Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8011,2,Mod(1,8011)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8011, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8011.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8011.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: | \(63.9681570592\) |
Analytic rank: | \(0\) |
Dimension: | \(358\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8011.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67959 | −1.89475 | −0.947377 | − | 0.320119i | \(-0.896277\pi\) | ||||
−0.947377 | + | 0.320119i | \(0.896277\pi\) | |||||||
\(3\) | −1.76320 | −1.01798 | −0.508992 | − | 0.860771i | \(-0.669982\pi\) | ||||
−0.508992 | + | 0.860771i | \(0.669982\pi\) | |||||||
\(4\) | 5.18019 | 2.59009 | ||||||||
\(5\) | −3.93630 | −1.76037 | −0.880184 | − | 0.474633i | \(-0.842581\pi\) | ||||
−0.880184 | + | 0.474633i | \(0.842581\pi\) | |||||||
\(6\) | 4.72465 | 1.92883 | ||||||||
\(7\) | −2.55729 | −0.966563 | −0.483282 | − | 0.875465i | \(-0.660555\pi\) | ||||
−0.483282 | + | 0.875465i | \(0.660555\pi\) | |||||||
\(8\) | −8.52159 | −3.01284 | ||||||||
\(9\) | 0.108876 | 0.0362919 | ||||||||
\(10\) | 10.5477 | 3.33546 | ||||||||
\(11\) | 1.40777 | 0.424459 | 0.212230 | − | 0.977220i | \(-0.431928\pi\) | ||||
0.212230 | + | 0.977220i | \(0.431928\pi\) | |||||||
\(12\) | −9.13371 | −2.63667 | ||||||||
\(13\) | −2.73241 | −0.757835 | −0.378917 | − | 0.925430i | \(-0.623704\pi\) | ||||
−0.378917 | + | 0.925430i | \(0.623704\pi\) | |||||||
\(14\) | 6.85247 | 1.83140 | ||||||||
\(15\) | 6.94049 | 1.79203 | ||||||||
\(16\) | 12.4740 | 3.11849 | ||||||||
\(17\) | −1.27752 | −0.309844 | −0.154922 | − | 0.987927i | \(-0.549513\pi\) | ||||
−0.154922 | + | 0.987927i | \(0.549513\pi\) | |||||||
\(18\) | −0.291742 | −0.0687642 | ||||||||
\(19\) | −3.42030 | −0.784672 | −0.392336 | − | 0.919822i | \(-0.628333\pi\) | ||||
−0.392336 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(20\) | −20.3908 | −4.55952 | ||||||||
\(21\) | 4.50901 | 0.983946 | ||||||||
\(22\) | −3.77225 | −0.804246 | ||||||||
\(23\) | 5.50852 | 1.14861 | 0.574303 | − | 0.818643i | \(-0.305273\pi\) | ||||
0.574303 | + | 0.818643i | \(0.305273\pi\) | |||||||
\(24\) | 15.0253 | 3.06702 | ||||||||
\(25\) | 10.4945 | 2.09889 | ||||||||
\(26\) | 7.32174 | 1.43591 | ||||||||
\(27\) | 5.09763 | 0.981040 | ||||||||
\(28\) | −13.2472 | −2.50349 | ||||||||
\(29\) | 4.57184 | 0.848970 | 0.424485 | − | 0.905435i | \(-0.360455\pi\) | ||||
0.424485 | + | 0.905435i | \(0.360455\pi\) | |||||||
\(30\) | −18.5976 | −3.39545 | ||||||||
\(31\) | −6.23935 | −1.12062 | −0.560310 | − | 0.828283i | \(-0.689318\pi\) | ||||
−0.560310 | + | 0.828283i | \(0.689318\pi\) | |||||||
\(32\) | −16.3819 | −2.89594 | ||||||||
\(33\) | −2.48218 | −0.432093 | ||||||||
\(34\) | 3.42322 | 0.587078 | ||||||||
\(35\) | 10.0662 | 1.70151 | ||||||||
\(36\) | 0.563996 | 0.0939993 | ||||||||
\(37\) | −3.97944 | −0.654215 | −0.327108 | − | 0.944987i | \(-0.606074\pi\) | ||||
−0.327108 | + | 0.944987i | \(0.606074\pi\) | |||||||
\(38\) | 9.16500 | 1.48676 | ||||||||
\(39\) | 4.81779 | 0.771464 | ||||||||
\(40\) | 33.5435 | 5.30370 | ||||||||
\(41\) | 9.88896 | 1.54440 | 0.772198 | − | 0.635382i | \(-0.219157\pi\) | ||||
0.772198 | + | 0.635382i | \(0.219157\pi\) | |||||||
\(42\) | −12.0823 | −1.86434 | ||||||||
\(43\) | 0.0738129 | 0.0112564 | 0.00562818 | − | 0.999984i | \(-0.498208\pi\) | ||||
0.00562818 | + | 0.999984i | \(0.498208\pi\) | |||||||
\(44\) | 7.29252 | 1.09939 | ||||||||
\(45\) | −0.428567 | −0.0638870 | ||||||||
\(46\) | −14.7606 | −2.17633 | ||||||||
\(47\) | −3.58950 | −0.523583 | −0.261791 | − | 0.965125i | \(-0.584313\pi\) | ||||
−0.261791 | + | 0.965125i | \(0.584313\pi\) | |||||||
\(48\) | −21.9941 | −3.17458 | ||||||||
\(49\) | −0.460288 | −0.0657554 | ||||||||
\(50\) | −28.1208 | −3.97689 | ||||||||
\(51\) | 2.25252 | 0.315416 | ||||||||
\(52\) | −14.1544 | −1.96286 | ||||||||
\(53\) | −0.0891657 | −0.0122479 | −0.00612393 | − | 0.999981i | \(-0.501949\pi\) | ||||
−0.00612393 | + | 0.999981i | \(0.501949\pi\) | |||||||
\(54\) | −13.6595 | −1.85883 | ||||||||
\(55\) | −5.54141 | −0.747204 | ||||||||
\(56\) | 21.7921 | 2.91210 | ||||||||
\(57\) | 6.03068 | 0.798783 | ||||||||
\(58\) | −12.2507 | −1.60859 | ||||||||
\(59\) | −0.736911 | −0.0959376 | −0.0479688 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479688 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(60\) | 35.9530 | 4.64152 | ||||||||
\(61\) | 12.7896 | 1.63754 | 0.818770 | − | 0.574122i | \(-0.194657\pi\) | ||||
0.818770 | + | 0.574122i | \(0.194657\pi\) | |||||||
\(62\) | 16.7189 | 2.12330 | ||||||||
\(63\) | −0.278426 | −0.0350784 | ||||||||
\(64\) | 18.9488 | 2.36860 | ||||||||
\(65\) | 10.7556 | 1.33407 | ||||||||
\(66\) | 6.65123 | 0.818710 | ||||||||
\(67\) | −0.110608 | −0.0135129 | −0.00675646 | − | 0.999977i | \(-0.502151\pi\) | ||||
−0.00675646 | + | 0.999977i | \(0.502151\pi\) | |||||||
\(68\) | −6.61778 | −0.802524 | ||||||||
\(69\) | −9.71263 | −1.16926 | ||||||||
\(70\) | −26.9734 | −3.22394 | ||||||||
\(71\) | −10.3081 | −1.22334 | −0.611672 | − | 0.791111i | \(-0.709503\pi\) | ||||
−0.611672 | + | 0.791111i | \(0.709503\pi\) | |||||||
\(72\) | −0.927793 | −0.109341 | ||||||||
\(73\) | −5.98043 | −0.699956 | −0.349978 | − | 0.936758i | \(-0.613811\pi\) | ||||
−0.349978 | + | 0.936758i | \(0.613811\pi\) | |||||||
\(74\) | 10.6632 | 1.23958 | ||||||||
\(75\) | −18.5038 | −2.13664 | ||||||||
\(76\) | −17.7178 | −2.03237 | ||||||||
\(77\) | −3.60008 | −0.410267 | ||||||||
\(78\) | −12.9097 | −1.46173 | ||||||||
\(79\) | −1.36862 | −0.153982 | −0.0769911 | − | 0.997032i | \(-0.524531\pi\) | ||||
−0.0769911 | + | 0.997032i | \(0.524531\pi\) | |||||||
\(80\) | −49.1013 | −5.48969 | ||||||||
\(81\) | −9.31477 | −1.03497 | ||||||||
\(82\) | −26.4983 | −2.92625 | ||||||||
\(83\) | −2.90034 | −0.318353 | −0.159177 | − | 0.987250i | \(-0.550884\pi\) | ||||
−0.159177 | + | 0.987250i | \(0.550884\pi\) | |||||||
\(84\) | 23.3575 | 2.54851 | ||||||||
\(85\) | 5.02870 | 0.545439 | ||||||||
\(86\) | −0.197788 | −0.0213280 | ||||||||
\(87\) | −8.06108 | −0.864238 | ||||||||
\(88\) | −11.9965 | −1.27883 | ||||||||
\(89\) | 18.5008 | 1.96108 | 0.980541 | − | 0.196317i | \(-0.0628981\pi\) | ||||
0.980541 | + | 0.196317i | \(0.0628981\pi\) | |||||||
\(90\) | 1.14838 | 0.121050 | ||||||||
\(91\) | 6.98756 | 0.732495 | ||||||||
\(92\) | 28.5352 | 2.97500 | ||||||||
\(93\) | 11.0012 | 1.14077 | ||||||||
\(94\) | 9.61838 | 0.992061 | ||||||||
\(95\) | 13.4633 | 1.38131 | ||||||||
\(96\) | 28.8846 | 2.94802 | ||||||||
\(97\) | −13.4129 | −1.36187 | −0.680936 | − | 0.732343i | \(-0.738427\pi\) | ||||
−0.680936 | + | 0.732343i | \(0.738427\pi\) | |||||||
\(98\) | 1.23338 | 0.124590 | ||||||||
\(99\) | 0.153272 | 0.0154044 | ||||||||
\(100\) | 54.3633 | 5.43633 | ||||||||
\(101\) | −0.619098 | −0.0616025 | −0.0308013 | − | 0.999526i | \(-0.509806\pi\) | ||||
−0.0308013 | + | 0.999526i | \(0.509806\pi\) | |||||||
\(102\) | −6.03583 | −0.597636 | ||||||||
\(103\) | −5.13500 | −0.505967 | −0.252983 | − | 0.967471i | \(-0.581412\pi\) | ||||
−0.252983 | + | 0.967471i | \(0.581412\pi\) | |||||||
