Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8003,2,Mod(1,8003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8003 = 53 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8003.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: | \(63.9042767376\) |
Analytic rank: | \(0\) |
Dimension: | \(172\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.39169 | −1.69118 | −0.845591 | − | 0.533832i | \(-0.820751\pi\) | ||||
−0.845591 | + | 0.533832i | \(0.820751\pi\) | |||||||
\(3\) | −2.70490 | −1.56168 | −0.780838 | − | 0.624733i | \(-0.785208\pi\) | ||||
−0.780838 | + | 0.624733i | \(0.785208\pi\) | |||||||
\(4\) | 3.72019 | 1.86009 | ||||||||
\(5\) | 3.87028 | 1.73084 | 0.865421 | − | 0.501045i | \(-0.167051\pi\) | ||||
0.865421 | + | 0.501045i | \(0.167051\pi\) | |||||||
\(6\) | 6.46929 | 2.64108 | ||||||||
\(7\) | −0.448223 | −0.169412 | −0.0847061 | − | 0.996406i | \(-0.526995\pi\) | ||||
−0.0847061 | + | 0.996406i | \(0.526995\pi\) | |||||||
\(8\) | −4.11416 | −1.45457 | ||||||||
\(9\) | 4.31650 | 1.43883 | ||||||||
\(10\) | −9.25652 | −2.92717 | ||||||||
\(11\) | 1.05036 | 0.316694 | 0.158347 | − | 0.987384i | \(-0.449384\pi\) | ||||
0.158347 | + | 0.987384i | \(0.449384\pi\) | |||||||
\(12\) | −10.0627 | −2.90486 | ||||||||
\(13\) | −1.18419 | −0.328437 | −0.164218 | − | 0.986424i | \(-0.552510\pi\) | ||||
−0.164218 | + | 0.986424i | \(0.552510\pi\) | |||||||
\(14\) | 1.07201 | 0.286507 | ||||||||
\(15\) | −10.4687 | −2.70302 | ||||||||
\(16\) | 2.39942 | 0.599855 | ||||||||
\(17\) | 4.93717 | 1.19744 | 0.598719 | − | 0.800959i | \(-0.295677\pi\) | ||||
0.598719 | + | 0.800959i | \(0.295677\pi\) | |||||||
\(18\) | −10.3237 | −2.43333 | ||||||||
\(19\) | −3.82010 | −0.876392 | −0.438196 | − | 0.898879i | \(-0.644382\pi\) | ||||
−0.438196 | + | 0.898879i | \(0.644382\pi\) | |||||||
\(20\) | 14.3982 | 3.21953 | ||||||||
\(21\) | 1.21240 | 0.264567 | ||||||||
\(22\) | −2.51213 | −0.535587 | ||||||||
\(23\) | −1.26401 | −0.263565 | −0.131782 | − | 0.991279i | \(-0.542070\pi\) | ||||
−0.131782 | + | 0.991279i | \(0.542070\pi\) | |||||||
\(24\) | 11.1284 | 2.27157 | ||||||||
\(25\) | 9.97908 | 1.99582 | ||||||||
\(26\) | 2.83223 | 0.555446 | ||||||||
\(27\) | −3.56101 | −0.685316 | ||||||||
\(28\) | −1.66747 | −0.315123 | ||||||||
\(29\) | 7.55593 | 1.40310 | 0.701551 | − | 0.712619i | \(-0.252491\pi\) | ||||
0.701551 | + | 0.712619i | \(0.252491\pi\) | |||||||
\(30\) | 25.0380 | 4.57129 | ||||||||
\(31\) | −5.15642 | −0.926120 | −0.463060 | − | 0.886327i | \(-0.653249\pi\) | ||||
−0.463060 | + | 0.886327i | \(0.653249\pi\) | |||||||
\(32\) | 2.48964 | 0.440111 | ||||||||
\(33\) | −2.84111 | −0.494574 | ||||||||
\(34\) | −11.8082 | −2.02509 | ||||||||
\(35\) | −1.73475 | −0.293226 | ||||||||
\(36\) | 16.0582 | 2.67637 | ||||||||
\(37\) | 3.83586 | 0.630611 | 0.315306 | − | 0.948990i | \(-0.397893\pi\) | ||||
0.315306 | + | 0.948990i | \(0.397893\pi\) | |||||||
\(38\) | 9.13651 | 1.48214 | ||||||||
\(39\) | 3.20313 | 0.512912 | ||||||||
\(40\) | −15.9229 | −2.51764 | ||||||||
\(41\) | −3.73658 | −0.583555 | −0.291778 | − | 0.956486i | \(-0.594247\pi\) | ||||
−0.291778 | + | 0.956486i | \(0.594247\pi\) | |||||||
\(42\) | −2.89968 | −0.447431 | ||||||||
\(43\) | −10.6396 | −1.62252 | −0.811261 | − | 0.584684i | \(-0.801219\pi\) | ||||
−0.811261 | + | 0.584684i | \(0.801219\pi\) | |||||||
\(44\) | 3.90752 | 0.589081 | ||||||||
\(45\) | 16.7061 | 2.49039 | ||||||||
\(46\) | 3.02313 | 0.445736 | ||||||||
\(47\) | −6.33948 | −0.924709 | −0.462354 | − | 0.886695i | \(-0.652995\pi\) | ||||
−0.462354 | + | 0.886695i | \(0.652995\pi\) | |||||||
\(48\) | −6.49020 | −0.936779 | ||||||||
\(49\) | −6.79910 | −0.971299 | ||||||||
\(50\) | −23.8669 | −3.37529 | ||||||||
\(51\) | −13.3546 | −1.87001 | ||||||||
\(52\) | −4.40543 | −0.610923 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 8.51683 | 1.15899 | ||||||||
\(55\) | 4.06517 | 0.548148 | ||||||||
\(56\) | 1.84406 | 0.246423 | ||||||||
\(57\) | 10.3330 | 1.36864 | ||||||||
\(58\) | −18.0715 | −2.37290 | ||||||||
\(59\) | −2.84970 | −0.370999 | −0.185499 | − | 0.982644i | \(-0.559390\pi\) | ||||
−0.185499 | + | 0.982644i | \(0.559390\pi\) | |||||||
\(60\) | −38.9457 | −5.02786 | ||||||||
\(61\) | −15.1761 | −1.94310 | −0.971550 | − | 0.236835i | \(-0.923890\pi\) | ||||
−0.971550 | + | 0.236835i | \(0.923890\pi\) | |||||||
\(62\) | 12.3326 | 1.56624 | ||||||||
\(63\) | −1.93475 | −0.243756 | ||||||||
\(64\) | −10.7533 | −1.34416 | ||||||||
\(65\) | −4.58317 | −0.568472 | ||||||||
\(66\) | 6.79506 | 0.836414 | ||||||||
\(67\) | 14.2853 | 1.74522 | 0.872612 | − | 0.488415i | \(-0.162425\pi\) | ||||
0.872612 | + | 0.488415i | \(0.162425\pi\) | |||||||
\(68\) | 18.3672 | 2.22735 | ||||||||
\(69\) | 3.41903 | 0.411603 | ||||||||
\(70\) | 4.14898 | 0.495898 | ||||||||
\(71\) | 13.8121 | 1.63919 | 0.819595 | − | 0.572944i | \(-0.194199\pi\) | ||||
0.819595 | + | 0.572944i | \(0.194199\pi\) | |||||||
\(72\) | −17.7588 | −2.09289 | ||||||||
\(73\) | 10.5536 | 1.23521 | 0.617605 | − | 0.786488i | \(-0.288103\pi\) | ||||
0.617605 | + | 0.786488i | \(0.288103\pi\) | |||||||
\(74\) | −9.17419 | −1.06648 | ||||||||
\(75\) | −26.9925 | −3.11682 | ||||||||
\(76\) | −14.2115 | −1.63017 | ||||||||
\(77\) | −0.470793 | −0.0536519 | ||||||||
\(78\) | −7.66090 | −0.867426 | ||||||||
\(79\) | −14.9888 | −1.68637 | −0.843184 | − | 0.537626i | \(-0.819321\pi\) | ||||
−0.843184 | + | 0.537626i | \(0.819321\pi\) | |||||||
\(80\) | 9.28643 | 1.03825 | ||||||||
\(81\) | −3.31733 | −0.368592 | ||||||||
\(82\) | 8.93673 | 0.986897 | ||||||||
\(83\) | 8.77655 | 0.963352 | 0.481676 | − | 0.876349i | \(-0.340028\pi\) | ||||
0.481676 | + | 0.876349i | \(0.340028\pi\) | |||||||
\(84\) | 4.51035 | 0.492120 | ||||||||
\(85\) | 19.1082 | 2.07258 | ||||||||
\(86\) | 25.4466 | 2.74398 | ||||||||
\(87\) | −20.4381 | −2.19119 | ||||||||
\(88\) | −4.32133 | −0.460655 | ||||||||
\(89\) | 5.60844 | 0.594494 | 0.297247 | − | 0.954801i | \(-0.403932\pi\) | ||||
0.297247 | + | 0.954801i | \(0.403932\pi\) | |||||||
\(90\) | −39.9558 | −4.21171 | ||||||||
\(91\) | 0.530783 | 0.0556412 | ||||||||
\(92\) | −4.70236 | −0.490255 | ||||||||
\(93\) | 13.9476 | 1.44630 | ||||||||
\(94\) | 15.1621 | 1.56385 | ||||||||
\(95\) | −14.7849 | −1.51690 | ||||||||
\(96\) | −6.73425 | −0.687311 | ||||||||
\(97\) | −0.789133 | −0.0801243 | −0.0400622 | − | 0.999197i | \(-0.512756\pi\) | ||||
−0.0400622 | + | 0.999197i | \(0.512756\pi\) | |||||||
\(98\) | 16.2613 | 1.64264 | ||||||||
\(99\) | 4.53386 | 0.455670 | ||||||||
\(100\) | 37.1241 | 3.71241 | ||||||||
\(101\) | 4.23498 | 0.421396 | 0.210698 | − | 0.977551i | \(-0.432426\pi\) | ||||
0.210698 | + | 0.977551i | \(0.432426\pi\) | |||||||
\(102\) | 31.9400 | 3.16253 | ||||||||
\(103\) | 10.3585 | 1.02066 | 0.510329 | − | 0.859979i | \(-0.329524\pi\) | ||||
0.510329 | + | 0.859979i | \(0.329524\pi\) | |||||||
\(104\) | 4.87196 | 0.477735 | ||||||||
\(105\) | 4.69233 | 0.457924 | ||||||||
\(106\) | 2.39169 | 0.232302 | ||||||||
\(107\) | −4.66932 | −0.451400 | −0.225700 | − | 0.974197i | \(-0.572467\pi\) | ||||
