Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(124,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.124");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.e (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 202.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.202 |
Dual form | 363.2.e.g.124.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | 0.835853 | − | 0.548953i | \(-0.184973\pi\) |
−0.263792 | + | 0.964580i | \(0.584973\pi\) | |||||||
\(3\) | −0.309017 | + | 0.951057i | −0.178411 | + | 0.549093i | ||||
\(4\) | −0.309017 | − | 0.951057i | −0.154508 | − | 0.475528i | ||||
\(5\) | 1.61803 | − | 1.17557i | 0.723607 | − | 0.525731i | −0.163928 | − | 0.986472i | \(-0.552416\pi\) |
0.887535 | + | 0.460741i | \(0.152416\pi\) | |||||||
\(6\) | −0.809017 | + | 0.587785i | −0.330280 | + | 0.239962i | ||||
\(7\) | −1.23607 | − | 3.80423i | −0.467190 | − | 1.43786i | −0.856208 | − | 0.516632i | \(-0.827186\pi\) |
0.389018 | − | 0.921230i | \(-0.372814\pi\) | |||||||
\(8\) | 0.927051 | − | 2.85317i | 0.327762 | − | 1.00875i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −1.61803 | − | 1.17557i | −0.448762 | − | 0.326045i | 0.340345 | − | 0.940301i | \(-0.389456\pi\) |
−0.789107 | + | 0.614256i | \(0.789456\pi\) | |||||||
\(14\) | 1.23607 | − | 3.80423i | 0.330353 | − | 1.01672i | ||||
\(15\) | 0.618034 | + | 1.90211i | 0.159576 | + | 0.491123i | ||||
\(16\) | 0.809017 | − | 0.587785i | 0.202254 | − | 0.146946i | ||||
\(17\) | −1.61803 | + | 1.17557i | −0.392431 | + | 0.285118i | −0.766451 | − | 0.642303i | \(-0.777979\pi\) |
0.374020 | + | 0.927421i | \(0.377979\pi\) | |||||||
\(18\) | −0.309017 | − | 0.951057i | −0.0728360 | − | 0.224166i | ||||
\(19\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(20\) | −1.61803 | − | 1.17557i | −0.361803 | − | 0.262866i | ||||
\(21\) | 4.00000 | 0.872872 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 2.42705 | + | 1.76336i | 0.495420 | + | 0.359943i | ||||
\(25\) | −0.309017 | + | 0.951057i | −0.0618034 | + | 0.190211i | ||||
\(26\) | −0.618034 | − | 1.90211i | −0.121206 | − | 0.373035i | ||||
\(27\) | 0.809017 | − | 0.587785i | 0.155695 | − | 0.113119i | ||||
\(28\) | −3.23607 | + | 2.35114i | −0.611559 | + | 0.444324i | ||||
\(29\) | 1.85410 | + | 5.70634i | 0.344298 | + | 1.05964i | 0.961958 | + | 0.273196i | \(0.0880806\pi\) |
−0.617660 | + | 0.786445i | \(0.711919\pi\) | |||||||
\(30\) | −0.618034 | + | 1.90211i | −0.112837 | + | 0.347277i | ||||
\(31\) | 6.47214 | + | 4.70228i | 1.16243 | + | 0.844555i | 0.990083 | − | 0.140482i | \(-0.0448651\pi\) |
0.172347 | + | 0.985036i | \(0.444865\pi\) | |||||||
\(32\) | −5.00000 | −0.883883 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | −6.47214 | − | 4.70228i | −1.09399 | − | 0.794831i | ||||
\(36\) | −0.309017 | + | 0.951057i | −0.0515028 | + | 0.158509i | ||||
\(37\) | 1.85410 | + | 5.70634i | 0.304812 | + | 0.938116i | 0.979747 | + | 0.200239i | \(0.0641718\pi\) |
−0.674935 | + | 0.737878i | \(0.735828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.61803 | − | 1.17557i | 0.259093 | − | 0.188242i | ||||
\(40\) | −1.85410 | − | 5.70634i | −0.293159 | − | 0.902251i | ||||
\(41\) | 0.618034 | − | 1.90211i | 0.0965207 | − | 0.297060i | −0.891126 | − | 0.453755i | \(-0.850084\pi\) |
0.987647 | + | 0.156695i | \(0.0500840\pi\) | |||||||
\(42\) | 3.23607 | + | 2.35114i | 0.499336 | + | 0.362789i | ||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | −0.298142 | ||||||||
\(46\) | 6.47214 | + | 4.70228i | 0.954264 | + | 0.693314i | ||||
\(47\) | 2.47214 | − | 7.60845i | 0.360598 | − | 1.10981i | −0.592094 | − | 0.805869i | \(-0.701699\pi\) |
0.952692 | − | 0.303938i | \(-0.0983015\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −7.28115 | + | 5.29007i | −1.04016 | + | 0.755724i | ||||
\(50\) | −0.809017 | + | 0.587785i | −0.114412 | + | 0.0831254i | ||||
\(51\) | −0.618034 | − | 1.90211i | −0.0865421 | − | 0.266349i | ||||
\(52\) | −0.618034 | + | 1.90211i | −0.0857059 | + | 0.263776i | ||||
\(53\) | −4.85410 | − | 3.52671i | −0.666762 | − | 0.484431i | 0.202178 | − | 0.979349i | \(-0.435198\pi\) |
−0.868940 | + | 0.494918i | \(0.835198\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −12.0000 | −1.60357 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.85410 | + | 5.70634i | −0.243456 | + | 0.749279i | ||||
\(59\) | −1.23607 | − | 3.80423i | −0.160922 | − | 0.495268i | 0.837790 | − | 0.545992i | \(-0.183847\pi\) |
−0.998713 | + | 0.0507240i | \(0.983847\pi\) | |||||||
\(60\) | 1.61803 | − | 1.17557i | 0.208887 | − | 0.151765i | ||||
\(61\) | 4.85410 | − | 3.52671i | 0.621504 | − | 0.451549i | −0.231942 | − | 0.972730i | \(-0.574508\pi\) |
0.853447 | + | 0.521180i | \(0.174508\pi\) | |||||||
\(62\) | 2.47214 | + | 7.60845i | 0.313962 | + | 0.966274i | ||||
\(63\) | −1.23607 | + | 3.80423i | −0.155730 | + | 0.479287i | ||||
\(64\) | −5.66312 | − | 4.11450i | −0.707890 | − | 0.514312i | ||||
\(65\) | −4.00000 | −0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 1.61803 | + | 1.17557i | 0.196215 | + | 0.142559i | ||||
\(69\) | −2.47214 | + | 7.60845i | −0.297610 | + | 0.915950i | ||||
\(70\) | −2.47214 | − | 7.60845i | −0.295477 | − | 0.909384i | ||||
\(71\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(72\) | −2.42705 | + | 1.76336i | −0.286031 | + | 0.207813i | ||||
\(73\) | 4.32624 | + | 13.3148i | 0.506348 | + | 1.55838i | 0.798493 | + | 0.602004i | \(0.205631\pi\) |
−0.292145 | + | 0.956374i | \(0.594369\pi\) | |||||||
\(74\) | −1.85410 | + | 5.70634i | −0.215535 | + | 0.663348i | ||||
\(75\) | −0.809017 | − | 0.587785i | −0.0934172 | − | 0.0678716i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2.00000 | 0.226455 | ||||||||
\(79\) | −3.23607 | − | 2.35114i | −0.364086 | − | 0.264524i | 0.390668 | − | 0.920532i | \(-0.372244\pi\) |
−0.754754 | + | 0.656007i | \(0.772244\pi\) | |||||||
\(80\) | 0.618034 | − | 1.90211i | 0.0690983 | − | 0.212663i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 1.61803 | − | 1.17557i | 0.178682 | − | 0.129820i | ||||
\(83\) | 9.70820 | − | 7.05342i | 1.06561 | − | 0.774214i | 0.0904951 | − | 0.995897i | \(-0.471155\pi\) |
0.975119 | + | 0.221683i | \(0.0711551\pi\) | |||||||
\(84\) | −1.23607 | − | 3.80423i | −0.134866 | − | 0.415075i | ||||
\(85\) | −1.23607 | + | 3.80423i | −0.134070 | + | 0.412626i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | −1.61803 | − | 1.17557i | −0.170556 | − | 0.123916i | ||||
\(91\) | −2.47214 | + | 7.60845i | −0.259150 | + | 0.797582i | ||||
\(92\) | −2.47214 | − | 7.60845i | −0.257738 | − | 0.793236i | ||||
