Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, 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("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.2 | ||
Root | \(0.199632 - 0.145041i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.151 |
Dual form | 375.2.g.c.226.2 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0762527 | − | 0.234682i | −0.0539188 | − | 0.165945i | 0.920471 | − | 0.390811i | \(-0.127805\pi\) |
−0.974390 | + | 0.224866i | \(0.927805\pi\) | |||||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | 1.56877 | − | 1.13978i | 0.784386 | − | 0.569890i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.199632 | + | 0.145041i | 0.0814995 | + | 0.0592129i | ||||
\(7\) | 1.24676 | 0.471231 | 0.235615 | − | 0.971846i | \(-0.424289\pi\) | ||||
0.235615 | + | 0.971846i | \(0.424289\pi\) | |||||||
\(8\) | −0.786373 | − | 0.571334i | −0.278025 | − | 0.201997i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.794084 | + | 2.44394i | 0.239425 | + | 0.736876i | 0.996503 | + | 0.0835513i | \(0.0266262\pi\) |
−0.757078 | + | 0.653324i | \(0.773374\pi\) | |||||||
\(12\) | −0.599218 | + | 1.84420i | −0.172979 | + | 0.532376i | ||||
\(13\) | 1.44659 | − | 4.45215i | 0.401212 | − | 1.23480i | −0.522805 | − | 0.852452i | \(-0.675115\pi\) |
0.924017 | − | 0.382351i | \(-0.124885\pi\) | |||||||
\(14\) | −0.0950687 | − | 0.292592i | −0.0254082 | − | 0.0781984i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.12432 | − | 3.46029i | 0.281079 | − | 0.865073i | ||||
\(17\) | 4.72397 | + | 3.43216i | 1.14573 | + | 0.832422i | 0.987907 | − | 0.155046i | \(-0.0495526\pi\) |
0.157823 | + | 0.987467i | \(0.449553\pi\) | |||||||
\(18\) | −0.246759 | −0.0581616 | ||||||||
\(19\) | −3.37244 | − | 2.45022i | −0.773692 | − | 0.562120i | 0.129387 | − | 0.991594i | \(-0.458699\pi\) |
−0.903079 | + | 0.429474i | \(0.858699\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00865 | + | 0.732827i | −0.220105 | + | 0.159916i | ||||
\(22\) | 0.512997 | − | 0.372714i | 0.109371 | − | 0.0794629i | ||||
\(23\) | −0.496117 | − | 1.52689i | −0.103447 | − | 0.318379i | 0.885915 | − | 0.463847i | \(-0.153531\pi\) |
−0.989363 | + | 0.145468i | \(0.953531\pi\) | |||||||
\(24\) | 0.972011 | 0.198411 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.15514 | −0.226542 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 1.95588 | − | 1.42103i | 0.369627 | − | 0.268550i | ||||
\(29\) | 2.60158 | − | 1.89016i | 0.483102 | − | 0.350994i | −0.319423 | − | 0.947612i | \(-0.603489\pi\) |
0.802525 | + | 0.596618i | \(0.203489\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.43739 | + | 5.40358i | 1.33579 | + | 0.970512i | 0.999587 | + | 0.0287236i | \(0.00914425\pi\) |
0.336207 | + | 0.941788i | \(0.390856\pi\) | |||||||
\(32\) | −2.84182 | −0.502368 | ||||||||
\(33\) | −2.07894 | − | 1.51044i | −0.361897 | − | 0.262934i | ||||
\(34\) | 0.445250 | − | 1.37034i | 0.0763598 | − | 0.235011i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.599218 | − | 1.84420i | −0.0998697 | − | 0.307367i | ||||
\(37\) | 0.394857 | − | 1.21524i | 0.0649141 | − | 0.199785i | −0.913339 | − | 0.407200i | \(-0.866505\pi\) |
0.978253 | + | 0.207415i | \(0.0665051\pi\) | |||||||
\(38\) | −0.317865 | + | 0.978287i | −0.0515645 | + | 0.158699i | ||||
\(39\) | 1.44659 | + | 4.45215i | 0.231640 | + | 0.712914i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.68719 | − | 8.27031i | 0.419668 | − | 1.29161i | −0.488340 | − | 0.872654i | \(-0.662397\pi\) |
0.908008 | − | 0.418953i | \(-0.137603\pi\) | |||||||
\(42\) | 0.248893 | + | 0.180832i | 0.0384051 | + | 0.0279029i | ||||
\(43\) | 3.88086 | 0.591825 | 0.295913 | − | 0.955215i | \(-0.404376\pi\) | ||||
0.295913 | + | 0.955215i | \(0.404376\pi\) | |||||||
\(44\) | 4.03129 | + | 2.92891i | 0.607740 | + | 0.441549i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.320503 | + | 0.232859i | −0.0472556 | + | 0.0343332i | ||||
\(47\) | −2.59656 | + | 1.88651i | −0.378747 | + | 0.275176i | −0.760829 | − | 0.648953i | \(-0.775207\pi\) |
0.382082 | + | 0.924129i | \(0.375207\pi\) | |||||||
\(48\) | 1.12432 | + | 3.46029i | 0.162281 | + | 0.499450i | ||||
\(49\) | −5.44559 | −0.777942 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.83914 | −0.817643 | ||||||||
\(52\) | −2.80510 | − | 8.63320i | −0.388997 | − | 1.19721i | ||||
\(53\) | −10.7877 | + | 7.83770i | −1.48180 | + | 1.07659i | −0.504829 | + | 0.863219i | \(0.668444\pi\) |
−0.976971 | + | 0.213371i | \(0.931556\pi\) | |||||||
\(54\) | 0.199632 | − | 0.145041i | 0.0271665 | − | 0.0197376i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.980418 | − | 0.712315i | −0.131014 | − | 0.0951871i | ||||
\(57\) | 4.16857 | 0.552141 | ||||||||
\(58\) | −0.641964 | − | 0.466414i | −0.0842940 | − | 0.0612432i | ||||
\(59\) | −1.97548 | + | 6.07990i | −0.257186 | + | 0.791536i | 0.736206 | + | 0.676758i | \(0.236616\pi\) |
−0.993391 | + | 0.114778i | \(0.963384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.18258 | + | 3.63961i | 0.151414 | + | 0.466005i | 0.997780 | − | 0.0665973i | \(-0.0212143\pi\) |
−0.846366 | + | 0.532602i | \(0.821214\pi\) | |||||||
\(62\) | 0.701000 | − | 2.15746i | 0.0890271 | − | 0.273997i | ||||
\(63\) | 0.385270 | − | 1.18574i | 0.0485394 | − | 0.149389i | ||||
\(64\) | −2.03194 | − | 6.25366i | −0.253992 | − | 0.781708i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.195947 | + | 0.603064i | −0.0241195 | + | 0.0742321i | ||||
\(67\) | −8.19034 | − | 5.95063i | −1.00061 | − | 0.726985i | −0.0383907 | − | 0.999263i | \(-0.512223\pi\) |
−0.962219 | + | 0.272277i | \(0.912223\pi\) | |||||||
\(68\) | 11.3227 | 1.37308 | ||||||||
\(69\) | 1.29885 | + | 0.943670i | 0.156363 | + | 0.113605i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.2284 | + | 8.15794i | −1.33257 | + | 0.968169i | −0.332888 | + | 0.942966i | \(0.608023\pi\) |
−0.999682 | + | 0.0252028i | \(0.991977\pi\) | |||||||
\(72\) | −0.786373 | + | 0.571334i | −0.0926750 | + | 0.0673323i | ||||
\(73\) | 3.51704 | + | 10.8243i | 0.411638 | + | 1.26689i | 0.915223 | + | 0.402947i | \(0.132014\pi\) |
−0.503585 | + | 0.863946i | \(0.667986\pi\) | |||||||
\(74\) | −0.315305 | −0.0366534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.08332 | −0.927220 | ||||||||
\(77\) | 0.990032 | + | 3.04700i | 0.112825 | + | 0.347238i | ||||
\(78\) | 0.934531 | − | 0.678976i | 0.105815 | − | 0.0768789i | ||||
\(79\) | −9.29008 | + | 6.74964i | −1.04522 | + | 0.759394i | −0.971297 | − | 0.237871i | \(-0.923551\pi\) |
−0.0739188 | + | 0.997264i | \(0.523551\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −2.14580 | −0.236964 | ||||||||
\(83\) | −2.29137 | − | 1.66478i | −0.251511 | − | 0.182733i | 0.454885 | − | 0.890550i | \(-0.349680\pi\) |
−0.706396 | + | 0.707817i | \(0.749680\pi\) | |||||||
\(84\) | −0.747080 | + | 2.29928i | −0.0815131 | + | 0.250872i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.295926 | − | 0.910766i | −0.0319105 | − | 0.0982105i | ||||
\(87\) | −0.993717 | + | 3.05835i | −0.106538 | + | 0.327889i | ||||
\(88\) | 0.771858 | − | 2.37554i | 0.0822804 | − | 0.253233i | ||||
\(89\) | −0.426682 | − | 1.31319i | −0.0452282 | − | 0.139198i | 0.925892 | − | 0.377788i | \(-0.123315\pi\) |
−0.971121 | + | 0.238589i | \(0.923315\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.80355 | − | 5.55075i | 0.189063 | − | 0.581877i | ||||
\(92\) | −2.51861 | − | 1.82988i | −0.262584 | − | 0.190778i | ||||
\(93\) | −9.19312 | −0.953282 | ||||||||
\(94\) | 0.640724 | + | 0.465513i | 0.0660857 | + | 0.0480140i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.29908 | − | 1.67038i | 0.234649 | − | 0.170483i | ||||
\(97\) | 0.0246815 | − | 0.0179322i | 0.00250603 | − | 0.00182074i | −0.586532 | − | 0.809926i | \(-0.699507\pi\) |
0.589038 | + | 0.808106i | \(0.299507\pi\) | |||||||
\(98\) | 0.415241 | + | 1.27798i | 0.0419457 | + | 0.129096i | ||||
\(99\) | 2.56971 | 0.258266 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.2308 | −1.11750 | −0.558751 | − | 0.829336i | \(-0.688719\pi\) | ||||
−0.558751 | + | 0.829336i | \(0.688719\pi\) | |||||||
\(102\) | 0.445250 | + | 1.37034i | 0.0440864 | + | 0.135684i | ||||
\(103\) | −0.583288 | + | 0.423783i | −0.0574730 | + | 0.0417566i | −0.616151 | − | 0.787628i | \(-0.711309\pi\) |
0.558678 | + | 0.829385i | \(0.311309\pi\) | |||||||
\(104\) | −3.68122 | + | 2.67456i | −0.360973 | + | 0.262262i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.66195 | + | 1.93402i | 0.258552 | + | 0.187849i | ||||
\(107\) | −2.11668 | −0.204627 | −0.102313 | − | 0.994752i | \(-0.532624\pi\) | ||||
−0.102313 | + | 0.994752i | \(0.532624\pi\) | |||||||
\(108\) | 1.56877 | + | 1.13978i | 0.150955 | + | 0.109675i | ||||
\(109\) | 0.690602 | − | 2.12545i | 0.0661477 | − | 0.203582i | −0.912520 | − | 0.409033i | \(-0.865866\pi\) |
0.978667 | + | 0.205451i | \(0.0658662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.394857 | + | 1.21524i | 0.0374782 | + | 0.115346i | ||||
\(112\) | 1.40175 | − | 4.31415i | 0.132453 | − | 0.407649i | ||||
\(113\) | 0.973217 | − | 2.99525i | 0.0915526 | − | 0.281770i | −0.894787 | − | 0.446493i | \(-0.852673\pi\) |
0.986340 | + | 0.164723i | \(0.0526729\pi\) | |||||||
\(114\) | −0.317865 | − | 0.978287i | −0.0297708 | − | 0.0916250i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.92693 | − | 5.93047i | 0.178911 | − | 0.550630i | ||||