\(104\) | 23.2845 | 2.28323 | ||||||||
\(105\) | −17.7488 | −1.73211 | ||||||||
\(106\) | 0.238927 | 0.0232067 | ||||||||
\(107\) | −3.57501 | −0.345609 | −0.172805 | − | 0.984956i | \(-0.555283\pi\) | ||||
−0.172805 | + | 0.984956i | \(0.555283\pi\) | |||||||
\(108\) | 26.4067 | 2.54099 | ||||||||
\(109\) | −2.41004 | −0.230840 | −0.115420 | − | 0.993317i | \(-0.536821\pi\) | ||||
−0.115420 | + | 0.993317i | \(0.536821\pi\) | |||||||
\(110\) | 14.8487 | 1.41577 | ||||||||
\(111\) | 7.01654 | 0.665981 | ||||||||
\(112\) | −31.8995 | −3.01422 | ||||||||
\(113\) | −14.3872 | −1.35343 | −0.676716 | − | 0.736244i | \(-0.736598\pi\) | ||||
−0.676716 | + | 0.736244i | \(0.736598\pi\) | |||||||
\(114\) | −16.1597 | −1.51350 | ||||||||
\(115\) | −21.6832 | −2.02197 | ||||||||
\(116\) | 23.6830 | 2.19891 | ||||||||
\(117\) | −0.297493 | −0.0275032 | ||||||||
\(118\) | 1.97462 | 0.181778 | ||||||||
\(119\) | 3.26698 | 0.299483 | ||||||||
\(120\) | −59.1440 | −5.39908 | ||||||||
\(121\) | −9.01818 | −0.819834 | ||||||||
\(122\) | −34.2708 | −3.10273 | ||||||||
\(123\) | −17.4362 | −1.57217 | ||||||||
\(124\) | −32.3210 | −2.90251 | ||||||||
\(125\) | −21.6279 | −1.93445 | ||||||||
\(126\) | 0.746067 | 0.0664649 | ||||||||
\(127\) | 8.49452 | 0.753767 | 0.376883 | − | 0.926261i | \(-0.376996\pi\) | ||||
0.376883 | + | 0.926261i | \(0.376996\pi\) | |||||||
\(128\) | −18.0112 | −1.59198 | ||||||||
\(129\) | −0.130147 | −0.0114588 | ||||||||
\(130\) | −28.8206 | −2.52773 | ||||||||
\(131\) | 4.17126 | 0.364445 | 0.182222 | − | 0.983257i | \(-0.441671\pi\) | ||||
0.182222 | + | 0.983257i | \(0.441671\pi\) | |||||||
\(132\) | −12.8582 | −1.11916 | ||||||||
\(133\) | 8.74670 | 0.758435 | ||||||||
\(134\) | 0.296384 | 0.0256037 | ||||||||
\(135\) | −20.0658 | −1.72699 | ||||||||
\(136\) | 10.8865 | 0.933509 | ||||||||
\(137\) | 3.18442 | 0.272064 | 0.136032 | − | 0.990704i | \(-0.456565\pi\) | ||||
0.136032 | + | 0.990704i | \(0.456565\pi\) | |||||||
\(138\) | 26.0258 | 2.21547 | ||||||||
\(139\) | −22.1332 | −1.87731 | −0.938656 | − | 0.344856i | \(-0.887928\pi\) | ||||
−0.938656 | + | 0.344856i | \(0.887928\pi\) | |||||||
\(140\) | 52.1451 | 4.40706 | ||||||||
\(141\) | 6.32901 | 0.532999 | ||||||||
\(142\) | 27.6214 | 2.31794 | ||||||||
\(143\) | −3.84661 | −0.321670 | ||||||||
\(144\) | 1.35811 | 0.113176 | ||||||||
\(145\) | −17.9961 | −1.49450 | ||||||||
\(146\) | 16.0251 | 1.32624 | ||||||||
\(147\) | 0.811579 | 0.0669379 | ||||||||
\(148\) | −20.6142 | −1.69448 | ||||||||
\(149\) | 0.910743 | 0.0746110 | 0.0373055 | − | 0.999304i | \(-0.488123\pi\) | ||||
0.0373055 | + | 0.999304i | \(0.488123\pi\) | |||||||
\(150\) | 49.5827 | 4.04841 | ||||||||
\(151\) | 3.94541 | 0.321073 | 0.160536 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160536 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(152\) | 29.1464 | 2.36409 | ||||||||
\(153\) | −0.139091 | −0.0112448 | ||||||||
\(154\) | 9.64672 | 0.777355 | ||||||||
\(155\) | 24.5599 | 1.97270 | ||||||||
\(156\) | 24.9571 | 1.99816 | ||||||||
\(157\) | −16.8836 | −1.34746 | −0.673729 | − | 0.738979i | \(-0.735308\pi\) | ||||
−0.673729 | + | 0.738979i | \(0.735308\pi\) | |||||||
\(158\) | 3.66735 | 0.291759 | ||||||||
\(159\) | 0.157217 | 0.0124681 | ||||||||
\(160\) | 64.4842 | 5.09792 | ||||||||
\(161\) | −14.0869 | −1.11020 | ||||||||
\(162\) | 24.9597 | 1.96102 | ||||||||
\(163\) | 6.60610 | 0.517430 | 0.258715 | − | 0.965954i | \(-0.416701\pi\) | ||||
0.258715 | + | 0.965954i | \(0.416701\pi\) | |||||||
\(164\) | 51.2267 | 4.00013 | ||||||||
\(165\) | 9.77062 | 0.760642 | ||||||||
\(166\) | 7.77170 | 0.603201 | ||||||||
\(167\) | −5.52442 | −0.427493 | −0.213746 | − | 0.976889i | \(-0.568567\pi\) | ||||
−0.213746 | + | 0.976889i | \(0.568567\pi\) | |||||||
\(168\) | −38.4239 | −2.96447 | ||||||||
\(169\) | −5.53392 | −0.425686 | ||||||||
\(170\) | −13.4748 | −1.03347 | ||||||||
\(171\) | −0.372388 | −0.0284772 | ||||||||
\(172\) | 0.382365 | 0.0291550 | ||||||||
\(173\) | −22.9879 | −1.74774 | −0.873868 | − | 0.486163i | \(-0.838396\pi\) | ||||
−0.873868 | + | 0.486163i | \(0.838396\pi\) | |||||||
\(174\) | 21.6004 | 1.63752 | ||||||||
\(175\) | −26.8373 | −2.02871 | ||||||||
\(176\) | 17.5605 | 1.32367 | ||||||||
\(177\) | 1.29932 | 0.0976630 | ||||||||
\(178\) | −49.5745 | −3.71577 | ||||||||
\(179\) | −4.90666 | −0.366741 | −0.183371 | − | 0.983044i | \(-0.558701\pi\) | ||||
−0.183371 | + | 0.983044i | \(0.558701\pi\) | |||||||
\(180\) | −2.22006 | −0.165473 | ||||||||
\(181\) | 19.4443 | 1.44528 | 0.722642 | − | 0.691223i | \(-0.242928\pi\) | ||||
0.722642 | + | 0.691223i | \(0.242928\pi\) | |||||||
\(182\) | −18.7238 | −1.38790 | ||||||||
\(183\) | −22.5506 | −1.66699 | ||||||||
\(184\) | −46.9414 | −3.46057 | ||||||||
\(185\) | 15.6643 | 1.15166 | ||||||||
\(186\) | −29.4787 | −2.16149 | ||||||||
\(187\) | −1.79845 | −0.131516 | ||||||||
\(188\) | −18.5943 | −1.35613 | ||||||||
\(189\) | −13.0361 | −0.948237 | ||||||||
\(190\) | −36.0762 | −2.61724 | ||||||||
\(191\) | 11.9773 | 0.866643 | 0.433322 | − | 0.901239i | \(-0.357341\pi\) | ||||
0.433322 | + | 0.901239i | \(0.357341\pi\) | |||||||
\(192\) | −33.4106 | −2.41120 | ||||||||
\(193\) | −14.5795 | −1.04946 | −0.524728 | − | 0.851270i | \(-0.675833\pi\) | ||||
−0.524728 | + | 0.851270i | \(0.675833\pi\) | |||||||
\(194\) | 35.9410 | 2.58041 | ||||||||
\(195\) | −18.9643 | −1.35806 | ||||||||
\(196\) | −2.38438 | −0.170313 | ||||||||
\(197\) | −5.12730 | −0.365305 | −0.182653 | − | 0.983178i | \(-0.558468\pi\) | ||||
−0.182653 | + | 0.983178i | \(0.558468\pi\) | |||||||
\(198\) | −0.410706 | −0.0291876 | ||||||||
\(199\) | 17.9179 | 1.27016 | 0.635082 | − | 0.772445i | \(-0.280966\pi\) | ||||
0.635082 | + | 0.772445i | \(0.280966\pi\) | |||||||
\(200\) | −89.4295 | −6.32362 | ||||||||
\(201\) | 0.195024 | 0.0137559 | ||||||||
\(202\) | 1.65893 | 0.116722 | ||||||||
\(203\) | −11.6915 | −0.820583 | ||||||||
\(204\) | 11.6685 | 0.816957 | ||||||||
\(205\) | −38.9259 | −2.71870 | ||||||||
\(206\) | 13.7597 | 0.958683 | ||||||||
\(207\) | 0.599744 | 0.0416851 | ||||||||
\(208\) | −34.0840 | −2.36330 | ||||||||
\(209\) | −4.81501 | −0.333061 | ||||||||
\(210\) | 47.5595 | 3.28192 | ||||||||
\(211\) | 3.05004 | 0.209974 | 0.104987 | − | 0.994474i | \(-0.466520\pi\) | ||||
0.104987 | + | 0.994474i | \(0.466520\pi\) | |||||||
\(212\) | −0.461895 | −0.0317231 | ||||||||
\(213\) | 18.1752 | 1.24535 | ||||||||
\(214\) | 9.57955 | 0.654845 | ||||||||
\(215\) | −0.290550 | −0.0198153 | ||||||||
\(216\) | −43.4399 | −2.95571 | ||||||||
\(217\) | 15.9558 | 1.08315 | ||||||||
\(218\) | 6.45790 | 0.437384 | ||||||||
\(219\) | 10.5447 | 0.712544 | ||||||||
\(220\) | −28.7056 | −1.93533 | ||||||||
\(221\) | 3.49071 | 0.234810 | ||||||||
\(222\) | −18.8014 | −1.26187 | ||||||||
\(223\) | −15.8701 | −1.06274 | −0.531370 | − | 0.847140i | \(-0.678323\pi\) | ||||
−0.531370 | + | 0.847140i | \(0.678323\pi\) | |||||||
\(224\) | 41.8933 | 2.79911 | ||||||||
\(225\) | 1.14259 | 0.0761727 | ||||||||
\(226\) | 38.5517 | 2.56442 | ||||||||
\(227\) | 3.30990 | 0.219686 | 0.109843 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109843 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(228\) | 31.2401 | 2.06892 | ||||||||
