Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} - 105 x^{18} + 103 x^{17} + 4500 x^{16} - 4345 x^{15} - 101844 x^{14} + 95592 x^{13} + 1317797 x^{12} - 1160501 x^{11} - 9914845 x^{10} + 7570653 x^{9} + \cdots + 150528 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(2.10393\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.10393 | −0.743850 | −0.371925 | − | 0.928263i | \(-0.621302\pi\) | ||||
−0.371925 | + | 0.928263i | \(0.621302\pi\) | |||||||
\(3\) | −1.35130 | −0.260057 | −0.130029 | − | 0.991510i | \(-0.541507\pi\) | ||||
−0.130029 | + | 0.991510i | \(0.541507\pi\) | |||||||
\(4\) | −3.57349 | −0.446686 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 2.84303 | 0.193444 | ||||||||
\(7\) | −13.9401 | −0.752694 | −0.376347 | − | 0.926479i | \(-0.622820\pi\) | ||||
−0.376347 | + | 0.926479i | \(0.622820\pi\) | |||||||
\(8\) | 24.3498 | 1.07612 | ||||||||
\(9\) | −25.1740 | −0.932370 | ||||||||
\(10\) | 10.5196 | 0.332660 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 4.82885 | 0.116164 | ||||||||
\(13\) | 44.0744 | 0.940310 | 0.470155 | − | 0.882584i | \(-0.344198\pi\) | ||||
0.470155 | + | 0.882584i | \(0.344198\pi\) | |||||||
\(14\) | 29.3289 | 0.559892 | ||||||||
\(15\) | 6.75648 | 0.116301 | ||||||||
\(16\) | −22.6422 | −0.353785 | ||||||||
\(17\) | −43.5563 | −0.621410 | −0.310705 | − | 0.950506i | \(-0.600565\pi\) | ||||
−0.310705 | + | 0.950506i | \(0.600565\pi\) | |||||||
\(18\) | 52.9643 | 0.693544 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 17.8675 | 0.199764 | ||||||||
\(21\) | 18.8372 | 0.195743 | ||||||||
\(22\) | 23.1432 | 0.224279 | ||||||||
\(23\) | −78.4251 | −0.710989 | −0.355495 | − | 0.934678i | \(-0.615688\pi\) | ||||
−0.355495 | + | 0.934678i | \(0.615688\pi\) | |||||||
\(24\) | −32.9038 | −0.279852 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −92.7293 | −0.699450 | ||||||||
\(27\) | 70.5025 | 0.502527 | ||||||||
\(28\) | 49.8148 | 0.336218 | ||||||||
\(29\) | 20.2635 | 0.129753 | 0.0648764 | − | 0.997893i | \(-0.479335\pi\) | ||||
0.0648764 | + | 0.997893i | \(0.479335\pi\) | |||||||
\(30\) | −14.2151 | −0.0865106 | ||||||||
\(31\) | 277.768 | 1.60931 | 0.804655 | − | 0.593743i | \(-0.202350\pi\) | ||||
0.804655 | + | 0.593743i | \(0.202350\pi\) | |||||||
\(32\) | −147.161 | −0.812955 | ||||||||
\(33\) | 14.8643 | 0.0784102 | ||||||||
\(34\) | 91.6394 | 0.462236 | ||||||||
\(35\) | 69.7004 | 0.336615 | ||||||||
\(36\) | 89.9591 | 0.416477 | ||||||||
\(37\) | 118.093 | 0.524713 | 0.262357 | − | 0.964971i | \(-0.415500\pi\) | ||||
0.262357 | + | 0.964971i | \(0.415500\pi\) | |||||||
\(38\) | −39.9746 | −0.170651 | ||||||||
\(39\) | −59.5576 | −0.244534 | ||||||||
\(40\) | −121.749 | −0.481255 | ||||||||
\(41\) | 293.707 | 1.11876 | 0.559381 | − | 0.828911i | \(-0.311039\pi\) | ||||
0.559381 | + | 0.828911i | \(0.311039\pi\) | |||||||
\(42\) | −39.6321 | −0.145604 | ||||||||
\(43\) | 171.485 | 0.608168 | 0.304084 | − | 0.952645i | \(-0.401650\pi\) | ||||
0.304084 | + | 0.952645i | \(0.401650\pi\) | |||||||
\(44\) | 39.3084 | 0.134681 | ||||||||
\(45\) | 125.870 | 0.416969 | ||||||||
\(46\) | 165.001 | 0.528870 | ||||||||
\(47\) | 265.721 | 0.824668 | 0.412334 | − | 0.911033i | \(-0.364714\pi\) | ||||
0.412334 | + | 0.911033i | \(0.364714\pi\) | |||||||
\(48\) | 30.5964 | 0.0920042 | ||||||||
\(49\) | −148.674 | −0.433452 | ||||||||
\(50\) | −52.5982 | −0.148770 | ||||||||
\(51\) | 58.8575 | 0.161602 | ||||||||
\(52\) | −157.499 | −0.420024 | ||||||||
\(53\) | −384.897 | −0.997542 | −0.498771 | − | 0.866734i | \(-0.666215\pi\) | ||||
−0.498771 | + | 0.866734i | \(0.666215\pi\) | |||||||
\(54\) | −148.332 | −0.373805 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | −339.438 | −0.809987 | ||||||||
\(57\) | −25.6746 | −0.0596612 | ||||||||
\(58\) | −42.6329 | −0.0965168 | ||||||||
\(59\) | −472.620 | −1.04288 | −0.521440 | − | 0.853288i | \(-0.674605\pi\) | ||||
−0.521440 | + | 0.853288i | \(0.674605\pi\) | |||||||
\(60\) | −24.1442 | −0.0519501 | ||||||||
\(61\) | 617.674 | 1.29648 | 0.648238 | − | 0.761438i | \(-0.275506\pi\) | ||||
0.648238 | + | 0.761438i | \(0.275506\pi\) | |||||||
\(62\) | −584.404 | −1.19709 | ||||||||
\(63\) | 350.928 | 0.701789 | ||||||||
\(64\) | 490.753 | 0.958502 | ||||||||
\(65\) | −220.372 | −0.420520 | ||||||||
\(66\) | −31.2733 | −0.0583254 | ||||||||
\(67\) | −24.8664 | −0.0453420 | −0.0226710 | − | 0.999743i | \(-0.507217\pi\) | ||||
−0.0226710 | + | 0.999743i | \(0.507217\pi\) | |||||||
\(68\) | 155.648 | 0.277575 | ||||||||
\(69\) | 105.976 | 0.184898 | ||||||||
\(70\) | −146.645 | −0.250391 | ||||||||
\(71\) | 828.984 | 1.38567 | 0.692833 | − | 0.721098i | \(-0.256362\pi\) | ||||
0.692833 | + | 0.721098i | \(0.256362\pi\) | |||||||
\(72\) | −612.981 | −1.00334 | ||||||||
\(73\) | −350.335 | −0.561693 | −0.280847 | − | 0.959753i | \(-0.590615\pi\) | ||||
−0.280847 | + | 0.959753i | \(0.590615\pi\) | |||||||
\(74\) | −248.459 | −0.390308 | ||||||||
\(75\) | −33.7824 | −0.0520114 | ||||||||
\(76\) | −67.8963 | −0.102477 | ||||||||
\(77\) | 153.341 | 0.226946 | ||||||||
\(78\) | 125.305 | 0.181897 | ||||||||
\(79\) | −475.784 | −0.677593 | −0.338797 | − | 0.940860i | \(-0.610020\pi\) | ||||
−0.338797 | + | 0.940860i | \(0.610020\pi\) | |||||||
\(80\) | 113.211 | 0.158217 | ||||||||
\(81\) | 584.428 | 0.801685 | ||||||||
\(82\) | −617.937 | −0.832192 | ||||||||
\(83\) | 757.088 | 1.00122 | 0.500609 | − | 0.865673i | \(-0.333109\pi\) | ||||
0.500609 | + | 0.865673i | \(0.333109\pi\) | |||||||
\(84\) | −67.3145 | −0.0874359 | ||||||||
\(85\) | 217.782 | 0.277903 | ||||||||
\(86\) | −360.792 | −0.452386 | ||||||||
\(87\) | −27.3820 | −0.0337432 | ||||||||
\(88\) | −267.848 | −0.324462 | ||||||||
\(89\) | −182.170 | −0.216966 | −0.108483 | − | 0.994098i | \(-0.534599\pi\) | ||||
−0.108483 | + | 0.994098i | \(0.534599\pi\) | |||||||
\(90\) | −264.821 | −0.310162 | ||||||||
\(91\) | −614.400 | −0.707766 | ||||||||
\(92\) | 280.251 | 0.317589 | ||||||||
\(93\) | −375.347 | −0.418513 | ||||||||
\(94\) | −559.058 | −0.613430 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | 198.858 | 0.211415 | ||||||||
\(97\) | 161.592 | 0.169146 | 0.0845730 | − | 0.996417i | \(-0.473047\pi\) | ||||
0.0845730 | + | 0.996417i | \(0.473047\pi\) | |||||||
\(98\) | 312.800 | 0.322424 | ||||||||
\(99\) | 276.914 | 0.281120 | ||||||||
\(100\) | −89.3373 | −0.0893373 | ||||||||
\(101\) | −409.325 | −0.403261 | −0.201630 | − | 0.979462i | \(-0.564624\pi\) | ||||
−0.201630 | + | 0.979462i | \(0.564624\pi\) | |||||||
\(102\) | −123.832 | −0.120208 | ||||||||
\(103\) | −151.866 | −0.145279 | −0.0726397 | − | 0.997358i | \(-0.523142\pi\) | ||||
−0.0726397 | + | 0.997358i | \(0.523142\pi\) | |||||||
\(104\) | 1073.20 | 1.01189 | ||||||||
\(105\) | −94.1859 | −0.0875391 | ||||||||
\(106\) | 809.796 | 0.742022 | ||||||||
\(107\) | −1472.78 | −1.33064 | −0.665322 | − | 0.746556i | \(-0.731706\pi\) | ||||
−0.665322 | + | 0.746556i | \(0.731706\pi\) | |||||||
\(108\) | −251.940 | −0.224472 | ||||||||
\(109\) | −737.377 | −0.647962 | −0.323981 | − | 0.946064i | \(-0.605021\pi\) | ||||
−0.323981 | + | 0.946064i | \(0.605021\pi\) | |||||||
