Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + \cdots + 4096 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.6 | ||
Root | \(-0.226426 - 0.392182i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.g.501.6 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.226426 | − | 0.392182i | 0.130727 | − | 0.226426i | −0.793230 | − | 0.608922i | \(-0.791602\pi\) |
0.923957 | + | 0.382496i | \(0.124935\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.54366 | −0.961414 | −0.480707 | − | 0.876881i | \(-0.659620\pi\) | ||||
−0.480707 | + | 0.876881i | \(0.659620\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.39746 | + | 2.42048i | 0.465821 | + | 0.806825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.22377 | 0.670491 | 0.335246 | − | 0.942131i | \(-0.391181\pi\) | ||||
0.335246 | + | 0.942131i | \(0.391181\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51096 | − | 6.08116i | −0.973765 | − | 1.68661i | −0.683953 | − | 0.729526i | \(-0.739741\pi\) |
−0.289812 | − | 0.957084i | \(-0.593593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.27878 | + | 2.21492i | −0.310151 | + | 0.537197i | −0.978395 | − | 0.206745i | \(-0.933713\pi\) |
0.668244 | + | 0.743942i | \(0.267046\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.70498 | + | 3.41805i | −0.620565 | + | 0.784155i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.575952 | + | 0.997578i | −0.125683 | + | 0.217689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.01448 | + | 6.95328i | 0.837076 | + | 1.44986i | 0.892329 | + | 0.451387i | \(0.149070\pi\) |
−0.0552521 | + | 0.998472i | \(0.517596\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.62425 | 0.505036 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.941734 | + | 1.63113i | 0.174876 | + | 0.302893i | 0.940118 | − | 0.340849i | \(-0.110714\pi\) |
−0.765243 | + | 0.643742i | \(0.777381\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.98111 | 1.07424 | 0.537120 | − | 0.843506i | \(-0.319512\pi\) | ||||
0.537120 | + | 0.843506i | \(0.319512\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.503519 | − | 0.872121i | 0.0876515 | − | 0.151817i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.86105 | 0.470353 | 0.235177 | − | 0.971953i | \(-0.424433\pi\) | ||||
0.235177 | + | 0.971953i | \(0.424433\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.17989 | −0.509190 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.67524 | + | 6.36571i | −0.573977 | + | 0.994157i | 0.422175 | + | 0.906514i | \(0.361267\pi\) |
−0.996152 | + | 0.0876426i | \(0.972067\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84706 | − | 3.19919i | 0.281673 | − | 0.487873i | −0.690124 | − | 0.723691i | \(-0.742444\pi\) |
0.971797 | + | 0.235819i | \(0.0757772\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.36448 | + | 4.09540i | 0.344895 | + | 0.597376i | 0.985335 | − | 0.170633i | \(-0.0545812\pi\) |
−0.640440 | + | 0.768008i | \(0.721248\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.529782 | −0.0756832 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.579100 | + | 1.00303i | 0.0810903 | + | 0.140453i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.14549 | + | 8.91226i | 0.706788 | + | 1.22419i | 0.966042 | + | 0.258383i | \(0.0831898\pi\) |
−0.259255 | + | 0.965809i | \(0.583477\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.728020 | + | 1.83478i | 0.0964286 | + | 0.243023i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.73666 | − | 6.47208i | 0.486472 | − | 0.842593i | −0.513408 | − | 0.858145i | \(-0.671617\pi\) |
0.999879 | + | 0.0155515i | \(0.00495040\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.17839 | + | 7.23719i | 0.534988 | + | 0.926627i | 0.999164 | + | 0.0408838i | \(0.0130174\pi\) |
−0.464176 | + | 0.885743i | \(0.653649\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.55467 | − | 6.15687i | −0.447847 | − | 0.775693i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.17997 | − | 10.7040i | −0.755004 | − | 1.30771i | −0.945372 | − | 0.325993i | \(-0.894302\pi\) |
0.190368 | − | 0.981713i | \(-0.439032\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.63593 | 0.437715 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.13931 | + | 7.16950i | −0.491246 | + | 0.850863i | −0.999949 | − | 0.0100790i | \(-0.996792\pi\) |
0.508703 | + | 0.860942i | \(0.330125\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.32134 | + | 10.9489i | −0.739857 | + | 1.28147i | 0.212703 | + | 0.977117i | \(0.431773\pi\) |
−0.952559 | + | 0.304352i | \(0.901560\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.65651 | −0.644620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.13067 | − | 3.69043i | 0.239719 | − | 0.415206i | −0.720914 | − | 0.693024i | \(-0.756278\pi\) |
0.960634 | + | 0.277818i | \(0.0896112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.59819 | + | 6.23225i | −0.399799 | + | 0.692472i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.7613 | −1.62026 | −0.810132 | − | 0.586248i | \(-0.800604\pi\) | ||||
−0.810132 | + | 0.586248i | \(0.800604\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.852933 | 0.0914440 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.19403 | + | 12.4604i | 0.762566 | + | 1.32080i | 0.941524 | + | 0.336946i | \(0.109394\pi\) |
−0.178958 | + | 0.983857i | \(0.557273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.93069 | + | 15.4684i | 0.936191 | + | 1.62153i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.35428 | − | 2.34568i | 0.140432 | − | 0.243236i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.91488 | + | 5.04871i | −0.295961 | + | 0.512619i | −0.975208 | − | 0.221291i | \(-0.928973\pi\) |
0.679247 | + | 0.733910i | \(0.262306\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.10763 | + | 5.38258i | 0.312329 | + | 0.540969i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.47686 | + | 11.2183i | 0.644472 | + | 1.11626i | 0.984423 | + | 0.175815i | \(0.0562560\pi\) |
−0.339951 | + | 0.940443i | \(0.610411\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6116 | 1.63679 | 0.818394 | − | 0.574658i | \(-0.194865\pi\) | ||||
0.818394 | + | 0.574658i | \(0.194865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.59275 | 0.443998 | 0.221999 | − | 0.975047i | \(-0.428742\pi\) | ||||
0.221999 | + | 0.975047i | \(0.428742\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.30902 | − | 2.26728i | 0.125381 | − | 0.217166i | −0.796501 | − | 0.604637i | \(-0.793318\pi\) |
