Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(205,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.205");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bm (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 205.5 | ||
Root | \(1.45057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.205 |
Dual form | 546.2.bm.a.277.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.34064 | − | 1.35137i | −1.04677 | − | 0.604351i | −0.125024 | − | 0.992154i | \(-0.539901\pi\) |
−0.921742 | + | 0.387803i | \(0.873234\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | 1.65982 | + | 2.06034i | 0.627352 | + | 0.778736i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.35137 | − | 2.34064i | 0.427341 | − | 0.740176i | ||||
\(11\) | −4.41435 | − | 2.54863i | −1.33098 | − | 0.768440i | −0.345528 | − | 0.938408i | \(-0.612300\pi\) |
−0.985450 | + | 0.169968i | \(0.945633\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 0.313194 | − | 3.59192i | 0.0868644 | − | 0.996220i | ||||
\(14\) | −2.06034 | + | 1.65982i | −0.550649 | + | 0.443605i | ||||
\(15\) | −2.34064 | + | 1.35137i | −0.604351 | + | 0.348922i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.73328 | −1.39052 | −0.695262 | − | 0.718756i | \(-0.744712\pi\) | ||||
−0.695262 | + | 0.718756i | \(0.744712\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | −3.79715 | + | 2.19229i | −0.871127 | + | 0.502945i | −0.867723 | − | 0.497049i | \(-0.834417\pi\) |
−0.00340438 | + | 0.999994i | \(0.501084\pi\) | |||||||
\(20\) | 2.34064 | + | 1.35137i | 0.523383 | + | 0.302175i | ||||
\(21\) | 2.61422 | − | 0.407273i | 0.570469 | − | 0.0888742i | ||||
\(22\) | 2.54863 | − | 4.41435i | 0.543369 | − | 0.941143i | ||||
\(23\) | 7.46964 | 1.55753 | 0.778764 | − | 0.627317i | \(-0.215847\pi\) | ||||
0.778764 | + | 0.627317i | \(0.215847\pi\) | |||||||
\(24\) | −0.866025 | − | 0.500000i | −0.176777 | − | 0.102062i | ||||
\(25\) | 1.15240 | + | 1.99602i | 0.230480 | + | 0.399203i | ||||
\(26\) | 3.59192 | + | 0.313194i | 0.704434 | + | 0.0614224i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.65982 | − | 2.06034i | −0.313676 | − | 0.389368i | ||||
\(29\) | −4.18045 | − | 7.24074i | −0.776289 | − | 1.34457i | −0.934067 | − | 0.357098i | \(-0.883766\pi\) |
0.157778 | − | 0.987475i | \(-0.449567\pi\) | |||||||
\(30\) | −1.35137 | − | 2.34064i | −0.246725 | − | 0.427341i | ||||
\(31\) | −6.21147 | + | 3.58619i | −1.11561 | + | 0.644099i | −0.940277 | − | 0.340410i | \(-0.889434\pi\) |
−0.175335 | + | 0.984509i | \(0.556101\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −4.41435 | + | 2.54863i | −0.768440 | + | 0.443659i | ||||
\(34\) | − | 5.73328i | − | 0.983249i | ||||||
\(35\) | −1.10075 | − | 7.06555i | −0.186061 | − | 1.19430i | ||||
\(36\) | 0.500000 | + | 0.866025i | 0.0833333 | + | 0.144338i | ||||
\(37\) | − | 6.77410i | − | 1.11366i | −0.830628 | − | 0.556828i | \(-0.812018\pi\) | ||
0.830628 | − | 0.556828i | \(-0.187982\pi\) | |||||||
\(38\) | −2.19229 | − | 3.79715i | −0.355636 | − | 0.615980i | ||||
\(39\) | −2.95410 | − | 2.06720i | −0.473034 | − | 0.331016i | ||||
\(40\) | −1.35137 | + | 2.34064i | −0.213670 | + | 0.370088i | ||||
\(41\) | 3.29661 | − | 1.90330i | 0.514843 | − | 0.297245i | −0.219979 | − | 0.975505i | \(-0.570599\pi\) |
0.734822 | + | 0.678260i | \(0.237266\pi\) | |||||||
\(42\) | 0.407273 | + | 2.61422i | 0.0628436 | + | 0.403382i | ||||
\(43\) | 3.10694 | − | 5.38138i | 0.473804 | − | 0.820653i | −0.525746 | − | 0.850642i | \(-0.676214\pi\) |
0.999550 | + | 0.0299887i | \(0.00954714\pi\) | |||||||
\(44\) | 4.41435 | + | 2.54863i | 0.665489 | + | 0.384220i | ||||
\(45\) | 2.70274i | 0.402901i | ||||||||
\(46\) | 7.46964i | 1.10134i | ||||||||
\(47\) | −7.44186 | − | 4.29656i | −1.08551 | − | 0.626718i | −0.153130 | − | 0.988206i | \(-0.548935\pi\) |
−0.932377 | + | 0.361488i | \(0.882269\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | −1.49001 | + | 6.83958i | −0.212859 | + | 0.977083i | ||||
\(50\) | −1.99602 | + | 1.15240i | −0.282279 | + | 0.162974i | ||||
\(51\) | −2.86664 | + | 4.96516i | −0.401410 | + | 0.695262i | ||||
\(52\) | −0.313194 | + | 3.59192i | −0.0434322 | + | 0.498110i | ||||
\(53\) | 3.60339 | + | 6.24125i | 0.494963 | + | 0.857301i | 0.999983 | − | 0.00580635i | \(-0.00184823\pi\) |
−0.505020 | + | 0.863108i | \(0.668515\pi\) | |||||||
\(54\) | − | 1.00000i | − | 0.136083i | ||||||
\(55\) | 6.88828 | + | 11.9308i | 0.928815 | + | 1.60875i | ||||
\(56\) | 2.06034 | − | 1.65982i | 0.275325 | − | 0.221802i | ||||
\(57\) | 4.38458i | 0.580751i | ||||||||
\(58\) | 7.24074 | − | 4.18045i | 0.950756 | − | 0.548919i | ||||
\(59\) | − | 6.47957i | − | 0.843569i | −0.906696 | − | 0.421784i | \(-0.861404\pi\) | ||
0.906696 | − | 0.421784i | \(-0.138596\pi\) | |||||||
\(60\) | 2.34064 | − | 1.35137i | 0.302175 | − | 0.174461i | ||||
\(61\) | 2.32523 | + | 4.02741i | 0.297715 | + | 0.515657i | 0.975613 | − | 0.219499i | \(-0.0704422\pi\) |
−0.677898 | + | 0.735156i | \(0.737109\pi\) | |||||||
\(62\) | −3.58619 | − | 6.21147i | −0.455447 | − | 0.788857i | ||||
\(63\) | 0.954400 | − | 2.46761i | 0.120243 | − | 0.310890i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.58709 | + | 7.98416i | −0.692993 | + | 0.990313i | ||||
\(66\) | −2.54863 | − | 4.41435i | −0.313714 | − | 0.543369i | ||||
\(67\) | 5.25284 | + | 3.03273i | 0.641736 | + | 0.370507i | 0.785283 | − | 0.619137i | \(-0.212517\pi\) |
−0.143547 | + | 0.989644i | \(0.545851\pi\) | |||||||
\(68\) | 5.73328 | 0.695262 | ||||||||
\(69\) | 3.73482 | − | 6.46890i | 0.449620 | − | 0.778764i | ||||
\(70\) | 7.06555 | − | 1.10075i | 0.844494 | − | 0.131565i | ||||
\(71\) | 0.792408 | + | 0.457497i | 0.0940415 | + | 0.0542949i | 0.546283 | − | 0.837601i | \(-0.316042\pi\) |
−0.452242 | + | 0.891895i | \(0.649376\pi\) | |||||||
\(72\) | −0.866025 | + | 0.500000i | −0.102062 | + | 0.0589256i | ||||
\(73\) | 5.93963 | − | 3.42924i | 0.695181 | − | 0.401363i | −0.110369 | − | 0.993891i | \(-0.535203\pi\) |
0.805550 | + | 0.592528i | \(0.201870\pi\) | |||||||
\(74\) | 6.77410 | 0.787473 | ||||||||
\(75\) | 2.30480 | 0.266135 | ||||||||
\(76\) | 3.79715 | − | 2.19229i | 0.435563 | − | 0.251473i | ||||
\(77\) | −2.07597 | − | 13.3253i | −0.236579 | − | 1.51856i | ||||
\(78\) | 2.06720 | − | 2.95410i | 0.234064 | − | 0.334486i | ||||
\(79\) | −3.81342 | + | 6.60504i | −0.429044 | + | 0.743126i | −0.996789 | − | 0.0800791i | \(-0.974483\pi\) |
0.567745 | + | 0.823205i | \(0.307816\pi\) | |||||||
\(80\) | −2.34064 | − | 1.35137i | −0.261692 | − | 0.151088i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.90330 | + | 3.29661i | 0.210184 | + | 0.364049i | ||||
\(83\) | 15.3966i | 1.69000i | 0.534769 | + | 0.844999i | \(0.320399\pi\) | ||||
−0.534769 | + | 0.844999i | \(0.679601\pi\) | |||||||
\(84\) | −2.61422 | + | 0.407273i | −0.285234 | + | 0.0444371i | ||||
\(85\) | 13.4195 | + | 7.74778i | 1.45555 | + | 0.840365i | ||||
\(86\) | 5.38138 | + | 3.10694i | 0.580289 | + | 0.335030i | ||||
\(87\) | −8.36089 | −0.896382 | ||||||||
\(88\) | −2.54863 | + | 4.41435i | −0.271685 | + | 0.470572i | ||||
\(89\) | 10.3822i | 1.10052i | 0.834995 | + | 0.550258i | \(0.185471\pi\) | ||||
−0.834995 | + | 0.550258i | \(0.814529\pi\) | |||||||
\(90\) | −2.70274 | −0.284894 | ||||||||
\(91\) | 7.92043 | − | 5.31665i | 0.830287 | − | 0.557336i | ||||
\(92\) | −7.46964 | −0.778764 | ||||||||
\(93\) | 7.17238i | 0.743742i | ||||||||
\(94\) | 4.29656 | − | 7.44186i | 0.443156 | − | 0.767569i | ||||
\(95\) | 11.8504 | 1.21582 | ||||||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | −8.20116 | − | 4.73494i | −0.832702 | − | 0.480761i | 0.0220749 | − | 0.999756i | \(-0.492973\pi\) |
−0.854777 | + | 0.518996i | \(0.826306\pi\) | |||||||
\(98\) | −6.83958 | − | 1.49001i | −0.690902 | − | 0.150514i | ||||
\(99\) | 5.09726i | 0.512293i | ||||||||
\(100\) | −1.15240 | − | 1.99602i | −0.115240 | − | 0.199602i | ||||
\(101\) | 1.86105 | − | 3.22344i | 0.185182 | − | 0.320744i | −0.758456 | − | 0.651724i | \(-0.774046\pi\) |
0.943638 | + | 0.330980i | \(0.107379\pi\) | |||||||
\(102\) | −4.96516 | − | 2.86664i | −0.491625 | − | 0.283840i | ||||
\(103\) | 4.55465 | − | 7.88888i | 0.448783 | − | 0.777314i | −0.549525 | − | 0.835478i | \(-0.685191\pi\) |
0.998307 | + | 0.0581634i | \(0.0185244\pi\) | |||||||
\(104\) | −3.59192 | − | 0.313194i | −0.352217 | − | 0.0307112i | ||||
\(105\) | −6.66932 | − | 2.57949i | −0.650859 | − | 0.251733i | ||||
\(106\) | −6.24125 | + | 3.60339i | −0.606204 | + | 0.349992i | ||||
\(107\) | 10.5677 | 1.02162 | 0.510810 | − | 0.859693i | \(-0.329345\pi\) | ||||
0.510810 | + | 0.859693i | \(0.329345\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −3.27729 | + | 1.89214i | −0.313907 | + | 0.181235i | −0.648674 | − | 0.761067i | \(-0.724676\pi\) |
0.334766 | + | 0.942301i | \(0.391343\pi\) | |||||||
\(110\) | −11.9308 | + | 6.88828i | −1.13756 | + | 0.656771i | ||||
\(111\) | −5.86654 | − | 3.38705i | −0.556828 | − | 0.321485i | ||||
\(112\) | 1.65982 | + | 2.06034i | 0.156838 | + | 0.194684i | ||||
\(113\) | 0.849593 | − | 1.47154i | 0.0799230 | − | 0.138431i | −0.823294 | − | 0.567616i | \(-0.807866\pi\) |
0.903217 | + | 0.429185i | \(0.141199\pi\) | |||||||
\(114\) | −4.38458 | −0.410653 | ||||||||
\(115\) | −17.4838 | − | 10.0943i | −1.63037 | − | 0.941294i | ||||
\(116\) | 4.18045 | + | 7.24074i | 0.388145 | + | 0.672286i | ||||
\(117\) | −3.26729 | + | 1.52473i | −0.302061 | + | 0.140961i | ||||
\(118\) | 6.47957 | 0.596493 | ||||||||
\(119\) | −9.51619 | − | 11.8125i | −0.872348 | − | 1.08285i | ||||
\(120\) | 1.35137 | + | 2.34064i | 0.123363 | + | 0.213670i | ||||
\(121\) | 7.49101 | + | 12.9748i | 0.681001 | + | 1.17953i | ||||
