Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.a (trivial) |
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: | yes |
Analytic conductor: | \(37.7692401561\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.771947\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.228053 | −0.131666 | −0.0658332 | − | 0.997831i | \(-0.520971\pi\) | ||||
−0.0658332 | + | 0.997831i | \(0.520971\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0.228053 | 0.0931022 | ||||||||
\(7\) | −2.81890 | −1.06545 | −0.532723 | − | 0.846290i | \(-0.678831\pi\) | ||||
−0.532723 | + | 0.846290i | \(0.678831\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.94799 | −0.982664 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.228053 | −0.0658332 | ||||||||
\(13\) | 1.12433 | 0.311834 | 0.155917 | − | 0.987770i | \(-0.450167\pi\) | ||||
0.155917 | + | 0.987770i | \(0.450167\pi\) | |||||||
\(14\) | 2.81890 | 0.753384 | ||||||||
\(15\) | −0.228053 | −0.0588830 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.66554 | −0.403953 | −0.201977 | − | 0.979390i | \(-0.564736\pi\) | ||||
−0.201977 | + | 0.979390i | \(0.564736\pi\) | |||||||
\(18\) | 2.94799 | 0.694848 | ||||||||
\(19\) | 7.42051 | 1.70238 | 0.851190 | − | 0.524857i | \(-0.175881\pi\) | ||||
0.851190 | + | 0.524857i | \(0.175881\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.642859 | 0.140283 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −0.875665 | −0.182589 | −0.0912944 | − | 0.995824i | \(-0.529100\pi\) | ||||
−0.0912944 | + | 0.995824i | \(0.529100\pi\) | |||||||
\(24\) | 0.228053 | 0.0465511 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.12433 | −0.220500 | ||||||||
\(27\) | 1.35646 | 0.261050 | ||||||||
\(28\) | −2.81890 | −0.532723 | ||||||||
\(29\) | −4.72931 | −0.878210 | −0.439105 | − | 0.898436i | \(-0.644704\pi\) | ||||
−0.439105 | + | 0.898436i | \(0.644704\pi\) | |||||||
\(30\) | 0.228053 | 0.0416366 | ||||||||
\(31\) | −2.66066 | −0.477869 | −0.238935 | − | 0.971036i | \(-0.576798\pi\) | ||||
−0.238935 | + | 0.971036i | \(0.576798\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.228053 | −0.0396989 | ||||||||
\(34\) | 1.66554 | 0.285638 | ||||||||
\(35\) | −2.81890 | −0.476482 | ||||||||
\(36\) | −2.94799 | −0.491332 | ||||||||
\(37\) | −5.63729 | −0.926765 | −0.463383 | − | 0.886158i | \(-0.653364\pi\) | ||||
−0.463383 | + | 0.886158i | \(0.653364\pi\) | |||||||
\(38\) | −7.42051 | −1.20376 | ||||||||
\(39\) | −0.256408 | −0.0410581 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 7.80977 | 1.21968 | 0.609841 | − | 0.792524i | \(-0.291233\pi\) | ||||
0.609841 | + | 0.792524i | \(0.291233\pi\) | |||||||
\(42\) | −0.642859 | −0.0991953 | ||||||||
\(43\) | −1.00000 | −0.152499 | ||||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | −2.94799 | −0.439461 | ||||||||
\(46\) | 0.875665 | 0.129110 | ||||||||
\(47\) | 13.2060 | 1.92629 | 0.963146 | − | 0.268978i | \(-0.0866858\pi\) | ||||
0.963146 | + | 0.268978i | \(0.0866858\pi\) | |||||||
\(48\) | −0.228053 | −0.0329166 | ||||||||
\(49\) | 0.946220 | 0.135174 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0.379832 | 0.0531871 | ||||||||
\(52\) | 1.12433 | 0.155917 | ||||||||
\(53\) | −3.40667 | −0.467943 | −0.233971 | − | 0.972244i | \(-0.575172\pi\) | ||||
−0.233971 | + | 0.972244i | \(0.575172\pi\) | |||||||
\(54\) | −1.35646 | −0.184590 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 2.81890 | 0.376692 | ||||||||
\(57\) | −1.69227 | −0.224146 | ||||||||
\(58\) | 4.72931 | 0.620988 | ||||||||
\(59\) | 0.759347 | 0.0988586 | 0.0494293 | − | 0.998778i | \(-0.484260\pi\) | ||||
0.0494293 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(60\) | −0.228053 | −0.0294415 | ||||||||
\(61\) | 4.85201 | 0.621236 | 0.310618 | − | 0.950535i | \(-0.399464\pi\) | ||||
0.310618 | + | 0.950535i | \(0.399464\pi\) | |||||||
\(62\) | 2.66066 | 0.337905 | ||||||||
\(63\) | 8.31011 | 1.04697 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.12433 | 0.139457 | ||||||||
\(66\) | 0.228053 | 0.0280714 | ||||||||
\(67\) | −2.24757 | −0.274585 | −0.137292 | − | 0.990531i | \(-0.543840\pi\) | ||||
−0.137292 | + | 0.990531i | \(0.543840\pi\) | |||||||
\(68\) | −1.66554 | −0.201977 | ||||||||
\(69\) | 0.199698 | 0.0240408 | ||||||||
\(70\) | 2.81890 | 0.336923 | ||||||||
\(71\) | 7.41158 | 0.879593 | 0.439797 | − | 0.898097i | \(-0.355051\pi\) | ||||
0.439797 | + | 0.898097i | \(0.355051\pi\) | |||||||
\(72\) | 2.94799 | 0.347424 | ||||||||
\(73\) | 2.51101 | 0.293892 | 0.146946 | − | 0.989145i | \(-0.453056\pi\) | ||||
0.146946 | + | 0.989145i | \(0.453056\pi\) | |||||||
\(74\) | 5.63729 | 0.655322 | ||||||||
\(75\) | −0.228053 | −0.0263333 | ||||||||
\(76\) | 7.42051 | 0.851190 | ||||||||
\(77\) | −2.81890 | −0.321244 | ||||||||
\(78\) | 0.256408 | 0.0290325 | ||||||||
\(79\) | −10.7456 | −1.20898 | −0.604490 | − | 0.796613i | \(-0.706623\pi\) | ||||
−0.604490 | + | 0.796613i | \(0.706623\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 8.53463 | 0.948292 | ||||||||
\(82\) | −7.80977 | −0.862445 | ||||||||
\(83\) | −12.0367 | −1.32120 | −0.660602 | − | 0.750737i | \(-0.729699\pi\) | ||||
−0.660602 | + | 0.750737i | \(0.729699\pi\) | |||||||
\(84\) | 0.642859 | 0.0701417 | ||||||||
\(85\) | −1.66554 | −0.180653 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | 1.07853 | 0.115631 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | −5.21429 | −0.552714 | −0.276357 | − | 0.961055i | \(-0.589127\pi\) | ||||
−0.276357 | + | 0.961055i | \(0.589127\pi\) | |||||||
\(90\) | 2.94799 | 0.310746 | ||||||||
\(91\) | −3.16939 | −0.332242 | ||||||||
\(92\) | −0.875665 | −0.0912944 | ||||||||
\(93\) | 0.606772 | 0.0629194 | ||||||||
\(94\) | −13.2060 | −1.36209 | ||||||||
\(95\) | 7.42051 | 0.761328 | ||||||||
\(96\) | 0.228053 | 0.0232756 | ||||||||
\(97\) | −6.50507 | −0.660490 | −0.330245 | − | 0.943895i | \(-0.607131\pi\) | ||||
−0.330245 | + | 0.943895i | \(0.607131\pi\) | |||||||
\(98\) | −0.946220 | −0.0955827 | ||||||||
\(99\) | −2.94799 | −0.296284 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 4.52576 | 0.450330 | 0.225165 | − | 0.974321i | \(-0.427708\pi\) | ||||
0.225165 | + | 0.974321i | \(0.427708\pi\) | |||||||
\(102\) | −0.379832 | −0.0376089 | ||||||||
\(103\) | −2.63398 | −0.259534 | −0.129767 | − | 0.991545i | \(-0.541423\pi\) | ||||
−0.129767 | + | 0.991545i | \(0.541423\pi\) | |||||||
\(104\) | −1.12433 | −0.110250 | ||||||||
\(105\) | 0.642859 | 0.0627366 | ||||||||
\(106\) | 3.40667 | 0.330885 | ||||||||
\(107\) | −9.33164 | −0.902124 | −0.451062 | − | 0.892493i | \(-0.648955\pi\) | ||||
−0.451062 | + | 0.892493i | \(0.648955\pi\) | |||||||
\(108\) | 1.35646 | 0.130525 | ||||||||
\(109\) | −4.97087 | −0.476123 | −0.238061 | − | 0.971250i | \(-0.576512\pi\) | ||||
−0.238061 | + | 0.971250i | \(0.576512\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 1.28560 | 0.122024 | ||||||||
\(112\) | −2.81890 | −0.266361 | ||||||||
\(113\) | −8.23164 | −0.774367 | −0.387184 | − | 0.922003i | \(-0.626552\pi\) | ||||
−0.387184 | + | 0.922003i | \(0.626552\pi\) | |||||||
\(114\) | 1.69227 | 0.158495 | ||||||||
