Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(109,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bf (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: | \(2.51528766367\) |
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: | \( x^{16} + 8x^{14} + 26x^{12} - 96x^{10} - 781x^{8} - 2400x^{6} + 16250x^{4} + 125000x^{2} + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(1.46253 + 1.69145i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.109 |
Dual form | 315.2.bf.c.289.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.05774 | + | 1.18804i | −1.45505 | + | 0.840071i | −0.998761 | − | 0.0497633i | \(-0.984153\pi\) |
−0.456284 | + | 0.889834i | \(0.650820\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.82288 | − | 3.15731i | 0.911438 | − | 1.57866i | ||||
\(5\) | 0.733576 | + | 2.11231i | 0.328065 | + | 0.944655i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.03996 | + | 1.68480i | 0.771033 | + | 0.636796i | ||||
\(8\) | 3.91044i | 1.38255i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.01902 | − | 3.47508i | −1.27093 | − | 1.09892i | ||||
\(11\) | 1.80712 | − | 3.13003i | 0.544867 | − | 0.943738i | −0.453748 | − | 0.891130i | \(-0.649913\pi\) |
0.998615 | − | 0.0526080i | \(-0.0167534\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.36961i | − | 0.934561i | −0.884109 | − | 0.467280i | \(-0.845234\pi\) | ||
0.884109 | − | 0.467280i | \(-0.154766\pi\) | |||||||
\(14\) | −6.19933 | − | 1.04334i | −1.65684 | − | 0.278845i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(17\) | 4.71533 | + | 2.72240i | 1.14363 | + | 0.660278i | 0.947328 | − | 0.320265i | \(-0.103772\pi\) |
0.196307 | + | 0.980543i | \(0.437105\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.32288 | + | 4.02334i | 0.532904 | + | 0.923017i | 0.999262 | + | 0.0384208i | \(0.0122327\pi\) |
−0.466357 | + | 0.884596i | \(0.654434\pi\) | |||||||
\(20\) | 8.00645 | + | 1.53436i | 1.79030 | + | 0.343092i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.58772i | 1.83091i | ||||||||
\(23\) | 0.599838 | − | 0.346317i | 0.125075 | − | 0.0722120i | −0.436157 | − | 0.899870i | \(-0.643661\pi\) |
0.561232 | + | 0.827658i | \(0.310328\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.92373 | + | 3.09908i | −0.784747 | + | 0.619817i | ||||
\(26\) | 4.00323 | + | 6.93379i | 0.785097 | + | 1.35983i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.03805 | − | 3.36961i | 1.70803 | − | 0.636796i | ||||
\(29\) | −8.00645 | −1.48676 | −0.743380 | − | 0.668869i | \(-0.766779\pi\) | ||||
−0.743380 | + | 0.668869i | \(0.766779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.50000 | + | 4.33013i | −0.449013 | + | 0.777714i | −0.998322 | − | 0.0579057i | \(-0.981558\pi\) |
0.549309 | + | 0.835619i | \(0.314891\pi\) | |||||||
\(32\) | −2.65758 | − | 1.53436i | −0.469799 | − | 0.271238i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.9373 | −2.21872 | ||||||||
\(35\) | −2.06237 | + | 5.54497i | −0.348604 | + | 0.937270i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.51902 | − | 2.60906i | 0.742923 | − | 0.428927i | −0.0802083 | − | 0.996778i | \(-0.525559\pi\) |
0.823131 | + | 0.567851i | \(0.192225\pi\) | |||||||
\(38\) | −9.55977 | − | 5.51934i | −1.55080 | − | 0.895355i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.26006 | + | 2.86860i | −1.30603 | + | 0.453565i | ||||
\(41\) | 5.17018 | 0.807446 | 0.403723 | − | 0.914881i | \(-0.367716\pi\) | ||||
0.403723 | + | 0.914881i | \(0.367716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.91514i | 1.35955i | 0.733422 | + | 0.679773i | \(0.237922\pi\) | ||||
−0.733422 | + | 0.679773i | \(0.762078\pi\) | |||||||
\(44\) | −6.58831 | − | 11.4113i | −0.993226 | − | 1.72032i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.822876 | + | 1.42526i | −0.121326 | + | 0.210143i | ||||
\(47\) | −3.38654 | + | 1.95522i | −0.493977 | + | 0.285198i | −0.726223 | − | 0.687459i | \(-0.758726\pi\) |
0.232246 | + | 0.972657i | \(0.425393\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.32288 | + | 6.87386i | 0.188982 | + | 0.981981i | ||||
\(50\) | 4.39221 | − | 11.0387i | 0.621152 | − | 1.56110i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −10.6389 | − | 6.14237i | −1.47535 | − | 0.851794i | ||||
\(53\) | 5.57340 | + | 3.21780i | 0.765565 | + | 0.441999i | 0.831290 | − | 0.555839i | \(-0.187603\pi\) |
−0.0657253 | + | 0.997838i | \(0.520936\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.93725 | + | 1.52110i | 1.07026 | + | 0.205104i | ||||
\(56\) | −6.58831 | + | 7.97713i | −0.880400 | + | 1.06599i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 16.4752 | − | 9.51198i | 2.16330 | − | 1.24898i | ||||
\(59\) | 0.388984 | − | 0.673739i | 0.0506414 | − | 0.0877134i | −0.839594 | − | 0.543215i | \(-0.817207\pi\) |
0.890235 | + | 0.455502i | \(0.150540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.82288 | − | 4.88936i | −0.361432 | − | 0.626019i | 0.626765 | − | 0.779209i | \(-0.284379\pi\) |
−0.988197 | + | 0.153190i | \(0.951045\pi\) | |||||||
\(62\) | − | 11.8804i | − | 1.50881i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.2915 | 1.41144 | ||||||||
\(65\) | 7.11766 | − | 2.47186i | 0.882838 | − | 0.306597i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.9562 | − | 6.90292i | −1.46068 | − | 0.843326i | −0.461641 | − | 0.887067i | \(-0.652739\pi\) |
−0.999043 | + | 0.0437409i | \(0.986072\pi\) | |||||||
\(68\) | 17.1909 | − | 9.92518i | 2.08470 | − | 1.20360i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.34381 | − | 13.8603i | −0.280139 | − | 1.65662i | ||||
\(71\) | 8.00645 | 0.950191 | 0.475095 | − | 0.879934i | \(-0.342414\pi\) | ||||
0.475095 | + | 0.879934i | \(0.342414\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.31731 | − | 0.760548i | −0.154179 | − | 0.0890154i | 0.420926 | − | 0.907095i | \(-0.361705\pi\) |
−0.575105 | + | 0.818080i | \(0.695039\pi\) | |||||||
\(74\) | −6.19933 | + | 10.7376i | −0.720658 | + | 1.24822i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 16.9373 | 1.94284 | ||||||||
\(77\) | 8.95993 | − | 3.34048i | 1.02108 | − | 0.380683i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.96863 | − | 8.60591i | −0.559014 | − | 0.968241i | −0.997579 | − | 0.0695415i | \(-0.977846\pi\) |
0.438565 | − | 0.898700i | \(-0.355487\pi\) | |||||||
\(80\) | 2.92506 | − | 3.38290i | 0.327031 | − | 0.378220i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.6389 | + | 6.14237i | −1.17487 | + | 0.678312i | ||||
\(83\) | 3.76135i | 0.412861i | 0.978461 | + | 0.206431i | \(0.0661848\pi\) | ||||
−0.978461 | + | 0.206431i | \(0.933815\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.29150 | + | 11.9573i | −0.248548 | + | 1.29695i | ||||
\(86\) | −10.5915 | − | 18.3451i | −1.14212 | − | 1.97820i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 12.2398 | + | 7.06663i | 1.30476 | + | 0.753305i | ||||
\(89\) | −1.80712 | − | 3.13003i | −0.191554 | − | 0.331782i | 0.754211 | − | 0.656632i | \(-0.228020\pi\) |
−0.945766 | + | 0.324850i | \(0.894686\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.67712 | − | 6.87386i | 0.595124 | − | 0.720577i | ||||
\(92\) | − | 2.52517i | − | 0.263267i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.64575 | − | 8.04668i | 0.479173 | − | 0.829951i | ||||
\(95\) | −6.79455 | + | 7.85806i | −0.697106 | + | 0.806220i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.2847i | − | 1.24733i | −0.781693 | − | 0.623664i | \(-0.785644\pi\) | ||
0.781693 | − | 0.623664i | \(-0.214356\pi\) | |||||||
\(98\) | −10.8886 | − | 12.5730i | −1.09991 | − | 1.27007i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.63230 | + | 18.0377i | 0.263230 | + | 1.80377i | ||||
\(101\) | 8.39544 | − | 14.5413i | 0.835377 | − | 1.44692i | −0.0583461 | − | 0.998296i | \(-0.518583\pi\) |
0.893723 | − | 0.448619i | \(-0.148084\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3554 | − | 5.97867i | 1.02034 | − | 0.589095i | 0.106140 | − | 0.994351i | \(-0.466151\pi\) |
0.914203 | + | 0.405256i | \(0.132818\pi\) | |||||||
\(104\) | 13.1766 | 1.29207 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.2915 | −1.48524 | ||||||||
\(107\) | −6.90219 | + | 3.98498i | −0.667260 | + | 0.385243i | −0.795038 | − | 0.606560i | \(-0.792549\pi\) |
0.127778 | + | 0.991803i | \(0.459216\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.61438 | − | 11.4564i | 0.633543 | − | 1.09733i | −0.353279 | − | 0.935518i | \(-0.614933\pi\) |
0.986822 | − | 0.161810i | \(-0.0517332\pi\) | |||||||
\(110\) | −18.1400 | + | 6.29975i | −1.72958 | + | 0.600657i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.878205 | − | 5.21812i | 0.0829825 | − | 0.493066i | ||||