\(93\) | −6.47214 | + | 4.70228i | −0.671129 | + | 0.487604i | ||||
\(94\) | 6.47214 | − | 4.70228i | 0.667550 | − | 0.485003i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.54508 | − | 4.75528i | 0.157695 | − | 0.485334i | ||||
\(97\) | −1.61803 | − | 1.17557i | −0.164286 | − | 0.119361i | 0.502604 | − | 0.864517i | \(-0.332375\pi\) |
−0.666891 | + | 0.745155i | \(0.732375\pi\) | |||||||
\(98\) | −9.00000 | −0.909137 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 1.61803 | + | 1.17557i | 0.161000 | + | 0.116974i | 0.665368 | − | 0.746515i | \(-0.268274\pi\) |
−0.504368 | + | 0.863489i | \(0.668274\pi\) | |||||||
\(102\) | 0.618034 | − | 1.90211i | 0.0611945 | − | 0.188337i | ||||
\(103\) | 2.47214 | + | 7.60845i | 0.243587 | + | 0.749683i | 0.995866 | + | 0.0908382i | \(0.0289546\pi\) |
−0.752279 | + | 0.658845i | \(0.771045\pi\) | |||||||
\(104\) | −4.85410 | + | 3.52671i | −0.475984 | + | 0.345823i | ||||
\(105\) | 6.47214 | − | 4.70228i | 0.631616 | − | 0.458896i | ||||
\(106\) | −1.85410 | − | 5.70634i | −0.180086 | − | 0.554249i | ||||
\(107\) | 3.70820 | − | 11.4127i | 0.358486 | − | 1.10331i | −0.595475 | − | 0.803374i | \(-0.703036\pi\) |
0.953961 | − | 0.299932i | \(-0.0969638\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | −0.569495 | ||||||||
\(112\) | −3.23607 | − | 2.35114i | −0.305780 | − | 0.222162i | ||||
\(113\) | −1.85410 | + | 5.70634i | −0.174419 | + | 0.536807i | −0.999606 | − | 0.0280521i | \(-0.991070\pi\) |
0.825187 | + | 0.564859i | \(0.191070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9443 | − | 9.40456i | 1.20706 | − | 0.876980i | ||||
\(116\) | 4.85410 | − | 3.52671i | 0.450692 | − | 0.327447i | ||||
\(117\) | 0.618034 | + | 1.90211i | 0.0571373 | + | 0.175850i | ||||
\(118\) | 1.23607 | − | 3.80423i | 0.113789 | − | 0.350207i | ||||
\(119\) | 6.47214 | + | 4.70228i | 0.593300 | + | 0.431057i | ||||
\(120\) | 6.00000 | 0.547723 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.00000 | 0.543214 | ||||||||
\(123\) | 1.61803 | + | 1.17557i | 0.145893 | + | 0.105998i | ||||
\(124\) | 2.47214 | − | 7.60845i | 0.222004 | − | 0.683259i | ||||
\(125\) | 3.70820 | + | 11.4127i | 0.331672 | + | 1.02078i | ||||
\(126\) | −3.23607 | + | 2.35114i | −0.288292 | + | 0.209456i | ||||
\(127\) | −3.23607 | + | 2.35114i | −0.287155 | + | 0.208630i | −0.722032 | − | 0.691860i | \(-0.756792\pi\) |
0.434877 | + | 0.900490i | \(0.356792\pi\) | |||||||
\(128\) | 0.927051 | + | 2.85317i | 0.0819405 | + | 0.252187i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.23607 | − | 2.35114i | −0.283822 | − | 0.206209i | ||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.23607 | − | 2.35114i | −0.279554 | − | 0.203108i | ||||
\(135\) | 0.618034 | − | 1.90211i | 0.0531919 | − | 0.163708i | ||||
\(136\) | 1.85410 | + | 5.70634i | 0.158988 | + | 0.489315i | ||||
\(137\) | −1.61803 | + | 1.17557i | −0.138238 | + | 0.100436i | −0.654755 | − | 0.755841i | \(-0.727228\pi\) |
0.516517 | + | 0.856277i | \(0.327228\pi\) | |||||||
\(138\) | −6.47214 | + | 4.70228i | −0.550945 | + | 0.400285i | ||||
\(139\) | 2.47214 | + | 7.60845i | 0.209684 | + | 0.645340i | 0.999488 | + | 0.0319820i | \(0.0101819\pi\) |
−0.789805 | + | 0.613359i | \(0.789818\pi\) | |||||||
\(140\) | −2.47214 | + | 7.60845i | −0.208934 | + | 0.643032i | ||||
\(141\) | 6.47214 | + | 4.70228i | 0.545052 | + | 0.396004i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 9.70820 | + | 7.05342i | 0.806222 | + | 0.585755i | ||||
\(146\) | −4.32624 | + | 13.3148i | −0.358042 | + | 1.10194i | ||||
\(147\) | −2.78115 | − | 8.55951i | −0.229386 | − | 0.705976i | ||||
\(148\) | 4.85410 | − | 3.52671i | 0.399005 | − | 0.289894i | ||||
\(149\) | −17.7984 | + | 12.9313i | −1.45810 | + | 1.05937i | −0.474247 | + | 0.880392i | \(0.657280\pi\) |
−0.983853 | + | 0.178979i | \(0.942720\pi\) | |||||||
\(150\) | −0.309017 | − | 0.951057i | −0.0252311 | − | 0.0776534i | ||||
\(151\) | −6.18034 | + | 19.0211i | −0.502949 | + | 1.54792i | 0.301243 | + | 0.953548i | \(0.402599\pi\) |
−0.804192 | + | 0.594370i | \(0.797401\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 16.0000 | 1.28515 | ||||||||
\(156\) | −1.61803 | − | 1.17557i | −0.129546 | − | 0.0941210i | ||||
\(157\) | 4.32624 | − | 13.3148i | 0.345271 | − | 1.06264i | −0.616167 | − | 0.787616i | \(-0.711315\pi\) |
0.961438 | − | 0.275020i | \(-0.0886846\pi\) | |||||||
\(158\) | −1.23607 | − | 3.80423i | −0.0983363 | − | 0.302648i | ||||
\(159\) | 4.85410 | − | 3.52671i | 0.384955 | − | 0.279686i | ||||
\(160\) | −8.09017 | + | 5.87785i | −0.639584 | + | 0.464685i | ||||
\(161\) | −9.88854 | − | 30.4338i | −0.779326 | − | 2.39852i | ||||
\(162\) | −0.309017 | + | 0.951057i | −0.0242787 | + | 0.0747221i | ||||
\(163\) | −3.23607 | − | 2.35114i | −0.253468 | − | 0.184156i | 0.453794 | − | 0.891107i | \(-0.350070\pi\) |
−0.707263 | + | 0.706951i | \(0.750070\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(168\) | 3.70820 | − | 11.4127i | 0.286094 | − | 0.880507i | ||||
\(169\) | −2.78115 | − | 8.55951i | −0.213935 | − | 0.658424i | ||||
\(170\) | −3.23607 | + | 2.35114i | −0.248195 | + | 0.180324i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.85410 | − | 5.70634i | 0.140965 | − | 0.433845i | −0.855505 | − | 0.517794i | \(-0.826753\pi\) |
0.996470 | + | 0.0839492i | \(0.0267533\pi\) | |||||||
\(174\) | −4.85410 | − | 3.52671i | −0.367989 | − | 0.267359i | ||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.00000 | 0.300658 | ||||||||
\(178\) | −4.85410 | − | 3.52671i | −0.363830 | − | 0.264338i | ||||
\(179\) | 3.70820 | − | 11.4127i | 0.277164 | − | 0.853024i | −0.711474 | − | 0.702712i | \(-0.751972\pi\) |
0.988639 | − | 0.150312i | \(-0.0480277\pi\) | |||||||
\(180\) | 0.618034 | + | 1.90211i | 0.0460655 | + | 0.141775i | ||||
\(181\) | −17.7984 | + | 12.9313i | −1.32294 | + | 0.961174i | −0.323052 | + | 0.946381i | \(0.604709\pi\) |
−0.999891 | + | 0.0147930i | \(0.995291\pi\) | |||||||
\(182\) | −6.47214 | + | 4.70228i | −0.479747 | + | 0.348556i | ||||
\(183\) | 1.85410 | + | 5.70634i | 0.137059 | + | 0.421825i | ||||
\(184\) | 7.41641 | − | 22.8254i | 0.546745 | − | 1.68271i | ||||
\(185\) | 9.70820 | + | 7.05342i | 0.713761 | + | 0.518578i | ||||
\(186\) | −8.00000 | −0.586588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | −3.23607 | − | 2.35114i | −0.235389 | − | 0.171020i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.47214 | + | 7.60845i | 0.178877 | + | 0.550528i | 0.999789 | − | 0.0205267i | \(-0.00653431\pi\) |
−0.820912 | + | 0.571055i | \(0.806534\pi\) | |||||||
