Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,4,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1859.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(109.684550701\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + 941923 x^{9} - 2799440 x^{8} - 6021311 x^{7} + 15765187 x^{6} + \cdots + 2596992 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 143) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-2.47248\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47248 | 0.874152 | 0.437076 | − | 0.899425i | \(-0.356014\pi\) | ||||
0.437076 | + | 0.899425i | \(0.356014\pi\) | |||||||
\(3\) | 6.49330 | 1.24964 | 0.624818 | − | 0.780770i | \(-0.285173\pi\) | ||||
0.624818 | + | 0.780770i | \(0.285173\pi\) | |||||||
\(4\) | −1.88686 | −0.235858 | ||||||||
\(5\) | 10.7576 | 0.962189 | 0.481095 | − | 0.876669i | \(-0.340239\pi\) | ||||
0.481095 | + | 0.876669i | \(0.340239\pi\) | |||||||
\(6\) | 16.0545 | 1.09237 | ||||||||
\(7\) | −24.9760 | −1.34858 | −0.674290 | − | 0.738467i | \(-0.735550\pi\) | ||||
−0.674290 | + | 0.738467i | \(0.735550\pi\) | |||||||
\(8\) | −24.4450 | −1.08033 | ||||||||
\(9\) | 15.1629 | 0.561590 | ||||||||
\(10\) | 26.5979 | 0.841100 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −12.2520 | −0.294737 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −61.7527 | −1.17886 | ||||||||
\(15\) | 69.8523 | 1.20239 | ||||||||
\(16\) | −45.3448 | −0.708513 | ||||||||
\(17\) | 99.6374 | 1.42151 | 0.710754 | − | 0.703441i | \(-0.248354\pi\) | ||||
0.710754 | + | 0.703441i | \(0.248354\pi\) | |||||||
\(18\) | 37.4900 | 0.490916 | ||||||||
\(19\) | −87.2296 | −1.05325 | −0.526627 | − | 0.850096i | \(-0.676544\pi\) | ||||
−0.526627 | + | 0.850096i | \(0.676544\pi\) | |||||||
\(20\) | −20.2981 | −0.226940 | ||||||||
\(21\) | −162.177 | −1.68523 | ||||||||
\(22\) | 27.1972 | 0.263567 | ||||||||
\(23\) | 95.5895 | 0.866600 | 0.433300 | − | 0.901250i | \(-0.357349\pi\) | ||||
0.433300 | + | 0.901250i | \(0.357349\pi\) | |||||||
\(24\) | −158.729 | −1.35002 | ||||||||
\(25\) | −9.27403 | −0.0741922 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −76.8616 | −0.547852 | ||||||||
\(28\) | 47.1264 | 0.318073 | ||||||||
\(29\) | −43.7369 | −0.280060 | −0.140030 | − | 0.990147i | \(-0.544720\pi\) | ||||
−0.140030 | + | 0.990147i | \(0.544720\pi\) | |||||||
\(30\) | 172.708 | 1.05107 | ||||||||
\(31\) | −183.927 | −1.06562 | −0.532810 | − | 0.846235i | \(-0.678864\pi\) | ||||
−0.532810 | + | 0.846235i | \(0.678864\pi\) | |||||||
\(32\) | 83.4462 | 0.460980 | ||||||||
\(33\) | 71.4263 | 0.376779 | ||||||||
\(34\) | 246.351 | 1.24261 | ||||||||
\(35\) | −268.682 | −1.29759 | ||||||||
\(36\) | −28.6104 | −0.132456 | ||||||||
\(37\) | −263.861 | −1.17239 | −0.586195 | − | 0.810170i | \(-0.699375\pi\) | ||||
−0.586195 | + | 0.810170i | \(0.699375\pi\) | |||||||
\(38\) | −215.673 | −0.920705 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −262.970 | −1.03948 | ||||||||
\(41\) | 61.8766 | 0.235695 | 0.117848 | − | 0.993032i | \(-0.462401\pi\) | ||||
0.117848 | + | 0.993032i | \(0.462401\pi\) | |||||||
\(42\) | −400.979 | −1.47315 | ||||||||
\(43\) | −207.867 | −0.737195 | −0.368598 | − | 0.929589i | \(-0.620162\pi\) | ||||
−0.368598 | + | 0.929589i | \(0.620162\pi\) | |||||||
\(44\) | −20.7555 | −0.0711138 | ||||||||
\(45\) | 163.117 | 0.540356 | ||||||||
\(46\) | 236.343 | 0.757540 | ||||||||
\(47\) | 122.424 | 0.379943 | 0.189972 | − | 0.981790i | \(-0.439160\pi\) | ||||
0.189972 | + | 0.981790i | \(0.439160\pi\) | |||||||
\(48\) | −294.438 | −0.885384 | ||||||||
\(49\) | 280.803 | 0.818668 | ||||||||
\(50\) | −22.9298 | −0.0648553 | ||||||||
\(51\) | 646.976 | 1.77637 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −315.428 | −0.817499 | −0.408749 | − | 0.912647i | \(-0.634035\pi\) | ||||
−0.408749 | + | 0.912647i | \(0.634035\pi\) | |||||||
\(54\) | −190.038 | −0.478906 | ||||||||
\(55\) | 118.334 | 0.290111 | ||||||||
\(56\) | 610.540 | 1.45691 | ||||||||
\(57\) | −566.408 | −1.31618 | ||||||||
\(58\) | −108.139 | −0.244815 | ||||||||
\(59\) | −209.700 | −0.462723 | −0.231362 | − | 0.972868i | \(-0.574318\pi\) | ||||
−0.231362 | + | 0.972868i | \(0.574318\pi\) | |||||||
\(60\) | −131.802 | −0.283592 | ||||||||
\(61\) | 52.8547 | 0.110940 | 0.0554700 | − | 0.998460i | \(-0.482334\pi\) | ||||
0.0554700 | + | 0.998460i | \(0.482334\pi\) | |||||||
\(62\) | −454.754 | −0.931514 | ||||||||
\(63\) | −378.710 | −0.757350 | ||||||||
\(64\) | 569.077 | 1.11148 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 176.600 | 0.329363 | ||||||||
\(67\) | −286.699 | −0.522773 | −0.261387 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261387 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(68\) | −188.002 | −0.335274 | ||||||||
\(69\) | 620.691 | 1.08293 | ||||||||
\(70\) | −664.311 | −1.13429 | ||||||||
\(71\) | −777.192 | −1.29909 | −0.649547 | − | 0.760321i | \(-0.725042\pi\) | ||||
−0.649547 | + | 0.760321i | \(0.725042\pi\) | |||||||
\(72\) | −370.659 | −0.606702 | ||||||||
\(73\) | −824.682 | −1.32222 | −0.661108 | − | 0.750291i | \(-0.729913\pi\) | ||||
−0.661108 | + | 0.750291i | \(0.729913\pi\) | |||||||
\(74\) | −652.389 | −1.02485 | ||||||||
\(75\) | −60.2191 | −0.0927133 | ||||||||
\(76\) | 164.590 | 0.248418 | ||||||||
\(77\) | −274.737 | −0.406612 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −860.840 | −1.22598 | −0.612988 | − | 0.790092i | \(-0.710033\pi\) | ||||
−0.612988 | + | 0.790092i | \(0.710033\pi\) | |||||||
\(80\) | −487.802 | −0.681724 | ||||||||
\(81\) | −908.485 | −1.24621 | ||||||||
\(82\) | 152.988 | 0.206033 | ||||||||
\(83\) | 1424.92 | 1.88440 | 0.942202 | − | 0.335045i | \(-0.108751\pi\) | ||||
0.942202 | + | 0.335045i | \(0.108751\pi\) | |||||||
\(84\) | 306.006 | 0.397476 | ||||||||
\(85\) | 1071.86 | 1.36776 | ||||||||
\(86\) | −513.946 | −0.644421 | ||||||||
\(87\) | −283.997 | −0.349973 | ||||||||
\(88\) | −268.895 | −0.325731 | ||||||||
\(89\) | −434.711 | −0.517744 | −0.258872 | − | 0.965912i | \(-0.583351\pi\) | ||||
−0.258872 | + | 0.965912i | \(0.583351\pi\) | |||||||
\(90\) | 403.303 | 0.472354 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −180.364 | −0.204394 | ||||||||
\(93\) | −1194.29 | −1.33164 | ||||||||
\(94\) | 302.690 | 0.332128 | ||||||||
\(95\) | −938.381 | −1.01343 | ||||||||
\(96\) | 541.841 | 0.576057 | ||||||||
\(97\) | 1111.26 | 1.16321 | 0.581606 | − | 0.813470i | \(-0.302424\pi\) | ||||
0.581606 | + | 0.813470i | \(0.302424\pi\) | |||||||
\(98\) | 694.279 | 0.715640 | ||||||||
\(99\) | 166.792 | 0.169326 | ||||||||
\(100\) | 17.4988 | 0.0174988 | ||||||||
\(101\) | −741.078 | −0.730099 | −0.365050 | − | 0.930988i | \(-0.618948\pi\) | ||||
−0.365050 | + | 0.930988i | \(0.618948\pi\) | |||||||
\(102\) | 1599.63 | 1.55281 | ||||||||
\(103\) | −517.376 | −0.494937 | −0.247469 | − | 0.968896i | \(-0.579599\pi\) | ||||
−0.247469 | + | 0.968896i | \(0.579599\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1744.64 | −1.62151 | ||||||||
\(106\) | −779.889 | −0.714618 | ||||||||
\(107\) | 1361.03 | 1.22968 | 0.614838 | − | 0.788653i | \(-0.289221\pi\) | ||||