\(113\) | 12.8712i | 1.21082i | 0.795913 | + | 0.605411i | \(0.206991\pi\) | ||||
−0.795913 | + | 0.605411i | \(0.793009\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17156 | + | 1.01300i | 0.109248 | + | 0.0944624i | ||||
\(116\) | −14.5948 | + | 25.2789i | −1.35509 | + | 2.34708i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.84851i | 0.170169i | ||||||||
\(119\) | 5.03238 | + | 13.4980i | 0.461317 | + | 1.23736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.03137 | − | 1.78639i | −0.0937612 | − | 0.162399i | ||||
\(122\) | 11.6175 | + | 6.70738i | 1.05180 | + | 0.607257i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.11438 | + | 15.7866i | 0.818495 | + | 1.41768i | ||||
\(125\) | −9.42459 | − | 6.01474i | −0.842961 | − | 0.537975i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.36961i | − | 0.299004i | −0.988761 | − | 0.149502i | \(-0.952233\pi\) | ||
0.988761 | − | 0.149502i | \(-0.0477671\pi\) | |||||||
\(128\) | −17.9199 | + | 10.3460i | −1.58391 | + | 0.914469i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.7097 | + | 13.5425i | −1.02701 | + | 1.18776i | ||||
\(131\) | −5.81035 | − | 10.0638i | −0.507652 | − | 0.879280i | −0.999961 | − | 0.00885883i | \(-0.997180\pi\) |
0.492308 | − | 0.870421i | \(-0.336153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.03996 | + | 12.1210i | −0.176887 | + | 1.05103i | ||||
\(134\) | 32.8038 | 2.83381 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −10.6458 | + | 18.4390i | −0.912866 | + | 1.58113i | ||||
\(137\) | −2.78670 | − | 1.60890i | −0.238084 | − | 0.137458i | 0.376212 | − | 0.926534i | \(-0.377226\pi\) |
−0.614296 | + | 0.789076i | \(0.710560\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.2288 | −1.63096 | −0.815481 | − | 0.578784i | \(-0.803527\pi\) | ||||
−0.815481 | + | 0.578784i | \(0.803527\pi\) | |||||||
\(140\) | 13.7478 | + | 16.6193i | 1.16190 | + | 1.40459i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.4752 | + | 9.51198i | −1.38257 | + | 0.798228i | ||||
\(143\) | −10.5470 | − | 6.08929i | −0.881981 | − | 0.509212i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.87334 | − | 16.9121i | −0.487754 | − | 1.40448i | ||||
\(146\) | 3.61424 | 0.299117 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 19.0240i | − | 1.56376i | ||||||
\(149\) | 2.19610 | + | 3.80376i | 0.179912 | + | 0.311617i | 0.941850 | − | 0.336033i | \(-0.109085\pi\) |
−0.761938 | + | 0.647650i | \(0.775752\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.46863 | + | 6.00784i | −0.282273 | + | 0.488911i | −0.971944 | − | 0.235212i | \(-0.924422\pi\) |
0.689671 | + | 0.724123i | \(0.257755\pi\) | |||||||
\(152\) | −15.7330 | + | 9.08345i | −1.27612 | + | 0.736765i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −14.4686 | + | 17.5186i | −1.16592 | + | 1.41169i | ||||
\(155\) | −10.9805 | − | 2.10431i | −0.881977 | − | 0.169022i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.2398 | + | 7.06663i | 0.976839 | + | 0.563978i | 0.901314 | − | 0.433165i | \(-0.142603\pi\) |
0.0755249 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(158\) | 20.4483 | + | 11.8059i | 1.62678 | + | 0.939223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.29150 | − | 6.73921i | 0.102102 | − | 0.532782i | ||||
\(161\) | 1.80712 | + | 0.304137i | 0.142421 | + | 0.0239693i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.03805 | + | 5.21812i | −0.707914 | + | 0.408715i | −0.810288 | − | 0.586031i | \(-0.800690\pi\) |
0.102374 | + | 0.994746i | \(0.467356\pi\) | |||||||
\(164\) | 9.42459 | − | 16.3239i | 0.735937 | − | 1.27468i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.46863 | − | 7.73989i | −0.346833 | − | 0.600732i | ||||
\(167\) | 12.4239i | 0.961393i | 0.876887 | + | 0.480697i | \(0.159616\pi\) | ||||
−0.876887 | + | 0.480697i | \(0.840384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.64575 | 0.126596 | ||||||||
\(170\) | −9.49045 | − | 27.3275i | −0.727885 | − | 2.09593i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 28.1479 | + | 16.2512i | 2.14626 | + | 1.23914i | ||||
\(173\) | 21.3064 | − | 12.3013i | 1.61990 | − | 0.935247i | 0.632950 | − | 0.774193i | \(-0.281844\pi\) |
0.986945 | − | 0.161055i | \(-0.0514895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2256 | − | 0.288713i | −0.999762 | − | 0.0218247i | ||||
\(176\) | −7.22848 | −0.544867 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.43719 | + | 4.29386i | 0.557441 | + | 0.321839i | ||||
\(179\) | −0.777967 | + | 1.34748i | −0.0581480 | + | 0.100715i | −0.893634 | − | 0.448796i | \(-0.851853\pi\) |
0.835486 | + | 0.549512i | \(0.185186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.35425 | 0.546637 | 0.273319 | − | 0.961924i | \(-0.411879\pi\) | ||||
0.273319 | + | 0.961924i | \(0.411879\pi\) | |||||||
\(182\) | −3.51565 | + | 20.8893i | −0.260597 | + | 1.54842i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.35425 | + | 2.34563i | 0.0998365 | + | 0.172922i | ||||
\(185\) | 8.82619 | + | 7.63165i | 0.648915 | + | 0.561090i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.0423 | − | 9.83940i | 1.24626 | − | 0.719528i | ||||
\(188\) | 14.2565i | 1.03976i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.64575 | − | 24.2421i | 0.337038 | − | 1.75871i | ||||
\(191\) | 3.61424 | + | 6.26005i | 0.261517 | + | 0.452961i | 0.966645 | − | 0.256119i | \(-0.0824438\pi\) |
−0.705128 | + | 0.709080i | \(0.749110\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.7588 | − | 9.67569i | −1.20632 | − | 0.696471i | −0.244370 | − | 0.969682i | \(-0.578581\pi\) |
−0.961954 | + | 0.273211i | \(0.911914\pi\) | |||||||
\(194\) | 14.5948 | + | 25.2789i | 1.04784 | + | 1.81492i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 24.1144 | + | 8.35347i | 1.72246 | + | 0.596676i | ||||
\(197\) | − | 14.1074i | − | 1.00511i | −0.864545 | − | 0.502555i | \(-0.832394\pi\) | ||
0.864545 | − | 0.502555i | \(-0.167606\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.17712 | − | 10.6991i | 0.437885 | − | 0.758439i | −0.559641 | − | 0.828735i | \(-0.689061\pi\) |
0.997526 | + | 0.0702963i | \(0.0223945\pi\) | |||||||
\(200\) | −12.1188 | − | 15.3435i | −0.856926 | − | 1.08495i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 39.8964i | 2.80710i | ||||||||
\(203\) | −16.3328 | − | 13.4893i | −1.14634 | − | 0.946763i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.79272 | + | 10.9210i | 0.264895 | + | 0.762758i | ||||
\(206\) | −14.2058 | + | 24.6051i | −0.989764 | + | 1.71432i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.83633 | + | 3.36961i | −0.404677 | + | 0.233640i | ||||
\(209\) | 16.7909 | 1.16145 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.937254 | 0.0645232 | 0.0322616 | − | 0.999479i | \(-0.489729\pi\) | ||||
0.0322616 | + | 0.999479i | \(0.489729\pi\) | |||||||
\(212\) | 20.3192 | − | 11.7313i | 1.39553 | − | 0.805709i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.46863 | − | 16.4001i | 0.647262 | − | 1.12109i | ||||
\(215\) | −18.8316 | + | 6.53993i | −1.28430 | + | 0.446020i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.3953 | + | 4.62128i | −0.841449 | + | 0.313713i | ||||
\(218\) | 31.4326i | 2.12888i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 19.2712 | − | 22.2876i | 1.29926 | − | 1.50263i | ||||
\(221\) | 9.17340 | − | 15.8888i | 0.617070 | − | 1.06880i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | −2.83627 | − | 7.60753i | −0.189507 | − | 0.508299i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.2915 | − | 26.4857i | −1.01718 | − | 1.76180i | ||||
\(227\) | −20.4483 | − | 11.8059i | −1.35720 | − | 0.783582i | −0.367957 | − | 0.929843i | \(-0.619943\pi\) |
−0.989246 | + | 0.146261i | \(0.953276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.14575 | + | 7.18065i | 0.273959 | + | 0.474511i | 0.969872 | − | 0.243615i | \(-0.0783334\pi\) |
−0.695913 | + | 0.718126i | \(0.745000\pi\) | |||||||
\(230\) | −3.61424 | − | 0.692633i | −0.238316 | − | 0.0456709i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 31.3087i | − | 2.05552i | ||||||
\(233\) | −6.04412 | + | 3.48957i | −0.395963 | + | 0.228610i | −0.684741 | − | 0.728787i | \(-0.740085\pi\) |
0.288777 | + | 0.957396i | \(0.406751\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.61431 | − | 5.71912i | −0.431470 | − | 0.373075i | ||||
\(236\) | −1.41814 | − | 2.45629i | −0.0923129 | − | 0.159891i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −26.3915 | − | 21.7967i | −1.71071 | − | 1.41287i | ||||
\(239\) | −13.1766 | −0.852325 | −0.426163 | − | 0.904647i | \(-0.640135\pi\) | ||||
