Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.05256 | −1.78635 | −0.893174 | − | 0.449710i | \(-0.851527\pi\) | ||||
−0.893174 | + | 0.449710i | \(0.851527\pi\) | |||||||
\(3\) | 9.36203 | 1.80172 | 0.900861 | − | 0.434107i | \(-0.142936\pi\) | ||||
0.900861 | + | 0.434107i | \(0.142936\pi\) | |||||||
\(4\) | 17.5283 | 2.19104 | ||||||||
\(5\) | 14.1438 | 1.26506 | 0.632531 | − | 0.774535i | \(-0.282016\pi\) | ||||
0.632531 | + | 0.774535i | \(0.282016\pi\) | |||||||
\(6\) | −47.3022 | −3.21851 | ||||||||
\(7\) | −13.7151 | −0.740546 | −0.370273 | − | 0.928923i | \(-0.620736\pi\) | ||||
−0.370273 | + | 0.928923i | \(0.620736\pi\) | |||||||
\(8\) | −48.1425 | −2.12762 | ||||||||
\(9\) | 60.6475 | 2.24620 | ||||||||
\(10\) | −71.4625 | −2.25984 | ||||||||
\(11\) | 10.3705 | 0.284257 | 0.142129 | − | 0.989848i | \(-0.454605\pi\) | ||||
0.142129 | + | 0.989848i | \(0.454605\pi\) | |||||||
\(12\) | 164.101 | 3.94765 | ||||||||
\(13\) | −61.4205 | −1.31038 | −0.655192 | − | 0.755463i | \(-0.727412\pi\) | ||||
−0.655192 | + | 0.755463i | \(0.727412\pi\) | |||||||
\(14\) | 69.2963 | 1.32287 | ||||||||
\(15\) | 132.415 | 2.27929 | ||||||||
\(16\) | 103.016 | 1.60963 | ||||||||
\(17\) | −24.4390 | −0.348666 | −0.174333 | − | 0.984687i | \(-0.555777\pi\) | ||||
−0.174333 | + | 0.984687i | \(0.555777\pi\) | |||||||
\(18\) | −306.425 | −4.01251 | ||||||||
\(19\) | −65.5106 | −0.791008 | −0.395504 | − | 0.918464i | \(-0.629430\pi\) | ||||
−0.395504 | + | 0.918464i | \(0.629430\pi\) | |||||||
\(20\) | 247.918 | 2.77181 | ||||||||
\(21\) | −128.401 | −1.33426 | ||||||||
\(22\) | −52.3977 | −0.507783 | ||||||||
\(23\) | 23.4730 | 0.212803 | 0.106401 | − | 0.994323i | \(-0.466067\pi\) | ||||
0.106401 | + | 0.994323i | \(0.466067\pi\) | |||||||
\(24\) | −450.711 | −3.83338 | ||||||||
\(25\) | 75.0480 | 0.600384 | ||||||||
\(26\) | 310.331 | 2.34080 | ||||||||
\(27\) | 315.009 | 2.24532 | ||||||||
\(28\) | −240.403 | −1.62257 | ||||||||
\(29\) | −236.538 | −1.51462 | −0.757310 | − | 0.653055i | \(-0.773487\pi\) | ||||
−0.757310 | + | 0.653055i | \(0.773487\pi\) | |||||||
\(30\) | −669.034 | −4.07161 | ||||||||
\(31\) | −210.270 | −1.21824 | −0.609122 | − | 0.793076i | \(-0.708478\pi\) | ||||
−0.609122 | + | 0.793076i | \(0.708478\pi\) | |||||||
\(32\) | −135.354 | −0.747735 | ||||||||
\(33\) | 97.0891 | 0.512153 | ||||||||
\(34\) | 123.479 | 0.622840 | ||||||||
\(35\) | −193.984 | −0.936837 | ||||||||
\(36\) | 1063.05 | 4.92153 | ||||||||
\(37\) | −316.642 | −1.40691 | −0.703455 | − | 0.710740i | \(-0.748360\pi\) | ||||
−0.703455 | + | 0.710740i | \(0.748360\pi\) | |||||||
\(38\) | 330.996 | 1.41302 | ||||||||
\(39\) | −575.020 | −2.36095 | ||||||||
\(40\) | −680.919 | −2.69157 | ||||||||
\(41\) | 13.2054 | 0.0503008 | 0.0251504 | − | 0.999684i | \(-0.491994\pi\) | ||||
0.0251504 | + | 0.999684i | \(0.491994\pi\) | |||||||
\(42\) | 648.754 | 2.38345 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 181.778 | 0.622820 | ||||||||
\(45\) | 857.789 | 2.84159 | ||||||||
\(46\) | −118.599 | −0.380140 | ||||||||
\(47\) | 450.216 | 1.39725 | 0.698625 | − | 0.715488i | \(-0.253796\pi\) | ||||
0.698625 | + | 0.715488i | \(0.253796\pi\) | |||||||
\(48\) | 964.439 | 2.90010 | ||||||||
\(49\) | −154.896 | −0.451592 | ||||||||
\(50\) | −379.185 | −1.07250 | ||||||||
\(51\) | −228.798 | −0.628200 | ||||||||
\(52\) | −1076.60 | −2.87111 | ||||||||
\(53\) | −205.541 | −0.532701 | −0.266351 | − | 0.963876i | \(-0.585818\pi\) | ||||
−0.266351 | + | 0.963876i | \(0.585818\pi\) | |||||||
\(54\) | −1591.60 | −4.01092 | ||||||||
\(55\) | 146.679 | 0.359603 | ||||||||
\(56\) | 660.279 | 1.57560 | ||||||||
\(57\) | −613.312 | −1.42518 | ||||||||
\(58\) | 1195.12 | 2.70564 | ||||||||
\(59\) | 334.558 | 0.738232 | 0.369116 | − | 0.929383i | \(-0.379661\pi\) | ||||
0.369116 | + | 0.929383i | \(0.379661\pi\) | |||||||
\(60\) | 2321.01 | 4.99403 | ||||||||
\(61\) | 811.774 | 1.70389 | 0.851943 | − | 0.523634i | \(-0.175424\pi\) | ||||
0.851943 | + | 0.523634i | \(0.175424\pi\) | |||||||
\(62\) | 1062.40 | 2.17621 | ||||||||
\(63\) | −831.787 | −1.66342 | ||||||||
\(64\) | −140.242 | −0.273910 | ||||||||
\(65\) | −868.722 | −1.65772 | ||||||||
\(66\) | −490.548 | −0.914884 | ||||||||
\(67\) | −113.497 | −0.206952 | −0.103476 | − | 0.994632i | \(-0.532997\pi\) | ||||
−0.103476 | + | 0.994632i | \(0.532997\pi\) | |||||||
\(68\) | −428.375 | −0.763943 | ||||||||
\(69\) | 219.755 | 0.383411 | ||||||||
\(70\) | 980.116 | 1.67352 | ||||||||
\(71\) | −53.8087 | −0.0899425 | −0.0449712 | − | 0.998988i | \(-0.514320\pi\) | ||||
−0.0449712 | + | 0.998988i | \(0.514320\pi\) | |||||||
\(72\) | −2919.72 | −4.77907 | ||||||||
\(73\) | −108.423 | −0.173835 | −0.0869174 | − | 0.996216i | \(-0.527702\pi\) | ||||
−0.0869174 | + | 0.996216i | \(0.527702\pi\) | |||||||
\(74\) | 1599.85 | 2.51323 | ||||||||
\(75\) | 702.602 | 1.08173 | ||||||||
\(76\) | −1148.29 | −1.73313 | ||||||||
\(77\) | −142.233 | −0.210506 | ||||||||
\(78\) | 2905.32 | 4.21748 | ||||||||
\(79\) | −723.417 | −1.03026 | −0.515132 | − | 0.857111i | \(-0.672257\pi\) | ||||
−0.515132 | + | 0.857111i | \(0.672257\pi\) | |||||||
\(80\) | 1457.04 | 2.03628 | ||||||||
\(81\) | 1311.64 | 1.79923 | ||||||||
\(82\) | −66.7209 | −0.0898548 | ||||||||
\(83\) | 191.269 | 0.252945 | 0.126473 | − | 0.991970i | \(-0.459634\pi\) | ||||
0.126473 | + | 0.991970i | \(0.459634\pi\) | |||||||
\(84\) | −2250.66 | −2.92342 | ||||||||
\(85\) | −345.661 | −0.441085 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2214.47 | −2.72893 | ||||||||
\(88\) | −499.263 | −0.604791 | ||||||||
\(89\) | 419.159 | 0.499221 | 0.249611 | − | 0.968346i | \(-0.419697\pi\) | ||||
0.249611 | + | 0.968346i | \(0.419697\pi\) | |||||||
\(90\) | −4334.03 | −5.07607 | ||||||||
\(91\) | 842.389 | 0.970399 | ||||||||
\(92\) | 411.443 | 0.466260 | ||||||||
\(93\) | −1968.55 | −2.19494 | ||||||||
\(94\) | −2274.74 | −2.49598 | ||||||||
\(95\) | −926.571 | −1.00068 | ||||||||
\(96\) | −1267.19 | −1.34721 | ||||||||
\(97\) | −953.469 | −0.998043 | −0.499021 | − | 0.866590i | \(-0.666307\pi\) | ||||
−0.499021 | + | 0.866590i | \(0.666307\pi\) | |||||||
\(98\) | 782.621 | 0.806701 | ||||||||
\(99\) | 628.947 | 0.638500 | ||||||||
\(100\) | 1315.47 | 1.31547 | ||||||||
\(101\) | −1393.87 | −1.37322 | −0.686612 | − | 0.727024i | \(-0.740903\pi\) | ||||
−0.686612 | + | 0.727024i | \(0.740903\pi\) | |||||||
\(102\) | 1156.02 | 1.12218 | ||||||||
\(103\) | −1470.15 | −1.40639 | −0.703197 | − | 0.710995i | \(-0.748245\pi\) | ||||
−0.703197 | + | 0.710995i | \(0.748245\pi\) | |||||||
\(104\) | 2956.94 | 2.78800 | ||||||||
\(105\) | −1816.08 | −1.68792 | ||||||||
\(106\) | 1038.51 | 0.951590 | ||||||||
\(107\) | −1071.54 | −0.968124 | −0.484062 | − | 0.875034i | \(-0.660839\pi\) | ||||
−0.484062 | + | 0.875034i | \(0.660839\pi\) | |||||||
\(108\) | 5521.59 | 4.91958 | ||||||||
\(109\) | −1637.65 | −1.43907 | −0.719536 | − | 0.694455i | \(-0.755645\pi\) | ||||
−0.719536 | + | 0.694455i | \(0.755645\pi\) | |||||||
\(110\) | −741.104 | −0.642377 | ||||||||
\(111\) | −2964.41 | −2.53486 | ||||||||
