Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(701,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.e (of order \(2\), degree \(1\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.9 | ||
Character | \(\chi\) | \(=\) | 1050.701 |
Dual form | 1050.3.e.e.701.11 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −2.46556 | + | 1.70910i | −0.821853 | + | 0.569700i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.41703 | + | 3.48683i | 0.402838 | + | 0.581138i | ||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.15796 | − | 8.42777i | 0.350885 | − | 0.936419i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.66621i | − | 0.242382i | −0.992629 | − | 0.121191i | \(-0.961329\pi\) | ||
0.992629 | − | 0.121191i | \(-0.0386714\pi\) | |||||||
\(12\) | 4.93112 | − | 3.41820i | 0.410927 | − | 0.284850i | ||||
\(13\) | 5.56242 | 0.427878 | 0.213939 | − | 0.976847i | \(-0.431371\pi\) | ||||
0.213939 | + | 0.976847i | \(0.431371\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 18.5525i | 1.09132i | 0.838005 | + | 0.545662i | \(0.183722\pi\) | ||||
−0.838005 | + | 0.545662i | \(0.816278\pi\) | |||||||
\(18\) | −11.9187 | − | 4.46603i | −0.662148 | − | 0.248113i | ||||
\(19\) | −0.634999 | −0.0334210 | −0.0167105 | − | 0.999860i | \(-0.505319\pi\) | ||||
−0.0167105 | + | 0.999860i | \(0.505319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.52326 | − | 4.52185i | 0.310631 | − | 0.215326i | ||||
\(22\) | −3.77058 | −0.171390 | ||||||||
\(23\) | − | 15.6144i | − | 0.678885i | −0.940627 | − | 0.339442i | \(-0.889762\pi\) | ||
0.940627 | − | 0.339442i | \(-0.110238\pi\) | |||||||
\(24\) | −4.83406 | − | 6.97365i | −0.201419 | − | 0.290569i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 7.86645i | − | 0.302556i | ||||||
\(27\) | 6.61774 | + | 26.1764i | 0.245101 | + | 0.969497i | ||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | − | 43.3517i | − | 1.49489i | −0.664325 | − | 0.747444i | \(-0.731281\pi\) | ||
0.664325 | − | 0.747444i | \(-0.268719\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 13.5411 | 0.436811 | 0.218406 | − | 0.975858i | \(-0.429914\pi\) | ||||
0.218406 | + | 0.975858i | \(0.429914\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 4.55681 | + | 6.57369i | 0.138085 | + | 0.199203i | ||||
\(34\) | 26.2372 | 0.771683 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.31593 | + | 16.8555i | −0.175442 | + | 0.468209i | ||||
\(37\) | −35.0014 | −0.945984 | −0.472992 | − | 0.881067i | \(-0.656826\pi\) | ||||
−0.472992 | + | 0.881067i | \(0.656826\pi\) | |||||||
\(38\) | 0.898024i | 0.0236322i | ||||||||
\(39\) | −13.7145 | + | 9.50672i | −0.351653 | + | 0.243762i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 15.6116i | − | 0.380770i | −0.981710 | − | 0.190385i | \(-0.939026\pi\) | ||
0.981710 | − | 0.190385i | \(-0.0609736\pi\) | |||||||
\(42\) | −6.39486 | − | 9.22528i | −0.152259 | − | 0.219649i | ||||
\(43\) | 64.4699 | 1.49930 | 0.749650 | − | 0.661835i | \(-0.230222\pi\) | ||||
0.749650 | + | 0.661835i | \(0.230222\pi\) | |||||||
\(44\) | 5.33241i | 0.121191i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22.0820 | −0.480044 | ||||||||
\(47\) | 52.5576i | 1.11825i | 0.829084 | + | 0.559124i | \(0.188862\pi\) | ||||
−0.829084 | + | 0.559124i | \(0.811138\pi\) | |||||||
\(48\) | −9.86224 | + | 6.83639i | −0.205463 | + | 0.142425i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −31.7081 | − | 45.7423i | −0.621727 | − | 0.896908i | ||||
\(52\) | −11.1248 | −0.213939 | ||||||||
\(53\) | 51.6056i | 0.973691i | 0.873488 | + | 0.486846i | \(0.161853\pi\) | ||||
−0.873488 | + | 0.486846i | \(0.838147\pi\) | |||||||
\(54\) | 37.0191 | − | 9.35890i | 0.685538 | − | 0.173313i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | 1.56563 | − | 1.08528i | 0.0274672 | − | 0.0190399i | ||||
\(58\) | −61.3086 | −1.05705 | ||||||||
\(59\) | 32.9384i | 0.558277i | 0.960251 | + | 0.279139i | \(0.0900489\pi\) | ||||
−0.960251 | + | 0.279139i | \(0.909951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −104.197 | −1.70815 | −0.854077 | − | 0.520147i | \(-0.825877\pi\) | ||||
−0.854077 | + | 0.520147i | \(0.825877\pi\) | |||||||
\(62\) | − | 19.1501i | − | 0.308872i | ||||||
\(63\) | −8.35519 | + | 22.2978i | −0.132622 | + | 0.353933i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9.29660 | − | 6.44430i | 0.140858 | − | 0.0976409i | ||||
\(67\) | −113.588 | −1.69535 | −0.847673 | − | 0.530519i | \(-0.821997\pi\) | ||||
−0.847673 | + | 0.530519i | \(0.821997\pi\) | |||||||
\(68\) | − | 37.1050i | − | 0.545662i | ||||||
\(69\) | 26.6865 | + | 38.4981i | 0.386760 | + | 0.557944i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36.8746i | 0.519361i | 0.965695 | + | 0.259680i | \(0.0836172\pi\) | ||||
−0.965695 | + | 0.259680i | \(0.916383\pi\) | |||||||
\(72\) | 23.8373 | + | 8.93207i | 0.331074 | + | 0.124057i | ||||
\(73\) | −144.926 | −1.98529 | −0.992645 | − | 0.121058i | \(-0.961371\pi\) | ||||
−0.992645 | + | 0.121058i | \(0.961371\pi\) | |||||||
\(74\) | 49.4995i | 0.668912i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.27000 | 0.0167105 | ||||||||
\(77\) | 7.05412i | 0.0916119i | ||||||||
\(78\) | 13.4445 | + | 19.3952i | 0.172366 | + | 0.248656i | ||||
\(79\) | −57.9487 | −0.733528 | −0.366764 | − | 0.930314i | \(-0.619534\pi\) | ||||
−0.366764 | + | 0.930314i | \(0.619534\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −61.0545 | − | 53.2292i | −0.753760 | − | 0.657150i | ||||
\(82\) | −22.0781 | −0.269245 | ||||||||
\(83\) | 45.0936i | 0.543296i | 0.962397 | + | 0.271648i | \(0.0875686\pi\) | ||||
−0.962397 | + | 0.271648i | \(0.912431\pi\) | |||||||
\(84\) | −13.0465 | + | 9.04370i | −0.155316 | + | 0.107663i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 91.1742i | − | 1.06016i | ||||||
\(87\) | 74.0924 | + | 106.886i | 0.851637 | + | 1.22858i | ||||
\(88\) | 7.54117 | 0.0856951 | ||||||||
\(89\) | − | 80.9733i | − | 0.909813i | −0.890539 | − | 0.454906i | \(-0.849673\pi\) | ||
0.890539 | − | 0.454906i | \(-0.150327\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.7168 | −0.161723 | ||||||||
\(92\) | 31.2287i | 0.339442i | ||||||||
\(93\) | −33.3865 | + | 23.1432i | −0.358995 | + | 0.248851i | ||||
\(94\) | 74.3277 | 0.790720 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.66812 | + | 13.9473i | 0.100710 | + | 0.145284i | ||||
\(97\) | −96.2255 | −0.992016 | −0.496008 | − | 0.868318i | \(-0.665201\pi\) | ||||
−0.496008 | + | 0.868318i | \(0.665201\pi\) | |||||||
\(98\) | − | 9.89949i | − | 0.101015i | ||||||
\(99\) | −22.4702 | − | 8.41978i | −0.226971 | − | 0.0850483i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 91.9696i | 0.910590i | 0.890341 | + | 0.455295i | \(0.150466\pi\) | ||||
−0.890341 | + | 0.455295i | \(0.849534\pi\) | |||||||
\(102\) | −64.6894 | + | 44.8420i | −0.634210 | + | 0.439627i | ||||
\(103\) | 30.6043 | 0.297129 | 0.148565 | − | 0.988903i | \(-0.452535\pi\) | ||||
0.148565 | + | 0.988903i | \(0.452535\pi\) | |||||||
\(104\) | 15.7329i | 0.151278i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 72.9814 | 0.688504 | ||||||||
\(107\) | 190.645i | 1.78173i | 0.454270 | + | 0.890864i | \(0.349900\pi\) | ||||
−0.454270 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(108\) | −13.2355 | − | 52.3529i | −0.122551 | − | 0.484749i | ||||
\(109\) | −73.9965 | −0.678867 | −0.339433 | − | 0.940630i | \(-0.610235\pi\) | ||||
−0.339433 | + | 0.940630i | \(0.610235\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 86.2980 | − | 59.8208i | 0.777460 | − | 0.538927i | ||||
\(112\) | −10.5830 | −0.0944911 | ||||||||
\(113\) | 128.861i | 1.14037i | 0.821518 | + | 0.570183i | \(0.193128\pi\) | ||||
−0.821518 | + | 0.570183i | \(0.806872\pi\) | |||||||
\(114\) | −1.53481 | − | 2.21413i | −0.0134633 | − | 0.0194222i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 86.7035i | 0.747444i | ||||||||
\(117\) | 17.5659 | − | 46.8788i | 0.150136 | − | 0.400673i | ||||
\(118\) | 46.5819 | 0.394762 | ||||||||