\(122\) | −4.02741 | + | 2.32523i | −0.364625 | + | 0.210516i | ||||
\(123\) | − | 3.80659i | − | 0.343229i | ||||||
\(124\) | 6.21147 | − | 3.58619i | 0.557806 | − | 0.322050i | ||||
\(125\) | 7.28442i | 0.651538i | ||||||||
\(126\) | 2.46761 | + | 0.954400i | 0.219833 | + | 0.0850247i | ||||
\(127\) | 3.11451 | + | 5.39450i | 0.276368 | + | 0.478684i | 0.970479 | − | 0.241184i | \(-0.0775357\pi\) |
−0.694111 | + | 0.719868i | \(0.744202\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −3.10694 | − | 5.38138i | −0.273551 | − | 0.473804i | ||||
\(130\) | −7.98416 | − | 5.58709i | −0.700257 | − | 0.490020i | ||||
\(131\) | −0.358468 | + | 0.620884i | −0.0313195 | + | 0.0542469i | −0.881260 | − | 0.472631i | \(-0.843304\pi\) |
0.849941 | + | 0.526878i | \(0.176638\pi\) | |||||||
\(132\) | 4.41435 | − | 2.54863i | 0.384220 | − | 0.221830i | ||||
\(133\) | −10.8194 | − | 4.18464i | −0.938165 | − | 0.362854i | ||||
\(134\) | −3.03273 | + | 5.25284i | −0.261988 | + | 0.453776i | ||||
\(135\) | 2.34064 | + | 1.35137i | 0.201450 | + | 0.116307i | ||||
\(136\) | 5.73328i | 0.491625i | ||||||||
\(137\) | − | 10.0557i | − | 0.859120i | −0.903038 | − | 0.429560i | \(-0.858669\pi\) | ||
0.903038 | − | 0.429560i | \(-0.141331\pi\) | |||||||
\(138\) | 6.46890 | + | 3.73482i | 0.550670 | + | 0.317929i | ||||
\(139\) | 8.84682 | − | 15.3231i | 0.750377 | − | 1.29969i | −0.197263 | − | 0.980351i | \(-0.563205\pi\) |
0.947640 | − | 0.319341i | \(-0.103462\pi\) | |||||||
\(140\) | 1.10075 | + | 7.06555i | 0.0930306 | + | 0.597148i | ||||
\(141\) | −7.44186 | + | 4.29656i | −0.626718 | + | 0.361836i | ||||
\(142\) | −0.457497 | + | 0.792408i | −0.0383923 | + | 0.0664974i | ||||
\(143\) | −10.5370 | + | 15.0578i | −0.881150 | + | 1.25920i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 22.5973i | 1.87660i | ||||||||
\(146\) | 3.42924 | + | 5.93963i | 0.283806 | + | 0.491567i | ||||
\(147\) | 5.17824 | + | 4.71018i | 0.427094 | + | 0.388489i | ||||
\(148\) | 6.77410i | 0.556828i | ||||||||
\(149\) | −20.1710 | + | 11.6457i | −1.65247 | + | 0.954055i | −0.676420 | + | 0.736516i | \(0.736469\pi\) |
−0.976052 | + | 0.217538i | \(0.930197\pi\) | |||||||
\(150\) | 2.30480i | 0.188186i | ||||||||
\(151\) | 15.8610 | − | 9.15737i | 1.29075 | − | 0.745216i | 0.311964 | − | 0.950094i | \(-0.399013\pi\) |
0.978788 | + | 0.204878i | \(0.0656798\pi\) | |||||||
\(152\) | 2.19229 | + | 3.79715i | 0.177818 | + | 0.307990i | ||||
\(153\) | 2.86664 | + | 4.96516i | 0.231754 | + | 0.401410i | ||||
\(154\) | 13.3253 | − | 2.07597i | 1.07379 | − | 0.167287i | ||||
\(155\) | 19.3851 | 1.55705 | ||||||||
\(156\) | 2.95410 | + | 2.06720i | 0.236517 | + | 0.165508i | ||||
\(157\) | −1.91775 | − | 3.32164i | −0.153053 | − | 0.265096i | 0.779295 | − | 0.626657i | \(-0.215577\pi\) |
−0.932348 | + | 0.361561i | \(0.882244\pi\) | |||||||
\(158\) | −6.60504 | − | 3.81342i | −0.525469 | − | 0.303380i | ||||
\(159\) | 7.20677 | 0.571534 | ||||||||
\(160\) | 1.35137 | − | 2.34064i | 0.106835 | − | 0.185044i | ||||
\(161\) | 12.3982 | + | 15.3900i | 0.977118 | + | 1.21290i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 9.03020 | − | 5.21359i | 0.707300 | − | 0.408360i | −0.102761 | − | 0.994706i | \(-0.532768\pi\) |
0.810061 | + | 0.586346i | \(0.199434\pi\) | |||||||
\(164\) | −3.29661 | + | 1.90330i | −0.257422 | + | 0.148622i | ||||
\(165\) | 13.7766 | 1.07250 | ||||||||
\(166\) | −15.3966 | −1.19501 | ||||||||
\(167\) | −1.90573 | + | 1.10027i | −0.147470 | + | 0.0851418i | −0.571919 | − | 0.820310i | \(-0.693801\pi\) |
0.424449 | + | 0.905452i | \(0.360468\pi\) | |||||||
\(168\) | −0.407273 | − | 2.61422i | −0.0314218 | − | 0.201691i | ||||
\(169\) | −12.8038 | − | 2.24994i | −0.984909 | − | 0.173072i | ||||
\(170\) | −7.74778 | + | 13.4195i | −0.594227 | + | 1.02923i | ||||
\(171\) | 3.79715 | + | 2.19229i | 0.290376 | + | 0.167648i | ||||
\(172\) | −3.10694 | + | 5.38138i | −0.236902 | + | 0.410326i | ||||
\(173\) | −10.7383 | − | 18.5992i | −0.816415 | − | 1.41407i | −0.908308 | − | 0.418303i | \(-0.862625\pi\) |
0.0918931 | − | 0.995769i | \(-0.470708\pi\) | |||||||
\(174\) | − | 8.36089i | − | 0.633838i | ||||||
\(175\) | −2.19970 | + | 5.68736i | −0.166282 | + | 0.429924i | ||||
\(176\) | −4.41435 | − | 2.54863i | −0.332744 | − | 0.192110i | ||||
\(177\) | −5.61147 | − | 3.23979i | −0.421784 | − | 0.243517i | ||||
\(178\) | −10.3822 | −0.778182 | ||||||||
\(179\) | 9.33910 | − | 16.1758i | 0.698037 | − | 1.20904i | −0.271109 | − | 0.962549i | \(-0.587390\pi\) |
0.969146 | − | 0.246487i | \(-0.0792763\pi\) | |||||||
\(180\) | − | 2.70274i | − | 0.201450i | ||||||
\(181\) | 1.97032 | 0.146452 | 0.0732262 | − | 0.997315i | \(-0.476670\pi\) | ||||
0.0732262 | + | 0.997315i | \(0.476670\pi\) | |||||||
\(182\) | 5.31665 | + | 7.92043i | 0.394096 | + | 0.587102i | ||||
\(183\) | 4.65046 | 0.343772 | ||||||||
\(184\) | − | 7.46964i | − | 0.550670i | ||||||
\(185\) | −9.15432 | + | 15.8557i | −0.673039 | + | 1.16574i | ||||
\(186\) | −7.17238 | −0.525905 | ||||||||
\(187\) | 25.3087 | + | 14.6120i | 1.85076 | + | 1.06853i | ||||
\(188\) | 7.44186 | + | 4.29656i | 0.542753 | + | 0.313359i | ||||
\(189\) | −1.65982 | − | 2.06034i | −0.120734 | − | 0.149868i | ||||
\(190\) | 11.8504i | 0.859716i | ||||||||
\(191\) | −1.85473 | − | 3.21249i | −0.134204 | − | 0.232448i | 0.791089 | − | 0.611701i | \(-0.209514\pi\) |
−0.925293 | + | 0.379253i | \(0.876181\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | 2.58076 | + | 1.49000i | 0.185767 | + | 0.107253i | 0.589999 | − | 0.807404i | \(-0.299128\pi\) |
−0.404232 | + | 0.914656i | \(0.632461\pi\) | |||||||
\(194\) | 4.73494 | − | 8.20116i | 0.339949 | − | 0.588809i | ||||
\(195\) | 4.12094 | + | 8.83064i | 0.295107 | + | 0.632375i | ||||
\(196\) | 1.49001 | − | 6.83958i | 0.106430 | − | 0.488541i | ||||
\(197\) | −12.8922 | + | 7.44330i | −0.918529 | + | 0.530313i | −0.883165 | − | 0.469062i | \(-0.844592\pi\) |
−0.0353634 | + | 0.999375i | \(0.511259\pi\) | |||||||
\(198\) | −5.09726 | −0.362246 | ||||||||
\(199\) | −2.66427 | −0.188865 | −0.0944327 | − | 0.995531i | \(-0.530104\pi\) | ||||
−0.0944327 | + | 0.995531i | \(0.530104\pi\) | |||||||
\(200\) | 1.99602 | − | 1.15240i | 0.141140 | − | 0.0814870i | ||||
\(201\) | 5.25284 | − | 3.03273i | 0.370507 | − | 0.213912i | ||||
\(202\) | 3.22344 | + | 1.86105i | 0.226800 | + | 0.130943i | ||||
\(203\) | 7.97963 | − | 20.6315i | 0.560060 | − | 1.44804i | ||||
\(204\) | 2.86664 | − | 4.96516i | 0.200705 | − | 0.347631i | ||||
\(205\) | −10.2882 | −0.718561 | ||||||||
\(206\) | 7.88888 | + | 4.55465i | 0.549644 | + | 0.317337i | ||||
\(207\) | −3.73482 | − | 6.46890i | −0.259588 | − | 0.449620i | ||||
\(208\) | 0.313194 | − | 3.59192i | 0.0217161 | − | 0.249055i | ||||
\(209\) | 22.3493 | 1.54593 | ||||||||
\(210\) | 2.57949 | − | 6.66932i | 0.178002 | − | 0.460227i | ||||
\(211\) | −3.24329 | − | 5.61754i | −0.223277 | − | 0.386728i | 0.732524 | − | 0.680741i | \(-0.238342\pi\) |
−0.955801 | + | 0.294014i | \(0.905009\pi\) | |||||||
\(212\) | −3.60339 | − | 6.24125i | −0.247482 | − | 0.428651i | ||||
\(213\) | 0.792408 | − | 0.457497i | 0.0542949 | − | 0.0313472i | ||||
\(214\) | 10.5677i | 0.722395i | ||||||||
\(215\) | −14.5445 | + | 8.39725i | −0.991925 | + | 0.572688i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −17.6987 | − | 6.84532i | −1.20146 | − | 0.464691i | ||||
\(218\) | −1.89214 | − | 3.27729i | −0.128152 | − | 0.221966i | ||||
\(219\) | − | 6.85849i | − | 0.463454i | ||||||
\(220\) | −6.88828 | − | 11.9308i | −0.464408 | − | 0.804377i | ||||
\(221\) | −1.79563 | + | 20.5935i | −0.120787 | + | 1.38527i | ||||
\(222\) | 3.38705 | − | 5.86654i | 0.227324 | − | 0.393737i | ||||
\(223\) | −22.5859 | + | 13.0400i | −1.51247 | + | 0.873223i | −0.512572 | + | 0.858644i | \(0.671307\pi\) |
−0.999894 | + | 0.0145787i | \(0.995359\pi\) | |||||||
\(224\) | −2.06034 | + | 1.65982i | −0.137662 | + | 0.110901i | ||||
\(225\) | 1.15240 | − | 1.99602i | 0.0768267 | − | 0.133068i | ||||
\(226\) | 1.47154 | + | 0.849593i | 0.0978852 | + | 0.0565141i | ||||
\(227\) | − | 11.6727i | − | 0.774743i | −0.921924 | − | 0.387372i | \(-0.873383\pi\) | ||
0.921924 | − | 0.387372i | \(-0.126617\pi\) | |||||||
\(228\) | − | 4.38458i | − | 0.290376i | ||||||
\(229\) | −10.4614 | − | 6.03988i | −0.691307 | − | 0.399126i | 0.112794 | − | 0.993618i | \(-0.464020\pi\) |
−0.804102 | + | 0.594492i | \(0.797353\pi\) | |||||||
\(230\) | 10.0943 | − | 17.4838i | 0.665595 | − | 1.15284i | ||||
\(231\) | −12.5781 | − | 4.86482i | −0.827576 | − | 0.320082i | ||||
\(232\) | −7.24074 | + | 4.18045i | −0.475378 | + | 0.274460i | ||||
\(233\) | −4.65865 | + | 8.06902i | −0.305199 | + | 0.528619i | −0.977306 | − | 0.211835i | \(-0.932056\pi\) |
0.672107 | + | 0.740454i | \(0.265389\pi\) | |||||||
\(234\) | −1.52473 | − | 3.26729i | −0.0996745 | − | 0.213590i | ||||
\(235\) | 11.6125 | + | 20.1134i | 0.757515 | + | 1.31205i | ||||
\(236\) | 6.47957i | 0.421784i | ||||||||
\(237\) | 3.81342 | + | 6.60504i | 0.247709 | + | 0.429044i | ||||
\(238\) | 11.8125 | − | 9.51619i | 0.765691 | − | 0.616843i | ||||
\(239\) | − | 16.8139i | − | 1.08760i | −0.839215 | − | 0.543799i | \(-0.816985\pi\) | ||
0.839215 | − | 0.543799i | \(-0.183015\pi\) | |||||||
\(240\) | −2.34064 | + | 1.35137i | −0.151088 | + | 0.0872305i | ||||
\(241\) | − | 22.3511i | − | 1.43976i | −0.694098 | − | 0.719881i | \(-0.744196\pi\) | ||
0.694098 | − | 0.719881i | \(-0.255804\pi\) | |||||||
\(242\) | −12.9748 | + | 7.49101i | −0.834052 | + | 0.481540i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.32523 | − | 4.02741i | −0.148857 | − | 0.257829i | ||||
\(245\) | 12.7304 | − | 13.9954i | 0.813315 | − | 0.894136i | ||||
