Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(139,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.b (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: | \(1.83655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.11574317056.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 45x^{4} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 139.5 | ||
Root | \(0.386289 + 0.386289i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.139 |
Dual form | 230.2.b.b.139.4 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − | 3.25886i | − | 1.88150i | −0.339095 | − | 0.940752i | \(-0.610121\pi\) | ||
0.339095 | − | 0.940752i | \(-0.389879\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.386289 | − | 2.20245i | 0.172754 | − | 0.984965i | ||||
\(6\) | 3.25886 | 1.33042 | ||||||||
\(7\) | 1.44270i | 0.545290i | 0.962115 | + | 0.272645i | \(0.0878984\pi\) | ||||
−0.962115 | + | 0.272645i | \(0.912102\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −7.62018 | −2.54006 | ||||||||
\(10\) | 2.20245 | + | 0.386289i | 0.696475 | + | 0.122155i | ||||
\(11\) | −2.03144 | −0.612502 | −0.306251 | − | 0.951951i | \(-0.599075\pi\) | ||||
−0.306251 | + | 0.951951i | \(0.599075\pi\) | |||||||
\(12\) | 3.25886i | 0.940752i | ||||||||
\(13\) | − | 0.557299i | − | 0.154567i | −0.997009 | − | 0.0772835i | \(-0.975375\pi\) | ||
0.997009 | − | 0.0772835i | \(-0.0246246\pi\) | |||||||
\(14\) | −1.44270 | −0.385578 | ||||||||
\(15\) | −7.17748 | − | 1.25886i | −1.85322 | − | 0.325037i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.91861i | − | 0.950403i | −0.879877 | − | 0.475202i | \(-0.842375\pi\) | ||
0.879877 | − | 0.475202i | \(-0.157625\pi\) | |||||||
\(18\) | − | 7.62018i | − | 1.79609i | ||||||
\(19\) | 6.73300 | 1.54466 | 0.772328 | − | 0.635224i | \(-0.219092\pi\) | ||||
0.772328 | + | 0.635224i | \(0.219092\pi\) | |||||||
\(20\) | −0.386289 | + | 2.20245i | −0.0863768 | + | 0.492483i | ||||
\(21\) | 4.70156 | 1.02596 | ||||||||
\(22\) | − | 2.03144i | − | 0.433104i | ||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | −3.25886 | −0.665212 | ||||||||
\(25\) | −4.70156 | − | 1.70156i | −0.940312 | − | 0.340312i | ||||
\(26\) | 0.557299 | 0.109295 | ||||||||
\(27\) | 15.0565i | 2.89763i | ||||||||
\(28\) | − | 1.44270i | − | 0.272645i | ||||||
\(29\) | 9.69520 | 1.80035 | 0.900176 | − | 0.435525i | \(-0.143437\pi\) | ||||
0.900176 | + | 0.435525i | \(0.143437\pi\) | |||||||
\(30\) | 1.25886 | − | 7.17748i | 0.229836 | − | 1.31042i | ||||
\(31\) | −3.07502 | −0.552290 | −0.276145 | − | 0.961116i | \(-0.589057\pi\) | ||||
−0.276145 | + | 0.961116i | \(0.589057\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 6.62018i | 1.15242i | ||||||||
\(34\) | 3.91861 | 0.672037 | ||||||||
\(35\) | 3.17748 | + | 0.557299i | 0.537091 | + | 0.0942007i | ||||
\(36\) | 7.62018 | 1.27003 | ||||||||
\(37\) | − | 3.65798i | − | 0.601368i | −0.953724 | − | 0.300684i | \(-0.902785\pi\) | ||
0.953724 | − | 0.300684i | \(-0.0972150\pi\) | |||||||
\(38\) | 6.73300i | 1.09224i | ||||||||
\(39\) | −1.81616 | −0.290818 | ||||||||
\(40\) | −2.20245 | − | 0.386289i | −0.348238 | − | 0.0610776i | ||||
\(41\) | 7.03321 | 1.09840 | 0.549202 | − | 0.835690i | \(-0.314932\pi\) | ||||
0.549202 | + | 0.835690i | \(0.314932\pi\) | |||||||
\(42\) | 4.70156i | 0.725467i | ||||||||
\(43\) | 5.06465i | 0.772352i | 0.922425 | + | 0.386176i | \(0.126204\pi\) | ||||
−0.922425 | + | 0.386176i | \(0.873796\pi\) | |||||||
\(44\) | 2.03144 | 0.306251 | ||||||||
\(45\) | −2.94359 | + | 16.7830i | −0.438804 | + | 2.50187i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 0.659753i | 0.0962348i | 0.998842 | + | 0.0481174i | \(0.0153222\pi\) | ||||
−0.998842 | + | 0.0481174i | \(0.984678\pi\) | |||||||
\(48\) | − | 3.25886i | − | 0.470376i | ||||||
\(49\) | 4.91861 | 0.702659 | ||||||||
\(50\) | 1.70156 | − | 4.70156i | 0.240637 | − | 0.664901i | ||||
\(51\) | −12.7702 | −1.78819 | ||||||||
\(52\) | 0.557299i | 0.0772835i | ||||||||
\(53\) | − | 11.1275i | − | 1.52848i | −0.644930 | − | 0.764242i | \(-0.723113\pi\) | ||
0.644930 | − | 0.764242i | \(-0.276887\pi\) | |||||||
\(54\) | −15.0565 | −2.04893 | ||||||||
\(55\) | −0.784722 | + | 4.47414i | −0.105812 | + | 0.603293i | ||||
\(56\) | 1.44270 | 0.192789 | ||||||||
\(57\) | − | 21.9419i | − | 2.90628i | ||||||
\(58\) | 9.69520i | 1.27304i | ||||||||
\(59\) | −10.7226 | −1.39597 | −0.697984 | − | 0.716114i | \(-0.745919\pi\) | ||||
−0.697984 | + | 0.716114i | \(0.745919\pi\) | |||||||
\(60\) | 7.17748 | + | 1.25886i | 0.926608 | + | 0.162518i | ||||
\(61\) | 1.73937 | 0.222703 | 0.111351 | − | 0.993781i | \(-0.464482\pi\) | ||||
0.111351 | + | 0.993781i | \(0.464482\pi\) | |||||||
\(62\) | − | 3.07502i | − | 0.390528i | ||||||
\(63\) | − | 10.9936i | − | 1.38507i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.22742 | − | 0.215278i | −0.152243 | − | 0.0267020i | ||||
\(66\) | −6.62018 | −0.814887 | ||||||||
\(67\) | 12.0129i | 1.46761i | 0.679359 | + | 0.733806i | \(0.262258\pi\) | ||||
−0.679359 | + | 0.733806i | \(0.737742\pi\) | |||||||
\(68\) | 3.91861i | 0.475202i | ||||||||
\(69\) | −3.25886 | −0.392321 | ||||||||
\(70\) | −0.557299 | + | 3.17748i | −0.0666100 | + | 0.379781i | ||||
\(71\) | 12.4363 | 1.47592 | 0.737961 | − | 0.674844i | \(-0.235789\pi\) | ||||
0.737961 | + | 0.674844i | \(0.235789\pi\) | |||||||
\(72\) | 7.62018i | 0.898046i | ||||||||
\(73\) | 9.26464i | 1.08434i | 0.840267 | + | 0.542172i | \(0.182398\pi\) | ||||
−0.840267 | + | 0.542172i | \(0.817602\pi\) | |||||||
\(74\) | 3.65798 | 0.425231 | ||||||||
\(75\) | −5.54515 | + | 15.3217i | −0.640299 | + | 1.76920i | ||||
\(76\) | −6.73300 | −0.772328 | ||||||||
\(77\) | − | 2.93076i | − | 0.333991i | ||||||
\(78\) | − | 1.81616i | − | 0.205640i | ||||||
\(79\) | −5.92439 | −0.666546 | −0.333273 | − | 0.942830i | \(-0.608153\pi\) | ||||
−0.333273 | + | 0.942830i | \(0.608153\pi\) | |||||||
\(80\) | 0.386289 | − | 2.20245i | 0.0431884 | − | 0.246241i | ||||
\(81\) | 26.2066 | 2.91184 | ||||||||
\(82\) | 7.03321i | 0.776688i | ||||||||
\(83\) | 11.3775i | 1.24884i | 0.781089 | + | 0.624420i | \(0.214664\pi\) | ||||
−0.781089 | + | 0.624420i | \(0.785336\pi\) | |||||||
\(84\) | −4.70156 | −0.512982 | ||||||||
\(85\) | −8.63055 | − | 1.51372i | −0.936114 | − | 0.164186i | ||||
\(86\) | −5.06465 | −0.546135 | ||||||||
\(87\) | − | 31.5953i | − | 3.38737i | ||||||
\(88\) | 2.03144i | 0.216552i | ||||||||
\(89\) | −5.25308 | −0.556826 | −0.278413 | − | 0.960462i | \(-0.589808\pi\) | ||||
−0.278413 | + | 0.960462i | \(0.589808\pi\) | |||||||
\(90\) | −16.7830 | − | 2.94359i | −1.76909 | − | 0.310281i | ||||
\(91\) | 0.804016 | 0.0842838 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 10.0211i | 1.03914i | ||||||||
\(94\) | −0.659753 | −0.0680483 | ||||||||
\(95\) | 2.60088 | − | 14.8291i | 0.266845 | − | 1.52143i | ||||
\(96\) | 3.25886 | 0.332606 | ||||||||
\(97\) | − | 0.0813861i | − | 0.00826350i | −0.999991 | − | 0.00413175i | \(-0.998685\pi\) | ||
0.999991 | − | 0.00413175i | \(-0.00131518\pi\) | |||||||
\(98\) | 4.91861i | 0.496855i | ||||||||
\(99\) | 15.4799 | 1.55579 | ||||||||
\(100\) | 4.70156 | + | 1.70156i | 0.470156 | + | 0.170156i | ||||
\(101\) | 8.31281 | 0.827156 | 0.413578 | − | 0.910469i | \(-0.364279\pi\) | ||||
0.413578 | + | 0.910469i | \(0.364279\pi\) | |||||||
\(102\) | − | 12.7702i | − | 1.26444i | ||||||
\(103\) | 6.36991i | 0.627646i | 0.949481 | + | 0.313823i | \(0.101610\pi\) | ||||
−0.949481 | + | 0.313823i | \(0.898390\pi\) | |||||||
\(104\) | −0.557299 | −0.0546477 | ||||||||
\(105\) | 1.81616 | − | 10.3550i | 0.177239 | − | 1.01054i | ||||
\(106\) | 11.1275 | 1.08080 | ||||||||
\(107\) | − | 16.9226i | − | 1.63597i | −0.575239 | − | 0.817986i | \(-0.695091\pi\) | ||
0.575239 | − | 0.817986i | \(-0.304909\pi\) | |||||||
\(108\) | − | 15.0565i | − | 1.44881i | ||||||
\(109\) | 0.218825 | 0.0209597 | 0.0104798 | − | 0.999945i | \(-0.496664\pi\) | ||||
0.0104798 | + | 0.999945i | \(0.496664\pi\) | |||||||
\(110\) | −4.47414 | − | 0.784722i | −0.426592 | − | 0.0748203i | ||||
\(111\) | −11.9208 | −1.13148 | ||||||||
\(112\) | 1.44270i | 0.136322i | ||||||||