\(110\) | −115.716 | −0.100301 | ||||||||
\(111\) | −159.579 | −0.136455 | ||||||||
\(112\) | 315.634 | 0.266292 | ||||||||
\(113\) | 1092.53 | 0.909525 | 0.454763 | − | 0.890613i | \(-0.349724\pi\) | ||||
0.454763 | + | 0.890613i | \(0.349724\pi\) | |||||||
\(114\) | 54.0175 | 0.0443790 | ||||||||
\(115\) | 392.125 | 0.317964 | ||||||||
\(116\) | −72.4114 | −0.0579589 | ||||||||
\(117\) | −1109.53 | −0.876717 | ||||||||
\(118\) | 994.358 | 0.775746 | ||||||||
\(119\) | 607.179 | 0.467731 | ||||||||
\(120\) | 164.519 | 0.125154 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1299.54 | −0.964384 | ||||||||
\(123\) | −396.885 | −0.290942 | ||||||||
\(124\) | −992.602 | −0.718857 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −738.326 | −0.522026 | ||||||||
\(127\) | −215.621 | −0.150656 | −0.0753278 | − | 0.997159i | \(-0.524000\pi\) | ||||
−0.0753278 | + | 0.997159i | \(0.524000\pi\) | |||||||
\(128\) | 144.777 | 0.0999732 | ||||||||
\(129\) | −231.727 | −0.158158 | ||||||||
\(130\) | 463.646 | 0.312804 | ||||||||
\(131\) | −683.511 | −0.455868 | −0.227934 | − | 0.973677i | \(-0.573197\pi\) | ||||
−0.227934 | + | 0.973677i | \(0.573197\pi\) | |||||||
\(132\) | −53.1173 | −0.0350248 | ||||||||
\(133\) | −264.862 | −0.172680 | ||||||||
\(134\) | 52.3171 | 0.0337277 | ||||||||
\(135\) | −352.513 | −0.224737 | ||||||||
\(136\) | −1060.59 | −0.668710 | ||||||||
\(137\) | 353.862 | 0.220675 | 0.110337 | − | 0.993894i | \(-0.464807\pi\) | ||||
0.110337 | + | 0.993894i | \(0.464807\pi\) | |||||||
\(138\) | −222.965 | −0.137536 | ||||||||
\(139\) | −456.332 | −0.278457 | −0.139229 | − | 0.990260i | \(-0.544462\pi\) | ||||
−0.139229 | + | 0.990260i | \(0.544462\pi\) | |||||||
\(140\) | −249.074 | −0.150361 | ||||||||
\(141\) | −359.068 | −0.214461 | ||||||||
\(142\) | −1744.12 | −1.03073 | ||||||||
\(143\) | −484.818 | −0.283514 | ||||||||
\(144\) | 569.995 | 0.329858 | ||||||||
\(145\) | −101.317 | −0.0580273 | ||||||||
\(146\) | 737.079 | 0.417816 | ||||||||
\(147\) | 200.903 | 0.112722 | ||||||||
\(148\) | −422.005 | −0.234382 | ||||||||
\(149\) | −2470.77 | −1.35848 | −0.679238 | − | 0.733918i | \(-0.737690\pi\) | ||||
−0.679238 | + | 0.733918i | \(0.737690\pi\) | |||||||
\(150\) | 71.0757 | 0.0386887 | ||||||||
\(151\) | −2923.75 | −1.57570 | −0.787852 | − | 0.615865i | \(-0.788807\pi\) | ||||
−0.787852 | + | 0.615865i | \(0.788807\pi\) | |||||||
\(152\) | 462.646 | 0.246878 | ||||||||
\(153\) | 1096.49 | 0.579384 | ||||||||
\(154\) | −322.618 | −0.168814 | ||||||||
\(155\) | −1388.84 | −0.719705 | ||||||||
\(156\) | 212.828 | 0.109230 | ||||||||
\(157\) | 693.959 | 0.352764 | 0.176382 | − | 0.984322i | \(-0.443561\pi\) | ||||
0.176382 | + | 0.984322i | \(0.443561\pi\) | |||||||
\(158\) | 1001.01 | 0.504028 | ||||||||
\(159\) | 520.111 | 0.259418 | ||||||||
\(160\) | 735.803 | 0.363565 | ||||||||
\(161\) | 1093.25 | 0.535157 | ||||||||
\(162\) | −1229.59 | −0.596334 | ||||||||
\(163\) | 3123.87 | 1.50110 | 0.750552 | − | 0.660811i | \(-0.229788\pi\) | ||||
0.750552 | + | 0.660811i | \(0.229788\pi\) | |||||||
\(164\) | −1049.56 | −0.499736 | ||||||||
\(165\) | −74.3213 | −0.0350661 | ||||||||
\(166\) | −1592.86 | −0.744757 | ||||||||
\(167\) | −715.299 | −0.331446 | −0.165723 | − | 0.986172i | \(-0.552996\pi\) | ||||
−0.165723 | + | 0.986172i | \(0.552996\pi\) | |||||||
\(168\) | 458.681 | 0.210643 | ||||||||
\(169\) | −254.449 | −0.115817 | ||||||||
\(170\) | −458.197 | −0.206718 | ||||||||
\(171\) | −478.306 | −0.213900 | ||||||||
\(172\) | −612.801 | −0.271661 | ||||||||
\(173\) | 1071.76 | 0.471008 | 0.235504 | − | 0.971873i | \(-0.424326\pi\) | ||||
0.235504 | + | 0.971873i | \(0.424326\pi\) | |||||||
\(174\) | 57.6097 | 0.0250999 | ||||||||
\(175\) | −348.502 | −0.150539 | ||||||||
\(176\) | 249.064 | 0.106670 | ||||||||
\(177\) | 638.650 | 0.271208 | ||||||||
\(178\) | 383.272 | 0.161390 | ||||||||
\(179\) | 1302.68 | 0.543948 | 0.271974 | − | 0.962305i | \(-0.412324\pi\) | ||||
0.271974 | + | 0.962305i | \(0.412324\pi\) | |||||||
\(180\) | −449.795 | −0.186254 | ||||||||
\(181\) | −1133.87 | −0.465634 | −0.232817 | − | 0.972521i | \(-0.574794\pi\) | ||||
−0.232817 | + | 0.972521i | \(0.574794\pi\) | |||||||
\(182\) | 1292.65 | 0.526472 | ||||||||
\(183\) | −834.660 | −0.337158 | ||||||||
\(184\) | −1909.63 | −0.765109 | ||||||||
\(185\) | −590.465 | −0.234659 | ||||||||
\(186\) | 789.703 | 0.311311 | ||||||||
\(187\) | 479.120 | 0.187362 | ||||||||
\(188\) | −949.552 | −0.368368 | ||||||||
\(189\) | −982.811 | −0.378249 | ||||||||
\(190\) | 199.873 | 0.0763174 | ||||||||
\(191\) | −3282.67 | −1.24359 | −0.621794 | − | 0.783181i | \(-0.713596\pi\) | ||||
−0.621794 | + | 0.783181i | \(0.713596\pi\) | |||||||
\(192\) | −663.153 | −0.249265 | ||||||||
\(193\) | −2704.78 | −1.00878 | −0.504390 | − | 0.863476i | \(-0.668283\pi\) | ||||
−0.504390 | + | 0.863476i | \(0.668283\pi\) | |||||||
\(194\) | −339.977 | −0.125819 | ||||||||
\(195\) | 297.788 | 0.109359 | ||||||||
\(196\) | 531.286 | 0.193617 | ||||||||
\(197\) | −3177.48 | −1.14917 | −0.574584 | − | 0.818446i | \(-0.694836\pi\) | ||||
−0.574584 | + | 0.818446i | \(0.694836\pi\) | |||||||
\(198\) | −582.607 | −0.209111 | ||||||||
\(199\) | −2469.85 | −0.879814 | −0.439907 | − | 0.898043i | \(-0.644989\pi\) | ||||
−0.439907 | + | 0.898043i | \(0.644989\pi\) | |||||||
\(200\) | 608.745 | 0.215224 | ||||||||
\(201\) | 33.6019 | 0.0117915 | ||||||||
\(202\) | 861.190 | 0.299966 | ||||||||
\(203\) | −282.475 | −0.0976642 | ||||||||
\(204\) | −210.327 | −0.0721854 | ||||||||
\(205\) | −1468.53 | −0.500326 | ||||||||
\(206\) | 319.514 | 0.108066 | ||||||||
\(207\) | 1974.27 | 0.662905 | ||||||||
\(208\) | −997.942 | −0.332667 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | 198.160 | 0.0651160 | ||||||||
\(211\) | −3087.64 | −1.00740 | −0.503701 | − | 0.863878i | \(-0.668029\pi\) | ||||
−0.503701 | + | 0.863878i | \(0.668029\pi\) | |||||||
\(212\) | 1375.43 | 0.445589 | ||||||||
\(213\) | −1120.20 | −0.360352 | ||||||||
\(214\) | 3098.62 | 0.989801 | ||||||||
\(215\) | −857.426 | −0.271981 | ||||||||
\(216\) | 1716.72 | 0.540778 | ||||||||
\(217\) | −3872.11 | −1.21132 | ||||||||
\(218\) | 1551.39 | 0.481987 | ||||||||
\(219\) | 473.406 | 0.146072 | ||||||||
\(220\) | −196.542 | −0.0602312 | ||||||||
\(221\) | −1919.72 | −0.584318 | ||||||||
\(222\) | 335.742 | 0.101502 | ||||||||
\(223\) | −2151.13 | −0.645965 | −0.322983 | − | 0.946405i | \(-0.604686\pi\) | ||||
−0.322983 | + | 0.946405i | \(0.604686\pi\) | |||||||
\(224\) | 2051.43 | 0.611906 | ||||||||
\(225\) | −629.350 | −0.186474 | ||||||||
\(226\) | −2298.60 | −0.676551 | ||||||||
\(227\) | 4431.47 | 1.29571 | 0.647856 | − | 0.761763i | \(-0.275666\pi\) | ||||
0.647856 | + | 0.761763i | \(0.275666\pi\) | |||||||
\(228\) | 91.7481 | 0.0266498 | ||||||||
\(229\) | 5246.32 | 1.51392 | 0.756958 | − | 0.653463i | \(-0.226685\pi\) | ||||
0.756958 | + | 0.653463i | \(0.226685\pi\) | |||||||
\(230\) | −825.003 | −0.236518 | ||||||||
\(231\) | −207.209 | −0.0590188 | ||||||||
\(232\) | 493.411 | 0.139629 | ||||||||
\(233\) | 5077.70 | 1.42769 | 0.713844 | − | 0.700305i | \(-0.246953\pi\) | ||||
