Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77548 | −1.96256 | −0.981279 | − | 0.192591i | \(-0.938311\pi\) | ||||
−0.981279 | + | 0.192591i | \(0.938311\pi\) | |||||||
\(3\) | −0.417524 | −0.241058 | −0.120529 | − | 0.992710i | \(-0.538459\pi\) | ||||
−0.120529 | + | 0.992710i | \(0.538459\pi\) | |||||||
\(4\) | 5.70327 | 2.85163 | ||||||||
\(5\) | 0.239845 | 0.107262 | 0.0536310 | − | 0.998561i | \(-0.482921\pi\) | ||||
0.0536310 | + | 0.998561i | \(0.482921\pi\) | |||||||
\(6\) | 1.15883 | 0.473090 | ||||||||
\(7\) | 2.35024 | 0.888306 | 0.444153 | − | 0.895951i | \(-0.353505\pi\) | ||||
0.444153 | + | 0.895951i | \(0.353505\pi\) | |||||||
\(8\) | −10.2783 | −3.63394 | ||||||||
\(9\) | −2.82567 | −0.941891 | ||||||||
\(10\) | −0.665684 | −0.210508 | ||||||||
\(11\) | 5.59006 | 1.68547 | 0.842733 | − | 0.538332i | \(-0.180945\pi\) | ||||
0.842733 | + | 0.538332i | \(0.180945\pi\) | |||||||
\(12\) | −2.38125 | −0.687409 | ||||||||
\(13\) | 1.16037 | 0.321827 | 0.160914 | − | 0.986968i | \(-0.448556\pi\) | ||||
0.160914 | + | 0.986968i | \(0.448556\pi\) | |||||||
\(14\) | −6.52303 | −1.74335 | ||||||||
\(15\) | −0.100141 | −0.0258563 | ||||||||
\(16\) | 17.1207 | 4.28019 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 7.84259 | 1.84852 | ||||||||
\(19\) | −5.90000 | −1.35355 | −0.676777 | − | 0.736188i | \(-0.736624\pi\) | ||||
−0.676777 | + | 0.736188i | \(0.736624\pi\) | |||||||
\(20\) | 1.36790 | 0.305872 | ||||||||
\(21\) | −0.981281 | −0.214133 | ||||||||
\(22\) | −15.5151 | −3.30783 | ||||||||
\(23\) | 6.51052 | 1.35754 | 0.678768 | − | 0.734352i | \(-0.262514\pi\) | ||||
0.678768 | + | 0.734352i | \(0.262514\pi\) | |||||||
\(24\) | 4.29146 | 0.875990 | ||||||||
\(25\) | −4.94247 | −0.988495 | ||||||||
\(26\) | −3.22057 | −0.631605 | ||||||||
\(27\) | 2.43236 | 0.468108 | ||||||||
\(28\) | 13.4040 | 2.53312 | ||||||||
\(29\) | −0.502806 | −0.0933688 | −0.0466844 | − | 0.998910i | \(-0.514866\pi\) | ||||
−0.0466844 | + | 0.998910i | \(0.514866\pi\) | |||||||
\(30\) | 0.277939 | 0.0507445 | ||||||||
\(31\) | 7.71016 | 1.38479 | 0.692393 | − | 0.721520i | \(-0.256556\pi\) | ||||
0.692393 | + | 0.721520i | \(0.256556\pi\) | |||||||
\(32\) | −26.9615 | −4.76617 | ||||||||
\(33\) | −2.33399 | −0.406295 | ||||||||
\(34\) | −2.77548 | −0.475990 | ||||||||
\(35\) | 0.563692 | 0.0952814 | ||||||||
\(36\) | −16.1156 | −2.68593 | ||||||||
\(37\) | 4.01127 | 0.659449 | 0.329724 | − | 0.944077i | \(-0.393044\pi\) | ||||
0.329724 | + | 0.944077i | \(0.393044\pi\) | |||||||
\(38\) | 16.3753 | 2.65643 | ||||||||
\(39\) | −0.484481 | −0.0775790 | ||||||||
\(40\) | −2.46521 | −0.389784 | ||||||||
\(41\) | 6.35057 | 0.991793 | 0.495896 | − | 0.868382i | \(-0.334840\pi\) | ||||
0.495896 | + | 0.868382i | \(0.334840\pi\) | |||||||
\(42\) | 2.72352 | 0.420249 | ||||||||
\(43\) | −1.67505 | −0.255443 | −0.127722 | − | 0.991810i | \(-0.540766\pi\) | ||||
−0.127722 | + | 0.991810i | \(0.540766\pi\) | |||||||
\(44\) | 31.8816 | 4.80633 | ||||||||
\(45\) | −0.677724 | −0.101029 | ||||||||
\(46\) | −18.0698 | −2.66425 | ||||||||
\(47\) | −4.93976 | −0.720538 | −0.360269 | − | 0.932849i | \(-0.617315\pi\) | ||||
−0.360269 | + | 0.932849i | \(0.617315\pi\) | |||||||
\(48\) | −7.14833 | −1.03177 | ||||||||
\(49\) | −1.47639 | −0.210913 | ||||||||
\(50\) | 13.7177 | 1.93998 | ||||||||
\(51\) | −0.417524 | −0.0584651 | ||||||||
\(52\) | 6.61788 | 0.917734 | ||||||||
\(53\) | 4.29153 | 0.589487 | 0.294744 | − | 0.955576i | \(-0.404766\pi\) | ||||
0.294744 | + | 0.955576i | \(0.404766\pi\) | |||||||
\(54\) | −6.75096 | −0.918689 | ||||||||
\(55\) | 1.34075 | 0.180786 | ||||||||
\(56\) | −24.1565 | −3.22805 | ||||||||
\(57\) | 2.46340 | 0.326285 | ||||||||
\(58\) | 1.39553 | 0.183242 | ||||||||
\(59\) | 1.89886 | 0.247210 | 0.123605 | − | 0.992331i | \(-0.460554\pi\) | ||||
0.123605 | + | 0.992331i | \(0.460554\pi\) | |||||||
\(60\) | −0.571132 | −0.0737328 | ||||||||
\(61\) | 0.183132 | 0.0234476 | 0.0117238 | − | 0.999931i | \(-0.496268\pi\) | ||||
0.0117238 | + | 0.999931i | \(0.496268\pi\) | |||||||
\(62\) | −21.3994 | −2.71772 | ||||||||
\(63\) | −6.64100 | −0.836687 | ||||||||
\(64\) | 40.5896 | 5.07371 | ||||||||
\(65\) | 0.278308 | 0.0345198 | ||||||||
\(66\) | 6.47792 | 0.797377 | ||||||||
\(67\) | −12.3784 | −1.51227 | −0.756134 | − | 0.654417i | \(-0.772914\pi\) | ||||
−0.756134 | + | 0.654417i | \(0.772914\pi\) | |||||||
\(68\) | 5.70327 | 0.691623 | ||||||||
\(69\) | −2.71830 | −0.327245 | ||||||||
\(70\) | −1.56452 | −0.186995 | ||||||||
\(71\) | 15.2216 | 1.80648 | 0.903238 | − | 0.429139i | \(-0.141183\pi\) | ||||
0.903238 | + | 0.429139i | \(0.141183\pi\) | |||||||
\(72\) | 29.0432 | 3.42278 | ||||||||
\(73\) | −9.63390 | −1.12756 | −0.563781 | − | 0.825924i | \(-0.690654\pi\) | ||||
−0.563781 | + | 0.825924i | \(0.690654\pi\) | |||||||
\(74\) | −11.1332 | −1.29421 | ||||||||
\(75\) | 2.06360 | 0.238284 | ||||||||
\(76\) | −33.6493 | −3.85984 | ||||||||
\(77\) | 13.1380 | 1.49721 | ||||||||
\(78\) | 1.34466 | 0.152253 | ||||||||
\(79\) | −5.10093 | −0.573900 | −0.286950 | − | 0.957946i | \(-0.592641\pi\) | ||||
−0.286950 | + | 0.957946i | \(0.592641\pi\) | |||||||
\(80\) | 4.10632 | 0.459101 | ||||||||
\(81\) | 7.46145 | 0.829050 | ||||||||
\(82\) | −17.6259 | −1.94645 | ||||||||
\(83\) | −1.18038 | −0.129563 | −0.0647815 | − | 0.997899i | \(-0.520635\pi\) | ||||
−0.0647815 | + | 0.997899i | \(0.520635\pi\) | |||||||
\(84\) | −5.59651 | −0.610629 | ||||||||
\(85\) | 0.239845 | 0.0260148 | ||||||||
\(86\) | 4.64907 | 0.501322 | ||||||||
\(87\) | 0.209934 | 0.0225073 | ||||||||
\(88\) | −57.4565 | −6.12488 | ||||||||
\(89\) | 11.5484 | 1.22413 | 0.612063 | − | 0.790809i | \(-0.290340\pi\) | ||||
0.612063 | + | 0.790809i | \(0.290340\pi\) | |||||||
\(90\) | 1.88101 | 0.198275 | ||||||||
\(91\) | 2.72713 | 0.285881 | ||||||||
\(92\) | 37.1312 | 3.87120 | ||||||||
\(93\) | −3.21918 | −0.333814 | ||||||||
\(94\) | 13.7102 | 1.41410 | ||||||||
\(95\) | −1.41509 | −0.145185 | ||||||||
\(96\) | 11.2571 | 1.14892 | ||||||||
\(97\) | 15.1467 | 1.53791 | 0.768956 | − | 0.639301i | \(-0.220776\pi\) | ||||
0.768956 | + | 0.639301i | \(0.220776\pi\) | |||||||
\(98\) | 4.09768 | 0.413929 | ||||||||
\(99\) | −15.7957 | −1.58753 | ||||||||
\(100\) | −28.1883 | −2.81883 | ||||||||
\(101\) | 8.33018 | 0.828884 | 0.414442 | − | 0.910076i | \(-0.363977\pi\) | ||||
0.414442 | + | 0.910076i | \(0.363977\pi\) | |||||||
\(102\) | 1.15883 | 0.114741 | ||||||||
\(103\) | 7.42252 | 0.731363 | 0.365682 | − | 0.930740i | \(-0.380836\pi\) | ||||
0.365682 | + | 0.930740i | \(0.380836\pi\) | |||||||
\(104\) | −11.9266 | −1.16950 | ||||||||
\(105\) | −0.235355 | −0.0229683 | ||||||||
\(106\) | −11.9110 | −1.15690 | ||||||||
\(107\) | −0.957372 | −0.0925526 | −0.0462763 | − | 0.998929i | \(-0.514735\pi\) | ||||
−0.0462763 | + | 0.998929i | \(0.514735\pi\) | |||||||
\(108\) | 13.8724 | 1.33487 | ||||||||
\(109\) | −16.6683 | −1.59653 | −0.798267 | − | 0.602304i | \(-0.794249\pi\) | ||||
−0.798267 | + | 0.602304i | \(0.794249\pi\) | |||||||
\(110\) | −3.72121 | −0.354804 | ||||||||
\(111\) | −1.67480 | −0.158965 | ||||||||