\(246\) | 3.80659 | 0.242699 | ||||||||
\(247\) | 6.68528 | + | 14.3257i | 0.425374 | + | 0.911522i | ||||
\(248\) | 3.58619 | + | 6.21147i | 0.227723 | + | 0.394429i | ||||
\(249\) | 13.3339 | + | 7.69830i | 0.844999 | + | 0.487860i | ||||
\(250\) | −7.28442 | −0.460707 | ||||||||
\(251\) | 3.75155 | − | 6.49788i | 0.236796 | − | 0.410143i | −0.722997 | − | 0.690851i | \(-0.757236\pi\) |
0.959793 | + | 0.280708i | \(0.0905694\pi\) | |||||||
\(252\) | −0.954400 | + | 2.46761i | −0.0601215 | + | 0.155445i | ||||
\(253\) | −32.9736 | − | 19.0373i | −2.07304 | − | 1.19687i | ||||
\(254\) | −5.39450 | + | 3.11451i | −0.338481 | + | 0.195422i | ||||
\(255\) | 13.4195 | − | 7.74778i | 0.840365 | − | 0.485185i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.03753 | −0.438989 | −0.219494 | − | 0.975614i | \(-0.570441\pi\) | ||||
−0.219494 | + | 0.975614i | \(0.570441\pi\) | |||||||
\(258\) | 5.38138 | − | 3.10694i | 0.335030 | − | 0.193430i | ||||
\(259\) | 13.9570 | − | 11.2438i | 0.867244 | − | 0.698654i | ||||
\(260\) | 5.58709 | − | 7.98416i | 0.346497 | − | 0.495157i | ||||
\(261\) | −4.18045 | + | 7.24074i | −0.258763 | + | 0.448191i | ||||
\(262\) | −0.620884 | − | 0.358468i | −0.0383583 | − | 0.0221462i | ||||
\(263\) | 11.9643 | − | 20.7228i | 0.737750 | − | 1.27782i | −0.215757 | − | 0.976447i | \(-0.569222\pi\) |
0.953506 | − | 0.301373i | \(-0.0974449\pi\) | |||||||
\(264\) | 2.54863 | + | 4.41435i | 0.156857 | + | 0.271685i | ||||
\(265\) | − | 19.4780i | − | 1.19653i | ||||||
\(266\) | 4.18464 | − | 10.8194i | 0.256577 | − | 0.663383i | ||||
\(267\) | 8.99129 | + | 5.19112i | 0.550258 | + | 0.317692i | ||||
\(268\) | −5.25284 | − | 3.03273i | −0.320868 | − | 0.185253i | ||||
\(269\) | −1.59963 | −0.0975312 | −0.0487656 | − | 0.998810i | \(-0.515529\pi\) | ||||
−0.0487656 | + | 0.998810i | \(0.515529\pi\) | |||||||
\(270\) | −1.35137 | + | 2.34064i | −0.0822417 | + | 0.142447i | ||||
\(271\) | − | 20.0012i | − | 1.21498i | −0.794326 | − | 0.607492i | \(-0.792176\pi\) | ||
0.794326 | − | 0.607492i | \(-0.207824\pi\) | |||||||
\(272\) | −5.73328 | −0.347631 | ||||||||
\(273\) | −0.644135 | − | 9.51762i | −0.0389848 | − | 0.576033i | ||||
\(274\) | 10.0557 | 0.607490 | ||||||||
\(275\) | − | 11.7482i | − | 0.708441i | ||||||
\(276\) | −3.73482 | + | 6.46890i | −0.224810 | + | 0.389382i | ||||
\(277\) | −18.1117 | −1.08822 | −0.544112 | − | 0.839012i | \(-0.683133\pi\) | ||||
−0.544112 | + | 0.839012i | \(0.683133\pi\) | |||||||
\(278\) | 15.3231 | + | 8.84682i | 0.919021 | + | 0.530597i | ||||
\(279\) | 6.21147 | + | 3.58619i | 0.371871 | + | 0.214700i | ||||
\(280\) | −7.06555 | + | 1.10075i | −0.422247 | + | 0.0657826i | ||||
\(281\) | 11.0176i | 0.657253i | 0.944460 | + | 0.328626i | \(0.106586\pi\) | ||||
−0.944460 | + | 0.328626i | \(0.893414\pi\) | |||||||
\(282\) | −4.29656 | − | 7.44186i | −0.255856 | − | 0.443156i | ||||
\(283\) | 6.74682 | − | 11.6858i | 0.401057 | − | 0.694651i | −0.592797 | − | 0.805352i | \(-0.701976\pi\) |
0.993854 | + | 0.110701i | \(0.0353096\pi\) | |||||||
\(284\) | −0.792408 | − | 0.457497i | −0.0470208 | − | 0.0271474i | ||||
\(285\) | 5.92518 | − | 10.2627i | 0.350978 | − | 0.607911i | ||||
\(286\) | −15.0578 | − | 10.5370i | −0.890386 | − | 0.623067i | ||||
\(287\) | 9.39320 | + | 3.63301i | 0.554463 | + | 0.214450i | ||||
\(288\) | 0.866025 | − | 0.500000i | 0.0510310 | − | 0.0294628i | ||||
\(289\) | 15.8705 | 0.933557 | ||||||||
\(290\) | −22.5973 | −1.32696 | ||||||||
\(291\) | −8.20116 | + | 4.73494i | −0.480761 | + | 0.277567i | ||||
\(292\) | −5.93963 | + | 3.42924i | −0.347590 | + | 0.200681i | ||||
\(293\) | 4.13569 | + | 2.38774i | 0.241610 | + | 0.139494i | 0.615916 | − | 0.787811i | \(-0.288786\pi\) |
−0.374307 | + | 0.927305i | \(0.622119\pi\) | |||||||
\(294\) | −4.71018 | + | 5.17824i | −0.274703 | + | 0.302001i | ||||
\(295\) | −8.75630 | + | 15.1664i | −0.509811 | + | 0.883019i | ||||
\(296\) | −6.77410 | −0.393737 | ||||||||
\(297\) | 4.41435 | + | 2.54863i | 0.256147 | + | 0.147886i | ||||
\(298\) | −11.6457 | − | 20.1710i | −0.674619 | − | 1.16847i | ||||
\(299\) | 2.33945 | − | 26.8304i | 0.135294 | − | 1.55164i | ||||
\(300\) | −2.30480 | −0.133068 | ||||||||
\(301\) | 16.2444 | − | 2.53075i | 0.936314 | − | 0.145870i | ||||
\(302\) | 9.15737 | + | 15.8610i | 0.526947 | + | 0.912699i | ||||
\(303\) | −1.86105 | − | 3.22344i | −0.106915 | − | 0.185182i | ||||
\(304\) | −3.79715 | + | 2.19229i | −0.217782 | + | 0.125736i | ||||
\(305\) | − | 12.5690i | − | 0.719697i | ||||||
\(306\) | −4.96516 | + | 2.86664i | −0.283840 | + | 0.163875i | ||||
\(307\) | − | 6.26422i | − | 0.357518i | −0.983893 | − | 0.178759i | \(-0.942792\pi\) | ||
0.983893 | − | 0.178759i | \(-0.0572082\pi\) | |||||||
\(308\) | 2.07597 | + | 13.3253i | 0.118290 | + | 0.759281i | ||||
\(309\) | −4.55465 | − | 7.88888i | −0.259105 | − | 0.448783i | ||||
\(310\) | 19.3851i | 1.10100i | ||||||||
\(311\) | 2.99213 | + | 5.18252i | 0.169668 | + | 0.293874i | 0.938303 | − | 0.345814i | \(-0.112397\pi\) |
−0.768635 | + | 0.639688i | \(0.779064\pi\) | |||||||
\(312\) | −2.06720 | + | 2.95410i | −0.117032 | + | 0.167243i | ||||
\(313\) | 14.3286 | − | 24.8179i | 0.809902 | − | 1.40279i | −0.103030 | − | 0.994678i | \(-0.532854\pi\) |
0.912931 | − | 0.408113i | \(-0.133813\pi\) | |||||||
\(314\) | 3.32164 | − | 1.91775i | 0.187451 | − | 0.108225i | ||||
\(315\) | −5.56857 | + | 4.48605i | −0.313753 | + | 0.252760i | ||||
\(316\) | 3.81342 | − | 6.60504i | 0.214522 | − | 0.371563i | ||||
\(317\) | 22.2694 | + | 12.8572i | 1.25077 | + | 0.722134i | 0.971263 | − | 0.238009i | \(-0.0764949\pi\) |
0.279509 | + | 0.960143i | \(0.409828\pi\) | |||||||
\(318\) | 7.20677i | 0.404136i | ||||||||
\(319\) | 42.6176i | 2.38613i | ||||||||
\(320\) | 2.34064 | + | 1.35137i | 0.130846 | + | 0.0755439i | ||||
\(321\) | 5.28386 | − | 9.15192i | 0.294917 | − | 0.510810i | ||||
\(322\) | −15.3900 | + | 12.3982i | −0.857652 | + | 0.690927i | ||||
\(323\) | 21.7701 | − | 12.5690i | 1.21132 | − | 0.699358i | ||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 7.53046 | − | 3.51419i | 0.417715 | − | 0.194932i | ||||
\(326\) | 5.21359 | + | 9.03020i | 0.288754 | + | 0.500137i | ||||
\(327\) | 3.78429i | 0.209272i | ||||||||
\(328\) | −1.90330 | − | 3.29661i | −0.105092 | − | 0.182025i | ||||
\(329\) | −3.49975 | − | 22.4643i | −0.192947 | − | 1.23850i | ||||
\(330\) | 13.7766i | 0.758374i | ||||||||
\(331\) | −0.762189 | + | 0.440050i | −0.0418937 | + | 0.0241873i | −0.520801 | − | 0.853678i | \(-0.674366\pi\) |
0.478907 | + | 0.877866i | \(0.341033\pi\) | |||||||
\(332\) | − | 15.3966i | − | 0.844999i | ||||||
\(333\) | −5.86654 | + | 3.38705i | −0.321485 | + | 0.185609i | ||||
\(334\) | −1.10027 | − | 1.90573i | −0.0602043 | − | 0.104277i | ||||
\(335\) | −8.19667 | − | 14.1971i | −0.447832 | − | 0.775668i | ||||
\(336\) | 2.61422 | − | 0.407273i | 0.142617 | − | 0.0222186i | ||||
\(337\) | 16.4964 | 0.898617 | 0.449308 | − | 0.893377i | \(-0.351670\pi\) | ||||
0.449308 | + | 0.893377i | \(0.351670\pi\) | |||||||
\(338\) | 2.24994 | − | 12.8038i | 0.122381 | − | 0.696436i | ||||
\(339\) | −0.849593 | − | 1.47154i | −0.0461435 | − | 0.0799230i | ||||
\(340\) | −13.4195 | − | 7.74778i | −0.727777 | − | 0.420182i | ||||
\(341\) | 36.5595 | 1.97981 | ||||||||
\(342\) | −2.19229 | + | 3.79715i | −0.118545 | + | 0.205327i | ||||
\(343\) | −16.5650 | + | 8.28251i | −0.894427 | + | 0.447214i | ||||
\(344\) | −5.38138 | − | 3.10694i | −0.290145 | − | 0.167515i | ||||
\(345\) | −17.4838 | + | 10.0943i | −0.941294 | + | 0.543456i | ||||
\(346\) | 18.5992 | − | 10.7383i | 0.999900 | − | 0.577292i | ||||
\(347\) | −5.59149 | −0.300167 | −0.150084 | − | 0.988673i | \(-0.547954\pi\) | ||||
−0.150084 | + | 0.988673i | \(0.547954\pi\) | |||||||
\(348\) | 8.36089 | 0.448191 | ||||||||
\(349\) | −11.1268 | + | 6.42408i | −0.595606 | + | 0.343873i | −0.767311 | − | 0.641275i | \(-0.778406\pi\) |
0.171705 | + | 0.985148i | \(0.445072\pi\) | |||||||
\(350\) | −5.68736 | − | 2.19970i | −0.304002 | − | 0.117579i | ||||
\(351\) | −0.313194 | + | 3.59192i | −0.0167171 | + | 0.191723i | ||||
\(352\) | 2.54863 | − | 4.41435i | 0.135842 | − | 0.235286i | ||||
\(353\) | 15.9755 | + | 9.22345i | 0.850289 | + | 0.490915i | 0.860748 | − | 0.509031i | \(-0.169996\pi\) |
−0.0104593 | + | 0.999945i | \(0.503329\pi\) | |||||||
\(354\) | 3.23979 | − | 5.61147i | 0.172193 | − | 0.298247i | ||||
\(355\) | −1.23649 | − | 2.14167i | −0.0656263 | − | 0.113668i | ||||
\(356\) | − | 10.3822i | − | 0.550258i | ||||||
\(357\) | −14.9880 | + | 2.33501i | −0.793251 | + | 0.123582i | ||||
\(358\) | 16.1758 | + | 9.33910i | 0.854917 | + | 0.493587i | ||||
\(359\) | 9.96875 | + | 5.75546i | 0.526130 | + | 0.303761i | 0.739439 | − | 0.673223i | \(-0.235091\pi\) |
−0.213309 | + | 0.976985i | \(0.568424\pi\) | |||||||
\(360\) | 2.70274 | 0.142447 | ||||||||
\(361\) | 0.112254 | − | 0.194430i | 0.00590811 | − | 0.0102331i | ||||
\(362\) | 1.97032i | 0.103557i | ||||||||
\(363\) | 14.9820 | 0.786352 | ||||||||
\(364\) | −7.92043 | + | 5.31665i | −0.415143 | + | 0.278668i | ||||
\(365\) | −18.5367 | −0.970256 | ||||||||
\(366\) | 4.65046i | 0.243083i | ||||||||
\(367\) | −3.00680 | + | 5.20794i | −0.156954 | + | 0.271852i | −0.933769 | − | 0.357877i | \(-0.883501\pi\) |
0.776815 | + | 0.629729i | \(0.216834\pi\) | |||||||
\(368\) | 7.46964 | 0.389382 | ||||||||
\(369\) | −3.29661 | − | 1.90330i | −0.171614 | − | 0.0990816i | ||||
\(370\) | −15.8557 | − | 9.15432i | −0.824301 | − | 0.475910i | ||||
\(371\) | −6.87814 | + | 17.7835i | −0.357095 | + | 0.923275i | ||||
\(372\) | − | 7.17238i | − | 0.371871i | ||||||
