Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 570x^{3} - 189x^{2} + 63838x + 254320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-8.37318\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 6.37318 | 0.570035 | 0.285017 | − | 0.958522i | \(-0.408001\pi\) | ||||
0.285017 | + | 0.958522i | \(0.408001\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 12.7464 | 0.403076 | ||||||||
\(11\) | 28.9207 | 0.792720 | 0.396360 | − | 0.918095i | \(-0.370273\pi\) | ||||
0.396360 | + | 0.918095i | \(0.370273\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −16.9261 | −0.361113 | −0.180557 | − | 0.983565i | \(-0.557790\pi\) | ||||
−0.180557 | + | 0.983565i | \(0.557790\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 19.1196 | 0.329110 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 82.8604 | 1.18215 | 0.591077 | − | 0.806615i | \(-0.298703\pi\) | ||||
0.591077 | + | 0.806615i | \(0.298703\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 120.424 | 1.45406 | 0.727032 | − | 0.686603i | \(-0.240899\pi\) | ||||
0.727032 | + | 0.686603i | \(0.240899\pi\) | |||||||
\(20\) | 25.4927 | 0.285017 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 57.8414 | 0.560538 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 24.0000 | 0.204124 | ||||||||
\(25\) | −84.3825 | −0.675060 | ||||||||
\(26\) | −33.8523 | −0.255345 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | −97.6183 | −0.625078 | −0.312539 | − | 0.949905i | \(-0.601180\pi\) | ||||
−0.312539 | + | 0.949905i | \(0.601180\pi\) | |||||||
\(30\) | 38.2391 | 0.232716 | ||||||||
\(31\) | −205.858 | −1.19268 | −0.596342 | − | 0.802731i | \(-0.703380\pi\) | ||||
−0.596342 | + | 0.802731i | \(0.703380\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 86.7622 | 0.457677 | ||||||||
\(34\) | 165.721 | 0.835909 | ||||||||
\(35\) | −44.6123 | −0.215453 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 53.2574 | 0.236634 | 0.118317 | − | 0.992976i | \(-0.462250\pi\) | ||||
0.118317 | + | 0.992976i | \(0.462250\pi\) | |||||||
\(38\) | 240.849 | 1.02818 | ||||||||
\(39\) | −50.7784 | −0.208489 | ||||||||
\(40\) | 50.9855 | 0.201538 | ||||||||
\(41\) | 295.035 | 1.12382 | 0.561910 | − | 0.827198i | \(-0.310067\pi\) | ||||
0.561910 | + | 0.827198i | \(0.310067\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | 247.467 | 0.877637 | 0.438819 | − | 0.898576i | \(-0.355397\pi\) | ||||
0.438819 | + | 0.898576i | \(0.355397\pi\) | |||||||
\(44\) | 115.683 | 0.396360 | ||||||||
\(45\) | 57.3587 | 0.190012 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 281.174 | 0.872628 | 0.436314 | − | 0.899794i | \(-0.356284\pi\) | ||||
0.436314 | + | 0.899794i | \(0.356284\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −168.765 | −0.477340 | ||||||||
\(51\) | 248.581 | 0.682517 | ||||||||
\(52\) | −67.7046 | −0.180557 | ||||||||
\(53\) | 648.786 | 1.68147 | 0.840733 | − | 0.541451i | \(-0.182125\pi\) | ||||
0.840733 | + | 0.541451i | \(0.182125\pi\) | |||||||
\(54\) | 54.0000 | 0.136083 | ||||||||
\(55\) | 184.317 | 0.451878 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 361.273 | 0.839505 | ||||||||
\(58\) | −195.237 | −0.441997 | ||||||||
\(59\) | 46.1774 | 0.101895 | 0.0509473 | − | 0.998701i | \(-0.483776\pi\) | ||||
0.0509473 | + | 0.998701i | \(0.483776\pi\) | |||||||
\(60\) | 76.4782 | 0.164555 | ||||||||
\(61\) | −175.417 | −0.368195 | −0.184097 | − | 0.982908i | \(-0.558936\pi\) | ||||
−0.184097 | + | 0.982908i | \(0.558936\pi\) | |||||||
\(62\) | −411.716 | −0.843354 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −107.873 | −0.205847 | ||||||||
\(66\) | 173.524 | 0.323627 | ||||||||
\(67\) | −141.982 | −0.258894 | −0.129447 | − | 0.991586i | \(-0.541320\pi\) | ||||
−0.129447 | + | 0.991586i | \(0.541320\pi\) | |||||||
\(68\) | 331.442 | 0.591077 | ||||||||
\(69\) | −69.0000 | −0.120386 | ||||||||
\(70\) | −89.2246 | −0.152348 | ||||||||
\(71\) | 125.012 | 0.208961 | 0.104480 | − | 0.994527i | \(-0.466682\pi\) | ||||
0.104480 | + | 0.994527i | \(0.466682\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 66.9851 | 0.107397 | 0.0536987 | − | 0.998557i | \(-0.482899\pi\) | ||||
0.0536987 | + | 0.998557i | \(0.482899\pi\) | |||||||
\(74\) | 106.515 | 0.167326 | ||||||||
\(75\) | −253.148 | −0.389746 | ||||||||
\(76\) | 481.697 | 0.727032 | ||||||||
\(77\) | −202.445 | −0.299620 | ||||||||
\(78\) | −101.557 | −0.147424 | ||||||||
\(79\) | −1263.29 | −1.79913 | −0.899564 | − | 0.436789i | \(-0.856116\pi\) | ||||
−0.899564 | + | 0.436789i | \(0.856116\pi\) | |||||||
\(80\) | 101.971 | 0.142509 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 590.069 | 0.794661 | ||||||||
\(83\) | 350.820 | 0.463945 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | 528.085 | 0.673869 | ||||||||
\(86\) | 494.935 | 0.620583 | ||||||||
\(87\) | −292.855 | −0.360889 | ||||||||
\(88\) | 231.366 | 0.280269 | ||||||||
\(89\) | −50.5168 | −0.0601660 | −0.0300830 | − | 0.999547i | \(-0.509577\pi\) | ||||
−0.0300830 | + | 0.999547i | \(0.509577\pi\) | |||||||
\(90\) | 114.717 | 0.134359 | ||||||||
\(91\) | 118.483 | 0.136488 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | −617.574 | −0.688596 | ||||||||
\(94\) | 562.349 | 0.617041 | ||||||||
\(95\) | 767.486 | 0.828868 | ||||||||
\(96\) | 96.0000 | 0.102062 | ||||||||
\(97\) | 1181.85 | 1.23710 | 0.618548 | − | 0.785747i | \(-0.287721\pi\) | ||||
0.618548 | + | 0.785747i | \(0.287721\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 260.286 | 0.264240 | ||||||||
\(100\) | −337.530 | −0.337530 | ||||||||
\(101\) | −771.445 | −0.760017 | −0.380008 | − | 0.924983i | \(-0.624079\pi\) | ||||
−0.380008 | + | 0.924983i | \(0.624079\pi\) | |||||||
\(102\) | 497.163 | 0.482612 | ||||||||
\(103\) | −697.034 | −0.666804 | −0.333402 | − | 0.942785i | \(-0.608197\pi\) | ||||
−0.333402 | + | 0.942785i | \(0.608197\pi\) | |||||||
\(104\) | −135.409 | −0.127673 | ||||||||
\(105\) | −133.837 | −0.124392 | ||||||||
\(106\) | 1297.57 | 1.18898 | ||||||||
\(107\) | 1452.92 | 1.31271 | 0.656353 | − | 0.754454i | \(-0.272098\pi\) | ||||
0.656353 | + | 0.754454i | \(0.272098\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 820.745 | 0.721221 | 0.360611 | − | 0.932716i | \(-0.382568\pi\) | ||||
0.360611 | + | 0.932716i | \(0.382568\pi\) | |||||||
\(110\) | 368.634 | 0.319526 | ||||||||
\(111\) | 159.772 | 0.136621 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | 69.2069 | 0.0576145 | 0.0288072 | − | 0.999585i | \(-0.490829\pi\) | ||||
0.0288072 | + | 0.999585i | \(0.490829\pi\) | |||||||
\(114\) | 722.546 | 0.593620 | ||||||||
\(115\) | −146.583 | −0.118860 | ||||||||
\(116\) | −390.473 | −0.312539 | ||||||||
\(117\) | −152.335 | −0.120371 | ||||||||
\(118\) | 92.3548 | 0.0720504 | ||||||||
\(119\) | −580.023 | −0.446812 | ||||||||
\(120\) | 152.956 | 0.116358 | ||||||||
\(121\) | −494.592 | −0.371594 | ||||||||
\(122\) | −350.834 | −0.260353 | ||||||||
\(123\) | 885.104 | 0.648838 | ||||||||
\(124\) | −823.432 | −0.596342 | ||||||||
\(125\) | −1334.43 | −0.954843 | ||||||||
