Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(136,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.136");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.et (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 136.7 | ||
Character | \(\chi\) | \(=\) | 819.136 |
Dual form | 819.2.et.c.271.7 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20543 | − | 1.20543i | 0.852365 | − | 0.852365i | −0.138059 | − | 0.990424i | \(-0.544086\pi\) |
0.990424 | + | 0.138059i | \(0.0440862\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 0.906108i | − | 0.453054i | ||||||
\(5\) | −0.363968 | + | 1.35835i | −0.162772 | + | 0.607472i | 0.835542 | + | 0.549426i | \(0.185154\pi\) |
−0.998314 | + | 0.0580459i | \(0.981513\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.864271 | − | 2.50061i | 0.326664 | − | 0.945141i | ||||
\(8\) | 1.31861 | + | 1.31861i | 0.466198 | + | 0.466198i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.19865 | + | 2.07613i | 0.379047 | + | 0.656529i | ||||
\(11\) | −0.392515 | + | 1.46489i | −0.118348 | + | 0.441680i | −0.999516 | − | 0.0311237i | \(-0.990091\pi\) |
0.881168 | + | 0.472804i | \(0.156758\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37191 | − | 3.33435i | −0.380500 | − | 0.924781i | ||||
\(14\) | −1.97248 | − | 4.05611i | −0.527169 | − | 1.08404i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.99118 | 1.24780 | ||||||||
\(17\) | 5.17026 | 1.25397 | 0.626986 | − | 0.779031i | \(-0.284288\pi\) | ||||
0.626986 | + | 0.779031i | \(0.284288\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.68519 | − | 1.25539i | 1.07486 | − | 0.288007i | 0.322370 | − | 0.946614i | \(-0.395521\pi\) |
0.752487 | + | 0.658607i | \(0.228854\pi\) | |||||||
\(20\) | 1.23081 | + | 0.329795i | 0.275218 | + | 0.0737443i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.29267 | + | 2.23896i | 0.275597 | + | 0.477348i | ||||
\(23\) | − | 2.14980i | − | 0.448264i | −0.974559 | − | 0.224132i | \(-0.928045\pi\) | ||
0.974559 | − | 0.224132i | \(-0.0719547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.61749 | + | 1.51121i | 0.523498 | + | 0.302242i | ||||
\(26\) | −5.67305 | − | 2.36557i | −1.11258 | − | 0.463927i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.26582 | − | 0.783122i | −0.428200 | − | 0.147996i | ||||
\(29\) | 0.744307 | − | 1.28918i | 0.138214 | − | 0.239394i | −0.788606 | − | 0.614898i | \(-0.789197\pi\) |
0.926821 | + | 0.375504i | \(0.122530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.89045 | − | 0.506544i | 0.339534 | − | 0.0909779i | −0.0850231 | − | 0.996379i | \(-0.527096\pi\) |
0.424557 | + | 0.905401i | \(0.360430\pi\) | |||||||
\(32\) | 3.37929 | − | 3.37929i | 0.597380 | − | 0.597380i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.23237 | − | 6.23237i | 1.06884 | − | 1.06884i | ||||
\(35\) | 3.08213 | + | 2.08412i | 0.520975 | + | 0.352281i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.70890 | + | 6.70890i | 1.10294 | + | 1.10294i | 0.994055 | + | 0.108882i | \(0.0347270\pi\) |
0.108882 | + | 0.994055i | \(0.465273\pi\) | |||||||
\(38\) | 4.13437 | − | 7.16094i | 0.670684 | − | 1.16166i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.27106 | + | 1.31120i | −0.359086 | + | 0.207318i | ||||
\(41\) | −6.34762 | + | 1.70084i | −0.991331 | + | 0.265626i | −0.717810 | − | 0.696239i | \(-0.754855\pi\) |
−0.273522 | + | 0.961866i | \(0.588188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27334 | + | 4.19927i | −1.10917 | + | 0.640382i | −0.938615 | − | 0.344965i | \(-0.887891\pi\) |
−0.170559 | + | 0.985347i | \(0.554557\pi\) | |||||||
\(44\) | 1.32735 | + | 0.355661i | 0.200105 | + | 0.0536179i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.59143 | − | 2.59143i | −0.382085 | − | 0.382085i | ||||
\(47\) | −6.20311 | − | 1.66212i | −0.904817 | − | 0.242445i | −0.223733 | − | 0.974650i | \(-0.571824\pi\) |
−0.681084 | + | 0.732206i | \(0.738491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.50607 | − | 4.32240i | −0.786582 | − | 0.617486i | ||||
\(50\) | 4.97684 | − | 1.33354i | 0.703832 | − | 0.188591i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.02128 | + | 1.24310i | −0.418976 | + | 0.172387i | ||||
\(53\) | −1.87579 | + | 3.24897i | −0.257660 | + | 0.446280i | −0.965615 | − | 0.259978i | \(-0.916285\pi\) |
0.707955 | + | 0.706258i | \(0.249618\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.84696 | − | 1.06635i | −0.249045 | − | 0.143786i | ||||
\(56\) | 4.43695 | − | 2.15769i | 0.592913 | − | 0.288333i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.656802 | − | 2.45122i | −0.0862423 | − | 0.321861i | ||||
\(59\) | 5.98603 | − | 5.98603i | 0.779315 | − | 0.779315i | −0.200399 | − | 0.979714i | \(-0.564224\pi\) |
0.979714 | + | 0.200399i | \(0.0642239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.79969 | − | 1.61640i | −0.358463 | − | 0.206959i | 0.309943 | − | 0.950755i | \(-0.399690\pi\) |
−0.668407 | + | 0.743796i | \(0.733023\pi\) | |||||||
\(62\) | 1.66819 | − | 2.88940i | 0.211861 | − | 0.366954i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.83539i | 0.229423i | ||||||||
\(65\) | 5.02854 | − | 0.649937i | 0.623713 | − | 0.0806147i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5811 | − | 3.37110i | −1.53703 | − | 0.411845i | −0.611723 | − | 0.791072i | \(-0.709523\pi\) |
−0.925304 | + | 0.379227i | \(0.876190\pi\) | |||||||
\(68\) | − | 4.68481i | − | 0.568117i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.22754 | − | 1.20302i | 0.744333 | − | 0.143789i | ||||
\(71\) | 2.71213 | + | 0.726713i | 0.321870 | + | 0.0862449i | 0.416137 | − | 0.909302i | \(-0.363384\pi\) |
−0.0942662 | + | 0.995547i | \(0.530050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.82844 | − | 14.2879i | −0.448085 | − | 1.67228i | −0.707660 | − | 0.706554i | \(-0.750249\pi\) |
0.259574 | − | 0.965723i | \(-0.416418\pi\) | |||||||
\(74\) | 16.1742 | 1.88021 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.13752 | − | 4.24529i | −0.130483 | − | 0.486968i | ||||
\(77\) | 3.32387 | + | 2.24759i | 0.378790 | + | 0.256136i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.67744 | + | 6.36951i | 0.413744 | + | 0.716626i | 0.995296 | − | 0.0968836i | \(-0.0308874\pi\) |
−0.581551 | + | 0.813510i | \(0.697554\pi\) | |||||||
\(80\) | −1.81663 | + | 6.77977i | −0.203106 | + | 0.758001i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.60135 | + | 9.70182i | −0.618566 | + | 1.07139i | ||||
\(83\) | −0.0684765 | − | 0.0684765i | −0.00751627 | − | 0.00751627i | 0.703339 | − | 0.710855i | \(-0.251692\pi\) |
−0.710855 | + | 0.703339i | \(0.751692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.88181 | + | 7.02301i | −0.204111 | + | 0.761753i | ||||
\(86\) | −3.70557 | + | 13.8294i | −0.399582 | + | 1.49126i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.44918 | + | 1.41404i | −0.261084 | + | 0.150737i | ||||
\(89\) | −7.89157 | + | 7.89157i | −0.836505 | + | 0.836505i | −0.988397 | − | 0.151892i | \(-0.951463\pi\) |
0.151892 | + | 0.988397i | \(0.451463\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.52359 | + | 0.548833i | −0.998344 | + | 0.0575333i | ||||
\(92\) | −1.94795 | −0.203088 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.48096 | + | 5.47383i | −0.977886 | + | 0.564583i | ||||
\(95\) | 6.82105i | 0.699825i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.39415 | + | 12.6671i | −0.344624 | + | 1.28615i | 0.548428 | + | 0.836198i | \(0.315227\pi\) |
−0.893051 | + | 0.449955i | \(0.851440\pi\) | |||||||
\(98\) | −11.8475 | + | 1.42683i | −1.19678 | + | 0.144131i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.36932 | − | 2.37173i | 0.136932 | − | 0.237173i | ||||
\(101\) | −8.59776 | − | 14.8918i | −0.855509 | − | 1.48179i | −0.876172 | − | 0.481999i | \(-0.839911\pi\) |
0.0206627 | − | 0.999787i | \(-0.493422\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.176474 | + | 0.305661i | 0.0173885 | + | 0.0301177i | 0.874589 | − | 0.484866i | \(-0.161131\pi\) |
−0.857200 | + | 0.514983i | \(0.827798\pi\) | |||||||
\(104\) | 2.58768 | − | 6.20570i | 0.253743 | − | 0.608519i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.65526 | + | 6.17753i | 0.160773 | + | 0.600014i | ||||
\(107\) | −13.4093 | −1.29633 | −0.648164 | − | 0.761500i | \(-0.724463\pi\) | ||||
−0.648164 | + | 0.761500i | \(0.724463\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.54648 | + | 9.50358i | 0.243908 | + | 0.910277i | 0.973929 | + | 0.226853i | \(0.0728436\pi\) |
−0.730021 | + | 0.683425i | \(0.760490\pi\) | |||||||
\(110\) | −3.51178 | + | 0.940979i | −0.334835 | + | 0.0897188i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.31373 | − | 12.4810i | 0.407610 | − | 1.17934i | ||||
\(113\) | −0.325800 | − | 0.564301i | −0.0306486 | − | 0.0530850i | 0.850294 | − | 0.526308i | \(-0.176424\pi\) |
