Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(209,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.2 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.209 |
Dual form | 546.2.g.a.209.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.618034 | − | 1.61803i | 0.356822 | − | 0.934172i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.23607 | 1.44721 | 0.723607 | − | 0.690212i | \(-0.242483\pi\) | ||||
0.723607 | + | 0.690212i | \(0.242483\pi\) | |||||||
\(6\) | −1.61803 | − | 0.618034i | −0.660560 | − | 0.252311i | ||||
\(7\) | 2.61803 | − | 0.381966i | 0.989524 | − | 0.144370i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.23607 | − | 2.00000i | −0.745356 | − | 0.666667i | ||||
\(10\) | − | 3.23607i | − | 1.02333i | ||||||
\(11\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(12\) | −0.618034 | + | 1.61803i | −0.178411 | + | 0.467086i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | −0.381966 | − | 2.61803i | −0.102085 | − | 0.699699i | ||||
\(15\) | 2.00000 | − | 5.23607i | 0.516398 | − | 1.35195i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.47214 | 0.599581 | 0.299791 | − | 0.954005i | \(-0.403083\pi\) | ||||
0.299791 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(18\) | −2.00000 | + | 2.23607i | −0.471405 | + | 0.527046i | ||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | −3.23607 | −0.723607 | ||||||||
\(21\) | 1.00000 | − | 4.47214i | 0.218218 | − | 0.975900i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.23607i | − | 0.674767i | −0.941367 | − | 0.337383i | \(-0.890458\pi\) | ||
0.941367 | − | 0.337383i | \(-0.109542\pi\) | |||||||
\(24\) | 1.61803 | + | 0.618034i | 0.330280 | + | 0.126156i | ||||
\(25\) | 5.47214 | 1.09443 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | −4.61803 | + | 2.38197i | −0.888741 | + | 0.458410i | ||||
\(28\) | −2.61803 | + | 0.381966i | −0.494762 | + | 0.0721848i | ||||
\(29\) | − | 5.70820i | − | 1.05999i | −0.848002 | − | 0.529993i | \(-0.822194\pi\) | ||
0.848002 | − | 0.529993i | \(-0.177806\pi\) | |||||||
\(30\) | −5.23607 | − | 2.00000i | −0.955971 | − | 0.365148i | ||||
\(31\) | 7.23607i | 1.29964i | 0.760090 | + | 0.649818i | \(0.225155\pi\) | ||||
−0.760090 | + | 0.649818i | \(0.774845\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.47214i | − | 0.423968i | ||||||
\(35\) | 8.47214 | − | 1.23607i | 1.43205 | − | 0.208934i | ||||
\(36\) | 2.23607 | + | 2.00000i | 0.372678 | + | 0.333333i | ||||
\(37\) | −9.23607 | −1.51840 | −0.759200 | − | 0.650857i | \(-0.774410\pi\) | ||||
−0.759200 | + | 0.650857i | \(0.774410\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 1.61803 | + | 0.618034i | 0.259093 | + | 0.0989646i | ||||
\(40\) | 3.23607i | 0.511667i | ||||||||
\(41\) | −5.23607 | −0.817736 | −0.408868 | − | 0.912593i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912593i | \(0.634076\pi\) | |||||||
\(42\) | −4.47214 | − | 1.00000i | −0.690066 | − | 0.154303i | ||||
\(43\) | −10.4721 | −1.59699 | −0.798493 | − | 0.602004i | \(-0.794369\pi\) | ||||
−0.798493 | + | 0.602004i | \(0.794369\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.23607 | − | 6.47214i | −1.07869 | − | 0.964809i | ||||
\(46\) | −3.23607 | −0.477132 | ||||||||
\(47\) | −6.47214 | −0.944058 | −0.472029 | − | 0.881583i | \(-0.656478\pi\) | ||||
−0.472029 | + | 0.881583i | \(0.656478\pi\) | |||||||
\(48\) | 0.618034 | − | 1.61803i | 0.0892055 | − | 0.233543i | ||||
\(49\) | 6.70820 | − | 2.00000i | 0.958315 | − | 0.285714i | ||||
\(50\) | − | 5.47214i | − | 0.773877i | ||||||
\(51\) | 1.52786 | − | 4.00000i | 0.213944 | − | 0.560112i | ||||
\(52\) | − | 1.00000i | − | 0.138675i | ||||||
\(53\) | − | 3.23607i | − | 0.444508i | −0.974989 | − | 0.222254i | \(-0.928659\pi\) | ||
0.974989 | − | 0.222254i | \(-0.0713414\pi\) | |||||||
\(54\) | 2.38197 | + | 4.61803i | 0.324145 | + | 0.628435i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.381966 | + | 2.61803i | 0.0510424 | + | 0.349850i | ||||
\(57\) | 9.70820 | + | 3.70820i | 1.28588 | + | 0.491164i | ||||
\(58\) | −5.70820 | −0.749524 | ||||||||
\(59\) | −4.47214 | −0.582223 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(60\) | −2.00000 | + | 5.23607i | −0.258199 | + | 0.675973i | ||||
\(61\) | 4.47214i | 0.572598i | 0.958140 | + | 0.286299i | \(0.0924251\pi\) | ||||
−0.958140 | + | 0.286299i | \(0.907575\pi\) | |||||||
\(62\) | 7.23607 | 0.918982 | ||||||||
\(63\) | −6.61803 | − | 4.38197i | −0.833794 | − | 0.552076i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.23607i | 0.401385i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.94427 | 0.848378 | 0.424189 | − | 0.905574i | \(-0.360559\pi\) | ||||
0.424189 | + | 0.905574i | \(0.360559\pi\) | |||||||
\(68\) | −2.47214 | −0.299791 | ||||||||
\(69\) | −5.23607 | − | 2.00000i | −0.630349 | − | 0.240772i | ||||
\(70\) | −1.23607 | − | 8.47214i | −0.147738 | − | 1.01261i | ||||
\(71\) | 14.4721i | 1.71753i | 0.512373 | + | 0.858763i | \(0.328767\pi\) | ||||
−0.512373 | + | 0.858763i | \(0.671233\pi\) | |||||||
\(72\) | 2.00000 | − | 2.23607i | 0.235702 | − | 0.263523i | ||||
\(73\) | − | 3.23607i | − | 0.378753i | −0.981905 | − | 0.189377i | \(-0.939353\pi\) | ||
0.981905 | − | 0.189377i | \(-0.0606467\pi\) | |||||||
\(74\) | 9.23607i | 1.07367i | ||||||||
\(75\) | 3.38197 | − | 8.85410i | 0.390516 | − | 1.02238i | ||||
\(76\) | − | 6.00000i | − | 0.688247i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.618034 | − | 1.61803i | 0.0699786 | − | 0.183206i | ||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 3.23607 | 0.361803 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 5.23607i | 0.578227i | ||||||||
\(83\) | 14.0000 | 1.53670 | 0.768350 | − | 0.640030i | \(-0.221078\pi\) | ||||
0.768350 | + | 0.640030i | \(0.221078\pi\) | |||||||
\(84\) | −1.00000 | + | 4.47214i | −0.109109 | + | 0.487950i | ||||
\(85\) | 8.00000 | 0.867722 | ||||||||
\(86\) | 10.4721i | 1.12924i | ||||||||
\(87\) | −9.23607 | − | 3.52786i | −0.990210 | − | 0.378227i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.18034 | 0.655115 | 0.327557 | − | 0.944831i | \(-0.393775\pi\) | ||||
0.327557 | + | 0.944831i | \(0.393775\pi\) | |||||||
\(90\) | −6.47214 | + | 7.23607i | −0.682223 | + | 0.762749i | ||||
\(91\) | 0.381966 | + | 2.61803i | 0.0400409 | + | 0.274445i | ||||
\(92\) | 3.23607i | 0.337383i | ||||||||
\(93\) | 11.7082 | + | 4.47214i | 1.21408 | + | 0.463739i | ||||
\(94\) | 6.47214i | 0.667550i | ||||||||
\(95\) | 19.4164i | 1.99208i | ||||||||
\(96\) | −1.61803 | − | 0.618034i | −0.165140 | − | 0.0630778i | ||||
\(97\) | − | 0.763932i | − | 0.0775655i | −0.999248 | − | 0.0387828i | \(-0.987652\pi\) | ||
0.999248 | − | 0.0387828i | \(-0.0123480\pi\) | |||||||
\(98\) | −2.00000 | − | 6.70820i | −0.202031 | − | 0.677631i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.47214 | −0.547214 | ||||||||
\(101\) | 18.1803 | 1.80901 | 0.904506 | − | 0.426461i | \(-0.140240\pi\) | ||||
0.904506 | + | 0.426461i | \(0.140240\pi\) | |||||||
\(102\) | −4.00000 | − | 1.52786i | −0.396059 | − | 0.151281i | ||||
\(103\) | − | 7.70820i | − | 0.759512i | −0.925087 | − | 0.379756i | \(-0.876008\pi\) | ||
0.925087 | − | 0.379756i | \(-0.123992\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 3.23607 | − | 14.4721i | 0.315808 | − | 1.41234i | ||||
\(106\) | −3.23607 | −0.314315 | ||||||||
\(107\) | − | 2.47214i | − | 0.238990i | −0.992835 | − | 0.119495i | \(-0.961872\pi\) | ||
0.992835 | − | 0.119495i | \(-0.0381276\pi\) | |||||||
\(108\) | 4.61803 | − | 2.38197i | 0.444371 | − | 0.229205i | ||||
\(109\) | 6.18034 | 0.591969 | 0.295985 | − | 0.955193i | \(-0.404352\pi\) | ||||
0.295985 | + | 0.955193i | \(0.404352\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.70820 | + | 14.9443i | −0.541799 | + | 1.41845i | ||||
\(112\) | 2.61803 | − | 0.381966i | 0.247381 | − | 0.0360924i | ||||
\(113\) | − | 16.0000i | − | 1.50515i | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||
0.658505 | − | 0.752577i | \(-0.271189\pi\) | |||||||
\(114\) | 3.70820 | − | 9.70820i | 0.347305 | − | 0.909257i | ||||
\(115\) | − | 10.4721i | − | 0.976532i | ||||||
\(116\) | 5.70820i | 0.529993i | ||||||||
\(117\) | 2.00000 | − | 2.23607i | 0.184900 | − | 0.206725i | ||||
\(118\) | 4.47214i | 0.411693i | ||||||||
\(119\) | 6.47214 | − | 0.944272i | 0.593300 | − | 0.0865613i | ||||
\(120\) | 5.23607 | + | 2.00000i | 0.477985 | + | 0.182574i | ||||
\(121\) | 11.0000 | 1.00000 | ||||||||
\(122\) | 4.47214 | 0.404888 | ||||||||
