Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(671,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.h (of order \(2\), degree \(1\), 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.20 | ||
Character | \(\chi\) | \(=\) | 2240.671 |
Dual form | 2240.2.h.e.671.19 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.59614i | 1.49888i | 0.662070 | + | 0.749442i | \(0.269678\pi\) | ||||
−0.662070 | + | 0.749442i | \(0.730322\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.28275 | − | 1.33755i | 0.862799 | − | 0.505547i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.73996 | −1.24665 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.05894 | −0.922306 | −0.461153 | − | 0.887321i | \(-0.652564\pi\) | ||||
−0.461153 | + | 0.887321i | \(0.652564\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.11716 | 1.69660 | 0.848298 | − | 0.529519i | \(-0.177628\pi\) | ||||
0.848298 | + | 0.529519i | \(0.177628\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.59614i | − | 0.670321i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.25746i | − | 0.304980i | −0.988305 | − | 0.152490i | \(-0.951271\pi\) | ||
0.988305 | − | 0.152490i | \(-0.0487292\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.37720i | 0.774784i | 0.921915 | + | 0.387392i | \(0.126624\pi\) | ||||
−0.921915 | + | 0.387392i | \(0.873376\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.47247 | + | 5.92635i | 0.757756 | + | 1.29324i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.24285i | 0.884695i | 0.896844 | + | 0.442348i | \(0.145854\pi\) | ||||
−0.896844 | + | 0.442348i | \(0.854146\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.92104i | − | 0.369704i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.52586i | 0.283345i | 0.989914 | + | 0.141673i | \(0.0452480\pi\) | ||||
−0.989914 | + | 0.141673i | \(0.954752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.46731 | −1.70038 | −0.850190 | − | 0.526476i | \(-0.823513\pi\) | ||||
−0.850190 | + | 0.526476i | \(0.823513\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 7.94145i | − | 1.38243i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.28275 | + | 1.33755i | −0.385856 | + | 0.226087i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.12779i | 0.514206i | 0.966384 | + | 0.257103i | \(0.0827680\pi\) | ||||
−0.966384 | + | 0.257103i | \(0.917232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.8810i | 2.54300i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.19570i | − | 0.499085i | −0.968364 | − | 0.249543i | \(-0.919720\pi\) | ||
0.968364 | − | 0.249543i | \(-0.0802803\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.7755 | 1.64325 | 0.821623 | − | 0.570031i | \(-0.193069\pi\) | ||||
0.821623 | + | 0.570031i | \(0.193069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.73996 | 0.557520 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.89284 | 1.15129 | 0.575645 | − | 0.817700i | \(-0.304751\pi\) | ||||
0.575645 | + | 0.817700i | \(0.304751\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.42191 | − | 6.10660i | 0.488845 | − | 0.872371i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.26456 | 0.457129 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.5951i | 1.73007i | 0.501710 | + | 0.865036i | \(0.332704\pi\) | ||||
−0.501710 | + | 0.865036i | \(0.667296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.05894 | 0.412468 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.76770 | −1.16131 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.5828i | 1.89852i | 0.314497 | + | 0.949259i | \(0.398164\pi\) | ||||
−0.314497 | + | 0.949259i | \(0.601836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.274335 | −0.0351250 | −0.0175625 | − | 0.999846i | \(-0.505591\pi\) | ||||
−0.0175625 | + | 0.999846i | \(0.505591\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.53740 | + | 5.00239i | −1.07561 | + | 0.630242i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.11716 | −0.758741 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7513 | −1.31348 | −0.656740 | − | 0.754117i | \(-0.728065\pi\) | ||||
−0.656740 | + | 0.754117i | \(0.728065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.0150 | −1.32606 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.23258i | 0.858350i | 0.903221 | + | 0.429175i | \(0.141196\pi\) | ||||
−0.903221 | + | 0.429175i | \(0.858804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.742408i | 0.0868922i | 0.999056 | + | 0.0434461i | \(0.0138337\pi\) | ||||
−0.999056 | + | 0.0434461i | \(0.986166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.59614i | 0.299777i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.98281 | + | 4.09149i | −0.795765 | + | 0.466269i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.1284i | 1.13953i | 0.821807 | + | 0.569765i | \(0.192966\pi\) | ||||
−0.821807 | + | 0.569765i | \(0.807034\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.23258 | −0.692509 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.15502i | 0.675601i | 0.941218 | + | 0.337801i | \(0.109683\pi\) | ||||
−0.941218 | + | 0.337801i | \(0.890317\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.25746i | 0.136391i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.96135 | −0.424702 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.78158i | 0.612846i | 0.951895 | + | 0.306423i | \(0.0991322\pi\) | ||||
−0.951895 | + | 0.306423i | \(0.900868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9640 | − | 8.18202i | 1.46382 | − | 0.857709i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 24.5785i | − | 2.54867i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 3.37720i | − | 0.346494i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.3036i | − | 1.45231i | −0.687533 | − | 0.726153i | \(-0.741306\pi\) | ||
0.687533 | − | 0.726153i | \(-0.258694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.4403 | 1.14980 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.31463 | 0.230314 | 0.115157 | − | 0.993347i | \(-0.463263\pi\) | ||||
0.115157 | + | 0.993347i | \(0.463263\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.8344 | 1.36315 | 0.681573 | − | 0.731750i | \(-0.261296\pi\) | ||||
0.681573 | + | 0.731750i | \(0.261296\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.47247 | − | 5.92635i | −0.338879 | − | 0.578353i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6267 | −1.31734 | −0.658672 | − | 0.752430i | \(-0.728882\pi\) | ||||
−0.658672 | + | 0.752430i | \(0.728882\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.26068i | − | 0.695447i | −0.937597 | − | 0.347723i | \(-0.886955\pi\) | ||
0.937597 | − | 0.347723i | \(-0.113045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.12020 | −0.770736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.04766 | −0.851133 | −0.425566 | − | 0.904927i | \(-0.639925\pi\) | ||||