\(113\) | − | 0.580599i | − | 0.0546182i | −0.999627 | − | 0.0273091i | \(-0.991306\pi\) | ||
0.999627 | − | 0.0273091i | \(-0.00869384\pi\) | |||||||
\(114\) | 21.9419 | 2.05505 | ||||||||
\(115\) | −2.20245 | − | 0.386289i | −0.205379 | − | 0.0360216i | ||||
\(116\) | −9.69520 | −0.900176 | ||||||||
\(117\) | 4.24672i | 0.392609i | ||||||||
\(118\) | − | 10.7226i | − | 0.987098i | ||||||
\(119\) | 5.65339 | 0.518245 | ||||||||
\(120\) | −1.25886 | + | 7.17748i | −0.114918 | + | 0.655211i | ||||
\(121\) | −6.87326 | −0.624842 | ||||||||
\(122\) | 1.73937i | 0.157475i | ||||||||
\(123\) | − | 22.9203i | − | 2.06665i | ||||||
\(124\) | 3.07502 | 0.276145 | ||||||||
\(125\) | −5.56376 | + | 9.69766i | −0.497638 | + | 0.867385i | ||||
\(126\) | 10.9936 | 0.979391 | ||||||||
\(127\) | 1.56944i | 0.139266i | 0.997573 | + | 0.0696328i | \(0.0221828\pi\) | ||||
−0.997573 | + | 0.0696328i | \(0.977817\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 16.5050 | 1.45318 | ||||||||
\(130\) | 0.215278 | − | 1.22742i | 0.0188812 | − | 0.107652i | ||||
\(131\) | 15.9208 | 1.39101 | 0.695505 | − | 0.718521i | \(-0.255181\pi\) | ||||
0.695505 | + | 0.718521i | \(0.255181\pi\) | |||||||
\(132\) | − | 6.62018i | − | 0.576212i | ||||||
\(133\) | 9.71371i | 0.842285i | ||||||||
\(134\) | −12.0129 | −1.03776 | ||||||||
\(135\) | 33.1612 | + | 5.81616i | 2.85406 | + | 0.500575i | ||||
\(136\) | −3.91861 | −0.336018 | ||||||||
\(137\) | − | 6.47013i | − | 0.552781i | −0.961045 | − | 0.276390i | \(-0.910862\pi\) | ||
0.961045 | − | 0.276390i | \(-0.0891383\pi\) | |||||||
\(138\) | − | 3.25886i | − | 0.277413i | ||||||
\(139\) | 0.656206 | 0.0556586 | 0.0278293 | − | 0.999613i | \(-0.491141\pi\) | ||||
0.0278293 | + | 0.999613i | \(0.491141\pi\) | |||||||
\(140\) | −3.17748 | − | 0.557299i | −0.268546 | − | 0.0471004i | ||||
\(141\) | 2.15004 | 0.181066 | ||||||||
\(142\) | 12.4363i | 1.04363i | ||||||||
\(143\) | 1.13212i | 0.0946725i | ||||||||
\(144\) | −7.62018 | −0.635015 | ||||||||
\(145\) | 3.74514 | − | 21.3532i | 0.311017 | − | 1.77328i | ||||
\(146\) | −9.26464 | −0.766747 | ||||||||
\(147\) | − | 16.0291i | − | 1.32206i | ||||||
\(148\) | 3.65798i | 0.300684i | ||||||||
\(149\) | −23.8349 | −1.95263 | −0.976314 | − | 0.216357i | \(-0.930582\pi\) | ||||
−0.976314 | + | 0.216357i | \(0.930582\pi\) | |||||||
\(150\) | −15.3217 | − | 5.54515i | −1.25101 | − | 0.452760i | ||||
\(151\) | −14.8669 | −1.20985 | −0.604925 | − | 0.796282i | \(-0.706797\pi\) | ||||
−0.604925 | + | 0.796282i | \(0.706797\pi\) | |||||||
\(152\) | − | 6.73300i | − | 0.546118i | ||||||
\(153\) | 29.8605i | 2.41408i | ||||||||
\(154\) | 2.93076 | 0.236167 | ||||||||
\(155\) | −1.18785 | + | 6.77258i | −0.0954101 | + | 0.543987i | ||||
\(156\) | 1.81616 | 0.145409 | ||||||||
\(157\) | 8.24213i | 0.657793i | 0.944366 | + | 0.328897i | \(0.106677\pi\) | ||||
−0.944366 | + | 0.328897i | \(0.893323\pi\) | |||||||
\(158\) | − | 5.92439i | − | 0.471319i | ||||||
\(159\) | −36.2631 | −2.87585 | ||||||||
\(160\) | 2.20245 | + | 0.386289i | 0.174119 | + | 0.0305388i | ||||
\(161\) | 1.44270 | 0.113701 | ||||||||
\(162\) | 26.2066i | 2.05898i | ||||||||
\(163\) | 10.3154i | 0.807962i | 0.914767 | + | 0.403981i | \(0.132374\pi\) | ||||
−0.914767 | + | 0.403981i | \(0.867626\pi\) | |||||||
\(164\) | −7.03321 | −0.549202 | ||||||||
\(165\) | 14.5806 | + | 2.55730i | 1.13510 | + | 0.199085i | ||||
\(166\) | −11.3775 | −0.883063 | ||||||||
\(167\) | − | 4.65975i | − | 0.360582i | −0.983613 | − | 0.180291i | \(-0.942296\pi\) | ||
0.983613 | − | 0.180291i | \(-0.0577040\pi\) | |||||||
\(168\) | − | 4.70156i | − | 0.362733i | ||||||
\(169\) | 12.6894 | 0.976109 | ||||||||
\(170\) | 1.51372 | − | 8.63055i | 0.116097 | − | 0.661933i | ||||
\(171\) | −51.3067 | −3.92352 | ||||||||
\(172\) | − | 5.06465i | − | 0.386176i | ||||||
\(173\) | − | 2.80402i | − | 0.213185i | −0.994303 | − | 0.106593i | \(-0.966006\pi\) | ||
0.994303 | − | 0.106593i | \(-0.0339941\pi\) | |||||||
\(174\) | 31.5953 | 2.39523 | ||||||||
\(175\) | 2.45485 | − | 6.78295i | 0.185569 | − | 0.512743i | ||||
\(176\) | −2.03144 | −0.153125 | ||||||||
\(177\) | 34.9436i | 2.62652i | ||||||||
\(178\) | − | 5.25308i | − | 0.393735i | ||||||
\(179\) | 4.44212 | 0.332019 | 0.166010 | − | 0.986124i | \(-0.446912\pi\) | ||||
0.166010 | + | 0.986124i | \(0.446912\pi\) | |||||||
\(180\) | 2.94359 | − | 16.7830i | 0.219402 | − | 1.25093i | ||||
\(181\) | 2.42019 | 0.179891 | 0.0899455 | − | 0.995947i | \(-0.471331\pi\) | ||||
0.0899455 | + | 0.995947i | \(0.471331\pi\) | |||||||
\(182\) | 0.804016i | 0.0595976i | ||||||||
\(183\) | − | 5.66835i | − | 0.419016i | ||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −8.05651 | − | 1.41304i | −0.592327 | − | 0.103888i | ||||
\(186\) | −10.0211 | −0.734780 | ||||||||
\(187\) | 7.96042i | 0.582124i | ||||||||
\(188\) | − | 0.659753i | − | 0.0481174i | ||||||
\(189\) | −21.7220 | −1.58005 | ||||||||
\(190\) | 14.8291 | + | 2.60088i | 1.07582 | + | 0.188688i | ||||
\(191\) | −20.8934 | −1.51179 | −0.755897 | − | 0.654690i | \(-0.772799\pi\) | ||||
−0.755897 | + | 0.654690i | \(0.772799\pi\) | |||||||
\(192\) | 3.25886i | 0.235188i | ||||||||
\(193\) | 2.88540i | 0.207696i | 0.994593 | + | 0.103848i | \(0.0331155\pi\) | ||||
−0.994593 | + | 0.103848i | \(0.966884\pi\) | |||||||
\(194\) | 0.0813861 | 0.00584318 | ||||||||
\(195\) | −0.701562 | + | 4.00000i | −0.0502399 | + | 0.286446i | ||||
\(196\) | −4.91861 | −0.351330 | ||||||||
\(197\) | 19.0925i | 1.36029i | 0.733079 | + | 0.680144i | \(0.238083\pi\) | ||||
−0.733079 | + | 0.680144i | \(0.761917\pi\) | |||||||
\(198\) | 15.4799i | 1.10011i | ||||||||
\(199\) | −6.58060 | −0.466486 | −0.233243 | − | 0.972418i | \(-0.574934\pi\) | ||||
−0.233243 | + | 0.972418i | \(0.574934\pi\) | |||||||
\(200\) | −1.70156 | + | 4.70156i | −0.120319 | + | 0.332451i | ||||
\(201\) | 39.1485 | 2.76132 | ||||||||
\(202\) | 8.31281i | 0.584888i | ||||||||
\(203\) | 13.9873i | 0.981714i | ||||||||
\(204\) | 12.7702 | 0.894094 | ||||||||
\(205\) | 2.71685 | − | 15.4903i | 0.189753 | − | 1.08189i | ||||
\(206\) | −6.36991 | −0.443813 | ||||||||
\(207\) | 7.62018i | 0.529639i | ||||||||
\(208\) | − | 0.557299i | − | 0.0386417i | ||||||
\(209\) | −13.6777 | −0.946105 | ||||||||
\(210\) | 10.3550 | + | 1.81616i | 0.714559 | + | 0.125327i | ||||
\(211\) | 6.55986 | 0.451599 | 0.225800 | − | 0.974174i | \(-0.427501\pi\) | ||||
0.225800 | + | 0.974174i | \(0.427501\pi\) | |||||||
\(212\) | 11.1275i | 0.764242i | ||||||||
\(213\) | − | 40.5283i | − | 2.77695i | ||||||
\(214\) | 16.9226 | 1.15681 | ||||||||
\(215\) | 11.1546 | + | 1.95642i | 0.760740 | + | 0.133427i | ||||
\(216\) | 15.0565 | 1.02447 | ||||||||
\(217\) | − | 4.43634i | − | 0.301158i | ||||||
\(218\) | 0.218825i | 0.0148207i | ||||||||
\(219\) | 30.1922 | 2.04020 | ||||||||
\(220\) | 0.784722 | − | 4.47414i | 0.0529059 | − | 0.301646i | ||||
\(221\) | −2.18384 | −0.146901 | ||||||||
\(222\) | − | 11.9208i | − | 0.800075i | ||||||
\(223\) | − | 20.2094i | − | 1.35332i | −0.736296 | − | 0.676660i | \(-0.763427\pi\) | ||
0.736296 | − | 0.676660i | \(-0.236573\pi\) | |||||||
\(224\) | −1.44270 | −0.0963945 | ||||||||
\(225\) | 35.8267 | + | 12.9662i | 2.38845 | + | 0.864414i | ||||
\(226\) | 0.580599 | 0.0386209 | ||||||||
\(227\) | 15.0098i | 0.996234i | 0.867110 | + | 0.498117i | \(0.165975\pi\) | ||||
−0.867110 | + | 0.498117i | \(0.834025\pi\) | |||||||
\(228\) | 21.9419i | 1.45314i | ||||||||
\(229\) | −13.7081 | −0.905859 | −0.452929 | − | 0.891546i | \(-0.649621\pi\) | ||||
−0.452929 | + | 0.891546i | \(0.649621\pi\) | |||||||
\(230\) | 0.386289 | − | 2.20245i | 0.0254711 | − | 0.145225i | ||||
\(231\) | −9.55093 | −0.628405 | ||||||||
\(232\) | − | 9.69520i | − | 0.636521i | ||||||
\(233\) | 9.19822i | 0.602595i | 0.953530 | + | 0.301298i | \(0.0974198\pi\) | ||||
−0.953530 | + | 0.301298i | \(0.902580\pi\) | |||||||
\(234\) | −4.24672 | −0.277617 | ||||||||
\(235\) | 1.45307 | + | 0.254855i | 0.0947880 | + | 0.0166249i | ||||
\(236\) | 10.7226 | 0.697984 | ||||||||
\(237\) | 19.3068i | 1.25411i | ||||||||
\(238\) | 5.65339i | 0.366455i | ||||||||
