Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6037,2,Mod(1,6037)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6037, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6037.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6037 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6037.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: | \(48.2056877002\) |
Analytic rank: | \(1\) |
Dimension: | \(243\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6037.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79753 | −1.97815 | −0.989077 | − | 0.147398i | \(-0.952910\pi\) | ||||
−0.989077 | + | 0.147398i | \(0.952910\pi\) | |||||||
\(3\) | −2.64112 | −1.52485 | −0.762427 | − | 0.647074i | \(-0.775992\pi\) | ||||
−0.762427 | + | 0.647074i | \(0.775992\pi\) | |||||||
\(4\) | 5.82619 | 2.91310 | ||||||||
\(5\) | −2.23668 | −1.00028 | −0.500138 | − | 0.865946i | \(-0.666717\pi\) | ||||
−0.500138 | + | 0.865946i | \(0.666717\pi\) | |||||||
\(6\) | 7.38863 | 3.01640 | ||||||||
\(7\) | −3.27355 | −1.23728 | −0.618642 | − | 0.785673i | \(-0.712317\pi\) | ||||
−0.618642 | + | 0.785673i | \(0.712317\pi\) | |||||||
\(8\) | −10.7039 | −3.78440 | ||||||||
\(9\) | 3.97554 | 1.32518 | ||||||||
\(10\) | 6.25720 | 1.97870 | ||||||||
\(11\) | 2.82619 | 0.852129 | 0.426064 | − | 0.904693i | \(-0.359900\pi\) | ||||
0.426064 | + | 0.904693i | \(0.359900\pi\) | |||||||
\(12\) | −15.3877 | −4.44204 | ||||||||
\(13\) | 0.422688 | 0.117232 | 0.0586162 | − | 0.998281i | \(-0.481331\pi\) | ||||
0.0586162 | + | 0.998281i | \(0.481331\pi\) | |||||||
\(14\) | 9.15785 | 2.44754 | ||||||||
\(15\) | 5.90736 | 1.52527 | ||||||||
\(16\) | 18.2921 | 4.57303 | ||||||||
\(17\) | −1.15037 | −0.279006 | −0.139503 | − | 0.990222i | \(-0.544550\pi\) | ||||
−0.139503 | + | 0.990222i | \(0.544550\pi\) | |||||||
\(18\) | −11.1217 | −2.62141 | ||||||||
\(19\) | 6.14718 | 1.41026 | 0.705130 | − | 0.709078i | \(-0.250889\pi\) | ||||
0.705130 | + | 0.709078i | \(0.250889\pi\) | |||||||
\(20\) | −13.0313 | −2.91390 | ||||||||
\(21\) | 8.64584 | 1.88668 | ||||||||
\(22\) | −7.90636 | −1.68564 | ||||||||
\(23\) | 5.61831 | 1.17150 | 0.585749 | − | 0.810492i | \(-0.300800\pi\) | ||||
0.585749 | + | 0.810492i | \(0.300800\pi\) | |||||||
\(24\) | 28.2703 | 5.77065 | ||||||||
\(25\) | 0.00275197 | 0.000550393 0 | ||||||||
\(26\) | −1.18248 | −0.231904 | ||||||||
\(27\) | −2.57651 | −0.495850 | ||||||||
\(28\) | −19.0723 | −3.60433 | ||||||||
\(29\) | −5.43869 | −1.00994 | −0.504970 | − | 0.863137i | \(-0.668497\pi\) | ||||
−0.504970 | + | 0.863137i | \(0.668497\pi\) | |||||||
\(30\) | −16.5260 | −3.01723 | ||||||||
\(31\) | −9.76944 | −1.75464 | −0.877321 | − | 0.479904i | \(-0.840672\pi\) | ||||
−0.877321 | + | 0.479904i | \(0.840672\pi\) | |||||||
\(32\) | −29.7650 | −5.26176 | ||||||||
\(33\) | −7.46432 | −1.29937 | ||||||||
\(34\) | 3.21820 | 0.551916 | ||||||||
\(35\) | 7.32188 | 1.23762 | ||||||||
\(36\) | 23.1622 | 3.86037 | ||||||||
\(37\) | −4.78322 | −0.786357 | −0.393179 | − | 0.919462i | \(-0.628625\pi\) | ||||
−0.393179 | + | 0.919462i | \(0.628625\pi\) | |||||||
\(38\) | −17.1969 | −2.78971 | ||||||||
\(39\) | −1.11637 | −0.178762 | ||||||||
\(40\) | 23.9412 | 3.78544 | ||||||||
\(41\) | −3.27748 | −0.511857 | −0.255929 | − | 0.966696i | \(-0.582381\pi\) | ||||
−0.255929 | + | 0.966696i | \(0.582381\pi\) | |||||||
\(42\) | −24.1870 | −3.73214 | ||||||||
\(43\) | −1.13266 | −0.172729 | −0.0863644 | − | 0.996264i | \(-0.527525\pi\) | ||||
−0.0863644 | + | 0.996264i | \(0.527525\pi\) | |||||||
\(44\) | 16.4659 | 2.48233 | ||||||||
\(45\) | −8.89202 | −1.32554 | ||||||||
\(46\) | −15.7174 | −2.31740 | ||||||||
\(47\) | −9.62890 | −1.40452 | −0.702260 | − | 0.711921i | \(-0.747826\pi\) | ||||
−0.702260 | + | 0.711921i | \(0.747826\pi\) | |||||||
\(48\) | −48.3117 | −6.97320 | ||||||||
\(49\) | 3.71610 | 0.530871 | ||||||||
\(50\) | −0.00769871 | −0.00108876 | ||||||||
\(51\) | 3.03827 | 0.425443 | ||||||||
\(52\) | 2.46266 | 0.341509 | ||||||||
\(53\) | 5.77106 | 0.792716 | 0.396358 | − | 0.918096i | \(-0.370274\pi\) | ||||
0.396358 | + | 0.918096i | \(0.370274\pi\) | |||||||
\(54\) | 7.20788 | 0.980868 | ||||||||
\(55\) | −6.32130 | −0.852363 | ||||||||
\(56\) | 35.0397 | 4.68237 | ||||||||
\(57\) | −16.2355 | −2.15044 | ||||||||
\(58\) | 15.2149 | 1.99782 | ||||||||
\(59\) | −2.67824 | −0.348677 | −0.174338 | − | 0.984686i | \(-0.555779\pi\) | ||||
−0.174338 | + | 0.984686i | \(0.555779\pi\) | |||||||
\(60\) | 34.4174 | 4.44327 | ||||||||
\(61\) | 13.5696 | 1.73741 | 0.868705 | − | 0.495330i | \(-0.164953\pi\) | ||||
0.868705 | + | 0.495330i | \(0.164953\pi\) | |||||||
\(62\) | 27.3303 | 3.47095 | ||||||||
\(63\) | −13.0141 | −1.63962 | ||||||||
\(64\) | 46.6843 | 5.83554 | ||||||||
\(65\) | −0.945418 | −0.117265 | ||||||||
\(66\) | 20.8817 | 2.57036 | ||||||||
\(67\) | 12.9183 | 1.57822 | 0.789112 | − | 0.614249i | \(-0.210541\pi\) | ||||
0.789112 | + | 0.614249i | \(0.210541\pi\) | |||||||
\(68\) | −6.70227 | −0.812770 | ||||||||
\(69\) | −14.8387 | −1.78636 | ||||||||
\(70\) | −20.4832 | −2.44821 | ||||||||
\(71\) | −7.11005 | −0.843808 | −0.421904 | − | 0.906640i | \(-0.638638\pi\) | ||||
−0.421904 | + | 0.906640i | \(0.638638\pi\) | |||||||
\(72\) | −42.5537 | −5.01500 | ||||||||
\(73\) | −14.5251 | −1.70003 | −0.850017 | − | 0.526755i | \(-0.823409\pi\) | ||||
−0.850017 | + | 0.526755i | \(0.823409\pi\) | |||||||
\(74\) | 13.3812 | 1.55554 | ||||||||
\(75\) | −0.00726828 | −0.000839269 0 | ||||||||
\(76\) | 35.8146 | 4.10822 | ||||||||
\(77\) | −9.25167 | −1.05433 | ||||||||
\(78\) | 3.12308 | 0.353620 | ||||||||
\(79\) | 7.07259 | 0.795729 | 0.397864 | − | 0.917444i | \(-0.369751\pi\) | ||||
0.397864 | + | 0.917444i | \(0.369751\pi\) | |||||||
\(80\) | −40.9137 | −4.57429 | ||||||||
\(81\) | −5.12172 | −0.569080 | ||||||||
\(82\) | 9.16887 | 1.01253 | ||||||||
\(83\) | −9.72765 | −1.06775 | −0.533874 | − | 0.845564i | \(-0.679264\pi\) | ||||
−0.533874 | + | 0.845564i | \(0.679264\pi\) | |||||||
\(84\) | 50.3723 | 5.49607 | ||||||||
\(85\) | 2.57301 | 0.279082 | ||||||||
\(86\) | 3.16865 | 0.341684 | ||||||||
\(87\) | 14.3643 | 1.54001 | ||||||||
\(88\) | −30.2513 | −3.22479 | ||||||||
\(89\) | −7.16245 | −0.759218 | −0.379609 | − | 0.925147i | \(-0.623942\pi\) | ||||
−0.379609 | + | 0.925147i | \(0.623942\pi\) | |||||||
\(90\) | 24.8757 | 2.62213 | ||||||||
\(91\) | −1.38369 | −0.145050 | ||||||||
\(92\) | 32.7333 | 3.41269 | ||||||||
\(93\) | 25.8023 | 2.67557 | ||||||||
\(94\) | 26.9372 | 2.77836 | ||||||||
\(95\) | −13.7493 | −1.41065 | ||||||||
\(96\) | 78.6131 | 8.02341 | ||||||||
\(97\) | 13.9886 | 1.42032 | 0.710162 | − | 0.704038i | \(-0.248622\pi\) | ||||
0.710162 | + | 0.704038i | \(0.248622\pi\) | |||||||
\(98\) | −10.3959 | −1.05015 | ||||||||
\(99\) | 11.2356 | 1.12922 | ||||||||
\(100\) | 0.0160335 | 0.00160335 | ||||||||
\(101\) | 8.80707 | 0.876337 | 0.438168 | − | 0.898893i | \(-0.355627\pi\) | ||||
0.438168 | + | 0.898893i | \(0.355627\pi\) | |||||||
\(102\) | −8.49965 | −0.841591 | ||||||||
\(103\) | 16.3924 | 1.61519 | 0.807595 | − | 0.589738i | \(-0.200769\pi\) | ||||
0.807595 | + | 0.589738i | \(0.200769\pi\) | |||||||