0.921882 | + | 0.387471i | \(0.126651\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.647816 | − | 1.12205i | 0.0614880 | − | 0.106500i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.509357 | 0.0479163 | 0.0239581 | − | 0.999713i | \(-0.492373\pi\) | ||||
0.0239581 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.81286 | − | 16.9964i | 0.907200 | − | 1.57132i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.25279 | − | 5.63401i | 0.298183 | − | 0.516468i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.05486 | −0.550441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.66434 | + | 2.88273i | 0.150069 | + | 0.259927i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.367242 | − | 0.636081i | −0.0325874 | − | 0.0564431i | 0.849272 | − | 0.527956i | \(-0.177041\pi\) |
−0.881859 | + | 0.471513i | \(0.843708\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.836444 | − | 1.44876i | −0.0736448 | − | 0.127556i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.84274 | − | 4.92377i | 0.248371 | − | 0.430192i | −0.714703 | − | 0.699428i | \(-0.753438\pi\) |
0.963074 | + | 0.269236i | \(0.0867713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.88055 | − | 8.69437i | 0.596620 | − | 0.753898i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.39993 | + | 16.2812i | 0.803091 | + | 1.39099i | 0.917573 | + | 0.397568i | \(0.130146\pi\) |
−0.114482 | + | 0.993425i | \(0.536521\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.05362 | − | 3.55697i | −0.174186 | − | 0.301698i | 0.765694 | − | 0.643206i | \(-0.222396\pi\) |
−0.939879 | + | 0.341507i | \(0.889063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.14152 | 0.180349 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.80756 | − | 13.5231i | −0.652901 | − | 1.13086i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.119957 | + | 0.207771i | −0.00989385 | + | 0.0171367i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.08175 | − | 3.60570i | 0.170544 | − | 0.295391i | −0.768066 | − | 0.640370i | \(-0.778781\pi\) |
0.938610 | + | 0.344980i | \(0.112114\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7955 | 1.44818 | 0.724090 | − | 0.689706i | \(-0.242260\pi\) | ||||
0.724090 | + | 0.689706i | \(0.242260\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.14821 | −0.577899 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.67476 | − | 8.09693i | 0.373087 | − | 0.646205i | −0.616952 | − | 0.787001i | \(-0.711633\pi\) |
0.990039 | + | 0.140796i | \(0.0449660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.66030 | 0.369586 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2115 | − | 17.6868i | −0.804777 | − | 1.39391i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.55215 | −0.121574 | −0.0607869 | − | 0.998151i | \(-0.519361\pi\) | ||||
−0.0607869 | + | 0.998151i | \(0.519361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.05980 | − | 7.03177i | −0.314157 | − | 0.544135i | 0.665101 | − | 0.746753i | \(-0.268388\pi\) |
−0.979258 | + | 0.202618i | \(0.935055\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.1537 | + | 31.4431i | −1.39644 | + | 2.41870i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.0534 | − | 1.77073i | −0.921748 | − | 0.135411i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.365686 | + | 0.633386i | −0.0278026 | + | 0.0481555i | −0.879592 | − | 0.475729i | \(-0.842184\pi\) |
0.851789 | + | 0.523884i | \(0.175518\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.69216 | − | 2.93090i | −0.127190 | − | 0.220300i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.68858 | 0.200954 | 0.100477 | − | 0.994939i | \(-0.467963\pi\) | ||||
0.100477 | + | 0.994939i | \(0.467963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.75090 | + | 4.76469i | 0.204473 | + | 0.354157i | 0.949965 | − | 0.312358i | \(-0.101119\pi\) |
−0.745492 | + | 0.666515i | \(0.767785\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.78439 | 0.279750 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.84372 | + | 4.92547i | −0.207953 | + | 0.360186i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.67520 | −0.485549 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.39845 | 0.680048 | 0.340024 | − | 0.940417i | \(-0.389565\pi\) | ||||
0.340024 | + | 0.940417i | \(0.389565\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.77864 | − | 10.0089i | 0.415956 | − | 0.720457i | −0.579572 | − | 0.814921i | \(-0.696780\pi\) |
0.995528 | + | 0.0944641i | \(0.0301138\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.11825 | −0.364660 | −0.182330 | − | 0.983237i | \(-0.558364\pi\) | ||||
−0.182330 | + | 0.983237i | \(0.558364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.71897 | − | 11.6376i | −0.476295 | − | 0.824968i | 0.523336 | − | 0.852127i | \(-0.324687\pi\) |
−0.999631 | + | 0.0271588i | \(0.991354\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.59723 | −0.394798 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.39545 | − | 4.14905i | −0.168128 | − | 0.291206i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.2202 | + | 19.4339i | −0.779855 | + | 1.35075i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.01524 | + | 7.60096i | −0.416083 | + | 0.525769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.54063 | − | 4.40050i | 0.174904 | − | 0.302943i | −0.765224 | − | 0.643764i | \(-0.777372\pi\) |
0.940128 | + | 0.340821i | \(0.110705\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.87450 | + | 3.24673i | 0.128438 | + | 0.222462i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.2139 | −1.03279 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.86263 | + | 4.95823i | 0.193439 | + | 0.335046i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9590 | 1.20806 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8464 | + | 20.5186i | −0.793295 | + | 1.37403i | 0.130621 | + | 0.991432i | \(0.458303\pi\) |
−0.923916 | + | 0.382595i | \(0.875030\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.0306 | −1.26310 | −0.631551 | − | 0.775334i | \(-0.717582\pi\) | ||||
−0.631551 | + | 0.775334i | \(0.717582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.9233 | −1.84523 | −0.922613 | − | 0.385727i | \(-0.873951\pi\) | ||||
−0.922613 | + | 0.385727i | \(0.873951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.28078 | + | 2.21838i | −0.0842694 | + | 0.145959i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.08296 | − | 12.2680i | 0.464020 | − | 0.803706i | −0.535137 | − | 0.844765i | \(-0.679740\pi\) |
0.999157 | + | 0.0410592i | \(0.0130732\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.964881 | − | 1.67122i | −0.0626757 | − | 0.108558i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.0237 | 1.10117 | 0.550585 | − | 0.834779i | \(-0.314405\pi\) | ||||
