Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} + \cdots - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 2001) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.98240\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.98240 | −1.40177 | −0.700883 | − | 0.713277i | \(-0.747210\pi\) | ||||
−0.700883 | + | 0.713277i | \(0.747210\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.92989 | 0.964946 | ||||||||
\(5\) | 0.252916 | 0.113107 | 0.0565537 | − | 0.998400i | \(-0.481989\pi\) | ||||
0.0565537 | + | 0.998400i | \(0.481989\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.21499 | −0.459222 | −0.229611 | − | 0.973283i | \(-0.573745\pi\) | ||||
−0.229611 | + | 0.973283i | \(0.573745\pi\) | |||||||
\(8\) | 0.138982 | 0.0491377 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.501379 | −0.158550 | ||||||||
\(11\) | −2.73986 | −0.826100 | −0.413050 | − | 0.910708i | \(-0.635536\pi\) | ||||
−0.413050 | + | 0.910708i | \(0.635536\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.01158 | −1.66731 | −0.833656 | − | 0.552285i | \(-0.813756\pi\) | ||||
−0.833656 | + | 0.552285i | \(0.813756\pi\) | |||||||
\(14\) | 2.40858 | 0.643721 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.13530 | −1.03383 | ||||||||
\(17\) | −0.539671 | −0.130889 | −0.0654447 | − | 0.997856i | \(-0.520847\pi\) | ||||
−0.0654447 | + | 0.997856i | \(0.520847\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.87659 | 0.889351 | 0.444675 | − | 0.895692i | \(-0.353319\pi\) | ||||
0.444675 | + | 0.895692i | \(0.353319\pi\) | |||||||
\(20\) | 0.488100 | 0.109143 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.43149 | 1.15800 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93603 | −0.987207 | ||||||||
\(26\) | 11.9173 | 2.33718 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.34479 | −0.443124 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4153 | −1.87064 | −0.935320 | − | 0.353803i | \(-0.884888\pi\) | ||||
−0.935320 | + | 0.353803i | \(0.884888\pi\) | |||||||
\(32\) | 7.91984 | 1.40004 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.06984 | 0.183476 | ||||||||
\(35\) | −0.307289 | −0.0519414 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.48518 | −0.737360 | −0.368680 | − | 0.929556i | \(-0.620190\pi\) | ||||
−0.368680 | + | 0.929556i | \(0.620190\pi\) | |||||||
\(38\) | −7.68494 | −1.24666 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.0351509 | 0.00555784 | ||||||||
\(41\) | 7.22607 | 1.12852 | 0.564261 | − | 0.825596i | \(-0.309161\pi\) | ||||
0.564261 | + | 0.825596i | \(0.309161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.16164 | 0.939641 | 0.469821 | − | 0.882762i | \(-0.344319\pi\) | ||||
0.469821 | + | 0.882762i | \(0.344319\pi\) | |||||||
\(44\) | −5.28764 | −0.797141 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.98240 | −0.292288 | ||||||||
\(47\) | −11.5319 | −1.68210 | −0.841050 | − | 0.540957i | \(-0.818062\pi\) | ||||
−0.841050 | + | 0.540957i | \(0.818062\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.52381 | −0.789115 | ||||||||
\(50\) | 9.78517 | 1.38383 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −11.6017 | −1.60887 | ||||||||
\(53\) | 3.65289 | 0.501763 | 0.250881 | − | 0.968018i | \(-0.419280\pi\) | ||||
0.250881 | + | 0.968018i | \(0.419280\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.692955 | −0.0934380 | ||||||||
\(56\) | −0.168862 | −0.0225651 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.98240 | −0.260301 | ||||||||
\(59\) | −4.78769 | −0.623304 | −0.311652 | − | 0.950196i | \(-0.600882\pi\) | ||||
−0.311652 | + | 0.950196i | \(0.600882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.30130 | −0.294651 | −0.147325 | − | 0.989088i | \(-0.547066\pi\) | ||||
−0.147325 | + | 0.989088i | \(0.547066\pi\) | |||||||
\(62\) | 20.6472 | 2.62220 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.42965 | −0.928706 | ||||||||
\(65\) | −1.52042 | −0.188585 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2382 | −1.61731 | −0.808653 | − | 0.588286i | \(-0.799803\pi\) | ||||
−0.808653 | + | 0.588286i | \(0.799803\pi\) | |||||||
\(68\) | −1.04151 | −0.126301 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.609169 | 0.0728096 | ||||||||
\(71\) | 10.9508 | 1.29962 | 0.649808 | − | 0.760098i | \(-0.274849\pi\) | ||||
0.649808 | + | 0.760098i | \(0.274849\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.281971 | 0.0330022 | 0.0165011 | − | 0.999864i | \(-0.494747\pi\) | ||||
0.0165011 | + | 0.999864i | \(0.494747\pi\) | |||||||
\(74\) | 8.89141 | 1.03361 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.48140 | 0.858175 | ||||||||
\(77\) | 3.32890 | 0.379363 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.98574 | −1.12348 | −0.561742 | − | 0.827313i | \(-0.689868\pi\) | ||||
−0.561742 | + | 0.827313i | \(0.689868\pi\) | |||||||
\(80\) | −1.04588 | −0.116933 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.3249 | −1.58192 | ||||||||
\(83\) | 0.778208 | 0.0854194 | 0.0427097 | − | 0.999088i | \(-0.486401\pi\) | ||||
0.0427097 | + | 0.999088i | \(0.486401\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.136491 | −0.0148046 | ||||||||
\(86\) | −12.2148 | −1.31716 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.380793 | −0.0405927 | ||||||||
\(89\) | −8.11723 | −0.860425 | −0.430213 | − | 0.902728i | \(-0.641561\pi\) | ||||
−0.430213 | + | 0.902728i | \(0.641561\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.30398 | 0.765666 | ||||||||
\(92\) | 1.92989 | 0.201205 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.8608 | 2.35791 | ||||||||
\(95\) | 0.980452 | 0.100592 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8074 | 1.80807 | 0.904033 | − | 0.427463i | \(-0.140593\pi\) | ||||
0.904033 | + | 0.427463i | \(0.140593\pi\) | |||||||
\(98\) | 10.9504 | 1.10615 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.52601 | −0.952601 | ||||||||
\(101\) | 9.49058 | 0.944348 | 0.472174 | − | 0.881505i | \(-0.343469\pi\) | ||||
0.472174 | + | 0.881505i | \(0.343469\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.0335 | 1.97396 | 0.986979 | − | 0.160849i | \(-0.0514234\pi\) | ||||
0.986979 | + | 0.160849i | \(0.0514234\pi\) | |||||||
\(104\) | −0.835504 | −0.0819279 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.24147 | −0.703354 | ||||||||
\(107\) | 19.9506 | 1.92870 | 0.964350 | − | 0.264630i | \(-0.0852498\pi\) | ||||
0.964350 | + | 0.264630i | \(0.0852498\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.56520 | 0.341484 | 0.170742 | − | 0.985316i | \(-0.445384\pi\) | ||||
0.170742 | + | 0.985316i | \(0.445384\pi\) | |||||||