\(123\) | −3.23607 | + | 8.47214i | −0.291786 | + | 0.763907i | ||||
\(124\) | − | 7.23607i | − | 0.649818i | ||||||
\(125\) | 1.52786 | 0.136656 | ||||||||
\(126\) | −4.38197 | + | 6.61803i | −0.390377 | + | 0.589581i | ||||
\(127\) | −3.05573 | −0.271152 | −0.135576 | − | 0.990767i | \(-0.543288\pi\) | ||||
−0.135576 | + | 0.990767i | \(0.543288\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −6.47214 | + | 16.9443i | −0.569840 | + | 1.49186i | ||||
\(130\) | 3.23607 | 0.283822 | ||||||||
\(131\) | −5.23607 | −0.457477 | −0.228739 | − | 0.973488i | \(-0.573460\pi\) | ||||
−0.228739 | + | 0.973488i | \(0.573460\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.29180 | + | 15.7082i | 0.198724 | + | 1.36207i | ||||
\(134\) | − | 6.94427i | − | 0.599894i | ||||||
\(135\) | −14.9443 | + | 7.70820i | −1.28620 | + | 0.663417i | ||||
\(136\) | 2.47214i | 0.211984i | ||||||||
\(137\) | 7.52786i | 0.643149i | 0.946884 | + | 0.321574i | \(0.104212\pi\) | ||||
−0.946884 | + | 0.321574i | \(0.895788\pi\) | |||||||
\(138\) | −2.00000 | + | 5.23607i | −0.170251 | + | 0.445724i | ||||
\(139\) | 12.1803i | 1.03312i | 0.856250 | + | 0.516561i | \(0.172788\pi\) | ||||
−0.856250 | + | 0.516561i | \(0.827212\pi\) | |||||||
\(140\) | −8.47214 | + | 1.23607i | −0.716026 | + | 0.104467i | ||||
\(141\) | −4.00000 | + | 10.4721i | −0.336861 | + | 0.881913i | ||||
\(142\) | 14.4721 | 1.21447 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.23607 | − | 2.00000i | −0.186339 | − | 0.166667i | ||||
\(145\) | − | 18.4721i | − | 1.53403i | ||||||
\(146\) | −3.23607 | −0.267819 | ||||||||
\(147\) | 0.909830 | − | 12.0902i | 0.0750415 | − | 0.997180i | ||||
\(148\) | 9.23607 | 0.759200 | ||||||||
\(149\) | − | 17.4164i | − | 1.42681i | −0.700753 | − | 0.713404i | \(-0.747153\pi\) | ||
0.700753 | − | 0.713404i | \(-0.252847\pi\) | |||||||
\(150\) | −8.85410 | − | 3.38197i | −0.722934 | − | 0.276136i | ||||
\(151\) | 3.70820 | 0.301769 | 0.150885 | − | 0.988551i | \(-0.451788\pi\) | ||||
0.150885 | + | 0.988551i | \(0.451788\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | −5.52786 | − | 4.94427i | −0.446901 | − | 0.399721i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.4164i | 1.88085i | ||||||||
\(156\) | −1.61803 | − | 0.618034i | −0.129546 | − | 0.0494823i | ||||
\(157\) | 5.41641i | 0.432276i | 0.976363 | + | 0.216138i | \(0.0693462\pi\) | ||||
−0.976363 | + | 0.216138i | \(0.930654\pi\) | |||||||
\(158\) | 8.94427i | 0.711568i | ||||||||
\(159\) | −5.23607 | − | 2.00000i | −0.415247 | − | 0.158610i | ||||
\(160\) | − | 3.23607i | − | 0.255834i | ||||||
\(161\) | −1.23607 | − | 8.47214i | −0.0974158 | − | 0.667698i | ||||
\(162\) | 8.94427 | − | 1.00000i | 0.702728 | − | 0.0785674i | ||||
\(163\) | −9.41641 | −0.737550 | −0.368775 | − | 0.929519i | \(-0.620223\pi\) | ||||
−0.368775 | + | 0.929519i | \(0.620223\pi\) | |||||||
\(164\) | 5.23607 | 0.408868 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 14.0000i | − | 1.08661i | ||||||
\(167\) | 16.9443 | 1.31119 | 0.655594 | − | 0.755114i | \(-0.272418\pi\) | ||||
0.655594 | + | 0.755114i | \(0.272418\pi\) | |||||||
\(168\) | 4.47214 | + | 1.00000i | 0.345033 | + | 0.0771517i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | − | 8.00000i | − | 0.613572i | ||||||
\(171\) | 12.0000 | − | 13.4164i | 0.917663 | − | 1.02598i | ||||
\(172\) | 10.4721 | 0.798493 | ||||||||
\(173\) | −18.7639 | −1.42660 | −0.713298 | − | 0.700861i | \(-0.752799\pi\) | ||||
−0.713298 | + | 0.700861i | \(0.752799\pi\) | |||||||
\(174\) | −3.52786 | + | 9.23607i | −0.267447 | + | 0.700185i | ||||
\(175\) | 14.3262 | − | 2.09017i | 1.08296 | − | 0.158002i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.76393 | + | 7.23607i | −0.207750 | + | 0.543896i | ||||
\(178\) | − | 6.18034i | − | 0.463236i | ||||||
\(179\) | 10.4721i | 0.782724i | 0.920237 | + | 0.391362i | \(0.127996\pi\) | ||||
−0.920237 | + | 0.391362i | \(0.872004\pi\) | |||||||
\(180\) | 7.23607 | + | 6.47214i | 0.539345 | + | 0.482405i | ||||
\(181\) | 4.47214i | 0.332411i | 0.986091 | + | 0.166206i | \(0.0531515\pi\) | ||||
−0.986091 | + | 0.166206i | \(0.946848\pi\) | |||||||
\(182\) | 2.61803 | − | 0.381966i | 0.194062 | − | 0.0283132i | ||||
\(183\) | 7.23607 | + | 2.76393i | 0.534906 | + | 0.204316i | ||||
\(184\) | 3.23607 | 0.238566 | ||||||||
\(185\) | −29.8885 | −2.19745 | ||||||||
\(186\) | 4.47214 | − | 11.7082i | 0.327913 | − | 0.858487i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 6.47214 | 0.472029 | ||||||||
\(189\) | −11.1803 | + | 8.00000i | −0.813250 | + | 0.581914i | ||||
\(190\) | 19.4164 | 1.40861 | ||||||||
\(191\) | − | 21.7082i | − | 1.57075i | −0.619020 | − | 0.785375i | \(-0.712470\pi\) | ||
0.619020 | − | 0.785375i | \(-0.287530\pi\) | |||||||
\(192\) | −0.618034 | + | 1.61803i | −0.0446028 | + | 0.116772i | ||||
\(193\) | 11.8885 | 0.855756 | 0.427878 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427878 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(194\) | −0.763932 | −0.0548471 | ||||||||
\(195\) | 5.23607 | + | 2.00000i | 0.374963 | + | 0.143223i | ||||
\(196\) | −6.70820 | + | 2.00000i | −0.479157 | + | 0.142857i | ||||
\(197\) | 25.4164i | 1.81084i | 0.424513 | + | 0.905422i | \(0.360445\pi\) | ||||
−0.424513 | + | 0.905422i | \(0.639555\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.7082i | 1.96418i | 0.188406 | + | 0.982091i | \(0.439668\pi\) | ||||
−0.188406 | + | 0.982091i | \(0.560332\pi\) | |||||||
\(200\) | 5.47214i | 0.386938i | ||||||||
\(201\) | 4.29180 | − | 11.2361i | 0.302720 | − | 0.792531i | ||||
\(202\) | − | 18.1803i | − | 1.27916i | ||||||
\(203\) | −2.18034 | − | 14.9443i | −0.153030 | − | 1.04888i | ||||
\(204\) | −1.52786 | + | 4.00000i | −0.106972 | + | 0.280056i | ||||
\(205\) | −16.9443 | −1.18344 | ||||||||
\(206\) | −7.70820 | −0.537056 | ||||||||
\(207\) | −6.47214 | + | 7.23607i | −0.449845 | + | 0.502941i | ||||
\(208\) | 1.00000i | 0.0693375i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −14.4721 | − | 3.23607i | −0.998672 | − | 0.223310i | ||||
\(211\) | −25.8885 | −1.78224 | −0.891120 | − | 0.453767i | \(-0.850080\pi\) | ||||
−0.891120 | + | 0.453767i | \(0.850080\pi\) | |||||||
\(212\) | 3.23607i | 0.222254i | ||||||||
\(213\) | 23.4164 | + | 8.94427i | 1.60447 | + | 0.612851i | ||||
\(214\) | −2.47214 | −0.168992 | ||||||||
\(215\) | −33.8885 | −2.31118 | ||||||||
\(216\) | −2.38197 | − | 4.61803i | −0.162072 | − | 0.314217i | ||||
\(217\) | 2.76393 | + | 18.9443i | 0.187628 | + | 1.28602i | ||||
\(218\) | − | 6.18034i | − | 0.418585i | ||||||
\(219\) | −5.23607 | − | 2.00000i | −0.353821 | − | 0.135147i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.47214i | 0.166294i | ||||||||
\(222\) | 14.9443 | + | 5.70820i | 1.00299 | + | 0.383110i | ||||
\(223\) | − | 8.76393i | − | 0.586876i | −0.955978 | − | 0.293438i | \(-0.905201\pi\) | ||
0.955978 | − | 0.293438i | \(-0.0947995\pi\) | |||||||
\(224\) | −0.381966 | − | 2.61803i | −0.0255212 | − | 0.174925i | ||||
\(225\) | −12.2361 | − | 10.9443i | −0.815738 | − | 0.729618i | ||||
\(226\) | −16.0000 | −1.06430 | ||||||||
\(227\) | 3.52786 | 0.234153 | 0.117076 | − | 0.993123i | \(-0.462648\pi\) | ||||
0.117076 | + | 0.993123i | \(0.462648\pi\) | |||||||
\(228\) | −9.70820 | − | 3.70820i | −0.642942 | − | 0.245582i | ||||
\(229\) | − | 2.94427i | − | 0.194563i | −0.995257 | − | 0.0972815i | \(-0.968985\pi\) | ||
0.995257 | − | 0.0972815i | \(-0.0310147\pi\) | |||||||
\(230\) | −10.4721 | −0.690512 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.70820 | 0.374762 | ||||||||
\(233\) | − | 7.05573i | − | 0.462236i | −0.972926 | − | 0.231118i | \(-0.925762\pi\) | ||
0.972926 | − | 0.231118i | \(-0.0742384\pi\) | |||||||
\(234\) | −2.23607 | − | 2.00000i | −0.146176 | − | 0.130744i | ||||
\(235\) | −20.9443 | −1.36625 | ||||||||
\(236\) | 4.47214 | 0.291111 | ||||||||
\(237\) | −5.52786 | + | 14.4721i | −0.359073 | + | 0.940066i | ||||
\(238\) | −0.944272 | − | 6.47214i | −0.0612081 | − | 0.419526i | ||||
\(239\) | − | 0.583592i | − | 0.0377494i | −0.999822 | − | 0.0188747i | \(-0.993992\pi\) | ||
0.999822 | − | 0.0188747i | \(-0.00600837\pi\) | |||||||
\(240\) | 2.00000 | − | 5.23607i | 0.129099 | − | 0.337987i | ||||
\(241\) | − | 10.6525i | − | 0.686186i | −0.939301 | − | 0.343093i | \(-0.888525\pi\) | ||
0.939301 | − | 0.343093i | \(-0.111475\pi\) | |||||||
\(242\) | − | 11.0000i | − | 0.707107i | ||||||
\(243\) | 15.0902 | + | 3.90983i | 0.968035 | + | 0.250816i | ||||