\(112\) | 40.2378 | 3.80211 | ||||||||
\(113\) | −9.04641 | −0.851015 | −0.425507 | − | 0.904955i | \(-0.639904\pi\) | ||||
−0.425507 | + | 0.904955i | \(0.639904\pi\) | |||||||
\(114\) | −6.83710 | −0.640353 | ||||||||
\(115\) | 1.56152 | 0.145612 | ||||||||
\(116\) | −2.86764 | −0.266254 | ||||||||
\(117\) | −3.27881 | −0.303126 | ||||||||
\(118\) | −5.27024 | −0.485165 | ||||||||
\(119\) | 2.35024 | 0.215446 | ||||||||
\(120\) | 1.02928 | 0.0939604 | ||||||||
\(121\) | 20.2488 | 1.84080 | ||||||||
\(122\) | −0.508278 | −0.0460174 | ||||||||
\(123\) | −2.65152 | −0.239079 | ||||||||
\(124\) | 43.9731 | 3.94890 | ||||||||
\(125\) | −2.38465 | −0.213290 | ||||||||
\(126\) | 18.4319 | 1.64205 | ||||||||
\(127\) | −8.74568 | −0.776054 | −0.388027 | − | 0.921648i | \(-0.626843\pi\) | ||||
−0.388027 | + | 0.921648i | \(0.626843\pi\) | |||||||
\(128\) | −58.7325 | −5.19127 | ||||||||
\(129\) | 0.699375 | 0.0615765 | ||||||||
\(130\) | −0.772437 | −0.0677472 | ||||||||
\(131\) | 4.70655 | 0.411213 | 0.205607 | − | 0.978635i | \(-0.434083\pi\) | ||||
0.205607 | + | 0.978635i | \(0.434083\pi\) | |||||||
\(132\) | −13.3113 | −1.15860 | ||||||||
\(133\) | −13.8664 | −1.20237 | ||||||||
\(134\) | 34.3561 | 2.96791 | ||||||||
\(135\) | 0.583390 | 0.0502102 | ||||||||
\(136\) | −10.2783 | −0.881360 | ||||||||
\(137\) | −1.03190 | −0.0881610 | −0.0440805 | − | 0.999028i | \(-0.514036\pi\) | ||||
−0.0440805 | + | 0.999028i | \(0.514036\pi\) | |||||||
\(138\) | 7.54458 | 0.642237 | ||||||||
\(139\) | 5.12493 | 0.434691 | 0.217346 | − | 0.976095i | \(-0.430260\pi\) | ||||
0.217346 | + | 0.976095i | \(0.430260\pi\) | |||||||
\(140\) | 3.21489 | 0.271708 | ||||||||
\(141\) | 2.06247 | 0.173691 | ||||||||
\(142\) | −42.2473 | −3.54532 | ||||||||
\(143\) | 6.48651 | 0.542429 | ||||||||
\(144\) | −48.3776 | −4.03147 | ||||||||
\(145\) | −0.120596 | −0.0100149 | ||||||||
\(146\) | 26.7387 | 2.21291 | ||||||||
\(147\) | 0.616429 | 0.0508422 | ||||||||
\(148\) | 22.8774 | 1.88051 | ||||||||
\(149\) | 6.35458 | 0.520587 | 0.260294 | − | 0.965530i | \(-0.416181\pi\) | ||||
0.260294 | + | 0.965530i | \(0.416181\pi\) | |||||||
\(150\) | −5.72748 | −0.467647 | ||||||||
\(151\) | −14.8664 | −1.20981 | −0.604905 | − | 0.796298i | \(-0.706789\pi\) | ||||
−0.604905 | + | 0.796298i | \(0.706789\pi\) | |||||||
\(152\) | 60.6422 | 4.91873 | ||||||||
\(153\) | −2.82567 | −0.228442 | ||||||||
\(154\) | −36.4641 | −2.93836 | ||||||||
\(155\) | 1.84924 | 0.148535 | ||||||||
\(156\) | −2.76312 | −0.221227 | ||||||||
\(157\) | 19.7081 | 1.57288 | 0.786440 | − | 0.617667i | \(-0.211922\pi\) | ||||
0.786440 | + | 0.617667i | \(0.211922\pi\) | |||||||
\(158\) | 14.1575 | 1.12631 | ||||||||
\(159\) | −1.79182 | −0.142101 | ||||||||
\(160\) | −6.46659 | −0.511229 | ||||||||
\(161\) | 15.3013 | 1.20591 | ||||||||
\(162\) | −20.7091 | −1.62706 | ||||||||
\(163\) | 17.8742 | 1.40001 | 0.700006 | − | 0.714137i | \(-0.253181\pi\) | ||||
0.700006 | + | 0.714137i | \(0.253181\pi\) | |||||||
\(164\) | 36.2190 | 2.82823 | ||||||||
\(165\) | −0.559795 | −0.0435800 | ||||||||
\(166\) | 3.27610 | 0.254275 | ||||||||
\(167\) | 7.76350 | 0.600757 | 0.300379 | − | 0.953820i | \(-0.402887\pi\) | ||||
0.300379 | + | 0.953820i | \(0.402887\pi\) | |||||||
\(168\) | 10.0859 | 0.778147 | ||||||||
\(169\) | −11.6536 | −0.896427 | ||||||||
\(170\) | −0.665684 | −0.0510556 | ||||||||
\(171\) | 16.6715 | 1.27490 | ||||||||
\(172\) | −9.55327 | −0.728430 | ||||||||
\(173\) | −4.35396 | −0.331026 | −0.165513 | − | 0.986208i | \(-0.552928\pi\) | ||||
−0.165513 | + | 0.986208i | \(0.552928\pi\) | |||||||
\(174\) | −0.582666 | −0.0441718 | ||||||||
\(175\) | −11.6160 | −0.878086 | ||||||||
\(176\) | 95.7060 | 7.21411 | ||||||||
\(177\) | −0.792820 | −0.0595920 | ||||||||
\(178\) | −32.0523 | −2.40242 | ||||||||
\(179\) | 9.29452 | 0.694705 | 0.347352 | − | 0.937735i | \(-0.387081\pi\) | ||||
0.347352 | + | 0.937735i | \(0.387081\pi\) | |||||||
\(180\) | −3.86524 | −0.288098 | ||||||||
\(181\) | 24.2494 | 1.80245 | 0.901223 | − | 0.433356i | \(-0.142671\pi\) | ||||
0.901223 | + | 0.433356i | \(0.142671\pi\) | |||||||
\(182\) | −7.56909 | −0.561058 | ||||||||
\(183\) | −0.0764620 | −0.00565224 | ||||||||
\(184\) | −66.9173 | −4.93321 | ||||||||
\(185\) | 0.962083 | 0.0707338 | ||||||||
\(186\) | 8.93476 | 0.655129 | ||||||||
\(187\) | 5.59006 | 0.408786 | ||||||||
\(188\) | −28.1728 | −2.05471 | ||||||||
\(189\) | 5.71662 | 0.415823 | ||||||||
\(190\) | 3.92754 | 0.284934 | ||||||||
\(191\) | 9.19880 | 0.665602 | 0.332801 | − | 0.942997i | \(-0.392006\pi\) | ||||
0.332801 | + | 0.942997i | \(0.392006\pi\) | |||||||
\(192\) | −16.9472 | −1.22306 | ||||||||
\(193\) | 8.53210 | 0.614154 | 0.307077 | − | 0.951685i | \(-0.400649\pi\) | ||||
0.307077 | + | 0.951685i | \(0.400649\pi\) | |||||||
\(194\) | −42.0393 | −3.01824 | ||||||||
\(195\) | −0.116200 | −0.00832128 | ||||||||
\(196\) | −8.42025 | −0.601446 | ||||||||
\(197\) | 0.380134 | 0.0270835 | 0.0135417 | − | 0.999908i | \(-0.495689\pi\) | ||||
0.0135417 | + | 0.999908i | \(0.495689\pi\) | |||||||
\(198\) | 43.8405 | 3.11561 | ||||||||
\(199\) | −1.38504 | −0.0981827 | −0.0490913 | − | 0.998794i | \(-0.515633\pi\) | ||||
−0.0490913 | + | 0.998794i | \(0.515633\pi\) | |||||||
\(200\) | 50.8004 | 3.59213 | ||||||||
\(201\) | 5.16830 | 0.364544 | ||||||||
\(202\) | −23.1202 | −1.62673 | ||||||||
\(203\) | −1.18171 | −0.0829400 | ||||||||
\(204\) | −2.38125 | −0.166721 | ||||||||
\(205\) | 1.52315 | 0.106382 | ||||||||
\(206\) | −20.6010 | −1.43534 | ||||||||
\(207\) | −18.3966 | −1.27865 | ||||||||
\(208\) | 19.8663 | 1.37748 | ||||||||
\(209\) | −32.9814 | −2.28137 | ||||||||
\(210\) | 0.653223 | 0.0450767 | ||||||||
\(211\) | 14.0694 | 0.968578 | 0.484289 | − | 0.874908i | \(-0.339078\pi\) | ||||
0.484289 | + | 0.874908i | \(0.339078\pi\) | |||||||
\(212\) | 24.4758 | 1.68100 | ||||||||
\(213\) | −6.35541 | −0.435465 | ||||||||
\(214\) | 2.65716 | 0.181640 | ||||||||
\(215\) | −0.401753 | −0.0273993 | ||||||||
\(216\) | −25.0006 | −1.70108 | ||||||||
\(217\) | 18.1207 | 1.23011 | ||||||||
\(218\) | 46.2625 | 3.13329 | ||||||||
\(219\) | 4.02239 | 0.271808 | ||||||||
\(220\) | 7.64664 | 0.515537 | ||||||||
\(221\) | 1.16037 | 0.0780546 | ||||||||
\(222\) | 4.64838 | 0.311979 | ||||||||
\(223\) | 4.20622 | 0.281669 | 0.140835 | − | 0.990033i | \(-0.455021\pi\) | ||||
0.140835 | + | 0.990033i | \(0.455021\pi\) | |||||||
\(224\) | −63.3660 | −4.23382 | ||||||||
\(225\) | 13.9658 | 0.931055 | ||||||||
\(226\) | 25.1081 | 1.67017 | ||||||||
\(227\) | 1.99235 | 0.132237 | 0.0661184 | − | 0.997812i | \(-0.478938\pi\) | ||||
0.0661184 | + | 0.997812i | \(0.478938\pi\) | |||||||
\(228\) | 14.0494 | 0.930445 | ||||||||
\(229\) | −26.1501 | −1.72805 | −0.864025 | − | 0.503449i | \(-0.832064\pi\) | ||||
−0.864025 | + | 0.503449i | \(0.832064\pi\) | |||||||
\(230\) | −4.33395 | −0.285772 | ||||||||
\(231\) | −5.48542 | −0.360914 | ||||||||
\(232\) | 5.16801 | 0.339297 | ||||||||
\(233\) | 13.6353 | 0.893279 | 0.446640 | − | 0.894714i | \(-0.352621\pi\) | ||||
0.446640 | + | 0.894714i | \(0.352621\pi\) | |||||||
