Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [640,3,Mod(353,640)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(640, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("640.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 640 = 2^{7} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 640.t (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.4387369191\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 417.10 | ||
Character | \(\chi\) | \(=\) | 640.417 |
Dual form | 640.3.t.a.353.10 |
$q$-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 \(\left(\mathbb{Z}/640\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(261\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.24645 | −0.415485 | −0.207742 | − | 0.978184i | \(-0.566612\pi\) | ||||
−0.207742 | + | 0.978184i | \(0.566612\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.50036 | − | 4.76958i | −0.300072 | − | 0.953917i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.62600 | + | 3.62600i | −0.518000 | + | 0.518000i | −0.916966 | − | 0.398966i | \(-0.869369\pi\) |
0.398966 | + | 0.916966i | \(0.369369\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.44635 | −0.827372 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.10832 | − | 9.10832i | 0.828029 | − | 0.828029i | −0.159215 | − | 0.987244i | \(-0.550896\pi\) |
0.987244 | + | 0.159215i | \(0.0508963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.59167 | 0.737821 | 0.368910 | − | 0.929465i | \(-0.379731\pi\) | ||||
0.368910 | + | 0.929465i | \(0.379731\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.87013 | + | 5.94507i | 0.124675 | + | 0.396338i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.5630 | − | 14.5630i | −0.856648 | − | 0.856648i | 0.134294 | − | 0.990942i | \(-0.457123\pi\) |
−0.990942 | + | 0.134294i | \(0.957123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.1736 | + | 10.1736i | −0.535454 | + | 0.535454i | −0.922190 | − | 0.386736i | \(-0.873602\pi\) |
0.386736 | + | 0.922190i | \(0.373602\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.51965 | − | 4.51965i | 0.215221 | − | 0.215221i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.9529 | + | 20.9529i | 0.910996 | + | 0.910996i | 0.996351 | − | 0.0853546i | \(-0.0272023\pi\) |
−0.0853546 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.4978 | + | 14.3122i | −0.819914 | + | 0.572487i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 20.4996 | 0.759246 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −15.9714 | + | 15.9714i | −0.550737 | + | 0.550737i | −0.926654 | − | 0.375916i | \(-0.877328\pi\) |
0.375916 | + | 0.926654i | \(0.377328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −22.3264 | −0.720208 | −0.360104 | − | 0.932912i | \(-0.617259\pi\) | ||||
−0.360104 | + | 0.932912i | \(0.617259\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.3531 | + | 11.3531i | −0.344034 | + | 0.344034i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 22.7348 | + | 11.8542i | 0.649566 | + | 0.338692i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −28.7135 | −0.776041 | −0.388020 | − | 0.921651i | \(-0.626841\pi\) | ||||
−0.388020 | + | 0.921651i | \(0.626841\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.9556 | −0.306553 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 71.4731i | 1.74325i | 0.490177 | + | 0.871623i | \(0.336932\pi\) | ||||
−0.490177 | + | 0.871623i | \(0.663068\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 18.1083i | − | 0.421123i | −0.977581 | − | 0.210561i | \(-0.932471\pi\) | ||
0.977581 | − | 0.210561i | \(-0.0675292\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1722 | + | 35.5160i | 0.248271 | + | 0.789244i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52.4024 | + | 52.4024i | 1.11495 | + | 1.11495i | 0.992472 | + | 0.122474i | \(0.0390827\pi\) |
0.122474 | + | 0.992472i | \(0.460917\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22.7042i | 0.463352i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 18.1521 | + | 18.1521i | 0.355924 | + | 0.355924i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 24.3168i | − | 0.458808i | −0.973331 | − | 0.229404i | \(-0.926322\pi\) | ||
0.973331 | − | 0.229404i | \(-0.0736776\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −57.1086 | − | 29.7771i | −1.03834 | − | 0.541402i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.6810 | − | 12.6810i | 0.222473 | − | 0.222473i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 48.9777 | + | 48.9777i | 0.830131 | + | 0.830131i | 0.987534 | − | 0.157403i | \(-0.0503123\pi\) |
−0.157403 | + | 0.987534i | \(0.550312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42.1700 | − | 42.1700i | −0.691311 | − | 0.691311i | 0.271209 | − | 0.962520i | \(-0.412576\pi\) |
−0.962520 | + | 0.271209i | \(0.912576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 27.0005 | − | 27.0005i | 0.428579 | − | 0.428579i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.3909 | − | 45.7483i | −0.221399 | − | 0.703819i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 73.7087i | 1.10013i | 0.835122 | + | 0.550065i | \(0.185397\pi\) | ||||
−0.835122 | + | 0.550065i | \(0.814603\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −26.1169 | − | 26.1169i | −0.378505 | − | 0.378505i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28.6304i | 0.403244i | 0.979463 | + | 0.201622i | \(0.0646213\pi\) | ||||
−0.979463 | + | 0.201622i | \(0.935379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.24608 | − | 9.24608i | −0.126659 | − | 0.126659i | 0.640936 | − | 0.767594i | \(-0.278546\pi\) |
−0.767594 | + | 0.640936i | \(0.778546\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.5496 | − | 17.8395i | 0.340662 | − | 0.237860i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 66.0535i | 0.857838i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 85.8203i | 1.08633i | 0.839625 | + | 0.543166i | \(0.182775\pi\) | ||||
−0.839625 | + | 0.543166i | \(0.817225\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 41.4653 | 0.511917 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −71.8998 | −0.866263 | −0.433131 | − | 0.901331i | \(-0.642591\pi\) | ||||
−0.433131 | + | 0.901331i | \(0.642591\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −47.6097 | + | 91.3092i | −0.560115 | + | 1.07423i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 19.9076 | − | 19.9076i | 0.228823 | − | 0.228823i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −124.642 | −1.40047 | −0.700233 | − | 0.713914i | \(-0.746921\pi\) | ||||
−0.700233 | + | 0.713914i | \(0.746921\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −34.7794 | + | 34.7794i | −0.382191 | + | 0.382191i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.8289 | 0.299236 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 63.7881 | + | 33.2599i | 0.671454 | + | 0.350104i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.5684 | + | 19.5684i | 0.201736 | + | 0.201736i | 0.800743 | − | 0.599008i | \(-0.204438\pi\) |
−0.599008 | + | 0.800743i | \(0.704438\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −67.8237 | + | 67.8237i | −0.685088 | + | 0.685088i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −52.5412 | + | 52.5412i | −0.520210 | + | 0.520210i | −0.917635 | − | 0.397425i | \(-0.869904\pi\) |
0.397425 | + | 0.917635i | \(0.369904\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −21.9304 | − | 21.9304i | −0.212916 | − | 0.212916i | 0.592589 | − | 0.805505i | \(-0.298106\pi\) |
−0.805505 | + | 0.592589i | \(0.798106\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −28.3379 | − | 14.7757i | −0.269885 | − | 0.140721i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −172.582 | −1.61291 | −0.806456 | − | 0.591294i | \(-0.798617\pi\) | ||||
−0.806456 | + | 0.591294i | \(0.798617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 33.6276 | − | 33.6276i | 0.308510 | − | 0.308510i | −0.535821 | − | 0.844331i | \(-0.679998\pi\) |