\(239\) | 2.72618 | 0.176342 | 0.0881709 | − | 0.996105i | \(-0.471898\pi\) | ||||
0.0881709 | + | 0.996105i | \(0.471898\pi\) | |||||||
\(240\) | −7.17748 | − | 1.25886i | −0.463304 | − | 0.0812591i | ||||
\(241\) | 3.26109 | 0.210066 | 0.105033 | − | 0.994469i | \(-0.466505\pi\) | ||||
0.105033 | + | 0.994469i | \(0.466505\pi\) | |||||||
\(242\) | − | 6.87326i | − | 0.441830i | ||||||
\(243\) | − | 40.2340i | − | 2.58101i | ||||||
\(244\) | −1.73937 | −0.111351 | ||||||||
\(245\) | 1.90000 | − | 10.8330i | 0.121387 | − | 0.692095i | ||||
\(246\) | 22.9203 | 1.46134 | ||||||||
\(247\) | − | 3.75229i | − | 0.238753i | ||||||
\(248\) | 3.07502i | 0.195264i | ||||||||
\(249\) | 37.0776 | 2.34970 | ||||||||
\(250\) | −9.69766 | − | 5.56376i | −0.613334 | − | 0.351883i | ||||
\(251\) | 19.9941 | 1.26202 | 0.631008 | − | 0.775776i | \(-0.282641\pi\) | ||||
0.631008 | + | 0.775776i | \(0.282641\pi\) | |||||||
\(252\) | 10.9936i | 0.692534i | ||||||||
\(253\) | 2.03144i | 0.127715i | ||||||||
\(254\) | −1.56944 | −0.0984756 | ||||||||
\(255\) | −4.93299 | + | 28.1258i | −0.308916 | + | 1.76130i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 26.7935i | − | 1.67133i | −0.549237 | − | 0.835667i | \(-0.685081\pi\) | ||
0.549237 | − | 0.835667i | \(-0.314919\pi\) | |||||||
\(258\) | 16.5050i | 1.02756i | ||||||||
\(259\) | 5.27737 | 0.327920 | ||||||||
\(260\) | 1.22742 | + | 0.215278i | 0.0761215 | + | 0.0133510i | ||||
\(261\) | −73.8791 | −4.57300 | ||||||||
\(262\) | 15.9208i | 0.983593i | ||||||||
\(263\) | 15.8267i | 0.975918i | 0.872867 | + | 0.487959i | \(0.162258\pi\) | ||||
−0.872867 | + | 0.487959i | \(0.837742\pi\) | |||||||
\(264\) | 6.62018 | 0.407444 | ||||||||
\(265\) | −24.5078 | − | 4.29844i | −1.50550 | − | 0.264051i | ||||
\(266\) | −9.71371 | −0.595586 | ||||||||
\(267\) | 17.1191i | 1.04767i | ||||||||
\(268\) | − | 12.0129i | − | 0.733806i | ||||||
\(269\) | −12.0872 | −0.736967 | −0.368484 | − | 0.929634i | \(-0.620123\pi\) | ||||
−0.368484 | + | 0.929634i | \(0.620123\pi\) | |||||||
\(270\) | −5.81616 | + | 33.1612i | −0.353960 | + | 2.01813i | ||||
\(271\) | 8.40254 | 0.510418 | 0.255209 | − | 0.966886i | \(-0.417856\pi\) | ||||
0.255209 | + | 0.966886i | \(0.417856\pi\) | |||||||
\(272\) | − | 3.91861i | − | 0.237601i | ||||||
\(273\) | − | 2.62018i | − | 0.158580i | ||||||
\(274\) | 6.47013 | 0.390875 | ||||||||
\(275\) | 9.55093 | + | 3.45662i | 0.575943 | + | 0.208442i | ||||
\(276\) | 3.25886 | 0.196160 | ||||||||
\(277\) | − | 13.8488i | − | 0.832093i | −0.909343 | − | 0.416046i | \(-0.863415\pi\) | ||
0.909343 | − | 0.416046i | \(-0.136585\pi\) | |||||||
\(278\) | 0.656206i | 0.0393566i | ||||||||
\(279\) | 23.4322 | 1.40285 | ||||||||
\(280\) | 0.557299 | − | 3.17748i | 0.0333050 | − | 0.189890i | ||||
\(281\) | −8.15004 | −0.486191 | −0.243095 | − | 0.970002i | \(-0.578163\pi\) | ||||
−0.243095 | + | 0.970002i | \(0.578163\pi\) | |||||||
\(282\) | 2.15004i | 0.128033i | ||||||||
\(283\) | 17.3532i | 1.03154i | 0.856727 | + | 0.515770i | \(0.172494\pi\) | ||||
−0.856727 | + | 0.515770i | \(0.827506\pi\) | |||||||
\(284\) | −12.4363 | −0.737961 | ||||||||
\(285\) | −48.3259 | − | 8.47591i | −2.86258 | − | 0.502070i | ||||
\(286\) | −1.13212 | −0.0669436 | ||||||||
\(287\) | 10.1468i | 0.598948i | ||||||||
\(288\) | − | 7.62018i | − | 0.449023i | ||||||
\(289\) | 1.64446 | 0.0967332 | ||||||||
\(290\) | 21.3532 | + | 3.74514i | 1.25390 | + | 0.219922i | ||||
\(291\) | −0.265226 | −0.0155478 | ||||||||
\(292\) | − | 9.26464i | − | 0.542172i | ||||||
\(293\) | − | 7.02252i | − | 0.410260i | −0.978735 | − | 0.205130i | \(-0.934238\pi\) | ||
0.978735 | − | 0.205130i | \(-0.0657617\pi\) | |||||||
\(294\) | 16.0291 | 0.934835 | ||||||||
\(295\) | −4.14203 | + | 23.6160i | −0.241158 | + | 1.37498i | ||||
\(296\) | −3.65798 | −0.212616 | ||||||||
\(297\) | − | 30.5864i | − | 1.77480i | ||||||
\(298\) | − | 23.8349i | − | 1.38072i | ||||||
\(299\) | −0.557299 | −0.0322294 | ||||||||
\(300\) | 5.54515 | − | 15.3217i | 0.320150 | − | 0.884601i | ||||
\(301\) | −7.30678 | −0.421156 | ||||||||
\(302\) | − | 14.8669i | − | 0.855494i | ||||||
\(303\) | − | 27.0903i | − | 1.55630i | ||||||
\(304\) | 6.73300 | 0.386164 | ||||||||
\(305\) | 0.671897 | − | 3.83086i | 0.0384727 | − | 0.219355i | ||||
\(306\) | −29.8605 | −1.70701 | ||||||||
\(307\) | 16.4156i | 0.936887i | 0.883493 | + | 0.468444i | \(0.155185\pi\) | ||||
−0.883493 | + | 0.468444i | \(0.844815\pi\) | |||||||
\(308\) | 2.93076i | 0.166995i | ||||||||
\(309\) | 20.7587 | 1.18092 | ||||||||
\(310\) | −6.77258 | − | 1.18785i | −0.384657 | − | 0.0674651i | ||||
\(311\) | 7.35181 | 0.416883 | 0.208441 | − | 0.978035i | \(-0.433161\pi\) | ||||
0.208441 | + | 0.978035i | \(0.433161\pi\) | |||||||
\(312\) | 1.81616i | 0.102820i | ||||||||
\(313\) | − | 4.08972i | − | 0.231165i | −0.993298 | − | 0.115582i | \(-0.963127\pi\) | ||
0.993298 | − | 0.115582i | \(-0.0368734\pi\) | |||||||
\(314\) | −8.24213 | −0.465130 | ||||||||
\(315\) | −24.2129 | − | 4.24672i | −1.36424 | − | 0.239275i | ||||
\(316\) | 5.92439 | 0.333273 | ||||||||
\(317\) | 8.91580i | 0.500761i | 0.968148 | + | 0.250381i | \(0.0805557\pi\) | ||||
−0.968148 | + | 0.250381i | \(0.919444\pi\) | |||||||
\(318\) | − | 36.2631i | − | 2.03353i | ||||||
\(319\) | −19.6952 | −1.10272 | ||||||||
\(320\) | −0.386289 | + | 2.20245i | −0.0215942 | + | 0.123121i | ||||
\(321\) | −55.1485 | −3.07809 | ||||||||
\(322\) | 1.44270i | 0.0803986i | ||||||||
\(323\) | − | 26.3840i | − | 1.46805i | ||||||
\(324\) | −26.2066 | −1.45592 | ||||||||
\(325\) | −0.948279 | + | 2.62018i | −0.0526011 | + | 0.145341i | ||||
\(326\) | −10.3154 | −0.571316 | ||||||||
\(327\) | − | 0.713121i | − | 0.0394357i | ||||||
\(328\) | − | 7.03321i | − | 0.388344i | ||||||
\(329\) | −0.951826 | −0.0524759 | ||||||||
\(330\) | −2.55730 | + | 14.5806i | −0.140775 | + | 0.802636i | ||||
\(331\) | 21.3240 | 1.17207 | 0.586036 | − | 0.810285i | \(-0.300688\pi\) | ||||
0.586036 | + | 0.810285i | \(0.300688\pi\) | |||||||
\(332\) | − | 11.3775i | − | 0.624420i | ||||||
\(333\) | 27.8744i | 1.52751i | ||||||||
\(334\) | 4.65975 | 0.254970 | ||||||||
\(335\) | 26.4579 | + | 4.64046i | 1.44555 | + | 0.253535i | ||||
\(336\) | 4.70156 | 0.256491 | ||||||||
\(337\) | − | 3.15417i | − | 0.171819i | −0.996303 | − | 0.0859094i | \(-0.972620\pi\) | ||
0.996303 | − | 0.0859094i | \(-0.0273796\pi\) | |||||||
\(338\) | 12.6894i | 0.690213i | ||||||||
\(339\) | −1.89209 | −0.102764 | ||||||||
\(340\) | 8.63055 | + | 1.51372i | 0.468057 | + | 0.0820928i | ||||
\(341\) | 6.24672 | 0.338279 | ||||||||
\(342\) | − | 51.3067i | − | 2.77435i | ||||||
\(343\) | 17.1950i | 0.928443i | ||||||||
\(344\) | 5.06465 | 0.273068 | ||||||||
\(345\) | −1.25886 | + | 7.17748i | −0.0677748 | + | 0.386422i | ||||
\(346\) | 2.80402 | 0.150745 | ||||||||
\(347\) | − | 3.54739i | − | 0.190434i | −0.995457 | − | 0.0952169i | \(-0.969646\pi\) | ||
0.995457 | − | 0.0952169i | \(-0.0303545\pi\) | |||||||
\(348\) | 31.5953i | 1.69369i | ||||||||
\(349\) | 18.9726 | 1.01558 | 0.507789 | − | 0.861481i | \(-0.330463\pi\) | ||||
0.507789 | + | 0.861481i | \(0.330463\pi\) | |||||||
\(350\) | 6.78295 | + | 2.45485i | 0.362564 | + | 0.131217i | ||||
\(351\) | 8.39098 | 0.447877 | ||||||||
\(352\) | − | 2.03144i | − | 0.108276i | ||||||
\(353\) | 33.5710i | 1.78680i | 0.449257 | + | 0.893402i | \(0.351689\pi\) | ||||
−0.449257 | + | 0.893402i | \(0.648311\pi\) | |||||||
\(354\) | −34.9436 | −1.85723 | ||||||||
\(355\) | 4.80402 | − | 27.3904i | 0.254971 | − | 1.45373i | ||||
\(356\) | 5.25308 | 0.278413 | ||||||||
\(357\) | − | 18.4236i | − | 0.975081i | ||||||
\(358\) | 4.44212i | 0.234773i | ||||||||
\(359\) | 3.53243 | 0.186434 | 0.0932171 | − | 0.995646i | \(-0.470285\pi\) | ||||
0.0932171 | + | 0.995646i | \(0.470285\pi\) | |||||||
\(360\) | 16.7830 | + | 2.94359i | 0.884544 | + | 0.155141i | ||||
\(361\) | 26.3333 | 1.38596 | ||||||||
\(362\) | 2.42019i | 0.127202i | ||||||||
\(363\) | 22.3990i | 1.17564i | ||||||||
\(364\) | −0.804016 | −0.0421419 | ||||||||
\(365\) | 20.4049 | + | 3.57883i | 1.06804 | + | 0.187324i | ||||
\(366\) | 5.66835 | 0.296289 | ||||||||