\(234\) | 9.10027 | 0.594903 | ||||||||
\(235\) | −1.18478 | −0.0772863 | ||||||||
\(236\) | 10.8297 | 0.704954 | ||||||||
\(237\) | 2.12976 | 0.138343 | ||||||||
\(238\) | −6.52303 | −0.422825 | ||||||||
\(239\) | −18.4831 | −1.19557 | −0.597785 | − | 0.801656i | \(-0.703952\pi\) | ||||
−0.597785 | + | 0.801656i | \(0.703952\pi\) | |||||||
\(240\) | −1.71449 | −0.110670 | ||||||||
\(241\) | 4.28271 | 0.275874 | 0.137937 | − | 0.990441i | \(-0.455953\pi\) | ||||
0.137937 | + | 0.990441i | \(0.455953\pi\) | |||||||
\(242\) | −56.1999 | −3.61267 | ||||||||
\(243\) | −10.4124 | −0.667957 | ||||||||
\(244\) | 1.04445 | 0.0668641 | ||||||||
\(245\) | −0.354105 | −0.0226229 | ||||||||
\(246\) | 7.35923 | 0.469207 | ||||||||
\(247\) | −6.84616 | −0.435611 | ||||||||
\(248\) | −79.2477 | −5.03223 | ||||||||
\(249\) | 0.492835 | 0.0312322 | ||||||||
\(250\) | 6.61855 | 0.418594 | ||||||||
\(251\) | −30.4674 | −1.92309 | −0.961543 | − | 0.274654i | \(-0.911437\pi\) | ||||
−0.961543 | + | 0.274654i | \(0.911437\pi\) | |||||||
\(252\) | −37.8754 | −2.38593 | ||||||||
\(253\) | 36.3942 | 2.28808 | ||||||||
\(254\) | 24.2734 | 1.52305 | ||||||||
\(255\) | −0.100141 | −0.00627108 | ||||||||
\(256\) | 81.8314 | 5.11446 | ||||||||
\(257\) | −9.26754 | −0.578093 | −0.289047 | − | 0.957315i | \(-0.593338\pi\) | ||||
−0.289047 | + | 0.957315i | \(0.593338\pi\) | |||||||
\(258\) | −1.94110 | −0.120848 | ||||||||
\(259\) | 9.42744 | 0.585792 | ||||||||
\(260\) | 1.58726 | 0.0984380 | ||||||||
\(261\) | 1.42077 | 0.0879432 | ||||||||
\(262\) | −13.0629 | −0.807030 | ||||||||
\(263\) | 7.38379 | 0.455304 | 0.227652 | − | 0.973743i | \(-0.426895\pi\) | ||||
0.227652 | + | 0.973743i | \(0.426895\pi\) | |||||||
\(264\) | 23.9895 | 1.47645 | ||||||||
\(265\) | 1.02930 | 0.0632296 | ||||||||
\(266\) | 38.4859 | 2.35972 | ||||||||
\(267\) | −4.82173 | −0.295085 | ||||||||
\(268\) | −70.5976 | −4.31243 | ||||||||
\(269\) | −13.6180 | −0.830306 | −0.415153 | − | 0.909752i | \(-0.636272\pi\) | ||||
−0.415153 | + | 0.909752i | \(0.636272\pi\) | |||||||
\(270\) | −1.61918 | −0.0985404 | ||||||||
\(271\) | 6.71299 | 0.407785 | 0.203893 | − | 0.978993i | \(-0.434641\pi\) | ||||
0.203893 | + | 0.978993i | \(0.434641\pi\) | |||||||
\(272\) | 17.1207 | 1.03810 | ||||||||
\(273\) | −1.13864 | −0.0689139 | ||||||||
\(274\) | 2.86401 | 0.173021 | ||||||||
\(275\) | −27.6287 | −1.66607 | ||||||||
\(276\) | −15.5032 | −0.933183 | ||||||||
\(277\) | −4.73918 | −0.284749 | −0.142375 | − | 0.989813i | \(-0.545474\pi\) | ||||
−0.142375 | + | 0.989813i | \(0.545474\pi\) | |||||||
\(278\) | −14.2241 | −0.853106 | ||||||||
\(279\) | −21.7864 | −1.30432 | ||||||||
\(280\) | −5.79382 | −0.346247 | ||||||||
\(281\) | 31.6506 | 1.88811 | 0.944057 | − | 0.329782i | \(-0.106975\pi\) | ||||
0.944057 | + | 0.329782i | \(0.106975\pi\) | |||||||
\(282\) | −5.72433 | −0.340879 | ||||||||
\(283\) | −33.4717 | −1.98969 | −0.994844 | − | 0.101418i | \(-0.967662\pi\) | ||||
−0.994844 | + | 0.101418i | \(0.967662\pi\) | |||||||
\(284\) | 86.8131 | 5.15141 | ||||||||
\(285\) | 0.590833 | 0.0349979 | ||||||||
\(286\) | −18.0032 | −1.06455 | ||||||||
\(287\) | 14.9253 | 0.881015 | ||||||||
\(288\) | 76.1845 | 4.48922 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0.334710 | 0.0196549 | ||||||||
\(291\) | −6.32411 | −0.370726 | ||||||||
\(292\) | −54.9447 | −3.21540 | ||||||||
\(293\) | −8.12392 | −0.474604 | −0.237302 | − | 0.971436i | \(-0.576263\pi\) | ||||
−0.237302 | + | 0.971436i | \(0.576263\pi\) | |||||||
\(294\) | −1.71088 | −0.0997807 | ||||||||
\(295\) | 0.455432 | 0.0265163 | ||||||||
\(296\) | −41.2292 | −2.39640 | ||||||||
\(297\) | 13.5970 | 0.788980 | ||||||||
\(298\) | −17.6370 | −1.02168 | ||||||||
\(299\) | 7.55458 | 0.436893 | ||||||||
\(300\) | 11.7693 | 0.679500 | ||||||||
\(301\) | −3.93677 | −0.226912 | ||||||||
\(302\) | 41.2613 | 2.37432 | ||||||||
\(303\) | −3.47805 | −0.199809 | ||||||||
\(304\) | −101.012 | −5.79346 | ||||||||
\(305\) | 0.0439233 | 0.00251504 | ||||||||
\(306\) | 7.84259 | 0.448331 | ||||||||
\(307\) | −29.0418 | −1.65750 | −0.828752 | − | 0.559615i | \(-0.810949\pi\) | ||||
−0.828752 | + | 0.559615i | \(0.810949\pi\) | |||||||
\(308\) | 74.9293 | 4.26949 | ||||||||
\(309\) | −3.09908 | −0.176301 | ||||||||
\(310\) | −5.13253 | −0.291508 | ||||||||
\(311\) | −19.9040 | −1.12865 | −0.564326 | − | 0.825552i | \(-0.690864\pi\) | ||||
−0.564326 | + | 0.825552i | \(0.690864\pi\) | |||||||
\(312\) | 4.97966 | 0.281918 | ||||||||
\(313\) | −11.5980 | −0.655557 | −0.327779 | − | 0.944755i | \(-0.606300\pi\) | ||||
−0.327779 | + | 0.944755i | \(0.606300\pi\) | |||||||
\(314\) | −54.6994 | −3.08687 | ||||||||
\(315\) | −1.59281 | −0.0897447 | ||||||||
\(316\) | −29.0920 | −1.63655 | ||||||||
\(317\) | −25.3477 | −1.42367 | −0.711835 | − | 0.702347i | \(-0.752136\pi\) | ||||
−0.711835 | + | 0.702347i | \(0.752136\pi\) | |||||||
\(318\) | 4.97315 | 0.278881 | ||||||||
\(319\) | −2.81072 | −0.157370 | ||||||||
\(320\) | 9.73522 | 0.544216 | ||||||||
\(321\) | 0.399726 | 0.0223105 | ||||||||
\(322\) | −42.4683 | −2.36666 | ||||||||
\(323\) | −5.90000 | −0.328285 | ||||||||
\(324\) | 42.5547 | 2.36415 | ||||||||
\(325\) | −5.73508 | −0.318125 | ||||||||
\(326\) | −49.6093 | −2.74761 | ||||||||
\(327\) | 6.95942 | 0.384857 | ||||||||
\(328\) | −65.2733 | −3.60412 | ||||||||
\(329\) | −11.6096 | −0.640058 | ||||||||
\(330\) | 1.55370 | 0.0855282 | ||||||||
\(331\) | −15.2938 | −0.840623 | −0.420311 | − | 0.907380i | \(-0.638079\pi\) | ||||
−0.420311 | + | 0.907380i | \(0.638079\pi\) | |||||||
\(332\) | −6.73200 | −0.369466 | ||||||||
\(333\) | −11.3345 | −0.621129 | ||||||||
\(334\) | −21.5474 | −1.17902 | ||||||||
\(335\) | −2.96891 | −0.162209 | ||||||||
\(336\) | −16.8003 | −0.916529 | ||||||||
\(337\) | 31.8640 | 1.73574 | 0.867872 | − | 0.496788i | \(-0.165487\pi\) | ||||
0.867872 | + | 0.496788i | \(0.165487\pi\) | |||||||
\(338\) | 32.3442 | 1.75929 | ||||||||
\(339\) | 3.77710 | 0.205144 | ||||||||
\(340\) | 1.36790 | 0.0741848 | ||||||||
\(341\) | 43.1003 | 2.33401 | ||||||||
\(342\) | −46.2713 | −2.50207 | ||||||||
\(343\) | −19.9215 | −1.07566 | ||||||||
\(344\) | 17.2167 | 0.928265 | ||||||||
\(345\) | −0.651971 | −0.0351009 | ||||||||
\(346\) | 12.0843 | 0.649657 | ||||||||
\(347\) | −12.9847 | −0.697056 | −0.348528 | − | 0.937298i | \(-0.613318\pi\) | ||||
−0.348528 | + | 0.937298i | \(0.613318\pi\) | |||||||
\(348\) | 1.19731 | 0.0641825 | ||||||||
\(349\) | 8.02647 | 0.429647 | 0.214824 | − | 0.976653i | \(-0.431082\pi\) | ||||
0.214824 | + | 0.976653i | \(0.431082\pi\) | |||||||
\(350\) | 32.2399 | 1.72329 | ||||||||
\(351\) | 2.82243 | 0.150650 | ||||||||
\(352\) | −150.717 | −8.03322 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | 2.20045 | 0.116953 | ||||||||
\(355\) | 3.65083 | 0.193766 | ||||||||
\(356\) | 65.8636 | 3.49076 | ||||||||
\(357\) | −0.981281 | −0.0519349 | ||||||||
\(358\) | −25.7967 | −1.36340 | ||||||||
\(359\) | 3.45667 | 0.182436 | 0.0912181 | − | 0.995831i | \(-0.470924\pi\) | ||||
0.0912181 | + | 0.995831i | \(0.470924\pi\) | |||||||
\(360\) | 6.96587 | 0.367134 | ||||||||