\(119\) | − | 49.0853i | − | 0.412482i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 113.891 | 0.941251 | ||||||||
\(122\) | 147.357i | 1.20785i | ||||||||
\(123\) | 26.6817 | + | 38.4912i | 0.216924 | + | 0.312937i | ||||
\(124\) | −27.0823 | −0.218406 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 31.5338 | + | 11.8160i | 0.250268 | + | 0.0937779i | ||||
\(127\) | −95.8035 | −0.754358 | −0.377179 | − | 0.926140i | \(-0.623106\pi\) | ||||
−0.377179 | + | 0.926140i | \(0.623106\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −158.954 | + | 110.185i | −1.23220 | + | 0.854150i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 148.465i | 1.13332i | 0.823952 | + | 0.566660i | \(0.191765\pi\) | ||||
−0.823952 | + | 0.566660i | \(0.808235\pi\) | |||||||
\(132\) | −9.11361 | − | 13.1474i | −0.0690425 | − | 0.0996013i | ||||
\(133\) | 1.68005 | 0.0126320 | ||||||||
\(134\) | 160.638i | 1.19879i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −52.4744 | −0.385842 | ||||||||
\(137\) | − | 115.295i | − | 0.841572i | −0.907160 | − | 0.420786i | \(-0.861754\pi\) | ||
0.907160 | − | 0.420786i | \(-0.138246\pi\) | |||||||
\(138\) | 54.4445 | − | 37.7404i | 0.394526 | − | 0.273481i | ||||
\(139\) | −95.1005 | −0.684176 | −0.342088 | − | 0.939668i | \(-0.611134\pi\) | ||||
−0.342088 | + | 0.939668i | \(0.611134\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −89.8262 | − | 129.584i | −0.637065 | − | 0.919035i | ||||
\(142\) | 52.1486 | 0.367244 | ||||||||
\(143\) | − | 14.8305i | − | 0.103710i | ||||||
\(144\) | 12.6319 | − | 33.7111i | 0.0877212 | − | 0.234105i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 204.957i | 1.40381i | ||||||||
\(147\) | −17.2589 | + | 11.9637i | −0.117408 | + | 0.0813857i | ||||
\(148\) | 70.0028 | 0.472992 | ||||||||
\(149\) | − | 179.342i | − | 1.20364i | −0.798632 | − | 0.601820i | \(-0.794442\pi\) | ||
0.798632 | − | 0.601820i | \(-0.205558\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 45.6621 | 0.302398 | 0.151199 | − | 0.988503i | \(-0.451687\pi\) | ||||
0.151199 | + | 0.988503i | \(0.451687\pi\) | |||||||
\(152\) | − | 1.79605i | − | 0.0118161i | ||||||
\(153\) | 156.356 | + | 58.5882i | 1.02194 | + | 0.382929i | ||||
\(154\) | 9.97603 | 0.0647794 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 27.4289 | − | 19.0134i | 0.175827 | − | 0.121881i | ||||
\(157\) | 223.977 | 1.42661 | 0.713303 | − | 0.700856i | \(-0.247198\pi\) | ||||
0.713303 | + | 0.700856i | \(0.247198\pi\) | |||||||
\(158\) | 81.9518i | 0.518683i | ||||||||
\(159\) | −88.1991 | − | 127.237i | −0.554711 | − | 0.800231i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 41.3117i | 0.256594i | ||||||||
\(162\) | −75.2774 | + | 86.3441i | −0.464675 | + | 0.532989i | ||||
\(163\) | −300.309 | −1.84239 | −0.921195 | − | 0.389102i | \(-0.872785\pi\) | ||||
−0.921195 | + | 0.389102i | \(0.872785\pi\) | |||||||
\(164\) | 31.2231i | 0.190385i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 63.7719 | 0.384168 | ||||||||
\(167\) | 125.443i | 0.751158i | 0.926790 | + | 0.375579i | \(0.122556\pi\) | ||||
−0.926790 | + | 0.375579i | \(0.877444\pi\) | |||||||
\(168\) | 12.7897 | + | 18.4506i | 0.0761293 | + | 0.109825i | ||||
\(169\) | −138.060 | −0.816920 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00530 | + | 5.35163i | −0.0117269 | + | 0.0312961i | ||||
\(172\) | −128.940 | −0.749650 | ||||||||
\(173\) | − | 195.635i | − | 1.13084i | −0.824804 | − | 0.565419i | \(-0.808714\pi\) | ||
0.824804 | − | 0.565419i | \(-0.191286\pi\) | |||||||
\(174\) | 151.160 | − | 104.782i | 0.868736 | − | 0.602198i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 10.6648i | − | 0.0605956i | ||||||
\(177\) | −56.2949 | − | 81.2115i | −0.318050 | − | 0.458822i | ||||
\(178\) | −114.514 | −0.643335 | ||||||||
\(179\) | 164.110i | 0.916815i | 0.888742 | + | 0.458408i | \(0.151580\pi\) | ||||
−0.888742 | + | 0.458408i | \(0.848420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 113.029 | 0.624468 | 0.312234 | − | 0.950005i | \(-0.398923\pi\) | ||||
0.312234 | + | 0.950005i | \(0.398923\pi\) | |||||||
\(182\) | 20.8127i | 0.114355i | ||||||||
\(183\) | 256.905 | − | 178.084i | 1.40385 | − | 0.973135i | ||||
\(184\) | 44.1641 | 0.240022 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 32.7294 | + | 47.2156i | 0.175964 | + | 0.253847i | ||||
\(187\) | 49.4648 | 0.264518 | ||||||||
\(188\) | − | 105.115i | − | 0.559124i | ||||||
\(189\) | −17.5089 | − | 69.2563i | −0.0926397 | − | 0.366436i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 196.398i | 1.02826i | 0.857711 | + | 0.514132i | \(0.171886\pi\) | ||||
−0.857711 | + | 0.514132i | \(0.828114\pi\) | |||||||
\(192\) | 19.7245 | − | 13.6728i | 0.102732 | − | 0.0712124i | ||||
\(193\) | −282.304 | −1.46272 | −0.731358 | − | 0.681994i | \(-0.761113\pi\) | ||||
−0.731358 | + | 0.681994i | \(0.761113\pi\) | |||||||
\(194\) | 136.083i | 0.701461i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | − | 286.761i | − | 1.45564i | −0.685767 | − | 0.727821i | \(-0.740533\pi\) | ||
0.685767 | − | 0.727821i | \(-0.259467\pi\) | |||||||
\(198\) | −11.9074 | + | 31.7776i | −0.0601382 | + | 0.160493i | ||||
\(199\) | 74.9133 | 0.376449 | 0.188224 | − | 0.982126i | \(-0.439727\pi\) | ||||
0.188224 | + | 0.982126i | \(0.439727\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 280.058 | − | 194.133i | 1.39333 | − | 0.965838i | ||||
\(202\) | 130.065 | 0.643884 | ||||||||
\(203\) | 114.698i | 0.565014i | ||||||||
\(204\) | 63.4162 | + | 91.4847i | 0.310864 | + | 0.448454i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 43.2810i | − | 0.210102i | ||||||
\(207\) | −131.594 | − | 49.3096i | −0.635720 | − | 0.238210i | ||||
\(208\) | 22.2497 | 0.106970 | ||||||||
\(209\) | 1.69304i | 0.00810066i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −136.746 | −0.648083 | −0.324042 | − | 0.946043i | \(-0.605042\pi\) | ||||
−0.324042 | + | 0.946043i | \(0.605042\pi\) | |||||||
\(212\) | − | 103.211i | − | 0.486846i | ||||||
\(213\) | −63.0224 | − | 90.9166i | −0.295880 | − | 0.426838i | ||||
\(214\) | 269.613 | 1.25987 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −74.0381 | + | 18.7178i | −0.342769 | + | 0.0866565i | ||||
\(217\) | −35.8265 | −0.165099 | ||||||||
\(218\) | 104.647i | 0.480031i | ||||||||
\(219\) | 357.324 | − | 247.693i | 1.63162 | − | 1.13102i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 103.197i | 0.466954i | ||||||||
\(222\) | −84.5994 | − | 122.044i | −0.381079 | − | 0.549747i | ||||
\(223\) | 25.8662 | 0.115992 | 0.0579959 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579959 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 182.238 | 0.806361 | ||||||||
\(227\) | 24.3393i | 0.107222i | 0.998562 | + | 0.0536109i | \(0.0170730\pi\) | ||||
−0.998562 | + | 0.0536109i | \(0.982927\pi\) | |||||||
\(228\) | −3.13126 | + | 2.17055i | −0.0137336 | + | 0.00951997i | ||||
\(229\) | 241.018 | 1.05248 | 0.526239 | − | 0.850336i | \(-0.323602\pi\) | ||||
0.526239 | + | 0.850336i | \(0.323602\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0562 | − | 17.3923i | −0.0521913 | − | 0.0752915i | ||||
\(232\) | 122.617 | 0.528523 | ||||||||
\(233\) | − | 24.9582i | − | 0.107117i | −0.998565 | − | 0.0535584i | \(-0.982944\pi\) | ||
0.998565 | − | 0.0535584i | \(-0.0170563\pi\) | |||||||
\(234\) | −66.2966 | − | 24.8420i | −0.283319 | − | 0.106162i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 65.8767i | − | 0.279139i | ||||||
\(237\) | 142.876 | − | 99.0401i | 0.602852 | − | 0.417891i | ||||
\(238\) | −69.4172 | −0.291669 | ||||||||
\(239\) | 240.780i | 1.00745i | 0.863864 | + | 0.503725i | \(0.168037\pi\) | ||||
−0.863864 | + | 0.503725i | \(0.831963\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −147.382 | −0.611543 | −0.305771 | − | 0.952105i | \(-0.598914\pi\) | ||||
−0.305771 | + | 0.952105i | \(0.598914\pi\) | |||||||
\(242\) | − | 161.067i | − | 0.665565i | ||||||
\(243\) | 241.507 | + | 26.8914i | 0.993858 | + | 0.110664i | ||||