\(112\) | −1412.88 | −1.19200 | ||||||||
\(113\) | 1051.03 | 0.874980 | 0.437490 | − | 0.899223i | \(-0.355868\pi\) | ||||
0.437490 | + | 0.899223i | \(0.355868\pi\) | |||||||
\(114\) | 3098.79 | 2.54586 | ||||||||
\(115\) | 331.998 | 0.269209 | ||||||||
\(116\) | −4146.12 | −3.31860 | ||||||||
\(117\) | −3725.00 | −2.94339 | ||||||||
\(118\) | −1690.37 | −1.31874 | ||||||||
\(119\) | 335.183 | 0.258203 | ||||||||
\(120\) | −6374.79 | −4.84946 | ||||||||
\(121\) | −1223.45 | −0.919198 | ||||||||
\(122\) | −4101.54 | −3.04374 | ||||||||
\(123\) | 123.629 | 0.0906281 | ||||||||
\(124\) | −3685.68 | −2.66923 | ||||||||
\(125\) | −706.512 | −0.505539 | ||||||||
\(126\) | 4202.65 | 2.97144 | ||||||||
\(127\) | 316.221 | 0.220946 | 0.110473 | − | 0.993879i | \(-0.464763\pi\) | ||||
0.110473 | + | 0.993879i | \(0.464763\pi\) | |||||||
\(128\) | 1791.42 | 1.23703 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4389.27 | 2.96126 | ||||||||
\(131\) | −1798.72 | −1.19965 | −0.599826 | − | 0.800130i | \(-0.704764\pi\) | ||||
−0.599826 | + | 0.800130i | \(0.704764\pi\) | |||||||
\(132\) | 1701.81 | 1.12215 | ||||||||
\(133\) | 898.484 | 0.585778 | ||||||||
\(134\) | 573.448 | 0.369689 | ||||||||
\(135\) | 4455.44 | 2.84047 | ||||||||
\(136\) | 1176.55 | 0.741829 | ||||||||
\(137\) | 2412.04 | 1.50419 | 0.752096 | − | 0.659054i | \(-0.229043\pi\) | ||||
0.752096 | + | 0.659054i | \(0.229043\pi\) | |||||||
\(138\) | −1110.32 | −0.684907 | ||||||||
\(139\) | 2424.03 | 1.47916 | 0.739582 | − | 0.673066i | \(-0.235023\pi\) | ||||
0.739582 | + | 0.673066i | \(0.235023\pi\) | |||||||
\(140\) | −3400.22 | −2.05265 | ||||||||
\(141\) | 4214.93 | 2.51746 | ||||||||
\(142\) | 271.871 | 0.160669 | ||||||||
\(143\) | −636.963 | −0.372486 | ||||||||
\(144\) | 6247.67 | 3.61555 | ||||||||
\(145\) | −3345.55 | −1.91609 | ||||||||
\(146\) | 547.813 | 0.310530 | ||||||||
\(147\) | −1450.14 | −0.813643 | ||||||||
\(148\) | −5550.21 | −3.08260 | ||||||||
\(149\) | −263.130 | −0.144674 | −0.0723372 | − | 0.997380i | \(-0.523046\pi\) | ||||
−0.0723372 | + | 0.997380i | \(0.523046\pi\) | |||||||
\(150\) | −3549.94 | −1.93234 | ||||||||
\(151\) | 1149.48 | 0.619493 | 0.309746 | − | 0.950819i | \(-0.399756\pi\) | ||||
0.309746 | + | 0.950819i | \(0.399756\pi\) | |||||||
\(152\) | 3153.84 | 1.68296 | ||||||||
\(153\) | −1482.16 | −0.783176 | ||||||||
\(154\) | 718.639 | 0.376036 | ||||||||
\(155\) | −2974.02 | −1.54116 | ||||||||
\(156\) | −10079.2 | −5.17294 | ||||||||
\(157\) | −945.081 | −0.480418 | −0.240209 | − | 0.970721i | \(-0.577216\pi\) | ||||
−0.240209 | + | 0.970721i | \(0.577216\pi\) | |||||||
\(158\) | 3655.11 | 1.84041 | ||||||||
\(159\) | −1924.28 | −0.959780 | ||||||||
\(160\) | −1914.43 | −0.945932 | ||||||||
\(161\) | −321.935 | −0.157590 | ||||||||
\(162\) | −6627.13 | −3.21405 | ||||||||
\(163\) | −1316.21 | −0.632476 | −0.316238 | − | 0.948680i | \(-0.602420\pi\) | ||||
−0.316238 | + | 0.948680i | \(0.602420\pi\) | |||||||
\(164\) | 231.468 | 0.110211 | ||||||||
\(165\) | 1373.21 | 0.647906 | ||||||||
\(166\) | −966.396 | −0.451849 | ||||||||
\(167\) | −1745.74 | −0.808917 | −0.404459 | − | 0.914556i | \(-0.632540\pi\) | ||||
−0.404459 | + | 0.914556i | \(0.632540\pi\) | |||||||
\(168\) | 6181.55 | 2.83879 | ||||||||
\(169\) | 1575.48 | 0.717105 | ||||||||
\(170\) | 1746.47 | 0.787931 | ||||||||
\(171\) | −3973.05 | −1.77677 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1020.88 | 0.448646 | 0.224323 | − | 0.974515i | \(-0.427983\pi\) | ||||
0.224323 | + | 0.974515i | \(0.427983\pi\) | |||||||
\(174\) | 11188.8 | 4.87482 | ||||||||
\(175\) | −1029.29 | −0.444612 | ||||||||
\(176\) | 1068.33 | 0.457548 | ||||||||
\(177\) | 3132.14 | 1.33009 | ||||||||
\(178\) | −2117.82 | −0.891784 | ||||||||
\(179\) | 1448.99 | 0.605043 | 0.302521 | − | 0.953143i | \(-0.402172\pi\) | ||||
0.302521 | + | 0.953143i | \(0.402172\pi\) | |||||||
\(180\) | 15035.6 | 6.22605 | ||||||||
\(181\) | −1207.52 | −0.495882 | −0.247941 | − | 0.968775i | \(-0.579754\pi\) | ||||
−0.247941 | + | 0.968775i | \(0.579754\pi\) | |||||||
\(182\) | −4256.22 | −1.73347 | ||||||||
\(183\) | 7599.85 | 3.06993 | ||||||||
\(184\) | −1130.05 | −0.452763 | ||||||||
\(185\) | −4478.53 | −1.77983 | ||||||||
\(186\) | 9946.23 | 3.92093 | ||||||||
\(187\) | −253.445 | −0.0991109 | ||||||||
\(188\) | 7891.54 | 3.06143 | ||||||||
\(189\) | −4320.38 | −1.66276 | ||||||||
\(190\) | 4681.55 | 1.78756 | ||||||||
\(191\) | 4420.48 | 1.67463 | 0.837316 | − | 0.546719i | \(-0.184123\pi\) | ||||
0.837316 | + | 0.546719i | \(0.184123\pi\) | |||||||
\(192\) | −1312.95 | −0.493510 | ||||||||
\(193\) | 3256.05 | 1.21438 | 0.607192 | − | 0.794556i | \(-0.292296\pi\) | ||||
0.607192 | + | 0.794556i | \(0.292296\pi\) | |||||||
\(194\) | 4817.46 | 1.78285 | ||||||||
\(195\) | −8132.99 | −2.98675 | ||||||||
\(196\) | −2715.07 | −0.989457 | ||||||||
\(197\) | −4223.73 | −1.52755 | −0.763777 | − | 0.645480i | \(-0.776657\pi\) | ||||
−0.763777 | + | 0.645480i | \(0.776657\pi\) | |||||||
\(198\) | −3177.79 | −1.14058 | ||||||||
\(199\) | 4105.07 | 1.46232 | 0.731158 | − | 0.682208i | \(-0.238980\pi\) | ||||
0.731158 | + | 0.682208i | \(0.238980\pi\) | |||||||
\(200\) | −3613.00 | −1.27739 | ||||||||
\(201\) | −1062.56 | −0.372871 | ||||||||
\(202\) | 7042.63 | 2.45306 | ||||||||
\(203\) | 3244.14 | 1.12165 | ||||||||
\(204\) | −4010.46 | −1.37641 | ||||||||
\(205\) | 186.775 | 0.0636337 | ||||||||
\(206\) | 7428.04 | 2.51231 | ||||||||
\(207\) | 1423.58 | 0.477998 | ||||||||
\(208\) | −6327.30 | −2.10923 | ||||||||
\(209\) | −679.379 | −0.224850 | ||||||||
\(210\) | 9175.87 | 3.01522 | ||||||||
\(211\) | −4020.06 | −1.31162 | −0.655811 | − | 0.754925i | \(-0.727673\pi\) | ||||
−0.655811 | + | 0.754925i | \(0.727673\pi\) | |||||||
\(212\) | −3602.78 | −1.16717 | ||||||||
\(213\) | −503.758 | −0.162051 | ||||||||
\(214\) | 5413.99 | 1.72941 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −15165.3 | −4.77717 | ||||||||
\(217\) | 2883.87 | 0.902166 | ||||||||
\(218\) | 8274.34 | 2.57068 | ||||||||
\(219\) | −1015.06 | −0.313202 | ||||||||
\(220\) | 2571.04 | 0.787906 | ||||||||
\(221\) | 1501.06 | 0.456887 | ||||||||
\(222\) | 14977.9 | 4.52815 | ||||||||
\(223\) | 924.761 | 0.277698 | 0.138849 | − | 0.990314i | \(-0.455660\pi\) | ||||
0.138849 | + | 0.990314i | \(0.455660\pi\) | |||||||
\(224\) | 1856.40 | 0.553732 | ||||||||
\(225\) | 4551.48 | 1.34859 | ||||||||
\(226\) | −5310.40 | −1.56302 | ||||||||
\(227\) | 3472.29 | 1.01526 | 0.507630 | − | 0.861575i | \(-0.330522\pi\) | ||||
0.507630 | + | 0.861575i | \(0.330522\pi\) | |||||||
\(228\) | −10750.3 | −3.12263 | ||||||||
\(229\) | 2118.36 | 0.611289 | 0.305644 | − | 0.952146i | \(-0.401128\pi\) | ||||
0.305644 | + | 0.952146i | \(0.401128\pi\) | |||||||
\(230\) | −1677.44 | −0.480901 | ||||||||
\(231\) | −1331.59 | −0.379273 | ||||||||
\(232\) | 11387.5 | 3.22253 | ||||||||
\(233\) | −3691.16 | −1.03784 | −0.518919 | − | 0.854824i | \(-0.673665\pi\) | ||||
−0.518919 | + | 0.854824i | \(0.673665\pi\) | |||||||
\(234\) | 18820.8 | 5.25792 | ||||||||