\(361\) | 15.8101 | 0.832108 | ||||||||
\(362\) | −67.3037 | −3.53740 | ||||||||
\(363\) | −8.45435 | −0.443738 | ||||||||
\(364\) | 15.5536 | 0.815229 | ||||||||
\(365\) | −2.31064 | −0.120945 | ||||||||
\(366\) | 0.212219 | 0.0110928 | ||||||||
\(367\) | −32.7225 | −1.70810 | −0.854052 | − | 0.520188i | \(-0.825862\pi\) | ||||
−0.854052 | + | 0.520188i | \(0.825862\pi\) | |||||||
\(368\) | 111.465 | 5.81051 | ||||||||
\(369\) | −17.9446 | −0.934161 | ||||||||
\(370\) | −2.67024 | −0.138819 | ||||||||
\(371\) | 10.0861 | 0.523645 | ||||||||
\(372\) | −18.3599 | −0.951914 | ||||||||
\(373\) | 1.99013 | 0.103045 | 0.0515226 | − | 0.998672i | \(-0.483593\pi\) | ||||
0.0515226 | + | 0.998672i | \(0.483593\pi\) | |||||||
\(374\) | −15.5151 | −0.802265 | ||||||||
\(375\) | 0.995651 | 0.0514152 | ||||||||
\(376\) | 50.7725 | 2.61839 | ||||||||
\(377\) | −0.583439 | −0.0300486 | ||||||||
\(378\) | −15.8663 | −0.816077 | ||||||||
\(379\) | 25.5095 | 1.31034 | 0.655168 | − | 0.755483i | \(-0.272598\pi\) | ||||
0.655168 | + | 0.755483i | \(0.272598\pi\) | |||||||
\(380\) | −8.07062 | −0.414014 | ||||||||
\(381\) | 3.65153 | 0.187074 | ||||||||
\(382\) | −25.5310 | −1.30628 | ||||||||
\(383\) | 19.5482 | 0.998864 | 0.499432 | − | 0.866353i | \(-0.333542\pi\) | ||||
0.499432 | + | 0.866353i | \(0.333542\pi\) | |||||||
\(384\) | 24.5223 | 1.25140 | ||||||||
\(385\) | 3.15107 | 0.160594 | ||||||||
\(386\) | −23.6806 | −1.20531 | ||||||||
\(387\) | 4.73315 | 0.240600 | ||||||||
\(388\) | 86.3856 | 4.38557 | ||||||||
\(389\) | 36.6173 | 1.85657 | 0.928285 | − | 0.371871i | \(-0.121284\pi\) | ||||
0.928285 | + | 0.371871i | \(0.121284\pi\) | |||||||
\(390\) | 0.322511 | 0.0163310 | ||||||||
\(391\) | 6.51052 | 0.329251 | ||||||||
\(392\) | 15.1748 | 0.766445 | ||||||||
\(393\) | −1.96510 | −0.0991262 | ||||||||
\(394\) | −1.05505 | −0.0531529 | ||||||||
\(395\) | −1.22343 | −0.0615576 | ||||||||
\(396\) | −90.0870 | −4.52704 | ||||||||
\(397\) | −21.7361 | −1.09090 | −0.545452 | − | 0.838142i | \(-0.683642\pi\) | ||||
−0.545452 | + | 0.838142i | \(0.683642\pi\) | |||||||
\(398\) | 3.84414 | 0.192689 | ||||||||
\(399\) | 5.78956 | 0.289841 | ||||||||
\(400\) | −84.6188 | −4.23094 | ||||||||
\(401\) | 11.7473 | 0.586633 | 0.293317 | − | 0.956015i | \(-0.405241\pi\) | ||||
0.293317 | + | 0.956015i | \(0.405241\pi\) | |||||||
\(402\) | −14.3445 | −0.715439 | ||||||||
\(403\) | 8.94661 | 0.445662 | ||||||||
\(404\) | 47.5093 | 2.36368 | ||||||||
\(405\) | 1.78959 | 0.0889255 | ||||||||
\(406\) | 3.27982 | 0.162775 | ||||||||
\(407\) | 22.4232 | 1.11148 | ||||||||
\(408\) | 4.29146 | 0.212459 | ||||||||
\(409\) | −28.6002 | −1.41419 | −0.707095 | − | 0.707119i | \(-0.749995\pi\) | ||||
−0.707095 | + | 0.707119i | \(0.749995\pi\) | |||||||
\(410\) | −4.22748 | −0.208780 | ||||||||
\(411\) | 0.430843 | 0.0212519 | ||||||||
\(412\) | 42.3327 | 2.08558 | ||||||||
\(413\) | 4.46277 | 0.219599 | ||||||||
\(414\) | 51.0593 | 2.50943 | ||||||||
\(415\) | −0.283107 | −0.0138972 | ||||||||
\(416\) | −31.2852 | −1.53389 | ||||||||
\(417\) | −2.13978 | −0.104786 | ||||||||
\(418\) | 91.5390 | 4.47732 | ||||||||
\(419\) | 10.9524 | 0.535060 | 0.267530 | − | 0.963550i | \(-0.413793\pi\) | ||||
0.267530 | + | 0.963550i | \(0.413793\pi\) | |||||||
\(420\) | −1.34229 | −0.0654973 | ||||||||
\(421\) | 19.6046 | 0.955470 | 0.477735 | − | 0.878504i | \(-0.341458\pi\) | ||||
0.477735 | + | 0.878504i | \(0.341458\pi\) | |||||||
\(422\) | −39.0493 | −1.90089 | ||||||||
\(423\) | 13.9581 | 0.678668 | ||||||||
\(424\) | −44.1098 | −2.14216 | ||||||||
\(425\) | −4.94247 | −0.239745 | ||||||||
\(426\) | 17.6393 | 0.854626 | ||||||||
\(427\) | 0.430403 | 0.0208287 | ||||||||
\(428\) | −5.46015 | −0.263926 | ||||||||
\(429\) | −2.70828 | −0.130757 | ||||||||
\(430\) | 1.11506 | 0.0537728 | ||||||||
\(431\) | −12.7253 | −0.612956 | −0.306478 | − | 0.951878i | \(-0.599151\pi\) | ||||
−0.306478 | + | 0.951878i | \(0.599151\pi\) | |||||||
\(432\) | 41.6438 | 2.00359 | ||||||||
\(433\) | 29.8667 | 1.43530 | 0.717650 | − | 0.696404i | \(-0.245218\pi\) | ||||
0.717650 | + | 0.696404i | \(0.245218\pi\) | |||||||
\(434\) | −50.2936 | −2.41417 | ||||||||
\(435\) | 0.0503516 | 0.00241417 | ||||||||
\(436\) | −95.0638 | −4.55273 | ||||||||
\(437\) | −38.4121 | −1.83750 | ||||||||
\(438\) | −11.1640 | −0.533439 | ||||||||
\(439\) | 33.7453 | 1.61058 | 0.805288 | − | 0.592884i | \(-0.202011\pi\) | ||||
0.805288 | + | 0.592884i | \(0.202011\pi\) | |||||||
\(440\) | −13.7807 | −0.656967 | ||||||||
\(441\) | 4.17179 | 0.198657 | ||||||||
\(442\) | −3.22057 | −0.153187 | ||||||||
\(443\) | −14.9084 | −0.708319 | −0.354159 | − | 0.935185i | \(-0.615233\pi\) | ||||
−0.354159 | + | 0.935185i | \(0.615233\pi\) | |||||||
\(444\) | −9.55185 | −0.453311 | ||||||||
\(445\) | 2.76982 | 0.131302 | ||||||||
\(446\) | −11.6743 | −0.552793 | ||||||||
\(447\) | −2.65319 | −0.125492 | ||||||||
\(448\) | 95.3953 | 4.50700 | ||||||||
\(449\) | 13.0950 | 0.617994 | 0.308997 | − | 0.951063i | \(-0.400007\pi\) | ||||
0.308997 | + | 0.951063i | \(0.400007\pi\) | |||||||
\(450\) | −38.7618 | −1.82725 | ||||||||
\(451\) | 35.5001 | 1.67163 | ||||||||
\(452\) | −51.5941 | −2.42678 | ||||||||
\(453\) | 6.20708 | 0.291634 | ||||||||
\(454\) | −5.52971 | −0.259522 | ||||||||
\(455\) | 0.654089 | 0.0306642 | ||||||||
\(456\) | −25.3196 | −1.18570 | ||||||||
\(457\) | 32.6396 | 1.52682 | 0.763408 | − | 0.645917i | \(-0.223525\pi\) | ||||
0.763408 | + | 0.645917i | \(0.223525\pi\) | |||||||
\(458\) | 72.5791 | 3.39140 | ||||||||
\(459\) | 2.43236 | 0.113533 | ||||||||
\(460\) | 8.90574 | 0.415232 | ||||||||
\(461\) | 17.1339 | 0.798004 | 0.399002 | − | 0.916950i | \(-0.369357\pi\) | ||||
0.399002 | + | 0.916950i | \(0.369357\pi\) | |||||||
\(462\) | 15.2246 | 0.708315 | ||||||||
\(463\) | −5.86312 | −0.272482 | −0.136241 | − | 0.990676i | \(-0.543502\pi\) | ||||
−0.136241 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(464\) | −8.60841 | −0.399636 | ||||||||
\(465\) | −0.772105 | −0.0358055 | ||||||||
\(466\) | −37.8445 | −1.75311 | ||||||||
\(467\) | −19.9019 | −0.920949 | −0.460474 | − | 0.887673i | \(-0.652321\pi\) | ||||
−0.460474 | + | 0.887673i | \(0.652321\pi\) | |||||||
\(468\) | −18.7000 | −0.864406 | ||||||||
\(469\) | −29.0923 | −1.34336 | ||||||||
\(470\) | 3.28832 | 0.151679 | ||||||||
\(471\) | −8.22862 | −0.379155 | ||||||||
\(472\) | −19.5171 | −0.898348 | ||||||||
\(473\) | −9.36364 | −0.430541 | ||||||||
\(474\) | −5.91111 | −0.271506 | ||||||||
\(475\) | 29.1606 | 1.33798 | ||||||||
\(476\) | 13.4040 | 0.614373 | ||||||||
\(477\) | −12.1265 | −0.555233 | ||||||||
\(478\) | 51.2993 | 2.34638 | ||||||||
\(479\) | 1.69085 | 0.0772568 | 0.0386284 | − | 0.999254i | \(-0.487701\pi\) | ||||
0.0386284 | + | 0.999254i | \(0.487701\pi\) | |||||||
\(480\) | 2.69996 | 0.123236 | ||||||||
\(481\) | 4.65454 | 0.212229 | ||||||||
\(482\) | −11.8866 | −0.541418 | ||||||||
\(483\) | −6.38865 | −0.290693 | ||||||||
\(484\) | 115.484 | 5.24928 | ||||||||
\(485\) | 3.63286 | 0.164960 | ||||||||
\(486\) | 28.8994 | 1.31090 | ||||||||
