Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), degree \(2\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.9 | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.j.508.9 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.672613 | − | 1.16500i | 0.475609 | − | 0.823779i | −0.524000 | − | 0.851718i | \(-0.675561\pi\) |
0.999610 | + | 0.0279386i | \(0.00889429\pi\) | |||||||
\(3\) | −1.02505 | − | 1.77544i | −0.591814 | − | 1.02505i | −0.993988 | − | 0.109489i | \(-0.965079\pi\) |
0.402174 | − | 0.915563i | \(-0.368255\pi\) | |||||||
\(4\) | 0.0951832 | + | 0.164862i | 0.0475916 | + | 0.0824311i | ||||
\(5\) | 1.78389 | − | 3.08979i | 0.797779 | − | 1.38179i | −0.123280 | − | 0.992372i | \(-0.539341\pi\) |
0.921059 | − | 0.389422i | \(-0.127325\pi\) | |||||||
\(6\) | −2.75785 | −1.12589 | ||||||||
\(7\) | −2.62255 | + | 0.349630i | −0.991230 | + | 0.132148i | ||||
\(8\) | 2.94654 | 1.04176 | ||||||||
\(9\) | −0.601462 | + | 1.04176i | −0.200487 | + | 0.347254i | ||||
\(10\) | −2.39973 | − | 4.15646i | −0.758862 | − | 1.31439i | ||||
\(11\) | 0.639336 | + | 1.10736i | 0.192767 | + | 0.333882i | 0.946166 | − | 0.323681i | \(-0.104920\pi\) |
−0.753399 | + | 0.657563i | \(0.771587\pi\) | |||||||
\(12\) | 0.195135 | − | 0.337984i | 0.0563307 | − | 0.0975677i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.35664 | + | 3.29043i | −0.362578 | + | 0.879406i | ||||
\(15\) | −7.31431 | −1.88855 | ||||||||
\(16\) | 1.79151 | − | 3.10299i | 0.447878 | − | 0.775748i | ||||
\(17\) | −3.86960 | − | 6.70234i | −0.938515 | − | 1.62556i | −0.768242 | − | 0.640159i | \(-0.778868\pi\) |
−0.170273 | − | 0.985397i | \(-0.554465\pi\) | |||||||
\(18\) | 0.809103 | + | 1.40141i | 0.190707 | + | 0.330315i | ||||
\(19\) | −0.471939 | + | 0.817422i | −0.108270 | + | 0.187530i | −0.915070 | − | 0.403296i | \(-0.867865\pi\) |
0.806799 | + | 0.590826i | \(0.201198\pi\) | |||||||
\(20\) | 0.679185 | 0.151870 | ||||||||
\(21\) | 3.30899 | + | 4.29779i | 0.722082 | + | 0.937855i | ||||
\(22\) | 1.72010 | 0.366727 | ||||||||
\(23\) | −0.823637 | + | 1.42658i | −0.171740 | + | 0.297463i | −0.939028 | − | 0.343840i | \(-0.888272\pi\) |
0.767288 | + | 0.641303i | \(0.221606\pi\) | |||||||
\(24\) | −3.02035 | − | 5.23141i | −0.616527 | − | 1.06786i | ||||
\(25\) | −3.86451 | − | 6.69354i | −0.772903 | − | 1.33871i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.68419 | −0.709023 | ||||||||
\(28\) | −0.307263 | − | 0.399080i | −0.0580673 | − | 0.0754190i | ||||
\(29\) | 4.04484 | 0.751107 | 0.375554 | − | 0.926801i | \(-0.377453\pi\) | ||||
0.375554 | + | 0.926801i | \(0.377453\pi\) | |||||||
\(30\) | −4.91970 | + | 8.52117i | −0.898210 | + | 1.55575i | ||||
\(31\) | −2.57610 | − | 4.46193i | −0.462681 | − | 0.801387i | 0.536413 | − | 0.843956i | \(-0.319779\pi\) |
−0.999094 | + | 0.0425691i | \(0.986446\pi\) | |||||||
\(32\) | 0.536547 | + | 0.929326i | 0.0948490 | + | 0.164283i | ||||
\(33\) | 1.31071 | − | 2.27021i | 0.228164 | − | 0.395192i | ||||
\(34\) | −10.4110 | −1.78547 | ||||||||
\(35\) | −3.59805 | + | 8.72681i | −0.608182 | + | 1.47510i | ||||
\(36\) | −0.228996 | −0.0381661 | ||||||||
\(37\) | −0.528041 | + | 0.914594i | −0.0868094 | + | 0.150358i | −0.906161 | − | 0.422933i | \(-0.861000\pi\) |
0.819351 | + | 0.573292i | \(0.194334\pi\) | |||||||
\(38\) | 0.634865 | + | 1.09962i | 0.102989 | + | 0.178382i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.25629 | − | 9.10417i | 0.831093 | − | 1.43950i | ||||
\(41\) | −4.19882 | −0.655746 | −0.327873 | − | 0.944722i | \(-0.606332\pi\) | ||||
−0.327873 | + | 0.944722i | \(0.606332\pi\) | |||||||
\(42\) | 7.23260 | − | 0.964227i | 1.11601 | − | 0.148784i | ||||
\(43\) | 3.83065 | 0.584168 | 0.292084 | − | 0.956393i | \(-0.405651\pi\) | ||||
0.292084 | + | 0.956393i | \(0.405651\pi\) | |||||||
\(44\) | −0.121708 | + | 0.210805i | −0.0183482 | + | 0.0317800i | ||||
\(45\) | 2.14588 | + | 3.71678i | 0.319889 | + | 0.554064i | ||||
\(46\) | 1.10798 | + | 1.91908i | 0.163363 | + | 0.282952i | ||||
\(47\) | −0.447109 | + | 0.774415i | −0.0652175 | + | 0.112960i | −0.896790 | − | 0.442456i | \(-0.854107\pi\) |
0.831573 | + | 0.555416i | \(0.187441\pi\) | |||||||
\(48\) | −7.34558 | −1.06024 | ||||||||
\(49\) | 6.75552 | − | 1.83384i | 0.965074 | − | 0.261977i | ||||
\(50\) | −10.3973 | −1.47040 | ||||||||
\(51\) | −7.93308 | + | 13.7405i | −1.11085 | + | 1.92405i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0399961 | + | 0.0692754i | 0.00549389 | + | 0.00951570i | 0.868759 | − | 0.495235i | \(-0.164918\pi\) |
−0.863265 | + | 0.504750i | \(0.831585\pi\) | |||||||
\(54\) | −2.47804 | + | 4.29208i | −0.337218 | + | 0.584079i | ||||
\(55\) | 4.56202 | 0.615142 | ||||||||
\(56\) | −7.72744 | + | 1.03020i | −1.03262 | + | 0.137666i | ||||
\(57\) | 1.93505 | 0.256303 | ||||||||
\(58\) | 2.72061 | − | 4.71224i | 0.357234 | − | 0.618747i | ||||
\(59\) | 5.59237 | + | 9.68627i | 0.728064 | + | 1.26104i | 0.957700 | + | 0.287768i | \(0.0929132\pi\) |
−0.229636 | + | 0.973277i | \(0.573754\pi\) | |||||||
\(60\) | −0.696200 | − | 1.20585i | −0.0898790 | − | 0.155675i | ||||
\(61\) | 3.81196 | − | 6.60251i | 0.488072 | − | 0.845365i | −0.511834 | − | 0.859084i | \(-0.671034\pi\) |
0.999906 | + | 0.0137195i | \(0.00436719\pi\) | |||||||
\(62\) | −6.93087 | −0.880221 | ||||||||
\(63\) | 1.21313 | − | 2.94236i | 0.152840 | − | 0.370703i | ||||
\(64\) | 8.60961 | 1.07620 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.76319 | − | 3.05394i | −0.217034 | − | 0.375914i | ||||
\(67\) | 3.16052 | + | 5.47418i | 0.386119 | + | 0.668777i | 0.991924 | − | 0.126836i | \(-0.0404822\pi\) |
−0.605805 | + | 0.795613i | \(0.707149\pi\) | |||||||
\(68\) | 0.736641 | − | 1.27590i | 0.0893309 | − | 0.154726i | ||||
\(69\) | 3.37708 | 0.406553 | ||||||||
\(70\) | 7.74664 | + | 10.0615i | 0.925900 | + | 1.20258i | ||||
\(71\) | −11.4240 | −1.35578 | −0.677889 | − | 0.735165i | \(-0.737105\pi\) | ||||
−0.677889 | + | 0.735165i | \(0.737105\pi\) | |||||||
\(72\) | −1.77223 | + | 3.06959i | −0.208859 | + | 0.361755i | ||||
\(73\) | 0.380253 | + | 0.658617i | 0.0445052 | + | 0.0770853i | 0.887420 | − | 0.460962i | \(-0.152496\pi\) |
−0.842915 | + | 0.538047i | \(0.819162\pi\) | |||||||
\(74\) | 0.710335 | + | 1.23034i | 0.0825747 | + | 0.143024i | ||||
\(75\) | −7.92265 | + | 13.7224i | −0.914829 | + | 1.58453i | ||||
\(76\) | −0.179683 | −0.0206110 | ||||||||
\(77\) | −2.06386 | − | 2.68058i | −0.235198 | − | 0.305481i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.42765 | − | 2.47277i | 0.160624 | − | 0.278208i | −0.774469 | − | 0.632612i | \(-0.781983\pi\) |
0.935093 | + | 0.354404i | \(0.115316\pi\) | |||||||
\(80\) | −6.39172 | − | 11.0708i | −0.714616 | − | 1.23775i | ||||
\(81\) | 5.58087 | + | 9.66636i | 0.620097 | + | 1.07404i | ||||
\(82\) | −2.82418 | + | 4.89163i | −0.311879 | + | 0.540190i | ||||
\(83\) | 2.32483 | 0.255183 | 0.127591 | − | 0.991827i | \(-0.459275\pi\) | ||||
0.127591 | + | 0.991827i | \(0.459275\pi\) | |||||||
\(84\) | −0.393583 | + | 0.954606i | −0.0429434 | + | 0.104156i | ||||
\(85\) | −27.6117 | −2.99491 | ||||||||
\(86\) | 2.57654 | − | 4.46270i | 0.277836 | − | 0.481226i | ||||
\(87\) | −4.14617 | − | 7.18137i | −0.444516 | − | 0.769924i | ||||
\(88\) | 1.88383 | + | 3.26289i | 0.200817 | + | 0.347825i | ||||
\(89\) | −3.78813 | + | 6.56124i | −0.401541 | + | 0.695490i | −0.993912 | − | 0.110176i | \(-0.964859\pi\) |
0.592371 | + | 0.805665i | \(0.298192\pi\) | |||||||
\(90\) | 5.77339 | 0.608569 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.313586 | −0.0326936 | ||||||||
\(93\) | −5.28127 | + | 9.14742i | −0.547642 | + | 0.948544i | ||||
\(94\) | 0.601462 | + | 1.04176i | 0.0620361 | + | 0.107450i | ||||
\(95\) | 1.68377 | + | 2.91638i | 0.172751 | + | 0.299214i | ||||
\(96\) | 1.09998 | − | 1.90522i | 0.112266 | − | 0.194450i | ||||
\(97\) | 0.478557 | 0.0485901 | 0.0242951 | − | 0.999705i | \(-0.492266\pi\) | ||||
0.0242951 | + | 0.999705i | \(0.492266\pi\) | |||||||
\(98\) | 2.40742 | − | 9.10365i | 0.243187 | − | 0.919607i | ||||
\(99\) | −1.53815 | −0.154589 | ||||||||
\(100\) | 0.735674 | − | 1.27422i | 0.0735674 | − | 0.127422i | ||||
\(101\) | −1.43918 | − | 2.49273i | −0.143204 | − | 0.248036i | 0.785498 | − | 0.618865i | \(-0.212407\pi\) |
−0.928701 | + | 0.370829i | \(0.879074\pi\) | |||||||
\(102\) | 10.6718 | + | 18.4841i | 1.05666 | + | 1.83020i | ||||
\(103\) | 5.66755 | − | 9.81649i | 0.558441 | − | 0.967248i | −0.439186 | − | 0.898396i | \(-0.644733\pi\) |
0.997627 | − | 0.0688516i | \(-0.0219335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 19.1821 | − | 2.55730i | 1.87198 | − | 0.249567i | ||||
\(106\) | 0.107608 | 0.0104518 | ||||||||
\(107\) | 3.28603 | − | 5.69157i | 0.317673 | − | 0.550225i | −0.662329 | − | 0.749213i | \(-0.730432\pi\) |
0.980002 | + | 0.198988i | \(0.0637653\pi\) | |||||||
\(108\) | −0.350673 | − | 0.607384i | −0.0337435 | − | 0.0584455i | ||||
\(109\) | 2.91957 | + | 5.05684i | 0.279644 | + | 0.484358i | 0.971296 | − | 0.237873i | \(-0.0764502\pi\) |
−0.691652 | + | 0.722231i | \(0.743117\pi\) | |||||||
\(110\) | 3.06847 | − | 5.31475i | 0.292567 | − | 0.506741i | ||||
\(111\) | 2.16508 | 0.205500 | ||||||||
\(112\) | −3.61343 | + | 8.76412i | −0.341437 | + | 0.828131i | ||||
\(113\) | 6.53233 | 0.614510 | 0.307255 | − | 0.951627i | \(-0.400590\pi\) | ||||
0.307255 | + | 0.951627i | \(0.400590\pi\) | |||||||
\(114\) | 1.30154 | − | 2.25433i | 0.121900 | − | 0.211137i | ||||
\(115\) | 2.93855 | + | 5.08973i | 0.274022 | + | 0.474619i | ||||