\(192\) | 5.66312 | − | 4.11450i | 0.408700 | − | 0.296938i | ||||
\(193\) | −11.3262 | + | 8.22899i | −0.815280 | + | 0.592336i | −0.915357 | − | 0.402644i | \(-0.868091\pi\) |
0.100076 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(194\) | −0.618034 | − | 1.90211i | −0.0443723 | − | 0.136564i | ||||
\(195\) | 1.23607 | − | 3.80423i | 0.0885167 | − | 0.272426i | ||||
\(196\) | 7.28115 | + | 5.29007i | 0.520082 | + | 0.377862i | ||||
\(197\) | 14.0000 | 0.997459 | 0.498729 | − | 0.866758i | \(-0.333800\pi\) | ||||
0.498729 | + | 0.866758i | \(0.333800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 2.42705 | + | 1.76336i | 0.171618 | + | 0.124688i | ||||
\(201\) | 1.23607 | − | 3.80423i | 0.0871855 | − | 0.268329i | ||||
\(202\) | 0.618034 | + | 1.90211i | 0.0434847 | + | 0.133832i | ||||
\(203\) | 19.4164 | − | 14.1068i | 1.36276 | − | 0.990106i | ||||
\(204\) | −1.61803 | + | 1.17557i | −0.113285 | + | 0.0823064i | ||||
\(205\) | −1.23607 | − | 3.80423i | −0.0863307 | − | 0.265699i | ||||
\(206\) | −2.47214 | + | 7.60845i | −0.172242 | + | 0.530106i | ||||
\(207\) | −6.47214 | − | 4.70228i | −0.449845 | − | 0.326831i | ||||
\(208\) | −2.00000 | −0.138675 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 8.00000 | 0.552052 | ||||||||
\(211\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(212\) | −1.85410 | + | 5.70634i | −0.127340 | + | 0.391913i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.70820 | − | 7.05342i | 0.663639 | − | 0.482162i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.927051 | − | 2.85317i | −0.0630778 | − | 0.194134i | ||||
\(217\) | 9.88854 | − | 30.4338i | 0.671278 | − | 2.06598i | ||||
\(218\) | 1.61803 | + | 1.17557i | 0.109587 | + | 0.0796197i | ||||
\(219\) | −14.0000 | −0.946032 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000 | 0.269069 | ||||||||
\(222\) | −4.85410 | − | 3.52671i | −0.325786 | − | 0.236697i | ||||
\(223\) | 4.94427 | − | 15.2169i | 0.331093 | − | 1.01900i | −0.637522 | − | 0.770432i | \(-0.720040\pi\) |
0.968615 | − | 0.248567i | \(-0.0799596\pi\) | |||||||
\(224\) | 6.18034 | + | 19.0211i | 0.412941 | + | 1.27090i | ||||
\(225\) | 0.809017 | − | 0.587785i | 0.0539345 | − | 0.0391857i | ||||
\(226\) | −4.85410 | + | 3.52671i | −0.322890 | + | 0.234593i | ||||
\(227\) | −3.70820 | − | 11.4127i | −0.246122 | − | 0.757486i | −0.995450 | − | 0.0952867i | \(-0.969623\pi\) |
0.749328 | − | 0.662199i | \(-0.230377\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.85410 | − | 3.52671i | −0.320768 | − | 0.233052i | 0.415735 | − | 0.909486i | \(-0.363524\pi\) |
−0.736503 | + | 0.676434i | \(0.763524\pi\) | |||||||
\(230\) | 16.0000 | 1.05501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 18.0000 | 1.18176 | ||||||||
\(233\) | 24.2705 | + | 17.6336i | 1.59001 | + | 1.15521i | 0.903921 | + | 0.427698i | \(0.140675\pi\) |
0.686092 | + | 0.727514i | \(0.259325\pi\) | |||||||
\(234\) | −0.618034 | + | 1.90211i | −0.0404021 | + | 0.124345i | ||||
\(235\) | −4.94427 | − | 15.2169i | −0.322529 | − | 0.992641i | ||||
\(236\) | −3.23607 | + | 2.35114i | −0.210650 | + | 0.153046i | ||||
\(237\) | 3.23607 | − | 2.35114i | 0.210205 | − | 0.152723i | ||||
\(238\) | 2.47214 | + | 7.60845i | 0.160245 | + | 0.493183i | ||||
\(239\) | −7.41641 | + | 22.8254i | −0.479728 | + | 1.47645i | 0.359747 | + | 0.933050i | \(0.382863\pi\) |
−0.839474 | + | 0.543400i | \(0.817137\pi\) | |||||||
\(240\) | 1.61803 | + | 1.17557i | 0.104444 | + | 0.0758827i | ||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −4.85410 | − | 3.52671i | −0.310752 | − | 0.225775i | ||||
\(245\) | −5.56231 | + | 17.1190i | −0.355363 | + | 1.09369i | ||||
\(246\) | 0.618034 | + | 1.90211i | 0.0394044 | + | 0.121274i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 19.4164 | − | 14.1068i | 1.23294 | − | 0.895786i | ||||
\(249\) | 3.70820 | + | 11.4127i | 0.234998 | + | 0.723249i | ||||
\(250\) | −3.70820 | + | 11.4127i | −0.234527 | + | 0.721801i | ||||
\(251\) | −3.23607 | − | 2.35114i | −0.204259 | − | 0.148403i | 0.480953 | − | 0.876746i | \(-0.340291\pi\) |
−0.685212 | + | 0.728343i | \(0.740291\pi\) | |||||||
\(252\) | 4.00000 | 0.251976 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −4.00000 | −0.250982 | ||||||||
\(255\) | −3.23607 | − | 2.35114i | −0.202650 | − | 0.147234i | ||||
\(256\) | −5.25329 | + | 16.1680i | −0.328331 | + | 1.01050i | ||||
\(257\) | −4.32624 | − | 13.3148i | −0.269863 | − | 0.830554i | −0.990533 | − | 0.137275i | \(-0.956166\pi\) |
0.720670 | − | 0.693279i | \(-0.243834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.4164 | − | 14.1068i | 1.20648 | − | 0.876557i | ||||
\(260\) | 1.23607 | + | 3.80423i | 0.0766577 | + | 0.235928i | ||||
\(261\) | 1.85410 | − | 5.70634i | 0.114766 | − | 0.353214i | ||||
\(262\) | 9.70820 | + | 7.05342i | 0.599775 | + | 0.435762i | ||||
\(263\) | 16.0000 | 0.986602 | 0.493301 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493301 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | −0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.85410 | − | 5.70634i | 0.113469 | − | 0.349222i | ||||
\(268\) | 1.23607 | + | 3.80423i | 0.0755049 | + | 0.232380i | ||||
\(269\) | 1.61803 | − | 1.17557i | 0.0986533 | − | 0.0716758i | −0.537365 | − | 0.843350i | \(-0.680580\pi\) |
0.636018 | + | 0.771674i | \(0.280580\pi\) | |||||||
\(270\) | 1.61803 | − | 1.17557i | 0.0984704 | − | 0.0715429i | ||||
\(271\) | −6.18034 | − | 19.0211i | −0.375429 | − | 1.15545i | −0.943189 | − | 0.332257i | \(-0.892190\pi\) |
0.567760 | − | 0.823194i | \(-0.307810\pi\) | |||||||
\(272\) | −0.618034 | + | 1.90211i | −0.0374738 | + | 0.115333i | ||||
\(273\) | −6.47214 | − | 4.70228i | −0.391711 | − | 0.284595i | ||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.00000 | 0.481543 | ||||||||
\(277\) | −21.0344 | − | 15.2824i | −1.26384 | − | 0.918231i | −0.264898 | − | 0.964277i | \(-0.585338\pi\) |
−0.998939 | + | 0.0460451i | \(0.985338\pi\) | |||||||
\(278\) | −2.47214 | + | 7.60845i | −0.148269 | + | 0.456325i | ||||
\(279\) | −2.47214 | − | 7.60845i | −0.148003 | − | 0.455506i | ||||
\(280\) | −19.4164 | + | 14.1068i | −1.16035 | + | 0.843045i | ||||
\(281\) | −14.5623 | + | 10.5801i | −0.868714 | + | 0.631158i | −0.930242 | − | 0.366947i | \(-0.880403\pi\) |
0.0615273 | + | 0.998105i | \(0.480403\pi\) | |||||||
\(282\) | 2.47214 | + | 7.60845i | 0.147214 | + | 0.453077i | ||||
\(283\) | −4.94427 | + | 15.2169i | −0.293906 | + | 0.904551i | 0.689680 | + | 0.724114i | \(0.257751\pi\) |
−0.983587 | + | 0.180437i | \(0.942249\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 4.04508 | + | 2.93893i | 0.238359 | + | 0.173178i | ||||