−0.880943 | + | 0.473223i | \(0.843091\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.92018 | + | 0.782460i | 0.272308 | + | 0.0729647i | ||||
\(116\) | −1.16813 | − | 0.674422i | −0.108458 | − | 0.0626185i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 14.4315i | − | 1.32852i | ||||||
\(119\) | 4.46850 | − | 12.9288i | 0.409627 | − | 1.18518i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.53445 | + | 4.35002i | 0.684950 | + | 0.395456i | ||||
\(122\) | −5.32327 | + | 1.42637i | −0.481947 | + | 0.129137i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.458983 | − | 1.71295i | −0.0412179 | − | 0.153827i | ||||
\(125\) | −7.97733 | + | 7.97733i | −0.713514 | + | 0.713514i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.63609 | − | 0.944595i | −0.145179 | − | 0.0838192i | 0.425651 | − | 0.904887i | \(-0.360045\pi\) |
−0.570830 | + | 0.821068i | \(0.693378\pi\) | |||||||
\(128\) | 8.97101 | + | 8.97101i | 0.792933 | + | 0.792933i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.27808 | − | 6.84498i | 0.462918 | − | 0.600345i | ||||
\(131\) | −8.89476 | + | 5.13539i | −0.777139 | + | 0.448681i | −0.835415 | − | 0.549619i | \(-0.814773\pi\) |
0.0582763 | + | 0.998300i | \(0.481440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.910028 | − | 12.8008i | 0.0789095 | − | 1.10997i | ||||
\(134\) | −19.2292 | + | 11.1020i | −1.66115 | + | 0.959066i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.81754 | + | 6.81754i | 0.584599 | + | 0.584599i | ||||
\(137\) | −6.59189 | − | 6.59189i | −0.563183 | − | 0.563183i | 0.367027 | − | 0.930210i | \(-0.380376\pi\) |
−0.930210 | + | 0.367027i | \(0.880376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.141825 | − | 0.0818824i | 0.0120294 | − | 0.00694518i | −0.493973 | − | 0.869477i | \(-0.664456\pi\) |
0.506003 | + | 0.862532i | \(0.331123\pi\) | |||||||
\(140\) | 1.88844 | − | 2.79274i | 0.159602 | − | 0.236030i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.14527 | − | 2.39327i | 0.347863 | − | 0.200839i | ||||
\(143\) | 5.42294 | − | 0.700913i | 0.453489 | − | 0.0586133i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.48025 | + | 1.48025i | 0.122928 | + | 0.122928i | ||||
\(146\) | −21.8380 | − | 12.6082i | −1.80732 | − | 1.04346i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.07899 | − | 6.07899i | 0.499690 | − | 0.499690i | ||||
\(149\) | 5.39257 | + | 20.1254i | 0.441777 | + | 1.64873i | 0.724309 | + | 0.689476i | \(0.242159\pi\) |
−0.282532 | + | 0.959258i | \(0.591174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.50140 | − | 0.938197i | 0.284940 | − | 0.0763494i | −0.113518 | − | 0.993536i | \(-0.536212\pi\) |
0.398458 | + | 0.917187i | \(0.369545\pi\) | |||||||
\(152\) | 7.83330 | + | 4.52256i | 0.635365 | + | 0.366828i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.71598 | − | 1.29738i | 0.541189 | − | 0.104546i | ||||
\(155\) | 2.75225i | 0.221066i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8664 | + | 7.42842i | 1.02685 | + | 0.592852i | 0.916081 | − | 0.400994i | \(-0.131335\pi\) |
0.110770 | + | 0.993846i | \(0.464668\pi\) | |||||||
\(158\) | 12.1109 | + | 3.24510i | 0.963489 | + | 0.258166i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.36030 | + | 5.82021i | 0.265655 | + | 0.460128i | ||||
\(161\) | −5.37581 | − | 1.85801i | −0.423673 | − | 0.146432i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.5228 | + | 4.15931i | −1.21584 | + | 0.325782i | −0.809050 | − | 0.587740i | \(-0.800018\pi\) |
−0.406787 | + | 0.913523i | \(0.633351\pi\) | |||||||
\(164\) | 1.54114 | + | 5.75162i | 0.120343 | + | 0.449126i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.165087 | −0.0128132 | ||||||||
\(167\) | −3.41310 | − | 12.7379i | −0.264114 | − | 0.985686i | −0.962791 | − | 0.270249i | \(-0.912894\pi\) |
0.698677 | − | 0.715438i | \(-0.253773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.23572 | + | 9.14885i | −0.710440 | + | 0.703758i | ||||
\(170\) | 6.19734 | + | 10.7341i | 0.475315 | + | 0.823269i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.80499 | + | 6.59043i | 0.290128 | + | 0.502516i | ||||
\(173\) | 7.01638 | − | 12.1527i | 0.533445 | − | 0.923954i | −0.465791 | − | 0.884895i | \(-0.654230\pi\) |
0.999237 | − | 0.0390600i | \(-0.0124363\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.04116 | − | 5.23922i | 0.456668 | − | 0.396048i | ||||
\(176\) | −1.95912 | + | 7.31152i | −0.147674 | + | 0.551127i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.0254i | 1.42602i | ||||||||
\(179\) | 15.5849 | − | 8.99797i | 1.16487 | − | 0.672540i | 0.212406 | − | 0.977182i | \(-0.431870\pi\) |
0.952467 | + | 0.304642i | \(0.0985368\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8428 | 1.10325 | 0.551627 | − | 0.834091i | \(-0.314007\pi\) | ||||
0.551627 | + | 0.834091i | \(0.314007\pi\) | |||||||
\(182\) | −10.8184 | + | 12.1416i | −0.801914 | + | 0.899993i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.83474 | − | 2.83474i | 0.208980 | − | 0.208980i | ||||
\(185\) | −11.5549 | + | 6.67120i | −0.849530 | + | 0.490476i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.02941 | + | 7.57385i | −0.148405 | + | 0.553854i | ||||
\(188\) | −1.50606 | + | 5.62069i | −0.109841 | + | 0.409931i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.22228 | + | 8.22228i | 0.596507 | + | 0.596507i | ||||
\(191\) | 7.23283 | − | 12.5276i | 0.523349 | − | 0.906468i | −0.476281 | − | 0.879293i | \(-0.658016\pi\) |
0.999631 | − | 0.0271748i | \(-0.00865108\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.69718 | − | 17.5301i | 0.338111 | − | 1.26185i | −0.562346 | − | 0.826902i | \(-0.690101\pi\) |
0.900457 | − | 0.434945i | \(-0.143232\pi\) | |||||||
\(194\) | 11.1779 | + | 19.3607i | 0.802527 | + | 1.39002i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.91656 | + | 4.98909i | −0.279754 | + | 0.356364i | ||||
\(197\) | 6.18216 | + | 23.0721i | 0.440460 | + | 1.64382i | 0.727651 | + | 0.685947i | \(0.240612\pi\) |
−0.287191 | + | 0.957873i | \(0.592721\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.98353 | 0.211497 | 0.105749 | − | 0.994393i | \(-0.466276\pi\) | ||||
0.105749 | + | 0.994393i | \(0.466276\pi\) | |||||||
\(200\) | 1.45875 | + | 5.44413i | 0.103149 | + | 0.384958i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −28.3149 | − | 7.58695i | −1.99223 | − | 0.533816i | ||||
\(203\) | −2.58044 | − | 2.97542i | −0.181112 | − | 0.208833i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 9.24133i | − | 0.645442i | ||||||
\(206\) | 0.581178 | + | 0.155726i | 0.0404926 | + | 0.0108500i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.84746 | − | 16.6423i | −0.474786 | − | 1.15394i | ||||
\(209\) | 7.35604i | 0.508828i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.05578 | + | 3.56072i | −0.141526 | + | 0.245130i | −0.928071 | − | 0.372402i | \(-0.878534\pi\) |
0.786546 | + | 0.617532i | \(0.211867\pi\) | |||||||
\(212\) | 2.94392 | + | 1.69967i | 0.202189 | + | 0.116734i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −16.1640 | + | 16.1640i | −1.10495 | + | 1.10495i | ||||
\(215\) | −3.05680 | − | 11.4081i | −0.208472 | − | 0.778028i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.367191 | − | 5.16506i | 0.0249265 | − | 0.350627i | ||||
\(218\) | 14.5255 | + | 8.38628i | 0.983788 | + | 0.567990i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.966224 | + | 1.67355i | −0.0651428 | + | 0.112831i | ||||
\(221\) | −7.09313 | − | 17.2394i | −0.477136 | − | 1.15965i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.9482 | + | 4.54125i | −1.13493 | + | 0.304105i | −0.776912 | − | 0.629609i | \(-0.783215\pi\) |
−0.358022 | + | 0.933713i | \(0.616549\pi\) | |||||||
\(224\) | −5.52966 | − | 11.3709i | −0.369466 | − | 0.759751i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.07295 | − | 0.287496i | −0.0713717 | − | 0.0191240i | ||||
\(227\) | 4.90655 | + | 4.90655i | 0.325659 | + | 0.325659i | 0.850933 | − | 0.525274i | \(-0.176037\pi\) |
−0.525274 | + | 0.850933i | \(0.676037\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.65510 | + | 2.31913i | 0.571945 | + | 0.153252i | 0.533189 | − | 0.845996i | \(-0.320994\pi\) |
0.0387566 | + | 0.999249i | \(0.487660\pi\) | |||||||
\(230\) | 4.46326 | − | 2.57686i | 0.294299 | − | 0.169913i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.68137 | − | 0.718470i | 0.176040 | − | 0.0471699i | ||||
\(233\) | −5.51653 | + | 3.18497i | −0.361400 | + | 0.208654i | −0.669695 | − | 0.742636i | \(-0.733575\pi\) |
0.308295 | + | 0.951291i | \(0.400242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.51547 | − | 7.82103i | 0.294557 | − | 0.510188i | ||||
\(236\) | −5.42399 | − | 5.42399i | −0.353072 | − | 0.353072i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.1983 | − | 20.9712i | −0.661055 | − | 1.35936i | ||||