\(116\) | 0.385001 | + | 0.666841i | 0.0357464 | + | 0.0619146i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0460 | 1.38510 | ||||||||
\(119\) | 12.4915 | + | 16.2243i | 1.14510 | + | 1.48728i | ||||
\(120\) | −21.5519 | −1.96741 | ||||||||
\(121\) | 4.68250 | − | 8.11033i | 0.425682 | − | 0.737302i | ||||
\(122\) | −5.12795 | − | 8.88187i | −0.464263 | − | 0.804127i | ||||
\(123\) | 4.30401 | + | 7.45477i | 0.388080 | + | 0.672174i | ||||
\(124\) | 0.490402 | − | 0.849402i | 0.0440394 | − | 0.0762786i | ||||
\(125\) | −9.73656 | −0.870865 | ||||||||
\(126\) | −2.61188 | − | 3.39237i | −0.232685 | − | 0.302216i | ||||
\(127\) | 14.7164 | 1.30586 | 0.652932 | − | 0.757416i | \(-0.273539\pi\) | ||||
0.652932 | + | 0.757416i | \(0.273539\pi\) | |||||||
\(128\) | 4.71784 | − | 8.17154i | 0.417002 | − | 0.722269i | ||||
\(129\) | −3.92661 | − | 6.80109i | −0.345719 | − | 0.598802i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.59335 | + | 9.68796i | −0.488693 | + | 0.846441i | −0.999915 | − | 0.0130074i | \(-0.995860\pi\) |
0.511222 | + | 0.859448i | \(0.329193\pi\) | |||||||
\(132\) | 0.499028 | 0.0434349 | ||||||||
\(133\) | 0.951888 | − | 2.30873i | 0.0825391 | − | 0.200193i | ||||
\(134\) | 8.50322 | 0.734566 | ||||||||
\(135\) | −6.57219 | + | 11.3834i | −0.565644 | + | 0.979724i | ||||
\(136\) | −11.4019 | − | 19.7487i | −0.977706 | − | 1.69344i | ||||
\(137\) | −8.81541 | − | 15.2687i | −0.753151 | − | 1.30450i | −0.946288 | − | 0.323324i | \(-0.895200\pi\) |
0.193137 | − | 0.981172i | \(-0.438134\pi\) | |||||||
\(138\) | 2.27147 | − | 3.93430i | 0.193360 | − | 0.334910i | ||||
\(139\) | −5.85710 | −0.496793 | −0.248396 | − | 0.968658i | \(-0.579904\pi\) | ||||
−0.248396 | + | 0.968658i | \(0.579904\pi\) | |||||||
\(140\) | −1.78119 | + | 0.237463i | −0.150538 | + | 0.0200693i | ||||
\(141\) | 1.83324 | 0.154386 | ||||||||
\(142\) | −7.68392 | + | 13.3089i | −0.644820 | + | 1.11686i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.15506 | + | 3.73267i | 0.179588 | + | 0.311055i | ||||
\(145\) | 7.21554 | − | 12.4977i | 0.599218 | − | 1.03788i | ||||
\(146\) | 1.02305 | 0.0846684 | ||||||||
\(147\) | −10.1806 | − | 10.1142i | −0.839685 | − | 0.834209i | ||||
\(148\) | −0.201043 | −0.0165256 | ||||||||
\(149\) | −5.23948 | + | 9.07505i | −0.429235 | + | 0.743457i | −0.996805 | − | 0.0798677i | \(-0.974550\pi\) |
0.567570 | + | 0.823325i | \(0.307884\pi\) | |||||||
\(150\) | 10.6578 | + | 18.4598i | 0.870203 | + | 1.50724i | ||||
\(151\) | −2.35703 | − | 4.08249i | −0.191812 | − | 0.332229i | 0.754039 | − | 0.656830i | \(-0.228103\pi\) |
−0.945851 | + | 0.324602i | \(0.894770\pi\) | |||||||
\(152\) | −1.39059 | + | 2.40857i | −0.112791 | + | 0.195361i | ||||
\(153\) | 9.30967 | 0.752642 | ||||||||
\(154\) | −4.51105 | + | 0.601399i | −0.363511 | + | 0.0484621i | ||||
\(155\) | −18.3819 | −1.47647 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.50105 | − | 7.79604i | −0.359223 | − | 0.622192i | 0.628608 | − | 0.777722i | \(-0.283625\pi\) |
−0.987831 | + | 0.155530i | \(0.950291\pi\) | |||||||
\(158\) | −1.92052 | − | 3.32643i | −0.152788 | − | 0.264637i | ||||
\(159\) | 0.0819962 | − | 0.142022i | 0.00650272 | − | 0.0112630i | ||||
\(160\) | 3.82856 | 0.302674 | ||||||||
\(161\) | 1.66125 | − | 4.02925i | 0.130925 | − | 0.317549i | ||||
\(162\) | 15.0151 | 1.17970 | ||||||||
\(163\) | 6.01619 | − | 10.4203i | 0.471224 | − | 0.816185i | −0.528234 | − | 0.849099i | \(-0.677146\pi\) |
0.999458 | + | 0.0329144i | \(0.0104789\pi\) | |||||||
\(164\) | −0.399657 | − | 0.692227i | −0.0312080 | − | 0.0540538i | ||||
\(165\) | −4.67630 | − | 8.09959i | −0.364050 | − | 0.630553i | ||||
\(166\) | 1.56371 | − | 2.70842i | 0.121367 | − | 0.210214i | ||||
\(167\) | 19.4220 | 1.50292 | 0.751459 | − | 0.659780i | \(-0.229350\pi\) | ||||
0.751459 | + | 0.659780i | \(0.229350\pi\) | |||||||
\(168\) | 9.75008 | + | 12.6636i | 0.752235 | + | 0.977019i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −18.5720 | + | 32.1677i | −1.42441 | + | 2.46715i | ||||
\(171\) | −0.567707 | − | 0.983297i | −0.0434136 | − | 0.0751946i | ||||
\(172\) | 0.364613 | + | 0.631528i | 0.0278015 | + | 0.0481536i | ||||
\(173\) | −7.18976 | + | 12.4530i | −0.546627 | + | 0.946786i | 0.451875 | + | 0.892081i | \(0.350755\pi\) |
−0.998503 | + | 0.0547049i | \(0.982578\pi\) | |||||||
\(174\) | −11.1551 | −0.845663 | ||||||||
\(175\) | 12.4751 | + | 16.2030i | 0.943031 | + | 1.22483i | ||||
\(176\) | 4.58152 | 0.345345 | ||||||||
\(177\) | 11.4649 | − | 19.8578i | 0.861757 | − | 1.49261i | ||||
\(178\) | 5.09589 | + | 8.82635i | 0.381953 | + | 0.661563i | ||||
\(179\) | −2.71303 | − | 4.69911i | −0.202781 | − | 0.351228i | 0.746642 | − | 0.665226i | \(-0.231665\pi\) |
−0.949424 | + | 0.313998i | \(0.898331\pi\) | |||||||
\(180\) | −0.408504 | + | 0.707550i | −0.0304481 | + | 0.0527376i | ||||
\(181\) | 15.4902 | 1.15138 | 0.575688 | − | 0.817669i | \(-0.304734\pi\) | ||||
0.575688 | + | 0.817669i | \(0.304734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.6298 | −1.15539 | ||||||||
\(184\) | −2.42688 | + | 4.20348i | −0.178912 | + | 0.309885i | ||||
\(185\) | 1.88393 | + | 3.26307i | 0.138509 | + | 0.239905i | ||||
\(186\) | 7.10450 | + | 12.3054i | 0.520927 | + | 0.902272i | ||||
\(187\) | 4.94795 | − | 8.57010i | 0.361830 | − | 0.626707i | ||||
\(188\) | −0.170229 | −0.0124152 | ||||||||
\(189\) | 9.66197 | − | 1.28810i | 0.702805 | − | 0.0936957i | ||||
\(190\) | 4.53011 | 0.328649 | ||||||||
\(191\) | −2.37311 | + | 4.11035i | −0.171712 | + | 0.297414i | −0.939019 | − | 0.343866i | \(-0.888263\pi\) |
0.767306 | + | 0.641281i | \(0.221597\pi\) | |||||||
\(192\) | −8.82529 | − | 15.2859i | −0.636911 | − | 1.10316i | ||||
\(193\) | −10.5196 | − | 18.2204i | −0.757215 | − | 1.31154i | −0.944266 | − | 0.329185i | \(-0.893226\pi\) |
0.187050 | − | 0.982350i | \(-0.440107\pi\) | |||||||
\(194\) | 0.321884 | − | 0.557519i | 0.0231099 | − | 0.0400276i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.945343 | + | 0.939178i | 0.0675245 | + | 0.0670842i | ||||
\(197\) | 5.81209 | 0.414094 | 0.207047 | − | 0.978331i | \(-0.433615\pi\) | ||||
0.207047 | + | 0.978331i | \(0.433615\pi\) | |||||||
\(198\) | −1.03458 | + | 1.79194i | −0.0735242 | + | 0.127348i | ||||
\(199\) | −5.30909 | − | 9.19562i | −0.376352 | − | 0.651860i | 0.614177 | − | 0.789168i | \(-0.289488\pi\) |
−0.990528 | + | 0.137309i | \(0.956155\pi\) | |||||||
\(200\) | −11.3869 | − | 19.7228i | −0.805178 | − | 1.39461i | ||||
\(201\) | 6.47939 | − | 11.2226i | 0.457021 | − | 0.791583i | ||||
\(202\) | −3.87204 | −0.272436 | ||||||||
\(203\) | −10.6078 | + | 1.41420i | −0.744520 | + | 0.0992571i | ||||
\(204\) | −3.02038 | −0.211469 | ||||||||
\(205\) | −7.49023 | + | 12.9735i | −0.523140 | + | 0.906106i | ||||
\(206\) | −7.62414 | − | 13.2054i | −0.531199 | − | 0.920064i | ||||
\(207\) | −0.990773 | − | 1.71607i | −0.0688635 | − | 0.119275i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.20691 | −0.0834837 | ||||||||
\(210\) | 9.92290 | − | 24.0673i | 0.684745 | − | 1.66080i | ||||
\(211\) | −4.66549 | −0.321186 | −0.160593 | − | 0.987021i | \(-0.551341\pi\) | ||||
−0.160593 | + | 0.987021i | \(0.551341\pi\) | |||||||
\(212\) | −0.00761392 | + | 0.0131877i | −0.000522926 | + | 0.000905735i | ||||
\(213\) | 11.7102 | + | 20.2826i | 0.802368 | + | 1.38974i | ||||
\(214\) | −4.42046 | − | 7.65645i | −0.302176 | − | 0.523384i | ||||
\(215\) | 6.83344 | − | 11.8359i | 0.466037 | − | 0.807200i | ||||
\(216\) | −10.8556 | −0.738631 | ||||||||
\(217\) | 8.31596 | + | 10.8010i | 0.564524 | + | 0.733216i | ||||
\(218\) | 7.85497 | 0.532005 | ||||||||
\(219\) | 0.779558 | − | 1.35023i | 0.0526776 | − | 0.0912403i | ||||
\(220\) | 0.434227 | + | 0.752104i | 0.0292756 | + | 0.0507068i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.45626 | − | 2.52232i | 0.0977377 | − | 0.169287i | ||||
\(223\) | 24.2254 | 1.62225 | 0.811126 | − | 0.584871i | \(-0.198855\pi\) | ||||
0.811126 | + | 0.584871i | \(0.198855\pi\) | |||||||
\(224\) | −1.73204 | − | 2.24961i | −0.115727 | − | 0.150308i | ||||
\(225\) | 9.29744 | 0.619829 | ||||||||
\(226\) | 4.39373 | − | 7.61017i | 0.292267 | − | 0.506221i | ||||
\(227\) | 7.68764 | + | 13.3154i | 0.510247 | + | 0.883773i | 0.999930 | + | 0.0118726i | \(0.00377926\pi\) |
−0.489683 | + | 0.871901i | \(0.662887\pi\) | |||||||
\(228\) | 0.184184 | + | 0.319016i | 0.0121979 | + | 0.0211274i | ||||
\(229\) | 8.17573 | − | 14.1608i | 0.540268 | − | 0.935771i | −0.458621 | − | 0.888632i | \(-0.651656\pi\) |
0.998888 | − | 0.0471389i | \(-0.0150103\pi\) | |||||||
\(230\) | 7.90604 | 0.521309 | ||||||||
\(231\) | −2.64366 | + | 6.41199i | −0.173940 | + | 0.421878i | ||||
\(232\) | 11.9183 | 0.782473 | ||||||||
\(233\) | 14.5554 | − | 25.2106i | 0.953554 | − | 1.65160i | 0.215911 | − | 0.976413i | \(-0.430728\pi\) |
0.737643 | − | 0.675191i | \(-0.235939\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.59518 | + | 2.76294i | 0.104058 | + | 0.180234i | ||||
\(236\) | −1.06460 | + | 1.84394i | −0.0692995 | + | 0.120030i | ||||
\(237\) | −5.85368 | −0.380237 | ||||||||
\(238\) | 27.3033 | − | 3.63998i | 1.76981 | − | 0.235945i | ||||
\(239\) | −8.65409 | −0.559787 | −0.279893 | − | 0.960031i | \(-0.590299\pi\) | ||||
−0.279893 | + | 0.960031i | \(0.590299\pi\) | |||||||
\(240\) | −13.1037 | + | 22.6963i | −0.845840 | + | 1.46504i | ||||
\(241\) | 9.09909 | + | 15.7601i | 0.586124 | + | 1.01520i | 0.994734 | + | 0.102487i | \(0.0326801\pi\) |
−0.408611 | + | 0.912709i | \(0.633987\pi\) | |||||||
\(242\) | −6.29902 | − | 10.9102i | −0.404916 | − | 0.701336i | ||||
\(243\) | 5.91508 | − | 10.2452i | 0.379453 | − | 0.657231i | ||||