\(126\) | −126.000 | −0.0890871 | ||||||||
\(127\) | 601.354 | 0.420170 | 0.210085 | − | 0.977683i | \(-0.432626\pi\) | ||||
0.210085 | + | 0.977683i | \(0.432626\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 742.402 | 0.506704 | ||||||||
\(130\) | −215.747 | −0.145556 | ||||||||
\(131\) | −629.859 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(132\) | 347.049 | 0.228839 | ||||||||
\(133\) | −842.970 | −0.549585 | ||||||||
\(134\) | −283.964 | −0.183065 | ||||||||
\(135\) | 172.076 | 0.109703 | ||||||||
\(136\) | 662.883 | 0.417954 | ||||||||
\(137\) | −204.273 | −0.127388 | −0.0636941 | − | 0.997969i | \(-0.520288\pi\) | ||||
−0.0636941 | + | 0.997969i | \(0.520288\pi\) | |||||||
\(138\) | −138.000 | −0.0851257 | ||||||||
\(139\) | −1162.94 | −0.709636 | −0.354818 | − | 0.934935i | \(-0.615457\pi\) | ||||
−0.354818 | + | 0.934935i | \(0.615457\pi\) | |||||||
\(140\) | −178.449 | −0.107726 | ||||||||
\(141\) | 843.523 | 0.503812 | ||||||||
\(142\) | 250.024 | 0.147758 | ||||||||
\(143\) | −489.516 | −0.286262 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −622.140 | −0.356316 | ||||||||
\(146\) | 133.970 | 0.0759415 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | 213.030 | 0.118317 | ||||||||
\(149\) | 257.111 | 0.141365 | 0.0706824 | − | 0.997499i | \(-0.477482\pi\) | ||||
0.0706824 | + | 0.997499i | \(0.477482\pi\) | |||||||
\(150\) | −506.295 | −0.275592 | ||||||||
\(151\) | −2140.16 | −1.15340 | −0.576700 | − | 0.816956i | \(-0.695660\pi\) | ||||
−0.576700 | + | 0.816956i | \(0.695660\pi\) | |||||||
\(152\) | 963.395 | 0.514090 | ||||||||
\(153\) | 745.744 | 0.394051 | ||||||||
\(154\) | −404.890 | −0.211863 | ||||||||
\(155\) | −1311.97 | −0.679871 | ||||||||
\(156\) | −203.114 | −0.104244 | ||||||||
\(157\) | 1670.08 | 0.848961 | 0.424481 | − | 0.905437i | \(-0.360457\pi\) | ||||
0.424481 | + | 0.905437i | \(0.360457\pi\) | |||||||
\(158\) | −2526.58 | −1.27218 | ||||||||
\(159\) | 1946.36 | 0.970794 | ||||||||
\(160\) | 203.942 | 0.100769 | ||||||||
\(161\) | 161.000 | 0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1853.08 | 0.890454 | 0.445227 | − | 0.895418i | \(-0.353123\pi\) | ||||
0.445227 | + | 0.895418i | \(0.353123\pi\) | |||||||
\(164\) | 1180.14 | 0.561910 | ||||||||
\(165\) | 552.951 | 0.260892 | ||||||||
\(166\) | 701.639 | 0.328059 | ||||||||
\(167\) | 198.010 | 0.0917513 | 0.0458756 | − | 0.998947i | \(-0.485392\pi\) | ||||
0.0458756 | + | 0.998947i | \(0.485392\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | −1910.51 | −0.869597 | ||||||||
\(170\) | 1056.17 | 0.476497 | ||||||||
\(171\) | 1083.82 | 0.484688 | ||||||||
\(172\) | 989.869 | 0.438819 | ||||||||
\(173\) | −3012.81 | −1.32405 | −0.662023 | − | 0.749484i | \(-0.730302\pi\) | ||||
−0.662023 | + | 0.749484i | \(0.730302\pi\) | |||||||
\(174\) | −585.710 | −0.255187 | ||||||||
\(175\) | 590.678 | 0.255149 | ||||||||
\(176\) | 462.732 | 0.198180 | ||||||||
\(177\) | 138.532 | 0.0588289 | ||||||||
\(178\) | −101.034 | −0.0425438 | ||||||||
\(179\) | 3551.92 | 1.48314 | 0.741572 | − | 0.670874i | \(-0.234081\pi\) | ||||
0.741572 | + | 0.670874i | \(0.234081\pi\) | |||||||
\(180\) | 229.435 | 0.0950058 | ||||||||
\(181\) | −134.196 | −0.0551091 | −0.0275545 | − | 0.999620i | \(-0.508772\pi\) | ||||
−0.0275545 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(182\) | 236.966 | 0.0965115 | ||||||||
\(183\) | −526.252 | −0.212577 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 339.419 | 0.134890 | ||||||||
\(186\) | −1235.15 | −0.486911 | ||||||||
\(187\) | 2396.38 | 0.937117 | ||||||||
\(188\) | 1124.70 | 0.436314 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 1534.97 | 0.586098 | ||||||||
\(191\) | −1424.26 | −0.539561 | −0.269781 | − | 0.962922i | \(-0.586951\pi\) | ||||
−0.269781 | + | 0.962922i | \(0.586951\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −1334.01 | −0.497534 | −0.248767 | − | 0.968563i | \(-0.580025\pi\) | ||||
−0.248767 | + | 0.968563i | \(0.580025\pi\) | |||||||
\(194\) | 2363.69 | 0.874759 | ||||||||
\(195\) | −323.620 | −0.118846 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −2132.06 | −0.771082 | −0.385541 | − | 0.922691i | \(-0.625985\pi\) | ||||
−0.385541 | + | 0.922691i | \(0.625985\pi\) | |||||||
\(198\) | 520.573 | 0.186846 | ||||||||
\(199\) | −0.162290 | −5.78111e−5 0 | −2.89056e−5 | − | 1.00000i | \(-0.500009\pi\) | ||||
−2.89056e−5 | 1.00000i | \(0.500009\pi\) | ||||||||
\(200\) | −675.060 | −0.238670 | ||||||||
\(201\) | −425.946 | −0.149472 | ||||||||
\(202\) | −1542.89 | −0.537413 | ||||||||
\(203\) | 683.328 | 0.236257 | ||||||||
\(204\) | 994.325 | 0.341258 | ||||||||
\(205\) | 1880.31 | 0.640617 | ||||||||
\(206\) | −1394.07 | −0.471502 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | −270.818 | −0.0902783 | ||||||||
\(209\) | 3482.76 | 1.15267 | ||||||||
\(210\) | −267.674 | −0.0879583 | ||||||||
\(211\) | 2208.49 | 0.720562 | 0.360281 | − | 0.932844i | \(-0.382681\pi\) | ||||
0.360281 | + | 0.932844i | \(0.382681\pi\) | |||||||
\(212\) | 2595.15 | 0.840733 | ||||||||
\(213\) | 375.036 | 0.120644 | ||||||||
\(214\) | 2905.85 | 0.928223 | ||||||||
\(215\) | 1577.15 | 0.500284 | ||||||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 1441.01 | 0.450792 | ||||||||
\(218\) | 1641.49 | 0.509980 | ||||||||
\(219\) | 200.955 | 0.0620060 | ||||||||
\(220\) | 737.268 | 0.225939 | ||||||||
\(221\) | −1402.51 | −0.426891 | ||||||||
\(222\) | 319.545 | 0.0966055 | ||||||||
\(223\) | 480.772 | 0.144372 | 0.0721858 | − | 0.997391i | \(-0.477003\pi\) | ||||
0.0721858 | + | 0.997391i | \(0.477003\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −759.443 | −0.225020 | ||||||||
\(226\) | 138.414 | 0.0407396 | ||||||||
\(227\) | 182.925 | 0.0534853 | 0.0267427 | − | 0.999642i | \(-0.491487\pi\) | ||||
0.0267427 | + | 0.999642i | \(0.491487\pi\) | |||||||
\(228\) | 1445.09 | 0.419752 | ||||||||
\(229\) | −4460.78 | −1.28723 | −0.643617 | − | 0.765348i | \(-0.722567\pi\) | ||||
−0.643617 | + | 0.765348i | \(0.722567\pi\) | |||||||
\(230\) | −293.166 | −0.0840471 | ||||||||
\(231\) | −607.335 | −0.172986 | ||||||||
\(232\) | −780.947 | −0.220999 | ||||||||
\(233\) | −872.569 | −0.245339 | −0.122669 | − | 0.992448i | \(-0.539145\pi\) | ||||
−0.122669 | + | 0.992448i | \(0.539145\pi\) | |||||||
\(234\) | −304.671 | −0.0851152 | ||||||||
\(235\) | 1791.98 | 0.497428 | ||||||||
\(236\) | 184.710 | 0.0509473 | ||||||||
\(237\) | −3789.87 | −1.03873 | ||||||||
\(238\) | −1160.05 | −0.315944 | ||||||||
\(239\) | −390.246 | −0.105619 | −0.0528094 | − | 0.998605i | \(-0.516818\pi\) | ||||
−0.0528094 | + | 0.998605i | \(0.516818\pi\) | |||||||
\(240\) | 305.913 | 0.0822775 | ||||||||
\(241\) | −2464.82 | −0.658809 | −0.329404 | − | 0.944189i | \(-0.606848\pi\) | ||||
−0.329404 | + | 0.944189i | \(0.606848\pi\) | |||||||
\(242\) | −989.184 | −0.262757 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −701.669 | −0.184097 | ||||||||
\(245\) | 312.286 | 0.0814336 | ||||||||
\(246\) | 1770.21 | 0.458798 | ||||||||