0.713844 | + | 0.700305i | \(0.246953\pi\) | |||||||
\(234\) | 2334.37 | 0.652147 | ||||||||
\(235\) | −1328.61 | −0.368803 | ||||||||
\(236\) | 1688.90 | 0.465840 | ||||||||
\(237\) | 642.925 | 0.176213 | ||||||||
\(238\) | −1277.46 | −0.347922 | ||||||||
\(239\) | −3494.23 | −0.945702 | −0.472851 | − | 0.881142i | \(-0.656775\pi\) | ||||
−0.472851 | + | 0.881142i | \(0.656775\pi\) | |||||||
\(240\) | −152.982 | −0.0411455 | ||||||||
\(241\) | −131.158 | −0.0350566 | −0.0175283 | − | 0.999846i | \(-0.505580\pi\) | ||||
−0.0175283 | + | 0.999846i | \(0.505580\pi\) | |||||||
\(242\) | −254.575 | −0.0676228 | ||||||||
\(243\) | −2693.30 | −0.711010 | ||||||||
\(244\) | −2207.25 | −0.579118 | ||||||||
\(245\) | 743.371 | 0.193846 | ||||||||
\(246\) | 835.016 | 0.216417 | ||||||||
\(247\) | 837.413 | 0.215722 | ||||||||
\(248\) | 6763.59 | 1.73181 | ||||||||
\(249\) | −1023.05 | −0.260374 | ||||||||
\(250\) | 262.991 | 0.0665320 | ||||||||
\(251\) | −1093.75 | −0.275048 | −0.137524 | − | 0.990498i | \(-0.543914\pi\) | ||||
−0.137524 | + | 0.990498i | \(0.543914\pi\) | |||||||
\(252\) | −1254.04 | −0.313480 | ||||||||
\(253\) | 862.676 | 0.214371 | ||||||||
\(254\) | 453.651 | 0.112065 | ||||||||
\(255\) | −294.288 | −0.0722706 | ||||||||
\(256\) | −4230.62 | −1.03287 | ||||||||
\(257\) | −1440.11 | −0.349540 | −0.174770 | − | 0.984609i | \(-0.555918\pi\) | ||||
−0.174770 | + | 0.984609i | \(0.555918\pi\) | |||||||
\(258\) | 487.537 | 0.117646 | ||||||||
\(259\) | −1646.23 | −0.394948 | ||||||||
\(260\) | 787.497 | 0.187840 | ||||||||
\(261\) | −510.113 | −0.120978 | ||||||||
\(262\) | 1438.06 | 0.339097 | ||||||||
\(263\) | −5960.11 | −1.39740 | −0.698699 | − | 0.715415i | \(-0.746237\pi\) | ||||
−0.698699 | + | 0.715415i | \(0.746237\pi\) | |||||||
\(264\) | 361.941 | 0.0843786 | ||||||||
\(265\) | 1924.49 | 0.446114 | ||||||||
\(266\) | 557.249 | 0.128448 | ||||||||
\(267\) | 246.166 | 0.0564236 | ||||||||
\(268\) | 88.8599 | 0.0202537 | ||||||||
\(269\) | −2603.80 | −0.590173 | −0.295087 | − | 0.955471i | \(-0.595349\pi\) | ||||
−0.295087 | + | 0.955471i | \(0.595349\pi\) | |||||||
\(270\) | 741.661 | 0.167171 | ||||||||
\(271\) | 5159.24 | 1.15646 | 0.578231 | − | 0.815873i | \(-0.303743\pi\) | ||||
0.578231 | + | 0.815873i | \(0.303743\pi\) | |||||||
\(272\) | 986.213 | 0.219845 | ||||||||
\(273\) | 830.237 | 0.184059 | ||||||||
\(274\) | −744.500 | −0.164149 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −378.703 | −0.0825914 | ||||||||
\(277\) | −3966.30 | −0.860331 | −0.430165 | − | 0.902750i | \(-0.641545\pi\) | ||||
−0.430165 | + | 0.902750i | \(0.641545\pi\) | |||||||
\(278\) | 960.090 | 0.207131 | ||||||||
\(279\) | −6992.53 | −1.50047 | ||||||||
\(280\) | 1697.19 | 0.362237 | ||||||||
\(281\) | −6393.99 | −1.35742 | −0.678708 | − | 0.734409i | \(-0.737460\pi\) | ||||
−0.678708 | + | 0.734409i | \(0.737460\pi\) | |||||||
\(282\) | 755.453 | 0.159527 | ||||||||
\(283\) | 3112.65 | 0.653808 | 0.326904 | − | 0.945058i | \(-0.393995\pi\) | ||||
0.326904 | + | 0.945058i | \(0.393995\pi\) | |||||||
\(284\) | −2962.37 | −0.618958 | ||||||||
\(285\) | 128.373 | 0.0266813 | ||||||||
\(286\) | 1020.02 | 0.210892 | ||||||||
\(287\) | −4094.29 | −0.842085 | ||||||||
\(288\) | 3704.62 | 0.757976 | ||||||||
\(289\) | −3015.84 | −0.613850 | ||||||||
\(290\) | 213.164 | 0.0431636 | ||||||||
\(291\) | −218.358 | −0.0439876 | ||||||||
\(292\) | 1251.92 | 0.250901 | ||||||||
\(293\) | 4021.36 | 0.801810 | 0.400905 | − | 0.916120i | \(-0.368696\pi\) | ||||
0.400905 | + | 0.916120i | \(0.368696\pi\) | |||||||
\(294\) | −422.685 | −0.0838486 | ||||||||
\(295\) | 2363.10 | 0.466390 | ||||||||
\(296\) | 2875.54 | 0.564653 | ||||||||
\(297\) | −775.528 | −0.151517 | ||||||||
\(298\) | 5198.31 | 1.01050 | ||||||||
\(299\) | −3456.54 | −0.668551 | ||||||||
\(300\) | 120.721 | 0.0232328 | ||||||||
\(301\) | −2390.52 | −0.457764 | ||||||||
\(302\) | 6151.35 | 1.17209 | ||||||||
\(303\) | 553.119 | 0.104871 | ||||||||
\(304\) | −430.202 | −0.0811638 | ||||||||
\(305\) | −3088.37 | −0.579802 | ||||||||
\(306\) | −2306.93 | −0.430975 | ||||||||
\(307\) | 2712.90 | 0.504343 | 0.252172 | − | 0.967683i | \(-0.418855\pi\) | ||||
0.252172 | + | 0.967683i | \(0.418855\pi\) | |||||||
\(308\) | −547.962 | −0.101374 | ||||||||
\(309\) | 205.216 | 0.0377809 | ||||||||
\(310\) | 2922.02 | 0.535353 | ||||||||
\(311\) | −8728.35 | −1.59144 | −0.795722 | − | 0.605662i | \(-0.792908\pi\) | ||||
−0.795722 | + | 0.605662i | \(0.792908\pi\) | |||||||
\(312\) | −1450.21 | −0.263148 | ||||||||
\(313\) | −10402.1 | −1.87847 | −0.939233 | − | 0.343279i | \(-0.888462\pi\) | ||||
−0.939233 | + | 0.343279i | \(0.888462\pi\) | |||||||
\(314\) | −1460.04 | −0.262404 | ||||||||
\(315\) | −1754.64 | −0.313850 | ||||||||
\(316\) | 1700.21 | 0.302672 | ||||||||
\(317\) | 277.488 | 0.0491650 | 0.0245825 | − | 0.999698i | \(-0.492174\pi\) | ||||
0.0245825 | + | 0.999698i | \(0.492174\pi\) | |||||||
\(318\) | −1094.27 | −0.192968 | ||||||||
\(319\) | −222.898 | −0.0391220 | ||||||||
\(320\) | −2453.77 | −0.428655 | ||||||||
\(321\) | 1990.16 | 0.346044 | ||||||||
\(322\) | −2300.12 | −0.398077 | ||||||||
\(323\) | −827.571 | −0.142561 | ||||||||
\(324\) | −2088.45 | −0.358102 | ||||||||
\(325\) | 1101.86 | 0.188062 | ||||||||
\(326\) | −6572.38 | −1.11660 | ||||||||
\(327\) | 996.415 | 0.168507 | ||||||||
\(328\) | 7151.69 | 1.20392 | ||||||||
\(329\) | −3704.17 | −0.620723 | ||||||||
\(330\) | 156.367 | 0.0260839 | ||||||||
\(331\) | 6416.27 | 1.06547 | 0.532734 | − | 0.846283i | \(-0.321165\pi\) | ||||
0.532734 | + | 0.846283i | \(0.321165\pi\) | |||||||
\(332\) | −2705.45 | −0.447231 | ||||||||
\(333\) | −2972.88 | −0.489227 | ||||||||
\(334\) | 1504.94 | 0.246546 | ||||||||
\(335\) | 124.332 | 0.0202776 | ||||||||
\(336\) | −426.516 | −0.0692510 | ||||||||
\(337\) | 10858.3 | 1.75517 | 0.877584 | − | 0.479423i | \(-0.159154\pi\) | ||||
0.877584 | + | 0.479423i | \(0.159154\pi\) | |||||||
\(338\) | 535.342 | 0.0861502 | ||||||||
\(339\) | −1476.33 | −0.236528 | ||||||||
\(340\) | −778.241 | −0.124135 | ||||||||
\(341\) | −3055.45 | −0.485225 | ||||||||
\(342\) | 1006.32 | 0.159110 | ||||||||
\(343\) | 6853.98 | 1.07895 | ||||||||
\(344\) | 4175.62 | 0.654461 | ||||||||
\(345\) | −529.878 | −0.0826888 | ||||||||
\(346\) | −2254.90 | −0.350359 | ||||||||
\(347\) | −4827.37 | −0.746821 | −0.373411 | − | 0.927666i | \(-0.621812\pi\) | ||||
−0.373411 | + | 0.927666i | \(0.621812\pi\) | |||||||
\(348\) | 97.8492 | 0.0150726 | ||||||||
\(349\) | 12166.2 | 1.86603 | 0.933013 | − | 0.359843i | \(-0.117170\pi\) | ||||
0.933013 | + | 0.359843i | \(0.117170\pi\) | |||||||
\(350\) | 733.223 | 0.111978 | ||||||||
\(351\) | 3107.36 | 0.472531 | ||||||||
\(352\) | 1618.77 | 0.245115 | ||||||||
\(353\) | 3040.19 | 0.458394 | 0.229197 | − | 0.973380i | \(-0.426390\pi\) | ||||
0.229197 | + | 0.973380i | \(0.426390\pi\) | |||||||
\(354\) | −1343.67 | −0.201738 | ||||||||
\(355\) | −4144.92 | −0.619689 | ||||||||
\(356\) | 650.983 | 0.0969158 | ||||||||
\(357\) | −820.479 | −0.121637 | ||||||||
\(358\) | −2740.74 | −0.404616 | ||||||||
\(359\) | 176.300 | 0.0259186 | 0.0129593 | − | 0.999916i | \(-0.495875\pi\) | ||||
