Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
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: | \( x^{5} - x^{4} - 37x^{3} + 21x^{2} + 288x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.227497\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.227497 | −0.0804324 | −0.0402162 | − | 0.999191i | \(-0.512805\pi\) | ||||
−0.0402162 | + | 0.999191i | \(0.512805\pi\) | |||||||
\(3\) | −1.80858 | −0.348062 | −0.174031 | − | 0.984740i | \(-0.555679\pi\) | ||||
−0.174031 | + | 0.984740i | \(0.555679\pi\) | |||||||
\(4\) | −7.94824 | −0.993531 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0.411448 | 0.0279955 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.62818 | 0.160345 | ||||||||
\(9\) | −23.7290 | −0.878853 | ||||||||
\(10\) | 1.13749 | 0.0359705 | ||||||||
\(11\) | 17.7019 | 0.485211 | 0.242605 | − | 0.970125i | \(-0.421998\pi\) | ||||
0.242605 | + | 0.970125i | \(0.421998\pi\) | |||||||
\(12\) | 14.3751 | 0.345810 | ||||||||
\(13\) | −62.3178 | −1.32953 | −0.664763 | − | 0.747054i | \(-0.731467\pi\) | ||||
−0.664763 | + | 0.747054i | \(0.731467\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.04291 | 0.155658 | ||||||||
\(16\) | 62.7606 | 0.980634 | ||||||||
\(17\) | 87.1623 | 1.24353 | 0.621764 | − | 0.783205i | \(-0.286416\pi\) | ||||
0.621764 | + | 0.783205i | \(0.286416\pi\) | |||||||
\(18\) | 5.39829 | 0.0706883 | ||||||||
\(19\) | −101.724 | −1.22826 | −0.614131 | − | 0.789204i | \(-0.710493\pi\) | ||||
−0.614131 | + | 0.789204i | \(0.710493\pi\) | |||||||
\(20\) | 39.7412 | 0.444320 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.02713 | −0.0390267 | ||||||||
\(23\) | 93.6396 | 0.848922 | 0.424461 | − | 0.905446i | \(-0.360464\pi\) | ||||
0.424461 | + | 0.905446i | \(0.360464\pi\) | |||||||
\(24\) | −6.56187 | −0.0558098 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 14.1771 | 0.106937 | ||||||||
\(27\) | 91.7477 | 0.653957 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 297.385 | 1.90424 | 0.952122 | − | 0.305718i | \(-0.0988963\pi\) | ||||
0.952122 | + | 0.305718i | \(0.0988963\pi\) | |||||||
\(30\) | −2.05724 | −0.0125200 | ||||||||
\(31\) | 91.2779 | 0.528838 | 0.264419 | − | 0.964408i | \(-0.414820\pi\) | ||||
0.264419 | + | 0.964408i | \(0.414820\pi\) | |||||||
\(32\) | −43.3033 | −0.239219 | ||||||||
\(33\) | −32.0153 | −0.168883 | ||||||||
\(34\) | −19.8292 | −0.100020 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 188.604 | 0.873167 | ||||||||
\(37\) | 281.210 | 1.24948 | 0.624738 | − | 0.780835i | \(-0.285206\pi\) | ||||
0.624738 | + | 0.780835i | \(0.285206\pi\) | |||||||
\(38\) | 23.1418 | 0.0987921 | ||||||||
\(39\) | 112.707 | 0.462757 | ||||||||
\(40\) | −18.1409 | −0.0717082 | ||||||||
\(41\) | −271.754 | −1.03514 | −0.517570 | − | 0.855641i | \(-0.673163\pi\) | ||||
−0.517570 | + | 0.855641i | \(0.673163\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.81066 | −0.0277003 | −0.0138502 | − | 0.999904i | \(-0.504409\pi\) | ||||
−0.0138502 | + | 0.999904i | \(0.504409\pi\) | |||||||
\(44\) | −140.699 | −0.482072 | ||||||||
\(45\) | 118.645 | 0.393035 | ||||||||
\(46\) | −21.3028 | −0.0682809 | ||||||||
\(47\) | −92.4524 | −0.286927 | −0.143464 | − | 0.989656i | \(-0.545824\pi\) | ||||
−0.143464 | + | 0.989656i | \(0.545824\pi\) | |||||||
\(48\) | −113.508 | −0.341321 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.68743 | −0.0160865 | ||||||||
\(51\) | −157.640 | −0.432825 | ||||||||
\(52\) | 495.317 | 1.32092 | ||||||||
\(53\) | 180.304 | 0.467295 | 0.233648 | − | 0.972321i | \(-0.424934\pi\) | ||||
0.233648 | + | 0.972321i | \(0.424934\pi\) | |||||||
\(54\) | −20.8723 | −0.0525994 | ||||||||
\(55\) | −88.5094 | −0.216993 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 183.975 | 0.427511 | ||||||||
\(58\) | −67.6544 | −0.153163 | ||||||||
\(59\) | −99.7011 | −0.220000 | −0.110000 | − | 0.993932i | \(-0.535085\pi\) | ||||
−0.110000 | + | 0.993932i | \(0.535085\pi\) | |||||||
\(60\) | −71.8753 | −0.154651 | ||||||||
\(61\) | 434.218 | 0.911408 | 0.455704 | − | 0.890131i | \(-0.349388\pi\) | ||||
0.455704 | + | 0.890131i | \(0.349388\pi\) | |||||||
\(62\) | −20.7655 | −0.0425358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −492.233 | −0.961393 | ||||||||
\(65\) | 311.589 | 0.594582 | ||||||||
\(66\) | 7.28340 | 0.0135837 | ||||||||
\(67\) | −461.554 | −0.841609 | −0.420805 | − | 0.907151i | \(-0.638252\pi\) | ||||
−0.420805 | + | 0.907151i | \(0.638252\pi\) | |||||||
\(68\) | −692.787 | −1.23548 | ||||||||
\(69\) | −169.355 | −0.295478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 518.417 | 0.866546 | 0.433273 | − | 0.901263i | \(-0.357359\pi\) | ||||
0.433273 | + | 0.901263i | \(0.357359\pi\) | |||||||
\(72\) | −86.0932 | −0.140919 | ||||||||
\(73\) | −542.866 | −0.870380 | −0.435190 | − | 0.900339i | \(-0.643319\pi\) | ||||
−0.435190 | + | 0.900339i | \(0.643319\pi\) | |||||||
\(74\) | −63.9744 | −0.100498 | ||||||||
\(75\) | −45.2146 | −0.0696124 | ||||||||
\(76\) | 808.524 | 1.22032 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −25.6405 | −0.0372207 | ||||||||
\(79\) | 239.701 | 0.341373 | 0.170687 | − | 0.985325i | \(-0.445401\pi\) | ||||
0.170687 | + | 0.985325i | \(0.445401\pi\) | |||||||
\(80\) | −313.803 | −0.438553 | ||||||||
\(81\) | 474.751 | 0.651235 | ||||||||
\(82\) | 61.8232 | 0.0832589 | ||||||||
\(83\) | 299.184 | 0.395660 | 0.197830 | − | 0.980236i | \(-0.436611\pi\) | ||||
0.197830 | + | 0.980236i | \(0.436611\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −435.812 | −0.556122 | ||||||||
\(86\) | 1.77690 | 0.00222801 | ||||||||
\(87\) | −537.846 | −0.662795 | ||||||||
\(88\) | 64.2257 | 0.0778009 | ||||||||
\(89\) | 1054.36 | 1.25575 | 0.627876 | − | 0.778314i | \(-0.283925\pi\) | ||||
0.627876 | + | 0.778314i | \(0.283925\pi\) | |||||||
\(90\) | −26.9914 | −0.0316128 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −744.271 | −0.843430 | ||||||||
\(93\) | −165.084 | −0.184069 | ||||||||
\(94\) | 21.0327 | 0.0230782 | ||||||||
\(95\) | 508.618 | 0.549296 | ||||||||
\(96\) | 78.3176 | 0.0832631 | ||||||||
\(97\) | 288.854 | 0.302358 | 0.151179 | − | 0.988506i | \(-0.451693\pi\) | ||||
0.151179 | + | 0.988506i | \(0.451693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −420.049 | −0.426429 | ||||||||
\(100\) | −198.706 | −0.198706 | ||||||||
\(101\) | 354.839 | 0.349582 | 0.174791 | − | 0.984606i | \(-0.444075\pi\) | ||||
0.174791 | + | 0.984606i | \(0.444075\pi\) | |||||||
\(102\) | 35.8627 | 0.0348131 | ||||||||
\(103\) | −1064.15 | −1.01799 | −0.508997 | − | 0.860768i | \(-0.669984\pi\) | ||||
−0.508997 | + | 0.860768i | \(0.669984\pi\) | |||||||
\(104\) | −226.100 | −0.213182 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −41.0186 | −0.0375857 | ||||||||
\(107\) | −1393.71 | −1.25920 | −0.629601 | − | 0.776918i | \(-0.716782\pi\) | ||||
−0.629601 | + | 0.776918i | \(0.716782\pi\) | |||||||
\(108\) | −729.233 | −0.649727 | ||||||||
\(109\) | −144.484 | −0.126964 | −0.0634818 | − | 0.997983i | \(-0.520220\pi\) | ||||
−0.0634818 | + | 0.997983i | \(0.520220\pi\) | |||||||
\(110\) | 20.1357 | 0.0174533 | ||||||||
\(111\) | −508.591 | −0.434895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2023.91 | −1.68489 | −0.842447 | − | 0.538780i | \(-0.818886\pi\) | ||||