\(110\) | 1.37371 | 0.130978 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.02434 | 0.474755 | ||||||||
\(113\) | −5.36104 | −0.504324 | −0.252162 | − | 0.967685i | \(-0.581142\pi\) | ||||
−0.252162 | + | 0.967685i | \(0.581142\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.252916 | 0.0235845 | ||||||||
\(116\) | 1.92989 | 0.179186 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.49109 | 0.873726 | ||||||||
\(119\) | 0.655693 | 0.0601073 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.49315 | −0.317559 | ||||||||
\(122\) | 4.56208 | 0.413031 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −20.1004 | −1.80507 | ||||||||
\(125\) | −2.51298 | −0.224768 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.509875 | 0.0452441 | 0.0226220 | − | 0.999744i | \(-0.492799\pi\) | ||||
0.0226220 | + | 0.999744i | \(0.492799\pi\) | |||||||
\(128\) | −1.11118 | −0.0982151 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.01408 | 0.264352 | ||||||||
\(131\) | −22.2670 | −1.94548 | −0.972739 | − | 0.231901i | \(-0.925505\pi\) | ||||
−0.972739 | + | 0.231901i | \(0.925505\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.71001 | −0.408409 | ||||||||
\(134\) | 26.2434 | 2.26708 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.0750048 | −0.00643161 | ||||||||
\(137\) | −12.6651 | −1.08206 | −0.541028 | − | 0.841005i | \(-0.681965\pi\) | ||||
−0.541028 | + | 0.841005i | \(0.681965\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.725814 | −0.0615627 | −0.0307814 | − | 0.999526i | \(-0.509800\pi\) | ||||
−0.0307814 | + | 0.999526i | \(0.509800\pi\) | |||||||
\(140\) | −0.593035 | −0.0501206 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −21.7087 | −1.82176 | ||||||||
\(143\) | 16.4709 | 1.37737 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.252916 | 0.0210035 | ||||||||
\(146\) | −0.558978 | −0.0462614 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.65592 | −0.711512 | ||||||||
\(149\) | 7.39238 | 0.605607 | 0.302804 | − | 0.953053i | \(-0.402077\pi\) | ||||
0.302804 | + | 0.953053i | \(0.402077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.47925 | 0.201759 | 0.100879 | − | 0.994899i | \(-0.467834\pi\) | ||||
0.100879 | + | 0.994899i | \(0.467834\pi\) | |||||||
\(152\) | 0.538778 | 0.0437007 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.59919 | −0.531778 | ||||||||
\(155\) | −2.63419 | −0.211583 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.9461 | 0.873597 | 0.436798 | − | 0.899559i | \(-0.356112\pi\) | ||||
0.436798 | + | 0.899559i | \(0.356112\pi\) | |||||||
\(158\) | 19.7957 | 1.57486 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.00305 | 0.158355 | ||||||||
\(161\) | −1.21499 | −0.0957544 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.5371 | −1.45194 | −0.725971 | − | 0.687726i | \(-0.758609\pi\) | ||||
−0.725971 | + | 0.687726i | \(0.758609\pi\) | |||||||
\(164\) | 13.9455 | 1.08896 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.54272 | −0.119738 | ||||||||
\(167\) | 8.98050 | 0.694932 | 0.347466 | − | 0.937693i | \(-0.387042\pi\) | ||||
0.347466 | + | 0.937693i | \(0.387042\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 23.1391 | 1.77993 | ||||||||
\(170\) | 0.270580 | 0.0207525 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.8913 | 0.906703 | ||||||||
\(173\) | −4.52117 | −0.343738 | −0.171869 | − | 0.985120i | \(-0.554981\pi\) | ||||
−0.171869 | + | 0.985120i | \(0.554981\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.99721 | 0.453347 | ||||||||
\(176\) | 11.3302 | 0.854043 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 16.0916 | 1.20611 | ||||||||
\(179\) | 19.6654 | 1.46986 | 0.734932 | − | 0.678141i | \(-0.237214\pi\) | ||||
0.734932 | + | 0.678141i | \(0.237214\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.0323 | 0.820023 | 0.410011 | − | 0.912080i | \(-0.365525\pi\) | ||||
0.410011 | + | 0.912080i | \(0.365525\pi\) | |||||||
\(182\) | −14.4794 | −1.07328 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.138982 | 0.0102459 | ||||||||
\(185\) | −1.13437 | −0.0834009 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.47862 | 0.108128 | ||||||||
\(188\) | −22.2553 | −1.62314 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.94364 | −0.141007 | ||||||||
\(191\) | −2.35924 | −0.170708 | −0.0853542 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853542 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.0547 | 1.22763 | 0.613814 | − | 0.789451i | \(-0.289635\pi\) | ||||
0.613814 | + | 0.789451i | \(0.289635\pi\) | |||||||
\(194\) | −35.3013 | −2.53448 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.6604 | −0.761454 | ||||||||
\(197\) | −5.51284 | −0.392774 | −0.196387 | − | 0.980527i | \(-0.562921\pi\) | ||||
−0.196387 | + | 0.980527i | \(0.562921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.5760 | −1.10415 | −0.552076 | − | 0.833794i | \(-0.686164\pi\) | ||||
−0.552076 | + | 0.833794i | \(0.686164\pi\) | |||||||
\(200\) | −0.686022 | −0.0485091 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −18.8141 | −1.32375 | ||||||||
\(203\) | −1.21499 | −0.0852753 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.82759 | 0.127644 | ||||||||
\(206\) | −39.7143 | −2.76703 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 24.8597 | 1.72371 | ||||||||
\(209\) | −10.6213 | −0.734693 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.675563 | 0.0465077 | 0.0232538 | − | 0.999730i | \(-0.492597\pi\) | ||||
0.0232538 | + | 0.999730i | \(0.492597\pi\) | |||||||
\(212\) | 7.04968 | 0.484174 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −39.5500 | −2.70358 | ||||||||
\(215\) | 1.55838 | 0.106280 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.6544 | 0.859039 | ||||||||
\(218\) | −7.06763 | −0.478680 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.33733 | −0.0901626 | ||||||||
\(221\) | 3.24427 | 0.218233 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.68120 | 0.447407 | 0.223703 | − | 0.974657i | \(-0.428185\pi\) | ||||
0.223703 | + | 0.974657i | \(0.428185\pi\) | |||||||
\(224\) | −9.62250 | −0.642930 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.6277 | 0.706944 | ||||||||
\(227\) | 1.10336 | 0.0732325 | 0.0366163 | − | 0.999329i | \(-0.488342\pi\) | ||||
0.0366163 | + | 0.999329i | \(0.488342\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.1398 | −1.59520 | −0.797602 | − | 0.603184i | \(-0.793899\pi\) | ||||
−0.797602 | + | 0.603184i | \(0.793899\pi\) | |||||||
\(230\) | −0.501379 | −0.0330600 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.138982 | 0.00912465 | ||||||||
\(233\) | −17.4274 | −1.14171 | −0.570855 | − | 0.821051i | \(-0.693388\pi\) | ||||