0.0129593 | + | 0.999916i | \(0.495875\pi\) | |||||||
\(360\) | 3064.91 | 0.448708 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 2385.58 | 0.346362 | ||||||||
\(363\) | −163.507 | −0.0236416 | ||||||||
\(364\) | 2195.55 | 0.316149 | ||||||||
\(365\) | 1751.67 | 0.251197 | ||||||||
\(366\) | 1756.06 | 0.250795 | ||||||||
\(367\) | −860.001 | −0.122321 | −0.0611604 | − | 0.998128i | \(-0.519480\pi\) | ||||
−0.0611604 | + | 0.998128i | \(0.519480\pi\) | |||||||
\(368\) | 1775.72 | 0.251537 | ||||||||
\(369\) | −7393.77 | −1.04310 | ||||||||
\(370\) | 1242.30 | 0.174551 | ||||||||
\(371\) | 5365.50 | 0.750844 | ||||||||
\(372\) | 1341.30 | 0.186944 | ||||||||
\(373\) | −9198.13 | −1.27684 | −0.638420 | − | 0.769688i | \(-0.720412\pi\) | ||||
−0.638420 | + | 0.769688i | \(0.720412\pi\) | |||||||
\(374\) | −1008.03 | −0.139369 | ||||||||
\(375\) | 168.912 | 0.0232602 | ||||||||
\(376\) | 6470.25 | 0.887441 | ||||||||
\(377\) | 893.100 | 0.122008 | ||||||||
\(378\) | 2067.76 | 0.281360 | ||||||||
\(379\) | −7433.64 | −1.00749 | −0.503747 | − | 0.863851i | \(-0.668046\pi\) | ||||
−0.503747 | + | 0.863851i | \(0.668046\pi\) | |||||||
\(380\) | 339.482 | 0.0458291 | ||||||||
\(381\) | 291.368 | 0.0391791 | ||||||||
\(382\) | 6906.49 | 0.925044 | ||||||||
\(383\) | 9654.84 | 1.28809 | 0.644046 | − | 0.764987i | \(-0.277255\pi\) | ||||
0.644046 | + | 0.764987i | \(0.277255\pi\) | |||||||
\(384\) | −195.636 | −0.0259987 | ||||||||
\(385\) | −766.704 | −0.101493 | ||||||||
\(386\) | 5690.67 | 0.750382 | ||||||||
\(387\) | −4316.97 | −0.567038 | ||||||||
\(388\) | −577.447 | −0.0755552 | ||||||||
\(389\) | 11358.3 | 1.48044 | 0.740218 | − | 0.672367i | \(-0.234722\pi\) | ||||
0.740218 | + | 0.672367i | \(0.234722\pi\) | |||||||
\(390\) | −626.524 | −0.0813468 | ||||||||
\(391\) | 3415.91 | 0.441816 | ||||||||
\(392\) | −3620.18 | −0.466446 | ||||||||
\(393\) | 923.626 | 0.118552 | ||||||||
\(394\) | 6685.18 | 0.854809 | ||||||||
\(395\) | 2378.92 | 0.303029 | ||||||||
\(396\) | −989.550 | −0.125573 | ||||||||
\(397\) | 4939.10 | 0.624399 | 0.312199 | − | 0.950017i | \(-0.398934\pi\) | ||||
0.312199 | + | 0.950017i | \(0.398934\pi\) | |||||||
\(398\) | 5196.38 | 0.654450 | ||||||||
\(399\) | 357.906 | 0.0449066 | ||||||||
\(400\) | −566.056 | −0.0707570 | ||||||||
\(401\) | −1507.40 | −0.187721 | −0.0938604 | − | 0.995585i | \(-0.529921\pi\) | ||||
−0.0938604 | + | 0.995585i | \(0.529921\pi\) | |||||||
\(402\) | −70.6959 | −0.00877112 | ||||||||
\(403\) | 12242.5 | 1.51325 | ||||||||
\(404\) | 1462.72 | 0.180131 | ||||||||
\(405\) | −2922.14 | −0.358524 | ||||||||
\(406\) | 594.306 | 0.0726475 | ||||||||
\(407\) | −1299.02 | −0.158207 | ||||||||
\(408\) | 1433.17 | 0.173903 | ||||||||
\(409\) | 11953.9 | 1.44519 | 0.722597 | − | 0.691270i | \(-0.242948\pi\) | ||||
0.722597 | + | 0.691270i | \(0.242948\pi\) | |||||||
\(410\) | 3089.69 | 0.372168 | ||||||||
\(411\) | −478.172 | −0.0573881 | ||||||||
\(412\) | 542.691 | 0.0648943 | ||||||||
\(413\) | 6588.36 | 0.784969 | ||||||||
\(414\) | −4153.72 | −0.493102 | ||||||||
\(415\) | −3785.44 | −0.447759 | ||||||||
\(416\) | −6486.01 | −0.764430 | ||||||||
\(417\) | 616.640 | 0.0724148 | ||||||||
\(418\) | 439.721 | 0.0514532 | ||||||||
\(419\) | 13232.6 | 1.54285 | 0.771424 | − | 0.636321i | \(-0.219545\pi\) | ||||
0.771424 | + | 0.636321i | \(0.219545\pi\) | |||||||
\(420\) | 336.573 | 0.0391025 | ||||||||
\(421\) | −840.471 | −0.0972970 | −0.0486485 | − | 0.998816i | \(-0.515491\pi\) | ||||
−0.0486485 | + | 0.998816i | \(0.515491\pi\) | |||||||
\(422\) | 6496.17 | 0.749357 | ||||||||
\(423\) | −6689.26 | −0.768896 | ||||||||
\(424\) | −9372.17 | −1.07347 | ||||||||
\(425\) | −1088.91 | −0.124282 | ||||||||
\(426\) | 2356.83 | 0.268048 | ||||||||
\(427\) | −8610.42 | −0.975849 | ||||||||
\(428\) | 5262.97 | 0.594381 | ||||||||
\(429\) | 655.133 | 0.0737299 | ||||||||
\(430\) | 1803.96 | 0.202313 | ||||||||
\(431\) | −9747.18 | −1.08934 | −0.544669 | − | 0.838651i | \(-0.683345\pi\) | ||||
−0.544669 | + | 0.838651i | \(0.683345\pi\) | |||||||
\(432\) | −1596.33 | −0.177786 | ||||||||
\(433\) | 7573.69 | 0.840574 | 0.420287 | − | 0.907391i | \(-0.361929\pi\) | ||||
0.420287 | + | 0.907391i | \(0.361929\pi\) | |||||||
\(434\) | 8146.63 | 0.901039 | ||||||||
\(435\) | 136.910 | 0.0150904 | ||||||||
\(436\) | 2635.01 | 0.289436 | ||||||||
\(437\) | −1490.08 | −0.163112 | ||||||||
\(438\) | −996.012 | −0.108656 | ||||||||
\(439\) | 652.502 | 0.0709390 | 0.0354695 | − | 0.999371i | \(-0.488707\pi\) | ||||
0.0354695 | + | 0.999371i | \(0.488707\pi\) | |||||||
\(440\) | 1339.24 | 0.145104 | ||||||||
\(441\) | 3742.72 | 0.404138 | ||||||||
\(442\) | 4038.95 | 0.434645 | ||||||||
\(443\) | −6013.35 | −0.644927 | −0.322464 | − | 0.946582i | \(-0.604511\pi\) | ||||
−0.322464 | + | 0.946582i | \(0.604511\pi\) | |||||||
\(444\) | 570.253 | 0.0609528 | ||||||||
\(445\) | 910.850 | 0.0970302 | ||||||||
\(446\) | 4525.82 | 0.480501 | ||||||||
\(447\) | 3338.74 | 0.353281 | ||||||||
\(448\) | −6841.14 | −0.721458 | ||||||||
\(449\) | −4456.99 | −0.468459 | −0.234230 | − | 0.972181i | \(-0.575257\pi\) | ||||
−0.234230 | + | 0.972181i | \(0.575257\pi\) | |||||||
\(450\) | 1324.11 | 0.138709 | ||||||||
\(451\) | −3230.77 | −0.337320 | ||||||||
\(452\) | −3904.14 | −0.406273 | ||||||||
\(453\) | 3950.85 | 0.409773 | ||||||||
\(454\) | −9323.48 | −0.963816 | ||||||||
\(455\) | 3072.00 | 0.316522 | ||||||||
\(456\) | −625.172 | −0.0642025 | ||||||||
\(457\) | −2578.27 | −0.263909 | −0.131954 | − | 0.991256i | \(-0.542125\pi\) | ||||
−0.131954 | + | 0.991256i | \(0.542125\pi\) | |||||||
\(458\) | −11037.9 | −1.12613 | ||||||||
\(459\) | −3070.83 | −0.312275 | ||||||||
\(460\) | −1401.26 | −0.142030 | ||||||||
\(461\) | −4415.71 | −0.446117 | −0.223059 | − | 0.974805i | \(-0.571604\pi\) | ||||
−0.223059 | + | 0.974805i | \(0.571604\pi\) | |||||||
\(462\) | 435.953 | 0.0439012 | ||||||||
\(463\) | 7177.27 | 0.720423 | 0.360211 | − | 0.932871i | \(-0.382705\pi\) | ||||
0.360211 | + | 0.932871i | \(0.382705\pi\) | |||||||
\(464\) | −458.810 | −0.0459046 | ||||||||
\(465\) | 1876.73 | 0.187165 | ||||||||
\(466\) | −10683.1 | −1.06199 | ||||||||
\(467\) | 9415.10 | 0.932931 | 0.466466 | − | 0.884539i | \(-0.345527\pi\) | ||||
0.466466 | + | 0.884539i | \(0.345527\pi\) | |||||||
\(468\) | 3964.89 | 0.391618 | ||||||||
\(469\) | 346.640 | 0.0341286 | ||||||||
\(470\) | 2795.29 | 0.274334 | ||||||||
\(471\) | −937.744 | −0.0917388 | ||||||||
\(472\) | −11508.2 | −1.12226 | ||||||||
\(473\) | −1886.34 | −0.183370 | ||||||||
\(474\) | −1352.67 | −0.131076 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | −2169.75 | −0.208929 | ||||||||
\(477\) | 9689.41 | 0.930079 | ||||||||
\(478\) | 7351.60 | 0.703461 | ||||||||
\(479\) | 14544.7 | 1.38740 | 0.693701 | − | 0.720263i | \(-0.255979\pi\) | ||||
0.693701 | + | 0.720263i | \(0.255979\pi\) | |||||||
\(480\) | −994.288 | −0.0945476 | ||||||||
\(481\) | 5204.88 | 0.493393 | ||||||||
\(482\) | 275.947 | 0.0260768 | ||||||||
\(483\) | −1477.31 | −0.139171 | ||||||||
\(484\) | −432.392 | −0.0406079 | ||||||||
\(485\) | −807.959 | −0.0756444 | ||||||||