\(235\) | 6367.78 | 1.76761 | ||||||||
\(236\) | 5864.24 | 1.61750 | ||||||||
\(237\) | −6772.65 | −1.85625 | ||||||||
\(238\) | −1693.53 | −0.461241 | ||||||||
\(239\) | 4854.95 | 1.31398 | 0.656988 | − | 0.753901i | \(-0.271830\pi\) | ||||
0.656988 | + | 0.753901i | \(0.271830\pi\) | |||||||
\(240\) | 13640.9 | 3.66881 | ||||||||
\(241\) | 2585.98 | 0.691193 | 0.345597 | − | 0.938383i | \(-0.387677\pi\) | ||||
0.345597 | + | 0.938383i | \(0.387677\pi\) | |||||||
\(242\) | 6181.56 | 1.64201 | ||||||||
\(243\) | 3774.36 | 0.996400 | ||||||||
\(244\) | 14229.1 | 3.73329 | ||||||||
\(245\) | −2190.82 | −0.571292 | ||||||||
\(246\) | −624.643 | −0.161893 | ||||||||
\(247\) | 4023.69 | 1.03652 | ||||||||
\(248\) | 10122.9 | 2.59196 | ||||||||
\(249\) | 1790.66 | 0.455737 | ||||||||
\(250\) | 3569.69 | 0.903069 | ||||||||
\(251\) | −2636.94 | −0.663116 | −0.331558 | − | 0.943435i | \(-0.607574\pi\) | ||||
−0.331558 | + | 0.943435i | \(0.607574\pi\) | |||||||
\(252\) | −14579.8 | −3.64462 | ||||||||
\(253\) | 243.427 | 0.0604907 | ||||||||
\(254\) | −1597.73 | −0.394686 | ||||||||
\(255\) | −3236.09 | −0.794712 | ||||||||
\(256\) | −7929.30 | −1.93586 | ||||||||
\(257\) | −7352.59 | −1.78460 | −0.892299 | − | 0.451444i | \(-0.850909\pi\) | ||||
−0.892299 | + | 0.451444i | \(0.850909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4342.78 | 1.04188 | ||||||||
\(260\) | −15227.2 | −3.63213 | ||||||||
\(261\) | −14345.4 | −3.40215 | ||||||||
\(262\) | 9088.11 | 2.14300 | ||||||||
\(263\) | −298.863 | −0.0700710 | −0.0350355 | − | 0.999386i | \(-0.511154\pi\) | ||||
−0.0350355 | + | 0.999386i | \(0.511154\pi\) | |||||||
\(264\) | −4674.11 | −1.08967 | ||||||||
\(265\) | −2907.13 | −0.673901 | ||||||||
\(266\) | −4539.64 | −1.04640 | ||||||||
\(267\) | 3924.17 | 0.899459 | ||||||||
\(268\) | −1989.41 | −0.453442 | ||||||||
\(269\) | −3228.02 | −0.731657 | −0.365828 | − | 0.930682i | \(-0.619214\pi\) | ||||
−0.365828 | + | 0.930682i | \(0.619214\pi\) | |||||||
\(270\) | −22511.3 | −5.07406 | ||||||||
\(271\) | −5962.95 | −1.33662 | −0.668309 | − | 0.743883i | \(-0.732982\pi\) | ||||
−0.668309 | + | 0.743883i | \(0.732982\pi\) | |||||||
\(272\) | −2517.61 | −0.561222 | ||||||||
\(273\) | 7886.46 | 1.74839 | ||||||||
\(274\) | −12187.0 | −2.68701 | ||||||||
\(275\) | 778.287 | 0.170664 | ||||||||
\(276\) | 3851.94 | 0.840071 | ||||||||
\(277\) | 1771.14 | 0.384179 | 0.192089 | − | 0.981377i | \(-0.438474\pi\) | ||||
0.192089 | + | 0.981377i | \(0.438474\pi\) | |||||||
\(278\) | −12247.6 | −2.64230 | ||||||||
\(279\) | −12752.4 | −2.73643 | ||||||||
\(280\) | 9338.88 | 1.99323 | ||||||||
\(281\) | −981.025 | −0.208267 | −0.104134 | − | 0.994563i | \(-0.533207\pi\) | ||||
−0.104134 | + | 0.994563i | \(0.533207\pi\) | |||||||
\(282\) | −21296.2 | −4.49706 | ||||||||
\(283\) | 8076.55 | 1.69647 | 0.848235 | − | 0.529620i | \(-0.177666\pi\) | ||||
0.848235 | + | 0.529620i | \(0.177666\pi\) | |||||||
\(284\) | −943.177 | −0.197068 | ||||||||
\(285\) | −8674.58 | −1.80294 | ||||||||
\(286\) | 3218.29 | 0.665390 | ||||||||
\(287\) | −181.113 | −0.0372501 | ||||||||
\(288\) | −8208.91 | −1.67957 | ||||||||
\(289\) | −4315.74 | −0.878432 | ||||||||
\(290\) | 16903.6 | 3.42281 | ||||||||
\(291\) | −8926.41 | −1.79820 | ||||||||
\(292\) | −1900.47 | −0.380879 | ||||||||
\(293\) | −4573.34 | −0.911869 | −0.455934 | − | 0.890013i | \(-0.650695\pi\) | ||||
−0.455934 | + | 0.890013i | \(0.650695\pi\) | |||||||
\(294\) | 7326.92 | 1.45345 | ||||||||
\(295\) | 4731.93 | 0.933910 | ||||||||
\(296\) | 15243.9 | 2.99337 | ||||||||
\(297\) | 3266.81 | 0.638247 | ||||||||
\(298\) | 1329.48 | 0.258439 | ||||||||
\(299\) | −1441.72 | −0.278853 | ||||||||
\(300\) | 12315.4 | 2.37011 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −5807.82 | −1.10663 | ||||||||
\(303\) | −13049.5 | −2.47417 | ||||||||
\(304\) | −6748.64 | −1.27323 | ||||||||
\(305\) | 11481.6 | 2.15552 | ||||||||
\(306\) | 7488.72 | 1.39903 | ||||||||
\(307\) | 4509.23 | 0.838290 | 0.419145 | − | 0.907919i | \(-0.362330\pi\) | ||||
0.419145 | + | 0.907919i | \(0.362330\pi\) | |||||||
\(308\) | −2493.10 | −0.461227 | ||||||||
\(309\) | −13763.6 | −2.53393 | ||||||||
\(310\) | 15026.4 | 2.75304 | ||||||||
\(311\) | −720.198 | −0.131314 | −0.0656571 | − | 0.997842i | \(-0.520914\pi\) | ||||
−0.0656571 | + | 0.997842i | \(0.520914\pi\) | |||||||
\(312\) | 27682.9 | 5.02320 | ||||||||
\(313\) | 8593.59 | 1.55188 | 0.775940 | − | 0.630807i | \(-0.217276\pi\) | ||||
0.775940 | + | 0.630807i | \(0.217276\pi\) | |||||||
\(314\) | 4775.08 | 0.858195 | ||||||||
\(315\) | −11764.7 | −2.10433 | ||||||||
\(316\) | −12680.3 | −2.25735 | ||||||||
\(317\) | −57.3605 | −0.0101630 | −0.00508152 | − | 0.999987i | \(-0.501618\pi\) | ||||
−0.00508152 | + | 0.999987i | \(0.501618\pi\) | |||||||
\(318\) | 9722.51 | 1.71450 | ||||||||
\(319\) | −2453.02 | −0.430542 | ||||||||
\(320\) | −1983.56 | −0.346514 | ||||||||
\(321\) | −10031.7 | −1.74429 | ||||||||
\(322\) | 1626.59 | 0.281511 | ||||||||
\(323\) | 1601.01 | 0.275798 | ||||||||
\(324\) | 22990.9 | 3.94219 | ||||||||
\(325\) | −4609.49 | −0.786734 | ||||||||
\(326\) | 6650.24 | 1.12982 | ||||||||
\(327\) | −15331.8 | −2.59281 | ||||||||
\(328\) | −635.740 | −0.107021 | ||||||||
\(329\) | −6174.76 | −1.03473 | ||||||||
\(330\) | −6938.23 | −1.15739 | ||||||||
\(331\) | −3284.93 | −0.545487 | −0.272743 | − | 0.962087i | \(-0.587931\pi\) | ||||
−0.272743 | + | 0.962087i | \(0.587931\pi\) | |||||||
\(332\) | 3352.62 | 0.554214 | ||||||||
\(333\) | −19203.6 | −3.16021 | ||||||||
\(334\) | 8820.43 | 1.44501 | ||||||||
\(335\) | −1605.28 | −0.261808 | ||||||||
\(336\) | −13227.4 | −2.14766 | ||||||||
\(337\) | 4713.15 | 0.761844 | 0.380922 | − | 0.924607i | \(-0.375607\pi\) | ||||
0.380922 | + | 0.924607i | \(0.375607\pi\) | |||||||
\(338\) | −7960.20 | −1.28100 | ||||||||
\(339\) | 9839.78 | 1.57647 | ||||||||
\(340\) | −6058.86 | −0.966436 | ||||||||
\(341\) | −2180.61 | −0.346295 | ||||||||
\(342\) | 20074.1 | 3.17393 | ||||||||
\(343\) | 6828.69 | 1.07497 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3108.18 | 0.485040 | ||||||||
\(346\) | −5158.03 | −0.801438 | ||||||||
\(347\) | −75.9955 | −0.0117569 | −0.00587846 | − | 0.999983i | \(-0.501871\pi\) | ||||
−0.00587846 | + | 0.999983i | \(0.501871\pi\) | |||||||
\(348\) | −38816.1 | −5.97920 | ||||||||
\(349\) | −8798.79 | −1.34954 | −0.674769 | − | 0.738029i | \(-0.735757\pi\) | ||||
−0.674769 | + | 0.738029i | \(0.735757\pi\) | |||||||
\(350\) | 5200.55 | 0.794232 | ||||||||
\(351\) | −19348.0 | −2.94222 | ||||||||
\(352\) | −1403.70 | −0.212549 | ||||||||
\(353\) | 2914.96 | 0.439511 | 0.219756 | − | 0.975555i | \(-0.429474\pi\) | ||||
0.219756 | + | 0.975555i | \(0.429474\pi\) | |||||||
\(354\) | −15825.3 | −2.37600 | ||||||||
\(355\) | −761.061 | −0.113783 | ||||||||
\(356\) | 7347.15 | 1.09382 | ||||||||
\(357\) | 3137.99 | 0.465211 | ||||||||
\(358\) | −7321.11 | −1.08082 | ||||||||
\(359\) | 4644.90 | 0.682864 | 0.341432 | − | 0.939906i | \(-0.389088\pi\) | ||||
0.341432 | + | 0.939906i | \(0.389088\pi\) | |||||||