\(373\) | −4.79186 | − | 8.29975i | −0.248113 | − | 0.429745i | 0.714889 | − | 0.699238i | \(-0.246477\pi\) |
−0.963002 | + | 0.269493i | \(0.913144\pi\) | |||||||
\(374\) | −14.6120 | + | 25.3087i | −0.755568 | + | 1.30868i | ||||
\(375\) | 6.30849 | + | 3.64221i | 0.325769 | + | 0.188083i | ||||
\(376\) | −4.29656 | + | 7.44186i | −0.221578 | + | 0.383785i | ||||
\(377\) | −27.3175 | + | 12.7481i | −1.40692 | + | 0.656559i | ||||
\(378\) | 2.06034 | − | 1.65982i | 0.105973 | − | 0.0853718i | ||||
\(379\) | −21.9503 | + | 12.6730i | −1.12751 | + | 0.650969i | −0.943308 | − | 0.331919i | \(-0.892304\pi\) |
−0.184203 | + | 0.982888i | \(0.558971\pi\) | |||||||
\(380\) | −11.8504 | −0.607911 | ||||||||
\(381\) | 6.22903 | 0.319123 | ||||||||
\(382\) | 3.21249 | − | 1.85473i | 0.164365 | − | 0.0948964i | ||||
\(383\) | −0.247581 | + | 0.142941i | −0.0126508 | + | 0.00730394i | −0.506312 | − | 0.862350i | \(-0.668992\pi\) |
0.493661 | + | 0.869654i | \(0.335658\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | −13.1483 | + | 33.9952i | −0.670101 | + | 1.73256i | ||||
\(386\) | −1.49000 | + | 2.58076i | −0.0758390 | + | 0.131357i | ||||
\(387\) | −6.21388 | −0.315869 | ||||||||
\(388\) | 8.20116 | + | 4.73494i | 0.416351 | + | 0.240380i | ||||
\(389\) | −1.66201 | − | 2.87869i | −0.0842674 | − | 0.145955i | 0.820811 | − | 0.571199i | \(-0.193522\pi\) |
−0.905079 | + | 0.425244i | \(0.860188\pi\) | |||||||
\(390\) | −8.83064 | + | 4.12094i | −0.447157 | + | 0.208672i | ||||
\(391\) | −42.8255 | −2.16578 | ||||||||
\(392\) | 6.83958 | + | 1.49001i | 0.345451 | + | 0.0752571i | ||||
\(393\) | 0.358468 | + | 0.620884i | 0.0180823 | + | 0.0313195i | ||||
\(394\) | −7.44330 | − | 12.8922i | −0.374988 | − | 0.649498i | ||||
\(395\) | 17.8517 | − | 10.3067i | 0.898217 | − | 0.518586i | ||||
\(396\) | − | 5.09726i | − | 0.256147i | ||||||
\(397\) | −26.3981 | + | 15.2409i | −1.32488 | + | 0.764921i | −0.984503 | − | 0.175368i | \(-0.943889\pi\) |
−0.340378 | + | 0.940289i | \(0.610555\pi\) | |||||||
\(398\) | − | 2.66427i | − | 0.133548i | ||||||
\(399\) | −9.03372 | + | 7.27759i | −0.452252 | + | 0.364335i | ||||
\(400\) | 1.15240 | + | 1.99602i | 0.0576200 | + | 0.0998008i | ||||
\(401\) | − | 19.5601i | − | 0.976783i | −0.872625 | − | 0.488392i | \(-0.837584\pi\) | ||
0.872625 | − | 0.488392i | \(-0.162416\pi\) | |||||||
\(402\) | 3.03273 | + | 5.25284i | 0.151259 | + | 0.261988i | ||||
\(403\) | 10.9359 | + | 23.4343i | 0.544757 | + | 1.16734i | ||||
\(404\) | −1.86105 | + | 3.22344i | −0.0925908 | + | 0.160372i | ||||
\(405\) | 2.34064 | − | 1.35137i | 0.116307 | − | 0.0671501i | ||||
\(406\) | 20.6315 | + | 7.97963i | 1.02392 | + | 0.396022i | ||||
\(407\) | −17.2647 | + | 29.9033i | −0.855778 | + | 1.48225i | ||||
\(408\) | 4.96516 | + | 2.86664i | 0.245812 | + | 0.141920i | ||||
\(409\) | − | 17.0474i | − | 0.842942i | −0.906842 | − | 0.421471i | \(-0.861514\pi\) | ||
0.906842 | − | 0.421471i | \(-0.138486\pi\) | |||||||
\(410\) | − | 10.2882i | − | 0.508099i | ||||||
\(411\) | −8.70853 | − | 5.02787i | −0.429560 | − | 0.248007i | ||||
\(412\) | −4.55465 | + | 7.88888i | −0.224391 | + | 0.388657i | ||||
\(413\) | 13.3501 | − | 10.7549i | 0.656917 | − | 0.529214i | ||||
\(414\) | 6.46890 | − | 3.73482i | 0.317929 | − | 0.183557i | ||||
\(415\) | 20.8065 | − | 36.0379i | 1.02135 | − | 1.76903i | ||||
\(416\) | 3.59192 | + | 0.313194i | 0.176109 | + | 0.0153556i | ||||
\(417\) | −8.84682 | − | 15.3231i | −0.433231 | − | 0.750377i | ||||
\(418\) | 22.3493i | 1.09314i | ||||||||
\(419\) | 4.16216 | + | 7.20908i | 0.203335 | + | 0.352186i | 0.949601 | − | 0.313461i | \(-0.101489\pi\) |
−0.746266 | + | 0.665648i | \(0.768155\pi\) | |||||||
\(420\) | 6.66932 | + | 2.57949i | 0.325429 | + | 0.125866i | ||||
\(421\) | − | 35.9805i | − | 1.75358i | −0.480873 | − | 0.876790i | \(-0.659680\pi\) | ||
0.480873 | − | 0.876790i | \(-0.340320\pi\) | |||||||
\(422\) | 5.61754 | − | 3.24329i | 0.273458 | − | 0.157881i | ||||
\(423\) | 8.59312i | 0.417812i | ||||||||
\(424\) | 6.24125 | − | 3.60339i | 0.303102 | − | 0.174996i | ||||
\(425\) | −6.60703 | − | 11.4437i | −0.320488 | − | 0.555102i | ||||
\(426\) | 0.457497 | + | 0.792408i | 0.0221658 | + | 0.0383923i | ||||
\(427\) | −4.43839 | + | 11.4755i | −0.214789 | + | 0.555340i | ||||
\(428\) | −10.5677 | −0.510810 | ||||||||
\(429\) | 7.77192 | + | 16.6542i | 0.375232 | + | 0.804074i | ||||
\(430\) | −8.39725 | − | 14.5445i | −0.404951 | − | 0.701397i | ||||
\(431\) | −5.37734 | − | 3.10461i | −0.259018 | − | 0.149544i | 0.364869 | − | 0.931059i | \(-0.381114\pi\) |
−0.623886 | + | 0.781515i | \(0.714447\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −3.98578 | + | 6.90357i | −0.191544 | + | 0.331764i | −0.945762 | − | 0.324860i | \(-0.894683\pi\) |
0.754218 | + | 0.656624i | \(0.228016\pi\) | |||||||
\(434\) | 6.84532 | − | 17.6987i | 0.328586 | − | 0.849564i | ||||
\(435\) | 19.5698 | + | 11.2987i | 0.938302 | + | 0.541729i | ||||
\(436\) | 3.27729 | − | 1.89214i | 0.156954 | − | 0.0906173i | ||||
\(437\) | −28.3634 | + | 16.3756i | −1.35681 | + | 0.783352i | ||||
\(438\) | 6.85849 | 0.327711 | ||||||||
\(439\) | 14.1623 | 0.675928 | 0.337964 | − | 0.941159i | \(-0.390262\pi\) | ||||
0.337964 | + | 0.941159i | \(0.390262\pi\) | |||||||
\(440\) | 11.9308 | − | 6.88828i | 0.568781 | − | 0.328386i | ||||
\(441\) | 6.66826 | − | 2.12940i | 0.317536 | − | 0.101400i | ||||
\(442\) | −20.5935 | − | 1.79563i | −0.979532 | − | 0.0854094i | ||||
\(443\) | −13.7918 | + | 23.8880i | −0.655267 | + | 1.13495i | 0.326560 | + | 0.945176i | \(0.394110\pi\) |
−0.981827 | + | 0.189779i | \(0.939223\pi\) | |||||||
\(444\) | 5.86654 | + | 3.38705i | 0.278414 | + | 0.160742i | ||||
\(445\) | 14.0303 | − | 24.3011i | 0.665098 | − | 1.15198i | ||||
\(446\) | −13.0400 | − | 22.5859i | −0.617462 | − | 1.06948i | ||||
\(447\) | 23.2914i | 1.10165i | ||||||||
\(448\) | −1.65982 | − | 2.06034i | −0.0784190 | − | 0.0973420i | ||||
\(449\) | 2.53224 | + | 1.46199i | 0.119504 | + | 0.0689957i | 0.558560 | − | 0.829464i | \(-0.311354\pi\) |
−0.439056 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(450\) | 1.99602 | + | 1.15240i | 0.0940931 | + | 0.0543247i | ||||
\(451\) | −19.4032 | −0.913660 | ||||||||
\(452\) | −0.849593 | + | 1.47154i | −0.0399615 | + | 0.0692153i | ||||
\(453\) | − | 18.3147i | − | 0.860501i | ||||||
\(454\) | 11.6727 | 0.547826 | ||||||||
\(455\) | −25.7236 | + | 1.74093i | −1.20594 | + | 0.0816161i | ||||
\(456\) | 4.38458 | 0.205327 | ||||||||
\(457\) | 20.9436i | 0.979702i | 0.871806 | + | 0.489851i | \(0.162949\pi\) | ||||
−0.871806 | + | 0.489851i | \(0.837051\pi\) | |||||||
\(458\) | 6.03988 | − | 10.4614i | 0.282225 | − | 0.488828i | ||||
\(459\) | 5.73328 | 0.267606 | ||||||||
\(460\) | 17.4838 | + | 10.0943i | 0.815184 | + | 0.470647i | ||||
\(461\) | 15.9388 | + | 9.20229i | 0.742346 | + | 0.428593i | 0.822922 | − | 0.568155i | \(-0.192343\pi\) |
−0.0805759 | + | 0.996748i | \(0.525676\pi\) | |||||||
\(462\) | 4.86482 | − | 12.5781i | 0.226332 | − | 0.585184i | ||||
\(463\) | 28.8633i | 1.34139i | 0.741732 | + | 0.670697i | \(0.234005\pi\) | ||||
−0.741732 | + | 0.670697i | \(0.765995\pi\) | |||||||
\(464\) | −4.18045 | − | 7.24074i | −0.194072 | − | 0.336143i | ||||
\(465\) | 9.69254 | − | 16.7880i | 0.449481 | − | 0.778524i | ||||
\(466\) | −8.06902 | − | 4.65865i | −0.373790 | − | 0.215808i | ||||
\(467\) | −16.8772 | + | 29.2322i | −0.780983 | + | 1.35270i | 0.150386 | + | 0.988627i | \(0.451948\pi\) |
−0.931369 | + | 0.364075i | \(0.881385\pi\) | |||||||
\(468\) | 3.26729 | − | 1.52473i | 0.151031 | − | 0.0704805i | ||||
\(469\) | 2.47030 | + | 15.8564i | 0.114068 | + | 0.732181i | ||||
\(470\) | −20.1134 | + | 11.6125i | −0.927762 | + | 0.535644i | ||||
\(471\) | −3.83550 | −0.176731 | ||||||||
\(472\) | −6.47957 | −0.298247 | ||||||||
\(473\) | −27.4303 | + | 15.8369i | −1.26125 | + | 0.728180i | ||||
\(474\) | −6.60504 | + | 3.81342i | −0.303380 | + | 0.175156i | ||||
\(475\) | −8.75168 | − | 5.05279i | −0.401555 | − | 0.231838i | ||||
\(476\) | 9.51619 | + | 11.8125i | 0.436174 | + | 0.541426i | ||||
\(477\) | 3.60339 | − | 6.24125i | 0.164988 | − | 0.285767i | ||||
\(478\) | 16.8139 | 0.769048 | ||||||||
\(479\) | 15.0874 | + | 8.71070i | 0.689360 | + | 0.398002i | 0.803372 | − | 0.595477i | \(-0.203037\pi\) |
−0.114012 | + | 0.993479i | \(0.536370\pi\) | |||||||
\(480\) | −1.35137 | − | 2.34064i | −0.0616813 | − | 0.106835i | ||||
\(481\) | −24.3321 | − | 2.12161i | −1.10945 | − | 0.0967371i | ||||
\(482\) | 22.3511 | 1.01807 | ||||||||
\(483\) | 19.5273 | − | 3.04218i | 0.888522 | − | 0.138424i | ||||
\(484\) | −7.49101 | − | 12.9748i | −0.340500 | − | 0.589764i | ||||
\(485\) | 12.7973 | + | 22.1656i | 0.581096 | + | 1.00649i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | − | 38.2660i | − | 1.73400i | −0.498312 | − | 0.866998i | \(-0.666046\pi\) | ||
0.498312 | − | 0.866998i | \(-0.333954\pi\) | |||||||
\(488\) | 4.02741 | − | 2.32523i | 0.182312 | − | 0.105258i | ||||
\(489\) | − | 10.4272i | − | 0.471533i | ||||||
\(490\) | 13.9954 | + | 12.7304i | 0.632250 | + | 0.575100i | ||||
\(491\) | −18.3883 | − | 31.8494i | −0.829851 | − | 1.43734i | −0.898155 | − | 0.439679i | \(-0.855092\pi\) |
0.0683042 | − | 0.997665i | \(-0.478241\pi\) | |||||||
\(492\) | 3.80659i | 0.171614i | ||||||||
\(493\) | 23.9677 | + | 41.5132i | 1.07945 | + | 1.86966i | ||||
\(494\) | −14.3257 | + | 6.68528i | −0.644544 | + | 0.300785i | ||||
\(495\) | 6.88828 | − | 11.9308i | 0.309605 | − | 0.536252i | ||||
\(496\) | −6.21147 | + | 3.58619i | −0.278903 | + | 0.161025i | ||||
\(497\) | 0.372652 | + | 2.39199i | 0.0167157 | + | 0.107296i | ||||