0.550585 | + | 0.834779i | \(0.314405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.59549 | − | 14.8878i | −0.553684 | − | 0.959009i | −0.998005 | − | 0.0631409i | \(-0.979888\pi\) |
0.444321 | − | 0.895868i | \(-0.353445\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.56582 | + | 9.64028i | 0.357047 | + | 0.618424i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.2828 | + | 4.44876i | 1.92685 | + | 0.283068i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.34235 | + | 5.78911i | −0.211813 | + | 0.366870i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.8853 | − | 20.5860i | −0.750195 | − | 1.29938i | −0.947728 | − | 0.319079i | \(-0.896626\pi\) |
0.197534 | − | 0.980296i | \(-0.436707\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.92727 | + | 15.4625i | 0.561252 | + | 0.972118i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.716409 | + | 1.24086i | 0.0446884 | + | 0.0774026i | 0.887504 | − | 0.460799i | \(-0.152437\pi\) |
−0.842816 | + | 0.538202i | \(0.819104\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.27754 | −0.452204 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.63208 | + | 4.55889i | −0.162921 | + | 0.282188i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.56505 | − | 6.17484i | 0.219830 | − | 0.380757i | −0.734926 | − | 0.678148i | \(-0.762783\pi\) |
0.954756 | + | 0.297390i | \(0.0961163\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.51567 | 0.398753 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.13452 | − | 15.8214i | 0.556941 | − | 0.964651i | −0.440808 | − | 0.897601i | \(-0.645308\pi\) |
0.997750 | − | 0.0670494i | \(-0.0213585\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90265 | − | 5.02754i | 0.176324 | − | 0.305401i | −0.764295 | − | 0.644867i | \(-0.776913\pi\) |
0.940619 | + | 0.339465i | \(0.110246\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.08857 | 0.489543 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.72209 | 0.343807 | 0.171904 | − | 0.985114i | \(-0.445008\pi\) | ||||
0.171904 | + | 0.985114i | \(0.445008\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.35838 | + | 14.4771i | 0.500403 | + | 0.866724i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.07155 | + | 5.32009i | 0.183233 | + | 0.317370i | 0.942980 | − | 0.332850i | \(-0.108010\pi\) |
−0.759746 | + | 0.650220i | \(0.774677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.22632 | + | 14.2484i | −0.489004 | + | 0.846980i | −0.999920 | − | 0.0126510i | \(-0.995973\pi\) |
0.510916 | + | 0.859631i | \(0.329306\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.34858 | − | 16.1922i | 0.551829 | − | 0.955796i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.22942 | + | 9.05763i | 0.307613 | + | 0.532801i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.32001 | + | 2.28632i | 0.0773803 | + | 0.134027i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −19.5684 | −1.14320 | −0.571599 | − | 0.820533i | \(-0.693677\pi\) | ||||
−0.571599 | + | 0.820533i | \(0.693677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.83571 | 0.338622 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 28.1893 | − | 48.8253i | 1.63023 | − | 2.82364i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.69829 | + | 8.13767i | −0.270805 | + | 0.469047i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.86613 | 0.337000 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3994 | + | 24.9405i | −0.821817 | + | 1.42343i | 0.0825100 | + | 0.996590i | \(0.473706\pi\) |
−0.904327 | + | 0.426839i | \(0.859627\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.76130 | − | 6.51476i | 0.213973 | − | 0.370612i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4309 | −1.10182 | −0.550911 | − | 0.834564i | \(-0.685720\pi\) | ||||
−0.550911 | + | 0.834564i | \(0.685720\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.81885 | − | 8.34649i | −0.272377 | − | 0.471772i | 0.697093 | − | 0.716981i | \(-0.254477\pi\) |
−0.969470 | + | 0.245209i | \(0.921143\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.115348 | + | 0.199789i | 0.00647860 | + | 0.0112213i | 0.869247 | − | 0.494379i | \(-0.164604\pi\) |
−0.862768 | + | 0.505600i | \(0.831271\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.09420 | + | 3.62726i | 0.117253 | + | 0.203087i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.03992 | − | 1.80119i | 0.0580427 | − | 0.100533i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.11163 | − | 10.3623i | −0.228777 | − | 0.576572i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.592791 | − | 1.02674i | −0.0327814 | − | 0.0567791i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.01444 | − | 10.4173i | −0.331587 | − | 0.574325i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.1135 | −0.665820 | −0.332910 | − | 0.942959i | \(-0.608031\pi\) | ||||
−0.332910 | + | 0.942959i | \(0.608031\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.99821 | + | 6.92510i | 0.219100 | + | 0.379493i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.57090 | − | 9.64909i | 0.303466 | − | 0.525619i | −0.673452 | − | 0.739231i | \(-0.735189\pi\) |
0.976919 | + | 0.213611i | \(0.0685226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.115332 | − | 0.199761i | 0.00626396 | − | 0.0108495i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.3006 | 0.720268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1532 | 1.03418 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.84478 | − | 4.92730i | 0.152716 | − | 0.264511i | −0.779509 | − | 0.626391i | \(-0.784532\pi\) |
0.932225 | + | 0.361880i | \(0.117865\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.369374 | 0.0197722 | 0.00988608 | − | 0.999951i | \(-0.496853\pi\) | ||||
0.00988608 | + | 0.999951i | \(0.496853\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.21362 | − | 15.9585i | −0.491787 | − | 0.851799i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.87124 | 0.0995962 | 0.0497981 | − | 0.998759i | \(-0.484142\pi\) | ||||
0.0497981 | + | 0.998759i | \(0.484142\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.47304 | − | 2.55137i | −0.0779613 | − | 0.135033i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.47802 | − | 14.6844i | 0.447453 | − | 0.775011i | −0.550767 | − | 0.834659i | \(-0.685665\pi\) |
0.998219 | + | 0.0596485i | \(0.0189980\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.36618 | − | 18.4915i | −0.229799 | − | 0.973238i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.37098 | + | 2.37460i | −0.0719577 | + | 0.124634i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.89237 | − | 3.27769i | −0.0987812 | − | 0.171094i | 0.812399 | − | 0.583102i | \(-0.198161\pi\) |