0.614838 | + | 0.788653i | \(0.289221\pi\) | |||||||
\(108\) | 145.027 | 0.129215 | ||||||||
\(109\) | −1918.88 | −1.68620 | −0.843098 | − | 0.537759i | \(-0.819271\pi\) | ||||
−0.843098 | + | 0.537759i | \(0.819271\pi\) | |||||||
\(110\) | 292.577 | 0.253601 | ||||||||
\(111\) | −1713.33 | −1.46506 | ||||||||
\(112\) | 1132.53 | 0.955486 | ||||||||
\(113\) | 104.069 | 0.0866368 | 0.0433184 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433184 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(114\) | −1400.43 | −1.15055 | ||||||||
\(115\) | 1028.31 | 0.833833 | ||||||||
\(116\) | 82.5256 | 0.0660544 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −518.479 | −0.404491 | ||||||||
\(119\) | −2488.55 | −1.91702 | ||||||||
\(120\) | −1707.54 | −1.29897 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 130.682 | 0.0969785 | ||||||||
\(123\) | 401.783 | 0.294533 | ||||||||
\(124\) | 347.045 | 0.251335 | ||||||||
\(125\) | −1444.47 | −1.03358 | ||||||||
\(126\) | −936.352 | −0.662039 | ||||||||
\(127\) | −2482.43 | −1.73449 | −0.867244 | − | 0.497883i | \(-0.834111\pi\) | ||||
−0.867244 | + | 0.497883i | \(0.834111\pi\) | |||||||
\(128\) | 739.461 | 0.510623 | ||||||||
\(129\) | −1349.74 | −0.921226 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −915.026 | −0.610276 | −0.305138 | − | 0.952308i | \(-0.598703\pi\) | ||||
−0.305138 | + | 0.952308i | \(0.598703\pi\) | |||||||
\(132\) | −134.772 | −0.0888664 | ||||||||
\(133\) | 2178.65 | 1.42040 | ||||||||
\(134\) | −708.856 | −0.456984 | ||||||||
\(135\) | −826.846 | −0.527138 | ||||||||
\(136\) | −2435.64 | −1.53569 | ||||||||
\(137\) | −2936.58 | −1.83131 | −0.915653 | − | 0.401971i | \(-0.868325\pi\) | ||||
−0.915653 | + | 0.401971i | \(0.868325\pi\) | |||||||
\(138\) | 1534.64 | 0.946649 | ||||||||
\(139\) | 2905.10 | 1.77272 | 0.886359 | − | 0.462999i | \(-0.153227\pi\) | ||||
0.886359 | + | 0.462999i | \(0.153227\pi\) | |||||||
\(140\) | 506.967 | 0.306047 | ||||||||
\(141\) | 794.933 | 0.474791 | ||||||||
\(142\) | −1921.59 | −1.13561 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −687.561 | −0.397894 | ||||||||
\(145\) | −470.505 | −0.269471 | ||||||||
\(146\) | −2039.01 | −1.15582 | ||||||||
\(147\) | 1823.34 | 1.02304 | ||||||||
\(148\) | 497.869 | 0.276517 | ||||||||
\(149\) | 1617.42 | 0.889288 | 0.444644 | − | 0.895707i | \(-0.353330\pi\) | ||||
0.444644 | + | 0.895707i | \(0.353330\pi\) | |||||||
\(150\) | −148.890 | −0.0810455 | ||||||||
\(151\) | −1869.40 | −1.00748 | −0.503741 | − | 0.863855i | \(-0.668043\pi\) | ||||
−0.503741 | + | 0.863855i | \(0.668043\pi\) | |||||||
\(152\) | 2132.33 | 1.13786 | ||||||||
\(153\) | 1510.80 | 0.798305 | ||||||||
\(154\) | −679.279 | −0.355441 | ||||||||
\(155\) | −1978.61 | −1.02533 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1248.10 | −0.634455 | −0.317228 | − | 0.948349i | \(-0.602752\pi\) | ||||
−0.317228 | + | 0.948349i | \(0.602752\pi\) | |||||||
\(158\) | −2128.41 | −1.07169 | ||||||||
\(159\) | −2048.17 | −1.02158 | ||||||||
\(160\) | 897.681 | 0.443550 | ||||||||
\(161\) | −2387.45 | −1.16868 | ||||||||
\(162\) | −2246.21 | −1.08937 | ||||||||
\(163\) | 2868.84 | 1.37856 | 0.689278 | − | 0.724497i | \(-0.257928\pi\) | ||||
0.689278 | + | 0.724497i | \(0.257928\pi\) | |||||||
\(164\) | −116.753 | −0.0555906 | ||||||||
\(165\) | 768.376 | 0.362533 | ||||||||
\(166\) | 3523.09 | 1.64726 | ||||||||
\(167\) | 1661.77 | 0.770009 | 0.385005 | − | 0.922915i | \(-0.374200\pi\) | ||||
0.385005 | + | 0.922915i | \(0.374200\pi\) | |||||||
\(168\) | 3964.42 | 1.82061 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2650.15 | 1.19563 | ||||||||
\(171\) | −1322.66 | −0.591498 | ||||||||
\(172\) | 392.216 | 0.173873 | ||||||||
\(173\) | 834.458 | 0.366721 | 0.183360 | − | 0.983046i | \(-0.441302\pi\) | ||||
0.183360 | + | 0.983046i | \(0.441302\pi\) | |||||||
\(174\) | −702.176 | −0.305930 | ||||||||
\(175\) | 231.629 | 0.100054 | ||||||||
\(176\) | −498.793 | −0.213625 | ||||||||
\(177\) | −1361.65 | −0.578236 | ||||||||
\(178\) | −1074.81 | −0.452587 | ||||||||
\(179\) | 1133.04 | 0.473116 | 0.236558 | − | 0.971617i | \(-0.423981\pi\) | ||||
0.236558 | + | 0.971617i | \(0.423981\pi\) | |||||||
\(180\) | −307.779 | −0.127447 | ||||||||
\(181\) | 4414.26 | 1.81276 | 0.906380 | − | 0.422464i | \(-0.138835\pi\) | ||||
0.906380 | + | 0.422464i | \(0.138835\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 343.201 | 0.138635 | ||||||||
\(184\) | −2336.69 | −0.936212 | ||||||||
\(185\) | −2838.51 | −1.12806 | ||||||||
\(186\) | −2952.86 | −1.16405 | ||||||||
\(187\) | 1096.01 | 0.428600 | ||||||||
\(188\) | −230.997 | −0.0896126 | ||||||||
\(189\) | 1919.70 | 0.738823 | ||||||||
\(190\) | −2320.12 | −0.885892 | ||||||||
\(191\) | 2556.25 | 0.968398 | 0.484199 | − | 0.874958i | \(-0.339111\pi\) | ||||
0.484199 | + | 0.874958i | \(0.339111\pi\) | |||||||
\(192\) | 3695.19 | 1.38894 | ||||||||
\(193\) | −2067.33 | −0.771033 | −0.385516 | − | 0.922701i | \(-0.625977\pi\) | ||||
−0.385516 | + | 0.922701i | \(0.625977\pi\) | |||||||
\(194\) | 2747.57 | 1.01682 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −529.837 | −0.193089 | ||||||||
\(197\) | 3312.55 | 1.19802 | 0.599009 | − | 0.800742i | \(-0.295561\pi\) | ||||
0.599009 | + | 0.800742i | \(0.295561\pi\) | |||||||
\(198\) | 412.390 | 0.148017 | ||||||||
\(199\) | −120.572 | −0.0429503 | −0.0214751 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214751 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(200\) | 226.704 | 0.0801519 | ||||||||
\(201\) | −1861.62 | −0.653277 | ||||||||
\(202\) | −1832.30 | −0.638218 | ||||||||
\(203\) | 1092.38 | 0.377684 | ||||||||
\(204\) | −1220.75 | −0.418970 | ||||||||
\(205\) | 665.644 | 0.226783 | ||||||||
\(206\) | −1279.20 | −0.432651 | ||||||||
\(207\) | 1449.42 | 0.486674 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −959.525 | −0.317568 | ||||||||
\(210\) | −4313.57 | −1.41745 | ||||||||
\(211\) | 4845.63 | 1.58098 | 0.790491 | − | 0.612474i | \(-0.209826\pi\) | ||||
0.790491 | + | 0.612474i | \(0.209826\pi\) | |||||||
\(212\) | 595.170 | 0.192814 | ||||||||
\(213\) | −5046.54 | −1.62340 | ||||||||
\(214\) | 3365.11 | 1.07492 | ||||||||
\(215\) | −2236.15 | −0.709321 | ||||||||
\(216\) | 1878.88 | 0.591860 | ||||||||
\(217\) | 4593.76 | 1.43707 | ||||||||
\(218\) | −4744.39 | −1.47399 | ||||||||
\(219\) | −5354.91 | −1.65229 | ||||||||
\(220\) | −223.279 | −0.0684250 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4236.16 | −1.28069 | ||||||||
\(223\) | 1683.59 | 0.505569 | 0.252784 | − | 0.967523i | \(-0.418654\pi\) | ||||
0.252784 | + | 0.967523i | \(0.418654\pi\) | |||||||
\(224\) | −2084.16 | −0.621668 | ||||||||
\(225\) | −140.622 | −0.0416657 | ||||||||
\(226\) | 257.307 | 0.0757338 | ||||||||
\(227\) | −1577.15 | −0.461142 | −0.230571 | − | 0.973056i | \(-0.574059\pi\) | ||||
−0.230571 | + | 0.973056i | \(0.574059\pi\) | |||||||
\(228\) | 1068.73 | 0.310433 | ||||||||
\(229\) | −2368.16 | −0.683374 | −0.341687 | − | 0.939814i | \(-0.610998\pi\) | ||||
−0.341687 | + | 0.939814i | \(0.610998\pi\) | |||||||
\(230\) | 2542.48 | 0.728897 | ||||||||
