Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(1\) |
Dimension: | \(108\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.23728 | −1.58199 | −0.790997 | − | 0.611819i | \(-0.790438\pi\) | ||||
−0.790997 | + | 0.611819i | \(0.790438\pi\) | |||||||
\(3\) | 2.31482 | 1.33646 | 0.668232 | − | 0.743953i | \(-0.267051\pi\) | ||||
0.668232 | + | 0.743953i | \(0.267051\pi\) | |||||||
\(4\) | 3.00542 | 1.50271 | ||||||||
\(5\) | −4.05108 | −1.81170 | −0.905848 | − | 0.423602i | \(-0.860766\pi\) | ||||
−0.905848 | + | 0.423602i | \(0.860766\pi\) | |||||||
\(6\) | −5.17891 | −2.11428 | ||||||||
\(7\) | −5.18040 | −1.95801 | −0.979004 | − | 0.203841i | \(-0.934657\pi\) | ||||
−0.979004 | + | 0.203841i | \(0.934657\pi\) | |||||||
\(8\) | −2.24940 | −0.795281 | ||||||||
\(9\) | 2.35841 | 0.786138 | ||||||||
\(10\) | 9.06339 | 2.86610 | ||||||||
\(11\) | 4.76756 | 1.43747 | 0.718737 | − | 0.695282i | \(-0.244720\pi\) | ||||
0.718737 | + | 0.695282i | \(0.244720\pi\) | |||||||
\(12\) | 6.95701 | 2.00832 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 11.5900 | 3.09756 | ||||||||
\(15\) | −9.37753 | −2.42127 | ||||||||
\(16\) | −0.978307 | −0.244577 | ||||||||
\(17\) | 2.33346 | 0.565947 | 0.282974 | − | 0.959128i | \(-0.408679\pi\) | ||||
0.282974 | + | 0.959128i | \(0.408679\pi\) | |||||||
\(18\) | −5.27643 | −1.24367 | ||||||||
\(19\) | −4.10318 | −0.941334 | −0.470667 | − | 0.882311i | \(-0.655987\pi\) | ||||
−0.470667 | + | 0.882311i | \(0.655987\pi\) | |||||||
\(20\) | −12.1752 | −2.72245 | ||||||||
\(21\) | −11.9917 | −2.61681 | ||||||||
\(22\) | −10.6664 | −2.27408 | ||||||||
\(23\) | −4.26438 | −0.889184 | −0.444592 | − | 0.895733i | \(-0.646651\pi\) | ||||
−0.444592 | + | 0.895733i | \(0.646651\pi\) | |||||||
\(24\) | −5.20696 | −1.06287 | ||||||||
\(25\) | 11.4112 | 2.28225 | ||||||||
\(26\) | 2.23728 | 0.438766 | ||||||||
\(27\) | −1.48516 | −0.285820 | ||||||||
\(28\) | −15.5693 | −2.94231 | ||||||||
\(29\) | 3.99786 | 0.742383 | 0.371192 | − | 0.928556i | \(-0.378949\pi\) | ||||
0.371192 | + | 0.928556i | \(0.378949\pi\) | |||||||
\(30\) | 20.9802 | 3.83043 | ||||||||
\(31\) | −2.65455 | −0.476772 | −0.238386 | − | 0.971171i | \(-0.576618\pi\) | ||||
−0.238386 | + | 0.971171i | \(0.576618\pi\) | |||||||
\(32\) | 6.68754 | 1.18220 | ||||||||
\(33\) | 11.0361 | 1.92113 | ||||||||
\(34\) | −5.22060 | −0.895326 | ||||||||
\(35\) | 20.9862 | 3.54732 | ||||||||
\(36\) | 7.08801 | 1.18134 | ||||||||
\(37\) | 10.7176 | 1.76197 | 0.880983 | − | 0.473148i | \(-0.156882\pi\) | ||||
0.880983 | + | 0.473148i | \(0.156882\pi\) | |||||||
\(38\) | 9.17996 | 1.48919 | ||||||||
\(39\) | −2.31482 | −0.370669 | ||||||||
\(40\) | 9.11248 | 1.44081 | ||||||||
\(41\) | −4.21707 | −0.658595 | −0.329298 | − | 0.944226i | \(-0.606812\pi\) | ||||
−0.329298 | + | 0.944226i | \(0.606812\pi\) | |||||||
\(42\) | 26.8288 | 4.13978 | ||||||||
\(43\) | 4.21943 | 0.643458 | 0.321729 | − | 0.946832i | \(-0.395736\pi\) | ||||
0.321729 | + | 0.946832i | \(0.395736\pi\) | |||||||
\(44\) | 14.3285 | 2.16010 | ||||||||
\(45\) | −9.55411 | −1.42424 | ||||||||
\(46\) | 9.54060 | 1.40668 | ||||||||
\(47\) | 2.37423 | 0.346317 | 0.173158 | − | 0.984894i | \(-0.444603\pi\) | ||||
0.173158 | + | 0.984894i | \(0.444603\pi\) | |||||||
\(48\) | −2.26461 | −0.326868 | ||||||||
\(49\) | 19.8366 | 2.83380 | ||||||||
\(50\) | −25.5301 | −3.61050 | ||||||||
\(51\) | 5.40155 | 0.756368 | ||||||||
\(52\) | −3.00542 | −0.416776 | ||||||||
\(53\) | 9.09971 | 1.24994 | 0.624970 | − | 0.780648i | \(-0.285111\pi\) | ||||
0.624970 | + | 0.780648i | \(0.285111\pi\) | |||||||
\(54\) | 3.32272 | 0.452165 | ||||||||
\(55\) | −19.3138 | −2.60427 | ||||||||
\(56\) | 11.6528 | 1.55717 | ||||||||
\(57\) | −9.49814 | −1.25806 | ||||||||
\(58\) | −8.94432 | −1.17445 | ||||||||
\(59\) | 2.78313 | 0.362333 | 0.181167 | − | 0.983452i | \(-0.442013\pi\) | ||||
0.181167 | + | 0.983452i | \(0.442013\pi\) | |||||||
\(60\) | −28.1834 | −3.63846 | ||||||||
\(61\) | 4.15230 | 0.531648 | 0.265824 | − | 0.964022i | \(-0.414356\pi\) | ||||
0.265824 | + | 0.964022i | \(0.414356\pi\) | |||||||
\(62\) | 5.93897 | 0.754250 | ||||||||
\(63\) | −12.2175 | −1.53926 | ||||||||
\(64\) | −13.0053 | −1.62566 | ||||||||
\(65\) | 4.05108 | 0.502474 | ||||||||
\(66\) | −24.6908 | −3.03922 | ||||||||
\(67\) | −4.83531 | −0.590727 | −0.295364 | − | 0.955385i | \(-0.595441\pi\) | ||||
−0.295364 | + | 0.955385i | \(0.595441\pi\) | |||||||
\(68\) | 7.01302 | 0.850453 | ||||||||
\(69\) | −9.87128 | −1.18836 | ||||||||
\(70\) | −46.9520 | −5.61184 | ||||||||
\(71\) | −12.3965 | −1.47119 | −0.735596 | − | 0.677421i | \(-0.763098\pi\) | ||||
−0.735596 | + | 0.677421i | \(0.763098\pi\) | |||||||
\(72\) | −5.30500 | −0.625201 | ||||||||
\(73\) | 5.46936 | 0.640141 | 0.320070 | − | 0.947394i | \(-0.396293\pi\) | ||||
0.320070 | + | 0.947394i | \(0.396293\pi\) | |||||||
\(74\) | −23.9783 | −2.78742 | ||||||||
\(75\) | 26.4150 | 3.05014 | ||||||||
\(76\) | −12.3318 | −1.41455 | ||||||||
\(77\) | −24.6979 | −2.81459 | ||||||||
\(78\) | 5.17891 | 0.586396 | ||||||||
\(79\) | −1.71267 | −0.192691 | −0.0963454 | − | 0.995348i | \(-0.530715\pi\) | ||||
−0.0963454 | + | 0.995348i | \(0.530715\pi\) | |||||||
\(80\) | 3.96320 | 0.443099 | ||||||||
\(81\) | −10.5131 | −1.16813 | ||||||||
\(82\) | 9.43475 | 1.04189 | ||||||||
\(83\) | 7.89643 | 0.866746 | 0.433373 | − | 0.901215i | \(-0.357323\pi\) | ||||
0.433373 | + | 0.901215i | \(0.357323\pi\) | |||||||
\(84\) | −36.0401 | −3.93230 | ||||||||
\(85\) | −9.45303 | −1.02532 | ||||||||
\(86\) | −9.44005 | −1.01795 | ||||||||
\(87\) | 9.25434 | 0.992169 | ||||||||
\(88\) | −10.7241 | −1.14320 | ||||||||
\(89\) | 12.6072 | 1.33636 | 0.668181 | − | 0.743999i | \(-0.267073\pi\) | ||||
0.668181 | + | 0.743999i | \(0.267073\pi\) | |||||||
\(90\) | 21.3752 | 2.25315 | ||||||||
\(91\) | 5.18040 | 0.543054 | ||||||||
\(92\) | −12.8162 | −1.33618 | ||||||||
\(93\) | −6.14482 | −0.637188 | ||||||||
\(94\) | −5.31181 | −0.547871 | ||||||||
\(95\) | 16.6223 | 1.70541 | ||||||||
\(96\) | 15.4805 | 1.57997 | ||||||||
\(97\) | −4.61728 | −0.468814 | −0.234407 | − | 0.972139i | \(-0.575315\pi\) | ||||
−0.234407 | + | 0.972139i | \(0.575315\pi\) | |||||||
\(98\) | −44.3799 | −4.48305 | ||||||||
\(99\) | 11.2439 | 1.13005 | ||||||||
\(100\) | 34.2955 | 3.42955 | ||||||||
\(101\) | −13.4320 | −1.33654 | −0.668268 | − | 0.743921i | \(-0.732964\pi\) | ||||
−0.668268 | + | 0.743921i | \(0.732964\pi\) | |||||||
\(102\) | −12.0848 | −1.19657 | ||||||||
\(103\) | −2.27315 | −0.223980 | −0.111990 | − | 0.993709i | \(-0.535722\pi\) | ||||
−0.111990 | + | 0.993709i | \(0.535722\pi\) | |||||||
\(104\) | 2.24940 | 0.220571 | ||||||||
\(105\) | 48.5794 | 4.74086 | ||||||||
\(106\) | −20.3586 | −1.97740 | ||||||||
\(107\) | 4.41560 | 0.426872 | 0.213436 | − | 0.976957i | \(-0.431534\pi\) | ||||
0.213436 | + | 0.976957i | \(0.431534\pi\) | |||||||
\(108\) | −4.46353 | −0.429503 | ||||||||
\(109\) | −10.1279 | −0.970078 | −0.485039 | − | 0.874492i | \(-0.661195\pi\) | ||||
−0.485039 | + | 0.874492i | \(0.661195\pi\) | |||||||