\(229\) | 17.7221 | 1.17111 | 0.585554 | − | 0.810634i | \(-0.300877\pi\) | ||||
0.585554 | + | 0.810634i | \(0.300877\pi\) | |||||||
\(230\) | 58.1020 | 3.83114 | ||||||||
\(231\) | 6.34765 | 0.417645 | ||||||||
\(232\) | −38.9594 | −2.55781 | ||||||||
\(233\) | 14.4415 | 0.946096 | 0.473048 | − | 0.881037i | \(-0.343154\pi\) | ||||
0.473048 | + | 0.881037i | \(0.343154\pi\) | |||||||
\(234\) | 0.797158 | 0.0521119 | ||||||||
\(235\) | 14.1294 | 0.921698 | ||||||||
\(236\) | −3.81734 | −0.248487 | ||||||||
\(237\) | 2.41316 | 0.156751 | ||||||||
\(238\) | −8.75416 | −0.567448 | ||||||||
\(239\) | −11.9333 | −0.771898 | −0.385949 | − | 0.922520i | \(-0.626126\pi\) | ||||
−0.385949 | + | 0.922520i | \(0.626126\pi\) | |||||||
\(240\) | 86.5754 | 5.58842 | ||||||||
\(241\) | −5.94809 | −0.383150 | −0.191575 | − | 0.981478i | \(-0.561360\pi\) | ||||
−0.191575 | + | 0.981478i | \(0.561360\pi\) | |||||||
\(242\) | 24.1650 | 1.55338 | ||||||||
\(243\) | 1.13092 | 0.0725483 | ||||||||
\(244\) | 66.2525 | 4.24138 | ||||||||
\(245\) | 1.81183 | 0.115754 | ||||||||
\(246\) | 46.7219 | 2.97888 | ||||||||
\(247\) | 9.34568 | 0.594652 | ||||||||
\(248\) | 53.1692 | 3.37625 | ||||||||
\(249\) | 5.11387 | 0.324078 | ||||||||
\(250\) | 57.9537 | 3.66531 | ||||||||
\(251\) | −9.09108 | −0.573824 | −0.286912 | − | 0.957957i | \(-0.592629\pi\) | ||||
−0.286912 | + | 0.957957i | \(0.592629\pi\) | |||||||
\(252\) | −1.44230 | −0.0908563 | ||||||||
\(253\) | 7.75474 | 0.487537 | ||||||||
\(254\) | −22.7618 | −1.42820 | ||||||||
\(255\) | −8.86660 | −0.555248 | ||||||||
\(256\) | 10.3650 | 0.647810 | ||||||||
\(257\) | 7.43202 | 0.463597 | 0.231798 | − | 0.972764i | \(-0.425539\pi\) | ||||
0.231798 | + | 0.972764i | \(0.425539\pi\) | |||||||
\(258\) | 0.348740 | 0.0217116 | ||||||||
\(259\) | 10.1766 | 0.632341 | ||||||||
\(260\) | 55.7160 | 3.45536 | ||||||||
\(261\) | 0.497762 | 0.0308107 | ||||||||
\(262\) | −11.1773 | −0.690533 | ||||||||
\(263\) | 31.0762 | 1.91624 | 0.958121 | − | 0.286365i | \(-0.0924470\pi\) | ||||
0.958121 | + | 0.286365i | \(0.0924470\pi\) | |||||||
\(264\) | 21.1522 | 1.30183 | ||||||||
\(265\) | 0.350983 | 0.0215607 | ||||||||
\(266\) | −23.4375 | −1.43705 | ||||||||
\(267\) | −32.6206 | −1.99635 | ||||||||
\(268\) | −0.572970 | −0.0349997 | ||||||||
\(269\) | −3.47735 | −0.212018 | −0.106009 | − | 0.994365i | \(-0.533807\pi\) | ||||
−0.106009 | + | 0.994365i | \(0.533807\pi\) | |||||||
\(270\) | 53.7681 | 3.27222 | ||||||||
\(271\) | −13.6748 | −0.830683 | −0.415342 | − | 0.909665i | \(-0.636338\pi\) | ||||
−0.415342 | + | 0.909665i | \(0.636338\pi\) | |||||||
\(272\) | −15.9357 | −0.966245 | ||||||||
\(273\) | −12.3205 | −0.745669 | ||||||||
\(274\) | −8.53294 | −0.515494 | ||||||||
\(275\) | 14.7738 | 0.890894 | ||||||||
\(276\) | −50.3133 | −3.02850 | ||||||||
\(277\) | −10.8085 | −0.649419 | −0.324709 | − | 0.945814i | \(-0.605267\pi\) | ||||
−0.324709 | + | 0.945814i | \(0.605267\pi\) | |||||||
\(278\) | 59.3078 | 3.55704 | ||||||||
\(279\) | −0.679313 | −0.0406694 | ||||||||
\(280\) | −85.7804 | −5.12636 | ||||||||
\(281\) | −11.1885 | −0.667449 | −0.333724 | − | 0.942671i | \(-0.608305\pi\) | ||||
−0.333724 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(282\) | −16.9591 | −1.00990 | ||||||||
\(283\) | −26.1812 | −1.55631 | −0.778156 | − | 0.628071i | \(-0.783845\pi\) | ||||
−0.778156 | + | 0.628071i | \(0.783845\pi\) | |||||||
\(284\) | −53.3978 | −3.16858 | ||||||||
\(285\) | −23.7386 | −1.40615 | ||||||||
\(286\) | 10.3073 | 0.609486 | ||||||||
\(287\) | −25.2889 | −1.49276 | ||||||||
\(288\) | −1.78359 | −0.105099 | ||||||||
\(289\) | −15.3679 | −0.903997 | ||||||||
\(290\) | 48.2223 | 2.83171 | ||||||||
\(291\) | 23.6496 | 1.38636 | ||||||||
\(292\) | −30.9797 | −1.81295 | ||||||||
\(293\) | −4.87985 | −0.285084 | −0.142542 | − | 0.989789i | \(-0.545528\pi\) | ||||
−0.142542 | + | 0.989789i | \(0.545528\pi\) | |||||||
\(294\) | −2.17470 | −0.126831 | ||||||||
\(295\) | 2.90070 | 0.168885 | ||||||||
\(296\) | 33.9111 | 1.97104 | ||||||||
\(297\) | 7.17630 | 0.416411 | ||||||||
\(298\) | −2.44042 | −0.141370 | ||||||||
\(299\) | −15.0516 | −0.870454 | ||||||||
\(300\) | −95.8534 | −5.53410 | ||||||||
\(301\) | −0.188761 | −0.0108800 | ||||||||
\(302\) | −10.5721 | −0.608354 | ||||||||
\(303\) | 1.09159 | 0.0627104 | ||||||||
\(304\) | −42.6648 | −2.44699 | ||||||||
\(305\) | −50.3437 | −2.88267 | ||||||||
\(306\) | 0.372705 | 0.0213061 | ||||||||
\(307\) | 14.8391 | 0.846914 | 0.423457 | − | 0.905916i | \(-0.360817\pi\) | ||||
0.423457 | + | 0.905916i | \(0.360817\pi\) | |||||||
\(308\) | −18.6491 | −1.06263 | ||||||||
\(309\) | 9.05404 | 0.515066 | ||||||||
\(310\) | −65.8105 | −3.73779 | ||||||||
\(311\) | −3.82519 | −0.216907 | −0.108453 | − | 0.994102i | \(-0.534590\pi\) | ||||
−0.108453 | + | 0.994102i | \(0.534590\pi\) | |||||||
\(312\) | −41.0553 | −2.32430 | ||||||||
\(313\) | 14.6682 | 0.829094 | 0.414547 | − | 0.910028i | \(-0.363940\pi\) | ||||
0.414547 | + | 0.910028i | \(0.363940\pi\) | |||||||
\(314\) | 45.2411 | 2.55310 | ||||||||
\(315\) | 1.09597 | 0.0617508 | ||||||||
\(316\) | −7.08973 | −0.398829 | ||||||||
\(317\) | 30.7893 | 1.72930 | 0.864649 | − | 0.502377i | \(-0.167541\pi\) | ||||
0.864649 | + | 0.502377i | \(0.167541\pi\) | |||||||
\(318\) | −0.421277 | −0.0236240 | ||||||||
\(319\) | 6.43611 | 0.360353 | ||||||||
\(320\) | −74.5883 | −4.16961 | ||||||||
\(321\) | 6.30346 | 0.351825 | ||||||||
\(322\) | 37.7470 | 2.10356 | ||||||||
\(323\) | 4.36950 | 0.243125 | ||||||||
\(324\) | −48.2523 | −2.68068 | ||||||||
\(325\) | −28.6752 | −1.59061 | ||||||||
\(326\) | −17.7016 | −0.980402 | ||||||||
\(327\) | 4.24938 | 0.234991 | ||||||||
\(328\) | −84.2697 | −4.65301 | ||||||||
\(329\) | 9.17938 | 0.506076 | ||||||||
\(330\) | −26.1812 | −1.44123 | ||||||||
\(331\) | −21.9532 | −1.20666 | −0.603329 | − | 0.797492i | \(-0.706159\pi\) | ||||
−0.603329 | + | 0.797492i | \(0.706159\pi\) | |||||||
\(332\) | −15.0243 | −0.824565 | ||||||||
\(333\) | −0.433263 | −0.0237427 | ||||||||
\(334\) | 14.8032 | 0.809994 | ||||||||
\(335\) | 0.435386 | 0.0237877 | ||||||||
\(336\) | 56.2452 | 3.06843 | ||||||||
\(337\) | −27.1026 | −1.47637 | −0.738185 | − | 0.674598i | \(-0.764317\pi\) | ||||
−0.738185 | + | 0.674598i | \(0.764317\pi\) | |||||||
\(338\) | 14.8286 | 0.806571 | ||||||||
\(339\) | 25.3675 | 1.37777 | ||||||||
\(340\) | 26.0496 | 1.41274 | ||||||||
\(341\) | −8.78358 | −0.475657 | ||||||||
\(342\) | 0.997845 | 0.0539573 | ||||||||
\(343\) | 19.0781 | 1.03012 | ||||||||
\(344\) | −0.629003 | −0.0339136 | ||||||||
\(345\) | 38.2318 | 2.05833 | ||||||||
\(346\) | 61.5980 | 3.31153 | ||||||||
\(347\) | −16.9744 | −0.911236 | −0.455618 | − | 0.890175i | \(-0.650582\pi\) | ||||
−0.455618 | + | 0.890175i | \(0.650582\pi\) | |||||||
\(348\) | −41.7579 | −2.23846 | ||||||||
\(349\) | −28.2467 | −1.51201 | −0.756005 | − | 0.654565i | \(-0.772852\pi\) | ||||
−0.756005 | + | 0.654565i | \(0.772852\pi\) | |||||||
\(350\) | 71.9130 | 3.84391 | ||||||||
\(351\) | −13.9288 | −0.743466 | ||||||||
\(352\) | −23.0620 | −1.22921 | ||||||||
\(353\) | −16.2422 | −0.864486 | −0.432243 | − | 0.901757i | \(-0.642278\pi\) | ||||