\(247\) | −2038.32 | −0.525082 | ||||||||
\(248\) | −1646.86 | −0.421677 | ||||||||
\(249\) | 1052.46 | 0.267859 | ||||||||
\(250\) | −2668.87 | −0.675176 | ||||||||
\(251\) | −2362.35 | −0.594065 | −0.297033 | − | 0.954867i | \(-0.595997\pi\) | ||||
−0.297033 | + | 0.954867i | \(0.595997\pi\) | |||||||
\(252\) | −252.000 | −0.0629941 | ||||||||
\(253\) | −665.177 | −0.165294 | ||||||||
\(254\) | 1202.71 | 0.297105 | ||||||||
\(255\) | 1584.25 | 0.389058 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −483.197 | −0.117280 | −0.0586400 | − | 0.998279i | \(-0.518676\pi\) | ||||
−0.0586400 | + | 0.998279i | \(0.518676\pi\) | |||||||
\(258\) | 1484.80 | 0.358294 | ||||||||
\(259\) | −372.802 | −0.0894394 | ||||||||
\(260\) | −431.494 | −0.102924 | ||||||||
\(261\) | −878.565 | −0.208359 | ||||||||
\(262\) | −1259.72 | −0.297044 | ||||||||
\(263\) | −8108.56 | −1.90112 | −0.950561 | − | 0.310536i | \(-0.899491\pi\) | ||||
−0.950561 | + | 0.310536i | \(0.899491\pi\) | |||||||
\(264\) | 694.097 | 0.161813 | ||||||||
\(265\) | 4134.83 | 0.958494 | ||||||||
\(266\) | −1685.94 | −0.388615 | ||||||||
\(267\) | −151.551 | −0.0347369 | ||||||||
\(268\) | −567.928 | −0.129447 | ||||||||
\(269\) | 387.516 | 0.0878338 | 0.0439169 | − | 0.999035i | \(-0.486016\pi\) | ||||
0.0439169 | + | 0.999035i | \(0.486016\pi\) | |||||||
\(270\) | 344.152 | 0.0775719 | ||||||||
\(271\) | 2754.53 | 0.617439 | 0.308720 | − | 0.951153i | \(-0.400100\pi\) | ||||
0.308720 | + | 0.951153i | \(0.400100\pi\) | |||||||
\(272\) | 1325.77 | 0.295538 | ||||||||
\(273\) | 355.449 | 0.0788013 | ||||||||
\(274\) | −408.545 | −0.0900771 | ||||||||
\(275\) | −2440.40 | −0.535134 | ||||||||
\(276\) | −276.000 | −0.0601929 | ||||||||
\(277\) | 556.992 | 0.120817 | 0.0604087 | − | 0.998174i | \(-0.480760\pi\) | ||||
0.0604087 | + | 0.998174i | \(0.480760\pi\) | |||||||
\(278\) | −2325.88 | −0.501789 | ||||||||
\(279\) | −1852.72 | −0.397561 | ||||||||
\(280\) | −356.898 | −0.0761741 | ||||||||
\(281\) | −1490.30 | −0.316385 | −0.158192 | − | 0.987408i | \(-0.550567\pi\) | ||||
−0.158192 | + | 0.987408i | \(0.550567\pi\) | |||||||
\(282\) | 1687.05 | 0.356249 | ||||||||
\(283\) | −4110.93 | −0.863496 | −0.431748 | − | 0.901994i | \(-0.642103\pi\) | ||||
−0.431748 | + | 0.901994i | \(0.642103\pi\) | |||||||
\(284\) | 500.049 | 0.104480 | ||||||||
\(285\) | 2302.46 | 0.478547 | ||||||||
\(286\) | −979.033 | −0.202418 | ||||||||
\(287\) | −2065.24 | −0.424764 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 1952.85 | 0.397487 | ||||||||
\(290\) | −1244.28 | −0.251954 | ||||||||
\(291\) | 3545.54 | 0.714238 | ||||||||
\(292\) | 267.941 | 0.0536987 | ||||||||
\(293\) | −311.055 | −0.0620206 | −0.0310103 | − | 0.999519i | \(-0.509872\pi\) | ||||
−0.0310103 | + | 0.999519i | \(0.509872\pi\) | |||||||
\(294\) | 294.000 | 0.0583212 | ||||||||
\(295\) | 294.297 | 0.0580835 | ||||||||
\(296\) | 426.060 | 0.0836629 | ||||||||
\(297\) | 780.859 | 0.152559 | ||||||||
\(298\) | 514.222 | 0.0999600 | ||||||||
\(299\) | 389.301 | 0.0752973 | ||||||||
\(300\) | −1012.59 | −0.194873 | ||||||||
\(301\) | −1732.27 | −0.331716 | ||||||||
\(302\) | −4280.31 | −0.815577 | ||||||||
\(303\) | −2314.34 | −0.438796 | ||||||||
\(304\) | 1926.79 | 0.363516 | ||||||||
\(305\) | −1117.97 | −0.209884 | ||||||||
\(306\) | 1491.49 | 0.278636 | ||||||||
\(307\) | −2619.45 | −0.486970 | −0.243485 | − | 0.969905i | \(-0.578291\pi\) | ||||
−0.243485 | + | 0.969905i | \(0.578291\pi\) | |||||||
\(308\) | −809.780 | −0.149810 | ||||||||
\(309\) | −2091.10 | −0.384980 | ||||||||
\(310\) | −2623.94 | −0.480741 | ||||||||
\(311\) | −3302.48 | −0.602142 | −0.301071 | − | 0.953602i | \(-0.597344\pi\) | ||||
−0.301071 | + | 0.953602i | \(0.597344\pi\) | |||||||
\(312\) | −406.228 | −0.0737119 | ||||||||
\(313\) | 2582.00 | 0.466272 | 0.233136 | − | 0.972444i | \(-0.425101\pi\) | ||||
0.233136 | + | 0.972444i | \(0.425101\pi\) | |||||||
\(314\) | 3340.16 | 0.600306 | ||||||||
\(315\) | −401.511 | −0.0718176 | ||||||||
\(316\) | −5053.16 | −0.899564 | ||||||||
\(317\) | −8388.53 | −1.48627 | −0.743134 | − | 0.669143i | \(-0.766662\pi\) | ||||
−0.743134 | + | 0.669143i | \(0.766662\pi\) | |||||||
\(318\) | 3892.72 | 0.686455 | ||||||||
\(319\) | −2823.19 | −0.495512 | ||||||||
\(320\) | 407.884 | 0.0712544 | ||||||||
\(321\) | 4358.77 | 0.757891 | ||||||||
\(322\) | 322.000 | 0.0557278 | ||||||||
\(323\) | 9978.41 | 1.71893 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 1428.27 | 0.243773 | ||||||||
\(326\) | 3706.15 | 0.629646 | ||||||||
\(327\) | 2462.24 | 0.416397 | ||||||||
\(328\) | 2360.28 | 0.397331 | ||||||||
\(329\) | −1968.22 | −0.329822 | ||||||||
\(330\) | 1105.90 | 0.184479 | ||||||||
\(331\) | 7161.59 | 1.18923 | 0.594617 | − | 0.804009i | \(-0.297304\pi\) | ||||
0.594617 | + | 0.804009i | \(0.297304\pi\) | |||||||
\(332\) | 1403.28 | 0.231973 | ||||||||
\(333\) | 479.317 | 0.0788781 | ||||||||
\(334\) | 396.020 | 0.0648780 | ||||||||
\(335\) | −904.878 | −0.147578 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | −9443.05 | −1.52640 | −0.763198 | − | 0.646165i | \(-0.776372\pi\) | ||||
−0.763198 | + | 0.646165i | \(0.776372\pi\) | |||||||
\(338\) | −3821.01 | −0.614898 | ||||||||
\(339\) | 207.621 | 0.0332637 | ||||||||
\(340\) | 2112.34 | 0.336934 | ||||||||
\(341\) | −5953.56 | −0.945464 | ||||||||
\(342\) | 2167.64 | 0.342726 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 1979.74 | 0.310292 | ||||||||
\(345\) | −439.750 | −0.0686241 | ||||||||
\(346\) | −6025.63 | −0.936242 | ||||||||
\(347\) | 3779.31 | 0.584680 | 0.292340 | − | 0.956314i | \(-0.405566\pi\) | ||||
0.292340 | + | 0.956314i | \(0.405566\pi\) | |||||||
\(348\) | −1171.42 | −0.180445 | ||||||||
\(349\) | 11136.7 | 1.70812 | 0.854060 | − | 0.520175i | \(-0.174133\pi\) | ||||
0.854060 | + | 0.520175i | \(0.174133\pi\) | |||||||
\(350\) | 1181.36 | 0.180417 | ||||||||
\(351\) | −457.006 | −0.0694962 | ||||||||
\(352\) | 925.463 | 0.140135 | ||||||||
\(353\) | −1545.29 | −0.232996 | −0.116498 | − | 0.993191i | \(-0.537167\pi\) | ||||
−0.116498 | + | 0.993191i | \(0.537167\pi\) | |||||||
\(354\) | 277.064 | 0.0415983 | ||||||||
\(355\) | 796.726 | 0.119115 | ||||||||
\(356\) | −202.067 | −0.0300830 | ||||||||
\(357\) | −1740.07 | −0.257967 | ||||||||
\(358\) | 7103.83 | 1.04874 | ||||||||
\(359\) | 2526.49 | 0.371429 | 0.185715 | − | 0.982604i | \(-0.440540\pi\) | ||||
0.185715 | + | 0.982604i | \(0.440540\pi\) | |||||||
\(360\) | 458.869 | 0.0671793 | ||||||||
\(361\) | 7643.02 | 1.11430 | ||||||||
\(362\) | −268.393 | −0.0389680 | ||||||||
\(363\) | −1483.78 | −0.214540 | ||||||||
\(364\) | 473.932 | 0.0682439 | ||||||||
\(365\) | 426.909 | 0.0612203 | ||||||||
\(366\) | −1052.50 | −0.150315 | ||||||||
\(367\) | −9346.59 | −1.32940 | −0.664698 | − | 0.747112i | \(-0.731440\pi\) | ||||
−0.664698 | + | 0.747112i | \(0.731440\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 2655.31 | 0.374607 | ||||||||
\(370\) | 678.839 | 0.0953815 | ||||||||