−0.225700 | + | 0.974197i | \(0.572467\pi\) | |||||||
\(108\) | −13.2476 | −1.27475 | ||||||||
\(109\) | 6.48667 | 0.621310 | 0.310655 | − | 0.950523i | \(-0.399452\pi\) | ||||
0.310655 | + | 0.950523i | \(0.399452\pi\) | |||||||
\(110\) | −9.72264 | −0.927017 | ||||||||
\(111\) | −10.3756 | −0.984811 | ||||||||
\(112\) | −1.07547 | −0.101623 | ||||||||
\(113\) | 10.2030 | 0.959821 | 0.479911 | − | 0.877317i | \(-0.340669\pi\) | ||||
0.479911 | + | 0.877317i | \(0.340669\pi\) | |||||||
\(114\) | −24.7134 | −2.31462 | ||||||||
\(115\) | −4.89208 | −0.456189 | ||||||||
\(116\) | 28.1095 | 2.60990 | ||||||||
\(117\) | −5.11158 | −0.472565 | ||||||||
\(118\) | 6.81559 | 0.627426 | ||||||||
\(119\) | −2.21295 | −0.202861 | ||||||||
\(120\) | 43.0700 | 3.93174 | ||||||||
\(121\) | −9.89675 | −0.899705 | ||||||||
\(122\) | 36.2965 | 3.28613 | ||||||||
\(123\) | 10.1071 | 0.911324 | ||||||||
\(124\) | −19.1828 | −1.72267 | ||||||||
\(125\) | 19.2705 | 1.72360 | ||||||||
\(126\) | 4.62733 | 0.412236 | ||||||||
\(127\) | 17.4823 | 1.55130 | 0.775652 | − | 0.631161i | \(-0.217421\pi\) | ||||
0.775652 | + | 0.631161i | \(0.217421\pi\) | |||||||
\(128\) | 20.7393 | 1.83311 | ||||||||
\(129\) | 28.7791 | 2.53386 | ||||||||
\(130\) | 10.9615 | 0.961389 | ||||||||
\(131\) | 1.59621 | 0.139462 | 0.0697309 | − | 0.997566i | \(-0.477786\pi\) | ||||
0.0697309 | + | 0.997566i | \(0.477786\pi\) | |||||||
\(132\) | −10.5695 | −0.919953 | ||||||||
\(133\) | 1.71226 | 0.148472 | ||||||||
\(134\) | −34.1660 | −2.95149 | ||||||||
\(135\) | −13.7821 | −1.18617 | ||||||||
\(136\) | −20.3123 | −1.74176 | ||||||||
\(137\) | 16.3099 | 1.39345 | 0.696723 | − | 0.717340i | \(-0.254641\pi\) | ||||
0.696723 | + | 0.717340i | \(0.254641\pi\) | |||||||
\(138\) | −8.17726 | −0.696095 | ||||||||
\(139\) | −3.52706 | −0.299161 | −0.149581 | − | 0.988750i | \(-0.547792\pi\) | ||||
−0.149581 | + | 0.988750i | \(0.547792\pi\) | |||||||
\(140\) | −6.45359 | −0.545428 | ||||||||
\(141\) | 17.1477 | 1.44410 | ||||||||
\(142\) | −33.0342 | −2.77217 | ||||||||
\(143\) | −1.24383 | −0.104014 | ||||||||
\(144\) | 10.3571 | 0.863091 | ||||||||
\(145\) | 29.2436 | 2.42855 | ||||||||
\(146\) | −25.2411 | −2.08897 | ||||||||
\(147\) | 18.3909 | 1.51686 | ||||||||
\(148\) | 14.2701 | 1.17300 | ||||||||
\(149\) | 0.588110 | 0.0481798 | 0.0240899 | − | 0.999710i | \(-0.492331\pi\) | ||||
0.0240899 | + | 0.999710i | \(0.492331\pi\) | |||||||
\(150\) | 64.5576 | 5.27111 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 15.7165 | 1.27478 | ||||||||
\(153\) | 21.3113 | 1.72291 | ||||||||
\(154\) | 1.12599 | 0.0907350 | ||||||||
\(155\) | −19.9568 | −1.60297 | ||||||||
\(156\) | 11.9163 | 0.954064 | ||||||||
\(157\) | 13.3085 | 1.06213 | 0.531067 | − | 0.847330i | \(-0.321791\pi\) | ||||
0.531067 | + | 0.847330i | \(0.321791\pi\) | |||||||
\(158\) | 35.8485 | 2.85195 | ||||||||
\(159\) | 2.70490 | 0.214513 | ||||||||
\(160\) | 9.63563 | 0.761763 | ||||||||
\(161\) | 0.566559 | 0.0446511 | ||||||||
\(162\) | 7.93402 | 0.623355 | ||||||||
\(163\) | −21.5246 | −1.68594 | −0.842968 | − | 0.537964i | \(-0.819193\pi\) | ||||
−0.842968 | + | 0.537964i | \(0.819193\pi\) | |||||||
\(164\) | −13.9008 | −1.08547 | ||||||||
\(165\) | −10.9959 | −0.856029 | ||||||||
\(166\) | −20.9908 | −1.62920 | ||||||||
\(167\) | −14.8656 | −1.15034 | −0.575169 | − | 0.818035i | \(-0.695064\pi\) | ||||
−0.575169 | + | 0.818035i | \(0.695064\pi\) | |||||||
\(168\) | −4.98800 | −0.384833 | ||||||||
\(169\) | −11.5977 | −0.892129 | ||||||||
\(170\) | −45.7010 | −3.50510 | ||||||||
\(171\) | −16.4895 | −1.26098 | ||||||||
\(172\) | −39.5813 | −3.01804 | ||||||||
\(173\) | 20.9921 | 1.59600 | 0.797999 | − | 0.602658i | \(-0.205892\pi\) | ||||
0.797999 | + | 0.602658i | \(0.205892\pi\) | |||||||
\(174\) | 48.8816 | 3.70570 | ||||||||
\(175\) | −4.47285 | −0.338116 | ||||||||
\(176\) | 2.52024 | 0.189970 | ||||||||
\(177\) | 7.70815 | 0.579380 | ||||||||
\(178\) | −13.4137 | −1.00540 | ||||||||
\(179\) | 7.23183 | 0.540532 | 0.270266 | − | 0.962786i | \(-0.412888\pi\) | ||||
0.270266 | + | 0.962786i | \(0.412888\pi\) | |||||||
\(180\) | 62.1497 | 4.63237 | ||||||||
\(181\) | −1.10604 | −0.0822113 | −0.0411057 | − | 0.999155i | \(-0.513088\pi\) | ||||
−0.0411057 | + | 0.999155i | \(0.513088\pi\) | |||||||
\(182\) | −1.26947 | −0.0940993 | ||||||||
\(183\) | 41.0499 | 3.03449 | ||||||||
\(184\) | 5.20034 | 0.383374 | ||||||||
\(185\) | 14.8459 | 1.09149 | ||||||||
\(186\) | −33.3584 | −2.44596 | ||||||||
\(187\) | 5.18578 | 0.379222 | ||||||||
\(188\) | −23.5841 | −1.72005 | ||||||||
\(189\) | 1.59612 | 0.116101 | ||||||||
\(190\) | 35.3609 | 2.56535 | ||||||||
\(191\) | 18.4150 | 1.33246 | 0.666230 | − | 0.745746i | \(-0.267907\pi\) | ||||
0.666230 | + | 0.745746i | \(0.267907\pi\) | |||||||
\(192\) | 29.0866 | 2.09915 | ||||||||
\(193\) | −25.1176 | −1.80800 | −0.904002 | − | 0.427528i | \(-0.859385\pi\) | ||||
−0.904002 | + | 0.427528i | \(0.859385\pi\) | |||||||
\(194\) | 1.88736 | 0.135505 | ||||||||
\(195\) | 12.3970 | 0.887769 | ||||||||
\(196\) | −25.2939 | −1.80671 | ||||||||
\(197\) | 5.07158 | 0.361335 | 0.180668 | − | 0.983544i | \(-0.442174\pi\) | ||||
0.180668 | + | 0.983544i | \(0.442174\pi\) | |||||||
\(198\) | −10.8436 | −0.770621 | ||||||||
\(199\) | 24.3833 | 1.72848 | 0.864241 | − | 0.503077i | \(-0.167799\pi\) | ||||
0.864241 | + | 0.503077i | \(0.167799\pi\) | |||||||
\(200\) | −41.0555 | −2.90306 | ||||||||
\(201\) | −38.6403 | −2.72547 | ||||||||
\(202\) | −10.1288 | −0.712657 | ||||||||
\(203\) | −3.38674 | −0.237703 | ||||||||
\(204\) | −49.6814 | −3.47840 | ||||||||
\(205\) | −14.4616 | −1.01004 | ||||||||
\(206\) | −24.7744 | −1.72612 | ||||||||
\(207\) | −5.45611 | −0.379226 | ||||||||
\(208\) | −2.84138 | −0.197014 | ||||||||
\(209\) | −4.01247 | −0.277548 | ||||||||
\(210\) | −11.2226 | −0.774433 | ||||||||
\(211\) | 16.4126 | 1.12989 | 0.564944 | − | 0.825129i | \(-0.308898\pi\) | ||||
0.564944 | + | 0.825129i | \(0.308898\pi\) | |||||||
\(212\) | −3.72019 | −0.255504 | ||||||||
\(213\) | −37.3603 | −2.55988 | ||||||||
\(214\) | 11.1676 | 0.763400 | ||||||||
\(215\) | −41.1782 | −2.80833 | ||||||||
\(216\) | 14.6505 | 0.996843 | ||||||||
\(217\) | 2.31122 | 0.156896 | ||||||||
\(218\) | −15.5141 | −1.05075 | ||||||||
\(219\) | −28.5466 | −1.92900 | ||||||||
\(220\) | 15.1232 | 1.01961 | ||||||||
\(221\) | −5.84656 | −0.393283 | ||||||||
\(222\) | 24.8153 | 1.66549 | ||||||||
\(223\) | −12.3841 | −0.829299 | −0.414650 | − | 0.909981i | \(-0.636096\pi\) | ||||
−0.414650 | + | 0.909981i | \(0.636096\pi\) | |||||||
\(224\) | −1.11592 | −0.0745602 | ||||||||
\(225\) | 43.0747 | 2.87165 | ||||||||
\(226\) | −24.4025 | −1.62323 | ||||||||
\(227\) | 24.8458 | 1.64908 | 0.824538 | − | 0.565807i | \(-0.191435\pi\) | ||||
0.824538 | + | 0.565807i | \(0.191435\pi\) | |||||||
\(228\) | 38.4407 | 2.54580 | ||||||||
\(229\) | −7.16757 | −0.473646 | −0.236823 | − | 0.971553i | \(-0.576106\pi\) | ||||
−0.236823 | + | 0.971553i | \(0.576106\pi\) | |||||||
\(230\) | 11.7004 | 0.771498 | ||||||||
\(231\) | 1.27345 | 0.0837869 | ||||||||
\(232\) | −31.0863 | −2.04092 | ||||||||