\(104\) | −4.52440 | −0.443654 | ||||||||
\(105\) | −19.3380 | −1.88720 | ||||||||
\(106\) | −16.1447 | −1.56811 | ||||||||
\(107\) | −12.9633 | −1.25321 | −0.626603 | − | 0.779339i | \(-0.715555\pi\) | ||||
−0.626603 | + | 0.779339i | \(0.715555\pi\) | |||||||
\(108\) | −15.0113 | −1.44446 | ||||||||
\(109\) | 10.4638 | 1.00225 | 0.501124 | − | 0.865376i | \(-0.332920\pi\) | ||||
0.501124 | + | 0.865376i | \(0.332920\pi\) | |||||||
\(110\) | 17.6840 | 1.68611 | ||||||||
\(111\) | 12.6331 | 1.19908 | ||||||||
\(112\) | −59.8801 | −5.65813 | ||||||||
\(113\) | 3.38229 | 0.318179 | 0.159089 | − | 0.987264i | \(-0.449144\pi\) | ||||
0.159089 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(114\) | 45.4192 | 4.25390 | ||||||||
\(115\) | −12.5664 | −1.17182 | ||||||||
\(116\) | −31.6869 | −2.94205 | ||||||||
\(117\) | 1.68041 | 0.155354 | ||||||||
\(118\) | 7.49245 | 0.689736 | ||||||||
\(119\) | 3.76579 | 0.345209 | ||||||||
\(120\) | −63.2317 | −5.77224 | ||||||||
\(121\) | −3.01264 | −0.273877 | ||||||||
\(122\) | −37.9614 | −3.43687 | ||||||||
\(123\) | 8.65624 | 0.780507 | ||||||||
\(124\) | −56.9186 | −5.11144 | ||||||||
\(125\) | 11.1773 | 0.999725 | ||||||||
\(126\) | 36.4074 | 3.24343 | ||||||||
\(127\) | 2.21220 | 0.196301 | 0.0981504 | − | 0.995172i | \(-0.468707\pi\) | ||||
0.0981504 | + | 0.995172i | \(0.468707\pi\) | |||||||
\(128\) | −71.0710 | −6.28185 | ||||||||
\(129\) | 2.99149 | 0.263386 | ||||||||
\(130\) | 2.64484 | 0.231968 | ||||||||
\(131\) | 14.6174 | 1.27712 | 0.638562 | − | 0.769570i | \(-0.279530\pi\) | ||||
0.638562 | + | 0.769570i | \(0.279530\pi\) | |||||||
\(132\) | −43.4886 | −3.78519 | ||||||||
\(133\) | −20.1231 | −1.74489 | ||||||||
\(134\) | −36.1394 | −3.12197 | ||||||||
\(135\) | 5.76284 | 0.495987 | ||||||||
\(136\) | 12.3134 | 1.05587 | ||||||||
\(137\) | 0.779217 | 0.0665730 | 0.0332865 | − | 0.999446i | \(-0.489403\pi\) | ||||
0.0332865 | + | 0.999446i | \(0.489403\pi\) | |||||||
\(138\) | 41.5116 | 3.53370 | ||||||||
\(139\) | 4.40686 | 0.373785 | 0.186892 | − | 0.982380i | \(-0.440158\pi\) | ||||
0.186892 | + | 0.982380i | \(0.440158\pi\) | |||||||
\(140\) | 42.6587 | 3.60532 | ||||||||
\(141\) | 25.4311 | 2.14169 | ||||||||
\(142\) | 19.8906 | 1.66918 | ||||||||
\(143\) | 1.19460 | 0.0998972 | ||||||||
\(144\) | 72.7210 | 6.06008 | ||||||||
\(145\) | 12.1646 | 1.01022 | ||||||||
\(146\) | 40.6345 | 3.36293 | ||||||||
\(147\) | −9.81468 | −0.809501 | ||||||||
\(148\) | −27.8680 | −2.29073 | ||||||||
\(149\) | −18.6521 | −1.52804 | −0.764019 | − | 0.645194i | \(-0.776776\pi\) | ||||
−0.764019 | + | 0.645194i | \(0.776776\pi\) | |||||||
\(150\) | 0.0203333 | 0.00166020 | ||||||||
\(151\) | −14.9523 | −1.21680 | −0.608401 | − | 0.793630i | \(-0.708189\pi\) | ||||
−0.608401 | + | 0.793630i | \(0.708189\pi\) | |||||||
\(152\) | −65.7987 | −5.33698 | ||||||||
\(153\) | −4.57333 | −0.369732 | ||||||||
\(154\) | 25.8818 | 2.08562 | ||||||||
\(155\) | 21.8511 | 1.75513 | ||||||||
\(156\) | −6.50419 | −0.520752 | ||||||||
\(157\) | 2.70182 | 0.215629 | 0.107814 | − | 0.994171i | \(-0.465615\pi\) | ||||
0.107814 | + | 0.994171i | \(0.465615\pi\) | |||||||
\(158\) | −19.7858 | −1.57407 | ||||||||
\(159\) | −15.2421 | −1.20878 | ||||||||
\(160\) | 66.5749 | 5.26321 | ||||||||
\(161\) | −18.3918 | −1.44948 | ||||||||
\(162\) | 14.3282 | 1.12573 | ||||||||
\(163\) | −1.44916 | −0.113507 | −0.0567535 | − | 0.998388i | \(-0.518075\pi\) | ||||
−0.0567535 | + | 0.998388i | \(0.518075\pi\) | |||||||
\(164\) | −19.0952 | −1.49109 | ||||||||
\(165\) | 16.6953 | 1.29973 | ||||||||
\(166\) | 27.2134 | 2.11217 | ||||||||
\(167\) | 18.2220 | 1.41006 | 0.705029 | − | 0.709179i | \(-0.250934\pi\) | ||||
0.705029 | + | 0.709179i | \(0.250934\pi\) | |||||||
\(168\) | −92.5441 | −7.13994 | ||||||||
\(169\) | −12.8213 | −0.986257 | ||||||||
\(170\) | −7.19808 | −0.552068 | ||||||||
\(171\) | 24.4383 | 1.86885 | ||||||||
\(172\) | −6.59908 | −0.503175 | ||||||||
\(173\) | 12.3339 | 0.937731 | 0.468866 | − | 0.883270i | \(-0.344663\pi\) | ||||
0.468866 | + | 0.883270i | \(0.344663\pi\) | |||||||
\(174\) | −40.1845 | −3.04638 | ||||||||
\(175\) | −0.00900868 | −0.000680992 0 | ||||||||
\(176\) | 51.6970 | 3.89681 | ||||||||
\(177\) | 7.07355 | 0.531681 | ||||||||
\(178\) | 20.0372 | 1.50185 | ||||||||
\(179\) | −5.34467 | −0.399480 | −0.199740 | − | 0.979849i | \(-0.564010\pi\) | ||||
−0.199740 | + | 0.979849i | \(0.564010\pi\) | |||||||
\(180\) | −51.8066 | −3.86143 | ||||||||
\(181\) | 25.4686 | 1.89307 | 0.946534 | − | 0.322603i | \(-0.104558\pi\) | ||||
0.946534 | + | 0.322603i | \(0.104558\pi\) | |||||||
\(182\) | 3.87091 | 0.286931 | ||||||||
\(183\) | −35.8390 | −2.64930 | ||||||||
\(184\) | −60.1378 | −4.43342 | ||||||||
\(185\) | 10.6986 | 0.786574 | ||||||||
\(186\) | −72.1828 | −5.29270 | ||||||||
\(187\) | −3.25116 | −0.237749 | ||||||||
\(188\) | −56.0998 | −4.09150 | ||||||||
\(189\) | 8.43433 | 0.613507 | ||||||||
\(190\) | 38.4641 | 2.79048 | ||||||||
\(191\) | −17.1770 | −1.24288 | −0.621441 | − | 0.783461i | \(-0.713452\pi\) | ||||
−0.621441 | + | 0.783461i | \(0.713452\pi\) | |||||||
\(192\) | −123.299 | −8.89835 | ||||||||
\(193\) | 6.72782 | 0.484279 | 0.242140 | − | 0.970241i | \(-0.422151\pi\) | ||||
0.242140 | + | 0.970241i | \(0.422151\pi\) | |||||||
\(194\) | −39.1335 | −2.80962 | ||||||||
\(195\) | 2.49697 | 0.178812 | ||||||||
\(196\) | 21.6507 | 1.54648 | ||||||||
\(197\) | −0.563334 | −0.0401359 | −0.0200679 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200679 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(198\) | −31.4320 | −2.23378 | ||||||||
\(199\) | 11.0840 | 0.785720 | 0.392860 | − | 0.919598i | \(-0.371486\pi\) | ||||
0.392860 | + | 0.919598i | \(0.371486\pi\) | |||||||
\(200\) | −0.0294567 | −0.00208291 | ||||||||
\(201\) | −34.1189 | −2.40656 | ||||||||
\(202\) | −24.6381 | −1.73353 | ||||||||
\(203\) | 17.8038 | 1.24958 | ||||||||
\(204\) | 17.7015 | 1.23935 | ||||||||
\(205\) | 7.33069 | 0.511998 | ||||||||
\(206\) | −45.8582 | −3.19510 | ||||||||
\(207\) | 22.3358 | 1.55244 | ||||||||
\(208\) | 7.73185 | 0.536107 | ||||||||
\(209\) | 17.3731 | 1.20172 | ||||||||
\(210\) | 54.0987 | 3.73317 | ||||||||
\(211\) | 14.7909 | 1.01824 | 0.509122 | − | 0.860694i | \(-0.329970\pi\) | ||||
0.509122 | + | 0.860694i | \(0.329970\pi\) | |||||||
\(212\) | 33.6233 | 2.30926 | ||||||||
\(213\) | 18.7785 | 1.28668 | ||||||||
\(214\) | 36.2652 | 2.47903 | ||||||||
\(215\) | 2.53340 | 0.172776 | ||||||||
\(216\) | 27.5787 | 1.87649 | ||||||||
\(217\) | 31.9807 | 2.17099 | ||||||||
\(218\) | −29.2727 | −1.98260 | ||||||||
\(219\) | 38.3626 | 2.59230 | ||||||||
\(220\) | −36.8291 | −2.48302 | ||||||||
\(221\) | −0.486247 | −0.0327085 | ||||||||
\(222\) | −35.3415 | −2.37196 | ||||||||
\(223\) | 13.2955 | 0.890335 | 0.445168 | − | 0.895447i | \(-0.353144\pi\) | ||||
0.445168 | + | 0.895447i | \(0.353144\pi\) | |||||||
\(224\) | 97.4371 | 6.51029 | ||||||||
\(225\) | 0.0109405 | 0.000729369 0 | ||||||||
\(226\) | −9.46206 | −0.629407 | ||||||||
\(227\) | −16.1507 | −1.07196 | −0.535978 | − | 0.844232i | \(-0.680057\pi\) | ||||
−0.535978 | + | 0.844232i | \(0.680057\pi\) | |||||||