\(289\) | −4.01722 | + | 12.3637i | −0.236307 | + | 0.727279i | ||||
\(290\) | 3.70820 | + | 11.4127i | 0.217753 | + | 0.670176i | ||||
\(291\) | 1.61803 | − | 1.17557i | 0.0948508 | − | 0.0689132i | ||||
\(292\) | 11.3262 | − | 8.22899i | 0.662818 | − | 0.481565i | ||||
\(293\) | 1.85410 | + | 5.70634i | 0.108318 | + | 0.333368i | 0.990495 | − | 0.137550i | \(-0.0439228\pi\) |
−0.882177 | + | 0.470918i | \(0.843923\pi\) | |||||||
\(294\) | 2.78115 | − | 8.55951i | 0.162200 | − | 0.499201i | ||||
\(295\) | −6.47214 | − | 4.70228i | −0.376822 | − | 0.273777i | ||||
\(296\) | 18.0000 | 1.04623 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −22.0000 | −1.27443 | ||||||||
\(299\) | −12.9443 | − | 9.40456i | −0.748587 | − | 0.543880i | ||||
\(300\) | −0.309017 | + | 0.951057i | −0.0178411 | + | 0.0549093i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −16.1803 | + | 11.7557i | −0.931074 | + | 0.676465i | ||||
\(303\) | −1.61803 | + | 1.17557i | −0.0929536 | + | 0.0675348i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.70820 | − | 11.4127i | 0.212331 | − | 0.653488i | ||||
\(306\) | 1.61803 | + | 1.17557i | 0.0924968 | + | 0.0672029i | ||||
\(307\) | −32.0000 | −1.82634 | −0.913168 | − | 0.407583i | \(-0.866372\pi\) | ||||
−0.913168 | + | 0.407583i | \(0.866372\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 12.9443 | + | 9.40456i | 0.735185 | + | 0.534143i | ||||
\(311\) | −7.41641 | + | 22.8254i | −0.420546 | + | 1.29431i | 0.486649 | + | 0.873597i | \(0.338219\pi\) |
−0.907195 | + | 0.420710i | \(0.861781\pi\) | |||||||
\(312\) | −1.85410 | − | 5.70634i | −0.104968 | − | 0.323058i | ||||
\(313\) | 17.7984 | − | 12.9313i | 1.00602 | − | 0.730919i | 0.0426523 | − | 0.999090i | \(-0.486419\pi\) |
0.963371 | + | 0.268171i | \(0.0864192\pi\) | |||||||
\(314\) | 11.3262 | − | 8.22899i | 0.639177 | − | 0.464389i | ||||
\(315\) | 2.47214 | + | 7.60845i | 0.139289 | + | 0.428688i | ||||
\(316\) | −1.23607 | + | 3.80423i | −0.0695343 | + | 0.214004i | ||||
\(317\) | −17.7984 | − | 12.9313i | −0.999656 | − | 0.726293i | −0.0376418 | − | 0.999291i | \(-0.511985\pi\) |
−0.962014 | + | 0.272999i | \(0.911985\pi\) | |||||||
\(318\) | 6.00000 | 0.336463 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −14.0000 | −0.782624 | ||||||||
\(321\) | 9.70820 | + | 7.05342i | 0.541859 | + | 0.393684i | ||||
\(322\) | 9.88854 | − | 30.4338i | 0.551067 | − | 1.69601i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.809017 | − | 0.587785i | 0.0449454 | − | 0.0326547i | ||||
\(325\) | 1.61803 | − | 1.17557i | 0.0897524 | − | 0.0652089i | ||||
\(326\) | −1.23607 | − | 3.80423i | −0.0684595 | − | 0.210697i | ||||
\(327\) | −0.618034 | + | 1.90211i | −0.0341774 | + | 0.105187i | ||||
\(328\) | −4.85410 | − | 3.52671i | −0.268023 | − | 0.194730i | ||||
\(329\) | −32.0000 | −1.76422 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.0000 | −1.09930 | −0.549650 | − | 0.835395i | \(-0.685239\pi\) | ||||
−0.549650 | + | 0.835395i | \(0.685239\pi\) | |||||||
\(332\) | −9.70820 | − | 7.05342i | −0.532807 | − | 0.387107i | ||||
\(333\) | 1.85410 | − | 5.70634i | 0.101604 | − | 0.312705i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.47214 | + | 4.70228i | −0.353611 | + | 0.256913i | ||||
\(336\) | 3.23607 | − | 2.35114i | 0.176542 | − | 0.128265i | ||||
\(337\) | 6.79837 | + | 20.9232i | 0.370331 | + | 1.13976i | 0.946575 | + | 0.322484i | \(0.104518\pi\) |
−0.576244 | + | 0.817278i | \(0.695482\pi\) | |||||||
\(338\) | 2.78115 | − | 8.55951i | 0.151275 | − | 0.465576i | ||||
\(339\) | −4.85410 | − | 3.52671i | −0.263639 | − | 0.191545i | ||||
\(340\) | 4.00000 | 0.216930 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.47214 | + | 4.70228i | 0.349462 | + | 0.253899i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.94427 | + | 15.2169i | 0.266191 | + | 0.819251i | ||||
\(346\) | 4.85410 | − | 3.52671i | 0.260958 | − | 0.189597i | ||||
\(347\) | 3.23607 | − | 2.35114i | 0.173721 | − | 0.126216i | −0.497527 | − | 0.867448i | \(-0.665758\pi\) |
0.671248 | + | 0.741233i | \(0.265758\pi\) | |||||||
\(348\) | 1.85410 | + | 5.70634i | 0.0993903 | + | 0.305892i | ||||
\(349\) | −1.85410 | + | 5.70634i | −0.0992478 | + | 0.305453i | −0.988337 | − | 0.152280i | \(-0.951338\pi\) |
0.889090 | + | 0.457733i | \(0.151338\pi\) | |||||||
\(350\) | 3.23607 | + | 2.35114i | 0.172975 | + | 0.125674i | ||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | 3.23607 | + | 2.35114i | 0.171995 | + | 0.124962i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.85410 | + | 5.70634i | 0.0982672 | + | 0.302435i | ||||
\(357\) | −6.47214 | + | 4.70228i | −0.342542 | + | 0.248871i | ||||
\(358\) | 9.70820 | − | 7.05342i | 0.513095 | − | 0.372785i | ||||
\(359\) | 2.47214 | + | 7.60845i | 0.130474 | + | 0.401559i | 0.994859 | − | 0.101273i | \(-0.0322915\pi\) |
−0.864384 | + | 0.502832i | \(0.832292\pi\) | |||||||
\(360\) | −1.85410 | + | 5.70634i | −0.0977198 | + | 0.300750i | ||||
\(361\) | 15.3713 | + | 11.1679i | 0.809017 | + | 0.587785i | ||||
\(362\) | −22.0000 | −1.15629 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.00000 | 0.419314 | ||||||||
\(365\) | 22.6525 | + | 16.4580i | 1.18568 | + | 0.861450i | ||||
\(366\) | −1.85410 | + | 5.70634i | −0.0969155 | + | 0.298275i | ||||
\(367\) | −9.88854 | − | 30.4338i | −0.516178 | − | 1.58863i | −0.781129 | − | 0.624370i | \(-0.785356\pi\) |
0.264951 | − | 0.964262i | \(-0.414644\pi\) | |||||||
\(368\) | 6.47214 | − | 4.70228i | 0.337383 | − | 0.245123i | ||||
\(369\) | −1.61803 | + | 1.17557i | −0.0842315 | + | 0.0611978i | ||||
\(370\) | 3.70820 | + | 11.4127i | 0.192780 | + | 0.593317i | ||||
\(371\) | −7.41641 | + | 22.8254i | −0.385041 | + | 1.18503i | ||||
\(372\) | 6.47214 | + | 4.70228i | 0.335565 | + | 0.243802i | ||||
\(373\) | 2.00000 | 0.103556 | 0.0517780 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517780 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | −19.4164 | − | 14.1068i | −1.00132 | − | 0.727505i | ||||
\(377\) | 3.70820 | − | 11.4127i | 0.190982 | − | 0.587783i | ||||
\(378\) | −1.23607 | − | 3.80423i | −0.0635765 | − | 0.195668i | ||||
\(379\) | −22.6525 | + | 16.4580i | −1.16358 | + | 0.845390i | −0.990226 | − | 0.139470i | \(-0.955460\pi\) |
−0.173353 | + | 0.984860i | \(0.555460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.23607 | − | 3.80423i | −0.0633257 | − | 0.194896i | ||||
\(382\) | −2.47214 | + | 7.60845i | −0.126485 | + | 0.389282i | ||||
\(383\) | 12.9443 | + | 9.40456i | 0.661421 | + | 0.480551i | 0.867143 | − | 0.498060i | \(-0.165954\pi\) |