\(231\) | −1783.95 | −0.508117 | ||||||||
\(232\) | 1069.15 | 0.302557 | ||||||||
\(233\) | 4037.46 | 1.13521 | 0.567603 | − | 0.823302i | \(-0.307871\pi\) | ||||
0.567603 | + | 0.823302i | \(0.307871\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1316.98 | 0.365577 | ||||||||
\(236\) | 395.676 | 0.109137 | ||||||||
\(237\) | −5589.69 | −1.53202 | ||||||||
\(238\) | −6152.88 | −1.67576 | ||||||||
\(239\) | 4072.68 | 1.10226 | 0.551129 | − | 0.834420i | \(-0.314197\pi\) | ||||
0.551129 | + | 0.834420i | \(0.314197\pi\) | |||||||
\(240\) | −3167.44 | −0.851906 | ||||||||
\(241\) | −4726.49 | −1.26332 | −0.631659 | − | 0.775246i | \(-0.717626\pi\) | ||||
−0.631659 | + | 0.775246i | \(0.717626\pi\) | |||||||
\(242\) | 299.170 | 0.0794684 | ||||||||
\(243\) | −3823.80 | −1.00945 | ||||||||
\(244\) | −99.7295 | −0.0261661 | ||||||||
\(245\) | 3020.77 | 0.787713 | ||||||||
\(246\) | 993.400 | 0.257467 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4496.09 | 1.15122 | ||||||||
\(249\) | 9252.45 | 2.35482 | ||||||||
\(250\) | −3571.41 | −0.903503 | ||||||||
\(251\) | −1098.64 | −0.276276 | −0.138138 | − | 0.990413i | \(-0.544112\pi\) | ||||
−0.138138 | + | 0.990413i | \(0.544112\pi\) | |||||||
\(252\) | 714.575 | 0.178627 | ||||||||
\(253\) | 1051.48 | 0.261290 | ||||||||
\(254\) | −6137.75 | −1.51621 | ||||||||
\(255\) | 6959.90 | 1.70920 | ||||||||
\(256\) | −2724.32 | −0.665118 | ||||||||
\(257\) | 670.252 | 0.162682 | 0.0813408 | − | 0.996686i | \(-0.474080\pi\) | ||||
0.0813408 | + | 0.996686i | \(0.474080\pi\) | |||||||
\(258\) | −3337.20 | −0.805292 | ||||||||
\(259\) | 6590.19 | 1.58106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −663.181 | −0.157279 | ||||||||
\(262\) | −2262.38 | −0.533474 | ||||||||
\(263\) | −7002.52 | −1.64180 | −0.820900 | − | 0.571071i | \(-0.806528\pi\) | ||||
−0.820900 | + | 0.571071i | \(0.806528\pi\) | |||||||
\(264\) | −1746.02 | −0.407045 | ||||||||
\(265\) | −3393.25 | −0.786588 | ||||||||
\(266\) | 5386.66 | 1.24164 | ||||||||
\(267\) | −2822.71 | −0.646992 | ||||||||
\(268\) | 540.961 | 0.123300 | ||||||||
\(269\) | −498.594 | −0.113011 | −0.0565053 | − | 0.998402i | \(-0.517996\pi\) | ||||
−0.0565053 | + | 0.998402i | \(0.517996\pi\) | |||||||
\(270\) | −2044.36 | −0.460798 | ||||||||
\(271\) | 1788.15 | 0.400822 | 0.200411 | − | 0.979712i | \(-0.435772\pi\) | ||||
0.200411 | + | 0.979712i | \(0.435772\pi\) | |||||||
\(272\) | −4518.04 | −1.00716 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7260.62 | −1.60084 | ||||||||
\(275\) | −102.014 | −0.0223698 | ||||||||
\(276\) | −1171.16 | −0.255419 | ||||||||
\(277\) | 2880.64 | 0.624840 | 0.312420 | − | 0.949944i | \(-0.398860\pi\) | ||||
0.312420 | + | 0.949944i | \(0.398860\pi\) | |||||||
\(278\) | 7182.80 | 1.54963 | ||||||||
\(279\) | −2788.87 | −0.598442 | ||||||||
\(280\) | 6567.95 | 1.40182 | ||||||||
\(281\) | 6128.45 | 1.30104 | 0.650521 | − | 0.759489i | \(-0.274551\pi\) | ||||
0.650521 | + | 0.759489i | \(0.274551\pi\) | |||||||
\(282\) | 1965.45 | 0.415039 | ||||||||
\(283\) | 7039.28 | 1.47859 | 0.739296 | − | 0.673380i | \(-0.235158\pi\) | ||||
0.739296 | + | 0.673380i | \(0.235158\pi\) | |||||||
\(284\) | 1466.46 | 0.306402 | ||||||||
\(285\) | −6093.19 | −1.26642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1545.43 | −0.317854 | ||||||||
\(288\) | 1265.29 | 0.258882 | ||||||||
\(289\) | 5014.61 | 1.02068 | ||||||||
\(290\) | −1163.31 | −0.235559 | ||||||||
\(291\) | 7215.76 | 1.45359 | ||||||||
\(292\) | 1556.06 | 0.311855 | ||||||||
\(293\) | −5273.69 | −1.05151 | −0.525755 | − | 0.850636i | \(-0.676217\pi\) | ||||
−0.525755 | + | 0.850636i | \(0.676217\pi\) | |||||||
\(294\) | 4508.16 | 0.894290 | ||||||||
\(295\) | −2255.87 | −0.445227 | ||||||||
\(296\) | 6450.08 | 1.26656 | ||||||||
\(297\) | −845.477 | −0.165184 | ||||||||
\(298\) | 3999.02 | 0.777373 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 113.625 | 0.0218672 | ||||||||
\(301\) | 5191.69 | 0.994167 | ||||||||
\(302\) | −4622.05 | −0.880692 | ||||||||
\(303\) | −4812.04 | −0.912358 | ||||||||
\(304\) | 3955.41 | 0.746245 | ||||||||
\(305\) | 568.589 | 0.106745 | ||||||||
\(306\) | 3735.41 | 0.697840 | ||||||||
\(307\) | −215.715 | −0.0401026 | −0.0200513 | − | 0.999799i | \(-0.506383\pi\) | ||||
−0.0200513 | + | 0.999799i | \(0.506383\pi\) | |||||||
\(308\) | 518.390 | 0.0959027 | ||||||||
\(309\) | −3359.48 | −0.618492 | ||||||||
\(310\) | −4892.07 | −0.896292 | ||||||||
\(311\) | 7314.80 | 1.33371 | 0.666855 | − | 0.745187i | \(-0.267640\pi\) | ||||
0.666855 | + | 0.745187i | \(0.267640\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −420.725 | −0.0759769 | −0.0379884 | − | 0.999278i | \(-0.512095\pi\) | ||||
−0.0379884 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(314\) | −3085.91 | −0.554611 | ||||||||
\(315\) | −4074.02 | −0.728713 | ||||||||
\(316\) | 1624.29 | 0.289156 | ||||||||
\(317\) | −7647.34 | −1.35494 | −0.677472 | − | 0.735548i | \(-0.736925\pi\) | ||||
−0.677472 | + | 0.735548i | \(0.736925\pi\) | |||||||
\(318\) | −5064.05 | −0.893013 | ||||||||
\(319\) | −481.106 | −0.0844413 | ||||||||
\(320\) | 6121.91 | 1.06945 | ||||||||
\(321\) | 8837.55 | 1.53665 | ||||||||
\(322\) | −5902.91 | −1.02160 | ||||||||
\(323\) | −8691.33 | −1.49721 | ||||||||
\(324\) | 1714.19 | 0.293928 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7093.13 | 1.20507 | ||||||||
\(327\) | −12459.9 | −2.10713 | ||||||||
\(328\) | −1512.58 | −0.254628 | ||||||||
\(329\) | −3057.66 | −0.512384 | ||||||||
\(330\) | 1899.79 | 0.316909 | ||||||||
\(331\) | −9264.16 | −1.53838 | −0.769191 | − | 0.639019i | \(-0.779340\pi\) | ||||
−0.769191 | + | 0.639019i | \(0.779340\pi\) | |||||||
\(332\) | −2688.63 | −0.444452 | ||||||||
\(333\) | −4000.90 | −0.658403 | ||||||||
\(334\) | 4108.68 | 0.673105 | ||||||||
\(335\) | −3084.19 | −0.503007 | ||||||||
\(336\) | 7353.89 | 1.19401 | ||||||||
\(337\) | −3367.62 | −0.544350 | −0.272175 | − | 0.962248i | \(-0.587743\pi\) | ||||
−0.272175 | + | 0.962248i | \(0.587743\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 675.749 | 0.108265 | ||||||||
\(340\) | −2022.45 | −0.322597 | ||||||||
\(341\) | −2023.19 | −0.321296 | ||||||||
\(342\) | −3270.24 | −0.517059 | ||||||||
\(343\) | 1553.44 | 0.244541 | ||||||||
\(344\) | 5081.31 | 0.796413 | ||||||||
\(345\) | 6677.15 | 1.04199 | ||||||||
\(346\) | 2063.18 | 0.320570 | ||||||||
\(347\) | −4548.38 | −0.703660 | −0.351830 | − | 0.936064i | \(-0.614440\pi\) | ||||
−0.351830 | + | 0.936064i | \(0.614440\pi\) | |||||||
\(348\) | 535.864 | 0.0825440 | ||||||||
\(349\) | −11551.2 | −1.77169 | −0.885845 | − | 0.463980i | \(-0.846421\pi\) | ||||
−0.885845 | + | 0.463980i | \(0.846421\pi\) | |||||||
\(350\) | 572.696 | 0.0874626 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 917.909 | 0.138991 | ||||||||
\(353\) | −4656.01 | −0.702024 | −0.351012 | − | 0.936371i | \(-0.614162\pi\) | ||||
−0.351012 | + | 0.936371i | \(0.614162\pi\) | |||||||
\(354\) | −3366.64 | −0.505466 | ||||||||
\(355\) | −8360.72 | −1.24997 | ||||||||
\(356\) | 820.240 | 0.122114 | ||||||||
\(357\) | −16158.9 | −2.39557 | ||||||||