−0.570855 | + | 0.821051i | \(0.693388\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.91660 | −0.190258 | ||||||||
\(236\) | −9.23972 | −0.601455 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.29984 | −0.0842563 | ||||||||
\(239\) | −18.1500 | −1.17402 | −0.587012 | − | 0.809578i | \(-0.699696\pi\) | ||||
−0.587012 | + | 0.809578i | \(0.699696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.6333 | −1.39353 | −0.696763 | − | 0.717301i | \(-0.745377\pi\) | ||||
−0.696763 | + | 0.717301i | \(0.745377\pi\) | |||||||
\(242\) | 6.92481 | 0.445144 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.44125 | −0.284322 | ||||||||
\(245\) | −1.39706 | −0.0892548 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.3044 | −1.48282 | ||||||||
\(248\) | −1.44754 | −0.0919190 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.98172 | 0.315072 | ||||||||
\(251\) | 6.85515 | 0.432693 | 0.216347 | − | 0.976317i | \(-0.430586\pi\) | ||||
0.216347 | + | 0.976317i | \(0.430586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.73986 | −0.172254 | ||||||||
\(254\) | −1.01077 | −0.0634216 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.0621 | 1.06638 | ||||||||
\(257\) | 20.4624 | 1.27641 | 0.638206 | − | 0.769866i | \(-0.279677\pi\) | ||||
0.638206 | + | 0.769866i | \(0.279677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.44944 | 0.338612 | ||||||||
\(260\) | −2.93425 | −0.181975 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 44.1420 | 2.72710 | ||||||||
\(263\) | 2.15812 | 0.133075 | 0.0665376 | − | 0.997784i | \(-0.478805\pi\) | ||||
0.0665376 | + | 0.997784i | \(0.478805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.923874 | 0.0567531 | ||||||||
\(266\) | 9.33709 | 0.572494 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −25.5483 | −1.56061 | ||||||||
\(269\) | −12.6541 | −0.771534 | −0.385767 | − | 0.922596i | \(-0.626063\pi\) | ||||
−0.385767 | + | 0.922596i | \(0.626063\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.3290 | 1.17415 | 0.587075 | − | 0.809532i | \(-0.300279\pi\) | ||||
0.587075 | + | 0.809532i | \(0.300279\pi\) | |||||||
\(272\) | 2.23170 | 0.135317 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.1073 | 1.51679 | ||||||||
\(275\) | 13.5241 | 0.815531 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.8131 | 1.79130 | 0.895649 | − | 0.444761i | \(-0.146712\pi\) | ||||
0.895649 | + | 0.444761i | \(0.146712\pi\) | |||||||
\(278\) | 1.43885 | 0.0862965 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0427079 | −0.00255228 | ||||||||
\(281\) | 11.6049 | 0.692290 | 0.346145 | − | 0.938181i | \(-0.387491\pi\) | ||||
0.346145 | + | 0.938181i | \(0.387491\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1145 | −1.55235 | −0.776173 | − | 0.630520i | \(-0.782842\pi\) | ||||
−0.776173 | + | 0.630520i | \(0.782842\pi\) | |||||||
\(284\) | 21.1338 | 1.25406 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −32.6518 | −1.93074 | ||||||||
\(287\) | −8.77957 | −0.518242 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7088 | −0.982868 | ||||||||
\(290\) | −0.501379 | −0.0294420 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.544174 | 0.0318454 | ||||||||
\(293\) | −20.6073 | −1.20389 | −0.601945 | − | 0.798537i | \(-0.705608\pi\) | ||||
−0.601945 | + | 0.798537i | \(0.705608\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.21088 | −0.0705003 | ||||||||
\(296\) | −0.623362 | −0.0362322 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.6546 | −0.848919 | ||||||||
\(299\) | −6.01158 | −0.347658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.48631 | −0.431504 | ||||||||
\(302\) | −4.91486 | −0.282819 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.0309 | −0.919434 | ||||||||
\(305\) | −0.582035 | −0.0333272 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.5171 | 1.11390 | 0.556950 | − | 0.830546i | \(-0.311972\pi\) | ||||
0.556950 | + | 0.830546i | \(0.311972\pi\) | |||||||
\(308\) | 6.42441 | 0.366065 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.22201 | 0.296590 | ||||||||
\(311\) | 19.7794 | 1.12159 | 0.560794 | − | 0.827955i | \(-0.310496\pi\) | ||||
0.560794 | + | 0.827955i | \(0.310496\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.3721 | 1.20802 | 0.604012 | − | 0.796975i | \(-0.293568\pi\) | ||||
0.604012 | + | 0.796975i | \(0.293568\pi\) | |||||||
\(314\) | −21.6996 | −1.22458 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −19.2714 | −1.08410 | ||||||||
\(317\) | −6.33500 | −0.355809 | −0.177905 | − | 0.984048i | \(-0.556932\pi\) | ||||
−0.177905 | + | 0.984048i | \(0.556932\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.73986 | −0.153403 | ||||||||
\(320\) | −1.87908 | −0.105044 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.40858 | 0.134225 | ||||||||
\(323\) | −2.09208 | −0.116407 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.6733 | 1.64598 | ||||||||
\(326\) | 36.7479 | 2.03528 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.00430 | 0.0554530 | ||||||||
\(329\) | 14.0111 | 0.772457 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.92635 | −0.160847 | −0.0804233 | − | 0.996761i | \(-0.525627\pi\) | ||||
−0.0804233 | + | 0.996761i | \(0.525627\pi\) | |||||||
\(332\) | 1.50186 | 0.0824251 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.8029 | −0.974131 | ||||||||
\(335\) | −3.34816 | −0.182929 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.2207 | 1.31938 | 0.659691 | − | 0.751537i | \(-0.270687\pi\) | ||||
0.659691 | + | 0.751537i | \(0.270687\pi\) | |||||||
\(338\) | −45.8708 | −2.49504 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.263413 | −0.0142856 | ||||||||
\(341\) | 28.5364 | 1.54534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.2163 | 0.821601 | ||||||||
\(344\) | 0.856360 | 0.0461718 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.96274 | 0.481840 | ||||||||
\(347\) | −1.43278 | −0.0769156 | −0.0384578 | − | 0.999260i | \(-0.512245\pi\) | ||||
−0.0384578 | + | 0.999260i | \(0.512245\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.1966 | −1.02757 | −0.513786 | − | 0.857919i | \(-0.671757\pi\) | ||||
−0.513786 | + | 0.857919i | \(0.671757\pi\) | |||||||
\(350\) | −11.8888 | −0.635486 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −21.6993 | −1.15657 | ||||||||
\(353\) | −10.2050 | −0.543155 | −0.271577 | − | 0.962417i | \(-0.587545\pi\) | ||||
−0.271577 | + | 0.962417i | \(0.587545\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.76962 | 0.146996 | ||||||||
\(356\) | −15.6654 | −0.830264 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −38.9847 | −2.06040 | ||||||||