−0.432243 | + | 0.901757i | \(0.642278\pi\) | |||||||
\(354\) | −3.48165 | −0.185047 | ||||||||
\(355\) | 40.5757 | 2.15353 | ||||||||
\(356\) | 95.8376 | 5.07938 | ||||||||
\(357\) | −5.76034 | −0.304869 | ||||||||
\(358\) | 13.1478 | 0.694884 | ||||||||
\(359\) | −31.8933 | −1.68326 | −0.841631 | − | 0.540053i | \(-0.818404\pi\) | ||||
−0.841631 | + | 0.540053i | \(0.818404\pi\) | |||||||
\(360\) | 3.65207 | 0.192481 | ||||||||
\(361\) | −7.30152 | −0.384291 | ||||||||
\(362\) | −52.1027 | −2.73846 | ||||||||
\(363\) | 15.9009 | 0.834578 | ||||||||
\(364\) | 36.1969 | 1.89723 | ||||||||
\(365\) | 23.5408 | 1.23218 | ||||||||
\(366\) | 60.4263 | 3.15853 | ||||||||
\(367\) | −1.84572 | −0.0963458 | −0.0481729 | − | 0.998839i | \(-0.515340\pi\) | ||||
−0.0481729 | + | 0.998839i | \(0.515340\pi\) | |||||||
\(368\) | 68.7132 | 3.58192 | ||||||||
\(369\) | 1.07667 | 0.0560490 | ||||||||
\(370\) | −41.9737 | −2.18211 | ||||||||
\(371\) | 0.228022 | 0.0118383 | ||||||||
\(372\) | 56.9884 | 2.95471 | ||||||||
\(373\) | 6.89626 | 0.357075 | 0.178537 | − | 0.983933i | \(-0.442863\pi\) | ||||
0.178537 | + | 0.983933i | \(0.442863\pi\) | |||||||
\(374\) | 4.81911 | 0.249190 | ||||||||
\(375\) | 38.1342 | 1.96924 | ||||||||
\(376\) | 30.5883 | 1.57747 | ||||||||
\(377\) | −12.4922 | −0.643379 | ||||||||
\(378\) | 34.9314 | 1.79668 | ||||||||
\(379\) | −13.2930 | −0.682817 | −0.341408 | − | 0.939915i | \(-0.610904\pi\) | ||||
−0.341408 | + | 0.939915i | \(0.610904\pi\) | |||||||
\(380\) | 69.7427 | 3.57772 | ||||||||
\(381\) | −14.9775 | −0.767323 | ||||||||
\(382\) | −32.0941 | −1.64208 | ||||||||
\(383\) | −3.78187 | −0.193245 | −0.0966223 | − | 0.995321i | \(-0.530804\pi\) | ||||
−0.0966223 | + | 0.995321i | \(0.530804\pi\) | |||||||
\(384\) | 31.7574 | 1.62061 | ||||||||
\(385\) | 14.1710 | 0.722220 | ||||||||
\(386\) | 39.0671 | 1.98846 | ||||||||
\(387\) | 0.00803642 | 0.000408514 0 | ||||||||
\(388\) | −69.4813 | −3.52738 | ||||||||
\(389\) | −6.19540 | −0.314119 | −0.157060 | − | 0.987589i | \(-0.550202\pi\) | ||||
−0.157060 | + | 0.987589i | \(0.550202\pi\) | |||||||
\(390\) | 50.8164 | 2.57319 | ||||||||
\(391\) | −7.03724 | −0.355888 | ||||||||
\(392\) | 3.92238 | 0.198110 | ||||||||
\(393\) | −7.35477 | −0.370999 | ||||||||
\(394\) | 13.7391 | 0.692164 | ||||||||
\(395\) | 5.38732 | 0.271065 | ||||||||
\(396\) | 0.793978 | 0.0398989 | ||||||||
\(397\) | −1.44165 | −0.0723543 | −0.0361771 | − | 0.999345i | \(-0.511518\pi\) | ||||
−0.0361771 | + | 0.999345i | \(0.511518\pi\) | |||||||
\(398\) | −48.0125 | −2.40665 | ||||||||
\(399\) | −15.4222 | −0.772075 | ||||||||
\(400\) | 130.908 | 6.54538 | ||||||||
\(401\) | 15.7940 | 0.788716 | 0.394358 | − | 0.918957i | \(-0.370967\pi\) | ||||
0.394358 | + | 0.918957i | \(0.370967\pi\) | |||||||
\(402\) | −0.522584 | −0.0260641 | ||||||||
\(403\) | 17.0485 | 0.849245 | ||||||||
\(404\) | −3.20704 | −0.159556 | ||||||||
\(405\) | 36.6657 | 1.82194 | ||||||||
\(406\) | 31.3284 | 1.55480 | ||||||||
\(407\) | −5.60214 | −0.277688 | ||||||||
\(408\) | −19.1951 | −0.950297 | ||||||||
\(409\) | −0.0784059 | −0.00387692 | −0.00193846 | − | 0.999998i | \(-0.500617\pi\) | ||||
−0.00193846 | + | 0.999998i | \(0.500617\pi\) | |||||||
\(410\) | 104.305 | 5.15128 | ||||||||
\(411\) | −5.61478 | −0.276957 | ||||||||
\(412\) | −26.6003 | −1.31050 | ||||||||
\(413\) | 1.88449 | 0.0927298 | ||||||||
\(414\) | −1.60707 | −0.0789830 | ||||||||
\(415\) | 11.4166 | 0.560418 | ||||||||
\(416\) | 44.7622 | 2.19465 | ||||||||
\(417\) | 39.0252 | 1.91107 | ||||||||
\(418\) | 12.9022 | 0.631069 | ||||||||
\(419\) | −10.3094 | −0.503648 | −0.251824 | − | 0.967773i | \(-0.581030\pi\) | ||||
−0.251824 | + | 0.967773i | \(0.581030\pi\) | |||||||
\(420\) | −91.9422 | −4.48632 | ||||||||
\(421\) | 10.5306 | 0.513228 | 0.256614 | − | 0.966514i | \(-0.417393\pi\) | ||||
0.256614 | + | 0.966514i | \(0.417393\pi\) | |||||||
\(422\) | −8.17285 | −0.397848 | ||||||||
\(423\) | −0.390809 | −0.0190018 | ||||||||
\(424\) | 0.759834 | 0.0369008 | ||||||||
\(425\) | −13.4069 | −0.650328 | ||||||||
\(426\) | −48.7021 | −2.35962 | ||||||||
\(427\) | −32.7066 | −1.58279 | ||||||||
\(428\) | −18.5192 | −0.895161 | ||||||||
\(429\) | 6.78235 | 0.327455 | ||||||||
\(430\) | 0.778553 | 0.0375452 | ||||||||
\(431\) | −8.94280 | −0.430759 | −0.215380 | − | 0.976530i | \(-0.569099\pi\) | ||||
−0.215380 | + | 0.976530i | \(0.569099\pi\) | |||||||
\(432\) | 63.5877 | 3.05937 | ||||||||
\(433\) | −26.0613 | −1.25243 | −0.626213 | − | 0.779652i | \(-0.715396\pi\) | ||||
−0.626213 | + | 0.779652i | \(0.715396\pi\) | |||||||
\(434\) | −42.7550 | −2.05230 | ||||||||
\(435\) | 31.7308 | 1.52138 | ||||||||
\(436\) | −12.4844 | −0.597896 | ||||||||
\(437\) | −18.8408 | −0.901279 | ||||||||
\(438\) | −28.2554 | −1.35010 | ||||||||
\(439\) | 19.8924 | 0.949410 | 0.474705 | − | 0.880145i | \(-0.342555\pi\) | ||||
0.474705 | + | 0.880145i | \(0.342555\pi\) | |||||||
\(440\) | 47.2217 | 2.25120 | ||||||||
\(441\) | −0.0501141 | −0.00238638 | ||||||||
\(442\) | −9.35365 | −0.444908 | ||||||||
\(443\) | 14.2506 | 0.677066 | 0.338533 | − | 0.940954i | \(-0.390069\pi\) | ||||
0.338533 | + | 0.940954i | \(0.390069\pi\) | |||||||
\(444\) | 36.3470 | 1.72495 | ||||||||
\(445\) | −72.8247 | −3.45222 | ||||||||
\(446\) | 42.5253 | 2.01363 | ||||||||
\(447\) | −1.60582 | −0.0759528 | ||||||||
\(448\) | −48.4576 | −2.28941 | ||||||||
\(449\) | −2.89085 | −0.136428 | −0.0682139 | − | 0.997671i | \(-0.521730\pi\) | ||||
−0.0682139 | + | 0.997671i | \(0.521730\pi\) | |||||||
\(450\) | −3.06167 | −0.144329 | ||||||||
\(451\) | 13.9214 | 0.655533 | ||||||||
\(452\) | −74.5283 | −3.50552 | ||||||||
\(453\) | −6.95655 | −0.326847 | ||||||||
\(454\) | −8.86917 | −0.416251 | ||||||||
\(455\) | −27.5051 | −1.28946 | ||||||||
\(456\) | −51.3910 | −2.40660 | ||||||||
\(457\) | −39.7598 | −1.85989 | −0.929943 | − | 0.367703i | \(-0.880144\pi\) | ||||
−0.929943 | + | 0.367703i | \(0.880144\pi\) | |||||||
\(458\) | −47.4878 | −2.21896 | ||||||||
\(459\) | −6.51232 | −0.303969 | ||||||||
\(460\) | −112.323 | −5.23709 | ||||||||
\(461\) | 15.5939 | 0.726281 | 0.363140 | − | 0.931734i | \(-0.381705\pi\) | ||||
0.363140 | + | 0.931734i | \(0.381705\pi\) | |||||||
\(462\) | −17.0091 | −0.791335 | ||||||||
\(463\) | 17.3940 | 0.808366 | 0.404183 | − | 0.914678i | \(-0.367556\pi\) | ||||
0.404183 | + | 0.914678i | \(0.367556\pi\) | |||||||
\(464\) | 57.0291 | 2.64751 | ||||||||
\(465\) | −43.3041 | −2.00818 | ||||||||
\(466\) | −38.6973 | −1.79262 | ||||||||
\(467\) | 29.8479 | 1.38120 | 0.690598 | − | 0.723239i | \(-0.257347\pi\) | ||||
0.690598 | + | 0.723239i | \(0.257347\pi\) | |||||||
\(468\) | −1.54107 | −0.0712360 | ||||||||
\(469\) | 0.282856 | 0.0130611 | ||||||||
\(470\) | −37.8608 | −1.74639 | ||||||||
\(471\) | 29.7692 | 1.37169 | ||||||||
\(472\) | 6.27965 | 0.289045 | ||||||||
\(473\) | 0.103912 | 0.00477787 | ||||||||
\(474\) | −6.46627 | −0.297006 | ||||||||
\(475\) | −35.8942 | −1.64694 | ||||||||
\(476\) | 16.9236 | 0.775690 | ||||||||
\(477\) | −0.00970797 | −0.000444497 0 | ||||||||
\(478\) | 31.9762 | 1.46256 | ||||||||
\(479\) | −17.3541 | −0.792928 | −0.396464 | − | 0.918050i | \(-0.629763\pi\) | ||||