\(117\) | −3.78722 | − | 2.75158i | −0.350129 | − | 0.254383i | ||||
\(118\) | 1.57748 | 0.145219 | ||||||||
\(119\) | 5.88965 | + | 4.27908i | 0.539903 | + | 0.392262i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.55691 | − | 2.58425i | 0.323356 | − | 0.234932i | ||||
\(122\) | 0.763975 | − | 0.555061i | 0.0691671 | − | 0.0502528i | ||||
\(123\) | 2.68719 | + | 8.27031i | 0.242296 | + | 0.745709i | ||||
\(124\) | 17.8265 | 1.60086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.307649 | −0.0274075 | ||||||||
\(127\) | 4.83929 | + | 14.8938i | 0.429418 | + | 1.32161i | 0.898700 | + | 0.438564i | \(0.144513\pi\) |
−0.469282 | + | 0.883048i | \(0.655487\pi\) | |||||||
\(128\) | −5.91084 | + | 4.29448i | −0.522450 | + | 0.379582i | ||||
\(129\) | −3.13968 | + | 2.28111i | −0.276433 | + | 0.200841i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1000 | + | 8.79116i | 1.05718 | + | 0.768087i | 0.973565 | − | 0.228411i | \(-0.0733530\pi\) |
0.0836161 | + | 0.996498i | \(0.473353\pi\) | |||||||
\(132\) | −4.98295 | −0.433710 | ||||||||
\(133\) | −4.20463 | − | 3.05484i | −0.364587 | − | 0.264888i | ||||
\(134\) | −0.771969 | + | 2.37588i | −0.0666879 | + | 0.205244i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.75389 | − | 5.39792i | −0.150395 | − | 0.462868i | ||||
\(137\) | 3.24300 | − | 9.98092i | 0.277068 | − | 0.852727i | −0.711597 | − | 0.702588i | \(-0.752028\pi\) |
0.988665 | − | 0.150139i | \(-0.0479723\pi\) | |||||||
\(138\) | 0.122421 | − | 0.376774i | 0.0104212 | − | 0.0320731i | ||||
\(139\) | 3.84749 | + | 11.8414i | 0.326340 | + | 1.00437i | 0.970832 | + | 0.239761i | \(0.0770690\pi\) |
−0.644492 | + | 0.764611i | \(0.722931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.991798 | − | 3.05244i | 0.0835244 | − | 0.257062i | ||||
\(142\) | 2.77072 | + | 2.01304i | 0.232513 | + | 0.168931i | ||||
\(143\) | 12.0295 | 1.00596 | ||||||||
\(144\) | −2.94350 | − | 2.13858i | −0.245292 | − | 0.178215i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.27209 | − | 1.65077i | 0.188039 | − | 0.136619i | ||||
\(147\) | 4.40558 | − | 3.20084i | 0.363366 | − | 0.264001i | ||||
\(148\) | −0.765671 | − | 2.35649i | −0.0629378 | − | 0.193703i | ||||
\(149\) | −17.0680 | −1.39826 | −0.699131 | − | 0.714994i | \(-0.746430\pi\) | ||||
−0.699131 | + | 0.714994i | \(0.746430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.57516 | −0.128185 | −0.0640923 | − | 0.997944i | \(-0.520415\pi\) | ||||
−0.0640923 | + | 0.997944i | \(0.520415\pi\) | |||||||
\(152\) | 1.25210 | + | 3.85358i | 0.101559 | + | 0.312567i | ||||
\(153\) | 4.72397 | − | 3.43216i | 0.381910 | − | 0.277474i | ||||
\(154\) | 0.639584 | − | 0.464685i | 0.0515391 | − | 0.0374454i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.34384 | + | 5.33561i | 0.587978 | + | 0.427191i | ||||
\(157\) | 9.20058 | 0.734286 | 0.367143 | − | 0.930164i | \(-0.380336\pi\) | ||||
0.367143 | + | 0.930164i | \(0.380336\pi\) | |||||||
\(158\) | 2.29241 | + | 1.66553i | 0.182374 | + | 0.132503i | ||||
\(159\) | 4.12052 | − | 12.6817i | 0.326779 | − | 1.00572i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.618538 | − | 1.90366i | −0.0487476 | − | 0.150030i | ||||
\(162\) | −0.0762527 | + | 0.234682i | −0.00599098 | + | 0.0184383i | ||||
\(163\) | 1.41553 | − | 4.35656i | 0.110873 | − | 0.341232i | −0.880191 | − | 0.474620i | \(-0.842586\pi\) |
0.991064 | + | 0.133388i | \(0.0425855\pi\) | |||||||
\(164\) | −5.21075 | − | 16.0370i | −0.406891 | − | 1.25228i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.215970 | + | 0.664687i | −0.0167625 | + | 0.0515897i | ||||
\(167\) | 0.115310 | + | 0.0837776i | 0.00892296 | + | 0.00648291i | 0.592238 | − | 0.805763i | \(-0.298245\pi\) |
−0.583315 | + | 0.812246i | \(0.698245\pi\) | |||||||
\(168\) | 1.21186 | 0.0934973 | ||||||||
\(169\) | −7.21176 | − | 5.23965i | −0.554751 | − | 0.403050i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.37244 | + | 2.45022i | −0.257897 | + | 0.187373i | ||||
\(172\) | 6.08819 | − | 4.42333i | 0.464220 | − | 0.337275i | ||||
\(173\) | −7.60885 | − | 23.4176i | −0.578490 | − | 1.78041i | −0.623974 | − | 0.781445i | \(-0.714483\pi\) |
0.0454831 | − | 0.998965i | \(-0.485517\pi\) | |||||||
\(174\) | 0.793511 | 0.0601559 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.34955 | 0.704749 | ||||||||
\(177\) | −1.97548 | − | 6.07990i | −0.148486 | − | 0.456993i | ||||
\(178\) | −0.275647 | + | 0.200269i | −0.0206606 | + | 0.0150108i | ||||
\(179\) | 19.5420 | − | 14.1981i | 1.46064 | − | 1.06122i | 0.477446 | − | 0.878661i | \(-0.341563\pi\) |
0.983195 | − | 0.182557i | \(-0.0584373\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.59218 | − | 1.15679i | −0.118346 | − | 0.0859834i | 0.527038 | − | 0.849842i | \(-0.323303\pi\) |
−0.645384 | + | 0.763858i | \(0.723303\pi\) | |||||||
\(182\) | −1.44019 | −0.106754 | ||||||||
\(183\) | −3.09604 | − | 2.24940i | −0.228866 | − | 0.166281i | ||||
\(184\) | −0.482231 | + | 1.48415i | −0.0355505 | + | 0.109413i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.701000 | + | 2.15746i | 0.0513998 | + | 0.158192i | ||||
\(187\) | −4.63677 | + | 14.2705i | −0.339074 | + | 1.04356i | ||||
\(188\) | −1.92320 | + | 5.91901i | −0.140264 | + | 0.431689i | ||||
\(189\) | 0.385270 | + | 1.18574i | 0.0280242 | + | 0.0862498i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.40061 | + | 7.38832i | −0.173702 | + | 0.534600i | −0.999572 | − | 0.0292607i | \(-0.990685\pi\) |
0.825870 | + | 0.563861i | \(0.190685\pi\) | |||||||
\(192\) | 5.31968 | + | 3.86498i | 0.383915 | + | 0.278931i | ||||
\(193\) | −14.3458 | −1.03264 | −0.516318 | − | 0.856397i | \(-0.672698\pi\) | ||||
−0.516318 | + | 0.856397i | \(0.672698\pi\) | |||||||
\(194\) | −0.00609039 | − | 0.00442493i | −0.000437265 | − | 0.000317691i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54290 | + | 6.20678i | −0.610207 | + | 0.443341i | ||||
\(197\) | 0.132307 | − | 0.0961264i | 0.00942645 | − | 0.00684872i | −0.583062 | − | 0.812428i | \(-0.698146\pi\) |
0.592489 | + | 0.805579i | \(0.298146\pi\) | |||||||
\(198\) | −0.195947 | − | 0.603064i | −0.0139254 | − | 0.0428579i | ||||
\(199\) | 4.96974 | 0.352295 | 0.176148 | − | 0.984364i | \(-0.443636\pi\) | ||||
0.176148 | + | 0.984364i | \(0.443636\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.1238 | 0.714079 | ||||||||
\(202\) | 0.856375 | + | 2.63565i | 0.0602543 | + | 0.185444i | ||||
\(203\) | 3.24355 | − | 2.35658i | 0.227652 | − | 0.165399i | ||||
\(204\) | −9.16029 | + | 6.65534i | −0.641348 | + | 0.465967i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.143931 | + | 0.104572i | 0.0100282 | + | 0.00728590i | ||||
\(207\) | −1.60547 | −0.111588 | ||||||||
\(208\) | −13.7793 | − | 10.0112i | −0.955423 | − | 0.694155i | ||||
\(209\) | 3.31020 | − | 10.1877i | 0.228971 | − | 0.704701i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.01784 | + | 3.13260i | 0.0700713 | + | 0.215657i | 0.979960 | − | 0.199196i | \(-0.0638330\pi\) |
−0.909888 | + | 0.414853i | \(0.863833\pi\) | |||||||
\(212\) | −7.99015 | + | 24.5911i | −0.548766 | + | 1.68893i | ||||
\(213\) | 4.28888 | − | 13.1998i | 0.293869 | − | 0.904437i | ||||
\(214\) | 0.161402 | + | 0.496745i | 0.0110332 | + | 0.0339568i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.300368 | − | 0.924437i | 0.0204374 | − | 0.0629000i | ||||
\(217\) | 9.27263 | + | 6.73696i | 0.629467 | + | 0.457335i | ||||
\(218\) | −0.551465 | −0.0373500 | ||||||||
\(219\) | −9.20773 | − | 6.68981i | −0.622201 | − | 0.452055i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.1141 | − | 16.0669i | 1.48756 | − | 1.08077i | ||||
\(222\) | 0.255087 | − | 0.185331i | 0.0171203 | − | 0.0124386i | ||||
\(223\) | 4.87419 | + | 15.0012i | 0.326400 | + | 1.00456i | 0.970805 | + | 0.239872i | \(0.0771053\pi\) |
−0.644404 | + | 0.764685i | \(0.722895\pi\) | |||||||
\(224\) | −3.54307 | −0.236731 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.777142 | −0.0516947 | ||||||||
\(227\) | −4.18427 | − | 12.8779i | −0.277720 | − | 0.854734i | −0.988487 | − | 0.151307i | \(-0.951652\pi\) |
0.710767 | − | 0.703428i | \(-0.248348\pi\) | |||||||
\(228\) | 6.53954 | − | 4.75125i | 0.433092 | − | 0.314660i | ||||
\(229\) | 11.9596 | − | 8.68915i | 0.790312 | − | 0.574195i | −0.117744 | − | 0.993044i | \(-0.537566\pi\) |
0.908056 | + | 0.418849i | \(0.137566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.59194 | − | 1.88315i | −0.170537 | − | 0.123902i | ||||
\(232\) | −3.12573 | −0.205214 | ||||||||
\(233\) | 0.419864 | + | 0.305049i | 0.0275062 | + | 0.0199844i | 0.601453 | − | 0.798908i | \(-0.294589\pi\) |
−0.573947 | + | 0.818892i | \(0.694589\pi\) | |||||||
\(234\) | −0.356959 | + | 1.09861i | −0.0233351 | + | 0.0718182i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.83067 | + | 11.7896i | 0.249356 | + | 0.767438i | ||||
\(237\) | 3.54849 | − | 10.9211i | 0.230500 | − | 0.709405i | ||||
\(238\) | 0.555120 | − | 1.70848i | 0.0359831 | − | 0.110745i | ||||
\(239\) | 2.54331 | + | 7.82750i | 0.164513 | + | 0.506319i | 0.999000 | − | 0.0447086i | \(-0.0142359\pi\) |
−0.834487 | + | 0.551027i | \(0.814236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.395906 | + | 1.21847i | −0.0255025 | + | 0.0784888i | −0.962998 | − | 0.269509i | \(-0.913138\pi\) |