−0.842447 | + | 0.538780i | \(0.818886\pi\) | |||||||
\(114\) | −41.8539 | −0.0343858 | ||||||||
\(115\) | −468.198 | −0.379650 | ||||||||
\(116\) | −2363.69 | −1.89193 | ||||||||
\(117\) | 1478.74 | 1.16846 | ||||||||
\(118\) | 22.6817 | 0.0176951 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 32.8093 | 0.0249589 | ||||||||
\(121\) | −1017.64 | −0.764570 | ||||||||
\(122\) | −98.7834 | −0.0733068 | ||||||||
\(123\) | 491.489 | 0.360293 | ||||||||
\(124\) | −725.499 | −0.525417 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1606.56 | 1.12252 | 0.561258 | − | 0.827641i | \(-0.310318\pi\) | ||||
0.561258 | + | 0.827641i | \(0.310318\pi\) | |||||||
\(128\) | 458.408 | 0.316546 | ||||||||
\(129\) | 14.1262 | 0.00964143 | ||||||||
\(130\) | −70.8856 | −0.0478237 | ||||||||
\(131\) | 2848.32 | 1.89969 | 0.949843 | − | 0.312726i | \(-0.101242\pi\) | ||||
0.949843 | + | 0.312726i | \(0.101242\pi\) | |||||||
\(132\) | 254.466 | 0.167791 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 105.002 | 0.0676927 | ||||||||
\(135\) | −458.738 | −0.292459 | ||||||||
\(136\) | 316.241 | 0.199393 | ||||||||
\(137\) | 841.717 | 0.524910 | 0.262455 | − | 0.964944i | \(-0.415468\pi\) | ||||
0.262455 | + | 0.964944i | \(0.415468\pi\) | |||||||
\(138\) | 38.5278 | 0.0237660 | ||||||||
\(139\) | 2429.10 | 1.48226 | 0.741128 | − | 0.671363i | \(-0.234291\pi\) | ||||
0.741128 | + | 0.671363i | \(0.234291\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 167.208 | 0.0998684 | ||||||||
\(142\) | −117.938 | −0.0696984 | ||||||||
\(143\) | −1103.14 | −0.645100 | ||||||||
\(144\) | −1489.25 | −0.861833 | ||||||||
\(145\) | −1486.93 | −0.851604 | ||||||||
\(146\) | 123.501 | 0.0700067 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2235.12 | −1.24139 | ||||||||
\(149\) | −577.947 | −0.317767 | −0.158884 | − | 0.987297i | \(-0.550789\pi\) | ||||
−0.158884 | + | 0.987297i | \(0.550789\pi\) | |||||||
\(150\) | 10.2862 | 0.00559909 | ||||||||
\(151\) | 783.616 | 0.422316 | 0.211158 | − | 0.977452i | \(-0.432276\pi\) | ||||
0.211158 | + | 0.977452i | \(0.432276\pi\) | |||||||
\(152\) | −369.072 | −0.196945 | ||||||||
\(153\) | −2068.28 | −1.09288 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −456.389 | −0.236504 | ||||||||
\(156\) | −895.822 | −0.459764 | ||||||||
\(157\) | −1372.40 | −0.697642 | −0.348821 | − | 0.937189i | \(-0.613418\pi\) | ||||
−0.348821 | + | 0.937189i | \(0.613418\pi\) | |||||||
\(158\) | −54.5314 | −0.0274575 | ||||||||
\(159\) | −326.095 | −0.162648 | ||||||||
\(160\) | 216.517 | 0.106982 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −108.004 | −0.0523804 | ||||||||
\(163\) | 3754.78 | 1.80428 | 0.902139 | − | 0.431445i | \(-0.141996\pi\) | ||||
0.902139 | + | 0.431445i | \(0.141996\pi\) | |||||||
\(164\) | 2159.96 | 1.02844 | ||||||||
\(165\) | 160.077 | 0.0755270 | ||||||||
\(166\) | −68.0636 | −0.0318239 | ||||||||
\(167\) | −1945.55 | −0.901505 | −0.450752 | − | 0.892649i | \(-0.648844\pi\) | ||||
−0.450752 | + | 0.892649i | \(0.648844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1686.50 | 0.767639 | ||||||||
\(170\) | 99.1459 | 0.0447303 | ||||||||
\(171\) | 2413.80 | 1.07946 | ||||||||
\(172\) | 62.0810 | 0.0275211 | ||||||||
\(173\) | −2067.34 | −0.908538 | −0.454269 | − | 0.890864i | \(-0.650100\pi\) | ||||
−0.454269 | + | 0.890864i | \(0.650100\pi\) | |||||||
\(174\) | 122.359 | 0.0533102 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1110.98 | 0.475814 | ||||||||
\(177\) | 180.318 | 0.0765735 | ||||||||
\(178\) | −239.864 | −0.101003 | ||||||||
\(179\) | 2395.92 | 1.00044 | 0.500222 | − | 0.865897i | \(-0.333252\pi\) | ||||
0.500222 | + | 0.865897i | \(0.333252\pi\) | |||||||
\(180\) | −943.021 | −0.390492 | ||||||||
\(181\) | 1319.40 | 0.541826 | 0.270913 | − | 0.962604i | \(-0.412674\pi\) | ||||
0.270913 | + | 0.962604i | \(0.412674\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −785.319 | −0.317227 | ||||||||
\(184\) | 339.742 | 0.136120 | ||||||||
\(185\) | −1406.05 | −0.558782 | ||||||||
\(186\) | 37.5561 | 0.0148051 | ||||||||
\(187\) | 1542.94 | 0.603373 | ||||||||
\(188\) | 734.834 | 0.285071 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −115.709 | −0.0441812 | ||||||||
\(191\) | 2108.07 | 0.798611 | 0.399306 | − | 0.916818i | \(-0.369251\pi\) | ||||
0.399306 | + | 0.916818i | \(0.369251\pi\) | |||||||
\(192\) | 890.244 | 0.334624 | ||||||||
\(193\) | 3631.62 | 1.35445 | 0.677227 | − | 0.735774i | \(-0.263181\pi\) | ||||
0.677227 | + | 0.735774i | \(0.263181\pi\) | |||||||
\(194\) | −65.7135 | −0.0243194 | ||||||||
\(195\) | −563.534 | −0.206951 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3280.46 | 1.18641 | 0.593206 | − | 0.805051i | \(-0.297862\pi\) | ||||
0.593206 | + | 0.805051i | \(0.297862\pi\) | |||||||
\(198\) | 95.5599 | 0.0342987 | ||||||||
\(199\) | −648.733 | −0.231093 | −0.115546 | − | 0.993302i | \(-0.536862\pi\) | ||||
−0.115546 | + | 0.993302i | \(0.536862\pi\) | |||||||
\(200\) | 90.7045 | 0.0320689 | ||||||||
\(201\) | 834.759 | 0.292932 | ||||||||
\(202\) | −80.7249 | −0.0281177 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1252.96 | 0.430024 | ||||||||
\(205\) | 1358.77 | 0.462929 | ||||||||
\(206\) | 242.090 | 0.0818798 | ||||||||
\(207\) | −2221.98 | −0.746078 | ||||||||
\(208\) | −3911.10 | −1.30378 | ||||||||
\(209\) | −1800.70 | −0.595966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5072.33 | 1.65495 | 0.827474 | − | 0.561504i | \(-0.189777\pi\) | ||||
0.827474 | + | 0.561504i | \(0.189777\pi\) | |||||||
\(212\) | −1433.10 | −0.464272 | ||||||||
\(213\) | −937.600 | −0.301612 | ||||||||
\(214\) | 317.064 | 0.101281 | ||||||||
\(215\) | 39.0533 | 0.0123880 | ||||||||
\(216\) | 332.877 | 0.104858 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 32.8697 | 0.0102120 | ||||||||
\(219\) | 981.819 | 0.302946 | ||||||||
\(220\) | 703.495 | 0.215589 | ||||||||
\(221\) | −5431.76 | −1.65330 | ||||||||
\(222\) | 115.703 | 0.0349796 | ||||||||
\(223\) | −163.717 | −0.0491629 | −0.0245814 | − | 0.999698i | \(-0.507825\pi\) | ||||
−0.0245814 | + | 0.999698i | \(0.507825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −593.226 | −0.175771 | ||||||||
\(226\) | 460.433 | 0.135520 | ||||||||
\(227\) | 6326.62 | 1.84984 | 0.924918 | − | 0.380166i | \(-0.124133\pi\) | ||||
0.924918 | + | 0.380166i | \(0.124133\pi\) | |||||||
\(228\) | −1462.28 | −0.424746 | ||||||||
\(229\) | 3484.47 | 1.00550 | 0.502752 | − | 0.864431i | \(-0.332321\pi\) | ||||
0.502752 | + | 0.864431i | \(0.332321\pi\) | |||||||
\(230\) | 106.514 | 0.0305361 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1078.97 | 0.305335 | ||||||||
\(233\) | −4496.13 | −1.26417 | −0.632084 | − | 0.774900i | \(-0.717800\pi\) | ||||
−0.632084 | + | 0.774900i | \(0.717800\pi\) | |||||||
\(234\) | −336.409 | −0.0939819 | ||||||||
\(235\) | 462.262 | 0.128318 | ||||||||
\(236\) | 792.449 | 0.218576 | ||||||||
\(237\) | −433.519 | −0.118819 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1529.73 | −0.414016 | −0.207008 | − | 0.978339i | \(-0.566373\pi\) | ||||
−0.207008 | + | 0.978339i | \(0.566373\pi\) | |||||||
\(240\) | 567.538 | 0.152644 | ||||||||