\(228\) | −94.5909 | −6.26443 | ||||||||
\(229\) | 8.61353 | 0.569198 | 0.284599 | − | 0.958647i | \(-0.408140\pi\) | ||||
0.284599 | + | 0.958647i | \(0.408140\pi\) | |||||||
\(230\) | 35.1549 | 2.31804 | ||||||||
\(231\) | 24.4348 | 1.60769 | ||||||||
\(232\) | 58.2152 | 3.82202 | ||||||||
\(233\) | −8.99808 | −0.589484 | −0.294742 | − | 0.955577i | \(-0.595234\pi\) | ||||
−0.294742 | + | 0.955577i | \(0.595234\pi\) | |||||||
\(234\) | −4.70100 | −0.307314 | ||||||||
\(235\) | 21.5368 | 1.40491 | ||||||||
\(236\) | −15.6039 | −1.01573 | ||||||||
\(237\) | −18.6796 | −1.21337 | ||||||||
\(238\) | −10.5349 | −0.682877 | ||||||||
\(239\) | −23.5695 | −1.52459 | −0.762293 | − | 0.647232i | \(-0.775926\pi\) | ||||
−0.762293 | + | 0.647232i | \(0.775926\pi\) | |||||||
\(240\) | 108.058 | 6.97512 | ||||||||
\(241\) | 17.2330 | 1.11007 | 0.555036 | − | 0.831826i | \(-0.312704\pi\) | ||||
0.555036 | + | 0.831826i | \(0.312704\pi\) | |||||||
\(242\) | 8.42797 | 0.541770 | ||||||||
\(243\) | 21.2566 | 1.36361 | ||||||||
\(244\) | 79.0591 | 5.06124 | ||||||||
\(245\) | −8.31174 | −0.531017 | ||||||||
\(246\) | −24.2161 | −1.54396 | ||||||||
\(247\) | 2.59834 | 0.165328 | ||||||||
\(248\) | 104.571 | 6.64026 | ||||||||
\(249\) | 25.6919 | 1.62816 | ||||||||
\(250\) | −31.2688 | −1.97761 | ||||||||
\(251\) | 11.9339 | 0.753260 | 0.376630 | − | 0.926364i | \(-0.377083\pi\) | ||||
0.376630 | + | 0.926364i | \(0.377083\pi\) | |||||||
\(252\) | −75.8226 | −4.77638 | ||||||||
\(253\) | 15.8784 | 0.998267 | ||||||||
\(254\) | −6.18870 | −0.388313 | ||||||||
\(255\) | −6.79564 | −0.425560 | ||||||||
\(256\) | 105.455 | 6.59092 | ||||||||
\(257\) | 0.0265183 | 0.00165416 | 0.000827082 | − | 1.00000i | \(-0.499737\pi\) | ||||
0.000827082 | 1.00000i | \(0.499737\pi\) | ||||||||
\(258\) | −8.36880 | −0.521019 | ||||||||
\(259\) | 15.6581 | 0.972947 | ||||||||
\(260\) | −5.50819 | −0.341603 | ||||||||
\(261\) | −21.6217 | −1.33835 | ||||||||
\(262\) | −40.8925 | −2.52635 | ||||||||
\(263\) | 12.1668 | 0.750236 | 0.375118 | − | 0.926977i | \(-0.377602\pi\) | ||||
0.375118 | + | 0.926977i | \(0.377602\pi\) | |||||||
\(264\) | 79.8973 | 4.91734 | ||||||||
\(265\) | −12.9080 | −0.792934 | ||||||||
\(266\) | 56.2949 | 3.45166 | ||||||||
\(267\) | 18.9169 | 1.15770 | ||||||||
\(268\) | 75.2646 | 4.59752 | ||||||||
\(269\) | 10.7221 | 0.653736 | 0.326868 | − | 0.945070i | \(-0.394007\pi\) | ||||
0.326868 | + | 0.945070i | \(0.394007\pi\) | |||||||
\(270\) | −16.1217 | −0.981138 | ||||||||
\(271\) | −15.7125 | −0.954466 | −0.477233 | − | 0.878777i | \(-0.658360\pi\) | ||||
−0.477233 | + | 0.878777i | \(0.658360\pi\) | |||||||
\(272\) | −21.0427 | −1.27590 | ||||||||
\(273\) | 3.65449 | 0.221180 | ||||||||
\(274\) | −2.17988 | −0.131692 | ||||||||
\(275\) | 0.00777758 | 0.000469006 0 | ||||||||
\(276\) | −86.4528 | −5.20385 | ||||||||
\(277\) | −22.9353 | −1.37805 | −0.689025 | − | 0.724738i | \(-0.741961\pi\) | ||||
−0.689025 | + | 0.724738i | \(0.741961\pi\) | |||||||
\(278\) | −12.3283 | −0.739404 | ||||||||
\(279\) | −38.8387 | −2.32522 | ||||||||
\(280\) | −78.3727 | −4.68366 | ||||||||
\(281\) | 11.0329 | 0.658169 | 0.329084 | − | 0.944301i | \(-0.393260\pi\) | ||||
0.329084 | + | 0.944301i | \(0.393260\pi\) | |||||||
\(282\) | −71.1444 | −4.23659 | ||||||||
\(283\) | −6.44214 | −0.382946 | −0.191473 | − | 0.981498i | \(-0.561326\pi\) | ||||
−0.191473 | + | 0.981498i | \(0.561326\pi\) | |||||||
\(284\) | −41.4245 | −2.45809 | ||||||||
\(285\) | 36.3136 | 2.15103 | ||||||||
\(286\) | −3.34192 | −0.197612 | ||||||||
\(287\) | 10.7290 | 0.633312 | ||||||||
\(288\) | −118.332 | −6.97277 | ||||||||
\(289\) | −15.6767 | −0.922156 | ||||||||
\(290\) | −34.0310 | −1.99837 | ||||||||
\(291\) | −36.9455 | −2.16579 | ||||||||
\(292\) | −84.6260 | −4.95236 | ||||||||
\(293\) | 7.89948 | 0.461492 | 0.230746 | − | 0.973014i | \(-0.425883\pi\) | ||||
0.230746 | + | 0.973014i | \(0.425883\pi\) | |||||||
\(294\) | 27.4569 | 1.60132 | ||||||||
\(295\) | 5.99036 | 0.348772 | ||||||||
\(296\) | 51.1991 | 2.97589 | ||||||||
\(297\) | −7.28172 | −0.422528 | ||||||||
\(298\) | 52.1798 | 3.02269 | ||||||||
\(299\) | 2.37479 | 0.137338 | ||||||||
\(300\) | −0.0423464 | −0.00244487 | ||||||||
\(301\) | 3.70781 | 0.213715 | ||||||||
\(302\) | 41.8296 | 2.40702 | ||||||||
\(303\) | −23.2606 | −1.33628 | ||||||||
\(304\) | 112.445 | 6.44916 | ||||||||
\(305\) | −30.3509 | −1.73789 | ||||||||
\(306\) | 12.7941 | 0.731387 | ||||||||
\(307\) | 18.9821 | 1.08336 | 0.541682 | − | 0.840584i | \(-0.317788\pi\) | ||||
0.541682 | + | 0.840584i | \(0.317788\pi\) | |||||||
\(308\) | −53.9020 | −3.07135 | ||||||||
\(309\) | −43.2943 | −2.46293 | ||||||||
\(310\) | −61.1293 | −3.47191 | ||||||||
\(311\) | 0.972350 | 0.0551369 | 0.0275685 | − | 0.999620i | \(-0.491224\pi\) | ||||
0.0275685 | + | 0.999620i | \(0.491224\pi\) | |||||||
\(312\) | 11.9495 | 0.676508 | ||||||||
\(313\) | −2.76853 | −0.156487 | −0.0782434 | − | 0.996934i | \(-0.524931\pi\) | ||||
−0.0782434 | + | 0.996934i | \(0.524931\pi\) | |||||||
\(314\) | −7.55843 | −0.426547 | ||||||||
\(315\) | 29.1084 | 1.64007 | ||||||||
\(316\) | 41.2063 | 2.31803 | ||||||||
\(317\) | 27.5905 | 1.54963 | 0.774817 | − | 0.632185i | \(-0.217842\pi\) | ||||
0.774817 | + | 0.632185i | \(0.217842\pi\) | |||||||
\(318\) | 42.6402 | 2.39114 | ||||||||
\(319\) | −15.3708 | −0.860599 | ||||||||
\(320\) | −104.418 | −5.83715 | ||||||||
\(321\) | 34.2376 | 1.91096 | ||||||||
\(322\) | 51.4516 | 2.86729 | ||||||||
\(323\) | −7.07152 | −0.393470 | ||||||||
\(324\) | −29.8401 | −1.65778 | ||||||||
\(325\) | 0.00116322 | 6.45239e−5 0 | ||||||||
\(326\) | 4.05407 | 0.224534 | ||||||||
\(327\) | −27.6361 | −1.52828 | ||||||||
\(328\) | 35.0818 | 1.93707 | ||||||||
\(329\) | 31.5206 | 1.73779 | ||||||||
\(330\) | −46.7057 | −2.57107 | ||||||||
\(331\) | 18.2967 | 1.00568 | 0.502838 | − | 0.864381i | \(-0.332289\pi\) | ||||
0.502838 | + | 0.864381i | \(0.332289\pi\) | |||||||
\(332\) | −56.6751 | −3.11045 | ||||||||
\(333\) | −19.0159 | −1.04206 | ||||||||
\(334\) | −50.9765 | −2.78931 | ||||||||
\(335\) | −28.8942 | −1.57866 | ||||||||
\(336\) | 158.151 | 8.62783 | ||||||||
\(337\) | −10.1901 | −0.555091 | −0.277546 | − | 0.960712i | \(-0.589521\pi\) | ||||
−0.277546 | + | 0.960712i | \(0.589521\pi\) | |||||||
\(338\) | 35.8681 | 1.95097 | ||||||||
\(339\) | −8.93304 | −0.485176 | ||||||||
\(340\) | 14.9909 | 0.812993 | ||||||||
\(341\) | −27.6103 | −1.49518 | ||||||||
\(342\) | −68.3670 | −3.69687 | ||||||||
\(343\) | 10.7500 | 0.580445 | ||||||||
\(344\) | 12.1239 | 0.653675 | ||||||||
\(345\) | 33.1894 | 1.78686 | ||||||||
\(346\) | −34.5046 | −1.85498 | ||||||||
\(347\) | −15.3601 | −0.824572 | −0.412286 | − | 0.911054i | \(-0.635270\pi\) | ||||
−0.412286 | + | 0.911054i | \(0.635270\pi\) | |||||||
\(348\) | 83.6890 | 4.48620 | ||||||||
\(349\) | −23.8658 | −1.27751 | −0.638754 | − | 0.769411i | \(-0.720550\pi\) | ||||
−0.638754 | + | 0.769411i | \(0.720550\pi\) | |||||||
\(350\) | 0.0252021 | 0.00134711 | ||||||||
\(351\) | −1.08906 | −0.0581297 | ||||||||
\(352\) | −84.1216 | −4.48370 | ||||||||
\(353\) | 1.38749 | 0.0738485 | 0.0369242 | − | 0.999318i | \(-0.488244\pi\) | ||||