\(244\) | − | 4.47214i | − | 0.286299i | ||||||
\(245\) | 21.7082 | − | 6.47214i | 1.38689 | − | 0.413490i | ||||
\(246\) | 8.47214 | + | 3.23607i | 0.540164 | + | 0.206324i | ||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | −7.23607 | −0.459491 | ||||||||
\(249\) | 8.65248 | − | 22.6525i | 0.548328 | − | 1.43554i | ||||
\(250\) | − | 1.52786i | − | 0.0966306i | ||||||
\(251\) | 14.7639 | 0.931891 | 0.465946 | − | 0.884813i | \(-0.345714\pi\) | ||||
0.465946 | + | 0.884813i | \(0.345714\pi\) | |||||||
\(252\) | 6.61803 | + | 4.38197i | 0.416897 | + | 0.276038i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.05573i | 0.191733i | ||||||||
\(255\) | 4.94427 | − | 12.9443i | 0.309622 | − | 0.810602i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.47214 | 0.154208 | 0.0771038 | − | 0.997023i | \(-0.475433\pi\) | ||||
0.0771038 | + | 0.997023i | \(0.475433\pi\) | |||||||
\(258\) | 16.9443 | + | 6.47214i | 1.05490 | + | 0.402938i | ||||
\(259\) | −24.1803 | + | 3.52786i | −1.50249 | + | 0.219211i | ||||
\(260\) | − | 3.23607i | − | 0.200692i | ||||||
\(261\) | −11.4164 | + | 12.7639i | −0.706658 | + | 0.790068i | ||||
\(262\) | 5.23607i | 0.323485i | ||||||||
\(263\) | − | 17.7082i | − | 1.09193i | −0.837806 | − | 0.545967i | \(-0.816162\pi\) | ||
0.837806 | − | 0.545967i | \(-0.183838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.4721i | − | 0.643298i | ||||||
\(266\) | 15.7082 | − | 2.29180i | 0.963132 | − | 0.140519i | ||||
\(267\) | 3.81966 | − | 10.0000i | 0.233759 | − | 0.611990i | ||||
\(268\) | −6.94427 | −0.424189 | ||||||||
\(269\) | 8.29180 | 0.505560 | 0.252780 | − | 0.967524i | \(-0.418655\pi\) | ||||
0.252780 | + | 0.967524i | \(0.418655\pi\) | |||||||
\(270\) | 7.70820 | + | 14.9443i | 0.469106 | + | 0.909479i | ||||
\(271\) | 3.81966i | 0.232028i | 0.993248 | + | 0.116014i | \(0.0370117\pi\) | ||||
−0.993248 | + | 0.116014i | \(0.962988\pi\) | |||||||
\(272\) | 2.47214 | 0.149895 | ||||||||
\(273\) | 4.47214 | + | 1.00000i | 0.270666 | + | 0.0605228i | ||||
\(274\) | 7.52786 | 0.454775 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.23607 | + | 2.00000i | 0.315174 | + | 0.120386i | ||||
\(277\) | 32.4721 | 1.95106 | 0.975531 | − | 0.219863i | \(-0.0705610\pi\) | ||||
0.975531 | + | 0.219863i | \(0.0705610\pi\) | |||||||
\(278\) | 12.1803 | 0.730528 | ||||||||
\(279\) | 14.4721 | − | 16.1803i | 0.866424 | − | 0.968692i | ||||
\(280\) | 1.23607 | + | 8.47214i | 0.0738692 | + | 0.506307i | ||||
\(281\) | − | 4.47214i | − | 0.266785i | −0.991063 | − | 0.133393i | \(-0.957413\pi\) | ||
0.991063 | − | 0.133393i | \(-0.0425871\pi\) | |||||||
\(282\) | 10.4721 | + | 4.00000i | 0.623607 | + | 0.238197i | ||||
\(283\) | − | 21.1246i | − | 1.25573i | −0.778323 | − | 0.627864i | \(-0.783929\pi\) | ||
0.778323 | − | 0.627864i | \(-0.216071\pi\) | |||||||
\(284\) | − | 14.4721i | − | 0.858763i | ||||||
\(285\) | 31.4164 | + | 12.0000i | 1.86095 | + | 0.710819i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.7082 | + | 2.00000i | −0.809170 | + | 0.118056i | ||||
\(288\) | −2.00000 | + | 2.23607i | −0.117851 | + | 0.131762i | ||||
\(289\) | −10.8885 | −0.640503 | ||||||||
\(290\) | −18.4721 | −1.08472 | ||||||||
\(291\) | −1.23607 | − | 0.472136i | −0.0724596 | − | 0.0276771i | ||||
\(292\) | 3.23607i | 0.189377i | ||||||||
\(293\) | −14.2918 | −0.834936 | −0.417468 | − | 0.908692i | \(-0.637082\pi\) | ||||
−0.417468 | + | 0.908692i | \(0.637082\pi\) | |||||||
\(294\) | −12.0902 | − | 0.909830i | −0.705113 | − | 0.0530624i | ||||
\(295\) | −14.4721 | −0.842600 | ||||||||
\(296\) | − | 9.23607i | − | 0.536836i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.4164 | −1.00891 | ||||||||
\(299\) | 3.23607 | 0.187147 | ||||||||
\(300\) | −3.38197 | + | 8.85410i | −0.195258 | + | 0.511192i | ||||
\(301\) | −27.4164 | + | 4.00000i | −1.58026 | + | 0.230556i | ||||
\(302\) | − | 3.70820i | − | 0.213383i | ||||||
\(303\) | 11.2361 | − | 29.4164i | 0.645495 | − | 1.68993i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 14.4721i | 0.828672i | ||||||||
\(306\) | −4.94427 | + | 5.52786i | −0.282645 | + | 0.316007i | ||||
\(307\) | − | 18.0000i | − | 1.02731i | −0.857996 | − | 0.513657i | \(-0.828290\pi\) | ||
0.857996 | − | 0.513657i | \(-0.171710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.4721 | − | 4.76393i | −0.709515 | − | 0.271011i | ||||
\(310\) | 23.4164 | 1.32996 | ||||||||
\(311\) | −22.4721 | −1.27428 | −0.637139 | − | 0.770749i | \(-0.719882\pi\) | ||||
−0.637139 | + | 0.770749i | \(0.719882\pi\) | |||||||
\(312\) | −0.618034 | + | 1.61803i | −0.0349893 | + | 0.0916031i | ||||
\(313\) | − | 10.4721i | − | 0.591920i | −0.955200 | − | 0.295960i | \(-0.904360\pi\) | ||
0.955200 | − | 0.295960i | \(-0.0956395\pi\) | |||||||
\(314\) | 5.41641 | 0.305666 | ||||||||
\(315\) | −21.4164 | − | 14.1803i | −1.20668 | − | 0.798972i | ||||
\(316\) | 8.94427 | 0.503155 | ||||||||
\(317\) | − | 6.94427i | − | 0.390029i | −0.980800 | − | 0.195015i | \(-0.937525\pi\) | ||
0.980800 | − | 0.195015i | \(-0.0624754\pi\) | |||||||
\(318\) | −2.00000 | + | 5.23607i | −0.112154 | + | 0.293624i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −3.23607 | −0.180902 | ||||||||
\(321\) | −4.00000 | − | 1.52786i | −0.223258 | − | 0.0852771i | ||||
\(322\) | −8.47214 | + | 1.23607i | −0.472134 | + | 0.0688834i | ||||
\(323\) | 14.8328i | 0.825320i | ||||||||
\(324\) | −1.00000 | − | 8.94427i | −0.0555556 | − | 0.496904i | ||||
\(325\) | 5.47214i | 0.303539i | ||||||||
\(326\) | 9.41641i | 0.521527i | ||||||||
\(327\) | 3.81966 | − | 10.0000i | 0.211228 | − | 0.553001i | ||||
\(328\) | − | 5.23607i | − | 0.289113i | ||||||
\(329\) | −16.9443 | + | 2.47214i | −0.934168 | + | 0.136293i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.3607 | 0.789334 | 0.394667 | − | 0.918824i | \(-0.370860\pi\) | ||||
0.394667 | + | 0.918824i | \(0.370860\pi\) | |||||||
\(332\) | −14.0000 | −0.768350 | ||||||||
\(333\) | 20.6525 | + | 18.4721i | 1.13175 | + | 1.01227i | ||||
\(334\) | − | 16.9443i | − | 0.927149i | ||||||
\(335\) | 22.4721 | 1.22778 | ||||||||
\(336\) | 1.00000 | − | 4.47214i | 0.0545545 | − | 0.243975i | ||||
\(337\) | −19.8885 | −1.08340 | −0.541699 | − | 0.840573i | \(-0.682219\pi\) | ||||
−0.541699 | + | 0.840573i | \(0.682219\pi\) | |||||||
\(338\) | 1.00000i | 0.0543928i | ||||||||
\(339\) | −25.8885 | − | 9.88854i | −1.40607 | − | 0.537072i | ||||
\(340\) | −8.00000 | −0.433861 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −13.4164 | − | 12.0000i | −0.725476 | − | 0.648886i | ||||
\(343\) | 16.7984 | − | 7.79837i | 0.907027 | − | 0.421073i | ||||
\(344\) | − | 10.4721i | − | 0.564620i | ||||||
\(345\) | −16.9443 | − | 6.47214i | −0.912249 | − | 0.348448i | ||||
\(346\) | 18.7639i | 1.00876i | ||||||||
\(347\) | 24.3607i | 1.30775i | 0.756603 | + | 0.653875i | \(0.226858\pi\) | ||||
−0.756603 | + | 0.653875i | \(0.773142\pi\) | |||||||
\(348\) | 9.23607 | + | 3.52786i | 0.495105 | + | 0.189113i | ||||
\(349\) | − | 35.3050i | − | 1.88983i | −0.327315 | − | 0.944915i | \(-0.606144\pi\) | ||
0.327315 | − | 0.944915i | \(-0.393856\pi\) | |||||||
\(350\) | −2.09017 | − | 14.3262i | −0.111724 | − | 0.765770i | ||||
\(351\) | −2.38197 | − | 4.61803i | −0.127140 | − | 0.246492i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.1246 | 1.01790 | 0.508950 | − | 0.860796i | \(-0.330034\pi\) | ||||
0.508950 | + | 0.860796i | \(0.330034\pi\) | |||||||
\(354\) | 7.23607 | + | 2.76393i | 0.384593 | + | 0.146901i | ||||
\(355\) | 46.8328i | 2.48563i | ||||||||
\(356\) | −6.18034 | −0.327557 | ||||||||
\(357\) | 2.47214 | − | 11.0557i | 0.130839 | − | 0.585131i | ||||
\(358\) | 10.4721 | 0.553470 | ||||||||
\(359\) | − | 21.8885i | − | 1.15523i | −0.816308 | − | 0.577617i | \(-0.803983\pi\) | ||
0.816308 | − | 0.577617i | \(-0.196017\pi\) | |||||||
\(360\) | 6.47214 | − | 7.23607i | 0.341112 | − | 0.381374i | ||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 4.47214 | 0.235050 | ||||||||
\(363\) | 6.79837 | − | 17.7984i | 0.356822 | − | 0.934172i | ||||
\(364\) | −0.381966 | − | 2.61803i | −0.0200205 | − | 0.137222i | ||||
\(365\) | − | 10.4721i | − | 0.548137i | ||||||
\(366\) | 2.76393 | − | 7.23607i | 0.144473 | − | 0.378235i | ||||
\(367\) | 12.6525i | 0.660454i | 0.943902 | + | 0.330227i | \(0.107125\pi\) | ||||
−0.943902 | + | 0.330227i | \(0.892875\pi\) | |||||||
\(368\) | − | 3.23607i | − | 0.168692i | ||||||
\(369\) | 11.7082 | + | 10.4721i | 0.609505 | + | 0.545158i | ||||