−0.425566 | + | 0.904927i | \(0.639925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.24285i | − | 0.395648i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.8779 | −2.11507 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.68192 | − | 2.87048i | −0.154182 | − | 0.263136i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.64287 | −0.149352 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.29651 | 0.748071 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 9.27159i | − | 0.822721i | −0.911473 | − | 0.411360i | \(-0.865054\pi\) | ||
0.911473 | − | 0.411360i | \(-0.134946\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 27.9747i | 2.46303i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 9.14476i | − | 0.798981i | −0.916737 | − | 0.399490i | \(-0.869187\pi\) | ||
0.916737 | − | 0.399490i | \(-0.130813\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.51718 | + | 7.70932i | 0.391689 | + | 0.668483i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.92104i | 0.165337i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.7481 | −1.00371 | −0.501853 | − | 0.864953i | \(-0.667348\pi\) | ||||
−0.501853 | + | 0.864953i | \(0.667348\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.2894i | − | 0.957552i | −0.877937 | − | 0.478776i | \(-0.841081\pi\) | ||
0.877937 | − | 0.478776i | \(-0.158919\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.4910i | 1.72565i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −18.7121 | −1.56478 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.52586i | − | 0.126716i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.8536 | + | 8.88378i | 1.30758 | + | 0.732721i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 18.6432i | − | 1.52731i | −0.645624 | − | 0.763655i | \(-0.723403\pi\) | ||
0.645624 | − | 0.763655i | \(-0.276597\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.29824i | 0.268407i | 0.990954 | + | 0.134204i | \(0.0428476\pi\) | ||||
−0.990954 | + | 0.134204i | \(0.957152\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.70286i | 0.380204i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.46731 | 0.760433 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.308165 | 0.0245943 | 0.0122971 | − | 0.999924i | \(-0.496086\pi\) | ||||
0.0122971 | + | 0.999924i | \(0.496086\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −32.6987 | −2.59318 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.67503 | + | 9.68537i | 0.447255 | + | 0.763314i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.8164 | −1.00386 | −0.501929 | − | 0.864909i | \(-0.667376\pi\) | ||||
−0.501929 | + | 0.864909i | \(0.667376\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.94145i | 0.618241i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.34267 | 0.645575 | 0.322788 | − | 0.946471i | \(-0.395380\pi\) | ||||
0.322788 | + | 0.946471i | \(0.395380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 24.4197 | 1.87844 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 12.6306i | − | 0.965887i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.924877 | −0.0703171 | −0.0351585 | − | 0.999382i | \(-0.511194\pi\) | ||||
−0.0351585 | + | 0.999382i | \(0.511194\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.28275 | − | 1.33755i | 0.172560 | − | 0.101109i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −37.8590 | −2.84566 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.99825 | 0.224100 | 0.112050 | − | 0.993703i | \(-0.464258\pi\) | ||||
0.112050 | + | 0.993703i | \(0.464258\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.52021 | 0.112997 | 0.0564983 | − | 0.998403i | \(-0.482006\pi\) | ||||
0.0564983 | + | 0.998403i | \(0.482006\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.712214i | − | 0.0526484i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.12779i | − | 0.229960i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.84651i | 0.281285i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.56949 | − | 4.38526i | −0.186903 | − | 0.318981i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.77816i | 0.345736i | 0.984945 | + | 0.172868i | \(0.0553034\pi\) | ||||
−0.984945 | + | 0.172868i | \(0.944697\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3979 | 1.03638 | 0.518191 | − | 0.855265i | \(-0.326606\pi\) | ||||
0.518191 | + | 0.855265i | \(0.326606\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 15.8810i | − | 1.13726i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.8023i | 1.48210i | 0.671449 | + | 0.741050i | \(0.265672\pi\) | ||||
−0.671449 | + | 0.741050i | \(0.734328\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.94052 | 0.350224 | 0.175112 | − | 0.984549i | \(-0.443971\pi\) | ||||
0.175112 | + | 0.984549i | \(0.443971\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 27.9119i | − | 1.96875i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.04092 | + | 3.48316i | 0.143244 | + | 0.244470i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.19570i | 0.223198i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 15.8681i | − | 1.10291i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.3307i | − | 0.714588i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.89937 | 0.337287 | 0.168643 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168643 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −18.7768 | −1.28657 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7755 | −0.734882 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.6115 | + | 12.6630i | −1.46709 | + | 0.859622i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.92740 | −0.130241 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.69211i | − | 0.517428i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.08814 | 0.206797 | 0.103399 | − | 0.994640i | \(-0.467028\pi\) | ||||
0.103399 | + | 0.994640i | \(0.467028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.73996 | −0.249331 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.04747i | 0.135896i | 0.997689 | + | 0.0679478i | \(0.0216451\pi\) | ||||
−0.997689 | + | 0.0679478i | \(0.978355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.06904 | 0.599299 | 0.299649 | − | 0.954049i | \(-0.403130\pi\) | ||||
0.299649 | + | 0.954049i | \(0.403130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.6221 | − | 18.1284i | −0.698883 | − | 1.19276i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8301 | −0.840529 | −0.420265 | − | 0.907402i | \(-0.638063\pi\) | ||||
−0.420265 | + | 0.907402i | \(0.638063\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.89284 | −0.514872 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.2947 | −1.70802 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.4982i | 0.937811i | 0.883248 | + | 0.468905i | \(0.155351\pi\) | ||||