\(359\) | 23.1960 | 1.22424 | 0.612119 | − | 0.790766i | \(-0.290317\pi\) | ||||
0.612119 | + | 0.790766i | \(0.290317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.97204 | −0.209055 | ||||||||
\(362\) | −21.8703 | −1.14948 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.0959 | 0.738826 | ||||||||
\(365\) | 0.0713150 | 0.00373280 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.1544 | 1.31305 | 0.656524 | − | 0.754305i | \(-0.272026\pi\) | ||||
0.656524 | + | 0.754305i | \(0.272026\pi\) | |||||||
\(368\) | −4.13530 | −0.215567 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.24878 | 0.116908 | ||||||||
\(371\) | −4.43821 | −0.230420 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −28.6093 | −1.48133 | −0.740667 | − | 0.671872i | \(-0.765491\pi\) | ||||
−0.740667 | + | 0.671872i | \(0.765491\pi\) | |||||||
\(374\) | −2.93122 | −0.151570 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.60273 | −0.0826546 | ||||||||
\(377\) | −6.01158 | −0.309612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.9594 | 1.64165 | 0.820823 | − | 0.571183i | \(-0.193515\pi\) | ||||
0.820823 | + | 0.571183i | \(0.193515\pi\) | |||||||
\(380\) | 1.89217 | 0.0970660 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.67694 | 0.239293 | ||||||||
\(383\) | 23.7993 | 1.21609 | 0.608043 | − | 0.793904i | \(-0.291955\pi\) | ||||
0.608043 | + | 0.793904i | \(0.291955\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.841931 | 0.0429088 | ||||||||
\(386\) | −33.8092 | −1.72085 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 34.3663 | 1.74468 | ||||||||
\(389\) | 22.9294 | 1.16257 | 0.581283 | − | 0.813701i | \(-0.302551\pi\) | ||||
0.581283 | + | 0.813701i | \(0.302551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.539671 | −0.0272923 | ||||||||
\(392\) | −0.767713 | −0.0387753 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.9286 | 0.550576 | ||||||||
\(395\) | −2.52555 | −0.127074 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.5659 | −1.23293 | −0.616465 | − | 0.787382i | \(-0.711436\pi\) | ||||
−0.616465 | + | 0.787382i | \(0.711436\pi\) | |||||||
\(398\) | 30.8778 | 1.54776 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 20.4120 | 1.02060 | ||||||||
\(401\) | 10.0873 | 0.503736 | 0.251868 | − | 0.967762i | \(-0.418955\pi\) | ||||
0.251868 | + | 0.967762i | \(0.418955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 62.6123 | 3.11894 | ||||||||
\(404\) | 18.3158 | 0.911245 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.40858 | 0.119536 | ||||||||
\(407\) | 12.2888 | 0.609133 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.20177 | −0.108871 | −0.0544353 | − | 0.998517i | \(-0.517336\pi\) | ||||
−0.0544353 | + | 0.998517i | \(0.517336\pi\) | |||||||
\(410\) | −3.62300 | −0.178927 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 38.6625 | 1.90476 | ||||||||
\(413\) | 5.81698 | 0.286235 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.196821 | 0.00966157 | ||||||||
\(416\) | −47.6107 | −2.33431 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 21.0557 | 1.02987 | ||||||||
\(419\) | −29.3618 | −1.43442 | −0.717209 | − | 0.696858i | \(-0.754581\pi\) | ||||
−0.717209 | + | 0.696858i | \(0.754581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.6470 | 0.762587 | 0.381293 | − | 0.924454i | \(-0.375479\pi\) | ||||
0.381293 | + | 0.924454i | \(0.375479\pi\) | |||||||
\(422\) | −1.33923 | −0.0651928 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.507688 | 0.0246555 | ||||||||
\(425\) | 2.66383 | 0.129215 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.79604 | 0.135310 | ||||||||
\(428\) | 38.5026 | 1.86109 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.08932 | −0.148980 | ||||||||
\(431\) | 38.3036 | 1.84502 | 0.922509 | − | 0.385976i | \(-0.126135\pi\) | ||||
0.922509 | + | 0.385976i | \(0.126135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.99905 | 0.432467 | 0.216233 | − | 0.976342i | \(-0.430623\pi\) | ||||
0.216233 | + | 0.976342i | \(0.430623\pi\) | |||||||
\(434\) | −25.0861 | −1.20417 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.88044 | 0.329513 | ||||||||
\(437\) | 3.87659 | 0.185442 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.33310 | −0.397717 | −0.198859 | − | 0.980028i | \(-0.563723\pi\) | ||||
−0.198859 | + | 0.980028i | \(0.563723\pi\) | |||||||
\(440\) | −0.0963086 | −0.00459133 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.43143 | −0.305912 | ||||||||
\(443\) | −14.4427 | −0.686192 | −0.343096 | − | 0.939300i | \(-0.611476\pi\) | ||||
−0.343096 | + | 0.939300i | \(0.611476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.05298 | −0.0973205 | ||||||||
\(446\) | −13.2448 | −0.627159 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.02692 | 0.426482 | ||||||||
\(449\) | −32.1523 | −1.51736 | −0.758682 | − | 0.651462i | \(-0.774156\pi\) | ||||
−0.758682 | + | 0.651462i | \(0.774156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.7984 | −0.932272 | ||||||||
\(452\) | −10.3462 | −0.486645 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.18729 | −0.102655 | ||||||||
\(455\) | 1.84729 | 0.0866025 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.45644 | −0.302020 | −0.151010 | − | 0.988532i | \(-0.548252\pi\) | ||||
−0.151010 | + | 0.988532i | \(0.548252\pi\) | |||||||
\(458\) | 47.8547 | 2.23610 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.488100 | 0.0227578 | ||||||||
\(461\) | 17.1311 | 0.797876 | 0.398938 | − | 0.916978i | \(-0.369379\pi\) | ||||
0.398938 | + | 0.916978i | \(0.369379\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.2500 | −0.755200 | −0.377600 | − | 0.925969i | \(-0.623251\pi\) | ||||
−0.377600 | + | 0.925969i | \(0.623251\pi\) | |||||||
\(464\) | −4.13530 | −0.191977 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 34.5481 | 1.60041 | ||||||||
\(467\) | −2.20551 | −0.102059 | −0.0510295 | − | 0.998697i | \(-0.516250\pi\) | ||||
−0.0510295 | + | 0.998697i | \(0.516250\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0843 | 0.742702 | ||||||||
\(470\) | 5.78186 | 0.266697 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.665405 | −0.0306278 | ||||||||
\(473\) | −16.8820 | −0.776237 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.1350 | −0.877973 | ||||||||
\(476\) | 1.26542 | 0.0580002 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.9804 | 1.64571 | ||||||||
\(479\) | 42.1804 | 1.92727 | 0.963637 | − | 0.267216i | \(-0.0861037\pi\) | ||||
0.963637 | + | 0.267216i | \(0.0861037\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.9630 | 1.22941 | ||||||||
\(482\) | 42.8858 | 1.95340 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.74141 | −0.306428 | ||||||||