\(370\) | 29.8885i | 1.55383i | ||||||||
\(371\) | −1.23607 | − | 8.47214i | −0.0641735 | − | 0.439851i | ||||
\(372\) | −11.7082 | − | 4.47214i | −0.607042 | − | 0.231869i | ||||
\(373\) | 17.4164 | 0.901787 | 0.450894 | − | 0.892578i | \(-0.351105\pi\) | ||||
0.450894 | + | 0.892578i | \(0.351105\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.944272 | − | 2.47214i | 0.0487620 | − | 0.127661i | ||||
\(376\) | − | 6.47214i | − | 0.333775i | ||||||
\(377\) | 5.70820 | 0.293987 | ||||||||
\(378\) | 8.00000 | + | 11.1803i | 0.411476 | + | 0.575055i | ||||
\(379\) | −30.0000 | −1.54100 | −0.770498 | − | 0.637442i | \(-0.779993\pi\) | ||||
−0.770498 | + | 0.637442i | \(0.779993\pi\) | |||||||
\(380\) | − | 19.4164i | − | 0.996041i | ||||||
\(381\) | −1.88854 | + | 4.94427i | −0.0967530 | + | 0.253303i | ||||
\(382\) | −21.7082 | −1.11069 | ||||||||
\(383\) | −30.4721 | −1.55705 | −0.778527 | − | 0.627611i | \(-0.784033\pi\) | ||||
−0.778527 | + | 0.627611i | \(0.784033\pi\) | |||||||
\(384\) | 1.61803 | + | 0.618034i | 0.0825700 | + | 0.0315389i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 11.8885i | − | 0.605111i | ||||||
\(387\) | 23.4164 | + | 20.9443i | 1.19032 | + | 1.06466i | ||||
\(388\) | 0.763932i | 0.0387828i | ||||||||
\(389\) | − | 32.5410i | − | 1.64990i | −0.565209 | − | 0.824948i | \(-0.691205\pi\) | ||
0.565209 | − | 0.824948i | \(-0.308795\pi\) | |||||||
\(390\) | 2.00000 | − | 5.23607i | 0.101274 | − | 0.265139i | ||||
\(391\) | − | 8.00000i | − | 0.404577i | ||||||
\(392\) | 2.00000 | + | 6.70820i | 0.101015 | + | 0.338815i | ||||
\(393\) | −3.23607 | + | 8.47214i | −0.163238 | + | 0.427363i | ||||
\(394\) | 25.4164 | 1.28046 | ||||||||
\(395\) | −28.9443 | −1.45634 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.8328i | 1.44708i | 0.690284 | + | 0.723539i | \(0.257486\pi\) | ||||
−0.690284 | + | 0.723539i | \(0.742514\pi\) | |||||||
\(398\) | 27.7082 | 1.38889 | ||||||||
\(399\) | 26.8328 | + | 6.00000i | 1.34332 | + | 0.300376i | ||||
\(400\) | 5.47214 | 0.273607 | ||||||||
\(401\) | 18.9443i | 0.946032i | 0.881054 | + | 0.473016i | \(0.156835\pi\) | ||||
−0.881054 | + | 0.473016i | \(0.843165\pi\) | |||||||
\(402\) | −11.2361 | − | 4.29180i | −0.560404 | − | 0.214055i | ||||
\(403\) | −7.23607 | −0.360454 | ||||||||
\(404\) | −18.1803 | −0.904506 | ||||||||
\(405\) | 3.23607 | + | 28.9443i | 0.160802 | + | 1.43825i | ||||
\(406\) | −14.9443 | + | 2.18034i | −0.741672 | + | 0.108208i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.00000 | + | 1.52786i | 0.198030 | + | 0.0756405i | ||||
\(409\) | − | 5.70820i | − | 0.282253i | −0.989992 | − | 0.141126i | \(-0.954928\pi\) | ||
0.989992 | − | 0.141126i | \(-0.0450724\pi\) | |||||||
\(410\) | 16.9443i | 0.836818i | ||||||||
\(411\) | 12.1803 | + | 4.65248i | 0.600812 | + | 0.229490i | ||||
\(412\) | 7.70820i | 0.379756i | ||||||||
\(413\) | −11.7082 | + | 1.70820i | −0.576123 | + | 0.0840552i | ||||
\(414\) | 7.23607 | + | 6.47214i | 0.355633 | + | 0.318088i | ||||
\(415\) | 45.3050 | 2.22393 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | 19.7082 | + | 7.52786i | 0.965115 | + | 0.368641i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.7082 | −0.571983 | −0.285992 | − | 0.958232i | \(-0.592323\pi\) | ||||
−0.285992 | + | 0.958232i | \(0.592323\pi\) | |||||||
\(420\) | −3.23607 | + | 14.4721i | −0.157904 | + | 0.706168i | ||||
\(421\) | 14.7639 | 0.719550 | 0.359775 | − | 0.933039i | \(-0.382853\pi\) | ||||
0.359775 | + | 0.933039i | \(0.382853\pi\) | |||||||
\(422\) | 25.8885i | 1.26023i | ||||||||
\(423\) | 14.4721 | + | 12.9443i | 0.703659 | + | 0.629372i | ||||
\(424\) | 3.23607 | 0.157157 | ||||||||
\(425\) | 13.5279 | 0.656198 | ||||||||
\(426\) | 8.94427 | − | 23.4164i | 0.433351 | − | 1.13453i | ||||
\(427\) | 1.70820 | + | 11.7082i | 0.0826658 | + | 0.566600i | ||||
\(428\) | 2.47214i | 0.119495i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.8885i | 1.63425i | ||||||||
\(431\) | − | 20.0000i | − | 0.963366i | −0.876346 | − | 0.481683i | \(-0.840026\pi\) | ||
0.876346 | − | 0.481683i | \(-0.159974\pi\) | |||||||
\(432\) | −4.61803 | + | 2.38197i | −0.222185 | + | 0.114602i | ||||
\(433\) | − | 19.4164i | − | 0.933093i | −0.884497 | − | 0.466547i | \(-0.845498\pi\) | ||
0.884497 | − | 0.466547i | \(-0.154502\pi\) | |||||||
\(434\) | 18.9443 | − | 2.76393i | 0.909354 | − | 0.132673i | ||||
\(435\) | −29.8885 | − | 11.4164i | −1.43305 | − | 0.547375i | ||||
\(436\) | −6.18034 | −0.295985 | ||||||||
\(437\) | 19.4164 | 0.928813 | ||||||||
\(438\) | −2.00000 | + | 5.23607i | −0.0955637 | + | 0.250189i | ||||
\(439\) | 34.5410i | 1.64855i | 0.566188 | + | 0.824276i | \(0.308418\pi\) | ||||
−0.566188 | + | 0.824276i | \(0.691582\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.0000 | − | 8.94427i | −0.904762 | − | 0.425918i | ||||
\(442\) | 2.47214 | 0.117588 | ||||||||
\(443\) | 29.5279i | 1.40291i | 0.712713 | + | 0.701456i | \(0.247466\pi\) | ||||
−0.712713 | + | 0.701456i | \(0.752534\pi\) | |||||||
\(444\) | 5.70820 | − | 14.9443i | 0.270899 | − | 0.709224i | ||||
\(445\) | 20.0000 | 0.948091 | ||||||||
\(446\) | −8.76393 | −0.414984 | ||||||||
\(447\) | −28.1803 | − | 10.7639i | −1.33288 | − | 0.509117i | ||||
\(448\) | −2.61803 | + | 0.381966i | −0.123690 | + | 0.0180462i | ||||
\(449\) | 18.3607i | 0.866494i | 0.901275 | + | 0.433247i | \(0.142632\pi\) | ||||
−0.901275 | + | 0.433247i | \(0.857368\pi\) | |||||||
\(450\) | −10.9443 | + | 12.2361i | −0.515918 | + | 0.576814i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 16.0000i | 0.752577i | ||||||||
\(453\) | 2.29180 | − | 6.00000i | 0.107678 | − | 0.281905i | ||||
\(454\) | − | 3.52786i | − | 0.165571i | ||||||
\(455\) | 1.23607 | + | 8.47214i | 0.0579478 | + | 0.397180i | ||||
\(456\) | −3.70820 | + | 9.70820i | −0.173653 | + | 0.454628i | ||||
\(457\) | 26.9443 | 1.26040 | 0.630200 | − | 0.776433i | \(-0.282973\pi\) | ||||
0.630200 | + | 0.776433i | \(0.282973\pi\) | |||||||
\(458\) | −2.94427 | −0.137577 | ||||||||
\(459\) | −11.4164 | + | 5.88854i | −0.532872 | + | 0.274854i | ||||
\(460\) | 10.4721i | 0.488266i | ||||||||
\(461\) | −20.7639 | −0.967073 | −0.483536 | − | 0.875324i | \(-0.660648\pi\) | ||||
−0.483536 | + | 0.875324i | \(0.660648\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.7082 | 0.730022 | 0.365011 | − | 0.931003i | \(-0.381065\pi\) | ||||
0.365011 | + | 0.931003i | \(0.381065\pi\) | |||||||
\(464\) | − | 5.70820i | − | 0.264997i | ||||||
\(465\) | 37.8885 | + | 14.4721i | 1.75704 | + | 0.671129i | ||||
\(466\) | −7.05573 | −0.326850 | ||||||||
\(467\) | −18.1803 | −0.841286 | −0.420643 | − | 0.907226i | \(-0.638195\pi\) | ||||
−0.420643 | + | 0.907226i | \(0.638195\pi\) | |||||||
\(468\) | −2.00000 | + | 2.23607i | −0.0924500 | + | 0.103362i | ||||
\(469\) | 18.1803 | − | 2.65248i | 0.839490 | − | 0.122480i | ||||
\(470\) | 20.9443i | 0.966087i | ||||||||
\(471\) | 8.76393 | + | 3.34752i | 0.403821 | + | 0.154246i | ||||
\(472\) | − | 4.47214i | − | 0.205847i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 14.4721 | + | 5.52786i | 0.664727 | + | 0.253903i | ||||
\(475\) | 32.8328i | 1.50647i | ||||||||
\(476\) | −6.47214 | + | 0.944272i | −0.296650 | + | 0.0432806i | ||||
\(477\) | −6.47214 | + | 7.23607i | −0.296339 | + | 0.331317i | ||||
\(478\) | −0.583592 | −0.0266929 | ||||||||
\(479\) | 14.4721 | 0.661249 | 0.330624 | − | 0.943762i | \(-0.392741\pi\) | ||||
0.330624 | + | 0.943762i | \(0.392741\pi\) | |||||||
\(480\) | −5.23607 | − | 2.00000i | −0.238993 | − | 0.0912871i | ||||
\(481\) | − | 9.23607i | − | 0.421128i | ||||||
\(482\) | −10.6525 | −0.485207 | ||||||||
\(483\) | −14.4721 | − | 3.23607i | −0.658505 | − | 0.147246i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | − | 2.47214i | − | 0.112254i | ||||||
\(486\) | 3.90983 | − | 15.0902i | 0.177353 | − | 0.684504i | ||||
\(487\) | 10.7639 | 0.487760 | 0.243880 | − | 0.969805i | \(-0.421580\pi\) | ||||
0.243880 | + | 0.969805i | \(0.421580\pi\) | |||||||
\(488\) | −4.47214 | −0.202444 | ||||||||
\(489\) | −5.81966 | + | 15.2361i | −0.263174 | + | 0.688999i | ||||
\(490\) | −6.47214 | − | 21.7082i | −0.292381 | − | 0.980677i | ||||
\(491\) | 3.41641i | 0.154180i | 0.997024 | + | 0.0770902i | \(0.0245629\pi\) | ||||
−0.997024 | + | 0.0770902i | \(0.975437\pi\) | |||||||
\(492\) | 3.23607 | − | 8.47214i | 0.145893 | − | 0.381953i | ||||
\(493\) | − | 14.1115i | − | 0.635548i | ||||||
