Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3420,2,Mod(1189,3420)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3420, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3420.1189");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3420.bj (of order \(6\), 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: | \(27.3088374913\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
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: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2629.3 | ||
Root | \(-0.392182 + 0.226426i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3420.2629 |
Dual form | 3420.2.bj.c.1189.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times\).
\(n\) | \(1711\) | \(1901\) | \(2737\) | \(3061\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.82467 | − | 1.29251i | −0.816018 | − | 0.578027i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.54366i | 0.961414i | 0.876881 | + | 0.480707i | \(0.159620\pi\) | ||||
−0.876881 | + | 0.480707i | \(0.840380\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.22377 | −0.670491 | −0.335246 | − | 0.942131i | \(-0.608819\pi\) | ||||
−0.335246 | + | 0.942131i | \(0.608819\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.08116 | − | 3.51096i | −1.68661 | − | 0.973765i | −0.957084 | − | 0.289812i | \(-0.906407\pi\) |
−0.729526 | − | 0.683953i | \(-0.760259\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.21492 | − | 1.27878i | 0.537197 | − | 0.310151i | −0.206745 | − | 0.978395i | \(-0.566287\pi\) |
0.743942 | + | 0.668244i | \(0.232954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.70498 | + | 3.41805i | 0.620565 | + | 0.784155i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.95328 | − | 4.01448i | −1.44986 | − | 0.837076i | −0.451387 | − | 0.892329i | \(-0.649070\pi\) |
−0.998472 | + | 0.0552521i | \(0.982404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.65885 | + | 4.71680i | 0.331769 | + | 0.943361i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.941734 | − | 1.63113i | 0.174876 | − | 0.302893i | −0.765243 | − | 0.643742i | \(-0.777381\pi\) |
0.940118 | + | 0.340849i | \(0.110714\pi\) | |||||||
\(30\) | 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 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.28770 | − | 4.64135i | 0.555723 | − | 0.784531i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.86105i | − | 0.470353i | −0.971953 | − | 0.235177i | \(-0.924433\pi\) | ||
0.971953 | − | 0.235177i | \(-0.0755669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.67524 | + | 6.36571i | 0.573977 | + | 0.994157i | 0.996152 | + | 0.0876426i | \(0.0279333\pi\) |
−0.422175 | + | 0.906514i | \(0.638733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.19919 | + | 1.84706i | −0.487873 | + | 0.281673i | −0.723691 | − | 0.690124i | \(-0.757556\pi\) |
0.235819 | + | 0.971797i | \(0.424223\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.09540 | + | 2.36448i | 0.597376 | + | 0.344895i | 0.768008 | − | 0.640440i | \(-0.221248\pi\) |
−0.170633 | + | 0.985335i | \(0.554581\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.529782 | 0.0756832 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.91226 | − | 5.14549i | −1.22419 | − | 0.706788i | −0.258383 | − | 0.966042i | \(-0.583190\pi\) |
−0.965809 | + | 0.259255i | \(0.916523\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.05764 | + | 2.87424i | 0.547133 | + | 0.387562i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.73666 | + | 6.47208i | 0.486472 | + | 0.842593i | 0.999879 | − | 0.0155515i | \(-0.00495040\pi\) |
−0.513408 | + | 0.858145i | \(0.671617\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.17839 | − | 7.23719i | 0.534988 | − | 0.926627i | −0.464176 | − | 0.885743i | \(-0.653649\pi\) |
0.999164 | − | 0.0408838i | \(-0.0130174\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.55817 | + | 14.2663i | 0.813441 | + | 1.76952i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.7040 | + | 6.17997i | 1.30771 | + | 0.755004i | 0.981713 | − | 0.190368i | \(-0.0609682\pi\) |
0.325993 | + | 0.945372i | \(0.394302\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.13931 | + | 7.16950i | 0.491246 | + | 0.850863i | 0.999949 | − | 0.0100790i | \(-0.00320829\pi\) |
−0.508703 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9489 | − | 6.32134i | 1.28147 | − | 0.739857i | 0.304352 | − | 0.952559i | \(-0.401560\pi\) |
0.977117 | + | 0.212703i | \(0.0682266\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.65651i | − | 0.644620i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.13067 | − | 3.69043i | −0.239719 | − | 0.415206i | 0.720914 | − | 0.693024i | \(-0.243722\pi\) |
−0.960634 | + | 0.277818i | \(0.910389\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.7613i | 1.62026i | 0.586248 | + | 0.810132i | \(0.300604\pi\) | ||||
−0.586248 | + | 0.810132i | \(0.699396\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.69434 | − | 0.529441i | −0.617638 | − | 0.0574259i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.19403 | − | 12.4604i | 0.762566 | − | 1.32080i | −0.178958 | − | 0.983857i | \(-0.557273\pi\) |
0.941524 | − | 0.336946i | \(-0.109394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.93069 | − | 15.4684i | 0.936191 | − | 1.62153i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.517834 | − | 9.73303i | −0.0531286 | − | 0.998588i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.04871 | + | 2.91488i | −0.512619 | + | 0.295961i | −0.733910 | − | 0.679247i | \(-0.762306\pi\) |
0.221291 | + | 0.975208i | \(0.428973\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.47686 | + | 11.2183i | −0.644472 | + | 1.11626i | 0.339951 | + | 0.940443i | \(0.389589\pi\) |
