Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(491,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.491");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.q (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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.4 | ||
Character | \(\chi\) | \(=\) | 637.491 |
Dual form | 637.2.q.j.589.4 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.04719 | + | 1.18194i | −1.44758 | + | 0.835761i | −0.998337 | − | 0.0576484i | \(-0.981640\pi\) |
−0.449243 | + | 0.893409i | \(0.648306\pi\) | |||||||
\(3\) | 1.49347 | + | 2.58676i | 0.862252 | + | 1.49347i | 0.869750 | + | 0.493493i | \(0.164280\pi\) |
−0.00749727 | + | 0.999972i | \(0.502386\pi\) | |||||||
\(4\) | 1.79399 | − | 3.10727i | 0.896993 | − | 1.55364i | ||||
\(5\) | 3.20263i | 1.43226i | 0.697967 | + | 0.716130i | \(0.254088\pi\) | ||||
−0.697967 | + | 0.716130i | \(0.745912\pi\) | |||||||
\(6\) | −6.11481 | − | 3.53039i | −2.49636 | − | 1.44127i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.75379i | 1.32716i | ||||||||
\(9\) | −2.96088 | + | 5.12839i | −0.986959 | + | 1.70946i | ||||
\(10\) | −3.78533 | − | 6.55639i | −1.19703 | − | 2.07331i | ||||
\(11\) | −3.19878 | + | 1.84682i | −0.964469 | + | 0.556837i | −0.897546 | − | 0.440922i | \(-0.854652\pi\) |
−0.0669235 | + | 0.997758i | \(0.521318\pi\) | |||||||
\(12\) | 10.7170 | 3.09374 | ||||||||
\(13\) | 2.99897 | − | 2.00154i | 0.831765 | − | 0.555127i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.28443 | + | 4.78302i | −2.13903 | + | 1.23497i | ||||
\(16\) | −0.848797 | − | 1.47016i | −0.212199 | − | 0.367540i | ||||
\(17\) | 0.733403 | − | 1.27029i | 0.177876 | − | 0.308091i | −0.763277 | − | 0.646072i | \(-0.776411\pi\) |
0.941153 | + | 0.337981i | \(0.109744\pi\) | |||||||
\(18\) | − | 13.9984i | − | 3.29945i | ||||||
\(19\) | −5.11958 | − | 2.95579i | −1.17451 | − | 0.678105i | −0.219774 | − | 0.975551i | \(-0.570532\pi\) |
−0.954739 | + | 0.297445i | \(0.903865\pi\) | |||||||
\(20\) | 9.95145 | + | 5.74547i | 2.22521 | + | 1.28473i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.36567 | − | 7.56157i | 0.930764 | − | 1.61213i | ||||
\(23\) | −0.345203 | − | 0.597908i | −0.0719797 | − | 0.124673i | 0.827789 | − | 0.561039i | \(-0.189598\pi\) |
−0.899769 | + | 0.436367i | \(0.856265\pi\) | |||||||
\(24\) | −9.71014 | + | 5.60615i | −1.98207 | + | 1.14435i | ||||
\(25\) | −5.25684 | −1.05137 | ||||||||
\(26\) | −3.77375 | + | 7.64215i | −0.740093 | + | 1.49875i | ||||
\(27\) | −8.72707 | −1.67952 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.39239 | + | 4.14374i | 0.444256 | + | 0.769474i | 0.998000 | − | 0.0632132i | \(-0.0201348\pi\) |
−0.553744 | + | 0.832687i | \(0.686801\pi\) | |||||||
\(30\) | 11.3065 | − | 19.5835i | 2.06428 | − | 3.57543i | ||||
\(31\) | 2.10879i | 0.378750i | 0.981905 | + | 0.189375i | \(0.0606462\pi\) | ||||
−0.981905 | + | 0.189375i | \(0.939354\pi\) | |||||||
\(32\) | −3.02646 | − | 1.74733i | −0.535007 | − | 0.308886i | ||||
\(33\) | −9.55454 | − | 5.51632i | −1.66323 | − | 0.960267i | ||||
\(34\) | 3.46737i | 0.594649i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.6235 | + | 18.4005i | 1.77059 | + | 3.06675i | ||||
\(37\) | 1.09027 | − | 0.629465i | 0.179238 | − | 0.103483i | −0.407696 | − | 0.913118i | \(-0.633668\pi\) |
0.586935 | + | 0.809634i | \(0.300334\pi\) | |||||||
\(38\) | 13.9743 | 2.26694 | ||||||||
\(39\) | 9.65636 | + | 4.76838i | 1.54626 | + | 0.763552i | ||||
\(40\) | −12.0220 | −1.90084 | ||||||||
\(41\) | 0.224704 | − | 0.129733i | 0.0350928 | − | 0.0202609i | −0.482351 | − | 0.875978i | \(-0.660217\pi\) |
0.517444 | + | 0.855717i | \(0.326884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.80608 | + | 4.86027i | −0.427923 | + | 0.741184i | −0.996688 | − | 0.0813155i | \(-0.974088\pi\) |
0.568766 | + | 0.822500i | \(0.307421\pi\) | |||||||
\(44\) | 13.2527i | 1.99791i | ||||||||
\(45\) | −16.4243 | − | 9.48259i | −2.44839 | − | 1.41358i | ||||
\(46\) | 1.41339 | + | 0.816021i | 0.208393 | + | 0.120316i | ||||
\(47\) | 11.6216i | 1.69518i | 0.530653 | + | 0.847589i | \(0.321947\pi\) | ||||
−0.530653 | + | 0.847589i | \(0.678053\pi\) | |||||||
\(48\) | 2.53530 | − | 4.39126i | 0.365939 | − | 0.633824i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 10.7617 | − | 6.21329i | 1.52194 | − | 0.878692i | ||||
\(51\) | 4.38125 | 0.613497 | ||||||||
\(52\) | −0.839222 | − | 12.9094i | −0.116379 | − | 1.79021i | ||||
\(53\) | 0.485623 | 0.0667055 | 0.0333527 | − | 0.999444i | \(-0.489382\pi\) | ||||
0.0333527 | + | 0.999444i | \(0.489382\pi\) | |||||||
\(54\) | 17.8659 | − | 10.3149i | 2.43125 | − | 1.40368i | ||||
\(55\) | −5.91467 | − | 10.2445i | −0.797534 | − | 1.38137i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 17.6575i | − | 2.33879i | ||||||
\(58\) | −9.79535 | − | 5.65535i | −1.28619 | − | 0.742583i | ||||
\(59\) | 7.55939 | + | 4.36441i | 0.984148 | + | 0.568198i | 0.903520 | − | 0.428546i | \(-0.140974\pi\) |
0.0806283 | + | 0.996744i | \(0.474307\pi\) | |||||||
\(60\) | 34.3226i | 4.43103i | ||||||||
\(61\) | 5.73161 | − | 9.92744i | 0.733858 | − | 1.27108i | −0.221365 | − | 0.975191i | \(-0.571051\pi\) |
0.955223 | − | 0.295888i | \(-0.0956154\pi\) | |||||||
\(62\) | −2.49247 | − | 4.31709i | −0.316545 | − | 0.548271i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.6562 | 1.45702 | ||||||||
\(65\) | 6.41019 | + | 9.60460i | 0.795087 | + | 1.19130i | ||||
\(66\) | 26.0799 | 3.21022 | ||||||||
\(67\) | 0.296094 | − | 0.170950i | 0.0361736 | − | 0.0208849i | −0.481804 | − | 0.876279i | \(-0.660018\pi\) |
0.517978 | + | 0.855394i | \(0.326685\pi\) | |||||||
\(68\) | −2.63143 | − | 4.55777i | −0.319108 | − | 0.552711i | ||||
\(69\) | 1.03110 | − | 1.78591i | 0.124129 | − | 0.214998i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.10638 | − | 4.10287i | −0.843372 | − | 0.486921i | 0.0150373 | − | 0.999887i | \(-0.495213\pi\) |
−0.858409 | + | 0.512966i | \(0.828547\pi\) | |||||||
\(72\) | −19.2509 | − | 11.1145i | −2.26874 | − | 1.30986i | ||||
\(73\) | − | 0.259823i | − | 0.0304100i | −0.999884 | − | 0.0152050i | \(-0.995160\pi\) | ||
0.999884 | − | 0.0152050i | \(-0.00484008\pi\) | |||||||
\(74\) | −1.48799 | + | 2.57727i | −0.172975 | + | 0.299601i | ||||
\(75\) | −7.85090 | − | 13.5982i | −0.906544 | − | 1.57018i | ||||
\(76\) | −18.3689 | + | 10.6053i | −2.10706 | + | 1.21651i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −25.4043 | + | 1.65151i | −2.87648 | + | 0.186996i | ||||
\(79\) | 10.1259 | 1.13925 | 0.569627 | − | 0.821903i | \(-0.307088\pi\) | ||||
0.569627 | + | 0.821903i | \(0.307088\pi\) | |||||||
\(80\) | 4.70838 | − | 2.71838i | 0.526413 | − | 0.303924i | ||||
\(81\) | −4.15094 | − | 7.18964i | −0.461216 | − | 0.798849i | ||||
\(82\) | −0.306674 | + | 0.531175i | −0.0338665 | + | 0.0586584i | ||||
\(83\) | − | 10.0995i | − | 1.10857i | −0.832327 | − | 0.554285i | \(-0.812992\pi\) | ||
0.832327 | − | 0.554285i | \(-0.187008\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.06827 | + | 2.34882i | 0.441266 | + | 0.254765i | ||||
\(86\) | − | 13.2665i | − | 1.43056i | ||||||
\(87\) | −7.14590 | + | 12.3771i | −0.766121 | + | 1.32696i | ||||
\(88\) | −6.93256 | − | 12.0075i | −0.739014 | − | 1.28001i | ||||
\(89\) | 2.16722 | − | 1.25125i | 0.229725 | − | 0.132632i | −0.380720 | − | 0.924690i | \(-0.624324\pi\) |
0.610445 | + | 0.792059i | \(0.290991\pi\) | |||||||
\(90\) | 44.8316 | 4.72566 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.47715 | −0.258261 | ||||||||
\(93\) | −5.45493 | + | 3.14941i | −0.565650 | + | 0.326578i | ||||
\(94\) | −13.7360 | − | 23.7915i | −1.41676 | − | 2.45391i | ||||
\(95\) | 9.46631 | − | 16.3961i | 0.971223 | − | 1.68221i | ||||
\(96\) | − | 10.4383i | − | 1.06535i | ||||||
\(97\) | 4.58314 | + | 2.64607i | 0.465347 | + | 0.268668i | 0.714290 | − | 0.699850i | \(-0.246750\pi\) |
−0.248943 | + | 0.968518i | \(0.580083\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 21.8728i | − | 2.19830i | ||||||
\(100\) | −9.43069 | + | 16.3344i | −0.943069 | + | 1.63344i | ||||
\(101\) | −6.00425 | − | 10.3997i | −0.597445 | − | 1.03480i | −0.993197 | − | 0.116447i | \(-0.962849\pi\) |
0.395752 | − | 0.918357i | \(-0.370484\pi\) | |||||||
\(102\) | −8.96924 | + | 5.17839i | −0.888087 | + | 0.512737i | ||||
\(103\) | −8.36022 | −0.823756 | −0.411878 | − | 0.911239i | \(-0.635127\pi\) | ||||
−0.411878 | + | 0.911239i | \(0.635127\pi\) | |||||||
\(104\) | 7.51336 | + | 11.2575i | 0.736745 | + | 1.10389i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.994162 | + | 0.573980i | −0.0965616 | + | 0.0557498i | ||||
\(107\) | −5.14150 | − | 8.90534i | −0.497048 | − | 0.860912i | 0.502947 | − | 0.864317i | \(-0.332249\pi\) |
−0.999994 | + | 0.00340581i | \(0.998916\pi\) | |||||||
\(108\) | −15.6562 | + | 27.1174i | −1.50652 | + | 2.60937i | ||||
\(109\) | 19.7427i | 1.89101i | 0.325604 | + | 0.945506i | \(0.394432\pi\) | ||||
−0.325604 | + | 0.945506i | \(0.605568\pi\) | |||||||
\(110\) | 24.2169 | + | 13.9816i | 2.30899 | + | 1.33310i | ||||
\(111\) | 3.25655 | + | 1.88017i | 0.309098 | + | 0.178458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.53549 | + | 2.65954i | −0.144446 | + | 0.250189i | −0.929166 | − | 0.369662i | \(-0.879473\pi\) |
