Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,4,Mod(1,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("77.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.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: | \(4.54314707044\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 42x^{3} + 18x^{2} + 368x + 352 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.18888\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 77.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.18888 | −0.773886 | −0.386943 | − | 0.922104i | \(-0.626469\pi\) | ||||
−0.386943 | + | 0.922104i | \(0.626469\pi\) | |||||||
\(3\) | 6.48496 | 1.24803 | 0.624016 | − | 0.781412i | \(-0.285500\pi\) | ||||
0.624016 | + | 0.781412i | \(0.285500\pi\) | |||||||
\(4\) | −3.20880 | −0.401100 | ||||||||
\(5\) | 7.60736 | 0.680423 | 0.340212 | − | 0.940349i | \(-0.389501\pi\) | ||||
0.340212 | + | 0.940349i | \(0.389501\pi\) | |||||||
\(6\) | −14.1948 | −0.965834 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 24.5347 | 1.08429 | ||||||||
\(9\) | 15.0547 | 0.557582 | ||||||||
\(10\) | −16.6516 | −0.526570 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −20.8090 | −0.500586 | ||||||||
\(13\) | 0.174238 | 0.00371730 | 0.00185865 | − | 0.999998i | \(-0.499408\pi\) | ||||
0.00185865 | + | 0.999998i | \(0.499408\pi\) | |||||||
\(14\) | −15.3222 | −0.292501 | ||||||||
\(15\) | 49.3335 | 0.849190 | ||||||||
\(16\) | −28.0332 | −0.438018 | ||||||||
\(17\) | 128.863 | 1.83846 | 0.919231 | − | 0.393719i | \(-0.128812\pi\) | ||||
0.919231 | + | 0.393719i | \(0.128812\pi\) | |||||||
\(18\) | −32.9530 | −0.431505 | ||||||||
\(19\) | 141.685 | 1.71078 | 0.855388 | − | 0.517988i | \(-0.173319\pi\) | ||||
0.855388 | + | 0.517988i | \(0.173319\pi\) | |||||||
\(20\) | −24.4105 | −0.272918 | ||||||||
\(21\) | 45.3947 | 0.471712 | ||||||||
\(22\) | −24.0777 | −0.233335 | ||||||||
\(23\) | −133.369 | −1.20910 | −0.604550 | − | 0.796567i | \(-0.706647\pi\) | ||||
−0.604550 | + | 0.796567i | \(0.706647\pi\) | |||||||
\(24\) | 159.107 | 1.35323 | ||||||||
\(25\) | −67.1280 | −0.537024 | ||||||||
\(26\) | −0.381386 | −0.00287677 | ||||||||
\(27\) | −77.4647 | −0.552151 | ||||||||
\(28\) | −22.4616 | −0.151602 | ||||||||
\(29\) | −177.002 | −1.13340 | −0.566698 | − | 0.823925i | \(-0.691779\pi\) | ||||
−0.566698 | + | 0.823925i | \(0.691779\pi\) | |||||||
\(30\) | −107.985 | −0.657176 | ||||||||
\(31\) | 48.2757 | 0.279696 | 0.139848 | − | 0.990173i | \(-0.455339\pi\) | ||||
0.139848 | + | 0.990173i | \(0.455339\pi\) | |||||||
\(32\) | −134.917 | −0.745316 | ||||||||
\(33\) | 71.3346 | 0.376296 | ||||||||
\(34\) | −282.065 | −1.42276 | ||||||||
\(35\) | 53.2515 | 0.257176 | ||||||||
\(36\) | −48.3076 | −0.223647 | ||||||||
\(37\) | 161.625 | 0.718136 | 0.359068 | − | 0.933311i | \(-0.383095\pi\) | ||||
0.359068 | + | 0.933311i | \(0.383095\pi\) | |||||||
\(38\) | −310.131 | −1.32394 | ||||||||
\(39\) | 1.12993 | 0.00463931 | ||||||||
\(40\) | 186.645 | 0.737778 | ||||||||
\(41\) | −195.689 | −0.745402 | −0.372701 | − | 0.927952i | \(-0.621568\pi\) | ||||
−0.372701 | + | 0.927952i | \(0.621568\pi\) | |||||||
\(42\) | −99.3636 | −0.365051 | ||||||||
\(43\) | −488.447 | −1.73227 | −0.866133 | − | 0.499814i | \(-0.833402\pi\) | ||||
−0.866133 | + | 0.499814i | \(0.833402\pi\) | |||||||
\(44\) | −35.2968 | −0.120936 | ||||||||
\(45\) | 114.527 | 0.379392 | ||||||||
\(46\) | 291.928 | 0.935705 | ||||||||
\(47\) | −171.705 | −0.532889 | −0.266444 | − | 0.963850i | \(-0.585849\pi\) | ||||
−0.266444 | + | 0.963850i | \(0.585849\pi\) | |||||||
\(48\) | −181.794 | −0.546660 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 146.935 | 0.415596 | ||||||||
\(51\) | 835.671 | 2.29446 | ||||||||
\(52\) | −0.559095 | −0.00149101 | ||||||||
\(53\) | −431.477 | −1.11826 | −0.559131 | − | 0.829079i | \(-0.688865\pi\) | ||||
−0.559131 | + | 0.829079i | \(0.688865\pi\) | |||||||
\(54\) | 169.561 | 0.427302 | ||||||||
\(55\) | 83.6810 | 0.205155 | ||||||||
\(56\) | 171.743 | 0.409824 | ||||||||
\(57\) | 918.821 | 2.13510 | ||||||||
\(58\) | 387.437 | 0.877120 | ||||||||
\(59\) | 194.176 | 0.428468 | 0.214234 | − | 0.976782i | \(-0.431275\pi\) | ||||
0.214234 | + | 0.976782i | \(0.431275\pi\) | |||||||
\(60\) | −158.301 | −0.340610 | ||||||||
\(61\) | 585.008 | 1.22791 | 0.613955 | − | 0.789341i | \(-0.289577\pi\) | ||||
0.613955 | + | 0.789341i | \(0.289577\pi\) | |||||||
\(62\) | −105.670 | −0.216453 | ||||||||
\(63\) | 105.383 | 0.210746 | ||||||||
\(64\) | 519.582 | 1.01481 | ||||||||
\(65\) | 1.32549 | 0.00252934 | ||||||||
\(66\) | −156.143 | −0.291210 | ||||||||
\(67\) | 155.905 | 0.284281 | 0.142140 | − | 0.989847i | \(-0.454602\pi\) | ||||
0.142140 | + | 0.989847i | \(0.454602\pi\) | |||||||
\(68\) | −413.496 | −0.737408 | ||||||||
\(69\) | −864.891 | −1.50899 | ||||||||
\(70\) | −116.561 | −0.199025 | ||||||||
\(71\) | −374.994 | −0.626811 | −0.313405 | − | 0.949619i | \(-0.601470\pi\) | ||||
−0.313405 | + | 0.949619i | \(0.601470\pi\) | |||||||
\(72\) | 369.364 | 0.604582 | ||||||||
\(73\) | 210.419 | 0.337365 | 0.168683 | − | 0.985670i | \(-0.446049\pi\) | ||||
0.168683 | + | 0.985670i | \(0.446049\pi\) | |||||||
\(74\) | −353.778 | −0.555755 | ||||||||
\(75\) | −435.323 | −0.670223 | ||||||||
\(76\) | −454.639 | −0.686193 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | −2.47327 | −0.00359029 | ||||||||
\(79\) | −7.00618 | −0.00997793 | −0.00498897 | − | 0.999988i | \(-0.501588\pi\) | ||||
−0.00498897 | + | 0.999988i | \(0.501588\pi\) | |||||||
\(80\) | −213.258 | −0.298038 | ||||||||
\(81\) | −908.833 | −1.24668 | ||||||||
\(82\) | 428.339 | 0.576856 | ||||||||
\(83\) | −93.6417 | −0.123837 | −0.0619187 | − | 0.998081i | \(-0.519722\pi\) | ||||
−0.0619187 | + | 0.998081i | \(0.519722\pi\) | |||||||
\(84\) | −145.663 | −0.189204 | ||||||||
\(85\) | 980.307 | 1.25093 | ||||||||
\(86\) | 1069.15 | 1.34058 | ||||||||
\(87\) | −1147.85 | −1.41451 | ||||||||
\(88\) | 269.882 | 0.326926 | ||||||||
\(89\) | −307.119 | −0.365781 | −0.182891 | − | 0.983133i | \(-0.558545\pi\) | ||||
−0.182891 | + | 0.983133i | \(0.558545\pi\) | |||||||
\(90\) | −250.685 | −0.293606 | ||||||||
\(91\) | 1.21967 | 0.00140501 | ||||||||
\(92\) | 427.954 | 0.484970 | ||||||||
\(93\) | 313.066 | 0.349069 | ||||||||
\(94\) | 375.842 | 0.412395 | ||||||||
\(95\) | 1077.85 | 1.16405 | ||||||||
\(96\) | −874.929 | −0.930178 | ||||||||
\(97\) | 965.991 | 1.01115 | 0.505575 | − | 0.862783i | \(-0.331280\pi\) | ||||
0.505575 | + | 0.862783i | \(0.331280\pi\) | |||||||
\(98\) | −107.255 | −0.110555 | ||||||||
\(99\) | 165.602 | 0.168117 | ||||||||
\(100\) | 215.401 | 0.215401 | ||||||||
\(101\) | −577.986 | −0.569424 | −0.284712 | − | 0.958613i | \(-0.591898\pi\) | ||||
−0.284712 | + | 0.958613i | \(0.591898\pi\) | |||||||
\(102\) | −1829.18 | −1.77565 | ||||||||
\(103\) | 133.232 | 0.127453 | 0.0637267 | − | 0.997967i | \(-0.479701\pi\) | ||||
0.0637267 | + | 0.997967i | \(0.479701\pi\) | |||||||
\(104\) | 4.27488 | 0.00403064 | ||||||||
\(105\) | 345.334 | 0.320963 | ||||||||
\(106\) | 944.451 | 0.865408 | ||||||||
\(107\) | 8.33627 | 0.00753175 | 0.00376587 | − | 0.999993i | \(-0.498801\pi\) | ||||
0.00376587 | + | 0.999993i | \(0.498801\pi\) | |||||||
\(108\) | 248.569 | 0.221468 | ||||||||