−0.984423 | + | 0.175815i | \(0.943744\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.6116i | 1.63679i | 0.574658 | + | 0.818394i | \(0.305135\pi\) | ||||
−0.574658 | + | 0.818394i | \(0.694865\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.59275i | 0.443998i | 0.975047 | + | 0.221999i | \(0.0712582\pi\) | ||||
−0.975047 | + | 0.221999i | \(0.928742\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.30902 | − | 2.26728i | −0.125381 | − | 0.217166i | 0.796501 | − | 0.604637i | \(-0.206682\pi\) |
−0.921882 | + | 0.387471i | \(0.873349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 0.509357i | − | 0.0479163i | −0.999713 | − | 0.0239581i | \(-0.992373\pi\) | ||
0.999713 | − | 0.0239581i | \(-0.00762684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.49870 | + | 16.3123i | 0.699257 | + | 1.52113i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.25279 | + | 5.63401i | 0.298183 | + | 0.516468i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.05486 | −0.550441 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.06966 | − | 10.7507i | 0.274559 | − | 0.961570i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.636081 | + | 0.367242i | 0.0564431 | + | 0.0325874i | 0.527956 | − | 0.849272i | \(-0.322959\pi\) |
−0.471513 | + | 0.881859i | \(0.656292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.84274 | − | 4.92377i | −0.248371 | − | 0.430192i | 0.714703 | − | 0.699428i | \(-0.246562\pi\) |
−0.963074 | + | 0.269236i | \(0.913229\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.69437 | + | 6.88055i | −0.753898 | + | 0.596620i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.2812 | + | 9.39993i | 1.39099 | + | 0.803091i | 0.993425 | − | 0.114482i | \(-0.0365209\pi\) |
0.397568 | + | 0.917573i | \(0.369854\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.05362 | − | 3.55697i | 0.174186 | − | 0.301698i | −0.765694 | − | 0.643206i | \(-0.777604\pi\) |
0.939879 | + | 0.341507i | \(0.110937\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.5231 | + | 7.80756i | 1.13086 | + | 0.652901i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.82660 | + | 1.75908i | −0.317782 | + | 0.146084i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.08175 | + | 3.60570i | 0.170544 | + | 0.295391i | 0.938610 | − | 0.344980i | \(-0.112114\pi\) |
−0.768066 | + | 0.640370i | \(0.778781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.7955 | 1.44818 | 0.724090 | − | 0.689706i | \(-0.242260\pi\) | ||||
0.724090 | + | 0.689706i | \(0.242260\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.9136 | − | 7.73064i | −0.876599 | − | 0.620940i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.09693 | − | 4.67476i | 0.646205 | − | 0.373087i | −0.140796 | − | 0.990039i | \(-0.544966\pi\) |
0.787001 | + | 0.616952i | \(0.211633\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.2115 | − | 17.6868i | 0.804777 | − | 1.39391i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.55215i | − | 0.121574i | −0.998151 | − | 0.0607869i | \(-0.980639\pi\) | ||
0.998151 | − | 0.0607869i | \(-0.0193610\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.03177 | − | 4.05980i | −0.544135 | − | 0.314157i | 0.202618 | − | 0.979258i | \(-0.435055\pi\) |
−0.746753 | + | 0.665101i | \(0.768388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.1537 | + | 31.4431i | 1.39644 | + | 2.41870i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.633386 | + | 0.365686i | −0.0481555 | + | 0.0278026i | −0.523884 | − | 0.851789i | \(-0.675518\pi\) |
0.475729 | + | 0.879592i | \(0.342184\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.9980 | + | 4.21954i | −0.906960 | + | 0.318968i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 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 | −0.745492 | − | 0.666515i | \(-0.767785\pi\) |
0.949965 | + | 0.312358i | \(0.101119\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.69793 | + | 5.22047i | −0.271877 | + | 0.383817i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.92547 | + | 2.84372i | −0.360186 | + | 0.207953i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.39845 | −0.680048 | −0.340024 | − | 0.940417i | \(-0.610435\pi\) | ||||
−0.340024 | + | 0.940417i | \(0.610435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0089 | + | 5.77864i | −0.720457 | + | 0.415956i | −0.814921 | − | 0.579572i | \(-0.803220\pi\) |
0.0944641 | + | 0.995528i | \(0.469886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.11825i | − | 0.364660i | −0.983237 | − | 0.182330i | \(-0.941636\pi\) | ||
0.983237 | − | 0.182330i | \(-0.0583639\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.71897 | − | 11.6376i | 0.476295 | − | 0.824968i | −0.523336 | − | 0.852127i | \(-0.675313\pi\) |
0.999631 | + | 0.0271588i | \(0.00864598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.14905 | + | 2.39545i | 0.291206 | + | 0.168128i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52162 | − | 16.3656i | 0.106275 | − | 1.14302i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.01524 | − | 7.60096i | −0.416083 | − | 0.525769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.54063 | + | 4.40050i | 0.174904 | + | 0.302943i | 0.940128 | − | 0.340821i | \(-0.110705\pi\) |
−0.765224 | + | 0.643764i | \(0.777372\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.22481 | + | 0.764716i | 0.560927 | + | 0.0521532i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.2139i | 1.03279i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.9590 | −1.20806 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.5186 | − | 11.8464i | 1.37403 | − | 0.793295i | 0.382595 | − | 0.923916i | \(-0.375030\pi\) |