\(487\) | 5.03381 | 0.228104 | 0.114052 | − | 0.993475i | \(-0.463617\pi\) | ||||
0.114052 | + | 0.993475i | \(0.463617\pi\) | |||||||
\(488\) | −1.88229 | −0.0852073 | ||||||||
\(489\) | −7.46290 | −0.337484 | ||||||||
\(490\) | 0.982809 | 0.0443988 | ||||||||
\(491\) | 37.8067 | 1.70619 | 0.853095 | − | 0.521755i | \(-0.174722\pi\) | ||||
0.853095 | + | 0.521755i | \(0.174722\pi\) | |||||||
\(492\) | −15.1223 | −0.681767 | ||||||||
\(493\) | −0.502806 | −0.0226452 | ||||||||
\(494\) | 19.0014 | 0.854911 | ||||||||
\(495\) | −3.78851 | −0.170281 | ||||||||
\(496\) | 132.004 | 5.92714 | ||||||||
\(497\) | 35.7745 | 1.60470 | ||||||||
\(498\) | −1.36785 | −0.0612950 | ||||||||
\(499\) | −10.7086 | −0.479382 | −0.239691 | − | 0.970849i | \(-0.577046\pi\) | ||||
−0.239691 | + | 0.970849i | \(0.577046\pi\) | |||||||
\(500\) | −13.6003 | −0.608225 | ||||||||
\(501\) | −3.24145 | −0.144817 | ||||||||
\(502\) | 84.5616 | 3.77417 | ||||||||
\(503\) | 10.1697 | 0.453445 | 0.226723 | − | 0.973959i | \(-0.427199\pi\) | ||||
0.226723 | + | 0.973959i | \(0.427199\pi\) | |||||||
\(504\) | 68.2584 | 3.04047 | ||||||||
\(505\) | 1.99795 | 0.0889077 | ||||||||
\(506\) | −101.011 | −4.49049 | ||||||||
\(507\) | 4.86564 | 0.216091 | ||||||||
\(508\) | −49.8790 | −2.21302 | ||||||||
\(509\) | 13.4689 | 0.597000 | 0.298500 | − | 0.954410i | \(-0.403514\pi\) | ||||
0.298500 | + | 0.954410i | \(0.403514\pi\) | |||||||
\(510\) | 0.277939 | 0.0123074 | ||||||||
\(511\) | −22.6419 | −1.00162 | ||||||||
\(512\) | −109.656 | −4.84616 | ||||||||
\(513\) | −14.3509 | −0.633609 | ||||||||
\(514\) | 25.7218 | 1.13454 | ||||||||
\(515\) | 1.78026 | 0.0784474 | ||||||||
\(516\) | 3.98872 | 0.175594 | ||||||||
\(517\) | −27.6135 | −1.21444 | ||||||||
\(518\) | −26.1656 | −1.14965 | ||||||||
\(519\) | 1.81789 | 0.0797963 | ||||||||
\(520\) | −2.86054 | −0.125443 | ||||||||
\(521\) | −13.9958 | −0.613168 | −0.306584 | − | 0.951844i | \(-0.599186\pi\) | ||||
−0.306584 | + | 0.951844i | \(0.599186\pi\) | |||||||
\(522\) | −3.94330 | −0.172594 | ||||||||
\(523\) | −20.8191 | −0.910356 | −0.455178 | − | 0.890400i | \(-0.650424\pi\) | ||||
−0.455178 | + | 0.890400i | \(0.650424\pi\) | |||||||
\(524\) | 26.8427 | 1.17263 | ||||||||
\(525\) | 4.84996 | 0.211669 | ||||||||
\(526\) | −20.4935 | −0.893561 | ||||||||
\(527\) | 7.71016 | 0.335860 | ||||||||
\(528\) | −39.9596 | −1.73902 | ||||||||
\(529\) | 19.3868 | 0.842906 | ||||||||
\(530\) | −2.85681 | −0.124092 | ||||||||
\(531\) | −5.36556 | −0.232845 | ||||||||
\(532\) | −79.0838 | −3.42872 | ||||||||
\(533\) | 7.36898 | 0.319186 | ||||||||
\(534\) | 13.3826 | 0.579122 | ||||||||
\(535\) | −0.229621 | −0.00992738 | ||||||||
\(536\) | 127.230 | 5.49549 | ||||||||
\(537\) | −3.88069 | −0.167464 | ||||||||
\(538\) | 37.7965 | 1.62952 | ||||||||
\(539\) | −8.25310 | −0.355486 | ||||||||
\(540\) | 3.32723 | 0.143181 | ||||||||
\(541\) | −34.5215 | −1.48419 | −0.742097 | − | 0.670293i | \(-0.766169\pi\) | ||||
−0.742097 | + | 0.670293i | \(0.766169\pi\) | |||||||
\(542\) | −18.6317 | −0.800302 | ||||||||
\(543\) | −10.1247 | −0.434494 | ||||||||
\(544\) | −26.9615 | −1.15597 | ||||||||
\(545\) | −3.99781 | −0.171247 | ||||||||
\(546\) | 3.16028 | 0.135248 | ||||||||
\(547\) | 11.9374 | 0.510404 | 0.255202 | − | 0.966888i | \(-0.417858\pi\) | ||||
0.255202 | + | 0.966888i | \(0.417858\pi\) | |||||||
\(548\) | −5.88519 | −0.251403 | ||||||||
\(549\) | −0.517471 | −0.0220851 | ||||||||
\(550\) | 76.6829 | 3.26977 | ||||||||
\(551\) | 2.96656 | 0.126380 | ||||||||
\(552\) | 27.9396 | 1.18919 | ||||||||
\(553\) | −11.9884 | −0.509799 | ||||||||
\(554\) | 13.1535 | 0.558837 | ||||||||
\(555\) | −0.401693 | −0.0170509 | ||||||||
\(556\) | 29.2289 | 1.23958 | ||||||||
\(557\) | 2.70884 | 0.114777 | 0.0573886 | − | 0.998352i | \(-0.481723\pi\) | ||||
0.0573886 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(558\) | 60.4677 | 2.55980 | ||||||||
\(559\) | −1.94367 | −0.0822086 | ||||||||
\(560\) | 9.65083 | 0.407822 | ||||||||
\(561\) | −2.33399 | −0.0985409 | ||||||||
\(562\) | −87.8454 | −3.70553 | ||||||||
\(563\) | 17.5082 | 0.737884 | 0.368942 | − | 0.929452i | \(-0.379720\pi\) | ||||
0.368942 | + | 0.929452i | \(0.379720\pi\) | |||||||
\(564\) | 11.7628 | 0.495304 | ||||||||
\(565\) | −2.16974 | −0.0912815 | ||||||||
\(566\) | 92.9000 | 3.90488 | ||||||||
\(567\) | 17.5362 | 0.736450 | ||||||||
\(568\) | −156.453 | −6.56463 | ||||||||
\(569\) | 39.8886 | 1.67222 | 0.836108 | − | 0.548564i | \(-0.184825\pi\) | ||||
0.836108 | + | 0.548564i | \(0.184825\pi\) | |||||||
\(570\) | −1.63984 | −0.0686855 | ||||||||
\(571\) | 29.9927 | 1.25516 | 0.627579 | − | 0.778553i | \(-0.284046\pi\) | ||||
0.627579 | + | 0.778553i | \(0.284046\pi\) | |||||||
\(572\) | 36.9943 | 1.54681 | ||||||||
\(573\) | −3.84072 | −0.160448 | ||||||||
\(574\) | −41.4249 | −1.72904 | ||||||||
\(575\) | −32.1781 | −1.34192 | ||||||||
\(576\) | −114.693 | −4.77888 | ||||||||
\(577\) | −16.4032 | −0.682876 | −0.341438 | − | 0.939904i | \(-0.610914\pi\) | ||||
−0.341438 | + | 0.939904i | \(0.610914\pi\) | |||||||
\(578\) | −2.77548 | −0.115445 | ||||||||
\(579\) | −3.56236 | −0.148047 | ||||||||
\(580\) | −0.687789 | −0.0285589 | ||||||||
\(581\) | −2.77416 | −0.115092 | ||||||||
\(582\) | 17.5524 | 0.727571 | ||||||||
\(583\) | 23.9899 | 0.993561 | ||||||||
\(584\) | 99.0205 | 4.09750 | ||||||||
\(585\) | −0.786407 | −0.0325139 | ||||||||
\(586\) | 22.5477 | 0.931439 | ||||||||
\(587\) | 30.8716 | 1.27421 | 0.637104 | − | 0.770778i | \(-0.280132\pi\) | ||||
0.637104 | + | 0.770778i | \(0.280132\pi\) | |||||||
\(588\) | 3.51566 | 0.144983 | ||||||||
\(589\) | −45.4900 | −1.87438 | ||||||||
\(590\) | −1.26404 | −0.0520397 | ||||||||
\(591\) | −0.158715 | −0.00652868 | ||||||||
\(592\) | 68.6759 | 2.82256 | ||||||||
\(593\) | −3.85567 | −0.158334 | −0.0791668 | − | 0.996861i | \(-0.525226\pi\) | ||||
−0.0791668 | + | 0.996861i | \(0.525226\pi\) | |||||||
\(594\) | −37.7383 | −1.54842 | ||||||||
\(595\) | 0.563692 | 0.0231091 | ||||||||
\(596\) | 36.2419 | 1.48452 | ||||||||
\(597\) | 0.578287 | 0.0236677 | ||||||||
\(598\) | −20.9676 | −0.857427 | ||||||||
\(599\) | −37.0008 | −1.51181 | −0.755906 | − | 0.654681i | \(-0.772803\pi\) | ||||
−0.755906 | + | 0.654681i | \(0.772803\pi\) | |||||||
\(600\) | −21.2104 | −0.865911 | ||||||||
\(601\) | 40.9313 | 1.66962 | 0.834810 | − | 0.550538i | \(-0.185577\pi\) | ||||
0.834810 | + | 0.550538i | \(0.185577\pi\) | |||||||
\(602\) | 10.9264 | 0.445327 | ||||||||
\(603\) | 34.9774 | 1.42439 | ||||||||
\(604\) | −84.7871 | −3.44994 | ||||||||
\(605\) | 4.85656 | 0.197447 | ||||||||
\(606\) | 9.65326 | 0.392137 | ||||||||
\(607\) | −42.9922 | −1.74500 | −0.872500 | − | 0.488614i | \(-0.837503\pi\) | ||||
−0.872500 | + | 0.488614i | \(0.837503\pi\) | |||||||
\(608\) | 159.073 | 6.45127 | ||||||||
\(609\) | 0.493394 | 0.0199933 | ||||||||
\(610\) | −0.121908 | −0.00493591 | ||||||||
\(611\) | −5.73192 | −0.231889 | ||||||||
\(612\) | −16.1156 | −0.651434 | ||||||||
\(613\) | −37.9419 | −1.53246 | −0.766229 | − | 0.642567i | \(-0.777869\pi\) | ||||
−0.766229 | + | 0.642567i | \(0.777869\pi\) | |||||||