\(239\) | 11.4926 | − | 11.4926i | 0.743396 | − | 0.743396i | −0.229834 | − | 0.973230i | \(-0.573818\pi\) |
0.973230 | + | 0.229834i | \(0.0738183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.164298 | + | 0.164298i | −0.0105834 | + | 0.0105834i | −0.712379 | − | 0.701795i | \(-0.752382\pi\) |
0.701795 | + | 0.712379i | \(0.252382\pi\) | |||||||
\(242\) | 14.3259 | − | 3.83860i | 0.920901 | − | 0.246755i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.46463 | + | 2.53682i | −0.0937636 | + | 0.162403i | ||||
\(245\) | 7.87537 | − | 5.90595i | 0.503139 | − | 0.377317i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.6136 | − | 13.8998i | −0.675326 | − | 0.884421i | ||||
\(248\) | 3.16069 | + | 1.82482i | 0.200704 | + | 0.115876i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.2322i | 1.21635i | ||||||||
\(251\) | −4.39247 | − | 7.60798i | −0.277250 | − | 0.480211i | 0.693450 | − | 0.720504i | \(-0.256090\pi\) |
−0.970700 | + | 0.240293i | \(0.922756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.14922 | + | 0.843830i | 0.197989 | + | 0.0530511i | ||||
\(254\) | −3.11082 | + | 0.833542i | −0.195190 | + | 0.0523011i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.9570 | 1.12231 | ||||||||
\(257\) | −22.7247 | −1.41753 | −0.708763 | − | 0.705447i | \(-0.750746\pi\) | ||||
−0.708763 | + | 0.705447i | \(0.750746\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.5746 | − | 10.9780i | 1.40272 | − | 0.682141i | ||||
\(260\) | −0.588913 | − | 4.55640i | −0.0365228 | − | 0.282576i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.53164 | + | 16.9123i | −0.279966 | + | 1.04485i | ||||
\(263\) | −4.09771 | − | 7.09745i | −0.252676 | − | 0.437647i | 0.711586 | − | 0.702599i | \(-0.247977\pi\) |
−0.964262 | + | 0.264952i | \(0.914644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.73050 | − | 3.73050i | −0.229163 | − | 0.229163i | ||||
\(266\) | −14.3335 | − | 16.5274i | −0.878843 | − | 1.01336i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.05458 | + | 11.3998i | −0.186588 | + | 0.696356i | ||||
\(269\) | 24.5019i | 1.49391i | 0.664875 | + | 0.746954i | \(0.268485\pi\) | ||||
−0.664875 | + | 0.746954i | \(0.731515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.87162 | + | 5.87162i | −0.356675 | + | 0.356675i | −0.862586 | − | 0.505910i | \(-0.831157\pi\) |
0.505910 | + | 0.862586i | \(0.331157\pi\) | |||||||
\(272\) | 25.8057 | 1.56470 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.8921 | −0.960076 | ||||||||
\(275\) | −3.24115 | + | 3.24115i | −0.195449 | + | 0.195449i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.49932i | 0.0900852i | 0.998985 | + | 0.0450426i | \(0.0143424\pi\) | ||||
−0.998985 | + | 0.0450426i | \(0.985658\pi\) | |||||||
\(278\) | 0.0722558 | − | 0.269662i | 0.00433362 | − | 0.0161733i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.31598 | + | 6.81226i | 0.0786447 | + | 0.407110i | ||||
\(281\) | −19.5020 | − | 19.5020i | −1.16339 | − | 1.16339i | −0.983728 | − | 0.179665i | \(-0.942499\pi\) |
−0.179665 | − | 0.983728i | \(-0.557501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.83136 | − | 13.5643i | −0.465526 | − | 0.806315i | 0.533699 | − | 0.845674i | \(-0.320802\pi\) |
−0.999225 | + | 0.0393597i | \(0.987468\pi\) | |||||||
\(284\) | 0.658480 | − | 2.45748i | 0.0390736 | − | 0.145825i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.69205 | − | 7.38185i | 0.336578 | − | 0.436498i | ||||
\(287\) | −1.23293 | + | 17.3429i | −0.0727775 | + | 1.02372i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.73158 | 0.572446 | ||||||||
\(290\) | 3.56866 | 0.209559 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.9464 | + | 3.46898i | −0.757631 | + | 0.203007i | ||||
\(293\) | −13.6614 | − | 3.66056i | −0.798107 | − | 0.213852i | −0.163354 | − | 0.986567i | \(-0.552231\pi\) |
−0.634753 | + | 0.772715i | \(0.718898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.95239 | + | 10.3098i | 0.346562 | + | 0.600263i | ||||
\(296\) | 17.6928i | 1.02837i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.7600 | + | 17.7593i | 1.78188 | + | 1.02877i | ||||
\(299\) | −7.16818 | + | 2.94933i | −0.414546 | + | 0.170564i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.21458 | + | 21.8171i | 0.242924 | + | 1.25752i | ||||
\(302\) | 3.08975 | − | 5.35161i | 0.177795 | − | 0.307950i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 23.3847 | − | 6.26590i | 1.34120 | − | 0.359374i | ||||
\(305\) | 3.21464 | − | 3.21464i | 0.184069 | − | 0.184069i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.977336 | − | 0.977336i | 0.0557795 | − | 0.0557795i | −0.678667 | − | 0.734446i | \(-0.737442\pi\) |
0.734446 | + | 0.678667i | \(0.237442\pi\) | |||||||
\(308\) | 2.03655 | − | 3.01178i | 0.116043 | − | 0.171612i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.31764 | + | 3.31764i | 0.188429 | + | 0.188429i | ||||
\(311\) | 4.20663 | − | 7.28609i | 0.238536 | − | 0.413156i | −0.721759 | − | 0.692145i | \(-0.756666\pi\) |
0.960294 | + | 0.278989i | \(0.0899992\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4104 | + | 8.31988i | −0.814527 | + | 0.470267i | −0.848525 | − | 0.529155i | \(-0.822509\pi\) |
0.0339987 | + | 0.999422i | \(0.489176\pi\) | |||||||
\(314\) | 24.4639 | − | 6.55509i | 1.38058 | − | 0.369925i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.77146 | − | 3.33216i | 0.324670 | − | 0.187448i | ||||
\(317\) | 8.06223 | + | 2.16027i | 0.452820 | + | 0.121333i | 0.478019 | − | 0.878350i | \(-0.341355\pi\) |
−0.0251986 | + | 0.999682i | \(0.508022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.59635 | + | 1.59635i | 0.0893783 | + | 0.0893783i | ||||
\(320\) | −2.49310 | − | 0.668023i | −0.139368 | − | 0.0373436i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.71984 | + | 4.24045i | −0.485937 | + | 0.236311i | ||||
\(323\) | 24.2237 | − | 6.49071i | 1.34784 | − | 0.361153i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.44793 | − | 10.8009i | 0.0803166 | − | 0.599124i | ||||
\(326\) | −13.6978 | + | 23.7253i | −0.758652 | + | 1.31402i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6128 | − | 6.12727i | −0.585991 | − | 0.338322i | ||||
\(329\) | −9.51747 | + | 14.0750i | −0.524715 | + | 0.775981i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.91640 | + | 7.15210i | 0.105335 | + | 0.393115i | 0.998383 | − | 0.0568462i | \(-0.0181045\pi\) |
−0.893048 | + | 0.449961i | \(0.851438\pi\) | |||||||
\(332\) | −0.0620471 | + | 0.0620471i | −0.00340528 | + | 0.00340528i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.4688 | − | 11.2403i | −1.06529 | − | 0.615043i | ||||
\(335\) | 9.15825 | − | 15.8626i | 0.500369 | − | 0.866664i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 27.7667i | − | 1.51255i | −0.654256 | − | 0.756273i | \(-0.727018\pi\) | ||
0.654256 | − | 0.756273i | \(-0.272982\pi\) | |||||||
\(338\) | −0.104718 | + | 22.1613i | −0.00569593 | + | 1.20541i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.36361 | + | 1.70512i | 0.345115 | + | 0.0924733i | ||||
\(341\) | 2.96812i | 0.160733i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5674 | + | 10.0328i | −0.840559 | + | 0.541720i | ||||
\(344\) | −15.1279 | − | 4.05350i | −0.815640 | − | 0.218550i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.19149 | − | 23.1070i | −0.332856 | − | 1.24224i | ||||
\(347\) | 10.8321 | 0.581499 | 0.290750 | − | 0.956799i | \(-0.406095\pi\) | ||||
0.290750 | + | 0.956799i | \(0.406095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.622157 | + | 2.32192i | 0.0333033 | + | 0.124290i | 0.980576 | − | 0.196138i | \(-0.0628401\pi\) |
−0.947273 | + | 0.320428i | \(0.896173\pi\) | |||||||
\(350\) | 0.966677 | − | 13.5977i | 0.0516710 | − | 0.726826i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.62386 | + | 6.27671i | 0.193152 | + | 0.334550i | ||||
\(353\) | −3.11894 | + | 11.6401i | −0.166005 | + | 0.619538i | 0.831905 | + | 0.554918i | \(0.187250\pi\) |
−0.997910 | + | 0.0646202i | \(0.979416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.97426 | + | 3.41952i | −0.104783 | + | 0.181489i | ||||
\(356\) | 7.15062 | + | 7.15062i | 0.378982 | + | 0.378982i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.94011 | − | 29.6329i | 0.419648 | − | 1.56615i | ||||
\(359\) | 7.12307 | − | 26.5837i | 0.375941 | − | 1.40303i | −0.476023 | − | 0.879433i | \(-0.657922\pi\) |
0.851965 | − | 0.523599i | \(-0.175411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.92054 | − | 2.26352i | 0.206344 | − | 0.119133i | ||||
\(362\) | 17.8919 | − | 17.8919i | 0.940376 | − | 0.940376i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.497302 | + | 8.62940i | 0.0260657 | + | 0.452303i | ||||
\(365\) | 20.8014 | 1.08880 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.2228 | − | 7.05683i | 0.638024 | − | 0.368363i | −0.145829 | − | 0.989310i | \(-0.546585\pi\) |