\(485\) | 4.50377 | 0.204506 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.8033 | −1.84897 | −0.924486 | − | 0.381216i | \(-0.875506\pi\) | ||||
−0.924486 | + | 0.381216i | \(0.875506\pi\) | |||||||
\(488\) | −0.319840 | −0.0144785 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.76952 | 0.125114 | ||||||||
\(491\) | 2.69191 | 0.121484 | 0.0607421 | − | 0.998153i | \(-0.480653\pi\) | ||||
0.0607421 | + | 0.998153i | \(0.480653\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.539671 | −0.0243056 | ||||||||
\(494\) | 46.1986 | 2.07857 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 43.0703 | 1.93392 | ||||||||
\(497\) | −13.3050 | −0.596812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.6818 | −1.50780 | −0.753902 | − | 0.656987i | \(-0.771831\pi\) | ||||
−0.753902 | + | 0.656987i | \(0.771831\pi\) | |||||||
\(500\) | −4.84978 | −0.216889 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −13.5896 | −0.606534 | ||||||||
\(503\) | 31.2381 | 1.39284 | 0.696418 | − | 0.717636i | \(-0.254776\pi\) | ||||
0.696418 | + | 0.717636i | \(0.254776\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.40032 | 0.106813 | ||||||||
\(506\) | 5.43149 | 0.241459 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.984004 | 0.0436581 | ||||||||
\(509\) | 20.3750 | 0.903107 | 0.451553 | − | 0.892244i | \(-0.350870\pi\) | ||||
0.451553 | + | 0.892244i | \(0.350870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.342591 | −0.0151553 | ||||||||
\(512\) | −31.6014 | −1.39660 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −40.5646 | −1.78923 | ||||||||
\(515\) | 5.06679 | 0.223269 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.5958 | 1.38958 | ||||||||
\(518\) | −10.8029 | −0.474654 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.211312 | −0.00926666 | ||||||||
\(521\) | −23.0113 | −1.00814 | −0.504071 | − | 0.863662i | \(-0.668165\pi\) | ||||
−0.504071 | + | 0.863662i | \(0.668165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.1568 | 1.36239 | 0.681197 | − | 0.732100i | \(-0.261460\pi\) | ||||
0.681197 | + | 0.732100i | \(0.261460\pi\) | |||||||
\(524\) | −42.9729 | −1.87728 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.27824 | −0.186540 | ||||||||
\(527\) | 5.62082 | 0.244847 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −1.83148 | −0.0795545 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.08980 | −0.394093 | ||||||||
\(533\) | −43.4401 | −1.88160 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.04583 | 0.218150 | ||||||||
\(536\) | −1.83988 | −0.0794707 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 25.0854 | 1.08151 | ||||||||
\(539\) | 15.1345 | 0.651888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.06950 | 0.174962 | 0.0874808 | − | 0.996166i | \(-0.472118\pi\) | ||||
0.0874808 | + | 0.996166i | \(0.472118\pi\) | |||||||
\(542\) | −38.3176 | −1.64588 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.27411 | −0.183251 | ||||||||
\(545\) | 0.901695 | 0.0386244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.2713 | −1.25155 | −0.625776 | − | 0.780003i | \(-0.715217\pi\) | ||||
−0.625776 | + | 0.780003i | \(0.715217\pi\) | |||||||
\(548\) | −24.4423 | −1.04412 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −26.8100 | −1.14318 | ||||||||
\(551\) | 3.87659 | 0.165148 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.1325 | 0.515928 | ||||||||
\(554\) | −59.1014 | −2.51098 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.40074 | −0.0594047 | ||||||||
\(557\) | 14.7898 | 0.626664 | 0.313332 | − | 0.949644i | \(-0.398555\pi\) | ||||
0.313332 | + | 0.949644i | \(0.398555\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.0412 | −1.56667 | ||||||||
\(560\) | 1.27073 | 0.0536983 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.0055 | −0.970428 | ||||||||
\(563\) | −22.0614 | −0.929776 | −0.464888 | − | 0.885369i | \(-0.653905\pi\) | ||||
−0.464888 | + | 0.885369i | \(0.653905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.35589 | −0.0570428 | ||||||||
\(566\) | 51.7693 | 2.17602 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.52196 | 0.0638602 | ||||||||
\(569\) | −26.5470 | −1.11291 | −0.556454 | − | 0.830879i | \(-0.687838\pi\) | ||||
−0.556454 | + | 0.830879i | \(0.687838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.2014 | 0.426914 | 0.213457 | − | 0.976952i | \(-0.431528\pi\) | ||||
0.213457 | + | 0.976952i | \(0.431528\pi\) | |||||||
\(572\) | 31.7870 | 1.32908 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.4046 | 0.726454 | ||||||||
\(575\) | −4.93603 | −0.205847 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.63413 | 0.0680295 | 0.0340148 | − | 0.999421i | \(-0.489171\pi\) | ||||
0.0340148 | + | 0.999421i | \(0.489171\pi\) | |||||||
\(578\) | 33.1234 | 1.37775 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.488100 | 0.0202673 | ||||||||
\(581\) | −0.945512 | −0.0392264 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0084 | −0.414506 | ||||||||
\(584\) | 0.0391891 | 0.00162165 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.8518 | 1.68757 | ||||||||
\(587\) | −15.9913 | −0.660032 | −0.330016 | − | 0.943975i | \(-0.607054\pi\) | ||||
−0.330016 | + | 0.943975i | \(0.607054\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.3758 | −1.66366 | ||||||||
\(590\) | 2.40045 | 0.0988249 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 18.5476 | 0.762301 | ||||||||
\(593\) | 44.3566 | 1.82151 | 0.910753 | − | 0.412952i | \(-0.135502\pi\) | ||||
0.910753 | + | 0.412952i | \(0.135502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.165835 | 0.00679858 | ||||||||
\(596\) | 14.2665 | 0.584378 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.9173 | 0.487336 | ||||||||
\(599\) | 28.0776 | 1.14722 | 0.573610 | − | 0.819129i | \(-0.305543\pi\) | ||||
0.573610 | + | 0.819129i | \(0.305543\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0537 | −0.981171 | −0.490586 | − | 0.871393i | \(-0.663217\pi\) | ||||
−0.490586 | + | 0.871393i | \(0.663217\pi\) | |||||||
\(602\) | 14.8408 | 0.604867 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.78469 | 0.194686 | ||||||||
\(605\) | −0.883474 | −0.0359183 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.6340 | 1.73046 | 0.865229 | − | 0.501376i | \(-0.167173\pi\) | ||||
0.865229 | + | 0.501376i | \(0.167173\pi\) | |||||||
\(608\) | 30.7020 | 1.24513 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.15382 | 0.0467169 | ||||||||
\(611\) | 69.3249 | 2.80459 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.6653 | 1.44051 | 0.720254 | − | 0.693711i | \(-0.244025\pi\) | ||||