−0.426163 | + | 0.904647i | \(0.640135\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.885622 | + | 1.53394i | −0.0570479 | + | 0.0988099i | −0.893139 | − | 0.449781i | \(-0.851502\pi\) |
0.836091 | + | 0.548591i | \(0.184835\pi\) | |||||||
\(242\) | 4.24460 | + | 2.45062i | 0.272854 | + | 0.157532i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −20.5830 | −1.31769 | ||||||||
\(245\) | −13.5493 | + | 7.83683i | −0.865634 | + | 0.500676i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.5571 | − | 7.82718i | 0.862616 | − | 0.498031i | ||||
\(248\) | −16.9327 | − | 9.77609i | −1.07523 | − | 0.620782i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 26.5391 | + | 1.18002i | 1.67848 | + | 0.0746311i | ||||
\(251\) | 10.8427 | 0.684387 | 0.342193 | − | 0.939630i | \(-0.388830\pi\) | ||||
0.342193 | + | 0.939630i | \(0.388830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.50334i | − | 0.157384i | ||||||
\(254\) | 4.00323 | + | 6.93379i | 0.251185 | + | 0.435065i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.2915 | − | 23.0216i | 0.830719 | − | 1.43885i | ||||
\(257\) | 5.44428 | − | 3.14326i | 0.339605 | − | 0.196071i | −0.320492 | − | 0.947251i | \(-0.603848\pi\) |
0.660097 | + | 0.751180i | \(0.270515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.6144 | + | 2.29129i | 0.845956 | + | 0.142374i | ||||
\(260\) | 5.17018 | − | 26.9786i | 0.320641 | − | 1.67314i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.9124 | + | 13.8058i | 1.47731 | + | 0.852928i | ||||
\(263\) | −4.58621 | − | 2.64785i | −0.282798 | − | 0.163273i | 0.351891 | − | 0.936041i | \(-0.385539\pi\) |
−0.634689 | + | 0.772767i | \(0.718872\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.70850 | + | 14.1333i | −0.166382 | + | 0.868199i | ||||
\(266\) | −10.2026 | − | 27.3656i | −0.625559 | − | 1.67789i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −43.5894 | + | 25.1663i | −2.66264 | + | 1.53728i | ||||
\(269\) | −5.03238 | + | 8.71634i | −0.306830 | + | 0.531444i | −0.977667 | − | 0.210160i | \(-0.932602\pi\) |
0.670837 | + | 0.741604i | \(0.265935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.11438 | + | 3.66221i | 0.128439 | + | 0.222463i | 0.923072 | − | 0.384627i | \(-0.125670\pi\) |
−0.794633 | + | 0.607090i | \(0.792337\pi\) | |||||||
\(272\) | − | 10.8896i | − | 0.660278i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.64575 | 0.461897 | ||||||||
\(275\) | 2.60955 | + | 17.8818i | 0.157362 | + | 1.07831i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.15364 | − | 4.13015i | −0.429820 | − | 0.248157i | 0.269450 | − | 0.963014i | \(-0.413158\pi\) |
−0.699270 | + | 0.714858i | \(0.746492\pi\) | |||||||
\(278\) | 39.5679 | − | 22.8445i | 2.37312 | − | 1.37012i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −21.6832 | − | 8.06475i | −1.29582 | − | 0.481961i | ||||
\(281\) | −29.1895 | −1.74130 | −0.870651 | − | 0.491902i | \(-0.836302\pi\) | ||||
−0.870651 | + | 0.491902i | \(0.836302\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.0280 | + | 12.7179i | 1.30943 | + | 0.755999i | 0.982001 | − | 0.188877i | \(-0.0604846\pi\) |
0.327429 | + | 0.944876i | \(0.393818\pi\) | |||||||
\(284\) | 14.5948 | − | 25.2789i | 0.866040 | − | 1.50003i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.9373 | 1.71110 | ||||||||
\(287\) | 10.5470 | + | 8.71073i | 0.622567 | + | 0.514178i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.32288 | + | 10.9515i | 0.371934 | + | 0.644208i | ||||
\(290\) | 32.1781 | + | 27.8231i | 1.88956 | + | 1.63383i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.80257 | + | 2.77277i | −0.281049 | + | 0.162264i | ||||
\(293\) | − | 27.3730i | − | 1.59915i | −0.600566 | − | 0.799575i | \(-0.705058\pi\) | ||
0.600566 | − | 0.799575i | \(-0.294942\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.70850 | + | 0.327416i | 0.0994726 | + | 0.0190629i | ||||
\(296\) | 10.2026 | + | 17.6713i | 0.593012 | + | 1.02713i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.03805 | − | 5.21812i | −0.523560 | − | 0.302277i | ||||
\(299\) | −1.16695 | − | 2.02122i | −0.0674865 | − | 0.116890i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.0203 | + | 18.1865i | −0.865753 | + | 1.04825i | ||||
\(302\) | − | 16.4835i | − | 0.948517i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.64575 | − | 8.04668i | 0.266452 | − | 0.461509i | ||||
\(305\) | 8.25708 | − | 9.54952i | 0.472799 | − | 0.546804i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.8480i | − | 0.961568i | −0.876839 | − | 0.480784i | \(-0.840352\pi\) | ||
0.876839 | − | 0.480784i | \(-0.159648\pi\) | |||||||
\(308\) | 5.78589 | − | 34.3786i | 0.329682 | − | 1.95890i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 25.0951 | − | 8.71517i | 1.42531 | − | 0.494988i | ||||
\(311\) | 8.39544 | − | 14.5413i | 0.476061 | − | 0.824563i | −0.523562 | − | 0.851987i | \(-0.675397\pi\) |
0.999624 | + | 0.0274247i | \(0.00873065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.31731 | + | 0.760548i | −0.0744586 | + | 0.0429887i | −0.536767 | − | 0.843730i | \(-0.680355\pi\) |
0.462308 | + | 0.886719i | \(0.347021\pi\) | |||||||
\(314\) | −33.5817 | −1.89513 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −36.2288 | −2.03803 | ||||||||
\(317\) | 17.3200 | − | 9.99972i | 0.972790 | − | 0.561640i | 0.0727041 | − | 0.997354i | \(-0.476837\pi\) |
0.900086 | + | 0.435713i | \(0.143504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −14.4686 | + | 25.0604i | −0.810088 | + | 1.40311i | ||||
\(320\) | 8.28317 | + | 23.8512i | 0.463043 | + | 1.33332i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.07992 | + | 1.52110i | −0.227365 | + | 0.0847673i | ||||
\(323\) | 25.2951i | 1.40746i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.4427 | + | 13.2214i | 0.579256 | + | 0.733393i | ||||
\(326\) | 12.3987 | − | 21.4751i | 0.686698 | − | 1.18940i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.2176i | 1.11633i | ||||||||
\(329\) | −10.2026 | − | 1.71708i | −0.562485 | − | 0.0946657i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.79150 | + | 3.10297i | 0.0984699 | + | 0.170555i | 0.911051 | − | 0.412293i | \(-0.135272\pi\) |
−0.812582 | + | 0.582847i | \(0.801939\pi\) | |||||||
\(332\) | 11.8757 | + | 6.85647i | 0.651766 | + | 0.376297i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.7601 | − | 25.5653i | −0.807638 | − | 1.39887i | ||||
\(335\) | 5.81035 | − | 30.3191i | 0.317453 | − | 1.65651i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 10.1088i | − | 0.550663i | −0.961349 | − | 0.275331i | \(-0.911212\pi\) | ||
0.961349 | − | 0.275331i | \(-0.0887875\pi\) | |||||||
\(338\) | −3.38654 | + | 1.95522i | −0.184203 | + | 0.106350i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 33.5759 | + | 29.0317i | 1.82091 | + | 1.57447i | ||||
\(341\) | 9.03561 | + | 15.6501i | 0.489305 | + | 0.847502i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.88249 | + | 16.2512i | −0.479610 | + | 0.877482i | ||||
\(344\) | −34.8621 | −1.87964 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −29.2288 | + | 50.6257i | −1.57135 | + | 2.72165i | ||||
\(347\) | −23.4933 | − | 13.5638i | −1.26118 | − | 0.728145i | −0.287881 | − | 0.957666i | \(-0.592951\pi\) |
−0.973304 | + | 0.229521i | \(0.926284\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.87451 | 0.314455 | 0.157228 | − | 0.987562i | \(-0.449744\pi\) | ||||
0.157228 | + | 0.987562i | \(0.449744\pi\) | |||||||
\(350\) | 27.5579 | − | 15.1184i | 1.47303 | − | 0.808115i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.60515 | + | 5.54553i | −0.511956 | + | 0.295578i | ||||
\(353\) | −5.44428 | − | 3.14326i | −0.289770 | − | 0.167299i | 0.348068 | − | 0.937469i | \(-0.386838\pi\) |
−0.637838 | + | 0.770171i | \(0.720171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.87334 | + | 16.9121i | 0.311724 | + | 0.897603i | ||||
\(356\) | −13.1766 | −0.698360 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.69702i | − | 0.195394i | ||||||
\(359\) | −3.22526 | − | 5.58631i | −0.170223 | − | 0.294834i | 0.768275 | − | 0.640120i | \(-0.221115\pi\) |
−0.938498 | + | 0.345286i | \(0.887782\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.29150 | + | 2.23695i | −0.0679738 | + | 0.117734i | ||||
\(362\) | −15.1332 | + | 8.73714i | −0.795382 | + | 0.459214i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −11.3542 | − | 30.4547i | −0.595124 | − | 1.59626i | ||||
\(365\) | 0.640170 | − | 3.34048i | 0.0335080 | − | 0.174849i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.6289 | − | 13.6421i | −1.23342 | − | 0.712114i | −0.265676 | − | 0.964062i | \(-0.585595\pi\) |
−0.967741 | + | 0.251949i | \(0.918929\pi\) | |||||||