0.784720 | + | 0.619851i | \(0.212807\pi\) | |||||||
\(114\) | 20.8702 | + | 36.1482i | 1.95467 | + | 3.38559i | ||||
\(115\) | 1.91488 | − | 1.10556i | 0.178563 | − | 0.103094i | ||||
\(116\) | 17.1677 | 1.59398 | ||||||||
\(117\) | 1.38509 | + | 21.3062i | 0.128052 | + | 1.96976i | ||||
\(118\) | −20.6340 | −1.89951 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −17.9544 | − | 31.0980i | −1.63901 | − | 2.83884i | ||||
\(121\) | 1.32147 | − | 2.28886i | 0.120134 | − | 0.208078i | ||||
\(122\) | 27.0978i | 2.45332i | ||||||||
\(123\) | 0.671174 | + | 0.387503i | 0.0605178 | + | 0.0349399i | ||||
\(124\) | 6.55259 | + | 3.78314i | 0.588440 | + | 0.339736i | ||||
\(125\) | − | 0.822557i | − | 0.0735717i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.23647 | + | 15.9980i | 0.819604 | + | 1.41960i | 0.905974 | + | 0.423333i | \(0.139140\pi\) |
−0.0863703 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(128\) | −17.8094 | + | 10.2823i | −1.57415 | + | 0.908833i | ||||
\(129\) | −16.7631 | −1.47591 | ||||||||
\(130\) | −24.4750 | − | 12.0859i | −2.14660 | − | 1.06001i | ||||
\(131\) | 12.5565 | 1.09707 | 0.548535 | − | 0.836128i | \(-0.315186\pi\) | ||||
0.548535 | + | 0.836128i | \(0.315186\pi\) | |||||||
\(132\) | −34.2814 | + | 19.7924i | −2.98381 | + | 1.72271i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.404107 | + | 0.699934i | −0.0349095 | + | 0.0604650i | ||||
\(135\) | − | 27.9496i | − | 2.40552i | ||||||
\(136\) | 4.76840 | + | 2.75304i | 0.408887 | + | 0.236071i | ||||
\(137\) | 15.3386 | + | 8.85577i | 1.31047 | + | 0.756600i | 0.982174 | − | 0.187975i | \(-0.0601926\pi\) |
0.328295 | + | 0.944575i | \(0.393526\pi\) | |||||||
\(138\) | 4.87479i | 0.414970i | ||||||||
\(139\) | −3.73758 | + | 6.47367i | −0.317017 | + | 0.549090i | −0.979864 | − | 0.199665i | \(-0.936015\pi\) |
0.662847 | + | 0.748755i | \(0.269348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −30.0622 | + | 17.3564i | −2.53169 | + | 1.46167i | ||||
\(142\) | 19.3974 | 1.62780 | ||||||||
\(143\) | −5.89658 | + | 11.9410i | −0.493097 | + | 0.998561i | ||||
\(144\) | 10.0527 | 0.837727 | ||||||||
\(145\) | −13.2709 | + | 7.66194i | −1.10209 | + | 0.636290i | ||||
\(146\) | 0.307096 | + | 0.531906i | 0.0254155 | + | 0.0440209i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.51700i | − | 0.371295i | ||||||
\(149\) | 6.42234 | + | 3.70794i | 0.526139 | + | 0.303766i | 0.739443 | − | 0.673220i | \(-0.235089\pi\) |
−0.213304 | + | 0.976986i | \(0.568422\pi\) | |||||||
\(150\) | 32.1445 | + | 18.5587i | 2.62459 | + | 1.51531i | ||||
\(151\) | − | 6.07902i | − | 0.494703i | −0.968926 | − | 0.247352i | \(-0.920440\pi\) | ||
0.968926 | − | 0.247352i | \(-0.0795603\pi\) | |||||||
\(152\) | 11.0954 | − | 19.2178i | 0.899957 | − | 1.55877i | ||||
\(153\) | 4.34303 | + | 7.52235i | 0.351113 | + | 0.608146i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.75368 | −0.542468 | ||||||||
\(156\) | 32.1400 | − | 21.4505i | 2.57326 | − | 1.71742i | ||||
\(157\) | 9.38366 | 0.748897 | 0.374449 | − | 0.927248i | \(-0.377832\pi\) | ||||
0.374449 | + | 0.927248i | \(0.377832\pi\) | |||||||
\(158\) | −20.7296 | + | 11.9683i | −1.64916 | + | 0.952144i | ||||
\(159\) | 0.725261 | + | 1.25619i | 0.0575170 | + | 0.0996223i | ||||
\(160\) | 5.59604 | − | 9.69262i | 0.442405 | − | 0.766269i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 16.9955 | + | 9.81236i | 1.33529 | + | 0.770932i | ||||
\(163\) | −21.3669 | − | 12.3362i | −1.67358 | − | 0.966244i | −0.965606 | − | 0.260008i | \(-0.916275\pi\) |
−0.707977 | − | 0.706235i | \(-0.750392\pi\) | |||||||
\(164\) | − | 0.930955i | − | 0.0726954i | ||||||
\(165\) | 17.6667 | − | 30.5997i | 1.37535 | − | 2.38218i | ||||
\(166\) | 11.9371 | + | 20.6757i | 0.926499 | + | 1.60474i | ||||
\(167\) | −1.47685 | + | 0.852661i | −0.114282 | + | 0.0659809i | −0.556052 | − | 0.831148i | \(-0.687684\pi\) |
0.441769 | + | 0.897129i | \(0.354351\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.98767 | − | 12.0051i | 0.383667 | − | 0.923472i | ||||
\(170\) | −11.1047 | −0.851691 | ||||||||
\(171\) | 30.3169 | − | 17.5035i | 2.31839 | − | 1.33852i | ||||
\(172\) | 10.0681 | + | 17.4385i | 0.767687 | + | 1.32967i | ||||
\(173\) | −1.44853 | + | 2.50893i | −0.110130 | + | 0.190751i | −0.915823 | − | 0.401583i | \(-0.868460\pi\) |
0.805693 | + | 0.592334i | \(0.201793\pi\) | |||||||
\(174\) | − | 33.7842i | − | 2.56118i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.43023 | + | 3.13515i | 0.409319 | + | 0.236321i | ||||
\(177\) | 26.0724i | 1.95972i | ||||||||
\(178\) | −2.95780 | + | 5.12307i | −0.221697 | + | 0.383990i | ||||
\(179\) | 7.75589 | + | 13.4336i | 0.579702 | + | 1.00407i | 0.995513 | + | 0.0946230i | \(0.0301646\pi\) |
−0.415811 | + | 0.909451i | \(0.636502\pi\) | |||||||
\(180\) | −58.9300 | + | 34.0233i | −4.39238 | + | 2.53594i | ||||
\(181\) | −19.4473 | −1.44551 | −0.722754 | − | 0.691105i | \(-0.757124\pi\) | ||||
−0.722754 | + | 0.691105i | \(0.757124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34.2398 | 2.53108 | ||||||||
\(184\) | 2.24442 | − | 1.29582i | 0.165461 | − | 0.0955289i | ||||
\(185\) | 2.01594 | + | 3.49172i | 0.148215 | + | 0.256716i | ||||
\(186\) | 7.44485 | − | 12.8949i | 0.545883 | − | 0.945496i | ||||
\(187\) | 5.41785i | 0.396192i | ||||||||
\(188\) | 36.1114 | + | 20.8489i | 2.63369 | + | 1.52056i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 44.7546i | 3.24684i | ||||||||
\(191\) | −8.68967 | + | 15.0510i | −0.628763 | + | 1.08905i | 0.359038 | + | 0.933323i | \(0.383105\pi\) |
−0.987800 | + | 0.155726i | \(0.950228\pi\) | |||||||
\(192\) | 17.4081 | + | 30.1516i | 1.25632 | + | 2.17601i | ||||
\(193\) | −10.0967 | + | 5.82935i | −0.726778 | + | 0.419605i | −0.817242 | − | 0.576294i | \(-0.804498\pi\) |
0.0904643 | + | 0.995900i | \(0.471165\pi\) | |||||||
\(194\) | −12.5101 | −0.898169 | ||||||||
\(195\) | −15.2714 | + | 30.9257i | −1.09361 | + | 2.21464i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.36568 | + | 3.09787i | −0.382289 | + | 0.220714i | −0.678814 | − | 0.734311i | \(-0.737506\pi\) |
0.296525 | + | 0.955025i | \(0.404172\pi\) | |||||||
\(198\) | 25.8524 | + | 44.7777i | 1.83725 | + | 3.18221i | ||||
\(199\) | −4.74100 | + | 8.21165i | −0.336081 | + | 0.582109i | −0.983692 | − | 0.179862i | \(-0.942435\pi\) |
0.647611 | + | 0.761971i | \(0.275768\pi\) | |||||||
\(200\) | − | 19.7331i | − | 1.39534i | ||||||
\(201\) | 0.884412 | + | 0.510616i | 0.0623816 | + | 0.0360161i | ||||
\(202\) | 24.5836 | + | 14.1934i | 1.72970 | + | 0.998642i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 7.85990 | − | 13.6137i | 0.550303 | − | 0.953152i | ||||
\(205\) | 0.415486 | + | 0.719643i | 0.0290188 | + | 0.0502621i | ||||
\(206\) | 17.1149 | − | 9.88131i | 1.19245 | − | 0.688464i | ||||
\(207\) | 4.08841 | 0.284164 | ||||||||
\(208\) | −5.48810 | − | 2.71007i | −0.380531 | − | 0.187909i | ||||
\(209\) | 21.8352 | 1.51038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.19094 | + | 2.06276i | 0.0819874 | + | 0.142006i | 0.904104 | − | 0.427314i | \(-0.140540\pi\) |
−0.822116 | + | 0.569320i | \(0.807207\pi\) | |||||||
\(212\) | 0.871201 | − | 1.50896i | 0.0598343 | − | 0.103636i | ||||
\(213\) | − | 24.5100i | − | 1.67939i | ||||||
\(214\) | 21.0512 | + | 12.1539i | 1.43903 | + | 0.830826i | ||||
\(215\) | −15.5656 | − | 8.98683i | −1.06157 | − | 0.612897i | ||||
\(216\) | − | 32.7595i | − | 2.22900i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −23.3348 | − | 40.4171i | −1.58043 | − | 2.73739i | ||||
\(219\) | 0.672099 | − | 0.388036i | 0.0454162 | − | 0.0262211i | ||||
\(220\) | −42.4434 | −2.86153 | ||||||||
\(221\) | −0.343084 | − | 5.27751i | −0.0230783 | − | 0.355003i | ||||
\(222\) | −8.88901 | −0.596592 | ||||||||
\(223\) | −1.99812 | + | 1.15362i | −0.133804 | + | 0.0772518i | −0.565408 | − | 0.824811i | \(-0.691281\pi\) |
0.431604 | + | 0.902063i | \(0.357948\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.5648 | − | 26.9591i | 1.03766 | − | 1.79727i | ||||
\(226\) | − | 7.25944i | − | 0.482891i | ||||||
\(227\) | −4.52103 | − | 2.61022i | −0.300072 | − | 0.173246i | 0.342403 | − | 0.939553i | \(-0.388759\pi\) |
−0.642475 | + | 0.766307i | \(0.722092\pi\) | |||||||
\(228\) | −54.8667 | − | 31.6773i | −3.63363 | − | 2.09788i | ||||
\(229\) | − | 15.9037i | − | 1.05095i | −0.850810 | − | 0.525473i | \(-0.823888\pi\) | ||
0.850810 | − | 0.525473i | \(-0.176112\pi\) | |||||||
\(230\) | −2.61341 | + | 4.52656i | −0.172323 | + | 0.298473i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.5547 | + | 8.98052i | −1.02122 | + | 0.589600i | ||||
\(233\) | −18.5787 | −1.21713 | −0.608564 | − | 0.793505i | \(-0.708254\pi\) | ||||
−0.608564 | + | 0.793505i | \(0.708254\pi\) | |||||||
\(234\) | −28.0183 | − | 41.9807i | −1.83161 | − | 2.74436i | ||||
\(235\) | −37.2196 | −2.42794 | ||||||||
\(236\) | 27.1229 | − | 15.6594i | 1.76555 | − | 1.01934i | ||||
\(237\) | 15.1227 | + | 26.1933i | 0.982324 | + | 1.70144i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.30548i | − | 0.213814i | −0.994269 | − | 0.106907i | \(-0.965905\pi\) | ||
0.994269 | − | 0.106907i | \(-0.0340946\pi\) | |||||||