\(115\) | −0.875665 | −0.0816562 | ||||||||
\(116\) | −4.72931 | −0.439105 | ||||||||
\(117\) | −3.31453 | −0.306428 | ||||||||
\(118\) | −0.759347 | −0.0699036 | ||||||||
\(119\) | 4.69500 | 0.430390 | ||||||||
\(120\) | 0.228053 | 0.0208183 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.85201 | −0.439280 | ||||||||
\(123\) | −1.78104 | −0.160591 | ||||||||
\(124\) | −2.66066 | −0.238935 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −8.31011 | −0.740323 | ||||||||
\(127\) | −20.1915 | −1.79171 | −0.895854 | − | 0.444348i | \(-0.853435\pi\) | ||||
−0.895854 | + | 0.444348i | \(0.853435\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.228053 | 0.0200789 | ||||||||
\(130\) | −1.12433 | −0.0986107 | ||||||||
\(131\) | −17.5653 | −1.53469 | −0.767345 | − | 0.641235i | \(-0.778422\pi\) | ||||
−0.767345 | + | 0.641235i | \(0.778422\pi\) | |||||||
\(132\) | −0.228053 | −0.0198495 | ||||||||
\(133\) | −20.9177 | −1.81379 | ||||||||
\(134\) | 2.24757 | 0.194161 | ||||||||
\(135\) | 1.35646 | 0.116745 | ||||||||
\(136\) | 1.66554 | 0.142819 | ||||||||
\(137\) | −10.6093 | −0.906413 | −0.453206 | − | 0.891406i | \(-0.649720\pi\) | ||||
−0.453206 | + | 0.891406i | \(0.649720\pi\) | |||||||
\(138\) | −0.199698 | −0.0169994 | ||||||||
\(139\) | −1.26492 | −0.107289 | −0.0536445 | − | 0.998560i | \(-0.517084\pi\) | ||||
−0.0536445 | + | 0.998560i | \(0.517084\pi\) | |||||||
\(140\) | −2.81890 | −0.238241 | ||||||||
\(141\) | −3.01167 | −0.253628 | ||||||||
\(142\) | −7.41158 | −0.621966 | ||||||||
\(143\) | 1.12433 | 0.0940216 | ||||||||
\(144\) | −2.94799 | −0.245666 | ||||||||
\(145\) | −4.72931 | −0.392748 | ||||||||
\(146\) | −2.51101 | −0.207813 | ||||||||
\(147\) | −0.215788 | −0.0177979 | ||||||||
\(148\) | −5.63729 | −0.463383 | ||||||||
\(149\) | 9.56881 | 0.783907 | 0.391954 | − | 0.919985i | \(-0.371799\pi\) | ||||
0.391954 | + | 0.919985i | \(0.371799\pi\) | |||||||
\(150\) | 0.228053 | 0.0186204 | ||||||||
\(151\) | 15.7568 | 1.28227 | 0.641136 | − | 0.767428i | \(-0.278464\pi\) | ||||
0.641136 | + | 0.767428i | \(0.278464\pi\) | |||||||
\(152\) | −7.42051 | −0.601882 | ||||||||
\(153\) | 4.91000 | 0.396950 | ||||||||
\(154\) | 2.81890 | 0.227154 | ||||||||
\(155\) | −2.66066 | −0.213710 | ||||||||
\(156\) | −0.256408 | −0.0205291 | ||||||||
\(157\) | −4.47588 | −0.357214 | −0.178607 | − | 0.983920i | \(-0.557159\pi\) | ||||
−0.178607 | + | 0.983920i | \(0.557159\pi\) | |||||||
\(158\) | 10.7456 | 0.854877 | ||||||||
\(159\) | 0.776902 | 0.0616123 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 2.46842 | 0.194539 | ||||||||
\(162\) | −8.53463 | −0.670544 | ||||||||
\(163\) | 15.5677 | 1.21936 | 0.609679 | − | 0.792648i | \(-0.291298\pi\) | ||||
0.609679 | + | 0.792648i | \(0.291298\pi\) | |||||||
\(164\) | 7.80977 | 0.609841 | ||||||||
\(165\) | −0.228053 | −0.0177539 | ||||||||
\(166\) | 12.0367 | 0.934232 | ||||||||
\(167\) | −6.01893 | −0.465759 | −0.232879 | − | 0.972506i | \(-0.574815\pi\) | ||||
−0.232879 | + | 0.972506i | \(0.574815\pi\) | |||||||
\(168\) | −0.642859 | −0.0495977 | ||||||||
\(169\) | −11.7359 | −0.902759 | ||||||||
\(170\) | 1.66554 | 0.127741 | ||||||||
\(171\) | −21.8756 | −1.67287 | ||||||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | −4.00241 | −0.304298 | −0.152149 | − | 0.988358i | \(-0.548619\pi\) | ||||
−0.152149 | + | 0.988358i | \(0.548619\pi\) | |||||||
\(174\) | −1.07853 | −0.0817633 | ||||||||
\(175\) | −2.81890 | −0.213089 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −0.173171 | −0.0130164 | ||||||||
\(178\) | 5.21429 | 0.390828 | ||||||||
\(179\) | −0.139202 | −0.0104044 | −0.00520221 | − | 0.999986i | \(-0.501656\pi\) | ||||
−0.00520221 | + | 0.999986i | \(0.501656\pi\) | |||||||
\(180\) | −2.94799 | −0.219730 | ||||||||
\(181\) | 6.05904 | 0.450365 | 0.225182 | − | 0.974317i | \(-0.427702\pi\) | ||||
0.225182 | + | 0.974317i | \(0.427702\pi\) | |||||||
\(182\) | 3.16939 | 0.234931 | ||||||||
\(183\) | −1.10651 | −0.0817959 | ||||||||
\(184\) | 0.875665 | 0.0645549 | ||||||||
\(185\) | −5.63729 | −0.414462 | ||||||||
\(186\) | −0.606772 | −0.0444907 | ||||||||
\(187\) | −1.66554 | −0.121796 | ||||||||
\(188\) | 13.2060 | 0.963146 | ||||||||
\(189\) | −3.82372 | −0.278135 | ||||||||
\(190\) | −7.42051 | −0.538340 | ||||||||
\(191\) | −16.1843 | −1.17106 | −0.585528 | − | 0.810653i | \(-0.699113\pi\) | ||||
−0.585528 | + | 0.810653i | \(0.699113\pi\) | |||||||
\(192\) | −0.228053 | −0.0164583 | ||||||||
\(193\) | 25.5558 | 1.83954 | 0.919772 | − | 0.392452i | \(-0.128373\pi\) | ||||
0.919772 | + | 0.392452i | \(0.128373\pi\) | |||||||
\(194\) | 6.50507 | 0.467037 | ||||||||
\(195\) | −0.256408 | −0.0183617 | ||||||||
\(196\) | 0.946220 | 0.0675872 | ||||||||
\(197\) | 19.6077 | 1.39699 | 0.698495 | − | 0.715615i | \(-0.253853\pi\) | ||||
0.698495 | + | 0.715615i | \(0.253853\pi\) | |||||||
\(198\) | 2.94799 | 0.209505 | ||||||||
\(199\) | −21.6580 | −1.53529 | −0.767647 | − | 0.640873i | \(-0.778573\pi\) | ||||
−0.767647 | + | 0.640873i | \(0.778573\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0.512565 | 0.0361536 | ||||||||
\(202\) | −4.52576 | −0.318431 | ||||||||
\(203\) | 13.3315 | 0.935685 | ||||||||
\(204\) | 0.379832 | 0.0265935 | ||||||||
\(205\) | 7.80977 | 0.545458 | ||||||||
\(206\) | 2.63398 | 0.183518 | ||||||||
\(207\) | 2.58145 | 0.179423 | ||||||||
\(208\) | 1.12433 | 0.0779586 | ||||||||
\(209\) | 7.42051 | 0.513287 | ||||||||
\(210\) | −0.642859 | −0.0443615 | ||||||||
\(211\) | 12.3193 | 0.848098 | 0.424049 | − | 0.905639i | \(-0.360608\pi\) | ||||
0.424049 | + | 0.905639i | \(0.360608\pi\) | |||||||
\(212\) | −3.40667 | −0.233971 | ||||||||
\(213\) | −1.69023 | −0.115813 | ||||||||
\(214\) | 9.33164 | 0.637898 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | −1.35646 | −0.0922952 | ||||||||
\(217\) | 7.50016 | 0.509144 | ||||||||
\(218\) | 4.97087 | 0.336670 | ||||||||
\(219\) | −0.572644 | −0.0386957 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | −1.87263 | −0.125966 | ||||||||
\(222\) | −1.28560 | −0.0862839 | ||||||||
\(223\) | −20.5666 | −1.37724 | −0.688620 | − | 0.725123i | \(-0.741783\pi\) | ||||
−0.688620 | + | 0.725123i | \(0.741783\pi\) | |||||||
\(224\) | 2.81890 | 0.188346 | ||||||||
\(225\) | −2.94799 | −0.196533 | ||||||||
\(226\) | 8.23164 | 0.547560 | ||||||||
\(227\) | −24.9903 | −1.65866 | −0.829331 | − | 0.558757i | \(-0.811278\pi\) | ||||
−0.829331 | + | 0.558757i | \(0.811278\pi\) | |||||||
\(228\) | −1.69227 | −0.112073 | ||||||||
\(229\) | −23.3892 | −1.54560 | −0.772801 | − | 0.634648i | \(-0.781145\pi\) | ||||
−0.772801 | + | 0.634648i | \(0.781145\pi\) | |||||||
\(230\) | 0.875665 | 0.0577397 | ||||||||
\(231\) | 0.642859 | 0.0422970 | ||||||||
\(232\) | 4.72931 | 0.310494 | ||||||||
\(233\) | −7.48056 | −0.490068 | −0.245034 | − | 0.969514i | \(-0.578799\pi\) | ||||
−0.245034 | + | 0.969514i | \(0.578799\pi\) | |||||||
\(234\) | 3.31453 | 0.216678 | ||||||||
\(235\) | 13.2060 | 0.861464 | ||||||||
\(236\) | 0.759347 | 0.0494293 | ||||||||
\(237\) | 2.45057 | 0.159182 | ||||||||
\(238\) | −4.69500 | −0.304332 | ||||||||