\(486\) | 5666.51 | 0.528885 | ||||||||
\(487\) | −925.751 | −0.0861392 | −0.0430696 | − | 0.999072i | \(-0.513714\pi\) | ||||
−0.0430696 | + | 0.999072i | \(0.513714\pi\) | |||||||
\(488\) | 15040.2 | 1.39516 | ||||||||
\(489\) | −4221.27 | −0.390373 | ||||||||
\(490\) | −1564.00 | −0.144192 | ||||||||
\(491\) | 3372.03 | 0.309934 | 0.154967 | − | 0.987920i | \(-0.450473\pi\) | ||||
0.154967 | + | 0.987920i | \(0.450473\pi\) | |||||||
\(492\) | 1418.26 | 0.129960 | ||||||||
\(493\) | −882.603 | −0.0806297 | ||||||||
\(494\) | −1761.86 | −0.160465 | ||||||||
\(495\) | −1384.57 | −0.125721 | ||||||||
\(496\) | −6289.29 | −0.569349 | ||||||||
\(497\) | −11556.1 | −1.04298 | ||||||||
\(498\) | 2152.42 | 0.193679 | ||||||||
\(499\) | 2491.89 | 0.223552 | 0.111776 | − | 0.993733i | \(-0.464346\pi\) | ||||
0.111776 | + | 0.993733i | \(0.464346\pi\) | |||||||
\(500\) | 446.686 | 0.0399529 | ||||||||
\(501\) | 966.580 | 0.0861949 | ||||||||
\(502\) | 2301.18 | 0.204595 | ||||||||
\(503\) | −6378.28 | −0.565395 | −0.282697 | − | 0.959209i | \(-0.591229\pi\) | ||||
−0.282697 | + | 0.959209i | \(0.591229\pi\) | |||||||
\(504\) | 8545.01 | 0.755208 | ||||||||
\(505\) | 2046.62 | 0.180344 | ||||||||
\(506\) | −1815.01 | −0.159460 | ||||||||
\(507\) | 343.836 | 0.0301189 | ||||||||
\(508\) | 770.520 | 0.0672958 | ||||||||
\(509\) | −6553.75 | −0.570707 | −0.285353 | − | 0.958422i | \(-0.592111\pi\) | ||||
−0.285353 | + | 0.958422i | \(0.592111\pi\) | |||||||
\(510\) | 619.160 | 0.0537585 | ||||||||
\(511\) | 4883.70 | 0.422783 | ||||||||
\(512\) | 7742.71 | 0.668326 | ||||||||
\(513\) | 1339.55 | 0.115288 | ||||||||
\(514\) | 3029.89 | 0.260005 | ||||||||
\(515\) | 759.329 | 0.0649709 | ||||||||
\(516\) | 828.075 | 0.0706472 | ||||||||
\(517\) | −2922.93 | −0.248647 | ||||||||
\(518\) | 3463.54 | 0.293782 | ||||||||
\(519\) | −1448.26 | −0.122489 | ||||||||
\(520\) | −5366.01 | −0.452529 | ||||||||
\(521\) | −5965.32 | −0.501623 | −0.250811 | − | 0.968036i | \(-0.580697\pi\) | ||||
−0.250811 | + | 0.968036i | \(0.580697\pi\) | |||||||
\(522\) | 1073.24 | 0.0899894 | ||||||||
\(523\) | 17544.9 | 1.46689 | 0.733446 | − | 0.679748i | \(-0.237911\pi\) | ||||
0.733446 | + | 0.679748i | \(0.237911\pi\) | |||||||
\(524\) | 2442.52 | 0.203630 | ||||||||
\(525\) | 470.930 | 0.0391487 | ||||||||
\(526\) | 12539.6 | 1.03946 | ||||||||
\(527\) | −12098.6 | −1.00004 | ||||||||
\(528\) | −336.560 | −0.0277403 | ||||||||
\(529\) | −6016.51 | −0.494494 | ||||||||
\(530\) | −4048.98 | −0.331842 | ||||||||
\(531\) | 11897.7 | 0.972350 | ||||||||
\(532\) | 946.480 | 0.0771337 | ||||||||
\(533\) | 12944.9 | 1.05198 | ||||||||
\(534\) | −517.914 | −0.0419707 | ||||||||
\(535\) | 7363.90 | 0.595082 | ||||||||
\(536\) | −605.491 | −0.0487934 | ||||||||
\(537\) | −1760.30 | −0.141458 | ||||||||
\(538\) | 5478.21 | 0.439001 | ||||||||
\(539\) | 1635.42 | 0.130691 | ||||||||
\(540\) | 1259.70 | 0.100387 | ||||||||
\(541\) | 14642.0 | 1.16361 | 0.581803 | − | 0.813330i | \(-0.302347\pi\) | ||||
0.581803 | + | 0.813330i | \(0.302347\pi\) | |||||||
\(542\) | −10854.7 | −0.860235 | ||||||||
\(543\) | 1532.19 | 0.121091 | ||||||||
\(544\) | 6409.78 | 0.505178 | ||||||||
\(545\) | 3686.88 | 0.289778 | ||||||||
\(546\) | −1746.76 | −0.136913 | ||||||||
\(547\) | −10032.1 | −0.784171 | −0.392086 | − | 0.919929i | \(-0.628246\pi\) | ||||
−0.392086 | + | 0.919929i | \(0.628246\pi\) | |||||||
\(548\) | −1264.52 | −0.0985725 | ||||||||
\(549\) | −15549.3 | −1.20880 | ||||||||
\(550\) | 578.580 | 0.0448559 | ||||||||
\(551\) | 385.006 | 0.0297674 | ||||||||
\(552\) | 2580.48 | 0.198972 | ||||||||
\(553\) | 6632.47 | 0.510020 | ||||||||
\(554\) | 8344.80 | 0.639957 | ||||||||
\(555\) | 797.894 | 0.0610247 | ||||||||
\(556\) | 1630.70 | 0.124383 | ||||||||
\(557\) | 1967.94 | 0.149702 | 0.0748512 | − | 0.997195i | \(-0.476152\pi\) | ||||
0.0748512 | + | 0.997195i | \(0.476152\pi\) | |||||||
\(558\) | 14711.8 | 1.11613 | ||||||||
\(559\) | 7558.10 | 0.571867 | ||||||||
\(560\) | −1578.17 | −0.119089 | ||||||||
\(561\) | −647.433 | −0.0487248 | ||||||||
\(562\) | 13452.5 | 1.00971 | ||||||||
\(563\) | −10183.1 | −0.762288 | −0.381144 | − | 0.924516i | \(-0.624470\pi\) | ||||
−0.381144 | + | 0.924516i | \(0.624470\pi\) | |||||||
\(564\) | 1283.13 | 0.0957968 | ||||||||
\(565\) | −5462.64 | −0.406752 | ||||||||
\(566\) | −6548.78 | −0.486335 | ||||||||
\(567\) | −8146.98 | −0.603423 | ||||||||
\(568\) | 20185.6 | 1.49114 | ||||||||
\(569\) | −23440.2 | −1.72700 | −0.863502 | − | 0.504345i | \(-0.831734\pi\) | ||||
−0.863502 | + | 0.504345i | \(0.831734\pi\) | |||||||
\(570\) | −270.088 | −0.0198469 | ||||||||
\(571\) | 3958.88 | 0.290147 | 0.145074 | − | 0.989421i | \(-0.453658\pi\) | ||||
0.145074 | + | 0.989421i | \(0.453658\pi\) | |||||||
\(572\) | 1732.49 | 0.126642 | ||||||||
\(573\) | 4435.85 | 0.323404 | ||||||||
\(574\) | 8614.09 | 0.626386 | ||||||||
\(575\) | −1960.63 | −0.142198 | ||||||||
\(576\) | −12354.2 | −0.893679 | ||||||||
\(577\) | 24216.8 | 1.74724 | 0.873620 | − | 0.486609i | \(-0.161766\pi\) | ||||
0.873620 | + | 0.486609i | \(0.161766\pi\) | |||||||
\(578\) | 6345.12 | 0.456613 | ||||||||
\(579\) | 3654.96 | 0.262340 | ||||||||
\(580\) | 362.057 | 0.0259200 | ||||||||
\(581\) | −10553.9 | −0.753611 | ||||||||
\(582\) | 459.410 | 0.0327202 | ||||||||
\(583\) | 4233.87 | 0.300770 | ||||||||
\(584\) | −8530.58 | −0.604448 | ||||||||
\(585\) | 5547.64 | 0.392080 | ||||||||
\(586\) | −8460.64 | −0.596427 | ||||||||
\(587\) | −16503.0 | −1.16040 | −0.580199 | − | 0.814475i | \(-0.697025\pi\) | ||||
−0.580199 | + | 0.814475i | \(0.697025\pi\) | |||||||
\(588\) | −717.925 | −0.0503515 | ||||||||
\(589\) | 5277.59 | 0.369201 | ||||||||
\(590\) | −4971.79 | −0.346924 | ||||||||
\(591\) | 4293.71 | 0.298849 | ||||||||
\(592\) | −2673.89 | −0.185636 | ||||||||
\(593\) | 4271.85 | 0.295824 | 0.147912 | − | 0.989001i | \(-0.452745\pi\) | ||||
0.147912 | + | 0.989001i | \(0.452745\pi\) | |||||||
\(594\) | 1631.65 | 0.112706 | ||||||||
\(595\) | −3035.89 | −0.209176 | ||||||||
\(596\) | 8829.26 | 0.606813 | ||||||||
\(597\) | 3337.50 | 0.228802 | ||||||||
\(598\) | 7272.30 | 0.497302 | ||||||||
\(599\) | −18163.3 | −1.23895 | −0.619476 | − | 0.785016i | \(-0.712655\pi\) | ||||
−0.619476 | + | 0.785016i | \(0.712655\pi\) | |||||||
\(600\) | −822.594 | −0.0559705 | ||||||||
\(601\) | −25285.8 | −1.71619 | −0.858094 | − | 0.513492i | \(-0.828352\pi\) | ||||
−0.858094 | + | 0.513492i | \(0.828352\pi\) | |||||||
\(602\) | 5029.47 | 0.340508 | ||||||||
\(603\) | 625.987 | 0.0422755 | ||||||||
\(604\) | 10448.0 | 0.703845 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | −1163.72 | −0.0780082 | ||||||||
\(607\) | −599.666 | −0.0400983 | −0.0200492 | − | 0.999799i | \(-0.506382\pi\) | ||||
−0.0200492 | + | 0.999799i | \(0.506382\pi\) | |||||||
\(608\) | −2796.05 | −0.186505 | ||||||||
\(609\) | 381.707 | 0.0253983 | ||||||||
\(610\) | 6497.70 | 0.431286 | ||||||||
\(611\) | 11711.5 | 0.775444 | ||||||||
\(612\) | −3918.29 | −0.258803 | ||||||||
\(613\) | 17067.6 | 1.12456 | 0.562280 | − | 0.826947i | \(-0.309924\pi\) | ||||