0.0369242 | + | 0.999318i | \(0.488244\pi\) | |||||||
\(354\) | −19.7885 | −1.05175 | ||||||||
\(355\) | 15.9029 | 0.844040 | ||||||||
\(356\) | −41.7298 | −2.21168 | ||||||||
\(357\) | −9.94591 | −0.526393 | ||||||||
\(358\) | 14.9519 | 0.790233 | ||||||||
\(359\) | 19.3823 | 1.02296 | 0.511479 | − | 0.859296i | \(-0.329098\pi\) | ||||
0.511479 | + | 0.859296i | \(0.329098\pi\) | |||||||
\(360\) | 95.1792 | 5.01638 | ||||||||
\(361\) | 18.7878 | 0.988831 | ||||||||
\(362\) | −71.2493 | −3.74478 | ||||||||
\(363\) | 7.95676 | 0.417622 | ||||||||
\(364\) | −8.06163 | −0.422544 | ||||||||
\(365\) | 32.4881 | 1.70050 | ||||||||
\(366\) | 100.261 | 5.24072 | ||||||||
\(367\) | −3.77179 | −0.196886 | −0.0984429 | − | 0.995143i | \(-0.531386\pi\) | ||||
−0.0984429 | + | 0.995143i | \(0.531386\pi\) | |||||||
\(368\) | 102.771 | 5.35730 | ||||||||
\(369\) | −13.0298 | −0.678302 | ||||||||
\(370\) | −29.9296 | −1.55596 | ||||||||
\(371\) | −18.8918 | −0.980814 | ||||||||
\(372\) | 150.329 | 7.79420 | ||||||||
\(373\) | 21.1980 | 1.09759 | 0.548797 | − | 0.835956i | \(-0.315086\pi\) | ||||
0.548797 | + | 0.835956i | \(0.315086\pi\) | |||||||
\(374\) | 9.09524 | 0.470304 | ||||||||
\(375\) | −29.5205 | −1.52443 | ||||||||
\(376\) | 103.067 | 5.31526 | ||||||||
\(377\) | −2.29887 | −0.118398 | ||||||||
\(378\) | −23.5953 | −1.21361 | ||||||||
\(379\) | −34.5944 | −1.77700 | −0.888498 | − | 0.458881i | \(-0.848251\pi\) | ||||
−0.888498 | + | 0.458881i | \(0.848251\pi\) | |||||||
\(380\) | −80.1060 | −4.10935 | ||||||||
\(381\) | −5.84269 | −0.299330 | ||||||||
\(382\) | 48.0531 | 2.45861 | ||||||||
\(383\) | 21.7843 | 1.11312 | 0.556562 | − | 0.830806i | \(-0.312120\pi\) | ||||
0.556562 | + | 0.830806i | \(0.312120\pi\) | |||||||
\(384\) | 187.707 | 9.57890 | ||||||||
\(385\) | 20.6930 | 1.05462 | ||||||||
\(386\) | −18.8213 | −0.957979 | ||||||||
\(387\) | −4.50293 | −0.228897 | ||||||||
\(388\) | 81.5000 | 4.13754 | ||||||||
\(389\) | 9.60999 | 0.487246 | 0.243623 | − | 0.969870i | \(-0.421664\pi\) | ||||
0.243623 | + | 0.969870i | \(0.421664\pi\) | |||||||
\(390\) | −6.98535 | −0.353717 | ||||||||
\(391\) | −6.46313 | −0.326854 | ||||||||
\(392\) | −39.7767 | −2.00903 | ||||||||
\(393\) | −38.6063 | −1.94743 | ||||||||
\(394\) | 1.57594 | 0.0793949 | ||||||||
\(395\) | −15.8191 | −0.795948 | ||||||||
\(396\) | 65.4609 | 3.28953 | ||||||||
\(397\) | −26.2362 | −1.31676 | −0.658378 | − | 0.752687i | \(-0.728757\pi\) | ||||
−0.658378 | + | 0.752687i | \(0.728757\pi\) | |||||||
\(398\) | −31.0077 | −1.55428 | ||||||||
\(399\) | 53.1475 | 2.66070 | ||||||||
\(400\) | 0.0503393 | 0.00251696 | ||||||||
\(401\) | 23.7476 | 1.18590 | 0.592948 | − | 0.805240i | \(-0.297964\pi\) | ||||
0.592948 | + | 0.805240i | \(0.297964\pi\) | |||||||
\(402\) | 95.4487 | 4.76055 | ||||||||
\(403\) | −4.12942 | −0.205701 | ||||||||
\(404\) | 51.3117 | 2.55285 | ||||||||
\(405\) | 11.4557 | 0.569236 | ||||||||
\(406\) | −49.8068 | −2.47187 | ||||||||
\(407\) | −13.5183 | −0.670078 | ||||||||
\(408\) | −32.5213 | −1.61004 | ||||||||
\(409\) | 34.6401 | 1.71284 | 0.856421 | − | 0.516278i | \(-0.172683\pi\) | ||||
0.856421 | + | 0.516278i | \(0.172683\pi\) | |||||||
\(410\) | −20.5079 | −1.01281 | ||||||||
\(411\) | −2.05801 | −0.101514 | ||||||||
\(412\) | 95.5052 | 4.70520 | ||||||||
\(413\) | 8.76732 | 0.431412 | ||||||||
\(414\) | −62.4851 | −3.07098 | ||||||||
\(415\) | 21.7577 | 1.06804 | ||||||||
\(416\) | −12.5813 | −0.616849 | ||||||||
\(417\) | −11.6391 | −0.569967 | ||||||||
\(418\) | −48.6018 | −2.37719 | ||||||||
\(419\) | −36.0734 | −1.76230 | −0.881150 | − | 0.472836i | \(-0.843230\pi\) | ||||
−0.881150 | + | 0.472836i | \(0.843230\pi\) | |||||||
\(420\) | −112.667 | −5.49758 | ||||||||
\(421\) | −13.6957 | −0.667486 | −0.333743 | − | 0.942664i | \(-0.608312\pi\) | ||||
−0.333743 | + | 0.942664i | \(0.608312\pi\) | |||||||
\(422\) | −41.3779 | −2.01424 | ||||||||
\(423\) | −38.2801 | −1.86124 | ||||||||
\(424\) | −61.7728 | −2.99995 | ||||||||
\(425\) | −0.00316578 | −0.000153563 0 | ||||||||
\(426\) | −52.5336 | −2.54526 | ||||||||
\(427\) | −44.4207 | −2.14967 | ||||||||
\(428\) | −75.5264 | −3.65071 | ||||||||
\(429\) | −3.15508 | −0.152329 | ||||||||
\(430\) | −7.08727 | −0.341778 | ||||||||
\(431\) | 30.8116 | 1.48414 | 0.742072 | − | 0.670320i | \(-0.233843\pi\) | ||||
0.742072 | + | 0.670320i | \(0.233843\pi\) | |||||||
\(432\) | −47.1299 | −2.26754 | ||||||||
\(433\) | 2.14577 | 0.103119 | 0.0515596 | − | 0.998670i | \(-0.483581\pi\) | ||||
0.0515596 | + | 0.998670i | \(0.483581\pi\) | |||||||
\(434\) | −89.4670 | −4.29455 | ||||||||
\(435\) | −32.1283 | −1.54043 | ||||||||
\(436\) | 60.9639 | 2.91964 | ||||||||
\(437\) | 34.5367 | 1.65212 | ||||||||
\(438\) | −107.321 | −5.12798 | ||||||||
\(439\) | −6.08630 | −0.290483 | −0.145242 | − | 0.989396i | \(-0.546396\pi\) | ||||
−0.145242 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(440\) | 67.6625 | 3.22568 | ||||||||
\(441\) | 14.7735 | 0.703499 | ||||||||
\(442\) | 1.36029 | 0.0647025 | ||||||||
\(443\) | −32.8131 | −1.55900 | −0.779499 | − | 0.626404i | \(-0.784526\pi\) | ||||
−0.779499 | + | 0.626404i | \(0.784526\pi\) | |||||||
\(444\) | 73.6028 | 3.49303 | ||||||||
\(445\) | 16.0201 | 0.759427 | ||||||||
\(446\) | −37.1947 | −1.76122 | ||||||||
\(447\) | 49.2624 | 2.33003 | ||||||||
\(448\) | −152.823 | −7.22022 | ||||||||
\(449\) | −0.0255115 | −0.00120396 | −0.000601980 | − | 1.00000i | \(-0.500192\pi\) | ||||
−0.000601980 | 1.00000i | \(0.500192\pi\) | ||||||||
\(450\) | −0.0306065 | −0.00144281 | ||||||||
\(451\) | −9.26280 | −0.436168 | ||||||||
\(452\) | 19.7058 | 0.926885 | ||||||||
\(453\) | 39.4909 | 1.85544 | ||||||||
\(454\) | 45.1820 | 2.12050 | ||||||||
\(455\) | 3.09487 | 0.145090 | ||||||||
\(456\) | 173.783 | 8.13812 | ||||||||
\(457\) | 9.36383 | 0.438021 | 0.219011 | − | 0.975722i | \(-0.429717\pi\) | ||||
0.219011 | + | 0.975722i | \(0.429717\pi\) | |||||||
\(458\) | −24.0966 | −1.12596 | ||||||||
\(459\) | 2.96394 | 0.138345 | ||||||||
\(460\) | −73.2141 | −3.41363 | ||||||||
\(461\) | −2.49901 | −0.116390 | −0.0581952 | − | 0.998305i | \(-0.518535\pi\) | ||||
−0.0581952 | + | 0.998305i | \(0.518535\pi\) | |||||||
\(462\) | −68.3571 | −3.18026 | ||||||||
\(463\) | −4.08859 | −0.190013 | −0.0950065 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950065 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(464\) | −99.4852 | −4.61849 | ||||||||
\(465\) | −57.7116 | −2.67631 | ||||||||
\(466\) | 25.1724 | 1.16609 | ||||||||
\(467\) | −9.92113 | −0.459095 | −0.229547 | − | 0.973297i | \(-0.573725\pi\) | ||||
−0.229547 | + | 0.973297i | \(0.573725\pi\) | |||||||
\(468\) | 9.79039 | 0.452561 | ||||||||
\(469\) | −42.2887 | −1.95271 | ||||||||
\(470\) | −60.2499 | −2.77912 | ||||||||
\(471\) | −7.13584 | −0.328802 | ||||||||
\(472\) | 28.6675 | 1.31953 | ||||||||
\(473\) | −3.20111 | −0.147187 | ||||||||
\(474\) | 52.2568 | 2.40023 | ||||||||
\(475\) | 0.0169168 | 0.000776197 0 | ||||||||
\(476\) | 21.9402 | 1.00563 | ||||||||
\(477\) | 22.9430 | 1.05049 | ||||||||
\(478\) | 65.9365 | 3.01587 | ||||||||
\(479\) | 0.0492393 | 0.00224980 | 0.00112490 | − | 0.999999i | \(-0.499642\pi\) | ||||