0.991432 | + | 0.130621i | \(0.0416971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 19.0306i | − | 1.26310i | −0.775334 | − | 0.631551i | \(-0.782418\pi\) | ||
0.775334 | − | 0.631551i | \(-0.217582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.9233 | 1.84523 | 0.922613 | − | 0.385727i | \(-0.126049\pi\) | ||||
0.922613 | + | 0.385727i | \(0.126049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.2680 | − | 7.08296i | 0.803706 | − | 0.464020i | −0.0410592 | − | 0.999157i | \(-0.513073\pi\) |
0.844765 | + | 0.535137i | \(0.179740\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.41665 | − | 9.60774i | −0.288110 | − | 0.626740i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 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 | 0.444321 | + | 0.895868i | \(0.353445\pi\) |
−0.998005 | + | 0.0631409i | \(0.979888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.966678 | − | 0.684748i | −0.0617588 | − | 0.0437469i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.44876 | − | 30.2828i | −0.283068 | − | 1.92685i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.8853 | − | 20.5860i | 0.750195 | − | 1.29938i | −0.197534 | − | 0.980296i | \(-0.563293\pi\) |
0.947728 | − | 0.319079i | \(-0.103374\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4625 | + | 8.92727i | 0.972118 | + | 0.561252i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.24086 | + | 0.716409i | 0.0774026 | + | 0.0446884i | 0.538202 | − | 0.842816i | \(-0.319104\pi\) |
−0.460799 | + | 0.887504i | \(0.652437\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.27754 | 0.452204 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.17484 | − | 3.56505i | 0.380757 | − | 0.219830i | −0.297390 | − | 0.954756i | \(-0.596116\pi\) |
0.678148 | + | 0.734926i | \(0.262783\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.61134 | + | 20.9080i | 0.590420 | + | 1.28437i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 9.13452 | + | 15.8214i | 0.556941 | + | 0.964651i | 0.997750 | + | 0.0670494i | \(0.0213585\pi\) |
−0.440808 | + | 0.897601i | \(0.645308\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.90265 | + | 5.02754i | 0.176324 | + | 0.305401i | 0.940619 | − | 0.339465i | \(-0.110246\pi\) |
−0.764295 | + | 0.644867i | \(0.776913\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.68889 | − | 10.4891i | −0.222448 | − | 0.632515i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.72209i | − | 0.343807i | −0.985114 | − | 0.171904i | \(-0.945008\pi\) | ||
0.985114 | − | 0.171904i | \(-0.0549918\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.07155 | + | 5.32009i | −0.183233 | + | 0.317370i | −0.942980 | − | 0.332850i | \(-0.891990\pi\) |
0.759746 | + | 0.650220i | \(0.225323\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.2484 | − | 8.22632i | 0.846980 | − | 0.489004i | −0.0126510 | − | 0.999920i | \(-0.504027\pi\) |
0.859631 | + | 0.510916i | \(0.170694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.1922 | + | 9.34858i | −0.955796 | + | 0.551829i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.22942 | + | 9.05763i | −0.307613 | + | 0.532801i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.5684i | 1.14320i | 0.820533 | + | 0.571599i | \(0.193677\pi\) | ||||
−0.820533 | + | 0.571599i | \(0.806323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.54705 | − | 16.6391i | 0.0900726 | − | 0.968765i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −16.9783 | + | 7.80488i | −0.972175 | + | 0.446906i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.9405 | + | 14.3994i | −1.42343 | + | 0.821817i | −0.996590 | − | 0.0825100i | \(-0.973706\pi\) |
−0.426839 | + | 0.904327i | \(0.640373\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.4309 | 1.10182 | 0.550911 | − | 0.834564i | \(-0.314280\pi\) | ||||
0.550911 | + | 0.834564i | \(0.314280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.34649 | − | 4.81885i | −0.471772 | − | 0.272377i | 0.245209 | − | 0.969470i | \(-0.421143\pi\) |
−0.716981 | + | 0.697093i | \(0.754477\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.199789 | + | 0.115348i | 0.0112213 | + | 0.00647860i | 0.505600 | − | 0.862768i | \(-0.331271\pi\) |
−0.494379 | + | 0.869247i | \(0.664604\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.09420 | + | 3.62726i | −0.117253 | + | 0.203087i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.3623 | + | 4.11163i | 0.576572 | + | 0.228777i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.47279 | − | 34.5078i | 0.359046 | − | 1.91415i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.5437 | − | 25.1115i | −0.630698 | − | 1.37199i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.64909 | − | 5.57090i | 0.525619 | − | 0.303466i | −0.213611 | − | 0.976919i | \(-0.568523\pi\) |
0.739231 | + | 0.673452i | \(0.235189\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.3006 | −0.720268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.1532i | 1.03418i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.92730 | + | 2.84478i | −0.264511 | + | 0.152716i | −0.626391 | − | 0.779509i | \(-0.715468\pi\) |
0.361880 | + | 0.932225i | \(0.382135\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.369374 | −0.0197722 | −0.00988608 | − | 0.999951i | \(-0.503147\pi\) | ||||
−0.00988608 | + | 0.999951i | \(0.503147\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.87124i | − | 0.0995962i | −0.998759 | − | 0.0497981i | \(-0.984142\pi\) | ||
0.998759 | − | 0.0497981i | \(-0.0158578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.71375 | − | 18.4321i | 0.0909566 | − | 0.978273i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.47802 | + | 14.6844i | 0.447453 | + | 0.775011i | 0.998219 | − | 0.0596485i | \(-0.0189980\pi\) |