−0.911180 | + | 0.412008i | \(0.864828\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.5441 | −1.06948 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.0884 | − | 22.6698i | −0.679516 | − | 1.17696i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.51203 | −0.233624 | −0.116812 | − | 0.993154i | \(-0.537268\pi\) | ||||
−0.116812 | + | 0.993154i | \(0.537268\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.61278 | − | 11.4537i | 0.340575 | − | 0.589894i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.64242 | 0.238465 | 0.119233 | − | 0.992866i | \(-0.461957\pi\) | ||||
0.119233 | + | 0.992866i | \(0.461957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.332612 | −0.0170403 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.99088 | + | 12.1086i | −0.357218 | + | 0.618719i | −0.987495 | − | 0.157651i | \(-0.949608\pi\) |
0.630277 | + | 0.776370i | \(0.282941\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.3248 | 0.524837 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.93460 | − | 6.81492i | −0.199492 | − | 0.345530i | 0.748872 | − | 0.662715i | \(-0.230596\pi\) |
−0.948364 | + | 0.317185i | \(0.897263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.5346 | −1.03848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.28734 | − | 2.22974i | −0.0649378 | − | 0.112476i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.48528 | + | 14.6969i | −0.425864 | + | 0.737618i | −0.996501 | − | 0.0835846i | \(-0.973363\pi\) |
0.570637 | + | 0.821203i | \(0.306696\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.85184 | − | 4.66706i | −0.0927078 | − | 0.233645i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.16651 | + | 12.4128i | −0.357878 | + | 0.619864i | −0.987606 | − | 0.156952i | \(-0.949833\pi\) |
0.629728 | + | 0.776816i | \(0.283166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.9994 | − | 36.3721i | −1.04606 | − | 1.81182i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.36231 | 0.315368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.122530 | + | 0.212228i | 0.00605872 | + | 0.0104940i | 0.869039 | − | 0.494744i | \(-0.164738\pi\) |
−0.862980 | + | 0.505238i | \(0.831405\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.51357 | 0.419943 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.50480 | + | 16.4628i | −0.467701 | + | 0.810081i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.85997 | −0.0910832 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.4690 | −1.24424 | −0.622122 | − | 0.782920i | \(-0.713729\pi\) | ||||
−0.622122 | + | 0.782920i | \(0.713729\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.02703 | + | 5.24297i | −0.147529 | + | 0.255527i | −0.930313 | − | 0.366765i | \(-0.880465\pi\) |
0.782785 | + | 0.622292i | \(0.213798\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.60855 | + | 11.4463i | −0.321318 | + | 0.556540i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.6284 | − | 18.4090i | −0.514345 | − | 0.890872i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.07134 | −0.341408 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.1005 | − | 19.2267i | −0.534694 | − | 0.926117i | −0.999178 | − | 0.0405356i | \(-0.987094\pi\) |
0.464484 | − | 0.885581i | \(-0.346240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1298 | − | 21.0094i | −0.582920 | − | 1.00965i | −0.995131 | − | 0.0985593i | \(-0.968577\pi\) |
0.412211 | − | 0.911089i | \(-0.364757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −34.6258 | − | 5.08677i | −1.65637 | − | 0.243333i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9487 | − | 20.6957i | 0.570279 | − | 0.987753i | −0.426258 | − | 0.904602i | \(-0.640168\pi\) |
0.996537 | − | 0.0831509i | \(-0.0264983\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.740350 | − | 1.28232i | −0.0352548 | − | 0.0610631i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3356 | + | 17.9017i | 0.491057 | + | 0.850536i | 0.999947 | − | 0.0102958i | \(-0.00327733\pi\) |
−0.508890 | + | 0.860832i | \(0.669944\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.942727 | − | 1.63285i | −0.0445895 | − | 0.0772312i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.64143 | −0.313429 | −0.156714 | − | 0.987644i | \(-0.550090\pi\) | ||||
−0.156714 | + | 0.987644i | \(0.550090\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.17289 | + | 14.1559i | −0.384846 | + | 0.666573i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.02937 | − | 6.97908i | 0.189316 | − | 0.327906i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3433 | −0.670952 | −0.335476 | − | 0.942049i | \(-0.608897\pi\) | ||||
−0.335476 | + | 0.942049i | \(0.608897\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.35584 | + | 5.81249i | −0.156637 | + | 0.271304i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.3682 | − | 23.1544i | 0.622618 | − | 1.07841i | −0.366378 | − | 0.930466i | \(-0.619402\pi\) |
0.988996 | − | 0.147940i | \(-0.0472643\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0950 | 0.562101 | 0.281051 | − | 0.959693i | \(-0.409317\pi\) | ||||
0.281051 | + | 0.959693i | \(0.409317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.3169 | 1.26408 | 0.632038 | − | 0.774938i | \(-0.282219\pi\) | ||||
0.632038 | + | 0.774938i | \(0.282219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.7198 | + | 27.2274i | 0.725871 | + | 1.25725i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.11698 | − | 3.66671i | −0.0975452 | − | 0.168953i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.10742 | − | 7.11427i | 0.188860 | − | 0.327114i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.3813 | + | 24.9091i | −0.658473 | + | 1.14051i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.69624 | − | 6.40208i | −0.168886 | − | 0.292519i | 0.769143 | − | 0.639077i | \(-0.220684\pi\) |
−0.938028 | + | 0.346559i | \(0.887350\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0450 | − | 17.3985i | −0.458013 | − | 0.793302i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.24858 | −0.420825 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.9424 | −0.586477 | −0.293239 | − | 0.956039i | \(-0.594733\pi\) | ||||
−0.293239 | + | 0.956039i | \(0.594733\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.351447 | + | 0.608725i | −0.0158930 | + | 0.0275275i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.59974 | − | 9.69903i | 0.252713 | − | 0.437711i | −0.711559 | − | 0.702626i | \(-0.752011\pi\) |