\(110\) | 43.2103 | 4.11994 | ||||||||
\(111\) | 24.8094 | 2.35481 | ||||||||
\(112\) | 5.06802 | 0.478883 | ||||||||
\(113\) | −7.44268 | −0.700148 | −0.350074 | − | 0.936722i | \(-0.613844\pi\) | ||||
−0.350074 | + | 0.936722i | \(0.613844\pi\) | |||||||
\(114\) | 21.2500 | 1.99024 | ||||||||
\(115\) | 17.2753 | 1.61093 | ||||||||
\(116\) | 12.0152 | 1.11559 | ||||||||
\(117\) | −2.35841 | −0.218035 | ||||||||
\(118\) | −6.22665 | −0.573209 | ||||||||
\(119\) | −12.0883 | −1.10813 | ||||||||
\(120\) | 21.0938 | 1.92559 | ||||||||
\(121\) | 11.7297 | 1.06633 | ||||||||
\(122\) | −9.28986 | −0.841064 | ||||||||
\(123\) | −9.76177 | −0.880189 | ||||||||
\(124\) | −7.97803 | −0.716449 | ||||||||
\(125\) | −25.9724 | −2.32304 | ||||||||
\(126\) | 27.3340 | 2.43511 | ||||||||
\(127\) | −13.7762 | −1.22244 | −0.611222 | − | 0.791459i | \(-0.709322\pi\) | ||||
−0.611222 | + | 0.791459i | \(0.709322\pi\) | |||||||
\(128\) | 15.7213 | 1.38958 | ||||||||
\(129\) | 9.76725 | 0.859959 | ||||||||
\(130\) | −9.06339 | −0.794912 | ||||||||
\(131\) | 1.68587 | 0.147295 | 0.0736477 | − | 0.997284i | \(-0.476536\pi\) | ||||
0.0736477 | + | 0.997284i | \(0.476536\pi\) | |||||||
\(132\) | 33.1680 | 2.88690 | ||||||||
\(133\) | 21.2561 | 1.84314 | ||||||||
\(134\) | 10.8179 | 0.934528 | ||||||||
\(135\) | 6.01651 | 0.517818 | ||||||||
\(136\) | −5.24887 | −0.450087 | ||||||||
\(137\) | −21.2511 | −1.81560 | −0.907800 | − | 0.419402i | \(-0.862240\pi\) | ||||
−0.907800 | + | 0.419402i | \(0.862240\pi\) | |||||||
\(138\) | 22.0848 | 1.87998 | ||||||||
\(139\) | 17.6191 | 1.49444 | 0.747218 | − | 0.664579i | \(-0.231389\pi\) | ||||
0.747218 | + | 0.664579i | \(0.231389\pi\) | |||||||
\(140\) | 63.0723 | 5.33058 | ||||||||
\(141\) | 5.49592 | 0.462840 | ||||||||
\(142\) | 27.7344 | 2.32742 | ||||||||
\(143\) | −4.76756 | −0.398684 | ||||||||
\(144\) | −2.30725 | −0.192271 | ||||||||
\(145\) | −16.1956 | −1.34497 | ||||||||
\(146\) | −12.2365 | −1.01270 | ||||||||
\(147\) | 45.9182 | 3.78727 | ||||||||
\(148\) | 32.2109 | 2.64772 | ||||||||
\(149\) | −15.4843 | −1.26852 | −0.634262 | − | 0.773118i | \(-0.718696\pi\) | ||||
−0.634262 | + | 0.773118i | \(0.718696\pi\) | |||||||
\(150\) | −59.0977 | −4.82531 | ||||||||
\(151\) | 13.7230 | 1.11676 | 0.558381 | − | 0.829585i | \(-0.311423\pi\) | ||||
0.558381 | + | 0.829585i | \(0.311423\pi\) | |||||||
\(152\) | 9.22968 | 0.748626 | ||||||||
\(153\) | 5.50326 | 0.444912 | ||||||||
\(154\) | 55.2561 | 4.45266 | ||||||||
\(155\) | 10.7538 | 0.863766 | ||||||||
\(156\) | −6.95701 | −0.557007 | ||||||||
\(157\) | 16.4529 | 1.31309 | 0.656543 | − | 0.754288i | \(-0.272018\pi\) | ||||
0.656543 | + | 0.754288i | \(0.272018\pi\) | |||||||
\(158\) | 3.83173 | 0.304836 | ||||||||
\(159\) | 21.0642 | 1.67050 | ||||||||
\(160\) | −27.0917 | −2.14179 | ||||||||
\(161\) | 22.0912 | 1.74103 | ||||||||
\(162\) | 23.5208 | 1.84797 | ||||||||
\(163\) | 9.61840 | 0.753371 | 0.376686 | − | 0.926341i | \(-0.377064\pi\) | ||||
0.376686 | + | 0.926341i | \(0.377064\pi\) | |||||||
\(164\) | −12.6740 | −0.989676 | ||||||||
\(165\) | −44.7080 | −3.48051 | ||||||||
\(166\) | −17.6665 | −1.37119 | ||||||||
\(167\) | 5.90000 | 0.456556 | 0.228278 | − | 0.973596i | \(-0.426690\pi\) | ||||
0.228278 | + | 0.973596i | \(0.426690\pi\) | |||||||
\(168\) | 26.9741 | 2.08110 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 21.1491 | 1.62206 | ||||||||
\(171\) | −9.67699 | −0.740018 | ||||||||
\(172\) | 12.6812 | 0.966929 | ||||||||
\(173\) | 10.1804 | 0.774001 | 0.387000 | − | 0.922080i | \(-0.373511\pi\) | ||||
0.387000 | + | 0.922080i | \(0.373511\pi\) | |||||||
\(174\) | −20.7045 | −1.56961 | ||||||||
\(175\) | −59.1148 | −4.46866 | ||||||||
\(176\) | −4.66414 | −0.351573 | ||||||||
\(177\) | 6.44247 | 0.484246 | ||||||||
\(178\) | −28.2058 | −2.11412 | ||||||||
\(179\) | −23.8854 | −1.78528 | −0.892639 | − | 0.450773i | \(-0.851149\pi\) | ||||
−0.892639 | + | 0.450773i | \(0.851149\pi\) | |||||||
\(180\) | −28.7141 | −2.14022 | ||||||||
\(181\) | −2.16112 | −0.160635 | −0.0803173 | − | 0.996769i | \(-0.525593\pi\) | ||||
−0.0803173 | + | 0.996769i | \(0.525593\pi\) | |||||||
\(182\) | −11.5900 | −0.859108 | ||||||||
\(183\) | 9.61185 | 0.710529 | ||||||||
\(184\) | 9.59227 | 0.707151 | ||||||||
\(185\) | −43.4179 | −3.19215 | ||||||||
\(186\) | 13.7477 | 1.00803 | ||||||||
\(187\) | 11.1249 | 0.813535 | ||||||||
\(188\) | 7.13554 | 0.520413 | ||||||||
\(189\) | 7.69374 | 0.559637 | ||||||||
\(190\) | −37.1887 | −2.69795 | ||||||||
\(191\) | −13.9001 | −1.00578 | −0.502888 | − | 0.864352i | \(-0.667729\pi\) | ||||
−0.502888 | + | 0.864352i | \(0.667729\pi\) | |||||||
\(192\) | −30.1049 | −2.17264 | ||||||||
\(193\) | −19.8790 | −1.43092 | −0.715461 | − | 0.698653i | \(-0.753783\pi\) | ||||
−0.715461 | + | 0.698653i | \(0.753783\pi\) | |||||||
\(194\) | 10.3302 | 0.741662 | ||||||||
\(195\) | 9.37753 | 0.671539 | ||||||||
\(196\) | 59.6171 | 4.25837 | ||||||||
\(197\) | −5.78525 | −0.412182 | −0.206091 | − | 0.978533i | \(-0.566074\pi\) | ||||
−0.206091 | + | 0.978533i | \(0.566074\pi\) | |||||||
\(198\) | −25.1557 | −1.78774 | ||||||||
\(199\) | 23.9044 | 1.69454 | 0.847268 | − | 0.531166i | \(-0.178246\pi\) | ||||
0.847268 | + | 0.531166i | \(0.178246\pi\) | |||||||
\(200\) | −25.6684 | −1.81503 | ||||||||
\(201\) | −11.1929 | −0.789486 | ||||||||
\(202\) | 30.0512 | 2.11439 | ||||||||
\(203\) | −20.7105 | −1.45359 | ||||||||
\(204\) | 16.2339 | 1.13660 | ||||||||
\(205\) | 17.0837 | 1.19317 | ||||||||
\(206\) | 5.08566 | 0.354335 | ||||||||
\(207\) | −10.0572 | −0.699021 | ||||||||
\(208\) | 0.978307 | 0.0678334 | ||||||||
\(209\) | −19.5622 | −1.35314 | ||||||||
\(210\) | −108.686 | −7.50002 | ||||||||
\(211\) | −22.8017 | −1.56974 | −0.784868 | − | 0.619663i | \(-0.787269\pi\) | ||||
−0.784868 | + | 0.619663i | \(0.787269\pi\) | |||||||
\(212\) | 27.3484 | 1.87830 | ||||||||
\(213\) | −28.6957 | −1.96620 | ||||||||
\(214\) | −9.87893 | −0.675310 | ||||||||
\(215\) | −17.0933 | −1.16575 | ||||||||
\(216\) | 3.34072 | 0.227307 | ||||||||
\(217\) | 13.7516 | 0.933523 | ||||||||
\(218\) | 22.6590 | 1.53466 | ||||||||
\(219\) | 12.6606 | 0.855525 | ||||||||
\(220\) | −58.0459 | −3.91346 | ||||||||
\(221\) | −2.33346 | −0.156965 | ||||||||
\(222\) | −55.5056 | −3.72529 | ||||||||
\(223\) | −9.12272 | −0.610903 | −0.305451 | − | 0.952208i | \(-0.598807\pi\) | ||||
−0.305451 | + | 0.952208i | \(0.598807\pi\) | |||||||
\(224\) | −34.6441 | −2.31476 | ||||||||
\(225\) | 26.9124 | 1.79416 | ||||||||
\(226\) | 16.6513 | 1.10763 | ||||||||
\(227\) | 18.0198 | 1.19602 | 0.598008 | − | 0.801490i | \(-0.295959\pi\) | ||||
0.598008 | + | 0.801490i | \(0.295959\pi\) | |||||||
\(228\) | −28.5459 | −1.89050 | ||||||||
\(229\) | −19.7012 | −1.30189 | −0.650946 | − | 0.759124i | \(-0.725628\pi\) | ||||
−0.650946 | + | 0.759124i | \(0.725628\pi\) | |||||||
\(230\) | −38.6497 | −2.54849 | ||||||||
\(231\) | −57.1713 | −3.76160 | ||||||||
\(232\) | −8.99276 | −0.590404 | ||||||||
\(233\) | −5.44325 | −0.356599 | −0.178300 | − | 0.983976i | \(-0.557060\pi\) | ||||