−0.205721 | + | 0.978611i | \(0.565954\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.618034 | + | 1.90211i | −0.0313759 | + | 0.0965652i | ||||
\(389\) | −5.56231 | − | 17.1190i | −0.282020 | − | 0.867969i | −0.987276 | − | 0.159016i | \(-0.949168\pi\) |
0.705256 | − | 0.708953i | \(-0.250832\pi\) | |||||||
\(390\) | 3.23607 | − | 2.35114i | 0.163865 | − | 0.119055i | ||||
\(391\) | −12.9443 | + | 9.40456i | −0.654620 | + | 0.475609i | ||||
\(392\) | 8.34346 | + | 25.6785i | 0.421408 | + | 1.29696i | ||||
\(393\) | −3.70820 | + | 11.4127i | −0.187054 | + | 0.575693i | ||||
\(394\) | 11.3262 | + | 8.22899i | 0.570608 | + | 0.414571i | ||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.309017 | + | 0.951057i | 0.0154508 | + | 0.0475528i | ||||
\(401\) | −21.0344 | + | 15.2824i | −1.05041 | + | 0.763167i | −0.972290 | − | 0.233777i | \(-0.924892\pi\) |
−0.0781195 | + | 0.996944i | \(0.524892\pi\) | |||||||
\(402\) | 3.23607 | − | 2.35114i | 0.161400 | − | 0.117264i | ||||
\(403\) | −4.94427 | − | 15.2169i | −0.246292 | − | 0.758008i | ||||
\(404\) | 0.618034 | − | 1.90211i | 0.0307483 | − | 0.0946337i | ||||
\(405\) | 1.61803 | + | 1.17557i | 0.0804008 | + | 0.0584146i | ||||
\(406\) | 24.0000 | 1.19110 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.00000 | −0.297044 | ||||||||
\(409\) | 14.5623 | + | 10.5801i | 0.720060 | + | 0.523154i | 0.886403 | − | 0.462914i | \(-0.153196\pi\) |
−0.166344 | + | 0.986068i | \(0.553196\pi\) | |||||||
\(410\) | 1.23607 | − | 3.80423i | 0.0610450 | − | 0.187877i | ||||
\(411\) | −0.618034 | − | 1.90211i | −0.0304854 | − | 0.0938243i | ||||
\(412\) | 6.47214 | − | 4.70228i | 0.318859 | − | 0.231665i | ||||
\(413\) | −12.9443 | + | 9.40456i | −0.636946 | + | 0.462768i | ||||
\(414\) | −2.47214 | − | 7.60845i | −0.121499 | − | 0.373935i | ||||
\(415\) | 7.41641 | − | 22.8254i | 0.364057 | − | 1.12045i | ||||
\(416\) | 8.09017 | + | 5.87785i | 0.396653 | + | 0.288185i | ||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.00000 | −0.195413 | −0.0977064 | − | 0.995215i | \(-0.531151\pi\) | ||||
−0.0977064 | + | 0.995215i | \(0.531151\pi\) | |||||||
\(420\) | −6.47214 | − | 4.70228i | −0.315808 | − | 0.229448i | ||||
\(421\) | −8.03444 | + | 24.7275i | −0.391575 | + | 1.20514i | 0.540022 | + | 0.841651i | \(0.318416\pi\) |
−0.931597 | + | 0.363492i | \(0.881584\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.47214 | + | 4.70228i | −0.314686 | + | 0.228633i | ||||
\(424\) | −14.5623 | + | 10.5801i | −0.707208 | + | 0.513817i | ||||
\(425\) | −0.618034 | − | 1.90211i | −0.0299791 | − | 0.0922660i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.4164 | − | 14.1068i | −0.939626 | − | 0.682678i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.4164 | − | 14.1068i | −0.935255 | − | 0.679503i | 0.0120185 | − | 0.999928i | \(-0.496174\pi\) |
−0.947274 | + | 0.320425i | \(0.896174\pi\) | |||||||
\(432\) | 0.309017 | − | 0.951057i | 0.0148676 | − | 0.0457577i | ||||
\(433\) | 10.5066 | + | 32.3359i | 0.504914 | + | 1.55397i | 0.800915 | + | 0.598778i | \(0.204347\pi\) |
−0.296001 | + | 0.955188i | \(0.595653\pi\) | |||||||
\(434\) | 25.8885 | − | 18.8091i | 1.24269 | − | 0.902867i | ||||
\(435\) | −9.70820 | + | 7.05342i | −0.465473 | + | 0.338186i | ||||
\(436\) | −0.618034 | − | 1.90211i | −0.0295985 | − | 0.0910947i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −11.3262 | − | 8.22899i | −0.541189 | − | 0.393197i | ||||
\(439\) | 20.0000 | 0.954548 | 0.477274 | − | 0.878755i | \(-0.341625\pi\) | ||||
0.477274 | + | 0.878755i | \(0.341625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.00000 | 0.428571 | ||||||||
\(442\) | 3.23607 | + | 2.35114i | 0.153924 | + | 0.111832i | ||||
\(443\) | 8.65248 | − | 26.6296i | 0.411092 | − | 1.26521i | −0.504609 | − | 0.863348i | \(-0.668363\pi\) |
0.915700 | − | 0.401862i | \(-0.131637\pi\) | |||||||
\(444\) | 1.85410 | + | 5.70634i | 0.0879918 | + | 0.270811i | ||||
\(445\) | −9.70820 | + | 7.05342i | −0.460213 | + | 0.334364i | ||||
\(446\) | 12.9443 | − | 9.40456i | 0.612929 | − | 0.445319i | ||||
\(447\) | −6.79837 | − | 20.9232i | −0.321552 | − | 0.989635i | ||||
\(448\) | −8.65248 | + | 26.6296i | −0.408791 | + | 1.25813i | ||||
\(449\) | −1.61803 | − | 1.17557i | −0.0763597 | − | 0.0554786i | 0.548950 | − | 0.835855i | \(-0.315028\pi\) |
−0.625310 | + | 0.780376i | \(0.715028\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | −16.1803 | − | 11.7557i | −0.760219 | − | 0.552331i | ||||
\(454\) | 3.70820 | − | 11.4127i | 0.174035 | − | 0.535624i | ||||
\(455\) | 4.94427 | + | 15.2169i | 0.231791 | + | 0.713379i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.5623 | − | 10.5801i | 0.681196 | − | 0.494918i | −0.192558 | − | 0.981286i | \(-0.561678\pi\) |
0.873754 | + | 0.486368i | \(0.161678\pi\) | |||||||
\(458\) | −1.85410 | − | 5.70634i | −0.0866365 | − | 0.266640i | ||||
\(459\) | −0.618034 | + | 1.90211i | −0.0288474 | + | 0.0887830i | ||||
\(460\) | −12.9443 | − | 9.40456i | −0.603530 | − | 0.438490i | ||||
\(461\) | 30.0000 | 1.39724 | 0.698620 | − | 0.715493i | \(-0.253798\pi\) | ||||
0.698620 | + | 0.715493i | \(0.253798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 4.85410 | + | 3.52671i | 0.225346 | + | 0.163723i | ||||
\(465\) | −4.94427 | + | 15.2169i | −0.229285 | + | 0.705667i | ||||
\(466\) | 9.27051 | + | 28.5317i | 0.429448 | + | 1.32171i | ||||
\(467\) | 9.70820 | − | 7.05342i | 0.449242 | − | 0.326393i | −0.340054 | − | 0.940406i | \(-0.610445\pi\) |
0.789296 | + | 0.614012i | \(0.210445\pi\) | |||||||
\(468\) | 1.61803 | − | 1.17557i | 0.0747936 | − | 0.0543408i | ||||
\(469\) | 4.94427 | + | 15.2169i | 0.228305 | + | 0.702651i | ||||
\(470\) | 4.94427 | − | 15.2169i | 0.228062 | − | 0.701903i | ||||
\(471\) | 11.3262 | + | 8.22899i | 0.521885 | + | 0.379172i | ||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.00000 | 0.183726 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.47214 | − | 7.60845i | 0.113310 | − | 0.348733i | ||||
\(477\) | 1.85410 | + | 5.70634i | 0.0848935 | + | 0.261275i | ||||
\(478\) | −19.4164 | + | 14.1068i | −0.888086 | + | 0.645232i | ||||
\(479\) | 6.47214 | − | 4.70228i | 0.295719 | − | 0.214853i | −0.430025 | − | 0.902817i | \(-0.641495\pi\) |
0.725745 | + | 0.687964i | \(0.241495\pi\) | |||||||
\(480\) | −3.09017 | − | 9.51057i | −0.141046 | − | 0.434096i | ||||
\(481\) | 3.70820 | − | 11.4127i | 0.169080 | − | 0.520373i | ||||
\(482\) | −8.09017 | − | 5.87785i | −0.368497 | − | 0.267729i | ||||