\(239\) | 10.7522 | 0.695499 | 0.347750 | − | 0.937587i | \(-0.386946\pi\) | ||||
0.347750 | + | 0.937587i | \(0.386946\pi\) | |||||||
\(240\) | −0.228053 | −0.0147208 | ||||||||
\(241\) | 10.8505 | 0.698944 | 0.349472 | − | 0.936947i | \(-0.386361\pi\) | ||||
0.349472 | + | 0.936947i | \(0.386361\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | −6.01572 | −0.385909 | ||||||||
\(244\) | 4.85201 | 0.310618 | ||||||||
\(245\) | 0.946220 | 0.0604518 | ||||||||
\(246\) | 1.78104 | 0.113555 | ||||||||
\(247\) | 8.34313 | 0.530861 | ||||||||
\(248\) | 2.66066 | 0.168952 | ||||||||
\(249\) | 2.74501 | 0.173958 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −1.64877 | −0.104069 | −0.0520346 | − | 0.998645i | \(-0.516571\pi\) | ||||
−0.0520346 | + | 0.998645i | \(0.516571\pi\) | |||||||
\(252\) | 8.31011 | 0.523487 | ||||||||
\(253\) | −0.875665 | −0.0550526 | ||||||||
\(254\) | 20.1915 | 1.26693 | ||||||||
\(255\) | 0.379832 | 0.0237860 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.6789 | −1.35229 | −0.676146 | − | 0.736767i | \(-0.736351\pi\) | ||||
−0.676146 | + | 0.736767i | \(0.736351\pi\) | |||||||
\(258\) | −0.228053 | −0.0141980 | ||||||||
\(259\) | 15.8910 | 0.987418 | ||||||||
\(260\) | 1.12433 | 0.0697283 | ||||||||
\(261\) | 13.9420 | 0.862986 | ||||||||
\(262\) | 17.5653 | 1.08519 | ||||||||
\(263\) | −15.0436 | −0.927631 | −0.463815 | − | 0.885932i | \(-0.653520\pi\) | ||||
−0.463815 | + | 0.885932i | \(0.653520\pi\) | |||||||
\(264\) | 0.228053 | 0.0140357 | ||||||||
\(265\) | −3.40667 | −0.209270 | ||||||||
\(266\) | 20.9177 | 1.28255 | ||||||||
\(267\) | 1.18914 | 0.0727739 | ||||||||
\(268\) | −2.24757 | −0.137292 | ||||||||
\(269\) | 17.5715 | 1.07135 | 0.535677 | − | 0.844423i | \(-0.320056\pi\) | ||||
0.535677 | + | 0.844423i | \(0.320056\pi\) | |||||||
\(270\) | −1.35646 | −0.0825513 | ||||||||
\(271\) | −5.85055 | −0.355396 | −0.177698 | − | 0.984085i | \(-0.556865\pi\) | ||||
−0.177698 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(272\) | −1.66554 | −0.100988 | ||||||||
\(273\) | 0.722789 | 0.0437452 | ||||||||
\(274\) | 10.6093 | 0.640930 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.199698 | 0.0120204 | ||||||||
\(277\) | 5.20593 | 0.312794 | 0.156397 | − | 0.987694i | \(-0.450012\pi\) | ||||
0.156397 | + | 0.987694i | \(0.450012\pi\) | |||||||
\(278\) | 1.26492 | 0.0758648 | ||||||||
\(279\) | 7.84362 | 0.469585 | ||||||||
\(280\) | 2.81890 | 0.168462 | ||||||||
\(281\) | 0.709992 | 0.0423546 | 0.0211773 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211773 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(282\) | 3.01167 | 0.179342 | ||||||||
\(283\) | −12.9171 | −0.767843 | −0.383921 | − | 0.923366i | \(-0.625427\pi\) | ||||
−0.383921 | + | 0.923366i | \(0.625427\pi\) | |||||||
\(284\) | 7.41158 | 0.439797 | ||||||||
\(285\) | −1.69227 | −0.100241 | ||||||||
\(286\) | −1.12433 | −0.0664833 | ||||||||
\(287\) | −22.0150 | −1.29950 | ||||||||
\(288\) | 2.94799 | 0.173712 | ||||||||
\(289\) | −14.2260 | −0.836822 | ||||||||
\(290\) | 4.72931 | 0.277714 | ||||||||
\(291\) | 1.48350 | 0.0869644 | ||||||||
\(292\) | 2.51101 | 0.146946 | ||||||||
\(293\) | 31.7028 | 1.85210 | 0.926049 | − | 0.377402i | \(-0.123183\pi\) | ||||
0.926049 | + | 0.377402i | \(0.123183\pi\) | |||||||
\(294\) | 0.215788 | 0.0125850 | ||||||||
\(295\) | 0.759347 | 0.0442109 | ||||||||
\(296\) | 5.63729 | 0.327661 | ||||||||
\(297\) | 1.35646 | 0.0787096 | ||||||||
\(298\) | −9.56881 | −0.554306 | ||||||||
\(299\) | −0.984541 | −0.0569375 | ||||||||
\(300\) | −0.228053 | −0.0131666 | ||||||||
\(301\) | 2.81890 | 0.162479 | ||||||||
\(302\) | −15.7568 | −0.906703 | ||||||||
\(303\) | −1.03211 | −0.0592933 | ||||||||
\(304\) | 7.42051 | 0.425595 | ||||||||
\(305\) | 4.85201 | 0.277825 | ||||||||
\(306\) | −4.91000 | −0.280686 | ||||||||
\(307\) | −12.5516 | −0.716360 | −0.358180 | − | 0.933653i | \(-0.616603\pi\) | ||||
−0.358180 | + | 0.933653i | \(0.616603\pi\) | |||||||
\(308\) | −2.81890 | −0.160622 | ||||||||
\(309\) | 0.600688 | 0.0341719 | ||||||||
\(310\) | 2.66066 | 0.151116 | ||||||||
\(311\) | −31.6930 | −1.79715 | −0.898573 | − | 0.438823i | \(-0.855395\pi\) | ||||
−0.898573 | + | 0.438823i | \(0.855395\pi\) | |||||||
\(312\) | 0.256408 | 0.0145162 | ||||||||
\(313\) | −29.8594 | −1.68775 | −0.843877 | − | 0.536536i | \(-0.819732\pi\) | ||||
−0.843877 | + | 0.536536i | \(0.819732\pi\) | |||||||
\(314\) | 4.47588 | 0.252589 | ||||||||
\(315\) | 8.31011 | 0.468221 | ||||||||
\(316\) | −10.7456 | −0.604490 | ||||||||
\(317\) | 21.6465 | 1.21579 | 0.607894 | − | 0.794018i | \(-0.292014\pi\) | ||||
0.607894 | + | 0.794018i | \(0.292014\pi\) | |||||||
\(318\) | −0.776902 | −0.0435665 | ||||||||
\(319\) | −4.72931 | −0.264790 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 2.12811 | 0.118779 | ||||||||
\(322\) | −2.46842 | −0.137559 | ||||||||
\(323\) | −12.3592 | −0.687682 | ||||||||
\(324\) | 8.53463 | 0.474146 | ||||||||
\(325\) | 1.12433 | 0.0623669 | ||||||||
\(326\) | −15.5677 | −0.862216 | ||||||||
\(327\) | 1.13362 | 0.0626894 | ||||||||
\(328\) | −7.80977 | −0.431223 | ||||||||
\(329\) | −37.2264 | −2.05236 | ||||||||
\(330\) | 0.228053 | 0.0125539 | ||||||||
\(331\) | −30.4783 | −1.67524 | −0.837621 | − | 0.546252i | \(-0.816054\pi\) | ||||
−0.837621 | + | 0.546252i | \(0.816054\pi\) | |||||||
\(332\) | −12.0367 | −0.660602 | ||||||||
\(333\) | 16.6187 | 0.910699 | ||||||||
\(334\) | 6.01893 | 0.329341 | ||||||||
\(335\) | −2.24757 | −0.122798 | ||||||||
\(336\) | 0.642859 | 0.0350708 | ||||||||
\(337\) | −23.7603 | −1.29431 | −0.647154 | − | 0.762359i | \(-0.724041\pi\) | ||||
−0.647154 | + | 0.762359i | \(0.724041\pi\) | |||||||
\(338\) | 11.7359 | 0.638347 | ||||||||
\(339\) | 1.87725 | 0.101958 | ||||||||
\(340\) | −1.66554 | −0.0903267 | ||||||||
\(341\) | −2.66066 | −0.144083 | ||||||||
\(342\) | 21.8756 | 1.18290 | ||||||||
\(343\) | 17.0650 | 0.921425 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 0.199698 | 0.0107514 | ||||||||
\(346\) | 4.00241 | 0.215171 | ||||||||
\(347\) | −14.2525 | −0.765112 | −0.382556 | − | 0.923932i | \(-0.624956\pi\) | ||||
−0.382556 | + | 0.923932i | \(0.624956\pi\) | |||||||
\(348\) | 1.07853 | 0.0578154 | ||||||||
\(349\) | −5.27164 | −0.282184 | −0.141092 | − | 0.989996i | \(-0.545061\pi\) | ||||
−0.141092 | + | 0.989996i | \(0.545061\pi\) | |||||||
\(350\) | 2.81890 | 0.150677 | ||||||||
\(351\) | 1.52511 | 0.0814044 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −21.3297 | −1.13526 | −0.567632 | − | 0.823282i | \(-0.692140\pi\) | ||||
−0.567632 | + | 0.823282i | \(0.692140\pi\) | |||||||
\(354\) | 0.173171 | 0.00920395 | ||||||||
\(355\) | 7.41158 | 0.393366 | ||||||||
\(356\) | −5.21429 | −0.276357 | ||||||||
\(357\) | −1.07071 | −0.0566679 | ||||||||
\(358\) | 0.139202 | 0.00735704 | ||||||||
\(359\) | 4.53953 | 0.239587 | 0.119794 | − | 0.992799i | \(-0.461777\pi\) | ||||
0.119794 | + | 0.992799i | \(0.461777\pi\) | |||||||
\(360\) | 2.94799 | 0.155373 | ||||||||
\(361\) | 36.0639 | 1.89810 | ||||||||
\(362\) | −6.05904 | −0.318456 | ||||||||
\(363\) | −0.228053 | −0.0119697 | ||||||||