\(233\) | 11.4617 | 0.750878 | 0.375439 | − | 0.926847i | \(-0.377492\pi\) | ||||
0.375439 | + | 0.926847i | \(0.377492\pi\) | |||||||
\(234\) | 12.2253 | 0.799194 | ||||||||
\(235\) | −24.5356 | −1.60053 | ||||||||
\(236\) | −10.6014 | −0.690093 | ||||||||
\(237\) | 40.5431 | 2.63356 | ||||||||
\(238\) | 5.29269 | 0.343074 | ||||||||
\(239\) | 24.2458 | 1.56833 | 0.784164 | − | 0.620554i | \(-0.213092\pi\) | ||||
0.784164 | + | 0.620554i | \(0.213092\pi\) | |||||||
\(240\) | −25.1189 | −1.62142 | ||||||||
\(241\) | 24.2028 | 1.55904 | 0.779521 | − | 0.626376i | \(-0.215463\pi\) | ||||
0.779521 | + | 0.626376i | \(0.215463\pi\) | |||||||
\(242\) | 23.6700 | 1.52156 | ||||||||
\(243\) | 19.6561 | 1.26094 | ||||||||
\(244\) | −56.4579 | −3.61435 | ||||||||
\(245\) | −26.3144 | −1.68117 | ||||||||
\(246\) | −24.1730 | −1.54121 | ||||||||
\(247\) | 4.52375 | 0.287839 | ||||||||
\(248\) | 21.2143 | 1.34711 | ||||||||
\(249\) | −23.7397 | −1.50444 | ||||||||
\(250\) | −46.0890 | −2.91492 | ||||||||
\(251\) | −19.3814 | −1.22334 | −0.611671 | − | 0.791112i | \(-0.709502\pi\) | ||||
−0.611671 | + | 0.791112i | \(0.709502\pi\) | |||||||
\(252\) | −7.19765 | −0.453409 | ||||||||
\(253\) | −1.32766 | −0.0834694 | ||||||||
\(254\) | −41.8123 | −2.62353 | ||||||||
\(255\) | −51.6859 | −3.23670 | ||||||||
\(256\) | −28.0954 | −1.75596 | ||||||||
\(257\) | 25.8622 | 1.61324 | 0.806621 | − | 0.591069i | \(-0.201294\pi\) | ||||
0.806621 | + | 0.591069i | \(0.201294\pi\) | |||||||
\(258\) | −68.8306 | −4.28521 | ||||||||
\(259\) | −1.71932 | −0.106833 | ||||||||
\(260\) | −17.0502 | −1.05741 | ||||||||
\(261\) | 32.6152 | 2.01883 | ||||||||
\(262\) | −3.81765 | −0.235855 | ||||||||
\(263\) | −19.8085 | −1.22144 | −0.610722 | − | 0.791845i | \(-0.709121\pi\) | ||||
−0.610722 | + | 0.791845i | \(0.709121\pi\) | |||||||
\(264\) | 11.6888 | 0.719394 | ||||||||
\(265\) | −3.87028 | −0.237750 | ||||||||
\(266\) | −4.09519 | −0.251092 | ||||||||
\(267\) | −15.1703 | −0.928407 | ||||||||
\(268\) | 53.1439 | 3.24628 | ||||||||
\(269\) | −27.2617 | −1.66218 | −0.831088 | − | 0.556141i | \(-0.812281\pi\) | ||||
−0.831088 | + | 0.556141i | \(0.812281\pi\) | |||||||
\(270\) | 32.9625 | 2.00604 | ||||||||
\(271\) | −14.4840 | −0.879842 | −0.439921 | − | 0.898036i | \(-0.644994\pi\) | ||||
−0.439921 | + | 0.898036i | \(0.644994\pi\) | |||||||
\(272\) | 11.8463 | 0.718289 | ||||||||
\(273\) | −1.43572 | −0.0868935 | ||||||||
\(274\) | −39.0082 | −2.35657 | ||||||||
\(275\) | 10.4816 | 0.632063 | ||||||||
\(276\) | 12.7194 | 0.765620 | ||||||||
\(277\) | 7.69069 | 0.462089 | 0.231044 | − | 0.972943i | \(-0.425786\pi\) | ||||
0.231044 | + | 0.972943i | \(0.425786\pi\) | |||||||
\(278\) | 8.43564 | 0.505936 | ||||||||
\(279\) | −22.2577 | −1.33253 | ||||||||
\(280\) | 7.13703 | 0.426519 | ||||||||
\(281\) | −10.4230 | −0.621787 | −0.310893 | − | 0.950445i | \(-0.600628\pi\) | ||||
−0.310893 | + | 0.950445i | \(0.600628\pi\) | |||||||
\(282\) | −41.0120 | −2.44223 | ||||||||
\(283\) | 3.74403 | 0.222560 | 0.111280 | − | 0.993789i | \(-0.464505\pi\) | ||||
0.111280 | + | 0.993789i | \(0.464505\pi\) | |||||||
\(284\) | 51.3834 | 3.04905 | ||||||||
\(285\) | 39.9917 | 2.36890 | ||||||||
\(286\) | 2.97485 | 0.175906 | ||||||||
\(287\) | 1.67482 | 0.0988614 | ||||||||
\(288\) | 10.7466 | 0.633247 | ||||||||
\(289\) | 7.37560 | 0.433859 | ||||||||
\(290\) | −69.9417 | −4.10712 | ||||||||
\(291\) | 2.13453 | 0.125128 | ||||||||
\(292\) | 39.2615 | 2.29761 | ||||||||
\(293\) | −3.97012 | −0.231937 | −0.115968 | − | 0.993253i | \(-0.536997\pi\) | ||||
−0.115968 | + | 0.993253i | \(0.536997\pi\) | |||||||
\(294\) | −43.9853 | −2.56528 | ||||||||
\(295\) | −11.0291 | −0.642141 | ||||||||
\(296\) | −15.7813 | −0.917271 | ||||||||
\(297\) | −3.74032 | −0.217036 | ||||||||
\(298\) | −1.40658 | −0.0814808 | ||||||||
\(299\) | 1.49684 | 0.0865643 | ||||||||
\(300\) | −100.417 | −5.79758 | ||||||||
\(301\) | 4.76891 | 0.274875 | ||||||||
\(302\) | −2.39169 | −0.137626 | ||||||||
\(303\) | −11.4552 | −0.658084 | ||||||||
\(304\) | −9.16603 | −0.525708 | ||||||||
\(305\) | −58.7358 | −3.36320 | ||||||||
\(306\) | −50.9700 | −2.91376 | ||||||||
\(307\) | 17.2052 | 0.981954 | 0.490977 | − | 0.871172i | \(-0.336640\pi\) | ||||
0.490977 | + | 0.871172i | \(0.336640\pi\) | |||||||
\(308\) | −1.75144 | −0.0997975 | ||||||||
\(309\) | −28.0189 | −1.59394 | ||||||||
\(310\) | 47.7305 | 2.71091 | ||||||||
\(311\) | 5.78665 | 0.328131 | 0.164066 | − | 0.986449i | \(-0.447539\pi\) | ||||
0.164066 | + | 0.986449i | \(0.447539\pi\) | |||||||
\(312\) | −13.1782 | −0.746068 | ||||||||
\(313\) | −17.7720 | −1.00453 | −0.502266 | − | 0.864713i | \(-0.667500\pi\) | ||||
−0.502266 | + | 0.864713i | \(0.667500\pi\) | |||||||
\(314\) | −31.8298 | −1.79626 | ||||||||
\(315\) | −7.48804 | −0.421903 | ||||||||
\(316\) | −55.7610 | −3.13680 | ||||||||
\(317\) | −17.4780 | −0.981660 | −0.490830 | − | 0.871255i | \(-0.663306\pi\) | ||||
−0.490830 | + | 0.871255i | \(0.663306\pi\) | |||||||
\(318\) | −6.46929 | −0.362780 | ||||||||
\(319\) | 7.93642 | 0.444354 | ||||||||
\(320\) | −41.6183 | −2.32653 | ||||||||
\(321\) | 12.6301 | 0.704941 | ||||||||
\(322\) | −1.35503 | −0.0755131 | ||||||||
\(323\) | −18.8605 | −1.04943 | ||||||||
\(324\) | −12.3411 | −0.685615 | ||||||||
\(325\) | −11.8172 | −0.655499 | ||||||||
\(326\) | 51.4801 | 2.85122 | ||||||||
\(327\) | −17.5458 | −0.970286 | ||||||||
\(328\) | 15.3729 | 0.848824 | ||||||||
\(329\) | 2.84150 | 0.156657 | ||||||||
\(330\) | 26.2988 | 1.44770 | ||||||||
\(331\) | 29.1935 | 1.60462 | 0.802309 | − | 0.596908i | \(-0.203604\pi\) | ||||
0.802309 | + | 0.596908i | \(0.203604\pi\) | |||||||
\(332\) | 32.6504 | 1.79192 | ||||||||
\(333\) | 16.5575 | 0.907345 | ||||||||
\(334\) | 35.5540 | 1.94543 | ||||||||
\(335\) | 55.2880 | 3.02071 | ||||||||
\(336\) | 2.90905 | 0.158702 | ||||||||
\(337\) | 29.1847 | 1.58979 | 0.794896 | − | 0.606745i | \(-0.207525\pi\) | ||||
0.794896 | + | 0.606745i | \(0.207525\pi\) | |||||||
\(338\) | 27.7381 | 1.50875 | ||||||||
\(339\) | −27.5982 | −1.49893 | ||||||||
\(340\) | 71.0862 | 3.85519 | ||||||||
\(341\) | −5.41607 | −0.293297 | ||||||||
\(342\) | 39.4377 | 2.13255 | ||||||||
\(343\) | 6.18507 | 0.333962 | ||||||||
\(344\) | 43.7729 | 2.36008 | ||||||||
\(345\) | 13.2326 | 0.712420 | ||||||||
\(346\) | −50.2066 | −2.69912 | ||||||||
\(347\) | −22.5446 | −1.21026 | −0.605130 | − | 0.796127i | \(-0.706879\pi\) | ||||
−0.605130 | + | 0.796127i | \(0.706879\pi\) | |||||||
\(348\) | −76.0334 | −4.07582 | ||||||||
\(349\) | 15.5629 | 0.833060 | 0.416530 | − | 0.909122i | \(-0.363246\pi\) | ||||
0.416530 | + | 0.909122i | \(0.363246\pi\) | |||||||
\(350\) | 10.6977 | 0.571815 | ||||||||
\(351\) | 4.21692 | 0.225083 | ||||||||
\(352\) | 2.61501 | 0.139381 | ||||||||
\(353\) | −0.142293 | −0.00757352 | −0.00378676 | − | 0.999993i | \(-0.501205\pi\) | ||||
−0.00378676 | + | 0.999993i | \(0.501205\pi\) | |||||||
\(354\) | −18.4355 | −0.979837 | ||||||||
\(355\) | 53.4565 | 2.83718 | ||||||||
\(356\) | 20.8645 | 1.10581 | ||||||||
\(357\) | 5.98581 | 0.316803 | ||||||||
\(358\) | −17.2963 | −0.914138 | ||||||||