−0.550767 | + | 0.834659i | \(0.685665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.36618 | + | 18.4915i | −0.229799 | + | 0.973238i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −28.1485 | − | 2.61715i | −1.47336 | − | 0.136988i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.27769 | + | 1.89237i | 0.171094 | + | 0.0987812i | 0.583102 | − | 0.812399i | \(-0.301839\pi\) |
−0.412008 | + | 0.911180i | \(0.635172\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0884 | − | 22.6698i | 0.679516 | − | 1.17696i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.51203i | − | 0.233624i | −0.993154 | − | 0.116812i | \(-0.962732\pi\) | ||
0.993154 | − | 0.116812i | \(-0.0372675\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −11.4537 | + | 6.61278i | −0.589894 | + | 0.340575i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.64242 | −0.238465 | −0.119233 | − | 0.992866i | \(-0.538043\pi\) | ||||
−0.119233 | + | 0.992866i | \(0.538043\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.1086 | + | 6.99088i | −0.618719 | + | 0.357218i | −0.776370 | − | 0.630277i | \(-0.782941\pi\) |
0.157651 | + | 0.987495i | \(0.449608\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.31109 | + | 10.3213i | −0.372608 | + | 0.526021i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.93460 | + | 6.81492i | −0.199492 | + | 0.345530i | −0.948364 | − | 0.317185i | \(-0.897263\pi\) |
0.748872 | + | 0.662715i | \(0.230596\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.5346 | −1.03848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.882139 | + | 9.48774i | −0.0443852 | + | 0.477380i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.6969 | + | 8.48528i | −0.737618 | + | 0.425864i | −0.821203 | − | 0.570637i | \(-0.806696\pi\) |
0.0835846 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.16651 | + | 12.4128i | 0.357878 | + | 0.619864i | 0.987606 | − | 0.156952i | \(-0.0501669\pi\) |
−0.629728 | + | 0.776816i | \(0.716834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.3721 | − | 20.9994i | −1.81182 | − | 1.04606i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.36231i | 0.315368i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.122530 | + | 0.212228i | −0.00605872 | + | 0.0104940i | −0.869039 | − | 0.494744i | \(-0.835262\pi\) |
0.862980 | + | 0.505238i | \(0.168595\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.4628 | + | 9.50480i | −0.810081 | + | 0.467701i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.0791 | − | 26.9345i | 0.936556 | − | 1.32216i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 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 | 0.782785 | − | 0.622292i | \(-0.213798\pi\) |
−0.930313 | + | 0.366765i | \(0.880465\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.70598 | + | 8.32603i | 0.470809 | + | 0.403872i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.4090 | + | 10.6284i | 0.890872 | + | 0.514345i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.1005 | − | 19.2267i | 0.534694 | − | 0.926117i | −0.464484 | − | 0.885581i | \(-0.653760\pi\) |
0.999178 | − | 0.0405356i | \(-0.0129064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0094 | − | 12.1298i | −1.00965 | − | 0.582920i | −0.0985593 | − | 0.995131i | \(-0.531423\pi\) |
−0.911089 | + | 0.412211i | \(0.864757\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.08677 | − | 34.6258i | −0.243333 | − | 1.65637i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.9487 | − | 20.6957i | −0.570279 | − | 0.987753i | −0.996537 | − | 0.0831509i | \(-0.973502\pi\) |
0.426258 | − | 0.904602i | \(-0.359832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.9017 | − | 10.3356i | −0.850536 | − | 0.491057i | 0.0102958 | − | 0.999947i | \(-0.496723\pi\) |
−0.860832 | + | 0.508890i | \(0.830056\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.2319 | + | 13.4378i | −1.38573 | + | 0.637015i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −36.2886 | + | 16.6818i | −1.70124 | + | 0.782053i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.3433i | 0.670952i | 0.942049 | + | 0.335476i | \(0.108897\pi\) | ||||
−0.942049 | + | 0.335476i | \(0.891103\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.3682 | − | 23.1544i | −0.622618 | − | 1.07841i | −0.988996 | − | 0.147940i | \(-0.952736\pi\) |
0.366378 | − | 0.930466i | \(-0.380598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0950i | 0.562101i | 0.959693 | + | 0.281051i | \(0.0906829\pi\) | ||||
−0.959693 | + | 0.281051i | \(0.909317\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 27.3169i | 1.26408i | 0.774938 | + | 0.632038i | \(0.217781\pi\) | ||||
−0.774938 | + | 0.632038i | \(0.782219\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.7198 | + | 27.2274i | −0.725871 | + | 1.25725i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.11427 | − | 4.10742i | 0.327114 | − | 0.188860i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.6351 | + | 18.4289i | −0.533857 | + | 0.845575i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.69624 | + | 6.40208i | −0.168886 | + | 0.292519i | −0.938028 | − | 0.346559i | \(-0.887350\pi\) |
0.769143 | + | 0.639077i | \(0.220684\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0450 | + | 17.3985i | −0.458013 | + | 0.793302i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.9797 | + | 1.20681i | 0.589379 | + | 0.0547986i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.9424i | 0.586477i | 0.956039 | + | 0.293239i | \(0.0947330\pi\) | ||||
−0.956039 | + | 0.293239i | \(0.905267\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.59974 | − | 9.69903i | −0.252713 | − | 0.437711i | 0.711559 | − | 0.702626i | \(-0.247989\pi\) |
