\(959\) | 10.0000 | 0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0424 | −0.969109 | ||||||||
\(962\) | 4.00000i | 0.128965i | ||||||||
\(963\) | 16.1235i | 0.519572i | ||||||||
\(964\) | 8.51806 | 0.274348 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.27131 | −0.105253 | ||||||||
\(967\) | 48.7299i | 1.56705i | 0.621361 | + | 0.783524i | \(0.286580\pi\) | ||||
−0.621361 | + | 0.783524i | \(0.713420\pi\) | |||||||
\(968\) | − 1.00000i | − 0.0321412i | ||||||||
\(969\) | 2.18731 | 0.0702665 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.9865 | −0.833948 | −0.416974 | − | 0.908918i | \(-0.636909\pi\) | ||||
−0.416974 | + | 0.908918i | \(0.636909\pi\) | |||||||
\(972\) | 14.8536i | 0.476431i | ||||||||
\(973\) | − 14.1825i | − 0.454669i | ||||||||
\(974\) | 36.1396 | 1.15799 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.9572 | −0.382739 | ||||||||
\(977\) | 2.67115i | 0.0854578i | 0.999087 | + | 0.0427289i | \(0.0136052\pi\) | ||||
−0.999087 | + | 0.0427289i | \(0.986395\pi\) | |||||||
\(978\) | − 27.4145i | − 0.876620i | ||||||||
\(979\) | −13.0790 | −0.418005 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.30429 | −0.169353 | ||||||||
\(982\) | 2.54262i | 0.0811381i | ||||||||
\(983\) | 8.33558i | 0.265864i | 0.991125 | + | 0.132932i | \(0.0424391\pi\) | ||||
−0.991125 | + | 0.132932i | \(0.957561\pi\) | |||||||
\(984\) | 7.13650 | 0.227503 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.421268 | 0.0134159 | ||||||||
\(987\) | 11.4145i | 0.363329i | ||||||||
\(988\) | − 30.5426i | − 0.971690i | ||||||||
\(989\) | 29.5359 | 0.939187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.2730 | 1.46991 | 0.734955 | − | 0.678116i | \(-0.237203\pi\) | ||||
0.734955 | + | 0.678116i | \(0.237203\pi\) | |||||||
\(992\) | 0.978577i | 0.0310699i | ||||||||
\(993\) | 4.36496i | 0.138518i | ||||||||
\(994\) | −0.335577 | −0.0106438 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.95715 | −0.0620148 | ||||||||
\(997\) | 35.8715i | 1.13606i | 0.823008 | + | 0.568030i | \(0.192294\pi\) | ||||
−0.823008 | + | 0.568030i | \(0.807706\pi\) | |||||||
\(998\) | − 3.13650i | − 0.0992842i | ||||||||
\(999\) | 4.58546 | 0.145078 |
(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 | 3850.2.c.ba.1849.5 | 6 | ||
5.2 | odd | 4 | 3850.2.a.bt.1.2 | 3 | |||
5.3 | odd | 4 | 770.2.a.m.1.2 | ✓ | 3 | ||
5.4 | even | 2 | inner | 3850.2.c.ba.1849.2 | 6 | ||
15.8 | even | 4 | 6930.2.a.ce.1.3 | 3 | |||
20.3 | even | 4 | 6160.2.a.bf.1.2 | 3 | |||
35.13 | even | 4 | 5390.2.a.ca.1.2 | 3 | |||
55.43 | even | 4 | 8470.2.a.ci.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.m.1.2 | ✓ | 3 | 5.3 | odd | 4 | ||
3850.2.a.bt.1.2 | 3 | 5.2 | odd | 4 | |||
3850.2.c.ba.1849.2 | 6 | 5.4 | even | 2 | inner | ||
3850.2.c.ba.1849.5 | 6 | 1.1 | even | 1 | trivial | ||
5390.2.a.ca.1.2 | 3 | 35.13 | even | 4 | |||
6160.2.a.bf.1.2 | 3 | 20.3 | even | 4 | |||
6930.2.a.ce.1.3 | 3 | 15.8 | even | 4 | |||
8470.2.a.ci.1.2 | 3 | 55.43 | even | 4 |