0.783853 | + | 0.620946i | \(0.213252\pi\) | |||||||
\(368\) | − | 10.7301i | − | 0.559343i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.88689 | + | 21.9702i | −0.306045 | + | 1.14218i | ||||
\(371\) | 6.50320 | + | 7.49861i | 0.337629 | + | 0.389308i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9945 | + | 25.9713i | −0.776387 | + | 1.34474i | 0.157624 | + | 0.987499i | \(0.449616\pi\) |
−0.934012 | + | 0.357243i | \(0.883717\pi\) | |||||||
\(374\) | 6.68342 | + | 11.5760i | 0.345591 | + | 0.598582i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.98778 | − | 10.3711i | −0.308796 | − | 0.534851i | ||||
\(377\) | −5.31969 | − | 0.713140i | −0.273978 | − | 0.0367286i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.76234 | − | 25.2374i | −0.347358 | − | 1.29636i | −0.889833 | − | 0.456286i | \(-0.849179\pi\) |
0.542475 | − | 0.840072i | \(-0.317487\pi\) | |||||||
\(380\) | 6.18061 | 0.317058 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.38250 | − | 23.8198i | −0.326557 | − | 1.21873i | ||||
\(383\) | −30.7142 | + | 8.22985i | −1.56942 | + | 0.420526i | −0.935632 | − | 0.352978i | \(-0.885169\pi\) |
−0.633792 | + | 0.773504i | \(0.718502\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.26279 | + | 3.69692i | −0.217252 | + | 0.188413i | ||||
\(386\) | −15.4692 | − | 26.7934i | −0.787360 | − | 1.36375i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 11.4778 | + | 3.07546i | 0.582697 | + | 0.156133i | ||||
\(389\) | −12.1261 | − | 7.00102i | −0.614818 | − | 0.354966i | 0.160030 | − | 0.987112i | \(-0.448841\pi\) |
−0.774849 | + | 0.632147i | \(0.782174\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 11.1150i | − | 0.562111i | ||||||
\(392\) | −1.56080 | − | 12.9599i | −0.0788321 | − | 0.654574i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 35.2639 | + | 20.3596i | 1.77657 | + | 1.02570i | ||||
\(395\) | −9.99049 | + | 2.67694i | −0.502676 | + | 0.134692i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.60637 | − | 17.1912i | −0.231187 | − | 0.862802i | −0.979831 | − | 0.199829i | \(-0.935961\pi\) |
0.748644 | − | 0.662973i | \(-0.230705\pi\) | |||||||
\(398\) | 3.59643 | − | 3.59643i | 0.180273 | − | 0.180273i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 13.0644 | + | 7.54272i | 0.653218 | + | 0.377136i | ||||
\(401\) | −1.38205 | − | 1.38205i | −0.0690162 | − | 0.0690162i | 0.671756 | − | 0.740772i | \(-0.265540\pi\) |
−0.740772 | + | 0.671756i | \(0.765540\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.28252 | − | 5.60847i | −0.213327 | − | 0.279378i | ||||
\(404\) | −13.4935 | + | 7.79050i | −0.671329 | + | 0.387592i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.69718 | − | 0.476112i | −0.332376 | − | 0.0236290i | ||||
\(407\) | −12.4611 | + | 7.19444i | −0.617675 | + | 0.356615i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0600 | − | 11.0600i | −0.546882 | − | 0.546882i | 0.378656 | − | 0.925538i | \(-0.376387\pi\) |
−0.925538 | + | 0.378656i | \(0.876387\pi\) | |||||||
\(410\) | −11.1397 | − | 11.1397i | −0.550153 | − | 0.550153i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.276962 | − | 0.159904i | 0.0136449 | − | 0.00787791i | ||||
\(413\) | −9.79517 | − | 20.1423i | −0.481989 | − | 0.991136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.117938 | − | 0.0680917i | 0.00578936 | − | 0.00334249i | ||||
\(416\) | −15.9038 | − | 6.63164i | −0.779749 | − | 0.325143i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.86717 | + | 8.86717i | 0.433707 | + | 0.433707i | ||||
\(419\) | 32.1543 | + | 18.5643i | 1.57084 | + | 0.906924i | 0.996066 | + | 0.0886099i | \(0.0282425\pi\) |
0.574772 | + | 0.818314i | \(0.305091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.1846 | + | 23.1846i | −1.12995 | + | 1.12995i | −0.139764 | + | 0.990185i | \(0.544634\pi\) |
−0.990185 | + | 0.139764i | \(0.955366\pi\) | |||||||
\(422\) | 1.81409 | + | 6.77028i | 0.0883085 | + | 0.329572i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.75755 | + | 1.81068i | −0.328176 | + | 0.0879344i | ||||
\(425\) | 13.5331 | + | 7.81334i | 0.656451 | + | 0.379002i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.46167 | + | 5.60391i | −0.312702 | + | 0.271192i | ||||
\(428\) | 12.1503i | 0.587307i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.4364 | − | 10.0669i | −0.840859 | − | 0.485470i | ||||
\(431\) | 15.9999 | + | 4.28716i | 0.770688 | + | 0.206505i | 0.622675 | − | 0.782480i | \(-0.286046\pi\) |
0.148012 | + | 0.988986i | \(0.452712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.814551 | + | 1.41084i | 0.0391448 | + | 0.0678008i | 0.884934 | − | 0.465716i | \(-0.154203\pi\) |
−0.845789 | + | 0.533517i | \(0.820870\pi\) | |||||||
\(434\) | −5.78347 | − | 6.66872i | −0.277616 | − | 0.320109i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.61126 | − | 2.30738i | 0.412405 | − | 0.110504i | ||||
\(437\) | −2.69885 | − | 10.0722i | −0.129103 | − | 0.481820i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.9803 | 1.33543 | 0.667713 | − | 0.744419i | \(-0.267273\pi\) | ||||
0.667713 | + | 0.744419i | \(0.267273\pi\) | |||||||
\(440\) | −1.02933 | − | 3.84151i | −0.0490714 | − | 0.183137i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −29.3311 | − | 12.2306i | −1.39514 | − | 0.581751i | ||||
\(443\) | −12.7182 | − | 22.0285i | −0.604258 | − | 1.04661i | −0.992168 | − | 0.124908i | \(-0.960136\pi\) |
0.387910 | − | 0.921697i | \(-0.373197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.84723 | − | 13.5918i | −0.371994 | − | 0.644313i | ||||
\(446\) | −14.9556 | + | 25.9039i | −0.708170 | + | 1.22659i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.58958 | + | 1.58627i | 0.216837 | + | 0.0749443i | ||||
\(449\) | 0.665392 | − | 2.48328i | 0.0314018 | − | 0.117193i | −0.948446 | − | 0.316939i | \(-0.897345\pi\) |
0.979848 | + | 0.199746i | \(0.0640116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.96615i | − | 0.469288i | ||||||
\(452\) | −0.511318 | + | 0.295209i | −0.0240504 | + | 0.0138855i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.8290 | 0.555162 | ||||||||
\(455\) | 2.72078 | − | 13.1361i | 0.127552 | − | 0.615831i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0248 | + | 10.0248i | −0.468940 | + | 0.468940i | −0.901571 | − | 0.432631i | \(-0.857585\pi\) |
0.432631 | + | 0.901571i | \(0.357585\pi\) | |||||||
\(458\) | 13.2286 | − | 7.63755i | 0.618133 | − | 0.356879i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.708993 | − | 2.64600i | 0.0330570 | − | 0.123370i | ||||
\(461\) | −10.8132 | + | 40.3552i | −0.503619 | + | 1.87953i | −0.0285297 | + | 0.999593i | \(0.509083\pi\) |
−0.475089 | + | 0.879938i | \(0.657584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.6177 | + | 19.6177i | 0.911713 | + | 0.911713i | 0.996407 | − | 0.0846939i | \(-0.0269912\pi\) |
−0.0846939 | + | 0.996407i | \(0.526991\pi\) | |||||||
\(464\) | 3.71497 | − | 6.43452i | 0.172463 | − | 0.298715i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.81053 | + | 10.4890i | −0.130195 | + | 0.485895i | ||||
\(467\) | 14.6509 | + | 25.3761i | 0.677962 | + | 1.17426i | 0.975594 | + | 0.219584i | \(0.0704700\pi\) |
−0.297632 | + | 0.954681i | \(0.596197\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.3033 | + | 28.5469i | −0.891342 | + | 1.31817i | ||||
\(470\) | −3.98461 | − | 14.8707i | −0.183796 | − | 0.685937i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 15.7865 | 0.726630 | ||||||||
\(473\) | −3.29655 | − | 12.3029i | −0.151576 | − | 0.565688i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.1606 | + | 3.79432i | 0.649733 | + | 0.174095i | ||||
\(476\) | −11.7149 | − | 4.04894i | −0.536950 | − | 0.185583i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 27.7070i | − | 1.26729i | ||||||
\(479\) | 8.64079 | + | 2.31529i | 0.394808 | + | 0.105788i | 0.450760 | − | 0.892645i | \(-0.351153\pi\) |
−0.0559526 | + | 0.998433i | \(0.517820\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.1658 | − | 31.5738i | 0.600308 | − | 1.43964i | ||||
\(482\) | 0.396098i | 0.0180418i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.94159 | − | 6.82703i | 0.179163 | − | 0.310319i | ||||
\(485\) | −15.9710 | − | 9.22088i | −0.725207 | − | 0.418698i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.5064 | − | 14.5064i | 0.657346 | − | 0.657346i | −0.297406 | − | 0.954751i | \(-0.596121\pi\) |
0.954751 | + | 0.297406i | \(0.0961214\pi\) | |||||||
\(488\) | −1.56029 | − | 5.82309i | −0.0706311 | − | 0.263599i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.37399 | − | 16.6124i | 0.107246 | − | 0.750470i | ||||
\(491\) | 27.6274 | + | 15.9507i | 1.24681 | + | 0.719845i | 0.970472 | − | 0.241216i | \(-0.0775461\pi\) |