\(358\) | 2801.43 | 0.413575 | ||||||||
\(359\) | 4795.68 | 0.705031 | 0.352516 | − | 0.935806i | \(-0.385326\pi\) | ||||
0.352516 | + | 0.935806i | \(0.385326\pi\) | |||||||
\(360\) | −3987.40 | −0.583762 | ||||||||
\(361\) | 749.997 | 0.109345 | ||||||||
\(362\) | 10914.2 | 1.58463 | ||||||||
\(363\) | 785.689 | 0.113603 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8871.60 | −1.27222 | ||||||||
\(366\) | 848.557 | 0.121188 | ||||||||
\(367\) | 2731.53 | 0.388515 | 0.194257 | − | 0.980951i | \(-0.437770\pi\) | ||||
0.194257 | + | 0.980951i | \(0.437770\pi\) | |||||||
\(368\) | −4334.49 | −0.613997 | ||||||||
\(369\) | 938.232 | 0.132364 | ||||||||
\(370\) | −7018.14 | −0.986096 | ||||||||
\(371\) | 7878.15 | 1.10246 | ||||||||
\(372\) | 2253.46 | 0.314077 | ||||||||
\(373\) | 11335.3 | 1.57351 | 0.786757 | − | 0.617263i | \(-0.211758\pi\) | ||||
0.786757 | + | 0.617263i | \(0.211758\pi\) | |||||||
\(374\) | 2709.86 | 0.374662 | ||||||||
\(375\) | −9379.35 | −1.29159 | ||||||||
\(376\) | −2992.65 | −0.410463 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4746.41 | 0.645843 | ||||||||
\(379\) | 10699.6 | 1.45014 | 0.725071 | − | 0.688674i | \(-0.241807\pi\) | ||||
0.725071 | + | 0.688674i | \(0.241807\pi\) | |||||||
\(380\) | 1770.60 | 0.239025 | ||||||||
\(381\) | −16119.2 | −2.16748 | ||||||||
\(382\) | 6320.28 | 0.846528 | ||||||||
\(383\) | −6729.49 | −0.897809 | −0.448905 | − | 0.893580i | \(-0.648186\pi\) | ||||
−0.448905 | + | 0.893580i | \(0.648186\pi\) | |||||||
\(384\) | 4801.54 | 0.638092 | ||||||||
\(385\) | −2955.51 | −0.391238 | ||||||||
\(386\) | −5111.41 | −0.674000 | ||||||||
\(387\) | −3151.87 | −0.414002 | ||||||||
\(388\) | −2096.80 | −0.274353 | ||||||||
\(389\) | 8798.11 | 1.14674 | 0.573370 | − | 0.819296i | \(-0.305636\pi\) | ||||
0.573370 | + | 0.819296i | \(0.305636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9524.29 | 1.23188 | ||||||||
\(392\) | −6864.24 | −0.884429 | ||||||||
\(393\) | −5941.54 | −0.762623 | ||||||||
\(394\) | 8190.20 | 1.04725 | ||||||||
\(395\) | −9260.57 | −1.17962 | ||||||||
\(396\) | −314.714 | −0.0399369 | ||||||||
\(397\) | −3726.62 | −0.471118 | −0.235559 | − | 0.971860i | \(-0.575692\pi\) | ||||
−0.235559 | + | 0.971860i | \(0.575692\pi\) | |||||||
\(398\) | −298.111 | −0.0375451 | ||||||||
\(399\) | 14146.6 | 1.77498 | ||||||||
\(400\) | 420.529 | 0.0525662 | ||||||||
\(401\) | 7708.28 | 0.959932 | 0.479966 | − | 0.877287i | \(-0.340649\pi\) | ||||
0.479966 | + | 0.877287i | \(0.340649\pi\) | |||||||
\(402\) | −4602.81 | −0.571063 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1398.31 | 0.172200 | ||||||||
\(405\) | −9773.11 | −1.19909 | ||||||||
\(406\) | 2700.87 | 0.330153 | ||||||||
\(407\) | −2902.47 | −0.353489 | ||||||||
\(408\) | −15815.3 | −1.91906 | ||||||||
\(409\) | −6777.35 | −0.819360 | −0.409680 | − | 0.912229i | \(-0.634360\pi\) | ||||
−0.409680 | + | 0.912229i | \(0.634360\pi\) | |||||||
\(410\) | 1645.79 | 0.198243 | ||||||||
\(411\) | −19068.1 | −2.28847 | ||||||||
\(412\) | 976.218 | 0.116735 | ||||||||
\(413\) | 5237.49 | 0.624019 | ||||||||
\(414\) | 3583.65 | 0.425427 | ||||||||
\(415\) | 15328.7 | 1.81315 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18863.7 | 2.21525 | ||||||||
\(418\) | −2372.40 | −0.277603 | ||||||||
\(419\) | 15203.6 | 1.77266 | 0.886329 | − | 0.463055i | \(-0.153247\pi\) | ||||
0.886329 | + | 0.463055i | \(0.153247\pi\) | |||||||
\(420\) | 3291.89 | 0.382447 | ||||||||
\(421\) | 504.983 | 0.0584593 | 0.0292296 | − | 0.999573i | \(-0.490695\pi\) | ||||
0.0292296 | + | 0.999573i | \(0.490695\pi\) | |||||||
\(422\) | 11980.7 | 1.38202 | ||||||||
\(423\) | 1856.30 | 0.213372 | ||||||||
\(424\) | 7710.66 | 0.883166 | ||||||||
\(425\) | −924.040 | −0.105465 | ||||||||
\(426\) | −12477.5 | −1.41909 | ||||||||
\(427\) | −1320.10 | −0.149612 | ||||||||
\(428\) | −2568.07 | −0.290029 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5528.82 | −0.620055 | ||||||||
\(431\) | −6636.70 | −0.741714 | −0.370857 | − | 0.928690i | \(-0.620936\pi\) | ||||
−0.370857 | + | 0.928690i | \(0.620936\pi\) | |||||||
\(432\) | 3485.28 | 0.388161 | ||||||||
\(433\) | −4418.04 | −0.490341 | −0.245170 | − | 0.969480i | \(-0.578844\pi\) | ||||
−0.245170 | + | 0.969480i | \(0.578844\pi\) | |||||||
\(434\) | 11358.0 | 1.25622 | ||||||||
\(435\) | −3055.13 | −0.336741 | ||||||||
\(436\) | 3620.67 | 0.397703 | ||||||||
\(437\) | −8338.23 | −0.912750 | ||||||||
\(438\) | −13239.9 | −1.44435 | ||||||||
\(439\) | 8127.71 | 0.883632 | 0.441816 | − | 0.897106i | \(-0.354334\pi\) | ||||
0.441816 | + | 0.897106i | \(0.354334\pi\) | |||||||
\(440\) | −2892.67 | −0.313415 | ||||||||
\(441\) | 4257.80 | 0.459756 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16067.6 | −1.72324 | −0.861620 | − | 0.507554i | \(-0.830550\pi\) | ||||
−0.861620 | + | 0.507554i | \(0.830550\pi\) | |||||||
\(444\) | 3232.81 | 0.345546 | ||||||||
\(445\) | −4676.45 | −0.498168 | ||||||||
\(446\) | 4162.65 | 0.441944 | ||||||||
\(447\) | 10502.4 | 1.11129 | ||||||||
\(448\) | −14213.3 | −1.49892 | ||||||||
\(449\) | −6330.96 | −0.665426 | −0.332713 | − | 0.943028i | \(-0.607964\pi\) | ||||
−0.332713 | + | 0.943028i | \(0.607964\pi\) | |||||||
\(450\) | −347.683 | −0.0364221 | ||||||||
\(451\) | 680.643 | 0.0710648 | ||||||||
\(452\) | −196.363 | −0.0204340 | ||||||||
\(453\) | −12138.6 | −1.25898 | ||||||||
\(454\) | −3899.47 | −0.403108 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 13845.9 | 1.42191 | ||||||||
\(457\) | −7781.66 | −0.796523 | −0.398261 | − | 0.917272i | \(-0.630386\pi\) | ||||
−0.398261 | + | 0.917272i | \(0.630386\pi\) | |||||||
\(458\) | −5855.23 | −0.597373 | ||||||||
\(459\) | −7658.29 | −0.778776 | ||||||||
\(460\) | −1940.29 | −0.196666 | ||||||||
\(461\) | 16672.3 | 1.68439 | 0.842197 | − | 0.539171i | \(-0.181262\pi\) | ||||
0.842197 | + | 0.539171i | \(0.181262\pi\) | |||||||
\(462\) | −4410.76 | −0.444172 | ||||||||
\(463\) | −287.484 | −0.0288564 | −0.0144282 | − | 0.999896i | \(-0.504593\pi\) | ||||
−0.0144282 | + | 0.999896i | \(0.504593\pi\) | |||||||
\(464\) | 1983.24 | 0.198426 | ||||||||
\(465\) | −12847.7 | −1.28129 | ||||||||
\(466\) | 9982.53 | 0.992343 | ||||||||
\(467\) | −3349.86 | −0.331934 | −0.165967 | − | 0.986131i | \(-0.553075\pi\) | ||||
−0.165967 | + | 0.986131i | \(0.553075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7160.60 | 0.705002 | ||||||||
\(470\) | 3256.21 | 0.319570 | ||||||||
\(471\) | −8104.31 | −0.792838 | ||||||||
\(472\) | 5126.13 | 0.499893 | ||||||||
\(473\) | −2286.54 | −0.222273 | ||||||||
\(474\) | −13820.4 | −1.33922 | ||||||||
\(475\) | 808.970 | 0.0781433 | ||||||||
\(476\) | 4695.55 | 0.452143 | ||||||||
\(477\) | −4782.82 | −0.459099 | ||||||||
\(478\) | 10069.6 | 0.963542 | ||||||||
\(479\) | 8197.72 | 0.781970 | 0.390985 | − | 0.920397i | \(-0.372134\pi\) | ||||
0.390985 | + | 0.920397i | \(0.372134\pi\) | |||||||
\(480\) | 5828.91 | 0.554276 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −11686.1 | −1.10433 | ||||||||
\(483\) | −15502.4 | −1.46042 | ||||||||
\(484\) | −228.310 | −0.0214416 | ||||||||