−0.964272 | + | 0.264915i | \(0.914656\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 4.81710i | − | 0.216951i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.2368 | + | 10.5290i | −0.818032 | + | 0.472291i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.9699 | − | 22.4645i | −0.580611 | − | 1.00565i | −0.995407 | − | 0.0957335i | \(-0.969480\pi\) |
0.414796 | − | 0.909914i | \(-0.363853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.6079 | + | 13.6300i | 1.05262 | + | 0.607733i | 0.923383 | − | 0.383881i | \(-0.125413\pi\) |
0.129241 | + | 0.991613i | \(0.458746\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.3178 | − | 12.0982i | 1.17113 | − | 0.538364i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.6203 | + | 21.8591i | −0.559386 | + | 0.968885i | 0.438161 | + | 0.898896i | \(0.355630\pi\) |
−0.997548 | + | 0.0699892i | \(0.977704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0794 | + | 27.8503i | 0.711309 | + | 1.23202i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.4706 | − | 30.3107i | 0.946107 | − | 1.33565i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.10722 | − | 5.25806i | −0.400535 | − | 0.231249i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.8142 | 1.08713 | 0.543565 | − | 0.839367i | \(-0.317074\pi\) | ||||
0.543565 | + | 0.839367i | \(0.317074\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.33581 | + | 3.08063i | 0.233318 | + | 0.134706i | 0.612102 | − | 0.790779i | \(-0.290324\pi\) |
−0.378784 | + | 0.925485i | \(0.623658\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.2477 | − | 7.64855i | 0.577078 | − | 0.333176i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.7321 | + | 35.9090i | 0.901394 | + | 1.56126i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 51.6145i | − | 2.23567i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.93617 | − | 8.38026i | 0.256643 | − | 0.362310i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.17811 | −0.0507449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.27394 | + | 5.67063i | −0.140758 | + | 0.243799i | −0.927782 | − | 0.373122i | \(-0.878287\pi\) |
0.787025 | + | 0.616922i | \(0.211620\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.541957 | + | 5.82895i | −0.0232149 | + | 0.249685i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.5323 | + | 11.2770i | 0.835141 | + | 0.482169i | 0.855610 | − | 0.517621i | \(-0.173182\pi\) |
−0.0204683 | + | 0.999791i | \(0.506516\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.12266 | − | 1.19328i | 0.346037 | − | 0.0508353i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.38722 | − | 5.41971i | 0.399185 | − | 0.230470i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.0691 | + | 8.12281i | 0.596128 | + | 0.344175i | 0.767517 | − | 0.641029i | \(-0.221492\pi\) |
−0.171389 | + | 0.985203i | \(0.554825\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.9397 | 1.09713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 32.4581i | − | 1.36795i | −0.729506 | − | 0.683974i | \(-0.760250\pi\) | ||
0.729506 | − | 0.683974i | \(-0.239750\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.658348 | + | 0.929409i | −0.0276969 | + | 0.0391005i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.40108 | − | 39.4566i | 0.308646 | − | 1.64546i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 44.5844i | − | 1.85607i | −0.372489 | − | 0.928037i | \(-0.621496\pi\) | ||
0.372489 | − | 0.928037i | \(-0.378504\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.5478 | −1.55774 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.8188 | + | 11.4424i | 0.820810 | + | 0.473895i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.6246 | + | 7.28884i | −0.521074 | + | 0.300842i | −0.737374 | − | 0.675485i | \(-0.763935\pi\) |
0.216300 | + | 0.976327i | \(0.430601\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.1788 | + | 20.4438i | 0.666635 | + | 0.842371i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20.5520 | − | 11.8657i | −0.843968 | − | 0.487265i | 0.0146433 | − | 0.999893i | \(-0.495339\pi\) |
−0.858611 | + | 0.512628i | \(0.828672\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.34672 | − | 14.4845i | 0.0552101 | − | 0.593805i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.86173 | − | 17.0810i | 0.402939 | − | 0.697911i | −0.591140 | − | 0.806569i | \(-0.701322\pi\) |
0.994079 | + | 0.108658i | \(0.0346552\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.0351 | −1.83702 | −0.918509 | − | 0.395400i | \(-0.870606\pi\) | ||||
−0.918509 | + | 0.395400i | \(0.870606\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.0481 | + | 7.82595i | 0.449170 | + | 0.318170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.24160i | − | 0.293928i | −0.989142 | − | 0.146964i | \(-0.953050\pi\) | ||
0.989142 | − | 0.146964i | \(-0.0469501\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.6032 | − | 28.7576i | −0.671693 | − | 1.16341i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.8788 | − | 18.4052i | 1.28757 | − | 0.743381i | 0.309352 | − | 0.950947i | \(-0.399888\pi\) |
0.978221 | + | 0.207567i | \(0.0665544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.7741 | + | 18.3448i | 1.27918 | + | 0.738533i | 0.976697 | − | 0.214623i | \(-0.0688524\pi\) |
0.302479 | + | 0.953156i | \(0.402186\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.1569 | −0.970948 | −0.485474 | − | 0.874251i | \(-0.661353\pi\) | ||||