\(367\) | − | 8.07444i | − | 0.421482i | −0.977542 | − | 0.210741i | \(-0.932412\pi\) | ||
0.977542 | − | 0.210741i | \(-0.0675877\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | −53.5943 | −2.79001 | ||||||||
\(370\) | 1.41304 | − | 8.05651i | 0.0734602 | − | 0.418838i | ||||
\(371\) | 16.0537 | 0.833466 | ||||||||
\(372\) | − | 10.0211i | − | 0.519568i | ||||||
\(373\) | − | 1.31459i | − | 0.0680668i | −0.999421 | − | 0.0340334i | \(-0.989165\pi\) | ||
0.999421 | − | 0.0340334i | \(-0.0108353\pi\) | |||||||
\(374\) | −7.96042 | −0.411624 | ||||||||
\(375\) | 31.6033 | + | 18.1315i | 1.63199 | + | 0.936308i | ||||
\(376\) | 0.659753 | 0.0340242 | ||||||||
\(377\) | − | 5.40312i | − | 0.278275i | ||||||
\(378\) | − | 21.7220i | − | 1.11726i | ||||||
\(379\) | −0.311952 | −0.0160239 | −0.00801196 | − | 0.999968i | \(-0.502550\pi\) | ||||
−0.00801196 | + | 0.999968i | \(0.502550\pi\) | |||||||
\(380\) | −2.60088 | + | 14.8291i | −0.133422 | + | 0.760716i | ||||
\(381\) | 5.11460 | 0.262029 | ||||||||
\(382\) | − | 20.8934i | − | 1.06900i | ||||||
\(383\) | 10.6805i | 0.545748i | 0.962050 | + | 0.272874i | \(0.0879742\pi\) | ||||
−0.962050 | + | 0.272874i | \(0.912026\pi\) | |||||||
\(384\) | −3.25886 | −0.166303 | ||||||||
\(385\) | −6.45485 | − | 1.13212i | −0.328969 | − | 0.0576981i | ||||
\(386\) | −2.88540 | −0.146863 | ||||||||
\(387\) | − | 38.5935i | − | 1.96182i | ||||||
\(388\) | 0.0813861i | 0.00413175i | ||||||||
\(389\) | 7.86867 | 0.398957 | 0.199479 | − | 0.979902i | \(-0.436075\pi\) | ||||
0.199479 | + | 0.979902i | \(0.436075\pi\) | |||||||
\(390\) | −4.00000 | − | 0.701562i | −0.202548 | − | 0.0355250i | ||||
\(391\) | −3.91861 | −0.198173 | ||||||||
\(392\) | − | 4.91861i | − | 0.248428i | ||||||
\(393\) | − | 51.8838i | − | 2.61719i | ||||||
\(394\) | −19.0925 | −0.961868 | ||||||||
\(395\) | −2.28853 | + | 13.0482i | −0.115148 | + | 0.656525i | ||||
\(396\) | −15.4799 | −0.777895 | ||||||||
\(397\) | − | 29.2334i | − | 1.46718i | −0.679591 | − | 0.733591i | \(-0.737843\pi\) | ||
0.679591 | − | 0.733591i | \(-0.262157\pi\) | |||||||
\(398\) | − | 6.58060i | − | 0.329856i | ||||||
\(399\) | 31.6556 | 1.58476 | ||||||||
\(400\) | −4.70156 | − | 1.70156i | −0.235078 | − | 0.0850781i | ||||
\(401\) | 23.7130 | 1.18417 | 0.592086 | − | 0.805874i | \(-0.298304\pi\) | ||||
0.592086 | + | 0.805874i | \(0.298304\pi\) | |||||||
\(402\) | 39.1485i | 1.95255i | ||||||||
\(403\) | 1.71371i | 0.0853658i | ||||||||
\(404\) | −8.31281 | −0.413578 | ||||||||
\(405\) | 10.1233 | − | 57.7186i | 0.503031 | − | 2.86806i | ||||
\(406\) | −13.9873 | −0.694177 | ||||||||
\(407\) | 7.43096i | 0.368339i | ||||||||
\(408\) | 12.7702i | 0.632220i | ||||||||
\(409\) | 33.2509 | 1.64415 | 0.822076 | − | 0.569378i | \(-0.192816\pi\) | ||||
0.822076 | + | 0.569378i | \(0.192816\pi\) | |||||||
\(410\) | 15.4903 | + | 2.71685i | 0.765011 | + | 0.134176i | ||||
\(411\) | −21.0853 | −1.04006 | ||||||||
\(412\) | − | 6.36991i | − | 0.313823i | ||||||
\(413\) | − | 15.4695i | − | 0.761207i | ||||||
\(414\) | −7.62018 | −0.374511 | ||||||||
\(415\) | 25.0583 | + | 4.39499i | 1.23006 | + | 0.215741i | ||||
\(416\) | 0.557299 | 0.0273238 | ||||||||
\(417\) | − | 2.13848i | − | 0.104722i | ||||||
\(418\) | − | 13.6777i | − | 0.668997i | ||||||
\(419\) | −7.28229 | −0.355763 | −0.177882 | − | 0.984052i | \(-0.556924\pi\) | ||||
−0.177882 | + | 0.984052i | \(0.556924\pi\) | |||||||
\(420\) | −1.81616 | + | 10.3550i | −0.0886195 | + | 0.505270i | ||||
\(421\) | −2.71515 | −0.132329 | −0.0661643 | − | 0.997809i | \(-0.521076\pi\) | ||||
−0.0661643 | + | 0.997809i | \(0.521076\pi\) | |||||||
\(422\) | 6.55986i | 0.319329i | ||||||||
\(423\) | − | 5.02743i | − | 0.244442i | ||||||
\(424\) | −11.1275 | −0.540401 | ||||||||
\(425\) | −6.66777 | + | 18.4236i | −0.323434 | + | 0.893676i | ||||
\(426\) | 40.5283 | 1.96360 | ||||||||
\(427\) | 2.50938i | 0.121438i | ||||||||
\(428\) | 16.9226i | 0.817986i | ||||||||
\(429\) | 3.68942 | 0.178127 | ||||||||
\(430\) | −1.95642 | + | 11.1546i | −0.0943468 | + | 0.537924i | ||||
\(431\) | 10.3336 | 0.497750 | 0.248875 | − | 0.968536i | \(-0.419939\pi\) | ||||
0.248875 | + | 0.968536i | \(0.419939\pi\) | |||||||
\(432\) | 15.0565i | 0.724407i | ||||||||
\(433\) | 28.4153i | 1.36555i | 0.730628 | + | 0.682775i | \(0.239227\pi\) | ||||
−0.730628 | + | 0.682775i | \(0.760773\pi\) | |||||||
\(434\) | 4.43634 | 0.212951 | ||||||||
\(435\) | −69.5870 | − | 12.2049i | −3.33644 | − | 0.585181i | ||||
\(436\) | −0.218825 | −0.0104798 | ||||||||
\(437\) | − | 6.73300i | − | 0.322083i | ||||||
\(438\) | 30.1922i | 1.44264i | ||||||||
\(439\) | −6.37313 | −0.304173 | −0.152087 | − | 0.988367i | \(-0.548599\pi\) | ||||
−0.152087 | + | 0.988367i | \(0.548599\pi\) | |||||||
\(440\) | 4.47414 | + | 0.784722i | 0.213296 | + | 0.0374101i | ||||
\(441\) | −37.4807 | −1.78480 | ||||||||
\(442\) | − | 2.18384i | − | 0.103875i | ||||||
\(443\) | − | 9.43114i | − | 0.448087i | −0.974579 | − | 0.224044i | \(-0.928074\pi\) | ||
0.974579 | − | 0.224044i | \(-0.0719258\pi\) | |||||||
\(444\) | 11.9208 | 0.565738 | ||||||||
\(445\) | −2.02921 | + | 11.5696i | −0.0961936 | + | 0.548454i | ||||
\(446\) | 20.2094 | 0.956942 | ||||||||
\(447\) | 77.6745i | 3.67388i | ||||||||
\(448\) | − | 1.44270i | − | 0.0681612i | ||||||
\(449\) | −11.3185 | −0.534154 | −0.267077 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267077 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(450\) | −12.9662 | + | 35.8267i | −0.611233 | + | 1.68889i | ||||
\(451\) | −14.2875 | −0.672774 | ||||||||
\(452\) | 0.580599i | 0.0273091i | ||||||||
\(453\) | 48.4491i | 2.27634i | ||||||||
\(454\) | −15.0098 | −0.704444 | ||||||||
\(455\) | 0.310582 | − | 1.77080i | 0.0145603 | − | 0.0830166i | ||||
\(456\) | −21.9419 | −1.02752 | ||||||||
\(457\) | − | 4.96456i | − | 0.232232i | −0.993236 | − | 0.116116i | \(-0.962956\pi\) | ||
0.993236 | − | 0.116116i | \(-0.0370445\pi\) | |||||||
\(458\) | − | 13.7081i | − | 0.640539i | ||||||
\(459\) | 59.0007 | 2.75391 | ||||||||
\(460\) | 2.20245 | + | 0.386289i | 0.102690 | + | 0.0180108i | ||||
\(461\) | 19.9128 | 0.927433 | 0.463717 | − | 0.885984i | \(-0.346516\pi\) | ||||
0.463717 | + | 0.885984i | \(0.346516\pi\) | |||||||
\(462\) | − | 9.55093i | − | 0.444350i | ||||||
\(463\) | − | 29.9046i | − | 1.38978i | −0.719114 | − | 0.694892i | \(-0.755452\pi\) | ||
0.719114 | − | 0.694892i | \(-0.244548\pi\) | |||||||
\(464\) | 9.69520 | 0.450088 | ||||||||
\(465\) | 22.0709 | + | 3.87102i | 1.02351 | + | 0.179514i | ||||
\(466\) | −9.19822 | −0.426099 | ||||||||
\(467\) | − | 15.1032i | − | 0.698895i | −0.936956 | − | 0.349447i | \(-0.886369\pi\) | ||
0.936956 | − | 0.349447i | \(-0.113631\pi\) | |||||||
\(468\) | − | 4.24672i | − | 0.196305i | ||||||
\(469\) | −17.3311 | −0.800274 | ||||||||
\(470\) | −0.254855 | + | 1.45307i | −0.0117556 | + | 0.0670252i | ||||
\(471\) | 26.8599 | 1.23764 | ||||||||
\(472\) | 10.7226i | 0.493549i | ||||||||
\(473\) | − | 10.2885i | − | 0.473067i | ||||||
\(474\) | −19.3068 | −0.886790 | ||||||||
\(475\) | −31.6556 | − | 11.4566i | −1.45246 | − | 0.525666i | ||||
\(476\) | −5.65339 | −0.259123 | ||||||||
\(477\) | 84.7937i | 3.88244i | ||||||||
\(478\) | 2.72618i | 0.124692i | ||||||||
\(479\) | −28.6678 | −1.30986 | −0.654932 | − | 0.755688i | \(-0.727303\pi\) | ||||
−0.654932 | + | 0.755688i | \(0.727303\pi\) | |||||||
\(480\) | 1.25886 | − | 7.17748i | 0.0574589 | − | 0.327605i | ||||
\(481\) | −2.03859 | −0.0929516 | ||||||||
\(482\) | 3.26109i | 0.148539i | ||||||||
\(483\) | − | 4.70156i | − | 0.213928i | ||||||
\(484\) | 6.87326 | 0.312421 | ||||||||
\(485\) | −0.179249 | − | 0.0314385i | −0.00813926 | − | 0.00142755i | ||||
\(486\) | 40.2340 | 1.82505 | ||||||||
\(487\) | − | 9.15319i | − | 0.414770i | −0.978259 | − | 0.207385i | \(-0.933505\pi\) | ||
0.978259 | − | 0.207385i | \(-0.0664954\pi\) | |||||||
\(488\) | − | 1.73937i | − | 0.0787374i | ||||||
\(489\) | 33.6164 | 1.52018 | ||||||||
\(490\) | 10.8330 | + | 1.90000i | 0.489385 | + | 0.0858335i | ||||
\(491\) | −20.8098 | −0.939133 | −0.469566 | − | 0.882897i | \(-0.655590\pi\) | ||||