\(368\) | −1.19968 | − | 0.692633i | −0.0625374 | − | 0.0361060i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.2288 | − | 5.21812i | −1.41556 | − | 0.271277i | ||||
\(371\) | 5.94814 | + | 15.9543i | 0.308812 | + | 0.828304i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.48527 | − | 2.01222i | 0.180460 | − | 0.104189i | −0.407049 | − | 0.913406i | \(-0.633442\pi\) |
0.587509 | + | 0.809218i | \(0.300109\pi\) | |||||||
\(374\) | −23.3792 | + | 40.4939i | −1.20891 | + | 2.09389i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.64575 | − | 13.2428i | −0.394300 | − | 0.682947i | ||||
\(377\) | 26.9786i | 1.38947i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.29150 | −0.425906 | −0.212953 | − | 0.977062i | \(-0.568308\pi\) | ||||
−0.212953 | + | 0.977062i | \(0.568308\pi\) | |||||||
\(380\) | 12.4248 | + | 35.7768i | 0.637377 | + | 1.83531i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.8744 | − | 8.58772i | −0.761039 | − | 0.439386i | ||||
\(383\) | −16.2037 | + | 9.35523i | −0.827972 | + | 0.478030i | −0.853158 | − | 0.521653i | \(-0.825316\pi\) |
0.0251859 | + | 0.999683i | \(0.491982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.6289 | + | 16.4757i | 0.694595 | + | 0.839679i | ||||
\(386\) | 45.9804 | 2.34034 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −38.7868 | − | 22.3936i | −1.96910 | − | 1.13686i | ||||
\(389\) | 5.55916 | − | 9.62875i | 0.281861 | − | 0.488197i | −0.689982 | − | 0.723826i | \(-0.742382\pi\) |
0.971843 | + | 0.235629i | \(0.0757151\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.77124 | 0.190720 | ||||||||
\(392\) | −26.8798 | + | 5.17302i | −1.35763 | + | 0.261277i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.7601 | + | 29.0294i | 0.844363 | + | 1.46248i | ||||
\(395\) | 14.5335 | − | 16.8084i | 0.731261 | − | 0.845722i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.8643 | − | 16.0875i | 1.39847 | − | 0.807408i | 0.404239 | − | 0.914654i | \(-0.367537\pi\) |
0.994233 | + | 0.107246i | \(0.0342032\pi\) | |||||||
\(398\) | 29.3547i | 1.47142i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.29150 | + | 3.69702i | 0.464575 | + | 0.184851i | ||||
\(401\) | 5.94814 | + | 10.3025i | 0.297036 | + | 0.514482i | 0.975456 | − | 0.220192i | \(-0.0706685\pi\) |
−0.678420 | + | 0.734674i | \(0.737335\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.5908 | + | 8.42402i | 0.726821 | + | 0.419630i | ||||
\(404\) | −30.6077 | − | 53.0140i | −1.52279 | − | 2.63755i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 49.6346 | + | 8.35347i | 2.46333 | + | 0.414576i | ||||
\(407\) | − | 18.8595i | − | 0.934833i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.20850 | − | 3.82523i | 0.109203 | − | 0.189145i | −0.806245 | − | 0.591582i | \(-0.798503\pi\) |
0.915448 | + | 0.402437i | \(0.131837\pi\) | |||||||
\(410\) | −20.7791 | − | 17.9668i | −1.02620 | − | 0.887317i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 43.5935i | − | 2.14770i | ||||||
\(413\) | 1.92863 | − | 0.719041i | 0.0949016 | − | 0.0353817i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.94514 | + | 2.75923i | −0.390012 | + | 0.135445i | ||||
\(416\) | −5.17018 | + | 8.95501i | −0.253489 | + | 0.439055i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −34.5513 | + | 19.9482i | −1.68996 | + | 0.975699i | ||||
\(419\) | −26.3533 | −1.28744 | −0.643720 | − | 0.765261i | \(-0.722610\pi\) | ||||
−0.643720 | + | 0.765261i | \(0.722610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2288 | 0.839678 | 0.419839 | − | 0.907599i | \(-0.362086\pi\) | ||||
0.419839 | + | 0.907599i | \(0.362086\pi\) | |||||||
\(422\) | −1.92863 | + | 1.11349i | −0.0938842 | + | 0.0542041i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.5830 | + | 21.7944i | −0.611085 | + | 1.05843i | ||||
\(425\) | −26.9386 | + | 3.93124i | −1.30671 | + | 0.190693i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.47906 | − | 14.7301i | 0.119970 | − | 0.712839i | ||||
\(428\) | 29.0565i | 1.40450i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 30.9809 | − | 35.8302i | 1.49403 | − | 1.72788i | ||||
\(431\) | −15.3727 | + | 26.6264i | −0.740478 | + | 1.28255i | 0.211799 | + | 0.977313i | \(0.432068\pi\) |
−0.952278 | + | 0.305233i | \(0.901266\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 7.72146i | − | 0.371070i | −0.982638 | − | 0.185535i | \(-0.940598\pi\) | ||
0.982638 | − | 0.185535i | \(-0.0594018\pi\) | |||||||
\(434\) | 20.0161 | − | 24.2355i | 0.960805 | − | 1.16334i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −24.1144 | − | 41.7673i | −1.15487 | − | 2.00029i | ||||
\(437\) | 2.78670 | + | 1.60890i | 0.133306 | + | 0.0769642i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.88562 | + | 3.26599i | 0.0899958 | + | 0.155877i | 0.907509 | − | 0.420032i | \(-0.137981\pi\) |
−0.817513 | + | 0.575910i | \(0.804648\pi\) | |||||||
\(440\) | −5.94814 | + | 31.0381i | −0.283567 | + | 1.47968i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 43.5935i | 2.07353i | ||||||||
\(443\) | 3.64477 | − | 2.10431i | 0.173168 | − | 0.0999787i | −0.410911 | − | 0.911676i | \(-0.634789\pi\) |
0.584079 | + | 0.811697i | \(0.301456\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.28593 | − | 6.11332i | 0.250577 | − | 0.289799i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 23.0342 | + | 19.0240i | 1.08826 | + | 0.898798i | ||||
\(449\) | −10.3404 | −0.487991 | −0.243996 | − | 0.969776i | \(-0.578458\pi\) | ||||
−0.243996 | + | 0.969776i | \(0.578458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.34313 | − | 16.1828i | 0.439951 | − | 0.762018i | ||||
\(452\) | 40.6384 | + | 23.4626i | 1.91147 | + | 1.10359i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 56.1033 | 2.63306 | ||||||||
\(455\) | 18.6844 | + | 6.94937i | 0.875936 | + | 0.325791i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.35106 | + | 1.35739i | −0.109978 | + | 0.0634959i | −0.553980 | − | 0.832530i | \(-0.686892\pi\) |
0.444002 | + | 0.896026i | \(0.353558\pi\) | |||||||
\(458\) | −17.0618 | − | 9.85063i | −0.797245 | − | 0.460290i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.33395 | − | 1.85240i | 0.248697 | − | 0.0863687i | ||||
\(461\) | −10.8427 | −0.504996 | −0.252498 | − | 0.967597i | \(-0.581252\pi\) | ||||
−0.252498 | + | 0.967597i | \(0.581252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.1999i | 0.985242i | 0.870244 | + | 0.492621i | \(0.163961\pi\) | ||||
−0.870244 | + | 0.492621i | \(0.836039\pi\) | |||||||
\(464\) | 8.00645 | + | 13.8676i | 0.371690 | + | 0.643786i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.29150 | − | 14.3613i | 0.384096 | − | 0.665275i | ||||
\(467\) | 10.3721 | − | 5.98833i | 0.479964 | − | 0.277107i | −0.240438 | − | 0.970665i | \(-0.577291\pi\) |
0.720401 | + | 0.693557i | \(0.243958\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.7601 | − | 34.2255i | −0.589208 | − | 1.58039i | ||||
\(470\) | 20.4051 | + | 3.91044i | 0.941218 | + | 0.180375i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.63461 | + | 1.52110i | 0.121268 | + | 0.0700141i | ||||
\(473\) | 27.9046 | + | 16.1107i | 1.28306 | + | 0.740773i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.5830 | − | 8.58772i | −0.990296 | − | 0.394032i | ||||
\(476\) | 51.7907 | + | 8.71634i | 2.37383 | + | 0.399513i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.1141 | − | 15.6544i | 1.24017 | − | 0.716014i | ||||
\(479\) | 13.8168 | − | 23.9314i | 0.631306 | − | 1.09345i | −0.355979 | − | 0.934494i | \(-0.615853\pi\) |
0.987285 | − | 0.158960i | \(-0.0508140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.79150 | − | 15.2273i | −0.400858 | − | 0.694306i | ||||
\(482\) | − | 4.20861i | − | 0.191697i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.52026 | −0.341830 | ||||||||
\(485\) | 25.9492 | − | 9.01179i | 1.17829 | − | 0.409204i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.48527 | + | 2.01222i | 0.157933 | + | 0.0911824i | 0.576883 | − | 0.816827i | \(-0.304269\pi\) |
−0.418951 | + | 0.908009i | \(0.637602\pi\) | |||||||
\(488\) | 19.1195 | − | 11.0387i | 0.865501 | − | 0.499697i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 18.5706 | − | 32.2233i | 0.838934 | − | 1.45570i | ||||
\(491\) | −7.50408 | −0.338654 | −0.169327 | − | 0.985560i | \(-0.554159\pi\) | ||||
−0.169327 | + | 0.985560i | \(0.554159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.7530 | − | 21.7967i | −1.70031 | − | 0.981675i | ||||
\(494\) | −18.5980 | + | 32.2127i | −0.836763 | + | 1.44932i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.0000 | 0.449013 | ||||||||