\(364\) | −3.16939 | −0.166121 | ||||||||
\(365\) | 2.51101 | 0.131432 | ||||||||
\(366\) | 1.10651 | 0.0578384 | ||||||||
\(367\) | −3.89111 | −0.203114 | −0.101557 | − | 0.994830i | \(-0.532382\pi\) | ||||
−0.101557 | + | 0.994830i | \(0.532382\pi\) | |||||||
\(368\) | −0.875665 | −0.0456472 | ||||||||
\(369\) | −23.0232 | −1.19854 | ||||||||
\(370\) | 5.63729 | 0.293069 | ||||||||
\(371\) | 9.60308 | 0.498567 | ||||||||
\(372\) | 0.606772 | 0.0314597 | ||||||||
\(373\) | 23.0020 | 1.19100 | 0.595500 | − | 0.803356i | \(-0.296954\pi\) | ||||
0.595500 | + | 0.803356i | \(0.296954\pi\) | |||||||
\(374\) | 1.66554 | 0.0861231 | ||||||||
\(375\) | −0.228053 | −0.0117766 | ||||||||
\(376\) | −13.2060 | −0.681047 | ||||||||
\(377\) | −5.31732 | −0.273856 | ||||||||
\(378\) | 3.82372 | 0.196671 | ||||||||
\(379\) | 9.10158 | 0.467517 | 0.233758 | − | 0.972295i | \(-0.424898\pi\) | ||||
0.233758 | + | 0.972295i | \(0.424898\pi\) | |||||||
\(380\) | 7.42051 | 0.380664 | ||||||||
\(381\) | 4.60474 | 0.235908 | ||||||||
\(382\) | 16.1843 | 0.828061 | ||||||||
\(383\) | 12.0564 | 0.616051 | 0.308025 | − | 0.951378i | \(-0.400332\pi\) | ||||
0.308025 | + | 0.951378i | \(0.400332\pi\) | |||||||
\(384\) | 0.228053 | 0.0116378 | ||||||||
\(385\) | −2.81890 | −0.143665 | ||||||||
\(386\) | −25.5558 | −1.30075 | ||||||||
\(387\) | 2.94799 | 0.149855 | ||||||||
\(388\) | −6.50507 | −0.330245 | ||||||||
\(389\) | 27.1985 | 1.37902 | 0.689510 | − | 0.724277i | \(-0.257826\pi\) | ||||
0.689510 | + | 0.724277i | \(0.257826\pi\) | |||||||
\(390\) | 0.256408 | 0.0129837 | ||||||||
\(391\) | 1.45846 | 0.0737573 | ||||||||
\(392\) | −0.946220 | −0.0477913 | ||||||||
\(393\) | 4.00582 | 0.202067 | ||||||||
\(394\) | −19.6077 | −0.987821 | ||||||||
\(395\) | −10.7456 | −0.540672 | ||||||||
\(396\) | −2.94799 | −0.148142 | ||||||||
\(397\) | −17.7469 | −0.890693 | −0.445346 | − | 0.895358i | \(-0.646919\pi\) | ||||
−0.445346 | + | 0.895358i | \(0.646919\pi\) | |||||||
\(398\) | 21.6580 | 1.08562 | ||||||||
\(399\) | 4.77034 | 0.238816 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 6.79422 | 0.339287 | 0.169644 | − | 0.985505i | \(-0.445738\pi\) | ||||
0.169644 | + | 0.985505i | \(0.445738\pi\) | |||||||
\(402\) | −0.512565 | −0.0255644 | ||||||||
\(403\) | −2.99148 | −0.149016 | ||||||||
\(404\) | 4.52576 | 0.225165 | ||||||||
\(405\) | 8.53463 | 0.424089 | ||||||||
\(406\) | −13.3315 | −0.661629 | ||||||||
\(407\) | −5.63729 | −0.279430 | ||||||||
\(408\) | −0.379832 | −0.0188045 | ||||||||
\(409\) | −5.47349 | −0.270647 | −0.135323 | − | 0.990801i | \(-0.543207\pi\) | ||||
−0.135323 | + | 0.990801i | \(0.543207\pi\) | |||||||
\(410\) | −7.80977 | −0.385697 | ||||||||
\(411\) | 2.41948 | 0.119344 | ||||||||
\(412\) | −2.63398 | −0.129767 | ||||||||
\(413\) | −2.14053 | −0.105328 | ||||||||
\(414\) | −2.58145 | −0.126872 | ||||||||
\(415\) | −12.0367 | −0.590860 | ||||||||
\(416\) | −1.12433 | −0.0551250 | ||||||||
\(417\) | 0.288468 | 0.0141264 | ||||||||
\(418\) | −7.42051 | −0.362949 | ||||||||
\(419\) | −1.27871 | −0.0624689 | −0.0312344 | − | 0.999512i | \(-0.509944\pi\) | ||||
−0.0312344 | + | 0.999512i | \(0.509944\pi\) | |||||||
\(420\) | 0.642859 | 0.0313683 | ||||||||
\(421\) | −11.6440 | −0.567492 | −0.283746 | − | 0.958899i | \(-0.591577\pi\) | ||||
−0.283746 | + | 0.958899i | \(0.591577\pi\) | |||||||
\(422\) | −12.3193 | −0.599696 | ||||||||
\(423\) | −38.9312 | −1.89290 | ||||||||
\(424\) | 3.40667 | 0.165443 | ||||||||
\(425\) | −1.66554 | −0.0807906 | ||||||||
\(426\) | 1.69023 | 0.0818921 | ||||||||
\(427\) | −13.6773 | −0.661893 | ||||||||
\(428\) | −9.33164 | −0.451062 | ||||||||
\(429\) | −0.256408 | −0.0123795 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 26.0044 | 1.25259 | 0.626295 | − | 0.779586i | \(-0.284571\pi\) | ||||
0.626295 | + | 0.779586i | \(0.284571\pi\) | |||||||
\(432\) | 1.35646 | 0.0652626 | ||||||||
\(433\) | 1.06003 | 0.0509419 | 0.0254710 | − | 0.999676i | \(-0.491891\pi\) | ||||
0.0254710 | + | 0.999676i | \(0.491891\pi\) | |||||||
\(434\) | −7.50016 | −0.360019 | ||||||||
\(435\) | 1.07853 | 0.0517117 | ||||||||
\(436\) | −4.97087 | −0.238061 | ||||||||
\(437\) | −6.49788 | −0.310836 | ||||||||
\(438\) | 0.572644 | 0.0273620 | ||||||||
\(439\) | 15.3574 | 0.732970 | 0.366485 | − | 0.930424i | \(-0.380561\pi\) | ||||
0.366485 | + | 0.930424i | \(0.380561\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −2.78945 | −0.132831 | ||||||||
\(442\) | 1.87263 | 0.0890717 | ||||||||
\(443\) | −13.0010 | −0.617697 | −0.308848 | − | 0.951111i | \(-0.599944\pi\) | ||||
−0.308848 | + | 0.951111i | \(0.599944\pi\) | |||||||
\(444\) | 1.28560 | 0.0610119 | ||||||||
\(445\) | −5.21429 | −0.247181 | ||||||||
\(446\) | 20.5666 | 0.973855 | ||||||||
\(447\) | −2.18219 | −0.103214 | ||||||||
\(448\) | −2.81890 | −0.133181 | ||||||||
\(449\) | −22.9889 | −1.08491 | −0.542457 | − | 0.840084i | \(-0.682506\pi\) | ||||
−0.542457 | + | 0.840084i | \(0.682506\pi\) | |||||||
\(450\) | 2.94799 | 0.138970 | ||||||||
\(451\) | 7.80977 | 0.367748 | ||||||||
\(452\) | −8.23164 | −0.387184 | ||||||||
\(453\) | −3.59339 | −0.168832 | ||||||||
\(454\) | 24.9903 | 1.17285 | ||||||||
\(455\) | −3.16939 | −0.148583 | ||||||||
\(456\) | 1.69227 | 0.0792477 | ||||||||
\(457\) | −17.3573 | −0.811942 | −0.405971 | − | 0.913886i | \(-0.633067\pi\) | ||||
−0.405971 | + | 0.913886i | \(0.633067\pi\) | |||||||
\(458\) | 23.3892 | 1.09291 | ||||||||
\(459\) | −2.25923 | −0.105452 | ||||||||
\(460\) | −0.875665 | −0.0408281 | ||||||||
\(461\) | 2.22579 | 0.103665 | 0.0518327 | − | 0.998656i | \(-0.483494\pi\) | ||||
0.0518327 | + | 0.998656i | \(0.483494\pi\) | |||||||
\(462\) | −0.642859 | −0.0299085 | ||||||||
\(463\) | −12.5943 | −0.585306 | −0.292653 | − | 0.956219i | \(-0.594538\pi\) | ||||
−0.292653 | + | 0.956219i | \(0.594538\pi\) | |||||||
\(464\) | −4.72931 | −0.219553 | ||||||||
\(465\) | 0.606772 | 0.0281384 | ||||||||
\(466\) | 7.48056 | 0.346530 | ||||||||
\(467\) | −15.4563 | −0.715232 | −0.357616 | − | 0.933869i | \(-0.616410\pi\) | ||||
−0.357616 | + | 0.933869i | \(0.616410\pi\) | |||||||
\(468\) | −3.31453 | −0.153214 | ||||||||
\(469\) | 6.33569 | 0.292555 | ||||||||
\(470\) | −13.2060 | −0.609147 | ||||||||
\(471\) | 1.02074 | 0.0470331 | ||||||||
\(472\) | −0.759347 | −0.0349518 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −2.45057 | −0.112559 | ||||||||
\(475\) | 7.42051 | 0.340476 | ||||||||
\(476\) | 4.69500 | 0.215195 | ||||||||
\(477\) | 10.0428 | 0.459830 | ||||||||
\(478\) | −10.7522 | −0.491792 | ||||||||
\(479\) | 16.3881 | 0.748793 | 0.374397 | − | 0.927269i | \(-0.377850\pi\) | ||||
0.374397 | + | 0.927269i | \(0.377850\pi\) | |||||||
\(480\) | 0.228053 | 0.0104091 | ||||||||
\(481\) | −6.33820 | −0.288997 | ||||||||
\(482\) | −10.8505 | −0.494228 | ||||||||
\(483\) | −0.562930 | −0.0256142 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.50507 | −0.295380 | ||||||||
\(486\) | 6.01572 | 0.272879 | ||||||||
\(487\) | −3.92891 | −0.178036 | −0.0890178 | − | 0.996030i | \(-0.528373\pi\) | ||||
−0.0890178 | + | 0.996030i | \(0.528373\pi\) | |||||||