−0.883248 | + | 0.468905i | \(0.844649\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.632410i | 0.0407371i | 0.999793 | + | 0.0203686i | \(0.00648396\pi\) | ||||
−0.999793 | + | 0.0203686i | \(0.993516\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 21.9438i | − | 1.40770i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.42191 | + | 6.10660i | −0.218618 | + | 0.390136i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.6589i | 1.31449i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.9793 | −1.01265 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.77158i | − | 0.616777i | −0.951261 | − | 0.308388i | \(-0.900210\pi\) | ||
0.951261 | − | 0.308388i | \(-0.0997897\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 12.9786i | − | 0.815960i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.26456 | −0.204434 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.31038i | − | 0.206496i | −0.994656 | − | 0.103248i | \(-0.967077\pi\) | ||
0.994656 | − | 0.103248i | \(-0.0329235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.18359 | + | 7.13998i | 0.259955 | + | 0.443657i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 5.70666i | − | 0.353233i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2314i | 1.74082i | 0.492324 | + | 0.870412i | \(0.336148\pi\) | ||||
−0.492324 | + | 0.870412i | \(0.663852\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 12.5951i | − | 0.773711i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0098 | −0.918585 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 28.0436 | 1.70985 | 0.854925 | − | 0.518751i | \(-0.173603\pi\) | ||||
0.854925 | + | 0.518751i | \(0.173603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.79282 | 0.534126 | 0.267063 | − | 0.963679i | \(-0.413947\pi\) | ||||
0.267063 | + | 0.963679i | \(0.413947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.2417 | + | 36.2525i | 1.28561 | + | 2.19410i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.05894 | −0.184461 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 18.3990i | − | 1.10549i | −0.833351 | − | 0.552744i | \(-0.813581\pi\) | ||
0.833351 | − | 0.552744i | \(-0.186419\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 35.4074 | 2.11978 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.1469 | 1.85807 | 0.929035 | − | 0.369991i | \(-0.120639\pi\) | ||||
0.929035 | + | 0.369991i | \(0.120639\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.8362i | 1.77358i | 0.462172 | + | 0.886790i | \(0.347070\pi\) | ||||
−0.462172 | + | 0.886790i | \(0.652930\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 8.76770 | 0.519354 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.27442 | − | 7.29500i | −0.252311 | − | 0.430610i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.4188 | 0.906987 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 37.1341 | 2.17684 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.5550 | −0.967156 | −0.483578 | − | 0.875301i | \(-0.660663\pi\) | ||||
−0.483578 | + | 0.875301i | \(0.660663\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 14.5828i | − | 0.849043i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.87635i | 0.340981i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.9542i | 1.50097i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.5978 | − | 14.4128i | 1.41779 | − | 0.830738i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00911i | 0.345215i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.274335 | 0.0157084 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.4879i | 1.28345i | 0.766933 | + | 0.641727i | \(0.221782\pi\) | ||||
−0.766933 | + | 0.641727i | \(0.778218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.9161i | 2.04320i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.02754 | −0.171676 | −0.0858380 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858380 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.0675i | 1.30385i | 0.758282 | + | 0.651926i | \(0.226039\pi\) | ||||
−0.758282 | + | 0.651926i | \(0.773961\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.53740 | − | 5.00239i | 0.481028 | − | 0.281853i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 10.8809i | − | 0.611135i | −0.952170 | − | 0.305567i | \(-0.901154\pi\) | ||
0.952170 | − | 0.305567i | \(-0.0988462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.66752i | − | 0.261331i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 35.3769i | − | 1.97455i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.24671 | 0.236293 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.11716 | 0.339319 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.8498 | 1.04239 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.0174 | − | 10.5571i | 0.993332 | − | 0.582031i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.3053 | −1.83062 | −0.915312 | − | 0.402745i | \(-0.868056\pi\) | ||||
−0.915312 | + | 0.402745i | \(0.868056\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 11.6978i | − | 0.641037i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.7513 | 0.587406 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.3149 | 0.779783 | 0.389892 | − | 0.920861i | \(-0.372512\pi\) | ||||
0.389892 | + | 0.920861i | \(0.372512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 23.4890i | − | 1.27575i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.9600 | 1.56827 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.356507 | − | 18.5168i | −0.0192496 | − | 0.999815i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.0150 | 0.593030 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.7204 | −1.05865 | −0.529324 | − | 0.848420i | \(-0.677554\pi\) | ||||
−0.529324 | + | 0.848420i | \(0.677554\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.99879 | −0.535223 | −0.267612 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267612 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 11.7513i | − | 0.627239i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 37.0563i | − | 1.97231i | −0.165839 | − | 0.986153i | \(-0.553033\pi\) | ||
0.165839 | − | 0.986153i | \(-0.446967\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.23258i | − | 0.383866i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.45217 | − | 4.36651i | 0.394411 | − | 0.231100i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.8233i | − | 0.782343i | −0.920318 | − | 0.391172i | \(-0.872070\pi\) | ||
0.920318 | − | 0.391172i | \(-0.127930\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.59449 | 0.399710 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.26512i | − | 0.223861i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 0.742408i | − | 0.0388594i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.3172 | 1.47814 | 0.739072 | − | 0.673626i | \(-0.235264\pi\) | ||||