\(240\) | 14.0636 | + | 8.11962i | 0.907801 | + | 0.524119i | ||||
\(241\) | 11.3994 | + | 6.58143i | 0.734298 | + | 0.423947i | 0.819993 | − | 0.572374i | \(-0.193977\pi\) |
−0.0856942 | + | 0.996321i | \(0.527311\pi\) | |||||||
\(242\) | 6.24763i | 0.401613i | ||||||||
\(243\) | −0.692028 | + | 1.19863i | −0.0443936 | + | 0.0768920i | ||||
\(244\) | −20.5649 | − | 35.6194i | −1.31653 | − | 2.28030i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.83203 | −0.116806 | ||||||||
\(247\) | −21.2696 | + | 1.38271i | −1.35335 | + | 0.0879799i | ||||
\(248\) | −7.91595 | −0.502664 | ||||||||
\(249\) | 26.1251 | − | 15.0833i | 1.65561 | − | 0.955866i | ||||
\(250\) | 0.972216 | + | 1.68393i | 0.0614884 | + | 0.106501i | ||||
\(251\) | 1.86214 | − | 3.22532i | 0.117537 | − | 0.203580i | −0.801254 | − | 0.598324i | \(-0.795833\pi\) |
0.918791 | + | 0.394744i | \(0.129167\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.20846 | + | 1.27505i | 0.138844 | + | 0.0801619i | ||||
\(254\) | −37.8176 | − | 21.8340i | −2.37289 | − | 1.36999i | ||||
\(255\) | 14.0315i | 0.878688i | ||||||||
\(256\) | 12.6500 | − | 21.9105i | 0.790625 | − | 1.36940i | ||||
\(257\) | −8.51637 | − | 14.7508i | −0.531236 | − | 0.920128i | −0.999335 | − | 0.0364524i | \(-0.988394\pi\) |
0.468099 | − | 0.883676i | \(-0.344939\pi\) | |||||||
\(258\) | 34.3173 | − | 19.8131i | 2.13650 | − | 1.23351i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 41.3439 | − | 2.68772i | 2.56404 | − | 0.166685i | ||||
\(261\) | −28.3343 | −1.75385 | ||||||||
\(262\) | −25.7056 | + | 14.8411i | −1.58810 | + | 0.916888i | ||||
\(263\) | −4.64186 | − | 8.03993i | −0.286229 | − | 0.495763i | 0.686677 | − | 0.726962i | \(-0.259068\pi\) |
−0.972906 | + | 0.231199i | \(0.925735\pi\) | |||||||
\(264\) | 20.7071 | − | 35.8657i | 1.27443 | − | 2.20738i | ||||
\(265\) | 1.55527i | 0.0955396i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.47333 | + | 3.73738i | 0.396162 | + | 0.228724i | ||||
\(268\) | − | 1.22673i | − | 0.0749343i | ||||||
\(269\) | 11.0680 | − | 19.1704i | 0.674829 | − | 1.16884i | −0.301690 | − | 0.953406i | \(-0.597551\pi\) |
0.976519 | − | 0.215431i | \(-0.0691158\pi\) | |||||||
\(270\) | 33.0348 | + | 57.2180i | 2.01044 | + | 3.48218i | ||||
\(271\) | 23.0544 | − | 13.3105i | 1.40045 | − | 0.808553i | 0.406016 | − | 0.913866i | \(-0.366918\pi\) |
0.994439 | + | 0.105313i | \(0.0335845\pi\) | |||||||
\(272\) | −2.49004 | −0.150981 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −41.8681 | −2.52935 | ||||||||
\(275\) | 16.8155 | − | 9.70842i | 1.01401 | − | 0.585440i | ||||
\(276\) | −3.69954 | − | 6.40780i | −0.222686 | − | 0.385704i | ||||
\(277\) | −0.840618 | + | 1.45599i | −0.0505079 | + | 0.0874822i | −0.890174 | − | 0.455621i | \(-0.849417\pi\) |
0.839666 | + | 0.543103i | \(0.182751\pi\) | |||||||
\(278\) | − | 17.6704i | − | 1.05980i | ||||||
\(279\) | −10.8147 | − | 6.24387i | −0.647459 | − | 0.373811i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6730i | 1.71049i | 0.518227 | + | 0.855243i | \(0.326592\pi\) | ||||
−0.518227 | + | 0.855243i | \(0.673408\pi\) | |||||||
\(282\) | 41.0286 | − | 71.0636i | 2.44322 | − | 4.23178i | ||||
\(283\) | 1.79156 | + | 3.10307i | 0.106497 | + | 0.184458i | 0.914349 | − | 0.404927i | \(-0.132703\pi\) |
−0.807852 | + | 0.589386i | \(0.799370\pi\) | |||||||
\(284\) | −25.4975 | + | 14.7210i | −1.51300 | + | 0.873529i | ||||
\(285\) | 56.5504 | 3.34976 | ||||||||
\(286\) | −2.04225 | − | 31.4150i | −0.120761 | − | 1.85761i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 17.9219 | − | 10.3472i | 1.05606 | − | 0.609716i | ||||
\(289\) | 7.42424 | + | 12.8592i | 0.436720 | + | 0.756421i | ||||
\(290\) | 18.1120 | − | 31.3709i | 1.06357 | − | 1.84216i | ||||
\(291\) | 15.8073i | 0.926639i | ||||||||
\(292\) | −0.807341 | − | 0.466118i | −0.0472460 | − | 0.0272775i | ||||
\(293\) | −14.2382 | − | 8.22041i | −0.831803 | − | 0.480242i | 0.0226667 | − | 0.999743i | \(-0.492784\pi\) |
−0.854470 | + | 0.519501i | \(0.826118\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.9776 | + | 24.2099i | −0.813807 | + | 1.40956i | ||||
\(296\) | 2.36288 | + | 4.09262i | 0.137339 | + | 0.237879i | ||||
\(297\) | 27.9160 | − | 16.1173i | 1.61985 | − | 0.935221i | ||||
\(298\) | −17.5303 | −1.01550 | ||||||||
\(299\) | −2.23199 | − | 1.10217i | −0.129079 | − | 0.0637404i | ||||
\(300\) | −56.3376 | −3.25265 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.18506 | + | 12.4449i | 0.413454 | + | 0.716123i | ||||
\(303\) | 17.9343 | − | 31.0631i | 1.03030 | − | 1.78453i | ||||
\(304\) | 10.0355i | 0.575574i | ||||||||
\(305\) | 31.7939 | + | 18.3562i | 1.82051 | + | 1.05107i | ||||
\(306\) | −17.7820 | − | 10.2664i | −1.01653 | − | 0.586893i | ||||
\(307\) | 3.52583i | 0.201230i | 0.994925 | + | 0.100615i | \(0.0320810\pi\) | ||||
−0.994925 | + | 0.100615i | \(0.967919\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4857 | − | 21.6258i | −0.710286 | − | 1.23025i | ||||
\(310\) | 13.8260 | − | 7.98247i | 0.785267 | − | 0.453374i | ||||
\(311\) | −14.3241 | −0.812245 | −0.406123 | − | 0.913819i | \(-0.633119\pi\) | ||||
−0.406123 | + | 0.913819i | \(0.633119\pi\) | |||||||
\(312\) | −17.8995 | + | 36.2479i | −1.01336 | + | 2.05213i | ||||
\(313\) | 6.71897 | 0.379779 | 0.189889 | − | 0.981805i | \(-0.439187\pi\) | ||||
0.189889 | + | 0.981805i | \(0.439187\pi\) | |||||||
\(314\) | −19.2101 | + | 11.0910i | −1.08409 | + | 0.625899i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.1657 | − | 31.4640i | 1.02190 | − | 1.76999i | ||||
\(317\) | 3.95457i | 0.222111i | 0.993814 | + | 0.111055i | \(0.0354231\pi\) | ||||
−0.993814 | + | 0.111055i | \(0.964577\pi\) | |||||||
\(318\) | −2.96949 | − | 1.71444i | −0.166521 | − | 0.0961409i | ||||
\(319\) | −15.3055 | − | 8.83662i | −0.856942 | − | 0.494756i | ||||
\(320\) | 37.3303i | 2.08683i | ||||||||
\(321\) | 15.3573 | − | 26.5996i | 0.857161 | − | 1.48465i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.50944 | + | 4.33558i | −0.417836 | + | 0.241238i | ||||
\(324\) | −29.7869 | −1.65483 | ||||||||
\(325\) | −15.7651 | + | 10.5218i | −0.874491 | + | 0.583643i | ||||
\(326\) | 58.3227 | 3.23020 | ||||||||
\(327\) | −51.0697 | + | 29.4851i | −2.82416 | + | 1.63053i | ||||
\(328\) | 0.486989 | + | 0.843490i | 0.0268895 | + | 0.0465740i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 83.5243i | 4.59786i | ||||||||
\(331\) | 10.2189 | + | 5.89989i | 0.561682 | + | 0.324287i | 0.753820 | − | 0.657080i | \(-0.228209\pi\) |
−0.192138 | + | 0.981368i | \(0.561542\pi\) | |||||||
\(332\) | −31.3821 | − | 18.1184i | −1.72231 | − | 0.994379i | ||||
\(333\) | 7.45507i | 0.408535i | ||||||||
\(334\) | 2.01560 | − | 3.49111i | 0.110288 | − | 0.191025i | ||||
\(335\) | 0.547490 | + | 0.948280i | 0.0299125 | + | 0.0518101i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.7135 | 1.50965 | 0.754824 | − | 0.655927i | \(-0.227722\pi\) | ||||
0.754824 | + | 0.655927i | \(0.227722\pi\) | |||||||
\(338\) | 3.97870 | + | 30.4719i | 0.216413 | + | 1.65745i | ||||
\(339\) | −9.17278 | −0.498197 | ||||||||
\(340\) | 14.5968 | − | 8.42749i | 0.791625 | − | 0.457045i | ||||
\(341\) | −3.89455 | − | 6.74556i | −0.210902 | − | 0.365293i | ||||
\(342\) | −41.3763 | + | 71.6658i | −2.23737 | + | 3.87524i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −18.2444 | − | 10.5334i | −0.983673 | − | 0.567924i | ||||
\(345\) | 5.71961 | + | 3.30222i | 0.307933 | + | 0.177785i | ||||
\(346\) | − | 6.84834i | − | 0.368169i | ||||||
\(347\) | −14.6894 | + | 25.4428i | −0.788569 | + | 1.36584i | 0.138275 | + | 0.990394i | \(0.455844\pi\) |
−0.926844 | + | 0.375447i | \(0.877489\pi\) | |||||||
\(348\) | 25.6393 | + | 44.4086i | 1.37441 | + | 2.38055i | ||||
\(349\) | 17.7934 | − | 10.2730i | 0.952458 | − | 0.549902i | 0.0586146 | − | 0.998281i | \(-0.481332\pi\) |
0.893844 | + | 0.448379i | \(0.147998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −26.1722 | + | 17.4676i | −1.39697 | + | 0.932350i | ||||
\(352\) | 12.9080 | 0.687997 | ||||||||
\(353\) | 3.02392 | − | 1.74586i | 0.160947 | − | 0.0929229i | −0.417363 | − | 0.908740i | \(-0.637046\pi\) |
0.578310 | + | 0.815817i | \(0.303712\pi\) | |||||||
\(354\) | −30.8161 | − | 53.3751i | −1.63786 | − | 2.83685i | ||||
\(355\) | 13.1400 | − | 22.7591i | 0.697397 | − | 1.20793i | ||||
\(356\) | − | 8.97886i | − | 0.475879i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.7555 | − | 18.3341i | −1.67833 | − | 0.968985i | ||||
\(359\) | − | 24.4864i | − | 1.29234i | −0.763193 | − | 0.646170i | \(-0.776370\pi\) | ||
0.763193 | − | 0.646170i | \(-0.223630\pi\) | |||||||
\(360\) | 35.5956 | − | 61.6534i | 1.87605 | − | 3.24942i | ||||
\(361\) | 7.97342 | + | 13.8104i | 0.419654 | + | 0.726861i | ||||
\(362\) | 39.8123 | − | 22.9857i | 2.09249 | − | 1.20810i | ||||
\(363\) | 7.89429 | 0.414343 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.832116 | 0.0435550 | ||||||||
\(366\) | −70.0954 | + | 40.4696i | −3.66394 | + | 2.11538i | ||||
\(367\) | 0.750181 | + | 1.29935i | 0.0391591 | + | 0.0678256i | 0.884941 | − | 0.465704i | \(-0.154199\pi\) |
−0.845782 | + | 0.533529i | \(0.820865\pi\) | |||||||
\(368\) | −0.586014 | + | 1.01501i | −0.0305481 | + | 0.0529108i | ||||