\(244\) | 208.395 | 0.854077 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 54.4348 | − | 37.7336i | 0.221280 | − | 0.153389i | ||||
\(247\) | −3.53213 | −0.0143001 | ||||||||
\(248\) | 38.3001i | 0.154436i | ||||||||
\(249\) | −77.0693 | − | 111.181i | −0.309515 | − | 0.446509i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 387.525i | − | 1.54393i | −0.635668 | − | 0.771963i | \(-0.719275\pi\) | ||
0.635668 | − | 0.771963i | \(-0.280725\pi\) | |||||||
\(252\) | 16.7104 | − | 44.5956i | 0.0663110 | − | 0.176966i | ||||
\(253\) | −41.6311 | −0.164550 | ||||||||
\(254\) | 135.487i | 0.533412i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 11.2525i | − | 0.0437839i | −0.999760 | − | 0.0218919i | \(-0.993031\pi\) | ||
0.999760 | − | 0.0218919i | \(-0.00696897\pi\) | |||||||
\(258\) | 155.826 | + | 224.795i | 0.603975 | + | 0.871300i | ||||
\(259\) | 92.6050 | 0.357548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −365.358 | − | 136.903i | −1.39984 | − | 0.524533i | ||||
\(262\) | 209.961 | 0.801378 | ||||||||
\(263\) | − | 308.658i | − | 1.17361i | −0.809730 | − | 0.586803i | \(-0.800386\pi\) | ||
0.809730 | − | 0.586803i | \(-0.199614\pi\) | |||||||
\(264\) | −18.5932 | + | 12.8886i | −0.0704288 | + | 0.0488204i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 2.37595i | − | 0.00893214i | ||||||
\(267\) | 138.391 | + | 199.644i | 0.518320 | + | 0.747732i | ||||
\(268\) | 227.176 | 0.847673 | ||||||||
\(269\) | 198.926i | 0.739503i | 0.929131 | + | 0.369751i | \(0.120557\pi\) | ||||
−0.929131 | + | 0.369751i | \(0.879443\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −176.341 | −0.650706 | −0.325353 | − | 0.945593i | \(-0.605483\pi\) | ||||
−0.325353 | + | 0.945593i | \(0.605483\pi\) | |||||||
\(272\) | 74.2101i | 0.272831i | ||||||||
\(273\) | 36.2851 | − | 25.1524i | 0.132912 | − | 0.0921334i | ||||
\(274\) | −163.052 | −0.595082 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −53.3729 | − | 76.9962i | −0.193380 | − | 0.278972i | ||||
\(277\) | −433.093 | −1.56351 | −0.781757 | − | 0.623583i | \(-0.785676\pi\) | ||||
−0.781757 | + | 0.623583i | \(0.785676\pi\) | |||||||
\(278\) | 134.492i | 0.483786i | ||||||||
\(279\) | 42.7624 | − | 114.122i | 0.153270 | − | 0.409038i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 281.134i | 1.00048i | 0.865887 | + | 0.500239i | \(0.166754\pi\) | ||||
−0.865887 | + | 0.500239i | \(0.833246\pi\) | |||||||
\(282\) | −183.259 | + | 127.033i | −0.649856 | + | 0.450473i | ||||
\(283\) | 113.795 | 0.402101 | 0.201050 | − | 0.979581i | \(-0.435565\pi\) | ||||
0.201050 | + | 0.979581i | \(0.435565\pi\) | |||||||
\(284\) | − | 73.7492i | − | 0.259680i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.9736 | −0.0733341 | ||||||||
\(287\) | 41.3043i | 0.143917i | ||||||||
\(288\) | −47.6747 | − | 17.8641i | −0.165537 | − | 0.0620283i | ||||
\(289\) | −55.1959 | −0.190989 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 237.250 | − | 164.459i | 0.815291 | − | 0.565151i | ||||
\(292\) | 289.852 | 0.992645 | ||||||||
\(293\) | − | 355.330i | − | 1.21273i | −0.795187 | − | 0.606365i | \(-0.792627\pi\) | ||
0.795187 | − | 0.606365i | \(-0.207373\pi\) | |||||||
\(294\) | 16.9192 | + | 24.4078i | 0.0575483 | + | 0.0830197i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 98.9989i | − | 0.334456i | ||||||
\(297\) | 69.7917 | − | 17.6443i | 0.234989 | − | 0.0594083i | ||||
\(298\) | −253.628 | −0.851102 | ||||||||
\(299\) | − | 86.8535i | − | 0.290480i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −170.571 | −0.566682 | ||||||||
\(302\) | − | 64.5759i | − | 0.213828i | ||||||
\(303\) | −157.185 | − | 226.756i | −0.518763 | − | 0.748371i | ||||
\(304\) | −2.54000 | −0.00835525 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 82.8562 | − | 221.121i | 0.270772 | − | 0.722618i | ||||
\(307\) | 404.490 | 1.31756 | 0.658778 | − | 0.752337i | \(-0.271074\pi\) | ||||
0.658778 | + | 0.752337i | \(0.271074\pi\) | |||||||
\(308\) | − | 14.1082i | − | 0.0458059i | ||||||
\(309\) | −75.4567 | + | 52.3058i | −0.244196 | + | 0.169274i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 530.330i | 1.70524i | 0.522530 | + | 0.852621i | \(0.324988\pi\) | ||||
−0.522530 | + | 0.852621i | \(0.675012\pi\) | |||||||
\(312\) | −26.8891 | − | 38.7904i | −0.0861829 | − | 0.124328i | ||||
\(313\) | 561.172 | 1.79288 | 0.896440 | − | 0.443165i | \(-0.146144\pi\) | ||||
0.896440 | + | 0.443165i | \(0.146144\pi\) | |||||||
\(314\) | − | 316.751i | − | 1.00876i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 115.897 | 0.366764 | ||||||||
\(317\) | − | 264.560i | − | 0.834574i | −0.908775 | − | 0.417287i | \(-0.862981\pi\) | ||
0.908775 | − | 0.417287i | \(-0.137019\pi\) | |||||||
\(318\) | −179.940 | + | 124.732i | −0.565849 | + | 0.392240i | ||||
\(319\) | −115.585 | −0.362334 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −325.831 | − | 470.046i | −1.01505 | − | 1.46432i | ||||
\(322\) | 58.4236 | 0.181440 | ||||||||
\(323\) | − | 11.7808i | − | 0.0364732i | ||||||
\(324\) | 122.109 | + | 106.458i | 0.376880 | + | 0.328575i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 424.702i | 1.30277i | ||||||||
\(327\) | 182.443 | − | 126.467i | 0.557929 | − | 0.386750i | ||||
\(328\) | 44.1561 | 0.134622 | ||||||||
\(329\) | − | 139.054i | − | 0.422658i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 540.436 | 1.63274 | 0.816369 | − | 0.577530i | \(-0.195984\pi\) | ||||
0.816369 | + | 0.577530i | \(0.195984\pi\) | |||||||
\(332\) | − | 90.1871i | − | 0.271648i | ||||||
\(333\) | −110.533 | + | 294.984i | −0.331931 | + | 0.885837i | ||||
\(334\) | 177.404 | 0.531149 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 26.0930 | − | 18.0874i | 0.0776578 | − | 0.0538315i | ||||
\(337\) | 444.323 | 1.31847 | 0.659233 | − | 0.751939i | \(-0.270881\pi\) | ||||
0.659233 | + | 0.751939i | \(0.270881\pi\) | |||||||
\(338\) | 195.246i | 0.577650i | ||||||||
\(339\) | −220.237 | − | 317.715i | −0.649666 | − | 0.937214i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 36.1035i | − | 0.105875i | ||||||
\(342\) | 7.56834 | + | 2.83593i | 0.0221297 | + | 0.00829219i | ||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | 182.348i | 0.530082i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −276.670 | −0.799624 | ||||||||
\(347\) | − | 253.956i | − | 0.731861i | −0.930642 | − | 0.365931i | \(-0.880751\pi\) | ||
0.930642 | − | 0.365931i | \(-0.119249\pi\) | |||||||
\(348\) | −148.185 | − | 213.773i | −0.425818 | − | 0.614289i | ||||
\(349\) | −415.627 | −1.19091 | −0.595454 | − | 0.803389i | \(-0.703028\pi\) | ||||
−0.595454 | + | 0.803389i | \(0.703028\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 36.8106 | + | 145.604i | 0.104874 | + | 0.414827i | ||||
\(352\) | −15.0823 | −0.0428475 | ||||||||
\(353\) | 278.041i | 0.787652i | 0.919185 | + | 0.393826i | \(0.128849\pi\) | ||||
−0.919185 | + | 0.393826i | \(0.871151\pi\) | |||||||
\(354\) | −114.850 | + | 79.6130i | −0.324436 | + | 0.224895i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 161.947i | 0.454906i | ||||||||
\(357\) | 83.8917 | + | 121.023i | 0.234991 | + | 0.339000i | ||||
\(358\) | 232.086 | 0.648286 | ||||||||
\(359\) | 81.6150i | 0.227340i | 0.993519 | + | 0.113670i | \(0.0362606\pi\) | ||||
−0.993519 | + | 0.113670i | \(0.963739\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −360.597 | −0.998883 | ||||||||
\(362\) | − | 159.847i | − | 0.441565i | ||||||
\(363\) | −280.806 | + | 194.652i | −0.773570 | + | 0.536230i | ||||
\(364\) | 29.4335 | 0.0808614 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −251.848 | − | 363.318i | −0.688110 | − | 0.992673i | ||||
\(367\) | −514.501 | −1.40191 | −0.700955 | − | 0.713206i | \(-0.747242\pi\) | ||||
−0.700955 | + | 0.713206i | \(0.747242\pi\) | |||||||
\(368\) | − | 62.4574i | − | 0.169721i | ||||||
\(369\) | −131.571 | − | 49.3007i | −0.356560 | − | 0.133606i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 136.536i | − | 0.368021i | ||||||