\(109\) | −317.052 | −0.278606 | −0.139303 | − | 0.990250i | \(-0.544486\pi\) | ||||
−0.139303 | + | 0.990250i | \(0.544486\pi\) | |||||||
\(110\) | −183.168 | −0.158767 | ||||||||
\(111\) | 1048.13 | 0.896256 | ||||||||
\(112\) | −196.232 | −0.165555 | ||||||||
\(113\) | −2170.00 | −1.80652 | −0.903260 | − | 0.429093i | \(-0.858833\pi\) | ||||
−0.903260 | + | 0.429093i | \(0.858833\pi\) | |||||||
\(114\) | −2011.19 | −1.65232 | ||||||||
\(115\) | −1014.58 | −0.822700 | ||||||||
\(116\) | 567.966 | 0.454606 | ||||||||
\(117\) | 2.62310 | 0.00207270 | ||||||||
\(118\) | −425.028 | −0.331585 | ||||||||
\(119\) | 902.040 | 0.694873 | ||||||||
\(120\) | 1210.38 | 0.920769 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1280.51 | −0.950263 | ||||||||
\(123\) | −1269.03 | −0.930285 | ||||||||
\(124\) | −154.907 | −0.112186 | ||||||||
\(125\) | −1461.59 | −1.04583 | ||||||||
\(126\) | −230.671 | −0.163094 | ||||||||
\(127\) | 1301.24 | 0.909184 | 0.454592 | − | 0.890700i | \(-0.349785\pi\) | ||||
0.454592 | + | 0.890700i | \(0.349785\pi\) | |||||||
\(128\) | −57.9688 | −0.0400294 | ||||||||
\(129\) | −3167.56 | −2.16192 | ||||||||
\(130\) | −2.90134 | −0.00195742 | ||||||||
\(131\) | 2522.22 | 1.68220 | 0.841098 | − | 0.540883i | \(-0.181910\pi\) | ||||
0.841098 | + | 0.540883i | \(0.181910\pi\) | |||||||
\(132\) | −228.899 | −0.150932 | ||||||||
\(133\) | 991.794 | 0.646612 | ||||||||
\(134\) | −341.257 | −0.220001 | ||||||||
\(135\) | −589.302 | −0.375696 | ||||||||
\(136\) | 3161.62 | 1.99343 | ||||||||
\(137\) | 2574.70 | 1.60563 | 0.802815 | − | 0.596228i | \(-0.203334\pi\) | ||||
0.802815 | + | 0.596228i | \(0.203334\pi\) | |||||||
\(138\) | 1893.14 | 1.16779 | ||||||||
\(139\) | −2741.49 | −1.67288 | −0.836438 | − | 0.548061i | \(-0.815366\pi\) | ||||
−0.836438 | + | 0.548061i | \(0.815366\pi\) | |||||||
\(140\) | −170.874 | −0.103153 | ||||||||
\(141\) | −1113.50 | −0.665062 | ||||||||
\(142\) | 820.816 | 0.485080 | ||||||||
\(143\) | 1.91662 | 0.00112081 | ||||||||
\(144\) | −422.031 | −0.244231 | ||||||||
\(145\) | −1346.52 | −0.771189 | ||||||||
\(146\) | −460.582 | −0.261082 | ||||||||
\(147\) | 317.763 | 0.178290 | ||||||||
\(148\) | −518.624 | −0.288045 | ||||||||
\(149\) | −1021.98 | −0.561907 | −0.280954 | − | 0.959721i | \(-0.590651\pi\) | ||||
−0.280954 | + | 0.959721i | \(0.590651\pi\) | |||||||
\(150\) | 952.869 | 0.518676 | ||||||||
\(151\) | 1016.40 | 0.547769 | 0.273885 | − | 0.961763i | \(-0.411691\pi\) | ||||
0.273885 | + | 0.961763i | \(0.411691\pi\) | |||||||
\(152\) | 3476.20 | 1.85498 | ||||||||
\(153\) | 1940.00 | 1.02509 | ||||||||
\(154\) | −168.544 | −0.0881925 | ||||||||
\(155\) | 367.251 | 0.190312 | ||||||||
\(156\) | −3.62571 | −0.00186083 | ||||||||
\(157\) | −1580.49 | −0.803422 | −0.401711 | − | 0.915767i | \(-0.631584\pi\) | ||||
−0.401711 | + | 0.915767i | \(0.631584\pi\) | |||||||
\(158\) | 15.3357 | 0.00772178 | ||||||||
\(159\) | −2798.11 | −1.39563 | ||||||||
\(160\) | −1026.36 | −0.507130 | ||||||||
\(161\) | −933.581 | −0.456997 | ||||||||
\(162\) | 1989.33 | 0.964792 | ||||||||
\(163\) | 768.358 | 0.369218 | 0.184609 | − | 0.982812i | \(-0.440898\pi\) | ||||
0.184609 | + | 0.982812i | \(0.440898\pi\) | |||||||
\(164\) | 627.927 | 0.298981 | ||||||||
\(165\) | 542.668 | 0.256040 | ||||||||
\(166\) | 204.970 | 0.0958361 | ||||||||
\(167\) | 3092.73 | 1.43307 | 0.716534 | − | 0.697552i | \(-0.245727\pi\) | ||||
0.716534 | + | 0.697552i | \(0.245727\pi\) | |||||||
\(168\) | 1113.75 | 0.511473 | ||||||||
\(169\) | −2196.97 | −0.999986 | ||||||||
\(170\) | −2145.77 | −0.968079 | ||||||||
\(171\) | 2133.03 | 0.953898 | ||||||||
\(172\) | 1567.33 | 0.694812 | ||||||||
\(173\) | −1327.46 | −0.583380 | −0.291690 | − | 0.956513i | \(-0.594218\pi\) | ||||
−0.291690 | + | 0.956513i | \(0.594218\pi\) | |||||||
\(174\) | 2512.51 | 1.09467 | ||||||||
\(175\) | −469.896 | −0.202976 | ||||||||
\(176\) | −308.365 | −0.132067 | ||||||||
\(177\) | 1259.23 | 0.534741 | ||||||||
\(178\) | 672.247 | 0.283073 | ||||||||
\(179\) | 3141.37 | 1.31171 | 0.655857 | − | 0.754885i | \(-0.272307\pi\) | ||||
0.655857 | + | 0.754885i | \(0.272307\pi\) | |||||||
\(180\) | −367.494 | −0.152174 | ||||||||
\(181\) | −3683.36 | −1.51261 | −0.756303 | − | 0.654221i | \(-0.772997\pi\) | ||||
−0.756303 | + | 0.654221i | \(0.772997\pi\) | |||||||
\(182\) | −2.66970 | −0.00108732 | ||||||||
\(183\) | 3793.75 | 1.53247 | ||||||||
\(184\) | −3272.16 | −1.31102 | ||||||||
\(185\) | 1229.54 | 0.488636 | ||||||||
\(186\) | −685.264 | −0.270140 | ||||||||
\(187\) | 1417.49 | 0.554317 | ||||||||
\(188\) | 550.968 | 0.213742 | ||||||||
\(189\) | −542.253 | −0.208694 | ||||||||
\(190\) | −2359.28 | −0.900843 | ||||||||
\(191\) | −2862.38 | −1.08437 | −0.542185 | − | 0.840259i | \(-0.682403\pi\) | ||||
−0.542185 | + | 0.840259i | \(0.682403\pi\) | |||||||
\(192\) | 3369.47 | 1.26651 | ||||||||
\(193\) | 2023.91 | 0.754839 | 0.377420 | − | 0.926042i | \(-0.376811\pi\) | ||||
0.377420 | + | 0.926042i | \(0.376811\pi\) | |||||||
\(194\) | −2114.44 | −0.782515 | ||||||||
\(195\) | 8.59576 | 0.00315669 | ||||||||
\(196\) | −157.231 | −0.0573001 | ||||||||
\(197\) | −4767.82 | −1.72433 | −0.862165 | − | 0.506628i | \(-0.830892\pi\) | ||||
−0.862165 | + | 0.506628i | \(0.830892\pi\) | |||||||
\(198\) | −362.483 | −0.130104 | ||||||||
\(199\) | 3546.72 | 1.26342 | 0.631709 | − | 0.775205i | \(-0.282354\pi\) | ||||
0.631709 | + | 0.775205i | \(0.282354\pi\) | |||||||
\(200\) | −1646.97 | −0.582291 | ||||||||
\(201\) | 1011.04 | 0.354791 | ||||||||
\(202\) | 1265.14 | 0.440669 | ||||||||
\(203\) | −1239.02 | −0.428384 | ||||||||
\(204\) | −2681.50 | −0.920308 | ||||||||
\(205\) | −1488.68 | −0.507189 | ||||||||
\(206\) | −291.628 | −0.0986343 | ||||||||
\(207\) | −2007.83 | −0.674173 | ||||||||
\(208\) | −4.88444 | −0.00162824 | ||||||||
\(209\) | 1558.53 | 0.515818 | ||||||||
\(210\) | −755.895 | −0.248389 | ||||||||
\(211\) | 1453.49 | 0.474230 | 0.237115 | − | 0.971482i | \(-0.423798\pi\) | ||||
0.237115 | + | 0.971482i | \(0.423798\pi\) | |||||||
\(212\) | 1384.52 | 0.448536 | ||||||||
\(213\) | −2431.82 | −0.782279 | ||||||||
\(214\) | −18.2471 | −0.00582872 | ||||||||
\(215\) | −3715.79 | −1.17867 | ||||||||
\(216\) | −1900.57 | −0.598693 | ||||||||
\(217\) | 337.930 | 0.105715 | ||||||||
\(218\) | 693.989 | 0.215610 | ||||||||
\(219\) | 1364.56 | 0.421042 | ||||||||
\(220\) | −268.516 | −0.0822879 | ||||||||
\(221\) | 22.4528 | 0.00683411 | ||||||||
\(222\) | −2294.24 | −0.693600 | ||||||||
\(223\) | 6440.10 | 1.93391 | 0.966953 | − | 0.254955i | \(-0.0820606\pi\) | ||||
0.966953 | + | 0.254955i | \(0.0820606\pi\) | |||||||
\(224\) | −944.416 | −0.281703 | ||||||||
\(225\) | −1010.59 | −0.299435 | ||||||||
\(226\) | 4749.88 | 1.39804 | ||||||||
\(227\) | −1313.21 | −0.383970 | −0.191985 | − | 0.981398i | \(-0.561492\pi\) | ||||
−0.191985 | + | 0.981398i | \(0.561492\pi\) | |||||||
\(228\) | −2948.31 | −0.856390 | ||||||||
\(229\) | −3780.00 | −1.09078 | −0.545392 | − | 0.838181i | \(-0.683619\pi\) | ||||
−0.545392 | + | 0.838181i | \(0.683619\pi\) | |||||||
\(230\) | 2220.80 | 0.636676 | ||||||||
\(231\) | 499.342 | 0.142226 | ||||||||
\(232\) | −4342.70 | −1.22893 | ||||||||