\(614\) | 80.6049 | 3.25295 | ||||||||
\(615\) | −0.635954 | −0.0256441 | ||||||||
\(616\) | −135.036 | −5.44077 | ||||||||
\(617\) | −7.15323 | −0.287978 | −0.143989 | − | 0.989579i | \(-0.545993\pi\) | ||||
−0.143989 | + | 0.989579i | \(0.545993\pi\) | |||||||
\(618\) | 8.60144 | 0.346000 | ||||||||
\(619\) | 30.1405 | 1.21145 | 0.605724 | − | 0.795675i | \(-0.292883\pi\) | ||||
0.605724 | + | 0.795675i | \(0.292883\pi\) | |||||||
\(620\) | 10.5467 | 0.423567 | ||||||||
\(621\) | 15.8359 | 0.635474 | ||||||||
\(622\) | 55.2431 | 2.21504 | ||||||||
\(623\) | 27.1414 | 1.08740 | ||||||||
\(624\) | −8.29467 | −0.332053 | ||||||||
\(625\) | 24.1404 | 0.965617 | ||||||||
\(626\) | 32.1900 | 1.28657 | ||||||||
\(627\) | 13.7705 | 0.549942 | ||||||||
\(628\) | 112.401 | 4.48528 | ||||||||
\(629\) | 4.01127 | 0.159940 | ||||||||
\(630\) | 4.42081 | 0.176129 | ||||||||
\(631\) | 14.3719 | 0.572138 | 0.286069 | − | 0.958209i | \(-0.407651\pi\) | ||||
0.286069 | + | 0.958209i | \(0.407651\pi\) | |||||||
\(632\) | 52.4291 | 2.08552 | ||||||||
\(633\) | −5.87432 | −0.233483 | ||||||||
\(634\) | 70.3520 | 2.79403 | ||||||||
\(635\) | −2.09761 | −0.0832410 | ||||||||
\(636\) | −10.2192 | −0.405219 | ||||||||
\(637\) | −1.71315 | −0.0678775 | ||||||||
\(638\) | 7.80108 | 0.308848 | ||||||||
\(639\) | −43.0114 | −1.70150 | ||||||||
\(640\) | −14.0867 | −0.556826 | ||||||||
\(641\) | 15.0912 | 0.596068 | 0.298034 | − | 0.954555i | \(-0.403669\pi\) | ||||
0.298034 | + | 0.954555i | \(0.403669\pi\) | |||||||
\(642\) | −1.10943 | −0.0437857 | ||||||||
\(643\) | 29.7690 | 1.17398 | 0.586988 | − | 0.809596i | \(-0.300314\pi\) | ||||
0.586988 | + | 0.809596i | \(0.300314\pi\) | |||||||
\(644\) | 87.2672 | 3.43881 | ||||||||
\(645\) | 0.167742 | 0.00660482 | ||||||||
\(646\) | 16.3753 | 0.644278 | ||||||||
\(647\) | 14.8389 | 0.583375 | 0.291688 | − | 0.956514i | \(-0.405783\pi\) | ||||
0.291688 | + | 0.956514i | \(0.405783\pi\) | |||||||
\(648\) | −76.6913 | −3.01272 | ||||||||
\(649\) | 10.6147 | 0.416665 | ||||||||
\(650\) | 15.9176 | 0.624338 | ||||||||
\(651\) | −7.56584 | −0.296529 | ||||||||
\(652\) | 101.941 | 3.99232 | ||||||||
\(653\) | −14.1951 | −0.555495 | −0.277748 | − | 0.960654i | \(-0.589588\pi\) | ||||
−0.277748 | + | 0.960654i | \(0.589588\pi\) | |||||||
\(654\) | −19.3157 | −0.755304 | ||||||||
\(655\) | 1.12884 | 0.0441075 | ||||||||
\(656\) | 108.727 | 4.24506 | ||||||||
\(657\) | 27.2223 | 1.06204 | ||||||||
\(658\) | 32.2222 | 1.25615 | ||||||||
\(659\) | 35.8400 | 1.39613 | 0.698064 | − | 0.716035i | \(-0.254045\pi\) | ||||
0.698064 | + | 0.716035i | \(0.254045\pi\) | |||||||
\(660\) | −3.19266 | −0.124274 | ||||||||
\(661\) | 42.4626 | 1.65160 | 0.825802 | − | 0.563960i | \(-0.190723\pi\) | ||||
0.825802 | + | 0.563960i | \(0.190723\pi\) | |||||||
\(662\) | 42.4475 | 1.64977 | ||||||||
\(663\) | −0.484481 | −0.0188157 | ||||||||
\(664\) | 12.1323 | 0.470824 | ||||||||
\(665\) | −3.32579 | −0.128969 | ||||||||
\(666\) | 31.4588 | 1.21900 | ||||||||
\(667\) | −3.27353 | −0.126752 | ||||||||
\(668\) | 44.2773 | 1.71314 | ||||||||
\(669\) | −1.75620 | −0.0678986 | ||||||||
\(670\) | 8.24013 | 0.318344 | ||||||||
\(671\) | 1.02372 | 0.0395202 | ||||||||
\(672\) | 26.4568 | 1.02060 | ||||||||
\(673\) | 19.6567 | 0.757711 | 0.378855 | − | 0.925456i | \(-0.376318\pi\) | ||||
0.378855 | + | 0.925456i | \(0.376318\pi\) | |||||||
\(674\) | −88.4378 | −3.40650 | ||||||||
\(675\) | −12.0219 | −0.462722 | ||||||||
\(676\) | −66.4633 | −2.55628 | ||||||||
\(677\) | −11.5452 | −0.443719 | −0.221859 | − | 0.975079i | \(-0.571213\pi\) | ||||
−0.221859 | + | 0.975079i | \(0.571213\pi\) | |||||||
\(678\) | −10.4832 | −0.402607 | ||||||||
\(679\) | 35.5983 | 1.36614 | ||||||||
\(680\) | −2.46521 | −0.0945364 | ||||||||
\(681\) | −0.831854 | −0.0318767 | ||||||||
\(682\) | −119.624 | −4.58063 | ||||||||
\(683\) | 30.8821 | 1.18167 | 0.590836 | − | 0.806791i | \(-0.298798\pi\) | ||||
0.590836 | + | 0.806791i | \(0.298798\pi\) | |||||||
\(684\) | 95.0820 | 3.63555 | ||||||||
\(685\) | −0.247496 | −0.00945632 | ||||||||
\(686\) | 55.2917 | 2.11105 | ||||||||
\(687\) | 10.9183 | 0.416560 | ||||||||
\(688\) | −28.6781 | −1.09334 | ||||||||
\(689\) | 4.97975 | 0.189713 | ||||||||
\(690\) | 1.80953 | 0.0688876 | ||||||||
\(691\) | −26.1020 | −0.992967 | −0.496483 | − | 0.868046i | \(-0.665376\pi\) | ||||
−0.496483 | + | 0.868046i | \(0.665376\pi\) | |||||||
\(692\) | −24.8318 | −0.943965 | ||||||||
\(693\) | −37.1236 | −1.41021 | ||||||||
\(694\) | 36.0387 | 1.36801 | ||||||||
\(695\) | 1.22919 | 0.0466258 | ||||||||
\(696\) | −2.15777 | −0.0817901 | ||||||||
\(697\) | 6.35057 | 0.240545 | ||||||||
\(698\) | −22.2773 | −0.843207 | ||||||||
\(699\) | −5.69308 | −0.215332 | ||||||||
\(700\) | −66.2491 | −2.50398 | ||||||||
\(701\) | −10.9713 | −0.414379 | −0.207189 | − | 0.978301i | \(-0.566432\pi\) | ||||
−0.207189 | + | 0.978301i | \(0.566432\pi\) | |||||||
\(702\) | −7.83358 | −0.295659 | ||||||||
\(703\) | −23.6665 | −0.892600 | ||||||||
\(704\) | 226.898 | 8.55156 | ||||||||
\(705\) | 0.494673 | 0.0186305 | ||||||||
\(706\) | 2.77548 | 0.104456 | ||||||||
\(707\) | 19.5779 | 0.736303 | ||||||||
\(708\) | −4.52167 | −0.169935 | ||||||||
\(709\) | 49.2734 | 1.85050 | 0.925251 | − | 0.379356i | \(-0.123854\pi\) | ||||
0.925251 | + | 0.379356i | \(0.123854\pi\) | |||||||
\(710\) | −10.1328 | −0.380277 | ||||||||
\(711\) | 14.4136 | 0.540551 | ||||||||
\(712\) | −118.698 | −4.44840 | ||||||||
\(713\) | 50.1972 | 1.87990 | ||||||||
\(714\) | 2.72352 | 0.101925 | ||||||||
\(715\) | 1.55576 | 0.0581820 | ||||||||
\(716\) | 53.0091 | 1.98104 | ||||||||
\(717\) | 7.71713 | 0.288202 | ||||||||
\(718\) | −9.59391 | −0.358042 | ||||||||
\(719\) | 44.0695 | 1.64351 | 0.821757 | − | 0.569838i | \(-0.192994\pi\) | ||||
0.821757 | + | 0.569838i | \(0.192994\pi\) | |||||||
\(720\) | −11.6031 | −0.432423 | ||||||||
\(721\) | 17.4447 | 0.649674 | ||||||||
\(722\) | −43.8804 | −1.63306 | ||||||||
\(723\) | −1.78814 | −0.0665015 | ||||||||
\(724\) | 138.301 | 5.13992 | ||||||||
\(725\) | 2.48511 | 0.0922945 | ||||||||
\(726\) | 23.4648 | 0.870862 | ||||||||
\(727\) | 6.11096 | 0.226643 | 0.113321 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113321 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(728\) | −28.0304 | −1.03888 | ||||||||
\(729\) | −18.0369 | −0.668034 | ||||||||
\(730\) | 6.41313 | 0.237361 | ||||||||
\(731\) | −1.67505 | −0.0619540 | ||||||||
\(732\) | −0.436084 | −0.0161181 | ||||||||
\(733\) | −18.1496 | −0.670372 | −0.335186 | − | 0.942152i | \(-0.608799\pi\) | ||||
−0.335186 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(734\) | 90.8207 | 3.35225 | ||||||||
\(735\) | 0.147847 | 0.00545343 | ||||||||
\(736\) | −175.534 | −6.47025 | ||||||||
\(737\) | −69.1962 | −2.54888 | ||||||||
\(738\) | 49.8049 | 1.83335 | ||||||||
\(739\) | 39.7553 | 1.46242 | 0.731211 | − | 0.682152i | \(-0.238956\pi\) | ||||
0.731211 | + | 0.682152i | \(0.238956\pi\) | |||||||
\(740\) | 5.48702 | 0.201707 | ||||||||
\(741\) | 2.85844 | 0.105007 | ||||||||
\(742\) | −27.9938 | −1.02768 | ||||||||