−0.396464 | + | 0.918050i | \(0.629763\pi\) | |||||||
\(480\) | −113.698 | −5.18960 | ||||||||
\(481\) | 10.8735 | 0.495787 | ||||||||
\(482\) | 15.9384 | 0.725975 | ||||||||
\(483\) | 24.8380 | 1.13017 | ||||||||
\(484\) | −46.7159 | −2.12345 | ||||||||
\(485\) | 52.7972 | 2.39740 | ||||||||
\(486\) | −3.03039 | −0.137461 | ||||||||
\(487\) | −24.5512 | −1.11252 | −0.556260 | − | 0.831008i | \(-0.687764\pi\) | ||||
−0.556260 | + | 0.831008i | \(0.687764\pi\) | |||||||
\(488\) | −108.988 | −4.93364 | ||||||||
\(489\) | −11.6479 | −0.526735 | ||||||||
\(490\) | −4.85496 | −0.219325 | ||||||||
\(491\) | 28.7218 | 1.29620 | 0.648098 | − | 0.761557i | \(-0.275565\pi\) | ||||
0.648098 | + | 0.761557i | \(0.275565\pi\) | |||||||
\(492\) | −90.3229 | −4.07207 | ||||||||
\(493\) | −5.84061 | −0.263048 | ||||||||
\(494\) | −25.0426 | −1.12672 | ||||||||
\(495\) | −0.603324 | −0.0271174 | ||||||||
\(496\) | −77.8295 | −3.49465 | ||||||||
\(497\) | 26.3607 | 1.18244 | ||||||||
\(498\) | −13.7031 | −0.614049 | ||||||||
\(499\) | 2.55228 | 0.114256 | 0.0571279 | − | 0.998367i | \(-0.481806\pi\) | ||||
0.0571279 | + | 0.998367i | \(0.481806\pi\) | |||||||
\(500\) | −112.036 | −5.01042 | ||||||||
\(501\) | 9.74067 | 0.435181 | ||||||||
\(502\) | 24.3604 | 1.08726 | ||||||||
\(503\) | −25.6503 | −1.14369 | −0.571845 | − | 0.820362i | \(-0.693772\pi\) | ||||
−0.571845 | + | 0.820362i | \(0.693772\pi\) | |||||||
\(504\) | 2.37263 | 0.105685 | ||||||||
\(505\) | 2.43696 | 0.108443 | ||||||||
\(506\) | −20.7795 | −0.923762 | ||||||||
\(507\) | 9.75741 | 0.433342 | ||||||||
\(508\) | 44.0032 | 1.95233 | ||||||||
\(509\) | −34.4210 | −1.52568 | −0.762841 | − | 0.646586i | \(-0.776196\pi\) | ||||
−0.762841 | + | 0.646586i | \(0.776196\pi\) | |||||||
\(510\) | 23.7588 | 1.05206 | ||||||||
\(511\) | 15.2937 | 0.676552 | ||||||||
\(512\) | 8.24862 | 0.364541 | ||||||||
\(513\) | −17.4354 | −0.769794 | ||||||||
\(514\) | −19.9147 | −0.878402 | ||||||||
\(515\) | 20.2129 | 0.890687 | ||||||||
\(516\) | −0.674186 | −0.0296794 | ||||||||
\(517\) | −5.05320 | −0.222239 | ||||||||
\(518\) | −27.2690 | −1.19813 | ||||||||
\(519\) | 40.5322 | 1.77917 | ||||||||
\(520\) | −91.6548 | −4.01933 | ||||||||
\(521\) | 4.67049 | 0.204618 | 0.102309 | − | 0.994753i | \(-0.467377\pi\) | ||||
0.102309 | + | 0.994753i | \(0.467377\pi\) | |||||||
\(522\) | −1.33380 | −0.0583787 | ||||||||
\(523\) | −12.3436 | −0.539747 | −0.269874 | − | 0.962896i | \(-0.586982\pi\) | ||||
−0.269874 | + | 0.962896i | \(0.586982\pi\) | |||||||
\(524\) | 21.6079 | 0.943946 | ||||||||
\(525\) | 47.3196 | 2.06520 | ||||||||
\(526\) | −83.2714 | −3.63081 | ||||||||
\(527\) | 7.97088 | 0.347217 | ||||||||
\(528\) | −30.9627 | −1.34748 | ||||||||
\(529\) | 7.34383 | 0.319297 | ||||||||
\(530\) | −0.940490 | −0.0408523 | ||||||||
\(531\) | −0.0802316 | −0.00348175 | ||||||||
\(532\) | 45.3095 | 1.96442 | ||||||||
\(533\) | −27.0207 | −1.17040 | ||||||||
\(534\) | 87.4098 | 3.78259 | ||||||||
\(535\) | 14.0723 | 0.608399 | ||||||||
\(536\) | 0.942556 | 0.0407122 | ||||||||
\(537\) | 8.65143 | 0.373337 | ||||||||
\(538\) | 9.31786 | 0.401721 | ||||||||
\(539\) | −0.647980 | −0.0279105 | ||||||||
\(540\) | −103.945 | −4.47307 | ||||||||
\(541\) | −20.7266 | −0.891105 | −0.445552 | − | 0.895256i | \(-0.646993\pi\) | ||||
−0.445552 | + | 0.895256i | \(0.646993\pi\) | |||||||
\(542\) | 36.6428 | 1.57394 | ||||||||
\(543\) | −34.2842 | −1.47128 | ||||||||
\(544\) | 20.9282 | 0.897289 | ||||||||
\(545\) | 9.48663 | 0.406362 | ||||||||
\(546\) | 33.0138 | 1.41286 | ||||||||
\(547\) | 25.1093 | 1.07360 | 0.536798 | − | 0.843711i | \(-0.319634\pi\) | ||||
0.536798 | + | 0.843711i | \(0.319634\pi\) | |||||||
\(548\) | 16.4959 | 0.704671 | ||||||||
\(549\) | 1.39247 | 0.0594293 | ||||||||
\(550\) | −39.5877 | −1.68803 | ||||||||
\(551\) | −15.6371 | −0.666163 | ||||||||
\(552\) | 82.7671 | 3.52280 | ||||||||
\(553\) | 3.49996 | 0.148834 | ||||||||
\(554\) | 28.9623 | 1.23049 | ||||||||
\(555\) | −27.6192 | −1.17237 | ||||||||
\(556\) | −114.654 | −4.86241 | ||||||||
\(557\) | 9.08336 | 0.384874 | 0.192437 | − | 0.981309i | \(-0.438361\pi\) | ||||
0.192437 | + | 0.981309i | \(0.438361\pi\) | |||||||
\(558\) | 1.82028 | 0.0770585 | ||||||||
\(559\) | −0.201687 | −0.00853046 | ||||||||
\(560\) | 125.566 | 5.30614 | ||||||||
\(561\) | 3.17103 | 0.133881 | ||||||||
\(562\) | 29.9805 | 1.26465 | ||||||||
\(563\) | −26.3365 | −1.10995 | −0.554976 | − | 0.831866i | \(-0.687273\pi\) | ||||
−0.554976 | + | 0.831866i | \(0.687273\pi\) | |||||||
\(564\) | 32.7855 | 1.38052 | ||||||||
\(565\) | 56.6323 | 2.38254 | ||||||||
\(566\) | 70.1549 | 2.94883 | ||||||||
\(567\) | 23.8205 | 1.00037 | ||||||||
\(568\) | 87.8413 | 3.68574 | ||||||||
\(569\) | −11.2263 | −0.470632 | −0.235316 | − | 0.971919i | \(-0.575613\pi\) | ||||
−0.235316 | + | 0.971919i | \(0.575613\pi\) | |||||||
\(570\) | 63.6096 | 2.66431 | ||||||||
\(571\) | 20.4743 | 0.856823 | 0.428412 | − | 0.903584i | \(-0.359073\pi\) | ||||
0.428412 | + | 0.903584i | \(0.359073\pi\) | |||||||
\(572\) | −19.9262 | −0.833156 | ||||||||
\(573\) | −21.1183 | −0.882229 | ||||||||
\(574\) | 67.7638 | 2.82841 | ||||||||
\(575\) | 57.8090 | 2.41080 | ||||||||
\(576\) | 2.06306 | 0.0859610 | ||||||||
\(577\) | −25.8342 | −1.07549 | −0.537746 | − | 0.843107i | \(-0.680724\pi\) | ||||
−0.537746 | + | 0.843107i | \(0.680724\pi\) | |||||||
\(578\) | 41.1798 | 1.71285 | ||||||||
\(579\) | 25.7066 | 1.06833 | ||||||||
\(580\) | −93.2234 | −3.87089 | ||||||||
\(581\) | 7.41699 | 0.307708 | ||||||||
\(582\) | −63.3712 | −2.62682 | ||||||||
\(583\) | −0.125525 | −0.00519871 | ||||||||
\(584\) | 50.9628 | 2.10885 | ||||||||
\(585\) | 1.17102 | 0.0484158 | ||||||||
\(586\) | 13.0760 | 0.540164 | ||||||||
\(587\) | −28.0740 | −1.15874 | −0.579368 | − | 0.815066i | \(-0.696701\pi\) | ||||
−0.579368 | + | 0.815066i | \(0.696701\pi\) | |||||||
\(588\) | 4.20413 | 0.173376 | ||||||||
\(589\) | 21.3405 | 0.879319 | ||||||||
\(590\) | −7.77269 | −0.319996 | ||||||||
\(591\) | 9.04046 | 0.371875 | ||||||||
\(592\) | −49.6394 | −2.04017 | ||||||||
\(593\) | −26.2442 | −1.07772 | −0.538859 | − | 0.842396i | \(-0.681145\pi\) | ||||
−0.538859 | + | 0.842396i | \(0.681145\pi\) | |||||||
\(594\) | −19.2295 | −0.788997 | ||||||||
\(595\) | −12.8598 | −0.527201 | ||||||||
\(596\) | 4.71782 | 0.193250 | ||||||||
\(597\) | −31.5928 | −1.29301 | ||||||||
\(598\) | 40.3320 | 1.64930 | ||||||||
\(599\) | 22.7241 | 0.928482 | 0.464241 | − | 0.885709i | \(-0.346327\pi\) | ||||
0.464241 | + | 0.885709i | \(0.346327\pi\) | |||||||
\(600\) | 157.682 | 6.43735 | ||||||||
\(601\) | 4.57880 | 0.186773 | 0.0933866 | − | 0.995630i | \(-0.470231\pi\) | ||||
0.0933866 | + | 0.995630i | \(0.470231\pi\) | |||||||
\(602\) | 0.505801 | 0.0206149 | ||||||||
\(603\) | −0.0120425 | −0.000490409 0 | ||||||||
\(604\) | 20.4380 | 0.831609 | ||||||||
\(605\) | 35.4983 | 1.44321 | ||||||||
\(606\) | −2.92502 | −0.118821 | ||||||||
\(607\) | 26.3845 | 1.07091 | 0.535457 | − | 0.844562i | \(-0.320139\pi\) | ||||
0.535457 | + | 0.844562i | \(0.320139\pi\) | |||||||
\(608\) | 56.0311 | 2.27236 | ||||||||
\(609\) | 20.6145 | 0.835341 | ||||||||