\(360\) | −41296.1 | −6.04582 | ||||||||
\(361\) | −2567.36 | −0.374306 | ||||||||
\(362\) | 6101.09 | 0.885818 | ||||||||
\(363\) | −11454.0 | −1.65614 | ||||||||
\(364\) | 14765.7 | 2.12619 | ||||||||
\(365\) | −1533.52 | −0.219912 | ||||||||
\(366\) | −38398.7 | −5.48397 | ||||||||
\(367\) | 285.848 | 0.0406571 | 0.0203285 | − | 0.999793i | \(-0.493529\pi\) | ||||
0.0203285 | + | 0.999793i | \(0.493529\pi\) | |||||||
\(368\) | 2418.10 | 0.342533 | ||||||||
\(369\) | 800.873 | 0.112986 | ||||||||
\(370\) | 22628.1 | 3.17940 | ||||||||
\(371\) | 2819.01 | 0.394490 | ||||||||
\(372\) | −34505.5 | −4.80921 | ||||||||
\(373\) | 10360.3 | 1.43816 | 0.719080 | − | 0.694927i | \(-0.244563\pi\) | ||||
0.719080 | + | 0.694927i | \(0.244563\pi\) | |||||||
\(374\) | 1280.55 | 0.177047 | ||||||||
\(375\) | −6614.39 | −0.910841 | ||||||||
\(376\) | −21674.5 | −2.97281 | ||||||||
\(377\) | 14528.3 | 1.98473 | ||||||||
\(378\) | 21829.0 | 2.97027 | ||||||||
\(379\) | 3278.07 | 0.444283 | 0.222141 | − | 0.975014i | \(-0.428695\pi\) | ||||
0.222141 | + | 0.975014i | \(0.428695\pi\) | |||||||
\(380\) | −16241.2 | −2.19252 | ||||||||
\(381\) | 2960.47 | 0.398083 | ||||||||
\(382\) | −22334.7 | −2.99148 | ||||||||
\(383\) | 8473.04 | 1.13042 | 0.565212 | − | 0.824946i | \(-0.308794\pi\) | ||||
0.565212 | + | 0.824946i | \(0.308794\pi\) | |||||||
\(384\) | 16771.3 | 2.22879 | ||||||||
\(385\) | −2011.72 | −0.266303 | ||||||||
\(386\) | −16451.4 | −2.16931 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16712.7 | −2.18675 | ||||||||
\(389\) | 4236.19 | 0.552142 | 0.276071 | − | 0.961137i | \(-0.410967\pi\) | ||||
0.276071 | + | 0.961137i | \(0.410967\pi\) | |||||||
\(390\) | 41092.4 | 5.33537 | ||||||||
\(391\) | −573.657 | −0.0741971 | ||||||||
\(392\) | 7457.08 | 0.960815 | ||||||||
\(393\) | −16839.6 | −2.16144 | ||||||||
\(394\) | 21340.6 | 2.72874 | ||||||||
\(395\) | −10231.9 | −1.30335 | ||||||||
\(396\) | 11024.4 | 1.39898 | ||||||||
\(397\) | 11874.3 | 1.50114 | 0.750571 | − | 0.660789i | \(-0.229778\pi\) | ||||
0.750571 | + | 0.660789i | \(0.229778\pi\) | |||||||
\(398\) | −20741.1 | −2.61221 | ||||||||
\(399\) | 8411.63 | 1.05541 | ||||||||
\(400\) | 7731.15 | 0.966394 | ||||||||
\(401\) | 2340.65 | 0.291487 | 0.145744 | − | 0.989322i | \(-0.453443\pi\) | ||||
0.145744 | + | 0.989322i | \(0.453443\pi\) | |||||||
\(402\) | 5368.64 | 0.666078 | ||||||||
\(403\) | 12914.9 | 1.59637 | ||||||||
\(404\) | −24432.3 | −3.00879 | ||||||||
\(405\) | 18551.6 | 2.27614 | ||||||||
\(406\) | −16391.2 | −2.00365 | ||||||||
\(407\) | −3283.74 | −0.399924 | ||||||||
\(408\) | 11014.9 | 1.33657 | ||||||||
\(409\) | 7241.71 | 0.875501 | 0.437750 | − | 0.899097i | \(-0.355775\pi\) | ||||
0.437750 | + | 0.899097i | \(0.355775\pi\) | |||||||
\(410\) | −943.690 | −0.113672 | ||||||||
\(411\) | 22581.6 | 2.71014 | ||||||||
\(412\) | −25769.4 | −3.08147 | ||||||||
\(413\) | −4588.49 | −0.546695 | ||||||||
\(414\) | −7192.72 | −0.853872 | ||||||||
\(415\) | 2705.27 | 0.319992 | ||||||||
\(416\) | 8313.54 | 0.979819 | ||||||||
\(417\) | 22693.9 | 2.66505 | ||||||||
\(418\) | 3432.60 | 0.401660 | ||||||||
\(419\) | −7303.95 | −0.851602 | −0.425801 | − | 0.904817i | \(-0.640008\pi\) | ||||
−0.425801 | + | 0.904817i | \(0.640008\pi\) | |||||||
\(420\) | −31832.9 | −3.69831 | ||||||||
\(421\) | −13018.6 | −1.50710 | −0.753551 | − | 0.657390i | \(-0.771661\pi\) | ||||
−0.753551 | + | 0.657390i | \(0.771661\pi\) | |||||||
\(422\) | 20311.6 | 2.34302 | ||||||||
\(423\) | 27304.5 | 3.13851 | ||||||||
\(424\) | 9895.23 | 1.13338 | ||||||||
\(425\) | −1834.10 | −0.209334 | ||||||||
\(426\) | 2545.27 | 0.289480 | ||||||||
\(427\) | −11133.6 | −1.26181 | ||||||||
\(428\) | −18782.2 | −2.12120 | ||||||||
\(429\) | −5963.26 | −0.671117 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6513.96 | −0.727996 | −0.363998 | − | 0.931400i | \(-0.618589\pi\) | ||||
−0.363998 | + | 0.931400i | \(0.618589\pi\) | |||||||
\(432\) | 32451.0 | 3.61412 | ||||||||
\(433\) | −3136.65 | −0.348124 | −0.174062 | − | 0.984735i | \(-0.555689\pi\) | ||||
−0.174062 | + | 0.984735i | \(0.555689\pi\) | |||||||
\(434\) | −14570.9 | −1.61158 | ||||||||
\(435\) | −31321.2 | −3.45226 | ||||||||
\(436\) | −28705.4 | −3.15307 | ||||||||
\(437\) | −1537.73 | −0.168329 | ||||||||
\(438\) | 5128.64 | 0.559488 | ||||||||
\(439\) | 670.745 | 0.0729223 | 0.0364612 | − | 0.999335i | \(-0.488391\pi\) | ||||
0.0364612 | + | 0.999335i | \(0.488391\pi\) | |||||||
\(440\) | −7061.49 | −0.765099 | ||||||||
\(441\) | −9394.06 | −1.01437 | ||||||||
\(442\) | −7584.17 | −0.816159 | ||||||||
\(443\) | 3012.53 | 0.323091 | 0.161546 | − | 0.986865i | \(-0.448352\pi\) | ||||
0.161546 | + | 0.986865i | \(0.448352\pi\) | |||||||
\(444\) | −51961.2 | −5.55399 | ||||||||
\(445\) | 5928.51 | 0.631547 | ||||||||
\(446\) | −4672.41 | −0.496065 | ||||||||
\(447\) | −2463.43 | −0.260663 | ||||||||
\(448\) | 1923.43 | 0.202843 | ||||||||
\(449\) | 12542.4 | 1.31829 | 0.659147 | − | 0.752014i | \(-0.270917\pi\) | ||||
0.659147 | + | 0.752014i | \(0.270917\pi\) | |||||||
\(450\) | −22996.6 | −2.40905 | ||||||||
\(451\) | 136.947 | 0.0142984 | ||||||||
\(452\) | 18422.8 | 1.91712 | ||||||||
\(453\) | 10761.5 | 1.11615 | ||||||||
\(454\) | −17544.0 | −1.81361 | ||||||||
\(455\) | 11914.6 | 1.22762 | ||||||||
\(456\) | 29526.4 | 3.03223 | ||||||||
\(457\) | 9096.37 | 0.931094 | 0.465547 | − | 0.885023i | \(-0.345858\pi\) | ||||
0.465547 | + | 0.885023i | \(0.345858\pi\) | |||||||
\(458\) | −10703.1 | −1.09197 | ||||||||
\(459\) | −7698.50 | −0.782866 | ||||||||
\(460\) | 5819.38 | 0.589848 | ||||||||
\(461\) | 13699.3 | 1.38403 | 0.692016 | − | 0.721882i | \(-0.256723\pi\) | ||||
0.692016 | + | 0.721882i | \(0.256723\pi\) | |||||||
\(462\) | 6727.92 | 0.677513 | ||||||||
\(463\) | −18592.6 | −1.86625 | −0.933124 | − | 0.359555i | \(-0.882928\pi\) | ||||
−0.933124 | + | 0.359555i | \(0.882928\pi\) | |||||||
\(464\) | −24367.2 | −2.43797 | ||||||||
\(465\) | −27842.9 | −2.77674 | ||||||||
\(466\) | 18649.8 | 1.85394 | ||||||||
\(467\) | −1536.60 | −0.152260 | −0.0761299 | − | 0.997098i | \(-0.524256\pi\) | ||||
−0.0761299 | + | 0.997098i | \(0.524256\pi\) | |||||||
\(468\) | −65293.1 | −6.44909 | ||||||||
\(469\) | 1556.62 | 0.153258 | ||||||||
\(470\) | −32173.6 | −3.15757 | ||||||||
\(471\) | −8847.87 | −0.865581 | ||||||||
\(472\) | −16106.4 | −1.57068 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 34219.2 | 3.31591 | ||||||||
\(475\) | −4916.44 | −0.474909 | ||||||||
\(476\) | 5875.21 | 0.565735 | ||||||||
\(477\) | −12465.5 | −1.19656 | ||||||||
\(478\) | −24529.9 | −2.34722 | ||||||||
\(479\) | −11184.2 | −1.06685 | −0.533424 | − | 0.845848i | \(-0.679095\pi\) | ||||
−0.533424 | + | 0.845848i | \(0.679095\pi\) | |||||||
\(480\) | −17923.0 | −1.70431 | ||||||||
\(481\) | 19448.3 | 1.84359 | ||||||||
\(482\) | −13065.8 | −1.23471 | ||||||||
\(483\) | −3013.96 | −0.283934 | ||||||||
\(484\) | −21445.1 | −2.01400 | ||||||||
\(485\) | −13485.7 | −1.26259 | ||||||||
\(486\) | −19070.2 | −1.77992 | ||||||||