−0.469566 | + | 0.882897i | \(0.655590\pi\) | |||||||
\(492\) | 22.9203i | 1.03333i | ||||||||
\(493\) | − | 37.9917i | − | 1.71106i | ||||||
\(494\) | 3.75229 | 0.168824 | ||||||||
\(495\) | 5.97972 | − | 34.0937i | 0.268768 | − | 1.53240i | ||||
\(496\) | −3.07502 | −0.138073 | ||||||||
\(497\) | 17.9419i | 0.804805i | ||||||||
\(498\) | 37.0776i | 1.66149i | ||||||||
\(499\) | 18.1293 | 0.811579 | 0.405789 | − | 0.913967i | \(-0.366997\pi\) | ||||
0.405789 | + | 0.913967i | \(0.366997\pi\) | |||||||
\(500\) | 5.56376 | − | 9.69766i | 0.248819 | − | 0.433692i | ||||
\(501\) | −15.1855 | −0.678438 | ||||||||
\(502\) | 19.9941i | 0.892380i | ||||||||
\(503\) | − | 26.4296i | − | 1.17844i | −0.807974 | − | 0.589218i | \(-0.799436\pi\) | ||
0.807974 | − | 0.589218i | \(-0.200564\pi\) | |||||||
\(504\) | −10.9936 | −0.489695 | ||||||||
\(505\) | 3.21115 | − | 18.3085i | 0.142894 | − | 0.814720i | ||||
\(506\) | −2.03144 | −0.0903085 | ||||||||
\(507\) | − | 41.3531i | − | 1.83655i | ||||||
\(508\) | − | 1.56944i | − | 0.0696328i | ||||||
\(509\) | 12.0501 | 0.534113 | 0.267057 | − | 0.963681i | \(-0.413949\pi\) | ||||
0.267057 | + | 0.963681i | \(0.413949\pi\) | |||||||
\(510\) | −28.1258 | − | 4.93299i | −1.24543 | − | 0.218437i | ||||
\(511\) | −13.3661 | −0.591282 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 101.376i | 4.47584i | ||||||||
\(514\) | 26.7935 | 1.18181 | ||||||||
\(515\) | 14.0294 | + | 2.46062i | 0.618209 | + | 0.108428i | ||||
\(516\) | −16.5050 | −0.726592 | ||||||||
\(517\) | − | 1.34025i | − | 0.0589440i | ||||||
\(518\) | 5.27737i | 0.231874i | ||||||||
\(519\) | −9.13790 | −0.401109 | ||||||||
\(520\) | −0.215278 | + | 1.22742i | −0.00944058 | + | 0.0538260i | ||||
\(521\) | −25.3697 | −1.11146 | −0.555732 | − | 0.831361i | \(-0.687562\pi\) | ||||
−0.555732 | + | 0.831361i | \(0.687562\pi\) | |||||||
\(522\) | − | 73.8791i | − | 3.23360i | ||||||
\(523\) | − | 25.0018i | − | 1.09325i | −0.837377 | − | 0.546626i | \(-0.815912\pi\) | ||
0.837377 | − | 0.546626i | \(-0.184088\pi\) | |||||||
\(524\) | −15.9208 | −0.695505 | ||||||||
\(525\) | −22.1047 | − | 8.00000i | −0.964728 | − | 0.349149i | ||||
\(526\) | −15.8267 | −0.690078 | ||||||||
\(527\) | 12.0498i | 0.524898i | ||||||||
\(528\) | 6.62018i | 0.288106i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 4.29844 | − | 24.5078i | 0.186712 | − | 1.06455i | ||||
\(531\) | 81.7083 | 3.54584 | ||||||||
\(532\) | − | 9.71371i | − | 0.421143i | ||||||
\(533\) | − | 3.91960i | − | 0.169777i | ||||||
\(534\) | −17.1191 | −0.740814 | ||||||||
\(535\) | −37.2712 | − | 6.53702i | −1.61137 | − | 0.282620i | ||||
\(536\) | 12.0129 | 0.518880 | ||||||||
\(537\) | − | 14.4762i | − | 0.624696i | ||||||
\(538\) | − | 12.0872i | − | 0.521115i | ||||||
\(539\) | −9.99186 | −0.430380 | ||||||||
\(540\) | −33.1612 | − | 5.81616i | −1.42703 | − | 0.250288i | ||||
\(541\) | 24.7900 | 1.06580 | 0.532902 | − | 0.846177i | \(-0.321101\pi\) | ||||
0.532902 | + | 0.846177i | \(0.321101\pi\) | |||||||
\(542\) | 8.40254i | 0.360920i | ||||||||
\(543\) | − | 7.88705i | − | 0.338466i | ||||||
\(544\) | 3.91861 | 0.168009 | ||||||||
\(545\) | 0.0845298 | − | 0.481952i | 0.00362086 | − | 0.0206445i | ||||
\(546\) | 2.62018 | 0.112133 | ||||||||
\(547\) | 30.9508i | 1.32336i | 0.749785 | + | 0.661681i | \(0.230157\pi\) | ||||
−0.749785 | + | 0.661681i | \(0.769843\pi\) | |||||||
\(548\) | 6.47013i | 0.276390i | ||||||||
\(549\) | −13.2543 | −0.565678 | ||||||||
\(550\) | −3.45662 | + | 9.55093i | −0.147391 | + | 0.407253i | ||||
\(551\) | 65.2778 | 2.78093 | ||||||||
\(552\) | 3.25886i | 0.138706i | ||||||||
\(553\) | − | 8.54713i | − | 0.363461i | ||||||
\(554\) | 13.8488 | 0.588379 | ||||||||
\(555\) | −4.60489 | + | 26.2551i | −0.195467 | + | 1.11447i | ||||
\(556\) | −0.656206 | −0.0278293 | ||||||||
\(557\) | 7.45307i | 0.315797i | 0.987455 | + | 0.157898i | \(0.0504718\pi\) | ||||
−0.987455 | + | 0.157898i | \(0.949528\pi\) | |||||||
\(558\) | 23.4322i | 0.991964i | ||||||||
\(559\) | 2.82252 | 0.119380 | ||||||||
\(560\) | 3.17748 | + | 0.557299i | 0.134273 | + | 0.0235502i | ||||
\(561\) | 25.9419 | 1.09527 | ||||||||
\(562\) | − | 8.15004i | − | 0.343789i | ||||||
\(563\) | − | 7.96161i | − | 0.335542i | −0.985826 | − | 0.167771i | \(-0.946343\pi\) | ||
0.985826 | − | 0.167771i | \(-0.0536569\pi\) | |||||||
\(564\) | −2.15004 | −0.0905331 | ||||||||
\(565\) | −1.27874 | − | 0.224279i | −0.0537970 | − | 0.00943549i | ||||
\(566\) | −17.3532 | −0.729408 | ||||||||
\(567\) | 37.8082i | 1.58780i | ||||||||
\(568\) | − | 12.4363i | − | 0.521817i | ||||||
\(569\) | −32.3873 | −1.35774 | −0.678872 | − | 0.734257i | \(-0.737531\pi\) | ||||
−0.678872 | + | 0.734257i | \(0.737531\pi\) | |||||||
\(570\) | 8.47591 | − | 48.3259i | 0.355017 | − | 2.02415i | ||||
\(571\) | −6.38994 | −0.267410 | −0.133705 | − | 0.991021i | \(-0.542688\pi\) | ||||
−0.133705 | + | 0.991021i | \(0.542688\pi\) | |||||||
\(572\) | − | 1.13212i | − | 0.0473363i | ||||||
\(573\) | 68.0887i | 2.84445i | ||||||||
\(574\) | −10.1468 | −0.423520 | ||||||||
\(575\) | −1.70156 | + | 4.70156i | −0.0709600 | + | 0.196069i | ||||
\(576\) | 7.62018 | 0.317507 | ||||||||
\(577\) | 39.1728i | 1.63078i | 0.578910 | + | 0.815392i | \(0.303478\pi\) | ||||
−0.578910 | + | 0.815392i | \(0.696522\pi\) | |||||||
\(578\) | 1.64446i | 0.0684007i | ||||||||
\(579\) | 9.40312 | 0.390781 | ||||||||
\(580\) | −3.74514 | + | 21.3532i | −0.155509 | + | 0.886642i | ||||
\(581\) | −16.4143 | −0.680979 | ||||||||
\(582\) | − | 0.265226i | − | 0.0109940i | ||||||
\(583\) | 22.6049i | 0.936199i | ||||||||
\(584\) | 9.26464 | 0.383374 | ||||||||
\(585\) | 9.35318 | + | 1.64046i | 0.386706 | + | 0.0678246i | ||||
\(586\) | 7.02252 | 0.290097 | ||||||||
\(587\) | 21.3811i | 0.882491i | 0.897386 | + | 0.441246i | \(0.145463\pi\) | ||||
−0.897386 | + | 0.441246i | \(0.854537\pi\) | |||||||
\(588\) | 16.0291i | 0.661028i | ||||||||
\(589\) | −20.7041 | −0.853098 | ||||||||
\(590\) | −23.6160 | − | 4.14203i | −0.972257 | − | 0.170525i | ||||
\(591\) | 62.2199 | 2.55939 | ||||||||
\(592\) | − | 3.65798i | − | 0.150342i | ||||||
\(593\) | − | 2.45130i | − | 0.100663i | −0.998733 | − | 0.0503314i | \(-0.983972\pi\) | ||
0.998733 | − | 0.0503314i | \(-0.0160277\pi\) | |||||||
\(594\) | 30.5864 | 1.25497 | ||||||||
\(595\) | 2.18384 | − | 12.4513i | 0.0895287 | − | 0.510453i | ||||
\(596\) | 23.8349 | 0.976314 | ||||||||
\(597\) | 21.4453i | 0.877696i | ||||||||
\(598\) | − | 0.557299i | − | 0.0227897i | ||||||
\(599\) | −38.5828 | −1.57645 | −0.788226 | − | 0.615386i | \(-0.789000\pi\) | ||||
−0.788226 | + | 0.615386i | \(0.789000\pi\) | |||||||
\(600\) | 15.3217 | + | 5.54515i | 0.625507 | + | 0.226380i | ||||
\(601\) | −35.3416 | −1.44162 | −0.720808 | − | 0.693135i | \(-0.756229\pi\) | ||||
−0.720808 | + | 0.693135i | \(0.756229\pi\) | |||||||
\(602\) | − | 7.30678i | − | 0.297802i | ||||||
\(603\) | − | 91.5406i | − | 3.72782i | ||||||
\(604\) | 14.8669 | 0.604925 | ||||||||
\(605\) | −2.65506 | + | 15.1380i | −0.107944 | + | 0.615447i | ||||
\(606\) | 27.0903 | 1.10047 | ||||||||
\(607\) | 17.8129i | 0.723005i | 0.932371 | + | 0.361502i | \(0.117736\pi\) | ||||
−0.932371 | + | 0.361502i | \(0.882264\pi\) | |||||||
\(608\) | 6.73300i | 0.273059i | ||||||||
\(609\) | 45.5826 | 1.84710 | ||||||||
\(610\) | 3.83086 | + | 0.671897i | 0.155107 | + | 0.0272043i | ||||
\(611\) | 0.367680 | 0.0148747 | ||||||||
\(612\) | − | 29.8605i | − | 1.20704i | ||||||
\(613\) | − | 37.7547i | − | 1.52490i | −0.647048 | − | 0.762450i | \(-0.723997\pi\) | ||
0.647048 | − | 0.762450i | \(-0.276003\pi\) | |||||||
\(614\) | −16.4156 | −0.662479 | ||||||||
\(615\) | −50.4807 | − | 8.85384i | −2.03558 | − | 0.357021i | ||||
\(616\) | −2.93076 | −0.118084 | ||||||||
\(617\) | − | 23.1248i | − | 0.930971i | −0.885055 | − | 0.465486i | \(-0.845880\pi\) | ||
0.885055 | − | 0.465486i | \(-0.154120\pi\) | |||||||
\(618\) | 20.7587i | 0.835036i | ||||||||
\(619\) | −19.5428 | −0.785491 | −0.392746 | − | 0.919647i | \(-0.628475\pi\) | ||||
−0.392746 | + | 0.919647i | \(0.628475\pi\) | |||||||
\(620\) | 1.18785 | − | 6.77258i | 0.0477050 | − | 0.271993i | ||||