\(498\) | −7.69830 | + | 13.3339i | −0.344969 | + | 0.597504i | ||||
\(499\) | 26.0698 | + | 15.0514i | 1.16704 | + | 0.673793i | 0.952982 | − | 0.303027i | \(-0.0979973\pi\) |
0.214062 | + | 0.976820i | \(0.431331\pi\) | |||||||
\(500\) | − | 7.28442i | − | 0.325769i | ||||||
\(501\) | 2.20055i | 0.0983133i | ||||||||
\(502\) | 6.49788 | + | 3.75155i | 0.290015 | + | 0.167440i | ||||
\(503\) | 3.90097 | − | 6.75668i | 0.173936 | − | 0.301265i | −0.765857 | − | 0.643011i | \(-0.777685\pi\) |
0.939792 | + | 0.341746i | \(0.111018\pi\) | |||||||
\(504\) | −2.46761 | − | 0.954400i | −0.109916 | − | 0.0425123i | ||||
\(505\) | −8.71211 | + | 5.02994i | −0.387684 | + | 0.223829i | ||||
\(506\) | 19.0373 | − | 32.9736i | 0.846313 | − | 1.46586i | ||||
\(507\) | −8.35041 | + | 9.96346i | −0.370855 | + | 0.442493i | ||||
\(508\) | −3.11451 | − | 5.39450i | −0.138184 | − | 0.239342i | ||||
\(509\) | 21.9997i | 0.975121i | 0.873089 | + | 0.487561i | \(0.162113\pi\) | ||||
−0.873089 | + | 0.487561i | \(0.837887\pi\) | |||||||
\(510\) | 7.74778 | + | 13.4195i | 0.343077 | + | 0.594227i | ||||
\(511\) | 16.9241 | + | 6.54574i | 0.748679 | + | 0.289567i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.79715 | − | 2.19229i | 0.167648 | − | 0.0967919i | ||||
\(514\) | − | 7.03753i | − | 0.310412i | ||||||
\(515\) | −21.3216 | + | 12.3100i | −0.939541 | + | 0.542444i | ||||
\(516\) | 3.10694 | + | 5.38138i | 0.136775 | + | 0.236902i | ||||
\(517\) | 21.9007 | + | 37.9331i | 0.963190 | + | 1.66829i | ||||
\(518\) | 11.2438 | + | 13.9570i | 0.494023 | + | 0.613234i | ||||
\(519\) | −21.4765 | −0.942714 | ||||||||
\(520\) | 7.98416 | + | 5.58709i | 0.350129 | + | 0.245010i | ||||
\(521\) | 13.9174 | + | 24.1056i | 0.609732 | + | 1.05609i | 0.991284 | + | 0.131740i | \(0.0420563\pi\) |
−0.381552 | + | 0.924347i | \(0.624610\pi\) | |||||||
\(522\) | −7.24074 | − | 4.18045i | −0.316919 | − | 0.182973i | ||||
\(523\) | −9.68552 | −0.423518 | −0.211759 | − | 0.977322i | \(-0.567919\pi\) | ||||
−0.211759 | + | 0.977322i | \(0.567919\pi\) | |||||||
\(524\) | 0.358468 | − | 0.620884i | 0.0156597 | − | 0.0271234i | ||||
\(525\) | 3.82555 | + | 4.74868i | 0.166961 | + | 0.207249i | ||||
\(526\) | 20.7228 | + | 11.9643i | 0.903555 | + | 0.521668i | ||||
\(527\) | 35.6121 | − | 20.5606i | 1.55129 | − | 0.895635i | ||||
\(528\) | −4.41435 | + | 2.54863i | −0.192110 | + | 0.110915i | ||||
\(529\) | 32.7956 | 1.42590 | ||||||||
\(530\) | 19.4780 | 0.846071 | ||||||||
\(531\) | −5.61147 | + | 3.23979i | −0.243517 | + | 0.140595i | ||||
\(532\) | 10.8194 | + | 4.18464i | 0.469082 | + | 0.181427i | ||||
\(533\) | −5.80402 | − | 12.4373i | −0.251400 | − | 0.538717i | ||||
\(534\) | −5.19112 | + | 8.99129i | −0.224642 | + | 0.389091i | ||||
\(535\) | −24.7353 | − | 14.2809i | −1.06940 | − | 0.617418i | ||||
\(536\) | 3.03273 | − | 5.25284i | 0.130994 | − | 0.226888i | ||||
\(537\) | −9.33910 | − | 16.1758i | −0.403012 | − | 0.698037i | ||||
\(538\) | − | 1.59963i | − | 0.0689649i | ||||||
\(539\) | 24.0090 | − | 26.3948i | 1.03414 | − | 1.13691i | ||||
\(540\) | −2.34064 | − | 1.35137i | −0.100725 | − | 0.0581537i | ||||
\(541\) | 0.964894 | + | 0.557082i | 0.0414840 | + | 0.0239508i | 0.520599 | − | 0.853802i | \(-0.325709\pi\) |
−0.479115 | + | 0.877752i | \(0.659042\pi\) | |||||||
\(542\) | 20.0012 | 0.859124 | ||||||||
\(543\) | 0.985158 | − | 1.70634i | 0.0422772 | − | 0.0732262i | ||||
\(544\) | − | 5.73328i | − | 0.245812i | ||||||
\(545\) | 10.2279 | 0.438117 | ||||||||
\(546\) | 9.51762 | − | 0.644135i | 0.407317 | − | 0.0275664i | ||||
\(547\) | −18.4164 | −0.787430 | −0.393715 | − | 0.919233i | \(-0.628810\pi\) | ||||
−0.393715 | + | 0.919233i | \(0.628810\pi\) | |||||||
\(548\) | 10.0557i | 0.429560i | ||||||||
\(549\) | 2.32523 | − | 4.02741i | 0.0992383 | − | 0.171886i | ||||
\(550\) | 11.7482 | 0.500943 | ||||||||
\(551\) | 31.7476 | + | 18.3295i | 1.35249 | + | 0.780862i | ||||
\(552\) | −6.46890 | − | 3.73482i | −0.275335 | − | 0.158965i | ||||
\(553\) | −19.9382 | + | 3.10621i | −0.847860 | + | 0.132089i | ||||
\(554\) | − | 18.1117i | − | 0.769491i | ||||||
\(555\) | 9.15432 | + | 15.8557i | 0.388579 | + | 0.673039i | ||||
\(556\) | −8.84682 | + | 15.3231i | −0.375189 | + | 0.649846i | ||||
\(557\) | −29.1335 | − | 16.8202i | −1.23443 | − | 0.712696i | −0.266476 | − | 0.963841i | \(-0.585859\pi\) |
−0.967949 | + | 0.251145i | \(0.919193\pi\) | |||||||
\(558\) | −3.58619 | + | 6.21147i | −0.151816 | + | 0.262952i | ||||
\(559\) | −18.3564 | − | 12.8453i | −0.776394 | − | 0.543299i | ||||
\(560\) | −1.10075 | − | 7.06555i | −0.0465153 | − | 0.298574i | ||||
\(561\) | 25.3087 | − | 14.6120i | 1.06853 | − | 0.616919i | ||||
\(562\) | −11.0176 | −0.464748 | ||||||||
\(563\) | −1.55896 | −0.0657024 | −0.0328512 | − | 0.999460i | \(-0.510459\pi\) | ||||
−0.0328512 | + | 0.999460i | \(0.510459\pi\) | |||||||
\(564\) | 7.44186 | − | 4.29656i | 0.313359 | − | 0.180918i | ||||
\(565\) | −3.97718 | + | 2.29623i | −0.167321 | + | 0.0966030i | ||||
\(566\) | 11.6858 | + | 6.74682i | 0.491193 | + | 0.283590i | ||||
\(567\) | −2.61422 | + | 0.407273i | −0.109787 | + | 0.0171039i | ||||
\(568\) | 0.457497 | − | 0.792408i | 0.0191961 | − | 0.0332487i | ||||
\(569\) | −5.20659 | −0.218272 | −0.109136 | − | 0.994027i | \(-0.534808\pi\) | ||||
−0.109136 | + | 0.994027i | \(0.534808\pi\) | |||||||
\(570\) | 10.2627 | + | 5.92518i | 0.429858 | + | 0.248179i | ||||
\(571\) | 5.99348 | + | 10.3810i | 0.250819 | + | 0.434432i | 0.963752 | − | 0.266801i | \(-0.0859666\pi\) |
−0.712932 | + | 0.701233i | \(0.752633\pi\) | |||||||
\(572\) | 10.5370 | − | 15.0578i | 0.440575 | − | 0.629598i | ||||
\(573\) | −3.70946 | −0.154965 | ||||||||
\(574\) | −3.63301 | + | 9.39320i | −0.151639 | + | 0.392065i | ||||
\(575\) | 8.60802 | + | 14.9095i | 0.358979 | + | 0.621770i | ||||
\(576\) | 0.500000 | + | 0.866025i | 0.0208333 | + | 0.0360844i | ||||
\(577\) | 0.299900 | − | 0.173147i | 0.0124850 | − | 0.00720821i | −0.493745 | − | 0.869607i | \(-0.664372\pi\) |
0.506230 | + | 0.862399i | \(0.331039\pi\) | |||||||
\(578\) | 15.8705i | 0.660125i | ||||||||
\(579\) | 2.58076 | − | 1.49000i | 0.107253 | − | 0.0619223i | ||||
\(580\) | − | 22.5973i | − | 0.938302i | ||||||
\(581\) | −31.7223 | + | 25.5556i | −1.31606 | + | 1.06022i | ||||
\(582\) | −4.73494 | − | 8.20116i | −0.196270 | − | 0.339949i | ||||
\(583\) | − | 36.7348i | − | 1.52140i | ||||||
\(584\) | −3.42924 | − | 5.93963i | −0.141903 | − | 0.245783i | ||||
\(585\) | 9.70803 | + | 0.846482i | 0.401378 | + | 0.0349977i | ||||
\(586\) | −2.38774 | + | 4.13569i | −0.0986368 | + | 0.170844i | ||||
\(587\) | 25.5443 | − | 14.7480i | 1.05433 | − | 0.608715i | 0.130468 | − | 0.991453i | \(-0.458352\pi\) |
0.923857 | + | 0.382738i | \(0.125019\pi\) | |||||||
\(588\) | −5.17824 | − | 4.71018i | −0.213547 | − | 0.194245i | ||||
\(589\) | 15.7239 | − | 27.2347i | 0.647893 | − | 1.12218i | ||||
\(590\) | −15.1664 | − | 8.75630i | −0.624389 | − | 0.360491i | ||||
\(591\) | 14.8866i | 0.612353i | ||||||||
\(592\) | − | 6.77410i | − | 0.278414i | ||||||
\(593\) | −2.79980 | − | 1.61647i | −0.114974 | − | 0.0663803i | 0.441410 | − | 0.897305i | \(-0.354478\pi\) |
−0.556384 | + | 0.830925i | \(0.687812\pi\) | |||||||
\(594\) | −2.54863 | + | 4.41435i | −0.104571 | + | 0.181123i | ||||
\(595\) | 6.31092 | + | 40.5087i | 0.258723 | + | 1.66070i | ||||
\(596\) | 20.1710 | − | 11.6457i | 0.826236 | − | 0.477027i | ||||
\(597\) | −1.33214 | + | 2.30733i | −0.0545207 | + | 0.0944327i | ||||
\(598\) | 26.8304 | + | 2.33945i | 1.09718 | + | 0.0956672i | ||||
\(599\) | −6.64023 | − | 11.5012i | −0.271312 | − | 0.469927i | 0.697886 | − | 0.716209i | \(-0.254124\pi\) |
−0.969198 | + | 0.246282i | \(0.920791\pi\) | |||||||
\(600\) | − | 2.30480i | − | 0.0940931i | ||||||
\(601\) | 3.58901 | + | 6.21634i | 0.146399 | + | 0.253570i | 0.929894 | − | 0.367828i | \(-0.119898\pi\) |
−0.783495 | + | 0.621398i | \(0.786565\pi\) | |||||||
\(602\) | 2.53075 | + | 16.2444i | 0.103146 | + | 0.662074i | ||||
\(603\) | − | 6.06546i | − | 0.247004i | ||||||
\(604\) | −15.8610 | + | 9.15737i | −0.645376 | + | 0.372608i | ||||
\(605\) | − | 40.4925i | − | 1.64625i | ||||||
\(606\) | 3.22344 | − | 1.86105i | 0.130943 | − | 0.0756001i | ||||
\(607\) | −20.2069 | − | 34.9994i | −0.820174 | − | 1.42058i | −0.905552 | − | 0.424235i | \(-0.860543\pi\) |
0.0853783 | − | 0.996349i | \(-0.472790\pi\) | |||||||
\(608\) | −2.19229 | − | 3.79715i | −0.0889090 | − | 0.153995i | ||||
\(609\) | −13.8775 | − | 17.2263i | −0.562347 | − | 0.698045i | ||||
\(610\) | 12.5690 | 0.508903 | ||||||||
\(611\) | −17.7637 | + | 25.3849i | −0.718641 | + | 1.02696i | ||||
\(612\) | −2.86664 | − | 4.96516i | −0.115877 | − | 0.200705i | ||||
\(613\) | −7.43967 | − | 4.29529i | −0.300485 | − | 0.173485i | 0.342176 | − | 0.939636i | \(-0.388836\pi\) |
−0.642661 | + | 0.766151i | \(0.722170\pi\) | |||||||
\(614\) | 6.26422 | 0.252803 | ||||||||
\(615\) | −5.14411 | + | 8.90987i | −0.207431 | + | 0.359280i | ||||
\(616\) | −13.3253 | + | 2.07597i | −0.536893 | + | 0.0836434i | ||||
\(617\) | 31.7545 | + | 18.3335i | 1.27839 | + | 0.738079i | 0.976552 | − | 0.215281i | \(-0.0690666\pi\) |
0.301838 | + | 0.953359i | \(0.402400\pi\) | |||||||
\(618\) | 7.88888 | − | 4.55465i | 0.317337 | − | 0.183215i | ||||
\(619\) | 4.95870 | − | 2.86291i | 0.199307 | − | 0.115070i | −0.397025 | − | 0.917808i | \(-0.629957\pi\) |
0.596332 | + | 0.802738i | \(0.296624\pi\) | |||||||
\(620\) | −19.3851 | −0.778524 | ||||||||
\(621\) | −7.46964 | −0.299747 | ||||||||
\(622\) | −5.18252 | + | 2.99213i | −0.207800 | + | 0.119974i | ||||
\(623\) | −21.3910 | + | 17.2326i | −0.857011 | + | 0.690411i | ||||