\(371\) | −4541.50 | −0.635534 | ||||||||
\(372\) | −2470.30 | −0.344298 | ||||||||
\(373\) | −854.068 | −0.118558 | −0.0592788 | − | 0.998241i | \(-0.518880\pi\) | ||||
−0.0592788 | + | 0.998241i | \(0.518880\pi\) | |||||||
\(374\) | 4792.77 | 0.662642 | ||||||||
\(375\) | −4003.30 | −0.551279 | ||||||||
\(376\) | 2249.40 | 0.308521 | ||||||||
\(377\) | 1652.30 | 0.225724 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | −8329.55 | −1.12892 | −0.564459 | − | 0.825461i | \(-0.690915\pi\) | ||||
−0.564459 | + | 0.825461i | \(0.690915\pi\) | |||||||
\(380\) | 3069.95 | 0.414434 | ||||||||
\(381\) | 1804.06 | 0.242585 | ||||||||
\(382\) | −2848.53 | −0.381527 | ||||||||
\(383\) | −5517.75 | −0.736145 | −0.368073 | − | 0.929797i | \(-0.619982\pi\) | ||||
−0.368073 | + | 0.929797i | \(0.619982\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | −1290.22 | −0.170794 | ||||||||
\(386\) | −2668.02 | −0.351809 | ||||||||
\(387\) | 2227.21 | 0.292546 | ||||||||
\(388\) | 4727.39 | 0.618548 | ||||||||
\(389\) | −7467.34 | −0.973289 | −0.486644 | − | 0.873600i | \(-0.661779\pi\) | ||||
−0.486644 | + | 0.873600i | \(0.661779\pi\) | |||||||
\(390\) | −647.241 | −0.0840367 | ||||||||
\(391\) | −1905.79 | −0.246496 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −1889.58 | −0.242536 | ||||||||
\(394\) | −4264.12 | −0.545237 | ||||||||
\(395\) | −8051.17 | −1.02557 | ||||||||
\(396\) | 1041.15 | 0.132120 | ||||||||
\(397\) | 665.468 | 0.0841281 | 0.0420641 | − | 0.999115i | \(-0.486607\pi\) | ||||
0.0420641 | + | 0.999115i | \(0.486607\pi\) | |||||||
\(398\) | −0.324580 | −4.08786e−5 0 | ||||||||
\(399\) | −2528.91 | −0.317303 | ||||||||
\(400\) | −1350.12 | −0.168765 | ||||||||
\(401\) | 2329.48 | 0.290096 | 0.145048 | − | 0.989425i | \(-0.453666\pi\) | ||||
0.145048 | + | 0.989425i | \(0.453666\pi\) | |||||||
\(402\) | −851.892 | −0.105693 | ||||||||
\(403\) | 3484.38 | 0.430693 | ||||||||
\(404\) | −3085.78 | −0.380008 | ||||||||
\(405\) | 516.228 | 0.0633372 | ||||||||
\(406\) | 1366.66 | 0.167059 | ||||||||
\(407\) | 1540.24 | 0.187585 | ||||||||
\(408\) | 1988.65 | 0.241306 | ||||||||
\(409\) | −14563.3 | −1.76065 | −0.880327 | − | 0.474368i | \(-0.842677\pi\) | ||||
−0.880327 | + | 0.474368i | \(0.842677\pi\) | |||||||
\(410\) | 3760.62 | 0.452985 | ||||||||
\(411\) | −612.818 | −0.0735476 | ||||||||
\(412\) | −2788.14 | −0.333402 | ||||||||
\(413\) | −323.242 | −0.0385126 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | 2235.84 | 0.264465 | ||||||||
\(416\) | −541.637 | −0.0638364 | ||||||||
\(417\) | −3488.83 | −0.409709 | ||||||||
\(418\) | 6965.52 | 0.815059 | ||||||||
\(419\) | 49.9148 | 0.00581980 | 0.00290990 | − | 0.999996i | \(-0.499074\pi\) | ||||
0.00290990 | + | 0.999996i | \(0.499074\pi\) | |||||||
\(420\) | −535.347 | −0.0621959 | ||||||||
\(421\) | 3418.01 | 0.395686 | 0.197843 | − | 0.980234i | \(-0.436606\pi\) | ||||
0.197843 | + | 0.980234i | \(0.436606\pi\) | |||||||
\(422\) | 4416.98 | 0.509514 | ||||||||
\(423\) | 2530.57 | 0.290876 | ||||||||
\(424\) | 5190.29 | 0.594488 | ||||||||
\(425\) | −6991.97 | −0.798025 | ||||||||
\(426\) | 750.073 | 0.0853079 | ||||||||
\(427\) | 1227.92 | 0.139165 | ||||||||
\(428\) | 5811.70 | 0.656353 | ||||||||
\(429\) | −1468.55 | −0.165273 | ||||||||
\(430\) | 3154.31 | 0.353754 | ||||||||
\(431\) | 10313.8 | 1.15267 | 0.576333 | − | 0.817215i | \(-0.304483\pi\) | ||||
0.576333 | + | 0.817215i | \(0.304483\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −6900.83 | −0.765896 | −0.382948 | − | 0.923770i | \(-0.625091\pi\) | ||||
−0.382948 | + | 0.923770i | \(0.625091\pi\) | |||||||
\(434\) | 2882.01 | 0.318758 | ||||||||
\(435\) | −1866.42 | −0.205719 | ||||||||
\(436\) | 3282.98 | 0.360611 | ||||||||
\(437\) | −2769.76 | −0.303193 | ||||||||
\(438\) | 401.911 | 0.0438448 | ||||||||
\(439\) | −11796.9 | −1.28254 | −0.641272 | − | 0.767313i | \(-0.721593\pi\) | ||||
−0.641272 | + | 0.767313i | \(0.721593\pi\) | |||||||
\(440\) | 1474.54 | 0.159763 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −2805.02 | −0.301857 | ||||||||
\(443\) | −17906.3 | −1.92044 | −0.960220 | − | 0.279244i | \(-0.909916\pi\) | ||||
−0.960220 | + | 0.279244i | \(0.909916\pi\) | |||||||
\(444\) | 639.089 | 0.0683104 | ||||||||
\(445\) | −321.953 | −0.0342967 | ||||||||
\(446\) | 961.543 | 0.102086 | ||||||||
\(447\) | 771.333 | 0.0816170 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −2508.58 | −0.263668 | −0.131834 | − | 0.991272i | \(-0.542087\pi\) | ||||
−0.131834 | + | 0.991272i | \(0.542087\pi\) | |||||||
\(450\) | −1518.89 | −0.159113 | ||||||||
\(451\) | 8532.61 | 0.890876 | ||||||||
\(452\) | 276.827 | 0.0288072 | ||||||||
\(453\) | −6420.47 | −0.665916 | ||||||||
\(454\) | 365.850 | 0.0378198 | ||||||||
\(455\) | 755.114 | 0.0778029 | ||||||||
\(456\) | 2890.18 | 0.296810 | ||||||||
\(457\) | −704.625 | −0.0721247 | −0.0360623 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360623 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(458\) | −8921.56 | −0.910212 | ||||||||
\(459\) | 2237.23 | 0.227506 | ||||||||
\(460\) | −586.333 | −0.0594302 | ||||||||
\(461\) | −5794.80 | −0.585446 | −0.292723 | − | 0.956197i | \(-0.594561\pi\) | ||||
−0.292723 | + | 0.956197i | \(0.594561\pi\) | |||||||
\(462\) | −1214.67 | −0.122319 | ||||||||
\(463\) | 19201.0 | 1.92731 | 0.963655 | − | 0.267151i | \(-0.0860823\pi\) | ||||
0.963655 | + | 0.267151i | \(0.0860823\pi\) | |||||||
\(464\) | −1561.89 | −0.156270 | ||||||||
\(465\) | −3935.91 | −0.392524 | ||||||||
\(466\) | −1745.14 | −0.173481 | ||||||||
\(467\) | −14602.0 | −1.44690 | −0.723449 | − | 0.690377i | \(-0.757445\pi\) | ||||
−0.723449 | + | 0.690377i | \(0.757445\pi\) | |||||||
\(468\) | −609.341 | −0.0601855 | ||||||||
\(469\) | 993.874 | 0.0978525 | ||||||||
\(470\) | 3583.95 | 0.351735 | ||||||||
\(471\) | 5010.24 | 0.490148 | ||||||||
\(472\) | 369.419 | 0.0360252 | ||||||||
\(473\) | 7156.93 | 0.695721 | ||||||||
\(474\) | −7579.73 | −0.734491 | ||||||||
\(475\) | −10161.7 | −0.981581 | ||||||||
\(476\) | −2320.09 | −0.223406 | ||||||||
\(477\) | 5839.08 | 0.560488 | ||||||||
\(478\) | −780.491 | −0.0746838 | ||||||||
\(479\) | 9139.21 | 0.871777 | 0.435889 | − | 0.900001i | \(-0.356434\pi\) | ||||
0.435889 | + | 0.900001i | \(0.356434\pi\) | |||||||
\(480\) | 611.826 | 0.0581789 | ||||||||
\(481\) | −901.443 | −0.0854517 | ||||||||
\(482\) | −4929.64 | −0.465848 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | −1978.37 | −0.185797 | ||||||||
\(485\) | 7532.13 | 0.705188 | ||||||||
\(486\) | 486.000 | 0.0453609 | ||||||||
\(487\) | −6675.76 | −0.621165 | −0.310583 | − | 0.950546i | \(-0.600524\pi\) | ||||
−0.310583 | + | 0.950546i | \(0.600524\pi\) | |||||||
\(488\) | −1403.34 | −0.130176 | ||||||||
\(489\) | 5559.23 | 0.514104 | ||||||||
\(490\) | 624.572 | 0.0575822 | ||||||||
\(491\) | −52.2053 | −0.00479835 | −0.00239918 | − | 0.999997i | \(-0.500764\pi\) | ||||
−0.00239918 | + | 0.999997i | \(0.500764\pi\) | |||||||
\(492\) | 3540.41 | 0.324419 | ||||||||
