Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,2,Mod(37,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("198.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.f (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.58103796002\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 163.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 198.163 |
Dual form | 198.2.f.b.181.1 |
$q$-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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(155\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.951057i | 0.218508 | − | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 1.11803 | + | 3.44095i | 0.500000 | + | 1.53884i | 0.809017 | + | 0.587785i | \(0.200000\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.11803 | + | 2.26538i | 1.17851 | + | 0.856235i | 0.992002 | − | 0.126219i | \(-0.0402844\pi\) |
0.186504 | + | 0.982454i | \(0.440284\pi\) | |||||||
\(8\) | −0.809017 | + | 0.587785i | −0.286031 | + | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.61803 | 1.14412 | ||||||||
\(11\) | −3.23607 | + | 0.726543i | −0.975711 | + | 0.219061i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | − | 6.15537i | 0.554700 | − | 1.70719i | −0.142034 | − | 0.989862i | \(-0.545364\pi\) |
0.696734 | − | 0.717330i | \(-0.254636\pi\) | |||||||
\(14\) | 3.11803 | − | 2.26538i | 0.833330 | − | 0.605449i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −1.00000 | − | 3.07768i | −0.242536 | − | 0.746448i | −0.996032 | − | 0.0889958i | \(-0.971634\pi\) |
0.753496 | − | 0.657452i | \(-0.228366\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.61803 | + | 1.17557i | −0.371202 | + | 0.269694i | −0.757709 | − | 0.652592i | \(-0.773682\pi\) |
0.386507 | + | 0.922287i | \(0.373682\pi\) | |||||||
\(20\) | 1.11803 | − | 3.44095i | 0.250000 | − | 0.769421i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.309017 | + | 3.30220i | −0.0658826 | + | 0.704031i | ||||
\(23\) | 2.76393 | 0.576320 | 0.288160 | − | 0.957582i | \(-0.406957\pi\) | ||||
0.288160 | + | 0.957582i | \(0.406957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.54508 | + | 4.75528i | −1.30902 | + | 0.951057i | ||||
\(26\) | −5.23607 | − | 3.80423i | −1.02688 | − | 0.746070i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.19098 | − | 3.66547i | −0.225075 | − | 0.692708i | ||||
\(29\) | −0.309017 | − | 0.224514i | −0.0573830 | − | 0.0416912i | 0.558724 | − | 0.829354i | \(-0.311291\pi\) |
−0.616107 | + | 0.787662i | \(0.711291\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0450850 | − | 0.138757i | 0.00809750 | − | 0.0249215i | −0.946926 | − | 0.321451i | \(-0.895829\pi\) |
0.955024 | + | 0.296530i | \(0.0958294\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.23607 | −0.554981 | ||||||||
\(35\) | −4.30902 | + | 13.2618i | −0.728357 | + | 2.24165i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 2.17963i | −0.493197 | − | 0.358329i | 0.313215 | − | 0.949682i | \(-0.398594\pi\) |
−0.806412 | + | 0.591354i | \(0.798594\pi\) | |||||||
\(38\) | 0.618034 | + | 1.90211i | 0.100258 | + | 0.308563i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.92705 | − | 2.12663i | −0.462807 | − | 0.336249i | ||||
\(41\) | 5.47214 | − | 3.97574i | 0.854604 | − | 0.620906i | −0.0718076 | − | 0.997419i | \(-0.522877\pi\) |
0.926412 | + | 0.376512i | \(0.122877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 3.04508 | + | 1.31433i | 0.459064 | + | 0.198142i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.854102 | − | 2.62866i | 0.125930 | − | 0.387574i | ||||
\(47\) | −3.85410 | + | 2.80017i | −0.562179 | + | 0.408447i | −0.832256 | − | 0.554392i | \(-0.812951\pi\) |
0.270077 | + | 0.962839i | \(0.412951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.42705 | + | 7.46969i | 0.346722 | + | 1.06710i | ||||
\(50\) | 2.50000 | + | 7.69421i | 0.353553 | + | 1.08813i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.23607 | + | 3.80423i | −0.726112 | + | 0.527551i | ||||
\(53\) | 2.89919 | − | 8.92278i | 0.398234 | − | 1.22564i | −0.528180 | − | 0.849132i | \(-0.677125\pi\) |
0.926414 | − | 0.376506i | \(-0.122875\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.11803 | − | 10.3229i | −0.824956 | − | 1.39193i | ||||
\(56\) | −3.85410 | −0.515026 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.309017 | + | 0.224514i | −0.0405759 | + | 0.0294801i | ||||
\(59\) | −9.97214 | − | 7.24518i | −1.29826 | − | 0.943242i | −0.298324 | − | 0.954465i | \(-0.596428\pi\) |
−0.999937 | + | 0.0112223i | \(0.996428\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.854102 | + | 2.62866i | 0.109357 | + | 0.336565i | 0.990728 | − | 0.135859i | \(-0.0433793\pi\) |
−0.881372 | + | 0.472423i | \(0.843379\pi\) | |||||||
\(62\) | −0.118034 | − | 0.0857567i | −0.0149903 | − | 0.0108911i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 23.4164 | 2.90445 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.9443 | −1.33706 | −0.668528 | − | 0.743687i | \(-0.733075\pi\) | ||||
−0.668528 | + | 0.743687i | \(0.733075\pi\) | |||||||
\(68\) | −1.00000 | + | 3.07768i | −0.121268 | + | 0.373224i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 11.2812 | + | 8.19624i | 1.34836 | + | 0.979638i | ||||
\(71\) | −0.236068 | − | 0.726543i | −0.0280161 | − | 0.0862247i | 0.936071 | − | 0.351812i | \(-0.114434\pi\) |
−0.964087 | + | 0.265587i | \(0.914434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.92705 | + | 1.40008i | 0.225544 | + | 0.163867i | 0.694819 | − | 0.719185i | \(-0.255485\pi\) |
−0.469275 | + | 0.883052i | \(0.655485\pi\) | |||||||
\(74\) | −3.00000 | + | 2.17963i | −0.348743 | + | 0.253377i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | −11.7361 | − | 5.06555i | −1.33745 | − | 0.577273i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.20820 | + | 6.79615i | −0.248442 | + | 0.764627i | 0.746609 | + | 0.665263i | \(0.231681\pi\) |
−0.995051 | + | 0.0993636i | \(0.968319\pi\) | |||||||
\(80\) | −2.92705 | + | 2.12663i | −0.327254 | + | 0.237764i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.09017 | − | 6.43288i | −0.230821 | − | 0.710393i | ||||
\(83\) | 2.40983 | + | 7.41669i | 0.264513 | + | 0.814088i | 0.991805 | + | 0.127760i | \(0.0407786\pi\) |
−0.727292 | + | 0.686328i | \(0.759221\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.47214 | − | 6.88191i | 1.02740 | − | 0.746448i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.19098 | − | 2.48990i | 0.233560 | − | 0.265424i | ||||
\(89\) | −6.18034 | −0.655115 | −0.327557 | − | 0.944831i | \(-0.606225\pi\) | ||||
−0.327557 | + | 0.944831i | \(0.606225\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.1803 | − | 14.6619i | 2.11547 | − | 1.53698i | ||||
\(92\) | −2.23607 | − | 1.62460i | −0.233126 | − | 0.169376i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.47214 | + | 4.53077i | 0.151839 | + | 0.467313i | ||||
\(95\) | −5.85410 | − | 4.25325i | −0.600618 | − | 0.436375i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.20820 | + | 6.79615i | −0.224209 | + | 0.690045i | 0.774162 | + | 0.632988i | \(0.218172\pi\) |
−0.998371 | + | 0.0570570i | \(0.981828\pi\) | |||||||
\(98\) | 7.85410 | 0.793384 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.09017 | 0.809017 | ||||||||
\(101\) | 1.82624 | − | 5.62058i | 0.181717 | − | 0.559269i | −0.818159 | − | 0.574992i | \(-0.805005\pi\) |
0.999876 | + | 0.0157233i | \(0.00500509\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.35410 | + | 4.61653i | 0.626088 | + | 0.454880i | 0.855043 | − | 0.518557i | \(-0.173531\pi\) |
−0.228955 | + | 0.973437i | \(0.573531\pi\) | |||||||
\(104\) | 2.00000 | + | 6.15537i | 0.196116 | + | 0.603583i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.59017 | − | 5.51458i | −0.737222 | − | 0.535623i | ||||
\(107\) | 11.2082 | − | 8.14324i | 1.08354 | − | 0.787236i | 0.105242 | − | 0.994447i | \(-0.466438\pi\) |
0.978296 | + | 0.207210i | \(0.0664384\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.76393 | 0.456302 | 0.228151 | − | 0.973626i | \(-0.426732\pi\) | ||||
0.228151 | + | 0.973626i | \(0.426732\pi\) | |||||||
\(110\) | −11.7082 | + | 2.62866i | −1.11633 | + | 0.250632i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.19098 | + | 3.66547i | −0.112537 | + | 0.346354i | ||||
\(113\) | 7.85410 | − | 5.70634i | 0.738852 | − | 0.536807i | −0.153500 | − | 0.988149i | \(-0.549054\pi\) |
0.892351 | + | 0.451341i | \(0.149054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.09017 | + | 9.51057i | 0.288160 | + | 0.886865i | ||||
\(116\) | 0.118034 | + | 0.363271i | 0.0109592 | + | 0.0337289i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −9.97214 | + | 7.24518i | −0.918010 | + | 0.666973i | ||||
\(119\) | 3.85410 | − | 11.8617i | 0.353305 | − | 1.08736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.94427 | − | 4.70228i | 0.904025 | − | 0.427480i | ||||
\(122\) | 2.76393 | 0.250235 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.118034 | + | 0.0857567i | −0.0105998 | + | 0.00770118i | ||||
\(125\) | −9.04508 | − | 6.57164i | −0.809017 | − | 0.587785i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.291796 | + | 0.898056i | 0.0258927 | + | 0.0796896i | 0.963168 | − | 0.268901i | \(-0.0866604\pi\) |
−0.937275 | + | 0.348590i | \(0.886660\pi\) | |||||||
\(128\) | −0.809017 | − | 0.587785i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.23607 | − | 22.2703i | 0.634645 | − | 1.95324i | ||||
\(131\) | −11.0902 | −0.968953 | −0.484476 | − | 0.874804i | \(-0.660990\pi\) | ||||
−0.484476 | + | 0.874804i | \(0.660990\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.70820 | −0.668386 | ||||||||
\(134\) | −3.38197 | + | 10.4086i | −0.292157 | + | 0.899168i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.61803 | + | 1.90211i | 0.224495 | + | 0.163105i | ||||
\(137\) | 5.09017 | + | 15.6659i | 0.434883 | + | 1.33843i | 0.893207 | + | 0.449646i | \(0.148450\pi\) |
−0.458324 | + | 0.888785i | \(0.651550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | − | 2.17963i | −0.254457 | − | 0.184874i | 0.453243 | − | 0.891387i | \(-0.350267\pi\) |
−0.707700 | + | 0.706513i | \(0.750267\pi\) | |||||||
\(140\) | 11.2812 | − | 8.19624i | 0.953431 | − | 0.692708i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.763932 | −0.0641078 | ||||||||
\(143\) | −2.00000 | + | 21.3723i | −0.167248 | + | 1.78724i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.427051 | − | 1.31433i | 0.0354647 | − | 0.109149i | ||||
\(146\) | 1.92705 | − | 1.40008i | 0.159484 | − | 0.115872i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.14590 | + | 3.52671i | 0.0941922 | + | 0.289894i | ||||
\(149\) | 3.28115 | + | 10.0984i | 0.268803 | + | 0.827289i | 0.990793 | + | 0.135386i | \(0.0432275\pi\) |
−0.721990 | + | 0.691903i | \(0.756773\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3992 | − | 7.55545i | 0.846274 | − | 0.614854i | −0.0778423 | − | 0.996966i | \(-0.524803\pi\) |
0.924116 | + | 0.382112i | \(0.124803\pi\) | |||||||
\(152\) | 0.618034 | − | 1.90211i | 0.0501292 | − | 0.154282i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.44427 | + | 9.59632i | −0.680459 | + | 0.773294i | ||||
\(155\) | 0.527864 | 0.0423991 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7082 | + | 9.23305i | −1.01423 | + | 0.736878i | −0.965091 | − | 0.261915i | \(-0.915646\pi\) |
−0.0491340 | + | 0.998792i | \(0.515646\pi\) | |||||||
\(158\) | 5.78115 | + | 4.20025i | 0.459924 | + | 0.334154i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.11803 | + | 3.44095i | 0.0883883 | + | 0.272031i | ||||
\(161\) | 8.61803 | + | 6.26137i | 0.679196 | + | 0.493465i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.76393 | + | 20.8172i | −0.529792 | + | 1.63053i | 0.224848 | + | 0.974394i | \(0.427811\pi\) |
−0.754640 | + | 0.656139i | \(0.772189\pi\) | |||||||
\(164\) | −6.76393 | −0.528174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.79837 | 0.605271 | ||||||||
\(167\) | −6.38197 | + | 19.6417i | −0.493851 | + | 1.51992i | 0.324888 | + | 0.945753i | \(0.394673\pi\) |
−0.818739 | + | 0.574166i | \(0.805327\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −23.3713 | − | 16.9803i | −1.79779 | − | 1.30617i | ||||
\(170\) | −3.61803 | − | 11.1352i | −0.277491 | − | 0.854028i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8262 | + | 10.0453i | −1.05119 | + | 0.763734i | −0.972438 | − | 0.233160i | \(-0.925093\pi\) |
−0.0787511 | + | 0.996894i | \(0.525093\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −31.1803 | −2.35701 | ||||||||
\(176\) | −1.69098 | − | 2.85317i | −0.127463 | − | 0.215066i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.90983 | + | 5.87785i | −0.143148 | + | 0.440564i | ||||
\(179\) | 16.0172 | − | 11.6372i | 1.19718 | − | 0.869805i | 0.203179 | − | 0.979142i | \(-0.434873\pi\) |
0.994005 | + | 0.109337i | \(0.0348728\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.52786 | − | 23.1684i | −0.559542 | − | 1.72209i | −0.683637 | − | 0.729822i | \(-0.739603\pi\) |
0.124095 | − | 0.992270i | \(-0.460397\pi\) | |||||||
\(182\) | −7.70820 | − | 23.7234i | −0.571370 | − | 1.75850i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.23607 | + | 1.62460i | −0.164845 | + | 0.119767i | ||||
\(185\) | 4.14590 | − | 12.7598i | 0.304812 | − | 0.938116i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.47214 | + | 9.23305i | 0.400162 | + | 0.675188i | ||||
\(188\) | 4.76393 | 0.347445 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.85410 | + | 4.25325i | −0.424701 | + | 0.308563i | ||||
\(191\) | −12.3262 | − | 8.95554i | −0.891895 | − | 0.648000i | 0.0444762 | − | 0.999010i | \(-0.485838\pi\) |
−0.936371 | + | 0.351011i | \(0.885838\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.89919 | − | 5.84510i | −0.136706 | − | 0.420739i | 0.859145 | − | 0.511732i | \(-0.170996\pi\) |
−0.995852 | + | 0.0909928i | \(0.970996\pi\) | |||||||
\(194\) | 5.78115 | + | 4.20025i | 0.415063 | + | 0.301561i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.42705 | − | 7.46969i | 0.173361 | − | 0.533550i | ||||
\(197\) | 0.381966 | 0.0272140 | 0.0136070 | − | 0.999907i | \(-0.495669\pi\) | ||||
0.0136070 | + | 0.999907i | \(0.495669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.79837 | 0.694588 | 0.347294 | − | 0.937756i | \(-0.387101\pi\) | ||||
0.347294 | + | 0.937756i | \(0.387101\pi\) | |||||||
\(200\) | 2.50000 | − | 7.69421i | 0.176777 | − | 0.544063i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.78115 | − | 3.47371i | −0.336401 | − | 0.244409i | ||||
\(203\) | −0.454915 | − | 1.40008i | −0.0319288 | − | 0.0982667i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.7984 | + | 14.3844i | 1.38278 | + | 1.00465i | ||||
\(206\) | 6.35410 | − | 4.61653i | 0.442711 | − | 0.321649i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.47214 | 0.448762 | ||||||||
\(209\) | 4.38197 | − | 4.97980i | 0.303107 | − | 0.344460i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.14590 | − | 6.60440i | 0.147730 | − | 0.454665i | −0.849622 | − | 0.527392i | \(-0.823170\pi\) |
0.997352 | + | 0.0727265i | \(0.0231700\pi\) | |||||||
\(212\) | −7.59017 | + | 5.51458i | −0.521295 | + | 0.378743i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.28115 | − | 13.1760i | −0.292654 | − | 0.900695i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.454915 | − | 0.330515i | 0.0308816 | − | 0.0224368i | ||||
\(218\) | 1.47214 | − | 4.53077i | 0.0997056 | − | 0.306862i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.11803 | + | 11.9475i | −0.0753778 | + | 0.805498i | ||||
\(221\) | −20.9443 | −1.40886 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.16312 | + | 5.20431i | −0.479678 | + | 0.348506i | −0.801201 | − | 0.598395i | \(-0.795805\pi\) |
0.321523 | + | 0.946902i | \(0.395805\pi\) | |||||||
\(224\) | 3.11803 | + | 2.26538i | 0.208332 | + | 0.151362i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00000 | − | 9.23305i | −0.199557 | − | 0.614173i | ||||
\(227\) | 8.16312 | + | 5.93085i | 0.541805 | + | 0.393645i | 0.824755 | − | 0.565490i | \(-0.191313\pi\) |
−0.282950 | + | 0.959135i | \(0.591313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.47214 | + | 16.8415i | −0.361609 | + | 1.11292i | 0.590468 | + | 0.807061i | \(0.298943\pi\) |
−0.952077 | + | 0.305857i | \(0.901057\pi\) | |||||||
\(230\) | 10.0000 | 0.659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.381966 | 0.0250773 | ||||||||
\(233\) | 4.29180 | − | 13.2088i | 0.281165 | − | 0.865337i | −0.706357 | − | 0.707856i | \(-0.749663\pi\) |
0.987522 | − | 0.157481i | \(-0.0503373\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.9443 | − | 10.1311i | −0.909624 | − | 0.660881i | ||||
\(236\) | 3.80902 | + | 11.7229i | 0.247946 | + | 0.763099i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.0902 | − | 7.33094i | −0.654049 | − | 0.475194i | ||||
\(239\) | −10.8541 | + | 7.88597i | −0.702093 | + | 0.510101i | −0.880613 | − | 0.473836i | \(-0.842869\pi\) |
0.178520 | + | 0.983936i | \(0.442869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.5066 | 0.676788 | 0.338394 | − | 0.941004i | \(-0.390116\pi\) | ||||
0.338394 | + | 0.941004i | \(0.390116\pi\) | |||||||
\(242\) | −1.39919 | − | 10.9106i | −0.0899431 | − | 0.701363i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.854102 | − | 2.62866i | 0.0546783 | − | 0.168282i | ||||
\(245\) | −22.9894 | + | 16.7027i | −1.46874 | + | 1.06710i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.00000 | + | 12.3107i | 0.254514 | + | 0.783313i | ||||
\(248\) | 0.0450850 | + | 0.138757i | 0.00286290 | + | 0.00881110i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.04508 | + | 6.57164i | −0.572061 | + | 0.415627i | ||||
\(251\) | −6.11803 | + | 18.8294i | −0.386167 | + | 1.18850i | 0.549463 | + | 0.835518i | \(0.314832\pi\) |
−0.935630 | + | 0.352982i | \(0.885168\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.94427 | + | 2.00811i | −0.562322 | + | 0.126249i | ||||
\(254\) | 0.944272 | 0.0592489 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 12.0902 | + | 8.78402i | 0.754164 | + | 0.547932i | 0.897115 | − | 0.441798i | \(-0.145659\pi\) |
−0.142951 | + | 0.989730i | \(0.545659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.41641 | − | 13.5923i | −0.274422 | − | 0.844585i | ||||
\(260\) | −18.9443 | − | 13.7638i | −1.17487 | − | 0.853596i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.42705 | + | 10.5474i | −0.211724 | + | 0.651619i | ||||
\(263\) | 14.9443 | 0.921503 | 0.460752 | − | 0.887529i | \(-0.347580\pi\) | ||||
0.460752 | + | 0.887529i | \(0.347580\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 33.9443 | 2.08518 | ||||||||
\(266\) | −2.38197 | + | 7.33094i | −0.146048 | + | 0.449489i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.85410 | + | 6.43288i | 0.540850 | + | 0.392951i | ||||
\(269\) | 2.14590 | + | 6.60440i | 0.130838 | + | 0.402677i | 0.994919 | − | 0.100675i | \(-0.0321001\pi\) |
−0.864082 | + | 0.503352i | \(0.832100\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.9443 | + | 13.7638i | 1.15078 | + | 0.836092i | 0.988585 | − | 0.150666i | \(-0.0481417\pi\) |
0.162198 | + | 0.986758i | \(0.448142\pi\) | |||||||
\(272\) | 2.61803 | − | 1.90211i | 0.158742 | − | 0.115333i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.4721 | 0.995118 | ||||||||
\(275\) | 17.7254 | − | 20.1437i | 1.06888 | − | 1.21471i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.32624 | + | 13.3148i | −0.259938 | + | 0.800008i | 0.732878 | + | 0.680360i | \(0.238177\pi\) |
−0.992816 | + | 0.119648i | \(0.961823\pi\) | |||||||
\(278\) | −3.00000 | + | 2.17963i | −0.179928 | + | 0.130725i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.30902 | − | 13.2618i | −0.257513 | − | 0.792544i | ||||
\(281\) | 2.76393 | + | 8.50651i | 0.164882 | + | 0.507456i | 0.999028 | − | 0.0440891i | \(-0.0140386\pi\) |
−0.834145 | + | 0.551545i | \(0.814039\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.4164 | − | 16.2865i | 1.33252 | − | 0.968130i | 0.332833 | − | 0.942986i | \(-0.391995\pi\) |
0.999684 | − | 0.0251447i | \(-0.00800465\pi\) | |||||||
\(284\) | −0.236068 | + | 0.726543i | −0.0140081 | + | 0.0431124i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.7082 | + | 8.50651i | 1.16537 | + | 0.503000i | ||||
\(287\) | 26.0689 | 1.53880 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.28115 | − | 3.83698i | 0.310656 | − | 0.225705i | ||||
\(290\) | −1.11803 | − | 0.812299i | −0.0656532 | − | 0.0476999i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −0.736068 | − | 2.26538i | −0.0430751 | − | 0.132572i | ||||
\(293\) | −19.5902 | − | 14.2331i | −1.14447 | − | 0.831506i | −0.156734 | − | 0.987641i | \(-0.550097\pi\) |
−0.987736 | + | 0.156135i | \(0.950097\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.7812 | − | 42.4140i | 0.802370 | − | 2.46944i | ||||
\(296\) | 3.70820 | 0.215535 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.6180 | 0.615086 | ||||||||
\(299\) | 5.52786 | − | 17.0130i | 0.319685 | − | 0.983888i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.97214 | − | 12.2250i | −0.228571 | − | 0.703468i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.61803 | − | 1.17557i | −0.0928006 | − | 0.0674236i | ||||
\(305\) | −8.09017 | + | 5.87785i | −0.463242 | + | 0.336565i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.3607 | −1.16205 | −0.581023 | − | 0.813887i | \(-0.697347\pi\) | ||||
−0.581023 | + | 0.813887i | \(0.697347\pi\) | |||||||
\(308\) | 6.51722 | + | 10.9964i | 0.371353 | + | 0.626578i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.163119 | − | 0.502029i | 0.00926453 | − | 0.0285133i | ||||
\(311\) | 9.09017 | − | 6.60440i | 0.515456 | − | 0.374501i | −0.299433 | − | 0.954117i | \(-0.596798\pi\) |
0.814889 | + | 0.579616i | \(0.196798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.50000 | − | 10.7719i | −0.197832 | − | 0.608863i | −0.999932 | − | 0.0116738i | \(-0.996284\pi\) |
0.802100 | − | 0.597190i | \(-0.203716\pi\) | |||||||
\(314\) | 4.85410 | + | 14.9394i | 0.273933 | + | 0.843079i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.78115 | − | 4.20025i | 0.325215 | − | 0.236283i | ||||
\(317\) | −10.1459 | + | 31.2259i | −0.569850 | + | 1.75382i | 0.0832297 | + | 0.996530i | \(0.473476\pi\) |
−0.653080 | + | 0.757289i | \(0.726524\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.16312 | + | 0.502029i | 0.0651222 | + | 0.0281082i | ||||
\(320\) | 3.61803 | 0.202254 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.61803 | − | 6.26137i | 0.480264 | − | 0.348932i | ||||
\(323\) | 5.23607 | + | 3.80423i | 0.291343 | + | 0.211673i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.1803 | + | 49.7980i | 0.897524 | + | 2.76229i | ||||
\(326\) | 17.7082 | + | 12.8658i | 0.980767 | + | 0.712569i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.09017 | + | 6.43288i | −0.115410 | + | 0.355196i | ||||
\(329\) | −18.3607 | −1.01226 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.29180 | −0.455758 | −0.227879 | − | 0.973689i | \(-0.573179\pi\) | ||||
−0.227879 | + | 0.973689i | \(0.573179\pi\) | |||||||
\(332\) | 2.40983 | − | 7.41669i | 0.132257 | − | 0.407044i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.7082 | + | 12.1392i | 0.914232 | + | 0.664229i | ||||
\(335\) | −12.2361 | − | 37.6587i | −0.668528 | − | 2.05752i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.5623 | − | 13.4863i | −1.01115 | − | 0.734646i | −0.0467026 | − | 0.998909i | \(-0.514871\pi\) |
−0.964451 | + | 0.264263i | \(0.914871\pi\) | |||||||
\(338\) | −23.3713 | + | 16.9803i | −1.27123 | + | 0.923604i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −11.7082 | −0.634967 | ||||||||
\(341\) | −0.0450850 | + | 0.481784i | −0.00244149 | + | 0.0260901i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.01722 | + | 3.13068i | −0.0549248 | + | 0.169041i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.28115 | + | 16.2537i | 0.283917 | + | 0.873805i | ||||
\(347\) | −3.62868 | − | 11.1679i | −0.194798 | − | 0.599525i | −0.999979 | − | 0.00649662i | \(-0.997932\pi\) |
0.805181 | − | 0.593029i | \(-0.202068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.61803 | − | 6.26137i | 0.461313 | − | 0.335163i | −0.332733 | − | 0.943021i | \(-0.607971\pi\) |
0.794046 | + | 0.607858i | \(0.207971\pi\) | |||||||
\(350\) | −9.63525 | + | 29.6543i | −0.515026 | + | 1.58509i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.23607 | + | 0.726543i | −0.172483 | + | 0.0387248i | ||||
\(353\) | 24.6525 | 1.31212 | 0.656059 | − | 0.754709i | \(-0.272222\pi\) | ||||
0.656059 | + | 0.754709i | \(0.272222\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.23607 | − | 1.62460i | 0.118678 | − | 0.0862247i | ||||
\(356\) | 5.00000 | + | 3.63271i | 0.264999 | + | 0.192533i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.11803 | − | 18.8294i | −0.323348 | − | 0.995163i | ||||
\(359\) | −10.8541 | − | 7.88597i | −0.572858 | − | 0.416205i | 0.263285 | − | 0.964718i | \(-0.415194\pi\) |
−0.836142 | + | 0.548513i | \(0.815194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.63525 | + | 14.2658i | −0.243961 | + | 0.750834i | ||||
\(362\) | −24.3607 | −1.28037 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −24.9443 | −1.30744 | ||||||||
\(365\) | −2.66312 | + | 8.19624i | −0.139394 | + | 0.429011i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.39919 | + | 3.19620i | 0.229636 | + | 0.166840i | 0.696653 | − | 0.717408i | \(-0.254672\pi\) |