\(241\) | 4572.40 | 1.22213 | 0.611067 | − | 0.791579i | \(-0.290741\pi\) | ||||
0.611067 | + | 0.791579i | \(0.290741\pi\) | |||||||
\(242\) | 231.511 | 0.0614963 | ||||||||
\(243\) | −3335.81 | −0.880627 | ||||||||
\(244\) | −3451.27 | −0.905512 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −111.812 | −0.0289793 | ||||||||
\(247\) | 6339.18 | 1.63301 | ||||||||
\(248\) | 331.173 | 0.0847963 | ||||||||
\(249\) | −541.100 | −0.137714 | ||||||||
\(250\) | 28.4372 | 0.00719409 | ||||||||
\(251\) | −537.143 | −0.135076 | −0.0675382 | − | 0.997717i | \(-0.521514\pi\) | ||||
−0.0675382 | + | 0.997717i | \(0.521514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1657.60 | 0.411906 | ||||||||
\(254\) | −365.489 | −0.0902866 | ||||||||
\(255\) | 788.201 | 0.193565 | ||||||||
\(256\) | 3833.58 | 0.935932 | ||||||||
\(257\) | −878.553 | −0.213240 | −0.106620 | − | 0.994300i | \(-0.534003\pi\) | ||||
−0.106620 | + | 0.994300i | \(0.534003\pi\) | |||||||
\(258\) | −3.21368 | −0.000775484 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −2476.58 | −0.590736 | ||||||||
\(261\) | −7056.67 | −1.67355 | ||||||||
\(262\) | −647.985 | −0.152796 | ||||||||
\(263\) | 3714.03 | 0.870786 | 0.435393 | − | 0.900241i | \(-0.356609\pi\) | ||||
0.435393 | + | 0.900241i | \(0.356609\pi\) | |||||||
\(264\) | −116.157 | −0.0270795 | ||||||||
\(265\) | −901.519 | −0.208981 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1906.90 | −0.437079 | ||||||||
\(268\) | 3668.55 | 0.836165 | ||||||||
\(269\) | −154.460 | −0.0350096 | −0.0175048 | − | 0.999847i | \(-0.505572\pi\) | ||||
−0.0175048 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(270\) | 104.362 | 0.0235232 | ||||||||
\(271\) | 2406.30 | 0.539382 | 0.269691 | − | 0.962947i | \(-0.413079\pi\) | ||||
0.269691 | + | 0.962947i | \(0.413079\pi\) | |||||||
\(272\) | 5470.36 | 1.21944 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −191.488 | −0.0422198 | ||||||||
\(275\) | 442.547 | 0.0970422 | ||||||||
\(276\) | 1346.08 | 0.293566 | ||||||||
\(277\) | 1449.76 | 0.314467 | 0.157234 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157234 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(278\) | −552.614 | −0.119222 | ||||||||
\(279\) | −2165.94 | −0.464771 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2037.07 | 0.432460 | 0.216230 | − | 0.976342i | \(-0.430624\pi\) | ||||
0.216230 | + | 0.976342i | \(0.430624\pi\) | |||||||
\(282\) | −38.0393 | −0.00803266 | ||||||||
\(283\) | −7366.22 | −1.54727 | −0.773633 | − | 0.633634i | \(-0.781563\pi\) | ||||
−0.773633 | + | 0.633634i | \(0.781563\pi\) | |||||||
\(284\) | −4120.51 | −0.860940 | ||||||||
\(285\) | −919.877 | −0.191189 | ||||||||
\(286\) | 250.962 | 0.0518870 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1027.55 | 0.210239 | ||||||||
\(289\) | 2684.27 | 0.546361 | ||||||||
\(290\) | 338.272 | 0.0684966 | ||||||||
\(291\) | −522.417 | −0.105239 | ||||||||
\(292\) | 4314.84 | 0.864749 | ||||||||
\(293\) | −542.935 | −0.108255 | −0.0541273 | − | 0.998534i | \(-0.517238\pi\) | ||||
−0.0541273 | + | 0.998534i | \(0.517238\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 498.506 | 0.0983868 | ||||||||
\(296\) | 1020.28 | 0.200346 | ||||||||
\(297\) | 1624.11 | 0.317307 | ||||||||
\(298\) | 131.481 | 0.0255588 | ||||||||
\(299\) | −5835.41 | −1.12866 | ||||||||
\(300\) | 359.377 | 0.0691620 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −178.271 | −0.0339679 | ||||||||
\(303\) | −641.756 | −0.121676 | ||||||||
\(304\) | −6384.23 | −1.20448 | ||||||||
\(305\) | −2171.09 | −0.407594 | ||||||||
\(306\) | 470.527 | 0.0879028 | ||||||||
\(307\) | 5314.23 | 0.987945 | 0.493972 | − | 0.869478i | \(-0.335544\pi\) | ||||
0.493972 | + | 0.869478i | \(0.335544\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1924.60 | 0.354325 | ||||||||
\(310\) | 103.827 | 0.0190226 | ||||||||
\(311\) | −8840.00 | −1.61180 | −0.805901 | − | 0.592051i | \(-0.798318\pi\) | ||||
−0.805901 | + | 0.592051i | \(0.798318\pi\) | |||||||
\(312\) | 408.921 | 0.0742006 | ||||||||
\(313\) | −1896.34 | −0.342453 | −0.171226 | − | 0.985232i | \(-0.554773\pi\) | ||||
−0.171226 | + | 0.985232i | \(0.554773\pi\) | |||||||
\(314\) | 312.218 | 0.0561130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1905.20 | −0.339165 | ||||||||
\(317\) | −6072.81 | −1.07597 | −0.537985 | − | 0.842954i | \(-0.680814\pi\) | ||||
−0.537985 | + | 0.842954i | \(0.680814\pi\) | |||||||
\(318\) | 74.1856 | 0.0130821 | ||||||||
\(319\) | 5264.28 | 0.923960 | ||||||||
\(320\) | 2461.17 | 0.429948 | ||||||||
\(321\) | 2520.63 | 0.438280 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8866.46 | −1.52738 | ||||||||
\(324\) | −3773.43 | −0.647022 | ||||||||
\(325\) | −1557.94 | −0.265905 | ||||||||
\(326\) | −854.203 | −0.145122 | ||||||||
\(327\) | 261.311 | 0.0441912 | ||||||||
\(328\) | −985.971 | −0.165979 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −36.4170 | −0.00607482 | ||||||||
\(331\) | 3341.78 | 0.554927 | 0.277463 | − | 0.960736i | \(-0.410506\pi\) | ||||
0.277463 | + | 0.960736i | \(0.410506\pi\) | |||||||
\(332\) | −2377.99 | −0.393100 | ||||||||
\(333\) | −6672.83 | −1.09810 | ||||||||
\(334\) | 442.608 | 0.0725102 | ||||||||
\(335\) | 2307.77 | 0.376379 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8568.87 | −1.38509 | −0.692547 | − | 0.721373i | \(-0.743511\pi\) | ||||
−0.692547 | + | 0.721373i | \(0.743511\pi\) | |||||||
\(338\) | −383.675 | −0.0617431 | ||||||||
\(339\) | 3660.40 | 0.586447 | ||||||||
\(340\) | 3463.94 | 0.552525 | ||||||||
\(341\) | 1615.79 | 0.256598 | ||||||||
\(342\) | −549.133 | −0.0868237 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −28.3385 | −0.00444160 | ||||||||
\(345\) | 846.775 | 0.132142 | ||||||||
\(346\) | 470.315 | 0.0730760 | ||||||||
\(347\) | −6246.73 | −0.966403 | −0.483202 | − | 0.875509i | \(-0.660526\pi\) | ||||
−0.483202 | + | 0.875509i | \(0.660526\pi\) | |||||||
\(348\) | 4274.93 | 0.658507 | ||||||||
\(349\) | 7091.01 | 1.08760 | 0.543801 | − | 0.839214i | \(-0.316985\pi\) | ||||
0.543801 | + | 0.839214i | \(0.316985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5717.51 | −0.869453 | ||||||||
\(352\) | −766.550 | −0.116072 | ||||||||
\(353\) | 7289.22 | 1.09905 | 0.549527 | − | 0.835476i | \(-0.314808\pi\) | ||||
0.549527 | + | 0.835476i | \(0.314808\pi\) | |||||||
\(354\) | −41.0218 | −0.00615899 | ||||||||
\(355\) | −2592.09 | −0.387531 | ||||||||
\(356\) | −8380.31 | −1.24763 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −545.065 | −0.0804681 | ||||||||
\(359\) | −8668.21 | −1.27435 | −0.637174 | − | 0.770720i | \(-0.719897\pi\) | ||||
−0.637174 | + | 0.770720i | \(0.719897\pi\) | |||||||
\(360\) | 430.466 | 0.0630210 | ||||||||
\(361\) | 3488.68 | 0.508628 | ||||||||
\(362\) | −300.161 | −0.0435804 | ||||||||
\(363\) | 1840.49 | 0.266118 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2714.33 | 0.389246 | ||||||||
\(366\) | 178.658 | 0.0255153 | ||||||||
\(367\) | −3777.62 | −0.537302 | −0.268651 | − | 0.963238i | \(-0.586578\pi\) | ||||
−0.268651 | + | 0.963238i | \(0.586578\pi\) | |||||||
\(368\) | 5876.88 | 0.832482 | ||||||||
\(369\) | 6448.45 | 0.909737 | ||||||||
