Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [891,2,Mod(82,891)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(891, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("891.82");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 891.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: | \(7.11467082010\) |
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: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 487.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 891.487 |
Dual form | 891.2.f.b.730.1 |
$q$-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 \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(650\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.11803 | − | 1.53884i | 1.49768 | − | 1.08813i | 0.526381 | − | 0.850249i | \(-0.323549\pi\) |
0.971295 | − | 0.237877i | \(-0.0764514\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 4.61653i | 0.750000 | − | 2.30826i | ||||
\(5\) | −2.61803 | − | 1.90211i | −1.17082 | − | 0.850651i | −0.179714 | − | 0.983719i | \(-0.557517\pi\) |
−0.991107 | + | 0.133068i | \(0.957517\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | −0.992318 | − | 0.123716i | \(-0.960519\pi\) |
0.875520 | + | 0.483181i | \(0.160519\pi\) | |||||||
\(8\) | −2.30902 | − | 7.10642i | −0.816361 | − | 2.51250i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.47214 | −2.67912 | ||||||||
\(11\) | −0.809017 | − | 3.21644i | −0.243928 | − | 0.969793i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | + | 1.45309i | −0.554700 | + | 0.403013i | −0.829515 | − | 0.558484i | \(-0.811383\pi\) |
0.274815 | + | 0.961497i | \(0.411383\pi\) | |||||||
\(14\) | 0.809017 | + | 2.48990i | 0.216219 | + | 0.665453i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −7.97214 | − | 5.79210i | −1.99303 | − | 1.44802i | ||||
\(17\) | 1.50000 | + | 1.08981i | 0.363803 | + | 0.264319i | 0.754637 | − | 0.656143i | \(-0.227813\pi\) |
−0.390833 | + | 0.920461i | \(0.627813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.309017 | + | 0.951057i | 0.0708934 | + | 0.218187i | 0.980226 | − | 0.197884i | \(-0.0634068\pi\) |
−0.909332 | + | 0.416071i | \(0.863407\pi\) | |||||||
\(20\) | −12.7082 | + | 9.23305i | −2.84164 | + | 2.06457i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.66312 | − | 5.56758i | −1.42058 | − | 1.18701i | ||||
\(23\) | 2.38197 | 0.496674 | 0.248337 | − | 0.968674i | \(-0.420116\pi\) | ||||
0.248337 | + | 0.968674i | \(0.420116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.69098 | + | 5.20431i | 0.338197 | + | 1.04086i | ||||
\(26\) | −2.00000 | + | 6.15537i | −0.392232 | + | 1.20717i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.92705 | + | 2.85317i | 0.742143 | + | 0.539198i | ||||
\(29\) | 0.572949 | − | 1.76336i | 0.106394 | − | 0.327447i | −0.883661 | − | 0.468127i | \(-0.844929\pi\) |
0.990055 | + | 0.140680i | \(0.0449289\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.30902 | − | 0.951057i | 0.235106 | − | 0.170815i | −0.463994 | − | 0.885838i | \(-0.653584\pi\) |
0.699100 | + | 0.715024i | \(0.253584\pi\) | |||||||
\(32\) | −10.8541 | −1.91875 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.85410 | 0.832472 | ||||||||
\(35\) | 2.61803 | − | 1.90211i | 0.442529 | − | 0.321516i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.88197 | − | 5.79210i | 0.309393 | − | 0.952215i | −0.668608 | − | 0.743615i | \(-0.733109\pi\) |
0.978001 | − | 0.208599i | \(-0.0668905\pi\) | |||||||
\(38\) | 2.11803 | + | 1.53884i | 0.343590 | + | 0.249633i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.47214 | + | 22.9969i | −1.18145 | + | 3.63612i | ||||
\(41\) | −3.54508 | − | 10.9106i | −0.553649 | − | 1.70396i | −0.699484 | − | 0.714648i | \(-0.746587\pi\) |
0.145835 | − | 0.989309i | \(-0.453413\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.85410 | −0.740244 | −0.370122 | − | 0.928983i | \(-0.620684\pi\) | ||||
−0.370122 | + | 0.928983i | \(0.620684\pi\) | |||||||
\(44\) | −16.0623 | − | 1.08981i | −2.42148 | − | 0.164296i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.04508 | − | 3.66547i | 0.743857 | − | 0.540444i | ||||
\(47\) | −1.83688 | − | 5.65334i | −0.267937 | − | 0.824624i | −0.991002 | − | 0.133845i | \(-0.957268\pi\) |
0.723066 | − | 0.690779i | \(-0.242732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.85410 | + | 3.52671i | 0.693443 | + | 0.503816i | ||||
\(50\) | 11.5902 | + | 8.42075i | 1.63910 | + | 1.19087i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.70820 | + | 11.4127i | 0.514235 | + | 1.58265i | ||||
\(53\) | 5.73607 | − | 4.16750i | 0.787910 | − | 0.572450i | −0.119433 | − | 0.992842i | \(-0.538108\pi\) |
0.907342 | + | 0.420393i | \(0.138108\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | + | 9.95959i | −0.539360 | + | 1.34295i | ||||
\(56\) | 7.47214 | 0.998506 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50000 | − | 4.61653i | −0.196960 | − | 0.606179i | ||||
\(59\) | −0.190983 | + | 0.587785i | −0.0248639 | + | 0.0765231i | −0.962718 | − | 0.270505i | \(-0.912809\pi\) |
0.937855 | + | 0.347028i | \(0.112809\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.35410 | − | 2.43690i | −0.429449 | − | 0.312013i | 0.351980 | − | 0.936008i | \(-0.385509\pi\) |
−0.781428 | + | 0.623995i | \(0.785509\pi\) | |||||||
\(62\) | 1.30902 | − | 4.02874i | 0.166245 | − | 0.511650i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.04508 | + | 5.11855i | −0.880636 | + | 0.639819i | ||||
\(65\) | 8.00000 | 0.992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.00000 | 0.733017 | 0.366508 | − | 0.930415i | \(-0.380553\pi\) | ||||
0.366508 | + | 0.930415i | \(0.380553\pi\) | |||||||
\(68\) | 7.28115 | − | 5.29007i | 0.882969 | − | 0.641515i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.61803 | − | 8.05748i | 0.312915 | − | 0.963053i | ||||
\(71\) | 11.3992 | + | 8.28199i | 1.35283 | + | 0.982892i | 0.998865 | + | 0.0476350i | \(0.0151684\pi\) |
0.353970 | + | 0.935257i | \(0.384832\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.11803 | + | 6.51864i | −0.247897 | + | 0.762949i | 0.747249 | + | 0.664544i | \(0.231374\pi\) |
−0.995146 | + | 0.0984051i | \(0.968626\pi\) | |||||||
\(74\) | −4.92705 | − | 15.1639i | −0.572758 | − | 1.76277i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.85410 | 0.556804 | ||||||||
\(77\) | 3.30902 | + | 0.224514i | 0.377097 | + | 0.0255857i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.73607 | − | 5.62058i | 0.870376 | − | 0.632365i | −0.0603121 | − | 0.998180i | \(-0.519210\pi\) |
0.930688 | + | 0.365815i | \(0.119210\pi\) | |||||||
\(80\) | 9.85410 | + | 30.3278i | 1.10172 | + | 3.39075i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −24.2984 | − | 17.6538i | −2.68331 | − | 1.94954i | ||||
\(83\) | 11.5172 | + | 8.36775i | 1.26418 | + | 0.918480i | 0.998955 | − | 0.0457068i | \(-0.0145540\pi\) |
0.265224 | + | 0.964187i | \(0.414554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.85410 | − | 5.70634i | −0.201106 | − | 0.618939i | ||||
\(86\) | −10.2812 | + | 7.46969i | −1.10865 | + | 0.805478i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20.9894 | + | 13.1760i | −2.23747 | + | 1.40457i | ||||
\(89\) | −11.2361 | −1.19102 | −0.595510 | − | 0.803348i | \(-0.703050\pi\) | ||||
−0.595510 | + | 0.803348i | \(0.703050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.763932 | − | 2.35114i | −0.0800818 | − | 0.246467i | ||||
\(92\) | 3.57295 | − | 10.9964i | 0.372506 | − | 1.14645i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.5902 | − | 9.14729i | −1.29858 | − | 0.943471i | ||||
\(95\) | 1.00000 | − | 3.07768i | 0.102598 | − | 0.315764i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.85410 | + | 3.52671i | −0.492859 | + | 0.358083i | −0.806283 | − | 0.591530i | \(-0.798524\pi\) |
0.313423 | + | 0.949613i | \(0.398524\pi\) | |||||||
\(98\) | 15.7082 | 1.58677 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 26.5623 | 2.65623 | ||||||||
\(101\) | −0.381966 | + | 0.277515i | −0.0380070 | + | 0.0276137i | −0.606627 | − | 0.794987i | \(-0.707478\pi\) |
0.568620 | + | 0.822601i | \(0.307478\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.78115 | + | 5.48183i | −0.175502 | + | 0.540140i | −0.999656 | − | 0.0262257i | \(-0.991651\pi\) |
0.824154 | + | 0.566366i | \(0.191651\pi\) | |||||||
\(104\) | 14.9443 | + | 10.8576i | 1.46541 | + | 1.06468i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.73607 | − | 17.6538i | 0.557136 | − | 1.71469i | ||||
\(107\) | −4.64590 | − | 14.2986i | −0.449136 | − | 1.38230i | −0.877884 | − | 0.478874i | \(-0.841045\pi\) |
0.428748 | − | 0.903424i | \(-0.358955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8541 | 1.32698 | 0.663491 | − | 0.748184i | \(-0.269074\pi\) | ||||
0.663491 | + | 0.748184i | \(0.269074\pi\) | |||||||