\(493\) | −8088.70 | −0.738938 | ||||||||
\(494\) | −4076.64 | −0.371289 | ||||||||
\(495\) | 1658.85 | 0.150626 | ||||||||
\(496\) | −3293.73 | −0.298171 | ||||||||
\(497\) | −875.085 | −0.0789797 | ||||||||
\(498\) | 2104.92 | 0.189405 | ||||||||
\(499\) | 20762.2 | 1.86262 | 0.931308 | − | 0.364233i | \(-0.118669\pi\) | ||||
0.931308 | + | 0.364233i | \(0.118669\pi\) | |||||||
\(500\) | −5337.73 | −0.477421 | ||||||||
\(501\) | 594.030 | 0.0529726 | ||||||||
\(502\) | −4724.70 | −0.420068 | ||||||||
\(503\) | −5576.17 | −0.494293 | −0.247146 | − | 0.968978i | \(-0.579493\pi\) | ||||
−0.247146 | + | 0.968978i | \(0.579493\pi\) | |||||||
\(504\) | −504.000 | −0.0445435 | ||||||||
\(505\) | −4916.56 | −0.433236 | ||||||||
\(506\) | −1330.35 | −0.116880 | ||||||||
\(507\) | −5731.52 | −0.502062 | ||||||||
\(508\) | 2405.42 | 0.210085 | ||||||||
\(509\) | −7807.52 | −0.679887 | −0.339943 | − | 0.940446i | \(-0.610408\pi\) | ||||
−0.339943 | + | 0.940446i | \(0.610408\pi\) | |||||||
\(510\) | 3168.51 | 0.275106 | ||||||||
\(511\) | −468.896 | −0.0405924 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 3251.46 | 0.279835 | ||||||||
\(514\) | −966.393 | −0.0829295 | ||||||||
\(515\) | −4442.33 | −0.380102 | ||||||||
\(516\) | 2969.61 | 0.253352 | ||||||||
\(517\) | 8131.77 | 0.691750 | ||||||||
\(518\) | −745.604 | −0.0632432 | ||||||||
\(519\) | −9038.44 | −0.764438 | ||||||||
\(520\) | −862.988 | −0.0727779 | ||||||||
\(521\) | −16370.3 | −1.37657 | −0.688287 | − | 0.725438i | \(-0.741637\pi\) | ||||
−0.688287 | + | 0.725438i | \(0.741637\pi\) | |||||||
\(522\) | −1757.13 | −0.147332 | ||||||||
\(523\) | 8164.48 | 0.682615 | 0.341308 | − | 0.939952i | \(-0.389130\pi\) | ||||
0.341308 | + | 0.939952i | \(0.389130\pi\) | |||||||
\(524\) | −2519.44 | −0.210042 | ||||||||
\(525\) | 1772.03 | 0.147310 | ||||||||
\(526\) | −16217.1 | −1.34430 | ||||||||
\(527\) | −17057.5 | −1.40993 | ||||||||
\(528\) | 1388.19 | 0.114419 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 8269.67 | 0.677758 | ||||||||
\(531\) | 415.597 | 0.0339649 | ||||||||
\(532\) | −3371.88 | −0.274792 | ||||||||
\(533\) | −4993.80 | −0.405826 | ||||||||
\(534\) | −303.101 | −0.0245627 | ||||||||
\(535\) | 9259.76 | 0.748288 | ||||||||
\(536\) | −1135.86 | −0.0915327 | ||||||||
\(537\) | 10655.7 | 0.856293 | ||||||||
\(538\) | 775.033 | 0.0621079 | ||||||||
\(539\) | 1417.12 | 0.113246 | ||||||||
\(540\) | 688.304 | 0.0548516 | ||||||||
\(541\) | 13369.8 | 1.06250 | 0.531251 | − | 0.847215i | \(-0.321722\pi\) | ||||
0.531251 | + | 0.847215i | \(0.321722\pi\) | |||||||
\(542\) | 5509.07 | 0.436595 | ||||||||
\(543\) | −402.589 | −0.0318172 | ||||||||
\(544\) | 2651.53 | 0.208977 | ||||||||
\(545\) | 5230.76 | 0.411121 | ||||||||
\(546\) | 710.898 | 0.0557209 | ||||||||
\(547\) | 10035.3 | 0.784425 | 0.392212 | − | 0.919875i | \(-0.371710\pi\) | ||||
0.392212 | + | 0.919875i | \(0.371710\pi\) | |||||||
\(548\) | −817.090 | −0.0636941 | ||||||||
\(549\) | −1578.76 | −0.122732 | ||||||||
\(550\) | −4880.81 | −0.378397 | ||||||||
\(551\) | −11755.6 | −0.908904 | ||||||||
\(552\) | −552.000 | −0.0425628 | ||||||||
\(553\) | 8843.02 | 0.680006 | ||||||||
\(554\) | 1113.98 | 0.0854308 | ||||||||
\(555\) | 1018.26 | 0.0778787 | ||||||||
\(556\) | −4651.77 | −0.354818 | ||||||||
\(557\) | 290.769 | 0.0221190 | 0.0110595 | − | 0.999939i | \(-0.496480\pi\) | ||||
0.0110595 | + | 0.999939i | \(0.496480\pi\) | |||||||
\(558\) | −3705.44 | −0.281118 | ||||||||
\(559\) | −4188.67 | −0.316926 | ||||||||
\(560\) | −713.797 | −0.0538632 | ||||||||
\(561\) | 7189.15 | 0.541045 | ||||||||
\(562\) | −2980.61 | −0.223718 | ||||||||
\(563\) | −20957.4 | −1.56882 | −0.784411 | − | 0.620241i | \(-0.787035\pi\) | ||||
−0.784411 | + | 0.620241i | \(0.787035\pi\) | |||||||
\(564\) | 3374.09 | 0.251906 | ||||||||
\(565\) | 441.068 | 0.0328423 | ||||||||
\(566\) | −8221.86 | −0.610584 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 1000.10 | 0.0738788 | ||||||||
\(569\) | 15884.9 | 1.17035 | 0.585176 | − | 0.810906i | \(-0.301025\pi\) | ||||
0.585176 | + | 0.810906i | \(0.301025\pi\) | |||||||
\(570\) | 4604.92 | 0.338384 | ||||||||
\(571\) | 22011.3 | 1.61322 | 0.806608 | − | 0.591087i | \(-0.201301\pi\) | ||||
0.806608 | + | 0.591087i | \(0.201301\pi\) | |||||||
\(572\) | −1958.07 | −0.143131 | ||||||||
\(573\) | −4272.79 | −0.311516 | ||||||||
\(574\) | −4130.48 | −0.300354 | ||||||||
\(575\) | 1940.80 | 0.140760 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −14098.7 | −1.01722 | −0.508611 | − | 0.860997i | \(-0.669841\pi\) | ||||
−0.508611 | + | 0.860997i | \(0.669841\pi\) | |||||||
\(578\) | 3905.70 | 0.281065 | ||||||||
\(579\) | −4002.02 | −0.287251 | ||||||||
\(580\) | −2488.56 | −0.178158 | ||||||||
\(581\) | −2455.74 | −0.175355 | ||||||||
\(582\) | 7091.08 | 0.505043 | ||||||||
\(583\) | 18763.4 | 1.33293 | ||||||||
\(584\) | 535.881 | 0.0379707 | ||||||||
\(585\) | −970.861 | −0.0686157 | ||||||||
\(586\) | −622.110 | −0.0438552 | ||||||||
\(587\) | −12148.3 | −0.854201 | −0.427100 | − | 0.904204i | \(-0.640465\pi\) | ||||
−0.427100 | + | 0.904204i | \(0.640465\pi\) | |||||||
\(588\) | 588.000 | 0.0412393 | ||||||||
\(589\) | −24790.3 | −1.73424 | ||||||||
\(590\) | 588.594 | 0.0410712 | ||||||||
\(591\) | −6396.19 | −0.445184 | ||||||||
\(592\) | 852.119 | 0.0591586 | ||||||||
\(593\) | −18128.5 | −1.25539 | −0.627696 | − | 0.778459i | \(-0.716002\pi\) | ||||
−0.627696 | + | 0.778459i | \(0.716002\pi\) | |||||||
\(594\) | 1561.72 | 0.107876 | ||||||||
\(595\) | −3696.59 | −0.254698 | ||||||||
\(596\) | 1028.44 | 0.0706824 | ||||||||
\(597\) | −0.486869 | −3.33773e−5 0 | ||||||||
\(598\) | 778.603 | 0.0532432 | ||||||||
\(599\) | 14228.3 | 0.970539 | 0.485270 | − | 0.874365i | \(-0.338721\pi\) | ||||
0.485270 | + | 0.874365i | \(0.338721\pi\) | |||||||
\(600\) | −2025.18 | −0.137796 | ||||||||
\(601\) | 3578.66 | 0.242889 | 0.121445 | − | 0.992598i | \(-0.461247\pi\) | ||||
0.121445 | + | 0.992598i | \(0.461247\pi\) | |||||||
\(602\) | −3464.54 | −0.234558 | ||||||||
\(603\) | −1277.84 | −0.0862978 | ||||||||
\(604\) | −8560.63 | −0.576700 | ||||||||
\(605\) | −3152.13 | −0.211822 | ||||||||
\(606\) | −4628.67 | −0.310275 | ||||||||
\(607\) | 3990.26 | 0.266820 | 0.133410 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133410 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(608\) | 3853.58 | 0.257045 | ||||||||
\(609\) | 2049.98 | 0.136403 | ||||||||
\(610\) | −2235.93 | −0.148410 | ||||||||
\(611\) | −4759.20 | −0.315117 | ||||||||
\(612\) | 2982.98 | 0.197026 | ||||||||
\(613\) | 19913.4 | 1.31207 | 0.656033 | − | 0.754732i | \(-0.272233\pi\) | ||||
0.656033 | + | 0.754732i | \(0.272233\pi\) | |||||||
\(614\) | −5238.90 | −0.344340 | ||||||||
\(615\) | 5640.93 | 0.369860 | ||||||||
\(616\) | −1619.56 | −0.105932 | ||||||||
\(617\) | −27505.9 | −1.79472 | −0.897362 | − | 0.441295i | \(-0.854519\pi\) | ||||
−0.897362 | + | 0.441295i | \(0.854519\pi\) | |||||||
\(618\) | −4182.21 | −0.272222 | ||||||||