\(359\) | −19.8288 | −1.04652 | −0.523261 | − | 0.852173i | \(-0.675285\pi\) | ||||
−0.523261 | + | 0.852173i | \(0.675285\pi\) | |||||||
\(360\) | −68.7314 | −3.62246 | ||||||||
\(361\) | −4.40681 | −0.231937 | ||||||||
\(362\) | 2.64531 | 0.139034 | ||||||||
\(363\) | 26.7698 | 1.40505 | ||||||||
\(364\) | 1.97461 | 0.103498 | ||||||||
\(365\) | 40.8456 | 2.13796 | ||||||||
\(366\) | −98.1786 | −5.13188 | ||||||||
\(367\) | 14.5906 | 0.761623 | 0.380812 | − | 0.924653i | \(-0.375645\pi\) | ||||
0.380812 | + | 0.924653i | \(0.375645\pi\) | |||||||
\(368\) | −3.03289 | −0.158101 | ||||||||
\(369\) | −16.1289 | −0.839638 | ||||||||
\(370\) | −35.5067 | −1.84591 | ||||||||
\(371\) | 0.448223 | 0.0232706 | ||||||||
\(372\) | 51.8877 | 2.69025 | ||||||||
\(373\) | −24.6611 | −1.27690 | −0.638452 | − | 0.769662i | \(-0.720425\pi\) | ||||
−0.638452 | + | 0.769662i | \(0.720425\pi\) | |||||||
\(374\) | −12.4028 | −0.641333 | ||||||||
\(375\) | −52.1247 | −2.69171 | ||||||||
\(376\) | 26.0816 | 1.34506 | ||||||||
\(377\) | −8.94770 | −0.460830 | ||||||||
\(378\) | −3.81744 | −0.196348 | ||||||||
\(379\) | 27.3965 | 1.40726 | 0.703631 | − | 0.710565i | \(-0.251561\pi\) | ||||
0.703631 | + | 0.710565i | \(0.251561\pi\) | |||||||
\(380\) | −55.0025 | −2.82157 | ||||||||
\(381\) | −47.2879 | −2.42263 | ||||||||
\(382\) | −44.0429 | −2.25343 | ||||||||
\(383\) | −3.00462 | −0.153529 | −0.0767644 | − | 0.997049i | \(-0.524459\pi\) | ||||
−0.0767644 | + | 0.997049i | \(0.524459\pi\) | |||||||
\(384\) | −56.0977 | −2.86273 | ||||||||
\(385\) | −1.82210 | −0.0928629 | ||||||||
\(386\) | 60.0735 | 3.05766 | ||||||||
\(387\) | −45.9258 | −2.33454 | ||||||||
\(388\) | −2.93572 | −0.149039 | ||||||||
\(389\) | 32.5015 | 1.64789 | 0.823945 | − | 0.566670i | \(-0.191769\pi\) | ||||
0.823945 | + | 0.566670i | \(0.191769\pi\) | |||||||
\(390\) | −29.6499 | −1.50138 | ||||||||
\(391\) | −6.24064 | −0.315602 | ||||||||
\(392\) | 27.9725 | 1.41283 | ||||||||
\(393\) | −4.31760 | −0.217794 | ||||||||
\(394\) | −12.1297 | −0.611083 | ||||||||
\(395\) | −58.0107 | −2.91884 | ||||||||
\(396\) | 16.8668 | 0.847589 | ||||||||
\(397\) | 6.67097 | 0.334806 | 0.167403 | − | 0.985889i | \(-0.446462\pi\) | ||||
0.167403 | + | 0.985889i | \(0.446462\pi\) | |||||||
\(398\) | −58.3172 | −2.92318 | ||||||||
\(399\) | −4.63149 | −0.231864 | ||||||||
\(400\) | 23.9440 | 1.19720 | ||||||||
\(401\) | 3.37448 | 0.168514 | 0.0842569 | − | 0.996444i | \(-0.473148\pi\) | ||||
0.0842569 | + | 0.996444i | \(0.473148\pi\) | |||||||
\(402\) | 92.4156 | 4.60927 | ||||||||
\(403\) | 6.10621 | 0.304172 | ||||||||
\(404\) | 15.7549 | 0.783836 | ||||||||
\(405\) | −12.8390 | −0.637974 | ||||||||
\(406\) | 8.10004 | 0.401998 | ||||||||
\(407\) | 4.02901 | 0.199711 | ||||||||
\(408\) | 54.9427 | 2.72007 | ||||||||
\(409\) | −7.74593 | −0.383012 | −0.191506 | − | 0.981491i | \(-0.561337\pi\) | ||||
−0.191506 | + | 0.981491i | \(0.561337\pi\) | |||||||
\(410\) | 34.5877 | 1.70816 | ||||||||
\(411\) | −44.1166 | −2.17611 | ||||||||
\(412\) | 38.5357 | 1.89852 | ||||||||
\(413\) | 1.27730 | 0.0628517 | ||||||||
\(414\) | 13.0493 | 0.641339 | ||||||||
\(415\) | 33.9677 | 1.66741 | ||||||||
\(416\) | −2.94822 | −0.144549 | ||||||||
\(417\) | 9.54035 | 0.467193 | ||||||||
\(418\) | 9.59658 | 0.469384 | ||||||||
\(419\) | −35.1455 | −1.71697 | −0.858486 | − | 0.512837i | \(-0.828594\pi\) | ||||
−0.858486 | + | 0.512837i | \(0.828594\pi\) | |||||||
\(420\) | 17.4563 | 0.851782 | ||||||||
\(421\) | 2.27247 | 0.110753 | 0.0553767 | − | 0.998466i | \(-0.482364\pi\) | ||||
0.0553767 | + | 0.998466i | \(0.482364\pi\) | |||||||
\(422\) | −39.2538 | −1.91085 | ||||||||
\(423\) | −27.3644 | −1.33050 | ||||||||
\(424\) | 4.11416 | 0.199801 | ||||||||
\(425\) | 49.2684 | 2.38987 | ||||||||
\(426\) | 89.3542 | 4.32923 | ||||||||
\(427\) | 6.80227 | 0.329185 | ||||||||
\(428\) | −17.3707 | −0.839647 | ||||||||
\(429\) | 3.36443 | 0.162436 | ||||||||
\(430\) | 98.4856 | 4.74940 | ||||||||
\(431\) | 2.13556 | 0.102866 | 0.0514331 | − | 0.998676i | \(-0.483621\pi\) | ||||
0.0514331 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(432\) | −8.54435 | −0.411090 | ||||||||
\(433\) | 29.4260 | 1.41412 | 0.707061 | − | 0.707153i | \(-0.250021\pi\) | ||||
0.707061 | + | 0.707153i | \(0.250021\pi\) | |||||||
\(434\) | −5.52774 | −0.265340 | ||||||||
\(435\) | −79.1011 | −3.79261 | ||||||||
\(436\) | 24.1316 | 1.15570 | ||||||||
\(437\) | 4.82866 | 0.230986 | ||||||||
\(438\) | 68.2746 | 3.26229 | ||||||||
\(439\) | 8.95868 | 0.427574 | 0.213787 | − | 0.976880i | \(-0.431420\pi\) | ||||
0.213787 | + | 0.976880i | \(0.431420\pi\) | |||||||
\(440\) | −16.7248 | −0.797321 | ||||||||
\(441\) | −29.3483 | −1.39754 | ||||||||
\(442\) | 13.9832 | 0.665112 | ||||||||
\(443\) | −10.3797 | −0.493153 | −0.246576 | − | 0.969123i | \(-0.579306\pi\) | ||||
−0.246576 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(444\) | −38.5993 | −1.83184 | ||||||||
\(445\) | 21.7063 | 1.02898 | ||||||||
\(446\) | 29.6189 | 1.40250 | ||||||||
\(447\) | −1.59078 | −0.0752413 | ||||||||
\(448\) | 4.81987 | 0.227718 | ||||||||
\(449\) | −24.7946 | −1.17013 | −0.585065 | − | 0.810986i | \(-0.698931\pi\) | ||||
−0.585065 | + | 0.810986i | \(0.698931\pi\) | |||||||
\(450\) | −103.021 | −4.85648 | ||||||||
\(451\) | −3.92473 | −0.184808 | ||||||||
\(452\) | 37.9572 | 1.78536 | ||||||||
\(453\) | −2.70490 | −0.127087 | ||||||||
\(454\) | −59.4235 | −2.78888 | ||||||||
\(455\) | 2.05428 | 0.0963061 | ||||||||
\(456\) | −42.5116 | −1.99079 | ||||||||
\(457\) | 10.3022 | 0.481916 | 0.240958 | − | 0.970536i | \(-0.422538\pi\) | ||||
0.240958 | + | 0.970536i | \(0.422538\pi\) | |||||||
\(458\) | 17.1426 | 0.801021 | ||||||||
\(459\) | −17.5813 | −0.820624 | ||||||||
\(460\) | −18.1995 | −0.848554 | ||||||||
\(461\) | −14.7074 | −0.684994 | −0.342497 | − | 0.939519i | \(-0.611273\pi\) | ||||
−0.342497 | + | 0.939519i | \(0.611273\pi\) | |||||||
\(462\) | −3.04570 | −0.141699 | ||||||||
\(463\) | −20.3812 | −0.947196 | −0.473598 | − | 0.880741i | \(-0.657045\pi\) | ||||
−0.473598 | + | 0.880741i | \(0.657045\pi\) | |||||||
\(464\) | 18.1299 | 0.841657 | ||||||||
\(465\) | 53.9812 | 2.50332 | ||||||||
\(466\) | −27.4127 | −1.26987 | ||||||||
\(467\) | 37.1890 | 1.72090 | 0.860451 | − | 0.509533i | \(-0.170182\pi\) | ||||
0.860451 | + | 0.509533i | \(0.170182\pi\) | |||||||
\(468\) | −19.0160 | −0.879016 | ||||||||
\(469\) | −6.40298 | −0.295662 | ||||||||
\(470\) | 58.6816 | 2.70678 | ||||||||
\(471\) | −35.9982 | −1.65871 | ||||||||
\(472\) | 11.7241 | 0.539645 | ||||||||
\(473\) | −11.1754 | −0.513843 | ||||||||
\(474\) | −96.9667 | −4.45383 | ||||||||
\(475\) | −38.1211 | −1.74912 | ||||||||
\(476\) | −8.23259 | −0.377340 | ||||||||
\(477\) | −4.31650 | −0.197639 | ||||||||
\(478\) | −57.9884 | −2.65233 | ||||||||
\(479\) | −13.3152 | −0.608386 | −0.304193 | − | 0.952610i | \(-0.598387\pi\) | ||||
−0.304193 | + | 0.952610i | \(0.598387\pi\) | |||||||
\(480\) | −26.0634 | −1.18963 | ||||||||
\(481\) | −4.54240 | −0.207116 | ||||||||
\(482\) | −57.8857 | −2.63662 | ||||||||