0.720254 | + | 0.693711i | \(0.244025\pi\) | |||||||
\(614\) | −38.6906 | −1.56143 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.462658 | 0.0186410 | ||||||||
\(617\) | 21.7432 | 0.875350 | 0.437675 | − | 0.899133i | \(-0.355802\pi\) | ||||
0.437675 | + | 0.899133i | \(0.355802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.1222 | −0.768588 | −0.384294 | − | 0.923211i | \(-0.625555\pi\) | ||||
−0.384294 | + | 0.923211i | \(0.625555\pi\) | |||||||
\(620\) | −5.08370 | −0.204166 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −39.2106 | −1.57220 | ||||||||
\(623\) | 9.86233 | 0.395126 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0446 | 0.961784 | ||||||||
\(626\) | −42.3680 | −1.69337 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 21.1249 | 0.842973 | ||||||||
\(629\) | 2.42052 | 0.0965126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.64264 | −0.264439 | −0.132220 | − | 0.991220i | \(-0.542210\pi\) | ||||
−0.132220 | + | 0.991220i | \(0.542210\pi\) | |||||||
\(632\) | −1.38784 | −0.0552054 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 12.5585 | 0.498761 | ||||||||
\(635\) | 0.128956 | 0.00511744 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.2068 | 1.31570 | ||||||||
\(638\) | 5.43149 | 0.215035 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.281034 | −0.0111089 | ||||||||
\(641\) | 40.3737 | 1.59466 | 0.797332 | − | 0.603541i | \(-0.206244\pi\) | ||||
0.797332 | + | 0.603541i | \(0.206244\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0493 | 0.790666 | 0.395333 | − | 0.918538i | \(-0.370629\pi\) | ||||
0.395333 | + | 0.918538i | \(0.370629\pi\) | |||||||
\(644\) | −2.34479 | −0.0923978 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.14734 | 0.163175 | ||||||||
\(647\) | 40.1626 | 1.57896 | 0.789478 | − | 0.613779i | \(-0.210351\pi\) | ||||
0.789478 | + | 0.613779i | \(0.210351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1176 | 0.514911 | ||||||||
\(650\) | −58.8243 | −2.30728 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −35.7747 | −1.40104 | ||||||||
\(653\) | −12.0476 | −0.471457 | −0.235729 | − | 0.971819i | \(-0.575748\pi\) | ||||
−0.235729 | + | 0.971819i | \(0.575748\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.63168 | −0.220048 | ||||||||
\(656\) | −29.8820 | −1.16669 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −27.7755 | −1.08280 | ||||||||
\(659\) | −3.01463 | −0.117433 | −0.0587166 | − | 0.998275i | \(-0.518701\pi\) | ||||
−0.0587166 | + | 0.998275i | \(0.518701\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.9576 | 0.581781 | 0.290891 | − | 0.956756i | \(-0.406048\pi\) | ||||
0.290891 | + | 0.956756i | \(0.406048\pi\) | |||||||
\(662\) | 5.80118 | 0.225469 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.108157 | 0.00419732 | ||||||||
\(665\) | −1.19124 | −0.0461941 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 17.3314 | 0.670572 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.63737 | 0.256424 | ||||||||
\(671\) | 6.30524 | 0.243411 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2877 | −0.627845 | −0.313922 | − | 0.949449i | \(-0.601643\pi\) | ||||
−0.313922 | + | 0.949449i | \(0.601643\pi\) | |||||||
\(674\) | −48.0149 | −1.84947 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 44.6559 | 1.71753 | ||||||||
\(677\) | 40.9529 | 1.57395 | 0.786974 | − | 0.616986i | \(-0.211646\pi\) | ||||
0.786974 | + | 0.616986i | \(0.211646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.6357 | −0.830303 | ||||||||
\(680\) | −0.0189699 | −0.000727463 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −56.5705 | −2.16620 | ||||||||
\(683\) | −10.0867 | −0.385957 | −0.192979 | − | 0.981203i | \(-0.561815\pi\) | ||||
−0.192979 | + | 0.981203i | \(0.561815\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.20321 | −0.122389 | ||||||||
\(686\) | −30.1646 | −1.15169 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −25.4802 | −0.971425 | ||||||||
\(689\) | −21.9596 | −0.836595 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.48669 | −0.246765 | −0.123383 | − | 0.992359i | \(-0.539374\pi\) | ||||
−0.123383 | + | 0.992359i | \(0.539374\pi\) | |||||||
\(692\) | −8.72537 | −0.331689 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.84034 | 0.107818 | ||||||||
\(695\) | −0.183570 | −0.00696320 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.89970 | −0.147712 | ||||||||
\(698\) | 38.0553 | 1.44041 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.5740 | 0.437455 | ||||||||
\(701\) | 14.3536 | 0.542129 | 0.271064 | − | 0.962561i | \(-0.412624\pi\) | ||||
0.271064 | + | 0.962561i | \(0.412624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.3872 | −0.655772 | ||||||||
\(704\) | 20.3562 | 0.767204 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.2303 | 0.761376 | ||||||||
\(707\) | −11.5309 | −0.433665 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.9482 | 1.38762 | 0.693808 | − | 0.720160i | \(-0.255931\pi\) | ||||
0.693808 | + | 0.720160i | \(0.255931\pi\) | |||||||
\(710\) | −5.49049 | −0.206054 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.12815 | −0.0422793 | ||||||||
\(713\) | −10.4153 | −0.390055 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.16575 | 0.155790 | ||||||||
\(716\) | 37.9521 | 1.41834 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −45.9836 | −1.71609 | ||||||||
\(719\) | 17.1679 | 0.640256 | 0.320128 | − | 0.947374i | \(-0.396274\pi\) | ||||
0.320128 | + | 0.947374i | \(0.396274\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.3404 | −0.906484 | ||||||||
\(722\) | 7.87416 | 0.293046 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.2911 | 0.791277 | ||||||||
\(725\) | −4.93603 | −0.183320 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.1921 | −0.860146 | −0.430073 | − | 0.902794i | \(-0.641512\pi\) | ||||
−0.430073 | + | 0.902794i | \(0.641512\pi\) | |||||||
\(728\) | 1.01513 | 0.0376231 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.141375 | −0.00523251 | ||||||||
\(731\) | −3.32526 | −0.122989 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.3741 | 1.71287 | 0.856434 | − | 0.516257i | \(-0.172675\pi\) | ||||
0.856434 | + | 0.516257i | \(0.172675\pi\) | |||||||
\(734\) | −49.8659 | −1.84059 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.91984 | 0.291929 | ||||||||
\(737\) | 36.2709 | 1.33606 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.51225 | −0.276342 | −0.138171 | − | 0.990408i | \(-0.544122\pi\) | ||||
−0.138171 | + | 0.990408i | \(0.544122\pi\) | |||||||
\(740\) | −2.18922 | −0.0804773 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.79829 | 0.322995 | ||||||||