0.844331 | + | 0.535821i | \(0.179998\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 35.7901 | 0.322433 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 33.7854 | − | 33.7854i | 0.298986 | − | 0.298986i | −0.541631 | − | 0.840617i | \(-0.682193\pi\) |
0.840617 | + | 0.541631i | \(0.182193\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 68.4997 | − | 131.374i | 0.595650 | − | 1.14238i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −71.4229 | −0.610452 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 105.611 | 0.887487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 44.9229i | − | 0.371264i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 89.0880i | − | 0.724292i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 99.0172 | + | 76.2928i | 0.792138 | + | 0.610342i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −104.424 | − | 104.424i | −0.822234 | − | 0.822234i | 0.164194 | − | 0.986428i | \(-0.447498\pi\) |
−0.986428 | + | 0.164194i | \(0.947498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.5711i | 0.174970i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.2047 | − | 21.2047i | −0.161868 | − | 0.161868i | 0.621526 | − | 0.783394i | \(-0.286513\pi\) |
−0.783394 | + | 0.621526i | \(0.786513\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 73.7792i | − | 0.554731i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −30.7568 | − | 97.7747i | −0.227828 | − | 0.724257i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 192.446 | − | 192.446i | 1.40471 | − | 1.40471i | 0.620531 | − | 0.784182i | \(-0.286917\pi\) |
0.784182 | − | 0.620531i | \(-0.213083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 100.158 | + | 100.158i | 0.720563 | + | 0.720563i | 0.968720 | − | 0.248157i | \(-0.0798249\pi\) |
−0.248157 | + | 0.968720i | \(0.579825\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −65.3173 | − | 65.3173i | −0.463243 | − | 0.463243i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 87.3640 | − | 87.3640i | 0.610937 | − | 0.610937i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 100.140 | + | 52.2140i | 0.690618 | + | 0.360097i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 28.2998i | − | 0.192516i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 96.2282 | + | 96.2282i | 0.645827 | + | 0.645827i | 0.951982 | − | 0.306155i | \(-0.0990426\pi\) |
−0.306155 | + | 0.951982i | \(0.599043\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 153.137i | 1.01415i | 0.861902 | + | 0.507075i | \(0.169273\pi\) | ||||
−0.861902 | + | 0.507075i | \(0.830727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 108.441 | + | 108.441i | 0.708767 | + | 0.708767i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 33.4977 | + | 106.488i | 0.216114 | + | 0.687018i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 125.408i | − | 0.798778i | −0.916782 | − | 0.399389i | \(-0.869222\pi\) | ||
0.916782 | − | 0.399389i | \(-0.130778\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30.3098i | 0.190628i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −151.951 | −0.943792 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 170.310 | 1.04485 | 0.522424 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522424 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 71.1833 | + | 37.1158i | 0.431414 | + | 0.224945i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 100.234 | − | 100.234i | 0.600206 | − | 0.600206i | −0.340161 | − | 0.940367i | \(-0.610482\pi\) |
0.940367 | + | 0.340161i | \(0.110482\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −76.9999 | −0.455621 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 75.7565 | − | 75.7565i | 0.443020 | − | 0.443020i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −230.629 | −1.33312 | −0.666559 | − | 0.745452i | \(-0.732234\pi\) | ||||
−0.666559 | + | 0.745452i | \(0.732234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.4292 | − | 126.221i | 0.128167 | − | 0.721264i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −61.0485 | − | 61.0485i | −0.344907 | − | 0.344907i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 141.787 | − | 141.787i | 0.792106 | − | 0.792106i | −0.189731 | − | 0.981836i | \(-0.560761\pi\) |
0.981836 | + | 0.189731i | \(0.0607615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 222.974 | − | 222.974i | 1.23190 | − | 1.23190i | 0.268665 | − | 0.963234i | \(-0.413418\pi\) |
0.963234 | − | 0.268665i | \(-0.0865825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 52.5630 | + | 52.5630i | 0.287229 | + | 0.287229i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 43.0806 | + | 136.951i | 0.232868 | + | 0.740278i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −265.289 | −1.41866 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −74.3317 | + | 74.3317i | −0.393289 | + | 0.393289i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −360.691 | −1.88843 | −0.944217 | − | 0.329325i | \(-0.893179\pi\) | ||||
−0.944217 | + | 0.329325i | \(0.893179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.2248 | − | 24.2248i | 0.125517 | − | 0.125517i | −0.641558 | − | 0.767075i | \(-0.721712\pi\) |
0.767075 | + | 0.641558i | \(0.221712\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 17.9377 | + | 57.0231i | 0.0919880 | + | 0.292426i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 169.208 | 0.858922 | 0.429461 | − | 0.903085i | \(-0.358704\pi\) | ||||
0.429461 | + | 0.903085i | \(0.358704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −176.493 | −0.886899 | −0.443450 | − | 0.896299i | \(-0.646245\pi\) | ||||
−0.443450 | + | 0.896299i | \(0.646245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 91.8746i | − | 0.457087i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 115.824i | − | 0.570564i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 340.897 | − | 107.235i | 1.66291 | − | 0.523099i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −156.023 | − | 156.023i | −0.753733 | − | 0.753733i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 185.329i | 0.886744i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −242.205 | − | 242.205i | −1.14789 | − | 1.14789i | −0.986967 | − | 0.160925i | \(-0.948552\pi\) |
−0.160925 | − | 0.986967i | \(-0.551448\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 35.6864i | − | 0.167542i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −86.3689 | + | 27.1689i | −0.401716 | + | 0.126367i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 80.9557 | − | 80.9557i | 0.373068 | − | 0.373068i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.5248 | + | 11.5248i | 0.0526248 | + | 0.0526248i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −139.684 | − | 139.684i | −0.632052 | − | 0.632052i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −112.186 | + | 112.186i | −0.503076 | + | 0.503076i | −0.912392 | − | 0.409316i | \(-0.865767\pi\) |
0.409316 | + | 0.912392i | \(0.365767\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 152.634 | − | 106.573i | 0.678374 | − | 0.473660i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.50408i | − | 0.0154365i | −0.999970 | − | 0.00771824i | \(-0.997543\pi\) | ||
0.999970 | − | 0.00771824i | \(-0.00245682\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.5594 | − | 12.5594i | −0.0548445 | − | 0.0548445i | 0.679153 | − | 0.733997i | \(-0.262347\pi\) |
−0.733997 | + | 0.679153i | \(0.762347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 82.3327i | − | 0.356419i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 137.748 | + | 137.748i | 0.591192 | + | 0.591192i | 0.937953 | − | 0.346761i | \(-0.112719\pi\) |
−0.346761 | + | 0.937953i | \(0.612719\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 171.315 | − | 328.560i | 0.729001 | − | 1.39813i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 106.971i | − | 0.451355i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 93.2096i | 0.389998i | 0.980803 | + | 0.194999i | \(0.0624704\pi\) | ||||