0.739072 | + | 0.673626i | \(0.235264\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.9518i | 0.622186i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.8466 | + | 28.7515i | 0.874632 | + | 1.49270i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.43536i | 0.436767i | 0.975863 | + | 0.218383i | \(0.0700783\pi\) | ||||
−0.975863 | + | 0.218383i | \(0.929922\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 2.59614i | − | 0.134064i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.33394i | 0.480722i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1855 | −0.523196 | −0.261598 | − | 0.965177i | \(-0.584249\pi\) | ||||
−0.261598 | + | 0.965177i | \(0.584249\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.0704 | 1.23316 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 37.5763 | 1.92006 | 0.960031 | − | 0.279895i | \(-0.0902998\pi\) | ||||
0.960031 | + | 0.279895i | \(0.0902998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.98281 | − | 4.09149i | 0.355877 | − | 0.208522i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −40.2999 | −2.04856 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 4.88157i | − | 0.247505i | −0.992313 | − | 0.123753i | \(-0.960507\pi\) | ||
0.992313 | − | 0.123753i | \(-0.0394929\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.33523 | 0.269814 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.7411 | 1.19758 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 10.1284i | − | 0.509614i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.4288 | 1.12567 | 0.562835 | − | 0.826569i | \(-0.309711\pi\) | ||||
0.562835 | + | 0.826569i | \(0.309711\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −20.0145 | + | 11.7273i | −1.00198 | + | 0.587097i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.25212 | 0.212341 | 0.106170 | − | 0.994348i | \(-0.466141\pi\) | ||||
0.106170 | + | 0.994348i | \(0.466141\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −57.9131 | −2.88486 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.23258 | 0.309699 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.56775i | − | 0.474256i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.7723i | 1.37325i | 0.727010 | + | 0.686627i | \(0.240909\pi\) | ||||
−0.727010 | + | 0.686627i | \(0.759091\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 30.4997i | − | 1.50444i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.5052 | + | 33.2889i | 0.959789 | + | 1.63804i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 6.15502i | − | 0.302138i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 29.3088 | 1.43526 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.91246i | 0.484255i | 0.970244 | + | 0.242128i | \(0.0778453\pi\) | ||||
−0.970244 | + | 0.242128i | \(0.922155\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.1235i | 1.61434i | 0.590318 | + | 0.807171i | \(0.299002\pi\) | ||||
−0.590318 | + | 0.807171i | \(0.700998\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −29.5189 | −1.43526 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 1.25746i | − | 0.0609960i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.626240 | + | 0.366938i | −0.0303059 | + | 0.0177574i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 48.5792i | − | 2.34542i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 24.9585i | − | 1.20221i | −0.799171 | − | 0.601104i | \(-0.794728\pi\) | ||
0.799171 | − | 0.601104i | \(-0.205272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.83379i | − | 0.232297i | −0.993232 | − | 0.116149i | \(-0.962945\pi\) | ||
0.993232 | − | 0.116149i | \(-0.0370549\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.96135 | 0.189932 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3290 | −0.685447 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.2643 | −0.871708 | −0.435854 | − | 0.900017i | \(-0.643554\pi\) | ||||
−0.435854 | + | 0.900017i | \(0.643554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.7978 | + | 22.8384i | −0.609420 | + | 1.08754i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2979 | 1.24945 | 0.624725 | − | 0.780844i | \(-0.285211\pi\) | ||||
0.624725 | + | 0.780844i | \(0.285211\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 5.78158i | − | 0.274073i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 48.4004 | 2.28926 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −38.9639 | −1.83882 | −0.919411 | − | 0.393299i | \(-0.871334\pi\) | ||||
−0.919411 | + | 0.393299i | \(0.871334\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.77548i | 0.460309i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.56271 | −0.402311 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.9640 | + | 8.18202i | −0.654641 | + | 0.383579i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.8688 | 1.67787 | 0.838936 | − | 0.544230i | \(-0.183178\pi\) | ||||
0.838936 | + | 0.544230i | \(0.183178\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.41564 | −0.112752 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.9750 | 1.58237 | 0.791187 | − | 0.611574i | \(-0.209463\pi\) | ||||
0.791187 | + | 0.611574i | \(0.209463\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.8826i | − | 0.738125i | −0.929405 | − | 0.369063i | \(-0.879679\pi\) | ||
0.929405 | − | 0.369063i | \(-0.120321\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.5785i | 1.13980i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.1435i | 0.608209i | 0.952639 | + | 0.304105i | \(0.0983572\pi\) | ||||
−0.952639 | + | 0.304105i | \(0.901643\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.5425 | + | 14.3804i | −1.13327 | + | 0.664026i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.800041i | 0.0368639i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.9616 | −1.51558 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.37720i | 0.154957i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 47.1052i | − | 2.15680i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.5908 | 1.03220 | 0.516100 | − | 0.856528i | \(-0.327383\pi\) | ||||
0.516100 | + | 0.856528i | \(0.327383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1332i | 0.872400i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.1446 | + | 14.7332i | −1.14412 | + | 0.670383i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.3036i | 0.649491i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 25.3997i | − | 1.15097i | −0.817812 | − | 0.575485i | \(-0.804813\pi\) | ||
0.817812 | − | 0.575485i | \(-0.195187\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 33.2732i | − | 1.50467i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.4146 | −0.560264 | −0.280132 | − | 0.959961i | \(-0.590378\pi\) | ||||