0.964272 | + | 0.264915i | \(0.0853439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.81710 | −0.216951 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.5290 | − | 18.2368i | 0.472291 | − | 0.818032i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.9699 | − | 22.4645i | 0.580611 | − | 1.00565i | −0.414796 | − | 0.909914i | \(-0.636147\pi\) |
0.995407 | − | 0.0957335i | \(-0.0305196\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.67698 | −0.164275 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.6300 | − | 23.6079i | −0.607733 | − | 1.05262i | −0.991613 | − | 0.129241i | \(-0.958746\pi\) |
0.383881 | − | 0.923383i | \(-0.374587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.22093 | + | 14.2391i | 0.365104 | + | 0.632379i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.6203 | − | 21.8591i | −0.559386 | − | 0.968885i | −0.997548 | − | 0.0699892i | \(-0.977704\pi\) |
0.438161 | − | 0.898896i | \(-0.355630\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0794 | − | 27.8503i | 0.711309 | − | 1.23202i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.09853 | + | 8.96981i | −0.313408 | + | 0.396027i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.25806 | + | 9.10722i | 0.231249 | + | 0.400535i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.165602 | + | 0.286831i | 0.00726911 | + | 0.0125905i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.8142 | −1.08713 | −0.543565 | − | 0.839367i | \(-0.682926\pi\) | ||||
−0.543565 | + | 0.839367i | \(0.682926\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.08063 | + | 5.33581i | 0.134706 | + | 0.233318i | 0.925485 | − | 0.378784i | \(-0.123658\pi\) |
−0.790779 | + | 0.612102i | \(0.790324\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.64855 | + | 13.2477i | −0.333176 | + | 0.577078i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.7321 | + | 35.9090i | −0.901394 | + | 1.56126i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.8874 | 0.906434 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 51.6145 | 2.23567 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.608765 | − | 1.05441i | 0.0262702 | − | 0.0455013i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.17811 | −0.0507449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.27394 | − | 5.67063i | −0.140758 | − | 0.243799i | 0.787025 | − | 0.616922i | \(-0.211620\pi\) |
−0.927782 | + | 0.373122i | \(0.878287\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.49150 | 0.106921 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2770 | − | 19.5323i | −0.482169 | − | 0.835141i | 0.517621 | − | 0.855610i | \(-0.326818\pi\) |
−0.999791 | + | 0.0204683i | \(0.993484\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.6783 | + | 20.2274i | −0.498417 | + | 0.863284i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.12266 | − | 1.19328i | −0.346037 | − | 0.0508353i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.41971 | + | 9.38722i | −0.230470 | + | 0.399185i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.12281 | + | 14.0691i | 0.344175 | + | 0.596128i | 0.985203 | − | 0.171389i | \(-0.0548254\pi\) |
−0.641029 | + | 0.767517i | \(0.721492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.9397 | −1.09713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.28779 | + | 2.23051i | 0.0543703 | + | 0.0941722i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.4581 | 1.36795 | 0.683974 | − | 0.729506i | \(-0.260250\pi\) | ||||
0.683974 | + | 0.729506i | \(0.260250\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.15258 | − | 15.8527i | 0.384372 | − | 0.665752i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.5422 | 1.07078 | 0.535392 | − | 0.844604i | \(-0.320164\pi\) | ||||
0.535392 | + | 0.844604i | \(0.320164\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.9974 | 1.08796 | 0.543979 | − | 0.839099i | \(-0.316917\pi\) | ||||
0.543979 | + | 0.839099i | \(0.316917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.12806 | − | 3.68590i | 0.0889008 | − | 0.153981i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.5844 | 1.85607 | 0.928037 | − | 0.372489i | \(-0.121496\pi\) | ||||
0.928037 | + | 0.372489i | \(0.121496\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.61687 | − | 4.53256i | −0.108754 | − | 0.188367i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.5478 | 1.55774 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.4424 | + | 19.8188i | 0.473895 | + | 0.820810i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.28884 | − | 12.6246i | 0.300842 | − | 0.521074i | −0.675485 | − | 0.737374i | \(-0.736065\pi\) |
0.976327 | + | 0.216300i | \(0.0693988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.1788 | + | 20.4438i | −0.666635 | + | 0.842371i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.15891 | + | 2.00728i | −0.0476710 | + | 0.0825686i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8657 | + | 20.5520i | 0.487265 | + | 0.843968i | 0.999893 | − | 0.0146433i | \(-0.00466126\pi\) |
−0.512628 | + | 0.858611i | \(0.671328\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.08541 | −0.249059 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.86173 | + | 17.0810i | 0.402939 | + | 0.697911i | 0.994079 | − | 0.108658i | \(-0.0346552\pi\) |
−0.591140 | + | 0.806569i | \(0.701322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.0351 | −1.83702 | −0.918509 | − | 0.395400i | \(-0.870606\pi\) | ||||
−0.918509 | + | 0.395400i | \(0.870606\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.2726 | − | 29.9170i | 0.703393 | − | 1.21831i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.24160 | 0.293928 | 0.146964 | − | 0.989142i | \(-0.453050\pi\) | ||||
0.146964 | + | 0.989142i | \(0.453050\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.16957 | −0.0879156 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6032 | − | 28.7576i | 0.671693 | − | 1.16341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.4052 | + | 31.8788i | −0.743381 | + | 1.28757i | 0.207567 | + | 0.978221i | \(0.433446\pi\) |
−0.950947 | + | 0.309352i | \(0.899888\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.3448 | + | 31.7741i | 0.738533 | + | 1.27918i | 0.953156 | + | 0.302479i | \(0.0978143\pi\) |
−0.214623 | + | 0.976697i | \(0.568852\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1569 | 0.970948 | 0.485474 | − | 0.874251i | \(-0.338647\pi\) | ||||