\(494\) | 6.00000i | 0.269953i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.23607i | 0.324909i | ||||||||
\(497\) | 5.52786 | + | 37.8885i | 0.247959 | + | 1.69953i | ||||
\(498\) | −22.6525 | − | 8.65248i | −1.01508 | − | 0.387727i | ||||
\(499\) | −10.0000 | −0.447661 | −0.223831 | − | 0.974628i | \(-0.571856\pi\) | ||||
−0.223831 | + | 0.974628i | \(0.571856\pi\) | |||||||
\(500\) | −1.52786 | −0.0683282 | ||||||||
\(501\) | 10.4721 | − | 27.4164i | 0.467861 | − | 1.22487i | ||||
\(502\) | − | 14.7639i | − | 0.658947i | ||||||
\(503\) | −4.94427 | −0.220454 | −0.110227 | − | 0.993906i | \(-0.535158\pi\) | ||||
−0.110227 | + | 0.993906i | \(0.535158\pi\) | |||||||
\(504\) | 4.38197 | − | 6.61803i | 0.195188 | − | 0.294791i | ||||
\(505\) | 58.8328 | 2.61803 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.618034 | + | 1.61803i | −0.0274479 | + | 0.0718594i | ||||
\(508\) | 3.05573 | 0.135576 | ||||||||
\(509\) | −7.23607 | −0.320733 | −0.160367 | − | 0.987058i | \(-0.551268\pi\) | ||||
−0.160367 | + | 0.987058i | \(0.551268\pi\) | |||||||
\(510\) | −12.9443 | − | 4.94427i | −0.573182 | − | 0.218936i | ||||
\(511\) | −1.23607 | − | 8.47214i | −0.0546804 | − | 0.374785i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −14.2918 | − | 27.7082i | −0.630998 | − | 1.22335i | ||||
\(514\) | − | 2.47214i | − | 0.109041i | ||||||
\(515\) | − | 24.9443i | − | 1.09918i | ||||||
\(516\) | 6.47214 | − | 16.9443i | 0.284920 | − | 0.745930i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.52786 | + | 24.1803i | 0.155005 | + | 1.06242i | ||||
\(519\) | −11.5967 | + | 30.3607i | −0.509041 | + | 1.33269i | ||||
\(520\) | −3.23607 | −0.141911 | ||||||||
\(521\) | −34.8328 | −1.52605 | −0.763027 | − | 0.646367i | \(-0.776288\pi\) | ||||
−0.763027 | + | 0.646367i | \(0.776288\pi\) | |||||||
\(522\) | 12.7639 | + | 11.4164i | 0.558662 | + | 0.499683i | ||||
\(523\) | 2.29180i | 0.100213i | 0.998744 | + | 0.0501066i | \(0.0159561\pi\) | ||||
−0.998744 | + | 0.0501066i | \(0.984044\pi\) | |||||||
\(524\) | 5.23607 | 0.228739 | ||||||||
\(525\) | 5.47214 | − | 24.4721i | 0.238824 | − | 1.06805i | ||||
\(526\) | −17.7082 | −0.772114 | ||||||||
\(527\) | 17.8885i | 0.779237i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5279 | 0.544690 | ||||||||
\(530\) | −10.4721 | −0.454881 | ||||||||
\(531\) | 10.0000 | + | 8.94427i | 0.433963 | + | 0.388148i | ||||
\(532\) | −2.29180 | − | 15.7082i | −0.0993620 | − | 0.681037i | ||||
\(533\) | − | 5.23607i | − | 0.226799i | ||||||
\(534\) | −10.0000 | − | 3.81966i | −0.432742 | − | 0.165293i | ||||
\(535\) | − | 8.00000i | − | 0.345870i | ||||||
\(536\) | 6.94427i | 0.299947i | ||||||||
\(537\) | 16.9443 | + | 6.47214i | 0.731199 | + | 0.279293i | ||||
\(538\) | − | 8.29180i | − | 0.357485i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14.9443 | − | 7.70820i | 0.643099 | − | 0.331708i | ||||
\(541\) | −28.6525 | −1.23187 | −0.615933 | − | 0.787798i | \(-0.711221\pi\) | ||||
−0.615933 | + | 0.787798i | \(0.711221\pi\) | |||||||
\(542\) | 3.81966 | 0.164068 | ||||||||
\(543\) | 7.23607 | + | 2.76393i | 0.310529 | + | 0.118612i | ||||
\(544\) | − | 2.47214i | − | 0.105992i | ||||||
\(545\) | 20.0000 | 0.856706 | ||||||||
\(546\) | 1.00000 | − | 4.47214i | 0.0427960 | − | 0.191390i | ||||
\(547\) | 22.4721 | 0.960839 | 0.480420 | − | 0.877039i | \(-0.340484\pi\) | ||||
0.480420 | + | 0.877039i | \(0.340484\pi\) | |||||||
\(548\) | − | 7.52786i | − | 0.321574i | ||||||
\(549\) | 8.94427 | − | 10.0000i | 0.381732 | − | 0.426790i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.2492 | 1.45907 | ||||||||
\(552\) | 2.00000 | − | 5.23607i | 0.0851257 | − | 0.222862i | ||||
\(553\) | −23.4164 | + | 3.41641i | −0.995767 | + | 0.145280i | ||||
\(554\) | − | 32.4721i | − | 1.37961i | ||||||
\(555\) | −18.4721 | + | 48.3607i | −0.784099 | + | 2.05280i | ||||
\(556\) | − | 12.1803i | − | 0.516561i | ||||||
\(557\) | 22.0000i | 0.932170i | 0.884740 | + | 0.466085i | \(0.154336\pi\) | ||||
−0.884740 | + | 0.466085i | \(0.845664\pi\) | |||||||
\(558\) | −16.1803 | − | 14.4721i | −0.684968 | − | 0.612654i | ||||
\(559\) | − | 10.4721i | − | 0.442924i | ||||||
\(560\) | 8.47214 | − | 1.23607i | 0.358013 | − | 0.0522334i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.47214 | −0.188646 | ||||||||
\(563\) | −9.81966 | −0.413849 | −0.206925 | − | 0.978357i | \(-0.566346\pi\) | ||||
−0.206925 | + | 0.978357i | \(0.566346\pi\) | |||||||
\(564\) | 4.00000 | − | 10.4721i | 0.168430 | − | 0.440956i | ||||
\(565\) | − | 51.7771i | − | 2.17828i | ||||||
\(566\) | −21.1246 | −0.887934 | ||||||||
\(567\) | 6.03444 | + | 23.0344i | 0.253423 | + | 0.967356i | ||||
\(568\) | −14.4721 | −0.607237 | ||||||||
\(569\) | 8.36068i | 0.350498i | 0.984524 | + | 0.175249i | \(0.0560730\pi\) | ||||
−0.984524 | + | 0.175249i | \(0.943927\pi\) | |||||||
\(570\) | 12.0000 | − | 31.4164i | 0.502625 | − | 1.31589i | ||||
\(571\) | −22.4721 | −0.940430 | −0.470215 | − | 0.882552i | \(-0.655824\pi\) | ||||
−0.470215 | + | 0.882552i | \(0.655824\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.1246 | − | 13.4164i | −1.46735 | − | 0.560478i | ||||
\(574\) | 2.00000 | + | 13.7082i | 0.0834784 | + | 0.572169i | ||||
\(575\) | − | 17.7082i | − | 0.738483i | ||||||
\(576\) | 2.23607 | + | 2.00000i | 0.0931695 | + | 0.0833333i | ||||
\(577\) | − | 2.87539i | − | 0.119704i | −0.998207 | − | 0.0598520i | \(-0.980937\pi\) | ||
0.998207 | − | 0.0598520i | \(-0.0190629\pi\) | |||||||
\(578\) | 10.8885i | 0.452904i | ||||||||
\(579\) | 7.34752 | − | 19.2361i | 0.305353 | − | 0.799424i | ||||
\(580\) | 18.4721i | 0.767014i | ||||||||
\(581\) | 36.6525 | − | 5.34752i | 1.52060 | − | 0.221853i | ||||
\(582\) | −0.472136 | + | 1.23607i | −0.0195707 | + | 0.0512367i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.23607 | 0.133909 | ||||||||
\(585\) | 6.47214 | − | 7.23607i | 0.267590 | − | 0.299175i | ||||
\(586\) | 14.2918i | 0.590389i | ||||||||
\(587\) | −5.41641 | −0.223559 | −0.111780 | − | 0.993733i | \(-0.535655\pi\) | ||||
−0.111780 | + | 0.993733i | \(0.535655\pi\) | |||||||
\(588\) | −0.909830 | + | 12.0902i | −0.0375208 | + | 0.498590i | ||||
\(589\) | −43.4164 | −1.78894 | ||||||||
\(590\) | 14.4721i | 0.595808i | ||||||||
\(591\) | 41.1246 | + | 15.7082i | 1.69164 | + | 0.646149i | ||||
\(592\) | −9.23607 | −0.379600 | ||||||||
\(593\) | −40.0689 | −1.64543 | −0.822716 | − | 0.568453i | \(-0.807542\pi\) | ||||
−0.822716 | + | 0.568453i | \(0.807542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.9443 | − | 3.05573i | 0.858631 | − | 0.125273i | ||||
\(596\) | 17.4164i | 0.713404i | ||||||||
\(597\) | 44.8328 | + | 17.1246i | 1.83488 | + | 0.700864i | ||||
\(598\) | − | 3.23607i | − | 0.132333i | ||||||
\(599\) | − | 32.5410i | − | 1.32959i | −0.747026 | − | 0.664795i | \(-0.768519\pi\) | ||
0.747026 | − | 0.664795i | \(-0.231481\pi\) | |||||||
\(600\) | 8.85410 | + | 3.38197i | 0.361467 | + | 0.138068i | ||||
\(601\) | − | 3.41641i | − | 0.139358i | −0.997569 | − | 0.0696791i | \(-0.977802\pi\) | ||
0.997569 | − | 0.0696791i | \(-0.0221975\pi\) | |||||||
\(602\) | 4.00000 | + | 27.4164i | 0.163028 | + | 1.11741i | ||||
\(603\) | −15.5279 | − | 13.8885i | −0.632344 | − | 0.565585i | ||||
\(604\) | −3.70820 | −0.150885 | ||||||||
\(605\) | 35.5967 | 1.44721 | ||||||||
\(606\) | −29.4164 | − | 11.2361i | −1.19496 | − | 0.456434i | ||||
\(607\) | − | 23.1246i | − | 0.938599i | −0.883039 | − | 0.469300i | \(-0.844506\pi\) | ||
0.883039 | − | 0.469300i | \(-0.155494\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | −25.5279 | − | 5.70820i | −1.03444 | − | 0.231308i | ||||
\(610\) | 14.4721 | 0.585960 | ||||||||
\(611\) | − | 6.47214i | − | 0.261835i | ||||||
\(612\) | 5.52786 | + | 4.94427i | 0.223451 | + | 0.199860i | ||||
\(613\) | 15.7082 | 0.634448 | 0.317224 | − | 0.948351i | \(-0.397249\pi\) | ||||
0.317224 | + | 0.948351i | \(0.397249\pi\) | |||||||
\(614\) | −18.0000 | −0.726421 | ||||||||
\(615\) | −10.4721 | + | 27.4164i | −0.422277 | + | 1.10554i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 33.7771i | − | 1.35981i | −0.733298 | − | 0.679907i | \(-0.762020\pi\) | ||
0.733298 | − | 0.679907i | \(-0.237980\pi\) | |||||||
\(618\) | −4.76393 | + | 12.4721i | −0.191633 | + | 0.501703i | ||||
\(619\) | − | 8.47214i | − | 0.340524i | −0.985399 | − | 0.170262i | \(-0.945539\pi\) | ||
0.985399 | − | 0.170262i | \(-0.0544614\pi\) | |||||||
\(620\) | − | 23.4164i | − | 0.940426i | ||||||