−0.280132 | + | 0.959961i | \(0.590378\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.91872 | 0.0864146 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.4403 | −0.514204 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.67395 | + | 16.5102i | 0.433936 | + | 0.740583i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.3343 | −0.910290 | −0.455145 | − | 0.890417i | \(-0.650413\pi\) | ||||
−0.455145 | + | 0.890417i | \(0.650413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.6588i | 0.967642i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.07370 | 0.137050 | 0.0685248 | − | 0.997649i | \(-0.478171\pi\) | ||||
0.0685248 | + | 0.997649i | \(0.478171\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.31463 | −0.103000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 63.3970i | 2.81556i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.3148 | −1.43233 | −0.716163 | − | 0.697933i | \(-0.754103\pi\) | ||||
−0.716163 | + | 0.697933i | \(0.754103\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.993008 | + | 1.69473i | 0.0439281 | + | 0.0749706i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.48775 | 0.286441 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.8344 | −0.609618 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.1438 | −1.06184 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 2.40111i | − | 0.105397i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 25.7947i | − | 1.13009i | −0.825062 | − | 0.565043i | \(-0.808860\pi\) | ||
0.825062 | − | 0.565043i | \(-0.191140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11.7945i | − | 0.515736i | −0.966180 | − | 0.257868i | \(-0.916980\pi\) | ||
0.966180 | − | 0.257868i | \(-0.0830200\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.47247 | + | 5.92635i | 0.151551 | + | 0.258647i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.9048i | 0.518582i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.99824 | 0.217315 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 54.5390i | − | 2.36679i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19.5486i | − | 0.846746i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6267 | 0.589134 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.78390i | 0.335900i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.4674 | + | 18.6797i | −0.450864 | + | 0.804593i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.07521i | 0.0892204i | 0.999004 | + | 0.0446102i | \(0.0142046\pi\) | ||||
−0.999004 | + | 0.0446102i | \(0.985795\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.94669i | 0.169369i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.26068i | 0.311013i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.5339 | 0.749697 | 0.374849 | − | 0.927086i | \(-0.377695\pi\) | ||||
0.374849 | + | 0.927086i | \(0.377695\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.02600 | 0.0437887 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.15314 | −0.219531 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.5472 | + | 23.1206i | 0.576086 | + | 0.983186i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.12020 | 0.344683 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 17.9855i | − | 0.762068i | −0.924561 | − | 0.381034i | \(-0.875568\pi\) | ||
0.924561 | − | 0.381034i | \(-0.124432\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 65.9154 | 2.78792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.98609 | −0.421613 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 26.5159i | − | 1.11751i | −0.829332 | − | 0.558756i | \(-0.811279\pi\) | ||
0.829332 | − | 0.558756i | \(-0.188721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.04766 | 0.380638 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.2274 | + | 8.33640i | −0.597496 | + | 0.350096i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.60242 | −0.402554 | −0.201277 | − | 0.979534i | \(-0.564509\pi\) | ||||
−0.201277 | + | 0.979534i | \(0.564509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4225 | 0.603563 | 0.301782 | − | 0.953377i | \(-0.402419\pi\) | ||||
0.301782 | + | 0.953377i | \(0.402419\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.4048 | −0.518218 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.24285i | 0.176939i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.6880i | 1.40245i | 0.712940 | + | 0.701225i | \(0.247363\pi\) | ||||
−0.712940 | + | 0.701225i | \(0.752637\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37.3789i | 1.55342i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.23266 | + | 14.0504i | 0.341548 | + | 0.582908i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 38.5277i | − | 1.59566i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.8779 | 0.945887 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.5627i | − | 1.38528i | −0.721283 | − | 0.692641i | \(-0.756447\pi\) | ||
0.721283 | − | 0.692641i | \(-0.243553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 31.9731i | − | 1.31743i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −54.0057 | −2.22150 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.5203i | − | 1.00693i | −0.864016 | − | 0.503464i | \(-0.832059\pi\) | ||
0.864016 | − | 0.503464i | \(-0.167941\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.68192 | + | 2.87048i | 0.0689521 | + | 0.117678i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.8263i | 0.524945i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.17590i | 0.129764i | 0.997893 | + | 0.0648818i | \(0.0206670\pi\) | ||||
−0.997893 | + | 0.0648818i | \(0.979333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.334920i | 0.0136617i | 0.999977 | + | 0.00683083i | \(0.00217434\pi\) | ||||
−0.999977 | + | 0.00683083i | \(0.997826\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 40.2094 | 1.63745 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.64287 | 0.0667921 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.55422 | −0.225439 | −0.112719 | − | 0.993627i | \(-0.535956\pi\) | ||||
−0.112719 | + | 0.993627i | \(0.535956\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.04279 | + | 5.29851i | −0.366432 | + | 0.214707i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 48.2818 | 1.95327 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.100256i | 0.00404931i | 0.999998 | + | 0.00202465i | \(0.000644468\pi\) | ||||
−0.999998 | + | 0.00202465i | \(0.999356\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.29651 | −0.334547 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6533 | 0.549660 | 0.274830 | − | 0.961493i | \(-0.411378\pi\) | ||||
0.274830 | + | 0.961493i | \(0.411378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 21.7703i | − | 0.875024i | −0.899213 | − | 0.437512i | \(-0.855860\pi\) | ||