\(487\) | 5611.36 | 0.522125 | 0.261063 | − | 0.965322i | \(-0.415927\pi\) | ||||
0.261063 | + | 0.965322i | \(0.415927\pi\) | |||||||
\(488\) | −39080.8 | −3.62522 | ||||||||
\(489\) | −12322.4 | −1.13955 | ||||||||
\(490\) | 11069.3 | 1.02053 | ||||||||
\(491\) | 6705.50 | 0.616324 | 0.308162 | − | 0.951334i | \(-0.400286\pi\) | ||||
0.308162 | + | 0.951334i | \(0.400286\pi\) | |||||||
\(492\) | 2167.01 | 0.198570 | ||||||||
\(493\) | 5780.75 | 0.528097 | ||||||||
\(494\) | −20329.9 | −1.85159 | ||||||||
\(495\) | 8895.72 | 0.807743 | ||||||||
\(496\) | −21661.2 | −1.96092 | ||||||||
\(497\) | 737.991 | 0.0666065 | ||||||||
\(498\) | −9047.42 | −0.814106 | ||||||||
\(499\) | 1528.07 | 0.137086 | 0.0685430 | − | 0.997648i | \(-0.478165\pi\) | ||||
0.0685430 | + | 0.997648i | \(0.478165\pi\) | |||||||
\(500\) | −12384.0 | −1.10766 | ||||||||
\(501\) | −16343.6 | −1.45744 | ||||||||
\(502\) | 13323.3 | 1.18456 | ||||||||
\(503\) | −16420.3 | −1.45556 | −0.727779 | − | 0.685812i | \(-0.759447\pi\) | ||||
−0.727779 | + | 0.685812i | \(0.759447\pi\) | |||||||
\(504\) | 40044.3 | 3.53912 | ||||||||
\(505\) | −19714.7 | −1.73722 | ||||||||
\(506\) | −1229.93 | −0.108058 | ||||||||
\(507\) | 14749.7 | 1.29202 | ||||||||
\(508\) | 5542.83 | 0.484101 | ||||||||
\(509\) | −13005.9 | −1.13257 | −0.566284 | − | 0.824210i | \(-0.691620\pi\) | ||||
−0.566284 | + | 0.824210i | \(0.691620\pi\) | |||||||
\(510\) | 16350.5 | 1.41963 | ||||||||
\(511\) | 1487.03 | 0.128733 | ||||||||
\(512\) | 25731.9 | 2.22109 | ||||||||
\(513\) | −20636.4 | −1.77606 | ||||||||
\(514\) | 37149.4 | 3.18792 | ||||||||
\(515\) | −20793.6 | −1.77918 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4668.97 | 0.397178 | ||||||||
\(518\) | −21942.1 | −1.86116 | ||||||||
\(519\) | 9557.47 | 0.808336 | ||||||||
\(520\) | 41822.4 | 3.52699 | ||||||||
\(521\) | −3433.05 | −0.288685 | −0.144342 | − | 0.989528i | \(-0.546107\pi\) | ||||
−0.144342 | + | 0.989528i | \(0.546107\pi\) | |||||||
\(522\) | 72481.2 | 6.07742 | ||||||||
\(523\) | 14300.7 | 1.19565 | 0.597826 | − | 0.801626i | \(-0.296031\pi\) | ||||
0.597826 | + | 0.801626i | \(0.296031\pi\) | |||||||
\(524\) | −31528.5 | −2.62849 | ||||||||
\(525\) | −9636.25 | −0.801068 | ||||||||
\(526\) | 1510.02 | 0.125171 | ||||||||
\(527\) | 5138.79 | 0.424761 | ||||||||
\(528\) | 10001.7 | 0.824374 | ||||||||
\(529\) | −11616.0 | −0.954715 | ||||||||
\(530\) | 14688.4 | 1.20382 | ||||||||
\(531\) | 20290.1 | 1.65822 | ||||||||
\(532\) | 15748.9 | 1.28346 | ||||||||
\(533\) | −811.081 | −0.0659134 | ||||||||
\(534\) | −19827.1 | −1.60675 | ||||||||
\(535\) | −15155.6 | −1.22474 | ||||||||
\(536\) | 5464.01 | 0.440316 | ||||||||
\(537\) | 13565.5 | 1.09012 | ||||||||
\(538\) | 16309.7 | 1.30699 | ||||||||
\(539\) | −1606.35 | −0.128368 | ||||||||
\(540\) | 78096.4 | 6.22358 | ||||||||
\(541\) | 2506.39 | 0.199184 | 0.0995918 | − | 0.995028i | \(-0.468246\pi\) | ||||
0.0995918 | + | 0.995028i | \(0.468246\pi\) | |||||||
\(542\) | 30128.2 | 2.38767 | ||||||||
\(543\) | −11304.9 | −0.893441 | ||||||||
\(544\) | 3307.93 | 0.260710 | ||||||||
\(545\) | −23162.7 | −1.82052 | ||||||||
\(546\) | −39846.8 | −3.12323 | ||||||||
\(547\) | 3120.71 | 0.243934 | 0.121967 | − | 0.992534i | \(-0.461080\pi\) | ||||
0.121967 | + | 0.992534i | \(0.461080\pi\) | |||||||
\(548\) | 42279.0 | 3.29575 | ||||||||
\(549\) | 49232.1 | 3.82728 | ||||||||
\(550\) | −3932.34 | −0.304865 | ||||||||
\(551\) | 15495.7 | 1.19808 | ||||||||
\(552\) | −10579.6 | −0.815753 | ||||||||
\(553\) | 9921.74 | 0.762957 | ||||||||
\(554\) | −8948.79 | −0.686277 | ||||||||
\(555\) | −41928.2 | −3.20676 | ||||||||
\(556\) | 42489.3 | 3.24091 | ||||||||
\(557\) | 4921.10 | 0.374351 | 0.187176 | − | 0.982326i | \(-0.440067\pi\) | ||||
0.187176 | + | 0.982326i | \(0.440067\pi\) | |||||||
\(558\) | 64432.0 | 4.88821 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −19983.5 | −1.50796 | ||||||||
\(561\) | −2372.76 | −0.178570 | ||||||||
\(562\) | 4956.69 | 0.372038 | ||||||||
\(563\) | −13911.2 | −1.04136 | −0.520680 | − | 0.853752i | \(-0.674321\pi\) | ||||
−0.520680 | + | 0.853752i | \(0.674321\pi\) | |||||||
\(564\) | 73880.8 | 5.51586 | ||||||||
\(565\) | 14865.6 | 1.10690 | ||||||||
\(566\) | −40807.2 | −3.03049 | ||||||||
\(567\) | −17989.3 | −1.33241 | ||||||||
\(568\) | 2590.48 | 0.191363 | ||||||||
\(569\) | −2045.35 | −0.150695 | −0.0753476 | − | 0.997157i | \(-0.524007\pi\) | ||||
−0.0753476 | + | 0.997157i | \(0.524007\pi\) | |||||||
\(570\) | 43828.8 | 3.22068 | ||||||||
\(571\) | −19012.8 | −1.39345 | −0.696725 | − | 0.717339i | \(-0.745360\pi\) | ||||
−0.696725 | + | 0.717339i | \(0.745360\pi\) | |||||||
\(572\) | −11164.9 | −0.816133 | ||||||||
\(573\) | 41384.7 | 3.01722 | ||||||||
\(574\) | 915.084 | 0.0665416 | ||||||||
\(575\) | 1761.60 | 0.127763 | ||||||||
\(576\) | −8505.33 | −0.615258 | ||||||||
\(577\) | −4056.31 | −0.292663 | −0.146331 | − | 0.989236i | \(-0.546747\pi\) | ||||
−0.146331 | + | 0.989236i | \(0.546747\pi\) | |||||||
\(578\) | 21805.5 | 1.56919 | ||||||||
\(579\) | 30483.3 | 2.18798 | ||||||||
\(580\) | −58642.0 | −4.19824 | ||||||||
\(581\) | −2623.27 | −0.187318 | ||||||||
\(582\) | 45101.2 | 3.21221 | ||||||||
\(583\) | −2131.56 | −0.151424 | ||||||||
\(584\) | 5219.75 | 0.369854 | ||||||||
\(585\) | −52685.8 | −3.72357 | ||||||||
\(586\) | 23107.1 | 1.62892 | ||||||||
\(587\) | 19491.1 | 1.37050 | 0.685249 | − | 0.728309i | \(-0.259693\pi\) | ||||
0.685249 | + | 0.728309i | \(0.259693\pi\) | |||||||
\(588\) | −25418.6 | −1.78273 | ||||||||
\(589\) | 13774.9 | 0.963642 | ||||||||
\(590\) | −23908.3 | −1.66829 | ||||||||
\(591\) | −39542.6 | −2.75223 | ||||||||
\(592\) | −32619.2 | −2.26460 | ||||||||
\(593\) | 5465.18 | 0.378462 | 0.189231 | − | 0.981933i | \(-0.439400\pi\) | ||||
0.189231 | + | 0.981933i | \(0.439400\pi\) | |||||||
\(594\) | −16505.7 | −1.14013 | ||||||||
\(595\) | 4740.78 | 0.326643 | ||||||||
\(596\) | −4612.24 | −0.316988 | ||||||||
\(597\) | 38431.8 | 2.63469 | ||||||||
\(598\) | 7284.40 | 0.498129 | ||||||||
\(599\) | −25500.9 | −1.73946 | −0.869731 | − | 0.493526i | \(-0.835708\pi\) | ||||
−0.869731 | + | 0.493526i | \(0.835708\pi\) | |||||||
\(600\) | −33825.0 | −2.30150 | ||||||||
\(601\) | −24308.3 | −1.64985 | −0.824923 | − | 0.565245i | \(-0.808781\pi\) | ||||
−0.824923 | + | 0.565245i | \(0.808781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6883.29 | −0.464858 | ||||||||
\(604\) | 20148.5 | 1.35733 | ||||||||
\(605\) | −17304.3 | −1.16284 | ||||||||
\(606\) | 65933.3 | 4.41973 | ||||||||
\(607\) | −2862.31 | −0.191397 | −0.0956983 | − | 0.995410i | \(-0.530508\pi\) | ||||
−0.0956983 | + | 0.995410i | \(0.530508\pi\) | |||||||
\(608\) | 8867.15 | 0.591464 | ||||||||
\(609\) | 30371.7 | 2.02090 | ||||||||
\(610\) | −58011.5 | −3.85052 | ||||||||
\(611\) | −27652.5 | −1.83093 | ||||||||
\(612\) | −25979.9 | −1.71597 | ||||||||
\(613\) | 20771.8 | 1.36862 | 0.684312 | − | 0.729189i | \(-0.260103\pi\) | ||||
0.684312 | + | 0.729189i | \(0.260103\pi\) | |||||||
\(614\) | −22783.1 | −1.49748 | ||||||||