\(370\) | 319.872 | 0.0449442 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1312.12 | 0.182878 | ||||||||
\(373\) | −1742.13 | −0.241834 | −0.120917 | − | 0.992663i | \(-0.538584\pi\) | ||||
−0.120917 | + | 0.992663i | \(0.538584\pi\) | |||||||
\(374\) | −351.014 | −0.0485308 | ||||||||
\(375\) | 226.073 | 0.0311316 | ||||||||
\(376\) | −335.434 | −0.0460072 | ||||||||
\(377\) | −18532.4 | −2.53174 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3471.30 | −0.470471 | −0.235236 | − | 0.971938i | \(-0.575586\pi\) | ||||
−0.235236 | + | 0.971938i | \(0.575586\pi\) | |||||||
\(380\) | −4042.62 | −0.545742 | ||||||||
\(381\) | −2905.60 | −0.390705 | ||||||||
\(382\) | −479.580 | −0.0642342 | ||||||||
\(383\) | 14445.1 | 1.92718 | 0.963591 | − | 0.267382i | \(-0.0861586\pi\) | ||||
0.963591 | + | 0.267382i | \(0.0861586\pi\) | |||||||
\(384\) | −829.069 | −0.110178 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −826.183 | −0.108942 | ||||||||
\(387\) | 185.339 | 0.0243445 | ||||||||
\(388\) | −2295.88 | −0.300402 | ||||||||
\(389\) | −7729.56 | −1.00747 | −0.503733 | − | 0.863860i | \(-0.668040\pi\) | ||||
−0.503733 | + | 0.863860i | \(0.668040\pi\) | |||||||
\(390\) | 128.202 | 0.0166456 | ||||||||
\(391\) | 8161.85 | 1.05566 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5151.43 | −0.661209 | ||||||||
\(394\) | −746.296 | −0.0954260 | ||||||||
\(395\) | −1198.51 | −0.152667 | ||||||||
\(396\) | 3338.65 | 0.423670 | ||||||||
\(397\) | −10069.6 | −1.27300 | −0.636499 | − | 0.771278i | \(-0.719618\pi\) | ||||
−0.636499 | + | 0.771278i | \(0.719618\pi\) | |||||||
\(398\) | 147.585 | 0.0185874 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1569.01 | 0.196127 | ||||||||
\(401\) | 1503.17 | 0.187194 | 0.0935972 | − | 0.995610i | \(-0.470163\pi\) | ||||
0.0935972 | + | 0.995610i | \(0.470163\pi\) | |||||||
\(402\) | −189.905 | −0.0235612 | ||||||||
\(403\) | −5688.23 | −0.703104 | ||||||||
\(404\) | −2820.35 | −0.347321 | ||||||||
\(405\) | −2373.75 | −0.291241 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4977.94 | 0.606259 | ||||||||
\(408\) | −571.948 | −0.0694010 | ||||||||
\(409\) | −613.381 | −0.0741559 | −0.0370779 | − | 0.999312i | \(-0.511805\pi\) | ||||
−0.0370779 | + | 0.999312i | \(0.511805\pi\) | |||||||
\(410\) | −309.116 | −0.0372345 | ||||||||
\(411\) | −1522.32 | −0.182701 | ||||||||
\(412\) | 8458.10 | 1.01141 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 505.494 | 0.0600089 | ||||||||
\(415\) | −1495.92 | −0.176944 | ||||||||
\(416\) | 2698.57 | 0.318048 | ||||||||
\(417\) | −4393.23 | −0.515917 | ||||||||
\(418\) | 409.654 | 0.0479350 | ||||||||
\(419\) | 12334.4 | 1.43813 | 0.719065 | − | 0.694943i | \(-0.244571\pi\) | ||||
0.719065 | + | 0.694943i | \(0.244571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2432.22 | −0.281566 | −0.140783 | − | 0.990040i | \(-0.544962\pi\) | ||||
−0.140783 | + | 0.990040i | \(0.544962\pi\) | |||||||
\(422\) | −1153.94 | −0.133111 | ||||||||
\(423\) | 2193.81 | 0.252167 | ||||||||
\(424\) | 654.175 | 0.0749282 | ||||||||
\(425\) | 2179.06 | 0.248705 | ||||||||
\(426\) | 213.301 | 0.0242594 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11077.5 | 1.25106 | ||||||||
\(429\) | 1995.12 | 0.224535 | ||||||||
\(430\) | −8.88452 | −0.000996394 0 | ||||||||
\(431\) | −1310.48 | −0.146458 | −0.0732292 | − | 0.997315i | \(-0.523330\pi\) | ||||
−0.0732292 | + | 0.997315i | \(0.523330\pi\) | |||||||
\(432\) | 5758.13 | 0.641292 | ||||||||
\(433\) | 4954.86 | 0.549920 | 0.274960 | − | 0.961456i | \(-0.411335\pi\) | ||||
0.274960 | + | 0.961456i | \(0.411335\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2689.23 | 0.296411 | ||||||||
\(436\) | 1148.39 | 0.126142 | ||||||||
\(437\) | −9525.36 | −1.04270 | ||||||||
\(438\) | −223.361 | −0.0243667 | ||||||||
\(439\) | −8195.34 | −0.890984 | −0.445492 | − | 0.895286i | \(-0.646971\pi\) | ||||
−0.445492 | + | 0.895286i | \(0.646971\pi\) | |||||||
\(440\) | −321.128 | −0.0347936 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1235.71 | 0.132979 | ||||||||
\(443\) | 2956.70 | 0.317104 | 0.158552 | − | 0.987351i | \(-0.449317\pi\) | ||||
0.158552 | + | 0.987351i | \(0.449317\pi\) | |||||||
\(444\) | 4042.41 | 0.432081 | ||||||||
\(445\) | −5271.80 | −0.561589 | ||||||||
\(446\) | 37.2452 | 0.00395429 | ||||||||
\(447\) | 1045.27 | 0.110603 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10453.5 | −1.09873 | −0.549364 | − | 0.835583i | \(-0.685130\pi\) | ||||
−0.549364 | + | 0.835583i | \(0.685130\pi\) | |||||||
\(450\) | 134.957 | 0.0141377 | ||||||||
\(451\) | −4810.55 | −0.502262 | ||||||||
\(452\) | 16086.5 | 1.67399 | ||||||||
\(453\) | −1417.23 | −0.146992 | ||||||||
\(454\) | −1439.29 | −0.148787 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 667.497 | 0.0685491 | ||||||||
\(457\) | 2245.19 | 0.229816 | 0.114908 | − | 0.993376i | \(-0.463343\pi\) | ||||
0.114908 | + | 0.993376i | \(0.463343\pi\) | |||||||
\(458\) | −792.707 | −0.0808751 | ||||||||
\(459\) | 7996.94 | 0.813214 | ||||||||
\(460\) | 3721.35 | 0.377194 | ||||||||
\(461\) | −12441.1 | −1.25692 | −0.628459 | − | 0.777842i | \(-0.716314\pi\) | ||||
−0.628459 | + | 0.777842i | \(0.716314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17086.0 | 1.71502 | 0.857510 | − | 0.514468i | \(-0.172010\pi\) | ||||
0.857510 | + | 0.514468i | \(0.172010\pi\) | |||||||
\(464\) | 18664.1 | 1.86737 | ||||||||
\(465\) | 825.418 | 0.0823179 | ||||||||
\(466\) | 1022.86 | 0.101680 | ||||||||
\(467\) | −11709.1 | −1.16024 | −0.580121 | − | 0.814531i | \(-0.696995\pi\) | ||||
−0.580121 | + | 0.814531i | \(0.696995\pi\) | |||||||
\(468\) | −11753.4 | −1.16090 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −105.163 | −0.0103209 | ||||||||
\(471\) | 2482.11 | 0.242823 | ||||||||
\(472\) | −361.734 | −0.0352757 | ||||||||
\(473\) | −138.263 | −0.0134405 | ||||||||
\(474\) | 98.6245 | 0.00955690 | ||||||||
\(475\) | −2543.09 | −0.245652 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4278.44 | −0.410684 | ||||||||
\(478\) | 348.009 | 0.0333003 | ||||||||
\(479\) | 11692.0 | 1.11528 | 0.557641 | − | 0.830082i | \(-0.311707\pi\) | ||||
0.557641 | + | 0.830082i | \(0.311707\pi\) | |||||||
\(480\) | −391.588 | −0.0372364 | ||||||||
\(481\) | −17524.4 | −1.66121 | ||||||||
\(482\) | −1040.21 | −0.0982992 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8088.48 | 0.759624 | ||||||||
\(485\) | −1444.27 | −0.135218 | ||||||||
\(486\) | 758.888 | 0.0708310 | ||||||||
\(487\) | 7128.84 | 0.663324 | 0.331662 | − | 0.943398i | \(-0.392391\pi\) | ||||
0.331662 | + | 0.943398i | \(0.392391\pi\) | |||||||
\(488\) | 1575.42 | 0.146139 | ||||||||
\(489\) | −6790.84 | −0.628001 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4330.34 | −0.398015 | −0.199008 | − | 0.979998i | \(-0.563772\pi\) | ||||
−0.199008 | + | 0.979998i | \(0.563772\pi\) | |||||||
\(492\) | −3906.47 | −0.357962 | ||||||||
\(493\) | 25920.8 | 2.36798 | ||||||||
\(494\) | −1442.15 | −0.131347 | ||||||||
\(495\) | 2100.24 | 0.190705 | ||||||||
\(496\) | 5728.65 | 0.518597 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 123.099 | 0.0110767 | ||||||||
\(499\) | 9635.67 | 0.864433 | 0.432216 | − | 0.901770i | \(-0.357732\pi\) | ||||