\(233\) | 2322.65 | 0.653055 | 0.326527 | − | 0.945188i | \(-0.394121\pi\) | ||||
0.326527 | + | 0.945188i | \(0.394121\pi\) | |||||||
\(234\) | −5.74166 | −0.00160403 | ||||||||
\(235\) | −1306.22 | −0.362590 | ||||||||
\(236\) | −623.073 | −0.171859 | ||||||||
\(237\) | −45.4348 | −0.0124528 | ||||||||
\(238\) | −1974.46 | −0.537753 | ||||||||
\(239\) | 2204.79 | 0.596718 | 0.298359 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298359 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(240\) | −1382.97 | −0.371960 | ||||||||
\(241\) | −4610.39 | −1.23229 | −0.616144 | − | 0.787634i | \(-0.711306\pi\) | ||||
−0.616144 | + | 0.787634i | \(0.711306\pi\) | |||||||
\(242\) | −264.855 | −0.0703533 | ||||||||
\(243\) | −3802.20 | −1.00375 | ||||||||
\(244\) | −1877.17 | −0.492516 | ||||||||
\(245\) | 372.761 | 0.0972033 | ||||||||
\(246\) | 2777.76 | 0.719934 | ||||||||
\(247\) | 24.6869 | 0.00635946 | ||||||||
\(248\) | 1184.43 | 0.303272 | ||||||||
\(249\) | −607.263 | −0.154553 | ||||||||
\(250\) | 3199.24 | 0.809351 | ||||||||
\(251\) | 4981.12 | 1.25261 | 0.626306 | − | 0.779577i | \(-0.284566\pi\) | ||||
0.626306 | + | 0.779577i | \(0.284566\pi\) | |||||||
\(252\) | −338.154 | −0.0845304 | ||||||||
\(253\) | −1467.06 | −0.364557 | ||||||||
\(254\) | −2848.26 | −0.703605 | ||||||||
\(255\) | 6357.25 | 1.56120 | ||||||||
\(256\) | −4029.77 | −0.983829 | ||||||||
\(257\) | 2726.08 | 0.661665 | 0.330833 | − | 0.943689i | \(-0.392670\pi\) | ||||
0.330833 | + | 0.943689i | \(0.392670\pi\) | |||||||
\(258\) | 6933.40 | 1.67308 | ||||||||
\(259\) | 1131.38 | 0.271430 | ||||||||
\(260\) | −4.25324 | −0.00101452 | ||||||||
\(261\) | −2664.72 | −0.631962 | ||||||||
\(262\) | −5520.84 | −1.30183 | ||||||||
\(263\) | −4228.84 | −0.991489 | −0.495744 | − | 0.868468i | \(-0.665105\pi\) | ||||
−0.495744 | + | 0.868468i | \(0.665105\pi\) | |||||||
\(264\) | 1750.17 | 0.408014 | ||||||||
\(265\) | −3282.40 | −0.760892 | ||||||||
\(266\) | −2170.92 | −0.500404 | ||||||||
\(267\) | −1991.65 | −0.456507 | ||||||||
\(268\) | −500.268 | −0.114025 | ||||||||
\(269\) | −2396.04 | −0.543081 | −0.271541 | − | 0.962427i | \(-0.587533\pi\) | ||||
−0.271541 | + | 0.962427i | \(0.587533\pi\) | |||||||
\(270\) | 1289.91 | 0.290746 | ||||||||
\(271\) | −2461.68 | −0.551795 | −0.275897 | − | 0.961187i | \(-0.588975\pi\) | ||||
−0.275897 | + | 0.961187i | \(0.588975\pi\) | |||||||
\(272\) | −3612.43 | −0.805279 | ||||||||
\(273\) | 7.90948 | 0.00175349 | ||||||||
\(274\) | −5635.71 | −1.24258 | ||||||||
\(275\) | −738.408 | −0.161919 | ||||||||
\(276\) | 2775.26 | 0.605258 | ||||||||
\(277\) | 5890.54 | 1.27772 | 0.638860 | − | 0.769323i | \(-0.279406\pi\) | ||||
0.638860 | + | 0.769323i | \(0.279406\pi\) | |||||||
\(278\) | 6000.79 | 1.29462 | ||||||||
\(279\) | 726.777 | 0.155953 | ||||||||
\(280\) | 1306.51 | 0.278854 | ||||||||
\(281\) | −1964.26 | −0.417004 | −0.208502 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208502 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(282\) | 2437.32 | 0.514682 | ||||||||
\(283\) | 8513.60 | 1.78827 | 0.894136 | − | 0.447796i | \(-0.147791\pi\) | ||||
0.894136 | + | 0.447796i | \(0.147791\pi\) | |||||||
\(284\) | 1203.28 | 0.251414 | ||||||||
\(285\) | 6989.80 | 1.45277 | ||||||||
\(286\) | −4.19524 | −0.000867378 0 | ||||||||
\(287\) | −1369.82 | −0.281735 | ||||||||
\(288\) | −2031.13 | −0.415575 | ||||||||
\(289\) | 11692.6 | 2.37994 | ||||||||
\(290\) | 2947.37 | 0.596813 | ||||||||
\(291\) | 6264.42 | 1.26195 | ||||||||
\(292\) | −675.193 | −0.135317 | ||||||||
\(293\) | 5219.58 | 1.04072 | 0.520360 | − | 0.853947i | \(-0.325798\pi\) | ||||
0.520360 | + | 0.853947i | \(0.325798\pi\) | |||||||
\(294\) | −695.545 | −0.137976 | ||||||||
\(295\) | 1477.17 | 0.291539 | ||||||||
\(296\) | 3965.43 | 0.778669 | ||||||||
\(297\) | −852.111 | −0.166480 | ||||||||
\(298\) | 2237.00 | 0.434852 | ||||||||
\(299\) | −23.2379 | −0.00449459 | ||||||||
\(300\) | 1396.86 | 0.268827 | ||||||||
\(301\) | −3419.13 | −0.654735 | ||||||||
\(302\) | −2224.77 | −0.423911 | ||||||||
\(303\) | −3748.22 | −0.710659 | ||||||||
\(304\) | −3971.87 | −0.749350 | ||||||||
\(305\) | 4450.37 | 0.835499 | ||||||||
\(306\) | −4246.42 | −0.793306 | ||||||||
\(307\) | 2887.29 | 0.536764 | 0.268382 | − | 0.963313i | \(-0.413511\pi\) | ||||
0.268382 | + | 0.963313i | \(0.413511\pi\) | |||||||
\(308\) | −247.078 | −0.0457096 | ||||||||
\(309\) | 864.001 | 0.159066 | ||||||||
\(310\) | −803.868 | −0.147279 | ||||||||
\(311\) | −5876.90 | −1.07154 | −0.535769 | − | 0.844364i | \(-0.679978\pi\) | ||||
−0.535769 | + | 0.844364i | \(0.679978\pi\) | |||||||
\(312\) | 27.7224 | 0.00503036 | ||||||||
\(313\) | −7683.14 | −1.38747 | −0.693733 | − | 0.720233i | \(-0.744035\pi\) | ||||
−0.693733 | + | 0.720233i | \(0.744035\pi\) | |||||||
\(314\) | 3459.51 | 0.621757 | ||||||||
\(315\) | 801.687 | 0.143397 | ||||||||
\(316\) | 22.4814 | 0.00400215 | ||||||||
\(317\) | −9642.33 | −1.70841 | −0.854207 | − | 0.519933i | \(-0.825957\pi\) | ||||
−0.854207 | + | 0.519933i | \(0.825957\pi\) | |||||||
\(318\) | 6124.73 | 1.08006 | ||||||||
\(319\) | −1947.03 | −0.341732 | ||||||||
\(320\) | 3952.65 | 0.690499 | ||||||||
\(321\) | 54.0604 | 0.00939986 | ||||||||
\(322\) | 2043.50 | 0.353663 | ||||||||
\(323\) | 18257.9 | 3.14519 | ||||||||
\(324\) | 2916.27 | 0.500046 | ||||||||
\(325\) | −11.6962 | −0.00199628 | ||||||||
\(326\) | −1681.84 | −0.285732 | ||||||||
\(327\) | −2056.07 | −0.347710 | ||||||||
\(328\) | −4801.17 | −0.808233 | ||||||||
\(329\) | −1201.94 | −0.201413 | ||||||||
\(330\) | −1187.84 | −0.198146 | ||||||||
\(331\) | −2069.87 | −0.343717 | −0.171859 | − | 0.985122i | \(-0.554977\pi\) | ||||
−0.171859 | + | 0.985122i | \(0.554977\pi\) | |||||||
\(332\) | 300.478 | 0.0496713 | ||||||||
\(333\) | 2433.22 | 0.400420 | ||||||||
\(334\) | −6769.61 | −1.10903 | ||||||||
\(335\) | 1186.03 | 0.193431 | ||||||||
\(336\) | −1272.56 | −0.206618 | ||||||||
\(337\) | 7547.59 | 1.22001 | 0.610005 | − | 0.792397i | \(-0.291167\pi\) | ||||
0.610005 | + | 0.792397i | \(0.291167\pi\) | |||||||
\(338\) | 4808.90 | 0.773875 | ||||||||
\(339\) | −14072.4 | −2.25459 | ||||||||
\(340\) | −3145.61 | −0.501749 | ||||||||
\(341\) | 531.033 | 0.0843315 | ||||||||
\(342\) | −4668.94 | −0.738208 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −11983.9 | −1.87828 | ||||||||
\(345\) | −6579.54 | −1.02675 | ||||||||
\(346\) | 2905.65 | 0.451469 | ||||||||
\(347\) | −6353.22 | −0.982877 | −0.491439 | − | 0.870912i | \(-0.663529\pi\) | ||||
−0.491439 | + | 0.870912i | \(0.663529\pi\) | |||||||
\(348\) | 3683.23 | 0.567362 | ||||||||
\(349\) | −1352.47 | −0.207439 | −0.103719 | − | 0.994607i | \(-0.533074\pi\) | ||||
−0.103719 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(350\) | 1028.55 | 0.157080 | ||||||||
\(351\) | −13.4973 | −0.00205251 | ||||||||
\(352\) | −1484.08 | −0.224721 | ||||||||
\(353\) | 4203.80 | 0.633840 | 0.316920 | − | 0.948452i | \(-0.397351\pi\) | ||||
0.316920 | + | 0.948452i | \(0.397351\pi\) | |||||||
\(354\) | −2756.29 | −0.413829 | ||||||||
\(355\) | −2852.71 | −0.426497 | ||||||||
\(356\) | 985.484 | 0.146715 | ||||||||
\(357\) | 5849.70 | 0.867223 | ||||||||
\(358\) | −6876.08 | −1.01512 | ||||||||
\(359\) | −11100.7 | −1.63195 | −0.815976 | − | 0.578086i | \(-0.803800\pi\) | ||||