−0.485474 | + | 0.874251i | \(0.661353\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.6951 | + | 18.2992i | 1.26984 | + | 0.733142i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.4965 | + | 15.6489i | −0.779858 | + | 0.625956i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.65866 | − | 6.33699i | −0.145880 | − | 0.252672i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.11258 | + | 12.3193i | −0.283147 | + | 0.490426i | −0.972158 | − | 0.234325i | \(-0.924712\pi\) |
0.689011 | + | 0.724751i | \(0.258045\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.685976 | − | 1.49223i | −0.0272221 | − | 0.0592175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.22169 | − | 1.86004i | −0.127648 | − | 0.0736976i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.1834 | − | 17.6382i | −0.402222 | − | 0.696668i | 0.591772 | − | 0.806105i | \(-0.298429\pi\) |
−0.993994 | + | 0.109437i | \(0.965095\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0041 | + | 5.77586i | −0.394523 | + | 0.227778i | −0.684118 | − | 0.729371i | \(-0.739813\pi\) |
0.289595 | + | 0.957149i | \(0.406479\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.1233i | 0.515932i | 0.966154 | + | 0.257966i | \(0.0830522\pi\) | ||||
−0.966154 | + | 0.257966i | \(0.916948\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.30946 | − | 14.3924i | −0.326175 | − | 0.564952i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4406i | 0.760769i | 0.924828 | + | 0.380385i | \(0.124208\pi\) | ||||
−0.924828 | + | 0.380385i | \(0.875792\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.17695 | + | 12.6585i | −0.0459872 | + | 0.494610i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7848 | − | 23.8759i | 0.536979 | − | 0.930074i | −0.462086 | − | 0.886835i | \(-0.652899\pi\) |
0.999065 | − | 0.0432391i | \(-0.0137677\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88006 | − | 6.72046i | 0.150917 | − | 0.261396i | −0.780648 | − | 0.624971i | \(-0.785111\pi\) |
0.931565 | + | 0.363575i | \(0.118444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 24.7575 | − | 1.31719i | 0.960056 | − | 0.0510786i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.0963 | + | 7.56114i | −0.507090 | + | 0.292769i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.29178 | + | 16.0938i | −0.358705 | + | 0.621295i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 24.2617i | − | 0.935220i | −0.883935 | − | 0.467610i | \(-0.845115\pi\) | ||
0.883935 | − | 0.467610i | \(-0.154885\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.88851i | 0.187881i | 0.995578 | + | 0.0939403i | \(0.0299463\pi\) | ||||
−0.995578 | + | 0.0939403i | \(0.970054\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.41446 | − | 12.8422i | −0.284541 | − | 0.492839i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 0.560031i | − | 0.0214290i | −0.999943 | − | 0.0107145i | \(-0.996589\pi\) | ||
0.999943 | − | 0.0107145i | \(-0.00341060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.5583 | − | 38.1953i | −0.670867 | − | 1.45937i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.34459 | + | 3.83598i | −0.316528 | + | 0.145507i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.2807 | + | 9.39969i | 0.616677 | + | 0.356039i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.23926 | − | 2.14647i | −0.0468064 | − | 0.0810710i | 0.841673 | − | 0.539987i | \(-0.181571\pi\) |
−0.888479 | + | 0.458916i | \(0.848238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.77921 | − | 7.73907i | 0.368830 | − | 0.291885i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28.5354 | − | 16.4749i | −1.07319 | − | 0.619604i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.1966 | + | 28.0533i | −0.608276 | + | 1.05356i | 0.383249 | + | 0.923645i | \(0.374805\pi\) |
−0.991525 | + | 0.129919i | \(0.958528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.5884 | − | 24.0110i | −1.55750 | − | 0.899221i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.5838 | − | 31.7249i | −0.545405 | − | 1.18644i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.64373 | − | 14.9714i | −0.322357 | − | 0.558338i | 0.658617 | − | 0.752478i | \(-0.271142\pi\) |
−0.980974 | + | 0.194140i | \(0.937808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.2542 | −1.57363 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.25592 | + | 1.73618i | 0.343756 | + | 0.0644800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4031 | + | 9.47034i | −0.608358 | + | 0.351236i | −0.772323 | − | 0.635231i | \(-0.780905\pi\) |
0.163965 | + | 0.986466i | \(0.447572\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.72397 | + | 8.18216i | −0.174722 | + | 0.302628i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.542118i | 0.0200236i | 0.999950 | + | 0.0100118i | \(0.00318690\pi\) | ||||
−0.999950 | + | 0.0100118i | \(0.996813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.8033 | − | 13.7428i | −0.876805 | − | 0.506224i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.87033 | − | 4.97156i | −0.105587 | − | 0.182882i | 0.808391 | − | 0.588646i | \(-0.200339\pi\) |
−0.913978 | + | 0.405764i | \(0.867005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.9290 | + | 11.5060i | −0.731125 | + | 0.422115i | −0.818834 | − | 0.574031i | \(-0.805379\pi\) |
0.0877087 | + | 0.996146i | \(0.472046\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.861885 | − | 9.26990i | 0.0315770 | − | 0.339623i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.6824 | −0.426866 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.9704 | − | 44.9821i | 0.947674 | − | 1.64142i | 0.197368 | − | 0.980330i | \(-0.436761\pi\) |
0.750306 | − | 0.661090i | \(-0.229906\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.4710 | − | 23.0009i | −1.18174 | − | 0.837087i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0229 | + | 6.36406i | −0.400633 | + | 0.231306i | −0.686757 | − | 0.726887i | \(-0.740966\pi\) |