\(369\) | 1.53649i | 0.0799865i | ||||||||
\(370\) | −8.25403 | − | 4.76547i | −0.429107 | − | 0.247745i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 22.6000i | 1.17175i | ||||||||
\(373\) | −4.53512 | + | 7.85506i | −0.234820 | + | 0.406720i | −0.959220 | − | 0.282660i | \(-0.908783\pi\) |
0.724401 | + | 0.689379i | \(0.242117\pi\) | |||||||
\(374\) | −6.40360 | − | 11.0914i | −0.331122 | − | 0.573520i | ||||
\(375\) | 2.12775 | − | 1.22846i | 0.109877 | − | 0.0634374i | ||||
\(376\) | −43.6249 | −2.24978 | ||||||||
\(377\) | 15.4686 | + | 7.63850i | 0.796672 | + | 0.393403i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2870 | − | 12.2900i | 1.09344 | − | 0.631297i | 0.158949 | − | 0.987287i | \(-0.449189\pi\) |
0.934490 | + | 0.355989i | \(0.115856\pi\) | |||||||
\(380\) | −33.9648 | − | 58.8288i | −1.74236 | − | 3.01786i | ||||
\(381\) | −27.5887 | + | 47.7850i | −1.41341 | + | 2.44810i | ||||
\(382\) | − | 41.0828i | − | 2.10198i | ||||||
\(383\) | 4.67467 | + | 2.69892i | 0.238865 | + | 0.137909i | 0.614655 | − | 0.788796i | \(-0.289295\pi\) |
−0.375790 | + | 0.926705i | \(0.622629\pi\) | |||||||
\(384\) | −53.1955 | − | 30.7124i | −2.71462 | − | 1.56729i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.7799 | − | 23.8675i | 0.701380 | − | 1.21483i | ||||
\(387\) | −16.6169 | − | 28.7813i | −0.844684 | − | 1.46304i | ||||
\(388\) | 16.4442 | − | 9.49404i | 0.834826 | − | 0.481987i | ||||
\(389\) | −21.2762 | −1.07875 | −0.539373 | − | 0.842067i | \(-0.681339\pi\) | ||||
−0.539373 | + | 0.842067i | \(0.681339\pi\) | |||||||
\(390\) | −5.28916 | − | 81.3607i | −0.267827 | − | 4.11986i | ||||
\(391\) | −1.01269 | −0.0512140 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.7527 | + | 32.4807i | 0.945951 | + | 1.63843i | ||||
\(394\) | 7.32303 | − | 12.6839i | 0.368929 | − | 0.639004i | ||||
\(395\) | 32.4295i | 1.63171i | ||||||||
\(396\) | −67.9648 | − | 39.2395i | −3.41536 | − | 1.97186i | ||||
\(397\) | 16.3574 | + | 9.44396i | 0.820955 | + | 0.473979i | 0.850746 | − | 0.525578i | \(-0.176151\pi\) |
−0.0297906 | + | 0.999556i | \(0.509484\pi\) | |||||||
\(398\) | − | 22.4144i | − | 1.12353i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.46199 | + | 7.72839i | 0.223099 | + | 0.386420i | ||||
\(401\) | 9.12779 | − | 5.26993i | 0.455820 | − | 0.263168i | −0.254465 | − | 0.967082i | \(-0.581899\pi\) |
0.710285 | + | 0.703914i | \(0.248566\pi\) | |||||||
\(402\) | −2.41408 | −0.120403 | ||||||||
\(403\) | 4.22083 | + | 6.32421i | 0.210255 | + | 0.315031i | ||||
\(404\) | −43.0861 | −2.14361 | ||||||||
\(405\) | 23.0258 | − | 13.2939i | 1.14416 | − | 0.660581i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.32501 | + | 4.02704i | −0.115247 | + | 0.199613i | ||||
\(408\) | 16.4463i | 0.814212i | ||||||||
\(409\) | 28.2798 | + | 16.3274i | 1.39835 | + | 0.807337i | 0.994220 | − | 0.107366i | \(-0.0342415\pi\) |
0.404128 | + | 0.914702i | \(0.367575\pi\) | |||||||
\(410\) | −1.70116 | − | 0.982163i | −0.0840141 | − | 0.0485056i | ||||
\(411\) | 52.9031i | 2.60952i | ||||||||
\(412\) | −14.9981 | + | 25.9775i | −0.738904 | + | 1.27982i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.36974 | + | 4.83227i | −0.411350 | + | 0.237493i | ||||
\(415\) | 32.3451 | 1.58776 | ||||||||
\(416\) | −12.5736 | + | 0.817394i | −0.616471 | + | 0.0400760i | ||||
\(417\) | −22.3278 | −1.09340 | ||||||||
\(418\) | −44.7008 | + | 25.8080i | −2.18639 | + | 1.26231i | ||||
\(419\) | 18.0683 | + | 31.2952i | 0.882693 | + | 1.52887i | 0.848336 | + | 0.529459i | \(0.177605\pi\) |
0.0343572 | + | 0.999410i | \(0.489062\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 36.6781i | − | 1.78758i | −0.448485 | − | 0.893791i | \(-0.648036\pi\) | ||
0.448485 | − | 0.893791i | \(-0.351964\pi\) | |||||||
\(422\) | −4.87614 | − | 2.81524i | −0.237367 | − | 0.137044i | ||||
\(423\) | −59.5999 | − | 34.4100i | −2.89784 | − | 1.67307i | ||||
\(424\) | 1.82293i | 0.0885291i | ||||||||
\(425\) | −3.85538 | + | 6.67772i | −0.187013 | + | 0.323917i | ||||
\(426\) | 28.9694 | + | 50.1765i | 1.40357 | + | 2.43106i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −36.8951 | −1.78339 | ||||||||
\(429\) | −39.6949 | + | 2.58052i | −1.91649 | + | 0.124589i | ||||
\(430\) | 42.4877 | 2.04894 | ||||||||
\(431\) | 8.91469 | − | 5.14690i | 0.429405 | − | 0.247917i | −0.269688 | − | 0.962948i | \(-0.586921\pi\) |
0.699093 | + | 0.715030i | \(0.253587\pi\) | |||||||
\(432\) | 7.40751 | + | 12.8302i | 0.356394 | + | 0.617292i | ||||
\(433\) | 13.9823 | − | 24.2180i | 0.671946 | − | 1.16385i | −0.305405 | − | 0.952223i | \(-0.598792\pi\) |
0.977351 | − | 0.211623i | \(-0.0678748\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −39.6392 | − | 22.8857i | −1.90055 | − | 1.09728i | ||||
\(436\) | 61.3461 | + | 35.4182i | 2.93795 | + | 1.69622i | ||||
\(437\) | 4.08139i | 0.195239i | ||||||||
\(438\) | −0.917275 | + | 1.58877i | −0.0438291 | + | 0.0759142i | ||||
\(439\) | 8.37605 | + | 14.5077i | 0.399767 | + | 0.692417i | 0.993697 | − | 0.112100i | \(-0.0357577\pi\) |
−0.593930 | + | 0.804517i | \(0.702424\pi\) | |||||||
\(440\) | 38.4557 | − | 22.2024i | 1.83331 | − | 1.05846i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.94008 | + | 10.3985i | 0.330106 | + | 0.494608i | ||||
\(443\) | 6.02660 | 0.286332 | 0.143166 | − | 0.989699i | \(-0.454272\pi\) | ||||
0.143166 | + | 0.989699i | \(0.454272\pi\) | |||||||
\(444\) | 11.6844 | − | 6.74599i | 0.554517 | − | 0.320150i | ||||
\(445\) | 4.00727 | + | 6.94080i | 0.189963 | + | 0.329026i | ||||
\(446\) | 2.72702 | − | 4.72334i | 0.129128 | − | 0.223657i | ||||
\(447\) | 22.1507i | 1.04769i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9665 | + | 14.9918i | 1.22544 | + | 0.707506i | 0.966072 | − | 0.258274i | \(-0.0831537\pi\) |
0.259364 | + | 0.965780i | \(0.416487\pi\) | |||||||
\(450\) | 73.5871i | 3.46893i | ||||||||
\(451\) | −0.479186 | + | 0.829974i | −0.0225640 | + | 0.0390819i | ||||
\(452\) | 5.50928 | + | 9.54236i | 0.259135 | + | 0.448835i | ||||
\(453\) | 15.7249 | − | 9.07880i | 0.738822 | − | 0.426559i | ||||
\(454\) | 12.3405 | 0.579170 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 66.2825 | 3.10396 | ||||||||
\(457\) | 25.3924 | − | 14.6603i | 1.18780 | − | 0.685779i | 0.229998 | − | 0.973191i | \(-0.426128\pi\) |
0.957807 | + | 0.287412i | \(0.0927948\pi\) | |||||||
\(458\) | 18.7973 | + | 32.5579i | 0.878340 | + | 1.52133i | ||||
\(459\) | −6.40046 | + | 11.0859i | −0.298748 | + | 0.517446i | ||||
\(460\) | − | 7.93341i | − | 0.369897i | ||||||
\(461\) | −7.31156 | − | 4.22133i | −0.340533 | − | 0.196607i | 0.319974 | − | 0.947426i | \(-0.396326\pi\) |
−0.660508 | + | 0.750819i | \(0.729659\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.17390i | − | 0.240452i | −0.992747 | − | 0.120226i | \(-0.961638\pi\) | ||
0.992747 | − | 0.120226i | \(-0.0383619\pi\) | |||||||
\(464\) | 4.06131 | − | 7.03439i | 0.188541 | − | 0.326563i | ||||
\(465\) | −10.0864 | − | 17.4701i | −0.467745 | − | 0.810158i | ||||
\(466\) | 38.0340 | − | 21.9589i | 1.76189 | − | 1.01723i | ||||
\(467\) | −40.3608 | −1.86768 | −0.933839 | − | 0.357694i | \(-0.883563\pi\) | ||||
−0.933839 | + | 0.357694i | \(0.883563\pi\) | |||||||
\(468\) | 68.6890 | + | 33.9192i | 3.17515 | + | 1.56791i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 76.1954 | − | 43.9914i | 3.51463 | − | 2.02917i | ||||
\(471\) | 14.0142 | + | 24.2732i | 0.645739 | + | 1.11845i | ||||
\(472\) | −16.3831 | + | 28.3763i | −0.754092 | + | 1.30613i | ||||
\(473\) | − | 20.7293i | − | 0.953132i | ||||||
\(474\) | −61.9180 | − | 35.7484i | −2.84399 | − | 1.64198i | ||||
\(475\) | 26.9128 | + | 15.5381i | 1.23484 | + | 0.712938i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.43787 | + | 2.49046i | −0.0658356 | + | 0.114031i | ||||
\(478\) | 3.90689 | + | 6.76693i | 0.178697 | + | 0.309512i | ||||
\(479\) | −6.50156 | + | 3.75368i | −0.297064 | + | 0.171510i | −0.641123 | − | 0.767438i | \(-0.721531\pi\) |
0.344059 | + | 0.938948i | \(0.388198\pi\) | |||||||
\(480\) | 33.4299 | 1.52586 | ||||||||
\(481\) | 2.00978 | − | 4.06996i | 0.0916379 | − | 0.185574i | ||||
\(482\) | −31.1156 | −1.41727 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.74140 | − | 8.21235i | −0.215518 | − | 0.373289i | ||||
\(485\) | −8.47440 | + | 14.6781i | −0.384803 | + | 0.666498i | ||||
\(486\) | − | 3.27176i | − | 0.148410i | ||||||
\(487\) | −4.00620 | − | 2.31298i | −0.181538 | − | 0.104811i | 0.406477 | − | 0.913661i | \(-0.366757\pi\) |
−0.588015 | + | 0.808850i | \(0.700091\pi\) | |||||||
\(488\) | 37.2655 | + | 21.5152i | 1.68693 | + | 0.973950i | ||||
\(489\) | − | 73.6946i | − | 3.33258i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.5862 | + | 28.7282i | 0.748525 | + | 1.29648i | 0.948529 | + | 0.316689i | \(0.102571\pi\) |
−0.200004 | + | 0.979795i | \(0.564096\pi\) | |||||||
\(492\) | 2.40815 | − | 1.39035i | 0.108568 | − | 0.0626818i | ||||
\(493\) | 7.01835 | 0.316090 | ||||||||
\(494\) | 41.9086 | − | 27.9702i | 1.88556 | − | 1.25844i | ||||
\(495\) | 70.0505 | 3.14853 | ||||||||
\(496\) | 3.10026 | − | 1.78994i | 0.139206 | − | 0.0803705i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −35.6553 | + | 61.7568i | −1.59775 | + | 2.76739i | ||||