\(621\) | 7.70820 | + | 14.9443i | 0.309320 | + | 0.599693i | ||||
\(622\) | 22.4721i | 0.901051i | ||||||||
\(623\) | 16.1803 | − | 2.36068i | 0.648252 | − | 0.0945786i | ||||
\(624\) | 1.61803 | + | 0.618034i | 0.0647732 | + | 0.0247412i | ||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | −10.4721 | −0.418551 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 5.41641i | − | 0.216138i | ||||||
\(629\) | −22.8328 | −0.910404 | ||||||||
\(630\) | −14.1803 | + | 21.4164i | −0.564958 | + | 0.853250i | ||||
\(631\) | 25.8197 | 1.02786 | 0.513932 | − | 0.857831i | \(-0.328188\pi\) | ||||
0.513932 | + | 0.857831i | \(0.328188\pi\) | |||||||
\(632\) | − | 8.94427i | − | 0.355784i | ||||||
\(633\) | −16.0000 | + | 41.8885i | −0.635943 | + | 1.66492i | ||||
\(634\) | −6.94427 | −0.275792 | ||||||||
\(635\) | −9.88854 | −0.392415 | ||||||||
\(636\) | 5.23607 | + | 2.00000i | 0.207624 | + | 0.0793052i | ||||
\(637\) | 2.00000 | + | 6.70820i | 0.0792429 | + | 0.265789i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.9443 | − | 32.3607i | 1.14502 | − | 1.28017i | ||||
\(640\) | 3.23607i | 0.127917i | ||||||||
\(641\) | 34.4721i | 1.36157i | 0.732484 | + | 0.680784i | \(0.238361\pi\) | ||||
−0.732484 | + | 0.680784i | \(0.761639\pi\) | |||||||
\(642\) | −1.52786 | + | 4.00000i | −0.0603000 | + | 0.157867i | ||||
\(643\) | 31.8885i | 1.25756i | 0.777583 | + | 0.628781i | \(0.216446\pi\) | ||||
−0.777583 | + | 0.628781i | \(0.783554\pi\) | |||||||
\(644\) | 1.23607 | + | 8.47214i | 0.0487079 | + | 0.333849i | ||||
\(645\) | −20.9443 | + | 54.8328i | −0.824680 | + | 2.15904i | ||||
\(646\) | 14.8328 | 0.583589 | ||||||||
\(647\) | 20.3607 | 0.800461 | 0.400230 | − | 0.916415i | \(-0.368930\pi\) | ||||
0.400230 | + | 0.916415i | \(0.368930\pi\) | |||||||
\(648\) | −8.94427 | + | 1.00000i | −0.351364 | + | 0.0392837i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.47214 | 0.214635 | ||||||||
\(651\) | 32.3607 | + | 7.23607i | 1.26832 | + | 0.283604i | ||||
\(652\) | 9.41641 | 0.368775 | ||||||||
\(653\) | − | 5.34752i | − | 0.209265i | −0.994511 | − | 0.104632i | \(-0.966633\pi\) | ||
0.994511 | − | 0.104632i | \(-0.0333666\pi\) | |||||||
\(654\) | −10.0000 | − | 3.81966i | −0.391031 | − | 0.149361i | ||||
\(655\) | −16.9443 | −0.662067 | ||||||||
\(656\) | −5.23607 | −0.204434 | ||||||||
\(657\) | −6.47214 | + | 7.23607i | −0.252502 | + | 0.282306i | ||||
\(658\) | 2.47214 | + | 16.9443i | 0.0963739 | + | 0.660556i | ||||
\(659\) | − | 1.88854i | − | 0.0735672i | −0.999323 | − | 0.0367836i | \(-0.988289\pi\) | ||
0.999323 | − | 0.0367836i | \(-0.0117112\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.4164i | 1.29975i | 0.760042 | + | 0.649874i | \(0.225178\pi\) | ||||
−0.760042 | + | 0.649874i | \(0.774822\pi\) | |||||||
\(662\) | − | 14.3607i | − | 0.558144i | ||||||
\(663\) | 4.00000 | + | 1.52786i | 0.155347 | + | 0.0593373i | ||||
\(664\) | 14.0000i | 0.543305i | ||||||||
\(665\) | 7.41641 | + | 50.8328i | 0.287596 | + | 1.97121i | ||||
\(666\) | 18.4721 | − | 20.6525i | 0.715781 | − | 0.800267i | ||||
\(667\) | −18.4721 | −0.715244 | ||||||||
\(668\) | −16.9443 | −0.655594 | ||||||||
\(669\) | −14.1803 | − | 5.41641i | −0.548244 | − | 0.209410i | ||||
\(670\) | − | 22.4721i | − | 0.868174i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.47214 | − | 1.00000i | −0.172516 | − | 0.0385758i | ||||
\(673\) | −12.8328 | −0.494669 | −0.247334 | − | 0.968930i | \(-0.579555\pi\) | ||||
−0.247334 | + | 0.968930i | \(0.579555\pi\) | |||||||
\(674\) | 19.8885i | 0.766078i | ||||||||
\(675\) | −25.2705 | + | 13.0344i | −0.972662 | + | 0.501696i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 8.65248 | 0.332542 | 0.166271 | − | 0.986080i | \(-0.446827\pi\) | ||||
0.166271 | + | 0.986080i | \(0.446827\pi\) | |||||||
\(678\) | −9.88854 | + | 25.8885i | −0.379767 | + | 0.994244i | ||||
\(679\) | −0.291796 | − | 2.00000i | −0.0111981 | − | 0.0767530i | ||||
\(680\) | 8.00000i | 0.306786i | ||||||||
\(681\) | 2.18034 | − | 5.70820i | 0.0835508 | − | 0.218739i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 42.8328i | − | 1.63895i | −0.573113 | − | 0.819476i | \(-0.694265\pi\) | ||
0.573113 | − | 0.819476i | \(-0.305735\pi\) | |||||||
\(684\) | −12.0000 | + | 13.4164i | −0.458831 | + | 0.512989i | ||||
\(685\) | 24.3607i | 0.930774i | ||||||||
\(686\) | −7.79837 | − | 16.7984i | −0.297743 | − | 0.641365i | ||||
\(687\) | −4.76393 | − | 1.81966i | −0.181755 | − | 0.0694244i | ||||
\(688\) | −10.4721 | −0.399246 | ||||||||
\(689\) | 3.23607 | 0.123284 | ||||||||
\(690\) | −6.47214 | + | 16.9443i | −0.246390 | + | 0.645057i | ||||
\(691\) | 10.0000i | 0.380418i | 0.981744 | + | 0.190209i | \(0.0609166\pi\) | ||||
−0.981744 | + | 0.190209i | \(0.939083\pi\) | |||||||
\(692\) | 18.7639 | 0.713298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.3607 | 0.924719 | ||||||||
\(695\) | 39.4164i | 1.49515i | ||||||||
\(696\) | 3.52786 | − | 9.23607i | 0.133723 | − | 0.350092i | ||||
\(697\) | −12.9443 | −0.490299 | ||||||||
\(698\) | −35.3050 | −1.33631 | ||||||||
\(699\) | −11.4164 | − | 4.36068i | −0.431808 | − | 0.164936i | ||||
\(700\) | −14.3262 | + | 2.09017i | −0.541481 | + | 0.0790010i | ||||
\(701\) | − | 12.7639i | − | 0.482087i | −0.970514 | − | 0.241044i | \(-0.922510\pi\) | ||
0.970514 | − | 0.241044i | \(-0.0774897\pi\) | |||||||
\(702\) | −4.61803 | + | 2.38197i | −0.174296 | + | 0.0899015i | ||||
\(703\) | − | 55.4164i | − | 2.09007i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.9443 | + | 33.8885i | −0.487509 | + | 1.27632i | ||||
\(706\) | − | 19.1246i | − | 0.719764i | ||||||
\(707\) | 47.5967 | − | 6.94427i | 1.79006 | − | 0.261166i | ||||
\(708\) | 2.76393 | − | 7.23607i | 0.103875 | − | 0.271948i | ||||
\(709\) | 2.76393 | 0.103802 | 0.0519008 | − | 0.998652i | \(-0.483472\pi\) | ||||
0.0519008 | + | 0.998652i | \(0.483472\pi\) | |||||||
\(710\) | 46.8328 | 1.75760 | ||||||||
\(711\) | 20.0000 | + | 17.8885i | 0.750059 | + | 0.670873i | ||||
\(712\) | 6.18034i | 0.231618i | ||||||||
\(713\) | 23.4164 | 0.876951 | ||||||||
\(714\) | −11.0557 | − | 2.47214i | −0.413750 | − | 0.0925174i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 10.4721i | − | 0.391362i | ||||||
\(717\) | −0.944272 | − | 0.360680i | −0.0352645 | − | 0.0134698i | ||||
\(718\) | −21.8885 | −0.816873 | ||||||||
\(719\) | 44.7214 | 1.66783 | 0.833913 | − | 0.551896i | \(-0.186096\pi\) | ||||
0.833913 | + | 0.551896i | \(0.186096\pi\) | |||||||
\(720\) | −7.23607 | − | 6.47214i | −0.269672 | − | 0.241202i | ||||
\(721\) | −2.94427 | − | 20.1803i | −0.109650 | − | 0.751555i | ||||
\(722\) | 17.0000i | 0.632674i | ||||||||
\(723\) | −17.2361 | − | 6.58359i | −0.641016 | − | 0.244846i | ||||
\(724\) | − | 4.47214i | − | 0.166206i | ||||||
\(725\) | − | 31.2361i | − | 1.16008i | ||||||
\(726\) | −17.7984 | − | 6.79837i | −0.660560 | − | 0.252311i | ||||
\(727\) | 38.1803i | 1.41603i | 0.706197 | + | 0.708015i | \(0.250409\pi\) | ||||
−0.706197 | + | 0.708015i | \(0.749591\pi\) | |||||||
\(728\) | −2.61803 | + | 0.381966i | −0.0970308 | + | 0.0141566i | ||||
\(729\) | 15.6525 | − | 22.0000i | 0.579721 | − | 0.814815i | ||||
\(730\) | −10.4721 | −0.387591 | ||||||||
\(731\) | −25.8885 | −0.957522 | ||||||||
\(732\) | −7.23607 | − | 2.76393i | −0.267453 | − | 0.102158i | ||||
\(733\) | 14.0000i | 0.517102i | 0.965998 | + | 0.258551i | \(0.0832450\pi\) | ||||
−0.965998 | + | 0.258551i | \(0.916755\pi\) | |||||||
\(734\) | 12.6525 | 0.467011 | ||||||||
\(735\) | 2.94427 | − | 39.1246i | 0.108601 | − | 1.44313i | ||||
\(736\) | −3.23607 | −0.119283 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.4721 | − | 11.7082i | 0.385485 | − | 0.430985i | ||||
\(739\) | −16.8328 | −0.619205 | −0.309603 | − | 0.950866i | \(-0.600196\pi\) | ||||
−0.309603 | + | 0.950866i | \(0.600196\pi\) | |||||||
\(740\) | 29.8885 | 1.09872 | ||||||||
\(741\) | −3.70820 | + | 9.70820i | −0.136224 | + | 0.356640i | ||||
\(742\) | −8.47214 | + | 1.23607i | −0.311022 | + | 0.0453775i | ||||
\(743\) | − | 17.3050i | − | 0.634857i | −0.948282 | − | 0.317429i | \(-0.897181\pi\) | ||
0.948282 | − | 0.317429i | \(-0.102819\pi\) | |||||||
\(744\) | −4.47214 | + | 11.7082i | −0.163956 | + | 0.429244i | ||||
\(745\) | − | 56.3607i | − | 2.06490i | ||||||
\(746\) | − | 17.4164i | − | 0.637660i | ||||||
\(747\) | −31.3050 | − | 28.0000i | −1.14539 | − | 1.02447i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.944272 | − | 6.47214i | −0.0345029 | − | 0.236487i | ||||