\(372\) | 66.7730 | − | 46.2863i | 0.179497 | − | 0.124426i | ||||
\(373\) | −80.1359 | −0.214842 | −0.107421 | − | 0.994214i | \(-0.534259\pi\) | ||||
−0.107421 | + | 0.994214i | \(0.534259\pi\) | |||||||
\(374\) | − | 69.9538i | − | 0.187042i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −148.655 | −0.395360 | ||||||||
\(377\) | − | 241.140i | − | 0.639630i | ||||||
\(378\) | −97.9432 | + | 24.7613i | −0.259109 | + | 0.0655061i | ||||
\(379\) | −706.877 | −1.86511 | −0.932556 | − | 0.361026i | \(-0.882427\pi\) | ||||
−0.932556 | + | 0.361026i | \(0.882427\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 236.209 | − | 163.738i | 0.619972 | − | 0.429758i | ||||
\(382\) | 277.749 | 0.727092 | ||||||||
\(383\) | − | 49.2802i | − | 0.128669i | −0.997928 | − | 0.0643345i | \(-0.979508\pi\) | ||
0.997928 | − | 0.0643345i | \(-0.0204924\pi\) | |||||||
\(384\) | −19.3362 | − | 27.8946i | −0.0503548 | − | 0.0726422i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 399.238i | 1.03430i | ||||||||
\(387\) | 203.594 | − | 543.337i | 0.526081 | − | 1.40397i | ||||
\(388\) | 192.451 | 0.496008 | ||||||||
\(389\) | − | 2.68340i | − | 0.00689821i | −0.999994 | − | 0.00344911i | \(-0.998902\pi\) | ||
0.999994 | − | 0.00344911i | \(-0.00109789\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 289.686 | 0.740884 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | −253.741 | − | 366.049i | −0.645652 | − | 0.931423i | ||||
\(394\) | −405.542 | −1.02929 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 44.9403 | + | 16.8396i | 0.113486 | + | 0.0425241i | ||||
\(397\) | −372.015 | −0.937065 | −0.468532 | − | 0.883446i | \(-0.655217\pi\) | ||||
−0.468532 | + | 0.883446i | \(0.655217\pi\) | |||||||
\(398\) | − | 105.943i | − | 0.266190i | ||||||
\(399\) | −4.14226 | + | 2.87137i | −0.0103816 | + | 0.00719642i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 119.122i | 0.297062i | 0.988908 | + | 0.148531i | \(0.0474545\pi\) | ||||
−0.988908 | + | 0.148531i | \(0.952545\pi\) | |||||||
\(402\) | −274.546 | − | 396.062i | −0.682950 | − | 0.985230i | ||||
\(403\) | 75.3215 | 0.186902 | ||||||||
\(404\) | − | 183.939i | − | 0.455295i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 162.207 | 0.399525 | ||||||||
\(407\) | 93.3209i | 0.229290i | ||||||||
\(408\) | 129.379 | − | 89.6840i | 0.317105 | − | 0.219814i | ||||
\(409\) | −198.033 | −0.484189 | −0.242095 | − | 0.970253i | \(-0.577834\pi\) | ||||
−0.242095 | + | 0.970253i | \(0.577834\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 197.051 | + | 284.268i | 0.479443 | + | 0.691649i | ||||
\(412\) | −61.2086 | −0.148565 | ||||||||
\(413\) | − | 87.1467i | − | 0.211009i | ||||||
\(414\) | −69.7342 | + | 186.102i | −0.168440 | + | 0.449522i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 31.4658i | − | 0.0756389i | ||||||
\(417\) | 234.476 | − | 162.536i | 0.562292 | − | 0.389775i | ||||
\(418\) | 2.39432 | 0.00572803 | ||||||||
\(419\) | − | 229.736i | − | 0.548295i | −0.961688 | − | 0.274148i | \(-0.911604\pi\) | ||
0.961688 | − | 0.274148i | \(-0.0883957\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −590.500 | −1.40261 | −0.701306 | − | 0.712860i | \(-0.747399\pi\) | ||||
−0.701306 | + | 0.712860i | \(0.747399\pi\) | |||||||
\(422\) | 193.387i | 0.458264i | ||||||||
\(423\) | 442.944 | + | 165.975i | 1.04715 | + | 0.392376i | ||||
\(424\) | −145.963 | −0.344252 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −128.575 | + | 89.1271i | −0.301820 | + | 0.209219i | ||||
\(427\) | 275.680 | 0.645622 | ||||||||
\(428\) | − | 381.290i | − | 0.890864i | ||||||
\(429\) | 25.3469 | + | 36.5656i | 0.0590836 | + | 0.0852345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 414.879i | − | 0.962597i | −0.876557 | − | 0.481298i | \(-0.840165\pi\) | ||
0.876557 | − | 0.481298i | \(-0.159835\pi\) | |||||||
\(432\) | 26.4710 | + | 104.706i | 0.0612754 | + | 0.242374i | ||||
\(433\) | 219.764 | 0.507538 | 0.253769 | − | 0.967265i | \(-0.418330\pi\) | ||||
0.253769 | + | 0.967265i | \(0.418330\pi\) | |||||||
\(434\) | 50.6663i | 0.116743i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 147.993 | 0.339433 | ||||||||
\(437\) | 9.91510i | 0.0226890i | ||||||||
\(438\) | −350.291 | − | 505.333i | −0.799751 | − | 1.15373i | ||||
\(439\) | 638.375 | 1.45416 | 0.727079 | − | 0.686554i | \(-0.240877\pi\) | ||||
0.727079 | + | 0.686554i | \(0.240877\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 22.1057 | − | 58.9944i | 0.0501264 | − | 0.133774i | ||||
\(442\) | 145.942 | 0.330186 | ||||||||
\(443\) | 299.160i | 0.675305i | 0.941271 | + | 0.337652i | \(0.109633\pi\) | ||||
−0.941271 | + | 0.337652i | \(0.890367\pi\) | |||||||
\(444\) | −172.596 | + | 119.642i | −0.388730 | + | 0.269463i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 36.5803i | − | 0.0820185i | ||||||
\(447\) | 306.514 | + | 442.179i | 0.685713 | + | 0.989216i | ||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | 580.653i | 1.29321i | 0.762823 | + | 0.646607i | \(0.223813\pi\) | ||||
−0.762823 | + | 0.646607i | \(0.776187\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.6236 | −0.0922918 | ||||||||
\(452\) | − | 257.723i | − | 0.570183i | ||||||
\(453\) | −112.583 | + | 78.0410i | −0.248527 | + | 0.172276i | ||||
\(454\) | 34.4210 | 0.0758172 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.06962 | + | 4.42826i | 0.00673163 | + | 0.00971111i | ||||
\(457\) | −563.314 | −1.23264 | −0.616318 | − | 0.787498i | \(-0.711376\pi\) | ||||
−0.616318 | + | 0.787498i | \(0.711376\pi\) | |||||||
\(458\) | − | 340.850i | − | 0.744215i | ||||||
\(459\) | −485.639 | + | 122.776i | −1.05804 | + | 0.267485i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 138.227i | 0.299842i | 0.988698 | + | 0.149921i | \(0.0479020\pi\) | ||||
−0.988698 | + | 0.149921i | \(0.952098\pi\) | |||||||
\(462\) | −24.5965 | + | 17.0500i | −0.0532391 | + | 0.0369048i | ||||
\(463\) | −154.802 | −0.334346 | −0.167173 | − | 0.985928i | \(-0.553464\pi\) | ||||
−0.167173 | + | 0.985928i | \(0.553464\pi\) | |||||||
\(464\) | − | 173.407i | − | 0.373722i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −35.2963 | −0.0757431 | ||||||||
\(467\) | − | 462.873i | − | 0.991162i | −0.868562 | − | 0.495581i | \(-0.834955\pi\) | ||
0.868562 | − | 0.495581i | \(-0.165045\pi\) | |||||||
\(468\) | −35.1318 | + | 93.7575i | −0.0750680 | + | 0.200337i | ||||
\(469\) | 300.526 | 0.640781 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −552.229 | + | 382.799i | −1.17246 | + | 0.812737i | ||||
\(472\) | −93.1637 | −0.197381 | ||||||||
\(473\) | − | 171.890i | − | 0.363404i | ||||||
\(474\) | −140.064 | − | 202.057i | −0.295493 | − | 0.426281i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 98.1707i | 0.206241i | ||||||||
\(477\) | 434.920 | + | 162.969i | 0.911782 | + | 0.341653i | ||||
\(478\) | 340.515 | 0.712374 | ||||||||
\(479\) | 836.942i | 1.74727i | 0.486582 | + | 0.873635i | \(0.338243\pi\) | ||||
−0.486582 | + | 0.873635i | \(0.661757\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −194.692 | −0.404766 | ||||||||
\(482\) | 208.429i | 0.432426i | ||||||||
\(483\) | −70.6058 | − | 101.856i | −0.146182 | − | 0.210883i | ||||
\(484\) | −227.783 | −0.470625 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 38.0302 | − | 341.543i | 0.0782515 | − | 0.702764i | ||||
\(487\) | 212.042 | 0.435405 | 0.217703 | − | 0.976015i | \(-0.430144\pi\) | ||||
0.217703 | + | 0.976015i | \(0.430144\pi\) | |||||||
\(488\) | − | 294.715i | − | 0.603924i | ||||||
\(489\) | 740.431 | − | 513.258i | 1.51417 | − | 1.04961i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 79.1998i | − | 0.161303i | −0.996742 | − | 0.0806516i | \(-0.974300\pi\) | ||
0.996742 | − | 0.0806516i | \(-0.0257001\pi\) | |||||||
\(492\) | −53.3634 | − | 76.9824i | −0.108462 | − | 0.156468i | ||||
\(493\) | 804.284 | 1.63141 | ||||||||
\(494\) | 4.99519i | 0.0101117i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 54.1646 | 0.109203 | ||||||||