\(244\) | 1.45134 | 0.0929124 | ||||||||
\(245\) | 6.38491 | − | 24.1445i | 0.407917 | − | 1.54253i | ||||
\(246\) | 11.5797 | 0.738297 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.59057 | − | 13.1473i | −0.482002 | − | 0.834851i | ||||
\(249\) | −2.38307 | − | 4.12759i | −0.151021 | − | 0.261576i | ||||
\(250\) | −6.54894 | + | 11.3431i | −0.414191 | + | 0.717400i | ||||
\(251\) | 15.8720 | 1.00183 | 0.500915 | − | 0.865497i | \(-0.332997\pi\) | ||||
0.500915 | + | 0.865497i | \(0.332997\pi\) | |||||||
\(252\) | 0.600554 | − | 0.0800639i | 0.0378313 | − | 0.00504355i | ||||
\(253\) | −2.10632 | −0.132423 | ||||||||
\(254\) | 9.89841 | − | 17.1446i | 0.621082 | − | 1.07574i | ||||
\(255\) | 28.3034 | + | 49.0230i | 1.77243 | + | 3.06994i | ||||
\(256\) | 2.26304 | + | 3.91971i | 0.141440 | + | 0.244982i | ||||
\(257\) | 12.1634 | − | 21.0676i | 0.758730 | − | 1.31416i | −0.184769 | − | 0.982782i | \(-0.559154\pi\) |
0.943499 | − | 0.331376i | \(-0.107513\pi\) | |||||||
\(258\) | −10.5644 | −0.657708 | ||||||||
\(259\) | 1.06504 | − | 2.58319i | 0.0661786 | − | 0.160511i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.43282 | + | 4.21376i | −0.150588 | + | 0.260825i | ||||
\(262\) | 7.52432 | + | 13.0325i | 0.464854 | + | 0.805150i | ||||
\(263\) | −7.71727 | − | 13.3667i | −0.475867 | − | 0.824226i | 0.523751 | − | 0.851872i | \(-0.324532\pi\) |
−0.999618 | + | 0.0276456i | \(0.991199\pi\) | |||||||
\(264\) | 3.86204 | − | 6.68925i | 0.237692 | − | 0.411695i | ||||
\(265\) | 0.285395 | 0.0175317 | ||||||||
\(266\) | −2.04942 | − | 2.66183i | −0.125658 | − | 0.163207i | ||||
\(267\) | 15.5321 | 0.950550 | ||||||||
\(268\) | −0.601656 | + | 1.04210i | −0.0367520 | + | 0.0636563i | ||||
\(269\) | 6.52035 | + | 11.2936i | 0.397553 | + | 0.688582i | 0.993423 | − | 0.114499i | \(-0.0365261\pi\) |
−0.595870 | + | 0.803081i | \(0.703193\pi\) | |||||||
\(270\) | 8.84108 | + | 15.3132i | 0.538051 | + | 0.931931i | ||||
\(271\) | −13.4853 | + | 23.3572i | −0.819174 | + | 1.41885i | 0.0871168 | + | 0.996198i | \(0.472235\pi\) |
−0.906291 | + | 0.422654i | \(0.861099\pi\) | |||||||
\(272\) | −27.7298 | −1.68136 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −23.7174 | −1.43282 | ||||||||
\(275\) | 4.94145 | − | 8.55884i | 0.297980 | − | 0.516117i | ||||
\(276\) | 0.321442 | + | 0.556753i | 0.0193485 | + | 0.0335126i | ||||
\(277\) | −6.35073 | − | 10.9998i | −0.381578 | − | 0.660913i | 0.609710 | − | 0.792625i | \(-0.291286\pi\) |
−0.991288 | + | 0.131712i | \(0.957953\pi\) | |||||||
\(278\) | −3.93956 | + | 6.82352i | −0.236279 | + | 0.409248i | ||||
\(279\) | 6.19770 | 0.371047 | ||||||||
\(280\) | −10.6018 | + | 25.7139i | −0.633579 | + | 1.53670i | ||||
\(281\) | 26.7216 | 1.59408 | 0.797038 | − | 0.603930i | \(-0.206399\pi\) | ||||
0.797038 | + | 0.603930i | \(0.206399\pi\) | |||||||
\(282\) | 1.23306 | − | 2.13572i | 0.0734276 | − | 0.127180i | ||||
\(283\) | −7.37113 | − | 12.7672i | −0.438168 | − | 0.758929i | 0.559380 | − | 0.828911i | \(-0.311039\pi\) |
−0.997548 | + | 0.0699819i | \(0.977706\pi\) | |||||||
\(284\) | −1.08737 | − | 1.88338i | −0.0645236 | − | 0.111758i | ||||
\(285\) | 3.45191 | − | 5.97888i | 0.204473 | − | 0.354158i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.0116 | − | 1.46803i | 0.649995 | − | 0.0866553i | ||||
\(288\) | −1.29085 | −0.0760641 | ||||||||
\(289\) | −21.4476 | + | 37.1483i | −1.26162 | + | 2.18519i | ||||
\(290\) | −9.70653 | − | 16.8122i | −0.569987 | − | 0.987247i | ||||
\(291\) | −0.490546 | − | 0.849651i | −0.0287563 | − | 0.0498074i | ||||
\(292\) | −0.0723874 | + | 0.125379i | −0.00423615 | + | 0.00733723i | ||||
\(293\) | −11.5831 | −0.676689 | −0.338345 | − | 0.941022i | \(-0.609867\pi\) | ||||
−0.338345 | + | 0.941022i | \(0.609867\pi\) | |||||||
\(294\) | −18.6307 | + | 5.05747i | −1.08657 | + | 0.294957i | ||||
\(295\) | 39.9046 | 2.32334 | ||||||||
\(296\) | −1.55589 | + | 2.69489i | −0.0904344 | + | 0.156637i | ||||
\(297\) | −2.35544 | − | 4.07974i | −0.136676 | − | 0.236730i | ||||
\(298\) | 7.04829 | + | 12.2080i | 0.408297 | + | 0.707190i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.01641 | −0.174153 | ||||||||
\(301\) | −10.0461 | + | 1.33931i | −0.579045 | + | 0.0771964i | ||||
\(302\) | −6.34147 | −0.364911 | ||||||||
\(303\) | −2.95047 | + | 5.11036i | −0.169500 | + | 0.293582i | ||||
\(304\) | 1.69097 | + | 2.92885i | 0.0969838 | + | 0.167981i | ||||
\(305\) | −13.6002 | − | 23.5563i | −0.778746 | − | 1.34883i | ||||
\(306\) | 6.26180 | − | 10.8458i | 0.357963 | − | 0.620011i | ||||
\(307\) | 29.3335 | 1.67415 | 0.837076 | − | 0.547086i | \(-0.184263\pi\) | ||||
0.837076 | + | 0.547086i | \(0.184263\pi\) | |||||||
\(308\) | 0.245482 | − | 0.595398i | 0.0139876 | − | 0.0339260i | ||||
\(309\) | −23.2381 | −1.32197 | ||||||||
\(310\) | −12.3639 | + | 21.4149i | −0.702222 | + | 1.21628i | ||||
\(311\) | 0.0753271 | + | 0.130470i | 0.00427141 | + | 0.00739830i | 0.868153 | − | 0.496296i | \(-0.165307\pi\) |
−0.863882 | + | 0.503695i | \(0.831974\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.26057 | − | 9.11157i | 0.297345 | − | 0.515016i | −0.678183 | − | 0.734893i | \(-0.737232\pi\) |
0.975528 | + | 0.219877i | \(0.0705656\pi\) | |||||||
\(314\) | −12.1099 | −0.683399 | ||||||||
\(315\) | −6.92718 | − | 8.99716i | −0.390302 | − | 0.506933i | ||||
\(316\) | 0.543555 | 0.0305773 | ||||||||
\(317\) | 0.753380 | − | 1.30489i | 0.0423140 | − | 0.0732901i | −0.844093 | − | 0.536197i | \(-0.819860\pi\) |
0.886407 | + | 0.462907i | \(0.153194\pi\) | |||||||
\(318\) | −0.110303 | − | 0.191051i | −0.00618551 | − | 0.0107136i | ||||
\(319\) | 2.58601 | + | 4.47910i | 0.144789 | + | 0.250782i | ||||
\(320\) | 15.3586 | − | 26.6018i | 0.858571 | − | 1.48709i | ||||
\(321\) | −13.4734 | −0.752012 | ||||||||
\(322\) | −3.57669 | − | 4.64549i | −0.199321 | − | 0.258883i | ||||
\(323\) | 7.30486 | 0.406453 | ||||||||
\(324\) | −1.06241 | + | 1.84015i | −0.0590228 | + | 0.102231i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.09314 | − | 14.0177i | −0.448237 | − | 0.776370i | ||||
\(327\) | 5.98542 | − | 10.3671i | 0.330995 | − | 0.573299i | ||||
\(328\) | −12.3720 | −0.683129 | ||||||||
\(329\) | 0.901805 | − | 2.18726i | 0.0497181 | − | 0.120588i | ||||
\(330\) | −12.5814 | −0.692582 | ||||||||
\(331\) | 12.6254 | − | 21.8679i | 0.693957 | − | 1.20197i | −0.276574 | − | 0.960993i | \(-0.589199\pi\) |
0.970531 | − | 0.240976i | \(-0.0774675\pi\) | |||||||
\(332\) | 0.221284 | + | 0.383276i | 0.0121446 | + | 0.0210350i | ||||
\(333\) | −0.635193 | − | 1.10019i | −0.0348084 | − | 0.0602899i | ||||
\(334\) | 13.0635 | − | 22.6266i | 0.714802 | − | 1.23807i | ||||
\(335\) | 22.5520 | 1.23215 | ||||||||
\(336\) | 19.2641 | − | 2.56823i | 1.05094 | − | 0.140109i | ||||
\(337\) | −32.1811 | −1.75302 | −0.876509 | − | 0.481386i | \(-0.840134\pi\) | ||||
−0.876509 | + | 0.481386i | \(0.840134\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.69598 | − | 11.5978i | −0.363676 | − | 0.629905i | ||||
\(340\) | −2.62817 | − | 4.55213i | −0.142533 | − | 0.246874i | ||||
\(341\) | 3.29398 | − | 5.70535i | 0.178379 | − | 0.308962i | ||||
\(342\) | −1.52739 | −0.0825917 | ||||||||
\(343\) | −17.0755 | + | 7.17127i | −0.921991 | + | 0.387212i | ||||
\(344\) | 11.2871 | 0.608562 | ||||||||
\(345\) | 6.02434 | − | 10.4345i | 0.324340 | − | 0.561773i | ||||
\(346\) | 9.67185 | + | 16.7521i | 0.519962 | + | 0.900600i | ||||
\(347\) | −12.3819 | − | 21.4461i | −0.664695 | − | 1.15128i | −0.979368 | − | 0.202085i | \(-0.935228\pi\) |
0.314673 | − | 0.949200i | \(-0.398105\pi\) | |||||||
\(348\) | 0.789291 | − | 1.36709i | 0.0423104 | − | 0.0732838i | ||||
\(349\) | 11.5556 | 0.618559 | 0.309280 | − | 0.950971i | \(-0.399912\pi\) | ||||
0.309280 | + | 0.950971i | \(0.399912\pi\) | |||||||
\(350\) | 27.2674 | − | 3.63520i | 1.45750 | − | 0.194310i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.686067 | + | 1.18830i | −0.0365675 | + | 0.0633368i | ||||
\(353\) | −10.0442 | − | 17.3971i | −0.534599 | − | 0.925953i | −0.999183 | − | 0.0404237i | \(-0.987129\pi\) |
0.464583 | − | 0.885529i | \(-0.346204\pi\) | |||||||
\(354\) | −15.4229 | − | 26.7133i | −0.819719 | − | 1.41980i | ||||
\(355\) | −20.3791 | + | 35.2977i | −1.08161 | + | 1.87340i | ||||
\(356\) | −1.44227 | −0.0764399 | ||||||||
\(357\) | 16.0008 | − | 38.8087i | 0.846852 | − | 2.05398i | ||||
\(358\) | −7.29928 | −0.385779 | ||||||||
\(359\) | −7.52551 | + | 13.0346i | −0.397181 | + | 0.687938i | −0.993377 | − | 0.114901i | \(-0.963345\pi\) |
0.596196 | + | 0.802839i | \(0.296678\pi\) | |||||||
\(360\) | 6.32292 | + | 10.9516i | 0.333247 | + | 0.577201i | ||||
\(361\) | 9.05455 | + | 15.6829i | 0.476555 | + | 0.825418i | ||||
\(362\) | 10.4189 | − | 18.0461i | 0.547606 | − | 0.948481i | ||||
\(363\) | −19.1992 | −1.00770 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.71331 | 0.142021 | ||||||||
\(366\) | −10.5128 | + | 18.2087i | −0.549514 | + | 0.951787i | ||||
\(367\) | −4.50178 | − | 7.79731i | −0.234991 | − | 0.407016i | 0.724279 | − | 0.689507i | \(-0.242173\pi\) |
−0.959270 | + | 0.282491i | \(0.908839\pi\) | |||||||
\(368\) | 2.95112 | + | 5.11148i | 0.153838 | + | 0.266454i | ||||
\(369\) | 2.52543 | − | 4.37418i | 0.131469 | − | 0.227711i | ||||
\(370\) | 5.06863 | 0.263506 | ||||||||
\(371\) | −0.129113 | − | 0.167694i | −0.00670319 | − | 0.00870624i | ||||
\(372\) | −2.01075 | −0.104253 | ||||||||
\(373\) | 8.06953 | − | 13.9768i | 0.417824 | − | 0.723693i | −0.577896 | − | 0.816110i | \(-0.696126\pi\) |
0.995720 | + | 0.0924174i | \(0.0294594\pi\) | |||||||