0.485474 | + | 0.874251i | \(0.338647\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.5350 | + | 18.2471i | 0.422754 | + | 0.732231i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.2992 | − | 31.6951i | −0.733142 | − | 1.26984i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.61895 | + | 4.08013i | 0.0646545 | + | 0.162945i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.65866 | + | 6.33699i | −0.145880 | + | 0.252672i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.11258 | − | 12.3193i | −0.283147 | − | 0.490426i | 0.689011 | − | 0.724751i | \(-0.258045\pi\) |
−0.972158 | + | 0.234325i | \(0.924712\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.15053 | − | 1.99278i | −0.0457295 | − | 0.0792058i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.86004 | + | 3.22169i | 0.0736976 | + | 0.127648i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.1381 | −0.915330 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.1834 | − | 17.6382i | 0.402222 | − | 0.696668i | −0.591772 | − | 0.806105i | \(-0.701571\pi\) |
0.993994 | + | 0.109437i | \(0.0349048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.77586 | − | 10.0041i | 0.227778 | − | 0.394523i | −0.729371 | − | 0.684118i | \(-0.760187\pi\) |
0.957149 | + | 0.289595i | \(0.0935207\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1233 | 0.515932 | 0.257966 | − | 0.966154i | \(-0.416948\pi\) | ||||
0.257966 | + | 0.966154i | \(0.416948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.30946 | − | 14.3924i | 0.326175 | − | 0.564952i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.44483 | + | 5.96663i | −0.135014 | + | 0.233851i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4406 | −0.760769 | −0.380385 | − | 0.924828i | \(-0.624208\pi\) | ||||
−0.380385 | + | 0.924828i | \(0.624208\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −35.3353 | −1.37856 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7848 | + | 23.8759i | 0.536979 | + | 0.930074i | 0.999065 | + | 0.0432391i | \(0.0137677\pi\) |
−0.462086 | + | 0.886835i | \(0.652899\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88006 | + | 6.72046i | 0.150917 | + | 0.261396i | 0.931565 | − | 0.363575i | \(-0.118444\pi\) |
−0.780648 | + | 0.624971i | \(0.785111\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.06640 | − | 7.04320i | 0.157926 | − | 0.273535i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.56114 | + | 13.0963i | −0.292769 | + | 0.507090i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.36468 | + | 9.29190i | 0.207411 | + | 0.359246i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.29178 | + | 16.0938i | 0.358705 | + | 0.621295i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.2617 | −0.935220 | −0.467610 | − | 0.883935i | \(-0.654885\pi\) | ||||
−0.467610 | + | 0.883935i | \(0.654885\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.88851 | 0.187881 | 0.0939403 | − | 0.995578i | \(-0.470054\pi\) | ||||
0.0939403 | + | 0.995578i | \(0.470054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.41446 | − | 12.8422i | 0.284541 | − | 0.492839i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.30902 | + | 7.46344i | −0.165122 | + | 0.286000i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.560031 | 0.0214290 | 0.0107145 | − | 0.999943i | \(-0.496589\pi\) | ||||
0.0107145 | + | 0.999943i | \(0.496589\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.32257 | + | 10.9510i | −0.241221 | + | 0.417807i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.1312 | − | 62.5811i | 1.37649 | − | 2.38415i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5255 | −0.552576 | −0.276288 | − | 0.961075i | \(-0.589104\pi\) | ||||
−0.276288 | + | 0.961075i | \(0.589104\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.90477 | − | 13.6915i | −0.300277 | − | 0.520095i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.39969 | − | 16.2807i | −0.356039 | − | 0.616677i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.20754 | − | 5.55561i | −0.121320 | − | 0.210133i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23926 | − | 2.14647i | 0.0468064 | − | 0.0810710i | −0.841673 | − | 0.539987i | \(-0.818429\pi\) |
0.888479 | + | 0.458916i | \(0.151762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.73907 | + | 9.77921i | −0.291885 | + | 0.368830i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.4749 | − | 28.5354i | −0.619604 | − | 1.07319i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.1966 | + | 28.0533i | 0.608276 | + | 1.05356i | 0.991525 | + | 0.129919i | \(0.0414718\pi\) |
−0.383249 | + | 0.923645i | \(0.625195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.9101 | 0.446665 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0110 | + | 41.5884i | 0.899221 | + | 1.55750i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.85461 | − | 6.67637i | 0.143953 | − | 0.249334i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.64373 | + | 14.9714i | −0.322357 | + | 0.558338i | −0.980974 | − | 0.194140i | \(-0.937808\pi\) |
0.658617 | + | 0.752478i | \(0.271142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.2542 | −1.57363 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.78497 | −0.289526 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.47034 | + | 16.4031i | −0.351236 | + | 0.608358i | −0.986466 | − | 0.163965i | \(-0.947572\pi\) |
0.635231 | + | 0.772323i | \(0.280905\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.5481 | −0.612894 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.72397 | + | 8.18216i | 0.174722 | + | 0.302628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.542118 | 0.0200236 | 0.0100118 | − | 0.999950i | \(-0.496813\pi\) | ||||
0.0100118 | + | 0.999950i | \(0.496813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.7428 | − | 23.8033i | −0.506224 | − | 0.876805i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.87033 | − | 4.97156i | 0.105587 | − | 0.182882i | −0.808391 | − | 0.588646i | \(-0.799661\pi\) |
0.913978 | + | 0.405764i | \(0.132995\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.60154 | − | 10.8690i | 0.315985 | − | 0.399284i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.5060 | + | 19.9290i | −0.422115 | + | 0.731125i | −0.996146 | − | 0.0877087i | \(-0.972046\pi\) |
0.574031 | + | 0.818834i | \(0.305379\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.6284 | − | 35.7294i | −0.754752 | − | 1.30727i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.6824 | −0.426866 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.9704 | + | 44.9821i | 0.947674 | + | 1.64142i | 0.750306 | + | 0.661090i | \(0.229906\pi\) |
0.197368 | + | 0.980330i | \(0.436761\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.7646 | −0.392283 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.36406 | + | 11.0229i | −0.231306 | + | 0.400633i | −0.958193 | − | 0.286124i | \(-0.907633\pi\) |