\(750\) | −2.47214 | − | 0.944272i | −0.0902696 | − | 0.0344799i | ||||
\(751\) | 33.3050 | 1.21531 | 0.607657 | − | 0.794199i | \(-0.292109\pi\) | ||||
0.607657 | + | 0.794199i | \(0.292109\pi\) | |||||||
\(752\) | −6.47214 | −0.236015 | ||||||||
\(753\) | 9.12461 | − | 23.8885i | 0.332519 | − | 0.870547i | ||||
\(754\) | − | 5.70820i | − | 0.207881i | ||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 11.1803 | − | 8.00000i | 0.406625 | − | 0.290957i | ||||
\(757\) | 10.3607 | 0.376565 | 0.188283 | − | 0.982115i | \(-0.439708\pi\) | ||||
0.188283 | + | 0.982115i | \(0.439708\pi\) | |||||||
\(758\) | 30.0000i | 1.08965i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.4164 | −0.704307 | ||||||||
\(761\) | −39.7082 | −1.43942 | −0.719711 | − | 0.694274i | \(-0.755726\pi\) | ||||
−0.719711 | + | 0.694274i | \(0.755726\pi\) | |||||||
\(762\) | 4.94427 | + | 1.88854i | 0.179112 | + | 0.0684147i | ||||
\(763\) | 16.1803 | − | 2.36068i | 0.585768 | − | 0.0854623i | ||||
\(764\) | 21.7082i | 0.785375i | ||||||||
\(765\) | −17.8885 | − | 16.0000i | −0.646762 | − | 0.578481i | ||||
\(766\) | 30.4721i | 1.10100i | ||||||||
\(767\) | − | 4.47214i | − | 0.161479i | ||||||
\(768\) | 0.618034 | − | 1.61803i | 0.0223014 | − | 0.0583858i | ||||
\(769\) | − | 52.5410i | − | 1.89468i | −0.320233 | − | 0.947339i | \(-0.603761\pi\) | ||
0.320233 | − | 0.947339i | \(-0.396239\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.52786 | − | 4.00000i | 0.0550247 | − | 0.144056i | ||||
\(772\) | −11.8885 | −0.427878 | ||||||||
\(773\) | −14.2918 | −0.514040 | −0.257020 | − | 0.966406i | \(-0.582741\pi\) | ||||
−0.257020 | + | 0.966406i | \(0.582741\pi\) | |||||||
\(774\) | 20.9443 | − | 23.4164i | 0.752826 | − | 0.841685i | ||||
\(775\) | 39.5967i | 1.42236i | ||||||||
\(776\) | 0.763932 | 0.0274236 | ||||||||
\(777\) | −9.23607 | + | 41.3050i | −0.331342 | + | 1.48181i | ||||
\(778\) | −32.5410 | −1.16665 | ||||||||
\(779\) | − | 31.4164i | − | 1.12561i | ||||||
\(780\) | −5.23607 | − | 2.00000i | −0.187481 | − | 0.0716115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −8.00000 | −0.286079 | ||||||||
\(783\) | 13.5967 | + | 26.3607i | 0.485908 | + | 0.942054i | ||||
\(784\) | 6.70820 | − | 2.00000i | 0.239579 | − | 0.0714286i | ||||
\(785\) | 17.5279i | 0.625596i | ||||||||
\(786\) | 8.47214 | + | 3.23607i | 0.302191 | + | 0.115427i | ||||
\(787\) | 18.5836i | 0.662434i | 0.943555 | + | 0.331217i | \(0.107459\pi\) | ||||
−0.943555 | + | 0.331217i | \(0.892541\pi\) | |||||||
\(788\) | − | 25.4164i | − | 0.905422i | ||||||
\(789\) | −28.6525 | − | 10.9443i | −1.02006 | − | 0.389626i | ||||
\(790\) | 28.9443i | 1.02979i | ||||||||
\(791\) | −6.11146 | − | 41.8885i | −0.217298 | − | 1.48939i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.47214 | −0.158810 | ||||||||
\(794\) | 28.8328 | 1.02324 | ||||||||
\(795\) | −16.9443 | − | 6.47214i | −0.600951 | − | 0.229543i | ||||
\(796\) | − | 27.7082i | − | 0.982091i | ||||||
\(797\) | −27.1246 | −0.960803 | −0.480402 | − | 0.877049i | \(-0.659509\pi\) | ||||
−0.480402 | + | 0.877049i | \(0.659509\pi\) | |||||||
\(798\) | 6.00000 | − | 26.8328i | 0.212398 | − | 0.949871i | ||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | − | 5.47214i | − | 0.193469i | ||||||
\(801\) | −13.8197 | − | 12.3607i | −0.488294 | − | 0.436743i | ||||
\(802\) | 18.9443 | 0.668945 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −4.29180 | + | 11.2361i | −0.151360 | + | 0.396266i | ||||
\(805\) | −4.00000 | − | 27.4164i | −0.140981 | − | 0.966301i | ||||
\(806\) | 7.23607i | 0.254880i | ||||||||
\(807\) | 5.12461 | − | 13.4164i | 0.180395 | − | 0.472280i | ||||
\(808\) | 18.1803i | 0.639582i | ||||||||
\(809\) | − | 27.4164i | − | 0.963910i | −0.876196 | − | 0.481955i | \(-0.839927\pi\) | ||
0.876196 | − | 0.481955i | \(-0.160073\pi\) | |||||||
\(810\) | 28.9443 | − | 3.23607i | 1.01700 | − | 0.113704i | ||||
\(811\) | − | 31.3050i | − | 1.09927i | −0.835406 | − | 0.549633i | \(-0.814768\pi\) | ||
0.835406 | − | 0.549633i | \(-0.185232\pi\) | |||||||
\(812\) | 2.18034 | + | 14.9443i | 0.0765149 | + | 0.524441i | ||||
\(813\) | 6.18034 | + | 2.36068i | 0.216754 | + | 0.0827927i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.4721 | −1.06739 | ||||||||
\(816\) | 1.52786 | − | 4.00000i | 0.0534859 | − | 0.140028i | ||||
\(817\) | − | 62.8328i | − | 2.19824i | ||||||
\(818\) | −5.70820 | −0.199583 | ||||||||
\(819\) | 4.38197 | − | 6.61803i | 0.153118 | − | 0.231253i | ||||
\(820\) | 16.9443 | 0.591720 | ||||||||
\(821\) | 18.9443i | 0.661160i | 0.943778 | + | 0.330580i | \(0.107244\pi\) | ||||
−0.943778 | + | 0.330580i | \(0.892756\pi\) | |||||||
\(822\) | 4.65248 | − | 12.1803i | 0.162274 | − | 0.424838i | ||||
\(823\) | 15.0557 | 0.524810 | 0.262405 | − | 0.964958i | \(-0.415484\pi\) | ||||
0.262405 | + | 0.964958i | \(0.415484\pi\) | |||||||
\(824\) | 7.70820 | 0.268528 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.70820 | + | 11.7082i | 0.0594360 | + | 0.407381i | ||||
\(827\) | − | 36.9443i | − | 1.28468i | −0.766421 | − | 0.642339i | \(-0.777964\pi\) | ||
0.766421 | − | 0.642339i | \(-0.222036\pi\) | |||||||
\(828\) | 6.47214 | − | 7.23607i | 0.224922 | − | 0.251471i | ||||
\(829\) | 2.58359i | 0.0897319i | 0.998993 | + | 0.0448659i | \(0.0142861\pi\) | ||||
−0.998993 | + | 0.0448659i | \(0.985714\pi\) | |||||||
\(830\) | − | 45.3050i | − | 1.57256i | ||||||
\(831\) | 20.0689 | − | 52.5410i | 0.696182 | − | 1.82263i | ||||
\(832\) | − | 1.00000i | − | 0.0346688i | ||||||
\(833\) | 16.5836 | − | 4.94427i | 0.574587 | − | 0.171309i | ||||
\(834\) | 7.52786 | − | 19.7082i | 0.260669 | − | 0.682439i | ||||
\(835\) | 54.8328 | 1.89757 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.2361 | − | 33.4164i | −0.595766 | − | 1.15504i | ||||
\(838\) | 11.7082i | 0.404453i | ||||||||
\(839\) | 44.7214 | 1.54395 | 0.771976 | − | 0.635651i | \(-0.219268\pi\) | ||||
0.771976 | + | 0.635651i | \(0.219268\pi\) | |||||||
\(840\) | 14.4721 | + | 3.23607i | 0.499336 | + | 0.111655i | ||||
\(841\) | −3.58359 | −0.123572 | ||||||||
\(842\) | − | 14.7639i | − | 0.508799i | ||||||
\(843\) | −7.23607 | − | 2.76393i | −0.249223 | − | 0.0951949i | ||||
\(844\) | 25.8885 | 0.891120 | ||||||||
\(845\) | −3.23607 | −0.111324 | ||||||||
\(846\) | 12.9443 | − | 14.4721i | 0.445033 | − | 0.497562i | ||||
\(847\) | 28.7984 | − | 4.20163i | 0.989524 | − | 0.144370i | ||||
\(848\) | − | 3.23607i | − | 0.111127i | ||||||
\(849\) | −34.1803 | − | 13.0557i | −1.17307 | − | 0.448071i | ||||
\(850\) | − | 13.5279i | − | 0.464002i | ||||||
\(851\) | 29.8885i | 1.02457i | ||||||||
\(852\) | −23.4164 | − | 8.94427i | −0.802233 | − | 0.306426i | ||||
\(853\) | − | 27.3050i | − | 0.934904i | −0.884019 | − | 0.467452i | \(-0.845172\pi\) | ||
0.884019 | − | 0.467452i | \(-0.154828\pi\) | |||||||
\(854\) | 11.7082 | − | 1.70820i | 0.400646 | − | 0.0584535i | ||||
\(855\) | 38.8328 | − | 43.4164i | 1.32805 | − | 1.48481i | ||||
\(856\) | 2.47214 | 0.0844959 | ||||||||
\(857\) | −36.7214 | −1.25438 | −0.627189 | − | 0.778867i | \(-0.715795\pi\) | ||||
−0.627189 | + | 0.778867i | \(0.715795\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 5.70820i | − | 0.194761i | −0.995247 | − | 0.0973807i | \(-0.968954\pi\) | ||
0.995247 | − | 0.0973807i | \(-0.0310464\pi\) | |||||||
\(860\) | 33.8885 | 1.15559 | ||||||||
\(861\) | −5.23607 | + | 23.4164i | −0.178445 | + | 0.798029i | ||||
\(862\) | −20.0000 | −0.681203 | ||||||||
\(863\) | 45.3050i | 1.54220i | 0.636715 | + | 0.771099i | \(0.280293\pi\) | ||||
−0.636715 | + | 0.771099i | \(0.719707\pi\) | |||||||
\(864\) | 2.38197 | + | 4.61803i | 0.0810361 | + | 0.157109i | ||||
\(865\) | −60.7214 | −2.06459 | ||||||||
\(866\) | −19.4164 | −0.659796 | ||||||||
\(867\) | −6.72949 | + | 17.6180i | −0.228545 | + | 0.598340i | ||||
\(868\) | −2.76393 | − | 18.9443i | −0.0938140 | − | 0.643010i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −11.4164 | + | 29.8885i | −0.387052 | + | 1.01332i | ||||
\(871\) | 6.94427i | 0.235298i | ||||||||
\(872\) | 6.18034i | 0.209293i | ||||||||
\(873\) | −1.52786 | + | 1.70820i | −0.0517104 | + | 0.0578139i | ||||
\(874\) | − | 19.4164i | − | 0.656770i | ||||||
\(875\) | 4.00000 | − | 0.583592i | 0.135225 | − | 0.0197290i | ||||
\(876\) | 5.23607 | + | 2.00000i | 0.176910 | + | 0.0675737i | ||||
\(877\) | −0.291796 | −0.00985325 | −0.00492663 | − | 0.999988i | \(-0.501568\pi\) | ||||