\(619\) | 4744.88 | 0.308098 | 0.154049 | − | 0.988063i | \(-0.450769\pi\) | ||||
0.154049 | + | 0.988063i | \(0.450769\pi\) | |||||||
\(620\) | −5247.88 | −0.339936 | ||||||||
\(621\) | −621.000 | −0.0401286 | ||||||||
\(622\) | −6604.95 | −0.425779 | ||||||||
\(623\) | 353.618 | 0.0227406 | ||||||||
\(624\) | −812.455 | −0.0521222 | ||||||||
\(625\) | 2043.23 | 0.130766 | ||||||||
\(626\) | 5163.99 | 0.329704 | ||||||||
\(627\) | 10448.3 | 0.665493 | ||||||||
\(628\) | 6680.32 | 0.424481 | ||||||||
\(629\) | 4412.93 | 0.279738 | ||||||||
\(630\) | −803.021 | −0.0507827 | ||||||||
\(631\) | −11363.0 | −0.716887 | −0.358443 | − | 0.933551i | \(-0.616692\pi\) | ||||
−0.358443 | + | 0.933551i | \(0.616692\pi\) | |||||||
\(632\) | −10106.3 | −0.636088 | ||||||||
\(633\) | 6625.47 | 0.416017 | ||||||||
\(634\) | −16777.1 | −1.05095 | ||||||||
\(635\) | 3832.54 | 0.239511 | ||||||||
\(636\) | 7785.44 | 0.485397 | ||||||||
\(637\) | −829.381 | −0.0515876 | ||||||||
\(638\) | −5646.38 | −0.350380 | ||||||||
\(639\) | 1125.11 | 0.0696536 | ||||||||
\(640\) | 815.768 | 0.0503844 | ||||||||
\(641\) | 25292.0 | 1.55846 | 0.779231 | − | 0.626737i | \(-0.215610\pi\) | ||||
0.779231 | + | 0.626737i | \(0.215610\pi\) | |||||||
\(642\) | 8717.55 | 0.535910 | ||||||||
\(643\) | 10026.2 | 0.614920 | 0.307460 | − | 0.951561i | \(-0.400521\pi\) | ||||
0.307460 | + | 0.951561i | \(0.400521\pi\) | |||||||
\(644\) | 644.000 | 0.0394055 | ||||||||
\(645\) | 4731.46 | 0.288839 | ||||||||
\(646\) | 19956.8 | 1.21547 | ||||||||
\(647\) | −21651.9 | −1.31565 | −0.657825 | − | 0.753171i | \(-0.728523\pi\) | ||||
−0.657825 | + | 0.753171i | \(0.728523\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 1335.48 | 0.0807740 | ||||||||
\(650\) | 2856.54 | 0.172374 | ||||||||
\(651\) | 4323.02 | 0.260265 | ||||||||
\(652\) | 7412.30 | 0.445227 | ||||||||
\(653\) | 15782.4 | 0.945810 | 0.472905 | − | 0.881114i | \(-0.343205\pi\) | ||||
0.472905 | + | 0.881114i | \(0.343205\pi\) | |||||||
\(654\) | 4924.47 | 0.294437 | ||||||||
\(655\) | −4014.21 | −0.239463 | ||||||||
\(656\) | 4720.55 | 0.280955 | ||||||||
\(657\) | 602.866 | 0.0357992 | ||||||||
\(658\) | −3936.44 | −0.233220 | ||||||||
\(659\) | −23510.0 | −1.38971 | −0.694856 | − | 0.719149i | \(-0.744532\pi\) | ||||
−0.694856 | + | 0.719149i | \(0.744532\pi\) | |||||||
\(660\) | 2211.80 | 0.130446 | ||||||||
\(661\) | −14625.4 | −0.860607 | −0.430303 | − | 0.902684i | \(-0.641593\pi\) | ||||
−0.430303 | + | 0.902684i | \(0.641593\pi\) | |||||||
\(662\) | 14323.2 | 0.840916 | ||||||||
\(663\) | −4207.52 | −0.246466 | ||||||||
\(664\) | 2806.56 | 0.164029 | ||||||||
\(665\) | −5372.40 | −0.313283 | ||||||||
\(666\) | 958.634 | 0.0557752 | ||||||||
\(667\) | 2245.22 | 0.130338 | ||||||||
\(668\) | 792.040 | 0.0458756 | ||||||||
\(669\) | 1442.32 | 0.0833530 | ||||||||
\(670\) | −1809.76 | −0.104354 | ||||||||
\(671\) | −5073.19 | −0.291875 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | 780.954 | 0.0447304 | 0.0223652 | − | 0.999750i | \(-0.492880\pi\) | ||||
0.0223652 | + | 0.999750i | \(0.492880\pi\) | |||||||
\(674\) | −18886.1 | −1.07933 | ||||||||
\(675\) | −2278.33 | −0.129915 | ||||||||
\(676\) | −7642.02 | −0.434799 | ||||||||
\(677\) | 4460.64 | 0.253230 | 0.126615 | − | 0.991952i | \(-0.459589\pi\) | ||||
0.126615 | + | 0.991952i | \(0.459589\pi\) | |||||||
\(678\) | 415.241 | 0.0235210 | ||||||||
\(679\) | −8272.93 | −0.467579 | ||||||||
\(680\) | 4224.68 | 0.238249 | ||||||||
\(681\) | 548.776 | 0.0308798 | ||||||||
\(682\) | −11907.1 | −0.668544 | ||||||||
\(683\) | 6334.14 | 0.354860 | 0.177430 | − | 0.984133i | \(-0.443222\pi\) | ||||
0.177430 | + | 0.984133i | \(0.443222\pi\) | |||||||
\(684\) | 4335.28 | 0.242344 | ||||||||
\(685\) | −1301.87 | −0.0726157 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | −13382.3 | −0.743185 | ||||||||
\(688\) | 3959.48 | 0.219409 | ||||||||
\(689\) | −10981.5 | −0.607199 | ||||||||
\(690\) | −879.499 | −0.0485246 | ||||||||
\(691\) | 12284.8 | 0.676319 | 0.338160 | − | 0.941089i | \(-0.390196\pi\) | ||||
0.338160 | + | 0.941089i | \(0.390196\pi\) | |||||||
\(692\) | −12051.3 | −0.662023 | ||||||||
\(693\) | −1822.01 | −0.0998734 | ||||||||
\(694\) | 7558.62 | 0.413431 | ||||||||
\(695\) | −7411.64 | −0.404517 | ||||||||
\(696\) | −2342.84 | −0.127594 | ||||||||
\(697\) | 24446.7 | 1.32853 | ||||||||
\(698\) | 22273.4 | 1.20782 | ||||||||
\(699\) | −2617.71 | −0.141646 | ||||||||
\(700\) | 2362.71 | 0.127574 | ||||||||
\(701\) | 2673.42 | 0.144042 | 0.0720211 | − | 0.997403i | \(-0.477055\pi\) | ||||
0.0720211 | + | 0.997403i | \(0.477055\pi\) | |||||||
\(702\) | −914.012 | −0.0491413 | ||||||||
\(703\) | 6413.49 | 0.344082 | ||||||||
\(704\) | 1850.93 | 0.0990901 | ||||||||
\(705\) | 5375.93 | 0.287190 | ||||||||
\(706\) | −3090.58 | −0.164753 | ||||||||
\(707\) | 5400.12 | 0.287259 | ||||||||
\(708\) | 554.129 | 0.0294145 | ||||||||
\(709\) | 27586.6 | 1.46127 | 0.730633 | − | 0.682770i | \(-0.239225\pi\) | ||||
0.730633 | + | 0.682770i | \(0.239225\pi\) | |||||||
\(710\) | 1593.45 | 0.0842270 | ||||||||
\(711\) | −11369.6 | −0.599709 | ||||||||
\(712\) | −404.135 | −0.0212719 | ||||||||
\(713\) | 4734.73 | 0.248692 | ||||||||
\(714\) | −3480.14 | −0.182410 | ||||||||
\(715\) | −3119.78 | −0.163179 | ||||||||
\(716\) | 14207.7 | 0.741572 | ||||||||
\(717\) | −1170.74 | −0.0609790 | ||||||||
\(718\) | 5052.98 | 0.262640 | ||||||||
\(719\) | 1930.24 | 0.100119 | 0.0500597 | − | 0.998746i | \(-0.484059\pi\) | ||||
0.0500597 | + | 0.998746i | \(0.484059\pi\) | |||||||
\(720\) | 917.739 | 0.0475029 | ||||||||
\(721\) | 4879.24 | 0.252028 | ||||||||
\(722\) | 15286.0 | 0.787932 | ||||||||
\(723\) | −7394.46 | −0.380363 | ||||||||
\(724\) | −536.786 | −0.0275545 | ||||||||
\(725\) | 8237.28 | 0.421965 | ||||||||
\(726\) | −2967.55 | −0.151703 | ||||||||
\(727\) | 12608.0 | 0.643197 | 0.321598 | − | 0.946876i | \(-0.395780\pi\) | ||||
0.321598 | + | 0.946876i | \(0.395780\pi\) | |||||||
\(728\) | 947.864 | 0.0482558 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 853.817 | 0.0432893 | ||||||||
\(731\) | 20505.2 | 1.03750 | ||||||||
\(732\) | −2105.01 | −0.106289 | ||||||||
\(733\) | 14282.8 | 0.719709 | 0.359854 | − | 0.933008i | \(-0.382826\pi\) | ||||
0.359854 | + | 0.933008i | \(0.382826\pi\) | |||||||
\(734\) | −18693.2 | −0.940025 | ||||||||
\(735\) | 936.858 | 0.0470157 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −4106.22 | −0.205230 | ||||||||
\(738\) | 5310.62 | 0.264887 | ||||||||
\(739\) | 13569.5 | 0.675455 | 0.337727 | − | 0.941244i | \(-0.390342\pi\) | ||||
0.337727 | + | 0.941244i | \(0.390342\pi\) | |||||||
\(740\) | 1357.68 | 0.0674449 | ||||||||
\(741\) | −6114.96 | −0.303156 | ||||||||
\(742\) | −9083.01 | −0.449390 | ||||||||
\(743\) | −2460.58 | −0.121494 | −0.0607469 | − | 0.998153i | \(-0.519348\pi\) | ||||
−0.0607469 | + | 0.998153i | \(0.519348\pi\) | |||||||
\(744\) | −4940.59 | −0.243455 | ||||||||
\(745\) | 1638.62 | 0.0805829 | ||||||||