\(624\) | −2.95410 | − | 2.06720i | −0.118259 | − | 0.0827541i | ||||
\(625\) | 15.6059 | − | 27.0303i | 0.624238 | − | 1.08121i | ||||
\(626\) | 24.8179 | + | 14.3286i | 0.991923 | + | 0.572687i | ||||
\(627\) | 11.1747 | − | 19.3551i | 0.446273 | − | 0.772967i | ||||
\(628\) | 1.91775 | + | 3.32164i | 0.0765266 | + | 0.132548i | ||||
\(629\) | 38.8378i | 1.54856i | ||||||||
\(630\) | −4.48605 | − | 5.56857i | −0.178729 | − | 0.221857i | ||||
\(631\) | −15.3218 | − | 8.84605i | −0.609952 | − | 0.352156i | 0.162995 | − | 0.986627i | \(-0.447885\pi\) |
−0.772947 | + | 0.634471i | \(0.781218\pi\) | |||||||
\(632\) | 6.60504 | + | 3.81342i | 0.262735 | + | 0.151690i | ||||
\(633\) | −6.48658 | −0.257818 | ||||||||
\(634\) | −12.8572 | + | 22.2694i | −0.510626 | + | 0.884430i | ||||
\(635\) | − | 16.8354i | − | 0.668094i | ||||||
\(636\) | −7.20677 | −0.285767 | ||||||||
\(637\) | 24.1006 | + | 7.49414i | 0.954900 | + | 0.296928i | ||||
\(638\) | −42.6176 | −1.68725 | ||||||||
\(639\) | − | 0.914994i | − | 0.0361966i | ||||||
\(640\) | −1.35137 | + | 2.34064i | −0.0534176 | + | 0.0925220i | ||||
\(641\) | 23.6951 | 0.935901 | 0.467950 | − | 0.883755i | \(-0.344993\pi\) | ||||
0.467950 | + | 0.883755i | \(0.344993\pi\) | |||||||
\(642\) | 9.15192 | + | 5.28386i | 0.361198 | + | 0.208537i | ||||
\(643\) | −11.0433 | − | 6.37588i | −0.435507 | − | 0.251440i | 0.266183 | − | 0.963923i | \(-0.414237\pi\) |
−0.701690 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(644\) | −12.3982 | − | 15.3900i | −0.488559 | − | 0.606452i | ||||
\(645\) | 16.7945i | 0.661283i | ||||||||
\(646\) | 12.5690 | + | 21.7701i | 0.494521 | + | 0.856535i | ||||
\(647\) | −3.70342 | + | 6.41451i | −0.145597 | + | 0.252181i | −0.929595 | − | 0.368582i | \(-0.879843\pi\) |
0.783999 | + | 0.620762i | \(0.213177\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | −16.5140 | + | 28.6031i | −0.648232 | + | 1.12277i | ||||
\(650\) | 3.51419 | + | 7.53046i | 0.137838 | + | 0.295369i | ||||
\(651\) | −14.7776 | + | 11.9048i | −0.579178 | + | 0.466588i | ||||
\(652\) | −9.03020 | + | 5.21359i | −0.353650 | + | 0.204180i | ||||
\(653\) | −40.1506 | −1.57121 | −0.785606 | − | 0.618727i | \(-0.787649\pi\) | ||||
−0.785606 | + | 0.618727i | \(0.787649\pi\) | |||||||
\(654\) | −3.78429 | −0.147977 | ||||||||
\(655\) | 1.67809 | − | 0.968844i | 0.0655683 | − | 0.0378559i | ||||
\(656\) | 3.29661 | − | 1.90330i | 0.128711 | − | 0.0743112i | ||||
\(657\) | −5.93963 | − | 3.42924i | −0.231727 | − | 0.133788i | ||||
\(658\) | 22.4643 | − | 3.49975i | 0.875749 | − | 0.136434i | ||||
\(659\) | 17.0035 | − | 29.4509i | 0.662361 | − | 1.14724i | −0.317633 | − | 0.948214i | \(-0.602888\pi\) |
0.979994 | − | 0.199029i | \(-0.0637788\pi\) | |||||||
\(660\) | −13.7766 | −0.536252 | ||||||||
\(661\) | −10.0528 | − | 5.80401i | −0.391010 | − | 0.225750i | 0.291588 | − | 0.956544i | \(-0.405816\pi\) |
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(662\) | −0.440050 | − | 0.762189i | −0.0171030 | − | 0.0296233i | ||||
\(663\) | 16.9367 | + | 11.8518i | 0.657766 | + | 0.460286i | ||||
\(664\) | 15.3966 | 0.597504 | ||||||||
\(665\) | 19.6694 | + | 24.4158i | 0.762748 | + | 0.946804i | ||||
\(666\) | −3.38705 | − | 5.86654i | −0.131246 | − | 0.227324i | ||||
\(667\) | −31.2264 | − | 54.0858i | −1.20909 | − | 2.09421i | ||||
\(668\) | 1.90573 | − | 1.10027i | 0.0737350 | − | 0.0425709i | ||||
\(669\) | 26.0800i | 1.00831i | ||||||||
\(670\) | 14.1971 | − | 8.19667i | 0.548480 | − | 0.316665i | ||||
\(671\) | − | 23.7046i | − | 0.915104i | ||||||
\(672\) | 0.407273 | + | 2.61422i | 0.0157109 | + | 0.100846i | ||||
\(673\) | −5.22869 | − | 9.05635i | −0.201551 | − | 0.349097i | 0.747477 | − | 0.664287i | \(-0.231265\pi\) |
−0.949028 | + | 0.315191i | \(0.897932\pi\) | |||||||
\(674\) | 16.4964i | 0.635418i | ||||||||
\(675\) | −1.15240 | − | 1.99602i | −0.0443559 | − | 0.0768267i | ||||
\(676\) | 12.8038 | + | 2.24994i | 0.492455 | + | 0.0865361i | ||||
\(677\) | 2.49022 | − | 4.31318i | 0.0957068 | − | 0.165769i | −0.814197 | − | 0.580589i | \(-0.802822\pi\) |
0.909903 | + | 0.414820i | \(0.136156\pi\) | |||||||
\(678\) | 1.47154 | − | 0.849593i | 0.0565141 | − | 0.0326284i | ||||
\(679\) | −3.85683 | − | 24.7563i | −0.148012 | − | 0.950061i | ||||
\(680\) | 7.74778 | − | 13.4195i | 0.297114 | − | 0.514616i | ||||
\(681\) | −10.1088 | − | 5.83634i | −0.387372 | − | 0.223649i | ||||
\(682\) | 36.5595i | 1.39993i | ||||||||
\(683\) | 16.0329i | 0.613481i | 0.951793 | + | 0.306741i | \(0.0992384\pi\) | ||||
−0.951793 | + | 0.306741i | \(0.900762\pi\) | |||||||
\(684\) | −3.79715 | − | 2.19229i | −0.145188 | − | 0.0838242i | ||||
\(685\) | −13.5890 | + | 23.5369i | −0.519210 | + | 0.899298i | ||||
\(686\) | −8.28251 | − | 16.5650i | −0.316228 | − | 0.632456i | ||||
\(687\) | −10.4614 | + | 6.03988i | −0.399126 | + | 0.230436i | ||||
\(688\) | 3.10694 | − | 5.38138i | 0.118451 | − | 0.205163i | ||||
\(689\) | 23.5466 | − | 10.9884i | 0.897056 | − | 0.418623i | ||||
\(690\) | −10.0943 | − | 17.4838i | −0.384282 | − | 0.665595i | ||||
\(691\) | − | 36.4604i | − | 1.38702i | −0.720447 | − | 0.693510i | \(-0.756063\pi\) | ||
0.720447 | − | 0.693510i | \(-0.243937\pi\) | |||||||
\(692\) | 10.7383 | + | 18.5992i | 0.408207 | + | 0.707036i | ||||
\(693\) | −10.5021 | + | 8.46051i | −0.398941 | + | 0.321388i | ||||
\(694\) | − | 5.59149i | − | 0.212250i | ||||||
\(695\) | −41.4145 | + | 23.9106i | −1.57094 | + | 0.906982i | ||||
\(696\) | 8.36089i | 0.316919i | ||||||||
\(697\) | −18.9004 | + | 10.9121i | −0.715902 | + | 0.413326i | ||||
\(698\) | −6.42408 | − | 11.1268i | −0.243155 | − | 0.421157i | ||||
\(699\) | 4.65865 | + | 8.06902i | 0.176206 | + | 0.305199i | ||||
\(700\) | 2.19970 | − | 5.68736i | 0.0831409 | − | 0.214962i | ||||
\(701\) | 11.4738 | 0.433360 | 0.216680 | − | 0.976243i | \(-0.430477\pi\) | ||||
0.216680 | + | 0.976243i | \(0.430477\pi\) | |||||||
\(702\) | −3.59192 | − | 0.313194i | −0.135568 | − | 0.0118208i | ||||
\(703\) | 14.8508 | + | 25.7223i | 0.560108 | + | 0.970135i | ||||
\(704\) | 4.41435 | + | 2.54863i | 0.166372 | + | 0.0960550i | ||||
\(705\) | 23.2250 | 0.874703 | ||||||||
\(706\) | −9.22345 | + | 15.9755i | −0.347129 | + | 0.601245i | ||||
\(707\) | 9.73039 | − | 1.51591i | 0.365949 | − | 0.0570117i | ||||
\(708\) | 5.61147 | + | 3.23979i | 0.210892 | + | 0.121759i | ||||
\(709\) | 36.2974 | − | 20.9563i | 1.36318 | − | 0.787030i | 0.373131 | − | 0.927779i | \(-0.378284\pi\) |
0.990045 | + | 0.140749i | \(0.0449509\pi\) | |||||||
\(710\) | 2.14167 | − | 1.23649i | 0.0803755 | − | 0.0464048i | ||||
\(711\) | 7.62685 | 0.286029 | ||||||||
\(712\) | 10.3822 | 0.389091 | ||||||||
\(713\) | −46.3975 | + | 26.7876i | −1.73760 | + | 1.00320i | ||||
\(714\) | −2.33501 | − | 14.9880i | −0.0873855 | − | 0.560913i | ||||
\(715\) | 45.0120 | − | 21.0055i | 1.68336 | − | 0.785561i | ||||
\(716\) | −9.33910 | + | 16.1758i | −0.349019 | + | 0.604518i | ||||
\(717\) | −14.5612 | − | 8.40693i | −0.543799 | − | 0.313963i | ||||
\(718\) | −5.75546 | + | 9.96875i | −0.214792 | + | 0.372030i | ||||
\(719\) | 18.1215 | + | 31.3873i | 0.675817 | + | 1.17055i | 0.976229 | + | 0.216739i | \(0.0695422\pi\) |
−0.300413 | + | 0.953809i | \(0.597124\pi\) | |||||||
\(720\) | 2.70274i | 0.100725i | ||||||||
\(721\) | 23.8137 | − | 3.70997i | 0.886867 | − | 0.138166i | ||||
\(722\) | 0.194430 | + | 0.112254i | 0.00723593 | + | 0.00417766i | ||||
\(723\) | −19.3566 | − | 11.1756i | −0.719881 | − | 0.415623i | ||||
\(724\) | −1.97032 | −0.0732262 | ||||||||
\(725\) | 9.63509 | − | 16.6885i | 0.357838 | − | 0.619794i | ||||
\(726\) | 14.9820i | 0.556035i | ||||||||
\(727\) | −6.41054 | −0.237754 | −0.118877 | − | 0.992909i | \(-0.537929\pi\) | ||||
−0.118877 | + | 0.992909i | \(0.537929\pi\) | |||||||
\(728\) | −5.31665 | − | 7.92043i | −0.197048 | − | 0.293551i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 18.5367i | − | 0.686074i | ||||||
\(731\) | −17.8130 | + | 30.8529i | −0.658836 | + | 1.14114i | ||||
\(732\) | −4.65046 | −0.171886 | ||||||||
\(733\) | −23.5129 | − | 13.5752i | −0.868469 | − | 0.501411i | −0.00162955 | − | 0.999999i | \(-0.500519\pi\) |
−0.866839 | + | 0.498588i | \(0.833852\pi\) | |||||||
\(734\) | −5.20794 | − | 3.00680i | −0.192228 | − | 0.110983i | ||||
\(735\) | −5.75521 | − | 18.0226i | −0.212284 | − | 0.664772i | ||||
\(736\) | 7.46964i | 0.275335i | ||||||||
\(737\) | −15.4586 | − | 26.7751i | −0.569425 | − | 0.986272i | ||||
\(738\) | 1.90330 | − | 3.29661i | 0.0700613 | − | 0.121350i | ||||
\(739\) | 17.1766 | + | 9.91693i | 0.631853 | + | 0.364800i | 0.781469 | − | 0.623944i | \(-0.214471\pi\) |
−0.149617 | + | 0.988744i | \(0.547804\pi\) | |||||||
\(740\) | 9.15432 | − | 15.8557i | 0.336519 | − | 0.582869i | ||||
\(741\) | 15.7491 | + | 1.37322i | 0.578556 | + | 0.0504466i | ||||
\(742\) | −17.7835 | − | 6.87814i | −0.652854 | − | 0.252504i | ||||
\(743\) | 31.4762 | − | 18.1728i | 1.15475 | − | 0.666696i | 0.204710 | − | 0.978823i | \(-0.434375\pi\) |
0.950040 | + | 0.312127i | \(0.101041\pi\) | |||||||
\(744\) | 7.17238 | 0.262952 | ||||||||
\(745\) | 62.9507 | 2.30634 | ||||||||
\(746\) | 8.29975 | − | 4.79186i | 0.303875 | − | 0.175442i | ||||
\(747\) | 13.3339 | − | 7.69830i | 0.487860 | − | 0.281666i | ||||
\(748\) | −25.3087 | − | 14.6120i | −0.925378 | − | 0.534267i | ||||
\(749\) | 17.5405 | + | 21.7731i | 0.640916 | + | 0.795573i | ||||
\(750\) | −3.64221 | + | 6.30849i | −0.132995 | + | 0.230354i | ||||
\(751\) | 0.923620 | 0.0337034 | 0.0168517 | − | 0.999858i | \(-0.494636\pi\) | ||||
0.0168517 | + | 0.999858i | \(0.494636\pi\) | |||||||
\(752\) | −7.44186 | − | 4.29656i | −0.271377 | − | 0.156679i | ||||