0.562280 | + | 0.826947i | \(0.309924\pi\) | |||||||
\(614\) | −5707.74 | −0.375156 | ||||||||
\(615\) | 1984.42 | 0.130113 | ||||||||
\(616\) | 3733.82 | 0.244220 | ||||||||
\(617\) | 10691.4 | 0.697600 | 0.348800 | − | 0.937197i | \(-0.386589\pi\) | ||||
0.348800 | + | 0.937197i | \(0.386589\pi\) | |||||||
\(618\) | −431.759 | −0.0281034 | ||||||||
\(619\) | −19853.6 | −1.28915 | −0.644573 | − | 0.764543i | \(-0.722965\pi\) | ||||
−0.644573 | + | 0.764543i | \(0.722965\pi\) | |||||||
\(620\) | 4963.01 | 0.321483 | ||||||||
\(621\) | −5529.17 | −0.357291 | ||||||||
\(622\) | 18363.8 | 1.18380 | ||||||||
\(623\) | 2539.46 | 0.163309 | ||||||||
\(624\) | 1348.52 | 0.0865125 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 21885.2 | 1.39730 | ||||||||
\(627\) | 282.421 | 0.0179885 | ||||||||
\(628\) | −2479.86 | −0.157575 | ||||||||
\(629\) | −5143.70 | −0.326062 | ||||||||
\(630\) | 3691.63 | 0.233457 | ||||||||
\(631\) | 5829.93 | 0.367806 | 0.183903 | − | 0.982944i | \(-0.441127\pi\) | ||||
0.183903 | + | 0.982944i | \(0.441127\pi\) | |||||||
\(632\) | −11585.2 | −0.729171 | ||||||||
\(633\) | 4172.32 | 0.261982 | ||||||||
\(634\) | −583.815 | −0.0365714 | ||||||||
\(635\) | 1078.10 | 0.0673752 | ||||||||
\(636\) | −1858.61 | −0.115878 | ||||||||
\(637\) | −6552.72 | −0.407580 | ||||||||
\(638\) | 468.962 | 0.0291009 | ||||||||
\(639\) | −20868.8 | −1.29195 | ||||||||
\(640\) | −723.883 | −0.0447094 | ||||||||
\(641\) | −14587.1 | −0.898840 | −0.449420 | − | 0.893320i | \(-0.648369\pi\) | ||||
−0.449420 | + | 0.893320i | \(0.648369\pi\) | |||||||
\(642\) | −4187.16 | −0.257405 | ||||||||
\(643\) | 3107.91 | 0.190613 | 0.0953065 | − | 0.995448i | \(-0.469617\pi\) | ||||
0.0953065 | + | 0.995448i | \(0.469617\pi\) | |||||||
\(644\) | −3906.73 | −0.239047 | ||||||||
\(645\) | 1158.64 | 0.0707306 | ||||||||
\(646\) | 1741.15 | 0.106044 | ||||||||
\(647\) | −30018.7 | −1.82405 | −0.912023 | − | 0.410139i | \(-0.865480\pi\) | ||||
−0.912023 | + | 0.410139i | \(0.865480\pi\) | |||||||
\(648\) | 14230.7 | 0.862708 | ||||||||
\(649\) | 5198.82 | 0.314440 | ||||||||
\(650\) | −2318.23 | −0.139890 | ||||||||
\(651\) | 5232.37 | 0.315012 | ||||||||
\(652\) | −11163.1 | −0.670523 | ||||||||
\(653\) | −15017.8 | −0.899987 | −0.449994 | − | 0.893032i | \(-0.648574\pi\) | ||||
−0.449994 | + | 0.893032i | \(0.648574\pi\) | |||||||
\(654\) | −2096.38 | −0.125344 | ||||||||
\(655\) | 3417.56 | 0.203870 | ||||||||
\(656\) | −6650.17 | −0.395801 | ||||||||
\(657\) | 8819.33 | 0.523706 | ||||||||
\(658\) | 7793.31 | 0.461725 | ||||||||
\(659\) | −12515.7 | −0.739822 | −0.369911 | − | 0.929067i | \(-0.620612\pi\) | ||||
−0.369911 | + | 0.929067i | \(0.620612\pi\) | |||||||
\(660\) | 265.587 | 0.0156635 | ||||||||
\(661\) | −8228.73 | −0.484207 | −0.242103 | − | 0.970250i | \(-0.577837\pi\) | ||||
−0.242103 | + | 0.970250i | \(0.577837\pi\) | |||||||
\(662\) | −13499.4 | −0.792549 | ||||||||
\(663\) | 2594.11 | 0.151956 | ||||||||
\(664\) | 18434.9 | 1.07743 | ||||||||
\(665\) | 1324.31 | 0.0772247 | ||||||||
\(666\) | 6254.71 | 0.363912 | ||||||||
\(667\) | −1589.16 | −0.0922529 | ||||||||
\(668\) | 2556.11 | 0.148052 | ||||||||
\(669\) | 2906.81 | 0.167988 | ||||||||
\(670\) | −261.585 | −0.0150835 | ||||||||
\(671\) | −6794.41 | −0.390902 | ||||||||
\(672\) | −2772.09 | −0.159131 | ||||||||
\(673\) | 10839.5 | 0.620848 | 0.310424 | − | 0.950598i | \(-0.399529\pi\) | ||||
0.310424 | + | 0.950598i | \(0.399529\pi\) | |||||||
\(674\) | −22845.2 | −1.30558 | ||||||||
\(675\) | 1762.56 | 0.100505 | ||||||||
\(676\) | 909.272 | 0.0517337 | ||||||||
\(677\) | 26166.0 | 1.48544 | 0.742719 | − | 0.669604i | \(-0.233536\pi\) | ||||
0.742719 | + | 0.669604i | \(0.233536\pi\) | |||||||
\(678\) | 3106.09 | 0.175942 | ||||||||
\(679\) | −2252.60 | −0.127315 | ||||||||
\(680\) | 5302.94 | 0.299056 | ||||||||
\(681\) | −5988.22 | −0.336959 | ||||||||
\(682\) | 6428.44 | 0.360935 | ||||||||
\(683\) | 21585.3 | 1.20928 | 0.604641 | − | 0.796498i | \(-0.293317\pi\) | ||||
0.604641 | + | 0.796498i | \(0.293317\pi\) | |||||||
\(684\) | 1709.22 | 0.0955464 | ||||||||
\(685\) | −1769.31 | −0.0986888 | ||||||||
\(686\) | −14420.3 | −0.802578 | ||||||||
\(687\) | −7089.34 | −0.393705 | ||||||||
\(688\) | −3882.80 | −0.215161 | ||||||||
\(689\) | −16964.1 | −0.937999 | ||||||||
\(690\) | 1114.82 | 0.0615081 | ||||||||
\(691\) | 12782.1 | 0.703696 | 0.351848 | − | 0.936057i | \(-0.385553\pi\) | ||||
0.351848 | + | 0.936057i | \(0.385553\pi\) | |||||||
\(692\) | −3829.92 | −0.210393 | ||||||||
\(693\) | −3860.20 | −0.211597 | ||||||||
\(694\) | 10156.4 | 0.555523 | ||||||||
\(695\) | 2281.66 | 0.124530 | ||||||||
\(696\) | −666.745 | −0.0363116 | ||||||||
\(697\) | −12792.8 | −0.695210 | ||||||||
\(698\) | −25596.8 | −1.38804 | ||||||||
\(699\) | −6861.48 | −0.371280 | ||||||||
\(700\) | 1245.37 | 0.0672436 | ||||||||
\(701\) | −17148.3 | −0.923943 | −0.461971 | − | 0.886895i | \(-0.652858\pi\) | ||||
−0.461971 | + | 0.886895i | \(0.652858\pi\) | |||||||
\(702\) | −6537.65 | −0.351492 | ||||||||
\(703\) | 2243.77 | 0.120377 | ||||||||
\(704\) | −5398.28 | −0.288999 | ||||||||
\(705\) | 1795.34 | 0.0959098 | ||||||||
\(706\) | −6396.34 | −0.340977 | ||||||||
\(707\) | 5706.02 | 0.303532 | ||||||||
\(708\) | −2282.21 | −0.121145 | ||||||||
\(709\) | −20910.8 | −1.10765 | −0.553824 | − | 0.832634i | \(-0.686832\pi\) | ||||
−0.553824 | + | 0.832634i | \(0.686832\pi\) | |||||||
\(710\) | 8720.61 | 0.460956 | ||||||||
\(711\) | 11977.4 | 0.631768 | ||||||||
\(712\) | −4435.80 | −0.233481 | ||||||||
\(713\) | −21784.0 | −1.14420 | ||||||||
\(714\) | 1726.23 | 0.0904796 | ||||||||
\(715\) | 2424.09 | 0.126791 | ||||||||
\(716\) | −4655.11 | −0.242974 | ||||||||
\(717\) | 4721.74 | 0.245937 | ||||||||
\(718\) | −370.922 | −0.0192795 | ||||||||
\(719\) | −25881.4 | −1.34244 | −0.671218 | − | 0.741260i | \(-0.734229\pi\) | ||||
−0.671218 | + | 0.741260i | \(0.734229\pi\) | |||||||
\(720\) | −2849.98 | −0.147517 | ||||||||
\(721\) | 2117.02 | 0.109351 | ||||||||
\(722\) | −759.518 | −0.0391500 | ||||||||
\(723\) | 177.233 | 0.00911671 | ||||||||
\(724\) | 4051.87 | 0.207992 | ||||||||
\(725\) | 506.587 | 0.0259506 | ||||||||
\(726\) | 344.006 | 0.0175858 | ||||||||
\(727\) | 5329.67 | 0.271893 | 0.135947 | − | 0.990716i | \(-0.456592\pi\) | ||||
0.135947 | + | 0.990716i | \(0.456592\pi\) | |||||||
\(728\) | −14960.5 | −0.761640 | ||||||||
\(729\) | −12140.1 | −0.616781 | ||||||||
\(730\) | −3685.40 | −0.186853 | ||||||||
\(731\) | −7469.26 | −0.377922 | ||||||||
\(732\) | 2982.65 | 0.150604 | ||||||||
\(733\) | 15533.6 | 0.782738 | 0.391369 | − | 0.920234i | \(-0.372002\pi\) | ||||
0.391369 | + | 0.920234i | \(0.372002\pi\) | |||||||
\(734\) | 1809.38 | 0.0909883 | ||||||||
\(735\) | −1004.51 | −0.0504110 | ||||||||
\(736\) | 11541.1 | 0.578003 | ||||||||
\(737\) | 273.530 | 0.0136711 | ||||||||
\(738\) | 15555.9 | 0.775911 | ||||||||
\(739\) | −18629.2 | −0.927315 | −0.463658 | − | 0.886014i | \(-0.653463\pi\) | ||||
−0.463658 | + | 0.886014i | \(0.653463\pi\) | |||||||
\(740\) | 2110.02 | 0.104819 | ||||||||
\(741\) | −1131.59 | −0.0561000 | ||||||||
\(742\) | −11288.6 | −0.558515 | ||||||||