\(110\) | 6.85410 | + | 27.2501i | 0.653513 | + | 2.59820i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.97214 | − | 5.79210i | 0.753296 | − | 0.547302i | ||||
\(113\) | 3.94427 | + | 12.1392i | 0.371046 | + | 1.14196i | 0.946108 | + | 0.323852i | \(0.104978\pi\) |
−0.575062 | + | 0.818110i | \(0.695022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.23607 | − | 4.53077i | −0.581516 | − | 0.422496i | ||||
\(116\) | −7.28115 | − | 5.29007i | −0.676038 | − | 0.491170i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.500000 | + | 1.53884i | 0.0460287 | + | 0.141662i | ||||
\(119\) | −1.50000 | + | 1.08981i | −0.137505 | + | 0.0999031i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.69098 | + | 5.20431i | −0.880998 | + | 0.473119i | ||||
\(122\) | −10.8541 | −0.982684 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.42705 | − | 7.46969i | −0.217956 | − | 0.670798i | ||||
\(125\) | 0.472136 | − | 1.45309i | 0.0422291 | − | 0.129968i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.73607 | − | 5.62058i | −0.686465 | − | 0.498746i | 0.189031 | − | 0.981971i | \(-0.439465\pi\) |
−0.875496 | + | 0.483225i | \(0.839465\pi\) | |||||||
\(128\) | −0.336881 | + | 1.03681i | −0.0297764 | + | 0.0916422i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 16.9443 | − | 12.3107i | 1.48611 | − | 1.07972i | ||||
\(131\) | 16.7639 | 1.46467 | 0.732336 | − | 0.680944i | \(-0.238430\pi\) | ||||
0.732336 | + | 0.680944i | \(0.238430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 12.7082 | − | 9.23305i | 1.09782 | − | 0.797614i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.28115 | − | 13.1760i | 0.367106 | − | 1.12984i | ||||
\(137\) | 5.16312 | + | 3.75123i | 0.441115 | + | 0.320489i | 0.786078 | − | 0.618128i | \(-0.212108\pi\) |
−0.344963 | + | 0.938616i | \(0.612108\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.14590 | + | 3.52671i | −0.0971938 | + | 0.299132i | −0.987819 | − | 0.155606i | \(-0.950267\pi\) |
0.890625 | + | 0.454738i | \(0.150267\pi\) | |||||||
\(140\) | −4.85410 | − | 14.9394i | −0.410246 | − | 1.26261i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 36.8885 | 3.09562 | ||||||||
\(143\) | 6.29180 | + | 5.25731i | 0.526146 | + | 0.439638i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.85410 | + | 3.52671i | −0.403111 | + | 0.292877i | ||||
\(146\) | 5.54508 | + | 17.0660i | 0.458914 | + | 1.41239i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.9164 | − | 17.3763i | −1.96592 | − | 1.42832i | ||||
\(149\) | −5.80902 | − | 4.22050i | −0.475893 | − | 0.345757i | 0.323840 | − | 0.946112i | \(-0.395026\pi\) |
−0.799734 | + | 0.600355i | \(0.795026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.50000 | − | 10.7719i | −0.284826 | − | 0.876604i | −0.986451 | − | 0.164058i | \(-0.947542\pi\) |
0.701625 | − | 0.712547i | \(-0.252458\pi\) | |||||||
\(152\) | 6.04508 | − | 4.39201i | 0.490321 | − | 0.356239i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.35410 | − | 4.61653i | 0.592610 | − | 0.372010i | ||||
\(155\) | −5.23607 | −0.420571 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.28115 | + | 13.1760i | 0.341673 | + | 1.05156i | 0.963341 | + | 0.268281i | \(0.0864555\pi\) |
−0.621668 | + | 0.783281i | \(0.713545\pi\) | |||||||
\(158\) | 7.73607 | − | 23.8092i | 0.615449 | − | 1.89416i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 28.4164 | + | 20.6457i | 2.24651 | + | 1.63219i | ||||
\(161\) | −0.736068 | + | 2.26538i | −0.0580103 | + | 0.178537i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.89919 | + | 4.28601i | −0.462060 | + | 0.335706i | −0.794339 | − | 0.607475i | \(-0.792182\pi\) |
0.332279 | + | 0.943181i | \(0.392182\pi\) | |||||||
\(164\) | −55.6869 | −4.34842 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 37.2705 | 2.89275 | ||||||||
\(167\) | 8.28115 | − | 6.01661i | 0.640815 | − | 0.465579i | −0.219315 | − | 0.975654i | \(-0.570382\pi\) |
0.860130 | + | 0.510075i | \(0.170382\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.12868 | + | 6.55139i | −0.163744 | + | 0.503953i | ||||
\(170\) | −12.7082 | − | 9.23305i | −0.974675 | − | 0.708143i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.28115 | + | 22.4091i | −0.555183 | + | 1.70868i | ||||
\(173\) | −3.68034 | − | 11.3269i | −0.279811 | − | 0.861170i | −0.987906 | − | 0.155053i | \(-0.950445\pi\) |
0.708095 | − | 0.706117i | \(-0.249555\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.47214 | −0.413655 | ||||||||
\(176\) | −12.1803 | + | 30.3278i | −0.918128 | + | 2.28604i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −23.7984 | + | 17.2905i | −1.78376 | + | 1.29598i | ||||
\(179\) | −7.09017 | − | 21.8213i | −0.529944 | − | 1.63100i | −0.754327 | − | 0.656499i | \(-0.772036\pi\) |
0.224382 | − | 0.974501i | \(-0.427964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.0623 | + | 12.3965i | 1.26823 | + | 0.921424i | 0.999131 | − | 0.0416882i | \(-0.0132736\pi\) |
0.269101 | + | 0.963112i | \(0.413274\pi\) | |||||||
\(182\) | −5.23607 | − | 3.80423i | −0.388123 | − | 0.281988i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.50000 | − | 16.9273i | −0.405465 | − | 1.24789i | ||||
\(185\) | −15.9443 | + | 11.5842i | −1.17225 | + | 0.851687i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29180 | − | 5.70634i | 0.167593 | − | 0.417289i | ||||
\(188\) | −28.8541 | −2.10440 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.61803 | − | 8.05748i | −0.189932 | − | 0.584551i | ||||
\(191\) | −3.69098 | + | 11.3597i | −0.267070 | + | 0.821957i | 0.724139 | + | 0.689654i | \(0.242237\pi\) |
−0.991209 | + | 0.132303i | \(0.957763\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.89919 | + | 6.46564i | 0.640577 | + | 0.465407i | 0.860049 | − | 0.510212i | \(-0.170433\pi\) |
−0.219471 | + | 0.975619i | \(0.570433\pi\) | |||||||
\(194\) | −4.85410 | + | 14.9394i | −0.348504 | + | 1.07259i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 23.5623 | − | 17.1190i | 1.68302 | − | 1.22279i | ||||
\(197\) | 3.76393 | 0.268169 | 0.134085 | − | 0.990970i | \(-0.457191\pi\) | ||||
0.134085 | + | 0.990970i | \(0.457191\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.8541 | −0.982091 | −0.491046 | − | 0.871134i | \(-0.663385\pi\) | ||||
−0.491046 | + | 0.871134i | \(0.663385\pi\) | |||||||
\(200\) | 33.0795 | − | 24.0337i | 2.33908 | − | 1.69944i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.381966 | + | 1.17557i | −0.0268750 | + | 0.0827129i | ||||
\(203\) | 1.50000 | + | 1.08981i | 0.105279 | + | 0.0764899i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.4721 | + | 35.3076i | −0.801249 | + | 2.46599i | ||||
\(206\) | 4.66312 | + | 14.3516i | 0.324895 | + | 0.999924i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.3607 | 1.68911 | ||||||||
\(209\) | 2.80902 | − | 1.76336i | 0.194304 | − | 0.121974i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.32624 | + | 6.77591i | −0.642045 | + | 0.466473i | −0.860552 | − | 0.509363i | \(-0.829881\pi\) |
0.218507 | + | 0.975835i | \(0.429881\pi\) | |||||||
\(212\) | −10.6353 | − | 32.7319i | −0.730432 | − | 2.24804i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −31.8435 | − | 23.1356i | −2.17677 | − | 1.58152i | ||||
\(215\) | 12.7082 | + | 9.23305i | 0.866692 | + | 0.629689i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.500000 | + | 1.53884i | 0.0339422 | + | 0.104463i | ||||
\(218\) | 29.3435 | − | 21.3193i | 1.98739 | − | 1.44392i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 39.9787 | + | 33.4055i | 2.69536 | + | 2.25220i | ||||
\(221\) | −4.58359 | −0.308326 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.95492 | + | 21.4050i | 0.465736 | + | 1.43339i | 0.858055 | + | 0.513558i | \(0.171673\pi\) |
−0.392320 | + | 0.919829i | \(0.628327\pi\) | |||||||
\(224\) | 3.35410 | − | 10.3229i | 0.224105 | − | 0.689725i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27.0344 | + | 19.6417i | 1.79830 | + | 1.30654i | ||||
\(227\) | −4.44427 | + | 13.6781i | −0.294977 | + | 0.907845i | 0.688253 | + | 0.725471i | \(0.258378\pi\) |
−0.983229 | + | 0.182374i | \(0.941622\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.85410 | − | 7.15942i | 0.651177 | − | 0.473108i | −0.212495 | − | 0.977162i | \(-0.568159\pi\) |
0.863672 | + | 0.504054i | \(0.168159\pi\) | |||||||
\(230\) | −20.1803 | −1.33065 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.8541 | −0.909566 | ||||||||
\(233\) | −23.5623 | + | 17.1190i | −1.54362 | + | 1.12150i | −0.595603 | + | 0.803279i | \(0.703087\pi\) |
−0.948015 | + | 0.318225i | \(0.896913\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.94427 | + | 18.2946i | −0.387762 | + | 1.19341i | ||||
\(236\) | 2.42705 | + | 1.76336i | 0.157988 | + | 0.114785i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.50000 | + | 4.61653i | −0.0972306 | + | 0.299245i | ||||