\(497\) | 16.3328 | + | 13.4893i | 0.732628 | + | 0.605078i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.50000 | − | 4.33013i | −0.111915 | − | 0.193843i | 0.804627 | − | 0.593780i | \(-0.202365\pi\) |
−0.916542 | + | 0.399937i | \(0.869032\pi\) | |||||||
\(500\) | −36.1703 | + | 18.7923i | −1.61758 | + | 0.840415i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.3116 | + | 12.8816i | −0.995814 | + | 0.574933i | ||||
\(503\) | 12.8712i | 0.573899i | 0.957946 | + | 0.286949i | \(0.0926412\pi\) | ||||
−0.957946 | + | 0.286949i | \(0.907359\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.8745 | + | 7.06663i | 1.64089 | + | 0.314461i | ||||
\(506\) | 2.97407 | + | 5.15124i | 0.132214 | + | 0.229001i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.6389 | − | 6.14237i | −0.472025 | − | 0.272524i | ||||
\(509\) | −7.22848 | − | 12.5201i | −0.320397 | − | 0.554944i | 0.660173 | − | 0.751114i | \(-0.270483\pi\) |
−0.980570 | + | 0.196170i | \(0.937150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.40588 | − | 3.77089i | −0.0621925 | − | 0.166814i | ||||
\(512\) | 21.7792i | 0.962512i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.46863 | + | 12.9360i | −0.329427 | + | 0.570584i | ||||
\(515\) | 20.2252 | + | 17.4879i | 0.891231 | + | 0.770611i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.1333i | 0.621580i | ||||||||
\(518\) | −30.7371 | + | 11.4595i | −1.35051 | + | 0.503503i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.66605 | + | 27.8332i | 0.423884 | + | 1.22056i | ||||
\(521\) | −0.777967 | + | 1.34748i | −0.0340834 | + | 0.0590341i | −0.882564 | − | 0.470192i | \(-0.844185\pi\) |
0.848481 | + | 0.529227i | \(0.177518\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.9562 | + | 6.90292i | −0.522809 | + | 0.301844i | −0.738083 | − | 0.674710i | \(-0.764269\pi\) |
0.215274 | + | 0.976554i | \(0.430935\pi\) | |||||||
\(524\) | −42.3662 | −1.85077 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.5830 | 0.548645 | ||||||||
\(527\) | −23.5766 | + | 13.6120i | −1.02701 | + | 0.592947i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.2601 | + | 19.5031i | −0.489571 | + | 0.847962i | ||||
\(530\) | −11.2175 | − | 32.3004i | −0.487256 | − | 1.40304i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 34.5513 | + | 28.5359i | 1.49799 | + | 1.23719i | ||||
\(533\) | − | 17.4215i | − | 0.754607i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.4808 | − | 11.6563i | −0.582826 | − | 0.503946i | ||||
\(536\) | 26.9934 | − | 46.7540i | 1.16594 | − | 2.01946i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 23.9147i | − | 1.03103i | ||||||
\(539\) | 23.9060 | + | 8.28127i | 1.02970 | + | 0.356700i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.20850 | − | 7.28933i | −0.180937 | − | 0.313393i | 0.761263 | − | 0.648444i | \(-0.224580\pi\) |
−0.942200 | + | 0.335051i | \(0.891246\pi\) | |||||||
\(542\) | −8.70170 | − | 5.02393i | −0.373770 | − | 0.215796i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.35425 | − | 14.4700i | −0.358185 | − | 0.620395i | ||||
\(545\) | 29.0517 | + | 5.56747i | 1.24444 | + | 0.238484i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.9569i | 1.15259i | 0.817241 | + | 0.576296i | \(0.195502\pi\) | ||||
−0.817241 | + | 0.576296i | \(0.804498\pi\) | |||||||
\(548\) | −10.1596 | + | 5.86565i | −0.433997 | + | 0.250568i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.6141 | − | 33.6959i | −1.13483 | − | 1.43680i | ||||
\(551\) | −18.5980 | − | 32.2127i | −0.792301 | − | 1.37231i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.36347 | − | 25.9269i | 0.185554 | − | 1.10252i | ||||
\(554\) | 19.6271 | 0.833877 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −35.0516 | + | 60.7112i | −1.48652 | + | 2.57473i | ||||
\(557\) | −38.9680 | − | 22.4982i | −1.65113 | − | 0.953280i | −0.976609 | − | 0.215023i | \(-0.931017\pi\) |
−0.674520 | − | 0.738257i | \(-0.735649\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 30.0405 | 1.27058 | ||||||||
\(560\) | 11.6665 | − | 1.97284i | 0.493001 | − | 0.0833678i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 60.0646 | − | 34.6783i | 2.53367 | − | 1.46282i | ||||
\(563\) | 13.5461 | + | 7.82087i | 0.570902 | + | 0.329610i | 0.757509 | − | 0.652824i | \(-0.226416\pi\) |
−0.186608 | + | 0.982435i | \(0.559749\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.1880 | + | 9.44200i | −1.14381 | + | 0.397228i | ||||
\(566\) | −60.4374 | −2.54037 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 31.3087i | 1.31368i | ||||||||
\(569\) | 11.3695 | + | 19.6926i | 0.476635 | + | 0.825555i | 0.999642 | − | 0.0267732i | \(-0.00852318\pi\) |
−0.523007 | + | 0.852328i | \(0.675190\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2601 | − | 28.1634i | 0.680465 | − | 1.17860i | −0.294374 | − | 0.955690i | \(-0.595111\pi\) |
0.974839 | − | 0.222910i | \(-0.0715556\pi\) | |||||||
\(572\) | −38.4516 | + | 22.2000i | −1.60774 | + | 0.928230i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32.0516 | − | 5.39426i | −1.33781 | − | 0.225152i | ||||
\(575\) | −1.28034 | + | 3.21780i | −0.0533939 | + | 0.134192i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.55278 | + | 3.20590i | 0.231165 | + | 0.133463i | 0.611109 | − | 0.791546i | \(-0.290724\pi\) |
−0.379944 | + | 0.925009i | \(0.624057\pi\) | |||||||
\(578\) | −26.0217 | − | 15.0237i | −1.08236 | − | 0.624902i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −64.1033 | − | 12.2847i | −2.66174 | − | 0.510096i | ||||
\(581\) | −6.33713 | + | 7.67300i | −0.262908 | + | 0.318329i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.1436 | − | 11.6299i | 0.834263 | − | 0.481662i | ||||
\(584\) | 2.97407 | − | 5.15124i | 0.123068 | − | 0.213160i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.5203 | + | 56.3267i | 1.34340 | + | 2.32684i | ||||
\(587\) | 13.3185i | 0.549712i | 0.961485 | + | 0.274856i | \(0.0886302\pi\) | ||||
−0.961485 | + | 0.274856i | \(0.911370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.2288 | −0.957124 | ||||||||
\(590\) | −3.90464 | + | 1.35602i | −0.160751 | + | 0.0558266i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.03805 | − | 5.21812i | −0.371461 | − | 0.214463i | ||||
\(593\) | −11.2759 | + | 6.51015i | −0.463046 | + | 0.267340i | −0.713324 | − | 0.700834i | \(-0.752811\pi\) |
0.250278 | + | 0.968174i | \(0.419478\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.8203 | + | 20.5317i | −1.01753 | + | 0.841720i | ||||
\(596\) | 16.0129 | 0.655914 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.80257 | + | 2.77277i | 0.196392 | + | 0.113387i | ||||
\(599\) | −5.03238 | + | 8.71634i | −0.205617 | + | 0.356140i | −0.950329 | − | 0.311246i | \(-0.899254\pi\) |
0.744712 | + | 0.667386i | \(0.232587\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.1033 | −1.43189 | −0.715946 | − | 0.698156i | \(-0.754004\pi\) | ||||
−0.715946 | + | 0.698156i | \(0.754004\pi\) | |||||||
\(602\) | 9.30154 | − | 55.2679i | 0.379102 | − | 2.25255i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.6458 | + | 21.9031i | 0.514548 | + | 0.891224i | ||||
\(605\) | 3.01683 | − | 3.48904i | 0.122651 | − | 0.141849i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.6289 | + | 13.6421i | −0.959066 | + | 0.553717i | −0.895886 | − | 0.444285i | \(-0.853458\pi\) |
−0.0631807 | + | 0.998002i | \(0.520124\pi\) | |||||||
\(608\) | − | 14.2565i | − | 0.578176i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.64575 | + | 29.4602i | −0.228590 | + | 1.19281i | ||||
\(611\) | 6.58831 | + | 11.4113i | 0.266535 | + | 0.461652i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.9081 | − | 9.18456i | −0.642523 | − | 0.370961i | 0.143063 | − | 0.989714i | \(-0.454305\pi\) |
−0.785586 | + | 0.618753i | \(0.787638\pi\) | |||||||
\(614\) | 20.0161 | + | 34.6690i | 0.807785 | + | 1.39913i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.0627 | + | 35.0372i | 0.526313 | + | 1.41169i | ||||
\(617\) | 30.1964i | 1.21566i | 0.794067 | + | 0.607831i | \(0.207960\pi\) | ||||
−0.794067 | + | 0.607831i | \(0.792040\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.50000 | − | 11.2583i | 0.261257 | − | 0.452510i | −0.705319 | − | 0.708890i | \(-0.749196\pi\) |
0.966576 | + | 0.256379i | \(0.0825296\pi\) | |||||||
\(620\) | −26.6601 | + | 30.8331i | −1.07069 | + | 1.23829i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 39.8964i | 1.59970i | ||||||||
\(623\) | 1.58702 | − | 9.42977i | 0.0635827 | − | 0.377796i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.79137 | − | 24.3200i | 0.231655 | − | 0.972798i | ||||
\(626\) | 1.80712 | − | 3.13003i | 0.0722271 | − | 0.125101i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.6231 | − | 25.7632i | 1.78066 | − | 1.02806i | ||||