\(485\) | 11954.5 | 1.11923 | ||||||||
\(486\) | −9454.26 | −0.882415 | ||||||||
\(487\) | 10583.9 | 0.984806 | 0.492403 | − | 0.870367i | \(-0.336119\pi\) | ||||
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(488\) | −1292.03 | −0.119852 | ||||||||
\(489\) | 18628.2 | 1.72269 | ||||||||
\(490\) | 7468.77 | 0.688581 | ||||||||
\(491\) | 7023.97 | 0.645596 | 0.322798 | − | 0.946468i | \(-0.395377\pi\) | ||||
0.322798 | + | 0.946468i | \(0.395377\pi\) | |||||||
\(492\) | −758.110 | −0.0694680 | ||||||||
\(493\) | −4357.83 | −0.398108 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1794.29 | 0.162924 | ||||||||
\(496\) | 8340.13 | 0.755006 | ||||||||
\(497\) | 19411.2 | 1.75193 | ||||||||
\(498\) | 22876.5 | 2.05847 | ||||||||
\(499\) | −14779.1 | −1.32586 | −0.662928 | − | 0.748683i | \(-0.730687\pi\) | ||||
−0.662928 | + | 0.748683i | \(0.730687\pi\) | |||||||
\(500\) | 2725.51 | 0.243777 | ||||||||
\(501\) | 10790.4 | 0.962231 | ||||||||
\(502\) | −2716.35 | −0.241507 | ||||||||
\(503\) | 13506.3 | 1.19725 | 0.598624 | − | 0.801030i | \(-0.295714\pi\) | ||||
0.598624 | + | 0.801030i | \(0.295714\pi\) | |||||||
\(504\) | 9257.59 | 0.818186 | ||||||||
\(505\) | −7972.22 | −0.702493 | ||||||||
\(506\) | 2599.77 | 0.228407 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4684.01 | 0.409093 | ||||||||
\(509\) | 9756.32 | 0.849590 | 0.424795 | − | 0.905290i | \(-0.360346\pi\) | ||||
0.424795 | + | 0.905290i | \(0.360346\pi\) | |||||||
\(510\) | 17208.2 | 1.49410 | ||||||||
\(511\) | 20597.3 | 1.78311 | ||||||||
\(512\) | −12651.5 | −1.09204 | ||||||||
\(513\) | 6704.60 | 0.577028 | ||||||||
\(514\) | 1657.18 | 0.142209 | ||||||||
\(515\) | −5565.72 | −0.476223 | ||||||||
\(516\) | 2546.78 | 0.217278 | ||||||||
\(517\) | 1346.66 | 0.114557 | ||||||||
\(518\) | 16294.1 | 1.38209 | ||||||||
\(519\) | 5418.39 | 0.458267 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20113.6 | −1.69135 | −0.845675 | − | 0.533698i | \(-0.820802\pi\) | ||||
−0.845675 | + | 0.533698i | \(0.820802\pi\) | |||||||
\(522\) | −1639.70 | −0.137486 | ||||||||
\(523\) | 7449.01 | 0.622797 | 0.311398 | − | 0.950279i | \(-0.399203\pi\) | ||||
0.311398 | + | 0.950279i | \(0.399203\pi\) | |||||||
\(524\) | 1726.53 | 0.143939 | ||||||||
\(525\) | 1504.03 | 0.125031 | ||||||||
\(526\) | −17313.6 | −1.43518 | ||||||||
\(527\) | −18326.0 | −1.51479 | ||||||||
\(528\) | −3238.81 | −0.266953 | ||||||||
\(529\) | −3029.64 | −0.249005 | ||||||||
\(530\) | −8389.74 | −0.687598 | ||||||||
\(531\) | −3179.68 | −0.259861 | ||||||||
\(532\) | −4110.81 | −0.335012 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6979.08 | −0.565570 | ||||||||
\(535\) | 14641.4 | 1.18318 | ||||||||
\(536\) | 7008.36 | 0.564767 | ||||||||
\(537\) | 7357.20 | 0.591223 | ||||||||
\(538\) | −1232.76 | −0.0987884 | ||||||||
\(539\) | 3088.83 | 0.246838 | ||||||||
\(540\) | 1560.15 | 0.124330 | ||||||||
\(541\) | −12994.4 | −1.03267 | −0.516335 | − | 0.856387i | \(-0.672704\pi\) | ||||
−0.516335 | + | 0.856387i | \(0.672704\pi\) | |||||||
\(542\) | 4421.17 | 0.350379 | ||||||||
\(543\) | 28663.1 | 2.26529 | ||||||||
\(544\) | 8314.37 | 0.655286 | ||||||||
\(545\) | −20642.6 | −1.62244 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7228.20 | 0.565001 | 0.282501 | − | 0.959267i | \(-0.408836\pi\) | ||||
0.282501 | + | 0.959267i | \(0.408836\pi\) | |||||||
\(548\) | 5540.92 | 0.431928 | ||||||||
\(549\) | 801.432 | 0.0623029 | ||||||||
\(550\) | −252.228 | −0.0195546 | ||||||||
\(551\) | 3815.15 | 0.294975 | ||||||||
\(552\) | −15172.8 | −1.16992 | ||||||||
\(553\) | 21500.4 | 1.65333 | ||||||||
\(554\) | 7122.31 | 0.546205 | ||||||||
\(555\) | −18431.3 | −1.40966 | ||||||||
\(556\) | −5481.54 | −0.418110 | ||||||||
\(557\) | −21258.3 | −1.61713 | −0.808565 | − | 0.588407i | \(-0.799755\pi\) | ||||
−0.808565 | + | 0.588407i | \(0.799755\pi\) | |||||||
\(558\) | −6895.41 | −0.523129 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 12183.4 | 0.919359 | ||||||||
\(561\) | 7116.73 | 0.535595 | ||||||||
\(562\) | 15152.4 | 1.13731 | ||||||||
\(563\) | 4193.52 | 0.313918 | 0.156959 | − | 0.987605i | \(-0.449831\pi\) | ||||
0.156959 | + | 0.987605i | \(0.449831\pi\) | |||||||
\(564\) | −1499.93 | −0.111983 | ||||||||
\(565\) | 1119.53 | 0.0833610 | ||||||||
\(566\) | 17404.5 | 1.29252 | ||||||||
\(567\) | 22690.4 | 1.68061 | ||||||||
\(568\) | 18998.5 | 1.40345 | ||||||||
\(569\) | −12696.3 | −0.935427 | −0.467713 | − | 0.883880i | \(-0.654922\pi\) | ||||
−0.467713 | + | 0.883880i | \(0.654922\pi\) | |||||||
\(570\) | −15065.3 | −1.10704 | ||||||||
\(571\) | 5206.70 | 0.381600 | 0.190800 | − | 0.981629i | \(-0.438892\pi\) | ||||
0.190800 | + | 0.981629i | \(0.438892\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16598.5 | 1.21015 | ||||||||
\(574\) | −3821.05 | −0.277853 | ||||||||
\(575\) | −886.500 | −0.0642950 | ||||||||
\(576\) | 8628.89 | 0.624196 | ||||||||
\(577\) | −5567.86 | −0.401721 | −0.200860 | − | 0.979620i | \(-0.564374\pi\) | ||||
−0.200860 | + | 0.979620i | \(0.564374\pi\) | |||||||
\(578\) | 12398.5 | 0.892232 | ||||||||
\(579\) | −13423.8 | −0.963510 | ||||||||
\(580\) | 887.778 | 0.0635568 | ||||||||
\(581\) | −35588.9 | −2.54127 | ||||||||
\(582\) | 17840.8 | 1.27066 | ||||||||
\(583\) | −3469.71 | −0.246485 | ||||||||
\(584\) | 20159.4 | 1.42843 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13039.1 | −0.919179 | ||||||||
\(587\) | −19446.1 | −1.36734 | −0.683669 | − | 0.729792i | \(-0.739617\pi\) | ||||
−0.683669 | + | 0.729792i | \(0.739617\pi\) | |||||||
\(588\) | −3440.39 | −0.241291 | ||||||||
\(589\) | 16043.8 | 1.12237 | ||||||||
\(590\) | −5577.59 | −0.389196 | ||||||||
\(591\) | 21509.4 | 1.49709 | ||||||||
\(592\) | 11964.7 | 0.830653 | ||||||||
\(593\) | −629.272 | −0.0435769 | −0.0217884 | − | 0.999763i | \(-0.506936\pi\) | ||||
−0.0217884 | + | 0.999763i | \(0.506936\pi\) | |||||||
\(594\) | −2090.42 | −0.144396 | ||||||||
\(595\) | −26770.8 | −1.84453 | ||||||||
\(596\) | −3051.85 | −0.209746 | ||||||||
\(597\) | −782.909 | −0.0536722 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25701.5 | −1.75315 | −0.876574 | − | 0.481268i | \(-0.840176\pi\) | ||||
−0.876574 | + | 0.481268i | \(0.840176\pi\) | |||||||
\(600\) | 1472.06 | 0.100161 | ||||||||
\(601\) | 11196.3 | 0.759913 | 0.379957 | − | 0.925004i | \(-0.375939\pi\) | ||||
0.379957 | + | 0.925004i | \(0.375939\pi\) | |||||||
\(602\) | 12836.3 | 0.869053 | ||||||||
\(603\) | −4347.20 | −0.293585 | ||||||||
\(604\) | 3527.30 | 0.237622 | ||||||||
\(605\) | 1301.67 | 0.0874717 | ||||||||
\(606\) | −11897.7 | −0.797540 | ||||||||
\(607\) | 5856.62 | 0.391619 | 0.195810 | − | 0.980642i | \(-0.437267\pi\) | ||||
0.195810 | + | 0.980642i | \(0.437267\pi\) | |||||||
\(608\) | −7278.98 | −0.485529 | ||||||||
\(609\) | 7093.12 | 0.471967 | ||||||||
\(610\) | 1405.82 | 0.0933117 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2850.67 | −0.188287 | ||||||||
\(613\) | 18626.4 | 1.22727 | 0.613633 | − | 0.789592i | \(-0.289708\pi\) | ||||
0.613633 | + | 0.789592i | \(0.289708\pi\) | |||||||
\(614\) | −533.350 | −0.0350558 | ||||||||