−0.178300 | + | 0.983976i | \(0.557060\pi\) | |||||||
\(234\) | 5.27643 | 0.344931 | ||||||||
\(235\) | −9.61818 | −0.627421 | ||||||||
\(236\) | 8.36448 | 0.544481 | ||||||||
\(237\) | −3.96454 | −0.257524 | ||||||||
\(238\) | 27.0448 | 1.75305 | ||||||||
\(239\) | 20.7066 | 1.33940 | 0.669701 | − | 0.742631i | \(-0.266422\pi\) | ||||
0.669701 | + | 0.742631i | \(0.266422\pi\) | |||||||
\(240\) | 9.17411 | 0.592186 | ||||||||
\(241\) | 17.3696 | 1.11887 | 0.559437 | − | 0.828873i | \(-0.311017\pi\) | ||||
0.559437 | + | 0.828873i | \(0.311017\pi\) | |||||||
\(242\) | −26.2425 | −1.68693 | ||||||||
\(243\) | −19.8806 | −1.27534 | ||||||||
\(244\) | 12.4794 | 0.798912 | ||||||||
\(245\) | −80.3595 | −5.13398 | ||||||||
\(246\) | 21.8398 | 1.39245 | ||||||||
\(247\) | 4.10318 | 0.261079 | ||||||||
\(248\) | 5.97114 | 0.379168 | ||||||||
\(249\) | 18.2789 | 1.15838 | ||||||||
\(250\) | 58.1075 | 3.67504 | ||||||||
\(251\) | 0.151593 | 0.00956849 | 0.00478424 | − | 0.999989i | \(-0.498477\pi\) | ||||
0.00478424 | + | 0.999989i | \(0.498477\pi\) | |||||||
\(252\) | −36.7187 | −2.31306 | ||||||||
\(253\) | −20.3307 | −1.27818 | ||||||||
\(254\) | 30.8213 | 1.93390 | ||||||||
\(255\) | −21.8821 | −1.37031 | ||||||||
\(256\) | −9.16248 | −0.572655 | ||||||||
\(257\) | −12.2224 | −0.762414 | −0.381207 | − | 0.924490i | \(-0.624492\pi\) | ||||
−0.381207 | + | 0.924490i | \(0.624492\pi\) | |||||||
\(258\) | −21.8521 | −1.36045 | ||||||||
\(259\) | −55.5216 | −3.44994 | ||||||||
\(260\) | 12.1752 | 0.755072 | ||||||||
\(261\) | 9.42860 | 0.583615 | ||||||||
\(262\) | −3.77177 | −0.233020 | ||||||||
\(263\) | 14.9432 | 0.921438 | 0.460719 | − | 0.887546i | \(-0.347592\pi\) | ||||
0.460719 | + | 0.887546i | \(0.347592\pi\) | |||||||
\(264\) | −24.8245 | −1.52784 | ||||||||
\(265\) | −36.8636 | −2.26451 | ||||||||
\(266\) | −47.5559 | −2.91584 | ||||||||
\(267\) | 29.1835 | 1.78600 | ||||||||
\(268\) | −14.5321 | −0.887691 | ||||||||
\(269\) | −6.31809 | −0.385221 | −0.192610 | − | 0.981275i | \(-0.561695\pi\) | ||||
−0.192610 | + | 0.981275i | \(0.561695\pi\) | |||||||
\(270\) | −13.4606 | −0.819186 | ||||||||
\(271\) | 4.57214 | 0.277738 | 0.138869 | − | 0.990311i | \(-0.455653\pi\) | ||||
0.138869 | + | 0.990311i | \(0.455653\pi\) | |||||||
\(272\) | −2.28284 | −0.138418 | ||||||||
\(273\) | 11.9917 | 0.725772 | ||||||||
\(274\) | 47.5446 | 2.87227 | ||||||||
\(275\) | 54.4038 | 3.28067 | ||||||||
\(276\) | −29.6673 | −1.78576 | ||||||||
\(277\) | 19.6717 | 1.18196 | 0.590978 | − | 0.806688i | \(-0.298742\pi\) | ||||
0.590978 | + | 0.806688i | \(0.298742\pi\) | |||||||
\(278\) | −39.4189 | −2.36419 | ||||||||
\(279\) | −6.26053 | −0.374808 | ||||||||
\(280\) | −47.2063 | −2.82112 | ||||||||
\(281\) | −14.7252 | −0.878431 | −0.439216 | − | 0.898382i | \(-0.644744\pi\) | ||||
−0.439216 | + | 0.898382i | \(0.644744\pi\) | |||||||
\(282\) | −12.2959 | −0.732211 | ||||||||
\(283\) | −12.9654 | −0.770713 | −0.385357 | − | 0.922768i | \(-0.625922\pi\) | ||||
−0.385357 | + | 0.922768i | \(0.625922\pi\) | |||||||
\(284\) | −37.2566 | −2.21077 | ||||||||
\(285\) | 38.4777 | 2.27922 | ||||||||
\(286\) | 10.6664 | 0.630716 | ||||||||
\(287\) | 21.8461 | 1.28953 | ||||||||
\(288\) | 15.7720 | 0.929372 | ||||||||
\(289\) | −11.5550 | −0.679704 | ||||||||
\(290\) | 36.2341 | 2.12774 | ||||||||
\(291\) | −10.6882 | −0.626554 | ||||||||
\(292\) | 16.4377 | 0.961945 | ||||||||
\(293\) | 7.55562 | 0.441404 | 0.220702 | − | 0.975341i | \(-0.429165\pi\) | ||||
0.220702 | + | 0.975341i | \(0.429165\pi\) | |||||||
\(294\) | −102.732 | −5.99144 | ||||||||
\(295\) | −11.2747 | −0.656438 | ||||||||
\(296\) | −24.1082 | −1.40126 | ||||||||
\(297\) | −7.08060 | −0.410858 | ||||||||
\(298\) | 34.6427 | 2.00680 | ||||||||
\(299\) | 4.26438 | 0.246615 | ||||||||
\(300\) | 79.3880 | 4.58347 | ||||||||
\(301\) | −21.8584 | −1.25990 | ||||||||
\(302\) | −30.7022 | −1.76671 | ||||||||
\(303\) | −31.0927 | −1.78623 | ||||||||
\(304\) | 4.01417 | 0.230228 | ||||||||
\(305\) | −16.8213 | −0.963185 | ||||||||
\(306\) | −12.3123 | −0.703849 | ||||||||
\(307\) | 25.8501 | 1.47534 | 0.737671 | − | 0.675160i | \(-0.235925\pi\) | ||||
0.737671 | + | 0.675160i | \(0.235925\pi\) | |||||||
\(308\) | −74.2275 | −4.22950 | ||||||||
\(309\) | −5.26194 | −0.299341 | ||||||||
\(310\) | −24.0592 | −1.36647 | ||||||||
\(311\) | −31.8760 | −1.80752 | −0.903761 | − | 0.428037i | \(-0.859205\pi\) | ||||
−0.903761 | + | 0.428037i | \(0.859205\pi\) | |||||||
\(312\) | 5.20696 | 0.294786 | ||||||||
\(313\) | 14.2861 | 0.807498 | 0.403749 | − | 0.914870i | \(-0.367707\pi\) | ||||
0.403749 | + | 0.914870i | \(0.367707\pi\) | |||||||
\(314\) | −36.8098 | −2.07730 | ||||||||
\(315\) | 49.4941 | 2.78868 | ||||||||
\(316\) | −5.14730 | −0.289558 | ||||||||
\(317\) | −19.0659 | −1.07085 | −0.535424 | − | 0.844583i | \(-0.679848\pi\) | ||||
−0.535424 | + | 0.844583i | \(0.679848\pi\) | |||||||
\(318\) | −47.1265 | −2.64273 | ||||||||
\(319\) | 19.0600 | 1.06716 | ||||||||
\(320\) | 52.6854 | 2.94520 | ||||||||
\(321\) | 10.2213 | 0.570500 | ||||||||
\(322\) | −49.4241 | −2.75430 | ||||||||
\(323\) | −9.57461 | −0.532745 | ||||||||
\(324\) | −31.5963 | −1.75535 | ||||||||
\(325\) | −11.4112 | −0.632981 | ||||||||
\(326\) | −21.5190 | −1.19183 | ||||||||
\(327\) | −23.4443 | −1.29648 | ||||||||
\(328\) | 9.48585 | 0.523769 | ||||||||
\(329\) | −12.2995 | −0.678091 | ||||||||
\(330\) | 100.024 | 5.50615 | ||||||||
\(331\) | 32.3698 | 1.77921 | 0.889604 | − | 0.456733i | \(-0.150981\pi\) | ||||
0.889604 | + | 0.456733i | \(0.150981\pi\) | |||||||
\(332\) | 23.7321 | 1.30247 | ||||||||
\(333\) | 25.2766 | 1.38515 | ||||||||
\(334\) | −13.2000 | −0.722269 | ||||||||
\(335\) | 19.5882 | 1.07022 | ||||||||
\(336\) | 11.7316 | 0.640010 | ||||||||
\(337\) | 0.342077 | 0.0186341 | 0.00931705 | − | 0.999957i | \(-0.497034\pi\) | ||||
0.00931705 | + | 0.999957i | \(0.497034\pi\) | |||||||
\(338\) | −2.23728 | −0.121692 | ||||||||
\(339\) | −17.2285 | −0.935723 | ||||||||
\(340\) | −28.4103 | −1.54076 | ||||||||
\(341\) | −12.6557 | −0.685347 | ||||||||
\(342\) | 21.6501 | 1.17070 | ||||||||
\(343\) | −66.4986 | −3.59059 | ||||||||
\(344\) | −9.49118 | −0.511730 | ||||||||
\(345\) | 39.9893 | 2.15295 | ||||||||
\(346\) | −22.7764 | −1.22446 | ||||||||
\(347\) | 27.2775 | 1.46434 | 0.732168 | − | 0.681124i | \(-0.238509\pi\) | ||||
0.732168 | + | 0.681124i | \(0.238509\pi\) | |||||||
\(348\) | 27.8131 | 1.49094 | ||||||||
\(349\) | −12.9125 | −0.691188 | −0.345594 | − | 0.938384i | \(-0.612322\pi\) | ||||
−0.345594 | + | 0.938384i | \(0.612322\pi\) | |||||||
\(350\) | 132.256 | 7.06939 | ||||||||
\(351\) | 1.48516 | 0.0792721 | ||||||||
\(352\) | 31.8833 | 1.69938 | ||||||||
\(353\) | −3.34223 | −0.177889 | −0.0889446 | − | 0.996037i | \(-0.528349\pi\) | ||||
−0.0889446 | + | 0.996037i | \(0.528349\pi\) | |||||||
\(354\) | −14.4136 | −0.766074 | ||||||||
\(355\) | 50.2191 | 2.66535 | ||||||||
\(356\) | 37.8899 | 2.00816 | ||||||||
\(357\) | −27.9822 | −1.48098 | ||||||||
\(358\) | 53.4383 | 2.82430 | ||||||||
