Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + 15565376 x^{4} + 6775664 x^{3} - 75006848 x^{2} + \cdots + 49172480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-5.43261\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.43261 | 1.31391 | 0.656956 | − | 0.753929i | \(-0.271844\pi\) | ||||
0.656956 | + | 0.753929i | \(0.271844\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 23.2437 | 0.726366 | ||||||||
\(5\) | 48.3022 | 0.864057 | 0.432028 | − | 0.901860i | \(-0.357798\pi\) | ||||
0.432028 | + | 0.901860i | \(0.357798\pi\) | |||||||
\(6\) | 66.8935 | 0.758588 | ||||||||
\(7\) | 120.542 | 0.929808 | 0.464904 | − | 0.885361i | \(-0.346089\pi\) | ||||
0.464904 | + | 0.885361i | \(0.346089\pi\) | |||||||
\(8\) | −65.0821 | −0.359531 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 359.012 | 1.13529 | ||||||||
\(11\) | −192.015 | −0.478468 | −0.239234 | − | 0.970962i | \(-0.576896\pi\) | ||||
−0.239234 | + | 0.970962i | \(0.576896\pi\) | |||||||
\(12\) | 209.193 | 0.419368 | ||||||||
\(13\) | 600.307 | 0.985178 | 0.492589 | − | 0.870262i | \(-0.336051\pi\) | ||||
0.492589 | + | 0.870262i | \(0.336051\pi\) | |||||||
\(14\) | 895.942 | 1.22169 | ||||||||
\(15\) | 434.720 | 0.498863 | ||||||||
\(16\) | −1227.53 | −1.19876 | ||||||||
\(17\) | 2195.23 | 1.84229 | 0.921146 | − | 0.389218i | \(-0.127255\pi\) | ||||
0.921146 | + | 0.389218i | \(0.127255\pi\) | |||||||
\(18\) | 602.041 | 0.437971 | ||||||||
\(19\) | −393.685 | −0.250187 | −0.125093 | − | 0.992145i | \(-0.539923\pi\) | ||||
−0.125093 | + | 0.992145i | \(0.539923\pi\) | |||||||
\(20\) | 1122.72 | 0.627621 | ||||||||
\(21\) | 1084.88 | 0.536825 | ||||||||
\(22\) | −1427.17 | −0.628665 | ||||||||
\(23\) | −212.558 | −0.0837834 | −0.0418917 | − | 0.999122i | \(-0.513338\pi\) | ||||
−0.0418917 | + | 0.999122i | \(0.513338\pi\) | |||||||
\(24\) | −585.739 | −0.207575 | ||||||||
\(25\) | −791.894 | −0.253406 | ||||||||
\(26\) | 4461.85 | 1.29444 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 2801.84 | 0.675381 | ||||||||
\(29\) | −320.477 | −0.0707623 | −0.0353812 | − | 0.999374i | \(-0.511265\pi\) | ||||
−0.0353812 | + | 0.999374i | \(0.511265\pi\) | |||||||
\(30\) | 3231.11 | 0.655463 | ||||||||
\(31\) | −1196.80 | −0.223675 | −0.111837 | − | 0.993727i | \(-0.535674\pi\) | ||||
−0.111837 | + | 0.993727i | \(0.535674\pi\) | |||||||
\(32\) | −7041.12 | −1.21553 | ||||||||
\(33\) | −1728.13 | −0.276244 | ||||||||
\(34\) | 16316.3 | 2.42061 | ||||||||
\(35\) | 5822.45 | 0.803407 | ||||||||
\(36\) | 1882.74 | 0.242122 | ||||||||
\(37\) | 1866.98 | 0.224200 | 0.112100 | − | 0.993697i | \(-0.464242\pi\) | ||||
0.112100 | + | 0.993697i | \(0.464242\pi\) | |||||||
\(38\) | −2926.10 | −0.328724 | ||||||||
\(39\) | 5402.76 | 0.568793 | ||||||||
\(40\) | −3143.61 | −0.310655 | ||||||||
\(41\) | −10116.5 | −0.939879 | −0.469939 | − | 0.882699i | \(-0.655724\pi\) | ||||
−0.469939 | + | 0.882699i | \(0.655724\pi\) | |||||||
\(42\) | 8063.48 | 0.705341 | ||||||||
\(43\) | 18212.6 | 1.50211 | 0.751053 | − | 0.660242i | \(-0.229546\pi\) | ||||
0.751053 | + | 0.660242i | \(0.229546\pi\) | |||||||
\(44\) | −4463.14 | −0.347543 | ||||||||
\(45\) | 3912.48 | 0.288019 | ||||||||
\(46\) | −1579.86 | −0.110084 | ||||||||
\(47\) | 19027.8 | 1.25645 | 0.628224 | − | 0.778033i | \(-0.283782\pi\) | ||||
0.628224 | + | 0.778033i | \(0.283782\pi\) | |||||||
\(48\) | −11047.8 | −0.692104 | ||||||||
\(49\) | −2276.61 | −0.135456 | ||||||||
\(50\) | −5885.84 | −0.332953 | ||||||||
\(51\) | 19757.1 | 1.06365 | ||||||||
\(52\) | 13953.4 | 0.715600 | ||||||||
\(53\) | −18428.0 | −0.901131 | −0.450566 | − | 0.892743i | \(-0.648778\pi\) | ||||
−0.450566 | + | 0.892743i | \(0.648778\pi\) | |||||||
\(54\) | 5418.37 | 0.252863 | ||||||||
\(55\) | −9274.74 | −0.413424 | ||||||||
\(56\) | −7845.13 | −0.334295 | ||||||||
\(57\) | −3543.16 | −0.144445 | ||||||||
\(58\) | −2381.98 | −0.0929755 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 10104.5 | 0.362357 | ||||||||
\(61\) | −16435.9 | −0.565547 | −0.282773 | − | 0.959187i | \(-0.591254\pi\) | ||||
−0.282773 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(62\) | −8895.35 | −0.293889 | ||||||||
\(63\) | 9763.91 | 0.309936 | ||||||||
\(64\) | −13053.0 | −0.398345 | ||||||||
\(65\) | 28996.2 | 0.851250 | ||||||||
\(66\) | −12844.5 | −0.362960 | ||||||||
\(67\) | 10398.4 | 0.282995 | 0.141497 | − | 0.989939i | \(-0.454808\pi\) | ||||
0.141497 | + | 0.989939i | \(0.454808\pi\) | |||||||
\(68\) | 51025.3 | 1.33818 | ||||||||
\(69\) | −1913.02 | −0.0483724 | ||||||||
\(70\) | 43276.0 | 1.05561 | ||||||||
\(71\) | −16382.6 | −0.385688 | −0.192844 | − | 0.981229i | \(-0.561771\pi\) | ||||
−0.192844 | + | 0.981229i | \(0.561771\pi\) | |||||||
\(72\) | −5271.65 | −0.119844 | ||||||||
\(73\) | −68804.3 | −1.51115 | −0.755577 | − | 0.655060i | \(-0.772643\pi\) | ||||
−0.755577 | + | 0.655060i | \(0.772643\pi\) | |||||||
\(74\) | 13876.6 | 0.294580 | ||||||||
\(75\) | −7127.05 | −0.146304 | ||||||||
\(76\) | −9150.69 | −0.181727 | ||||||||
\(77\) | −23145.9 | −0.444884 | ||||||||
\(78\) | 40156.6 | 0.747344 | ||||||||
\(79\) | −3498.36 | −0.0630662 | −0.0315331 | − | 0.999503i | \(-0.510039\pi\) | ||||
−0.0315331 | + | 0.999503i | \(0.510039\pi\) | |||||||
\(80\) | −59292.4 | −1.03580 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −75192.2 | −1.23492 | ||||||||
\(83\) | −95365.4 | −1.51948 | −0.759741 | − | 0.650226i | \(-0.774674\pi\) | ||||
−0.759741 | + | 0.650226i | \(0.774674\pi\) | |||||||
\(84\) | 25216.6 | 0.389931 | ||||||||
\(85\) | 106035. | 1.59184 | ||||||||
\(86\) | 135367. | 1.97364 | ||||||||
\(87\) | −2884.29 | −0.0408546 | ||||||||
\(88\) | 12496.7 | 0.172024 | ||||||||
\(89\) | −19992.9 | −0.267548 | −0.133774 | − | 0.991012i | \(-0.542710\pi\) | ||||
−0.133774 | + | 0.991012i | \(0.542710\pi\) | |||||||
\(90\) | 29080.0 | 0.378432 | ||||||||
\(91\) | 72362.2 | 0.916027 | ||||||||
\(92\) | −4940.64 | −0.0608574 | ||||||||
\(93\) | −10771.2 | −0.129139 | ||||||||
\(94\) | 141426. | 1.65086 | ||||||||
\(95\) | −19015.8 | −0.216176 | ||||||||
\(96\) | −63370.0 | −0.701788 | ||||||||
\(97\) | −99691.0 | −1.07579 | −0.537894 | − | 0.843012i | \(-0.680780\pi\) | ||||
−0.537894 | + | 0.843012i | \(0.680780\pi\) | |||||||
\(98\) | −16921.2 | −0.177978 | ||||||||
\(99\) | −15553.2 | −0.159489 | ||||||||
\(100\) | −18406.6 | −0.184066 | ||||||||
\(101\) | −77792.2 | −0.758809 | −0.379405 | − | 0.925231i | \(-0.623871\pi\) | ||||
−0.379405 | + | 0.925231i | \(0.623871\pi\) | |||||||
\(102\) | 146847. | 1.39754 | ||||||||
\(103\) | −53809.1 | −0.499761 | −0.249880 | − | 0.968277i | \(-0.580391\pi\) | ||||
−0.249880 | + | 0.968277i | \(0.580391\pi\) | |||||||
\(104\) | −39069.2 | −0.354202 | ||||||||
\(105\) | 52402.1 | 0.463847 | ||||||||
\(106\) | −136968. | −1.18401 | ||||||||
\(107\) | −90583.1 | −0.764870 | −0.382435 | − | 0.923982i | \(-0.624914\pi\) | ||||
−0.382435 | + | 0.923982i | \(0.624914\pi\) | |||||||
\(108\) | 16944.7 | 0.139789 | ||||||||
\(109\) | 206631. | 1.66583 | 0.832913 | − | 0.553405i | \(-0.186672\pi\) | ||||
0.832913 | + | 0.553405i | \(0.186672\pi\) | |||||||
\(110\) | −68935.6 | −0.543202 | ||||||||
\(111\) | 16802.9 | 0.129442 | ||||||||
\(112\) | −147969. | −1.11462 | ||||||||
\(113\) | 83781.9 | 0.617240 | 0.308620 | − | 0.951185i | \(-0.400133\pi\) | ||||