\(488\) | −4.85201 | −0.219640 | ||||||||
\(489\) | −3.55026 | −0.160548 | ||||||||
\(490\) | −0.946220 | −0.0427459 | ||||||||
\(491\) | 9.17767 | 0.414183 | 0.207091 | − | 0.978322i | \(-0.433600\pi\) | ||||
0.207091 | + | 0.978322i | \(0.433600\pi\) | |||||||
\(492\) | −1.78104 | −0.0802956 | ||||||||
\(493\) | 7.87686 | 0.354756 | ||||||||
\(494\) | −8.34313 | −0.375375 | ||||||||
\(495\) | −2.94799 | −0.132502 | ||||||||
\(496\) | −2.66066 | −0.119467 | ||||||||
\(497\) | −20.8925 | −0.937159 | ||||||||
\(498\) | −2.74501 | −0.123007 | ||||||||
\(499\) | −39.8502 | −1.78394 | −0.891969 | − | 0.452096i | \(-0.850676\pi\) | ||||
−0.891969 | + | 0.452096i | \(0.850676\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 1.37264 | 0.0613248 | ||||||||
\(502\) | 1.64877 | 0.0735881 | ||||||||
\(503\) | −25.6544 | −1.14387 | −0.571937 | − | 0.820297i | \(-0.693808\pi\) | ||||
−0.571937 | + | 0.820297i | \(0.693808\pi\) | |||||||
\(504\) | −8.31011 | −0.370162 | ||||||||
\(505\) | 4.52576 | 0.201394 | ||||||||
\(506\) | 0.875665 | 0.0389281 | ||||||||
\(507\) | 2.67640 | 0.118863 | ||||||||
\(508\) | −20.1915 | −0.895854 | ||||||||
\(509\) | 21.5400 | 0.954746 | 0.477373 | − | 0.878701i | \(-0.341589\pi\) | ||||
0.477373 | + | 0.878701i | \(0.341589\pi\) | |||||||
\(510\) | −0.379832 | −0.0168192 | ||||||||
\(511\) | −7.07830 | −0.313126 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 10.0656 | 0.444407 | ||||||||
\(514\) | 21.6789 | 0.956215 | ||||||||
\(515\) | −2.63398 | −0.116067 | ||||||||
\(516\) | 0.228053 | 0.0100395 | ||||||||
\(517\) | 13.2060 | 0.580799 | ||||||||
\(518\) | −15.8910 | −0.698210 | ||||||||
\(519\) | 0.912762 | 0.0400658 | ||||||||
\(520\) | −1.12433 | −0.0493053 | ||||||||
\(521\) | −11.6344 | −0.509713 | −0.254857 | − | 0.966979i | \(-0.582028\pi\) | ||||
−0.254857 | + | 0.966979i | \(0.582028\pi\) | |||||||
\(522\) | −13.9420 | −0.610223 | ||||||||
\(523\) | −1.08302 | −0.0473570 | −0.0236785 | − | 0.999720i | \(-0.507538\pi\) | ||||
−0.0236785 | + | 0.999720i | \(0.507538\pi\) | |||||||
\(524\) | −17.5653 | −0.767345 | ||||||||
\(525\) | 0.642859 | 0.0280567 | ||||||||
\(526\) | 15.0436 | 0.655934 | ||||||||
\(527\) | 4.43145 | 0.193037 | ||||||||
\(528\) | −0.228053 | −0.00992473 | ||||||||
\(529\) | −22.2332 | −0.966661 | ||||||||
\(530\) | 3.40667 | 0.147976 | ||||||||
\(531\) | −2.23855 | −0.0971447 | ||||||||
\(532\) | −20.9177 | −0.906897 | ||||||||
\(533\) | 8.78080 | 0.380339 | ||||||||
\(534\) | −1.18914 | −0.0514589 | ||||||||
\(535\) | −9.33164 | −0.403442 | ||||||||
\(536\) | 2.24757 | 0.0970803 | ||||||||
\(537\) | 0.0317454 | 0.00136991 | ||||||||
\(538\) | −17.5715 | −0.757562 | ||||||||
\(539\) | 0.946220 | 0.0407566 | ||||||||
\(540\) | 1.35646 | 0.0583726 | ||||||||
\(541\) | −16.5158 | −0.710072 | −0.355036 | − | 0.934853i | \(-0.615531\pi\) | ||||
−0.355036 | + | 0.934853i | \(0.615531\pi\) | |||||||
\(542\) | 5.85055 | 0.251303 | ||||||||
\(543\) | −1.38178 | −0.0592979 | ||||||||
\(544\) | 1.66554 | 0.0714095 | ||||||||
\(545\) | −4.97087 | −0.212929 | ||||||||
\(546\) | −0.722789 | −0.0309325 | ||||||||
\(547\) | −20.5525 | −0.878759 | −0.439380 | − | 0.898301i | \(-0.644802\pi\) | ||||
−0.439380 | + | 0.898301i | \(0.644802\pi\) | |||||||
\(548\) | −10.6093 | −0.453206 | ||||||||
\(549\) | −14.3037 | −0.610466 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −35.0939 | −1.49505 | ||||||||
\(552\) | −0.199698 | −0.00849971 | ||||||||
\(553\) | 30.2909 | 1.28810 | ||||||||
\(554\) | −5.20593 | −0.221179 | ||||||||
\(555\) | 1.28560 | 0.0545707 | ||||||||
\(556\) | −1.26492 | −0.0536445 | ||||||||
\(557\) | 18.4175 | 0.780377 | 0.390188 | − | 0.920735i | \(-0.372410\pi\) | ||||
0.390188 | + | 0.920735i | \(0.372410\pi\) | |||||||
\(558\) | −7.84362 | −0.332047 | ||||||||
\(559\) | −1.12433 | −0.0475543 | ||||||||
\(560\) | −2.81890 | −0.119120 | ||||||||
\(561\) | 0.379832 | 0.0160365 | ||||||||
\(562\) | −0.709992 | −0.0299492 | ||||||||
\(563\) | −26.4824 | −1.11610 | −0.558049 | − | 0.829808i | \(-0.688450\pi\) | ||||
−0.558049 | + | 0.829808i | \(0.688450\pi\) | |||||||
\(564\) | −3.01167 | −0.126814 | ||||||||
\(565\) | −8.23164 | −0.346308 | ||||||||
\(566\) | 12.9171 | 0.542947 | ||||||||
\(567\) | −24.0583 | −1.01035 | ||||||||
\(568\) | −7.41158 | −0.310983 | ||||||||
\(569\) | 28.7858 | 1.20676 | 0.603381 | − | 0.797453i | \(-0.293820\pi\) | ||||
0.603381 | + | 0.797453i | \(0.293820\pi\) | |||||||
\(570\) | 1.69227 | 0.0708813 | ||||||||
\(571\) | 42.4795 | 1.77771 | 0.888855 | − | 0.458188i | \(-0.151501\pi\) | ||||
0.888855 | + | 0.458188i | \(0.151501\pi\) | |||||||
\(572\) | 1.12433 | 0.0470108 | ||||||||
\(573\) | 3.69088 | 0.154189 | ||||||||
\(574\) | 22.0150 | 0.918889 | ||||||||
\(575\) | −0.875665 | −0.0365178 | ||||||||
\(576\) | −2.94799 | −0.122833 | ||||||||
\(577\) | 31.9934 | 1.33190 | 0.665952 | − | 0.745995i | \(-0.268026\pi\) | ||||
0.665952 | + | 0.745995i | \(0.268026\pi\) | |||||||
\(578\) | 14.2260 | 0.591722 | ||||||||
\(579\) | −5.82807 | −0.242206 | ||||||||
\(580\) | −4.72931 | −0.196374 | ||||||||
\(581\) | 33.9304 | 1.40767 | ||||||||
\(582\) | −1.48350 | −0.0614931 | ||||||||
\(583\) | −3.40667 | −0.141090 | ||||||||
\(584\) | −2.51101 | −0.103906 | ||||||||
\(585\) | −3.31453 | −0.137039 | ||||||||
\(586\) | −31.7028 | −1.30963 | ||||||||
\(587\) | 33.9644 | 1.40186 | 0.700930 | − | 0.713230i | \(-0.252769\pi\) | ||||
0.700930 | + | 0.713230i | \(0.252769\pi\) | |||||||
\(588\) | −0.215788 | −0.00889896 | ||||||||
\(589\) | −19.7435 | −0.813516 | ||||||||
\(590\) | −0.759347 | −0.0312618 | ||||||||
\(591\) | −4.47159 | −0.183937 | ||||||||
\(592\) | −5.63729 | −0.231691 | ||||||||
\(593\) | 4.34754 | 0.178532 | 0.0892660 | − | 0.996008i | \(-0.471548\pi\) | ||||
0.0892660 | + | 0.996008i | \(0.471548\pi\) | |||||||
\(594\) | −1.35646 | −0.0556561 | ||||||||
\(595\) | 4.69500 | 0.192476 | ||||||||
\(596\) | 9.56881 | 0.391954 | ||||||||
\(597\) | 4.93917 | 0.202147 | ||||||||
\(598\) | 0.984541 | 0.0402609 | ||||||||
\(599\) | −46.5405 | −1.90159 | −0.950796 | − | 0.309819i | \(-0.899732\pi\) | ||||
−0.950796 | + | 0.309819i | \(0.899732\pi\) | |||||||
\(600\) | 0.228053 | 0.00931022 | ||||||||
\(601\) | 6.17544 | 0.251902 | 0.125951 | − | 0.992036i | \(-0.459802\pi\) | ||||
0.125951 | + | 0.992036i | \(0.459802\pi\) | |||||||
\(602\) | −2.81890 | −0.114890 | ||||||||
\(603\) | 6.62583 | 0.269824 | ||||||||
\(604\) | 15.7568 | 0.641136 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 1.03211 | 0.0419267 | ||||||||
\(607\) | −11.5532 | −0.468929 | −0.234464 | − | 0.972125i | \(-0.575334\pi\) | ||||
−0.234464 | + | 0.972125i | \(0.575334\pi\) | |||||||
\(608\) | −7.42051 | −0.300941 | ||||||||
\(609\) | −3.04028 | −0.123198 | ||||||||
\(610\) | −4.85201 | −0.196452 | ||||||||
\(611\) | 14.8480 | 0.600684 | ||||||||
\(612\) | 4.91000 | 0.198475 | ||||||||
\(613\) | −9.44772 | −0.381590 | −0.190795 | − | 0.981630i | \(-0.561107\pi\) | ||||
−0.190795 | + | 0.981630i | \(0.561107\pi\) | |||||||
\(614\) | 12.5516 | 0.506543 | ||||||||
\(615\) | −1.78104 | −0.0718185 | ||||||||