0.276337 | + | 0.961061i | \(0.410879\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.84826 | − | 6.66538i | 0.173317 | − | 0.300194i | ||||
\(494\) | −29.5490 | − | 3.96125i | −1.32947 | − | 0.178225i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.43557 | − | 2.52825i | 0.423669 | − | 0.113522i | ||||
\(497\) | 4.16124 | − | 6.15389i | 0.186657 | − | 0.276040i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.1352 | − | 5.93111i | −0.990907 | − | 0.265513i | −0.273276 | − | 0.961936i | \(-0.588107\pi\) |
−0.717632 | + | 0.696423i | \(0.754774\pi\) | |||||||
\(500\) | 7.22832 | + | 7.22832i | 0.323260 | + | 0.323260i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.4657 | − | 3.87606i | −0.645634 | − | 0.172997i | ||||
\(503\) | 23.9880 | − | 13.8495i | 1.06957 | − | 0.617518i | 0.141508 | − | 0.989937i | \(-0.454805\pi\) |
0.928065 | + | 0.372419i | \(0.121472\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.3575 | − | 6.25863i | 1.03940 | − | 0.278505i | ||||
\(506\) | 4.81332 | − | 2.77897i | 0.213978 | − | 0.123540i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.855905 | + | 1.48247i | −0.0379746 | + | 0.0657740i | ||||
\(509\) | −30.4769 | − | 30.4769i | −1.35087 | − | 1.35087i | −0.884693 | − | 0.466174i | \(-0.845632\pi\) |
−0.466174 | − | 0.884693i | \(-0.654368\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −39.0373 | − | 2.77522i | −1.72691 | − | 0.122768i | ||||
\(512\) | 3.70385 | − | 3.70385i | 0.163689 | − | 0.163689i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.3929 | + | 27.3929i | −1.20825 | + | 1.20825i | ||||
\(515\) | −0.479425 | + | 0.128462i | −0.0211260 | + | 0.00566070i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.86963 | − | 8.43445i | 0.214166 | − | 0.370947i | ||||
\(518\) | 13.9789 | − | 40.4453i | 0.614196 | − | 1.77706i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.48768 | + | 5.77365i | 0.328356 | + | 0.253191i | ||||
\(521\) | −1.66737 | − | 0.962655i | −0.0730487 | − | 0.0421747i | 0.463031 | − | 0.886342i | \(-0.346762\pi\) |
−0.536079 | + | 0.844168i | \(0.680095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.27342i | 0.0556829i | 0.999612 | + | 0.0278414i | \(0.00886335\pi\) | ||||
−0.999612 | + | 0.0278414i | \(0.991137\pi\) | |||||||
\(524\) | 4.65322 | + | 8.05961i | 0.203277 | + | 0.352086i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.4949 | − | 3.61596i | −0.588408 | − | 0.157663i | ||||
\(527\) | 9.77410 | − | 2.61896i | 0.425766 | − | 0.114084i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.3784 | 0.799059 | ||||||||
\(530\) | −8.99370 | −0.390661 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −11.5989 | − | 0.824584i | −0.502877 | − | 0.0357502i | ||||
\(533\) | 14.3795 | + | 18.8317i | 0.622847 | + | 0.815694i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.88057 | − | 18.2145i | 0.211006 | − | 0.787483i | ||||
\(536\) | −12.1444 | − | 21.0347i | −0.524557 | − | 0.908560i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 29.5353 | + | 29.5353i | 1.27336 | + | 1.27336i | ||||
\(539\) | 8.49305 | − | 6.36917i | 0.365822 | − | 0.274339i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.06372 | + | 22.6301i | −0.260700 | + | 0.972944i | 0.704131 | + | 0.710070i | \(0.251337\pi\) |
−0.964830 | + | 0.262874i | \(0.915330\pi\) | |||||||
\(542\) | 14.1556i | 0.608036i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 17.4718 | − | 17.4718i | 0.749098 | − | 0.749098i | ||||
\(545\) | −13.8360 | −0.592669 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.4093 | 1.68502 | 0.842510 | − | 0.538680i | \(-0.181077\pi\) | ||||
0.842510 | + | 0.538680i | \(0.181077\pi\) | |||||||
\(548\) | −5.97296 | + | 5.97296i | −0.255152 | + | 0.255152i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.81395i | 0.333188i | ||||||||
\(551\) | 1.86880 | − | 6.97444i | 0.0796134 | − | 0.297121i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.1059 | − | 3.69085i | 0.812468 | − | 0.156951i | ||||
\(554\) | 1.80732 | + | 1.80732i | 0.0767855 | + | 0.0767855i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.0741943 | − | 0.128508i | −0.00314654 | − | 0.00544997i | ||||
\(557\) | −3.89152 | + | 14.5233i | −0.164889 | + | 0.615374i | 0.833165 | + | 0.553024i | \(0.186526\pi\) |
−0.998054 | + | 0.0623501i | \(0.980140\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.9802 | + | 18.4908i | 1.01425 | + | 0.782078i | ||||
\(560\) | 15.3835 | + | 10.4022i | 0.650070 | + | 0.439575i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −47.0165 | −1.98327 | ||||||||
\(563\) | 17.2519 | 0.727081 | 0.363541 | − | 0.931578i | \(-0.381568\pi\) | ||||
0.363541 | + | 0.931578i | \(0.381568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.885099 | − | 0.237161i | 0.0372364 | − | 0.00997746i | ||||
\(566\) | −25.7909 | − | 6.91066i | −1.08407 | − | 0.290477i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.61798 | + | 4.53448i | 0.109848 | + | 0.190263i | ||||
\(569\) | − | 10.5691i | − | 0.443081i | −0.975151 | − | 0.221540i | \(-0.928892\pi\) | ||
0.975151 | − | 0.221540i | \(-0.0711085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.73797 | − | 2.73547i | −0.198278 | − | 0.114476i | 0.397574 | − | 0.917570i | \(-0.369852\pi\) |
−0.595852 | + | 0.803094i | \(0.703185\pi\) | |||||||
\(572\) | −0.635102 | − | 4.91376i | −0.0265550 | − | 0.205455i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 19.4194 | + | 22.3918i | 0.810549 | + | 0.934615i | ||||
\(575\) | 3.24880 | − | 5.62708i | 0.135484 | − | 0.234665i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.3289 | + | 5.17915i | −0.804671 | + | 0.215611i | −0.637634 | − | 0.770340i | \(-0.720087\pi\) |
−0.167037 | + | 0.985951i | \(0.553420\pi\) | |||||||
\(578\) | 11.7307 | − | 11.7307i | 0.487933 | − | 0.487933i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.34126 | − | 1.34126i | 0.0556930 | − | 0.0556930i | ||||
\(581\) | −0.230415 | + | 0.112051i | −0.00955923 | + | 0.00464864i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.02310 | − | 4.02310i | −0.166620 | − | 0.166620i | ||||
\(584\) | 13.7920 | − | 23.8884i | 0.570716 | − | 0.988508i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.8803 | + | 12.0553i | −0.862559 | + | 0.497999i | ||||
\(587\) | 1.59431 | − | 0.427193i | 0.0658041 | − | 0.0176321i | −0.225767 | − | 0.974181i | \(-0.572489\pi\) |
0.291571 | + | 0.956549i | \(0.405822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.22120 | − | 4.74651i | 0.338748 | − | 0.195577i | ||||
\(590\) | 19.6029 | + | 5.25259i | 0.807040 | + | 0.216246i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.4854 | + | 33.4854i | 1.37624 | + | 1.37624i | ||||
\(593\) | 34.8670 | + | 9.34258i | 1.43182 | + | 0.383654i | 0.889660 | − | 0.456624i | \(-0.150941\pi\) |
0.542156 | + | 0.840278i | \(0.317608\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.9354 | + | 10.7755i | 0.653288 | + | 0.441751i | ||||
\(596\) | 18.2357 | − | 4.88625i | 0.746965 | − | 0.200149i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.08551 | + | 12.1959i | −0.207962 | + | 0.498728i | ||||
\(599\) | 5.29544 | − | 9.17197i | 0.216366 | − | 0.374757i | −0.737328 | − | 0.675534i | \(-0.763913\pi\) |
0.953694 | + | 0.300778i | \(0.0972463\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.1270 | − | 13.9297i | −0.984160 | − | 0.568205i | −0.0806362 | − | 0.996744i | \(-0.525695\pi\) |
−0.903523 | + | 0.428539i | \(0.859029\pi\) | |||||||
\(602\) | 31.3793 | + | 21.2185i | 1.27892 | + | 0.864802i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.850107 | − | 3.17264i | −0.0345904 | − | 0.129093i | ||||
\(605\) | −8.65115 | + | 8.65115i | −0.351719 | + | 0.351719i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.2975 | + | 11.1414i | 0.783262 | + | 0.452216i | 0.837585 | − | 0.546307i | \(-0.183967\pi\) |
−0.0543233 | + | 0.998523i | \(0.517300\pi\) | |||||||
\(608\) | 11.5903 | − | 20.0750i | 0.470049 | − | 0.814148i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 7.75001i | − | 0.313789i | ||||||
\(611\) | 2.96804 | + | 22.9636i | 0.120074 | + | 0.929007i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.2994 | − | 9.99436i | −1.50651 | − | 0.403668i | −0.591236 | − | 0.806499i | \(-0.701360\pi\) |
−0.915275 | + | 0.402831i | \(0.868026\pi\) | |||||||
\(614\) | − | 2.35621i | − | 0.0950890i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.41919 | + | 7.34656i | 0.0571809 | + | 0.296001i | ||||
\(617\) | −19.0276 | − | 5.09843i | −0.766022 | − | 0.205255i | −0.145409 | − | 0.989372i | \(-0.546450\pi\) |
−0.620613 | + | 0.784117i | \(0.713116\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.15720 | − | 34.1751i | −0.368059 | − | 1.37361i | −0.863226 | − | 0.504817i | \(-0.831560\pi\) |
0.495167 | − | 0.868798i | \(-0.335107\pi\) | |||||||