0.726887 | + | 0.686757i | \(0.240966\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.08547 | 0.293484 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.6089 | −0.384573 | −0.192287 | − | 0.981339i | \(-0.561590\pi\) | ||||
−0.192287 | + | 0.981339i | \(0.561590\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.32969 | + | 5.76720i | −0.120543 | + | 0.208787i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −52.4770 | −1.89484 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.8089 | − | 18.7215i | −0.389777 | − | 0.675114i | 0.602642 | − | 0.798012i | \(-0.294115\pi\) |
−0.992419 | + | 0.122898i | \(0.960781\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.648856 | 0.0233680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.6637 | − | 37.5227i | −0.779190 | − | 1.34960i | −0.932409 | − | 0.361404i | \(-0.882298\pi\) |
0.153220 | − | 0.988192i | \(-0.451036\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.64783 | + | 2.85412i | −0.0591154 | + | 0.102391i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.8169 | − | 29.7813i | −0.423384 | − | 1.06703i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.20487 | + | 15.9433i | −0.329376 | + | 0.570496i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.47134 | + | 4.28049i | 0.0883185 | + | 0.152972i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.0046 | 1.03390 | 0.516950 | − | 0.856015i | \(-0.327067\pi\) | ||||
0.516950 | + | 0.856015i | \(0.327067\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.61444 | − | 2.79629i | −0.0574756 | − | 0.0995507i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.29563 | −0.0460674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 29.3403 | − | 50.8189i | 1.04191 | − | 1.80463i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.2045 | 0.503150 | 0.251575 | − | 0.967838i | \(-0.419051\pi\) | ||||
0.251575 | + | 0.967838i | \(0.419051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0946 | −0.427878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.1068 | + | 34.8260i | −0.710438 | + | 1.23052i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.0572 | + | 24.3478i | −0.496067 | + | 0.859214i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.13659 | − | 7.16478i | −0.145615 | − | 0.252212i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.9781 | 0.526603 | 0.263301 | − | 0.964714i | \(-0.415189\pi\) | ||||
0.263301 | + | 0.964714i | \(0.415189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.5388 | + | 35.5742i | 0.721214 | + | 1.24918i | 0.960513 | + | 0.278233i | \(0.0897489\pi\) |
−0.239300 | + | 0.970946i | \(0.576918\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.31447 | − | 2.27674i | −0.0461006 | − | 0.0798486i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.93877 | + | 14.9671i | 0.207771 | + | 0.523632i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.9606 | + | 43.2330i | −0.872194 | + | 1.51068i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.5219 | + | 37.2771i | 0.751120 | + | 1.30098i | 0.947280 | + | 0.320407i | \(0.103820\pi\) |
−0.196160 | + | 0.980572i | \(0.562847\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.18105 | − | 12.4379i | −0.250316 | − | 0.433559i | 0.713297 | − | 0.700862i | \(-0.247201\pi\) |
−0.963613 | + | 0.267302i | \(0.913868\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.1891 | + | 38.4326i | 0.771590 | + | 1.33643i | 0.936691 | + | 0.350157i | \(0.113872\pi\) |
−0.165101 | + | 0.986277i | \(0.552795\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.6112 | 1.23683 | 0.618413 | − | 0.785853i | \(-0.287776\pi\) | ||||
0.618413 | + | 0.785853i | \(0.287776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.29563 | − | 2.24410i | 0.0449450 | − | 0.0778470i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.677477 | − | 1.17342i | 0.0234732 | − | 0.0406567i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.6959 | 0.542530 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.1147 | − | 36.5718i | 0.728962 | − | 1.26260i | −0.228361 | − | 0.973577i | \(-0.573337\pi\) |
0.957322 | − | 0.289022i | \(-0.0933301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7263 | − | 22.0426i | 0.438837 | − | 0.760088i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.78192 | 0.0958144 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.4015 | 0.529202 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.72531 | + | 6.45242i | 0.127852 | + | 0.221447i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4856 | + | 19.8937i | 0.393722 | + | 0.681946i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.90917 | − | 17.1632i | 0.339284 | − | 0.587656i | −0.645015 | − | 0.764170i | \(-0.723149\pi\) |
0.984298 | + | 0.176514i | \(0.0564821\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.7082 | − | 44.5279i | 0.878175 | − | 1.52104i | 0.0248328 | − | 0.999692i | \(-0.492095\pi\) |
0.853342 | − | 0.521352i | \(-0.174572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.5243 | + | 18.2286i | 0.359084 | + | 0.621951i | 0.987808 | − | 0.155677i | \(-0.0497559\pi\) |
−0.628724 | + | 0.777628i | \(0.716423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.23353 | − | 7.33268i | −0.144278 | − | 0.249897i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.8358 | 1.32199 | 0.660994 | − | 0.750391i | \(-0.270135\pi\) | ||||
0.660994 | + | 0.750391i | \(0.270135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.73631 | 0.160854 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.73812 | − | 8.20667i | 0.160730 | − | 0.278392i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.3953 | + | 75.1628i | −1.47039 | + | 2.54679i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −16.2937 | −0.551459 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0379 | − | 22.5823i | 0.440259 | − | 0.762551i | −0.557450 | − | 0.830211i | \(-0.688220\pi\) |
0.997708 | + | 0.0676600i | \(0.0215533\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.43080 | + | 7.67437i | −0.149447 | + | 0.258850i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.23096 | 0.277308 | 0.138654 | − | 0.990341i | \(-0.455722\pi\) | ||||
0.138654 | + | 0.990341i | \(0.455722\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.4326 | + | 28.4622i | 0.553003 | + | 0.957828i | 0.998056 | + | 0.0623244i | \(0.0198513\pi\) |
−0.445053 | + | 0.895504i | \(0.646815\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7.11165 | + | 12.3177i | 0.238786 | + | 0.413589i | 0.960366 | − | 0.278741i | \(-0.0899173\pi\) |