\(616\) | 2.81890 | 0.113577 | ||||||||
\(617\) | −1.03392 | −0.0416239 | −0.0208120 | − | 0.999783i | \(-0.506625\pi\) | ||||
−0.0208120 | + | 0.999783i | \(0.506625\pi\) | |||||||
\(618\) | −0.600688 | −0.0241632 | ||||||||
\(619\) | −25.0261 | −1.00588 | −0.502941 | − | 0.864321i | \(-0.667749\pi\) | ||||
−0.502941 | + | 0.864321i | \(0.667749\pi\) | |||||||
\(620\) | −2.66066 | −0.106855 | ||||||||
\(621\) | −1.18780 | −0.0476649 | ||||||||
\(622\) | 31.6930 | 1.27077 | ||||||||
\(623\) | 14.6986 | 0.588887 | ||||||||
\(624\) | −0.256408 | −0.0102645 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 29.8594 | 1.19342 | ||||||||
\(627\) | −1.69227 | −0.0675827 | ||||||||
\(628\) | −4.47588 | −0.178607 | ||||||||
\(629\) | 9.38914 | 0.374370 | ||||||||
\(630\) | −8.31011 | −0.331083 | ||||||||
\(631\) | −12.3126 | −0.490158 | −0.245079 | − | 0.969503i | \(-0.578814\pi\) | ||||
−0.245079 | + | 0.969503i | \(0.578814\pi\) | |||||||
\(632\) | 10.7456 | 0.427439 | ||||||||
\(633\) | −2.80946 | −0.111666 | ||||||||
\(634\) | −21.6465 | −0.859693 | ||||||||
\(635\) | −20.1915 | −0.801276 | ||||||||
\(636\) | 0.776902 | 0.0308062 | ||||||||
\(637\) | 1.06387 | 0.0421520 | ||||||||
\(638\) | 4.72931 | 0.187235 | ||||||||
\(639\) | −21.8493 | −0.864345 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 9.17973 | 0.362578 | 0.181289 | − | 0.983430i | \(-0.441973\pi\) | ||||
0.181289 | + | 0.983430i | \(0.441973\pi\) | |||||||
\(642\) | −2.12811 | −0.0839897 | ||||||||
\(643\) | 0.391841 | 0.0154527 | 0.00772635 | − | 0.999970i | \(-0.497541\pi\) | ||||
0.00772635 | + | 0.999970i | \(0.497541\pi\) | |||||||
\(644\) | 2.46842 | 0.0972693 | ||||||||
\(645\) | 0.228053 | 0.00897957 | ||||||||
\(646\) | 12.3592 | 0.486265 | ||||||||
\(647\) | −30.6471 | −1.20486 | −0.602431 | − | 0.798171i | \(-0.705801\pi\) | ||||
−0.602431 | + | 0.798171i | \(0.705801\pi\) | |||||||
\(648\) | −8.53463 | −0.335272 | ||||||||
\(649\) | 0.759347 | 0.0298070 | ||||||||
\(650\) | −1.12433 | −0.0441000 | ||||||||
\(651\) | −1.71043 | −0.0670371 | ||||||||
\(652\) | 15.5677 | 0.609679 | ||||||||
\(653\) | 22.1546 | 0.866977 | 0.433488 | − | 0.901159i | \(-0.357283\pi\) | ||||
0.433488 | + | 0.901159i | \(0.357283\pi\) | |||||||
\(654\) | −1.13362 | −0.0443281 | ||||||||
\(655\) | −17.5653 | −0.686334 | ||||||||
\(656\) | 7.80977 | 0.304920 | ||||||||
\(657\) | −7.40245 | −0.288797 | ||||||||
\(658\) | 37.2264 | 1.45124 | ||||||||
\(659\) | 32.6360 | 1.27132 | 0.635659 | − | 0.771970i | \(-0.280729\pi\) | ||||
0.635659 | + | 0.771970i | \(0.280729\pi\) | |||||||
\(660\) | −0.228053 | −0.00887695 | ||||||||
\(661\) | −13.2055 | −0.513633 | −0.256816 | − | 0.966460i | \(-0.582674\pi\) | ||||
−0.256816 | + | 0.966460i | \(0.582674\pi\) | |||||||
\(662\) | 30.4783 | 1.18457 | ||||||||
\(663\) | 0.427058 | 0.0165855 | ||||||||
\(664\) | 12.0367 | 0.467116 | ||||||||
\(665\) | −20.9177 | −0.811153 | ||||||||
\(666\) | −16.6187 | −0.643961 | ||||||||
\(667\) | 4.14129 | 0.160351 | ||||||||
\(668\) | −6.01893 | −0.232879 | ||||||||
\(669\) | 4.69027 | 0.181336 | ||||||||
\(670\) | 2.24757 | 0.0868313 | ||||||||
\(671\) | 4.85201 | 0.187310 | ||||||||
\(672\) | −0.642859 | −0.0247988 | ||||||||
\(673\) | 10.7752 | 0.415353 | 0.207677 | − | 0.978198i | \(-0.433410\pi\) | ||||
0.207677 | + | 0.978198i | \(0.433410\pi\) | |||||||
\(674\) | 23.7603 | 0.915214 | ||||||||
\(675\) | 1.35646 | 0.0522100 | ||||||||
\(676\) | −11.7359 | −0.451380 | ||||||||
\(677\) | −16.0165 | −0.615564 | −0.307782 | − | 0.951457i | \(-0.599587\pi\) | ||||
−0.307782 | + | 0.951457i | \(0.599587\pi\) | |||||||
\(678\) | −1.87725 | −0.0720953 | ||||||||
\(679\) | 18.3372 | 0.703716 | ||||||||
\(680\) | 1.66554 | 0.0638706 | ||||||||
\(681\) | 5.69910 | 0.218390 | ||||||||
\(682\) | 2.66066 | 0.101882 | ||||||||
\(683\) | −2.47119 | −0.0945576 | −0.0472788 | − | 0.998882i | \(-0.515055\pi\) | ||||
−0.0472788 | + | 0.998882i | \(0.515055\pi\) | |||||||
\(684\) | −21.8756 | −0.836434 | ||||||||
\(685\) | −10.6093 | −0.405360 | ||||||||
\(686\) | −17.0650 | −0.651546 | ||||||||
\(687\) | 5.33398 | 0.203504 | ||||||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | −3.83024 | −0.145921 | ||||||||
\(690\) | −0.199698 | −0.00760238 | ||||||||
\(691\) | −34.7962 | −1.32371 | −0.661855 | − | 0.749632i | \(-0.730231\pi\) | ||||
−0.661855 | + | 0.749632i | \(0.730231\pi\) | |||||||
\(692\) | −4.00241 | −0.152149 | ||||||||
\(693\) | 8.31011 | 0.315675 | ||||||||
\(694\) | 14.2525 | 0.541016 | ||||||||
\(695\) | −1.26492 | −0.0479811 | ||||||||
\(696\) | −1.07853 | −0.0408817 | ||||||||
\(697\) | −13.0075 | −0.492694 | ||||||||
\(698\) | 5.27164 | 0.199534 | ||||||||
\(699\) | 1.70596 | 0.0645255 | ||||||||
\(700\) | −2.81890 | −0.106545 | ||||||||
\(701\) | 22.8672 | 0.863683 | 0.431841 | − | 0.901950i | \(-0.357864\pi\) | ||||
0.431841 | + | 0.901950i | \(0.357864\pi\) | |||||||
\(702\) | −1.52511 | −0.0575616 | ||||||||
\(703\) | −41.8316 | −1.57771 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −3.01167 | −0.113426 | ||||||||
\(706\) | 21.3297 | 0.802753 | ||||||||
\(707\) | −12.7577 | −0.479802 | ||||||||
\(708\) | −0.173171 | −0.00650818 | ||||||||
\(709\) | 13.4279 | 0.504294 | 0.252147 | − | 0.967689i | \(-0.418863\pi\) | ||||
0.252147 | + | 0.967689i | \(0.418863\pi\) | |||||||
\(710\) | −7.41158 | −0.278152 | ||||||||
\(711\) | 31.6781 | 1.18802 | ||||||||
\(712\) | 5.21429 | 0.195414 | ||||||||
\(713\) | 2.32985 | 0.0872536 | ||||||||
\(714\) | 1.07071 | 0.0400703 | ||||||||
\(715\) | 1.12433 | 0.0420477 | ||||||||
\(716\) | −0.139202 | −0.00520221 | ||||||||
\(717\) | −2.45206 | −0.0915739 | ||||||||
\(718\) | −4.53953 | −0.169414 | ||||||||
\(719\) | 3.01743 | 0.112531 | 0.0562656 | − | 0.998416i | \(-0.482081\pi\) | ||||
0.0562656 | + | 0.998416i | \(0.482081\pi\) | |||||||
\(720\) | −2.94799 | −0.109865 | ||||||||
\(721\) | 7.42495 | 0.276520 | ||||||||
\(722\) | −36.0639 | −1.34216 | ||||||||
\(723\) | −2.47449 | −0.0920274 | ||||||||
\(724\) | 6.05904 | 0.225182 | ||||||||
\(725\) | −4.72931 | −0.175642 | ||||||||
\(726\) | 0.228053 | 0.00846384 | ||||||||
\(727\) | −40.5835 | −1.50516 | −0.752579 | − | 0.658502i | \(-0.771190\pi\) | ||||
−0.752579 | + | 0.658502i | \(0.771190\pi\) | |||||||
\(728\) | 3.16939 | 0.117465 | ||||||||
\(729\) | −24.2320 | −0.897481 | ||||||||
\(730\) | −2.51101 | −0.0929368 | ||||||||
\(731\) | 1.66554 | 0.0616023 | ||||||||
\(732\) | −1.10651 | −0.0408979 | ||||||||
\(733\) | 48.4636 | 1.79004 | 0.895022 | − | 0.446021i | \(-0.147160\pi\) | ||||
0.895022 | + | 0.446021i | \(0.147160\pi\) | |||||||
\(734\) | 3.89111 | 0.143623 | ||||||||
\(735\) | −0.215788 | −0.00795947 | ||||||||
\(736\) | 0.875665 | 0.0322775 | ||||||||
\(737\) | −2.24757 | −0.0827904 | ||||||||
\(738\) | 23.0232 | 0.847494 | ||||||||
\(739\) | 34.9368 | 1.28517 | 0.642586 | − | 0.766213i | \(-0.277861\pi\) | ||||
0.642586 | + | 0.766213i | \(0.277861\pi\) | |||||||
\(740\) | −5.63729 | −0.207231 | ||||||||
\(741\) | −1.90268 | −0.0698965 | ||||||||
\(742\) | −9.60308 | −0.352540 | ||||||||
\(743\) | −41.3831 | −1.51820 | −0.759100 | − | 0.650974i | \(-0.774361\pi\) | ||||