0.937495 | + | 0.347998i | \(0.113138\pi\) | |||||||
\(242\) | −0.877700 | − | 0.637686i | −0.0564207 | − | 0.0409920i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.00356 | + | 4.36184i | 0.384339 | + | 0.279238i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.73599 | − | 1.26127i | 0.110682 | − | 0.0804155i | ||||
\(247\) | −15.7873 | + | 11.4701i | −1.00452 | + | 0.729828i | ||||
\(248\) | −2.76132 | − | 8.49846i | −0.175344 | − | 0.539653i | ||||
\(249\) | 2.83229 | 0.179489 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.63494 | 0.292555 | 0.146277 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146277 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(252\) | −0.747080 | − | 2.29928i | −0.0470616 | − | 0.144841i | ||||
\(253\) | 3.33767 | − | 2.42496i | 0.209837 | − | 0.152456i | ||||
\(254\) | 3.12630 | − | 2.27139i | 0.196161 | − | 0.142519i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.18081 | − | 6.67025i | −0.573801 | − | 0.416891i | ||||
\(257\) | 18.3001 | 1.14153 | 0.570766 | − | 0.821113i | \(-0.306647\pi\) | ||||
0.570766 | + | 0.821113i | \(0.306647\pi\) | |||||||
\(258\) | 0.774744 | + | 0.562885i | 0.0482335 | + | 0.0350437i | ||||
\(259\) | 0.492291 | − | 1.51512i | 0.0305895 | − | 0.0941448i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.993717 | − | 3.05835i | −0.0615095 | − | 0.189307i | ||||
\(262\) | 1.14047 | − | 3.51000i | 0.0704583 | − | 0.216848i | ||||
\(263\) | −5.15027 | + | 15.8509i | −0.317579 | + | 0.977409i | 0.657100 | + | 0.753803i | \(0.271783\pi\) |
−0.974680 | + | 0.223606i | \(0.928217\pi\) | |||||||
\(264\) | 0.771858 | + | 2.37554i | 0.0475046 | + | 0.146204i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.396301 | + | 1.21969i | −0.0242988 | + | 0.0747839i | ||||
\(267\) | 1.11707 | + | 0.811598i | 0.0683635 | + | 0.0496690i | ||||
\(268\) | −19.6312 | −1.19917 | ||||||||
\(269\) | −2.12942 | − | 1.54712i | −0.129833 | − | 0.0943294i | 0.520973 | − | 0.853573i | \(-0.325569\pi\) |
−0.650807 | + | 0.759244i | \(0.725569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.69192 | + | 2.68233i | −0.224268 | + | 0.162940i | −0.694246 | − | 0.719738i | \(-0.744262\pi\) |
0.469978 | + | 0.882678i | \(0.344262\pi\) | |||||||
\(272\) | 17.1875 | − | 12.4875i | 1.04215 | − | 0.757164i | ||||
\(273\) | 1.80355 | + | 5.55075i | 0.109156 | + | 0.335947i | ||||
\(274\) | −2.58963 | −0.156445 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.11318 | 0.187391 | ||||||||
\(277\) | −0.389132 | − | 1.19762i | −0.0233807 | − | 0.0719583i | 0.938685 | − | 0.344775i | \(-0.112045\pi\) |
−0.962066 | + | 0.272817i | \(0.912045\pi\) | |||||||
\(278\) | 2.48557 | − | 1.80587i | 0.149075 | − | 0.108309i | ||||
\(279\) | 7.43739 | − | 5.40358i | 0.445265 | − | 0.323504i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.8543 | − | 7.88611i | −0.647513 | − | 0.470446i | 0.214910 | − | 0.976634i | \(-0.431054\pi\) |
−0.862423 | + | 0.506188i | \(0.831054\pi\) | |||||||
\(282\) | −0.791979 | −0.0471617 | ||||||||
\(283\) | 19.4884 | + | 14.1591i | 1.15846 | + | 0.841674i | 0.989583 | − | 0.143962i | \(-0.0459844\pi\) |
0.168882 | + | 0.985636i | \(0.445984\pi\) | |||||||
\(284\) | −8.31661 | + | 25.5959i | −0.493500 | + | 1.51884i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.917281 | − | 2.82310i | −0.0542400 | − | 0.166934i | ||||
\(287\) | 3.35028 | − | 10.3111i | 0.197761 | − | 0.608644i | ||||
\(288\) | −0.878171 | + | 2.70273i | −0.0517467 | + | 0.159260i | ||||
\(289\) | 5.28283 | + | 16.2589i | 0.310754 | + | 0.956404i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.00942751 | + | 0.0290149i | −0.000552651 | + | 0.00170088i | ||||
\(292\) | 17.8548 | + | 12.9723i | 1.04487 | + | 0.759145i | ||||
\(293\) | 32.1727 | 1.87955 | 0.939776 | − | 0.341792i | \(-0.111034\pi\) | ||||
0.939776 | + | 0.341792i | \(0.111034\pi\) | |||||||
\(294\) | −1.08712 | − | 0.789836i | −0.0634019 | − | 0.0460641i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00481 | + | 0.730041i | −0.0584037 | + | 0.0424328i | ||||
\(297\) | −2.07894 | + | 1.51044i | −0.120632 | + | 0.0876445i | ||||
\(298\) | 1.30148 | + | 4.00554i | 0.0753926 | + | 0.232035i | ||||
\(299\) | −7.51561 | −0.434639 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.83849 | 0.278886 | ||||||||
\(302\) | 0.120110 | + | 0.369661i | 0.00691156 | + | 0.0212716i | ||||
\(303\) | 9.08587 | − | 6.60127i | 0.521970 | − | 0.379233i | ||||
\(304\) | −12.2702 | + | 8.91482i | −0.703744 | + | 0.511300i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.16568 | − | 0.846917i | −0.0666375 | − | 0.0484150i | ||||
\(307\) | −20.2962 | −1.15837 | −0.579183 | − | 0.815198i | \(-0.696628\pi\) | ||||
−0.579183 | + | 0.815198i | \(0.696628\pi\) | |||||||
\(308\) | 5.02605 | + | 3.65164i | 0.286386 | + | 0.208071i | ||||
\(309\) | 0.222796 | − | 0.685696i | 0.0126744 | − | 0.0390079i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.78554 | − | 17.8061i | −0.328068 | − | 1.00969i | −0.970037 | − | 0.242959i | \(-0.921882\pi\) |
0.641969 | − | 0.766731i | \(-0.278118\pi\) | |||||||
\(312\) | 1.40610 | − | 4.32753i | 0.0796048 | − | 0.244998i | ||||
\(313\) | −7.68955 | + | 23.6660i | −0.434639 | + | 1.33768i | 0.458817 | + | 0.888531i | \(0.348274\pi\) |
−0.893456 | + | 0.449151i | \(0.851726\pi\) | |||||||
\(314\) | −0.701569 | − | 2.15921i | −0.0395919 | − | 0.121851i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.88092 | + | 21.1773i | −0.387082 | + | 1.19132i | ||||
\(317\) | −20.3775 | − | 14.8052i | −1.14452 | − | 0.831540i | −0.156775 | − | 0.987634i | \(-0.550110\pi\) |
−0.987742 | + | 0.156094i | \(0.950110\pi\) | |||||||
\(318\) | −3.29036 | −0.184514 | ||||||||
\(319\) | 6.68532 | + | 4.85717i | 0.374306 | + | 0.271949i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.71243 | − | 1.24415i | 0.0955783 | − | 0.0694417i | ||||
\(322\) | −0.399590 | + | 0.290319i | −0.0222683 | + | 0.0161788i | ||||
\(323\) | −7.52174 | − | 23.1496i | −0.418521 | − | 1.28808i | ||||
\(324\) | −1.93911 | −0.107728 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.13034 | −0.0626039 | ||||||||
\(327\) | 0.690602 | + | 2.12545i | 0.0381904 | + | 0.117538i | ||||
\(328\) | −6.83824 | + | 4.96827i | −0.377579 | + | 0.274327i | ||||
\(329\) | −3.23728 | + | 2.35202i | −0.178477 | + | 0.129671i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.6097 | − | 17.8800i | −1.35267 | − | 0.982773i | −0.998874 | − | 0.0474508i | \(-0.984890\pi\) |
−0.353797 | − | 0.935322i | \(-0.615110\pi\) | |||||||
\(332\) | −5.49212 | −0.301419 | ||||||||
\(333\) | −1.03375 | − | 0.751062i | −0.0566491 | − | 0.0411580i | ||||
\(334\) | 0.0108684 | − | 0.0334494i | 0.000594691 | − | 0.00183027i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.40175 | + | 4.31415i | 0.0764719 | + | 0.235356i | ||||
\(337\) | 1.41361 | − | 4.35066i | 0.0770045 | − | 0.236995i | −0.905143 | − | 0.425107i | \(-0.860237\pi\) |
0.982148 | + | 0.188111i | \(0.0602366\pi\) | |||||||
\(338\) | −0.679734 | + | 2.09200i | −0.0369726 | + | 0.113790i | ||||
\(339\) | 0.973217 | + | 2.99525i | 0.0528579 | + | 0.162680i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.30011 | + | 22.4674i | −0.395323 | + | 1.21668i | ||||
\(342\) | 0.832181 | + | 0.604615i | 0.0449992 | + | 0.0326938i | ||||
\(343\) | −15.5167 | −0.837821 | ||||||||
\(344\) | −3.05180 | − | 2.21726i | −0.164542 | − | 0.119547i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.91550 | + | 3.57132i | −0.264259 | + | 0.191995i | ||||
\(347\) | −13.6038 | + | 9.88377i | −0.730293 | + | 0.530589i | −0.889656 | − | 0.456631i | \(-0.849056\pi\) |
0.159363 | + | 0.987220i | \(0.449056\pi\) | |||||||
\(348\) | 1.92693 | + | 5.93047i | 0.103294 | + | 0.317906i | ||||
\(349\) | 0.373581 | 0.0199973 | 0.00999866 | − | 0.999950i | \(-0.496817\pi\) | ||||
0.00999866 | + | 0.999950i | \(0.496817\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.68126 | 0.249867 | ||||||||
\(352\) | −2.25665 | − | 6.94524i | −0.120280 | − | 0.370183i | ||||
\(353\) | −19.3909 | + | 14.0883i | −1.03208 | + | 0.749847i | −0.968723 | − | 0.248144i | \(-0.920179\pi\) |
−0.0633526 | + | 0.997991i | \(0.520179\pi\) | |||||||
\(354\) | −1.27621 | + | 0.927218i | −0.0678296 | + | 0.0492811i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.16612 | − | 1.57378i | −0.114804 | − | 0.0834101i | ||||
\(357\) | −7.28000 | −0.385299 | ||||||||
\(358\) | −4.82218 | − | 3.50352i | −0.254860 | − | 0.185167i | ||||
\(359\) | −1.46789 | + | 4.51771i | −0.0774724 | + | 0.238435i | −0.982291 | − | 0.187362i | \(-0.940006\pi\) |
0.904819 | + | 0.425797i | \(0.140006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.501540 | − | 1.54358i | −0.0263969 | − | 0.0812412i | ||||
\(362\) | −0.150069 | + | 0.461865i | −0.00788744 | + | 0.0242751i | ||||
\(363\) | −1.35862 | + | 4.18140i | −0.0713090 | + | 0.219467i | ||||
\(364\) | −3.49728 | − | 10.7635i | −0.183307 | − | 0.564162i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.291813 | + | 0.898107i | −0.0152533 | + | 0.0469448i | ||||
\(367\) | −14.0526 | − | 10.2098i | −0.733540 | − | 0.532948i | 0.157141 | − | 0.987576i | \(-0.449772\pi\) |
−0.890681 | + | 0.454628i | \(0.849772\pi\) | |||||||
\(368\) | −5.84128 | −0.304498 | ||||||||