\(483\) | 32.0000 | 1.45605 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.00000 | −0.181631 | ||||||||
\(486\) | −0.809017 | − | 0.587785i | −0.0366978 | − | 0.0266625i | ||||
\(487\) | −4.94427 | + | 15.2169i | −0.224046 | + | 0.689544i | 0.774341 | + | 0.632769i | \(0.218082\pi\) |
−0.998387 | + | 0.0567748i | \(0.981918\pi\) | |||||||
\(488\) | −5.56231 | − | 17.1190i | −0.251794 | − | 0.774942i | ||||
\(489\) | 3.23607 | − | 2.35114i | 0.146340 | − | 0.106322i | ||||
\(490\) | −14.5623 | + | 10.5801i | −0.657858 | + | 0.477962i | ||||
\(491\) | −1.23607 | − | 3.80423i | −0.0557830 | − | 0.171682i | 0.919283 | − | 0.393597i | \(-0.128769\pi\) |
−0.975066 | + | 0.221915i | \(0.928769\pi\) | |||||||
\(492\) | 0.618034 | − | 1.90211i | 0.0278631 | − | 0.0857539i | ||||
\(493\) | −9.70820 | − | 7.05342i | −0.437236 | − | 0.317670i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3.70820 | + | 11.4127i | −0.166169 | + | 0.511414i | ||||
\(499\) | −1.23607 | − | 3.80423i | −0.0553340 | − | 0.170301i | 0.919570 | − | 0.392926i | \(-0.128537\pi\) |
−0.974904 | + | 0.222626i | \(0.928537\pi\) | |||||||
\(500\) | 9.70820 | − | 7.05342i | 0.434164 | − | 0.315439i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.23607 | − | 3.80423i | −0.0551684 | − | 0.169791i | ||||
\(503\) | 9.88854 | − | 30.4338i | 0.440908 | − | 1.35698i | −0.446001 | − | 0.895033i | \(-0.647152\pi\) |
0.886909 | − | 0.461944i | \(-0.152848\pi\) | |||||||
\(504\) | 9.70820 | + | 7.05342i | 0.432438 | + | 0.314184i | ||||
\(505\) | 4.00000 | 0.177998 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.00000 | 0.399704 | ||||||||
\(508\) | 3.23607 | + | 2.35114i | 0.143577 | + | 0.104315i | ||||
\(509\) | 9.27051 | − | 28.5317i | 0.410908 | − | 1.26465i | −0.504952 | − | 0.863147i | \(-0.668490\pi\) |
0.915860 | − | 0.401498i | \(-0.131510\pi\) | |||||||
\(510\) | −1.23607 | − | 3.80423i | −0.0547340 | − | 0.168454i | ||||
\(511\) | 45.3050 | − | 32.9160i | 2.00417 | − | 1.45612i | ||||
\(512\) | −8.89919 | + | 6.46564i | −0.393292 | + | 0.285744i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.32624 | − | 13.3148i | 0.190822 | − | 0.587290i | ||||
\(515\) | 12.9443 | + | 9.40456i | 0.570393 | + | 0.414415i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 24.0000 | 1.05450 | ||||||||
\(519\) | 4.85410 | + | 3.52671i | 0.213071 | + | 0.154805i | ||||
\(520\) | −3.70820 | + | 11.4127i | −0.162615 | + | 0.500479i | ||||
\(521\) | −9.27051 | − | 28.5317i | −0.406148 | − | 1.25000i | −0.919933 | − | 0.392077i | \(-0.871757\pi\) |
0.513784 | − | 0.857920i | \(-0.328243\pi\) | |||||||
\(522\) | 4.85410 | − | 3.52671i | 0.212458 | − | 0.154360i | ||||
\(523\) | −12.9443 | + | 9.40456i | −0.566013 | + | 0.411233i | −0.833655 | − | 0.552286i | \(-0.813756\pi\) |
0.267641 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(524\) | −3.70820 | − | 11.4127i | −0.161994 | − | 0.498565i | ||||
\(525\) | −1.23607 | + | 3.80423i | −0.0539464 | + | 0.166030i | ||||
\(526\) | 12.9443 | + | 9.40456i | 0.564397 | + | 0.410058i | ||||
\(527\) | −16.0000 | −0.696971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | −9.70820 | − | 7.05342i | −0.421697 | − | 0.306381i | ||||
\(531\) | −1.23607 | + | 3.80423i | −0.0536408 | + | 0.165089i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.23607 | + | 2.35114i | −0.140170 | + | 0.101839i | ||||
\(534\) | 4.85410 | − | 3.52671i | 0.210058 | − | 0.152616i | ||||
\(535\) | −7.41641 | − | 22.8254i | −0.320639 | − | 0.986826i | ||||
\(536\) | −3.70820 | + | 11.4127i | −0.160170 | + | 0.492953i | ||||
\(537\) | 9.70820 | + | 7.05342i | 0.418940 | + | 0.304378i | ||||
\(538\) | 2.00000 | 0.0862261 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.00000 | −0.0860663 | ||||||||
\(541\) | 37.2148 | + | 27.0381i | 1.59999 | + | 1.16246i | 0.887535 | + | 0.460740i | \(0.152416\pi\) |
0.712453 | + | 0.701719i | \(0.247584\pi\) | |||||||
\(542\) | 6.18034 | − | 19.0211i | 0.265468 | − | 0.817028i | ||||
\(543\) | −6.79837 | − | 20.9232i | −0.291746 | − | 0.897902i | ||||
\(544\) | 8.09017 | − | 5.87785i | 0.346863 | − | 0.252011i | ||||
\(545\) | 3.23607 | − | 2.35114i | 0.138618 | − | 0.100712i | ||||
\(546\) | −2.47214 | − | 7.60845i | −0.105798 | − | 0.325612i | ||||
\(547\) | −2.47214 | + | 7.60845i | −0.105701 | + | 0.325314i | −0.989894 | − | 0.141807i | \(-0.954709\pi\) |
0.884193 | + | 0.467121i | \(0.154709\pi\) | |||||||
\(548\) | 1.61803 | + | 1.17557i | 0.0691190 | + | 0.0502179i | ||||
\(549\) | −6.00000 | −0.256074 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 19.4164 | + | 14.1068i | 0.826417 | + | 0.600427i | ||||
\(553\) | −4.94427 | + | 15.2169i | −0.210252 | + | 0.647089i | ||||
\(554\) | −8.03444 | − | 24.7275i | −0.341351 | − | 1.05057i | ||||
\(555\) | −9.70820 | + | 7.05342i | −0.412090 | + | 0.299401i | ||||
\(556\) | 6.47214 | − | 4.70228i | 0.274480 | − | 0.199421i | ||||
\(557\) | 4.32624 | + | 13.3148i | 0.183309 | + | 0.564166i | 0.999915 | − | 0.0130289i | \(-0.00414735\pi\) |
−0.816607 | + | 0.577195i | \(0.804147\pi\) | |||||||
\(558\) | 2.47214 | − | 7.60845i | 0.104654 | − | 0.322091i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8.00000 | −0.338062 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.0000 | −0.759284 | ||||||||
\(563\) | −35.5967 | − | 25.8626i | −1.50022 | − | 1.08998i | −0.970292 | − | 0.241936i | \(-0.922217\pi\) |
−0.529932 | − | 0.848040i | \(-0.677783\pi\) | |||||||
\(564\) | 2.47214 | − | 7.60845i | 0.104096 | − | 0.320374i | ||||
\(565\) | 3.70820 | + | 11.4127i | 0.156005 | + | 0.480135i | ||||
\(566\) | −12.9443 | + | 9.40456i | −0.544088 | + | 0.395303i | ||||
\(567\) | 3.23607 | − | 2.35114i | 0.135902 | − | 0.0987386i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.9787 | − | 39.9444i | 0.544096 | − | 1.67456i | −0.179034 | − | 0.983843i | \(-0.557297\pi\) |
0.723130 | − | 0.690712i | \(-0.242703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | 0.669579 | 0.334790 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334790 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | −6.47214 | − | 4.70228i | −0.270142 | − | 0.196269i | ||||
\(575\) | −2.47214 | + | 7.60845i | −0.103095 | + | 0.317294i | ||||
\(576\) | 2.16312 | + | 6.65740i | 0.0901300 | + | 0.277391i | ||||
\(577\) | 24.2705 | − | 17.6336i | 1.01039 | − | 0.734095i | 0.0461028 | − | 0.998937i | \(-0.485320\pi\) |
0.964292 | + | 0.264842i | \(0.0853198\pi\) | |||||||
\(578\) | −10.5172 | + | 7.64121i | −0.437459 | + | 0.317832i | ||||
\(579\) | −4.32624 | − | 13.3148i | −0.179792 | − | 0.553344i | ||||
\(580\) | 3.70820 | − | 11.4127i | 0.153975 | − | 0.473886i | ||||
\(581\) | −38.8328 | − | 28.2137i | −1.61106 | − | 1.17050i | ||||
\(582\) | 2.00000 | 0.0829027 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 42.0000 | 1.73797 | ||||||||
\(585\) | 3.23607 | + | 2.35114i | 0.133795 | + | 0.0972077i | ||||
\(586\) | −1.85410 | + | 5.70634i | −0.0765922 | + | 0.235727i | ||||
\(587\) | 8.65248 | + | 26.6296i | 0.357126 | + | 1.09912i | 0.954767 | + | 0.297356i | \(0.0961050\pi\) |
−0.597641 | + | 0.801764i | \(0.703895\pi\) | |||||||
\(588\) | −7.28115 | + | 5.29007i | −0.300270 | + | 0.218159i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −2.47214 | − | 7.60845i | −0.101776 | − | 0.313235i | ||||
\(591\) | −4.32624 | + | 13.3148i | −0.177958 | + | 0.547697i | ||||
\(592\) | 4.85410 | + | 3.52671i | 0.199502 | + | 0.144947i | ||||
\(593\) | −38.0000 | −1.56047 | −0.780236 | − | 0.625485i | \(-0.784901\pi\) | ||||
−0.780236 | + | 0.625485i | \(0.784901\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.0000 | 0.655936 | ||||||||
\(596\) | 17.7984 | + | 12.9313i | 0.729050 | + | 0.529686i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.94427 | − | 15.2169i | −0.202186 | − | 0.622265i | ||||
\(599\) | 6.47214 | − | 4.70228i | 0.264444 | − | 0.192130i | −0.447660 | − | 0.894204i | \(-0.647742\pi\) |
0.712104 | + | 0.702074i | \(0.247742\pi\) | |||||||
\(600\) | −2.42705 | + | 1.76336i | −0.0990839 | + | 0.0719887i | ||||
\(601\) | −8.03444 | − | 24.7275i | −0.327732 | − | 1.00865i | −0.970192 | − | 0.242336i | \(-0.922086\pi\) |
0.642461 | − | 0.766319i | \(-0.277914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.23607 | + | 2.35114i | 0.131783 | + | 0.0957459i | ||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.00000 | −0.0812444 | ||||||||
\(607\) | −3.23607 | − | 2.35114i | −0.131348 | − | 0.0954299i | 0.520171 | − | 0.854062i | \(-0.325868\pi\) |
−0.651519 | + | 0.758632i | \(0.725868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.41641 | + | 22.8254i | 0.300528 | + | 0.924930i | ||||
\(610\) | 9.70820 | − | 7.05342i | 0.393074 | − | 0.285585i | ||||
\(611\) | −12.9443 | + | 9.40456i | −0.523669 | + | 0.380468i | ||||
\(612\) | −0.618034 | − | 1.90211i | −0.0249825 | − | 0.0768884i | ||||
\(613\) | −4.32624 | + | 13.3148i | −0.174735 | + | 0.537779i | −0.999621 | − | 0.0275195i | \(-0.991239\pi\) |
0.824886 | + | 0.565299i | \(0.191239\pi\) | |||||||
\(614\) | −25.8885 | − | 18.8091i | −1.04478 | − | 0.759075i | ||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | −6.47214 | − | 4.70228i | −0.260347 | − | 0.189154i | ||||
\(619\) | 13.5967 | − | 41.8465i | 0.546499 | − | 1.68195i | −0.170898 | − | 0.985289i | \(-0.554667\pi\) |
0.717398 | − | 0.696664i | \(-0.245333\pi\) | |||||||
\(620\) | −4.94427 | − | 15.2169i | −0.198567 | − | 0.611126i | ||||
\(621\) | 6.47214 | − | 4.70228i | 0.259718 | − | 0.188696i | ||||
\(622\) | −19.4164 | + | 14.1068i | −0.778527 | + | 0.565633i | ||||
\(623\) | 7.41641 | + | 22.8254i | 0.297132 | + | 0.914479i | ||||
\(624\) | 0.618034 | − | 1.90211i | 0.0247412 | − | 0.0761455i | ||||
\(625\) | 15.3713 | + | 11.1679i | 0.614853 | + | 0.446717i | ||||
\(626\) | 22.0000 | 0.879297 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.0000 | −0.558661 | ||||||||
\(629\) | −9.70820 | − | 7.05342i | −0.387091 | − | 0.281238i | ||||
\(630\) | −2.47214 | + | 7.60845i | −0.0984923 | + | 0.303128i | ||||
\(631\) | 4.94427 | + | 15.2169i | 0.196828 | + | 0.605775i | 0.999950 | + | 0.00996082i | \(0.00317068\pi\) |
−0.803122 | + | 0.595815i | \(0.796829\pi\) | |||||||
\(632\) | −9.70820 | + | 7.05342i | −0.386172 | + | 0.280570i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.79837 | − | 20.9232i | −0.269998 | − | 0.830968i | ||||
\(635\) | −2.47214 | + | 7.60845i | −0.0981037 | + | 0.301932i | ||||
\(636\) | −4.85410 | − | 3.52671i | −0.192478 | − | 0.139843i | ||||
\(637\) | 18.0000 | 0.713186 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 4.85410 | + | 3.52671i | 0.191875 | + | 0.139406i | ||||
\(641\) | 5.56231 | − | 17.1190i | 0.219698 | − | 0.676161i | −0.779089 | − | 0.626914i | \(-0.784318\pi\) |
0.998787 | − | 0.0492469i | \(-0.0156821\pi\) | |||||||
\(642\) | 3.70820 | + | 11.4127i | 0.146351 | + | 0.450422i | ||||
\(643\) | −16.1803 | + | 11.7557i | −0.638090 | + | 0.463600i | −0.859194 | − | 0.511651i | \(-0.829034\pi\) |
0.221103 | + | 0.975250i | \(0.429034\pi\) | |||||||
\(644\) | −25.8885 | + | 18.8091i | −1.02015 | + | 0.741183i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.47214 | − | 4.70228i | −0.254446 | − | 0.184866i | 0.453249 | − | 0.891384i | \(-0.350265\pi\) |
−0.707695 | + | 0.706518i | \(0.750265\pi\) | |||||||
\(648\) | 3.00000 | 0.117851 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | 0.0784465 | ||||||||
\(651\) | 25.8885 | + | 18.8091i | 1.01465 | + | 0.737188i | ||||
\(652\) | −1.23607 | + | 3.80423i | −0.0484082 | + | 0.148985i | ||||
\(653\) | −0.618034 | − | 1.90211i | −0.0241855 | − | 0.0744354i | 0.938235 | − | 0.345998i | \(-0.112460\pi\) |
−0.962421 | + | 0.271563i | \(0.912460\pi\) | |||||||
\(654\) | −1.61803 | + | 1.17557i | −0.0632701 | + | 0.0459684i | ||||
\(655\) | 19.4164 | − | 14.1068i | 0.758662 | − | 0.551200i | ||||
\(656\) | −0.618034 | − | 1.90211i | −0.0241302 | − | 0.0742650i | ||||
\(657\) | 4.32624 | − | 13.3148i | 0.168783 | − | 0.519459i | ||||
\(658\) | −25.8885 | − | 18.8091i | −1.00924 | − | 0.733256i | ||||
\(659\) | −4.00000 | −0.155818 | −0.0779089 | − | 0.996960i | \(-0.524824\pi\) | ||||
−0.0779089 | + | 0.996960i | \(0.524824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26.0000 | −1.01128 | −0.505641 | − | 0.862744i | \(-0.668744\pi\) | ||||
−0.505641 | + | 0.862744i | \(0.668744\pi\) | |||||||
\(662\) | −16.1803 | − | 11.7557i | −0.628867 | − | 0.456898i | ||||
\(663\) | −1.23607 | + | 3.80423i | −0.0480049 | + | 0.147744i | ||||
\(664\) | −11.1246 | − | 34.2380i | −0.431719 | − | 1.32869i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.85410 | − | 3.52671i | 0.188093 | − | 0.136657i | ||||
\(667\) | 14.8328 | + | 45.6507i | 0.574329 | + | 1.76760i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.9443 | + | 9.40456i | 0.500454 | + | 0.363601i | ||||
\(670\) | −8.00000 | −0.309067 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −20.0000 | −0.771517 | ||||||||
\(673\) | −37.2148 | − | 27.0381i | −1.43452 | − | 1.04224i | −0.989152 | − | 0.146898i | \(-0.953071\pi\) |
−0.445373 | − | 0.895345i | \(-0.646929\pi\) | |||||||
\(674\) | −6.79837 | + | 20.9232i | −0.261864 | + | 0.805933i | ||||