\(497\) | − | 97.5611i | − | 0.196300i | ||||||
\(498\) | −157.233 | + | 108.992i | −0.315730 | + | 0.218860i | ||||
\(499\) | 259.432 | 0.519905 | 0.259952 | − | 0.965621i | \(-0.416293\pi\) | ||||
0.259952 | + | 0.965621i | \(0.416293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −214.395 | − | 309.288i | −0.427934 | − | 0.617341i | ||||
\(502\) | −548.044 | −1.09172 | ||||||||
\(503\) | 175.890i | 0.349683i | 0.984597 | + | 0.174841i | \(0.0559412\pi\) | ||||
−0.984597 | + | 0.174841i | \(0.944059\pi\) | |||||||
\(504\) | −63.0676 | − | 23.6320i | −0.125134 | − | 0.0468890i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 58.8752i | 0.116354i | ||||||||
\(507\) | 340.394 | − | 235.957i | 0.671388 | − | 0.465399i | ||||
\(508\) | 191.607 | 0.377179 | ||||||||
\(509\) | − | 577.094i | − | 1.13378i | −0.823794 | − | 0.566890i | \(-0.808147\pi\) | ||
0.823794 | − | 0.566890i | \(-0.191853\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 383.439 | 0.750369 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −4.20226 | − | 16.6220i | −0.00819154 | − | 0.0324016i | ||||
\(514\) | −15.9134 | −0.0309599 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 317.909 | − | 220.371i | 0.616102 | − | 0.427075i | ||||
\(517\) | 140.129 | 0.271043 | ||||||||
\(518\) | − | 130.963i | − | 0.252825i | ||||||
\(519\) | 334.360 | + | 482.350i | 0.644238 | + | 0.929383i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 198.309i | − | 0.380631i | −0.981723 | − | 0.190316i | \(-0.939049\pi\) | ||
0.981723 | − | 0.190316i | \(-0.0609512\pi\) | |||||||
\(522\) | −193.610 | + | 516.695i | −0.370901 | + | 0.989837i | ||||
\(523\) | −307.722 | −0.588378 | −0.294189 | − | 0.955747i | \(-0.595049\pi\) | ||||
−0.294189 | + | 0.955747i | \(0.595049\pi\) | |||||||
\(524\) | − | 296.930i | − | 0.566660i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −436.509 | −0.829864 | ||||||||
\(527\) | 251.222i | 0.476703i | ||||||||
\(528\) | 18.2272 | + | 26.2947i | 0.0345213 | + | 0.0498007i | ||||
\(529\) | 285.192 | 0.539115 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 277.597 | + | 104.018i | 0.522781 | + | 0.195891i | ||||
\(532\) | −3.36010 | −0.00631598 | ||||||||
\(533\) | − | 86.8380i | − | 0.162923i | ||||||
\(534\) | 282.340 | − | 195.715i | 0.528726 | − | 0.366507i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 321.276i | − | 0.599395i | ||||||
\(537\) | −280.480 | − | 404.623i | −0.522309 | − | 0.753487i | ||||
\(538\) | 281.324 | 0.522907 | ||||||||
\(539\) | − | 18.6634i | − | 0.0346260i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 229.692 | 0.424569 | 0.212284 | − | 0.977208i | \(-0.431910\pi\) | ||||
0.212284 | + | 0.977208i | \(0.431910\pi\) | |||||||
\(542\) | 249.384i | 0.460118i | ||||||||
\(543\) | −278.679 | + | 193.177i | −0.513221 | + | 0.355759i | ||||
\(544\) | 104.949 | 0.192921 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −35.5709 | − | 51.3148i | −0.0651482 | − | 0.0939832i | ||||
\(547\) | −296.031 | −0.541191 | −0.270596 | − | 0.962693i | \(-0.587221\pi\) | ||||
−0.270596 | + | 0.962693i | \(0.587221\pi\) | |||||||
\(548\) | 230.591i | 0.420786i | ||||||||
\(549\) | −329.052 | + | 878.151i | −0.599365 | + | 1.59955i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.5283i | 0.0499606i | ||||||||
\(552\) | −108.889 | + | 75.4807i | −0.197263 | + | 0.136740i | ||||
\(553\) | 153.318 | 0.277247 | ||||||||
\(554\) | 612.487i | 1.10557i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 190.201 | 0.342088 | ||||||||
\(557\) | 659.047i | 1.18321i | 0.806228 | + | 0.591604i | \(0.201505\pi\) | ||||
−0.806228 | + | 0.591604i | \(0.798495\pi\) | |||||||
\(558\) | −161.392 | − | 60.4752i | −0.289234 | − | 0.108379i | ||||
\(559\) | 358.608 | 0.641518 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −121.958 | + | 84.5403i | −0.217395 | + | 0.150696i | ||||
\(562\) | 397.584 | 0.707444 | ||||||||
\(563\) | 1041.64i | 1.85016i | 0.379774 | + | 0.925079i | \(0.376002\pi\) | ||||
−0.379774 | + | 0.925079i | \(0.623998\pi\) | |||||||
\(564\) | 179.652 | + | 259.168i | 0.318533 | + | 0.459518i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 160.930i | − | 0.284328i | ||||||
\(567\) | 161.535 | + | 140.831i | 0.284894 | + | 0.248379i | ||||
\(568\) | −104.297 | −0.183622 | ||||||||
\(569\) | − | 143.782i | − | 0.252692i | −0.991986 | − | 0.126346i | \(-0.959675\pi\) | ||
0.991986 | − | 0.126346i | \(-0.0403250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 198.901 | 0.348337 | 0.174169 | − | 0.984716i | \(-0.444276\pi\) | ||||
0.174169 | + | 0.984716i | \(0.444276\pi\) | |||||||
\(572\) | 29.6611i | 0.0518551i | ||||||||
\(573\) | −335.664 | − | 484.232i | −0.585801 | − | 0.845082i | ||||
\(574\) | 58.4131 | 0.101765 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −25.2637 | + | 67.4221i | −0.0438606 | + | 0.117052i | ||||
\(577\) | −55.7825 | −0.0966767 | −0.0483384 | − | 0.998831i | \(-0.515393\pi\) | ||||
−0.0483384 | + | 0.998831i | \(0.515393\pi\) | |||||||
\(578\) | 78.0588i | 0.135050i | ||||||||
\(579\) | 696.037 | − | 482.486i | 1.20214 | − | 0.833308i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 119.306i | − | 0.205347i | ||||||
\(582\) | −232.580 | − | 335.522i | −0.399622 | − | 0.576498i | ||||
\(583\) | 137.591 | 0.236005 | ||||||||
\(584\) | − | 409.913i | − | 0.701906i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −502.512 | −0.857529 | ||||||||
\(587\) | − | 679.045i | − | 1.15681i | −0.815751 | − | 0.578403i | \(-0.803676\pi\) | ||
0.815751 | − | 0.578403i | \(-0.196324\pi\) | |||||||
\(588\) | 34.5178 | − | 23.9274i | 0.0587038 | − | 0.0406928i | ||||
\(589\) | −8.59862 | −0.0145987 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 490.104 | + | 707.027i | 0.829278 | + | 1.19632i | ||||
\(592\) | −140.006 | −0.236496 | ||||||||
\(593\) | 794.933i | 1.34053i | 0.742123 | + | 0.670264i | \(0.233819\pi\) | ||||
−0.742123 | + | 0.670264i | \(0.766181\pi\) | |||||||
\(594\) | −24.9527 | − | 98.7004i | −0.0420080 | − | 0.166162i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 358.685i | 0.601820i | ||||||||
\(597\) | −184.703 | + | 128.034i | −0.309386 | + | 0.214463i | ||||
\(598\) | −122.829 | −0.205400 | ||||||||
\(599\) | 525.925i | 0.878004i | 0.898486 | + | 0.439002i | \(0.144668\pi\) | ||||
−0.898486 | + | 0.439002i | \(0.855332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 169.552 | 0.282116 | 0.141058 | − | 0.990001i | \(-0.454950\pi\) | ||||
0.141058 | + | 0.990001i | \(0.454950\pi\) | |||||||
\(602\) | 241.224i | 0.400705i | ||||||||
\(603\) | −358.707 | + | 957.295i | −0.594871 | + | 1.58755i | ||||
\(604\) | −91.3242 | −0.151199 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −320.682 | + | 222.293i | −0.529178 | + | 0.366821i | ||||
\(607\) | −29.1399 | −0.0480064 | −0.0240032 | − | 0.999712i | \(-0.507641\pi\) | ||||
−0.0240032 | + | 0.999712i | \(0.507641\pi\) | |||||||
\(608\) | 3.59210i | 0.00590806i | ||||||||
\(609\) | −196.030 | − | 282.794i | −0.321888 | − | 0.464359i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 292.348i | 0.478474i | ||||||||
\(612\) | −312.713 | − | 117.176i | −0.510968 | − | 0.191465i | ||||
\(613\) | 167.118 | 0.272623 | 0.136311 | − | 0.990666i | \(-0.456475\pi\) | ||||
0.136311 | + | 0.990666i | \(0.456475\pi\) | |||||||
\(614\) | − | 572.035i | − | 0.931653i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −19.9521 | −0.0323897 | ||||||||
\(617\) | 872.471i | 1.41405i | 0.707187 | + | 0.707027i | \(0.249964\pi\) | ||||
−0.707187 | + | 0.707027i | \(0.750036\pi\) | |||||||
\(618\) | 73.9715 | + | 106.712i | 0.119695 | + | 0.172673i | ||||
\(619\) | 852.170 | 1.37669 | 0.688344 | − | 0.725384i | \(-0.258338\pi\) | ||||
0.688344 | + | 0.725384i | \(0.258338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 408.728 | − | 103.332i | 0.658177 | − | 0.166396i | ||||
\(622\) | 750.000 | 1.20579 | ||||||||