\(620\) | 2.49384 | 0.100155 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.71207 | − | 13.8536i | −0.148840 | − | 0.555480i | ||||
\(623\) | 12.9133 | + | 26.5542i | 0.517359 | + | 1.06387i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.376462 | − | 0.652052i | −0.0150585 | − | 0.0260821i | ||||
\(626\) | −7.34174 | + | 27.3997i | −0.293435 | + | 1.09511i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.73095 | − | 11.6583i | 0.268594 | − | 0.465219i | ||||
\(629\) | 34.6868 | + | 34.6868i | 1.38305 | + | 1.38305i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.11023 | − | 4.14343i | 0.0441976 | − | 0.164948i | −0.940300 | − | 0.340348i | \(-0.889455\pi\) |
0.984497 | + | 0.175400i | \(0.0561219\pi\) | |||||||
\(632\) | −3.54979 | + | 13.2480i | −0.141203 | + | 0.526976i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.3225 | − | 7.11439i | 0.489388 | − | 0.282548i | ||||
\(635\) | 1.87857 | − | 1.87857i | 0.0745489 | − | 0.0745489i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.85854 | + | 24.2891i | −0.271745 | + | 0.962369i | ||||
\(638\) | 3.84856 | 0.152366 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.4509 | + | 8.92060i | −0.610752 | + | 0.352618i | ||||
\(641\) | 35.3132i | 1.39479i | 0.716689 | + | 0.697393i | \(0.245657\pi\) | ||||
−0.716689 | + | 0.697393i | \(0.754343\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.90713 | + | 10.8495i | −0.114646 | + | 0.427864i | −0.999260 | − | 0.0384591i | \(-0.987755\pi\) |
0.884614 | + | 0.466323i | \(0.154422\pi\) | |||||||
\(644\) | −1.68356 | + | 4.87106i | −0.0663414 | + | 0.191947i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 21.3758 | − | 37.0239i | 0.841019 | − | 1.45669i | ||||
\(647\) | −6.78354 | − | 11.7494i | −0.266689 | − | 0.461918i | 0.701316 | − | 0.712851i | \(-0.252596\pi\) |
−0.968005 | + | 0.250932i | \(0.919263\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.41925 | + | 11.1185i | 0.251978 | + | 0.436438i | ||||
\(650\) | −11.2743 | − | 14.7650i | −0.442213 | − | 0.579131i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.76878 | + | 14.0653i | 0.147597 | + | 0.550839i | ||||
\(653\) | 14.6552 | 0.573501 | 0.286751 | − | 0.958005i | \(-0.407425\pi\) | ||||
0.286751 | + | 0.958005i | \(0.407425\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.73824 | − | 13.9513i | −0.146065 | − | 0.545123i | ||||
\(656\) | −31.6821 | + | 8.48920i | −1.23698 | + | 0.331448i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.49379 | + | 28.4390i | 0.214170 | + | 1.10867i | ||||
\(659\) | 25.1178 | + | 43.5054i | 0.978452 | + | 1.69473i | 0.668037 | + | 0.744128i | \(0.267135\pi\) |
0.310415 | + | 0.950601i | \(0.399532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.25098 | − | 0.335198i | −0.0486574 | − | 0.0130377i | 0.234408 | − | 0.972138i | \(-0.424685\pi\) |
−0.283066 | + | 0.959101i | \(0.591351\pi\) | |||||||
\(662\) | 10.9314 | + | 6.31125i | 0.424861 | + | 0.245294i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 0.180587i | − | 0.00700814i | ||||||
\(665\) | 17.0568 | + | 5.89523i | 0.661433 | + | 0.228607i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.77147 | − | 1.60011i | −0.107312 | − | 0.0619566i | ||||
\(668\) | −11.5419 | + | 3.09264i | −0.446569 | + | 0.119658i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8.08155 | − | 30.1607i | −0.312217 | − | 1.16521i | ||||
\(671\) | 3.46677 | − | 3.46677i | 0.133833 | − | 0.133833i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.6264 | + | 11.3313i | 0.756543 | + | 0.436790i | 0.828053 | − | 0.560650i | \(-0.189449\pi\) |
−0.0715103 | + | 0.997440i | \(0.522782\pi\) | |||||||
\(674\) | −33.4707 | − | 33.4707i | −1.28924 | − | 1.28924i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.28984 | + | 8.36856i | 0.318840 | + | 0.321868i | ||||
\(677\) | 23.6738 | − | 13.6681i | 0.909859 | − | 0.525307i | 0.0294729 | − | 0.999566i | \(-0.490617\pi\) |
0.880386 | + | 0.474258i | \(0.157284\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.7421 | + | 19.4353i | 1.10302 | + | 0.745857i | ||||
\(680\) | −11.7420 | + | 6.77923i | −0.450284 | + | 0.259972i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.57785 | + | 3.57785i | 0.137003 | + | 0.137003i | ||||
\(683\) | −20.0961 | − | 20.0961i | −0.768954 | − | 0.768954i | 0.208968 | − | 0.977922i | \(-0.432989\pi\) |
−0.977922 | + | 0.208968i | \(0.932989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3533 | − | 6.55485i | 0.433788 | − | 0.250448i | ||||
\(686\) | −6.67152 | + | 30.8591i | −0.254720 | + | 1.17821i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −36.3026 | + | 20.9593i | −1.38402 | + | 0.799066i | ||||
\(689\) | 13.4066 | + | 1.79725i | 0.510751 | + | 0.0684697i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.07012 | + | 7.07012i | 0.268960 | + | 0.268960i | 0.828681 | − | 0.559721i | \(-0.189092\pi\) |
−0.559721 | + | 0.828681i | \(0.689092\pi\) | |||||||
\(692\) | −11.0117 | − | 6.35759i | −0.418601 | − | 0.241679i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0573 | − | 13.0573i | 0.495650 | − | 0.495650i | ||||
\(695\) | 0.0596052 | + | 0.222450i | 0.00226096 | + | 0.00843800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −32.8188 | + | 8.79378i | −1.24310 | + | 0.333088i | ||||
\(698\) | 3.54887 | + | 2.04894i | 0.134327 | + | 0.0775536i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.74730 | − | 5.47394i | −0.179431 | − | 0.206895i | ||||
\(701\) | − | 36.1836i | − | 1.36664i | −0.730121 | − | 0.683318i | \(-0.760536\pi\) | ||
0.730121 | − | 0.683318i | \(-0.239464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.8548 | + | 23.0102i | 1.50315 | + | 0.867846i | ||||
\(704\) | −2.68864 | − | 0.720418i | −0.101332 | − | 0.0271518i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.2716 | + | 17.7909i | 0.386576 | + | 0.669569i | ||||
\(707\) | −44.6692 | + | 8.62911i | −1.67996 | + | 0.324531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.8750 | + | 8.27293i | −1.15954 | + | 0.310697i | −0.786780 | − | 0.617233i | \(-0.788253\pi\) |
−0.372755 | + | 0.927930i | \(0.621587\pi\) | |||||||
\(710\) | 1.74215 | + | 6.50180i | 0.0653818 | + | 0.244008i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −20.8118 | −0.779954 | ||||||||
\(713\) | −1.08897 | − | 4.06408i | −0.0407822 | − | 0.152201i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.02169 | + | 7.62135i | −0.0382092 | + | 0.285022i | ||||
\(716\) | −8.15313 | − | 14.1216i | −0.304697 | − | 0.527750i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.4583 | − | 40.6310i | −0.875457 | − | 1.51634i | ||||
\(719\) | 10.5168 | − | 18.2157i | 0.392212 | − | 0.679330i | −0.600529 | − | 0.799603i | \(-0.705043\pi\) |
0.992741 | + | 0.120272i | \(0.0383768\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.916860 | − | 0.177117i | 0.0341456 | − | 0.00659619i | ||||
\(722\) | 1.99741 | − | 7.45444i | 0.0743359 | − | 0.277425i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 13.4491i | − | 0.499833i | ||||||
\(725\) | 3.89643 | − | 2.24961i | 0.144710 | − | 0.0835482i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.1689 | −1.15599 | −0.577995 | − | 0.816040i | \(-0.696165\pi\) | ||||
−0.577995 | + | 0.816040i | \(0.696165\pi\) | |||||||
\(728\) | −13.2816 | − | 11.8342i | −0.492248 | − | 0.438604i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 25.0746 | − | 25.0746i | 0.928053 | − | 0.928053i | ||||
\(731\) | −37.6051 | + | 21.7113i | −1.39087 | + | 0.803021i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.40351 | − | 5.23797i | 0.0518398 | − | 0.193469i | −0.935150 | − | 0.354252i | \(-0.884735\pi\) |
0.986990 | + | 0.160783i | \(0.0514021\pi\) | |||||||
\(734\) | 6.22718 | − | 23.2402i | 0.229849 | − | 0.857810i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.26481 | − | 7.26481i | −0.267784 | − | 0.267784i | ||||
\(737\) | 9.87655 | − | 17.1067i | 0.363807 | − | 0.630133i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.93352 | − | 29.6083i | 0.291839 | − | 1.08916i | −0.651856 | − | 0.758343i | \(-0.726009\pi\) |
0.943695 | − | 0.330816i | \(-0.107324\pi\) | |||||||
\(740\) | 6.04482 | + | 10.4699i | 0.222212 | + | 0.384883i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.8782 | + | 1.19989i | 0.619617 | + | 0.0440494i | ||||
\(743\) | 1.70775 | + | 6.37341i | 0.0626512 | + | 0.233818i | 0.990150 | − | 0.140008i | \(-0.0447127\pi\) |
−0.927499 | + | 0.373825i | \(0.878046\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.3000 | −1.07347 | ||||||||
\(746\) | 13.2317 | + | 49.3813i | 0.484446 | + | 1.80798i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.86272 | + | 1.83886i | 0.250926 | + | 0.0672354i | ||||
\(749\) | −11.5893 | + | 33.5315i | −0.423463 | + | 1.22521i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 8.46455i | − | 0.308876i | −0.988002 | − | 0.154438i | \(-0.950643\pi\) | ||
