Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.3 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.b.1249.2 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | 0.935414 | + | 0.353553i | \(0.115027\pi\) | ||||
−0.935414 | + | 0.353553i | \(0.884973\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | − 4.47214i | − 1.69031i | −0.534522 | − | 0.845154i | \(-0.679509\pi\) | ||||
0.534522 | − | 0.845154i | \(-0.320491\pi\) | |||||||
\(8\) | 3.00000i | 1.06066i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23607 | −0.372689 | −0.186344 | − | 0.982485i | \(-0.559664\pi\) | ||||
−0.186344 | + | 0.982485i | \(0.559664\pi\) | |||||||
\(12\) | − 1.00000i | − 0.288675i | ||||||||
\(13\) | − 5.61803i | − 1.55816i | −0.626923 | − | 0.779081i | \(-0.715686\pi\) | ||||
0.626923 | − | 0.779081i | \(-0.284314\pi\) | |||||||
\(14\) | 4.47214 | 1.19523 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.85410i | 0.934757i | 0.884057 | + | 0.467379i | \(0.154801\pi\) | ||||
−0.884057 | + | 0.467379i | \(0.845199\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | −1.23607 | −0.283573 | −0.141787 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141787 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.47214 | −0.975900 | ||||||||
\(22\) | − 1.23607i | − 0.263531i | ||||||||
\(23\) | − 4.47214i | − 0.932505i | −0.884652 | − | 0.466252i | \(-0.845604\pi\) | ||||
0.884652 | − | 0.466252i | \(-0.154396\pi\) | |||||||
\(24\) | 3.00000 | 0.612372 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.61803 | 1.10179 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 4.47214i | − 0.845154i | ||||||||
\(29\) | −6.61803 | −1.22894 | −0.614469 | − | 0.788941i | \(-0.710630\pi\) | ||||
−0.614469 | + | 0.788941i | \(0.710630\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.76393 | 0.496417 | 0.248208 | − | 0.968707i | \(-0.420158\pi\) | ||||
0.248208 | + | 0.968707i | \(0.420158\pi\) | |||||||
\(32\) | 5.00000i | 0.883883i | ||||||||
\(33\) | 1.23607i | 0.215172i | ||||||||
\(34\) | −3.85410 | −0.660973 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − 3.09017i | − 0.508021i | −0.967201 | − | 0.254010i | \(-0.918250\pi\) | ||||
0.967201 | − | 0.254010i | \(-0.0817497\pi\) | |||||||
\(38\) | − 1.23607i | − 0.200517i | ||||||||
\(39\) | −5.61803 | −0.899605 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.61803 | −0.565042 | −0.282521 | − | 0.959261i | \(-0.591171\pi\) | ||||
−0.282521 | + | 0.959261i | \(0.591171\pi\) | |||||||
\(42\) | − 4.47214i | − 0.690066i | ||||||||
\(43\) | − 7.70820i | − 1.17549i | −0.809046 | − | 0.587745i | \(-0.800016\pi\) | ||||
0.809046 | − | 0.587745i | \(-0.199984\pi\) | |||||||
\(44\) | −1.23607 | −0.186344 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.47214 | 0.659380 | ||||||||
\(47\) | − 0.763932i | − 0.111431i | −0.998447 | − | 0.0557155i | \(-0.982256\pi\) | ||||
0.998447 | − | 0.0557155i | \(-0.0177440\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −13.0000 | −1.85714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.85410 | 0.539682 | ||||||||
\(52\) | − 5.61803i | − 0.779081i | ||||||||
\(53\) | − 3.61803i | − 0.496975i | −0.968635 | − | 0.248488i | \(-0.920066\pi\) | ||||
0.968635 | − | 0.248488i | \(-0.0799335\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 13.4164 | 1.79284 | ||||||||
\(57\) | 1.23607i | 0.163721i | ||||||||
\(58\) | − 6.61803i | − 0.868990i | ||||||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.61803 | 0.207168 | 0.103584 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103584 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(62\) | 2.76393i | 0.351020i | ||||||||
\(63\) | 4.47214i | 0.563436i | ||||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.23607 | −0.152149 | ||||||||
\(67\) | 0.763932i | 0.0933292i | 0.998911 | + | 0.0466646i | \(0.0148592\pi\) | ||||
−0.998911 | + | 0.0466646i | \(0.985141\pi\) | |||||||
\(68\) | 3.85410i | 0.467379i | ||||||||
\(69\) | −4.47214 | −0.538382 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.23607 | −0.621407 | −0.310703 | − | 0.950507i | \(-0.600565\pi\) | ||||
−0.310703 | + | 0.950507i | \(0.600565\pi\) | |||||||
\(72\) | − 3.00000i | − 0.353553i | ||||||||
\(73\) | 8.09017i | 0.946883i | 0.880825 | + | 0.473441i | \(0.156988\pi\) | ||||
−0.880825 | + | 0.473441i | \(0.843012\pi\) | |||||||
\(74\) | 3.09017 | 0.359225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23607 | −0.141787 | ||||||||
\(77\) | 5.52786i | 0.629959i | ||||||||
\(78\) | − 5.61803i | − 0.636117i | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 3.61803i | − 0.399545i | ||||||||
\(83\) | − 12.4721i | − 1.36899i | −0.729015 | − | 0.684497i | \(-0.760022\pi\) | ||||
0.729015 | − | 0.684497i | \(-0.239978\pi\) | |||||||
\(84\) | −4.47214 | −0.487950 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.70820 | 0.831197 | ||||||||
\(87\) | 6.61803i | 0.709528i | ||||||||
\(88\) | − 3.70820i | − 0.395296i | ||||||||
\(89\) | −5.38197 | −0.570487 | −0.285244 | − | 0.958455i | \(-0.592075\pi\) | ||||
−0.285244 | + | 0.958455i | \(0.592075\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.1246 | −2.63377 | ||||||||
\(92\) | − 4.47214i | − 0.466252i | ||||||||
\(93\) | − 2.76393i | − 0.286606i | ||||||||
\(94\) | 0.763932 | 0.0787936 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.00000 | 0.510310 | ||||||||
\(97\) | 2.14590i | 0.217883i | 0.994048 | + | 0.108941i | \(0.0347461\pi\) | ||||
−0.994048 | + | 0.108941i | \(0.965254\pi\) | |||||||
\(98\) | − 13.0000i | − 1.31320i | ||||||||
\(99\) | 1.23607 | 0.124230 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.56231 | 0.354463 | 0.177231 | − | 0.984169i | \(-0.443286\pi\) | ||||
0.177231 | + | 0.984169i | \(0.443286\pi\) | |||||||
\(102\) | 3.85410i | 0.381613i | ||||||||
\(103\) | − 3.23607i | − 0.318859i | −0.987209 | − | 0.159430i | \(-0.949034\pi\) | ||||
0.987209 | − | 0.159430i | \(-0.0509655\pi\) | |||||||
\(104\) | 16.8541 | 1.65268 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.61803 | 0.351415 | ||||||||
\(107\) | 7.52786i | 0.727746i | 0.931449 | + | 0.363873i | \(0.118546\pi\) | ||||
−0.931449 | + | 0.363873i | \(0.881454\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 7.90983 | 0.757624 | 0.378812 | − | 0.925474i | \(-0.376333\pi\) | ||||
0.378812 | + | 0.925474i | \(0.376333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.09017 | −0.293306 | ||||||||
\(112\) | 4.47214i | 0.422577i | ||||||||
\(113\) | − 18.3262i | − 1.72399i | −0.506919 | − | 0.861994i | \(-0.669216\pi\) | ||||
0.506919 | − | 0.861994i | \(-0.330784\pi\) | |||||||
\(114\) | −1.23607 | −0.115768 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.61803 | −0.614469 | ||||||||
\(117\) | 5.61803i | 0.519387i | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | 17.2361 | 1.58003 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.47214 | −0.861103 | ||||||||
\(122\) | 1.61803i | 0.146490i | ||||||||
\(123\) | 3.61803i | 0.326227i | ||||||||