\(483\) | −1.53249 | −0.0697306 | ||||||||
\(484\) | −36.8178 | −1.67354 | ||||||||
\(485\) | −3.05417 | −0.138683 | ||||||||
\(486\) | −47.0112 | −2.13247 | ||||||||
\(487\) | −38.6096 | −1.74957 | −0.874783 | − | 0.484515i | \(-0.838996\pi\) | ||||
−0.874783 | + | 0.484515i | \(0.838996\pi\) | |||||||
\(488\) | 62.4368 | 2.82638 | ||||||||
\(489\) | 58.2219 | 2.63289 | ||||||||
\(490\) | 62.9360 | 2.84316 | ||||||||
\(491\) | −34.0796 | −1.53799 | −0.768996 | − | 0.639253i | \(-0.779244\pi\) | ||||
−0.768996 | + | 0.639253i | \(0.779244\pi\) | |||||||
\(492\) | 37.6002 | 1.69515 | ||||||||
\(493\) | 37.3049 | 1.68013 | ||||||||
\(494\) | −10.8194 | −0.486788 | ||||||||
\(495\) | 17.5473 | 0.788693 | ||||||||
\(496\) | −12.3724 | −0.555538 | ||||||||
\(497\) | −6.19088 | −0.277699 | ||||||||
\(498\) | 56.7781 | 2.54429 | ||||||||
\(499\) | 17.5904 | 0.787456 | 0.393728 | − | 0.919227i | \(-0.371185\pi\) | ||||
0.393728 | + | 0.919227i | \(0.371185\pi\) | |||||||
\(500\) | 71.6897 | 3.20606 | ||||||||
\(501\) | 40.2101 | 1.79646 | ||||||||
\(502\) | 46.3543 | 2.06889 | ||||||||
\(503\) | −2.42370 | −0.108068 | −0.0540338 | − | 0.998539i | \(-0.517208\pi\) | ||||
−0.0540338 | + | 0.998539i | \(0.517208\pi\) | |||||||
\(504\) | 7.95988 | 0.354561 | ||||||||
\(505\) | 16.3906 | 0.729370 | ||||||||
\(506\) | 3.17536 | 0.141162 | ||||||||
\(507\) | 31.3706 | 1.39322 | ||||||||
\(508\) | 65.0374 | 2.88557 | ||||||||
\(509\) | 22.4246 | 0.993954 | 0.496977 | − | 0.867764i | \(-0.334443\pi\) | ||||
0.496977 | + | 0.867764i | \(0.334443\pi\) | |||||||
\(510\) | 123.617 | 5.47384 | ||||||||
\(511\) | −4.73038 | −0.209260 | ||||||||
\(512\) | 25.7169 | 1.13654 | ||||||||
\(513\) | 13.6034 | 0.600605 | ||||||||
\(514\) | −61.8545 | −2.72828 | ||||||||
\(515\) | 40.0905 | 1.76660 | ||||||||
\(516\) | 107.064 | 4.71321 | ||||||||
\(517\) | −6.65871 | −0.292850 | ||||||||
\(518\) | 4.11208 | 0.180674 | ||||||||
\(519\) | −56.7815 | −2.49243 | ||||||||
\(520\) | 18.8559 | 0.826885 | ||||||||
\(521\) | 16.5027 | 0.722997 | 0.361499 | − | 0.932373i | \(-0.382265\pi\) | ||||
0.361499 | + | 0.932373i | \(0.382265\pi\) | |||||||
\(522\) | −78.0055 | −3.41421 | ||||||||
\(523\) | 14.6709 | 0.641512 | 0.320756 | − | 0.947162i | \(-0.396063\pi\) | ||||
0.320756 | + | 0.947162i | \(0.396063\pi\) | |||||||
\(524\) | 5.93821 | 0.259412 | ||||||||
\(525\) | 12.0986 | 0.528028 | ||||||||
\(526\) | 47.3758 | 2.06568 | ||||||||
\(527\) | −25.4581 | −1.10897 | ||||||||
\(528\) | −6.81701 | −0.296672 | ||||||||
\(529\) | −21.4023 | −0.930534 | ||||||||
\(530\) | 9.25652 | 0.402078 | ||||||||
\(531\) | −12.3007 | −0.533806 | ||||||||
\(532\) | 6.36992 | 0.276171 | ||||||||
\(533\) | 4.42483 | 0.191661 | ||||||||
\(534\) | 36.2827 | 1.57010 | ||||||||
\(535\) | −18.0716 | −0.781303 | ||||||||
\(536\) | −58.7718 | −2.53856 | ||||||||
\(537\) | −19.5614 | −0.844136 | ||||||||
\(538\) | 65.2016 | 2.81104 | ||||||||
\(539\) | −7.14147 | −0.307605 | ||||||||
\(540\) | −51.2720 | −2.20639 | ||||||||
\(541\) | 6.83314 | 0.293780 | 0.146890 | − | 0.989153i | \(-0.453074\pi\) | ||||
0.146890 | + | 0.989153i | \(0.453074\pi\) | |||||||
\(542\) | 34.6413 | 1.48797 | ||||||||
\(543\) | 2.99173 | 0.128387 | ||||||||
\(544\) | 12.2918 | 0.527006 | ||||||||
\(545\) | 25.1052 | 1.07539 | ||||||||
\(546\) | 3.43379 | 0.146953 | ||||||||
\(547\) | −18.1637 | −0.776623 | −0.388311 | − | 0.921528i | \(-0.626941\pi\) | ||||
−0.388311 | + | 0.921528i | \(0.626941\pi\) | |||||||
\(548\) | 60.6757 | 2.59194 | ||||||||
\(549\) | −65.5076 | −2.79580 | ||||||||
\(550\) | −25.0687 | −1.06893 | ||||||||
\(551\) | −28.8645 | −1.22967 | ||||||||
\(552\) | −14.0664 | −0.598707 | ||||||||
\(553\) | 6.71830 | 0.285691 | ||||||||
\(554\) | −18.3938 | −0.781476 | ||||||||
\(555\) | −40.1566 | −1.70455 | ||||||||
\(556\) | −13.1213 | −0.556468 | ||||||||
\(557\) | −8.68874 | −0.368154 | −0.184077 | − | 0.982912i | \(-0.558930\pi\) | ||||
−0.184077 | + | 0.982912i | \(0.558930\pi\) | |||||||
\(558\) | 53.2335 | 2.25355 | ||||||||
\(559\) | 12.5993 | 0.532896 | ||||||||
\(560\) | −4.16239 | −0.175893 | ||||||||
\(561\) | −14.0270 | −0.592222 | ||||||||
\(562\) | 24.9287 | 1.05155 | ||||||||
\(563\) | −9.24161 | −0.389487 | −0.194744 | − | 0.980854i | \(-0.562388\pi\) | ||||
−0.194744 | + | 0.980854i | \(0.562388\pi\) | |||||||
\(564\) | 63.7926 | 2.68615 | ||||||||
\(565\) | 39.4886 | 1.66130 | ||||||||
\(566\) | −8.95457 | −0.376389 | ||||||||
\(567\) | 1.48690 | 0.0624440 | ||||||||
\(568\) | −56.8250 | −2.38432 | ||||||||
\(569\) | −7.89008 | −0.330769 | −0.165385 | − | 0.986229i | \(-0.552887\pi\) | ||||
−0.165385 | + | 0.986229i | \(0.552887\pi\) | |||||||
\(570\) | −95.6477 | −4.00624 | ||||||||
\(571\) | 7.40686 | 0.309967 | 0.154984 | − | 0.987917i | \(-0.450467\pi\) | ||||
0.154984 | + | 0.987917i | \(0.450467\pi\) | |||||||
\(572\) | −4.62726 | −0.193476 | ||||||||
\(573\) | −49.8107 | −2.08087 | ||||||||
\(574\) | −4.00565 | −0.167192 | ||||||||
\(575\) | −12.6137 | −0.526027 | ||||||||
\(576\) | −46.4166 | −1.93403 | ||||||||
\(577\) | 46.4834 | 1.93513 | 0.967566 | − | 0.252620i | \(-0.0812922\pi\) | ||||
0.967566 | + | 0.252620i | \(0.0812922\pi\) | |||||||
\(578\) | −17.6402 | −0.733734 | ||||||||
\(579\) | 67.9407 | 2.82352 | ||||||||
\(580\) | 108.792 | 4.51733 | ||||||||
\(581\) | −3.93385 | −0.163204 | ||||||||
\(582\) | −5.10513 | −0.211615 | ||||||||
\(583\) | −1.05036 | −0.0435013 | ||||||||
\(584\) | −43.4194 | −1.79671 | ||||||||
\(585\) | −19.7832 | −0.817937 | ||||||||
\(586\) | 9.49530 | 0.392247 | ||||||||
\(587\) | −8.39052 | −0.346314 | −0.173157 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173157 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(588\) | 68.4176 | 2.82149 | ||||||||
\(589\) | 19.6981 | 0.811644 | ||||||||
\(590\) | 26.3783 | 1.08598 | ||||||||
\(591\) | −13.7181 | −0.564289 | ||||||||
\(592\) | 9.20383 | 0.378275 | ||||||||
\(593\) | 23.3843 | 0.960278 | 0.480139 | − | 0.877193i | \(-0.340586\pi\) | ||||
0.480139 | + | 0.877193i | \(0.340586\pi\) | |||||||
\(594\) | 8.94570 | 0.367046 | ||||||||
\(595\) | −8.56474 | −0.351120 | ||||||||
\(596\) | 2.18788 | 0.0896190 | ||||||||
\(597\) | −65.9543 | −2.69933 | ||||||||
\(598\) | −3.57997 | −0.146396 | ||||||||
\(599\) | −11.7449 | −0.479883 | −0.239942 | − | 0.970787i | \(-0.577128\pi\) | ||||
−0.239942 | + | 0.970787i | \(0.577128\pi\) | |||||||
\(600\) | 111.051 | 4.53365 | ||||||||
\(601\) | −11.9460 | −0.487289 | −0.243645 | − | 0.969865i | \(-0.578343\pi\) | ||||
−0.243645 | + | 0.969865i | \(0.578343\pi\) | |||||||
\(602\) | −11.4058 | −0.464864 | ||||||||
\(603\) | 61.6624 | 2.51109 | ||||||||
\(604\) | 3.72019 | 0.151372 | ||||||||
\(605\) | −38.3032 | −1.55725 | ||||||||
\(606\) | 27.3973 | 1.11294 | ||||||||
\(607\) | 17.7751 | 0.721470 | 0.360735 | − | 0.932668i | \(-0.382526\pi\) | ||||
0.360735 | + | 0.932668i | \(0.382526\pi\) | |||||||
\(608\) | −9.51070 | −0.385710 | ||||||||
\(609\) | 9.16081 | 0.371215 | ||||||||
\(610\) | 140.478 | 5.68778 | ||||||||
\(611\) | 7.50718 | 0.303708 | ||||||||
\(612\) | 79.2819 | 3.20478 | ||||||||