0.432216 | + | 0.901770i | \(0.357732\pi\) | |||||||
\(500\) | 993.531 | 0.0888641 | ||||||||
\(501\) | 3518.69 | 0.313779 | ||||||||
\(502\) | 122.199 | 0.0108645 | ||||||||
\(503\) | 18763.3 | 1.66325 | 0.831626 | − | 0.555335i | \(-0.187410\pi\) | ||||
0.831626 | + | 0.555335i | \(0.187410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1774.19 | −0.156338 | ||||||||
\(506\) | −377.099 | −0.0331306 | ||||||||
\(507\) | −3050.18 | −0.267186 | ||||||||
\(508\) | −12769.4 | −1.11525 | ||||||||
\(509\) | 15804.5 | 1.37627 | 0.688137 | − | 0.725580i | \(-0.258429\pi\) | ||||
0.688137 | + | 0.725580i | \(0.258429\pi\) | |||||||
\(510\) | −179.314 | −0.0155689 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −4539.39 | −0.391826 | ||||||||
\(513\) | −9332.90 | −0.803231 | ||||||||
\(514\) | 199.869 | 0.0171514 | ||||||||
\(515\) | 5320.73 | 0.455261 | ||||||||
\(516\) | −112.279 | −0.00957906 | ||||||||
\(517\) | −1636.58 | −0.139220 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3738.96 | 0.316228 | ||||||||
\(520\) | 1130.50 | 0.0953380 | ||||||||
\(521\) | 9451.64 | 0.794787 | 0.397393 | − | 0.917648i | \(-0.369915\pi\) | ||||
0.397393 | + | 0.917648i | \(0.369915\pi\) | |||||||
\(522\) | 1605.37 | 0.134608 | ||||||||
\(523\) | 2704.59 | 0.226125 | 0.113062 | − | 0.993588i | \(-0.463934\pi\) | ||||
0.113062 | + | 0.993588i | \(0.463934\pi\) | |||||||
\(524\) | −22639.2 | −1.88740 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −844.931 | −0.0700394 | ||||||||
\(527\) | 7955.99 | 0.657625 | ||||||||
\(528\) | −2009.30 | −0.165613 | ||||||||
\(529\) | −3398.62 | −0.279331 | ||||||||
\(530\) | 205.093 | 0.0168088 | ||||||||
\(531\) | 2365.81 | 0.193347 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16935.1 | 1.37625 | ||||||||
\(534\) | 433.814 | 0.0351553 | ||||||||
\(535\) | 6968.53 | 0.563132 | ||||||||
\(536\) | −1674.60 | −0.134947 | ||||||||
\(537\) | −4333.22 | −0.348216 | ||||||||
\(538\) | 35.1392 | 0.00281591 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3646.16 | 0.290567 | ||||||||
\(541\) | 60.7636 | 0.00482889 | 0.00241445 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241445 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(542\) | −547.427 | −0.0433838 | ||||||||
\(543\) | −2386.25 | −0.188589 | ||||||||
\(544\) | −3774.42 | −0.297476 | ||||||||
\(545\) | 722.419 | 0.0567799 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14267.4 | 1.11523 | 0.557614 | − | 0.830100i | \(-0.311717\pi\) | ||||
0.557614 | + | 0.830100i | \(0.311717\pi\) | |||||||
\(548\) | −6690.17 | −0.521515 | ||||||||
\(549\) | −10303.6 | −0.800994 | ||||||||
\(550\) | −100.678 | −0.00780534 | ||||||||
\(551\) | −30251.1 | −2.33891 | ||||||||
\(552\) | −614.451 | −0.0473782 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −329.816 | −0.0252934 | ||||||||
\(555\) | 2542.95 | 0.194491 | ||||||||
\(556\) | −19307.1 | −1.47267 | ||||||||
\(557\) | −19601.8 | −1.49112 | −0.745559 | − | 0.666439i | \(-0.767818\pi\) | ||||
−0.745559 | + | 0.666439i | \(0.767818\pi\) | |||||||
\(558\) | 492.744 | 0.0373827 | ||||||||
\(559\) | 486.743 | 0.0368283 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2790.53 | −0.210011 | ||||||||
\(562\) | −463.427 | −0.0347838 | ||||||||
\(563\) | 7081.18 | 0.530082 | 0.265041 | − | 0.964237i | \(-0.414615\pi\) | ||||
0.265041 | + | 0.964237i | \(0.414615\pi\) | |||||||
\(564\) | −1329.01 | −0.0992223 | ||||||||
\(565\) | 10119.5 | 0.753507 | ||||||||
\(566\) | 1675.79 | 0.124450 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1880.91 | 0.138946 | ||||||||
\(569\) | −12034.6 | −0.886669 | −0.443334 | − | 0.896356i | \(-0.646205\pi\) | ||||
−0.443334 | + | 0.896356i | \(0.646205\pi\) | |||||||
\(570\) | 209.270 | 0.0153778 | ||||||||
\(571\) | 4179.38 | 0.306308 | 0.153154 | − | 0.988202i | \(-0.451057\pi\) | ||||
0.153154 | + | 0.988202i | \(0.451057\pi\) | |||||||
\(572\) | 8768.04 | 0.640927 | ||||||||
\(573\) | −3812.62 | −0.277966 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2340.99 | 0.169784 | ||||||||
\(576\) | 11680.2 | 0.844923 | ||||||||
\(577\) | 16691.6 | 1.20430 | 0.602151 | − | 0.798382i | \(-0.294311\pi\) | ||||
0.602151 | + | 0.798382i | \(0.294311\pi\) | |||||||
\(578\) | −610.664 | −0.0439451 | ||||||||
\(579\) | −6568.09 | −0.471434 | ||||||||
\(580\) | 11818.5 | 0.846095 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 118.848 | 0.00846465 | ||||||||
\(583\) | 3191.72 | 0.226737 | ||||||||
\(584\) | −1969.62 | −0.139561 | ||||||||
\(585\) | −7393.70 | −0.522550 | ||||||||
\(586\) | 123.516 | 0.00870718 | ||||||||
\(587\) | −8878.89 | −0.624311 | −0.312156 | − | 0.950031i | \(-0.601051\pi\) | ||||
−0.312156 | + | 0.950031i | \(0.601051\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9285.11 | −0.649552 | ||||||||
\(590\) | −113.409 | −0.00791349 | ||||||||
\(591\) | −5932.99 | −0.412945 | ||||||||
\(592\) | 17648.9 | 1.22528 | ||||||||
\(593\) | 23777.1 | 1.64656 | 0.823278 | − | 0.567639i | \(-0.192143\pi\) | ||||
0.823278 | + | 0.567639i | \(0.192143\pi\) | |||||||
\(594\) | −369.480 | −0.0255218 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4593.67 | 0.315711 | ||||||||
\(597\) | 1173.29 | 0.0804346 | ||||||||
\(598\) | 1327.54 | 0.0907812 | ||||||||
\(599\) | 12709.4 | 0.866934 | 0.433467 | − | 0.901169i | \(-0.357290\pi\) | ||||
0.433467 | + | 0.901169i | \(0.357290\pi\) | |||||||
\(600\) | −164.047 | −0.0111620 | ||||||||
\(601\) | −13296.4 | −0.902446 | −0.451223 | − | 0.892411i | \(-0.649012\pi\) | ||||
−0.451223 | + | 0.892411i | \(0.649012\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10952.2 | 0.739651 | ||||||||
\(604\) | −6228.37 | −0.419584 | ||||||||
\(605\) | 5088.22 | 0.341926 | ||||||||
\(606\) | 145.998 | 0.00978672 | ||||||||
\(607\) | −5838.48 | −0.390406 | −0.195203 | − | 0.980763i | \(-0.562537\pi\) | ||||
−0.195203 | + | 0.980763i | \(0.562537\pi\) | |||||||
\(608\) | 4404.97 | 0.293824 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 493.917 | 0.0327838 | ||||||||
\(611\) | 5761.43 | 0.381477 | ||||||||
\(612\) | 16439.2 | 1.08581 | ||||||||
\(613\) | 4270.31 | 0.281364 | 0.140682 | − | 0.990055i | \(-0.455070\pi\) | ||||
0.140682 | + | 0.990055i | \(0.455070\pi\) | |||||||
\(614\) | −1208.97 | −0.0794628 | ||||||||
\(615\) | −2457.44 | −0.161128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2869.54 | −0.187234 | −0.0936168 | − | 0.995608i | \(-0.529843\pi\) | ||||
−0.0936168 | + | 0.995608i | \(0.529843\pi\) | |||||||
\(618\) | −437.841 | −0.0284992 | ||||||||
\(619\) | −6882.06 | −0.446871 | −0.223436 | − | 0.974719i | \(-0.571727\pi\) | ||||
−0.223436 | + | 0.974719i | \(0.571727\pi\) | |||||||
\(620\) | 3627.49 | 0.234974 | ||||||||
\(621\) | 8591.22 | 0.555159 | ||||||||
\(622\) | 2011.07 | 0.129641 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7073.54 | 0.453796 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 431.413 | 0.0275443 | ||||||||
\(627\) | 3256.71 | 0.207433 | ||||||||
\(628\) | 10908.2 | 0.693129 | ||||||||
\(629\) | 24510.9 | 1.55376 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28101.9 | −1.77293 | −0.886467 | − | 0.462793i | \(-0.846847\pi\) | ||||