\(615\) | 4322.23 | 0.283397 | ||||||||
\(616\) | 6715.94 | 0.439274 | ||||||||
\(617\) | −6014.29 | −0.392425 | −0.196213 | − | 0.980561i | \(-0.562864\pi\) | ||||
−0.196213 | + | 0.980561i | \(0.562864\pi\) | |||||||
\(618\) | −8306.23 | −0.540656 | ||||||||
\(619\) | 13605.2 | 0.883427 | 0.441713 | − | 0.897156i | \(-0.354371\pi\) | ||||
0.441713 | + | 0.897156i | \(0.354371\pi\) | |||||||
\(620\) | 3733.37 | 0.241832 | ||||||||
\(621\) | −7347.16 | −0.474769 | ||||||||
\(622\) | 18085.7 | 1.16587 | ||||||||
\(623\) | 10857.4 | 0.698220 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14379.7 | −0.920303 | ||||||||
\(626\) | −1040.23 | −0.0664153 | ||||||||
\(627\) | −6230.49 | −0.396845 | ||||||||
\(628\) | 2355.00 | 0.149641 | ||||||||
\(629\) | −26290.4 | −1.66656 | ||||||||
\(630\) | −10072.9 | −0.637006 | ||||||||
\(631\) | −15244.3 | −0.961751 | −0.480876 | − | 0.876789i | \(-0.659681\pi\) | ||||
−0.480876 | + | 0.876789i | \(0.659681\pi\) | |||||||
\(632\) | 21043.3 | 1.32446 | ||||||||
\(633\) | 31464.1 | 1.97565 | ||||||||
\(634\) | −18907.9 | −1.18443 | ||||||||
\(635\) | −26705.0 | −1.66891 | ||||||||
\(636\) | 3864.62 | 0.240947 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1189.52 | −0.0738146 | ||||||||
\(639\) | −11784.5 | −0.729559 | ||||||||
\(640\) | 7954.82 | 0.491315 | ||||||||
\(641\) | −25338.9 | −1.56135 | −0.780677 | − | 0.624934i | \(-0.785126\pi\) | ||||
−0.780677 | + | 0.624934i | \(0.785126\pi\) | |||||||
\(642\) | 21850.6 | 1.34326 | ||||||||
\(643\) | 11455.3 | 0.702570 | 0.351285 | − | 0.936269i | \(-0.385745\pi\) | ||||
0.351285 | + | 0.936269i | \(0.385745\pi\) | |||||||
\(644\) | 4504.79 | 0.275642 | ||||||||
\(645\) | −14520.0 | −0.886393 | ||||||||
\(646\) | −21489.1 | −1.30879 | ||||||||
\(647\) | −12557.8 | −0.763058 | −0.381529 | − | 0.924357i | \(-0.624602\pi\) | ||||
−0.381529 | + | 0.924357i | \(0.624602\pi\) | |||||||
\(648\) | 22207.9 | 1.34631 | ||||||||
\(649\) | −2306.71 | −0.139516 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29828.7 | 1.79582 | ||||||||
\(652\) | −5413.10 | −0.325143 | ||||||||
\(653\) | −3738.25 | −0.224026 | −0.112013 | − | 0.993707i | \(-0.535730\pi\) | ||||
−0.112013 | + | 0.993707i | \(0.535730\pi\) | |||||||
\(654\) | −30806.7 | −1.84195 | ||||||||
\(655\) | −9843.49 | −0.587201 | ||||||||
\(656\) | −2805.79 | −0.166993 | ||||||||
\(657\) | −12504.6 | −0.742543 | ||||||||
\(658\) | −7559.99 | −0.447901 | ||||||||
\(659\) | 16091.1 | 0.951171 | 0.475586 | − | 0.879669i | \(-0.342236\pi\) | ||||
0.475586 | + | 0.879669i | \(0.342236\pi\) | |||||||
\(660\) | −1449.82 | −0.0855063 | ||||||||
\(661\) | 13820.8 | 0.813265 | 0.406633 | − | 0.913592i | \(-0.366703\pi\) | ||||
0.406633 | + | 0.913592i | \(0.366703\pi\) | |||||||
\(662\) | −22905.4 | −1.34478 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −34832.3 | −2.03577 | ||||||||
\(665\) | 23437.0 | 1.36669 | ||||||||
\(666\) | −9892.13 | −0.575544 | ||||||||
\(667\) | −4180.79 | −0.242700 | ||||||||
\(668\) | −3135.53 | −0.181613 | ||||||||
\(669\) | 10932.1 | 0.631777 | ||||||||
\(670\) | −7625.58 | −0.439705 | ||||||||
\(671\) | 581.401 | 0.0334497 | ||||||||
\(672\) | −13533.1 | −0.776859 | ||||||||
\(673\) | −20587.0 | −1.17916 | −0.589578 | − | 0.807712i | \(-0.700706\pi\) | ||||
−0.589578 | + | 0.807712i | \(0.700706\pi\) | |||||||
\(674\) | −8326.35 | −0.475844 | ||||||||
\(675\) | 712.816 | 0.0406464 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3979.12 | −0.225894 | −0.112947 | − | 0.993601i | \(-0.536029\pi\) | ||||
−0.112947 | + | 0.993601i | \(0.536029\pi\) | |||||||
\(678\) | 1670.77 | 0.0946397 | ||||||||
\(679\) | −27754.9 | −1.56868 | ||||||||
\(680\) | −26201.6 | −1.47763 | ||||||||
\(681\) | −10240.9 | −0.576259 | ||||||||
\(682\) | −5002.30 | −0.280862 | ||||||||
\(683\) | −26072.1 | −1.46064 | −0.730322 | − | 0.683103i | \(-0.760630\pi\) | ||||
−0.730322 | + | 0.683103i | \(0.760630\pi\) | |||||||
\(684\) | 2495.67 | 0.139509 | ||||||||
\(685\) | −31590.5 | −1.76206 | ||||||||
\(686\) | 3840.83 | 0.213766 | ||||||||
\(687\) | −15377.2 | −0.853969 | ||||||||
\(688\) | 9425.69 | 0.522312 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 16509.1 | 0.910856 | ||||||||
\(691\) | −13017.8 | −0.716675 | −0.358337 | − | 0.933592i | \(-0.616656\pi\) | ||||
−0.358337 | + | 0.933592i | \(0.616656\pi\) | |||||||
\(692\) | −1574.51 | −0.0864940 | ||||||||
\(693\) | −4165.81 | −0.228349 | ||||||||
\(694\) | −11245.8 | −0.615106 | ||||||||
\(695\) | 31252.0 | 1.70569 | ||||||||
\(696\) | 6942.32 | 0.378086 | ||||||||
\(697\) | 6165.22 | 0.335042 | ||||||||
\(698\) | −28560.0 | −1.54873 | ||||||||
\(699\) | 26216.5 | 1.41859 | ||||||||
\(700\) | −437.052 | −0.0235986 | ||||||||
\(701\) | −13900.1 | −0.748927 | −0.374464 | − | 0.927242i | \(-0.622173\pi\) | ||||
−0.374464 | + | 0.927242i | \(0.622173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 23016.4 | 1.23482 | ||||||||
\(704\) | 6259.85 | 0.335124 | ||||||||
\(705\) | 8551.58 | 0.456838 | ||||||||
\(706\) | −11511.9 | −0.613676 | ||||||||
\(707\) | 18509.2 | 0.984597 | ||||||||
\(708\) | 2569.24 | 0.136381 | ||||||||
\(709\) | −23353.6 | −1.23704 | −0.618520 | − | 0.785769i | \(-0.712268\pi\) | ||||
−0.618520 | + | 0.785769i | \(0.712268\pi\) | |||||||
\(710\) | −20671.7 | −1.09267 | ||||||||
\(711\) | −13052.9 | −0.688496 | ||||||||
\(712\) | 10626.5 | 0.559334 | ||||||||
\(713\) | −17581.5 | −0.923466 | ||||||||
\(714\) | −39952.5 | −2.09409 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2137.90 | −0.111588 | ||||||||
\(717\) | 26445.1 | 1.37742 | ||||||||
\(718\) | 11857.2 | 0.616305 | ||||||||
\(719\) | −18288.9 | −0.948624 | −0.474312 | − | 0.880357i | \(-0.657303\pi\) | ||||
−0.474312 | + | 0.880357i | \(0.657303\pi\) | |||||||
\(720\) | −7396.51 | −0.382849 | ||||||||
\(721\) | 12922.0 | 0.667463 | ||||||||
\(722\) | 1854.35 | 0.0955842 | ||||||||
\(723\) | −30690.5 | −1.57869 | ||||||||
\(724\) | −8329.11 | −0.427554 | ||||||||
\(725\) | 405.618 | 0.0207783 | ||||||||
\(726\) | 1942.60 | 0.0993066 | ||||||||
\(727\) | −18378.0 | −0.937555 | −0.468777 | − | 0.883316i | \(-0.655305\pi\) | ||||
−0.468777 | + | 0.883316i | \(0.655305\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −300.001 | −0.0152416 | ||||||||
\(730\) | −21934.8 | −1.11211 | ||||||||
\(731\) | −20711.3 | −1.04793 | ||||||||
\(732\) | −647.574 | −0.0326981 | ||||||||
\(733\) | 12956.4 | 0.652874 | 0.326437 | − | 0.945219i | \(-0.394152\pi\) | ||||
0.326437 | + | 0.945219i | \(0.394152\pi\) | |||||||
\(734\) | 6753.65 | 0.339621 | ||||||||
\(735\) | 19614.7 | 0.984355 | ||||||||
\(736\) | 7976.59 | 0.399485 | ||||||||
\(737\) | −3153.69 | −0.157622 | ||||||||
\(738\) | 2319.75 | 0.115706 | ||||||||
\(739\) | 30833.2 | 1.53480 | 0.767400 | − | 0.641169i | \(-0.221550\pi\) | ||||
0.767400 | + | 0.641169i | \(0.221550\pi\) | |||||||
\(740\) | 5355.87 | 0.266062 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19478.5 | 0.963720 | ||||||||
\(743\) | 28532.4 | 1.40882 | 0.704410 | − | 0.709793i | \(-0.251212\pi\) | ||||
0.704410 | + | 0.709793i | \(0.251212\pi\) | |||||||