\(743\) | 19.5439 | 0.716997 | 0.358499 | − | 0.933530i | \(-0.383289\pi\) | ||||
0.358499 | + | 0.933530i | \(0.383289\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.86965 | 0.0684987 | ||||||||
\(746\) | 56.7150 | 2.07648 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.85358 | 0.104337 | ||||||||
\(749\) | −24.2397 | −0.885701 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4707 | −0.856457 | −0.428228 | − | 0.903671i | \(-0.640862\pi\) | ||||
−0.428228 | + | 0.903671i | \(0.640862\pi\) | |||||||
\(752\) | 47.6879 | 1.73900 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.9173 | 0.434003 | ||||||||
\(755\) | 0.627043 | 0.0228204 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.8600 | 1.95757 | 0.978787 | − | 0.204880i | \(-0.0656803\pi\) | ||||
0.978787 | + | 0.204880i | \(0.0656803\pi\) | |||||||
\(758\) | −63.3562 | −2.30120 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.136266 | 0.00494287 | ||||||||
\(761\) | −3.33811 | −0.121006 | −0.0605032 | − | 0.998168i | \(-0.519271\pi\) | ||||
−0.0605032 | + | 0.998168i | \(0.519271\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.33166 | −0.156817 | ||||||||
\(764\) | −4.55307 | −0.164724 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47.1796 | −1.70467 | ||||||||
\(767\) | 28.7816 | 1.03924 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.2700 | −0.586712 | −0.293356 | − | 0.956003i | \(-0.594772\pi\) | ||||
−0.293356 | + | 0.956003i | \(0.594772\pi\) | |||||||
\(770\) | −1.66904 | −0.0601480 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 32.9138 | 1.18459 | ||||||||
\(773\) | 36.7642 | 1.32232 | 0.661159 | − | 0.750246i | \(-0.270065\pi\) | ||||
0.661159 | + | 0.750246i | \(0.270065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.4102 | 1.84671 | ||||||||
\(776\) | 2.47491 | 0.0888442 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −45.4551 | −1.62965 | ||||||||
\(779\) | 28.0125 | 1.00365 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −30.0036 | −1.07361 | ||||||||
\(782\) | 1.06984 | 0.0382574 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 22.8426 | 0.815808 | ||||||||
\(785\) | 2.76845 | 0.0988103 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2569 | −0.757727 | −0.378863 | − | 0.925453i | \(-0.623685\pi\) | ||||
−0.378863 | + | 0.925453i | \(0.623685\pi\) | |||||||
\(788\) | −10.6392 | −0.379005 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.00664 | 0.178128 | ||||||||
\(791\) | 6.51359 | 0.231597 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.8344 | 0.491275 | ||||||||
\(794\) | 48.6994 | 1.72828 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −30.0600 | −1.06545 | ||||||||
\(797\) | 47.3125 | 1.67589 | 0.837947 | − | 0.545752i | \(-0.183756\pi\) | ||||
0.837947 | + | 0.545752i | \(0.183756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.22343 | 0.220169 | ||||||||
\(800\) | −39.0926 | −1.38213 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.9970 | −0.706120 | ||||||||
\(803\) | −0.772562 | −0.0272631 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.307289 | −0.0108305 | ||||||||
\(806\) | −124.122 | −4.37202 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.31902 | 0.0464031 | ||||||||
\(809\) | −7.50118 | −0.263727 | −0.131864 | − | 0.991268i | \(-0.542096\pi\) | ||||
−0.131864 | + | 0.991268i | \(0.542096\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.5896 | 1.00392 | 0.501959 | − | 0.864891i | \(-0.332613\pi\) | ||||
0.501959 | + | 0.864891i | \(0.332613\pi\) | |||||||
\(812\) | −2.34479 | −0.0822861 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.3612 | −0.853861 | ||||||||
\(815\) | −4.68834 | −0.164225 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.8862 | 0.835671 | ||||||||
\(818\) | 4.36478 | 0.152611 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.52705 | 0.123170 | ||||||||
\(821\) | 27.1303 | 0.946853 | 0.473426 | − | 0.880833i | \(-0.343017\pi\) | ||||
0.473426 | + | 0.880833i | \(0.343017\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.22868 | 0.182260 | 0.0911301 | − | 0.995839i | \(-0.470952\pi\) | ||||
0.0911301 | + | 0.995839i | \(0.470952\pi\) | |||||||
\(824\) | 2.78430 | 0.0969958 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −11.5316 | −0.401234 | ||||||||
\(827\) | −7.46403 | −0.259550 | −0.129775 | − | 0.991543i | \(-0.541425\pi\) | ||||
−0.129775 | + | 0.991543i | \(0.541425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.68393 | 0.232143 | 0.116071 | − | 0.993241i | \(-0.462970\pi\) | ||||
0.116071 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(830\) | −0.390177 | −0.0135433 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 44.6639 | 1.54844 | ||||||||
\(833\) | 2.98104 | 0.103287 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.27131 | 0.0786020 | ||||||||
\(836\) | −20.4980 | −0.708938 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 58.2067 | 2.01072 | ||||||||
\(839\) | 23.6750 | 0.817352 | 0.408676 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408676 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −31.0185 | −1.06897 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.30376 | 0.0448774 | ||||||||
\(845\) | 5.85224 | 0.201323 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.24413 | 0.145830 | ||||||||
\(848\) | −15.1058 | −0.518735 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.28077 | −0.181129 | ||||||||
\(851\) | −4.48518 | −0.153750 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.3533 | 1.79254 | 0.896271 | − | 0.443507i | \(-0.146266\pi\) | ||||
0.896271 | + | 0.443507i | \(0.146266\pi\) | |||||||
\(854\) | −5.54287 | −0.189673 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.77279 | 0.0947720 | ||||||||
\(857\) | 52.5066 | 1.79359 | 0.896796 | − | 0.442444i | \(-0.145888\pi\) | ||||
0.896796 | + | 0.442444i | \(0.145888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.4193 | −0.662577 | −0.331288 | − | 0.943530i | \(-0.607483\pi\) | ||||
−0.331288 | + | 0.943530i | \(0.607483\pi\) | |||||||
\(860\) | 3.00750 | 0.102555 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −75.9328 | −2.58628 | ||||||||
\(863\) | −25.1140 | −0.854891 | −0.427445 | − | 0.904041i | \(-0.640586\pi\) | ||||
−0.427445 | + | 0.904041i | \(0.640586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.14348 | −0.0388793 | ||||||||
\(866\) | −17.8397 | −0.606217 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24.4217 | 0.828926 | ||||||||
\(869\) | 27.3595 | 0.928109 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 79.5825 | 2.69655 | ||||||||