\(499\) | 28.3940i | 1.27109i | 0.772063 | + | 0.635546i | \(0.219225\pi\) | ||||
−0.772063 | + | 0.635546i | \(0.780775\pi\) | |||||||
\(500\) | −2.55591 | − | 1.47565i | −0.114304 | − | 0.0659933i | ||||
\(501\) | −4.41125 | − | 2.54684i | −0.197080 | − | 0.113784i | ||||
\(502\) | 8.80378i | 0.392932i | ||||||||
\(503\) | 15.2455 | − | 26.4059i | 0.679762 | − | 1.17738i | −0.295290 | − | 0.955408i | \(-0.595416\pi\) |
0.975052 | − | 0.221975i | \(-0.0712503\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.3063 | − | 19.2294i | 1.48211 | − | 0.855696i | ||||
\(506\) | −6.02817 | −0.267985 | ||||||||
\(507\) | 38.5033 | − | 5.02735i | 1.70999 | − | 0.223272i | ||||
\(508\) | 66.2804 | 2.94072 | ||||||||
\(509\) | 15.3716 | − | 8.87482i | 0.681336 | − | 0.393370i | −0.119022 | − | 0.992892i | \(-0.537976\pi\) |
0.800358 | + | 0.599522i | \(0.204643\pi\) | |||||||
\(510\) | −16.5845 | − | 28.7251i | −0.734373 | − | 1.27197i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.6773i | 0.825428i | ||||||||
\(513\) | 44.6789 | + | 25.7954i | 1.97262 | + | 1.13889i | ||||
\(514\) | 34.8692 | + | 20.1317i | 1.53801 | + | 0.887973i | ||||
\(515\) | − | 26.7747i | − | 1.17983i | ||||||
\(516\) | −30.0728 | + | 52.0876i | −1.32388 | + | 2.29303i | ||||
\(517\) | −21.4629 | − | 37.1748i | −0.943937 | − | 1.63495i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.65333 | −0.379839 | ||||||||
\(520\) | −36.0536 | + | 24.0625i | −1.58106 | + | 1.05521i | ||||
\(521\) | −3.82051 | −0.167380 | −0.0836898 | − | 0.996492i | \(-0.526670\pi\) | ||||
−0.0836898 | + | 0.996492i | \(0.526670\pi\) | |||||||
\(522\) | 58.0056 | − | 33.4895i | 2.53884 | − | 1.46580i | ||||
\(523\) | 9.98769 | + | 17.2992i | 0.436731 | + | 0.756441i | 0.997435 | − | 0.0715758i | \(-0.0228028\pi\) |
−0.560704 | + | 0.828016i | \(0.689469\pi\) | |||||||
\(524\) | 22.5262 | − | 39.0166i | 0.984063 | − | 1.70445i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.0055 | + | 10.9728i | 0.828679 | + | 0.478438i | ||||
\(527\) | 2.67878 | + | 1.54659i | 0.116689 | + | 0.0673707i | ||||
\(528\) | 18.7289i | 0.815072i | ||||||||
\(529\) | 11.2617 | − | 19.5058i | 0.489638 | − | 0.848078i | ||||
\(530\) | −1.83824 | − | 3.18393i | −0.0798483 | − | 0.138301i | ||||
\(531\) | −44.7648 | + | 25.8450i | −1.94263 | + | 1.12158i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.414215 | − | 0.838819i | 0.0179416 | − | 0.0363333i | ||||
\(534\) | −17.6695 | −0.764634 | ||||||||
\(535\) | 28.5205 | − | 16.4663i | 1.23305 | − | 0.711901i | ||||
\(536\) | 0.641710 | + | 1.11147i | 0.0277176 | + | 0.0480084i | ||||
\(537\) | −23.1663 | + | 40.1252i | −0.999700 | + | 1.73153i | ||||
\(538\) | 52.3271i | 2.25598i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −86.8469 | − | 50.1411i | −3.73730 | − | 2.15773i | ||||
\(541\) | − | 35.0586i | − | 1.50729i | −0.657284 | − | 0.753643i | \(-0.728295\pi\) | ||
0.657284 | − | 0.753643i | \(-0.271705\pi\) | |||||||
\(542\) | −31.4645 | + | 54.4980i | −1.35151 | + | 2.34089i | ||||
\(543\) | −29.0439 | − | 50.3055i | −1.24639 | − | 2.15882i | ||||
\(544\) | −4.43922 | + | 2.56299i | −0.190330 | + | 0.109887i | ||||
\(545\) | −63.2287 | −2.70842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.0737 | −1.62792 | −0.813958 | − | 0.580924i | \(-0.802691\pi\) | ||||
−0.813958 | + | 0.580924i | \(0.802691\pi\) | |||||||
\(548\) | 55.0346 | − | 31.7743i | 2.35096 | − | 1.35733i | ||||
\(549\) | 33.9412 | + | 58.7878i | 1.44857 | + | 2.50900i | ||||
\(550\) | −22.9496 | + | 39.7499i | −0.978576 | + | 1.69494i | ||||
\(551\) | − | 28.2856i | − | 1.20501i | ||||||
\(552\) | 6.70393 | + | 3.87051i | 0.285338 | + | 0.164740i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 3.97426i | − | 0.168850i | ||||||
\(555\) | −6.02148 | + | 10.4295i | −0.255598 | + | 0.442708i | ||||
\(556\) | 13.4103 | + | 23.2274i | 0.568724 | + | 0.985059i | ||||
\(557\) | −19.4379 | + | 11.2225i | −0.823610 | + | 0.475511i | −0.851660 | − | 0.524095i | \(-0.824404\pi\) |
0.0280499 | + | 0.999607i | \(0.491070\pi\) | |||||||
\(558\) | 29.5196 | 1.24967 | ||||||||
\(559\) | 1.31268 | + | 20.1923i | 0.0555203 | + | 0.854043i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.0147 | + | 8.09137i | −0.591699 | + | 0.341618i | ||||
\(562\) | −33.8899 | − | 58.6990i | −1.42956 | − | 2.47607i | ||||
\(563\) | 15.1092 | − | 26.1700i | 0.636779 | − | 1.10293i | −0.349357 | − | 0.936990i | \(-0.613600\pi\) |
0.986135 | − | 0.165943i | \(-0.0530669\pi\) | |||||||
\(564\) | 124.548i | 5.24444i | ||||||||
\(565\) | −8.51753 | − | 4.91760i | −0.358335 | − | 0.206885i | ||||
\(566\) | −7.33531 | − | 4.23504i | −0.308326 | − | 0.178012i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.4013 | − | 26.6758i | 0.646224 | − | 1.11929i | ||||
\(569\) | −7.50755 | − | 13.0035i | −0.314733 | − | 0.545134i | 0.664648 | − | 0.747157i | \(-0.268582\pi\) |
−0.979381 | + | 0.202023i | \(0.935248\pi\) | |||||||
\(570\) | −115.769 | + | 66.8394i | −4.84904 | + | 2.79960i | ||||
\(571\) | −24.1365 | −1.01008 | −0.505041 | − | 0.863096i | \(-0.668523\pi\) | ||||
−0.505041 | + | 0.863096i | \(0.668523\pi\) | |||||||
\(572\) | 26.5257 | + | 39.7444i | 1.10910 | + | 1.66180i | ||||
\(573\) | −51.9109 | −2.16861 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.81467 | + | 3.14311i | 0.0756771 | + | 0.131077i | ||||
\(576\) | −34.5124 | + | 59.7773i | −1.43802 | + | 2.49072i | ||||
\(577\) | − | 45.4117i | − | 1.89051i | −0.326326 | − | 0.945257i | \(-0.605811\pi\) | ||
0.326326 | − | 0.945257i | \(-0.394189\pi\) | |||||||
\(578\) | −30.3976 | − | 17.5501i | −1.26437 | − | 0.729987i | ||||
\(579\) | −30.1582 | − | 17.4118i | −1.25333 | − | 0.723612i | ||||
\(580\) | 54.9816i | 2.28299i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −18.6833 | − | 32.3605i | −0.774449 | − | 1.34138i | ||||
\(583\) | −1.55340 | + | 0.896858i | −0.0643354 | + | 0.0371441i | ||||
\(584\) | 0.975320 | 0.0403590 | ||||||||
\(585\) | −68.2359 | + | 4.43593i | −2.82121 | + | 0.183403i | ||||
\(586\) | 38.8643 | 1.60547 | ||||||||
\(587\) | 26.2185 | − | 15.1373i | 1.08215 | − | 0.624781i | 0.150677 | − | 0.988583i | \(-0.451855\pi\) |
0.931476 | + | 0.363802i | \(0.118521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.23315 | − | 10.7961i | 0.256832 | − | 0.444847i | ||||
\(590\) | − | 66.0830i | − | 2.72059i | ||||||
\(591\) | −16.0269 | − | 9.25313i | −0.659259 | − | 0.380623i | ||||
\(592\) | −1.85083 | − | 1.06858i | −0.0760685 | − | 0.0439182i | ||||
\(593\) | − | 29.8218i | − | 1.22463i | −0.790612 | − | 0.612317i | \(-0.790238\pi\) | ||
0.790612 | − | 0.612317i | \(-0.209762\pi\) | |||||||
\(594\) | −38.0995 | + | 65.9903i | −1.56324 | + | 2.70761i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.0432 | − | 13.3040i | 0.943885 | − | 0.544952i | ||||
\(597\) | −28.3221 | −1.15915 | ||||||||
\(598\) | 5.87201 | − | 0.381732i | 0.240124 | − | 0.0156102i | ||||
\(599\) | 22.6191 | 0.924191 | 0.462096 | − | 0.886830i | \(-0.347098\pi\) | ||||
0.462096 | + | 0.886830i | \(0.347098\pi\) | |||||||
\(600\) | 51.0446 | − | 29.4706i | 2.08389 | − | 1.20313i | ||||
\(601\) | 22.3912 | + | 38.7826i | 0.913355 | + | 1.58198i | 0.809292 | + | 0.587406i | \(0.199851\pi\) |
0.104062 | + | 0.994571i | \(0.466816\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.02465i | 0.0824500i | ||||||||
\(604\) | −18.8892 | − | 10.9057i | −0.768589 | − | 0.443745i | ||||
\(605\) | 7.33036 | + | 4.23219i | 0.298022 | + | 0.172063i | ||||
\(606\) | 84.7892i | 3.44433i | ||||||||
\(607\) | 2.15014 | − | 3.72415i | 0.0872715 | − | 0.151159i | −0.819085 | − | 0.573672i | \(-0.805519\pi\) |
0.906357 | + | 0.422513i | \(0.138852\pi\) | |||||||
\(608\) | 10.3295 | + | 17.8912i | 0.418915 | + | 0.725582i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −86.7842 | −3.51379 | ||||||||
\(611\) | 23.2610 | + | 34.8527i | 0.941040 | + | 1.40999i | ||||
\(612\) | 31.1653 | 1.25978 | ||||||||
\(613\) | −20.5300 | + | 11.8530i | −0.829201 | + | 0.478739i | −0.853579 | − | 0.520964i | \(-0.825573\pi\) |
0.0243783 | + | 0.999703i | \(0.492239\pi\) | |||||||
\(614\) | −4.16734 | − | 7.21805i | −0.168180 | − | 0.291297i | ||||
\(615\) | −1.24103 | + | 2.14952i | −0.0500431 | + | 0.0866772i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.2808 | + | 5.93560i | 0.413888 | + | 0.238958i | 0.692459 | − | 0.721458i | \(-0.256527\pi\) |
−0.278571 | + | 0.960416i | \(0.589861\pi\) | |||||||
\(618\) | 51.1211 | + | 29.5148i | 2.05639 | + | 1.18726i | ||||
\(619\) | 6.30946i | 0.253599i | 0.991928 | + | 0.126799i | \(0.0404704\pi\) | ||||
−0.991928 | + | 0.126799i | \(0.959530\pi\) | |||||||
\(620\) | −12.1160 | + | 20.9855i | −0.486590 | + | 0.842799i | ||||
\(621\) | 3.01261 | + | 5.21799i | 0.120892 | + | 0.209391i | ||||
\(622\) | 29.3241 | − | 16.9303i | 1.17579 | − | 0.678843i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.18601 | − | 18.2438i | −0.0474782 | − | 0.730336i | ||||
\(625\) | −23.6498 | −0.945994 | ||||||||
\(626\) | −13.7550 | + | 7.94145i | −0.549760 | + | 0.317404i | ||||
\(627\) | 32.6102 | + | 56.4825i | 1.30232 | + | 2.25569i | ||||