\(621\) | 15.0565 | 0.604197 | ||||||||
\(622\) | 7.35181i | 0.294781i | ||||||||
\(623\) | − | 7.57863i | − | 0.303631i | ||||||
\(624\) | −1.81616 | −0.0727046 | ||||||||
\(625\) | 19.2094 | + | 16.0000i | 0.768375 | + | 0.640000i | ||||
\(626\) | 4.08972 | 0.163458 | ||||||||
\(627\) | 44.5736i | 1.78010i | ||||||||
\(628\) | − | 8.24213i | − | 0.328897i | ||||||
\(629\) | −14.3342 | −0.571542 | ||||||||
\(630\) | 4.24672 | − | 24.2129i | 0.169193 | − | 0.964666i | ||||
\(631\) | −26.4807 | −1.05418 | −0.527090 | − | 0.849809i | \(-0.676717\pi\) | ||||
−0.527090 | + | 0.849809i | \(0.676717\pi\) | |||||||
\(632\) | 5.92439i | 0.235660i | ||||||||
\(633\) | − | 21.3777i | − | 0.849686i | ||||||
\(634\) | −8.91580 | −0.354092 | ||||||||
\(635\) | 3.45662 | + | 0.606258i | 0.137172 | + | 0.0240586i | ||||
\(636\) | 36.2631 | 1.43792 | ||||||||
\(637\) | − | 2.74114i | − | 0.108608i | ||||||
\(638\) | − | 19.6952i | − | 0.779740i | ||||||
\(639\) | −94.7671 | −3.74893 | ||||||||
\(640\) | −2.20245 | − | 0.386289i | −0.0870594 | − | 0.0152694i | ||||
\(641\) | −35.9594 | −1.42031 | −0.710156 | − | 0.704044i | \(-0.751376\pi\) | ||||
−0.710156 | + | 0.704044i | \(0.751376\pi\) | |||||||
\(642\) | − | 55.1485i | − | 2.17654i | ||||||
\(643\) | 14.6934i | 0.579452i | 0.957110 | + | 0.289726i | \(0.0935642\pi\) | ||||
−0.957110 | + | 0.289726i | \(0.906436\pi\) | |||||||
\(644\) | −1.44270 | −0.0568504 | ||||||||
\(645\) | 6.37569 | − | 36.3514i | 0.251043 | − | 1.43134i | ||||
\(646\) | 26.3840 | 1.03807 | ||||||||
\(647\) | − | 26.7763i | − | 1.05269i | −0.850272 | − | 0.526343i | \(-0.823563\pi\) | ||
0.850272 | − | 0.526343i | \(-0.176437\pi\) | |||||||
\(648\) | − | 26.2066i | − | 1.02949i | ||||||
\(649\) | 21.7824 | 0.855033 | ||||||||
\(650\) | −2.62018 | − | 0.948279i | −0.102772 | − | 0.0371946i | ||||
\(651\) | −14.4574 | −0.566630 | ||||||||
\(652\) | − | 10.3154i | − | 0.403981i | ||||||
\(653\) | 18.8331i | 0.736996i | 0.929629 | + | 0.368498i | \(0.120128\pi\) | ||||
−0.929629 | + | 0.368498i | \(0.879872\pi\) | |||||||
\(654\) | 0.713121 | 0.0278853 | ||||||||
\(655\) | 6.15004 | − | 35.0649i | 0.240302 | − | 1.37010i | ||||
\(656\) | 7.03321 | 0.274601 | ||||||||
\(657\) | − | 70.5982i | − | 2.75430i | ||||||
\(658\) | − | 0.951826i | − | 0.0371060i | ||||||
\(659\) | 18.0885 | 0.704629 | 0.352315 | − | 0.935882i | \(-0.385395\pi\) | ||||
0.352315 | + | 0.935882i | \(0.385395\pi\) | |||||||
\(660\) | −14.5806 | − | 2.55730i | −0.567549 | − | 0.0995427i | ||||
\(661\) | 30.3235 | 1.17945 | 0.589724 | − | 0.807605i | \(-0.299237\pi\) | ||||
0.589724 | + | 0.807605i | \(0.299237\pi\) | |||||||
\(662\) | 21.3240i | 0.828780i | ||||||||
\(663\) | 7.11683i | 0.276395i | ||||||||
\(664\) | 11.3775 | 0.441531 | ||||||||
\(665\) | 21.3939 | + | 3.75229i | 0.829621 | + | 0.145508i | ||||
\(666\) | −27.8744 | −1.08011 | ||||||||
\(667\) | − | 9.69520i | − | 0.375400i | ||||||
\(668\) | 4.65975i | 0.180291i | ||||||||
\(669\) | −65.8595 | −2.54628 | ||||||||
\(670\) | −4.64046 | + | 26.4579i | −0.179277 | + | 1.02216i | ||||
\(671\) | −3.53341 | −0.136406 | ||||||||
\(672\) | 4.70156i | 0.181367i | ||||||||
\(673\) | 11.1496i | 0.429787i | 0.976637 | + | 0.214894i | \(0.0689404\pi\) | ||||
−0.976637 | + | 0.214894i | \(0.931060\pi\) | |||||||
\(674\) | 3.15417 | 0.121494 | ||||||||
\(675\) | 25.6196 | − | 70.7891i | 0.986099 | − | 2.72467i | ||||
\(676\) | −12.6894 | −0.488055 | ||||||||
\(677\) | 43.5275i | 1.67290i | 0.548045 | + | 0.836449i | \(0.315372\pi\) | ||||
−0.548045 | + | 0.836449i | \(0.684628\pi\) | |||||||
\(678\) | − | 1.89209i | − | 0.0726654i | ||||||
\(679\) | 0.117416 | 0.00450600 | ||||||||
\(680\) | −1.51372 | + | 8.63055i | −0.0580484 | + | 0.330966i | ||||
\(681\) | 48.9148 | 1.87442 | ||||||||
\(682\) | 6.24672i | 0.239199i | ||||||||
\(683\) | 24.1375i | 0.923596i | 0.886985 | + | 0.461798i | \(0.152795\pi\) | ||||
−0.886985 | + | 0.461798i | \(0.847205\pi\) | |||||||
\(684\) | 51.3067 | 1.96176 | ||||||||
\(685\) | −14.2501 | − | 2.49934i | −0.544470 | − | 0.0954948i | ||||
\(686\) | −17.1950 | −0.656508 | ||||||||
\(687\) | 44.6729i | 1.70438i | ||||||||
\(688\) | 5.06465i | 0.193088i | ||||||||
\(689\) | −6.20136 | −0.236253 | ||||||||
\(690\) | −7.17748 | − | 1.25886i | −0.273242 | − | 0.0479240i | ||||
\(691\) | −20.8241 | −0.792186 | −0.396093 | − | 0.918210i | \(-0.629634\pi\) | ||||
−0.396093 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(692\) | 2.80402i | 0.106593i | ||||||||
\(693\) | 22.3329i | 0.848356i | ||||||||
\(694\) | 3.54739 | 0.134657 | ||||||||
\(695\) | 0.253485 | − | 1.44526i | 0.00961523 | − | 0.0548218i | ||||
\(696\) | −31.5953 | −1.19762 | ||||||||
\(697\) | − | 27.5604i | − | 1.04393i | ||||||
\(698\) | 18.9726i | 0.718122i | ||||||||
\(699\) | 29.9757 | 1.13379 | ||||||||
\(700\) | −2.45485 | + | 6.78295i | −0.0927844 | + | 0.256371i | ||||
\(701\) | −31.5301 | −1.19087 | −0.595437 | − | 0.803402i | \(-0.703021\pi\) | ||||
−0.595437 | + | 0.803402i | \(0.703021\pi\) | |||||||
\(702\) | 8.39098i | 0.316697i | ||||||||
\(703\) | − | 24.6292i | − | 0.928907i | ||||||
\(704\) | 2.03144 | 0.0765627 | ||||||||
\(705\) | 0.830537 | − | 4.73536i | 0.0312798 | − | 0.178344i | ||||
\(706\) | −33.5710 | −1.26346 | ||||||||
\(707\) | 11.9929i | 0.451040i | ||||||||
\(708\) | − | 34.9436i | − | 1.31326i | ||||||
\(709\) | −3.12175 | −0.117240 | −0.0586199 | − | 0.998280i | \(-0.518670\pi\) | ||||
−0.0586199 | + | 0.998280i | \(0.518670\pi\) | |||||||
\(710\) | 27.3904 | + | 4.80402i | 1.02794 | + | 0.180292i | ||||
\(711\) | 45.1449 | 1.69307 | ||||||||
\(712\) | 5.25308i | 0.196868i | ||||||||
\(713\) | 3.07502i | 0.115160i | ||||||||
\(714\) | 18.4236 | 0.689486 | ||||||||
\(715\) | 2.49343 | + | 0.437325i | 0.0932491 | + | 0.0163550i | ||||
\(716\) | −4.44212 | −0.166010 | ||||||||
\(717\) | − | 8.88423i | − | 0.331788i | ||||||
\(718\) | 3.53243i | 0.131829i | ||||||||
\(719\) | −20.3945 | −0.760588 | −0.380294 | − | 0.924866i | \(-0.624177\pi\) | ||||
−0.380294 | + | 0.924866i | \(0.624177\pi\) | |||||||
\(720\) | −2.94359 | + | 16.7830i | −0.109701 | + | 0.625467i | ||||
\(721\) | −9.18988 | −0.342249 | ||||||||
\(722\) | 26.3333i | 0.980024i | ||||||||
\(723\) | − | 10.6275i | − | 0.395239i | ||||||
\(724\) | −2.42019 | −0.0899455 | ||||||||
\(725\) | −45.5826 | − | 16.4970i | −1.69289 | − | 0.612682i | ||||
\(726\) | −22.3990 | −0.831305 | ||||||||
\(727\) | − | 39.8896i | − | 1.47942i | −0.672924 | − | 0.739712i | \(-0.734962\pi\) | ||
0.672924 | − | 0.739712i | \(-0.265038\pi\) | |||||||
\(728\) | − | 0.804016i | − | 0.0297988i | ||||||
\(729\) | −52.4973 | −1.94434 | ||||||||
\(730\) | −3.57883 | + | 20.4049i | −0.132458 | + | 0.755219i | ||||
\(731\) | 19.8464 | 0.734046 | ||||||||
\(732\) | 5.66835i | 0.209508i | ||||||||
\(733\) | 22.7761i | 0.841255i | 0.907233 | + | 0.420628i | \(0.138190\pi\) | ||||
−0.907233 | + | 0.420628i | \(0.861810\pi\) | |||||||
\(734\) | 8.07444 | 0.298033 | ||||||||
\(735\) | −35.3032 | − | 6.19185i | −1.30218 | − | 0.228390i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | − | 24.4035i | − | 0.898915i | ||||||
\(738\) | − | 53.5943i | − | 1.97283i | ||||||
\(739\) | −33.7661 | −1.24211 | −0.621053 | − | 0.783769i | \(-0.713295\pi\) | ||||
−0.621053 | + | 0.783769i | \(0.713295\pi\) | |||||||
\(740\) | 8.05651 | + | 1.41304i | 0.296163 | + | 0.0519442i | ||||
\(741\) | −12.2282 | −0.449214 | ||||||||
\(742\) | 16.0537i | 0.589350i | ||||||||
\(743\) | − | 47.5880i | − | 1.74584i | −0.487868 | − | 0.872918i | \(-0.662225\pi\) | ||
0.487868 | − | 0.872918i | \(-0.337775\pi\) | |||||||
\(744\) | 10.0211 | 0.367390 | ||||||||
\(745\) | −9.20714 | + | 52.4951i | −0.337324 | + | 1.92327i | ||||
\(746\) | 1.31459 | 0.0481305 | ||||||||
\(747\) | − | 86.6983i | − | 3.17212i | ||||||
\(748\) | − | 7.96042i | − | 0.291062i | ||||||
\(749\) | 24.4143 | 0.892078 | ||||||||
\(750\) | −18.1315 | + | 31.6033i | −0.662070 | + | 1.15399i | ||||
\(751\) | 51.2698 | 1.87086 | 0.935430 | − | 0.353512i | \(-0.115013\pi\) | ||||
0.935430 | + | 0.353512i | \(0.115013\pi\) | |||||||