\(239\) | 0.472136 | + | 1.45309i | 0.0305399 | + | 0.0939923i | 0.965165 | − | 0.261643i | \(-0.0842644\pi\) |
−0.934625 | + | 0.355636i | \(0.884264\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.8328 | 1.72845 | 0.864227 | − | 0.503102i | \(-0.167808\pi\) | ||||
0.864227 | + | 0.503102i | \(0.167808\pi\) | |||||||
\(242\) | −12.5172 | + | 25.9358i | −0.804637 | + | 1.66722i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.2812 | + | 11.8290i | −1.04229 | + | 0.757271i | ||||
\(245\) | −6.00000 | − | 18.4661i | −0.383326 | − | 1.17976i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | − | 1.45309i | −0.127257 | − | 0.0924576i | ||||
\(248\) | −9.78115 | − | 7.10642i | −0.621104 | − | 0.451258i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.23607 | − | 3.80423i | −0.0781758 | − | 0.240600i | ||||
\(251\) | −0.354102 | + | 0.257270i | −0.0223507 | + | 0.0162387i | −0.598905 | − | 0.800820i | \(-0.704397\pi\) |
0.576554 | + | 0.817059i | \(0.304397\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.92705 | − | 7.66145i | −0.121153 | − | 0.481671i | ||||
\(254\) | −25.0344 | −1.57080 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.50000 | − | 13.8496i | −0.281250 | − | 0.865598i | ||||
\(257\) | −8.06231 | + | 24.8132i | −0.502913 | + | 1.54781i | 0.301339 | + | 0.953517i | \(0.402567\pi\) |
−0.804251 | + | 0.594289i | \(0.797433\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.92705 | + | 3.57971i | 0.306152 | + | 0.222432i | ||||
\(260\) | 12.0000 | − | 36.9322i | 0.744208 | − | 2.29044i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 35.5066 | − | 25.7970i | 2.19360 | − | 1.59375i | ||||
\(263\) | 0.708204 | 0.0436697 | 0.0218349 | − | 0.999762i | \(-0.493049\pi\) | ||||
0.0218349 | + | 0.999762i | \(0.493049\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.9443 | −1.40946 | ||||||||
\(266\) | −2.11803 | + | 1.53884i | −0.129865 | + | 0.0943524i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.00000 | − | 27.6992i | 0.549762 | − | 1.69199i | ||||
\(269\) | −9.92705 | − | 7.21242i | −0.605263 | − | 0.439749i | 0.242480 | − | 0.970156i | \(-0.422039\pi\) |
−0.847743 | + | 0.530407i | \(0.822039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.70820 | − | 14.4904i | 0.286003 | − | 0.880227i | −0.700093 | − | 0.714051i | \(-0.746858\pi\) |
0.986096 | − | 0.166175i | \(-0.0531418\pi\) | |||||||
\(272\) | −5.64590 | − | 17.3763i | −0.342333 | − | 1.05359i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.7082 | 1.00938 | ||||||||
\(275\) | 15.3713 | − | 9.64932i | 0.926926 | − | 0.581876i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.9443 | − | 8.67802i | 0.717662 | − | 0.521412i | −0.167975 | − | 0.985791i | \(-0.553723\pi\) |
0.885636 | + | 0.464380i | \(0.153723\pi\) | |||||||
\(278\) | 3.00000 | + | 9.23305i | 0.179928 | + | 0.553762i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.5623 | − | 14.2128i | −1.16907 | − | 0.849380i | ||||
\(281\) | −5.11803 | − | 3.71847i | −0.305316 | − | 0.221825i | 0.424568 | − | 0.905396i | \(-0.360426\pi\) |
−0.729884 | + | 0.683571i | \(0.760426\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.25329 | − | 16.1680i | −0.312276 | − | 0.961086i | −0.976861 | − | 0.213874i | \(-0.931392\pi\) |
0.664586 | − | 0.747212i | \(-0.268608\pi\) | |||||||
\(284\) | 55.3328 | − | 40.2016i | 3.28340 | − | 2.38553i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.4164 | + | 1.45309i | 1.26638 | + | 0.0859227i | ||||
\(287\) | 11.4721 | 0.677179 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.19098 | − | 12.8985i | −0.246528 | − | 0.758736i | ||||
\(290\) | −4.85410 | + | 14.9394i | −0.285043 | + | 0.877271i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 26.9164 | + | 19.5559i | 1.57516 | + | 1.14442i | ||||
\(293\) | −2.10739 | + | 6.48588i | −0.123115 | + | 0.378909i | −0.993553 | − | 0.113369i | \(-0.963836\pi\) |
0.870438 | + | 0.492278i | \(0.163836\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.61803 | − | 1.17557i | 0.0942056 | − | 0.0684444i | ||||
\(296\) | −45.5066 | −2.64502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.7984 | −1.08896 | ||||||||
\(299\) | −4.76393 | + | 3.46120i | −0.275505 | + | 0.200166i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50000 | − | 4.61653i | 0.0864586 | − | 0.266092i | ||||
\(302\) | −23.9894 | − | 17.4293i | −1.38043 | − | 1.00294i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.04508 | − | 9.37181i | 0.174648 | − | 0.537510i | ||||
\(305\) | 4.14590 | + | 12.7598i | 0.237393 | + | 0.730622i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.14590 | 0.0653999 | 0.0326999 | − | 0.999465i | \(-0.489589\pi\) | ||||
0.0326999 | + | 0.999465i | \(0.489589\pi\) | |||||||
\(308\) | 6.00000 | − | 14.9394i | 0.341882 | − | 0.851251i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.0902 | + | 8.05748i | −0.629879 | + | 0.457634i | ||||
\(311\) | −2.21885 | − | 6.82891i | −0.125819 | − | 0.387232i | 0.868230 | − | 0.496162i | \(-0.165258\pi\) |
−0.994049 | + | 0.108930i | \(0.965258\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.42705 | + | 3.21644i | 0.250232 | + | 0.181804i | 0.705829 | − | 0.708382i | \(-0.250574\pi\) |
−0.455598 | + | 0.890186i | \(0.650574\pi\) | |||||||
\(314\) | 29.3435 | + | 21.3193i | 1.65595 | + | 1.20312i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.3435 | − | 44.1446i | −0.806883 | − | 2.48333i | ||||
\(317\) | −2.47214 | + | 1.79611i | −0.138849 | + | 0.100880i | −0.655042 | − | 0.755593i | \(-0.727349\pi\) |
0.516193 | + | 0.856473i | \(0.327349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.13525 | − | 0.416272i | −0.343508 | − | 0.0233067i | ||||
\(320\) | 28.1803 | 1.57533 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.92705 | + | 5.93085i | 0.107390 | + | 0.330514i | ||||
\(323\) | −0.572949 | + | 1.76336i | −0.0318797 | + | 0.0981157i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.9443 | − | 7.95148i | −0.607079 | − | 0.441069i | ||||
\(326\) | −5.89919 | + | 18.1558i | −0.326726 | + | 1.00556i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −69.3500 | + | 50.3858i | −3.82922 | + | 2.78209i | ||||
\(329\) | 5.94427 | 0.327718 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.4164 | −0.682467 | −0.341234 | − | 0.939978i | \(-0.610845\pi\) | ||||
−0.341234 | + | 0.939978i | \(0.610845\pi\) | |||||||
\(332\) | 55.9058 | − | 40.6179i | 3.06823 | − | 2.22920i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.28115 | − | 25.4868i | 0.453125 | − | 1.39457i | ||||
\(335\) | −15.7082 | − | 11.4127i | −0.858231 | − | 0.623541i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.781153 | + | 2.40414i | −0.0425521 | + | 0.130962i | −0.970076 | − | 0.242803i | \(-0.921933\pi\) |
0.927524 | + | 0.373765i | \(0.121933\pi\) | |||||||
\(338\) | 5.57295 | + | 17.1518i | 0.303128 | + | 0.932933i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −29.1246 | −1.57950 | ||||||||
\(341\) | −4.11803 | − | 3.44095i | −0.223004 | − | 0.186338i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.5172 | + | 7.64121i | −0.567877 | + | 0.412586i | ||||
\(344\) | 11.2082 | + | 34.4953i | 0.604306 | + | 1.85986i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −25.2254 | − | 18.3273i | −1.35613 | − | 0.985284i | ||||
\(347\) | −21.7533 | − | 15.8047i | −1.16778 | − | 0.848440i | −0.177037 | − | 0.984204i | \(-0.556651\pi\) |
−0.990741 | + | 0.135764i | \(0.956651\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.35410 | − | 10.3229i | −0.179541 | − | 0.552570i | 0.820271 | − | 0.571975i | \(-0.193823\pi\) |
−0.999812 | + | 0.0194052i | \(0.993823\pi\) | |||||||
\(350\) | −11.5902 | + | 8.42075i | −0.619521 | + | 0.450108i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.78115 | + | 34.9116i | 0.468037 | + | 1.86079i | ||||
\(353\) | 10.4164 | 0.554409 | 0.277205 | − | 0.960811i | \(-0.410592\pi\) | ||||
0.277205 | + | 0.960811i | \(0.410592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.0902 | − | 43.3651i | −0.747829 | − | 2.30158i | ||||
\(356\) | −16.8541 | + | 51.8716i | −0.893266 | + | 2.74919i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −48.5967 | − | 35.3076i | −2.56842 | − | 1.86606i | ||||
\(359\) | −4.98936 | + | 15.3557i | −0.263328 | + | 0.810441i | 0.728746 | + | 0.684784i | \(0.240104\pi\) |
−0.992074 | + | 0.125656i | \(0.959896\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.5623 | − | 10.5801i | 0.766437 | − | 0.556849i | ||||
\(362\) | 55.2148 | 2.90202 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.0000 | −0.628971 | ||||||||
\(365\) | 17.9443 | − | 13.0373i | 0.939246 | − | 0.682402i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.218847 | − | 0.673542i | 0.0114237 | − | 0.0351586i | −0.945182 | − | 0.326544i | \(-0.894116\pi\) |