−0.980803 | + | 0.194999i | \(0.937530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −180.914 | −0.750682 | −0.375341 | − | 0.926887i | \(-0.622474\pi\) | ||||
−0.375341 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −236.181 | −0.971939 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 108.290 | − | 34.0645i | 0.441999 | − | 0.139039i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −97.5821 | + | 97.5821i | −0.395069 | + | 0.395069i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 89.6199 | 0.359919 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −218.622 | + | 218.622i | −0.871005 | + | 0.871005i | −0.992582 | − | 0.121577i | \(-0.961205\pi\) |
0.121577 | + | 0.992582i | \(0.461205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 381.692 | 1.50866 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 59.3434 | − | 113.813i | 0.232719 | − | 0.446325i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −97.0001 | − | 97.0001i | −0.377432 | − | 0.377432i | 0.492743 | − | 0.870175i | \(-0.335994\pi\) |
−0.870175 | + | 0.492743i | \(0.835994\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 104.115 | − | 104.115i | 0.401989 | − | 0.401989i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 118.929 | − | 118.929i | 0.455665 | − | 0.455665i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 62.4735 | + | 62.4735i | 0.237542 | + | 0.237542i | 0.815831 | − | 0.578290i | \(-0.196280\pi\) |
−0.578290 | + | 0.815831i | \(0.696280\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −115.981 | + | 36.4839i | −0.437664 | + | 0.137675i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 155.360 | 0.581873 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −315.384 | + | 315.384i | −1.17243 | + | 1.17243i | −0.190804 | + | 0.981628i | \(0.561109\pi\) |
−0.981628 | + | 0.190804i | \(0.938891\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 113.916 | 0.420354 | 0.210177 | − | 0.977663i | \(-0.432596\pi\) | ||||
0.210177 | + | 0.977663i | \(0.432596\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 43.3509 | − | 43.3509i | 0.158795 | − | 0.158795i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −56.3410 | + | 317.061i | −0.204876 | + | 1.15295i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.5970 | 0.0960179 | 0.0480089 | − | 0.998847i | \(-0.484712\pi\) | ||||
0.0480089 | + | 0.998847i | \(0.484712\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 166.251 | 0.595880 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 335.487i | − | 1.19390i | −0.802278 | − | 0.596951i | \(-0.796379\pi\) | ||
0.802278 | − | 0.596951i | \(-0.203621\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 165.652i | − | 0.585342i | −0.956213 | − | 0.292671i | \(-0.905456\pi\) | ||
0.956213 | − | 0.292671i | \(-0.0945441\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −79.5090 | − | 41.4569i | −0.278979 | − | 0.145463i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −259.161 | − | 259.161i | −0.903001 | − | 0.903001i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 135.163i | 0.467690i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.3911 | − | 24.3911i | −0.0838182 | − | 0.0838182i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 331.620i | 1.13181i | 0.824471 | + | 0.565905i | \(0.191473\pi\) | ||||
−0.824471 | + | 0.565905i | \(0.808527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 160.119 | − | 307.088i | 0.542777 | − | 1.04097i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 186.717 | − | 186.717i | 0.628677 | − | 0.628677i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 200.973 | + | 200.973i | 0.672152 | + | 0.672152i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 65.6606 | + | 65.6606i | 0.218142 | + | 0.218142i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 65.4902 | − | 65.4902i | 0.216139 | − | 0.216139i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −137.863 | + | 264.403i | −0.452010 | + | 0.866896i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 164.676i | − | 0.536404i | −0.963363 | − | 0.268202i | \(-0.913570\pi\) | ||
0.963363 | − | 0.268202i | \(-0.0864295\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.3352 | + | 27.3352i | 0.0884635 | + | 0.0884635i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 573.207i | 1.84311i | 0.388250 | + | 0.921554i | \(0.373080\pi\) | ||||
−0.388250 | + | 0.921554i | \(0.626920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.3002 | + | 14.3002i | 0.0456875 | + | 0.0456875i | 0.729581 | − | 0.683894i | \(-0.239715\pi\) |
−0.683894 | + | 0.729581i | \(0.739715\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −169.291 | − | 88.2706i | −0.537433 | − | 0.280224i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 297.136i | − | 0.937338i | −0.883374 | − | 0.468669i | \(-0.844734\pi\) | ||
0.883374 | − | 0.468669i | \(-0.155266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 290.945i | 0.912053i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 215.115 | 0.670140 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 296.318 | 0.917392 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −196.609 | + | 137.278i | −0.604949 | + | 0.422393i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −41.9152 | + | 41.9152i | −0.128181 | + | 0.128181i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −380.023 | −1.15508 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −114.533 | + | 114.533i | −0.346020 | + | 0.346020i | −0.858625 | − | 0.512605i | \(-0.828681\pi\) |
0.512605 | + | 0.858625i | \(0.328681\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 213.811 | 0.642075 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 351.560 | − | 110.590i | 1.04943 | − | 0.330118i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 128.010 | + | 128.010i | 0.379850 | + | 0.379850i | 0.871048 | − | 0.491198i | \(-0.163441\pi\) |
−0.491198 | + | 0.871048i | \(0.663441\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −42.1120 | + | 42.1120i | −0.124224 | + | 0.124224i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −203.356 | + | 203.356i | −0.596353 | + | 0.596353i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −260.000 | − | 260.000i | −0.758016 | − | 0.758016i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −85.3818 | + | 163.751i | −0.247484 | + | 0.474641i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −402.112 | −1.15882 | −0.579412 | − | 0.815035i | \(-0.696718\pi\) | ||||
−0.579412 | + | 0.815035i | \(0.696718\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −183.939 | + | 183.939i | −0.527047 | + | 0.527047i | −0.919691 | − | 0.392644i | \(-0.871561\pi\) |
0.392644 | + | 0.919691i | \(0.371561\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 196.626 | 0.560187 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.3150 | + | 24.3150i | −0.0688810 | + | 0.0688810i | −0.740708 | − | 0.671827i | \(-0.765510\pi\) |
0.671827 | + | 0.740708i | \(0.265510\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 136.555 | − | 42.9558i | 0.384661 | − | 0.121002i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −131.639 | −0.368737 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 574.715 | 1.60088 | 0.800439 | − | 0.599414i | \(-0.204600\pi\) | ||||
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 153.994i | 0.426577i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 55.9944i | 0.154254i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.2275 | + | 57.9724i | −0.0828151 | + | 0.158829i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 380.075 | + | 380.075i | 1.03563 | + | 1.03563i | 0.999341 | + | 0.0362850i | \(0.0115524\pi\) |