0.899213 | − | 0.437512i | \(-0.144140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.15068 | 0.327076 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.73316 | + | 13.1979i | 0.309822 | + | 0.528763i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.8199 | 1.07108 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.93309 | 0.156823 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 22.1194i | − | 0.880559i | −0.897861 | − | 0.440280i | \(-0.854879\pi\) | ||
0.897861 | − | 0.440280i | \(-0.145121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.7195i | 0.505554i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.27159i | 0.367932i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.9324 | − | 37.3550i | 0.829372 | − | 1.48006i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 27.0496i | − | 1.07006i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.4852 | 1.04610 | 0.523050 | − | 0.852302i | \(-0.324794\pi\) | ||||
0.523050 | + | 0.852302i | \(0.324794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 39.9374i | − | 1.57498i | −0.616330 | − | 0.787488i | \(-0.711381\pi\) | ||
0.616330 | − | 0.787488i | \(-0.288619\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 27.9747i | − | 1.10150i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −45.2321 | −1.77826 | −0.889128 | − | 0.457658i | \(-0.848688\pi\) | ||||
−0.889128 | + | 0.457658i | \(0.848688\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 44.6079i | − | 1.75101i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.8750 | − | 56.1066i | −1.28847 | − | 2.19899i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 9.97322i | − | 0.390282i | −0.980775 | − | 0.195141i | \(-0.937484\pi\) | ||
0.980775 | − | 0.195141i | \(-0.0625165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.14476i | 0.357315i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.77657i | − | 0.108324i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −33.7753 | −1.31570 | −0.657850 | − | 0.753149i | \(-0.728534\pi\) | ||||
−0.657850 | + | 0.753149i | \(0.728534\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0667 | 0.702715 | 0.351357 | − | 0.936241i | \(-0.385720\pi\) | ||||
0.351357 | + | 0.936241i | \(0.385720\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.9698 | 0.775564 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.51718 | − | 7.70932i | −0.175169 | − | 0.298955i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.47400 | −0.250674 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.01727i | 0.309965i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.839176 | 0.0323960 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.7732 | −1.45605 | −0.728024 | − | 0.685551i | \(-0.759561\pi\) | ||||
−0.728024 | + | 0.685551i | \(0.759561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.92104i | − | 0.0739409i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −36.0391 | −1.38510 | −0.692548 | − | 0.721371i | \(-0.743512\pi\) | ||||
−0.692548 | + | 0.721371i | \(0.743512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −19.1317 | − | 32.6515i | −0.734209 | − | 1.25305i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.31553 | −0.203692 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.2784 | 0.431554 | 0.215777 | − | 0.976443i | \(-0.430772\pi\) | ||||
0.215777 | + | 0.976443i | \(0.430772\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.7481 | 0.448871 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.5445i | 0.898280i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 77.0463i | 2.93523i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.4353i | − | 0.815438i | −0.913107 | − | 0.407719i | \(-0.866324\pi\) | ||
0.913107 | − | 0.407719i | \(-0.133676\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 26.1154 | − | 15.3020i | 0.992043 | − | 0.581276i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.2894i | 0.428230i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.01848 | −0.152211 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 33.3088i | − | 1.25986i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.09861i | − | 0.0414940i | −0.999785 | − | 0.0207470i | \(-0.993396\pi\) | ||
0.999785 | − | 0.0207470i | \(-0.00660446\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.5632 | −0.398399 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 20.4910i | − | 0.771734i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.28373 | − | 3.09594i | 0.198715 | − | 0.116435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.7287i | 0.778481i | 0.921136 | + | 0.389240i | \(0.127262\pi\) | ||||
−0.921136 | + | 0.389240i | \(0.872738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 37.8797i | − | 1.42060i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 40.1684i | − | 1.50432i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.7121 | 0.699791 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.6394 | −1.40567 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.5825 | 0.991361 | 0.495680 | − | 0.868505i | \(-0.334919\pi\) | ||||
0.495680 | + | 0.868505i | \(0.334919\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.5806 | − | 18.5043i | 1.17612 | − | 0.689134i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.64183 | −0.0610602 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.52586i | 0.0566691i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.08151 | −0.0771989 | −0.0385995 | − | 0.999255i | \(-0.512290\pi\) | ||||
−0.0385995 | + | 0.999255i | \(0.512290\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 38.2715 | 1.41746 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 13.5498i | − | 0.501157i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.11229 | 0.0780191 | 0.0390096 | − | 0.999239i | \(-0.487580\pi\) | ||||
0.0390096 | + | 0.999239i | \(0.487580\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.8536 | − | 8.88378i | −0.584769 | − | 0.327683i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 32.8876 | 1.21143 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.6264 | 0.501255 | 0.250628 | − | 0.968084i | \(-0.419363\pi\) | ||||
0.250628 | + | 0.968084i | \(0.419363\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −53.6335 | −1.97028 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 42.8070i | − | 1.57044i | −0.619219 | − | 0.785218i | \(-0.712551\pi\) | ||
0.619219 | − | 0.785218i | \(-0.287449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.6432i | 0.683034i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 23.0195i | − | 0.842241i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.1064 | + | 18.2264i | −1.13660 | + | 0.665979i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.3283i | − | 0.924244i | −0.886816 | − | 0.462122i | \(-0.847088\pi\) | ||