\(615\) | 1748.59 | 0.114650 | ||||||||
\(616\) | 6847.44 | 0.447875 | ||||||||
\(617\) | −18855.6 | −1.23030 | −0.615152 | − | 0.788408i | \(-0.710905\pi\) | ||||
−0.615152 | + | 0.788408i | \(0.710905\pi\) | |||||||
\(618\) | 69541.5 | 4.52649 | ||||||||
\(619\) | −5019.16 | −0.325908 | −0.162954 | − | 0.986634i | \(-0.552102\pi\) | ||||
−0.162954 | + | 0.986634i | \(0.552102\pi\) | |||||||
\(620\) | −52129.7 | −3.37674 | ||||||||
\(621\) | 7394.21 | 0.477809 | ||||||||
\(622\) | 3638.84 | 0.234573 | ||||||||
\(623\) | −5748.80 | −0.369696 | ||||||||
\(624\) | −59236.3 | −3.80024 | ||||||||
\(625\) | −19373.8 | −1.23992 | ||||||||
\(626\) | −43419.6 | −2.77220 | ||||||||
\(627\) | −6360.36 | −0.405117 | ||||||||
\(628\) | −16565.7 | −1.05262 | ||||||||
\(629\) | 7738.42 | 0.490542 | ||||||||
\(630\) | 59441.6 | 3.75906 | ||||||||
\(631\) | 7678.40 | 0.484425 | 0.242213 | − | 0.970223i | \(-0.422127\pi\) | ||||
0.242213 | + | 0.970223i | \(0.422127\pi\) | |||||||
\(632\) | 34827.1 | 2.19201 | ||||||||
\(633\) | −37635.9 | −2.36318 | ||||||||
\(634\) | 289.817 | 0.0181547 | ||||||||
\(635\) | 4472.58 | 0.279510 | ||||||||
\(636\) | −33729.4 | −2.10292 | ||||||||
\(637\) | 9513.79 | 0.591759 | ||||||||
\(638\) | 12394.0 | 0.769098 | ||||||||
\(639\) | −3263.36 | −0.202029 | ||||||||
\(640\) | 25337.5 | 1.56493 | ||||||||
\(641\) | 30358.4 | 1.87065 | 0.935324 | − | 0.353792i | \(-0.115108\pi\) | ||||
0.935324 | + | 0.353792i | \(0.115108\pi\) | |||||||
\(642\) | 50686.0 | 3.11591 | ||||||||
\(643\) | 1310.34 | 0.0803654 | 0.0401827 | − | 0.999192i | \(-0.487206\pi\) | ||||
0.0401827 | + | 0.999192i | \(0.487206\pi\) | |||||||
\(644\) | −5642.98 | −0.345287 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8089.21 | −0.492671 | ||||||||
\(647\) | −16438.0 | −0.998834 | −0.499417 | − | 0.866362i | \(-0.666452\pi\) | ||||
−0.499417 | + | 0.866362i | \(0.666452\pi\) | |||||||
\(648\) | −63145.6 | −3.82808 | ||||||||
\(649\) | 3469.54 | 0.209848 | ||||||||
\(650\) | 23289.7 | 1.40538 | ||||||||
\(651\) | 26998.9 | 1.62545 | ||||||||
\(652\) | −23071.0 | −1.38578 | ||||||||
\(653\) | 8211.20 | 0.492081 | 0.246041 | − | 0.969260i | \(-0.420870\pi\) | ||||
0.246041 | + | 0.969260i | \(0.420870\pi\) | |||||||
\(654\) | 77464.6 | 4.63166 | ||||||||
\(655\) | −25440.7 | −1.51764 | ||||||||
\(656\) | 1360.37 | 0.0809655 | ||||||||
\(657\) | −6575.58 | −0.390469 | ||||||||
\(658\) | 31198.3 | 1.84838 | ||||||||
\(659\) | −18816.5 | −1.11227 | −0.556136 | − | 0.831091i | \(-0.687717\pi\) | ||||
−0.556136 | + | 0.831091i | \(0.687717\pi\) | |||||||
\(660\) | 24070.1 | 1.41959 | ||||||||
\(661\) | 10768.9 | 0.633677 | 0.316838 | − | 0.948480i | \(-0.397379\pi\) | ||||
0.316838 | + | 0.948480i | \(0.397379\pi\) | |||||||
\(662\) | 16597.3 | 0.974430 | ||||||||
\(663\) | 14052.9 | 0.823183 | ||||||||
\(664\) | −9208.15 | −0.538171 | ||||||||
\(665\) | 12708.0 | 0.741046 | ||||||||
\(666\) | 97027.1 | 5.64523 | ||||||||
\(667\) | −5552.26 | −0.322315 | ||||||||
\(668\) | −30599.9 | −1.77237 | ||||||||
\(669\) | 8657.63 | 0.500334 | ||||||||
\(670\) | 8110.76 | 0.467680 | ||||||||
\(671\) | 8418.52 | 0.484342 | ||||||||
\(672\) | 17379.7 | 0.997671 | ||||||||
\(673\) | −24154.4 | −1.38348 | −0.691740 | − | 0.722146i | \(-0.743156\pi\) | ||||
−0.691740 | + | 0.722146i | \(0.743156\pi\) | |||||||
\(674\) | −23813.4 | −1.36092 | ||||||||
\(675\) | 23640.8 | 1.34805 | ||||||||
\(676\) | 27615.6 | 1.57121 | ||||||||
\(677\) | 926.147 | 0.0525771 | 0.0262886 | − | 0.999654i | \(-0.491631\pi\) | ||||
0.0262886 | + | 0.999654i | \(0.491631\pi\) | |||||||
\(678\) | −49716.1 | −2.81613 | ||||||||
\(679\) | 13076.9 | 0.739096 | ||||||||
\(680\) | 16641.0 | 0.938460 | ||||||||
\(681\) | 32507.7 | 1.82922 | ||||||||
\(682\) | 11017.7 | 0.618604 | ||||||||
\(683\) | −14605.3 | −0.818237 | −0.409119 | − | 0.912481i | \(-0.634164\pi\) | ||||
−0.409119 | + | 0.912481i | \(0.634164\pi\) | |||||||
\(684\) | −69641.1 | −3.89297 | ||||||||
\(685\) | 34115.5 | 1.90290 | ||||||||
\(686\) | −34502.4 | −1.92027 | ||||||||
\(687\) | 19832.1 | 1.10137 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12624.4 | 0.698043 | ||||||||
\(690\) | −15704.2 | −0.866450 | ||||||||
\(691\) | −14706.2 | −0.809627 | −0.404813 | − | 0.914399i | \(-0.632664\pi\) | ||||
−0.404813 | + | 0.914399i | \(0.632664\pi\) | |||||||
\(692\) | 17894.3 | 0.983003 | ||||||||
\(693\) | −8626.06 | −0.472839 | ||||||||
\(694\) | 383.972 | 0.0210020 | ||||||||
\(695\) | 34285.1 | 1.87124 | ||||||||
\(696\) | 106610. | 5.80611 | ||||||||
\(697\) | −322.726 | −0.0175382 | ||||||||
\(698\) | 44456.4 | 2.41075 | ||||||||
\(699\) | −34556.8 | −1.86990 | ||||||||
\(700\) | −18041.8 | −0.974164 | ||||||||
\(701\) | −6588.69 | −0.354995 | −0.177497 | − | 0.984121i | \(-0.556800\pi\) | ||||
−0.177497 | + | 0.984121i | \(0.556800\pi\) | |||||||
\(702\) | 97757.0 | 5.25584 | ||||||||
\(703\) | 20743.4 | 1.11288 | ||||||||
\(704\) | −1454.38 | −0.0778610 | ||||||||
\(705\) | 59615.3 | 3.18474 | ||||||||
\(706\) | −14728.0 | −0.785121 | ||||||||
\(707\) | 19117.1 | 1.01694 | ||||||||
\(708\) | 54901.2 | 2.91428 | ||||||||
\(709\) | −7624.16 | −0.403852 | −0.201926 | − | 0.979401i | \(-0.564720\pi\) | ||||
−0.201926 | + | 0.979401i | \(0.564720\pi\) | |||||||
\(710\) | 3845.30 | 0.203256 | ||||||||
\(711\) | −43873.5 | −2.31418 | ||||||||
\(712\) | −20179.3 | −1.06215 | ||||||||
\(713\) | −4935.67 | −0.259246 | ||||||||
\(714\) | −15854.9 | −0.831029 | ||||||||
\(715\) | −9009.10 | −0.471218 | ||||||||
\(716\) | 25398.4 | 1.32567 | ||||||||
\(717\) | 45452.1 | 2.36742 | ||||||||
\(718\) | −23468.6 | −1.21983 | ||||||||
\(719\) | −31629.6 | −1.64059 | −0.820296 | − | 0.571939i | \(-0.806192\pi\) | ||||
−0.820296 | + | 0.571939i | \(0.806192\pi\) | |||||||
\(720\) | 88366.0 | 4.57390 | ||||||||
\(721\) | 20163.3 | 1.04150 | ||||||||
\(722\) | 12971.8 | 0.668641 | ||||||||
\(723\) | 24210.0 | 1.24534 | ||||||||
\(724\) | −21165.9 | −1.08650 | ||||||||
\(725\) | −17751.7 | −0.909355 | ||||||||
\(726\) | 57872.0 | 2.95844 | ||||||||
\(727\) | 23784.0 | 1.21334 | 0.606670 | − | 0.794954i | \(-0.292505\pi\) | ||||
0.606670 | + | 0.794954i | \(0.292505\pi\) | |||||||
\(728\) | −40554.7 | −2.06464 | ||||||||
\(729\) | −78.6220 | −0.00399441 | ||||||||
\(730\) | 7748.18 | 0.392840 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 133213. | 6.72635 | ||||||||
\(733\) | −13440.2 | −0.677252 | −0.338626 | − | 0.940921i | \(-0.609962\pi\) | ||||
−0.338626 | + | 0.940921i | \(0.609962\pi\) | |||||||
\(734\) | −1444.26 | −0.0726277 | ||||||||
\(735\) | −20510.5 | −1.02931 | ||||||||
\(736\) | −3177.18 | −0.159120 | ||||||||
\(737\) | −1177.02 | −0.0588278 | ||||||||
\(738\) | −4046.46 | −0.201832 | ||||||||
\(739\) | 28469.7 | 1.41715 | 0.708575 | − | 0.705636i | \(-0.249338\pi\) | ||||
0.708575 | + | 0.705636i | \(0.249338\pi\) | |||||||
\(740\) | −78501.3 | −3.89968 | ||||||||
\(741\) | 37669.9 | 1.86753 | ||||||||
\(742\) | −14243.2 | −0.704696 | ||||||||
\(743\) | −3370.81 | −0.166437 | −0.0832187 | − | 0.996531i | \(-0.526520\pi\) | ||||