\(359\) | 4.65572 | 0.245720 | 0.122860 | − | 0.992424i | \(-0.460793\pi\) | ||||
0.122860 | + | 0.992424i | \(0.460793\pi\) | |||||||
\(360\) | 21.4910 | 1.13267 | ||||||||
\(361\) | −2.16391 | −0.113890 | ||||||||
\(362\) | 4.83502 | 0.254123 | ||||||||
\(363\) | 27.1521 | 1.42512 | ||||||||
\(364\) | 15.5693 | 0.816051 | ||||||||
\(365\) | −22.1568 | −1.15974 | ||||||||
\(366\) | −21.5044 | −1.12405 | ||||||||
\(367\) | −30.3387 | −1.58366 | −0.791832 | − | 0.610738i | \(-0.790873\pi\) | ||||
−0.791832 | + | 0.610738i | \(0.790873\pi\) | |||||||
\(368\) | 4.17187 | 0.217474 | ||||||||
\(369\) | −9.94558 | −0.517746 | ||||||||
\(370\) | 97.1380 | 5.04996 | ||||||||
\(371\) | −47.1401 | −2.44739 | ||||||||
\(372\) | −18.4677 | −0.957508 | ||||||||
\(373\) | −6.25855 | −0.324055 | −0.162028 | − | 0.986786i | \(-0.551803\pi\) | ||||
−0.162028 | + | 0.986786i | \(0.551803\pi\) | |||||||
\(374\) | −24.8895 | −1.28701 | ||||||||
\(375\) | −60.1215 | −3.10466 | ||||||||
\(376\) | −5.34058 | −0.275419 | ||||||||
\(377\) | −3.99786 | −0.205900 | ||||||||
\(378\) | −17.2130 | −0.885343 | ||||||||
\(379\) | 33.5344 | 1.72254 | 0.861272 | − | 0.508144i | \(-0.169668\pi\) | ||||
0.861272 | + | 0.508144i | \(0.169668\pi\) | |||||||
\(380\) | 49.9569 | 2.56274 | ||||||||
\(381\) | −31.8896 | −1.63375 | ||||||||
\(382\) | 31.0984 | 1.59113 | ||||||||
\(383\) | −18.7163 | −0.956356 | −0.478178 | − | 0.878263i | \(-0.658703\pi\) | ||||
−0.478178 | + | 0.878263i | \(0.658703\pi\) | |||||||
\(384\) | 36.3921 | 1.85713 | ||||||||
\(385\) | 100.053 | 5.09918 | ||||||||
\(386\) | 44.4749 | 2.26371 | ||||||||
\(387\) | 9.95117 | 0.505846 | ||||||||
\(388\) | −13.8769 | −0.704491 | ||||||||
\(389\) | −6.80394 | −0.344974 | −0.172487 | − | 0.985012i | \(-0.555180\pi\) | ||||
−0.172487 | + | 0.985012i | \(0.555180\pi\) | |||||||
\(390\) | −20.9802 | −1.06237 | ||||||||
\(391\) | −9.95075 | −0.503231 | ||||||||
\(392\) | −44.6203 | −2.25366 | ||||||||
\(393\) | 3.90250 | 0.196855 | ||||||||
\(394\) | 12.9432 | 0.652069 | ||||||||
\(395\) | 6.93817 | 0.349097 | ||||||||
\(396\) | 33.7926 | 1.69814 | ||||||||
\(397\) | −3.70357 | −0.185877 | −0.0929385 | − | 0.995672i | \(-0.529626\pi\) | ||||
−0.0929385 | + | 0.995672i | \(0.529626\pi\) | |||||||
\(398\) | −53.4807 | −2.68075 | ||||||||
\(399\) | 49.2042 | 2.46329 | ||||||||
\(400\) | −11.1637 | −0.558184 | ||||||||
\(401\) | −37.5645 | −1.87588 | −0.937942 | − | 0.346793i | \(-0.887271\pi\) | ||||
−0.937942 | + | 0.346793i | \(0.887271\pi\) | |||||||
\(402\) | 25.0416 | 1.24896 | ||||||||
\(403\) | 2.65455 | 0.132233 | ||||||||
\(404\) | −40.3688 | −2.00842 | ||||||||
\(405\) | 42.5895 | 2.11629 | ||||||||
\(406\) | 46.3352 | 2.29958 | ||||||||
\(407\) | 51.0970 | 2.53278 | ||||||||
\(408\) | −12.1502 | −0.601526 | ||||||||
\(409\) | −16.5389 | −0.817798 | −0.408899 | − | 0.912580i | \(-0.634087\pi\) | ||||
−0.408899 | + | 0.912580i | \(0.634087\pi\) | |||||||
\(410\) | −38.2209 | −1.88760 | ||||||||
\(411\) | −49.1925 | −2.42649 | ||||||||
\(412\) | −6.83175 | −0.336576 | ||||||||
\(413\) | −14.4178 | −0.709451 | ||||||||
\(414\) | 22.5007 | 1.10585 | ||||||||
\(415\) | −31.9891 | −1.57028 | ||||||||
\(416\) | −6.68754 | −0.327883 | ||||||||
\(417\) | 40.7852 | 1.99726 | ||||||||
\(418\) | 43.7660 | 2.14067 | ||||||||
\(419\) | −22.4658 | −1.09752 | −0.548762 | − | 0.835979i | \(-0.684901\pi\) | ||||
−0.548762 | + | 0.835979i | \(0.684901\pi\) | |||||||
\(420\) | 146.001 | 7.12413 | ||||||||
\(421\) | 4.90331 | 0.238973 | 0.119486 | − | 0.992836i | \(-0.461875\pi\) | ||||
0.119486 | + | 0.992836i | \(0.461875\pi\) | |||||||
\(422\) | 51.0138 | 2.48331 | ||||||||
\(423\) | 5.59941 | 0.272253 | ||||||||
\(424\) | −20.4688 | −0.994055 | ||||||||
\(425\) | 26.6276 | 1.29163 | ||||||||
\(426\) | 64.2002 | 3.11051 | ||||||||
\(427\) | −21.5106 | −1.04097 | ||||||||
\(428\) | 13.2707 | 0.641464 | ||||||||
\(429\) | −11.0361 | −0.532827 | ||||||||
\(430\) | 38.2424 | 1.84421 | ||||||||
\(431\) | −24.0006 | −1.15607 | −0.578034 | − | 0.816013i | \(-0.696180\pi\) | ||||
−0.578034 | + | 0.816013i | \(0.696180\pi\) | |||||||
\(432\) | 1.45294 | 0.0699048 | ||||||||
\(433\) | −35.1582 | −1.68960 | −0.844798 | − | 0.535085i | \(-0.820279\pi\) | ||||
−0.844798 | + | 0.535085i | \(0.820279\pi\) | |||||||
\(434\) | −30.7663 | −1.47683 | ||||||||
\(435\) | −37.4900 | −1.79751 | ||||||||
\(436\) | −30.4386 | −1.45774 | ||||||||
\(437\) | 17.4975 | 0.837019 | ||||||||
\(438\) | −28.3253 | −1.35344 | ||||||||
\(439\) | 4.02707 | 0.192201 | 0.0961007 | − | 0.995372i | \(-0.469363\pi\) | ||||
0.0961007 | + | 0.995372i | \(0.469363\pi\) | |||||||
\(440\) | 43.4443 | 2.07113 | ||||||||
\(441\) | 46.7828 | 2.22775 | ||||||||
\(442\) | 5.22060 | 0.248319 | ||||||||
\(443\) | −13.3329 | −0.633465 | −0.316733 | − | 0.948515i | \(-0.602586\pi\) | ||||
−0.316733 | + | 0.948515i | \(0.602586\pi\) | |||||||
\(444\) | 74.5626 | 3.53859 | ||||||||
\(445\) | −51.0728 | −2.42108 | ||||||||
\(446\) | 20.4101 | 0.966445 | ||||||||
\(447\) | −35.8434 | −1.69534 | ||||||||
\(448\) | 67.3725 | 3.18305 | ||||||||
\(449\) | −11.7911 | −0.556455 | −0.278228 | − | 0.960515i | \(-0.589747\pi\) | ||||
−0.278228 | + | 0.960515i | \(0.589747\pi\) | |||||||
\(450\) | −60.2105 | −2.83835 | ||||||||
\(451\) | −20.1051 | −0.946714 | ||||||||
\(452\) | −22.3683 | −1.05212 | ||||||||
\(453\) | 31.7663 | 1.49251 | ||||||||
\(454\) | −40.3153 | −1.89209 | ||||||||
\(455\) | −20.9862 | −0.983849 | ||||||||
\(456\) | 21.3651 | 1.00051 | ||||||||
\(457\) | 34.4444 | 1.61124 | 0.805621 | − | 0.592431i | \(-0.201832\pi\) | ||||
0.805621 | + | 0.592431i | \(0.201832\pi\) | |||||||
\(458\) | 44.0771 | 2.05959 | ||||||||
\(459\) | −3.46557 | −0.161759 | ||||||||
\(460\) | 51.9195 | 2.42076 | ||||||||
\(461\) | −1.82312 | −0.0849112 | −0.0424556 | − | 0.999098i | \(-0.513518\pi\) | ||||
−0.0424556 | + | 0.999098i | \(0.513518\pi\) | |||||||
\(462\) | 127.908 | 5.95083 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | −3.91113 | −0.181570 | ||||||||
\(465\) | 24.8932 | 1.15439 | ||||||||
\(466\) | 12.1781 | 0.564138 | ||||||||
\(467\) | 24.6044 | 1.13856 | 0.569278 | − | 0.822145i | \(-0.307223\pi\) | ||||
0.569278 | + | 0.822145i | \(0.307223\pi\) | |||||||
\(468\) | −7.08801 | −0.327643 | ||||||||
\(469\) | 25.0489 | 1.15665 | ||||||||
\(470\) | 21.5185 | 0.992577 | ||||||||
\(471\) | 38.0857 | 1.75489 | ||||||||
\(472\) | −6.26037 | −0.288157 | ||||||||
\(473\) | 20.1164 | 0.924954 | ||||||||
\(474\) | 8.86978 | 0.407402 | ||||||||
\(475\) | −46.8223 | −2.14836 | ||||||||
\(476\) | −36.3302 | −1.66519 | ||||||||
\(477\) | 21.4609 | 0.982626 | ||||||||
\(478\) | −46.3265 | −2.11893 | ||||||||
\(479\) | −26.1509 | −1.19486 | −0.597432 | − | 0.801920i | \(-0.703812\pi\) | ||||
−0.597432 | + | 0.801920i | \(0.703812\pi\) | |||||||
\(480\) | −62.7126 | −2.86243 | ||||||||
\(481\) | −10.7176 | −0.488682 | ||||||||
\(482\) | −38.8606 | −1.77005 | ||||||||
\(483\) | 51.1372 | 2.32682 | ||||||||
\(484\) | 35.2525 | 1.60239 | ||||||||
\(485\) | 18.7050 | 0.849349 | ||||||||
\(486\) | 44.4784 | 2.01758 | ||||||||