\(629\) | 28.4116 | 1.13284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.1660 | −1.55917 | −0.779587 | − | 0.626294i | \(-0.784571\pi\) | ||||
−0.779587 | + | 0.626294i | \(0.784571\pi\) | |||||||
\(632\) | 33.6529 | − | 19.4295i | 1.33864 | − | 0.772864i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −23.7601 | + | 41.1538i | −0.943635 | + | 1.63442i | ||||
\(635\) | 7.11766 | − | 2.47186i | 0.282456 | − | 0.0980928i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.1622 | − | 4.45757i | 0.917720 | − | 0.176615i | ||||
\(638\) | − | 68.7572i | − | 2.72212i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −34.9996 | − | 30.2628i | −1.38348 | − | 1.19624i | ||||
\(641\) | −1.02915 | + | 1.78255i | −0.0406491 | + | 0.0704064i | −0.885634 | − | 0.464384i | \(-0.846276\pi\) |
0.844985 | + | 0.534790i | \(0.179609\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.0302i | 1.53920i | 0.638526 | + | 0.769600i | \(0.279544\pi\) | ||||
−0.638526 | + | 0.769600i | \(0.720456\pi\) | |||||||
\(644\) | 4.25441 | − | 5.15124i | 0.167647 | − | 0.202987i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.0516 | − | 52.0510i | −1.18237 | − | 2.04792i | ||||
\(647\) | 35.1942 | + | 20.3194i | 1.38362 | + | 0.798836i | 0.992587 | − | 0.121538i | \(-0.0387827\pi\) |
0.391038 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.40588 | − | 2.43506i | −0.0551857 | − | 0.0955844i | ||||
\(650\) | −37.1960 | − | 14.8000i | −1.45895 | − | 0.580504i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 38.0479i | 1.49007i | ||||||||
\(653\) | 12.0049 | − | 6.93101i | 0.469787 | − | 0.271231i | −0.246364 | − | 0.969177i | \(-0.579236\pi\) |
0.716150 | + | 0.697946i | \(0.245902\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.9956 | − | 19.6558i | 0.664073 | − | 0.768017i | ||||
\(656\) | −5.17018 | − | 8.95501i | −0.201861 | − | 0.349634i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 23.0342 | − | 8.58772i | 0.897967 | − | 0.334784i | ||||
\(659\) | 26.3533 | 1.02658 | 0.513289 | − | 0.858216i | \(-0.328427\pi\) | ||||
0.513289 | + | 0.858216i | \(0.328427\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.67712 | + | 11.5651i | −0.259710 | + | 0.449831i | −0.966164 | − | 0.257928i | \(-0.916960\pi\) |
0.706454 | + | 0.707759i | \(0.250294\pi\) | |||||||
\(662\) | −7.37291 | − | 4.25675i | −0.286556 | − | 0.165443i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.7085 | −0.570800 | ||||||||
\(665\) | −27.0999 | + | 4.58266i | −1.05089 | + | 0.177708i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.80257 | + | 2.77277i | −0.185956 | + | 0.107362i | ||||
\(668\) | 39.2263 | + | 22.6473i | 1.51771 | + | 0.876250i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.0640 | + | 69.2918i | 0.929675 | + | 2.67698i | ||||
\(671\) | −20.4051 | −0.787731 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 10.1088i | − | 0.389666i | −0.980836 | − | 0.194833i | \(-0.937583\pi\) | ||
0.980836 | − | 0.194833i | \(-0.0624165\pi\) | |||||||
\(674\) | 12.0097 | + | 20.8014i | 0.462595 | + | 0.801239i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | − | 5.19615i | 0.115385 | − | 0.199852i | ||||
\(677\) | 39.3554 | − | 22.7218i | 1.51255 | − | 0.873271i | 0.512658 | − | 0.858593i | \(-0.328661\pi\) |
0.999892 | − | 0.0146783i | \(-0.00467241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.6974 | − | 25.0604i | 0.794293 | − | 0.961730i | ||||
\(680\) | −46.7584 | − | 8.96077i | −1.79310 | − | 0.343630i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −37.1859 | − | 21.4693i | −1.42392 | − | 0.822102i | ||||
\(683\) | 20.9648 | + | 12.1040i | 0.802196 | + | 0.463148i | 0.844238 | − | 0.535968i | \(-0.180053\pi\) |
−0.0420428 | + | 0.999116i | \(0.513387\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.35425 | − | 7.06663i | 0.0517432 | − | 0.270002i | ||||
\(686\) | −1.02915 | − | 43.9936i | −0.0392933 | − | 1.67968i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 15.4415 | − | 8.91514i | 0.588701 | − | 0.339887i | ||||
\(689\) | 10.8427 | − | 18.7802i | 0.413075 | − | 0.715467i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.85425 | − | 3.21165i | −0.0705389 | − | 0.122177i | 0.828599 | − | 0.559843i | \(-0.189139\pi\) |
−0.899138 | + | 0.437666i | \(0.855805\pi\) | |||||||
\(692\) | − | 89.6946i | − | 3.40968i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 64.4575 | 2.44677 | ||||||||
\(695\) | −14.1057 | − | 40.6172i | −0.535061 | − | 1.54070i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.3791 | + | 14.0753i | 0.923423 | + | 0.533139i | ||||
\(698\) | −12.0882 | + | 6.97915i | −0.457547 | + | 0.264165i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −25.0202 | + | 41.2311i | −0.945674 | + | 1.55839i | ||||
\(701\) | −42.8685 | −1.61912 | −0.809561 | − | 0.587036i | \(-0.800295\pi\) | ||||
−0.809561 | + | 0.587036i | \(0.800295\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.9943 | + | 12.1210i | 0.791813 | + | 0.457154i | ||||
\(704\) | 20.4051 | − | 35.3427i | 0.769047 | − | 1.33203i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.9373 | 0.562171 | ||||||||
\(707\) | 41.6256 | − | 15.5191i | 1.56549 | − | 0.583654i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.82288 | − | 10.0855i | −0.218683 | − | 0.378770i | 0.735723 | − | 0.677283i | \(-0.236843\pi\) |
−0.954405 | + | 0.298513i | \(0.903509\pi\) | |||||||
\(710\) | −32.1781 | − | 27.8231i | −1.20762 | − | 1.04418i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.2398 | − | 7.06663i | 0.458704 | − | 0.264833i | ||||
\(713\) | 3.46317i | 0.129697i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.12549 | − | 26.7454i | 0.191683 | − | 1.00022i | ||||
\(716\) | 2.83627 | + | 4.91257i | 0.105997 | + | 0.183591i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.2735 | + | 7.66347i | 0.495363 | + | 0.285998i | ||||
\(719\) | −2.97407 | − | 5.15124i | −0.110914 | − | 0.192109i | 0.805225 | − | 0.592969i | \(-0.202045\pi\) |
−0.916139 | + | 0.400861i | \(0.868711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.1974 | + | 5.25049i | 1.16185 | + | 0.195539i | ||||
\(722\) | − | 6.13742i | − | 0.228411i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.4059 | − | 23.2197i | 0.498226 | − | 0.862952i | ||||
\(725\) | 31.4152 | − | 24.8127i | 1.16673 | − | 0.921519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 20.0062i | − | 0.741989i | −0.928635 | − | 0.370995i | \(-0.879017\pi\) | ||
0.928635 | − | 0.370995i | \(-0.120983\pi\) | |||||||
\(728\) | 26.8798 | + | 22.2000i | 0.996232 | + | 0.822788i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.65132 | + | 7.63441i | 0.0981298 | + | 0.282562i | ||||
\(731\) | −24.2705 | + | 42.0378i | −0.897678 | + | 1.55482i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.7925 | + | 10.2725i | −0.657182 | + | 0.379424i | −0.791203 | − | 0.611554i | \(-0.790545\pi\) |
0.134020 | + | 0.990979i | \(0.457211\pi\) | |||||||
\(734\) | 64.8296 | 2.39290 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.12549 | −0.0783467 | ||||||||
\(737\) | −43.2126 | + | 24.9488i | −1.59176 | + | 0.919002i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.96863 | + | 3.40976i | −0.0724171 | + | 0.125430i | −0.899960 | − | 0.435972i | \(-0.856405\pi\) |
0.827543 | + | 0.561402i | \(0.189738\pi\) | |||||||
\(740\) | 40.1846 | − | 13.9555i | 1.47721 | − | 0.513015i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −31.1941 | − | 25.7632i | −1.14517 | − | 0.945796i | ||||
\(743\) | − | 4.90125i | − | 0.179809i | −0.995950 | − | 0.0899047i | \(-0.971344\pi\) | ||
0.995950 | − | 0.0899047i | \(-0.0286562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.42373 | + | 7.42921i | −0.235347 | + | 0.272185i | ||||
\(746\) | −4.78119 | + | 8.28127i | −0.175052 | + | 0.303199i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 71.7440i | − | 2.62322i | ||||||
\(749\) | −20.7941 | − | 3.49963i | −0.759800 | − | 0.127874i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.7288 | + | 22.0469i | 0.464479 | + | 0.804501i | 0.999178 | − | 0.0405415i | \(-0.0129083\pi\) |
−0.534699 | + | 0.845043i | \(0.679575\pi\) | |||||||
\(752\) | 6.77307 | + | 3.91044i | 0.246989 | + | 0.142599i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.0516 | − | 55.5151i | −1.16725 | − | 2.02174i | ||||
\(755\) | −15.2349 | − | 2.91962i | −0.554456 | − | 0.106256i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 33.6961i | − | 1.22470i | −0.790585 | − | 0.612352i | \(-0.790223\pi\) | ||
0.790585 | − | 0.612352i | \(-0.209777\pi\) | |||||||