−0.886467 | + | 0.462793i | \(0.846847\pi\) | |||||||
\(632\) | 869.679 | 0.0547373 | ||||||||
\(633\) | −9173.74 | −0.576024 | ||||||||
\(634\) | 1381.55 | 0.0865429 | ||||||||
\(635\) | −8032.82 | −0.502004 | ||||||||
\(636\) | 2591.88 | 0.161595 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1197.61 | −0.0743164 | ||||||||
\(639\) | −12301.5 | −0.761567 | ||||||||
\(640\) | −2292.04 | −0.141564 | ||||||||
\(641\) | 13677.8 | 0.842809 | 0.421404 | − | 0.906873i | \(-0.361537\pi\) | ||||
0.421404 | + | 0.906873i | \(0.361537\pi\) | |||||||
\(642\) | −573.437 | −0.0352520 | ||||||||
\(643\) | −17919.1 | −1.09901 | −0.549503 | − | 0.835492i | \(-0.685183\pi\) | ||||
−0.549503 | + | 0.835492i | \(0.685183\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −70.6311 | −0.00431178 | ||||||||
\(646\) | 2017.10 | 0.122851 | ||||||||
\(647\) | −31488.2 | −1.91334 | −0.956669 | − | 0.291176i | \(-0.905953\pi\) | ||||
−0.956669 | + | 0.291176i | \(0.905953\pi\) | |||||||
\(648\) | 1722.48 | 0.104422 | ||||||||
\(649\) | −1764.90 | −0.106746 | ||||||||
\(650\) | 354.428 | 0.0213874 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29843.9 | −1.79261 | ||||||||
\(653\) | −1110.46 | −0.0665477 | −0.0332739 | − | 0.999446i | \(-0.510593\pi\) | ||||
−0.0332739 | + | 0.999446i | \(0.510593\pi\) | |||||||
\(654\) | −59.4475 | −0.00355441 | ||||||||
\(655\) | −14241.6 | −0.849566 | ||||||||
\(656\) | −17055.4 | −1.01509 | ||||||||
\(657\) | 12881.7 | 0.764936 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12793.3 | 0.756230 | 0.378115 | − | 0.925759i | \(-0.376572\pi\) | ||||
0.378115 | + | 0.925759i | \(0.376572\pi\) | |||||||
\(660\) | −1272.33 | −0.0750384 | ||||||||
\(661\) | −2039.60 | −0.120017 | −0.0600086 | − | 0.998198i | \(-0.519113\pi\) | ||||
−0.0600086 | + | 0.998198i | \(0.519113\pi\) | |||||||
\(662\) | −760.246 | −0.0446341 | ||||||||
\(663\) | 9823.79 | 0.575452 | ||||||||
\(664\) | 1085.50 | 0.0634419 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1518.05 | 0.0883232 | ||||||||
\(667\) | 27847.1 | 1.61656 | ||||||||
\(668\) | 15463.7 | 0.895672 | ||||||||
\(669\) | 296.096 | 0.0171117 | ||||||||
\(670\) | −525.012 | −0.0302731 | ||||||||
\(671\) | 7686.48 | 0.442225 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4039.94 | −0.231394 | −0.115697 | − | 0.993285i | \(-0.536910\pi\) | ||||
−0.115697 | + | 0.993285i | \(0.536910\pi\) | |||||||
\(674\) | 1949.40 | 0.111406 | ||||||||
\(675\) | 2293.69 | 0.130791 | ||||||||
\(676\) | −13404.7 | −0.762673 | ||||||||
\(677\) | 1121.55 | 0.0636701 | 0.0318351 | − | 0.999493i | \(-0.489865\pi\) | ||||
0.0318351 | + | 0.999493i | \(0.489865\pi\) | |||||||
\(678\) | −832.731 | −0.0471694 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1581.20 | −0.0891712 | ||||||||
\(681\) | −11442.2 | −0.643858 | ||||||||
\(682\) | −367.588 | −0.0206388 | ||||||||
\(683\) | −10232.0 | −0.573232 | −0.286616 | − | 0.958046i | \(-0.592530\pi\) | ||||
−0.286616 | + | 0.958046i | \(0.592530\pi\) | |||||||
\(684\) | −19185.5 | −1.07248 | ||||||||
\(685\) | −4208.59 | −0.234747 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6301.95 | −0.349977 | ||||||||
\(688\) | −490.201 | −0.0271639 | ||||||||
\(689\) | −11236.1 | −0.621281 | ||||||||
\(690\) | −192.639 | −0.0106285 | ||||||||
\(691\) | 22514.6 | 1.23950 | 0.619750 | − | 0.784799i | \(-0.287234\pi\) | ||||
0.619750 | + | 0.784799i | \(0.287234\pi\) | |||||||
\(692\) | 16431.7 | 0.902661 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1421.11 | 0.0777302 | ||||||||
\(695\) | −12145.5 | −0.662885 | ||||||||
\(696\) | −1951.40 | −0.106276 | ||||||||
\(697\) | −23686.7 | −1.28723 | ||||||||
\(698\) | −1613.19 | −0.0874785 | ||||||||
\(699\) | 8131.62 | 0.440009 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19172.5 | −1.03300 | −0.516501 | − | 0.856287i | \(-0.672766\pi\) | ||||
−0.516501 | + | 0.856287i | \(0.672766\pi\) | |||||||
\(702\) | 1300.72 | 0.0699322 | ||||||||
\(703\) | −28605.6 | −1.53468 | ||||||||
\(704\) | −8713.45 | −0.466478 | ||||||||
\(705\) | −836.039 | −0.0446625 | ||||||||
\(706\) | −1658.28 | −0.0883996 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1433.21 | −0.0760781 | ||||||||
\(709\) | −26333.2 | −1.39487 | −0.697437 | − | 0.716646i | \(-0.745676\pi\) | ||||
−0.697437 | + | 0.716646i | \(0.745676\pi\) | |||||||
\(710\) | 589.692 | 0.0311701 | ||||||||
\(711\) | −5687.88 | −0.300017 | ||||||||
\(712\) | 3825.41 | 0.201353 | ||||||||
\(713\) | 8547.23 | 0.448943 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5515.71 | 0.288498 | ||||||||
\(716\) | −19043.3 | −0.993971 | ||||||||
\(717\) | 2766.64 | 0.144103 | ||||||||
\(718\) | 1971.99 | 0.102499 | ||||||||
\(719\) | 17047.7 | 0.884246 | 0.442123 | − | 0.896955i | \(-0.354226\pi\) | ||||
0.442123 | + | 0.896955i | \(0.354226\pi\) | |||||||
\(720\) | 7446.24 | 0.385423 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −793.666 | −0.0409102 | ||||||||
\(723\) | −8269.57 | −0.425378 | ||||||||
\(724\) | −10486.9 | −0.538321 | ||||||||
\(725\) | 7434.64 | 0.380849 | ||||||||
\(726\) | −418.707 | −0.0214045 | ||||||||
\(727\) | −16021.2 | −0.817325 | −0.408662 | − | 0.912686i | \(-0.634005\pi\) | ||||
−0.408662 | + | 0.912686i | \(0.634005\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6785.17 | −0.344722 | ||||||||
\(730\) | −617.503 | −0.0313080 | ||||||||
\(731\) | −680.795 | −0.0344461 | ||||||||
\(732\) | 6241.91 | 0.315174 | ||||||||
\(733\) | 7544.16 | 0.380150 | 0.190075 | − | 0.981770i | \(-0.439127\pi\) | ||||
0.190075 | + | 0.981770i | \(0.439127\pi\) | |||||||
\(734\) | 859.397 | 0.0432165 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4054.91 | −0.203079 | ||||||||
\(737\) | −8170.38 | −0.408358 | ||||||||
\(738\) | −1467.00 | −0.0731723 | ||||||||
\(739\) | 17543.9 | 0.873291 | 0.436645 | − | 0.899634i | \(-0.356166\pi\) | ||||
0.436645 | + | 0.899634i | \(0.356166\pi\) | |||||||
\(740\) | 11175.6 | 0.555167 | ||||||||
\(741\) | −11464.9 | −0.568387 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26595.9 | −1.31320 | −0.656600 | − | 0.754239i | \(-0.728006\pi\) | ||||
−0.656600 | + | 0.754239i | \(0.728006\pi\) | |||||||
\(744\) | −598.953 | −0.0295144 | ||||||||
\(745\) | 2889.74 | 0.142110 | ||||||||
\(746\) | 396.330 | 0.0194513 | ||||||||
\(747\) | −7099.36 | −0.347727 | ||||||||
\(748\) | −12263.6 | −0.599470 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −51.4310 | −0.00250399 | ||||||||
\(751\) | 9616.06 | 0.467237 | 0.233619 | − | 0.972328i | \(-0.424943\pi\) | ||||
0.233619 | + | 0.972328i | \(0.424943\pi\) | |||||||
\(752\) | −5802.37 | −0.281370 | ||||||||
\(753\) | 971.468 | 0.0470149 | ||||||||
\(754\) | 4216.07 | 0.203634 | ||||||||
\(755\) | −3918.08 | −0.188866 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8519.83 | 0.409060 | 0.204530 | − | 0.978860i | \(-0.434433\pi\) | ||||
0.204530 | + | 0.978860i | \(0.434433\pi\) | |||||||
\(758\) | 789.711 | 0.0378411 | ||||||||
\(759\) | −2997.90 | −0.143369 | ||||||||
\(760\) | 1845.36 | 0.0880765 | ||||||||
\(761\) | −4228.45 | −0.201421 | −0.100710 | − | 0.994916i | \(-0.532112\pi\) | ||||
−0.100710 | + | 0.994916i | \(0.532112\pi\) | |||||||