−0.815976 | + | 0.578086i | \(0.803800\pi\) | |||||||
\(360\) | 2809.88 | 0.411372 | ||||||||
\(361\) | 13215.6 | 1.92675 | ||||||||
\(362\) | 8062.43 | 1.17059 | ||||||||
\(363\) | 784.680 | 0.113457 | ||||||||
\(364\) | −3.91367 | −0.000563549 0 | ||||||||
\(365\) | 1600.73 | 0.229551 | ||||||||
\(366\) | −8304.07 | −1.18596 | ||||||||
\(367\) | −4963.35 | −0.705953 | −0.352977 | − | 0.935632i | \(-0.614830\pi\) | ||||
−0.352977 | + | 0.935632i | \(0.614830\pi\) | |||||||
\(368\) | 3738.74 | 0.529607 | ||||||||
\(369\) | −2946.04 | −0.415623 | ||||||||
\(370\) | −2691.32 | −0.378149 | ||||||||
\(371\) | −3020.34 | −0.422663 | ||||||||
\(372\) | −1004.57 | −0.140012 | ||||||||
\(373\) | −8882.54 | −1.23303 | −0.616515 | − | 0.787343i | \(-0.711456\pi\) | ||||
−0.616515 | + | 0.787343i | \(0.711456\pi\) | |||||||
\(374\) | −3102.72 | −0.428978 | ||||||||
\(375\) | −9478.34 | −1.30522 | ||||||||
\(376\) | −4212.74 | −0.577807 | ||||||||
\(377\) | −30.8405 | −0.00421317 | ||||||||
\(378\) | 1186.93 | 0.161505 | ||||||||
\(379\) | −1218.83 | −0.165190 | −0.0825952 | − | 0.996583i | \(-0.526321\pi\) | ||||
−0.0825952 | + | 0.996583i | \(0.526321\pi\) | |||||||
\(380\) | −3458.60 | −0.466901 | ||||||||
\(381\) | 8438.49 | 1.13469 | ||||||||
\(382\) | 6265.41 | 0.839179 | ||||||||
\(383\) | 112.614 | 0.0150243 | 0.00751214 | − | 0.999972i | \(-0.497609\pi\) | ||||
0.00751214 | + | 0.999972i | \(0.497609\pi\) | |||||||
\(384\) | −375.926 | −0.0499580 | ||||||||
\(385\) | 585.767 | 0.0775414 | ||||||||
\(386\) | −4430.09 | −0.584159 | ||||||||
\(387\) | −7353.43 | −0.965880 | ||||||||
\(388\) | −3099.68 | −0.405573 | ||||||||
\(389\) | 12656.2 | 1.64961 | 0.824804 | − | 0.565419i | \(-0.191286\pi\) | ||||
0.824804 | + | 0.565419i | \(0.191286\pi\) | |||||||
\(390\) | −18.8151 | −0.00244292 | ||||||||
\(391\) | −17186.3 | −2.22288 | ||||||||
\(392\) | 1202.20 | 0.154899 | ||||||||
\(393\) | 16356.5 | 2.09943 | ||||||||
\(394\) | 10436.2 | 1.33443 | ||||||||
\(395\) | −53.2985 | −0.00678922 | ||||||||
\(396\) | −531.384 | −0.0674320 | ||||||||
\(397\) | 3707.14 | 0.468655 | 0.234327 | − | 0.972158i | \(-0.424711\pi\) | ||||
0.234327 | + | 0.972158i | \(0.424711\pi\) | |||||||
\(398\) | −7763.35 | −0.977742 | ||||||||
\(399\) | 6431.74 | 0.806992 | ||||||||
\(400\) | 1881.81 | 0.235226 | ||||||||
\(401\) | 5671.06 | 0.706232 | 0.353116 | − | 0.935579i | \(-0.385122\pi\) | ||||
0.353116 | + | 0.935579i | \(0.385122\pi\) | |||||||
\(402\) | −2213.04 | −0.274568 | ||||||||
\(403\) | 8.41146 | 0.00103971 | ||||||||
\(404\) | 1854.64 | 0.228396 | ||||||||
\(405\) | −6913.82 | −0.848273 | ||||||||
\(406\) | 2712.06 | 0.331520 | ||||||||
\(407\) | 1777.88 | 0.216526 | ||||||||
\(408\) | 20503.0 | 2.48786 | ||||||||
\(409\) | 260.465 | 0.0314894 | 0.0157447 | − | 0.999876i | \(-0.494988\pi\) | ||||
0.0157447 | + | 0.999876i | \(0.494988\pi\) | |||||||
\(410\) | 3258.53 | 0.392506 | ||||||||
\(411\) | 16696.8 | 2.00388 | ||||||||
\(412\) | −427.514 | −0.0511216 | ||||||||
\(413\) | 1359.23 | 0.161946 | ||||||||
\(414\) | 4394.90 | 0.521733 | ||||||||
\(415\) | −712.366 | −0.0842619 | ||||||||
\(416\) | −23.5076 | −0.00277056 | ||||||||
\(417\) | −17778.4 | −2.08780 | ||||||||
\(418\) | −3411.44 | −0.399184 | ||||||||
\(419\) | 4153.96 | 0.484330 | 0.242165 | − | 0.970235i | \(-0.422142\pi\) | ||||
0.242165 | + | 0.970235i | \(0.422142\pi\) | |||||||
\(420\) | −1108.11 | −0.128739 | ||||||||
\(421\) | 4240.11 | 0.490856 | 0.245428 | − | 0.969415i | \(-0.421072\pi\) | ||||
0.245428 | + | 0.969415i | \(0.421072\pi\) | |||||||
\(422\) | −3181.52 | −0.367000 | ||||||||
\(423\) | −2584.97 | −0.297129 | ||||||||
\(424\) | −10586.2 | −1.21252 | ||||||||
\(425\) | −8650.31 | −0.987298 | ||||||||
\(426\) | 5322.96 | 0.605395 | ||||||||
\(427\) | 4095.05 | 0.464107 | ||||||||
\(428\) | −26.7494 | −0.00302099 | ||||||||
\(429\) | 12.4292 | 0.00139880 | ||||||||
\(430\) | 8133.42 | 0.912159 | ||||||||
\(431\) | 1012.17 | 0.113119 | 0.0565595 | − | 0.998399i | \(-0.481987\pi\) | ||||
0.0565595 | + | 0.998399i | \(0.481987\pi\) | |||||||
\(432\) | 2171.58 | 0.241852 | ||||||||
\(433\) | 1604.50 | 0.178077 | 0.0890386 | − | 0.996028i | \(-0.471621\pi\) | ||||
0.0890386 | + | 0.996028i | \(0.471621\pi\) | |||||||
\(434\) | −739.688 | −0.0818114 | ||||||||
\(435\) | −8732.13 | −0.962469 | ||||||||
\(436\) | 1017.36 | 0.111749 | ||||||||
\(437\) | −18896.3 | −2.06850 | ||||||||
\(438\) | −2986.85 | −0.325839 | ||||||||
\(439\) | 10671.6 | 1.16020 | 0.580099 | − | 0.814546i | \(-0.303014\pi\) | ||||
0.580099 | + | 0.814546i | \(0.303014\pi\) | |||||||
\(440\) | 2053.09 | 0.222448 | ||||||||
\(441\) | 737.681 | 0.0796546 | ||||||||
\(442\) | −49.1465 | −0.00528882 | ||||||||
\(443\) | 2193.74 | 0.235277 | 0.117638 | − | 0.993056i | \(-0.462468\pi\) | ||||
0.117638 | + | 0.993056i | \(0.462468\pi\) | |||||||
\(444\) | −3363.25 | −0.359489 | ||||||||
\(445\) | −2336.37 | −0.248886 | ||||||||
\(446\) | −14096.6 | −1.49662 | ||||||||
\(447\) | −6627.52 | −0.701278 | ||||||||
\(448\) | 3637.07 | 0.383561 | ||||||||
\(449\) | −7070.36 | −0.743143 | −0.371571 | − | 0.928404i | \(-0.621181\pi\) | ||||
−0.371571 | + | 0.928404i | \(0.621181\pi\) | |||||||
\(450\) | 2212.07 | 0.231729 | ||||||||
\(451\) | −2152.58 | −0.224747 | ||||||||
\(452\) | 6963.12 | 0.724596 | ||||||||
\(453\) | 6591.29 | 0.683633 | ||||||||
\(454\) | 2874.47 | 0.297149 | ||||||||
\(455\) | 9.27844 | 0.000956000 0 | ||||||||
\(456\) | 22543.0 | 2.31507 | ||||||||
\(457\) | 16245.8 | 1.66290 | 0.831451 | − | 0.555599i | \(-0.187511\pi\) | ||||
0.831451 | + | 0.555599i | \(0.187511\pi\) | |||||||
\(458\) | 8273.98 | 0.844143 | ||||||||
\(459\) | −9982.32 | −1.01511 | ||||||||
\(460\) | 3255.60 | 0.329985 | ||||||||
\(461\) | −5235.18 | −0.528908 | −0.264454 | − | 0.964398i | \(-0.585192\pi\) | ||||
−0.264454 | + | 0.964398i | \(0.585192\pi\) | |||||||
\(462\) | −1093.00 | −0.110067 | ||||||||
\(463\) | −11093.9 | −1.11355 | −0.556777 | − | 0.830662i | \(-0.687962\pi\) | ||||
−0.556777 | + | 0.830662i | \(0.687962\pi\) | |||||||
\(464\) | 4961.93 | 0.496448 | ||||||||
\(465\) | 2381.61 | 0.237515 | ||||||||
\(466\) | −5084.00 | −0.505390 | ||||||||
\(467\) | −7813.14 | −0.774195 | −0.387097 | − | 0.922039i | \(-0.626522\pi\) | ||||
−0.387097 | + | 0.922039i | \(0.626522\pi\) | |||||||
\(468\) | −8.41702 | −0.000831361 0 | ||||||||
\(469\) | 1091.33 | 0.107448 | ||||||||
\(470\) | 2859.17 | 0.280603 | ||||||||
\(471\) | −10249.4 | −1.00270 | ||||||||
\(472\) | 4764.06 | 0.464584 | ||||||||
\(473\) | −5372.91 | −0.522298 | ||||||||
\(474\) | 99.4513 | 0.00963703 | ||||||||
\(475\) | −9511.02 | −0.918728 | ||||||||
\(476\) | −2894.47 | −0.278714 | ||||||||
\(477\) | −6495.76 | −0.623523 | ||||||||
\(478\) | −4826.01 | −0.461792 | ||||||||
\(479\) | 5298.54 | 0.505420 | 0.252710 | − | 0.967542i | \(-0.418678\pi\) | ||||
0.252710 | + | 0.967542i | \(0.418678\pi\) | |||||||
\(480\) | −6655.90 | −0.632915 | ||||||||
\(481\) | 28.1612 | 0.00266953 | ||||||||
\(482\) | 10091.6 | 0.953650 | ||||||||
\(483\) | −6054.23 | −0.570346 | ||||||||
\(484\) | −388.265 | −0.0364637 | ||||||||
\(485\) | 7348.65 | 0.688010 | ||||||||
\(486\) | 8322.56 | 0.776788 | ||||||||