0.308620 | + | 0.951185i | \(0.400133\pi\) | |||||||
\(114\) | −26334.9 | −0.189789 | ||||||||
\(115\) | −10267.0 | −0.0723936 | ||||||||
\(116\) | −7449.08 | −0.0513993 | ||||||||
\(117\) | 48624.8 | 0.328393 | ||||||||
\(118\) | −25872.9 | −0.171057 | ||||||||
\(119\) | 264618. | 1.71298 | ||||||||
\(120\) | −28292.5 | −0.179357 | ||||||||
\(121\) | −124181. | −0.771068 | ||||||||
\(122\) | −122162. | −0.743079 | ||||||||
\(123\) | −91048.7 | −0.542639 | ||||||||
\(124\) | −27818.1 | −0.162470 | ||||||||
\(125\) | −189195. | −1.08301 | ||||||||
\(126\) | 72571.3 | 0.407229 | ||||||||
\(127\) | −230499. | −1.26812 | −0.634059 | − | 0.773285i | \(-0.718612\pi\) | ||||
−0.634059 | + | 0.773285i | \(0.718612\pi\) | |||||||
\(128\) | 128298. | 0.692142 | ||||||||
\(129\) | 163913. | 0.867241 | ||||||||
\(130\) | 215517. | 1.11847 | ||||||||
\(131\) | 186771. | 0.950892 | 0.475446 | − | 0.879745i | \(-0.342287\pi\) | ||||
0.475446 | + | 0.879745i | \(0.342287\pi\) | |||||||
\(132\) | −40168.2 | −0.200654 | ||||||||
\(133\) | −47455.6 | −0.232626 | ||||||||
\(134\) | 77287.0 | 0.371830 | ||||||||
\(135\) | 35212.3 | 0.166288 | ||||||||
\(136\) | −142870. | −0.662361 | ||||||||
\(137\) | 111807. | 0.508941 | 0.254471 | − | 0.967081i | \(-0.418099\pi\) | ||||
0.254471 | + | 0.967081i | \(0.418099\pi\) | |||||||
\(138\) | −14218.8 | −0.0635571 | ||||||||
\(139\) | 195432. | 0.857942 | 0.428971 | − | 0.903318i | \(-0.358876\pi\) | ||||
0.428971 | + | 0.903318i | \(0.358876\pi\) | |||||||
\(140\) | 135335. | 0.583568 | ||||||||
\(141\) | 171250. | 0.725410 | ||||||||
\(142\) | −121765. | −0.506760 | ||||||||
\(143\) | −115268. | −0.471376 | ||||||||
\(144\) | −99429.8 | −0.399586 | ||||||||
\(145\) | −15479.8 | −0.0611427 | ||||||||
\(146\) | −511396. | −1.98552 | ||||||||
\(147\) | −20489.5 | −0.0782057 | ||||||||
\(148\) | 43395.6 | 0.162851 | ||||||||
\(149\) | −371327. | −1.37022 | −0.685111 | − | 0.728438i | \(-0.740246\pi\) | ||||
−0.685111 | + | 0.728438i | \(0.740246\pi\) | |||||||
\(150\) | −52972.6 | −0.192231 | ||||||||
\(151\) | −405248. | −1.44637 | −0.723184 | − | 0.690655i | \(-0.757322\pi\) | ||||
−0.723184 | + | 0.690655i | \(0.757322\pi\) | |||||||
\(152\) | 25621.8 | 0.0899500 | ||||||||
\(153\) | 177814. | 0.614097 | ||||||||
\(154\) | −172034. | −0.584538 | ||||||||
\(155\) | −57808.1 | −0.193268 | ||||||||
\(156\) | 125580. | 0.413152 | ||||||||
\(157\) | 93561.5 | 0.302934 | 0.151467 | − | 0.988462i | \(-0.451600\pi\) | ||||
0.151467 | + | 0.988462i | \(0.451600\pi\) | |||||||
\(158\) | −26001.9 | −0.0828634 | ||||||||
\(159\) | −165852. | −0.520268 | ||||||||
\(160\) | −340102. | −1.05029 | ||||||||
\(161\) | −25622.2 | −0.0779026 | ||||||||
\(162\) | 48765.4 | 0.145990 | ||||||||
\(163\) | −314860. | −0.928216 | −0.464108 | − | 0.885779i | \(-0.653625\pi\) | ||||
−0.464108 | + | 0.885779i | \(0.653625\pi\) | |||||||
\(164\) | −235146. | −0.682696 | ||||||||
\(165\) | −83472.7 | −0.238690 | ||||||||
\(166\) | −708814. | −1.99647 | ||||||||
\(167\) | 82055.5 | 0.227676 | 0.113838 | − | 0.993499i | \(-0.463686\pi\) | ||||
0.113838 | + | 0.993499i | \(0.463686\pi\) | |||||||
\(168\) | −70606.2 | −0.193005 | ||||||||
\(169\) | −10924.8 | −0.0294238 | ||||||||
\(170\) | 788114. | 2.09154 | ||||||||
\(171\) | −31888.5 | −0.0833956 | ||||||||
\(172\) | 423328. | 1.09108 | ||||||||
\(173\) | −138981. | −0.353053 | −0.176527 | − | 0.984296i | \(-0.556486\pi\) | ||||
−0.176527 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(174\) | −21437.8 | −0.0536794 | ||||||||
\(175\) | −95456.5 | −0.235619 | ||||||||
\(176\) | 235704. | 0.573568 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | −148600. | −0.351535 | ||||||||
\(179\) | 377160. | 0.879819 | 0.439909 | − | 0.898042i | \(-0.355011\pi\) | ||||
0.439909 | + | 0.898042i | \(0.355011\pi\) | |||||||
\(180\) | 90940.6 | 0.209207 | ||||||||
\(181\) | −395990. | −0.898438 | −0.449219 | − | 0.893422i | \(-0.648298\pi\) | ||||
−0.449219 | + | 0.893422i | \(0.648298\pi\) | |||||||
\(182\) | 537840. | 1.20358 | ||||||||
\(183\) | −147923. | −0.326519 | ||||||||
\(184\) | 13833.7 | 0.0301228 | ||||||||
\(185\) | 90179.5 | 0.193722 | ||||||||
\(186\) | −80058.2 | −0.169677 | ||||||||
\(187\) | −421517. | −0.881478 | ||||||||
\(188\) | 442277. | 0.912640 | ||||||||
\(189\) | 87875.2 | 0.178942 | ||||||||
\(190\) | −141337. | −0.284036 | ||||||||
\(191\) | 611684. | 1.21323 | 0.606616 | − | 0.794995i | \(-0.292527\pi\) | ||||
0.606616 | + | 0.794995i | \(0.292527\pi\) | |||||||
\(192\) | −117477. | −0.229984 | ||||||||
\(193\) | 374856. | 0.724388 | 0.362194 | − | 0.932103i | \(-0.382028\pi\) | ||||
0.362194 | + | 0.932103i | \(0.382028\pi\) | |||||||
\(194\) | −740965. | −1.41349 | ||||||||
\(195\) | 260965. | 0.491469 | ||||||||
\(196\) | −52916.9 | −0.0983908 | ||||||||
\(197\) | 527822. | 0.968997 | 0.484498 | − | 0.874792i | \(-0.339002\pi\) | ||||
0.484498 | + | 0.874792i | \(0.339002\pi\) | |||||||
\(198\) | −115601. | −0.209555 | ||||||||
\(199\) | 167623. | 0.300055 | 0.150028 | − | 0.988682i | \(-0.452064\pi\) | ||||
0.150028 | + | 0.988682i | \(0.452064\pi\) | |||||||
\(200\) | 51538.1 | 0.0911074 | ||||||||
\(201\) | 93585.3 | 0.163387 | ||||||||
\(202\) | −578199. | −0.997009 | ||||||||
\(203\) | −38631.0 | −0.0657954 | ||||||||
\(204\) | 459228. | 0.772597 | ||||||||
\(205\) | −488651. | −0.812108 | ||||||||
\(206\) | −399942. | −0.656642 | ||||||||
\(207\) | −17217.2 | −0.0279278 | ||||||||
\(208\) | −736894. | −1.18099 | ||||||||
\(209\) | 75593.3 | 0.119706 | ||||||||
\(210\) | 389484. | 0.609455 | ||||||||
\(211\) | −256097. | −0.396003 | −0.198001 | − | 0.980202i | \(-0.563445\pi\) | ||||
−0.198001 | + | 0.980202i | \(0.563445\pi\) | |||||||
\(212\) | −428335. | −0.654551 | ||||||||
\(213\) | −147443. | −0.222677 | ||||||||
\(214\) | −673269. | −1.00497 | ||||||||
\(215\) | 879709. | 1.29790 | ||||||||
\(216\) | −47444.9 | −0.0691918 | ||||||||
\(217\) | −144265. | −0.207975 | ||||||||
\(218\) | 1.53581e6 | 2.18875 | ||||||||
\(219\) | −619239. | −0.872465 | ||||||||
\(220\) | −215579. | −0.300297 | ||||||||
\(221\) | 1.31781e6 | 1.81499 | ||||||||
\(222\) | 124889. | 0.170076 | ||||||||
\(223\) | 615040. | 0.828212 | 0.414106 | − | 0.910229i | \(-0.364094\pi\) | ||||
0.414106 | + | 0.910229i | \(0.364094\pi\) | |||||||
\(224\) | −848751. | −1.13021 | ||||||||
\(225\) | −64143.4 | −0.0844687 | ||||||||
\(226\) | 622718. | 0.810999 | ||||||||
\(227\) | 1.04368e6 | 1.34432 | 0.672161 | − | 0.740405i | \(-0.265366\pi\) | ||||
0.672161 | + | 0.740405i | \(0.265366\pi\) | |||||||
\(228\) | −82356.2 | −0.104920 | ||||||||
\(229\) | −608125. | −0.766309 | −0.383154 | − | 0.923684i | \(-0.625162\pi\) | ||||
−0.383154 | + | 0.923684i | \(0.625162\pi\) | |||||||
\(230\) | −76310.9 | −0.0951189 | ||||||||
\(231\) | −208313. | −0.256854 | ||||||||
\(232\) | 20857.3 | 0.0254413 | ||||||||
\(233\) | 1.00513e6 | 1.21292 | 0.606462 | − | 0.795113i | \(-0.292588\pi\) | ||||
0.606462 | + | 0.795113i | \(0.292588\pi\) | |||||||
\(234\) | 361410. | 0.431479 | ||||||||
\(235\) | 919086. | 1.08564 | ||||||||
\(236\) | −80911.3 | −0.0945648 | ||||||||
\(237\) | −31485.2 | −0.0364113 | ||||||||
\(238\) | 1.96680e6 | 2.25070 | ||||||||
\(239\) | 1.22727e6 | 1.38978 | 0.694891 | − | 0.719115i | \(-0.255453\pi\) | ||||