\(487\) | 24.7109 | 1.11976 | 0.559879 | − | 0.828575i | \(-0.310848\pi\) | ||||
0.559879 | + | 0.828575i | \(0.310848\pi\) | |||||||
\(488\) | −9.34017 | −0.422810 | ||||||||
\(489\) | 22.2649 | 1.00685 | ||||||||
\(490\) | 179.787 | 8.12193 | ||||||||
\(491\) | 4.13862 | 0.186774 | 0.0933868 | − | 0.995630i | \(-0.470231\pi\) | ||||
0.0933868 | + | 0.995630i | \(0.470231\pi\) | |||||||
\(492\) | −29.3382 | −1.32267 | ||||||||
\(493\) | 9.32884 | 0.420150 | ||||||||
\(494\) | −9.17996 | −0.413026 | ||||||||
\(495\) | −45.5499 | −2.04731 | ||||||||
\(496\) | 2.59697 | 0.116607 | ||||||||
\(497\) | 64.2188 | 2.88060 | ||||||||
\(498\) | −40.8949 | −1.83254 | ||||||||
\(499\) | 13.5710 | 0.607523 | 0.303761 | − | 0.952748i | \(-0.401757\pi\) | ||||
0.303761 | + | 0.952748i | \(0.401757\pi\) | |||||||
\(500\) | −78.0578 | −3.49085 | ||||||||
\(501\) | 13.6575 | 0.610171 | ||||||||
\(502\) | −0.339157 | −0.0151373 | ||||||||
\(503\) | −34.9153 | −1.55679 | −0.778397 | − | 0.627772i | \(-0.783967\pi\) | ||||
−0.778397 | + | 0.627772i | \(0.783967\pi\) | |||||||
\(504\) | 27.4821 | 1.22415 | ||||||||
\(505\) | 54.4141 | 2.42140 | ||||||||
\(506\) | 45.4854 | 2.02207 | ||||||||
\(507\) | 2.31482 | 0.102805 | ||||||||
\(508\) | −41.4033 | −1.83698 | ||||||||
\(509\) | −29.2652 | −1.29716 | −0.648579 | − | 0.761147i | \(-0.724636\pi\) | ||||
−0.648579 | + | 0.761147i | \(0.724636\pi\) | |||||||
\(510\) | 48.9564 | 2.16782 | ||||||||
\(511\) | −28.3335 | −1.25340 | ||||||||
\(512\) | −10.9437 | −0.483646 | ||||||||
\(513\) | 6.09389 | 0.269052 | ||||||||
\(514\) | 27.3450 | 1.20614 | ||||||||
\(515\) | 9.20870 | 0.405784 | ||||||||
\(516\) | 29.3547 | 1.29227 | ||||||||
\(517\) | 11.3193 | 0.497822 | ||||||||
\(518\) | 124.217 | 5.45779 | ||||||||
\(519\) | 23.5658 | 1.03442 | ||||||||
\(520\) | −9.11248 | −0.399608 | ||||||||
\(521\) | 16.7702 | 0.734716 | 0.367358 | − | 0.930080i | \(-0.380262\pi\) | ||||
0.367358 | + | 0.930080i | \(0.380262\pi\) | |||||||
\(522\) | −21.0944 | −0.923277 | ||||||||
\(523\) | −29.9038 | −1.30760 | −0.653800 | − | 0.756667i | \(-0.726826\pi\) | ||||
−0.653800 | + | 0.756667i | \(0.726826\pi\) | |||||||
\(524\) | 5.06675 | 0.221342 | ||||||||
\(525\) | −136.840 | −5.97220 | ||||||||
\(526\) | −33.4321 | −1.45771 | ||||||||
\(527\) | −6.19429 | −0.269828 | ||||||||
\(528\) | −10.7967 | −0.469865 | ||||||||
\(529\) | −4.81510 | −0.209352 | ||||||||
\(530\) | 82.4742 | 3.58245 | ||||||||
\(531\) | 6.56378 | 0.284844 | ||||||||
\(532\) | 63.8835 | 2.76970 | ||||||||
\(533\) | 4.21707 | 0.182661 | ||||||||
\(534\) | −65.2916 | −2.82544 | ||||||||
\(535\) | −17.8879 | −0.773363 | ||||||||
\(536\) | 10.8765 | 0.469795 | ||||||||
\(537\) | −55.2905 | −2.38596 | ||||||||
\(538\) | 14.1353 | 0.609417 | ||||||||
\(539\) | 94.5721 | 4.07351 | ||||||||
\(540\) | 18.0821 | 0.778130 | ||||||||
\(541\) | −45.8945 | −1.97316 | −0.986580 | − | 0.163280i | \(-0.947793\pi\) | ||||
−0.986580 | + | 0.163280i | \(0.947793\pi\) | |||||||
\(542\) | −10.2292 | −0.439380 | ||||||||
\(543\) | −5.00261 | −0.214682 | ||||||||
\(544\) | 15.6051 | 0.669063 | ||||||||
\(545\) | 41.0290 | 1.75749 | ||||||||
\(546\) | −26.8288 | −1.14817 | ||||||||
\(547\) | −1.25473 | −0.0536485 | −0.0268242 | − | 0.999640i | \(-0.508539\pi\) | ||||
−0.0268242 | + | 0.999640i | \(0.508539\pi\) | |||||||
\(548\) | −63.8683 | −2.72832 | ||||||||
\(549\) | 9.79284 | 0.417948 | ||||||||
\(550\) | −121.716 | −5.19000 | ||||||||
\(551\) | −16.4039 | −0.698831 | ||||||||
\(552\) | 22.2044 | 0.945083 | ||||||||
\(553\) | 8.87234 | 0.377290 | ||||||||
\(554\) | −44.0110 | −1.86985 | ||||||||
\(555\) | −100.505 | −4.26619 | ||||||||
\(556\) | 52.9529 | 2.24570 | ||||||||
\(557\) | −14.6619 | −0.621246 | −0.310623 | − | 0.950533i | \(-0.600538\pi\) | ||||
−0.310623 | + | 0.950533i | \(0.600538\pi\) | |||||||
\(558\) | 14.0066 | 0.592945 | ||||||||
\(559\) | −4.21943 | −0.178463 | ||||||||
\(560\) | −20.5310 | −0.867591 | ||||||||
\(561\) | 25.7522 | 1.08726 | ||||||||
\(562\) | 32.9443 | 1.38967 | ||||||||
\(563\) | 4.13193 | 0.174140 | 0.0870700 | − | 0.996202i | \(-0.472250\pi\) | ||||
0.0870700 | + | 0.996202i | \(0.472250\pi\) | |||||||
\(564\) | 16.5175 | 0.695513 | ||||||||
\(565\) | 30.1509 | 1.26846 | ||||||||
\(566\) | 29.0072 | 1.21926 | ||||||||
\(567\) | 54.4622 | 2.28720 | ||||||||
\(568\) | 27.8846 | 1.17001 | ||||||||
\(569\) | −40.3252 | −1.69052 | −0.845260 | − | 0.534355i | \(-0.820555\pi\) | ||||
−0.845260 | + | 0.534355i | \(0.820555\pi\) | |||||||
\(570\) | −86.0854 | −3.60572 | ||||||||
\(571\) | −11.9777 | −0.501251 | −0.250626 | − | 0.968084i | \(-0.580636\pi\) | ||||
−0.250626 | + | 0.968084i | \(0.580636\pi\) | |||||||
\(572\) | −14.3285 | −0.599105 | ||||||||
\(573\) | −32.1763 | −1.34418 | ||||||||
\(574\) | −48.8758 | −2.04004 | ||||||||
\(575\) | −48.6618 | −2.02934 | ||||||||
\(576\) | −30.6718 | −1.27799 | ||||||||
\(577\) | −12.1989 | −0.507849 | −0.253924 | − | 0.967224i | \(-0.581721\pi\) | ||||
−0.253924 | + | 0.967224i | \(0.581721\pi\) | |||||||
\(578\) | 25.8517 | 1.07529 | ||||||||
\(579\) | −46.0164 | −1.91238 | ||||||||
\(580\) | −48.6746 | −2.02110 | ||||||||
\(581\) | −40.9067 | −1.69710 | ||||||||
\(582\) | 23.9125 | 0.991205 | ||||||||
\(583\) | 43.3834 | 1.79676 | ||||||||
\(584\) | −12.3028 | −0.509092 | ||||||||
\(585\) | 9.55411 | 0.395014 | ||||||||
\(586\) | −16.9040 | −0.698299 | ||||||||
\(587\) | 7.92549 | 0.327120 | 0.163560 | − | 0.986533i | \(-0.447702\pi\) | ||||
0.163560 | + | 0.986533i | \(0.447702\pi\) | |||||||
\(588\) | 138.003 | 5.69116 | ||||||||
\(589\) | 10.8921 | 0.448801 | ||||||||
\(590\) | 25.2246 | 1.03848 | ||||||||
\(591\) | −13.3918 | −0.550866 | ||||||||
\(592\) | −10.4851 | −0.430936 | ||||||||
\(593\) | 13.0362 | 0.535333 | 0.267667 | − | 0.963512i | \(-0.413747\pi\) | ||||
0.267667 | + | 0.963512i | \(0.413747\pi\) | |||||||
\(594\) | 15.8413 | 0.649976 | ||||||||
\(595\) | 48.9705 | 2.00759 | ||||||||
\(596\) | −46.5368 | −1.90622 | ||||||||
\(597\) | 55.3344 | 2.26469 | ||||||||
\(598\) | −9.54060 | −0.390144 | ||||||||
\(599\) | −22.1148 | −0.903587 | −0.451793 | − | 0.892123i | \(-0.649216\pi\) | ||||
−0.451793 | + | 0.892123i | \(0.649216\pi\) | |||||||
\(600\) | −59.4178 | −2.42572 | ||||||||
\(601\) | −27.4156 | −1.11831 | −0.559153 | − | 0.829064i | \(-0.688874\pi\) | ||||
−0.559153 | + | 0.829064i | \(0.688874\pi\) | |||||||
\(602\) | 48.9033 | 1.99315 | ||||||||
\(603\) | −11.4037 | −0.464393 | ||||||||
\(604\) | 41.2433 | 1.67817 | ||||||||
\(605\) | −47.5178 | −1.93187 | ||||||||
\(606\) | 69.5631 | 2.82581 | ||||||||
\(607\) | −0.144931 | −0.00588257 | −0.00294129 | − | 0.999996i | \(-0.500936\pi\) | ||||
−0.00294129 | + | 0.999996i | \(0.500936\pi\) | |||||||
\(608\) | −27.4402 | −1.11285 | ||||||||
\(609\) | −47.9412 | −1.94267 | ||||||||
\(610\) | 37.6339 | 1.52375 | ||||||||
\(611\) | −2.37423 | −0.0960510 | ||||||||
\(612\) | 16.5396 | 0.668573 | ||||||||
\(613\) | 8.19498 | 0.330992 | 0.165496 | − | 0.986210i | \(-0.447078\pi\) | ||||
0.165496 | + | 0.986210i | \(0.447078\pi\) | |||||||