0.00112490 | + | 0.999999i | \(0.499642\pi\) | |||||||
\(480\) | −175.833 | −8.02562 | ||||||||
\(481\) | −2.02181 | −0.0921866 | ||||||||
\(482\) | −48.2097 | −2.19589 | ||||||||
\(483\) | 48.5750 | 2.21024 | ||||||||
\(484\) | −17.5522 | −0.797828 | ||||||||
\(485\) | −31.2880 | −1.42071 | ||||||||
\(486\) | −59.4661 | −2.69744 | ||||||||
\(487\) | 11.4807 | 0.520239 | 0.260120 | − | 0.965576i | \(-0.416238\pi\) | ||||
0.260120 | + | 0.965576i | \(0.416238\pi\) | |||||||
\(488\) | −145.248 | −6.57505 | ||||||||
\(489\) | 3.82741 | 0.173082 | ||||||||
\(490\) | 23.2524 | 1.05043 | ||||||||
\(491\) | −6.08443 | −0.274586 | −0.137293 | − | 0.990530i | \(-0.543840\pi\) | ||||
−0.137293 | + | 0.990530i | \(0.543840\pi\) | |||||||
\(492\) | 50.4329 | 2.27369 | ||||||||
\(493\) | 6.25651 | 0.281779 | ||||||||
\(494\) | −7.26893 | −0.327045 | ||||||||
\(495\) | −25.1305 | −1.12953 | ||||||||
\(496\) | −178.704 | −8.02403 | ||||||||
\(497\) | 23.2751 | 1.04403 | ||||||||
\(498\) | −71.8740 | −3.22075 | ||||||||
\(499\) | 15.5579 | 0.696467 | 0.348233 | − | 0.937408i | \(-0.386782\pi\) | ||||
0.348233 | + | 0.937408i | \(0.386782\pi\) | |||||||
\(500\) | 65.1209 | 2.91229 | ||||||||
\(501\) | −48.1265 | −2.15013 | ||||||||
\(502\) | −33.3854 | −1.49006 | ||||||||
\(503\) | 30.9593 | 1.38041 | 0.690204 | − | 0.723615i | \(-0.257521\pi\) | ||||
0.690204 | + | 0.723615i | \(0.257521\pi\) | |||||||
\(504\) | 139.302 | 6.20498 | ||||||||
\(505\) | −19.6986 | −0.876578 | ||||||||
\(506\) | −44.4204 | −1.97473 | ||||||||
\(507\) | 33.8627 | 1.50390 | ||||||||
\(508\) | 12.8887 | 0.571843 | ||||||||
\(509\) | −29.8788 | −1.32435 | −0.662177 | − | 0.749348i | \(-0.730367\pi\) | ||||
−0.662177 | + | 0.749348i | \(0.730367\pi\) | |||||||
\(510\) | 19.0110 | 0.841823 | ||||||||
\(511\) | 47.5486 | 2.10343 | ||||||||
\(512\) | −152.871 | −6.75601 | ||||||||
\(513\) | −15.8383 | −0.699277 | ||||||||
\(514\) | −0.0741857 | −0.00327219 | ||||||||
\(515\) | −36.6646 | −1.61563 | ||||||||
\(516\) | 17.4290 | 0.767269 | ||||||||
\(517\) | −27.2131 | −1.19683 | ||||||||
\(518\) | −43.8040 | −1.92464 | ||||||||
\(519\) | −32.5754 | −1.42990 | ||||||||
\(520\) | 10.1197 | 0.443776 | ||||||||
\(521\) | 19.5999 | 0.858689 | 0.429344 | − | 0.903141i | \(-0.358745\pi\) | ||||
0.429344 | + | 0.903141i | \(0.358745\pi\) | |||||||
\(522\) | 60.4875 | 2.64747 | ||||||||
\(523\) | 11.0580 | 0.483532 | 0.241766 | − | 0.970335i | \(-0.422273\pi\) | ||||
0.241766 | + | 0.970335i | \(0.422273\pi\) | |||||||
\(524\) | 85.1635 | 3.72038 | ||||||||
\(525\) | 0.0237931 | 0.00103841 | ||||||||
\(526\) | −34.0370 | −1.48408 | ||||||||
\(527\) | 11.2385 | 0.489555 | ||||||||
\(528\) | −136.538 | −5.94206 | ||||||||
\(529\) | 8.56539 | 0.372408 | ||||||||
\(530\) | 36.1106 | 1.56855 | ||||||||
\(531\) | −10.6474 | −0.462059 | ||||||||
\(532\) | −117.241 | −5.08303 | ||||||||
\(533\) | −1.38535 | −0.0600063 | ||||||||
\(534\) | −52.9207 | −2.29010 | ||||||||
\(535\) | 28.9947 | 1.25355 | ||||||||
\(536\) | −138.276 | −5.97263 | ||||||||
\(537\) | 14.1159 | 0.609148 | ||||||||
\(538\) | −29.9953 | −1.29319 | ||||||||
\(539\) | 10.5024 | 0.452371 | ||||||||
\(540\) | 33.5754 | 1.44486 | ||||||||
\(541\) | 15.7541 | 0.677320 | 0.338660 | − | 0.940909i | \(-0.390026\pi\) | ||||
0.338660 | + | 0.940909i | \(0.390026\pi\) | |||||||
\(542\) | 43.9562 | 1.88808 | ||||||||
\(543\) | −67.2658 | −2.88665 | ||||||||
\(544\) | 34.2407 | 1.46806 | ||||||||
\(545\) | −23.4041 | −1.00252 | ||||||||
\(546\) | −10.2236 | −0.437528 | ||||||||
\(547\) | −32.8539 | −1.40473 | −0.702366 | − | 0.711816i | \(-0.747873\pi\) | ||||
−0.702366 | + | 0.711816i | \(0.747873\pi\) | |||||||
\(548\) | 4.53986 | 0.193933 | ||||||||
\(549\) | 53.9465 | 2.30238 | ||||||||
\(550\) | −0.0217580 | −0.000927766 0 | ||||||||
\(551\) | −33.4326 | −1.42428 | ||||||||
\(552\) | 158.831 | 6.76031 | ||||||||
\(553\) | −23.1525 | −0.984542 | ||||||||
\(554\) | 64.1623 | 2.72599 | ||||||||
\(555\) | −28.2562 | −1.19941 | ||||||||
\(556\) | 25.6752 | 1.08887 | ||||||||
\(557\) | −8.96768 | −0.379973 | −0.189986 | − | 0.981787i | \(-0.560844\pi\) | ||||
−0.189986 | + | 0.981787i | \(0.560844\pi\) | |||||||
\(558\) | 108.653 | 4.59963 | ||||||||
\(559\) | −0.478761 | −0.0202494 | ||||||||
\(560\) | 133.933 | 5.65969 | ||||||||
\(561\) | 8.58673 | 0.362532 | ||||||||
\(562\) | −30.8650 | −1.30196 | ||||||||
\(563\) | −41.0777 | −1.73122 | −0.865610 | − | 0.500719i | \(-0.833069\pi\) | ||||
−0.865610 | + | 0.500719i | \(0.833069\pi\) | |||||||
\(564\) | 148.167 | 6.23894 | ||||||||
\(565\) | −7.56510 | −0.318266 | ||||||||
\(566\) | 18.0221 | 0.757526 | ||||||||
\(567\) | 16.7662 | 0.704113 | ||||||||
\(568\) | 76.1053 | 3.19331 | ||||||||
\(569\) | −21.9102 | −0.918524 | −0.459262 | − | 0.888301i | \(-0.651886\pi\) | ||||
−0.459262 | + | 0.888301i | \(0.651886\pi\) | |||||||
\(570\) | −101.588 | −4.25507 | ||||||||
\(571\) | −19.4488 | −0.813905 | −0.406952 | − | 0.913449i | \(-0.633409\pi\) | ||||
−0.406952 | + | 0.913449i | \(0.633409\pi\) | |||||||
\(572\) | 6.95995 | 0.291010 | ||||||||
\(573\) | 45.3665 | 1.89521 | ||||||||
\(574\) | −30.0147 | −1.25279 | ||||||||
\(575\) | 0.0154614 | 0.000644785 0 | ||||||||
\(576\) | 185.595 | 7.73314 | ||||||||
\(577\) | 44.3100 | 1.84465 | 0.922325 | − | 0.386415i | \(-0.126287\pi\) | ||||
0.922325 | + | 0.386415i | \(0.126287\pi\) | |||||||
\(578\) | 43.8559 | 1.82417 | ||||||||
\(579\) | −17.7690 | −0.738455 | ||||||||
\(580\) | 70.8735 | 2.94286 | ||||||||
\(581\) | 31.8439 | 1.32111 | ||||||||
\(582\) | 103.356 | 4.28426 | ||||||||
\(583\) | 16.3101 | 0.675496 | ||||||||
\(584\) | 155.475 | 6.43361 | ||||||||
\(585\) | −3.75855 | −0.155397 | ||||||||
\(586\) | −22.0991 | −0.912903 | ||||||||
\(587\) | −0.695373 | −0.0287011 | −0.0143506 | − | 0.999897i | \(-0.504568\pi\) | ||||
−0.0143506 | + | 0.999897i | \(0.504568\pi\) | |||||||
\(588\) | −57.1822 | −2.35815 | ||||||||
\(589\) | −60.0545 | −2.47450 | ||||||||
\(590\) | −16.7582 | −0.689926 | ||||||||
\(591\) | 1.48783 | 0.0612013 | ||||||||
\(592\) | −87.4953 | −3.59603 | ||||||||
\(593\) | −25.7659 | −1.05808 | −0.529040 | − | 0.848597i | \(-0.677448\pi\) | ||||
−0.529040 | + | 0.848597i | \(0.677448\pi\) | |||||||
\(594\) | 20.3709 | 0.835826 | ||||||||
\(595\) | −8.42287 | −0.345304 | ||||||||
\(596\) | −108.671 | −4.45132 | ||||||||
\(597\) | −29.2741 | −1.19811 | ||||||||
\(598\) | −6.64355 | −0.271675 | ||||||||
\(599\) | 15.7179 | 0.642217 | 0.321109 | − | 0.947042i | \(-0.395945\pi\) | ||||
0.321109 | + | 0.947042i | \(0.395945\pi\) | |||||||
\(600\) | 0.0777989 | 0.00317613 | ||||||||
\(601\) | 11.4825 | 0.468380 | 0.234190 | − | 0.972191i | \(-0.424756\pi\) | ||||
0.234190 | + | 0.972191i | \(0.424756\pi\) | |||||||
\(602\) | −10.3727 | −0.422760 | ||||||||
\(603\) | 51.3572 | 2.09143 | ||||||||
\(604\) | −87.1150 | −3.54466 | ||||||||
\(605\) | 6.73833 | 0.273952 | ||||||||
\(606\) | 65.0722 | 2.64338 | ||||||||
\(607\) | −1.25150 | −0.0507969 | −0.0253985 | − | 0.999677i | \(-0.508085\pi\) | ||||
−0.0253985 | + | 0.999677i | \(0.508085\pi\) | |||||||
\(608\) | −182.971 | −7.42044 | ||||||||