0.694891 | + | 0.719115i | \(0.255453\pi\) | |||||||
\(240\) | −533631. | −0.598017 | ||||||||
\(241\) | 1.34998e6 | 1.49721 | 0.748607 | − | 0.663014i | \(-0.230723\pi\) | ||||
0.748607 | + | 0.663014i | \(0.230723\pi\) | |||||||
\(242\) | −922991. | −1.01312 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −382031. | −0.410794 | ||||||||
\(245\) | −109965. | −0.117042 | ||||||||
\(246\) | −676730. | −0.712980 | ||||||||
\(247\) | −236332. | −0.246479 | ||||||||
\(248\) | 77890.3 | 0.0804182 | ||||||||
\(249\) | −858289. | −0.877273 | ||||||||
\(250\) | −1.40621e6 | −1.42299 | ||||||||
\(251\) | 448506. | 0.449350 | 0.224675 | − | 0.974434i | \(-0.427868\pi\) | ||||
0.224675 | + | 0.974434i | \(0.427868\pi\) | |||||||
\(252\) | 226949. | 0.225127 | ||||||||
\(253\) | 40814.3 | 0.0400877 | ||||||||
\(254\) | −1.71321e6 | −1.66620 | ||||||||
\(255\) | 954312. | 0.919052 | ||||||||
\(256\) | 1.37128e6 | 1.30776 | ||||||||
\(257\) | 656292. | 0.619818 | 0.309909 | − | 0.950766i | \(-0.399701\pi\) | ||||
0.309909 | + | 0.950766i | \(0.399701\pi\) | |||||||
\(258\) | 1.21830e6 | 1.13948 | ||||||||
\(259\) | 225050. | 0.208463 | ||||||||
\(260\) | 673978. | 0.618319 | ||||||||
\(261\) | −25958.6 | −0.0235874 | ||||||||
\(262\) | 1.38820e6 | 1.24939 | ||||||||
\(263\) | 1.25395e6 | 1.11787 | 0.558934 | − | 0.829212i | \(-0.311211\pi\) | ||||
0.558934 | + | 0.829212i | \(0.311211\pi\) | |||||||
\(264\) | 112471. | 0.0993183 | ||||||||
\(265\) | −890113. | −0.778628 | ||||||||
\(266\) | −352719. | −0.305650 | ||||||||
\(267\) | −179936. | −0.154469 | ||||||||
\(268\) | 241697. | 0.205558 | ||||||||
\(269\) | 295417. | 0.248917 | 0.124459 | − | 0.992225i | \(-0.460281\pi\) | ||||
0.124459 | + | 0.992225i | \(0.460281\pi\) | |||||||
\(270\) | 261720. | 0.218488 | ||||||||
\(271\) | 1.36641e6 | 1.13021 | 0.565103 | − | 0.825020i | \(-0.308836\pi\) | ||||
0.565103 | + | 0.825020i | \(0.308836\pi\) | |||||||
\(272\) | −2.69471e6 | −2.20846 | ||||||||
\(273\) | 651260. | 0.528868 | ||||||||
\(274\) | 831018. | 0.668704 | ||||||||
\(275\) | 152055. | 0.121247 | ||||||||
\(276\) | −44465.8 | −0.0351361 | ||||||||
\(277\) | −180534. | −0.141371 | −0.0706853 | − | 0.997499i | \(-0.522519\pi\) | ||||
−0.0706853 | + | 0.997499i | \(0.522519\pi\) | |||||||
\(278\) | 1.45257e6 | 1.12726 | ||||||||
\(279\) | −96940.8 | −0.0745583 | ||||||||
\(280\) | −378937. | −0.288850 | ||||||||
\(281\) | 748821. | 0.565734 | 0.282867 | − | 0.959159i | \(-0.408715\pi\) | ||||
0.282867 | + | 0.959159i | \(0.408715\pi\) | |||||||
\(282\) | 1.27284e6 | 0.953125 | ||||||||
\(283\) | −1.43420e6 | −1.06450 | −0.532248 | − | 0.846589i | \(-0.678652\pi\) | ||||
−0.532248 | + | 0.846589i | \(0.678652\pi\) | |||||||
\(284\) | −380792. | −0.280151 | ||||||||
\(285\) | −171143. | −0.124809 | ||||||||
\(286\) | −856741. | −0.619347 | ||||||||
\(287\) | −1.21947e6 | −0.873907 | ||||||||
\(288\) | −570330. | −0.405177 | ||||||||
\(289\) | 3.39919e6 | 2.39404 | ||||||||
\(290\) | −115055. | −0.0803361 | ||||||||
\(291\) | −897219. | −0.621107 | ||||||||
\(292\) | −1.59927e6 | −1.09765 | ||||||||
\(293\) | −1.99988e6 | −1.36093 | −0.680465 | − | 0.732781i | \(-0.738222\pi\) | ||||
−0.680465 | + | 0.732781i | \(0.738222\pi\) | |||||||
\(294\) | −152291. | −0.102755 | ||||||||
\(295\) | −168140. | −0.112491 | ||||||||
\(296\) | −121507. | −0.0806070 | ||||||||
\(297\) | −139979. | −0.0920812 | ||||||||
\(298\) | −2.75993e6 | −1.80035 | ||||||||
\(299\) | −127600. | −0.0825416 | ||||||||
\(300\) | −165659. | −0.106270 | ||||||||
\(301\) | 2.19538e6 | 1.39667 | ||||||||
\(302\) | −3.01205e6 | −1.90040 | ||||||||
\(303\) | −700130. | −0.438099 | ||||||||
\(304\) | 483259. | 0.299914 | ||||||||
\(305\) | −793890. | −0.488665 | ||||||||
\(306\) | 1.32162e6 | 0.806870 | ||||||||
\(307\) | 2.66083e6 | 1.61128 | 0.805639 | − | 0.592407i | \(-0.201822\pi\) | ||||
0.805639 | + | 0.592407i | \(0.201822\pi\) | |||||||
\(308\) | −537996. | −0.323148 | ||||||||
\(309\) | −484282. | −0.288537 | ||||||||
\(310\) | −429665. | −0.253937 | ||||||||
\(311\) | −2.11645e6 | −1.24082 | −0.620408 | − | 0.784279i | \(-0.713033\pi\) | ||||
−0.620408 | + | 0.784279i | \(0.713033\pi\) | |||||||
\(312\) | −351623. | −0.204499 | ||||||||
\(313\) | 725870. | 0.418792 | 0.209396 | − | 0.977831i | \(-0.432850\pi\) | ||||
0.209396 | + | 0.977831i | \(0.432850\pi\) | |||||||
\(314\) | 695407. | 0.398029 | ||||||||
\(315\) | 471619. | 0.267802 | ||||||||
\(316\) | −81314.8 | −0.0458091 | ||||||||
\(317\) | −1.20622e6 | −0.674186 | −0.337093 | − | 0.941471i | \(-0.609444\pi\) | ||||
−0.337093 | + | 0.941471i | \(0.609444\pi\) | |||||||
\(318\) | −1.23271e6 | −0.683587 | ||||||||
\(319\) | 61536.4 | 0.0338575 | ||||||||
\(320\) | −630487. | −0.344192 | ||||||||
\(321\) | −815248. | −0.441598 | ||||||||
\(322\) | −190440. | −0.102357 | ||||||||
\(323\) | −864229. | −0.460917 | ||||||||
\(324\) | 152502. | 0.0807073 | ||||||||
\(325\) | −475379. | −0.249650 | ||||||||
\(326\) | −2.34023e6 | −1.21959 | ||||||||
\(327\) | 1.85968e6 | 0.961765 | ||||||||
\(328\) | 658405. | 0.337916 | ||||||||
\(329\) | 2.29365e6 | 1.16826 | ||||||||
\(330\) | −620420. | −0.313618 | ||||||||
\(331\) | −1.12789e6 | −0.565845 | −0.282923 | − | 0.959143i | \(-0.591304\pi\) | ||||
−0.282923 | + | 0.959143i | \(0.591304\pi\) | |||||||
\(332\) | −2.21665e6 | −1.10370 | ||||||||
\(333\) | 151226. | 0.0747334 | ||||||||
\(334\) | 609887. | 0.299146 | ||||||||
\(335\) | 502264. | 0.244523 | ||||||||
\(336\) | −1.33172e6 | −0.643524 | ||||||||
\(337\) | −2.51669e6 | −1.20713 | −0.603567 | − | 0.797312i | \(-0.706255\pi\) | ||||
−0.603567 | + | 0.797312i | \(0.706255\pi\) | |||||||
\(338\) | −81200.1 | −0.0386603 | ||||||||
\(339\) | 754037. | 0.356364 | ||||||||
\(340\) | 2.46464e6 | 1.15626 | ||||||||
\(341\) | 229803. | 0.107021 | ||||||||
\(342\) | −237014. | −0.109575 | ||||||||
\(343\) | −2.30038e6 | −1.05576 | ||||||||
\(344\) | −1.18531e6 | −0.540054 | ||||||||
\(345\) | −92403.3 | −0.0417965 | ||||||||
\(346\) | −1.03299e6 | −0.463881 | ||||||||
\(347\) | 3.97910e6 | 1.77403 | 0.887015 | − | 0.461741i | \(-0.152775\pi\) | ||||
0.887015 | + | 0.461741i | \(0.152775\pi\) | |||||||
\(348\) | −67041.7 | −0.0296754 | ||||||||
\(349\) | −1.16212e6 | −0.510726 | −0.255363 | − | 0.966845i | \(-0.582195\pi\) | ||||
−0.255363 | + | 0.966845i | \(0.582195\pi\) | |||||||
\(350\) | −709491. | −0.309583 | ||||||||
\(351\) | 437624. | 0.189598 | ||||||||
\(352\) | 1.35200e6 | 0.581593 | ||||||||
\(353\) | −2.71947e6 | −1.16158 | −0.580788 | − | 0.814055i | \(-0.697256\pi\) | ||||
−0.580788 | + | 0.814055i | \(0.697256\pi\) | |||||||
\(354\) | −232856. | −0.0987597 | ||||||||
\(355\) | −791315. | −0.333256 | ||||||||
\(356\) | −464710. | −0.194338 | ||||||||
\(357\) | 2.38156e6 | 0.988988 | ||||||||
\(358\) | 2.80329e6 | 1.15601 | ||||||||
\(359\) | −2.66436e6 | −1.09108 | −0.545540 | − | 0.838085i | \(-0.683675\pi\) | ||||
−0.545540 | + | 0.838085i | \(0.683675\pi\) | |||||||
\(360\) | −254633. | −0.103552 | ||||||||
\(361\) | −2.32111e6 | −0.937407 | ||||||||
\(362\) | −2.94324e6 | −1.18047 | ||||||||
\(363\) | −1.11763e6 | −0.445176 | ||||||||
\(364\) | 1.68197e6 | 0.665371 | ||||||||
\(365\) | −3.32340e6 | −1.30572 | ||||||||