\(743\) | −12.1880 | −0.447136 | −0.223568 | − | 0.974688i | \(-0.571770\pi\) | ||||
−0.223568 | + | 0.974688i | \(0.571770\pi\) | |||||||
\(744\) | 33.0878 | 1.21306 | ||||||||
\(745\) | 1.52411 | 0.0558392 | ||||||||
\(746\) | −5.52357 | −0.202232 | ||||||||
\(747\) | 3.33536 | 0.122034 | ||||||||
\(748\) | 31.8816 | 1.16571 | ||||||||
\(749\) | −2.25005 | −0.0822151 | ||||||||
\(750\) | −2.76340 | −0.100905 | ||||||||
\(751\) | 21.4953 | 0.784374 | 0.392187 | − | 0.919886i | \(-0.371719\pi\) | ||||
0.392187 | + | 0.919886i | \(0.371719\pi\) | |||||||
\(752\) | −84.5723 | −3.08404 | ||||||||
\(753\) | 12.7209 | 0.463575 | ||||||||
\(754\) | 1.61932 | 0.0589722 | ||||||||
\(755\) | −3.56563 | −0.129767 | ||||||||
\(756\) | 32.6034 | 1.18578 | ||||||||
\(757\) | 10.3877 | 0.377546 | 0.188773 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188773 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(758\) | −70.8010 | −2.57161 | ||||||||
\(759\) | −15.1955 | −0.551560 | ||||||||
\(760\) | 14.5447 | 0.527593 | ||||||||
\(761\) | 16.9604 | 0.614814 | 0.307407 | − | 0.951578i | \(-0.400539\pi\) | ||||
0.307407 | + | 0.951578i | \(0.400539\pi\) | |||||||
\(762\) | −10.1347 | −0.367143 | ||||||||
\(763\) | −39.1744 | −1.41821 | ||||||||
\(764\) | 52.4632 | 1.89805 | ||||||||
\(765\) | −0.677724 | −0.0245032 | ||||||||
\(766\) | −54.2554 | −1.96033 | ||||||||
\(767\) | 2.20337 | 0.0795591 | ||||||||
\(768\) | −34.1666 | −1.23288 | ||||||||
\(769\) | 22.1586 | 0.799061 | 0.399530 | − | 0.916720i | \(-0.369173\pi\) | ||||
0.399530 | + | 0.916720i | \(0.369173\pi\) | |||||||
\(770\) | −8.74573 | −0.315174 | ||||||||
\(771\) | 3.86942 | 0.139354 | ||||||||
\(772\) | 48.6608 | 1.75134 | ||||||||
\(773\) | −27.6299 | −0.993778 | −0.496889 | − | 0.867814i | \(-0.665524\pi\) | ||||
−0.496889 | + | 0.867814i | \(0.665524\pi\) | |||||||
\(774\) | −13.1367 | −0.472191 | ||||||||
\(775\) | −38.1073 | −1.36885 | ||||||||
\(776\) | −155.683 | −5.58868 | ||||||||
\(777\) | −3.93618 | −0.141210 | ||||||||
\(778\) | −101.630 | −3.64362 | ||||||||
\(779\) | −37.4684 | −1.34245 | ||||||||
\(780\) | −0.662722 | −0.0237292 | ||||||||
\(781\) | 85.0899 | 3.04476 | ||||||||
\(782\) | −18.0698 | −0.646174 | ||||||||
\(783\) | −1.22301 | −0.0437067 | ||||||||
\(784\) | −25.2769 | −0.902746 | ||||||||
\(785\) | 4.72689 | 0.168710 | ||||||||
\(786\) | 5.45409 | 0.194541 | ||||||||
\(787\) | 0.761315 | 0.0271380 | 0.0135690 | − | 0.999908i | \(-0.495681\pi\) | ||||
0.0135690 | + | 0.999908i | \(0.495681\pi\) | |||||||
\(788\) | 2.16801 | 0.0772321 | ||||||||
\(789\) | −3.08291 | −0.109755 | ||||||||
\(790\) | 3.39561 | 0.120810 | ||||||||
\(791\) | −21.2612 | −0.755961 | ||||||||
\(792\) | 162.353 | 5.76897 | ||||||||
\(793\) | 0.212500 | 0.00754609 | ||||||||
\(794\) | 60.3281 | 2.14096 | ||||||||
\(795\) | −0.429759 | −0.0152420 | ||||||||
\(796\) | −7.89924 | −0.279981 | ||||||||
\(797\) | −25.4190 | −0.900387 | −0.450194 | − | 0.892931i | \(-0.648645\pi\) | ||||
−0.450194 | + | 0.892931i | \(0.648645\pi\) | |||||||
\(798\) | −16.0688 | −0.568829 | ||||||||
\(799\) | −4.93976 | −0.174756 | ||||||||
\(800\) | 133.257 | 4.71134 | ||||||||
\(801\) | −32.6320 | −1.15299 | ||||||||
\(802\) | −32.6044 | −1.15130 | ||||||||
\(803\) | −53.8541 | −1.90047 | ||||||||
\(804\) | 29.4762 | 1.03955 | ||||||||
\(805\) | 3.66993 | 0.129348 | ||||||||
\(806\) | −24.8311 | −0.874638 | ||||||||
\(807\) | 5.68586 | 0.200152 | ||||||||
\(808\) | −85.6204 | −3.01212 | ||||||||
\(809\) | −3.56651 | −0.125392 | −0.0626958 | − | 0.998033i | \(-0.519970\pi\) | ||||
−0.0626958 | + | 0.998033i | \(0.519970\pi\) | |||||||
\(810\) | −4.96697 | −0.174522 | ||||||||
\(811\) | 15.2051 | 0.533923 | 0.266962 | − | 0.963707i | \(-0.413980\pi\) | ||||
0.266962 | + | 0.963707i | \(0.413980\pi\) | |||||||
\(812\) | −6.73963 | −0.236515 | ||||||||
\(813\) | −2.80284 | −0.0982998 | ||||||||
\(814\) | −62.2352 | −2.18134 | ||||||||
\(815\) | 4.28703 | 0.150168 | ||||||||
\(816\) | −7.14833 | −0.250241 | ||||||||
\(817\) | 9.88281 | 0.345756 | ||||||||
\(818\) | 79.3792 | 2.77543 | ||||||||
\(819\) | −7.70599 | −0.269269 | ||||||||
\(820\) | 8.68695 | 0.303362 | ||||||||
\(821\) | 33.2592 | 1.16075 | 0.580376 | − | 0.814348i | \(-0.302905\pi\) | ||||
0.580376 | + | 0.814348i | \(0.302905\pi\) | |||||||
\(822\) | −1.19579 | −0.0417081 | ||||||||
\(823\) | 4.12682 | 0.143852 | 0.0719259 | − | 0.997410i | \(-0.477085\pi\) | ||||
0.0719259 | + | 0.997410i | \(0.477085\pi\) | |||||||
\(824\) | −76.2912 | −2.65773 | ||||||||
\(825\) | 11.5357 | 0.401620 | ||||||||
\(826\) | −12.3863 | −0.430975 | ||||||||
\(827\) | −29.5582 | −1.02784 | −0.513919 | − | 0.857839i | \(-0.671807\pi\) | ||||
−0.513919 | + | 0.857839i | \(0.671807\pi\) | |||||||
\(828\) | −104.921 | −3.64625 | ||||||||
\(829\) | −9.75878 | −0.338937 | −0.169468 | − | 0.985536i | \(-0.554205\pi\) | ||||
−0.169468 | + | 0.985536i | \(0.554205\pi\) | |||||||
\(830\) | 0.785757 | 0.0272740 | ||||||||
\(831\) | 1.97872 | 0.0686411 | ||||||||
\(832\) | 47.0988 | 1.63286 | ||||||||
\(833\) | −1.47639 | −0.0511539 | ||||||||
\(834\) | 5.93892 | 0.205648 | ||||||||
\(835\) | 1.86204 | 0.0644384 | ||||||||
\(836\) | −188.102 | −6.50563 | ||||||||
\(837\) | 18.7539 | 0.648230 | ||||||||
\(838\) | −30.3981 | −1.05009 | ||||||||
\(839\) | 49.5613 | 1.71105 | 0.855523 | − | 0.517765i | \(-0.173236\pi\) | ||||
0.855523 | + | 0.517765i | \(0.173236\pi\) | |||||||
\(840\) | 2.41906 | 0.0834655 | ||||||||
\(841\) | −28.7472 | −0.991282 | ||||||||
\(842\) | −54.4121 | −1.87517 | ||||||||
\(843\) | −13.2149 | −0.455145 | ||||||||
\(844\) | 80.2416 | 2.76203 | ||||||||
\(845\) | −2.79505 | −0.0961525 | ||||||||
\(846\) | −38.7405 | −1.33193 | ||||||||
\(847\) | 47.5894 | 1.63519 | ||||||||
\(848\) | 73.4742 | 2.52312 | ||||||||
\(849\) | 13.9753 | 0.479630 | ||||||||
\(850\) | 13.7177 | 0.470514 | ||||||||
\(851\) | 26.1155 | 0.895226 | ||||||||
\(852\) | −36.2466 | −1.24179 | ||||||||
\(853\) | −33.2986 | −1.14012 | −0.570061 | − | 0.821602i | \(-0.693081\pi\) | ||||
−0.570061 | + | 0.821602i | \(0.693081\pi\) | |||||||
\(854\) | −1.19457 | −0.0408775 | ||||||||
\(855\) | 3.99857 | 0.136748 | ||||||||
\(856\) | 9.84019 | 0.336331 | ||||||||
\(857\) | 9.25640 | 0.316192 | 0.158096 | − | 0.987424i | \(-0.449464\pi\) | ||||
0.158096 | + | 0.987424i | \(0.449464\pi\) | |||||||
\(858\) | 7.51676 | 0.256618 | ||||||||
\(859\) | 16.2887 | 0.555764 | 0.277882 | − | 0.960615i | \(-0.410368\pi\) | ||||
0.277882 | + | 0.960615i | \(0.410368\pi\) | |||||||
\(860\) | −2.29130 | −0.0781328 | ||||||||
\(861\) | −6.23170 | −0.212376 | ||||||||
\(862\) | 35.3188 | 1.20296 | ||||||||
\(863\) | −28.7258 | −0.977839 | −0.488919 | − | 0.872329i | \(-0.662609\pi\) | ||||
−0.488919 | + | 0.872329i | \(0.662609\pi\) | |||||||
\(864\) | −65.5802 | −2.23108 | ||||||||
\(865\) | −1.04428 | −0.0355065 | ||||||||
\(866\) | −82.8942 | −2.81686 | ||||||||
\(867\) | −0.417524 | −0.0141799 | ||||||||
\(868\) | 103.347 | 3.50784 | ||||||||
\(869\) | −28.5145 | −0.967289 | ||||||||
\(870\) | −0.139750 | −0.00473796 | ||||||||
\(871\) | −14.3635 | −0.486689 | ||||||||