\(743\) | −12179.0 | −0.601350 | −0.300675 | − | 0.953727i | \(-0.597212\pi\) | ||||
−0.300675 | + | 0.953727i | \(0.597212\pi\) | |||||||
\(744\) | −9139.62 | −0.450369 | ||||||||
\(745\) | 12353.8 | 0.607529 | ||||||||
\(746\) | 19352.2 | 0.949778 | ||||||||
\(747\) | −19058.9 | −0.933507 | ||||||||
\(748\) | −1712.13 | −0.0836921 | ||||||||
\(749\) | 20530.7 | 1.00157 | ||||||||
\(750\) | −355.379 | −0.0173021 | ||||||||
\(751\) | −17345.0 | −0.842779 | −0.421389 | − | 0.906880i | \(-0.638457\pi\) | ||||
−0.421389 | + | 0.906880i | \(0.638457\pi\) | |||||||
\(752\) | −6016.52 | −0.291755 | ||||||||
\(753\) | 1477.98 | 0.0715282 | ||||||||
\(754\) | −1879.02 | −0.0907557 | ||||||||
\(755\) | 14618.7 | 0.704676 | ||||||||
\(756\) | 3512.07 | 0.168959 | ||||||||
\(757\) | −8740.90 | −0.419674 | −0.209837 | − | 0.977736i | \(-0.567293\pi\) | ||||
−0.209837 | + | 0.977736i | \(0.567293\pi\) | |||||||
\(758\) | 15639.8 | 0.749426 | ||||||||
\(759\) | −1165.73 | −0.0557488 | ||||||||
\(760\) | −2313.23 | −0.110407 | ||||||||
\(761\) | 12237.7 | 0.582940 | 0.291470 | − | 0.956580i | \(-0.405856\pi\) | ||||
0.291470 | + | 0.956580i | \(0.405856\pi\) | |||||||
\(762\) | −613.017 | −0.0291434 | ||||||||
\(763\) | 10279.1 | 0.487717 | ||||||||
\(764\) | 11730.6 | 0.555494 | ||||||||
\(765\) | −5482.44 | −0.259108 | ||||||||
\(766\) | −20313.1 | −0.958148 | ||||||||
\(767\) | −20830.4 | −0.980630 | ||||||||
\(768\) | 5716.83 | 0.268604 | ||||||||
\(769\) | −30994.0 | −1.45341 | −0.726704 | − | 0.686950i | \(-0.758949\pi\) | ||||
−0.726704 | + | 0.686950i | \(0.758949\pi\) | |||||||
\(770\) | 1613.09 | 0.0754958 | ||||||||
\(771\) | 1946.02 | 0.0909003 | ||||||||
\(772\) | 9665.52 | 0.450608 | ||||||||
\(773\) | 3179.76 | 0.147953 | 0.0739767 | − | 0.997260i | \(-0.476431\pi\) | ||||
0.0739767 | + | 0.997260i | \(0.476431\pi\) | |||||||
\(774\) | 9082.58 | 0.421791 | ||||||||
\(775\) | 6944.20 | 0.321862 | ||||||||
\(776\) | 3934.72 | 0.182021 | ||||||||
\(777\) | 2224.54 | 0.102709 | ||||||||
\(778\) | −23897.1 | −1.10122 | ||||||||
\(779\) | 5580.42 | 0.256662 | ||||||||
\(780\) | −1064.14 | −0.0488492 | ||||||||
\(781\) | −9118.83 | −0.417794 | ||||||||
\(782\) | −7186.82 | −0.328645 | ||||||||
\(783\) | 1428.63 | 0.0652043 | ||||||||
\(784\) | 3366.31 | 0.153349 | ||||||||
\(785\) | −3469.80 | −0.157761 | ||||||||
\(786\) | −1943.24 | −0.0881847 | ||||||||
\(787\) | −4618.33 | −0.209181 | −0.104591 | − | 0.994515i | \(-0.533353\pi\) | ||||
−0.104591 | + | 0.994515i | \(0.533353\pi\) | |||||||
\(788\) | 11354.7 | 0.513317 | ||||||||
\(789\) | 8053.87 | 0.363403 | ||||||||
\(790\) | −5005.07 | −0.225408 | ||||||||
\(791\) | −15229.9 | −0.684594 | ||||||||
\(792\) | 6742.79 | 0.302519 | ||||||||
\(793\) | 27223.6 | 1.21909 | ||||||||
\(794\) | −10391.5 | −0.464459 | ||||||||
\(795\) | −2600.55 | −0.116015 | ||||||||
\(796\) | 8825.99 | 0.393001 | ||||||||
\(797\) | −11910.6 | −0.529356 | −0.264678 | − | 0.964337i | \(-0.585266\pi\) | ||||
−0.264678 | + | 0.964337i | \(0.585266\pi\) | |||||||
\(798\) | −753.009 | −0.0334038 | ||||||||
\(799\) | −11573.8 | −0.512457 | ||||||||
\(800\) | −3679.02 | −0.162591 | ||||||||
\(801\) | 4585.95 | 0.202293 | ||||||||
\(802\) | 3171.46 | 0.139636 | ||||||||
\(803\) | 3853.68 | 0.169357 | ||||||||
\(804\) | −120.076 | −0.00526711 | ||||||||
\(805\) | −5466.26 | −0.239330 | ||||||||
\(806\) | −25757.2 | −1.12563 | ||||||||
\(807\) | 3518.51 | 0.153479 | ||||||||
\(808\) | −9966.97 | −0.433956 | ||||||||
\(809\) | 14183.9 | 0.616417 | 0.308208 | − | 0.951319i | \(-0.400271\pi\) | ||||
0.308208 | + | 0.951319i | \(0.400271\pi\) | |||||||
\(810\) | 6147.97 | 0.266688 | ||||||||
\(811\) | −9815.70 | −0.425001 | −0.212501 | − | 0.977161i | \(-0.568161\pi\) | ||||
−0.212501 | + | 0.977161i | \(0.568161\pi\) | |||||||
\(812\) | 1009.42 | 0.0436253 | ||||||||
\(813\) | −6971.66 | −0.300746 | ||||||||
\(814\) | 2733.05 | 0.117682 | ||||||||
\(815\) | −15619.3 | −0.671314 | ||||||||
\(816\) | −1332.67 | −0.0571723 | ||||||||
\(817\) | 3258.22 | 0.139523 | ||||||||
\(818\) | −25150.2 | −1.07501 | ||||||||
\(819\) | 15466.9 | 0.659900 | ||||||||
\(820\) | 5247.79 | 0.223489 | ||||||||
\(821\) | −28522.4 | −1.21247 | −0.606236 | − | 0.795285i | \(-0.707321\pi\) | ||||
−0.606236 | + | 0.795285i | \(0.707321\pi\) | |||||||
\(822\) | 1006.04 | 0.0426882 | ||||||||
\(823\) | −36441.1 | −1.54345 | −0.771724 | − | 0.635957i | \(-0.780605\pi\) | ||||
−0.771724 | + | 0.635957i | \(0.780605\pi\) | |||||||
\(824\) | −3697.90 | −0.156338 | ||||||||
\(825\) | 371.607 | 0.0156820 | ||||||||
\(826\) | −13861.4 | −0.583899 | ||||||||
\(827\) | 17468.3 | 0.734502 | 0.367251 | − | 0.930122i | \(-0.380299\pi\) | ||||
0.367251 | + | 0.930122i | \(0.380299\pi\) | |||||||
\(828\) | −7055.05 | −0.296111 | ||||||||
\(829\) | 23483.0 | 0.983834 | 0.491917 | − | 0.870642i | \(-0.336296\pi\) | ||||
0.491917 | + | 0.870642i | \(0.336296\pi\) | |||||||
\(830\) | 7964.29 | 0.333066 | ||||||||
\(831\) | 5359.64 | 0.223735 | ||||||||
\(832\) | 21629.6 | 0.901289 | ||||||||
\(833\) | 6475.70 | 0.269351 | ||||||||
\(834\) | −1297.37 | −0.0538658 | ||||||||
\(835\) | 3576.49 | 0.148227 | ||||||||
\(836\) | 746.860 | 0.0308979 | ||||||||
\(837\) | 19583.4 | 0.808721 | ||||||||
\(838\) | −27840.4 | −1.14765 | ||||||||
\(839\) | −3723.45 | −0.153216 | −0.0766078 | − | 0.997061i | \(-0.524409\pi\) | ||||
−0.0766078 | + | 0.997061i | \(0.524409\pi\) | |||||||
\(840\) | −2293.41 | −0.0942024 | ||||||||
\(841\) | −23978.4 | −0.983164 | ||||||||
\(842\) | 1768.29 | 0.0723744 | ||||||||
\(843\) | 8640.18 | 0.353005 | ||||||||
\(844\) | 11033.7 | 0.449993 | ||||||||
\(845\) | 1272.25 | 0.0517948 | ||||||||
\(846\) | 14073.7 | 0.571944 | ||||||||
\(847\) | −1686.75 | −0.0684267 | ||||||||
\(848\) | 8714.94 | 0.352915 | ||||||||
\(849\) | −4206.11 | −0.170027 | ||||||||
\(850\) | 2290.98 | 0.0924472 | ||||||||
\(851\) | −9261.46 | −0.373065 | ||||||||
\(852\) | 4003.04 | 0.160965 | ||||||||
\(853\) | 15522.6 | 0.623076 | 0.311538 | − | 0.950234i | \(-0.399156\pi\) | ||||
0.311538 | + | 0.950234i | \(0.399156\pi\) | |||||||
\(854\) | 18115.7 | 0.725886 | ||||||||
\(855\) | 2391.53 | 0.0956592 | ||||||||
\(856\) | −35861.9 | −1.43193 | ||||||||
\(857\) | −41729.3 | −1.66330 | −0.831649 | − | 0.555302i | \(-0.812603\pi\) | ||||
−0.831649 | + | 0.555302i | \(0.812603\pi\) | |||||||
\(858\) | −1378.35 | −0.0548440 | ||||||||
\(859\) | −10863.6 | −0.431502 | −0.215751 | − | 0.976448i | \(-0.569220\pi\) | ||||
−0.215751 | + | 0.976448i | \(0.569220\pi\) | |||||||
\(860\) | 3064.00 | 0.121490 | ||||||||
\(861\) | 5532.60 | 0.218990 | ||||||||
\(862\) | 20507.3 | 0.810305 | ||||||||
\(863\) | −29609.2 | −1.16791 | −0.583956 | − | 0.811785i | \(-0.698496\pi\) | ||||
−0.583956 | + | 0.811785i | \(0.698496\pi\) | |||||||
\(864\) | −10375.2 | −0.408532 | ||||||||
\(865\) | −5358.80 | −0.210641 | ||||||||
\(866\) | −15934.5 | −0.625261 | ||||||||
\(867\) | 4075.30 | 0.159636 | ||||||||
\(868\) | 13836.9 | 0.541079 | ||||||||
\(869\) | 5233.62 | 0.204302 | ||||||||
\(870\) | −288.048 | −0.0112250 | ||||||||
\(871\) | −1095.97 | −0.0426355 | ||||||||