\(613\) | −40.4649 | −1.63436 | −0.817182 | − | 0.576380i | \(-0.804465\pi\) | ||||
−0.817182 | + | 0.576380i | \(0.804465\pi\) | |||||||
\(614\) | −41.1496 | −1.66066 | ||||||||
\(615\) | 39.1172 | 1.57736 | ||||||||
\(616\) | 1.93692 | 0.0780406 | ||||||||
\(617\) | −46.9633 | −1.89067 | −0.945336 | − | 0.326097i | \(-0.894266\pi\) | ||||
−0.945336 | + | 0.326097i | \(0.894266\pi\) | |||||||
\(618\) | 67.0124 | 2.69564 | ||||||||
\(619\) | 35.1944 | 1.41458 | 0.707291 | − | 0.706922i | \(-0.249917\pi\) | ||||
0.707291 | + | 0.706922i | \(0.249917\pi\) | |||||||
\(620\) | −74.2430 | −2.98167 | ||||||||
\(621\) | 4.50115 | 0.180625 | ||||||||
\(622\) | −13.8399 | −0.554929 | ||||||||
\(623\) | −2.51383 | −0.100715 | ||||||||
\(624\) | 7.68565 | 0.307672 | ||||||||
\(625\) | 24.6867 | 0.987468 | ||||||||
\(626\) | 42.5051 | 1.69885 | ||||||||
\(627\) | 10.8533 | 0.433440 | ||||||||
\(628\) | 49.5101 | 1.97567 | ||||||||
\(629\) | 18.9383 | 0.755118 | ||||||||
\(630\) | 17.9091 | 0.713515 | ||||||||
\(631\) | 28.4848 | 1.13396 | 0.566981 | − | 0.823731i | \(-0.308111\pi\) | ||||
0.566981 | + | 0.823731i | \(0.308111\pi\) | |||||||
\(632\) | 61.6661 | 2.45295 | ||||||||
\(633\) | −44.3944 | −1.76452 | ||||||||
\(634\) | 41.8019 | 1.66016 | ||||||||
\(635\) | 67.6614 | 2.68506 | ||||||||
\(636\) | 10.0627 | 0.399014 | ||||||||
\(637\) | 8.05145 | 0.319010 | ||||||||
\(638\) | −18.9815 | −0.751483 | ||||||||
\(639\) | 59.6197 | 2.35852 | ||||||||
\(640\) | 80.2669 | 3.17283 | ||||||||
\(641\) | 24.5148 | 0.968276 | 0.484138 | − | 0.874992i | \(-0.339133\pi\) | ||||
0.484138 | + | 0.874992i | \(0.339133\pi\) | |||||||
\(642\) | −30.2072 | −1.19218 | ||||||||
\(643\) | −48.8650 | −1.92705 | −0.963524 | − | 0.267620i | \(-0.913763\pi\) | ||||
−0.963524 | + | 0.267620i | \(0.913763\pi\) | |||||||
\(644\) | 2.10770 | 0.0830552 | ||||||||
\(645\) | 111.383 | 4.38571 | ||||||||
\(646\) | 45.1085 | 1.77477 | ||||||||
\(647\) | 45.3741 | 1.78384 | 0.891920 | − | 0.452192i | \(-0.149358\pi\) | ||||
0.891920 | + | 0.452192i | \(0.149358\pi\) | |||||||
\(648\) | 13.6480 | 0.536144 | ||||||||
\(649\) | −2.99319 | −0.117493 | ||||||||
\(650\) | 28.2630 | 1.10857 | ||||||||
\(651\) | −6.25164 | −0.245021 | ||||||||
\(652\) | −80.0755 | −3.13600 | ||||||||
\(653\) | −6.56459 | −0.256892 | −0.128446 | − | 0.991716i | \(-0.540999\pi\) | ||||
−0.128446 | + | 0.991716i | \(0.540999\pi\) | |||||||
\(654\) | 41.9642 | 1.64093 | ||||||||
\(655\) | 6.17780 | 0.241386 | ||||||||
\(656\) | −8.96561 | −0.350048 | ||||||||
\(657\) | 45.5548 | 1.77726 | ||||||||
\(658\) | −6.79599 | −0.264935 | ||||||||
\(659\) | 6.21299 | 0.242024 | 0.121012 | − | 0.992651i | \(-0.461386\pi\) | ||||
0.121012 | + | 0.992651i | \(0.461386\pi\) | |||||||
\(660\) | −40.9068 | −1.59229 | ||||||||
\(661\) | −15.9371 | −0.619880 | −0.309940 | − | 0.950756i | \(-0.600309\pi\) | ||||
−0.309940 | + | 0.950756i | \(0.600309\pi\) | |||||||
\(662\) | −69.8218 | −2.71370 | ||||||||
\(663\) | 15.8144 | 0.614180 | ||||||||
\(664\) | −36.1081 | −1.40127 | ||||||||
\(665\) | 6.62692 | 0.256981 | ||||||||
\(666\) | −39.6004 | −1.53448 | ||||||||
\(667\) | −9.55079 | −0.369808 | ||||||||
\(668\) | −55.3030 | −2.13974 | ||||||||
\(669\) | 33.4977 | 1.29510 | ||||||||
\(670\) | −132.232 | −5.10856 | ||||||||
\(671\) | −15.9403 | −0.615368 | ||||||||
\(672\) | 3.01844 | 0.116439 | ||||||||
\(673\) | 0.102951 | 0.00396847 | 0.00198424 | − | 0.999998i | \(-0.499368\pi\) | ||||
0.00198424 | + | 0.999998i | \(0.499368\pi\) | |||||||
\(674\) | −69.8008 | −2.68863 | ||||||||
\(675\) | −35.5356 | −1.36777 | ||||||||
\(676\) | −43.1456 | −1.65944 | ||||||||
\(677\) | 14.3249 | 0.550551 | 0.275276 | − | 0.961365i | \(-0.411231\pi\) | ||||
0.275276 | + | 0.961365i | \(0.411231\pi\) | |||||||
\(678\) | 66.0064 | 2.53496 | ||||||||
\(679\) | 0.353707 | 0.0135740 | ||||||||
\(680\) | −78.6142 | −3.01472 | ||||||||
\(681\) | −67.2055 | −2.57532 | ||||||||
\(682\) | 12.9536 | 0.496018 | ||||||||
\(683\) | 43.0990 | 1.64914 | 0.824569 | − | 0.565762i | \(-0.191418\pi\) | ||||
0.824569 | + | 0.565762i | \(0.191418\pi\) | |||||||
\(684\) | −61.3439 | −2.34554 | ||||||||
\(685\) | 63.1238 | 2.41184 | ||||||||
\(686\) | −14.7928 | −0.564791 | ||||||||
\(687\) | 19.3876 | 0.739682 | ||||||||
\(688\) | −25.5288 | −0.973278 | ||||||||
\(689\) | 1.18419 | 0.0451142 | ||||||||
\(690\) | −31.6483 | −1.20483 | ||||||||
\(691\) | 13.0820 | 0.497661 | 0.248831 | − | 0.968547i | \(-0.419954\pi\) | ||||
0.248831 | + | 0.968547i | \(0.419954\pi\) | |||||||
\(692\) | 78.0945 | 2.96871 | ||||||||
\(693\) | −2.03218 | −0.0771961 | ||||||||
\(694\) | 53.9198 | 2.04677 | ||||||||
\(695\) | −13.6507 | −0.517801 | ||||||||
\(696\) | 84.0854 | 3.18725 | ||||||||
\(697\) | −18.4481 | −0.698771 | ||||||||
\(698\) | −37.2215 | −1.40886 | ||||||||
\(699\) | −31.0027 | −1.17263 | ||||||||
\(700\) | −16.6398 | −0.628927 | ||||||||
\(701\) | 34.2201 | 1.29247 | 0.646237 | − | 0.763137i | \(-0.276342\pi\) | ||||
0.646237 | + | 0.763137i | \(0.276342\pi\) | |||||||
\(702\) | −10.0856 | −0.380656 | ||||||||
\(703\) | −14.6534 | −0.552663 | ||||||||
\(704\) | −11.2948 | −0.425688 | ||||||||
\(705\) | 66.3664 | 2.49950 | ||||||||
\(706\) | 0.340322 | 0.0128082 | ||||||||
\(707\) | −1.89821 | −0.0713896 | ||||||||
\(708\) | 28.6758 | 1.07770 | ||||||||
\(709\) | 25.8747 | 0.971747 | 0.485873 | − | 0.874029i | \(-0.338502\pi\) | ||||
0.485873 | + | 0.874029i | \(0.338502\pi\) | |||||||
\(710\) | −127.852 | −4.79818 | ||||||||
\(711\) | −64.6990 | −2.42640 | ||||||||
\(712\) | −23.0740 | −0.864735 | ||||||||
\(713\) | 6.51778 | 0.244093 | ||||||||
\(714\) | −14.3162 | −0.535771 | ||||||||
\(715\) | −4.81396 | −0.180032 | ||||||||
\(716\) | 26.9038 | 1.00544 | ||||||||
\(717\) | −65.5824 | −2.44922 | ||||||||
\(718\) | 47.4243 | 1.76986 | ||||||||
\(719\) | 36.1869 | 1.34954 | 0.674772 | − | 0.738026i | \(-0.264242\pi\) | ||||
0.674772 | + | 0.738026i | \(0.264242\pi\) | |||||||
\(720\) | 40.0849 | 1.49387 | ||||||||
\(721\) | −4.64293 | −0.172912 | ||||||||
\(722\) | 10.5397 | 0.392248 | ||||||||
\(723\) | −65.4663 | −2.43472 | ||||||||
\(724\) | −4.11468 | −0.152921 | ||||||||
\(725\) | 75.4013 | 2.80033 | ||||||||
\(726\) | −64.0250 | −2.37619 | ||||||||
\(727\) | 28.7514 | 1.06633 | 0.533165 | − | 0.846012i | \(-0.321003\pi\) | ||||
0.533165 | + | 0.846012i | \(0.321003\pi\) | |||||||
\(728\) | −2.18372 | −0.0809342 | ||||||||
\(729\) | −43.2158 | −1.60058 | ||||||||
\(730\) | −97.6900 | −3.61567 | ||||||||
\(731\) | −52.5294 | −1.94287 | ||||||||
\(732\) | 152.713 | 5.64444 | ||||||||
\(733\) | −44.2125 | −1.63303 | −0.816513 | − | 0.577327i | \(-0.804096\pi\) | ||||
−0.816513 | + | 0.577327i | \(0.804096\pi\) | |||||||
\(734\) | −34.8962 | −1.28804 | ||||||||
\(735\) | 71.1780 | 2.62544 | ||||||||
\(736\) | −3.14694 | −0.115998 | ||||||||
\(737\) | 15.0046 | 0.552702 | ||||||||
\(738\) | 38.5754 | 1.41998 | ||||||||
\(739\) | −10.6665 | −0.392375 | −0.196188 | − | 0.980566i | \(-0.562856\pi\) | ||||
−0.196188 | + | 0.980566i | \(0.562856\pi\) | |||||||
\(740\) | 55.2294 | 2.03027 | ||||||||