\(744\) | 29194.5 | 1.43860 | ||||||||
\(745\) | 17399.5 | 0.855664 | ||||||||
\(746\) | 28026.3 | 1.37549 | ||||||||
\(747\) | 21606.0 | 1.05826 | ||||||||
\(748\) | −2068.02 | −0.101089 | ||||||||
\(749\) | −33993.1 | −1.65832 | ||||||||
\(750\) | −23190.2 | −1.12905 | ||||||||
\(751\) | 19355.4 | 0.940464 | 0.470232 | − | 0.882543i | \(-0.344170\pi\) | ||||
0.470232 | + | 0.882543i | \(0.344170\pi\) | |||||||
\(752\) | −5551.28 | −0.269195 | ||||||||
\(753\) | −7133.77 | −0.345244 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20110.3 | −0.969387 | ||||||||
\(756\) | −3622.21 | −0.174257 | ||||||||
\(757\) | −21781.8 | −1.04580 | −0.522902 | − | 0.852393i | \(-0.675151\pi\) | ||||
−0.522902 | + | 0.852393i | \(0.675151\pi\) | |||||||
\(758\) | 26454.6 | 1.26765 | ||||||||
\(759\) | 6827.61 | 0.326517 | ||||||||
\(760\) | 22938.7 | 1.09484 | ||||||||
\(761\) | 1847.78 | 0.0880182 | 0.0440091 | − | 0.999031i | \(-0.485987\pi\) | ||||
0.0440091 | + | 0.999031i | \(0.485987\pi\) | |||||||
\(762\) | −39854.2 | −1.89471 | ||||||||
\(763\) | 47926.1 | 2.27397 | ||||||||
\(764\) | −4823.30 | −0.228404 | ||||||||
\(765\) | 16252.5 | 0.768120 | ||||||||
\(766\) | −16638.5 | −0.784822 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −17689.8 | −0.831155 | ||||||||
\(769\) | −3741.48 | −0.175450 | −0.0877251 | − | 0.996145i | \(-0.527960\pi\) | ||||
−0.0877251 | + | 0.996145i | \(0.527960\pi\) | |||||||
\(770\) | −7307.42 | −0.342001 | ||||||||
\(771\) | 4352.15 | 0.203293 | ||||||||
\(772\) | 3900.76 | 0.181854 | ||||||||
\(773\) | −16469.9 | −0.766338 | −0.383169 | − | 0.923678i | \(-0.625167\pi\) | ||||
−0.383169 | + | 0.923678i | \(0.625167\pi\) | |||||||
\(774\) | −7792.93 | −0.361901 | ||||||||
\(775\) | 1705.74 | 0.0790607 | ||||||||
\(776\) | −27164.8 | −1.25665 | ||||||||
\(777\) | 42792.1 | 1.97575 | ||||||||
\(778\) | 21753.1 | 1.00243 | ||||||||
\(779\) | −5397.47 | −0.248247 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8549.11 | −0.391692 | ||||||||
\(782\) | 23548.6 | 1.07685 | ||||||||
\(783\) | 3361.69 | 0.153432 | ||||||||
\(784\) | −12733.0 | −0.580037 | ||||||||
\(785\) | −13426.6 | −0.610466 | ||||||||
\(786\) | −14690.3 | −0.666649 | ||||||||
\(787\) | 32554.4 | 1.47451 | 0.737254 | − | 0.675616i | \(-0.236122\pi\) | ||||
0.737254 | + | 0.675616i | \(0.236122\pi\) | |||||||
\(788\) | −6250.33 | −0.282562 | ||||||||
\(789\) | −45469.4 | −2.05165 | ||||||||
\(790\) | −22896.5 | −1.03117 | ||||||||
\(791\) | −2599.23 | −0.116837 | ||||||||
\(792\) | −4077.24 | −0.182928 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −9213.98 | −0.411829 | ||||||||
\(795\) | −22033.4 | −0.982949 | ||||||||
\(796\) | 227.502 | 0.0101302 | ||||||||
\(797\) | 316.849 | 0.0140820 | 0.00704101 | − | 0.999975i | \(-0.497759\pi\) | ||||
0.00704101 | + | 0.999975i | \(0.497759\pi\) | |||||||
\(798\) | 34977.2 | 1.55160 | ||||||||
\(799\) | 12198.0 | 0.540092 | ||||||||
\(800\) | −773.883 | −0.0342011 | ||||||||
\(801\) | −6591.49 | −0.290760 | ||||||||
\(802\) | 19058.5 | 0.839127 | ||||||||
\(803\) | −9071.50 | −0.398663 | ||||||||
\(804\) | 3512.62 | 0.154080 | ||||||||
\(805\) | −25683.2 | −1.12449 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3237.52 | −0.141222 | ||||||||
\(808\) | 18115.7 | 0.788746 | ||||||||
\(809\) | 17621.3 | 0.765798 | 0.382899 | − | 0.923790i | \(-0.374926\pi\) | ||||
0.382899 | + | 0.923790i | \(0.374926\pi\) | |||||||
\(810\) | −24163.8 | −1.04818 | ||||||||
\(811\) | 35740.6 | 1.54750 | 0.773751 | − | 0.633490i | \(-0.218378\pi\) | ||||
0.773751 | + | 0.633490i | \(0.218378\pi\) | |||||||
\(812\) | −2061.16 | −0.0890797 | ||||||||
\(813\) | 11611.0 | 0.500881 | ||||||||
\(814\) | −7176.28 | −0.309003 | ||||||||
\(815\) | 30861.8 | 1.32643 | ||||||||
\(816\) | −29337.0 | −1.25858 | ||||||||
\(817\) | 18132.1 | 0.776454 | ||||||||
\(818\) | −16756.8 | −0.716246 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1255.98 | −0.0534886 | ||||||||
\(821\) | −4653.75 | −0.197828 | −0.0989142 | − | 0.995096i | \(-0.531537\pi\) | ||||
−0.0989142 | + | 0.995096i | \(0.531537\pi\) | |||||||
\(822\) | −47145.4 | −2.00047 | ||||||||
\(823\) | 34143.4 | 1.44613 | 0.723065 | − | 0.690780i | \(-0.242733\pi\) | ||||
0.723065 | + | 0.690780i | \(0.242733\pi\) | |||||||
\(824\) | 12647.3 | 0.534695 | ||||||||
\(825\) | −662.410 | −0.0279541 | ||||||||
\(826\) | 12949.6 | 0.545488 | ||||||||
\(827\) | −10628.8 | −0.446914 | −0.223457 | − | 0.974714i | \(-0.571734\pi\) | ||||
−0.223457 | + | 0.974714i | \(0.571734\pi\) | |||||||
\(828\) | −2734.85 | −0.114786 | ||||||||
\(829\) | 17652.2 | 0.739549 | 0.369775 | − | 0.929122i | \(-0.379435\pi\) | ||||
0.369775 | + | 0.929122i | \(0.379435\pi\) | |||||||
\(830\) | 37900.0 | 1.58497 | ||||||||
\(831\) | 18704.8 | 0.780823 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27978.5 | 1.16374 | ||||||||
\(834\) | 46640.1 | 1.93647 | ||||||||
\(835\) | 17876.6 | 0.740894 | ||||||||
\(836\) | 1810.49 | 0.0749010 | ||||||||
\(837\) | 14136.9 | 0.583802 | ||||||||
\(838\) | 37590.5 | 1.54957 | ||||||||
\(839\) | −31051.9 | −1.27775 | −0.638874 | − | 0.769312i | \(-0.720599\pi\) | ||||
−0.638874 | + | 0.769312i | \(0.720599\pi\) | |||||||
\(840\) | 42647.7 | 1.75177 | ||||||||
\(841\) | −22476.1 | −0.921566 | ||||||||
\(842\) | 1248.56 | 0.0511023 | ||||||||
\(843\) | 39793.9 | 1.62583 | ||||||||
\(844\) | −9143.05 | −0.372887 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4589.66 | 0.186520 | ||||||||
\(847\) | −3022.10 | −0.122598 | ||||||||
\(848\) | 14303.0 | 0.579208 | ||||||||
\(849\) | 45708.2 | 1.84770 | ||||||||
\(850\) | −2284.67 | −0.0921923 | ||||||||
\(851\) | −25222.3 | −1.01599 | ||||||||
\(852\) | 9522.13 | 0.382891 | ||||||||
\(853\) | 27998.0 | 1.12384 | 0.561918 | − | 0.827193i | \(-0.310064\pi\) | ||||
0.561918 | + | 0.827193i | \(0.310064\pi\) | |||||||
\(854\) | −3263.92 | −0.130783 | ||||||||
\(855\) | −14228.6 | −0.569133 | ||||||||
\(856\) | −33270.3 | −1.32845 | ||||||||
\(857\) | −39389.9 | −1.57005 | −0.785025 | − | 0.619464i | \(-0.787350\pi\) | ||||
−0.785025 | + | 0.619464i | \(0.787350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32534.3 | 1.29226 | 0.646132 | − | 0.763226i | \(-0.276385\pi\) | ||||
0.646132 | + | 0.763226i | \(0.276385\pi\) | |||||||
\(860\) | 4219.31 | 0.167299 | ||||||||
\(861\) | −10035.0 | −0.397202 | ||||||||
\(862\) | −16409.1 | −0.648371 | ||||||||
\(863\) | 23046.9 | 0.909067 | 0.454533 | − | 0.890730i | \(-0.349806\pi\) | ||||
0.454533 | + | 0.890730i | \(0.349806\pi\) | |||||||
\(864\) | −6413.81 | −0.252549 | ||||||||
\(865\) | 8976.77 | 0.352855 | ||||||||
\(866\) | −10923.5 | −0.428633 | ||||||||
\(867\) | 32561.4 | 1.27548 | ||||||||
\(868\) | −8667.80 | −0.338945 | ||||||||
\(869\) | −9469.24 | −0.369646 | ||||||||
\(870\) | −7553.73 | −0.294362 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 46907.1 | 1.82165 | ||||||||
\(873\) | 16850.0 | 0.653249 | ||||||||
\(874\) | −20616.1 | −0.797882 | ||||||||
\(875\) | 36077.1 | 1.39386 | ||||||||
\(876\) | 10104.0 | 0.389705 | ||||||||