−0.467018 | + | 0.884248i | \(0.654672\pi\) | |||||||
\(368\) | 0.854102 | + | 2.62866i | 0.0445231 | + | 0.137028i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.8541 | − | 7.88597i | −0.564278 | − | 0.409972i | ||||
\(371\) | 29.2533 | − | 21.2538i | 1.51876 | − | 1.10344i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.70820 | 0.0884474 | 0.0442237 | − | 0.999022i | \(-0.485919\pi\) | ||||
0.0442237 | + | 0.999022i | \(0.485919\pi\) | |||||||
\(374\) | 10.4721 | − | 2.35114i | 0.541501 | − | 0.121575i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.47214 | − | 4.53077i | 0.0759196 | − | 0.233657i | ||||
\(377\) | −2.00000 | + | 1.45309i | −0.103005 | + | 0.0748377i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.90983 | + | 27.4216i | 0.457667 | + | 1.40855i | 0.867975 | + | 0.496608i | \(0.165421\pi\) |
−0.410308 | + | 0.911947i | \(0.634579\pi\) | |||||||
\(380\) | 2.23607 | + | 6.88191i | 0.114708 | + | 0.353035i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.3262 | + | 8.95554i | −0.630665 | + | 0.458205i | ||||
\(383\) | 5.05573 | − | 15.5599i | 0.258336 | − | 0.795075i | −0.734818 | − | 0.678264i | \(-0.762733\pi\) |
0.993154 | − | 0.116812i | \(-0.0372673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.30902 | − | 46.0467i | 0.219608 | − | 2.34676i | ||||
\(386\) | −6.14590 | −0.312818 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.78115 | − | 4.20025i | 0.293494 | − | 0.213236i | ||||
\(389\) | 6.85410 | + | 4.97980i | 0.347517 | + | 0.252486i | 0.747827 | − | 0.663894i | \(-0.231097\pi\) |
−0.400310 | + | 0.916380i | \(0.631097\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.76393 | − | 8.50651i | −0.139778 | − | 0.430193i | ||||
\(392\) | −6.35410 | − | 4.61653i | −0.320931 | − | 0.233170i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.118034 | − | 0.363271i | 0.00594647 | − | 0.0183013i | ||||
\(395\) | −25.8541 | −1.30086 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −31.4164 | −1.57674 | −0.788372 | − | 0.615199i | \(-0.789076\pi\) | ||||
−0.788372 | + | 0.615199i | \(0.789076\pi\) | |||||||
\(398\) | 3.02786 | − | 9.31881i | 0.151773 | − | 0.467110i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.54508 | − | 4.75528i | −0.327254 | − | 0.237764i | ||||
\(401\) | −4.03444 | − | 12.4167i | −0.201470 | − | 0.620062i | −0.999840 | − | 0.0178943i | \(-0.994304\pi\) |
0.798369 | − | 0.602168i | \(-0.205696\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.763932 | − | 0.555029i | −0.0380542 | − | 0.0276480i | ||||
\(404\) | −4.78115 | + | 3.47371i | −0.237871 | + | 0.172824i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.47214 | −0.0730609 | ||||||||
\(407\) | 11.2918 | + | 4.87380i | 0.559714 | + | 0.241585i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.79180 | + | 20.9030i | −0.335833 | + | 1.03359i | 0.630478 | + | 0.776207i | \(0.282859\pi\) |
−0.966310 | + | 0.257379i | \(0.917141\pi\) | |||||||
\(410\) | 19.7984 | − | 14.3844i | 0.977772 | − | 0.710393i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.42705 | − | 7.46969i | −0.119572 | − | 0.368005i | ||||
\(413\) | −14.6803 | − | 45.1814i | −0.722372 | − | 2.22323i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.8262 | + | 16.5842i | −1.12050 | + | 0.814088i | ||||
\(416\) | 2.00000 | − | 6.15537i | 0.0980581 | − | 0.301792i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.38197 | − | 5.70634i | −0.165417 | − | 0.279106i | ||||
\(419\) | −13.1459 | −0.642219 | −0.321110 | − | 0.947042i | \(-0.604056\pi\) | ||||
−0.321110 | + | 0.947042i | \(0.604056\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8541 | − | 10.0656i | 0.675208 | − | 0.490567i | −0.196557 | − | 0.980492i | \(-0.562976\pi\) |
0.871764 | + | 0.489925i | \(0.162976\pi\) | |||||||
\(422\) | −5.61803 | − | 4.08174i | −0.273482 | − | 0.198696i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.89919 | + | 8.92278i | 0.140797 | + | 0.433328i | ||||
\(425\) | 21.1803 | + | 15.3884i | 1.02740 | + | 0.746448i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.29180 | + | 10.1311i | −0.159301 | + | 0.490279i | ||||
\(428\) | −13.8541 | −0.669663 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.5623 | − | 38.6628i | 0.605105 | − | 1.86232i | 0.109038 | − | 0.994038i | \(-0.465223\pi\) |
0.496067 | − | 0.868284i | \(-0.334777\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2082 | + | 7.41669i | 0.490575 | + | 0.356424i | 0.805405 | − | 0.592724i | \(-0.201948\pi\) |
−0.314830 | + | 0.949148i | \(0.601948\pi\) | |||||||
\(434\) | −0.173762 | − | 0.534785i | −0.00834085 | − | 0.0256705i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.85410 | − | 2.80017i | −0.184578 | − | 0.134104i | ||||
\(437\) | −4.47214 | + | 3.24920i | −0.213931 | + | 0.155430i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.8541 | −0.756675 | −0.378338 | − | 0.925668i | \(-0.623504\pi\) | ||||
−0.378338 | + | 0.925668i | \(0.623504\pi\) | |||||||
\(440\) | 11.0172 | + | 4.75528i | 0.525225 | + | 0.226699i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.47214 | + | 19.9192i | −0.307848 | + | 0.947459i | ||||
\(443\) | −26.2082 | + | 19.0414i | −1.24519 | + | 0.904683i | −0.997933 | − | 0.0642670i | \(-0.979529\pi\) |
−0.247257 | + | 0.968950i | \(0.579529\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.90983 | − | 21.2663i | −0.327557 | − | 1.00812i | ||||
\(446\) | 2.73607 | + | 8.42075i | 0.129557 | + | 0.398734i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.11803 | − | 2.26538i | 0.147313 | − | 0.107029i | ||||
\(449\) | −4.41641 | + | 13.5923i | −0.208423 | + | 0.641461i | 0.791132 | + | 0.611645i | \(0.209492\pi\) |
−0.999555 | + | 0.0298154i | \(0.990508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.8197 | + | 16.8415i | −0.697831 | + | 0.793035i | ||||
\(452\) | −9.70820 | −0.456636 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.16312 | − | 5.93085i | 0.383114 | − | 0.278349i | ||||
\(455\) | 73.0132 | + | 53.0472i | 3.42291 | + | 2.48689i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.791796 | − | 2.43690i | −0.0370387 | − | 0.113993i | 0.930828 | − | 0.365458i | \(-0.119088\pi\) |
−0.967866 | + | 0.251465i | \(0.919088\pi\) | |||||||
\(458\) | 14.3262 | + | 10.4086i | 0.669421 | + | 0.486363i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.09017 | − | 9.51057i | 0.144080 | − | 0.443432i | ||||
\(461\) | −32.4721 | −1.51238 | −0.756189 | − | 0.654353i | \(-0.772941\pi\) | ||||
−0.756189 | + | 0.654353i | \(0.772941\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2705 | −0.709681 | −0.354840 | − | 0.934927i | \(-0.615465\pi\) | ||||
−0.354840 | + | 0.934927i | \(0.615465\pi\) | |||||||
\(464\) | 0.118034 | − | 0.363271i | 0.00547959 | − | 0.0168644i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.2361 | − | 8.16348i | −0.520501 | − | 0.378166i | ||||
\(467\) | 8.75329 | + | 26.9399i | 0.405054 | + | 1.24663i | 0.920850 | + | 0.389916i | \(0.127496\pi\) |
−0.515796 | + | 0.856711i | \(0.672504\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −34.1246 | − | 24.7930i | −1.57573 | − | 1.14483i | ||||
\(470\) | −13.9443 | + | 10.1311i | −0.643201 | + | 0.467313i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12.3262 | 0.567361 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.00000 | − | 15.3884i | 0.229416 | − | 0.706069i | ||||
\(476\) | −10.0902 | + | 7.33094i | −0.462482 | + | 0.336013i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.14590 | + | 12.7598i | 0.189629 | + | 0.583618i | ||||
\(479\) | −8.76393 | − | 26.9726i | −0.400434 | − | 1.23241i | −0.924648 | − | 0.380823i | \(-0.875641\pi\) |
0.524214 | − | 0.851587i | \(-0.324359\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.4164 | + | 14.1068i | −0.885312 | + | 0.643217i | ||||
\(482\) | 3.24671 | − | 9.99235i | 0.147884 | − | 0.455139i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8090 | − | 2.04087i | −0.491319 | − | 0.0927668i | ||||
\(485\) | −25.8541 | −1.17397 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3541 | − | 7.52270i | 0.469189 | − | 0.340886i | −0.327936 | − | 0.944700i | \(-0.606353\pi\) |
0.797125 | + | 0.603814i | \(0.206353\pi\) | |||||||
\(488\) | −2.23607 | − | 1.62460i | −0.101222 | − | 0.0735421i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.78115 | + | 27.0256i | 0.396692 | + | 1.22089i | ||||
\(491\) | 19.4164 | + | 14.1068i | 0.876250 | + | 0.636633i | 0.932257 | − | 0.361797i | \(-0.117837\pi\) |