\(124\) | 2.76393 | 0.248208 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.47214 | −0.398410 | ||||||||
\(127\) | − 3.70820i | − 0.329050i | −0.986373 | − | 0.164525i | \(-0.947391\pi\) | ||||
0.986373 | − | 0.164525i | \(-0.0526091\pi\) | |||||||
\(128\) | 3.00000i | 0.265165i | ||||||||
\(129\) | −7.70820 | −0.678670 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.18034 | −0.714720 | −0.357360 | − | 0.933967i | \(-0.616323\pi\) | ||||
−0.357360 | + | 0.933967i | \(0.616323\pi\) | |||||||
\(132\) | 1.23607i | 0.107586i | ||||||||
\(133\) | 5.52786i | 0.479327i | ||||||||
\(134\) | −0.763932 | −0.0659937 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −11.5623 | −0.991460 | ||||||||
\(137\) | − 7.61803i | − 0.650853i | −0.945567 | − | 0.325426i | \(-0.894492\pi\) | ||||
0.945567 | − | 0.325426i | \(-0.105508\pi\) | |||||||
\(138\) | − 4.47214i | − 0.380693i | ||||||||
\(139\) | 22.9443 | 1.94611 | 0.973054 | − | 0.230578i | \(-0.0740616\pi\) | ||||
0.973054 | + | 0.230578i | \(0.0740616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.763932 | −0.0643347 | ||||||||
\(142\) | − 5.23607i | − 0.439401i | ||||||||
\(143\) | 6.94427i | 0.580709i | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.09017 | −0.669547 | ||||||||
\(147\) | 13.0000i | 1.07222i | ||||||||
\(148\) | − 3.09017i | − 0.254010i | ||||||||
\(149\) | 18.8541 | 1.54459 | 0.772294 | − | 0.635265i | \(-0.219109\pi\) | ||||
0.772294 | + | 0.635265i | \(0.219109\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.52786 | 0.612609 | 0.306304 | − | 0.951934i | \(-0.400907\pi\) | ||||
0.306304 | + | 0.951934i | \(0.400907\pi\) | |||||||
\(152\) | − 3.70820i | − 0.300775i | ||||||||
\(153\) | − 3.85410i | − 0.311586i | ||||||||
\(154\) | −5.52786 | −0.445448 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.61803 | −0.449803 | ||||||||
\(157\) | 10.7984i | 0.861804i | 0.902399 | + | 0.430902i | \(0.141805\pi\) | ||||
−0.902399 | + | 0.430902i | \(0.858195\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.61803 | −0.286929 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.0000 | −1.57622 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 14.9443i | 1.17053i | 0.810844 | + | 0.585263i | \(0.199009\pi\) | ||||
−0.810844 | + | 0.585263i | \(0.800991\pi\) | |||||||
\(164\) | −3.61803 | −0.282521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.4721 | 0.968025 | ||||||||
\(167\) | 3.41641i | 0.264370i | 0.991225 | + | 0.132185i | \(0.0421992\pi\) | ||||
−0.991225 | + | 0.132185i | \(0.957801\pi\) | |||||||
\(168\) | − 13.4164i | − 1.03510i | ||||||||
\(169\) | −18.5623 | −1.42787 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.23607 | 0.0945245 | ||||||||
\(172\) | − 7.70820i | − 0.587745i | ||||||||
\(173\) | − 21.0902i | − 1.60346i | −0.597689 | − | 0.801728i | \(-0.703914\pi\) | ||||
0.597689 | − | 0.801728i | \(-0.296086\pi\) | |||||||
\(174\) | −6.61803 | −0.501712 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.23607 | 0.0931721 | ||||||||
\(177\) | − 4.00000i | − 0.300658i | ||||||||
\(178\) | − 5.38197i | − 0.403395i | ||||||||
\(179\) | 16.1803 | 1.20938 | 0.604688 | − | 0.796463i | \(-0.293298\pi\) | ||||
0.604688 | + | 0.796463i | \(0.293298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.7984 | 1.09995 | 0.549977 | − | 0.835180i | \(-0.314636\pi\) | ||||
0.549977 | + | 0.835180i | \(0.314636\pi\) | |||||||
\(182\) | − 25.1246i | − 1.86236i | ||||||||
\(183\) | − 1.61803i | − 0.119609i | ||||||||
\(184\) | 13.4164 | 0.989071 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.76393 | 0.202661 | ||||||||
\(187\) | − 4.76393i | − 0.348373i | ||||||||
\(188\) | − 0.763932i | − 0.0557155i | ||||||||
\(189\) | 4.47214 | 0.325300 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.65248 | 0.481356 | 0.240678 | − | 0.970605i | \(-0.422630\pi\) | ||||
0.240678 | + | 0.970605i | \(0.422630\pi\) | |||||||
\(192\) | 7.00000i | 0.505181i | ||||||||
\(193\) | − 23.3262i | − 1.67906i | −0.543314 | − | 0.839530i | \(-0.682831\pi\) | ||||
0.543314 | − | 0.839530i | \(-0.317169\pi\) | |||||||
\(194\) | −2.14590 | −0.154067 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.0000 | −0.928571 | ||||||||
\(197\) | 7.61803i | 0.542762i | 0.962472 | + | 0.271381i | \(0.0874804\pi\) | ||||
−0.962472 | + | 0.271381i | \(0.912520\pi\) | |||||||
\(198\) | 1.23607i | 0.0878435i | ||||||||
\(199\) | −12.6525 | −0.896910 | −0.448455 | − | 0.893805i | \(-0.648026\pi\) | ||||
−0.448455 | + | 0.893805i | \(0.648026\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.763932 | 0.0538836 | ||||||||
\(202\) | 3.56231i | 0.250643i | ||||||||
\(203\) | 29.5967i | 2.07728i | ||||||||
\(204\) | 3.85410 | 0.269841 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.23607 | 0.225468 | ||||||||
\(207\) | 4.47214i | 0.310835i | ||||||||
\(208\) | 5.61803i | 0.389541i | ||||||||
\(209\) | 1.52786 | 0.105685 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.8885 | 1.23150 | 0.615749 | − | 0.787942i | \(-0.288854\pi\) | ||||
0.615749 | + | 0.787942i | \(0.288854\pi\) | |||||||
\(212\) | − 3.61803i | − 0.248488i | ||||||||
\(213\) | 5.23607i | 0.358769i | ||||||||
\(214\) | −7.52786 | −0.514594 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.00000 | −0.204124 | ||||||||
\(217\) | − 12.3607i | − 0.839098i | ||||||||
\(218\) | 7.90983i | 0.535721i | ||||||||
\(219\) | 8.09017 | 0.546683 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.6525 | 1.45650 | ||||||||
\(222\) | − 3.09017i | − 0.207399i | ||||||||
\(223\) | − 8.18034i | − 0.547796i | −0.961759 | − | 0.273898i | \(-0.911687\pi\) | ||||
0.961759 | − | 0.273898i | \(-0.0883131\pi\) | |||||||
\(224\) | 22.3607 | 1.49404 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.3262 | 1.21904 | ||||||||
\(227\) | − 20.0000i | − 1.32745i | −0.747978 | − | 0.663723i | \(-0.768975\pi\) | ||||
0.747978 | − | 0.663723i | \(-0.231025\pi\) | |||||||
\(228\) | 1.23607i | 0.0818606i | ||||||||
\(229\) | −21.9787 | −1.45239 | −0.726197 | − | 0.687487i | \(-0.758714\pi\) | ||||
−0.726197 | + | 0.687487i | \(0.758714\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.52786 | 0.363707 | ||||||||
\(232\) | − 19.8541i | − 1.30349i | ||||||||
\(233\) | − 12.3820i | − 0.811170i | −0.914057 | − | 0.405585i | \(-0.867068\pi\) | ||||
0.914057 | − | 0.405585i | \(-0.132932\pi\) | |||||||
\(234\) | −5.61803 | −0.367262 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.00000 | 0.260378 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 17.2361i | 1.11725i | ||||||||
\(239\) | 24.9443 | 1.61351 | 0.806755 | − | 0.590886i | \(-0.201222\pi\) | ||||
0.806755 | + | 0.590886i | \(0.201222\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.0344 | 1.80586 | 0.902929 | − | 0.429791i | \(-0.141413\pi\) | ||||
0.902929 | + | 0.429791i | \(0.141413\pi\) | |||||||
\(242\) | − 9.47214i | − 0.608892i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 1.61803 | 0.103584 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.61803 | −0.230677 | ||||||||