\(752\) | 0.659753i | 0.0240587i | ||||||||
\(753\) | − | 65.1580i | − | 2.37449i | ||||||
\(754\) | 5.40312 | 0.196770 | ||||||||
\(755\) | −5.74291 | + | 32.7436i | −0.209006 | + | 1.19166i | ||||
\(756\) | 21.7220 | 0.790023 | ||||||||
\(757\) | − | 26.2807i | − | 0.955189i | −0.878580 | − | 0.477594i | \(-0.841509\pi\) | ||
0.878580 | − | 0.477594i | \(-0.158491\pi\) | |||||||
\(758\) | − | 0.311952i | − | 0.0113306i | ||||||
\(759\) | 6.62018 | 0.240297 | ||||||||
\(760\) | −14.8291 | − | 2.60088i | −0.537908 | − | 0.0943439i | ||||
\(761\) | −7.18003 | −0.260276 | −0.130138 | − | 0.991496i | \(-0.541542\pi\) | ||||
−0.130138 | + | 0.991496i | \(0.541542\pi\) | |||||||
\(762\) | 5.11460i | 0.185282i | ||||||||
\(763\) | 0.315700i | 0.0114291i | ||||||||
\(764\) | 20.8934 | 0.755897 | ||||||||
\(765\) | 65.7663 | + | 11.5348i | 2.37779 | + | 0.417041i | ||||
\(766\) | −10.6805 | −0.385902 | ||||||||
\(767\) | 5.97571i | 0.215770i | ||||||||
\(768\) | − | 3.25886i | − | 0.117594i | ||||||
\(769\) | 32.2666 | 1.16356 | 0.581782 | − | 0.813345i | \(-0.302356\pi\) | ||||
0.581782 | + | 0.813345i | \(0.302356\pi\) | |||||||
\(770\) | 1.13212 | − | 6.45485i | 0.0407987 | − | 0.232616i | ||||
\(771\) | −87.3164 | −3.14462 | ||||||||
\(772\) | − | 2.88540i | − | 0.103848i | ||||||
\(773\) | − | 3.75316i | − | 0.134992i | −0.997720 | − | 0.0674958i | \(-0.978499\pi\) | ||
0.997720 | − | 0.0674958i | \(-0.0215009\pi\) | |||||||
\(774\) | 38.5935 | 1.38722 | ||||||||
\(775\) | 14.4574 | + | 5.23234i | 0.519325 | + | 0.187951i | ||||
\(776\) | −0.0813861 | −0.00292159 | ||||||||
\(777\) | − | 17.1982i | − | 0.616983i | ||||||
\(778\) | 7.86867i | 0.282105i | ||||||||
\(779\) | 47.3546 | 1.69666 | ||||||||
\(780\) | 0.701562 | − | 4.00000i | 0.0251200 | − | 0.143223i | ||||
\(781\) | −25.2637 | −0.904005 | ||||||||
\(782\) | − | 3.91861i | − | 0.140129i | ||||||
\(783\) | 145.976i | 5.21675i | ||||||||
\(784\) | 4.91861 | 0.175665 | ||||||||
\(785\) | 18.1529 | + | 3.18384i | 0.647903 | + | 0.113636i | ||||
\(786\) | 51.8838 | 1.85063 | ||||||||
\(787\) | − | 21.9373i | − | 0.781981i | −0.920395 | − | 0.390991i | \(-0.872133\pi\) | ||
0.920395 | − | 0.390991i | \(-0.127867\pi\) | |||||||
\(788\) | − | 19.0925i | − | 0.680144i | ||||||
\(789\) | 51.5771 | 1.83619 | ||||||||
\(790\) | −13.0482 | − | 2.28853i | −0.464233 | − | 0.0814221i | ||||
\(791\) | 0.837631 | 0.0297827 | ||||||||
\(792\) | − | 15.4799i | − | 0.550055i | ||||||
\(793\) | − | 0.969347i | − | 0.0344225i | ||||||
\(794\) | 29.2334 | 1.03745 | ||||||||
\(795\) | −14.0080 | + | 79.8676i | −0.496813 | + | 2.83261i | ||||
\(796\) | 6.58060 | 0.233243 | ||||||||
\(797\) | − | 7.57883i | − | 0.268456i | −0.990950 | − | 0.134228i | \(-0.957145\pi\) | ||
0.990950 | − | 0.134228i | \(-0.0428554\pi\) | |||||||
\(798\) | 31.6556i | 1.12060i | ||||||||
\(799\) | 2.58532 | 0.0914619 | ||||||||
\(800\) | 1.70156 | − | 4.70156i | 0.0601593 | − | 0.166225i | ||||
\(801\) | 40.0294 | 1.41437 | ||||||||
\(802\) | 23.7130i | 0.837337i | ||||||||
\(803\) | − | 18.8205i | − | 0.664163i | ||||||
\(804\) | −39.1485 | −1.38066 | ||||||||
\(805\) | 0.557299 | − | 3.17748i | 0.0196422 | − | 0.111991i | ||||
\(806\) | −1.71371 | −0.0603627 | ||||||||
\(807\) | 39.3904i | 1.38661i | ||||||||
\(808\) | − | 8.31281i | − | 0.292444i | ||||||
\(809\) | −18.9835 | −0.667423 | −0.333712 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333712 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(810\) | 57.7186 | + | 10.1233i | 2.02802 | + | 0.355696i | ||||
\(811\) | 14.1851 | 0.498106 | 0.249053 | − | 0.968490i | \(-0.419881\pi\) | ||||
0.249053 | + | 0.968490i | \(0.419881\pi\) | |||||||
\(812\) | − | 13.9873i | − | 0.490857i | ||||||
\(813\) | − | 27.3827i | − | 0.960354i | ||||||
\(814\) | −7.43096 | −0.260455 | ||||||||
\(815\) | 22.7191 | + | 3.98471i | 0.795815 | + | 0.139578i | ||||
\(816\) | −12.7702 | −0.447047 | ||||||||
\(817\) | 34.1003i | 1.19302i | ||||||||
\(818\) | 33.2509i | 1.16259i | ||||||||
\(819\) | −6.12674 | −0.214086 | ||||||||
\(820\) | −2.71685 | + | 15.4903i | −0.0948765 | + | 0.540944i | ||||
\(821\) | −44.8294 | −1.56456 | −0.782278 | − | 0.622930i | \(-0.785942\pi\) | ||||
−0.782278 | + | 0.622930i | \(0.785942\pi\) | |||||||
\(822\) | − | 21.0853i | − | 0.735433i | ||||||
\(823\) | − | 15.7652i | − | 0.549539i | −0.961510 | − | 0.274770i | \(-0.911398\pi\) | ||
0.961510 | − | 0.274770i | \(-0.0886016\pi\) | |||||||
\(824\) | 6.36991 | 0.221906 | ||||||||
\(825\) | 11.2646 | − | 31.1252i | 0.392184 | − | 1.08364i | ||||
\(826\) | 15.4695 | 0.538254 | ||||||||
\(827\) | − | 11.4332i | − | 0.397573i | −0.980043 | − | 0.198786i | \(-0.936300\pi\) | ||
0.980043 | − | 0.198786i | \(-0.0637000\pi\) | |||||||
\(828\) | − | 7.62018i | − | 0.264819i | ||||||
\(829\) | 28.3924 | 0.986108 | 0.493054 | − | 0.869999i | \(-0.335881\pi\) | ||||
0.493054 | + | 0.869999i | \(0.335881\pi\) | |||||||
\(830\) | −4.39499 | + | 25.0583i | −0.152552 | + | 0.869786i | ||||
\(831\) | −45.1313 | −1.56559 | ||||||||
\(832\) | 0.557299i | 0.0193209i | ||||||||
\(833\) | − | 19.2741i | − | 0.667810i | ||||||
\(834\) | 2.13848 | 0.0740496 | ||||||||
\(835\) | −10.2629 | − | 1.80001i | −0.355161 | − | 0.0622919i | ||||
\(836\) | 13.6777 | 0.473052 | ||||||||
\(837\) | − | 46.2991i | − | 1.60033i | ||||||
\(838\) | − | 7.28229i | − | 0.251562i | ||||||
\(839\) | −54.3340 | −1.87582 | −0.937908 | − | 0.346883i | \(-0.887240\pi\) | ||||
−0.937908 | + | 0.346883i | \(0.887240\pi\) | |||||||
\(840\) | −10.3550 | − | 1.81616i | −0.357280 | − | 0.0626635i | ||||
\(841\) | 64.9969 | 2.24127 | ||||||||
\(842\) | − | 2.71515i | − | 0.0935704i | ||||||
\(843\) | 26.5599i | 0.914770i | ||||||||
\(844\) | −6.55986 | −0.225800 | ||||||||
\(845\) | 4.90178 | − | 27.9478i | 0.168626 | − | 0.961433i | ||||
\(846\) | 5.02743 | 0.172847 | ||||||||
\(847\) | − | 9.91606i | − | 0.340720i | ||||||
\(848\) | − | 11.1275i | − | 0.382121i | ||||||
\(849\) | 56.5516 | 1.94085 | ||||||||
\(850\) | −18.4236 | − | 6.66777i | −0.631925 | − | 0.228702i | ||||
\(851\) | −3.65798 | −0.125394 | ||||||||
\(852\) | 40.5283i | 1.38848i | ||||||||
\(853\) | 46.8542i | 1.60426i | 0.597150 | + | 0.802129i | \(0.296300\pi\) | ||||
−0.597150 | + | 0.802129i | \(0.703700\pi\) | |||||||
\(854\) | −2.50938 | −0.0858694 | ||||||||
\(855\) | −19.8192 | + | 113.000i | −0.677802 | + | 3.86453i | ||||
\(856\) | −16.9226 | −0.578403 | ||||||||
\(857\) | 28.5356i | 0.974756i | 0.873191 | + | 0.487378i | \(0.162047\pi\) | ||||
−0.873191 | + | 0.487378i | \(0.837953\pi\) | |||||||
\(858\) | 3.68942i | 0.125955i | ||||||||
\(859\) | −19.4417 | −0.663343 | −0.331671 | − | 0.943395i | \(-0.607613\pi\) | ||||
−0.331671 | + | 0.943395i | \(0.607613\pi\) | |||||||
\(860\) | −11.1546 | − | 1.95642i | −0.380370 | − | 0.0667133i | ||||
\(861\) | 33.0671 | 1.12692 | ||||||||
\(862\) | 10.3336i | 0.351962i | ||||||||
\(863\) | − | 1.94514i | − | 0.0662132i | −0.999452 | − | 0.0331066i | \(-0.989460\pi\) | ||
0.999452 | − | 0.0331066i | \(-0.0105401\pi\) | |||||||
\(864\) | −15.0565 | −0.512233 | ||||||||
\(865\) | −6.17570 | − | 1.08316i | −0.209980 | − | 0.0368285i | ||||
\(866\) | −28.4153 | −0.965590 | ||||||||
\(867\) | − | 5.35908i | − | 0.182004i | ||||||
\(868\) | 4.43634i | 0.150579i | ||||||||
\(869\) | 12.0350 | 0.408261 | ||||||||
\(870\) | 12.2049 | − | 69.5870i | 0.413785 | − | 2.35922i | ||||
\(871\) | 6.69479 | 0.226844 | ||||||||
\(872\) | − | 0.218825i | − | 0.00741036i | ||||||
\(873\) | 0.620176i | 0.0209898i | ||||||||
\(874\) | 6.73300 | 0.227747 | ||||||||
\(875\) | −13.9908 | − | 8.02685i | −0.472976 | − | 0.271357i | ||||
\(876\) | −30.1922 | −1.02010 | ||||||||
\(877\) | − | 38.6457i | − | 1.30497i | −0.757800 | − | 0.652486i | \(-0.773726\pi\) | ||
0.757800 | − | 0.652486i | \(-0.226274\pi\) | |||||||
\(878\) | − | 6.37313i | − | 0.215083i | ||||||
\(879\) | −22.8854 | −0.771905 | ||||||||
\(880\) | −0.784722 | + | 4.47414i | −0.0264530 | + | 0.150823i | ||||
\(881\) | −54.6889 | −1.84252 | −0.921258 | − | 0.388952i | \(-0.872837\pi\) | ||||
−0.921258 | + | 0.388952i | \(0.872837\pi\) | |||||||