0.0362850 | + | 0.999341i | \(0.488448\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 532.214i | − | 1.44231i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 88.1727 | + | 88.1727i | 0.237662 | + | 0.237662i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.18922i | 0.00318825i | 0.999999 | + | 0.00159413i | \(0.000507426\pi\) | ||||
−0.999999 | + | 0.00159413i | \(0.999493\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −123.421 | − | 95.0955i | −0.329121 | − | 0.253588i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −153.192 | + | 153.192i | −0.406345 | + | 0.406345i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 241.146 | + | 241.146i | 0.636269 | + | 0.636269i | 0.949633 | − | 0.313364i | \(-0.101456\pi\) |
−0.313364 | + | 0.949633i | \(0.601456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 130.159 | + | 130.159i | 0.341626 | + | 0.341626i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.5247 | + | 18.5247i | −0.0483675 | + | 0.0483675i | −0.730877 | − | 0.682509i | \(-0.760889\pi\) |
0.682509 | + | 0.730877i | \(0.260889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 315.048 | − | 99.1040i | 0.818306 | − | 0.257413i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 134.841i | 0.348425i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −420.008 | − | 420.008i | −1.07971 | − | 1.07971i | −0.996535 | − | 0.0831763i | \(-0.973494\pi\) |
−0.0831763 | − | 0.996535i | \(-0.526506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 610.275i | − | 1.56081i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.4307 | + | 26.4307i | 0.0672537 | + | 0.0672537i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 409.327 | − | 128.761i | 1.03627 | − | 0.325978i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 146.340i | − | 0.368615i | −0.982869 | − | 0.184307i | \(-0.940996\pi\) | ||
0.982869 | − | 0.184307i | \(-0.0590042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 91.9625i | 0.230482i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −132.278 | −0.329871 | −0.164936 | − | 0.986304i | \(-0.552742\pi\) | ||||
−0.164936 | + | 0.986304i | \(0.552742\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −214.148 | −0.531384 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −62.2128 | − | 197.772i | −0.153612 | − | 0.488326i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −261.532 | + | 261.532i | −0.642584 | + | 0.642584i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −306.287 | −0.748867 | −0.374433 | − | 0.927254i | \(-0.622163\pi\) | ||||
−0.374433 | + | 0.927254i | \(0.622163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −239.875 | + | 239.875i | −0.583637 | + | 0.583637i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −355.187 | −0.860016 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 107.876 | + | 342.932i | 0.259941 | + | 0.826343i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −124.843 | − | 124.843i | −0.299383 | − | 0.299383i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −347.061 | + | 347.061i | −0.828309 | + | 0.828309i | −0.987283 | − | 0.158974i | \(-0.949181\pi\) |
0.158974 | + | 0.987283i | \(0.449181\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −303.635 | + | 303.635i | −0.721222 | + | 0.721222i | −0.968854 | − | 0.247632i | \(-0.920348\pi\) |
0.247632 | + | 0.968854i | \(0.420348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −390.207 | − | 390.207i | −0.922475 | − | 0.922475i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 506.939 | + | 90.0819i | 1.19280 | + | 0.211957i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 305.817 | 0.716198 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −108.895 | + | 108.895i | −0.253835 | + | 0.253835i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −131.782 | −0.305760 | −0.152880 | − | 0.988245i | \(-0.548855\pi\) | ||||
−0.152880 | + | 0.988245i | \(0.548855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 322.889 | − | 322.889i | 0.745701 | − | 0.745701i | −0.227967 | − | 0.973669i | \(-0.573208\pi\) |
0.973669 | + | 0.227967i | \(0.0732080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −124.820 | − | 65.0824i | −0.286941 | − | 0.149615i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −426.335 | −0.975594 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −423.768 | −0.965304 | −0.482652 | − | 0.875812i | \(-0.660326\pi\) | ||||
−0.482652 | + | 0.875812i | \(0.660326\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 169.064i | − | 0.383364i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 758.450i | 1.71208i | 0.516912 | + | 0.856038i | \(0.327081\pi\) | ||||
−0.516912 | + | 0.856038i | \(0.672919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 187.007 | + | 594.488i | 0.420241 | + | 1.33593i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −119.944 | − | 119.944i | −0.268331 | − | 0.268331i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 516.303i | 1.14989i | 0.818191 | + | 0.574947i | \(0.194977\pi\) | ||||
−0.818191 | + | 0.574947i | \(0.805023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 650.999 | + | 650.999i | 1.44346 | + | 1.44346i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 190.878i | − | 0.421364i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 218.065 | + | 113.702i | 0.479263 | + | 0.249894i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −612.830 | + | 612.830i | −1.34099 | + | 1.34099i | −0.445905 | + | 0.895080i | \(0.647118\pi\) |
−0.895080 | + | 0.445905i | \(0.852882\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −298.536 | − | 298.536i | −0.650406 | − | 0.650406i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −193.692 | − | 193.692i | −0.420156 | − | 0.420156i | 0.465102 | − | 0.885257i | \(-0.346018\pi\) |
−0.885257 | + | 0.465102i | \(0.846018\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 159.340 | − | 159.340i | 0.344146 | − | 0.344146i | −0.513777 | − | 0.857924i | \(-0.671754\pi\) |
0.857924 | + | 0.513777i | \(0.171754\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −41.7534 | − | 132.732i | −0.0897922 | − | 0.285446i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 190.782i | − | 0.408528i | −0.978916 | − | 0.204264i | \(-0.934520\pi\) | ||
0.978916 | − | 0.204264i | \(-0.0654801\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −267.268 | − | 267.268i | −0.569867 | − | 0.569867i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 156.316i | 0.331880i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −164.936 | − | 164.936i | −0.348702 | − | 0.348702i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 62.9307 | − | 354.144i | 0.132486 | − | 0.745567i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 181.071i | 0.379605i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 246.542i | 0.514701i | 0.966318 | + | 0.257350i | \(0.0828494\pi\) | ||||
−0.966318 | + | 0.257350i | \(0.917151\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −275.410 | −0.572579 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 189.399 | 0.392131 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 63.9734 | − | 122.693i | 0.131904 | − | 0.252974i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −118.580 | + | 118.580i | −0.243491 | + | 0.243491i | −0.818293 | − | 0.574802i | \(-0.805079\pi\) |
0.574802 | + | 0.818293i | \(0.305079\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −212.284 | −0.434118 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 273.453 | − | 273.453i | 0.556930 | − | 0.556930i | −0.371502 | − | 0.928432i | \(-0.621157\pi\) |
0.928432 | + | 0.371502i | \(0.121157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 465.183 | 0.943576 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 425.251 | + | 221.731i | 0.859093 | + | 0.447941i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −103.814 | − | 103.814i | −0.208881 | − | 0.208881i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −458.148 | + | 458.148i | −0.918133 | + | 0.918133i | −0.996894 | − | 0.0787603i | \(-0.974904\pi\) |