\(762\) | 661.017 | 0.0314253 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16755.5 | −0.793444 | ||||||||
\(765\) | 10341.4 | 0.488750 | ||||||||
\(766\) | −3286.22 | −0.155008 | ||||||||
\(767\) | 6213.15 | 0.292495 | ||||||||
\(768\) | −6933.34 | −0.325762 | ||||||||
\(769\) | −25293.4 | −1.18609 | −0.593046 | − | 0.805169i | \(-0.702075\pi\) | ||||
−0.593046 | + | 0.805169i | \(0.702075\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1588.94 | 0.0742207 | ||||||||
\(772\) | −28865.0 | −1.34569 | ||||||||
\(773\) | 15296.8 | 0.711756 | 0.355878 | − | 0.934533i | \(-0.384182\pi\) | ||||
0.355878 | + | 0.934533i | \(0.384182\pi\) | |||||||
\(774\) | −42.1642 | −0.00195809 | ||||||||
\(775\) | 2281.95 | 0.105768 | ||||||||
\(776\) | 1048.02 | 0.0484814 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1758.45 | 0.0810329 | ||||||||
\(779\) | 27643.7 | 1.27142 | ||||||||
\(780\) | 4479.11 | 0.205613 | ||||||||
\(781\) | 9176.96 | 0.420458 | ||||||||
\(782\) | −1856.80 | −0.0849092 | ||||||||
\(783\) | 27284.4 | 1.24529 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6862.02 | 0.311995 | ||||||||
\(786\) | 1171.94 | 0.0531826 | ||||||||
\(787\) | 16789.8 | 0.760474 | 0.380237 | − | 0.924889i | \(-0.375842\pi\) | ||||
0.380237 | + | 0.924889i | \(0.375842\pi\) | |||||||
\(788\) | −26073.9 | −1.17874 | ||||||||
\(789\) | −6717.12 | −0.303087 | ||||||||
\(790\) | 272.657 | 0.0122794 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1524.01 | −0.0683755 | ||||||||
\(793\) | −27059.5 | −1.21174 | ||||||||
\(794\) | 2290.81 | 0.102390 | ||||||||
\(795\) | 1630.47 | 0.0727382 | ||||||||
\(796\) | 5156.29 | 0.229598 | ||||||||
\(797\) | −18124.8 | −0.805537 | −0.402768 | − | 0.915302i | \(-0.631952\pi\) | ||||
−0.402768 | + | 0.915302i | \(0.631952\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8058.37 | −0.356802 | ||||||||
\(800\) | −1082.58 | −0.0478439 | ||||||||
\(801\) | −25018.9 | −1.10362 | ||||||||
\(802\) | −341.968 | −0.0150565 | ||||||||
\(803\) | −9609.76 | −0.422318 | ||||||||
\(804\) | −6634.87 | −0.291037 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1294.06 | 0.0565524 | ||||||||
\(807\) | 279.353 | 0.0121855 | ||||||||
\(808\) | 1287.42 | 0.0560536 | ||||||||
\(809\) | −10777.9 | −0.468395 | −0.234197 | − | 0.972189i | \(-0.575246\pi\) | ||||
−0.234197 | + | 0.972189i | \(0.575246\pi\) | |||||||
\(810\) | 540.022 | 0.0234252 | ||||||||
\(811\) | 11986.8 | 0.519007 | 0.259503 | − | 0.965742i | \(-0.416441\pi\) | ||||
0.259503 | + | 0.965742i | \(0.416441\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4352.00 | −0.187738 | ||||||||
\(814\) | −1132.47 | −0.0487629 | ||||||||
\(815\) | −18773.9 | −0.806898 | ||||||||
\(816\) | −9893.59 | −0.424442 | ||||||||
\(817\) | 794.528 | 0.0340233 | ||||||||
\(818\) | 139.543 | 0.00596454 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10799.8 | −0.459934 | ||||||||
\(821\) | 10740.4 | 0.456570 | 0.228285 | − | 0.973594i | \(-0.426688\pi\) | ||||
0.228285 | + | 0.973594i | \(0.426688\pi\) | |||||||
\(822\) | 346.322 | 0.0146951 | ||||||||
\(823\) | 32400.9 | 1.37233 | 0.686163 | − | 0.727448i | \(-0.259294\pi\) | ||||
0.686163 | + | 0.727448i | \(0.259294\pi\) | |||||||
\(824\) | −3860.92 | −0.163230 | ||||||||
\(825\) | −800.383 | −0.0337767 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3825.30 | 0.160845 | 0.0804225 | − | 0.996761i | \(-0.474373\pi\) | ||||
0.0804225 | + | 0.996761i | \(0.474373\pi\) | |||||||
\(828\) | 17660.8 | 0.741251 | ||||||||
\(829\) | 31836.3 | 1.33380 | 0.666900 | − | 0.745147i | \(-0.267621\pi\) | ||||
0.666900 | + | 0.745147i | \(0.267621\pi\) | |||||||
\(830\) | 340.318 | 0.0142321 | ||||||||
\(831\) | −2622.01 | −0.109454 | ||||||||
\(832\) | 30674.9 | 1.27820 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 999.448 | 0.0414965 | ||||||||
\(835\) | 9727.76 | 0.403165 | ||||||||
\(836\) | 14312.4 | 0.592111 | ||||||||
\(837\) | 8374.53 | 0.345838 | ||||||||
\(838\) | −2806.05 | −0.115672 | ||||||||
\(839\) | 6354.36 | 0.261474 | 0.130737 | − | 0.991417i | \(-0.458266\pi\) | ||||
0.130737 | + | 0.991417i | \(0.458266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 64049.1 | 2.62615 | ||||||||
\(842\) | 553.324 | 0.0226470 | ||||||||
\(843\) | −3684.20 | −0.150523 | ||||||||
\(844\) | −40316.2 | −1.64424 | ||||||||
\(845\) | −8432.52 | −0.343299 | ||||||||
\(846\) | −499.085 | −0.0202824 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 11316.0 | 0.458245 | ||||||||
\(849\) | 13322.4 | 0.538544 | ||||||||
\(850\) | −495.730 | −0.0200040 | ||||||||
\(851\) | 26332.4 | 1.06071 | ||||||||
\(852\) | 7452.28 | 0.299661 | ||||||||
\(853\) | 16620.2 | 0.667135 | 0.333568 | − | 0.942726i | \(-0.391747\pi\) | ||||
0.333568 | + | 0.942726i | \(0.391747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12069.0 | −0.482750 | ||||||||
\(856\) | −5056.62 | −0.201906 | ||||||||
\(857\) | −34440.5 | −1.37277 | −0.686385 | − | 0.727238i | \(-0.740804\pi\) | ||||
−0.686385 | + | 0.727238i | \(0.740804\pi\) | |||||||
\(858\) | −453.885 | −0.0180599 | ||||||||
\(859\) | 29192.5 | 1.15953 | 0.579765 | − | 0.814784i | \(-0.303144\pi\) | ||||
0.579765 | + | 0.814784i | \(0.303144\pi\) | |||||||
\(860\) | −310.405 | −0.0123078 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 298.130 | 0.0117800 | ||||||||
\(863\) | 26062.4 | 1.02801 | 0.514006 | − | 0.857786i | \(-0.328161\pi\) | ||||
0.514006 | + | 0.857786i | \(0.328161\pi\) | |||||||
\(864\) | −3972.98 | −0.156439 | ||||||||
\(865\) | 10336.7 | 0.406311 | ||||||||
\(866\) | −1127.22 | −0.0442314 | ||||||||
\(867\) | −4854.72 | −0.190167 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4243.16 | 0.165638 | ||||||||
\(870\) | −611.793 | −0.0238411 | ||||||||
\(871\) | 28763.0 | 1.11894 | ||||||||
\(872\) | −524.214 | −0.0203579 | ||||||||
\(873\) | −6854.23 | −0.265728 | ||||||||
\(874\) | 2166.99 | 0.0838668 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7803.74 | −0.300986 | ||||||||
\(877\) | −29048.5 | −1.11847 | −0.559236 | − | 0.829009i | \(-0.688905\pi\) | ||||
−0.559236 | + | 0.829009i | \(0.688905\pi\) | |||||||
\(878\) | 1864.42 | 0.0716640 | ||||||||
\(879\) | 981.943 | 0.0376793 | ||||||||
\(880\) | −5554.90 | −0.212791 | ||||||||
\(881\) | 24440.9 | 0.934660 | 0.467330 | − | 0.884083i | \(-0.345216\pi\) | ||||
0.467330 | + | 0.884083i | \(0.345216\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38951.9 | 1.48453 | 0.742264 | − | 0.670108i | \(-0.233752\pi\) | ||||
0.742264 | + | 0.670108i | \(0.233752\pi\) | |||||||
\(884\) | 43173.0 | 1.64261 | ||||||||
\(885\) | −901.589 | −0.0342447 | ||||||||
\(886\) | −672.642 | −0.0255055 | ||||||||
\(887\) | 3143.83 | 0.119007 | 0.0595036 | − | 0.998228i | \(-0.481048\pi\) | ||||
0.0595036 | + | 0.998228i | \(0.481048\pi\) | |||||||
\(888\) | −1845.26 | −0.0697330 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1199.32 | 0.0451700 | ||||||||
\(891\) | 8403.98 | 0.315986 | ||||||||
\(892\) | 1301.26 | 0.0488448 | ||||||||
\(893\) | 9404.59 | 0.352422 | ||||||||
\(894\) | −237.795 | −0.00889604 | ||||||||
\(895\) | −11979.6 | −0.447412 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10553.8 | 0.392845 | ||||||||
\(898\) | 2378.13 | 0.0883734 | ||||||||