\(614\) | −57.8339 | −2.33398 | ||||||||
\(615\) | 39.5457 | 1.59464 | ||||||||
\(616\) | 55.5554 | 2.23839 | ||||||||
\(617\) | −41.5308 | −1.67197 | −0.835983 | − | 0.548756i | \(-0.815102\pi\) | ||||
−0.835983 | + | 0.548756i | \(0.815102\pi\) | |||||||
\(618\) | 11.7724 | 0.473556 | ||||||||
\(619\) | 36.8619 | 1.48161 | 0.740803 | − | 0.671723i | \(-0.234445\pi\) | ||||
0.740803 | + | 0.671723i | \(0.234445\pi\) | |||||||
\(620\) | 32.3196 | 1.29799 | ||||||||
\(621\) | 6.33329 | 0.254146 | ||||||||
\(622\) | 71.3155 | 2.85949 | ||||||||
\(623\) | −65.3104 | −2.61661 | ||||||||
\(624\) | 2.26461 | 0.0906569 | ||||||||
\(625\) | 48.1600 | 1.92640 | ||||||||
\(626\) | −31.9620 | −1.27746 | ||||||||
\(627\) | −45.2830 | −1.80843 | ||||||||
\(628\) | 49.4479 | 1.97319 | ||||||||
\(629\) | 25.0091 | 0.997180 | ||||||||
\(630\) | −110.732 | −4.41168 | ||||||||
\(631\) | −16.9892 | −0.676330 | −0.338165 | − | 0.941087i | \(-0.609806\pi\) | ||||
−0.338165 | + | 0.941087i | \(0.609806\pi\) | |||||||
\(632\) | 3.85248 | 0.153243 | ||||||||
\(633\) | −52.7820 | −2.09790 | ||||||||
\(634\) | 42.6557 | 1.69408 | ||||||||
\(635\) | 55.8086 | 2.21470 | ||||||||
\(636\) | 63.3068 | 2.51028 | ||||||||
\(637\) | −19.8366 | −0.785953 | ||||||||
\(638\) | −42.6426 | −1.68824 | ||||||||
\(639\) | −29.2360 | −1.15656 | ||||||||
\(640\) | −63.6884 | −2.51750 | ||||||||
\(641\) | 7.62227 | 0.301062 | 0.150531 | − | 0.988605i | \(-0.451902\pi\) | ||||
0.150531 | + | 0.988605i | \(0.451902\pi\) | |||||||
\(642\) | −22.8680 | −0.902528 | ||||||||
\(643\) | 15.2419 | 0.601083 | 0.300542 | − | 0.953769i | \(-0.402833\pi\) | ||||
0.300542 | + | 0.953769i | \(0.402833\pi\) | |||||||
\(644\) | 66.3932 | 2.61626 | ||||||||
\(645\) | −39.5679 | −1.55798 | ||||||||
\(646\) | 21.4211 | 0.842800 | ||||||||
\(647\) | 2.21709 | 0.0871628 | 0.0435814 | − | 0.999050i | \(-0.486123\pi\) | ||||
0.0435814 | + | 0.999050i | \(0.486123\pi\) | |||||||
\(648\) | 23.6482 | 0.928988 | ||||||||
\(649\) | 13.2688 | 0.520845 | ||||||||
\(650\) | 25.5301 | 1.00137 | ||||||||
\(651\) | 31.8327 | 1.24762 | ||||||||
\(652\) | 28.9073 | 1.13210 | ||||||||
\(653\) | −28.5694 | −1.11801 | −0.559003 | − | 0.829166i | \(-0.688816\pi\) | ||||
−0.559003 | + | 0.829166i | \(0.688816\pi\) | |||||||
\(654\) | 52.4515 | 2.05102 | ||||||||
\(655\) | −6.82960 | −0.266854 | ||||||||
\(656\) | 4.12559 | 0.161077 | ||||||||
\(657\) | 12.8990 | 0.503239 | ||||||||
\(658\) | 27.5173 | 1.07274 | ||||||||
\(659\) | −30.0421 | −1.17028 | −0.585138 | − | 0.810934i | \(-0.698960\pi\) | ||||
−0.585138 | + | 0.810934i | \(0.698960\pi\) | |||||||
\(660\) | −134.366 | −5.23019 | ||||||||
\(661\) | −2.02342 | −0.0787018 | −0.0393509 | − | 0.999225i | \(-0.512529\pi\) | ||||
−0.0393509 | + | 0.999225i | \(0.512529\pi\) | |||||||
\(662\) | −72.4203 | −2.81470 | ||||||||
\(663\) | −5.40155 | −0.209779 | ||||||||
\(664\) | −17.7622 | −0.689307 | ||||||||
\(665\) | −86.1102 | −3.33921 | ||||||||
\(666\) | −56.5508 | −2.19130 | ||||||||
\(667\) | −17.0484 | −0.660115 | ||||||||
\(668\) | 17.7320 | 0.686070 | ||||||||
\(669\) | −21.1175 | −0.816450 | ||||||||
\(670\) | −43.8243 | −1.69308 | ||||||||
\(671\) | 19.7964 | 0.764230 | ||||||||
\(672\) | −80.1951 | −3.09359 | ||||||||
\(673\) | −19.8977 | −0.767002 | −0.383501 | − | 0.923541i | \(-0.625282\pi\) | ||||
−0.383501 | + | 0.923541i | \(0.625282\pi\) | |||||||
\(674\) | −0.765321 | −0.0294791 | ||||||||
\(675\) | −16.9475 | −0.652310 | ||||||||
\(676\) | 3.00542 | 0.115593 | ||||||||
\(677\) | −7.19902 | −0.276681 | −0.138340 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138340 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(678\) | 38.5449 | 1.48031 | ||||||||
\(679\) | 23.9194 | 0.917942 | ||||||||
\(680\) | 21.2636 | 0.815422 | ||||||||
\(681\) | 41.7127 | 1.59843 | ||||||||
\(682\) | 28.3144 | 1.08422 | ||||||||
\(683\) | 32.9422 | 1.26050 | 0.630249 | − | 0.776393i | \(-0.282953\pi\) | ||||
0.630249 | + | 0.776393i | \(0.282953\pi\) | |||||||
\(684\) | −29.0834 | −1.11203 | ||||||||
\(685\) | 86.0897 | 3.28932 | ||||||||
\(686\) | 148.776 | 5.68029 | ||||||||
\(687\) | −45.6048 | −1.73993 | ||||||||
\(688\) | −4.12790 | −0.157375 | ||||||||
\(689\) | −9.09971 | −0.346671 | ||||||||
\(690\) | −89.4673 | −3.40596 | ||||||||
\(691\) | 9.51279 | 0.361884 | 0.180942 | − | 0.983494i | \(-0.442085\pi\) | ||||
0.180942 | + | 0.983494i | \(0.442085\pi\) | |||||||
\(692\) | 30.5963 | 1.16310 | ||||||||
\(693\) | −58.2478 | −2.21265 | ||||||||
\(694\) | −61.0275 | −2.31657 | ||||||||
\(695\) | −71.3765 | −2.70747 | ||||||||
\(696\) | −20.8167 | −0.789054 | ||||||||
\(697\) | −9.84036 | −0.372730 | ||||||||
\(698\) | 28.8888 | 1.09346 | ||||||||
\(699\) | −12.6002 | −0.476582 | ||||||||
\(700\) | −177.664 | −6.71508 | ||||||||
\(701\) | 3.19747 | 0.120767 | 0.0603833 | − | 0.998175i | \(-0.480768\pi\) | ||||
0.0603833 | + | 0.998175i | \(0.480768\pi\) | |||||||
\(702\) | −3.32272 | −0.125408 | ||||||||
\(703\) | −43.9763 | −1.65860 | ||||||||
\(704\) | −62.0035 | −2.33684 | ||||||||
\(705\) | −22.2644 | −0.838526 | ||||||||
\(706\) | 7.47751 | 0.281420 | ||||||||
\(707\) | 69.5832 | 2.61695 | ||||||||
\(708\) | 19.3623 | 0.727680 | ||||||||
\(709\) | 25.8807 | 0.971971 | 0.485985 | − | 0.873967i | \(-0.338461\pi\) | ||||
0.485985 | + | 0.873967i | \(0.338461\pi\) | |||||||
\(710\) | −112.354 | −4.21658 | ||||||||
\(711\) | −4.03919 | −0.151481 | ||||||||
\(712\) | −28.3586 | −1.06278 | ||||||||
\(713\) | 11.3200 | 0.423938 | ||||||||
\(714\) | 62.6040 | 2.34290 | ||||||||
\(715\) | 19.3138 | 0.722294 | ||||||||
\(716\) | −71.7855 | −2.68275 | ||||||||
\(717\) | 47.9322 | 1.79006 | ||||||||
\(718\) | −10.4161 | −0.388727 | ||||||||
\(719\) | 35.2863 | 1.31596 | 0.657978 | − | 0.753037i | \(-0.271412\pi\) | ||||
0.657978 | + | 0.753037i | \(0.271412\pi\) | |||||||
\(720\) | 9.34686 | 0.348337 | ||||||||
\(721\) | 11.7758 | 0.438554 | ||||||||
\(722\) | 4.84127 | 0.180173 | ||||||||
\(723\) | 40.2075 | 1.49533 | ||||||||
\(724\) | −6.49505 | −0.241387 | ||||||||
\(725\) | 45.6205 | 1.69430 | ||||||||
\(726\) | −60.7469 | −2.25453 | ||||||||
\(727\) | 8.34614 | 0.309541 | 0.154771 | − | 0.987950i | \(-0.450536\pi\) | ||||
0.154771 | + | 0.987950i | \(0.450536\pi\) | |||||||
\(728\) | −11.6528 | −0.431881 | ||||||||
\(729\) | −14.4806 | −0.536320 | ||||||||
\(730\) | 49.5710 | 1.83470 | ||||||||
\(731\) | 9.84588 | 0.364163 | ||||||||
\(732\) | 28.8876 | 1.06772 | ||||||||
\(733\) | 32.2322 | 1.19052 | 0.595262 | − | 0.803532i | \(-0.297048\pi\) | ||||
0.595262 | + | 0.803532i | \(0.297048\pi\) | |||||||
\(734\) | 67.8760 | 2.50535 | ||||||||
\(735\) | −186.018 | −6.86138 | ||||||||
\(736\) | −28.5182 | −1.05119 | ||||||||
\(737\) | −23.0527 | −0.849156 | ||||||||
\(738\) | 22.2510 | 0.819072 | ||||||||
\(739\) | −11.4776 | −0.422209 | −0.211104 | − | 0.977464i | \(-0.567706\pi\) | ||||
−0.211104 | + | 0.977464i | \(0.567706\pi\) | |||||||
\(740\) | −130.489 | −4.79687 | ||||||||
\(741\) | 9.49814 | 0.348923 | ||||||||
\(742\) | 105.466 | 3.87177 | ||||||||