0.988002 | − | 0.154438i | \(-0.0493567\pi\) | |||||||
\(752\) | −30.9609 | − | 8.29594i | −1.12903 | − | 0.302522i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.27213 | + | 5.55285i | −0.264835 | + | 0.202223i | ||||
\(755\) | 5.09759i | 0.185520i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.5330 | − | 23.4399i | 0.491866 | − | 0.851937i | −0.508090 | − | 0.861304i | \(-0.669648\pi\) |
0.999956 | + | 0.00936661i | \(0.00298153\pi\) | |||||||
\(758\) | −38.5734 | − | 22.2703i | −1.40105 | − | 0.808895i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.99429 | + | 8.99429i | −0.326257 | + | 0.326257i | ||||
\(761\) | 4.69735 | + | 17.5308i | 0.170279 | + | 0.635489i | 0.997308 | + | 0.0733299i | \(0.0233626\pi\) |
−0.827029 | + | 0.562159i | \(0.809971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.9656 | + | 1.84593i | 0.940016 | + | 0.0668270i | ||||
\(764\) | −11.3514 | − | 6.55373i | −0.410679 | − | 0.237105i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −27.1033 | + | 46.9442i | −0.979281 | + | 1.69616i | ||||
\(767\) | −28.1718 | − | 11.7472i | −1.01723 | − | 0.424167i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.4162 | − | 10.5616i | 1.42139 | − | 0.380859i | 0.535411 | − | 0.844592i | \(-0.320157\pi\) |
0.885975 | + | 0.463732i | \(0.153490\pi\) | |||||||
\(770\) | −0.682111 | + | 9.59485i | −0.0245816 | + | 0.345774i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.8842 | − | 4.25616i | −0.571684 | − | 0.153182i | ||||
\(773\) | 7.87836 | + | 7.87836i | 0.283365 | + | 0.283365i | 0.834449 | − | 0.551085i | \(-0.185786\pi\) |
−0.551085 | + | 0.834449i | \(0.685786\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.71372 | + | 1.53099i | 0.205243 | + | 0.0549946i | ||||
\(776\) | −21.1785 | + | 12.2274i | −0.760265 | + | 0.438939i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.0564 | + | 6.17793i | −0.826610 | + | 0.221490i | ||||
\(779\) | −27.6046 | + | 15.9375i | −0.989037 | + | 0.571021i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.12910 | + | 3.68772i | −0.0761853 | + | 0.131957i | ||||
\(782\) | −13.3983 | − | 13.3983i | −0.479124 | − | 0.479124i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.4818 | − | 21.5739i | −0.981494 | − | 0.770497i | ||||
\(785\) | −14.7733 | + | 14.7733i | −0.527283 | + | 0.527283i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.429238 | + | 0.429238i | −0.0153007 | + | 0.0153007i | −0.714716 | − | 0.699415i | \(-0.753444\pi\) |
0.699415 | + | 0.714716i | \(0.253444\pi\) | |||||||
\(788\) | 20.9058 | − | 5.60170i | 0.744739 | − | 0.199552i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.81594 | + | 15.2697i | −0.313657 | + | 0.543270i | ||||
\(791\) | −1.69267 | + | 0.326988i | −0.0601846 | + | 0.0116263i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.54872 | + | 11.5527i | −0.0549966 | + | 0.410248i | ||||
\(794\) | −26.2754 | − | 15.1701i | −0.932478 | − | 0.538367i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 2.70340i | − | 0.0958196i | ||||||
\(797\) | 25.9638 | + | 44.9707i | 0.919687 | + | 1.59294i | 0.799891 | + | 0.600145i | \(0.204891\pi\) |
0.119796 | + | 0.992799i | \(0.461776\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0717 | − | 8.59358i | −1.13461 | − | 0.304019i | ||||
\(800\) | 13.9521 | − | 3.73845i | 0.493280 | − | 0.132174i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.33192 | −0.117654 | ||||||||
\(803\) | 22.4329 | 0.791641 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.48045 | − | 6.62596i | 0.157915 | − | 0.233535i | ||||
\(806\) | −11.9229 | − | 1.59834i | −0.419965 | − | 0.0562992i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.29931 | − | 30.9734i | 0.291969 | − | 1.08964i | ||||
\(809\) | 3.61649 | + | 6.26395i | 0.127149 | + | 0.220229i | 0.922571 | − | 0.385827i | \(-0.126084\pi\) |
−0.795422 | + | 0.606056i | \(0.792751\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.2728 | + | 25.2728i | 0.887448 | + | 0.887448i | 0.994277 | − | 0.106830i | \(-0.0340700\pi\) |
−0.106830 | + | 0.994277i | \(0.534070\pi\) | |||||||
\(812\) | −2.69605 | + | 2.33816i | −0.0946128 | + | 0.0820533i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.34861 | + | 23.6933i | −0.222519 | + | 0.830451i | ||||
\(815\) | − | 22.5992i | − | 0.791615i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.8053 | + | 28.8053i | −1.00777 | + | 1.00777i | ||||
\(818\) | −26.6641 | −0.932287 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.37364 | −0.292420 | ||||||||
\(821\) | −26.1285 | + | 26.1285i | −0.911890 | + | 0.911890i | −0.996421 | − | 0.0845305i | \(-0.973061\pi\) |
0.0845305 | + | 0.996421i | \(0.473061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.9126i | 0.798683i | 0.916802 | + | 0.399341i | \(0.130761\pi\) | ||||
−0.916802 | + | 0.399341i | \(0.869239\pi\) | |||||||
\(824\) | −0.170348 | + | 0.635746i | −0.00593434 | + | 0.0221473i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.0874 | − | 12.4727i | −1.25564 | − | 0.433980i | ||||
\(827\) | 1.34175 | + | 1.34175i | 0.0466571 | + | 0.0466571i | 0.730050 | − | 0.683393i | \(-0.239497\pi\) |
−0.683393 | + | 0.730050i | \(0.739497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.94656 | + | 6.83564i | 0.137070 | + | 0.237412i | 0.926386 | − | 0.376575i | \(-0.122898\pi\) |
−0.789317 | + | 0.613987i | \(0.789565\pi\) | |||||||
\(830\) | 0.0600864 | − | 0.224246i | 0.00208563 | − | 0.00778368i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.11982 | − | 2.51799i | 0.212166 | − | 0.0872955i | ||||
\(833\) | −28.4678 | − | 22.3479i | −0.986351 | − | 0.774310i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.5447 | 0.641767 | ||||||||
\(836\) | 6.66536 | 0.230526 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 61.1375 | − | 16.3817i | 2.11196 | − | 0.565898i | ||||
\(839\) | −20.2818 | − | 5.43449i | −0.700205 | − | 0.187619i | −0.108883 | − | 0.994055i | \(-0.534727\pi\) |
−0.591322 | + | 0.806435i | \(0.701394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.3920 | + | 23.1956i | 0.461794 | + | 0.799850i | ||||
\(842\) | 55.8947i | 1.92626i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.22639 | + | 1.86276i | 0.111057 | + | 0.0641188i | ||||
\(845\) | −9.06582 | − | 15.8752i | −0.311874 | − | 0.546124i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.3895 | − | 15.0811i | 0.597510 | − | 0.518193i | ||||
\(848\) | −9.36243 | + | 16.2162i | −0.321507 | + | 0.556867i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25.7316 | − | 6.89475i | 0.882585 | − | 0.236488i | ||||
\(851\) | 14.4228 | − | 14.4228i | 0.494407 | − | 0.494407i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.56250 | + | 5.56250i | −0.190456 | + | 0.190456i | −0.795893 | − | 0.605437i | \(-0.792998\pi\) |
0.605437 | + | 0.795893i | \(0.292998\pi\) | |||||||
\(854\) | −1.03397 | + | 14.5442i | −0.0353816 | + | 0.497692i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.6816 | − | 17.6816i | −0.604346 | − | 0.604346i | ||||
\(857\) | 7.92167 | − | 13.7207i | 0.270599 | − | 0.468691i | −0.698416 | − | 0.715692i | \(-0.746112\pi\) |
0.969015 | + | 0.247000i | \(0.0794449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0070 | + | 12.7057i | −0.750867 | + | 0.433514i | −0.826007 | − | 0.563659i | \(-0.809393\pi\) |
0.0751398 | + | 0.997173i | \(0.476060\pi\) | |||||||
\(860\) | −10.3370 | + | 2.76979i | −0.352489 | + | 0.0944491i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.4546 | − | 14.1188i | 0.832925 | − | 0.480890i | ||||
\(863\) | −31.5462 | − | 8.45278i | −1.07385 | − | 0.287736i | −0.321773 | − | 0.946817i | \(-0.604279\pi\) |
−0.752072 | + | 0.659081i | \(0.770946\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.9539 | + | 13.9539i | 0.474447 | + | 0.474447i | ||||
\(866\) | 2.68255 | + | 0.718787i | 0.0911568 | + | 0.0244254i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.68010 | − | 0.332714i | −0.158853 | − | 0.0112931i | ||||
\(869\) | −10.7741 | + | 2.88690i | −0.365485 | + | 0.0979315i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.01975 | + | 46.5746i | 0.203971 | + | 1.57812i | ||||
\(872\) | −9.17368 | + | 15.8893i | −0.310660 | + | 0.538079i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −15.3946 | − | 8.88808i | −0.520730 | − | 0.300644i | ||||
\(875\) | 13.0536 | + | 26.8427i | 0.441292 | + | 0.907450i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.8921 | − | 44.3819i | −0.401568 | − | 1.49867i | −0.810299 | − | 0.586016i | \(-0.800696\pi\) |
0.408732 | − | 0.912654i | \(-0.365971\pi\) | |||||||
\(878\) | 33.7282 | − | 33.7282i | 1.13827 | − | 1.13827i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.21854 | − | 5.32233i | −0.310757 | − | 0.179416i | ||||
\(881\) | −16.3535 | + | 28.3251i | −0.550963 | + | 0.954296i | 0.447242 | + | 0.894413i | \(0.352406\pi\) |