−0.0560065 | + | 0.998430i | \(0.517837\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.381966 | + | 1.17557i | −0.0172029 | + | 0.0529450i | ||||
\(494\) | 12.9443 | 0.582390 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.145898 | 0.00655102 | ||||||||
\(497\) | 0.909830 | − | 2.80017i | 0.0408115 | − | 0.125605i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3262 | + | 12.5882i | 0.775629 | + | 0.563527i | 0.903664 | − | 0.428242i | \(-0.140867\pi\) |
−0.128035 | + | 0.991770i | \(0.540867\pi\) | |||||||
\(500\) | 3.45492 | + | 10.6331i | 0.154508 | + | 0.475528i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.0172 | + | 11.6372i | 0.714884 | + | 0.519393i | ||||
\(503\) | −28.2705 | + | 20.5397i | −1.26052 | + | 0.915821i | −0.998783 | − | 0.0493181i | \(-0.984295\pi\) |
−0.261737 | + | 0.965139i | \(0.584295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 21.3820 | 0.951485 | ||||||||
\(506\) | −0.854102 | + | 9.12705i | −0.0379695 | + | 0.405747i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.291796 | − | 0.898056i | 0.0129464 | − | 0.0398448i | ||||
\(509\) | 19.0623 | − | 13.8496i | 0.844922 | − | 0.613872i | −0.0788193 | − | 0.996889i | \(-0.525115\pi\) |
0.923741 | + | 0.383017i | \(0.125115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.83688 | + | 8.73102i | 0.125496 | + | 0.386238i | ||||
\(512\) | 0.309017 | + | 0.951057i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.0902 | − | 8.78402i | 0.533275 | − | 0.387447i | ||||
\(515\) | −8.78115 | + | 27.0256i | −0.386944 | + | 1.19089i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4377 | − | 11.8617i | 0.459049 | − | 0.521677i | ||||
\(518\) | −14.2918 | −0.627945 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.9443 | + | 13.7638i | −0.830761 | + | 0.603583i | ||||
\(521\) | 24.3262 | + | 17.6740i | 1.06575 | + | 0.774314i | 0.975144 | − | 0.221573i | \(-0.0711190\pi\) |
0.0906080 | + | 0.995887i | \(0.471119\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.76393 | − | 30.0503i | −0.426947 | − | 1.31401i | −0.901118 | − | 0.433575i | \(-0.857252\pi\) |
0.474171 | − | 0.880433i | \(-0.342748\pi\) | |||||||
\(524\) | 8.97214 | + | 6.51864i | 0.391950 | + | 0.284768i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.61803 | − | 14.2128i | 0.201356 | − | 0.619710i | ||||
\(527\) | −0.472136 | −0.0205666 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3607 | −0.667856 | ||||||||
\(530\) | 10.4894 | − | 32.2829i | 0.455629 | − | 1.40228i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.23607 | + | 4.53077i | 0.270368 | + | 0.196434i | ||||
\(533\) | −13.5279 | − | 41.6345i | −0.585957 | − | 1.80339i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.5517 | + | 29.4625i | 1.75320 | + | 1.27378i | ||||
\(536\) | 8.85410 | − | 6.43288i | 0.382439 | − | 0.277858i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.94427 | 0.299389 | ||||||||
\(539\) | −13.2812 | − | 22.4091i | −0.572060 | − | 0.965228i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.1803 | − | 37.4872i | 0.523674 | − | 1.61170i | −0.243250 | − | 0.969964i | \(-0.578214\pi\) |
0.766924 | − | 0.641738i | \(-0.221786\pi\) | |||||||
\(542\) | 18.9443 | − | 13.7638i | 0.813726 | − | 0.591207i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | − | 3.07768i | −0.0428746 | − | 0.131955i | ||||
\(545\) | 5.32624 | + | 16.3925i | 0.228151 | + | 0.702176i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.14590 | + | 3.73871i | −0.220023 | + | 0.159856i | −0.692337 | − | 0.721574i | \(-0.743419\pi\) |
0.472314 | + | 0.881430i | \(0.343419\pi\) | |||||||
\(548\) | 5.09017 | − | 15.6659i | 0.217441 | − | 0.669215i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −13.6803 | − | 23.0826i | −0.583332 | − | 0.984247i | ||||
\(551\) | 0.763932 | 0.0325446 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −22.2812 | + | 16.1882i | −0.947491 | + | 0.688393i | ||||
\(554\) | 11.3262 | + | 8.22899i | 0.481206 | + | 0.349616i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.14590 | + | 3.52671i | 0.0485969 | + | 0.149566i | ||||
\(557\) | 7.59017 | + | 5.51458i | 0.321606 | + | 0.233660i | 0.736860 | − | 0.676045i | \(-0.236307\pi\) |
−0.415255 | + | 0.909705i | \(0.636307\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −13.9443 | −0.589253 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.94427 | 0.377291 | ||||||||
\(563\) | 1.81966 | − | 5.60034i | 0.0766895 | − | 0.236026i | −0.905361 | − | 0.424642i | \(-0.860400\pi\) |
0.982051 | + | 0.188616i | \(0.0604000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 28.4164 | + | 20.6457i | 1.19549 | + | 0.868572i | ||||
\(566\) | −8.56231 | − | 26.3521i | −0.359901 | − | 1.10766i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.618034 | + | 0.449028i | 0.0259321 | + | 0.0188408i | ||||
\(569\) | 13.4721 | − | 9.78808i | 0.564781 | − | 0.410338i | −0.268424 | − | 0.963301i | \(-0.586503\pi\) |
0.833206 | + | 0.552963i | \(0.186503\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.7639 | 1.37113 | 0.685564 | − | 0.728012i | \(-0.259556\pi\) | ||||
0.685564 | + | 0.728012i | \(0.259556\pi\) | |||||||
\(572\) | 14.1803 | − | 16.1150i | 0.592910 | − | 0.673800i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.05573 | − | 24.7930i | 0.336240 | − | 1.03484i | ||||
\(575\) | −18.0902 | + | 13.1433i | −0.754412 | + | 0.548113i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.8435 | + | 33.3727i | 0.451419 | + | 1.38933i | 0.875288 | + | 0.483602i | \(0.160672\pi\) |
−0.423869 | + | 0.905723i | \(0.639328\pi\) | |||||||
\(578\) | −2.01722 | − | 6.20837i | −0.0839053 | − | 0.258234i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.11803 | + | 0.812299i | −0.0464238 | + | 0.0337289i | ||||
\(581\) | −9.28773 | + | 28.5847i | −0.385320 | + | 1.18589i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.89919 | + | 30.9811i | −0.120072 | + | 1.28311i | ||||
\(584\) | −2.38197 | −0.0985665 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.5902 | + | 14.2331i | −0.809262 | + | 0.587964i | ||||
\(587\) | −34.1976 | − | 24.8460i | −1.41148 | − | 1.02550i | −0.993105 | − | 0.117231i | \(-0.962598\pi\) |
−0.418380 | − | 0.908272i | \(-0.637402\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0901699 | + | 0.277515i | 0.00371539 | + | 0.0114348i | ||||
\(590\) | −36.0795 | − | 26.2133i | −1.48537 | − | 1.07918i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.14590 | − | 3.52671i | 0.0470961 | − | 0.144947i | ||||
\(593\) | −9.70820 | −0.398668 | −0.199334 | − | 0.979932i | \(-0.563878\pi\) | ||||
−0.199334 | + | 0.979932i | \(0.563878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 45.1246 | 1.84993 | ||||||||
\(596\) | 3.28115 | − | 10.0984i | 0.134401 | − | 0.413645i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.4721 | − | 10.5146i | −0.591810 | − | 0.429975i | ||||
\(599\) | 2.72949 | + | 8.40051i | 0.111524 | + | 0.343235i | 0.991206 | − | 0.132327i | \(-0.0422448\pi\) |
−0.879682 | + | 0.475562i | \(0.842245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.44427 | − | 3.95550i | −0.222076 | − | 0.161348i | 0.471184 | − | 0.882035i | \(-0.343827\pi\) |
−0.693261 | + | 0.720687i | \(0.743827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.8541 | −0.523026 | ||||||||
\(605\) | 27.2984 | + | 28.9605i | 1.10984 | + | 1.17741i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.0000 | − | 36.9322i | 0.487065 | − | 1.49903i | −0.341903 | − | 0.939735i | \(-0.611071\pi\) |
0.828968 | − | 0.559297i | \(-0.188929\pi\) | |||||||
\(608\) | −1.61803 | + | 1.17557i | −0.0656199 | + | 0.0476757i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.09017 | + | 9.51057i | 0.125117 | + | 0.385072i | ||||
\(611\) | 9.52786 | + | 29.3238i | 0.385456 | + | 1.18631i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.9443 | − | 20.3027i | 1.12866 | − | 0.820018i | 0.143160 | − | 0.989700i | \(-0.454274\pi\) |
0.985499 | + | 0.169681i | \(0.0542738\pi\) | |||||||
\(614\) | −6.29180 | + | 19.3642i | −0.253916 | + | 0.781474i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.4721 | − | 2.80017i | 0.502517 | − | 0.112822i | ||||
\(617\) | 32.0689 | 1.29104 | 0.645522 | − | 0.763741i | \(-0.276640\pi\) | ||||
0.645522 | + | 0.763741i | \(0.276640\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.61803 | + | 1.90211i | −0.105228 | + | 0.0764524i | −0.639155 | − | 0.769078i | \(-0.720716\pi\) |