−0.00492663 | + | 0.999988i | \(0.501568\pi\) | |||||||
\(878\) | 34.5410 | 1.16570 | ||||||||
\(879\) | −8.83282 | + | 23.1246i | −0.297923 | + | 0.779974i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.4721 | 0.891869 | 0.445934 | − | 0.895066i | \(-0.352871\pi\) | ||||
0.445934 | + | 0.895066i | \(0.352871\pi\) | |||||||
\(882\) | −8.94427 | + | 19.0000i | −0.301169 | + | 0.639763i | ||||
\(883\) | 9.52786 | 0.320638 | 0.160319 | − | 0.987065i | \(-0.448748\pi\) | ||||
0.160319 | + | 0.987065i | \(0.448748\pi\) | |||||||
\(884\) | − | 2.47214i | − | 0.0831469i | ||||||
\(885\) | −8.94427 | + | 23.4164i | −0.300658 | + | 0.787134i | ||||
\(886\) | 29.5279 | 0.992008 | ||||||||
\(887\) | 45.8885 | 1.54079 | 0.770393 | − | 0.637569i | \(-0.220060\pi\) | ||||
0.770393 | + | 0.637569i | \(0.220060\pi\) | |||||||
\(888\) | −14.9443 | − | 5.70820i | −0.501497 | − | 0.191555i | ||||
\(889\) | −8.00000 | + | 1.16718i | −0.268311 | + | 0.0391461i | ||||
\(890\) | − | 20.0000i | − | 0.670402i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.76393i | 0.293438i | ||||||||
\(893\) | − | 38.8328i | − | 1.29949i | ||||||
\(894\) | −10.7639 | + | 28.1803i | −0.360000 | + | 0.942492i | ||||
\(895\) | 33.8885i | 1.13277i | ||||||||
\(896\) | 0.381966 | + | 2.61803i | 0.0127606 | + | 0.0874624i | ||||
\(897\) | 2.00000 | − | 5.23607i | 0.0667781 | − | 0.174827i | ||||
\(898\) | 18.3607 | 0.612704 | ||||||||
\(899\) | 41.3050 | 1.37760 | ||||||||
\(900\) | 12.2361 | + | 10.9443i | 0.407869 | + | 0.364809i | ||||
\(901\) | − | 8.00000i | − | 0.266519i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.4721 | + | 46.8328i | −0.348491 | + | 1.55850i | ||||
\(904\) | 16.0000 | 0.532152 | ||||||||
\(905\) | 14.4721i | 0.481070i | ||||||||
\(906\) | −6.00000 | − | 2.29180i | −0.199337 | − | 0.0761398i | ||||
\(907\) | −18.8328 | −0.625333 | −0.312667 | − | 0.949863i | \(-0.601222\pi\) | ||||
−0.312667 | + | 0.949863i | \(0.601222\pi\) | |||||||
\(908\) | −3.52786 | −0.117076 | ||||||||
\(909\) | −40.6525 | − | 36.3607i | −1.34836 | − | 1.20601i | ||||
\(910\) | 8.47214 | − | 1.23607i | 0.280849 | − | 0.0409753i | ||||
\(911\) | − | 1.70820i | − | 0.0565953i | −0.999600 | − | 0.0282977i | \(-0.990991\pi\) | ||
0.999600 | − | 0.0282977i | \(-0.00900863\pi\) | |||||||
\(912\) | 9.70820 | + | 3.70820i | 0.321471 | + | 0.122791i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 26.9443i | − | 0.891237i | ||||||
\(915\) | 23.4164 | + | 8.94427i | 0.774123 | + | 0.295689i | ||||
\(916\) | 2.94427i | 0.0972815i | ||||||||
\(917\) | −13.7082 | + | 2.00000i | −0.452685 | + | 0.0660458i | ||||
\(918\) | 5.88854 | + | 11.4164i | 0.194351 | + | 0.376798i | ||||
\(919\) | −44.7214 | −1.47522 | −0.737611 | − | 0.675226i | \(-0.764046\pi\) | ||||
−0.737611 | + | 0.675226i | \(0.764046\pi\) | |||||||
\(920\) | 10.4721 | 0.345256 | ||||||||
\(921\) | −29.1246 | − | 11.1246i | −0.959689 | − | 0.366568i | ||||
\(922\) | 20.7639i | 0.683824i | ||||||||
\(923\) | −14.4721 | −0.476356 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −50.5410 | −1.66178 | ||||||||
\(926\) | − | 15.7082i | − | 0.516204i | ||||||
\(927\) | −15.4164 | + | 17.2361i | −0.506341 | + | 0.566107i | ||||
\(928\) | −5.70820 | −0.187381 | ||||||||
\(929\) | 42.7639 | 1.40304 | 0.701520 | − | 0.712650i | \(-0.252505\pi\) | ||||
0.701520 | + | 0.712650i | \(0.252505\pi\) | |||||||
\(930\) | 14.4721 | − | 37.8885i | 0.474560 | − | 1.24241i | ||||
\(931\) | 12.0000 | + | 40.2492i | 0.393284 | + | 1.31912i | ||||
\(932\) | 7.05573i | 0.231118i | ||||||||
\(933\) | −13.8885 | + | 36.3607i | −0.454691 | + | 1.19040i | ||||
\(934\) | 18.1803i | 0.594879i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.23607 | + | 2.00000i | 0.0730882 | + | 0.0653720i | ||||
\(937\) | − | 10.1115i | − | 0.330327i | −0.986266 | − | 0.165163i | \(-0.947185\pi\) | ||
0.986266 | − | 0.165163i | \(-0.0528152\pi\) | |||||||
\(938\) | −2.65248 | − | 18.1803i | −0.0866064 | − | 0.593609i | ||||
\(939\) | −16.9443 | − | 6.47214i | −0.552955 | − | 0.211210i | ||||
\(940\) | 20.9443 | 0.683127 | ||||||||
\(941\) | −51.0132 | −1.66298 | −0.831491 | − | 0.555539i | \(-0.812512\pi\) | ||||
−0.831491 | + | 0.555539i | \(0.812512\pi\) | |||||||
\(942\) | 3.34752 | − | 8.76393i | 0.109068 | − | 0.285544i | ||||
\(943\) | 16.9443i | 0.551781i | ||||||||
\(944\) | −4.47214 | −0.145556 | ||||||||
\(945\) | −36.1803 | + | 25.8885i | −1.17695 | + | 0.842154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.0557i | 0.749210i | 0.927184 | + | 0.374605i | \(0.122222\pi\) | ||||
−0.927184 | + | 0.374605i | \(0.877778\pi\) | |||||||
\(948\) | 5.52786 | − | 14.4721i | 0.179537 | − | 0.470033i | ||||
\(949\) | 3.23607 | 0.105047 | ||||||||
\(950\) | 32.8328 | 1.06524 | ||||||||
\(951\) | −11.2361 | − | 4.29180i | −0.364354 | − | 0.139171i | ||||
\(952\) | 0.944272 | + | 6.47214i | 0.0306040 | + | 0.209763i | ||||
\(953\) | − | 17.3050i | − | 0.560562i | −0.959918 | − | 0.280281i | \(-0.909572\pi\) | ||
0.959918 | − | 0.280281i | \(-0.0904277\pi\) | |||||||
\(954\) | 7.23607 | + | 6.47214i | 0.234276 | + | 0.209543i | ||||
\(955\) | − | 70.2492i | − | 2.27321i | ||||||
\(956\) | 0.583592i | 0.0188747i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 14.4721i | − | 0.467573i | ||||||
\(959\) | 2.87539 | + | 19.7082i | 0.0928511 | + | 0.636411i | ||||
\(960\) | −2.00000 | + | 5.23607i | −0.0645497 | + | 0.168993i | ||||
\(961\) | −21.3607 | −0.689054 | ||||||||
\(962\) | −9.23607 | −0.297783 | ||||||||
\(963\) | −4.94427 | + | 5.52786i | −0.159327 | + | 0.178133i | ||||
\(964\) | 10.6525i | 0.343093i | ||||||||
\(965\) | 38.4721 | 1.23846 | ||||||||
\(966\) | −3.23607 | + | 14.4721i | −0.104119 | + | 0.465633i | ||||
\(967\) | 34.1803 | 1.09917 | 0.549583 | − | 0.835439i | \(-0.314787\pi\) | ||||
0.549583 | + | 0.835439i | \(0.314787\pi\) | |||||||
\(968\) | 11.0000i | 0.353553i | ||||||||
\(969\) | 24.0000 | + | 9.16718i | 0.770991 | + | 0.294492i | ||||
\(970\) | −2.47214 | −0.0793755 | ||||||||
\(971\) | 0.291796 | 0.00936418 | 0.00468209 | − | 0.999989i | \(-0.498510\pi\) | ||||
0.00468209 | + | 0.999989i | \(0.498510\pi\) | |||||||
\(972\) | −15.0902 | − | 3.90983i | −0.484017 | − | 0.125408i | ||||
\(973\) | 4.65248 | + | 31.8885i | 0.149152 | + | 1.02230i | ||||
\(974\) | − | 10.7639i | − | 0.344899i | ||||||
\(975\) | 8.85410 | + | 3.38197i | 0.283558 | + | 0.108310i | ||||
\(976\) | 4.47214i | 0.143150i | ||||||||
\(977\) | − | 21.4164i | − | 0.685172i | −0.939487 | − | 0.342586i | \(-0.888697\pi\) | ||
0.939487 | − | 0.342586i | \(-0.111303\pi\) | |||||||
\(978\) | 15.2361 | + | 5.81966i | 0.487196 | + | 0.186092i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −21.7082 | + | 6.47214i | −0.693443 | + | 0.206745i | ||||
\(981\) | −13.8197 | − | 12.3607i | −0.441228 | − | 0.394646i | ||||
\(982\) | 3.41641 | 0.109022 | ||||||||
\(983\) | 61.8885 | 1.97394 | 0.986969 | − | 0.160911i | \(-0.0514431\pi\) | ||||
0.986969 | + | 0.160911i | \(0.0514431\pi\) | |||||||
\(984\) | −8.47214 | − | 3.23607i | −0.270082 | − | 0.103162i | ||||
\(985\) | 82.2492i | 2.62068i | ||||||||
\(986\) | −14.1115 | −0.449400 | ||||||||
\(987\) | −6.47214 | + | 28.9443i | −0.206010 | + | 0.921306i | ||||
\(988\) | 6.00000 | 0.190885 | ||||||||
\(989\) | 33.8885i | 1.07759i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.3607 | 0.773842 | 0.386921 | − | 0.922113i | \(-0.373539\pi\) | ||||
0.386921 | + | 0.922113i | \(0.373539\pi\) | |||||||
\(992\) | 7.23607 | 0.229745 | ||||||||
\(993\) | 8.87539 | − | 23.2361i | 0.281652 | − | 0.737374i | ||||
\(994\) | 37.8885 | − | 5.52786i | 1.20175 | − | 0.175333i | ||||
\(995\) | 89.6656i | 2.84259i | ||||||||
\(996\) | −8.65248 | + | 22.6525i | −0.274164 | + | 0.717771i | ||||
\(997\) | − | 46.9443i | − | 1.48674i | −0.668880 | − | 0.743370i | \(-0.733226\pi\) | ||
0.668880 | − | 0.743370i | \(-0.266774\pi\) | |||||||
\(998\) | 10.0000i | 0.316544i | ||||||||
\(999\) | 42.6525 | − | 22.0000i | 1.34946 | − | 0.696049i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 546.2.g.a.209.2 | ✓ | 4 | |
3.2 | odd | 2 | 546.2.g.b.209.3 | yes | 4 | ||
7.6 | odd | 2 | 546.2.g.b.209.1 | yes | 4 | ||
21.20 | even | 2 | inner | 546.2.g.a.209.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.g.a.209.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
546.2.g.a.209.4 | yes | 4 | 21.20 | even | 2 | inner | |
546.2.g.b.209.1 | yes | 4 | 7.6 | odd | 2 | ||
546.2.g.b.209.3 | yes | 4 | 3.2 | odd | 2 |