0.886816 | − | 0.462122i | \(-0.152912\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.3684 | 0.924477 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.29824i | − | 0.120035i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 37.2852i | − | 1.35516i | −0.735451 | − | 0.677578i | \(-0.763030\pi\) | ||
0.735451 | − | 0.677578i | \(-0.236970\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.6944 | 1.22303 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.5390i | 1.03454i | 0.855823 | + | 0.517268i | \(0.173051\pi\) | ||||
−0.855823 | + | 0.517268i | \(0.826949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.71153 | − | 16.5743i | −0.351581 | − | 0.600031i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 4.70286i | − | 0.170032i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 89.2053i | 3.22102i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.7803i | 0.929660i | 0.885400 | + | 0.464830i | \(0.153885\pi\) | ||||
−0.885400 | + | 0.464830i | \(0.846115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.59421 | 0.309513 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.8642 | 1.07414 | 0.537070 | − | 0.843538i | \(-0.319531\pi\) | ||||
0.537070 | + | 0.843538i | \(0.319531\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.46731 | −0.340076 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.5364 | + | 10.8612i | −0.664990 | + | 0.389643i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.7925 | 0.386683 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 22.1241i | − | 0.791661i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.93124 | 0.104754 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.308165 | −0.0109989 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 0.839063i | − | 0.0299094i | −0.999888 | − | 0.0149547i | \(-0.995240\pi\) | ||
0.999888 | − | 0.0149547i | \(-0.00476040\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −73.2928 | −2.60929 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.6536 | + | 12.1017i | −0.734357 | + | 0.430287i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.67815 | −0.0595930 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 32.6987 | 1.15970 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.39992 | −0.0850096 | −0.0425048 | − | 0.999096i | \(-0.513534\pi\) | ||||
−0.0425048 | + | 0.999096i | \(0.513534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.92497i | − | 0.351120i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 21.6229i | − | 0.764007i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.27098i | − | 0.0801412i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.67503 | − | 9.68537i | −0.200018 | − | 0.341364i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.8053i | 2.56287i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.4961 | −1.10734 | −0.553672 | − | 0.832735i | \(-0.686774\pi\) | ||||
−0.553672 | + | 0.832735i | \(0.686774\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.89901i | 0.312486i | 0.987719 | + | 0.156243i | \(0.0499384\pi\) | ||||
−0.987719 | + | 0.156243i | \(0.950062\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.8274i | 0.800592i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.8164 | 0.448939 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36.3910i | 1.27316i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −52.2247 | + | 30.6004i | −1.82488 | + | 1.06927i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.8802i | 0.868326i | 0.900834 | + | 0.434163i | \(0.142956\pi\) | ||||
−0.900834 | + | 0.434163i | \(0.857044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 38.0624i | − | 1.32677i | −0.748277 | − | 0.663386i | \(-0.769119\pi\) | ||
0.748277 | − | 0.663386i | \(-0.230881\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 7.94145i | − | 0.276486i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.3847 | 0.987031 | 0.493516 | − | 0.869737i | \(-0.335712\pi\) | ||||
0.493516 | + | 0.869737i | \(0.335712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.3879 | 1.09015 | 0.545074 | − | 0.838388i | \(-0.316502\pi\) | ||||
0.545074 | + | 0.838388i | \(0.316502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 47.7664 | 1.65700 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.67882 | − | 4.30293i | −0.266056 | − | 0.149088i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.34267 | −0.288710 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.1871i | 0.628638i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.4588 | −0.361079 | −0.180539 | − | 0.983568i | \(-0.557784\pi\) | ||||
−0.180539 | + | 0.983568i | \(0.557784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.6717 | 0.919715 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 80.8619i | 2.78503i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −24.4197 | −0.840063 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.75026 | + | 2.19742i | −0.128861 | + | 0.0755043i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −77.4592 | −2.65839 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −13.2708 | −0.454916 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.0347 | −0.583256 | −0.291628 | − | 0.956532i | \(-0.594197\pi\) | ||||
−0.291628 | + | 0.956532i | \(0.594197\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.6306i | 0.431958i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.2852i | 1.47859i | 0.673379 | + | 0.739297i | \(0.264842\pi\) | ||||
−0.673379 | + | 0.739297i | \(0.735158\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.0541i | − | 0.786597i | −0.919411 | − | 0.393298i | \(-0.871334\pi\) | ||
0.919411 | − | 0.393298i | \(-0.128666\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.9389 | − | 11.0970i | 0.645435 | − | 0.378185i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.3924i | − | 0.830327i | −0.909747 | − | 0.415163i | \(-0.863724\pi\) | ||
0.909747 | − | 0.415163i | \(-0.136276\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.924877 | 0.0314468 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.0294i | 1.35947i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 30.9821i | − | 1.05100i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −65.7675 | −2.22845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 53.4947i | 1.81052i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.28275 | + | 1.33755i | −0.0771711 | + | 0.0452175i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 57.3223i | 1.93564i | 0.251649 | + | 0.967819i | \(0.419027\pi\) | ||||
−0.251649 | + | 0.967819i | \(0.580973\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 42.9793i | − | 1.44965i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 44.0539i | − | 1.48421i | −0.670282 | − | 0.742107i | \(-0.733827\pi\) | ||
0.670282 | − | 0.742107i | \(-0.266173\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.5580 | −1.49950 | −0.749749 | − | 0.661723i | \(-0.769826\pi\) | ||||