\(872\) | −17955.0 | −0.697284 | ||||||||
\(873\) | −4067.91 | −0.157707 | ||||||||
\(874\) | 3135.01 | 0.121331 | ||||||||
\(875\) | 1742.51 | 0.0673230 | ||||||||
\(876\) | −1691.71 | −0.0652485 | ||||||||
\(877\) | −20633.9 | −0.794477 | −0.397239 | − | 0.917715i | \(-0.630031\pi\) | ||||
−0.397239 | + | 0.917715i | \(0.630031\pi\) | |||||||
\(878\) | −1372.82 | −0.0527680 | ||||||||
\(879\) | −5434.05 | −0.208516 | ||||||||
\(880\) | −1245.32 | −0.0477043 | ||||||||
\(881\) | −26074.6 | −0.997134 | −0.498567 | − | 0.866851i | \(-0.666140\pi\) | ||||
−0.498567 | + | 0.866851i | \(0.666140\pi\) | |||||||
\(882\) | −7874.41 | −0.300618 | ||||||||
\(883\) | −8802.66 | −0.335485 | −0.167742 | − | 0.985831i | \(-0.553648\pi\) | ||||
−0.167742 | + | 0.985831i | \(0.553648\pi\) | |||||||
\(884\) | 6860.10 | 0.261007 | ||||||||
\(885\) | −3193.25 | −0.121288 | ||||||||
\(886\) | 12651.6 | 0.479729 | ||||||||
\(887\) | 6551.53 | 0.248003 | 0.124002 | − | 0.992282i | \(-0.460427\pi\) | ||||
0.124002 | + | 0.992282i | \(0.460427\pi\) | |||||||
\(888\) | −3885.71 | −0.146842 | ||||||||
\(889\) | 3005.77 | 0.113398 | ||||||||
\(890\) | −1916.36 | −0.0721759 | ||||||||
\(891\) | −6428.71 | −0.241717 | ||||||||
\(892\) | 7687.04 | 0.288544 | ||||||||
\(893\) | 5048.70 | 0.189192 | ||||||||
\(894\) | −7024.46 | −0.262789 | ||||||||
\(895\) | −6513.39 | −0.243261 | ||||||||
\(896\) | −2018.20 | −0.0752492 | ||||||||
\(897\) | 4670.80 | 0.173861 | ||||||||
\(898\) | 9377.17 | 0.348464 | ||||||||
\(899\) | 5628.55 | 0.208813 | ||||||||
\(900\) | 2248.98 | 0.0832954 | ||||||||
\(901\) | 16764.7 | 0.619882 | ||||||||
\(902\) | 6797.31 | 0.250915 | ||||||||
\(903\) | 3230.30 | 0.119045 | ||||||||
\(904\) | 26602.8 | 0.978757 | ||||||||
\(905\) | 5669.34 | 0.208238 | ||||||||
\(906\) | −8312.30 | −0.304810 | ||||||||
\(907\) | −27373.0 | −1.00210 | −0.501050 | − | 0.865418i | \(-0.667053\pi\) | ||||
−0.501050 | + | 0.865418i | \(0.667053\pi\) | |||||||
\(908\) | −15835.8 | −0.578777 | ||||||||
\(909\) | 10304.3 | 0.375988 | ||||||||
\(910\) | −6463.27 | −0.235445 | ||||||||
\(911\) | −27648.6 | −1.00553 | −0.502766 | − | 0.864422i | \(-0.667684\pi\) | ||||
−0.502766 | + | 0.864422i | \(0.667684\pi\) | |||||||
\(912\) | 581.331 | 0.0211072 | ||||||||
\(913\) | −8327.96 | −0.301879 | ||||||||
\(914\) | 5424.49 | 0.196309 | ||||||||
\(915\) | 4173.30 | 0.150782 | ||||||||
\(916\) | −18747.7 | −0.676246 | ||||||||
\(917\) | 9528.20 | 0.343129 | ||||||||
\(918\) | 6460.81 | 0.232286 | ||||||||
\(919\) | 13285.7 | 0.476883 | 0.238442 | − | 0.971157i | \(-0.423363\pi\) | ||||
0.238442 | + | 0.971157i | \(0.423363\pi\) | |||||||
\(920\) | 9548.17 | 0.342167 | ||||||||
\(921\) | −3665.93 | −0.131158 | ||||||||
\(922\) | 9290.33 | 0.331844 | ||||||||
\(923\) | 36537.0 | 1.30296 | ||||||||
\(924\) | 740.460 | 0.0263629 | ||||||||
\(925\) | 2952.33 | 0.104943 | ||||||||
\(926\) | −15100.4 | −0.535887 | ||||||||
\(927\) | 3823.07 | 0.135454 | ||||||||
\(928\) | −2981.99 | −0.105483 | ||||||||
\(929\) | −26022.5 | −0.919021 | −0.459510 | − | 0.888172i | \(-0.651975\pi\) | ||||
−0.459510 | + | 0.888172i | \(0.651975\pi\) | |||||||
\(930\) | −3948.51 | −0.139222 | ||||||||
\(931\) | −2824.81 | −0.0994408 | ||||||||
\(932\) | −18145.1 | −0.637729 | ||||||||
\(933\) | 11794.6 | 0.413866 | ||||||||
\(934\) | −19808.7 | −0.693961 | ||||||||
\(935\) | −2395.60 | −0.0837909 | ||||||||
\(936\) | −27016.8 | −0.943452 | ||||||||
\(937\) | 46641.3 | 1.62615 | 0.813075 | − | 0.582158i | \(-0.197792\pi\) | ||||
0.813075 | + | 0.582158i | \(0.197792\pi\) | |||||||
\(938\) | −729.304 | −0.0253866 | ||||||||
\(939\) | 14056.3 | 0.488509 | ||||||||
\(940\) | 4747.76 | 0.164739 | ||||||||
\(941\) | −27230.8 | −0.943357 | −0.471679 | − | 0.881771i | \(-0.656352\pi\) | ||||
−0.471679 | + | 0.881771i | \(0.656352\pi\) | |||||||
\(942\) | 1972.95 | 0.0682400 | ||||||||
\(943\) | −23034.0 | −0.795428 | ||||||||
\(944\) | 10701.2 | 0.368955 | ||||||||
\(945\) | 4914.06 | 0.169158 | ||||||||
\(946\) | 3968.71 | 0.136400 | ||||||||
\(947\) | −37535.1 | −1.28799 | −0.643996 | − | 0.765029i | \(-0.722725\pi\) | ||||
−0.643996 | + | 0.765029i | \(0.722725\pi\) | |||||||
\(948\) | −2297.49 | −0.0787120 | ||||||||
\(949\) | −15440.8 | −0.528166 | ||||||||
\(950\) | −999.365 | −0.0341302 | ||||||||
\(951\) | −374.969 | −0.0127857 | ||||||||
\(952\) | 14784.7 | 0.503334 | ||||||||
\(953\) | 2383.13 | 0.0810044 | 0.0405022 | − | 0.999179i | \(-0.487104\pi\) | ||||
0.0405022 | + | 0.999179i | \(0.487104\pi\) | |||||||
\(954\) | −20385.8 | −0.691839 | ||||||||
\(955\) | 16413.3 | 0.556150 | ||||||||
\(956\) | 12486.6 | 0.422432 | ||||||||
\(957\) | 301.202 | 0.0101739 | ||||||||
\(958\) | −30601.1 | −1.03202 | ||||||||
\(959\) | −4932.86 | −0.166101 | ||||||||
\(960\) | 3315.76 | 0.111475 | ||||||||
\(961\) | 47364.1 | 1.58988 | ||||||||
\(962\) | −10950.7 | −0.367011 | ||||||||
\(963\) | 37075.8 | 1.24065 | ||||||||
\(964\) | 468.692 | 0.0156593 | ||||||||
\(965\) | 13523.9 | 0.451140 | ||||||||
\(966\) | 3108.15 | 0.103523 | ||||||||
\(967\) | 21589.3 | 0.717957 | 0.358979 | − | 0.933346i | \(-0.383125\pi\) | ||||
0.358979 | + | 0.933346i | \(0.383125\pi\) | |||||||
\(968\) | 2946.32 | 0.0978289 | ||||||||
\(969\) | 1118.29 | 0.0370740 | ||||||||
\(970\) | 1699.89 | 0.0562681 | ||||||||
\(971\) | −36213.7 | −1.19686 | −0.598431 | − | 0.801174i | \(-0.704209\pi\) | ||||
−0.598431 | + | 0.801174i | \(0.704209\pi\) | |||||||
\(972\) | 9624.50 | 0.317599 | ||||||||
\(973\) | 6361.31 | 0.209593 | ||||||||
\(974\) | 1947.71 | 0.0640747 | ||||||||
\(975\) | −1488.94 | −0.0489069 | ||||||||
\(976\) | −13985.5 | −0.458673 | ||||||||
\(977\) | 29395.9 | 0.962599 | 0.481300 | − | 0.876556i | \(-0.340165\pi\) | ||||
0.481300 | + | 0.876556i | \(0.340165\pi\) | |||||||
\(978\) | 8881.24 | 0.290379 | ||||||||
\(979\) | 2003.87 | 0.0654177 | ||||||||
\(980\) | −2656.43 | −0.0865883 | ||||||||
\(981\) | 18562.7 | 0.604141 | ||||||||
\(982\) | −7094.50 | −0.230544 | ||||||||
\(983\) | 33250.4 | 1.07886 | 0.539432 | − | 0.842029i | \(-0.318639\pi\) | ||||
0.539432 | + | 0.842029i | \(0.318639\pi\) | |||||||
\(984\) | −9664.05 | −0.313088 | ||||||||
\(985\) | 15887.4 | 0.513923 | ||||||||
\(986\) | 1856.93 | 0.0599764 | ||||||||
\(987\) | 5005.44 | 0.161423 | ||||||||
\(988\) | −2992.49 | −0.0963601 | ||||||||
\(989\) | −13448.7 | −0.432401 | ||||||||
\(990\) | 2913.03 | 0.0935175 | ||||||||
\(991\) | −33387.9 | −1.07024 | −0.535118 | − | 0.844778i | \(-0.679733\pi\) | ||||
−0.535118 | + | 0.844778i | \(0.679733\pi\) | |||||||
\(992\) | −40876.5 | −1.30830 | ||||||||
\(993\) | −8670.28 | −0.277083 | ||||||||
\(994\) | 24313.2 | 0.775823 | ||||||||
\(995\) | 12349.3 | 0.393465 | ||||||||
\(996\) | 3655.86 | 0.116306 | ||||||||
\(997\) | −22983.7 | −0.730092 | −0.365046 | − | 0.930990i | \(-0.618947\pi\) | ||||
−0.365046 | + | 0.930990i | \(0.618947\pi\) | |||||||
\(998\) | −5242.76 | −0.166289 | ||||||||
\(999\) | 8325.86 | 0.263682 |
(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 | 1045.4.a.c.1.7 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.c.1.7 | ✓ | 20 | 1.1 | even | 1 | trivial |