\(374\) | −6.65611 | − | 11.5287i | −0.344179 | − | 0.596136i | ||||
\(375\) | 9.98048 | + | 17.2867i | 0.515390 | + | 0.892681i | ||||
\(376\) | −1.31742 | + | 2.28184i | −0.0679409 | + | 0.117677i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.99813 | − | 12.1226i | 0.257076 | − | 0.623519i | ||||
\(379\) | −15.6655 | −0.804685 | −0.402342 | − | 0.915489i | \(-0.631804\pi\) | ||||
−0.402342 | + | 0.915489i | \(0.631804\pi\) | |||||||
\(380\) | −0.320534 | + | 0.555181i | −0.0164430 | + | 0.0284802i | ||||
\(381\) | −15.0850 | − | 26.1280i | −0.772829 | − | 1.33858i | ||||
\(382\) | 3.19237 | + | 5.52935i | 0.163336 | + | 0.282906i | ||||
\(383\) | −12.3164 | + | 21.3327i | −0.629339 | + | 1.09005i | 0.358345 | + | 0.933589i | \(0.383341\pi\) |
−0.987685 | + | 0.156459i | \(0.949992\pi\) | |||||||
\(384\) | −19.3441 | −0.987151 | ||||||||
\(385\) | −11.9641 | + | 1.59502i | −0.609747 | + | 0.0812896i | ||||
\(386\) | −28.3024 | −1.44055 | ||||||||
\(387\) | −2.30399 | + | 3.99062i | −0.117118 | + | 0.202855i | ||||
\(388\) | 0.0455506 | + | 0.0788960i | 0.00231248 | + | 0.00400534i | ||||
\(389\) | 9.42834 | + | 16.3304i | 0.478036 | + | 0.827982i | 0.999683 | − | 0.0251791i | \(-0.00801560\pi\) |
−0.521647 | + | 0.853161i | \(0.674682\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.7486 | 0.644724 | ||||||||
\(392\) | 19.9054 | − | 5.40348i | 1.00537 | − | 0.272917i | ||||
\(393\) | 22.9339 | 1.15686 | ||||||||
\(394\) | 3.90929 | − | 6.77108i | 0.196947 | − | 0.341122i | ||||
\(395\) | −5.09355 | − | 8.82229i | −0.256284 | − | 0.443897i | ||||
\(396\) | −0.146406 | − | 0.253582i | −0.00735716 | − | 0.0127430i | ||||
\(397\) | −7.25149 | + | 12.5600i | −0.363942 | + | 0.630366i | −0.988606 | − | 0.150528i | \(-0.951903\pi\) |
0.624664 | + | 0.780894i | \(0.285236\pi\) | |||||||
\(398\) | −14.2839 | −0.715985 | ||||||||
\(399\) | −5.07476 | + | 0.676550i | −0.254056 | + | 0.0338699i | ||||
\(400\) | −27.6933 | −1.38467 | ||||||||
\(401\) | −10.4945 | + | 18.1770i | −0.524069 | + | 0.907714i | 0.475539 | + | 0.879695i | \(0.342253\pi\) |
−0.999607 | + | 0.0280189i | \(0.991080\pi\) | |||||||
\(402\) | −8.71624 | − | 15.0970i | −0.434727 | − | 0.752968i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.273971 | − | 0.474532i | 0.0136306 | − | 0.0236089i | ||||
\(405\) | 39.8226 | 1.97880 | ||||||||
\(406\) | −5.48739 | + | 13.3093i | −0.272335 | + | 0.660528i | ||||
\(407\) | −1.35038 | −0.0669360 | ||||||||
\(408\) | −23.3751 | + | 40.4869i | −1.15724 | + | 2.00440i | ||||
\(409\) | 10.7138 | + | 18.5568i | 0.529763 | + | 0.917576i | 0.999397 | + | 0.0347148i | \(0.0110523\pi\) |
−0.469635 | + | 0.882861i | \(0.655614\pi\) | |||||||
\(410\) | 10.0761 | + | 17.4522i | 0.497621 | + | 0.861905i | ||||
\(411\) | −18.0725 | + | 31.3025i | −0.891451 | + | 1.54404i | ||||
\(412\) | 2.15782 | 0.106308 | ||||||||
\(413\) | −18.0529 | − | 23.4474i | −0.888323 | − | 1.15377i | ||||
\(414\) | −2.66563 | −0.131009 | ||||||||
\(415\) | 4.14723 | − | 7.18321i | 0.203580 | − | 0.352610i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00383 | + | 10.3989i | 0.294009 | + | 0.509238i | ||||
\(418\) | −0.811784 | + | 1.40605i | −0.0397056 | + | 0.0687722i | ||||
\(419\) | 7.96406 | 0.389070 | 0.194535 | − | 0.980896i | \(-0.437680\pi\) | ||||
0.194535 | + | 0.980896i | \(0.437680\pi\) | |||||||
\(420\) | 2.24742 | + | 2.91900i | 0.109663 | + | 0.142432i | ||||
\(421\) | 2.81786 | 0.137334 | 0.0686670 | − | 0.997640i | \(-0.478125\pi\) | ||||
0.0686670 | + | 0.997640i | \(0.478125\pi\) | |||||||
\(422\) | −3.13807 | + | 5.43530i | −0.152759 | + | 0.264586i | ||||
\(423\) | −0.537838 | − | 0.931562i | −0.0261506 | − | 0.0452941i | ||||
\(424\) | 0.117850 | + | 0.204122i | 0.00572331 | + | 0.00991306i | ||||
\(425\) | −29.9082 | + | 51.8026i | −1.45076 | + | 2.51279i | ||||
\(426\) | 31.5057 | 1.52645 | ||||||||
\(427\) | −7.68862 | + | 18.6482i | −0.372078 | + | 0.902448i | ||||
\(428\) | 1.25110 | 0.0604742 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9.19253 | − | 15.9219i | −0.443303 | − | 0.767823i | ||||
\(431\) | 2.86813 | + | 4.96775i | 0.138153 | + | 0.239288i | 0.926797 | − | 0.375561i | \(-0.122550\pi\) |
−0.788645 | + | 0.614849i | \(0.789217\pi\) | |||||||
\(432\) | −6.60028 | + | 11.4320i | −0.317556 | + | 0.550023i | ||||
\(433\) | −24.5257 | −1.17863 | −0.589314 | − | 0.807904i | \(-0.700602\pi\) | ||||
−0.589314 | + | 0.807904i | \(0.700602\pi\) | |||||||
\(434\) | 18.1765 | − | 2.42324i | 0.872502 | − | 0.116319i | ||||
\(435\) | −29.5852 | −1.41850 | ||||||||
\(436\) | −0.555788 | + | 0.962653i | −0.0266174 | + | 0.0461027i | ||||
\(437\) | −0.777413 | − | 1.34652i | −0.0371887 | − | 0.0644128i | ||||
\(438\) | −1.04868 | − | 1.81637i | −0.0501079 | − | 0.0867895i | ||||
\(439\) | −18.3211 | + | 31.7332i | −0.874420 | + | 1.51454i | −0.0170416 | + | 0.999855i | \(0.505425\pi\) |
−0.857379 | + | 0.514686i | \(0.827909\pi\) | |||||||
\(440\) | 13.4422 | 0.640830 | ||||||||
\(441\) | −2.15276 | + | 8.14063i | −0.102512 | + | 0.387649i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.5467 | + | 23.4635i | −0.643622 | + | 1.11479i | 0.340996 | + | 0.940065i | \(0.389236\pi\) |
−0.984618 | + | 0.174721i | \(0.944098\pi\) | |||||||
\(444\) | 0.206079 | + | 0.356939i | 0.00978008 | + | 0.0169396i | ||||
\(445\) | 13.5152 | + | 23.4090i | 0.640682 | + | 1.10969i | ||||
\(446\) | 16.2943 | − | 28.2226i | 0.771558 | − | 1.33638i | ||||
\(447\) | 21.4830 | 1.01611 | ||||||||
\(448\) | −22.5791 | + | 3.01018i | −1.06676 | + | 0.142217i | ||||
\(449\) | 27.4324 | 1.29461 | 0.647307 | − | 0.762229i | \(-0.275895\pi\) | ||||
0.647307 | + | 0.762229i | \(0.275895\pi\) | |||||||
\(450\) | 6.25358 | − | 10.8315i | 0.294796 | − | 0.510602i | ||||
\(451\) | −2.68446 | − | 4.64962i | −0.126406 | − | 0.218942i | ||||
\(452\) | 0.621768 | + | 1.07693i | 0.0292455 | + | 0.0506547i | ||||
\(453\) | −4.83215 | + | 8.36953i | −0.227034 | + | 0.393235i | ||||
\(454\) | 20.6832 | 0.970712 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.70169 | 0.267006 | ||||||||
\(457\) | −19.8320 | + | 34.3500i | −0.927700 | + | 1.60682i | −0.140539 | + | 0.990075i | \(0.544884\pi\) |
−0.787161 | + | 0.616748i | \(0.788450\pi\) | |||||||
\(458\) | −10.9982 | − | 19.0495i | −0.513913 | − | 0.890123i | ||||
\(459\) | 14.2563 | + | 24.6927i | 0.665429 | + | 1.15256i | ||||
\(460\) | −0.559402 | + | 0.968913i | −0.0260823 | + | 0.0451758i | ||||
\(461\) | 4.89580 | 0.228020 | 0.114010 | − | 0.993480i | \(-0.463630\pi\) | ||||
0.114010 | + | 0.993480i | \(0.463630\pi\) | |||||||
\(462\) | 5.69181 | + | 7.39265i | 0.264807 | + | 0.343937i | ||||
\(463\) | 4.71193 | 0.218982 | 0.109491 | − | 0.993988i | \(-0.465078\pi\) | ||||
0.109491 | + | 0.993988i | \(0.465078\pi\) | |||||||
\(464\) | 7.24638 | − | 12.5511i | 0.336405 | − | 0.582670i | ||||
\(465\) | 18.8424 | + | 32.6360i | 0.873794 | + | 1.51346i | ||||
\(466\) | −19.5803 | − | 33.9140i | −0.907038 | − | 1.57104i | ||||
\(467\) | −16.0081 | + | 27.7268i | −0.740765 | + | 1.28304i | 0.211383 | + | 0.977403i | \(0.432203\pi\) |
−0.952147 | + | 0.305639i | \(0.901130\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2025 | − | 13.2513i | −0.471110 | − | 0.611887i | ||||
\(470\) | 4.29176 | 0.197964 | ||||||||
\(471\) | −9.22761 | + | 15.9827i | −0.425186 | + | 0.736444i | ||||
\(472\) | 16.4781 | + | 28.5410i | 0.758467 | + | 1.31370i | ||||
\(473\) | 2.44907 | + | 4.24191i | 0.112608 | + | 0.195043i | ||||
\(474\) | −3.93726 | + | 6.81953i | −0.180844 | + | 0.313232i | ||||
\(475\) | 7.29526 | 0.334730 | ||||||||
\(476\) | −1.48578 | + | 3.60366i | −0.0681008 | + | 0.165174i | ||||
\(477\) | −0.0962247 | −0.00440582 | ||||||||
\(478\) | −5.82086 | + | 10.0820i | −0.266240 | + | 0.461141i | ||||
\(479\) | −9.01224 | − | 15.6097i | −0.411780 | − | 0.713224i | 0.583305 | − | 0.812254i | \(-0.301759\pi\) |
−0.995084 | + | 0.0990298i | \(0.968426\pi\) | |||||||
\(480\) | −3.92447 | − | 6.79738i | −0.179127 | − | 0.310257i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 24.4807 | 1.11506 | ||||||||
\(483\) | −8.85657 | + | 1.18073i | −0.402988 | + | 0.0537250i | ||||
\(484\) | 1.78278 | 0.0810355 | ||||||||
\(485\) | 0.853693 | − | 1.47864i | 0.0387642 | − | 0.0671416i | ||||
\(486\) | −7.95712 | − | 13.7821i | −0.360942 | − | 0.625170i | ||||
\(487\) | 8.80020 | + | 15.2424i | 0.398775 | + | 0.690699i | 0.993575 | − | 0.113175i | \(-0.0361021\pi\) |
−0.594800 | + | 0.803874i | \(0.702769\pi\) | |||||||
\(488\) | 11.2321 | − | 19.4545i | 0.508453 | − | 0.880666i | ||||
\(489\) | −24.6676 | −1.11551 | ||||||||
\(490\) | −23.8337 | − | 23.6783i | −1.07670 | − | 1.06968i | ||||
\(491\) | 3.86360 | 0.174362 | 0.0871810 | − | 0.996192i | \(-0.472214\pi\) | ||||
0.0871810 | + | 0.996192i | \(0.472214\pi\) | |||||||
\(492\) | −0.819339 | + | 1.41914i | −0.0369387 | + | 0.0639796i | ||||
\(493\) | −15.6519 | − | 27.1099i | −0.704926 | − | 1.22097i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.74388 | + | 4.75254i | −0.123328 | + | 0.213611i | ||||
\(496\) | −18.4605 | −0.828899 | ||||||||
\(497\) | 29.9599 | − | 3.99416i | 1.34389 | − | 0.179163i | ||||
\(498\) | −6.41153 | −0.287308 | ||||||||
\(499\) | −6.32363 | + | 10.9528i | −0.283084 | + | 0.490317i | −0.972143 | − | 0.234389i | \(-0.924691\pi\) |
0.689058 | + | 0.724706i | \(0.258024\pi\) | |||||||
\(500\) | −0.926757 | − | 1.60519i | −0.0414458 | − | 0.0717863i | ||||
\(501\) | −19.9085 | − | 34.4826i | −0.889448 | − | 1.54057i | ||||
\(502\) | 10.6757 | − | 18.4908i | 0.476480 | − | 0.825287i | ||||