\(366\) | −1.09945e6 | −0.429017 | ||||||||
\(367\) | −4.17455e6 | −1.61787 | −0.808936 | − | 0.587897i | \(-0.799956\pi\) | ||||
−0.808936 | + | 0.587897i | \(0.799956\pi\) | |||||||
\(368\) | 260921. | 0.100436 | ||||||||
\(369\) | −819439. | −0.313293 | ||||||||
\(370\) | 670269. | 0.254533 | ||||||||
\(371\) | −2.22135e6 | −0.837879 | ||||||||
\(372\) | −250363. | −0.0938020 | ||||||||
\(373\) | −2.61953e6 | −0.974879 | −0.487440 | − | 0.873157i | \(-0.662069\pi\) | ||||
−0.487440 | + | 0.873157i | \(0.662069\pi\) | |||||||
\(374\) | −3.13297e6 | −1.15818 | ||||||||
\(375\) | −1.70275e6 | −0.625278 | ||||||||
\(376\) | −1.23837e6 | −0.451732 | ||||||||
\(377\) | −192385. | −0.0697135 | ||||||||
\(378\) | 653142. | 0.235114 | ||||||||
\(379\) | 1.25240e6 | 0.447864 | 0.223932 | − | 0.974605i | \(-0.428111\pi\) | ||||
0.223932 | + | 0.974605i | \(0.428111\pi\) | |||||||
\(380\) | −441999. | −0.157023 | ||||||||
\(381\) | −2.07449e6 | −0.732148 | ||||||||
\(382\) | 4.54641e6 | 1.59408 | ||||||||
\(383\) | 5.09439e6 | 1.77458 | 0.887289 | − | 0.461214i | \(-0.152586\pi\) | ||||
0.887289 | + | 0.461214i | \(0.152586\pi\) | |||||||
\(384\) | 1.15468e6 | 0.399609 | ||||||||
\(385\) | −1.11800e6 | −0.384405 | ||||||||
\(386\) | 2.78616e6 | 0.951783 | ||||||||
\(387\) | 1.47522e6 | 0.500702 | ||||||||
\(388\) | −2.31719e6 | −0.781416 | ||||||||
\(389\) | 2.50585e6 | 0.839615 | 0.419808 | − | 0.907613i | \(-0.362098\pi\) | ||||
0.419808 | + | 0.907613i | \(0.362098\pi\) | |||||||
\(390\) | 1.93965e6 | 0.645748 | ||||||||
\(391\) | −466615. | −0.154353 | ||||||||
\(392\) | 148167. | 0.0487008 | ||||||||
\(393\) | 1.68094e6 | 0.548998 | ||||||||
\(394\) | 3.92310e6 | 1.27318 | ||||||||
\(395\) | −168978. | −0.0544927 | ||||||||
\(396\) | −361514. | −0.115848 | ||||||||
\(397\) | 3.27595e6 | 1.04318 | 0.521592 | − | 0.853195i | \(-0.325338\pi\) | ||||
0.521592 | + | 0.853195i | \(0.325338\pi\) | |||||||
\(398\) | 1.24588e6 | 0.394246 | ||||||||
\(399\) | −427100. | −0.134307 | ||||||||
\(400\) | 972073. | 0.303773 | ||||||||
\(401\) | 6.06788e6 | 1.88441 | 0.942206 | − | 0.335033i | \(-0.108748\pi\) | ||||
0.942206 | + | 0.335033i | \(0.108748\pi\) | |||||||
\(402\) | 695583. | 0.214676 | ||||||||
\(403\) | −718447. | −0.220360 | ||||||||
\(404\) | −1.80818e6 | −0.551173 | ||||||||
\(405\) | 316911. | 0.0960063 | ||||||||
\(406\) | −287129. | −0.0864494 | ||||||||
\(407\) | −358488. | −0.107273 | ||||||||
\(408\) | −1.28583e6 | −0.382414 | ||||||||
\(409\) | −325513. | −0.0962189 | −0.0481095 | − | 0.998842i | \(-0.515320\pi\) | ||||
−0.0481095 | + | 0.998842i | \(0.515320\pi\) | |||||||
\(410\) | −3.63195e6 | −1.06704 | ||||||||
\(411\) | 1.00626e6 | 0.293837 | ||||||||
\(412\) | −1.25072e6 | −0.363009 | ||||||||
\(413\) | −419607. | −0.121051 | ||||||||
\(414\) | −127969. | −0.0366947 | ||||||||
\(415\) | −4.60636e6 | −1.31292 | ||||||||
\(416\) | −4.22683e6 | −1.19752 | ||||||||
\(417\) | 1.75888e6 | 0.495333 | ||||||||
\(418\) | 561855. | 0.157284 | ||||||||
\(419\) | 5.62708e6 | 1.56584 | 0.782921 | − | 0.622121i | \(-0.213729\pi\) | ||||
0.782921 | + | 0.622121i | \(0.213729\pi\) | |||||||
\(420\) | 1.21802e6 | 0.336923 | ||||||||
\(421\) | 1.40296e6 | 0.385780 | 0.192890 | − | 0.981220i | \(-0.438214\pi\) | ||||
0.192890 | + | 0.981220i | \(0.438214\pi\) | |||||||
\(422\) | −1.90347e6 | −0.520313 | ||||||||
\(423\) | 1.54125e6 | 0.418816 | ||||||||
\(424\) | 1.19933e6 | 0.323985 | ||||||||
\(425\) | −1.73839e6 | −0.466848 | ||||||||
\(426\) | −1.09589e6 | −0.292578 | ||||||||
\(427\) | −1.98122e6 | −0.525850 | ||||||||
\(428\) | −2.10549e6 | −0.555576 | ||||||||
\(429\) | −1.03741e6 | −0.272149 | ||||||||
\(430\) | 6.53853e6 | 1.70533 | ||||||||
\(431\) | −1.55865e6 | −0.404163 | −0.202082 | − | 0.979369i | \(-0.564771\pi\) | ||||
−0.202082 | + | 0.979369i | \(0.564771\pi\) | |||||||
\(432\) | −894868. | −0.230701 | ||||||||
\(433\) | 2.65215e6 | 0.679795 | 0.339898 | − | 0.940462i | \(-0.389608\pi\) | ||||
0.339898 | + | 0.940462i | \(0.389608\pi\) | |||||||
\(434\) | −1.07226e6 | −0.273261 | ||||||||
\(435\) | −139318. | −0.0353007 | ||||||||
\(436\) | 4.80287e6 | 1.21000 | ||||||||
\(437\) | 83680.9 | 0.0209615 | ||||||||
\(438\) | −4.60256e6 | −1.14634 | ||||||||
\(439\) | 2.58237e6 | 0.639525 | 0.319763 | − | 0.947498i | \(-0.396397\pi\) | ||||
0.319763 | + | 0.947498i | \(0.396397\pi\) | |||||||
\(440\) | 603620. | 0.148639 | ||||||||
\(441\) | −184406. | −0.0451521 | ||||||||
\(442\) | 9.79479e6 | 2.38473 | ||||||||
\(443\) | 4.79743e6 | 1.16145 | 0.580723 | − | 0.814101i | \(-0.302770\pi\) | ||||
0.580723 | + | 0.814101i | \(0.302770\pi\) | |||||||
\(444\) | 390561. | 0.0940223 | ||||||||
\(445\) | −965704. | −0.231177 | ||||||||
\(446\) | 4.57136e6 | 1.08820 | ||||||||
\(447\) | −3.34194e6 | −0.791098 | ||||||||
\(448\) | −1.57343e6 | −0.370384 | ||||||||
\(449\) | 4.66201e6 | 1.09133 | 0.545667 | − | 0.838002i | \(-0.316276\pi\) | ||||
0.545667 | + | 0.838002i | \(0.316276\pi\) | |||||||
\(450\) | −476753. | −0.110984 | ||||||||
\(451\) | 1.94252e6 | 0.449702 | ||||||||
\(452\) | 1.94740e6 | 0.448342 | ||||||||
\(453\) | −3.64724e6 | −0.835061 | ||||||||
\(454\) | 7.75728e6 | 1.76632 | ||||||||
\(455\) | 3.49526e6 | 0.791499 | ||||||||
\(456\) | 230596. | 0.0519327 | ||||||||
\(457\) | −3.52146e6 | −0.788738 | −0.394369 | − | 0.918952i | \(-0.629037\pi\) | ||||
−0.394369 | + | 0.918952i | \(0.629037\pi\) | |||||||
\(458\) | −4.51995e6 | −1.00686 | ||||||||
\(459\) | 1.60032e6 | 0.354549 | ||||||||
\(460\) | −238644. | −0.0525843 | ||||||||
\(461\) | −3.24447e6 | −0.711037 | −0.355518 | − | 0.934669i | \(-0.615696\pi\) | ||||
−0.355518 | + | 0.934669i | \(0.615696\pi\) | |||||||
\(462\) | −1.54831e6 | −0.337483 | ||||||||
\(463\) | 3.08362e6 | 0.668511 | 0.334255 | − | 0.942483i | \(-0.391515\pi\) | ||||
0.334255 | + | 0.942483i | \(0.391515\pi\) | |||||||
\(464\) | 393395. | 0.0848269 | ||||||||
\(465\) | −520273. | −0.111583 | ||||||||
\(466\) | 7.47076e6 | 1.59367 | ||||||||
\(467\) | −4.71258e6 | −0.999923 | −0.499962 | − | 0.866048i | \(-0.666653\pi\) | ||||
−0.499962 | + | 0.866048i | \(0.666653\pi\) | |||||||
\(468\) | 1.13022e6 | 0.238533 | ||||||||
\(469\) | 1.25344e6 | 0.263131 | ||||||||
\(470\) | 6.83121e6 | 1.42644 | ||||||||
\(471\) | 842054. | 0.174899 | ||||||||
\(472\) | 226551. | 0.0468070 | ||||||||
\(473\) | −3.49709e6 | −0.718710 | ||||||||
\(474\) | −234017. | −0.0478412 | ||||||||
\(475\) | 311756. | 0.0633989 | ||||||||
\(476\) | 6.15070e6 | 1.24425 | ||||||||
\(477\) | −1.49267e6 | −0.300377 | ||||||||
\(478\) | 9.12184e6 | 1.82605 | ||||||||
\(479\) | −1.95384e6 | −0.389089 | −0.194545 | − | 0.980894i | \(-0.562323\pi\) | ||||
−0.194545 | + | 0.980894i | \(0.562323\pi\) | |||||||
\(480\) | −3.06091e6 | −0.606385 | ||||||||
\(481\) | 1.12076e6 | 0.220877 | ||||||||
\(482\) | 1.00339e7 | 1.96721 | ||||||||
\(483\) | −230600. | −0.0449771 | ||||||||
\(484\) | −2.88643e6 | −0.560078 | ||||||||
\(485\) | −4.81530e6 | −0.929542 | ||||||||
\(486\) | 438888. | 0.0842875 | ||||||||
\(487\) | −3.00669e6 | −0.574468 | −0.287234 | − | 0.957860i | \(-0.592736\pi\) | ||||
−0.287234 | + | 0.957860i | \(0.592736\pi\) | |||||||
\(488\) | 1.06968e6 | 0.203332 | ||||||||
\(489\) | −2.83374e6 | −0.535906 | ||||||||
\(490\) | −817331. | −0.153783 | ||||||||