0.286124 | + | 0.958193i | \(0.407633\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6089 | 0.384573 | 0.192287 | − | 0.981339i | \(-0.438410\pi\) | ||||
0.192287 | + | 0.981339i | \(0.438410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.76720 | − | 3.32969i | 0.208787 | − | 0.120543i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 52.4770i | − | 1.89484i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8089 | − | 18.7215i | 0.389777 | − | 0.675114i | −0.602642 | − | 0.798012i | \(-0.705885\pi\) |
0.992419 | + | 0.122898i | \(0.0392187\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.5227 | + | 21.6637i | 1.34960 | + | 0.779190i | 0.988192 | − | 0.153220i | \(-0.0489642\pi\) |
0.361404 | + | 0.932409i | \(0.382298\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.92175 | + | 28.2117i | 0.356400 | + | 1.01340i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.8164 | − | 1.93544i | −0.742969 | − | 0.0690788i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.0046i | − | 1.03390i | −0.856015 | − | 0.516950i | \(-0.827067\pi\) | ||
0.856015 | − | 0.516950i | \(-0.172933\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.29563 | 0.0460674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −50.8189 | + | 29.3403i | −1.80463 | + | 1.04191i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 14.2045i | 0.503150i | 0.967838 | + | 0.251575i | \(0.0809485\pi\) | ||||
−0.967838 | + | 0.251575i | \(0.919051\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0946 | 0.427878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.3478 | + | 14.0572i | −0.859214 | + | 0.496067i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −41.4929 | + | 19.0742i | −1.46243 | + | 0.672276i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | −0.239300 | − | 0.970946i | \(-0.576918\pi\) |
0.960513 | − | 0.278233i | \(-0.0897489\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00617 | + | 2.83216i | −0.0702729 | + | 0.0992063i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.9671 | − | 5.93877i | −0.523632 | − | 0.207771i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.5219 | + | 37.2771i | −0.751120 | + | 1.30098i | 0.196160 | + | 0.980572i | \(0.437153\pi\) |
−0.947280 | + | 0.320407i | \(0.896180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4379 | − | 7.18105i | −0.433559 | − | 0.250316i | 0.267302 | − | 0.963613i | \(-0.413868\pi\) |
−0.700862 | + | 0.713297i | \(0.747201\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.4326 | + | 22.1891i | 1.33643 | + | 0.771590i | 0.986277 | − | 0.165101i | \(-0.0527951\pi\) |
0.350157 | + | 0.936691i | \(0.386128\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −35.6112 | −1.23683 | −0.618413 | − | 0.785853i | \(-0.712224\pi\) | ||||
−0.618413 | + | 0.785853i | \(0.712224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.17342 | − | 0.677477i | 0.0406567 | − | 0.0234732i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.58335 | + | 16.4964i | 0.262433 | + | 0.570882i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 21.1147 | + | 36.5718i | 0.728962 | + | 1.26260i | 0.957322 | + | 0.289022i | \(0.0933301\pi\) |
−0.228361 | + | 0.973577i | \(0.573337\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7263 | + | 22.0426i | 0.438837 | + | 0.760088i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.51596 | − | 80.8370i | 0.258557 | − | 2.78088i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 15.4015i | − | 0.529202i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4856 | + | 19.8937i | −0.393722 | + | 0.681946i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1632 | + | 9.90917i | −0.587656 | + | 0.339284i | −0.764170 | − | 0.645015i | \(-0.776851\pi\) |
0.176514 | + | 0.984298i | \(0.443518\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.5279 | + | 25.7082i | −1.52104 | + | 0.878175i | −0.521352 | + | 0.853342i | \(0.674572\pi\) |
−0.999692 | + | 0.0248328i | \(0.992095\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.5243 | + | 18.2286i | −0.359084 | + | 0.621951i | −0.987808 | − | 0.155677i | \(-0.950244\pi\) |
0.628724 | + | 0.777628i | \(0.283577\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 38.8358i | − | 1.32199i | −0.750391 | − | 0.660994i | \(-0.770135\pi\) | ||
0.750391 | − | 0.660994i | \(-0.229865\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.62837 | + | 0.151401i | 0.0553663 | + | 0.00514778i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.3461 | + | 7.80817i | 0.924467 | + | 0.263964i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.5823 | − | 13.0379i | 0.762551 | − | 0.440259i | −0.0676600 | − | 0.997708i | \(-0.521553\pi\) |
0.830211 | + | 0.557450i | \(0.188220\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.23096 | −0.277308 | −0.138654 | − | 0.990341i | \(-0.544278\pi\) | ||||
−0.138654 | + | 0.990341i | \(0.544278\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.4622 | + | 16.4326i | 0.957828 | + | 0.553003i | 0.895504 | − | 0.445053i | \(-0.146815\pi\) |
0.0623244 | + | 0.998056i | \(0.480149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.3177 | + | 7.11165i | 0.413589 | + | 0.238786i | 0.692331 | − | 0.721580i | \(-0.256584\pi\) |