−0.759100 | + | 0.650974i | \(0.774361\pi\) | |||||||
\(744\) | −0.606772 | −0.0222454 | ||||||||
\(745\) | 9.56881 | 0.350574 | ||||||||
\(746\) | −23.0020 | −0.842164 | ||||||||
\(747\) | 35.4842 | 1.29830 | ||||||||
\(748\) | −1.66554 | −0.0608982 | ||||||||
\(749\) | 26.3050 | 0.961164 | ||||||||
\(750\) | 0.228053 | 0.00832732 | ||||||||
\(751\) | 24.2343 | 0.884322 | 0.442161 | − | 0.896936i | \(-0.354212\pi\) | ||||
0.442161 | + | 0.896936i | \(0.354212\pi\) | |||||||
\(752\) | 13.2060 | 0.481573 | ||||||||
\(753\) | 0.376006 | 0.0137024 | ||||||||
\(754\) | 5.31732 | 0.193646 | ||||||||
\(755\) | 15.7568 | 0.573449 | ||||||||
\(756\) | −3.82372 | −0.139067 | ||||||||
\(757\) | −34.1443 | −1.24100 | −0.620498 | − | 0.784208i | \(-0.713069\pi\) | ||||
−0.620498 | + | 0.784208i | \(0.713069\pi\) | |||||||
\(758\) | −9.10158 | −0.330584 | ||||||||
\(759\) | 0.199698 | 0.00724858 | ||||||||
\(760\) | −7.42051 | −0.269170 | ||||||||
\(761\) | 15.2944 | 0.554421 | 0.277211 | − | 0.960809i | \(-0.410590\pi\) | ||||
0.277211 | + | 0.960809i | \(0.410590\pi\) | |||||||
\(762\) | −4.60474 | −0.166812 | ||||||||
\(763\) | 14.0124 | 0.507283 | ||||||||
\(764\) | −16.1843 | −0.585528 | ||||||||
\(765\) | 4.91000 | 0.177521 | ||||||||
\(766\) | −12.0564 | −0.435614 | ||||||||
\(767\) | 0.853760 | 0.0308275 | ||||||||
\(768\) | −0.228053 | −0.00822915 | ||||||||
\(769\) | −5.86852 | −0.211624 | −0.105812 | − | 0.994386i | \(-0.533744\pi\) | ||||
−0.105812 | + | 0.994386i | \(0.533744\pi\) | |||||||
\(770\) | 2.81890 | 0.101586 | ||||||||
\(771\) | 4.94394 | 0.178052 | ||||||||
\(772\) | 25.5558 | 0.919772 | ||||||||
\(773\) | −1.03649 | −0.0372801 | −0.0186401 | − | 0.999826i | \(-0.505934\pi\) | ||||
−0.0186401 | + | 0.999826i | \(0.505934\pi\) | |||||||
\(774\) | −2.94799 | −0.105963 | ||||||||
\(775\) | −2.66066 | −0.0955739 | ||||||||
\(776\) | 6.50507 | 0.233519 | ||||||||
\(777\) | −3.62399 | −0.130010 | ||||||||
\(778\) | −27.1985 | −0.975114 | ||||||||
\(779\) | 57.9525 | 2.07636 | ||||||||
\(780\) | −0.256408 | −0.00918087 | ||||||||
\(781\) | 7.41158 | 0.265207 | ||||||||
\(782\) | −1.45846 | −0.0521543 | ||||||||
\(783\) | −6.41510 | −0.229257 | ||||||||
\(784\) | 0.946220 | 0.0337936 | ||||||||
\(785\) | −4.47588 | −0.159751 | ||||||||
\(786\) | −4.00582 | −0.142883 | ||||||||
\(787\) | −0.328194 | −0.0116989 | −0.00584943 | − | 0.999983i | \(-0.501862\pi\) | ||||
−0.00584943 | + | 0.999983i | \(0.501862\pi\) | |||||||
\(788\) | 19.6077 | 0.698495 | ||||||||
\(789\) | 3.43075 | 0.122138 | ||||||||
\(790\) | 10.7456 | 0.382313 | ||||||||
\(791\) | 23.2042 | 0.825046 | ||||||||
\(792\) | 2.94799 | 0.104752 | ||||||||
\(793\) | 5.45528 | 0.193723 | ||||||||
\(794\) | 17.7469 | 0.629815 | ||||||||
\(795\) | 0.776902 | 0.0275539 | ||||||||
\(796\) | −21.6580 | −0.767647 | ||||||||
\(797\) | 17.5447 | 0.621466 | 0.310733 | − | 0.950497i | \(-0.399425\pi\) | ||||
0.310733 | + | 0.950497i | \(0.399425\pi\) | |||||||
\(798\) | −4.77034 | −0.168868 | ||||||||
\(799\) | −21.9951 | −0.778132 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 15.3717 | 0.543132 | ||||||||
\(802\) | −6.79422 | −0.239912 | ||||||||
\(803\) | 2.51101 | 0.0886117 | ||||||||
\(804\) | 0.512565 | 0.0180768 | ||||||||
\(805\) | 2.46842 | 0.0870003 | ||||||||
\(806\) | 2.99148 | 0.105370 | ||||||||
\(807\) | −4.00723 | −0.141061 | ||||||||
\(808\) | −4.52576 | −0.159216 | ||||||||
\(809\) | 25.6981 | 0.903495 | 0.451748 | − | 0.892146i | \(-0.350801\pi\) | ||||
0.451748 | + | 0.892146i | \(0.350801\pi\) | |||||||
\(810\) | −8.53463 | −0.299876 | ||||||||
\(811\) | −33.9530 | −1.19225 | −0.596125 | − | 0.802892i | \(-0.703294\pi\) | ||||
−0.596125 | + | 0.802892i | \(0.703294\pi\) | |||||||
\(812\) | 13.3315 | 0.467843 | ||||||||
\(813\) | 1.33424 | 0.0467937 | ||||||||
\(814\) | 5.63729 | 0.197587 | ||||||||
\(815\) | 15.5677 | 0.545313 | ||||||||
\(816\) | 0.379832 | 0.0132968 | ||||||||
\(817\) | −7.42051 | −0.259611 | ||||||||
\(818\) | 5.47349 | 0.191376 | ||||||||
\(819\) | 9.34334 | 0.326483 | ||||||||
\(820\) | 7.80977 | 0.272729 | ||||||||
\(821\) | −9.62751 | −0.336003 | −0.168001 | − | 0.985787i | \(-0.553731\pi\) | ||||
−0.168001 | + | 0.985787i | \(0.553731\pi\) | |||||||
\(822\) | −2.41948 | −0.0843890 | ||||||||
\(823\) | 16.0071 | 0.557971 | 0.278986 | − | 0.960295i | \(-0.410002\pi\) | ||||
0.278986 | + | 0.960295i | \(0.410002\pi\) | |||||||
\(824\) | 2.63398 | 0.0917592 | ||||||||
\(825\) | −0.228053 | −0.00793978 | ||||||||
\(826\) | 2.14053 | 0.0744784 | ||||||||
\(827\) | 43.8703 | 1.52552 | 0.762759 | − | 0.646682i | \(-0.223844\pi\) | ||||
0.762759 | + | 0.646682i | \(0.223844\pi\) | |||||||
\(828\) | 2.58145 | 0.0897117 | ||||||||
\(829\) | −51.3496 | −1.78344 | −0.891722 | − | 0.452583i | \(-0.850503\pi\) | ||||
−0.891722 | + | 0.452583i | \(0.850503\pi\) | |||||||
\(830\) | 12.0367 | 0.417801 | ||||||||
\(831\) | −1.18723 | −0.0411845 | ||||||||
\(832\) | 1.12433 | 0.0389793 | ||||||||
\(833\) | −1.57597 | −0.0546041 | ||||||||
\(834\) | −0.288468 | −0.00998885 | ||||||||
\(835\) | −6.01893 | −0.208294 | ||||||||
\(836\) | 7.42051 | 0.256644 | ||||||||
\(837\) | −3.60908 | −0.124748 | ||||||||
\(838\) | 1.27871 | 0.0441722 | ||||||||
\(839\) | 42.5718 | 1.46974 | 0.734871 | − | 0.678207i | \(-0.237243\pi\) | ||||
0.734871 | + | 0.678207i | \(0.237243\pi\) | |||||||
\(840\) | −0.642859 | −0.0221808 | ||||||||
\(841\) | −6.63365 | −0.228747 | ||||||||
\(842\) | 11.6440 | 0.401278 | ||||||||
\(843\) | −0.161916 | −0.00557668 | ||||||||
\(844\) | 12.3193 | 0.424049 | ||||||||
\(845\) | −11.7359 | −0.403726 | ||||||||
\(846\) | 38.9312 | 1.33848 | ||||||||
\(847\) | −2.81890 | −0.0968587 | ||||||||
\(848\) | −3.40667 | −0.116986 | ||||||||
\(849\) | 2.94579 | 0.101099 | ||||||||
\(850\) | 1.66554 | 0.0571276 | ||||||||
\(851\) | 4.93638 | 0.169217 | ||||||||
\(852\) | −1.69023 | −0.0579064 | ||||||||
\(853\) | 10.7587 | 0.368372 | 0.184186 | − | 0.982891i | \(-0.441035\pi\) | ||||
0.184186 | + | 0.982891i | \(0.441035\pi\) | |||||||
\(854\) | 13.6773 | 0.468029 | ||||||||
\(855\) | −21.8756 | −0.748129 | ||||||||
\(856\) | 9.33164 | 0.318949 | ||||||||
\(857\) | −43.8362 | −1.49741 | −0.748707 | − | 0.662901i | \(-0.769325\pi\) | ||||
−0.748707 | + | 0.662901i | \(0.769325\pi\) | |||||||
\(858\) | 0.256408 | 0.00875362 | ||||||||
\(859\) | 16.8246 | 0.574047 | 0.287023 | − | 0.957924i | \(-0.407334\pi\) | ||||
0.287023 | + | 0.957924i | \(0.407334\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 5.02059 | 0.171101 | ||||||||
\(862\) | −26.0044 | −0.885715 | ||||||||
\(863\) | 17.2444 | 0.587008 | 0.293504 | − | 0.955958i | \(-0.405179\pi\) | ||||
0.293504 | + | 0.955958i | \(0.405179\pi\) | |||||||
\(864\) | −1.35646 | −0.0461476 | ||||||||
\(865\) | −4.00241 | −0.136086 | ||||||||
\(866\) | −1.06003 | −0.0360214 | ||||||||
\(867\) | 3.24427 | 0.110181 | ||||||||
\(868\) | 7.50016 | 0.254572 | ||||||||
\(869\) | −10.7456 | −0.364521 | ||||||||
\(870\) | −1.07853 | −0.0365657 | ||||||||
\(871\) | −2.52702 | −0.0856249 | ||||||||