\(753\) | −3.75155 | − | 6.49788i | −0.136714 | − | 0.236796i | ||||
\(754\) | −12.7481 | − | 27.3175i | −0.464258 | − | 0.994844i | ||||
\(755\) | −49.4999 | −1.80149 | ||||||||
\(756\) | 1.65982 | + | 2.06034i | 0.0603670 | + | 0.0749339i | ||||
\(757\) | 1.33975 | + | 2.32051i | 0.0486940 | + | 0.0843405i | 0.889345 | − | 0.457237i | \(-0.151161\pi\) |
−0.840651 | + | 0.541577i | \(0.817827\pi\) | |||||||
\(758\) | −12.6730 | − | 21.9503i | −0.460305 | − | 0.797271i | ||||
\(759\) | −32.9736 | + | 19.0373i | −1.19687 | + | 0.691012i | ||||
\(760\) | − | 11.8504i | − | 0.429858i | ||||||
\(761\) | −13.0650 | + | 7.54307i | −0.473605 | + | 0.273436i | −0.717748 | − | 0.696303i | \(-0.754827\pi\) |
0.244143 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(762\) | 6.22903i | 0.225654i | ||||||||
\(763\) | −9.33817 | − | 3.61172i | −0.338064 | − | 0.130753i | ||||
\(764\) | 1.85473 | + | 3.21249i | 0.0671019 | + | 0.116224i | ||||
\(765\) | − | 15.4956i | − | 0.560243i | ||||||
\(766\) | −0.142941 | − | 0.247581i | −0.00516466 | − | 0.00894546i | ||||
\(767\) | −23.2741 | − | 2.02936i | −0.840380 | − | 0.0732761i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 17.7838 | − | 10.2675i | 0.641301 | − | 0.370256i | −0.143814 | − | 0.989605i | \(-0.545937\pi\) |
0.785116 | + | 0.619349i | \(0.212603\pi\) | |||||||
\(770\) | −33.9952 | − | 13.1483i | −1.22510 | − | 0.473833i | ||||
\(771\) | −3.51876 | + | 6.09468i | −0.126725 | + | 0.219494i | ||||
\(772\) | −2.58076 | − | 1.49000i | −0.0928834 | − | 0.0536263i | ||||
\(773\) | 18.0867i | 0.650532i | 0.945623 | + | 0.325266i | \(0.105454\pi\) | ||||
−0.945623 | + | 0.325266i | \(0.894546\pi\) | |||||||
\(774\) | − | 6.21388i | − | 0.223353i | ||||||
\(775\) | −14.3162 | − | 8.26546i | −0.514253 | − | 0.296904i | ||||
\(776\) | −4.73494 | + | 8.20116i | −0.169975 | + | 0.294405i | ||||
\(777\) | −2.75891 | − | 17.7090i | −0.0989753 | − | 0.635306i | ||||
\(778\) | 2.87869 | − | 1.66201i | 0.103206 | − | 0.0595860i | ||||
\(779\) | −8.34515 | + | 14.4542i | −0.298996 | + | 0.517876i | ||||
\(780\) | −4.12094 | − | 8.83064i | −0.147553 | − | 0.316188i | ||||
\(781\) | −2.33198 | − | 4.03911i | −0.0834448 | − | 0.144531i | ||||
\(782\) | − | 42.8255i | − | 1.53144i | ||||||
\(783\) | 4.18045 | + | 7.24074i | 0.149397 | + | 0.258763i | ||||
\(784\) | −1.49001 | + | 6.83958i | −0.0532148 | + | 0.244271i | ||||
\(785\) | 10.3664i | 0.369991i | ||||||||
\(786\) | −0.620884 | + | 0.358468i | −0.0221462 | + | 0.0127861i | ||||
\(787\) | 35.0577i | 1.24967i | 0.780757 | + | 0.624835i | \(0.214834\pi\) | ||||
−0.780757 | + | 0.624835i | \(0.785166\pi\) | |||||||
\(788\) | 12.8922 | − | 7.44330i | 0.459264 | − | 0.265156i | ||||
\(789\) | −11.9643 | − | 20.7228i | −0.425940 | − | 0.737750i | ||||
\(790\) | 10.3067 | + | 17.8517i | 0.366696 | + | 0.635135i | ||||
\(791\) | 4.44204 | − | 0.692032i | 0.157941 | − | 0.0246058i | ||||
\(792\) | 5.09726 | 0.181123 | ||||||||
\(793\) | 15.1944 | − | 7.09068i | 0.539569 | − | 0.251797i | ||||
\(794\) | −15.2409 | − | 26.3981i | −0.540881 | − | 0.936833i | ||||
\(795\) | −16.8685 | − | 9.73901i | −0.598263 | − | 0.345407i | ||||
\(796\) | 2.66427 | 0.0944327 | ||||||||
\(797\) | −8.96425 | + | 15.5265i | −0.317530 | + | 0.549978i | −0.979972 | − | 0.199135i | \(-0.936187\pi\) |
0.662442 | + | 0.749113i | \(0.269520\pi\) | |||||||
\(798\) | −7.27759 | − | 9.03372i | −0.257624 | − | 0.319790i | ||||
\(799\) | 42.6663 | + | 24.6334i | 1.50942 | + | 0.871466i | ||||
\(800\) | −1.99602 | + | 1.15240i | −0.0705698 | + | 0.0407435i | ||||
\(801\) | 8.99129 | − | 5.19112i | 0.317692 | − | 0.183419i | ||||
\(802\) | 19.5601 | 0.690690 | ||||||||
\(803\) | −34.9595 | −1.23369 | ||||||||
\(804\) | −5.25284 | + | 3.03273i | −0.185253 | + | 0.106956i | ||||
\(805\) | −8.22223 | − | 52.7771i | −0.289796 | − | 1.86015i | ||||
\(806\) | −23.4343 | + | 10.9359i | −0.825437 | + | 0.385202i | ||||
\(807\) | −0.799815 | + | 1.38532i | −0.0281548 | + | 0.0487656i | ||||
\(808\) | −3.22344 | − | 1.86105i | −0.113400 | − | 0.0654716i | ||||
\(809\) | −10.3413 | + | 17.9116i | −0.363580 | + | 0.629739i | −0.988547 | − | 0.150912i | \(-0.951779\pi\) |
0.624967 | + | 0.780651i | \(0.285112\pi\) | |||||||
\(810\) | 1.35137 | + | 2.34064i | 0.0474823 | + | 0.0822417i | ||||
\(811\) | − | 16.2377i | − | 0.570182i | −0.958500 | − | 0.285091i | \(-0.907976\pi\) | ||
0.958500 | − | 0.285091i | \(-0.0920239\pi\) | |||||||
\(812\) | −7.97963 | + | 20.6315i | −0.280030 | + | 0.724022i | ||||
\(813\) | −17.3215 | − | 10.0006i | −0.607492 | − | 0.350736i | ||||
\(814\) | −29.9033 | − | 17.2647i | −1.04811 | − | 0.605126i | ||||
\(815\) | −28.1819 | −0.987171 | ||||||||
\(816\) | −2.86664 | + | 4.96516i | −0.100352 | + | 0.173816i | ||||
\(817\) | 27.2452i | 0.953190i | ||||||||
\(818\) | 17.0474 | 0.596050 | ||||||||
\(819\) | −8.56457 | − | 4.20097i | −0.299270 | − | 0.146794i | ||||
\(820\) | 10.2882 | 0.359280 | ||||||||
\(821\) | − | 41.5159i | − | 1.44891i | −0.689320 | − | 0.724457i | \(-0.742091\pi\) | ||
0.689320 | − | 0.724457i | \(-0.257909\pi\) | |||||||
\(822\) | 5.02787 | − | 8.70853i | 0.175367 | − | 0.303745i | ||||
\(823\) | −17.9495 | −0.625682 | −0.312841 | − | 0.949806i | \(-0.601281\pi\) | ||||
−0.312841 | + | 0.949806i | \(0.601281\pi\) | |||||||
\(824\) | −7.88888 | − | 4.55465i | −0.274822 | − | 0.158669i | ||||
\(825\) | −10.1742 | − | 5.87408i | −0.354220 | − | 0.204509i | ||||
\(826\) | 10.7549 | + | 13.3501i | 0.374211 | + | 0.464511i | ||||
\(827\) | − | 0.0414259i | − | 0.00144052i | −1.00000 | 0.000720261i | \(-0.999771\pi\) | |||
1.00000 | 0.000720261i | \(-0.000229266\pi\) | ||||||||
\(828\) | 3.73482 | + | 6.46890i | 0.129794 | + | 0.224810i | ||||
\(829\) | 1.75746 | − | 3.04402i | 0.0610393 | − | 0.105723i | −0.833891 | − | 0.551929i | \(-0.813892\pi\) |
0.894930 | + | 0.446206i | \(0.147225\pi\) | |||||||
\(830\) | 36.0379 | + | 20.8065i | 1.25089 | + | 0.722204i | ||||
\(831\) | −9.05583 | + | 15.6852i | −0.314143 | + | 0.544112i | ||||
\(832\) | −0.313194 | + | 3.59192i | −0.0108581 | + | 0.124528i | ||||
\(833\) | 8.54267 | − | 39.2132i | 0.295986 | − | 1.35866i | ||||
\(834\) | 15.3231 | − | 8.84682i | 0.530597 | − | 0.306340i | ||||
\(835\) | 5.94751 | 0.205822 | ||||||||
\(836\) | −22.3493 | −0.772967 | ||||||||
\(837\) | 6.21147 | − | 3.58619i | 0.214700 | − | 0.123957i | ||||
\(838\) | −7.20908 | + | 4.16216i | −0.249033 | + | 0.143779i | ||||
\(839\) | −1.59236 | − | 0.919352i | −0.0549745 | − | 0.0317395i | 0.472261 | − | 0.881459i | \(-0.343438\pi\) |
−0.527235 | + | 0.849719i | \(0.676771\pi\) | |||||||
\(840\) | −2.57949 | + | 6.66932i | −0.0890010 | + | 0.230113i | ||||
\(841\) | −20.4523 | + | 35.4243i | −0.705250 | + | 1.22153i | ||||
\(842\) | 35.9805 | 1.23997 | ||||||||
\(843\) | 9.54149 | + | 5.50878i | 0.328626 | + | 0.189732i | ||||
\(844\) | 3.24329 | + | 5.61754i | 0.111639 | + | 0.193364i | ||||
\(845\) | 26.9286 | + | 22.5690i | 0.926374 | + | 0.776397i | ||||
\(846\) | −8.59312 | −0.295438 | ||||||||
\(847\) | −14.2988 | + | 36.9698i | −0.491314 | + | 1.27030i | ||||
\(848\) | 3.60339 | + | 6.24125i | 0.123741 | + | 0.214325i | ||||
\(849\) | −6.74682 | − | 11.6858i | −0.231550 | − | 0.401057i | ||||
\(850\) | 11.4437 | − | 6.60703i | 0.392516 | − | 0.226619i | ||||
\(851\) | − | 50.6001i | − | 1.73455i | ||||||
\(852\) | −0.792408 | + | 0.457497i | −0.0271474 | + | 0.0156736i | ||||
\(853\) | − | 3.88953i | − | 0.133175i | −0.997781 | − | 0.0665875i | \(-0.978789\pi\) | ||
0.997781 | − | 0.0665875i | \(-0.0212111\pi\) | |||||||
\(854\) | −11.4755 | − | 4.43839i | −0.392685 | − | 0.151879i | ||||
\(855\) | −5.92518 | − | 10.2627i | −0.202637 | − | 0.350978i | ||||
\(856\) | − | 10.5677i | − | 0.361198i | ||||||
\(857\) | 3.14373 | + | 5.44510i | 0.107388 | + | 0.186001i | 0.914711 | − | 0.404108i | \(-0.132418\pi\) |
−0.807323 | + | 0.590109i | \(0.799085\pi\) | |||||||
\(858\) | −16.6542 | + | 7.77192i | −0.568566 | + | 0.265329i | ||||
\(859\) | −3.28045 | + | 5.68190i | −0.111927 | + | 0.193864i | −0.916547 | − | 0.399926i | \(-0.869036\pi\) |
0.804620 | + | 0.593790i | \(0.202369\pi\) | |||||||
\(860\) | 14.5445 | − | 8.39725i | 0.495962 | − | 0.286344i | ||||
\(861\) | 7.84288 | − | 6.31825i | 0.267285 | − | 0.215325i | ||||
\(862\) | 3.10461 | − | 5.37734i | 0.105743 | − | 0.183153i | ||||
\(863\) | −11.3137 | − | 6.53197i | −0.385123 | − | 0.222351i | 0.294922 | − | 0.955521i | \(-0.404706\pi\) |
−0.680045 | + | 0.733170i | \(0.738040\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 58.0454i | 1.97360i | ||||||||
\(866\) | −6.90357 | − | 3.98578i | −0.234593 | − | 0.135442i | ||||
\(867\) | 7.93524 | − | 13.7442i | 0.269495 | − | 0.466779i | ||||
\(868\) | 17.6987 | + | 6.84532i | 0.600732 | + | 0.232345i | ||||
\(869\) | 33.6676 | − | 19.4380i | 1.14210 | − | 0.659389i | ||||
\(870\) | −11.2987 | + | 19.5698i | −0.383060 | + | 0.663480i | ||||
\(871\) | 12.5385 | − | 17.9180i | 0.424850 | − | 0.607127i | ||||
\(872\) | 1.89214 | + | 3.27729i | 0.0640761 | + | 0.110983i | ||||
\(873\) | 9.46989i | 0.320507i | ||||||||
\(874\) | −16.3756 | − | 28.3634i | −0.553913 | − | 0.959406i | ||||
\(875\) | −15.0084 | + | 12.0908i | −0.507376 | + | 0.408744i | ||||
\(876\) | 6.85849i | 0.231727i | ||||||||
\(877\) | −4.28533 | + | 2.47413i | −0.144705 | + | 0.0835456i | −0.570605 | − | 0.821225i | \(-0.693291\pi\) |
0.425899 | + | 0.904771i | \(0.359958\pi\) | |||||||
\(878\) | 14.1623i | 0.477953i | ||||||||
\(879\) | 4.13569 | − | 2.38774i | 0.139494 | − | 0.0805366i | ||||
\(880\) | 6.88828 | + | 11.9308i | 0.232204 | + | 0.402189i | ||||
\(881\) | −5.49446 | − | 9.51669i | −0.185113 | − | 0.320625i | 0.758501 | − | 0.651671i | \(-0.225932\pi\) |