0.0787603 | + | 0.996894i | \(0.474904\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −124.938 | + | 124.938i | −0.249377 | + | 0.249377i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 424.905 | + | 424.905i | 0.844742 | + | 0.844742i | 0.989471 | − | 0.144729i | \(-0.0462311\pi\) |
−0.144729 | + | 0.989471i | \(0.546231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 329.430 | + | 171.769i | 0.652337 | + | 0.340137i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 95.9769 | 0.189304 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −36.5107 | + | 36.5107i | −0.0717303 | + | 0.0717303i | −0.742062 | − | 0.670331i | \(-0.766152\pi\) |
0.670331 | + | 0.742062i | \(0.266152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 67.0526 | 0.131218 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −208.556 | + | 208.556i | −0.406541 | + | 0.406541i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −71.6953 | + | 137.502i | −0.139214 | + | 0.266995i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 954.596 | 1.84641 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 287.469 | 0.553891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 220.060i | − | 0.422381i | −0.977445 | − | 0.211190i | \(-0.932266\pi\) | ||
0.977445 | − | 0.211190i | \(-0.0677340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 558.669i | − | 1.06820i | −0.845421 | − | 0.534100i | \(-0.820650\pi\) | ||
0.845421 | − | 0.534100i | \(-0.179350\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −27.9570 | + | 157.329i | −0.0532515 | + | 0.299674i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 325.140 | + | 325.140i | 0.616964 | + | 0.616964i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 349.049i | 0.659828i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −364.705 | − | 364.705i | −0.686827 | − | 0.686827i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 685.546i | 1.28620i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 258.934 | + | 823.142i | 0.483989 | + | 1.53858i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −176.731 | + | 176.731i | −0.329108 | + | 0.329108i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 206.797 | + | 206.797i | 0.383669 | + | 0.383669i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −304.353 | − | 304.353i | −0.562575 | − | 0.562575i | 0.367463 | − | 0.930038i | \(-0.380226\pi\) |
−0.930038 | + | 0.367463i | \(0.880226\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −277.927 | + | 277.927i | −0.511835 | + | 0.511835i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −210.843 | − | 109.936i | −0.386868 | − | 0.201718i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 72.4546i | − | 0.132458i | −0.997804 | − | 0.0662290i | \(-0.978903\pi\) | ||
0.997804 | − | 0.0662290i | \(-0.0210968\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 314.012 | + | 314.012i | 0.571972 | + | 0.571972i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 324.974i | − | 0.589790i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −311.184 | − | 311.184i | −0.562721 | − | 0.562721i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −53.6980 | − | 170.704i | −0.0967532 | − | 0.307574i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 219.766i | − | 0.394553i | −0.980348 | − | 0.197276i | \(-0.936790\pi\) | ||
0.980348 | − | 0.197276i | \(-0.0632096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 173.689i | − | 0.310713i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 330.671 | 0.589431 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 102.644 | 0.182316 | 0.0911581 | − | 0.995836i | \(-0.470943\pi\) | ||||
0.0911581 | + | 0.995836i | \(0.470943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −211.833 | − | 110.452i | −0.374925 | − | 0.195491i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −150.353 | + | 150.353i | −0.265173 | + | 0.265173i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 146.493 | 0.257457 | 0.128729 | − | 0.991680i | \(-0.458910\pi\) | ||||
0.128729 | + | 0.991680i | \(0.458910\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 163.098 | − | 163.098i | 0.285635 | − | 0.285635i | −0.549716 | − | 0.835351i | \(-0.685264\pi\) |
0.835351 | + | 0.549716i | \(0.185264\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 449.585 | 0.784616 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −729.371 | − | 129.608i | −1.26847 | − | 0.225405i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −298.200 | − | 298.200i | −0.516811 | − | 0.516811i | 0.399794 | − | 0.916605i | \(-0.369082\pi\) |
−0.916605 | + | 0.399794i | \(0.869082\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −30.1951 | + | 30.1951i | −0.0521504 | + | 0.0521504i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 260.709 | − | 260.709i | 0.448724 | − | 0.448724i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −221.485 | − | 221.485i | −0.379906 | − | 0.379906i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 107.160 | + | 340.658i | 0.183180 | + | 0.582321i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 738.236 | 1.25764 | 0.628821 | − | 0.777550i | \(-0.283538\pi\) | ||||
0.628821 | + | 0.777550i | \(0.283538\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 227.141 | − | 227.141i | 0.385639 | − | 0.385639i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −210.910 | −0.356869 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −632.549 | + | 632.549i | −1.06669 | + | 1.06669i | −0.0690814 | + | 0.997611i | \(0.522007\pi\) |
−0.997611 | + | 0.0690814i | \(0.977993\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −158.454 | − | 503.720i | −0.266310 | − | 0.846589i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 219.990 | 0.368493 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 419.874 | 0.700958 | 0.350479 | − | 0.936571i | \(-0.386019\pi\) | ||||
0.350479 | + | 0.936571i | \(0.386019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 230.628i | 0.383741i | 0.981420 | + | 0.191871i | \(0.0614554\pi\) | ||||
−0.981420 | + | 0.191871i | \(0.938545\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 548.861i | − | 0.910217i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −214.264 | + | 67.4005i | −0.354155 | + | 0.111406i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −641.727 | − | 641.727i | −1.05721 | − | 1.05721i | −0.998261 | − | 0.0589500i | \(-0.981225\pi\) |
−0.0589500 | − | 0.998261i | \(-0.518775\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 144.370i | 0.237061i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 502.627 | + | 502.627i | 0.822630 | + | 0.822630i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 724.254i | − | 1.18149i | −0.806858 | − | 0.590746i | \(-0.798834\pi\) | ||
0.806858 | − | 0.590746i | \(-0.201166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −424.912 | + | 133.664i | −0.690914 | + | 0.217340i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −102.268 | + | 102.268i | −0.165750 | + | 0.165750i | −0.785108 | − | 0.619358i | \(-0.787393\pi\) |
0.619358 | + | 0.785108i | \(0.287393\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.61045 | + | 1.61045i | 0.00260170 | + | 0.00260170i | 0.708406 | − | 0.705805i | \(-0.249414\pi\) |
−0.705805 | + | 0.708406i | \(0.749414\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 429.527 | + | 429.527i | 0.691670 | + | 0.691670i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 451.950 | − | 451.950i | 0.725442 | − | 0.725442i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 215.323 | − | 586.738i | 0.344517 | − | 0.938780i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 231.005i | − | 0.368429i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 418.155 | + | 418.155i | 0.664794 | + | 0.664794i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 333.003i | − | 0.527738i | −0.964559 | − | 0.263869i | \(-0.915001\pi\) | ||