\(741\) | −12.2363 | −0.449512 | ||||||||
\(742\) | −1.07201 | −0.0393547 | ||||||||
\(743\) | 39.1946 | 1.43791 | 0.718956 | − | 0.695056i | \(-0.244620\pi\) | ||||
0.718956 | + | 0.695056i | \(0.244620\pi\) | |||||||
\(744\) | −57.3827 | −2.10375 | ||||||||
\(745\) | 2.27615 | 0.0833917 | ||||||||
\(746\) | 58.9817 | 2.15947 | ||||||||
\(747\) | 37.8840 | 1.38610 | ||||||||
\(748\) | 19.2921 | 0.705388 | ||||||||
\(749\) | 2.09290 | 0.0764727 | ||||||||
\(750\) | 124.666 | 4.55217 | ||||||||
\(751\) | −42.5715 | −1.55346 | −0.776728 | − | 0.629836i | \(-0.783122\pi\) | ||||
−0.776728 | + | 0.629836i | \(0.783122\pi\) | |||||||
\(752\) | −15.2111 | −0.554691 | ||||||||
\(753\) | 52.4247 | 1.91046 | ||||||||
\(754\) | 21.4001 | 0.779347 | ||||||||
\(755\) | 3.87028 | 0.140854 | ||||||||
\(756\) | 5.93788 | 0.215959 | ||||||||
\(757\) | −2.67333 | −0.0971637 | −0.0485818 | − | 0.998819i | \(-0.515470\pi\) | ||||
−0.0485818 | + | 0.998819i | \(0.515470\pi\) | |||||||
\(758\) | −65.5239 | −2.37994 | ||||||||
\(759\) | 3.59120 | 0.130352 | ||||||||
\(760\) | 60.8273 | 2.20644 | ||||||||
\(761\) | 14.5742 | 0.528315 | 0.264158 | − | 0.964479i | \(-0.414906\pi\) | ||||
0.264158 | + | 0.964479i | \(0.414906\pi\) | |||||||
\(762\) | 113.098 | 4.09711 | ||||||||
\(763\) | −2.90747 | −0.105258 | ||||||||
\(764\) | 68.5071 | 2.47850 | ||||||||
\(765\) | 82.4807 | 2.98209 | ||||||||
\(766\) | 7.18612 | 0.259645 | ||||||||
\(767\) | 3.37459 | 0.121850 | ||||||||
\(768\) | 75.9952 | 2.74224 | ||||||||
\(769\) | 3.55851 | 0.128323 | 0.0641615 | − | 0.997940i | \(-0.479563\pi\) | ||||
0.0641615 | + | 0.997940i | \(0.479563\pi\) | |||||||
\(770\) | 4.35791 | 0.157048 | ||||||||
\(771\) | −69.9548 | −2.51936 | ||||||||
\(772\) | −93.4422 | −3.36306 | ||||||||
\(773\) | −24.1279 | −0.867820 | −0.433910 | − | 0.900956i | \(-0.642866\pi\) | ||||
−0.433910 | + | 0.900956i | \(0.642866\pi\) | |||||||
\(774\) | 109.840 | 3.94813 | ||||||||
\(775\) | −51.4564 | −1.84837 | ||||||||
\(776\) | 3.24662 | 0.116547 | ||||||||
\(777\) | 4.65059 | 0.166839 | ||||||||
\(778\) | −77.7335 | −2.78688 | ||||||||
\(779\) | 14.2741 | 0.511423 | ||||||||
\(780\) | 46.1193 | 1.65133 | ||||||||
\(781\) | 14.5076 | 0.519122 | ||||||||
\(782\) | 14.9257 | 0.533741 | ||||||||
\(783\) | −26.9067 | −0.961568 | ||||||||
\(784\) | −16.3139 | −0.582639 | ||||||||
\(785\) | 51.5076 | 1.83839 | ||||||||
\(786\) | 10.3264 | 0.368329 | ||||||||
\(787\) | −10.2574 | −0.365637 | −0.182819 | − | 0.983147i | \(-0.558522\pi\) | ||||
−0.182819 | + | 0.983147i | \(0.558522\pi\) | |||||||
\(788\) | 18.8672 | 0.672117 | ||||||||
\(789\) | 53.5800 | 1.90750 | ||||||||
\(790\) | 138.744 | 4.93628 | ||||||||
\(791\) | −4.57323 | −0.162605 | ||||||||
\(792\) | −18.6530 | −0.662806 | ||||||||
\(793\) | 17.9714 | 0.638185 | ||||||||
\(794\) | −15.9549 | −0.566218 | ||||||||
\(795\) | 10.4687 | 0.371288 | ||||||||
\(796\) | 90.7103 | 3.21514 | ||||||||
\(797\) | −13.6241 | −0.482590 | −0.241295 | − | 0.970452i | \(-0.577572\pi\) | ||||
−0.241295 | + | 0.970452i | \(0.577572\pi\) | |||||||
\(798\) | 11.0771 | 0.392125 | ||||||||
\(799\) | −31.2991 | −1.10728 | ||||||||
\(800\) | 24.8444 | 0.878381 | ||||||||
\(801\) | 24.2088 | 0.855378 | ||||||||
\(802\) | −8.07073 | −0.284987 | ||||||||
\(803\) | 11.0851 | 0.391184 | ||||||||
\(804\) | −143.749 | −5.06964 | ||||||||
\(805\) | 2.19274 | 0.0772840 | ||||||||
\(806\) | −14.6042 | −0.514410 | ||||||||
\(807\) | 73.7403 | 2.59578 | ||||||||
\(808\) | −17.4234 | −0.612952 | ||||||||
\(809\) | −36.9906 | −1.30052 | −0.650261 | − | 0.759711i | \(-0.725340\pi\) | ||||
−0.650261 | + | 0.759711i | \(0.725340\pi\) | |||||||
\(810\) | 30.7069 | 1.07893 | ||||||||
\(811\) | −34.3246 | −1.20530 | −0.602650 | − | 0.798006i | \(-0.705888\pi\) | ||||
−0.602650 | + | 0.798006i | \(0.705888\pi\) | |||||||
\(812\) | −12.5993 | −0.442149 | ||||||||
\(813\) | 39.1779 | 1.37403 | ||||||||
\(814\) | −9.63616 | −0.337747 | ||||||||
\(815\) | −83.3062 | −2.91809 | ||||||||
\(816\) | −32.0432 | −1.12174 | ||||||||
\(817\) | 40.6443 | 1.42197 | ||||||||
\(818\) | 18.5259 | 0.647742 | ||||||||
\(819\) | 2.29112 | 0.0800584 | ||||||||
\(820\) | −53.7999 | −1.87877 | ||||||||
\(821\) | 14.7819 | 0.515893 | 0.257947 | − | 0.966159i | \(-0.416954\pi\) | ||||
0.257947 | + | 0.966159i | \(0.416954\pi\) | |||||||
\(822\) | 105.513 | 3.68020 | ||||||||
\(823\) | 26.9333 | 0.938835 | 0.469417 | − | 0.882976i | \(-0.344464\pi\) | ||||
0.469417 | + | 0.882976i | \(0.344464\pi\) | |||||||
\(824\) | −42.6167 | −1.48462 | ||||||||
\(825\) | −28.3517 | −0.987079 | ||||||||
\(826\) | −3.05490 | −0.106294 | ||||||||
\(827\) | 47.7838 | 1.66161 | 0.830803 | − | 0.556567i | \(-0.187882\pi\) | ||||
0.830803 | + | 0.556567i | \(0.187882\pi\) | |||||||
\(828\) | −20.2977 | −0.705395 | ||||||||
\(829\) | 28.8466 | 1.00188 | 0.500942 | − | 0.865481i | \(-0.332987\pi\) | ||||
0.500942 | + | 0.865481i | \(0.332987\pi\) | |||||||
\(830\) | −81.2403 | −2.81989 | ||||||||
\(831\) | −20.8026 | −0.721633 | ||||||||
\(832\) | 12.7340 | 0.441472 | ||||||||
\(833\) | −33.5683 | −1.16307 | ||||||||
\(834\) | −22.8176 | −0.790108 | ||||||||
\(835\) | −57.5342 | −1.99105 | ||||||||
\(836\) | −14.9271 | −0.516266 | ||||||||
\(837\) | 18.3620 | 0.634685 | ||||||||
\(838\) | 84.0573 | 2.90371 | ||||||||
\(839\) | −23.6771 | −0.817424 | −0.408712 | − | 0.912663i | \(-0.634022\pi\) | ||||
−0.408712 | + | 0.912663i | \(0.634022\pi\) | |||||||
\(840\) | −19.3050 | −0.666085 | ||||||||
\(841\) | 28.0921 | 0.968695 | ||||||||
\(842\) | −5.43505 | −0.187304 | ||||||||
\(843\) | 28.1933 | 0.971030 | ||||||||
\(844\) | 61.0578 | 2.10170 | ||||||||
\(845\) | −44.8863 | −1.54414 | ||||||||
\(846\) | 65.4472 | 2.25012 | ||||||||
\(847\) | 4.43595 | 0.152421 | ||||||||
\(848\) | −2.39942 | −0.0823964 | ||||||||
\(849\) | −10.1272 | −0.347566 | ||||||||
\(850\) | −117.835 | −4.04170 | ||||||||
\(851\) | −4.84857 | −0.166207 | ||||||||
\(852\) | −138.987 | −4.76162 | ||||||||
\(853\) | 21.3528 | 0.731107 | 0.365553 | − | 0.930790i | \(-0.380880\pi\) | ||||
0.365553 | + | 0.930790i | \(0.380880\pi\) | |||||||
\(854\) | −16.2689 | −0.556711 | ||||||||
\(855\) | −63.8189 | −2.18256 | ||||||||
\(856\) | 19.2103 | 0.656595 | ||||||||
\(857\) | 47.6593 | 1.62801 | 0.814006 | − | 0.580857i | \(-0.197282\pi\) | ||||
0.814006 | + | 0.580857i | \(0.197282\pi\) | |||||||
\(858\) | −8.04667 | −0.274709 | ||||||||
\(859\) | 15.5311 | 0.529914 | 0.264957 | − | 0.964260i | \(-0.414642\pi\) | ||||
0.264957 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(860\) | −153.191 | −5.22376 | ||||||||
\(861\) | −4.53022 | −0.154389 | ||||||||
\(862\) | −5.10759 | −0.173965 | ||||||||
\(863\) | 25.8022 | 0.878318 | 0.439159 | − | 0.898409i | \(-0.355277\pi\) | ||||
0.439159 | + | 0.898409i | \(0.355277\pi\) | |||||||
\(864\) | −8.86564 | −0.301615 | ||||||||
\(865\) | 81.2453 | 2.76242 | ||||||||
\(866\) | −70.3778 | −2.39154 | ||||||||
\(867\) | −19.9503 | −0.677547 | ||||||||
\(868\) | 8.59819 | 0.291842 | ||||||||
\(869\) | −15.7435 | −0.534063 | ||||||||
\(870\) | 189.185 | 6.41399 | ||||||||