\(247\) | 6.94427i | 0.441853i | ||||||||
\(248\) | 8.29180i | 0.526530i | ||||||||
\(249\) | −12.4721 | −0.790390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.05573 | −0.571592 | −0.285796 | − | 0.958290i | \(-0.592258\pi\) | ||||
−0.285796 | + | 0.958290i | \(0.592258\pi\) | |||||||
\(252\) | 4.47214i | 0.281718i | ||||||||
\(253\) | 5.52786i | 0.347534i | ||||||||
\(254\) | 3.70820 | 0.232673 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | 11.7984i | 0.735962i | 0.929833 | + | 0.367981i | \(0.119951\pi\) | ||||
−0.929833 | + | 0.367981i | \(0.880049\pi\) | |||||||
\(258\) | − 7.70820i | − 0.479892i | ||||||||
\(259\) | −13.8197 | −0.858712 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.61803 | 0.409646 | ||||||||
\(262\) | − 8.18034i | − 0.505383i | ||||||||
\(263\) | 23.8885i | 1.47303i | 0.676421 | + | 0.736515i | \(0.263530\pi\) | ||||
−0.676421 | + | 0.736515i | \(0.736470\pi\) | |||||||
\(264\) | −3.70820 | −0.228224 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.52786 | −0.338935 | ||||||||
\(267\) | 5.38197i | 0.329371i | ||||||||
\(268\) | 0.763932i | 0.0466646i | ||||||||
\(269\) | 6.85410 | 0.417902 | 0.208951 | − | 0.977926i | \(-0.432995\pi\) | ||||
0.208951 | + | 0.977926i | \(0.432995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.180340 | −0.0109549 | −0.00547743 | − | 0.999985i | \(-0.501744\pi\) | ||||
−0.00547743 | + | 0.999985i | \(0.501744\pi\) | |||||||
\(272\) | − 3.85410i | − 0.233689i | ||||||||
\(273\) | 25.1246i | 1.52061i | ||||||||
\(274\) | 7.61803 | 0.460222 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −4.47214 | −0.269191 | ||||||||
\(277\) | 18.7984i | 1.12948i | 0.825267 | + | 0.564742i | \(0.191024\pi\) | ||||
−0.825267 | + | 0.564742i | \(0.808976\pi\) | |||||||
\(278\) | 22.9443i | 1.37611i | ||||||||
\(279\) | −2.76393 | −0.165472 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.6180 | −1.17031 | −0.585157 | − | 0.810920i | \(-0.698967\pi\) | ||||
−0.585157 | + | 0.810920i | \(0.698967\pi\) | |||||||
\(282\) | − 0.763932i | − 0.0454915i | ||||||||
\(283\) | − 13.7082i | − 0.814868i | −0.913235 | − | 0.407434i | \(-0.866424\pi\) | ||||
0.913235 | − | 0.407434i | \(-0.133576\pi\) | |||||||
\(284\) | −5.23607 | −0.310703 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.94427 | −0.410623 | ||||||||
\(287\) | 16.1803i | 0.955095i | ||||||||
\(288\) | − 5.00000i | − 0.294628i | ||||||||
\(289\) | 2.14590 | 0.126229 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.14590 | 0.125795 | ||||||||
\(292\) | 8.09017i | 0.473441i | ||||||||
\(293\) | 20.7984i | 1.21505i | 0.794299 | + | 0.607527i | \(0.207838\pi\) | ||||
−0.794299 | + | 0.607527i | \(0.792162\pi\) | |||||||
\(294\) | −13.0000 | −0.758175 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.27051 | 0.538837 | ||||||||
\(297\) | − 1.23607i | − 0.0717239i | ||||||||
\(298\) | 18.8541i | 1.09219i | ||||||||
\(299\) | −25.1246 | −1.45299 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.4721 | −1.98694 | ||||||||
\(302\) | 7.52786i | 0.433180i | ||||||||
\(303\) | − 3.56231i | − 0.204649i | ||||||||
\(304\) | 1.23607 | 0.0708934 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.85410 | 0.220324 | ||||||||
\(307\) | 32.6525i | 1.86358i | 0.363004 | + | 0.931788i | \(0.381751\pi\) | ||||
−0.363004 | + | 0.931788i | \(0.618249\pi\) | |||||||
\(308\) | 5.52786i | 0.314979i | ||||||||
\(309\) | −3.23607 | −0.184093 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7082 | 1.00414 | 0.502070 | − | 0.864827i | \(-0.332572\pi\) | ||||
0.502070 | + | 0.864827i | \(0.332572\pi\) | |||||||
\(312\) | − 16.8541i | − 0.954176i | ||||||||
\(313\) | 0.472136i | 0.0266867i | 0.999911 | + | 0.0133434i | \(0.00424745\pi\) | ||||
−0.999911 | + | 0.0133434i | \(0.995753\pi\) | |||||||
\(314\) | −10.7984 | −0.609387 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.8328i | 1.61941i | 0.586836 | + | 0.809706i | \(0.300373\pi\) | ||||
−0.586836 | + | 0.809706i | \(0.699627\pi\) | |||||||
\(318\) | − 3.61803i | − 0.202889i | ||||||||
\(319\) | 8.18034 | 0.458011 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.52786 | 0.420164 | ||||||||
\(322\) | − 20.0000i | − 1.11456i | ||||||||
\(323\) | − 4.76393i | − 0.265072i | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.9443 | −0.827687 | ||||||||
\(327\) | − 7.90983i | − 0.437415i | ||||||||
\(328\) | − 10.8541i | − 0.599318i | ||||||||
\(329\) | −3.41641 | −0.188353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.94427 | −0.381692 | −0.190846 | − | 0.981620i | \(-0.561123\pi\) | ||||
−0.190846 | + | 0.981620i | \(0.561123\pi\) | |||||||
\(332\) | − 12.4721i | − 0.684497i | ||||||||
\(333\) | 3.09017i | 0.169340i | ||||||||
\(334\) | −3.41641 | −0.186938 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.47214 | 0.243975 | ||||||||
\(337\) | 2.94427i | 0.160385i | 0.996779 | + | 0.0801924i | \(0.0255535\pi\) | ||||
−0.996779 | + | 0.0801924i | \(0.974447\pi\) | |||||||
\(338\) | − 18.5623i | − 1.00966i | ||||||||
\(339\) | −18.3262 | −0.995345 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.41641 | −0.185009 | ||||||||
\(342\) | 1.23607i | 0.0668389i | ||||||||
\(343\) | 26.8328i | 1.44884i | ||||||||
\(344\) | 23.1246 | 1.24680 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.0902 | 1.13381 | ||||||||
\(347\) | − 20.2918i | − 1.08932i | −0.838657 | − | 0.544660i | \(-0.816659\pi\) | ||||
0.838657 | − | 0.544660i | \(-0.183341\pi\) | |||||||
\(348\) | 6.61803i | 0.354764i | ||||||||
\(349\) | 4.03444 | 0.215959 | 0.107979 | − | 0.994153i | \(-0.465562\pi\) | ||||
0.107979 | + | 0.994153i | \(0.465562\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.61803 | 0.299868 | ||||||||
\(352\) | − 6.18034i | − 0.329413i | ||||||||
\(353\) | − 14.3607i | − 0.764342i | −0.924092 | − | 0.382171i | \(-0.875177\pi\) | ||||
0.924092 | − | 0.382171i | \(-0.124823\pi\) | |||||||
\(354\) | 4.00000 | 0.212598 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.38197 | −0.285244 | ||||||||
\(357\) | − 17.2361i | − 0.912229i | ||||||||
\(358\) | 16.1803i | 0.855158i | ||||||||
\(359\) | 37.4164 | 1.97476 | 0.987381 | − | 0.158361i | \(-0.0506211\pi\) | ||||
0.987381 | + | 0.158361i | \(0.0506211\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | 14.7984i | 0.777785i | ||||||||
\(363\) | 9.47214i | 0.497158i | ||||||||
\(364\) | −25.1246 | −1.31689 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.61803 | 0.0845760 | ||||||||
\(367\) | − 6.00000i | − 0.313197i | −0.987662 | − | 0.156599i | \(-0.949947\pi\) | ||||
0.987662 | − | 0.156599i | \(-0.0500529\pi\) | |||||||
\(368\) | 4.47214i | 0.233126i | ||||||||
\(369\) | 3.61803 | 0.188347 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.1803 | −0.840041 | ||||||||
\(372\) | − 2.76393i | − 0.143303i | ||||||||
\(373\) | − 2.58359i | − 0.133773i | −0.997761 | − | 0.0668867i | \(-0.978693\pi\) | ||||
0.997761 | − | 0.0668867i | \(-0.0213066\pi\) | |||||||