−0.278741 | + | 0.960366i | \(0.589917\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.934139 | + | 1.61798i | −0.0313300 | + | 0.0542652i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.99605 | + | 20.3942i | 0.100259 | + | 0.682465i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.90578 | − | 3.47501i | −0.163982 | − | 0.116157i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.63262 | − | 9.75598i | 0.187858 | − | 0.325380i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.3199 | −0.876843 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.1779 | + | 5.13844i | −0.371565 | + | 0.170808i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9008 | − | 22.4594i | 1.29168 | − | 0.745752i | 0.312729 | − | 0.949842i | \(-0.398757\pi\) |
0.978952 | + | 0.204090i | \(0.0654236\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.3516 | −1.27064 | −0.635322 | − | 0.772247i | \(-0.719133\pi\) | ||||
−0.635322 | + | 0.772247i | \(0.719133\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 32.8257i | − | 1.08637i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.5244 | − | 7.23097i | 0.413593 | − | 0.238788i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3727 | 1.19983 | 0.599913 | − | 0.800065i | \(-0.295202\pi\) | ||||
0.599913 | + | 0.800065i | \(0.295202\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 58.1318i | − | 1.91343i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.4950 | − | 4.74604i | 0.443713 | − | 0.156049i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.96542 | − | 3.40421i | −0.0644834 | − | 0.111689i | 0.831981 | − | 0.554804i | \(-0.187207\pi\) |
−0.896465 | + | 0.443115i | \(0.853873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.43305 | + | 1.81082i | 0.0469663 | + | 0.0593473i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.6629 | + | 1.17735i | 0.414121 | + | 0.0385036i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −46.8937 | − | 27.0741i | −1.53195 | − | 0.884473i | −0.999272 | − | 0.0381558i | \(-0.987852\pi\) |
−0.532680 | − | 0.846317i | \(-0.678815\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.9969 | + | 25.9755i | −0.488886 | + | 0.846776i | −0.999918 | − | 0.0127858i | \(-0.995930\pi\) |
0.511032 | + | 0.859562i | \(0.329263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 59.0167i | − | 1.92185i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.1378 | − | 19.7095i | 1.10933 | − | 0.640472i | 0.170674 | − | 0.985328i | \(-0.445406\pi\) |
0.938656 | + | 0.344856i | \(0.112072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −88.7758 | −2.88179 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.14860 | + | 0.663142i | −0.0372067 | + | 0.0214813i | −0.518488 | − | 0.855085i | \(-0.673505\pi\) |
0.481281 | + | 0.876566i | \(0.340172\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.1491 | + | 12.1476i | 0.554931 | + | 0.393086i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.9103 | + | 41.4138i | −0.772102 | + | 1.33732i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.77372 | 0.153991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 25.7319 | + | 2.39247i | 0.828339 | + | 0.0770162i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.18431 | − | 3.57052i | 0.198874 | − | 0.114820i | −0.397256 | − | 0.917708i | \(-0.630038\pi\) |
0.596130 | + | 0.802888i | \(0.296704\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.5252 | + | 21.6943i | 0.401953 | + | 0.696202i | 0.993962 | − | 0.109729i | \(-0.0349983\pi\) |
−0.592009 | + | 0.805931i | \(0.701665\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.04773 | + | 5.22371i | 0.290057 | + | 0.167464i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 0.00409135i | − | 0.000130894i | −1.00000 | 6.54469e-5i | \(-0.999979\pi\) | |||
1.00000 | 6.54469e-5i | \(-2.08324e-5\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.9979 | + | 27.7091i | −0.511294 | + | 0.885587i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38.4495 | + | 22.1988i | −1.22635 | + | 0.708033i | −0.966264 | − | 0.257553i | \(-0.917084\pi\) |
−0.260084 | + | 0.965586i | \(0.583750\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.61538 | + | 9.33912i | −0.210783 | + | 0.297569i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 29.6599 | 0.943128 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.7636 | + | 41.1598i | 0.754877 | + | 1.30749i | 0.945435 | + | 0.325810i | \(0.105637\pi\) |
−0.190558 | + | 0.981676i | \(0.561030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.3016 | + | 12.5505i | −0.865519 | + | 0.397877i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.6381 | + | 14.8021i | 0.811965 | + | 0.468788i | 0.847638 | − | 0.530575i | \(-0.178024\pi\) |
−0.0356725 | + | 0.999364i | \(0.511357\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 3420.2.bj.c.2629.3 | 20 | ||
3.2 | odd | 2 | 380.2.r.a.349.5 | yes | 20 | ||
5.4 | even | 2 | inner | 3420.2.bj.c.2629.5 | 20 | ||
15.2 | even | 4 | 1900.2.i.g.501.6 | 20 | |||
15.8 | even | 4 | 1900.2.i.g.501.5 | 20 | |||
15.14 | odd | 2 | 380.2.r.a.349.6 | yes | 20 | ||
19.11 | even | 3 | inner | 3420.2.bj.c.1189.5 | 20 | ||
57.11 | odd | 6 | 380.2.r.a.49.6 | yes | 20 | ||
95.49 | even | 6 | inner | 3420.2.bj.c.1189.3 | 20 | ||
285.68 | even | 12 | 1900.2.i.g.201.5 | 20 | |||
285.182 | even | 12 | 1900.2.i.g.201.6 | 20 | |||
285.239 | odd | 6 | 380.2.r.a.49.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.r.a.49.5 | ✓ | 20 | 285.239 | odd | 6 | ||
380.2.r.a.49.6 | yes | 20 | 57.11 | odd | 6 | ||
380.2.r.a.349.5 | yes | 20 | 3.2 | odd | 2 | ||
380.2.r.a.349.6 | yes | 20 | 15.14 | odd | 2 | ||
1900.2.i.g.201.5 | 20 | 285.68 | even | 12 | |||
1900.2.i.g.201.6 | 20 | 285.182 | even | 12 | |||
1900.2.i.g.501.5 | 20 | 15.8 | even | 4 | |||
1900.2.i.g.501.6 | 20 | 15.2 | even | 4 | |||
3420.2.bj.c.1189.3 | 20 | 95.49 | even | 6 | inner | ||
3420.2.bj.c.1189.5 | 20 | 19.11 | even | 3 | inner | ||
3420.2.bj.c.2629.3 | 20 | 1.1 | even | 1 | trivial | ||
3420.2.bj.c.2629.5 | 20 | 5.4 | even | 2 | inner |