\(628\) | 16.8341 | − | 29.1576i | 0.671756 | − | 1.16351i | ||||
\(629\) | − | 1.84661i | − | 0.0736290i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.2293 | − | 6.48324i | −0.447032 | − | 0.258094i | 0.259544 | − | 0.965731i | \(-0.416428\pi\) |
−0.706576 | + | 0.707637i | \(0.749761\pi\) | |||||||
\(632\) | 38.0105i | 1.51198i | ||||||||
\(633\) | −3.55724 | + | 6.16132i | −0.141388 | + | 0.244891i | ||||
\(634\) | −4.67408 | − | 8.09574i | −0.185631 | − | 0.321523i | ||||
\(635\) | −51.2358 | + | 29.5810i | −2.03323 | + | 1.17389i | ||||
\(636\) | 5.20443 | 0.206369 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 41.7776 | 1.65399 | ||||||||
\(639\) | 42.0822 | − | 24.2962i | 1.66475 | − | 0.961141i | ||||
\(640\) | −32.9303 | − | 57.0370i | −1.30169 | − | 2.25459i | ||||
\(641\) | 16.7277 | − | 28.9732i | 0.660704 | − | 1.14437i | −0.319727 | − | 0.947510i | \(-0.603591\pi\) |
0.980431 | − | 0.196863i | \(-0.0630754\pi\) | |||||||
\(642\) | 72.6059i | 2.86553i | ||||||||
\(643\) | −5.35385 | − | 3.09105i | −0.211135 | − | 0.121899i | 0.390704 | − | 0.920517i | \(-0.372232\pi\) |
−0.601839 | + | 0.798618i | \(0.705565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 53.6861i | − | 2.11389i | ||||||
\(646\) | 10.2488 | − | 17.7515i | 0.403234 | − | 0.698422i | ||||
\(647\) | −18.2114 | − | 31.5430i | −0.715963 | − | 1.24008i | −0.962587 | − | 0.270974i | \(-0.912654\pi\) |
0.246623 | − | 0.969111i | \(-0.420679\pi\) | |||||||
\(648\) | 26.9884 | − | 15.5817i | 1.06020 | − | 0.612109i | ||||
\(649\) | −32.2411 | −1.26557 | ||||||||
\(650\) | 19.8380 | − | 40.1735i | 0.778110 | − | 1.57574i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −76.6638 | + | 44.2618i | −3.00238 | + | 1.73343i | ||||
\(653\) | 20.0564 | + | 34.7387i | 0.784867 | + | 1.35943i | 0.929079 | + | 0.369882i | \(0.120602\pi\) |
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(654\) | 69.6995 | − | 120.723i | 2.72547 | − | 4.72065i | ||||
\(655\) | 40.2139i | 1.57129i | ||||||||
\(656\) | −0.381456 | − | 0.220234i | −0.0148933 | − | 0.00859868i | ||||
\(657\) | 1.33247 | + | 0.769303i | 0.0519847 | + | 0.0300134i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0636 | + | 20.8948i | −0.469933 | + | 0.813948i | −0.999409 | − | 0.0343773i | \(-0.989055\pi\) |
0.529476 | + | 0.848325i | \(0.322389\pi\) | |||||||
\(660\) | −63.3877 | − | 109.791i | −2.46736 | − | 4.27360i | ||||
\(661\) | 6.99297 | − | 4.03739i | 0.271995 | − | 0.157036i | −0.357799 | − | 0.933799i | \(-0.616473\pi\) |
0.629794 | + | 0.776762i | \(0.283139\pi\) | |||||||
\(662\) | −27.8934 | −1.08411 | ||||||||
\(663\) | 13.1392 | − | 8.76924i | 0.510286 | − | 0.340569i | ||||
\(664\) | 37.9115 | 1.47125 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.81148 | − | 15.2619i | −0.341438 | − | 0.591388i | ||||
\(667\) | 1.65172 | − | 2.86086i | 0.0639548 | − | 0.110773i | ||||
\(668\) | 6.11864i | 0.236737i | ||||||||
\(669\) | −5.96825 | − | 3.44577i | −0.230746 | − | 0.133221i | ||||
\(670\) | −2.24163 | − | 1.29420i | −0.0866016 | − | 0.0499995i | ||||
\(671\) | 42.3410i | 1.63455i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.130865 | + | 0.226665i | 0.00504449 | + | 0.00873731i | 0.868537 | − | 0.495625i | \(-0.165061\pi\) |
−0.863492 | + | 0.504362i | \(0.831728\pi\) | |||||||
\(674\) | −56.7347 | + | 32.7558i | −2.18534 | + | 1.26171i | ||||
\(675\) | 45.8768 | 1.76580 | ||||||||
\(676\) | −28.3554 | − | 37.0351i | −1.09059 | − | 1.42443i | ||||
\(677\) | 13.8129 | 0.530874 | 0.265437 | − | 0.964128i | \(-0.414484\pi\) | ||||
0.265437 | + | 0.964128i | \(0.414484\pi\) | |||||||
\(678\) | 18.7784 | − | 10.8417i | 0.721181 | − | 0.416374i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −8.81697 | + | 15.2714i | −0.338115 | + | 0.585633i | ||||
\(681\) | − | 15.5931i | − | 0.597528i | ||||||
\(682\) | 15.9458 | + | 9.20629i | 0.610595 | + | 0.352527i | ||||
\(683\) | −15.2050 | − | 8.77861i | −0.581803 | − | 0.335904i | 0.180046 | − | 0.983658i | \(-0.442375\pi\) |
−0.761850 | + | 0.647754i | \(0.775709\pi\) | |||||||
\(684\) | − | 125.604i | − | 4.80258i | ||||||
\(685\) | −28.3618 | + | 49.1240i | −1.08365 | + | 1.87693i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.1390 | − | 23.7516i | 1.56955 | − | 0.906181i | ||||
\(688\) | 9.52716 | 0.363220 | ||||||||
\(689\) | 1.45637 | − | 0.971995i | 0.0554833 | − | 0.0370301i | ||||
\(690\) | −15.6122 | −0.594345 | ||||||||
\(691\) | 32.1966 | − | 18.5887i | 1.22482 | − | 0.707148i | 0.258875 | − | 0.965911i | \(-0.416648\pi\) |
0.965941 | + | 0.258763i | \(0.0833149\pi\) | |||||||
\(692\) | 5.19729 | + | 9.00198i | 0.197571 | + | 0.342204i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 69.4483i | − | 2.63622i | ||||||
\(695\) | −20.7328 | − | 11.9701i | −0.786439 | − | 0.454051i | ||||
\(696\) | −46.4609 | − | 26.8242i | −1.76109 | − | 1.01677i | ||||
\(697\) | − | 0.380586i | − | 0.0144157i | ||||||
\(698\) | −24.2843 | + | 42.0616i | −0.919173 | + | 1.59206i | ||||
\(699\) | −27.7466 | − | 48.0585i | −1.04947 | − | 1.81774i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.8575 | −1.65647 | −0.828237 | − | 0.560378i | \(-0.810656\pi\) | ||||
−0.828237 | + | 0.560378i | \(0.810656\pi\) | |||||||
\(702\) | 32.9338 | − | 66.6935i | 1.24300 | − | 2.51719i | ||||
\(703\) | −7.44227 | −0.280691 | ||||||||
\(704\) | −37.2855 | + | 21.5268i | −1.40525 | + | 0.811322i | ||||
\(705\) | −55.5861 | − | 96.2779i | −2.09349 | − | 3.62604i | ||||
\(706\) | −4.12703 | + | 7.14822i | −0.155323 | + | 0.269027i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 81.0141 | + | 46.7735i | 3.04470 | + | 1.75786i | ||||
\(709\) | 30.8017 | + | 17.7834i | 1.15678 | + | 0.667870i | 0.950531 | − | 0.310629i | \(-0.100540\pi\) |
0.206253 | + | 0.978499i | \(0.433873\pi\) | |||||||
\(710\) | 62.1228i | 2.33143i | ||||||||
\(711\) | −29.9816 | + | 51.9296i | −1.12440 | + | 1.94751i | ||||
\(712\) | 4.69691 | + | 8.13528i | 0.176024 | + | 0.304883i | ||||
\(713\) | 1.26086 | − | 0.727960i | 0.0472197 | − | 0.0272623i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.2428 | − | 18.8846i | −1.43020 | − | 0.706243i | ||||
\(716\) | 55.6558 | 2.07996 | ||||||||
\(717\) | 8.55047 | − | 4.93661i | 0.319323 | − | 0.184361i | ||||
\(718\) | 28.9415 | + | 50.1282i | 1.08009 | + | 1.87077i | ||||
\(719\) | −4.99828 | + | 8.65727i | −0.186404 | + | 0.322862i | −0.944049 | − | 0.329806i | \(-0.893017\pi\) |
0.757645 | + | 0.652667i | \(0.226350\pi\) | |||||||
\(720\) | 32.1952i | 1.19984i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −32.6462 | − | 18.8483i | −1.21496 | − | 0.701460i | ||||
\(723\) | 39.3166i | 1.46220i | ||||||||
\(724\) | −34.8882 | + | 60.4282i | −1.29661 | + | 2.24580i | ||||
\(725\) | −12.5764 | − | 21.7830i | −0.467076 | − | 0.809000i | ||||
\(726\) | −16.1611 | + | 9.33061i | −0.599795 | + | 0.346292i | ||||
\(727\) | 39.8985 | 1.47975 | 0.739877 | − | 0.672742i | \(-0.234884\pi\) | ||||
0.739877 | + | 0.672742i | \(0.234884\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0397 | −1.07555 | ||||||||
\(730\) | −1.70350 | + | 0.983515i | −0.0630493 | + | 0.0364015i | ||||
\(731\) | 4.11597 | + | 7.12907i | 0.152235 | + | 0.263678i | ||||
\(732\) | 61.4258 | − | 106.393i | 2.27036 | − | 3.93238i | ||||
\(733\) | − | 6.81455i | − | 0.251701i | −0.992049 | − | 0.125850i | \(-0.959834\pi\) | ||
0.992049 | − | 0.125850i | \(-0.0401660\pi\) | |||||||
\(734\) | −3.07152 | − | 1.77335i | −0.113372 | − | 0.0654554i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.41272i | 0.0889342i | ||||||||
\(737\) | −0.631427 | + | 1.09366i | −0.0232589 | + | 0.0402856i | ||||
\(738\) | −1.81605 | − | 3.14548i | −0.0668496 | − | 0.115787i | ||||
\(739\) | 22.4174 | − | 12.9427i | 0.824638 | − | 0.476105i | −0.0273755 | − | 0.999625i | \(-0.508715\pi\) |
0.852013 | + | 0.523520i | \(0.175382\pi\) | |||||||
\(740\) | 14.4663 | 0.531791 | ||||||||
\(741\) | −35.3422 | − | 52.9543i | −1.29833 | − | 1.94533i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.38738 | + | 1.37836i | −0.0875846 | + | 0.0505670i | −0.543153 | − | 0.839634i | \(-0.682770\pi\) |
0.455568 | + | 0.890201i | \(0.349436\pi\) | |||||||
\(744\) | −11.8222 | − | 20.4766i | −0.433423 | − | 0.750710i | ||||
\(745\) | −11.8752 | + | 20.5684i | −0.435072 | + | 0.753567i | ||||
\(746\) | − | 21.4410i | − | 0.785012i | ||||||
\(747\) | 51.7944 | + | 29.9035i | 1.89506 | + | 1.09411i | ||||
\(748\) | 16.8347 | + | 9.71954i | 0.615539 | + | 0.355382i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.90394 | + | 5.02978i | −0.106037 | + | 0.183661i | ||||
\(751\) | 13.1874 | + | 22.8413i | 0.481216 | + | 0.833491i | 0.999768 | − | 0.0215556i | \(-0.00686189\pi\) |
−0.518552 | + | 0.855046i | \(0.673529\pi\) | |||||||
\(752\) | 17.0855 | − | 9.86435i | 0.623046 | − | 0.359716i | ||||
\(753\) | 11.1242 | 0.405387 | ||||||||
\(754\) | −40.6954 | + | 2.64556i | −1.48204 | + | 0.0963455i | ||||
\(755\) | 19.4688 | 0.708544 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.39345 | − | 12.8058i | −0.268720 | − | 0.465436i | 0.699812 | − | 0.714327i | \(-0.253267\pi\) |
−0.968531 | + | 0.248891i | \(0.919934\pi\) | |||||||
\(758\) | −29.0523 | + | 50.3201i | −1.05523 | + | 1.82771i | ||||