\(872\) | 171.322 | 5.80171 | ||||||||
\(873\) | −42.7996 | −1.44855 | ||||||||
\(874\) | 106.612 | 3.60620 | ||||||||
\(875\) | −5.60450 | −0.189467 | ||||||||
\(876\) | 22.9408 | 0.775096 | ||||||||
\(877\) | −40.0300 | −1.35172 | −0.675858 | − | 0.737032i | \(-0.736227\pi\) | ||||
−0.675858 | + | 0.737032i | \(0.736227\pi\) | |||||||
\(878\) | −93.6593 | −3.16085 | ||||||||
\(879\) | 3.39193 | 0.114407 | ||||||||
\(880\) | 22.9546 | 0.773799 | ||||||||
\(881\) | −57.1257 | −1.92461 | −0.962307 | − | 0.271966i | \(-0.912326\pi\) | ||||
−0.962307 | + | 0.271966i | \(0.912326\pi\) | |||||||
\(882\) | −11.5787 | −0.389876 | ||||||||
\(883\) | −16.5703 | −0.557635 | −0.278818 | − | 0.960344i | \(-0.589943\pi\) | ||||
−0.278818 | + | 0.960344i | \(0.589943\pi\) | |||||||
\(884\) | 6.61788 | 0.222583 | ||||||||
\(885\) | −0.190154 | −0.00639196 | ||||||||
\(886\) | 41.3779 | 1.39012 | ||||||||
\(887\) | 8.19913 | 0.275300 | 0.137650 | − | 0.990481i | \(-0.456045\pi\) | ||||
0.137650 | + | 0.990481i | \(0.456045\pi\) | |||||||
\(888\) | 17.2142 | 0.577670 | ||||||||
\(889\) | −20.5544 | −0.689373 | ||||||||
\(890\) | −7.68758 | −0.257688 | ||||||||
\(891\) | 41.7099 | 1.39734 | ||||||||
\(892\) | 23.9892 | 0.803218 | ||||||||
\(893\) | 29.1446 | 0.975287 | ||||||||
\(894\) | 7.36387 | 0.246285 | ||||||||
\(895\) | 2.22924 | 0.0745154 | ||||||||
\(896\) | −138.035 | −4.61143 | ||||||||
\(897\) | −3.15422 | −0.105316 | ||||||||
\(898\) | −36.3450 | −1.21285 | ||||||||
\(899\) | −3.87672 | −0.129296 | ||||||||
\(900\) | 79.6508 | 2.65503 | ||||||||
\(901\) | 4.29153 | 0.142972 | ||||||||
\(902\) | −98.5296 | −3.28068 | ||||||||
\(903\) | 1.64370 | 0.0546988 | ||||||||
\(904\) | 92.9821 | 3.09254 | ||||||||
\(905\) | 5.81610 | 0.193334 | ||||||||
\(906\) | −17.2276 | −0.572349 | ||||||||
\(907\) | 19.0545 | 0.632694 | 0.316347 | − | 0.948643i | \(-0.397544\pi\) | ||||
0.316347 | + | 0.948643i | \(0.397544\pi\) | |||||||
\(908\) | 11.3629 | 0.377091 | ||||||||
\(909\) | −23.5384 | −0.780719 | ||||||||
\(910\) | −1.81541 | −0.0601802 | ||||||||
\(911\) | −12.4631 | −0.412920 | −0.206460 | − | 0.978455i | \(-0.566194\pi\) | ||||
−0.206460 | + | 0.978455i | \(0.566194\pi\) | |||||||
\(912\) | 42.1752 | 1.39656 | ||||||||
\(913\) | −6.59837 | −0.218374 | ||||||||
\(914\) | −90.5904 | −2.99646 | ||||||||
\(915\) | −0.0183390 | −0.000606270 0 | ||||||||
\(916\) | −149.141 | −4.92777 | ||||||||
\(917\) | 11.0615 | 0.365283 | ||||||||
\(918\) | −6.75096 | −0.222815 | ||||||||
\(919\) | 22.1311 | 0.730038 | 0.365019 | − | 0.931000i | \(-0.381063\pi\) | ||||
0.365019 | + | 0.931000i | \(0.381063\pi\) | |||||||
\(920\) | −16.0498 | −0.529146 | ||||||||
\(921\) | 12.1257 | 0.399554 | ||||||||
\(922\) | −47.5547 | −1.56613 | ||||||||
\(923\) | 17.6627 | 0.581374 | ||||||||
\(924\) | −31.2848 | −1.02919 | ||||||||
\(925\) | −19.8256 | −0.651862 | ||||||||
\(926\) | 16.2730 | 0.534762 | ||||||||
\(927\) | −20.9736 | −0.688864 | ||||||||
\(928\) | 13.5564 | 0.445012 | ||||||||
\(929\) | 49.6112 | 1.62769 | 0.813845 | − | 0.581082i | \(-0.197371\pi\) | ||||
0.813845 | + | 0.581082i | \(0.197371\pi\) | |||||||
\(930\) | 2.14296 | 0.0702704 | ||||||||
\(931\) | 8.71070 | 0.285482 | ||||||||
\(932\) | 77.7659 | 2.54731 | ||||||||
\(933\) | 8.31040 | 0.272070 | ||||||||
\(934\) | 55.2372 | 1.80742 | ||||||||
\(935\) | 1.34075 | 0.0438471 | ||||||||
\(936\) | 33.7007 | 1.10154 | ||||||||
\(937\) | 17.9491 | 0.586371 | 0.293185 | − | 0.956056i | \(-0.405285\pi\) | ||||
0.293185 | + | 0.956056i | \(0.405285\pi\) | |||||||
\(938\) | 80.7449 | 2.63641 | ||||||||
\(939\) | 4.84244 | 0.158027 | ||||||||
\(940\) | −6.75710 | −0.220392 | ||||||||
\(941\) | 18.2934 | 0.596349 | 0.298174 | − | 0.954511i | \(-0.403622\pi\) | ||||
0.298174 | + | 0.954511i | \(0.403622\pi\) | |||||||
\(942\) | 22.8383 | 0.744113 | ||||||||
\(943\) | 41.3455 | 1.34640 | ||||||||
\(944\) | 32.5099 | 1.05811 | ||||||||
\(945\) | 1.37110 | 0.0446020 | ||||||||
\(946\) | 25.9886 | 0.844961 | ||||||||
\(947\) | 51.1789 | 1.66309 | 0.831546 | − | 0.555456i | \(-0.187456\pi\) | ||||
0.831546 | + | 0.555456i | \(0.187456\pi\) | |||||||
\(948\) | 12.1466 | 0.394504 | ||||||||
\(949\) | −11.1788 | −0.362881 | ||||||||
\(950\) | −80.9346 | −2.62587 | ||||||||
\(951\) | 10.5833 | 0.343187 | ||||||||
\(952\) | −24.1565 | −0.782917 | ||||||||
\(953\) | 14.5224 | 0.470426 | 0.235213 | − | 0.971944i | \(-0.424421\pi\) | ||||
0.235213 | + | 0.971944i | \(0.424421\pi\) | |||||||
\(954\) | 33.6567 | 1.08968 | ||||||||
\(955\) | 2.20629 | 0.0713937 | ||||||||
\(956\) | −105.414 | −3.40933 | ||||||||
\(957\) | 1.17354 | 0.0379352 | ||||||||
\(958\) | −4.69290 | −0.151621 | ||||||||
\(959\) | −2.42520 | −0.0783139 | ||||||||
\(960\) | −4.06469 | −0.131187 | ||||||||
\(961\) | 28.4466 | 0.917633 | ||||||||
\(962\) | −12.9186 | −0.416511 | ||||||||
\(963\) | 2.70522 | 0.0871745 | ||||||||
\(964\) | 24.4255 | 0.786691 | ||||||||
\(965\) | 2.04638 | 0.0658753 | ||||||||
\(966\) | 17.7315 | 0.570503 | ||||||||
\(967\) | 23.1948 | 0.745893 | 0.372946 | − | 0.927853i | \(-0.378348\pi\) | ||||
0.372946 | + | 0.927853i | \(0.378348\pi\) | |||||||
\(968\) | −208.124 | −6.68934 | ||||||||
\(969\) | 2.46340 | 0.0791357 | ||||||||
\(970\) | −10.0829 | −0.323743 | ||||||||
\(971\) | 16.8217 | 0.539833 | 0.269916 | − | 0.962884i | \(-0.413004\pi\) | ||||
0.269916 | + | 0.962884i | \(0.413004\pi\) | |||||||
\(972\) | −59.3848 | −1.90477 | ||||||||
\(973\) | 12.0448 | 0.386139 | ||||||||
\(974\) | −13.9712 | −0.447667 | ||||||||
\(975\) | 2.39453 | 0.0766865 | ||||||||
\(976\) | 3.13535 | 0.100360 | ||||||||
\(977\) | −54.9587 | −1.75828 | −0.879142 | − | 0.476560i | \(-0.841884\pi\) | ||||
−0.879142 | + | 0.476560i | \(0.841884\pi\) | |||||||
\(978\) | 20.7131 | 0.662332 | ||||||||
\(979\) | 64.5562 | 2.06322 | ||||||||
\(980\) | −2.01955 | −0.0645123 | ||||||||
\(981\) | 47.0992 | 1.50376 | ||||||||
\(982\) | −104.931 | −3.34850 | ||||||||
\(983\) | 18.3612 | 0.585632 | 0.292816 | − | 0.956169i | \(-0.405408\pi\) | ||||
0.292816 | + | 0.956169i | \(0.405408\pi\) | |||||||
\(984\) | 27.2532 | 0.868800 | ||||||||
\(985\) | 0.0911733 | 0.00290502 | ||||||||
\(986\) | 1.39553 | 0.0444426 | ||||||||
\(987\) | 4.84729 | 0.154291 | ||||||||
\(988\) | −39.0455 | −1.24220 | ||||||||
\(989\) | −10.9055 | −0.346773 | ||||||||
\(990\) | 10.5149 | 0.334187 | ||||||||
\(991\) | −23.6819 | −0.752282 | −0.376141 | − | 0.926563i | \(-0.622749\pi\) | ||||
−0.376141 | + | 0.926563i | \(0.622749\pi\) | |||||||
\(992\) | −207.878 | −6.60013 | ||||||||
\(993\) | 6.38553 | 0.202639 | ||||||||
\(994\) | −99.2912 | −3.14932 | ||||||||
\(995\) | −0.332194 | −0.0105313 | ||||||||
\(996\) | 2.81077 | 0.0890628 | ||||||||
\(997\) | −18.6026 | −0.589149 | −0.294575 | − | 0.955628i | \(-0.595178\pi\) | ||||
−0.294575 | + | 0.955628i | \(0.595178\pi\) | |||||||
\(998\) | 29.7214 | 0.940816 | ||||||||
\(999\) | 9.75686 | 0.308693 |
(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 | 6001.2.a.d.1.1 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.d.1.1 | ✓ | 121 | 1.1 | even | 1 | trivial |