\(487\) | 5580.89 | 0.519290 | 0.259645 | − | 0.965704i | \(-0.416394\pi\) | ||||
0.259645 | + | 0.965704i | \(0.416394\pi\) | |||||||
\(488\) | 14353.0 | 1.33141 | ||||||||
\(489\) | 4982.77 | 0.460795 | ||||||||
\(490\) | −815.929 | −0.0752243 | ||||||||
\(491\) | 16718.8 | 1.53668 | 0.768341 | − | 0.640041i | \(-0.221083\pi\) | ||||
0.768341 | + | 0.640041i | \(0.221083\pi\) | |||||||
\(492\) | 4072.08 | 0.373138 | ||||||||
\(493\) | −22809.0 | −2.08371 | ||||||||
\(494\) | −54.0366 | −0.00492150 | ||||||||
\(495\) | 1259.79 | 0.114391 | ||||||||
\(496\) | −1353.32 | −0.122512 | ||||||||
\(497\) | −2624.96 | −0.236912 | ||||||||
\(498\) | 1329.23 | 0.119606 | ||||||||
\(499\) | 19594.4 | 1.75784 | 0.878922 | − | 0.476965i | \(-0.158263\pi\) | ||||
0.878922 | + | 0.476965i | \(0.158263\pi\) | |||||||
\(500\) | 4689.95 | 0.419482 | ||||||||
\(501\) | 20056.2 | 1.78851 | ||||||||
\(502\) | −10903.1 | −0.969379 | ||||||||
\(503\) | 9008.04 | 0.798506 | 0.399253 | − | 0.916841i | \(-0.369269\pi\) | ||||
0.399253 | + | 0.916841i | \(0.369269\pi\) | |||||||
\(504\) | 2585.54 | 0.228511 | ||||||||
\(505\) | −4396.95 | −0.387449 | ||||||||
\(506\) | 3211.21 | 0.282126 | ||||||||
\(507\) | −14247.3 | −1.24801 | ||||||||
\(508\) | −4175.42 | −0.364674 | ||||||||
\(509\) | −3379.88 | −0.294324 | −0.147162 | − | 0.989112i | \(-0.547014\pi\) | ||||
−0.147162 | + | 0.989112i | \(0.547014\pi\) | |||||||
\(510\) | −13915.3 | −1.20819 | ||||||||
\(511\) | 1472.93 | 0.127512 | ||||||||
\(512\) | 9284.42 | 0.801401 | ||||||||
\(513\) | −10975.6 | −0.944606 | ||||||||
\(514\) | −5967.05 | −0.512053 | ||||||||
\(515\) | 1013.54 | 0.0867222 | ||||||||
\(516\) | 10164.1 | 0.867148 | ||||||||
\(517\) | −1888.76 | −0.160672 | ||||||||
\(518\) | −2476.45 | −0.210056 | ||||||||
\(519\) | −8608.51 | −0.728076 | ||||||||
\(520\) | 32.5206 | 0.00274254 | ||||||||
\(521\) | −736.886 | −0.0619646 | −0.0309823 | − | 0.999520i | \(-0.509864\pi\) | ||||
−0.0309823 | + | 0.999520i | \(0.509864\pi\) | |||||||
\(522\) | 5832.75 | 0.489066 | ||||||||
\(523\) | 9541.00 | 0.797703 | 0.398852 | − | 0.917015i | \(-0.369409\pi\) | ||||
0.398852 | + | 0.917015i | \(0.369409\pi\) | |||||||
\(524\) | −8093.32 | −0.674729 | ||||||||
\(525\) | −3047.26 | −0.253320 | ||||||||
\(526\) | 9256.43 | 0.767299 | ||||||||
\(527\) | 6220.95 | 0.514210 | ||||||||
\(528\) | −1999.73 | −0.164824 | ||||||||
\(529\) | 5620.20 | 0.461922 | ||||||||
\(530\) | 7184.78 | 0.588843 | ||||||||
\(531\) | 2923.27 | 0.238906 | ||||||||
\(532\) | −3182.47 | −0.259356 | ||||||||
\(533\) | −34.0964 | −0.00277088 | ||||||||
\(534\) | 4359.49 | 0.353284 | ||||||||
\(535\) | 63.4170 | 0.00512478 | ||||||||
\(536\) | 3825.08 | 0.308243 | ||||||||
\(537\) | 20371.7 | 1.63706 | ||||||||
\(538\) | 5244.64 | 0.420283 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 1890.95 | 0.150692 | ||||||||
\(541\) | 16721.0 | 1.32882 | 0.664411 | − | 0.747368i | \(-0.268683\pi\) | ||||
0.664411 | + | 0.747368i | \(0.268683\pi\) | |||||||
\(542\) | 5388.32 | 0.427026 | ||||||||
\(543\) | −23886.4 | −1.88778 | ||||||||
\(544\) | −17385.7 | −1.37023 | ||||||||
\(545\) | −2411.93 | −0.189570 | ||||||||
\(546\) | −17.3129 | −0.00135700 | ||||||||
\(547\) | 8958.59 | 0.700259 | 0.350129 | − | 0.936701i | \(-0.386138\pi\) | ||||
0.350129 | + | 0.936701i | \(0.386138\pi\) | |||||||
\(548\) | −8261.70 | −0.644019 | ||||||||
\(549\) | 8807.13 | 0.684661 | ||||||||
\(550\) | 1616.29 | 0.125307 | ||||||||
\(551\) | −25078.5 | −1.93899 | ||||||||
\(552\) | −21219.9 | −1.63619 | ||||||||
\(553\) | −49.0432 | −0.00377130 | ||||||||
\(554\) | −12893.7 | −0.988809 | ||||||||
\(555\) | 7973.53 | 0.609834 | ||||||||
\(556\) | 8796.89 | 0.670992 | ||||||||
\(557\) | −14329.6 | −1.09006 | −0.545031 | − | 0.838416i | \(-0.683482\pi\) | ||||
−0.545031 | + | 0.838416i | \(0.683482\pi\) | |||||||
\(558\) | −1590.83 | −0.120690 | ||||||||
\(559\) | −85.1059 | −0.00643935 | ||||||||
\(560\) | −1492.81 | −0.112648 | ||||||||
\(561\) | 9192.38 | 0.691805 | ||||||||
\(562\) | 4299.54 | 0.322713 | ||||||||
\(563\) | 15791.2 | 1.18209 | 0.591047 | − | 0.806637i | \(-0.298715\pi\) | ||||
0.591047 | + | 0.806637i | \(0.298715\pi\) | |||||||
\(564\) | 3573.01 | 0.266757 | ||||||||
\(565\) | −16508.0 | −1.22920 | ||||||||
\(566\) | −18635.2 | −1.38392 | ||||||||
\(567\) | −6361.83 | −0.471202 | ||||||||
\(568\) | −9200.37 | −0.679646 | ||||||||
\(569\) | −13996.4 | −1.03121 | −0.515605 | − | 0.856826i | \(-0.672433\pi\) | ||||
−0.515605 | + | 0.856826i | \(0.672433\pi\) | |||||||
\(570\) | −15299.8 | −1.12428 | ||||||||
\(571\) | −6642.54 | −0.486833 | −0.243417 | − | 0.969922i | \(-0.578268\pi\) | ||||
−0.243417 | + | 0.969922i | \(0.578268\pi\) | |||||||
\(572\) | −6.15005 | −0.000449557 0 | ||||||||
\(573\) | −18562.4 | −1.35333 | ||||||||
\(574\) | 2998.38 | 0.218031 | ||||||||
\(575\) | 8952.78 | 0.649316 | ||||||||
\(576\) | 7822.16 | 0.565839 | ||||||||
\(577\) | −85.5448 | −0.00617206 | −0.00308603 | − | 0.999995i | \(-0.500982\pi\) | ||||
−0.00308603 | + | 0.999995i | \(0.500982\pi\) | |||||||
\(578\) | −25593.8 | −1.84180 | ||||||||
\(579\) | 13125.0 | 0.942063 | ||||||||
\(580\) | 4320.72 | 0.309324 | ||||||||
\(581\) | −655.492 | −0.0468062 | ||||||||
\(582\) | −13712.1 | −0.976603 | ||||||||
\(583\) | −4746.25 | −0.337169 | ||||||||
\(584\) | 5162.57 | 0.365802 | ||||||||
\(585\) | 19.9549 | 0.00141031 | ||||||||
\(586\) | −11425.0 | −0.805399 | ||||||||
\(587\) | 11205.0 | 0.787869 | 0.393934 | − | 0.919139i | \(-0.371114\pi\) | ||||
0.393934 | + | 0.919139i | \(0.371114\pi\) | |||||||
\(588\) | −1019.64 | −0.0715123 | ||||||||
\(589\) | 6839.93 | 0.478497 | ||||||||
\(590\) | −3233.35 | −0.225618 | ||||||||
\(591\) | −30919.1 | −2.15202 | ||||||||
\(592\) | −4530.87 | −0.314556 | ||||||||
\(593\) | 11664.6 | 0.807773 | 0.403886 | − | 0.914809i | \(-0.367659\pi\) | ||||
0.403886 | + | 0.914809i | \(0.367659\pi\) | |||||||
\(594\) | 1865.17 | 0.128836 | ||||||||
\(595\) | 6862.15 | 0.472808 | ||||||||
\(596\) | 3279.34 | 0.225381 | ||||||||
\(597\) | 23000.3 | 1.57679 | ||||||||
\(598\) | 50.8649 | 0.00347830 | ||||||||
\(599\) | −20545.1 | −1.40142 | −0.700711 | − | 0.713445i | \(-0.747134\pi\) | ||||
−0.700711 | + | 0.713445i | \(0.747134\pi\) | |||||||
\(600\) | −10680.5 | −0.726718 | ||||||||
\(601\) | 3885.01 | 0.263682 | 0.131841 | − | 0.991271i | \(-0.457911\pi\) | ||||
0.131841 | + | 0.991271i | \(0.457911\pi\) | |||||||
\(602\) | 7484.06 | 0.506690 | ||||||||
\(603\) | 2347.11 | 0.158510 | ||||||||
\(604\) | −3261.42 | −0.219710 | ||||||||
\(605\) | 920.491 | 0.0618567 | ||||||||
\(606\) | 8204.40 | 0.549969 | ||||||||
\(607\) | 8439.80 | 0.564351 | 0.282175 | − | 0.959363i | \(-0.408944\pi\) | ||||
0.282175 | + | 0.959363i | \(0.408944\pi\) | |||||||
\(608\) | −19115.6 | −1.27507 | ||||||||
\(609\) | −8034.97 | −0.534636 | ||||||||
\(610\) | −9741.32 | −0.646581 | ||||||||
\(611\) | −29.9175 | −0.00198091 | ||||||||
\(612\) | −6225.06 | −0.411165 | ||||||||
\(613\) | 17997.8 | 1.18584 | 0.592922 | − | 0.805260i | \(-0.297974\pi\) | ||||
0.592922 | + | 0.805260i | \(0.297974\pi\) | |||||||
\(614\) | −6319.94 | −0.415394 | ||||||||
\(615\) | −9654.01 | −0.632987 | ||||||||
\(616\) | 1889.17 | 0.123567 | ||||||||