\(746\) | −1708.14 | −0.0838328 | ||||||||
\(747\) | 3157.38 | 0.154648 | ||||||||
\(748\) | 9585.53 | 0.468559 | ||||||||
\(749\) | −10170.5 | −0.496156 | ||||||||
\(750\) | −8006.60 | −0.389813 | ||||||||
\(751\) | 31279.9 | 1.51987 | 0.759933 | − | 0.650002i | \(-0.225232\pi\) | ||||
0.759933 | + | 0.650002i | \(0.225232\pi\) | |||||||
\(752\) | 4498.79 | 0.218157 | ||||||||
\(753\) | −7087.06 | −0.342984 | ||||||||
\(754\) | 3304.60 | 0.159611 | ||||||||
\(755\) | −13639.6 | −0.657479 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 8111.98 | 0.389478 | 0.194739 | − | 0.980855i | \(-0.437614\pi\) | ||||
0.194739 | + | 0.980855i | \(0.437614\pi\) | |||||||
\(758\) | −16659.1 | −0.798266 | ||||||||
\(759\) | −1995.53 | −0.0954323 | ||||||||
\(760\) | 6139.89 | 0.293049 | ||||||||
\(761\) | −11611.8 | −0.553123 | −0.276562 | − | 0.960996i | \(-0.589195\pi\) | ||||
−0.276562 | + | 0.960996i | \(0.589195\pi\) | |||||||
\(762\) | 3608.12 | 0.171534 | ||||||||
\(763\) | −5745.22 | −0.272596 | ||||||||
\(764\) | −5697.06 | −0.269781 | ||||||||
\(765\) | 4752.76 | 0.224623 | ||||||||
\(766\) | −11035.5 | −0.520533 | ||||||||
\(767\) | −781.605 | −0.0367955 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −27763.2 | −1.30191 | −0.650953 | − | 0.759118i | \(-0.725630\pi\) | ||||
−0.650953 | + | 0.759118i | \(0.725630\pi\) | |||||||
\(770\) | −2580.44 | −0.120770 | ||||||||
\(771\) | −1449.59 | −0.0677117 | ||||||||
\(772\) | −5336.03 | −0.248767 | ||||||||
\(773\) | −18274.2 | −0.850292 | −0.425146 | − | 0.905125i | \(-0.639777\pi\) | ||||
−0.425146 | + | 0.905125i | \(0.639777\pi\) | |||||||
\(774\) | 4454.41 | 0.206861 | ||||||||
\(775\) | 17370.8 | 0.805133 | ||||||||
\(776\) | 9454.78 | 0.437380 | ||||||||
\(777\) | −1118.41 | −0.0516378 | ||||||||
\(778\) | −14934.7 | −0.688219 | ||||||||
\(779\) | 35529.3 | 1.63411 | ||||||||
\(780\) | −1294.48 | −0.0594229 | ||||||||
\(781\) | 3615.44 | 0.165647 | ||||||||
\(782\) | −3811.58 | −0.174299 | ||||||||
\(783\) | −2635.69 | −0.120296 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 10643.7 | 0.483938 | ||||||||
\(786\) | −3779.15 | −0.171499 | ||||||||
\(787\) | 17073.2 | 0.773310 | 0.386655 | − | 0.922224i | \(-0.373630\pi\) | ||||
0.386655 | + | 0.922224i | \(0.373630\pi\) | |||||||
\(788\) | −8528.25 | −0.385541 | ||||||||
\(789\) | −24325.7 | −1.09761 | ||||||||
\(790\) | −16102.3 | −0.725184 | ||||||||
\(791\) | −484.448 | −0.0217762 | ||||||||
\(792\) | 2082.29 | 0.0934230 | ||||||||
\(793\) | 2969.14 | 0.132960 | ||||||||
\(794\) | 1330.94 | 0.0594876 | ||||||||
\(795\) | 12404.5 | 0.553387 | ||||||||
\(796\) | −0.649159 | −2.89056e−5 0 | ||||||||
\(797\) | 8355.89 | 0.371368 | 0.185684 | − | 0.982609i | \(-0.440550\pi\) | ||||
0.185684 | + | 0.982609i | \(0.440550\pi\) | |||||||
\(798\) | −5057.82 | −0.224367 | ||||||||
\(799\) | 23298.2 | 1.03158 | ||||||||
\(800\) | −2700.24 | −0.119335 | ||||||||
\(801\) | −454.652 | −0.0200553 | ||||||||
\(802\) | 4658.95 | 0.205129 | ||||||||
\(803\) | 1937.26 | 0.0851362 | ||||||||
\(804\) | −1703.78 | −0.0747361 | ||||||||
\(805\) | 1026.08 | 0.0449250 | ||||||||
\(806\) | 6968.77 | 0.304546 | ||||||||
\(807\) | 1162.55 | 0.0507109 | ||||||||
\(808\) | −6171.56 | −0.268706 | ||||||||
\(809\) | 1365.06 | 0.0593237 | 0.0296618 | − | 0.999560i | \(-0.490557\pi\) | ||||
0.0296618 | + | 0.999560i | \(0.490557\pi\) | |||||||
\(810\) | 1032.46 | 0.0447862 | ||||||||
\(811\) | 6369.46 | 0.275785 | 0.137893 | − | 0.990447i | \(-0.455967\pi\) | ||||
0.137893 | + | 0.990447i | \(0.455967\pi\) | |||||||
\(812\) | 2733.31 | 0.118129 | ||||||||
\(813\) | 8263.60 | 0.356479 | ||||||||
\(814\) | 3080.49 | 0.132643 | ||||||||
\(815\) | 11810.0 | 0.507590 | ||||||||
\(816\) | 3977.30 | 0.170629 | ||||||||
\(817\) | 29801.1 | 1.27614 | ||||||||
\(818\) | −29126.5 | −1.24497 | ||||||||
\(819\) | 1066.35 | 0.0454960 | ||||||||
\(820\) | 7521.24 | 0.320309 | ||||||||
\(821\) | 21449.4 | 0.911803 | 0.455901 | − | 0.890030i | \(-0.349317\pi\) | ||||
0.455901 | + | 0.890030i | \(0.349317\pi\) | |||||||
\(822\) | −1225.64 | −0.0520060 | ||||||||
\(823\) | −28555.4 | −1.20945 | −0.604725 | − | 0.796434i | \(-0.706717\pi\) | ||||
−0.604725 | + | 0.796434i | \(0.706717\pi\) | |||||||
\(824\) | −5576.28 | −0.235751 | ||||||||
\(825\) | −7321.21 | −0.308960 | ||||||||
\(826\) | −646.484 | −0.0272325 | ||||||||
\(827\) | −3612.76 | −0.151908 | −0.0759540 | − | 0.997111i | \(-0.524200\pi\) | ||||
−0.0759540 | + | 0.997111i | \(0.524200\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | −4348.21 | −0.182171 | −0.0910854 | − | 0.995843i | \(-0.529034\pi\) | ||||
−0.0910854 | + | 0.995843i | \(0.529034\pi\) | |||||||
\(830\) | 4471.68 | 0.187005 | ||||||||
\(831\) | 1670.98 | 0.0697540 | ||||||||
\(832\) | −1083.27 | −0.0451391 | ||||||||
\(833\) | 4060.16 | 0.168879 | ||||||||
\(834\) | −6977.65 | −0.289708 | ||||||||
\(835\) | 1261.95 | 0.0523014 | ||||||||
\(836\) | 13931.0 | 0.576333 | ||||||||
\(837\) | −5558.17 | −0.229532 | ||||||||
\(838\) | 99.8295 | 0.00411522 | ||||||||
\(839\) | 47629.6 | 1.95990 | 0.979949 | − | 0.199247i | \(-0.0638496\pi\) | ||||
0.979949 | + | 0.199247i | \(0.0638496\pi\) | |||||||
\(840\) | −1070.69 | −0.0439791 | ||||||||
\(841\) | −14859.7 | −0.609277 | ||||||||
\(842\) | 6836.03 | 0.279792 | ||||||||
\(843\) | −4470.91 | −0.182665 | ||||||||
\(844\) | 8833.96 | 0.360281 | ||||||||
\(845\) | −12176.0 | −0.495701 | ||||||||
\(846\) | 5061.14 | 0.205680 | ||||||||
\(847\) | 3462.14 | 0.140449 | ||||||||
\(848\) | 10380.6 | 0.420366 | ||||||||
\(849\) | −12332.8 | −0.498540 | ||||||||
\(850\) | −13983.9 | −0.564289 | ||||||||
\(851\) | −1224.92 | −0.0493417 | ||||||||
\(852\) | 1500.15 | 0.0603218 | ||||||||
\(853\) | −16383.9 | −0.657647 | −0.328824 | − | 0.944391i | \(-0.606652\pi\) | ||||
−0.328824 | + | 0.944391i | \(0.606652\pi\) | |||||||
\(854\) | 2455.84 | 0.0984042 | ||||||||
\(855\) | 6907.38 | 0.276289 | ||||||||
\(856\) | 11623.4 | 0.464112 | ||||||||
\(857\) | −28121.4 | −1.12090 | −0.560449 | − | 0.828189i | \(-0.689371\pi\) | ||||
−0.560449 | + | 0.828189i | \(0.689371\pi\) | |||||||
\(858\) | −2937.10 | −0.116866 | ||||||||
\(859\) | 31385.2 | 1.24662 | 0.623311 | − | 0.781974i | \(-0.285787\pi\) | ||||
0.623311 | + | 0.781974i | \(0.285787\pi\) | |||||||
\(860\) | 6308.62 | 0.250142 | ||||||||
\(861\) | −6195.72 | −0.245238 | ||||||||
\(862\) | 20627.6 | 0.815058 | ||||||||
\(863\) | 27621.2 | 1.08950 | 0.544748 | − | 0.838600i | \(-0.316625\pi\) | ||||
0.544748 | + | 0.838600i | \(0.316625\pi\) | |||||||
\(864\) | 864.000 | 0.0340207 | ||||||||
\(865\) | −19201.2 | −0.754752 | ||||||||
\(866\) | −13801.7 | −0.541570 | ||||||||
\(867\) | 5858.55 | 0.229489 | ||||||||
\(868\) | 5764.02 | 0.225396 | ||||||||
\(869\) | −36535.2 | −1.42621 | ||||||||
\(870\) | −3732.84 | −0.145466 | ||||||||
\(871\) | 2403.21 | 0.0934898 | ||||||||
\(872\) | 6565.96 | 0.254990 | ||||||||
\(873\) | 10636.6 | 0.412366 | ||||||||
\(874\) | −5539.52 | −0.214390 | ||||||||
\(875\) | 9341.03 | 0.360897 | ||||||||