\(491\) | 600072. | 0.112331 | 0.0561655 | − | 0.998421i | \(-0.482113\pi\) | ||||
0.0561655 | + | 0.998421i | \(0.482113\pi\) | |||||||
\(492\) | −2.11631e6 | −0.394155 | ||||||||
\(493\) | −703522. | −0.130365 | ||||||||
\(494\) | −1.75656e6 | −0.323851 | ||||||||
\(495\) | −751254. | −0.137808 | ||||||||
\(496\) | 1.46911e6 | 0.268132 | ||||||||
\(497\) | −1.97479e6 | −0.358616 | ||||||||
\(498\) | −6.37933e6 | −1.15266 | ||||||||
\(499\) | −9.20598e6 | −1.65508 | −0.827540 | − | 0.561407i | \(-0.810260\pi\) | ||||
−0.827540 | + | 0.561407i | \(0.810260\pi\) | |||||||
\(500\) | −4.39759e6 | −0.786664 | ||||||||
\(501\) | 738500. | 0.131449 | ||||||||
\(502\) | 3.33357e6 | 0.590406 | ||||||||
\(503\) | −5.84921e6 | −1.03081 | −0.515403 | − | 0.856948i | \(-0.672358\pi\) | ||||
−0.515403 | + | 0.856948i | \(0.672358\pi\) | |||||||
\(504\) | −635456. | −0.111432 | ||||||||
\(505\) | −3.75754e6 | −0.655654 | ||||||||
\(506\) | 303357. | 0.0526717 | ||||||||
\(507\) | −98323.6 | −0.0169878 | ||||||||
\(508\) | −5.35765e6 | −0.921118 | ||||||||
\(509\) | 7.98607e6 | 1.36628 | 0.683139 | − | 0.730289i | \(-0.260614\pi\) | ||||
0.683139 | + | 0.730289i | \(0.260614\pi\) | |||||||
\(510\) | 7.09303e6 | 1.20755 | ||||||||
\(511\) | −8.29381e6 | −1.40508 | ||||||||
\(512\) | 6.08669e6 | 1.02614 | ||||||||
\(513\) | −286996. | −0.0481485 | ||||||||
\(514\) | 4.87796e6 | 0.814387 | ||||||||
\(515\) | −2.59910e6 | −0.431822 | ||||||||
\(516\) | 3.80995e6 | 0.629935 | ||||||||
\(517\) | −3.65362e6 | −0.601170 | ||||||||
\(518\) | 1.67271e6 | 0.273903 | ||||||||
\(519\) | −1.25083e6 | −0.203835 | ||||||||
\(520\) | −1.88713e6 | −0.306051 | ||||||||
\(521\) | −2.58297e6 | −0.416893 | −0.208446 | − | 0.978034i | \(-0.566841\pi\) | ||||
−0.208446 | + | 0.978034i | \(0.566841\pi\) | |||||||
\(522\) | −192941. | −0.0309918 | ||||||||
\(523\) | −4.44025e6 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(524\) | 4.34125e6 | 0.690695 | ||||||||
\(525\) | −859109. | −0.136035 | ||||||||
\(526\) | 9.32011e6 | 1.46878 | ||||||||
\(527\) | −2.62725e6 | −0.412074 | ||||||||
\(528\) | 2.12133e6 | 0.331149 | ||||||||
\(529\) | −6.39116e6 | −0.992980 | ||||||||
\(530\) | −6.61586e6 | −1.02305 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | −1.10304e6 | −0.168971 | ||||||||
\(533\) | −6.07302e6 | −0.925948 | ||||||||
\(534\) | −1.33740e6 | −0.202959 | ||||||||
\(535\) | −4.37537e6 | −0.660891 | ||||||||
\(536\) | −676748. | −0.101745 | ||||||||
\(537\) | 3.39444e6 | 0.507964 | ||||||||
\(538\) | 2.19572e6 | 0.327056 | ||||||||
\(539\) | 437143. | 0.0648115 | ||||||||
\(540\) | 818465. | 0.120786 | ||||||||
\(541\) | 4.63492e6 | 0.680846 | 0.340423 | − | 0.940272i | \(-0.389430\pi\) | ||||
0.340423 | + | 0.940272i | \(0.389430\pi\) | |||||||
\(542\) | 1.01560e7 | 1.48499 | ||||||||
\(543\) | −3.56391e6 | −0.518713 | ||||||||
\(544\) | −1.54569e7 | −2.23936 | ||||||||
\(545\) | 9.98074e6 | 1.43937 | ||||||||
\(546\) | 4.84056e6 | 0.694887 | ||||||||
\(547\) | −1.30458e7 | −1.86425 | −0.932124 | − | 0.362138i | \(-0.882047\pi\) | ||||
−0.932124 | + | 0.362138i | \(0.882047\pi\) | |||||||
\(548\) | 2.59881e6 | 0.369677 | ||||||||
\(549\) | −1.33131e6 | −0.188516 | ||||||||
\(550\) | 1.13017e6 | 0.159308 | ||||||||
\(551\) | 126167. | 0.0177038 | ||||||||
\(552\) | 124504. | 0.0173914 | ||||||||
\(553\) | −421699. | −0.0586395 | ||||||||
\(554\) | −1.34184e6 | −0.185749 | ||||||||
\(555\) | 811615. | 0.111845 | ||||||||
\(556\) | 4.54256e6 | 0.623180 | ||||||||
\(557\) | −5.71867e6 | −0.781011 | −0.390506 | − | 0.920600i | \(-0.627700\pi\) | ||||
−0.390506 | + | 0.920600i | \(0.627700\pi\) | |||||||
\(558\) | −720523. | −0.0979631 | ||||||||
\(559\) | 1.09331e7 | 1.47984 | ||||||||
\(560\) | −7.14723e6 | −0.963091 | ||||||||
\(561\) | −3.79365e6 | −0.508921 | ||||||||
\(562\) | 5.56570e6 | 0.743325 | ||||||||
\(563\) | 5.22161e6 | 0.694278 | 0.347139 | − | 0.937814i | \(-0.387153\pi\) | ||||
0.347139 | + | 0.937814i | \(0.387153\pi\) | |||||||
\(564\) | 3.98049e6 | 0.526913 | ||||||||
\(565\) | 4.04685e6 | 0.533330 | ||||||||
\(566\) | −1.06599e7 | −1.39865 | ||||||||
\(567\) | 790876. | 0.103312 | ||||||||
\(568\) | 1.06621e6 | 0.138667 | ||||||||
\(569\) | −845736. | −0.109510 | −0.0547550 | − | 0.998500i | \(-0.517438\pi\) | ||||
−0.0547550 | + | 0.998500i | \(0.517438\pi\) | |||||||
\(570\) | −1.27204e6 | −0.163988 | ||||||||
\(571\) | −4.22254e6 | −0.541981 | −0.270990 | − | 0.962582i | \(-0.587351\pi\) | ||||
−0.270990 | + | 0.962582i | \(0.587351\pi\) | |||||||
\(572\) | −2.67925e6 | −0.342392 | ||||||||
\(573\) | 5.50516e6 | 0.700460 | ||||||||
\(574\) | −9.06382e6 | −1.14824 | ||||||||
\(575\) | 168324. | 0.0212312 | ||||||||
\(576\) | −1.05729e6 | −0.132782 | ||||||||
\(577\) | −8.12269e6 | −1.01569 | −0.507844 | − | 0.861449i | \(-0.669557\pi\) | ||||
−0.507844 | + | 0.861449i | \(0.669557\pi\) | |||||||
\(578\) | 2.52649e7 | 3.14555 | ||||||||
\(579\) | 3.37371e6 | 0.418226 | ||||||||
\(580\) | −359807. | −0.0444119 | ||||||||
\(581\) | −1.14955e7 | −1.41283 | ||||||||
\(582\) | −6.66868e6 | −0.816080 | ||||||||
\(583\) | 3.53844e6 | 0.431163 | ||||||||
\(584\) | 4.47793e6 | 0.543307 | ||||||||
\(585\) | 2.34869e6 | 0.283750 | ||||||||
\(586\) | −1.48644e7 | −1.78814 | ||||||||
\(587\) | 1.23310e7 | 1.47708 | 0.738539 | − | 0.674210i | \(-0.235516\pi\) | ||||
0.738539 | + | 0.674210i | \(0.235516\pi\) | |||||||
\(588\) | −476252. | −0.0568059 | ||||||||
\(589\) | 471162. | 0.0559605 | ||||||||
\(590\) | −1.24972e6 | −0.147803 | ||||||||
\(591\) | 4.75040e6 | 0.559450 | ||||||||
\(592\) | −2.29178e6 | −0.268762 | ||||||||
\(593\) | −1.45287e7 | −1.69664 | −0.848320 | − | 0.529484i | \(-0.822386\pi\) | ||||
−0.848320 | + | 0.529484i | \(0.822386\pi\) | |||||||
\(594\) | −1.04041e6 | −0.120987 | ||||||||
\(595\) | 1.27816e7 | 1.48011 | ||||||||
\(596\) | −8.63102e6 | −0.995283 | ||||||||
\(597\) | 1.50861e6 | 0.173237 | ||||||||
\(598\) | −948402. | −0.108452 | ||||||||
\(599\) | 8.46504e6 | 0.963967 | 0.481983 | − | 0.876180i | \(-0.339917\pi\) | ||||
0.481983 | + | 0.876180i | \(0.339917\pi\) | |||||||
\(600\) | 463843. | 0.0526009 | ||||||||
\(601\) | 4.80633e6 | 0.542785 | 0.271392 | − | 0.962469i | \(-0.412516\pi\) | ||||
0.271392 | + | 0.962469i | \(0.412516\pi\) | |||||||
\(602\) | 1.63174e7 | 1.83510 | ||||||||
\(603\) | 842268. | 0.0943315 | ||||||||
\(604\) | −9.41948e6 | −1.05059 | ||||||||
\(605\) | −5.99824e6 | −0.666247 | ||||||||
\(606\) | −5.20379e6 | −0.575623 | ||||||||
\(607\) | −7.55460e6 | −0.832223 | −0.416111 | − | 0.909314i | \(-0.636607\pi\) | ||||
−0.416111 | + | 0.909314i | \(0.636607\pi\) | |||||||
\(608\) | 2.77198e6 | 0.304110 | ||||||||
\(609\) | −347679. | −0.0379870 | ||||||||
\(610\) | −5.90068e6 | −0.642062 | ||||||||
\(611\) | 1.14225e7 | 1.23782 | ||||||||
\(612\) | 4.13305e6 | 0.446059 | ||||||||
\(613\) | 1.78145e7 | 1.91480 | 0.957399 | − | 0.288768i | \(-0.0932456\pi\) | ||||
0.957399 | + | 0.288768i | \(0.0932456\pi\) | |||||||
\(614\) | 1.97769e7 | 2.11708 | ||||||||
\(615\) | −4.39786e6 | −0.468871 | ||||||||
\(616\) | 1.50638e6 | 0.159950 | ||||||||
\(617\) | 1.13067e6 | 0.119570 | 0.0597851 | − | 0.998211i | \(-0.480958\pi\) | ||||
0.0597851 | + | 0.998211i | \(0.480958\pi\) | |||||||
\(618\) | −3.59948e6 | −0.379113 | ||||||||