\(503\) | 22.0360 | 0.982537 | 0.491268 | − | 0.871008i | \(-0.336533\pi\) | ||||
0.491268 | + | 0.871008i | \(0.336533\pi\) | |||||||
\(504\) | 3.57454 | − | 8.66978i | 0.159223 | − | 0.386183i | ||||
\(505\) | −10.2693 | −0.456980 | ||||||||
\(506\) | −1.41674 | + | 2.45387i | −0.0629818 | + | 0.109088i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.40075 | + | 2.42617i | 0.0621482 | + | 0.107644i | ||||
\(509\) | −7.83509 | + | 13.5708i | −0.347284 | + | 0.601514i | −0.985766 | − | 0.168123i | \(-0.946229\pi\) |
0.638482 | + | 0.769637i | \(0.279563\pi\) | |||||||
\(510\) | 76.1491 | 3.37194 | ||||||||
\(511\) | −1.22750 | − | 1.59431i | −0.0543016 | − | 0.0705280i | ||||
\(512\) | 24.9600 | 1.10309 | ||||||||
\(513\) | 1.73871 | − | 3.01154i | 0.0767661 | − | 0.132963i | ||||
\(514\) | −16.3625 | − | 28.3406i | −0.721718 | − | 1.25005i | ||||
\(515\) | −20.2206 | − | 35.0230i | −0.891025 | − | 1.54330i | ||||
\(516\) | 0.747495 | − | 1.29470i | 0.0329066 | − | 0.0569959i | ||||
\(517\) | −1.14341 | −0.0502871 | ||||||||
\(518\) | −2.29305 | − | 2.97826i | −0.100751 | − | 0.130857i | ||||
\(519\) | 29.4795 | 1.29401 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.6207 | + | 21.8598i | 0.552925 | + | 0.957694i | 0.998062 | + | 0.0622317i | \(0.0198218\pi\) |
−0.445137 | + | 0.895463i | \(0.646845\pi\) | |||||||
\(522\) | 3.27269 | + | 5.66846i | 0.143242 | + | 0.248102i | ||||
\(523\) | 6.62383 | − | 11.4728i | 0.289640 | − | 0.501671i | −0.684084 | − | 0.729403i | \(-0.739798\pi\) |
0.973724 | + | 0.227733i | \(0.0731312\pi\) | |||||||
\(524\) | −2.12957 | −0.0930307 | ||||||||
\(525\) | 15.9798 | − | 38.7578i | 0.697414 | − | 1.69153i | ||||
\(526\) | −20.7629 | −0.905307 | ||||||||
\(527\) | −19.9369 | + | 34.5318i | −0.868466 | + | 1.50423i | ||||
\(528\) | −4.69629 | − | 8.13422i | −0.204380 | − | 0.353996i | ||||
\(529\) | 10.1432 | + | 17.5686i | 0.441011 | + | 0.763853i | ||||
\(530\) | 0.191960 | − | 0.332485i | 0.00833822 | − | 0.0144422i | ||||
\(531\) | −13.4544 | −0.583871 | ||||||||
\(532\) | 0.471226 | − | 0.0628224i | 0.0204303 | − | 0.00272370i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 10.4471 | − | 18.0949i | 0.452091 | − | 0.783044i | ||||
\(535\) | −11.7238 | − | 20.3063i | −0.506865 | − | 0.877916i | ||||
\(536\) | 9.31258 | + | 16.1299i | 0.402242 | + | 0.696704i | ||||
\(537\) | −5.56200 | + | 9.63366i | −0.240018 | + | 0.415723i | ||||
\(538\) | 17.5427 | 0.756320 | ||||||||
\(539\) | 6.34977 | + | 6.30837i | 0.273504 | + | 0.271721i | ||||
\(540\) | −2.50225 | −0.107680 | ||||||||
\(541\) | 7.20170 | − | 12.4737i | 0.309625 | − | 0.536287i | −0.668655 | − | 0.743573i | \(-0.733130\pi\) |
0.978280 | + | 0.207286i | \(0.0664631\pi\) | |||||||
\(542\) | 18.1408 | + | 31.4208i | 0.779214 | + | 1.34964i | ||||
\(543\) | −15.8782 | − | 27.5019i | −0.681401 | − | 1.18022i | ||||
\(544\) | 4.15244 | − | 7.19224i | 0.178034 | − | 0.308365i | ||||
\(545\) | 20.8328 | 0.892377 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.00679 | 0.0858042 | 0.0429021 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429021 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(548\) | 1.67816 | − | 2.90665i | 0.0716873 | − | 0.124166i | ||||
\(549\) | 4.58550 | + | 7.94232i | 0.195704 | + | 0.338970i | ||||
\(550\) | −6.64736 | − | 11.5136i | −0.283445 | − | 0.490940i | ||||
\(551\) | −1.90892 | + | 3.30634i | −0.0813226 | + | 0.140855i | ||||
\(552\) | 9.95071 | 0.423530 | ||||||||
\(553\) | −2.87954 | + | 6.98411i | −0.122450 | + | 0.296994i | ||||
\(554\) | −17.0863 | −0.725928 | ||||||||
\(555\) | 3.86226 | − | 6.68962i | 0.163944 | − | 0.283959i | ||||
\(556\) | −0.557497 | − | 0.965614i | −0.0236432 | − | 0.0409512i | ||||
\(557\) | 4.28958 | + | 7.42977i | 0.181755 | + | 0.314810i | 0.942478 | − | 0.334267i | \(-0.108489\pi\) |
−0.760723 | + | 0.649077i | \(0.775155\pi\) | |||||||
\(558\) | 4.16865 | − | 7.22032i | 0.176473 | − | 0.305661i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 20.6333 | + | 26.7989i | 0.871915 | + | 1.13246i | ||||
\(561\) | −20.2876 | −0.856543 | ||||||||
\(562\) | 17.9733 | − | 31.1306i | 0.758157 | − | 1.31317i | ||||
\(563\) | 6.38718 | + | 11.0629i | 0.269188 | + | 0.466247i | 0.968652 | − | 0.248421i | \(-0.0799115\pi\) |
−0.699465 | + | 0.714667i | \(0.746578\pi\) | |||||||
\(564\) | 0.174493 | + | 0.302231i | 0.00734750 | + | 0.0127262i | ||||
\(565\) | 11.6530 | − | 20.1835i | 0.490243 | − | 0.849126i | ||||
\(566\) | −19.8317 | −0.833587 | ||||||||
\(567\) | −18.0158 | − | 23.3992i | −0.756591 | − | 0.982676i | ||||
\(568\) | −33.6612 | −1.41239 | ||||||||
\(569\) | 2.89558 | − | 5.01530i | 0.121389 | − | 0.210252i | −0.798927 | − | 0.601429i | \(-0.794598\pi\) |
0.920316 | + | 0.391176i | \(0.127932\pi\) | |||||||
\(570\) | −4.64360 | − | 8.04295i | −0.194499 | − | 0.336882i | ||||
\(571\) | 22.0666 | + | 38.2204i | 0.923458 | + | 1.59948i | 0.794023 | + | 0.607888i | \(0.207983\pi\) |
0.129435 | + | 0.991588i | \(0.458684\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.73025 | 0.406487 | ||||||||
\(574\) | 5.69630 | − | 13.8160i | 0.237759 | − | 0.576667i | ||||
\(575\) | 12.7318 | 0.530954 | ||||||||
\(576\) | −5.17835 | + | 8.96917i | −0.215765 | + | 0.373715i | ||||
\(577\) | −5.96649 | − | 10.3343i | −0.248388 | − | 0.430221i | 0.714691 | − | 0.699441i | \(-0.246568\pi\) |
−0.963079 | + | 0.269220i | \(0.913234\pi\) | |||||||
\(578\) | 28.8518 | + | 49.9729i | 1.20008 | + | 2.07860i | ||||
\(579\) | −21.5662 | + | 37.3538i | −0.896261 | + | 1.55237i | ||||
\(580\) | 2.74719 | 0.114071 | ||||||||
\(581\) | −6.09697 | + | 0.812829i | −0.252945 | + | 0.0337218i | ||||
\(582\) | −1.31979 | −0.0547071 | ||||||||
\(583\) | −0.0511420 | + | 0.0885805i | −0.00211808 | + | 0.00366863i | ||||
\(584\) | 1.12043 | + | 1.94064i | 0.0463637 | + | 0.0803043i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.79091 | + | 13.4943i | −0.321840 | + | 0.557443i | ||||
\(587\) | 20.3516 | 0.840000 | 0.420000 | − | 0.907524i | \(-0.362030\pi\) | ||||
0.420000 | + | 0.907524i | \(0.362030\pi\) | |||||||
\(588\) | 0.698431 | − | 2.64111i | 0.0288028 | − | 0.108917i | ||||
\(589\) | 4.86304 | 0.200378 | ||||||||
\(590\) | 26.8404 | − | 46.4889i | 1.10500 | − | 1.91392i | ||||
\(591\) | −5.95769 | − | 10.3190i | −0.245067 | − | 0.424468i | ||||
\(592\) | 1.89199 | + | 3.27701i | 0.0777601 | + | 0.134684i | ||||
\(593\) | −9.09000 | + | 15.7443i | −0.373282 | + | 0.646543i | −0.990068 | − | 0.140588i | \(-0.955101\pi\) |
0.616787 | + | 0.787130i | \(0.288434\pi\) | |||||||
\(594\) | −6.33719 | −0.260018 | ||||||||
\(595\) | 72.4131 | − | 9.65388i | 2.96865 | − | 0.395770i | ||||
\(596\) | −1.99484 | −0.0817120 | ||||||||
\(597\) | −10.8842 | + | 18.8520i | −0.445460 | + | 0.771560i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.1341 | + | 33.1412i | 0.781797 | + | 1.35411i | 0.930894 | + | 0.365290i | \(0.119030\pi\) |
−0.149096 | + | 0.988823i | \(0.547636\pi\) | |||||||
\(600\) | −23.3444 | + | 40.4337i | −0.953031 | + | 1.65070i | ||||
\(601\) | −26.8719 | −1.09613 | −0.548064 | − | 0.836436i | \(-0.684635\pi\) | ||||
−0.548064 | + | 0.836436i | \(0.684635\pi\) | |||||||
\(602\) | −5.19681 | + | 12.6045i | −0.211806 | + | 0.513721i | ||||
\(603\) | −7.60372 | −0.309648 | ||||||||
\(604\) | 0.448699 | − | 0.777170i | 0.0182573 | − | 0.0316226i | ||||
\(605\) | −16.7061 | − | 28.9358i | −0.679200 | − | 1.17641i | ||||
\(606\) | 3.96904 | + | 6.87459i | 0.161231 | + | 0.279261i | ||||
\(607\) | 4.70105 | − | 8.14245i | 0.190810 | − | 0.330492i | −0.754709 | − | 0.656059i | \(-0.772222\pi\) |
0.945519 | + | 0.325568i | \(0.105555\pi\) | |||||||
\(608\) | −1.01287 | −0.0410773 | ||||||||
\(609\) | 13.3843 | + | 17.3839i | 0.542361 | + | 0.704430i | ||||
\(610\) | −36.5908 | −1.48152 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.886124 | + | 1.53481i | 0.0358194 | + | 0.0620411i | ||||
\(613\) | 6.64469 | + | 11.5089i | 0.268376 | + | 0.464842i | 0.968443 | − | 0.249236i | \(-0.0801796\pi\) |
−0.700066 | + | 0.714078i | \(0.746846\pi\) | |||||||
\(614\) | 19.7301 | − | 34.1735i | 0.796242 | − | 1.37913i | ||||
\(615\) | 30.7115 | 1.23841 | ||||||||
\(616\) | −6.08123 | − | 7.89843i | −0.245020 | − | 0.318237i | ||||
\(617\) | 11.2261 | 0.451947 | 0.225973 | − | 0.974133i | \(-0.427444\pi\) | ||||
0.225973 | + | 0.974133i | \(0.427444\pi\) | |||||||
\(618\) | −15.6303 | + | 27.0724i | −0.628742 | + | 1.08901i | ||||
\(619\) | −4.64253 | − | 8.04109i | −0.186599 | − | 0.323199i | 0.757515 | − | 0.652817i | \(-0.226413\pi\) |
−0.944114 | + | 0.329619i | \(0.893080\pi\) | |||||||
\(620\) | −1.74965 | − | 3.03048i | −0.0702675 | − | 0.121707i | ||||
\(621\) | 3.03444 | − | 5.25580i | 0.121768 | − | 0.210908i | ||||
\(622\) | 0.202664 | 0.00812608 | ||||||||
\(623\) | 7.64055 | − | 18.5316i | 0.306112 | − | 0.742453i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.95363 | − | 3.38379i | 0.0781452 | − | 0.135351i | ||||
\(626\) | −7.07665 | − | 12.2571i | −0.282840 | − | 0.489893i | ||||
\(627\) | 1.23715 | + | 2.14280i | 0.0494068 | + | 0.0855752i | ||||
\(628\) | 0.856848 | − | 1.48410i | 0.0341920 | − | 0.0592222i | ||||
\(629\) | 8.17322 | 0.325888 | ||||||||
\(630\) | −15.1410 | + | 2.01855i | −0.603232 | + | 0.0804210i | ||||
\(631\) | 10.4026 | 0.414122 | 0.207061 | − | 0.978328i | \(-0.433610\pi\) | ||||
0.207061 | + | 0.978328i | \(0.433610\pi\) | |||||||
\(632\) | 4.20664 | − | 7.28611i | 0.167331 | − | 0.289826i | ||||
\(633\) | 4.78237 | + | 8.28331i | 0.190082 | + | 0.329232i | ||||
\(634\) | −1.01347 | − | 1.75538i | −0.0402499 | − | 0.0697149i | ||||