\(872\) | 0.495500 | 0.0167797 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.68494 | −0.259947 | ||||||||
\(875\) | 3.05324 | 0.103218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.4365 | −1.29791 | −0.648954 | − | 0.760828i | \(-0.724793\pi\) | ||||
−0.648954 | + | 0.760828i | \(0.724793\pi\) | |||||||
\(878\) | 16.5195 | 0.557506 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.86558 | 0.0965986 | ||||||||
\(881\) | −10.3064 | −0.347230 | −0.173615 | − | 0.984814i | \(-0.555545\pi\) | ||||
−0.173615 | + | 0.984814i | \(0.555545\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0404 | −0.876328 | −0.438164 | − | 0.898895i | \(-0.644371\pi\) | ||||
−0.438164 | + | 0.898895i | \(0.644371\pi\) | |||||||
\(884\) | 6.26109 | 0.210583 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.6311 | 0.961880 | ||||||||
\(887\) | 1.08373 | 0.0363882 | 0.0181941 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181941 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.619491 | −0.0207771 | ||||||||
\(890\) | 4.06981 | 0.136420 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.8940 | 0.431723 | ||||||||
\(893\) | −44.7045 | −1.49598 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.97370 | 0.166252 | ||||||||
\(896\) | 1.35006 | 0.0451025 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 63.7387 | 2.12699 | ||||||||
\(899\) | −10.4153 | −0.347369 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.97136 | −0.0656754 | ||||||||
\(902\) | 39.2483 | 1.30683 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.745090 | −0.0247813 | ||||||||
\(905\) | 2.79024 | 0.0927507 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.1863 | −0.935910 | −0.467955 | − | 0.883752i | \(-0.655009\pi\) | ||||
−0.467955 | + | 0.883752i | \(0.655009\pi\) | |||||||
\(908\) | 2.12936 | 0.0706654 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −3.66207 | −0.121396 | ||||||||
\(911\) | 36.4596 | 1.20796 | 0.603980 | − | 0.796999i | \(-0.293581\pi\) | ||||
0.603980 | + | 0.796999i | \(0.293581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.13218 | −0.0705649 | ||||||||
\(914\) | 12.7992 | 0.423361 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.5872 | −1.53929 | ||||||||
\(917\) | 27.0541 | 0.893406 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −46.5156 | −1.53441 | −0.767204 | − | 0.641403i | \(-0.778353\pi\) | ||||
−0.767204 | + | 0.641403i | \(0.778353\pi\) | |||||||
\(920\) | 0.0351509 | 0.00115889 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −33.9607 | −1.11844 | ||||||||
\(923\) | −65.8314 | −2.16687 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.1390 | 0.727927 | ||||||||
\(926\) | 32.2139 | 1.05861 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.91984 | 0.259981 | ||||||||
\(929\) | −1.73608 | −0.0569591 | −0.0284795 | − | 0.999594i | \(-0.509067\pi\) | ||||
−0.0284795 | + | 0.999594i | \(0.509067\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.4135 | −0.701801 | ||||||||
\(932\) | −33.6331 | −1.10169 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.37220 | 0.143063 | ||||||||
\(935\) | 0.373968 | 0.0122300 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.65638 | −0.282792 | −0.141396 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141396 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(938\) | −31.8853 | −1.04109 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.62872 | −0.183589 | ||||||||
\(941\) | −15.3813 | −0.501417 | −0.250708 | − | 0.968063i | \(-0.580664\pi\) | ||||
−0.250708 | + | 0.968063i | \(0.580664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.22607 | 0.235313 | ||||||||
\(944\) | 19.7985 | 0.644388 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 33.4669 | 1.08810 | ||||||||
\(947\) | −48.5352 | −1.57718 | −0.788591 | − | 0.614918i | \(-0.789189\pi\) | ||||
−0.788591 | + | 0.614918i | \(0.789189\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.69509 | −0.0550250 | ||||||||
\(950\) | 37.9331 | 1.23071 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0911298 | 0.00295353 | ||||||||
\(953\) | 46.7032 | 1.51286 | 0.756432 | − | 0.654072i | \(-0.226941\pi\) | ||||
0.756432 | + | 0.654072i | \(0.226941\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.596689 | −0.0193084 | ||||||||
\(956\) | −35.0275 | −1.13287 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −83.6183 | −2.70158 | ||||||||
\(959\) | 15.3880 | 0.496903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 77.4781 | 2.49929 | ||||||||
\(962\) | −53.4514 | −1.72334 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −41.7500 | −1.34468 | ||||||||
\(965\) | 4.31342 | 0.138854 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26.5967 | −0.855291 | −0.427645 | − | 0.903947i | \(-0.640657\pi\) | ||||
−0.427645 | + | 0.903947i | \(0.640657\pi\) | |||||||
\(968\) | −0.485487 | −0.0156041 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.92825 | −0.286669 | ||||||||
\(971\) | −44.5888 | −1.43092 | −0.715462 | − | 0.698652i | \(-0.753784\pi\) | ||||
−0.715462 | + | 0.698652i | \(0.753784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.881854 | 0.0282709 | ||||||||
\(974\) | 80.8882 | 2.59183 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.51656 | 0.304618 | ||||||||
\(977\) | 45.3191 | 1.44989 | 0.724944 | − | 0.688808i | \(-0.241866\pi\) | ||||
0.724944 | + | 0.688808i | \(0.241866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.2401 | 0.710797 | ||||||||
\(980\) | −2.69617 | −0.0861261 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.33643 | −0.170292 | ||||||||
\(983\) | −31.5879 | −1.00750 | −0.503749 | − | 0.863850i | \(-0.668046\pi\) | ||||
−0.503749 | + | 0.863850i | \(0.668046\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.39428 | −0.0444256 | ||||||||
\(986\) | 1.06984 | 0.0340707 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −44.9750 | −1.43085 | ||||||||
\(989\) | 6.16164 | 0.195929 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.9658 | −1.46015 | −0.730076 | − | 0.683366i | \(-0.760515\pi\) | ||||
−0.730076 | + | 0.683366i | \(0.760515\pi\) | |||||||
\(992\) | −82.4874 | −2.61898 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 26.3758 | 0.836591 | ||||||||
\(995\) | −3.93942 | −0.124888 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.2525 | −1.08479 | −0.542394 | − | 0.840125i | \(-0.682482\pi\) | ||||
−0.542394 | + | 0.840125i | \(0.682482\pi\) | |||||||
\(998\) | 66.7706 | 2.11359 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.p.1.2 | 14 | ||
3.2 | odd | 2 | 2001.2.a.m.1.13 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.m.1.13 | ✓ | 14 | 3.2 | odd | 2 | ||
6003.2.a.p.1.2 | 14 | 1.1 | even | 1 | trivial |