0.533927 | + | 0.845531i | \(0.320716\pi\) | |||||||
\(620\) | −0.427051 | − | 0.310271i | −0.0171508 | − | 0.0124608i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.47214 | − | 10.6861i | −0.139220 | − | 0.428475i | ||||
\(623\) | −19.2705 | − | 14.0008i | −0.772057 | − | 0.560932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −11.3262 | −0.452688 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.7082 | 0.626826 | ||||||||
\(629\) | −3.70820 | + | 11.4127i | −0.147856 | + | 0.455053i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6697 | − | 27.3686i | −1.49961 | − | 1.08953i | −0.970538 | − | 0.240950i | \(-0.922541\pi\) |
−0.529069 | − | 0.848579i | \(-0.677459\pi\) | |||||||
\(632\) | −2.20820 | − | 6.79615i | −0.0878376 | − | 0.270336i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.5623 | + | 19.2986i | 1.05492 | + | 0.766447i | ||||
\(635\) | −2.76393 | + | 2.00811i | −0.109683 | + | 0.0796896i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 50.8328 | 2.01407 | ||||||||
\(638\) | 0.836881 | − | 0.951057i | 0.0331324 | − | 0.0376527i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.11803 | − | 3.44095i | 0.0441942 | − | 0.136016i | ||||
\(641\) | −17.2361 | + | 12.5227i | −0.680784 | + | 0.494618i | −0.873618 | − | 0.486613i | \(-0.838232\pi\) |
0.192834 | + | 0.981231i | \(0.438232\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.27051 | − | 10.0656i | −0.128976 | − | 0.396948i | 0.865628 | − | 0.500687i | \(-0.166919\pi\) |
−0.994605 | + | 0.103739i | \(0.966919\pi\) | |||||||
\(644\) | −3.29180 | − | 10.1311i | −0.129715 | − | 0.399222i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.23607 | − | 3.80423i | 0.206010 | − | 0.149675i | ||||
\(647\) | −1.20163 | + | 3.69822i | −0.0472408 | + | 0.145392i | −0.971895 | − | 0.235417i | \(-0.924354\pi\) |
0.924654 | + | 0.380809i | \(0.124354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 37.5344 | + | 16.2007i | 1.47336 | + | 0.635934i | ||||
\(650\) | 52.3607 | 2.05375 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.7082 | − | 12.8658i | 0.693507 | − | 0.503862i | ||||
\(653\) | 3.54508 | + | 2.57565i | 0.138730 | + | 0.100793i | 0.654986 | − | 0.755641i | \(-0.272675\pi\) |
−0.516256 | + | 0.856434i | \(0.672675\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.3992 | − | 38.1608i | −0.484476 | − | 1.49106i | ||||
\(656\) | 5.47214 | + | 3.97574i | 0.213651 | + | 0.155227i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.67376 | + | 17.4620i | −0.221186 | + | 0.680741i | ||||
\(659\) | 4.20163 | 0.163672 | 0.0818361 | − | 0.996646i | \(-0.473922\pi\) | ||||
0.0818361 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1803 | −0.629342 | −0.314671 | − | 0.949201i | \(-0.601894\pi\) | ||||
−0.314671 | + | 0.949201i | \(0.601894\pi\) | |||||||
\(662\) | −2.56231 | + | 7.88597i | −0.0995868 | + | 0.306497i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.30902 | − | 4.58377i | −0.244837 | − | 0.177885i | ||||
\(665\) | −8.61803 | − | 26.5236i | −0.334193 | − | 1.02854i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.854102 | − | 0.620541i | −0.0330710 | − | 0.0240275i | ||||
\(668\) | 16.7082 | − | 12.1392i | 0.646460 | − | 0.469681i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −39.5967 | −1.52976 | ||||||||
\(671\) | −4.67376 | − | 7.88597i | −0.180429 | − | 0.304434i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0279 | + | 33.9403i | −0.425093 | + | 1.30830i | 0.477812 | + | 0.878462i | \(0.341430\pi\) |
−0.902905 | + | 0.429840i | \(0.858570\pi\) | |||||||
\(674\) | −18.5623 | + | 13.4863i | −0.714993 | + | 0.519473i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.92705 | + | 27.4746i | 0.343348 | + | 1.05672i | ||||
\(677\) | 6.51722 | + | 20.0579i | 0.250477 | + | 0.770889i | 0.994687 | + | 0.102944i | \(0.0328262\pi\) |
−0.744210 | + | 0.667946i | \(0.767174\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.2812 | + | 16.1882i | −0.855072 | + | 0.621246i | ||||
\(680\) | −3.61803 | + | 11.1352i | −0.138745 | + | 0.427014i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.444272 | + | 0.191758i | 0.0170121 | + | 0.00734279i | ||||
\(683\) | −16.3262 | −0.624706 | −0.312353 | − | 0.949966i | \(-0.601117\pi\) | ||||
−0.312353 | + | 0.949966i | \(0.601117\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −48.2148 | + | 35.0301i | −1.84219 | + | 1.33843i | ||||
\(686\) | 2.66312 | + | 1.93487i | 0.101678 | + | 0.0738736i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −49.1246 | − | 35.6911i | −1.87150 | − | 1.35972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.29180 | + | 3.97574i | −0.0491422 | + | 0.151244i | −0.972616 | − | 0.232416i | \(-0.925337\pi\) |
0.923474 | + | 0.383661i | \(0.125337\pi\) | |||||||
\(692\) | 17.0902 | 0.649671 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.7426 | −0.445745 | ||||||||
\(695\) | 4.14590 | − | 12.7598i | 0.157263 | − | 0.484005i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.7082 | − | 12.8658i | −0.670746 | − | 0.487326i | ||||
\(698\) | −3.29180 | − | 10.1311i | −0.124596 | − | 0.383468i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 25.2254 | + | 18.3273i | 0.953431 | + | 0.692708i | ||||
\(701\) | 14.5623 | − | 10.5801i | 0.550011 | − | 0.399606i | −0.277779 | − | 0.960645i | \(-0.589598\pi\) |
0.827789 | + | 0.561039i | \(0.189598\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.41641 | 0.279715 | ||||||||
\(704\) | −0.309017 | + | 3.30220i | −0.0116465 | + | 0.124456i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.61803 | − | 23.4459i | 0.286708 | − | 0.882398i | ||||
\(707\) | 18.4271 | − | 13.3880i | 0.693021 | − | 0.503509i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.90983 | − | 24.3440i | −0.297060 | − | 0.914256i | −0.982522 | − | 0.186148i | \(-0.940400\pi\) |
0.685462 | − | 0.728109i | \(-0.259600\pi\) | |||||||
\(710\) | −0.854102 | − | 2.62866i | −0.0320539 | − | 0.0986517i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.00000 | − | 3.63271i | 0.187383 | − | 0.136142i | ||||
\(713\) | 0.124612 | − | 0.383516i | 0.00466675 | − | 0.0143628i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −75.7771 | + | 17.0130i | −2.83390 | + | 0.636251i | ||||
\(716\) | −19.7984 | −0.739900 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.8541 | + | 7.88597i | −0.405071 | + | 0.294302i | ||||
\(719\) | 6.00000 | + | 4.35926i | 0.223762 | + | 0.162573i | 0.694019 | − | 0.719957i | \(-0.255839\pi\) |
−0.470256 | + | 0.882530i | \(0.655839\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.35410 | + | 28.7890i | 0.348365 | + | 1.07216i | ||||
\(722\) | 12.1353 | + | 8.81678i | 0.451627 | + | 0.328127i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.52786 | + | 23.1684i | −0.279771 | + | 0.861046i | ||||
\(725\) | 3.09017 | 0.114766 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | −7.70820 | + | 23.7234i | −0.285685 | + | 0.879248i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.97214 | + | 5.06555i | 0.258050 | + | 0.187485i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.0902 | − | 14.5964i | −0.742047 | − | 0.539129i | 0.151304 | − | 0.988487i | \(-0.451653\pi\) |
−0.893352 | + | 0.449358i | \(0.851653\pi\) | |||||||
\(734\) | 4.39919 | − | 3.19620i | 0.162377 | − | 0.117974i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.76393 | 0.101880 | ||||||||
\(737\) | 35.4164 | − | 7.95148i | 1.30458 | − | 0.292896i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6525 | − | 35.8626i | 0.428643 | − | 1.31923i | −0.470819 | − | 0.882230i | \(-0.656042\pi\) |
0.899462 | − | 0.436998i | \(-0.143958\pi\) | |||||||
\(740\) | −10.8541 | + | 7.88597i | −0.399005 | + | 0.289894i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.1738 | − | 34.3893i | −0.410202 | − | 1.26247i | ||||
\(743\) | 6.32624 | + | 19.4702i | 0.232087 | + | 0.714291i | 0.997494 | + | 0.0707447i | \(0.0225376\pi\) |
−0.765407 | + | 0.643546i | \(0.777462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.0795 | + | 22.5806i | −1.13867 | + | 0.827289i | ||||
\(746\) | 0.527864 | − | 1.62460i | 0.0193265 | − | 0.0594808i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.00000 | − | 10.6861i | 0.0365636 | − | 0.390724i | ||||
\(749\) | 53.3951 | 1.95102 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.7082 | − | 17.2250i | 0.865125 | − | 0.628550i | −0.0641496 | − | 0.997940i | \(-0.520433\pi\) |
0.929274 | + | 0.369390i | \(0.120433\pi\) | |||||||