\(635\) | 26.2523 | − | 45.4704i | 1.04179 | − | 1.80444i | ||||
\(636\) | 0.0312187 | 0.00123790 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6.95754 | 0.275452 | ||||||||
\(639\) | 6.87109 | − | 11.9011i | 0.271816 | − | 0.470800i | ||||
\(640\) | −16.8322 | − | 29.1542i | −0.665351 | − | 1.15242i | ||||
\(641\) | −7.42955 | − | 12.8684i | −0.293449 | − | 0.508269i | 0.681174 | − | 0.732122i | \(-0.261470\pi\) |
−0.974623 | + | 0.223853i | \(0.928137\pi\) | |||||||
\(642\) | −9.06239 | + | 15.6965i | −0.357664 | + | 0.619492i | ||||
\(643\) | −2.29722 | −0.0905935 | −0.0452968 | − | 0.998974i | \(-0.514423\pi\) | ||||
−0.0452968 | + | 0.998974i | \(0.514423\pi\) | |||||||
\(644\) | 0.822394 | − | 0.109639i | 0.0324069 | − | 0.00432038i | ||||
\(645\) | −28.0185 | −1.10323 | ||||||||
\(646\) | 4.91334 | − | 8.51016i | 0.193313 | − | 0.334828i | ||||
\(647\) | −3.99932 | − | 6.92703i | −0.157230 | − | 0.272330i | 0.776639 | − | 0.629946i | \(-0.216923\pi\) |
−0.933869 | + | 0.357616i | \(0.883590\pi\) | |||||||
\(648\) | 16.4443 | + | 28.4823i | 0.645991 | + | 1.11889i | ||||
\(649\) | −7.15081 | + | 12.3856i | −0.280694 | + | 0.486176i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.6522 | − | 25.8360i | 0.417491 | − | 1.01259i | ||||
\(652\) | 2.29056 | 0.0897053 | ||||||||
\(653\) | −1.99222 | + | 3.45062i | −0.0779615 | + | 0.135033i | −0.902370 | − | 0.430962i | \(-0.858174\pi\) |
0.824409 | + | 0.565995i | \(0.191508\pi\) | |||||||
\(654\) | −8.05175 | − | 13.9460i | −0.314848 | − | 0.545333i | ||||
\(655\) | 19.9558 | + | 34.5645i | 0.779738 | + | 1.35055i | ||||
\(656\) | −7.52225 | + | 13.0289i | −0.293695 | + | 0.508694i | ||||
\(657\) | −0.914831 | −0.0356910 | ||||||||
\(658\) | −1.94159 | − | 2.52178i | −0.0756912 | − | 0.0983094i | ||||
\(659\) | −27.5003 | −1.07126 | −0.535629 | − | 0.844453i | \(-0.679925\pi\) | ||||
−0.535629 | + | 0.844453i | \(0.679925\pi\) | |||||||
\(660\) | 0.890211 | − | 1.54189i | 0.0346514 | − | 0.0600180i | ||||
\(661\) | −3.49310 | − | 6.05023i | −0.135866 | − | 0.235327i | 0.790062 | − | 0.613027i | \(-0.210048\pi\) |
−0.925928 | + | 0.377700i | \(0.876715\pi\) | |||||||
\(662\) | −16.9841 | − | 29.4173i | −0.660105 | − | 1.14333i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.85019 | 0.265839 | ||||||||
\(665\) | −5.43543 | − | 7.05965i | −0.210777 | − | 0.273762i | ||||
\(666\) | −1.70896 | −0.0662207 | ||||||||
\(667\) | −3.33148 | + | 5.77029i | −0.128995 | + | 0.223427i | ||||
\(668\) | 1.84865 | + | 3.20195i | 0.0715263 | + | 0.123887i | ||||
\(669\) | −24.8323 | − | 43.0108i | −0.960071 | − | 1.66289i | ||||
\(670\) | 15.1688 | − | 26.2731i | 0.586022 | − | 1.01502i | ||||
\(671\) | 9.74849 | 0.376336 | ||||||||
\(672\) | −2.21862 | + | 5.38110i | −0.0855852 | + | 0.207581i | ||||
\(673\) | 5.45566 | 0.210300 | 0.105150 | − | 0.994456i | \(-0.466468\pi\) | ||||
0.105150 | + | 0.994456i | \(0.466468\pi\) | |||||||
\(674\) | −21.6455 | + | 37.4910i | −0.833752 | + | 1.44410i | ||||
\(675\) | 14.2376 | + | 24.6603i | 0.548006 | + | 0.949174i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.8961 | + | 29.2649i | −0.649371 | + | 1.12474i | 0.333903 | + | 0.942607i | \(0.391634\pi\) |
−0.983273 | + | 0.182135i | \(0.941699\pi\) | |||||||
\(678\) | −18.0152 | −0.691870 | ||||||||
\(679\) | −1.25504 | + | 0.167318i | −0.0481640 | + | 0.00642107i | ||||
\(680\) | −81.3590 | −3.11997 | ||||||||
\(681\) | 15.7605 | − | 27.2979i | 0.603942 | − | 1.04606i | ||||
\(682\) | −4.43115 | − | 7.67498i | −0.169678 | − | 0.293890i | ||||
\(683\) | −6.14942 | − | 10.6511i | −0.235301 | − | 0.407553i | 0.724059 | − | 0.689738i | \(-0.242274\pi\) |
−0.959360 | + | 0.282185i | \(0.908941\pi\) | |||||||
\(684\) | 0.108072 | − | 0.187187i | 0.00413225 | − | 0.00715726i | ||||
\(685\) | −62.9028 | −2.40339 | ||||||||
\(686\) | −3.13068 | + | 24.7165i | −0.119530 | + | 0.943679i | ||||
\(687\) | −33.5222 | −1.27895 | ||||||||
\(688\) | 6.86265 | − | 11.8865i | 0.261636 | − | 0.453167i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −8.10410 | − | 14.0367i | −0.308518 | − | 0.534369i | ||||
\(691\) | 5.54483 | − | 9.60393i | 0.210935 | − | 0.365351i | −0.741072 | − | 0.671425i | \(-0.765682\pi\) |
0.952008 | + | 0.306075i | \(0.0990157\pi\) | |||||||
\(692\) | −2.73738 | −0.104059 | ||||||||
\(693\) | 4.03386 | − | 0.537781i | 0.153234 | − | 0.0204286i | ||||
\(694\) | −33.3129 | −1.26454 | ||||||||
\(695\) | −10.4484 | + | 18.0972i | −0.396331 | + | 0.686465i | ||||
\(696\) | −12.2168 | − | 21.1602i | −0.463078 | − | 0.802075i | ||||
\(697\) | 16.2478 | + | 28.1419i | 0.615428 | + | 1.06595i | ||||
\(698\) | 7.77247 | − | 13.4623i | 0.294193 | − | 0.509556i | ||||
\(699\) | −59.6800 | −2.25731 | ||||||||
\(700\) | −1.48383 | + | 3.59893i | −0.0560836 | + | 0.136027i | ||||
\(701\) | −10.6470 | −0.402133 | −0.201066 | − | 0.979578i | \(-0.564441\pi\) | ||||
−0.201066 | + | 0.979578i | \(0.564441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.498406 | − | 0.863265i | −0.0187977 | − | 0.0325587i | ||||
\(704\) | 5.50443 | + | 9.53396i | 0.207456 | + | 0.359325i | ||||
\(705\) | 3.27029 | − | 5.66431i | 0.123166 | − | 0.213330i | ||||
\(706\) | −27.0235 | −1.01704 | ||||||||
\(707\) | 4.64585 | + | 6.03413i | 0.174725 | + | 0.226937i | ||||
\(708\) | 4.36508 | 0.164050 | ||||||||
\(709\) | 20.3535 | − | 35.2532i | 0.764391 | − | 1.32396i | −0.176178 | − | 0.984358i | \(-0.556373\pi\) |
0.940568 | − | 0.339605i | \(-0.110293\pi\) | |||||||
\(710\) | 27.4145 | + | 47.4833i | 1.02885 | + | 1.78202i | ||||
\(711\) | 1.71736 | + | 2.97455i | 0.0644060 | + | 0.111554i | ||||
\(712\) | −11.1619 | + | 19.3329i | −0.418309 | + | 0.724532i | ||||
\(713\) | 8.48708 | 0.317844 | ||||||||
\(714\) | −34.4498 | − | 44.7442i | −1.28925 | − | 1.67451i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.516470 | − | 0.894552i | 0.0193014 | − | 0.0334310i | ||||
\(717\) | 8.87089 | + | 15.3648i | 0.331290 | + | 0.573810i | ||||
\(718\) | 10.1235 | + | 17.5344i | 0.377806 | + | 0.654380i | ||||
\(719\) | 4.88769 | − | 8.46572i | 0.182280 | − | 0.315718i | −0.760377 | − | 0.649482i | \(-0.774986\pi\) |
0.942657 | + | 0.333764i | \(0.108319\pi\) | |||||||
\(720\) | 15.3775 | 0.573086 | ||||||||
\(721\) | −11.4313 | + | 27.7258i | −0.425724 | + | 1.03256i | ||||
\(722\) | 24.3608 | 0.906616 | ||||||||
\(723\) | 18.6541 | − | 32.3098i | 0.693752 | − | 1.20161i | ||||
\(724\) | 1.47441 | + | 2.55375i | 0.0547959 | + | 0.0949092i | ||||
\(725\) | −15.6313 | − | 27.0743i | −0.580533 | − | 1.00551i | ||||
\(726\) | −12.9136 | + | 22.3671i | −0.479270 | + | 0.830120i | ||||
\(727\) | 12.2091 | 0.452811 | 0.226406 | − | 0.974033i | \(-0.427303\pi\) | ||||
0.226406 | + | 0.974033i | \(0.427303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.23219 | 0.341933 | ||||||||
\(730\) | 1.82501 | − | 3.16101i | 0.0675467 | − | 0.116994i | ||||
\(731\) | −14.8231 | − | 25.6743i | −0.548251 | − | 0.949598i | ||||
\(732\) | −1.48770 | − | 2.57677i | −0.0549869 | − | 0.0952400i | ||||
\(733\) | −11.1577 | + | 19.3256i | −0.412118 | + | 0.713809i | −0.995121 | − | 0.0986608i | \(-0.968544\pi\) |
0.583003 | + | 0.812470i | \(0.301877\pi\) | |||||||
\(734\) | −12.1118 | −0.447055 | ||||||||
\(735\) | −49.4120 | + | 13.4133i | −1.82259 | + | 0.494757i | ||||
\(736\) | −1.76768 | −0.0651576 | ||||||||
\(737\) | −4.04126 | + | 6.99968i | −0.148862 | + | 0.257836i | ||||
\(738\) | −3.39728 | − | 5.88426i | −0.125056 | − | 0.216603i | ||||
\(739\) | 21.1865 | + | 36.6960i | 0.779357 | + | 1.34989i | 0.932313 | + | 0.361653i | \(0.117787\pi\) |
−0.152956 | + | 0.988233i | \(0.548879\pi\) | |||||||
\(740\) | −0.358637 | + | 0.621178i | −0.0131838 | + | 0.0228350i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.282206 | + | 0.0376229i | −0.0103601 | + | 0.00138118i | ||||
\(743\) | −30.9801 | −1.13655 | −0.568276 | − | 0.822838i | \(-0.692389\pi\) | ||||
−0.568276 | + | 0.822838i | \(0.692389\pi\) | |||||||
\(744\) | −15.5615 | + | 26.9532i | −0.570511 | + | 0.988153i | ||||
\(745\) | 18.6933 | + | 32.3778i | 0.684870 | + | 1.18623i | ||||
\(746\) | −10.8553 | − | 18.8020i | −0.397442 | − | 0.688390i | ||||
\(747\) | −1.39830 | + | 2.42192i | −0.0511609 | + | 0.0886133i | ||||
\(748\) | 1.88385 | 0.0688802 | ||||||||
\(749\) | −6.62783 | + | 16.0753i | −0.242176 | + | 0.587379i | ||||
\(750\) | 26.8520 | 0.980497 | ||||||||
\(751\) | −11.2830 | + | 19.5427i | −0.411722 | + | 0.713123i | −0.995078 | − | 0.0990930i | \(-0.968406\pi\) |
0.583356 | + | 0.812216i | \(0.301739\pi\) | |||||||
\(752\) | 1.60200 | + | 2.77475i | 0.0584190 | + | 0.101185i | ||||
\(753\) | −16.2696 | − | 28.1798i | −0.592897 | − | 1.02693i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.8187 | −0.612095 | ||||||||
\(756\) | 1.13202 | + | 1.47029i | 0.0411710 | + | 0.0534738i | ||||
\(757\) | 32.2808 | 1.17327 | 0.586633 | − | 0.809853i | \(-0.300453\pi\) | ||||
0.586633 | + | 0.809853i | \(0.300453\pi\) | |||||||
\(758\) | −10.5368 | + | 18.2504i | −0.382716 | + | 0.662883i | ||||
\(759\) | 2.15909 | + | 3.73966i | 0.0783701 | + | 0.135741i | ||||
\(760\) | 4.96130 | + | 8.59323i | 0.179965 | + | 0.311709i | ||||
\(761\) | −14.8758 | + | 25.7657i | −0.539249 | + | 0.934006i | 0.459696 | + | 0.888076i | \(0.347958\pi\) |
−0.998945 | + | 0.0459296i | \(0.985375\pi\) | |||||||
\(762\) | −40.5855 | −1.47026 | ||||||||
\(763\) | −9.42474 | − | 12.2411i | −0.341198 | − | 0.443156i | ||||
\(764\) | −0.903521 | −0.0326883 | ||||||||
\(765\) | 16.6074 | − | 28.7649i | 0.600442 | − | 1.04000i | ||||