\(609\) | −47.0221 | −1.90543 | ||||||||
\(610\) | 84.9077 | 3.43781 | ||||||||
\(611\) | −4.07002 | −0.164655 | ||||||||
\(612\) | −26.6451 | −1.07707 | ||||||||
\(613\) | 10.9114 | 0.440709 | 0.220355 | − | 0.975420i | \(-0.429279\pi\) | ||||
0.220355 | + | 0.975420i | \(0.429279\pi\) | |||||||
\(614\) | −53.1029 | −2.14306 | ||||||||
\(615\) | −19.3613 | −0.780722 | ||||||||
\(616\) | 99.0288 | 3.98999 | ||||||||
\(617\) | −0.774334 | −0.0311735 | −0.0155867 | − | 0.999879i | \(-0.504962\pi\) | ||||
−0.0155867 | + | 0.999879i | \(0.504962\pi\) | |||||||
\(618\) | 121.117 | 4.87205 | ||||||||
\(619\) | 21.4067 | 0.860407 | 0.430203 | − | 0.902732i | \(-0.358442\pi\) | ||||
0.430203 | + | 0.902732i | \(0.358442\pi\) | |||||||
\(620\) | 127.309 | 5.11285 | ||||||||
\(621\) | −14.4756 | −0.580888 | ||||||||
\(622\) | −2.72018 | −0.109069 | ||||||||
\(623\) | 23.4466 | 0.939369 | ||||||||
\(624\) | −20.4208 | −0.817485 | ||||||||
\(625\) | −25.0138 | −1.00055 | ||||||||
\(626\) | 7.74506 | 0.309555 | ||||||||
\(627\) | −45.8845 | −1.83245 | ||||||||
\(628\) | 15.7413 | 0.628147 | ||||||||
\(629\) | 5.50247 | 0.219398 | ||||||||
\(630\) | −81.4318 | −3.24432 | ||||||||
\(631\) | −28.2046 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(632\) | −75.7043 | −3.01135 | ||||||||
\(633\) | −39.0645 | −1.55267 | ||||||||
\(634\) | −77.1852 | −3.06542 | ||||||||
\(635\) | −4.94799 | −0.196355 | ||||||||
\(636\) | −88.8032 | −3.52128 | ||||||||
\(637\) | 1.57075 | 0.0622354 | ||||||||
\(638\) | 43.0003 | 1.70240 | ||||||||
\(639\) | −28.2663 | −1.11820 | ||||||||
\(640\) | 158.963 | 6.28358 | ||||||||
\(641\) | 39.9342 | 1.57731 | 0.788653 | − | 0.614838i | \(-0.210779\pi\) | ||||
0.788653 | + | 0.614838i | \(0.210779\pi\) | |||||||
\(642\) | −95.7808 | −3.78017 | ||||||||
\(643\) | 23.2143 | 0.915483 | 0.457742 | − | 0.889085i | \(-0.348658\pi\) | ||||
0.457742 | + | 0.889085i | \(0.348658\pi\) | |||||||
\(644\) | −107.154 | −4.22246 | ||||||||
\(645\) | −6.69102 | −0.263459 | ||||||||
\(646\) | 19.7828 | 0.778345 | ||||||||
\(647\) | 7.65966 | 0.301132 | 0.150566 | − | 0.988600i | \(-0.451890\pi\) | ||||
0.150566 | + | 0.988600i | \(0.451890\pi\) | |||||||
\(648\) | 54.8223 | 2.15362 | ||||||||
\(649\) | −7.56920 | −0.297117 | ||||||||
\(650\) | −0.00325415 | −0.000127638 0 | ||||||||
\(651\) | −84.4650 | −3.31044 | ||||||||
\(652\) | −8.44308 | −0.330657 | ||||||||
\(653\) | 36.0850 | 1.41211 | 0.706057 | − | 0.708155i | \(-0.250472\pi\) | ||||
0.706057 | + | 0.708155i | \(0.250472\pi\) | |||||||
\(654\) | 77.3129 | 3.02318 | ||||||||
\(655\) | −32.6944 | −1.27748 | ||||||||
\(656\) | −59.9521 | −2.34074 | ||||||||
\(657\) | −57.7451 | −2.25285 | ||||||||
\(658\) | −88.1801 | −3.43762 | ||||||||
\(659\) | 29.8589 | 1.16314 | 0.581569 | − | 0.813497i | \(-0.302439\pi\) | ||||
0.581569 | + | 0.813497i | \(0.302439\pi\) | |||||||
\(660\) | 97.2701 | 3.78624 | ||||||||
\(661\) | −24.8293 | −0.965749 | −0.482875 | − | 0.875689i | \(-0.660407\pi\) | ||||
−0.482875 | + | 0.875689i | \(0.660407\pi\) | |||||||
\(662\) | −51.1856 | −1.98938 | ||||||||
\(663\) | 1.28424 | 0.0498757 | ||||||||
\(664\) | 104.124 | 4.04078 | ||||||||
\(665\) | 45.0089 | 1.74537 | ||||||||
\(666\) | 53.1976 | 2.06136 | ||||||||
\(667\) | −30.5563 | −1.18314 | ||||||||
\(668\) | 106.165 | 4.10763 | ||||||||
\(669\) | −35.1152 | −1.35763 | ||||||||
\(670\) | 80.8324 | 3.12283 | ||||||||
\(671\) | 38.3503 | 1.48050 | ||||||||
\(672\) | −257.343 | −9.92724 | ||||||||
\(673\) | −39.9498 | −1.53995 | −0.769975 | − | 0.638074i | \(-0.779732\pi\) | ||||
−0.769975 | + | 0.638074i | \(0.779732\pi\) | |||||||
\(674\) | 28.5072 | 1.09806 | ||||||||
\(675\) | −0.00709048 | −0.000272913 0 | ||||||||
\(676\) | −74.6995 | −2.87306 | ||||||||
\(677\) | 28.6722 | 1.10196 | 0.550981 | − | 0.834518i | \(-0.314254\pi\) | ||||
0.550981 | + | 0.834518i | \(0.314254\pi\) | |||||||
\(678\) | 24.9905 | 0.959753 | ||||||||
\(679\) | −45.7922 | −1.75734 | ||||||||
\(680\) | −27.5412 | −1.05616 | ||||||||
\(681\) | 42.6559 | 1.63458 | ||||||||
\(682\) | 77.2407 | 2.95770 | ||||||||
\(683\) | 2.91588 | 0.111573 | 0.0557865 | − | 0.998443i | \(-0.482233\pi\) | ||||
0.0557865 | + | 0.998443i | \(0.482233\pi\) | |||||||
\(684\) | 142.382 | 5.44413 | ||||||||
\(685\) | −1.74286 | −0.0665913 | ||||||||
\(686\) | −30.0735 | −1.14821 | ||||||||
\(687\) | −22.7494 | −0.867944 | ||||||||
\(688\) | −20.7187 | −0.789894 | ||||||||
\(689\) | 2.43935 | 0.0929320 | ||||||||
\(690\) | −92.8483 | −3.53468 | ||||||||
\(691\) | −39.1964 | −1.49110 | −0.745550 | − | 0.666449i | \(-0.767813\pi\) | ||||
−0.745550 | + | 0.666449i | \(0.767813\pi\) | |||||||
\(692\) | 71.8598 | 2.73170 | ||||||||
\(693\) | −36.7803 | −1.39717 | ||||||||
\(694\) | 42.9703 | 1.63113 | ||||||||
\(695\) | −9.85674 | −0.373888 | ||||||||
\(696\) | −153.754 | −5.82802 | ||||||||
\(697\) | 3.77032 | 0.142811 | ||||||||
\(698\) | 66.7655 | 2.52711 | ||||||||
\(699\) | 23.7651 | 0.898877 | ||||||||
\(700\) | −0.0524863 | −0.00198380 | ||||||||
\(701\) | 9.94840 | 0.375746 | 0.187873 | − | 0.982193i | \(-0.439841\pi\) | ||||
0.187873 | + | 0.982193i | \(0.439841\pi\) | |||||||
\(702\) | 3.04668 | 0.114990 | ||||||||
\(703\) | −29.4033 | −1.10897 | ||||||||
\(704\) | 131.939 | 4.97263 | ||||||||
\(705\) | −56.8814 | −2.14228 | ||||||||
\(706\) | −3.88154 | −0.146084 | ||||||||
\(707\) | −28.8304 | −1.08428 | ||||||||
\(708\) | 41.2119 | 1.54884 | ||||||||
\(709\) | 0.345603 | 0.0129794 | 0.00648970 | − | 0.999979i | \(-0.497934\pi\) | ||||
0.00648970 | + | 0.999979i | \(0.497934\pi\) | |||||||
\(710\) | −44.4890 | −1.66964 | ||||||||
\(711\) | 28.1173 | 1.05448 | ||||||||
\(712\) | 76.6661 | 2.87318 | ||||||||
\(713\) | −54.8877 | −2.05556 | ||||||||
\(714\) | 27.8240 | 1.04129 | ||||||||
\(715\) | −2.67193 | −0.0999247 | ||||||||
\(716\) | −31.1391 | −1.16372 | ||||||||
\(717\) | 62.2500 | 2.32477 | ||||||||
\(718\) | −54.2226 | −2.02357 | ||||||||
\(719\) | −16.5347 | −0.616641 | −0.308320 | − | 0.951283i | \(-0.599767\pi\) | ||||
−0.308320 | + | 0.951283i | \(0.599767\pi\) | |||||||
\(720\) | −162.654 | −6.06175 | ||||||||
\(721\) | −53.6612 | −1.99845 | ||||||||
\(722\) | −52.5595 | −1.95606 | ||||||||
\(723\) | −45.5144 | −1.69270 | ||||||||
\(724\) | 148.385 | 5.51469 | ||||||||
\(725\) | −0.0149671 | −0.000555864 0 | ||||||||
\(726\) | −22.2593 | −0.826120 | ||||||||
\(727\) | −4.24350 | −0.157383 | −0.0786914 | − | 0.996899i | \(-0.525074\pi\) | ||||
−0.0786914 | + | 0.996899i | \(0.525074\pi\) | |||||||
\(728\) | 14.8108 | 0.548926 | ||||||||
\(729\) | −40.7763 | −1.51023 | ||||||||
\(730\) | −90.8864 | −3.36386 | ||||||||
\(731\) | 1.30298 | 0.0481923 | ||||||||
\(732\) | −208.805 | −7.71765 | ||||||||
\(733\) | 44.2526 | 1.63451 | 0.817254 | − | 0.576277i | \(-0.195495\pi\) | ||||
0.817254 | + | 0.576277i | \(0.195495\pi\) | |||||||
\(734\) | 10.5517 | 0.389471 | ||||||||
\(735\) | 21.9523 | 0.809724 | ||||||||
\(736\) | −167.229 | −6.16414 | ||||||||
\(737\) | 36.5096 | 1.34485 | ||||||||
\(738\) | 36.4512 | 1.34179 | ||||||||
\(739\) | −33.8978 | −1.24695 | −0.623474 | − | 0.781844i | \(-0.714279\pi\) | ||||
−0.623474 | + | 0.781844i | \(0.714279\pi\) | |||||||