−0.943615 | + | 0.331046i | \(0.892599\pi\) | |||||||
\(882\) | 2.12940 | + | 6.66826i | 0.0717006 | + | 0.224532i | ||||
\(883\) | 43.0985 | 1.45038 | 0.725190 | − | 0.688549i | \(-0.241752\pi\) | ||||
0.725190 | + | 0.688549i | \(0.241752\pi\) | |||||||
\(884\) | 1.79563 | − | 20.5935i | 0.0603936 | − | 0.692634i | ||||
\(885\) | 8.75630 | + | 15.1664i | 0.294340 | + | 0.509811i | ||||
\(886\) | −23.8880 | − | 13.7918i | −0.802534 | − | 0.463343i | ||||
\(887\) | −42.2975 | −1.42021 | −0.710106 | − | 0.704095i | \(-0.751353\pi\) | ||||
−0.710106 | + | 0.704095i | \(0.751353\pi\) | |||||||
\(888\) | −3.38705 | + | 5.86654i | −0.113662 | + | 0.196868i | ||||
\(889\) | −5.94498 | + | 15.3708i | −0.199388 | + | 0.515521i | ||||
\(890\) | 24.3011 | + | 14.0303i | 0.814575 | + | 0.470295i | ||||
\(891\) | 4.41435 | − | 2.54863i | 0.147886 | − | 0.0853822i | ||||
\(892\) | 22.5859 | − | 13.0400i | 0.756233 | − | 0.436611i | ||||
\(893\) | 37.6772 | 1.26082 | ||||||||
\(894\) | −23.2914 | −0.778983 | ||||||||
\(895\) | −43.7190 | + | 25.2412i | −1.46136 | + | 0.843719i | ||||
\(896\) | 2.06034 | − | 1.65982i | 0.0688312 | − | 0.0554506i | ||||
\(897\) | −22.0661 | − | 15.4412i | −0.736765 | − | 0.515567i | ||||
\(898\) | −1.46199 | + | 2.53224i | −0.0487873 | + | 0.0845021i | ||||
\(899\) | 51.9334 | + | 29.9838i | 1.73208 | + | 1.00001i | ||||
\(900\) | −1.15240 | + | 1.99602i | −0.0384133 | + | 0.0665339i | ||||
\(901\) | −20.6592 | − | 35.7828i | −0.688258 | − | 1.19210i | ||||
\(902\) | − | 19.4032i | − | 0.646055i | ||||||
\(903\) | 5.93053 | − | 15.3335i | 0.197356 | − | 0.510266i | ||||
\(904\) | −1.47154 | − | 0.849593i | −0.0489426 | − | 0.0282570i | ||||
\(905\) | −4.61180 | − | 2.66262i | −0.153301 | − | 0.0885086i | ||||
\(906\) | 18.3147 | 0.608466 | ||||||||
\(907\) | −16.5689 | + | 28.6982i | −0.550162 | + | 0.952908i | 0.448101 | + | 0.893983i | \(0.352101\pi\) |
−0.998262 | + | 0.0589251i | \(0.981233\pi\) | |||||||
\(908\) | 11.6727i | 0.387372i | ||||||||
\(909\) | −3.72210 | −0.123454 | ||||||||
\(910\) | −1.74093 | − | 25.7236i | −0.0577113 | − | 0.852731i | ||||
\(911\) | −26.0908 | −0.864426 | −0.432213 | − | 0.901772i | \(-0.642267\pi\) | ||||
−0.432213 | + | 0.901772i | \(0.642267\pi\) | |||||||
\(912\) | 4.38458i | 0.145188i | ||||||||
\(913\) | 39.2402 | − | 67.9661i | 1.29866 | − | 2.24935i | ||||
\(914\) | −20.9436 | −0.692754 | ||||||||
\(915\) | −10.8850 | − | 6.28449i | −0.359849 | − | 0.207759i | ||||
\(916\) | 10.4614 | + | 6.03988i | 0.345654 | + | 0.199563i | ||||
\(917\) | −1.87422 | + | 0.291988i | −0.0618923 | + | 0.00964230i | ||||
\(918\) | 5.73328i | 0.189226i | ||||||||
\(919\) | 23.1004 | + | 40.0111i | 0.762013 | + | 1.31984i | 0.941812 | + | 0.336141i | \(0.109122\pi\) |
−0.179799 | + | 0.983703i | \(0.557545\pi\) | |||||||
\(920\) | −10.0943 | + | 17.4838i | −0.332798 | + | 0.576422i | ||||
\(921\) | −5.42497 | − | 3.13211i | −0.178759 | − | 0.103207i | ||||
\(922\) | −9.20229 | + | 15.9388i | −0.303061 | + | 0.524918i | ||||
\(923\) | 1.89147 | − | 2.70298i | 0.0622585 | − | 0.0889698i | ||||
\(924\) | 12.5781 | + | 4.86482i | 0.413788 | + | 0.160041i | ||||
\(925\) | 13.5212 | − | 7.80648i | 0.444575 | − | 0.256675i | ||||
\(926\) | −28.8633 | −0.948508 | ||||||||
\(927\) | −9.10929 | −0.299188 | ||||||||
\(928\) | 7.24074 | − | 4.18045i | 0.237689 | − | 0.137230i | ||||
\(929\) | 2.74803 | − | 1.58658i | 0.0901599 | − | 0.0520539i | −0.454242 | − | 0.890878i | \(-0.650090\pi\) |
0.544402 | + | 0.838824i | \(0.316757\pi\) | |||||||
\(930\) | 16.7880 | + | 9.69254i | 0.550499 | + | 0.317831i | ||||
\(931\) | −9.33651 | − | 29.2375i | −0.305992 | − | 0.958220i | ||||
\(932\) | 4.65865 | − | 8.06902i | 0.152599 | − | 0.264310i | ||||
\(933\) | 5.98426 | 0.195916 | ||||||||
\(934\) | −29.2322 | − | 16.8772i | −0.956505 | − | 0.552239i | ||||
\(935\) | −39.4924 | − | 68.4029i | −1.29154 | − | 2.23701i | ||||
\(936\) | 1.52473 | + | 3.26729i | 0.0498373 | + | 0.106795i | ||||
\(937\) | 36.3959 | 1.18900 | 0.594501 | − | 0.804095i | \(-0.297350\pi\) | ||||
0.594501 | + | 0.804095i | \(0.297350\pi\) | |||||||
\(938\) | −15.8564 | + | 2.47030i | −0.517730 | + | 0.0806580i | ||||
\(939\) | −14.3286 | − | 24.8179i | −0.467597 | − | 0.809902i | ||||
\(940\) | −11.6125 | − | 20.1134i | −0.378757 | − | 0.656027i | ||||
\(941\) | 25.2928 | − | 14.6028i | 0.824521 | − | 0.476037i | −0.0274523 | − | 0.999623i | \(-0.508739\pi\) |
0.851973 | + | 0.523586i | \(0.175406\pi\) | |||||||
\(942\) | − | 3.83550i | − | 0.124967i | ||||||
\(943\) | 24.6245 | − | 14.2169i | 0.801883 | − | 0.462967i | ||||
\(944\) | − | 6.47957i | − | 0.210892i | ||||||
\(945\) | 1.10075 | + | 7.06555i | 0.0358075 | + | 0.229842i | ||||
\(946\) | −15.8369 | − | 27.4303i | −0.514901 | − | 0.891835i | ||||
\(947\) | 8.20811i | 0.266728i | 0.991067 | + | 0.133364i | \(0.0425779\pi\) | ||||
−0.991067 | + | 0.133364i | \(0.957422\pi\) | |||||||
\(948\) | −3.81342 | − | 6.60504i | −0.123854 | − | 0.214522i | ||||
\(949\) | −10.4573 | − | 22.4087i | −0.339459 | − | 0.727417i | ||||
\(950\) | 5.05279 | − | 8.75168i | 0.163934 | − | 0.283942i | ||||
\(951\) | 22.2694 | − | 12.8572i | 0.722134 | − | 0.416924i | ||||
\(952\) | −11.8125 | + | 9.51619i | −0.382846 | + | 0.308422i | ||||
\(953\) | −22.9551 | + | 39.7595i | −0.743590 | + | 1.28794i | 0.207261 | + | 0.978286i | \(0.433545\pi\) |
−0.950851 | + | 0.309649i | \(0.899788\pi\) | |||||||
\(954\) | 6.24125 | + | 3.60339i | 0.202068 | + | 0.116664i | ||||
\(955\) | 10.0257i | 0.324425i | ||||||||
\(956\) | 16.8139i | 0.543799i | ||||||||
\(957\) | 36.9079 | + | 21.3088i | 1.19306 | + | 0.688816i | ||||
\(958\) | −8.71070 | + | 15.0874i | −0.281430 | + | 0.487451i | ||||
\(959\) | 20.7183 | − | 16.6907i | 0.669028 | − | 0.538971i | ||||
\(960\) | 2.34064 | − | 1.35137i | 0.0755439 | − | 0.0436153i | ||||
\(961\) | 10.2215 | − | 17.7042i | 0.329727 | − | 0.571105i | ||||
\(962\) | 2.12161 | − | 24.3321i | 0.0684034 | − | 0.784497i | ||||
\(963\) | −5.28386 | − | 9.15192i | −0.170270 | − | 0.294917i | ||||
\(964\) | 22.3511i | 0.719881i | ||||||||
\(965\) | −4.02708 | − | 6.97511i | −0.129636 | − | 0.224537i | ||||
\(966\) | 3.04218 | + | 19.5273i | 0.0978807 | + | 0.628280i | ||||
\(967\) | − | 27.1219i | − | 0.872182i | −0.899903 | − | 0.436091i | \(-0.856363\pi\) | ||
0.899903 | − | 0.436091i | \(-0.143637\pi\) | |||||||
\(968\) | 12.9748 | − | 7.49101i | 0.417026 | − | 0.240770i | ||||
\(969\) | − | 25.1380i | − | 0.807549i | ||||||
\(970\) | −22.1656 | + | 12.7973i | −0.711695 | + | 0.410897i | ||||
\(971\) | 22.7273 | + | 39.3648i | 0.729353 | + | 1.26328i | 0.957157 | + | 0.289569i | \(0.0935120\pi\) |
−0.227805 | + | 0.973707i | \(0.573155\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 46.2550 | − | 7.20614i | 1.48287 | − | 0.231018i | ||||
\(974\) | 38.2660 | 1.22612 | ||||||||
\(975\) | 0.721850 | − | 8.27867i | 0.0231177 | − | 0.265130i | ||||
\(976\) | 2.32523 | + | 4.02741i | 0.0744287 | + | 0.128914i | ||||
\(977\) | −17.8075 | − | 10.2812i | −0.569714 | − | 0.328924i | 0.187321 | − | 0.982299i | \(-0.440019\pi\) |
−0.757035 | + | 0.653374i | \(0.773353\pi\) | |||||||
\(978\) | 10.4272 | 0.333424 | ||||||||
\(979\) | 26.4605 | − | 45.8309i | 0.845681 | − | 1.46476i | ||||
\(980\) | −12.7304 | + | 13.9954i | −0.406657 | + | 0.447068i | ||||
\(981\) | 3.27729 | + | 1.89214i | 0.104636 | + | 0.0604115i | ||||
\(982\) | 31.8494 | − | 18.3883i | 1.01636 | − | 0.586793i | ||||
\(983\) | 13.1471 | − | 7.59050i | 0.419329 | − | 0.242099i | −0.275461 | − | 0.961312i | \(-0.588831\pi\) |
0.694790 | + | 0.719213i | \(0.255497\pi\) | |||||||
\(984\) | −3.80659 | −0.121350 | ||||||||
\(985\) | 40.2346 | 1.28198 | ||||||||
\(986\) | −41.5132 | + | 23.9677i | −1.32205 | + | 0.763286i | ||||
\(987\) | −21.2045 | − | 8.20127i | −0.674947 | − | 0.261049i | ||||
\(988\) | −6.68528 | − | 14.3257i | −0.212687 | − | 0.455761i | ||||
\(989\) | 23.2077 | − | 40.1970i | 0.737963 | − | 1.27819i | ||||
\(990\) | 11.9308 | + | 6.88828i | 0.379187 | + | 0.218924i | ||||
\(991\) | −2.00473 | + | 3.47230i | −0.0636824 | + | 0.110301i | −0.896109 | − | 0.443835i | \(-0.853618\pi\) |
0.832426 | + | 0.554136i | \(0.186951\pi\) | |||||||
\(992\) | −3.58619 | − | 6.21147i | −0.113862 | − | 0.197214i | ||||
\(993\) | 0.880100i | 0.0279291i | ||||||||
\(994\) | −2.39199 | + | 0.372652i | −0.0758694 | + | 0.0118198i | ||||
\(995\) | 6.23611 | + | 3.60042i | 0.197698 | + | 0.114141i | ||||
\(996\) | −13.3339 | − | 7.69830i | −0.422499 | − | 0.243930i | ||||
\(997\) | −34.3896 | −1.08913 | −0.544565 | − | 0.838719i | \(-0.683305\pi\) | ||||
−0.544565 | + | 0.838719i | \(0.683305\pi\) | |||||||
\(998\) | −15.0514 | + | 26.0698i | −0.476444 | + | 0.825224i | ||||
\(999\) | 6.77410i | 0.214323i |
(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 | 546.2.bm.a.205.5 | yes | 16 | |
3.2 | odd | 2 | 1638.2.dt.a.1297.4 | 16 | |||
7.4 | even | 3 | 546.2.bd.a.361.4 | yes | 16 | ||
13.4 | even | 6 | 546.2.bd.a.121.4 | ✓ | 16 | ||
21.11 | odd | 6 | 1638.2.cr.a.361.5 | 16 | |||
39.17 | odd | 6 | 1638.2.cr.a.667.5 | 16 | |||
91.4 | even | 6 | inner | 546.2.bm.a.277.1 | yes | 16 | |
273.95 | odd | 6 | 1638.2.dt.a.1369.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bd.a.121.4 | ✓ | 16 | 13.4 | even | 6 | ||
546.2.bd.a.361.4 | yes | 16 | 7.4 | even | 3 | ||
546.2.bm.a.205.5 | yes | 16 | 1.1 | even | 1 | trivial | |
546.2.bm.a.277.1 | yes | 16 | 91.4 | even | 6 | inner | |
1638.2.cr.a.361.5 | 16 | 21.11 | odd | 6 | |||
1638.2.cr.a.667.5 | 16 | 39.17 | odd | 6 | |||
1638.2.dt.a.1297.4 | 16 | 3.2 | odd | 2 | |||
1638.2.dt.a.1369.8 | 16 | 273.95 | odd | 6 |