\(374\) | 4.76393 | 0.246337 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.29180 | 0.118190 | ||||||||
\(377\) | 37.1803i | 1.91488i | ||||||||
\(378\) | 4.47214i | 0.230022i | ||||||||
\(379\) | 3.41641 | 0.175489 | 0.0877445 | − | 0.996143i | \(-0.472034\pi\) | ||||
0.0877445 | + | 0.996143i | \(0.472034\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.70820 | −0.189977 | ||||||||
\(382\) | 6.65248i | 0.340370i | ||||||||
\(383\) | 32.8328i | 1.67768i | 0.544379 | + | 0.838839i | \(0.316765\pi\) | ||||
−0.544379 | + | 0.838839i | \(0.683235\pi\) | |||||||
\(384\) | 3.00000 | 0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.3262 | 1.18727 | ||||||||
\(387\) | 7.70820i | 0.391830i | ||||||||
\(388\) | 2.14590i | 0.108941i | ||||||||
\(389\) | 25.9098 | 1.31368 | 0.656840 | − | 0.754030i | \(-0.271893\pi\) | ||||
0.656840 | + | 0.754030i | \(0.271893\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.2361 | 0.871665 | ||||||||
\(392\) | − 39.0000i | − 1.96980i | ||||||||
\(393\) | 8.18034i | 0.412644i | ||||||||
\(394\) | −7.61803 | −0.383791 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.23607 | 0.0621148 | ||||||||
\(397\) | − 6.94427i | − 0.348523i | −0.984699 | − | 0.174262i | \(-0.944246\pi\) | ||||
0.984699 | − | 0.174262i | \(-0.0557538\pi\) | |||||||
\(398\) | − 12.6525i | − 0.634211i | ||||||||
\(399\) | 5.52786 | 0.276739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4508 | −1.12114 | −0.560571 | − | 0.828106i | \(-0.689418\pi\) | ||||
−0.560571 | + | 0.828106i | \(0.689418\pi\) | |||||||
\(402\) | 0.763932i | 0.0381015i | ||||||||
\(403\) | − 15.5279i | − 0.773498i | ||||||||
\(404\) | 3.56231 | 0.177231 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −29.5967 | −1.46886 | ||||||||
\(407\) | 3.81966i | 0.189334i | ||||||||
\(408\) | 11.5623i | 0.572419i | ||||||||
\(409\) | −1.20163 | −0.0594166 | −0.0297083 | − | 0.999559i | \(-0.509458\pi\) | ||||
−0.0297083 | + | 0.999559i | \(0.509458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.61803 | −0.375770 | ||||||||
\(412\) | − 3.23607i | − 0.159430i | ||||||||
\(413\) | − 17.8885i | − 0.880238i | ||||||||
\(414\) | −4.47214 | −0.219793 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.0902 | 1.37723 | ||||||||
\(417\) | − 22.9443i | − 1.12359i | ||||||||
\(418\) | 1.52786i | 0.0747303i | ||||||||
\(419\) | −15.0557 | −0.735520 | −0.367760 | − | 0.929921i | \(-0.619875\pi\) | ||||
−0.367760 | + | 0.929921i | \(0.619875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.8541 | 1.45500 | 0.727500 | − | 0.686108i | \(-0.240682\pi\) | ||||
0.727500 | + | 0.686108i | \(0.240682\pi\) | |||||||
\(422\) | 17.8885i | 0.870801i | ||||||||
\(423\) | 0.763932i | 0.0371436i | ||||||||
\(424\) | 10.8541 | 0.527122 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.23607 | −0.253688 | ||||||||
\(427\) | − 7.23607i | − 0.350178i | ||||||||
\(428\) | 7.52786i | 0.363873i | ||||||||
\(429\) | 6.94427 | 0.335273 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.6525 | 0.994795 | 0.497397 | − | 0.867523i | \(-0.334289\pi\) | ||||
0.497397 | + | 0.867523i | \(0.334289\pi\) | |||||||
\(432\) | − 1.00000i | − 0.0481125i | ||||||||
\(433\) | 21.9787i | 1.05623i | 0.849173 | + | 0.528115i | \(0.177101\pi\) | ||||
−0.849173 | + | 0.528115i | \(0.822899\pi\) | |||||||
\(434\) | 12.3607 | 0.593332 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.90983 | 0.378812 | ||||||||
\(437\) | 5.52786i | 0.264434i | ||||||||
\(438\) | 8.09017i | 0.386563i | ||||||||
\(439\) | −16.1803 | −0.772245 | −0.386123 | − | 0.922447i | \(-0.626186\pi\) | ||||
−0.386123 | + | 0.922447i | \(0.626186\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | 0.619048 | ||||||||
\(442\) | 21.6525i | 1.02990i | ||||||||
\(443\) | 35.2361i | 1.67412i | 0.547114 | + | 0.837058i | \(0.315726\pi\) | ||||
−0.547114 | + | 0.837058i | \(0.684274\pi\) | |||||||
\(444\) | −3.09017 | −0.146653 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.18034 | 0.387350 | ||||||||
\(447\) | − 18.8541i | − 0.891768i | ||||||||
\(448\) | 31.3050i | 1.47902i | ||||||||
\(449\) | −16.7984 | −0.792764 | −0.396382 | − | 0.918086i | \(-0.629734\pi\) | ||||
−0.396382 | + | 0.918086i | \(0.629734\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.47214 | 0.210585 | ||||||||
\(452\) | − 18.3262i | − 0.861994i | ||||||||
\(453\) | − 7.52786i | − 0.353690i | ||||||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.70820 | −0.173653 | ||||||||
\(457\) | − 22.3607i | − 1.04599i | −0.852336 | − | 0.522994i | \(-0.824815\pi\) | ||||
0.852336 | − | 0.522994i | \(-0.175185\pi\) | |||||||
\(458\) | − 21.9787i | − 1.02700i | ||||||||
\(459\) | −3.85410 | −0.179894 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.7984 | −1.52757 | −0.763786 | − | 0.645469i | \(-0.776662\pi\) | ||||
−0.763786 | + | 0.645469i | \(0.776662\pi\) | |||||||
\(462\) | 5.52786i | 0.257180i | ||||||||
\(463\) | − 18.7639i | − 0.872034i | −0.899938 | − | 0.436017i | \(-0.856389\pi\) | ||||
0.899938 | − | 0.436017i | \(-0.143611\pi\) | |||||||
\(464\) | 6.61803 | 0.307235 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.3820 | 0.573583 | ||||||||
\(467\) | 28.1803i | 1.30403i | 0.758206 | + | 0.652015i | \(0.226076\pi\) | ||||
−0.758206 | + | 0.652015i | \(0.773924\pi\) | |||||||
\(468\) | 5.61803i | 0.259694i | ||||||||
\(469\) | 3.41641 | 0.157755 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.7984 | 0.497563 | ||||||||
\(472\) | 12.0000i | 0.552345i | ||||||||
\(473\) | 9.52786i | 0.438092i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 17.2361 | 0.790014 | ||||||||
\(477\) | 3.61803i | 0.165658i | ||||||||
\(478\) | 24.9443i | 1.14092i | ||||||||
\(479\) | −18.9443 | −0.865586 | −0.432793 | − | 0.901493i | \(-0.642472\pi\) | ||||
−0.432793 | + | 0.901493i | \(0.642472\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3607 | −0.791579 | ||||||||
\(482\) | 28.0344i | 1.27693i | ||||||||
\(483\) | 20.0000i | 0.910032i | ||||||||
\(484\) | −9.47214 | −0.430552 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 9.70820i | 0.439921i | 0.975509 | + | 0.219960i | \(0.0705928\pi\) | ||||
−0.975509 | + | 0.219960i | \(0.929407\pi\) | |||||||
\(488\) | 4.85410i | 0.219735i | ||||||||
\(489\) | 14.9443 | 0.675803 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.88854 | 0.265746 | 0.132873 | − | 0.991133i | \(-0.457580\pi\) | ||||
0.132873 | + | 0.991133i | \(0.457580\pi\) | |||||||
\(492\) | 3.61803i | 0.163114i | ||||||||
\(493\) | − 25.5066i | − 1.14876i | ||||||||
\(494\) | −6.94427 | −0.312438 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.76393 | −0.124104 | ||||||||
\(497\) | 23.4164i | 1.05037i | ||||||||
\(498\) | − 12.4721i | − 0.558890i | ||||||||
\(499\) | 6.00000 | 0.268597 | 0.134298 | − | 0.990941i | \(-0.457122\pi\) | ||||
0.134298 | + | 0.990941i | \(0.457122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.41641 | 0.152634 | ||||||||
\(502\) | − 9.05573i | − 0.404177i | ||||||||
\(503\) | − 8.58359i | − 0.382723i | −0.981520 | − | 0.191362i | \(-0.938710\pi\) | ||||