\(610\) | 134.900 | 5.46195 | ||||||||
\(611\) | 9.80800 | 0.396789 | ||||||||
\(612\) | −0.720515 | −0.0291251 | ||||||||
\(613\) | −5.30786 | −0.214383 | −0.107191 | − | 0.994238i | \(-0.534186\pi\) | ||||
−0.107191 | + | 0.994238i | \(0.534186\pi\) | |||||||
\(614\) | −39.7627 | −1.60469 | ||||||||
\(615\) | 68.6342 | 2.76760 | ||||||||
\(616\) | 30.6784 | 1.23607 | ||||||||
\(617\) | 46.1306 | 1.85715 | 0.928575 | − | 0.371145i | \(-0.121035\pi\) | ||||
0.928575 | + | 0.371145i | \(0.121035\pi\) | |||||||
\(618\) | −24.2611 | −0.975924 | ||||||||
\(619\) | −32.5442 | −1.30806 | −0.654030 | − | 0.756468i | \(-0.726923\pi\) | ||||
−0.654030 | + | 0.756468i | \(0.726923\pi\) | |||||||
\(620\) | 127.225 | 5.10949 | ||||||||
\(621\) | 28.0804 | 1.12683 | ||||||||
\(622\) | 10.2499 | 0.410985 | ||||||||
\(623\) | −47.3118 | −1.89551 | ||||||||
\(624\) | 60.0970 | 2.40581 | ||||||||
\(625\) | 32.6614 | 1.30646 | ||||||||
\(626\) | −39.3046 | −1.57093 | ||||||||
\(627\) | 8.48982 | 0.339051 | ||||||||
\(628\) | −87.4602 | −3.49004 | ||||||||
\(629\) | 5.08380 | 0.202704 | ||||||||
\(630\) | −2.93674 | −0.117003 | ||||||||
\(631\) | 47.0883 | 1.87455 | 0.937277 | − | 0.348585i | \(-0.113338\pi\) | ||||
0.937277 | + | 0.348585i | \(0.113338\pi\) | |||||||
\(632\) | 11.6629 | 0.463924 | ||||||||
\(633\) | −5.37783 | −0.213750 | ||||||||
\(634\) | −82.5025 | −3.27659 | ||||||||
\(635\) | −33.4370 | −1.32691 | ||||||||
\(636\) | 0.814414 | 0.0322936 | ||||||||
\(637\) | 1.25770 | 0.0498317 | ||||||||
\(638\) | −17.2461 | −0.682781 | ||||||||
\(639\) | −1.12230 | −0.0443974 | ||||||||
\(640\) | 70.8976 | 2.80247 | ||||||||
\(641\) | −20.9382 | −0.827008 | −0.413504 | − | 0.910502i | \(-0.635695\pi\) | ||||
−0.413504 | + | 0.910502i | \(0.635695\pi\) | |||||||
\(642\) | −16.8907 | −0.666622 | ||||||||
\(643\) | −1.46300 | −0.0576951 | −0.0288475 | − | 0.999584i | \(-0.509184\pi\) | ||||
−0.0288475 | + | 0.999584i | \(0.509184\pi\) | |||||||
\(644\) | −72.9726 | −2.87553 | ||||||||
\(645\) | 0.512297 | 0.0201717 | ||||||||
\(646\) | −11.7085 | −0.460663 | ||||||||
\(647\) | −45.5453 | −1.79057 | −0.895285 | − | 0.445495i | \(-0.853028\pi\) | ||||
−0.895285 | + | 0.445495i | \(0.853028\pi\) | |||||||
\(648\) | 79.3767 | 3.11821 | ||||||||
\(649\) | −1.03740 | −0.0407216 | ||||||||
\(650\) | 76.8377 | 3.01382 | ||||||||
\(651\) | −28.1333 | −1.10263 | ||||||||
\(652\) | 34.2208 | 1.34019 | ||||||||
\(653\) | −1.62927 | −0.0637583 | −0.0318792 | − | 0.999492i | \(-0.510149\pi\) | ||||
−0.0318792 | + | 0.999492i | \(0.510149\pi\) | |||||||
\(654\) | −11.3866 | −0.445250 | ||||||||
\(655\) | −16.4193 | −0.641557 | ||||||||
\(656\) | 123.355 | 4.81619 | ||||||||
\(657\) | −0.651122 | −0.0254027 | ||||||||
\(658\) | −24.5970 | −0.958889 | ||||||||
\(659\) | 9.01689 | 0.351248 | 0.175624 | − | 0.984457i | \(-0.443806\pi\) | ||||
0.175624 | + | 0.984457i | \(0.443806\pi\) | |||||||
\(660\) | 50.6137 | 1.97013 | ||||||||
\(661\) | −40.8048 | −1.58712 | −0.793561 | − | 0.608491i | \(-0.791775\pi\) | ||||
−0.793561 | + | 0.608491i | \(0.791775\pi\) | |||||||
\(662\) | 58.8256 | 2.28632 | ||||||||
\(663\) | −6.15482 | −0.239033 | ||||||||
\(664\) | 24.7155 | 0.959146 | ||||||||
\(665\) | −34.4296 | −1.33512 | ||||||||
\(666\) | 1.16097 | 0.0449866 | ||||||||
\(667\) | 25.1841 | 0.975133 | ||||||||
\(668\) | −28.6176 | −1.10725 | ||||||||
\(669\) | 27.9822 | 1.08185 | ||||||||
\(670\) | −1.16666 | −0.0450718 | ||||||||
\(671\) | 18.0048 | 0.695069 | ||||||||
\(672\) | −73.8662 | −2.84945 | ||||||||
\(673\) | −25.9461 | −1.00015 | −0.500075 | − | 0.865982i | \(-0.666694\pi\) | ||||
−0.500075 | + | 0.865982i | \(0.666694\pi\) | |||||||
\(674\) | 72.6237 | 2.79736 | ||||||||
\(675\) | 53.4969 | 2.05910 | ||||||||
\(676\) | −28.6668 | −1.10257 | ||||||||
\(677\) | −25.9626 | −0.997825 | −0.498912 | − | 0.866652i | \(-0.666267\pi\) | ||||
−0.498912 | + | 0.866652i | \(0.666267\pi\) | |||||||
\(678\) | −67.9744 | −2.61054 | ||||||||
\(679\) | 34.3006 | 1.31634 | ||||||||
\(680\) | −42.8525 | −1.64332 | ||||||||
\(681\) | −5.83602 | −0.223637 | ||||||||
\(682\) | 23.5364 | 0.901254 | ||||||||
\(683\) | 6.35212 | 0.243057 | 0.121529 | − | 0.992588i | \(-0.461220\pi\) | ||||
0.121529 | + | 0.992588i | \(0.461220\pi\) | |||||||
\(684\) | −1.92904 | −0.0737586 | ||||||||
\(685\) | −12.5348 | −0.478932 | ||||||||
\(686\) | −51.1214 | −1.95182 | ||||||||
\(687\) | −31.2476 | −1.19217 | ||||||||
\(688\) | 0.920740 | 0.0351029 | ||||||||
\(689\) | 0.243637 | 0.00928185 | ||||||||
\(690\) | −102.446 | −3.90004 | ||||||||
\(691\) | 32.8473 | 1.24957 | 0.624785 | − | 0.780797i | \(-0.285187\pi\) | ||||
0.624785 | + | 0.780797i | \(0.285187\pi\) | |||||||
\(692\) | −119.082 | −4.52680 | ||||||||
\(693\) | −0.391960 | −0.0148893 | ||||||||
\(694\) | 45.4845 | 1.72657 | ||||||||
\(695\) | 87.1228 | 3.30476 | ||||||||
\(696\) | 68.6932 | 2.60381 | ||||||||
\(697\) | −12.6333 | −0.478521 | ||||||||
\(698\) | 75.6895 | 2.86489 | ||||||||
\(699\) | −25.4633 | −0.963110 | ||||||||
\(700\) | −139.022 | −5.25456 | ||||||||
\(701\) | 39.1416 | 1.47836 | 0.739179 | − | 0.673509i | \(-0.235214\pi\) | ||||
0.739179 | + | 0.673509i | \(0.235214\pi\) | |||||||
\(702\) | 37.3235 | 1.40869 | ||||||||
\(703\) | 13.6109 | 0.513344 | ||||||||
\(704\) | 26.6756 | 1.00538 | ||||||||
\(705\) | −24.9129 | −0.938274 | ||||||||
\(706\) | 43.5225 | 1.63799 | ||||||||
\(707\) | 1.58321 | 0.0595428 | ||||||||
\(708\) | 6.73073 | 0.252956 | ||||||||
\(709\) | 32.2835 | 1.21243 | 0.606217 | − | 0.795299i | \(-0.292686\pi\) | ||||
0.606217 | + | 0.795299i | \(0.292686\pi\) | |||||||
\(710\) | −108.726 | −4.08042 | ||||||||
\(711\) | −0.149010 | −0.00558830 | ||||||||
\(712\) | −157.656 | −5.90842 | ||||||||
\(713\) | −34.3696 | −1.28715 | ||||||||
\(714\) | 15.4353 | 0.577653 | ||||||||
\(715\) | 15.1414 | 0.566257 | ||||||||
\(716\) | −25.4174 | −0.949894 | ||||||||
\(717\) | 21.0407 | 0.785780 | ||||||||
\(718\) | 85.4608 | 3.18937 | ||||||||
\(719\) | −4.01496 | −0.149733 | −0.0748664 | − | 0.997194i | \(-0.523853\pi\) | ||||
−0.0748664 | + | 0.997194i | \(0.523853\pi\) | |||||||
\(720\) | −5.34593 | −0.199231 | ||||||||
\(721\) | 13.1317 | 0.489049 | ||||||||
\(722\) | 19.5651 | 0.728136 | ||||||||
\(723\) | 10.4877 | 0.390041 | ||||||||
\(724\) | 100.725 | 3.74342 | ||||||||
\(725\) | 47.9790 | 1.78190 | ||||||||
\(726\) | −42.6077 | −1.58132 | ||||||||
\(727\) | 3.12013 | 0.115719 | 0.0578597 | − | 0.998325i | \(-0.481572\pi\) | ||||
0.0578597 | + | 0.998325i | \(0.481572\pi\) | |||||||
\(728\) | −59.5451 | −2.20689 | ||||||||
\(729\) | 25.9503 | 0.961122 | ||||||||
\(730\) | −63.0795 | −2.33468 | ||||||||
\(731\) | −0.0942973 | −0.00348771 | ||||||||
\(732\) | −116.816 | −4.31766 | ||||||||
\(733\) | 50.5369 | 1.86662 | 0.933311 | − | 0.359068i | \(-0.116905\pi\) | ||||
0.933311 | + | 0.359068i | \(0.116905\pi\) | |||||||
\(734\) | 4.94577 | 0.182552 | ||||||||
\(735\) | −3.19462 | −0.117835 | ||||||||
\(736\) | −90.2402 | −3.32630 | ||||||||
\(737\) | −0.155711 | −0.00573568 | ||||||||
\(738\) | −2.88502 | −0.106199 | ||||||||
\(739\) | −0.672270 | −0.0247299 | −0.0123649 | − | 0.999924i | \(-0.503936\pi\) | ||||