\(617\) | −26336.6 | −1.71843 | −0.859214 | − | 0.511616i | \(-0.829047\pi\) | ||||
−0.859214 | + | 0.511616i | \(0.829047\pi\) | |||||||
\(618\) | −1891.20 | −0.123099 | ||||||||
\(619\) | 27875.5 | 1.81003 | 0.905016 | − | 0.425376i | \(-0.139858\pi\) | ||||
0.905016 | + | 0.425376i | \(0.139858\pi\) | |||||||
\(620\) | −1178.44 | −0.0763341 | ||||||||
\(621\) | 10331.4 | 0.667606 | ||||||||
\(622\) | 12863.8 | 0.829249 | ||||||||
\(623\) | −2149.83 | −0.138252 | ||||||||
\(624\) | −31.6754 | −0.00203210 | ||||||||
\(625\) | −2727.83 | −0.174581 | ||||||||
\(626\) | 16817.5 | 1.07374 | ||||||||
\(627\) | 10107.0 | 0.643757 | ||||||||
\(628\) | 5071.50 | 0.322253 | ||||||||
\(629\) | 20827.5 | 1.32027 | ||||||||
\(630\) | −1754.80 | −0.110973 | ||||||||
\(631\) | 8242.15 | 0.519992 | 0.259996 | − | 0.965610i | \(-0.416279\pi\) | ||||
0.259996 | + | 0.965610i | \(0.416279\pi\) | |||||||
\(632\) | −171.895 | −0.0108190 | ||||||||
\(633\) | 9425.84 | 0.591854 | ||||||||
\(634\) | 21105.9 | 1.32212 | ||||||||
\(635\) | 9899.00 | 0.618630 | ||||||||
\(636\) | 8978.59 | 0.559786 | ||||||||
\(637\) | 8.53766 | 0.000531043 0 | ||||||||
\(638\) | 4261.80 | 0.264462 | ||||||||
\(639\) | −5645.43 | −0.349499 | ||||||||
\(640\) | −440.990 | −0.0272370 | ||||||||
\(641\) | −7001.97 | −0.431453 | −0.215726 | − | 0.976454i | \(-0.569212\pi\) | ||||
−0.215726 | + | 0.976454i | \(0.569212\pi\) | |||||||
\(642\) | −118.332 | −0.00727442 | ||||||||
\(643\) | 2473.25 | 0.151688 | 0.0758442 | − | 0.997120i | \(-0.475835\pi\) | ||||
0.0758442 | + | 0.997120i | \(0.475835\pi\) | |||||||
\(644\) | 2995.68 | 0.183302 | ||||||||
\(645\) | −24096.8 | −1.47102 | ||||||||
\(646\) | −39964.4 | −2.43402 | ||||||||
\(647\) | 9153.21 | 0.556182 | 0.278091 | − | 0.960555i | \(-0.410298\pi\) | ||||
0.278091 | + | 0.960555i | \(0.410298\pi\) | |||||||
\(648\) | −22298.0 | −1.35177 | ||||||||
\(649\) | 2135.94 | 0.129188 | ||||||||
\(650\) | 25.6017 | 0.00154489 | ||||||||
\(651\) | 2191.46 | 0.131936 | ||||||||
\(652\) | −2465.51 | −0.148093 | ||||||||
\(653\) | 725.254 | 0.0434630 | 0.0217315 | − | 0.999764i | \(-0.493082\pi\) | ||||
0.0217315 | + | 0.999764i | \(0.493082\pi\) | |||||||
\(654\) | 4500.49 | 0.269088 | ||||||||
\(655\) | 19187.5 | 1.14461 | ||||||||
\(656\) | 5485.78 | 0.326499 | ||||||||
\(657\) | 3167.80 | 0.188109 | ||||||||
\(658\) | 2630.89 | 0.155871 | ||||||||
\(659\) | 14332.9 | 0.847242 | 0.423621 | − | 0.905840i | \(-0.360759\pi\) | ||||
0.423621 | + | 0.905840i | \(0.360759\pi\) | |||||||
\(660\) | −1741.32 | −0.102698 | ||||||||
\(661\) | 26773.3 | 1.57543 | 0.787715 | − | 0.616040i | \(-0.211264\pi\) | ||||
0.787715 | + | 0.616040i | \(0.211264\pi\) | |||||||
\(662\) | 4530.70 | 0.265998 | ||||||||
\(663\) | 145.606 | 0.00852919 | ||||||||
\(664\) | −2297.47 | −0.134276 | ||||||||
\(665\) | 7544.94 | 0.439970 | ||||||||
\(666\) | −5326.04 | −0.309879 | ||||||||
\(667\) | 23606.6 | 1.37039 | ||||||||
\(668\) | −9923.95 | −0.574804 | ||||||||
\(669\) | 41763.8 | 2.41358 | ||||||||
\(670\) | −2596.07 | −0.149694 | ||||||||
\(671\) | 6435.08 | 0.370229 | ||||||||
\(672\) | −6124.50 | −0.351574 | ||||||||
\(673\) | −25423.9 | −1.45619 | −0.728096 | − | 0.685475i | \(-0.759595\pi\) | ||||
−0.728096 | + | 0.685475i | \(0.759595\pi\) | |||||||
\(674\) | −16520.8 | −0.944149 | ||||||||
\(675\) | 5200.05 | 0.296519 | ||||||||
\(676\) | 7049.64 | 0.401095 | ||||||||
\(677\) | 9287.48 | 0.527248 | 0.263624 | − | 0.964625i | \(-0.415082\pi\) | ||||
0.263624 | + | 0.964625i | \(0.415082\pi\) | |||||||
\(678\) | 30802.8 | 1.74480 | ||||||||
\(679\) | 6761.94 | 0.382179 | ||||||||
\(680\) | 24051.6 | 1.35638 | ||||||||
\(681\) | −8516.15 | −0.479206 | ||||||||
\(682\) | −1162.37 | −0.0652629 | ||||||||
\(683\) | −31888.8 | −1.78652 | −0.893258 | − | 0.449544i | \(-0.851586\pi\) | ||||
−0.893258 | + | 0.449544i | \(0.851586\pi\) | |||||||
\(684\) | −6844.46 | −0.382609 | ||||||||
\(685\) | 19586.7 | 1.09251 | ||||||||
\(686\) | −750.786 | −0.0417859 | ||||||||
\(687\) | −24513.2 | −1.36133 | ||||||||
\(688\) | 13692.7 | 0.758763 | ||||||||
\(689\) | −75.1796 | −0.00415692 | ||||||||
\(690\) | 14401.8 | 0.794591 | ||||||||
\(691\) | −18650.3 | −1.02676 | −0.513379 | − | 0.858162i | \(-0.671606\pi\) | ||||
−0.513379 | + | 0.858162i | \(0.671606\pi\) | |||||||
\(692\) | 4259.55 | 0.233994 | ||||||||
\(693\) | 1159.21 | 0.0635424 | ||||||||
\(694\) | 13906.4 | 0.760635 | ||||||||
\(695\) | −20855.5 | −1.13826 | ||||||||
\(696\) | −28162.3 | −1.53375 | ||||||||
\(697\) | −25217.0 | −1.37039 | ||||||||
\(698\) | 2960.40 | 0.160534 | ||||||||
\(699\) | 15062.3 | 0.815033 | ||||||||
\(700\) | 1507.80 | 0.0814138 | ||||||||
\(701\) | 8566.01 | 0.461532 | 0.230766 | − | 0.973009i | \(-0.425877\pi\) | ||||
0.230766 | + | 0.973009i | \(0.425877\pi\) | |||||||
\(702\) | 29.5439 | 0.00158841 | ||||||||
\(703\) | 22899.8 | 1.22857 | ||||||||
\(704\) | 5715.40 | 0.305976 | ||||||||
\(705\) | −8470.81 | −0.452524 | ||||||||
\(706\) | −9201.61 | −0.490520 | ||||||||
\(707\) | −4045.90 | −0.215222 | ||||||||
\(708\) | −4040.61 | −0.214485 | ||||||||
\(709\) | 680.116 | 0.0360258 | 0.0180129 | − | 0.999838i | \(-0.494266\pi\) | ||||
0.0180129 | + | 0.999838i | \(0.494266\pi\) | |||||||
\(710\) | 6244.25 | 0.330060 | ||||||||
\(711\) | −105.476 | −0.00556352 | ||||||||
\(712\) | −7535.08 | −0.396614 | ||||||||
\(713\) | −6438.47 | −0.338180 | ||||||||
\(714\) | −12804.3 | −0.671132 | ||||||||
\(715\) | 14.5804 | 0.000762624 0 | ||||||||
\(716\) | −10080.0 | −0.526129 | ||||||||
\(717\) | 14297.9 | 0.744723 | ||||||||
\(718\) | 24298.0 | 1.26294 | ||||||||
\(719\) | 12557.6 | 0.651346 | 0.325673 | − | 0.945482i | \(-0.394409\pi\) | ||||
0.325673 | + | 0.945482i | \(0.394409\pi\) | |||||||
\(720\) | −3210.55 | −0.166181 | ||||||||
\(721\) | 932.621 | 0.0481728 | ||||||||
\(722\) | −28927.3 | −1.49109 | ||||||||
\(723\) | −29898.2 | −1.53793 | ||||||||
\(724\) | 11819.2 | 0.606707 | ||||||||
\(725\) | 11881.8 | 0.608661 | ||||||||
\(726\) | −1717.57 | −0.0878031 | ||||||||
\(727\) | 22253.6 | 1.13527 | 0.567635 | − | 0.823281i | \(-0.307859\pi\) | ||||
0.567635 | + | 0.823281i | \(0.307859\pi\) | |||||||
\(728\) | 29.9242 | 0.00152344 | ||||||||
\(729\) | −118.633 | −0.00602716 | ||||||||
\(730\) | −3503.81 | −0.177646 | ||||||||
\(731\) | −62942.6 | −3.18470 | ||||||||
\(732\) | −12173.4 | −0.614675 | ||||||||
\(733\) | 6852.72 | 0.345308 | 0.172654 | − | 0.984982i | \(-0.444766\pi\) | ||||
0.172654 | + | 0.984982i | \(0.444766\pi\) | |||||||
\(734\) | 10864.2 | 0.546327 | ||||||||
\(735\) | 2417.34 | 0.121313 | ||||||||
\(736\) | 17993.6 | 0.901161 | ||||||||
\(737\) | 1714.95 | 0.0857139 | ||||||||
\(738\) | 6448.53 | 0.321645 | ||||||||
\(739\) | −9133.20 | −0.454628 | −0.227314 | − | 0.973821i | \(-0.572994\pi\) | ||||
−0.227314 | + | 0.973821i | \(0.572994\pi\) | |||||||
\(740\) | −3945.36 | −0.195992 | ||||||||
\(741\) | 160.093 | 0.00793681 | ||||||||
\(742\) | 6611.16 | 0.327093 | ||||||||
\(743\) | −33458.7 | −1.65206 | −0.826031 | − | 0.563624i | \(-0.809407\pi\) | ||||
−0.826031 | + | 0.563624i | \(0.809407\pi\) | |||||||
\(744\) | 7680.99 | 0.378493 | ||||||||
\(745\) | −7774.60 | −0.382335 | ||||||||
\(746\) | 19442.8 | 0.954225 | ||||||||