0.981520 | − | 0.191362i | \(-0.0612904\pi\) | |||||||
\(504\) | −13.4164 | −0.597614 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.52786 | −0.245744 | ||||||||
\(507\) | 18.5623i | 0.824381i | ||||||||
\(508\) | − 3.70820i | − 0.164525i | ||||||||
\(509\) | −20.1459 | −0.892951 | −0.446476 | − | 0.894796i | \(-0.647321\pi\) | ||||
−0.446476 | + | 0.894796i | \(0.647321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.1803 | 1.60052 | ||||||||
\(512\) | − 11.0000i | − 0.486136i | ||||||||
\(513\) | − 1.23607i | − 0.0545737i | ||||||||
\(514\) | −11.7984 | −0.520404 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.70820 | −0.339335 | ||||||||
\(517\) | 0.944272i | 0.0415290i | ||||||||
\(518\) | − 13.8197i | − 0.607201i | ||||||||
\(519\) | −21.0902 | −0.925756 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0344 | −1.18440 | −0.592200 | − | 0.805791i | \(-0.701741\pi\) | ||||
−0.592200 | + | 0.805791i | \(0.701741\pi\) | |||||||
\(522\) | 6.61803i | 0.289663i | ||||||||
\(523\) | 25.7082i | 1.12414i | 0.827089 | + | 0.562071i | \(0.189995\pi\) | ||||
−0.827089 | + | 0.562071i | \(0.810005\pi\) | |||||||
\(524\) | −8.18034 | −0.357360 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.8885 | −1.04159 | ||||||||
\(527\) | 10.6525i | 0.464029i | ||||||||
\(528\) | − 1.23607i | − 0.0537930i | ||||||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 5.52786i | 0.239663i | ||||||||
\(533\) | 20.3262i | 0.880427i | ||||||||
\(534\) | −5.38197 | −0.232900 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.29180 | −0.0989905 | ||||||||
\(537\) | − 16.1803i | − 0.698233i | ||||||||
\(538\) | 6.85410i | 0.295501i | ||||||||
\(539\) | 16.0689 | 0.692136 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.6738 | −0.845841 | −0.422921 | − | 0.906167i | \(-0.638995\pi\) | ||||
−0.422921 | + | 0.906167i | \(0.638995\pi\) | |||||||
\(542\) | − 0.180340i | − 0.00774626i | ||||||||
\(543\) | − 14.7984i | − 0.635059i | ||||||||
\(544\) | −19.2705 | −0.826216 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −25.1246 | −1.07523 | ||||||||
\(547\) | 42.3607i | 1.81121i | 0.424120 | + | 0.905606i | \(0.360583\pi\) | ||||
−0.424120 | + | 0.905606i | \(0.639417\pi\) | |||||||
\(548\) | − 7.61803i | − 0.325426i | ||||||||
\(549\) | −1.61803 | −0.0690560 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.18034 | 0.348494 | ||||||||
\(552\) | − 13.4164i | − 0.571040i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.7984 | −0.798666 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.9443 | 0.973054 | ||||||||
\(557\) | − 11.2705i | − 0.477547i | −0.971075 | − | 0.238773i | \(-0.923255\pi\) | ||||
0.971075 | − | 0.238773i | \(-0.0767453\pi\) | |||||||
\(558\) | − 2.76393i | − 0.117007i | ||||||||
\(559\) | −43.3050 | −1.83160 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.76393 | −0.201133 | ||||||||
\(562\) | − 19.6180i | − 0.827537i | ||||||||
\(563\) | 26.4721i | 1.11567i | 0.829953 | + | 0.557834i | \(0.188367\pi\) | ||||
−0.829953 | + | 0.557834i | \(0.811633\pi\) | |||||||
\(564\) | −0.763932 | −0.0321673 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 13.7082 | 0.576199 | ||||||||
\(567\) | − 4.47214i | − 0.187812i | ||||||||
\(568\) | − 15.7082i | − 0.659102i | ||||||||
\(569\) | −3.27051 | −0.137107 | −0.0685535 | − | 0.997647i | \(-0.521838\pi\) | ||||
−0.0685535 | + | 0.997647i | \(0.521838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.7639 | −0.701549 | −0.350774 | − | 0.936460i | \(-0.614082\pi\) | ||||
−0.350774 | + | 0.936460i | \(0.614082\pi\) | |||||||
\(572\) | 6.94427i | 0.290355i | ||||||||
\(573\) | − 6.65248i | − 0.277911i | ||||||||
\(574\) | −16.1803 | −0.675354 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | − 13.0557i | − 0.543517i | −0.962365 | − | 0.271759i | \(-0.912395\pi\) | ||||
0.962365 | − | 0.271759i | \(-0.0876052\pi\) | |||||||
\(578\) | 2.14590i | 0.0892576i | ||||||||
\(579\) | −23.3262 | −0.969405 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −55.7771 | −2.31402 | ||||||||
\(582\) | 2.14590i | 0.0889503i | ||||||||
\(583\) | 4.47214i | 0.185217i | ||||||||
\(584\) | −24.2705 | −1.00432 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.7984 | −0.859173 | ||||||||
\(587\) | − 41.4164i | − 1.70944i | −0.519091 | − | 0.854719i | \(-0.673729\pi\) | ||||
0.519091 | − | 0.854719i | \(-0.326271\pi\) | |||||||
\(588\) | 13.0000i | 0.536111i | ||||||||
\(589\) | −3.41641 | −0.140771 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.61803 | 0.313364 | ||||||||
\(592\) | 3.09017i | 0.127005i | ||||||||
\(593\) | − 9.74265i | − 0.400083i | −0.979787 | − | 0.200041i | \(-0.935892\pi\) | ||||
0.979787 | − | 0.200041i | \(-0.0641076\pi\) | |||||||
\(594\) | 1.23607 | 0.0507165 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.8541 | 0.772294 | ||||||||
\(597\) | 12.6525i | 0.517831i | ||||||||
\(598\) | − 25.1246i | − 1.02742i | ||||||||
\(599\) | 3.52786 | 0.144145 | 0.0720723 | − | 0.997399i | \(-0.477039\pi\) | ||||
0.0720723 | + | 0.997399i | \(0.477039\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.67376 | −0.353810 | −0.176905 | − | 0.984228i | \(-0.556609\pi\) | ||||
−0.176905 | + | 0.984228i | \(0.556609\pi\) | |||||||
\(602\) | − 34.4721i | − 1.40498i | ||||||||
\(603\) | − 0.763932i | − 0.0311097i | ||||||||
\(604\) | 7.52786 | 0.306304 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.56231 | 0.144709 | ||||||||
\(607\) | − 34.7639i | − 1.41102i | −0.708698 | − | 0.705512i | \(-0.750717\pi\) | ||||
0.708698 | − | 0.705512i | \(-0.249283\pi\) | |||||||
\(608\) | − 6.18034i | − 0.250646i | ||||||||
\(609\) | 29.5967 | 1.19932 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.29180 | −0.173627 | ||||||||
\(612\) | − 3.85410i | − 0.155793i | ||||||||
\(613\) | − 1.49342i | − 0.0603188i | −0.999545 | − | 0.0301594i | \(-0.990399\pi\) | ||||
0.999545 | − | 0.0301594i | \(-0.00960148\pi\) | |||||||
\(614\) | −32.6525 | −1.31775 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.5836 | −0.668172 | ||||||||
\(617\) | − 19.9787i | − 0.804313i | −0.915571 | − | 0.402156i | \(-0.868261\pi\) | ||||
0.915571 | − | 0.402156i | \(-0.131739\pi\) | |||||||
\(618\) | − 3.23607i | − 0.130174i | ||||||||
\(619\) | 16.3607 | 0.657591 | 0.328796 | − | 0.944401i | \(-0.393357\pi\) | ||||
0.328796 | + | 0.944401i | \(0.393357\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.47214 | 0.179461 | ||||||||
\(622\) | 17.7082i | 0.710034i | ||||||||
\(623\) | 24.0689i | 0.964299i | ||||||||
\(624\) | 5.61803 | 0.224901 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.472136 | −0.0188703 | ||||||||
\(627\) | − 1.52786i | − 0.0610170i | ||||||||
\(628\) | 10.7984i | 0.430902i | ||||||||
\(629\) | 11.9098 | 0.474876 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7082 | 0.943809 | 0.471904 | − | 0.881650i | \(-0.343567\pi\) | ||||
0.471904 | + | 0.881650i | \(0.343567\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 17.8885i | − 0.711006i | ||||||||