0.956606 | + | 0.291385i | \(0.0941160\pi\) | |||||||
\(368\) | −18.9894 | − | 13.7966i | −0.989889 | − | 0.719196i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.9443 | + | 49.0714i | −0.828903 | + | 2.55110i | ||||
\(371\) | 2.19098 | + | 6.74315i | 0.113750 | + | 0.350087i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.6525 | 1.32823 | 0.664117 | − | 0.747628i | \(-0.268807\pi\) | ||||
0.664117 | + | 0.747628i | \(0.268807\pi\) | |||||||
\(374\) | −3.92705 | − | 15.6129i | −0.203063 | − | 0.807325i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −35.9336 | + | 26.1073i | −1.85314 | + | 1.34638i | ||||
\(377\) | 1.41641 | + | 4.35926i | 0.0729487 | + | 0.224513i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.11803 | + | 5.17155i | 0.365629 | + | 0.265645i | 0.755396 | − | 0.655269i | \(-0.227445\pi\) |
−0.389767 | + | 0.920913i | \(0.627445\pi\) | |||||||
\(380\) | −12.7082 | − | 9.23305i | −0.651917 | − | 0.473646i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.66312 | + | 29.7400i | 0.494408 | + | 1.52163i | ||||
\(383\) | −10.6353 | + | 7.72696i | −0.543436 | + | 0.394829i | −0.825360 | − | 0.564607i | \(-0.809028\pi\) |
0.281923 | + | 0.959437i | \(0.409028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.23607 | − | 6.88191i | −0.419749 | − | 0.350735i | ||||
\(386\) | 28.7984 | 1.46580 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.00000 | + | 27.6992i | 0.456906 | + | 1.40621i | ||||
\(389\) | 2.67376 | − | 8.22899i | 0.135565 | − | 0.417227i | −0.860112 | − | 0.510105i | \(-0.829607\pi\) |
0.995677 | + | 0.0928781i | \(0.0296067\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.57295 | + | 2.59590i | 0.180692 | + | 0.131280i | ||||
\(392\) | 13.8541 | − | 42.6385i | 0.699738 | − | 2.15357i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.97214 | − | 5.79210i | 0.401630 | − | 0.291802i | ||||
\(395\) | −30.9443 | −1.55698 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.1246 | 1.91342 | 0.956710 | − | 0.291044i | \(-0.0940026\pi\) | ||||
0.956710 | + | 0.291044i | \(0.0940026\pi\) | |||||||
\(398\) | −29.3435 | + | 21.3193i | −1.47085 | + | 1.06864i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.6631 | − | 51.2838i | 0.833156 | − | 2.56419i | ||||
\(401\) | 4.50000 | + | 3.26944i | 0.224719 | + | 0.163268i | 0.694448 | − | 0.719542i | \(-0.255648\pi\) |
−0.469729 | + | 0.882811i | \(0.655648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.23607 | + | 3.80423i | −0.0615729 | + | 0.189502i | ||||
\(404\) | 0.708204 | + | 2.17963i | 0.0352345 | + | 0.108441i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.85410 | 0.240905 | ||||||||
\(407\) | −20.1525 | − | 1.36733i | −0.998921 | − | 0.0677759i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.07295 | + | 5.13880i | −0.349735 | + | 0.254097i | −0.748758 | − | 0.662844i | \(-0.769349\pi\) |
0.399023 | + | 0.916941i | \(0.369349\pi\) | |||||||
\(410\) | 30.0344 | + | 92.4365i | 1.48330 | + | 4.56511i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.6353 | + | 16.4455i | 1.11516 | + | 0.810210i | ||||
\(413\) | −0.500000 | − | 0.363271i | −0.0246034 | − | 0.0178754i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2361 | − | 43.8141i | −0.698821 | − | 2.15075i | ||||
\(416\) | 21.7082 | − | 15.7719i | 1.06433 | − | 0.773283i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.23607 | − | 8.05748i | 0.158281 | − | 0.394104i | ||||
\(419\) | −3.09017 | −0.150965 | −0.0754823 | − | 0.997147i | \(-0.524050\pi\) | ||||
−0.0754823 | + | 0.997147i | \(0.524050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.78115 | + | 5.48183i | 0.0868081 | + | 0.267168i | 0.985032 | − | 0.172370i | \(-0.0551424\pi\) |
−0.898224 | + | 0.439537i | \(0.855142\pi\) | |||||||
\(422\) | −9.32624 | + | 28.7032i | −0.453994 | + | 1.39725i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −42.8607 | − | 31.1401i | −2.08150 | − | 1.51230i | ||||
\(425\) | −3.13525 | + | 9.64932i | −0.152082 | + | 0.468061i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.35410 | − | 2.43690i | 0.162316 | − | 0.117930i | ||||
\(428\) | −72.9787 | −3.52756 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 41.1246 | 1.98320 | ||||||||
\(431\) | −19.4721 | + | 14.1473i | −0.937940 | + | 0.681453i | −0.947924 | − | 0.318497i | \(-0.896822\pi\) |
0.00998408 | + | 0.999950i | \(0.496822\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.57295 | + | 26.3848i | −0.411990 | + | 1.26797i | 0.502926 | + | 0.864329i | \(0.332257\pi\) |
−0.914916 | + | 0.403644i | \(0.867743\pi\) | |||||||
\(434\) | 3.42705 | + | 2.48990i | 0.164504 | + | 0.119519i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.7812 | − | 63.9578i | 0.995237 | − | 3.06302i | ||||
\(437\) | 0.736068 | + | 2.26538i | 0.0352109 | + | 0.108368i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.7082 | 0.606529 | 0.303265 | − | 0.952906i | \(-0.401923\pi\) | ||||
0.303265 | + | 0.952906i | \(0.401923\pi\) | |||||||
\(440\) | 80.0132 | + | 5.42882i | 3.81448 | + | 0.258809i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.70820 | + | 7.05342i | −0.461772 | + | 0.335497i | ||||
\(443\) | 1.00000 | + | 3.07768i | 0.0475114 | + | 0.146225i | 0.971998 | − | 0.234990i | \(-0.0755057\pi\) |
−0.924486 | + | 0.381215i | \(0.875506\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.4164 | + | 21.3723i | 1.39447 | + | 1.01314i | ||||
\(446\) | 47.6697 | + | 34.6341i | 2.25723 | + | 1.63997i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.69098 | − | 8.28199i | −0.127137 | − | 0.391287i | ||||
\(449\) | 1.19098 | − | 0.865300i | 0.0562060 | − | 0.0408360i | −0.559328 | − | 0.828947i | \(-0.688941\pi\) |
0.615533 | + | 0.788111i | \(0.288941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −32.2254 | + | 20.2295i | −1.51744 | + | 0.952568i | ||||
\(452\) | 61.9574 | 2.91423 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.6353 | + | 35.8096i | 0.546070 | + | 1.68063i | ||||
\(455\) | −2.47214 | + | 7.60845i | −0.115896 | + | 0.356690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.809017 | + | 0.587785i | 0.0378442 | + | 0.0274954i | 0.606547 | − | 0.795048i | \(-0.292554\pi\) |
−0.568702 | + | 0.822543i | \(0.692554\pi\) | |||||||
\(458\) | 9.85410 | − | 30.3278i | 0.460452 | − | 1.41713i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −30.2705 | + | 21.9928i | −1.41137 | + | 1.02542i | ||||
\(461\) | −22.8541 | −1.06442 | −0.532211 | − | 0.846612i | \(-0.678639\pi\) | ||||
−0.532211 | + | 0.846612i | \(0.678639\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0000 | 0.790057 | 0.395029 | − | 0.918669i | \(-0.370735\pi\) | ||||
0.395029 | + | 0.918669i | \(0.370735\pi\) | |||||||
\(464\) | −14.7812 | + | 10.7391i | −0.686198 | + | 0.498552i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.5623 | + | 72.5173i | −1.09150 | + | 3.35930i | ||||
\(467\) | 4.23607 | + | 3.07768i | 0.196022 | + | 0.142418i | 0.681467 | − | 0.731849i | \(-0.261342\pi\) |
−0.485445 | + | 0.874267i | \(0.661342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.85410 | + | 5.70634i | −0.0856145 | + | 0.263494i | ||||
\(470\) | 15.5623 | + | 47.8959i | 0.717836 | + | 2.20927i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.61803 | 0.212562 | ||||||||
\(473\) | 3.92705 | + | 15.6129i | 0.180566 | + | 0.717883i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.42705 | + | 3.21644i | −0.203127 | + | 0.147580i | ||||
\(476\) | 2.78115 | + | 8.55951i | 0.127474 | + | 0.392324i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.23607 | + | 2.35114i | 0.148014 | + | 0.107539i | ||||
\(479\) | 13.1353 | + | 9.54332i | 0.600165 | + | 0.436045i | 0.845937 | − | 0.533282i | \(-0.179042\pi\) |
−0.245772 | + | 0.969328i | \(0.579042\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.65248 | + | 14.3188i | 0.212135 | + | 0.652883i | ||||
\(482\) | 56.8328 | − | 41.2915i | 2.58866 | − | 1.88077i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.48936 | + | 52.5451i | 0.431334 | + | 2.38842i | ||||
\(485\) | 19.4164 | 0.881654 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5000 | + | 32.3157i | 0.475800 | + | 1.46436i | 0.844875 | + | 0.534963i | \(0.179675\pi\) |
−0.369075 | + | 0.929400i | \(0.620325\pi\) | |||||||
\(488\) | −9.57295 | + | 29.4625i | −0.433347 | + | 1.33371i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −41.1246 | − | 29.8788i | −1.85782 | − | 1.34979i | ||||
\(491\) | −2.57295 | + | 7.91872i | −0.116116 | + | 0.357367i | −0.992178 | − | 0.124831i | \(-0.960161\pi\) |
0.876063 | + | 0.482198i | \(0.160161\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.78115 | − | 2.02063i | 0.125257 | − | 0.0910044i | ||||
\(494\) | −6.47214 | −0.291195 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.9443 | −0.715919 | ||||||||