0.964559 | − | 0.263869i | \(-0.0849987\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 301.898 | + | 301.898i | 0.476932 | + | 0.476932i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −341.385 | + | 654.731i | −0.537614 | + | 1.03107i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 217.772i | 0.341871i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 213.192i | − | 0.333633i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 90.2646 | 0.140818 | 0.0704092 | − | 0.997518i | \(-0.477570\pi\) | ||||
0.0704092 | + | 0.997518i | \(0.477570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −177.970 | −0.276781 | −0.138391 | − | 0.990378i | \(-0.544193\pi\) | ||||
−0.138391 | + | 0.990378i | \(0.544193\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 107.655 | − | 33.8648i | 0.166907 | − | 0.0525036i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −591.289 | + | 591.289i | −0.913893 | + | 0.913893i | −0.996576 | − | 0.0826827i | \(-0.973651\pi\) |
0.0826827 | + | 0.996576i | \(0.473651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 892.209 | 1.37474 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −100.908 | + | 100.908i | −0.155004 | + | 0.155004i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −390.593 | −0.598152 | −0.299076 | − | 0.954229i | \(-0.596678\pi\) | ||||
−0.299076 | + | 0.954229i | \(0.596678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −69.3230 | + | 132.952i | −0.105837 | + | 0.202981i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 68.8496 | + | 68.8496i | 0.104794 | + | 0.104794i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 766.873 | − | 766.873i | 1.16369 | − | 1.16369i | 0.180032 | − | 0.983661i | \(-0.442380\pi\) |
0.983661 | − | 0.180032i | \(-0.0576201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 48.7607 | − | 48.7607i | 0.0737680 | − | 0.0737680i | −0.669260 | − | 0.743028i | \(-0.733389\pi\) |
0.743028 | + | 0.669260i | \(0.233389\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 174.109 | + | 174.109i | 0.262608 | + | 0.262608i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −351.896 | + | 110.695i | −0.529167 | + | 0.166459i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −669.294 | −1.00344 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 139.835 | − | 139.835i | 0.209021 | − | 0.209021i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −768.195 | −1.14485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 290.185 | − | 290.185i | 0.431181 | − | 0.431181i | −0.457849 | − | 0.889030i | \(-0.651380\pi\) |
0.889030 | + | 0.457849i | \(0.151380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −420.198 | + | 293.394i | −0.622516 | + | 0.434658i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −407.637 | −0.602123 | −0.301061 | − | 0.953605i | \(-0.597341\pi\) | ||||
−0.301061 | + | 0.953605i | \(0.597341\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −141.910 | −0.208998 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.36768i | 0.00641362i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 684.730i | 1.00253i | 0.865293 | + | 0.501267i | \(0.167132\pi\) | ||||
−0.865293 | + | 0.501267i | \(0.832868\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1206.62 | − | 629.148i | −1.76149 | − | 0.918464i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.6547 | + | 15.6547i | 0.0227871 | + | 0.0227871i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 233.239i | − | 0.338518i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −405.351 | − | 405.351i | −0.586616 | − | 0.586616i | 0.350098 | − | 0.936713i | \(-0.386148\pi\) |
−0.936713 | + | 0.350098i | \(0.886148\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 491.858i | − | 0.709751i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 327.440 | − | 627.986i | 0.471136 | − | 0.903577i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1040.86 | − | 1040.86i | 1.49335 | − | 1.49335i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −171.696 | − | 171.696i | −0.245631 | − | 0.245631i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −87.8312 | − | 87.8312i | −0.125294 | − | 0.125294i | 0.641679 | − | 0.766973i | \(-0.278238\pi\) |
−0.766973 | + | 0.641679i | \(0.778238\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 292.121 | − | 292.121i | 0.415535 | − | 0.415535i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −213.537 | + | 409.536i | −0.302889 | + | 0.580901i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 381.029i | − | 0.538938i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −286.699 | − | 286.699i | −0.404370 | − | 0.404370i | 0.475400 | − | 0.879770i | \(-0.342304\pi\) |
−0.879770 | + | 0.475400i | \(0.842304\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 639.048i | − | 0.898802i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −467.804 | − | 467.804i | −0.656107 | − | 0.656107i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −547.767 | − | 285.612i | −0.766108 | − | 0.399458i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 116.182i | − | 0.162038i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 170.890i | 0.237677i | 0.992914 | + | 0.118839i | \(0.0379171\pi\) | ||||
−0.992914 | + | 0.118839i | \(0.962083\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 159.039 | 0.220581 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 225.502 | 0.311897 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 98.7936 | − | 555.964i | 0.136267 | − | 0.766847i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 510.540 | − | 510.540i | 0.702256 | − | 0.702256i | −0.262638 | − | 0.964894i | \(-0.584593\pi\) |
0.964894 | + | 0.262638i | \(0.0845926\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −78.7983 | −0.108091 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −263.711 | + | 263.711i | −0.360754 | + | 0.360754i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.0813496 | −0.000110982 | −5.54908e−5 | − | 1.00000i | \(-0.500018\pi\) | ||||
−5.54908e−5 | 1.00000i | \(0.500018\pi\) | ||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −134.978 | + | 42.4599i | −0.183644 | + | 0.0577686i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 671.362 | + | 671.362i | 0.910939 | + | 0.910939i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.3702 | − | 37.3702i | 0.0505685 | − | 0.0505685i | −0.681370 | − | 0.731939i | \(-0.738616\pi\) |
0.731939 | + | 0.681370i | \(0.238616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 121.632 | − | 121.632i | 0.164145 | − | 0.164145i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −217.733 | − | 217.733i | −0.293046 | − | 0.293046i | 0.545236 | − | 0.838282i | \(-0.316440\pi\) |
−0.838282 | + | 0.545236i | \(0.816440\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 314.591 | − | 603.345i | 0.422270 | − | 0.809859i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 535.391 | 0.716722 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 625.781 | − | 625.781i | 0.835488 | − | 0.835488i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 321.722 | 0.428391 | 0.214196 | − | 0.976791i | \(-0.431287\pi\) | ||||
0.214196 | + | 0.976791i | \(0.431287\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 272.503 | − | 272.503i | 0.361890 | − | 0.361890i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 730.398 | − | 229.760i | 0.967414 | − | 0.304318i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 794.309 | 1.04929 | 0.524643 | − | 0.851322i | \(-0.324199\pi\) | ||||
0.524643 | + | 0.851322i | \(0.324199\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −475.761 | −0.626826 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 413.877i | − | 0.543859i | −0.962317 | − | 0.271929i | \(-0.912338\pi\) | ||