\(634\) | −28.8328 | −1.14510 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.61803 | −0.143464 | ||||||||
\(637\) | 73.0344i | 2.89373i | ||||||||
\(638\) | 8.18034i | 0.323863i | ||||||||
\(639\) | 5.23607 | 0.207136 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.0557 | 0.831651 | 0.415826 | − | 0.909444i | \(-0.363493\pi\) | ||||
0.415826 | + | 0.909444i | \(0.363493\pi\) | |||||||
\(642\) | 7.52786i | 0.297101i | ||||||||
\(643\) | 21.8885i | 0.863200i | 0.902065 | + | 0.431600i | \(0.142051\pi\) | ||||
−0.902065 | + | 0.431600i | \(0.857949\pi\) | |||||||
\(644\) | −20.0000 | −0.788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.76393 | 0.187434 | ||||||||
\(647\) | − 34.3607i | − 1.35086i | −0.737425 | − | 0.675429i | \(-0.763959\pi\) | ||||
0.737425 | − | 0.675429i | \(-0.236041\pi\) | |||||||
\(648\) | 3.00000i | 0.117851i | ||||||||
\(649\) | −4.94427 | −0.194080 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.3607 | −0.484453 | ||||||||
\(652\) | 14.9443i | 0.585263i | ||||||||
\(653\) | 42.1033i | 1.64763i | 0.566858 | + | 0.823815i | \(0.308159\pi\) | ||||
−0.566858 | + | 0.823815i | \(0.691841\pi\) | |||||||
\(654\) | 7.90983 | 0.309299 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.61803 | 0.141260 | ||||||||
\(657\) | − 8.09017i | − 0.315628i | ||||||||
\(658\) | − 3.41641i | − 0.133185i | ||||||||
\(659\) | 33.4164 | 1.30172 | 0.650859 | − | 0.759198i | \(-0.274409\pi\) | ||||
0.650859 | + | 0.759198i | \(0.274409\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41641 | −0.0550919 | −0.0275459 | − | 0.999621i | \(-0.508769\pi\) | ||||
−0.0275459 | + | 0.999621i | \(0.508769\pi\) | |||||||
\(662\) | − 6.94427i | − 0.269897i | ||||||||
\(663\) | − 21.6525i | − 0.840912i | ||||||||
\(664\) | 37.4164 | 1.45204 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.09017 | −0.119742 | ||||||||
\(667\) | 29.5967i | 1.14599i | ||||||||
\(668\) | 3.41641i | 0.132185i | ||||||||
\(669\) | −8.18034 | −0.316270 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | − 22.3607i | − 0.862582i | ||||||||
\(673\) | − 5.20163i | − 0.200508i | −0.994962 | − | 0.100254i | \(-0.968034\pi\) | ||||
0.994962 | − | 0.100254i | \(-0.0319655\pi\) | |||||||
\(674\) | −2.94427 | −0.113409 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.5623 | −0.713935 | ||||||||
\(677\) | 10.5836i | 0.406760i | 0.979100 | + | 0.203380i | \(0.0651928\pi\) | ||||
−0.979100 | + | 0.203380i | \(0.934807\pi\) | |||||||
\(678\) | − 18.3262i | − 0.703815i | ||||||||
\(679\) | 9.59675 | 0.368289 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.0000 | −0.766402 | ||||||||
\(682\) | − 3.41641i | − 0.130821i | ||||||||
\(683\) | 19.4164i | 0.742948i | 0.928443 | + | 0.371474i | \(0.121148\pi\) | ||||
−0.928443 | + | 0.371474i | \(0.878852\pi\) | |||||||
\(684\) | 1.23607 | 0.0472622 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −26.8328 | −1.02448 | ||||||||
\(687\) | 21.9787i | 0.838540i | ||||||||
\(688\) | 7.70820i | 0.293873i | ||||||||
\(689\) | −20.3262 | −0.774368 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.7639 | −0.637730 | −0.318865 | − | 0.947800i | \(-0.603302\pi\) | ||||
−0.318865 | + | 0.947800i | \(0.603302\pi\) | |||||||
\(692\) | − 21.0902i | − 0.801728i | ||||||||
\(693\) | − 5.52786i | − 0.209986i | ||||||||
\(694\) | 20.2918 | 0.770266 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −19.8541 | −0.752568 | ||||||||
\(697\) | − 13.9443i | − 0.528177i | ||||||||
\(698\) | 4.03444i | 0.152706i | ||||||||
\(699\) | −12.3820 | −0.468329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.5623 | 0.776628 | 0.388314 | − | 0.921527i | \(-0.373058\pi\) | ||||
0.388314 | + | 0.921527i | \(0.373058\pi\) | |||||||
\(702\) | 5.61803i | 0.212039i | ||||||||
\(703\) | 3.81966i | 0.144061i | ||||||||
\(704\) | 8.65248 | 0.326102 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.3607 | 0.540471 | ||||||||
\(707\) | − 15.9311i | − 0.599151i | ||||||||
\(708\) | − 4.00000i | − 0.150329i | ||||||||
\(709\) | 40.2705 | 1.51239 | 0.756195 | − | 0.654346i | \(-0.227056\pi\) | ||||
0.756195 | + | 0.654346i | \(0.227056\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 16.1459i | − 0.605093i | ||||||||
\(713\) | − 12.3607i | − 0.462911i | ||||||||
\(714\) | 17.2361 | 0.645044 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.1803 | 0.604688 | ||||||||
\(717\) | − 24.9443i | − 0.931561i | ||||||||
\(718\) | 37.4164i | 1.39637i | ||||||||
\(719\) | 0.111456 | 0.00415661 | 0.00207831 | − | 0.999998i | \(-0.499338\pi\) | ||||
0.00207831 | + | 0.999998i | \(0.499338\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4721 | −0.538971 | ||||||||
\(722\) | − 17.4721i | − 0.650246i | ||||||||
\(723\) | − 28.0344i | − 1.04261i | ||||||||
\(724\) | 14.7984 | 0.549977 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.47214 | −0.351544 | ||||||||
\(727\) | 46.6525i | 1.73024i | 0.501561 | + | 0.865122i | \(0.332759\pi\) | ||||
−0.501561 | + | 0.865122i | \(0.667241\pi\) | |||||||
\(728\) | − 75.3738i | − 2.79354i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.7082 | 1.09880 | ||||||||
\(732\) | − 1.61803i | − 0.0598043i | ||||||||
\(733\) | − 29.4164i | − 1.08652i | −0.839565 | − | 0.543260i | \(-0.817190\pi\) | ||||
0.839565 | − | 0.543260i | \(-0.182810\pi\) | |||||||
\(734\) | 6.00000 | 0.221464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 22.3607 | 0.824226 | ||||||||
\(737\) | − 0.944272i | − 0.0347827i | ||||||||
\(738\) | 3.61803i | 0.133182i | ||||||||
\(739\) | −4.29180 | −0.157876 | −0.0789381 | − | 0.996880i | \(-0.525153\pi\) | ||||
−0.0789381 | + | 0.996880i | \(0.525153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.94427 | 0.255104 | ||||||||
\(742\) | − 16.1803i | − 0.593999i | ||||||||
\(743\) | − 41.1246i | − 1.50872i | −0.656463 | − | 0.754358i | \(-0.727948\pi\) | ||||
0.656463 | − | 0.754358i | \(-0.272052\pi\) | |||||||
\(744\) | 8.29180 | 0.303992 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.58359 | 0.0945920 | ||||||||
\(747\) | 12.4721i | 0.456332i | ||||||||
\(748\) | − 4.76393i | − 0.174187i | ||||||||
\(749\) | 33.6656 | 1.23012 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.6525 | 1.33747 | 0.668734 | − | 0.743502i | \(-0.266837\pi\) | ||||
0.668734 | + | 0.743502i | \(0.266837\pi\) | |||||||
\(752\) | 0.763932i | 0.0278577i | ||||||||
\(753\) | 9.05573i | 0.330009i | ||||||||
\(754\) | −37.1803 | −1.35403 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.47214 | 0.162650 | ||||||||
\(757\) | 29.6180i | 1.07649i | 0.842790 | + | 0.538243i | \(0.180912\pi\) | ||||
−0.842790 | + | 0.538243i | \(0.819088\pi\) | |||||||
\(758\) | 3.41641i | 0.124090i | ||||||||
\(759\) | 5.52786 | 0.200649 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.7426 | 1.18692 | 0.593460 | − | 0.804863i | \(-0.297762\pi\) | ||||
0.593460 | + | 0.804863i | \(0.297762\pi\) | |||||||
\(762\) | − 3.70820i | − 0.134334i | ||||||||
\(763\) | − 35.3738i | − 1.28062i | ||||||||