\(758\) | 17.0618 | − | 9.85063i | 0.619712 | − | 0.357791i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.7284 | − | 26.5696i | −1.11464 | − | 0.963782i | ||||
\(761\) | 20.7941 | + | 36.0164i | 0.753785 | + | 1.30559i | 0.945976 | + | 0.324237i | \(0.105108\pi\) |
−0.192191 | + | 0.981358i | \(0.561559\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.7949 | − | 12.2268i | 1.18726 | − | 0.442638i | ||||
\(764\) | 26.3533 | 0.953427 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 22.2288 | − | 38.5013i | 0.803158 | − | 1.39111i | ||||
\(767\) | −2.27024 | − | 1.31072i | −0.0819735 | − | 0.0473274i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.3542 | 0.697932 | 0.348966 | − | 0.937135i | \(-0.386533\pi\) | ||||
0.348966 | + | 0.937135i | \(0.386533\pi\) | |||||||
\(770\) | −47.6186 | − | 17.7110i | −1.71606 | − | 0.638262i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −61.0984 | + | 35.2752i | −2.19898 | + | 1.26958i | ||||
\(773\) | −20.9191 | − | 12.0776i | −0.752406 | − | 0.434402i | 0.0741565 | − | 0.997247i | \(-0.476374\pi\) |
−0.826563 | + | 0.562845i | \(0.809707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.61009 | − | 24.7380i | −0.129678 | − | 0.888614i | ||||
\(776\) | 48.0387 | 1.72449 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.4180i | 0.947131i | ||||||||
\(779\) | 12.0097 | + | 20.8014i | 0.430291 | + | 0.745286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.4686 | − | 25.0604i | 0.517728 | − | 0.896732i | ||||
\(782\) | −7.76026 | + | 4.48039i | −0.277506 | + | 0.160218i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 10.5830 | − | 9.16515i | 0.377964 | − | 0.327327i | ||||
\(785\) | −5.94814 | + | 31.0381i | −0.212298 | + | 1.10780i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7107 | − | 11.9573i | −0.738257 | − | 0.426233i | 0.0831783 | − | 0.996535i | \(-0.473493\pi\) |
−0.821435 | + | 0.570302i | \(0.806826\pi\) | |||||||
\(788\) | −44.5414 | − | 25.7160i | −1.58672 | − | 0.916095i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.93725 | + | 51.8538i | −0.353552 | + | 1.84487i | ||||
\(791\) | −21.6855 | + | 26.2568i | −0.771046 | + | 0.933583i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.4752 | + | 9.51198i | −0.585053 | + | 0.337780i | ||||
\(794\) | −38.2251 | + | 66.2079i | −1.35656 | + | 2.34963i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −22.5203 | − | 39.0062i | −0.798209 | − | 1.38254i | ||||
\(797\) | 23.6117i | 0.836369i | 0.908362 | + | 0.418185i | \(0.137334\pi\) | ||||
−0.908362 | + | 0.418185i | \(0.862666\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.2915 | −0.753239 | ||||||||
\(800\) | 15.1827 | − | 2.21566i | 0.536791 | − | 0.0783356i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.4795 | − | 14.1333i | −0.864402 | − | 0.499063i | ||||
\(803\) | −4.76107 | + | 2.74880i | −0.168014 | + | 0.0970032i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.683228 | + | 4.04031i | 0.0240806 | + | 0.142402i | ||||
\(806\) | −40.0323 | −1.41008 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 56.8629 | + | 32.8298i | 2.00043 | + | 1.15495i | ||||
\(809\) | 24.6595 | − | 42.7115i | 0.866983 | − | 1.50166i | 0.00191780 | − | 0.999998i | \(-0.499390\pi\) |
0.865065 | − | 0.501660i | \(-0.167277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.7712 | 0.483574 | 0.241787 | − | 0.970329i | \(-0.422267\pi\) | ||||
0.241787 | + | 0.970329i | \(0.422267\pi\) | |||||||
\(812\) | −72.3627 | + | 26.9786i | −2.53943 | + | 0.946763i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 22.4059 | + | 38.8081i | 0.785326 | + | 1.36022i | ||||
\(815\) | −17.6524 | − | 15.2633i | −0.618336 | − | 0.534650i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −35.8686 | + | 20.7088i | −1.25488 | + | 0.724508i | ||||
\(818\) | 10.4951i | 0.366954i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 41.3948 | + | 7.93289i | 1.44557 | + | 0.277029i | ||||
\(821\) | −6.97730 | − | 12.0850i | −0.243509 | − | 0.421771i | 0.718202 | − | 0.695835i | \(-0.244965\pi\) |
−0.961711 | + | 0.274064i | \(0.911632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.4838 | + | 18.7545i | 1.13231 | + | 0.653742i | 0.944516 | − | 0.328465i | \(-0.106531\pi\) |
0.187799 | + | 0.982208i | \(0.439865\pi\) | |||||||
\(824\) | 23.3792 | + | 40.4939i | 0.814452 | + | 1.41067i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.11438 | + | 3.77089i | −0.108363 | + | 0.131206i | ||||
\(827\) | 14.5018i | 0.504278i | 0.967691 | + | 0.252139i | \(0.0811341\pi\) | ||||
−0.967691 | + | 0.252139i | \(0.918866\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.5516 | + | 23.4721i | −0.470668 | + | 0.815220i | −0.999437 | − | 0.0335452i | \(-0.989320\pi\) |
0.528770 | + | 0.848765i | \(0.322654\pi\) | |||||||
\(830\) | 13.0710 | − | 15.1169i | 0.453701 | − | 0.524716i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 38.0479i | − | 1.31907i | ||||||
\(833\) | −12.4756 | + | 36.0139i | −0.432253 | + | 1.24781i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.2432 | + | 9.11390i | −0.908185 | + | 0.315399i | ||||
\(836\) | 30.6077 | − | 53.0140i | 1.05859 | − | 1.83353i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54.2283 | − | 31.3087i | 1.87328 | − | 1.08154i | ||||
\(839\) | 28.6872 | 0.990391 | 0.495195 | − | 0.868782i | \(-0.335096\pi\) | ||||
0.495195 | + | 0.868782i | \(0.335096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.1033 | 1.21046 | ||||||||
\(842\) | −35.4524 | + | 20.4684i | −1.22177 | + | 0.705389i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.70850 | − | 2.95920i | 0.0588089 | − | 0.101860i | ||||
\(845\) | 1.20728 | + | 3.47634i | 0.0415318 | + | 0.119590i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.905757 | − | 5.38183i | 0.0311222 | − | 0.184922i | ||||
\(848\) | − | 12.8712i | − | 0.441999i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 50.7623 | − | 40.0936i | 1.74113 | − | 1.37520i | ||||
\(851\) | 1.80712 | − | 3.13003i | 0.0619473 | − | 0.107296i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15.6544i | − | 0.535995i | −0.963420 | − | 0.267997i | \(-0.913638\pi\) | ||
0.963420 | − | 0.267997i | \(-0.0863619\pi\) | |||||||
\(854\) | 12.3987 | + | 33.2560i | 0.424273 | + | 1.13800i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.5830 | − | 26.9906i | −0.532616 | − | 0.922518i | ||||
\(857\) | −23.8806 | − | 13.7875i | −0.815746 | − | 0.470971i | 0.0332013 | − | 0.999449i | \(-0.489430\pi\) |
−0.848947 | + | 0.528478i | \(0.822763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.4686 | + | 28.5245i | 0.561902 | + | 0.973243i | 0.997330 | + | 0.0730199i | \(0.0232636\pi\) |
−0.435428 | + | 0.900223i | \(0.643403\pi\) | |||||||
\(860\) | −13.6790 | + | 71.3786i | −0.466450 | + | 2.43399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 73.0537i | − | 2.48822i | ||||||
\(863\) | 32.8782 | − | 18.9822i | 1.11919 | − | 0.646162i | 0.177993 | − | 0.984032i | \(-0.443040\pi\) |
0.941193 | + | 0.337869i | \(0.109706\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.6140 | + | 35.9819i | 1.41492 | + | 1.22342i | ||||
\(866\) | 9.17340 | + | 15.8888i | 0.311725 | + | 0.539923i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.00429 | + | 47.5599i | −0.271683 | + | 1.61429i | ||||
\(869\) | −35.9156 | −1.21835 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.2601 | + | 40.2877i | −0.788139 | + | 1.36510i | ||||
\(872\) | 44.7997 | + | 25.8651i | 1.51711 | + | 0.875903i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.64575 | −0.258621 | ||||||||
\(875\) | −9.09213 | − | 28.1484i | −0.307370 | − | 0.951590i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.6432 | + | 10.7637i | −0.629536 | + | 0.363463i | −0.780572 | − | 0.625065i | \(-0.785072\pi\) |
0.151036 | + | 0.988528i | \(0.451739\pi\) | |||||||
\(878\) | −7.76026 | − | 4.48039i | −0.261896 | − | 0.151206i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.30264 | − | 15.2688i | −0.178752 | − | 0.514712i | ||||
\(881\) | 24.5217 | 0.826158 | 0.413079 | − | 0.910695i | \(-0.364453\pi\) | ||||
0.413079 | + | 0.910695i | \(0.364453\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 35.8720i | − | 1.20719i | −0.797292 | − | 0.603594i | \(-0.793735\pi\) | ||
0.797292 | − | 0.603594i | \(-0.206265\pi\) | |||||||
\(884\) | −33.4439 | − | 57.9266i | −1.12484 | − | 1.94828i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.00000 | + | 8.66025i | −0.167978 | + | 0.290947i | ||||
\(887\) | 32.7948 | − | 18.9341i | 1.10114 | − | 0.635744i | 0.164621 | − | 0.986357i | \(-0.447360\pi\) |
0.936521 | + | 0.350612i | \(0.114027\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.67712 | − | 6.87386i | 0.190405 | − | 0.230542i | ||||