\(899\) | 27144.7 | 1.00704 | ||||||||
\(900\) | 4715.10 | 0.174633 | ||||||||
\(901\) | 15715.7 | 0.581094 | ||||||||
\(902\) | 1094.39 | 0.0403981 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7343.10 | −0.270163 | ||||||||
\(905\) | −6597.02 | −0.242312 | ||||||||
\(906\) | 322.417 | 0.0118229 | ||||||||
\(907\) | −12839.5 | −0.470044 | −0.235022 | − | 0.971990i | \(-0.575516\pi\) | ||||
−0.235022 | + | 0.971990i | \(0.575516\pi\) | |||||||
\(908\) | −50285.6 | −1.83787 | ||||||||
\(909\) | −8419.98 | −0.307231 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17451.4 | 0.634678 | 0.317339 | − | 0.948312i | \(-0.397211\pi\) | ||||
0.317339 | + | 0.948312i | \(0.397211\pi\) | |||||||
\(912\) | 11546.4 | 0.419232 | ||||||||
\(913\) | 5296.13 | 0.191978 | ||||||||
\(914\) | −510.775 | −0.0184846 | ||||||||
\(915\) | 3926.60 | 0.141868 | ||||||||
\(916\) | −27695.4 | −0.998998 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1819.28 | −0.0654088 | ||||||||
\(919\) | −7937.66 | −0.284918 | −0.142459 | − | 0.989801i | \(-0.545501\pi\) | ||||
−0.142459 | + | 0.989801i | \(0.545501\pi\) | |||||||
\(920\) | −1698.71 | −0.0608747 | ||||||||
\(921\) | −9611.22 | −0.343866 | ||||||||
\(922\) | 2830.31 | 0.101097 | ||||||||
\(923\) | −32306.6 | −1.15210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7030.24 | 0.249895 | ||||||||
\(926\) | −3887.02 | −0.137943 | ||||||||
\(927\) | 25251.2 | 0.894668 | ||||||||
\(928\) | −12877.8 | −0.455532 | ||||||||
\(929\) | −1781.40 | −0.0629127 | −0.0314563 | − | 0.999505i | \(-0.510015\pi\) | ||||
−0.0314563 | + | 0.999505i | \(0.510015\pi\) | |||||||
\(930\) | −187.780 | −0.00662103 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 35736.3 | 1.25599 | ||||||||
\(933\) | 15987.9 | 0.561007 | ||||||||
\(934\) | 2663.79 | 0.0933210 | ||||||||
\(935\) | −7714.69 | −0.269837 | ||||||||
\(936\) | 5365.14 | 0.187356 | ||||||||
\(937\) | −46363.0 | −1.61645 | −0.808225 | − | 0.588874i | \(-0.799571\pi\) | ||||
−0.808225 | + | 0.588874i | \(0.799571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3429.70 | 0.119195 | ||||||||
\(940\) | −3674.17 | −0.127488 | ||||||||
\(941\) | 16535.3 | 0.572833 | 0.286416 | − | 0.958105i | \(-0.407536\pi\) | ||||
0.286416 | + | 0.958105i | \(0.407536\pi\) | |||||||
\(942\) | −564.673 | −0.0195308 | ||||||||
\(943\) | −25446.9 | −0.878754 | ||||||||
\(944\) | −6257.30 | −0.215739 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.4545 | 0.00108105 | ||||||||
\(947\) | −2734.31 | −0.0938258 | −0.0469129 | − | 0.998899i | \(-0.514938\pi\) | ||||
−0.0469129 | + | 0.998899i | \(0.514938\pi\) | |||||||
\(948\) | 3445.72 | 0.118050 | ||||||||
\(949\) | 33830.2 | 1.15719 | ||||||||
\(950\) | 578.546 | 0.0197584 | ||||||||
\(951\) | 10983.2 | 0.374505 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35524.6 | −1.20751 | −0.603754 | − | 0.797171i | \(-0.706329\pi\) | ||||
−0.603754 | + | 0.797171i | \(0.706329\pi\) | |||||||
\(954\) | 973.332 | 0.0330323 | ||||||||
\(955\) | −10540.4 | −0.357150 | ||||||||
\(956\) | 12158.7 | 0.411338 | ||||||||
\(957\) | −9520.89 | −0.321595 | ||||||||
\(958\) | −2659.89 | −0.0897048 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −4451.22 | −0.149649 | ||||||||
\(961\) | −21459.4 | −0.720330 | ||||||||
\(962\) | 3986.74 | 0.133615 | ||||||||
\(963\) | 33071.3 | 1.10665 | ||||||||
\(964\) | −36342.6 | −1.21423 | ||||||||
\(965\) | −18158.1 | −0.605730 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9328.92 | 0.310236 | 0.155118 | − | 0.987896i | \(-0.450424\pi\) | ||||
0.155118 | + | 0.987896i | \(0.450424\pi\) | |||||||
\(968\) | −3692.19 | −0.122595 | ||||||||
\(969\) | 16035.7 | 0.531622 | ||||||||
\(970\) | 328.568 | 0.0108760 | ||||||||
\(971\) | 49138.1 | 1.62401 | 0.812007 | − | 0.583648i | \(-0.198375\pi\) | ||||
0.812007 | + | 0.583648i | \(0.198375\pi\) | |||||||
\(972\) | 26513.9 | 0.874930 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1621.79 | −0.0533527 | ||||||||
\(975\) | 2817.67 | 0.0925515 | ||||||||
\(976\) | 27251.8 | 0.893758 | ||||||||
\(977\) | 14771.3 | 0.483702 | 0.241851 | − | 0.970313i | \(-0.422245\pi\) | ||||
0.241851 | + | 0.970313i | \(0.422245\pi\) | |||||||
\(978\) | 1544.90 | 0.0505116 | ||||||||
\(979\) | 18664.1 | 0.609304 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3428.46 | 0.111582 | ||||||||
\(982\) | 985.141 | 0.0320133 | ||||||||
\(983\) | −20651.0 | −0.670054 | −0.335027 | − | 0.942208i | \(-0.608746\pi\) | ||||
−0.335027 | + | 0.942208i | \(0.608746\pi\) | |||||||
\(984\) | 1783.21 | 0.0577710 | ||||||||
\(985\) | −16402.3 | −0.530580 | ||||||||
\(986\) | −5896.91 | −0.190462 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −50385.4 | −1.62244 | ||||||||
\(989\) | −731.387 | −0.0235154 | ||||||||
\(990\) | −477.799 | −0.0153389 | ||||||||
\(991\) | −45941.4 | −1.47263 | −0.736315 | − | 0.676639i | \(-0.763436\pi\) | ||||
−0.736315 | + | 0.676639i | \(0.763436\pi\) | |||||||
\(992\) | −3952.63 | −0.126508 | ||||||||
\(993\) | −6043.88 | −0.193149 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3243.67 | 0.103348 | ||||||||
\(996\) | 4300.79 | 0.136823 | ||||||||
\(997\) | 9025.07 | 0.286687 | 0.143344 | − | 0.989673i | \(-0.454215\pi\) | ||||
0.143344 | + | 0.989673i | \(0.454215\pi\) | |||||||
\(998\) | −2192.09 | −0.0695284 | ||||||||
\(999\) | 25800.3 | 0.817103 |
(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 | 245.4.a.m.1.3 | 5 | ||
3.2 | odd | 2 | 2205.4.a.bu.1.3 | 5 | |||
5.4 | even | 2 | 1225.4.a.bg.1.3 | 5 | |||
7.2 | even | 3 | 35.4.e.c.11.3 | ✓ | 10 | ||
7.3 | odd | 6 | 245.4.e.o.226.3 | 10 | |||
7.4 | even | 3 | 35.4.e.c.16.3 | yes | 10 | ||
7.5 | odd | 6 | 245.4.e.o.116.3 | 10 | |||
7.6 | odd | 2 | 245.4.a.n.1.3 | 5 | |||
21.2 | odd | 6 | 315.4.j.g.46.3 | 10 | |||
21.11 | odd | 6 | 315.4.j.g.226.3 | 10 | |||
21.20 | even | 2 | 2205.4.a.bt.1.3 | 5 | |||
28.11 | odd | 6 | 560.4.q.n.401.3 | 10 | |||
28.23 | odd | 6 | 560.4.q.n.81.3 | 10 | |||
35.2 | odd | 12 | 175.4.k.d.74.5 | 20 | |||
35.4 | even | 6 | 175.4.e.d.51.3 | 10 | |||
35.9 | even | 6 | 175.4.e.d.151.3 | 10 | |||
35.18 | odd | 12 | 175.4.k.d.149.5 | 20 | |||
35.23 | odd | 12 | 175.4.k.d.74.6 | 20 | |||
35.32 | odd | 12 | 175.4.k.d.149.6 | 20 | |||
35.34 | odd | 2 | 1225.4.a.bf.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.4.e.c.11.3 | ✓ | 10 | 7.2 | even | 3 | ||
35.4.e.c.16.3 | yes | 10 | 7.4 | even | 3 | ||
175.4.e.d.51.3 | 10 | 35.4 | even | 6 | |||
175.4.e.d.151.3 | 10 | 35.9 | even | 6 | |||
175.4.k.d.74.5 | 20 | 35.2 | odd | 12 | |||
175.4.k.d.74.6 | 20 | 35.23 | odd | 12 | |||
175.4.k.d.149.5 | 20 | 35.18 | odd | 12 | |||
175.4.k.d.149.6 | 20 | 35.32 | odd | 12 | |||
245.4.a.m.1.3 | 5 | 1.1 | even | 1 | trivial | ||
245.4.a.n.1.3 | 5 | 7.6 | odd | 2 | |||
245.4.e.o.116.3 | 10 | 7.5 | odd | 6 | |||
245.4.e.o.226.3 | 10 | 7.3 | odd | 6 | |||
315.4.j.g.46.3 | 10 | 21.2 | odd | 6 | |||
315.4.j.g.226.3 | 10 | 21.11 | odd | 6 | |||
560.4.q.n.81.3 | 10 | 28.23 | odd | 6 | |||
560.4.q.n.401.3 | 10 | 28.11 | odd | 6 | |||
1225.4.a.bf.1.3 | 5 | 35.34 | odd | 2 | |||
1225.4.a.bg.1.3 | 5 | 5.4 | even | 2 | |||
2205.4.a.bt.1.3 | 5 | 21.20 | even | 2 | |||
2205.4.a.bu.1.3 | 5 | 3.2 | odd | 2 |