0.962317 | − | 0.271929i | \(-0.0876617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 243.867i | 0.319616i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 354.519 | − | 679.921i | 0.463423 | − | 0.888785i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 469.778 | + | 469.778i | 0.612488 | + | 0.612488i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1059.37i | − | 1.37760i | −0.724952 | − | 0.688799i | \(-0.758138\pi\) | ||
0.724952 | − | 0.688799i | \(-0.241862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 120.906 | + | 120.906i | 0.156817 | + | 0.156817i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1328.27i | 1.71833i | 0.511700 | + | 0.859164i | \(0.329016\pi\) | ||||
−0.511700 | + | 0.859164i | \(0.670984\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 457.644 | − | 319.540i | 0.590508 | − | 0.412310i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −129.775 | + | 129.775i | −0.167020 | + | 0.167020i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −727.141 | − | 727.141i | −0.933429 | − | 0.933429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 260.774 | + | 260.774i | 0.333898 | + | 0.333898i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −327.407 | + | 327.407i | −0.418145 | + | 0.418145i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −598.144 | + | 188.157i | −0.761967 | + | 0.239691i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 126.631i | 0.160903i | 0.996759 | + | 0.0804515i | \(0.0256362\pi\) | ||||
−0.996759 | + | 0.0804515i | \(0.974364\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −77.8703 | − | 77.8703i | −0.0986950 | − | 0.0986950i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 245.012i | 0.309750i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −404.480 | − | 404.480i | −0.510064 | − | 0.510064i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 144.565 | − | 45.4756i | 0.181843 | − | 0.0572020i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 123.005i | − | 0.154335i | −0.997018 | − | 0.0771677i | \(-0.975412\pi\) | ||
0.997018 | − | 0.0771677i | \(-0.0245877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1526.27i | − | 1.91023i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 928.124 | 1.15871 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −168.433 | −0.209754 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 227.980 | + | 724.741i | 0.283205 | + | 0.900299i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 393.112 | − | 393.112i | 0.487128 | − | 0.487128i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1294.86 | 1.60057 | 0.800285 | − | 0.599620i | \(-0.204682\pi\) | ||||
0.800285 | + | 0.599620i | \(0.204682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −596.423 | + | 596.423i | −0.735416 | + | 0.735416i | −0.971687 | − | 0.236271i | \(-0.924075\pi\) |
0.236271 | + | 0.971687i | \(0.424075\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −141.991 | −0.174651 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −255.526 | − | 812.308i | −0.313529 | − | 0.996697i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 184.227 | + | 184.227i | 0.225492 | + | 0.225492i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 258.980 | − | 258.980i | 0.316214 | − | 0.316214i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −113.969 | + | 113.969i | −0.138817 | + | 0.138817i | −0.773100 | − | 0.634284i | \(-0.781295\pi\) |
0.634284 | + | 0.773100i | \(0.281295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 704.375 | + | 704.375i | 0.855862 | + | 0.855862i | 0.990848 | − | 0.134985i | \(-0.0430987\pi\) |
−0.134985 | + | 0.990848i | \(0.543099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 70.2265 | − | 395.202i | 0.0851231 | − | 0.479033i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −307.918 | −0.372331 | −0.186166 | − | 0.982518i | \(-0.559606\pi\) | ||||
−0.186166 | + | 0.982518i | \(0.559606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −151.064 | + | 151.064i | −0.182224 | + | 0.182224i | −0.792324 | − | 0.610100i | \(-0.791129\pi\) |
0.610100 | + | 0.792324i | \(0.291129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −33.1519 | −0.0398940 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 330.642 | − | 330.642i | 0.396929 | − | 0.396929i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −628.464 | − | 327.689i | −0.752652 | − | 0.392442i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −457.684 | −0.546815 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −131.699 | −0.156972 | −0.0784859 | − | 0.996915i | \(-0.525009\pi\) | ||||
−0.0784859 | + | 0.996915i | \(0.525009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 330.830i | 0.393377i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 418.169i | 0.496048i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 115.528 | + | 367.257i | 0.136719 | + | 0.434624i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 162.890 | + | 162.890i | 0.192315 | + | 0.192315i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 206.478i | 0.243201i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −601.632 | − | 601.632i | −0.706970 | − | 0.706970i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 125.517i | 0.147147i | 0.997290 | + | 0.0735737i | \(0.0234404\pi\) | ||||
−0.997290 | + | 0.0735737i | \(0.976560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −474.989 | − | 247.665i | −0.555542 | − | 0.289666i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −146.932 | + | 146.932i | −0.171449 | + | 0.171449i | −0.787616 | − | 0.616167i | \(-0.788685\pi\) |
0.616167 | + | 0.787616i | \(0.288685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −117.232 | − | 117.232i | −0.136475 | − | 0.136475i | 0.635569 | − | 0.772044i | \(-0.280766\pi\) |
−0.772044 | + | 0.635569i | \(0.780766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 323.033 | + | 323.033i | 0.375183 | + | 0.375183i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 164.801 | − | 164.801i | 0.190963 | − | 0.190963i | −0.605149 | − | 0.796112i | \(-0.706886\pi\) |
0.796112 | + | 0.605149i | \(0.206886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 346.027 | + | 1100.01i | 0.400031 | + | 1.27168i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 168.474i | − | 0.194318i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 781.679 | + | 781.679i | 0.899515 | + | 0.899515i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 706.989i | 0.811698i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −145.713 | − | 145.713i | −0.166911 | − | 0.166911i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −635.674 | + | 82.3990i | −0.726485 | + | 0.0941703i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 362.710i | 0.413580i | 0.978385 | + | 0.206790i | \(0.0663017\pi\) | ||||
−0.978385 | + | 0.206790i | \(0.933698\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 413.350i | − | 0.470250i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −900.515 | −1.02215 | −0.511075 | − | 0.859536i | \(-0.670753\pi\) | ||||
−0.511075 | + | 0.859536i | \(0.670753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −374.768 | −0.424426 | −0.212213 | − | 0.977223i | \(-0.568067\pi\) | ||||
−0.212213 | + | 0.977223i | \(0.568067\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −199.581 | + | 382.771i | −0.225516 | + | 0.432509i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 493.146 | − | 493.146i | 0.555971 | − | 0.555971i | −0.372187 | − | 0.928158i | \(-0.621392\pi\) |