\(619\) | 39879.3 | 0.00418332 | 0.00209166 | − | 0.999998i | \(-0.499334\pi\) | ||||
0.00209166 | + | 0.999998i | \(0.499334\pi\) | |||||||
\(620\) | −1.34368e6 | −0.140383 | ||||||||
\(621\) | −154955. | −0.0161241 | ||||||||
\(622\) | −1.57308e7 | −1.63032 | ||||||||
\(623\) | −2.40999e6 | −0.248768 | ||||||||
\(624\) | −6.63204e6 | −0.681845 | ||||||||
\(625\) | −6.66386e6 | −0.682379 | ||||||||
\(626\) | 5.39511e6 | 0.550256 | ||||||||
\(627\) | 680339. | 0.0691125 | ||||||||
\(628\) | 2.17472e6 | 0.220041 | ||||||||
\(629\) | 4.09846e6 | 0.413042 | ||||||||
\(630\) | 3.50536e6 | 0.351869 | ||||||||
\(631\) | 7.70574e6 | 0.770443 | 0.385222 | − | 0.922824i | \(-0.374125\pi\) | ||||
0.385222 | + | 0.922824i | \(0.374125\pi\) | |||||||
\(632\) | 227681. | 0.0226743 | ||||||||
\(633\) | −2.30487e6 | −0.228632 | ||||||||
\(634\) | −8.96539e6 | −0.885821 | ||||||||
\(635\) | −1.11336e7 | −1.09573 | ||||||||
\(636\) | −3.85501e6 | −0.377905 | ||||||||
\(637\) | −1.36667e6 | −0.133449 | ||||||||
\(638\) | 457376. | 0.0444858 | ||||||||
\(639\) | −1.32699e6 | −0.128563 | ||||||||
\(640\) | 6.19709e6 | 0.598050 | ||||||||
\(641\) | 1.60378e7 | 1.54170 | 0.770848 | − | 0.637019i | \(-0.219833\pi\) | ||||
0.770848 | + | 0.637019i | \(0.219833\pi\) | |||||||
\(642\) | −6.05942e6 | −0.580221 | ||||||||
\(643\) | 2.62458e6 | 0.250341 | 0.125170 | − | 0.992135i | \(-0.460052\pi\) | ||||
0.125170 | + | 0.992135i | \(0.460052\pi\) | |||||||
\(644\) | −595555. | −0.0565858 | ||||||||
\(645\) | 7.91738e6 | 0.749346 | ||||||||
\(646\) | −6.42348e6 | −0.605605 | ||||||||
\(647\) | 1.06120e6 | 0.0996634 | 0.0498317 | − | 0.998758i | \(-0.484132\pi\) | ||||
0.0498317 | + | 0.998758i | \(0.484132\pi\) | |||||||
\(648\) | −427004. | −0.0399479 | ||||||||
\(649\) | 668404. | 0.0622912 | ||||||||
\(650\) | −3.53331e6 | −0.328018 | ||||||||
\(651\) | −1.29838e6 | −0.120074 | ||||||||
\(652\) | −7.31852e6 | −0.674224 | ||||||||
\(653\) | −1.18303e7 | −1.08571 | −0.542854 | − | 0.839827i | \(-0.682656\pi\) | ||||
−0.542854 | + | 0.839827i | \(0.682656\pi\) | |||||||
\(654\) | 1.38223e7 | 1.26367 | ||||||||
\(655\) | 9.02145e6 | 0.821624 | ||||||||
\(656\) | 1.24183e7 | 1.12669 | ||||||||
\(657\) | −5.57315e6 | −0.503718 | ||||||||
\(658\) | 1.70478e7 | 1.53499 | ||||||||
\(659\) | 3.08114e6 | 0.276375 | 0.138187 | − | 0.990406i | \(-0.455872\pi\) | ||||
0.138187 | + | 0.990406i | \(0.455872\pi\) | |||||||
\(660\) | −1.94022e6 | −0.173376 | ||||||||
\(661\) | −1.52738e7 | −1.35970 | −0.679850 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679850 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(662\) | −8.38318e6 | −0.743471 | ||||||||
\(663\) | 1.18603e7 | 1.04788 | ||||||||
\(664\) | 6.20658e6 | 0.546301 | ||||||||
\(665\) | −2.29221e6 | −0.201002 | ||||||||
\(666\) | 1.12400e6 | 0.0981932 | ||||||||
\(667\) | 68120.0 | 0.00592871 | ||||||||
\(668\) | 1.90727e6 | 0.165376 | ||||||||
\(669\) | 5.53536e6 | 0.478168 | ||||||||
\(670\) | 3.73314e6 | 0.321282 | ||||||||
\(671\) | 3.15593e6 | 0.270596 | ||||||||
\(672\) | −7.63876e6 | −0.652528 | ||||||||
\(673\) | 1.59289e6 | 0.135565 | 0.0677824 | − | 0.997700i | \(-0.478408\pi\) | ||||
0.0677824 | + | 0.997700i | \(0.478408\pi\) | |||||||
\(674\) | −1.87056e7 | −1.58607 | ||||||||
\(675\) | −577291. | −0.0487680 | ||||||||
\(676\) | −253934. | −0.0213724 | ||||||||
\(677\) | −1.45086e7 | −1.21662 | −0.608308 | − | 0.793701i | \(-0.708151\pi\) | ||||
−0.608308 | + | 0.793701i | \(0.708151\pi\) | |||||||
\(678\) | 5.60446e6 | 0.468231 | ||||||||
\(679\) | −1.20170e7 | −1.00028 | ||||||||
\(680\) | −6.90096e6 | −0.572318 | ||||||||
\(681\) | 9.39313e6 | 0.776145 | ||||||||
\(682\) | 1.70804e6 | 0.140617 | ||||||||
\(683\) | 1.08149e7 | 0.887094 | 0.443547 | − | 0.896251i | \(-0.353720\pi\) | ||||
0.443547 | + | 0.896251i | \(0.353720\pi\) | |||||||
\(684\) | −741206. | −0.0605757 | ||||||||
\(685\) | 5.40053e6 | 0.439754 | ||||||||
\(686\) | −1.70978e7 | −1.38717 | ||||||||
\(687\) | −5.47312e6 | −0.442429 | ||||||||
\(688\) | −2.23565e7 | −1.80066 | ||||||||
\(689\) | −1.10624e7 | −0.887775 | ||||||||
\(690\) | −686798. | −0.0549169 | ||||||||
\(691\) | 1.24968e7 | 0.995639 | 0.497820 | − | 0.867281i | \(-0.334134\pi\) | ||||
0.497820 | + | 0.867281i | \(0.334134\pi\) | |||||||
\(692\) | −3.23043e6 | −0.256446 | ||||||||
\(693\) | −1.87481e6 | −0.148295 | ||||||||
\(694\) | 2.95751e7 | 2.33092 | ||||||||
\(695\) | 9.43978e6 | 0.741310 | ||||||||
\(696\) | 187716. | 0.0146885 | ||||||||
\(697\) | −2.22081e7 | −1.73153 | ||||||||
\(698\) | −8.63759e6 | −0.671049 | ||||||||
\(699\) | 9.04619e6 | 0.700282 | ||||||||
\(700\) | −2.21876e6 | −0.171146 | ||||||||
\(701\) | −4.63586e6 | −0.356316 | −0.178158 | − | 0.984002i | \(-0.557014\pi\) | ||||
−0.178158 | + | 0.984002i | \(0.557014\pi\) | |||||||
\(702\) | 3.25269e6 | 0.249115 | ||||||||
\(703\) | −735003. | −0.0560920 | ||||||||
\(704\) | 2.50636e6 | 0.190595 | ||||||||
\(705\) | 8.27177e6 | 0.626796 | ||||||||
\(706\) | −2.02128e7 | −1.52621 | ||||||||
\(707\) | −9.37723e6 | −0.705547 | ||||||||
\(708\) | −728202. | −0.0545970 | ||||||||
\(709\) | −1.99355e7 | −1.48940 | −0.744699 | − | 0.667401i | \(-0.767407\pi\) | ||||
−0.744699 | + | 0.667401i | \(0.767407\pi\) | |||||||
\(710\) | −5.88153e6 | −0.437870 | ||||||||
\(711\) | −283367. | −0.0210221 | ||||||||
\(712\) | 1.30118e6 | 0.0961919 | ||||||||
\(713\) | 254390. | 0.0187403 | ||||||||
\(714\) | 1.77012e7 | 1.29944 | ||||||||
\(715\) | −5.56769e6 | −0.407296 | ||||||||
\(716\) | 8.76660e6 | 0.639070 | ||||||||
\(717\) | 1.10455e7 | 0.802391 | ||||||||
\(718\) | −1.98031e7 | −1.43358 | ||||||||
\(719\) | 4.81963e6 | 0.347689 | 0.173845 | − | 0.984773i | \(-0.444381\pi\) | ||||
0.173845 | + | 0.984773i | \(0.444381\pi\) | |||||||
\(720\) | −4.80268e6 | −0.345265 | ||||||||
\(721\) | −6.48625e6 | −0.464682 | ||||||||
\(722\) | −1.72519e7 | −1.23167 | ||||||||
\(723\) | 1.21498e7 | 0.864417 | ||||||||
\(724\) | −9.20428e6 | −0.652595 | ||||||||
\(725\) | 253784. | 0.0179316 | ||||||||
\(726\) | −8.30692e6 | −0.584923 | ||||||||
\(727\) | 3.77212e6 | 0.264697 | 0.132349 | − | 0.991203i | \(-0.457748\pi\) | ||||
0.132349 | + | 0.991203i | \(0.457748\pi\) | |||||||
\(728\) | −4.70949e6 | −0.329340 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.47016e7 | −1.71560 | ||||||||
\(731\) | 3.99809e7 | 2.76732 | ||||||||
\(732\) | −3.43828e6 | −0.237172 | ||||||||
\(733\) | −8.67096e6 | −0.596084 | −0.298042 | − | 0.954553i | \(-0.596333\pi\) | ||||
−0.298042 | + | 0.954553i | \(0.596333\pi\) | |||||||
\(734\) | −3.10278e7 | −2.12574 | ||||||||
\(735\) | −989689. | −0.0675742 | ||||||||
\(736\) | 1.49665e6 | 0.101841 | ||||||||
\(737\) | −1.99664e6 | −0.135404 | ||||||||
\(738\) | −6.09057e6 | −0.411639 | ||||||||
\(739\) | 2.67260e7 | 1.80021 | 0.900103 | − | 0.435678i | \(-0.143491\pi\) | ||||
0.900103 | + | 0.435678i | \(0.143491\pi\) | |||||||
\(740\) | 2.09611e6 | 0.140713 | ||||||||
\(741\) | −2.12698e6 | −0.142305 | ||||||||
\(742\) | −1.65104e7 | −1.10090 | ||||||||
\(743\) | 882576. | 0.0586516 | 0.0293258 | − | 0.999570i | \(-0.490664\pi\) | ||||
0.0293258 | + | 0.999570i | \(0.490664\pi\) | |||||||
\(744\) | 701013. | 0.0464294 | ||||||||
\(745\) | −1.79359e7 | −1.18395 | ||||||||
\(746\) | −1.94699e7 | −1.28091 | ||||||||