\(740\) | 62.3318 | 2.29136 | ||||||||
\(741\) | −6.86253 | −0.252101 | ||||||||
\(742\) | 52.8505 | 1.94020 | ||||||||
\(743\) | −41.5621 | −1.52476 | −0.762382 | − | 0.647127i | \(-0.775970\pi\) | ||||
−0.762382 | + | 0.647127i | \(0.775970\pi\) | |||||||
\(744\) | −276.185 | −10.1254 | ||||||||
\(745\) | 41.7188 | 1.52846 | ||||||||
\(746\) | −59.3022 | −2.17121 | ||||||||
\(747\) | −38.6726 | −1.41496 | ||||||||
\(748\) | −18.9419 | −0.692584 | ||||||||
\(749\) | 42.4358 | 1.55057 | ||||||||
\(750\) | 82.5847 | 3.01557 | ||||||||
\(751\) | −27.6375 | −1.00851 | −0.504253 | − | 0.863556i | \(-0.668232\pi\) | ||||
−0.504253 | + | 0.863556i | \(0.668232\pi\) | |||||||
\(752\) | −176.133 | −6.42291 | ||||||||
\(753\) | −31.5189 | −1.14861 | ||||||||
\(754\) | 6.43116 | 0.234209 | ||||||||
\(755\) | 33.4436 | 1.21714 | ||||||||
\(756\) | 49.1400 | 1.78721 | ||||||||
\(757\) | −45.0284 | −1.63658 | −0.818292 | − | 0.574803i | \(-0.805079\pi\) | ||||
−0.818292 | + | 0.574803i | \(0.805079\pi\) | |||||||
\(758\) | 96.7790 | 3.51517 | ||||||||
\(759\) | −41.9369 | −1.52221 | ||||||||
\(760\) | 147.171 | 5.33845 | ||||||||
\(761\) | 26.9088 | 0.975444 | 0.487722 | − | 0.872999i | \(-0.337828\pi\) | ||||
0.487722 | + | 0.872999i | \(0.337828\pi\) | |||||||
\(762\) | 16.3451 | 0.592121 | ||||||||
\(763\) | −34.2536 | −1.24006 | ||||||||
\(764\) | −100.076 | −3.62063 | ||||||||
\(765\) | 10.2291 | 0.369834 | ||||||||
\(766\) | −60.9422 | −2.20193 | ||||||||
\(767\) | −1.13206 | −0.0408762 | ||||||||
\(768\) | −278.519 | −10.0502 | ||||||||
\(769\) | −23.1620 | −0.835243 | −0.417622 | − | 0.908621i | \(-0.637136\pi\) | ||||
−0.417622 | + | 0.908621i | \(0.637136\pi\) | |||||||
\(770\) | −57.8895 | −2.08619 | ||||||||
\(771\) | −0.0700380 | −0.00252236 | ||||||||
\(772\) | 39.1976 | 1.41075 | ||||||||
\(773\) | −37.8677 | −1.36201 | −0.681003 | − | 0.732281i | \(-0.738456\pi\) | ||||
−0.681003 | + | 0.732281i | \(0.738456\pi\) | |||||||
\(774\) | 12.5971 | 0.452793 | ||||||||
\(775\) | −0.0268851 | −0.000965743 0 | ||||||||
\(776\) | −149.732 | −5.37507 | ||||||||
\(777\) | −41.3550 | −1.48360 | ||||||||
\(778\) | −26.8843 | −0.963847 | ||||||||
\(779\) | −20.1473 | −0.721851 | ||||||||
\(780\) | 14.5478 | 0.520895 | ||||||||
\(781\) | −20.0944 | −0.719033 | ||||||||
\(782\) | 18.0808 | 0.646569 | ||||||||
\(783\) | 14.0129 | 0.500779 | ||||||||
\(784\) | 67.9753 | 2.42769 | ||||||||
\(785\) | −6.04311 | −0.215688 | ||||||||
\(786\) | 108.002 | 3.85231 | ||||||||
\(787\) | −31.8704 | −1.13606 | −0.568029 | − | 0.823009i | \(-0.692294\pi\) | ||||
−0.568029 | + | 0.823009i | \(0.692294\pi\) | |||||||
\(788\) | −3.28209 | −0.116920 | ||||||||
\(789\) | −32.1340 | −1.14400 | ||||||||
\(790\) | 44.2546 | 1.57451 | ||||||||
\(791\) | −11.0721 | −0.393677 | ||||||||
\(792\) | −120.265 | −4.27343 | ||||||||
\(793\) | 5.73571 | 0.203681 | ||||||||
\(794\) | 73.3966 | 2.60475 | ||||||||
\(795\) | 34.0917 | 1.20911 | ||||||||
\(796\) | 64.5772 | 2.28888 | ||||||||
\(797\) | 47.5733 | 1.68513 | 0.842567 | − | 0.538592i | \(-0.181043\pi\) | ||||
0.842567 | + | 0.538592i | \(0.181043\pi\) | |||||||
\(798\) | −148.682 | −5.26328 | ||||||||
\(799\) | 11.0768 | 0.391869 | ||||||||
\(800\) | −0.0819123 | −0.00289604 | ||||||||
\(801\) | −28.4746 | −1.00610 | ||||||||
\(802\) | −66.4346 | −2.34589 | ||||||||
\(803\) | −41.0507 | −1.44865 | ||||||||
\(804\) | −198.783 | −7.01054 | ||||||||
\(805\) | 41.1366 | 1.44987 | ||||||||
\(806\) | 11.5522 | 0.406908 | ||||||||
\(807\) | −28.3183 | −0.996852 | ||||||||
\(808\) | −94.2700 | −3.31641 | ||||||||
\(809\) | −16.3622 | −0.575263 | −0.287631 | − | 0.957741i | \(-0.592868\pi\) | ||||
−0.287631 | + | 0.957741i | \(0.592868\pi\) | |||||||
\(810\) | −32.0476 | −1.12604 | ||||||||
\(811\) | −9.85742 | −0.346141 | −0.173070 | − | 0.984909i | \(-0.555369\pi\) | ||||
−0.173070 | + | 0.984909i | \(0.555369\pi\) | |||||||
\(812\) | 103.728 | 3.64015 | ||||||||
\(813\) | 41.4986 | 1.45542 | ||||||||
\(814\) | 37.8179 | 1.32552 | ||||||||
\(815\) | 3.24131 | 0.113538 | ||||||||
\(816\) | 55.5763 | 1.94556 | ||||||||
\(817\) | −6.96265 | −0.243592 | ||||||||
\(818\) | −96.9068 | −3.38827 | ||||||||
\(819\) | −5.50090 | −0.192217 | ||||||||
\(820\) | 42.7100 | 1.49150 | ||||||||
\(821\) | 4.40351 | 0.153684 | 0.0768418 | − | 0.997043i | \(-0.475516\pi\) | ||||
0.0768418 | + | 0.997043i | \(0.475516\pi\) | |||||||
\(822\) | 5.75734 | 0.200810 | ||||||||
\(823\) | −9.28162 | −0.323537 | −0.161768 | − | 0.986829i | \(-0.551720\pi\) | ||||
−0.161768 | + | 0.986829i | \(0.551720\pi\) | |||||||
\(824\) | −175.462 | −6.11252 | ||||||||
\(825\) | −0.0205416 | −0.000715165 0 | ||||||||
\(826\) | −24.5269 | −0.853399 | ||||||||
\(827\) | −14.3120 | −0.497677 | −0.248839 | − | 0.968545i | \(-0.580049\pi\) | ||||
−0.248839 | + | 0.968545i | \(0.580049\pi\) | |||||||
\(828\) | 130.133 | 4.52242 | ||||||||
\(829\) | 13.4431 | 0.466899 | 0.233450 | − | 0.972369i | \(-0.424999\pi\) | ||||
0.233450 | + | 0.972369i | \(0.424999\pi\) | |||||||
\(830\) | −60.8678 | −2.11275 | ||||||||
\(831\) | 60.5750 | 2.10132 | ||||||||
\(832\) | 19.7329 | 0.684115 | ||||||||
\(833\) | −4.27489 | −0.148116 | ||||||||
\(834\) | 32.5606 | 1.12748 | ||||||||
\(835\) | −40.7568 | −1.41045 | ||||||||
\(836\) | 101.219 | 3.50073 | ||||||||
\(837\) | 25.1711 | 0.870040 | ||||||||
\(838\) | 100.917 | 3.48610 | ||||||||
\(839\) | 27.4806 | 0.948735 | 0.474367 | − | 0.880327i | \(-0.342677\pi\) | ||||
0.474367 | + | 0.880327i | \(0.342677\pi\) | |||||||
\(840\) | 206.992 | 7.14190 | ||||||||
\(841\) | 0.579402 | 0.0199794 | ||||||||
\(842\) | 38.3141 | 1.32039 | ||||||||
\(843\) | −29.1393 | −1.00361 | ||||||||
\(844\) | 86.1743 | 2.96624 | ||||||||
\(845\) | 28.6773 | 0.986528 | ||||||||
\(846\) | 107.090 | 3.68182 | ||||||||
\(847\) | 9.86202 | 0.338863 | ||||||||
\(848\) | 105.565 | 3.62511 | ||||||||
\(849\) | 17.0145 | 0.583936 | ||||||||
\(850\) | 0.00885636 | 0.000303771 0 | ||||||||
\(851\) | −26.8736 | −0.921216 | ||||||||
\(852\) | 109.407 | 3.74823 | ||||||||
\(853\) | 29.0153 | 0.993466 | 0.496733 | − | 0.867903i | \(-0.334533\pi\) | ||||
0.496733 | + | 0.867903i | \(0.334533\pi\) | |||||||
\(854\) | 124.268 | 4.25238 | ||||||||
\(855\) | −54.6608 | −1.86936 | ||||||||
\(856\) | 138.757 | 4.74263 | ||||||||
\(857\) | 36.9710 | 1.26291 | 0.631453 | − | 0.775414i | \(-0.282459\pi\) | ||||
0.631453 | + | 0.775414i | \(0.282459\pi\) | |||||||
\(858\) | 8.82643 | 0.301329 | ||||||||
\(859\) | −32.4394 | −1.10682 | −0.553408 | − | 0.832910i | \(-0.686673\pi\) | ||||
−0.553408 | + | 0.832910i | \(0.686673\pi\) | |||||||
\(860\) | 14.7601 | 0.503314 | ||||||||
\(861\) | −28.3366 | −0.965709 | ||||||||
\(862\) | −86.1965 | −2.93587 | ||||||||
\(863\) | 42.9190 | 1.46098 | 0.730491 | − | 0.682923i | \(-0.239291\pi\) | ||||
0.730491 | + | 0.682923i | \(0.239291\pi\) | |||||||
\(864\) | 76.6899 | 2.60904 | ||||||||
\(865\) | −27.5871 | −0.937989 | ||||||||
\(866\) | −6.00287 | −0.203986 | ||||||||
\(867\) | 41.4040 | 1.40615 | ||||||||
\(868\) | 186.326 | 6.32430 | ||||||||
\(869\) | 19.9885 | 0.678063 | ||||||||
\(870\) | 89.8800 | 3.04722 | ||||||||