0.928158 | + | 0.372187i | \(0.121392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 757.281 | 0.851835 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 377.679 | − | 377.679i | 0.423882 | − | 0.423882i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1066.25 | −1.19401 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −888.996 | − | 463.533i | −0.993291 | − | 0.517914i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −250.504 | − | 250.504i | −0.279269 | − | 0.279269i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 356.584 | − | 356.584i | 0.396645 | − | 0.396645i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −354.126 | + | 354.126i | −0.393036 | + | 0.393036i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −81.8430 | − | 81.8430i | −0.0906345 | − | 0.0906345i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1398.03 | − | 728.951i | −1.54479 | − | 0.805470i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 107.286 | 0.118286 | 0.0591432 | − | 0.998250i | \(-0.481163\pi\) | ||||
0.0591432 | + | 0.998250i | \(0.481163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 391.240 | − | 391.240i | 0.430407 | − | 0.430407i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1193.83 | 1.31047 | 0.655233 | − | 0.755427i | \(-0.272570\pi\) | ||||
0.655233 | + | 0.755427i | \(0.272570\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −654.886 | + | 654.886i | −0.717291 | + | 0.717291i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 171.840 | − | 329.567i | 0.187803 | − | 0.360182i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 153.777 | 0.167695 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1001.83 | −1.09013 | −0.545064 | − | 0.838394i | \(-0.683495\pi\) | ||||
−0.545064 | + | 0.838394i | \(0.683495\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 205.261i | 0.222868i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 274.613i | 0.297522i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 588.565 | − | 410.953i | 0.636287 | − | 0.444273i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 163.301 | + | 163.301i | 0.176161 | + | 0.176161i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 527.162i | 0.567451i | 0.958905 | + | 0.283726i | \(0.0915705\pi\) | ||||
−0.958905 | + | 0.283726i | \(0.908429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −230.985 | − | 230.985i | −0.248104 | − | 0.248104i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 714.476i | − | 0.765784i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 398.029 | + | 1265.32i | 0.425699 | + | 1.35328i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 129.020 | − | 129.020i | 0.137694 | − | 0.137694i | −0.634900 | − | 0.772594i | \(-0.718959\pi\) |
0.772594 | + | 0.634900i | \(0.218959\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.8245 | − | 17.8245i | −0.0189825 | − | 0.0189825i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 381.136 | + | 381.136i | 0.405033 | + | 0.405033i | 0.880002 | − | 0.474969i | \(-0.157541\pi\) |
−0.474969 | + | 0.880002i | \(0.657541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1497.57 | + | 1497.57i | −1.58809 | + | 1.58809i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 466.055 | + | 243.007i | 0.493180 | + | 0.257150i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1038.55i | 1.09667i | 0.836259 | + | 0.548334i | \(0.184738\pi\) | ||||
−0.836259 | + | 0.548334i | \(0.815262\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −88.6854 | − | 88.6854i | −0.0934514 | − | 0.0934514i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 370.367i | 0.389450i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 871.876 | + | 871.876i | 0.914875 | + | 0.914875i | 0.996651 | − | 0.0817757i | \(-0.0260591\pi\) |
−0.0817757 | + | 0.996651i | \(0.526059\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 541.166 | + | 1720.34i | 0.566666 | + | 1.80141i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 362.650i | − | 0.378944i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1395.62i | 1.45528i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −462.530 | −0.481300 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1285.10 | 1.33448 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −151.888 | − | 79.1962i | −0.157397 | − | 0.0820686i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 866.285 | − | 866.285i | 0.895848 | − | 0.895848i | −0.0992181 | − | 0.995066i | \(-0.531634\pi\) |
0.995066 | + | 0.0992181i | \(0.0316342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −369.346 | −0.381162 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1165.60 | − | 1165.60i | 1.20041 | − | 1.20041i | 0.226371 | − | 0.974041i | \(-0.427314\pi\) |
0.974041 | − | 0.226371i | \(-0.0726862\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −726.347 | −0.746503 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 245.064 | − | 171.110i | 0.251347 | − | 0.175498i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 765.976 | + | 765.976i | 0.784008 | + | 0.784008i | 0.980504 | − | 0.196497i | \(-0.0629565\pi\) |
−0.196497 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1135.27 | + | 1135.27i | −1.15963 | + | 1.15963i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −250.403 | + | 250.403i | −0.255252 | + | 0.255252i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −212.053 | − | 212.053i | −0.215720 | − | 0.215720i | 0.590972 | − | 0.806692i | \(-0.298744\pi\) |
−0.806692 | + | 0.590972i | \(0.798744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −253.872 | − | 807.050i | −0.257738 | − | 0.819340i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 473.681 | 0.479920 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 379.421 | − | 379.421i | 0.383641 | − | 0.383641i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1530.97 | 1.54487 | 0.772435 | − | 0.635094i | \(-0.219039\pi\) | ||||
0.772435 | + | 0.635094i | \(0.219039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 142.760 | − | 142.760i | 0.143766 | − | 0.143766i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 264.803 | + | 841.798i | 0.266133 | + | 0.846028i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −834.620 | −0.837131 | −0.418565 | − | 0.908187i | \(-0.637467\pi\) | ||||
−0.418565 | + | 0.908187i | \(0.637467\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −588.616 | −0.589206 |
(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 | 640.3.t.a.417.10 | 44 | ||
4.3 | odd | 2 | 640.3.t.b.417.13 | 44 | |||
5.3 | odd | 4 | 640.3.i.a.33.10 | 44 | |||
8.3 | odd | 2 | 80.3.t.a.77.21 | yes | 44 | ||
8.5 | even | 2 | 320.3.t.a.17.13 | 44 | |||
16.3 | odd | 4 | 80.3.i.a.37.13 | yes | 44 | ||
16.5 | even | 4 | 640.3.i.a.97.13 | 44 | |||
16.11 | odd | 4 | 640.3.i.b.97.10 | 44 | |||
16.13 | even | 4 | 320.3.i.a.177.10 | 44 | |||
20.3 | even | 4 | 640.3.i.b.33.13 | 44 | |||
40.3 | even | 4 | 80.3.i.a.13.13 | ✓ | 44 | ||
40.13 | odd | 4 | 320.3.i.a.273.13 | 44 | |||
40.19 | odd | 2 | 400.3.t.b.157.2 | 44 | |||
40.27 | even | 4 | 400.3.i.b.93.10 | 44 | |||
80.3 | even | 4 | 80.3.t.a.53.21 | yes | 44 | ||
80.13 | odd | 4 | 320.3.t.a.113.13 | 44 | |||
80.19 | odd | 4 | 400.3.i.b.357.10 | 44 | |||
80.43 | even | 4 | 640.3.t.b.353.13 | 44 | |||
80.53 | odd | 4 | inner | 640.3.t.a.353.10 | 44 | ||
80.67 | even | 4 | 400.3.t.b.293.2 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.i.a.13.13 | ✓ | 44 | 40.3 | even | 4 | ||
80.3.i.a.37.13 | yes | 44 | 16.3 | odd | 4 | ||
80.3.t.a.53.21 | yes | 44 | 80.3 | even | 4 | ||
80.3.t.a.77.21 | yes | 44 | 8.3 | odd | 2 | ||
320.3.i.a.177.10 | 44 | 16.13 | even | 4 | |||
320.3.i.a.273.13 | 44 | 40.13 | odd | 4 | |||
320.3.t.a.17.13 | 44 | 8.5 | even | 2 | |||
320.3.t.a.113.13 | 44 | 80.13 | odd | 4 | |||
400.3.i.b.93.10 | 44 | 40.27 | even | 4 | |||
400.3.i.b.357.10 | 44 | 80.19 | odd | 4 | |||
400.3.t.b.157.2 | 44 | 40.19 | odd | 2 | |||
400.3.t.b.293.2 | 44 | 80.67 | even | 4 | |||
640.3.i.a.33.10 | 44 | 5.3 | odd | 4 | |||
640.3.i.a.97.13 | 44 | 16.5 | even | 4 | |||
640.3.i.b.33.13 | 44 | 20.3 | even | 4 | |||
640.3.i.b.97.10 | 44 | 16.11 | odd | 4 | |||
640.3.t.a.353.10 | 44 | 80.53 | odd | 4 | inner | ||
640.3.t.a.417.10 | 44 | 1.1 | even | 1 | trivial | ||
640.3.t.b.353.13 | 44 | 80.43 | even | 4 | |||
640.3.t.b.417.13 | 44 | 4.3 | odd | 2 |