−0.0123649 | + | 0.999924i | \(0.503936\pi\) | |||||||
\(740\) | 81.1438 | 2.98291 | ||||||||
\(741\) | −16.4783 | −0.605346 | ||||||||
\(742\) | −0.611005 | −0.0224307 | ||||||||
\(743\) | −35.7447 | −1.31135 | −0.655673 | − | 0.755045i | \(-0.727615\pi\) | ||||
−0.655673 | + | 0.755045i | \(0.727615\pi\) | |||||||
\(744\) | −93.7479 | −3.43697 | ||||||||
\(745\) | −3.58496 | −0.131343 | ||||||||
\(746\) | −18.4791 | −0.676569 | ||||||||
\(747\) | −0.315776 | −0.0115536 | ||||||||
\(748\) | −9.31633 | −0.340639 | ||||||||
\(749\) | 9.14233 | 0.334053 | ||||||||
\(750\) | −102.184 | −3.73123 | ||||||||
\(751\) | 12.4924 | 0.455855 | 0.227928 | − | 0.973678i | \(-0.426805\pi\) | ||||
0.227928 | + | 0.973678i | \(0.426805\pi\) | |||||||
\(752\) | −44.7754 | −1.63279 | ||||||||
\(753\) | 16.0294 | 0.584144 | ||||||||
\(754\) | 33.4738 | 1.21905 | ||||||||
\(755\) | −15.5303 | −0.565206 | ||||||||
\(756\) | −67.5295 | −2.45602 | ||||||||
\(757\) | 33.7346 | 1.22610 | 0.613052 | − | 0.790042i | \(-0.289941\pi\) | ||||
0.613052 | + | 0.790042i | \(0.289941\pi\) | |||||||
\(758\) | 35.6198 | 1.29377 | ||||||||
\(759\) | −13.6732 | −0.496305 | ||||||||
\(760\) | −114.729 | −4.16166 | ||||||||
\(761\) | 9.11708 | 0.330494 | 0.165247 | − | 0.986252i | \(-0.447158\pi\) | ||||
0.165247 | + | 0.986252i | \(0.447158\pi\) | |||||||
\(762\) | 40.1336 | 1.45389 | ||||||||
\(763\) | 6.16315 | 0.223121 | ||||||||
\(764\) | 62.0444 | 2.24469 | ||||||||
\(765\) | 0.547502 | 0.0197950 | ||||||||
\(766\) | 10.1339 | 0.366151 | ||||||||
\(767\) | 2.01354 | 0.0727049 | ||||||||
\(768\) | −18.2755 | −0.659460 | ||||||||
\(769\) | 14.6084 | 0.526792 | 0.263396 | − | 0.964688i | \(-0.415157\pi\) | ||||
0.263396 | + | 0.964688i | \(0.415157\pi\) | |||||||
\(770\) | −37.9724 | −1.36843 | ||||||||
\(771\) | −13.1041 | −0.471934 | ||||||||
\(772\) | −75.5246 | −2.71819 | ||||||||
\(773\) | −22.8709 | −0.822608 | −0.411304 | − | 0.911498i | \(-0.634927\pi\) | ||||
−0.411304 | + | 0.911498i | \(0.634927\pi\) | |||||||
\(774\) | −0.0215343 | −0.000774034 0 | ||||||||
\(775\) | −65.4786 | −2.35206 | ||||||||
\(776\) | 114.299 | 4.10310 | ||||||||
\(777\) | −17.9433 | −0.643713 | ||||||||
\(778\) | 16.6011 | 0.595179 | ||||||||
\(779\) | −33.8232 | −1.21184 | ||||||||
\(780\) | −98.2385 | −3.51750 | ||||||||
\(781\) | −14.5114 | −0.519260 | ||||||||
\(782\) | 18.8569 | 0.674321 | ||||||||
\(783\) | 23.3056 | 0.832873 | ||||||||
\(784\) | −5.74162 | −0.205058 | ||||||||
\(785\) | 66.4589 | 2.37202 | ||||||||
\(786\) | 19.7077 | 0.702952 | ||||||||
\(787\) | −41.3364 | −1.47348 | −0.736742 | − | 0.676174i | \(-0.763637\pi\) | ||||
−0.736742 | + | 0.676174i | \(0.763637\pi\) | |||||||
\(788\) | −26.5604 | −0.946175 | ||||||||
\(789\) | −54.7936 | −1.95070 | ||||||||
\(790\) | −14.4358 | −0.513602 | ||||||||
\(791\) | 36.7922 | 1.30818 | ||||||||
\(792\) | −1.30612 | −0.0464110 | ||||||||
\(793\) | −34.9464 | −1.24098 | ||||||||
\(794\) | 3.86302 | 0.137094 | ||||||||
\(795\) | −0.618853 | −0.0219485 | ||||||||
\(796\) | 92.8179 | 3.28984 | ||||||||
\(797\) | 8.82065 | 0.312444 | 0.156222 | − | 0.987722i | \(-0.450069\pi\) | ||||
0.156222 | + | 0.987722i | \(0.450069\pi\) | |||||||
\(798\) | 41.3251 | 1.46289 | ||||||||
\(799\) | 4.58565 | 0.162229 | ||||||||
\(800\) | −171.919 | −6.07827 | ||||||||
\(801\) | 2.01429 | 0.0711713 | ||||||||
\(802\) | −42.3215 | −1.49442 | ||||||||
\(803\) | −8.41908 | −0.297103 | ||||||||
\(804\) | 1.01026 | 0.0356292 | ||||||||
\(805\) | 55.4502 | 1.95436 | ||||||||
\(806\) | −45.6829 | −1.60911 | ||||||||
\(807\) | 6.13126 | 0.215831 | ||||||||
\(808\) | 5.27570 | 0.185598 | ||||||||
\(809\) | 22.8529 | 0.803464 | 0.401732 | − | 0.915757i | \(-0.368408\pi\) | ||||
0.401732 | + | 0.915757i | \(0.368408\pi\) | |||||||
\(810\) | −98.2491 | −3.45212 | ||||||||
\(811\) | 7.26827 | 0.255223 | 0.127612 | − | 0.991824i | \(-0.459269\pi\) | ||||
0.127612 | + | 0.991824i | \(0.459269\pi\) | |||||||
\(812\) | −60.5642 | −2.12539 | ||||||||
\(813\) | 24.1114 | 0.845623 | ||||||||
\(814\) | 15.0114 | 0.526150 | ||||||||
\(815\) | −26.0036 | −0.910866 | ||||||||
\(816\) | 28.0979 | 0.983623 | ||||||||
\(817\) | −0.252463 | −0.00883255 | ||||||||
\(818\) | 0.210095 | 0.00734582 | ||||||||
\(819\) | 0.760775 | 0.0265836 | ||||||||
\(820\) | −201.644 | −7.04170 | ||||||||
\(821\) | 55.1608 | 1.92512 | 0.962562 | − | 0.271062i | \(-0.0873750\pi\) | ||||
0.962562 | + | 0.271062i | \(0.0873750\pi\) | |||||||
\(822\) | 15.0453 | 0.524765 | ||||||||
\(823\) | −7.46788 | −0.260314 | −0.130157 | − | 0.991493i | \(-0.541548\pi\) | ||||
−0.130157 | + | 0.991493i | \(0.541548\pi\) | |||||||
\(824\) | 43.7584 | 1.52440 | ||||||||
\(825\) | −26.0492 | −0.906916 | ||||||||
\(826\) | −5.04966 | −0.175700 | ||||||||
\(827\) | −44.0972 | −1.53341 | −0.766706 | − | 0.641999i | \(-0.778105\pi\) | ||||
−0.766706 | + | 0.641999i | \(0.778105\pi\) | |||||||
\(828\) | 3.10679 | 0.107968 | ||||||||
\(829\) | 32.3580 | 1.12384 | 0.561920 | − | 0.827192i | \(-0.310063\pi\) | ||||
0.561920 | + | 0.827192i | \(0.310063\pi\) | |||||||
\(830\) | −30.5918 | −1.06186 | ||||||||
\(831\) | 19.0575 | 0.661098 | ||||||||
\(832\) | −51.7760 | −1.79501 | ||||||||
\(833\) | 0.588026 | 0.0203739 | ||||||||
\(834\) | −104.571 | −3.62101 | ||||||||
\(835\) | 21.7458 | 0.752544 | ||||||||
\(836\) | −24.9426 | −0.862659 | ||||||||
\(837\) | −31.8059 | −1.09937 | ||||||||
\(838\) | 27.6250 | 0.954290 | ||||||||
\(839\) | 37.1210 | 1.28156 | 0.640780 | − | 0.767725i | \(-0.278611\pi\) | ||||
0.640780 | + | 0.767725i | \(0.278611\pi\) | |||||||
\(840\) | 151.248 | 5.21856 | ||||||||
\(841\) | −8.09825 | −0.279250 | ||||||||
\(842\) | −28.2175 | −0.972441 | ||||||||
\(843\) | 19.7275 | 0.679452 | ||||||||
\(844\) | 15.7998 | 0.543851 | ||||||||
\(845\) | 21.7832 | 0.749364 | ||||||||
\(846\) | 1.04721 | 0.0360037 | ||||||||
\(847\) | 23.0621 | 0.792422 | ||||||||
\(848\) | −1.11225 | −0.0381948 | ||||||||
\(849\) | 46.1627 | 1.58430 | ||||||||
\(850\) | 35.9249 | 1.23221 | ||||||||
\(851\) | −21.9208 | −0.751436 | ||||||||
\(852\) | 94.1510 | 3.22556 | ||||||||
\(853\) | 23.5796 | 0.807352 | 0.403676 | − | 0.914902i | \(-0.367732\pi\) | ||||
0.403676 | + | 0.914902i | \(0.367732\pi\) | |||||||
\(854\) | 87.6403 | 2.99899 | ||||||||
\(855\) | 1.46583 | 0.0501303 | ||||||||
\(856\) | 30.4648 | 1.04127 | ||||||||
\(857\) | 6.10651 | 0.208595 | 0.104297 | − | 0.994546i | \(-0.466741\pi\) | ||||
0.104297 | + | 0.994546i | \(0.466741\pi\) | |||||||
\(858\) | −18.1739 | −0.620447 | ||||||||
\(859\) | 34.5877 | 1.18012 | 0.590059 | − | 0.807360i | \(-0.299105\pi\) | ||||
0.590059 | + | 0.807360i | \(0.299105\pi\) | |||||||
\(860\) | −1.50510 | −0.0513236 | ||||||||
\(861\) | 44.5894 | 1.51960 | ||||||||
\(862\) | 23.9630 | 0.816183 | ||||||||
\(863\) | 23.1648 | 0.788541 | 0.394270 | − | 0.918995i | \(-0.370997\pi\) | ||||
0.394270 | + | 0.918995i | \(0.370997\pi\) | |||||||
\(864\) | −83.5090 | −2.84103 | ||||||||
\(865\) | 90.4872 | 3.07666 | ||||||||
\(866\) | 69.8335 | 2.37304 | ||||||||
\(867\) | 27.0968 | 0.920255 | ||||||||
\(868\) | 82.6540 | 2.80546 | ||||||||
\(869\) | −1.92671 | −0.0653592 | ||||||||