\(871\) | 5.46041 | 0.185019 | ||||||||
\(872\) | −112.003 | −3.79290 | ||||||||
\(873\) | 55.6121 | 1.88218 | ||||||||
\(874\) | −96.6177 | −3.26814 | ||||||||
\(875\) | −36.5893 | −1.23694 | ||||||||
\(876\) | 223.508 | 7.55163 | ||||||||
\(877\) | 18.1102 | 0.611538 | 0.305769 | − | 0.952106i | \(-0.401086\pi\) | ||||
0.305769 | + | 0.952106i | \(0.401086\pi\) | |||||||
\(878\) | 17.0266 | 0.574621 | ||||||||
\(879\) | −20.8635 | −0.703708 | ||||||||
\(880\) | −115.630 | −3.89788 | ||||||||
\(881\) | 4.31254 | 0.145293 | 0.0726466 | − | 0.997358i | \(-0.476855\pi\) | ||||
0.0726466 | + | 0.997358i | \(0.476855\pi\) | |||||||
\(882\) | −41.3293 | −1.39163 | ||||||||
\(883\) | 15.1311 | 0.509202 | 0.254601 | − | 0.967046i | \(-0.418056\pi\) | ||||
0.254601 | + | 0.967046i | \(0.418056\pi\) | |||||||
\(884\) | −2.83297 | −0.0952830 | ||||||||
\(885\) | −15.8213 | −0.531827 | ||||||||
\(886\) | 91.7957 | 3.08394 | ||||||||
\(887\) | 12.9405 | 0.434500 | 0.217250 | − | 0.976116i | \(-0.430291\pi\) | ||||
0.217250 | + | 0.976116i | \(0.430291\pi\) | |||||||
\(888\) | −135.223 | −4.53779 | ||||||||
\(889\) | −7.24173 | −0.242880 | ||||||||
\(890\) | −44.8169 | −1.50226 | ||||||||
\(891\) | −14.4750 | −0.484929 | ||||||||
\(892\) | 77.4623 | 2.59363 | ||||||||
\(893\) | −59.1906 | −1.98074 | ||||||||
\(894\) | −137.813 | −4.60917 | ||||||||
\(895\) | 11.9543 | 0.399590 | ||||||||
\(896\) | 232.654 | 7.77243 | ||||||||
\(897\) | −6.27211 | −0.209420 | ||||||||
\(898\) | 0.0713692 | 0.00238162 | ||||||||
\(899\) | 53.1330 | 1.77208 | ||||||||
\(900\) | 0.0637417 | 0.00212472 | ||||||||
\(901\) | −6.63885 | −0.221172 | ||||||||
\(902\) | 25.9130 | 0.862808 | ||||||||
\(903\) | −9.79278 | −0.325883 | ||||||||
\(904\) | −36.2036 | −1.20412 | ||||||||
\(905\) | −56.9653 | −1.89359 | ||||||||
\(906\) | −110.477 | −3.67035 | ||||||||
\(907\) | −45.0235 | −1.49498 | −0.747490 | − | 0.664273i | \(-0.768741\pi\) | ||||
−0.747490 | + | 0.664273i | \(0.768741\pi\) | |||||||
\(908\) | −94.0968 | −3.12271 | ||||||||
\(909\) | 35.0128 | 1.16130 | ||||||||
\(910\) | −8.65800 | −0.287010 | ||||||||
\(911\) | −48.4297 | −1.60455 | −0.802274 | − | 0.596956i | \(-0.796377\pi\) | ||||
−0.802274 | + | 0.596956i | \(0.796377\pi\) | |||||||
\(912\) | −296.981 | −9.83402 | ||||||||
\(913\) | −27.4922 | −0.909859 | ||||||||
\(914\) | −26.1956 | −0.866474 | ||||||||
\(915\) | 80.1605 | 2.65003 | ||||||||
\(916\) | 50.1841 | 1.65813 | ||||||||
\(917\) | −47.8506 | −1.58017 | ||||||||
\(918\) | −8.29172 | −0.273668 | ||||||||
\(919\) | 2.26181 | 0.0746101 | 0.0373050 | − | 0.999304i | \(-0.488123\pi\) | ||||
0.0373050 | + | 0.999304i | \(0.488123\pi\) | |||||||
\(920\) | 134.509 | 4.43464 | ||||||||
\(921\) | −50.1340 | −1.65197 | ||||||||
\(922\) | 6.99105 | 0.230238 | ||||||||
\(923\) | −3.00533 | −0.0989217 | ||||||||
\(924\) | 142.362 | 4.68336 | ||||||||
\(925\) | −0.0131633 | −0.000432806 0 | ||||||||
\(926\) | 11.4380 | 0.375875 | ||||||||
\(927\) | 65.1685 | 2.14042 | ||||||||
\(928\) | 161.883 | 5.31406 | ||||||||
\(929\) | 46.4296 | 1.52331 | 0.761653 | − | 0.647985i | \(-0.224388\pi\) | ||||
0.761653 | + | 0.647985i | \(0.224388\pi\) | |||||||
\(930\) | 161.450 | 5.29415 | ||||||||
\(931\) | 22.8435 | 0.748666 | ||||||||
\(932\) | −52.4246 | −1.71722 | ||||||||
\(933\) | −2.56810 | −0.0840758 | ||||||||
\(934\) | 27.7547 | 0.908161 | ||||||||
\(935\) | 7.27182 | 0.237814 | ||||||||
\(936\) | −17.9869 | −0.587921 | ||||||||
\(937\) | −25.9335 | −0.847210 | −0.423605 | − | 0.905847i | \(-0.639236\pi\) | ||||
−0.423605 | + | 0.905847i | \(0.639236\pi\) | |||||||
\(938\) | 118.304 | 3.86276 | ||||||||
\(939\) | 7.31204 | 0.238619 | ||||||||
\(940\) | 125.478 | 4.09263 | ||||||||
\(941\) | 22.6401 | 0.738046 | 0.369023 | − | 0.929420i | \(-0.379692\pi\) | ||||
0.369023 | + | 0.929420i | \(0.379692\pi\) | |||||||
\(942\) | 19.9628 | 0.650422 | ||||||||
\(943\) | −18.4139 | −0.599640 | ||||||||
\(944\) | −48.9906 | −1.59451 | ||||||||
\(945\) | −18.8649 | −0.613676 | ||||||||
\(946\) | 8.95521 | 0.291159 | ||||||||
\(947\) | 13.5891 | 0.441587 | 0.220793 | − | 0.975321i | \(-0.429135\pi\) | ||||
0.220793 | + | 0.975321i | \(0.429135\pi\) | |||||||
\(948\) | −108.831 | −3.53466 | ||||||||
\(949\) | −6.13958 | −0.199299 | ||||||||
\(950\) | −0.0473254 | −0.00153544 | ||||||||
\(951\) | −72.8698 | −2.36297 | ||||||||
\(952\) | −40.3086 | −1.30641 | ||||||||
\(953\) | 27.6601 | 0.895997 | 0.447999 | − | 0.894034i | \(-0.352137\pi\) | ||||
0.447999 | + | 0.894034i | \(0.352137\pi\) | |||||||
\(954\) | −64.1839 | −2.07803 | ||||||||
\(955\) | 38.4194 | 1.24322 | ||||||||
\(956\) | −137.321 | −4.44126 | ||||||||
\(957\) | 40.5962 | 1.31229 | ||||||||
\(958\) | −0.137749 | −0.00445046 | ||||||||
\(959\) | −2.55080 | −0.0823697 | ||||||||
\(960\) | 275.781 | 8.90080 | ||||||||
\(961\) | 64.4419 | 2.07877 | ||||||||
\(962\) | 5.65608 | 0.182359 | ||||||||
\(963\) | −51.5359 | −1.66072 | ||||||||
\(964\) | 100.402 | 3.23375 | ||||||||
\(965\) | −15.0480 | −0.484413 | ||||||||
\(966\) | −135.890 | −4.37219 | ||||||||
\(967\) | −55.9798 | −1.80019 | −0.900094 | − | 0.435695i | \(-0.856503\pi\) | ||||
−0.900094 | + | 0.435695i | \(0.856503\pi\) | |||||||
\(968\) | 32.2470 | 1.03646 | ||||||||
\(969\) | 18.6768 | 0.599984 | ||||||||
\(970\) | 87.5292 | 2.81039 | ||||||||
\(971\) | 5.85159 | 0.187786 | 0.0938932 | − | 0.995582i | \(-0.470069\pi\) | ||||
0.0938932 | + | 0.995582i | \(0.470069\pi\) | |||||||
\(972\) | 123.845 | 3.97234 | ||||||||
\(973\) | −14.4260 | −0.462478 | ||||||||
\(974\) | −32.1176 | −1.02911 | ||||||||
\(975\) | −0.00307221 | −9.83896e−5 0 | ||||||||
\(976\) | 248.217 | 7.94523 | ||||||||
\(977\) | −3.14161 | −0.100509 | −0.0502545 | − | 0.998736i | \(-0.516003\pi\) | ||||
−0.0502545 | + | 0.998736i | \(0.516003\pi\) | |||||||
\(978\) | −10.7073 | −0.342382 | ||||||||
\(979\) | −20.2425 | −0.646952 | ||||||||
\(980\) | −48.4258 | −1.54690 | ||||||||
\(981\) | 41.5991 | 1.32816 | ||||||||
\(982\) | 17.0214 | 0.543174 | ||||||||
\(983\) | −41.9970 | −1.33950 | −0.669748 | − | 0.742588i | \(-0.733598\pi\) | ||||
−0.669748 | + | 0.742588i | \(0.733598\pi\) | |||||||
\(984\) | −92.6555 | −2.95375 | ||||||||
\(985\) | 1.26000 | 0.0401469 | ||||||||
\(986\) | −17.5028 | −0.557402 | ||||||||
\(987\) | −83.2499 | −2.64987 | ||||||||
\(988\) | 15.1384 | 0.481617 | ||||||||
\(989\) | −6.36363 | −0.202352 | ||||||||
\(990\) | 70.3035 | 2.23439 | ||||||||
\(991\) | −23.2422 | −0.738312 | −0.369156 | − | 0.929367i | \(-0.620353\pi\) | ||||
−0.369156 | + | 0.929367i | \(0.620353\pi\) | |||||||
\(992\) | 290.787 | 9.23251 | ||||||||
\(993\) | −48.3238 | −1.53351 | ||||||||
\(994\) | −65.1128 | −2.06525 | ||||||||
\(995\) | −24.7913 | −0.785937 | ||||||||
\(996\) | 149.686 | 4.74298 | ||||||||
\(997\) | 13.0472 | 0.413210 | 0.206605 | − | 0.978424i | \(-0.433758\pi\) | ||||
0.206605 | + | 0.978424i | \(0.433758\pi\) | |||||||
\(998\) | −43.5237 | −1.37772 | ||||||||
\(999\) | 12.3240 | 0.389915 |
(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 | 6037.2.a.a.1.3 | ✓ | 243 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6037.2.a.a.1.3 | ✓ | 243 | 1.1 | even | 1 | trivial |