\(872\) | 4.97087 | 0.168335 | ||||||||
\(873\) | 19.1769 | 0.649040 | ||||||||
\(874\) | 6.49788 | 0.219794 | ||||||||
\(875\) | −2.81890 | −0.0952964 | ||||||||
\(876\) | −0.572644 | −0.0193478 | ||||||||
\(877\) | −3.05479 | −0.103153 | −0.0515765 | − | 0.998669i | \(-0.516425\pi\) | ||||
−0.0515765 | + | 0.998669i | \(0.516425\pi\) | |||||||
\(878\) | −15.3574 | −0.518288 | ||||||||
\(879\) | −7.22992 | −0.243859 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 20.4644 | 0.689464 | 0.344732 | − | 0.938701i | \(-0.387970\pi\) | ||||
0.344732 | + | 0.938701i | \(0.387970\pi\) | |||||||
\(882\) | 2.78945 | 0.0939256 | ||||||||
\(883\) | −13.9109 | −0.468139 | −0.234070 | − | 0.972220i | \(-0.575204\pi\) | ||||
−0.234070 | + | 0.972220i | \(0.575204\pi\) | |||||||
\(884\) | −1.87263 | −0.0629832 | ||||||||
\(885\) | −0.173171 | −0.00582109 | ||||||||
\(886\) | 13.0010 | 0.436778 | ||||||||
\(887\) | 1.06369 | 0.0357152 | 0.0178576 | − | 0.999841i | \(-0.494315\pi\) | ||||
0.0178576 | + | 0.999841i | \(0.494315\pi\) | |||||||
\(888\) | −1.28560 | −0.0431420 | ||||||||
\(889\) | 56.9180 | 1.90897 | ||||||||
\(890\) | 5.21429 | 0.174784 | ||||||||
\(891\) | 8.53463 | 0.285921 | ||||||||
\(892\) | −20.5666 | −0.688620 | ||||||||
\(893\) | 97.9952 | 3.27928 | ||||||||
\(894\) | 2.18219 | 0.0729835 | ||||||||
\(895\) | −0.139202 | −0.00465300 | ||||||||
\(896\) | 2.81890 | 0.0941730 | ||||||||
\(897\) | 0.224527 | 0.00749675 | ||||||||
\(898\) | 22.9889 | 0.767150 | ||||||||
\(899\) | 12.5831 | 0.419670 | ||||||||
\(900\) | −2.94799 | −0.0982664 | ||||||||
\(901\) | 5.67395 | 0.189027 | ||||||||
\(902\) | −7.80977 | −0.260037 | ||||||||
\(903\) | −0.642859 | −0.0213930 | ||||||||
\(904\) | 8.23164 | 0.273780 | ||||||||
\(905\) | 6.05904 | 0.201409 | ||||||||
\(906\) | 3.59339 | 0.119382 | ||||||||
\(907\) | −30.2393 | −1.00408 | −0.502040 | − | 0.864844i | \(-0.667417\pi\) | ||||
−0.502040 | + | 0.864844i | \(0.667417\pi\) | |||||||
\(908\) | −24.9903 | −0.829331 | ||||||||
\(909\) | −13.3419 | −0.442523 | ||||||||
\(910\) | 3.16939 | 0.105064 | ||||||||
\(911\) | 40.3214 | 1.33591 | 0.667954 | − | 0.744202i | \(-0.267170\pi\) | ||||
0.667954 | + | 0.744202i | \(0.267170\pi\) | |||||||
\(912\) | −1.69227 | −0.0560366 | ||||||||
\(913\) | −12.0367 | −0.398358 | ||||||||
\(914\) | 17.3573 | 0.574130 | ||||||||
\(915\) | −1.10651 | −0.0365802 | ||||||||
\(916\) | −23.3892 | −0.772801 | ||||||||
\(917\) | 49.5150 | 1.63513 | ||||||||
\(918\) | 2.25923 | 0.0745659 | ||||||||
\(919\) | −35.9397 | −1.18554 | −0.592770 | − | 0.805372i | \(-0.701966\pi\) | ||||
−0.592770 | + | 0.805372i | \(0.701966\pi\) | |||||||
\(920\) | 0.875665 | 0.0288698 | ||||||||
\(921\) | 2.86244 | 0.0943205 | ||||||||
\(922\) | −2.22579 | −0.0733026 | ||||||||
\(923\) | 8.33310 | 0.274287 | ||||||||
\(924\) | 0.642859 | 0.0211485 | ||||||||
\(925\) | −5.63729 | −0.185353 | ||||||||
\(926\) | 12.5943 | 0.413874 | ||||||||
\(927\) | 7.76496 | 0.255035 | ||||||||
\(928\) | 4.72931 | 0.155247 | ||||||||
\(929\) | 48.4403 | 1.58928 | 0.794638 | − | 0.607084i | \(-0.207661\pi\) | ||||
0.794638 | + | 0.607084i | \(0.207661\pi\) | |||||||
\(930\) | −0.606772 | −0.0198968 | ||||||||
\(931\) | 7.02143 | 0.230118 | ||||||||
\(932\) | −7.48056 | −0.245034 | ||||||||
\(933\) | 7.22769 | 0.236624 | ||||||||
\(934\) | 15.4563 | 0.505745 | ||||||||
\(935\) | −1.66554 | −0.0544690 | ||||||||
\(936\) | 3.31453 | 0.108339 | ||||||||
\(937\) | 57.6303 | 1.88270 | 0.941350 | − | 0.337431i | \(-0.109558\pi\) | ||||
0.941350 | + | 0.337431i | \(0.109558\pi\) | |||||||
\(938\) | −6.33569 | −0.206868 | ||||||||
\(939\) | 6.80953 | 0.222221 | ||||||||
\(940\) | 13.2060 | 0.430732 | ||||||||
\(941\) | 24.7222 | 0.805920 | 0.402960 | − | 0.915218i | \(-0.367981\pi\) | ||||
0.402960 | + | 0.915218i | \(0.367981\pi\) | |||||||
\(942\) | −1.02074 | −0.0332574 | ||||||||
\(943\) | −6.83875 | −0.222700 | ||||||||
\(944\) | 0.759347 | 0.0247146 | ||||||||
\(945\) | −3.82372 | −0.124386 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 20.3291 | 0.660608 | 0.330304 | − | 0.943875i | \(-0.392849\pi\) | ||||
0.330304 | + | 0.943875i | \(0.392849\pi\) | |||||||
\(948\) | 2.45057 | 0.0795910 | ||||||||
\(949\) | 2.82322 | 0.0916456 | ||||||||
\(950\) | −7.42051 | −0.240753 | ||||||||
\(951\) | −4.93655 | −0.160079 | ||||||||
\(952\) | −4.69500 | −0.152166 | ||||||||
\(953\) | −23.9699 | −0.776461 | −0.388231 | − | 0.921562i | \(-0.626914\pi\) | ||||
−0.388231 | + | 0.921562i | \(0.626914\pi\) | |||||||
\(954\) | −10.0428 | −0.325149 | ||||||||
\(955\) | −16.1843 | −0.523712 | ||||||||
\(956\) | 10.7522 | 0.347750 | ||||||||
\(957\) | 1.07853 | 0.0348640 | ||||||||
\(958\) | −16.3881 | −0.529477 | ||||||||
\(959\) | 29.9066 | 0.965733 | ||||||||
\(960\) | −0.228053 | −0.00736038 | ||||||||
\(961\) | −23.9209 | −0.771641 | ||||||||
\(962\) | 6.33820 | 0.204352 | ||||||||
\(963\) | 27.5096 | 0.886484 | ||||||||
\(964\) | 10.8505 | 0.349472 | ||||||||
\(965\) | 25.5558 | 0.822670 | ||||||||
\(966\) | 0.562930 | 0.0181120 | ||||||||
\(967\) | 37.5049 | 1.20608 | 0.603038 | − | 0.797712i | \(-0.293957\pi\) | ||||
0.603038 | + | 0.797712i | \(0.293957\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 2.81854 | 0.0905446 | ||||||||
\(970\) | 6.50507 | 0.208865 | ||||||||
\(971\) | 53.6069 | 1.72033 | 0.860163 | − | 0.510019i | \(-0.170362\pi\) | ||||
0.860163 | + | 0.510019i | \(0.170362\pi\) | |||||||
\(972\) | −6.01572 | −0.192954 | ||||||||
\(973\) | 3.56569 | 0.114311 | ||||||||
\(974\) | 3.92891 | 0.125890 | ||||||||
\(975\) | −0.256408 | −0.00821162 | ||||||||
\(976\) | 4.85201 | 0.155309 | ||||||||
\(977\) | −16.9339 | −0.541763 | −0.270881 | − | 0.962613i | \(-0.587315\pi\) | ||||
−0.270881 | + | 0.962613i | \(0.587315\pi\) | |||||||
\(978\) | 3.55026 | 0.113525 | ||||||||
\(979\) | −5.21429 | −0.166650 | ||||||||
\(980\) | 0.946220 | 0.0302259 | ||||||||
\(981\) | 14.6541 | 0.467869 | ||||||||
\(982\) | −9.17767 | −0.292871 | ||||||||
\(983\) | 20.9921 | 0.669545 | 0.334772 | − | 0.942299i | \(-0.391341\pi\) | ||||
0.334772 | + | 0.942299i | \(0.391341\pi\) | |||||||
\(984\) | 1.78104 | 0.0567775 | ||||||||
\(985\) | 19.6077 | 0.624753 | ||||||||
\(986\) | −7.87686 | −0.250850 | ||||||||
\(987\) | 8.48960 | 0.270227 | ||||||||
\(988\) | 8.34313 | 0.265430 | ||||||||
\(989\) | 0.875665 | 0.0278445 | ||||||||
\(990\) | 2.94799 | 0.0936933 | ||||||||
\(991\) | −44.9992 | −1.42945 | −0.714723 | − | 0.699408i | \(-0.753447\pi\) | ||||
−0.714723 | + | 0.699408i | \(0.753447\pi\) | |||||||
\(992\) | 2.66066 | 0.0844762 | ||||||||
\(993\) | 6.95068 | 0.220573 | ||||||||
\(994\) | 20.8925 | 0.662671 | ||||||||
\(995\) | −21.6580 | −0.686605 | ||||||||
\(996\) | 2.74501 | 0.0869790 | ||||||||
\(997\) | −19.5085 | −0.617841 | −0.308921 | − | 0.951088i | \(-0.599968\pi\) | ||||
−0.308921 | + | 0.951088i | \(0.599968\pi\) | |||||||
\(998\) | 39.8502 | 1.26143 | ||||||||
\(999\) | −7.64675 | −0.241932 |
(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 | 4730.2.a.w.1.6 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.w.1.6 | ✓ | 8 | 1.1 | even | 1 | trivial |