\(747\) | −1409.75 | −0.0690496 | ||||||||
\(748\) | −4548.45 | −0.222337 | ||||||||
\(749\) | 58.3539 | 0.00284673 | ||||||||
\(750\) | 20746.9 | 1.01010 | ||||||||
\(751\) | −37530.0 | −1.82355 | −0.911776 | − | 0.410688i | \(-0.865289\pi\) | ||||
−0.911776 | + | 0.410688i | \(0.865289\pi\) | |||||||
\(752\) | 4813.44 | 0.233415 | ||||||||
\(753\) | 32302.4 | 1.56330 | ||||||||
\(754\) | 67.5062 | 0.00326052 | ||||||||
\(755\) | 7732.10 | 0.372715 | ||||||||
\(756\) | 1739.98 | 0.0837071 | ||||||||
\(757\) | 32174.8 | 1.54480 | 0.772399 | − | 0.635138i | \(-0.219057\pi\) | ||||
0.772399 | + | 0.635138i | \(0.219057\pi\) | |||||||
\(758\) | 2667.88 | 0.127839 | ||||||||
\(759\) | −9513.80 | −0.454979 | ||||||||
\(760\) | 26444.7 | 1.26217 | ||||||||
\(761\) | 4457.43 | 0.212328 | 0.106164 | − | 0.994349i | \(-0.466143\pi\) | ||||
0.106164 | + | 0.994349i | \(0.466143\pi\) | |||||||
\(762\) | −18470.8 | −0.878121 | ||||||||
\(763\) | −2219.37 | −0.105303 | ||||||||
\(764\) | 9184.82 | 0.434941 | ||||||||
\(765\) | 14758.2 | 0.697497 | ||||||||
\(766\) | −246.498 | −0.0116271 | ||||||||
\(767\) | 33.8329 | 0.00159274 | ||||||||
\(768\) | −26132.9 | −1.22785 | ||||||||
\(769\) | −38329.0 | −1.79737 | −0.898687 | − | 0.438591i | \(-0.855478\pi\) | ||||
−0.898687 | + | 0.438591i | \(0.855478\pi\) | |||||||
\(770\) | −1282.17 | −0.0600082 | ||||||||
\(771\) | 17678.5 | 0.825779 | ||||||||
\(772\) | −6494.32 | −0.302766 | ||||||||
\(773\) | −9529.23 | −0.443393 | −0.221696 | − | 0.975116i | \(-0.571159\pi\) | ||||
−0.221696 | + | 0.975116i | \(0.571159\pi\) | |||||||
\(774\) | 16095.8 | 0.747481 | ||||||||
\(775\) | −3240.65 | −0.150203 | ||||||||
\(776\) | 23700.3 | 1.09638 | ||||||||
\(777\) | 7336.94 | 0.338753 | ||||||||
\(778\) | −27703.0 | −1.27661 | ||||||||
\(779\) | −27726.1 | −1.27521 | ||||||||
\(780\) | −27.5821 | −0.00126615 | ||||||||
\(781\) | −4124.93 | −0.188991 | ||||||||
\(782\) | 37618.7 | 1.72026 | ||||||||
\(783\) | 13711.4 | 0.625806 | ||||||||
\(784\) | −1373.62 | −0.0625740 | ||||||||
\(785\) | −12023.4 | −0.546667 | ||||||||
\(786\) | −35802.5 | −1.62472 | ||||||||
\(787\) | 29705.1 | 1.34545 | 0.672726 | − | 0.739892i | \(-0.265123\pi\) | ||||
0.672726 | + | 0.739892i | \(0.265123\pi\) | |||||||
\(788\) | 15299.0 | 0.691629 | ||||||||
\(789\) | −27423.9 | −1.23741 | ||||||||
\(790\) | 116.664 | 0.00525408 | ||||||||
\(791\) | −15190.0 | −0.682801 | ||||||||
\(792\) | 4063.00 | 0.182288 | ||||||||
\(793\) | 101.931 | 0.00456451 | ||||||||
\(794\) | −8114.48 | −0.362685 | ||||||||
\(795\) | −21286.2 | −0.949617 | ||||||||
\(796\) | −11380.7 | −0.506758 | ||||||||
\(797\) | 8596.99 | 0.382084 | 0.191042 | − | 0.981582i | \(-0.438813\pi\) | ||||
0.191042 | + | 0.981582i | \(0.438813\pi\) | |||||||
\(798\) | −14078.3 | −0.624520 | ||||||||
\(799\) | −22126.4 | −0.979695 | ||||||||
\(800\) | 9056.69 | 0.400253 | ||||||||
\(801\) | −4623.59 | −0.203953 | ||||||||
\(802\) | −12413.3 | −0.546543 | ||||||||
\(803\) | 2314.61 | 0.101719 | ||||||||
\(804\) | −3244.22 | −0.142307 | ||||||||
\(805\) | −7102.09 | −0.310951 | ||||||||
\(806\) | −18.4117 | −0.000804620 0 | ||||||||
\(807\) | −15538.2 | −0.677783 | ||||||||
\(808\) | −14180.7 | −0.617422 | ||||||||
\(809\) | 16630.2 | 0.722727 | 0.361364 | − | 0.932425i | \(-0.382311\pi\) | ||||
0.361364 | + | 0.932425i | \(0.382311\pi\) | |||||||
\(810\) | 15133.5 | 0.656467 | ||||||||
\(811\) | 18584.2 | 0.804660 | 0.402330 | − | 0.915495i | \(-0.368201\pi\) | ||||
0.402330 | + | 0.915495i | \(0.368201\pi\) | |||||||
\(812\) | 3975.76 | 0.171825 | ||||||||
\(813\) | −15963.9 | −0.688657 | ||||||||
\(814\) | −3891.56 | −0.167567 | ||||||||
\(815\) | 5845.18 | 0.251224 | ||||||||
\(816\) | −23426.5 | −1.00501 | ||||||||
\(817\) | −69205.5 | −2.96352 | ||||||||
\(818\) | −570.127 | −0.0243692 | ||||||||
\(819\) | 18.3617 | 0.000783407 0 | ||||||||
\(820\) | 4776.87 | 0.203434 | ||||||||
\(821\) | −4088.88 | −0.173816 | −0.0869079 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869079 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(822\) | −36547.3 | −1.55077 | ||||||||
\(823\) | −12830.0 | −0.543410 | −0.271705 | − | 0.962381i | \(-0.587587\pi\) | ||||
−0.271705 | + | 0.962381i | \(0.587587\pi\) | |||||||
\(824\) | 3268.80 | 0.138197 | ||||||||
\(825\) | −4788.55 | −0.202080 | ||||||||
\(826\) | −2975.20 | −0.125327 | ||||||||
\(827\) | −13768.7 | −0.578942 | −0.289471 | − | 0.957187i | \(-0.593479\pi\) | ||||
−0.289471 | + | 0.957187i | \(0.593479\pi\) | |||||||
\(828\) | 6442.73 | 0.270411 | ||||||||
\(829\) | −10907.8 | −0.456987 | −0.228494 | − | 0.973545i | \(-0.573380\pi\) | ||||
−0.228494 | + | 0.973545i | \(0.573380\pi\) | |||||||
\(830\) | 1559.28 | 0.0652091 | ||||||||
\(831\) | 38199.9 | 1.59463 | ||||||||
\(832\) | 90.5308 | 0.00377234 | ||||||||
\(833\) | 6314.28 | 0.262637 | ||||||||
\(834\) | 38914.9 | 1.61572 | ||||||||
\(835\) | 23527.5 | 0.975093 | ||||||||
\(836\) | −5001.03 | −0.206895 | ||||||||
\(837\) | −3739.66 | −0.154434 | ||||||||
\(838\) | −9092.53 | −0.374817 | ||||||||
\(839\) | −27174.8 | −1.11821 | −0.559105 | − | 0.829097i | \(-0.688855\pi\) | ||||
−0.559105 | + | 0.829097i | \(0.688855\pi\) | |||||||
\(840\) | 8472.68 | 0.348018 | ||||||||
\(841\) | 6940.81 | 0.284588 | ||||||||
\(842\) | −9281.09 | −0.379866 | ||||||||
\(843\) | −12738.2 | −0.520434 | ||||||||
\(844\) | −4663.97 | −0.190214 | ||||||||
\(845\) | −16713.1 | −0.680414 | ||||||||
\(846\) | 5658.20 | 0.229944 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | 12095.7 | 0.489819 | ||||||||
\(849\) | 55210.3 | 2.23182 | ||||||||
\(850\) | 18934.5 | 0.764056 | ||||||||
\(851\) | −21555.7 | −0.868298 | ||||||||
\(852\) | 7803.23 | 0.313773 | ||||||||
\(853\) | −33975.1 | −1.36376 | −0.681878 | − | 0.731466i | \(-0.738837\pi\) | ||||
−0.681878 | + | 0.731466i | \(0.738837\pi\) | |||||||
\(854\) | −8963.58 | −0.359166 | ||||||||
\(855\) | 16226.7 | 0.649054 | ||||||||
\(856\) | 204.528 | 0.00816662 | ||||||||
\(857\) | 20423.7 | 0.814073 | 0.407037 | − | 0.913412i | \(-0.366562\pi\) | ||||
0.407037 | + | 0.913412i | \(0.366562\pi\) | |||||||
\(858\) | −27.2060 | −0.00108251 | ||||||||
\(859\) | −36704.2 | −1.45789 | −0.728947 | − | 0.684570i | \(-0.759990\pi\) | ||||
−0.728947 | + | 0.684570i | \(0.759990\pi\) | |||||||
\(860\) | 11923.2 | 0.472766 | ||||||||
\(861\) | −8883.24 | −0.351615 | ||||||||
\(862\) | −2215.51 | −0.0875413 | ||||||||
\(863\) | 26222.8 | 1.03434 | 0.517170 | − | 0.855883i | \(-0.326985\pi\) | ||||
0.517170 | + | 0.855883i | \(0.326985\pi\) | |||||||
\(864\) | 10451.3 | 0.411527 | ||||||||
\(865\) | −10098.5 | −0.396945 | ||||||||
\(866\) | −3512.06 | −0.137811 | ||||||||
\(867\) | 75826.4 | 2.97024 | ||||||||
\(868\) | −1084.35 | −0.0424024 | ||||||||
\(869\) | −77.0680 | −0.00300846 | ||||||||
\(870\) | 19113.6 | 0.744841 | ||||||||
\(871\) | 27.1645 | 0.00105676 | ||||||||
\(872\) | −7778.79 | −0.302091 | ||||||||
\(873\) | 14542.7 | 0.563799 | ||||||||
\(874\) | 41361.8 | 1.60078 | ||||||||
\(875\) | −10231.1 | −0.395285 | ||||||||
\(876\) | −4378.60 | −0.168880 | ||||||||
\(877\) | 44950.8 | 1.73076 | 0.865382 | − | 0.501113i | \(-0.167076\pi\) | ||||
0.865382 | + | 0.501113i | \(0.167076\pi\) | |||||||
\(878\) | −23358.8 | −0.897861 | ||||||||