−0.998205 | + | 0.0598832i | \(0.980927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 57.1171i | − | 1.92214i | −0.276302 | − | 0.961071i | \(-0.589109\pi\) | ||
0.276302 | − | 0.961071i | \(-0.410891\pi\) | |||||||
\(884\) | −15.6208 | + | 6.42714i | −0.525384 | + | 0.216168i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −41.8846 | − | 11.2229i | −1.40714 | − | 0.377042i | ||||
\(887\) | − | 26.1341i | − | 0.877498i | −0.898610 | − | 0.438749i | \(-0.855422\pi\) | ||
0.898610 | − | 0.438749i | \(-0.144578\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.77608 | + | 3.27482i | −0.126646 | + | 0.109834i | ||||
\(890\) | −25.8432 | − | 6.92466i | −0.866265 | − | 0.232115i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.11486 | + | 15.3569i | 0.137776 | + | 0.514186i | ||||
\(893\) | −31.1494 | −1.04237 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.54995 | + | 24.4448i | 0.218941 | + | 0.817098i | ||||
\(896\) | 30.1864 | − | 14.6796i | 1.00846 | − | 0.490411i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.19133 | − | 3.79549i | −0.0731256 | − | 0.126657i | ||||
\(899\) | 0.754048 | − | 2.81415i | 0.0251489 | − | 0.0938570i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.69834 | + | 16.7980i | −0.323098 | + | 0.559623i | ||||
\(902\) | −12.0135 | − | 12.0135i | −0.400004 | − | 0.400004i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.314490 | − | 1.17369i | 0.0104598 | − | 0.0390365i | ||||
\(905\) | −5.40230 | + | 20.1616i | −0.179578 | + | 0.670196i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.38851 | + | 5.42046i | −0.311740 | + | 0.179983i | −0.647705 | − | 0.761891i | \(-0.724271\pi\) |
0.335965 | + | 0.941875i | \(0.390938\pi\) | |||||||
\(908\) | 4.44587 | − | 4.44587i | 0.147541 | − | 0.147541i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.5549 | − | 19.1143i | −0.416192 | − | 0.633634i | ||||
\(911\) | −35.4311 | −1.17389 | −0.586943 | − | 0.809628i | \(-0.699669\pi\) | ||||
−0.586943 | + | 0.809628i | \(0.699669\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.127188 | − | 0.0734323i | 0.00420932 | − | 0.00243025i | ||||
\(914\) | 24.1683i | 0.799417i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.10138 | − | 7.84245i | 0.0694315 | − | 0.259122i | ||||
\(917\) | 5.15412 | + | 26.6807i | 0.170204 | + | 0.881074i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.75577 | − | 13.4334i | 0.255839 | − | 0.443126i | −0.709284 | − | 0.704923i | \(-0.750982\pi\) |
0.965123 | + | 0.261797i | \(0.0843149\pi\) | |||||||
\(920\) | 2.81881 | + | 4.88233i | 0.0929335 | + | 0.160966i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 35.6108 | + | 61.6797i | 1.17278 | + | 2.03131i | ||||
\(923\) | −1.29769 | − | 10.0402i | −0.0427139 | − | 0.330476i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.42193 | + | 27.6990i | 0.244032 | + | 0.910738i | ||||
\(926\) | 47.2955 | 1.55423 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.84128 | − | 6.87174i | −0.0604429 | − | 0.225576i | ||||
\(929\) | 53.2944 | − | 14.2802i | 1.74853 | − | 0.468518i | 0.764222 | − | 0.644954i | \(-0.223123\pi\) |
0.984312 | + | 0.176436i | \(0.0564567\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.2233 | − | 13.3390i | −1.02330 | − | 0.437168i | ||||
\(932\) | 2.88593 | + | 4.99857i | 0.0945317 | + | 0.163734i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 48.2496 | + | 12.9284i | 1.57877 | + | 0.423031i | ||||
\(935\) | −9.54928 | − | 5.51328i | −0.312295 | − | 0.180304i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.36357i | 0.142552i | 0.997457 | + | 0.0712758i | \(0.0227070\pi\) | ||||
−0.997457 | + | 0.0712758i | \(0.977293\pi\) | |||||||
\(938\) | 11.1425 | + | 57.6798i | 0.363815 | + | 1.88331i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.08669 | − | 4.09150i | −0.231142 | − | 0.133450i | ||||
\(941\) | 8.90484 | − | 2.38605i | 0.290290 | − | 0.0777829i | −0.110736 | − | 0.993850i | \(-0.535321\pi\) |
0.401025 | + | 0.916067i | \(0.368654\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.65646 | + | 13.6461i | 0.119071 | + | 0.444378i | ||||
\(944\) | 29.8774 | − | 29.8774i | 0.972426 | − | 0.972426i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18.8040 | − | 10.8565i | −0.611371 | − | 0.352975i | ||||
\(947\) | −39.0303 | − | 39.0303i | −1.26832 | − | 1.26832i | −0.946958 | − | 0.321357i | \(-0.895861\pi\) |
−0.321357 | − | 0.946958i | \(-0.604139\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.3886 | + | 32.3671i | −1.37599 | + | 1.05068i | ||||
\(950\) | 21.6433 | − | 12.4958i | 0.702203 | − | 0.405417i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 22.9402 | − | 11.1558i | 0.743496 | − | 0.361561i | ||||
\(953\) | 30.1513 | − | 17.4079i | 0.976697 | − | 0.563896i | 0.0754255 | − | 0.997151i | \(-0.475969\pi\) |
0.901271 | + | 0.433255i | \(0.142635\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.3844 | + | 14.3844i | 0.465467 | + | 0.465467i | ||||
\(956\) | −10.4136 | − | 10.4136i | −0.336798 | − | 0.336798i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.2068 | − | 7.62492i | 0.426691 | − | 0.246350i | ||||
\(959\) | −22.1809 | + | 10.7866i | −0.716259 | + | 0.348316i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.5296 | + | 13.5848i | −0.759019 | + | 0.438220i | ||||
\(962\) | −22.1895 | − | 53.9303i | −0.715419 | − | 1.73878i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.148872 | + | 0.148872i | 0.00479483 | + | 0.00479483i | ||||
\(965\) | 22.1024 | + | 12.7608i | 0.711502 | + | 0.410786i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.1180 | + | 24.1180i | −0.775583 | + | 0.775583i | −0.979076 | − | 0.203494i | \(-0.934770\pi\) |
0.203494 | + | 0.979076i | \(0.434770\pi\) | |||||||
\(968\) | 4.19902 | + | 15.6710i | 0.134962 | + | 0.503683i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −30.3670 | + | 8.13681i | −0.975026 | + | 0.261257i | ||||
\(971\) | 40.0392 | + | 23.1166i | 1.28492 | + | 0.741848i | 0.977743 | − | 0.209805i | \(-0.0672829\pi\) |
0.307175 | + | 0.951653i | \(0.400616\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.0821810 | − | 0.425416i | −0.00263460 | − | 0.0136382i | ||||
\(974\) | − | 34.9727i | − | 1.12060i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.9738 | − | 8.06776i | −0.447289 | − | 0.258243i | ||||
\(977\) | 7.76823 | + | 2.08149i | 0.248528 | + | 0.0665928i | 0.380932 | − | 0.924603i | \(-0.375603\pi\) |
−0.132404 | + | 0.991196i | \(0.542270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.46270 | − | 14.6578i | −0.270469 | − | 0.468466i | ||||
\(980\) | −5.35143 | − | 7.13593i | −0.170945 | − | 0.227949i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 52.5303 | − | 14.0754i | 1.67631 | − | 0.449165i | ||||
\(983\) | −2.20054 | − | 8.21252i | −0.0701863 | − | 0.261939i | 0.921912 | − | 0.387398i | \(-0.126626\pi\) |
−0.992099 | + | 0.125459i | \(0.959959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.5901 | −1.07027 | ||||||||
\(986\) | −3.39583 | − | 12.6734i | −0.108145 | − | 0.403604i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.5947 | + | 9.61705i | −0.400690 | + | 0.305959i | ||||
\(989\) | 9.02758 | + | 15.6362i | 0.287060 | + | 0.497203i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.44662 | + | 9.43383i | 0.173018 | + | 0.299675i | 0.939473 | − | 0.342622i | \(-0.111315\pi\) |
−0.766456 | + | 0.642297i | \(0.777982\pi\) | |||||||
\(992\) | 4.67661 | − | 8.10013i | 0.148483 | − | 0.257179i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.40200 | − | 12.4341i | −0.0761868 | − | 0.394387i | ||||
\(995\) | −1.08591 | + | 4.05268i | −0.0344257 | + | 0.128479i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 0.973665i | − | 0.0308363i | −0.999881 | − | 0.0154181i | \(-0.995092\pi\) | ||
0.999881 | − | 0.0154181i | \(-0.00490794\pi\) | |||||||
\(998\) | −33.8319 | + | 19.5328i | −1.07093 | + | 0.618301i | ||||
\(999\) | 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 | 819.2.et.c.136.7 | 36 | ||
3.2 | odd | 2 | 273.2.bt.a.136.3 | ✓ | 36 | ||
7.5 | odd | 6 | 819.2.gh.c.19.3 | 36 | |||
13.11 | odd | 12 | 819.2.gh.c.388.3 | 36 | |||
21.5 | even | 6 | 273.2.cg.a.19.7 | yes | 36 | ||
39.11 | even | 12 | 273.2.cg.a.115.7 | yes | 36 | ||
91.89 | even | 12 | inner | 819.2.et.c.271.7 | 36 | ||
273.89 | odd | 12 | 273.2.bt.a.271.3 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bt.a.136.3 | ✓ | 36 | 3.2 | odd | 2 | ||
273.2.bt.a.271.3 | yes | 36 | 273.89 | odd | 12 | ||
273.2.cg.a.19.7 | yes | 36 | 21.5 | even | 6 | ||
273.2.cg.a.115.7 | yes | 36 | 39.11 | even | 12 | ||
819.2.et.c.136.7 | 36 | 1.1 | even | 1 | trivial | ||
819.2.et.c.271.7 | 36 | 91.89 | even | 12 | inner | ||
819.2.gh.c.19.3 | 36 | 7.5 | odd | 6 | |||
819.2.gh.c.388.3 | 36 | 13.11 | odd | 12 |