\(747\) | −7.72460e6 | −0.506494 | ||||||||
\(748\) | −9.79762e6 | −0.640275 | ||||||||
\(749\) | −1.09191e7 | −0.711183 | ||||||||
\(750\) | −1.26559e7 | −0.821561 | ||||||||
\(751\) | 1.50079e7 | 0.971005 | 0.485502 | − | 0.874235i | \(-0.338637\pi\) | ||||
0.485502 | + | 0.874235i | \(0.338637\pi\) | |||||||
\(752\) | −2.33572e7 | −1.50618 | ||||||||
\(753\) | 4.03656e6 | 0.259432 | ||||||||
\(754\) | −1.42992e6 | −0.0915974 | ||||||||
\(755\) | −1.95744e7 | −1.24974 | ||||||||
\(756\) | 2.04254e6 | 0.129977 | ||||||||
\(757\) | −2.73466e7 | −1.73446 | −0.867228 | − | 0.497910i | \(-0.834101\pi\) | ||||
−0.867228 | + | 0.497910i | \(0.834101\pi\) | |||||||
\(758\) | 9.30862e6 | 0.588454 | ||||||||
\(759\) | 367329. | 0.0231446 | ||||||||
\(760\) | 1.23759e6 | 0.0777219 | ||||||||
\(761\) | 1.85952e7 | 1.16397 | 0.581983 | − | 0.813201i | \(-0.302277\pi\) | ||||
0.581983 | + | 0.813201i | \(0.302277\pi\) | |||||||
\(762\) | −1.54189e7 | −0.961979 | ||||||||
\(763\) | 2.49077e7 | 1.54890 | ||||||||
\(764\) | 1.42178e7 | 0.881250 | ||||||||
\(765\) | 8.58881e6 | 0.530615 | ||||||||
\(766\) | 3.78646e7 | 2.33164 | ||||||||
\(767\) | −2.08967e6 | −0.128259 | ||||||||
\(768\) | 1.23416e7 | 0.755035 | ||||||||
\(769\) | 1.69589e6 | 0.103414 | 0.0517072 | − | 0.998662i | \(-0.483534\pi\) | ||||
0.0517072 | + | 0.998662i | \(0.483534\pi\) | |||||||
\(770\) | −8.30964e6 | −0.505074 | ||||||||
\(771\) | 5.90663e6 | 0.357852 | ||||||||
\(772\) | 8.71305e6 | 0.526171 | ||||||||
\(773\) | −8.47019e6 | −0.509853 | −0.254926 | − | 0.966960i | \(-0.582051\pi\) | ||||
−0.254926 | + | 0.966960i | \(0.582051\pi\) | |||||||
\(774\) | 1.09647e7 | 0.657879 | ||||||||
\(775\) | 947739. | 0.0566806 | ||||||||
\(776\) | 6.48810e6 | 0.386780 | ||||||||
\(777\) | 2.02545e6 | 0.120356 | ||||||||
\(778\) | 1.86250e7 | 1.10318 | ||||||||
\(779\) | 3.98272e6 | 0.235145 | ||||||||
\(780\) | 6.06580e6 | 0.356987 | ||||||||
\(781\) | 3.14570e6 | 0.184539 | ||||||||
\(782\) | −3.46817e6 | −0.202807 | ||||||||
\(783\) | −233628. | −0.0136182 | ||||||||
\(784\) | 2.79461e6 | 0.162379 | ||||||||
\(785\) | 4.51923e6 | 0.261752 | ||||||||
\(786\) | 1.24938e7 | 0.721335 | ||||||||
\(787\) | −7.45024e6 | −0.428779 | −0.214389 | − | 0.976748i | \(-0.568776\pi\) | ||||
−0.214389 | + | 0.976748i | \(0.568776\pi\) | |||||||
\(788\) | 1.22686e7 | 0.703846 | ||||||||
\(789\) | 1.12855e7 | 0.645401 | ||||||||
\(790\) | −1.25595e6 | −0.0715987 | ||||||||
\(791\) | 1.00992e7 | 0.573915 | ||||||||
\(792\) | 1.01224e6 | 0.0573414 | ||||||||
\(793\) | −9.86658e6 | −0.557165 | ||||||||
\(794\) | 2.43489e7 | 1.37065 | ||||||||
\(795\) | −8.01101e6 | −0.449541 | ||||||||
\(796\) | 3.89618e6 | 0.217950 | ||||||||
\(797\) | 1.44140e7 | 0.803783 | 0.401892 | − | 0.915687i | \(-0.368353\pi\) | ||||
0.401892 | + | 0.915687i | \(0.368353\pi\) | |||||||
\(798\) | −3.17447e6 | −0.176467 | ||||||||
\(799\) | 4.17705e7 | 2.31474 | ||||||||
\(800\) | 5.57582e6 | 0.308023 | ||||||||
\(801\) | −1.61943e6 | −0.0891827 | ||||||||
\(802\) | 4.51002e7 | 2.47595 | ||||||||
\(803\) | 1.32114e7 | 0.723039 | ||||||||
\(804\) | 2.17527e6 | 0.118679 | ||||||||
\(805\) | −1.23761e6 | −0.0673122 | ||||||||
\(806\) | −5.33994e6 | −0.289533 | ||||||||
\(807\) | 2.65875e6 | 0.143712 | ||||||||
\(808\) | 5.06288e6 | 0.272816 | ||||||||
\(809\) | −2.19181e7 | −1.17742 | −0.588710 | − | 0.808344i | \(-0.700364\pi\) | ||||
−0.588710 | + | 0.808344i | \(0.700364\pi\) | |||||||
\(810\) | 2.35548e6 | 0.126144 | ||||||||
\(811\) | −1.90616e6 | −0.101767 | −0.0508836 | − | 0.998705i | \(-0.516204\pi\) | ||||
−0.0508836 | + | 0.998705i | \(0.516204\pi\) | |||||||
\(812\) | −897927. | −0.0477915 | ||||||||
\(813\) | 1.22977e7 | 0.652525 | ||||||||
\(814\) | −2.66451e6 | −0.140947 | ||||||||
\(815\) | −1.52085e7 | −0.802031 | ||||||||
\(816\) | −2.42524e7 | −1.27506 | ||||||||
\(817\) | −7.17002e6 | −0.375807 | ||||||||
\(818\) | −2.41941e6 | −0.126423 | ||||||||
\(819\) | 5.86134e6 | 0.305342 | ||||||||
\(820\) | −1.13581e7 | −0.589888 | ||||||||
\(821\) | −5.58709e6 | −0.289286 | −0.144643 | − | 0.989484i | \(-0.546203\pi\) | ||||
−0.144643 | + | 0.989484i | \(0.546203\pi\) | |||||||
\(822\) | 7.47916e6 | 0.386077 | ||||||||
\(823\) | 7.03605e6 | 0.362101 | 0.181050 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181050 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(824\) | 3.50201e6 | 0.179680 | ||||||||
\(825\) | 1.36850e6 | 0.0700018 | ||||||||
\(826\) | −3.11877e6 | −0.159050 | ||||||||
\(827\) | −1.36355e7 | −0.693276 | −0.346638 | − | 0.937999i | \(-0.612677\pi\) | ||||
−0.346638 | + | 0.937999i | \(0.612677\pi\) | |||||||
\(828\) | −400192. | −0.0202858 | ||||||||
\(829\) | 8.78197e6 | 0.443819 | 0.221909 | − | 0.975067i | \(-0.428771\pi\) | ||||
0.221909 | + | 0.975067i | \(0.428771\pi\) | |||||||
\(830\) | −3.42373e7 | −1.72506 | ||||||||
\(831\) | −1.62481e6 | −0.0816204 | ||||||||
\(832\) | −7.83578e6 | −0.392440 | ||||||||
\(833\) | −4.99770e6 | −0.249550 | ||||||||
\(834\) | 1.30731e7 | 0.650824 | ||||||||
\(835\) | 3.96346e6 | 0.196725 | ||||||||
\(836\) | 1.75707e6 | 0.0869507 | ||||||||
\(837\) | −872467. | −0.0430463 | ||||||||
\(838\) | 4.18239e7 | 2.05738 | ||||||||
\(839\) | 2.47541e7 | 1.21407 | 0.607034 | − | 0.794676i | \(-0.292359\pi\) | ||||
0.607034 | + | 0.794676i | \(0.292359\pi\) | |||||||
\(840\) | −3.41044e6 | −0.166768 | ||||||||
\(841\) | −2.04084e7 | −0.994993 | ||||||||
\(842\) | 1.04277e7 | 0.506882 | ||||||||
\(843\) | 6.73939e6 | 0.326627 | ||||||||
\(844\) | −5.95264e6 | −0.287643 | ||||||||
\(845\) | −527694. | −0.0254238 | ||||||||
\(846\) | 1.14555e7 | 0.550287 | ||||||||
\(847\) | −1.49691e7 | −0.716946 | ||||||||
\(848\) | 2.26209e7 | 1.08024 | ||||||||
\(849\) | −1.29078e7 | −0.614587 | ||||||||
\(850\) | −1.29208e7 | −0.613397 | ||||||||
\(851\) | −396843. | −0.0187843 | ||||||||
\(852\) | −3.42712e6 | −0.161745 | ||||||||
\(853\) | 3.15345e7 | 1.48393 | 0.741964 | − | 0.670439i | \(-0.233894\pi\) | ||||
0.741964 | + | 0.670439i | \(0.233894\pi\) | |||||||
\(854\) | −1.47256e7 | −0.690921 | ||||||||
\(855\) | −1.54028e6 | −0.0720585 | ||||||||
\(856\) | 5.89534e6 | 0.274995 | ||||||||
\(857\) | −3.48098e7 | −1.61901 | −0.809505 | − | 0.587113i | \(-0.800265\pi\) | ||||
−0.809505 | + | 0.587113i | \(0.800265\pi\) | |||||||
\(858\) | −7.71067e6 | −0.357580 | ||||||||
\(859\) | −3.28394e7 | −1.51849 | −0.759246 | − | 0.650803i | \(-0.774432\pi\) | ||||
−0.759246 | + | 0.650803i | \(0.774432\pi\) | |||||||
\(860\) | 2.04477e7 | 0.942754 | ||||||||
\(861\) | −1.09752e7 | −0.504550 | ||||||||
\(862\) | −1.15849e7 | −0.531035 | ||||||||
\(863\) | 2.13743e7 | 0.976935 | 0.488468 | − | 0.872582i | \(-0.337556\pi\) | ||||
0.488468 | + | 0.872582i | \(0.337556\pi\) | |||||||
\(864\) | −5.13297e6 | −0.233929 | ||||||||
\(865\) | −6.71309e6 | −0.305058 | ||||||||
\(866\) | 1.97124e7 | 0.893191 | ||||||||
\(867\) | 3.05927e7 | 1.38220 | ||||||||
\(868\) | −3.35325e6 | −0.151066 | ||||||||
\(869\) | 671736. | 0.0301752 | ||||||||
\(870\) | −1.03550e6 | −0.0463821 | ||||||||
\(871\) | 6.24221e6 | 0.278800 | ||||||||
\(872\) | −1.34480e7 | −0.598916 | ||||||||
\(873\) | −8.07497e6 | −0.358596 | ||||||||
\(874\) | 621967. | 0.0275416 | ||||||||
\(875\) | −2.28059e7 | −1.00700 | ||||||||