\(743\) | 26.6324 | 0.977047 | 0.488523 | − | 0.872551i | \(-0.337536\pi\) | ||||
0.488523 | + | 0.872551i | \(0.337536\pi\) | |||||||
\(744\) | 13.8221 | 0.506744 | ||||||||
\(745\) | 62.7281 | 2.29818 | ||||||||
\(746\) | 14.0021 | 0.512654 | ||||||||
\(747\) | 18.6230 | 0.681382 | ||||||||
\(748\) | 33.4350 | 1.22251 | ||||||||
\(749\) | −22.8746 | −0.835819 | ||||||||
\(750\) | 134.509 | 4.91156 | ||||||||
\(751\) | −6.48488 | −0.236637 | −0.118318 | − | 0.992976i | \(-0.537750\pi\) | ||||
−0.118318 | + | 0.992976i | \(0.537750\pi\) | |||||||
\(752\) | −2.32272 | −0.0847010 | ||||||||
\(753\) | 0.350912 | 0.0127879 | ||||||||
\(754\) | 8.94432 | 0.325733 | ||||||||
\(755\) | −55.5929 | −2.02323 | ||||||||
\(756\) | 23.1229 | 0.840971 | ||||||||
\(757\) | −16.9100 | −0.614605 | −0.307303 | − | 0.951612i | \(-0.599426\pi\) | ||||
−0.307303 | + | 0.951612i | \(0.599426\pi\) | |||||||
\(758\) | −75.0257 | −2.72506 | ||||||||
\(759\) | −47.0620 | −1.70824 | ||||||||
\(760\) | −37.3901 | −1.35628 | ||||||||
\(761\) | −20.6719 | −0.749355 | −0.374678 | − | 0.927155i | \(-0.622247\pi\) | ||||
−0.374678 | + | 0.927155i | \(0.622247\pi\) | |||||||
\(762\) | 71.3459 | 2.58459 | ||||||||
\(763\) | 52.4667 | 1.89942 | ||||||||
\(764\) | −41.7756 | −1.51139 | ||||||||
\(765\) | −22.2941 | −0.806046 | ||||||||
\(766\) | 41.8735 | 1.51295 | ||||||||
\(767\) | −2.78313 | −0.100493 | ||||||||
\(768\) | −21.2095 | −0.765333 | ||||||||
\(769\) | −31.3424 | −1.13023 | −0.565117 | − | 0.825011i | \(-0.691169\pi\) | ||||
−0.565117 | + | 0.825011i | \(0.691169\pi\) | |||||||
\(770\) | −223.847 | −8.06687 | ||||||||
\(771\) | −28.2928 | −1.01894 | ||||||||
\(772\) | −59.7447 | −2.15026 | ||||||||
\(773\) | 40.5333 | 1.45788 | 0.728941 | − | 0.684576i | \(-0.240013\pi\) | ||||
0.728941 | + | 0.684576i | \(0.240013\pi\) | |||||||
\(774\) | −22.2635 | −0.800246 | ||||||||
\(775\) | −30.2917 | −1.08811 | ||||||||
\(776\) | 10.3861 | 0.372839 | ||||||||
\(777\) | −128.523 | −4.61073 | ||||||||
\(778\) | 15.2223 | 0.545747 | ||||||||
\(779\) | 17.3034 | 0.619958 | ||||||||
\(780\) | 28.1834 | 1.00913 | ||||||||
\(781\) | −59.1010 | −2.11480 | ||||||||
\(782\) | 22.2626 | 0.796109 | ||||||||
\(783\) | −5.93746 | −0.212188 | ||||||||
\(784\) | −19.4063 | −0.693080 | ||||||||
\(785\) | −66.6521 | −2.37892 | ||||||||
\(786\) | −8.73098 | −0.311424 | ||||||||
\(787\) | 45.8375 | 1.63393 | 0.816965 | − | 0.576687i | \(-0.195655\pi\) | ||||
0.816965 | + | 0.576687i | \(0.195655\pi\) | |||||||
\(788\) | −17.3871 | −0.619389 | ||||||||
\(789\) | 34.5909 | 1.23147 | ||||||||
\(790\) | −15.5226 | −0.552270 | ||||||||
\(791\) | 38.5561 | 1.37090 | ||||||||
\(792\) | −25.2919 | −0.898710 | ||||||||
\(793\) | −4.15230 | −0.147453 | ||||||||
\(794\) | 8.28592 | 0.294056 | ||||||||
\(795\) | −85.3328 | −3.02644 | ||||||||
\(796\) | 71.8425 | 2.54639 | ||||||||
\(797\) | 30.5244 | 1.08123 | 0.540615 | − | 0.841270i | \(-0.318192\pi\) | ||||
0.540615 | + | 0.841270i | \(0.318192\pi\) | |||||||
\(798\) | −110.084 | −3.89691 | ||||||||
\(799\) | 5.54017 | 0.195997 | ||||||||
\(800\) | 76.3130 | 2.69807 | ||||||||
\(801\) | 29.7330 | 1.05056 | ||||||||
\(802\) | 84.0423 | 2.96764 | ||||||||
\(803\) | 26.0755 | 0.920186 | ||||||||
\(804\) | −33.6393 | −1.18637 | ||||||||
\(805\) | −89.4931 | −3.15422 | ||||||||
\(806\) | −5.93897 | −0.209191 | ||||||||
\(807\) | −14.6253 | −0.514834 | ||||||||
\(808\) | 30.2139 | 1.06292 | ||||||||
\(809\) | −5.23437 | −0.184031 | −0.0920153 | − | 0.995758i | \(-0.529331\pi\) | ||||
−0.0920153 | + | 0.995758i | \(0.529331\pi\) | |||||||
\(810\) | −95.2846 | −3.34796 | ||||||||
\(811\) | −39.1010 | −1.37302 | −0.686510 | − | 0.727120i | \(-0.740858\pi\) | ||||
−0.686510 | + | 0.727120i | \(0.740858\pi\) | |||||||
\(812\) | −62.2437 | −2.18432 | ||||||||
\(813\) | 10.5837 | 0.371187 | ||||||||
\(814\) | −114.318 | −4.00685 | ||||||||
\(815\) | −38.9649 | −1.36488 | ||||||||
\(816\) | −5.28437 | −0.184990 | ||||||||
\(817\) | −17.3131 | −0.605709 | ||||||||
\(818\) | 37.0022 | 1.29375 | ||||||||
\(819\) | 12.2175 | 0.426915 | ||||||||
\(820\) | 51.3435 | 1.79299 | ||||||||
\(821\) | −2.51187 | −0.0876647 | −0.0438324 | − | 0.999039i | \(-0.513957\pi\) | ||||
−0.0438324 | + | 0.999039i | \(0.513957\pi\) | |||||||
\(822\) | 110.057 | 3.83869 | ||||||||
\(823\) | 8.28117 | 0.288663 | 0.144332 | − | 0.989529i | \(-0.453897\pi\) | ||||
0.144332 | + | 0.989529i | \(0.453897\pi\) | |||||||
\(824\) | 5.11321 | 0.178127 | ||||||||
\(825\) | 125.935 | 4.38450 | ||||||||
\(826\) | 32.2565 | 1.12235 | ||||||||
\(827\) | 20.7902 | 0.722945 | 0.361473 | − | 0.932383i | \(-0.382274\pi\) | ||||
0.361473 | + | 0.932383i | \(0.382274\pi\) | |||||||
\(828\) | −30.2259 | −1.05042 | ||||||||
\(829\) | 49.4890 | 1.71882 | 0.859411 | − | 0.511285i | \(-0.170830\pi\) | ||||
0.859411 | + | 0.511285i | \(0.170830\pi\) | |||||||
\(830\) | 71.5684 | 2.48418 | ||||||||
\(831\) | 45.5365 | 1.57964 | ||||||||
\(832\) | 13.0053 | 0.450877 | ||||||||
\(833\) | 46.2878 | 1.60378 | ||||||||
\(834\) | −91.2479 | −3.15966 | ||||||||
\(835\) | −23.9014 | −0.827141 | ||||||||
\(836\) | −58.7925 | −2.03338 | ||||||||
\(837\) | 3.94244 | 0.136271 | ||||||||
\(838\) | 50.2622 | 1.73628 | ||||||||
\(839\) | −45.6574 | −1.57627 | −0.788135 | − | 0.615502i | \(-0.788953\pi\) | ||||
−0.788135 | + | 0.615502i | \(0.788953\pi\) | |||||||
\(840\) | −109.274 | −3.77032 | ||||||||
\(841\) | −13.0171 | −0.448867 | ||||||||
\(842\) | −10.9701 | −0.378053 | ||||||||
\(843\) | −34.0862 | −1.17399 | ||||||||
\(844\) | −68.5287 | −2.35885 | ||||||||
\(845\) | −4.05108 | −0.139361 | ||||||||
\(846\) | −12.5274 | −0.430702 | ||||||||
\(847\) | −60.7644 | −2.08789 | ||||||||
\(848\) | −8.90231 | −0.305707 | ||||||||
\(849\) | −30.0126 | −1.03003 | ||||||||
\(850\) | −59.5735 | −2.04335 | ||||||||
\(851\) | −45.7040 | −1.56671 | ||||||||
\(852\) | −86.2424 | −2.95462 | ||||||||
\(853\) | −20.9148 | −0.716108 | −0.358054 | − | 0.933701i | \(-0.616560\pi\) | ||||
−0.358054 | + | 0.933701i | \(0.616560\pi\) | |||||||
\(854\) | 48.1252 | 1.64681 | ||||||||
\(855\) | 39.2022 | 1.34069 | ||||||||
\(856\) | −9.93243 | −0.339484 | ||||||||
\(857\) | −45.5327 | −1.55537 | −0.777684 | − | 0.628655i | \(-0.783606\pi\) | ||||
−0.777684 | + | 0.628655i | \(0.783606\pi\) | |||||||
\(858\) | 24.6908 | 0.842929 | ||||||||
\(859\) | −30.0964 | −1.02688 | −0.513438 | − | 0.858127i | \(-0.671628\pi\) | ||||
−0.513438 | + | 0.858127i | \(0.671628\pi\) | |||||||
\(860\) | −51.3723 | −1.75178 | ||||||||
\(861\) | 50.5699 | 1.72342 | ||||||||
\(862\) | 53.6960 | 1.82889 | ||||||||
\(863\) | 0.389666 | 0.0132644 | 0.00663220 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663220 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(864\) | −9.93207 | −0.337896 | ||||||||
\(865\) | −41.2415 | −1.40225 | ||||||||
\(866\) | 78.6587 | 2.67293 | ||||||||
\(867\) | −26.7477 | −0.908400 | ||||||||
\(868\) | 41.3294 | 1.40281 | ||||||||
\(869\) | −8.16528 | −0.276988 | ||||||||
\(870\) | 83.8757 | 2.84365 | ||||||||
\(871\) | 4.83531 | 0.163838 | ||||||||