−0.721580 | + | 0.692331i | \(0.756584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.934139 | + | 1.61798i | 0.0313300 | + | 0.0542652i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.00154 | + | 13.8591i | −0.268062 | + | 0.464296i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.3942 | − | 2.99605i | −0.682465 | − | 0.100259i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.7656 | − | 22.1107i | −0.426231 | − | 0.738254i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.63262 | + | 9.75598i | 0.187858 | + | 0.325380i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.3199 | −0.876843 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.12763 | + | 3.68516i | 0.0708031 | + | 0.122635i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.4594 | − | 38.9008i | 0.745752 | − | 1.29168i | −0.204090 | − | 0.978952i | \(-0.565424\pi\) |
0.949842 | − | 0.312729i | \(-0.101243\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.1023 | + | 31.3542i | −0.600417 | + | 1.03995i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.3516 | 1.27064 | 0.635322 | − | 0.772247i | \(-0.280867\pi\) | ||||
0.635322 | + | 0.772247i | \(0.280867\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32.8257 | −1.08637 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.23097 | + | 12.5244i | −0.238788 | + | 0.413593i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.3727 | −1.19983 | −0.599913 | − | 0.800065i | \(-0.704798\pi\) | ||||
−0.599913 | + | 0.800065i | \(0.704798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.52081 | + | 11.2944i | 0.214868 | + | 0.372162i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 58.1318 | 1.91343 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.2140 | + | 40.2079i | 0.762449 | + | 1.32060i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.96542 | + | 3.40421i | −0.0644834 | + | 0.111689i | −0.896465 | − | 0.443115i | \(-0.853873\pi\) |
0.831981 | + | 0.554804i | \(0.187207\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43305 | − | 1.81082i | 0.0469663 | − | 0.0593473i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4.39966 | + | 7.62043i | −0.144038 | + | 0.249482i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.0741 | + | 46.8937i | 0.884473 | + | 1.53195i | 0.846317 | + | 0.532680i | \(0.178815\pi\) |
0.0381558 | + | 0.999272i | \(0.487852\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.36445 | −0.142429 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.9969 | + | 25.9755i | 0.488886 | + | 0.846776i | 0.999918 | − | 0.0127858i | \(-0.00406997\pi\) |
−0.511032 | + | 0.859562i | \(0.670737\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −59.0167 | −1.92185 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.7095 | + | 34.1378i | −0.640472 | + | 1.10933i | 0.344856 | + | 0.938656i | \(0.387928\pi\) |
−0.985328 | + | 0.170674i | \(0.945406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 88.7758 | 2.88179 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.104471 | 0.00338772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.663142 | + | 1.14860i | −0.0214813 | + | 0.0372067i | −0.876566 | − | 0.481281i | \(-0.840172\pi\) |
0.855085 | + | 0.518488i | \(0.173505\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.89673 | 0.0613124 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.9103 | − | 41.4138i | −0.772102 | − | 1.33732i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.77372 | 0.153991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.41820 | + | 11.1167i | 0.206824 | + | 0.358229i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.57052 | − | 6.18431i | 0.114820 | − | 0.198874i | −0.802888 | − | 0.596130i | \(-0.796704\pi\) |
0.917708 | + | 0.397256i | \(0.130038\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.99487 | − | 0.733782i | −0.160458 | − | 0.0235725i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.5252 | + | 21.6943i | −0.401953 | + | 0.696202i | −0.993962 | − | 0.109729i | \(-0.965002\pi\) |
0.592009 | + | 0.805931i | \(0.298335\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.22371 | + | 9.04773i | 0.167464 | + | 0.290057i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −0.00409135 | −0.000130894 | −6.54469e−5 | − | 1.00000i | \(-0.500021\pi\) | ||||
−6.54469e−5 | 1.00000i | \(0.500021\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.9979 | + | 27.7091i | 0.511294 | + | 0.885587i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.31720 | 0.233620 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.1988 | + | 38.4495i | −0.708033 | + | 1.22635i | 0.257553 | + | 0.966264i | \(0.417084\pi\) |
−0.965586 | + | 0.260084i | \(0.916250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.44731 | −0.173390 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.6599 | 0.943128 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7636 | − | 41.1598i | 0.754877 | − | 1.30749i | −0.190558 | − | 0.981676i | \(-0.561030\pi\) |
0.945435 | − | 0.325810i | \(-0.105637\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.74282 | + | 4.75071i | −0.0870408 | + | 0.150759i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.8021 | − | 25.6381i | −0.468788 | − | 0.811965i | 0.530575 | − | 0.847638i | \(-0.321976\pi\) |
−0.999364 | + | 0.0356725i | \(0.988643\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.50809 | 0.237545 |
(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 | 1900.2.i.g.201.6 | 20 | ||
5.2 | odd | 4 | 380.2.r.a.49.5 | ✓ | 20 | ||
5.3 | odd | 4 | 380.2.r.a.49.6 | yes | 20 | ||
5.4 | even | 2 | inner | 1900.2.i.g.201.5 | 20 | ||
15.2 | even | 4 | 3420.2.bj.c.1189.3 | 20 | |||
15.8 | even | 4 | 3420.2.bj.c.1189.5 | 20 | |||
19.7 | even | 3 | inner | 1900.2.i.g.501.6 | 20 | ||
95.7 | odd | 12 | 380.2.r.a.349.6 | yes | 20 | ||
95.64 | even | 6 | inner | 1900.2.i.g.501.5 | 20 | ||
95.83 | odd | 12 | 380.2.r.a.349.5 | yes | 20 | ||
285.83 | even | 12 | 3420.2.bj.c.2629.3 | 20 | |||
285.197 | even | 12 | 3420.2.bj.c.2629.5 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.5 | ✓ | 20 | 5.2 | odd | 4 | ||
380.2.r.a.49.6 | yes | 20 | 5.3 | odd | 4 | ||
380.2.r.a.349.5 | yes | 20 | 95.83 | odd | 12 | ||
380.2.r.a.349.6 | yes | 20 | 95.7 | odd | 12 | ||
1900.2.i.g.201.5 | 20 | 5.4 | even | 2 | inner | ||
1900.2.i.g.201.6 | 20 | 1.1 | even | 1 | trivial | ||
1900.2.i.g.501.5 | 20 | 95.64 | even | 6 | inner | ||
1900.2.i.g.501.6 | 20 | 19.7 | even | 3 | inner | ||
3420.2.bj.c.1189.3 | 20 | 15.2 | even | 4 | |||
3420.2.bj.c.1189.5 | 20 | 15.8 | even | 4 | |||
3420.2.bj.c.2629.3 | 20 | 285.83 | even | 12 | |||
3420.2.bj.c.2629.5 | 20 | 285.197 | even | 12 |