\(369\) | −7.03515 | − | 5.11134i | −0.366235 | − | 0.266085i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.4496 | + | 9.77172i | −0.698270 | + | 0.507323i | ||||
\(372\) | −14.4219 | + | 10.4781i | −0.747742 | + | 0.543266i | ||||
\(373\) | −0.651645 | − | 2.00556i | −0.0337409 | − | 0.103844i | 0.932768 | − | 0.360478i | \(-0.117386\pi\) |
−0.966509 | + | 0.256634i | \(0.917386\pi\) | |||||||
\(374\) | 3.70260 | 0.191457 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.11969 | 0.160886 | ||||||||
\(377\) | −4.65185 | − | 14.3169i | −0.239582 | − | 0.737359i | ||||
\(378\) | 0.248893 | − | 0.180832i | 0.0128017 | − | 0.00930097i | ||||
\(379\) | −10.0391 | + | 7.29380i | −0.515671 | + | 0.374657i | −0.814971 | − | 0.579502i | \(-0.803247\pi\) |
0.299299 | + | 0.954159i | \(0.403247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.6694 | − | 9.20488i | −0.649075 | − | 0.471580i | ||||
\(382\) | 1.91696 | 0.0980801 | ||||||||
\(383\) | 26.9448 | + | 19.5766i | 1.37682 | + | 1.00032i | 0.997170 | + | 0.0751836i | \(0.0239543\pi\) |
0.379646 | + | 0.925132i | \(0.376046\pi\) | |||||||
\(384\) | 2.25774 | − | 6.94861i | 0.115215 | − | 0.354595i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.09391 | + | 3.36671i | 0.0556785 | + | 0.171361i | ||||
\(387\) | 1.19925 | − | 3.69092i | 0.0609614 | − | 0.187620i | ||||
\(388\) | 0.0182810 | − | 0.0562631i | 0.000928076 | − | 0.00285633i | ||||
\(389\) | −5.24639 | − | 16.1467i | −0.266002 | − | 0.818671i | −0.991461 | − | 0.130405i | \(-0.958372\pi\) |
0.725459 | − | 0.688266i | \(-0.241628\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.89690 | − | 8.91573i | 0.146502 | − | 0.450888i | ||||
\(392\) | 4.28227 | + | 3.11125i | 0.216287 | + | 0.157142i | ||||
\(393\) | −14.9564 | −0.754451 | ||||||||
\(394\) | −0.0326478 | − | 0.0237200i | −0.00164477 | − | 0.00119500i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.03129 | − | 2.92891i | 0.202580 | − | 0.147183i | ||||
\(397\) | −0.701070 | + | 0.509357i | −0.0351857 | + | 0.0255639i | −0.605239 | − | 0.796044i | \(-0.706922\pi\) |
0.570053 | + | 0.821608i | \(0.306922\pi\) | |||||||
\(398\) | −0.378956 | − | 1.16631i | −0.0189953 | − | 0.0584617i | ||||
\(399\) | 5.19720 | 0.260186 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.68680 | 0.483736 | 0.241868 | − | 0.970309i | \(-0.422240\pi\) | ||||
0.241868 | + | 0.970309i | \(0.422240\pi\) | |||||||
\(402\) | −0.771969 | − | 2.37588i | −0.0385023 | − | 0.118498i | ||||
\(403\) | 34.8164 | − | 25.2956i | 1.73433 | − | 1.26006i | ||||
\(404\) | −17.6185 | + | 12.8006i | −0.876553 | + | 0.636853i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.800374 | − | 0.581506i | −0.0397219 | − | 0.0288597i | ||||
\(407\) | 3.28353 | 0.162759 | ||||||||
\(408\) | 4.59174 | + | 3.33610i | 0.227325 | + | 0.165161i | ||||
\(409\) | 0.469043 | − | 1.44357i | 0.0231927 | − | 0.0713797i | −0.938790 | − | 0.344489i | \(-0.888052\pi\) |
0.961983 | + | 0.273109i | \(0.0880521\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.24300 | + | 9.98092i | 0.159965 | + | 0.492322i | ||||
\(412\) | −0.432026 | + | 1.32964i | −0.0212844 | + | 0.0655066i | ||||
\(413\) | −2.46295 | + | 7.58017i | −0.121194 | + | 0.372996i | ||||
\(414\) | 0.122421 | + | 0.376774i | 0.00601667 | + | 0.0185174i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.11095 | + | 12.6522i | −0.201556 | + | 0.620325i | ||||
\(417\) | −10.0729 | − | 7.31837i | −0.493271 | − | 0.358382i | ||||
\(418\) | −2.64329 | −0.129287 | ||||||||
\(419\) | 24.7252 | + | 17.9639i | 1.20790 | + | 0.877594i | 0.995039 | − | 0.0994875i | \(-0.0317203\pi\) |
0.212866 | + | 0.977081i | \(0.431720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.64016 | − | 4.09782i | 0.274885 | − | 0.199715i | −0.441799 | − | 0.897114i | \(-0.645659\pi\) |
0.716683 | + | 0.697399i | \(0.245659\pi\) | |||||||
\(422\) | 0.657551 | − | 0.477739i | 0.0320091 | − | 0.0232560i | ||||
\(423\) | 0.991798 | + | 3.05244i | 0.0482228 | + | 0.148415i | ||||
\(424\) | 12.9611 | 0.629445 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.42480 | −0.165932 | ||||||||
\(427\) | 1.47439 | + | 4.53772i | 0.0713510 | + | 0.219596i | ||||
\(428\) | −3.32058 | + | 2.41255i | −0.160506 | + | 0.116615i | ||||
\(429\) | −9.73206 | + | 7.07076i | −0.469868 | + | 0.341379i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.85650 | − | 6.43463i | −0.426603 | − | 0.309945i | 0.353686 | − | 0.935364i | \(-0.384928\pi\) |
−0.780289 | + | 0.625419i | \(0.784928\pi\) | |||||||
\(432\) | 3.63837 | 0.175051 | ||||||||
\(433\) | 8.44561 | + | 6.13609i | 0.405870 | + | 0.294882i | 0.771928 | − | 0.635710i | \(-0.219293\pi\) |
−0.366058 | + | 0.930592i | \(0.619293\pi\) | |||||||
\(434\) | 0.873978 | − | 2.68983i | 0.0419523 | − | 0.129116i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.33915 | − | 4.12149i | −0.0641338 | − | 0.197384i | ||||
\(437\) | −2.06810 | + | 6.36495i | −0.0989305 | + | 0.304477i | ||||
\(438\) | −0.867861 | + | 2.67100i | −0.0414680 | + | 0.127625i | ||||
\(439\) | 4.76917 | + | 14.6780i | 0.227620 | + | 0.700543i | 0.998015 | + | 0.0629758i | \(0.0200591\pi\) |
−0.770395 | + | 0.637567i | \(0.779941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.68278 | + | 5.17907i | −0.0801324 | + | 0.246622i | ||||
\(442\) | −5.45686 | − | 3.96464i | −0.259556 | − | 0.188579i | ||||
\(443\) | −18.9105 | −0.898463 | −0.449231 | − | 0.893415i | \(-0.648302\pi\) | ||||
−0.449231 | + | 0.893415i | \(0.648302\pi\) | |||||||
\(444\) | 2.00455 | + | 1.45639i | 0.0951318 | + | 0.0691173i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.14884 | − | 2.28777i | 0.149102 | − | 0.108329i | ||||
\(447\) | 13.8083 | − | 10.0323i | 0.653109 | − | 0.474511i | ||||
\(448\) | −2.53334 | − | 7.79681i | −0.119689 | − | 0.368365i | ||||
\(449\) | −11.4152 | −0.538714 | −0.269357 | − | 0.963040i | \(-0.586811\pi\) | ||||
−0.269357 | + | 0.963040i | \(0.586811\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.3460 | 1.05223 | ||||||||
\(452\) | −1.88717 | − | 5.80813i | −0.0887652 | − | 0.273191i | ||||
\(453\) | 1.27433 | − | 0.925855i | 0.0598733 | − | 0.0435005i | ||||
\(454\) | −2.70314 | + | 1.96395i | −0.126865 | + | 0.0921725i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.27805 | − | 2.38164i | −0.153509 | − | 0.111531i | ||||
\(457\) | 33.9739 | 1.58923 | 0.794616 | − | 0.607112i | \(-0.207672\pi\) | ||||
0.794616 | + | 0.607112i | \(0.207672\pi\) | |||||||
\(458\) | −2.95114 | − | 2.14413i | −0.137898 | − | 0.100188i | ||||
\(459\) | −1.80439 | + | 5.55335i | −0.0842219 | + | 0.259208i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.62985 | − | 23.4823i | −0.355358 | − | 1.09368i | −0.955802 | − | 0.294012i | \(-0.905009\pi\) |
0.600444 | − | 0.799667i | \(-0.294991\pi\) | |||||||
\(462\) | −0.244299 | + | 0.751876i | −0.0113658 | + | 0.0349804i | ||||
\(463\) | 4.21237 | − | 12.9643i | 0.195765 | − | 0.602504i | −0.804202 | − | 0.594357i | \(-0.797407\pi\) |
0.999967 | − | 0.00814689i | \(-0.00259326\pi\) | |||||||
\(464\) | −3.61551 | − | 11.1274i | −0.167846 | − | 0.516576i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.0395737 | − | 0.121795i | 0.00183321 | − | 0.00564205i | ||||
\(467\) | 7.66232 | + | 5.56700i | 0.354570 | + | 0.257610i | 0.750784 | − | 0.660548i | \(-0.229676\pi\) |
−0.396214 | + | 0.918158i | \(0.629676\pi\) | |||||||
\(468\) | −9.07748 | −0.419607 | ||||||||
\(469\) | −10.2114 | − | 7.41900i | −0.471518 | − | 0.342578i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.44343 | + | 5.40797i | −0.342975 | + | 0.249186i | ||||
\(472\) | 5.02712 | − | 3.65241i | 0.231392 | − | 0.168116i | ||||
\(473\) | 3.08173 | + | 9.48459i | 0.141698 | + | 0.436102i | ||||
\(474\) | −2.83358 | −0.130150 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.1167 | 0.647039 | ||||||||
\(477\) | 4.12052 | + | 12.6817i | 0.188666 | + | 0.580654i | ||||
\(478\) | 1.64304 | − | 1.19374i | 0.0751508 | − | 0.0546002i | ||||
\(479\) | 20.8149 | − | 15.1229i | 0.951055 | − | 0.690982i | −1.08775e−6 | − | 1.00000i | \(-0.500000\pi\) |
0.951056 | + | 0.309018i | \(0.100000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83925 | − | 3.51592i | −0.220651 | − | 0.160312i | ||||
\(482\) | 0.316142 | 0.0143999 | ||||||||
\(483\) | 1.61935 | + | 1.17653i | 0.0736831 | + | 0.0535339i | ||||
\(484\) | 2.63451 | − | 8.10820i | 0.119751 | − | 0.368554i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.0762527 | − | 0.234682i | −0.00345889 | − | 0.0106454i | ||||
\(487\) | 8.77751 | − | 27.0144i | 0.397747 | − | 1.22414i | −0.529055 | − | 0.848588i | \(-0.677453\pi\) |
0.926802 | − | 0.375551i | \(-0.122547\pi\) | |||||||
\(488\) | 1.14948 | − | 3.53774i | 0.0520346 | − | 0.160146i | ||||
\(489\) | 1.41553 | + | 4.35656i | 0.0640126 | + | 0.197010i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.88593 | + | 5.80429i | −0.0851107 | + | 0.261944i | −0.984551 | − | 0.175101i | \(-0.943975\pi\) |
0.899440 | + | 0.437045i | \(0.143975\pi\) | |||||||
\(492\) | 13.6419 | + | 9.91144i | 0.615026 | + | 0.446842i | ||||
\(493\) | 18.7771 | 0.845679 | ||||||||
\(494\) | 3.89566 | + | 2.83036i | 0.175274 | + | 0.127344i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.0600 | − | 19.6602i | 1.21503 | − | 0.882770i | ||||
\(497\) | −13.9992 | + | 10.1710i | −0.627948 | + | 0.456231i | ||||