\(675\) | 0.309017 | + | 0.951057i | 0.0118941 | + | 0.0366062i | ||||
\(676\) | −7.28115 | + | 5.29007i | −0.280044 | + | 0.203464i | ||||
\(677\) | 14.5623 | − | 10.5801i | 0.559675 | − | 0.406628i | −0.271665 | − | 0.962392i | \(-0.587574\pi\) |
0.831340 | + | 0.555764i | \(0.187574\pi\) | |||||||
\(678\) | −1.85410 | − | 5.70634i | −0.0712064 | − | 0.219151i | ||||
\(679\) | −2.47214 | + | 7.60845i | −0.0948719 | + | 0.291986i | ||||
\(680\) | 9.70820 | + | 7.05342i | 0.372293 | + | 0.270486i | ||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000 | 0.765279 | 0.382639 | − | 0.923898i | \(-0.375015\pi\) | ||||
0.382639 | + | 0.923898i | \(0.375015\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.23607 | + | 3.80423i | −0.0472277 | + | 0.145352i | ||||
\(686\) | 2.47214 | + | 7.60845i | 0.0943866 | + | 0.290492i | ||||
\(687\) | 4.85410 | − | 3.52671i | 0.185196 | − | 0.134552i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.70820 | + | 11.4127i | 0.141271 | + | 0.434788i | ||||
\(690\) | −4.94427 | + | 15.2169i | −0.188225 | + | 0.579298i | ||||
\(691\) | 22.6525 | + | 16.4580i | 0.861741 | + | 0.626091i | 0.928358 | − | 0.371687i | \(-0.121221\pi\) |
−0.0666172 | + | 0.997779i | \(0.521221\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 12.9443 | + | 9.40456i | 0.491004 | + | 0.356735i | ||||
\(696\) | −5.56231 | + | 17.1190i | −0.210839 | + | 0.648895i | ||||
\(697\) | 1.23607 | + | 3.80423i | 0.0468194 | + | 0.144095i | ||||
\(698\) | −4.85410 | + | 3.52671i | −0.183730 | + | 0.133488i | ||||
\(699\) | −24.2705 | + | 17.6336i | −0.917995 | + | 0.666962i | ||||
\(700\) | −1.23607 | − | 3.80423i | −0.0467190 | − | 0.143786i | ||||
\(701\) | −15.4508 | + | 47.5528i | −0.583571 | + | 1.79605i | 0.0213660 | + | 0.999772i | \(0.493198\pi\) |
−0.604936 | + | 0.796274i | \(0.706802\pi\) | |||||||
\(702\) | −1.61803 | − | 1.17557i | −0.0610688 | − | 0.0443690i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0000 | 0.602595 | ||||||||
\(706\) | 14.5623 | + | 10.5801i | 0.548060 | + | 0.398189i | ||||
\(707\) | 2.47214 | − | 7.60845i | 0.0929742 | − | 0.286145i | ||||
\(708\) | −1.23607 | − | 3.80423i | −0.0464543 | − | 0.142972i | ||||
\(709\) | −30.7426 | + | 22.3358i | −1.15456 | + | 0.838840i | −0.989081 | − | 0.147373i | \(-0.952918\pi\) |
−0.165483 | + | 0.986213i | \(0.552918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.23607 | + | 3.80423i | 0.0463562 | + | 0.142670i | ||||
\(712\) | −5.56231 | + | 17.1190i | −0.208456 | + | 0.641562i | ||||
\(713\) | 51.7771 | + | 37.6183i | 1.93907 | + | 1.40881i | ||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −19.4164 | − | 14.1068i | −0.725119 | − | 0.526830i | ||||
\(718\) | −2.47214 | + | 7.60845i | −0.0922593 | + | 0.283945i | ||||
\(719\) | 7.41641 | + | 22.8254i | 0.276585 | + | 0.851242i | 0.988796 | + | 0.149276i | \(0.0476943\pi\) |
−0.712210 | + | 0.701966i | \(0.752306\pi\) | |||||||
\(720\) | −1.61803 | + | 1.17557i | −0.0603006 | + | 0.0438109i | ||||
\(721\) | 25.8885 | − | 18.8091i | 0.964140 | − | 0.700489i | ||||
\(722\) | 5.87132 | + | 18.0701i | 0.218508 | + | 0.672499i | ||||
\(723\) | 3.09017 | − | 9.51057i | 0.114925 | − | 0.353702i | ||||
\(724\) | 17.7984 | + | 12.9313i | 0.661471 | + | 0.480587i | ||||
\(725\) | −6.00000 | −0.222834 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 19.4164 | + | 14.1068i | 0.719620 | + | 0.522834i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 8.65248 | + | 26.6296i | 0.320242 | + | 0.985605i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 4.85410 | − | 3.52671i | 0.179413 | − | 0.130351i | ||||
\(733\) | −9.27051 | − | 28.5317i | −0.342414 | − | 1.05384i | −0.962954 | − | 0.269667i | \(-0.913086\pi\) |
0.620540 | − | 0.784175i | \(-0.286914\pi\) | |||||||
\(734\) | 9.88854 | − | 30.4338i | 0.364993 | − | 1.12333i | ||||
\(735\) | −14.5623 | − | 10.5801i | −0.537139 | − | 0.390254i | ||||
\(736\) | −40.0000 | −1.47442 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −2.00000 | −0.0736210 | ||||||||
\(739\) | 6.47214 | + | 4.70228i | 0.238081 | + | 0.172976i | 0.700428 | − | 0.713723i | \(-0.252992\pi\) |
−0.462347 | + | 0.886699i | \(0.652992\pi\) | |||||||
\(740\) | 3.70820 | − | 11.4127i | 0.136316 | − | 0.419538i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −19.4164 | + | 14.1068i | −0.712799 | + | 0.517879i | ||||
\(743\) | 32.3607 | − | 23.5114i | 1.18720 | − | 0.862550i | 0.194233 | − | 0.980955i | \(-0.437778\pi\) |
0.992965 | + | 0.118405i | \(0.0377783\pi\) | |||||||
\(744\) | 7.41641 | + | 22.8254i | 0.271899 | + | 0.836818i | ||||
\(745\) | −13.5967 | + | 41.8465i | −0.498146 | + | 1.53314i | ||||
\(746\) | 1.61803 | + | 1.17557i | 0.0592404 | + | 0.0430407i | ||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −48.0000 | −1.75388 | ||||||||
\(750\) | −9.70820 | − | 7.05342i | −0.354493 | − | 0.257555i | ||||
\(751\) | −2.47214 | + | 7.60845i | −0.0902095 | + | 0.277636i | −0.985976 | − | 0.166889i | \(-0.946628\pi\) |
0.895766 | + | 0.444526i | \(0.146628\pi\) | |||||||
\(752\) | −2.47214 | − | 7.60845i | −0.0901495 | − | 0.277452i | ||||
\(753\) | 3.23607 | − | 2.35114i | 0.117929 | − | 0.0856803i | ||||
\(754\) | 9.70820 | − | 7.05342i | 0.353552 | − | 0.256871i | ||||
\(755\) | 12.3607 | + | 38.0423i | 0.449851 | + | 1.38450i | ||||
\(756\) | −1.23607 | + | 3.80423i | −0.0449554 | + | 0.138358i | ||||
\(757\) | 8.09017 | + | 5.87785i | 0.294042 | + | 0.213634i | 0.725019 | − | 0.688729i | \(-0.241831\pi\) |
−0.430977 | + | 0.902363i | \(0.641831\pi\) | |||||||
\(758\) | −28.0000 | −1.01701 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.85410 | + | 3.52671i | 0.175961 | + | 0.127843i | 0.672280 | − | 0.740297i | \(-0.265315\pi\) |
−0.496319 | + | 0.868140i | \(0.665315\pi\) | |||||||
\(762\) | 1.23607 | − | 3.80423i | 0.0447780 | − | 0.137813i | ||||
\(763\) | −2.47214 | − | 7.60845i | −0.0894973 | − | 0.275444i | ||||
\(764\) | 6.47214 | − | 4.70228i | 0.234154 | − | 0.170123i | ||||
\(765\) | 3.23607 | − | 2.35114i | 0.117000 | − | 0.0850057i | ||||
\(766\) | 4.94427 | + | 15.2169i | 0.178644 | + | 0.549809i | ||||
\(767\) | −2.47214 | + | 7.60845i | −0.0892637 | + | 0.274725i | ||||
\(768\) | −13.7533 | − | 9.99235i | −0.496279 | − | 0.360568i | ||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | 0.504198 | ||||||||
\(772\) | 11.3262 | + | 8.22899i | 0.407640 | + | 0.296168i | ||||
\(773\) | 1.85410 | − | 5.70634i | 0.0666874 | − | 0.205243i | −0.912160 | − | 0.409834i | \(-0.865587\pi\) |
0.978847 | + | 0.204591i | \(0.0655866\pi\) | |||||||
\(774\) | 0 | 0 |