\(497\) | −11.3992 | + | 8.28199i | −0.511323 | + | 0.371498i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.57953 | − | 11.0167i | 0.160242 | − | 0.493173i | −0.838413 | − | 0.545036i | \(-0.816516\pi\) |
0.998654 | + | 0.0518631i | \(0.0165159\pi\) | |||||||
\(500\) | −6.00000 | − | 4.35926i | −0.268328 | − | 0.194952i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.354102 | + | 1.08981i | −0.0158043 | + | 0.0486408i | ||||
\(503\) | −5.70820 | − | 17.5680i | −0.254516 | − | 0.783320i | −0.993925 | − | 0.110063i | \(-0.964895\pi\) |
0.739408 | − | 0.673257i | \(-0.235105\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.52786 | 0.0679891 | ||||||||
\(506\) | −15.8713 | − | 13.2618i | −0.705566 | − | 0.589559i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −37.5517 | + | 27.2829i | −1.66609 | + | 1.21048i | ||||
\(509\) | −1.48936 | − | 4.58377i | −0.0660146 | − | 0.203172i | 0.912608 | − | 0.408835i | \(-0.134065\pi\) |
−0.978623 | + | 0.205663i | \(0.934065\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.54508 | − | 4.02874i | −0.245300 | − | 0.178221i | ||||
\(512\) | −32.6074 | − | 23.6907i | −1.44106 | − | 1.04699i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.1074 | + | 64.9619i | 0.931007 | + | 2.86535i | ||||
\(515\) | 15.0902 | − | 10.9637i | 0.664952 | − | 0.483116i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.6976 | + | 10.4819i | −0.734358 | + | 0.460992i | ||||
\(518\) | 15.9443 | 0.700551 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.4721 | − | 56.8514i | −0.810057 | − | 2.49310i | ||||
\(521\) | 1.34752 | − | 4.14725i | 0.0590361 | − | 0.181694i | −0.917190 | − | 0.398451i | \(-0.869548\pi\) |
0.976226 | + | 0.216757i | \(0.0695478\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(524\) | 25.1459 | − | 77.3911i | 1.09850 | − | 3.38085i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.50000 | − | 1.08981i | 0.0654031 | − | 0.0475181i | ||||
\(527\) | 3.00000 | 0.130682 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.3262 | −0.753315 | ||||||||
\(530\) | −48.5967 | + | 35.3076i | −2.11091 | + | 1.53366i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.50000 | + | 4.61653i | −0.0650332 | + | 0.200152i | ||||
\(533\) | 22.9443 | + | 16.6700i | 0.993827 | + | 0.722057i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.0344 | + | 46.2713i | −0.649996 | + | 2.00048i | ||||
\(536\) | −13.8541 | − | 42.6385i | −0.598406 | − | 1.84170i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −32.1246 | −1.38499 | ||||||||
\(539\) | 7.41641 | − | 18.4661i | 0.319447 | − | 0.795391i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6803 | − | 13.5721i | 0.803131 | − | 0.583508i | −0.108700 | − | 0.994075i | \(-0.534669\pi\) |
0.911831 | + | 0.410566i | \(0.134669\pi\) | |||||||
\(542\) | −12.3262 | − | 37.9363i | −0.529457 | − | 1.62950i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −16.2812 | − | 11.8290i | −0.698049 | − | 0.507162i | ||||
\(545\) | −36.2705 | − | 26.3521i | −1.55366 | − | 1.12880i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.15248 | − | 15.8577i | −0.220304 | − | 0.678026i | −0.998734 | − | 0.0502950i | \(-0.983984\pi\) |
0.778430 | − | 0.627731i | \(-0.216016\pi\) | |||||||
\(548\) | 25.0623 | − | 18.2088i | 1.07061 | − | 0.777843i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.7082 | − | 44.0916i | 0.755080 | − | 1.88007i | ||||
\(551\) | 1.85410 | 0.0789874 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.95492 | + | 9.09429i | 0.125656 | + | 0.386729i | ||||
\(554\) | 11.9443 | − | 36.7607i | 0.507463 | − | 1.56181i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.5623 | + | 10.5801i | 0.617579 | + | 0.448698i | ||||
\(557\) | 9.47214 | − | 29.1522i | 0.401347 | − | 1.23522i | −0.522560 | − | 0.852603i | \(-0.675023\pi\) |
0.923907 | − | 0.382617i | \(-0.124977\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.70820 | − | 7.05342i | 0.410613 | − | 0.298328i | ||||
\(560\) | −31.8885 | −1.34754 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.5623 | −0.698639 | ||||||||
\(563\) | −34.2254 | + | 24.8662i | −1.44243 | + | 1.04799i | −0.454902 | + | 0.890542i | \(0.650326\pi\) |
−0.987528 | + | 0.157445i | \(0.949674\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.7639 | − | 39.2833i | 0.536983 | − | 1.65266i | ||||
\(566\) | −36.0066 | − | 26.1603i | −1.51347 | − | 1.09960i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 32.5344 | − | 100.131i | 1.36511 | − | 4.20139i | ||||
\(569\) | 4.38854 | + | 13.5065i | 0.183977 | + | 0.566224i | 0.999929 | − | 0.0118958i | \(-0.00378663\pi\) |
−0.815952 | + | 0.578120i | \(0.803787\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.4721 | −1.14967 | −0.574837 | − | 0.818268i | \(-0.694934\pi\) | ||||
−0.574837 | + | 0.818268i | \(0.694934\pi\) | |||||||
\(572\) | 33.7082 | − | 21.1603i | 1.40941 | − | 0.884755i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.2984 | − | 17.6538i | 1.01419 | − | 0.736855i | ||||
\(575\) | 4.02786 | + | 12.3965i | 0.167974 | + | 0.516969i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.94427 | − | 5.04531i | −0.289094 | − | 0.210039i | 0.433780 | − | 0.901019i | \(-0.357179\pi\) |
−0.722874 | + | 0.690980i | \(0.757179\pi\) | |||||||
\(578\) | −28.7254 | − | 20.8702i | −1.19482 | − | 0.868088i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | + | 27.6992i | 0.373705 | + | 1.15014i | ||||
\(581\) | −11.5172 | + | 8.36775i | −0.477815 | + | 0.347153i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0451 | − | 15.0781i | −0.747351 | − | 0.624473i | ||||
\(584\) | 51.2148 | 2.11928 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.51722 | + | 16.9803i | 0.227914 | + | 0.701448i | ||||
\(587\) | −4.14590 | + | 12.7598i | −0.171120 | + | 0.526652i | −0.999435 | − | 0.0336102i | \(-0.989300\pi\) |
0.828315 | + | 0.560262i | \(0.189300\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.30902 | + | 0.951057i | 0.0539371 | + | 0.0391876i | ||||
\(590\) | 1.61803 | − | 4.97980i | 0.0666134 | − | 0.205015i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −48.5517 | + | 35.2748i | −1.99546 | + | 1.44979i | ||||
\(593\) | 6.94427 | 0.285167 | 0.142584 | − | 0.989783i | \(-0.454459\pi\) | ||||
0.142584 | + | 0.989783i | \(0.454459\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.00000 | 0.245976 | ||||||||
\(596\) | −28.1976 | + | 20.4867i | −1.15502 | + | 0.839169i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.76393 | + | 14.6619i | −0.194812 | + | 0.599569i | ||||
\(599\) | −25.3713 | − | 18.4333i | −1.03664 | − | 0.753166i | −0.0670165 | − | 0.997752i | \(-0.521348\pi\) |
−0.969628 | + | 0.244586i | \(0.921348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.63525 | + | 8.11048i | −0.107494 | + | 0.330833i | −0.990308 | − | 0.138890i | \(-0.955646\pi\) |
0.882813 | + | 0.469724i | \(0.155646\pi\) | |||||||
\(602\) | −3.92705 | − | 12.0862i | −0.160055 | − | 0.492598i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −54.9787 | −2.23705 | ||||||||
\(605\) | 35.2705 | + | 4.80828i | 1.43395 | + | 0.195485i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.6074 | − | 17.8783i | 0.998783 | − | 0.725658i | 0.0369562 | − | 0.999317i | \(-0.488234\pi\) |
0.961827 | + | 0.273658i | \(0.0882338\pi\) | |||||||
\(608\) | −3.35410 | − | 10.3229i | −0.136027 | − | 0.418647i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.4164 | + | 20.6457i | 1.15055 | + | 0.835921i | ||||
\(611\) | 11.8885 | + | 8.63753i | 0.480959 | + | 0.349437i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.06231 | + | 12.5025i | 0.164075 | + | 0.504971i | 0.998967 | − | 0.0454430i | \(-0.0144699\pi\) |
−0.834892 | + | 0.550414i | \(0.814470\pi\) | |||||||
\(614\) | 2.42705 | − | 1.76336i | 0.0979478 | − | 0.0711632i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.04508 | − | 24.0337i | −0.243563 | − | 0.968345i | ||||
\(617\) | 42.1591 | 1.69726 | 0.848630 | − | 0.528987i | \(-0.177428\pi\) | ||||
0.848630 | + | 0.528987i | \(0.177428\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.29837 | + | 7.07367i | 0.0923794 | + | 0.284315i | 0.986562 | − | 0.163388i | \(-0.0522423\pi\) |
−0.894182 | + | 0.447703i | \(0.852242\pi\) | |||||||
\(620\) | −7.85410 | + | 24.1724i | −0.315428 | + | 0.970789i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.2082 | − | 11.0494i | −0.609793 | − | 0.443041i | ||||
\(623\) | 3.47214 | − | 10.6861i | 0.139108 | − | 0.428131i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.1353 | − | 13.1760i | 0.725410 | − | 0.527041i | ||||
\(626\) | 14.3262 | 0.572592 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 67.2492 | 2.68354 | ||||||||
\(629\) | 9.13525 | − | 6.63715i | 0.364246 | − | 0.264641i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.69098 | − | 23.6704i | 0.306173 | − | 0.942304i | −0.673064 | − | 0.739585i | \(-0.735022\pi\) |
0.979237 | − | 0.202720i | \(-0.0649780\pi\) | |||||||
\(632\) | −57.8050 | − | 41.9978i | −2.29936 | − | 1.67058i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.47214 | + | 7.60845i | −0.0981811 | + | 0.302170i | ||||
\(635\) | 9.56231 | + | 29.4298i | 0.379469 | + | 1.16788i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8328 | −0.587698 | ||||||||
\(638\) | −13.6353 | + | 8.55951i | −0.539825 | + | 0.338874i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.85410 | − | 2.07363i | 0.112818 | − | 0.0819673i | ||||
\(641\) | 10.9549 | + | 33.7158i | 0.432693 | + | 1.33169i | 0.895432 | + | 0.445198i | \(0.146867\pi\) |
−0.462739 | + | 0.886495i | \(0.653133\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.118034 | + | 0.0857567i | 0.00465481 | + | 0.00338191i | 0.590110 | − | 0.807323i | \(-0.299084\pi\) |
−0.585455 | + | 0.810705i | \(0.699084\pi\) | |||||||
\(644\) | 9.35410 | + | 6.79615i | 0.368603 | + | 0.267806i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50000 | + | 4.61653i | 0.0590167 | + | 0.181635i | ||||
\(647\) | −14.7082 | + | 10.6861i | −0.578239 | + | 0.420115i | −0.838089 | − | 0.545534i | \(-0.816327\pi\) |
0.259850 | + | 0.965649i | \(0.416327\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.04508 | + | 0.138757i | 0.0802766 | + | 0.00544670i | ||||
\(650\) | −35.4164 | −1.38915 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.9377 | + | 33.6628i | 0.428353 | + | 1.31834i | ||||
\(653\) | 13.3992 | − | 41.2385i | 0.524351 | − | 1.61379i | −0.241246 | − | 0.970464i | \(-0.577556\pi\) |
0.765596 | − | 0.643321i | \(-0.222444\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −43.8885 | − | 31.8869i | −1.71487 | − | 1.24592i | ||||
\(656\) | −34.9336 | + | 107.515i | −1.36393 | + | 4.19774i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.5902 | − | 9.14729i | 0.490816 | − | 0.356599i | ||||
\(659\) | −36.9787 | −1.44049 | −0.720243 | − | 0.693722i | \(-0.755970\pi\) | ||||
−0.720243 | + | 0.693722i | \(0.755970\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.7082 | −0.688769 | −0.344385 | − | 0.938829i | \(-0.611912\pi\) | ||||
−0.344385 | + | 0.938829i | \(0.611912\pi\) | |||||||
\(662\) | −26.2984 | + | 19.1069i | −1.02212 | + | 0.742610i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 32.8713 | − | 101.168i | 1.27565 | − | 3.92606i | ||||
\(665\) | 2.61803 | + | 1.90211i | 0.101523 | + | 0.0737608i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.36475 | − | 4.20025i | 0.0528431 | − | 0.162634i | ||||
\(668\) | −15.3541 | − | 47.2551i | −0.594068 | − | 1.82835i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −50.8328 | −1.96384 | ||||||||
\(671\) | −5.12461 | + | 12.7598i | −0.197833 | + | 0.492585i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.63525 | − | 5.54734i | 0.294317 | − | 0.213834i | −0.430821 | − | 0.902438i | \(-0.641776\pi\) |
0.725138 | + | 0.688603i | \(0.241776\pi\) | |||||||
\(674\) | 2.04508 | + | 6.29412i | 0.0787737 | + | 0.242441i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 27.0517 | + | 19.6542i | 1.04045 | + | 0.755930i | ||||
\(677\) | −19.3713 | − | 14.0741i | −0.744500 | − | 0.540911i | 0.149617 | − | 0.988744i | \(-0.452196\pi\) |
−0.894117 | + | 0.447833i | \(0.852196\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.85410 | − | 5.70634i | −0.0711539 | − | 0.218989i | ||||
\(680\) | −36.2705 | + | 26.3521i | −1.39091 | + | 1.01056i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.0172 | − | 0.951057i | −0.536747 | − | 0.0364178i | ||||
\(683\) | −14.4721 | −0.553761 | −0.276880 | − | 0.960904i | \(-0.589301\pi\) | ||||
−0.276880 | + | 0.960904i | \(0.589301\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.38197 | − | 19.6417i | −0.243842 | − | 0.750470i | ||||
\(686\) | −10.5172 | + | 32.3687i | −0.401549 | + | 1.23584i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 38.6976 | + | 28.1154i | 1.47533 | + | 1.07189i | ||||
\(689\) | −5.41641 | + | 16.6700i | −0.206349 | + | 0.635076i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.9894 | − | 20.3355i | 1.06477 | − | 0.773597i | 0.0898012 | − | 0.995960i | \(-0.471377\pi\) |
0.974964 | + | 0.222362i | \(0.0713768\pi\) | |||||||
\(692\) | −57.8115 | −2.19766 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −70.3951 | −2.67216 | ||||||||
\(695\) | 9.70820 | − | 7.05342i | 0.368253 | − | 0.267552i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.57295 | − | 20.2295i | 0.248968 | − | 0.766245i | ||||
\(698\) | −22.9894 | − | 16.7027i | −0.870160 | − | 0.632208i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.20820 | + | 25.2623i | −0.310241 | + | 0.954823i | ||||
\(701\) | 12.8926 | + | 39.6794i | 0.486947 | + | 1.49867i | 0.829141 | + | 0.559040i | \(0.188830\pi\) |
−0.342194 | + | 0.939629i | \(0.611170\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.09017 | 0.229695 | ||||||||
\(704\) | 22.1631 | + | 18.5191i | 0.835304 | + | 0.697965i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.0623 | − | 16.0292i | 0.830326 | − | 0.603267i | ||||
\(707\) | −0.145898 | − | 0.449028i | −0.00548706 | − | 0.0168874i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.4615 | + | 17.7723i | 0.918671 | + | 0.667453i | 0.943193 | − | 0.332246i | \(-0.107806\pi\) |
−0.0245221 | + | 0.999699i | \(0.507806\pi\) | |||||||
\(710\) | −96.5755 | − | 70.1662i | −3.62441 | − | 2.63329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.9443 | + | 79.8483i | 0.972303 | + | 2.99244i | ||||
\(713\) | 3.11803 | − | 2.26538i | 0.116771 | − | 0.0848393i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.47214 | − | 25.7315i | −0.242044 | − | 0.962305i | ||||
\(716\) | −111.374 | −4.16224 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.0623 | + | 40.2016i | 0.487481 | + | 1.50031i | ||||
\(719\) | 9.14590 | − | 28.1482i | 0.341084 | − | 1.04975i | −0.622562 | − | 0.782570i | \(-0.713908\pi\) |
0.963647 | − | 0.267180i | \(-0.0860917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.66312 | − | 3.38795i | −0.173664 | − | 0.126174i | ||||
\(722\) | 14.5623 | − | 44.8182i | 0.541953 | − | 1.66796i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 82.8222 | − | 60.1738i | 3.07806 | − | 2.23634i | ||||
\(725\) | 10.1459 | 0.376809 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.8328 | −1.29188 | −0.645939 | − | 0.763389i | \(-0.723534\pi\) | ||||
−0.645939 | + | 0.763389i | \(0.723534\pi\) | |||||||
\(728\) | −14.9443 | + | 10.8576i | −0.553872 | + | 0.402411i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 17.9443 | − | 55.2268i | 0.664147 | − | 2.04404i | ||||
\(731\) | −7.28115 | − | 5.29007i | −0.269303 | − | 0.195660i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.2148 | − | 37.5932i | 0.451163 | − | 1.38854i | −0.424418 | − | 0.905466i | \(-0.639521\pi\) |
0.875581 | − | 0.483071i | \(-0.160479\pi\) | |||||||
\(734\) | −0.572949 | − | 1.76336i | −0.0211479 | − | 0.0650866i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25.8541 | −0.952995 | ||||||||
\(737\) | −4.85410 | − | 19.2986i | −0.178803 | − | 0.710875i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.8541 | − | 14.4248i | 0.730345 | − | 0.530627i | −0.159328 | − | 0.987226i | \(-0.550933\pi\) |
0.889673 | + | 0.456599i | \(0.150933\pi\) | |||||||
\(740\) | 29.5623 | + | 90.9834i | 1.08673 | + | 3.34462i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0172 | + | 10.9106i | 0.551300 | + | 0.400543i | ||||
\(743\) | −1.90983 | − | 1.38757i | −0.0700649 | − | 0.0509051i | 0.552201 | − | 0.833711i | \(-0.313788\pi\) |
−0.622266 | + | 0.782806i | \(0.713788\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.18034 | + | 22.0988i | 0.263067 | + | 0.809638i | ||||
\(746\) | 54.3328 | − | 39.4751i | 1.98927 | − | 1.44529i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.9058 | − | 19.1396i | −0.837518 | − | 0.699815i | ||||
\(749\) | 15.0344 | 0.549347 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.2188 | + | 46.8388i | 0.555344 | + | 1.70917i | 0.695034 | + | 0.718977i | \(0.255389\pi\) |
−0.139691 | + | 0.990195i | \(0.544611\pi\) | |||||||
\(752\) | −18.1008 | + | 55.7086i | −0.660069 | + | 2.03148i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.70820 | + | 7.05342i | 0.353552 | + | 0.256871i | ||||
\(755\) | −11.3262 | + | 34.8586i | −0.412204 | + | 1.26863i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.89919 | + | 6.46564i | −0.323446 | + | 0.234998i | −0.737645 | − | 0.675189i | \(-0.764062\pi\) |
0.414198 | + | 0.910187i | \(0.364062\pi\) | |||||||
\(758\) | 23.0344 | 0.836649 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.1803 | −0.877113 | ||||||||
\(761\) | 32.3435 | − | 23.4989i | 1.17245 | − | 0.851834i | 0.181149 | − | 0.983456i | \(-0.442018\pi\) |
0.991300 | + | 0.131621i | \(0.0420182\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.28115 | + | 13.1760i | −0.154988 | + | 0.477004i | ||||
\(764\) | 46.9058 | + | 34.0790i | 1.69699 | + | 1.23294i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.6353 | + | 32.7319i | −0.384267 | + | 1.18265i | ||||
\(767\) | −0.472136 | − | 1.45309i | −0.0170478 | − | 0.0524679i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.79837 | 0.317277 | 0.158639 | − | 0.987337i | \(-0.449289\pi\) | ||||
0.158639 | + | 0.987337i | \(0.449289\pi\) | |||||||
\(770\) | −28.0344 | − | 1.90211i | −1.01029 | − | 0.0685474i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 43.1976 | − | 31.3849i | 1.55471 | − | 1.12957i | ||||
\(773\) | −2.36475 | − | 7.27794i | −0.0850540 | − | 0.261769i | 0.899480 | − | 0.436961i | \(-0.143945\pi\) |
−0.984534 | + | 0.175192i | \(0.943945\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.16312 | + | 5.20431i | 0.257307 | + | 0.186944i | ||||
\(776\) | 36.2705 | + | 26.3521i | 1.30204 | + | 0.945984i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.00000 | − | 21.5438i | −0.250962 | − | 0.772382i | ||||
\(779\) | 9.28115 | − | 6.74315i | 0.332532 | − | 0.241599i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.4164 | − | 43.3651i | 0.623208 | − | 1.55172i | ||||
\(782\) | 11.5623 | 0.413467 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.2705 | − | 56.2308i | −0.652518 | − | 2.00824i | ||||
\(785\) | 13.8541 | − | 42.6385i | 0.494474 | − | 1.52183i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.1246 | − | 21.1603i | −1.03818 | − | 0.754282i | −0.0682508 | − | 0.997668i | \(-0.521742\pi\) |
−0.969929 | + | 0.243386i | \(0.921742\pi\) | |||||||
\(788\) | 5.64590 | − | 17.3763i | 0.201127 | − | 0.619005i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −65.5410 | + | 47.6183i | −2.33184 | + | 1.69418i | ||||
\(791\) | −12.7639 | −0.453833 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.2492 | 0.363961 | ||||||||
\(794\) | 80.7492 | − | 58.6677i | 2.86568 | − | 2.08204i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.7812 | + | 63.9578i | −0.736568 | + | 2.26692i | ||||
\(797\) | 7.50000 | + | 5.44907i | 0.265664 | + | 0.193016i | 0.712640 | − | 0.701530i | \(-0.247499\pi\) |
−0.446977 | + | 0.894546i | \(0.647499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.40576 | − | 10.4819i | 0.120487 | − | 0.370822i | ||||
\(800\) | −18.3541 | − | 56.4881i | −0.648915 | − | 1.99716i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.5623 | 0.514213 | ||||||||
\(803\) | 22.6803 | + | 1.53884i | 0.800372 | + | 0.0543045i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.23607 | − | 4.53077i | 0.219793 | − | 0.159689i | ||||
\(806\) | 3.23607 | + | 9.95959i | 0.113986 | + | 0.350812i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.85410 | + | 2.07363i | 0.100407 | + | 0.0729499i | ||||
\(809\) | 5.59017 | + | 4.06150i | 0.196540 | + | 0.142795i | 0.681703 | − | 0.731629i | \(-0.261240\pi\) |
−0.485163 | + | 0.874424i | \(0.661240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.9721 | − | 49.1572i | −0.560858 | − | 1.72614i | −0.679950 | − | 0.733259i | \(-0.737998\pi\) |
0.119092 | − | 0.992883i | \(-0.462002\pi\) | |||||||
\(812\) | 7.28115 | − | 5.29007i | 0.255518 | − | 0.185645i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −44.7877 | + | 28.1154i | −1.56981 | + | 0.985445i | ||||
\(815\) | 23.5967 | 0.826558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50000 | − | 4.61653i | −0.0524784 | − | 0.161512i | ||||
\(818\) | −7.07295 | + | 21.7683i | −0.247300 | + | 0.761111i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 145.790 | + | 105.923i | 5.09122 | + | 3.69899i | ||||
\(821\) | −4.08359 | + | 12.5680i | −0.142518 | + | 0.438626i | −0.996684 | − | 0.0813754i | \(-0.974069\pi\) |
0.854165 | + | 0.520002i | \(0.174069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.0689 | − | 32.7445i | 1.57100 | − | 1.14140i | 0.644814 | − | 0.764340i | \(-0.276935\pi\) |
0.926189 | − | 0.377061i | \(-0.123065\pi\) | |||||||
\(824\) | 43.0689 | 1.50038 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.61803 | −0.0562986 | ||||||||
\(827\) | 22.6246 | − | 16.4377i | 0.786735 | − | 0.571596i | −0.120258 | − | 0.992743i | \(-0.538372\pi\) |
0.906993 | + | 0.421146i | \(0.138372\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.27458 | + | 22.3888i | −0.252656 | + | 0.777597i | 0.741626 | + | 0.670814i | \(0.234055\pi\) |
−0.994282 | + | 0.106783i | \(0.965945\pi\) | |||||||
\(830\) | −97.5755 | − | 70.8927i | −3.38689 | − | 2.46072i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.65248 | − | 20.4742i | 0.230633 | − | 0.709816i | ||||
\(833\) | 3.43769 | + | 10.5801i | 0.119109 | + | 0.366580i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.1246 | −1.14632 | ||||||||
\(836\) | −3.92705 | − | 15.6129i | −0.135820 | − | 0.539985i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.54508 | + | 4.75528i | −0.226096 | + | 0.164269i | ||||
\(839\) | −9.48936 | − | 29.2052i | −0.327609 | − | 1.00828i | −0.970249 | − | 0.242109i | \(-0.922161\pi\) |
0.642640 | − | 0.766168i | \(-0.277839\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.6803 | + | 15.0251i | 0.713115 | + | 0.518108i | ||||
\(842\) | 12.2082 | + | 8.86978i | 0.420722 | + | 0.305673i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 17.2918 | + | 53.2187i | 0.595208 | + | 1.83186i | ||||
\(845\) | 18.0344 | − | 13.1028i | 0.620404 | − | 0.450750i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.95492 | − | 10.8249i | −0.0671717 | − | 0.371948i | ||||
\(848\) | −69.8673 | −2.39925 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8.20820 | + | 25.2623i | 0.281539 | + | 0.866488i | ||||
\(851\) | 4.48278 | − | 13.7966i | 0.153668 | − | 0.472941i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.9508 | + | 32.6587i | 1.53909 | + | 1.11821i | 0.950904 | + | 0.309485i | \(0.100157\pi\) |
0.588184 | + | 0.808727i | \(0.299843\pi\) | |||||||
\(854\) | 3.35410 | − | 10.3229i | 0.114775 | − | 0.353241i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −90.8845 | + | 66.0314i | −3.10637 | + | 2.25691i | ||||
\(857\) | −19.3607 | −0.661348 | −0.330674 | − | 0.943745i | \(-0.607276\pi\) | ||||
−0.330674 | + | 0.943745i | \(0.607276\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.4377 | −0.424369 | −0.212184 | − | 0.977230i | \(-0.568058\pi\) | ||||
−0.212184 | + | 0.977230i | \(0.568058\pi\) | |||||||
\(860\) | 61.6869 | − | 44.8182i | 2.10351 | − | 1.52829i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.4721 | + | 59.9291i | −0.663224 | + | 2.04119i | ||||
\(863\) | 33.5344 | + | 24.3642i | 1.14153 | + | 0.829367i | 0.987331 | − | 0.158674i | \(-0.0507217\pi\) |
0.154195 | + | 0.988041i | \(0.450722\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.9098 | + | 36.6547i | −0.404946 | + | 1.24630i | ||||
\(866\) | 22.4443 | + | 69.0764i | 0.762687 | + | 2.34731i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.85410 | 0.266586 | ||||||||
\(869\) | −24.3369 | − | 20.3355i | −0.825572 | − | 0.689833i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | + | 8.71851i | −0.406604 | + | 0.295415i | ||||
\(872\) | −31.9894 | − | 98.4531i | −1.08330 | − | 3.33404i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.04508 | + | 3.66547i | 0.170653 | + | 0.123986i | ||||
\(875\) | 1.23607 | + | 0.898056i | 0.0417867 | + | 0.0303598i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.6180 | − | 35.7566i | −0.392313 | − | 1.20742i | −0.931034 | − | 0.364932i | \(-0.881092\pi\) |
0.538721 | − | 0.842484i | \(-0.318908\pi\) | |||||||
\(878\) | 26.9164 | − | 19.5559i | 0.908385 | − | 0.659980i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 89.5755 | − | 56.2308i | 3.01959 | − | 1.89554i | ||||
\(881\) | 24.1803 | 0.814656 | 0.407328 | − | 0.913282i | \(-0.366461\pi\) | ||||
0.407328 | + | 0.913282i | \(0.366461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.34346 | − | 4.13474i | −0.0452110 | − | 0.139145i | 0.925903 | − | 0.377762i | \(-0.123306\pi\) |
−0.971114 | + | 0.238616i | \(0.923306\pi\) | |||||||
\(884\) | −6.87539 | + | 21.1603i | −0.231244 | + | 0.711697i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.85410 | + | 4.97980i | 0.230268 | + | 0.167300i | ||||
\(887\) | 7.73607 | − | 23.8092i | 0.259752 | − | 0.799434i | −0.733104 | − | 0.680116i | \(-0.761929\pi\) |
0.992856 | − | 0.119318i | \(-0.0380707\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.73607 | − | 5.62058i | 0.259459 | − | 0.188508i | ||||
\(890\) | 95.1935 | 3.19089 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 109.249 | 3.65793 | ||||||||
\(893\) | 4.80902 | − | 3.49396i | 0.160928 | − | 0.116921i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.9443 | + | 70.6152i | −0.766942 | + | 2.36041i | ||||
\(896\) | −0.881966 | − | 0.640786i | −0.0294644 | − | 0.0214072i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.19098 | − | 3.66547i | 0.0397436 | − | 0.122318i | ||||
\(899\) | −0.927051 | − | 2.85317i | −0.0309189 | − | 0.0951585i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.1459 | 0.437953 | ||||||||
\(902\) | −37.1246 | + | 92.4365i | −1.23611 | + | 3.07780i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 77.1591 | − | 56.0593i | 2.56627 | − | 1.86451i | ||||
\(905\) | −21.0902 | − | 64.9089i | −0.701061 | − | 2.15764i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.5066 | + | 24.3440i | 1.11257 | + | 0.808328i | 0.983066 | − | 0.183251i | \(-0.0586623\pi\) |
0.129502 | + | 0.991579i | \(0.458662\pi\) | |||||||
\(908\) | 56.4787 | + | 41.0342i | 1.87431 | + | 1.36177i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 6.47214 | + | 19.9192i | 0.214549 | + | 0.660315i | ||||
\(911\) | −2.57295 | + | 1.86936i | −0.0852456 | + | 0.0619346i | −0.629592 | − | 0.776926i | \(-0.716778\pi\) |
0.544346 | + | 0.838861i | \(0.316778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5967 | − | 43.8141i | 0.582367 | − | 1.45004i | ||||
\(914\) | 2.61803 | 0.0865969 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −18.2705 | − | 56.2308i | −0.603675 | − | 1.85792i | ||||
\(917\) | −5.18034 | + | 15.9434i | −0.171070 | + | 0.526499i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.1976 | − | 32.8380i | −1.49093 | − | 1.08322i | −0.973824 | − | 0.227303i | \(-0.927009\pi\) |
−0.517106 | − | 0.855922i | \(-0.672991\pi\) | |||||||
\(920\) | −17.7984 | + | 54.7778i | −0.586795 | + | 1.80597i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.4058 | + | 35.1688i | −1.59416 | + | 1.15822i | ||||
\(923\) | −34.8328 | −1.14654 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 33.3262 | 1.09576 | ||||||||
\(926\) | 36.0066 | − | 26.1603i | 1.18325 | − | 0.859681i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.21885 | + | 19.1396i | −0.204144 | + | 0.628290i | ||||
\(929\) | 11.9164 | + | 8.65778i | 0.390965 | + | 0.284052i | 0.765851 | − | 0.643018i | \(-0.222318\pi\) |
−0.374886 | + | 0.927071i | \(0.622318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.85410 | + | 5.70634i | −0.0607657 | + | 0.187018i | ||||
\(932\) | 43.6869 | + | 134.455i | 1.43101 | + | 4.40420i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.7082 | 0.448546 | ||||||||
\(935\) | −16.8541 | + | 10.5801i | −0.551188 | + | 0.346007i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.88197 | + | 3.54696i | −0.159487 | + | 0.115874i | −0.664666 | − | 0.747140i | \(-0.731426\pi\) |
0.505179 | + | 0.863014i | \(0.331426\pi\) | |||||||
\(938\) | 4.85410 | + | 14.9394i | 0.158492 | + | 0.487788i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 75.5410 | + | 54.8838i | 2.46388 | + | 1.79011i | ||||
\(941\) | 34.1074 | + | 24.7805i | 1.11187 | + | 0.807820i | 0.982957 | − | 0.183836i | \(-0.0588515\pi\) |
0.128912 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.44427 | − | 25.9888i | −0.274983 | − | 0.846312i | ||||
\(944\) | 4.92705 | − | 3.57971i | 0.160362 | − | 0.116510i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.3435 | + | 27.0256i | 1.05158 | + | 0.878678i | ||||
\(947\) | 23.2918 | 0.756882 | 0.378441 | − | 0.925625i | \(-0.376460\pi\) | ||||
0.378441 | + | 0.925625i | \(0.376460\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.23607 | − | 16.1150i | −0.169970 | − | 0.523114i | ||||
\(950\) | −4.42705 | + | 13.6251i | −0.143633 | + | 0.442055i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 11.2082 | + | 8.14324i | 0.363260 | + | 0.263924i | ||||
\(953\) | −14.6803 | + | 45.1814i | −0.475543 | + | 1.46357i | 0.369681 | + | 0.929159i | \(0.379467\pi\) |
−0.845224 | + | 0.534412i | \(0.820533\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.2705 | − | 22.7194i | 1.01189 | − | 0.735181i | ||||
\(956\) | 7.41641 | 0.239864 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 42.5066 | 1.37333 | ||||||||
\(959\) | −5.16312 | + | 3.75123i | −0.166726 | + | 0.121133i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.77051 | + | 26.9929i | −0.282920 | + | 0.870737i | ||||
\(962\) | 31.8885 | + | 23.1684i | 1.02813 | + | 0.746979i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 40.2492 | − | 123.874i | 1.29634 | − | 3.98972i | ||||
\(965\) | −11.0000 | − | 33.8545i | −0.354103 | − | 1.08982i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.4853 | −1.04466 | −0.522328 | − | 0.852744i | \(-0.674936\pi\) | ||||
−0.522328 | + | 0.852744i | \(0.674936\pi\) | |||||||
\(968\) | 59.3607 | + | 56.8514i | 1.90792 | + | 1.82727i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 41.1246 | − | 29.8788i | 1.32043 | − | 0.959350i | ||||
\(971\) | −7.50000 | − | 23.0826i | −0.240686 | − | 0.740757i | −0.996316 | − | 0.0857575i | \(-0.972669\pi\) |
0.755630 | − | 0.654999i | \(-0.227331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.00000 | − | 2.17963i | −0.0961756 | − | 0.0698757i | ||||
\(974\) | 71.9681 | + | 52.2879i | 2.30601 | + | 1.67541i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.6246 | + | 38.8546i | 0.404104 | + | 1.24370i | ||||
\(977\) | −16.3713 | + | 11.8945i | −0.523765 | + | 0.380538i | −0.818020 | − | 0.575189i | \(-0.804928\pi\) |
0.294255 | + | 0.955727i | \(0.404928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.09017 | + | 36.1401i | 0.290523 | + | 1.15504i | ||||
\(980\) | −94.2492 | −3.01068 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.73607 | + | 20.7315i | 0.214957 | + | 0.661568i | ||||
\(983\) | 15.9894 | − | 49.2102i | 0.509981 | − | 1.56956i | −0.282251 | − | 0.959341i | \(-0.591081\pi\) |
0.792232 | − | 0.610220i | \(-0.208919\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.85410 | − | 7.15942i | −0.313978 | − | 0.228118i | ||||
\(986\) | 2.78115 | − | 8.55951i | 0.0885700 | − | 0.272590i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.70820 | + | 7.05342i | −0.308859 | + | 0.224399i | ||||
\(989\) | −11.5623 | −0.367660 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.5967 | −0.908406 | −0.454203 | − | 0.890898i | \(-0.650076\pi\) | ||||
−0.454203 | + | 0.890898i | \(0.650076\pi\) | |||||||
\(992\) | −14.2082 | + | 10.3229i | −0.451111 | + | 0.327751i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.3992 | + | 35.0831i | −0.361560 | + | 1.11277i | ||||
\(995\) | 36.2705 | + | 26.3521i | 1.14985 | + | 0.835417i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.97214 | − | 9.14729i | 0.0941285 | − | 0.289698i | −0.892897 | − | 0.450261i | \(-0.851331\pi\) |
0.987026 | + | 0.160563i | \(0.0513310\pi\) | |||||||
\(998\) | −9.37132 | − | 28.8420i | −0.296644 | − | 0.912976i | ||||
\(999\) | 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 | 891.2.f.b.487.1 | 4 | ||
3.2 | odd | 2 | 891.2.f.a.487.1 | 4 | |||
9.2 | odd | 6 | 297.2.n.a.91.1 | 8 | |||
9.4 | even | 3 | 99.2.m.a.25.1 | yes | 8 | ||
9.5 | odd | 6 | 297.2.n.a.289.1 | 8 | |||
9.7 | even | 3 | 99.2.m.a.58.1 | yes | 8 | ||
11.2 | odd | 10 | 9801.2.a.bc.1.2 | 2 | |||
11.4 | even | 5 | inner | 891.2.f.b.730.1 | 4 | ||
11.9 | even | 5 | 9801.2.a.n.1.1 | 2 | |||
33.2 | even | 10 | 9801.2.a.m.1.1 | 2 | |||
33.20 | odd | 10 | 9801.2.a.bb.1.2 | 2 | |||
33.26 | odd | 10 | 891.2.f.a.730.1 | 4 | |||
99.4 | even | 15 | 99.2.m.a.70.1 | yes | 8 | ||
99.13 | odd | 30 | 1089.2.e.d.727.1 | 4 | |||
99.31 | even | 15 | 1089.2.e.g.727.2 | 4 | |||
99.59 | odd | 30 | 297.2.n.a.235.1 | 8 | |||
99.70 | even | 15 | 99.2.m.a.4.1 | ✓ | 8 | ||
99.79 | odd | 30 | 1089.2.e.d.364.1 | 4 | |||
99.92 | odd | 30 | 297.2.n.a.37.1 | 8 | |||
99.97 | even | 15 | 1089.2.e.g.364.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.a.4.1 | ✓ | 8 | 99.70 | even | 15 | ||
99.2.m.a.25.1 | yes | 8 | 9.4 | even | 3 | ||
99.2.m.a.58.1 | yes | 8 | 9.7 | even | 3 | ||
99.2.m.a.70.1 | yes | 8 | 99.4 | even | 15 | ||
297.2.n.a.37.1 | 8 | 99.92 | odd | 30 | |||
297.2.n.a.91.1 | 8 | 9.2 | odd | 6 | |||
297.2.n.a.235.1 | 8 | 99.59 | odd | 30 | |||
297.2.n.a.289.1 | 8 | 9.5 | odd | 6 | |||
891.2.f.a.487.1 | 4 | 3.2 | odd | 2 | |||
891.2.f.a.730.1 | 4 | 33.26 | odd | 10 | |||
891.2.f.b.487.1 | 4 | 1.1 | even | 1 | trivial | ||
891.2.f.b.730.1 | 4 | 11.4 | even | 5 | inner | ||
1089.2.e.d.364.1 | 4 | 99.79 | odd | 30 | |||
1089.2.e.d.727.1 | 4 | 99.13 | odd | 30 | |||
1089.2.e.g.364.2 | 4 | 99.97 | even | 15 | |||
1089.2.e.g.727.2 | 4 | 99.31 | even | 15 | |||
9801.2.a.m.1.1 | 2 | 33.2 | even | 10 | |||
9801.2.a.n.1.1 | 2 | 11.9 | even | 5 | |||
9801.2.a.bb.1.2 | 2 | 33.20 | odd | 10 | |||
9801.2.a.bc.1.2 | 2 | 11.2 | odd | 10 |