\(498\) | −0.215970 | − | 0.664687i | −0.00967784 | − | 0.0297853i | ||||
\(499\) | −20.3163 | −0.909481 | −0.454740 | − | 0.890624i | \(-0.650268\pi\) | ||||
−0.454740 | + | 0.890624i | \(0.650268\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.142531 | −0.00636782 | ||||||||
\(502\) | −0.353426 | − | 1.08773i | −0.0157742 | − | 0.0485480i | ||||
\(503\) | 11.8332 | − | 8.59734i | 0.527617 | − | 0.383336i | −0.291848 | − | 0.956465i | \(-0.594270\pi\) |
0.819466 | + | 0.573128i | \(0.194270\pi\) | |||||||
\(504\) | −0.980418 | + | 0.712315i | −0.0436713 | + | 0.0317290i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.823600 | − | 0.598380i | −0.0366135 | − | 0.0266012i | ||||
\(507\) | 8.91422 | 0.395894 | ||||||||
\(508\) | 24.5674 | + | 17.8493i | 1.09000 | + | 0.791934i | ||||
\(509\) | −1.33058 | + | 4.09510i | −0.0589768 | + | 0.181512i | −0.976205 | − | 0.216851i | \(-0.930422\pi\) |
0.917228 | + | 0.398363i | \(0.130422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.38490 | + | 13.4953i | 0.193977 | + | 0.596999i | ||||
\(512\) | −5.38081 | + | 16.5604i | −0.237800 | + | 0.731874i | ||||
\(513\) | 1.28816 | − | 3.96455i | 0.0568736 | − | 0.175039i | ||||
\(514\) | −1.39543 | − | 4.29471i | −0.0615500 | − | 0.189431i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.32548 | + | 7.15709i | −0.102374 | + | 0.315073i | ||||
\(517\) | −6.67241 | − | 4.84779i | −0.293452 | − | 0.213205i | ||||
\(518\) | −0.393109 | −0.0172722 | ||||||||
\(519\) | 19.9202 | + | 14.4729i | 0.874401 | + | 0.635290i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.0705 | − | 23.3006i | 1.40503 | − | 1.02082i | 0.411011 | − | 0.911630i | \(-0.365176\pi\) |
0.994021 | − | 0.109186i | \(-0.0348243\pi\) | |||||||
\(522\) | −0.641964 | + | 0.466414i | −0.0280980 | + | 0.0204144i | ||||
\(523\) | −11.2134 | − | 34.5114i | −0.490329 | − | 1.50908i | −0.824111 | − | 0.566428i | \(-0.808325\pi\) |
0.333782 | − | 0.942650i | \(-0.391675\pi\) | |||||||
\(524\) | 29.0021 | 1.26696 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.11264 | 0.179320 | ||||||||
\(527\) | 16.5880 | + | 51.0526i | 0.722585 | + | 2.22389i | ||||
\(528\) | −7.56395 | + | 5.49553i | −0.329179 | + | 0.239162i | ||||
\(529\) | 16.5221 | − | 12.0040i | 0.718353 | − | 0.521914i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.17187 | + | 3.75759i | 0.224440 | + | 0.163065i | ||||
\(532\) | −10.0779 | −0.436934 | ||||||||
\(533\) | −32.9334 | − | 23.9275i | −1.42650 | − | 1.03642i | ||||
\(534\) | 0.105288 | − | 0.324042i | 0.00455625 | − | 0.0140227i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.04087 | + | 9.35883i | 0.131346 | + | 0.404240i | ||||
\(537\) | −7.46440 | + | 22.9731i | −0.322113 | + | 0.991360i | ||||
\(538\) | −0.200706 | + | 0.617709i | −0.00865304 | + | 0.0266313i | ||||
\(539\) | −4.32426 | − | 13.3087i | −0.186259 | − | 0.573246i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.9294 | + | 36.7150i | −0.512886 | + | 1.57850i | 0.274211 | + | 0.961670i | \(0.411583\pi\) |
−0.787096 | + | 0.616830i | \(0.788417\pi\) | |||||||
\(542\) | 0.911014 | + | 0.661890i | 0.0391314 | + | 0.0284306i | ||||
\(543\) | 1.96805 | 0.0844570 | ||||||||
\(544\) | −13.4247 | − | 9.75359i | −0.575578 | − | 0.418182i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.16513 | − | 0.846520i | 0.0498632 | − | 0.0362277i | ||||
\(547\) | 8.38303 | − | 6.09063i | 0.358433 | − | 0.260416i | −0.393965 | − | 0.919125i | \(-0.628897\pi\) |
0.752398 | + | 0.658709i | \(0.228897\pi\) | |||||||
\(548\) | −6.28853 | − | 19.3541i | −0.268633 | − | 0.826766i | ||||
\(549\) | 3.82692 | 0.163329 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.4050 | −0.571073 | ||||||||
\(552\) | −0.482231 | − | 1.48415i | −0.0205251 | − | 0.0631698i | ||||
\(553\) | −11.5825 | + | 8.41517i | −0.492538 | + | 0.357850i | ||||
\(554\) | −0.251388 | + | 0.182644i | −0.0106805 | + | 0.00775981i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.5324 | + | 14.1911i | 0.828359 | + | 0.601838i | ||||
\(557\) | −12.6830 | −0.537398 | −0.268699 | − | 0.963224i | \(-0.586594\pi\) | ||||
−0.268699 | + | 0.963224i | \(0.586594\pi\) | |||||||
\(558\) | −1.83524 | − | 1.33338i | −0.0776920 | − | 0.0564465i | ||||
\(559\) | 5.61401 | − | 17.2781i | 0.237447 | − | 0.730788i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.63677 | − | 14.2705i | −0.195765 | − | 0.602502i | ||||
\(562\) | −1.02306 | + | 3.14864i | −0.0431550 | + | 0.132817i | ||||
\(563\) | −4.04480 | + | 12.4486i | −0.170468 | + | 0.524646i | −0.999398 | − | 0.0347068i | \(-0.988950\pi\) |
0.828930 | + | 0.559353i | \(0.188950\pi\) | |||||||
\(564\) | −1.92320 | − | 5.91901i | −0.0809815 | − | 0.249235i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.83685 | − | 5.65324i | 0.0772086 | − | 0.237624i | ||||
\(567\) | −1.00865 | − | 0.732827i | −0.0423593 | − | 0.0307758i | ||||
\(568\) | 13.4906 | 0.566055 | ||||||||
\(569\) | 2.09376 | + | 1.52120i | 0.0877748 | + | 0.0637721i | 0.630807 | − | 0.775940i | \(-0.282724\pi\) |
−0.543032 | + | 0.839712i | \(0.682724\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.55571 | − | 6.21609i | 0.358045 | − | 0.260135i | −0.394191 | − | 0.919029i | \(-0.628975\pi\) |
0.752236 | + | 0.658893i | \(0.228975\pi\) | |||||||
\(572\) | 18.8715 | − | 13.7110i | 0.789059 | − | 0.573285i | ||||
\(573\) | −2.40061 | − | 7.38832i | −0.100287 | − | 0.308652i | ||||
\(574\) | −2.67529 | −0.111665 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.57549 | −0.273979 | ||||||||
\(577\) | 0.00441597 | + | 0.0135910i | 0.000183839 | + | 0.000565800i | 0.951148 | − | 0.308734i | \(-0.0999053\pi\) |
−0.950965 | + | 0.309300i | \(0.899905\pi\) | |||||||
\(578\) | 3.41283 | − | 2.47957i | 0.141955 | − | 0.103136i | ||||
\(579\) | 11.6060 | − | 8.43227i | 0.482330 | − | 0.350433i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.85679 | − | 2.07558i | −0.118519 | − | 0.0861094i | ||||
\(582\) | 0.00752814 | 0.000312051 | ||||||||
\(583\) | −27.7212 | − | 20.1406i | −1.14809 | − | 0.834139i | ||||
\(584\) | 3.41860 | − | 10.5214i | 0.141463 | − | 0.435377i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.45326 | − | 7.55035i | −0.101343 | − | 0.311902i | ||||
\(587\) | 6.99581 | − | 21.5309i | 0.288748 | − | 0.888675i | −0.696502 | − | 0.717555i | \(-0.745261\pi\) |
0.985250 | − | 0.171120i | \(-0.0547387\pi\) | |||||||
\(588\) | 3.26310 | − | 10.0428i | 0.134568 | − | 0.414157i | ||||
\(589\) | −11.8422 | − | 36.4465i | −0.487949 | − | 1.50175i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.0505366 | + | 0.155536i | −0.00207880 | + | 0.00639788i | ||||
\(592\) | −3.76116 | − | 2.73264i | −0.154583 | − | 0.112311i | ||||
\(593\) | −12.7423 | −0.523264 | −0.261632 | − | 0.965168i | \(-0.584261\pi\) | ||||
−0.261632 | + | 0.965168i | \(0.584261\pi\) | |||||||
\(594\) | 0.512997 | + | 0.372714i | 0.0210485 | + | 0.0152926i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26.7758 | + | 19.4537i | −1.09678 | + | 0.796856i | ||||
\(597\) | −4.02060 | + | 2.92114i | −0.164552 | + | 0.119554i | ||||
\(598\) | 0.573086 | + | 1.76378i | 0.0234352 | + | 0.0721262i | ||||
\(599\) | −6.83599 | −0.279311 | −0.139656 | − | 0.990200i | \(-0.544600\pi\) | ||||
−0.139656 | + | 0.990200i | \(0.544600\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 31.8422 | 1.29887 | 0.649435 | − | 0.760417i | \(-0.275005\pi\) | ||||
0.649435 | + | 0.760417i | \(0.275005\pi\) | |||||||
\(602\) | −0.368948 | − | 1.13551i | −0.0150372 | − | 0.0462798i | ||||
\(603\) | −8.19034 | + | 5.95063i | −0.333537 | + | 0.242328i | ||||
\(604\) | −2.47107 | + | 1.79534i | −0.100546 | + | 0.0730511i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.24202 | − | 1.62892i | −0.0910758 | − | 0.0661705i | ||||
\(607\) | −27.7763 | −1.12741 | −0.563703 | − | 0.825977i | \(-0.690624\pi\) | ||||
−0.563703 | + | 0.825977i | \(0.690624\pi\) | |||||||
\(608\) | 9.58388 | + | 6.96310i | 0.388678 | + | 0.282391i | ||||
\(609\) | −1.23892 | + | 3.81302i | −0.0502038 | + | 0.154511i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.64286 | + | 14.2893i | 0.187830 | + | 0.578082i | ||||
\(612\) | 3.49892 | − | 10.7686i | 0.141435 | − | 0.435293i | ||||
\(613\) | 1.11769 | − | 3.43991i | 0.0451433 | − | 0.138937i | −0.925944 | − | 0.377660i | \(-0.876729\pi\) |
0.971088 | + | 0.238723i | \(0.0767289\pi\) | |||||||
\(614\) | 1.54764 | + | 4.76315i | 0.0624577 | + | 0.192225i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.962321 | − | 2.96172i | 0.0387730 | − | 0.119331i | ||||
\(617\) | 36.1166 | + | 26.2402i | 1.45400 | + | 1.05639i | 0.984876 | + | 0.173259i | \(0.0554297\pi\) |
0.469122 | + | 0.883133i | \(0.344570\pi\) | |||||||
\(618\) | −0.177909 | −0.00715655 | ||||||||
\(619\) | −16.5917 | − | 12.0546i | −0.666878 | − | 0.484515i | 0.202101 | − | 0.979365i | \(-0.435223\pi\) |
−0.868979 | + | 0.494850i | \(0.835223\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.29885 | − | 0.943670i | 0.0521211 | − | 0.0378682i | ||||
\(622\) | −3.73760 | + | 2.71552i | −0.149864 | + | 0.108883i | ||||
\(623\) | −0.531970 | − | 1.63724i | −0.0213129 | − | 0.0655945i | ||||
\(624\) | 17.0322 | 0.681832 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.14033 | 0.245417 | ||||||||
\(627\) | 3.31020 | + | 10.1877i | 0.132197 | + | 0.406859i | ||||