−0.0832187 | + | 0.996531i | \(0.526520\pi\) | |||||||
\(744\) | 94771.0 | 4.66999 | ||||||||
\(745\) | −3721.67 | −0.183022 | ||||||||
\(746\) | −52345.8 | −2.56906 | ||||||||
\(747\) | 11600.0 | 0.568167 | ||||||||
\(748\) | −4442.47 | −0.217156 | ||||||||
\(749\) | 14696.2 | 0.716940 | ||||||||
\(750\) | 33419.6 | 1.62708 | ||||||||
\(751\) | −2003.54 | −0.0973505 | −0.0486752 | − | 0.998815i | \(-0.515500\pi\) | ||||
−0.0486752 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(752\) | 46379.5 | 2.24905 | ||||||||
\(753\) | −24687.1 | −1.19475 | ||||||||
\(754\) | −73405.0 | −3.54543 | ||||||||
\(755\) | 16258.1 | 0.783697 | ||||||||
\(756\) | −75729.1 | −3.64318 | ||||||||
\(757\) | −4412.38 | −0.211850 | −0.105925 | − | 0.994374i | \(-0.533780\pi\) | ||||
−0.105925 | + | 0.994374i | \(0.533780\pi\) | |||||||
\(758\) | −16562.6 | −0.793644 | ||||||||
\(759\) | 2278.97 | 0.108988 | ||||||||
\(760\) | 44607.4 | 2.12905 | ||||||||
\(761\) | 10159.0 | 0.483921 | 0.241961 | − | 0.970286i | \(-0.422210\pi\) | ||||
0.241961 | + | 0.970286i | \(0.422210\pi\) | |||||||
\(762\) | −14957.9 | −0.711115 | ||||||||
\(763\) | 22460.6 | 1.06570 | ||||||||
\(764\) | 77483.7 | 3.66919 | ||||||||
\(765\) | −20963.5 | −0.990767 | ||||||||
\(766\) | −42810.5 | −2.01933 | ||||||||
\(767\) | −20548.7 | −0.967367 | ||||||||
\(768\) | −74234.3 | −3.48789 | ||||||||
\(769\) | 17334.7 | 0.812881 | 0.406440 | − | 0.913677i | \(-0.366770\pi\) | ||||
0.406440 | + | 0.913677i | \(0.366770\pi\) | |||||||
\(770\) | 10164.3 | 0.475710 | ||||||||
\(771\) | −68835.1 | −3.21535 | ||||||||
\(772\) | 57073.2 | 2.66076 | ||||||||
\(773\) | 11330.7 | 0.527213 | 0.263607 | − | 0.964630i | \(-0.415088\pi\) | ||||
0.263607 | + | 0.964630i | \(0.415088\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15780.3 | −0.731415 | ||||||||
\(776\) | 45902.4 | 2.12345 | ||||||||
\(777\) | 40657.2 | 1.87718 | ||||||||
\(778\) | −21403.6 | −0.986319 | ||||||||
\(779\) | −865.092 | −0.0397884 | ||||||||
\(780\) | −142558. | −6.54409 | ||||||||
\(781\) | −558.024 | −0.0255668 | ||||||||
\(782\) | 2898.43 | 0.132542 | ||||||||
\(783\) | −74511.6 | −3.40080 | ||||||||
\(784\) | −15956.8 | −0.726894 | ||||||||
\(785\) | −13367.1 | −0.607759 | ||||||||
\(786\) | 85083.1 | 3.86109 | ||||||||
\(787\) | 14755.8 | 0.668343 | 0.334172 | − | 0.942512i | \(-0.391543\pi\) | ||||
0.334172 | + | 0.942512i | \(0.391543\pi\) | |||||||
\(788\) | −74034.9 | −3.34694 | ||||||||
\(789\) | −2797.96 | −0.126249 | ||||||||
\(790\) | 51697.3 | 2.32824 | ||||||||
\(791\) | −14415.0 | −0.647962 | ||||||||
\(792\) | −30279.1 | −1.35848 | ||||||||
\(793\) | −49859.6 | −2.23274 | ||||||||
\(794\) | −59995.6 | −2.68156 | ||||||||
\(795\) | −27216.6 | −1.21418 | ||||||||
\(796\) | 71955.1 | 3.20400 | ||||||||
\(797\) | 21567.4 | 0.958538 | 0.479269 | − | 0.877668i | \(-0.340902\pi\) | ||||
0.479269 | + | 0.877668i | \(0.340902\pi\) | |||||||
\(798\) | −42500.3 | −1.88533 | ||||||||
\(799\) | −11002.8 | −0.487174 | ||||||||
\(800\) | −10158.1 | −0.448928 | ||||||||
\(801\) | 25420.9 | 1.12135 | ||||||||
\(802\) | −11826.3 | −0.520698 | ||||||||
\(803\) | −1124.40 | −0.0494138 | ||||||||
\(804\) | −18624.9 | −0.816976 | ||||||||
\(805\) | −4553.39 | −0.199361 | ||||||||
\(806\) | −65253.2 | −2.85167 | ||||||||
\(807\) | −30220.8 | −1.31824 | ||||||||
\(808\) | 67104.6 | 2.92170 | ||||||||
\(809\) | 27638.2 | 1.20112 | 0.600561 | − | 0.799579i | \(-0.294944\pi\) | ||||
0.600561 | + | 0.799579i | \(0.294944\pi\) | |||||||
\(810\) | −93733.1 | −4.06598 | ||||||||
\(811\) | 5477.83 | 0.237180 | 0.118590 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118590 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(812\) | 56864.4 | 2.45757 | ||||||||
\(813\) | −55825.3 | −2.40822 | ||||||||
\(814\) | 16591.3 | 0.714404 | ||||||||
\(815\) | −18616.3 | −0.800122 | ||||||||
\(816\) | −23569.9 | −1.01117 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −36589.2 | −1.56395 | ||||||||
\(819\) | 51088.8 | 2.17972 | ||||||||
\(820\) | 3273.85 | 0.139424 | ||||||||
\(821\) | −3043.53 | −0.129379 | −0.0646894 | − | 0.997905i | \(-0.520606\pi\) | ||||
−0.0646894 | + | 0.997905i | \(0.520606\pi\) | |||||||
\(822\) | −114095. | −4.84125 | ||||||||
\(823\) | 22867.8 | 0.968556 | 0.484278 | − | 0.874914i | \(-0.339082\pi\) | ||||
0.484278 | + | 0.874914i | \(0.339082\pi\) | |||||||
\(824\) | 70776.9 | 2.99227 | ||||||||
\(825\) | 7286.35 | 0.307489 | ||||||||
\(826\) | 23183.6 | 0.976587 | ||||||||
\(827\) | −13967.0 | −0.587281 | −0.293640 | − | 0.955916i | \(-0.594867\pi\) | ||||
−0.293640 | + | 0.955916i | \(0.594867\pi\) | |||||||
\(828\) | 24953.0 | 1.04732 | ||||||||
\(829\) | −4419.68 | −0.185165 | −0.0925825 | − | 0.995705i | \(-0.529512\pi\) | ||||
−0.0925825 | + | 0.995705i | \(0.529512\pi\) | |||||||
\(830\) | −13668.5 | −0.571617 | ||||||||
\(831\) | 16581.5 | 0.692183 | ||||||||
\(832\) | 8613.74 | 0.358927 | ||||||||
\(833\) | 3785.50 | 0.157455 | ||||||||
\(834\) | −114662. | −4.76070 | ||||||||
\(835\) | −24691.4 | −1.02333 | ||||||||
\(836\) | −11908.4 | −0.492656 | ||||||||
\(837\) | −66236.9 | −2.73534 | ||||||||
\(838\) | 36903.6 | 1.52126 | ||||||||
\(839\) | −16617.7 | −0.683797 | −0.341898 | − | 0.939737i | \(-0.611070\pi\) | ||||
−0.341898 | + | 0.939737i | \(0.611070\pi\) | |||||||
\(840\) | 87430.8 | 3.59125 | ||||||||
\(841\) | 31561.2 | 1.29408 | ||||||||
\(842\) | 65777.4 | 2.69221 | ||||||||
\(843\) | −9184.38 | −0.375240 | ||||||||
\(844\) | −70465.0 | −2.87382 | ||||||||
\(845\) | 22283.3 | 0.907183 | ||||||||
\(846\) | −137957. | −5.60647 | ||||||||
\(847\) | 16779.8 | 0.680708 | ||||||||
\(848\) | −21174.0 | −0.857449 | ||||||||
\(849\) | 75612.8 | 3.05657 | ||||||||
\(850\) | 9266.89 | 0.373943 | ||||||||
\(851\) | −7432.55 | −0.299394 | ||||||||
\(852\) | −8830.04 | −0.355061 | ||||||||
\(853\) | −12302.6 | −0.493825 | −0.246912 | − | 0.969038i | \(-0.579416\pi\) | ||||
−0.246912 | + | 0.969038i | \(0.579416\pi\) | |||||||
\(854\) | 56253.0 | 2.25403 | ||||||||
\(855\) | −56194.2 | −2.24772 | ||||||||
\(856\) | 51586.4 | 2.05980 | ||||||||
\(857\) | 39311.0 | 1.56690 | 0.783452 | − | 0.621452i | \(-0.213457\pi\) | ||||
0.783452 | + | 0.621452i | \(0.213457\pi\) | |||||||
\(858\) | 30129.7 | 1.19885 | ||||||||
\(859\) | 3412.44 | 0.135542 | 0.0677712 | − | 0.997701i | \(-0.478411\pi\) | ||||
0.0677712 | + | 0.997701i | \(0.478411\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1695.58 | −0.0671143 | ||||||||
\(862\) | 32912.1 | 1.30045 | ||||||||
\(863\) | −19362.2 | −0.763727 | −0.381863 | − | 0.924219i | \(-0.624718\pi\) | ||||
−0.381863 | + | 0.924219i | \(0.624718\pi\) | |||||||
\(864\) | −42637.9 | −1.67890 | ||||||||
\(865\) | 14439.1 | 0.567565 | ||||||||
\(866\) | 15848.1 | 0.621872 | ||||||||
\(867\) | −40404.0 | −1.58269 | ||||||||
\(868\) | 50549.5 | 1.97668 | ||||||||
\(869\) | −7502.22 | −0.292860 | ||||||||
\(870\) | 158252. | 6.16695 | ||||||||
\(871\) | 6971.02 | 0.271187 | ||||||||
\(872\) | 78840.8 | 3.06179 | ||||||||
\(873\) | −57825.6 | −2.24181 | ||||||||