\(759\) | 7.61699i | 0.276479i | ||||||||
\(760\) | 61.5476 | + | 35.5345i | 2.23257 | + | 1.28897i | ||||
\(761\) | 20.4564 | + | 11.8105i | 0.741543 | + | 0.428130i | 0.822630 | − | 0.568577i | \(-0.192506\pi\) |
−0.0810874 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(762\) | − | 130.433i | − | 4.72510i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 31.1783 | + | 54.0024i | 1.12799 | + | 1.95374i | ||||
\(765\) | −24.0913 | + | 13.9091i | −0.871023 | + | 0.502885i | ||||
\(766\) | −12.7599 | −0.461034 | ||||||||
\(767\) | 31.4059 | − | 2.04166i | 1.13400 | − | 0.0737201i | ||||
\(768\) | 75.5694 | 2.72687 | ||||||||
\(769\) | −0.990062 | + | 0.571613i | −0.0357026 | + | 0.0206129i | −0.517745 | − | 0.855535i | \(-0.673228\pi\) |
0.482042 | + | 0.876148i | \(0.339895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.4378 | − | 44.0596i | 0.916120 | − | 1.58677i | ||||
\(772\) | 41.8310i | 1.50553i | ||||||||
\(773\) | −15.0236 | − | 8.67389i | −0.540362 | − | 0.311978i | 0.204864 | − | 0.978791i | \(-0.434325\pi\) |
−0.745226 | + | 0.666812i | \(0.767658\pi\) | |||||||
\(774\) | 68.0358 | + | 39.2805i | 2.44550 | + | 1.41191i | ||||
\(775\) | − | 11.0856i | − | 0.398206i | ||||||
\(776\) | −9.93280 | + | 17.2041i | −0.356567 | + | 0.617592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 43.5564 | − | 25.1473i | 1.56157 | − | 0.901574i | ||||
\(779\) | −1.53385 | −0.0549560 | ||||||||
\(780\) | 68.6982 | + | 102.933i | 2.45979 | + | 3.68558i | ||||
\(781\) | 30.3090 | 1.08454 | ||||||||
\(782\) | 2.07317 | − | 1.19694i | 0.0741363 | − | 0.0428026i | ||||
\(783\) | −20.8785 | − | 36.1627i | −0.746138 | − | 1.29235i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.0524i | 1.07262i | ||||||||
\(786\) | −76.7808 | − | 44.3294i | −2.73868 | − | 1.58118i | ||||
\(787\) | −0.953072 | − | 0.550256i | −0.0339734 | − | 0.0196145i | 0.482917 | − | 0.875666i | \(-0.339577\pi\) |
−0.516890 | + | 0.856052i | \(0.672911\pi\) | |||||||
\(788\) | 22.2302i | 0.791917i | ||||||||
\(789\) | 13.8649 | − | 24.0147i | 0.493603 | − | 0.854946i | ||||
\(790\) | −38.3299 | − | 66.3894i | −1.36372 | − | 2.36203i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 82.1058 | 2.91750 | ||||||||
\(793\) | −2.68123 | − | 41.2442i | −0.0952134 | − | 1.46462i | ||||
\(794\) | −44.6489 | −1.58453 | ||||||||
\(795\) | −4.02311 | + | 2.32274i | −0.142685 | + | 0.0823792i | ||||
\(796\) | 17.0106 | + | 29.4632i | 0.602924 | + | 1.04429i | ||||
\(797\) | −6.31738 | + | 10.9420i | −0.223773 | + | 0.387587i | −0.955951 | − | 0.293527i | \(-0.905171\pi\) |
0.732177 | + | 0.681114i | \(0.238504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7628 | + | 8.52329i | 0.522269 | + | 0.301532i | ||||
\(800\) | 15.9096 | + | 9.18541i | 0.562489 | + | 0.324753i | ||||
\(801\) | 14.8191i | 0.523608i | ||||||||
\(802\) | −12.4575 | + | 21.5771i | −0.439891 | + | 0.761913i | ||||
\(803\) | 0.479845 | + | 0.831117i | 0.0169334 | + | 0.0293295i | ||||
\(804\) | 3.17325 | − | 1.83207i | 0.111912 | − | 0.0646123i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.1157 | − | 7.95805i | −0.567651 | − | 0.280310i | ||||
\(807\) | 66.1188 | 2.32749 | ||||||||
\(808\) | 39.0381 | − | 22.5387i | 1.37336 | − | 0.792907i | ||||
\(809\) | −20.6805 | − | 35.8197i | −0.727088 | − | 1.25935i | −0.958109 | − | 0.286404i | \(-0.907540\pi\) |
0.231021 | − | 0.972949i | \(-0.425793\pi\) | |||||||
\(810\) | −31.4254 | + | 54.4303i | −1.10417 | + | 1.91249i | ||||
\(811\) | 15.3408i | 0.538687i | 0.963044 | + | 0.269343i | \(0.0868067\pi\) | ||||
−0.963044 | + | 0.269343i | \(0.913193\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 68.8619 | + | 39.7574i | 2.41509 | + | 1.39435i | ||||
\(814\) | − | 10.9921i | − | 0.385275i | ||||||
\(815\) | 39.5082 | − | 68.4302i | 1.38391 | − | 2.39701i | ||||
\(816\) | −3.71879 | − | 6.44113i | −0.130184 | − | 0.225485i | ||||
\(817\) | 28.7319 | − | 16.5884i | 1.00520 | − | 0.580354i | ||||
\(818\) | −77.1922 | −2.69896 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.98150 | 0.104119 | ||||||||
\(821\) | −28.4471 | + | 16.4240i | −0.992812 | + | 0.573200i | −0.906114 | − | 0.423034i | \(-0.860965\pi\) |
−0.0866982 | + | 0.996235i | \(0.527632\pi\) | |||||||
\(822\) | −62.5286 | − | 108.303i | −2.18093 | − | 3.77749i | ||||
\(823\) | −16.2971 | + | 28.2273i | −0.568080 | + | 0.983943i | 0.428676 | + | 0.903458i | \(0.358980\pi\) |
−0.996756 | + | 0.0804850i | \(0.974353\pi\) | |||||||
\(824\) | − | 31.3825i | − | 1.09326i | ||||||
\(825\) | 50.2267 | + | 28.9984i | 1.74867 | + | 1.00959i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.24226i | − | 0.217065i | −0.994093 | − | 0.108532i | \(-0.965385\pi\) | ||
0.994093 | − | 0.108532i | \(-0.0346151\pi\) | |||||||
\(828\) | 7.33454 | − | 12.7038i | 0.254893 | − | 0.441488i | ||||
\(829\) | 10.8516 | + | 18.7954i | 0.376890 | + | 0.652792i | 0.990608 | − | 0.136733i | \(-0.0436602\pi\) |
−0.613718 | + | 0.789525i | \(0.710327\pi\) | |||||||
\(830\) | −66.2165 | + | 38.2301i | −2.29841 | + | 1.32699i | ||||
\(831\) | −5.02174 | −0.174202 | ||||||||
\(832\) | 34.9565 | − | 23.3303i | 1.21190 | − | 0.808831i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 45.7091 | − | 26.3902i | 1.58278 | − | 0.913817i | ||||
\(835\) | −2.73076 | − | 4.72981i | −0.0945017 | − | 0.163682i | ||||
\(836\) | 39.1721 | − | 67.8481i | 1.35480 | − | 2.34657i | ||||
\(837\) | − | 18.4036i | − | 0.636120i | ||||||
\(838\) | −73.9783 | − | 42.7114i | −2.55554 | − | 1.47544i | ||||
\(839\) | 2.86335 | + | 1.65316i | 0.0988540 | + | 0.0570734i | 0.548612 | − | 0.836077i | \(-0.315156\pi\) |
−0.449758 | + | 0.893150i | \(0.648490\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.05294 | − | 5.28784i | 0.105274 | − | 0.182339i | ||||
\(842\) | 43.3515 | + | 75.0870i | 1.49399 | + | 2.58767i | ||||
\(843\) | −74.1700 | + | 42.8221i | −2.55455 | + | 1.47487i | ||||
\(844\) | 8.54608 | 0.294168 | ||||||||
\(845\) | 38.4480 | + | 15.9737i | 1.32265 | + | 0.549511i | ||||
\(846\) | 162.683 | 5.59315 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.412196 | − | 0.713944i | −0.0141549 | − | 0.0245169i | ||||
\(849\) | −5.35126 | + | 9.26865i | −0.183655 | + | 0.318099i | ||||
\(850\) | − | 18.2274i | − | 0.625194i | ||||||
\(851\) | −0.752725 | − | 0.434586i | −0.0258031 | − | 0.0148974i | ||||
\(852\) | −76.1592 | − | 43.9705i | −2.60917 | − | 1.50640i | ||||
\(853\) | − | 1.65549i | − | 0.0566828i | −0.999598 | − | 0.0283414i | \(-0.990977\pi\) | ||
0.999598 | − | 0.0283414i | \(-0.00902255\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 56.0571 | + | 97.0938i | 1.91711 | + | 3.32054i | ||||
\(856\) | 33.4287 | − | 19.3001i | 1.14257 | − | 0.659664i | ||||
\(857\) | 48.2809 | 1.64924 | 0.824622 | − | 0.565683i | \(-0.191388\pi\) | ||||
0.824622 | + | 0.565683i | \(0.191388\pi\) | |||||||
\(858\) | 78.2129 | − | 52.2000i | 2.67015 | − | 1.78208i | ||||
\(859\) | −16.1342 | −0.550492 | −0.275246 | − | 0.961374i | \(-0.588759\pi\) | ||||
−0.275246 | + | 0.961374i | \(0.588759\pi\) | |||||||
\(860\) | −55.8491 | + | 32.2445i | −1.90444 | + | 1.09953i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.1667 | + | 21.0733i | −0.414399 | + | 0.717761i | ||||
\(863\) | − | 1.89828i | − | 0.0646181i | −0.999478 | − | 0.0323090i | \(-0.989714\pi\) | ||
0.999478 | − | 0.0323090i | \(-0.0102861\pi\) | |||||||
\(864\) | 26.4121 | + | 15.2490i | 0.898557 | + | 0.518782i | ||||
\(865\) | −8.03518 | − | 4.63911i | −0.273204 | − | 0.157735i | ||||
\(866\) | 66.1052i | 2.24635i | ||||||||
\(867\) | −22.1757 | + | 38.4094i | −0.753126 | + | 1.30445i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.3906 | + | 18.7007i | −1.09878 | + | 0.634378i | ||||
\(870\) | 108.198 | 3.66827 | ||||||||
\(871\) | 0.545815 | − | 1.10532i | 0.0184942 | − | 0.0374523i | ||||
\(872\) | −74.1101 | −2.50968 | ||||||||
\(873\) | −27.1402 | + | 15.6694i | −0.918556 | + | 0.530329i | ||||
\(874\) | −4.82398 | − | 8.35537i | −0.163173 | − | 0.282625i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 2.78453i | − | 0.0940804i | ||||||
\(877\) | −5.50805 | − | 3.18007i | −0.185994 | − | 0.107383i | 0.404112 | − | 0.914709i | \(-0.367581\pi\) |
−0.590106 | + | 0.807326i | \(0.700914\pi\) | |||||||
\(878\) | −34.2947 | − | 19.8001i | −1.15739 | − | 0.668219i | ||||
\(879\) | − | 49.1076i | − | 1.65636i | ||||||
\(880\) | −10.0407 | + | 17.3910i | −0.338472 | + | 0.586251i | ||||
\(881\) | 10.8083 | + | 18.7205i | 0.364140 | + | 0.630709i | 0.988638 | − | 0.150318i | \(-0.0480296\pi\) |
−0.624498 | + | 0.781027i | \(0.714696\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.14172 | 0.206685 | 0.103343 | − | 0.994646i | \(-0.467046\pi\) | ||||
0.103343 | + | 0.994646i | \(0.467046\pi\) | |||||||
\(884\) | −17.0141 | − | 8.40171i | −0.572248 | − | 0.282580i | ||||
\(885\) | −83.5002 | −2.80683 | ||||||||
\(886\) | −12.3376 | + | 7.12311i | −0.414489 | + | 0.239306i | ||||
\(887\) | −16.9316 | − | 29.3265i | −0.568509 | − | 0.984686i | −0.996714 | − | 0.0810044i | \(-0.974187\pi\) |
0.428205 | − | 0.903682i | \(-0.359146\pi\) | |||||||
\(888\) | −7.05775 | + | 12.2244i | −0.236843 | + | 0.410223i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −16.4073 | − | 9.47275i | −0.549974 | − | 0.317527i | ||||