\(890\) | −3.61424 | + | 18.8595i | −0.121150 | + | 0.632173i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.7330 | − | 9.08345i | −0.526485 | − | 0.303966i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.41699 | − | 0.654833i | −0.114218 | − | 0.0218886i | ||||
\(896\) | −53.9869 | − | 9.08594i | −1.80357 | − | 0.303540i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21.2778 | − | 12.2847i | 0.710050 | − | 0.409947i | ||||
\(899\) | 20.0161 | − | 34.6690i | 0.667575 | − | 1.15627i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.5203 | + | 30.3460i | 0.583684 | + | 1.01097i | ||||
\(902\) | 44.4001i | 1.47836i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50.3320 | −1.67402 | ||||||||
\(905\) | 5.39490 | + | 15.5345i | 0.179332 | + | 0.516383i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.51902 | + | 2.60906i | 0.150052 | + | 0.0866324i | 0.573146 | − | 0.819453i | \(-0.305723\pi\) |
−0.423094 | + | 0.906086i | \(0.639056\pi\) | |||||||
\(908\) | −74.5495 | + | 43.0412i | −2.47401 | + | 1.42837i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −46.7037 | + | 7.89773i | −1.54821 | + | 0.261807i | ||||
\(911\) | 37.1960 | 1.23236 | 0.616179 | − | 0.787606i | \(-0.288680\pi\) | ||||
0.616179 | + | 0.787606i | \(0.288680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7731 | + | 6.79721i | 0.389633 | + | 0.224955i | ||||
\(914\) | 3.22526 | − | 5.58631i | 0.106682 | − | 0.184779i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.2288 | 0.998786 | ||||||||
\(917\) | 5.10267 | − | 30.3191i | 0.168505 | − | 1.00122i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.4373 | + | 19.8099i | 0.377280 | + | 0.653468i | 0.990665 | − | 0.136315i | \(-0.0435260\pi\) |
−0.613385 | + | 0.789784i | \(0.710193\pi\) | |||||||
\(920\) | −3.96126 | + | 4.58129i | −0.130599 | + | 0.151041i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.3116 | − | 12.8816i | 0.734792 | − | 0.424232i | ||||
\(923\) | − | 26.9786i | − | 0.888011i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.64575 | + | 24.2421i | −0.317150 | + | 0.797075i | ||||
\(926\) | −25.1863 | − | 43.6240i | −0.827673 | − | 1.43357i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 21.2778 | + | 12.2847i | 0.698478 | + | 0.403267i | ||||
\(929\) | 27.3824 | + | 47.4277i | 0.898388 | + | 1.55605i | 0.829555 | + | 0.558425i | \(0.188594\pi\) |
0.0688327 | + | 0.997628i | \(0.478073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.5830 | + | 21.2895i | −0.805675 | + | 0.697735i | ||||
\(932\) | 25.4442i | 0.833454i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14.2288 | + | 24.6449i | −0.465579 | + | 0.806407i | ||||
\(935\) | 33.2857 | + | 28.7808i | 1.08856 | + | 0.941233i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.7023i | 1.75438i | 0.480146 | + | 0.877188i | \(0.340584\pi\) | ||||
−0.480146 | + | 0.877188i | \(0.659416\pi\) | |||||||
\(938\) | 66.9184 | + | 55.2679i | 2.18496 | + | 1.80456i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.1141 | + | 10.4582i | −0.982215 | + | 0.341109i | ||||
\(941\) | −17.9578 | + | 31.1039i | −0.585408 | + | 1.01396i | 0.409416 | + | 0.912348i | \(0.365732\pi\) |
−0.994824 | + | 0.101609i | \(0.967601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.10127 | − | 1.79052i | 0.100991 | − | 0.0583073i | ||||
\(944\) | −1.55593 | −0.0506414 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −76.5608 | −2.48921 | ||||||||
\(947\) | 18.7322 | − | 10.8150i | 0.608715 | − | 0.351442i | −0.163748 | − | 0.986502i | \(-0.552358\pi\) |
0.772462 | + | 0.635061i | \(0.219025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.56275 | + | 4.43881i | −0.0831903 | + | 0.144090i | ||||
\(950\) | 54.6149 | − | 7.97012i | 1.77194 | − | 0.258585i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −52.7830 | + | 19.6788i | −1.71071 | + | 0.637793i | ||||
\(953\) | 21.1828i | 0.686178i | 0.939303 | + | 0.343089i | \(0.111473\pi\) | ||||
−0.939303 | + | 0.343089i | \(0.888527\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.5719 | + | 12.2266i | −0.342098 | + | 0.395645i | ||||
\(956\) | −24.0194 | + | 41.6027i | −0.776841 | + | 1.34553i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 65.6596i | 2.12137i | ||||||||
\(959\) | −2.97407 | − | 7.97713i | −0.0960378 | − | 0.257595i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.00000 | + | 5.19615i | 0.0967742 | + | 0.167618i | ||||
\(962\) | 36.1813 | + | 20.8893i | 1.16653 | + | 0.673498i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.22876 | + | 5.59237i | 0.103991 | + | 0.180118i | ||||
\(965\) | 8.14425 | − | 42.4976i | 0.262173 | − | 1.36805i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.4846i | − | 1.07679i | −0.842692 | − | 0.538397i | \(-0.819030\pi\) | ||
0.842692 | − | 0.538397i | \(-0.180970\pi\) | |||||||
\(968\) | 6.98556 | − | 4.03312i | 0.224525 | − | 0.129629i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −42.6905 | + | 49.3727i | −1.37071 | + | 1.58526i | ||||
\(971\) | −29.8297 | − | 51.6666i | −0.957281 | − | 1.65806i | −0.729061 | − | 0.684449i | \(-0.760043\pi\) |
−0.228220 | − | 0.973610i | \(-0.573291\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −39.2259 | − | 32.3967i | −1.25752 | − | 1.03859i | ||||
\(974\) | −9.56239 | −0.306399 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.64575 | + | 9.77873i | −0.180716 | + | 0.313009i | ||||
\(977\) | −26.0675 | − | 15.0501i | −0.833972 | − | 0.481494i | 0.0212386 | − | 0.999774i | \(-0.493239\pi\) |
−0.855211 | + | 0.518280i | \(0.826572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.0627 | −0.417487 | ||||||||
\(980\) | 0.0445851 | + | 57.0650i | 0.00142422 | + | 1.82288i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.4415 | − | 8.91514i | 0.492757 | − | 0.284494i | ||||
\(983\) | 34.2527 | + | 19.7758i | 1.09249 | + | 0.630750i | 0.934239 | − | 0.356648i | \(-0.116081\pi\) |
0.158253 | + | 0.987399i | \(0.449414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.7992 | − | 10.3488i | 0.949482 | − | 0.329741i | ||||
\(986\) | 103.581 | 3.29871 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 57.0719i | − | 1.81570i | ||||||
\(989\) | 3.08746 | + | 5.34764i | 0.0981756 | + | 0.170045i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.1974 | + | 45.3752i | −0.832187 | + | 1.44139i | 0.0641128 | + | 0.997943i | \(0.479578\pi\) |
−0.896300 | + | 0.443448i | \(0.853755\pi\) | |||||||
\(992\) | 13.2879 | − | 7.67178i | 0.421892 | − | 0.243579i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −49.6346 | − | 8.35347i | −1.57432 | − | 0.264956i | ||||
\(995\) | 27.1312 | + | 5.19943i | 0.860118 | + | 0.164833i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.8643 | + | 16.0875i | 0.882473 | + | 0.509496i | 0.871473 | − | 0.490444i | \(-0.163165\pi\) |
0.0109997 | + | 0.999940i | \(0.496499\pi\) | |||||||
\(998\) | 10.2887 | + | 5.94020i | 0.325684 | + | 0.188034i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.bf.c.109.2 | yes | 16 | |
3.2 | odd | 2 | inner | 315.2.bf.c.109.7 | yes | 16 | |
5.4 | even | 2 | inner | 315.2.bf.c.109.8 | yes | 16 | |
7.2 | even | 3 | inner | 315.2.bf.c.289.8 | yes | 16 | |
7.3 | odd | 6 | 2205.2.d.r.1324.2 | 8 | |||
7.4 | even | 3 | 2205.2.d.p.1324.1 | 8 | |||
15.14 | odd | 2 | inner | 315.2.bf.c.109.1 | ✓ | 16 | |
21.2 | odd | 6 | inner | 315.2.bf.c.289.1 | yes | 16 | |
21.11 | odd | 6 | 2205.2.d.p.1324.8 | 8 | |||
21.17 | even | 6 | 2205.2.d.r.1324.7 | 8 | |||
35.4 | even | 6 | 2205.2.d.p.1324.7 | 8 | |||
35.9 | even | 6 | inner | 315.2.bf.c.289.2 | yes | 16 | |
35.24 | odd | 6 | 2205.2.d.r.1324.8 | 8 | |||
105.44 | odd | 6 | inner | 315.2.bf.c.289.7 | yes | 16 | |
105.59 | even | 6 | 2205.2.d.r.1324.1 | 8 | |||
105.74 | odd | 6 | 2205.2.d.p.1324.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bf.c.109.1 | ✓ | 16 | 15.14 | odd | 2 | inner | |
315.2.bf.c.109.2 | yes | 16 | 1.1 | even | 1 | trivial | |
315.2.bf.c.109.7 | yes | 16 | 3.2 | odd | 2 | inner | |
315.2.bf.c.109.8 | yes | 16 | 5.4 | even | 2 | inner | |
315.2.bf.c.289.1 | yes | 16 | 21.2 | odd | 6 | inner | |
315.2.bf.c.289.2 | yes | 16 | 35.9 | even | 6 | inner | |
315.2.bf.c.289.7 | yes | 16 | 105.44 | odd | 6 | inner | |
315.2.bf.c.289.8 | yes | 16 | 7.2 | even | 3 | inner | |
2205.2.d.p.1324.1 | 8 | 7.4 | even | 3 | |||
2205.2.d.p.1324.2 | 8 | 105.74 | odd | 6 | |||
2205.2.d.p.1324.7 | 8 | 35.4 | even | 6 | |||
2205.2.d.p.1324.8 | 8 | 21.11 | odd | 6 | |||
2205.2.d.r.1324.1 | 8 | 105.59 | even | 6 | |||
2205.2.d.r.1324.2 | 8 | 7.3 | odd | 6 | |||
2205.2.d.r.1324.7 | 8 | 21.17 | even | 6 | |||
2205.2.d.r.1324.8 | 8 | 35.24 | odd | 6 |