\(766\) | 16.5684 | + | 28.6972i | 0.598639 | + | 1.03687i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.63947 | − | 8.03581i | 0.167413 | − | 0.289967i | ||||
\(769\) | −41.8105 | −1.50773 | −0.753863 | − | 0.657032i | \(-0.771812\pi\) | ||||
−0.753863 | + | 0.657032i | \(0.771812\pi\) | |||||||
\(770\) | −6.18902 | + | 15.0110i | −0.223037 | + | 0.540959i | ||||
\(771\) | −49.8723 | −1.79611 | ||||||||
\(772\) | 2.00257 | − | 3.46856i | 0.0720742 | − | 0.124836i | ||||
\(773\) | −20.7168 | − | 35.8826i | −0.745132 | − | 1.29061i | −0.950133 | − | 0.311845i | \(-0.899053\pi\) |
0.205001 | − | 0.978762i | \(-0.434280\pi\) | |||||||
\(774\) | 3.09938 | + | 5.36829i | 0.111405 | + | 0.192959i | ||||
\(775\) | −19.9107 | + | 34.4864i | −0.715215 | + | 1.23879i | ||||
\(776\) | 1.41009 | 0.0506192 | ||||||||
\(777\) | −5.67802 | + | 0.756975i | −0.203698 | + | 0.0271563i | ||||
\(778\) | 25.3665 | 0.909433 | ||||||||
\(779\) | 1.98159 | − | 3.43221i | 0.0709978 | − | 0.122972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.30376 | − | 12.6505i | −0.261349 | − | 0.452670i | ||||
\(782\) | 8.57486 | − | 14.8521i | 0.306637 | − | 0.531110i | ||||
\(783\) | −14.9020 | −0.532552 | ||||||||
\(784\) | 6.41221 | − | 24.2477i | 0.229007 | − | 0.865989i | ||||
\(785\) | −32.1175 | −1.14632 | ||||||||
\(786\) | 15.4256 | − | 26.7180i | 0.550214 | − | 0.952998i | ||||
\(787\) | 11.9313 | + | 20.6657i | 0.425306 | + | 0.736651i | 0.996449 | − | 0.0841992i | \(-0.0268332\pi\) |
−0.571143 | + | 0.820851i | \(0.693500\pi\) | |||||||
\(788\) | 0.553213 | + | 0.958193i | 0.0197074 | + | 0.0341342i | ||||
\(789\) | −15.8212 | + | 27.4031i | −0.563250 | + | 0.975577i | ||||
\(790\) | −13.7040 | −0.487565 | ||||||||
\(791\) | −17.1314 | + | 2.28390i | −0.609121 | + | 0.0812061i | ||||
\(792\) | −4.53221 | −0.161045 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.75490 | + | 16.8960i | 0.346188 | + | 0.599616i | ||||
\(795\) | −0.292544 | − | 0.506701i | −0.0103755 | − | 0.0179708i | ||||
\(796\) | 1.01067 | − | 1.75054i | 0.0358223 | − | 0.0620461i | ||||
\(797\) | 50.8231 | 1.80025 | 0.900123 | − | 0.435636i | \(-0.143476\pi\) | ||||
0.900123 | + | 0.435636i | \(0.143476\pi\) | |||||||
\(798\) | −2.62517 | + | 6.36715i | −0.0929299 | + | 0.225395i | ||||
\(799\) | 6.92052 | 0.244830 | ||||||||
\(800\) | 4.14699 | − | 7.18279i | 0.146618 | − | 0.253950i | ||||
\(801\) | −4.55683 | − | 7.89267i | −0.161008 | − | 0.278874i | ||||
\(802\) | 14.1174 | + | 24.4521i | 0.498504 | + | 0.863434i | ||||
\(803\) | −0.486219 | + | 0.842156i | −0.0171583 | + | 0.0297190i | ||||
\(804\) | 2.46691 | 0.0870014 | ||||||||
\(805\) | −9.48602 | − | 12.3206i | −0.334338 | − | 0.434246i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.3674 | − | 23.1530i | 0.470555 | − | 0.815025i | ||||
\(808\) | −4.24060 | − | 7.34493i | −0.149184 | − | 0.258394i | ||||
\(809\) | −2.20588 | − | 3.82070i | −0.0775547 | − | 0.134329i | 0.824640 | − | 0.565658i | \(-0.191378\pi\) |
−0.902194 | + | 0.431330i | \(0.858045\pi\) | |||||||
\(810\) | 26.7852 | − | 46.3933i | 0.941136 | − | 1.63010i | ||||
\(811\) | −17.6493 | −0.619750 | −0.309875 | − | 0.950777i | \(-0.600287\pi\) | ||||
−0.309875 | + | 0.950777i | \(0.600287\pi\) | |||||||
\(812\) | −1.24283 | − | 1.61421i | −0.0436148 | − | 0.0566478i | ||||
\(813\) | 55.2926 | 1.93920 | ||||||||
\(814\) | −0.908285 | + | 1.57320i | −0.0318354 | + | 0.0551405i | ||||
\(815\) | −21.4644 | − | 37.1775i | −0.751866 | − | 1.30227i | ||||
\(816\) | 28.4244 | + | 49.2326i | 0.995054 | + | 1.72348i | ||||
\(817\) | −1.80783 | + | 3.13126i | −0.0632480 | + | 0.109549i | ||||
\(818\) | 28.8249 | 1.00784 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.85178 | −0.0995884 | ||||||||
\(821\) | 1.78022 | − | 3.08342i | 0.0621299 | − | 0.107612i | −0.833287 | − | 0.552840i | \(-0.813544\pi\) |
0.895417 | + | 0.445228i | \(0.146877\pi\) | |||||||
\(822\) | 24.3116 | + | 42.1089i | 0.847964 | + | 1.46872i | ||||
\(823\) | −10.9332 | − | 18.9369i | −0.381109 | − | 0.660100i | 0.610112 | − | 0.792315i | \(-0.291124\pi\) |
−0.991221 | + | 0.132215i | \(0.957791\pi\) | |||||||
\(824\) | 16.6997 | − | 28.9247i | 0.581760 | − | 1.00764i | ||||
\(825\) | −20.2610 | −0.705396 | ||||||||
\(826\) | −39.4589 | + | 5.26053i | −1.37295 | + | 0.183037i | ||||
\(827\) | 18.1361 | 0.630653 | 0.315327 | − | 0.948983i | \(-0.397886\pi\) | ||||
0.315327 | + | 0.948983i | \(0.397886\pi\) | |||||||
\(828\) | 0.188610 | − | 0.326682i | 0.00655465 | − | 0.0113530i | ||||
\(829\) | −15.4497 | − | 26.7596i | −0.536590 | − | 0.929401i | −0.999085 | − | 0.0427787i | \(-0.986379\pi\) |
0.462495 | − | 0.886622i | \(-0.346954\pi\) | |||||||
\(830\) | −5.57896 | − | 9.66305i | −0.193649 | − | 0.335409i | ||||
\(831\) | −13.0196 | + | 22.5507i | −0.451646 | + | 0.782275i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.4322 | − | 38.1816i | −1.33160 | − | 1.32291i | ||||
\(834\) | 16.1530 | 0.559333 | ||||||||
\(835\) | 34.6466 | − | 60.0097i | 1.19900 | − | 2.07672i | ||||
\(836\) | −0.114878 | − | 0.198974i | −0.00397313 | − | 0.00688165i | ||||
\(837\) | 9.49084 | + | 16.4386i | 0.328051 | + | 0.568202i | ||||
\(838\) | 5.35673 | − | 9.27813i | 0.185045 | − | 0.320508i | ||||
\(839\) | −15.3959 | −0.531526 | −0.265763 | − | 0.964038i | \(-0.585624\pi\) | ||||
−0.265763 | + | 0.964038i | \(0.585624\pi\) | |||||||
\(840\) | 56.5209 | − | 7.53518i | 1.95016 | − | 0.259989i | ||||
\(841\) | −12.6393 | −0.435838 | ||||||||
\(842\) | 1.89533 | − | 3.28280i | 0.0653173 | − | 0.113133i | ||||
\(843\) | −27.3910 | − | 47.4426i | −0.943396 | − | 1.63401i | ||||
\(844\) | −0.444076 | − | 0.769163i | −0.0152857 | − | 0.0264757i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.44703 | −0.0497498 | ||||||||
\(847\) | −9.44447 | + | 22.9069i | −0.324516 | + | 0.787089i | ||||
\(848\) | 0.286615 | 0.00984239 | ||||||||
\(849\) | −15.1116 | + | 26.1740i | −0.518628 | + | 0.898290i | ||||
\(850\) | 40.2333 | + | 69.6862i | 1.37999 | + | 2.39022i | ||||
\(851\) | −0.869829 | − | 1.50659i | −0.0298173 | − | 0.0516451i | ||||
\(852\) | −2.22922 | + | 3.86113i | −0.0763719 | + | 0.132280i | ||||
\(853\) | −23.7772 | −0.814116 | −0.407058 | − | 0.913402i | \(-0.633445\pi\) | ||||
−0.407058 | + | 0.913402i | \(0.633445\pi\) | |||||||
\(854\) | 16.5537 | + | 21.5002i | 0.566455 | + | 0.735723i | ||||
\(855\) | −4.05090 | −0.138538 | ||||||||
\(856\) | 9.68242 | − | 16.7704i | 0.330938 | − | 0.573202i | ||||
\(857\) | 15.0525 | + | 26.0717i | 0.514184 | + | 0.890592i | 0.999865 | + | 0.0164561i | \(0.00523837\pi\) |
−0.485681 | + | 0.874136i | \(0.661428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.56717 | − | 13.1067i | 0.258188 | − | 0.447195i | −0.707568 | − | 0.706645i | \(-0.750208\pi\) |
0.965757 | + | 0.259450i | \(0.0835411\pi\) | |||||||
\(860\) | 2.60172 | 0.0887178 | ||||||||
\(861\) | −13.8939 | − | 18.0457i | −0.473502 | − | 0.614995i | ||||
\(862\) | 7.71657 | 0.262827 | ||||||||
\(863\) | 9.13287 | − | 15.8186i | 0.310886 | − | 0.538471i | −0.667668 | − | 0.744459i | \(-0.732707\pi\) |
0.978555 | + | 0.205988i | \(0.0660408\pi\) | |||||||
\(864\) | −1.97674 | − | 3.42382i | −0.0672501 | − | 0.116481i | ||||
\(865\) | 25.6514 | + | 44.4296i | 0.872175 | + | 1.51065i | ||||
\(866\) | −16.4963 | + | 28.5724i | −0.560566 | + | 0.970929i | ||||
\(867\) | 87.9395 | 2.98658 | ||||||||
\(868\) | −0.989128 | + | 2.39906i | −0.0335732 | + | 0.0814293i | ||||
\(869\) | 3.65100 | 0.123852 | ||||||||
\(870\) | −19.8994 | + | 34.4668i | −0.674653 | + | 1.16853i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.60263 | + | 14.9002i | 0.291322 | + | 0.504584i | ||||
\(873\) | −0.287834 | + | 0.498543i | −0.00974171 | + | 0.0168731i | ||||
\(874\) | −2.09159 | −0.0707492 | ||||||||
\(875\) | 25.5346 | − | 3.40419i | 0.863227 | − | 0.115083i | ||||
\(876\) | 0.296803 | 0.0100281 | ||||||||
\(877\) | 3.49820 | − | 6.05906i | 0.118126 | − | 0.204600i | −0.800899 | − | 0.598799i | \(-0.795645\pi\) |
0.919025 | + | 0.394199i | \(0.128978\pi\) | |||||||
\(878\) | 24.6461 | + | 42.6883i | 0.831765 | + | 1.44066i | ||||
\(879\) | 11.8732 | + | 20.5650i | 0.400474 | + | 0.693641i | ||||
\(880\) | 8.17292 | − | 14.1559i | 0.275509 | − | 0.477195i | ||||
\(881\) | 25.7746 | 0.868368 | 0.434184 | − | 0.900824i | \(-0.357037\pi\) | ||||
0.434184 | + | 0.900824i | \(0.357037\pi\) | |||||||
\(882\) | 8.03587 | + | 7.98346i | 0.270582 | + | 0.268817i | ||||
\(883\) | 16.4526 | 0.553674 | 0.276837 | − | 0.960917i | \(-0.410714\pi\) | ||||
0.276837 | + | 0.960917i | \(0.410714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −40.9043 | − | 70.8484i | −1.37498 | − | 2.38154i | ||||
\(886\) | 18.2233 | + | 31.5637i | 0.612225 | + | 1.06040i | ||||
\(887\) | −27.6227 | + | 47.8440i | −0.927481 | + | 1.60644i | −0.139958 | + | 0.990157i | \(0.544697\pi\) |
−0.787522 | + | 0.616286i | \(0.788636\pi\) | |||||||
\(888\) | 6.37948 | 0.214081 | ||||||||
\(889\) | −38.5943 | + | 5.14527i | −1.29441 | + | 0.172567i | ||||
\(890\) | 36.3620 | 1.21886 | ||||||||
\(891\) | −7.13611 | + | 12.3601i | −0.239069 | + | 0.414079i | ||||
\(892\) | 2.30585 | + | 3.99385i | 0.0772056 | + | 0.133724i | ||||
\(893\) | −0.422016 | − | 0.730953i | −0.0141222 | − | 0.0244604i | ||||
\(894\) | 14.4497 | − | 25.0277i | 0.483271 | − | 0.837050i | ||||
\(895\) | −19.3590 | −0.647099 | ||||||||
\(896\) | −9.51575 | + | 23.0798i | −0.317899 | + | 0.771041i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.4514 | − | 31.9587i | 0.615731 | − | 1.06648i | ||||
\(899\) | −10.4199 | − | 18.0478i | −0.347523 | − | 0.601927i | ||||
\(900\) | 0.884960 | + | 1.53280i | 0.0294987 | + | 0.0510932i | ||||
\(901\) | 0.309538 | − | 0.536136i | 0.0103122 | − | 0.0178613i | ||||
\(902\) | −7.22241 | −0.240480 | ||||||||
\(903\) | 12.6756 | + | 16.4633i | 0.421817 | + | 0.547865i | ||||
\(904\) | 19.2478 | 0.640171 | ||||||||
\(905\) | 27.6328 | − | 47.8614i | 0.918544 | − | 1.59097i | ||||
\(906\) | 6.50034 | + | 11.2589i | 0.215959 | + | 0.374052i | ||||
\(907\) | −23.9212 | − | 41.4327i | −0.794290 | − | 1.37575i | −0.923289 | − | 0.384107i | \(-0.874510\pi\) |
0.128998 | − | 0.991645i | \(-0.458824\pi\) | |||||||
\(908\) | −1.46347 | + | 2.53480i | −0.0485669 | + | 0.0841204i | ||||
\(909\) | 3.46245 | 0.114842 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.0711 | −0.764380 | −0.382190 | − | 0.924084i | \(-0.624830\pi\) | ||||
−0.382190 | + | 0.924084i | \(0.624830\pi\) | |||||||
\(912\) | 3.46666 | − | 6.00444i | 0.114793 | − | 0.198827i | ||||
\(913\) | 1.48635 | + | 2.57443i | 0.0491909 | + | 0.0852011i | ||||
\(914\) | 26.6785 | + | 46.2085i | 0.882445 | + | 1.52844i | ||||
\(915\) | −27.8819 | + | 48.2928i | −0.921746 | + | 1.59651i | ||||
\(916\) | 3.11277 | 0.102849 | ||||||||
\(917\) | 11.2816 | − | 27.3627i | 0.372552 | − | 0.903597i | ||||
\(918\) | 38.3560 | 1.26594 | ||||||||
\(919\) | 21.7184 | − | 37.6174i | 0.716424 | − | 1.24088i | −0.245984 | − | 0.969274i | \(-0.579111\pi\) |
0.962408 | − | 0.271609i | \(-0.0875557\pi\) | |||||||
\(920\) | 8.65856 | + | 14.9971i | 0.285464 | + | 0.494439i | ||||
\(921\) | −30.0684 | − | 52.0799i | −0.990787 | − | 1.71609i | ||||
\(922\) | 3.29298 | − | 5.70360i | 0.108448 | − | 0.187838i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.30873 | + | 0.174475i | −0.0430539 | + | 0.00573981i | ||||
\(925\) | 8.16249 | 0.268381 | ||||||||
\(926\) | 3.16931 | − | 5.48940i | 0.104150 | − | 0.180393i | ||||
\(927\) | 6.81764 | + | 11.8085i | 0.223921 | + | 0.387842i | ||||
\(928\) | 2.17024 | + | 3.75897i | 0.0712418 | + | 0.123394i | ||||
\(929\) | −6.39095 | + | 11.0695i | −0.209680 | + | 0.363177i | −0.951614 | − | 0.307296i | \(-0.900576\pi\) |
0.741933 | + | 0.670474i | \(0.233909\pi\) | |||||||
\(930\) | 50.6945 | 1.66234 | ||||||||
\(931\) | −1.68917 | + | 6.38757i | −0.0553603 | + | 0.209344i | ||||
\(932\) | 5.54171 | 0.181525 | ||||||||
\(933\) | 0.154428 | − | 0.267478i | 0.00505576 | − | 0.00875683i | ||||
\(934\) | 21.5345 | + | 37.2988i | 0.704629 | + | 1.22045i | ||||
\(935\) | −17.6532 | − | 30.5762i | −0.577320 | − | 0.999948i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.2533 | 0.530971 | 0.265486 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265486 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(938\) | −22.3001 | + | 2.97298i | −0.728124 | + | 0.0970712i | ||||
\(939\) | −21.5694 | −0.703891 | ||||||||
\(940\) | −0.303669 | + | 0.525971i | −0.00990460 | + | 0.0171553i | ||||
\(941\) | −22.5744 | − | 39.1000i | −0.735905 | − | 1.27462i | −0.954325 | − | 0.298770i | \(-0.903424\pi\) |
0.218420 | − | 0.975855i | \(-0.429910\pi\) | |||||||
\(942\) | 12.4132 | + | 21.5003i | 0.404445 | + | 0.700519i | ||||
\(943\) | 3.45831 | − | 5.98997i | 0.112618 | − | 0.195060i | ||||
\(944\) | 40.0752 | 1.30434 | ||||||||
\(945\) | 13.2559 | − | 32.1512i | 0.431215 | − | 1.04588i | ||||
\(946\) | 6.58911 | 0.214230 | ||||||||
\(947\) | −9.92787 | + | 17.1956i | −0.322612 | + | 0.558781i | −0.981026 | − | 0.193875i | \(-0.937894\pi\) |
0.658414 | + | 0.752656i | \(0.271228\pi\) | |||||||
\(948\) | −0.557172 | − | 0.965050i | −0.0180961 | − | 0.0313434i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.90689 | − | 8.49898i | 0.159200 | − | 0.275743i | ||||
\(951\) | −3.08901 | −0.100168 | ||||||||
\(952\) | 36.8068 | + | 47.8055i | 1.19292 | + | 1.54938i | ||||
\(953\) | 15.7287 | 0.509501 | 0.254751 | − | 0.967007i | \(-0.418007\pi\) | ||||
0.254751 | + | 0.967007i | \(0.418007\pi\) | |||||||
\(954\) | −0.0647220 | + | 0.112102i | −0.00209545 | + | 0.00362943i | ||||
\(955\) | 8.46673 | + | 14.6648i | 0.273977 | + | 0.474542i | ||||
\(956\) | −0.823724 | − | 1.42673i | −0.0266412 | − | 0.0461438i | ||||
\(957\) | 5.30159 | − | 9.18262i | 0.171376 | − | 0.296832i | ||||
\(958\) | −24.2470 | −0.783385 | ||||||||
\(959\) | 28.4572 | + | 36.9609i | 0.918932 | + | 1.19353i | ||||
\(960\) | −62.9734 | −2.03246 | ||||||||
\(961\) | 2.22744 | − | 3.85804i | 0.0718529 | − | 0.124453i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.95285 | + | 6.84653i | 0.127379 | + | 0.220626i | ||||
\(964\) | −1.73216 | + | 3.00019i | −0.0557891 | + | 0.0966296i | ||||
\(965\) | −75.0629 | −2.41636 | ||||||||
\(966\) | −4.58149 | + | 11.1121i | −0.147407 | + | 0.357525i | ||||
\(967\) | 52.1912 | 1.67835 | 0.839177 | − | 0.543858i | \(-0.183037\pi\) | ||||
0.839177 | + | 0.543858i | \(0.183037\pi\) | |||||||
\(968\) | 13.7972 | − | 23.8974i | 0.443458 | − | 0.768091i | ||||
\(969\) | −7.48786 | − | 12.9693i | −0.240545 | − | 0.416635i | ||||
\(970\) | −1.14841 | − | 1.98910i | −0.0368732 | − | 0.0638663i | ||||
\(971\) | 11.2292 | − | 19.4495i | 0.360362 | − | 0.624165i | −0.627658 | − | 0.778489i | \(-0.715987\pi\) |
0.988020 | + | 0.154324i | \(0.0493198\pi\) | |||||||
\(972\) | 2.25207 | 0.0722350 | ||||||||
\(973\) | 15.3605 | − | 2.04782i | 0.492436 | − | 0.0656500i | ||||
\(974\) | 23.6765 | 0.758645 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.6584 | − | 23.6570i | −0.437193 | − | 0.757241i | ||||
\(977\) | −20.5172 | − | 35.5369i | −0.656405 | − | 1.13693i | −0.981540 | − | 0.191259i | \(-0.938743\pi\) |
0.325135 | − | 0.945668i | \(-0.394590\pi\) | |||||||
\(978\) | −16.5918 | + | 28.7378i | −0.530546 | + | 0.918933i | ||||
\(979\) | −9.68755 | −0.309616 | ||||||||
\(980\) | 4.58825 | − | 1.24552i | 0.146566 | − | 0.0397866i | ||||
\(981\) | −7.02404 | −0.224260 | ||||||||
\(982\) | 2.59871 | − | 4.50110i | 0.0829282 | − | 0.143636i | ||||
\(983\) | −13.4164 | − | 23.2379i | −0.427916 | − | 0.741173i | 0.568772 | − | 0.822496i | \(-0.307419\pi\) |
−0.996688 | + | 0.0813229i | \(0.974085\pi\) | |||||||
\(984\) | 12.6819 | + | 21.9658i | 0.404285 | + | 0.700243i | ||||
\(985\) | 10.3681 | − | 17.9581i | 0.330356 | − | 0.572193i | ||||
\(986\) | −42.1107 | −1.34108 | ||||||||
\(987\) | −4.80775 | + | 0.640954i | −0.153032 | + | 0.0204018i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.15506 | + | 5.46473i | −0.100325 | + | 0.173768i | ||||
\(990\) | 3.69114 | + | 6.39324i | 0.117312 | + | 0.203191i | ||||
\(991\) | −5.18755 | − | 8.98510i | −0.164788 | − | 0.285421i | 0.771792 | − | 0.635875i | \(-0.219361\pi\) |
−0.936580 | + | 0.350454i | \(0.886027\pi\) | |||||||
\(992\) | 2.76439 | − | 4.78807i | 0.0877696 | − | 0.152021i | ||||
\(993\) | −51.7669 | −1.64277 | ||||||||
\(994\) | 15.4983 | − | 37.5899i | 0.491575 | − | 1.19228i | ||||
\(995\) | −37.8833 | −1.20098 | ||||||||
\(996\) | 0.453656 | − | 0.785755i | 0.0143746 | − | 0.0248976i | ||||
\(997\) | 26.9549 | + | 46.6872i | 0.853669 | + | 1.47860i | 0.877874 | + | 0.478891i | \(0.158961\pi\) |
−0.0242056 | + | 0.999707i | \(0.507706\pi\) | |||||||
\(998\) | 8.50671 | + | 14.7341i | 0.269275 | + | 0.466398i | ||||
\(999\) | 1.94540 | − | 3.36954i | 0.0615499 | − | 0.106607i |
(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 | 1183.2.e.j.170.9 | 24 | ||
7.2 | even | 3 | 8281.2.a.cp.1.4 | 12 | |||
7.4 | even | 3 | inner | 1183.2.e.j.508.9 | 24 | ||
7.5 | odd | 6 | 8281.2.a.co.1.4 | 12 | |||
13.2 | odd | 12 | 91.2.u.b.30.5 | yes | 12 | ||
13.7 | odd | 12 | 91.2.k.b.23.2 | yes | 12 | ||
13.12 | even | 2 | inner | 1183.2.e.j.170.4 | 24 | ||
39.2 | even | 12 | 819.2.do.e.667.2 | 12 | |||
39.20 | even | 12 | 819.2.bm.f.478.5 | 12 | |||
91.2 | odd | 12 | 637.2.q.g.589.2 | 12 | |||
91.12 | odd | 6 | 8281.2.a.co.1.9 | 12 | |||
91.20 | even | 12 | 637.2.k.i.569.2 | 12 | |||
91.25 | even | 6 | inner | 1183.2.e.j.508.4 | 24 | ||
91.33 | even | 12 | 637.2.q.i.491.2 | 12 | |||
91.41 | even | 12 | 637.2.u.g.30.5 | 12 | |||
91.46 | odd | 12 | 91.2.u.b.88.5 | yes | 12 | ||
91.51 | even | 6 | 8281.2.a.cp.1.9 | 12 | |||
91.54 | even | 12 | 637.2.q.i.589.2 | 12 | |||
91.59 | even | 12 | 637.2.u.g.361.5 | 12 | |||
91.67 | odd | 12 | 91.2.k.b.4.5 | ✓ | 12 | ||
91.72 | odd | 12 | 637.2.q.g.491.2 | 12 | |||
91.80 | even | 12 | 637.2.k.i.459.5 | 12 | |||
273.137 | even | 12 | 819.2.do.e.361.2 | 12 | |||
273.158 | even | 12 | 819.2.bm.f.550.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.k.b.4.5 | ✓ | 12 | 91.67 | odd | 12 | ||
91.2.k.b.23.2 | yes | 12 | 13.7 | odd | 12 | ||
91.2.u.b.30.5 | yes | 12 | 13.2 | odd | 12 | ||
91.2.u.b.88.5 | yes | 12 | 91.46 | odd | 12 | ||
637.2.k.i.459.5 | 12 | 91.80 | even | 12 | |||
637.2.k.i.569.2 | 12 | 91.20 | even | 12 | |||
637.2.q.g.491.2 | 12 | 91.72 | odd | 12 | |||
637.2.q.g.589.2 | 12 | 91.2 | odd | 12 | |||
637.2.q.i.491.2 | 12 | 91.33 | even | 12 | |||
637.2.q.i.589.2 | 12 | 91.54 | even | 12 | |||
637.2.u.g.30.5 | 12 | 91.41 | even | 12 | |||
637.2.u.g.361.5 | 12 | 91.59 | even | 12 | |||
819.2.bm.f.478.5 | 12 | 39.20 | even | 12 | |||
819.2.bm.f.550.2 | 12 | 273.158 | even | 12 | |||
819.2.do.e.361.2 | 12 | 273.137 | even | 12 | |||
819.2.do.e.667.2 | 12 | 39.2 | even | 12 | |||
1183.2.e.j.170.4 | 24 | 13.12 | even | 2 | inner | ||
1183.2.e.j.170.9 | 24 | 1.1 | even | 1 | trivial | ||
1183.2.e.j.508.4 | 24 | 91.25 | even | 6 | inner | ||
1183.2.e.j.508.9 | 24 | 7.4 | even | 3 | inner | ||
8281.2.a.co.1.4 | 12 | 7.5 | odd | 6 | |||
8281.2.a.co.1.9 | 12 | 91.12 | odd | 6 | |||
8281.2.a.cp.1.4 | 12 | 7.2 | even | 3 | |||
8281.2.a.cp.1.9 | 12 | 91.51 | even | 6 |