−0.749749 | + | 0.661723i | \(0.769826\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 37.8590 | 1.27262 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.89650 | −0.0972550 | −0.0486275 | − | 0.998817i | \(-0.515485\pi\) | ||||
−0.0486275 | + | 0.998817i | \(0.515485\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.4012 | − | 21.1647i | −0.415924 | − | 0.709843i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.0651 | 0.638705 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.6557i | 0.892000i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.99825 | −0.100221 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −67.3808 | −2.24978 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 14.4458i | − | 0.481795i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.8379 | 0.527637 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 37.4176 | + | 63.8593i | 1.24518 | + | 2.12510i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.52021 | −0.0505336 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.2835 | −0.872728 | −0.436364 | − | 0.899770i | \(-0.643734\pi\) | ||||
−0.436364 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.65663 | −0.287122 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.5911i | 1.11292i | 0.830873 | + | 0.556462i | \(0.187842\pi\) | ||||
−0.830873 | + | 0.556462i | \(0.812158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.8279i | − | 0.623111i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.712214i | 0.0235451i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.2316 | − | 20.8752i | −0.403922 | − | 0.689360i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.6535i | − | 1.01117i | −0.862778 | − | 0.505583i | \(-0.831277\pi\) | ||
0.862778 | − | 0.505583i | \(-0.168723\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −58.3819 | −1.92375 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.2429i | 1.45627i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.12779i | 0.102841i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.7402 | −1.69937 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 59.1269i | − | 1.93989i | −0.243322 | − | 0.969946i | \(-0.578237\pi\) | ||
0.243322 | − | 0.969946i | \(-0.421763\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.6232 | + | 11.5565i | 0.675899 | + | 0.378749i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 7.85992i | − | 0.257322i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 3.84651i | − | 0.125794i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 16.3377i | − | 0.533730i | −0.963734 | − | 0.266865i | \(-0.914012\pi\) | ||
0.963734 | − | 0.266865i | \(-0.0859878\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −59.8866 | −1.95432 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.6773 | −0.804457 | −0.402228 | − | 0.915539i | \(-0.631764\pi\) | ||||
−0.402228 | + | 0.915539i | \(0.631764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5589 | 0.441538 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.56949 | + | 4.38526i | 0.0835855 | + | 0.142652i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.5781 | 0.928664 | 0.464332 | − | 0.885661i | \(-0.346294\pi\) | ||||
0.464332 | + | 0.885661i | \(0.346294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.54143i | 0.147421i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.2485 | 0.916020 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −20.9275 | −0.677908 | −0.338954 | − | 0.940803i | \(-0.610073\pi\) | ||||
−0.338954 | + | 0.940803i | \(0.610073\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 4.77816i | − | 0.154618i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.1176 | 0.391705 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.8179 | + | 15.7137i | −0.865996 | + | 0.507420i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 58.6300 | 1.89129 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.9634 | 1.64227 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −14.3979 | −0.463484 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.8079i | 0.701295i | 0.936508 | + | 0.350647i | \(0.114038\pi\) | ||||
−0.936508 | + | 0.350647i | \(0.885962\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.0251i | 0.354176i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 32.1900i | − | 1.03303i | −0.856279 | − | 0.516513i | \(-0.827230\pi\) | ||
0.856279 | − | 0.516513i | \(-0.172770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.1001 | − | 25.7708i | −0.484088 | − | 0.826175i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 15.8810i | 0.508600i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.4242 | 0.621435 | 0.310717 | − | 0.950502i | \(-0.399431\pi\) | ||||
0.310717 | + | 0.950502i | \(0.399431\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 17.6855i | − | 0.565232i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 27.1546i | 0.866981i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −57.5903 | −1.83685 | −0.918423 | − | 0.395599i | \(-0.870537\pi\) | ||||
−0.918423 | + | 0.395599i | \(0.870537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 20.8023i | − | 0.662816i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.4077 | + | 46.7758i | 0.872397 | + | 1.48889i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 45.7187i | 1.45377i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 61.5330i | 1.95466i | 0.211725 | + | 0.977329i | \(0.432092\pi\) | ||||
−0.211725 | + | 0.977329i | \(0.567908\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 86.4653i | − | 2.74389i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.94052 | −0.156625 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.2889 | 0.927589 | 0.463795 | − | 0.885943i | \(-0.346488\pi\) | ||||
0.463795 | + | 0.885943i | \(0.346488\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.00862 | 0.190104 |
(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 | 2240.2.h.e.671.20 | yes | 24 | |
4.3 | odd | 2 | inner | 2240.2.h.e.671.5 | ✓ | 24 | |
7.6 | odd | 2 | 2240.2.h.f.671.5 | yes | 24 | ||
8.3 | odd | 2 | 2240.2.h.f.671.6 | yes | 24 | ||
8.5 | even | 2 | 2240.2.h.f.671.19 | yes | 24 | ||
28.27 | even | 2 | 2240.2.h.f.671.20 | yes | 24 | ||
56.13 | odd | 2 | inner | 2240.2.h.e.671.6 | yes | 24 | |
56.27 | even | 2 | inner | 2240.2.h.e.671.19 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.h.e.671.5 | ✓ | 24 | 4.3 | odd | 2 | inner | |
2240.2.h.e.671.6 | yes | 24 | 56.13 | odd | 2 | inner | |
2240.2.h.e.671.19 | yes | 24 | 56.27 | even | 2 | inner | |
2240.2.h.e.671.20 | yes | 24 | 1.1 | even | 1 | trivial | |
2240.2.h.f.671.5 | yes | 24 | 7.6 | odd | 2 | ||
2240.2.h.f.671.6 | yes | 24 | 8.3 | odd | 2 | ||
2240.2.h.f.671.19 | yes | 24 | 8.5 | even | 2 | ||
2240.2.h.f.671.20 | yes | 24 | 28.27 | even | 2 |