\(876\) | −1.43934e7 | −0.633729 | ||||||||
\(877\) | 1.54465e7 | 0.678158 | 0.339079 | − | 0.940758i | \(-0.389885\pi\) | ||||
0.339079 | + | 0.940758i | \(0.389885\pi\) | |||||||
\(878\) | 1.91938e7 | 0.840280 | ||||||||
\(879\) | −1.79990e7 | −0.785733 | ||||||||
\(880\) | 1.13850e7 | 0.495595 | ||||||||
\(881\) | 4.43148e6 | 0.192357 | 0.0961787 | − | 0.995364i | \(-0.469338\pi\) | ||||
0.0961787 | + | 0.995364i | \(0.469338\pi\) | |||||||
\(882\) | −1.37062e6 | −0.0593259 | ||||||||
\(883\) | 6.63288e6 | 0.286286 | 0.143143 | − | 0.989702i | \(-0.454279\pi\) | ||||
0.143143 | + | 0.989702i | \(0.454279\pi\) | |||||||
\(884\) | 3.06309e7 | 1.31834 | ||||||||
\(885\) | −1.51326e6 | −0.0649465 | ||||||||
\(886\) | 3.56574e7 | 1.52604 | ||||||||
\(887\) | −1.88116e7 | −0.802818 | −0.401409 | − | 0.915899i | \(-0.631479\pi\) | ||||
−0.401409 | + | 0.915899i | \(0.631479\pi\) | |||||||
\(888\) | −1.09357e6 | −0.0465385 | ||||||||
\(889\) | −2.77848e7 | −1.17911 | ||||||||
\(890\) | −7.17770e6 | −0.303746 | ||||||||
\(891\) | −1.25981e6 | −0.0531631 | ||||||||
\(892\) | 1.42958e7 | 0.601585 | ||||||||
\(893\) | −7.49096e6 | −0.314347 | ||||||||
\(894\) | −2.48394e7 | −1.03943 | ||||||||
\(895\) | 1.82177e7 | 0.760213 | ||||||||
\(896\) | 1.54653e7 | 0.643560 | ||||||||
\(897\) | −1.14840e6 | −0.0476554 | ||||||||
\(898\) | 3.46509e7 | 1.43392 | ||||||||
\(899\) | 383547. | 0.0158278 | ||||||||
\(900\) | −1.49093e6 | −0.0613552 | ||||||||
\(901\) | −4.04537e7 | −1.66015 | ||||||||
\(902\) | 1.44380e7 | 0.590869 | ||||||||
\(903\) | 1.97584e7 | 0.806368 | ||||||||
\(904\) | −5.45270e6 | −0.221917 | ||||||||
\(905\) | −1.91272e7 | −0.776301 | ||||||||
\(906\) | −2.71085e7 | −1.09720 | ||||||||
\(907\) | 8.97079e6 | 0.362087 | 0.181043 | − | 0.983475i | \(-0.442053\pi\) | ||||
0.181043 | + | 0.983475i | \(0.442053\pi\) | |||||||
\(908\) | 2.42590e7 | 0.976470 | ||||||||
\(909\) | −6.30117e6 | −0.252936 | ||||||||
\(910\) | 2.59789e7 | 1.03996 | ||||||||
\(911\) | 4.68204e7 | 1.86913 | 0.934564 | − | 0.355794i | \(-0.115789\pi\) | ||||
0.934564 | + | 0.355794i | \(0.115789\pi\) | |||||||
\(912\) | 4.34933e6 | 0.173155 | ||||||||
\(913\) | 1.83116e7 | 0.727024 | ||||||||
\(914\) | −2.61737e7 | −1.03633 | ||||||||
\(915\) | −7.14501e6 | −0.282131 | ||||||||
\(916\) | −1.41351e7 | −0.556621 | ||||||||
\(917\) | 2.25138e7 | 0.884147 | ||||||||
\(918\) | 1.18946e7 | 0.465846 | ||||||||
\(919\) | −2.58264e7 | −1.00873 | −0.504366 | − | 0.863490i | \(-0.668274\pi\) | ||||
−0.504366 | + | 0.863490i | \(0.668274\pi\) | |||||||
\(920\) | 668200. | 0.0260278 | ||||||||
\(921\) | 2.39474e7 | 0.930272 | ||||||||
\(922\) | −2.41149e7 | −0.934240 | ||||||||
\(923\) | −9.83457e6 | −0.379971 | ||||||||
\(924\) | −4.84196e6 | −0.186570 | ||||||||
\(925\) | −1.47845e6 | −0.0568137 | ||||||||
\(926\) | 2.29193e7 | 0.878364 | ||||||||
\(927\) | −4.35853e6 | −0.166587 | ||||||||
\(928\) | 2.25652e6 | 0.0860139 | ||||||||
\(929\) | 4.55842e7 | 1.73291 | 0.866453 | − | 0.499259i | \(-0.166394\pi\) | ||||
0.866453 | + | 0.499259i | \(0.166394\pi\) | |||||||
\(930\) | −3.86699e6 | −0.146611 | ||||||||
\(931\) | 896268. | 0.0338894 | ||||||||
\(932\) | 2.33630e7 | 0.881026 | ||||||||
\(933\) | −1.90481e7 | −0.716386 | ||||||||
\(934\) | −3.50268e7 | −1.31381 | ||||||||
\(935\) | −2.03602e7 | −0.761647 | ||||||||
\(936\) | −3.16461e6 | −0.118067 | ||||||||
\(937\) | 1.83075e6 | 0.0681208 | 0.0340604 | − | 0.999420i | \(-0.489156\pi\) | ||||
0.0340604 | + | 0.999420i | \(0.489156\pi\) | |||||||
\(938\) | 9.31634e6 | 0.345731 | ||||||||
\(939\) | 6.53283e6 | 0.241790 | ||||||||
\(940\) | 2.13630e7 | 0.788573 | ||||||||
\(941\) | 6.42585e6 | 0.236568 | 0.118284 | − | 0.992980i | \(-0.462261\pi\) | ||||
0.118284 | + | 0.992980i | \(0.462261\pi\) | |||||||
\(942\) | 6.25866e6 | 0.229802 | ||||||||
\(943\) | 2.15035e6 | 0.0787463 | ||||||||
\(944\) | 4.27303e6 | 0.156065 | ||||||||
\(945\) | 4.24457e6 | 0.154616 | ||||||||
\(946\) | −2.59925e7 | −0.944322 | ||||||||
\(947\) | −2.39260e7 | −0.866953 | −0.433477 | − | 0.901165i | \(-0.642713\pi\) | ||||
−0.433477 | + | 0.901165i | \(0.642713\pi\) | |||||||
\(948\) | −731833. | −0.0264479 | ||||||||
\(949\) | −4.13037e7 | −1.48876 | ||||||||
\(950\) | 2.31716e6 | 0.0833006 | ||||||||
\(951\) | −1.08560e7 | −0.389241 | ||||||||
\(952\) | −1.72219e7 | −0.615869 | ||||||||
\(953\) | 3.98437e7 | 1.42111 | 0.710554 | − | 0.703643i | \(-0.248445\pi\) | ||||
0.710554 | + | 0.703643i | \(0.248445\pi\) | |||||||
\(954\) | −1.10944e7 | −0.394669 | ||||||||
\(955\) | 2.95457e7 | 1.04830 | ||||||||
\(956\) | 2.85264e7 | 1.00949 | ||||||||
\(957\) | 553827. | 0.0195476 | ||||||||
\(958\) | −1.45221e7 | −0.511230 | ||||||||
\(959\) | 1.34774e7 | 0.473218 | ||||||||
\(960\) | −5.67438e6 | −0.198720 | ||||||||
\(961\) | −2.71968e7 | −0.949970 | ||||||||
\(962\) | 8.33019e6 | 0.290213 | ||||||||
\(963\) | −7.33723e6 | −0.254957 | ||||||||
\(964\) | 3.13785e7 | 1.08752 | ||||||||
\(965\) | 1.81064e7 | 0.625913 | ||||||||
\(966\) | −1.71396e6 | −0.0590959 | ||||||||
\(967\) | 4.45202e7 | 1.53105 | 0.765527 | − | 0.643403i | \(-0.222478\pi\) | ||||
0.765527 | + | 0.643403i | \(0.222478\pi\) | |||||||
\(968\) | 8.08198e6 | 0.277223 | ||||||||
\(969\) | −7.77806e6 | −0.266111 | ||||||||
\(970\) | −3.57903e7 | −1.22134 | ||||||||
\(971\) | 4.02063e7 | 1.36850 | 0.684252 | − | 0.729245i | \(-0.260129\pi\) | ||||
0.684252 | + | 0.729245i | \(0.260129\pi\) | |||||||
\(972\) | 1.37252e6 | 0.0465964 | ||||||||
\(973\) | 2.35577e7 | 0.797722 | ||||||||
\(974\) | −2.23475e7 | −0.754801 | ||||||||
\(975\) | −4.27841e6 | −0.144136 | ||||||||
\(976\) | 2.01755e7 | 0.677954 | ||||||||
\(977\) | −1.46923e7 | −0.492440 | −0.246220 | − | 0.969214i | \(-0.579189\pi\) | ||||
−0.246220 | + | 0.969214i | \(0.579189\pi\) | |||||||
\(978\) | −2.10621e7 | −0.704133 | ||||||||
\(979\) | 3.83894e6 | 0.128013 | ||||||||
\(980\) | −2.55601e6 | −0.0850152 | ||||||||
\(981\) | 1.67371e7 | 0.555275 | ||||||||
\(982\) | 4.46010e6 | 0.147593 | ||||||||
\(983\) | −550436. | −0.0181687 | −0.00908433 | − | 0.999959i | \(-0.502892\pi\) | ||||
−0.00908433 | + | 0.999959i | \(0.502892\pi\) | |||||||
\(984\) | 5.92564e6 | 0.195096 | ||||||||
\(985\) | 2.54950e7 | 0.837268 | ||||||||
\(986\) | −5.22900e6 | −0.171288 | ||||||||
\(987\) | 2.06429e7 | 0.674493 | ||||||||
\(988\) | −5.49322e6 | −0.179034 | ||||||||
\(989\) | −3.87124e6 | −0.125852 | ||||||||
\(990\) | −5.58378e6 | −0.181067 | ||||||||
\(991\) | −3.24918e7 | −1.05097 | −0.525485 | − | 0.850803i | \(-0.676116\pi\) | ||||
−0.525485 | + | 0.850803i | \(0.676116\pi\) | |||||||
\(992\) | 8.42681e6 | 0.271884 | ||||||||
\(993\) | −1.01510e7 | −0.326691 | ||||||||
\(994\) | −1.46778e7 | −0.471190 | ||||||||
\(995\) | 8.09657e6 | 0.259265 | ||||||||
\(996\) | −1.99498e7 | −0.637221 | ||||||||
\(997\) | 619302. | 0.0197317 | 0.00986586 | − | 0.999951i | \(-0.496860\pi\) | ||||
0.00986586 | + | 0.999951i | \(0.496860\pi\) | |||||||
\(998\) | −6.84245e7 | −2.17463 | ||||||||
\(999\) | 1.36103e6 | 0.0431474 |
(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 | 177.6.a.c.1.9 | ✓ | 12 | |
3.2 | odd | 2 | 531.6.a.c.1.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.c.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
531.6.a.c.1.4 | 12 | 3.2 | odd | 2 |