\(879\) | 33848.8 | 1.29885 | ||||||||
\(880\) | −2345.84 | −0.0898617 | ||||||||
\(881\) | 3896.87 | 0.149023 | 0.0745113 | − | 0.997220i | \(-0.476260\pi\) | ||||
0.0745113 | + | 0.997220i | \(0.476260\pi\) | |||||||
\(882\) | −1614.70 | −0.0616436 | ||||||||
\(883\) | 6257.41 | 0.238481 | 0.119240 | − | 0.992865i | \(-0.461954\pi\) | ||||
0.119240 | + | 0.992865i | \(0.461954\pi\) | |||||||
\(884\) | −72.0466 | −0.00274117 | ||||||||
\(885\) | 9579.38 | 0.363850 | ||||||||
\(886\) | −4801.83 | −0.182077 | ||||||||
\(887\) | 40626.2 | 1.53787 | 0.768937 | − | 0.639324i | \(-0.220786\pi\) | ||||
0.768937 | + | 0.639324i | \(0.220786\pi\) | |||||||
\(888\) | 25715.7 | 0.971803 | ||||||||
\(889\) | 9108.68 | 0.343639 | ||||||||
\(890\) | 5114.02 | 0.192610 | ||||||||
\(891\) | −9997.16 | −0.375889 | ||||||||
\(892\) | −20665.0 | −0.775691 | ||||||||
\(893\) | −24328.0 | −0.911653 | ||||||||
\(894\) | 14506.9 | 0.542709 | ||||||||
\(895\) | 23897.5 | 0.892521 | ||||||||
\(896\) | −405.782 | −0.0151297 | ||||||||
\(897\) | −150.697 | −0.00560938 | ||||||||
\(898\) | 15476.2 | 0.575108 | ||||||||
\(899\) | −8544.91 | −0.317006 | ||||||||
\(900\) | 3242.80 | 0.120104 | ||||||||
\(901\) | −55601.4 | −2.05588 | ||||||||
\(902\) | 4711.73 | 0.173929 | ||||||||
\(903\) | −22172.9 | −0.817129 | ||||||||
\(904\) | −53240.5 | −1.95880 | ||||||||
\(905\) | −28020.6 | −1.02921 | ||||||||
\(906\) | −14427.5 | −0.529054 | ||||||||
\(907\) | 42366.9 | 1.55101 | 0.775506 | − | 0.631340i | \(-0.217495\pi\) | ||||
0.775506 | + | 0.631340i | \(0.217495\pi\) | |||||||
\(908\) | 4213.85 | 0.154010 | ||||||||
\(909\) | −8701.42 | −0.317501 | ||||||||
\(910\) | −20.3094 | −0.000739835 0 | ||||||||
\(911\) | 26231.4 | 0.953992 | 0.476996 | − | 0.878906i | \(-0.341726\pi\) | ||||
0.476996 | + | 0.878906i | \(0.341726\pi\) | |||||||
\(912\) | −25757.4 | −0.935213 | ||||||||
\(913\) | −1030.06 | −0.0373384 | ||||||||
\(914\) | −35560.1 | −1.28690 | ||||||||
\(915\) | 28860.5 | 1.04273 | ||||||||
\(916\) | 12129.3 | 0.437514 | ||||||||
\(917\) | 17655.6 | 0.635810 | ||||||||
\(918\) | 21850.1 | 0.785578 | ||||||||
\(919\) | 2542.24 | 0.0912522 | 0.0456261 | − | 0.998959i | \(-0.485472\pi\) | ||||
0.0456261 | + | 0.998959i | \(0.485472\pi\) | |||||||
\(920\) | −24892.5 | −0.892047 | ||||||||
\(921\) | 18724.0 | 0.669898 | ||||||||
\(922\) | 11459.2 | 0.409314 | ||||||||
\(923\) | −65.3381 | −0.00233004 | ||||||||
\(924\) | −1602.29 | −0.0570471 | ||||||||
\(925\) | −10849.6 | −0.385656 | ||||||||
\(926\) | 24283.2 | 0.861764 | ||||||||
\(927\) | 2005.76 | 0.0710657 | ||||||||
\(928\) | 23880.5 | 0.844739 | ||||||||
\(929\) | −20097.8 | −0.709782 | −0.354891 | − | 0.934908i | \(-0.615482\pi\) | ||||
−0.354891 | + | 0.934908i | \(0.615482\pi\) | |||||||
\(930\) | −5213.05 | −0.183809 | ||||||||
\(931\) | 6942.56 | 0.244396 | ||||||||
\(932\) | −7452.92 | −0.261941 | ||||||||
\(933\) | −38111.5 | −1.33731 | ||||||||
\(934\) | 17102.0 | 0.599138 | ||||||||
\(935\) | 10783.4 | 0.377170 | ||||||||
\(936\) | 64.3571 | 0.00224741 | ||||||||
\(937\) | −202.788 | −0.00707023 | −0.00353511 | − | 0.999994i | \(-0.501125\pi\) | ||||
−0.00353511 | + | 0.999994i | \(0.501125\pi\) | |||||||
\(938\) | −2388.80 | −0.0831525 | ||||||||
\(939\) | −49824.9 | −1.73160 | ||||||||
\(940\) | 4191.41 | 0.145435 | ||||||||
\(941\) | 12419.1 | 0.430235 | 0.215118 | − | 0.976588i | \(-0.430987\pi\) | ||||
0.215118 | + | 0.976588i | \(0.430987\pi\) | |||||||
\(942\) | 22434.8 | 0.775972 | ||||||||
\(943\) | 26098.8 | 0.901265 | ||||||||
\(944\) | −5443.37 | −0.187677 | ||||||||
\(945\) | −4125.11 | −0.142000 | ||||||||
\(946\) | 11760.7 | 0.404199 | ||||||||
\(947\) | 369.282 | 0.0126717 | 0.00633583 | − | 0.999980i | \(-0.497983\pi\) | ||||
0.00633583 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(948\) | 145.791 | 0.00499481 | ||||||||
\(949\) | 36.6629 | 0.00125409 | ||||||||
\(950\) | 20818.5 | 0.710990 | ||||||||
\(951\) | −62530.1 | −2.13215 | ||||||||
\(952\) | 22131.3 | 0.753445 | ||||||||
\(953\) | 25994.1 | 0.883558 | 0.441779 | − | 0.897124i | \(-0.354348\pi\) | ||||
0.441779 | + | 0.897124i | \(0.354348\pi\) | |||||||
\(954\) | 14218.5 | 0.482536 | ||||||||
\(955\) | −21775.2 | −0.737830 | ||||||||
\(956\) | −7074.72 | −0.239344 | ||||||||
\(957\) | −12626.4 | −0.426492 | ||||||||
\(958\) | −11597.9 | −0.391138 | ||||||||
\(959\) | 18022.9 | 0.606871 | ||||||||
\(960\) | 25632.8 | 0.861764 | ||||||||
\(961\) | −27460.5 | −0.921770 | ||||||||
\(962\) | −61.6416 | −0.00206591 | ||||||||
\(963\) | 125.500 | 0.00419957 | ||||||||
\(964\) | 14793.8 | 0.494271 | ||||||||
\(965\) | 15396.6 | 0.513610 | ||||||||
\(966\) | 13252.0 | 0.441383 | ||||||||
\(967\) | −53830.0 | −1.79013 | −0.895065 | − | 0.445937i | \(-0.852871\pi\) | ||||
−0.895065 | + | 0.445937i | \(0.852871\pi\) | |||||||
\(968\) | 2968.70 | 0.0985720 | ||||||||
\(969\) | 118402. | 3.92530 | ||||||||
\(970\) | −16085.3 | −0.532441 | ||||||||
\(971\) | −1349.54 | −0.0446022 | −0.0223011 | − | 0.999751i | \(-0.507099\pi\) | ||||
−0.0223011 | + | 0.999751i | \(0.507099\pi\) | |||||||
\(972\) | 12200.5 | 0.402605 | ||||||||
\(973\) | −19190.4 | −0.632288 | ||||||||
\(974\) | −12215.9 | −0.401872 | ||||||||
\(975\) | −75.8497 | −0.00249142 | ||||||||
\(976\) | −16399.6 | −0.537847 | ||||||||
\(977\) | 6611.71 | 0.216507 | 0.108253 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108253 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(978\) | −10906.7 | −0.356603 | ||||||||
\(979\) | −3378.31 | −0.110287 | ||||||||
\(980\) | −1196.12 | −0.0389883 | ||||||||
\(981\) | −4773.13 | −0.155346 | ||||||||
\(982\) | −36595.5 | −1.18922 | ||||||||
\(983\) | 40595.9 | 1.31720 | 0.658601 | − | 0.752493i | \(-0.271149\pi\) | ||||
0.658601 | + | 0.752493i | \(0.271149\pi\) | |||||||
\(984\) | −31135.4 | −1.00870 | ||||||||
\(985\) | −36270.5 | −1.17327 | ||||||||
\(986\) | 49926.2 | 1.61255 | ||||||||
\(987\) | −7794.51 | −0.251370 | ||||||||
\(988\) | −79.2153 | −0.00255078 | ||||||||
\(989\) | 65143.5 | 2.09448 | ||||||||
\(990\) | −2757.54 | −0.0885256 | ||||||||
\(991\) | −48877.7 | −1.56675 | −0.783376 | − | 0.621548i | \(-0.786504\pi\) | ||||
−0.783376 | + | 0.621548i | \(0.786504\pi\) | |||||||
\(992\) | −6513.19 | −0.208462 | ||||||||
\(993\) | −13423.0 | −0.428970 | ||||||||
\(994\) | 5745.71 | 0.183343 | ||||||||
\(995\) | 26981.2 | 0.859660 | ||||||||
\(996\) | 1948.59 | 0.0619913 | ||||||||
\(997\) | 13127.4 | 0.417000 | 0.208500 | − | 0.978022i | \(-0.433142\pi\) | ||||
0.208500 | + | 0.978022i | \(0.433142\pi\) | |||||||
\(998\) | −42889.7 | −1.36037 | ||||||||
\(999\) | −12520.2 | −0.396520 |
(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 | 77.4.a.e.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 693.4.a.o.1.4 | 5 | |||
4.3 | odd | 2 | 1232.4.a.y.1.2 | 5 | |||
5.4 | even | 2 | 1925.4.a.r.1.4 | 5 | |||
7.6 | odd | 2 | 539.4.a.h.1.2 | 5 | |||
11.10 | odd | 2 | 847.4.a.f.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.4.a.e.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
539.4.a.h.1.2 | 5 | 7.6 | odd | 2 | |||
693.4.a.o.1.4 | 5 | 3.2 | odd | 2 | |||
847.4.a.f.1.4 | 5 | 11.10 | odd | 2 | |||
1232.4.a.y.1.2 | 5 | 4.3 | odd | 2 | |||
1925.4.a.r.1.4 | 5 | 5.4 | even | 2 |