\(876\) | 803.822 | 0.0310030 | ||||||||
\(877\) | −15793.1 | −0.608092 | −0.304046 | − | 0.952657i | \(-0.598338\pi\) | ||||
−0.304046 | + | 0.952657i | \(0.598338\pi\) | |||||||
\(878\) | −23593.9 | −0.906896 | ||||||||
\(879\) | −933.165 | −0.0358076 | ||||||||
\(880\) | 2949.07 | 0.112970 | ||||||||
\(881\) | −8099.56 | −0.309740 | −0.154870 | − | 0.987935i | \(-0.549496\pi\) | ||||
−0.154870 | + | 0.987935i | \(0.549496\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | −15482.3 | −0.590057 | −0.295029 | − | 0.955488i | \(-0.595329\pi\) | ||||
−0.295029 | + | 0.955488i | \(0.595329\pi\) | |||||||
\(884\) | −5610.03 | −0.213445 | ||||||||
\(885\) | 882.891 | 0.0335345 | ||||||||
\(886\) | −35812.6 | −1.35796 | ||||||||
\(887\) | 33847.4 | 1.28127 | 0.640634 | − | 0.767846i | \(-0.278672\pi\) | ||||
0.640634 | + | 0.767846i | \(0.278672\pi\) | |||||||
\(888\) | 1278.18 | 0.0483028 | ||||||||
\(889\) | −4209.48 | −0.158809 | ||||||||
\(890\) | −643.906 | −0.0242514 | ||||||||
\(891\) | 2342.58 | 0.0880801 | ||||||||
\(892\) | 1923.09 | 0.0721858 | ||||||||
\(893\) | 33860.2 | 1.26886 | ||||||||
\(894\) | 1542.67 | 0.0577119 | ||||||||
\(895\) | 22637.0 | 0.845444 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 1167.90 | 0.0434729 | ||||||||
\(898\) | −5017.15 | −0.186442 | ||||||||
\(899\) | 20095.5 | 0.745520 | ||||||||
\(900\) | −3037.77 | −0.112510 | ||||||||
\(901\) | 53758.7 | 1.98775 | ||||||||
\(902\) | 17065.2 | 0.629944 | ||||||||
\(903\) | −5196.81 | −0.191516 | ||||||||
\(904\) | 553.655 | 0.0203698 | ||||||||
\(905\) | −855.259 | −0.0314141 | ||||||||
\(906\) | −12840.9 | −0.470874 | ||||||||
\(907\) | 37868.5 | 1.38633 | 0.693166 | − | 0.720778i | \(-0.256215\pi\) | ||||
0.693166 | + | 0.720778i | \(0.256215\pi\) | |||||||
\(908\) | 731.701 | 0.0267427 | ||||||||
\(909\) | −6943.01 | −0.253339 | ||||||||
\(910\) | 1510.23 | 0.0550149 | ||||||||
\(911\) | −32996.0 | −1.20001 | −0.600004 | − | 0.799997i | \(-0.704834\pi\) | ||||
−0.600004 | + | 0.799997i | \(0.704834\pi\) | |||||||
\(912\) | 5780.37 | 0.209876 | ||||||||
\(913\) | 10146.0 | 0.367779 | ||||||||
\(914\) | −1409.25 | −0.0509998 | ||||||||
\(915\) | −3353.90 | −0.121176 | ||||||||
\(916\) | −17843.1 | −0.643617 | ||||||||
\(917\) | 4409.01 | 0.158777 | ||||||||
\(918\) | 4474.46 | 0.160871 | ||||||||
\(919\) | −3997.67 | −0.143494 | −0.0717470 | − | 0.997423i | \(-0.522857\pi\) | ||||
−0.0717470 | + | 0.997423i | \(0.522857\pi\) | |||||||
\(920\) | −1172.67 | −0.0420235 | ||||||||
\(921\) | −7858.35 | −0.281152 | ||||||||
\(922\) | −11589.6 | −0.413973 | ||||||||
\(923\) | −2115.97 | −0.0754585 | ||||||||
\(924\) | −2429.34 | −0.0864929 | ||||||||
\(925\) | −4494.00 | −0.159742 | ||||||||
\(926\) | 38401.9 | 1.36281 | ||||||||
\(927\) | −6273.31 | −0.222268 | ||||||||
\(928\) | −3123.79 | −0.110499 | ||||||||
\(929\) | 16174.3 | 0.571218 | 0.285609 | − | 0.958346i | \(-0.407804\pi\) | ||||
0.285609 | + | 0.958346i | \(0.407804\pi\) | |||||||
\(930\) | −7871.82 | −0.277556 | ||||||||
\(931\) | 5900.79 | 0.207724 | ||||||||
\(932\) | −3490.28 | −0.122669 | ||||||||
\(933\) | −9907.43 | −0.347647 | ||||||||
\(934\) | −29204.1 | −1.02311 | ||||||||
\(935\) | 15272.6 | 0.534189 | ||||||||
\(936\) | −1218.68 | −0.0425576 | ||||||||
\(937\) | −37286.2 | −1.29999 | −0.649993 | − | 0.759940i | \(-0.725228\pi\) | ||||
−0.649993 | + | 0.759940i | \(0.725228\pi\) | |||||||
\(938\) | 1987.75 | 0.0691922 | ||||||||
\(939\) | 7745.99 | 0.269202 | ||||||||
\(940\) | 7167.91 | 0.248714 | ||||||||
\(941\) | −24276.8 | −0.841021 | −0.420511 | − | 0.907288i | \(-0.638149\pi\) | ||||
−0.420511 | + | 0.907288i | \(0.638149\pi\) | |||||||
\(942\) | 10020.5 | 0.346587 | ||||||||
\(943\) | −6785.79 | −0.234333 | ||||||||
\(944\) | 738.838 | 0.0254737 | ||||||||
\(945\) | −1204.53 | −0.0414639 | ||||||||
\(946\) | 14313.9 | 0.491949 | ||||||||
\(947\) | 45165.7 | 1.54983 | 0.774914 | − | 0.632066i | \(-0.217793\pi\) | ||||
0.774914 | + | 0.632066i | \(0.217793\pi\) | |||||||
\(948\) | −15159.5 | −0.519363 | ||||||||
\(949\) | −1133.80 | −0.0387826 | ||||||||
\(950\) | −20323.4 | −0.694083 | ||||||||
\(951\) | −25165.6 | −0.858097 | ||||||||
\(952\) | −4640.18 | −0.157972 | ||||||||
\(953\) | −5474.02 | −0.186066 | −0.0930330 | − | 0.995663i | \(-0.529656\pi\) | ||||
−0.0930330 | + | 0.995663i | \(0.529656\pi\) | |||||||
\(954\) | 11678.2 | 0.396325 | ||||||||
\(955\) | −9077.10 | −0.307569 | ||||||||
\(956\) | −1560.98 | −0.0528094 | ||||||||
\(957\) | −8469.58 | −0.286084 | ||||||||
\(958\) | 18278.4 | 0.616440 | ||||||||
\(959\) | 1429.91 | 0.0481482 | ||||||||
\(960\) | 1223.65 | 0.0411387 | ||||||||
\(961\) | 12586.5 | 0.422494 | ||||||||
\(962\) | −1802.89 | −0.0604235 | ||||||||
\(963\) | 13076.3 | 0.437569 | ||||||||
\(964\) | −9859.28 | −0.329404 | ||||||||
\(965\) | −8501.88 | −0.283611 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | −15869.0 | −0.527729 | −0.263865 | − | 0.964560i | \(-0.584997\pi\) | ||||
−0.263865 | + | 0.964560i | \(0.584997\pi\) | |||||||
\(968\) | −3956.74 | −0.131378 | ||||||||
\(969\) | 29935.2 | 0.992423 | ||||||||
\(970\) | 15064.3 | 0.498643 | ||||||||
\(971\) | 18857.4 | 0.623235 | 0.311618 | − | 0.950208i | \(-0.399129\pi\) | ||||
0.311618 | + | 0.950208i | \(0.399129\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 8140.59 | 0.268217 | ||||||||
\(974\) | −13351.5 | −0.439230 | ||||||||
\(975\) | 4284.81 | 0.140742 | ||||||||
\(976\) | −2806.68 | −0.0920487 | ||||||||
\(977\) | 10822.3 | 0.354387 | 0.177193 | − | 0.984176i | \(-0.443298\pi\) | ||||
0.177193 | + | 0.984176i | \(0.443298\pi\) | |||||||
\(978\) | 11118.5 | 0.363527 | ||||||||
\(979\) | −1460.98 | −0.0476948 | ||||||||
\(980\) | 1249.14 | 0.0407168 | ||||||||
\(981\) | 7386.71 | 0.240407 | ||||||||
\(982\) | −104.411 | −0.00339295 | ||||||||
\(983\) | −22249.4 | −0.721917 | −0.360958 | − | 0.932582i | \(-0.617550\pi\) | ||||
−0.360958 | + | 0.932582i | \(0.617550\pi\) | |||||||
\(984\) | 7080.83 | 0.229399 | ||||||||
\(985\) | −13588.0 | −0.439544 | ||||||||
\(986\) | −16177.4 | −0.522508 | ||||||||
\(987\) | −5904.66 | −0.190423 | ||||||||
\(988\) | −8153.28 | −0.262541 | ||||||||
\(989\) | −5691.75 | −0.183000 | ||||||||
\(990\) | 3317.71 | 0.106509 | ||||||||
\(991\) | 27607.4 | 0.884941 | 0.442470 | − | 0.896783i | \(-0.354102\pi\) | ||||
0.442470 | + | 0.896783i | \(0.354102\pi\) | |||||||
\(992\) | −6587.46 | −0.210839 | ||||||||
\(993\) | 21484.8 | 0.686605 | ||||||||
\(994\) | −1750.17 | −0.0558471 | ||||||||
\(995\) | −1.03430 | −3.29544e−5 0 | ||||||||
\(996\) | 4209.83 | 0.133929 | ||||||||
\(997\) | 51820.9 | 1.64612 | 0.823062 | − | 0.567952i | \(-0.192264\pi\) | ||||
0.823062 | + | 0.567952i | \(0.192264\pi\) | |||||||
\(998\) | 41524.5 | 1.31707 | ||||||||
\(999\) | 1437.95 | 0.0455403 |
(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 | 966.4.a.q.1.4 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.q.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial |