Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2013,4,Mod(1,2013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2013, 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("2013.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2013 = 3 \cdot 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2013.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: | \(118.770844842\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 2013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.121017 | −0.0427859 | −0.0213930 | − | 0.999771i | \(-0.506810\pi\) | ||||
−0.0213930 | + | 0.999771i | \(0.506810\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −7.98535 | −0.998169 | ||||||||
\(5\) | 12.2818 | 1.09851 | 0.549257 | − | 0.835654i | \(-0.314911\pi\) | ||||
0.549257 | + | 0.835654i | \(0.314911\pi\) | |||||||
\(6\) | −0.363050 | −0.0247025 | ||||||||
\(7\) | 1.74252 | 0.0940875 | 0.0470437 | − | 0.998893i | \(-0.485020\pi\) | ||||
0.0470437 | + | 0.998893i | \(0.485020\pi\) | |||||||
\(8\) | 1.93450 | 0.0854935 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −1.48630 | −0.0470009 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −23.9561 | −0.576293 | ||||||||
\(13\) | −16.8573 | −0.359644 | −0.179822 | − | 0.983699i | \(-0.557552\pi\) | ||||
−0.179822 | + | 0.983699i | \(0.557552\pi\) | |||||||
\(14\) | −0.210875 | −0.00402562 | ||||||||
\(15\) | 36.8453 | 0.634227 | ||||||||
\(16\) | 63.6487 | 0.994511 | ||||||||
\(17\) | −69.8432 | −0.996439 | −0.498219 | − | 0.867051i | \(-0.666013\pi\) | ||||
−0.498219 | + | 0.867051i | \(0.666013\pi\) | |||||||
\(18\) | −1.08915 | −0.0142620 | ||||||||
\(19\) | 76.4490 | 0.923084 | 0.461542 | − | 0.887118i | \(-0.347296\pi\) | ||||
0.461542 | + | 0.887118i | \(0.347296\pi\) | |||||||
\(20\) | −98.0742 | −1.09650 | ||||||||
\(21\) | 5.22757 | 0.0543214 | ||||||||
\(22\) | −1.33119 | −0.0129004 | ||||||||
\(23\) | −164.226 | −1.48885 | −0.744426 | − | 0.667705i | \(-0.767277\pi\) | ||||
−0.744426 | + | 0.667705i | \(0.767277\pi\) | |||||||
\(24\) | 5.80349 | 0.0493597 | ||||||||
\(25\) | 25.8415 | 0.206732 | ||||||||
\(26\) | 2.04001 | 0.0153877 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −13.9147 | −0.0939152 | ||||||||
\(29\) | −191.049 | −1.22334 | −0.611670 | − | 0.791113i | \(-0.709502\pi\) | ||||
−0.611670 | + | 0.791113i | \(0.709502\pi\) | |||||||
\(30\) | −4.45890 | −0.0271360 | ||||||||
\(31\) | 219.115 | 1.26949 | 0.634745 | − | 0.772722i | \(-0.281105\pi\) | ||||
0.634745 | + | 0.772722i | \(0.281105\pi\) | |||||||
\(32\) | −23.1785 | −0.128045 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | 8.45220 | 0.0426335 | ||||||||
\(35\) | 21.4013 | 0.103356 | ||||||||
\(36\) | −71.8682 | −0.332723 | ||||||||
\(37\) | 142.029 | 0.631066 | 0.315533 | − | 0.948915i | \(-0.397817\pi\) | ||||
0.315533 | + | 0.948915i | \(0.397817\pi\) | |||||||
\(38\) | −9.25162 | −0.0394950 | ||||||||
\(39\) | −50.5718 | −0.207640 | ||||||||
\(40\) | 23.7590 | 0.0939158 | ||||||||
\(41\) | −332.946 | −1.26823 | −0.634115 | − | 0.773239i | \(-0.718635\pi\) | ||||
−0.634115 | + | 0.773239i | \(0.718635\pi\) | |||||||
\(42\) | −0.632624 | −0.00232419 | ||||||||
\(43\) | −154.235 | −0.546993 | −0.273496 | − | 0.961873i | \(-0.588180\pi\) | ||||
−0.273496 | + | 0.961873i | \(0.588180\pi\) | |||||||
\(44\) | −87.8389 | −0.300959 | ||||||||
\(45\) | 110.536 | 0.366171 | ||||||||
\(46\) | 19.8742 | 0.0637019 | ||||||||
\(47\) | −356.693 | −1.10700 | −0.553500 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553500 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(48\) | 190.946 | 0.574181 | ||||||||
\(49\) | −339.964 | −0.991148 | ||||||||
\(50\) | −3.12725 | −0.00884521 | ||||||||
\(51\) | −209.530 | −0.575294 | ||||||||
\(52\) | 134.611 | 0.358985 | ||||||||
\(53\) | 422.804 | 1.09579 | 0.547893 | − | 0.836548i | \(-0.315430\pi\) | ||||
0.547893 | + | 0.836548i | \(0.315430\pi\) | |||||||
\(54\) | −3.26745 | −0.00823415 | ||||||||
\(55\) | 135.099 | 0.331214 | ||||||||
\(56\) | 3.37091 | 0.00804387 | ||||||||
\(57\) | 229.347 | 0.532943 | ||||||||
\(58\) | 23.1201 | 0.0523417 | ||||||||
\(59\) | −75.2931 | −0.166141 | −0.0830706 | − | 0.996544i | \(-0.526473\pi\) | ||||
−0.0830706 | + | 0.996544i | \(0.526473\pi\) | |||||||
\(60\) | −294.222 | −0.633066 | ||||||||
\(61\) | 61.0000 | 0.128037 | ||||||||
\(62\) | −26.5166 | −0.0543163 | ||||||||
\(63\) | 15.6827 | 0.0313625 | ||||||||
\(64\) | −506.385 | −0.989033 | ||||||||
\(65\) | −207.037 | −0.395073 | ||||||||
\(66\) | −3.99356 | −0.00744807 | ||||||||
\(67\) | 193.281 | 0.352433 | 0.176217 | − | 0.984351i | \(-0.443614\pi\) | ||||
0.176217 | + | 0.984351i | \(0.443614\pi\) | |||||||
\(68\) | 557.722 | 0.994615 | ||||||||
\(69\) | −492.679 | −0.859589 | ||||||||
\(70\) | −2.58991 | −0.00442220 | ||||||||
\(71\) | −202.723 | −0.338856 | −0.169428 | − | 0.985543i | \(-0.554192\pi\) | ||||
−0.169428 | + | 0.985543i | \(0.554192\pi\) | |||||||
\(72\) | 17.4105 | 0.0284978 | ||||||||
\(73\) | 322.488 | 0.517046 | 0.258523 | − | 0.966005i | \(-0.416764\pi\) | ||||
0.258523 | + | 0.966005i | \(0.416764\pi\) | |||||||
\(74\) | −17.1879 | −0.0270007 | ||||||||
\(75\) | 77.5244 | 0.119357 | ||||||||
\(76\) | −610.472 | −0.921395 | ||||||||
\(77\) | 19.1678 | 0.0283684 | ||||||||
\(78\) | 6.12004 | 0.00888408 | ||||||||
\(79\) | −25.9330 | −0.0369327 | −0.0184664 | − | 0.999829i | \(-0.505878\pi\) | ||||
−0.0184664 | + | 0.999829i | \(0.505878\pi\) | |||||||
\(80\) | 781.718 | 1.09248 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 40.2920 | 0.0542623 | ||||||||
\(83\) | −309.786 | −0.409680 | −0.204840 | − | 0.978795i | \(-0.565667\pi\) | ||||
−0.204840 | + | 0.978795i | \(0.565667\pi\) | |||||||
\(84\) | −41.7440 | −0.0542220 | ||||||||
\(85\) | −857.797 | −1.09460 | ||||||||
\(86\) | 18.6651 | 0.0234036 | ||||||||
\(87\) | −573.146 | −0.706295 | ||||||||
\(88\) | 21.2795 | 0.0257773 | ||||||||
\(89\) | 53.0787 | 0.0632171 | 0.0316086 | − | 0.999500i | \(-0.489937\pi\) | ||||
0.0316086 | + | 0.999500i | \(0.489937\pi\) | |||||||
\(90\) | −13.3767 | −0.0156670 | ||||||||
\(91\) | −29.3742 | −0.0338380 | ||||||||
\(92\) | 1311.41 | 1.48613 | ||||||||
\(93\) | 657.345 | 0.732940 | ||||||||
\(94\) | 43.1658 | 0.0473640 | ||||||||
\(95\) | 938.928 | 1.01402 | ||||||||
\(96\) | −69.5356 | −0.0739266 | ||||||||
\(97\) | −232.952 | −0.243842 | −0.121921 | − | 0.992540i | \(-0.538906\pi\) | ||||
−0.121921 | + | 0.992540i | \(0.538906\pi\) | |||||||
\(98\) | 41.1413 | 0.0424071 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −206.353 | −0.206353 | ||||||||
\(101\) | −712.709 | −0.702150 | −0.351075 | − | 0.936347i | \(-0.614184\pi\) | ||||
−0.351075 | + | 0.936347i | \(0.614184\pi\) | |||||||
\(102\) | 25.3566 | 0.0246145 | ||||||||
\(103\) | −180.969 | −0.173120 | −0.0865601 | − | 0.996247i | \(-0.527587\pi\) | ||||
−0.0865601 | + | 0.996247i | \(0.527587\pi\) | |||||||
\(104\) | −32.6104 | −0.0307472 | ||||||||
\(105\) | 64.2038 | 0.0596728 | ||||||||
\(106\) | −51.1664 | −0.0468842 | ||||||||
\(107\) | −663.869 | −0.599800 | −0.299900 | − | 0.953971i | \(-0.596953\pi\) | ||||
−0.299900 | + | 0.953971i | \(0.596953\pi\) | |||||||
\(108\) | −215.605 | −0.192098 | ||||||||
\(109\) | −1069.26 | −0.939605 | −0.469802 | − | 0.882772i | \(-0.655675\pi\) | ||||
−0.469802 | + | 0.882772i | \(0.655675\pi\) | |||||||
\(110\) | −16.3493 | −0.0141713 | ||||||||
\(111\) | 426.087 | 0.364346 | ||||||||
\(112\) | 110.909 | 0.0935711 | ||||||||
\(113\) | 1118.63 | 0.931254 | 0.465627 | − | 0.884981i | \(-0.345829\pi\) | ||||
0.465627 | + | 0.884981i | \(0.345829\pi\) | |||||||
\(114\) | −27.7548 | −0.0228025 | ||||||||
\(115\) | −2016.99 | −1.63552 | ||||||||
\(116\) | 1525.59 | 1.22110 | ||||||||
\(117\) | −151.715 | −0.119881 | ||||||||
\(118\) | 9.11173 | 0.00710850 | ||||||||
\(119\) | −121.703 | −0.0937524 | ||||||||
\(120\) | 71.2770 | 0.0542223 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −7.38203 | −0.00547817 | ||||||||
\(123\) | −998.837 | −0.732213 | ||||||||
\(124\) | −1749.71 | −1.26717 | ||||||||
\(125\) | −1217.84 | −0.871416 | ||||||||
\(126\) | −1.89787 | −0.00134187 | ||||||||
\(127\) | 2177.43 | 1.52138 | 0.760690 | − | 0.649115i | \(-0.224861\pi\) | ||||
0.760690 | + | 0.649115i | \(0.224861\pi\) | |||||||
\(128\) | 246.709 | 0.170361 | ||||||||
\(129\) | −462.706 | −0.315806 | ||||||||
\(130\) | 25.0550 | 0.0169036 | ||||||||
\(131\) | −181.805 | −0.121255 | −0.0606275 | − | 0.998160i | \(-0.519310\pi\) | ||||
−0.0606275 | + | 0.998160i | \(0.519310\pi\) | |||||||
\(132\) | −263.517 | −0.173759 | ||||||||
\(133\) | 133.214 | 0.0868507 | ||||||||
\(134\) | −23.3903 | −0.0150792 | ||||||||
\(135\) | 331.607 | 0.211409 | ||||||||
\(136\) | −135.111 | −0.0851890 | ||||||||
\(137\) | 485.808 | 0.302959 | 0.151480 | − | 0.988460i | \(-0.451596\pi\) | ||||
0.151480 | + | 0.988460i | \(0.451596\pi\) | |||||||
\(138\) | 59.6225 | 0.0367783 | ||||||||
\(139\) | −2549.57 | −1.55577 | −0.777883 | − | 0.628409i | \(-0.783707\pi\) | ||||
−0.777883 | + | 0.628409i | \(0.783707\pi\) | |||||||
\(140\) | −170.897 | −0.103167 | ||||||||
\(141\) | −1070.08 | −0.639127 | ||||||||
\(142\) | 24.5329 | 0.0144983 | ||||||||
\(143\) | −185.430 | −0.108437 | ||||||||
\(144\) | 572.839 | 0.331504 | ||||||||
\(145\) | −2346.41 | −1.34385 | ||||||||
\(146\) | −39.0265 | −0.0221223 | ||||||||
\(147\) | −1019.89 | −0.572239 | ||||||||
\(148\) | −1134.15 | −0.629911 | ||||||||
\(149\) | 573.498 | 0.315321 | 0.157660 | − | 0.987493i | \(-0.449605\pi\) | ||||
0.157660 | + | 0.987493i | \(0.449605\pi\) | |||||||
\(150\) | −9.38176 | −0.00510678 | ||||||||
\(151\) | −707.152 | −0.381107 | −0.190554 | − | 0.981677i | \(-0.561028\pi\) | ||||
−0.190554 | + | 0.981677i | \(0.561028\pi\) | |||||||
\(152\) | 147.890 | 0.0789177 | ||||||||
\(153\) | −628.589 | −0.332146 | ||||||||
\(154\) | −2.31962 | −0.00121377 | ||||||||
\(155\) | 2691.11 | 1.39455 | ||||||||
\(156\) | 403.834 | 0.207260 | ||||||||
\(157\) | 615.464 | 0.312862 | 0.156431 | − | 0.987689i | \(-0.450001\pi\) | ||||
0.156431 | + | 0.987689i | \(0.450001\pi\) | |||||||
\(158\) | 3.13832 | 0.00158020 | ||||||||
\(159\) | 1268.41 | 0.632652 | ||||||||
\(160\) | −284.673 | −0.140659 | ||||||||
\(161\) | −286.169 | −0.140082 | ||||||||
\(162\) | −9.80236 | −0.00475399 | ||||||||
\(163\) | 1668.64 | 0.801827 | 0.400914 | − | 0.916116i | \(-0.368693\pi\) | ||||
0.400914 | + | 0.916116i | \(0.368693\pi\) | |||||||
\(164\) | 2658.69 | 1.26591 | ||||||||
\(165\) | 405.298 | 0.191227 | ||||||||
\(166\) | 37.4893 | 0.0175285 | ||||||||
\(167\) | 1173.49 | 0.543756 | 0.271878 | − | 0.962332i | \(-0.412355\pi\) | ||||
0.271878 | + | 0.962332i | \(0.412355\pi\) | |||||||
\(168\) | 10.1127 | 0.00464413 | ||||||||
\(169\) | −1912.83 | −0.870656 | ||||||||
\(170\) | 103.808 | 0.0468335 | ||||||||
\(171\) | 688.041 | 0.307695 | ||||||||
\(172\) | 1231.62 | 0.545991 | ||||||||
\(173\) | −2845.67 | −1.25059 | −0.625297 | − | 0.780387i | \(-0.715022\pi\) | ||||
−0.625297 | + | 0.780387i | \(0.715022\pi\) | |||||||
\(174\) | 69.3603 | 0.0302195 | ||||||||
\(175\) | 45.0294 | 0.0194509 | ||||||||
\(176\) | 700.136 | 0.299856 | ||||||||
\(177\) | −225.879 | −0.0959216 | ||||||||
\(178\) | −6.42341 | −0.00270480 | ||||||||
\(179\) | 77.7021 | 0.0324454 | 0.0162227 | − | 0.999868i | \(-0.494836\pi\) | ||||
0.0162227 | + | 0.999868i | \(0.494836\pi\) | |||||||
\(180\) | −882.667 | −0.365501 | ||||||||
\(181\) | 1525.39 | 0.626416 | 0.313208 | − | 0.949685i | \(-0.398596\pi\) | ||||
0.313208 | + | 0.949685i | \(0.398596\pi\) | |||||||
\(182\) | 3.55477 | 0.00144779 | ||||||||
\(183\) | 183.000 | 0.0739221 | ||||||||
\(184\) | −317.696 | −0.127287 | ||||||||
\(185\) | 1744.37 | 0.693235 | ||||||||
\(186\) | −79.5498 | −0.0313595 | ||||||||
\(187\) | −768.275 | −0.300438 | ||||||||
\(188\) | 2848.32 | 1.10497 | ||||||||
\(189\) | 47.0482 | 0.0181071 | ||||||||
\(190\) | −113.626 | −0.0433858 | ||||||||
\(191\) | −3810.44 | −1.44353 | −0.721764 | − | 0.692139i | \(-0.756669\pi\) | ||||
−0.721764 | + | 0.692139i | \(0.756669\pi\) | |||||||
\(192\) | −1519.15 | −0.571018 | ||||||||
\(193\) | −979.479 | −0.365308 | −0.182654 | − | 0.983177i | \(-0.558469\pi\) | ||||
−0.182654 | + | 0.983177i | \(0.558469\pi\) | |||||||
\(194\) | 28.1911 | 0.0104330 | ||||||||
\(195\) | −621.111 | −0.228096 | ||||||||
\(196\) | 2714.73 | 0.989333 | ||||||||
\(197\) | −3359.40 | −1.21496 | −0.607481 | − | 0.794334i | \(-0.707820\pi\) | ||||
−0.607481 | + | 0.794334i | \(0.707820\pi\) | |||||||
\(198\) | −11.9807 | −0.00430015 | ||||||||
\(199\) | 1736.17 | 0.618463 | 0.309232 | − | 0.950987i | \(-0.399928\pi\) | ||||
0.309232 | + | 0.950987i | \(0.399928\pi\) | |||||||
\(200\) | 49.9903 | 0.0176742 | ||||||||
\(201\) | 579.843 | 0.203478 | ||||||||
\(202\) | 86.2497 | 0.0300421 | ||||||||
\(203\) | −332.907 | −0.115101 | ||||||||
\(204\) | 1673.17 | 0.574241 | ||||||||
\(205\) | −4089.16 | −1.39317 | ||||||||
\(206\) | 21.9003 | 0.00740710 | ||||||||
\(207\) | −1478.04 | −0.496284 | ||||||||
\(208\) | −1072.94 | −0.357670 | ||||||||
\(209\) | 840.939 | 0.278320 | ||||||||
\(210\) | −7.76974 | −0.00255316 | ||||||||
\(211\) | 3040.81 | 0.992122 | 0.496061 | − | 0.868288i | \(-0.334779\pi\) | ||||
0.496061 | + | 0.868288i | \(0.334779\pi\) | |||||||
\(212\) | −3376.24 | −1.09378 | ||||||||
\(213\) | −608.168 | −0.195639 | ||||||||
\(214\) | 80.3393 | 0.0256630 | ||||||||
\(215\) | −1894.28 | −0.600879 | ||||||||
\(216\) | 52.2314 | 0.0164532 | ||||||||
\(217\) | 381.813 | 0.119443 | ||||||||
\(218\) | 129.399 | 0.0402019 | ||||||||
\(219\) | 967.464 | 0.298517 | ||||||||
\(220\) | −1078.82 | −0.330608 | ||||||||
\(221\) | 1177.37 | 0.358363 | ||||||||
\(222\) | −51.5637 | −0.0155889 | ||||||||
\(223\) | −2735.36 | −0.821403 | −0.410702 | − | 0.911770i | \(-0.634716\pi\) | ||||
−0.410702 | + | 0.911770i | \(0.634716\pi\) | |||||||
\(224\) | −40.3892 | −0.0120474 | ||||||||
\(225\) | 232.573 | 0.0689106 | ||||||||
\(226\) | −135.373 | −0.0398445 | ||||||||
\(227\) | 3477.01 | 1.01664 | 0.508320 | − | 0.861168i | \(-0.330267\pi\) | ||||
0.508320 | + | 0.861168i | \(0.330267\pi\) | |||||||
\(228\) | −1831.42 | −0.531967 | ||||||||
\(229\) | −5465.48 | −1.57716 | −0.788579 | − | 0.614933i | \(-0.789183\pi\) | ||||
−0.788579 | + | 0.614933i | \(0.789183\pi\) | |||||||
\(230\) | 244.090 | 0.0699774 | ||||||||
\(231\) | 57.5033 | 0.0163785 | ||||||||
\(232\) | −369.583 | −0.104588 | ||||||||
\(233\) | 1431.51 | 0.402495 | 0.201247 | − | 0.979540i | \(-0.435501\pi\) | ||||
0.201247 | + | 0.979540i | \(0.435501\pi\) | |||||||
\(234\) | 18.3601 | 0.00512923 | ||||||||
\(235\) | −4380.81 | −1.21605 | ||||||||
\(236\) | 601.242 | 0.165837 | ||||||||
\(237\) | −77.7989 | −0.0213231 | ||||||||
\(238\) | 14.7282 | 0.00401128 | ||||||||
\(239\) | −4286.19 | −1.16004 | −0.580022 | − | 0.814601i | \(-0.696956\pi\) | ||||
−0.580022 | + | 0.814601i | \(0.696956\pi\) | |||||||
\(240\) | 2345.15 | 0.630746 | ||||||||
\(241\) | −4245.65 | −1.13480 | −0.567399 | − | 0.823443i | \(-0.692050\pi\) | ||||
−0.567399 | + | 0.823443i | \(0.692050\pi\) | |||||||
\(242\) | −14.6430 | −0.00388963 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −487.107 | −0.127802 | ||||||||
\(245\) | −4175.35 | −1.08879 | ||||||||
\(246\) | 120.876 | 0.0313284 | ||||||||
\(247\) | −1288.72 | −0.331981 | ||||||||
\(248\) | 423.877 | 0.108533 | ||||||||
\(249\) | −929.358 | −0.236529 | ||||||||
\(250\) | 147.379 | 0.0372843 | ||||||||
\(251\) | −3184.94 | −0.800922 | −0.400461 | − | 0.916314i | \(-0.631150\pi\) | ||||
−0.400461 | + | 0.916314i | \(0.631150\pi\) | |||||||
\(252\) | −125.232 | −0.0313051 | ||||||||
\(253\) | −1806.49 | −0.448906 | ||||||||
\(254\) | −263.505 | −0.0650936 | ||||||||
\(255\) | −2573.39 | −0.631968 | ||||||||
\(256\) | 4021.22 | 0.981744 | ||||||||
\(257\) | −5121.96 | −1.24319 | −0.621593 | − | 0.783340i | \(-0.713514\pi\) | ||||
−0.621593 | + | 0.783340i | \(0.713514\pi\) | |||||||
\(258\) | 55.9952 | 0.0135121 | ||||||||
\(259\) | 247.489 | 0.0593754 | ||||||||
\(260\) | 1653.26 | 0.394350 | ||||||||
\(261\) | −1719.44 | −0.407780 | ||||||||
\(262\) | 22.0015 | 0.00518800 | ||||||||
\(263\) | −2636.72 | −0.618203 | −0.309102 | − | 0.951029i | \(-0.600028\pi\) | ||||
−0.309102 | + | 0.951029i | \(0.600028\pi\) | |||||||
\(264\) | 63.8384 | 0.0148825 | ||||||||
\(265\) | 5192.78 | 1.20374 | ||||||||
\(266\) | −16.1212 | −0.00371599 | ||||||||
\(267\) | 159.236 | 0.0364984 | ||||||||
\(268\) | −1543.42 | −0.351788 | ||||||||
\(269\) | 864.055 | 0.195845 | 0.0979226 | − | 0.995194i | \(-0.468780\pi\) | ||||
0.0979226 | + | 0.995194i | \(0.468780\pi\) | |||||||
\(270\) | −40.1301 | −0.00904533 | ||||||||
\(271\) | 3207.44 | 0.718960 | 0.359480 | − | 0.933153i | \(-0.382954\pi\) | ||||
0.359480 | + | 0.933153i | \(0.382954\pi\) | |||||||
\(272\) | −4445.43 | −0.990970 | ||||||||
\(273\) | −88.1226 | −0.0195364 | ||||||||
\(274\) | −58.7910 | −0.0129624 | ||||||||
\(275\) | 284.256 | 0.0623320 | ||||||||
\(276\) | 3934.22 | 0.858015 | ||||||||
\(277\) | −4263.22 | −0.924736 | −0.462368 | − | 0.886688i | \(-0.653000\pi\) | ||||
−0.462368 | + | 0.886688i | \(0.653000\pi\) | |||||||
\(278\) | 308.541 | 0.0665649 | ||||||||
\(279\) | 1972.03 | 0.423163 | ||||||||
\(280\) | 41.4007 | 0.00883630 | ||||||||
\(281\) | −2447.29 | −0.519548 | −0.259774 | − | 0.965669i | \(-0.583648\pi\) | ||||
−0.259774 | + | 0.965669i | \(0.583648\pi\) | |||||||
\(282\) | 129.497 | 0.0273456 | ||||||||
\(283\) | 2701.84 | 0.567519 | 0.283759 | − | 0.958896i | \(-0.408418\pi\) | ||||
0.283759 | + | 0.958896i | \(0.408418\pi\) | |||||||
\(284\) | 1618.81 | 0.338236 | ||||||||
\(285\) | 2816.78 | 0.585445 | ||||||||
\(286\) | 22.4402 | 0.00463956 | ||||||||
\(287\) | −580.166 | −0.119324 | ||||||||
\(288\) | −208.607 | −0.0426815 | ||||||||
\(289\) | −34.9317 | −0.00711005 | ||||||||
\(290\) | 283.955 | 0.0574980 | ||||||||
\(291\) | −698.857 | −0.140783 | ||||||||
\(292\) | −2575.18 | −0.516100 | ||||||||
\(293\) | −1603.24 | −0.319666 | −0.159833 | − | 0.987144i | \(-0.551096\pi\) | ||||
−0.159833 | + | 0.987144i | \(0.551096\pi\) | |||||||
\(294\) | 123.424 | 0.0244838 | ||||||||
\(295\) | −924.731 | −0.182508 | ||||||||
\(296\) | 274.755 | 0.0539520 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −69.4029 | −0.0134913 | ||||||||
\(299\) | 2768.41 | 0.535456 | ||||||||
\(300\) | −619.060 | −0.119138 | ||||||||
\(301\) | −268.759 | −0.0514651 | ||||||||
\(302\) | 85.5773 | 0.0163060 | ||||||||
\(303\) | −2138.13 | −0.405387 | ||||||||
\(304\) | 4865.88 | 0.918018 | ||||||||
\(305\) | 749.187 | 0.140650 | ||||||||
\(306\) | 76.0698 | 0.0142112 | ||||||||
\(307\) | −2376.70 | −0.441842 | −0.220921 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220921 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(308\) | −153.061 | −0.0283165 | ||||||||
\(309\) | −542.906 | −0.0999510 | ||||||||
\(310\) | −325.670 | −0.0596672 | ||||||||
\(311\) | 2918.67 | 0.532163 | 0.266082 | − | 0.963951i | \(-0.414271\pi\) | ||||
0.266082 | + | 0.963951i | \(0.414271\pi\) | |||||||
\(312\) | −97.8311 | −0.0177519 | ||||||||
\(313\) | 3502.94 | 0.632582 | 0.316291 | − | 0.948662i | \(-0.397562\pi\) | ||||
0.316291 | + | 0.948662i | \(0.397562\pi\) | |||||||
\(314\) | −74.4815 | −0.0133861 | ||||||||
\(315\) | 192.611 | 0.0344521 | ||||||||
\(316\) | 207.084 | 0.0368651 | ||||||||
\(317\) | −10633.6 | −1.88405 | −0.942027 | − | 0.335538i | \(-0.891082\pi\) | ||||
−0.942027 | + | 0.335538i | \(0.891082\pi\) | |||||||
\(318\) | −153.499 | −0.0270686 | ||||||||
\(319\) | −2101.53 | −0.368851 | ||||||||
\(320\) | −6219.29 | −1.08647 | ||||||||
\(321\) | −1991.61 | −0.346295 | ||||||||
\(322\) | 34.6312 | 0.00599355 | ||||||||
\(323\) | −5339.44 | −0.919797 | ||||||||
\(324\) | −646.814 | −0.110908 | ||||||||
\(325\) | −435.617 | −0.0743498 | ||||||||
\(326\) | −201.933 | −0.0343069 | ||||||||
\(327\) | −3207.79 | −0.542481 | ||||||||
\(328\) | −644.083 | −0.108425 | ||||||||
\(329\) | −621.546 | −0.104155 | ||||||||
\(330\) | −49.0479 | −0.00818181 | ||||||||
\(331\) | −3504.69 | −0.581979 | −0.290990 | − | 0.956726i | \(-0.593984\pi\) | ||||
−0.290990 | + | 0.956726i | \(0.593984\pi\) | |||||||
\(332\) | 2473.75 | 0.408930 | ||||||||
\(333\) | 1278.26 | 0.210355 | ||||||||
\(334\) | −142.012 | −0.0232651 | ||||||||
\(335\) | 2373.83 | 0.387153 | ||||||||
\(336\) | 332.728 | 0.0540233 | ||||||||
\(337\) | −9204.75 | −1.48788 | −0.743938 | − | 0.668248i | \(-0.767044\pi\) | ||||
−0.743938 | + | 0.668248i | \(0.767044\pi\) | |||||||
\(338\) | 231.485 | 0.0372518 | ||||||||
\(339\) | 3355.89 | 0.537660 | ||||||||
\(340\) | 6849.81 | 1.09260 | ||||||||
\(341\) | 2410.26 | 0.382766 | ||||||||
\(342\) | −83.2645 | −0.0131650 | ||||||||
\(343\) | −1190.08 | −0.187342 | ||||||||
\(344\) | −298.368 | −0.0467643 | ||||||||
\(345\) | −6050.97 | −0.944270 | ||||||||
\(346\) | 344.375 | 0.0535078 | ||||||||
\(347\) | 9750.22 | 1.50841 | 0.754206 | − | 0.656638i | \(-0.228022\pi\) | ||||
0.754206 | + | 0.656638i | \(0.228022\pi\) | |||||||
\(348\) | 4576.77 | 0.705002 | ||||||||
\(349\) | 6118.70 | 0.938472 | 0.469236 | − | 0.883073i | \(-0.344529\pi\) | ||||
0.469236 | + | 0.883073i | \(0.344529\pi\) | |||||||
\(350\) | −5.44931 | −0.000832223 0 | ||||||||
\(351\) | −455.146 | −0.0692135 | ||||||||
\(352\) | −254.964 | −0.0386069 | ||||||||
\(353\) | 722.414 | 0.108924 | 0.0544621 | − | 0.998516i | \(-0.482656\pi\) | ||||
0.0544621 | + | 0.998516i | \(0.482656\pi\) | |||||||
\(354\) | 27.3352 | 0.00410409 | ||||||||
\(355\) | −2489.79 | −0.372238 | ||||||||
\(356\) | −423.852 | −0.0631014 | ||||||||
\(357\) | −365.110 | −0.0541280 | ||||||||
\(358\) | −9.40326 | −0.00138821 | ||||||||
\(359\) | −7019.48 | −1.03196 | −0.515980 | − | 0.856600i | \(-0.672572\pi\) | ||||
−0.515980 | + | 0.856600i | \(0.672572\pi\) | |||||||
\(360\) | 213.831 | 0.0313053 | ||||||||
\(361\) | −1014.55 | −0.147915 | ||||||||
\(362\) | −184.598 | −0.0268018 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 234.564 | 0.0337760 | ||||||||
\(365\) | 3960.72 | 0.567982 | ||||||||
\(366\) | −22.1461 | −0.00316283 | ||||||||
\(367\) | 4668.34 | 0.663993 | 0.331996 | − | 0.943281i | \(-0.392278\pi\) | ||||
0.331996 | + | 0.943281i | \(0.392278\pi\) | |||||||
\(368\) | −10452.8 | −1.48068 | ||||||||
\(369\) | −2996.51 | −0.422743 | ||||||||
\(370\) | −211.098 | −0.0296607 | ||||||||
\(371\) | 736.747 | 0.103100 | ||||||||
\(372\) | −5249.13 | −0.731599 | ||||||||
\(373\) | 4256.85 | 0.590915 | 0.295458 | − | 0.955356i | \(-0.404528\pi\) | ||||
0.295458 | + | 0.955356i | \(0.404528\pi\) | |||||||
\(374\) | 92.9742 | 0.0128545 | ||||||||
\(375\) | −3653.52 | −0.503112 | ||||||||
\(376\) | −690.021 | −0.0946413 | ||||||||
\(377\) | 3220.56 | 0.439966 | ||||||||
\(378\) | −5.69362 | −0.000774731 0 | ||||||||
\(379\) | 8557.53 | 1.15982 | 0.579909 | − | 0.814681i | \(-0.303088\pi\) | ||||
0.579909 | + | 0.814681i | \(0.303088\pi\) | |||||||
\(380\) | −7497.67 | −1.01216 | ||||||||
\(381\) | 6532.28 | 0.878369 | ||||||||
\(382\) | 461.128 | 0.0617627 | ||||||||
\(383\) | −5425.52 | −0.723841 | −0.361920 | − | 0.932209i | \(-0.617879\pi\) | ||||
−0.361920 | + | 0.932209i | \(0.617879\pi\) | |||||||
\(384\) | 740.128 | 0.0983581 | ||||||||
\(385\) | 235.414 | 0.0311631 | ||||||||
\(386\) | 118.533 | 0.0156300 | ||||||||
\(387\) | −1388.12 | −0.182331 | ||||||||
\(388\) | 1860.21 | 0.243396 | ||||||||
\(389\) | 10568.9 | 1.37754 | 0.688772 | − | 0.724978i | \(-0.258150\pi\) | ||||
0.688772 | + | 0.724978i | \(0.258150\pi\) | |||||||
\(390\) | 75.1649 | 0.00975928 | ||||||||
\(391\) | 11470.1 | 1.48355 | ||||||||
\(392\) | −657.659 | −0.0847367 | ||||||||
\(393\) | −545.416 | −0.0700066 | ||||||||
\(394\) | 406.544 | 0.0519833 | ||||||||
\(395\) | −318.502 | −0.0405711 | ||||||||
\(396\) | −790.550 | −0.100320 | ||||||||
\(397\) | −5550.64 | −0.701709 | −0.350855 | − | 0.936430i | \(-0.614109\pi\) | ||||
−0.350855 | + | 0.936430i | \(0.614109\pi\) | |||||||
\(398\) | −210.106 | −0.0264615 | ||||||||
\(399\) | 399.643 | 0.0501433 | ||||||||
\(400\) | 1644.78 | 0.205597 | ||||||||
\(401\) | 7943.46 | 0.989220 | 0.494610 | − | 0.869115i | \(-0.335311\pi\) | ||||
0.494610 | + | 0.869115i | \(0.335311\pi\) | |||||||
\(402\) | −70.1708 | −0.00870597 | ||||||||
\(403\) | −3693.68 | −0.456564 | ||||||||
\(404\) | 5691.23 | 0.700865 | ||||||||
\(405\) | 994.822 | 0.122057 | ||||||||
\(406\) | 40.2873 | 0.00492470 | ||||||||
\(407\) | 1562.32 | 0.190274 | ||||||||
\(408\) | −405.334 | −0.0491839 | ||||||||
\(409\) | −7808.41 | −0.944012 | −0.472006 | − | 0.881595i | \(-0.656470\pi\) | ||||
−0.472006 | + | 0.881595i | \(0.656470\pi\) | |||||||
\(410\) | 494.857 | 0.0596079 | ||||||||
\(411\) | 1457.43 | 0.174914 | ||||||||
\(412\) | 1445.10 | 0.172803 | ||||||||
\(413\) | −131.200 | −0.0156318 | ||||||||
\(414\) | 178.868 | 0.0212340 | ||||||||
\(415\) | −3804.72 | −0.450039 | ||||||||
\(416\) | 390.727 | 0.0460504 | ||||||||
\(417\) | −7648.71 | −0.898222 | ||||||||
\(418\) | −101.768 | −0.0119082 | ||||||||
\(419\) | −8549.04 | −0.996773 | −0.498386 | − | 0.866955i | \(-0.666074\pi\) | ||||
−0.498386 | + | 0.866955i | \(0.666074\pi\) | |||||||
\(420\) | −512.690 | −0.0595636 | ||||||||
\(421\) | −3141.87 | −0.363719 | −0.181859 | − | 0.983325i | \(-0.558212\pi\) | ||||
−0.181859 | + | 0.983325i | \(0.558212\pi\) | |||||||
\(422\) | −367.989 | −0.0424488 | ||||||||
\(423\) | −3210.24 | −0.369000 | ||||||||
\(424\) | 817.914 | 0.0936826 | ||||||||
\(425\) | −1804.85 | −0.205996 | ||||||||
\(426\) | 73.5986 | 0.00837057 | ||||||||
\(427\) | 106.294 | 0.0120467 | ||||||||
\(428\) | 5301.23 | 0.598702 | ||||||||
\(429\) | −556.290 | −0.0626059 | ||||||||
\(430\) | 229.240 | 0.0257091 | ||||||||
\(431\) | 8677.03 | 0.969740 | 0.484870 | − | 0.874586i | \(-0.338867\pi\) | ||||
0.484870 | + | 0.874586i | \(0.338867\pi\) | |||||||
\(432\) | 1718.52 | 0.191394 | ||||||||
\(433\) | −9027.50 | −1.00193 | −0.500963 | − | 0.865469i | \(-0.667021\pi\) | ||||
−0.500963 | + | 0.865469i | \(0.667021\pi\) | |||||||
\(434\) | −46.2058 | −0.00511048 | ||||||||
\(435\) | −7039.24 | −0.775875 | ||||||||
\(436\) | 8538.45 | 0.937885 | ||||||||
\(437\) | −12555.0 | −1.37434 | ||||||||
\(438\) | −117.079 | −0.0127723 | ||||||||
\(439\) | −4237.20 | −0.460661 | −0.230331 | − | 0.973112i | \(-0.573981\pi\) | ||||
−0.230331 | + | 0.973112i | \(0.573981\pi\) | |||||||
\(440\) | 261.349 | 0.0283167 | ||||||||
\(441\) | −3059.67 | −0.330383 | ||||||||
\(442\) | −142.481 | −0.0153329 | ||||||||
\(443\) | 5447.67 | 0.584258 | 0.292129 | − | 0.956379i | \(-0.405636\pi\) | ||||
0.292129 | + | 0.956379i | \(0.405636\pi\) | |||||||
\(444\) | −3402.46 | −0.363679 | ||||||||
\(445\) | 651.899 | 0.0694449 | ||||||||
\(446\) | 331.024 | 0.0351445 | ||||||||
\(447\) | 1720.49 | 0.182050 | ||||||||
\(448\) | −882.388 | −0.0930556 | ||||||||
\(449\) | −1337.51 | −0.140581 | −0.0702904 | − | 0.997527i | \(-0.522393\pi\) | ||||
−0.0702904 | + | 0.997527i | \(0.522393\pi\) | |||||||
\(450\) | −28.1453 | −0.00294840 | ||||||||
\(451\) | −3662.40 | −0.382386 | ||||||||
\(452\) | −8932.64 | −0.929549 | ||||||||
\(453\) | −2121.46 | −0.220032 | ||||||||
\(454\) | −420.777 | −0.0434979 | ||||||||
\(455\) | −360.767 | −0.0371715 | ||||||||
\(456\) | 443.671 | 0.0455632 | ||||||||
\(457\) | −14032.4 | −1.43635 | −0.718173 | − | 0.695865i | \(-0.755021\pi\) | ||||
−0.718173 | + | 0.695865i | \(0.755021\pi\) | |||||||
\(458\) | 661.415 | 0.0674801 | ||||||||
\(459\) | −1885.77 | −0.191765 | ||||||||
\(460\) | 16106.4 | 1.63253 | ||||||||
\(461\) | −4143.24 | −0.418589 | −0.209295 | − | 0.977853i | \(-0.567117\pi\) | ||||
−0.209295 | + | 0.977853i | \(0.567117\pi\) | |||||||
\(462\) | −6.95887 | −0.000700770 0 | ||||||||
\(463\) | −890.749 | −0.0894095 | −0.0447048 | − | 0.999000i | \(-0.514235\pi\) | ||||
−0.0447048 | + | 0.999000i | \(0.514235\pi\) | |||||||
\(464\) | −12160.0 | −1.21662 | ||||||||
\(465\) | 8073.34 | 0.805145 | ||||||||
\(466\) | −173.237 | −0.0172211 | ||||||||
\(467\) | 6408.35 | 0.634996 | 0.317498 | − | 0.948259i | \(-0.397157\pi\) | ||||
0.317498 | + | 0.948259i | \(0.397157\pi\) | |||||||
\(468\) | 1211.50 | 0.119662 | ||||||||
\(469\) | 336.797 | 0.0331596 | ||||||||
\(470\) | 530.152 | 0.0520300 | ||||||||
\(471\) | 1846.39 | 0.180631 | ||||||||
\(472\) | −145.654 | −0.0142040 | ||||||||
\(473\) | −1696.59 | −0.164924 | ||||||||
\(474\) | 9.41497 | 0.000912329 0 | ||||||||
\(475\) | 1975.55 | 0.190831 | ||||||||
\(476\) | 971.845 | 0.0935808 | ||||||||
\(477\) | 3805.24 | 0.365262 | ||||||||
\(478\) | 518.701 | 0.0496335 | ||||||||
\(479\) | −3289.13 | −0.313745 | −0.156873 | − | 0.987619i | \(-0.550141\pi\) | ||||
−0.156873 | + | 0.987619i | \(0.550141\pi\) | |||||||
\(480\) | −854.019 | −0.0812093 | ||||||||
\(481\) | −2394.22 | −0.226959 | ||||||||
\(482\) | 513.795 | 0.0485533 | ||||||||
\(483\) | −858.506 | −0.0808765 | ||||||||
\(484\) | −966.228 | −0.0907427 | ||||||||
\(485\) | −2861.06 | −0.267864 | ||||||||
\(486\) | −29.4071 | −0.00274472 | ||||||||
\(487\) | −2031.13 | −0.188992 | −0.0944960 | − | 0.995525i | \(-0.530124\pi\) | ||||
−0.0944960 | + | 0.995525i | \(0.530124\pi\) | |||||||
\(488\) | 118.004 | 0.0109463 | ||||||||
\(489\) | 5005.91 | 0.462935 | ||||||||
\(490\) | 505.288 | 0.0465848 | ||||||||
\(491\) | −2397.66 | −0.220377 | −0.110188 | − | 0.993911i | \(-0.535145\pi\) | ||||
−0.110188 | + | 0.993911i | \(0.535145\pi\) | |||||||
\(492\) | 7976.07 | 0.730872 | ||||||||
\(493\) | 13343.4 | 1.21898 | ||||||||
\(494\) | 155.957 | 0.0142041 | ||||||||
\(495\) | 1215.89 | 0.110405 | ||||||||
\(496\) | 13946.4 | 1.26252 | ||||||||
\(497\) | −353.249 | −0.0318821 | ||||||||
\(498\) | 112.468 | 0.0101201 | ||||||||
\(499\) | 5555.67 | 0.498409 | 0.249205 | − | 0.968451i | \(-0.419831\pi\) | ||||
0.249205 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(500\) | 9724.89 | 0.869821 | ||||||||
\(501\) | 3520.47 | 0.313938 | ||||||||
\(502\) | 385.431 | 0.0342682 | ||||||||
\(503\) | −10945.3 | −0.970231 | −0.485116 | − | 0.874450i | \(-0.661223\pi\) | ||||
−0.485116 | + | 0.874450i | \(0.661223\pi\) | |||||||
\(504\) | 30.3382 | 0.00268129 | ||||||||
\(505\) | −8753.31 | −0.771321 | ||||||||
\(506\) | 218.616 | 0.0192068 | ||||||||
\(507\) | −5738.50 | −0.502674 | ||||||||
\(508\) | −17387.5 | −1.51860 | ||||||||
\(509\) | 22545.5 | 1.96328 | 0.981641 | − | 0.190739i | \(-0.0610884\pi\) | ||||
0.981641 | + | 0.190739i | \(0.0610884\pi\) | |||||||
\(510\) | 311.423 | 0.0270393 | ||||||||
\(511\) | 561.943 | 0.0486476 | ||||||||
\(512\) | −2460.31 | −0.212366 | ||||||||
\(513\) | 2064.12 | 0.177648 | ||||||||
\(514\) | 619.843 | 0.0531909 | ||||||||
\(515\) | −2222.61 | −0.190175 | ||||||||
\(516\) | 3694.87 | 0.315228 | ||||||||
\(517\) | −3923.62 | −0.333773 | ||||||||
\(518\) | −29.9504 | −0.00254043 | ||||||||
\(519\) | −8537.02 | −0.722030 | ||||||||
\(520\) | −400.512 | −0.0337762 | ||||||||
\(521\) | −16194.6 | −1.36180 | −0.680901 | − | 0.732376i | \(-0.738411\pi\) | ||||
−0.680901 | + | 0.732376i | \(0.738411\pi\) | |||||||
\(522\) | 208.081 | 0.0174472 | ||||||||
\(523\) | −19813.0 | −1.65653 | −0.828264 | − | 0.560338i | \(-0.810671\pi\) | ||||
−0.828264 | + | 0.560338i | \(0.810671\pi\) | |||||||
\(524\) | 1451.78 | 0.121033 | ||||||||
\(525\) | 135.088 | 0.0112300 | ||||||||
\(526\) | 319.088 | 0.0264504 | ||||||||
\(527\) | −15303.7 | −1.26497 | ||||||||
\(528\) | 2100.41 | 0.173122 | ||||||||
\(529\) | 14803.3 | 1.21668 | ||||||||
\(530\) | −628.414 | −0.0515029 | ||||||||
\(531\) | −677.638 | −0.0553804 | ||||||||
\(532\) | −1063.76 | −0.0866917 | ||||||||
\(533\) | 5612.56 | 0.456111 | ||||||||
\(534\) | −19.2702 | −0.00156162 | ||||||||
\(535\) | −8153.47 | −0.658889 | ||||||||
\(536\) | 373.902 | 0.0301308 | ||||||||
\(537\) | 233.106 | 0.0187324 | ||||||||
\(538\) | −104.565 | −0.00837942 | ||||||||
\(539\) | −3739.60 | −0.298842 | ||||||||
\(540\) | −2648.00 | −0.211022 | ||||||||
\(541\) | 8648.83 | 0.687324 | 0.343662 | − | 0.939093i | \(-0.388333\pi\) | ||||
0.343662 | + | 0.939093i | \(0.388333\pi\) | |||||||
\(542\) | −388.154 | −0.0307613 | ||||||||
\(543\) | 4576.16 | 0.361661 | ||||||||
\(544\) | 1618.86 | 0.127589 | ||||||||
\(545\) | −13132.4 | −1.03217 | ||||||||
\(546\) | 10.6643 | 0.000835881 0 | ||||||||
\(547\) | 3905.53 | 0.305281 | 0.152640 | − | 0.988282i | \(-0.451222\pi\) | ||||
0.152640 | + | 0.988282i | \(0.451222\pi\) | |||||||
\(548\) | −3879.35 | −0.302405 | ||||||||
\(549\) | 549.000 | 0.0426790 | ||||||||
\(550\) | −34.3998 | −0.00266693 | ||||||||
\(551\) | −14605.5 | −1.12925 | ||||||||
\(552\) | −953.087 | −0.0734893 | ||||||||
\(553\) | −45.1888 | −0.00347491 | ||||||||
\(554\) | 515.921 | 0.0395657 | ||||||||
\(555\) | 5233.10 | 0.400239 | ||||||||
\(556\) | 20359.2 | 1.55292 | ||||||||
\(557\) | 12168.0 | 0.925629 | 0.462814 | − | 0.886455i | \(-0.346840\pi\) | ||||
0.462814 | + | 0.886455i | \(0.346840\pi\) | |||||||
\(558\) | −238.649 | −0.0181054 | ||||||||
\(559\) | 2599.99 | 0.196722 | ||||||||
\(560\) | 1362.16 | 0.102789 | ||||||||
\(561\) | −2304.82 | −0.173458 | ||||||||
\(562\) | 296.163 | 0.0222293 | ||||||||
\(563\) | −3022.51 | −0.226259 | −0.113129 | − | 0.993580i | \(-0.536087\pi\) | ||||
−0.113129 | + | 0.993580i | \(0.536087\pi\) | |||||||
\(564\) | 8544.96 | 0.637957 | ||||||||
\(565\) | 13738.7 | 1.02300 | ||||||||
\(566\) | −326.968 | −0.0242818 | ||||||||
\(567\) | 141.144 | 0.0104542 | ||||||||
\(568\) | −392.167 | −0.0289700 | ||||||||
\(569\) | −3762.70 | −0.277224 | −0.138612 | − | 0.990347i | \(-0.544264\pi\) | ||||
−0.138612 | + | 0.990347i | \(0.544264\pi\) | |||||||
\(570\) | −340.878 | −0.0250488 | ||||||||
\(571\) | 12185.9 | 0.893108 | 0.446554 | − | 0.894757i | \(-0.352651\pi\) | ||||
0.446554 | + | 0.894757i | \(0.352651\pi\) | |||||||
\(572\) | 1480.72 | 0.108238 | ||||||||
\(573\) | −11431.3 | −0.833422 | ||||||||
\(574\) | 70.2099 | 0.00510541 | ||||||||
\(575\) | −4243.85 | −0.307793 | ||||||||
\(576\) | −4557.46 | −0.329678 | ||||||||
\(577\) | 13987.7 | 1.00921 | 0.504606 | − | 0.863350i | \(-0.331638\pi\) | ||||
0.504606 | + | 0.863350i | \(0.331638\pi\) | |||||||
\(578\) | 4.22732 | 0.000304210 0 | ||||||||
\(579\) | −2938.44 | −0.210911 | ||||||||
\(580\) | 18736.9 | 1.34139 | ||||||||
\(581\) | −539.810 | −0.0385458 | ||||||||
\(582\) | 84.5734 | 0.00602351 | ||||||||
\(583\) | 4650.85 | 0.330392 | ||||||||
\(584\) | 623.852 | 0.0442041 | ||||||||
\(585\) | −1863.33 | −0.131691 | ||||||||
\(586\) | 194.019 | 0.0136772 | ||||||||
\(587\) | −11707.7 | −0.823214 | −0.411607 | − | 0.911361i | \(-0.635032\pi\) | ||||
−0.411607 | + | 0.911361i | \(0.635032\pi\) | |||||||
\(588\) | 8144.19 | 0.571192 | ||||||||
\(589\) | 16751.1 | 1.17185 | ||||||||
\(590\) | 111.908 | 0.00780878 | ||||||||
\(591\) | −10078.2 | −0.701459 | ||||||||
\(592\) | 9039.97 | 0.627602 | ||||||||
\(593\) | −17451.4 | −1.20851 | −0.604253 | − | 0.796793i | \(-0.706528\pi\) | ||||
−0.604253 | + | 0.796793i | \(0.706528\pi\) | |||||||
\(594\) | −35.9420 | −0.00248269 | ||||||||
\(595\) | −1494.73 | −0.102988 | ||||||||
\(596\) | −4579.58 | −0.314743 | ||||||||
\(597\) | 5208.52 | 0.357070 | ||||||||
\(598\) | −335.024 | −0.0229100 | ||||||||
\(599\) | 25119.7 | 1.71346 | 0.856730 | − | 0.515765i | \(-0.172492\pi\) | ||||
0.856730 | + | 0.515765i | \(0.172492\pi\) | |||||||
\(600\) | 149.971 | 0.0102042 | ||||||||
\(601\) | 19723.3 | 1.33865 | 0.669325 | − | 0.742970i | \(-0.266583\pi\) | ||||
0.669325 | + | 0.742970i | \(0.266583\pi\) | |||||||
\(602\) | 32.5244 | 0.00220198 | ||||||||
\(603\) | 1739.53 | 0.117478 | ||||||||
\(604\) | 5646.86 | 0.380410 | ||||||||
\(605\) | 1486.09 | 0.0998649 | ||||||||
\(606\) | 258.749 | 0.0173448 | ||||||||
\(607\) | −8435.56 | −0.564067 | −0.282034 | − | 0.959405i | \(-0.591009\pi\) | ||||
−0.282034 | + | 0.959405i | \(0.591009\pi\) | |||||||
\(608\) | −1771.98 | −0.118196 | ||||||||
\(609\) | −998.720 | −0.0664535 | ||||||||
\(610\) | −90.6642 | −0.00601785 | ||||||||
\(611\) | 6012.87 | 0.398125 | ||||||||
\(612\) | 5019.50 | 0.331538 | ||||||||
\(613\) | −20881.9 | −1.37588 | −0.687938 | − | 0.725769i | \(-0.741484\pi\) | ||||
−0.687938 | + | 0.725769i | \(0.741484\pi\) | |||||||
\(614\) | 287.621 | 0.0189046 | ||||||||
\(615\) | −12267.5 | −0.804345 | ||||||||
\(616\) | 37.0800 | 0.00242532 | ||||||||
\(617\) | 24440.1 | 1.59469 | 0.797343 | − | 0.603527i | \(-0.206238\pi\) | ||||
0.797343 | + | 0.603527i | \(0.206238\pi\) | |||||||
\(618\) | 65.7008 | 0.00427649 | ||||||||
\(619\) | −10033.3 | −0.651490 | −0.325745 | − | 0.945458i | \(-0.605615\pi\) | ||||
−0.325745 | + | 0.945458i | \(0.605615\pi\) | |||||||
\(620\) | −21489.5 | −1.39200 | ||||||||
\(621\) | −4434.12 | −0.286530 | ||||||||
\(622\) | −353.208 | −0.0227691 | ||||||||
\(623\) | 92.4908 | 0.00594794 | ||||||||
\(624\) | −3218.83 | −0.206501 | ||||||||
\(625\) | −18187.4 | −1.16399 | ||||||||
\(626\) | −423.915 | −0.0270656 | ||||||||
\(627\) | 2522.82 | 0.160688 | ||||||||
\(628\) | −4914.70 | −0.312290 | ||||||||
\(629\) | −9919.76 | −0.628819 | ||||||||
\(630\) | −23.3092 | −0.00147407 | ||||||||
\(631\) | 18323.2 | 1.15600 | 0.578001 | − | 0.816036i | \(-0.303833\pi\) | ||||
0.578001 | + | 0.816036i | \(0.303833\pi\) | |||||||
\(632\) | −50.1672 | −0.00315751 | ||||||||
\(633\) | 9122.42 | 0.572802 | ||||||||
\(634\) | 1286.85 | 0.0806109 | ||||||||
\(635\) | 26742.6 | 1.67126 | ||||||||
\(636\) | −10128.7 | −0.631494 | ||||||||
\(637\) | 5730.86 | 0.356460 | ||||||||
\(638\) | 254.321 | 0.0157816 | ||||||||
\(639\) | −1824.50 | −0.112952 | ||||||||
\(640\) | 3030.02 | 0.187144 | ||||||||
\(641\) | −7754.92 | −0.477849 | −0.238924 | − | 0.971038i | \(-0.576795\pi\) | ||||
−0.238924 | + | 0.971038i | \(0.576795\pi\) | |||||||
\(642\) | 241.018 | 0.0148165 | ||||||||
\(643\) | 7490.61 | 0.459410 | 0.229705 | − | 0.973260i | \(-0.426224\pi\) | ||||
0.229705 | + | 0.973260i | \(0.426224\pi\) | |||||||
\(644\) | 2285.16 | 0.139826 | ||||||||
\(645\) | −5682.84 | −0.346917 | ||||||||
\(646\) | 646.162 | 0.0393543 | ||||||||
\(647\) | −7986.04 | −0.485260 | −0.242630 | − | 0.970119i | \(-0.578010\pi\) | ||||
−0.242630 | + | 0.970119i | \(0.578010\pi\) | |||||||
\(648\) | 156.694 | 0.00949928 | ||||||||
\(649\) | −828.224 | −0.0500934 | ||||||||
\(650\) | 52.7170 | 0.00318112 | ||||||||
\(651\) | 1145.44 | 0.0689605 | ||||||||
\(652\) | −13324.7 | −0.800359 | ||||||||
\(653\) | 14331.3 | 0.858845 | 0.429423 | − | 0.903104i | \(-0.358717\pi\) | ||||
0.429423 | + | 0.903104i | \(0.358717\pi\) | |||||||
\(654\) | 388.197 | 0.0232106 | ||||||||
\(655\) | −2232.89 | −0.133200 | ||||||||
\(656\) | −21191.6 | −1.26127 | ||||||||
\(657\) | 2902.39 | 0.172349 | ||||||||
\(658\) | 75.2175 | 0.00445636 | ||||||||
\(659\) | 2526.46 | 0.149343 | 0.0746714 | − | 0.997208i | \(-0.476209\pi\) | ||||
0.0746714 | + | 0.997208i | \(0.476209\pi\) | |||||||
\(660\) | −3236.45 | −0.190877 | ||||||||
\(661\) | 4480.72 | 0.263661 | 0.131830 | − | 0.991272i | \(-0.457915\pi\) | ||||
0.131830 | + | 0.991272i | \(0.457915\pi\) | |||||||
\(662\) | 424.126 | 0.0249005 | ||||||||
\(663\) | 3532.10 | 0.206901 | ||||||||
\(664\) | −599.280 | −0.0350250 | ||||||||
\(665\) | 1636.10 | 0.0954066 | ||||||||
\(666\) | −154.691 | −0.00900025 | ||||||||
\(667\) | 31375.2 | 1.82137 | ||||||||
\(668\) | −9370.72 | −0.542761 | ||||||||
\(669\) | −8206.07 | −0.474237 | ||||||||
\(670\) | −287.273 | −0.0165647 | ||||||||
\(671\) | 671.000 | 0.0386046 | ||||||||
\(672\) | −121.168 | −0.00695556 | ||||||||
\(673\) | 29326.4 | 1.67972 | 0.839859 | − | 0.542805i | \(-0.182638\pi\) | ||||
0.839859 | + | 0.542805i | \(0.182638\pi\) | |||||||
\(674\) | 1113.93 | 0.0636602 | ||||||||
\(675\) | 697.720 | 0.0397856 | ||||||||
\(676\) | 15274.6 | 0.869063 | ||||||||
\(677\) | 4191.92 | 0.237974 | 0.118987 | − | 0.992896i | \(-0.462035\pi\) | ||||
0.118987 | + | 0.992896i | \(0.462035\pi\) | |||||||
\(678\) | −406.119 | −0.0230043 | ||||||||
\(679\) | −405.925 | −0.0229425 | ||||||||
\(680\) | −1659.40 | −0.0935813 | ||||||||
\(681\) | 10431.0 | 0.586957 | ||||||||
\(682\) | −291.682 | −0.0163770 | ||||||||
\(683\) | −11133.1 | −0.623715 | −0.311857 | − | 0.950129i | \(-0.600951\pi\) | ||||
−0.311857 | + | 0.950129i | \(0.600951\pi\) | |||||||
\(684\) | −5494.25 | −0.307132 | ||||||||
\(685\) | 5966.58 | 0.332805 | ||||||||
\(686\) | 144.020 | 0.00801560 | ||||||||
\(687\) | −16396.4 | −0.910573 | ||||||||
\(688\) | −9816.89 | −0.543990 | ||||||||
\(689\) | −7127.33 | −0.394092 | ||||||||
\(690\) | 732.269 | 0.0404015 | ||||||||
\(691\) | 11977.0 | 0.659373 | 0.329686 | − | 0.944091i | \(-0.393057\pi\) | ||||
0.329686 | + | 0.944091i | \(0.393057\pi\) | |||||||
\(692\) | 22723.7 | 1.24830 | ||||||||
\(693\) | 172.510 | 0.00945615 | ||||||||
\(694\) | −1179.94 | −0.0645388 | ||||||||
\(695\) | −31313.2 | −1.70903 | ||||||||
\(696\) | −1108.75 | −0.0603836 | ||||||||
\(697\) | 23254.0 | 1.26371 | ||||||||
\(698\) | −740.466 | −0.0401534 | ||||||||
\(699\) | 4294.53 | 0.232380 | ||||||||
\(700\) | −359.576 | −0.0194153 | ||||||||
\(701\) | −6225.75 | −0.335440 | −0.167720 | − | 0.985835i | \(-0.553640\pi\) | ||||
−0.167720 | + | 0.985835i | \(0.553640\pi\) | |||||||
\(702\) | 55.0804 | 0.00296136 | ||||||||
\(703\) | 10858.0 | 0.582527 | ||||||||
\(704\) | −5570.23 | −0.298205 | ||||||||
\(705\) | −13142.4 | −0.702089 | ||||||||
\(706\) | −87.4243 | −0.00466042 | ||||||||
\(707\) | −1241.91 | −0.0660635 | ||||||||
\(708\) | 1803.73 | 0.0957460 | ||||||||
\(709\) | 27441.1 | 1.45356 | 0.726778 | − | 0.686873i | \(-0.241017\pi\) | ||||
0.726778 | + | 0.686873i | \(0.241017\pi\) | |||||||
\(710\) | 301.307 | 0.0159265 | ||||||||
\(711\) | −233.397 | −0.0123109 | ||||||||
\(712\) | 102.680 | 0.00540465 | ||||||||
\(713\) | −35984.5 | −1.89008 | ||||||||
\(714\) | 44.1845 | 0.00231591 | ||||||||
\(715\) | −2277.41 | −0.119119 | ||||||||
\(716\) | −620.479 | −0.0323860 | ||||||||
\(717\) | −12858.6 | −0.669752 | ||||||||
\(718\) | 849.475 | 0.0441534 | ||||||||
\(719\) | −23378.4 | −1.21261 | −0.606305 | − | 0.795232i | \(-0.707349\pi\) | ||||
−0.606305 | + | 0.795232i | \(0.707349\pi\) | |||||||
\(720\) | 7035.46 | 0.364161 | ||||||||
\(721\) | −315.342 | −0.0162884 | ||||||||
\(722\) | 122.778 | 0.00632869 | ||||||||
\(723\) | −12736.9 | −0.655176 | ||||||||
\(724\) | −12180.8 | −0.625269 | ||||||||
\(725\) | −4936.98 | −0.252903 | ||||||||
\(726\) | −43.9291 | −0.00224568 | ||||||||
\(727\) | −5148.36 | −0.262644 | −0.131322 | − | 0.991340i | \(-0.541922\pi\) | ||||
−0.131322 | + | 0.991340i | \(0.541922\pi\) | |||||||
\(728\) | −56.8243 | −0.00289293 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −479.314 | −0.0243016 | ||||||||
\(731\) | 10772.3 | 0.545044 | ||||||||
\(732\) | −1461.32 | −0.0737868 | ||||||||
\(733\) | 25961.1 | 1.30818 | 0.654090 | − | 0.756416i | \(-0.273052\pi\) | ||||
0.654090 | + | 0.756416i | \(0.273052\pi\) | |||||||
\(734\) | −564.948 | −0.0284095 | ||||||||
\(735\) | −12526.0 | −0.628613 | ||||||||
\(736\) | 3806.53 | 0.190639 | ||||||||
\(737\) | 2126.09 | 0.106263 | ||||||||
\(738\) | 362.628 | 0.0180874 | ||||||||
\(739\) | −29417.0 | −1.46431 | −0.732154 | − | 0.681139i | \(-0.761485\pi\) | ||||
−0.732154 | + | 0.681139i | \(0.761485\pi\) | |||||||
\(740\) | −13929.4 | −0.691966 | ||||||||
\(741\) | −3866.17 | −0.191670 | ||||||||
\(742\) | −89.1588 | −0.00441122 | ||||||||
\(743\) | 15346.0 | 0.757725 | 0.378862 | − | 0.925453i | \(-0.376315\pi\) | ||||
0.378862 | + | 0.925453i | \(0.376315\pi\) | |||||||
\(744\) | 1271.63 | 0.0626616 | ||||||||
\(745\) | 7043.56 | 0.346384 | ||||||||
\(746\) | −515.150 | −0.0252828 | ||||||||
\(747\) | −2788.07 | −0.136560 | ||||||||
\(748\) | 6134.95 | 0.299888 | ||||||||
\(749\) | −1156.81 | −0.0564337 | ||||||||
\(750\) | 442.138 | 0.0215261 | ||||||||
\(751\) | 2725.82 | 0.132445 | 0.0662227 | − | 0.997805i | \(-0.478905\pi\) | ||||
0.0662227 | + | 0.997805i | \(0.478905\pi\) | |||||||
\(752\) | −22703.0 | −1.10092 | ||||||||
\(753\) | −9554.81 | −0.462413 | ||||||||
\(754\) | −389.742 | −0.0188244 | ||||||||
\(755\) | −8685.06 | −0.418651 | ||||||||
\(756\) | −375.696 | −0.0180740 | ||||||||
\(757\) | 12431.1 | 0.596852 | 0.298426 | − | 0.954433i | \(-0.403538\pi\) | ||||
0.298426 | + | 0.954433i | \(0.403538\pi\) | |||||||
\(758\) | −1035.61 | −0.0496239 | ||||||||
\(759\) | −5419.47 | −0.259176 | ||||||||
\(760\) | 1816.35 | 0.0866922 | ||||||||
\(761\) | −12914.2 | −0.615165 | −0.307583 | − | 0.951521i | \(-0.599520\pi\) | ||||
−0.307583 | + | 0.951521i | \(0.599520\pi\) | |||||||
\(762\) | −790.516 | −0.0375818 | ||||||||
\(763\) | −1863.22 | −0.0884050 | ||||||||
\(764\) | 30427.7 | 1.44089 | ||||||||
\(765\) | −7720.17 | −0.364867 | ||||||||
\(766\) | 656.579 | 0.0309702 | ||||||||
\(767\) | 1269.24 | 0.0597516 | ||||||||
\(768\) | 12063.7 | 0.566810 | ||||||||
\(769\) | 9189.99 | 0.430949 | 0.215474 | − | 0.976509i | \(-0.430870\pi\) | ||||
0.215474 | + | 0.976509i | \(0.430870\pi\) | |||||||
\(770\) | −28.4890 | −0.00133334 | ||||||||
\(771\) | −15365.9 | −0.717754 | ||||||||
\(772\) | 7821.49 | 0.364639 | ||||||||
\(773\) | −14080.3 | −0.655152 | −0.327576 | − | 0.944825i | \(-0.606232\pi\) | ||||
−0.327576 | + | 0.944825i | \(0.606232\pi\) | |||||||
\(774\) | 167.986 | 0.00780119 | ||||||||
\(775\) | 5662.25 | 0.262444 | ||||||||
\(776\) | −450.646 | −0.0208469 | ||||||||
\(777\) | 742.468 | 0.0342804 | ||||||||
\(778\) | −1279.01 | −0.0589395 | ||||||||
\(779\) | −25453.4 | −1.17068 | ||||||||
\(780\) | 4959.79 | 0.227678 | ||||||||
\(781\) | −2229.95 | −0.102169 | ||||||||
\(782\) | −1388.07 | −0.0634750 | ||||||||
\(783\) | −5158.31 | −0.235432 | ||||||||
\(784\) | −21638.3 | −0.985708 | ||||||||
\(785\) | 7558.98 | 0.343683 | ||||||||
\(786\) | 66.0045 | 0.00299530 | ||||||||
\(787\) | 19186.9 | 0.869046 | 0.434523 | − | 0.900661i | \(-0.356917\pi\) | ||||
0.434523 | + | 0.900661i | \(0.356917\pi\) | |||||||
\(788\) | 26826.0 | 1.21274 | ||||||||
\(789\) | −7910.17 | −0.356920 | ||||||||
\(790\) | 38.5441 | 0.00173587 | ||||||||
\(791\) | 1949.24 | 0.0876193 | ||||||||
\(792\) | 191.515 | 0.00859242 | ||||||||
\(793\) | −1028.29 | −0.0460477 | ||||||||
\(794\) | 671.721 | 0.0300233 | ||||||||
\(795\) | 15578.3 | 0.694977 | ||||||||
\(796\) | −13864.0 | −0.617331 | ||||||||
\(797\) | −22605.0 | −1.00465 | −0.502327 | − | 0.864678i | \(-0.667523\pi\) | ||||
−0.502327 | + | 0.864678i | \(0.667523\pi\) | |||||||
\(798\) | −48.3635 | −0.00214543 | ||||||||
\(799\) | 24912.6 | 1.10306 | ||||||||
\(800\) | −598.968 | −0.0264709 | ||||||||
\(801\) | 477.708 | 0.0210724 | ||||||||
\(802\) | −961.292 | −0.0423247 | ||||||||
\(803\) | 3547.37 | 0.155895 | ||||||||
\(804\) | −4630.25 | −0.203105 | ||||||||
\(805\) | −3514.65 | −0.153882 | ||||||||
\(806\) | 446.997 | 0.0195345 | ||||||||
\(807\) | 2592.17 | 0.113071 | ||||||||
\(808\) | −1378.73 | −0.0600293 | ||||||||
\(809\) | −2944.93 | −0.127983 | −0.0639915 | − | 0.997950i | \(-0.520383\pi\) | ||||
−0.0639915 | + | 0.997950i | \(0.520383\pi\) | |||||||
\(810\) | −120.390 | −0.00522232 | ||||||||
\(811\) | 26365.7 | 1.14158 | 0.570792 | − | 0.821095i | \(-0.306636\pi\) | ||||
0.570792 | + | 0.821095i | \(0.306636\pi\) | |||||||
\(812\) | 2658.38 | 0.114890 | ||||||||
\(813\) | 9622.32 | 0.415092 | ||||||||
\(814\) | −189.067 | −0.00814103 | ||||||||
\(815\) | 20493.8 | 0.880818 | ||||||||
\(816\) | −13336.3 | −0.572137 | ||||||||
\(817\) | −11791.1 | −0.504920 | ||||||||
\(818\) | 944.949 | 0.0403904 | ||||||||
\(819\) | −264.368 | −0.0112793 | ||||||||
\(820\) | 32653.4 | 1.39062 | ||||||||
\(821\) | 31011.2 | 1.31827 | 0.659134 | − | 0.752025i | \(-0.270923\pi\) | ||||
0.659134 | + | 0.752025i | \(0.270923\pi\) | |||||||
\(822\) | −176.373 | −0.00748384 | ||||||||
\(823\) | −5472.12 | −0.231769 | −0.115885 | − | 0.993263i | \(-0.536970\pi\) | ||||
−0.115885 | + | 0.993263i | \(0.536970\pi\) | |||||||
\(824\) | −350.083 | −0.0148006 | ||||||||
\(825\) | 852.769 | 0.0359874 | ||||||||
\(826\) | 15.8774 | 0.000668821 0 | ||||||||
\(827\) | 22579.7 | 0.949425 | 0.474712 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474712 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(828\) | 11802.7 | 0.495375 | ||||||||
\(829\) | −18629.2 | −0.780480 | −0.390240 | − | 0.920713i | \(-0.627608\pi\) | ||||
−0.390240 | + | 0.920713i | \(0.627608\pi\) | |||||||
\(830\) | 460.435 | 0.0192553 | ||||||||
\(831\) | −12789.6 | −0.533896 | ||||||||
\(832\) | 8536.27 | 0.355699 | ||||||||
\(833\) | 23744.1 | 0.987618 | ||||||||
\(834\) | 925.622 | 0.0384313 | ||||||||
\(835\) | 14412.5 | 0.597323 | ||||||||
\(836\) | −6715.20 | −0.277811 | ||||||||
\(837\) | 5916.10 | 0.244313 | ||||||||
\(838\) | 1034.58 | 0.0426478 | ||||||||
\(839\) | −20243.9 | −0.833011 | −0.416506 | − | 0.909133i | \(-0.636745\pi\) | ||||
−0.416506 | + | 0.909133i | \(0.636745\pi\) | |||||||
\(840\) | 124.202 | 0.00510164 | ||||||||
\(841\) | 12110.6 | 0.496558 | ||||||||
\(842\) | 380.220 | 0.0155620 | ||||||||
\(843\) | −7341.87 | −0.299961 | ||||||||
\(844\) | −24281.9 | −0.990306 | ||||||||
\(845\) | −23492.9 | −0.956428 | ||||||||
\(846\) | 388.492 | 0.0157880 | ||||||||
\(847\) | 210.845 | 0.00855341 | ||||||||
\(848\) | 26911.0 | 1.08977 | ||||||||
\(849\) | 8105.52 | 0.327657 | ||||||||
\(850\) | 218.417 | 0.00881371 | ||||||||
\(851\) | −23324.9 | −0.939564 | ||||||||
\(852\) | 4856.44 | 0.195280 | ||||||||
\(853\) | −2490.25 | −0.0999583 | −0.0499791 | − | 0.998750i | \(-0.515915\pi\) | ||||
−0.0499791 | + | 0.998750i | \(0.515915\pi\) | |||||||
\(854\) | −12.8634 | −0.000515428 0 | ||||||||
\(855\) | 8450.35 | 0.338007 | ||||||||
\(856\) | −1284.25 | −0.0512790 | ||||||||
\(857\) | −18458.1 | −0.735727 | −0.367863 | − | 0.929880i | \(-0.619911\pi\) | ||||
−0.367863 | + | 0.929880i | \(0.619911\pi\) | |||||||
\(858\) | 67.3205 | 0.00267865 | ||||||||
\(859\) | 18674.3 | 0.741743 | 0.370872 | − | 0.928684i | \(-0.379059\pi\) | ||||
0.370872 | + | 0.928684i | \(0.379059\pi\) | |||||||
\(860\) | 15126.5 | 0.599779 | ||||||||
\(861\) | −1740.50 | −0.0688920 | ||||||||
\(862\) | −1050.07 | −0.0414912 | ||||||||
\(863\) | −2813.94 | −0.110994 | −0.0554968 | − | 0.998459i | \(-0.517674\pi\) | ||||
−0.0554968 | + | 0.998459i | \(0.517674\pi\) | |||||||
\(864\) | −625.821 | −0.0246422 | ||||||||
\(865\) | −34949.9 | −1.37379 | ||||||||
\(866\) | 1092.48 | 0.0428683 | ||||||||
\(867\) | −104.795 | −0.00410499 | ||||||||
\(868\) | −3048.91 | −0.119224 | ||||||||
\(869\) | −285.263 | −0.0111356 | ||||||||
\(870\) | 851.866 | 0.0331965 | ||||||||
\(871\) | −3258.19 | −0.126750 | ||||||||
\(872\) | −2068.49 | −0.0803301 | ||||||||
\(873\) | −2096.57 | −0.0812808 | ||||||||
\(874\) | 1519.36 | 0.0588022 | ||||||||
\(875\) | −2122.12 | −0.0819893 | ||||||||
\(876\) | −7725.54 | −0.297970 | ||||||||
\(877\) | 11048.2 | 0.425396 | 0.212698 | − | 0.977118i | \(-0.431775\pi\) | ||||
0.212698 | + | 0.977118i | \(0.431775\pi\) | |||||||
\(878\) | 512.772 | 0.0197098 | ||||||||
\(879\) | −4809.72 | −0.184560 | ||||||||
\(880\) | 8598.90 | 0.329396 | ||||||||
\(881\) | 34885.2 | 1.33407 | 0.667033 | − | 0.745028i | \(-0.267564\pi\) | ||||
0.667033 | + | 0.745028i | \(0.267564\pi\) | |||||||
\(882\) | 370.272 | 0.0141357 | ||||||||
\(883\) | 3602.19 | 0.137286 | 0.0686429 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686429 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(884\) | −9401.68 | −0.357707 | ||||||||
\(885\) | −2774.19 | −0.105371 | ||||||||
\(886\) | −659.259 | −0.0249980 | ||||||||
\(887\) | −2451.75 | −0.0928091 | −0.0464046 | − | 0.998923i | \(-0.514776\pi\) | ||||
−0.0464046 | + | 0.998923i | \(0.514776\pi\) | |||||||
\(888\) | 824.265 | 0.0311492 | ||||||||
\(889\) | 3794.22 | 0.143143 | ||||||||
\(890\) | −78.8907 | −0.00297126 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 21842.8 | 0.819900 | ||||||||
\(893\) | −27268.8 | −1.02185 | ||||||||
\(894\) | −208.209 | −0.00778919 | ||||||||
\(895\) | 954.318 | 0.0356417 | ||||||||
\(896\) | 429.897 | 0.0160289 | ||||||||
\(897\) | 8305.23 | 0.309146 | ||||||||
\(898\) | 161.861 | 0.00601488 | ||||||||
\(899\) | −41861.6 | −1.55302 | ||||||||
\(900\) | −1857.18 | −0.0687844 | ||||||||
\(901\) | −29530.0 | −1.09188 | ||||||||
\(902\) | 443.213 | 0.0163607 | ||||||||
\(903\) | −806.277 | −0.0297134 | ||||||||
\(904\) | 2163.98 | 0.0796162 | ||||||||
\(905\) | 18734.4 | 0.688126 | ||||||||
\(906\) | 256.732 | 0.00941428 | ||||||||
\(907\) | −2791.01 | −0.102176 | −0.0510881 | − | 0.998694i | \(-0.516269\pi\) | ||||
−0.0510881 | + | 0.998694i | \(0.516269\pi\) | |||||||
\(908\) | −27765.2 | −1.01478 | ||||||||
\(909\) | −6414.38 | −0.234050 | ||||||||
\(910\) | 43.6589 | 0.00159041 | ||||||||
\(911\) | −3786.71 | −0.137716 | −0.0688579 | − | 0.997626i | \(-0.521936\pi\) | ||||
−0.0688579 | + | 0.997626i | \(0.521936\pi\) | |||||||
\(912\) | 14597.6 | 0.530018 | ||||||||
\(913\) | −3407.65 | −0.123523 | ||||||||
\(914\) | 1698.16 | 0.0614553 | ||||||||
\(915\) | 2247.56 | 0.0812045 | ||||||||
\(916\) | 43643.8 | 1.57427 | ||||||||
\(917\) | −316.800 | −0.0114086 | ||||||||
\(918\) | 228.209 | 0.00820483 | ||||||||
\(919\) | −14356.2 | −0.515306 | −0.257653 | − | 0.966237i | \(-0.582949\pi\) | ||||
−0.257653 | + | 0.966237i | \(0.582949\pi\) | |||||||
\(920\) | −3901.86 | −0.139827 | ||||||||
\(921\) | −7130.10 | −0.255098 | ||||||||
\(922\) | 501.401 | 0.0179097 | ||||||||
\(923\) | 3417.35 | 0.121867 | ||||||||
\(924\) | −459.184 | −0.0163485 | ||||||||
\(925\) | 3670.24 | 0.130461 | ||||||||
\(926\) | 107.796 | 0.00382547 | ||||||||
\(927\) | −1628.72 | −0.0577067 | ||||||||
\(928\) | 4428.23 | 0.156642 | ||||||||
\(929\) | 8242.35 | 0.291090 | 0.145545 | − | 0.989352i | \(-0.453506\pi\) | ||||
0.145545 | + | 0.989352i | \(0.453506\pi\) | |||||||
\(930\) | −977.011 | −0.0344489 | ||||||||
\(931\) | −25989.9 | −0.914913 | ||||||||
\(932\) | −11431.1 | −0.401758 | ||||||||
\(933\) | 8756.02 | 0.307245 | ||||||||
\(934\) | −775.518 | −0.0271689 | ||||||||
\(935\) | −9435.76 | −0.330035 | ||||||||
\(936\) | −293.493 | −0.0102491 | ||||||||
\(937\) | 31267.5 | 1.09015 | 0.545073 | − | 0.838389i | \(-0.316502\pi\) | ||||
0.545073 | + | 0.838389i | \(0.316502\pi\) | |||||||
\(938\) | −40.7581 | −0.00141876 | ||||||||
\(939\) | 10508.8 | 0.365221 | ||||||||
\(940\) | 34982.3 | 1.21383 | ||||||||
\(941\) | 53123.3 | 1.84035 | 0.920175 | − | 0.391508i | \(-0.128046\pi\) | ||||
0.920175 | + | 0.391508i | \(0.128046\pi\) | |||||||
\(942\) | −223.445 | −0.00772847 | ||||||||
\(943\) | 54678.5 | 1.88821 | ||||||||
\(944\) | −4792.31 | −0.165229 | ||||||||
\(945\) | 577.834 | 0.0198909 | ||||||||
\(946\) | 205.316 | 0.00705644 | ||||||||
\(947\) | 36728.8 | 1.26032 | 0.630161 | − | 0.776465i | \(-0.282989\pi\) | ||||
0.630161 | + | 0.776465i | \(0.282989\pi\) | |||||||
\(948\) | 621.252 | 0.0212841 | ||||||||
\(949\) | −5436.27 | −0.185952 | ||||||||
\(950\) | −239.075 | −0.00816487 | ||||||||
\(951\) | −31900.9 | −1.08776 | ||||||||
\(952\) | −235.435 | −0.00801522 | ||||||||
\(953\) | 18311.8 | 0.622432 | 0.311216 | − | 0.950339i | \(-0.399264\pi\) | ||||
0.311216 | + | 0.950339i | \(0.399264\pi\) | |||||||
\(954\) | −460.498 | −0.0156281 | ||||||||
\(955\) | −46798.9 | −1.58574 | ||||||||
\(956\) | 34226.7 | 1.15792 | ||||||||
\(957\) | −6304.60 | −0.212956 | ||||||||
\(958\) | 398.040 | 0.0134239 | ||||||||
\(959\) | 846.533 | 0.0285047 | ||||||||
\(960\) | −18657.9 | −0.627271 | ||||||||
\(961\) | 18220.3 | 0.611605 | ||||||||
\(962\) | 289.741 | 0.00971064 | ||||||||
\(963\) | −5974.82 | −0.199933 | ||||||||
\(964\) | 33903.0 | 1.13272 | ||||||||
\(965\) | −12029.7 | −0.401296 | ||||||||
\(966\) | 103.894 | 0.00346038 | ||||||||
\(967\) | 6955.76 | 0.231316 | 0.115658 | − | 0.993289i | \(-0.463102\pi\) | ||||
0.115658 | + | 0.993289i | \(0.463102\pi\) | |||||||
\(968\) | 234.074 | 0.00777214 | ||||||||
\(969\) | −16018.3 | −0.531045 | ||||||||
\(970\) | 346.237 | 0.0114608 | ||||||||
\(971\) | 40538.6 | 1.33980 | 0.669899 | − | 0.742452i | \(-0.266337\pi\) | ||||
0.669899 | + | 0.742452i | \(0.266337\pi\) | |||||||
\(972\) | −1940.44 | −0.0640326 | ||||||||
\(973\) | −4442.69 | −0.146378 | ||||||||
\(974\) | 245.800 | 0.00808620 | ||||||||
\(975\) | −1306.85 | −0.0429259 | ||||||||
\(976\) | 3882.57 | 0.127334 | ||||||||
\(977\) | 50218.9 | 1.64447 | 0.822235 | − | 0.569149i | \(-0.192727\pi\) | ||||
0.822235 | + | 0.569149i | \(0.192727\pi\) | |||||||
\(978\) | −605.800 | −0.0198071 | ||||||||
\(979\) | 583.865 | 0.0190607 | ||||||||
\(980\) | 33341.6 | 1.08680 | ||||||||
\(981\) | −9623.38 | −0.313202 | ||||||||
\(982\) | 290.157 | 0.00942902 | ||||||||
\(983\) | −10722.4 | −0.347907 | −0.173954 | − | 0.984754i | \(-0.555654\pi\) | ||||
−0.173954 | + | 0.984754i | \(0.555654\pi\) | |||||||
\(984\) | −1932.25 | −0.0625994 | ||||||||
\(985\) | −41259.4 | −1.33465 | ||||||||
\(986\) | −1614.78 | −0.0521553 | ||||||||
\(987\) | −1864.64 | −0.0601338 | ||||||||
\(988\) | 10290.9 | 0.331374 | ||||||||
\(989\) | 25329.5 | 0.814391 | ||||||||
\(990\) | −147.144 | −0.00472377 | ||||||||
\(991\) | 37188.0 | 1.19204 | 0.596022 | − | 0.802968i | \(-0.296747\pi\) | ||||
0.596022 | + | 0.802968i | \(0.296747\pi\) | |||||||
\(992\) | −5078.76 | −0.162551 | ||||||||
\(993\) | −10514.1 | −0.336006 | ||||||||
\(994\) | 42.7491 | 0.00136410 | ||||||||
\(995\) | 21323.3 | 0.679390 | ||||||||
\(996\) | 7421.25 | 0.236096 | ||||||||
\(997\) | 42702.9 | 1.35648 | 0.678242 | − | 0.734839i | \(-0.262742\pi\) | ||||
0.678242 | + | 0.734839i | \(0.262742\pi\) | |||||||
\(998\) | −672.330 | −0.0213249 | ||||||||
\(999\) | 3834.79 | 0.121449 |
(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 | 2013.4.a.a.1.19 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2013.4.a.a.1.19 | ✓ | 36 | 1.1 | even | 1 | trivial |