\(623\) | 214.235i | 0.343877i | ||||||||
\(624\) | −54.8579 | + | 38.0269i | −0.0879133 | + | 0.0609405i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 793.616i | − | 1.26776i | ||||||
\(627\) | −2.89357 | − | 4.17429i | −0.00461494 | − | 0.00665755i | ||||
\(628\) | −447.954 | −0.713303 | ||||||||
\(629\) | − | 649.364i | − | 1.03238i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 550.448 | 0.872343 | 0.436171 | − | 0.899864i | \(-0.356334\pi\) | ||||
0.436171 | + | 0.899864i | \(0.356334\pi\) | |||||||
\(632\) | − | 163.904i | − | 0.259341i | ||||||
\(633\) | 337.154 | − | 233.712i | 0.532629 | − | 0.369213i | ||||
\(634\) | −374.144 | −0.590133 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 176.398 | + | 254.473i | 0.277356 | + | 0.400115i | ||||
\(637\) | 38.9369 | 0.0611255 | ||||||||
\(638\) | 163.461i | 0.256209i | ||||||||
\(639\) | 310.771 | + | 116.449i | 0.486339 | + | 0.182236i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 56.3780i | 0.0879532i | 0.999033 | + | 0.0439766i | \(0.0140027\pi\) | ||||
−0.999033 | + | 0.0439766i | \(0.985997\pi\) | |||||||
\(642\) | −664.746 | + | 460.795i | −1.03543 | + | 0.717749i | ||||
\(643\) | −934.856 | −1.45390 | −0.726948 | − | 0.686692i | \(-0.759062\pi\) | ||||
−0.726948 | + | 0.686692i | \(0.759062\pi\) | |||||||
\(644\) | − | 82.6234i | − | 0.128297i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.6606 | −0.0257904 | ||||||||
\(647\) | 523.120i | 0.808532i | 0.914641 | + | 0.404266i | \(0.132473\pi\) | ||||
−0.914641 | + | 0.404266i | \(0.867527\pi\) | |||||||
\(648\) | 150.555 | − | 172.688i | 0.232338 | − | 0.266494i | ||||
\(649\) | 87.8204 | 0.135316 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 88.3324 | − | 61.2310i | 0.135687 | − | 0.0940569i | ||||
\(652\) | 600.619 | 0.921195 | ||||||||
\(653\) | − | 629.201i | − | 0.963554i | −0.876294 | − | 0.481777i | \(-0.839992\pi\) | ||
0.876294 | − | 0.481777i | \(-0.160008\pi\) | |||||||
\(654\) | −178.852 | − | 258.013i | −0.273474 | − | 0.394515i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 62.4462i | − | 0.0951924i | ||||||
\(657\) | −457.672 | + | 1221.40i | −0.696608 | + | 1.85906i | ||||
\(658\) | −196.653 | −0.298864 | ||||||||
\(659\) | 1205.86i | 1.82983i | 0.403644 | + | 0.914916i | \(0.367743\pi\) | ||||
−0.403644 | + | 0.914916i | \(0.632257\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 421.451 | 0.637596 | 0.318798 | − | 0.947823i | \(-0.396721\pi\) | ||||
0.318798 | + | 0.947823i | \(0.396721\pi\) | |||||||
\(662\) | − | 764.292i | − | 1.15452i | ||||||
\(663\) | −176.374 | − | 254.438i | −0.266024 | − | 0.383768i | ||||
\(664\) | −127.544 | −0.192084 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 417.170 | + | 156.317i | 0.626381 | + | 0.234711i | ||||
\(667\) | −676.909 | −1.01486 | ||||||||
\(668\) | − | 250.887i | − | 0.375579i | ||||||
\(669\) | −63.7745 | + | 44.2078i | −0.0953281 | + | 0.0660804i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 277.812i | 0.414026i | ||||||||
\(672\) | −25.5794 | − | 36.9011i | −0.0380647 | − | 0.0549124i | ||||
\(673\) | −208.482 | −0.309779 | −0.154890 | − | 0.987932i | \(-0.549502\pi\) | ||||
−0.154890 | + | 0.987932i | \(0.549502\pi\) | |||||||
\(674\) | − | 628.368i | − | 0.932297i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 276.119 | 0.408460 | ||||||||
\(677\) | 1253.11i | 1.85097i | 0.378784 | + | 0.925485i | \(0.376342\pi\) | ||||
−0.378784 | + | 0.925485i | \(0.623658\pi\) | |||||||
\(678\) | −449.317 | + | 311.462i | −0.662710 | + | 0.459383i | ||||
\(679\) | 254.589 | 0.374947 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −41.5983 | − | 60.0101i | −0.0610842 | − | 0.0881205i | ||||
\(682\) | −51.0580 | −0.0748651 | ||||||||
\(683\) | − | 982.114i | − | 1.43794i | −0.695041 | − | 0.718971i | \(-0.744614\pi\) | ||
0.695041 | − | 0.718971i | \(-0.255386\pi\) | |||||||
\(684\) | 4.01061 | − | 10.7033i | 0.00586346 | − | 0.0156480i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | −594.243 | + | 411.923i | −0.864983 | + | 0.599597i | ||||
\(688\) | 257.880 | 0.374825 | ||||||||
\(689\) | 287.052i | 0.416621i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 204.605 | 0.296099 | 0.148050 | − | 0.988980i | \(-0.452700\pi\) | ||||
0.148050 | + | 0.988980i | \(0.452700\pi\) | |||||||
\(692\) | 391.270i | 0.565419i | ||||||||
\(693\) | 59.4504 | + | 22.2766i | 0.0857871 | + | 0.0321452i | ||||
\(694\) | −359.148 | −0.517504 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −302.320 | + | 209.565i | −0.434368 | + | 0.301099i | ||||
\(697\) | 289.634 | 0.415543 | ||||||||
\(698\) | 587.785i | 0.842099i | ||||||||
\(699\) | 42.6561 | + | 61.5360i | 0.0610244 | + | 0.0880343i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 330.503i | 0.471473i | 0.971817 | + | 0.235736i | \(0.0757502\pi\) | ||||
−0.971817 | + | 0.235736i | \(0.924250\pi\) | |||||||
\(702\) | 205.915 | − | 52.0581i | 0.293327 | − | 0.0741568i | ||||
\(703\) | 22.2259 | 0.0316157 | ||||||||
\(704\) | 21.3296i | 0.0302978i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 393.210 | 0.556954 | ||||||||
\(707\) | − | 243.329i | − | 0.344171i | ||||||
\(708\) | 112.590 | + | 162.423i | 0.159025 | + | 0.229411i | ||||
\(709\) | −265.328 | −0.374229 | −0.187114 | − | 0.982338i | \(-0.559914\pi\) | ||||
−0.187114 | + | 0.982338i | \(0.559914\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −183.000 | + | 488.378i | −0.257384 | + | 0.686889i | ||||
\(712\) | 229.027 | 0.321667 | ||||||||
\(713\) | − | 211.436i | − | 0.296544i | ||||||
\(714\) | 171.152 | − | 118.641i | 0.239709 | − | 0.166164i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 328.220i | − | 0.458408i | ||||||
\(717\) | −411.517 | − | 593.658i | −0.573943 | − | 0.827975i | ||||
\(718\) | 115.421 | 0.160754 | ||||||||
\(719\) | − | 994.084i | − | 1.38259i | −0.722572 | − | 0.691296i | \(-0.757040\pi\) | ||
0.722572 | − | 0.691296i | \(-0.242960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −80.9713 | −0.112304 | ||||||||
\(722\) | 509.961i | 0.706317i | ||||||||
\(723\) | 363.379 | − | 251.890i | 0.502598 | − | 0.348396i | ||||
\(724\) | −226.057 | −0.312234 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 275.279 | + | 397.119i | 0.379172 | + | 0.546996i | ||||
\(727\) | −1244.89 | −1.71236 | −0.856182 | − | 0.516674i | \(-0.827170\pi\) | ||||
−0.856182 | + | 0.516674i | \(0.827170\pi\) | |||||||
\(728\) | − | 41.6253i | − | 0.0571776i | ||||||
\(729\) | −641.411 | + | 346.458i | −0.879851 | + | 0.475251i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1196.08i | 1.63622i | ||||||||
\(732\) | −513.810 | + | 356.167i | −0.701926 | + | 0.486567i | ||||
\(733\) | −822.707 | −1.12238 | −0.561192 | − | 0.827686i | \(-0.689657\pi\) | ||||
−0.561192 | + | 0.827686i | \(0.689657\pi\) | |||||||
\(734\) | 727.614i | 0.991300i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −88.3281 | −0.120011 | ||||||||
\(737\) | 302.849i | 0.410922i | ||||||||
\(738\) | −69.7217 | + | 186.069i | −0.0944739 | + | 0.252126i | ||||
\(739\) | 550.154 | 0.744458 | 0.372229 | − | 0.928141i | \(-0.378594\pi\) | ||||
0.372229 | + | 0.928141i | \(0.378594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.70868 | − | 6.03676i | 0.0117526 | − | 0.00814677i | ||||
\(742\) | −193.091 | −0.260230 | ||||||||
\(743\) | − | 356.858i | − | 0.480293i | −0.970737 | − | 0.240147i | \(-0.922805\pi\) | ||
0.970737 | − | 0.240147i | \(-0.0771955\pi\) | |||||||
\(744\) | −65.4587 | − | 94.4313i | −0.0879821 | − | 0.126924i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 113.329i | 0.151916i | ||||||||
\(747\) | 380.038 | + | 142.404i | 0.508752 | + | 0.190634i | ||||
\(748\) | −98.9296 | −0.132259 | ||||||||
\(749\) | − | 504.399i | − | 0.673430i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1027.14 | 1.36770 | 0.683850 | − | 0.729623i | \(-0.260304\pi\) | ||||
0.683850 | + | 0.729623i | \(0.260304\pi\) | |||||||
\(752\) | 210.231i | 0.279562i | ||||||||
\(753\) | 662.319 | + | 955.467i | 0.879574 | + | 1.26888i | ||||
\(754\) | −341.024 | −0.452287 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 35.0178 | + | 138.513i | 0.0463198 | + | 0.183218i | ||||
\(757\) | −799.336 | −1.05593 | −0.527963 | − | 0.849267i | \(-0.677044\pi\) | ||||
−0.527963 | + | 0.849267i | \(0.677044\pi\) | |||||||
\(758\) | 999.675i | 1.31883i | ||||||||
\(759\) | 102.644 | − | 71.1516i | 0.135236 | − | 0.0937439i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 799.993i | − | 1.05124i | −0.850720 | − | 0.525619i | \(-0.823834\pi\) | ||
0.850720 | − | 0.525619i | \(-0.176166\pi\) | |||||||
\(762\) | −231.560 | − | 334.050i | −0.303884 | − | 0.438386i | ||||
\(763\) | 195.776 | 0.256588 | ||||||||
\(764\) | − | 392.797i | − | 0.514132i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −69.6927 | −0.0909827 | ||||||||
\(767\) | 183.217i | 0.238875i | ||||||||
\(768\) | −39.4489 | + | 27.3456i | −0.0513658 | + | 0.0356062i | ||||
\(769\) | 1066.44 | 1.38679 | 0.693393 | − | 0.720560i | \(-0.256115\pi\) | ||||
0.693393 | + | 0.720560i | \(0.256115\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.2315 | + | 27.7436i | 0.0249436 | + | 0.0359839i | ||||
\(772\) | 564.608 | 0.731358 | ||||||||
\(773\) | 10.9234i | 0.0141311i | 0.999975 | + | 0.00706557i | \(0.00224906\pi\) | ||||
−0.999975 | + | 0.00706557i | \(0.997751\pi\) | |||||||
\(774\) | −768.395 | − | 287.925i | −0.992758 | − | 0.371996i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 272.167i | − | 0.350731i | ||||||
\(777\) | −228.323 | + | 158.271i | −0.293852 | + | 0.203695i | ||||
\(778\) | −3.79491 | −0.00487777 | ||||||||
\(779\) | 9.91332i | 0.0127257i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 98.3153 | 0.125884 | ||||||||
\(782\) | − | 409.677i | − | 0.523884i | ||||||
\(783\) | 1134.79 | − | 286.891i | 1.44929 | − | 0.366399i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −517.672 | + | 358.844i | −0.658615 | + | 0.456545i | ||||
\(787\) | 741.962 | 0.942772 | 0.471386 | − | 0.881927i | \(-0.343754\pi\) | ||||
0.471386 | + | 0.881927i | \(0.343754\pi\) | |||||||
\(788\) | 573.523i | 0.727821i | ||||||||
\(789\) | 527.527 | + | 761.015i | 0.668602 | + | 0.964531i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 340.935i | − | 0.431018i | ||||||
\(792\) | 23.8147 | − | 63.5552i | 0.0300691 | − | 0.0802465i | ||||
\(793\) | −579.589 | −0.730882 | ||||||||
\(794\) | 526.108i | 0.662605i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −149.827 | −0.188224 | ||||||||
\(797\) | − | 805.498i | − | 1.01066i | −0.862925 | − | 0.505331i | \(-0.831370\pi\) | ||
0.862925 | − | 0.505331i | \(-0.168630\pi\) | |||||||
\(798\) | 4.06073 | + | 5.85804i | 0.00508864 | + | 0.00734091i | ||||
\(799\) | −975.077 | −1.22037 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −682.424 | − | 255.711i | −0.851965 | − | 0.319239i | ||||
\(802\) | 168.464 | 0.210055 | ||||||||
\(803\) | 386.403i | 0.481199i | ||||||||
\(804\) | −560.117 | + | 388.267i | −0.696663 | + | 0.482919i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 106.521i | − | 0.132160i | ||||||
\(807\) | −339.985 | − | 490.464i | −0.421294 | − | 0.607762i | ||||
\(808\) | −260.129 | −0.321942 | ||||||||
\(809\) | − | 968.340i | − | 1.19696i | −0.801138 | − | 0.598480i | \(-0.795772\pi\) | ||
0.801138 | − | 0.598480i | \(-0.204228\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −542.257 | −0.668627 | −0.334314 | − | 0.942462i | \(-0.608504\pi\) | ||||
−0.334314 | + | 0.942462i | \(0.608504\pi\) | |||||||
\(812\) | − | 229.396i | − | 0.282507i | ||||||
\(813\) | 434.780 | − | 301.385i | 0.534784 | − | 0.370707i | ||||
\(814\) | 131.976 | 0.162132 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −126.832 | − | 182.969i | −0.155432 | − | 0.224227i | ||||
\(817\) | −40.9383 | −0.0501081 | ||||||||
\(818\) | 280.062i | 0.342374i | ||||||||
\(819\) | −46.4750 | + | 124.030i | −0.0567461 | + | 0.151440i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1034.06i | − | 1.25951i | −0.776793 | − | 0.629756i | \(-0.783155\pi\) | ||
0.776793 | − | 0.629756i | \(-0.216845\pi\) | |||||||
\(822\) | 402.015 | − | 278.673i | 0.489070 | − | 0.339018i | ||||
\(823\) | 352.261 | 0.428021 | 0.214010 | − | 0.976831i | \(-0.431347\pi\) | ||||
0.214010 | + | 0.976831i | \(0.431347\pi\) | |||||||
\(824\) | 86.5620i | 0.105051i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −123.244 | −0.149206 | ||||||||
\(827\) | − | 1125.16i | − | 1.36054i | −0.732964 | − | 0.680268i | \(-0.761864\pi\) | ||
0.732964 | − | 0.680268i | \(-0.238136\pi\) | |||||||
\(828\) | 263.188 | + | 98.6191i | 0.317860 | + | 0.119105i | ||||
\(829\) | −1107.76 | −1.33626 | −0.668128 | − | 0.744046i | \(-0.732904\pi\) | ||||
−0.668128 | + | 0.744046i | \(0.732904\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1067.82 | − | 740.200i | 1.28498 | − | 0.890733i | ||||
\(832\) | −44.4993 | −0.0534848 | ||||||||
\(833\) | 129.868i | 0.155904i | ||||||||
\(834\) | −229.861 | − | 331.599i | −0.275612 | − | 0.397601i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 3.38608i | − | 0.00405033i | ||||||
\(837\) | 89.6118 | + | 354.459i | 0.107063 | + | 0.423487i | ||||
\(838\) | −324.895 | −0.387703 | ||||||||
\(839\) | 13.3680i | 0.0159333i | 0.999968 | + | 0.00796664i | \(0.00253589\pi\) | ||||
−0.999968 | + | 0.00796664i | \(0.997464\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1038.37 | −1.23469 | ||||||||
\(842\) | 835.093i | 0.991797i | ||||||||
\(843\) | −480.486 | − | 693.153i | −0.569972 | − | 0.822246i | ||||
\(844\) | 273.491 | 0.324042 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 234.724 | − | 626.417i | 0.277452 | − | 0.740445i | ||||
\(847\) | −301.328 | −0.355759 | ||||||||
\(848\) | 206.423i | 0.243423i | ||||||||
\(849\) | −280.567 | + | 194.486i | −0.330468 | + | 0.229077i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 546.524i | 0.642214i | ||||||||
\(852\) | 126.045 | + | 181.833i | 0.147940 | + | 0.213419i | ||||
\(853\) | −498.127 | −0.583971 | −0.291985 | − | 0.956423i | \(-0.594316\pi\) | ||||
−0.291985 | + | 0.956423i | \(0.594316\pi\) | |||||||
\(854\) | − | 389.871i | − | 0.456523i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −539.225 | −0.629936 | ||||||||
\(857\) | 1519.40i | 1.77293i | 0.462799 | + | 0.886463i | \(0.346845\pi\) | ||||
−0.462799 | + | 0.886463i | \(0.653155\pi\) | |||||||
\(858\) | 51.7115 | − | 35.8459i | 0.0602699 | − | 0.0417784i | ||||
\(859\) | −964.144 | −1.12240 | −0.561201 | − | 0.827679i | \(-0.689661\pi\) | ||||
−0.561201 | + | 0.827679i | \(0.689661\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −70.5931 | − | 101.838i | −0.0819897 | − | 0.118279i | ||||
\(862\) | −586.728 | −0.680659 | ||||||||
\(863\) | − | 1169.35i | − | 1.35498i | −0.735532 | − | 0.677490i | \(-0.763068\pi\) | ||
0.735532 | − | 0.677490i | \(-0.236932\pi\) | |||||||
\(864\) | 148.076 | − | 37.4356i | 0.171385 | − | 0.0433282i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 310.793i | − | 0.358884i | ||||||
\(867\) | 136.089 | − | 94.3353i | 0.156965 | − | 0.108807i | ||||
\(868\) | 71.6530 | 0.0825495 | ||||||||
\(869\) | 154.503i | 0.177794i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −631.825 | −0.725402 | ||||||||
\(872\) | − | 209.294i | − | 0.240016i | ||||||
\(873\) | −303.877 | + | 810.966i | −0.348083 | + | 0.928942i | ||||
\(874\) | 14.0221 | 0.0160436 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −714.648 | + | 495.386i | −0.815809 | + | 0.565510i | ||||
\(877\) | 937.994 | 1.06955 | 0.534774 | − | 0.844995i | \(-0.320397\pi\) | ||||
0.534774 | + | 0.844995i | \(0.320397\pi\) | |||||||
\(878\) | − | 902.799i | − | 1.02824i | ||||||
\(879\) | 607.294 | + | 876.087i | 0.690892 | + | 0.996686i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 274.915i | − | 0.312049i | −0.987753 | − | 0.156024i | \(-0.950132\pi\) | ||
0.987753 | − | 0.156024i | \(-0.0498679\pi\) | |||||||
\(882\) | −83.4306 | − | 31.2622i | −0.0945926 | − | 0.0354447i | ||||
\(883\) | −1155.73 | −1.30886 | −0.654432 | − | 0.756121i | \(-0.727092\pi\) | ||||
−0.654432 | + | 0.756121i | \(0.727092\pi\) | |||||||
\(884\) | − | 206.394i | − | 0.233477i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 423.076 | 0.477512 | ||||||||
\(887\) | 887.696i | 1.00079i | 0.865799 | + | 0.500393i | \(0.166811\pi\) | ||||
−0.865799 | + | 0.500393i | \(0.833189\pi\) | |||||||
\(888\) | 169.199 | + | 244.088i | 0.190539 | + | 0.274873i | ||||
\(889\) | 253.472 | 0.285121 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −141.920 | + | 162.784i | −0.159282 | + | 0.182698i | ||||
\(892\) | −51.7323 | −0.0579959 | ||||||||
\(893\) | − | 33.3741i | − | 0.0373730i | ||||||
\(894\) | 625.336 | − | 433.476i | 0.699481 | − | 0.484873i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | 148.441 | + | 214.143i | 0.165486 | + | 0.238732i | ||||
\(898\) | 821.168 | 0.914441 | ||||||||
\(899\) | − | 587.032i | − | 0.652983i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −957.414 | −1.06261 | ||||||||
\(902\) | 58.8647i | 0.0652601i | ||||||||
\(903\) | 420.554 | − | 291.523i | 0.465729 | − | 0.322838i | ||||
\(904\) | −364.475 | −0.403180 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 110.367 | + | 159.216i | 0.121818 | + | 0.175735i | ||||
\(907\) | −326.166 | −0.359610 | −0.179805 | − | 0.983702i | \(-0.557547\pi\) | ||||
−0.179805 | + | 0.983702i | \(0.557547\pi\) | |||||||
\(908\) | − | 48.6787i | − | 0.0536109i | ||||||
\(909\) | 775.098 | + | 290.437i | 0.852693 | + | 0.319512i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 455.102i | − | 0.499563i | −0.968302 | − | 0.249782i | \(-0.919641\pi\) | ||
0.968302 | − | 0.249782i | \(-0.0803588\pi\) | |||||||
\(912\) | 6.26251 | − | 4.34110i | 0.00686679 | − | 0.00475998i | ||||
\(913\) | 120.229 | 0.131685 | ||||||||
\(914\) | 796.647i | 0.871605i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −482.035 | −0.526239 | ||||||||
\(917\) | − | 392.801i | − | 0.428355i | ||||||
\(918\) | 173.631 | + | 686.797i | 0.189141 | + | 0.748145i | ||||
\(919\) | 1354.04 | 1.47338 | 0.736690 | − | 0.676230i | \(-0.236388\pi\) | ||||
0.736690 | + | 0.676230i | \(0.236388\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −997.294 | + | 691.313i | −1.08284 | + | 0.750611i | ||||
\(922\) | 195.483 | 0.212021 | ||||||||
\(923\) | 205.112i | 0.222223i | ||||||||
\(924\) | 24.1124 | + | 34.7847i | 0.0260956 | + | 0.0376458i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 218.923i | 0.236418i | ||||||||
\(927\) | 96.6472 | − | 257.926i | 0.104258 | − | 0.278237i | ||||
\(928\) | −245.234 | −0.264261 | ||||||||
\(929\) | 1705.50i | 1.83585i | 0.396759 | + | 0.917923i | \(0.370135\pi\) | ||||
−0.396759 | + | 0.917923i | \(0.629865\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.44499 | −0.00477443 | ||||||||
\(932\) | 49.9165i | 0.0535584i | ||||||||
\(933\) | −906.386 | − | 1307.56i | −0.971475 | − | 1.40146i | ||||
\(934\) | −654.601 | −0.700857 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 132.593 | + | 49.6839i | 0.141659 | + | 0.0530811i | ||||
\(937\) | −445.015 | −0.474936 | −0.237468 | − | 0.971395i | \(-0.576317\pi\) | ||||
−0.237468 | + | 0.971395i | \(0.576317\pi\) | |||||||
\(938\) | − | 425.008i | − | 0.453100i | ||||||
\(939\) | −1383.60 | + | 959.098i | −1.47348 | + | 1.02140i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1110.66i | − | 1.18030i | −0.807294 | − | 0.590150i | \(-0.799069\pi\) | ||
0.807294 | − | 0.590150i | \(-0.200931\pi\) | |||||||
\(942\) | 541.359 | + | 780.969i | 0.574692 | + | 0.829054i | ||||
\(943\) | −243.764 | −0.258499 | ||||||||
\(944\) | 131.753i | 0.139569i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −243.089 | −0.256965 | ||||||||
\(947\) | − | 32.4631i | − | 0.0342799i | −0.999853 | − | 0.0171400i | \(-0.994544\pi\) | ||
0.999853 | − | 0.0171400i | \(-0.00545609\pi\) | |||||||
\(948\) | −285.752 | + | 198.080i | −0.301426 | + | 0.208945i | ||||
\(949\) | −806.140 | −0.849463 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 452.159 | + | 652.288i | 0.475456 | + | 0.685897i | ||||
\(952\) | 138.834 | 0.145834 | ||||||||
\(953\) | 458.990i | 0.481626i | 0.970572 | + | 0.240813i | \(0.0774141\pi\) | ||||
−0.970572 | + | 0.240813i | \(0.922586\pi\) | |||||||
\(954\) | 230.473 | − | 615.070i | 0.241585 | − | 0.644728i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 481.561i | − | 0.503725i | ||||||
\(957\) | 284.981 | − | 197.546i | 0.297785 | − | 0.206422i | ||||
\(958\) | 1183.61 | 1.23551 | ||||||||
\(959\) | 305.043i | 0.318084i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −777.637 | −0.809196 | ||||||||
\(962\) | 275.337i | 0.286213i | ||||||||
\(963\) | 1606.71 | + | 602.050i | 1.66844 | + | 0.625182i | ||||
\(964\) | 294.764 | 0.305771 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −144.047 | + | 99.8516i | −0.149117 | + | 0.103366i | ||||
\(967\) | −899.118 | −0.929802 | −0.464901 | − | 0.885363i | \(-0.653910\pi\) | ||||
−0.464901 | + | 0.885363i | \(0.653910\pi\) | |||||||
\(968\) | 322.133i | 0.332782i | ||||||||
\(969\) | 20.1346 | + | 29.0463i | 0.0207787 | + | 0.0299756i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1201.62i | − | 1.23750i | −0.785587 | − | 0.618752i | \(-0.787639\pi\) | ||
0.785587 | − | 0.618752i | \(-0.212361\pi\) | |||||||
\(972\) | −483.015 | − | 53.7829i | −0.496929 | − | 0.0553322i | ||||
\(973\) | 251.612 | 0.258594 | ||||||||
\(974\) | − | 299.873i | − | 0.307878i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −416.790 | −0.427039 | ||||||||
\(977\) | − | 227.188i | − | 0.232536i | −0.993218 | − | 0.116268i | \(-0.962907\pi\) | ||
0.993218 | − | 0.116268i | \(-0.0370932\pi\) | |||||||
\(978\) | −725.857 | − | 1047.13i | −0.742185 | − | 1.07068i | ||||
\(979\) | −215.891 | −0.220522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −233.678 | + | 623.625i | −0.238204 | + | 0.635704i | ||||
\(982\) | −112.005 | −0.114059 | ||||||||
\(983\) | − | 510.695i | − | 0.519527i | −0.965672 | − | 0.259763i | \(-0.916355\pi\) | ||
0.965672 | − | 0.259763i | \(-0.0836446\pi\) | |||||||
\(984\) | −108.870 | + | 75.4672i | −0.110640 | + | 0.0766943i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1137.43i | − | 1.15358i | ||||||
\(987\) | 237.658 | + | 342.847i | 0.240788 | + | 0.347363i | ||||
\(988\) | 7.06426 | 0.00715006 | ||||||||
\(989\) | − | 1006.66i | − | 1.01785i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1161.49 | 1.17204 | 0.586019 | − | 0.810297i | \(-0.300694\pi\) | ||||
0.586019 | + | 0.810297i | \(0.300694\pi\) | |||||||
\(992\) | − | 76.6003i | − | 0.0772180i | ||||||
\(993\) | −1332.48 | + | 923.659i | −1.34187 | + | 0.930170i | ||||
\(994\) | −137.972 | −0.138805 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 154.139 | + | 222.362i | 0.154758 | + | 0.223255i | ||||
\(997\) | 506.932 | 0.508457 | 0.254229 | − | 0.967144i | \(-0.418178\pi\) | ||||
0.254229 | + | 0.967144i | \(0.418178\pi\) | |||||||
\(998\) | − | 366.893i | − | 0.367628i | ||||||
\(999\) | −231.630 | − | 916.212i | −0.231862 | − | 0.917129i |
(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 | 1050.3.e.e.701.9 | 24 | ||
3.2 | odd | 2 | inner | 1050.3.e.e.701.11 | 24 | ||
5.2 | odd | 4 | 210.3.c.a.29.20 | yes | 24 | ||
5.3 | odd | 4 | 210.3.c.a.29.5 | ✓ | 24 | ||
5.4 | even | 2 | inner | 1050.3.e.e.701.12 | 24 | ||
15.2 | even | 4 | 210.3.c.a.29.6 | yes | 24 | ||
15.8 | even | 4 | 210.3.c.a.29.19 | yes | 24 | ||
15.14 | odd | 2 | inner | 1050.3.e.e.701.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.5 | ✓ | 24 | 5.3 | odd | 4 | ||
210.3.c.a.29.6 | yes | 24 | 15.2 | even | 4 | ||
210.3.c.a.29.19 | yes | 24 | 15.8 | even | 4 | ||
210.3.c.a.29.20 | yes | 24 | 5.2 | odd | 4 | ||
1050.3.e.e.701.9 | 24 | 1.1 | even | 1 | trivial | ||
1050.3.e.e.701.10 | 24 | 15.14 | odd | 2 | inner | ||
1050.3.e.e.701.11 | 24 | 3.2 | odd | 2 | inner | ||
1050.3.e.e.701.12 | 24 | 5.4 | even | 2 | inner |