\(871\) | −16.9165 | −0.573195 | ||||||||
\(872\) | −26.6872 | −0.903742 | ||||||||
\(873\) | −3.40629 | −0.115286 | ||||||||
\(874\) | −11.5487 | −0.390639 | ||||||||
\(875\) | −8.63746 | −0.291999 | ||||||||
\(876\) | −106.199 | −3.58812 | ||||||||
\(877\) | −49.9200 | −1.68568 | −0.842840 | − | 0.538164i | \(-0.819118\pi\) | ||||
−0.842840 | + | 0.538164i | \(0.819118\pi\) | |||||||
\(878\) | −21.4264 | −0.723106 | ||||||||
\(879\) | 10.7388 | 0.362210 | ||||||||
\(880\) | 9.75405 | 0.328809 | ||||||||
\(881\) | 32.6794 | 1.10100 | 0.550499 | − | 0.834836i | \(-0.314437\pi\) | ||||
0.550499 | + | 0.834836i | \(0.314437\pi\) | |||||||
\(882\) | 70.1921 | 2.36349 | ||||||||
\(883\) | 38.1763 | 1.28473 | 0.642367 | − | 0.766397i | \(-0.277952\pi\) | ||||
0.642367 | + | 0.766397i | \(0.277952\pi\) | |||||||
\(884\) | −21.7503 | −0.731542 | ||||||||
\(885\) | 29.8327 | 1.00282 | ||||||||
\(886\) | 24.8250 | 0.834011 | ||||||||
\(887\) | −25.1764 | −0.845341 | −0.422670 | − | 0.906283i | \(-0.638907\pi\) | ||||
−0.422670 | + | 0.906283i | \(0.638907\pi\) | |||||||
\(888\) | 42.6869 | 1.43248 | ||||||||
\(889\) | −7.83596 | −0.262810 | ||||||||
\(890\) | −51.9147 | −1.74018 | ||||||||
\(891\) | −3.48437 | −0.116731 | ||||||||
\(892\) | −46.0711 | −1.54257 | ||||||||
\(893\) | 24.2175 | 0.810407 | ||||||||
\(894\) | 3.80466 | 0.127247 | ||||||||
\(895\) | 27.9892 | 0.935576 | ||||||||
\(896\) | −9.29582 | −0.310551 | ||||||||
\(897\) | −4.04880 | −0.135185 | ||||||||
\(898\) | 59.3011 | 1.97890 | ||||||||
\(899\) | −38.9616 | −1.29944 | ||||||||
\(900\) | 160.246 | 5.34153 | ||||||||
\(901\) | −4.93717 | −0.164481 | ||||||||
\(902\) | 9.38675 | 0.312545 | ||||||||
\(903\) | −12.8994 | −0.429266 | ||||||||
\(904\) | −41.9769 | −1.39613 | ||||||||
\(905\) | −4.28069 | −0.142295 | ||||||||
\(906\) | 6.46929 | 0.214928 | ||||||||
\(907\) | 22.8623 | 0.759131 | 0.379566 | − | 0.925165i | \(-0.376073\pi\) | ||||
0.379566 | + | 0.925165i | \(0.376073\pi\) | |||||||
\(908\) | 92.4311 | 3.06743 | ||||||||
\(909\) | 18.2803 | 0.606319 | ||||||||
\(910\) | −4.91320 | −0.162871 | ||||||||
\(911\) | 27.1210 | 0.898558 | 0.449279 | − | 0.893391i | \(-0.351681\pi\) | ||||
0.449279 | + | 0.893391i | \(0.351681\pi\) | |||||||
\(912\) | 24.7932 | 0.820986 | ||||||||
\(913\) | 9.21850 | 0.305088 | ||||||||
\(914\) | −24.6396 | −0.815007 | ||||||||
\(915\) | 158.875 | 5.25223 | ||||||||
\(916\) | −26.6647 | −0.881026 | ||||||||
\(917\) | −0.715459 | −0.0236265 | ||||||||
\(918\) | 42.0490 | 1.38782 | ||||||||
\(919\) | 9.82933 | 0.324240 | 0.162120 | − | 0.986771i | \(-0.448167\pi\) | ||||
0.162120 | + | 0.986771i | \(0.448167\pi\) | |||||||
\(920\) | 20.1268 | 0.663561 | ||||||||
\(921\) | −46.5385 | −1.53349 | ||||||||
\(922\) | 35.1757 | 1.15845 | ||||||||
\(923\) | −16.3562 | −0.538370 | ||||||||
\(924\) | 4.73747 | 0.155851 | ||||||||
\(925\) | 38.2784 | 1.25858 | ||||||||
\(926\) | 48.7456 | 1.60188 | ||||||||
\(927\) | 44.7126 | 1.46856 | ||||||||
\(928\) | 18.8116 | 0.617521 | ||||||||
\(929\) | 20.1498 | 0.661095 | 0.330547 | − | 0.943789i | \(-0.392767\pi\) | ||||
0.330547 | + | 0.943789i | \(0.392767\pi\) | |||||||
\(930\) | −129.106 | −4.23357 | ||||||||
\(931\) | 25.9733 | 0.851239 | ||||||||
\(932\) | 42.6395 | 1.39670 | ||||||||
\(933\) | −15.6523 | −0.512435 | ||||||||
\(934\) | −88.9447 | −2.91036 | ||||||||
\(935\) | 20.0704 | 0.656373 | ||||||||
\(936\) | 21.0298 | 0.687381 | ||||||||
\(937\) | −9.61016 | −0.313950 | −0.156975 | − | 0.987603i | \(-0.550174\pi\) | ||||
−0.156975 | + | 0.987603i | \(0.550174\pi\) | |||||||
\(938\) | 15.3140 | 0.500018 | ||||||||
\(939\) | 48.0715 | 1.56876 | ||||||||
\(940\) | −91.2770 | −2.97713 | ||||||||
\(941\) | 19.3603 | 0.631129 | 0.315564 | − | 0.948904i | \(-0.397806\pi\) | ||||
0.315564 | + | 0.948904i | \(0.397806\pi\) | |||||||
\(942\) | 86.0966 | 2.80518 | ||||||||
\(943\) | 4.72308 | 0.153804 | ||||||||
\(944\) | −6.83761 | −0.222545 | ||||||||
\(945\) | 6.17745 | 0.200952 | ||||||||
\(946\) | 26.7280 | 0.869002 | ||||||||
\(947\) | −16.0894 | −0.522837 | −0.261418 | − | 0.965226i | \(-0.584190\pi\) | ||||
−0.261418 | + | 0.965226i | \(0.584190\pi\) | |||||||
\(948\) | 150.828 | 4.89867 | ||||||||
\(949\) | −12.4976 | −0.405688 | ||||||||
\(950\) | 91.1740 | 2.95807 | ||||||||
\(951\) | 47.2762 | 1.53304 | ||||||||
\(952\) | 9.10442 | 0.295076 | ||||||||
\(953\) | −59.4118 | −1.92454 | −0.962268 | − | 0.272104i | \(-0.912280\pi\) | ||||
−0.962268 | + | 0.272104i | \(0.912280\pi\) | |||||||
\(954\) | 10.3237 | 0.334243 | ||||||||
\(955\) | 71.2711 | 2.30628 | ||||||||
\(956\) | 90.1987 | 2.91724 | ||||||||
\(957\) | −21.4672 | −0.693937 | ||||||||
\(958\) | 31.8458 | 1.02889 | ||||||||
\(959\) | −7.31045 | −0.236067 | ||||||||
\(960\) | 112.573 | 3.63329 | ||||||||
\(961\) | −4.41133 | −0.142301 | ||||||||
\(962\) | 10.8640 | 0.350270 | ||||||||
\(963\) | −20.1551 | −0.649490 | ||||||||
\(964\) | 90.0391 | 2.89996 | ||||||||
\(965\) | −97.2122 | −3.12937 | ||||||||
\(966\) | 3.66523 | 0.117927 | ||||||||
\(967\) | 41.8590 | 1.34610 | 0.673048 | − | 0.739599i | \(-0.264985\pi\) | ||||
0.673048 | + | 0.739599i | \(0.264985\pi\) | |||||||
\(968\) | 40.7168 | 1.30869 | ||||||||
\(969\) | 51.0158 | 1.63886 | ||||||||
\(970\) | 7.30463 | 0.234537 | ||||||||
\(971\) | 37.4824 | 1.20287 | 0.601433 | − | 0.798923i | \(-0.294597\pi\) | ||||
0.601433 | + | 0.798923i | \(0.294597\pi\) | |||||||
\(972\) | 73.1242 | 2.34546 | ||||||||
\(973\) | 1.58091 | 0.0506816 | ||||||||
\(974\) | 92.3422 | 2.95883 | ||||||||
\(975\) | 31.9643 | 1.02368 | ||||||||
\(976\) | −36.4138 | −1.16558 | ||||||||
\(977\) | −14.8910 | −0.476407 | −0.238203 | − | 0.971215i | \(-0.576558\pi\) | ||||
−0.238203 | + | 0.971215i | \(0.576558\pi\) | |||||||
\(978\) | −139.249 | −4.45269 | ||||||||
\(979\) | 5.89086 | 0.188273 | ||||||||
\(980\) | −97.8946 | −3.12713 | ||||||||
\(981\) | 27.9997 | 0.893962 | ||||||||
\(982\) | 81.5080 | 2.60102 | ||||||||
\(983\) | 8.80561 | 0.280855 | 0.140428 | − | 0.990091i | \(-0.455152\pi\) | ||||
0.140428 | + | 0.990091i | \(0.455152\pi\) | |||||||
\(984\) | −41.5821 | −1.32559 | ||||||||
\(985\) | 19.6285 | 0.625415 | ||||||||
\(986\) | −89.2218 | −2.84140 | ||||||||
\(987\) | −7.68598 | −0.244648 | ||||||||
\(988\) | 16.8292 | 0.535408 | ||||||||
\(989\) | 13.4486 | 0.427640 | ||||||||
\(990\) | −41.9678 | −1.33382 | ||||||||
\(991\) | −37.3228 | −1.18560 | −0.592798 | − | 0.805351i | \(-0.701977\pi\) | ||||
−0.592798 | + | 0.805351i | \(0.701977\pi\) | |||||||
\(992\) | −12.8377 | −0.407596 | ||||||||
\(993\) | −78.9655 | −2.50590 | ||||||||
\(994\) | 14.8067 | 0.469639 | ||||||||
\(995\) | 94.3701 | 2.99173 | ||||||||
\(996\) | −88.3162 | −2.79841 | ||||||||
\(997\) | −10.7722 | −0.341161 | −0.170580 | − | 0.985344i | \(-0.554564\pi\) | ||||
−0.170580 | + | 0.985344i | \(0.554564\pi\) | |||||||
\(998\) | −42.0709 | −1.33173 | ||||||||
\(999\) | −13.6595 | −0.432168 |
(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 | 8003.2.a.c.1.16 | ✓ | 172 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8003.2.a.c.1.16 | ✓ | 172 | 1.1 | even | 1 | trivial |