\(628\) | 14.4336 | − | 10.4866i | 0.575964 | − | 0.418463i | ||||
\(629\) | 6.03621 | − | 4.38556i | 0.240679 | − | 0.174864i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.5288 | + | 22.1805i | 1.21533 | + | 0.882991i | 0.995704 | − | 0.0925923i | \(-0.0295153\pi\) |
0.219629 | + | 0.975583i | \(0.429515\pi\) | |||||||
\(632\) | 11.1618 | 0.443991 | ||||||||
\(633\) | −2.66475 | − | 1.93605i | −0.105914 | − | 0.0769512i | ||||
\(634\) | −1.92066 | + | 5.91117i | −0.0762790 | + | 0.234763i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.99015 | − | 24.5911i | −0.316830 | − | 0.975102i | ||||
\(637\) | −7.87754 | + | 24.2446i | −0.312119 | + | 0.960605i | ||||
\(638\) | 0.630115 | − | 1.93929i | 0.0249465 | − | 0.0767774i | ||||
\(639\) | 4.28888 | + | 13.1998i | 0.169666 | + | 0.522177i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.83865 | + | 8.73646i | −0.112120 | + | 0.345070i | −0.991335 | − | 0.131355i | \(-0.958067\pi\) |
0.879216 | + | 0.476424i | \(0.158067\pi\) | |||||||
\(642\) | −0.422557 | − | 0.307005i | −0.0166770 | − | 0.0121165i | ||||
\(643\) | −3.42111 | −0.134915 | −0.0674577 | − | 0.997722i | \(-0.521489\pi\) | ||||
−0.0674577 | + | 0.997722i | \(0.521489\pi\) | |||||||
\(644\) | −3.14010 | − | 2.28142i | −0.123737 | − | 0.0899005i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.85922 | + | 3.53043i | −0.191184 | + | 0.138903i | ||||
\(647\) | 2.64334 | − | 1.92050i | 0.103920 | − | 0.0755027i | −0.534611 | − | 0.845098i | \(-0.679542\pi\) |
0.638532 | + | 0.769595i | \(0.279542\pi\) | |||||||
\(648\) | 0.300368 | + | 0.924437i | 0.0117996 | + | 0.0363153i | ||||
\(649\) | −16.4276 | −0.644840 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.4616 | −0.449216 | ||||||||
\(652\) | −2.74487 | − | 8.44785i | −0.107498 | − | 0.330843i | ||||
\(653\) | 10.2229 | − | 7.42740i | 0.400054 | − | 0.290656i | −0.369509 | − | 0.929227i | \(-0.620474\pi\) |
0.769563 | + | 0.638571i | \(0.220474\pi\) | |||||||
\(654\) | 0.446145 | − | 0.324143i | 0.0174456 | − | 0.0126750i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −25.5965 | − | 18.5969i | −0.999374 | − | 0.726088i | ||||
\(657\) | 11.3814 | 0.444030 | ||||||||
\(658\) | 0.798829 | + | 0.580383i | 0.0311416 | + | 0.0226257i | ||||
\(659\) | −2.82719 | + | 8.70118i | −0.110131 | + | 0.338950i | −0.990901 | − | 0.134596i | \(-0.957026\pi\) |
0.880769 | + | 0.473546i | \(0.157026\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.97487 | + | 6.07804i | 0.0768137 | + | 0.236408i | 0.982089 | − | 0.188417i | \(-0.0603356\pi\) |
−0.905275 | + | 0.424825i | \(0.860336\pi\) | |||||||
\(662\) | −2.31955 | + | 7.13884i | −0.0901519 | + | 0.277459i | ||||
\(663\) | −8.44684 | + | 25.9967i | −0.328048 | + | 1.00963i | ||||
\(664\) | 0.850729 | + | 2.61827i | 0.0330147 | + | 0.101609i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0974345 | + | 0.299872i | −0.00377551 | + | 0.0116198i | ||||
\(667\) | −4.17676 | − | 3.03459i | −0.161725 | − | 0.117500i | ||||
\(668\) | 0.276383 | 0.0106936 | ||||||||
\(669\) | −12.7608 | − | 9.27127i | −0.493361 | − | 0.358448i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.95593 | + | 5.78032i | −0.307135 | + | 0.223147i | ||||
\(672\) | 2.86640 | − | 2.08256i | 0.110574 | − | 0.0803366i | ||||
\(673\) | 10.4158 | + | 32.0566i | 0.401500 | + | 1.23569i | 0.923782 | + | 0.382918i | \(0.125081\pi\) |
−0.522282 | + | 0.852773i | \(0.674919\pi\) | |||||||
\(674\) | −1.12881 | −0.0434802 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.2857 | −0.664833 | ||||||||
\(677\) | −2.84401 | − | 8.75295i | −0.109304 | − | 0.336403i | 0.881412 | − | 0.472347i | \(-0.156593\pi\) |
−0.990716 | + | 0.135944i | \(0.956593\pi\) | |||||||
\(678\) | 0.628721 | − | 0.456792i | 0.0241459 | − | 0.0175430i | ||||
\(679\) | 0.0307719 | − | 0.0223571i | 0.00118092 | − | 0.000857988i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.9546 | + | 7.95896i | 0.419780 | + | 0.304988i | ||||
\(682\) | 5.82935 | 0.223217 | ||||||||
\(683\) | 22.0227 | + | 16.0005i | 0.842677 | + | 0.612241i | 0.923117 | − | 0.384519i | \(-0.125633\pi\) |
−0.0804402 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(684\) | −2.49788 | + | 7.68769i | −0.0955089 | + | 0.293946i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.18319 | + | 3.64147i | 0.0451743 | + | 0.139032i | ||||
\(687\) | −4.56816 | + | 14.0593i | −0.174286 | + | 0.536397i | ||||
\(688\) | 4.36332 | − | 13.4289i | 0.166350 | − | 0.511972i | ||||
\(689\) | 19.2892 | + | 59.3662i | 0.734862 | + | 2.26167i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.21607 | − | 28.3642i | 0.350596 | − | 1.07902i | −0.607923 | − | 0.793996i | \(-0.707997\pi\) |
0.958519 | − | 0.285028i | \(-0.0920028\pi\) | |||||||
\(692\) | −38.6275 | − | 28.0645i | −1.46840 | − | 1.06685i | ||||
\(693\) | 3.20381 | 0.121703 | ||||||||
\(694\) | 3.35687 | + | 2.43891i | 0.127425 | + | 0.0925797i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.52877 | − | 1.83726i | 0.0958527 | − | 0.0696410i | ||||
\(697\) | 41.0792 | − | 29.8458i | 1.55599 | − | 1.13049i | ||||
\(698\) | −0.0284865 | − | 0.0876726i | −0.00107823 | − | 0.00331846i | ||||
\(699\) | −0.518980 | −0.0196296 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.1081 | −0.721704 | −0.360852 | − | 0.932623i | \(-0.617514\pi\) | ||||
−0.360852 | + | 0.932623i | \(0.617514\pi\) | |||||||
\(702\) | −0.356959 | − | 1.09861i | −0.0134725 | − | 0.0414642i | ||||
\(703\) | −4.30925 | + | 3.13086i | −0.162527 | + | 0.118082i | ||||
\(704\) | 13.6700 | − | 9.93187i | 0.515209 | − | 0.374322i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.78489 | + | 3.47642i | 0.180082 | + | 0.130837i | ||||
\(707\) | −14.0020 | −0.526601 | ||||||||
\(708\) | −10.0288 | − | 7.28637i | −0.376907 | − | 0.273839i | ||||
\(709\) | 4.48525 | − | 13.8042i | 0.168447 | − | 0.518427i | −0.830827 | − | 0.556531i | \(-0.812132\pi\) |
0.999274 | + | 0.0381042i | \(0.0121319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.54849 | + | 10.9211i | 0.133079 | + | 0.409575i | ||||
\(712\) | −0.414740 | + | 1.27644i | −0.0155430 | + | 0.0478365i | ||||
\(713\) | 4.56086 | − | 14.0369i | 0.170806 | − | 0.525685i | ||||
\(714\) | 0.555120 | + | 1.70848i | 0.0207748 | + | 0.0639384i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.4743 | − | 44.5473i | 0.540930 | − | 1.66481i | ||||
\(717\) | −6.65847 | − | 4.83766i | −0.248665 | − | 0.180666i | ||||
\(718\) | 1.17215 | 0.0437444 | ||||||||
\(719\) | −28.1139 | − | 20.4260i | −1.04847 | − | 0.761760i | −0.0765512 | − | 0.997066i | \(-0.524391\pi\) |
−0.971921 | + | 0.235306i | \(0.924391\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.727219 | + | 0.528356i | −0.0270831 | + | 0.0196770i | ||||
\(722\) | −0.324007 | + | 0.235405i | −0.0120583 | + | 0.00876086i | ||||
\(723\) | −0.395906 | − | 1.21847i | −0.0147239 | − | 0.0453155i | ||||
\(724\) | −3.81626 | −0.141830 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.08490 | 0.0402643 | ||||||||
\(727\) | −13.1727 | − | 40.5415i | −0.488550 | − | 1.50360i | −0.826773 | − | 0.562536i | \(-0.809826\pi\) |
0.338223 | − | 0.941066i | \(-0.390174\pi\) | |||||||
\(728\) | −4.58959 | + | 3.33453i | −0.170102 | + | 0.123586i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3330 | + | 13.3197i | 0.678072 | + | 0.492648i | ||||
\(732\) | −7.42081 | −0.274281 | ||||||||
\(733\) | 1.58754 | + | 1.15341i | 0.0586370 | + | 0.0426023i | 0.616718 | − | 0.787184i | \(-0.288462\pi\) |
−0.558081 | + | 0.829787i | \(0.688462\pi\) | |||||||
\(734\) | −1.32451 | + | 4.07642i | −0.0488885 | + | 0.150463i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.40987 | + | 4.33915i | 0.0519687 | + | 0.159943i | ||||
\(737\) | 8.03917 | − | 24.7420i | 0.296127 | − | 0.911384i | ||||
\(738\) | −0.663088 | + | 2.04077i | −0.0244086 | + | 0.0751219i | ||||
\(739\) | 3.81947 | + | 11.7551i | 0.140501 | + | 0.432419i | 0.996405 | − | 0.0847164i | \(-0.0269984\pi\) |
−0.855904 | + | 0.517135i | \(0.826998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.03021 | − | 18.5591i | 0.221525 | − | 0.681785i | ||||
\(742\) | 3.31881 | + | 2.41126i | 0.121838 | + | 0.0885201i | ||||
\(743\) | −8.63742 | −0.316876 | −0.158438 | − | 0.987369i | \(-0.550646\pi\) | ||||
−0.158438 | + | 0.987369i | \(0.550646\pi\) | |||||||
\(744\) | 7.22922 | + | 5.25234i | 0.265036 | + | 0.192560i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.420978 | + | 0.305858i | −0.0154131 | + | 0.0111983i | ||||
\(747\) | −2.29137 | + | 1.66478i | −0.0838369 | + | 0.0609110i | ||||
\(748\) | 8.99121 | + | 27.6721i | 0.328751 | + | 1.01179i | ||||
\(749\) | −2.63898 | −0.0964264 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3654 | −0.889105 | −0.444552 | − | 0.895753i | \(-0.646637\pi\) | ||||
−0.444552 | + | 0.895753i | \(0.646637\pi\) | |||||||
\(752\) | 3.60852 | + | 11.1059i | 0.131589 | + | 0.404990i | ||||
\(753\) | −3.74974 | + | 2.72435i | −0.136648 | + | 0.0992807i | ||||
\(754\) | −3.00520 | + | 2.18341i | −0.109443 | + | 0.0795150i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.95588 | + | 1.42103i | 0.0711347 | + | 0.0516824i | ||||
\(757\) | 5.18352 | 0.188398 | 0.0941991 | − | 0.995553i | \(-0.469971\pi\) | ||||
0.0941991 | + | 0.995553i | \(0.469971\pi\) | |||||||
\(758\) | 2.47723 | + | 1.79981i | 0.0899769 | + | 0.0653720i | ||||
\(759\) | −1.27488 | + | 3.92367i | −0.0462751 | + | 0.142420i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.66099 | + | 29.7335i | 0.350211 | + | 1.07784i | 0.958735 | + | 0.284302i | \(0.0917618\pi\) |
−0.608524 | + | 0.793535i | \(0.708238\pi\) | |||||||
\(762\) | −1.19414 | + | 3.67518i | −0.0432591 | + | 0.133138i | ||||
\(763\) | 0.861014 | − | 2.64993i | 0.0311708 | − | 0.0959339i | ||||
\(764\) | 4.65505 | + | 14.3268i | 0.168414 | + | 0.518324i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.53964 | − | 7.81622i | 0.0917611 | − | 0.282412i | ||||
\(767\) | 24.2109 | + | 17.5903i | 0.874205 | + | 0.635147i | ||||
\(768\) | 11.3481 | 0.409490 | ||||||||
\(769\) | 35.7497 | + | 25.9737i | 1.28917 | + | 0.936636i | 0.999788 | − | 0.0205786i | \(-0.00655083\pi\) |
0.289380 | + | 0.957214i | \(0.406551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.8051 | + | 10.7566i | −0.533193 | + | 0.387388i | ||||
\(772\) | −22.5054 | + | 16.3511i | −0.809986 | + | 0.588489i | ||||
\(773\) | 6.67110 | + | 20.5315i | 0.239943 | + | 0.738468i | 0.996427 | + | 0.0844563i | \(0.0269153\pi\) |
−0.756484 | + | 0.654012i | \(0.773085\pi\) | |||||||
\(774\) | −0.957636 | −0.0344215 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0296542 | −0.00106452 | ||||||||
\(777\) | 0.492291 | + | 1.51512i | 0.0176609 | + | 0.0543545i | ||||
\(778\) | −3.38929 | + | 2.46246i | −0.121512 | + | 0.0882835i | ||||
\(779\) | −29.3265 | + | 21.3070i | −1.05073 | + | 0.763401i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −28.8538 | − | 20.9635i | −1.03247 | − | 0.750135i | ||||
\(782\) | −2.31325 | −0.0827218 | ||||||||
\(783\) | 2.60158 | + | 1.89016i | 0.0929730 | + | 0.0675488i | ||||
\(784\) | −6.12257 | + | 18.8433i | −0.218663 | + | 0.672977i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.14047 | + | 3.51000i | 0.0406791 | + | 0.125197i | ||||
\(787\) | −4.45638 | + | 13.7153i | −0.158853 | + | 0.488899i | −0.998531 | − | 0.0541857i | \(-0.982744\pi\) |
0.839678 | + | 0.543085i | \(0.182744\pi\) | |||||||
\(788\) | 0.0979961 | − | 0.301601i | 0.00349097 | − | 0.0107441i | ||||
\(789\) | −5.15027 | − | 15.8509i | −0.183355 | − | 0.564307i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.21337 | − | 3.73436i | 0.0431424 | − | 0.132779i | ||||
\(792\) | −2.02075 | − | 1.46816i | −0.0718043 | − | 0.0521689i | ||||
\(793\) | 17.9148 | 0.636173 | ||||||||
\(794\) | 0.172995 | + | 0.125688i | 0.00613937 | + | 0.00446052i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.79639 | − | 5.66441i | 0.276336 | − | 0.200770i | ||||
\(797\) | −31.9211 | + | 23.1921i | −1.13070 | + | 0.821505i | −0.985797 | − | 0.167941i | \(-0.946288\pi\) |
−0.144907 | + | 0.989445i | \(0.546288\pi\) | |||||||
\(798\) | −0.396301 | − | 1.21969i | −0.0140289 | − | 0.0431765i | ||||
\(799\) | −18.7409 | −0.663004 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.38077 | −0.0487872 | ||||||||
\(802\) | −0.738645 | − | 2.27332i | −0.0260825 | − | 0.0802736i | ||||
\(803\) | −23.6612 | + | 17.1909i | −0.834986 | + | 0.606653i | ||||
\(804\) | 15.8820 | − | 11.5389i | 0.560114 | − | 0.406947i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.59125 | − | 6.24191i | −0.302614 | − | 0.219862i | ||||
\(807\) | 2.63211 | 0.0926547 | ||||||||
\(808\) | 8.83156 | + | 6.41650i | 0.310693 | + | 0.225732i | ||||
\(809\) | −1.84237 | + | 5.67024i | −0.0647744 | + | 0.199355i | −0.978206 | − | 0.207638i | \(-0.933423\pi\) |
0.913431 | + | 0.406993i | \(0.133423\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.1062 | − | 37.2590i | −0.425105 | − | 1.30834i | −0.902893 | − | 0.429865i | \(-0.858561\pi\) |
0.477788 | − | 0.878475i | \(-0.341439\pi\) | |||||||
\(812\) | 2.40241 | − | 7.39386i | 0.0843081 | − | 0.259474i | ||||
\(813\) | 1.41019 | − | 4.34011i | 0.0494574 | − | 0.152214i | ||||
\(814\) | −0.250378 | − | 0.770586i | −0.00877576 | − | 0.0270090i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.56505 | + | 20.2051i | −0.229823 | + | 0.707322i | ||||
\(817\) | −13.0880 | − | 9.50897i | −0.457890 | − | 0.332677i | ||||
\(818\) | −0.374544 | −0.0130956 | ||||||||
\(819\) | −4.72175 | − | 3.43055i | −0.164991 | − | 0.119873i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −16.6923 | + | 12.1277i | −0.582567 | + | 0.423260i | −0.839649 | − | 0.543130i | \(-0.817239\pi\) |
0.257082 | + | 0.966390i | \(0.417239\pi\) | |||||||
\(822\) | 2.09505 | − | 1.52214i | 0.0730733 | − | 0.0530909i | ||||
\(823\) | −12.0567 | − | 37.1066i | −0.420269 | − | 1.29345i | −0.907452 | − | 0.420155i | \(-0.861976\pi\) |
0.487183 | − | 0.873300i | \(-0.338024\pi\) | |||||||
\(824\) | 0.700803 | 0.0244136 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.96673 | 0.0684314 | ||||||||
\(827\) | −6.05598 | − | 18.6384i | −0.210587 | − | 0.648120i | −0.999438 | − | 0.0335352i | \(-0.989323\pi\) |
0.788850 | − | 0.614585i | \(-0.210677\pi\) | |||||||
\(828\) | −2.51861 | + | 1.82988i | −0.0875279 | + | 0.0635927i | ||||
\(829\) | 7.01831 | − | 5.09910i | 0.243756 | − | 0.177099i | −0.459199 | − | 0.888333i | \(-0.651864\pi\) |
0.702955 | + | 0.711234i | \(0.251864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.01876 | + | 0.740173i | 0.0353404 | + | 0.0256763i | ||||
\(832\) | −30.7816 | −1.06716 | ||||||||
\(833\) | −25.7248 | − | 18.6902i | −0.891311 | − | 0.647575i | ||||
\(834\) | −0.949404 | + | 2.92196i | −0.0328752 | + | 0.101179i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.41884 | − | 19.7551i | −0.222000 | − | 0.683246i | ||||
\(837\) | −2.84083 | + | 8.74318i | −0.0981935 | + | 0.302208i | ||||
\(838\) | 2.33044 | − | 7.17235i | 0.0805036 | − | 0.247765i | ||||
\(839\) | −1.19256 | − | 3.67033i | −0.0411718 | − | 0.126714i | 0.928358 | − | 0.371687i | \(-0.121221\pi\) |
−0.969530 | + | 0.244974i | \(0.921221\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.76596 | + | 17.7458i | −0.198826 | + | 0.611925i | ||||
\(842\) | −1.39176 | − | 1.01117i | −0.0479632 | − | 0.0348473i | ||||
\(843\) | 13.4167 | 0.462094 | ||||||||
\(844\) | 5.16724 | + | 3.75422i | 0.177864 | + | 0.129226i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.640724 | − | 0.465513i | 0.0220286 | − | 0.0160047i | ||||
\(847\) | 4.43461 | − | 3.22193i | 0.152375 | − | 0.110707i | ||||
\(848\) | 14.9920 | + | 46.1406i | 0.514827 | + | 1.58447i | ||||
\(849\) | −24.0890 | −0.826732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.05144 | −0.0703224 | ||||||||
\(852\) | −8.31661 | − | 25.5959i | −0.284922 | − | 0.876901i | ||||
\(853\) | −24.1004 | + | 17.5100i | −0.825183 | + | 0.599531i | −0.918192 | − | 0.396135i | \(-0.870351\pi\) |
0.0930093 | + | 0.995665i | \(0.470351\pi\) | |||||||
\(854\) | 0.952493 | − | 0.692027i | 0.0325936 | − | 0.0236807i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.66450 | + | 1.20933i | 0.0568913 | + | 0.0413340i | ||||
\(857\) | −36.2041 | −1.23671 | −0.618354 | − | 0.785899i | \(-0.712200\pi\) | ||||
−0.618354 | + | 0.785899i | \(0.712200\pi\) | |||||||
\(858\) | 2.40147 | + | 1.74477i | 0.0819850 | + | 0.0595656i | ||||
\(859\) | −11.6355 | + | 35.8104i | −0.396998 | + | 1.22184i | 0.530396 | + | 0.847750i | \(0.322043\pi\) |
−0.927394 | + | 0.374086i | \(0.877957\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.35028 | + | 10.3111i | 0.114177 | + | 0.351401i | ||||
\(862\) | −0.834757 | + | 2.56912i | −0.0284319 | + | 0.0875045i | ||||
\(863\) | 0.772275 | − | 2.37682i | 0.0262885 | − | 0.0809078i | −0.937051 | − | 0.349191i | \(-0.886456\pi\) |
0.963340 | + | 0.268283i | \(0.0864564\pi\) | |||||||
\(864\) | −0.878171 | − | 2.70273i | −0.0298760 | − | 0.0919488i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.796028 | − | 2.44992i | 0.0270501 | − | 0.0832518i | ||||
\(867\) | −13.8306 | − | 10.0485i | −0.469712 | − | 0.341266i | ||||
\(868\) | 22.2253 | 0.754376 | ||||||||
\(869\) | −23.8728 | − | 17.3446i | −0.809830 | − | 0.588376i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.3411 | + | 27.8565i | −1.29914 | + | 0.943881i | ||||
\(872\) | −1.75741 | + | 1.27684i | −0.0595136 | + | 0.0432391i | ||||
\(873\) | −0.00942751 | − | 0.0290149i | −0.000319073 | − | 0.000982006i | ||||
\(874\) | 1.65143 | 0.0558606 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22.0697 | −0.745668 | ||||||||
\(877\) | 10.0273 | + | 30.8609i | 0.338599 | + | 1.04210i | 0.964922 | + | 0.262537i | \(0.0845590\pi\) |
−0.626323 | + | 0.779563i | \(0.715441\pi\) | |||||||
\(878\) | 3.08100 | − | 2.23847i | 0.103979 | − | 0.0755449i | ||||
\(879\) | −26.0283 | + | 18.9107i | −0.877912 | + | 0.637841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.9099 | + | 19.5512i | 0.906619 | + | 0.658697i | 0.940157 | − | 0.340740i | \(-0.110678\pi\) |
−0.0335388 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(882\) | 1.34375 | 0.0452464 | ||||||||
\(883\) | −8.87730 | − | 6.44974i | −0.298745 | − | 0.217051i | 0.428307 | − | 0.903633i | \(-0.359110\pi\) |
−0.727052 | + | 0.686582i | \(0.759110\pi\) | |||||||
\(884\) | 16.3794 | − | 50.4105i | 0.550897 | − | 1.69549i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.44197 | + | 4.43794i | 0.0484440 | + | 0.149095i | ||||
\(887\) | 8.03604 | − | 24.7324i | 0.269824 | − | 0.830432i | −0.720719 | − | 0.693227i | \(-0.756188\pi\) |
0.990543 | − | 0.137205i | \(-0.0438118\pi\) | |||||||
\(888\) | 0.383805 | − | 1.18123i | 0.0128797 | − | 0.0396395i | ||||
\(889\) | 6.03343 | + | 18.5690i | 0.202355 | + | 0.622784i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.794084 | − | 2.44394i | 0.0266028 | − | 0.0818751i | ||||
\(892\) | 24.7446 | + | 17.9780i | 0.828511 | + | 0.601948i | ||||
\(893\) | 13.3791 | 0.447715 | ||||||||
\(894\) | −3.40731 | − | 2.47556i | −0.113958 | − | 0.0827951i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −7.36940 | + | 5.35418i | −0.246194 | + | 0.178871i | ||||
\(897\) | 6.08026 | − | 4.41757i | 0.203014 | − | 0.147498i | ||||
\(898\) | 0.870436 | + | 2.67893i | 0.0290468 | + | 0.0893970i | ||||
\(899\) | 29.5626 | 0.985969 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.8608 | −2.59392 | ||||||||
\(902\) | −1.70394 | − | 5.24420i | −0.0567351 | − | 0.174613i | ||||
\(903\) | −3.91442 | + | 2.84400i | −0.130264 | + | 0.0946423i | ||||
\(904\) | −2.47660 | + | 1.79936i | −0.0823705 | + | 0.0598457i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.314452 | − | 0.228463i | −0.0104470 | − | 0.00759018i | ||||
\(907\) | 55.0108 | 1.82660 | 0.913302 | − | 0.407283i | \(-0.133524\pi\) | ||||
0.913302 | + | 0.407283i | \(0.133524\pi\) | |||||||
\(908\) | −21.2421 | − | 15.4333i | −0.704944 | − | 0.512172i | ||||
\(909\) | −3.47049 | + | 10.6811i | −0.115109 | + | 0.354269i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.74142 | − | 11.5149i | −0.123959 | − | 0.381506i | 0.869751 | − | 0.493490i | \(-0.164279\pi\) |
−0.993710 | + | 0.111985i | \(0.964279\pi\) | |||||||
\(912\) | 4.68680 | − | 14.4245i | 0.155195 | − | 0.477642i | ||||
\(913\) | 2.24908 | − | 6.92195i | 0.0744336 | − | 0.229083i | ||||
\(914\) | −2.59060 | − | 7.97306i | −0.0856895 | − | 0.263725i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.85816 | − | 27.2626i | 0.292682 | − | 0.900782i | ||||
\(917\) | 15.0858 | + | 10.9605i | 0.498176 | + | 0.361946i | ||||
\(918\) | 1.44086 | 0.0475555 | ||||||||
\(919\) | −4.83138 | − | 3.51020i | −0.159372 | − | 0.115791i | 0.505241 | − | 0.862978i | \(-0.331404\pi\) |
−0.664613 | + | 0.747188i | \(0.731404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.4200 | − | 11.9298i | 0.541056 | − | 0.393100i | ||||
\(922\) | −4.92906 | + | 3.58117i | −0.162330 | + | 0.117940i | ||||
\(923\) | 20.0774 | + | 61.7918i | 0.660855 | + | 2.03390i | ||||
\(924\) | −6.21254 | −0.204378 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.36370 | −0.110538 | ||||||||
\(927\) | 0.222796 | + | 0.685696i | 0.00731758 | + | 0.0225212i | ||||
\(928\) | −7.39324 | + | 5.37150i | −0.242695 | + | 0.176328i | ||||
\(929\) | −37.9232 | + | 27.5528i | −1.24422 | + | 0.903979i | −0.997872 | − | 0.0652030i | \(-0.979230\pi\) |
−0.246348 | + | 0.969182i | \(0.579230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.3650 | + | 13.3429i | 0.601887 | + | 0.437297i | ||||
\(932\) | 1.00636 | 0.0329644 | ||||||||
\(933\) | 15.1468 | + | 11.0048i | 0.495882 | + | 0.360280i | ||||
\(934\) | 0.722201 | − | 2.22271i | 0.0236311 | − | 0.0727291i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.40610 | + | 4.32753i | 0.0459598 | + | 0.141450i | ||||
\(937\) | 6.00528 | − | 18.4823i | 0.196184 | − | 0.603792i | −0.803777 | − | 0.594931i | \(-0.797179\pi\) |
0.999961 | − | 0.00886093i | \(-0.00282056\pi\) | |||||||
\(938\) | −0.962459 | + | 2.96214i | −0.0314254 | + | 0.0967174i | ||||
\(939\) | −7.68955 | − | 23.6660i | −0.250939 | − | 0.772311i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.70867 | − | 20.6472i | 0.218696 | − | 0.673078i | −0.780174 | − | 0.625563i | \(-0.784870\pi\) |
0.998870 | − | 0.0475159i | \(-0.0151305\pi\) | |||||||
\(942\) | 1.83673 | + | 1.33446i | 0.0598440 | + | 0.0434792i | ||||
\(943\) | −13.9610 | −0.454633 | ||||||||
\(944\) | 18.8172 | + | 13.6715i | 0.612447 | + | 0.444969i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.99087 | − | 1.44645i | 0.0647287 | − | 0.0470282i | ||||
\(947\) | −5.10943 | + | 3.71222i | −0.166034 | + | 0.120631i | −0.667699 | − | 0.744431i | \(-0.732721\pi\) |
0.501665 | + | 0.865062i | \(0.332721\pi\) | |||||||
\(948\) | −6.88092 | − | 21.1773i | −0.223482 | − | 0.687807i | ||||
\(949\) | 53.2792 | 1.72952 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.1880 | 0.816778 | ||||||||
\(952\) | −2.18668 | − | 6.72990i | −0.0708707 | − | 0.218117i | ||||
\(953\) | 17.6380 | − | 12.8147i | 0.571350 | − | 0.415110i | −0.264245 | − | 0.964455i | \(-0.585123\pi\) |
0.835595 | + | 0.549345i | \(0.185123\pi\) | |||||||
\(954\) | 2.66195 | − | 1.93402i | 0.0861839 | − | 0.0626163i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.9115 | + | 9.38076i | 0.417588 | + | 0.303395i | ||||
\(957\) | −8.26351 | −0.267121 | ||||||||
\(958\) | −5.13625 | − | 3.73171i | −0.165945 | − | 0.120566i | ||||
\(959\) | 4.04324 | − | 12.4438i | 0.130563 | − | 0.401831i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.5366 | + | 50.8943i | 0.533437 | + | 1.64175i | ||||
\(962\) | −0.456116 | + | 1.40378i | −0.0147058 | + | 0.0452597i | ||||
\(963\) | −0.654089 | + | 2.01308i | −0.0210777 | + | 0.0648705i | ||||
\(964\) | 0.767705 | + | 2.36275i | 0.0247261 | + | 0.0760992i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.152630 | − | 0.469746i | 0.00491078 | − | 0.0151138i | ||||
\(967\) | −5.67338 | − | 4.12195i | −0.182444 | − | 0.132553i | 0.492815 | − | 0.870134i | \(-0.335968\pi\) |
−0.675259 | + | 0.737581i | \(0.735968\pi\) | |||||||
\(968\) | −4.27353 | −0.137356 | ||||||||
\(969\) | 19.6922 | + | 14.3072i | 0.632604 | + | 0.459614i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.99504 | + | 4.35565i | −0.192390 | + | 0.139779i | −0.679810 | − | 0.733388i | \(-0.737938\pi\) |
0.487420 | + | 0.873167i | \(0.337938\pi\) | |||||||
\(972\) | 1.56877 | − | 1.13978i | 0.0503184 | − | 0.0365585i | ||||
\(973\) | 4.79690 | + | 14.7633i | 0.153781 | + | 0.473291i | ||||
\(974\) | −7.00909 | −0.224586 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 13.9237 | 0.445688 | ||||||||
\(977\) | −12.1315 | − | 37.3370i | −0.388122 | − | 1.19452i | −0.934190 | − | 0.356776i | \(-0.883876\pi\) |
0.546068 | − | 0.837741i | \(-0.316124\pi\) | |||||||
\(978\) | 0.914467 | − | 0.664399i | 0.0292414 | − | 0.0212451i | ||||
\(979\) | 2.87054 | − | 2.08557i | 0.0917430 | − | 0.0666552i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.80802 | − | 1.31360i | −0.0577256 | − | 0.0419401i | ||||
\(982\) | 1.50597 | 0.0480573 | ||||||||
\(983\) | −14.8719 | − | 10.8051i | −0.474341 | − | 0.344629i | 0.324790 | − | 0.945786i | \(-0.394706\pi\) |
−0.799131 | + | 0.601158i | \(0.794706\pi\) | |||||||
\(984\) | 2.61198 | − | 8.03883i | 0.0832667 | − | 0.256269i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.43181 | − | 4.40665i | −0.0455980 | − | 0.140336i | ||||
\(987\) | 1.23653 | − | 3.80566i | 0.0393593 | − | 0.121135i | ||||
\(988\) | −11.6932 | + | 35.9881i | −0.372012 | + | 1.14493i | ||||
\(989\) | −1.92536 | − | 5.92564i | −0.0612228 | − | 0.188424i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.2128 | − | 49.8980i | 0.515018 | − | 1.58506i | −0.268233 | − | 0.963354i | \(-0.586440\pi\) |
0.783250 | − | 0.621707i | \(-0.213560\pi\) | |||||||
\(992\) | −21.1357 | − | 15.3560i | −0.671060 | − | 0.487554i | ||||
\(993\) | 30.4193 | 0.965326 | ||||||||
\(994\) | 3.45442 | + | 2.50978i | 0.109567 | + | 0.0796054i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.44322 | − | 3.22819i | 0.140789 | − | 0.102289i | ||||
\(997\) | −29.4256 | + | 21.3789i | −0.931917 | + | 0.677077i | −0.946461 | − | 0.322817i | \(-0.895370\pi\) |
0.0145444 | + | 0.999894i | \(0.495370\pi\) | |||||||
\(998\) | 1.54917 | + | 4.76785i | 0.0490381 | + | 0.150924i | ||||
\(999\) | 1.27778 | 0.0404273 |
(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 | 375.2.g.c.151.2 | 12 | ||
5.2 | odd | 4 | 375.2.i.d.349.4 | 24 | |||
5.3 | odd | 4 | 375.2.i.d.349.3 | 24 | |||
5.4 | even | 2 | 75.2.g.c.31.2 | ✓ | 12 | ||
15.14 | odd | 2 | 225.2.h.d.181.2 | 12 | |||
25.2 | odd | 20 | 1875.2.b.f.1249.5 | 12 | |||
25.3 | odd | 20 | 375.2.i.d.274.4 | 24 | |||
25.4 | even | 10 | 75.2.g.c.46.2 | yes | 12 | ||
25.11 | even | 5 | 1875.2.a.k.1.3 | 6 | |||
25.14 | even | 10 | 1875.2.a.j.1.4 | 6 | |||
25.21 | even | 5 | inner | 375.2.g.c.226.2 | 12 | ||
25.22 | odd | 20 | 375.2.i.d.274.3 | 24 | |||
25.23 | odd | 20 | 1875.2.b.f.1249.8 | 12 | |||
75.11 | odd | 10 | 5625.2.a.q.1.4 | 6 | |||
75.14 | odd | 10 | 5625.2.a.p.1.3 | 6 | |||
75.29 | odd | 10 | 225.2.h.d.46.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.2 | ✓ | 12 | 5.4 | even | 2 | ||
75.2.g.c.46.2 | yes | 12 | 25.4 | even | 10 | ||
225.2.h.d.46.2 | 12 | 75.29 | odd | 10 | |||
225.2.h.d.181.2 | 12 | 15.14 | odd | 2 | |||
375.2.g.c.151.2 | 12 | 1.1 | even | 1 | trivial | ||
375.2.g.c.226.2 | 12 | 25.21 | even | 5 | inner | ||
375.2.i.d.274.3 | 24 | 25.22 | odd | 20 | |||
375.2.i.d.274.4 | 24 | 25.3 | odd | 20 | |||
375.2.i.d.349.3 | 24 | 5.3 | odd | 4 | |||
375.2.i.d.349.4 | 24 | 5.2 | odd | 4 | |||
1875.2.a.j.1.4 | 6 | 25.14 | even | 10 | |||
1875.2.a.k.1.3 | 6 | 25.11 | even | 5 | |||
1875.2.b.f.1249.5 | 12 | 25.2 | odd | 20 | |||
1875.2.b.f.1249.8 | 12 | 25.23 | odd | 20 | |||
5625.2.a.p.1.3 | 6 | 75.14 | odd | 10 | |||
5625.2.a.q.1.4 | 6 | 75.11 | odd | 10 |