\(870\) | −85.0255 | −2.88263 | ||||||||
\(871\) | 0.302227 | 0.0102406 | ||||||||
\(872\) | 20.5373 | 0.695482 | ||||||||
\(873\) | −1.46034 | −0.0494249 | ||||||||
\(874\) | 50.4856 | 1.70770 | ||||||||
\(875\) | 55.3086 | 1.86977 | ||||||||
\(876\) | 54.6235 | 1.84556 | ||||||||
\(877\) | 49.6852 | 1.67775 | 0.838875 | − | 0.544324i | \(-0.183214\pi\) | ||||
0.838875 | + | 0.544324i | \(0.183214\pi\) | |||||||
\(878\) | −53.3033 | −1.79890 | ||||||||
\(879\) | 8.60415 | 0.290211 | ||||||||
\(880\) | −69.1234 | −2.33015 | ||||||||
\(881\) | −25.9924 | −0.875705 | −0.437853 | − | 0.899047i | \(-0.644261\pi\) | ||||
−0.437853 | + | 0.899047i | \(0.644261\pi\) | |||||||
\(882\) | 0.134285 | 0.00452161 | ||||||||
\(883\) | 52.3121 | 1.76044 | 0.880221 | − | 0.474564i | \(-0.157394\pi\) | ||||
0.880221 | + | 0.474564i | \(0.157394\pi\) | |||||||
\(884\) | 18.0825 | 0.608181 | ||||||||
\(885\) | −5.11452 | −0.171923 | ||||||||
\(886\) | −38.1857 | −1.28287 | ||||||||
\(887\) | 27.1327 | 0.911027 | 0.455514 | − | 0.890229i | \(-0.349456\pi\) | ||||
0.455514 | + | 0.890229i | \(0.349456\pi\) | |||||||
\(888\) | −59.7921 | −2.00649 | ||||||||
\(889\) | −21.7229 | −0.728563 | ||||||||
\(890\) | 195.140 | 6.54111 | ||||||||
\(891\) | −13.1131 | −0.439305 | ||||||||
\(892\) | −82.2101 | −2.75260 | ||||||||
\(893\) | 12.2772 | 0.410840 | ||||||||
\(894\) | 4.30294 | 0.143912 | ||||||||
\(895\) | 19.3141 | 0.645599 | ||||||||
\(896\) | 46.0598 | 1.53875 | ||||||||
\(897\) | 26.5389 | 0.886109 | ||||||||
\(898\) | 7.74629 | 0.258497 | ||||||||
\(899\) | −28.5253 | −0.951373 | ||||||||
\(900\) | 5.91883 | 0.197294 | ||||||||
\(901\) | 0.113911 | 0.00379492 | ||||||||
\(902\) | −37.3036 | −1.24207 | ||||||||
\(903\) | 0.332823 | 0.0110757 | ||||||||
\(904\) | 122.602 | 4.07767 | ||||||||
\(905\) | −76.5386 | −2.54423 | ||||||||
\(906\) | 18.6407 | 0.619295 | ||||||||
\(907\) | 37.8100 | 1.25546 | 0.627730 | − | 0.778431i | \(-0.283984\pi\) | ||||
0.627730 | + | 0.778431i | \(0.283984\pi\) | |||||||
\(908\) | 17.1459 | 0.569007 | ||||||||
\(909\) | −0.0674046 | −0.00223567 | ||||||||
\(910\) | 73.7024 | 2.44321 | ||||||||
\(911\) | −15.3308 | −0.507932 | −0.253966 | − | 0.967213i | \(-0.581735\pi\) | ||||
−0.253966 | + | 0.967213i | \(0.581735\pi\) | |||||||
\(912\) | 75.2266 | 2.49100 | ||||||||
\(913\) | −4.08301 | −0.135128 | ||||||||
\(914\) | 106.540 | 3.52403 | ||||||||
\(915\) | 88.7660 | 2.93451 | ||||||||
\(916\) | 91.8037 | 3.03328 | ||||||||
\(917\) | −10.6671 | −0.352259 | ||||||||
\(918\) | 17.4503 | 0.575946 | ||||||||
\(919\) | −31.3384 | −1.03376 | −0.516879 | − | 0.856059i | \(-0.672906\pi\) | ||||
−0.516879 | + | 0.856059i | \(0.672906\pi\) | |||||||
\(920\) | 184.775 | 6.09187 | ||||||||
\(921\) | −26.1644 | −0.862145 | ||||||||
\(922\) | −41.7852 | −1.37612 | ||||||||
\(923\) | 28.1659 | 0.927093 | ||||||||
\(924\) | 32.8820 | 1.08174 | ||||||||
\(925\) | −41.7620 | −1.37313 | ||||||||
\(926\) | −46.6087 | −1.53166 | ||||||||
\(927\) | −0.559076 | −0.0183625 | ||||||||
\(928\) | −74.8956 | −2.45857 | ||||||||
\(929\) | 40.4213 | 1.32618 | 0.663090 | − | 0.748540i | \(-0.269245\pi\) | ||||
0.663090 | + | 0.748540i | \(0.269245\pi\) | |||||||
\(930\) | 116.037 | 3.80501 | ||||||||
\(931\) | 1.57432 | 0.0515964 | ||||||||
\(932\) | 74.8098 | 2.45048 | ||||||||
\(933\) | 6.74458 | 0.220808 | ||||||||
\(934\) | −79.9800 | −2.61703 | ||||||||
\(935\) | 7.07926 | 0.231516 | ||||||||
\(936\) | 2.53511 | 0.0828628 | ||||||||
\(937\) | −46.1999 | −1.50928 | −0.754642 | − | 0.656136i | \(-0.772190\pi\) | ||||
−0.754642 | + | 0.656136i | \(0.772190\pi\) | |||||||
\(938\) | −0.757938 | −0.0247476 | ||||||||
\(939\) | −25.8629 | −0.844005 | ||||||||
\(940\) | 73.1927 | 2.38728 | ||||||||
\(941\) | 30.4574 | 0.992883 | 0.496441 | − | 0.868070i | \(-0.334640\pi\) | ||||
0.496441 | + | 0.868070i | \(0.334640\pi\) | |||||||
\(942\) | −79.7691 | −2.59902 | ||||||||
\(943\) | 54.4736 | 1.77390 | ||||||||
\(944\) | −9.19221 | −0.299181 | ||||||||
\(945\) | 51.3140 | 1.66925 | ||||||||
\(946\) | −0.278441 | −0.00905288 | ||||||||
\(947\) | −50.7411 | −1.64886 | −0.824431 | − | 0.565962i | \(-0.808505\pi\) | ||||
−0.824431 | + | 0.565962i | \(0.808505\pi\) | |||||||
\(948\) | 12.5006 | 0.406001 | ||||||||
\(949\) | 16.3410 | 0.530451 | ||||||||
\(950\) | 96.1818 | 3.12055 | ||||||||
\(951\) | −54.2876 | −1.76040 | ||||||||
\(952\) | −27.8399 | −0.902295 | ||||||||
\(953\) | 57.9225 | 1.87629 | 0.938147 | − | 0.346238i | \(-0.112541\pi\) | ||||
0.938147 | + | 0.346238i | \(0.112541\pi\) | |||||||
\(954\) | 0.0260133 | 0.000842213 0 | ||||||||
\(955\) | −47.1461 | −1.52561 | ||||||||
\(956\) | −61.8165 | −1.99929 | ||||||||
\(957\) | −11.3482 | −0.366834 | ||||||||
\(958\) | 46.5017 | 1.50240 | ||||||||
\(959\) | −8.14348 | −0.262967 | ||||||||
\(960\) | 131.514 | 4.24460 | ||||||||
\(961\) | 7.92946 | 0.255789 | ||||||||
\(962\) | −29.1364 | −0.939395 | ||||||||
\(963\) | −0.389231 | −0.0125428 | ||||||||
\(964\) | −30.8122 | −0.992395 | ||||||||
\(965\) | 57.3893 | 1.84743 | ||||||||
\(966\) | −66.5555 | −2.14139 | ||||||||
\(967\) | 34.0320 | 1.09440 | 0.547198 | − | 0.837003i | \(-0.315695\pi\) | ||||
0.547198 | + | 0.837003i | \(0.315695\pi\) | |||||||
\(968\) | 76.8492 | 2.47003 | ||||||||
\(969\) | −7.70430 | −0.247498 | ||||||||
\(970\) | −141.475 | −4.54248 | ||||||||
\(971\) | −29.1470 | −0.935372 | −0.467686 | − | 0.883895i | \(-0.654912\pi\) | ||||
−0.467686 | + | 0.883895i | \(0.654912\pi\) | |||||||
\(972\) | 5.85836 | 0.187907 | ||||||||
\(973\) | 56.6009 | 1.81454 | ||||||||
\(974\) | 65.7870 | 2.10795 | ||||||||
\(975\) | 50.5601 | 1.61922 | ||||||||
\(976\) | 159.537 | 5.10666 | ||||||||
\(977\) | −23.4948 | −0.751666 | −0.375833 | − | 0.926687i | \(-0.622643\pi\) | ||||
−0.375833 | + | 0.926687i | \(0.622643\pi\) | |||||||
\(978\) | 31.2115 | 0.998034 | ||||||||
\(979\) | 26.0449 | 0.832399 | ||||||||
\(980\) | 9.38562 | 0.299813 | ||||||||
\(981\) | −0.262394 | −0.00837760 | ||||||||
\(982\) | −76.9625 | −2.45597 | ||||||||
\(983\) | 8.10480 | 0.258503 | 0.129251 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129251 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(984\) | 148.584 | 4.73670 | ||||||||
\(985\) | 20.1826 | 0.643071 | ||||||||
\(986\) | 15.6504 | 0.498411 | ||||||||
\(987\) | −16.1851 | −0.515177 | ||||||||
\(988\) | 48.4124 | 1.54020 | ||||||||
\(989\) | 0.406600 | 0.0129291 | ||||||||
\(990\) | 1.61666 | 0.0513808 | ||||||||
\(991\) | −21.9803 | −0.698229 | −0.349114 | − | 0.937080i | \(-0.613518\pi\) | ||||
−0.349114 | + | 0.937080i | \(0.613518\pi\) | |||||||
\(992\) | 102.212 | 3.24525 | ||||||||
\(993\) | 38.7079 | 1.22836 | ||||||||
\(994\) | −70.6358 | −2.24043 | ||||||||
\(995\) | −70.5301 | −2.23595 | ||||||||
\(996\) | 26.4908 | 0.839394 | ||||||||
\(997\) | 12.2064 | 0.386579 | 0.193290 | − | 0.981142i | \(-0.438084\pi\) | ||||
0.193290 | + | 0.981142i | \(0.438084\pi\) | |||||||
\(998\) | −6.83906 | −0.216487 | ||||||||
\(999\) | −20.2857 | −0.641811 |
(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 | 8011.2.a.b.1.9 | ✓ | 358 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8011.2.a.b.1.9 | ✓ | 358 | 1.1 | even | 1 | trivial |