\(874\) | 7769.47 | 0.300694 | ||||||||
\(875\) | 9689.89 | 0.374375 | ||||||||
\(876\) | −17792.3 | −0.686239 | ||||||||
\(877\) | −16784.7 | −0.646272 | −0.323136 | − | 0.946353i | \(-0.604737\pi\) | ||||
−0.323136 | + | 0.946353i | \(0.604737\pi\) | |||||||
\(878\) | −3388.98 | −0.130265 | ||||||||
\(879\) | −42815.7 | −1.64293 | ||||||||
\(880\) | 15110.3 | 0.578827 | ||||||||
\(881\) | −21039.3 | −0.804578 | −0.402289 | − | 0.915513i | \(-0.631785\pi\) | ||||
−0.402289 | + | 0.915513i | \(0.631785\pi\) | |||||||
\(882\) | 47464.0 | 1.81202 | ||||||||
\(883\) | 20024.2 | 0.763157 | 0.381579 | − | 0.924336i | \(-0.375381\pi\) | ||||
0.381579 | + | 0.924336i | \(0.375381\pi\) | |||||||
\(884\) | 26311.0 | 1.00106 | ||||||||
\(885\) | 44300.4 | 1.68265 | ||||||||
\(886\) | −15221.0 | −0.577154 | ||||||||
\(887\) | 16204.3 | 0.613401 | 0.306700 | − | 0.951806i | \(-0.400775\pi\) | ||||
0.306700 | + | 0.951806i | \(0.400775\pi\) | |||||||
\(888\) | 142714. | 5.39322 | ||||||||
\(889\) | −4337.00 | −0.163620 | ||||||||
\(890\) | −29954.1 | −1.12816 | ||||||||
\(891\) | 13602.4 | 0.511445 | ||||||||
\(892\) | 16209.5 | 0.608447 | ||||||||
\(893\) | −29493.9 | −1.10524 | ||||||||
\(894\) | 12446.6 | 0.465635 | ||||||||
\(895\) | 20494.3 | 0.765417 | ||||||||
\(896\) | −24569.5 | −0.916080 | ||||||||
\(897\) | −13497.5 | −0.502416 | ||||||||
\(898\) | −63371.4 | −2.35493 | ||||||||
\(899\) | 49736.8 | 1.84518 | ||||||||
\(900\) | 79779.9 | 2.95481 | ||||||||
\(901\) | 5023.20 | 0.185735 | ||||||||
\(902\) | −691.931 | −0.0255419 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −50599.3 | −1.86162 | ||||||||
\(905\) | −17079.0 | −0.627322 | ||||||||
\(906\) | −54372.9 | −1.99384 | ||||||||
\(907\) | −13786.2 | −0.504699 | −0.252350 | − | 0.967636i | \(-0.581203\pi\) | ||||
−0.252350 | + | 0.967636i | \(0.581203\pi\) | |||||||
\(908\) | 60863.5 | 2.22448 | ||||||||
\(909\) | −84535.0 | −3.08454 | ||||||||
\(910\) | −60199.2 | −2.19295 | ||||||||
\(911\) | −23933.3 | −0.870412 | −0.435206 | − | 0.900331i | \(-0.643324\pi\) | ||||
−0.435206 | + | 0.900331i | \(0.643324\pi\) | |||||||
\(912\) | −63180.9 | −2.29400 | ||||||||
\(913\) | 1983.56 | 0.0719015 | ||||||||
\(914\) | −45959.9 | −1.66326 | ||||||||
\(915\) | 107491. | 3.88366 | ||||||||
\(916\) | 37131.3 | 1.33936 | ||||||||
\(917\) | 24669.6 | 0.888398 | ||||||||
\(918\) | 38897.1 | 1.39847 | ||||||||
\(919\) | −31897.7 | −1.14495 | −0.572475 | − | 0.819922i | \(-0.694017\pi\) | ||||
−0.572475 | + | 0.819922i | \(0.694017\pi\) | |||||||
\(920\) | −15983.2 | −0.572774 | ||||||||
\(921\) | 42215.5 | 1.51037 | ||||||||
\(922\) | −69216.4 | −2.47236 | ||||||||
\(923\) | 3304.96 | 0.117859 | ||||||||
\(924\) | −23340.5 | −0.831002 | ||||||||
\(925\) | −23763.4 | −0.844686 | ||||||||
\(926\) | 93940.3 | 3.33377 | ||||||||
\(927\) | −89161.2 | −3.15905 | ||||||||
\(928\) | 32016.5 | 1.13253 | ||||||||
\(929\) | −42084.6 | −1.48628 | −0.743138 | − | 0.669138i | \(-0.766663\pi\) | ||||
−0.743138 | + | 0.669138i | \(0.766663\pi\) | |||||||
\(930\) | 140678. | 4.96022 | ||||||||
\(931\) | 10147.3 | 0.357213 | ||||||||
\(932\) | −64700.0 | −2.27395 | ||||||||
\(933\) | −6742.51 | −0.236592 | ||||||||
\(934\) | 7763.75 | 0.271989 | ||||||||
\(935\) | −3584.69 | −0.125382 | ||||||||
\(936\) | 179331. | 6.26241 | ||||||||
\(937\) | −6000.64 | −0.209213 | −0.104606 | − | 0.994514i | \(-0.533358\pi\) | ||||
−0.104606 | + | 0.994514i | \(0.533358\pi\) | |||||||
\(938\) | −7864.90 | −0.273772 | ||||||||
\(939\) | 80453.4 | 2.79606 | ||||||||
\(940\) | 111617. | 3.87291 | ||||||||
\(941\) | −17755.8 | −0.615114 | −0.307557 | − | 0.951530i | \(-0.599511\pi\) | ||||
−0.307557 | + | 0.951530i | \(0.599511\pi\) | |||||||
\(942\) | 44704.4 | 1.54623 | ||||||||
\(943\) | 309.970 | 0.0107041 | ||||||||
\(944\) | 34464.8 | 1.18828 | ||||||||
\(945\) | −61106.7 | −2.10349 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28692.8 | 0.984572 | 0.492286 | − | 0.870434i | \(-0.336161\pi\) | ||||
0.492286 | + | 0.870434i | \(0.336161\pi\) | |||||||
\(948\) | −118713. | −4.06712 | ||||||||
\(949\) | 6659.39 | 0.227790 | ||||||||
\(950\) | 24840.6 | 0.848353 | ||||||||
\(951\) | −537.010 | −0.0183110 | ||||||||
\(952\) | −16136.6 | −0.549358 | ||||||||
\(953\) | −20739.6 | −0.704956 | −0.352478 | − | 0.935820i | \(-0.614661\pi\) | ||||
−0.352478 | + | 0.935820i | \(0.614661\pi\) | |||||||
\(954\) | 62982.8 | 2.13747 | ||||||||
\(955\) | 62522.6 | 2.11852 | ||||||||
\(956\) | 85099.2 | 2.87898 | ||||||||
\(957\) | −22965.3 | −0.775717 | ||||||||
\(958\) | 56508.9 | 1.90576 | ||||||||
\(959\) | −33081.3 | −1.11392 | ||||||||
\(960\) | −18570.1 | −0.624321 | ||||||||
\(961\) | 14422.4 | 0.484121 | ||||||||
\(962\) | −98263.8 | −3.29330 | ||||||||
\(963\) | −64986.0 | −2.17460 | ||||||||
\(964\) | 45327.9 | 1.51443 | ||||||||
\(965\) | 46053.1 | 1.53627 | ||||||||
\(966\) | 15228.2 | 0.507205 | ||||||||
\(967\) | −35018.1 | −1.16454 | −0.582268 | − | 0.812997i | \(-0.697835\pi\) | ||||
−0.582268 | + | 0.812997i | \(0.697835\pi\) | |||||||
\(968\) | 58900.0 | 1.95570 | ||||||||
\(969\) | 14988.7 | 0.496911 | ||||||||
\(970\) | 68137.4 | 2.25542 | ||||||||
\(971\) | −52435.4 | −1.73299 | −0.866495 | − | 0.499186i | \(-0.833633\pi\) | ||||
−0.866495 | + | 0.499186i | \(0.833633\pi\) | |||||||
\(972\) | 66158.2 | 2.18316 | ||||||||
\(973\) | −33245.9 | −1.09539 | ||||||||
\(974\) | −28351.7 | −0.932697 | ||||||||
\(975\) | −43154.2 | −1.41748 | ||||||||
\(976\) | 83625.8 | 2.74262 | ||||||||
\(977\) | 10021.8 | 0.328173 | 0.164086 | − | 0.986446i | \(-0.447532\pi\) | ||||
0.164086 | + | 0.986446i | \(0.447532\pi\) | |||||||
\(978\) | 62259.7 | 2.03563 | ||||||||
\(979\) | 4346.89 | 0.141907 | ||||||||
\(980\) | −38401.5 | −1.25173 | ||||||||
\(981\) | −99319.7 | −3.23245 | ||||||||
\(982\) | −33879.9 | −1.10097 | ||||||||
\(983\) | −54750.4 | −1.77647 | −0.888233 | − | 0.459394i | \(-0.848067\pi\) | ||||
−0.888233 | + | 0.459394i | \(0.848067\pi\) | |||||||
\(984\) | −5951.81 | −0.192822 | ||||||||
\(985\) | −59739.7 | −1.93245 | ||||||||
\(986\) | −29207.6 | −0.943366 | ||||||||
\(987\) | −57808.2 | −1.86429 | ||||||||
\(988\) | 70528.7 | 2.27107 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −44946.1 | −1.44291 | ||||||||
\(991\) | 49955.3 | 1.60130 | 0.800648 | − | 0.599135i | \(-0.204489\pi\) | ||||
0.800648 | + | 0.599135i | \(0.204489\pi\) | |||||||
\(992\) | 28461.0 | 0.910924 | ||||||||
\(993\) | −30753.6 | −0.982816 | ||||||||
\(994\) | −3728.74 | −0.118982 | ||||||||
\(995\) | 58061.5 | 1.84992 | ||||||||
\(996\) | 31387.3 | 0.998540 | ||||||||
\(997\) | −42986.1 | −1.36548 | −0.682740 | − | 0.730661i | \(-0.739212\pi\) | ||||
−0.682740 | + | 0.730661i | \(0.739212\pi\) | |||||||
\(998\) | −7720.68 | −0.244884 | ||||||||
\(999\) | −99745.1 | −3.15896 |
(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 | 1849.4.a.i.1.4 | ✓ | 50 | |
43.42 | odd | 2 | 1849.4.a.j.1.47 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.4 | ✓ | 50 | 1.1 | even | 1 | trivial | |
1849.4.a.j.1.47 | yes | 50 | 43.42 | odd | 2 |