\(877\) | −13302.0 | −0.512176 | −0.256088 | − | 0.966654i | \(-0.582434\pi\) | ||||
−0.256088 | + | 0.966654i | \(0.582434\pi\) | |||||||
\(878\) | 20095.6 | 0.772429 | ||||||||
\(879\) | −34243.7 | −1.31400 | ||||||||
\(880\) | −5365.82 | −0.205547 | ||||||||
\(881\) | −26136.9 | −0.999516 | −0.499758 | − | 0.866165i | \(-0.666578\pi\) | ||||
−0.499758 | + | 0.866165i | \(0.666578\pi\) | |||||||
\(882\) | 10527.3 | 0.401897 | ||||||||
\(883\) | 9479.63 | 0.361285 | 0.180643 | − | 0.983549i | \(-0.442182\pi\) | ||||
0.180643 | + | 0.983549i | \(0.442182\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14648.1 | −0.556372 | ||||||||
\(886\) | −39726.8 | −1.50637 | ||||||||
\(887\) | −11961.4 | −0.452790 | −0.226395 | − | 0.974036i | \(-0.572694\pi\) | ||||
−0.226395 | + | 0.974036i | \(0.572694\pi\) | |||||||
\(888\) | 41882.3 | 1.58275 | ||||||||
\(889\) | 62001.3 | 2.33910 | ||||||||
\(890\) | −11562.4 | −0.435475 | ||||||||
\(891\) | −9993.33 | −0.375745 | ||||||||
\(892\) | −3176.71 | −0.119242 | ||||||||
\(893\) | −10679.0 | −0.400177 | ||||||||
\(894\) | 25966.9 | 0.971434 | ||||||||
\(895\) | 12188.8 | 0.455227 | ||||||||
\(896\) | −18468.8 | −0.688615 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −15653.1 | −0.581684 | ||||||||
\(899\) | 8044.39 | 0.298438 | ||||||||
\(900\) | 265.334 | 0.00982717 | ||||||||
\(901\) | −31428.5 | −1.16208 | ||||||||
\(902\) | 1682.87 | 0.0621214 | ||||||||
\(903\) | 33711.2 | 1.24235 | ||||||||
\(904\) | −2543.96 | −0.0935962 | ||||||||
\(905\) | 47486.9 | 1.74422 | ||||||||
\(906\) | −30012.3 | −1.10054 | ||||||||
\(907\) | −17900.5 | −0.655321 | −0.327661 | − | 0.944795i | \(-0.606260\pi\) | ||||
−0.327661 | + | 0.944795i | \(0.606260\pi\) | |||||||
\(908\) | 2975.87 | 0.108764 | ||||||||
\(909\) | −11236.9 | −0.410017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −818.497 | −0.0297673 | −0.0148836 | − | 0.999889i | \(-0.504738\pi\) | ||||
−0.0148836 | + | 0.999889i | \(0.504738\pi\) | |||||||
\(912\) | 25683.7 | 0.932534 | ||||||||
\(913\) | 15674.1 | 0.568169 | ||||||||
\(914\) | −19240.0 | −0.696282 | ||||||||
\(915\) | 3692.02 | 0.133393 | ||||||||
\(916\) | 4468.40 | 0.161179 | ||||||||
\(917\) | 22853.7 | 0.823006 | ||||||||
\(918\) | −18934.9 | −0.680769 | ||||||||
\(919\) | 43051.4 | 1.54531 | 0.772653 | − | 0.634829i | \(-0.218929\pi\) | ||||
0.772653 | + | 0.634829i | \(0.218929\pi\) | |||||||
\(920\) | −25137.2 | −0.900813 | ||||||||
\(921\) | −1400.70 | −0.0501137 | ||||||||
\(922\) | 41221.8 | 1.47242 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3366.06 | 0.119843 | ||||||||
\(925\) | 2447.05 | 0.0869822 | ||||||||
\(926\) | −710.796 | −0.0252249 | ||||||||
\(927\) | −7844.94 | −0.277952 | ||||||||
\(928\) | −3649.68 | −0.129102 | ||||||||
\(929\) | 42221.7 | 1.49112 | 0.745559 | − | 0.666439i | \(-0.232182\pi\) | ||||
0.745559 | + | 0.666439i | \(0.232182\pi\) | |||||||
\(930\) | −31765.7 | −1.12004 | ||||||||
\(931\) | −24494.3 | −0.862265 | ||||||||
\(932\) | −7618.14 | −0.267747 | ||||||||
\(933\) | 47497.2 | 1.66665 | ||||||||
\(934\) | −8282.46 | −0.290161 | ||||||||
\(935\) | 11790.5 | 0.412395 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1130.59 | 0.0394181 | 0.0197091 | − | 0.999806i | \(-0.493726\pi\) | ||||
0.0197091 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(938\) | 17704.4 | 0.616279 | ||||||||
\(939\) | −2731.89 | −0.0949434 | ||||||||
\(940\) | −2484.97 | −0.0862243 | ||||||||
\(941\) | 17108.5 | 0.592692 | 0.296346 | − | 0.955081i | \(-0.404232\pi\) | ||||
0.296346 | + | 0.955081i | \(0.404232\pi\) | |||||||
\(942\) | −20037.7 | −0.693061 | ||||||||
\(943\) | 5914.76 | 0.204253 | ||||||||
\(944\) | 9508.83 | 0.327846 | ||||||||
\(945\) | 20651.3 | 0.710887 | ||||||||
\(946\) | −5653.40 | −0.194300 | ||||||||
\(947\) | 2802.40 | 0.0961624 | 0.0480812 | − | 0.998843i | \(-0.484689\pi\) | ||||
0.0480812 | + | 0.998843i | \(0.484689\pi\) | |||||||
\(948\) | 10547.0 | 0.361340 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2000.16 | 0.0683091 | ||||||||
\(951\) | −49656.5 | −1.69319 | ||||||||
\(952\) | 60832.6 | 2.07101 | ||||||||
\(953\) | 2705.21 | 0.0919521 | 0.0459760 | − | 0.998943i | \(-0.485360\pi\) | ||||
0.0459760 | + | 0.998943i | \(0.485360\pi\) | |||||||
\(954\) | −11825.4 | −0.401323 | ||||||||
\(955\) | 27499.2 | 0.931782 | ||||||||
\(956\) | −7684.59 | −0.259976 | ||||||||
\(957\) | −3123.97 | −0.105521 | ||||||||
\(958\) | 20268.7 | 0.683560 | ||||||||
\(959\) | 73344.1 | 2.46966 | ||||||||
\(960\) | 39751.4 | 1.33643 | ||||||||
\(961\) | 4038.04 | 0.135546 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20637.2 | 0.690575 | ||||||||
\(964\) | 8918.24 | 0.297964 | ||||||||
\(965\) | −22239.5 | −0.741879 | ||||||||
\(966\) | −38329.4 | −1.27663 | ||||||||
\(967\) | −59777.8 | −1.98792 | −0.993962 | − | 0.109723i | \(-0.965004\pi\) | ||||
−0.993962 | + | 0.109723i | \(0.965004\pi\) | |||||||
\(968\) | −2957.85 | −0.0982116 | ||||||||
\(969\) | −56435.4 | −1.87097 | ||||||||
\(970\) | 29557.3 | 0.978378 | ||||||||
\(971\) | 25271.6 | 0.835224 | 0.417612 | − | 0.908625i | \(-0.362867\pi\) | ||||
0.417612 | + | 0.908625i | \(0.362867\pi\) | |||||||
\(972\) | 7214.99 | 0.238087 | ||||||||
\(973\) | −72558.0 | −2.39065 | ||||||||
\(974\) | 26168.3 | 0.860870 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2396.69 | −0.0786025 | ||||||||
\(977\) | 50763.1 | 1.66229 | 0.831144 | − | 0.556057i | \(-0.187686\pi\) | ||||
0.831144 | + | 0.556057i | \(0.187686\pi\) | |||||||
\(978\) | 46057.8 | 1.50590 | ||||||||
\(979\) | −4781.82 | −0.156106 | ||||||||
\(980\) | −5699.77 | −0.185788 | ||||||||
\(981\) | −29095.9 | −0.946952 | ||||||||
\(982\) | 17366.6 | 0.564349 | ||||||||
\(983\) | −25390.8 | −0.823847 | −0.411924 | − | 0.911218i | \(-0.635143\pi\) | ||||
−0.411924 | + | 0.911218i | \(0.635143\pi\) | |||||||
\(984\) | −9821.61 | −0.318192 | ||||||||
\(985\) | 35635.1 | 1.15272 | ||||||||
\(986\) | −10774.6 | −0.348007 | ||||||||
\(987\) | −19854.3 | −0.640293 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −19869.9 | −0.638853 | ||||||||
\(990\) | 4436.33 | 0.142420 | ||||||||
\(991\) | 15905.8 | 0.509853 | 0.254927 | − | 0.966960i | \(-0.417949\pi\) | ||||
0.254927 | + | 0.966960i | \(0.417949\pi\) | |||||||
\(992\) | −15348.0 | −0.491229 | ||||||||
\(993\) | −60155.0 | −1.92242 | ||||||||
\(994\) | 47993.7 | 1.53146 | ||||||||
\(995\) | −1297.06 | −0.0413263 | ||||||||
\(996\) | −17458.1 | −0.555403 | ||||||||
\(997\) | 26353.4 | 0.837133 | 0.418567 | − | 0.908186i | \(-0.362533\pi\) | ||||
0.418567 | + | 0.908186i | \(0.362533\pi\) | |||||||
\(998\) | −36540.9 | −1.15900 | ||||||||
\(999\) | 20280.7 | 0.642296 |
(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 | 1859.4.a.f.1.12 | 17 | ||
13.4 | even | 6 | 143.4.e.a.133.12 | yes | 34 | ||
13.10 | even | 6 | 143.4.e.a.100.12 | ✓ | 34 | ||
13.12 | even | 2 | 1859.4.a.i.1.6 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.e.a.100.12 | ✓ | 34 | 13.10 | even | 6 | ||
143.4.e.a.133.12 | yes | 34 | 13.4 | even | 6 | ||
1859.4.a.f.1.12 | 17 | 1.1 | even | 1 | trivial | ||
1859.4.a.i.1.6 | 17 | 13.12 | even | 2 |