\(764\) | 6.65248 | 0.240678 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.8328 | −1.18630 | ||||||||
\(767\) | − 22.4721i | − 0.811422i | ||||||||
\(768\) | 17.0000i | 0.613435i | ||||||||
\(769\) | 50.3607 | 1.81605 | 0.908026 | − | 0.418913i | \(-0.137589\pi\) | ||||
0.908026 | + | 0.418913i | \(0.137589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.7984 | 0.424908 | ||||||||
\(772\) | − 23.3262i | − 0.839530i | ||||||||
\(773\) | − 28.9230i | − 1.04029i | −0.854079 | − | 0.520144i | \(-0.825878\pi\) | ||||
0.854079 | − | 0.520144i | \(-0.174122\pi\) | |||||||
\(774\) | −7.70820 | −0.277066 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.43769 | −0.231100 | ||||||||
\(777\) | 13.8197i | 0.495778i | ||||||||
\(778\) | 25.9098i | 0.928912i | ||||||||
\(779\) | 4.47214 | 0.160231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.47214 | 0.231591 | ||||||||
\(782\) | 17.2361i | 0.616361i | ||||||||
\(783\) | − 6.61803i | − 0.236509i | ||||||||
\(784\) | 13.0000 | 0.464286 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.18034 | −0.291783 | ||||||||
\(787\) | − 14.1803i | − 0.505475i | −0.967535 | − | 0.252737i | \(-0.918669\pi\) | ||||
0.967535 | − | 0.252737i | \(-0.0813308\pi\) | |||||||
\(788\) | 7.61803i | 0.271381i | ||||||||
\(789\) | 23.8885 | 0.850455 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −81.9574 | −2.91407 | ||||||||
\(792\) | 3.70820i | 0.131765i | ||||||||
\(793\) | − 9.09017i | − 0.322801i | ||||||||
\(794\) | 6.94427 | 0.246443 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.6525 | −0.448455 | ||||||||
\(797\) | − 49.1033i | − 1.73933i | −0.493643 | − | 0.869665i | \(-0.664335\pi\) | ||||
0.493643 | − | 0.869665i | \(-0.335665\pi\) | |||||||
\(798\) | 5.52786i | 0.195684i | ||||||||
\(799\) | 2.94427 | 0.104161 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.38197 | 0.190162 | ||||||||
\(802\) | − 22.4508i | − 0.792767i | ||||||||
\(803\) | − 10.0000i | − 0.352892i | ||||||||
\(804\) | 0.763932 | 0.0269418 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.5279 | 0.546946 | ||||||||
\(807\) | − 6.85410i | − 0.241276i | ||||||||
\(808\) | 10.6869i | 0.375964i | ||||||||
\(809\) | −28.2148 | −0.991979 | −0.495989 | − | 0.868329i | \(-0.665195\pi\) | ||||
−0.495989 | + | 0.868329i | \(0.665195\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.76393 | 0.167284 | 0.0836421 | − | 0.996496i | \(-0.473345\pi\) | ||||
0.0836421 | + | 0.996496i | \(0.473345\pi\) | |||||||
\(812\) | 29.5967i | 1.03864i | ||||||||
\(813\) | 0.180340i | 0.00632480i | ||||||||
\(814\) | −3.81966 | −0.133879 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.85410 | −0.134921 | ||||||||
\(817\) | 9.52786i | 0.333338i | ||||||||
\(818\) | − 1.20163i | − 0.0420139i | ||||||||
\(819\) | 25.1246 | 0.877925 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.9443 | 0.800761 | 0.400380 | − | 0.916349i | \(-0.368878\pi\) | ||||
0.400380 | + | 0.916349i | \(0.368878\pi\) | |||||||
\(822\) | − 7.61803i | − 0.265709i | ||||||||
\(823\) | 19.2361i | 0.670527i | 0.942124 | + | 0.335264i | \(0.108825\pi\) | ||||
−0.942124 | + | 0.335264i | \(0.891175\pi\) | |||||||
\(824\) | 9.70820 | 0.338201 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8885 | 0.622422 | ||||||||
\(827\) | − 36.0689i | − 1.25424i | −0.778923 | − | 0.627119i | \(-0.784234\pi\) | ||||
0.778923 | − | 0.627119i | \(-0.215766\pi\) | |||||||
\(828\) | 4.47214i | 0.155417i | ||||||||
\(829\) | −11.5066 | −0.399640 | −0.199820 | − | 0.979833i | \(-0.564036\pi\) | ||||
−0.199820 | + | 0.979833i | \(0.564036\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.7984 | 0.652108 | ||||||||
\(832\) | 39.3262i | 1.36339i | ||||||||
\(833\) | − 50.1033i | − 1.73598i | ||||||||
\(834\) | 22.9443 | 0.794495 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.52786 | 0.0528423 | ||||||||
\(837\) | 2.76393i | 0.0955355i | ||||||||
\(838\) | − 15.0557i | − 0.520091i | ||||||||
\(839\) | −14.0689 | −0.485712 | −0.242856 | − | 0.970062i | \(-0.578084\pi\) | ||||
−0.242856 | + | 0.970062i | \(0.578084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7984 | 0.510289 | ||||||||
\(842\) | 29.8541i | 1.02884i | ||||||||
\(843\) | 19.6180i | 0.675681i | ||||||||
\(844\) | 17.8885 | 0.615749 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.763932 | −0.0262645 | ||||||||
\(847\) | 42.3607i | 1.45553i | ||||||||
\(848\) | 3.61803i | 0.124244i | ||||||||
\(849\) | −13.7082 | −0.470464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.8197 | −0.473732 | ||||||||
\(852\) | 5.23607i | 0.179385i | ||||||||
\(853\) | − 23.1459i | − 0.792500i | −0.918143 | − | 0.396250i | \(-0.870311\pi\) | ||||
0.918143 | − | 0.396250i | \(-0.129689\pi\) | |||||||
\(854\) | 7.23607 | 0.247613 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.5836 | −0.771891 | ||||||||
\(857\) | − 12.4721i | − 0.426040i | −0.977048 | − | 0.213020i | \(-0.931670\pi\) | ||||
0.977048 | − | 0.213020i | \(-0.0683300\pi\) | |||||||
\(858\) | 6.94427i | 0.237074i | ||||||||
\(859\) | 23.4164 | 0.798958 | 0.399479 | − | 0.916742i | \(-0.369191\pi\) | ||||
0.399479 | + | 0.916742i | \(0.369191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.1803 | 0.551425 | ||||||||
\(862\) | 20.6525i | 0.703426i | ||||||||
\(863\) | − 10.8754i | − 0.370203i | −0.982719 | − | 0.185101i | \(-0.940739\pi\) | ||||
0.982719 | − | 0.185101i | \(-0.0592613\pi\) | |||||||
\(864\) | −5.00000 | −0.170103 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −21.9787 | −0.746867 | ||||||||
\(867\) | − 2.14590i | − 0.0728785i | ||||||||
\(868\) | − 12.3607i | − 0.419549i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.29180 | 0.145422 | ||||||||
\(872\) | 23.7295i | 0.803582i | ||||||||
\(873\) | − 2.14590i | − 0.0726276i | ||||||||
\(874\) | −5.52786 | −0.186983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.09017 | 0.273342 | ||||||||
\(877\) | − 33.2148i | − 1.12158i | −0.827957 | − | 0.560792i | \(-0.810497\pi\) | ||||
0.827957 | − | 0.560792i | \(-0.189503\pi\) | |||||||
\(878\) | − 16.1803i | − 0.546060i | ||||||||
\(879\) | 20.7984 | 0.701512 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.9443 | 1.44683 | 0.723415 | − | 0.690414i | \(-0.242572\pi\) | ||||
0.723415 | + | 0.690414i | \(0.242572\pi\) | |||||||
\(882\) | 13.0000i | 0.437733i | ||||||||
\(883\) | − 22.1803i | − 0.746428i | −0.927745 | − | 0.373214i | \(-0.878256\pi\) | ||||
0.927745 | − | 0.373214i | \(-0.121744\pi\) | |||||||
\(884\) | 21.6525 | 0.728252 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.2361 | −1.18378 | ||||||||
\(887\) | − 23.1246i | − 0.776448i | −0.921565 | − | 0.388224i | \(-0.873089\pi\) | ||||
0.921565 | − | 0.388224i | \(-0.126911\pi\) | |||||||
\(888\) | − 9.27051i | − 0.311098i | ||||||||
\(889\) | −16.5836 | −0.556196 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.23607 | −0.0414098 | ||||||||
\(892\) | − 8.18034i | − 0.273898i | ||||||||
\(893\) | 0.944272i | 0.0315989i | ||||||||