\(891\) | 26.5559 | + | 15.3321i | 0.889657 | + | 0.513643i | ||||
\(892\) | 8.27828i | 0.277177i | ||||||||
\(893\) | 34.3509 | − | 59.4975i | 1.14951 | − | 1.99101i | ||||
\(894\) | −26.1809 | − | 45.3467i | −0.875621 | − | 1.51662i | ||||
\(895\) | −43.0228 | + | 24.8392i | −1.43809 | + | 0.830284i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.482344 | − | 7.41968i | −0.0161050 | − | 0.247736i | ||||
\(898\) | −70.8778 | −2.36522 | ||||||||
\(899\) | −8.73829 | + | 5.04505i | −0.291438 | + | 0.168262i | ||||
\(900\) | −55.8462 | − | 96.7285i | −1.86154 | − | 3.22428i | ||||
\(901\) | 0.356158 | − | 0.616883i | 0.0118653 | − | 0.0205514i | ||||
\(902\) | − | 2.26548i | − | 0.0754323i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.98335 | − | 5.76389i | −0.332041 | − | 0.191704i | ||||
\(905\) | − | 62.2826i | − | 2.07034i | ||||||
\(906\) | −21.4613 | + | 37.1720i | −0.713003 | + | 1.23496i | ||||
\(907\) | −6.15858 | − | 10.6670i | −0.204492 | − | 0.354191i | 0.745479 | − | 0.666530i | \(-0.232221\pi\) |
−0.949971 | + | 0.312339i | \(0.898888\pi\) | |||||||
\(908\) | −16.2213 | + | 9.36539i | −0.538324 | + | 0.310802i | ||||
\(909\) | 71.1113 | 2.35861 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.7667 | 0.588636 | 0.294318 | − | 0.955708i | \(-0.404908\pi\) | ||||
0.294318 | + | 0.955708i | \(0.404908\pi\) | |||||||
\(912\) | −25.9593 | + | 14.9876i | −0.859599 | + | 0.496290i | ||||
\(913\) | 18.6520 | + | 32.3062i | 0.617292 | + | 1.06918i | ||||
\(914\) | −34.6553 | + | 60.0247i | −1.14630 | + | 1.98544i | ||||
\(915\) | 109.658i | 3.62517i | ||||||||
\(916\) | −49.4172 | − | 28.5310i | −1.63279 | − | 0.942691i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | − | 30.2599i | − | 0.998727i | ||||||
\(919\) | 12.1237 | − | 20.9988i | 0.399924 | − | 0.692688i | −0.593792 | − | 0.804618i | \(-0.702370\pi\) |
0.993716 | + | 0.111930i | \(0.0357033\pi\) | |||||||
\(920\) | 4.15002 | + | 7.18805i | 0.136822 | + | 0.236983i | ||||
\(921\) | −9.12048 | + | 5.26571i | −0.300530 | + | 0.173511i | ||||
\(922\) | 19.9575 | 0.657266 | ||||||||
\(923\) | −29.5239 | + | 1.91931i | −0.971790 | + | 0.0631749i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.73135 | + | 3.30899i | −0.188446 | + | 0.108799i | ||||
\(926\) | 6.11527 | + | 10.5920i | 0.200960 | + | 0.348073i | ||||
\(927\) | 24.7536 | − | 42.8744i | 0.813013 | − | 1.40818i | ||||
\(928\) | − | 16.7211i | − | 0.548898i | ||||||
\(929\) | 40.7740 | + | 23.5409i | 1.33775 | + | 0.772351i | 0.986474 | − | 0.163921i | \(-0.0524141\pi\) |
0.351277 | + | 0.936271i | \(0.385747\pi\) | |||||||
\(930\) | 41.2974 | + | 23.8431i | 1.35420 | + | 0.781846i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −33.3299 | + | 57.7290i | −1.09176 | + | 1.89098i | ||||
\(933\) | −21.3925 | − | 37.0530i | −0.700360 | − | 1.21306i | ||||
\(934\) | 82.6262 | − | 47.7043i | 2.70361 | − | 1.56093i | ||||
\(935\) | −17.3514 | −0.567450 | ||||||||
\(936\) | −79.9790 | + | 5.19933i | −2.61419 | + | 0.169945i | ||||
\(937\) | 29.4852 | 0.963240 | 0.481620 | − | 0.876380i | \(-0.340048\pi\) | ||||
0.481620 | + | 0.876380i | \(0.340048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.0345 | + | 17.3803i | 0.327465 | + | 0.567186i | ||||
\(940\) | −66.7713 | + | 115.651i | −2.17784 | + | 3.77213i | ||||
\(941\) | 48.3265i | 1.57540i | 0.616059 | + | 0.787700i | \(0.288728\pi\) | ||||
−0.616059 | + | 0.787700i | \(0.711272\pi\) | |||||||
\(942\) | −57.3793 | − | 33.1279i | −1.86952 | − | 1.07937i | ||||
\(943\) | −0.155137 | − | 0.0895682i | −0.00505194 | − | 0.00291674i | ||||
\(944\) | − | 14.8180i | − | 0.482285i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.5008 | + | 42.4367i | 0.796591 | + | 1.37974i | ||||
\(947\) | −2.35762 | + | 1.36117i | −0.0766125 | + | 0.0442322i | −0.537817 | − | 0.843062i | \(-0.680751\pi\) |
0.461204 | + | 0.887294i | \(0.347417\pi\) | |||||||
\(948\) | 108.520 | 3.52455 | ||||||||
\(949\) | −0.520046 | − | 0.779201i | −0.0168814 | − | 0.0252939i | ||||
\(950\) | −73.4608 | −2.38338 | ||||||||
\(951\) | −10.2295 | + | 5.90601i | −0.331714 | + | 0.191515i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 19.8192 | − | 34.3279i | 0.642008 | − | 1.11199i | −0.342976 | − | 0.939344i | \(-0.611435\pi\) |
0.984984 | − | 0.172646i | \(-0.0552316\pi\) | |||||||
\(954\) | − | 6.79793i | − | 0.220091i | ||||||
\(955\) | −48.2026 | − | 27.8298i | −1.55980 | − | 0.900551i | ||||
\(956\) | −10.2710 | − | 5.92998i | −0.332189 | − | 0.191789i | ||||
\(957\) | − | 52.7887i | − | 1.70642i | ||||||
\(958\) | 8.87327 | − | 15.3690i | 0.286682 | − | 0.496549i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −96.5645 | + | 55.7516i | −3.11661 | + | 1.79937i | ||||
\(961\) | 26.5530 | 0.856548 | ||||||||
\(962\) | 0.696076 | + | 10.7074i | 0.0224424 | + | 0.345221i | ||||
\(963\) | 60.8934 | 1.96226 | ||||||||
\(964\) | 40.9006 | − | 23.6140i | 1.31732 | − | 0.760555i | ||||
\(965\) | −18.6692 | − | 32.3361i | −0.600984 | − | 1.04093i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.7830i | 0.764810i | 0.923995 | + | 0.382405i | \(0.124904\pi\) | ||||
−0.923995 | + | 0.382405i | \(0.875096\pi\) | |||||||
\(968\) | 8.59188 | + | 4.96053i | 0.276154 | + | 0.159437i | ||||
\(969\) | −22.4302 | − | 12.9501i | −0.720561 | − | 0.416016i | ||||
\(970\) | − | 40.0651i | − | 1.28641i | ||||||
\(971\) | 18.6704 | − | 32.3380i | 0.599160 | − | 1.03778i | −0.393785 | − | 0.919203i | \(-0.628835\pi\) |
0.992945 | − | 0.118573i | \(-0.0378321\pi\) | |||||||
\(972\) | 2.48298 | + | 4.30064i | 0.0796416 | + | 0.137943i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10.9353 | 0.350389 | ||||||||
\(975\) | −50.7619 | − | 25.0666i | −1.62568 | − | 0.802774i | ||||
\(976\) | −19.4599 | −0.622896 | ||||||||
\(977\) | 43.7185 | − | 25.2409i | 1.39868 | − | 0.807527i | 0.404423 | − | 0.914572i | \(-0.367472\pi\) |
0.994254 | + | 0.107045i | \(0.0341389\pi\) | |||||||
\(978\) | 87.1029 | + | 150.867i | 2.78524 | + | 4.82418i | ||||
\(979\) | −4.62164 | + | 8.00492i | −0.147708 | + | 0.255838i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −101.248 | − | 58.4558i | −3.23261 | − | 1.86635i | ||||
\(982\) | −67.9102 | − | 39.2080i | −2.16710 | − | 1.25118i | ||||
\(983\) | − | 7.90270i | − | 0.252057i | −0.992027 | − | 0.126028i | \(-0.959777\pi\) | ||
0.992027 | − | 0.126028i | \(-0.0402231\pi\) | |||||||
\(984\) | −1.45460 | + | 2.51945i | −0.0463710 | + | 0.0803170i | ||||
\(985\) | −9.92135 | − | 17.1843i | −0.316120 | − | 0.547536i | ||||
\(986\) | −14.3679 | + | 8.29530i | −0.457566 | + | 0.264176i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −33.8609 | + | 68.5711i | −1.07726 | + | 2.18154i | ||||
\(989\) | 3.87466 | 0.123207 | ||||||||
\(990\) | −143.406 | + | 82.7957i | −4.55776 | + | 2.63142i | ||||
\(991\) | −2.93261 | − | 5.07942i | −0.0931573 | − | 0.161353i | 0.815681 | − | 0.578502i | \(-0.196363\pi\) |
−0.908838 | + | 0.417149i | \(0.863029\pi\) | |||||||
\(992\) | 3.68474 | − | 6.38216i | 0.116991 | − | 0.202634i | ||||
\(993\) | 35.2451i | 1.11847i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26.2989 | − | 15.1837i | −0.833731 | − | 0.481355i | ||||
\(996\) | − | 108.237i | − | 3.42962i | ||||||
\(997\) | 25.6600 | − | 44.4443i | 0.812659 | − | 1.40757i | −0.0983379 | − | 0.995153i | \(-0.531353\pi\) |
0.910997 | − | 0.412413i | \(-0.135314\pi\) | |||||||
\(998\) | −33.5602 | − | 58.1279i | −1.06233 | − | 1.84001i | ||||
\(999\) | −9.51482 | + | 5.49338i | −0.301035 | + | 0.173803i |
(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 | 637.2.q.j.491.4 | yes | 32 | |
7.2 | even | 3 | 637.2.u.j.361.13 | 32 | |||
7.3 | odd | 6 | 637.2.k.j.569.3 | 32 | |||
7.4 | even | 3 | 637.2.k.j.569.4 | 32 | |||
7.5 | odd | 6 | 637.2.u.j.361.14 | 32 | |||
7.6 | odd | 2 | inner | 637.2.q.j.491.3 | ✓ | 32 | |
13.2 | odd | 12 | 8281.2.a.cx.1.5 | 32 | |||
13.4 | even | 6 | inner | 637.2.q.j.589.4 | yes | 32 | |
13.11 | odd | 12 | 8281.2.a.cx.1.27 | 32 | |||
91.4 | even | 6 | 637.2.u.j.30.13 | 32 | |||
91.17 | odd | 6 | 637.2.u.j.30.14 | 32 | |||
91.30 | even | 6 | 637.2.k.j.459.14 | 32 | |||
91.41 | even | 12 | 8281.2.a.cx.1.6 | 32 | |||
91.69 | odd | 6 | inner | 637.2.q.j.589.3 | yes | 32 | |
91.76 | even | 12 | 8281.2.a.cx.1.28 | 32 | |||
91.82 | odd | 6 | 637.2.k.j.459.13 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.k.j.459.13 | 32 | 91.82 | odd | 6 | |||
637.2.k.j.459.14 | 32 | 91.30 | even | 6 | |||
637.2.k.j.569.3 | 32 | 7.3 | odd | 6 | |||
637.2.k.j.569.4 | 32 | 7.4 | even | 3 | |||
637.2.q.j.491.3 | ✓ | 32 | 7.6 | odd | 2 | inner | |
637.2.q.j.491.4 | yes | 32 | 1.1 | even | 1 | trivial | |
637.2.q.j.589.3 | yes | 32 | 91.69 | odd | 6 | inner | |
637.2.q.j.589.4 | yes | 32 | 13.4 | even | 6 | inner | |
637.2.u.j.30.13 | 32 | 91.4 | even | 6 | |||
637.2.u.j.30.14 | 32 | 91.17 | odd | 6 | |||
637.2.u.j.361.13 | 32 | 7.2 | even | 3 | |||
637.2.u.j.361.14 | 32 | 7.5 | odd | 6 | |||
8281.2.a.cx.1.5 | 32 | 13.2 | odd | 12 | |||
8281.2.a.cx.1.6 | 32 | 91.41 | even | 12 | |||
8281.2.a.cx.1.27 | 32 | 13.11 | odd | 12 | |||
8281.2.a.cx.1.28 | 32 | 91.76 | even | 12 |