\(752\) | −3.85410 | − | 2.80017i | −0.140545 | − | 0.102112i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.763932 | + | 2.35114i | 0.0278208 | + | 0.0856235i | ||||
\(755\) | 37.6246 | + | 27.3359i | 1.36930 | + | 0.994855i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5623 | − | 47.8959i | 0.565622 | − | 1.74080i | −0.100476 | − | 0.994940i | \(-0.532036\pi\) |
0.666097 | − | 0.745865i | \(-0.267964\pi\) | |||||||
\(758\) | 28.8328 | 1.04726 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.23607 | 0.262480 | ||||||||
\(761\) | −2.96556 | + | 9.12705i | −0.107501 | + | 0.330855i | −0.990309 | − | 0.138879i | \(-0.955650\pi\) |
0.882808 | + | 0.469734i | \(0.155650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.8541 | + | 10.7921i | 0.537755 | + | 0.390702i | ||||
\(764\) | 4.70820 | + | 14.4904i | 0.170337 | + | 0.524243i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.2361 | − | 9.61657i | −0.478239 | − | 0.347461i | ||||
\(767\) | −64.5410 | + | 46.8918i | −2.33044 | + | 1.69316i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.9787 | 0.792573 | 0.396286 | − | 0.918127i | \(-0.370299\pi\) | ||||
0.396286 | + | 0.918127i | \(0.370299\pi\) | |||||||
\(770\) | −42.4615 | − | 18.3273i | −1.53021 | − | 0.660472i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.89919 | + | 5.84510i | −0.0683532 | + | 0.210370i | ||||
\(773\) | 7.69098 | − | 5.58783i | 0.276625 | − | 0.200980i | −0.440819 | − | 0.897596i | \(-0.645312\pi\) |
0.717444 | + | 0.696616i | \(0.245312\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.364745 | + | 1.12257i | 0.0131020 | + | 0.0403239i | ||||
\(776\) | −2.20820 | − | 6.79615i | −0.0792699 | − | 0.243968i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.85410 | − | 4.97980i | 0.245731 | − | 0.178534i | ||||
\(779\) | −4.18034 | + | 12.8658i | −0.149776 | + | 0.460964i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.29180 | + | 2.17963i | 0.0462241 | + | 0.0779932i | ||||
\(782\) | −8.94427 | −0.319847 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.35410 | + | 4.61653i | −0.226932 | + | 0.164876i | ||||
\(785\) | −45.9787 | − | 33.4055i | −1.64105 | − | 1.19229i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.291796 | − | 0.898056i | −0.0104014 | − | 0.0320122i | 0.945721 | − | 0.324979i | \(-0.105357\pi\) |
−0.956123 | + | 0.292967i | \(0.905357\pi\) | |||||||
\(788\) | −0.309017 | − | 0.224514i | −0.0110083 | − | 0.00799798i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −7.98936 | + | 24.5887i | −0.284249 | + | 0.874827i | ||||
\(791\) | 37.4164 | 1.33037 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.8885 | 0.635241 | ||||||||
\(794\) | −9.70820 | + | 29.8788i | −0.344531 | + | 1.06036i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.92705 | − | 5.75934i | −0.280967 | − | 0.204134i | ||||
\(797\) | 10.5172 | + | 32.3687i | 0.372539 | + | 1.14656i | 0.945124 | + | 0.326712i | \(0.105941\pi\) |
−0.572585 | + | 0.819845i | \(0.694059\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.4721 | + | 9.06154i | 0.441232 | + | 0.320574i | ||||
\(800\) | −6.54508 | + | 4.75528i | −0.231404 | + | 0.168125i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.0557 | −0.461014 | ||||||||
\(803\) | −7.25329 | − | 3.13068i | −0.255963 | − | 0.110479i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9098 | + | 36.6547i | −0.419766 | + | 1.29191i | ||||
\(806\) | −0.763932 | + | 0.555029i | −0.0269084 | + | 0.0195501i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.82624 | + | 5.62058i | 0.0642468 | + | 0.197731i | ||||
\(809\) | −8.09017 | − | 24.8990i | −0.284435 | − | 0.875402i | −0.986567 | − | 0.163355i | \(-0.947768\pi\) |
0.702132 | − | 0.712047i | \(-0.252232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.2148 | + | 26.3116i | −1.27167 | + | 0.923925i | −0.999268 | − | 0.0382582i | \(-0.987819\pi\) |
−0.272405 | + | 0.962183i | \(0.587819\pi\) | |||||||
\(812\) | −0.454915 | + | 1.40008i | −0.0159644 | + | 0.0491333i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.12461 | − | 9.23305i | 0.284767 | − | 0.323618i | ||||
\(815\) | −79.1935 | −2.77403 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.7812 | + | 12.9188i | 0.621703 | + | 0.451694i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.56231 | − | 23.2744i | −0.264087 | − | 0.812777i | ||||
\(821\) | 21.3541 | + | 15.5147i | 0.745263 | + | 0.541465i | 0.894355 | − | 0.447358i | \(-0.147635\pi\) |
−0.149092 | + | 0.988823i | \(0.547635\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.73607 | − | 20.7315i | 0.234805 | − | 0.722654i | −0.762343 | − | 0.647174i | \(-0.775951\pi\) |
0.997147 | − | 0.0754806i | \(-0.0240491\pi\) | |||||||
\(824\) | −7.85410 | −0.273611 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −47.5066 | −1.65297 | ||||||||
\(827\) | 8.66312 | − | 26.6623i | 0.301246 | − | 0.927140i | −0.679805 | − | 0.733393i | \(-0.737936\pi\) |
0.981051 | − | 0.193748i | \(-0.0620643\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.61803 | − | 1.90211i | −0.0909281 | − | 0.0660631i | 0.541392 | − | 0.840770i | \(-0.317897\pi\) |
−0.632320 | + | 0.774707i | \(0.717897\pi\) | |||||||
\(830\) | 8.71885 | + | 26.8339i | 0.302636 | + | 0.931417i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.23607 | − | 3.80423i | −0.181528 | − | 0.131888i | ||||
\(833\) | 20.5623 | − | 14.9394i | 0.712442 | − | 0.517619i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −74.7214 | −2.58584 | ||||||||
\(836\) | −6.47214 | + | 1.45309i | −0.223844 | + | 0.0502560i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.06231 | + | 12.5025i | −0.140330 | + | 0.431891i | ||||
\(839\) | −1.32624 | + | 0.963568i | −0.0457868 | + | 0.0332661i | −0.610443 | − | 0.792060i | \(-0.709009\pi\) |
0.564656 | + | 0.825326i | \(0.309009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.91641 | − | 27.4419i | −0.307462 | − | 0.946272i | ||||
\(842\) | −5.29180 | − | 16.2865i | −0.182367 | − | 0.561269i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.61803 | + | 4.08174i | −0.193381 | + | 0.140499i | ||||
\(845\) | 32.2984 | − | 99.4042i | 1.11110 | − | 3.41961i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.6591 | + | 7.86572i | 1.43142 | + | 0.270269i | ||||
\(848\) | 9.38197 | 0.322178 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 21.1803 | − | 15.3884i | 0.726480 | − | 0.527818i | ||||
\(851\) | −8.29180 | − | 6.02434i | −0.284239 | − | 0.206512i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.88854 | + | 27.3561i | 0.304338 | + | 0.936656i | 0.979923 | + | 0.199374i | \(0.0638909\pi\) |
−0.675585 | + | 0.737282i | \(0.736109\pi\) | |||||||
\(854\) | 8.61803 | + | 6.26137i | 0.294903 | + | 0.214260i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.28115 | + | 13.1760i | −0.146327 | + | 0.450348i | ||||
\(857\) | −3.81966 | −0.130477 | −0.0652386 | − | 0.997870i | \(-0.520781\pi\) | ||||
−0.0652386 | + | 0.997870i | \(0.520781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.7214 | 1.38939 | 0.694697 | − | 0.719302i | \(-0.255538\pi\) | ||||
0.694697 | + | 0.719302i | \(0.255538\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.8885 | − | 23.8949i | −1.12019 | − | 0.813864i | ||||
\(863\) | 13.7984 | + | 42.4670i | 0.469702 | + | 1.44559i | 0.852971 | + | 0.521958i | \(0.174798\pi\) |
−0.383269 | + | 0.923637i | \(0.625202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.0238 | − | 36.3444i | −1.70086 | − | 1.23575i | ||||
\(866\) | 10.2082 | − | 7.41669i | 0.346889 | − | 0.252030i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.562306 | −0.0190859 | ||||||||
\(869\) | 2.20820 | − | 23.5972i | 0.0749082 | − | 0.800479i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.8885 | + | 67.3660i | −0.741665 | + | 2.28261i | ||||
\(872\) | −3.85410 | + | 2.80017i | −0.130516 | + | 0.0948257i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.70820 | + | 5.25731i | 0.0577809 | + | 0.177831i | ||||
\(875\) | −13.3156 | − | 40.9812i | −0.450149 | − | 1.38542i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.7082 | − | 7.77997i | 0.361590 | − | 0.262711i | −0.392125 | − | 0.919912i | \(-0.628260\pi\) |
0.753715 | + | 0.657201i | \(0.228260\pi\) | |||||||
\(878\) | −4.89919 | + | 15.0781i | −0.165340 | + | 0.508863i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.92705 | − | 9.00854i | 0.267221 | − | 0.303678i | ||||
\(881\) | −13.8885 | −0.467917 | −0.233958 | − | 0.972247i | \(-0.575168\pi\) | ||||