\(894\) | 18.8541 | 0.630575 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13.4164 | 0.448211 | ||||||||
\(897\) | 25.1246i | 0.838886i | ||||||||
\(898\) | − 16.7984i | − 0.560569i | ||||||||
\(899\) | −18.2918 | −0.610066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9443 | 0.464551 | ||||||||
\(902\) | 4.47214i | 0.148906i | ||||||||
\(903\) | 34.4721i | 1.14716i | ||||||||
\(904\) | 54.9787 | 1.82856 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.52786 | 0.250097 | ||||||||
\(907\) | 7.12461i | 0.236569i | 0.992980 | + | 0.118284i | \(0.0377395\pi\) | ||||
−0.992980 | + | 0.118284i | \(0.962261\pi\) | |||||||
\(908\) | − 20.0000i | − 0.663723i | ||||||||
\(909\) | −3.56231 | −0.118154 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.1803 | 0.602342 | 0.301171 | − | 0.953570i | \(-0.402623\pi\) | ||||
0.301171 | + | 0.953570i | \(0.402623\pi\) | |||||||
\(912\) | − 1.23607i | − 0.0409303i | ||||||||
\(913\) | 15.4164i | 0.510209i | ||||||||
\(914\) | 22.3607 | 0.739626 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −21.9787 | −0.726197 | ||||||||
\(917\) | 36.5836i | 1.20810i | ||||||||
\(918\) | − 3.85410i | − 0.127204i | ||||||||
\(919\) | −49.1935 | −1.62274 | −0.811372 | − | 0.584530i | \(-0.801279\pi\) | ||||
−0.811372 | + | 0.584530i | \(0.801279\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.6525 | 1.07594 | ||||||||
\(922\) | − 32.7984i | − 1.08016i | ||||||||
\(923\) | 29.4164i | 0.968253i | ||||||||
\(924\) | 5.52786 | 0.181853 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.7639 | 0.616621 | ||||||||
\(927\) | 3.23607i | 0.106286i | ||||||||
\(928\) | − 33.0902i | − 1.08624i | ||||||||
\(929\) | 9.09017 | 0.298239 | 0.149119 | − | 0.988819i | \(-0.452356\pi\) | ||||
0.149119 | + | 0.988819i | \(0.452356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.0689 | 0.526636 | ||||||||
\(932\) | − 12.3820i | − 0.405585i | ||||||||
\(933\) | − 17.7082i | − 0.579741i | ||||||||
\(934\) | −28.1803 | −0.922089 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −16.8541 | −0.550894 | ||||||||
\(937\) | − 48.6869i | − 1.59053i | −0.606260 | − | 0.795266i | \(-0.707331\pi\) | ||||
0.606260 | − | 0.795266i | \(-0.292669\pi\) | |||||||
\(938\) | 3.41641i | 0.111550i | ||||||||
\(939\) | 0.472136 | 0.0154076 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.3262 | −0.336626 | −0.168313 | − | 0.985734i | \(-0.553832\pi\) | ||||
−0.168313 | + | 0.985734i | \(0.553832\pi\) | |||||||
\(942\) | 10.7984i | 0.351830i | ||||||||
\(943\) | 16.1803i | 0.526904i | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.52786 | −0.309778 | ||||||||
\(947\) | 2.58359i | 0.0839555i | 0.999119 | + | 0.0419777i | \(0.0133659\pi\) | ||||
−0.999119 | + | 0.0419777i | \(0.986634\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.4508 | 1.47540 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.8328 | 0.934968 | ||||||||
\(952\) | 51.7082i | 1.67587i | ||||||||
\(953\) | 1.09017i | 0.0353141i | 0.999844 | + | 0.0176570i | \(0.00562070\pi\) | ||||
−0.999844 | + | 0.0176570i | \(0.994379\pi\) | |||||||
\(954\) | −3.61803 | −0.117138 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.9443 | 0.806755 | ||||||||
\(957\) | − 8.18034i | − 0.264433i | ||||||||
\(958\) | − 18.9443i | − 0.612062i | ||||||||
\(959\) | −34.0689 | −1.10014 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.3607 | −0.753570 | ||||||||
\(962\) | − 17.3607i | − 0.559731i | ||||||||
\(963\) | − 7.52786i | − 0.242582i | ||||||||
\(964\) | 28.0344 | 0.902929 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −20.0000 | −0.643489 | ||||||||
\(967\) | − 18.8328i | − 0.605623i | −0.953051 | − | 0.302811i | \(-0.902075\pi\) | ||||
0.953051 | − | 0.302811i | \(-0.0979252\pi\) | |||||||
\(968\) | − 28.4164i | − 0.913338i | ||||||||
\(969\) | −4.76393 | −0.153040 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.4164 | −1.07238 | −0.536192 | − | 0.844096i | \(-0.680138\pi\) | ||||
−0.536192 | + | 0.844096i | \(0.680138\pi\) | |||||||
\(972\) | − 1.00000i | − 0.0320750i | ||||||||
\(973\) | − 102.610i | − 3.28952i | ||||||||
\(974\) | −9.70820 | −0.311071 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.61803 | −0.0517920 | ||||||||
\(977\) | − 3.25735i | − 0.104212i | −0.998642 | − | 0.0521060i | \(-0.983407\pi\) | ||||
0.998642 | − | 0.0521060i | \(-0.0165934\pi\) | |||||||
\(978\) | 14.9443i | 0.477865i | ||||||||
\(979\) | 6.65248 | 0.212614 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.90983 | −0.252541 | ||||||||
\(982\) | 5.88854i | 0.187911i | ||||||||
\(983\) | − 8.29180i | − 0.264467i | −0.991219 | − | 0.132234i | \(-0.957785\pi\) | ||||
0.991219 | − | 0.132234i | \(-0.0422149\pi\) | |||||||
\(984\) | −10.8541 | −0.346016 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 25.5066 | 0.812295 | ||||||||
\(987\) | 3.41641i | 0.108745i | ||||||||
\(988\) | 6.94427i | 0.220927i | ||||||||
\(989\) | −34.4721 | −1.09615 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.1246 | 1.17930 | 0.589651 | − | 0.807658i | \(-0.299265\pi\) | ||||
0.589651 | + | 0.807658i | \(0.299265\pi\) | |||||||
\(992\) | 13.8197i | 0.438775i | ||||||||
\(993\) | 6.94427i | 0.220370i | ||||||||
\(994\) | −23.4164 | −0.742723 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −12.4721 | −0.395195 | ||||||||
\(997\) | − 17.4164i | − 0.551583i | −0.961217 | − | 0.275792i | \(-0.911060\pi\) | ||||
0.961217 | − | 0.275792i | \(-0.0889400\pi\) | |||||||
\(998\) | 6.00000i | 0.189927i | ||||||||
\(999\) | 3.09017 | 0.0977687 |
(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 | 1875.2.b.b.1249.3 | 4 | ||
5.2 | odd | 4 | 1875.2.a.a.1.2 | 2 | |||
5.3 | odd | 4 | 1875.2.a.d.1.1 | 2 | |||
5.4 | even | 2 | inner | 1875.2.b.b.1249.2 | 4 | ||
15.2 | even | 4 | 5625.2.a.h.1.2 | 2 | |||
15.8 | even | 4 | 5625.2.a.a.1.1 | 2 | |||
25.2 | odd | 20 | 375.2.g.a.226.1 | 4 | |||
25.9 | even | 10 | 375.2.i.a.349.2 | 8 | |||
25.11 | even | 5 | 375.2.i.a.274.2 | 8 | |||
25.12 | odd | 20 | 375.2.g.a.151.1 | 4 | |||
25.13 | odd | 20 | 75.2.g.a.31.1 | ✓ | 4 | ||
25.14 | even | 10 | 375.2.i.a.274.1 | 8 | |||
25.16 | even | 5 | 375.2.i.a.349.1 | 8 | |||
25.23 | odd | 20 | 75.2.g.a.46.1 | yes | 4 | ||
75.23 | even | 20 | 225.2.h.a.46.1 | 4 | |||
75.38 | even | 20 | 225.2.h.a.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.a.31.1 | ✓ | 4 | 25.13 | odd | 20 | ||
75.2.g.a.46.1 | yes | 4 | 25.23 | odd | 20 | ||
225.2.h.a.46.1 | 4 | 75.23 | even | 20 | |||
225.2.h.a.181.1 | 4 | 75.38 | even | 20 | |||
375.2.g.a.151.1 | 4 | 25.12 | odd | 20 | |||
375.2.g.a.226.1 | 4 | 25.2 | odd | 20 | |||
375.2.i.a.274.1 | 8 | 25.14 | even | 10 | |||
375.2.i.a.274.2 | 8 | 25.11 | even | 5 | |||
375.2.i.a.349.1 | 8 | 25.16 | even | 5 | |||
375.2.i.a.349.2 | 8 | 25.9 | even | 10 | |||
1875.2.a.a.1.2 | 2 | 5.2 | odd | 4 | |||
1875.2.a.d.1.1 | 2 | 5.3 | odd | 4 | |||
1875.2.b.b.1249.2 | 4 | 5.4 | even | 2 | inner | ||
1875.2.b.b.1249.3 | 4 | 1.1 | even | 1 | trivial | ||
5625.2.a.a.1.1 | 2 | 15.8 | even | 4 | |||
5625.2.a.h.1.2 | 2 | 15.2 | even | 4 |