\(882\) | − | 37.4807i | − | 1.26204i | ||||||
\(883\) | 14.6273i | 0.492247i | 0.969238 | + | 0.246123i | \(0.0791569\pi\) | ||||
−0.969238 | + | 0.246123i | \(0.920843\pi\) | |||||||
\(884\) | 2.18384 | 0.0734505 | ||||||||
\(885\) | 76.9614 | + | 13.4983i | 2.58703 | + | 0.453740i | ||||
\(886\) | 9.43114 | 0.316845 | ||||||||
\(887\) | 40.2666i | 1.35202i | 0.736892 | + | 0.676010i | \(0.236293\pi\) | ||||
−0.736892 | + | 0.676010i | \(0.763707\pi\) | |||||||
\(888\) | 11.9208i | 0.400037i | ||||||||
\(889\) | −2.26424 | −0.0759401 | ||||||||
\(890\) | −11.5696 | − | 2.02921i | −0.387815 | − | 0.0680191i | ||||
\(891\) | −53.2370 | −1.78351 | ||||||||
\(892\) | 20.2094i | 0.676660i | ||||||||
\(893\) | 4.44212i | 0.148650i | ||||||||
\(894\) | −77.6745 | −2.59782 | ||||||||
\(895\) | 1.71594 | − | 9.78353i | 0.0573575 | − | 0.327027i | ||||
\(896\) | 1.44270 | 0.0481973 | ||||||||
\(897\) | 1.81616i | 0.0606398i | ||||||||
\(898\) | − | 11.3185i | − | 0.377704i | ||||||
\(899\) | −29.8129 | −0.994317 | ||||||||
\(900\) | −35.8267 | − | 12.9662i | −1.19422 | − | 0.432207i | ||||
\(901\) | −43.6045 | −1.45268 | ||||||||
\(902\) | − | 14.2875i | − | 0.475723i | ||||||
\(903\) | 23.8118i | 0.792406i | ||||||||
\(904\) | −0.580599 | −0.0193104 | ||||||||
\(905\) | 0.934890 | − | 5.33034i | 0.0310768 | − | 0.177186i | ||||
\(906\) | −48.4491 | −1.60961 | ||||||||
\(907\) | 7.87090i | 0.261349i | 0.991425 | + | 0.130674i | \(0.0417143\pi\) | ||||
−0.991425 | + | 0.130674i | \(0.958286\pi\) | |||||||
\(908\) | − | 15.0098i | − | 0.498117i | ||||||
\(909\) | −63.3451 | −2.10102 | ||||||||
\(910\) | 1.77080 | + | 0.310582i | 0.0587016 | + | 0.0102957i | ||||
\(911\) | 0.586235 | 0.0194228 | 0.00971141 | − | 0.999953i | \(-0.496909\pi\) | ||||
0.00971141 | + | 0.999953i | \(0.496909\pi\) | |||||||
\(912\) | − | 21.9419i | − | 0.726569i | ||||||
\(913\) | − | 23.1126i | − | 0.764916i | ||||||
\(914\) | 4.96456 | 0.164213 | ||||||||
\(915\) | −12.4843 | − | 2.18962i | −0.412717 | − | 0.0723866i | ||||
\(916\) | 13.7081 | 0.452929 | ||||||||
\(917\) | 22.9690i | 0.758504i | ||||||||
\(918\) | 59.0007i | 1.94731i | ||||||||
\(919\) | 27.9422 | 0.921729 | 0.460865 | − | 0.887470i | \(-0.347539\pi\) | ||||
0.460865 | + | 0.887470i | \(0.347539\pi\) | |||||||
\(920\) | −0.386289 | + | 2.20245i | −0.0127356 | + | 0.0726126i | ||||
\(921\) | 53.4961 | 1.76276 | ||||||||
\(922\) | 19.9128i | 0.655794i | ||||||||
\(923\) | − | 6.93076i | − | 0.228129i | ||||||
\(924\) | 9.55093 | 0.314203 | ||||||||
\(925\) | −6.22428 | + | 17.1982i | −0.204653 | + | 0.565474i | ||||
\(926\) | 29.9046 | 0.982725 | ||||||||
\(927\) | − | 48.5399i | − | 1.59426i | ||||||
\(928\) | 9.69520i | 0.318260i | ||||||||
\(929\) | 4.79352 | 0.157270 | 0.0786351 | − | 0.996903i | \(-0.474944\pi\) | ||||
0.0786351 | + | 0.996903i | \(0.474944\pi\) | |||||||
\(930\) | −3.87102 | + | 22.0709i | −0.126936 | + | 0.723733i | ||||
\(931\) | 33.1170 | 1.08537 | ||||||||
\(932\) | − | 9.19822i | − | 0.301298i | ||||||
\(933\) | − | 23.9585i | − | 0.784367i | ||||||
\(934\) | 15.1032 | 0.494193 | ||||||||
\(935\) | 17.5324 | + | 3.07502i | 0.573372 | + | 0.100564i | ||||
\(936\) | 4.24672 | 0.138808 | ||||||||
\(937\) | 0.110466i | 0.00360877i | 0.999998 | + | 0.00180438i | \(0.000574353\pi\) | ||||
−0.999998 | + | 0.00180438i | \(0.999426\pi\) | |||||||
\(938\) | − | 17.3311i | − | 0.565879i | ||||||
\(939\) | −13.3278 | −0.434938 | ||||||||
\(940\) | −1.45307 | − | 0.254855i | −0.0473940 | − | 0.00831245i | ||||
\(941\) | 19.2077 | 0.626155 | 0.313077 | − | 0.949728i | \(-0.398640\pi\) | ||||
0.313077 | + | 0.949728i | \(0.398640\pi\) | |||||||
\(942\) | 26.8599i | 0.875144i | ||||||||
\(943\) | − | 7.03321i | − | 0.229033i | ||||||
\(944\) | −10.7226 | −0.348992 | ||||||||
\(945\) | −8.39098 | + | 47.8417i | −0.272959 | + | 1.55629i | ||||
\(946\) | 10.2885 | 0.334509 | ||||||||
\(947\) | 20.0933i | 0.652944i | 0.945207 | + | 0.326472i | \(0.105860\pi\) | ||||
−0.945207 | + | 0.326472i | \(0.894140\pi\) | |||||||
\(948\) | − | 19.3068i | − | 0.627055i | ||||||
\(949\) | 5.16318 | 0.167604 | ||||||||
\(950\) | 11.4566 | − | 31.6556i | 0.371702 | − | 1.02704i | ||||
\(951\) | 29.0553 | 0.942184 | ||||||||
\(952\) | − | 5.65339i | − | 0.183227i | ||||||
\(953\) | − | 55.4762i | − | 1.79705i | −0.438920 | − | 0.898526i | \(-0.644639\pi\) | ||
0.438920 | − | 0.898526i | \(-0.355361\pi\) | |||||||
\(954\) | −84.7937 | −2.74530 | ||||||||
\(955\) | −8.07089 | + | 46.0167i | −0.261168 | + | 1.48906i | ||||
\(956\) | −2.72618 | −0.0881709 | ||||||||
\(957\) | 64.1839i | 2.07477i | ||||||||
\(958\) | − | 28.6678i | − | 0.926213i | ||||||
\(959\) | 9.33447 | 0.301426 | ||||||||
\(960\) | 7.17748 | + | 1.25886i | 0.231652 | + | 0.0406296i | ||||
\(961\) | −21.5442 | −0.694976 | ||||||||
\(962\) | − | 2.03859i | − | 0.0657267i | ||||||
\(963\) | 128.953i | 4.15546i | ||||||||
\(964\) | −3.26109 | −0.105033 | ||||||||
\(965\) | 6.35495 | + | 1.11460i | 0.204573 | + | 0.0358802i | ||||
\(966\) | 4.70156 | 0.151270 | ||||||||
\(967\) | − | 2.86228i | − | 0.0920448i | −0.998940 | − | 0.0460224i | \(-0.985345\pi\) | ||
0.998940 | − | 0.0460224i | \(-0.0146546\pi\) | |||||||
\(968\) | 6.87326i | 0.220915i | ||||||||
\(969\) | −85.9819 | −2.76214 | ||||||||
\(970\) | 0.0314385 | − | 0.179249i | 0.00100943 | − | 0.00575533i | ||||
\(971\) | 42.5901 | 1.36678 | 0.683391 | − | 0.730052i | \(-0.260504\pi\) | ||||
0.683391 | + | 0.730052i | \(0.260504\pi\) | |||||||
\(972\) | 40.2340i | 1.29051i | ||||||||
\(973\) | 0.946709i | 0.0303501i | ||||||||
\(974\) | 9.15319 | 0.293287 | ||||||||
\(975\) | 8.53879 | + | 3.09031i | 0.273460 | + | 0.0989691i | ||||
\(976\) | 1.73937 | 0.0556757 | ||||||||
\(977\) | 42.5633i | 1.36172i | 0.732413 | + | 0.680861i | \(0.238394\pi\) | ||||
−0.732413 | + | 0.680861i | \(0.761606\pi\) | |||||||
\(978\) | 33.6164i | 1.07493i | ||||||||
\(979\) | 10.6713 | 0.341057 | ||||||||
\(980\) | −1.90000 | + | 10.8330i | −0.0606934 | + | 0.346047i | ||||
\(981\) | −1.66749 | −0.0532388 | ||||||||
\(982\) | − | 20.8098i | − | 0.664067i | ||||||
\(983\) | − | 32.6691i | − | 1.04198i | −0.853562 | − | 0.520991i | \(-0.825563\pi\) | ||
0.853562 | − | 0.520991i | \(-0.174437\pi\) | |||||||
\(984\) | −22.9203 | −0.730671 | ||||||||
\(985\) | 42.0503 | + | 7.37523i | 1.33984 | + | 0.234994i | ||||
\(986\) | 37.9917 | 1.20990 | ||||||||
\(987\) | 3.10187i | 0.0987336i | ||||||||
\(988\) | 3.75229i | 0.119376i | ||||||||
\(989\) | 5.06465 | 0.161047 | ||||||||
\(990\) | 34.0937 | + | 5.97972i | 1.08357 | + | 0.190048i | ||||
\(991\) | −4.39775 | −0.139699 | −0.0698495 | − | 0.997558i | \(-0.522252\pi\) | ||||
−0.0698495 | + | 0.997558i | \(0.522252\pi\) | |||||||
\(992\) | − | 3.07502i | − | 0.0976320i | ||||||
\(993\) | − | 69.4919i | − | 2.20526i | ||||||
\(994\) | −17.9419 | −0.569083 | ||||||||
\(995\) | −2.54201 | + | 14.4934i | −0.0805872 | + | 0.459473i | ||||
\(996\) | −37.0776 | −1.17485 | ||||||||
\(997\) | 33.4135i | 1.05822i | 0.848554 | + | 0.529108i | \(0.177473\pi\) | ||||
−0.848554 | + | 0.529108i | \(0.822527\pi\) | |||||||
\(998\) | 18.1293i | 0.573873i | ||||||||
\(999\) | 55.0764 | 1.74254 |
(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 | 230.2.b.b.139.5 | yes | 8 | |
3.2 | odd | 2 | 2070.2.d.f.829.2 | 8 | |||
4.3 | odd | 2 | 1840.2.e.e.369.8 | 8 | |||
5.2 | odd | 4 | 1150.2.a.r.1.1 | 4 | |||
5.3 | odd | 4 | 1150.2.a.s.1.4 | 4 | |||
5.4 | even | 2 | inner | 230.2.b.b.139.4 | ✓ | 8 | |
15.14 | odd | 2 | 2070.2.d.f.829.6 | 8 | |||
20.3 | even | 4 | 9200.2.a.cj.1.1 | 4 | |||
20.7 | even | 4 | 9200.2.a.cr.1.4 | 4 | |||
20.19 | odd | 2 | 1840.2.e.e.369.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.b.b.139.4 | ✓ | 8 | 5.4 | even | 2 | inner | |
230.2.b.b.139.5 | yes | 8 | 1.1 | even | 1 | trivial | |
1150.2.a.r.1.1 | 4 | 5.2 | odd | 4 | |||
1150.2.a.s.1.4 | 4 | 5.3 | odd | 4 | |||
1840.2.e.e.369.1 | 8 | 20.19 | odd | 2 | |||
1840.2.e.e.369.8 | 8 | 4.3 | odd | 2 | |||
2070.2.d.f.829.2 | 8 | 3.2 | odd | 2 | |||
2070.2.d.f.829.6 | 8 | 15.14 | odd | 2 | |||
9200.2.a.cj.1.1 | 4 | 20.3 | even | 4 | |||
9200.2.a.cr.1.4 | 4 | 20.7 | even | 4 |