−0.233958 | + | 0.972247i | \(0.575168\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.2705 | − | 26.3521i | 1.22060 | − | 0.886818i | 0.224450 | − | 0.974486i | \(-0.427941\pi\) |
0.996150 | + | 0.0876679i | \(0.0279414\pi\) | |||||||
\(884\) | 16.9443 | + | 12.3107i | 0.569898 | + | 0.414055i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0106 | + | 30.8096i | 0.336314 | + | 1.03507i | ||||
\(887\) | −24.3262 | − | 17.6740i | −0.816795 | − | 0.593436i | 0.0989976 | − | 0.995088i | \(-0.468436\pi\) |
−0.915793 | + | 0.401651i | \(0.868436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.12461 | + | 3.46120i | −0.0377183 | + | 0.116085i | ||||
\(890\) | −22.3607 | −0.749532 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.85410 | 0.296457 | ||||||||
\(893\) | 2.94427 | − | 9.06154i | 0.0985263 | − | 0.303233i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 57.9508 | + | 42.1038i | 1.93708 | + | 1.40737i | ||||
\(896\) | −1.19098 | − | 3.66547i | −0.0397879 | − | 0.122455i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.5623 | + | 8.40051i | 0.385839 | + | 0.280329i | ||||
\(899\) | −0.0450850 | + | 0.0327561i | −0.00150367 | + | 0.00109248i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.3607 | −1.01146 | ||||||||
\(902\) | 11.4377 | + | 19.2986i | 0.380834 | + | 0.642575i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00000 | + | 9.23305i | −0.0997785 | + | 0.307087i | ||||
\(905\) | 71.3050 | − | 51.8061i | 2.37026 | − | 1.72209i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.81966 | + | 17.9111i | 0.193239 | + | 0.594727i | 0.999993 | + | 0.00383991i | \(0.00122229\pi\) |
−0.806754 | + | 0.590887i | \(0.798778\pi\) | |||||||
\(908\) | −3.11803 | − | 9.59632i | −0.103476 | − | 0.318465i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 73.0132 | − | 53.0472i | 2.42036 | − | 1.75850i | ||||
\(911\) | 17.4164 | − | 53.6022i | 0.577031 | − | 1.77592i | −0.0521244 | − | 0.998641i | \(-0.516599\pi\) |
0.629156 | − | 0.777279i | \(-0.283401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.1869 | − | 22.2501i | −0.436423 | − | 0.736370i | ||||
\(914\) | −2.56231 | −0.0847535 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.3262 | − | 10.4086i | 0.473352 | − | 0.343911i | ||||
\(917\) | −34.5795 | − | 25.1235i | −1.14192 | − | 0.829651i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.91641 | − | 8.97578i | −0.0962034 | − | 0.296084i | 0.891362 | − | 0.453292i | \(-0.149751\pi\) |
−0.987565 | + | 0.157208i | \(0.949751\pi\) | |||||||
\(920\) | −8.09017 | − | 5.87785i | −0.266725 | − | 0.193787i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10.0344 | + | 30.8828i | −0.330467 | + | 1.01707i | ||||
\(923\) | −4.94427 | −0.162743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | 0.986394 | ||||||||
\(926\) | −4.71885 | + | 14.5231i | −0.155071 | + | 0.477259i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.309017 | − | 0.224514i | −0.0101440 | − | 0.00737003i | ||||
\(929\) | 0.742646 | + | 2.28563i | 0.0243654 | + | 0.0749890i | 0.962500 | − | 0.271282i | \(-0.0874477\pi\) |
−0.938134 | + | 0.346271i | \(0.887448\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.7082 | − | 9.23305i | −0.416495 | − | 0.302601i | ||||
\(932\) | −11.2361 | + | 8.16348i | −0.368050 | + | 0.267404i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.3262 | 0.926863 | ||||||||
\(935\) | −25.6525 | + | 29.1522i | −0.838926 | + | 0.953380i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.5517 | − | 32.4747i | 0.344708 | − | 1.06090i | −0.617032 | − | 0.786938i | \(-0.711665\pi\) |
0.961740 | − | 0.273964i | \(-0.0883348\pi\) | |||||||
\(938\) | −34.1246 | + | 24.7930i | −1.11421 | + | 0.809520i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.32624 | + | 16.3925i | 0.173723 | + | 0.534664i | ||||
\(941\) | 11.8541 | + | 36.4832i | 0.386433 | + | 1.18932i | 0.935436 | + | 0.353497i | \(0.115008\pi\) |
−0.549003 | + | 0.835820i | \(0.684992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.1246 | − | 10.9887i | 0.492525 | − | 0.357840i | ||||
\(944\) | 3.80902 | − | 11.7229i | 0.123973 | − | 0.381549i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.25735 | 0.138345 | 0.0691727 | − | 0.997605i | \(-0.477964\pi\) | ||||
0.0691727 | + | 0.997605i | \(0.477964\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.4721 | − | 9.06154i | 0.404863 | − | 0.294150i | ||||
\(950\) | −13.0902 | − | 9.51057i | −0.424701 | − | 0.308563i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.85410 | + | 11.8617i | 0.124912 | + | 0.384440i | ||||
\(953\) | 21.5623 | + | 15.6659i | 0.698472 | + | 0.507469i | 0.879434 | − | 0.476021i | \(-0.157921\pi\) |
−0.180962 | + | 0.983490i | \(0.557921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.0344 | − | 52.4266i | 0.551222 | − | 1.69649i | ||||
\(956\) | 13.4164 | 0.433918 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.3607 | −0.916292 | ||||||||
\(959\) | −19.6180 | + | 60.3781i | −0.633499 | + | 1.94971i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 25.0623 | + | 18.2088i | 0.808461 | + | 0.587382i | ||||
\(962\) | 7.41641 | + | 22.8254i | 0.239115 | + | 0.735919i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.50000 | − | 6.17561i | −0.273767 | − | 0.198903i | ||||
\(965\) | 17.9894 | − | 13.0700i | 0.579098 | − | 0.420739i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.5623 | 0.339661 | 0.169830 | − | 0.985473i | \(-0.445678\pi\) | ||||
0.169830 | + | 0.985473i | \(0.445678\pi\) | |||||||
\(968\) | −5.28115 | + | 9.64932i | −0.169743 | + | 0.310141i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.98936 | + | 24.5887i | −0.256523 | + | 0.789496i | ||||
\(971\) | −10.0000 | + | 7.26543i | −0.320915 | + | 0.233159i | −0.736566 | − | 0.676366i | \(-0.763554\pi\) |
0.415651 | + | 0.909524i | \(0.363554\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.41641 | − | 13.5923i | −0.141584 | − | 0.435749i | ||||
\(974\) | −3.95492 | − | 12.1720i | −0.126724 | − | 0.390015i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.23607 | + | 1.62460i | −0.0715748 | + | 0.0520021i | ||||
\(977\) | −3.90983 | + | 12.0332i | −0.125087 | + | 0.384977i | −0.993917 | − | 0.110133i | \(-0.964872\pi\) |
0.868830 | + | 0.495110i | \(0.164872\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | − | 4.49028i | 0.639203 | − | 0.143510i | ||||
\(980\) | 28.4164 | 0.907729 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.4164 | − | 14.1068i | 0.619602 | − | 0.450168i | ||||
\(983\) | −22.4164 | − | 16.2865i | −0.714972 | − | 0.519458i | 0.169802 | − | 0.985478i | \(-0.445687\pi\) |
−0.884774 | + | 0.466020i | \(0.845687\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.427051 | + | 1.31433i | 0.0136070 | + | 0.0418780i | ||||
\(986\) | 1.00000 | + | 0.726543i | 0.0318465 | + | 0.0231378i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | − | 12.3107i | 0.127257 | − | 0.391657i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.5623 | −1.22497 | −0.612486 | − | 0.790481i | \(-0.709830\pi\) | ||||
−0.612486 | + | 0.790481i | \(0.709830\pi\) | |||||||
\(992\) | 0.0450850 | − | 0.138757i | 0.00143145 | − | 0.00440555i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.38197 | − | 1.73060i | −0.0755514 | − | 0.0548913i | ||||
\(995\) | 10.9549 | + | 33.7158i | 0.347294 | + | 1.06886i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.94427 | − | 6.49839i | −0.283268 | − | 0.205806i | 0.437074 | − | 0.899426i | \(-0.356015\pi\) |
−0.720342 | + | 0.693620i | \(0.756015\pi\) | |||||||
\(998\) | 17.3262 | − | 12.5882i | 0.548452 | − | 0.398474i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 198.2.f.b.163.1 | ✓ | 4 | |
3.2 | odd | 2 | 198.2.f.d.163.1 | yes | 4 | ||
11.4 | even | 5 | 2178.2.a.bc.1.2 | 2 | |||
11.5 | even | 5 | inner | 198.2.f.b.181.1 | yes | 4 | |
11.7 | odd | 10 | 2178.2.a.u.1.2 | 2 | |||
33.5 | odd | 10 | 198.2.f.d.181.1 | yes | 4 | ||
33.26 | odd | 10 | 2178.2.a.n.1.1 | 2 | |||
33.29 | even | 10 | 2178.2.a.w.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
198.2.f.b.163.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
198.2.f.b.181.1 | yes | 4 | 11.5 | even | 5 | inner | |
198.2.f.d.163.1 | yes | 4 | 3.2 | odd | 2 | ||
198.2.f.d.181.1 | yes | 4 | 33.5 | odd | 10 | ||
2178.2.a.n.1.1 | 2 | 33.26 | odd | 10 | |||
2178.2.a.u.1.2 | 2 | 11.7 | odd | 10 | |||
2178.2.a.w.1.1 | 2 | 33.29 | even | 10 | |||
2178.2.a.bc.1.2 | 2 | 11.4 | even | 5 |