\(872\) | 22.7817 | 0.771485 | ||||||||
\(873\) | −10.8895 | −0.368552 | ||||||||
\(874\) | −39.1468 | −1.32416 | ||||||||
\(875\) | 134.547 | 4.54853 | ||||||||
\(876\) | 38.0504 | 1.28560 | ||||||||
\(877\) | 46.2964 | 1.56332 | 0.781659 | − | 0.623706i | \(-0.214374\pi\) | ||||
0.781659 | + | 0.623706i | \(0.214374\pi\) | |||||||
\(878\) | −9.00967 | −0.304062 | ||||||||
\(879\) | 17.4899 | 0.589921 | ||||||||
\(880\) | 18.8948 | 0.636944 | ||||||||
\(881\) | −19.2251 | −0.647710 | −0.323855 | − | 0.946107i | \(-0.604979\pi\) | ||||
−0.323855 | + | 0.946107i | \(0.604979\pi\) | |||||||
\(882\) | −104.666 | −3.52429 | ||||||||
\(883\) | 2.93154 | 0.0986543 | 0.0493271 | − | 0.998783i | \(-0.484292\pi\) | ||||
0.0493271 | + | 0.998783i | \(0.484292\pi\) | |||||||
\(884\) | −7.01302 | −0.235873 | ||||||||
\(885\) | −26.0989 | −0.877306 | ||||||||
\(886\) | 29.8294 | 1.00214 | ||||||||
\(887\) | 46.8097 | 1.57172 | 0.785858 | − | 0.618407i | \(-0.212222\pi\) | ||||
0.785858 | + | 0.618407i | \(0.212222\pi\) | |||||||
\(888\) | −55.8062 | −1.87273 | ||||||||
\(889\) | 71.3665 | 2.39355 | ||||||||
\(890\) | 114.264 | 3.83014 | ||||||||
\(891\) | −50.1220 | −1.67915 | ||||||||
\(892\) | −27.4176 | −0.918008 | ||||||||
\(893\) | −9.74188 | −0.326000 | ||||||||
\(894\) | 80.1918 | 2.68201 | ||||||||
\(895\) | 96.7616 | 3.23438 | ||||||||
\(896\) | −81.4429 | −2.72081 | ||||||||
\(897\) | 9.87128 | 0.329592 | ||||||||
\(898\) | 26.3799 | 0.880309 | ||||||||
\(899\) | −10.6125 | −0.353947 | ||||||||
\(900\) | 80.8829 | 2.69610 | ||||||||
\(901\) | 21.2338 | 0.707401 | ||||||||
\(902\) | 44.9808 | 1.49770 | ||||||||
\(903\) | −50.5983 | −1.68381 | ||||||||
\(904\) | 16.7415 | 0.556815 | ||||||||
\(905\) | 8.75485 | 0.291021 | ||||||||
\(906\) | −71.0701 | −2.36115 | ||||||||
\(907\) | 3.38813 | 0.112501 | 0.0562506 | − | 0.998417i | \(-0.482085\pi\) | ||||
0.0562506 | + | 0.998417i | \(0.482085\pi\) | |||||||
\(908\) | 54.1570 | 1.79726 | ||||||||
\(909\) | −31.6782 | −1.05070 | ||||||||
\(910\) | 46.9520 | 1.55644 | ||||||||
\(911\) | 25.9959 | 0.861283 | 0.430642 | − | 0.902523i | \(-0.358287\pi\) | ||||
0.430642 | + | 0.902523i | \(0.358287\pi\) | |||||||
\(912\) | 9.29210 | 0.307692 | ||||||||
\(913\) | 37.6468 | 1.24593 | ||||||||
\(914\) | −77.0618 | −2.54898 | ||||||||
\(915\) | −38.9384 | −1.28726 | ||||||||
\(916\) | −59.2103 | −1.95636 | ||||||||
\(917\) | −8.73350 | −0.288405 | ||||||||
\(918\) | 7.75344 | 0.255902 | ||||||||
\(919\) | −2.70131 | −0.0891079 | −0.0445539 | − | 0.999007i | \(-0.514187\pi\) | ||||
−0.0445539 | + | 0.999007i | \(0.514187\pi\) | |||||||
\(920\) | −38.8590 | −1.28114 | ||||||||
\(921\) | 59.8384 | 1.97174 | ||||||||
\(922\) | 4.07883 | 0.134329 | ||||||||
\(923\) | 12.3965 | 0.408035 | ||||||||
\(924\) | −171.824 | −5.65258 | ||||||||
\(925\) | 122.301 | 4.02124 | ||||||||
\(926\) | 2.23728 | 0.0735215 | ||||||||
\(927\) | −5.36102 | −0.176079 | ||||||||
\(928\) | 26.7358 | 0.877646 | ||||||||
\(929\) | 57.0827 | 1.87282 | 0.936411 | − | 0.350905i | \(-0.114126\pi\) | ||||
0.936411 | + | 0.350905i | \(0.114126\pi\) | |||||||
\(930\) | −55.6929 | −1.82624 | ||||||||
\(931\) | −81.3930 | −2.66755 | ||||||||
\(932\) | −16.3592 | −0.535865 | ||||||||
\(933\) | −73.7874 | −2.41569 | ||||||||
\(934\) | −55.0469 | −1.80119 | ||||||||
\(935\) | −45.0679 | −1.47388 | ||||||||
\(936\) | 5.30500 | 0.173399 | ||||||||
\(937\) | 18.5064 | 0.604579 | 0.302290 | − | 0.953216i | \(-0.402249\pi\) | ||||
0.302290 | + | 0.953216i | \(0.402249\pi\) | |||||||
\(938\) | −56.0413 | −1.82981 | ||||||||
\(939\) | 33.0698 | 1.07919 | ||||||||
\(940\) | −28.9066 | −0.942830 | ||||||||
\(941\) | −8.88120 | −0.289519 | −0.144759 | − | 0.989467i | \(-0.546241\pi\) | ||||
−0.144759 | + | 0.989467i | \(0.546241\pi\) | |||||||
\(942\) | −85.2082 | −2.77623 | ||||||||
\(943\) | 17.9832 | 0.585612 | ||||||||
\(944\) | −2.72276 | −0.0886183 | ||||||||
\(945\) | −31.1679 | −1.01389 | ||||||||
\(946\) | −45.0061 | −1.46327 | ||||||||
\(947\) | −28.3129 | −0.920046 | −0.460023 | − | 0.887907i | \(-0.652159\pi\) | ||||
−0.460023 | + | 0.887907i | \(0.652159\pi\) | |||||||
\(948\) | −11.9151 | −0.386984 | ||||||||
\(949\) | −5.46936 | −0.177543 | ||||||||
\(950\) | 104.755 | 3.39869 | ||||||||
\(951\) | −44.1342 | −1.43115 | ||||||||
\(952\) | 27.1913 | 0.881274 | ||||||||
\(953\) | −53.9944 | −1.74905 | −0.874524 | − | 0.484981i | \(-0.838826\pi\) | ||||
−0.874524 | + | 0.484981i | \(0.838826\pi\) | |||||||
\(954\) | −48.0139 | −1.55451 | ||||||||
\(955\) | 56.3104 | 1.82216 | ||||||||
\(956\) | 62.2321 | 2.01273 | ||||||||
\(957\) | 44.1206 | 1.42622 | ||||||||
\(958\) | 58.5068 | 1.89027 | ||||||||
\(959\) | 110.089 | 3.55496 | ||||||||
\(960\) | 121.957 | 3.93616 | ||||||||
\(961\) | −23.9534 | −0.772689 | ||||||||
\(962\) | 23.9783 | 0.773092 | ||||||||
\(963\) | 10.4138 | 0.335580 | ||||||||
\(964\) | 52.2028 | 1.68134 | ||||||||
\(965\) | 80.5314 | 2.59240 | ||||||||
\(966\) | −114.408 | −3.68102 | ||||||||
\(967\) | 41.3037 | 1.32824 | 0.664118 | − | 0.747628i | \(-0.268807\pi\) | ||||
0.664118 | + | 0.747628i | \(0.268807\pi\) | |||||||
\(968\) | −26.3847 | −0.848035 | ||||||||
\(969\) | −22.1635 | −0.711995 | ||||||||
\(970\) | −41.8482 | −1.34367 | ||||||||
\(971\) | 4.94888 | 0.158817 | 0.0794085 | − | 0.996842i | \(-0.474697\pi\) | ||||
0.0794085 | + | 0.996842i | \(0.474697\pi\) | |||||||
\(972\) | −59.7494 | −1.91646 | ||||||||
\(973\) | −91.2743 | −2.92612 | ||||||||
\(974\) | −55.2851 | −1.77145 | ||||||||
\(975\) | −26.4150 | −0.845957 | ||||||||
\(976\) | −4.06223 | −0.130029 | ||||||||
\(977\) | −24.3468 | −0.778925 | −0.389462 | − | 0.921042i | \(-0.627339\pi\) | ||||
−0.389462 | + | 0.921042i | \(0.627339\pi\) | |||||||
\(978\) | −49.8128 | −1.59284 | ||||||||
\(979\) | 60.1057 | 1.92099 | ||||||||
\(980\) | −241.514 | −7.71487 | ||||||||
\(981\) | −23.8858 | −0.762615 | ||||||||
\(982\) | −9.25926 | −0.295475 | ||||||||
\(983\) | −57.1539 | −1.82293 | −0.911464 | − | 0.411380i | \(-0.865047\pi\) | ||||
−0.911464 | + | 0.411380i | \(0.865047\pi\) | |||||||
\(984\) | 21.9581 | 0.699998 | ||||||||
\(985\) | 23.4365 | 0.746748 | ||||||||
\(986\) | −20.8712 | −0.664675 | ||||||||
\(987\) | −28.4711 | −0.906244 | ||||||||
\(988\) | 12.3318 | 0.392326 | ||||||||
\(989\) | −17.9933 | −0.572152 | ||||||||
\(990\) | 101.908 | 3.23884 | ||||||||
\(991\) | 22.8587 | 0.726130 | 0.363065 | − | 0.931764i | \(-0.381730\pi\) | ||||
0.363065 | + | 0.931764i | \(0.381730\pi\) | |||||||
\(992\) | −17.7524 | −0.563640 | ||||||||
\(993\) | 74.9305 | 2.37785 | ||||||||
\(994\) | −143.675 | −4.55710 | ||||||||
\(995\) | −96.8384 | −3.06998 | ||||||||
\(996\) | 54.9356 | 1.74070 | ||||||||
\(997\) | 40.4888 | 1.28229 | 0.641147 | − | 0.767418i | \(-0.278459\pi\) | ||||
0.641147 | + | 0.767418i | \(0.278459\pi\) | |||||||
\(998\) | −30.3622 | −0.961098 | ||||||||
\(999\) | −15.9174 | −0.503604 |
(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 | 6019.2.a.c.1.16 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.c.1.16 | ✓ | 108 | 1.1 | even | 1 | trivial |